LMFDB - Embedded newform 70.6.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [70,6,Mod(1,70)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(70, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("70.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 70 = 2 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	70.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:	$11.2268673869$
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	$\chi$	$=$	70.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

\(q+4.00000 q^{2} -11.0000 q^{3} +16.0000 q^{4} -25.0000 q^{5} -44.0000 q^{6} +49.0000 q^{7} +64.0000 q^{8} -122.000 q^{9} -100.000 q^{10} -267.000 q^{11} -176.000 q^{12} -1087.00 q^{13} +196.000 q^{14} +275.000 q^{15} +256.000 q^{16} -513.000 q^{17} -488.000 q^{18} -802.000 q^{19} -400.000 q^{20} -539.000 q^{21} -1068.00 q^{22} -1290.00 q^{23} -704.000 q^{24} +625.000 q^{25} -4348.00 q^{26} +4015.00 q^{27} +784.000 q^{28} +1779.00 q^{29} +1100.00 q^{30} -2584.00 q^{31} +1024.00 q^{32} +2937.00 q^{33} -2052.00 q^{34} -1225.00 q^{35} -1952.00 q^{36} +13862.0 q^{37} -3208.00 q^{38} +11957.0 q^{39} -1600.00 q^{40} -11904.0 q^{41} -2156.00 q^{42} -598.000 q^{43} -4272.00 q^{44} +3050.00 q^{45} -5160.00 q^{46} -17019.0 q^{47} -2816.00 q^{48} +2401.00 q^{49} +2500.00 q^{50} +5643.00 q^{51} -17392.0 q^{52} +27852.0 q^{53} +16060.0 q^{54} +6675.00 q^{55} +3136.00 q^{56} +8822.00 q^{57} +7116.00 q^{58} +30912.0 q^{59} +4400.00 q^{60} -1780.00 q^{61} -10336.0 q^{62} -5978.00 q^{63} +4096.00 q^{64} +27175.0 q^{65} +11748.0 q^{66} +25052.0 q^{67} -8208.00 q^{68} +14190.0 q^{69} -4900.00 q^{70} -51984.0 q^{71} -7808.00 q^{72} +47690.0 q^{73} +55448.0 q^{74} -6875.00 q^{75} -12832.0 q^{76} -13083.0 q^{77} +47828.0 q^{78} -102121. q^{79} -6400.00 q^{80} -14519.0 q^{81} -47616.0 q^{82} -83676.0 q^{83} -8624.00 q^{84} +12825.0 q^{85} -2392.00 q^{86} -19569.0 q^{87} -17088.0 q^{88} -32400.0 q^{89} +12200.0 q^{90} -53263.0 q^{91} -20640.0 q^{92} +28424.0 q^{93} -68076.0 q^{94} +20050.0 q^{95} -11264.0 q^{96} -148645. q^{97} +9604.00 q^{98} +32574.0 q^{99} +O(q^{100})\)

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 $

$2$	4.00000	0.707107
$2$	4.00000	0.707107
$3$	−11.0000	−0.705650	−0.352825	−	0.935689i	$-0.614779\pi$
$3$	−11.0000	−0.705650	−0.352825	+	0.935689i	$0.614779\pi$
$4$	16.0000	0.500000
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−44.0000	−0.498970
$7$	49.0000	0.377964
$7$	49.0000	0.377964
$8$	64.0000	0.353553
$9$	−122.000	−0.502058
$10$	−100.000	−0.316228
$11$	−267.000	−0.665318	−0.332659	−	0.943047i	$-0.607946\pi$
$11$	−267.000	−0.665318	−0.332659	+	0.943047i	$0.607946\pi$
$12$	−176.000	−0.352825
$13$	−1087.00	−1.78390	−0.891951	−	0.452131i	$-0.850664\pi$
$13$	−1087.00	−1.78390	−0.891951	+	0.452131i	$0.850664\pi$
$14$	196.000	0.267261
$15$	275.000	0.315576
$16$	256.000	0.250000
$17$	−513.000	−0.430522	−0.215261	−	0.976557i	$-0.569060\pi$
$17$	−513.000	−0.430522	−0.215261	+	0.976557i	$0.569060\pi$
$18$	−488.000	−0.355008
$19$	−802.000	−0.509672	−0.254836	−	0.966984i	$-0.582021\pi$
$19$	−802.000	−0.509672	−0.254836	+	0.966984i	$0.582021\pi$
$20$	−400.000	−0.223607
$21$	−539.000	−0.266711
$22$	−1068.00	−0.470451
$23$	−1290.00	−0.508476	−0.254238	−	0.967142i	$-0.581825\pi$
$23$	−1290.00	−0.508476	−0.254238	+	0.967142i	$0.581825\pi$
$24$	−704.000	−0.249485
$25$	625.000	0.200000
$26$	−4348.00	−1.26141
$27$	4015.00	1.05993
$28$	784.000	0.188982
$29$	1779.00	0.392809	0.196404	−	0.980523i	$-0.437074\pi$
$29$	1779.00	0.392809	0.196404	+	0.980523i	$0.437074\pi$
$30$	1100.00	0.223146
$31$	−2584.00	−0.482935	−0.241467	−	0.970409i	$-0.577629\pi$
$31$	−2584.00	−0.482935	−0.241467	+	0.970409i	$0.577629\pi$
$32$	1024.00	0.176777
$33$	2937.00	0.469482
$34$	−2052.00	−0.304425
$35$	−1225.00	−0.169031
$36$	−1952.00	−0.251029
$37$	13862.0	1.66464	0.832322	−	0.554292i	$-0.187011\pi$
$37$	13862.0	1.66464	0.832322	+	0.554292i	$0.187011\pi$
$38$	−3208.00	−0.360392
$39$	11957.0	1.25881
$40$	−1600.00	−0.158114
$41$	−11904.0	−1.10594	−0.552972	−	0.833200i	$-0.686506\pi$
$41$	−11904.0	−1.10594	−0.552972	+	0.833200i	$0.686506\pi$
$42$	−2156.00	−0.188593
$43$	−598.000	−0.0493208	−0.0246604	−	0.999696i	$-0.507850\pi$
$43$	−598.000	−0.0493208	−0.0246604	+	0.999696i	$0.507850\pi$
$44$	−4272.00	−0.332659
$45$	3050.00	0.224527
$46$	−5160.00	−0.359547
$47$	−17019.0	−1.12380	−0.561900	−	0.827205i	$-0.689930\pi$
$47$	−17019.0	−1.12380	−0.561900	+	0.827205i	$0.689930\pi$
$48$	−2816.00	−0.176413
$49$	2401.00	0.142857
$50$	2500.00	0.141421
$51$	5643.00	0.303798
$52$	−17392.0	−0.891951
$53$	27852.0	1.36197	0.680984	−	0.732299i	$-0.261552\pi$
$53$	27852.0	1.36197	0.680984	+	0.732299i	$0.261552\pi$
$54$	16060.0	0.749482
$55$	6675.00	0.297539
$56$	3136.00	0.133631
$57$	8822.00	0.359650
$58$	7116.00	0.277758
$59$	30912.0	1.15610	0.578052	−	0.816000i	$-0.303813\pi$
$59$	30912.0	1.15610	0.578052	+	0.816000i	$0.303813\pi$
$60$	4400.00	0.157788
$61$	−1780.00	−0.0612485	−0.0306242	−	0.999531i	$-0.509750\pi$
$61$	−1780.00	−0.0612485	−0.0306242	+	0.999531i	$0.509750\pi$
$62$	−10336.0	−0.341486
$63$	−5978.00	−0.189760
$64$	4096.00	0.125000
$65$	27175.0	0.797786
$66$	11748.0	0.331974
$67$	25052.0	0.681797	0.340899	−	0.940100i	$-0.389269\pi$
$67$	25052.0	0.681797	0.340899	+	0.940100i	$0.389269\pi$
$68$	−8208.00	−0.215261
$69$	14190.0	0.358806
$70$	−4900.00	−0.119523
$71$	−51984.0	−1.22384	−0.611919	−	0.790921i	$-0.709602\pi$
$71$	−51984.0	−1.22384	−0.611919	+	0.790921i	$0.709602\pi$
$72$	−7808.00	−0.177504
