LMFDB - Embedded newform 2280.4.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2280,4,Mod(1,2280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2280, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 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("2280.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2280 = 2^{3} \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2280.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:	$134.524354813$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2280.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-3.00000 q^{3} -5.00000 q^{5} +28.0000 q^{7} +9.00000 q^{9} +O(q^{10})$

$q-3.00000 q^{3} -5.00000 q^{5} +28.0000 q^{7} +9.00000 q^{9} +64.0000 q^{11} +2.00000 q^{13} +15.0000 q^{15} -74.0000 q^{17} -19.0000 q^{19} -84.0000 q^{21} -72.0000 q^{23} +25.0000 q^{25} -27.0000 q^{27} -310.000 q^{29} +248.000 q^{31} -192.000 q^{33} -140.000 q^{35} -158.000 q^{37} -6.00000 q^{39} -462.000 q^{41} +36.0000 q^{43} -45.0000 q^{45} -168.000 q^{47} +441.000 q^{49} +222.000 q^{51} +82.0000 q^{53} -320.000 q^{55} +57.0000 q^{57} -504.000 q^{59} -706.000 q^{61} +252.000 q^{63} -10.0000 q^{65} +844.000 q^{67} +216.000 q^{69} +224.000 q^{71} -894.000 q^{73} -75.0000 q^{75} +1792.00 q^{77} -1000.00 q^{79} +81.0000 q^{81} +892.000 q^{83} +370.000 q^{85} +930.000 q^{87} +266.000 q^{89} +56.0000 q^{91} -744.000 q^{93} +95.0000 q^{95} -822.000 q^{97} +576.000 q^{99} +O(q^{100})$

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 $

$2$	0	0
$2$	0	0
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	0	0
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	0	0
$7$	28.0000	1.51186	0.755929	−	0.654654i	$-0.227186\pi$
$7$	28.0000	1.51186	0.755929	+	0.654654i	$0.227186\pi$
$8$	0	0
$9$	9.00000	0.333333
$10$	0	0
$11$	64.0000	1.75425	0.877124	−	0.480264i	$-0.159459\pi$
$11$	64.0000	1.75425	0.877124	+	0.480264i	$0.159459\pi$
$12$	0	0
$13$	2.00000	0.0426692	0.0213346	−	0.999772i	$-0.493208\pi$
$13$	2.00000	0.0426692	0.0213346	+	0.999772i	$0.493208\pi$
$14$	0	0
$15$	15.0000	0.258199
$16$	0	0
$17$	−74.0000	−1.05574	−0.527872	−	0.849324i	$-0.677010\pi$
$17$	−74.0000	−1.05574	−0.527872	+	0.849324i	$0.677010\pi$
$18$	0	0
$19$	−19.0000	−0.229416
$19$	−19.0000	−0.229416
$20$	0	0
$21$	−84.0000	−0.872872
$22$	0	0
$23$	−72.0000	−0.652741	−0.326370	−	0.945242i	$-0.605826\pi$
$23$	−72.0000	−0.652741	−0.326370	+	0.945242i	$0.605826\pi$
$24$	0	0
$25$	25.0000	0.200000
$26$	0	0
$27$	−27.0000	−0.192450
$28$	0	0
$29$	−310.000	−1.98502	−0.992510	−	0.122167i	$-0.961016\pi$
$29$	−310.000	−1.98502	−0.992510	+	0.122167i	$0.961016\pi$
$30$	0	0
$31$	248.000	1.43684	0.718421	−	0.695608i	$-0.244865\pi$
$31$	248.000	1.43684	0.718421	+	0.695608i	$0.244865\pi$
$32$	0	0
$33$	−192.000	−1.01282
$34$	0	0
$35$	−140.000	−0.676123
$36$	0	0
$37$	−158.000	−0.702028	−0.351014	−	0.936370i	$-0.614163\pi$
$37$	−158.000	−0.702028	−0.351014	+	0.936370i	$0.614163\pi$
$38$	0	0
$39$	−6.00000	−0.0246351
$40$	0	0
$41$	−462.000	−1.75981	−0.879906	−	0.475148i	$-0.842394\pi$
$41$	−462.000	−1.75981	−0.879906	+	0.475148i	$0.842394\pi$
$42$	0	0
$43$	36.0000	0.127673	0.0638366	−	0.997960i	$-0.479666\pi$
$43$	36.0000	0.127673	0.0638366	+	0.997960i	$0.479666\pi$
$44$	0	0
$45$	−45.0000	−0.149071
$46$	0	0
$47$	−168.000	−0.521390	−0.260695	−	0.965421i	$-0.583952\pi$
$47$	−168.000	−0.521390	−0.260695	+	0.965421i	$0.583952\pi$
$48$	0	0
$49$	441.000	1.28571
$50$	0	0
$51$	222.000	0.609534
$52$	0	0
$53$	82.0000	0.212520	0.106260	−	0.994338i	$-0.466112\pi$
$53$	82.0000	0.212520	0.106260	+	0.994338i	$0.466112\pi$
$54$	0	0
$55$	−320.000	−0.784523
$56$	0	0
$57$	57.0000	0.132453
$58$	0	0
$59$	−504.000	−1.11212	−0.556061	−	0.831141i	$-0.687688\pi$
$59$	−504.000	−1.11212	−0.556061	+	0.831141i	$0.687688\pi$
$60$	0	0
$61$	−706.000	−1.48187	−0.740935	−	0.671577i	$-0.765617\pi$
$61$	−706.000	−1.48187	−0.740935	+	0.671577i	$0.765617\pi$
$62$	0	0
$63$	252.000	0.503953
$64$	0	0
$65$	−10.0000	−0.0190823
$66$	0	0
$67$	844.000	1.53897	0.769485	−	0.638665i	$-0.220513\pi$
$67$	844.000	1.53897	0.769485	+	0.638665i	$0.220513\pi$
$68$	0	0
$69$	216.000	0.376860
$70$	0	0
$71$	224.000	0.374421	0.187211	−	0.982320i	$-0.440055\pi$
$71$	224.000	0.374421	0.187211	+	0.982320i	$0.440055\pi$
$72$	0	0
$73$	−894.000	−1.43335	−0.716677	−	0.697406i	$-0.754338\pi$
