LMFDB - Embedded newform 154.4.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [154,4,Mod(1,154)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(154, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("154.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 154 = 2 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	154.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:	$9.08629414088$
Analytic rank:	$0$
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	$\chi$	$=$	154.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2.00000 q^{2} -10.0000 q^{3} +4.00000 q^{4} -14.0000 q^{5} -20.0000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +73.0000 q^{9} +O(q^{10})$

\(q+2.00000 q^{2} -10.0000 q^{3} +4.00000 q^{4} -14.0000 q^{5} -20.0000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +73.0000 q^{9} -28.0000 q^{10} -11.0000 q^{11} -40.0000 q^{12} -16.0000 q^{13} +14.0000 q^{14} +140.000 q^{15} +16.0000 q^{16} +108.000 q^{17} +146.000 q^{18} +116.000 q^{19} -56.0000 q^{20} -70.0000 q^{21} -22.0000 q^{22} +68.0000 q^{23} -80.0000 q^{24} +71.0000 q^{25} -32.0000 q^{26} -460.000 q^{27} +28.0000 q^{28} +122.000 q^{29} +280.000 q^{30} -262.000 q^{31} +32.0000 q^{32} +110.000 q^{33} +216.000 q^{34} -98.0000 q^{35} +292.000 q^{36} +130.000 q^{37} +232.000 q^{38} +160.000 q^{39} -112.000 q^{40} +204.000 q^{41} -140.000 q^{42} -396.000 q^{43} -44.0000 q^{44} -1022.00 q^{45} +136.000 q^{46} +166.000 q^{47} -160.000 q^{48} +49.0000 q^{49} +142.000 q^{50} -1080.00 q^{51} -64.0000 q^{52} +442.000 q^{53} -920.000 q^{54} +154.000 q^{55} +56.0000 q^{56} -1160.00 q^{57} +244.000 q^{58} +702.000 q^{59} +560.000 q^{60} +196.000 q^{61} -524.000 q^{62} +511.000 q^{63} +64.0000 q^{64} +224.000 q^{65} +220.000 q^{66} -416.000 q^{67} +432.000 q^{68} -680.000 q^{69} -196.000 q^{70} +492.000 q^{71} +584.000 q^{72} +408.000 q^{73} +260.000 q^{74} -710.000 q^{75} +464.000 q^{76} -77.0000 q^{77} +320.000 q^{78} +600.000 q^{79} -224.000 q^{80} +2629.00 q^{81} +408.000 q^{82} -1212.00 q^{83} -280.000 q^{84} -1512.00 q^{85} -792.000 q^{86} -1220.00 q^{87} -88.0000 q^{88} +1146.00 q^{89} -2044.00 q^{90} -112.000 q^{91} +272.000 q^{92} +2620.00 q^{93} +332.000 q^{94} -1624.00 q^{95} -320.000 q^{96} -482.000 q^{97} +98.0000 q^{98} -803.000 q^{99} +O(q^{100})\)

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 $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	−10.0000	−1.92450	−0.962250	−	0.272166i	$-0.912260\pi$
$3$	−10.0000	−1.92450	−0.962250	+	0.272166i	$0.912260\pi$
$4$	4.00000	0.500000
$5$	−14.0000	−1.25220	−0.626099	−	0.779744i	$-0.715349\pi$
$5$	−14.0000	−1.25220	−0.626099	+	0.779744i	$0.715349\pi$
$6$	−20.0000	−1.36083
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	8.00000	0.353553
$9$	73.0000	2.70370
$10$	−28.0000	−0.885438
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−40.0000	−0.962250
$13$	−16.0000	−0.341354	−0.170677	−	0.985327i	$-0.554595\pi$
$13$	−16.0000	−0.341354	−0.170677	+	0.985327i	$0.554595\pi$
$14$	14.0000	0.267261
$15$	140.000	2.40986
$16$	16.0000	0.250000
$17$	108.000	1.54081	0.770407	−	0.637552i	$-0.220053\pi$
$17$	108.000	1.54081	0.770407	+	0.637552i	$0.220053\pi$
$18$	146.000	1.91181
$19$	116.000	1.40064	0.700322	−	0.713827i	$-0.253040\pi$
$19$	116.000	1.40064	0.700322	+	0.713827i	$0.253040\pi$
$20$	−56.0000	−0.626099
$21$	−70.0000	−0.727393
$22$	−22.0000	−0.213201
$23$	68.0000	0.616477	0.308239	−	0.951309i	$-0.400260\pi$
$23$	68.0000	0.616477	0.308239	+	0.951309i	$0.400260\pi$
$24$	−80.0000	−0.680414
$25$	71.0000	0.568000
$26$	−32.0000	−0.241374
$27$	−460.000	−3.27878
$28$	28.0000	0.188982
$29$	122.000	0.781201	0.390601	−	0.920560i	$-0.372267\pi$
$29$	122.000	0.781201	0.390601	+	0.920560i	$0.372267\pi$
$30$	280.000	1.70403
$31$	−262.000	−1.51795	−0.758977	−	0.651117i	$-0.774301\pi$
$31$	−262.000	−1.51795	−0.758977	+	0.651117i	$0.774301\pi$
$32$	32.0000	0.176777
$33$	110.000	0.580259
$34$	216.000	1.08952
$35$	−98.0000	−0.473286
$36$	292.000	1.35185
$37$	130.000	0.577618	0.288809	−	0.957387i	$-0.406741\pi$
$37$	130.000	0.577618	0.288809	+	0.957387i	$0.406741\pi$
$38$	232.000	0.990404
$39$	160.000	0.656936
$40$	−112.000	−0.442719
$41$	204.000	0.777060	0.388530	−	0.921436i	$-0.372983\pi$
$41$	204.000	0.777060	0.388530	+	0.921436i	$0.372983\pi$
$42$	−140.000	−0.514344
$43$	−396.000	−1.40441	−0.702203	−	0.711977i	$-0.747800\pi$
$43$	−396.000	−1.40441	−0.702203	+	0.711977i	$0.747800\pi$
$44$	−44.0000	−0.150756
$45$	−1022.00	−3.38557
$46$	136.000	0.435915
$47$	166.000	0.515183	0.257591	−	0.966254i	$-0.417071\pi$
$47$	166.000	0.515183	0.257591	+	0.966254i	$0.417071\pi$
$48$	−160.000	−0.481125
$49$	49.0000	0.142857
$50$	142.000	0.401637
$51$	−1080.00	−2.96530
$52$	−64.0000	−0.170677
$53$	442.000	1.14554	0.572768	−	0.819718i	$-0.305870\pi$
$53$	442.000	1.14554	0.572768	+	0.819718i	$0.305870\pi$
$54$	−920.000	−2.31845
$55$	154.000	0.377552
$56$	56.0000	0.133631
$57$	−1160.00	−2.69554
$58$	244.000	0.552393
$59$	702.000	1.54903	0.774514	−	0.632557i	$-0.217995\pi$
$59$	702.000	1.54903	0.774514	+	0.632557i	$0.217995\pi$
$60$	560.000	1.20493
$61$	196.000	0.411397	0.205699	−	0.978615i	$-0.434053\pi$
$61$	196.000	0.411397	0.205699	+	0.978615i	$0.434053\pi$
$62$	−524.000	−1.07336
$63$	511.000	1.02190
$64$	64.0000	0.125000
$65$	224.000	0.427443
$66$	220.000	0.410305
