LMFDB - Embedded newform 1694.4.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1694,4,Mod(1,1694)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1694, 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("1694.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1694 = 2 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1694.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:	$99.9492355497$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 154)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1694.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

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

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
$11$	0	0
$11$	0	0
$12$	−40.0000	−0.962250
$13$	16.0000	0.341354	0.170677	−	0.985327i	$-0.445405\pi$
$13$	16.0000	0.341354	0.170677	+	0.985327i	$0.445405\pi$
$14$	14.0000	0.267261
$15$	140.000	2.40986
$16$	16.0000	0.250000
$17$	−108.000	−1.54081	−0.770407	−	0.637552i	$-0.779947\pi$
$17$	−108.000	−1.54081	−0.770407	+	0.637552i	$0.779947\pi$
$18$	−146.000	−1.91181
$19$	−116.000	−1.40064	−0.700322	−	0.713827i	$-0.746960\pi$
$19$	−116.000	−1.40064	−0.700322	+	0.713827i	$0.746960\pi$
$20$	−56.0000	−0.626099
$21$	70.0000	0.727393
$22$	0	0
$23$	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	$-0.627733\pi$
$29$	−122.000	−0.781201	−0.390601	+	0.920560i	$0.627733\pi$
$30$	−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
$33$	0	0
$34$	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	$-0.627017\pi$
$41$	−204.000	−0.777060	−0.388530	+	0.921436i	$0.627017\pi$
$42$	−140.000	−0.514344
$43$	396.000	1.40441	0.702203	−	0.711977i	$-0.252200\pi$
$43$	396.000	1.40441	0.702203	+	0.711977i	$0.252200\pi$
$44$	0	0
$45$	−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
$55$	0	0
$56$	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	$-0.565947\pi$
$61$	−196.000	−0.411397	−0.205699	+	0.978615i	$0.565947\pi$
$62$	524.000	1.07336
$63$	−511.000	−1.02190
$64$	64.0000	0.125000
$65$	−224.000	−0.427443
$66$	0	0
$67$	−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	$-0.606063\pi$
$73$	−408.000	−0.654148	−0.327074	+	0.944999i	$0.606063\pi$
$74$	−260.000	−0.408438
$75$	−710.000	−1.09312
$76$	−464.000	−0.700322
$77$	0	0
$78$	320.000	0.464524
$79$	−600.000	−0.854497	−0.427249	−	0.904134i	$-0.640517\pi$
$79$	−600.000	−0.854497	−0.427249	+	0.904134i	$0.640517\pi$
$80$	−224.000	−0.313050
$81$	2629.00	3.60631
$82$	408.000	0.549464
$83$	1212.00	1.60282	0.801411	−	0.598114i	$-0.204083\pi$
$83$	1212.00	1.60282	0.801411	+	0.598114i	$0.204083\pi$
$84$	280.000	0.363696
$85$	1512.00	1.92941
$86$	−792.000	−0.993065
$87$	1220.00	1.50342
$88$	0	0
$89$	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
$99$	0	0
$100$	284.000	0.284000
$101$	−1216.00	−1.19799	−0.598993	−	0.800754i	$-0.704432\pi$
$101$	−1216.00	−1.19799	−0.598993	+	0.800754i	$0.704432\pi$
$102$	−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	$-0.414421\pi$
$107$	588.000	0.531253	0.265627	+	0.964076i	$0.414421\pi$
$108$	−1840.00	−1.63939
$109$	−154.000	−0.135326	−0.0676630	−	0.997708i	$-0.521554\pi$
$109$	−154.000	−0.135326	−0.0676630	+	0.997708i	$0.521554\pi$
$110$	0	0
$111$	−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
$121$	0	0
$122$	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	$-0.507118\pi$
$127$	−64.0000	−0.0447172	−0.0223586	+	0.999750i	$0.507118\pi$
$128$	−128.000	−0.0883883
$129$	−3960.00	−2.70278
$130$	448.000	0.302248
$131$	1584.00	1.05645	0.528224	−	0.849105i	$-0.322858\pi$
$131$	1584.00	1.05645	0.528224	+	0.849105i	$0.322858\pi$
$132$	0	0
$133$	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	$-0.526836\pi$
$139$	−276.000	−0.168417	−0.0842087	+	0.996448i	$0.526836\pi$
$140$	392.000	0.236643
$141$	−1660.00	−0.991470