$73$	−894.000	−1.43335	−0.716677	+	0.697406i	$0.754338\pi$
$74$	0	0
$75$	−75.0000	−0.115470
$76$	0	0
$77$	1792.00	2.65217
$78$	0	0
$79$	−1000.00	−1.42416	−0.712081	−	0.702097i	$-0.752247\pi$
$79$	−1000.00	−1.42416	−0.712081	+	0.702097i	$0.752247\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	0	0
$83$	892.000	1.17964	0.589818	−	0.807537i	$-0.299200\pi$
$83$	892.000	1.17964	0.589818	+	0.807537i	$0.299200\pi$
$84$	0	0
$85$	370.000	0.472143
$86$	0	0
$87$	930.000	1.14605
$88$	0	0
$89$	266.000	0.316808	0.158404	−	0.987374i	$-0.449365\pi$
$89$	266.000	0.316808	0.158404	+	0.987374i	$0.449365\pi$
$90$	0	0
$91$	56.0000	0.0645098
$92$	0	0
$93$	−744.000	−0.829561
$94$	0	0
$95$	95.0000	0.102598
$96$	0	0
$97$	−822.000	−0.860427	−0.430214	−	0.902727i	$-0.641562\pi$
$97$	−822.000	−0.860427	−0.430214	+	0.902727i	$0.641562\pi$
$98$	0	0
$99$	576.000	0.584749
$100$	0	0
$101$	682.000	0.671896	0.335948	−	0.941880i	$-0.390943\pi$
$101$	682.000	0.671896	0.335948	+	0.941880i	$0.390943\pi$
$102$	0	0
$103$	1172.00	1.12117	0.560585	−	0.828097i	$-0.310576\pi$
$103$	1172.00	1.12117	0.560585	+	0.828097i	$0.310576\pi$
$104$	0	0
$105$	420.000	0.390360
$106$	0	0
$107$	−252.000	−0.227680	−0.113840	−	0.993499i	$-0.536315\pi$
$107$	−252.000	−0.227680	−0.113840	+	0.993499i	$0.536315\pi$
$108$	0	0
$109$	−434.000	−0.381373	−0.190687	−	0.981651i	$-0.561071\pi$
$109$	−434.000	−0.381373	−0.190687	+	0.981651i	$0.561071\pi$
$110$	0	0
$111$	474.000	0.405316
$112$	0	0
$113$	−1218.00	−1.01398	−0.506990	−	0.861952i	$-0.669242\pi$
$113$	−1218.00	−1.01398	−0.506990	+	0.861952i	$0.669242\pi$
$114$	0	0
$115$	360.000	0.291915
$116$	0	0
$117$	18.0000	0.0142231
$118$	0	0
$119$	−2072.00	−1.59613
$120$	0	0
$121$	2765.00	2.07739
$122$	0	0
$123$	1386.00	1.01603
$124$	0	0
$125$	−125.000	−0.0894427
$126$	0	0
$127$	1020.00	0.712680	0.356340	−	0.934356i	$-0.384024\pi$
$127$	1020.00	0.712680	0.356340	+	0.934356i	$0.384024\pi$
$128$	0	0
$129$	−108.000	−0.0737122
$130$	0	0
$131$	1632.00	1.08846	0.544231	−	0.838935i	$-0.316822\pi$
$131$	1632.00	1.08846	0.544231	+	0.838935i	$0.316822\pi$
$132$	0	0
$133$	−532.000	−0.346844
$134$	0	0
$135$	135.000	0.0860663
$136$	0	0
$137$	134.000	0.0835649	0.0417825	−	0.999127i	$-0.486696\pi$
$137$	134.000	0.0835649	0.0417825	+	0.999127i	$0.486696\pi$
$138$	0	0
$139$	2244.00	1.36931	0.684653	−	0.728869i	$-0.259954\pi$
$139$	2244.00	1.36931	0.684653	+	0.728869i	$0.259954\pi$
$140$	0	0
$141$	504.000	0.301025
$142$	0	0
$143$	128.000	0.0748524
$144$	0	0
$145$	1550.00	0.887728
$146$	0	0
$147$	−1323.00	−0.742307
$148$	0	0
$149$	−590.000	−0.324394	−0.162197	−	0.986758i	$-0.551858\pi$
$149$	−590.000	−0.324394	−0.162197	+	0.986758i	$0.551858\pi$
$150$	0	0
$151$	−3288.00	−1.77201	−0.886005	−	0.463675i	$-0.846531\pi$
$151$	−3288.00	−1.77201	−0.886005	+	0.463675i	$0.846531\pi$
$152$	0	0
$153$	−666.000	−0.351914
$154$	0	0
$155$	−1240.00	−0.642575
$156$	0	0
$157$	−1766.00	−0.897721	−0.448860	−	0.893602i	$-0.648170\pi$
$157$	−1766.00	−0.897721	−0.448860	+	0.893602i	$0.648170\pi$
$158$	0	0
$159$	−246.000	−0.122699
$160$	0	0
$161$	−2016.00	−0.986851
$162$	0	0
$163$	−1212.00	−0.582400	−0.291200	−	0.956662i	$-0.594054\pi$
$163$	−1212.00	−0.582400	−0.291200	+	0.956662i	$0.594054\pi$
$164$	0	0
$165$	960.000	0.452945
$166$	0	0
$167$	−1880.00	−0.871130	−0.435565	−	0.900157i	$-0.643451\pi$
$167$	−1880.00	−0.871130	−0.435565	+	0.900157i	$0.643451\pi$
$168$	0	0
$169$	−2193.00	−0.998179
$170$	0	0
$171$	−171.000	−0.0764719
$172$	0	0
$173$	1994.00	0.876306	0.438153	−	0.898900i	$-0.355633\pi$
$173$	1994.00	0.876306	0.438153	+	0.898900i	$0.355633\pi$
$174$	0	0
$175$	700.000	0.302372
$176$	0	0
$177$	1512.00	0.642084
$178$	0	0
$179$	−2928.00	−1.22262	−0.611310	−	0.791391i	$-0.709357\pi$
$179$	−2928.00	−1.22262	−0.611310	+	0.791391i	$0.709357\pi$
$180$	0	0
$181$	2422.00	0.994618	0.497309	−	0.867574i	$-0.334322\pi$
$181$	2422.00	0.994618	0.497309	+	0.867574i	$0.334322\pi$
$182$	0	0
$183$	2118.00	0.855558
$184$	0	0
$185$	790.000	0.313957
$186$	0	0
$187$	−4736.00	−1.85204
$188$	0	0
$189$	−756.000	−0.290957
$190$	0	0
$191$	−848.000	−0.321252	−0.160626	−	0.987015i	$-0.551351\pi$
$191$	−848.000	−0.321252	−0.160626	+	0.987015i	$0.551351\pi$
$192$	0	0
$193$	−1118.00	−0.416971	−0.208485	−	0.978025i	$-0.566853\pi$
$193$	−1118.00	−0.416971	−0.208485	+	0.978025i	$0.566853\pi$
$194$	0	0
$195$	30.0000	0.0110172
$196$	0	0
