LMFDB - Embedded newform 1014.6.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,6,Mod(1,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, 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("1014.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	1014.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:	$162.629193290$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 78)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -24.0000 q^{5} +36.0000 q^{6} +238.000 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$

\(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -24.0000 q^{5} +36.0000 q^{6} +238.000 q^{7} +64.0000 q^{8} +81.0000 q^{9} -96.0000 q^{10} -24.0000 q^{11} +144.000 q^{12} +952.000 q^{14} -216.000 q^{15} +256.000 q^{16} -2262.00 q^{17} +324.000 q^{18} -1154.00 q^{19} -384.000 q^{20} +2142.00 q^{21} -96.0000 q^{22} -3744.00 q^{23} +576.000 q^{24} -2549.00 q^{25} +729.000 q^{27} +3808.00 q^{28} -6294.00 q^{29} -864.000 q^{30} -7010.00 q^{31} +1024.00 q^{32} -216.000 q^{33} -9048.00 q^{34} -5712.00 q^{35} +1296.00 q^{36} +5182.00 q^{37} -4616.00 q^{38} -1536.00 q^{40} +9252.00 q^{41} +8568.00 q^{42} -23044.0 q^{43} -384.000 q^{44} -1944.00 q^{45} -14976.0 q^{46} -27480.0 q^{47} +2304.00 q^{48} +39837.0 q^{49} -10196.0 q^{50} -20358.0 q^{51} -5130.00 q^{53} +2916.00 q^{54} +576.000 q^{55} +15232.0 q^{56} -10386.0 q^{57} -25176.0 q^{58} -10164.0 q^{59} -3456.00 q^{60} +37490.0 q^{61} -28040.0 q^{62} +19278.0 q^{63} +4096.00 q^{64} -864.000 q^{66} -26342.0 q^{67} -36192.0 q^{68} -33696.0 q^{69} -22848.0 q^{70} +28668.0 q^{71} +5184.00 q^{72} +26818.0 q^{73} +20728.0 q^{74} -22941.0 q^{75} -18464.0 q^{76} -5712.00 q^{77} +26168.0 q^{79} -6144.00 q^{80} +6561.00 q^{81} +37008.0 q^{82} +13308.0 q^{83} +34272.0 q^{84} +54288.0 q^{85} -92176.0 q^{86} -56646.0 q^{87} -1536.00 q^{88} +48264.0 q^{89} -7776.00 q^{90} -59904.0 q^{92} -63090.0 q^{93} -109920. q^{94} +27696.0 q^{95} +9216.00 q^{96} -73094.0 q^{97} +159348. q^{98} -1944.00 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	4.00000	0.707107
$2$	4.00000	0.707107
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	16.0000	0.500000
$5$	−24.0000	−0.429325	−0.214663	−	0.976688i	$-0.568865\pi$
$5$	−24.0000	−0.429325	−0.214663	+	0.976688i	$0.568865\pi$
$6$	36.0000	0.408248
$7$	238.000	1.83583	0.917914	−	0.396780i	$-0.129872\pi$
$7$	238.000	1.83583	0.917914	+	0.396780i	$0.129872\pi$
$8$	64.0000	0.353553
$9$	81.0000	0.333333
$10$	−96.0000	−0.303579
$11$	−24.0000	−0.0598039	−0.0299020	−	0.999553i	$-0.509520\pi$
$11$	−24.0000	−0.0598039	−0.0299020	+	0.999553i	$0.509520\pi$
$12$	144.000	0.288675
$13$	0	0
$13$	0	0
$14$	952.000	1.29813
$15$	−216.000	−0.247871
$16$	256.000	0.250000
$17$	−2262.00	−1.89832	−0.949162	−	0.314788i	$-0.898066\pi$
$17$	−2262.00	−1.89832	−0.949162	+	0.314788i	$0.898066\pi$
$18$	324.000	0.235702
$19$	−1154.00	−0.733368	−0.366684	−	0.930346i	$-0.619507\pi$
$19$	−1154.00	−0.733368	−0.366684	+	0.930346i	$0.619507\pi$
$20$	−384.000	−0.214663
$21$	2142.00	1.05992
$22$	−96.0000	−0.0422877
$23$	−3744.00	−1.47576	−0.737881	−	0.674931i	$-0.764173\pi$
$23$	−3744.00	−1.47576	−0.737881	+	0.674931i	$0.764173\pi$
$24$	576.000	0.204124
$25$	−2549.00	−0.815680
$26$	0	0
$27$	729.000	0.192450
$28$	3808.00	0.917914
$29$	−6294.00	−1.38973	−0.694867	−	0.719138i	$-0.744537\pi$
$29$	−6294.00	−1.38973	−0.694867	+	0.719138i	$0.744537\pi$
$30$	−864.000	−0.175271
$31$	−7010.00	−1.31013	−0.655064	−	0.755573i	$-0.727358\pi$
$31$	−7010.00	−1.31013	−0.655064	+	0.755573i	$0.727358\pi$
$32$	1024.00	0.176777
$33$	−216.000	−0.0345278
$34$	−9048.00	−1.34232
$35$	−5712.00	−0.788167
$36$	1296.00	0.166667
$37$	5182.00	0.622290	0.311145	−	0.950362i	$-0.399287\pi$
$37$	5182.00	0.622290	0.311145	+	0.950362i	$0.399287\pi$
$38$	−4616.00	−0.518569
$39$	0	0
$40$	−1536.00	−0.151789
$41$	9252.00	0.859560	0.429780	−	0.902934i	$-0.358591\pi$
$41$	9252.00	0.859560	0.429780	+	0.902934i	$0.358591\pi$
$42$	8568.00	0.749473
$43$	−23044.0	−1.90058	−0.950291	−	0.311362i	$-0.899215\pi$
$43$	−23044.0	−1.90058	−0.950291	+	0.311362i	$0.899215\pi$
$44$	−384.000	−0.0299020
$45$	−1944.00	−0.143108
$46$	−14976.0	−1.04352
$47$	−27480.0	−1.81456	−0.907282	−	0.420524i	$-0.861846\pi$
$47$	−27480.0	−1.81456	−0.907282	+	0.420524i	$0.861846\pi$
$48$	2304.00	0.144338
$49$	39837.0	2.37026
$50$	−10196.0	−0.576773
$51$	−20358.0	−1.09600
$52$	0	0
$53$	−5130.00	−0.250858	−0.125429	−	0.992103i	$-0.540031\pi$
$53$	−5130.00	−0.250858	−0.125429	+	0.992103i	$0.540031\pi$
$54$	2916.00	0.136083
$55$	576.000	0.0256753
$56$	15232.0	0.649063
$57$	−10386.0	−0.423410
$58$	−25176.0	−0.982690
$59$	−10164.0	−0.380132	−0.190066	−	0.981771i	$-0.560870\pi$
$59$	−10164.0	−0.380132	−0.190066	+	0.981771i	$0.560870\pi$
$60$	−3456.00	−0.123935
$61$	37490.0	1.29000	0.645002	−	0.764181i	$-0.276857\pi$
$61$	37490.0	1.29000	0.645002	+	0.764181i	$0.276857\pi$
$62$	−28040.0	−0.926401
$63$	19278.0	0.611942
$64$	4096.00	0.125000
$65$	0	0
$66$	−864.000	−0.0244148
$67$	−26342.0	−0.716905	−0.358453	−	0.933548i	$-0.616696\pi$
$67$	−26342.0	−0.716905	−0.358453	+	0.933548i	$0.616696\pi$
$68$	−36192.0	−0.949162
$69$	−33696.0	−0.852031
$70$	−22848.0	−0.557318
$71$	28668.0	0.674919	0.337459	−	0.941340i	$-0.390432\pi$
$71$	28668.0	0.674919	0.337459	+	0.941340i	$0.390432\pi$
$72$	5184.00	0.117851
