LMFDB - Embedded newform 847.6.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,6,Mod(1,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, 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("847.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	847.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:	$135.845095382$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 7)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	847.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+10.0000 q^{2} -14.0000 q^{3} +68.0000 q^{4} -56.0000 q^{5} -140.000 q^{6} +49.0000 q^{7} +360.000 q^{8} -47.0000 q^{9} +O(q^{10})$

\(q+10.0000 q^{2} -14.0000 q^{3} +68.0000 q^{4} -56.0000 q^{5} -140.000 q^{6} +49.0000 q^{7} +360.000 q^{8} -47.0000 q^{9} -560.000 q^{10} -952.000 q^{12} +140.000 q^{13} +490.000 q^{14} +784.000 q^{15} +1424.00 q^{16} +1722.00 q^{17} -470.000 q^{18} +98.0000 q^{19} -3808.00 q^{20} -686.000 q^{21} +1824.00 q^{23} -5040.00 q^{24} +11.0000 q^{25} +1400.00 q^{26} +4060.00 q^{27} +3332.00 q^{28} -3418.00 q^{29} +7840.00 q^{30} -7644.00 q^{31} +2720.00 q^{32} +17220.0 q^{34} -2744.00 q^{35} -3196.00 q^{36} -10398.0 q^{37} +980.000 q^{38} -1960.00 q^{39} -20160.0 q^{40} +17962.0 q^{41} -6860.00 q^{42} -10880.0 q^{43} +2632.00 q^{45} +18240.0 q^{46} +9324.00 q^{47} -19936.0 q^{48} +2401.00 q^{49} +110.000 q^{50} -24108.0 q^{51} +9520.00 q^{52} +2262.00 q^{53} +40600.0 q^{54} +17640.0 q^{56} -1372.00 q^{57} -34180.0 q^{58} -2730.00 q^{59} +53312.0 q^{60} -25648.0 q^{61} -76440.0 q^{62} -2303.00 q^{63} -18368.0 q^{64} -7840.00 q^{65} -48404.0 q^{67} +117096. q^{68} -25536.0 q^{69} -27440.0 q^{70} -58560.0 q^{71} -16920.0 q^{72} -68082.0 q^{73} -103980. q^{74} -154.000 q^{75} +6664.00 q^{76} -19600.0 q^{78} -31784.0 q^{79} -79744.0 q^{80} -45419.0 q^{81} +179620. q^{82} +20538.0 q^{83} -46648.0 q^{84} -96432.0 q^{85} -108800. q^{86} +47852.0 q^{87} -50582.0 q^{89} +26320.0 q^{90} +6860.00 q^{91} +124032. q^{92} +107016. q^{93} +93240.0 q^{94} -5488.00 q^{95} -38080.0 q^{96} -58506.0 q^{97} +24010.0 q^{98} +O(q^{100})\)

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 $

$2$	10.0000	1.76777	0.883883	−	0.467707i	$-0.154920\pi$
$2$	10.0000	1.76777	0.883883	+	0.467707i	$0.154920\pi$
$3$	−14.0000	−0.898100	−0.449050	−	0.893507i	$-0.648238\pi$
$3$	−14.0000	−0.898100	−0.449050	+	0.893507i	$0.648238\pi$
$4$	68.0000	2.12500
$5$	−56.0000	−1.00176	−0.500879	−	0.865517i	$-0.666990\pi$
$5$	−56.0000	−1.00176	−0.500879	+	0.865517i	$0.666990\pi$
$6$	−140.000	−1.58763
$7$	49.0000	0.377964
$7$	49.0000	0.377964
$8$	360.000	1.98874
$9$	−47.0000	−0.193416
$10$	−560.000	−1.77088
$11$	0	0
$11$	0	0
$12$	−952.000	−1.90846
$13$	140.000	0.229757	0.114879	−	0.993380i	$-0.463352\pi$
$13$	140.000	0.229757	0.114879	+	0.993380i	$0.463352\pi$
$14$	490.000	0.668153
$15$	784.000	0.899680
$16$	1424.00	1.39062
$17$	1722.00	1.44514	0.722572	−	0.691296i	$-0.242960\pi$
$17$	1722.00	1.44514	0.722572	+	0.691296i	$0.242960\pi$
$18$	−470.000	−0.341914
$19$	98.0000	0.0622791	0.0311395	−	0.999515i	$-0.490086\pi$
$19$	98.0000	0.0622791	0.0311395	+	0.999515i	$0.490086\pi$
$20$	−3808.00	−2.12874
$21$	−686.000	−0.339450
$22$	0	0
$23$	1824.00	0.718961	0.359480	−	0.933153i	$-0.382954\pi$
$23$	1824.00	0.718961	0.359480	+	0.933153i	$0.382954\pi$
$24$	−5040.00	−1.78609
$25$	11.0000	0.00352000
$26$	1400.00	0.406158
$27$	4060.00	1.07181
$28$	3332.00	0.803175
$29$	−3418.00	−0.754705	−0.377352	−	0.926070i	$-0.623165\pi$
$29$	−3418.00	−0.754705	−0.377352	+	0.926070i	$0.623165\pi$
$30$	7840.00	1.59042
$31$	−7644.00	−1.42862	−0.714310	−	0.699830i	$-0.753259\pi$
$31$	−7644.00	−1.42862	−0.714310	+	0.699830i	$0.753259\pi$
$32$	2720.00	0.469563
$33$	0	0
$34$	17220.0	2.55468
$35$	−2744.00	−0.378629
$36$	−3196.00	−0.411008
$37$	−10398.0	−1.24866	−0.624332	−	0.781159i	$-0.714629\pi$
$37$	−10398.0	−1.24866	−0.624332	+	0.781159i	$0.714629\pi$
$38$	980.000	0.110095
$39$	−1960.00	−0.206345
$40$	−20160.0	−1.99223
$41$	17962.0	1.66876	0.834382	−	0.551186i	$-0.185825\pi$
$41$	17962.0	1.66876	0.834382	+	0.551186i	$0.185825\pi$
$42$	−6860.00	−0.600069
$43$	−10880.0	−0.897342	−0.448671	−	0.893697i	$-0.648102\pi$
$43$	−10880.0	−0.897342	−0.448671	+	0.893697i	$0.648102\pi$
$44$	0	0
$45$	2632.00	0.193756
$46$	18240.0	1.27096
$47$	9324.00	0.615684	0.307842	−	0.951438i	$-0.400393\pi$
$47$	9324.00	0.615684	0.307842	+	0.951438i	$0.400393\pi$
$48$	−19936.0	−1.24892
$49$	2401.00	0.142857
$50$	110.000	0.00622254
$51$	−24108.0	−1.29788
$52$	9520.00	0.488235
$53$	2262.00	0.110612	0.0553061	−	0.998469i	$-0.482387\pi$
$53$	2262.00	0.110612	0.0553061	+	0.998469i	$0.482387\pi$
$54$	40600.0	1.89471
$55$	0	0
$56$	17640.0	0.751672
$57$	−1372.00	−0.0559329
$58$	−34180.0	−1.33414
$59$	−2730.00	−0.102102	−0.0510508	−	0.998696i	$-0.516257\pi$
$59$	−2730.00	−0.102102	−0.0510508	+	0.998696i	$0.516257\pi$
$60$	53312.0	1.91182
$61$	−25648.0	−0.882529	−0.441264	−	0.897377i	$-0.645470\pi$
$61$	−25648.0	−0.882529	−0.441264	+	0.897377i	$0.645470\pi$
$62$	−76440.0	−2.52547
$63$	−2303.00	−0.0731042
$64$	−18368.0	−0.560547
$65$	−7840.00	−0.230161
$66$	0	0
$67$	−48404.0	−1.31733	−0.658664	−	0.752437i	$-0.728878\pi$
$67$	−48404.0	−1.31733	−0.658664	+	0.752437i	$0.728878\pi$
$68$	117096.	3.07093
$69$	−25536.0	−0.645699
$70$	−27440.0	−0.669328
$71$	−58560.0	−1.37865	−0.689327	−	0.724450i	$-0.742094\pi$
$71$	−58560.0	−1.37865	−0.689327	+	0.724450i	$0.742094\pi$
$72$	−16920.0	−0.384653
