LMFDB - Embedded newform 1050.4.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,4,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, 4, names="a")

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

chi := DirichletCharacter("1050.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
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:	$61.9520055060$
Analytic rank:	$1$
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)

$f(q)$

$=$

$q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$

\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} -8.00000 q^{11} -12.0000 q^{12} +42.0000 q^{13} -14.0000 q^{14} +16.0000 q^{16} +2.00000 q^{17} -18.0000 q^{18} -124.000 q^{19} -21.0000 q^{21} +16.0000 q^{22} -76.0000 q^{23} +24.0000 q^{24} -84.0000 q^{26} -27.0000 q^{27} +28.0000 q^{28} +254.000 q^{29} -72.0000 q^{31} -32.0000 q^{32} +24.0000 q^{33} -4.00000 q^{34} +36.0000 q^{36} -398.000 q^{37} +248.000 q^{38} -126.000 q^{39} +462.000 q^{41} +42.0000 q^{42} -212.000 q^{43} -32.0000 q^{44} +152.000 q^{46} +264.000 q^{47} -48.0000 q^{48} +49.0000 q^{49} -6.00000 q^{51} +168.000 q^{52} +162.000 q^{53} +54.0000 q^{54} -56.0000 q^{56} +372.000 q^{57} -508.000 q^{58} -772.000 q^{59} +30.0000 q^{61} +144.000 q^{62} +63.0000 q^{63} +64.0000 q^{64} -48.0000 q^{66} +764.000 q^{67} +8.00000 q^{68} +228.000 q^{69} -236.000 q^{71} -72.0000 q^{72} -418.000 q^{73} +796.000 q^{74} -496.000 q^{76} -56.0000 q^{77} +252.000 q^{78} +552.000 q^{79} +81.0000 q^{81} -924.000 q^{82} -1036.00 q^{83} -84.0000 q^{84} +424.000 q^{86} -762.000 q^{87} +64.0000 q^{88} +30.0000 q^{89} +294.000 q^{91} -304.000 q^{92} +216.000 q^{93} -528.000 q^{94} +96.0000 q^{96} +1190.00 q^{97} -98.0000 q^{98} -72.0000 q^{99} +O(q^{100})\)

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 $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	4.00000	0.500000
$5$	0	0
$5$	0	0
$6$	6.00000	0.408248
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	0	0
$11$	−8.00000	−0.219281	−0.109640	−	0.993971i	$-0.534970\pi$
$11$	−8.00000	−0.219281	−0.109640	+	0.993971i	$0.534970\pi$
$12$	−12.0000	−0.288675
$13$	42.0000	0.896054	0.448027	−	0.894020i	$-0.352127\pi$
$13$	42.0000	0.896054	0.448027	+	0.894020i	$0.352127\pi$
$14$	−14.0000	−0.267261
$15$	0	0
$16$	16.0000	0.250000
$17$	2.00000	0.0285336	0.0142668	−	0.999898i	$-0.495459\pi$
$17$	2.00000	0.0285336	0.0142668	+	0.999898i	$0.495459\pi$
$18$	−18.0000	−0.235702
$19$	−124.000	−1.49724	−0.748620	−	0.663000i	$-0.769283\pi$
$19$	−124.000	−1.49724	−0.748620	+	0.663000i	$0.769283\pi$
$20$	0	0
$21$	−21.0000	−0.218218
$22$	16.0000	0.155055
$23$	−76.0000	−0.689004	−0.344502	−	0.938786i	$-0.611952\pi$
$23$	−76.0000	−0.689004	−0.344502	+	0.938786i	$0.611952\pi$
$24$	24.0000	0.204124
$25$	0	0
$26$	−84.0000	−0.633606
$27$	−27.0000	−0.192450
$28$	28.0000	0.188982
$29$	254.000	1.62644	0.813218	−	0.581960i	$-0.197714\pi$
$29$	254.000	1.62644	0.813218	+	0.581960i	$0.197714\pi$
$30$	0	0
$31$	−72.0000	−0.417148	−0.208574	−	0.978007i	$-0.566882\pi$
$31$	−72.0000	−0.417148	−0.208574	+	0.978007i	$0.566882\pi$
$32$	−32.0000	−0.176777
$33$	24.0000	0.126602
$34$	−4.00000	−0.0201763
$35$	0	0
$36$	36.0000	0.166667
$37$	−398.000	−1.76840	−0.884200	−	0.467109i	$-0.845296\pi$
$37$	−398.000	−1.76840	−0.884200	+	0.467109i	$0.845296\pi$
$38$	248.000	1.05871
$39$	−126.000	−0.517337
$40$	0	0
$41$	462.000	1.75981	0.879906	−	0.475148i	$-0.157606\pi$
$41$	462.000	1.75981	0.879906	+	0.475148i	$0.157606\pi$
$42$	42.0000	0.154303
$43$	−212.000	−0.751853	−0.375927	−	0.926649i	$-0.622676\pi$
$43$	−212.000	−0.751853	−0.375927	+	0.926649i	$0.622676\pi$
$44$	−32.0000	−0.109640
$45$	0	0
$46$	152.000	0.487200
$47$	264.000	0.819327	0.409663	−	0.912237i	$-0.365646\pi$
$47$	264.000	0.819327	0.409663	+	0.912237i	$0.365646\pi$
$48$	−48.0000	−0.144338
$49$	49.0000	0.142857
$50$	0	0
$51$	−6.00000	−0.0164739
$52$	168.000	0.448027
$53$	162.000	0.419857	0.209928	−	0.977717i	$-0.432677\pi$
$53$	162.000	0.419857	0.209928	+	0.977717i	$0.432677\pi$
$54$	54.0000	0.136083
$55$	0	0
$56$	−56.0000	−0.133631
$57$	372.000	0.864432
$58$	−508.000	−1.15006
$59$	−772.000	−1.70349	−0.851744	−	0.523958i	$-0.824455\pi$
$59$	−772.000	−1.70349	−0.851744	+	0.523958i	$0.824455\pi$
$60$	0	0
$61$	30.0000	0.0629690	0.0314845	−	0.999504i	$-0.489977\pi$
$61$	30.0000	0.0629690	0.0314845	+	0.999504i	$0.489977\pi$
$62$	144.000	0.294968
$63$	63.0000	0.125988
$64$	64.0000	0.125000
$65$	0	0
$66$	−48.0000	−0.0895211
$67$	764.000	1.39310	0.696548	−	0.717510i	$-0.254718\pi$
$67$	764.000	1.39310	0.696548	+	0.717510i	$0.254718\pi$
$68$	8.00000	0.0142668
$69$	228.000	0.397797
$70$	0	0
$71$	−236.000	−0.394480	−0.197240	−	0.980355i	$-0.563198\pi$
$71$	−236.000	−0.394480	−0.197240	+	0.980355i	$0.563198\pi$
$72$	−72.0000	−0.117851
$73$	−418.000	−0.670181	−0.335090	−	0.942186i	$-0.608767\pi$
$73$	−418.000	−0.670181	−0.335090	+	0.942186i	$0.608767\pi$
$74$	796.000	1.25045
$75$	0	0
$76$	−496.000	−0.748620
$77$	−56.0000	−0.0828804
$78$	252.000	0.365813
$79$	552.000	0.786137	0.393069	−	0.919509i	$-0.371413\pi$
