LMFDB - Embedded newform 1050.6.a.p.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,6,Mod(1,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1050.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	1050.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:	$168.403010804$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1050.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +36.0000 q^{6} +49.0000 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$

\(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +36.0000 q^{6} +49.0000 q^{7} +64.0000 q^{8} +81.0000 q^{9} +272.000 q^{11} +144.000 q^{12} -114.000 q^{13} +196.000 q^{14} +256.000 q^{16} +1022.00 q^{17} +324.000 q^{18} +960.000 q^{19} +441.000 q^{21} +1088.00 q^{22} +1296.00 q^{23} +576.000 q^{24} -456.000 q^{26} +729.000 q^{27} +784.000 q^{28} -1050.00 q^{29} -4348.00 q^{31} +1024.00 q^{32} +2448.00 q^{33} +4088.00 q^{34} +1296.00 q^{36} +5842.00 q^{37} +3840.00 q^{38} -1026.00 q^{39} +9322.00 q^{41} +1764.00 q^{42} +1196.00 q^{43} +4352.00 q^{44} +5184.00 q^{46} -20848.0 q^{47} +2304.00 q^{48} +2401.00 q^{49} +9198.00 q^{51} -1824.00 q^{52} -28274.0 q^{53} +2916.00 q^{54} +3136.00 q^{56} +8640.00 q^{57} -4200.00 q^{58} +28340.0 q^{59} +23782.0 q^{61} -17392.0 q^{62} +3969.00 q^{63} +4096.00 q^{64} +9792.00 q^{66} -15108.0 q^{67} +16352.0 q^{68} +11664.0 q^{69} +49372.0 q^{71} +5184.00 q^{72} +23986.0 q^{73} +23368.0 q^{74} +15360.0 q^{76} +13328.0 q^{77} -4104.00 q^{78} +50320.0 q^{79} +6561.00 q^{81} +37288.0 q^{82} -63364.0 q^{83} +7056.00 q^{84} +4784.00 q^{86} -9450.00 q^{87} +17408.0 q^{88} +2090.00 q^{89} -5586.00 q^{91} +20736.0 q^{92} -39132.0 q^{93} -83392.0 q^{94} +9216.00 q^{96} +43282.0 q^{97} +9604.00 q^{98} +22032.0 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	4.00000	0.707107
$2$	4.00000	0.707107
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	16.0000	0.500000
$5$	0	0
$5$	0	0
$6$	36.0000	0.408248
$7$	49.0000	0.377964
$7$	49.0000	0.377964
$8$	64.0000	0.353553
$9$	81.0000	0.333333
$10$	0	0
$11$	272.000	0.677778	0.338889	−	0.940826i	$-0.389949\pi$
$11$	272.000	0.677778	0.338889	+	0.940826i	$0.389949\pi$
$12$	144.000	0.288675
$13$	−114.000	−0.187088	−0.0935441	−	0.995615i	$-0.529820\pi$
$13$	−114.000	−0.187088	−0.0935441	+	0.995615i	$0.529820\pi$
$14$	196.000	0.267261
$15$	0	0
$16$	256.000	0.250000
$17$	1022.00	0.857687	0.428843	−	0.903379i	$-0.358921\pi$
$17$	1022.00	0.857687	0.428843	+	0.903379i	$0.358921\pi$
$18$	324.000	0.235702
$19$	960.000	0.610081	0.305040	−	0.952339i	$-0.401330\pi$
$19$	960.000	0.610081	0.305040	+	0.952339i	$0.401330\pi$
$20$	0	0
$21$	441.000	0.218218
$22$	1088.00	0.479261
$23$	1296.00	0.510841	0.255420	−	0.966830i	$-0.417786\pi$
$23$	1296.00	0.510841	0.255420	+	0.966830i	$0.417786\pi$
$24$	576.000	0.204124
$25$	0	0
$26$	−456.000	−0.132291
$27$	729.000	0.192450
$28$	784.000	0.188982
$29$	−1050.00	−0.231843	−0.115922	−	0.993258i	$-0.536982\pi$
$29$	−1050.00	−0.231843	−0.115922	+	0.993258i	$0.536982\pi$
$30$	0	0
$31$	−4348.00	−0.812616	−0.406308	−	0.913736i	$-0.633184\pi$
$31$	−4348.00	−0.812616	−0.406308	+	0.913736i	$0.633184\pi$
$32$	1024.00	0.176777
$33$	2448.00	0.391315
$34$	4088.00	0.606476
$35$	0	0
$36$	1296.00	0.166667
$37$	5842.00	0.701548	0.350774	−	0.936460i	$-0.385919\pi$
$37$	5842.00	0.701548	0.350774	+	0.936460i	$0.385919\pi$
$38$	3840.00	0.431392
$39$	−1026.00	−0.108015
$40$	0	0
$41$	9322.00	0.866063	0.433031	−	0.901379i	$-0.357444\pi$
$41$	9322.00	0.866063	0.433031	+	0.901379i	$0.357444\pi$
$42$	1764.00	0.154303
$43$	1196.00	0.0986416	0.0493208	−	0.998783i	$-0.484294\pi$
$43$	1196.00	0.0986416	0.0493208	+	0.998783i	$0.484294\pi$
$44$	4352.00	0.338889
$45$	0	0
$46$	5184.00	0.361219
$47$	−20848.0	−1.37664	−0.688319	−	0.725408i	$-0.741651\pi$
$47$	−20848.0	−1.37664	−0.688319	+	0.725408i	$0.741651\pi$
$48$	2304.00	0.144338
$49$	2401.00	0.142857
$50$	0	0
$51$	9198.00	0.495186
$52$	−1824.00	−0.0935441
$53$	−28274.0	−1.38260	−0.691302	−	0.722566i	$-0.742962\pi$
$53$	−28274.0	−1.38260	−0.691302	+	0.722566i	$0.742962\pi$
$54$	2916.00	0.136083
$55$	0	0
$56$	3136.00	0.133631
$57$	8640.00	0.352230
$58$	−4200.00	−0.163938
$59$	28340.0	1.05991	0.529956	−	0.848025i	$-0.322208\pi$
$59$	28340.0	1.05991	0.529956	+	0.848025i	$0.322208\pi$
$60$	0	0
$61$	23782.0	0.818321	0.409161	−	0.912462i	$-0.365822\pi$
$61$	23782.0	0.818321	0.409161	+	0.912462i	$0.365822\pi$
$62$	−17392.0	−0.574606
$63$	3969.00	0.125988
$64$	4096.00	0.125000
$65$	0	0
$66$	9792.00	0.276702
$67$	−15108.0	−0.411169	−0.205584	−	0.978639i	$-0.565909\pi$
$67$	−15108.0	−0.411169	−0.205584	+	0.978639i	$0.565909\pi$
$68$	16352.0	0.428843
$69$	11664.0	0.294934
$70$	0	0
$71$	49372.0	1.16234	0.581172	−	0.813781i	$-0.302594\pi$
$71$	49372.0	1.16234	0.581172	+	0.813781i	$0.302594\pi$
$72$	5184.00	0.117851
$73$	23986.0	0.526806	0.263403	−	0.964686i	$-0.415155\pi$
$73$	23986.0	0.526806	0.263403	+	0.964686i	$0.415155\pi$
$74$	23368.0	0.496069
$75$	0	0
$76$	15360.0	0.305040
$77$	13328.0	0.256176
$78$	−4104.00	−0.0763785
$79$	50320.0	0.907137	0.453569	−	0.891221i	$-0.350151\pi$
