LMFDB - Embedded newform 17.6.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,6,Mod(1,17)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("17.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	17.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:	$2.72652493682$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-6.00000 q^{2} +10.0000 q^{3} +4.00000 q^{4} -72.0000 q^{5} -60.0000 q^{6} -196.000 q^{7} +168.000 q^{8} -143.000 q^{9} +O(q^{10})$

\(q-6.00000 q^{2} +10.0000 q^{3} +4.00000 q^{4} -72.0000 q^{5} -60.0000 q^{6} -196.000 q^{7} +168.000 q^{8} -143.000 q^{9} +432.000 q^{10} +450.000 q^{11} +40.0000 q^{12} -142.000 q^{13} +1176.00 q^{14} -720.000 q^{15} -1136.00 q^{16} -289.000 q^{17} +858.000 q^{18} -244.000 q^{19} -288.000 q^{20} -1960.00 q^{21} -2700.00 q^{22} +2904.00 q^{23} +1680.00 q^{24} +2059.00 q^{25} +852.000 q^{26} -3860.00 q^{27} -784.000 q^{28} -6984.00 q^{29} +4320.00 q^{30} -436.000 q^{31} +1440.00 q^{32} +4500.00 q^{33} +1734.00 q^{34} +14112.0 q^{35} -572.000 q^{36} -8572.00 q^{37} +1464.00 q^{38} -1420.00 q^{39} -12096.0 q^{40} +16374.0 q^{41} +11760.0 q^{42} -19216.0 q^{43} +1800.00 q^{44} +10296.0 q^{45} -17424.0 q^{46} -19920.0 q^{47} -11360.0 q^{48} +21609.0 q^{49} -12354.0 q^{50} -2890.00 q^{51} -568.000 q^{52} +1146.00 q^{53} +23160.0 q^{54} -32400.0 q^{55} -32928.0 q^{56} -2440.00 q^{57} +41904.0 q^{58} +22008.0 q^{59} -2880.00 q^{60} +35780.0 q^{61} +2616.00 q^{62} +28028.0 q^{63} +27712.0 q^{64} +10224.0 q^{65} -27000.0 q^{66} +23264.0 q^{67} -1156.00 q^{68} +29040.0 q^{69} -84672.0 q^{70} -31704.0 q^{71} -24024.0 q^{72} -13966.0 q^{73} +51432.0 q^{74} +20590.0 q^{75} -976.000 q^{76} -88200.0 q^{77} +8520.00 q^{78} -51088.0 q^{79} +81792.0 q^{80} -3851.00 q^{81} -98244.0 q^{82} -64344.0 q^{83} -7840.00 q^{84} +20808.0 q^{85} +115296. q^{86} -69840.0 q^{87} +75600.0 q^{88} +70650.0 q^{89} -61776.0 q^{90} +27832.0 q^{91} +11616.0 q^{92} -4360.00 q^{93} +119520. q^{94} +17568.0 q^{95} +14400.0 q^{96} +62702.0 q^{97} -129654. q^{98} -64350.0 q^{99} +O(q^{100})\)

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 $

$2$	−6.00000	−1.06066	−0.530330	−	0.847791i	$-0.677932\pi$
$2$	−6.00000	−1.06066	−0.530330	+	0.847791i	$0.677932\pi$
$3$	10.0000	0.641500	0.320750	−	0.947164i	$-0.396065\pi$
$3$	10.0000	0.641500	0.320750	+	0.947164i	$0.396065\pi$
$4$	4.00000	0.125000
$5$	−72.0000	−1.28798	−0.643988	−	0.765036i	$-0.722721\pi$
$5$	−72.0000	−1.28798	−0.643988	+	0.765036i	$0.722721\pi$
$6$	−60.0000	−0.680414
$7$	−196.000	−1.51186	−0.755929	−	0.654654i	$-0.772814\pi$
$7$	−196.000	−1.51186	−0.755929	+	0.654654i	$0.772814\pi$
$8$	168.000	0.928078
$9$	−143.000	−0.588477
$10$	432.000	1.36610
$11$	450.000	1.12132	0.560662	−	0.828045i	$-0.310547\pi$
$11$	450.000	1.12132	0.560662	+	0.828045i	$0.310547\pi$
$12$	40.0000	0.0801875
$13$	−142.000	−0.233040	−0.116520	−	0.993188i	$-0.537174\pi$
$13$	−142.000	−0.233040	−0.116520	+	0.993188i	$0.537174\pi$
$14$	1176.00	1.60357
$15$	−720.000	−0.826236
$16$	−1136.00	−1.10938
$17$	−289.000	−0.242536
$17$	−289.000	−0.242536
$18$	858.000	0.624175
$19$	−244.000	−0.155062	−0.0775311	−	0.996990i	$-0.524704\pi$
$19$	−244.000	−0.155062	−0.0775311	+	0.996990i	$0.524704\pi$
$20$	−288.000	−0.160997
$21$	−1960.00	−0.969857
$22$	−2700.00	−1.18934
$23$	2904.00	1.14466	0.572331	−	0.820023i	$-0.306039\pi$
$23$	2904.00	1.14466	0.572331	+	0.820023i	$0.306039\pi$
$24$	1680.00	0.595362
$25$	2059.00	0.658880
$26$	852.000	0.247176
$27$	−3860.00	−1.01901
$28$	−784.000	−0.188982
$29$	−6984.00	−1.54209	−0.771044	−	0.636782i	$-0.780265\pi$
$29$	−6984.00	−1.54209	−0.771044	+	0.636782i	$0.780265\pi$
$30$	4320.00	0.876356
$31$	−436.000	−0.0814859	−0.0407429	−	0.999170i	$-0.512972\pi$
$31$	−436.000	−0.0814859	−0.0407429	+	0.999170i	$0.512972\pi$
$32$	1440.00	0.248592
$33$	4500.00	0.719329
$34$	1734.00	0.257248
$35$	14112.0	1.94724
$36$	−572.000	−0.0735597
$37$	−8572.00	−1.02939	−0.514693	−	0.857375i	$-0.672094\pi$
$37$	−8572.00	−1.02939	−0.514693	+	0.857375i	$0.672094\pi$
$38$	1464.00	0.164468
$39$	−1420.00	−0.149495
$40$	−12096.0	−1.19534
$41$	16374.0	1.52123	0.760615	−	0.649203i	$-0.224897\pi$
$41$	16374.0	1.52123	0.760615	+	0.649203i	$0.224897\pi$
$42$	11760.0	1.02869
$43$	−19216.0	−1.58486	−0.792432	−	0.609961i	$-0.791185\pi$
$43$	−19216.0	−1.58486	−0.792432	+	0.609961i	$0.791185\pi$
$44$	1800.00	0.140165
$45$	10296.0	0.757944
$46$	−17424.0	−1.21410
$47$	−19920.0	−1.31536	−0.657680	−	0.753297i	$-0.728462\pi$
$47$	−19920.0	−1.31536	−0.657680	+	0.753297i	$0.728462\pi$
$48$	−11360.0	−0.711664
$49$	21609.0	1.28571
$50$	−12354.0	−0.698848
$51$	−2890.00	−0.155587
$52$	−568.000	−0.0291300
$53$	1146.00	0.0560396	0.0280198	−	0.999607i	$-0.491080\pi$
$53$	1146.00	0.0560396	0.0280198	+	0.999607i	$0.491080\pi$
$54$	23160.0	1.08082
$55$	−32400.0	−1.44424
$56$	−32928.0	−1.40312
$57$	−2440.00	−0.0994724
$58$	41904.0	1.63563
$59$	22008.0	0.823096	0.411548	−	0.911388i	$-0.364988\pi$
$59$	22008.0	0.823096	0.411548	+	0.911388i	$0.364988\pi$
$60$	−2880.00	−0.103280
$61$	35780.0	1.23116	0.615582	−	0.788073i	$-0.288921\pi$
$61$	35780.0	1.23116	0.615582	+	0.788073i	$0.288921\pi$
$62$	2616.00	0.0864288
$63$	28028.0	0.889694
$64$	27712.0	0.845703
$65$	10224.0	0.300149
$66$	−27000.0	−0.762964
$67$	23264.0	0.633137	0.316568	−	0.948570i	$-0.397469\pi$
$67$	23264.0	0.633137	0.316568	+	0.948570i	$0.397469\pi$
$68$	−1156.00	−0.0303170
$69$	29040.0	0.734301
$70$	−84672.0	−2.06536
$71$	−31704.0	−0.746394	−0.373197	−	0.927752i	$-0.621738\pi$
$71$	−31704.0	−0.746394	−0.373197	+	0.927752i	$0.621738\pi$