$67$	−416.000	−0.758545	−0.379272	−	0.925285i	$-0.623826\pi$
$67$	−416.000	−0.758545	−0.379272	+	0.925285i	$0.623826\pi$
$68$	432.000	0.770407
$69$	−680.000	−1.18641
$70$	−196.000	−0.334664
$71$	492.000	0.822390	0.411195	−	0.911548i	$-0.365112\pi$
$71$	492.000	0.822390	0.411195	+	0.911548i	$0.365112\pi$
$72$	584.000	0.955904
$73$	408.000	0.654148	0.327074	−	0.944999i	$-0.393937\pi$
$73$	408.000	0.654148	0.327074	+	0.944999i	$0.393937\pi$
$74$	260.000	0.408438
$75$	−710.000	−1.09312
$76$	464.000	0.700322
$77$	−77.0000	−0.113961
$78$	320.000	0.464524
$79$	600.000	0.854497	0.427249	−	0.904134i	$-0.359483\pi$
$79$	600.000	0.854497	0.427249	+	0.904134i	$0.359483\pi$
$80$	−224.000	−0.313050
$81$	2629.00	3.60631
$82$	408.000	0.549464
$83$	−1212.00	−1.60282	−0.801411	−	0.598114i	$-0.795917\pi$
$83$	−1212.00	−1.60282	−0.801411	+	0.598114i	$0.795917\pi$
$84$	−280.000	−0.363696
$85$	−1512.00	−1.92941
$86$	−792.000	−0.993065
$87$	−1220.00	−1.50342
$88$	−88.0000	−0.106600
$89$	1146.00	1.36490	0.682448	−	0.730934i	$-0.260915\pi$
$89$	1146.00	1.36490	0.682448	+	0.730934i	$0.260915\pi$
$90$	−2044.00	−2.39396
$91$	−112.000	−0.129020
$92$	272.000	0.308239
$93$	2620.00	2.92130
$94$	332.000	0.364289
$95$	−1624.00	−1.75388
$96$	−320.000	−0.340207
$97$	−482.000	−0.504533	−0.252266	−	0.967658i	$-0.581176\pi$
$97$	−482.000	−0.504533	−0.252266	+	0.967658i	$0.581176\pi$
$98$	98.0000	0.101015
$99$	−803.000	−0.815197
$100$	284.000	0.284000
$101$	1216.00	1.19799	0.598993	−	0.800754i	$-0.295568\pi$
$101$	1216.00	1.19799	0.598993	+	0.800754i	$0.295568\pi$
$102$	−2160.00	−2.09678
$103$	1406.00	1.34502	0.672511	−	0.740087i	$-0.265216\pi$
$103$	1406.00	1.34502	0.672511	+	0.740087i	$0.265216\pi$
$104$	−128.000	−0.120687
$105$	980.000	0.910840
$106$	884.000	0.810016
$107$	−588.000	−0.531253	−0.265627	−	0.964076i	$-0.585579\pi$
$107$	−588.000	−0.531253	−0.265627	+	0.964076i	$0.585579\pi$
$108$	−1840.00	−1.63939
$109$	154.000	0.135326	0.0676630	−	0.997708i	$-0.478446\pi$
$109$	154.000	0.135326	0.0676630	+	0.997708i	$0.478446\pi$
$110$	308.000	0.266970
$111$	−1300.00	−1.11163
$112$	112.000	0.0944911
$113$	−1902.00	−1.58341	−0.791704	−	0.610905i	$-0.790806\pi$
$113$	−1902.00	−1.58341	−0.791704	+	0.610905i	$0.790806\pi$
$114$	−2320.00	−1.90603
$115$	−952.000	−0.771952
$116$	488.000	0.390601
$117$	−1168.00	−0.922920
$118$	1404.00	1.09533
$119$	756.000	0.582373
$120$	1120.00	0.852013
$121$	121.000	0.0909091
$122$	392.000	0.290902
$123$	−2040.00	−1.49545
$124$	−1048.00	−0.758977
$125$	756.000	0.540950
$126$	1022.00	0.722595
$127$	64.0000	0.0447172	0.0223586	−	0.999750i	$-0.492882\pi$
$127$	64.0000	0.0447172	0.0223586	+	0.999750i	$0.492882\pi$
$128$	128.000	0.0883883
$129$	3960.00	2.70278
$130$	448.000	0.302248
$131$	−1584.00	−1.05645	−0.528224	−	0.849105i	$-0.677142\pi$
$131$	−1584.00	−1.05645	−0.528224	+	0.849105i	$0.677142\pi$
$132$	440.000	0.290129
$133$	812.000	0.529393
$134$	−832.000	−0.536372
$135$	6440.00	4.10568
$136$	864.000	0.544760
$137$	998.000	0.622371	0.311186	−	0.950349i	$-0.399274\pi$
$137$	998.000	0.622371	0.311186	+	0.950349i	$0.399274\pi$
$138$	−1360.00	−0.838919
$139$	276.000	0.168417	0.0842087	−	0.996448i	$-0.473164\pi$
$139$	276.000	0.168417	0.0842087	+	0.996448i	$0.473164\pi$
$140$	−392.000	−0.236643
$141$	−1660.00	−0.991470
$142$	984.000	0.581517
$143$	176.000	0.102922
$144$	1168.00	0.675926
$145$	−1708.00	−0.978218
$146$	816.000	0.462552
$147$	−490.000	−0.274929
$148$	520.000	0.288809
$149$	1318.00	0.724663	0.362331	−	0.932049i	$-0.381981\pi$
$149$	1318.00	0.724663	0.362331	+	0.932049i	$0.381981\pi$
$150$	−1420.00	−0.772950
$151$	−984.000	−0.530310	−0.265155	−	0.964206i	$-0.585423\pi$
$151$	−984.000	−0.530310	−0.265155	+	0.964206i	$0.585423\pi$
$152$	928.000	0.495202
$153$	7884.00	4.16591
$154$	−154.000	−0.0805823
$155$	3668.00	1.90078
$156$	640.000	0.328468
$157$	1706.00	0.867221	0.433610	−	0.901101i	$-0.357239\pi$
$157$	1706.00	0.867221	0.433610	+	0.901101i	$0.357239\pi$
$158$	1200.00	0.604221
$159$	−4420.00	−2.20458
$160$	−448.000	−0.221359
$161$	476.000	0.233007
$162$	5258.00	2.55005
$163$	1168.00	0.561257	0.280628	−	0.959817i	$-0.409457\pi$
$163$	1168.00	0.561257	0.280628	+	0.959817i	$0.409457\pi$
$164$	816.000	0.388530
$165$	−1540.00	−0.726599
$166$	−2424.00	−1.13337
$167$	72.0000	0.0333624	0.0166812	−	0.999861i	$-0.494690\pi$
$167$	72.0000	0.0333624	0.0166812	+	0.999861i	$0.494690\pi$
$168$	−560.000	−0.257172
$169$	−1941.00	−0.883477
$170$	−3024.00	−1.36430
$171$	8468.00	3.78692
$172$	−1584.00	−0.702203
$173$	−4328.00	−1.90203	−0.951017	−	0.309140i	$-0.899959\pi$
$173$	−4328.00	−1.90203	−0.951017	+	0.309140i	$0.899959\pi$
$174$	−2440.00	−1.06308
$175$	497.000	0.214684
$176$	−176.000	−0.0753778
$177$	−7020.00	−2.98110
$178$	2292.00	0.965127
$179$	−1924.00	−0.803388	−0.401694	−	0.915774i	$-0.631579\pi$
$179$	−1924.00	−0.803388	−0.401694	+	0.915774i	$0.631579\pi$
$180$	−4088.00	−1.69279
$181$	2230.00	0.915771	0.457886	−	0.889011i	$-0.348607\pi$
$181$	2230.00	0.915771	0.457886	+	0.889011i	$0.348607\pi$
$182$	−224.000	−0.0912307
$183$	−1960.00	−0.791734
$184$	544.000	0.217958
$185$	−1820.00	−0.723292
$186$	5240.00	2.06567
$187$	−1188.00	−0.464573
$188$	664.000	0.257591
$189$	−3220.00	−1.23926
$190$	−3248.00	−1.24018
$191$	2176.00	0.824345	0.412172	−	0.911106i	$-0.364770\pi$
$191$	2176.00	0.824345	0.412172	+	0.911106i	$0.364770\pi$
$192$	−640.000	−0.240563