$79$	50320.0	0.907137	0.453569	+	0.891221i	$0.350151\pi$
$80$	0	0
$81$	6561.00	0.111111
$82$	37288.0	0.612399
$83$	−63364.0	−1.00960	−0.504798	−	0.863238i	$-0.668433\pi$
$83$	−63364.0	−1.00960	−0.504798	+	0.863238i	$0.668433\pi$
$84$	7056.00	0.109109
$85$	0	0
$86$	4784.00	0.0697501
$87$	−9450.00	−0.133855
$88$	17408.0	0.239631
$89$	2090.00	0.0279686	0.0139843	−	0.999902i	$-0.495549\pi$
$89$	2090.00	0.0279686	0.0139843	+	0.999902i	$0.495549\pi$
$90$	0	0
$91$	−5586.00	−0.0707127
$92$	20736.0	0.255420
$93$	−39132.0	−0.469164
$94$	−83392.0	−0.973430
$95$	0	0
$96$	9216.00	0.102062
$97$	43282.0	0.467066	0.233533	−	0.972349i	$-0.424971\pi$
$97$	43282.0	0.467066	0.233533	+	0.972349i	$0.424971\pi$
$98$	9604.00	0.101015
$99$	22032.0	0.225926
$100$	0	0
$101$	78582.0	0.766513	0.383257	−	0.923642i	$-0.374802\pi$
$101$	78582.0	0.766513	0.383257	+	0.923642i	$0.374802\pi$
$102$	36792.0	0.350149
$103$	7256.00	0.0673914	0.0336957	−	0.999432i	$-0.489272\pi$
$103$	7256.00	0.0673914	0.0336957	+	0.999432i	$0.489272\pi$
$104$	−7296.00	−0.0661457
$105$	0	0
$106$	−113096.	−0.977648
$107$	−187428.	−1.58261	−0.791307	−	0.611419i	$-0.790599\pi$
$107$	−187428.	−1.58261	−0.791307	+	0.611419i	$0.790599\pi$
$108$	11664.0	0.0962250
$109$	88830.0	0.716133	0.358066	−	0.933696i	$-0.383436\pi$
$109$	88830.0	0.716133	0.358066	+	0.933696i	$0.383436\pi$
$110$	0	0
$111$	52578.0	0.405039
$112$	12544.0	0.0944911
$113$	61226.0	0.451066	0.225533	−	0.974236i	$-0.427588\pi$
$113$	61226.0	0.451066	0.225533	+	0.974236i	$0.427588\pi$
$114$	34560.0	0.249064
$115$	0	0
$116$	−16800.0	−0.115922
$117$	−9234.00	−0.0623627
$118$	113360.	0.749471
$119$	50078.0	0.324175
$120$	0	0
$121$	−87067.0	−0.540618
$122$	95128.0	0.578640
$123$	83898.0	0.500022
$124$	−69568.0	−0.406308
$125$	0	0
$126$	15876.0	0.0890871
$127$	211112.	1.16146	0.580729	−	0.814097i	$-0.302768\pi$
$127$	211112.	1.16146	0.580729	+	0.814097i	$0.302768\pi$
$128$	16384.0	0.0883883
$129$	10764.0	0.0569507
$130$	0	0
$131$	65332.0	0.332620	0.166310	−	0.986074i	$-0.446815\pi$
$131$	65332.0	0.332620	0.166310	+	0.986074i	$0.446815\pi$
$132$	39168.0	0.195658
$133$	47040.0	0.230589
$134$	−60432.0	−0.290740
$135$	0	0
$136$	65408.0	0.303238
$137$	91722.0	0.417515	0.208758	−	0.977967i	$-0.433058\pi$
$137$	91722.0	0.417515	0.208758	+	0.977967i	$0.433058\pi$
$138$	46656.0	0.208550
$139$	233080.	1.02322	0.511609	−	0.859218i	$-0.329050\pi$
$139$	233080.	1.02322	0.511609	+	0.859218i	$0.329050\pi$
$140$	0	0
$141$	−187632.	−0.794802
$142$	197488.	0.821902
$143$	−31008.0	−0.126804
$144$	20736.0	0.0833333
$145$	0	0
$146$	95944.0	0.372508
$147$	21609.0	0.0824786
$148$	93472.0	0.350774
$149$	98070.0	0.361885	0.180942	−	0.983494i	$-0.442085\pi$
$149$	98070.0	0.361885	0.180942	+	0.983494i	$0.442085\pi$
$150$	0	0
$151$	−14608.0	−0.0521373	−0.0260686	−	0.999660i	$-0.508299\pi$
$151$	−14608.0	−0.0521373	−0.0260686	+	0.999660i	$0.508299\pi$
$152$	61440.0	0.215696
$153$	82782.0	0.285896
$154$	53312.0	0.181144
$155$	0	0
$156$	−16416.0	−0.0540077
$157$	−186778.	−0.604751	−0.302375	−	0.953189i	$-0.597780\pi$
$157$	−186778.	−0.604751	−0.302375	+	0.953189i	$0.597780\pi$
$158$	201280.	0.641443
$159$	−254466.	−0.798246
$160$	0	0
$161$	63504.0	0.193080
$162$	26244.0	0.0785674
$163$	53236.0	0.156941	0.0784705	−	0.996916i	$-0.474996\pi$
$163$	53236.0	0.156941	0.0784705	+	0.996916i	$0.474996\pi$
$164$	149152.	0.433031
$165$	0	0
$166$	−253456.	−0.713892
$167$	185952.	0.515952	0.257976	−	0.966151i	$-0.416944\pi$
$167$	185952.	0.515952	0.257976	+	0.966151i	$0.416944\pi$
$168$	28224.0	0.0771517
$169$	−358297.	−0.964998
$170$	0	0
$171$	77760.0	0.203360
$172$	19136.0	0.0493208
$173$	83546.0	0.212232	0.106116	−	0.994354i	$-0.466159\pi$
$173$	83546.0	0.212232	0.106116	+	0.994354i	$0.466159\pi$
$174$	−37800.0	−0.0946496
$175$	0	0
$176$	69632.0	0.169444
$177$	255060.	0.611940
$178$	8360.00	0.0197768
$179$	793560.	1.85117	0.925587	−	0.378535i	$-0.123572\pi$
$179$	793560.	1.85117	0.925587	+	0.378535i	$0.123572\pi$
$180$	0	0
$181$	−329498.	−0.747578	−0.373789	−	0.927514i	$-0.621942\pi$
$181$	−329498.	−0.747578	−0.373789	+	0.927514i	$0.621942\pi$
$182$	−22344.0	−0.0500014
$183$	214038.	0.472458
$184$	82944.0	0.180609
$185$	0	0
$186$	−156528.	−0.331749
$187$	277984.	0.581321
$188$	−333568.	−0.688319
$189$	35721.0	0.0727393
$190$	0	0
$191$	−41508.0	−0.0823282	−0.0411641	−	0.999152i	$-0.513107\pi$
$191$	−41508.0	−0.0823282	−0.0411641	+	0.999152i	$0.513107\pi$
$192$	36864.0	0.0721688
$193$	45646.0	0.0882083	0.0441042	−	0.999027i	$-0.485957\pi$
$193$	45646.0	0.0882083	0.0441042	+	0.999027i	$0.485957\pi$
$194$	173128.	0.330265
$195$	0	0
$196$	38416.0	0.0714286
$197$	185702.	0.340919	0.170459	−	0.985365i	$-0.445475\pi$
$197$	185702.	0.340919	0.170459	+	0.985365i	$0.445475\pi$
$198$	88128.0	0.159754
$199$	951500.	1.70324	0.851620	−	0.524159i	$-0.175620\pi$
$199$	951500.	1.70324	0.851620	+	0.524159i	$0.175620\pi$
$200$	0	0
$201$	−135972.	−0.237388
$202$	314328.	0.542007
$203$	−51450.0	−0.0876285
$204$	147168.	0.247593
$205$	0	0
$206$	29024.0	0.0476529
$207$	104976.	0.170280