$142$	−984.000	−0.581517
$143$	0	0
$144$	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	$-0.618019\pi$
$149$	−1318.00	−0.724663	−0.362331	+	0.932049i	$0.618019\pi$
$150$	1420.00	0.772950
$151$	984.000	0.530310	0.265155	−	0.964206i	$-0.414577\pi$
$151$	984.000	0.530310	0.265155	+	0.964206i	$0.414577\pi$
$152$	928.000	0.495202
$153$	−7884.00	−4.16591
$154$	0	0
$155$	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
$165$	0	0
$166$	−2424.00	−1.13337
$167$	−72.0000	−0.0333624	−0.0166812	−	0.999861i	$-0.505310\pi$
$167$	−72.0000	−0.0333624	−0.0166812	+	0.999861i	$0.505310\pi$
$168$	−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	$-0.100041\pi$
$173$	4328.00	1.90203	0.951017	+	0.309140i	$0.100041\pi$
$174$	−2440.00	−1.06308
$175$	−497.000	−0.214684
$176$	0	0
$177$	−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
$187$	0	0
$188$	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	$-0.301903\pi$
$193$	3126.00	1.16588	0.582939	+	0.812516i	$0.301903\pi$
$194$	964.000	0.356759
$195$	2240.00	0.822614
$196$	196.000	0.0714286
$197$	1122.00	0.405783	0.202891	−	0.979201i	$-0.434966\pi$
$197$	1122.00	0.405783	0.202891	+	0.979201i	$0.434966\pi$
$198$	0	0
$199$	−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
$209$	0	0
$210$	1960.00	0.644061
$211$	−3372.00	−1.10018	−0.550090	−	0.835105i	$-0.685407\pi$
$211$	−3372.00	−1.10018	−0.550090	+	0.835105i	$0.685407\pi$
$212$	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
$220$	0	0
$221$	−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	$-0.506702\pi$
$227$	−144.000	−0.0421040	−0.0210520	+	0.999778i	$0.506702\pi$
$228$	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
$231$	0	0
$232$	976.000	0.276196
$233$	−3790.00	−1.06563	−0.532814	−	0.846233i	$-0.678865\pi$
$233$	−3790.00	−1.06563	−0.532814	+	0.846233i	$0.678865\pi$
$234$	−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	$-0.595502\pi$
$239$	−2184.00	−0.591093	−0.295546	+	0.955328i	$0.595502\pi$
$240$	2240.00	0.602464
$241$	4268.00	1.14077	0.570386	−	0.821377i	$-0.306794\pi$
$241$	4268.00	1.14077	0.570386	+	0.821377i	$0.306794\pi$
$242$	0	0
$243$	−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
$253$	0	0
$254$	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	$-0.346332\pi$
$263$	3960.00	0.928457	0.464228	+	0.885716i	$0.346332\pi$
$264$	0	0
$265$	−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	$-0.321725\pi$
$271$	4740.00	1.06249	0.531244	+	0.847219i	$0.321725\pi$
$272$	−1728.00	−0.385204
$273$	1120.00	0.248298
$274$	−1996.00	−0.440083
$275$	0	0
$276$	−2720.00	−0.593206
$277$	−710.000	−0.154006	−0.0770032	−	0.997031i	$-0.524535\pi$
$277$	−710.000	−0.154006	−0.0770032	+	0.997031i	$0.524535\pi$
$278$	552.000	0.119089
$279$	−19126.0	−4.10410
$280$	−784.000	−0.167332
$281$	90.0000	0.0191066	0.00955329	−	0.999954i	$-0.496959\pi$
$281$	90.0000	0.0191066	0.00955329	+	0.999954i	$0.496959\pi$
$282$	3320.00	0.701075
$283$	3448.00	0.724248	0.362124	−	0.932130i	$-0.382052\pi$
$283$	3448.00	0.724248	0.362124	+	0.932130i	$0.382052\pi$
$284$	1968.00	0.411195
$285$	−16240.0	−3.37535
$286$	0	0
$287$	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	$-0.409817\pi$
$293$	2804.00	0.559083	0.279542	+	0.960134i	$0.409817\pi$
$294$	980.000	0.194404
$295$	−9828.00	−1.93969
$296$	−1040.00	−0.204219
$297$	0	0
$298$	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	$-0.539155\pi$
$307$	−1320.00	−0.245395	−0.122698	+	0.992444i	$0.539155\pi$
$308$	0	0
$309$	−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
$319$	0	0
$320$	−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
$330$	0	0
$331$	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	$-0.572821\pi$
$337$	−2806.00	−0.453568	−0.226784	+	0.973945i	$0.572821\pi$
$338$	3882.00	0.624713