$193$	−3126.00	−1.16588	−0.582939	−	0.812516i	$-0.698097\pi$
$193$	−3126.00	−1.16588	−0.582939	+	0.812516i	$0.698097\pi$
$194$	−964.000	−0.356759
$195$	−2240.00	−0.822614
$196$	196.000	0.0714286
$197$	−1122.00	−0.405783	−0.202891	−	0.979201i	$-0.565034\pi$
$197$	−1122.00	−0.405783	−0.202891	+	0.979201i	$0.565034\pi$
$198$	−1606.00	−0.576432
$199$	−5586.00	−1.98985	−0.994927	−	0.100597i	$-0.967925\pi$
$199$	−5586.00	−1.98985	−0.994927	+	0.100597i	$0.967925\pi$
$200$	568.000	0.200818
$201$	4160.00	1.45982
$202$	2432.00	0.847104
$203$	854.000	0.295266
$204$	−4320.00	−1.48265
$205$	−2856.00	−0.973033
$206$	2812.00	0.951074
$207$	4964.00	1.66677
$208$	−256.000	−0.0853385
$209$	−1276.00	−0.422310
$210$	1960.00	0.644061
$211$	3372.00	1.10018	0.550090	−	0.835105i	$-0.314593\pi$
$211$	3372.00	1.10018	0.550090	+	0.835105i	$0.314593\pi$
$212$	1768.00	0.572768
$213$	−4920.00	−1.58269
$214$	−1176.00	−0.375653
$215$	5544.00	1.75859
$216$	−3680.00	−1.15922
$217$	−1834.00	−0.573733
$218$	308.000	0.0956899
$219$	−4080.00	−1.25891
$220$	616.000	0.188776
$221$	−1728.00	−0.525963
$222$	−2600.00	−0.786039
$223$	606.000	0.181977	0.0909883	−	0.995852i	$-0.470997\pi$
$223$	606.000	0.181977	0.0909883	+	0.995852i	$0.470997\pi$
$224$	224.000	0.0668153
$225$	5183.00	1.53570
$226$	−3804.00	−1.11964
$227$	144.000	0.0421040	0.0210520	−	0.999778i	$-0.493298\pi$
$227$	144.000	0.0421040	0.0210520	+	0.999778i	$0.493298\pi$
$228$	−4640.00	−1.34777
$229$	−1010.00	−0.291453	−0.145726	−	0.989325i	$-0.546552\pi$
$229$	−1010.00	−0.291453	−0.145726	+	0.989325i	$0.546552\pi$
$230$	−1904.00	−0.545852
$231$	770.000	0.219317
$232$	976.000	0.276196
$233$	3790.00	1.06563	0.532814	−	0.846233i	$-0.321135\pi$
$233$	3790.00	1.06563	0.532814	+	0.846233i	$0.321135\pi$
$234$	−2336.00	−0.652603
$235$	−2324.00	−0.645111
$236$	2808.00	0.774514
$237$	−6000.00	−1.64448
$238$	1512.00	0.411800
$239$	2184.00	0.591093	0.295546	−	0.955328i	$-0.404498\pi$
$239$	2184.00	0.591093	0.295546	+	0.955328i	$0.404498\pi$
$240$	2240.00	0.602464
$241$	−4268.00	−1.14077	−0.570386	−	0.821377i	$-0.693206\pi$
$241$	−4268.00	−1.14077	−0.570386	+	0.821377i	$0.693206\pi$
$242$	242.000	0.0642824
$243$	−13870.0	−3.66157
$244$	784.000	0.205699
$245$	−686.000	−0.178885
$246$	−4080.00	−1.05744
$247$	−1856.00	−0.478115
$248$	−2096.00	−0.536678
$249$	12120.0	3.08463
$250$	1512.00	0.382509
$251$	7922.00	1.99216	0.996080	−	0.0884559i	$-0.0281932\pi$
$251$	7922.00	1.99216	0.996080	+	0.0884559i	$0.0281932\pi$
$252$	2044.00	0.510952
$253$	−748.000	−0.185875
$254$	128.000	0.0316198
$255$	15120.0	3.71314
$256$	256.000	0.0625000
$257$	4002.00	0.971354	0.485677	−	0.874138i	$-0.338573\pi$
$257$	4002.00	0.971354	0.485677	+	0.874138i	$0.338573\pi$
$258$	7920.00	1.91115
$259$	910.000	0.218319
$260$	896.000	0.213721
$261$	8906.00	2.11214
$262$	−3168.00	−0.747022
$263$	−3960.00	−0.928457	−0.464228	−	0.885716i	$-0.653668\pi$
$263$	−3960.00	−0.928457	−0.464228	+	0.885716i	$0.653668\pi$
$264$	880.000	0.205152
$265$	−6188.00	−1.43444
$266$	1624.00	0.374338
$267$	−11460.0	−2.62674
$268$	−1664.00	−0.379272
$269$	1878.00	0.425664	0.212832	−	0.977089i	$-0.431731\pi$
$269$	1878.00	0.425664	0.212832	+	0.977089i	$0.431731\pi$
$270$	12880.0	2.90315
$271$	−4740.00	−1.06249	−0.531244	−	0.847219i	$-0.678275\pi$
$271$	−4740.00	−1.06249	−0.531244	+	0.847219i	$0.678275\pi$
$272$	1728.00	0.385204
$273$	1120.00	0.248298
$274$	1996.00	0.440083
$275$	−781.000	−0.171258
$276$	−2720.00	−0.593206
$277$	710.000	0.154006	0.0770032	−	0.997031i	$-0.475465\pi$
$277$	710.000	0.154006	0.0770032	+	0.997031i	$0.475465\pi$
$278$	552.000	0.119089
$279$	−19126.0	−4.10410
$280$	−784.000	−0.167332
$281$	−90.0000	−0.0191066	−0.00955329	−	0.999954i	$-0.503041\pi$
$281$	−90.0000	−0.0191066	−0.00955329	+	0.999954i	$0.503041\pi$
$282$	−3320.00	−0.701075
$283$	−3448.00	−0.724248	−0.362124	−	0.932130i	$-0.617948\pi$
$283$	−3448.00	−0.724248	−0.362124	+	0.932130i	$0.617948\pi$
$284$	1968.00	0.411195
$285$	16240.0	3.37535
$286$	352.000	0.0727769
$287$	1428.00	0.293701
$288$	2336.00	0.477952
$289$	6751.00	1.37411
$290$	−3416.00	−0.691705
$291$	4820.00	0.970974
$292$	1632.00	0.327074
$293$	−2804.00	−0.559083	−0.279542	−	0.960134i	$-0.590183\pi$
$293$	−2804.00	−0.559083	−0.279542	+	0.960134i	$0.590183\pi$
$294$	−980.000	−0.194404
$295$	−9828.00	−1.93969
$296$	1040.00	0.204219
$297$	5060.00	0.988589
$298$	2636.00	0.512414
$299$	−1088.00	−0.210437
$300$	−2840.00	−0.546558
$301$	−2772.00	−0.530815
$302$	−1968.00	−0.374986
$303$	−12160.0	−2.30552
$304$	1856.00	0.350161
$305$	−2744.00	−0.515151
$306$	15768.0	2.94574
$307$	1320.00	0.245395	0.122698	−	0.992444i	$-0.460845\pi$
$307$	1320.00	0.245395	0.122698	+	0.992444i	$0.460845\pi$
$308$	−308.000	−0.0569803
$309$	−14060.0	−2.58850
$310$	7336.00	1.34405
$311$	−1066.00	−0.194364	−0.0971822	−	0.995267i	$-0.530983\pi$
$311$	−1066.00	−0.194364	−0.0971822	+	0.995267i	$0.530983\pi$
$312$	1280.00	0.232262
$313$	−9254.00	−1.67114	−0.835570	−	0.549384i	$-0.814863\pi$
$313$	−9254.00	−1.67114	−0.835570	+	0.549384i	$0.814863\pi$
$314$	3412.00	0.613218
$315$	−7154.00	−1.27963
$316$	2400.00	0.427249
$317$	−9722.00	−1.72253	−0.861265	−	0.508156i	$-0.830327\pi$
$317$	−9722.00	−1.72253	−0.861265	+	0.508156i	$0.830327\pi$
$318$	−8840.00	−1.55888
$319$	−1342.00	−0.235541
$320$	−896.000	−0.156525
$321$	5880.00	1.02240
$322$	952.000	0.164761