$197$	−3070.00	−1.11030	−0.555148	−	0.831751i	$-0.687339\pi$
$197$	−3070.00	−1.11030	−0.555148	+	0.831751i	$0.687339\pi$
$198$	0	0
$199$	−2888.00	−1.02877	−0.514384	−	0.857560i	$-0.671979\pi$
$199$	−2888.00	−1.02877	−0.514384	+	0.857560i	$0.671979\pi$
$200$	0	0
$201$	−2532.00	−0.888525
$202$	0	0
$203$	−8680.00	−3.00107
$204$	0	0
$205$	2310.00	0.787012
$206$	0	0
$207$	−648.000	−0.217580
$208$	0	0
$209$	−1216.00	−0.402452
$210$	0	0
$211$	−1876.00	−0.612081	−0.306041	−	0.952018i	$-0.599004\pi$
$211$	−1876.00	−0.612081	−0.306041	+	0.952018i	$0.599004\pi$
$212$	0	0
$213$	−672.000	−0.216172
$214$	0	0
$215$	−180.000	−0.0570972
$216$	0	0
$217$	6944.00	2.17230
$218$	0	0
$219$	2682.00	0.827547
$220$	0	0
$221$	−148.000	−0.0450478
$222$	0	0
$223$	5788.00	1.73809	0.869043	−	0.494737i	$-0.164735\pi$
$223$	5788.00	1.73809	0.869043	+	0.494737i	$0.164735\pi$
$224$	0	0
$225$	225.000	0.0666667
$226$	0	0
$227$	−188.000	−0.0549692	−0.0274846	−	0.999622i	$-0.508750\pi$
$227$	−188.000	−0.0549692	−0.0274846	+	0.999622i	$0.508750\pi$
$228$	0	0
$229$	2190.00	0.631962	0.315981	−	0.948766i	$-0.397666\pi$
$229$	2190.00	0.631962	0.315981	+	0.948766i	$0.397666\pi$
$230$	0	0
$231$	−5376.00	−1.53123
$232$	0	0
$233$	3918.00	1.10162	0.550808	−	0.834632i	$-0.314319\pi$
$233$	3918.00	1.10162	0.550808	+	0.834632i	$0.314319\pi$
$234$	0	0
$235$	840.000	0.233173
$236$	0	0
$237$	3000.00	0.822240
$238$	0	0
$239$	−5280.00	−1.42902	−0.714508	−	0.699627i	$-0.753349\pi$
$239$	−5280.00	−1.42902	−0.714508	+	0.699627i	$0.753349\pi$
$240$	0	0
$241$	−1150.00	−0.307378	−0.153689	−	0.988119i	$-0.549115\pi$
$241$	−1150.00	−0.307378	−0.153689	+	0.988119i	$0.549115\pi$
$242$	0	0
$243$	−243.000	−0.0641500
$244$	0	0
$245$	−2205.00	−0.574989
$246$	0	0
$247$	−38.0000	−0.00978900
$248$	0	0
$249$	−2676.00	−0.681063
$250$	0	0
$251$	1384.00	0.348037	0.174019	−	0.984742i	$-0.444325\pi$
$251$	1384.00	0.348037	0.174019	+	0.984742i	$0.444325\pi$
$252$	0	0
$253$	−4608.00	−1.14507
$254$	0	0
$255$	−1110.00	−0.272592
$256$	0	0
$257$	−2562.00	−0.621841	−0.310921	−	0.950436i	$-0.600637\pi$
$257$	−2562.00	−0.621841	−0.310921	+	0.950436i	$0.600637\pi$
$258$	0	0
$259$	−4424.00	−1.06137
$260$	0	0
$261$	−2790.00	−0.661673
$262$	0	0
$263$	−2840.00	−0.665863	−0.332931	−	0.942951i	$-0.608038\pi$
$263$	−2840.00	−0.665863	−0.332931	+	0.942951i	$0.608038\pi$
$264$	0	0
$265$	−410.000	−0.0950419
$266$	0	0
$267$	−798.000	−0.182909
$268$	0	0
$269$	−3574.00	−0.810077	−0.405038	−	0.914300i	$-0.632742\pi$
$269$	−3574.00	−0.810077	−0.405038	+	0.914300i	$0.632742\pi$
$270$	0	0
$271$	5248.00	1.17636	0.588180	−	0.808730i	$-0.299845\pi$
$271$	5248.00	1.17636	0.588180	+	0.808730i	$0.299845\pi$
$272$	0	0
$273$	−168.000	−0.0372448
$274$	0	0
$275$	1600.00	0.350850
$276$	0	0
$277$	−2902.00	−0.629474	−0.314737	−	0.949179i	$-0.601916\pi$
$277$	−2902.00	−0.629474	−0.314737	+	0.949179i	$0.601916\pi$
$278$	0	0
$279$	2232.00	0.478947
$280$	0	0
$281$	1658.00	0.351986	0.175993	−	0.984391i	$-0.443686\pi$
$281$	1658.00	0.351986	0.175993	+	0.984391i	$0.443686\pi$
$282$	0	0
$283$	2492.00	0.523442	0.261721	−	0.965144i	$-0.415710\pi$
$283$	2492.00	0.523442	0.261721	+	0.965144i	$0.415710\pi$
$284$	0	0
$285$	−285.000	−0.0592349
$286$	0	0
$287$	−12936.0	−2.66059
$288$	0	0
$289$	563.000	0.114594
$290$	0	0
$291$	2466.00	0.496768
$292$	0	0
$293$	−7230.00	−1.44157	−0.720787	−	0.693157i	$-0.756219\pi$
$293$	−7230.00	−1.44157	−0.720787	+	0.693157i	$0.756219\pi$
$294$	0	0
$295$	2520.00	0.497356
$296$	0	0
$297$	−1728.00	−0.337605
$298$	0	0
$299$	−144.000	−0.0278520
$300$	0	0
$301$	1008.00	0.193024
$302$	0	0
$303$	−2046.00	−0.387920
$304$	0	0
$305$	3530.00	0.662712
$306$	0	0
$307$	−6524.00	−1.21285	−0.606424	−	0.795141i	$-0.707397\pi$
$307$	−6524.00	−1.21285	−0.606424	+	0.795141i	$0.707397\pi$
$308$	0	0
$309$	−3516.00	−0.647308
$310$	0	0
$311$	7864.00	1.43385	0.716924	−	0.697152i	$-0.245550\pi$
$311$	7864.00	1.43385	0.716924	+	0.697152i	$0.245550\pi$
$312$	0	0
$313$	2386.00	0.430878	0.215439	−	0.976517i	$-0.430882\pi$
$313$	2386.00	0.430878	0.215439	+	0.976517i	$0.430882\pi$
$314$	0	0
$315$	−1260.00	−0.225374
$316$	0	0
$317$	1466.00	0.259744	0.129872	−	0.991531i	$-0.458543\pi$
$317$	1466.00	0.259744	0.129872	+	0.991531i	$0.458543\pi$
$318$	0	0
$319$	−19840.0	−3.48222
$320$	0	0
$321$	756.000	0.131451
$322$	0	0
$323$	1406.00	0.242204
$324$	0	0
$325$	50.0000	0.00853385
