LMFDB - Embedded newform 110.4.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [110,4,Mod(1,110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(110, 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("110.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 110 = 2 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	110.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:	$6.49021010063$
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	$\chi$	$=$	110.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2.00000 q^{2} -8.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} -16.0000 q^{6} +26.0000 q^{7} +8.00000 q^{8} +37.0000 q^{9} +O(q^{10})$

\(q+2.00000 q^{2} -8.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} -16.0000 q^{6} +26.0000 q^{7} +8.00000 q^{8} +37.0000 q^{9} -10.0000 q^{10} +11.0000 q^{11} -32.0000 q^{12} +92.0000 q^{13} +52.0000 q^{14} +40.0000 q^{15} +16.0000 q^{16} -84.0000 q^{17} +74.0000 q^{18} +80.0000 q^{19} -20.0000 q^{20} -208.000 q^{21} +22.0000 q^{22} +72.0000 q^{23} -64.0000 q^{24} +25.0000 q^{25} +184.000 q^{26} -80.0000 q^{27} +104.000 q^{28} -30.0000 q^{29} +80.0000 q^{30} -208.000 q^{31} +32.0000 q^{32} -88.0000 q^{33} -168.000 q^{34} -130.000 q^{35} +148.000 q^{36} +86.0000 q^{37} +160.000 q^{38} -736.000 q^{39} -40.0000 q^{40} -378.000 q^{41} -416.000 q^{42} +542.000 q^{43} +44.0000 q^{44} -185.000 q^{45} +144.000 q^{46} +216.000 q^{47} -128.000 q^{48} +333.000 q^{49} +50.0000 q^{50} +672.000 q^{51} +368.000 q^{52} -18.0000 q^{53} -160.000 q^{54} -55.0000 q^{55} +208.000 q^{56} -640.000 q^{57} -60.0000 q^{58} +420.000 q^{59} +160.000 q^{60} -718.000 q^{61} -416.000 q^{62} +962.000 q^{63} +64.0000 q^{64} -460.000 q^{65} -176.000 q^{66} -124.000 q^{67} -336.000 q^{68} -576.000 q^{69} -260.000 q^{70} +912.000 q^{71} +296.000 q^{72} -268.000 q^{73} +172.000 q^{74} -200.000 q^{75} +320.000 q^{76} +286.000 q^{77} -1472.00 q^{78} -940.000 q^{79} -80.0000 q^{80} -359.000 q^{81} -756.000 q^{82} -498.000 q^{83} -832.000 q^{84} +420.000 q^{85} +1084.00 q^{86} +240.000 q^{87} +88.0000 q^{88} +150.000 q^{89} -370.000 q^{90} +2392.00 q^{91} +288.000 q^{92} +1664.00 q^{93} +432.000 q^{94} -400.000 q^{95} -256.000 q^{96} +446.000 q^{97} +666.000 q^{98} +407.000 q^{99} +O(q^{100})\)

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
$3$	−8.00000	−1.53960	−0.769800	−	0.638285i	$-0.779644\pi$
$3$	−8.00000	−1.53960	−0.769800	+	0.638285i	$0.779644\pi$
$4$	4.00000	0.500000
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−16.0000	−1.08866