$323$	12528.0	2.15813
$324$	10516.0	1.80316
$325$	−1136.00	−0.193889
$326$	2336.00	0.396868
$327$	−1540.00	−0.260435
$328$	1632.00	0.274732
$329$	1162.00	0.194721
$330$	−3080.00	−0.513783
$331$	2620.00	0.435070	0.217535	−	0.976053i	$-0.430198\pi$
$331$	2620.00	0.435070	0.217535	+	0.976053i	$0.430198\pi$
$332$	−4848.00	−0.801411
$333$	9490.00	1.56171
$334$	144.000	0.0235908
$335$	5824.00	0.949848
$336$	−1120.00	−0.181848
$337$	2806.00	0.453568	0.226784	−	0.973945i	$-0.427179\pi$
$337$	2806.00	0.453568	0.226784	+	0.973945i	$0.427179\pi$
$338$	−3882.00	−0.624713
$339$	19020.0	3.04727
$340$	−6048.00	−0.964703
$341$	2882.00	0.457680
$342$	16936.0	2.67776
$343$	343.000	0.0539949
$344$	−3168.00	−0.496532
$345$	9520.00	1.48562
$346$	−8656.00	−1.34494
$347$	5564.00	0.860781	0.430391	−	0.902643i	$-0.358376\pi$
$347$	5564.00	0.860781	0.430391	+	0.902643i	$0.358376\pi$
$348$	−4880.00	−0.751711
$349$	10060.0	1.54298	0.771489	−	0.636242i	$-0.219512\pi$
$349$	10060.0	1.54298	0.771489	+	0.636242i	$0.219512\pi$
$350$	994.000	0.151804
$351$	7360.00	1.11922
$352$	−352.000	−0.0533002
$353$	−5102.00	−0.769269	−0.384635	−	0.923069i	$-0.625673\pi$
$353$	−5102.00	−0.769269	−0.384635	+	0.923069i	$0.625673\pi$
$354$	−14040.0	−2.10796
$355$	−6888.00	−1.02979
$356$	4584.00	0.682448
$357$	−7560.00	−1.12078
$358$	−3848.00	−0.568081
$359$	7976.00	1.17258	0.586291	−	0.810100i	$-0.300587\pi$
$359$	7976.00	1.17258	0.586291	+	0.810100i	$0.300587\pi$
$360$	−8176.00	−1.19698
$361$	6597.00	0.961802
$362$	4460.00	0.647548
$363$	−1210.00	−0.174955
$364$	−448.000	−0.0645098
$365$	−5712.00	−0.819123
$366$	−3920.00	−0.559841
$367$	−1234.00	−0.175516	−0.0877579	−	0.996142i	$-0.527970\pi$
$367$	−1234.00	−0.175516	−0.0877579	+	0.996142i	$0.527970\pi$
$368$	1088.00	0.154119
$369$	14892.0	2.10094
$370$	−3640.00	−0.511445
$371$	3094.00	0.432972
$372$	10480.0	1.46065
$373$	8030.00	1.11469	0.557343	−	0.830283i	$-0.311821\pi$
$373$	8030.00	1.11469	0.557343	+	0.830283i	$0.311821\pi$
$374$	−2376.00	−0.328503
$375$	−7560.00	−1.04106
$376$	1328.00	0.182145
$377$	−1952.00	−0.266666
$378$	−6440.00	−0.876291
$379$	−5184.00	−0.702597	−0.351298	−	0.936264i	$-0.614260\pi$
$379$	−5184.00	−0.702597	−0.351298	+	0.936264i	$0.614260\pi$
$380$	−6496.00	−0.876941
$381$	−640.000	−0.0860583
$382$	4352.00	0.582900
$383$	7570.00	1.00994	0.504972	−	0.863135i	$-0.331503\pi$
$383$	7570.00	1.00994	0.504972	+	0.863135i	$0.331503\pi$
$384$	−1280.00	−0.170103
$385$	1078.00	0.142701
$386$	−6252.00	−0.824400
$387$	−28908.0	−3.79710
$388$	−1928.00	−0.252266
$389$	−5370.00	−0.699922	−0.349961	−	0.936764i	$-0.613805\pi$
$389$	−5370.00	−0.699922	−0.349961	+	0.936764i	$0.613805\pi$
$390$	−4480.00	−0.581676
$391$	7344.00	0.949877
$392$	392.000	0.0505076
$393$	15840.0	2.03314
$394$	−2244.00	−0.286932
$395$	−8400.00	−1.07000
$396$	−3212.00	−0.407599
$397$	11442.0	1.44649	0.723246	−	0.690590i	$-0.242649\pi$
$397$	11442.0	1.44649	0.723246	+	0.690590i	$0.242649\pi$
$398$	−11172.0	−1.40704
$399$	−8120.00	−1.01882
$400$	1136.00	0.142000
$401$	2362.00	0.294146	0.147073	−	0.989126i	$-0.453015\pi$
$401$	2362.00	0.294146	0.147073	+	0.989126i	$0.453015\pi$
$402$	8320.00	1.03225
$403$	4192.00	0.518160
$404$	4864.00	0.598993
$405$	−36806.0	−4.51581
$406$	1708.00	0.208785
$407$	−1430.00	−0.174158
$408$	−8640.00	−1.04839
$409$	−16.0000	−0.00193435	−0.000967175	−	1.00000i	$-0.500308\pi$
$409$	−16.0000	−0.00193435	−0.000967175		1.00000i	$0.500308\pi$
$410$	−5712.00	−0.688038
$411$	−9980.00	−1.19775
$412$	5624.00	0.672511
$413$	4914.00	0.585477
$414$	9928.00	1.17859
$415$	16968.0	2.00705
$416$	−512.000	−0.0603434
$417$	−2760.00	−0.324119
$418$	−2552.00	−0.298618
$419$	9462.00	1.10322	0.551610	−	0.834102i	$-0.314014\pi$
$419$	9462.00	1.10322	0.551610	+	0.834102i	$0.314014\pi$
$420$	3920.00	0.455420
$421$	−6302.00	−0.729550	−0.364775	−	0.931096i	$-0.618854\pi$
$421$	−6302.00	−0.729550	−0.364775	+	0.931096i	$0.618854\pi$
$422$	6744.00	0.777945
$423$	12118.0	1.39290
$424$	3536.00	0.405008
$425$	7668.00	0.875183
$426$	−9840.00	−1.11913
$427$	1372.00	0.155494
$428$	−2352.00	−0.265627
$429$	−1760.00	−0.198074
$430$	11088.0	1.24351
$431$	7816.00	0.873512	0.436756	−	0.899580i	$-0.356127\pi$
$431$	7816.00	0.873512	0.436756	+	0.899580i	$0.356127\pi$
$432$	−7360.00	−0.819695
$433$	−9506.00	−1.05503	−0.527516	−	0.849545i	$-0.676877\pi$
$433$	−9506.00	−1.05503	−0.527516	+	0.849545i	$0.676877\pi$
$434$	−3668.00	−0.405690
$435$	17080.0	1.88258
$436$	616.000	0.0676630
$437$	7888.00	0.863465
$438$	−8160.00	−0.890182
$439$	−8228.00	−0.894535	−0.447268	−	0.894400i	$-0.647603\pi$
$439$	−8228.00	−0.894535	−0.447268	+	0.894400i	$0.647603\pi$
$440$	1232.00	0.133485
$441$	3577.00	0.386243
$442$	−3456.00	−0.371912
$443$	7668.00	0.822388	0.411194	−	0.911548i	$-0.365112\pi$
$443$	7668.00	0.822388	0.411194	+	0.911548i	$0.365112\pi$
$444$	−5200.00	−0.555813
$445$	−16044.0	−1.70912
$446$	1212.00	0.128677
$447$	−13180.0	−1.39461
$448$	448.000	0.0472456
$449$	−922.000	−0.0969084	−0.0484542	−	0.998825i	$-0.515429\pi$
$449$	−922.000	−0.0969084	−0.0484542	+	0.998825i	$0.515429\pi$
$450$	10366.0	1.08591
$451$	−2244.00	−0.234292
$452$	−7608.00	−0.791704
$453$	9840.00	1.02058
$454$	288.000	0.0297720
$455$	1568.00	0.161558
$456$	−9280.00	−0.953017
$457$	3386.00	0.346587	0.173294	−	0.984870i	$-0.444559\pi$
$457$	3386.00	0.346587	0.173294	+	0.984870i	$0.444559\pi$
