LMFDB - Embedded newform 1050.6.a.g.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 42)
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)

$f(q)$

$=$

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

\(q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -36.0000 q^{6} -49.0000 q^{7} +64.0000 q^{8} +81.0000 q^{9} -414.000 q^{11} -144.000 q^{12} +1054.00 q^{13} -196.000 q^{14} +256.000 q^{16} +1848.00 q^{17} +324.000 q^{18} +236.000 q^{19} +441.000 q^{21} -1656.00 q^{22} -2898.00 q^{23} -576.000 q^{24} +4216.00 q^{26} -729.000 q^{27} -784.000 q^{28} -6522.00 q^{29} +6200.00 q^{31} +1024.00 q^{32} +3726.00 q^{33} +7392.00 q^{34} +1296.00 q^{36} -9650.00 q^{37} +944.000 q^{38} -9486.00 q^{39} +8484.00 q^{41} +1764.00 q^{42} +10804.0 q^{43} -6624.00 q^{44} -11592.0 q^{46} -60.0000 q^{47} -2304.00 q^{48} +2401.00 q^{49} -16632.0 q^{51} +16864.0 q^{52} -22506.0 q^{53} -2916.00 q^{54} -3136.00 q^{56} -2124.00 q^{57} -26088.0 q^{58} -28176.0 q^{59} -35194.0 q^{61} +24800.0 q^{62} -3969.00 q^{63} +4096.00 q^{64} +14904.0 q^{66} +28216.0 q^{67} +29568.0 q^{68} +26082.0 q^{69} -6642.00 q^{71} +5184.00 q^{72} +52090.0 q^{73} -38600.0 q^{74} +3776.00 q^{76} +20286.0 q^{77} -37944.0 q^{78} +43340.0 q^{79} +6561.00 q^{81} +33936.0 q^{82} -25716.0 q^{83} +7056.00 q^{84} +43216.0 q^{86} +58698.0 q^{87} -26496.0 q^{88} +98724.0 q^{89} -51646.0 q^{91} -46368.0 q^{92} -55800.0 q^{93} -240.000 q^{94} -9216.00 q^{96} +148954. q^{97} +9604.00 q^{98} -33534.0 q^{99} +O(q^{100})\)

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
$11$	−414.000	−1.03162	−0.515809	−	0.856704i	$-0.672508\pi$
$11$	−414.000	−1.03162	−0.515809	+	0.856704i	$0.672508\pi$
$12$	−144.000	−0.288675
$13$	1054.00	1.72975	0.864873	−	0.501991i	$-0.167399\pi$
$13$	1054.00	1.72975	0.864873	+	0.501991i	$0.167399\pi$
$14$	−196.000	−0.267261
$15$	0	0
$16$	256.000	0.250000
$17$	1848.00	1.55089	0.775443	−	0.631418i	$-0.217527\pi$
$17$	1848.00	1.55089	0.775443	+	0.631418i	$0.217527\pi$
$18$	324.000	0.235702
$19$	236.000	0.149978	0.0749891	−	0.997184i	$-0.476108\pi$
$19$	236.000	0.149978	0.0749891	+	0.997184i	$0.476108\pi$
$20$	0	0
$21$	441.000	0.218218
$22$	−1656.00	−0.729464
$23$	−2898.00	−1.14230	−0.571148	−	0.820847i	$-0.693502\pi$
$23$	−2898.00	−1.14230	−0.571148	+	0.820847i	$0.693502\pi$
$24$	−576.000	−0.204124
$25$	0	0
$26$	4216.00	1.22311
$27$	−729.000	−0.192450
$28$	−784.000	−0.188982
$29$	−6522.00	−1.44008	−0.720039	−	0.693934i	$-0.755876\pi$
$29$	−6522.00	−1.44008	−0.720039	+	0.693934i	$0.755876\pi$
$30$	0	0
$31$	6200.00	1.15874	0.579372	−	0.815063i	$-0.303298\pi$
$31$	6200.00	1.15874	0.579372	+	0.815063i	$0.303298\pi$
$32$	1024.00	0.176777
$33$	3726.00	0.595605
$34$	7392.00	1.09664
$35$	0	0
$36$	1296.00	0.166667
$37$	−9650.00	−1.15884	−0.579419	−	0.815030i	$-0.696721\pi$
$37$	−9650.00	−1.15884	−0.579419	+	0.815030i	$0.696721\pi$
$38$	944.000	0.106051
$39$	−9486.00	−0.998669
$40$	0	0
$41$	8484.00	0.788208	0.394104	−	0.919066i	$-0.371055\pi$
$41$	8484.00	0.788208	0.394104	+	0.919066i	$0.371055\pi$
$42$	1764.00	0.154303
$43$	10804.0	0.891073	0.445537	−	0.895264i	$-0.353013\pi$
$43$	10804.0	0.891073	0.445537	+	0.895264i	$0.353013\pi$
$44$	−6624.00	−0.515809
$45$	0	0
$46$	−11592.0	−0.807725
$47$	−60.0000	−0.00396193	−0.00198096	−	0.999998i	$-0.500631\pi$
$47$	−60.0000	−0.00396193	−0.00198096	+	0.999998i	$0.500631\pi$
$48$	−2304.00	−0.144338
$49$	2401.00	0.142857
$50$	0	0
$51$	−16632.0	−0.895404
$52$	16864.0	0.864873
$53$	−22506.0	−1.10055	−0.550274	−	0.834984i	$-0.685477\pi$
$53$	−22506.0	−1.10055	−0.550274	+	0.834984i	$0.685477\pi$
$54$	−2916.00	−0.136083
$55$	0	0
$56$	−3136.00	−0.133631
$57$	−2124.00	−0.0865899
$58$	−26088.0	−1.01829
$59$	−28176.0	−1.05378	−0.526889	−	0.849934i	$-0.676642\pi$
$59$	−28176.0	−1.05378	−0.526889	+	0.849934i	$0.676642\pi$
$60$	0	0
$61$	−35194.0	−1.21100	−0.605500	−	0.795845i	$-0.707027\pi$
$61$	−35194.0	−1.21100	−0.605500	+	0.795845i	$0.707027\pi$
$62$	24800.0	0.819356
$63$	−3969.00	−0.125988
$64$	4096.00	0.125000
$65$	0	0
$66$	14904.0	0.421156
$67$	28216.0	0.767907	0.383953	−	0.923352i	$-0.374562\pi$
$67$	28216.0	0.767907	0.383953	+	0.923352i	$0.374562\pi$
$68$	29568.0	0.775443
$69$	26082.0	0.659505
$70$	0	0
$71$	−6642.00	−0.156370	−0.0781849	−	0.996939i	$-0.524912\pi$
$71$	−6642.00	−0.156370	−0.0781849	+	0.996939i	$0.524912\pi$
$72$	5184.00	0.117851
$73$	52090.0	1.14406	0.572028	−	0.820234i	$-0.306157\pi$
$73$	52090.0	1.14406	0.572028	+	0.820234i	$0.306157\pi$
$74$	−38600.0	−0.819423
$75$	0	0
$76$	3776.00	0.0749891
$77$	20286.0	0.389915
$78$	−37944.0	−0.706166
$79$	43340.0	0.781306	0.390653	−	0.920538i	$-0.372249\pi$
$79$	43340.0	0.781306	0.390653	+	0.920538i	$0.372249\pi$
$80$	0	0
$81$	6561.00	0.111111
$82$	33936.0	0.557347
$83$	−25716.0	−0.409740	−0.204870	−	0.978789i	$-0.565677\pi$
$83$	−25716.0	−0.409740	−0.204870	+	0.978789i	$0.565677\pi$
$84$	7056.00	0.109109
$85$	0	0
$86$	43216.0	0.630084
$87$	58698.0	0.831429
$88$	−26496.0	−0.364732
$89$	98724.0	1.32114	0.660568	−	0.750766i	$-0.270315\pi$
$89$	98724.0	1.32114	0.660568	+	0.750766i	$0.270315\pi$