$339$	19020.0	3.04727
$340$	6048.00	0.964703
$341$	0	0
$342$	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	$-0.641624\pi$
$347$	−5564.00	−0.860781	−0.430391	+	0.902643i	$0.641624\pi$
$348$	4880.00	0.751711
$349$	−10060.0	−1.54298	−0.771489	−	0.636242i	$-0.780488\pi$
$349$	−10060.0	−1.54298	−0.771489	+	0.636242i	$0.780488\pi$
$350$	994.000	0.151804
$351$	−7360.00	−1.11922
$352$	0	0
$353$	−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	$-0.699413\pi$
$359$	−7976.00	−1.17258	−0.586291	+	0.810100i	$0.699413\pi$
$360$	8176.00	1.19698
$361$	6597.00	0.961802
$362$	−4460.00	−0.647548
$363$	0	0
$364$	−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	$-0.688179\pi$
$373$	−8030.00	−1.11469	−0.557343	+	0.830283i	$0.688179\pi$
$374$	0	0
$375$	−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
$385$	0	0
$386$	−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
$396$	0	0
$397$	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
$407$	0	0
$408$	−8640.00	−1.04839
$409$	16.0000	0.00193435	0.000967175	−	1.00000i	$-0.499692\pi$
$409$	16.0000	0.00193435	0.000967175		1.00000i	$0.499692\pi$
$410$	−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
$418$	0	0
$419$	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
$429$	0	0
$430$	11088.0	1.24351
$431$	−7816.00	−0.873512	−0.436756	−	0.899580i	$-0.643873\pi$
$431$	−7816.00	−0.873512	−0.436756	+	0.899580i	$0.643873\pi$
$432$	−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	$-0.352397\pi$
$439$	8228.00	0.894535	0.447268	+	0.894400i	$0.352397\pi$
$440$	0	0
$441$	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
$451$	0	0
$452$	−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	$-0.555441\pi$
$457$	−3386.00	−0.346587	−0.173294	+	0.984870i	$0.555441\pi$
$458$	2020.00	0.206088
$459$	49680.0	5.05199
$460$	−3808.00	−0.385976
$461$	3300.00	0.333398	0.166699	−	0.986008i	$-0.446689\pi$
$461$	3300.00	0.333398	0.166699	+	0.986008i	$0.446689\pi$
$462$	0	0
$463$	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
$473$	0	0
$474$	−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	$-0.822655\pi$
$479$	−17796.0	−1.69754	−0.848768	+	0.528765i	$0.822655\pi$
$480$	−4480.00	−0.426006
$481$	2080.00	0.197172
$482$	−8536.00	−0.806648
$483$	4760.00	0.448421
$484$	0	0
$485$	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	$-0.208984\pi$
$491$	17236.0	1.58422	0.792108	+	0.610381i	$0.208984\pi$
$492$	8160.00	0.747726
$493$	13176.0	1.20369
$494$	3712.00	0.338078
$495$	0	0
$496$	−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	$-0.739673\pi$
$503$	−15428.0	−1.36760	−0.683798	+	0.729672i	$0.739673\pi$
$504$	4088.00	0.361298
$505$	17024.0	1.50011
$506$	0	0
$507$	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
$517$	0	0
$518$	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	$-0.513737\pi$
$523$	−1032.00	−0.0862834	−0.0431417	+	0.999069i	$0.513737\pi$
$524$	6336.00	0.528224
$525$	4970.00	0.413159
$526$	−7920.00	−0.656518
$527$	28296.0	2.33889
$528$	0	0
$529$	−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
$539$	0	0
$540$	25760.0	2.05284
$541$	−94.0000	−0.00747020	−0.00373510	−	0.999993i	$-0.501189\pi$
$541$	−94.0000	−0.00747020	−0.00373510	+	0.999993i	$0.501189\pi$
$542$	−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	$-0.349162\pi$
$547$	11676.0	0.912669	0.456334	+	0.889808i	$0.349162\pi$
$548$	3992.00	0.311186
$549$	−14308.0	−1.11230
$550$	0	0
$551$	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	$-0.477486\pi$
$557$	1858.00	0.141339	0.0706696	+	0.997500i	$0.477486\pi$
$558$	38252.0	2.90204
$559$	6336.00	0.479399
$560$	1568.00	0.118322
$561$	0	0
$562$	−180.000	−0.0135104
$563$	23028.0	1.72383	0.861913	−	0.507056i	$-0.169266\pi$
$563$	23028.0	1.72383	0.861913	+	0.507056i	$0.169266\pi$