$458$	−2020.00	−0.206088
$459$	−49680.0	−5.05199
$460$	−3808.00	−0.385976
$461$	−3300.00	−0.333398	−0.166699	−	0.986008i	$-0.553311\pi$
$461$	−3300.00	−0.333398	−0.166699	+	0.986008i	$0.553311\pi$
$462$	1540.00	0.155081
$463$	14236.0	1.42895	0.714474	−	0.699662i	$-0.246666\pi$
$463$	14236.0	1.42895	0.714474	+	0.699662i	$0.246666\pi$
$464$	1952.00	0.195300
$465$	−36680.0	−3.65805
$466$	7580.00	0.753512
$467$	3770.00	0.373565	0.186782	−	0.982401i	$-0.440194\pi$
$467$	3770.00	0.373565	0.186782	+	0.982401i	$0.440194\pi$
$468$	−4672.00	−0.461460
$469$	−2912.00	−0.286703
$470$	−4648.00	−0.456162
$471$	−17060.0	−1.66897
$472$	5616.00	0.547664
$473$	4356.00	0.423444
$474$	−12000.0	−1.16282
$475$	8236.00	0.795565
$476$	3024.00	0.291187
$477$	32266.0	3.09719
$478$	4368.00	0.417966
$479$	17796.0	1.69754	0.848768	−	0.528765i	$-0.177345\pi$
$479$	17796.0	1.69754	0.848768	+	0.528765i	$0.177345\pi$
$480$	4480.00	0.426006
$481$	−2080.00	−0.197172
$482$	−8536.00	−0.806648
$483$	−4760.00	−0.448421
$484$	484.000	0.0454545
$485$	6748.00	0.631775
$486$	−27740.0	−2.58912
$487$	−3684.00	−0.342788	−0.171394	−	0.985203i	$-0.554827\pi$
$487$	−3684.00	−0.342788	−0.171394	+	0.985203i	$0.554827\pi$
$488$	1568.00	0.145451
$489$	−11680.0	−1.08014
$490$	−1372.00	−0.126491
$491$	−17236.0	−1.58422	−0.792108	−	0.610381i	$-0.791016\pi$
$491$	−17236.0	−1.58422	−0.792108	+	0.610381i	$0.791016\pi$
$492$	−8160.00	−0.747726
$493$	13176.0	1.20369
$494$	−3712.00	−0.338078
$495$	11242.0	1.02079
$496$	−4192.00	−0.379489
$497$	3444.00	0.310834
$498$	24240.0	2.18117
$499$	13176.0	1.18204	0.591021	−	0.806656i	$-0.298725\pi$
$499$	13176.0	1.18204	0.591021	+	0.806656i	$0.298725\pi$
$500$	3024.00	0.270475
$501$	−720.000	−0.0642060
$502$	15844.0	1.40867
$503$	15428.0	1.36760	0.683798	−	0.729672i	$-0.260327\pi$
$503$	15428.0	1.36760	0.683798	+	0.729672i	$0.260327\pi$
$504$	4088.00	0.361298
$505$	−17024.0	−1.50011
$506$	−1496.00	−0.131433
$507$	19410.0	1.70025
$508$	256.000	0.0223586
$509$	−7842.00	−0.682889	−0.341445	−	0.939902i	$-0.610916\pi$
$509$	−7842.00	−0.682889	−0.341445	+	0.939902i	$0.610916\pi$
$510$	30240.0	2.62559
$511$	2856.00	0.247245
$512$	512.000	0.0441942
$513$	−53360.0	−4.59240
$514$	8004.00	0.686851
$515$	−19684.0	−1.68423
$516$	15840.0	1.35139
$517$	−1826.00	−0.155333
$518$	1820.00	0.154375
$519$	43280.0	3.66046
$520$	1792.00	0.151124
$521$	−17250.0	−1.45055	−0.725275	−	0.688460i	$-0.758287\pi$
$521$	−17250.0	−1.45055	−0.725275	+	0.688460i	$0.758287\pi$
$522$	17812.0	1.49351
$523$	1032.00	0.0862834	0.0431417	−	0.999069i	$-0.486263\pi$
$523$	1032.00	0.0862834	0.0431417	+	0.999069i	$0.486263\pi$
$524$	−6336.00	−0.528224
$525$	−4970.00	−0.413159
$526$	−7920.00	−0.656518
$527$	−28296.0	−2.33889
$528$	1760.00	0.145065
$529$	−7543.00	−0.619956
$530$	−12376.0	−1.01430
$531$	51246.0	4.18811
$532$	3248.00	0.264697
$533$	−3264.00	−0.265252
$534$	−22920.0	−1.85739
$535$	8232.00	0.665234
$536$	−3328.00	−0.268186
$537$	19240.0	1.54612
$538$	3756.00	0.300990
$539$	−539.000	−0.0430730
$540$	25760.0	2.05284
$541$	94.0000	0.00747020	0.00373510	−	0.999993i	$-0.498811\pi$
$541$	94.0000	0.00747020	0.00373510	+	0.999993i	$0.498811\pi$
$542$	−9480.00	−0.751293
$543$	−22300.0	−1.76240
$544$	3456.00	0.272380
$545$	−2156.00	−0.169455
$546$	2240.00	0.175574
$547$	−11676.0	−0.912669	−0.456334	−	0.889808i	$-0.650838\pi$
$547$	−11676.0	−0.912669	−0.456334	+	0.889808i	$0.650838\pi$
$548$	3992.00	0.311186
$549$	14308.0	1.11230
$550$	−1562.00	−0.121098
$551$	14152.0	1.09418
$552$	−5440.00	−0.419460
$553$	4200.00	0.322970
$554$	1420.00	0.108899
$555$	18200.0	1.39198
$556$	1104.00	0.0842087
$557$	−1858.00	−0.141339	−0.0706696	−	0.997500i	$-0.522514\pi$
$557$	−1858.00	−0.141339	−0.0706696	+	0.997500i	$0.522514\pi$
$558$	−38252.0	−2.90204
$559$	6336.00	0.479399
$560$	−1568.00	−0.118322
$561$	11880.0	0.894071
$562$	−180.000	−0.0135104
$563$	−23028.0	−1.72383	−0.861913	−	0.507056i	$-0.830734\pi$
$563$	−23028.0	−1.72383	−0.861913	+	0.507056i	$0.830734\pi$
$564$	−6640.00	−0.495735
$565$	26628.0	1.98274
$566$	−6896.00	−0.512121
$567$	18403.0	1.36306
$568$	3936.00	0.290759
$569$	−17066.0	−1.25737	−0.628685	−	0.777660i	$-0.716407\pi$
$569$	−17066.0	−1.25737	−0.628685	+	0.777660i	$0.716407\pi$
$570$	32480.0	2.38673
$571$	−10252.0	−0.751371	−0.375686	−	0.926747i	$-0.622593\pi$
$571$	−10252.0	−0.751371	−0.375686	+	0.926747i	$0.622593\pi$
$572$	704.000	0.0514610
$573$	−21760.0	−1.58645
$574$	2856.00	0.207678
$575$	4828.00	0.350159
$576$	4672.00	0.337963
$577$	2142.00	0.154545	0.0772726	−	0.997010i	$-0.475379\pi$
$577$	2142.00	0.154545	0.0772726	+	0.997010i	$0.475379\pi$
$578$	13502.0	0.971642
$579$	31260.0	2.24373
$580$	−6832.00	−0.489109
$581$	−8484.00	−0.605810
$582$	9640.00	0.686582
$583$	−4862.00	−0.345392
$584$	3264.00	0.231276
$585$	16352.0	1.15568
$586$	−5608.00	−0.395332
$587$	3474.00	0.244271	0.122136	−	0.992513i	$-0.461026\pi$
$587$	3474.00	0.244271	0.122136	+	0.992513i	$0.461026\pi$
$588$	−1960.00	−0.137464
$589$	−30392.0	−2.12611
$590$	−19656.0	−1.37157
$591$	11220.0	0.780929
$592$	2080.00	0.144405
$593$	−17424.0	−1.20661	−0.603303	−	0.797512i	$-0.706149\pi$
$593$	−17424.0	−1.20661	−0.603303	+	0.797512i	$0.706149\pi$
$594$	10120.0	0.699038
$595$	−10584.0	−0.729247
$596$	5272.00	0.362331
$597$	55860.0	3.82948
$598$	−2176.00	−0.148801
$599$	6916.00	0.471753	0.235877	−	0.971783i	$-0.424204\pi$