$90$	0	0
$91$	−51646.0	−0.653782
$92$	−46368.0	−0.571148
$93$	−55800.0	−0.669001
$94$	−240.000	−0.00280151
$95$	0	0
$96$	−9216.00	−0.102062
$97$	148954.	1.60740	0.803698	−	0.595038i	$-0.202863\pi$
$97$	148954.	1.60740	0.803698	+	0.595038i	$0.202863\pi$
$98$	9604.00	0.101015
$99$	−33534.0	−0.343872
$100$	0	0
$101$	48348.0	0.471601	0.235801	−	0.971801i	$-0.424229\pi$
$101$	48348.0	0.471601	0.235801	+	0.971801i	$0.424229\pi$
$102$	−66528.0	−0.633146
$103$	183592.	1.70514	0.852571	−	0.522611i	$-0.175042\pi$
$103$	183592.	1.70514	0.852571	+	0.522611i	$0.175042\pi$
$104$	67456.0	0.611557
$105$	0	0
$106$	−90024.0	−0.778204
$107$	2238.00	0.0188973	0.00944867	−	0.999955i	$-0.496992\pi$
$107$	2238.00	0.0188973	0.00944867	+	0.999955i	$0.496992\pi$
$108$	−11664.0	−0.0962250
$109$	60158.0	0.484984	0.242492	−	0.970153i	$-0.422035\pi$
$109$	60158.0	0.484984	0.242492	+	0.970153i	$0.422035\pi$
$110$	0	0
$111$	86850.0	0.669056
$112$	−12544.0	−0.0944911
$113$	7014.00	0.0516737	0.0258369	−	0.999666i	$-0.491775\pi$
$113$	7014.00	0.0516737	0.0258369	+	0.999666i	$0.491775\pi$
$114$	−8496.00	−0.0612283
$115$	0	0
$116$	−104352.	−0.720039
$117$	85374.0	0.576582
$118$	−112704.	−0.745134
$119$	−90552.0	−0.586180
$120$	0	0
$121$	10345.0	0.0642343
$122$	−140776.	−0.856306
$123$	−76356.0	−0.455072
$124$	99200.0	0.579372
$125$	0	0
$126$	−15876.0	−0.0890871
$127$	1780.00	0.00979289	0.00489644	−	0.999988i	$-0.498441\pi$
$127$	1780.00	0.00979289	0.00489644	+	0.999988i	$0.498441\pi$
$128$	16384.0	0.0883883
$129$	−97236.0	−0.514461
$130$	0	0
$131$	−265140.	−1.34989	−0.674943	−	0.737870i	$-0.735832\pi$
$131$	−265140.	−1.34989	−0.674943	+	0.737870i	$0.735832\pi$
$132$	59616.0	0.297802
$133$	−11564.0	−0.0566864
$134$	112864.	0.542992
$135$	0	0
$136$	118272.	0.548321
$137$	206730.	0.941027	0.470514	−	0.882393i	$-0.344069\pi$
$137$	206730.	0.941027	0.470514	+	0.882393i	$0.344069\pi$
$138$	104328.	0.466341
$139$	−236836.	−1.03971	−0.519853	−	0.854256i	$-0.674013\pi$
$139$	−236836.	−1.03971	−0.519853	+	0.854256i	$0.674013\pi$
$140$	0	0
$141$	540.000	0.00228742
$142$	−26568.0	−0.110570
$143$	−436356.	−1.78444
$144$	20736.0	0.0833333
$145$	0	0
$146$	208360.	0.808970
$147$	−21609.0	−0.0824786
$148$	−154400.	−0.579419
$149$	473706.	1.74801	0.874004	−	0.485919i	$-0.161515\pi$
$149$	473706.	1.74801	0.874004	+	0.485919i	$0.161515\pi$
$150$	0	0
$151$	394952.	1.40962	0.704810	−	0.709396i	$-0.251032\pi$
$151$	394952.	1.40962	0.704810	+	0.709396i	$0.251032\pi$
$152$	15104.0	0.0530253
$153$	149688.	0.516962
$154$	81144.0	0.275711
$155$	0	0
$156$	−151776.	−0.499335
$157$	145090.	0.469773	0.234887	−	0.972023i	$-0.424528\pi$
$157$	145090.	0.469773	0.234887	+	0.972023i	$0.424528\pi$
$158$	173360.	0.552467
$159$	202554.	0.635401
$160$	0	0
$161$	142002.	0.431747
$162$	26244.0	0.0785674
$163$	−530480.	−1.56387	−0.781934	−	0.623361i	$-0.785767\pi$
$163$	−530480.	−1.56387	−0.781934	+	0.623361i	$0.785767\pi$
$164$	135744.	0.394104
$165$	0	0
$166$	−102864.	−0.289730
$167$	312348.	0.866658	0.433329	−	0.901236i	$-0.357339\pi$
$167$	312348.	0.866658	0.433329	+	0.901236i	$0.357339\pi$
$168$	28224.0	0.0771517
$169$	739623.	1.99202
$170$	0	0
$171$	19116.0	0.0499927
$172$	172864.	0.445537
$173$	75108.0	0.190797	0.0953984	−	0.995439i	$-0.469588\pi$
$173$	75108.0	0.190797	0.0953984	+	0.995439i	$0.469588\pi$
$174$	234792.	0.587909
$175$	0	0
$176$	−105984.	−0.257904
$177$	253584.	0.608399
$178$	394896.	0.934185
$179$	386718.	0.902115	0.451057	−	0.892495i	$-0.351047\pi$
$179$	386718.	0.902115	0.451057	+	0.892495i	$0.351047\pi$
$180$	0	0
$181$	−417598.	−0.947462	−0.473731	−	0.880669i	$-0.657093\pi$
$181$	−417598.	−0.947462	−0.473731	+	0.880669i	$0.657093\pi$
$182$	−206584.	−0.462294
$183$	316746.	0.699171
$184$	−185472.	−0.403863
$185$	0	0
$186$	−223200.	−0.473055
$187$	−765072.	−1.59992
$188$	−960.000	−0.00198096
$189$	35721.0	0.0727393
$190$	0	0
$191$	−988050.	−1.95973	−0.979863	−	0.199669i	$-0.936013\pi$
$191$	−988050.	−1.95973	−0.979863	+	0.199669i	$0.936013\pi$
$192$	−36864.0	−0.0721688
$193$	409258.	0.790868	0.395434	−	0.918494i	$-0.370594\pi$
$193$	409258.	0.790868	0.395434	+	0.918494i	$0.370594\pi$
$194$	595816.	1.13660
$195$	0	0
$196$	38416.0	0.0714286
$197$	922230.	1.69307	0.846533	−	0.532337i	$-0.178686\pi$
$197$	922230.	1.69307	0.846533	+	0.532337i	$0.178686\pi$
$198$	−134136.	−0.243155
$199$	189488.	0.339195	0.169597	−	0.985513i	$-0.445753\pi$
$199$	189488.	0.339195	0.169597	+	0.985513i	$0.445753\pi$
$200$	0	0
$201$	−253944.	−0.443351
$202$	193392.	0.333473
$203$	319578.	0.544298
$204$	−266112.	−0.447702
$205$	0	0
$206$	734368.	1.20572
$207$	−234738.	−0.380765
$208$	269824.	0.432436
$209$	−97704.0	−0.154720
$210$	0	0
$211$	−611380.	−0.945377	−0.472689	−	0.881230i	$-0.656716\pi$
$211$	−611380.	−0.945377	−0.472689	+	0.881230i	$0.656716\pi$
$212$	−360096.	−0.550274
$213$	59778.0	0.0902802
$214$	8952.00	0.0133624
$215$	0	0
$216$	−46656.0	−0.0680414
$217$	−303800.	−0.437964
$218$	240632.	0.342935
$219$	−468810.	−0.660521
$220$	0	0
$221$	1.94779e6	2.68264
$222$	347400.	0.473094