$208$	−29184.0	−0.0467721
$209$	261120.	0.413499
$210$	0	0
$211$	−1.11355e6	−1.72188	−0.860940	−	0.508707i	$-0.830124\pi$
$211$	−1.11355e6	−1.72188	−0.860940	+	0.508707i	$0.830124\pi$
$212$	−452384.	−0.691302
$213$	444348.	0.671080
$214$	−749712.	−1.11908
$215$	0	0
$216$	46656.0	0.0680414
$217$	−213052.	−0.307140
$218$	355320.	0.506382
$219$	215874.	0.304152
$220$	0	0
$221$	−116508.	−0.160463
$222$	210312.	0.286406
$223$	−340984.	−0.459168	−0.229584	−	0.973289i	$-0.573737\pi$
$223$	−340984.	−0.459168	−0.229584	+	0.973289i	$0.573737\pi$
$224$	50176.0	0.0668153
$225$	0	0
$226$	244904.	0.318952
$227$	−315028.	−0.405774	−0.202887	−	0.979202i	$-0.565032\pi$
$227$	−315028.	−0.405774	−0.202887	+	0.979202i	$0.565032\pi$
$228$	138240.	0.176115
$229$	933310.	1.17608	0.588040	−	0.808832i	$-0.299900\pi$
$229$	933310.	1.17608	0.588040	+	0.808832i	$0.299900\pi$
$230$	0	0
$231$	119952.	0.147903
$232$	−67200.0	−0.0819689
$233$	−843294.	−1.01763	−0.508814	−	0.860876i	$-0.669916\pi$
$233$	−843294.	−1.01763	−0.508814	+	0.860876i	$0.669916\pi$
$234$	−36936.0	−0.0440971
$235$	0	0
$236$	453440.	0.529956
$237$	452880.	0.523736
$238$	200312.	0.229226
$239$	1.54682e6	1.75164	0.875820	−	0.482637i	$-0.160321\pi$
$239$	1.54682e6	1.75164	0.875820	+	0.482637i	$0.160321\pi$
$240$	0	0
$241$	73642.0	0.0816738	0.0408369	−	0.999166i	$-0.486998\pi$
$241$	73642.0	0.0816738	0.0408369	+	0.999166i	$0.486998\pi$
$242$	−348268.	−0.382274
$243$	59049.0	0.0641500
$244$	380512.	0.409161
$245$	0	0
$246$	335592.	0.353569
$247$	−109440.	−0.114139
$248$	−278272.	−0.287303
$249$	−570276.	−0.582890
$250$	0	0
$251$	−1.53131e6	−1.53419	−0.767093	−	0.641535i	$-0.778298\pi$
$251$	−1.53131e6	−1.53419	−0.767093	+	0.641535i	$0.778298\pi$
$252$	63504.0	0.0629941
$253$	352512.	0.346236
$254$	844448.	0.821275
$255$	0	0
$256$	65536.0	0.0625000
$257$	−702778.	−0.663721	−0.331860	−	0.943329i	$-0.607676\pi$
$257$	−702778.	−0.663721	−0.331860	+	0.943329i	$0.607676\pi$
$258$	43056.0	0.0402703
$259$	286258.	0.265160
$260$	0	0
$261$	−85050.0	−0.0772811
$262$	261328.	0.235198
$263$	−336904.	−0.300343	−0.150171	−	0.988660i	$-0.547983\pi$
$263$	−336904.	−0.300343	−0.150171	+	0.988660i	$0.547983\pi$
$264$	156672.	0.138351
$265$	0	0
$266$	188160.	0.163051
$267$	18810.0	0.0161477
$268$	−241728.	−0.205584
$269$	2.11203e6	1.77959	0.889794	−	0.456363i	$-0.150848\pi$
$269$	2.11203e6	1.77959	0.889794	+	0.456363i	$0.150848\pi$
$270$	0	0
$271$	−119748.	−0.0990478	−0.0495239	−	0.998773i	$-0.515770\pi$
$271$	−119748.	−0.0990478	−0.0495239	+	0.998773i	$0.515770\pi$
$272$	261632.	0.214422
$273$	−50274.0	−0.0408260
$274$	366888.	0.295228
$275$	0	0
$276$	186624.	0.147467
$277$	107202.	0.0839467	0.0419733	−	0.999119i	$-0.486636\pi$
$277$	107202.	0.0839467	0.0419733	+	0.999119i	$0.486636\pi$
$278$	932320.	0.723524
$279$	−352188.	−0.270872
$280$	0	0
$281$	−2.11480e6	−1.59773	−0.798864	−	0.601511i	$-0.794566\pi$
$281$	−2.11480e6	−1.59773	−0.798864	+	0.601511i	$0.794566\pi$
$282$	−750528.	−0.562010
$283$	−1.71112e6	−1.27003	−0.635017	−	0.772498i	$-0.719007\pi$
$283$	−1.71112e6	−1.27003	−0.635017	+	0.772498i	$0.719007\pi$
$284$	789952.	0.581172
$285$	0	0
$286$	−124032.	−0.0896641
$287$	456778.	0.327341
$288$	82944.0	0.0589256
$289$	−375373.	−0.264374
$290$	0	0
$291$	389538.	0.269661
$292$	383776.	0.263403
$293$	2.37887e6	1.61883	0.809414	−	0.587238i	$-0.199785\pi$
$293$	2.37887e6	1.61883	0.809414	+	0.587238i	$0.199785\pi$
$294$	86436.0	0.0583212
$295$	0	0
$296$	373888.	0.248035
$297$	198288.	0.130438
$298$	392280.	0.255891
$299$	−147744.	−0.0955723
$300$	0	0
$301$	58604.0	0.0372830
$302$	−58432.0	−0.0368666
$303$	707238.	0.442547
$304$	245760.	0.152520
$305$	0	0
$306$	331128.	0.202159
$307$	4172.00	0.00252638	0.00126319	−	0.999999i	$-0.499598\pi$
$307$	4172.00	0.00252638	0.00126319	+	0.999999i	$0.499598\pi$
$308$	213248.	0.128088
$309$	65304.0	0.0389084
$310$	0	0
$311$	187512.	0.109933	0.0549665	−	0.998488i	$-0.482495\pi$
$311$	187512.	0.109933	0.0549665	+	0.998488i	$0.482495\pi$
$312$	−65664.0	−0.0381892
$313$	1.87883e6	1.08399	0.541996	−	0.840381i	$-0.317669\pi$
$313$	1.87883e6	1.08399	0.541996	+	0.840381i	$0.317669\pi$
$314$	−747112.	−0.427624
$315$	0	0
$316$	805120.	0.453569
$317$	−371978.	−0.207907	−0.103953	−	0.994582i	$-0.533149\pi$
$317$	−371978.	−0.207907	−0.103953	+	0.994582i	$0.533149\pi$
$318$	−1.01786e6	−0.564445
$319$	−285600.	−0.157138
$320$	0	0
$321$	−1.68685e6	−0.913723
$322$	254016.	0.136528
$323$	981120.	0.523258
$324$	104976.	0.0555556
$325$	0	0
$326$	212944.	0.110974
$327$	799470.	0.413459
$328$	596608.	0.306199
$329$	−1.02155e6	−0.520320
$330$	0	0
$331$	1.83113e6	0.918649	0.459325	−	0.888269i	$-0.348091\pi$
$331$	1.83113e6	0.918649	0.459325	+	0.888269i	$0.348091\pi$
$332$	−1.01382e6	−0.504798
$333$	473202.	0.233849
$334$	743808.	0.364833
$335$	0	0
$336$	112896.	0.0545545
$337$	−406258.	−0.194862	−0.0974310	−	0.995242i	$-0.531063\pi$
$337$	−406258.	−0.194862	−0.0974310	+	0.995242i	$0.531063\pi$
$338$	−1.43319e6	−0.682357
$339$	551034.	0.260423
$340$	0	0
$341$	−1.18266e6	−0.550773