$73$	47690.0	1.04742	0.523709	−	0.851897i	$-0.324548\pi$
$73$	47690.0	1.04742	0.523709	+	0.851897i	$0.324548\pi$
$74$	55448.0	1.17708
$75$	−6875.00	−0.141130
$76$	−12832.0	−0.254836
$77$	−13083.0	−0.251467
$78$	47828.0	0.890114
$79$	−102121.	−1.84097	−0.920486	−	0.390775i	$-0.872207\pi$
$79$	−102121.	−1.84097	−0.920486	+	0.390775i	$0.872207\pi$
$80$	−6400.00	−0.111803
$81$	−14519.0	−0.245881
$82$	−47616.0	−0.782021
$83$	−83676.0	−1.33323	−0.666616	−	0.745401i	$-0.732258\pi$
$83$	−83676.0	−1.33323	−0.666616	+	0.745401i	$0.732258\pi$
$84$	−8624.00	−0.133355
$85$	12825.0	0.192535
$86$	−2392.00	−0.0348751
$87$	−19569.0	−0.277185
$88$	−17088.0	−0.235226
$89$	−32400.0	−0.433581	−0.216790	−	0.976218i	$-0.569559\pi$
$89$	−32400.0	−0.433581	−0.216790	+	0.976218i	$0.569559\pi$
$90$	12200.0	0.158765
$91$	−53263.0	−0.674252
$92$	−20640.0	−0.254238
$93$	28424.0	0.340783
$94$	−68076.0	−0.794647
$95$	20050.0	0.227932
$96$	−11264.0	−0.124743
$97$	−148645.	−1.60406	−0.802031	−	0.597283i	$-0.796247\pi$
$97$	−148645.	−1.60406	−0.802031	+	0.597283i	$0.796247\pi$
$98$	9604.00	0.101015
$99$	32574.0	0.334028
$100$	10000.0	0.100000
$101$	−41310.0	−0.402951	−0.201475	−	0.979494i	$-0.564574\pi$
$101$	−41310.0	−0.402951	−0.201475	+	0.979494i	$0.564574\pi$
$102$	22572.0	0.214817
$103$	108785.	1.01036	0.505180	−	0.863014i	$-0.331426\pi$
$103$	108785.	1.01036	0.505180	+	0.863014i	$0.331426\pi$
$104$	−69568.0	−0.630705
$105$	13475.0	0.119277
$106$	111408.	0.963056
$107$	−106098.	−0.895876	−0.447938	−	0.894065i	$-0.647841\pi$
$107$	−106098.	−0.895876	−0.447938	+	0.894065i	$0.647841\pi$
$108$	64240.0	0.529964
$109$	−124111.	−1.00056	−0.500281	−	0.865863i	$-0.666770\pi$
$109$	−124111.	−1.00056	−0.500281	+	0.865863i	$0.666770\pi$
$110$	26700.0	0.210392
$111$	−152482.	−1.17466
$112$	12544.0	0.0944911
$113$	192834.	1.42065	0.710326	−	0.703873i	$-0.248548\pi$
$113$	192834.	1.42065	0.710326	+	0.703873i	$0.248548\pi$
$114$	35288.0	0.254311
$115$	32250.0	0.227397
$116$	28464.0	0.196404
$117$	132614.	0.895622
$118$	123648.	0.817489
$119$	−25137.0	−0.162722
$120$	17600.0	0.111573
$121$	−89762.0	−0.557351
$122$	−7120.00	−0.0433092
$123$	130944.	0.780410
$124$	−41344.0	−0.241467
$125$	−15625.0	−0.0894427
$126$	−23912.0	−0.134181
$127$	99248.0	0.546025	0.273012	−	0.962010i	$-0.411980\pi$
$127$	99248.0	0.546025	0.273012	+	0.962010i	$0.411980\pi$
$128$	16384.0	0.0883883
$129$	6578.00	0.0348032
$130$	108700.	0.564120
$131$	−276810.	−1.40930	−0.704650	−	0.709555i	$-0.748896\pi$
$131$	−276810.	−1.40930	−0.704650	+	0.709555i	$0.748896\pi$
$132$	46992.0	0.234741
$133$	−39298.0	−0.192638
$134$	100208.	0.482104
$135$	−100375.	−0.474014
$136$	−32832.0	−0.152212
$137$	237744.	1.08220	0.541101	−	0.840958i	$-0.318008\pi$
$137$	237744.	1.08220	0.541101	+	0.840958i	$0.318008\pi$
$138$	56760.0	0.253714
$139$	160478.	0.704496	0.352248	−	0.935907i	$-0.385417\pi$
$139$	160478.	0.704496	0.352248	+	0.935907i	$0.385417\pi$
$140$	−19600.0	−0.0845154
$141$	187209.	0.793011
$142$	−207936.	−0.865384
$143$	290229.	1.18686
$144$	−31232.0	−0.125514
$145$	−44475.0	−0.175669
$146$	190760.	0.740637
$147$	−26411.0	−0.100807
$148$	221792.	0.832322
$149$	−99678.0	−0.367819	−0.183909	−	0.982943i	$-0.558875\pi$
$149$	−99678.0	−0.367819	−0.183909	+	0.982943i	$0.558875\pi$
$150$	−27500.0	−0.0997940
$151$	−206017.	−0.735293	−0.367647	−	0.929966i	$-0.619836\pi$
$151$	−206017.	−0.735293	−0.367647	+	0.929966i	$0.619836\pi$
$152$	−51328.0	−0.180196
$153$	62586.0	0.216147
$154$	−52332.0	−0.177814
$155$	64600.0	0.215975
$156$	191312.	0.629406
$157$	581150.	1.88165	0.940826	−	0.338891i	$-0.110052\pi$
$157$	581150.	1.88165	0.940826	+	0.338891i	$0.110052\pi$
$158$	−408484.	−1.30176
$159$	−306372.	−0.961073
$160$	−25600.0	−0.0790569
$161$	−63210.0	−0.192186
$162$	−58076.0	−0.173864
$163$	346610.	1.02181	0.510907	−	0.859636i	$-0.329310\pi$
$163$	346610.	1.02181	0.510907	+	0.859636i	$0.329310\pi$
$164$	−190464.	−0.552972
$165$	−73425.0	−0.209959
$166$	−334704.	−0.942737
$167$	−448887.	−1.24551	−0.622753	−	0.782418i	$-0.713986\pi$
$167$	−448887.	−1.24551	−0.622753	+	0.782418i	$0.713986\pi$
$168$	−34496.0	−0.0942965
$169$	810276.	2.18231
$170$	51300.0	0.136143
$171$	97844.0	0.255884
$172$	−9568.00	−0.0246604
$173$	−262509.	−0.666851	−0.333426	−	0.942776i	$-0.608205\pi$
$173$	−262509.	−0.666851	−0.333426	+	0.942776i	$0.608205\pi$
$174$	−78276.0	−0.196000
$175$	30625.0	0.0755929
$176$	−68352.0	−0.166330
$177$	−340032.	−0.815805
$178$	−129600.	−0.306588
$179$	−111012.	−0.258963	−0.129481	−	0.991582i	$-0.541331\pi$
$179$	−111012.	−0.258963	−0.129481	+	0.991582i	$0.541331\pi$
$180$	48800.0	0.112263
$181$	112772.	0.255861	0.127931	−	0.991783i	$-0.459166\pi$
$181$	112772.	0.255861	0.127931	+	0.991783i	$0.459166\pi$
$182$	−213052.	−0.476768
$183$	19580.0	0.0432200
$184$	−82560.0	−0.179773
$185$	−346550.	−0.744452
$186$	113696.	0.240970
$187$	136971.	0.286434
$188$	−272304.	−0.561900
$189$	196735.	0.400615
$190$	80200.0	0.161172
$191$	−731991.	−1.45185	−0.725926	−	0.687773i	$-0.758589\pi$
$191$	−731991.	−1.45185	−0.725926	+	0.687773i	$0.758589\pi$
$192$	−45056.0	−0.0882063
$193$	−186040.	−0.359512	−0.179756	−	0.983711i	$-0.557531\pi$
$193$	−186040.	−0.359512	−0.179756	+	0.983711i	$0.557531\pi$
$194$	−594580.	−1.13424
$195$	−298925.	−0.562958
$196$	38416.0	0.0714286
$197$	121356.	0.222790	0.111395	−	0.993776i	$-0.464468\pi$
$197$	121356.	0.222790	0.111395	+	0.993776i	$0.464468\pi$
$198$	130296.	0.236194
$199$	648584.	1.16100	0.580502	−	0.814259i	$-0.302856\pi$
$199$	648584.	1.16100	0.580502	+	0.814259i	$0.302856\pi$