$72$	−24024.0	−0.546153
$73$	−13966.0	−0.306736	−0.153368	−	0.988169i	$-0.549012\pi$
$73$	−13966.0	−0.306736	−0.153368	+	0.988169i	$0.549012\pi$
$74$	51432.0	1.09183
$75$	20590.0	0.422672
$76$	−976.000	−0.0193828
$77$	−88200.0	−1.69528
$78$	8520.00	0.158563
$79$	−51088.0	−0.920982	−0.460491	−	0.887664i	$-0.652327\pi$
$79$	−51088.0	−0.920982	−0.460491	+	0.887664i	$0.652327\pi$
$80$	81792.0	1.42885
$81$	−3851.00	−0.0652170
$82$	−98244.0	−1.61351
$83$	−64344.0	−1.02521	−0.512605	−	0.858625i	$-0.671319\pi$
$83$	−64344.0	−1.02521	−0.512605	+	0.858625i	$0.671319\pi$
$84$	−7840.00	−0.121232
$85$	20808.0	0.312380
$86$	115296.	1.68100
$87$	−69840.0	−0.989250
$88$	75600.0	1.04067
$89$	70650.0	0.945447	0.472723	−	0.881211i	$-0.343271\pi$
$89$	70650.0	0.945447	0.472723	+	0.881211i	$0.343271\pi$
$90$	−61776.0	−0.803921
$91$	27832.0	0.352323
$92$	11616.0	0.143083
$93$	−4360.00	−0.0522732
$94$	119520.	1.39515
$95$	17568.0	0.199716
$96$	14400.0	0.159472
$97$	62702.0	0.676631	0.338316	−	0.941033i	$-0.390143\pi$
$97$	62702.0	0.676631	0.338316	+	0.941033i	$0.390143\pi$
$98$	−129654.	−1.36371
$99$	−64350.0	−0.659873
$100$	8236.00	0.0823600
$101$	−85470.0	−0.833701	−0.416850	−	0.908975i	$-0.636866\pi$
$101$	−85470.0	−0.833701	−0.416850	+	0.908975i	$0.636866\pi$
$102$	17340.0	0.165025
$103$	−181792.	−1.68842	−0.844212	−	0.536009i	$-0.819931\pi$
$103$	−181792.	−1.68842	−0.844212	+	0.536009i	$0.819931\pi$
$104$	−23856.0	−0.216279
$105$	141120.	1.24915
$106$	−6876.00	−0.0594390
$107$	82638.0	0.697783	0.348891	−	0.937163i	$-0.386558\pi$
$107$	82638.0	0.697783	0.348891	+	0.937163i	$0.386558\pi$
$108$	−15440.0	−0.127376
$109$	245576.	1.97979	0.989896	−	0.141794i	$-0.0452869\pi$
$109$	245576.	1.97979	0.989896	+	0.141794i	$0.0452869\pi$
$110$	194400.	1.53184
$111$	−85720.0	−0.660351
$112$	222656.	1.67722
$113$	−187014.	−1.37777	−0.688887	−	0.724869i	$-0.741900\pi$
$113$	−187014.	−1.37777	−0.688887	+	0.724869i	$0.741900\pi$
$114$	14640.0	0.105506
$115$	−209088.	−1.47430
$116$	−27936.0	−0.192761
$117$	20306.0	0.137139
$118$	−132048.	−0.873025
$119$	56644.0	0.366679
$120$	−120960.	−0.766812
$121$	41449.0	0.257366
$122$	−214680.	−1.30585
$123$	163740.	0.975870
$124$	−1744.00	−0.0101857
$125$	76752.0	0.439354
$126$	−168168.	−0.943663
$127$	102848.	0.565831	0.282915	−	0.959145i	$-0.408698\pi$
$127$	102848.	0.565831	0.282915	+	0.959145i	$0.408698\pi$
$128$	−212352.	−1.14560
$129$	−192160.	−1.01669
$130$	−61344.0	−0.318356
$131$	128286.	0.653132	0.326566	−	0.945174i	$-0.394108\pi$
$131$	128286.	0.653132	0.326566	+	0.945174i	$0.394108\pi$
$132$	18000.0	0.0899161
$133$	47824.0	0.234432
$134$	−139584.	−0.671543
$135$	277920.	1.31246
$136$	−48552.0	−0.225092
$137$	23334.0	0.106215	0.0531077	−	0.998589i	$-0.483087\pi$
$137$	23334.0	0.106215	0.0531077	+	0.998589i	$0.483087\pi$
$138$	−174240.	−0.778843
$139$	−17338.0	−0.0761136	−0.0380568	−	0.999276i	$-0.512117\pi$
$139$	−17338.0	−0.0761136	−0.0380568	+	0.999276i	$0.512117\pi$
$140$	56448.0	0.243404
$141$	−199200.	−0.843804
$142$	190224.	0.791670
$143$	−63900.0	−0.261313
$144$	162448.	0.652842
$145$	502848.	1.98617
$146$	83796.0	0.325343
$147$	216090.	0.824786
$148$	−34288.0	−0.128673
$149$	51990.0	0.191847	0.0959233	−	0.995389i	$-0.469420\pi$
$149$	51990.0	0.191847	0.0959233	+	0.995389i	$0.469420\pi$
$150$	−123540.	−0.448311
$151$	131504.	0.469350	0.234675	−	0.972074i	$-0.424597\pi$
$151$	131504.	0.469350	0.234675	+	0.972074i	$0.424597\pi$
$152$	−40992.0	−0.143910
$153$	41327.0	0.142727
$154$	529200.	1.79812
$155$	31392.0	0.104952
$156$	−5680.00	−0.0186869
$157$	−598882.	−1.93906	−0.969532	−	0.244965i	$-0.921224\pi$
$157$	−598882.	−1.93906	−0.969532	+	0.244965i	$0.921224\pi$
$158$	306528.	0.976849
$159$	11460.0	0.0359494
$160$	−103680.	−0.320181
$161$	−569184.	−1.73057
$162$	23106.0	0.0691731
$163$	−321946.	−0.949104	−0.474552	−	0.880227i	$-0.657390\pi$
$163$	−321946.	−0.949104	−0.474552	+	0.880227i	$0.657390\pi$
$164$	65496.0	0.190154
$165$	−324000.	−0.926478
$166$	386064.	1.08740
$167$	339516.	0.942039	0.471020	−	0.882123i	$-0.343886\pi$
$167$	339516.	0.942039	0.471020	+	0.882123i	$0.343886\pi$
$168$	−329280.	−0.900103
$169$	−351129.	−0.945692
$170$	−124848.	−0.331329
$171$	34892.0	0.0912506
$172$	−76864.0	−0.198108
$173$	252432.	0.641253	0.320626	−	0.947206i	$-0.396107\pi$
$173$	252432.	0.641253	0.320626	+	0.947206i	$0.396107\pi$
$174$	419040.	1.04926
$175$	−403564.	−0.996133
$176$	−511200.	−1.24397
$177$	220080.	0.528016
$178$	−423900.	−1.00280
$179$	−555108.	−1.29493	−0.647463	−	0.762097i	$-0.724170\pi$
$179$	−555108.	−1.29493	−0.647463	+	0.762097i	$0.724170\pi$
$180$	41184.0	0.0947430
$181$	1508.00	0.00342141	0.00171070	−	0.999999i	$-0.499455\pi$
$181$	1508.00	0.00342141	0.00171070	+	0.999999i	$0.499455\pi$
$182$	−166992.	−0.373695
$183$	357800.	0.789792
$184$	487872.	1.06233
$185$	617184.	1.32582
$186$	26160.0	0.0554441
$187$	−130050.	−0.271961
$188$	−79680.0	−0.164420
$189$	756560.	1.54060
$190$	−105408.	−0.211831
$191$	−392856.	−0.779202	−0.389601	−	0.920984i	$-0.627387\pi$
$191$	−392856.	−0.779202	−0.389601	+	0.920984i	$0.627387\pi$
$192$	277120.	0.542519
$193$	−390538.	−0.754692	−0.377346	−	0.926072i	$-0.623163\pi$
$193$	−390538.	−0.754692	−0.377346	+	0.926072i	$0.623163\pi$
$194$	−376212.	−0.717676
$195$	102240.	0.192546
$196$	86436.0	0.160714
$197$	205212.	0.376736	0.188368	−	0.982099i	$-0.439680\pi$
$197$	205212.	0.376736	0.188368	+	0.982099i	$0.439680\pi$
$198$	386100.	0.699901
$199$	−405160.	−0.725260	−0.362630	−	0.931933i	$-0.618121\pi$