$223$	783256.	1.05473	0.527365	−	0.849639i	$-0.323180\pi$
$223$	783256.	1.05473	0.527365	+	0.849639i	$0.323180\pi$
$224$	−50176.0	−0.0668153
$225$	0	0
$226$	28056.0	0.0365388
$227$	−80712.0	−0.103962	−0.0519809	−	0.998648i	$-0.516553\pi$
$227$	−80712.0	−0.103962	−0.0519809	+	0.998648i	$0.516553\pi$
$228$	−33984.0	−0.0432950
$229$	152738.	0.192468	0.0962340	−	0.995359i	$-0.469320\pi$
$229$	152738.	0.192468	0.0962340	+	0.995359i	$0.469320\pi$
$230$	0	0
$231$	−182574.	−0.225117
$232$	−417408.	−0.509144
$233$	354282.	0.427523	0.213761	−	0.976886i	$-0.431428\pi$
$233$	354282.	0.427523	0.213761	+	0.976886i	$0.431428\pi$
$234$	341496.	0.407705
$235$	0	0
$236$	−450816.	−0.526889
$237$	−390060.	−0.451087
$238$	−362208.	−0.414492
$239$	275370.	0.311833	0.155916	−	0.987770i	$-0.450167\pi$
$239$	275370.	0.311833	0.155916	+	0.987770i	$0.450167\pi$
$240$	0	0
$241$	−584698.	−0.648469	−0.324234	−	0.945977i	$-0.605107\pi$
$241$	−584698.	−0.648469	−0.324234	+	0.945977i	$0.605107\pi$
$242$	41380.0	0.0454205
$243$	−59049.0	−0.0641500
$244$	−563104.	−0.605500
$245$	0	0
$246$	−305424.	−0.321785
$247$	248744.	0.259424
$248$	396800.	0.409678
$249$	231444.	0.236563
$250$	0	0
$251$	−184752.	−0.185099	−0.0925497	−	0.995708i	$-0.529502\pi$
$251$	−184752.	−0.185099	−0.0925497	+	0.995708i	$0.529502\pi$
$252$	−63504.0	−0.0629941
$253$	1.19977e6	1.17841
$254$	7120.00	0.00692462
$255$	0	0
$256$	65536.0	0.0625000
$257$	−235980.	−0.222865	−0.111433	−	0.993772i	$-0.535544\pi$
$257$	−235980.	−0.222865	−0.111433	+	0.993772i	$0.535544\pi$
$258$	−388944.	−0.363779
$259$	472850.	0.438000
$260$	0	0
$261$	−528282.	−0.480026
$262$	−1.06056e6	−0.954513
$263$	244494.	0.217961	0.108981	−	0.994044i	$-0.465241\pi$
$263$	244494.	0.217961	0.108981	+	0.994044i	$0.465241\pi$
$264$	238464.	0.210578
$265$	0	0
$266$	−46256.0	−0.0400833
$267$	−888516.	−0.762759
$268$	451456.	0.383953
$269$	1.52779e6	1.28731	0.643656	−	0.765315i	$-0.277417\pi$
$269$	1.52779e6	1.28731	0.643656	+	0.765315i	$0.277417\pi$
$270$	0	0
$271$	2.07056e6	1.71263	0.856317	−	0.516450i	$-0.172747\pi$
$271$	2.07056e6	1.71263	0.856317	+	0.516450i	$0.172747\pi$
$272$	473088.	0.387721
$273$	464814.	0.377461
$274$	826920.	0.665407
$275$	0	0
$276$	417312.	0.329753
$277$	2.40727e6	1.88506	0.942530	−	0.334120i	$-0.108439\pi$
$277$	2.40727e6	1.88506	0.942530	+	0.334120i	$0.108439\pi$
$278$	−947344.	−0.735183
$279$	502200.	0.386248
$280$	0	0
$281$	341886.	0.258295	0.129147	−	0.991625i	$-0.458776\pi$
$281$	341886.	0.258295	0.129147	+	0.991625i	$0.458776\pi$
$282$	2160.00	0.00161745
$283$	−578564.	−0.429423	−0.214712	−	0.976678i	$-0.568881\pi$
$283$	−578564.	−0.429423	−0.214712	+	0.976678i	$0.568881\pi$
$284$	−106272.	−0.0781849
$285$	0	0
$286$	−1.74542e6	−1.26179
$287$	−415716.	−0.297915
$288$	82944.0	0.0589256
$289$	1.99525e6	1.40525
$290$	0	0
$291$	−1.34059e6	−0.928030
$292$	833440.	0.572028
$293$	−780540.	−0.531161	−0.265580	−	0.964089i	$-0.585564\pi$
$293$	−780540.	−0.531161	−0.265580	+	0.964089i	$0.585564\pi$
$294$	−86436.0	−0.0583212
$295$	0	0
$296$	−617600.	−0.409711
$297$	301806.	0.198535
$298$	1.89482e6	1.23603
$299$	−3.05449e6	−1.97588
$300$	0	0
$301$	−529396.	−0.336794
$302$	1.57981e6	0.996752
$303$	−435132.	−0.272279
$304$	60416.0	0.0374945
$305$	0	0
$306$	598752.	0.365547
$307$	2.24825e6	1.36144	0.680721	−	0.732543i	$-0.261667\pi$
$307$	2.24825e6	1.36144	0.680721	+	0.732543i	$0.261667\pi$
$308$	324576.	0.194957
$309$	−1.65233e6	−0.984465
$310$	0	0
$311$	581412.	0.340865	0.170433	−	0.985369i	$-0.445483\pi$
$311$	581412.	0.340865	0.170433	+	0.985369i	$0.445483\pi$
$312$	−607104.	−0.353083
$313$	2.00407e6	1.15625	0.578125	−	0.815948i	$-0.303784\pi$
$313$	2.00407e6	1.15625	0.578125	+	0.815948i	$0.303784\pi$
$314$	580360.	0.332180
$315$	0	0
$316$	693440.	0.390653
$317$	1.27832e6	0.714481	0.357241	−	0.934012i	$-0.383718\pi$
$317$	1.27832e6	0.714481	0.357241	+	0.934012i	$0.383718\pi$
$318$	810216.	0.449296
$319$	2.70011e6	1.48561
$320$	0	0
$321$	−20142.0	−0.0109104
$322$	568008.	0.305292
$323$	436128.	0.232599
$324$	104976.	0.0555556
$325$	0	0
$326$	−2.12192e6	−1.10582
$327$	−541422.	−0.280005
$328$	542976.	0.278674
$329$	2940.00	0.00149747
$330$	0	0
$331$	2.59812e6	1.30343	0.651716	−	0.758463i	$-0.274049\pi$
$331$	2.59812e6	1.30343	0.651716	+	0.758463i	$0.274049\pi$
$332$	−411456.	−0.204870
$333$	−781650.	−0.386280
$334$	1.24939e6	0.612819
$335$	0	0
$336$	112896.	0.0545545
$337$	−3.06190e6	−1.46864	−0.734321	−	0.678802i	$-0.762499\pi$
$337$	−3.06190e6	−1.46864	−0.734321	+	0.678802i	$0.762499\pi$
$338$	2.95849e6	1.40857
$339$	−63126.0	−0.0298338
$340$	0	0
$341$	−2.56680e6	−1.19538
$342$	76464.0	0.0353502
$343$	−117649.	−0.0539949
$344$	691456.	0.315042
$345$	0	0
$346$	300432.	0.134914
$347$	1.42550e6	0.635540	0.317770	−	0.948168i	$-0.397066\pi$
$347$	1.42550e6	0.635540	0.317770	+	0.948168i	$0.397066\pi$
$348$	939168.	0.415715
$349$	2.93322e6	1.28908	0.644542	−	0.764569i	$-0.277048\pi$
$349$	2.93322e6	1.28908	0.644542	+	0.764569i	$0.277048\pi$
$350$	0	0
$351$	−768366.	−0.332890
$352$	−423936.	−0.182366
$353$	2.01276e6	0.859716	0.429858	−	0.902896i	$-0.358564\pi$