$326$	0	0
$327$	1302.00	0.220186
$328$	0	0
$329$	−4704.00	−0.788267
$330$	0	0
$331$	124.000	0.0205911	0.0102956	−	0.999947i	$-0.496723\pi$
$331$	124.000	0.0205911	0.0102956	+	0.999947i	$0.496723\pi$
$332$	0	0
$333$	−1422.00	−0.234009
$334$	0	0
$335$	−4220.00	−0.688248
$336$	0	0
$337$	6754.00	1.09173	0.545866	−	0.837872i	$-0.316201\pi$
$337$	6754.00	1.09173	0.545866	+	0.837872i	$0.316201\pi$
$338$	0	0
$339$	3654.00	0.585422
$340$	0	0
$341$	15872.0	2.52058
$342$	0	0
$343$	2744.00	0.431959
$344$	0	0
$345$	−1080.00	−0.168537
$346$	0	0
$347$	−5572.00	−0.862019	−0.431010	−	0.902347i	$-0.641842\pi$
$347$	−5572.00	−0.862019	−0.431010	+	0.902347i	$0.641842\pi$
$348$	0	0
$349$	2878.00	0.441421	0.220710	−	0.975339i	$-0.429162\pi$
$349$	2878.00	0.441421	0.220710	+	0.975339i	$0.429162\pi$
$350$	0	0
$351$	−54.0000	−0.00821170
$352$	0	0
$353$	−6090.00	−0.918238	−0.459119	−	0.888375i	$-0.651835\pi$
$353$	−6090.00	−0.918238	−0.459119	+	0.888375i	$0.651835\pi$
$354$	0	0
$355$	−1120.00	−0.167446
$356$	0	0
$357$	6216.00	0.921528
$358$	0	0
$359$	−8240.00	−1.21139	−0.605697	−	0.795695i	$-0.707106\pi$
$359$	−8240.00	−1.21139	−0.605697	+	0.795695i	$0.707106\pi$
$360$	0	0
$361$	361.000	0.0526316
$362$	0	0
$363$	−8295.00	−1.19938
$364$	0	0
$365$	4470.00	0.641015
$366$	0	0
$367$	−2748.00	−0.390857	−0.195428	−	0.980718i	$-0.562610\pi$
$367$	−2748.00	−0.390857	−0.195428	+	0.980718i	$0.562610\pi$
$368$	0	0
$369$	−4158.00	−0.586604
$370$	0	0
$371$	2296.00	0.321300
$372$	0	0
$373$	4458.00	0.618838	0.309419	−	0.950926i	$-0.399865\pi$
$373$	4458.00	0.618838	0.309419	+	0.950926i	$0.399865\pi$
$374$	0	0
$375$	375.000	0.0516398
$376$	0	0
$377$	−620.000	−0.0846993
$378$	0	0
$379$	−9788.00	−1.32659	−0.663293	−	0.748360i	$-0.730842\pi$
$379$	−9788.00	−1.32659	−0.663293	+	0.748360i	$0.730842\pi$
$380$	0	0
$381$	−3060.00	−0.411466
$382$	0	0
$383$	−9640.00	−1.28611	−0.643056	−	0.765819i	$-0.722334\pi$
$383$	−9640.00	−1.28611	−0.643056	+	0.765819i	$0.722334\pi$
$384$	0	0
$385$	−8960.00	−1.18609
$386$	0	0
$387$	324.000	0.0425577
$388$	0	0
$389$	2274.00	0.296392	0.148196	−	0.988958i	$-0.452653\pi$
$389$	2274.00	0.296392	0.148196	+	0.988958i	$0.452653\pi$
$390$	0	0
$391$	5328.00	0.689127
$392$	0	0
$393$	−4896.00	−0.628424
$394$	0	0
$395$	5000.00	0.636905
$396$	0	0
$397$	14306.0	1.80856	0.904279	−	0.426942i	$-0.140409\pi$
$397$	14306.0	1.80856	0.904279	+	0.426942i	$0.140409\pi$
$398$	0	0
$399$	1596.00	0.200250
$400$	0	0
$401$	−2318.00	−0.288667	−0.144333	−	0.989529i	$-0.546104\pi$
$401$	−2318.00	−0.288667	−0.144333	+	0.989529i	$0.546104\pi$
$402$	0	0
$403$	496.000	0.0613090
$404$	0	0
$405$	−405.000	−0.0496904
$406$	0	0
$407$	−10112.0	−1.23153
$408$	0	0
$409$	−3590.00	−0.434020	−0.217010	−	0.976169i	$-0.569630\pi$
$409$	−3590.00	−0.434020	−0.217010	+	0.976169i	$0.569630\pi$
$410$	0	0
$411$	−402.000	−0.0482462
$412$	0	0
$413$	−14112.0	−1.68137
$414$	0	0
$415$	−4460.00	−0.527549
$416$	0	0
$417$	−6732.00	−0.790569
$418$	0	0
$419$	9024.00	1.05215	0.526075	−	0.850438i	$-0.323663\pi$
$419$	9024.00	1.05215	0.526075	+	0.850438i	$0.323663\pi$
$420$	0	0
$421$	−13042.0	−1.50981	−0.754903	−	0.655837i	$-0.772316\pi$
$421$	−13042.0	−1.50981	−0.754903	+	0.655837i	$0.772316\pi$
$422$	0	0
$423$	−1512.00	−0.173797
$424$	0	0
$425$	−1850.00	−0.211149
$426$	0	0
$427$	−19768.0	−2.24038
$428$	0	0
$429$	−384.000	−0.0432161
$430$	0	0
$431$	7264.00	0.811820	0.405910	−	0.913913i	$-0.366955\pi$
$431$	7264.00	0.811820	0.405910	+	0.913913i	$0.366955\pi$
$432$	0	0
$433$	9042.00	1.00354	0.501768	−	0.865002i	$-0.332683\pi$
$433$	9042.00	1.00354	0.501768	+	0.865002i	$0.332683\pi$
$434$	0	0
$435$	−4650.00	−0.512530
$436$	0	0
$437$	1368.00	0.149749
$438$	0	0
$439$	15720.0	1.70905	0.854527	−	0.519407i	$-0.173847\pi$
$439$	15720.0	1.70905	0.854527	+	0.519407i	$0.173847\pi$
$440$	0	0
$441$	3969.00	0.428571
$442$	0	0
$443$	13116.0	1.40668	0.703341	−	0.710853i	$-0.251691\pi$
$443$	13116.0	1.40668	0.703341	+	0.710853i	$0.251691\pi$
$444$	0	0
$445$	−1330.00	−0.141681
$446$	0	0
$447$	1770.00	0.187289
$448$	0	0
$449$	−926.000	−0.0973288	−0.0486644	−	0.998815i	$-0.515496\pi$
$449$	−926.000	−0.0973288	−0.0486644	+	0.998815i	$0.515496\pi$
$450$	0	0
$451$	−29568.0	−3.08715
$452$	0	0
$453$	9864.00	1.02307
$454$	0	0
$455$	−280.000	−0.0288497
$456$	0	0
$457$	−7318.00	−0.749063	−0.374531	−	0.927214i	$-0.622196\pi$