$199$	−405160.	−0.725260	−0.362630	+	0.931933i	$0.618121\pi$
$200$	345912.	0.611492
$201$	232640.	0.406157
$202$	512820.	0.884273
$203$	1.36886e6	2.33142
$204$	−11560.0	−0.0194483
$205$	−1.17893e6	−1.95931
$206$	1.09075e6	1.79084
$207$	−415272.	−0.673607
$208$	161312.	0.258528
$209$	−109800.	−0.173875
$210$	−846720.	−1.32493
$211$	−269662.	−0.416978	−0.208489	−	0.978025i	$-0.566855\pi$
$211$	−269662.	−0.416978	−0.208489	+	0.978025i	$0.566855\pi$
$212$	4584.00	0.00700495
$213$	−317040.	−0.478812
$214$	−495828.	−0.740111
$215$	1.38355e6	2.04126
$216$	−648480.	−0.945719
$217$	85456.0	0.123195
$218$	−1.47346e6	−2.09989
$219$	−139660.	−0.196771
$220$	−129600.	−0.180530
$221$	41038.0	0.0565204
$222$	514320.	0.700408
$223$	−455656.	−0.613585	−0.306793	−	0.951776i	$-0.599256\pi$
$223$	−455656.	−0.613585	−0.306793	+	0.951776i	$0.599256\pi$
$224$	−282240.	−0.375836
$225$	−294437.	−0.387736
$226$	1.12208e6	1.46135
$227$	792366.	1.02061	0.510307	−	0.859993i	$-0.329532\pi$
$227$	792366.	1.02061	0.510307	+	0.859993i	$0.329532\pi$
$228$	−9760.00	−0.0124341
$229$	−179794.	−0.226562	−0.113281	−	0.993563i	$-0.536136\pi$
$229$	−179794.	−0.226562	−0.113281	+	0.993563i	$0.536136\pi$
$230$	1.25453e6	1.56373
$231$	−882000.	−1.08752
$232$	−1.17331e6	−1.43118
$233$	245154.	0.295835	0.147917	−	0.989000i	$-0.452743\pi$
$233$	245154.	0.295835	0.147917	+	0.989000i	$0.452743\pi$
$234$	−121836.	−0.145457
$235$	1.43424e6	1.69415
$236$	88032.0	0.102887
$237$	−510880.	−0.590810
$238$	−339864.	−0.388922
$239$	−334536.	−0.378833	−0.189417	−	0.981897i	$-0.560660\pi$
$239$	−334536.	−0.378833	−0.189417	+	0.981897i	$0.560660\pi$
$240$	817920.	0.916606
$241$	−882922.	−0.979219	−0.489609	−	0.871942i	$-0.662861\pi$
$241$	−882922.	−0.979219	−0.489609	+	0.871942i	$0.662861\pi$
$242$	−248694.	−0.272978
$243$	899470.	0.977172
$244$	143120.	0.153895
$245$	−1.55585e6	−1.65597
$246$	−982440.	−1.03507
$247$	34648.0	0.0361356
$248$	−73248.0	−0.0756252
$249$	−643440.	−0.657673
$250$	−460512.	−0.466005
$251$	−146928.	−0.147204	−0.0736021	−	0.997288i	$-0.523449\pi$
$251$	−146928.	−0.147204	−0.0736021	+	0.997288i	$0.523449\pi$
$252$	112112.	0.111212
$253$	1.30680e6	1.28354
$254$	−617088.	−0.600154
$255$	208080.	0.200392
$256$	387328.	0.369385
$257$	−737082.	−0.696118	−0.348059	−	0.937473i	$-0.613159\pi$
$257$	−737082.	−0.696118	−0.348059	+	0.937473i	$0.613159\pi$
$258$	1.15296e6	1.07836
$259$	1.68011e6	1.55628
$260$	40896.0	0.0375187
$261$	998712.	0.907484
$262$	−769716.	−0.692751
$263$	−1.08214e6	−0.964700	−0.482350	−	0.875978i	$-0.660217\pi$
$263$	−1.08214e6	−0.964700	−0.482350	+	0.875978i	$0.660217\pi$
$264$	756000.	0.667593
$265$	−82512.0	−0.0721776
$266$	−286944.	−0.248653
$267$	706500.	0.606504
$268$	93056.0	0.0791421
$269$	1.51939e6	1.28023	0.640117	−	0.768278i	$-0.278886\pi$
$269$	1.51939e6	1.28023	0.640117	+	0.768278i	$0.278886\pi$
$270$	−1.66752e6	−1.39207
$271$	395624.	0.327235	0.163617	−	0.986524i	$-0.447684\pi$
$271$	395624.	0.327235	0.163617	+	0.986524i	$0.447684\pi$
$272$	328304.	0.269063
$273$	278320.	0.226015
$274$	−140004.	−0.112659
$275$	926550.	0.738817
$276$	116160.	0.0917876
$277$	−1.15178e6	−0.901921	−0.450961	−	0.892544i	$-0.648919\pi$
$277$	−1.15178e6	−0.901921	−0.450961	+	0.892544i	$0.648919\pi$
$278$	104028.	0.0807306
$279$	62348.0	0.0479526
$280$	2.37082e6	1.80719
$281$	1.37261e6	1.03701	0.518505	−	0.855075i	$-0.326489\pi$
$281$	1.37261e6	1.03701	0.518505	+	0.855075i	$0.326489\pi$
$282$	1.19520e6	0.894989
$283$	229754.	0.170529	0.0852643	−	0.996358i	$-0.472827\pi$
$283$	229754.	0.170529	0.0852643	+	0.996358i	$0.472827\pi$
$284$	−126816.	−0.0932993
$285$	175680.	0.128118
$286$	383400.	0.277164
$287$	−3.20930e6	−2.29988
$288$	−205920.	−0.146291
$289$	83521.0	0.0588235
$290$	−3.01709e6	−2.10665
$291$	627020.	0.434059
$292$	−55864.0	−0.0383420
$293$	761526.	0.518222	0.259111	−	0.965848i	$-0.416570\pi$
$293$	761526.	0.518222	0.259111	+	0.965848i	$0.416570\pi$
$294$	−1.29654e6	−0.874818
$295$	−1.58458e6	−1.06013
$296$	−1.44010e6	−0.955349
$297$	−1.73700e6	−1.14264
$298$	−311940.	−0.203484
$299$	−412368.	−0.266752
$300$	82360.0	0.0528340
$301$	3.76634e6	2.39609
$302$	−789024.	−0.497821
$303$	−854700.	−0.534819
$304$	277184.	0.172022
$305$	−2.57616e6	−1.58571
$306$	−247962.	−0.151385
$307$	599348.	0.362939	0.181469	−	0.983397i	$-0.441915\pi$
$307$	599348.	0.362939	0.181469	+	0.983397i	$0.441915\pi$
$308$	−352800.	−0.211910
$309$	−1.81792e6	−1.08312
$310$	−188352.	−0.111318
$311$	847548.	0.496894	0.248447	−	0.968646i	$-0.420080\pi$
$311$	847548.	0.496894	0.248447	+	0.968646i	$0.420080\pi$
$312$	−238560.	−0.138743
$313$	2.00008e6	1.15395	0.576974	−	0.816763i	$-0.304233\pi$
$313$	2.00008e6	1.15395	0.576974	+	0.816763i	$0.304233\pi$
$314$	3.59329e6	2.05669
$315$	−2.01802e6	−1.14590
$316$	−204352.	−0.115123
$317$	194460.	0.108688	0.0543441	−	0.998522i	$-0.482693\pi$
$317$	194460.	0.108688	0.0543441	+	0.998522i	$0.482693\pi$
$318$	−68760.0	−0.0381301
$319$	−3.14280e6	−1.72918
$320$	−1.99526e6	−1.08924
$321$	826380.	0.447628
$322$	3.41510e6	1.83554
$323$	70516.0	0.0376081
$324$	−15404.0	−0.00815213
$325$	−292378.	−0.153545
$326$	1.93168e6	1.00668
$327$	2.45576e6	1.27004
$328$	2.75083e6	1.41182
$329$	3.90432e6	1.98864
$330$	1.94400e6	0.982678
$331$	−1.82342e6	−0.914778	−0.457389	−	0.889267i	$-0.651215\pi$
$331$	−1.82342e6	−0.914778	−0.457389	+	0.889267i	$0.651215\pi$
$332$	−257376.	−0.128151
$333$	1.22580e6	0.605770
$334$	−2.03710e6	−0.999184
$335$	−1.67501e6	−0.815464
$336$	2.22656e6	1.07594
$337$	−2.59269e6	−1.24359	−0.621794	−	0.783181i	$-0.713596\pi$