$7$	26.0000	1.40387	0.701934	−	0.712242i	$-0.252320\pi$
$7$	26.0000	1.40387	0.701934	+	0.712242i	$0.252320\pi$
$8$	8.00000	0.353553
$9$	37.0000	1.37037
$10$	−10.0000	−0.316228
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−32.0000	−0.769800
$13$	92.0000	1.96279	0.981393	−	0.192012i	$-0.0615011\pi$
$13$	92.0000	1.96279	0.981393	+	0.192012i	$0.0615011\pi$
$14$	52.0000	0.992685
$15$	40.0000	0.688530
$16$	16.0000	0.250000
$17$	−84.0000	−1.19841	−0.599206	−	0.800595i	$-0.704517\pi$
$17$	−84.0000	−1.19841	−0.599206	+	0.800595i	$0.704517\pi$
$18$	74.0000	0.968998
$19$	80.0000	0.965961	0.482980	−	0.875631i	$-0.339554\pi$
$19$	80.0000	0.965961	0.482980	+	0.875631i	$0.339554\pi$
$20$	−20.0000	−0.223607
$21$	−208.000	−2.16140
$22$	22.0000	0.213201
$23$	72.0000	0.652741	0.326370	−	0.945242i	$-0.394174\pi$
$23$	72.0000	0.652741	0.326370	+	0.945242i	$0.394174\pi$
$24$	−64.0000	−0.544331
$25$	25.0000	0.200000
$26$	184.000	1.38790
$27$	−80.0000	−0.570222
$28$	104.000	0.701934
$29$	−30.0000	−0.192099	−0.0960493	−	0.995377i	$-0.530621\pi$
$29$	−30.0000	−0.192099	−0.0960493	+	0.995377i	$0.530621\pi$
$30$	80.0000	0.486864
$31$	−208.000	−1.20509	−0.602547	−	0.798084i	$-0.705847\pi$
$31$	−208.000	−1.20509	−0.602547	+	0.798084i	$0.705847\pi$
$32$	32.0000	0.176777
$33$	−88.0000	−0.464207
$34$	−168.000	−0.847405
$35$	−130.000	−0.627829
$36$	148.000	0.685185
$37$	86.0000	0.382117	0.191058	−	0.981579i	$-0.438808\pi$
$37$	86.0000	0.382117	0.191058	+	0.981579i	$0.438808\pi$
$38$	160.000	0.683038
$39$	−736.000	−3.02191
$40$	−40.0000	−0.158114
$41$	−378.000	−1.43985	−0.719923	−	0.694054i	$-0.755823\pi$
$41$	−378.000	−1.43985	−0.719923	+	0.694054i	$0.755823\pi$
$42$	−416.000	−1.52834
$43$	542.000	1.92219	0.961096	−	0.276216i	$-0.0890805\pi$
$43$	542.000	1.92219	0.961096	+	0.276216i	$0.0890805\pi$
$44$	44.0000	0.150756
$45$	−185.000	−0.612848
$46$	144.000	0.461557
$47$	216.000	0.670358	0.335179	−	0.942154i	$-0.391203\pi$
$47$	216.000	0.670358	0.335179	+	0.942154i	$0.391203\pi$
$48$	−128.000	−0.384900
$49$	333.000	0.970845
$50$	50.0000	0.141421
$51$	672.000	1.84507
$52$	368.000	0.981393
$53$	−18.0000	−0.0466508	−0.0233254	−	0.999728i	$-0.507425\pi$
$53$	−18.0000	−0.0466508	−0.0233254	+	0.999728i	$0.507425\pi$
$54$	−160.000	−0.403208
$55$	−55.0000	−0.134840
$56$	208.000	0.496342
$57$	−640.000	−1.48719
$58$	−60.0000	−0.135834
$59$	420.000	0.926769	0.463384	−	0.886157i	$-0.346635\pi$
$59$	420.000	0.926769	0.463384	+	0.886157i	$0.346635\pi$
$60$	160.000	0.344265