$79$	552.000	0.786137	0.393069	+	0.919509i	$0.371413\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	−924.000	−1.24437
$83$	−1036.00	−1.37007	−0.685035	−	0.728510i	$-0.740213\pi$
$83$	−1036.00	−1.37007	−0.685035	+	0.728510i	$0.740213\pi$
$84$	−84.0000	−0.109109
$85$	0	0
$86$	424.000	0.531641
$87$	−762.000	−0.939023
$88$	64.0000	0.0775275
$89$	30.0000	0.0357303	0.0178651	−	0.999840i	$-0.494313\pi$
$89$	30.0000	0.0357303	0.0178651	+	0.999840i	$0.494313\pi$
$90$	0	0
$91$	294.000	0.338677
$92$	−304.000	−0.344502
$93$	216.000	0.240840
$94$	−528.000	−0.579352
$95$	0	0
$96$	96.0000	0.102062
$97$	1190.00	1.24563	0.622815	−	0.782369i	$-0.285989\pi$
$97$	1190.00	1.24563	0.622815	+	0.782369i	$0.285989\pi$
$98$	−98.0000	−0.101015
$99$	−72.0000	−0.0730937
$100$	0	0
$101$	1370.00	1.34970	0.674852	−	0.737953i	$-0.264207\pi$
$101$	1370.00	1.34970	0.674852	+	0.737953i	$0.264207\pi$
$102$	12.0000	0.0116488
$103$	−464.000	−0.443876	−0.221938	−	0.975061i	$-0.571238\pi$
$103$	−464.000	−0.443876	−0.221938	+	0.975061i	$0.571238\pi$
$104$	−336.000	−0.316803
$105$	0	0
$106$	−324.000	−0.296884
$107$	2136.00	1.92986	0.964930	−	0.262509i	$-0.0845500\pi$
$107$	2136.00	1.92986	0.964930	+	0.262509i	$0.0845500\pi$
$108$	−108.000	−0.0962250
$109$	−1226.00	−1.07733	−0.538667	−	0.842518i	$-0.681072\pi$
$109$	−1226.00	−1.07733	−0.538667	+	0.842518i	$0.681072\pi$
$110$	0	0
$111$	1194.00	1.02099
$112$	112.000	0.0944911
$113$	−338.000	−0.281384	−0.140692	−	0.990053i	$-0.544933\pi$
$113$	−338.000	−0.281384	−0.140692	+	0.990053i	$0.544933\pi$
$114$	−744.000	−0.611245
$115$	0	0
$116$	1016.00	0.813218
$117$	378.000	0.298685
$118$	1544.00	1.20455
$119$	14.0000	0.0107847
$120$	0	0
$121$	−1267.00	−0.951916
$122$	−60.0000	−0.0445258
$123$	−1386.00	−1.01603
$124$	−288.000	−0.208574
$125$	0	0
$126$	−126.000	−0.0890871
$127$	−2088.00	−1.45890	−0.729449	−	0.684035i	$-0.760223\pi$
$127$	−2088.00	−1.45890	−0.729449	+	0.684035i	$0.760223\pi$
$128$	−128.000	−0.0883883
$129$	636.000	0.434083
$130$	0	0
$131$	−292.000	−0.194749	−0.0973747	−	0.995248i	$-0.531045\pi$
$131$	−292.000	−0.194749	−0.0973747	+	0.995248i	$0.531045\pi$
$132$	96.0000	0.0633010
$133$	−868.000	−0.565903
$134$	−1528.00	−0.985068
$135$	0	0
$136$	−16.0000	−0.0100882
$137$	−818.000	−0.510120	−0.255060	−	0.966925i	$-0.582095\pi$
$137$	−818.000	−0.510120	−0.255060	+	0.966925i	$0.582095\pi$
$138$	−456.000	−0.281285
$139$	−2156.00	−1.31561	−0.657804	−	0.753189i	$-0.728515\pi$
$139$	−2156.00	−1.31561	−0.657804	+	0.753189i	$0.728515\pi$
$140$	0	0
$141$	−792.000	−0.473039
$142$	472.000	0.278939
$143$	−336.000	−0.196488
$144$	144.000	0.0833333
$145$	0	0
$146$	836.000	0.473889
$147$	−147.000	−0.0824786
$148$	−1592.00	−0.884200
$149$	−2850.00	−1.56699	−0.783494	−	0.621400i	$-0.786564\pi$
$149$	−2850.00	−1.56699	−0.783494	+	0.621400i	$0.786564\pi$
$150$	0	0
$151$	1672.00	0.901096	0.450548	−	0.892752i	$-0.351229\pi$
$151$	1672.00	0.901096	0.450548	+	0.892752i	$0.351229\pi$
$152$	992.000	0.529354
$153$	18.0000	0.00951120
$154$	112.000	0.0586053
$155$	0	0
$156$	−504.000	−0.258669
$157$	−446.000	−0.226718	−0.113359	−	0.993554i	$-0.536161\pi$
$157$	−446.000	−0.226718	−0.113359	+	0.993554i	$0.536161\pi$
$158$	−1104.00	−0.555883
$159$	−486.000	−0.242404
$160$	0	0
$161$	−532.000	−0.260419
$162$	−162.000	−0.0785674
$163$	−2708.00	−1.30127	−0.650635	−	0.759391i	$-0.725497\pi$
$163$	−2708.00	−1.30127	−0.650635	+	0.759391i	$0.725497\pi$
$164$	1848.00	0.879906
$165$	0	0
$166$	2072.00	0.968785
$167$	−896.000	−0.415177	−0.207589	−	0.978216i	$-0.566561\pi$
$167$	−896.000	−0.415177	−0.207589	+	0.978216i	$0.566561\pi$
$168$	168.000	0.0771517
$169$	−433.000	−0.197087
$170$	0	0
$171$	−1116.00	−0.499080
$172$	−848.000	−0.375927
$173$	−4034.00	−1.77283	−0.886414	−	0.462893i	$-0.846811\pi$
$173$	−4034.00	−1.77283	−0.886414	+	0.462893i	$0.846811\pi$
$174$	1524.00	0.663989
$175$	0	0
$176$	−128.000	−0.0548202
$177$	2316.00	0.983510
$178$	−60.0000	−0.0252651
$179$	−3480.00	−1.45311	−0.726557	−	0.687106i	$-0.758881\pi$
$179$	−3480.00	−1.45311	−0.726557	+	0.687106i	$0.758881\pi$
$180$	0	0
$181$	−2898.00	−1.19009	−0.595046	−	0.803692i	$-0.702866\pi$
$181$	−2898.00	−1.19009	−0.595046	+	0.803692i	$0.702866\pi$
$182$	−588.000	−0.239481
$183$	−90.0000	−0.0363551
$184$	608.000	0.243600
$185$	0	0
$186$	−432.000	−0.170300
$187$	−16.0000	−0.00625688
$188$	1056.00	0.409663
$189$	−189.000	−0.0727393
$190$	0	0
$191$	2652.00	1.00467	0.502335	−	0.864673i	$-0.332474\pi$
$191$	2652.00	1.00467	0.502335	+	0.864673i	$0.332474\pi$
$192$	−192.000	−0.0721688
$193$	−146.000	−0.0544524	−0.0272262	−	0.999629i	$-0.508667\pi$
$193$	−146.000	−0.0544524	−0.0272262	+	0.999629i	$0.508667\pi$
$194$	−2380.00	−0.880794
$195$	0	0
$196$	196.000	0.0714286
$197$	2546.00	0.920787	0.460393	−	0.887715i	$-0.347708\pi$
$197$	2546.00	0.920787	0.460393	+	0.887715i	$0.347708\pi$
$198$	144.000	0.0516850
$199$	−2536.00	−0.903378	−0.451689	−	0.892175i	$-0.649178\pi$
$199$	−2536.00	−0.903378	−0.451689	+	0.892175i	$0.649178\pi$
$200$	0	0
$201$	−2292.00	−0.804305
$202$	−2740.00	−0.954385
$203$	1778.00	0.614735