$599$	6916.00	0.471753	0.235877	+	0.971783i	$0.424204\pi$
$600$	−5680.00	−0.386475
$601$	16468.0	1.11771	0.558855	−	0.829265i	$-0.311241\pi$
$601$	16468.0	1.11771	0.558855	+	0.829265i	$0.311241\pi$
$602$	−5544.00	−0.375343
$603$	−30368.0	−2.05088
$604$	−3936.00	−0.265155
$605$	−1694.00	−0.113836
$606$	−24320.0	−1.63025
$607$	−17176.0	−1.14852	−0.574261	−	0.818673i	$-0.694710\pi$
$607$	−17176.0	−1.14852	−0.574261	+	0.818673i	$0.694710\pi$
$608$	3712.00	0.247601
$609$	−8540.00	−0.568240
$610$	−5488.00	−0.364267
$611$	−2656.00	−0.175860
$612$	31536.0	2.08295
$613$	11402.0	0.751260	0.375630	−	0.926770i	$-0.377426\pi$
$613$	11402.0	0.751260	0.375630	+	0.926770i	$0.377426\pi$
$614$	2640.00	0.173521
$615$	28560.0	1.87260
$616$	−616.000	−0.0402911
$617$	3654.00	0.238419	0.119209	−	0.992869i	$-0.461964\pi$
$617$	3654.00	0.238419	0.119209	+	0.992869i	$0.461964\pi$
$618$	−28120.0	−1.83034
$619$	−11318.0	−0.734909	−0.367455	−	0.930041i	$-0.619771\pi$
$619$	−11318.0	−0.734909	−0.367455	+	0.930041i	$0.619771\pi$
$620$	14672.0	0.950390
$621$	−31280.0	−2.02129
$622$	−2132.00	−0.137436
$623$	8022.00	0.515882
$624$	2560.00	0.164234
$625$	−19459.0	−1.24538
$626$	−18508.0	−1.18167
$627$	12760.0	0.812736
$628$	6824.00	0.433610
$629$	14040.0	0.890002
$630$	−14308.0	−0.904832
$631$	−23872.0	−1.50607	−0.753034	−	0.657981i	$-0.771411\pi$
$631$	−23872.0	−1.50607	−0.753034	+	0.657981i	$0.771411\pi$
$632$	4800.00	0.302110
$633$	−33720.0	−2.11730
$634$	−19444.0	−1.21801
$635$	−896.000	−0.0559948
$636$	−17680.0	−1.10229
$637$	−784.000	−0.0487649
$638$	−2684.00	−0.166553
$639$	35916.0	2.22350
$640$	−1792.00	−0.110680
$641$	−27026.0	−1.66531	−0.832654	−	0.553793i	$-0.813180\pi$
$641$	−27026.0	−1.66531	−0.832654	+	0.553793i	$0.813180\pi$
$642$	11760.0	0.722944
$643$	6498.00	0.398532	0.199266	−	0.979945i	$-0.436144\pi$
$643$	6498.00	0.398532	0.199266	+	0.979945i	$0.436144\pi$
$644$	1904.00	0.116503
$645$	−55440.0	−3.38442
$646$	25056.0	1.52603
$647$	−6422.00	−0.390224	−0.195112	−	0.980781i	$-0.562507\pi$
$647$	−6422.00	−0.390224	−0.195112	+	0.980781i	$0.562507\pi$
$648$	21032.0	1.27502
$649$	−7722.00	−0.467049
$650$	−2272.00	−0.137100
$651$	18340.0	1.10415
$652$	4672.00	0.280628
$653$	23670.0	1.41850	0.709249	−	0.704958i	$-0.249034\pi$
$653$	23670.0	1.41850	0.709249	+	0.704958i	$0.249034\pi$
$654$	−3080.00	−0.184155
$655$	22176.0	1.32288
$656$	3264.00	0.194265
$657$	29784.0	1.76862
$658$	2324.00	0.137688
$659$	−9812.00	−0.580002	−0.290001	−	0.957026i	$-0.593656\pi$
$659$	−9812.00	−0.580002	−0.290001	+	0.957026i	$0.593656\pi$
$660$	−6160.00	−0.363300
$661$	−5190.00	−0.305397	−0.152699	−	0.988273i	$-0.548796\pi$
$661$	−5190.00	−0.305397	−0.152699	+	0.988273i	$0.548796\pi$
$662$	5240.00	0.307641
$663$	17280.0	1.01222
$664$	−9696.00	−0.566683
$665$	−11368.0	−0.662905
$666$	18980.0	1.10429
$667$	8296.00	0.481593
$668$	288.000	0.0166812
$669$	−6060.00	−0.350214
$670$	11648.0	0.671644
$671$	−2156.00	−0.124041
$672$	−2240.00	−0.128586
$673$	94.0000	0.00538400	0.00269200	−	0.999996i	$-0.499143\pi$
$673$	94.0000	0.00538400	0.00269200	+	0.999996i	$0.499143\pi$
$674$	5612.00	0.320721
$675$	−32660.0	−1.86235
$676$	−7764.00	−0.441739
$677$	−12432.0	−0.705762	−0.352881	−	0.935668i	$-0.614798\pi$
$677$	−12432.0	−0.705762	−0.352881	+	0.935668i	$0.614798\pi$
$678$	38040.0	2.15475
$679$	−3374.00	−0.190695
$680$	−12096.0	−0.682148
$681$	−1440.00	−0.0810293
$682$	5764.00	0.323629
$683$	−2308.00	−0.129302	−0.0646509	−	0.997908i	$-0.520593\pi$
$683$	−2308.00	−0.129302	−0.0646509	+	0.997908i	$0.520593\pi$
$684$	33872.0	1.89346
$685$	−13972.0	−0.779332
$686$	686.000	0.0381802
$687$	10100.0	0.560901
$688$	−6336.00	−0.351101
$689$	−7072.00	−0.391033
$690$	19040.0	1.05049
$691$	26446.0	1.45594	0.727969	−	0.685610i	$-0.240464\pi$
$691$	26446.0	1.45594	0.727969	+	0.685610i	$0.240464\pi$
$692$	−17312.0	−0.951017
$693$	−5621.00	−0.308116
$694$	11128.0	0.608664
$695$	−3864.00	−0.210892
$696$	−9760.00	−0.531540
$697$	22032.0	1.19730
$698$	20120.0	1.09105
$699$	−37900.0	−2.05080
$700$	1988.00	0.107342
$701$	26450.0	1.42511	0.712555	−	0.701616i	$-0.247538\pi$
$701$	26450.0	1.42511	0.712555	+	0.701616i	$0.247538\pi$
$702$	14720.0	0.791411
$703$	15080.0	0.809037
$704$	−704.000	−0.0376889
$705$	23240.0	1.24152
$706$	−10204.0	−0.543956
$707$	8512.00	0.452796
$708$	−28080.0	−1.49055
$709$	17102.0	0.905894	0.452947	−	0.891537i	$-0.350373\pi$
$709$	17102.0	0.905894	0.452947	+	0.891537i	$0.350373\pi$
$710$	−13776.0	−0.728175
$711$	43800.0	2.31031
$712$	9168.00	0.482564
$713$	−17816.0	−0.935785
$714$	−15120.0	−0.792509
$715$	−2464.00	−0.128879
$716$	−7696.00	−0.401694
$717$	−21840.0	−1.13756
$718$	15952.0	0.829141
$719$	−16854.0	−0.874198	−0.437099	−	0.899413i	$-0.643994\pi$
$719$	−16854.0	−0.874198	−0.437099	+	0.899413i	$0.643994\pi$
$720$	−16352.0	−0.846393
$721$	9842.00	0.508371
$722$	13194.0	0.680097
$723$	42680.0	2.19542
$724$	8920.00	0.457886
$725$	8662.00	0.443722
$726$	−2420.00	−0.123712
$727$	−34670.0	−1.76869	−0.884346	−	0.466832i	$-0.845395\pi$
$727$	−34670.0	−1.76869	−0.884346	+	0.466832i	$0.845395\pi$
$728$	−896.000	−0.0456153
$729$	67717.0	3.44038
$730$	−11424.0	−0.579207
$731$	−42768.0	−2.16393
$732$	−7840.00	−0.395867
$733$	11716.0	0.590369	0.295184	−	0.955440i	$-0.404619\pi$
$733$	11716.0	0.590369	0.295184	+	0.955440i	$0.404619\pi$