$73$	−68082.0	−1.49529	−0.747645	−	0.664099i	$-0.768815\pi$
$73$	−68082.0	−1.49529	−0.747645	+	0.664099i	$0.768815\pi$
$74$	−103980.	−2.20735
$75$	−154.000	−0.00316131
$76$	6664.00	0.132343
$77$	0	0
$78$	−19600.0	−0.364770
$79$	−31784.0	−0.572982	−0.286491	−	0.958083i	$-0.592489\pi$
$79$	−31784.0	−0.572982	−0.286491	+	0.958083i	$0.592489\pi$
$80$	−79744.0	−1.39307
$81$	−45419.0	−0.769175
$82$	179620.	2.94999
$83$	20538.0	0.327237	0.163619	−	0.986524i	$-0.447683\pi$
$83$	20538.0	0.327237	0.163619	+	0.986524i	$0.447683\pi$
$84$	−46648.0	−0.721331
$85$	−96432.0	−1.44768
$86$	−108800.	−1.58629
$87$	47852.0	0.677801
$88$	0	0
$89$	−50582.0	−0.676894	−0.338447	−	0.940985i	$-0.609902\pi$
$89$	−50582.0	−0.676894	−0.338447	+	0.940985i	$0.609902\pi$
$90$	26320.0	0.342515
$91$	6860.00	0.0868402
$92$	124032.	1.52779
$93$	107016.	1.28304
$94$	93240.0	1.08839
$95$	−5488.00	−0.0623886
$96$	−38080.0	−0.421715
$97$	−58506.0	−0.631351	−0.315676	−	0.948867i	$-0.602231\pi$
$97$	−58506.0	−0.631351	−0.315676	+	0.948867i	$0.602231\pi$
$98$	24010.0	0.252538
$99$	0	0
$100$	748.000	0.00748000
$101$	−38696.0	−0.377453	−0.188726	−	0.982030i	$-0.560436\pi$
$101$	−38696.0	−0.377453	−0.188726	+	0.982030i	$0.560436\pi$
$102$	−241080.	−2.29436
$103$	53060.0	0.492804	0.246402	−	0.969168i	$-0.420752\pi$
$103$	53060.0	0.492804	0.246402	+	0.969168i	$0.420752\pi$
$104$	50400.0	0.456927
$105$	38416.0	0.340047
$106$	22620.0	0.195537
$107$	146324.	1.23554	0.617769	−	0.786360i	$-0.288037\pi$
$107$	146324.	1.23554	0.617769	+	0.786360i	$0.288037\pi$
$108$	276080.	2.27759
$109$	−92898.0	−0.748928	−0.374464	−	0.927241i	$-0.622173\pi$
$109$	−92898.0	−0.748928	−0.374464	+	0.927241i	$0.622173\pi$
$110$	0	0
$111$	145572.	1.12143
$112$	69776.0	0.525607
$113$	−83354.0	−0.614088	−0.307044	−	0.951695i	$-0.599340\pi$
$113$	−83354.0	−0.614088	−0.307044	+	0.951695i	$0.599340\pi$
$114$	−13720.0	−0.0988762
$115$	−102144.	−0.720225
$116$	−232424.	−1.60375
$117$	−6580.00	−0.0444387
$118$	−27300.0	−0.180492
$119$	84378.0	0.546213
$120$	282240.	1.78923
$121$	0	0
$122$	−256480.	−1.56011
$123$	−251468.	−1.49872
$124$	−519792.	−3.03582
$125$	174384.	0.998232
$126$	−23030.0	−0.129231
$127$	−60384.0	−0.332210	−0.166105	−	0.986108i	$-0.553119\pi$
$127$	−60384.0	−0.332210	−0.166105	+	0.986108i	$0.553119\pi$
$128$	−270720.	−1.46048
$129$	152320.	0.805903
$130$	−78400.0	−0.406872
$131$	61586.0	0.313548	0.156774	−	0.987635i	$-0.449891\pi$
$131$	61586.0	0.313548	0.156774	+	0.987635i	$0.449891\pi$
$132$	0	0
$133$	4802.00	0.0235393
$134$	−484040.	−2.32873
$135$	−227360.	−1.07369
$136$	619920.	2.87401
$137$	−204462.	−0.930703	−0.465352	−	0.885126i	$-0.654072\pi$
$137$	−204462.	−0.930703	−0.465352	+	0.885126i	$0.654072\pi$
$138$	−255360.	−1.14145
$139$	35406.0	0.155432	0.0777159	−	0.996976i	$-0.475237\pi$
$139$	35406.0	0.155432	0.0777159	+	0.996976i	$0.475237\pi$
$140$	−186592.	−0.804587
$141$	−130536.	−0.552946
$142$	−585600.	−2.43714
$143$	0	0
$144$	−66928.0	−0.268969
$145$	191408.	0.756032
$146$	−680820.	−2.64332
$147$	−33614.0	−0.128300
$148$	−707064.	−2.65341
$149$	20226.0	0.0746353	0.0373177	−	0.999303i	$-0.488119\pi$
$149$	20226.0	0.0746353	0.0373177	+	0.999303i	$0.488119\pi$
$150$	−1540.00	−0.00558847
$151$	−70904.0	−0.253063	−0.126531	−	0.991963i	$-0.540384\pi$
$151$	−70904.0	−0.253063	−0.126531	+	0.991963i	$0.540384\pi$
$152$	35280.0	0.123857
$153$	−80934.0	−0.279513
$154$	0	0
$155$	428064.	1.43113
$156$	−133280.	−0.438484
$157$	293524.	0.950374	0.475187	−	0.879885i	$-0.342380\pi$
$157$	293524.	0.950374	0.475187	+	0.879885i	$0.342380\pi$
$158$	−317840.	−1.01290
$159$	−31668.0	−0.0993408
$160$	−152320.	−0.470389
$161$	89376.0	0.271742
$162$	−454190.	−1.35972
$163$	13192.0	0.0388903	0.0194452	−	0.999811i	$-0.493810\pi$
$163$	13192.0	0.0388903	0.0194452	+	0.999811i	$0.493810\pi$
$164$	1.22142e6	3.54612
$165$	0	0
$166$	205380.	0.578479
$167$	−493612.	−1.36960	−0.684801	−	0.728730i	$-0.740111\pi$
$167$	−493612.	−1.36960	−0.684801	+	0.728730i	$0.740111\pi$
$168$	−246960.	−0.675077
$169$	−351693.	−0.947212
$170$	−964320.	−2.55917
$171$	−4606.00	−0.0120457
$172$	−739840.	−1.90685
$173$	−240716.	−0.611490	−0.305745	−	0.952113i	$-0.598906\pi$
$173$	−240716.	−0.611490	−0.305745	+	0.952113i	$0.598906\pi$
$174$	478520.	1.19819
$175$	539.000	0.00133043
$176$	0	0
$177$	38220.0	0.0916975
$178$	−505820.	−1.19659
$179$	294932.	0.688001	0.344001	−	0.938969i	$-0.388218\pi$
$179$	294932.	0.688001	0.344001	+	0.938969i	$0.388218\pi$
$180$	178976.	0.411731
$181$	−336980.	−0.764553	−0.382277	−	0.924048i	$-0.624860\pi$
$181$	−336980.	−0.764553	−0.382277	+	0.924048i	$0.624860\pi$
$182$	68600.0	0.153513
$183$	359072.	0.792600
$184$	656640.	1.42982
$185$	582288.	1.25086
$186$	1.07016e6	2.26812
$187$	0	0
$188$	634032.	1.30833
$189$	198940.	0.405105
$190$	−54880.0	−0.110288
$191$	358264.	0.710591	0.355296	−	0.934754i	$-0.384380\pi$
$191$	358264.	0.710591	0.355296	+	0.934754i	$0.384380\pi$
$192$	257152.	0.503427
$193$	989554.	1.91226	0.956128	−	0.292948i	$-0.0946362\pi$
$193$	989554.	1.91226	0.956128	+	0.292948i	$0.0946362\pi$
$194$	−585060.	−1.11608
$195$	109760.	0.206708
$196$	163268.	0.303571
$197$	990050.	1.81757	0.908786	−	0.417263i	$-0.137011\pi$
$197$	990050.	1.81757	0.908786	+	0.417263i	$0.137011\pi$
$198$	0	0
$199$	−840756.	−1.50500	−0.752501	−	0.658591i	$-0.771153\pi$
$199$	−840756.	−1.50500	−0.752501	+	0.658591i	$0.771153\pi$
$200$	3960.00	0.00700036
$201$	677656.	1.18309
$202$	−386960.	−0.667249