$61$	−718.000	−1.50706	−0.753529	−	0.657415i	$-0.771650\pi$
$61$	−718.000	−1.50706	−0.753529	+	0.657415i	$0.771650\pi$
$62$	−416.000	−0.852130
$63$	962.000	1.92382
$64$	64.0000	0.125000
$65$	−460.000	−0.877784
$66$	−176.000	−0.328244
$67$	−124.000	−0.226105	−0.113052	−	0.993589i	$-0.536063\pi$
$67$	−124.000	−0.226105	−0.113052	+	0.993589i	$0.536063\pi$
$68$	−336.000	−0.599206
$69$	−576.000	−1.00496
$70$	−260.000	−0.443942
$71$	912.000	1.52443	0.762215	−	0.647324i	$-0.224112\pi$
$71$	912.000	1.52443	0.762215	+	0.647324i	$0.224112\pi$
$72$	296.000	0.484499
$73$	−268.000	−0.429685	−0.214843	−	0.976649i	$-0.568924\pi$
$73$	−268.000	−0.429685	−0.214843	+	0.976649i	$0.568924\pi$
$74$	172.000	0.270197
$75$	−200.000	−0.307920
$76$	320.000	0.482980
$77$	286.000	0.423282
$78$	−1472.00	−2.13681
$79$	−940.000	−1.33871	−0.669356	−	0.742942i	$-0.733430\pi$
$79$	−940.000	−1.33871	−0.669356	+	0.742942i	$0.733430\pi$
$80$	−80.0000	−0.111803
$81$	−359.000	−0.492455
$82$	−756.000	−1.01812
$83$	−498.000	−0.658586	−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−498.000	−0.658586	−0.329293	+	0.944228i	$0.606810\pi$
$84$	−832.000	−1.08070
$85$	420.000	0.535946
$86$	1084.00	1.35919
$87$	240.000	0.295755
$88$	88.0000	0.106600
$89$	150.000	0.178651	0.0893257	−	0.996002i	$-0.471529\pi$
$89$	150.000	0.178651	0.0893257	+	0.996002i	$0.471529\pi$
$90$	−370.000	−0.433349
$91$	2392.00	2.75549
$92$	288.000	0.326370
$93$	1664.00	1.85536
$94$	432.000	0.474015
$95$	−400.000	−0.431991
$96$	−256.000	−0.272166
$97$	446.000	0.466850	0.233425	−	0.972375i	$-0.425007\pi$
$97$	446.000	0.466850	0.233425	+	0.972375i	$0.425007\pi$
$98$	666.000	0.686491
$99$	407.000	0.413182
$100$	100.000	0.100000
$101$	−498.000	−0.490622	−0.245311	−	0.969444i	$-0.578890\pi$
$101$	−498.000	−0.490622	−0.245311	+	0.969444i	$0.578890\pi$
$102$	1344.00	1.30466
$103$	−988.000	−0.945151	−0.472575	−	0.881290i	$-0.656676\pi$
$103$	−988.000	−0.945151	−0.472575	+	0.881290i	$0.656676\pi$
$104$	736.000	0.693949
$105$	1040.00	0.966606
$106$	−36.0000	−0.0329871
$107$	1686.00	1.52329	0.761644	−	0.647996i	$-0.224393\pi$
$107$	1686.00	1.52329	0.761644	+	0.647996i	$0.224393\pi$
$108$	−320.000	−0.285111
$109$	350.000	0.307559	0.153779	−	0.988105i	$-0.450855\pi$
$109$	350.000	0.307559	0.153779	+	0.988105i	$0.450855\pi$
$110$	−110.000	−0.0953463
$111$	−688.000	−0.588307
$112$	416.000	0.350967
$113$	−498.000	−0.414583	−0.207292	−	0.978279i	$-0.566465\pi$
$113$	−498.000	−0.414583	−0.207292	+	0.978279i	$0.566465\pi$
$114$	−1280.00	−1.05161
$115$	−360.000	−0.291915