$564$	−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	$-0.283593\pi$
$569$	17066.0	1.25737	0.628685	+	0.777660i	$0.283593\pi$
$570$	32480.0	2.38673
$571$	10252.0	0.751371	0.375686	−	0.926747i	$-0.377407\pi$
$571$	10252.0	0.751371	0.375686	+	0.926747i	$0.377407\pi$
$572$	0	0
$573$	−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
$583$	0	0
$584$	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	$-0.293851\pi$
$593$	17424.0	1.20661	0.603303	+	0.797512i	$0.293851\pi$
$594$	0	0
$595$	−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	$-0.688759\pi$
$601$	−16468.0	−1.11771	−0.558855	+	0.829265i	$0.688759\pi$
$602$	5544.00	0.375343
$603$	−30368.0	−2.05088
$604$	3936.00	0.265155
$605$	0	0
$606$	−24320.0	−1.63025
$607$	17176.0	1.14852	0.574261	−	0.818673i	$-0.305290\pi$
$607$	17176.0	1.14852	0.574261	+	0.818673i	$0.305290\pi$
$608$	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	$-0.622574\pi$
$613$	−11402.0	−0.751260	−0.375630	+	0.926770i	$0.622574\pi$
$614$	2640.00	0.173521
$615$	−28560.0	−1.87260
$616$	0	0
$617$	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
$627$	0	0
$628$	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
$638$	0	0
$639$	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
$649$	0	0
$650$	−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	$-0.406344\pi$
$659$	9812.00	0.580002	0.290001	+	0.957026i	$0.406344\pi$
$660$	0	0
$661$	−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
$671$	0	0
$672$	−2240.00	−0.128586
$673$	−94.0000	−0.00538400	−0.00269200	−	0.999996i	$-0.500857\pi$
$673$	−94.0000	−0.00538400	−0.00269200	+	0.999996i	$0.500857\pi$
$674$	5612.00	0.320721
$675$	−32660.0	−1.86235
$676$	−7764.00	−0.441739
$677$	12432.0	0.705762	0.352881	−	0.935668i	$-0.385202\pi$
$677$	12432.0	0.705762	0.352881	+	0.935668i	$0.385202\pi$
$678$	−38040.0	−2.15475
$679$	3374.00	0.190695
$680$	−12096.0	−0.682148
$681$	1440.00	0.0810293
$682$	0	0
$683$	−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
$693$	0	0
$694$	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	$-0.752462\pi$
$701$	−26450.0	−1.42511	−0.712555	+	0.701616i	$0.752462\pi$
$702$	14720.0	0.791411
$703$	−15080.0	−0.809037
$704$	0	0
$705$	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
$715$	0	0
$716$	−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
$726$	0	0
$727$	−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	$-0.595381\pi$
$733$	−11716.0	−0.590369	−0.295184	+	0.955440i	$0.595381\pi$
$734$	2468.00	0.124108
$735$	6860.00	0.344265
$736$	−2176.00	−0.108979
$737$	0	0
$738$	29784.0	1.48559
$739$	−29772.0	−1.48198	−0.740988	−	0.671518i	$-0.765643\pi$
$739$	−29772.0	−1.48198	−0.740988	+	0.671518i	$0.765643\pi$
$740$	−7280.00	−0.361646
$741$	18560.0	0.920133
$742$	6188.00	0.306157
$743$	24928.0	1.23085	0.615424	−	0.788196i	$-0.288985\pi$
$743$	24928.0	1.23085	0.615424	+	0.788196i	$0.288985\pi$
$744$	−20960.0	−1.03284
$745$	18452.0	0.907421
$746$	16060.0	0.788202
$747$	88476.0	4.33356
$748$	0	0
$749$	−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
$759$	0	0
$760$	−12992.0	−0.620091
$761$	808.000	0.0384888	0.0192444	−	0.999815i	$-0.493874\pi$
$761$	808.000	0.0384888	0.0192444	+	0.999815i	$0.493874\pi$
$762$	−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	$-0.682579\pi$
$769$	−23144.0	−1.08530	−0.542649	+	0.839960i	$0.682579\pi$
$770$	0	0
$771$	−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
$781$	0	0
$782$	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	$-0.679521\pi$
$787$	−23604.0	−1.06911	−0.534556	+	0.845133i	$0.679521\pi$
$788$	4488.00	0.202891
$789$	−39600.0	−1.78682
$790$	−16800.0	−0.756604
$791$	13314.0	0.598472
$792$	0	0
$793$	−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
$803$	0	0
$804$	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	$-0.436570\pi$