$73$	26818.0	0.589005	0.294503	−	0.955651i	$-0.404846\pi$
$73$	26818.0	0.589005	0.294503	+	0.955651i	$0.404846\pi$
$74$	20728.0	0.440026
$75$	−22941.0	−0.470933
$76$	−18464.0	−0.366684
$77$	−5712.00	−0.109790
$78$	0	0
$79$	26168.0	0.471740	0.235870	−	0.971785i	$-0.424206\pi$
$79$	26168.0	0.471740	0.235870	+	0.971785i	$0.424206\pi$
$80$	−6144.00	−0.107331
$81$	6561.00	0.111111
$82$	37008.0	0.607800
$83$	13308.0	0.212040	0.106020	−	0.994364i	$-0.466189\pi$
$83$	13308.0	0.212040	0.106020	+	0.994364i	$0.466189\pi$
$84$	34272.0	0.529958
$85$	54288.0	0.814998
$86$	−92176.0	−1.34391
$87$	−56646.0	−0.802363
$88$	−1536.00	−0.0211439
$89$	48264.0	0.645875	0.322937	−	0.946420i	$-0.395330\pi$
$89$	48264.0	0.645875	0.322937	+	0.946420i	$0.395330\pi$
$90$	−7776.00	−0.101193
$91$	0	0
$92$	−59904.0	−0.737881
$93$	−63090.0	−0.756403
$94$	−109920.	−1.28309
$95$	27696.0	0.314853
$96$	9216.00	0.102062
$97$	−73094.0	−0.788774	−0.394387	−	0.918945i	$-0.629043\pi$
$97$	−73094.0	−0.788774	−0.394387	+	0.918945i	$0.629043\pi$
$98$	159348.	1.67603
$99$	−1944.00	−0.0199346
$100$	−40784.0	−0.407840
$101$	51954.0	0.506775	0.253388	−	0.967365i	$-0.418455\pi$
$101$	51954.0	0.506775	0.253388	+	0.967365i	$0.418455\pi$
$102$	−81432.0	−0.774987
$103$	109088.	1.01317	0.506587	−	0.862189i	$-0.330907\pi$
$103$	109088.	1.01317	0.506587	+	0.862189i	$0.330907\pi$
$104$	0	0
$105$	−51408.0	−0.455048
$106$	−20520.0	−0.177383
$107$	40692.0	0.343597	0.171799	−	0.985132i	$-0.445042\pi$
$107$	40692.0	0.343597	0.171799	+	0.985132i	$0.445042\pi$
$108$	11664.0	0.0962250
$109$	−3422.00	−0.0275876	−0.0137938	−	0.999905i	$-0.504391\pi$
$109$	−3422.00	−0.0275876	−0.0137938	+	0.999905i	$0.504391\pi$
$110$	2304.00	0.0181552
$111$	46638.0	0.359280
$112$	60928.0	0.458957
$113$	−12570.0	−0.0926060	−0.0463030	−	0.998927i	$-0.514744\pi$
$113$	−12570.0	−0.0926060	−0.0463030	+	0.998927i	$0.514744\pi$
$114$	−41544.0	−0.299396
$115$	89856.0	0.633581
$116$	−100704.	−0.694867
$117$	0	0
$118$	−40656.0	−0.268794
$119$	−538356.	−3.48499
$120$	−13824.0	−0.0876356
$121$	−160475.	−0.996423
$122$	149960.	0.912170
$123$	83268.0	0.496267
$124$	−112160.	−0.655064
$125$	136176.	0.779517
$126$	77112.0	0.432709
$127$	289964.	1.59527	0.797636	−	0.603139i	$-0.206084\pi$
$127$	289964.	1.59527	0.797636	+	0.603139i	$0.206084\pi$
$128$	16384.0	0.0883883
$129$	−207396.	−1.09730
$130$	0	0
$131$	−101460.	−0.516555	−0.258278	−	0.966071i	$-0.583155\pi$
$131$	−101460.	−0.516555	−0.258278	+	0.966071i	$0.583155\pi$
$132$	−3456.00	−0.0172639
$133$	−274652.	−1.34634
$134$	−105368.	−0.506929
$135$	−17496.0	−0.0826236
$136$	−144768.	−0.671159
$137$	95076.0	0.432782	0.216391	−	0.976307i	$-0.430571\pi$
$137$	95076.0	0.432782	0.216391	+	0.976307i	$0.430571\pi$
$138$	−134784.	−0.602477
$139$	133712.	0.586994	0.293497	−	0.955960i	$-0.405181\pi$
$139$	133712.	0.586994	0.293497	+	0.955960i	$0.405181\pi$
$140$	−91392.0	−0.394083
$141$	−247320.	−1.04764
$142$	114672.	0.477240
$143$	0	0
$144$	20736.0	0.0833333
$145$	151056.	0.596648
$146$	107272.	0.416490
$147$	358533.	1.36847
$148$	82912.0	0.311145
$149$	−4980.00	−0.0183765	−0.00918827	−	0.999958i	$-0.502925\pi$
$149$	−4980.00	−0.0183765	−0.00918827	+	0.999958i	$0.502925\pi$
$150$	−91764.0	−0.333000
$151$	111370.	0.397490	0.198745	−	0.980051i	$-0.436313\pi$
$151$	111370.	0.397490	0.198745	+	0.980051i	$0.436313\pi$
$152$	−73856.0	−0.259285
$153$	−183222.	−0.632775
$154$	−22848.0	−0.0776330
$155$	168240.	0.562471
$156$	0	0
$157$	224882.	0.728124	0.364062	−	0.931375i	$-0.381390\pi$
$157$	224882.	0.728124	0.364062	+	0.931375i	$0.381390\pi$
$158$	104672.	0.333571
$159$	−46170.0	−0.144833
$160$	−24576.0	−0.0758947
$161$	−891072.	−2.70924
$162$	26244.0	0.0785674
$163$	645586.	1.90320	0.951601	−	0.307335i	$-0.0994371\pi$
$163$	645586.	1.90320	0.951601	+	0.307335i	$0.0994371\pi$
$164$	148032.	0.429780
$165$	5184.00	0.0148236
$166$	53232.0	0.149935
$167$	−605376.	−1.67971	−0.839854	−	0.542812i	$-0.817360\pi$
$167$	−605376.	−1.67971	−0.839854	+	0.542812i	$0.817360\pi$
$168$	137088.	0.374737
$169$	0	0
$170$	217152.	0.576291
$171$	−93474.0	−0.244456
$172$	−368704.	−0.950291
$173$	−557478.	−1.41616	−0.708080	−	0.706132i	$-0.750439\pi$
$173$	−557478.	−1.41616	−0.708080	+	0.706132i	$0.750439\pi$
$174$	−226584.	−0.567357
$175$	−606662.	−1.49745
$176$	−6144.00	−0.0149510
$177$	−91476.0	−0.219469
$178$	193056.	0.456702
$179$	−405060.	−0.944902	−0.472451	−	0.881357i	$-0.656631\pi$
$179$	−405060.	−0.944902	−0.472451	+	0.881357i	$0.656631\pi$
$180$	−31104.0	−0.0715542
$181$	−469870.	−1.06606	−0.533030	−	0.846097i	$-0.678947\pi$
$181$	−469870.	−1.06606	−0.533030	+	0.846097i	$0.678947\pi$
$182$	0	0
$183$	337410.	0.744784
$184$	−239616.	−0.521761
$185$	−124368.	−0.267165
$186$	−252360.	−0.534858
$187$	54288.0	0.113527
$188$	−439680.	−0.907282
$189$	173502.	0.353305
$190$	110784.	0.222635
$191$	−650160.	−1.28955	−0.644773	−	0.764374i	$-0.723048\pi$
$191$	−650160.	−1.28955	−0.644773	+	0.764374i	$0.723048\pi$
$192$	36864.0	0.0721688
$193$	231454.	0.447272	0.223636	−	0.974673i	$-0.428207\pi$
$193$	231454.	0.447272	0.223636	+	0.974673i	$0.428207\pi$
$194$	−292376.	−0.557747
$195$	0	0
$196$	637392.	1.18513
$197$	459168.	0.842958	0.421479	−	0.906838i	$-0.361511\pi$
$197$	459168.	0.842958	0.421479	+	0.906838i	$0.361511\pi$
$198$	−7776.00	−0.0140959
$199$	−128860.	−0.230667	−0.115333	−	0.993327i	$-0.536794\pi$