$353$	2.01276e6	0.859716	0.429858	+	0.902896i	$0.358564\pi$
$354$	1.01434e6	0.430203
$355$	0	0
$356$	1.57958e6	0.660568
$357$	814968.	0.338431
$358$	1.54687e6	0.637891
$359$	4.07710e6	1.66961	0.834806	−	0.550545i	$-0.185580\pi$
$359$	4.07710e6	1.66961	0.834806	+	0.550545i	$0.185580\pi$
$360$	0	0
$361$	−2.42040e6	−0.977507
$362$	−1.67039e6	−0.669957
$363$	−93105.0	−0.0370857
$364$	−826336.	−0.326891
$365$	0	0
$366$	1.26698e6	0.494389
$367$	−594752.	−0.230500	−0.115250	−	0.993337i	$-0.536767\pi$
$367$	−594752.	−0.230500	−0.115250	+	0.993337i	$0.536767\pi$
$368$	−741888.	−0.285574
$369$	687204.	0.262736
$370$	0	0
$371$	1.10279e6	0.415968
$372$	−892800.	−0.334501
$373$	−2.04522e6	−0.761147	−0.380573	−	0.924751i	$-0.624273\pi$
$373$	−2.04522e6	−0.761147	−0.380573	+	0.924751i	$0.624273\pi$
$374$	−3.06029e6	−1.13131
$375$	0	0
$376$	−3840.00	−0.00140075
$377$	−6.87419e6	−2.49097
$378$	142884.	0.0514344
$379$	−3.22198e6	−1.15219	−0.576096	−	0.817382i	$-0.695425\pi$
$379$	−3.22198e6	−1.15219	−0.576096	+	0.817382i	$0.695425\pi$
$380$	0	0
$381$	−16020.0	−0.00565393
$382$	−3.95220e6	−1.38574
$383$	1.72966e6	0.602508	0.301254	−	0.953544i	$-0.402595\pi$
$383$	1.72966e6	0.602508	0.301254	+	0.953544i	$0.402595\pi$
$384$	−147456.	−0.0510310
$385$	0	0
$386$	1.63703e6	0.559228
$387$	875124.	0.297024
$388$	2.38326e6	0.803698
$389$	−1.74919e6	−0.586087	−0.293043	−	0.956099i	$-0.594668\pi$
$389$	−1.74919e6	−0.586087	−0.293043	+	0.956099i	$0.594668\pi$
$390$	0	0
$391$	−5.35550e6	−1.77157
$392$	153664.	0.0505076
$393$	2.38626e6	0.779357
$394$	3.68892e6	1.19718
$395$	0	0
$396$	−536544.	−0.171936
$397$	−1.88205e6	−0.599313	−0.299657	−	0.954047i	$-0.596872\pi$
$397$	−1.88205e6	−0.599313	−0.299657	+	0.954047i	$0.596872\pi$
$398$	757952.	0.239847
$399$	104076.	0.0327279
$400$	0	0
$401$	4.18124e6	1.29851	0.649253	−	0.760573i	$-0.275082\pi$
$401$	4.18124e6	1.29851	0.649253	+	0.760573i	$0.275082\pi$
$402$	−1.01578e6	−0.313497
$403$	6.53480e6	2.00433
$404$	773568.	0.235801
$405$	0	0
$406$	1.27831e6	0.384877
$407$	3.99510e6	1.19548
$408$	−1.06445e6	−0.316573
$409$	−471682.	−0.139425	−0.0697126	−	0.997567i	$-0.522208\pi$
$409$	−471682.	−0.139425	−0.0697126	+	0.997567i	$0.522208\pi$
$410$	0	0
$411$	−1.86057e6	−0.543302
$412$	2.93747e6	0.852571
$413$	1.38062e6	0.398291
$414$	−938952.	−0.269242
$415$	0	0
$416$	1.07930e6	0.305779
$417$	2.13152e6	0.600275
$418$	−390816.	−0.109404
$419$	−3.54094e6	−0.985333	−0.492666	−	0.870218i	$-0.663978\pi$
$419$	−3.54094e6	−0.985333	−0.492666	+	0.870218i	$0.663978\pi$
$420$	0	0
$421$	2.72763e6	0.750032	0.375016	−	0.927018i	$-0.377637\pi$
$421$	2.72763e6	0.750032	0.375016	+	0.927018i	$0.377637\pi$
$422$	−2.44552e6	−0.668483
$423$	−4860.00	−0.00132064
$424$	−1.44038e6	−0.389102
$425$	0	0
$426$	239112.	0.0638377
$427$	1.72451e6	0.457715
$428$	35808.0	0.00944867
$429$	3.92720e6	1.03024
$430$	0	0
$431$	−4.76517e6	−1.23562	−0.617810	−	0.786327i	$-0.711980\pi$
$431$	−4.76517e6	−1.23562	−0.617810	+	0.786327i	$0.711980\pi$
$432$	−186624.	−0.0481125
$433$	−6.90300e6	−1.76937	−0.884684	−	0.466191i	$-0.845626\pi$
$433$	−6.90300e6	−1.76937	−0.884684	+	0.466191i	$0.845626\pi$
$434$	−1.21520e6	−0.309687
$435$	0	0
$436$	962528.	0.242492
$437$	−683928.	−0.171319
$438$	−1.87524e6	−0.467059
$439$	5.40126e6	1.33762	0.668811	−	0.743432i	$-0.266803\pi$
$439$	5.40126e6	1.33762	0.668811	+	0.743432i	$0.266803\pi$
$440$	0	0
$441$	194481.	0.0476190
$442$	7.79117e6	1.89691
$443$	4.05863e6	0.982586	0.491293	−	0.870994i	$-0.336524\pi$
$443$	4.05863e6	0.982586	0.491293	+	0.870994i	$0.336524\pi$
$444$	1.38960e6	0.334528
$445$	0	0
$446$	3.13302e6	0.745807
$447$	−4.26335e6	−1.00921
$448$	−200704.	−0.0472456
$449$	212994.	0.0498599	0.0249300	−	0.999689i	$-0.492064\pi$
$449$	212994.	0.0498599	0.0249300	+	0.999689i	$0.492064\pi$
$450$	0	0
$451$	−3.51238e6	−0.813129
$452$	112224.	0.0258369
$453$	−3.55457e6	−0.813844
$454$	−322848.	−0.0735120
$455$	0	0
$456$	−135936.	−0.0306142
$457$	916150.	0.205199	0.102600	−	0.994723i	$-0.467284\pi$
$457$	916150.	0.205199	0.102600	+	0.994723i	$0.467284\pi$
$458$	610952.	0.136095
$459$	−1.34719e6	−0.298468
$460$	0	0
$461$	−4.15835e6	−0.911315	−0.455657	−	0.890155i	$-0.650596\pi$
$461$	−4.15835e6	−0.911315	−0.455657	+	0.890155i	$0.650596\pi$
$462$	−730296.	−0.159182
$463$	−8.40799e6	−1.82280	−0.911401	−	0.411519i	$-0.864998\pi$
$463$	−8.40799e6	−1.82280	−0.911401	+	0.411519i	$0.864998\pi$
$464$	−1.66963e6	−0.360019
$465$	0	0
$466$	1.41713e6	0.302304
$467$	−72048.0	−0.0152873	−0.00764363	−	0.999971i	$-0.502433\pi$
$467$	−72048.0	−0.0152873	−0.00764363	+	0.999971i	$0.502433\pi$
$468$	1.36598e6	0.288291
$469$	−1.38258e6	−0.290241
$470$	0	0
$471$	−1.30581e6	−0.271224
$472$	−1.80326e6	−0.372567
$473$	−4.47286e6	−0.919247
$474$	−1.56024e6	−0.318967
$475$	0	0
$476$	−1.44883e6	−0.293090
$477$	−1.82299e6	−0.366849
$478$	1.10148e6	0.220499
$479$	4.80560e6	0.956994	0.478497	−	0.878089i	$-0.341182\pi$
$479$	4.80560e6	0.956994	0.478497	+	0.878089i	$0.341182\pi$
$480$	0	0
$481$	−1.01711e7	−2.00450
$482$	−2.33879e6	−0.458537
$483$	−1.27802e6	−0.249270