$809$	9110.00	0.395909	0.197955	+	0.980211i	$0.436570\pi$
$810$	73612.0	3.19316
$811$	28352.0	1.22759	0.613794	−	0.789466i	$-0.289643\pi$
$811$	28352.0	1.22759	0.613794	+	0.789466i	$0.289643\pi$
$812$	3416.00	0.147633
$813$	−47400.0	−2.04476
$814$	0	0
$815$	−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	$-0.403811\pi$
$821$	14002.0	0.595217	0.297609	+	0.954688i	$0.403811\pi$
$822$	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
$825$	0	0
$826$	9828.00	0.413995
$827$	−10500.0	−0.441500	−0.220750	−	0.975330i	$-0.570851\pi$
$827$	−10500.0	−0.441500	−0.220750	+	0.975330i	$0.570851\pi$
$828$	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
$836$	0	0
$837$	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
$847$	0	0
$848$	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	$-0.469442\pi$
$853$	4776.00	0.191708	0.0958541	+	0.995395i	$0.469442\pi$
$854$	−2744.00	−0.109951
$855$	118552.	4.74198
$856$	−4704.00	−0.187826
$857$	13024.0	0.519126	0.259563	−	0.965726i	$-0.416421\pi$
$857$	13024.0	0.519126	0.259563	+	0.965726i	$0.416421\pi$
$858$	0	0
$859$	−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
$869$	0	0
$870$	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	$-0.301010\pi$
$877$	30398.0	1.17043	0.585215	+	0.810878i	$0.301010\pi$
$878$	−16456.0	−0.632532
$879$	−28040.0	−1.07596
$880$	0	0
$881$	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	$-0.763484\pi$
$887$	−38908.0	−1.47283	−0.736416	+	0.676528i	$0.763484\pi$
$888$	10400.0	0.393019
$889$	448.000	0.0169015
$890$	32088.0	1.20853
$891$	0	0
$892$	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
$902$	0	0
$903$	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
$913$	0	0
$914$	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	$-0.336986\pi$
$919$	27304.0	0.980061	0.490030	+	0.871705i	$0.336986\pi$
$920$	7616.00	0.272926
$921$	13200.0	0.472264
$922$	−6600.00	−0.235748
$923$	7872.00	0.280726
$924$	0	0
$925$	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
$935$	0	0
$936$	−9344.00	−0.326301
$937$	−4736.00	−0.165121	−0.0825605	−	0.996586i	$-0.526310\pi$
$937$	−4736.00	−0.165121	−0.0825605	+	0.996586i	$0.526310\pi$
$938$	−5824.00	−0.202730
$939$	92540.0	3.21611
$940$	−9296.00	−0.322555
$941$	−19996.0	−0.692722	−0.346361	−	0.938101i	$-0.612583\pi$
$941$	−19996.0	−0.692722	−0.346361	+	0.938101i	$0.612583\pi$
$942$	34120.0	1.18014
$943$	−13872.0	−0.479040
$944$	11232.0	0.387257
$945$	−45080.0	−1.55180
$946$	0	0
$947$	−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	$-0.598883\pi$
$953$	−17986.0	−0.611357	−0.305679	+	0.952135i	$0.598883\pi$
$954$	−64532.0	−2.19004
$955$	−30464.0	−1.03224
$956$	−8736.00	−0.295546
$957$	0	0
$958$	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	$-0.576178\pi$
$967$	−14256.0	−0.474087	−0.237043	+	0.971499i	$0.576178\pi$
$968$	0	0
$969$	−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
$979$	0	0
$980$	−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
$990$	0	0
$991$	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	$-0.626368\pi$
$997$	−24344.0	−0.773302	−0.386651	+	0.922226i	$0.626368\pi$
$998$	−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	1694.4.a.a.1.1		1
11.10	odd	2		154.4.a.c.1.1	✓	1
33.32	even	2		1386.4.a.g.1.1		1
44.43	even	2		1232.4.a.i.1.1		1
77.76	even	2		1078.4.a.h.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.4.a.c.1.1	✓	1	11.10	odd	2
1078.4.a.h.1.1		1	77.76	even	2
1232.4.a.i.1.1		1	44.43	even	2
1386.4.a.g.1.1		1	33.32	even	2
1694.4.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:	\( N \)	\(=\)	\( 1694 = 2 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1694.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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