$200$	40000.0	0.0707107
$201$	−275572.	−0.481111
$202$	−165240.	−0.284929
$203$	87171.0	0.148468
$204$	90288.0	0.151899
$205$	297600.	0.494593
$206$	435140.	0.714432
$207$	157380.	0.255284
$208$	−278272.	−0.445976
$209$	214134.	0.339094
$210$	53900.0	0.0843413
$211$	−149773.	−0.231594	−0.115797	−	0.993273i	$-0.536942\pi$
$211$	−149773.	−0.231594	−0.115797	+	0.993273i	$0.536942\pi$
$212$	445632.	0.680984
$213$	571824.	0.863601
$214$	−424392.	−0.633480
$215$	14950.0	0.0220569
$216$	256960.	0.374741
$217$	−126616.	−0.182532
$218$	−496444.	−0.707504
$219$	−524590.	−0.739111
$220$	106800.	0.148770
$221$	557631.	0.768009
$222$	−609928.	−0.830608
$223$	−1.10096e6	−1.48255	−0.741274	−	0.671202i	$-0.765778\pi$
$223$	−1.10096e6	−1.48255	−0.741274	+	0.671202i	$0.765778\pi$
$224$	50176.0	0.0668153
$225$	−76250.0	−0.100412
$226$	771336.	1.00455
$227$	−695127.	−0.895364	−0.447682	−	0.894193i	$-0.647750\pi$
$227$	−695127.	−0.895364	−0.447682	+	0.894193i	$0.647750\pi$
$228$	141152.	0.179825
$229$	463736.	0.584362	0.292181	−	0.956363i	$-0.405619\pi$
$229$	463736.	0.584362	0.292181	+	0.956363i	$0.405619\pi$
$230$	129000.	0.160794
$231$	143913.	0.177448
$232$	113856.	0.138879
$233$	−1.57654e6	−1.90245	−0.951227	−	0.308492i	$-0.900176\pi$
$233$	−1.57654e6	−1.90245	−0.951227	+	0.308492i	$0.900176\pi$
$234$	530456.	0.633300
$235$	425475.	0.502579
$236$	494592.	0.578052
$237$	1.12333e6	1.29908
$238$	−100548.	−0.115062
$239$	−512037.	−0.579838	−0.289919	−	0.957051i	$-0.593628\pi$
$239$	−512037.	−0.579838	−0.289919	+	0.957051i	$0.593628\pi$
$240$	70400.0	0.0788941
$241$	989330.	1.09723	0.548616	−	0.836074i	$-0.315155\pi$
$241$	989330.	1.09723	0.548616	+	0.836074i	$0.315155\pi$
$242$	−359048.	−0.394107
$243$	−815936.	−0.886422
$244$	−28480.0	−0.0306242
$245$	−60025.0	−0.0638877
$246$	523776.	0.551833
$247$	871774.	0.909204
$248$	−165376.	−0.170743
$249$	920436.	0.940795
$250$	−62500.0	−0.0632456
$251$	−61230.0	−0.0613451	−0.0306726	−	0.999529i	$-0.509765\pi$
$251$	−61230.0	−0.0613451	−0.0306726	+	0.999529i	$0.509765\pi$
$252$	−95648.0	−0.0948800
$253$	344430.	0.338298
$254$	396992.	0.386098
$255$	−141075.	−0.135863
$256$	65536.0	0.0625000
$257$	1.33887e6	1.26446	0.632231	−	0.774780i	$-0.282139\pi$
$257$	1.33887e6	1.26446	0.632231	+	0.774780i	$0.282139\pi$
$258$	26312.0	0.0246096
$259$	679238.	0.629177
$260$	434800.	0.398893
$261$	−217038.	−0.197213
$262$	−1.10724e6	−0.996526
$263$	−1.65619e6	−1.47645	−0.738227	−	0.674553i	$-0.764337\pi$
$263$	−1.65619e6	−1.47645	−0.738227	+	0.674553i	$0.764337\pi$
$264$	187968.	0.165987
$265$	−696300.	−0.609090
$266$	−157192.	−0.136215
$267$	356400.	0.305956
$268$	400832.	0.340899
$269$	−750606.	−0.632457	−0.316229	−	0.948683i	$-0.602417\pi$
$269$	−750606.	−0.632457	−0.316229	+	0.948683i	$0.602417\pi$
$270$	−401500.	−0.335178
$271$	−557908.	−0.461466	−0.230733	−	0.973017i	$-0.574112\pi$
$271$	−557908.	−0.461466	−0.230733	+	0.973017i	$0.574112\pi$
$272$	−131328.	−0.107630
$273$	585893.	0.475786
$274$	950976.	0.765232
$275$	−166875.	−0.133064
$276$	227040.	0.179403
$277$	1.77256e6	1.38804	0.694018	−	0.719957i	$-0.255839\pi$
$277$	1.77256e6	1.38804	0.694018	+	0.719957i	$0.255839\pi$
$278$	641912.	0.498154
$279$	315248.	0.242461
$280$	−78400.0	−0.0597614
$281$	−1.09893e6	−0.830243	−0.415122	−	0.909766i	$-0.636261\pi$
$281$	−1.09893e6	−0.830243	−0.415122	+	0.909766i	$0.636261\pi$
$282$	748836.	0.560743
$283$	−320569.	−0.237933	−0.118967	−	0.992898i	$-0.537958\pi$
$283$	−320569.	−0.237933	−0.118967	+	0.992898i	$0.537958\pi$
$284$	−831744.	−0.611919
$285$	−220550.	−0.160840
$286$	1.16092e6	0.839239
$287$	−583296.	−0.418008
$288$	−124928.	−0.0887521
$289$	−1.15669e6	−0.814651
$290$	−177900.	−0.124217
$291$	1.63510e6	1.13191
$292$	763040.	0.523709
$293$	−1.62337e6	−1.10471	−0.552355	−	0.833609i	$-0.686271\pi$
$293$	−1.62337e6	−1.10471	−0.552355	+	0.833609i	$0.686271\pi$
$294$	−105644.	−0.0712814
$295$	−772800.	−0.517026
$296$	887168.	0.588541
$297$	−1.07200e6	−0.705189
$298$	−398712.	−0.260087
$299$	1.40223e6	0.907071
$300$	−110000.	−0.0705650
$301$	−29302.0	−0.0186415
$302$	−824068.	−0.519931
$303$	454410.	0.284342
$304$	−205312.	−0.127418
$305$	44500.0	0.0273912
$306$	250344.	0.152839
$307$	995087.	0.602581	0.301290	−	0.953532i	$-0.402583\pi$
$307$	995087.	0.602581	0.301290	+	0.953532i	$0.402583\pi$
$308$	−209328.	−0.125733
$309$	−1.19664e6	−0.712961
$310$	258400.	0.152717
$311$	1.34398e6	0.787939	0.393969	−	0.919124i	$-0.371102\pi$
$311$	1.34398e6	0.787939	0.393969	+	0.919124i	$0.371102\pi$
$312$	765248.	0.445057
$313$	1.91971e6	1.10758	0.553788	−	0.832658i	$-0.313182\pi$
$313$	1.91971e6	1.10758	0.553788	+	0.832658i	$0.313182\pi$
$314$	2.32460e6	1.33053
$315$	149450.	0.0848632
$316$	−1.63394e6	−0.920486
$317$	−1.91366e6	−1.06959	−0.534794	−	0.844983i	$-0.679611\pi$
$317$	−1.91366e6	−1.06959	−0.534794	+	0.844983i	$0.679611\pi$
$318$	−1.22549e6	−0.679581
$319$	−474993.	−0.261343
$320$	−102400.	−0.0559017
$321$	1.16708e6	0.632175
$322$	−252840.	−0.135896
$323$	411426.	0.219425
$324$	−232304.	−0.122940
$325$	−679375.	−0.356781
$326$	1.38644e6	0.722532
$327$	1.36522e6	0.706047
$328$	−761856.	−0.391010
$329$	−833931.	−0.424757
$330$	−293700.	−0.148463
$331$	−2.25694e6	−1.13227	−0.566135	−	0.824313i	$-0.691562\pi$
$331$	−2.25694e6	−1.13227	−0.566135	+	0.824313i	$0.691562\pi$
$332$	−1.33882e6	−0.666616
$333$	−1.69116e6	−0.835748
$334$	−1.79555e6	−0.880706
$335$	−626300.	−0.304909
$336$	−137984.	−0.0666777
$337$	−1.45016e6	−0.695571	−0.347786	−	0.937574i	$-0.613066\pi$