$203$	−167482.	−0.285252
$204$	−1.63934e6	−2.75800
$205$	−1.00587e6	−1.67170
$206$	530600.	0.871163
$207$	−85728.0	−0.139058
$208$	199360.	0.319506
$209$	0	0
$210$	384160.	0.601124
$211$	−1.15073e6	−1.77938	−0.889689	−	0.456568i	$-0.849079\pi$
$211$	−1.15073e6	−1.77938	−0.889689	+	0.456568i	$0.849079\pi$
$212$	153816.	0.235051
$213$	819840.	1.23817
$214$	1.46324e6	2.18414
$215$	609280.	0.898919
$216$	1.46160e6	2.13154
$217$	−374556.	−0.539967
$218$	−928980.	−1.32393
$219$	953148.	1.34292
$220$	0	0
$221$	241080.	0.332032
$222$	1.45572e6	1.98242
$223$	−824264.	−1.10995	−0.554976	−	0.831866i	$-0.687273\pi$
$223$	−824264.	−1.10995	−0.554976	+	0.831866i	$0.687273\pi$
$224$	133280.	0.177478
$225$	−517.000	−0.000680823 0
$226$	−833540.	−1.08556
$227$	−74382.0	−0.0958083	−0.0479042	−	0.998852i	$-0.515254\pi$
$227$	−74382.0	−0.0958083	−0.0479042	+	0.998852i	$0.515254\pi$
$228$	−93296.0	−0.118857
$229$	1.13196e6	1.42640	0.713199	−	0.700961i	$-0.247245\pi$
$229$	1.13196e6	1.42640	0.713199	+	0.700961i	$0.247245\pi$
$230$	−1.02144e6	−1.27319
$231$	0	0
$232$	−1.23048e6	−1.50091
$233$	198726.	0.239809	0.119904	−	0.992785i	$-0.461741\pi$
$233$	198726.	0.239809	0.119904	+	0.992785i	$0.461741\pi$
$234$	−65800.0	−0.0785572
$235$	−522144.	−0.616766
$236$	−185640.	−0.216966
$237$	444976.	0.514595
$238$	843780.	0.965577
$239$	−482904.	−0.546847	−0.273424	−	0.961894i	$-0.588156\pi$
$239$	−482904.	−0.546847	−0.273424	+	0.961894i	$0.588156\pi$
$240$	1.11642e6	1.25112
$241$	−805910.	−0.893807	−0.446904	−	0.894582i	$-0.647473\pi$
$241$	−805910.	−0.893807	−0.446904	+	0.894582i	$0.647473\pi$
$242$	0	0
$243$	−350714.	−0.381011
$244$	−1.74406e6	−1.87537
$245$	−134456.	−0.143108
$246$	−2.51468e6	−2.64938
$247$	13720.0	0.0143091
$248$	−2.75184e6	−2.84115
$249$	−287532.	−0.293892
$250$	1.74384e6	1.76464
$251$	430738.	0.431548	0.215774	−	0.976443i	$-0.430773\pi$
$251$	430738.	0.431548	0.215774	+	0.976443i	$0.430773\pi$
$252$	−156604.	−0.155347
$253$	0	0
$254$	−603840.	−0.587270
$255$	1.35005e6	1.30017
$256$	−2.11942e6	−2.02124
$257$	−1.17691e6	−1.11150	−0.555751	−	0.831349i	$-0.687569\pi$
$257$	−1.17691e6	−1.11150	−0.555751	+	0.831349i	$0.687569\pi$
$258$	1.52320e6	1.42465
$259$	−509502.	−0.471951
$260$	−533120.	−0.489093
$261$	160646.	0.145972
$262$	615860.	0.554279
$263$	−1.29098e6	−1.15088	−0.575438	−	0.817845i	$-0.695169\pi$
$263$	−1.29098e6	−1.15088	−0.575438	+	0.817845i	$0.695169\pi$
$264$	0	0
$265$	−126672.	−0.110807
$266$	48020.0	0.0416119
$267$	708148.	0.607919
$268$	−3.29147e6	−2.79932
$269$	−1.27756e6	−1.07646	−0.538232	−	0.842797i	$-0.680907\pi$
$269$	−1.27756e6	−1.07646	−0.538232	+	0.842797i	$0.680907\pi$
$270$	−2.27360e6	−1.89804
$271$	−1.65054e6	−1.36522	−0.682612	−	0.730781i	$-0.739156\pi$
$271$	−1.65054e6	−1.36522	−0.682612	+	0.730781i	$0.739156\pi$
$272$	2.45213e6	2.00965
$273$	−96040.0	−0.0779912
$274$	−2.04462e6	−1.64527
$275$	0	0
$276$	−1.73645e6	−1.37211
$277$	1.06409e6	0.833257	0.416628	−	0.909077i	$-0.363212\pi$
$277$	1.06409e6	0.833257	0.416628	+	0.909077i	$0.363212\pi$
$278$	354060.	0.274767
$279$	359268.	0.276317
$280$	−987840.	−0.752994
$281$	22342.0	0.0168794	0.00843969	−	0.999964i	$-0.497314\pi$
$281$	22342.0	0.0168794	0.00843969	+	0.999964i	$0.497314\pi$
$282$	−1.30536e6	−0.977479
$283$	2.49574e6	1.85239	0.926196	−	0.377042i	$-0.123059\pi$
$283$	2.49574e6	1.85239	0.926196	+	0.377042i	$0.123059\pi$
$284$	−3.98208e6	−2.92964
$285$	76832.0	0.0560312
$286$	0	0
$287$	880138.	0.630734
$288$	−127840.	−0.0908208
$289$	1.54543e6	1.08844
$290$	1.91408e6	1.33649
$291$	819084.	0.567017
$292$	−4.62958e6	−3.17749
$293$	1.93178e6	1.31458	0.657291	−	0.753637i	$-0.271702\pi$
$293$	1.93178e6	1.31458	0.657291	+	0.753637i	$0.271702\pi$
$294$	−336140.	−0.226805
$295$	152880.	0.102281
$296$	−3.74328e6	−2.48326
$297$	0	0
$298$	202260.	0.131938
$299$	255360.	0.165187
$300$	−10472.0	−0.00671779
$301$	−533120.	−0.339163
$302$	−709040.	−0.447356
$303$	541744.	0.338991
$304$	139552.	0.0866068
$305$	1.43629e6	0.884081
$306$	−809340.	−0.494114
$307$	459074.	0.277995	0.138997	−	0.990293i	$-0.455612\pi$
$307$	459074.	0.277995	0.138997	+	0.990293i	$0.455612\pi$
$308$	0	0
$309$	−742840.	−0.442587
$310$	4.28064e6	2.52991
$311$	667128.	0.391118	0.195559	−	0.980692i	$-0.437348\pi$
$311$	667128.	0.391118	0.195559	+	0.980692i	$0.437348\pi$
$312$	−705600.	−0.410367
$313$	−111034.	−0.0640612	−0.0320306	−	0.999487i	$-0.510197\pi$
$313$	−111034.	−0.0640612	−0.0320306	+	0.999487i	$0.510197\pi$
$314$	2.93524e6	1.68004
$315$	128968.	0.0732328
$316$	−2.16131e6	−1.21759
$317$	−68778.0	−0.0384416	−0.0192208	−	0.999815i	$-0.506119\pi$
$317$	−68778.0	−0.0384416	−0.0192208	+	0.999815i	$0.506119\pi$
$318$	−316680.	−0.175611
$319$	0	0
$320$	1.02861e6	0.561533
$321$	−2.04854e6	−1.10964
$322$	893760.	0.480376
$323$	168756.	0.0900022
$324$	−3.08849e6	−1.63450
$325$	1540.00	0.000808746 0
$326$	131920.	0.0687490
$327$	1.30057e6	0.672613
$328$	6.46632e6	3.31874
$329$	456876.	0.232707
$330$	0	0
$331$	−564448.	−0.283174	−0.141587	−	0.989926i	$-0.545221\pi$
$331$	−564448.	−0.283174	−0.141587	+	0.989926i	$0.545221\pi$
$332$	1.39658e6	0.695379
$333$	488706.	0.241511
$334$	−4.93612e6	−2.42114
$335$	2.71062e6	1.31965
$336$	−976864.	−0.472048
$337$	−2.07729e6	−0.996376	−0.498188	−	0.867069i	$-0.666001\pi$
$337$	−2.07729e6	−0.996376	−0.498188	+	0.867069i	$0.666001\pi$
$338$	−3.51693e6	−1.67445
$339$	1.16696e6	0.551512
$340$	−6.55738e6	−3.07633
$341$	0	0