$342$	311040.	0.143797
$343$	117649.	0.0539949
$344$	76544.0	0.0348751
$345$	0	0
$346$	334184.	0.150071
$347$	430132.	0.191769	0.0958844	−	0.995392i	$-0.469432\pi$
$347$	430132.	0.191769	0.0958844	+	0.995392i	$0.469432\pi$
$348$	−151200.	−0.0669274
$349$	−1.24313e6	−0.546327	−0.273164	−	0.961968i	$-0.588070\pi$
$349$	−1.24313e6	−0.546327	−0.273164	+	0.961968i	$0.588070\pi$
$350$	0	0
$351$	−83106.0	−0.0360051
$352$	278528.	0.119815
$353$	−362034.	−0.154637	−0.0773184	−	0.997006i	$-0.524636\pi$
$353$	−362034.	−0.154637	−0.0773184	+	0.997006i	$0.524636\pi$
$354$	1.02024e6	0.432707
$355$	0	0
$356$	33440.0	0.0139843
$357$	450702.	0.187163
$358$	3.17424e6	1.30898
$359$	−343820.	−0.140798	−0.0703988	−	0.997519i	$-0.522427\pi$
$359$	−343820.	−0.140798	−0.0703988	+	0.997519i	$0.522427\pi$
$360$	0	0
$361$	−1.55450e6	−0.627802
$362$	−1.31799e6	−0.528617
$363$	−783603.	−0.312126
$364$	−89376.0	−0.0353564
$365$	0	0
$366$	856152.	0.334078
$367$	−1.70769e6	−0.661825	−0.330913	−	0.943661i	$-0.607357\pi$
$367$	−1.70769e6	−0.661825	−0.330913	+	0.943661i	$0.607357\pi$
$368$	331776.	0.127710
$369$	755082.	0.288688
$370$	0	0
$371$	−1.38543e6	−0.522575
$372$	−626112.	−0.234582
$373$	1.23035e6	0.457884	0.228942	−	0.973440i	$-0.426473\pi$
$373$	1.23035e6	0.457884	0.228942	+	0.973440i	$0.426473\pi$
$374$	1.11194e6	0.411056
$375$	0	0
$376$	−1.33427e6	−0.486715
$377$	119700.	0.0433751
$378$	142884.	0.0514344
$379$	−2.49246e6	−0.891313	−0.445656	−	0.895204i	$-0.647030\pi$
$379$	−2.49246e6	−0.891313	−0.445656	+	0.895204i	$0.647030\pi$
$380$	0	0
$381$	1.90001e6	0.670568
$382$	−166032.	−0.0582148
$383$	1.17502e6	0.409305	0.204652	−	0.978835i	$-0.434394\pi$
$383$	1.17502e6	0.409305	0.204652	+	0.978835i	$0.434394\pi$
$384$	147456.	0.0510310
$385$	0	0
$386$	182584.	0.0623727
$387$	96876.0	0.0328805
$388$	692512.	0.233533
$389$	−2.90945e6	−0.974848	−0.487424	−	0.873165i	$-0.662063\pi$
$389$	−2.90945e6	−0.974848	−0.487424	+	0.873165i	$0.662063\pi$
$390$	0	0
$391$	1.32451e6	0.438141
$392$	153664.	0.0505076
$393$	587988.	0.192038
$394$	742808.	0.241066
$395$	0	0
$396$	352512.	0.112963
$397$	−363538.	−0.115764	−0.0578820	−	0.998323i	$-0.518435\pi$
$397$	−363538.	−0.115764	−0.0578820	+	0.998323i	$0.518435\pi$
$398$	3.80600e6	1.20437
$399$	423360.	0.133131
$400$	0	0
$401$	808322.	0.251029	0.125514	−	0.992092i	$-0.459942\pi$
$401$	808322.	0.251029	0.125514	+	0.992092i	$0.459942\pi$
$402$	−543888.	−0.167859
$403$	495672.	0.152031
$404$	1.25731e6	0.383257
$405$	0	0
$406$	−205800.	−0.0619627
$407$	1.58902e6	0.475493
$408$	588672.	0.175075
$409$	3.70665e6	1.09565	0.547827	−	0.836592i	$-0.315455\pi$
$409$	3.70665e6	1.09565	0.547827	+	0.836592i	$0.315455\pi$
$410$	0	0
$411$	825498.	0.241052
$412$	116096.	0.0336957
$413$	1.38866e6	0.400609
$414$	419904.	0.120406
$415$	0	0
$416$	−116736.	−0.0330728
$417$	2.09772e6	0.590755
$418$	1.04448e6	0.292388
$419$	3.21786e6	0.895431	0.447715	−	0.894176i	$-0.352238\pi$
$419$	3.21786e6	0.895431	0.447715	+	0.894176i	$0.352238\pi$
$420$	0	0
$421$	−3.05910e6	−0.841178	−0.420589	−	0.907251i	$-0.638177\pi$
$421$	−3.05910e6	−0.841178	−0.420589	+	0.907251i	$0.638177\pi$
$422$	−4.45419e6	−1.21755
$423$	−1.68869e6	−0.458879
$424$	−1.80954e6	−0.488824
$425$	0	0
$426$	1.77739e6	0.474525
$427$	1.16532e6	0.309296
$428$	−2.99885e6	−0.791307
$429$	−279072.	−0.0732104
$430$	0	0
$431$	−3.55283e6	−0.921257	−0.460629	−	0.887593i	$-0.652376\pi$
$431$	−3.55283e6	−0.921257	−0.460629	+	0.887593i	$0.652376\pi$
$432$	186624.	0.0481125
$433$	−1.96921e6	−0.504746	−0.252373	−	0.967630i	$-0.581211\pi$
$433$	−1.96921e6	−0.504746	−0.252373	+	0.967630i	$0.581211\pi$
$434$	−852208.	−0.217181
$435$	0	0
$436$	1.42128e6	0.358066
$437$	1.24416e6	0.311654
$438$	863496.	0.215068
$439$	1.92550e6	0.476850	0.238425	−	0.971161i	$-0.423369\pi$
$439$	1.92550e6	0.476850	0.238425	+	0.971161i	$0.423369\pi$
$440$	0	0
$441$	194481.	0.0476190
$442$	−466032.	−0.113465
$443$	7.23404e6	1.75134	0.875672	−	0.482907i	$-0.160419\pi$
$443$	7.23404e6	1.75134	0.875672	+	0.482907i	$0.160419\pi$
$444$	841248.	0.202519
$445$	0	0
$446$	−1.36394e6	−0.324681
$447$	882630.	0.208934
$448$	200704.	0.0472456
$449$	314610.	0.0736473	0.0368236	−	0.999322i	$-0.488276\pi$
$449$	314610.	0.0736473	0.0368236	+	0.999322i	$0.488276\pi$
$450$	0	0
$451$	2.53558e6	0.586998
$452$	979616.	0.225533
$453$	−131472.	−0.0301015
$454$	−1.26011e6	−0.286926
$455$	0	0
$456$	552960.	0.124532
$457$	−1.50786e6	−0.337730	−0.168865	−	0.985639i	$-0.554010\pi$
$457$	−1.50786e6	−0.337730	−0.168865	+	0.985639i	$0.554010\pi$
$458$	3.73324e6	0.831615
$459$	745038.	0.165062
$460$	0	0
$461$	−8.34330e6	−1.82846	−0.914230	−	0.405196i	$-0.867203\pi$
$461$	−8.34330e6	−1.82846	−0.914230	+	0.405196i	$0.867203\pi$
$462$	479808.	0.104583
$463$	6.39230e6	1.38581	0.692906	−	0.721028i	$-0.256330\pi$
$463$	6.39230e6	1.38581	0.692906	+	0.721028i	$0.256330\pi$
$464$	−268800.	−0.0579608
$465$	0	0
$466$	−3.37318e6	−0.719572
$467$	−2.04207e6	−0.433289	−0.216645	−	0.976251i	$-0.569511\pi$
$467$	−2.04207e6	−0.433289	−0.216645	+	0.976251i	$0.569511\pi$
$468$	−147744.	−0.0311814