$204$	−24.0000	−0.00823694
$205$	0	0
$206$	928.000	0.313868
$207$	−684.000	−0.229668
$208$	672.000	0.224014
$209$	992.000	0.328316
$210$	0	0
$211$	−1300.00	−0.424150	−0.212075	−	0.977253i	$-0.568022\pi$
$211$	−1300.00	−0.424150	−0.212075	+	0.977253i	$0.568022\pi$
$212$	648.000	0.209928
$213$	708.000	0.227753
$214$	−4272.00	−1.36462
$215$	0	0
$216$	216.000	0.0680414
$217$	−504.000	−0.157667
$218$	2452.00	0.761791
$219$	1254.00	0.386929
$220$	0	0
$221$	84.0000	0.0255677
$222$	−2388.00	−0.721946
$223$	−2576.00	−0.773550	−0.386775	−	0.922174i	$-0.626411\pi$
$223$	−2576.00	−0.773550	−0.386775	+	0.922174i	$0.626411\pi$
$224$	−224.000	−0.0668153
$225$	0	0
$226$	676.000	0.198968
$227$	1836.00	0.536826	0.268413	−	0.963304i	$-0.413501\pi$
$227$	1836.00	0.536826	0.268413	+	0.963304i	$0.413501\pi$
$228$	1488.00	0.432216
$229$	−1874.00	−0.540775	−0.270387	−	0.962752i	$-0.587152\pi$
$229$	−1874.00	−0.540775	−0.270387	+	0.962752i	$0.587152\pi$
$230$	0	0
$231$	168.000	0.0478510
$232$	−2032.00	−0.575032
$233$	−3730.00	−1.04876	−0.524379	−	0.851485i	$-0.675702\pi$
$233$	−3730.00	−1.04876	−0.524379	+	0.851485i	$0.675702\pi$
$234$	−756.000	−0.211202
$235$	0	0
$236$	−3088.00	−0.851744
$237$	−1656.00	−0.453877
$238$	−28.0000	−0.00762593
$239$	2004.00	0.542377	0.271188	−	0.962526i	$-0.412583\pi$
$239$	2004.00	0.542377	0.271188	+	0.962526i	$0.412583\pi$
$240$	0	0
$241$	−646.000	−0.172666	−0.0863330	−	0.996266i	$-0.527515\pi$
$241$	−646.000	−0.172666	−0.0863330	+	0.996266i	$0.527515\pi$
$242$	2534.00	0.673106
$243$	−243.000	−0.0641500
$244$	120.000	0.0314845
$245$	0	0
$246$	2772.00	0.718440
$247$	−5208.00	−1.34161
$248$	576.000	0.147484
$249$	3108.00	0.791010
$250$	0	0
$251$	1260.00	0.316855	0.158427	−	0.987371i	$-0.449358\pi$
$251$	1260.00	0.316855	0.158427	+	0.987371i	$0.449358\pi$
$252$	252.000	0.0629941
$253$	608.000	0.151086
$254$	4176.00	1.03160
$255$	0	0
$256$	256.000	0.0625000
$257$	−5910.00	−1.43446	−0.717229	−	0.696838i	$-0.754590\pi$
$257$	−5910.00	−1.43446	−0.717229	+	0.696838i	$0.754590\pi$
$258$	−1272.00	−0.306943
$259$	−2786.00	−0.668392
$260$	0	0
$261$	2286.00	0.542145
$262$	584.000	0.137709
$263$	−2988.00	−0.700563	−0.350281	−	0.936645i	$-0.613914\pi$
$263$	−2988.00	−0.700563	−0.350281	+	0.936645i	$0.613914\pi$
$264$	−192.000	−0.0447605
$265$	0	0
$266$	1736.00	0.400154
$267$	−90.0000	−0.0206289
$268$	3056.00	0.696548
$269$	−1318.00	−0.298736	−0.149368	−	0.988782i	$-0.547724\pi$
$269$	−1318.00	−0.298736	−0.149368	+	0.988782i	$0.547724\pi$
$270$	0	0
$271$	−5640.00	−1.26423	−0.632114	−	0.774876i	$-0.717812\pi$
$271$	−5640.00	−1.26423	−0.632114	+	0.774876i	$0.717812\pi$
$272$	32.0000	0.00713340
$273$	−882.000	−0.195535
$274$	1636.00	0.360709
$275$	0	0
$276$	912.000	0.198898
$277$	−6446.00	−1.39820	−0.699102	−	0.715022i	$-0.746417\pi$
$277$	−6446.00	−1.39820	−0.699102	+	0.715022i	$0.746417\pi$
$278$	4312.00	0.930275
$279$	−648.000	−0.139049
$280$	0	0
$281$	4930.00	1.04662	0.523308	−	0.852144i	$-0.324698\pi$
$281$	4930.00	1.04662	0.523308	+	0.852144i	$0.324698\pi$
$282$	1584.00	0.334489
$283$	6260.00	1.31491	0.657453	−	0.753496i	$-0.271634\pi$
$283$	6260.00	1.31491	0.657453	+	0.753496i	$0.271634\pi$
$284$	−944.000	−0.197240
$285$	0	0
$286$	672.000	0.138938
$287$	3234.00	0.665146
$288$	−288.000	−0.0589256
$289$	−4909.00	−0.999186
$290$	0	0
$291$	−3570.00	−0.719165
$292$	−1672.00	−0.335090
$293$	2310.00	0.460586	0.230293	−	0.973121i	$-0.426032\pi$
$293$	2310.00	0.460586	0.230293	+	0.973121i	$0.426032\pi$
$294$	294.000	0.0583212
$295$	0	0
$296$	3184.00	0.625224
$297$	216.000	0.0422006
$298$	5700.00	1.10803
$299$	−3192.00	−0.617385
$300$	0	0
$301$	−1484.00	−0.284174
$302$	−3344.00	−0.637171
$303$	−4110.00	−0.779252
$304$	−1984.00	−0.374310
$305$	0	0
$306$	−36.0000	−0.00672543
$307$	−196.000	−0.0364375	−0.0182187	−	0.999834i	$-0.505800\pi$
$307$	−196.000	−0.0364375	−0.0182187	+	0.999834i	$0.505800\pi$
$308$	−224.000	−0.0414402
$309$	1392.00	0.256272
$310$	0	0
$311$	−6736.00	−1.22818	−0.614089	−	0.789237i	$-0.710477\pi$
$311$	−6736.00	−1.22818	−0.614089	+	0.789237i	$0.710477\pi$
$312$	1008.00	0.182906
$313$	−394.000	−0.0711508	−0.0355754	−	0.999367i	$-0.511326\pi$
$313$	−394.000	−0.0711508	−0.0355754	+	0.999367i	$0.511326\pi$
$314$	892.000	0.160314
$315$	0	0
$316$	2208.00	0.393069
$317$	6714.00	1.18958	0.594788	−	0.803882i	$-0.297236\pi$
$317$	6714.00	1.18958	0.594788	+	0.803882i	$0.297236\pi$
$318$	972.000	0.171406
$319$	−2032.00	−0.356646
$320$	0	0
$321$	−6408.00	−1.11420
$322$	1064.00	0.184144
$323$	−248.000	−0.0427216
$324$	324.000	0.0555556
$325$	0	0
$326$	5416.00	0.920136
$327$	3678.00	0.622000
$328$	−3696.00	−0.622187
$329$	1848.00	0.309676
$330$	0	0
$331$	692.000	0.114912	0.0574558	−	0.998348i	$-0.481701\pi$
$331$	692.000	0.114912	0.0574558	+	0.998348i	$0.481701\pi$
$332$	−4144.00	−0.685035
$333$	−3582.00	−0.589467
$334$	1792.00	0.293574
$335$	0	0
$336$	−336.000	−0.0545545
$337$	1566.00	0.253132	0.126566	−	0.991958i	$-0.459604\pi$
$337$	1566.00	0.253132	0.126566	+	0.991958i	$0.459604\pi$
$338$	866.000	0.139362
$339$	1014.00	0.162457
$340$	0	0
$341$	576.000	0.0914726