$457$	−7318.00	−0.749063	−0.374531	+	0.927214i	$0.622196\pi$
$458$	0	0
$459$	1998.00	0.203178
$460$	0	0
$461$	−3286.00	−0.331983	−0.165992	−	0.986127i	$-0.553082\pi$
$461$	−3286.00	−0.331983	−0.165992	+	0.986127i	$0.553082\pi$
$462$	0	0
$463$	6316.00	0.633973	0.316986	−	0.948430i	$-0.397329\pi$
$463$	6316.00	0.633973	0.316986	+	0.948430i	$0.397329\pi$
$464$	0	0
$465$	3720.00	0.370991
$466$	0	0
$467$	−1620.00	−0.160524	−0.0802619	−	0.996774i	$-0.525576\pi$
$467$	−1620.00	−0.160524	−0.0802619	+	0.996774i	$0.525576\pi$
$468$	0	0
$469$	23632.0	2.32670
$470$	0	0
$471$	5298.00	0.518299
$472$	0	0
$473$	2304.00	0.223970
$474$	0	0
$475$	−475.000	−0.0458831
$476$	0	0
$477$	738.000	0.0708400
$478$	0	0
$479$	−17568.0	−1.67579	−0.837894	−	0.545833i	$-0.816213\pi$
$479$	−17568.0	−1.67579	−0.837894	+	0.545833i	$0.816213\pi$
$480$	0	0
$481$	−316.000	−0.0299550
$482$	0	0
$483$	6048.00	0.569759
$484$	0	0
$485$	4110.00	0.384795
$486$	0	0
$487$	9484.00	0.882466	0.441233	−	0.897393i	$-0.354541\pi$
$487$	9484.00	0.882466	0.441233	+	0.897393i	$0.354541\pi$
$488$	0	0
$489$	3636.00	0.336249
$490$	0	0
$491$	11080.0	1.01840	0.509199	−	0.860649i	$-0.329942\pi$
$491$	11080.0	1.01840	0.509199	+	0.860649i	$0.329942\pi$
$492$	0	0
$493$	22940.0	2.09567
$494$	0	0
$495$	−2880.00	−0.261508
$496$	0	0
$497$	6272.00	0.566072
$498$	0	0
$499$	−3564.00	−0.319733	−0.159866	−	0.987139i	$-0.551106\pi$
$499$	−3564.00	−0.319733	−0.159866	+	0.987139i	$0.551106\pi$
$500$	0	0
$501$	5640.00	0.502947
$502$	0	0
$503$	2144.00	0.190052	0.0950261	−	0.995475i	$-0.469707\pi$
$503$	2144.00	0.190052	0.0950261	+	0.995475i	$0.469707\pi$
$504$	0	0
$505$	−3410.00	−0.300481
$506$	0	0
$507$	6579.00	0.576299
$508$	0	0
$509$	−1286.00	−0.111986	−0.0559931	−	0.998431i	$-0.517832\pi$
$509$	−1286.00	−0.111986	−0.0559931	+	0.998431i	$0.517832\pi$
$510$	0	0
$511$	−25032.0	−2.16703
$512$	0	0
$513$	513.000	0.0441511
$514$	0	0
$515$	−5860.00	−0.501403
$516$	0	0
$517$	−10752.0	−0.914647
$518$	0	0
$519$	−5982.00	−0.505936
$520$	0	0
$521$	−2214.00	−0.186175	−0.0930874	−	0.995658i	$-0.529674\pi$
$521$	−2214.00	−0.186175	−0.0930874	+	0.995658i	$0.529674\pi$
$522$	0	0
$523$	11060.0	0.924704	0.462352	−	0.886697i	$-0.347006\pi$
$523$	11060.0	0.924704	0.462352	+	0.886697i	$0.347006\pi$
$524$	0	0
$525$	−2100.00	−0.174574
$526$	0	0
$527$	−18352.0	−1.51694
$528$	0	0
$529$	−6983.00	−0.573929
$530$	0	0
$531$	−4536.00	−0.370707
$532$	0	0
$533$	−924.000	−0.0750898
$534$	0	0
$535$	1260.00	0.101822
$536$	0	0
$537$	8784.00	0.705880
$538$	0	0
$539$	28224.0	2.25546
$540$	0	0
$541$	−17794.0	−1.41409	−0.707046	−	0.707168i	$-0.749973\pi$
$541$	−17794.0	−1.41409	−0.707046	+	0.707168i	$0.749973\pi$
$542$	0	0
$543$	−7266.00	−0.574243
$544$	0	0
$545$	2170.00	0.170555
$546$	0	0
$547$	−1196.00	−0.0934868	−0.0467434	−	0.998907i	$-0.514884\pi$
$547$	−1196.00	−0.0934868	−0.0467434	+	0.998907i	$0.514884\pi$
$548$	0	0
$549$	−6354.00	−0.493956
$550$	0	0
$551$	5890.00	0.455395
$552$	0	0
$553$	−28000.0	−2.15313
$554$	0	0
$555$	−2370.00	−0.181263
$556$	0	0
$557$	6090.00	0.463270	0.231635	−	0.972803i	$-0.425592\pi$
$557$	6090.00	0.463270	0.231635	+	0.972803i	$0.425592\pi$
$558$	0	0
$559$	72.0000	0.00544772
$560$	0	0
$561$	14208.0	1.06927
$562$	0	0
$563$	−19244.0	−1.44056	−0.720282	−	0.693681i	$-0.755988\pi$
$563$	−19244.0	−1.44056	−0.720282	+	0.693681i	$0.755988\pi$
$564$	0	0
$565$	6090.00	0.453466
$566$	0	0
$567$	2268.00	0.167984
$568$	0	0
$569$	−20886.0	−1.53882	−0.769408	−	0.638757i	$-0.779449\pi$
$569$	−20886.0	−1.53882	−0.769408	+	0.638757i	$0.779449\pi$
$570$	0	0
$571$	4684.00	0.343291	0.171646	−	0.985159i	$-0.445092\pi$
$571$	4684.00	0.343291	0.171646	+	0.985159i	$0.445092\pi$
$572$	0	0
$573$	2544.00	0.185475
$574$	0	0
$575$	−1800.00	−0.130548
$576$	0	0
$577$	−5790.00	−0.417748	−0.208874	−	0.977943i	$-0.566980\pi$
$577$	−5790.00	−0.417748	−0.208874	+	0.977943i	$0.566980\pi$
$578$	0	0
$579$	3354.00	0.240738
$580$	0	0
$581$	24976.0	1.78344
$582$	0	0
$583$	5248.00	0.372813
$584$	0	0
$585$	−90.0000	−0.00636076
$586$	0	0
$587$	7700.00	0.541419	0.270710	−	0.962661i	$-0.412742\pi$
$587$	7700.00	0.541419	0.270710	+	0.962661i	$0.412742\pi$
$588$	0	0
$589$	−4712.00	−0.329634
$590$	0	0
$591$	9210.00	0.641030
$592$	0	0
$593$	−3410.00	−0.236142	−0.118071	−	0.993005i	$-0.537671\pi$
$593$	−3410.00	−0.236142	−0.118071	+	0.993005i	$0.537671\pi$
$594$	0	0