$734$	−2468.00	−0.124108
$735$	6860.00	0.344265
$736$	2176.00	0.108979
$737$	4576.00	0.228710
$738$	29784.0	1.48559
$739$	29772.0	1.48198	0.740988	−	0.671518i	$-0.234357\pi$
$739$	29772.0	1.48198	0.740988	+	0.671518i	$0.234357\pi$
$740$	−7280.00	−0.361646
$741$	18560.0	0.920133
$742$	6188.00	0.306157
$743$	−24928.0	−1.23085	−0.615424	−	0.788196i	$-0.711015\pi$
$743$	−24928.0	−1.23085	−0.615424	+	0.788196i	$0.711015\pi$
$744$	20960.0	1.03284
$745$	−18452.0	−0.907421
$746$	16060.0	0.788202
$747$	−88476.0	−4.33356
$748$	−4752.00	−0.232287
$749$	−4116.00	−0.200795
$750$	−15120.0	−0.736139
$751$	−4652.00	−0.226037	−0.113019	−	0.993593i	$-0.536052\pi$
$751$	−4652.00	−0.226037	−0.113019	+	0.993593i	$0.536052\pi$
$752$	2656.00	0.128796
$753$	−79220.0	−3.83391
$754$	−3904.00	−0.188561
$755$	13776.0	0.664053
$756$	−12880.0	−0.619631
$757$	−1802.00	−0.0865189	−0.0432594	−	0.999064i	$-0.513774\pi$
$757$	−1802.00	−0.0865189	−0.0432594	+	0.999064i	$0.513774\pi$
$758$	−10368.0	−0.496811
$759$	7480.00	0.357716
$760$	−12992.0	−0.620091
$761$	−808.000	−0.0384888	−0.0192444	−	0.999815i	$-0.506126\pi$
$761$	−808.000	−0.0384888	−0.0192444	+	0.999815i	$0.506126\pi$
$762$	−1280.00	−0.0608524
$763$	1078.00	0.0511484
$764$	8704.00	0.412172
$765$	−110376.	−5.21654
$766$	15140.0	0.714139
$767$	−11232.0	−0.528767
$768$	−2560.00	−0.120281
$769$	23144.0	1.08530	0.542649	−	0.839960i	$-0.317421\pi$
$769$	23144.0	1.08530	0.542649	+	0.839960i	$0.317421\pi$
$770$	2156.00	0.100905
$771$	−40020.0	−1.86937
$772$	−12504.0	−0.582939
$773$	−27466.0	−1.27799	−0.638993	−	0.769212i	$-0.720649\pi$
$773$	−27466.0	−1.27799	−0.638993	+	0.769212i	$0.720649\pi$
$774$	−57816.0	−2.68495
$775$	−18602.0	−0.862198
$776$	−3856.00	−0.178379
$777$	−9100.00	−0.420155
$778$	−10740.0	−0.494920
$779$	23664.0	1.08838
$780$	−8960.00	−0.411307
$781$	−5412.00	−0.247960
$782$	14688.0	0.671665
$783$	−56120.0	−2.56139
$784$	784.000	0.0357143
$785$	−23884.0	−1.08593
$786$	31680.0	1.43764
$787$	23604.0	1.06911	0.534556	−	0.845133i	$-0.320479\pi$
$787$	23604.0	1.06911	0.534556	+	0.845133i	$0.320479\pi$
$788$	−4488.00	−0.202891
$789$	39600.0	1.78682
$790$	−16800.0	−0.756604
$791$	−13314.0	−0.598472
$792$	−6424.00	−0.288216
$793$	−3136.00	−0.140432
$794$	22884.0	1.02282
$795$	61880.0	2.76058
$796$	−22344.0	−0.994927
$797$	4122.00	0.183198	0.0915990	−	0.995796i	$-0.470802\pi$
$797$	4122.00	0.183198	0.0915990	+	0.995796i	$0.470802\pi$
$798$	−16240.0	−0.720413
$799$	17928.0	0.793801
$800$	2272.00	0.100409
$801$	83658.0	3.69027
$802$	4724.00	0.207993
$803$	−4488.00	−0.197233
$804$	16640.0	0.729910
$805$	−6664.00	−0.291770
$806$	8384.00	0.366394
$807$	−18780.0	−0.819191
$808$	9728.00	0.423552
$809$	−9110.00	−0.395909	−0.197955	−	0.980211i	$-0.563430\pi$
$809$	−9110.00	−0.395909	−0.197955	+	0.980211i	$0.563430\pi$
$810$	−73612.0	−3.19316
$811$	−28352.0	−1.22759	−0.613794	−	0.789466i	$-0.710357\pi$
$811$	−28352.0	−1.22759	−0.613794	+	0.789466i	$0.710357\pi$
$812$	3416.00	0.147633
$813$	47400.0	2.04476
$814$	−2860.00	−0.123149
$815$	−16352.0	−0.702804
$816$	−17280.0	−0.741325
$817$	−45936.0	−1.96707
$818$	−32.0000	−0.00136779
$819$	−8176.00	−0.348831
$820$	−11424.0	−0.486516
$821$	−14002.0	−0.595217	−0.297609	−	0.954688i	$-0.596189\pi$
$821$	−14002.0	−0.595217	−0.297609	+	0.954688i	$0.596189\pi$
$822$	−19960.0	−0.846940
$823$	−14848.0	−0.628881	−0.314440	−	0.949277i	$-0.601817\pi$
$823$	−14848.0	−0.628881	−0.314440	+	0.949277i	$0.601817\pi$
$824$	11248.0	0.475537
$825$	7810.00	0.329587
$826$	9828.00	0.413995
$827$	10500.0	0.441500	0.220750	−	0.975330i	$-0.429149\pi$
$827$	10500.0	0.441500	0.220750	+	0.975330i	$0.429149\pi$
$828$	19856.0	0.833386
$829$	23890.0	1.00089	0.500443	−	0.865770i	$-0.333171\pi$
$829$	23890.0	1.00089	0.500443	+	0.865770i	$0.333171\pi$
$830$	33936.0	1.41920
$831$	−7100.00	−0.296385
$832$	−1024.00	−0.0426692
$833$	5292.00	0.220116
$834$	−5520.00	−0.229187
$835$	−1008.00	−0.0417764
$836$	−5104.00	−0.211155
$837$	120520.	4.97704
$838$	18924.0	0.780094
$839$	−670.000	−0.0275697	−0.0137848	−	0.999905i	$-0.504388\pi$
$839$	−670.000	−0.0275697	−0.0137848	+	0.999905i	$0.504388\pi$
$840$	7840.00	0.322031
$841$	−9505.00	−0.389725
$842$	−12604.0	−0.515870
$843$	900.000	0.0367706
$844$	13488.0	0.550090
$845$	27174.0	1.10629
$846$	24236.0	0.984930
$847$	847.000	0.0343604
$848$	7072.00	0.286384
$849$	34480.0	1.39382
$850$	15336.0	0.618848
$851$	8840.00	0.356088
$852$	−19680.0	−0.791345
$853$	−4776.00	−0.191708	−0.0958541	−	0.995395i	$-0.530558\pi$
$853$	−4776.00	−0.191708	−0.0958541	+	0.995395i	$0.530558\pi$
$854$	2744.00	0.109951
$855$	−118552.	−4.74198
$856$	−4704.00	−0.187826
$857$	−13024.0	−0.519126	−0.259563	−	0.965726i	$-0.583579\pi$
$857$	−13024.0	−0.519126	−0.259563	+	0.965726i	$0.583579\pi$
$858$	−3520.00	−0.140059
$859$	−32998.0	−1.31068	−0.655342	−	0.755332i	$-0.727475\pi$
$859$	−32998.0	−1.31068	−0.655342	+	0.755332i	$0.727475\pi$
$860$	22176.0	0.879297
$861$	−14280.0	−0.565228
$862$	15632.0	0.617666
$863$	22272.0	0.878503	0.439251	−	0.898364i	$-0.355244\pi$
$863$	22272.0	0.878503	0.439251	+	0.898364i	$0.355244\pi$
$864$	−14720.0	−0.579612
$865$	60592.0	2.38172
$866$	−19012.0	−0.746021
$867$	−67510.0	−2.64447
$868$	−7336.00	−0.286866
$869$	−6600.00	−0.257641
$870$	34160.0	1.33119
$871$	6656.00	0.258932
$872$	1232.00	0.0478449
$873$	−35186.0	−1.36411
$874$	15776.0	0.610562