$337$	−2.59269e6	−1.24359	−0.621794	+	0.783181i	$0.713596\pi$
$338$	2.10677e6	1.00306
$339$	−1.87014e6	−0.883842
$340$	83232.0	0.0390475
$341$	−196200.	−0.0913720
$342$	−209352.	−0.0967858
$343$	−941192.	−0.431959
$344$	−3.22829e6	−1.47088
$345$	−2.09088e6	−0.945761
$346$	−1.51459e6	−0.680151
$347$	2.67418e6	1.19225	0.596125	−	0.802892i	$-0.296706\pi$
$347$	2.67418e6	1.19225	0.596125	+	0.802892i	$0.296706\pi$
$348$	−279360.	−0.123656
$349$	504122.	0.221550	0.110775	−	0.993846i	$-0.464667\pi$
$349$	504122.	0.221550	0.110775	+	0.993846i	$0.464667\pi$
$350$	2.42138e6	1.05656
$351$	548120.	0.237470
$352$	648000.	0.278752
$353$	1.00791e6	0.430512	0.215256	−	0.976558i	$-0.430941\pi$
$353$	1.00791e6	0.430512	0.215256	+	0.976558i	$0.430941\pi$
$354$	−1.32048e6	−0.560046
$355$	2.28269e6	0.961337
$356$	282600.	0.118181
$357$	566440.	0.235225
$358$	3.33065e6	1.37348
$359$	−4.74516e6	−1.94319	−0.971594	−	0.236655i	$-0.923949\pi$
$359$	−4.74516e6	−1.94319	−0.971594	+	0.236655i	$0.923949\pi$
$360$	1.72973e6	0.703431
$361$	−2.41656e6	−0.975956
$362$	−9048.00	−0.00362895
$363$	414490.	0.165100
$364$	111328.	0.0440404
$365$	1.00555e6	0.395068
$366$	−2.14680e6	−0.837701
$367$	155048.	0.0600898	0.0300449	−	0.999549i	$-0.490435\pi$
$367$	155048.	0.0600898	0.0300449	+	0.999549i	$0.490435\pi$
$368$	−3.29894e6	−1.26986
$369$	−2.34148e6	−0.895210
$370$	−3.70310e6	−1.40625
$371$	−224616.	−0.0847239
$372$	−17440.0	−0.00653415
$373$	3.89811e6	1.45071	0.725357	−	0.688373i	$-0.241675\pi$
$373$	3.89811e6	1.45071	0.725357	+	0.688373i	$0.241675\pi$
$374$	780300.	0.288458
$375$	767520.	0.281846
$376$	−3.34656e6	−1.22076
$377$	991728.	0.359368
$378$	−4.53936e6	−1.63405
$379$	−2.76828e6	−0.989946	−0.494973	−	0.868908i	$-0.664822\pi$
$379$	−2.76828e6	−0.989946	−0.494973	+	0.868908i	$0.664822\pi$
$380$	70272.0	0.0249645
$381$	1.02848e6	0.362981
$382$	2.35714e6	0.826468
$383$	−3.51362e6	−1.22393	−0.611967	−	0.790883i	$-0.709622\pi$
$383$	−3.51362e6	−1.22393	−0.611967	+	0.790883i	$0.709622\pi$
$384$	−2.12352e6	−0.734900
$385$	6.35040e6	2.18348
$386$	2.34323e6	0.800472
$387$	2.74789e6	0.932656
$388$	250808.	0.0845789
$389$	834366.	0.279565	0.139782	−	0.990182i	$-0.455360\pi$
$389$	834366.	0.279565	0.139782	+	0.990182i	$0.455360\pi$
$390$	−613440.	−0.204226
$391$	−839256.	−0.277621
$392$	3.63031e6	1.19324
$393$	1.28286e6	0.418984
$394$	−1.23127e6	−0.399589
$395$	3.67834e6	1.18620
$396$	−257400.	−0.0824842
$397$	−5.08080e6	−1.61792	−0.808958	−	0.587866i	$-0.799968\pi$
$397$	−5.08080e6	−1.61792	−0.808958	+	0.587866i	$0.799968\pi$
$398$	2.43096e6	0.769255
$399$	478240.	0.150388
$400$	−2.33902e6	−0.730945
$401$	649566.	0.201726	0.100863	−	0.994900i	$-0.467840\pi$
$401$	649566.	0.201726	0.100863	+	0.994900i	$0.467840\pi$
$402$	−1.39584e6	−0.430795
$403$	61912.0	0.0189894
$404$	−341880.	−0.104213
$405$	277272.	0.0839979
$406$	−8.21318e6	−2.47284
$407$	−3.85740e6	−1.15427
$408$	−485520.	−0.144397
$409$	3.33465e6	0.985693	0.492846	−	0.870116i	$-0.335956\pi$
$409$	3.33465e6	0.985693	0.492846	+	0.870116i	$0.335956\pi$
$410$	7.07357e6	2.07816
$411$	233340.	0.0681373
$412$	−727168.	−0.211053
$413$	−4.31357e6	−1.24440
$414$	2.49163e6	0.714468
$415$	4.63277e6	1.32044
$416$	−204480.	−0.0579319
$417$	−173380.	−0.0488269
$418$	658800.	0.184422
$419$	1.72532e6	0.480103	0.240051	−	0.970760i	$-0.422836\pi$
$419$	1.72532e6	0.480103	0.240051	+	0.970760i	$0.422836\pi$
$420$	564480.	0.156144
$421$	924722.	0.254276	0.127138	−	0.991885i	$-0.459421\pi$
$421$	924722.	0.254276	0.127138	+	0.991885i	$0.459421\pi$
$422$	1.61797e6	0.442272
$423$	2.84856e6	0.774060
$424$	192528.	0.0520091
$425$	−595051.	−0.159802
$426$	1.90224e6	0.507857
$427$	−7.01288e6	−1.86134
$428$	330552.	0.0872229
$429$	−639000.	−0.167632
$430$	−8.30131e6	−2.16509
$431$	4.83139e6	1.25279	0.626396	−	0.779505i	$-0.284529\pi$
$431$	4.83139e6	1.25279	0.626396	+	0.779505i	$0.284529\pi$
$432$	4.38496e6	1.13046
$433$	5.39952e6	1.38400	0.691999	−	0.721898i	$-0.256730\pi$
$433$	5.39952e6	1.38400	0.691999	+	0.721898i	$0.256730\pi$
$434$	−512736.	−0.130668
$435$	5.02848e6	1.27413
$436$	982304.	0.247474
$437$	−708576.	−0.177494
$438$	837960.	0.208707
$439$	3.78320e6	0.936910	0.468455	−	0.883487i	$-0.344811\pi$
$439$	3.78320e6	0.936910	0.468455	+	0.883487i	$0.344811\pi$
$440$	−5.44320e6	−1.34036
$441$	−3.09009e6	−0.756614
$442$	−246228.	−0.0599490
$443$	−4.20235e6	−1.01738	−0.508690	−	0.860950i	$-0.669870\pi$
$443$	−4.20235e6	−1.01738	−0.508690	+	0.860950i	$0.669870\pi$
$444$	−342880.	−0.0825439
$445$	−5.08680e6	−1.21771
$446$	2.73394e6	0.650805
$447$	519900.	0.123070
$448$	−5.43155e6	−1.27858
$449$	−3.72223e6	−0.871338	−0.435669	−	0.900107i	$-0.643488\pi$
$449$	−3.72223e6	−0.871338	−0.435669	+	0.900107i	$0.643488\pi$
$450$	1.76662e6	0.411256
$451$	7.36830e6	1.70579
$452$	−748056.	−0.172222
$453$	1.31504e6	0.301088
$454$	−4.75420e6	−1.08252
$455$	−2.00390e6	−0.453783
$456$	−409920.	−0.0923181
$457$	6.53743e6	1.46426	0.732128	−	0.681167i	$-0.238527\pi$
$457$	6.53743e6	1.46426	0.732128	+	0.681167i	$0.238527\pi$
$458$	1.07876e6	0.240305
$459$	1.11554e6	0.247146
$460$	−836352.	−0.184287
$461$	−2.83978e6	−0.622347	−0.311174	−	0.950353i	$-0.600722\pi$
$461$	−2.83978e6	−0.622347	−0.311174	+	0.950353i	$0.600722\pi$
$462$	5.29200e6	1.15349
$463$	−4.22901e6	−0.916824	−0.458412	−	0.888740i	$-0.651582\pi$
$463$	−4.22901e6	−0.916824	−0.458412	+	0.888740i	$0.651582\pi$
$464$	7.93382e6	1.71075
$465$	313920.	0.0673266
$466$	−1.47092e6	−0.313780
$467$	−4.02215e6	−0.853426	−0.426713	−	0.904387i	$-0.640329\pi$