$337$	−1.45016e6	−0.695571	−0.347786	+	0.937574i	$0.613066\pi$
$338$	3.24110e6	1.54313
$339$	−2.12117e6	−1.00248
$340$	205200.	0.0962676
$341$	689928.	0.321305
$342$	391376.	0.180938
$343$	117649.	0.0539949
$344$	−38272.0	−0.0174375
$345$	−354750.	−0.160463
$346$	−1.05004e6	−0.471535
$347$	856386.	0.381809	0.190904	−	0.981609i	$-0.438858\pi$
$347$	856386.	0.381809	0.190904	+	0.981609i	$0.438858\pi$
$348$	−313104.	−0.138593
$349$	−347602.	−0.152763	−0.0763816	−	0.997079i	$-0.524337\pi$
$349$	−347602.	−0.152763	−0.0763816	+	0.997079i	$0.524337\pi$
$350$	122500.	0.0534522
$351$	−4.36430e6	−1.89081
$352$	−273408.	−0.117613
$353$	−2.21860e6	−0.947640	−0.473820	−	0.880622i	$-0.657125\pi$
$353$	−2.21860e6	−0.947640	−0.473820	+	0.880622i	$0.657125\pi$
$354$	−1.36013e6	−0.576862
$355$	1.29960e6	0.547317
$356$	−518400.	−0.216790
$357$	276507.	0.114825
$358$	−444048.	−0.183114
$359$	2.94338e6	1.20534	0.602672	−	0.797989i	$-0.294103\pi$
$359$	2.94338e6	1.20534	0.602672	+	0.797989i	$0.294103\pi$
$360$	195200.	0.0793823
$361$	−1.83290e6	−0.740235
$362$	451088.	0.180921
$363$	987382.	0.393295
$364$	−852208.	−0.337126
$365$	−1.19225e6	−0.468420
$366$	78320.0	0.0305612
$367$	2.33000e6	0.903005	0.451503	−	0.892270i	$-0.350888\pi$
$367$	2.33000e6	0.903005	0.451503	+	0.892270i	$0.350888\pi$
$368$	−330240.	−0.127119
$369$	1.45229e6	0.555248
$370$	−1.38620e6	−0.526407
$371$	1.36475e6	0.514775
$372$	454784.	0.170391
$373$	1.69246e6	0.629865	0.314932	−	0.949114i	$-0.398018\pi$
$373$	1.69246e6	0.629865	0.314932	+	0.949114i	$0.398018\pi$
$374$	547884.	0.202539
$375$	171875.	0.0631153
$376$	−1.08922e6	−0.397324
$377$	−1.93377e6	−0.700732
$378$	786940.	0.283278
$379$	−1.50075e6	−0.536673	−0.268337	−	0.963325i	$-0.586474\pi$
$379$	−1.50075e6	−0.536673	−0.268337	+	0.963325i	$0.586474\pi$
$380$	320800.	0.113966
$381$	−1.09173e6	−0.385303
$382$	−2.92796e6	−1.02661
$383$	3.48522e6	1.21404	0.607020	−	0.794686i	$-0.292365\pi$
$383$	3.48522e6	1.21404	0.607020	+	0.794686i	$0.292365\pi$
$384$	−180224.	−0.0623713
$385$	327075.	0.112459
$386$	−744160.	−0.254213
$387$	72956.0	0.0247619
$388$	−2.37832e6	−0.802031
$389$	−3.60598e6	−1.20823	−0.604114	−	0.796898i	$-0.706473\pi$
$389$	−3.60598e6	−1.20823	−0.604114	+	0.796898i	$0.706473\pi$
$390$	−1.19570e6	−0.398071
$391$	661770.	0.218910
$392$	153664.	0.0505076
$393$	3.04491e6	0.994473
$394$	485424.	0.157536
$395$	2.55302e6	0.823308
$396$	521184.	0.167014
$397$	4.74380e6	1.51060	0.755302	−	0.655377i	$-0.227490\pi$
$397$	4.74380e6	1.51060	0.755302	+	0.655377i	$0.227490\pi$
$398$	2.59434e6	0.820953
$399$	432278.	0.135935
$400$	160000.	0.0500000
$401$	5.26539e6	1.63520	0.817598	−	0.575789i	$-0.195305\pi$
$401$	5.26539e6	1.63520	0.817598	+	0.575789i	$0.195305\pi$
$402$	−1.10229e6	−0.340197
$403$	2.80881e6	0.861508
$404$	−660960.	−0.201475
$405$	362975.	0.109961
$406$	348684.	0.104983
$407$	−3.70115e6	−1.10752
$408$	361152.	0.107409
$409$	1.37015e6	0.405004	0.202502	−	0.979282i	$-0.435093\pi$
$409$	1.37015e6	0.405004	0.202502	+	0.979282i	$0.435093\pi$
$410$	1.19040e6	0.349730
$411$	−2.61518e6	−0.763656
$412$	1.74056e6	0.505180
$413$	1.51469e6	0.436966
$414$	629520.	0.180513
$415$	2.09190e6	0.596239
$416$	−1.11309e6	−0.315352
$417$	−1.76526e6	−0.497128
$418$	856536.	0.239776
$419$	6.16429e6	1.71533	0.857666	−	0.514207i	$-0.171914\pi$
$419$	6.16429e6	1.71533	0.857666	+	0.514207i	$0.171914\pi$
$420$	215600.	0.0596383
$421$	2.45358e6	0.674677	0.337338	−	0.941383i	$-0.390473\pi$
$421$	2.45358e6	0.674677	0.337338	+	0.941383i	$0.390473\pi$
$422$	−599092.	−0.163762
$423$	2.07632e6	0.564213
$424$	1.78253e6	0.481528
$425$	−320625.	−0.0861043
$426$	2.28730e6	0.610658
$427$	−87220.0	−0.0231498
$428$	−1.69757e6	−0.447938
$429$	−3.19252e6	−0.837510
$430$	59800.0	0.0155966
$431$	7.66771e6	1.98826	0.994128	−	0.108207i	$-0.0345111\pi$
$431$	7.66771e6	1.98826	0.994128	+	0.108207i	$0.0345111\pi$
$432$	1.02784e6	0.264982
$433$	−5.00285e6	−1.28232	−0.641161	−	0.767406i	$-0.721547\pi$
$433$	−5.00285e6	−1.28232	−0.641161	+	0.767406i	$0.721547\pi$
$434$	−506464.	−0.129070
$435$	489225.	0.123961
$436$	−1.98578e6	−0.500281
$437$	1.03458e6	0.259156
$438$	−2.09836e6	−0.522630
$439$	1.86363e6	0.461527	0.230764	−	0.973010i	$-0.425878\pi$
$439$	1.86363e6	0.461527	0.230764	+	0.973010i	$0.425878\pi$
$440$	427200.	0.105196
$441$	−292922.	−0.0717225
$442$	2.23052e6	0.543064
$443$	2.60747e6	0.631263	0.315632	−	0.948882i	$-0.397784\pi$
$443$	2.60747e6	0.631263	0.315632	+	0.948882i	$0.397784\pi$
$444$	−2.43971e6	−0.587329
$445$	810000.	0.193903
$446$	−4.40384e6	−1.04832
$447$	1.09646e6	0.259551
$448$	200704.	0.0472456
$449$	−4.78007e6	−1.11897	−0.559484	−	0.828841i	$-0.689001\pi$
$449$	−4.78007e6	−1.11897	−0.559484	+	0.828841i	$0.689001\pi$
$450$	−305000.	−0.0710017
$451$	3.17837e6	0.735805
$452$	3.08534e6	0.710326
$453$	2.26619e6	0.518860
$454$	−2.78051e6	−0.633118
$455$	1.33157e6	0.301535
$456$	564608.	0.127155
$457$	−7.96757e6	−1.78458	−0.892289	−	0.451465i	$-0.850902\pi$
$457$	−7.96757e6	−1.78458	−0.892289	+	0.451465i	$0.850902\pi$
$458$	1.85494e6	0.413206
$459$	−2.05969e6	−0.456322
$460$	516000.	0.113699
$461$	1.77665e6	0.389358	0.194679	−	0.980867i	$-0.437633\pi$
$461$	1.77665e6	0.389358	0.194679	+	0.980867i	$0.437633\pi$
$462$	575652.	0.125474
$463$	−998548.	−0.216479	−0.108240	−	0.994125i	$-0.534521\pi$
$463$	−998548.	−0.216479	−0.108240	+	0.994125i	$0.534521\pi$
$464$	455424.	0.0982021
$465$	−710600.	−0.152403
$466$	−6.30614e6	−1.34524
$467$	−5.08478e6	−1.07890	−0.539449	−	0.842019i	$-0.681367\pi$
$467$	−5.08478e6	−1.07890	−0.539449	+	0.842019i	$0.681367\pi$