$469$	−740292.	−0.155407
$470$	0	0
$471$	−1.68100e6	−0.349153
$472$	1.81376e6	0.374735
$473$	325312.	0.0668571
$474$	1.81152e6	0.370337
$475$	0	0
$476$	801248.	0.162088
$477$	−2.29019e6	−0.460868
$478$	6.18728e6	1.23860
$479$	5.16528e6	1.02862	0.514310	−	0.857604i	$-0.328048\pi$
$479$	5.16528e6	1.02862	0.514310	+	0.857604i	$0.328048\pi$
$480$	0	0
$481$	−665988.	−0.131251
$482$	294568.	0.0577521
$483$	571536.	0.111475
$484$	−1.39307e6	−0.270309
$485$	0	0
$486$	236196.	0.0453609
$487$	3.11939e6	0.596002	0.298001	−	0.954566i	$-0.403680\pi$
$487$	3.11939e6	0.596002	0.298001	+	0.954566i	$0.403680\pi$
$488$	1.52205e6	0.289320
$489$	479124.	0.0906099
$490$	0	0
$491$	−3.00677e6	−0.562855	−0.281427	−	0.959583i	$-0.590808\pi$
$491$	−3.00677e6	−0.562855	−0.281427	+	0.959583i	$0.590808\pi$
$492$	1.34237e6	0.250011
$493$	−1.07310e6	−0.198849
$494$	−437760.	−0.0807084
$495$	0	0
$496$	−1.11309e6	−0.203154
$497$	2.41923e6	0.439325
$498$	−2.28110e6	−0.412166
$499$	−226500.	−0.0407209	−0.0203604	−	0.999793i	$-0.506481\pi$
$499$	−226500.	−0.0407209	−0.0203604	+	0.999793i	$0.506481\pi$
$500$	0	0
$501$	1.67357e6	0.297885
$502$	−6.12523e6	−1.08483
$503$	−2.06918e6	−0.364652	−0.182326	−	0.983238i	$-0.558363\pi$
$503$	−2.06918e6	−0.364652	−0.182326	+	0.983238i	$0.558363\pi$
$504$	254016.	0.0445435
$505$	0	0
$506$	1.41005e6	0.244826
$507$	−3.22467e6	−0.557142
$508$	3.37779e6	0.580729
$509$	−978610.	−0.167423	−0.0837115	−	0.996490i	$-0.526677\pi$
$509$	−978610.	−0.167423	−0.0837115	+	0.996490i	$0.526677\pi$
$510$	0	0
$511$	1.17531e6	0.199114
$512$	262144.	0.0441942
$513$	699840.	0.117410
$514$	−2.81111e6	−0.469321
$515$	0	0
$516$	172224.	0.0284754
$517$	−5.67066e6	−0.933054
$518$	1.14503e6	0.187497
$519$	751914.	0.122532
$520$	0	0
$521$	−3.17380e6	−0.512254	−0.256127	−	0.966643i	$-0.582446\pi$
$521$	−3.17380e6	−0.512254	−0.256127	+	0.966643i	$0.582446\pi$
$522$	−340200.	−0.0546460
$523$	−1.22480e7	−1.95800	−0.979000	−	0.203862i	$-0.934651\pi$
$523$	−1.22480e7	−1.95800	−0.979000	+	0.203862i	$0.934651\pi$
$524$	1.04531e6	0.166310
$525$	0	0
$526$	−1.34762e6	−0.212374
$527$	−4.44366e6	−0.696970
$528$	626688.	0.0978288
$529$	−4.75673e6	−0.739042
$530$	0	0
$531$	2.29554e6	0.353304
$532$	752640.	0.115294
$533$	−1.06271e6	−0.162030
$534$	75240.0	0.0114181
$535$	0	0
$536$	−966912.	−0.145370
$537$	7.14204e6	1.06878
$538$	8.44812e6	1.25836
$539$	653072.	0.0968254
$540$	0	0
$541$	3.99742e6	0.587201	0.293601	−	0.955928i	$-0.405146\pi$
$541$	3.99742e6	0.587201	0.293601	+	0.955928i	$0.405146\pi$
$542$	−478992.	−0.0700374
$543$	−2.96548e6	−0.431614
$544$	1.04653e6	0.151619
$545$	0	0
$546$	−201096.	−0.0288683
$547$	−1.96799e6	−0.281225	−0.140613	−	0.990065i	$-0.544907\pi$
$547$	−1.96799e6	−0.281225	−0.140613	+	0.990065i	$0.544907\pi$
$548$	1.46755e6	0.208758
$549$	1.92634e6	0.272774
$550$	0	0
$551$	−1.00800e6	−0.141443
$552$	746496.	0.104275
$553$	2.46568e6	0.342866
$554$	428808.	0.0593593
$555$	0	0
$556$	3.72928e6	0.511609
$557$	1.10475e7	1.50878	0.754388	−	0.656429i	$-0.227934\pi$
$557$	1.10475e7	1.50878	0.754388	+	0.656429i	$0.227934\pi$
$558$	−1.40875e6	−0.191535
$559$	−136344.	−0.0184547
$560$	0	0
$561$	2.50186e6	0.335626
$562$	−8.45919e6	−1.12976
$563$	−1.03573e7	−1.37714	−0.688568	−	0.725172i	$-0.741760\pi$
$563$	−1.03573e7	−1.37714	−0.688568	+	0.725172i	$0.741760\pi$
$564$	−3.00211e6	−0.397401
$565$	0	0
$566$	−6.84450e6	−0.898050
$567$	321489.	0.0419961
$568$	3.15981e6	0.410951
$569$	−4.57575e6	−0.592491	−0.296245	−	0.955112i	$-0.595735\pi$
$569$	−4.57575e6	−0.592491	−0.296245	+	0.955112i	$0.595735\pi$
$570$	0	0
$571$	1.00453e7	1.28936	0.644680	−	0.764453i	$-0.276991\pi$
$571$	1.00453e7	1.28936	0.644680	+	0.764453i	$0.276991\pi$
$572$	−496128.	−0.0634021
$573$	−373572.	−0.0475322
$574$	1.82711e6	0.231465
$575$	0	0
$576$	331776.	0.0416667
$577$	−7.38072e6	−0.922909	−0.461455	−	0.887164i	$-0.652672\pi$
$577$	−7.38072e6	−0.922909	−0.461455	+	0.887164i	$0.652672\pi$
$578$	−1.50149e6	−0.186941
$579$	410814.	0.0509271
$580$	0	0
$581$	−3.10484e6	−0.381591
$582$	1.55815e6	0.190679
$583$	−7.69053e6	−0.937097
$584$	1.53510e6	0.186254
$585$	0	0
$586$	9.51546e6	1.14468
$587$	−1.05983e7	−1.26953	−0.634763	−	0.772707i	$-0.718902\pi$
$587$	−1.05983e7	−1.26953	−0.634763	+	0.772707i	$0.718902\pi$
$588$	345744.	0.0412393
$589$	−4.17408e6	−0.495761
$590$	0	0
$591$	1.67132e6	0.196830
$592$	1.49555e6	0.175387
$593$	−1.36804e7	−1.59757	−0.798786	−	0.601615i	$-0.794524\pi$
$593$	−1.36804e7	−1.59757	−0.798786	+	0.601615i	$0.794524\pi$
$594$	793152.	0.0922338
$595$	0	0
$596$	1.56912e6	0.180942
$597$	8.56350e6	0.983367
$598$	−590976.	−0.0675798
$599$	2.52474e6	0.287508	0.143754	−	0.989613i	$-0.454083\pi$
$599$	2.52474e6	0.287508	0.143754	+	0.989613i	$0.454083\pi$
$600$	0	0
$601$	1.12439e7	1.26979	0.634895	−	0.772599i	$-0.281044\pi$
$601$	1.12439e7	1.26979	0.634895	+	0.772599i	$0.281044\pi$
$602$	234416.	0.0263631
$603$	−1.22375e6	−0.137056
$604$	−233728.	−0.0260686
$605$	0	0
$606$	2.82895e6	0.312928
$607$	−1.80330e7	−1.98653	−0.993266	−	0.115858i	$-0.963038\pi$