$342$	2232.00	0.352903
$343$	343.000	0.0539949
$344$	1696.00	0.265820
$345$	0	0
$346$	8068.00	1.25358
$347$	5328.00	0.824271	0.412135	−	0.911123i	$-0.364783\pi$
$347$	5328.00	0.824271	0.412135	+	0.911123i	$0.364783\pi$
$348$	−3048.00	−0.469511
$349$	11326.0	1.73715	0.868577	−	0.495554i	$-0.165035\pi$
$349$	11326.0	1.73715	0.868577	+	0.495554i	$0.165035\pi$
$350$	0	0
$351$	−1134.00	−0.172446
$352$	256.000	0.0387638
$353$	2130.00	0.321157	0.160579	−	0.987023i	$-0.448664\pi$
$353$	2130.00	0.321157	0.160579	+	0.987023i	$0.448664\pi$
$354$	−4632.00	−0.695446
$355$	0	0
$356$	120.000	0.0178651
$357$	−42.0000	−0.00622654
$358$	6960.00	1.02751
$359$	3044.00	0.447510	0.223755	−	0.974645i	$-0.428168\pi$
$359$	3044.00	0.447510	0.223755	+	0.974645i	$0.428168\pi$
$360$	0	0
$361$	8517.00	1.24173
$362$	5796.00	0.841522
$363$	3801.00	0.549589
$364$	1176.00	0.169338
$365$	0	0
$366$	180.000	0.0257070
$367$	−12416.0	−1.76597	−0.882984	−	0.469404i	$-0.844469\pi$
$367$	−12416.0	−1.76597	−0.882984	+	0.469404i	$0.844469\pi$
$368$	−1216.00	−0.172251
$369$	4158.00	0.586604
$370$	0	0
$371$	1134.00	0.158691
$372$	864.000	0.120420
$373$	7442.00	1.03306	0.516531	−	0.856268i	$-0.327223\pi$
$373$	7442.00	1.03306	0.516531	+	0.856268i	$0.327223\pi$
$374$	32.0000	0.00442428
$375$	0	0
$376$	−2112.00	−0.289676
$377$	10668.0	1.45737
$378$	378.000	0.0514344
$379$	100.000	0.0135532	0.00677659	−	0.999977i	$-0.497843\pi$
$379$	100.000	0.0135532	0.00677659	+	0.999977i	$0.497843\pi$
$380$	0	0
$381$	6264.00	0.842295
$382$	−5304.00	−0.710409
$383$	−8080.00	−1.07799	−0.538993	−	0.842310i	$-0.681195\pi$
$383$	−8080.00	−1.07799	−0.538993	+	0.842310i	$0.681195\pi$
$384$	384.000	0.0510310
$385$	0	0
$386$	292.000	0.0385036
$387$	−1908.00	−0.250618
$388$	4760.00	0.622815
$389$	−5482.00	−0.714520	−0.357260	−	0.934005i	$-0.616289\pi$
$389$	−5482.00	−0.714520	−0.357260	+	0.934005i	$0.616289\pi$
$390$	0	0
$391$	−152.000	−0.0196598
$392$	−392.000	−0.0505076
$393$	876.000	0.112439
$394$	−5092.00	−0.651095
$395$	0	0
$396$	−288.000	−0.0365468
$397$	−10446.0	−1.32058	−0.660289	−	0.751011i	$-0.729566\pi$
$397$	−10446.0	−1.32058	−0.660289	+	0.751011i	$0.729566\pi$
$398$	5072.00	0.638785
$399$	2604.00	0.326724
$400$	0	0
$401$	−11334.0	−1.41145	−0.705727	−	0.708484i	$-0.749379\pi$
$401$	−11334.0	−1.41145	−0.705727	+	0.708484i	$0.749379\pi$
$402$	4584.00	0.568729
$403$	−3024.00	−0.373787
$404$	5480.00	0.674852
$405$	0	0
$406$	−3556.00	−0.434683
$407$	3184.00	0.387776
$408$	48.0000	0.00582440
$409$	8594.00	1.03899	0.519494	−	0.854474i	$-0.326121\pi$
$409$	8594.00	1.03899	0.519494	+	0.854474i	$0.326121\pi$
$410$	0	0
$411$	2454.00	0.294518
$412$	−1856.00	−0.221938
$413$	−5404.00	−0.643858
$414$	1368.00	0.162400
$415$	0	0
$416$	−1344.00	−0.158401
$417$	6468.00	0.759567
$418$	−1984.00	−0.232155
$419$	10500.0	1.22424	0.612122	−	0.790763i	$-0.290316\pi$
$419$	10500.0	1.22424	0.612122	+	0.790763i	$0.290316\pi$
$420$	0	0
$421$	−12066.0	−1.39682	−0.698410	−	0.715698i	$-0.746109\pi$
$421$	−12066.0	−1.39682	−0.698410	+	0.715698i	$0.746109\pi$
$422$	2600.00	0.299919
$423$	2376.00	0.273109
$424$	−1296.00	−0.148442
$425$	0	0
$426$	−1416.00	−0.161046
$427$	210.000	0.0238000
$428$	8544.00	0.964930
$429$	1008.00	0.113442
$430$	0	0
$431$	4332.00	0.484142	0.242071	−	0.970259i	$-0.422173\pi$
$431$	4332.00	0.484142	0.242071	+	0.970259i	$0.422173\pi$
$432$	−432.000	−0.0481125
$433$	1918.00	0.212871	0.106436	−	0.994320i	$-0.466056\pi$
$433$	1918.00	0.212871	0.106436	+	0.994320i	$0.466056\pi$
$434$	1008.00	0.111487
$435$	0	0
$436$	−4904.00	−0.538667
$437$	9424.00	1.03160
$438$	−2508.00	−0.273600
$439$	−7992.00	−0.868878	−0.434439	−	0.900701i	$-0.643053\pi$
$439$	−7992.00	−0.868878	−0.434439	+	0.900701i	$0.643053\pi$
$440$	0	0
$441$	441.000	0.0476190
$442$	−168.000	−0.0180791
$443$	−3184.00	−0.341482	−0.170741	−	0.985316i	$-0.554616\pi$
$443$	−3184.00	−0.341482	−0.170741	+	0.985316i	$0.554616\pi$
$444$	4776.00	0.510493
$445$	0	0
$446$	5152.00	0.546983
$447$	8550.00	0.904700
$448$	448.000	0.0472456
$449$	11426.0	1.20095	0.600475	−	0.799644i	$-0.294978\pi$
$449$	11426.0	1.20095	0.600475	+	0.799644i	$0.294978\pi$
$450$	0	0
$451$	−3696.00	−0.385893
$452$	−1352.00	−0.140692
$453$	−5016.00	−0.520248
$454$	−3672.00	−0.379594
$455$	0	0
$456$	−2976.00	−0.305623
$457$	16934.0	1.73335	0.866673	−	0.498877i	$-0.166254\pi$
$457$	16934.0	1.73335	0.866673	+	0.498877i	$0.166254\pi$
$458$	3748.00	0.382385
$459$	−54.0000	−0.00549129
$460$	0	0
$461$	−17038.0	−1.72134	−0.860671	−	0.509161i	$-0.829956\pi$
$461$	−17038.0	−1.72134	−0.860671	+	0.509161i	$0.829956\pi$
$462$	−336.000	−0.0338358
$463$	13592.0	1.36431	0.682153	−	0.731209i	$-0.261044\pi$
$463$	13592.0	1.36431	0.682153	+	0.731209i	$0.261044\pi$
$464$	4064.00	0.406609
$465$	0	0
$466$	7460.00	0.741583
$467$	−8612.00	−0.853353	−0.426676	−	0.904404i	$-0.640316\pi$
$467$	−8612.00	−0.853353	−0.426676	+	0.904404i	$0.640316\pi$
$468$	1512.00	0.149342
$469$	5348.00	0.526541
$470$	0	0
$471$	1338.00	0.130896
$472$	6176.00	0.602274
$473$	1696.00	0.164867
$474$	3312.00	0.320939
$475$	0	0