$199$	−128860.	−0.230667	−0.115333	+	0.993327i	$0.536794\pi$
$200$	−163136.	−0.288386
$201$	−237078.	−0.413905
$202$	207816.	0.358344
$203$	−1.49797e6	−2.55131
$204$	−325728.	−0.547999
$205$	−222048.	−0.369030
$206$	436352.	0.716422
$207$	−303264.	−0.491921
$208$	0	0
$209$	27696.0	0.0438583
$210$	−205632.	−0.321768
$211$	−675460.	−1.04446	−0.522232	−	0.852803i	$-0.674901\pi$
$211$	−675460.	−1.04446	−0.522232	+	0.852803i	$0.674901\pi$
$212$	−82080.0	−0.125429
$213$	258012.	0.389665
$214$	162768.	0.242960
$215$	553056.	0.815968
$216$	46656.0	0.0680414
$217$	−1.66838e6	−2.40517
$218$	−13688.0	−0.0195074
$219$	241362.	0.340062
$220$	9216.00	0.0128377
$221$	0	0
$222$	186552.	0.254049
$223$	−172058.	−0.231693	−0.115846	−	0.993267i	$-0.536958\pi$
$223$	−172058.	−0.231693	−0.115846	+	0.993267i	$0.536958\pi$
$224$	243712.	0.324532
$225$	−206469.	−0.271893
$226$	−50280.0	−0.0654823
$227$	−157536.	−0.202915	−0.101458	−	0.994840i	$-0.532351\pi$
$227$	−157536.	−0.202915	−0.101458	+	0.994840i	$0.532351\pi$
$228$	−166176.	−0.211705
$229$	505666.	0.637199	0.318599	−	0.947889i	$-0.396788\pi$
$229$	505666.	0.637199	0.318599	+	0.947889i	$0.396788\pi$
$230$	359424.	0.448010
$231$	−51408.0	−0.0633871
$232$	−402816.	−0.491345
$233$	881334.	1.06353	0.531766	−	0.846891i	$-0.321529\pi$
$233$	881334.	1.06353	0.531766	+	0.846891i	$0.321529\pi$
$234$	0	0
$235$	659520.	0.779037
$236$	−162624.	−0.190066
$237$	235512.	0.272359
$238$	−2.15342e6	−2.46426
$239$	722964.	0.818695	0.409347	−	0.912379i	$-0.365756\pi$
$239$	722964.	0.818695	0.409347	+	0.912379i	$0.365756\pi$
$240$	−55296.0	−0.0619677
$241$	921658.	1.02218	0.511090	−	0.859527i	$-0.329242\pi$
$241$	921658.	1.02218	0.511090	+	0.859527i	$0.329242\pi$
$242$	−641900.	−0.704578
$243$	59049.0	0.0641500
$244$	599840.	0.645002
$245$	−956088.	−1.01761
$246$	333072.	0.350914
$247$	0	0
$248$	−448640.	−0.463200
$249$	119772.	0.122421
$250$	544704.	0.551202
$251$	958236.	0.960037	0.480019	−	0.877258i	$-0.340630\pi$
$251$	958236.	0.960037	0.480019	+	0.877258i	$0.340630\pi$
$252$	308448.	0.305971
$253$	89856.0	0.0882563
$254$	1.15986e6	1.12803
$255$	488592.	0.470539
$256$	65536.0	0.0625000
$257$	−842058.	−0.795260	−0.397630	−	0.917546i	$-0.630167\pi$
$257$	−842058.	−0.795260	−0.397630	+	0.917546i	$0.630167\pi$
$258$	−829584.	−0.775910
$259$	1.23332e6	1.14242
$260$	0	0
$261$	−509814.	−0.463245
$262$	−405840.	−0.365260
$263$	−640488.	−0.570981	−0.285490	−	0.958382i	$-0.592156\pi$
$263$	−640488.	−0.570981	−0.285490	+	0.958382i	$0.592156\pi$
$264$	−13824.0	−0.0122074
$265$	123120.	0.107700
$266$	−1.09861e6	−0.952004
$267$	434376.	0.372896
$268$	−421472.	−0.358453
$269$	−833214.	−0.702063	−0.351031	−	0.936364i	$-0.614169\pi$
$269$	−833214.	−0.702063	−0.351031	+	0.936364i	$0.614169\pi$
$270$	−69984.0	−0.0584237
$271$	106774.	0.0883166	0.0441583	−	0.999025i	$-0.485939\pi$
$271$	106774.	0.0883166	0.0441583	+	0.999025i	$0.485939\pi$
$272$	−579072.	−0.474581
$273$	0	0
$274$	380304.	0.306023
$275$	61176.0	0.0487808
$276$	−539136.	−0.426016
$277$	2.23223e6	1.74799	0.873996	−	0.485933i	$-0.161520\pi$
$277$	2.23223e6	1.74799	0.873996	+	0.485933i	$0.161520\pi$
$278$	534848.	0.415067
$279$	−567810.	−0.436709
$280$	−365568.	−0.278659
$281$	8196.00	0.00619207	0.00309604	−	0.999995i	$-0.499014\pi$
$281$	8196.00	0.00619207	0.00309604	+	0.999995i	$0.499014\pi$
$282$	−989280.	−0.740792
$283$	−376624.	−0.279539	−0.139769	−	0.990184i	$-0.544636\pi$
$283$	−376624.	−0.279539	−0.139769	+	0.990184i	$0.544636\pi$
$284$	458688.	0.337459
$285$	249264.	0.181781
$286$	0	0
$287$	2.20198e6	1.57800
$288$	82944.0	0.0589256
$289$	3.69679e6	2.60363
$290$	604224.	0.421894
$291$	−657846.	−0.455399
$292$	429088.	0.294503
$293$	2.02564e6	1.37845	0.689227	−	0.724545i	$-0.257950\pi$
$293$	2.02564e6	1.37845	0.689227	+	0.724545i	$0.257950\pi$
$294$	1.43413e6	0.967656
$295$	243936.	0.163200
$296$	331648.	0.220013
$297$	−17496.0	−0.0115093
$298$	−19920.0	−0.0129942
$299$	0	0
$300$	−367056.	−0.235467
$301$	−5.48447e6	−3.48914
$302$	445480.	0.281068
$303$	467586.	0.292587
$304$	−295424.	−0.183342
$305$	−899760.	−0.553831
$306$	−732888.	−0.447439
$307$	−1.38168e6	−0.836685	−0.418343	−	0.908289i	$-0.637389\pi$
$307$	−1.38168e6	−0.836685	−0.418343	+	0.908289i	$0.637389\pi$
$308$	−91392.0	−0.0548948
$309$	981792.	0.584956
$310$	672960.	0.397727
$311$	2.60066e6	1.52470	0.762348	−	0.647167i	$-0.224046\pi$
$311$	2.60066e6	1.52470	0.762348	+	0.647167i	$0.224046\pi$
$312$	0	0
$313$	1.45467e6	0.839271	0.419636	−	0.907693i	$-0.362158\pi$
$313$	1.45467e6	0.839271	0.419636	+	0.907693i	$0.362158\pi$
$314$	899528.	0.514862
$315$	−462672.	−0.262722
$316$	418688.	0.235870
$317$	1.16304e6	0.650050	0.325025	−	0.945705i	$-0.394627\pi$
$317$	1.16304e6	0.650050	0.325025	+	0.945705i	$0.394627\pi$
$318$	−184680.	−0.102412
$319$	151056.	0.0831115
$320$	−98304.0	−0.0536656
$321$	366228.	0.198376
$322$	−3.56429e6	−1.91572
$323$	2.61035e6	1.39217
$324$	104976.	0.0555556
$325$	0	0
$326$	2.58234e6	1.34577
$327$	−30798.0	−0.0159277
$328$	592128.	0.303900
$329$	−6.54024e6	−3.33122
$330$	20736.0	0.0104819
$331$	−687110.	−0.344712	−0.172356	−	0.985035i	$-0.555138\pi$
$331$	−687110.	−0.344712	−0.172356	+	0.985035i	$0.555138\pi$
$332$	212928.	0.106020
$333$	419742.	0.207430
$334$	−2.42150e6	−1.18773
$335$	632208.	0.307785
$336$	548352.	0.264979
$337$	−2.53949e6	−1.21807	−0.609033	−	0.793145i	$-0.708442\pi$