$342$	−46060.0	−0.0212941
$343$	117649.	0.0539949
$344$	−3.91680e6	−1.78458
$345$	1.43002e6	0.646834
$346$	−2.40716e6	−1.08097
$347$	53248.0	0.0237399	0.0118700	−	0.999930i	$-0.496222\pi$
$347$	53248.0	0.0237399	0.0118700	+	0.999930i	$0.496222\pi$
$348$	3.25394e6	1.44033
$349$	2.27200e6	0.998494	0.499247	−	0.866460i	$-0.333610\pi$
$349$	2.27200e6	0.998494	0.499247	+	0.866460i	$0.333610\pi$
$350$	5390.00	0.00235190
$351$	568400.	0.246256
$352$	0	0
$353$	4.00645e6	1.71129	0.855644	−	0.517565i	$-0.173162\pi$
$353$	4.00645e6	1.71129	0.855644	+	0.517565i	$0.173162\pi$
$354$	382200.	0.162100
$355$	3.27936e6	1.38108
$356$	−3.43958e6	−1.43840
$357$	−1.18129e6	−0.490554
$358$	2.94932e6	1.21623
$359$	−73784.0	−0.0302152	−0.0151076	−	0.999886i	$-0.504809\pi$
$359$	−73784.0	−0.0302152	−0.0151076	+	0.999886i	$0.504809\pi$
$360$	947520.	0.385329
$361$	−2.46650e6	−0.996121
$362$	−3.36980e6	−1.35155
$363$	0	0
$364$	466480.	0.184535
$365$	3.81259e6	1.49792
$366$	3.59072e6	1.40113
$367$	1.40431e6	0.544250	0.272125	−	0.962262i	$-0.412274\pi$
$367$	1.40431e6	0.544250	0.272125	+	0.962262i	$0.412274\pi$
$368$	2.59738e6	0.999805
$369$	−844214.	−0.322765
$370$	5.82288e6	2.21123
$371$	110838.	0.0418075
$372$	7.27709e6	2.72647
$373$	1.60323e6	0.596657	0.298329	−	0.954463i	$-0.403571\pi$
$373$	1.60323e6	0.596657	0.298329	+	0.954463i	$0.403571\pi$
$374$	0	0
$375$	−2.44138e6	−0.896513
$376$	3.35664e6	1.22443
$377$	−478520.	−0.173399
$378$	1.98940e6	0.716131
$379$	−4.77012e6	−1.70581	−0.852906	−	0.522064i	$-0.825162\pi$
$379$	−4.77012e6	−1.70581	−0.852906	+	0.522064i	$0.825162\pi$
$380$	−373184.	−0.132576
$381$	845376.	0.298358
$382$	3.58264e6	1.25616
$383$	−2.23079e6	−0.777072	−0.388536	−	0.921434i	$-0.627019\pi$
$383$	−2.23079e6	−0.777072	−0.388536	+	0.921434i	$0.627019\pi$
$384$	3.79008e6	1.31166
$385$	0	0
$386$	9.89554e6	3.38042
$387$	511360.	0.173560
$388$	−3.97841e6	−1.34162
$389$	4.84024e6	1.62178	0.810892	−	0.585196i	$-0.198982\pi$
$389$	4.84024e6	1.62178	0.810892	+	0.585196i	$0.198982\pi$
$390$	1.09760e6	0.365412
$391$	3.14093e6	1.03900
$392$	864360.	0.284105
$393$	−862204.	−0.281597
$394$	9.90050e6	3.21304
$395$	1.77990e6	0.573989
$396$	0	0
$397$	995820.	0.317106	0.158553	−	0.987350i	$-0.449317\pi$
$397$	995820.	0.317106	0.158553	+	0.987350i	$0.449317\pi$
$398$	−8.40756e6	−2.66049
$399$	−67228.0	−0.0211406
$400$	15664.0	0.00489500
$401$	−3.31605e6	−1.02982	−0.514909	−	0.857245i	$-0.672174\pi$
$401$	−3.31605e6	−1.02982	−0.514909	+	0.857245i	$0.672174\pi$
$402$	6.77656e6	2.09143
$403$	−1.07016e6	−0.328236
$404$	−2.63133e6	−0.802087
$405$	2.54346e6	0.770527
$406$	−1.67482e6	−0.504258
$407$	0	0
$408$	−8.67888e6	−2.58115
$409$	−3.07273e6	−0.908274	−0.454137	−	0.890932i	$-0.650052\pi$
$409$	−3.07273e6	−0.908274	−0.454137	+	0.890932i	$0.650052\pi$
$410$	−1.00587e7	−2.95517
$411$	2.86247e6	0.835865
$412$	3.60808e6	1.04721
$413$	−133770.	−0.0385908
$414$	−857280.	−0.245823
$415$	−1.15013e6	−0.327813
$416$	380800.	0.107886
$417$	−495684.	−0.139593
$418$	0	0
$419$	2.81438e6	0.783154	0.391577	−	0.920145i	$-0.371930\pi$
$419$	2.81438e6	0.783154	0.391577	+	0.920145i	$0.371930\pi$
$420$	2.61229e6	0.722600
$421$	3.05802e6	0.840883	0.420441	−	0.907320i	$-0.361875\pi$
$421$	3.05802e6	0.840883	0.420441	+	0.907320i	$0.361875\pi$
$422$	−1.15073e7	−3.14552
$423$	−438228.	−0.119083
$424$	814320.	0.219979
$425$	18942.0	0.00508690
$426$	8.19840e6	2.18880
$427$	−1.25675e6	−0.333565
$428$	9.95003e6	2.62552
$429$	0	0
$430$	6.09280e6	1.58908
$431$	−1.93750e6	−0.502398	−0.251199	−	0.967936i	$-0.580825\pi$
$431$	−1.93750e6	−0.502398	−0.251199	+	0.967936i	$0.580825\pi$
$432$	5.78144e6	1.49048
$433$	3.94790e6	1.01192	0.505961	−	0.862557i	$-0.331138\pi$
$433$	3.94790e6	1.01192	0.505961	+	0.862557i	$0.331138\pi$
$434$	−3.74556e6	−0.954536
$435$	−2.67971e6	−0.678993
$436$	−6.31706e6	−1.59147
$437$	178752.	0.0447762
$438$	9.53148e6	2.37397
$439$	7.41770e6	1.83700	0.918498	−	0.395426i	$-0.129403\pi$
$439$	7.41770e6	1.83700	0.918498	+	0.395426i	$0.129403\pi$
$440$	0	0
$441$	−112847.	−0.0276308
$442$	2.41080e6	0.586956
$443$	1.40269e6	0.339589	0.169794	−	0.985480i	$-0.445690\pi$
$443$	1.40269e6	0.339589	0.169794	+	0.985480i	$0.445690\pi$
$444$	9.89890e6	2.38303
$445$	2.83259e6	0.678085
$446$	−8.24264e6	−1.96214
$447$	−283164.	−0.0670300
$448$	−900032.	−0.211867
$449$	−590574.	−0.138248	−0.0691239	−	0.997608i	$-0.522020\pi$
$449$	−590574.	−0.138248	−0.0691239	+	0.997608i	$0.522020\pi$
$450$	−5170.00	−0.00120354
$451$	0	0
$452$	−5.66807e6	−1.30494
$453$	992656.	0.227276
$454$	−743820.	−0.169367
$455$	−384160.	−0.0869929
$456$	−493920.	−0.111236
$457$	2.90484e6	0.650627	0.325313	−	0.945606i	$-0.394530\pi$
$457$	2.90484e6	0.650627	0.325313	+	0.945606i	$0.394530\pi$
$458$	1.13196e7	2.52154
$459$	6.99132e6	1.54891
$460$	−6.94579e6	−1.53048
$461$	922684.	0.202209	0.101105	−	0.994876i	$-0.467762\pi$
$461$	922684.	0.202209	0.101105	+	0.994876i	$0.467762\pi$
$462$	0	0
$463$	7.18235e6	1.55709	0.778546	−	0.627588i	$-0.215958\pi$
$463$	7.18235e6	1.55709	0.778546	+	0.627588i	$0.215958\pi$
$464$	−4.86723e6	−1.04951
$465$	−5.99290e6	−1.28530
$466$	1.98726e6	0.423926
$467$	−612570.	−0.129976	−0.0649881	−	0.997886i	$-0.520701\pi$
$467$	−612570.	−0.129976	−0.0649881	+	0.997886i	$0.520701\pi$
$468$	−447440.	−0.0944322
$469$	−2.37180e6	−0.497904
$470$	−5.22144e6	−1.09030
$471$	−4.10934e6	−0.853531
$472$	−982800.	−0.203053
$473$	0	0
$474$	4.44976e6	0.909684
$475$	1078.00	0.000219222 0