$484$	165520.	0.0321172
$485$	0	0
$486$	−236196.	−0.0453609
$487$	−4.41805e6	−0.844127	−0.422064	−	0.906566i	$-0.638694\pi$
$487$	−4.41805e6	−0.844127	−0.422064	+	0.906566i	$0.638694\pi$
$488$	−2.25242e6	−0.428153
$489$	4.77432e6	0.902899
$490$	0	0
$491$	−5.64998e6	−1.05765	−0.528826	−	0.848730i	$-0.677368\pi$
$491$	−5.64998e6	−1.05765	−0.528826	+	0.848730i	$0.677368\pi$
$492$	−1.22170e6	−0.227536
$493$	−1.20527e7	−2.23339
$494$	994976.	0.183441
$495$	0	0
$496$	1.58720e6	0.289686
$497$	325458.	0.0591022
$498$	925776.	0.167276
$499$	−9.22344e6	−1.65822	−0.829109	−	0.559087i	$-0.811152\pi$
$499$	−9.22344e6	−1.65822	−0.829109	+	0.559087i	$0.811152\pi$
$500$	0	0
$501$	−2.81113e6	−0.500365
$502$	−739008.	−0.130885
$503$	−1.45562e6	−0.256525	−0.128262	−	0.991740i	$-0.540940\pi$
$503$	−1.45562e6	−0.256525	−0.128262	+	0.991740i	$0.540940\pi$
$504$	−254016.	−0.0445435
$505$	0	0
$506$	4.79909e6	0.833264
$507$	−6.65661e6	−1.15009
$508$	28480.0	0.00489644
$509$	−367344.	−0.0628461	−0.0314231	−	0.999506i	$-0.510004\pi$
$509$	−367344.	−0.0628461	−0.0314231	+	0.999506i	$0.510004\pi$
$510$	0	0
$511$	−2.55241e6	−0.432412
$512$	262144.	0.0441942
$513$	−172044.	−0.0288633
$514$	−943920.	−0.157590
$515$	0	0
$516$	−1.55578e6	−0.257231
$517$	24840.0	0.00408719
$518$	1.89140e6	0.309713
$519$	−675972.	−0.110157
$520$	0	0
$521$	5.76362e6	0.930254	0.465127	−	0.885244i	$-0.346009\pi$
$521$	5.76362e6	0.930254	0.465127	+	0.885244i	$0.346009\pi$
$522$	−2.11313e6	−0.339429
$523$	−235100.	−0.0375836	−0.0187918	−	0.999823i	$-0.505982\pi$
$523$	−235100.	−0.0375836	−0.0187918	+	0.999823i	$0.505982\pi$
$524$	−4.24224e6	−0.674943
$525$	0	0
$526$	977976.	0.154122
$527$	1.14576e7	1.79708
$528$	953856.	0.148901
$529$	1.96206e6	0.304841
$530$	0	0
$531$	−2.28226e6	−0.351259
$532$	−185024.	−0.0283432
$533$	8.94214e6	1.36340
$534$	−3.55406e6	−0.539352
$535$	0	0
$536$	1.80582e6	0.271496
$537$	−3.48046e6	−0.520836
$538$	6.11117e6	0.910266
$539$	−994014.	−0.147374
$540$	0	0
$541$	109010.	0.0160130	0.00800651	−	0.999968i	$-0.497451\pi$
$541$	109010.	0.0160130	0.00800651	+	0.999968i	$0.497451\pi$
$542$	8.28224e6	1.21102
$543$	3.75838e6	0.547018
$544$	1.89235e6	0.274160
$545$	0	0
$546$	1.85926e6	0.266906
$547$	−1.61953e6	−0.231430	−0.115715	−	0.993282i	$-0.536916\pi$
$547$	−1.61953e6	−0.231430	−0.115715	+	0.993282i	$0.536916\pi$
$548$	3.30768e6	0.470514
$549$	−2.85071e6	−0.403667
$550$	0	0
$551$	−1.53919e6	−0.215980
$552$	1.66925e6	0.233170
$553$	−2.12366e6	−0.295306
$554$	9.62908e6	1.33294
$555$	0	0
$556$	−3.78938e6	−0.519853
$557$	6.62986e6	0.905454	0.452727	−	0.891649i	$-0.350451\pi$
$557$	6.62986e6	0.905454	0.452727	+	0.891649i	$0.350451\pi$
$558$	2.00880e6	0.273119
$559$	1.13874e7	1.54133
$560$	0	0
$561$	6.88565e6	0.923714
$562$	1.36754e6	0.182642
$563$	−7.85294e6	−1.04415	−0.522073	−	0.852901i	$-0.674841\pi$
$563$	−7.85294e6	−1.04415	−0.522073	+	0.852901i	$0.674841\pi$
$564$	8640.00	0.00114371
$565$	0	0
$566$	−2.31426e6	−0.303648
$567$	−321489.	−0.0419961
$568$	−425088.	−0.0552851
$569$	−2.48155e6	−0.321323	−0.160661	−	0.987010i	$-0.551363\pi$
$569$	−2.48155e6	−0.321323	−0.160661	+	0.987010i	$0.551363\pi$
$570$	0	0
$571$	1.13675e7	1.45907	0.729533	−	0.683945i	$-0.239737\pi$
$571$	1.13675e7	1.45907	0.729533	+	0.683945i	$0.239737\pi$
$572$	−6.98170e6	−0.892218
$573$	8.89245e6	1.13145
$574$	−1.66286e6	−0.210658
$575$	0	0
$576$	331776.	0.0416667
$577$	8.20505e6	1.02599	0.512993	−	0.858393i	$-0.328537\pi$
$577$	8.20505e6	1.02599	0.512993	+	0.858393i	$0.328537\pi$
$578$	7.98099e6	0.993658
$579$	−3.68332e6	−0.456608
$580$	0	0
$581$	1.26008e6	0.154867
$582$	−5.36234e6	−0.656217
$583$	9.31748e6	1.13534
$584$	3.33376e6	0.404485
$585$	0	0
$586$	−3.12216e6	−0.375587
$587$	1.38400e7	1.65783	0.828917	−	0.559371i	$-0.188957\pi$
$587$	1.38400e7	1.65783	0.828917	+	0.559371i	$0.188957\pi$
$588$	−345744.	−0.0412393
$589$	1.46320e6	0.173786
$590$	0	0
$591$	−8.30007e6	−0.977492
$592$	−2.47040e6	−0.289710
$593$	5.38951e6	0.629380	0.314690	−	0.949195i	$-0.398099\pi$
$593$	5.38951e6	0.629380	0.314690	+	0.949195i	$0.398099\pi$
$594$	1.20722e6	0.140385
$595$	0	0
$596$	7.57930e6	0.874004
$597$	−1.70539e6	−0.195834
$598$	−1.22180e7	−1.39716
$599$	−1.14885e7	−1.30827	−0.654134	−	0.756379i	$-0.726967\pi$
$599$	−1.14885e7	−1.30827	−0.654134	+	0.756379i	$0.726967\pi$
$600$	0	0
$601$	−2.79225e6	−0.315333	−0.157666	−	0.987492i	$-0.550397\pi$
$601$	−2.79225e6	−0.315333	−0.157666	+	0.987492i	$0.550397\pi$
$602$	−2.11758e6	−0.238149
$603$	2.28550e6	0.255969
$604$	6.31923e6	0.704810
$605$	0	0
$606$	−1.74053e6	−0.192530
$607$	−713888.	−0.0786427	−0.0393213	−	0.999227i	$-0.512520\pi$
$607$	−713888.	−0.0786427	−0.0393213	+	0.999227i	$0.512520\pi$
$608$	241664.	0.0265126
$609$	−2.87620e6	−0.314251
$610$	0	0
$611$	−63240.0	−0.00685313
$612$	2.39501e6	0.258481
$613$	−3.10972e6	−0.334249	−0.167124	−	0.985936i	$-0.553448\pi$
$613$	−3.10972e6	−0.334249	−0.167124	+	0.985936i	$0.553448\pi$
$614$	8.99301e6	0.962685
$615$	0	0
$616$	1.29830e6	0.137856
$617$	−3.62384e6	−0.383227	−0.191613	−	0.981470i	$-0.561372\pi$