$337$	−2.53949e6	−1.21807	−0.609033	+	0.793145i	$0.708442\pi$
$338$	0	0
$339$	−113130.	−0.0534661
$340$	868608.	0.407499
$341$	168240.	0.0783508
$342$	−373896.	−0.172856
$343$	5.48114e6	2.51557
$344$	−1.47482e6	−0.671957
$345$	808704.	0.365798
$346$	−2.22991e6	−1.00138
$347$	−1.39844e6	−0.623478	−0.311739	−	0.950168i	$-0.600912\pi$
$347$	−1.39844e6	−0.623478	−0.311739	+	0.950168i	$0.600912\pi$
$348$	−906336.	−0.401182
$349$	−3.45684e6	−1.51920	−0.759602	−	0.650388i	$-0.774606\pi$
$349$	−3.45684e6	−1.51920	−0.759602	+	0.650388i	$0.774606\pi$
$350$	−2.42665e6	−1.05886
$351$	0	0
$352$	−24576.0	−0.0105719
$353$	−1.48348e6	−0.633642	−0.316821	−	0.948485i	$-0.602615\pi$
$353$	−1.48348e6	−0.633642	−0.316821	+	0.948485i	$0.602615\pi$
$354$	−365904.	−0.155188
$355$	−688032.	−0.289760
$356$	772224.	0.322937
$357$	−4.84520e6	−2.01206
$358$	−1.62024e6	−0.668147
$359$	−876096.	−0.358770	−0.179385	−	0.983779i	$-0.557411\pi$
$359$	−876096.	−0.358770	−0.179385	+	0.983779i	$0.557411\pi$
$360$	−124416.	−0.0505964
$361$	−1.14438e6	−0.462172
$362$	−1.87948e6	−0.753818
$363$	−1.44428e6	−0.575285
$364$	0	0
$365$	−643632.	−0.252875
$366$	1.34964e6	0.526642
$367$	−2.49344e6	−0.966347	−0.483173	−	0.875525i	$-0.660516\pi$
$367$	−2.49344e6	−0.966347	−0.483173	+	0.875525i	$0.660516\pi$
$368$	−958464.	−0.368940
$369$	749412.	0.286520
$370$	−497472.	−0.188914
$371$	−1.22094e6	−0.460532
$372$	−1.00944e6	−0.378201
$373$	−4.91696e6	−1.82989	−0.914945	−	0.403580i	$-0.867766\pi$
$373$	−4.91696e6	−1.82989	−0.914945	+	0.403580i	$0.867766\pi$
$374$	217152.	0.0802758
$375$	1.22558e6	0.450054
$376$	−1.75872e6	−0.641545
$377$	0	0
$378$	694008.	0.249824
$379$	−781562.	−0.279489	−0.139745	−	0.990188i	$-0.544628\pi$
$379$	−781562.	−0.279489	−0.139745	+	0.990188i	$0.544628\pi$
$380$	443136.	0.157427
$381$	2.60968e6	0.921031
$382$	−2.60064e6	−0.911847
$383$	2.45299e6	0.854475	0.427237	−	0.904140i	$-0.359487\pi$
$383$	2.45299e6	0.854475	0.427237	+	0.904140i	$0.359487\pi$
$384$	147456.	0.0510310
$385$	137088.	0.0471354
$386$	925816.	0.316269
$387$	−1.86656e6	−0.633528
$388$	−1.16950e6	−0.394387
$389$	−605922.	−0.203022	−0.101511	−	0.994834i	$-0.532368\pi$
$389$	−605922.	−0.203022	−0.101511	+	0.994834i	$0.532368\pi$
$390$	0	0
$391$	8.46893e6	2.80147
$392$	2.54957e6	0.838014
$393$	−913140.	−0.298233
$394$	1.83667e6	0.596061
$395$	−628032.	−0.202530
$396$	−31104.0	−0.00996732
$397$	−1.09159e6	−0.347604	−0.173802	−	0.984781i	$-0.555605\pi$
$397$	−1.09159e6	−0.347604	−0.173802	+	0.984781i	$0.555605\pi$
$398$	−515440.	−0.163106
$399$	−2.47187e6	−0.777308
$400$	−652544.	−0.203920
$401$	2.65176e6	0.823518	0.411759	−	0.911293i	$-0.364914\pi$
$401$	2.65176e6	0.823518	0.411759	+	0.911293i	$0.364914\pi$
$402$	−948312.	−0.292675
$403$	0	0
$404$	831264.	0.253388
$405$	−157464.	−0.0477028
$406$	−5.99189e6	−1.80405
$407$	−124368.	−0.0372154
$408$	−1.30291e6	−0.387494
$409$	863866.	0.255351	0.127676	−	0.991816i	$-0.459248\pi$
$409$	863866.	0.255351	0.127676	+	0.991816i	$0.459248\pi$
$410$	−888192.	−0.260944
$411$	855684.	0.249867
$412$	1.74541e6	0.506587
$413$	−2.41903e6	−0.697857
$414$	−1.21306e6	−0.347840
$415$	−319392.	−0.0910340
$416$	0	0
$417$	1.20341e6	0.338901
$418$	110784.	0.0310125
$419$	4.38066e6	1.21900	0.609501	−	0.792785i	$-0.291370\pi$
$419$	4.38066e6	1.21900	0.609501	+	0.792785i	$0.291370\pi$
$420$	−822528.	−0.227524
$421$	−3.75006e6	−1.03118	−0.515588	−	0.856836i	$-0.672427\pi$
$421$	−3.75006e6	−1.03118	−0.515588	+	0.856836i	$0.672427\pi$
$422$	−2.70184e6	−0.738548
$423$	−2.22588e6	−0.604854
$424$	−328320.	−0.0886916
$425$	5.76584e6	1.54842
$426$	1.03205e6	0.275534
$427$	8.92262e6	2.36822
$428$	651072.	0.171799
$429$	0	0
$430$	2.21222e6	0.576976
$431$	−1.20864e6	−0.313403	−0.156702	−	0.987646i	$-0.550086\pi$
$431$	−1.20864e6	−0.313403	−0.156702	+	0.987646i	$0.550086\pi$
$432$	186624.	0.0481125
$433$	−1.23368e6	−0.316216	−0.158108	−	0.987422i	$-0.550539\pi$
$433$	−1.23368e6	−0.316216	−0.158108	+	0.987422i	$0.550539\pi$
$434$	−6.67352e6	−1.70071
$435$	1.35950e6	0.344475
$436$	−54752.0	−0.0137938
$437$	4.32058e6	1.08228
$438$	965448.	0.240460
$439$	−5.75831e6	−1.42605	−0.713024	−	0.701140i	$-0.752675\pi$
$439$	−5.75831e6	−1.42605	−0.713024	+	0.701140i	$0.752675\pi$
$440$	36864.0	0.00907759
$441$	3.22680e6	0.790087
$442$	0	0
$443$	2.04316e6	0.494643	0.247322	−	0.968933i	$-0.420450\pi$
$443$	2.04316e6	0.494643	0.247322	+	0.968933i	$0.420450\pi$
$444$	746208.	0.179640
$445$	−1.15834e6	−0.277290
$446$	−688232.	−0.163832
$447$	−44820.0	−0.0106097
$448$	974848.	0.229478
$449$	−452184.	−0.105852	−0.0529260	−	0.998598i	$-0.516855\pi$
$449$	−452184.	−0.105852	−0.0529260	+	0.998598i	$0.516855\pi$
$450$	−825876.	−0.192258
$451$	−222048.	−0.0514050
$452$	−201120.	−0.0463030
$453$	1.00233e6	0.229491
$454$	−630144.	−0.143483
$455$	0	0
$456$	−664704.	−0.149698
$457$	1.79300e6	0.401597	0.200798	−	0.979633i	$-0.435646\pi$
$457$	1.79300e6	0.401597	0.200798	+	0.979633i	$0.435646\pi$
$458$	2.02266e6	0.450568
$459$	−1.64900e6	−0.365333
$460$	1.43770e6	0.316791
$461$	−4.17074e6	−0.914032	−0.457016	−	0.889459i	$-0.651082\pi$
$461$	−4.17074e6	−0.914032	−0.457016	+	0.889459i	$0.651082\pi$
$462$	−205632.	−0.0448214
$463$	−1.31215e6	−0.284467	−0.142234	−	0.989833i	$-0.545428\pi$
$463$	−1.31215e6	−0.284467	−0.142234	+	0.989833i	$0.545428\pi$
$464$	−1.61126e6	−0.347434