$467$	−4.02215e6	−0.853426	−0.426713	+	0.904387i	$0.640329\pi$
$468$	81224.0	0.0171423
$469$	−4.55974e6	−0.957212
$470$	−8.60544e6	−1.79692
$471$	−5.98882e6	−1.24391
$472$	3.69734e6	0.763897
$473$	−8.64720e6	−1.77714
$474$	3.06528e6	0.626649
$475$	−502396.	−0.102167
$476$	226576.	0.0458349
$477$	−163878.	−0.0329780
$478$	2.00722e6	0.401813
$479$	−3.68606e6	−0.734047	−0.367024	−	0.930212i	$-0.619623\pi$
$479$	−3.68606e6	−0.734047	−0.367024	+	0.930212i	$0.619623\pi$
$480$	−1.03680e6	−0.205396
$481$	1.21722e6	0.239888
$482$	5.29753e6	1.03862
$483$	−5.69184e6	−1.11016
$484$	165796.	0.0321707
$485$	−4.51454e6	−0.871484
$486$	−5.39682e6	−1.03645
$487$	−2.22808e6	−0.425705	−0.212852	−	0.977084i	$-0.568275\pi$
$487$	−2.22808e6	−0.425705	−0.212852	+	0.977084i	$0.568275\pi$
$488$	6.01104e6	1.14262
$489$	−3.21946e6	−0.608851
$490$	9.33509e6	1.75642
$491$	2.01546e6	0.377286	0.188643	−	0.982046i	$-0.439591\pi$
$491$	2.01546e6	0.377286	0.188643	+	0.982046i	$0.439591\pi$
$492$	654960.	0.121984
$493$	2.01838e6	0.374011
$494$	−207888.	−0.0383276
$495$	4.63320e6	0.849900
$496$	495296.	0.0903984
$497$	6.21398e6	1.12844
$498$	3.86064e6	0.697567
$499$	1.58273e6	0.284548	0.142274	−	0.989827i	$-0.454559\pi$
$499$	1.58273e6	0.284548	0.142274	+	0.989827i	$0.454559\pi$
$500$	307008.	0.0549193
$501$	3.39516e6	0.604319
$502$	881568.	0.156134
$503$	1.64357e6	0.289646	0.144823	−	0.989458i	$-0.453739\pi$
$503$	1.64357e6	0.289646	0.144823	+	0.989458i	$0.453739\pi$
$504$	4.70870e6	0.825705
$505$	6.15384e6	1.07379
$506$	−7.84080e6	−1.36139
$507$	−3.51129e6	−0.606662
$508$	411392.	0.0707288
$509$	5.24456e6	0.897252	0.448626	−	0.893720i	$-0.351914\pi$
$509$	5.24456e6	0.897252	0.448626	+	0.893720i	$0.351914\pi$
$510$	−1.24848e6	−0.212548
$511$	2.73734e6	0.463741
$512$	4.47130e6	0.753804
$513$	941840.	0.158010
$514$	4.42249e6	0.738345
$515$	1.30890e7	2.17465
$516$	−768640.	−0.127086
$517$	−8.96400e6	−1.47494
$518$	−1.00807e7	−1.65069
$519$	2.52432e6	0.411364
$520$	1.71763e6	0.278562
$521$	4.17805e6	0.674340	0.337170	−	0.941444i	$-0.390530\pi$
$521$	4.17805e6	0.674340	0.337170	+	0.941444i	$0.390530\pi$
$522$	−5.99227e6	−0.962532
$523$	−4.38518e6	−0.701024	−0.350512	−	0.936558i	$-0.613992\pi$
$523$	−4.38518e6	−0.701024	−0.350512	+	0.936558i	$0.613992\pi$
$524$	513144.	0.0816415
$525$	−4.03564e6	−0.639020
$526$	6.49282e6	1.02322
$527$	126004.	0.0197632
$528$	−5.11200e6	−0.798006
$529$	1.99687e6	0.310250
$530$	495072.	0.0765559
$531$	−3.14714e6	−0.484373
$532$	191296.	0.0293040
$533$	−2.32511e6	−0.354507
$534$	−4.23900e6	−0.643295
$535$	−5.94994e6	−0.898727
$536$	3.90835e6	0.587600
$537$	−5.55108e6	−0.830695
$538$	−9.11635e6	−1.35789
$539$	9.72405e6	1.44170
$540$	1.11168e6	0.164057
$541$	−4.33056e6	−0.636138	−0.318069	−	0.948068i	$-0.603034\pi$
$541$	−4.33056e6	−0.636138	−0.318069	+	0.948068i	$0.603034\pi$
$542$	−2.37374e6	−0.347085
$543$	15080.0	0.00219483
$544$	−416160.	−0.0602925
$545$	−1.76815e7	−2.54992
$546$	−1.66992e6	−0.239725
$547$	−2.70020e6	−0.385858	−0.192929	−	0.981213i	$-0.561799\pi$
$547$	−2.70020e6	−0.385858	−0.192929	+	0.981213i	$0.561799\pi$
$548$	93336.0	0.0132769
$549$	−5.11654e6	−0.724512
$550$	−5.55930e6	−0.783634
$551$	1.70410e6	0.239120
$552$	4.87872e6	0.681488
$553$	1.00132e7	1.39239
$554$	6.91066e6	0.956632
$555$	6.17184e6	0.850515
$556$	−69352.0	−0.00951419
$557$	9.26997e6	1.26602	0.633010	−	0.774144i	$-0.281819\pi$
$557$	9.26997e6	1.26602	0.633010	+	0.774144i	$0.281819\pi$
$558$	−374088.	−0.0508614
$559$	2.72867e6	0.369336
$560$	−1.60312e7	−2.16021
$561$	−1.30050e6	−0.174463
$562$	−8.23568e6	−1.09991
$563$	8.11546e6	1.07905	0.539525	−	0.841969i	$-0.318604\pi$
$563$	8.11546e6	1.07905	0.539525	+	0.841969i	$0.318604\pi$
$564$	−796800.	−0.105475
$565$	1.34650e7	1.77454
$566$	−1.37852e6	−0.180873
$567$	754796.	0.0985989
$568$	−5.32627e6	−0.692712
$569$	−1.14498e7	−1.48257	−0.741286	−	0.671190i	$-0.765784\pi$
$569$	−1.14498e7	−1.48257	−0.741286	+	0.671190i	$0.765784\pi$
$570$	−1.05408e6	−0.135890
$571$	−429442.	−0.0551206	−0.0275603	−	0.999620i	$-0.508774\pi$
$571$	−429442.	−0.0551206	−0.0275603	+	0.999620i	$0.508774\pi$
$572$	−255600.	−0.0326641
$573$	−3.92856e6	−0.499858
$574$	1.92558e7	2.43940
$575$	5.97934e6	0.754194
$576$	−3.96282e6	−0.497677
$577$	−4.38411e6	−0.548204	−0.274102	−	0.961701i	$-0.588381\pi$
$577$	−4.38411e6	−0.548204	−0.274102	+	0.961701i	$0.588381\pi$
$578$	−501126.	−0.0623918
$579$	−3.90538e6	−0.484135
$580$	2.01139e6	0.248271
$581$	1.26114e7	1.54997
$582$	−3.76212e6	−0.460389
$583$	515700.	0.0628385
$584$	−2.34629e6	−0.284675
$585$	−1.46203e6	−0.176631
$586$	−4.56916e6	−0.549657
$587$	1.89188e6	0.226621	0.113310	−	0.993560i	$-0.463855\pi$
$587$	1.89188e6	0.226621	0.113310	+	0.993560i	$0.463855\pi$
$588$	864360.	0.103098
$589$	106384.	0.0126354
$590$	9.50746e6	1.12443
$591$	2.05212e6	0.241676
$592$	9.73779e6	1.14197
$593$	−1.32588e7	−1.54834	−0.774171	−	0.632977i	$-0.781833\pi$
$593$	−1.32588e7	−1.54834	−0.774171	+	0.632977i	$0.781833\pi$
$594$	1.04220e7	1.21195
$595$	−4.07837e6	−0.472274
$596$	207960.	0.0239808
$597$	−4.05160e6	−0.465255
$598$	2.47421e6	0.282933
$599$	9.69070e6	1.10354	0.551770	−	0.833996i	$-0.313953\pi$
$599$	9.69070e6	1.10354	0.551770	+	0.833996i	$0.313953\pi$
$600$	3.45912e6	0.392272
$601$	−3.95875e6	−0.447066	−0.223533	−	0.974696i	$-0.571759\pi$
$601$	−3.95875e6	−0.447066	−0.223533	+	0.974696i	$0.571759\pi$
$602$	−2.25980e7	−2.54144
$603$	−3.32675e6	−0.372587
$604$	526016.	0.0586687
$605$	−2.98433e6	−0.331481
$606$	5.12820e6	0.567262
$607$	−3.92350e6	−0.432217	−0.216109	−	0.976369i	$-0.569337\pi$