$617$	−3.62384e6	−0.383227	−0.191613	+	0.981470i	$0.561372\pi$
$618$	−6.60931e6	−0.696122
$619$	4.25196e6	0.446028	0.223014	−	0.974815i	$-0.428410\pi$
$619$	4.25196e6	0.446028	0.223014	+	0.974815i	$0.428410\pi$
$620$	0	0
$621$	2.11264e6	0.219835
$622$	2.32565e6	0.241028
$623$	−4.83748e6	−0.499343
$624$	−2.42842e6	−0.249667
$625$	0	0
$626$	8.01628e6	0.817593
$627$	879336.	0.0893277
$628$	2.32144e6	0.234887
$629$	−1.78332e7	−1.79723
$630$	0	0
$631$	−1.70299e7	−1.70270	−0.851349	−	0.524600i	$-0.824215\pi$
$631$	−1.70299e7	−1.70270	−0.851349	+	0.524600i	$0.824215\pi$
$632$	2.77376e6	0.276233
$633$	5.50242e6	0.545814
$634$	5.11327e6	0.505214
$635$	0	0
$636$	3.24086e6	0.317701
$637$	2.53065e6	0.247107
$638$	1.08004e7	1.05048
$639$	−538002.	−0.0521233
$640$	0	0
$641$	−1.80938e6	−0.173934	−0.0869669	−	0.996211i	$-0.527717\pi$
$641$	−1.80938e6	−0.173934	−0.0869669	+	0.996211i	$0.527717\pi$
$642$	−80568.0	−0.00771481
$643$	−1.53012e7	−1.45948	−0.729740	−	0.683725i	$-0.760359\pi$
$643$	−1.53012e7	−1.45948	−0.729740	+	0.683725i	$0.760359\pi$
$644$	2.27203e6	0.215874
$645$	0	0
$646$	1.74451e6	0.164472
$647$	−1.67546e7	−1.57352	−0.786762	−	0.617256i	$-0.788244\pi$
$647$	−1.67546e7	−1.57352	−0.786762	+	0.617256i	$0.788244\pi$
$648$	419904.	0.0392837
$649$	1.16649e7	1.08710
$650$	0	0
$651$	2.73420e6	0.252859
$652$	−8.48768e6	−0.781934
$653$	−1.47859e7	−1.35695	−0.678477	−	0.734622i	$-0.737360\pi$
$653$	−1.47859e7	−1.35695	−0.678477	+	0.734622i	$0.737360\pi$
$654$	−2.16569e6	−0.197994
$655$	0	0
$656$	2.17190e6	0.197052
$657$	4.21929e6	0.381352
$658$	11760.0	0.00105887
$659$	933762.	0.0837573	0.0418786	−	0.999123i	$-0.486666\pi$
$659$	933762.	0.0837573	0.0418786	+	0.999123i	$0.486666\pi$
$660$	0	0
$661$	6.09724e6	0.542787	0.271394	−	0.962468i	$-0.412516\pi$
$661$	6.09724e6	0.542787	0.271394	+	0.962468i	$0.412516\pi$
$662$	1.03925e7	0.921666
$663$	−1.75301e7	−1.54882
$664$	−1.64582e6	−0.144865
$665$	0	0
$666$	−3.12660e6	−0.273141
$667$	1.89008e7	1.64500
$668$	4.99757e6	0.433329
$669$	−7.04930e6	−0.608949
$670$	0	0
$671$	1.45703e7	1.24929
$672$	451584.	0.0385758
$673$	−2.09190e6	−0.178034	−0.0890171	−	0.996030i	$-0.528373\pi$
$673$	−2.09190e6	−0.178034	−0.0890171	+	0.996030i	$0.528373\pi$
$674$	−1.22476e7	−1.03849
$675$	0	0
$676$	1.18340e7	0.996010
$677$	−1.36453e6	−0.114423	−0.0572113	−	0.998362i	$-0.518221\pi$
$677$	−1.36453e6	−0.114423	−0.0572113	+	0.998362i	$0.518221\pi$
$678$	−252504.	−0.0210957
$679$	−7.29875e6	−0.607539
$680$	0	0
$681$	726408.	0.0600223
$682$	−1.02672e7	−0.845261
$683$	−1.15483e7	−0.947254	−0.473627	−	0.880726i	$-0.657055\pi$
$683$	−1.15483e7	−0.947254	−0.473627	+	0.880726i	$0.657055\pi$
$684$	305856.	0.0249964
$685$	0	0
$686$	−470596.	−0.0381802
$687$	−1.37464e6	−0.111121
$688$	2.76582e6	0.222768
$689$	−2.37213e7	−1.90367
$690$	0	0
$691$	4.17744e6	0.332824	0.166412	−	0.986056i	$-0.446782\pi$
$691$	4.17744e6	0.332824	0.166412	+	0.986056i	$0.446782\pi$
$692$	1.20173e6	0.0953984
$693$	1.64317e6	0.129972
$694$	5.70199e6	0.449395
$695$	0	0
$696$	3.75667e6	0.293955
$697$	1.56784e7	1.22242
$698$	1.17329e7	0.911520
$699$	−3.18854e6	−0.246830
$700$	0	0
$701$	−1.70278e7	−1.30877	−0.654385	−	0.756161i	$-0.727073\pi$
$701$	−1.70278e7	−1.30877	−0.654385	+	0.756161i	$0.727073\pi$
$702$	−3.07346e6	−0.235389
$703$	−2.27740e6	−0.173800
$704$	−1.69574e6	−0.128952
$705$	0	0
$706$	8.05104e6	0.607911
$707$	−2.36905e6	−0.178249
$708$	4.05734e6	0.304200
$709$	2.26932e7	1.69543	0.847715	−	0.530452i	$-0.177978\pi$
$709$	2.26932e7	1.69543	0.847715	+	0.530452i	$0.177978\pi$
$710$	0	0
$711$	3.51054e6	0.260435
$712$	6.31834e6	0.467092
$713$	−1.79676e7	−1.32363
$714$	3.25987e6	0.239307
$715$	0	0
$716$	6.18749e6	0.451057
$717$	−2.47833e6	−0.180037
$718$	1.63084e7	1.18059
$719$	5.12544e6	0.369751	0.184875	−	0.982762i	$-0.440812\pi$
$719$	5.12544e6	0.369751	0.184875	+	0.982762i	$0.440812\pi$
$720$	0	0
$721$	−8.99601e6	−0.644483
$722$	−9.68161e6	−0.691202
$723$	5.26228e6	0.374394
$724$	−6.68157e6	−0.473731
$725$	0	0
$726$	−372420.	−0.0262235
$727$	1.54328e7	1.08295	0.541476	−	0.840716i	$-0.317866\pi$
$727$	1.54328e7	1.08295	0.541476	+	0.840716i	$0.317866\pi$
$728$	−3.30534e6	−0.231147
$729$	531441.	0.0370370
$730$	0	0
$731$	1.99658e7	1.38195
$732$	5.06794e6	0.349586
$733$	6.84465e6	0.470535	0.235267	−	0.971931i	$-0.424403\pi$
$733$	6.84465e6	0.470535	0.235267	+	0.971931i	$0.424403\pi$
$734$	−2.37901e6	−0.162988
$735$	0	0
$736$	−2.96755e6	−0.201931
$737$	−1.16814e7	−0.792186
$738$	2.74882e6	0.185782
$739$	2.99389e6	0.201662	0.100831	−	0.994904i	$-0.467850\pi$
$739$	2.99389e6	0.201662	0.100831	+	0.994904i	$0.467850\pi$
$740$	0	0
$741$	−2.23870e6	−0.149779
$742$	4.41118e6	0.294134
$743$	−2.23250e7	−1.48361	−0.741804	−	0.670617i	$-0.766029\pi$
$743$	−2.23250e7	−1.48361	−0.741804	+	0.670617i	$0.766029\pi$
$744$	−3.57120e6	−0.236528
$745$	0	0
$746$	−8.18089e6	−0.538212
$747$	−2.08300e6	−0.136580
$748$	−1.22412e7	−0.799960
$749$	−109662.	−0.00714252
$750$	0	0
$751$	−1.41440e7	−0.915110	−0.457555	−	0.889181i	$-0.651275\pi$
$751$	−1.41440e7	−0.915110	−0.457555	+	0.889181i	$0.651275\pi$