$465$	1.51416e6	0.324743
$466$	3.52534e6	0.752031
$467$	−2.77297e6	−0.588374	−0.294187	−	0.955748i	$-0.595049\pi$
$467$	−2.77297e6	−0.588374	−0.294187	+	0.955748i	$0.595049\pi$
$468$	0	0
$469$	−6.26940e6	−1.31611
$470$	2.63808e6	0.550863
$471$	2.02394e6	0.420383
$472$	−650496.	−0.134397
$473$	553056.	0.113662
$474$	942048.	0.192587
$475$	2.94155e6	0.598193
$476$	−8.61370e6	−1.74250
$477$	−415530.	−0.0836193
$478$	2.89186e6	0.578904
$479$	−7.07737e6	−1.40940	−0.704698	−	0.709507i	$-0.748918\pi$
$479$	−7.07737e6	−1.40940	−0.704698	+	0.709507i	$0.748918\pi$
$480$	−221184.	−0.0438178
$481$	0	0
$482$	3.68663e6	0.722790
$483$	−8.01965e6	−1.56418
$484$	−2.56760e6	−0.498212
$485$	1.75426e6	0.338640
$486$	236196.	0.0453609
$487$	−1.60503e6	−0.306662	−0.153331	−	0.988175i	$-0.549000\pi$
$487$	−1.60503e6	−0.306662	−0.153331	+	0.988175i	$0.549000\pi$
$488$	2.39936e6	0.456085
$489$	5.81027e6	1.09881
$490$	−3.82435e6	−0.719561
$491$	−5.13335e6	−0.960942	−0.480471	−	0.877011i	$-0.659534\pi$
$491$	−5.13335e6	−0.960942	−0.480471	+	0.877011i	$0.659534\pi$
$492$	1.33229e6	0.248133
$493$	1.42370e7	2.63817
$494$	0	0
$495$	46656.0	0.00855844
$496$	−1.79456e6	−0.327532
$497$	6.82298e6	1.23903
$498$	479088.	0.0865649
$499$	9.61136e6	1.72796	0.863980	−	0.503527i	$-0.167964\pi$
$499$	9.61136e6	1.72796	0.863980	+	0.503527i	$0.167964\pi$
$500$	2.17882e6	0.389758
$501$	−5.44838e6	−0.969780
$502$	3.83294e6	0.678849
$503$	2.16924e6	0.382285	0.191143	−	0.981562i	$-0.438781\pi$
$503$	2.16924e6	0.382285	0.191143	+	0.981562i	$0.438781\pi$
$504$	1.23379e6	0.216354
$505$	−1.24690e6	−0.217571
$506$	359424.	0.0624066
$507$	0	0
$508$	4.63942e6	0.797636
$509$	−8.20505e6	−1.40374	−0.701870	−	0.712305i	$-0.747651\pi$
$509$	−8.20505e6	−1.40374	−0.701870	+	0.712305i	$0.747651\pi$
$510$	1.95437e6	0.332722
$511$	6.38268e6	1.08131
$512$	262144.	0.0441942
$513$	−841266.	−0.141137
$514$	−3.36823e6	−0.562334
$515$	−2.61811e6	−0.434981
$516$	−3.31834e6	−0.548651
$517$	659520.	0.108518
$518$	4.93326e6	0.807811
$519$	−5.01730e6	−0.817621
$520$	0	0
$521$	−8.54743e6	−1.37956	−0.689781	−	0.724018i	$-0.742293\pi$
$521$	−8.54743e6	−1.37956	−0.689781	+	0.724018i	$0.742293\pi$
$522$	−2.03926e6	−0.327563
$523$	−1.04792e7	−1.67523	−0.837613	−	0.546265i	$-0.816049\pi$
$523$	−1.04792e7	−1.67523	−0.837613	+	0.546265i	$0.816049\pi$
$524$	−1.62336e6	−0.258278
$525$	−5.45996e6	−0.864552
$526$	−2.56195e6	−0.403745
$527$	1.58566e7	2.48705
$528$	−55296.0	−0.00863195
$529$	7.58119e6	1.17787
$530$	492480.	0.0761551
$531$	−823284.	−0.126711
$532$	−4.39443e6	−0.673168
$533$	0	0
$534$	1.73750e6	0.263677
$535$	−976608.	−0.147515
$536$	−1.68589e6	−0.253464
$537$	−3.64554e6	−0.545539
$538$	−3.33286e6	−0.496433
$539$	−956088.	−0.141751
$540$	−279936.	−0.0413118
$541$	−3.85434e6	−0.566183	−0.283092	−	0.959093i	$-0.591360\pi$
$541$	−3.85434e6	−0.566183	−0.283092	+	0.959093i	$0.591360\pi$
$542$	427096.	0.0624493
$543$	−4.22883e6	−0.615490
$544$	−2.31629e6	−0.335579
$545$	82128.0	0.0118440
$546$	0	0
$547$	−9.92056e6	−1.41765	−0.708823	−	0.705386i	$-0.750774\pi$
$547$	−9.92056e6	−1.41765	−0.708823	+	0.705386i	$0.750774\pi$
$548$	1.52122e6	0.216391
$549$	3.03669e6	0.430001
$550$	244704.	0.0344933
$551$	7.26328e6	1.01919
$552$	−2.15654e6	−0.301239
$553$	6.22798e6	0.866033
$554$	8.92892e6	1.23602
$555$	−1.11931e6	−0.154248
$556$	2.13939e6	0.293497
$557$	−3.51577e6	−0.480156	−0.240078	−	0.970754i	$-0.577173\pi$
$557$	−3.51577e6	−0.480156	−0.240078	+	0.970754i	$0.577173\pi$
$558$	−2.27124e6	−0.308800
$559$	0	0
$560$	−1.46227e6	−0.197042
$561$	488592.	0.0655449
$562$	32784.0	0.00437846
$563$	8.86364e6	1.17853	0.589266	−	0.807939i	$-0.299417\pi$
$563$	8.86364e6	1.17853	0.589266	+	0.807939i	$0.299417\pi$
$564$	−3.95712e6	−0.523819
$565$	301680.	0.0397581
$566$	−1.50650e6	−0.197664
$567$	1.56152e6	0.203981
$568$	1.83475e6	0.238620
$569$	1.07245e6	0.138866	0.0694328	−	0.997587i	$-0.477881\pi$
$569$	1.07245e6	0.138866	0.0694328	+	0.997587i	$0.477881\pi$
$570$	997056.	0.128538
$571$	9.74492e6	1.25080	0.625400	−	0.780304i	$-0.284936\pi$
$571$	9.74492e6	1.25080	0.625400	+	0.780304i	$0.284936\pi$
$572$	0	0
$573$	−5.85144e6	−0.744520
$574$	8.80790e6	1.11582
$575$	9.54346e6	1.20375
$576$	331776.	0.0416667
$577$	8.89632e6	1.11243	0.556213	−	0.831040i	$-0.312254\pi$
$577$	8.89632e6	1.11243	0.556213	+	0.831040i	$0.312254\pi$
$578$	1.47871e7	1.84105
$579$	2.08309e6	0.258232
$580$	2.41690e6	0.298324
$581$	3.16730e6	0.389269
$582$	−2.63138e6	−0.322015
$583$	123120.	0.0150023
$584$	1.71635e6	0.208245
$585$	0	0
$586$	8.10254e6	0.974714
$587$	−2796.00	−0.000334921 0	−0.000167460	−	1.00000i	$-0.500053\pi$
$587$	−2796.00	−0.000334921 0	−0.000167460		1.00000i	$0.500053\pi$
$588$	5.73653e6	0.684236
$589$	8.08954e6	0.960806
$590$	975744.	0.115400
$591$	4.13251e6	0.486682
$592$	1.32659e6	0.155573
$593$	−5.54911e6	−0.648018	−0.324009	−	0.946054i	$-0.605031\pi$
$593$	−5.54911e6	−0.648018	−0.324009	+	0.946054i	$0.605031\pi$
$594$	−69984.0	−0.00813828
$595$	1.29205e7	1.49620
$596$	−79680.0	−0.00918827
$597$	−1.15974e6	−0.133176
$598$	0	0
$599$	−1.41044e7	−1.60616	−0.803079	−	0.595873i	$-0.796806\pi$
$599$	−1.41044e7	−1.60616	−0.803079	+	0.595873i	$0.796806\pi$
$600$	−1.46822e6	−0.166500
$601$	−7.39572e6	−0.835207	−0.417604	−	0.908629i	$-0.637130\pi$
$601$	−7.39572e6	−0.835207	−0.417604	+	0.908629i	$0.637130\pi$