$468$	2.12182e6	0.447811
$469$	1.22755e6	0.257695
$470$	1.70190e6	0.355377
$471$	−6.39265e6	−1.32779
$472$	1.97837e6	0.408745
$473$	159666.	0.0328140
$474$	4.49332e6	0.918590
$475$	−501250.	−0.101934
$476$	−402192.	−0.0813610
$477$	−3.39794e6	−0.683786
$478$	−2.04815e6	−0.410007
$479$	3.71936e6	0.740678	0.370339	−	0.928897i	$-0.379242\pi$
$479$	3.71936e6	0.740678	0.370339	+	0.928897i	$0.379242\pi$
$480$	281600.	0.0557866
$481$	−1.50680e7	−2.96956
$482$	3.95732e6	0.775860
$483$	695310.	0.135616
$484$	−1.43619e6	−0.278676
$485$	3.71612e6	0.717358
$486$	−3.26374e6	−0.626795
$487$	−9.12035e6	−1.74256	−0.871282	−	0.490782i	$-0.836711\pi$
$487$	−9.12035e6	−1.74256	−0.871282	+	0.490782i	$0.836711\pi$
$488$	−113920.	−0.0216546
$489$	−3.81271e6	−0.721044
$490$	−240100.	−0.0451754
$491$	−7.83774e6	−1.46719	−0.733596	−	0.679586i	$-0.762160\pi$
$491$	−7.83774e6	−1.46719	−0.733596	+	0.679586i	$0.762160\pi$
$492$	2.09510e6	0.390205
$493$	−912627.	−0.169113
$494$	3.48710e6	0.642905
$495$	−814350.	−0.149382
$496$	−661504.	−0.120734
$497$	−2.54722e6	−0.462567
$498$	3.68174e6	0.665243
$499$	−96103.0	−0.0172777	−0.00863884	−	0.999963i	$-0.502750\pi$
$499$	−96103.0	−0.0172777	−0.00863884	+	0.999963i	$0.502750\pi$
$500$	−250000.	−0.0447214
$501$	4.93776e6	0.878892
$502$	−244920.	−0.0433775
$503$	−2.37577e6	−0.418682	−0.209341	−	0.977843i	$-0.567132\pi$
$503$	−2.37577e6	−0.418682	−0.209341	+	0.977843i	$0.567132\pi$
$504$	−382592.	−0.0670903
$505$	1.03275e6	0.180205
$506$	1.37772e6	0.239213
$507$	−8.91304e6	−1.53995
$508$	1.58797e6	0.273012
$509$	5.91484e6	1.01193	0.505963	−	0.862555i	$-0.331137\pi$
$509$	5.91484e6	1.01193	0.505963	+	0.862555i	$0.331137\pi$
$510$	−564300.	−0.0960693
$511$	2.33681e6	0.395887
$512$	262144.	0.0441942
$513$	−3.22003e6	−0.540215
$514$	5.35548e6	0.894109
$515$	−2.71963e6	−0.451847
$516$	105248.	0.0174016
$517$	4.54407e6	0.747685
$518$	2.71695e6	0.444895
$519$	2.88760e6	0.470564
$520$	1.73920e6	0.282060
$521$	1.46099e6	0.235806	0.117903	−	0.993025i	$-0.462383\pi$
$521$	1.46099e6	0.235806	0.117903	+	0.993025i	$0.462383\pi$
$522$	−868152.	−0.139450
$523$	−2.90691e6	−0.464705	−0.232352	−	0.972632i	$-0.574642\pi$
$523$	−2.90691e6	−0.464705	−0.232352	+	0.972632i	$0.574642\pi$
$524$	−4.42896e6	−0.704650
$525$	−336875.	−0.0533422
$526$	−6.62474e6	−1.04401
$527$	1.32559e6	0.207914
$528$	751872.	0.117371
$529$	−4.77224e6	−0.741453
$530$	−2.78520e6	−0.430692
$531$	−3.77126e6	−0.580431
$532$	−628768.	−0.0963189
$533$	1.29396e7	1.97290
$534$	1.42560e6	0.216344
$535$	2.65245e6	0.400648
$536$	1.60333e6	0.241052
$537$	1.22113e6	0.182737
$538$	−3.00242e6	−0.447215
$539$	−641067.	−0.0950455
$540$	−1.60600e6	−0.237007
$541$	5.28092e6	0.775741	0.387870	−	0.921714i	$-0.373211\pi$
$541$	5.28092e6	0.775741	0.387870	+	0.921714i	$0.373211\pi$
$542$	−2.23163e6	−0.326305
$543$	−1.24049e6	−0.180549
$544$	−525312.	−0.0761062
$545$	3.10278e6	0.447465
$546$	2.34357e6	0.336432
$547$	1.31999e7	1.88626	0.943132	−	0.332419i	$-0.107865\pi$
$547$	1.31999e7	1.88626	0.943132	+	0.332419i	$0.107865\pi$
$548$	3.80390e6	0.541101
$549$	217160.	0.0307503
$550$	−667500.	−0.0940902
$551$	−1.42676e6	−0.200203
$552$	908160.	0.126857
$553$	−5.00393e6	−0.695822
$554$	7.09023e6	0.981490
$555$	3.81205e6	0.525323
$556$	2.56765e6	0.352248
$557$	−1.39920e7	−1.91091	−0.955457	−	0.295131i	$-0.904637\pi$
$557$	−1.39920e7	−1.91091	−0.955457	+	0.295131i	$0.904637\pi$
$558$	1.26099e6	0.171446
$559$	650026.	0.0879835
$560$	−313600.	−0.0422577
$561$	−1.50668e6	−0.202122
$562$	−4.39573e6	−0.587071
$563$	−5.12689e6	−0.681684	−0.340842	−	0.940121i	$-0.610712\pi$
$563$	−5.12689e6	−0.681684	−0.340842	+	0.940121i	$0.610712\pi$
$564$	2.99534e6	0.396505
$565$	−4.82085e6	−0.635335
$566$	−1.28228e6	−0.168244
$567$	−711431.	−0.0929341
$568$	−3.32698e6	−0.432692
$569$	−8.29102e6	−1.07356	−0.536781	−	0.843721i	$-0.680360\pi$
$569$	−8.29102e6	−1.07356	−0.536781	+	0.843721i	$0.680360\pi$
$570$	−882200.	−0.113731
$571$	6.21372e6	0.797556	0.398778	−	0.917048i	$-0.369434\pi$
$571$	6.21372e6	0.797556	0.398778	+	0.917048i	$0.369434\pi$
$572$	4.64366e6	0.593432
$573$	8.05190e6	1.02450
$574$	−2.33318e6	−0.295576
$575$	−806250.	−0.101695
$576$	−499712.	−0.0627572
$577$	1.14818e7	1.43572	0.717861	−	0.696186i	$-0.245121\pi$
$577$	1.14818e7	1.43572	0.717861	+	0.696186i	$0.245121\pi$
$578$	−4.62675e6	−0.576045
$579$	2.04644e6	0.253690
$580$	−711600.	−0.0878347
$581$	−4.10012e6	−0.503914
$582$	6.54038e6	0.800379
$583$	−7.43648e6	−0.906142
$584$	3.05216e6	0.370318
$585$	−3.31535e6	−0.400534
$586$	−6.49348e6	−0.781148
$587$	641856.	0.0768851	0.0384426	−	0.999261i	$-0.487760\pi$
$587$	641856.	0.0768851	0.0384426	+	0.999261i	$0.487760\pi$
$588$	−422576.	−0.0504036
$589$	2.07237e6	0.246138
$590$	−3.09120e6	−0.365592
$591$	−1.33492e6	−0.157212
$592$	3.54867e6	0.416161
$593$	−2.80572e6	−0.327648	−0.163824	−	0.986490i	$-0.552383\pi$
$593$	−2.80572e6	−0.327648	−0.163824	+	0.986490i	$0.552383\pi$
$594$	−4.28802e6	−0.498644
$595$	628425.	0.0727715
$596$	−1.59485e6	−0.183909
$597$	−7.13442e6	−0.819263
$598$	5.60892e6	0.641396
$599$	7.74415e6	0.881874	0.440937	−	0.897538i	$-0.354646\pi$
$599$	7.74415e6	0.881874	0.440937	+	0.897538i	$0.354646\pi$
$600$	−440000.	−0.0498970
$601$	2.88868e6	0.326222	0.163111	−	0.986608i	$-0.447847\pi$
$601$	2.88868e6	0.326222	0.163111	+	0.986608i	$0.447847\pi$
$602$	−117208.	−0.0131815
$603$	−3.05634e6	−0.342302
$604$	−3.29627e6	−0.367647
$605$	2.24405e6	0.249255
$606$	1.81764e6	0.201060
$607$	1.22095e7	1.34501	0.672504	−	0.740093i	$-0.265219\pi$