$476$	56.0000	0.00539234
$477$	1458.00	0.139952
$478$	−4008.00	−0.383518
$479$	7432.00	0.708928	0.354464	−	0.935070i	$-0.384663\pi$
$479$	7432.00	0.708928	0.354464	+	0.935070i	$0.384663\pi$
$480$	0	0
$481$	−16716.0	−1.58458
$482$	1292.00	0.122093
$483$	1596.00	0.150353
$484$	−5068.00	−0.475958
$485$	0	0
$486$	486.000	0.0453609
$487$	6616.00	0.615605	0.307802	−	0.951450i	$-0.400406\pi$
$487$	6616.00	0.615605	0.307802	+	0.951450i	$0.400406\pi$
$488$	−240.000	−0.0222629
$489$	8124.00	0.751288
$490$	0	0
$491$	17040.0	1.56620	0.783100	−	0.621896i	$-0.213637\pi$
$491$	17040.0	1.56620	0.783100	+	0.621896i	$0.213637\pi$
$492$	−5544.00	−0.508014
$493$	508.000	0.0464081
$494$	10416.0	0.948660
$495$	0	0
$496$	−1152.00	−0.104287
$497$	−1652.00	−0.149099
$498$	−6216.00	−0.559329
$499$	−2948.00	−0.264470	−0.132235	−	0.991218i	$-0.542215\pi$
$499$	−2948.00	−0.264470	−0.132235	+	0.991218i	$0.542215\pi$
$500$	0	0
$501$	2688.00	0.239703
$502$	−2520.00	−0.224050
$503$	−17304.0	−1.53389	−0.766946	−	0.641712i	$-0.778224\pi$
$503$	−17304.0	−1.53389	−0.766946	+	0.641712i	$0.778224\pi$
$504$	−504.000	−0.0445435
$505$	0	0
$506$	−1216.00	−0.106834
$507$	1299.00	0.113788
$508$	−8352.00	−0.729449
$509$	4650.00	0.404927	0.202463	−	0.979290i	$-0.435105\pi$
$509$	4650.00	0.404927	0.202463	+	0.979290i	$0.435105\pi$
$510$	0	0
$511$	−2926.00	−0.253305
$512$	−512.000	−0.0441942
$513$	3348.00	0.288144
$514$	11820.0	1.01431
$515$	0	0
$516$	2544.00	0.217041
$517$	−2112.00	−0.179663
$518$	5572.00	0.472625
$519$	12102.0	1.02354
$520$	0	0
$521$	16854.0	1.41725	0.708625	−	0.705585i	$-0.249316\pi$
$521$	16854.0	1.41725	0.708625	+	0.705585i	$0.249316\pi$
$522$	−4572.00	−0.383354
$523$	124.000	0.0103674	0.00518369	−	0.999987i	$-0.498350\pi$
$523$	124.000	0.0103674	0.00518369	+	0.999987i	$0.498350\pi$
$524$	−1168.00	−0.0973747
$525$	0	0
$526$	5976.00	0.495373
$527$	−144.000	−0.0119027
$528$	384.000	0.0316505
$529$	−6391.00	−0.525273
$530$	0	0
$531$	−6948.00	−0.567830
$532$	−3472.00	−0.282952
$533$	19404.0	1.57689
$534$	180.000	0.0145868
$535$	0	0
$536$	−6112.00	−0.492534
$537$	10440.0	0.838956
$538$	2636.00	0.211238
$539$	−392.000	−0.0313259
$540$	0	0
$541$	5382.00	0.427708	0.213854	−	0.976866i	$-0.431398\pi$
$541$	5382.00	0.427708	0.213854	+	0.976866i	$0.431398\pi$
$542$	11280.0	0.893944
$543$	8694.00	0.687100
$544$	−64.0000	−0.00504408
$545$	0	0
$546$	1764.00	0.138264
$547$	−17460.0	−1.36478	−0.682391	−	0.730987i	$-0.739060\pi$
$547$	−17460.0	−1.36478	−0.682391	+	0.730987i	$0.739060\pi$
$548$	−3272.00	−0.255060
$549$	270.000	0.0209897
$550$	0	0
$551$	−31496.0	−2.43516
$552$	−1824.00	−0.140642
$553$	3864.00	0.297132
$554$	12892.0	0.988680
$555$	0	0
$556$	−8624.00	−0.657804
$557$	9514.00	0.723736	0.361868	−	0.932229i	$-0.382139\pi$
$557$	9514.00	0.723736	0.361868	+	0.932229i	$0.382139\pi$
$558$	1296.00	0.0983227
$559$	−8904.00	−0.673701
$560$	0	0
$561$	48.0000	0.00361241
$562$	−9860.00	−0.740069
$563$	−3988.00	−0.298533	−0.149267	−	0.988797i	$-0.547691\pi$
$563$	−3988.00	−0.298533	−0.149267	+	0.988797i	$0.547691\pi$
$564$	−3168.00	−0.236519
$565$	0	0
$566$	−12520.0	−0.929779
$567$	567.000	0.0419961
$568$	1888.00	0.139470
$569$	11346.0	0.835939	0.417969	−	0.908461i	$-0.362742\pi$
$569$	11346.0	0.835939	0.417969	+	0.908461i	$0.362742\pi$
$570$	0	0
$571$	−8436.00	−0.618276	−0.309138	−	0.951017i	$-0.600041\pi$
$571$	−8436.00	−0.618276	−0.309138	+	0.951017i	$0.600041\pi$
$572$	−1344.00	−0.0982438
$573$	−7956.00	−0.580047
$574$	−6468.00	−0.470329
$575$	0	0
$576$	576.000	0.0416667
$577$	−2098.00	−0.151371	−0.0756853	−	0.997132i	$-0.524114\pi$
$577$	−2098.00	−0.151371	−0.0756853	+	0.997132i	$0.524114\pi$
$578$	9818.00	0.706531
$579$	438.000	0.0314381
$580$	0	0
$581$	−7252.00	−0.517838
$582$	7140.00	0.508527
$583$	−1296.00	−0.0920666
$584$	3344.00	0.236945
$585$	0	0
$586$	−4620.00	−0.325683
$587$	−9436.00	−0.663484	−0.331742	−	0.943370i	$-0.607636\pi$
$587$	−9436.00	−0.663484	−0.331742	+	0.943370i	$0.607636\pi$
$588$	−588.000	−0.0412393
$589$	8928.00	0.624570
$590$	0	0
$591$	−7638.00	−0.531616
$592$	−6368.00	−0.442100
$593$	1314.00	0.0909941	0.0454971	−	0.998964i	$-0.485513\pi$
$593$	1314.00	0.0909941	0.0454971	+	0.998964i	$0.485513\pi$
$594$	−432.000	−0.0298404
$595$	0	0
$596$	−11400.0	−0.783494
$597$	7608.00	0.521566
$598$	6384.00	0.436557
$599$	−8940.00	−0.609814	−0.304907	−	0.952382i	$-0.598625\pi$
$599$	−8940.00	−0.609814	−0.304907	+	0.952382i	$0.598625\pi$
$600$	0	0
$601$	16058.0	1.08988	0.544941	−	0.838474i	$-0.316552\pi$
$601$	16058.0	1.08988	0.544941	+	0.838474i	$0.316552\pi$
$602$	2968.00	0.200941
$603$	6876.00	0.464365
$604$	6688.00	0.450548
$605$	0	0
$606$	8220.00	0.551014
$607$	−3936.00	−0.263192	−0.131596	−	0.991303i	$-0.542010\pi$
$607$	−3936.00	−0.263192	−0.131596	+	0.991303i	$0.542010\pi$
$608$	3968.00	0.264677
$609$	−5334.00	−0.354917
$610$	0	0
$611$	11088.0	0.734161
$612$	72.0000	0.00475560
$613$	−174.000	−0.0114646	−0.00573230	−	0.999984i	$-0.501825\pi$
$613$	−174.000	−0.0114646	−0.00573230	+	0.999984i	$0.501825\pi$
$614$	392.000	0.0257652
$615$	0	0
$616$	448.000	0.0293027