$607$	−3.92350e6	−0.432217	−0.216109	+	0.976369i	$0.569337\pi$
$608$	−351360.	−0.0385472
$609$	1.36886e7	1.49561
$610$	1.54570e7	1.68190
$611$	2.82864e6	0.306531
$612$	165308.	0.0178408
$613$	1.50137e7	1.61375	0.806875	−	0.590722i	$-0.201157\pi$
$613$	1.50137e7	1.61375	0.806875	+	0.590722i	$0.201157\pi$
$614$	−3.59609e6	−0.384954
$615$	−1.17893e7	−1.25690
$616$	−1.48176e7	−1.57335
$617$	5.90027e6	0.623964	0.311982	−	0.950088i	$-0.399007\pi$
$617$	5.90027e6	0.623964	0.311982	+	0.950088i	$0.399007\pi$
$618$	1.09075e7	1.14883
$619$	1.52636e7	1.60114	0.800571	−	0.599238i	$-0.204530\pi$
$619$	1.52636e7	1.60114	0.800571	+	0.599238i	$0.204530\pi$
$620$	125568.	0.0131190
$621$	−1.12094e7	−1.16642
$622$	−5.08529e6	−0.527035
$623$	−1.38474e7	−1.42938
$624$	1.61312e6	0.165846
$625$	−1.19605e7	−1.22476
$626$	−1.20005e7	−1.22395
$627$	−1.09800e6	−0.111541
$628$	−2.39553e6	−0.242383
$629$	2.47731e6	0.249663
$630$	1.21081e7	1.21541
$631$	1.42765e7	1.42740	0.713702	−	0.700449i	$-0.247017\pi$
$631$	1.42765e7	1.42740	0.713702	+	0.700449i	$0.247017\pi$
$632$	−8.58278e6	−0.854743
$633$	−2.69662e6	−0.267492
$634$	−1.16676e6	−0.115281
$635$	−7.40506e6	−0.728776
$636$	45840.0	0.00449368
$637$	−3.06848e6	−0.299623
$638$	1.88568e7	1.83407
$639$	4.53367e6	0.439236
$640$	1.52893e7	1.47550
$641$	−3.51957e6	−0.338333	−0.169167	−	0.985587i	$-0.554108\pi$
$641$	−3.51957e6	−0.338333	−0.169167	+	0.985587i	$0.554108\pi$
$642$	−4.95828e6	−0.474781
$643$	−117478.	−0.0112054	−0.00560272	−	0.999984i	$-0.501783\pi$
$643$	−117478.	−0.0112054	−0.00560272	+	0.999984i	$0.501783\pi$
$644$	−2.27674e6	−0.216321
$645$	1.38355e7	1.30947
$646$	−423096.	−0.0398894
$647$	3.45269e6	0.324262	0.162131	−	0.986769i	$-0.448163\pi$
$647$	3.45269e6	0.324262	0.162131	+	0.986769i	$0.448163\pi$
$648$	−646968.	−0.0605265
$649$	9.90360e6	0.922957
$650$	1.75427e6	0.162859
$651$	854560.	0.0790297
$652$	−1.28778e6	−0.118638
$653$	−1.40017e7	−1.28499	−0.642494	−	0.766291i	$-0.722100\pi$
$653$	−1.40017e7	−1.28499	−0.642494	+	0.766291i	$0.722100\pi$
$654$	−1.47346e7	−1.34708
$655$	−9.23659e6	−0.841218
$656$	−1.86009e7	−1.68762
$657$	1.99714e6	0.180507
$658$	−2.34259e7	−2.10927
$659$	4.84952e6	0.434996	0.217498	−	0.976061i	$-0.430210\pi$
$659$	4.84952e6	0.434996	0.217498	+	0.976061i	$0.430210\pi$
$660$	−1.29600e6	−0.115810
$661$	1.01240e7	0.901258	0.450629	−	0.892711i	$-0.351200\pi$
$661$	1.01240e7	0.901258	0.450629	+	0.892711i	$0.351200\pi$
$662$	1.09405e7	0.970269
$663$	410380.	0.0362579
$664$	−1.08098e7	−0.951474
$665$	−3.44333e6	−0.301943
$666$	−7.35478e6	−0.642516
$667$	−2.02815e7	−1.76517
$668$	1.35806e6	0.117755
$669$	−4.55656e6	−0.393615
$670$	1.00500e7	0.864930
$671$	1.61010e7	1.38053
$672$	−2.82240e6	−0.241099
$673$	−1.40204e7	−1.19322	−0.596612	−	0.802530i	$-0.703487\pi$
$673$	−1.40204e7	−1.19322	−0.596612	+	0.802530i	$0.703487\pi$
$674$	1.55562e7	1.31902
$675$	−7.94774e6	−0.671404
$676$	−1.40452e6	−0.118212
$677$	7.67190e6	0.643326	0.321663	−	0.946854i	$-0.395758\pi$
$677$	7.67190e6	0.643326	0.321663	+	0.946854i	$0.395758\pi$
$678$	1.12208e7	0.937457
$679$	−1.22896e7	−1.02297
$680$	3.49574e6	0.289913
$681$	7.92366e6	0.654724
$682$	1.17720e6	0.0969146
$683$	−5.36631e6	−0.440174	−0.220087	−	0.975480i	$-0.570634\pi$
$683$	−5.36631e6	−0.440174	−0.220087	+	0.975480i	$0.570634\pi$
$684$	139568.	0.0114063
$685$	−1.68005e6	−0.136803
$686$	5.64715e6	0.458162
$687$	−1.79794e6	−0.145339
$688$	2.18294e7	1.75821
$689$	−162732.	−0.0130595
$690$	1.25453e7	1.00313
$691$	−1.31376e7	−1.04670	−0.523348	−	0.852119i	$-0.675317\pi$
$691$	−1.31376e7	−1.04670	−0.523348	+	0.852119i	$0.675317\pi$
$692$	1.00973e6	0.0801566
$693$	1.26126e7	0.997635
$694$	−1.60451e7	−1.26457
$695$	1.24834e6	0.0980324
$696$	−1.17331e7	−0.918101
$697$	−4.73209e6	−0.368953
$698$	−3.02473e6	−0.234989
$699$	2.45154e6	0.189778
$700$	−1.61426e6	−0.124517
$701$	−1.78160e6	−0.136935	−0.0684675	−	0.997653i	$-0.521811\pi$
$701$	−1.78160e6	−0.136935	−0.0684675	+	0.997653i	$0.521811\pi$
$702$	−3.28872e6	−0.251874
$703$	2.09157e6	0.159619
$704$	1.24704e7	0.948307
$705$	1.43424e7	1.08680
$706$	−6.04746e6	−0.456627
$707$	1.67521e7	1.26044
$708$	880320.	0.0660020
$709$	−1.16819e7	−0.872769	−0.436385	−	0.899760i	$-0.643741\pi$
$709$	−1.16819e7	−0.872769	−0.436385	+	0.899760i	$0.643741\pi$
$710$	−1.36961e7	−1.01965
$711$	7.30558e6	0.541977
$712$	1.18692e7	0.877448
$713$	−1.26614e6	−0.0932737
$714$	−3.39864e6	−0.249494
$715$	4.60080e6	0.336564
$716$	−2.22043e6	−0.161866
$717$	−3.34536e6	−0.243022
$718$	2.84710e7	2.06106
$719$	−1.62177e7	−1.16995	−0.584976	−	0.811051i	$-0.698896\pi$
$719$	−1.62177e7	−1.16995	−0.584976	+	0.811051i	$0.698896\pi$
$720$	−1.16963e7	−0.840844
$721$	3.56312e7	2.55266
$722$	1.44994e7	1.03516
$723$	−8.82922e6	−0.628169
$724$	6032.00	0.000427676 0
$725$	−1.43801e7	−1.01605
$726$	−2.48694e6	−0.175115
$727$	1.27353e7	0.893663	0.446832	−	0.894618i	$-0.352552\pi$
$727$	1.27353e7	0.893663	0.446832	+	0.894618i	$0.352552\pi$
$728$	4.67578e6	0.326983
$729$	9.93049e6	0.692073
$730$	−6.03331e6	−0.419033
$731$	5.55342e6	0.384386
$732$	1.43120e6	0.0987240
$733$	5.93825e6	0.408224	0.204112	−	0.978948i	$-0.434569\pi$
$733$	5.93825e6	0.408224	0.204112	+	0.978948i	$0.434569\pi$
$734$	−930288.	−0.0637349
$735$	−1.55585e7	−1.06230
$736$	4.18176e6	0.284554
$737$	1.04688e7	0.709951
$738$	1.40489e7	0.949514
$739$	−2.46285e7	−1.65892	−0.829462	−	0.558562i	$-0.811353\pi$
$739$	−2.46285e7	−1.65892	−0.829462	+	0.558562i	$0.811353\pi$
$740$	2.46874e6	0.165728
$741$	346480.	0.0231810
$742$	1.34770e6	0.0898633