$752$	−15360.0	−0.000990482 0
$753$	1.66277e6	0.106867
$754$	−2.74968e7	−1.76138
$755$	0	0
$756$	571536.	0.0363696
$757$	8.15367e6	0.517147	0.258573	−	0.965992i	$-0.416748\pi$
$757$	8.15367e6	0.517147	0.258573	+	0.965992i	$0.416748\pi$
$758$	−1.28879e7	−0.814723
$759$	−1.07979e7	−0.680357
$760$	0	0
$761$	−2.25745e6	−0.141305	−0.0706524	−	0.997501i	$-0.522508\pi$
$761$	−2.25745e6	−0.141305	−0.0706524	+	0.997501i	$0.522508\pi$
$762$	−64080.0	−0.00399793
$763$	−2.94774e6	−0.183307
$764$	−1.58088e7	−0.979863
$765$	0	0
$766$	6.91862e6	0.426037
$767$	−2.96975e7	−1.82277
$768$	−589824.	−0.0360844
$769$	−748774.	−0.0456599	−0.0228299	−	0.999739i	$-0.507268\pi$
$769$	−748774.	−0.0456599	−0.0228299	+	0.999739i	$0.507268\pi$
$770$	0	0
$771$	2.12382e6	0.128671
$772$	6.54813e6	0.395434
$773$	9.46225e6	0.569568	0.284784	−	0.958592i	$-0.408078\pi$
$773$	9.46225e6	0.569568	0.284784	+	0.958592i	$0.408078\pi$
$774$	3.50050e6	0.210028
$775$	0	0
$776$	9.53306e6	0.568300
$777$	−4.25565e6	−0.252879
$778$	−6.99674e6	−0.414426
$779$	2.00222e6	0.118214
$780$	0	0
$781$	2.74979e6	0.161314
$782$	−2.14220e7	−1.25269
$783$	4.75454e6	0.277143
$784$	614656.	0.0357143
$785$	0	0
$786$	9.54504e6	0.551089
$787$	1.99634e7	1.14894	0.574470	−	0.818525i	$-0.305208\pi$
$787$	1.99634e7	1.14894	0.574470	+	0.818525i	$0.305208\pi$
$788$	1.47557e7	0.846533
$789$	−2.20045e6	−0.125840
$790$	0	0
$791$	−343686.	−0.0195308
$792$	−2.14618e6	−0.121577
$793$	−3.70945e7	−2.09472
$794$	−7.52818e6	−0.423779
$795$	0	0
$796$	3.03181e6	0.169597
$797$	4.05368e6	0.226050	0.113025	−	0.993592i	$-0.463946\pi$
$797$	4.05368e6	0.226050	0.113025	+	0.993592i	$0.463946\pi$
$798$	416304.	0.0231421
$799$	−110880.	−0.00614450
$800$	0	0
$801$	7.99664e6	0.440379
$802$	1.67250e7	0.918182
$803$	−2.15653e7	−1.18023
$804$	−4.06310e6	−0.221676
$805$	0	0
$806$	2.61392e7	1.41728
$807$	−1.37501e7	−0.743229
$808$	3.09427e6	0.166736
$809$	1.85432e7	0.996124	0.498062	−	0.867141i	$-0.334045\pi$
$809$	1.85432e7	0.996124	0.498062	+	0.867141i	$0.334045\pi$
$810$	0	0
$811$	1.63648e7	0.873690	0.436845	−	0.899537i	$-0.356096\pi$
$811$	1.63648e7	0.873690	0.436845	+	0.899537i	$0.356096\pi$
$812$	5.11325e6	0.272149
$813$	−1.86350e7	−0.988790
$814$	1.59804e7	0.845331
$815$	0	0
$816$	−4.25779e6	−0.223851
$817$	2.54974e6	0.133642
$818$	−1.88673e6	−0.0985884
$819$	−4.18333e6	−0.217927
$820$	0	0
$821$	−5.45014e6	−0.282195	−0.141098	−	0.989996i	$-0.545063\pi$
$821$	−5.45014e6	−0.282195	−0.141098	+	0.989996i	$0.545063\pi$
$822$	−7.44228e6	−0.384173
$823$	2.19153e7	1.12784	0.563921	−	0.825829i	$-0.309292\pi$
$823$	2.19153e7	1.12784	0.563921	+	0.825829i	$0.309292\pi$
$824$	1.17499e7	0.602859
$825$	0	0
$826$	5.52250e6	0.281634
$827$	−8.11859e6	−0.412778	−0.206389	−	0.978470i	$-0.566171\pi$
$827$	−8.11859e6	−0.412778	−0.206389	+	0.978470i	$0.566171\pi$
$828$	−3.75581e6	−0.190383
$829$	1.60662e7	0.811943	0.405972	−	0.913886i	$-0.366933\pi$
$829$	1.60662e7	0.811943	0.405972	+	0.913886i	$0.366933\pi$
$830$	0	0
$831$	−2.16654e7	−1.08834
$832$	4.31718e6	0.216218
$833$	4.43705e6	0.221555
$834$	8.52610e6	0.424458
$835$	0	0
$836$	−1.56326e6	−0.0773600
$837$	−4.51980e6	−0.223000
$838$	−1.41637e7	−0.696736
$839$	−2.63504e7	−1.29236	−0.646178	−	0.763186i	$-0.723634\pi$
$839$	−2.63504e7	−1.29236	−0.646178	+	0.763186i	$0.723634\pi$
$840$	0	0
$841$	2.20253e7	1.07382
$842$	1.09105e7	0.530352
$843$	−3.07697e6	−0.149127
$844$	−9.78208e6	−0.472689
$845$	0	0
$846$	−19440.0	−0.000933835 0
$847$	−506905.	−0.0242783
$848$	−5.76154e6	−0.275137
$849$	5.20708e6	0.247927
$850$	0	0
$851$	2.79657e7	1.32374
$852$	956448.	0.0451401
$853$	−2.78129e7	−1.30880	−0.654400	−	0.756148i	$-0.727079\pi$
$853$	−2.78129e7	−1.30880	−0.654400	+	0.756148i	$0.727079\pi$
$854$	6.89802e6	0.323653
$855$	0	0
$856$	143232.	0.00668122
$857$	2.69363e6	0.125281	0.0626406	−	0.998036i	$-0.480048\pi$
$857$	2.69363e6	0.125281	0.0626406	+	0.998036i	$0.480048\pi$
$858$	1.57088e7	0.728493
$859$	−1.88389e7	−0.871109	−0.435555	−	0.900162i	$-0.643448\pi$
$859$	−1.88389e7	−0.871109	−0.435555	+	0.900162i	$0.643448\pi$
$860$	0	0
$861$	3.74144e6	0.172001
$862$	−1.90607e7	−0.873716
$863$	1.28630e7	0.587917	0.293959	−	0.955818i	$-0.405027\pi$
$863$	1.28630e7	0.587917	0.293959	+	0.955818i	$0.405027\pi$
$864$	−746496.	−0.0340207
$865$	0	0
$866$	−2.76120e7	−1.25113
$867$	−1.79572e7	−0.811319
$868$	−4.86080e6	−0.218982
$869$	−1.79428e7	−0.806009
$870$	0	0
$871$	2.97397e7	1.32828
$872$	3.85011e6	0.171468
$873$	1.20653e7	0.535799
$874$	−2.73571e6	−0.121141
$875$	0	0
$876$	−7.50096e6	−0.330260
$877$	1.58811e7	0.697240	0.348620	−	0.937264i	$-0.386650\pi$
$877$	1.58811e7	0.697240	0.348620	+	0.937264i	$0.386650\pi$
$878$	2.16050e7	0.945842
$879$	7.02486e6	0.306666
$880$	0	0
$881$	1.73681e7	0.753899	0.376950	−	0.926234i	$-0.376973\pi$
$881$	1.73681e7	0.753899	0.376950	+	0.926234i	$0.376973\pi$
$882$	777924.	0.0336718
$883$	−2.23513e7	−0.964721	−0.482361	−	0.875973i	$-0.660220\pi$
$883$	−2.23513e7	−0.964721	−0.482361	+	0.875973i	$0.660220\pi$
$884$	3.11647e7	1.34132
$885$	0	0
$886$	1.62345e7	0.694793