$476$	5.73770e6	1.16070
$477$	−106314.	−0.0213941
$478$	−4.82904e6	−0.966699
$479$	−2.60330e6	−0.518424	−0.259212	−	0.965820i	$-0.583463\pi$
$479$	−2.60330e6	−0.518424	−0.259212	+	0.965820i	$0.583463\pi$
$480$	2.13248e6	0.422456
$481$	−1.45572e6	−0.286890
$482$	−8.05910e6	−1.58004
$483$	−1.25126e6	−0.244051
$484$	0	0
$485$	3.27634e6	0.632461
$486$	−3.50714e6	−0.673539
$487$	5.46309e6	1.04380	0.521898	−	0.853008i	$-0.325224\pi$
$487$	5.46309e6	1.04380	0.521898	+	0.853008i	$0.325224\pi$
$488$	−9.23328e6	−1.75512
$489$	−184688.	−0.0349274
$490$	−1.34456e6	−0.252982
$491$	−1.64090e6	−0.307170	−0.153585	−	0.988135i	$-0.549082\pi$
$491$	−1.64090e6	−0.307170	−0.153585	+	0.988135i	$0.549082\pi$
$492$	−1.70998e7	−3.18478
$493$	−5.88580e6	−1.09066
$494$	137200.	0.0252951
$495$	0	0
$496$	−1.08851e7	−1.98667
$497$	−2.86944e6	−0.521082
$498$	−2.87532e6	−0.519533
$499$	2.99796e6	0.538983	0.269491	−	0.963003i	$-0.413144\pi$
$499$	2.99796e6	0.538983	0.269491	+	0.963003i	$0.413144\pi$
$500$	1.18581e7	2.12124
$501$	6.91057e6	1.23004
$502$	4.30738e6	0.762876
$503$	6.89405e6	1.21494	0.607469	−	0.794343i	$-0.292185\pi$
$503$	6.89405e6	1.21494	0.607469	+	0.794343i	$0.292185\pi$
$504$	−829080.	−0.145385
$505$	2.16698e6	0.378117
$506$	0	0
$507$	4.92370e6	0.850691
$508$	−4.10611e6	−0.705946
$509$	2.30476e6	0.394305	0.197152	−	0.980373i	$-0.436831\pi$
$509$	2.30476e6	0.394305	0.197152	+	0.980373i	$0.436831\pi$
$510$	1.35005e7	2.29839
$511$	−3.33602e6	−0.565166
$512$	−1.25312e7	−2.11260
$513$	397880.	0.0667511
$514$	−1.17691e7	−1.96488
$515$	−2.97136e6	−0.493671
$516$	1.03578e7	1.71254
$517$	0	0
$518$	−5.09502e6	−0.834299
$519$	3.37002e6	0.549180
$520$	−2.82240e6	−0.457731
$521$	−1.20960e7	−1.95231	−0.976155	−	0.217073i	$-0.930349\pi$
$521$	−1.20960e7	−1.95231	−0.976155	+	0.217073i	$0.930349\pi$
$522$	1.60646e6	0.258044
$523$	−5.48443e6	−0.876753	−0.438377	−	0.898791i	$-0.644446\pi$
$523$	−5.48443e6	−0.876753	−0.438377	+	0.898791i	$0.644446\pi$
$524$	4.18785e6	0.666289
$525$	−7546.00	−0.00119486
$526$	−1.29098e7	−2.03448
$527$	−1.31630e7	−2.06456
$528$	0	0
$529$	−3.10937e6	−0.483095
$530$	−1.26672e6	−0.195880
$531$	128310.	0.0197480
$532$	326536.	0.0500210
$533$	2.51468e6	0.383411
$534$	7.08148e6	1.07466
$535$	−8.19414e6	−1.23771
$536$	−1.74254e7	−2.61982
$537$	−4.12905e6	−0.617894
$538$	−1.27756e7	−1.90294
$539$	0	0
$540$	−1.54605e7	−2.28160
$541$	6.71799e6	0.986839	0.493420	−	0.869791i	$-0.335747\pi$
$541$	6.71799e6	0.986839	0.493420	+	0.869791i	$0.335747\pi$
$542$	−1.65054e7	−2.41340
$543$	4.71772e6	0.686646
$544$	4.68384e6	0.678586
$545$	5.20229e6	0.750245
$546$	−960400.	−0.137870
$547$	5.00235e6	0.714835	0.357418	−	0.933945i	$-0.383657\pi$
$547$	5.00235e6	0.714835	0.357418	+	0.933945i	$0.383657\pi$
$548$	−1.39034e7	−1.97774
$549$	1.20546e6	0.170695
$550$	0	0
$551$	−334964.	−0.0470023
$552$	−9.19296e6	−1.28413
$553$	−1.55742e6	−0.216567
$554$	1.06409e7	1.47300
$555$	−8.15203e6	−1.12340
$556$	2.40761e6	0.330293
$557$	−9.01961e6	−1.23183	−0.615913	−	0.787814i	$-0.711213\pi$
$557$	−9.01961e6	−1.23183	−0.615913	+	0.787814i	$0.711213\pi$
$558$	3.59268e6	0.488465
$559$	−1.52320e6	−0.206171
$560$	−3.90746e6	−0.526531
$561$	0	0
$562$	223420.	0.0298388
$563$	−1.24051e7	−1.64941	−0.824707	−	0.565561i	$-0.808660\pi$
$563$	−1.24051e7	−1.64941	−0.824707	+	0.565561i	$0.808660\pi$
$564$	−8.87645e6	−1.17501
$565$	4.66782e6	0.615167
$566$	2.49574e7	3.27460
$567$	−2.22553e6	−0.290721
$568$	−2.10816e7	−2.74178
$569$	−6.48804e6	−0.840103	−0.420052	−	0.907500i	$-0.637988\pi$
$569$	−6.48804e6	−0.840103	−0.420052	+	0.907500i	$0.637988\pi$
$570$	768320.	0.0990501
$571$	1.02285e7	1.31287	0.656435	−	0.754382i	$-0.272064\pi$
$571$	1.02285e7	1.31287	0.656435	+	0.754382i	$0.272064\pi$
$572$	0	0
$573$	−5.01570e6	−0.638182
$574$	8.80138e6	1.11499
$575$	20064.0	0.00253074
$576$	863296.	0.108419
$577$	2.65338e6	0.331787	0.165894	−	0.986144i	$-0.446949\pi$
$577$	2.65338e6	0.331787	0.165894	+	0.986144i	$0.446949\pi$
$578$	1.54543e7	1.92411
$579$	−1.38538e7	−1.71740
$580$	1.30157e7	1.60657
$581$	1.00636e6	0.123684
$582$	8.19084e6	1.00235
$583$	0	0
$584$	−2.45095e7	−2.97374
$585$	368480.	0.0445168
$586$	1.93178e7	2.32387
$587$	−1.43044e7	−1.71346	−0.856729	−	0.515766i	$-0.827507\pi$
$587$	−1.43044e7	−1.71346	−0.856729	+	0.515766i	$0.827507\pi$
$588$	−2.28575e6	−0.272638
$589$	−749112.	−0.0889731
$590$	1.52880e6	0.180809
$591$	−1.38607e7	−1.63236
$592$	−1.48068e7	−1.73642
$593$	1.00265e7	1.17088	0.585442	−	0.810714i	$-0.300921\pi$
$593$	1.00265e7	1.17088	0.585442	+	0.810714i	$0.300921\pi$
$594$	0	0
$595$	−4.72517e6	−0.547173
$596$	1.37537e6	0.158600
$597$	1.17706e7	1.35164
$598$	2.55360e6	0.292011
$599$	−7.52292e6	−0.856681	−0.428341	−	0.903617i	$-0.640902\pi$
$599$	−7.52292e6	−0.856681	−0.428341	+	0.903617i	$0.640902\pi$
$600$	−55440.0	−0.00628702
$601$	−3.38625e6	−0.382413	−0.191207	−	0.981550i	$-0.561240\pi$
$601$	−3.38625e6	−0.382413	−0.191207	+	0.981550i	$0.561240\pi$
$602$	−5.33120e6	−0.599562
$603$	2.27499e6	0.254792
$604$	−4.82147e6	−0.537759
$605$	0	0
$606$	5.41744e6	0.599256
$607$	6.90861e6	0.761060	0.380530	−	0.924769i	$-0.375742\pi$
$607$	6.90861e6	0.761060	0.380530	+	0.924769i	$0.375742\pi$
$608$	266560.	0.0292439
$609$	2.34475e6	0.256185
$610$	1.43629e7	1.56285
$611$	1.30536e6	0.141458
$612$	−5.50351e6	−0.593966
$613$	9.68896e6	1.04142	0.520710	−	0.853734i	$-0.325667\pi$
$613$	9.68896e6	1.04142	0.520710	+	0.853734i	$0.325667\pi$