$743$	−440628.	−0.0292820	−0.0146410	−	0.999893i	$-0.504661\pi$
$743$	−440628.	−0.0292820	−0.0146410	+	0.999893i	$0.504661\pi$
$744$	−732480.	−0.0485136
$745$	−3.74328e6	−0.247094
$746$	−2.33886e7	−1.53871
$747$	9.20119e6	0.603313
$748$	−520200.	−0.0339951
$749$	−1.61970e7	−1.05495
$750$	−4.60512e6	−0.298943
$751$	−5.22736e6	−0.338207	−0.169103	−	0.985598i	$-0.554087\pi$
$751$	−5.22736e6	−0.338207	−0.169103	+	0.985598i	$0.554087\pi$
$752$	2.26291e7	1.45923
$753$	−1.46928e6	−0.0944316
$754$	−5.95037e6	−0.381167
$755$	−9.46829e6	−0.604511
$756$	3.02624e6	0.192575
$757$	−1.60789e7	−1.01980	−0.509901	−	0.860233i	$-0.670318\pi$
$757$	−1.60789e7	−1.01980	−0.509901	+	0.860233i	$0.670318\pi$
$758$	1.66097e7	1.05000
$759$	1.30680e7	0.823388
$760$	2.95142e6	0.185352
$761$	−1.98848e7	−1.24468	−0.622341	−	0.782746i	$-0.713818\pi$
$761$	−1.98848e7	−1.24468	−0.622341	+	0.782746i	$0.713818\pi$
$762$	−6.17088e6	−0.384999
$763$	−4.81329e7	−2.99316
$764$	−1.57142e6	−0.0974002
$765$	−2.97554e6	−0.183828
$766$	2.10817e7	1.29818
$767$	−3.12514e6	−0.191814
$768$	3.87328e6	0.236960
$769$	−2.73915e7	−1.67032	−0.835160	−	0.550007i	$-0.814625\pi$
$769$	−2.73915e7	−1.67032	−0.835160	+	0.550007i	$0.814625\pi$
$770$	−3.81024e7	−2.31593
$771$	−7.37082e6	−0.446560
$772$	−1.56215e6	−0.0943366
$773$	2.30626e7	1.38822	0.694112	−	0.719867i	$-0.255797\pi$
$773$	2.30626e7	1.38822	0.694112	+	0.719867i	$0.255797\pi$
$774$	−1.64873e7	−0.989231
$775$	−897724.	−0.0536894
$776$	1.05339e7	0.627966
$777$	1.68011e7	0.998357
$778$	−5.00620e6	−0.296523
$779$	−3.99526e6	−0.235885
$780$	408960.	0.0240682
$781$	−1.42668e7	−0.836949
$782$	5.03554e6	0.294462
$783$	2.69582e7	1.57140
$784$	−2.45478e7	−1.42634
$785$	4.31195e7	2.49747
$786$	−7.69716e6	−0.444400
$787$	−642682.	−0.0369879	−0.0184939	−	0.999829i	$-0.505887\pi$
$787$	−642682.	−0.0369879	−0.0184939	+	0.999829i	$0.505887\pi$
$788$	820848.	0.0470920
$789$	−1.08214e7	−0.618856
$790$	−2.20700e7	−1.25816
$791$	3.66547e7	2.08300
$792$	−1.08108e7	−0.612414
$793$	−5.08076e6	−0.286910
$794$	3.04848e7	1.71606
$795$	−825120.	−0.0463020
$796$	−1.62064e6	−0.0906575
$797$	9.10785e6	0.507890	0.253945	−	0.967219i	$-0.418272\pi$
$797$	9.10785e6	0.507890	0.253945	+	0.967219i	$0.418272\pi$
$798$	−2.86944e6	−0.159511
$799$	5.75688e6	0.319022
$800$	2.96496e6	0.163792
$801$	−1.01030e7	−0.556374
$802$	−3.89740e6	−0.213963
$803$	−6.28470e6	−0.343950
$804$	930560.	0.0507697
$805$	4.09812e7	2.22893
$806$	−371472.	−0.0201413
$807$	1.51939e7	0.821270
$808$	−1.43590e7	−0.773739
$809$	−1.37190e7	−0.736972	−0.368486	−	0.929633i	$-0.620124\pi$
$809$	−1.37190e7	−0.736972	−0.368486	+	0.929633i	$0.620124\pi$
$810$	−1.66363e6	−0.0890932
$811$	2.74959e7	1.46796	0.733982	−	0.679168i	$-0.237659\pi$
$811$	2.74959e7	1.46796	0.733982	+	0.679168i	$0.237659\pi$
$812$	5.47546e6	0.291427
$813$	3.95624e6	0.209921
$814$	2.31444e7	1.22429
$815$	2.31801e7	1.22242
$816$	3.28304e6	0.172604
$817$	4.68870e6	0.245752
$818$	−2.00079e7	−1.04548
$819$	−3.97998e6	−0.207334
$820$	−4.71571e6	−0.244913
$821$	2.85504e7	1.47827	0.739136	−	0.673556i	$-0.235234\pi$
$821$	2.85504e7	1.47827	0.739136	+	0.673556i	$0.235234\pi$
$822$	−1.40004e6	−0.0722705
$823$	−58840.0	−0.00302812	−0.00151406	−	0.999999i	$-0.500482\pi$
$823$	−58840.0	−0.00302812	−0.00151406	+	0.999999i	$0.500482\pi$
$824$	−3.05411e7	−1.56699
$825$	9.26550e6	0.473952
$826$	2.58814e7	1.31989
$827$	−3.14197e7	−1.59749	−0.798745	−	0.601670i	$-0.794502\pi$
$827$	−3.14197e7	−1.59749	−0.798745	+	0.601670i	$0.794502\pi$
$828$	−1.66109e6	−0.0842009
$829$	9.55809e6	0.483042	0.241521	−	0.970396i	$-0.422354\pi$
$829$	9.55809e6	0.483042	0.241521	+	0.970396i	$0.422354\pi$
$830$	−2.77966e7	−1.40054
$831$	−1.15178e7	−0.578583
$832$	−3.93510e6	−0.197082
$833$	−6.24500e6	−0.311832
$834$	1.04028e6	0.0517887
$835$	−2.44452e7	−1.21332
$836$	−439200.	−0.0217343
$837$	1.68296e6	0.0830348
$838$	−1.03519e7	−0.509226
$839$	−82980.0	−0.00406976	−0.00203488	−	0.999998i	$-0.500648\pi$
$839$	−82980.0	−0.00406976	−0.00203488	+	0.999998i	$0.500648\pi$
$840$	2.37082e7	1.15931
$841$	2.82651e7	1.37804
$842$	−5.54833e6	−0.269701
$843$	1.37261e7	0.665242
$844$	−1.07865e6	−0.0521223
$845$	2.52813e7	1.21803
$846$	−1.70914e7	−0.821014
$847$	−8.12400e6	−0.389100
$848$	−1.30186e6	−0.0621689
$849$	2.29754e6	0.109394
$850$	3.57031e6	0.169495
$851$	−2.48931e7	−1.17830
$852$	−1.26816e6	−0.0598515
$853$	2.82115e7	1.32756	0.663779	−	0.747929i	$-0.268951\pi$
$853$	2.82115e7	1.32756	0.663779	+	0.747929i	$0.268951\pi$
$854$	4.20773e7	1.97425
$855$	−2.51222e6	−0.117528
$856$	1.38832e7	0.647597
$857$	3.64611e6	0.169581	0.0847906	−	0.996399i	$-0.472978\pi$
$857$	3.64611e6	0.169581	0.0847906	+	0.996399i	$0.472978\pi$
$858$	3.83400e6	0.177801
$859$	−1.98241e7	−0.916664	−0.458332	−	0.888781i	$-0.651553\pi$
$859$	−1.98241e7	−0.916664	−0.458332	+	0.888781i	$0.651553\pi$
$860$	5.53421e6	0.255158
$861$	−3.20930e7	−1.47538
$862$	−2.89884e7	−1.32879
$863$	−3.96712e7	−1.81321	−0.906605	−	0.421980i	$-0.861335\pi$
$863$	−3.96712e7	−1.81321	−0.906605	+	0.421980i	$0.861335\pi$
$864$	−5.55840e6	−0.253318
$865$	−1.81751e7	−0.825917
$866$	−3.23971e7	−1.46795
$867$	835210.	0.0377353
$868$	341824.	0.0153994
$869$	−2.29896e7	−1.03272
$870$	−3.01709e7	−1.35142
$871$	−3.30349e6	−0.147546
$872$	4.12568e7	1.83740
$873$	−8.96639e6	−0.398182
$874$	4.25146e6	0.188260
$875$	−1.50434e7	−0.664241
$876$	−558640.	−0.0245964
$877$	3.83641e7	1.68432	0.842162	−	0.539225i	$-0.181283\pi$
$877$	3.83641e7	1.68432	0.842162	+	0.539225i	$0.181283\pi$
$878$	−2.26992e7	−0.993743
$879$	7.61526e6	0.332439