$116$	−120.000	−0.0960493
$117$	3404.00	2.68974
$118$	840.000	0.655324
$119$	−2184.00	−1.68241
$120$	320.000	0.243432
$121$	121.000	0.0909091
$122$	−1436.00	−1.06565
$123$	3024.00	2.21679
$124$	−832.000	−0.602547
$125$	−125.000	−0.0894427
$126$	1924.00	1.36035
$127$	−514.000	−0.359135	−0.179567	−	0.983746i	$-0.557470\pi$
$127$	−514.000	−0.359135	−0.179567	+	0.983746i	$0.557470\pi$
$128$	128.000	0.0883883
$129$	−4336.00	−2.95941
$130$	−920.000	−0.620687
$131$	−2808.00	−1.87279	−0.936397	−	0.350942i	$-0.885862\pi$
$131$	−2808.00	−1.87279	−0.936397	+	0.350942i	$0.885862\pi$
$132$	−352.000	−0.232104
$133$	2080.00	1.35608
$134$	−248.000	−0.159880
$135$	400.000	0.255011
$136$	−672.000	−0.423702
$137$	−1194.00	−0.744601	−0.372300	−	0.928112i	$-0.621431\pi$
$137$	−1194.00	−0.744601	−0.372300	+	0.928112i	$0.621431\pi$
$138$	−1152.00	−0.710614
$139$	1820.00	1.11058	0.555289	−	0.831657i	$-0.312608\pi$
$139$	1820.00	1.11058	0.555289	+	0.831657i	$0.312608\pi$
$140$	−520.000	−0.313914
$141$	−1728.00	−1.03208
$142$	1824.00	1.07793
$143$	1012.00	0.591802
$144$	592.000	0.342593
$145$	150.000	0.0859091
$146$	−536.000	−0.303833
$147$	−2664.00	−1.49471
$148$	344.000	0.191058
$149$	390.000	0.214430	0.107215	−	0.994236i	$-0.465807\pi$
$149$	390.000	0.214430	0.107215	+	0.994236i	$0.465807\pi$
$150$	−400.000	−0.217732
$151$	−1348.00	−0.726481	−0.363241	−	0.931695i	$-0.618330\pi$
$151$	−1348.00	−0.726481	−0.363241	+	0.931695i	$0.618330\pi$
$152$	640.000	0.341519
$153$	−3108.00	−1.64227
$154$	572.000	0.299306
$155$	1040.00	0.538934
$156$	−2944.00	−1.51095
$157$	−2614.00	−1.32879	−0.664395	−	0.747382i	$-0.731311\pi$
$157$	−2614.00	−1.32879	−0.664395	+	0.747382i	$0.731311\pi$
$158$	−1880.00	−0.946612
$159$	144.000	0.0718235
$160$	−160.000	−0.0790569
$161$	1872.00	0.916362
$162$	−718.000	−0.348219
$163$	−208.000	−0.0999498	−0.0499749	−	0.998750i	$-0.515914\pi$
$163$	−208.000	−0.0999498	−0.0499749	+	0.998750i	$0.515914\pi$
$164$	−1512.00	−0.719923
$165$	440.000	0.207600
$166$	−996.000	−0.465690
$167$	−3714.00	−1.72095	−0.860473	−	0.509496i	$-0.829832\pi$
$167$	−3714.00	−1.72095	−0.860473	+	0.509496i	$0.829832\pi$
$168$	−1664.00	−0.764169
$169$	6267.00	2.85253
$170$	840.000	0.378971
$171$	2960.00	1.32372
$172$	2168.00	0.961096
$173$	312.000	0.137115	0.0685576	−	0.997647i	$-0.478160\pi$
$173$	312.000	0.137115	0.0685576	+	0.997647i	$0.478160\pi$
$174$	480.000	0.209130
$175$	650.000	0.280774
$176$	176.000	0.0753778
$177$	−3360.00	−1.42685
$178$	300.000	0.126326
$179$	−4020.00	−1.67860	−0.839299	−	0.543671i	$-0.817034\pi$