$875$	5292.00	0.204460
$876$	−16320.0	−0.629454
$877$	−30398.0	−1.17043	−0.585215	−	0.810878i	$-0.698990\pi$
$877$	−30398.0	−1.17043	−0.585215	+	0.810878i	$0.698990\pi$
$878$	−16456.0	−0.632532
$879$	28040.0	1.07596
$880$	2464.00	0.0943880
$881$	1630.00	0.0623338	0.0311669	−	0.999514i	$-0.490078\pi$
$881$	1630.00	0.0623338	0.0311669	+	0.999514i	$0.490078\pi$
$882$	7154.00	0.273115
$883$	−20228.0	−0.770925	−0.385462	−	0.922724i	$-0.625958\pi$
$883$	−20228.0	−0.770925	−0.385462	+	0.922724i	$0.625958\pi$
$884$	−6912.00	−0.262982
$885$	98280.0	3.73293
$886$	15336.0	0.581516
$887$	38908.0	1.47283	0.736416	−	0.676528i	$-0.236516\pi$
$887$	38908.0	1.47283	0.736416	+	0.676528i	$0.236516\pi$
$888$	−10400.0	−0.393019
$889$	448.000	0.0169015
$890$	−32088.0	−1.20853
$891$	−28919.0	−1.08734
$892$	2424.00	0.0909883
$893$	19256.0	0.721587
$894$	−26360.0	−0.986141
$895$	26936.0	1.00600
$896$	896.000	0.0334077
$897$	10880.0	0.404986
$898$	−1844.00	−0.0685246
$899$	−31964.0	−1.18583
$900$	20732.0	0.767852
$901$	47736.0	1.76506
$902$	−4488.00	−0.165670
$903$	27720.0	1.02155
$904$	−15216.0	−0.559819
$905$	−31220.0	−1.14673
$906$	19680.0	0.721660
$907$	−20936.0	−0.766448	−0.383224	−	0.923655i	$-0.625186\pi$
$907$	−20936.0	−0.766448	−0.383224	+	0.923655i	$0.625186\pi$
$908$	576.000	0.0210520
$909$	88768.0	3.23900
$910$	3136.00	0.114239
$911$	48204.0	1.75310	0.876548	−	0.481315i	$-0.159841\pi$
$911$	48204.0	1.75310	0.876548	+	0.481315i	$0.159841\pi$
$912$	−18560.0	−0.673885
$913$	13332.0	0.483269
$914$	6772.00	0.245074
$915$	27440.0	0.991408
$916$	−4040.00	−0.145726
$917$	−11088.0	−0.399300
$918$	−99360.0	−3.57230
$919$	−27304.0	−0.980061	−0.490030	−	0.871705i	$-0.663014\pi$
$919$	−27304.0	−0.980061	−0.490030	+	0.871705i	$0.663014\pi$
$920$	−7616.00	−0.272926
$921$	−13200.0	−0.472264
$922$	−6600.00	−0.235748
$923$	−7872.00	−0.280726
$924$	3080.00	0.109659
$925$	9230.00	0.328087
$926$	28472.0	1.01042
$927$	102638.	3.63654
$928$	3904.00	0.138098
$929$	30.0000	0.00105949	0.000529746	−	1.00000i	$-0.499831\pi$
$929$	30.0000	0.00105949	0.000529746		1.00000i	$0.499831\pi$
$930$	−73360.0	−2.58663
$931$	5684.00	0.200092
$932$	15160.0	0.532814
$933$	10660.0	0.374054
$934$	7540.00	0.264150
$935$	16632.0	0.581737
$936$	−9344.00	−0.326301
$937$	4736.00	0.165121	0.0825605	−	0.996586i	$-0.473690\pi$
$937$	4736.00	0.165121	0.0825605	+	0.996586i	$0.473690\pi$
$938$	−5824.00	−0.202730
$939$	92540.0	3.21611
$940$	−9296.00	−0.322555
$941$	19996.0	0.692722	0.346361	−	0.938101i	$-0.387417\pi$
$941$	19996.0	0.692722	0.346361	+	0.938101i	$0.387417\pi$
$942$	−34120.0	−1.18014
$943$	13872.0	0.479040
$944$	11232.0	0.387257
$945$	45080.0	1.55180
$946$	8712.00	0.299420
$947$	−1252.00	−0.0429615	−0.0214807	−	0.999769i	$-0.506838\pi$
$947$	−1252.00	−0.0429615	−0.0214807	+	0.999769i	$0.506838\pi$
$948$	−24000.0	−0.822240
$949$	−6528.00	−0.223296
$950$	16472.0	0.562550
$951$	97220.0	3.31501
$952$	6048.00	0.205900
$953$	17986.0	0.611357	0.305679	−	0.952135i	$-0.401117\pi$
$953$	17986.0	0.611357	0.305679	+	0.952135i	$0.401117\pi$
$954$	64532.0	2.19004
$955$	−30464.0	−1.03224
$956$	8736.00	0.295546
$957$	13420.0	0.453299
$958$	35592.0	1.20034
$959$	6986.00	0.235234
$960$	8960.00	0.301232
$961$	38853.0	1.30419
$962$	−4160.00	−0.139422
$963$	−42924.0	−1.43635
$964$	−17072.0	−0.570386
$965$	43764.0	1.45991
$966$	−9520.00	−0.317082
$967$	14256.0	0.474087	0.237043	−	0.971499i	$-0.423822\pi$
$967$	14256.0	0.474087	0.237043	+	0.971499i	$0.423822\pi$
$968$	968.000	0.0321412
$969$	−125280.	−4.15333
$970$	13496.0	0.446732
$971$	−50214.0	−1.65957	−0.829786	−	0.558082i	$-0.811537\pi$
$971$	−50214.0	−1.65957	−0.829786	+	0.558082i	$0.811537\pi$
$972$	−55480.0	−1.83078
$973$	1932.00	0.0636558
$974$	−7368.00	−0.242388
$975$	11360.0	0.373140
$976$	3136.00	0.102849
$977$	−35814.0	−1.17276	−0.586382	−	0.810034i	$-0.699448\pi$
$977$	−35814.0	−1.17276	−0.586382	+	0.810034i	$0.699448\pi$
$978$	−23360.0	−0.763773
$979$	−12606.0	−0.411532
$980$	−2744.00	−0.0894427
$981$	11242.0	0.365881
$982$	−34472.0	−1.12021
$983$	−19274.0	−0.625377	−0.312688	−	0.949856i	$-0.601230\pi$
$983$	−19274.0	−0.625377	−0.312688	+	0.949856i	$0.601230\pi$
$984$	−16320.0	−0.528722
$985$	15708.0	0.508120
$986$	26352.0	0.851135
$987$	−11620.0	−0.374740
$988$	−7424.00	−0.239058
$989$	−26928.0	−0.865784
$990$	22484.0	0.721806
$991$	59996.0	1.92314	0.961572	−	0.274553i	$-0.0885298\pi$
$991$	59996.0	1.92314	0.961572	+	0.274553i	$0.0885298\pi$
$992$	−8384.00	−0.268339
$993$	−26200.0	−0.837293
$994$	6888.00	0.219793
$995$	78204.0	2.49169
$996$	48480.0	1.54232
$997$	24344.0	0.773302	0.386651	−	0.922226i	$-0.373632\pi$
$997$	24344.0	0.773302	0.386651	+	0.922226i	$0.373632\pi$
$998$	26352.0	0.835830
$999$	−59800.0	−1.89388

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	154.4.a.c.1.1	✓	1
3.2	odd	2		1386.4.a.g.1.1		1
4.3	odd	2		1232.4.a.i.1.1		1
7.6	odd	2		1078.4.a.h.1.1		1
11.10	odd	2		1694.4.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.4.a.c.1.1	✓	1	1.1	even	1	trivial
1078.4.a.h.1.1		1	7.6	odd	2
1232.4.a.i.1.1		1	4.3	odd	2
1386.4.a.g.1.1		1	3.2	odd	2
1694.4.a.a.1.1		1	11.10	odd	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:	\( N \)	\(=\)	\( 154 = 2 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	154.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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