$617$	−16018.0	−1.04515	−0.522577	−	0.852592i	$-0.675029\pi$
$617$	−16018.0	−1.04515	−0.522577	+	0.852592i	$0.675029\pi$
$618$	−2784.00	−0.181212
$619$	−3068.00	−0.199214	−0.0996069	−	0.995027i	$-0.531759\pi$
$619$	−3068.00	−0.199214	−0.0996069	+	0.995027i	$0.531759\pi$
$620$	0	0
$621$	2052.00	0.132599
$622$	13472.0	0.868453
$623$	210.000	0.0135048
$624$	−2016.00	−0.129334
$625$	0	0
$626$	788.000	0.0503112
$627$	−2976.00	−0.189553
$628$	−1784.00	−0.113359
$629$	−796.000	−0.0504588
$630$	0	0
$631$	24656.0	1.55553	0.777765	−	0.628555i	$-0.216353\pi$
$631$	24656.0	1.55553	0.777765	+	0.628555i	$0.216353\pi$
$632$	−4416.00	−0.277942
$633$	3900.00	0.244883
$634$	−13428.0	−0.841158
$635$	0	0
$636$	−1944.00	−0.121202
$637$	2058.00	0.128008
$638$	4064.00	0.252187
$639$	−2124.00	−0.131493
$640$	0	0
$641$	7594.00	0.467933	0.233966	−	0.972245i	$-0.424829\pi$
$641$	7594.00	0.467933	0.233966	+	0.972245i	$0.424829\pi$
$642$	12816.0	0.787862
$643$	3724.00	0.228398	0.114199	−	0.993458i	$-0.463570\pi$
$643$	3724.00	0.228398	0.114199	+	0.993458i	$0.463570\pi$
$644$	−2128.00	−0.130210
$645$	0	0
$646$	496.000	0.0302088
$647$	−3792.00	−0.230416	−0.115208	−	0.993341i	$-0.536753\pi$
$647$	−3792.00	−0.230416	−0.115208	+	0.993341i	$0.536753\pi$
$648$	−648.000	−0.0392837
$649$	6176.00	0.373543
$650$	0	0
$651$	1512.00	0.0910291
$652$	−10832.0	−0.650635
$653$	−24702.0	−1.48034	−0.740171	−	0.672418i	$-0.765256\pi$
$653$	−24702.0	−1.48034	−0.740171	+	0.672418i	$0.765256\pi$
$654$	−7356.00	−0.439820
$655$	0	0
$656$	7392.00	0.439953
$657$	−3762.00	−0.223394
$658$	−3696.00	−0.218974
$659$	−20144.0	−1.19074	−0.595371	−	0.803451i	$-0.702995\pi$
$659$	−20144.0	−1.19074	−0.595371	+	0.803451i	$0.702995\pi$
$660$	0	0
$661$	−2522.00	−0.148403	−0.0742015	−	0.997243i	$-0.523641\pi$
$661$	−2522.00	−0.148403	−0.0742015	+	0.997243i	$0.523641\pi$
$662$	−1384.00	−0.0812548
$663$	−252.000	−0.0147615
$664$	8288.00	0.484393
$665$	0	0
$666$	7164.00	0.416816
$667$	−19304.0	−1.12062
$668$	−3584.00	−0.207589
$669$	7728.00	0.446609
$670$	0	0
$671$	−240.000	−0.0138079
$672$	672.000	0.0385758
$673$	10414.0	0.596479	0.298239	−	0.954491i	$-0.403601\pi$
$673$	10414.0	0.596479	0.298239	+	0.954491i	$0.403601\pi$
$674$	−3132.00	−0.178991
$675$	0	0
$676$	−1732.00	−0.0985435
$677$	22230.0	1.26199	0.630996	−	0.775786i	$-0.282647\pi$
$677$	22230.0	1.26199	0.630996	+	0.775786i	$0.282647\pi$
$678$	−2028.00	−0.114874
$679$	8330.00	0.470804
$680$	0	0
$681$	−5508.00	−0.309937
$682$	−1152.00	−0.0646809
$683$	−18192.0	−1.01918	−0.509588	−	0.860418i	$-0.670202\pi$
$683$	−18192.0	−1.01918	−0.509588	+	0.860418i	$0.670202\pi$
$684$	−4464.00	−0.249540
$685$	0	0
$686$	−686.000	−0.0381802
$687$	5622.00	0.312216
$688$	−3392.00	−0.187963
$689$	6804.00	0.376214
$690$	0	0
$691$	8108.00	0.446372	0.223186	−	0.974776i	$-0.428354\pi$
$691$	8108.00	0.446372	0.223186	+	0.974776i	$0.428354\pi$
$692$	−16136.0	−0.886414
$693$	−504.000	−0.0276268
$694$	−10656.0	−0.582848
$695$	0	0
$696$	6096.00	0.331995
$697$	924.000	0.0502138
$698$	−22652.0	−1.22835
$699$	11190.0	0.605500
$700$	0	0
$701$	−5794.00	−0.312177	−0.156089	−	0.987743i	$-0.549889\pi$
$701$	−5794.00	−0.312177	−0.156089	+	0.987743i	$0.549889\pi$
$702$	2268.00	0.121938
$703$	49352.0	2.64772
$704$	−512.000	−0.0274101
$705$	0	0
$706$	−4260.00	−0.227092
$707$	9590.00	0.510140
$708$	9264.00	0.491755
$709$	−1954.00	−0.103504	−0.0517518	−	0.998660i	$-0.516480\pi$
$709$	−1954.00	−0.103504	−0.0517518	+	0.998660i	$0.516480\pi$
$710$	0	0
$711$	4968.00	0.262046
$712$	−240.000	−0.0126326
$713$	5472.00	0.287417
$714$	84.0000	0.00440283
$715$	0	0
$716$	−13920.0	−0.726557
$717$	−6012.00	−0.313141
$718$	−6088.00	−0.316438
$719$	−32016.0	−1.66063	−0.830317	−	0.557292i	$-0.811840\pi$
$719$	−32016.0	−1.66063	−0.830317	+	0.557292i	$0.811840\pi$
$720$	0	0
$721$	−3248.00	−0.167770
$722$	−17034.0	−0.878033
$723$	1938.00	0.0996888
$724$	−11592.0	−0.595046
$725$	0	0
$726$	−7602.00	−0.388618
$727$	23072.0	1.17702	0.588510	−	0.808490i	$-0.299715\pi$
$727$	23072.0	1.17702	0.588510	+	0.808490i	$0.299715\pi$
$728$	−2352.00	−0.119740
$729$	729.000	0.0370370
$730$	0	0
$731$	−424.000	−0.0214531
$732$	−360.000	−0.0181776
$733$	−31782.0	−1.60149	−0.800747	−	0.599003i	$-0.795564\pi$
$733$	−31782.0	−1.60149	−0.800747	+	0.599003i	$0.795564\pi$
$734$	24832.0	1.24873
$735$	0	0
$736$	2432.00	0.121800
$737$	−6112.00	−0.305480
$738$	−8316.00	−0.414792
$739$	−24396.0	−1.21437	−0.607186	−	0.794559i	$-0.707702\pi$
$739$	−24396.0	−1.21437	−0.607186	+	0.794559i	$0.707702\pi$
$740$	0	0
$741$	15624.0	0.774578
$742$	−2268.00	−0.112211
$743$	32604.0	1.60986	0.804929	−	0.593371i	$-0.202203\pi$
$743$	32604.0	1.60986	0.804929	+	0.593371i	$0.202203\pi$
$744$	−1728.00	−0.0851499
$745$	0	0
$746$	−14884.0	−0.730485
$747$	−9324.00	−0.456690
$748$	−64.0000	−0.00312844
$749$	14952.0	0.729418
$750$	0	0
$751$	−7680.00	−0.373165	−0.186583	−	0.982439i	$-0.559741\pi$
$751$	−7680.00	−0.373165	−0.186583	+	0.982439i	$0.559741\pi$
$752$	4224.00	0.204832
$753$	−3780.00	−0.182936
$754$	−21336.0	−1.03052
$755$	0	0
$756$	−756.000	−0.0363696