$602$	−2.19379e7	−2.46720
$603$	−2.13370e6	−0.238968
$604$	1.78192e6	0.198745
$605$	3.85140e6	0.427790
$606$	1.87034e6	0.206890
$607$	2.44689e6	0.269552	0.134776	−	0.990876i	$-0.456968\pi$
$607$	2.44689e6	0.269552	0.134776	+	0.990876i	$0.456968\pi$
$608$	−1.18170e6	−0.129642
$609$	−1.34817e7	−1.47300
$610$	−3.59904e6	−0.391617
$611$	0	0
$612$	−2.93155e6	−0.316387
$613$	3.70159e6	0.397866	0.198933	−	0.980013i	$-0.436252\pi$
$613$	3.70159e6	0.397866	0.198933	+	0.980013i	$0.436252\pi$
$614$	−5.52673e6	−0.591626
$615$	−1.99843e6	−0.213060
$616$	−365568.	−0.0388165
$617$	1.55469e7	1.64411	0.822054	−	0.569410i	$-0.192828\pi$
$617$	1.55469e7	1.64411	0.822054	+	0.569410i	$0.192828\pi$
$618$	3.92717e6	0.413626
$619$	1.66849e7	1.75023	0.875117	−	0.483911i	$-0.160784\pi$
$619$	1.66849e7	1.75023	0.875117	+	0.483911i	$0.160784\pi$
$620$	2.69184e6	0.281235
$621$	−2.72938e6	−0.284010
$622$	1.04027e7	1.07812
$623$	1.14868e7	1.18571
$624$	0	0
$625$	4.69740e6	0.481014
$626$	5.81866e6	0.593455
$627$	249264.	0.0253216
$628$	3.59811e6	0.364062
$629$	−1.17217e7	−1.18131
$630$	−1.85069e6	−0.185773
$631$	−1.14295e7	−1.14275	−0.571377	−	0.820688i	$-0.693590\pi$
$631$	−1.14295e7	−1.14275	−0.571377	+	0.820688i	$0.693590\pi$
$632$	1.67475e6	0.166785
$633$	−6.07914e6	−0.603022
$634$	4.65216e6	0.459654
$635$	−6.95914e6	−0.684890
$636$	−738720.	−0.0724164
$637$	0	0
$638$	604224.	0.0587687
$639$	2.32211e6	0.224973
$640$	−393216.	−0.0379473
$641$	−7.16326e6	−0.688598	−0.344299	−	0.938860i	$-0.611883\pi$
$641$	−7.16326e6	−0.688598	−0.344299	+	0.938860i	$0.611883\pi$
$642$	1.46491e6	0.140273
$643$	−1.12894e7	−1.07682	−0.538409	−	0.842684i	$-0.680974\pi$
$643$	−1.12894e7	−1.07682	−0.538409	+	0.842684i	$0.680974\pi$
$644$	−1.42572e7	−1.35462
$645$	4.97750e6	0.471099
$646$	1.04414e7	0.984412
$647$	9.36372e6	0.879403	0.439701	−	0.898144i	$-0.355084\pi$
$647$	9.36372e6	0.879403	0.439701	+	0.898144i	$0.355084\pi$
$648$	419904.	0.0392837
$649$	243936.	0.0227334
$650$	0	0
$651$	−1.50154e7	−1.38863
$652$	1.03294e7	0.951601
$653$	−4.00520e6	−0.367571	−0.183785	−	0.982966i	$-0.558835\pi$
$653$	−4.00520e6	−0.367571	−0.183785	+	0.982966i	$0.558835\pi$
$654$	−123192.	−0.0112626
$655$	2.43504e6	0.221770
$656$	2.36851e6	0.214890
$657$	2.17226e6	0.196335
$658$	−2.61610e7	−2.35553
$659$	1.36299e7	1.22258	0.611290	−	0.791406i	$-0.290651\pi$
$659$	1.36299e7	1.22258	0.611290	+	0.791406i	$0.290651\pi$
$660$	82944.0	0.00741182
$661$	−1.85919e7	−1.65509	−0.827544	−	0.561401i	$-0.810263\pi$
$661$	−1.85919e7	−1.65509	−0.827544	+	0.561401i	$0.810263\pi$
$662$	−2.74844e6	−0.243748
$663$	0	0
$664$	851712.	0.0749674
$665$	6.59165e6	0.578016
$666$	1.67897e6	0.146675
$667$	2.35647e7	2.05092
$668$	−9.68602e6	−0.839854
$669$	−1.54852e6	−0.133768
$670$	2.52883e6	0.217637
$671$	−899760.	−0.0771472
$672$	2.19341e6	0.187368
$673$	6.14745e6	0.523187	0.261594	−	0.965178i	$-0.415752\pi$
$673$	6.14745e6	0.523187	0.261594	+	0.965178i	$0.415752\pi$
$674$	−1.01579e7	−0.861303
$675$	−1.85822e6	−0.156978
$676$	0	0
$677$	974550.	0.0817208	0.0408604	−	0.999165i	$-0.486990\pi$
$677$	974550.	0.0817208	0.0408604	+	0.999165i	$0.486990\pi$
$678$	−452520.	−0.0378062
$679$	−1.73964e7	−1.44805
$680$	3.47443e6	0.288145
$681$	−1.41782e6	−0.117153
$682$	672960.	0.0554024
$683$	−1.38486e7	−1.13593	−0.567967	−	0.823051i	$-0.692270\pi$
$683$	−1.38486e7	−1.13593	−0.567967	+	0.823051i	$0.692270\pi$
$684$	−1.49558e6	−0.122228
$685$	−2.28182e6	−0.185804
$686$	2.19246e7	1.77877
$687$	4.55099e6	0.367887
$688$	−5.89926e6	−0.475146
$689$	0	0
$690$	3.23482e6	0.258659
$691$	6.17139e6	0.491686	0.245843	−	0.969310i	$-0.420935\pi$
$691$	6.17139e6	0.491686	0.245843	+	0.969310i	$0.420935\pi$
$692$	−8.91965e6	−0.708080
$693$	−462672.	−0.0365965
$694$	−5.59378e6	−0.440866
$695$	−3.20909e6	−0.252011
$696$	−3.62534e6	−0.283678
$697$	−2.09280e7	−1.63172
$698$	−1.38274e7	−1.07424
$699$	7.93201e6	0.614031
$700$	−9.70659e6	−0.748724
$701$	−2.18574e7	−1.67998	−0.839989	−	0.542603i	$-0.817439\pi$
$701$	−2.18574e7	−1.67998	−0.839989	+	0.542603i	$0.817439\pi$
$702$	0	0
$703$	−5.98003e6	−0.456368
$704$	−98304.0	−0.00747549
$705$	5.93568e6	0.449777
$706$	−5.93390e6	−0.448052
$707$	1.23651e7	0.930352
$708$	−1.46362e6	−0.109735
$709$	−7.27281e6	−0.543358	−0.271679	−	0.962388i	$-0.587579\pi$
$709$	−7.27281e6	−0.543358	−0.271679	+	0.962388i	$0.587579\pi$
$710$	−2.75213e6	−0.204891
$711$	2.11961e6	0.157247
$712$	3.08890e6	0.228351
$713$	2.62454e7	1.93344
$714$	−1.93808e7	−1.42274
$715$	0	0
$716$	−6.48096e6	−0.472451
$717$	6.50668e6	0.472674
$718$	−3.50438e6	−0.253688
$719$	−1.08042e7	−0.779420	−0.389710	−	0.920938i	$-0.627425\pi$
$719$	−1.08042e7	−0.779420	−0.389710	+	0.920938i	$0.627425\pi$
$720$	−497664.	−0.0357771
$721$	2.59629e7	1.86001
$722$	−4.57753e6	−0.326805
$723$	8.29492e6	0.590156
$724$	−7.51792e6	−0.533030
$725$	1.60434e7	1.13358
$726$	−5.77710e6	−0.406788
$727$	5.28192e6	0.370643	0.185321	−	0.982678i	$-0.440667\pi$
$727$	5.28192e6	0.370643	0.185321	+	0.982678i	$0.440667\pi$
$728$	0	0
$729$	531441.	0.0370370
$730$	−2.57453e6	−0.178809
$731$	5.21255e7	3.60792
$732$	5.39856e6	0.372392
$733$	1.76844e7	1.21571	0.607854	−	0.794049i	$-0.292030\pi$
$733$	1.76844e7	1.21571	0.607854	+	0.794049i	$0.292030\pi$
$734$	−9.97374e6	−0.683310
$735$	−8.60479e6	−0.587519
$736$	−3.83386e6	−0.260880
$737$	632208.	0.0428737
$738$	2.99765e6	0.202600