$595$	10360.0	0.713813
$596$	0	0
$597$	8664.00	0.593960
$598$	0	0
$599$	−7928.00	−0.540783	−0.270392	−	0.962750i	$-0.587153\pi$
$599$	−7928.00	−0.540783	−0.270392	+	0.962750i	$0.587153\pi$
$600$	0	0
$601$	−25302.0	−1.71729	−0.858644	−	0.512572i	$-0.828693\pi$
$601$	−25302.0	−1.71729	−0.858644	+	0.512572i	$0.828693\pi$
$602$	0	0
$603$	7596.00	0.512990
$604$	0	0
$605$	−13825.0	−0.929035
$606$	0	0
$607$	9876.00	0.660386	0.330193	−	0.943913i	$-0.392886\pi$
$607$	9876.00	0.660386	0.330193	+	0.943913i	$0.392886\pi$
$608$	0	0
$609$	26040.0	1.73267
$610$	0	0
$611$	−336.000	−0.0222473
$612$	0	0
$613$	28330.0	1.86662	0.933310	−	0.359072i	$-0.116907\pi$
$613$	28330.0	1.86662	0.933310	+	0.359072i	$0.116907\pi$
$614$	0	0
$615$	−6930.00	−0.454381
$616$	0	0
$617$	−19394.0	−1.26543	−0.632717	−	0.774383i	$-0.718060\pi$
$617$	−19394.0	−1.26543	−0.632717	+	0.774383i	$0.718060\pi$
$618$	0	0
$619$	26932.0	1.74877	0.874385	−	0.485233i	$-0.161265\pi$
$619$	26932.0	1.74877	0.874385	+	0.485233i	$0.161265\pi$
$620$	0	0
$621$	1944.00	0.125620
$622$	0	0
$623$	7448.00	0.478969
$624$	0	0
$625$	625.000	0.0400000
$626$	0	0
$627$	3648.00	0.232356
$628$	0	0
$629$	11692.0	0.741161
$630$	0	0
$631$	−9168.00	−0.578403	−0.289202	−	0.957268i	$-0.593390\pi$
$631$	−9168.00	−0.578403	−0.289202	+	0.957268i	$0.593390\pi$
$632$	0	0
$633$	5628.00	0.353385
$634$	0	0
$635$	−5100.00	−0.318720
$636$	0	0
$637$	882.000	0.0548605
$638$	0	0
$639$	2016.00	0.124807
$640$	0	0
$641$	4394.00	0.270753	0.135376	−	0.990794i	$-0.456776\pi$
$641$	4394.00	0.270753	0.135376	+	0.990794i	$0.456776\pi$
$642$	0	0
$643$	4004.00	0.245571	0.122786	−	0.992433i	$-0.460817\pi$
$643$	4004.00	0.245571	0.122786	+	0.992433i	$0.460817\pi$
$644$	0	0
$645$	540.000	0.0329651
$646$	0	0
$647$	9648.00	0.586247	0.293124	−	0.956075i	$-0.405305\pi$
$647$	9648.00	0.586247	0.293124	+	0.956075i	$0.405305\pi$
$648$	0	0
$649$	−32256.0	−1.95094
$650$	0	0
$651$	−20832.0	−1.25418
$652$	0	0
$653$	19402.0	1.16272	0.581362	−	0.813645i	$-0.302520\pi$
$653$	19402.0	1.16272	0.581362	+	0.813645i	$0.302520\pi$
$654$	0	0
$655$	−8160.00	−0.486775
$656$	0	0
$657$	−8046.00	−0.477784
$658$	0	0
$659$	−3080.00	−0.182063	−0.0910317	−	0.995848i	$-0.529016\pi$
$659$	−3080.00	−0.182063	−0.0910317	+	0.995848i	$0.529016\pi$
$660$	0	0
$661$	−16618.0	−0.977860	−0.488930	−	0.872323i	$-0.662613\pi$
$661$	−16618.0	−0.977860	−0.488930	+	0.872323i	$0.662613\pi$
$662$	0	0
$663$	444.000	0.0260083
$664$	0	0
$665$	2660.00	0.155113
$666$	0	0
$667$	22320.0	1.29570
$668$	0	0
$669$	−17364.0	−1.00348
$670$	0	0
$671$	−45184.0	−2.59957
$672$	0	0
$673$	−17534.0	−1.00429	−0.502144	−	0.864784i	$-0.667455\pi$
$673$	−17534.0	−1.00429	−0.502144	+	0.864784i	$0.667455\pi$
$674$	0	0
$675$	−675.000	−0.0384900
$676$	0	0
$677$	−5550.00	−0.315072	−0.157536	−	0.987513i	$-0.550355\pi$
$677$	−5550.00	−0.315072	−0.157536	+	0.987513i	$0.550355\pi$
$678$	0	0
$679$	−23016.0	−1.30084
$680$	0	0
$681$	564.000	0.0317365
$682$	0	0
$683$	−7052.00	−0.395077	−0.197538	−	0.980295i	$-0.563295\pi$
$683$	−7052.00	−0.395077	−0.197538	+	0.980295i	$0.563295\pi$
$684$	0	0
$685$	−670.000	−0.0373714
$686$	0	0
$687$	−6570.00	−0.364863
$688$	0	0
$689$	164.000	0.00906807
$690$	0	0
$691$	30708.0	1.69058	0.845288	−	0.534312i	$-0.179429\pi$
$691$	30708.0	1.69058	0.845288	+	0.534312i	$0.179429\pi$
$692$	0	0
$693$	16128.0	0.884058
$694$	0	0
$695$	−11220.0	−0.612372
$696$	0	0
$697$	34188.0	1.85791
$698$	0	0
$699$	−11754.0	−0.636019
$700$	0	0
$701$	−2878.00	−0.155065	−0.0775325	−	0.996990i	$-0.524704\pi$
$701$	−2878.00	−0.155065	−0.0775325	+	0.996990i	$0.524704\pi$
$702$	0	0
$703$	3002.00	0.161056
$704$	0	0
$705$	−2520.00	−0.134622
$706$	0	0
$707$	19096.0	1.01581
$708$	0	0
$709$	20606.0	1.09150	0.545751	−	0.837948i	$-0.316245\pi$
$709$	20606.0	1.09150	0.545751	+	0.837948i	$0.316245\pi$
$710$	0	0
$711$	−9000.00	−0.474721
$712$	0	0
$713$	−17856.0	−0.937886
$714$	0	0
$715$	−640.000	−0.0334750
$716$	0	0
$717$	15840.0	0.825043
$718$	0	0
$719$	7368.00	0.382170	0.191085	−	0.981574i	$-0.438799\pi$
$719$	7368.00	0.382170	0.191085	+	0.981574i	$0.438799\pi$
$720$	0	0
$721$	32816.0	1.69505
$722$	0	0
$723$	3450.00	0.177465
$724$	0	0
$725$	−7750.00	−0.397004
$726$	0	0
$727$	−524.000	−0.0267319	−0.0133659	−	0.999911i	$-0.504255\pi$
$727$	−524.000	−0.0267319	−0.0133659	+	0.999911i	$0.504255\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	0	0