$757$	−366.000	−0.0175727	−0.00878633	−	0.999961i	$-0.502797\pi$
$757$	−366.000	−0.0175727	−0.00878633	+	0.999961i	$0.502797\pi$
$758$	−200.000	−0.00958355
$759$	−1824.00	−0.0872293
$760$	0	0
$761$	29374.0	1.39922	0.699610	−	0.714525i	$-0.253357\pi$
$761$	29374.0	1.39922	0.699610	+	0.714525i	$0.253357\pi$
$762$	−12528.0	−0.595593
$763$	−8582.00	−0.407194
$764$	10608.0	0.502335
$765$	0	0
$766$	16160.0	0.762251
$767$	−32424.0	−1.52642
$768$	−768.000	−0.0360844
$769$	−38990.0	−1.82837	−0.914184	−	0.405299i	$-0.867167\pi$
$769$	−38990.0	−1.82837	−0.914184	+	0.405299i	$0.867167\pi$
$770$	0	0
$771$	17730.0	0.828185
$772$	−584.000	−0.0272262
$773$	20470.0	0.952464	0.476232	−	0.879320i	$-0.342002\pi$
$773$	20470.0	0.952464	0.476232	+	0.879320i	$0.342002\pi$
$774$	3816.00	0.177214
$775$	0	0
$776$	−9520.00	−0.440397
$777$	8358.00	0.385896
$778$	10964.0	0.505242
$779$	−57288.0	−2.63486
$780$	0	0
$781$	1888.00	0.0865019
$782$	304.000	0.0139016
$783$	−6858.00	−0.313008
$784$	784.000	0.0357143
$785$	0	0
$786$	−1752.00	−0.0795061
$787$	−29916.0	−1.35501	−0.677503	−	0.735520i	$-0.736938\pi$
$787$	−29916.0	−1.35501	−0.677503	+	0.735520i	$0.736938\pi$
$788$	10184.0	0.460393
$789$	8964.00	0.404470
$790$	0	0
$791$	−2366.00	−0.106353
$792$	576.000	0.0258425
$793$	1260.00	0.0564236
$794$	20892.0	0.933790
$795$	0	0
$796$	−10144.0	−0.451689
$797$	−4914.00	−0.218398	−0.109199	−	0.994020i	$-0.534828\pi$
$797$	−4914.00	−0.218398	−0.109199	+	0.994020i	$0.534828\pi$
$798$	−5208.00	−0.231029
$799$	528.000	0.0233783
$800$	0	0
$801$	270.000	0.0119101
$802$	22668.0	0.998049
$803$	3344.00	0.146958
$804$	−9168.00	−0.402152
$805$	0	0
$806$	6048.00	0.264307
$807$	3954.00	0.172475
$808$	−10960.0	−0.477192
$809$	34250.0	1.48846	0.744231	−	0.667922i	$-0.232816\pi$
$809$	34250.0	1.48846	0.744231	+	0.667922i	$0.232816\pi$
$810$	0	0
$811$	−41804.0	−1.81003	−0.905017	−	0.425376i	$-0.860142\pi$
$811$	−41804.0	−1.81003	−0.905017	+	0.425376i	$0.860142\pi$
$812$	7112.00	0.307367
$813$	16920.0	0.729902
$814$	−6368.00	−0.274199
$815$	0	0
$816$	−96.0000	−0.00411847
$817$	26288.0	1.12570
$818$	−17188.0	−0.734675
$819$	2646.00	0.112892
$820$	0	0
$821$	30862.0	1.31193	0.655963	−	0.754793i	$-0.272263\pi$
$821$	30862.0	1.31193	0.655963	+	0.754793i	$0.272263\pi$
$822$	−4908.00	−0.208256
$823$	−10576.0	−0.447942	−0.223971	−	0.974596i	$-0.571902\pi$
$823$	−10576.0	−0.447942	−0.223971	+	0.974596i	$0.571902\pi$
$824$	3712.00	0.156934
$825$	0	0
$826$	10808.0	0.455277
$827$	10680.0	0.449069	0.224534	−	0.974466i	$-0.427914\pi$
$827$	10680.0	0.449069	0.224534	+	0.974466i	$0.427914\pi$
$828$	−2736.00	−0.114834
$829$	−1178.00	−0.0493530	−0.0246765	−	0.999695i	$-0.507856\pi$
$829$	−1178.00	−0.0493530	−0.0246765	+	0.999695i	$0.507856\pi$
$830$	0	0
$831$	19338.0	0.807254
$832$	2688.00	0.112007
$833$	98.0000	0.00407623
$834$	−12936.0	−0.537095
$835$	0	0
$836$	3968.00	0.164158
$837$	1944.00	0.0802801
$838$	−21000.0	−0.865672
$839$	−5600.00	−0.230433	−0.115217	−	0.993340i	$-0.536756\pi$
$839$	−5600.00	−0.230433	−0.115217	+	0.993340i	$0.536756\pi$
$840$	0	0
$841$	40127.0	1.64529
$842$	24132.0	0.987700
$843$	−14790.0	−0.604264
$844$	−5200.00	−0.212075
$845$	0	0
$846$	−4752.00	−0.193117
$847$	−8869.00	−0.359790
$848$	2592.00	0.104964
$849$	−18780.0	−0.759161
$850$	0	0
$851$	30248.0	1.21843
$852$	2832.00	0.113876
$853$	826.000	0.0331556	0.0165778	−	0.999863i	$-0.494723\pi$
$853$	826.000	0.0331556	0.0165778	+	0.999863i	$0.494723\pi$
$854$	−420.000	−0.0168292
$855$	0	0
$856$	−17088.0	−0.682308
$857$	−45918.0	−1.83026	−0.915128	−	0.403164i	$-0.867910\pi$
$857$	−45918.0	−1.83026	−0.915128	+	0.403164i	$0.867910\pi$
$858$	−2016.00	−0.0802157
$859$	42380.0	1.68334	0.841669	−	0.539994i	$-0.181574\pi$
$859$	42380.0	1.68334	0.841669	+	0.539994i	$0.181574\pi$
$860$	0	0
$861$	−9702.00	−0.384022
$862$	−8664.00	−0.342340
$863$	26524.0	1.04622	0.523110	−	0.852265i	$-0.324772\pi$
$863$	26524.0	1.04622	0.523110	+	0.852265i	$0.324772\pi$
$864$	864.000	0.0340207
$865$	0	0
$866$	−3836.00	−0.150523
$867$	14727.0	0.576880
$868$	−2016.00	−0.0788335
$869$	−4416.00	−0.172385
$870$	0	0
$871$	32088.0	1.24829
$872$	9808.00	0.380895
$873$	10710.0	0.415210
$874$	−18848.0	−0.729454
$875$	0	0
$876$	5016.00	0.193465
$877$	−20614.0	−0.793712	−0.396856	−	0.917881i	$-0.629899\pi$
$877$	−20614.0	−0.793712	−0.396856	+	0.917881i	$0.629899\pi$
$878$	15984.0	0.614389
$879$	−6930.00	−0.265919
$880$	0	0
$881$	−23730.0	−0.907473	−0.453737	−	0.891136i	$-0.649909\pi$
$881$	−23730.0	−0.907473	−0.453737	+	0.891136i	$0.649909\pi$
$882$	−882.000	−0.0336718
$883$	9028.00	0.344073	0.172036	−	0.985091i	$-0.444965\pi$
$883$	9028.00	0.344073	0.172036	+	0.985091i	$0.444965\pi$
$884$	336.000	0.0127838
$885$	0	0
$886$	6368.00	0.241464
$887$	−37200.0	−1.40818	−0.704089	−	0.710112i	$-0.748644\pi$
$887$	−37200.0	−1.40818	−0.704089	+	0.710112i	$0.748644\pi$
$888$	−9552.00	−0.360973
$889$	−14616.0	−0.551412
$890$	0	0
$891$	−648.000	−0.0243646
$892$	−10304.0	−0.386775
$893$	−32736.0	−1.22673
$894$	−17100.0	−0.639720
$895$	0	0
$896$	−896.000	−0.0334077
$897$	9576.00	0.356447