$739$	4.86907e6	0.327971	0.163985	−	0.986463i	$-0.447565\pi$
$739$	4.86907e6	0.327971	0.163985	+	0.986463i	$0.447565\pi$
$740$	−1.98989e6	−0.133582
$741$	0	0
$742$	−4.88376e6	−0.325645
$743$	−2.73229e6	−0.181575	−0.0907873	−	0.995870i	$-0.528938\pi$
$743$	−2.73229e6	−0.181575	−0.0907873	+	0.995870i	$0.528938\pi$
$744$	−4.03776e6	−0.267429
$745$	119520.	0.00788951
$746$	−1.96678e7	−1.29393
$747$	1.07795e6	0.0706800
$748$	868608.	0.0567636
$749$	9.68470e6	0.630785
$750$	4.90234e6	0.318236
$751$	−1.83506e6	−0.118727	−0.0593635	−	0.998236i	$-0.518907\pi$
$751$	−1.83506e6	−0.118727	−0.0593635	+	0.998236i	$0.518907\pi$
$752$	−7.03488e6	−0.453641
$753$	8.62412e6	0.554278
$754$	0	0
$755$	−2.67288e6	−0.170652
$756$	2.77603e6	0.176653
$757$	−2.61341e7	−1.65756	−0.828778	−	0.559577i	$-0.810963\pi$
$757$	−2.61341e7	−1.65756	−0.828778	+	0.559577i	$0.810963\pi$
$758$	−3.12625e6	−0.197629
$759$	808704.	0.0509548
$760$	1.77254e6	0.111317
$761$	2.81858e7	1.76429	0.882143	−	0.470981i	$-0.156100\pi$
$761$	2.81858e7	1.76429	0.882143	+	0.470981i	$0.156100\pi$
$762$	1.04387e7	0.651267
$763$	−814436.	−0.0506461
$764$	−1.04026e7	−0.644773
$765$	4.39733e6	0.271666
$766$	9.81197e6	0.604205
$767$	0	0
$768$	589824.	0.0360844
$769$	−1.14050e7	−0.695470	−0.347735	−	0.937593i	$-0.613049\pi$
$769$	−1.14050e7	−0.695470	−0.347735	+	0.937593i	$0.613049\pi$
$770$	548352.	0.0333298
$771$	−7.57852e6	−0.459144
$772$	3.70326e6	0.223636
$773$	−2.22191e6	−0.133745	−0.0668725	−	0.997762i	$-0.521302\pi$
$773$	−2.22191e6	−0.133745	−0.0668725	+	0.997762i	$0.521302\pi$
$774$	−7.46626e6	−0.447972
$775$	1.78685e7	1.06865
$776$	−4.67802e6	−0.278874
$777$	1.10998e7	0.659575
$778$	−2.42369e6	−0.143558
$779$	−1.06768e7	−0.630373
$780$	0	0
$781$	−688032.	−0.0403628
$782$	3.38757e7	1.98094
$783$	−4.58833e6	−0.267454
$784$	1.01983e7	0.592566
$785$	−5.39717e6	−0.312602
$786$	−3.65256e6	−0.210883
$787$	3.98114e6	0.229124	0.114562	−	0.993416i	$-0.463454\pi$
$787$	3.98114e6	0.229124	0.114562	+	0.993416i	$0.463454\pi$
$788$	7.34669e6	0.421479
$789$	−5.76439e6	−0.329656
$790$	−2.51213e6	−0.143210
$791$	−2.99166e6	−0.170009
$792$	−124416.	−0.00704796
$793$	0	0
$794$	−4.36638e6	−0.245793
$795$	1.10808e6	0.0621804
$796$	−2.06176e6	−0.115333
$797$	2.20126e7	1.22751	0.613755	−	0.789496i	$-0.289658\pi$
$797$	2.20126e7	1.22751	0.613755	+	0.789496i	$0.289658\pi$
$798$	−9.88747e6	−0.549640
$799$	6.21598e7	3.44463
$800$	−2.61018e6	−0.144193
$801$	3.90938e6	0.215292
$802$	1.06070e7	0.582315
$803$	−643632.	−0.0352248
$804$	−3.79325e6	−0.206953
$805$	2.13857e7	1.16315
$806$	0	0
$807$	−7.49893e6	−0.405336
$808$	3.32506e6	0.179172
$809$	−2.68804e7	−1.44399	−0.721995	−	0.691898i	$-0.756775\pi$
$809$	−2.68804e7	−1.44399	−0.721995	+	0.691898i	$0.756775\pi$
$810$	−629856.	−0.0337310
$811$	−8.80164e6	−0.469907	−0.234953	−	0.972007i	$-0.575494\pi$
$811$	−8.80164e6	−0.469907	−0.234953	+	0.972007i	$0.575494\pi$
$812$	−2.39676e7	−1.27566
$813$	960966.	0.0509896
$814$	−497472.	−0.0263153
$815$	−1.54941e7	−0.817093
$816$	−5.21165e6	−0.273999
$817$	2.65928e7	1.39383
$818$	3.45546e6	0.180561
$819$	0	0
$820$	−3.55277e6	−0.184515
$821$	−1.69316e7	−0.876677	−0.438338	−	0.898810i	$-0.644433\pi$
$821$	−1.69316e7	−0.876677	−0.438338	+	0.898810i	$0.644433\pi$
$822$	3.42274e6	0.176683
$823$	1.05941e7	0.545210	0.272605	−	0.962126i	$-0.412115\pi$
$823$	1.05941e7	0.545210	0.272605	+	0.962126i	$0.412115\pi$
$824$	6.98163e6	0.358211
$825$	550584.	0.0281636
$826$	−9.67613e6	−0.493459
$827$	2.54154e7	1.29221	0.646104	−	0.763249i	$-0.276397\pi$
$827$	2.54154e7	1.29221	0.646104	+	0.763249i	$0.276397\pi$
$828$	−4.85222e6	−0.245960
$829$	1.92970e7	0.975222	0.487611	−	0.873061i	$-0.337868\pi$
$829$	1.92970e7	0.975222	0.487611	+	0.873061i	$0.337868\pi$
$830$	−1.27757e6	−0.0643708
$831$	2.00901e7	1.00920
$832$	0	0
$833$	−9.01113e7	−4.49953
$834$	4.81363e6	0.239639
$835$	1.45290e7	0.721141
$836$	443136.	0.0219291
$837$	−5.11029e6	−0.252134
$838$	1.75226e7	0.861965
$839$	−2.67637e7	−1.31262	−0.656312	−	0.754489i	$-0.727885\pi$
$839$	−2.67637e7	−1.31262	−0.656312	+	0.754489i	$0.727885\pi$
$840$	−3.29011e6	−0.160884
$841$	1.91033e7	0.931361
$842$	−1.50002e7	−0.729152
$843$	73764.0	0.00357500
$844$	−1.08074e7	−0.522232
$845$	0	0
$846$	−8.90352e6	−0.427697
$847$	−3.81930e7	−1.82926
$848$	−1.31328e6	−0.0627145
$849$	−3.38962e6	−0.161392
$850$	2.30634e7	1.09490
$851$	−1.94014e7	−0.918352
$852$	4.12819e6	0.194832
$853$	−9.51435e6	−0.447720	−0.223860	−	0.974621i	$-0.571866\pi$
$853$	−9.51435e6	−0.447720	−0.223860	+	0.974621i	$0.571866\pi$
$854$	3.56905e7	1.67459
$855$	2.24338e6	0.104951
$856$	2.60429e6	0.121480
$857$	2.73757e7	1.27325	0.636623	−	0.771175i	$-0.280331\pi$
$857$	2.73757e7	1.27325	0.636623	+	0.771175i	$0.280331\pi$
$858$	0	0
$859$	1.05377e7	0.487261	0.243631	−	0.969868i	$-0.421662\pi$
$859$	1.05377e7	0.487261	0.243631	+	0.969868i	$0.421662\pi$
$860$	8.84890e6	0.407984
$861$	1.98178e7	0.911060
$862$	−4.83456e6	−0.221610
$863$	−3.82773e7	−1.74950	−0.874750	−	0.484574i	$-0.838975\pi$
$863$	−3.82773e7	−1.74950	−0.874750	+	0.484574i	$0.838975\pi$
$864$	746496.	0.0340207
$865$	1.33795e7	0.607993
$866$	−4.93473e6	−0.223598
$867$	3.32711e7	1.50321
$868$	−2.66941e7	−1.20258
$869$	−628032.	−0.0282119
$870$	5.43802e6	0.243580
$871$	0	0
$872$	−219008.	−0.00975369
$873$	−5.92061e6	−0.262925
$874$	1.72823e7	0.765285