$614$	4.59074e6	0.491430
$615$	1.40822e7	1.50135
$616$	0	0
$617$	−7.84742e6	−0.829877	−0.414939	−	0.909849i	$-0.636197\pi$
$617$	−7.84742e6	−0.829877	−0.414939	+	0.909849i	$0.636197\pi$
$618$	−7.42840e6	−0.782391
$619$	−1.01972e7	−1.06968	−0.534840	−	0.844953i	$-0.679628\pi$
$619$	−1.01972e7	−1.06968	−0.534840	+	0.844953i	$0.679628\pi$
$620$	2.91084e7	3.04115
$621$	7.40544e6	0.770587
$622$	6.67128e6	0.691406
$623$	−2.47852e6	−0.255842
$624$	−2.79104e6	−0.286949
$625$	−9.79988e6	−1.00351
$626$	−1.11034e6	−0.113245
$627$	0	0
$628$	1.99596e7	2.01954
$629$	−1.79054e7	−1.80450
$630$	1.28968e6	0.129459
$631$	−8.36258e6	−0.836116	−0.418058	−	0.908420i	$-0.637289\pi$
$631$	−8.36258e6	−0.836116	−0.418058	+	0.908420i	$0.637289\pi$
$632$	−1.14422e7	−1.13951
$633$	1.61102e7	1.59806
$634$	−687780.	−0.0679558
$635$	3.38150e6	0.332794
$636$	−2.15342e6	−0.211099
$637$	336140.	0.0328225
$638$	0	0
$639$	2.75232e6	0.266653
$640$	1.51603e7	1.46305
$641$	1.10283e6	0.106014	0.0530070	−	0.998594i	$-0.483119\pi$
$641$	1.10283e6	0.106014	0.0530070	+	0.998594i	$0.483119\pi$
$642$	−2.04854e7	−1.96158
$643$	1.71354e7	1.63443	0.817217	−	0.576330i	$-0.195516\pi$
$643$	1.71354e7	1.63443	0.817217	+	0.576330i	$0.195516\pi$
$644$	6.07757e6	0.577451
$645$	−8.52992e6	−0.807320
$646$	1.68756e6	0.159103
$647$	−54964.0	−0.00516200	−0.00258100	−	0.999997i	$-0.500822\pi$
$647$	−54964.0	−0.00516200	−0.00258100	+	0.999997i	$0.500822\pi$
$648$	−1.63508e7	−1.52969
$649$	0	0
$650$	15400.0	0.00142968
$651$	5.24378e6	0.484945
$652$	897056.	0.0826420
$653$	−485166.	−0.0445254	−0.0222627	−	0.999752i	$-0.507087\pi$
$653$	−485166.	−0.0445254	−0.0222627	+	0.999752i	$0.507087\pi$
$654$	1.30057e7	1.18902
$655$	−3.44882e6	−0.314099
$656$	2.55779e7	2.32063
$657$	3.19985e6	0.289212
$658$	4.56876e6	0.411371
$659$	2.72136e6	0.244103	0.122051	−	0.992524i	$-0.461053\pi$
$659$	2.72136e6	0.244103	0.122051	+	0.992524i	$0.461053\pi$
$660$	0	0
$661$	−2.14525e6	−0.190974	−0.0954869	−	0.995431i	$-0.530441\pi$
$661$	−2.14525e6	−0.190974	−0.0954869	+	0.995431i	$0.530441\pi$
$662$	−5.64448e6	−0.500586
$663$	−3.37512e6	−0.298198
$664$	7.39368e6	0.650789
$665$	−268912.	−0.0235807
$666$	4.88706e6	0.426935
$667$	−6.23443e6	−0.542603
$668$	−3.35656e7	−2.91041
$669$	1.15397e7	0.996848
$670$	2.71062e7	2.33283
$671$	0	0
$672$	−1.86592e6	−0.159393
$673$	−2.92796e6	−0.249188	−0.124594	−	0.992208i	$-0.539763\pi$
$673$	−2.92796e6	−0.249188	−0.124594	+	0.992208i	$0.539763\pi$
$674$	−2.07729e7	−1.76136
$675$	44660.0	0.00377276
$676$	−2.39151e7	−2.01282
$677$	1.34992e7	1.13198	0.565988	−	0.824414i	$-0.308495\pi$
$677$	1.34992e7	1.13198	0.565988	+	0.824414i	$0.308495\pi$
$678$	1.16696e7	0.974945
$679$	−2.86679e6	−0.238628
$680$	−3.47155e7	−2.87906
$681$	1.04135e6	0.0860455
$682$	0	0
$683$	−5.42972e6	−0.445375	−0.222688	−	0.974890i	$-0.571483\pi$
$683$	−5.42972e6	−0.445375	−0.222688	+	0.974890i	$0.571483\pi$
$684$	−313208.	−0.0255972
$685$	1.14499e7	0.932340
$686$	1.17649e6	0.0954504
$687$	−1.58474e7	−1.28105
$688$	−1.54931e7	−1.24787
$689$	316680.	0.0254140
$690$	1.43002e7	1.14345
$691$	2.08280e7	1.65940	0.829702	−	0.558207i	$-0.188510\pi$
$691$	2.08280e7	1.65940	0.829702	+	0.558207i	$0.188510\pi$
$692$	−1.63687e7	−1.29942
$693$	0	0
$694$	532480.	0.0419667
$695$	−1.98274e6	−0.155705
$696$	1.72267e7	1.34797
$697$	3.09306e7	2.41160
$698$	2.27200e7	1.76510
$699$	−2.78216e6	−0.215372
$700$	36652.0	0.00282717
$701$	−2.35141e7	−1.80731	−0.903655	−	0.428261i	$-0.859126\pi$
$701$	−2.35141e7	−1.80731	−0.903655	+	0.428261i	$0.859126\pi$
$702$	5.68400e6	0.435323
$703$	−1.01900e6	−0.0777656
$704$	0	0
$705$	7.31002e6	0.553918
$706$	4.00645e7	3.02516
$707$	−1.89610e6	−0.142664
$708$	2.59896e6	0.194857
$709$	−1.95747e7	−1.46244	−0.731221	−	0.682140i	$-0.761049\pi$
$709$	−1.95747e7	−1.46244	−0.731221	+	0.682140i	$0.761049\pi$
$710$	3.27936e7	2.44142
$711$	1.49385e6	0.110824
$712$	−1.82095e7	−1.34617
$713$	−1.39427e7	−1.02712
$714$	−1.18129e7	−0.867185
$715$	0	0
$716$	2.00554e7	1.46200
$717$	6.76066e6	0.491124
$718$	−737840.	−0.0534135
$719$	−2.61152e7	−1.88396	−0.941978	−	0.335674i	$-0.891036\pi$
$719$	−2.61152e7	−1.88396	−0.941978	+	0.335674i	$0.891036\pi$
$720$	3.74797e6	0.269442
$721$	2.59994e6	0.186262
$722$	−2.46650e7	−1.76091
$723$	1.12827e7	0.802729
$724$	−2.29146e7	−1.62468
$725$	−37598.0	−0.00265656
$726$	0	0
$727$	1.54126e7	1.08154	0.540768	−	0.841172i	$-0.318134\pi$
$727$	1.54126e7	1.08154	0.540768	+	0.841172i	$0.318134\pi$
$728$	2.46960e6	0.172702
$729$	1.59468e7	1.11136
$730$	3.81259e7	2.64797
$731$	−1.87354e7	−1.29679
$732$	2.44169e7	1.68427
$733$	1.69868e7	1.16776	0.583878	−	0.811841i	$-0.301535\pi$
$733$	1.69868e7	1.16776	0.583878	+	0.811841i	$0.301535\pi$
$734$	1.40431e7	0.962107
$735$	1.88238e6	0.128526
$736$	4.96128e6	0.337597
$737$	0	0
$738$	−8.44214e6	−0.570574
$739$	−2.01511e6	−0.135734	−0.0678669	−	0.997694i	$-0.521619\pi$
$739$	−2.01511e6	−0.135734	−0.0678669	+	0.997694i	$0.521619\pi$
$740$	3.95956e7	2.65808
$741$	−192080.	−0.0128510
$742$	1.10838e6	0.0739059
$743$	1.51381e7	1.00600	0.503001	−	0.864286i	$-0.332229\pi$
$743$	1.51381e7	1.00600	0.503001	+	0.864286i	$0.332229\pi$
$744$	3.85258e7	2.55164
$745$	−1.13266e6	−0.0747666
$746$	1.60323e7	1.05475
$747$	−965286.	−0.0632928
$748$	0	0
$749$	7.16988e6	0.466989
$750$	−2.44138e7	−1.58483
$751$	7.21401e6	0.466742	0.233371	−	0.972388i	$-0.425024\pi$
$751$	7.21401e6	0.466742	0.233371	+	0.972388i	$0.425024\pi$
$752$	1.32774e7	0.856185