$607$	1.22095e7	1.34501	0.672504	+	0.740093i	$0.265219\pi$
$608$	−821248.	−0.0900980
$609$	−958881.	−0.104766
$610$	178000.	0.0193685
$611$	1.84997e7	2.00475
$612$	1.00138e6	0.108073
$613$	1.51667e7	1.63019	0.815096	−	0.579326i	$-0.196684\pi$
$613$	1.51667e7	1.63019	0.815096	+	0.579326i	$0.196684\pi$
$614$	3.98035e6	0.426089
$615$	−3.27360e6	−0.349010
$616$	−837312.	−0.0889069
$617$	1.53927e7	1.62780	0.813899	−	0.581006i	$-0.197341\pi$
$617$	1.53927e7	1.62780	0.813899	+	0.581006i	$0.197341\pi$
$618$	−4.78654e6	−0.504139
$619$	−1.40843e7	−1.47744	−0.738720	−	0.674013i	$-0.764569\pi$
$619$	−1.40843e7	−1.47744	−0.738720	+	0.674013i	$0.764569\pi$
$620$	1.03360e6	0.107987
$621$	−5.17935e6	−0.538947
$622$	5.37593e6	0.557157
$623$	−1.58760e6	−0.163878
$624$	3.06099e6	0.314703
$625$	390625.	0.0400000
$626$	7.67882e6	0.783175
$627$	−2.35547e6	−0.239282
$628$	9.29840e6	0.940826
$629$	−7.11121e6	−0.716666
$630$	597800.	0.0600074
$631$	1.56178e7	1.56152	0.780760	−	0.624831i	$-0.214832\pi$
$631$	1.56178e7	1.56152	0.780760	+	0.624831i	$0.214832\pi$
$632$	−6.53574e6	−0.650882
$633$	1.64750e6	0.163424
$634$	−7.65463e6	−0.756312
$635$	−2.48120e6	−0.244190
$636$	−4.90195e6	−0.480536
$637$	−2.60989e6	−0.254843
$638$	−1.89997e6	−0.184797
$639$	6.34205e6	0.614437
$640$	−409600.	−0.0395285
$641$	4.04157e6	0.388513	0.194256	−	0.980951i	$-0.437771\pi$
$641$	4.04157e6	0.388513	0.194256	+	0.980951i	$0.437771\pi$
$642$	4.66831e6	0.447015
$643$	−1.71035e7	−1.63139	−0.815693	−	0.578485i	$-0.803644\pi$
$643$	−1.71035e7	−1.63139	−0.815693	+	0.578485i	$0.803644\pi$
$644$	−1.01136e6	−0.0960929
$645$	−164450.	−0.0155645
$646$	1.64570e6	0.155157
$647$	−8.83546e6	−0.829790	−0.414895	−	0.909869i	$-0.636182\pi$
$647$	−8.83546e6	−0.829790	−0.414895	+	0.909869i	$0.636182\pi$
$648$	−929216.	−0.0869319
$649$	−8.25350e6	−0.769178
$650$	−2.71750e6	−0.252282
$651$	1.39278e6	0.128804
$652$	5.54576e6	0.510907
$653$	9.36125e6	0.859115	0.429557	−	0.903040i	$-0.358670\pi$
$653$	9.36125e6	0.859115	0.429557	+	0.903040i	$0.358670\pi$
$654$	5.46088e6	0.499251
$655$	6.92025e6	0.630258
$656$	−3.04742e6	−0.276486
$657$	−5.81818e6	−0.525864
$658$	−3.33572e6	−0.300348
$659$	−366111.	−0.0328397	−0.0164199	−	0.999865i	$-0.505227\pi$
$659$	−366111.	−0.0328397	−0.0164199	+	0.999865i	$0.505227\pi$
$660$	−1.17480e6	−0.104979
$661$	2.05164e7	1.82640	0.913202	−	0.407508i	$-0.133602\pi$
$661$	2.05164e7	1.82640	0.913202	+	0.407508i	$0.133602\pi$
$662$	−9.02776e6	−0.800636
$663$	−6.13394e6	−0.541946
$664$	−5.35526e6	−0.471369
$665$	982450.	0.0861502
$666$	−6.76466e6	−0.590963
$667$	−2.29491e6	−0.199734
$668$	−7.18219e6	−0.622753
$669$	1.21105e7	1.04616
$670$	−2.50520e6	−0.215603
$671$	475260.	0.0407498
$672$	−551936.	−0.0471482
$673$	7.48189e6	0.636757	0.318378	−	0.947964i	$-0.396862\pi$
$673$	7.48189e6	0.636757	0.318378	+	0.947964i	$0.396862\pi$
$674$	−5.80065e6	−0.491843
$675$	2.50938e6	0.211985
$676$	1.29644e7	1.09115
$677$	1.21459e7	1.01849	0.509247	−	0.860621i	$-0.329924\pi$
$677$	1.21459e7	1.01849	0.509247	+	0.860621i	$0.329924\pi$
$678$	−8.48470e6	−0.708863
$679$	−7.28360e6	−0.606278
$680$	820800.	0.0680715
$681$	7.64640e6	0.631814
$682$	2.75971e6	0.227197
$683$	−1.15232e7	−0.945197	−0.472599	−	0.881278i	$-0.656684\pi$
$683$	−1.15232e7	−0.945197	−0.472599	+	0.881278i	$0.656684\pi$
$684$	1.56550e6	0.127942
$685$	−5.94360e6	−0.483975
$686$	470596.	0.0381802
$687$	−5.10110e6	−0.412355
$688$	−153088.	−0.0123302
$689$	−3.02751e7	−2.42962
$690$	−1.41900e6	−0.113464
$691$	−1.71185e7	−1.36386	−0.681931	−	0.731417i	$-0.738859\pi$
$691$	−1.71185e7	−1.36386	−0.681931	+	0.731417i	$0.738859\pi$
$692$	−4.20014e6	−0.333426
$693$	1.59613e6	0.126251
$694$	3.42554e6	0.269980
$695$	−4.01195e6	−0.315060
$696$	−1.25242e6	−0.0979999
$697$	6.10675e6	0.476133
$698$	−1.39041e6	−0.108020
$699$	1.73419e7	1.34247
$700$	490000.	0.0377964
$701$	9.72758e6	0.747669	0.373835	−	0.927495i	$-0.378043\pi$
$701$	9.72758e6	0.747669	0.373835	+	0.927495i	$0.378043\pi$
$702$	−1.74572e7	−1.33700
$703$	−1.11173e7	−0.848422
$704$	−1.09363e6	−0.0831648
$705$	−4.68022e6	−0.354645
$706$	−8.87442e6	−0.670082
$707$	−2.02419e6	−0.152301
$708$	−5.44051e6	−0.407903
$709$	−673813.	−0.0503412	−0.0251706	−	0.999683i	$-0.508013\pi$
$709$	−673813.	−0.0503412	−0.0251706	+	0.999683i	$0.508013\pi$
$710$	5.19840e6	0.387011
$711$	1.24588e7	0.924274
$712$	−2.07360e6	−0.153294
$713$	3.33336e6	0.245560
$714$	1.10603e6	0.0811934
$715$	−7.25572e6	−0.530781
$716$	−1.77619e6	−0.129481
$717$	5.63241e6	0.409163
$718$	1.17735e7	0.852307
$719$	2.77719e6	0.200347	0.100174	−	0.994970i	$-0.468060\pi$
$719$	2.77719e6	0.200347	0.100174	+	0.994970i	$0.468060\pi$
$720$	780800.	0.0561317
$721$	5.33046e6	0.381880
$722$	−7.33158e6	−0.523425
$723$	−1.08826e7	−0.774262
$724$	1.80435e6	0.127931
$725$	1.11188e6	0.0785617
$726$	3.94953e6	0.278102
$727$	1.16385e7	0.816700	0.408350	−	0.912825i	$-0.366104\pi$
$727$	1.16385e7	0.816700	0.408350	+	0.912825i	$0.366104\pi$
$728$	−3.40883e6	−0.238384
$729$	1.25034e7	0.871384
$730$	−4.76900e6	−0.331223
$731$	306774.	0.0212337
$732$	313280.	0.0216100
$733$	−1.32013e7	−0.907522	−0.453761	−	0.891123i	$-0.649918\pi$
$733$	−1.32013e7	−0.907522	−0.453761	+	0.891123i	$0.649918\pi$
$734$	9.31999e6	0.638521
$735$	660275.	0.0450823
$736$	−1.32096e6	−0.0898866
$737$	−6.68888e6	−0.453612
$738$	5.80915e6	0.392619
$739$	3.25476e6	0.219234	0.109617	−	0.993974i	$-0.465038\pi$
$739$	3.25476e6	0.219234	0.109617	+	0.993974i	$0.465038\pi$
$740$	−5.54480e6	−0.372226
$741$	−9.58951e6	−0.641580
$742$	5.45899e6	0.364001