$880$	3.68064e7	1.60220
$881$	−2.64738e7	−1.14915	−0.574575	−	0.818452i	$-0.694833\pi$
$881$	−2.64738e7	−1.14915	−0.574575	+	0.818452i	$0.694833\pi$
$882$	1.85405e7	0.802510
$883$	2.76564e7	1.19370	0.596848	−	0.802354i	$-0.296419\pi$
$883$	2.76564e7	1.19370	0.596848	+	0.802354i	$0.296419\pi$
$884$	164152.	0.00706505
$885$	−1.58458e7	−0.680072
$886$	2.52141e7	1.07909
$887$	5.91883e6	0.252596	0.126298	−	0.991992i	$-0.459690\pi$
$887$	5.91883e6	0.252596	0.126298	+	0.991992i	$0.459690\pi$
$888$	−1.44010e7	−0.612857
$889$	−2.01582e7	−0.855456
$890$	3.05208e7	1.29158
$891$	−1.73295e6	−0.0731294
$892$	−1.82262e6	−0.0766982
$893$	4.86048e6	0.203963
$894$	−3.11940e6	−0.130535
$895$	3.99678e7	1.66783
$896$	4.16210e7	1.73198
$897$	−4.12368e6	−0.171121
$898$	2.23334e7	0.924194
$899$	3.04502e6	0.125658
$900$	−1.17775e6	−0.0484670
$901$	−331194.	−0.0135916
$902$	−4.42098e7	−1.80927
$903$	3.76634e7	1.53709
$904$	−3.14184e7	−1.27868
$905$	−108576.	−0.00440669
$906$	−7.89024e6	−0.319352
$907$	−4.04616e7	−1.63315	−0.816573	−	0.577243i	$-0.804129\pi$
$907$	−4.04616e7	−1.63315	−0.816573	+	0.577243i	$0.804129\pi$
$908$	3.16946e6	0.127577
$909$	1.22222e7	0.490614
$910$	1.20234e7	0.481310
$911$	−1.02375e7	−0.408695	−0.204347	−	0.978898i	$-0.565507\pi$
$911$	−1.02375e7	−0.408695	−0.204347	+	0.978898i	$0.565507\pi$
$912$	2.77184e6	0.110352
$913$	−2.89548e7	−1.14959
$914$	−3.92246e7	−1.55308
$915$	−2.57616e7	−1.01723
$916$	−719176.	−0.0283202
$917$	−2.51441e7	−0.987443
$918$	−6.69324e6	−0.262138
$919$	−1.95081e7	−0.761948	−0.380974	−	0.924586i	$-0.624411\pi$
$919$	−1.95081e7	−0.761948	−0.380974	+	0.924586i	$0.624411\pi$
$920$	−3.51268e7	−1.36826
$921$	5.99348e6	0.232825
$922$	1.70387e7	0.660099
$923$	4.50197e6	0.173939
$924$	−3.52800e6	−0.135940
$925$	−1.76497e7	−0.678241
$926$	2.53740e7	0.972439
$927$	2.59963e7	0.993600
$928$	−1.00570e7	−0.383351
$929$	−6.77925e6	−0.257717	−0.128858	−	0.991663i	$-0.541131\pi$
$929$	−6.77925e6	−0.257717	−0.128858	+	0.991663i	$0.541131\pi$
$930$	−1.88352e6	−0.0714106
$931$	−5.27260e6	−0.199366
$932$	980616.	0.0369793
$933$	8.47548e6	0.318757
$934$	2.41329e7	0.905195
$935$	9.36360e6	0.350279
$936$	3.41141e6	0.127275
$937$	4.20612e7	1.56507	0.782533	−	0.622609i	$-0.213927\pi$
$937$	4.20612e7	1.56507	0.782533	+	0.622609i	$0.213927\pi$
$938$	2.73585e7	1.01528
$939$	2.00008e7	0.740258
$940$	5.73696e6	0.211769
$941$	−4.41336e7	−1.62478	−0.812391	−	0.583113i	$-0.801834\pi$
$941$	−4.41336e7	−1.62478	−0.812391	+	0.583113i	$0.801834\pi$
$942$	3.59329e7	1.31937
$943$	4.75501e7	1.74129
$944$	−2.50011e7	−0.913122
$945$	−5.44723e7	−1.98425
$946$	5.18832e7	1.88495
$947$	1.21508e7	0.440282	0.220141	−	0.975468i	$-0.429348\pi$
$947$	1.21508e7	0.440282	0.220141	+	0.975468i	$0.429348\pi$
$948$	−2.04352e6	−0.0738513
$949$	1.98317e6	0.0714817
$950$	3.01438e6	0.108365
$951$	1.94460e6	0.0697235
$952$	9.51619e6	0.340307
$953$	2.39119e7	0.852869	0.426435	−	0.904518i	$-0.359769\pi$
$953$	2.39119e7	0.852869	0.426435	+	0.904518i	$0.359769\pi$
$954$	983268.	0.0349785
$955$	2.82856e7	1.00359
$956$	−1.33814e6	−0.0473542
$957$	−3.14280e7	−1.10927
$958$	2.21164e7	0.778575
$959$	−4.57346e6	−0.160583
$960$	−1.99526e7	−0.698751
$961$	−2.84391e7	−0.993360
$962$	−7.30334e6	−0.254439
$963$	−1.18172e7	−0.410629
$964$	−3.53169e6	−0.122402
$965$	2.81187e7	0.972025
$966$	3.41510e7	1.17750
$967$	−4.71653e7	−1.62202	−0.811011	−	0.585031i	$-0.801082\pi$
$967$	−4.71653e7	−1.62202	−0.811011	+	0.585031i	$0.801082\pi$
$968$	6.96343e6	0.238855
$969$	705160.	0.0241256
$970$	2.70873e7	0.924349
$971$	3.76796e7	1.28250	0.641251	−	0.767331i	$-0.278416\pi$
$971$	3.76796e7	1.28250	0.641251	+	0.767331i	$0.278416\pi$
$972$	3.59788e6	0.122146
$973$	3.39825e6	0.115073
$974$	1.33685e7	0.451528
$975$	−2.92378e6	−0.0984993
$976$	−4.06461e7	−1.36582
$977$	−4.65997e7	−1.56188	−0.780938	−	0.624608i	$-0.785259\pi$
$977$	−4.65997e7	−1.56188	−0.780938	+	0.624608i	$0.785259\pi$
$978$	1.93168e7	0.645784
$979$	3.17925e7	1.06015
$980$	−6.22339e6	−0.206996
$981$	−3.51174e7	−1.16506
$982$	−1.20928e7	−0.400172
$983$	3.55297e7	1.17276	0.586378	−	0.810038i	$-0.300553\pi$
$983$	3.55297e7	1.17276	0.586378	+	0.810038i	$0.300553\pi$
$984$	2.75083e7	0.905683
$985$	−1.47753e7	−0.485227
$986$	−1.21103e7	−0.396699
$987$	3.90432e7	1.27571
$988$	138592.	0.00451696
$989$	−5.58033e7	−1.81413
$990$	−2.77992e7	−0.901456
$991$	3.01289e7	0.974538	0.487269	−	0.873252i	$-0.337993\pi$
$991$	3.01289e7	0.974538	0.487269	+	0.873252i	$0.337993\pi$
$992$	−627840.	−0.0202568
$993$	−1.82342e7	−0.586830
$994$	−3.72839e7	−1.19689
$995$	2.91715e7	0.934117
$996$	−2.57376e6	−0.0822091
$997$	−2.76127e7	−0.879774	−0.439887	−	0.898053i	$-0.644982\pi$
$997$	−2.76127e7	−0.879774	−0.439887	+	0.898053i	$0.644982\pi$
$998$	−9.49638e6	−0.301809
$999$	3.30879e7	1.04895

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.6.a.a.1.1	✓	1
3.2	odd	2		153.6.a.b.1.1		1
4.3	odd	2		272.6.a.a.1.1		1
5.4	even	2		425.6.a.b.1.1		1
7.6	odd	2		833.6.a.a.1.1		1
8.3	odd	2		1088.6.a.g.1.1		1
8.5	even	2		1088.6.a.d.1.1		1
17.16	even	2		289.6.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.6.a.a.1.1	✓	1	1.1	even	1	trivial
153.6.a.b.1.1		1	3.2	odd	2
272.6.a.a.1.1		1	4.3	odd	2
289.6.a.a.1.1		1	17.16	even	2
425.6.a.b.1.1		1	5.4	even	2
833.6.a.a.1.1		1	7.6	odd	2
1088.6.a.d.1.1		1	8.5	even	2
1088.6.a.g.1.1		1	8.3	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:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	17.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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