$898$	−22852.0	−0.849199
$899$	−18288.0	−0.678464
$900$	0	0
$901$	324.000	0.0119800
$902$	7392.00	0.272868
$903$	4452.00	0.164068
$904$	2704.00	0.0994842
$905$	0	0
$906$	10032.0	0.367871
$907$	−23988.0	−0.878179	−0.439090	−	0.898443i	$-0.644699\pi$
$907$	−23988.0	−0.878179	−0.439090	+	0.898443i	$0.644699\pi$
$908$	7344.00	0.268413
$909$	12330.0	0.449901
$910$	0	0
$911$	15276.0	0.555561	0.277781	−	0.960645i	$-0.410401\pi$
$911$	15276.0	0.555561	0.277781	+	0.960645i	$0.410401\pi$
$912$	5952.00	0.216108
$913$	8288.00	0.300430
$914$	−33868.0	−1.22566
$915$	0	0
$916$	−7496.00	−0.270387
$917$	−2044.00	−0.0736083
$918$	108.000	0.00388293
$919$	−10760.0	−0.386224	−0.193112	−	0.981177i	$-0.561858\pi$
$919$	−10760.0	−0.386224	−0.193112	+	0.981177i	$0.561858\pi$
$920$	0	0
$921$	588.000	0.0210372
$922$	34076.0	1.21717
$923$	−9912.00	−0.353475
$924$	672.000	0.0239255
$925$	0	0
$926$	−27184.0	−0.964710
$927$	−4176.00	−0.147959
$928$	−8128.00	−0.287516
$929$	−52890.0	−1.86788	−0.933942	−	0.357424i	$-0.883655\pi$
$929$	−52890.0	−1.86788	−0.933942	+	0.357424i	$0.883655\pi$
$930$	0	0
$931$	−6076.00	−0.213891
$932$	−14920.0	−0.524379
$933$	20208.0	0.709089
$934$	17224.0	0.603412
$935$	0	0
$936$	−3024.00	−0.105601
$937$	6118.00	0.213305	0.106652	−	0.994296i	$-0.465987\pi$
$937$	6118.00	0.213305	0.106652	+	0.994296i	$0.465987\pi$
$938$	−10696.0	−0.372321
$939$	1182.00	0.0410789
$940$	0	0
$941$	−32230.0	−1.11654	−0.558272	−	0.829658i	$-0.688535\pi$
$941$	−32230.0	−1.11654	−0.558272	+	0.829658i	$0.688535\pi$
$942$	−2676.00	−0.0925571
$943$	−35112.0	−1.21252
$944$	−12352.0	−0.425872
$945$	0	0
$946$	−3392.00	−0.116579
$947$	18544.0	0.636324	0.318162	−	0.948036i	$-0.396934\pi$
$947$	18544.0	0.636324	0.318162	+	0.948036i	$0.396934\pi$
$948$	−6624.00	−0.226938
$949$	−17556.0	−0.600518
$950$	0	0
$951$	−20142.0	−0.686802
$952$	−112.000	−0.00381296
$953$	−25930.0	−0.881380	−0.440690	−	0.897659i	$-0.645266\pi$
$953$	−25930.0	−0.881380	−0.440690	+	0.897659i	$0.645266\pi$
$954$	−2916.00	−0.0989612
$955$	0	0
$956$	8016.00	0.271188
$957$	6096.00	0.205910
$958$	−14864.0	−0.501288
$959$	−5726.00	−0.192807
$960$	0	0
$961$	−24607.0	−0.825988
$962$	33432.0	1.12047
$963$	19224.0	0.643286
$964$	−2584.00	−0.0863330
$965$	0	0
$966$	−3192.00	−0.106316
$967$	−8192.00	−0.272427	−0.136214	−	0.990680i	$-0.543493\pi$
$967$	−8192.00	−0.272427	−0.136214	+	0.990680i	$0.543493\pi$
$968$	10136.0	0.336553
$969$	744.000	0.0246653
$970$	0	0
$971$	−54444.0	−1.79937	−0.899686	−	0.436537i	$-0.856205\pi$
$971$	−54444.0	−1.79937	−0.899686	+	0.436537i	$0.856205\pi$
$972$	−972.000	−0.0320750
$973$	−15092.0	−0.497253
$974$	−13232.0	−0.435298
$975$	0	0
$976$	480.000	0.0157422
$977$	25446.0	0.833255	0.416627	−	0.909077i	$-0.363212\pi$
$977$	25446.0	0.833255	0.416627	+	0.909077i	$0.363212\pi$
$978$	−16248.0	−0.531241
$979$	−240.000	−0.00783497
$980$	0	0
$981$	−11034.0	−0.359112
$982$	−34080.0	−1.10747
$983$	−33192.0	−1.07697	−0.538484	−	0.842635i	$-0.681003\pi$
$983$	−33192.0	−1.07697	−0.538484	+	0.842635i	$0.681003\pi$
$984$	11088.0	0.359220
$985$	0	0
$986$	−1016.00	−0.0328154
$987$	−5544.00	−0.178792
$988$	−20832.0	−0.670804
$989$	16112.0	0.518030
$990$	0	0
$991$	11024.0	0.353369	0.176685	−	0.984268i	$-0.443463\pi$
$991$	11024.0	0.353369	0.176685	+	0.984268i	$0.443463\pi$
$992$	2304.00	0.0737420
$993$	−2076.00	−0.0663443
$994$	3304.00	0.105429
$995$	0	0
$996$	12432.0	0.395505
$997$	40714.0	1.29331	0.646653	−	0.762785i	$-0.276168\pi$
$997$	40714.0	1.29331	0.646653	+	0.762785i	$0.276168\pi$
$998$	5896.00	0.187009
$999$	10746.0	0.340329

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.4.a.d.1.1		1
5.2	odd	4		1050.4.g.n.799.1		2
5.3	odd	4		1050.4.g.n.799.2		2
5.4	even	2		42.4.a.b.1.1	✓	1
15.14	odd	2		126.4.a.c.1.1		1
20.19	odd	2		336.4.a.d.1.1		1
35.4	even	6		294.4.e.a.79.1		2
35.9	even	6		294.4.e.a.67.1		2
35.19	odd	6		294.4.e.d.67.1		2
35.24	odd	6		294.4.e.d.79.1		2
35.34	odd	2		294.4.a.h.1.1		1
40.19	odd	2		1344.4.a.t.1.1		1
40.29	even	2		1344.4.a.f.1.1		1
60.59	even	2		1008.4.a.j.1.1		1
105.44	odd	6		882.4.g.s.361.1		2
105.59	even	6		882.4.g.r.667.1		2
105.74	odd	6		882.4.g.s.667.1		2
105.89	even	6		882.4.g.r.361.1		2
105.104	even	2		882.4.a.d.1.1		1
140.139	even	2		2352.4.a.ba.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.4.a.b.1.1	✓	1	5.4	even	2
126.4.a.c.1.1		1	15.14	odd	2
294.4.a.h.1.1		1	35.34	odd	2
294.4.e.a.67.1		2	35.9	even	6
294.4.e.a.79.1		2	35.4	even	6
294.4.e.d.67.1		2	35.19	odd	6
294.4.e.d.79.1		2	35.24	odd	6
336.4.a.d.1.1		1	20.19	odd	2
882.4.a.d.1.1		1	105.104	even	2
882.4.g.r.361.1		2	105.89	even	6
882.4.g.r.667.1		2	105.59	even	6
882.4.g.s.361.1		2	105.44	odd	6
882.4.g.s.667.1		2	105.74	odd	6
1008.4.a.j.1.1		1	60.59	even	2
1050.4.a.d.1.1		1	1.1	even	1	trivial
1050.4.g.n.799.1		2	5.2	odd	4
1050.4.g.n.799.2		2	5.3	odd	4
1344.4.a.f.1.1		1	40.29	even	2
1344.4.a.t.1.1		1	40.19	odd	2
2352.4.a.ba.1.1		1	140.139	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1050.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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