$731$	−2664.00	−0.134790
$732$	0	0
$733$	−13326.0	−0.671497	−0.335748	−	0.941952i	$-0.608989\pi$
$733$	−13326.0	−0.671497	−0.335748	+	0.941952i	$0.608989\pi$
$734$	0	0
$735$	6615.00	0.331970
$736$	0	0
$737$	54016.0	2.69974
$738$	0	0
$739$	−31436.0	−1.56481	−0.782403	−	0.622772i	$-0.786006\pi$
$739$	−31436.0	−1.56481	−0.782403	+	0.622772i	$0.786006\pi$
$740$	0	0
$741$	114.000	0.00565168
$742$	0	0
$743$	−27088.0	−1.33750	−0.668750	−	0.743487i	$-0.733170\pi$
$743$	−27088.0	−1.33750	−0.668750	+	0.743487i	$0.733170\pi$
$744$	0	0
$745$	2950.00	0.145073
$746$	0	0
$747$	8028.00	0.393212
$748$	0	0
$749$	−7056.00	−0.344220
$750$	0	0
$751$	−30136.0	−1.46429	−0.732143	−	0.681151i	$-0.761480\pi$
$751$	−30136.0	−1.46429	−0.732143	+	0.681151i	$0.761480\pi$
$752$	0	0
$753$	−4152.00	−0.200939
$754$	0	0
$755$	16440.0	0.792467
$756$	0	0
$757$	12634.0	0.606593	0.303296	−	0.952896i	$-0.401913\pi$
$757$	12634.0	0.606593	0.303296	+	0.952896i	$0.401913\pi$
$758$	0	0
$759$	13824.0	0.661106
$760$	0	0
$761$	−27726.0	−1.32072	−0.660359	−	0.750950i	$-0.729596\pi$
$761$	−27726.0	−1.32072	−0.660359	+	0.750950i	$0.729596\pi$
$762$	0	0
$763$	−12152.0	−0.576582
$764$	0	0
$765$	3330.00	0.157381
$766$	0	0
$767$	−1008.00	−0.0474534
$768$	0	0
$769$	−15230.0	−0.714184	−0.357092	−	0.934069i	$-0.616232\pi$
$769$	−15230.0	−0.714184	−0.357092	+	0.934069i	$0.616232\pi$
$770$	0	0
$771$	7686.00	0.359020
$772$	0	0
$773$	11394.0	0.530160	0.265080	−	0.964226i	$-0.414602\pi$
$773$	11394.0	0.530160	0.265080	+	0.964226i	$0.414602\pi$
$774$	0	0
$775$	6200.00	0.287368
$776$	0	0
$777$	13272.0	0.612780
$778$	0	0
$779$	8778.00	0.403728
$780$	0	0
$781$	14336.0	0.656828
$782$	0	0
$783$	8370.00	0.382017
$784$	0	0
$785$	8830.00	0.401473
$786$	0	0
$787$	−4804.00	−0.217591	−0.108795	−	0.994064i	$-0.534699\pi$
$787$	−4804.00	−0.217591	−0.108795	+	0.994064i	$0.534699\pi$
$788$	0	0
$789$	8520.00	0.384436
$790$	0	0
$791$	−34104.0	−1.53299
$792$	0	0
$793$	−1412.00	−0.0632303
$794$	0	0
$795$	1230.00	0.0548725
$796$	0	0
$797$	40698.0	1.80878	0.904390	−	0.426708i	$-0.140327\pi$
$797$	40698.0	1.80878	0.904390	+	0.426708i	$0.140327\pi$
$798$	0	0
$799$	12432.0	0.550454
$800$	0	0
$801$	2394.00	0.105603
$802$	0	0
$803$	−57216.0	−2.51446
$804$	0	0
$805$	10080.0	0.441333
$806$	0	0
$807$	10722.0	0.467698
$808$	0	0
$809$	−37446.0	−1.62736	−0.813678	−	0.581316i	$-0.802538\pi$
$809$	−37446.0	−1.62736	−0.813678	+	0.581316i	$0.802538\pi$
$810$	0	0
$811$	17092.0	0.740051	0.370025	−	0.929022i	$-0.379349\pi$
$811$	17092.0	0.740051	0.370025	+	0.929022i	$0.379349\pi$
$812$	0	0
$813$	−15744.0	−0.679171
$814$	0	0
$815$	6060.00	0.260457
$816$	0	0
$817$	−684.000	−0.0292902
$818$	0	0
$819$	504.000	0.0215033
$820$	0	0
$821$	−29142.0	−1.23881	−0.619405	−	0.785072i	$-0.712626\pi$
$821$	−29142.0	−1.23881	−0.619405	+	0.785072i	$0.712626\pi$
$822$	0	0
$823$	6260.00	0.265140	0.132570	−	0.991174i	$-0.457677\pi$
$823$	6260.00	0.265140	0.132570	+	0.991174i	$0.457677\pi$
$824$	0	0
$825$	−4800.00	−0.202563
$826$	0	0
$827$	32844.0	1.38101	0.690507	−	0.723326i	$-0.257388\pi$
$827$	32844.0	1.38101	0.690507	+	0.723326i	$0.257388\pi$
$828$	0	0
$829$	−36322.0	−1.52173	−0.760866	−	0.648909i	$-0.775225\pi$
$829$	−36322.0	−1.52173	−0.760866	+	0.648909i	$0.775225\pi$
$830$	0	0
$831$	8706.00	0.363427
$832$	0	0
$833$	−32634.0	−1.35738
$834$	0	0
$835$	9400.00	0.389581
$836$	0	0
$837$	−6696.00	−0.276520
$838$	0	0
$839$	−44184.0	−1.81812	−0.909059	−	0.416667i	$-0.863198\pi$
$839$	−44184.0	−1.81812	−0.909059	+	0.416667i	$0.863198\pi$
$840$	0	0
$841$	71711.0	2.94030
$842$	0	0
$843$	−4974.00	−0.203219
$844$	0	0
$845$	10965.0	0.446399
$846$	0	0
$847$	77420.0	3.14071
$848$	0	0
$849$	−7476.00	−0.302209
$850$	0	0
$851$	11376.0	0.458242
$852$	0	0
$853$	2762.00	0.110866	0.0554332	−	0.998462i	$-0.482346\pi$
$853$	2762.00	0.110866	0.0554332	+	0.998462i	$0.482346\pi$
$854$	0	0
$855$	855.000	0.0341993
$856$	0	0
$857$	15326.0	0.610882	0.305441	−	0.952211i	$-0.401196\pi$
$857$	15326.0	0.610882	0.305441	+	0.952211i	$0.401196\pi$
$858$	0	0
$859$	19028.0	0.755794	0.377897	−	0.925848i	$-0.376647\pi$
$859$	19028.0	0.755794	0.377897	+	0.925848i	$0.376647\pi$
$860$	0	0
$861$	38808.0	1.53609
$862$	0	0
$863$	37232.0	1.46859	0.734294	−	0.678831i	$-0.237513\pi$
$863$	37232.0	1.46859	0.734294	+	0.678831i	$0.237513\pi$
$864$	0	0
$865$	−9970.00	−0.391896