$607$	−1.80330e7	−1.98653	−0.993266	+	0.115858i	$0.963038\pi$
$608$	983040.	0.107848
$609$	−463050.	−0.0505923
$610$	0	0
$611$	2.37667e6	0.257553
$612$	1.32451e6	0.142948
$613$	−1.00535e7	−1.08061	−0.540303	−	0.841470i	$-0.681690\pi$
$613$	−1.00535e7	−1.08061	−0.540303	+	0.841470i	$0.681690\pi$
$614$	16688.0	0.00178642
$615$	0	0
$616$	852992.	0.0905718
$617$	4.54104e6	0.480223	0.240111	−	0.970745i	$-0.422816\pi$
$617$	4.54104e6	0.480223	0.240111	+	0.970745i	$0.422816\pi$
$618$	261216.	0.0275124
$619$	4.14068e6	0.434355	0.217178	−	0.976132i	$-0.430315\pi$
$619$	4.14068e6	0.434355	0.217178	+	0.976132i	$0.430315\pi$
$620$	0	0
$621$	944784.	0.0983113
$622$	750048.	0.0777344
$623$	102410.	0.0105712
$624$	−262656.	−0.0270039
$625$	0	0
$626$	7.51530e6	0.766497
$627$	2.35008e6	0.238734
$628$	−2.98845e6	−0.302375
$629$	5.97052e6	0.601708
$630$	0	0
$631$	−1.06700e7	−1.06682	−0.533410	−	0.845857i	$-0.679090\pi$
$631$	−1.06700e7	−1.06682	−0.533410	+	0.845857i	$0.679090\pi$
$632$	3.22048e6	0.320721
$633$	−1.00219e7	−0.994128
$634$	−1.48791e6	−0.147012
$635$	0	0
$636$	−4.07146e6	−0.399123
$637$	−273714.	−0.0267269
$638$	−1.14240e6	−0.111113
$639$	3.99913e6	0.387448
$640$	0	0
$641$	−3.89020e6	−0.373961	−0.186981	−	0.982364i	$-0.559870\pi$
$641$	−3.89020e6	−0.373961	−0.186981	+	0.982364i	$0.559870\pi$
$642$	−6.74741e6	−0.646099
$643$	−275764.	−0.0263033	−0.0131516	−	0.999914i	$-0.504186\pi$
$643$	−275764.	−0.0263033	−0.0131516	+	0.999914i	$0.504186\pi$
$644$	1.01606e6	0.0965398
$645$	0	0
$646$	3.92448e6	0.369999
$647$	1.33170e7	1.25068	0.625339	−	0.780353i	$-0.284961\pi$
$647$	1.33170e7	1.25068	0.625339	+	0.780353i	$0.284961\pi$
$648$	419904.	0.0392837
$649$	7.70848e6	0.718385
$650$	0	0
$651$	−1.91747e6	−0.177327
$652$	851776.	0.0784705
$653$	−1.26550e7	−1.16139	−0.580696	−	0.814120i	$-0.697220\pi$
$653$	−1.26550e7	−1.16139	−0.580696	+	0.814120i	$0.697220\pi$
$654$	3.19788e6	0.292360
$655$	0	0
$656$	2.38643e6	0.216516
$657$	1.94287e6	0.175602
$658$	−4.08621e6	−0.367922
$659$	−2.06776e6	−0.185476	−0.0927378	−	0.995691i	$-0.529562\pi$
$659$	−2.06776e6	−0.185476	−0.0927378	+	0.995691i	$0.529562\pi$
$660$	0	0
$661$	−7.69666e6	−0.685170	−0.342585	−	0.939487i	$-0.611303\pi$
$661$	−7.69666e6	−0.685170	−0.342585	+	0.939487i	$0.611303\pi$
$662$	7.32453e6	0.649583
$663$	−1.04857e6	−0.0926434
$664$	−4.05530e6	−0.356946
$665$	0	0
$666$	1.89281e6	0.165356
$667$	−1.36080e6	−0.118435
$668$	2.97523e6	0.257976
$669$	−3.06886e6	−0.265101
$670$	0	0
$671$	6.46870e6	0.554640
$672$	451584.	0.0385758
$673$	6.09921e6	0.519082	0.259541	−	0.965732i	$-0.416429\pi$
$673$	6.09921e6	0.519082	0.259541	+	0.965732i	$0.416429\pi$
$674$	−1.62503e6	−0.137788
$675$	0	0
$676$	−5.73275e6	−0.482499
$677$	1.23234e7	1.03338	0.516690	−	0.856172i	$-0.327164\pi$
$677$	1.23234e7	1.03338	0.516690	+	0.856172i	$0.327164\pi$
$678$	2.20414e6	0.184147
$679$	2.12082e6	0.176534
$680$	0	0
$681$	−2.83525e6	−0.234274
$682$	−4.73062e6	−0.389455
$683$	−4.16388e6	−0.341544	−0.170772	−	0.985311i	$-0.554626\pi$
$683$	−4.16388e6	−0.341544	−0.170772	+	0.985311i	$0.554626\pi$
$684$	1.24416e6	0.101680
$685$	0	0
$686$	470596.	0.0381802
$687$	8.39979e6	0.679011
$688$	306176.	0.0246604
$689$	3.22324e6	0.258669
$690$	0	0
$691$	−3.13225e6	−0.249552	−0.124776	−	0.992185i	$-0.539821\pi$
$691$	−3.13225e6	−0.249552	−0.124776	+	0.992185i	$0.539821\pi$
$692$	1.33674e6	0.106116
$693$	1.07957e6	0.0853919
$694$	1.72053e6	0.135601
$695$	0	0
$696$	−604800.	−0.0473248
$697$	9.52708e6	0.742811
$698$	−4.97252e6	−0.386312
$699$	−7.58965e6	−0.587528
$700$	0	0
$701$	−7.49430e6	−0.576018	−0.288009	−	0.957628i	$-0.592993\pi$
$701$	−7.49430e6	−0.576018	−0.288009	+	0.957628i	$0.592993\pi$
$702$	−332424.	−0.0254595
$703$	5.60832e6	0.428001
$704$	1.11411e6	0.0847222
$705$	0	0
$706$	−1.44814e6	−0.109345
$707$	3.85052e6	0.289715
$708$	4.08096e6	0.305970
$709$	−2.40760e7	−1.79874	−0.899371	−	0.437186i	$-0.855975\pi$
$709$	−2.40760e7	−1.79874	−0.899371	+	0.437186i	$0.855975\pi$
$710$	0	0
$711$	4.07592e6	0.302379
$712$	133760.	0.00988841
$713$	−5.63501e6	−0.415117
$714$	1.80281e6	0.132344
$715$	0	0
$716$	1.26970e7	0.925587
$717$	1.39214e7	1.01131
$718$	−1.37528e6	−0.0995589
$719$	1.75788e6	0.126814	0.0634070	−	0.997988i	$-0.479803\pi$
$719$	1.75788e6	0.126814	0.0634070	+	0.997988i	$0.479803\pi$
$720$	0	0
$721$	355544.	0.0254715
$722$	−6.21800e6	−0.443923
$723$	662778.	0.0471544
$724$	−5.27197e6	−0.373789
$725$	0	0
$726$	−3.13441e6	−0.220706
$727$	−4.65437e6	−0.326606	−0.163303	−	0.986576i	$-0.552215\pi$
$727$	−4.65437e6	−0.326606	−0.163303	+	0.986576i	$0.552215\pi$
$728$	−357504.	−0.0250007
$729$	531441.	0.0370370
$730$	0	0
$731$	1.22231e6	0.0846036
$732$	3.42461e6	0.236229
$733$	−4.60131e6	−0.316317	−0.158158	−	0.987414i	$-0.550556\pi$
$733$	−4.60131e6	−0.316317	−0.158158	+	0.987414i	$0.550556\pi$
$734$	−6.83075e6	−0.467981
$735$	0	0
$736$	1.32710e6	0.0903047
$737$	−4.10938e6	−0.278681
$738$	3.02033e6	0.204133
$739$	−2.82994e7	−1.90619	−0.953094	−	0.302674i	$-0.902121\pi$
$739$	−2.82994e7	−1.90619	−0.953094	+	0.302674i	$0.902121\pi$
$740$	0	0
$741$	−984960.	−0.0658981