$753$	−6.03033e6	−0.387573
$754$	−4.78520e6	−0.306529
$755$	3.97062e6	0.253508
$756$	1.35279e7	0.860848
$757$	−1.09697e7	−0.695755	−0.347877	−	0.937540i	$-0.613097\pi$
$757$	−1.09697e7	−0.695755	−0.347877	+	0.937540i	$0.613097\pi$
$758$	−4.77012e7	−3.01548
$759$	0	0
$760$	−1.97568e6	−0.124075
$761$	−1.92442e7	−1.20459	−0.602293	−	0.798275i	$-0.705746\pi$
$761$	−1.92442e7	−1.20459	−0.602293	+	0.798275i	$0.705746\pi$
$762$	8.45376e6	0.527427
$763$	−4.55200e6	−0.283068
$764$	2.43620e7	1.51001
$765$	4.53230e6	0.280005
$766$	−2.23079e7	−1.37368
$767$	−382200.	−0.0234586
$768$	2.96719e7	1.81528
$769$	−8.21185e6	−0.500755	−0.250378	−	0.968148i	$-0.580555\pi$
$769$	−8.21185e6	−0.500755	−0.250378	+	0.968148i	$0.580555\pi$
$770$	0	0
$771$	1.64767e7	0.998241
$772$	6.72897e7	4.06355
$773$	1.86187e7	1.12073	0.560363	−	0.828247i	$-0.310662\pi$
$773$	1.86187e7	1.12073	0.560363	+	0.828247i	$0.310662\pi$
$774$	5.11360e6	0.306813
$775$	−84084.0	−0.00502874
$776$	−2.10622e7	−1.25559
$777$	7.13303e6	0.423859
$778$	4.84024e7	2.86694
$779$	1.76028e6	0.103929
$780$	7.46368e6	0.439255
$781$	0	0
$782$	3.14093e7	1.83671
$783$	−1.38771e7	−0.808898
$784$	3.41902e6	0.198661
$785$	−1.64373e7	−0.952045
$786$	−8.62204e6	−0.497799
$787$	−2.62501e7	−1.51075	−0.755377	−	0.655291i	$-0.772546\pi$
$787$	−2.62501e7	−1.51075	−0.755377	+	0.655291i	$0.772546\pi$
$788$	6.73234e7	3.86234
$789$	1.80737e7	1.03360
$790$	1.77990e7	1.01468
$791$	−4.08435e6	−0.232103
$792$	0	0
$793$	−3.59072e6	−0.202768
$794$	9.95820e6	0.560570
$795$	1.77341e6	0.0995155
$796$	−5.71714e7	−3.19813
$797$	−1.00373e7	−0.559720	−0.279860	−	0.960041i	$-0.590288\pi$
$797$	−1.00373e7	−0.559720	−0.279860	+	0.960041i	$0.590288\pi$
$798$	−672280.	−0.0373717
$799$	1.60559e7	0.889751
$800$	29920.0	0.00165286
$801$	2.37735e6	0.130922
$802$	−3.31605e7	−1.82048
$803$	0	0
$804$	4.60806e7	2.51407
$805$	−5.00506e6	−0.272220
$806$	−1.07016e7	−0.580245
$807$	1.78858e7	0.966772
$808$	−1.39306e7	−0.750655
$809$	−1.40884e7	−0.756816	−0.378408	−	0.925639i	$-0.623528\pi$
$809$	−1.40884e7	−0.756816	−0.378408	+	0.925639i	$0.623528\pi$
$810$	2.54346e7	1.36211
$811$	−1.81433e7	−0.968646	−0.484323	−	0.874889i	$-0.660934\pi$
$811$	−1.81433e7	−0.968646	−0.484323	+	0.874889i	$0.660934\pi$
$812$	−1.13888e7	−0.606160
$813$	2.31076e7	1.22611
$814$	0	0
$815$	−738752.	−0.0389587
$816$	−3.43298e7	−1.80487
$817$	−1.06624e6	−0.0558856
$818$	−3.07273e7	−1.60562
$819$	−322420.	−0.0167962
$820$	−6.83993e7	−3.55236
$821$	2.13669e7	1.10633	0.553164	−	0.833072i	$-0.313420\pi$
$821$	2.13669e7	1.10633	0.553164	+	0.833072i	$0.313420\pi$
$822$	2.86247e7	1.47761
$823$	1.78017e7	0.916142	0.458071	−	0.888916i	$-0.348541\pi$
$823$	1.78017e7	0.916142	0.458071	+	0.888916i	$0.348541\pi$
$824$	1.91016e7	0.980058
$825$	0	0
$826$	−1.33770e6	−0.0682195
$827$	−1.62921e7	−0.828350	−0.414175	−	0.910197i	$-0.635930\pi$
$827$	−1.62921e7	−0.828350	−0.414175	+	0.910197i	$0.635930\pi$
$828$	−5.82950e6	−0.295499
$829$	−2.08499e6	−0.105370	−0.0526851	−	0.998611i	$-0.516778\pi$
$829$	−2.08499e6	−0.105370	−0.0526851	+	0.998611i	$0.516778\pi$
$830$	−1.15013e7	−0.579497
$831$	−1.48973e7	−0.748348
$832$	−2.57152e6	−0.128790
$833$	4.13452e6	0.206449
$834$	−4.95684e6	−0.246769
$835$	2.76423e7	1.37201
$836$	0	0
$837$	−3.10346e7	−1.53120
$838$	2.81438e7	1.38443
$839$	−2.27850e7	−1.11749	−0.558745	−	0.829340i	$-0.688717\pi$
$839$	−2.27850e7	−1.11749	−0.558745	+	0.829340i	$0.688717\pi$
$840$	1.38298e7	0.676264
$841$	−8.82842e6	−0.430421
$842$	3.05802e7	1.48648
$843$	−312788.	−0.0151594
$844$	−7.82498e7	−3.78118
$845$	1.96948e7	0.948877
$846$	−4.38228e6	−0.210511
$847$	0	0
$848$	3.22109e6	0.153820
$849$	−3.49403e7	−1.66363
$850$	189420.	0.00899246
$851$	−1.89660e7	−0.897740
$852$	5.57491e7	2.63111
$853$	2.26975e7	1.06808	0.534042	−	0.845458i	$-0.320672\pi$
$853$	2.26975e7	1.06808	0.534042	+	0.845458i	$0.320672\pi$
$854$	−1.25675e7	−0.589664
$855$	257936.	0.0120669
$856$	5.26766e7	2.45716
$857$	−2.52900e7	−1.17624	−0.588120	−	0.808774i	$-0.700132\pi$
$857$	−2.52900e7	−1.17624	−0.588120	+	0.808774i	$0.700132\pi$
$858$	0	0
$859$	−1.03947e7	−0.480652	−0.240326	−	0.970692i	$-0.577254\pi$
$859$	−1.03947e7	−0.480652	−0.240326	+	0.970692i	$0.577254\pi$
$860$	4.14310e7	1.91020
$861$	−1.23219e7	−0.566462
$862$	−1.93750e7	−0.888122
$863$	4.33399e7	1.98089	0.990447	−	0.137892i	$-0.0440327\pi$
$863$	4.33399e7	1.98089	0.990447	+	0.137892i	$0.0440327\pi$
$864$	1.10432e7	0.503281
$865$	1.34801e7	0.612566
$866$	3.94790e7	1.78884
$867$	−2.16360e7	−0.977527
$868$	−2.54698e7	−1.14743
$869$	0	0
$870$	−2.67971e7	−1.20030
$871$	−6.77656e6	−0.302666
$872$	−3.34433e7	−1.48942
$873$	2.74978e6	0.122113
$874$	1.78752e6	0.0791539
$875$	8.54482e6	0.377296
$876$	6.48141e7	2.85370
$877$	−3.71659e7	−1.63172	−0.815861	−	0.578248i	$-0.803736\pi$
$877$	−3.71659e7	−1.63172	−0.815861	+	0.578248i	$0.803736\pi$
$878$	7.41770e7	3.24738
$879$	−2.70449e7	−1.18063
$880$	0	0
$881$	9.04785e6	0.392740	0.196370	−	0.980530i	$-0.437085\pi$
$881$	9.04785e6	0.392740	0.196370	+	0.980530i	$0.437085\pi$
$882$	−1.12847e6	−0.0488448
$883$	3.29679e7	1.42295	0.711474	−	0.702712i	$-0.248028\pi$
$883$	3.29679e7	1.42295	0.711474	+	0.702712i	$0.248028\pi$
$884$	1.63934e7	0.705569
$885$	−2.14032e6	−0.0918588
$886$	1.40269e7	0.600313
$887$	1.61099e7	0.687517	0.343758	−	0.939058i	$-0.388300\pi$
$887$	1.61099e7	0.687517	0.343758	+	0.939058i	$0.388300\pi$
$888$	5.24059e7	2.23022
$889$	−2.95882e6	−0.125564
$890$	2.83259e7	1.19870