$866$	0	0
$867$	−1689.00	−0.0661608
$868$	0	0
$869$	−64000.0	−2.49833
$870$	0	0
$871$	1688.00	0.0656667
$872$	0	0
$873$	−7398.00	−0.286809
$874$	0	0
$875$	−3500.00	−0.135225
$876$	0	0
$877$	2722.00	0.104807	0.0524033	−	0.998626i	$-0.483312\pi$
$877$	2722.00	0.104807	0.0524033	+	0.998626i	$0.483312\pi$
$878$	0	0
$879$	21690.0	0.832293
$880$	0	0
$881$	2874.00	0.109906	0.0549532	−	0.998489i	$-0.482499\pi$
$881$	2874.00	0.109906	0.0549532	+	0.998489i	$0.482499\pi$
$882$	0	0
$883$	−7964.00	−0.303522	−0.151761	−	0.988417i	$-0.548494\pi$
$883$	−7964.00	−0.303522	−0.151761	+	0.988417i	$0.548494\pi$
$884$	0	0
$885$	−7560.00	−0.287149
$886$	0	0
$887$	−45608.0	−1.72646	−0.863228	−	0.504814i	$-0.831561\pi$
$887$	−45608.0	−1.72646	−0.863228	+	0.504814i	$0.831561\pi$
$888$	0	0
$889$	28560.0	1.07747
$890$	0	0
$891$	5184.00	0.194916
$892$	0	0
$893$	3192.00	0.119615
$894$	0	0
$895$	14640.0	0.546772
$896$	0	0
$897$	432.000	0.0160803
$898$	0	0
$899$	−76880.0	−2.85216
$900$	0	0
$901$	−6068.00	−0.224367
$902$	0	0
$903$	−3024.00	−0.111442
$904$	0	0
$905$	−12110.0	−0.444807
$906$	0	0
$907$	36988.0	1.35410	0.677049	−	0.735938i	$-0.263259\pi$
$907$	36988.0	1.35410	0.677049	+	0.735938i	$0.263259\pi$
$908$	0	0
$909$	6138.00	0.223965
$910$	0	0
$911$	−25152.0	−0.914734	−0.457367	−	0.889278i	$-0.651207\pi$
$911$	−25152.0	−0.914734	−0.457367	+	0.889278i	$0.651207\pi$
$912$	0	0
$913$	57088.0	2.06937
$914$	0	0
$915$	−10590.0	−0.382617
$916$	0	0
$917$	45696.0	1.64560
$918$	0	0
$919$	47984.0	1.72236	0.861179	−	0.508303i	$-0.169727\pi$
$919$	47984.0	1.72236	0.861179	+	0.508303i	$0.169727\pi$
$920$	0	0
$921$	19572.0	0.700238
$922$	0	0
$923$	448.000	0.0159763
$924$	0	0
$925$	−3950.00	−0.140406
$926$	0	0
$927$	10548.0	0.373724
$928$	0	0
$929$	20634.0	0.728719	0.364359	−	0.931258i	$-0.381288\pi$
$929$	20634.0	0.728719	0.364359	+	0.931258i	$0.381288\pi$
$930$	0	0
$931$	−8379.00	−0.294963
$932$	0	0
$933$	−23592.0	−0.827832
$934$	0	0
$935$	23680.0	0.828255
$936$	0	0
$937$	31226.0	1.08870	0.544348	−	0.838859i	$-0.316777\pi$
$937$	31226.0	1.08870	0.544348	+	0.838859i	$0.316777\pi$
$938$	0	0
$939$	−7158.00	−0.248767
$940$	0	0
$941$	−19518.0	−0.676162	−0.338081	−	0.941117i	$-0.609778\pi$
$941$	−19518.0	−0.676162	−0.338081	+	0.941117i	$0.609778\pi$
$942$	0	0
$943$	33264.0	1.14870
$944$	0	0
$945$	3780.00	0.130120
$946$	0	0
$947$	−40572.0	−1.39220	−0.696100	−	0.717945i	$-0.745083\pi$
$947$	−40572.0	−1.39220	−0.696100	+	0.717945i	$0.745083\pi$
$948$	0	0
$949$	−1788.00	−0.0611601
$950$	0	0
$951$	−4398.00	−0.149963
$952$	0	0
$953$	−35194.0	−1.19627	−0.598135	−	0.801395i	$-0.704091\pi$
$953$	−35194.0	−1.19627	−0.598135	+	0.801395i	$0.704091\pi$
$954$	0	0
$955$	4240.00	0.143668
$956$	0	0
$957$	59520.0	2.01046
$958$	0	0
$959$	3752.00	0.126338
$960$	0	0
$961$	31713.0	1.06452
$962$	0	0
$963$	−2268.00	−0.0758933
$964$	0	0
$965$	5590.00	0.186475
$966$	0	0
$967$	36492.0	1.21355	0.606775	−	0.794873i	$-0.292463\pi$
$967$	36492.0	1.21355	0.606775	+	0.794873i	$0.292463\pi$
$968$	0	0
$969$	−4218.00	−0.139837
$970$	0	0
$971$	−26080.0	−0.861943	−0.430972	−	0.902365i	$-0.641829\pi$
$971$	−26080.0	−0.861943	−0.430972	+	0.902365i	$0.641829\pi$
$972$	0	0
$973$	62832.0	2.07020
$974$	0	0
$975$	−150.000	−0.00492702
$976$	0	0
$977$	−1514.00	−0.0495774	−0.0247887	−	0.999693i	$-0.507891\pi$
$977$	−1514.00	−0.0495774	−0.0247887	+	0.999693i	$0.507891\pi$
$978$	0	0
$979$	17024.0	0.555760
$980$	0	0
$981$	−3906.00	−0.127124
$982$	0	0
$983$	58688.0	1.90423	0.952114	−	0.305743i	$-0.0989047\pi$
$983$	58688.0	1.90423	0.952114	+	0.305743i	$0.0989047\pi$
$984$	0	0
$985$	15350.0	0.496540
$986$	0	0
$987$	14112.0	0.455106
$988$	0	0
$989$	−2592.00	−0.0833375
$990$	0	0
$991$	53104.0	1.70222	0.851112	−	0.524984i	$-0.175929\pi$
$991$	53104.0	1.70222	0.851112	+	0.524984i	$0.175929\pi$
$992$	0	0
$993$	−372.000	−0.0118883
$994$	0	0
$995$	14440.0	0.460079
$996$	0	0
$997$	−49406.0	−1.56941	−0.784706	−	0.619868i	$-0.787186\pi$
$997$	−49406.0	−1.56941	−0.784706	+	0.619868i	$0.787186\pi$
$998$	0	0
$999$	4266.00	0.135105

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2280.4.a.a.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2280.4.a.a.1.1	✓	1	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2280 = 2^{3} \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2280.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more