$875$	3.24099e7	1.43106
$876$	3.86179e6	0.170031
$877$	3.91309e7	1.71799	0.858995	−	0.511983i	$-0.171089\pi$
$877$	3.91309e7	1.71799	0.858995	+	0.511983i	$0.171089\pi$
$878$	−2.30332e7	−1.00837
$879$	1.82307e7	0.795851
$880$	147456.	0.00641883
$881$	−1.74541e7	−0.757633	−0.378816	−	0.925472i	$-0.623669\pi$
$881$	−1.74541e7	−0.757633	−0.378816	+	0.925472i	$0.623669\pi$
$882$	1.29072e7	0.558676
$883$	−7.42293e6	−0.320386	−0.160193	−	0.987086i	$-0.551212\pi$
$883$	−7.42293e6	−0.320386	−0.160193	+	0.987086i	$0.551212\pi$
$884$	0	0
$885$	2.19542e6	0.0942237
$886$	8.17262e6	0.349766
$887$	1.98525e7	0.847239	0.423619	−	0.905840i	$-0.360759\pi$
$887$	1.98525e7	0.847239	0.423619	+	0.905840i	$0.360759\pi$
$888$	2.98483e6	0.127024
$889$	6.90114e7	2.92864
$890$	−4.63334e6	−0.196074
$891$	−157464.	−0.00664488
$892$	−2.75293e6	−0.115846
$893$	3.17119e7	1.33074
$894$	−179280.	−0.00750219
$895$	9.72144e6	0.405670
$896$	3.89939e6	0.162266
$897$	0	0
$898$	−1.80874e6	−0.0748487
$899$	4.41209e7	1.82073
$900$	−3.30350e6	−0.135947
$901$	1.16041e7	0.476209
$902$	−888192.	−0.0363488
$903$	−4.93602e7	−2.01446
$904$	−804480.	−0.0327412
$905$	1.12769e7	0.457686
$906$	4.00932e6	0.162274
$907$	−1.80284e7	−0.727678	−0.363839	−	0.931462i	$-0.618534\pi$
$907$	−1.80284e7	−0.727678	−0.363839	+	0.931462i	$0.618534\pi$
$908$	−2.52058e6	−0.101458
$909$	4.20827e6	0.168925
$910$	0	0
$911$	−1.16246e7	−0.464070	−0.232035	−	0.972707i	$-0.574538\pi$
$911$	−1.16246e7	−0.464070	−0.232035	+	0.972707i	$0.574538\pi$
$912$	−2.65882e6	−0.105853
$913$	−319392.	−0.0126808
$914$	7.17201e6	0.283972
$915$	−8.09784e6	−0.319754
$916$	8.09066e6	0.318599
$917$	−2.41475e7	−0.948306
$918$	−6.59599e6	−0.258329
$919$	2.19382e7	0.856866	0.428433	−	0.903574i	$-0.359066\pi$
$919$	2.19382e7	0.856866	0.428433	+	0.903574i	$0.359066\pi$
$920$	5.75078e6	0.224005
$921$	−1.24351e7	−0.483061
$922$	−1.66830e7	−0.646318
$923$	0	0
$924$	−822528.	−0.0316935
$925$	−1.32089e7	−0.507590
$926$	−5.24862e6	−0.201149
$927$	8.83613e6	0.337725
$928$	−6.44506e6	−0.245673
$929$	2.92599e7	1.11233	0.556165	−	0.831072i	$-0.312272\pi$
$929$	2.92599e7	1.11233	0.556165	+	0.831072i	$0.312272\pi$
$930$	6.05664e6	0.229628
$931$	−4.59719e7	−1.73827
$932$	1.41013e7	0.531766
$933$	2.34060e7	0.880284
$934$	−1.10919e7	−0.416043
$935$	−1.30291e6	−0.0487401
$936$	0	0
$937$	2.31218e7	0.860343	0.430172	−	0.902747i	$-0.358453\pi$
$937$	2.31218e7	0.860343	0.430172	+	0.902747i	$0.358453\pi$
$938$	−2.50776e7	−0.930633
$939$	1.30920e7	0.484554
$940$	1.05523e7	0.389519
$941$	1.57256e7	0.578940	0.289470	−	0.957187i	$-0.406521\pi$
$941$	1.57256e7	0.578940	0.289470	+	0.957187i	$0.406521\pi$
$942$	8.09575e6	0.297256
$943$	−3.46395e7	−1.26851
$944$	−2.60198e6	−0.0950330
$945$	−4.16405e6	−0.151683
$946$	2.21222e6	0.0803713
$947$	−1.57405e7	−0.570352	−0.285176	−	0.958475i	$-0.592052\pi$
$947$	−1.57405e7	−0.570352	−0.285176	+	0.958475i	$0.592052\pi$
$948$	3.76819e6	0.136180
$949$	0	0
$950$	1.17662e7	0.422987
$951$	1.04674e7	0.375306
$952$	−3.44548e7	−1.23213
$953$	312414.	0.0111429	0.00557145	−	0.999984i	$-0.498227\pi$
$953$	312414.	0.0111429	0.00557145	+	0.999984i	$0.498227\pi$
$954$	−1.66212e6	−0.0591278
$955$	1.56038e7	0.553634
$956$	1.15674e7	0.409347
$957$	1.35950e6	0.0479845
$958$	−2.83095e7	−0.996594
$959$	2.26281e7	0.794514
$960$	−884736.	−0.0309839
$961$	2.05109e7	0.716436
$962$	0	0
$963$	3.29605e6	0.114532
$964$	1.47465e7	0.511090
$965$	−5.55490e6	−0.192025
$966$	−3.20786e7	−1.10604
$967$	−3.14651e7	−1.08209	−0.541045	−	0.840994i	$-0.681971\pi$
$967$	−3.14651e7	−1.08209	−0.541045	+	0.840994i	$0.681971\pi$
$968$	−1.02704e7	−0.352289
$969$	2.34931e7	0.803769
$970$	7.01702e6	0.239455
$971$	−5.61172e7	−1.91006	−0.955032	−	0.296504i	$-0.904179\pi$
$971$	−5.61172e7	−1.91006	−0.955032	+	0.296504i	$0.904179\pi$
$972$	944784.	0.0320750
$973$	3.18235e7	1.07762
$974$	−6.42010e6	−0.216843
$975$	0	0
$976$	9.59744e6	0.322501
$977$	−4.01018e7	−1.34409	−0.672044	−	0.740511i	$-0.734584\pi$
$977$	−4.01018e7	−1.34409	−0.672044	+	0.740511i	$0.734584\pi$
$978$	2.32411e7	0.776979
$979$	−1.15834e6	−0.0386258
$980$	−1.52974e7	−0.508807
$981$	−277182.	−0.00919586
$982$	−2.05334e7	−0.679488
$983$	3.82807e7	1.26356	0.631781	−	0.775147i	$-0.282324\pi$
$983$	3.82807e7	1.26356	0.631781	+	0.775147i	$0.282324\pi$
$984$	5.32915e6	0.175457
$985$	−1.10200e7	−0.361903
$986$	5.69481e7	1.86546
$987$	−5.88622e7	−1.92328
$988$	0	0
$989$	8.62767e7	2.80481
$990$	186624.	0.00605173
$991$	−1.87594e6	−0.0606785	−0.0303392	−	0.999540i	$-0.509659\pi$
$991$	−1.87594e6	−0.0606785	−0.0303392	+	0.999540i	$0.509659\pi$
$992$	−7.17824e6	−0.231600
$993$	−6.18399e6	−0.199020
$994$	2.72919e7	0.876130
$995$	3.09264e6	0.0990311
$996$	1.91635e6	0.0612106
$997$	1.34521e7	0.428601	0.214301	−	0.976768i	$-0.431253\pi$
$997$	1.34521e7	0.428601	0.214301	+	0.976768i	$0.431253\pi$
$998$	3.84454e7	1.22185
$999$	3.77768e6	0.119760

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.6.a.g.1.1		1
13.12	even	2		78.6.a.b.1.1	✓	1
39.38	odd	2		234.6.a.e.1.1		1
52.51	odd	2		624.6.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.6.a.b.1.1	✓	1	13.12	even	2
234.6.a.e.1.1		1	39.38	odd	2
624.6.a.c.1.1		1	52.51	odd	2
1014.6.a.g.1.1		1	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1014.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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