$743$	−7.61596e6	−0.506119	−0.253059	−	0.967451i	$-0.581437\pi$
$743$	−7.61596e6	−0.506119	−0.253059	+	0.967451i	$0.581437\pi$
$744$	1.81914e6	0.120485
$745$	2.49195e6	0.164493
$746$	6.76986e6	0.445382
$747$	1.02085e7	0.669359
$748$	2.19154e6	0.143217
$749$	−5.19880e6	−0.338609
$750$	687500.	0.0446292
$751$	655199.	0.0423910	0.0211955	−	0.999775i	$-0.493253\pi$
$751$	655199.	0.0423910	0.0211955	+	0.999775i	$0.493253\pi$
$752$	−4.35686e6	−0.280950
$753$	673530.	0.0432882
$754$	−7.73509e6	−0.495493
$755$	5.15042e6	0.328833
$756$	3.14776e6	0.200307
$757$	1.85111e7	1.17406	0.587032	−	0.809564i	$-0.300296\pi$
$757$	1.85111e7	1.17406	0.587032	+	0.809564i	$0.300296\pi$
$758$	−6.00299e6	−0.379485
$759$	−3.78873e6	−0.238720
$760$	1.28320e6	0.0805861
$761$	−1.85291e7	−1.15983	−0.579914	−	0.814678i	$-0.696914\pi$
$761$	−1.85291e7	−1.15983	−0.579914	+	0.814678i	$0.696914\pi$
$762$	−4.36691e6	−0.272450
$763$	−6.08144e6	−0.378177
$764$	−1.17119e7	−0.725926
$765$	−1.56465e6	−0.0966637
$766$	1.39409e7	0.858456
$767$	−3.36013e7	−2.06238
$768$	−720896.	−0.0441031
$769$	−1.48414e7	−0.905024	−0.452512	−	0.891758i	$-0.649472\pi$
$769$	−1.48414e7	−0.905024	−0.452512	+	0.891758i	$0.649472\pi$
$770$	1.30830e6	0.0795208
$771$	−1.47276e7	−0.892268
$772$	−2.97664e6	−0.179756
$773$	3.93042e6	0.236586	0.118293	−	0.992979i	$-0.462258\pi$
$773$	3.93042e6	0.236586	0.118293	+	0.992979i	$0.462258\pi$
$774$	291824.	0.0175093
$775$	−1.61500e6	−0.0965869
$776$	−9.51328e6	−0.567121
$777$	−7.47162e6	−0.443979
$778$	−1.44239e7	−0.854347
$779$	9.54701e6	0.563668
$780$	−4.78280e6	−0.281479
$781$	1.38797e7	0.814242
$782$	2.64708e6	0.154793
$783$	7.14269e6	0.416349
$784$	614656.	0.0357143
$785$	−1.45288e7	−0.841500
$786$	1.21796e7	0.703199
$787$	1.17824e7	0.678105	0.339053	−	0.940767i	$-0.389893\pi$
$787$	1.17824e7	0.678105	0.339053	+	0.940767i	$0.389893\pi$
$788$	1.94170e6	0.111395
$789$	1.82180e7	1.04186
$790$	1.02121e7	0.582167
$791$	9.44887e6	0.536956
$792$	2.08474e6	0.118097
$793$	1.93486e6	0.109261
$794$	1.89752e7	1.06816
$795$	7.65930e6	0.429805
$796$	1.03773e7	0.580502
$797$	−5.40952e6	−0.301657	−0.150828	−	0.988560i	$-0.548194\pi$
$797$	−5.40952e6	−0.301657	−0.150828	+	0.988560i	$0.548194\pi$
$798$	1.72911e6	0.0961205
$799$	8.73075e6	0.483821
$800$	640000.	0.0353553
$801$	3.95280e6	0.217683
$802$	2.10616e7	1.15626
$803$	−1.27332e7	−0.696867
$804$	−4.40915e6	−0.240555
$805$	1.58025e6	0.0859481
$806$	1.12352e7	0.609178
$807$	8.25667e6	0.446294
$808$	−2.64384e6	−0.142465
$809$	−7.12264e6	−0.382622	−0.191311	−	0.981529i	$-0.561274\pi$
$809$	−7.12264e6	−0.382622	−0.191311	+	0.981529i	$0.561274\pi$
$810$	1.45190e6	0.0777543
$811$	−3.03045e7	−1.61791	−0.808956	−	0.587869i	$-0.799967\pi$
$811$	−3.03045e7	−1.61791	−0.808956	+	0.587869i	$0.799967\pi$
$812$	1.39474e6	0.0742338
$813$	6.13699e6	0.325633
$814$	−1.48046e7	−0.783134
$815$	−8.66525e6	−0.456969
$816$	1.44461e6	0.0759494
$817$	479596.	0.0251374
$818$	5.48060e6	0.286381
$819$	6.49809e6	0.338513
$820$	4.76160e6	0.247297
$821$	2.82181e7	1.46106	0.730532	−	0.682878i	$-0.239272\pi$
$821$	2.82181e7	1.46106	0.730532	+	0.682878i	$0.239272\pi$
$822$	−1.04607e7	−0.539986
$823$	−2.64534e7	−1.36139	−0.680694	−	0.732567i	$-0.738322\pi$
$823$	−2.64534e7	−1.36139	−0.680694	+	0.732567i	$0.738322\pi$
$824$	6.96224e6	0.357216
$825$	1.83563e6	0.0938964
$826$	6.05875e6	0.308982
$827$	4.44481e6	0.225990	0.112995	−	0.993596i	$-0.463956\pi$
$827$	4.44481e6	0.225990	0.112995	+	0.993596i	$0.463956\pi$
$828$	2.51808e6	0.127642
$829$	−2.80386e6	−0.141700	−0.0708501	−	0.997487i	$-0.522571\pi$
$829$	−2.80386e6	−0.141700	−0.0708501	+	0.997487i	$0.522571\pi$
$830$	8.36760e6	0.421605
$831$	−1.94981e7	−0.979469
$832$	−4.45235e6	−0.222988
$833$	−1.23171e6	−0.0615031
$834$	−7.06103e6	−0.351522
$835$	1.12222e7	0.557007
$836$	3.42614e6	0.169547
$837$	−1.03748e7	−0.511876
$838$	2.46572e7	1.21292
$839$	2.59804e7	1.27421	0.637104	−	0.770778i	$-0.280132\pi$
$839$	2.59804e7	1.27421	0.637104	+	0.770778i	$0.280132\pi$
$840$	862400.	0.0421707
$841$	−1.73463e7	−0.845701
$842$	9.81434e6	0.477069
$843$	1.20883e7	0.585862
$844$	−2.39637e6	−0.115797
$845$	−2.02569e7	−0.975958
$846$	8.30527e6	0.398959
$847$	−4.39834e6	−0.210659
$848$	7.13011e6	0.340492
$849$	3.52626e6	0.167898
$850$	−1.28250e6	−0.0608850
$851$	−1.78820e7	−0.846431
$852$	9.14918e6	0.431801
$853$	1.18392e7	0.557121	0.278560	−	0.960419i	$-0.410143\pi$
$853$	1.18392e7	0.557121	0.278560	+	0.960419i	$0.410143\pi$
$854$	−348880.	−0.0163693
$855$	−2.44610e6	−0.114435
$856$	−6.79027e6	−0.316740
$857$	−2.99283e6	−0.139197	−0.0695985	−	0.997575i	$-0.522172\pi$
$857$	−2.99283e6	−0.139197	−0.0695985	+	0.997575i	$0.522172\pi$
$858$	−1.27701e7	−0.592209
$859$	2.80980e7	1.29925	0.649626	−	0.760254i	$-0.274926\pi$
$859$	2.80980e7	1.29925	0.649626	+	0.760254i	$0.274926\pi$
$860$	239200.	0.0110285
$861$	6.41626e6	0.294967
$862$	3.06708e7	1.40591
$863$	1.15833e7	0.529424	0.264712	−	0.964328i	$-0.414723\pi$
$863$	1.15833e7	0.529424	0.264712	+	0.964328i	$0.414723\pi$
$864$	4.11136e6	0.187370
$865$	6.56272e6	0.298225
$866$	−2.00114e7	−0.906739
$867$	1.27236e7	0.574859
$868$	−2.02586e6	−0.0912661
$869$	2.72663e7	1.22483
$870$	1.95690e6	0.0876538
$871$	−2.72315e7	−1.21626
$872$	−7.94310e6	−0.353752
$873$	1.81347e7	0.805331
$874$	4.13832e6	0.183251
$875$	−765625.	−0.0338062
$876$	−8.39344e6	−0.369556
$877$	4.12538e7	1.81119	0.905596	−	0.424141i	$-0.139424\pi$
$877$	4.12538e7	1.81119	0.905596	+	0.424141i	$0.139424\pi$
$878$	7.45450e6	0.326349
$879$	1.78571e7	0.779539
$880$	1.70880e6	0.0743849