$742$	−5.54170e6	−0.369516
$743$	−2.28144e7	−1.51613	−0.758067	−	0.652177i	$-0.773856\pi$
$743$	−2.28144e7	−1.51613	−0.758067	+	0.652177i	$0.773856\pi$
$744$	−2.50445e6	−0.165875
$745$	0	0
$746$	4.92138e6	0.323773
$747$	−5.13248e6	−0.336532
$748$	4.44774e6	0.290660
$749$	−9.18397e6	−0.598172
$750$	0	0
$751$	−1.00946e7	−0.653115	−0.326557	−	0.945177i	$-0.605889\pi$
$751$	−1.00946e7	−0.653115	−0.326557	+	0.945177i	$0.605889\pi$
$752$	−5.33709e6	−0.344160
$753$	−1.37818e7	−0.885763
$754$	478800.	0.0306708
$755$	0	0
$756$	571536.	0.0363696
$757$	1.59301e7	1.01037	0.505184	−	0.863012i	$-0.331425\pi$
$757$	1.59301e7	1.01037	0.505184	+	0.863012i	$0.331425\pi$
$758$	−9.96984e6	−0.630253
$759$	3.17261e6	0.199900
$760$	0	0
$761$	−1.67320e7	−1.04734	−0.523669	−	0.851922i	$-0.675437\pi$
$761$	−1.67320e7	−1.04734	−0.523669	+	0.851922i	$0.675437\pi$
$762$	7.60003e6	0.474163
$763$	4.35267e6	0.270673
$764$	−664128.	−0.0411641
$765$	0	0
$766$	4.70006e6	0.289422
$767$	−3.23076e6	−0.198297
$768$	589824.	0.0360844
$769$	−1.61242e7	−0.983243	−0.491622	−	0.870809i	$-0.663596\pi$
$769$	−1.61242e7	−0.983243	−0.491622	+	0.870809i	$0.663596\pi$
$770$	0	0
$771$	−6.32500e6	−0.383199
$772$	730336.	0.0441042
$773$	3.25255e6	0.195783	0.0978914	−	0.995197i	$-0.468790\pi$
$773$	3.25255e6	0.195783	0.0978914	+	0.995197i	$0.468790\pi$
$774$	387504.	0.0232500
$775$	0	0
$776$	2.77005e6	0.165133
$777$	2.57632e6	0.153090
$778$	−1.16378e7	−0.689322
$779$	8.94912e6	0.528368
$780$	0	0
$781$	1.34292e7	0.787811
$782$	5.29805e6	0.309813
$783$	−765450.	−0.0446182
$784$	614656.	0.0357143
$785$	0	0
$786$	2.35195e6	0.135791
$787$	3.08591e7	1.77601	0.888006	−	0.459832i	$-0.152091\pi$
$787$	3.08591e7	1.77601	0.888006	+	0.459832i	$0.152091\pi$
$788$	2.97123e6	0.170459
$789$	−3.03214e6	−0.173403
$790$	0	0
$791$	3.00007e6	0.170487
$792$	1.41005e6	0.0798769
$793$	−2.71115e6	−0.153098
$794$	−1.45415e6	−0.0818575
$795$	0	0
$796$	1.52240e7	0.851620
$797$	4.18180e6	0.233194	0.116597	−	0.993179i	$-0.462801\pi$
$797$	4.18180e6	0.233194	0.116597	+	0.993179i	$0.462801\pi$
$798$	1.69344e6	0.0941375
$799$	−2.13067e7	−1.18072
$800$	0	0
$801$	169290.	0.00932288
$802$	3.23329e6	0.177504
$803$	6.52419e6	0.357057
$804$	−2.17555e6	−0.118694
$805$	0	0
$806$	1.98269e6	0.107502
$807$	1.90083e7	1.02745
$808$	5.02925e6	0.271003
$809$	−2.08215e7	−1.11851	−0.559255	−	0.828996i	$-0.688913\pi$
$809$	−2.08215e7	−1.11851	−0.559255	+	0.828996i	$0.688913\pi$
$810$	0	0
$811$	−2.51593e7	−1.34322	−0.671609	−	0.740906i	$-0.734396\pi$
$811$	−2.51593e7	−1.34322	−0.671609	+	0.740906i	$0.734396\pi$
$812$	−823200.	−0.0438142
$813$	−1.07773e6	−0.0571853
$814$	6.35610e6	0.336225
$815$	0	0
$816$	2.35469e6	0.123796
$817$	1.14816e6	0.0601793
$818$	1.48266e7	0.774744
$819$	−452466.	−0.0235709
$820$	0	0
$821$	1.26600e7	0.655504	0.327752	−	0.944764i	$-0.393709\pi$
$821$	1.26600e7	0.655504	0.327752	+	0.944764i	$0.393709\pi$
$822$	3.30199e6	0.170450
$823$	−4.84854e6	−0.249524	−0.124762	−	0.992187i	$-0.539817\pi$
$823$	−4.84854e6	−0.249524	−0.124762	+	0.992187i	$0.539817\pi$
$824$	464384.	0.0238264
$825$	0	0
$826$	5.55464e6	0.283273
$827$	−1.50661e7	−0.766017	−0.383009	−	0.923745i	$-0.625112\pi$
$827$	−1.50661e7	−0.766017	−0.383009	+	0.923745i	$0.625112\pi$
$828$	1.67962e6	0.0851401
$829$	−2.73320e7	−1.38129	−0.690647	−	0.723192i	$-0.742674\pi$
$829$	−2.73320e7	−1.38129	−0.690647	+	0.723192i	$0.742674\pi$
$830$	0	0
$831$	964818.	0.0484666
$832$	−466944.	−0.0233860
$833$	2.45382e6	0.122527
$834$	8.39088e6	0.417727
$835$	0	0
$836$	4.17792e6	0.206749
$837$	−3.16969e6	−0.156388
$838$	1.28714e7	0.633165
$839$	3.87448e7	1.90024	0.950120	−	0.311884i	$-0.100960\pi$
$839$	3.87448e7	1.90024	0.950120	+	0.311884i	$0.100960\pi$
$840$	0	0
$841$	−1.94086e7	−0.946249
$842$	−1.22364e7	−0.594803
$843$	−1.90332e7	−0.922449
$844$	−1.78168e7	−0.860940
$845$	0	0
$846$	−6.75475e6	−0.324477
$847$	−4.26628e6	−0.204334
$848$	−7.23814e6	−0.345651
$849$	−1.54001e7	−0.733255
$850$	0	0
$851$	7.57123e6	0.358379
$852$	7.10957e6	0.335540
$853$	−3.24391e6	−0.152650	−0.0763250	−	0.997083i	$-0.524319\pi$
$853$	−3.24391e6	−0.152650	−0.0763250	+	0.997083i	$0.524319\pi$
$854$	4.66127e6	0.218706
$855$	0	0
$856$	−1.19954e7	−0.559539
$857$	5.56318e6	0.258745	0.129372	−	0.991596i	$-0.458704\pi$
$857$	5.56318e6	0.258745	0.129372	+	0.991596i	$0.458704\pi$
$858$	−1.11629e6	−0.0517676
$859$	−3.27631e7	−1.51496	−0.757482	−	0.652856i	$-0.773571\pi$
$859$	−3.27631e7	−1.51496	−0.757482	+	0.652856i	$0.773571\pi$
$860$	0	0
$861$	4.11100e6	0.188990
$862$	−1.42113e7	−0.651427
$863$	−2.48499e7	−1.13579	−0.567896	−	0.823101i	$-0.692242\pi$
$863$	−2.48499e7	−1.13579	−0.567896	+	0.823101i	$0.692242\pi$
$864$	746496.	0.0340207
$865$	0	0
$866$	−7.87686e6	−0.356910
$867$	−3.37836e6	−0.152636
$868$	−3.40883e6	−0.153570
$869$	1.36870e7	0.614837
$870$	0	0
$871$	1.72231e6	0.0769248
$872$	5.68512e6	0.253191
$873$	3.50584e6	0.155689
$874$	4.97664e6	0.220373
$875$	0	0
$876$	3.45398e6	0.152076
$877$	−1.75976e7	−0.772598	−0.386299	−	0.922374i	$-0.626247\pi$
$877$	−1.75976e7	−0.772598	−0.386299	+	0.922374i	$0.626247\pi$