$887$	8.91140e6	0.380309	0.190155	−	0.981754i	$-0.439101\pi$
$887$	8.91140e6	0.380309	0.190155	+	0.981754i	$0.439101\pi$
$888$	5.55840e6	0.236547
$889$	−87220.0	−0.00370136
$890$	0	0
$891$	−2.71625e6	−0.114624
$892$	1.25321e7	0.527365
$893$	−14160.0	−0.000594203 0
$894$	−1.70534e7	−0.713621
$895$	0	0
$896$	−802816.	−0.0334077
$897$	2.74904e7	1.14078
$898$	851976.	0.0352563
$899$	−4.04364e7	−1.66868
$900$	0	0
$901$	−4.15911e7	−1.70682
$902$	−1.40495e7	−0.574969
$903$	4.76456e6	0.194448
$904$	448896.	0.0182694
$905$	0	0
$906$	−1.42183e7	−0.575475
$907$	4.53327e6	0.182976	0.0914878	−	0.995806i	$-0.470838\pi$
$907$	4.53327e6	0.182976	0.0914878	+	0.995806i	$0.470838\pi$
$908$	−1.29139e6	−0.0519809
$909$	3.91619e6	0.157200
$910$	0	0
$911$	−9.83085e6	−0.392460	−0.196230	−	0.980558i	$-0.562870\pi$
$911$	−9.83085e6	−0.392460	−0.196230	+	0.980558i	$0.562870\pi$
$912$	−543744.	−0.0216475
$913$	1.06464e7	0.422695
$914$	3.66460e6	0.145098
$915$	0	0
$916$	2.44381e6	0.0962340
$917$	1.29919e7	0.510209
$918$	−5.38877e6	−0.211049
$919$	−4.82049e7	−1.88279	−0.941396	−	0.337304i	$-0.890485\pi$
$919$	−4.82049e7	−1.88279	−0.941396	+	0.337304i	$0.890485\pi$
$920$	0	0
$921$	−2.02343e7	−0.786029
$922$	−1.66334e7	−0.644397
$923$	−7.00067e6	−0.270480
$924$	−2.92118e6	−0.112559
$925$	0	0
$926$	−3.36320e7	−1.28892
$927$	1.48710e7	0.568381
$928$	−6.67853e6	−0.254572
$929$	−6.77017e6	−0.257371	−0.128686	−	0.991685i	$-0.541076\pi$
$929$	−6.77017e6	−0.257371	−0.128686	+	0.991685i	$0.541076\pi$
$930$	0	0
$931$	566636.	0.0214255
$932$	5.66851e6	0.213761
$933$	−5.23271e6	−0.196799
$934$	−288192.	−0.0108097
$935$	0	0
$936$	5.46394e6	0.203852
$937$	−1.25127e7	−0.465590	−0.232795	−	0.972526i	$-0.574787\pi$
$937$	−1.25127e7	−0.465590	−0.232795	+	0.972526i	$0.574787\pi$
$938$	−5.53034e6	−0.205232
$939$	−1.80366e7	−0.667562
$940$	0	0
$941$	−1.38659e7	−0.510473	−0.255236	−	0.966879i	$-0.582153\pi$
$941$	−1.38659e7	−0.510473	−0.255236	+	0.966879i	$0.582153\pi$
$942$	−5.22324e6	−0.191784
$943$	−2.45866e7	−0.900367
$944$	−7.21306e6	−0.263445
$945$	0	0
$946$	−1.78914e7	−0.650006
$947$	−4.89287e6	−0.177292	−0.0886460	−	0.996063i	$-0.528254\pi$
$947$	−4.89287e6	−0.177292	−0.0886460	+	0.996063i	$0.528254\pi$
$948$	−6.24096e6	−0.225544
$949$	5.49029e7	1.97893
$950$	0	0
$951$	−1.15049e7	−0.412506
$952$	−5.79533e6	−0.207246
$953$	1.40055e7	0.499535	0.249768	−	0.968306i	$-0.419646\pi$
$953$	1.40055e7	0.499535	0.249768	+	0.968306i	$0.419646\pi$
$954$	−7.29194e6	−0.259401
$955$	0	0
$956$	4.40592e6	0.155916
$957$	−2.43010e7	−0.857717
$958$	1.92224e7	0.676697
$959$	−1.01298e7	−0.355675
$960$	0	0
$961$	9.81085e6	0.342687
$962$	−4.06844e7	−1.41739
$963$	181278.	0.00629911
$964$	−9.35517e6	−0.324234
$965$	0	0
$966$	−5.11207e6	−0.176260
$967$	1.02386e7	0.352106	0.176053	−	0.984381i	$-0.443667\pi$
$967$	1.02386e7	0.352106	0.176053	+	0.984381i	$0.443667\pi$
$968$	662080.	0.0227103
$969$	−3.92515e6	−0.134291
$970$	0	0
$971$	1.17452e7	0.399773	0.199886	−	0.979819i	$-0.435943\pi$
$971$	1.17452e7	0.399773	0.199886	+	0.979819i	$0.435943\pi$
$972$	−944784.	−0.0320750
$973$	1.16050e7	0.392972
$974$	−1.76722e7	−0.596888
$975$	0	0
$976$	−9.00966e6	−0.302750
$977$	−2.26195e7	−0.758134	−0.379067	−	0.925369i	$-0.623755\pi$
$977$	−2.26195e7	−0.758134	−0.379067	+	0.925369i	$0.623755\pi$
$978$	1.90973e7	0.638446
$979$	−4.08717e7	−1.36291
$980$	0	0
$981$	4.87280e6	0.161661
$982$	−2.25999e7	−0.747873
$983$	−2.79575e7	−0.922813	−0.461407	−	0.887189i	$-0.652655\pi$
$983$	−2.79575e7	−0.922813	−0.461407	+	0.887189i	$0.652655\pi$
$984$	−4.88678e6	−0.160892
$985$	0	0
$986$	−4.82106e7	−1.57925
$987$	−26460.0	−0.000864564 0
$988$	3.97990e6	0.129712
$989$	−3.13100e7	−1.01787
$990$	0	0
$991$	−1.66475e7	−0.538474	−0.269237	−	0.963074i	$-0.586772\pi$
$991$	−1.66475e7	−0.538474	−0.269237	+	0.963074i	$0.586772\pi$
$992$	6.34880e6	0.204839
$993$	−2.33830e7	−0.752537
$994$	1.30183e6	0.0417916
$995$	0	0
$996$	3.70310e6	0.118282
$997$	5.17280e7	1.64812	0.824058	−	0.566505i	$-0.191705\pi$
$997$	5.17280e7	1.64812	0.824058	+	0.566505i	$0.191705\pi$
$998$	−3.68938e7	−1.17254
$999$	7.03485e6	0.223019

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.6.a.g.1.1		1
5.2	odd	4		1050.6.g.b.799.2		2
5.3	odd	4		1050.6.g.b.799.1		2
5.4	even	2		42.6.a.c.1.1	✓	1
15.14	odd	2		126.6.a.l.1.1		1
20.19	odd	2		336.6.a.b.1.1		1
35.4	even	6		294.6.e.l.79.1		2
35.9	even	6		294.6.e.l.67.1		2
35.19	odd	6		294.6.e.n.67.1		2
35.24	odd	6		294.6.e.n.79.1		2
35.34	odd	2		294.6.a.c.1.1		1
60.59	even	2		1008.6.a.ba.1.1		1
105.104	even	2		882.6.a.n.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.6.a.c.1.1	✓	1	5.4	even	2
126.6.a.l.1.1		1	15.14	odd	2
294.6.a.c.1.1		1	35.34	odd	2
294.6.e.l.67.1		2	35.9	even	6
294.6.e.l.79.1		2	35.4	even	6
294.6.e.n.67.1		2	35.19	odd	6
294.6.e.n.79.1		2	35.24	odd	6
336.6.a.b.1.1		1	20.19	odd	2
882.6.a.n.1.1		1	105.104	even	2
1008.6.a.ba.1.1		1	60.59	even	2
1050.6.a.g.1.1		1	1.1	even	1	trivial
1050.6.g.b.799.1		2	5.3	odd	4
1050.6.g.b.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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