$881$	−1.32541e7	−0.575321	−0.287661	−	0.957732i	$-0.592877\pi$
$881$	−1.32541e7	−0.575321	−0.287661	+	0.957732i	$0.592877\pi$
$882$	−1.17169e6	−0.0507155
$883$	−3.19208e7	−1.37776	−0.688878	−	0.724877i	$-0.741897\pi$
$883$	−3.19208e7	−1.37776	−0.688878	+	0.724877i	$0.741897\pi$
$884$	8.92210e6	0.384004
$885$	8.50080e6	0.364839
$886$	1.04299e7	0.446371
$887$	1.74303e7	0.743866	0.371933	−	0.928260i	$-0.378695\pi$
$887$	1.74303e7	0.743866	0.371933	+	0.928260i	$0.378695\pi$
$888$	−9.75885e6	−0.415304
$889$	4.86315e6	0.206378
$890$	3.24000e6	0.137110
$891$	3.87657e6	0.163589
$892$	−1.76153e7	−0.741274
$893$	1.36492e7	0.572769
$894$	4.38583e6	0.183530
$895$	2.77530e6	0.115812
$896$	802816.	0.0334077
$897$	−1.54245e7	−0.640075
$898$	−1.91203e7	−0.791230
$899$	−4.59694e6	−0.189701
$900$	−1.22000e6	−0.0502058
$901$	−1.42881e7	−0.586357
$902$	1.27135e7	0.520293
$903$	322322.	0.0131544
$904$	1.23414e7	0.502276
$905$	−2.81930e6	−0.114425
$906$	9.06475e6	0.366889
$907$	−3.15066e7	−1.27170	−0.635848	−	0.771815i	$-0.719349\pi$
$907$	−3.15066e7	−1.27170	−0.635848	+	0.771815i	$0.719349\pi$
$908$	−1.11220e7	−0.447682
$909$	5.03982e6	0.202304
$910$	5.32630e6	0.213217
$911$	−4.91214e7	−1.96099	−0.980494	−	0.196548i	$-0.937027\pi$
$911$	−4.91214e7	−1.96099	−0.980494	+	0.196548i	$0.937027\pi$
$912$	2.25843e6	0.0899125
$913$	2.23415e7	0.887024
$914$	−3.18703e7	−1.26189
$915$	−489500.	−0.0193286
$916$	7.41978e6	0.292181
$917$	−1.35637e7	−0.532665
$918$	−8.23878e6	−0.322668
$919$	−4.51238e7	−1.76245	−0.881226	−	0.472696i	$-0.843281\pi$
$919$	−4.51238e7	−1.76245	−0.881226	+	0.472696i	$0.843281\pi$
$920$	2.06400e6	0.0803971
$921$	−1.09460e7	−0.425211
$922$	7.10659e6	0.275318
$923$	5.65066e7	2.18321
$924$	2.30261e6	0.0887238
$925$	8.66375e6	0.332929
$926$	−3.99419e6	−0.153074
$927$	−1.32718e7	−0.507259
$928$	1.82170e6	0.0694394
$929$	−3.68196e7	−1.39972	−0.699858	−	0.714282i	$-0.746753\pi$
$929$	−3.68196e7	−1.39972	−0.699858	+	0.714282i	$0.746753\pi$
$930$	−2.84240e6	−0.107765
$931$	−1.92560e6	−0.0728102
$932$	−2.52246e7	−0.951227
$933$	−1.47838e7	−0.556009
$934$	−2.03391e7	−0.762896
$935$	−3.42428e6	−0.128097
$936$	8.48730e6	0.316650
$937$	1.71904e7	0.639641	0.319820	−	0.947478i	$-0.396377\pi$
$937$	1.71904e7	0.639641	0.319820	+	0.947478i	$0.396377\pi$
$938$	4.91019e6	0.182218
$939$	−2.11168e7	−0.781562
$940$	6.80760e6	0.251290
$941$	−8.10352e6	−0.298332	−0.149166	−	0.988812i	$-0.547659\pi$
$941$	−8.10352e6	−0.298332	−0.149166	+	0.988812i	$0.547659\pi$
$942$	−2.55706e7	−0.938888
$943$	1.53562e7	0.562346
$944$	7.91347e6	0.289026
$945$	−4.91838e6	−0.179160
$946$	638664.	0.0232030
$947$	1.83337e7	0.664317	0.332158	−	0.943224i	$-0.392223\pi$
$947$	1.83337e7	0.664317	0.332158	+	0.943224i	$0.392223\pi$
$948$	1.79733e7	0.649541
$949$	−5.18390e7	−1.86849
$950$	−2.00500e6	−0.0720784
$951$	2.10502e7	0.754755
$952$	−1.60877e6	−0.0575309
$953$	6.03035e6	0.215085	0.107542	−	0.994200i	$-0.465702\pi$
$953$	6.03035e6	0.215085	0.107542	+	0.994200i	$0.465702\pi$
$954$	−1.35918e7	−0.483510
$955$	1.82998e7	0.649288
$956$	−8.19259e6	−0.289919
$957$	5.22492e6	0.184417
$958$	1.48774e7	0.523738
$959$	1.16495e7	0.409034
$960$	1.12640e6	0.0394471
$961$	−2.19521e7	−0.766774
$962$	−6.02720e7	−2.09980
$963$	1.29440e7	0.449781
$964$	1.58293e7	0.548616
$965$	4.65100e6	0.160779
$966$	2.78124e6	0.0958949
$967$	−3.09228e7	−1.06344	−0.531720	−	0.846920i	$-0.678454\pi$
$967$	−3.09228e7	−1.06344	−0.531720	+	0.846920i	$0.678454\pi$
$968$	−5.74477e6	−0.197053
$969$	−4.52569e6	−0.154837
$970$	1.48645e7	0.507249
$971$	−2.47924e6	−0.0843859	−0.0421929	−	0.999109i	$-0.513434\pi$
$971$	−2.47924e6	−0.0843859	−0.0421929	+	0.999109i	$0.513434\pi$
$972$	−1.30550e7	−0.443211
$973$	7.86342e6	0.266274
$974$	−3.64814e7	−1.23218
$975$	7.47312e6	0.251762
$976$	−455680.	−0.0153121
$977$	−2.09758e6	−0.0703044	−0.0351522	−	0.999382i	$-0.511192\pi$
$977$	−2.09758e6	−0.0703044	−0.0351522	+	0.999382i	$0.511192\pi$
$978$	−1.52508e7	−0.509855
$979$	8.65080e6	0.288469
$980$	−960400.	−0.0319438
$981$	1.51415e7	0.502340
$982$	−3.13509e7	−1.03746
$983$	−4.45491e7	−1.47047	−0.735233	−	0.677814i	$-0.762927\pi$
$983$	−4.45491e7	−1.47047	−0.735233	+	0.677814i	$0.762927\pi$
$984$	8.38042e6	0.275917
$985$	−3.03390e6	−0.0996347
$986$	−3.65051e6	−0.119581
$987$	9.17324e6	0.299730
$988$	1.39484e7	0.454602
$989$	771420.	0.0250784
$990$	−3.25740e6	−0.105629
$991$	−1.95104e7	−0.631075	−0.315538	−	0.948913i	$-0.602185\pi$
$991$	−1.95104e7	−0.631075	−0.315538	+	0.948913i	$0.602185\pi$
$992$	−2.64602e6	−0.0853716
$993$	2.48263e7	0.798987
$994$	−1.01889e7	−0.327084
$995$	−1.62146e7	−0.519217
$996$	1.47270e7	0.470398
$997$	−2.00678e7	−0.639385	−0.319692	−	0.947521i	$-0.603580\pi$
$997$	−2.00678e7	−0.639385	−0.319692	+	0.947521i	$0.603580\pi$
$998$	−384412.	−0.0122172
$999$	5.56559e7	1.76440

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	70.6.a.f.1.1	✓	1
3.2	odd	2		630.6.a.e.1.1		1
4.3	odd	2		560.6.a.f.1.1		1
5.2	odd	4		350.6.c.b.99.2		2
5.3	odd	4		350.6.c.b.99.1		2
5.4	even	2		350.6.a.d.1.1		1
7.6	odd	2		490.6.a.l.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.6.a.f.1.1	✓	1	1.1	even	1	trivial
350.6.a.d.1.1		1	5.4	even	2
350.6.c.b.99.1		2	5.3	odd	4
350.6.c.b.99.2		2	5.2	odd	4
490.6.a.l.1.1		1	7.6	odd	2
560.6.a.f.1.1		1	4.3	odd	2
630.6.a.e.1.1		1	3.2	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:	\( N \)	\(=\)	\( 70 = 2 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	70.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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