$179$	−4020.00	−1.67860	−0.839299	+	0.543671i	$0.817034\pi$
$180$	−740.000	−0.306424
$181$	−1558.00	−0.639808	−0.319904	−	0.947450i	$-0.603651\pi$
$181$	−1558.00	−0.639808	−0.319904	+	0.947450i	$0.603651\pi$
$182$	4784.00	1.94843
$183$	5744.00	2.32027
$184$	576.000	0.230779
$185$	−430.000	−0.170888
$186$	3328.00	1.31194
$187$	−924.000	−0.361335
$188$	864.000	0.335179
$189$	−2080.00	−0.800517
$190$	−800.000	−0.305464
$191$	−2328.00	−0.881928	−0.440964	−	0.897525i	$-0.645363\pi$
$191$	−2328.00	−0.881928	−0.440964	+	0.897525i	$0.645363\pi$
$192$	−512.000	−0.192450
$193$	−988.000	−0.368486	−0.184243	−	0.982881i	$-0.558983\pi$
$193$	−988.000	−0.368486	−0.184243	+	0.982881i	$0.558983\pi$
$194$	892.000	0.330113
$195$	3680.00	1.35144
$196$	1332.00	0.485423
$197$	−1464.00	−0.529470	−0.264735	−	0.964321i	$-0.585285\pi$
$197$	−1464.00	−0.529470	−0.264735	+	0.964321i	$0.585285\pi$
$198$	814.000	0.292164
$199$	800.000	0.284977	0.142489	−	0.989796i	$-0.454490\pi$
$199$	800.000	0.284977	0.142489	+	0.989796i	$0.454490\pi$
$200$	200.000	0.0707107
$201$	992.000	0.348111
$202$	−996.000	−0.346922
$203$	−780.000	−0.269681
$204$	2688.00	0.922537
$205$	1890.00	0.643919
$206$	−1976.00	−0.668323
$207$	2664.00	0.894497
$208$	1472.00	0.490696
$209$	880.000	0.291248
$210$	2080.00	0.683494
$211$	3032.00	0.989249	0.494624	−	0.869107i	$-0.335306\pi$
$211$	3032.00	0.989249	0.494624	+	0.869107i	$0.335306\pi$
$212$	−72.0000	−0.0233254
$213$	−7296.00	−2.34701
$214$	3372.00	1.07713
$215$	−2710.00	−0.859630
$216$	−640.000	−0.201604
$217$	−5408.00	−1.69179
$218$	700.000	0.217477
$219$	2144.00	0.661544
$220$	−220.000	−0.0674200
$221$	−7728.00	−2.35222
$222$	−1376.00	−0.415996
$223$	−3088.00	−0.927299	−0.463650	−	0.886019i	$-0.653460\pi$
$223$	−3088.00	−0.927299	−0.463650	+	0.886019i	$0.653460\pi$
$224$	832.000	0.248171
$225$	925.000	0.274074
$226$	−996.000	−0.293155
$227$	−534.000	−0.156136	−0.0780679	−	0.996948i	$-0.524875\pi$
$227$	−534.000	−0.156136	−0.0780679	+	0.996948i	$0.524875\pi$
$228$	−2560.00	−0.743597
$229$	110.000	0.0317424	0.0158712	−	0.999874i	$-0.494948\pi$
$229$	110.000	0.0317424	0.0158712	+	0.999874i	$0.494948\pi$
$230$	−720.000	−0.206415
$231$	−2288.00	−0.651685
$232$	−240.000	−0.0679171
$233$	3312.00	0.931229	0.465614	−	0.884988i	$-0.345833\pi$
$233$	3312.00	0.931229	0.465614	+	0.884988i	$0.345833\pi$
$234$	6808.00	1.90194
$235$	−1080.00	−0.299793
$236$	1680.00	0.463384
$237$	7520.00	2.06108
$238$	−4368.00	−1.18964
$239$	3780.00	1.02305	0.511523	−	0.859270i	$-0.329082\pi$