$878$	7.70200e6	0.337184
$879$	2.14098e7	0.934631
$880$	0	0
$881$	2.07548e7	0.900905	0.450452	−	0.892800i	$-0.351263\pi$
$881$	2.07548e7	0.900905	0.450452	+	0.892800i	$0.351263\pi$
$882$	777924.	0.0336718
$883$	8.54944e6	0.369008	0.184504	−	0.982832i	$-0.440932\pi$
$883$	8.54944e6	0.369008	0.184504	+	0.982832i	$0.440932\pi$
$884$	−1.86413e6	−0.0802315
$885$	0	0
$886$	2.89361e7	1.23839
$887$	−8.69289e6	−0.370984	−0.185492	−	0.982646i	$-0.559388\pi$
$887$	−8.69289e6	−0.370984	−0.185492	+	0.982646i	$0.559388\pi$
$888$	3.36499e6	0.143203
$889$	1.03445e7	0.438990
$890$	0	0
$891$	1.78459e6	0.0753086
$892$	−5.45574e6	−0.229584
$893$	−2.00141e7	−0.839860
$894$	3.53052e6	0.147739
$895$	0	0
$896$	802816.	0.0334077
$897$	−1.32970e6	−0.0551787
$898$	1.25844e6	0.0520765
$899$	4.56540e6	0.188399
$900$	0	0
$901$	−2.88960e7	−1.18584
$902$	1.01423e7	0.415070
$903$	527436.	0.0215254
$904$	3.91846e6	0.159476
$905$	0	0
$906$	−525888.	−0.0212850
$907$	−3.55677e7	−1.43561	−0.717807	−	0.696242i	$-0.754854\pi$
$907$	−3.55677e7	−1.43561	−0.717807	+	0.696242i	$0.754854\pi$
$908$	−5.04045e6	−0.202887
$909$	6.36514e6	0.255504
$910$	0	0
$911$	−5.23727e6	−0.209078	−0.104539	−	0.994521i	$-0.533337\pi$
$911$	−5.23727e6	−0.209078	−0.104539	+	0.994521i	$0.533337\pi$
$912$	2.21184e6	0.0880576
$913$	−1.72350e7	−0.684281
$914$	−6.03143e6	−0.238811
$915$	0	0
$916$	1.49330e7	0.588040
$917$	3.20127e6	0.125718
$918$	2.98015e6	0.116716
$919$	−4.29864e7	−1.67897	−0.839485	−	0.543384i	$-0.817143\pi$
$919$	−4.29864e7	−1.67897	−0.839485	+	0.543384i	$0.817143\pi$
$920$	0	0
$921$	37548.0	0.00145861
$922$	−3.33732e7	−1.29292
$923$	−5.62841e6	−0.217461
$924$	1.91923e6	0.0739516
$925$	0	0
$926$	2.55692e7	0.979917
$927$	587736.	0.0224638
$928$	−1.07520e6	−0.0409845
$929$	−2.09911e7	−0.797986	−0.398993	−	0.916954i	$-0.630640\pi$
$929$	−2.09911e7	−0.797986	−0.398993	+	0.916954i	$0.630640\pi$
$930$	0	0
$931$	2.30496e6	0.0871544
$932$	−1.34927e7	−0.508814
$933$	1.68761e6	0.0634698
$934$	−8.16827e6	−0.306382
$935$	0	0
$936$	−590976.	−0.0220486
$937$	−2.98362e7	−1.11018	−0.555092	−	0.831789i	$-0.687317\pi$
$937$	−2.98362e7	−1.11018	−0.555092	+	0.831789i	$0.687317\pi$
$938$	−2.96117e6	−0.109889
$939$	1.69094e7	0.625843
$940$	0	0
$941$	1.51948e7	0.559397	0.279699	−	0.960088i	$-0.409765\pi$
$941$	1.51948e7	0.559397	0.279699	+	0.960088i	$0.409765\pi$
$942$	−6.72401e6	−0.246889
$943$	1.20813e7	0.442420
$944$	7.25504e6	0.264978
$945$	0	0
$946$	1.30125e6	0.0472751
$947$	3.58035e7	1.29733	0.648666	−	0.761073i	$-0.275327\pi$
$947$	3.58035e7	1.29733	0.648666	+	0.761073i	$0.275327\pi$
$948$	7.24608e6	0.261868
$949$	−2.73440e6	−0.0985592
$950$	0	0
$951$	−3.34780e6	−0.120035
$952$	3.20499e6	0.114613
$953$	−3.36211e7	−1.19917	−0.599583	−	0.800313i	$-0.704667\pi$
$953$	−3.36211e7	−1.19917	−0.599583	+	0.800313i	$0.704667\pi$
$954$	−9.16078e6	−0.325883
$955$	0	0
$956$	2.47491e7	0.875820
$957$	−2.57040e6	−0.0907237
$958$	2.06611e7	0.727344
$959$	4.49438e6	0.157806
$960$	0	0
$961$	−9.72405e6	−0.339655
$962$	−2.66395e6	−0.0928087
$963$	−1.51817e7	−0.527538
$964$	1.17827e6	0.0408369
$965$	0	0
$966$	2.28614e6	0.0788244
$967$	−1.51482e7	−0.520947	−0.260474	−	0.965481i	$-0.583879\pi$
$967$	−1.51482e7	−0.520947	−0.260474	+	0.965481i	$0.583879\pi$
$968$	−5.57229e6	−0.191137
$969$	8.83008e6	0.302103
$970$	0	0
$971$	−2.55320e7	−0.869035	−0.434517	−	0.900663i	$-0.643081\pi$
$971$	−2.55320e7	−0.869035	−0.434517	+	0.900663i	$0.643081\pi$
$972$	944784.	0.0320750
$973$	1.14209e7	0.386740
$974$	1.24776e7	0.421437
$975$	0	0
$976$	6.08819e6	0.204580
$977$	−4.25088e7	−1.42476	−0.712380	−	0.701793i	$-0.752383\pi$
$977$	−4.25088e7	−1.42476	−0.712380	+	0.701793i	$0.752383\pi$
$978$	1.91650e6	0.0640709
$979$	568480.	0.0189565
$980$	0	0
$981$	7.19523e6	0.238711
$982$	−1.20271e7	−0.397998
$983$	3.55964e7	1.17496	0.587479	−	0.809240i	$-0.300121\pi$
$983$	3.55964e7	1.17496	0.587479	+	0.809240i	$0.300121\pi$
$984$	5.36947e6	0.176784
$985$	0	0
$986$	−4.29240e6	−0.140607
$987$	−9.19397e6	−0.300407
$988$	−1.75104e6	−0.0570695
$989$	1.55002e6	0.0503901
$990$	0	0
$991$	1.66468e7	0.538450	0.269225	−	0.963077i	$-0.413232\pi$
$991$	1.66468e7	0.538450	0.269225	+	0.963077i	$0.413232\pi$
$992$	−4.45235e6	−0.143652
$993$	1.64802e7	0.530382
$994$	9.67691e6	0.310650
$995$	0	0
$996$	−9.12442e6	−0.291445
$997$	−3.67375e7	−1.17050	−0.585250	−	0.810853i	$-0.699004\pi$
$997$	−3.67375e7	−1.17050	−0.585250	+	0.810853i	$0.699004\pi$
$998$	−906000.	−0.0287940
$999$	4.25882e6	0.135013

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.6.a.p.1.1		1
5.2	odd	4		1050.6.g.p.799.2		2
5.3	odd	4		1050.6.g.p.799.1		2
5.4	even	2		210.6.a.b.1.1	✓	1
15.14	odd	2		630.6.a.g.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.6.a.b.1.1	✓	1	5.4	even	2
630.6.a.g.1.1		1	15.14	odd	2
1050.6.a.p.1.1		1	1.1	even	1	trivial
1050.6.g.p.799.1		2	5.3	odd	4
1050.6.g.p.799.2		2	5.2	odd	4

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1050.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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