$891$	0	0
$892$	−5.60500e7	−2.35865
$893$	913752.	0.0383442
$894$	−2.83164e6	−0.118493
$895$	−1.65162e7	−0.689211
$896$	−1.32653e7	−0.552009
$897$	−3.57504e6	−0.148354
$898$	−5.90574e6	−0.244390
$899$	2.61272e7	1.07819
$900$	−35156.0	−0.00144675
$901$	3.89516e6	0.159850
$902$	0	0
$903$	7.46368e6	0.304603
$904$	−3.00074e7	−1.22126
$905$	1.88709e7	0.765898
$906$	9.92656e6	0.401771
$907$	−4.47286e7	−1.80537	−0.902686	−	0.430300i	$-0.858408\pi$
$907$	−4.47286e7	−1.80537	−0.902686	+	0.430300i	$0.858408\pi$
$908$	−5.05798e6	−0.203593
$909$	1.81871e6	0.0730053
$910$	−3.84160e6	−0.153783
$911$	−6.60518e6	−0.263687	−0.131844	−	0.991271i	$-0.542090\pi$
$911$	−6.60518e6	−0.263687	−0.131844	+	0.991271i	$0.542090\pi$
$912$	−1.95373e6	−0.0777816
$913$	0	0
$914$	2.90484e7	1.15016
$915$	−2.01080e7	−0.793993
$916$	7.69730e7	3.03110
$917$	3.01771e6	0.118510
$918$	6.99132e7	2.73812
$919$	3.08930e7	1.20662	0.603311	−	0.797506i	$-0.293848\pi$
$919$	3.08930e7	1.20662	0.603311	+	0.797506i	$0.293848\pi$
$920$	−3.67718e7	−1.43234
$921$	−6.42704e6	−0.249667
$922$	9.22684e6	0.357459
$923$	−8.19840e6	−0.316756
$924$	0	0
$925$	−114378.	−0.00439530
$926$	7.18235e7	2.75258
$927$	−2.49382e6	−0.0953160
$928$	−9.29696e6	−0.354381
$929$	−4.87215e6	−0.185217	−0.0926087	−	0.995703i	$-0.529521\pi$
$929$	−4.87215e6	−0.185217	−0.0926087	+	0.995703i	$0.529521\pi$
$930$	−5.99290e7	−2.27211
$931$	235298.	0.00889701
$932$	1.35134e7	0.509593
$933$	−9.33979e6	−0.351264
$934$	−6.12570e6	−0.229767
$935$	0	0
$936$	−2.36880e6	−0.0883769
$937$	3.25004e7	1.20932	0.604658	−	0.796485i	$-0.293310\pi$
$937$	3.25004e7	1.20932	0.604658	+	0.796485i	$0.293310\pi$
$938$	−2.37180e7	−0.880177
$939$	1.55448e6	0.0575334
$940$	−3.55058e7	−1.31063
$941$	2.64040e6	0.0972066	0.0486033	−	0.998818i	$-0.484523\pi$
$941$	2.64040e6	0.0972066	0.0486033	+	0.998818i	$0.484523\pi$
$942$	−4.10934e7	−1.50884
$943$	3.27627e7	1.19978
$944$	−3.88752e6	−0.141985
$945$	−1.11406e7	−0.405817
$946$	0	0
$947$	−4.08179e7	−1.47903	−0.739513	−	0.673142i	$-0.764944\pi$
$947$	−4.08179e7	−1.47903	−0.739513	+	0.673142i	$0.764944\pi$
$948$	3.02584e7	1.09351
$949$	−9.53148e6	−0.343554
$950$	10780.0	0.000387534 0
$951$	962892.	0.0345244
$952$	3.03761e7	1.08627
$953$	6.71983e6	0.239677	0.119838	−	0.992793i	$-0.461762\pi$
$953$	6.71983e6	0.239677	0.119838	+	0.992793i	$0.461762\pi$
$954$	−1.06314e6	−0.0378198
$955$	−2.00628e7	−0.711841
$956$	−3.28375e7	−1.16205
$957$	0	0
$958$	−2.60330e7	−0.916454
$959$	−1.00186e7	−0.351773
$960$	−1.44005e7	−0.504313
$961$	2.98016e7	1.04095
$962$	−1.45572e7	−0.507154
$963$	−6.87723e6	−0.238972
$964$	−5.48019e7	−1.89934
$965$	−5.54150e7	−1.91562
$966$	−1.25126e7	−0.431426
$967$	2.78979e6	0.0959413	0.0479707	−	0.998849i	$-0.484725\pi$
$967$	2.78979e6	0.0959413	0.0479707	+	0.998849i	$0.484725\pi$
$968$	0	0
$969$	−2.36258e6	−0.0808310
$970$	3.27634e7	1.11804
$971$	3.33594e7	1.13545	0.567727	−	0.823217i	$-0.307823\pi$
$971$	3.33594e7	1.13545	0.567727	+	0.823217i	$0.307823\pi$
$972$	−2.38486e7	−0.809648
$973$	1.73489e6	0.0587477
$974$	5.46309e7	1.84519
$975$	−21560.0	−0.000726335 0
$976$	−3.65228e7	−1.22727
$977$	−7.60033e6	−0.254739	−0.127370	−	0.991855i	$-0.540653\pi$
$977$	−7.60033e6	−0.254739	−0.127370	+	0.991855i	$0.540653\pi$
$978$	−1.84688e6	−0.0617435
$979$	0	0
$980$	−9.14301e6	−0.304105
$981$	4.36621e6	0.144854
$982$	−1.64090e7	−0.543004
$983$	−5.79760e6	−0.191366	−0.0956829	−	0.995412i	$-0.530503\pi$
$983$	−5.79760e6	−0.191366	−0.0956829	+	0.995412i	$0.530503\pi$
$984$	−9.05285e7	−2.98056
$985$	−5.54428e7	−1.82077
$986$	−5.88580e7	−1.92803
$987$	−6.39626e6	−0.208994
$988$	932960.	0.0304068
$989$	−1.98451e7	−0.645153
$990$	0	0
$991$	1.26825e7	0.410224	0.205112	−	0.978739i	$-0.434244\pi$
$991$	1.26825e7	0.410224	0.205112	+	0.978739i	$0.434244\pi$
$992$	−2.07917e7	−0.670827
$993$	7.90227e6	0.254319
$994$	−2.86944e7	−0.921152
$995$	4.70823e7	1.50765
$996$	−1.95522e7	−0.624521
$997$	−1.44400e7	−0.460077	−0.230039	−	0.973182i	$-0.573885\pi$
$997$	−1.44400e7	−0.460077	−0.230039	+	0.973182i	$0.573885\pi$
$998$	2.99796e7	0.952796
$999$	−4.22159e7	−1.33833

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.6.a.b.1.1		1
11.10	odd	2		7.6.a.a.1.1	✓	1
33.32	even	2		63.6.a.e.1.1		1
44.43	even	2		112.6.a.g.1.1		1
55.32	even	4		175.6.b.a.99.1		2
55.43	even	4		175.6.b.a.99.2		2
55.54	odd	2		175.6.a.b.1.1		1
77.10	even	6		49.6.c.b.30.1		2
77.32	odd	6		49.6.c.c.30.1		2
77.54	even	6		49.6.c.b.18.1		2
77.65	odd	6		49.6.c.c.18.1		2
77.76	even	2		49.6.a.a.1.1		1
88.21	odd	2		448.6.a.m.1.1		1
88.43	even	2		448.6.a.c.1.1		1
132.131	odd	2		1008.6.a.y.1.1		1
231.230	odd	2		441.6.a.k.1.1		1
308.307	odd	2		784.6.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.6.a.a.1.1	✓	1	11.10	odd	2
49.6.a.a.1.1		1	77.76	even	2
49.6.c.b.18.1		2	77.54	even	6
49.6.c.b.30.1		2	77.10	even	6
49.6.c.c.18.1		2	77.65	odd	6
49.6.c.c.30.1		2	77.32	odd	6
63.6.a.e.1.1		1	33.32	even	2
112.6.a.g.1.1		1	44.43	even	2
175.6.a.b.1.1		1	55.54	odd	2
175.6.b.a.99.1		2	55.32	even	4
175.6.b.a.99.2		2	55.43	even	4
441.6.a.k.1.1		1	231.230	odd	2
448.6.a.c.1.1		1	88.43	even	2
448.6.a.m.1.1		1	88.21	odd	2
784.6.a.c.1.1		1	308.307	odd	2
847.6.a.b.1.1		1	1.1	even	1	trivial
1008.6.a.y.1.1		1	132.131	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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	847.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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