$239$	3780.00	1.02305	0.511523	+	0.859270i	$0.329082\pi$
$240$	640.000	0.172133
$241$	5222.00	1.39576	0.697881	−	0.716214i	$-0.254126\pi$
$241$	5222.00	1.39576	0.697881	+	0.716214i	$0.254126\pi$
$242$	242.000	0.0642824
$243$	5032.00	1.32841
$244$	−2872.00	−0.753529
$245$	−1665.00	−0.434175
$246$	6048.00	1.56751
$247$	7360.00	1.89597
$248$	−1664.00	−0.426065
$249$	3984.00	1.01396
$250$	−250.000	−0.0632456
$251$	−1548.00	−0.389278	−0.194639	−	0.980875i	$-0.562354\pi$
$251$	−1548.00	−0.389278	−0.194639	+	0.980875i	$0.562354\pi$
$252$	3848.00	0.961910
$253$	792.000	0.196809
$254$	−1028.00	−0.253947
$255$	−3360.00	−0.825143
$256$	256.000	0.0625000
$257$	4626.00	1.12281	0.561405	−	0.827541i	$-0.310261\pi$
$257$	4626.00	1.12281	0.561405	+	0.827541i	$0.310261\pi$
$258$	−8672.00	−2.09262
$259$	2236.00	0.536441
$260$	−1840.00	−0.438892
$261$	−1110.00	−0.263246
$262$	−5616.00	−1.32427
$263$	4962.00	1.16338	0.581692	−	0.813409i	$-0.302391\pi$
$263$	4962.00	1.16338	0.581692	+	0.813409i	$0.302391\pi$
$264$	−704.000	−0.164122
$265$	90.0000	0.0208629
$266$	4160.00	0.958895
$267$	−1200.00	−0.275052
$268$	−496.000	−0.113052
$269$	1590.00	0.360387	0.180193	−	0.983631i	$-0.442328\pi$
$269$	1590.00	0.360387	0.180193	+	0.983631i	$0.442328\pi$
$270$	800.000	0.180320
$271$	6212.00	1.39244	0.696222	−	0.717827i	$-0.254863\pi$
$271$	6212.00	1.39244	0.696222	+	0.717827i	$0.254863\pi$
$272$	−1344.00	−0.299603
$273$	−19136.0	−4.24236
$274$	−2388.00	−0.526512
$275$	275.000	0.0603023
$276$	−2304.00	−0.502480
$277$	1556.00	0.337513	0.168756	−	0.985658i	$-0.446025\pi$
$277$	1556.00	0.337513	0.168756	+	0.985658i	$0.446025\pi$
$278$	3640.00	0.785297
$279$	−7696.00	−1.65142
$280$	−1040.00	−0.221971
$281$	−3258.00	−0.691658	−0.345829	−	0.938297i	$-0.612402\pi$
$281$	−3258.00	−0.691658	−0.345829	+	0.938297i	$0.612402\pi$
$282$	−3456.00	−0.729794
$283$	2222.00	0.466729	0.233364	−	0.972389i	$-0.425027\pi$
$283$	2222.00	0.466729	0.233364	+	0.972389i	$0.425027\pi$
$284$	3648.00	0.762215
$285$	3200.00	0.665093
$286$	2024.00	0.418467
$287$	−9828.00	−2.02135
$288$	1184.00	0.242250
$289$	2143.00	0.436190
$290$	300.000	0.0607469
$291$	−3568.00	−0.718762
$292$	−1072.00	−0.214843
$293$	−3948.00	−0.787183	−0.393592	−	0.919285i	$-0.628768\pi$
$293$	−3948.00	−0.787183	−0.393592	+	0.919285i	$0.628768\pi$
$294$	−5328.00	−1.05692
$295$	−2100.00	−0.414463
$296$	688.000	0.135099
$297$	−880.000	−0.171929
$298$	780.000	0.151625
$299$	6624.00	1.28119
$300$	−800.000	−0.153960
$301$	14092.0	2.69850
$302$	−2696.00	−0.513700
$303$	3984.00	0.755362
$304$	1280.00	0.241490
$305$	3590.00	0.673976
$306$	−6216.00	−1.16126
$307$	1406.00	0.261383	0.130692	−	0.991423i	$-0.458280\pi$
$307$	1406.00	0.261383	0.130692	+	0.991423i	$0.458280\pi$
$308$	1144.00	0.211641
$309$	7904.00	1.45515
$310$	2080.00	0.381084
$311$	−768.000	−0.140030	−0.0700149	−	0.997546i	$-0.522305\pi$
$311$	−768.000	−0.140030	−0.0700149	+	0.997546i	$0.522305\pi$
$312$	−5888.00	−1.06840
$313$	1082.00	0.195394	0.0976969	−	0.995216i	$-0.468852\pi$
$313$	1082.00	0.195394	0.0976969	+	0.995216i	$0.468852\pi$
$314$	−5228.00	−0.939596
$315$	−4810.00	−0.860358
$316$	−3760.00	−0.669356
$317$	3186.00	0.564491	0.282245	−	0.959342i	$-0.408921\pi$
$317$	3186.00	0.564491	0.282245	+	0.959342i	$0.408921\pi$
$318$	288.000	0.0507869
$319$	−330.000	−0.0579199
$320$	−320.000	−0.0559017
$321$	−13488.0	−2.34525
$322$	3744.00	0.647966
$323$	−6720.00	−1.15762
$324$	−1436.00	−0.246228
$325$	2300.00	0.392557
$326$	−416.000	−0.0706752
$327$	−2800.00	−0.473518
$328$	−3024.00	−0.509062
$329$	5616.00	0.941095
$330$	880.000	0.146795
$331$	−5908.00	−0.981067	−0.490533	−	0.871422i	$-0.663198\pi$
$331$	−5908.00	−0.981067	−0.490533	+	0.871422i	$0.663198\pi$
$332$	−1992.00	−0.329293
$333$	3182.00	0.523641
$334$	−7428.00	−1.21689
$335$	620.000	0.101117
$336$	−3328.00	−0.540349
$337$	−9364.00	−1.51362	−0.756809	−	0.653636i	$-0.773243\pi$
$337$	−9364.00	−1.51362	−0.756809	+	0.653636i	$0.773243\pi$
$338$	12534.0	2.01704
$339$	3984.00	0.638293
$340$	1680.00	0.267973
$341$	−2288.00	−0.363349
$342$	5920.00	0.936014
$343$	−260.000	−0.0409291
$344$	4336.00	0.679597
$345$	2880.00	0.449432
$346$	624.000	0.0969551
$347$	−8274.00	−1.28003	−0.640017	−	0.768361i	$-0.721073\pi$
$347$	−8274.00	−1.28003	−0.640017	+	0.768361i	$0.721073\pi$
$348$	960.000	0.147878
$349$	−2470.00	−0.378843	−0.189421	−	0.981896i	$-0.560661\pi$
$349$	−2470.00	−0.378843	−0.189421	+	0.981896i	$0.560661\pi$
$350$	1300.00	0.198537
$351$	−7360.00	−1.11922
$352$	352.000	0.0533002
$353$	3402.00	0.512947	0.256473	−	0.966551i	$-0.417439\pi$
$353$	3402.00	0.512947	0.256473	+	0.966551i	$0.417439\pi$
$354$	−6720.00	−1.00894
$355$	−4560.00	−0.681746
$356$	600.000	0.0893257
$357$	17472.0	2.59024
$358$	−8040.00	−1.18695
$359$	8220.00	1.20845	0.604227	−	0.796812i	$-0.293482\pi$
$359$	8220.00	1.20845	0.604227	+	0.796812i	$0.293482\pi$
$360$	−1480.00	−0.216675
$361$	−459.000	−0.0669194
$362$	−3116.00	−0.452412
$363$	−968.000	−0.139964
$364$	9568.00	1.37775
$365$	1340.00	0.192161
$366$	11488.0	1.64068
$367$	8696.00	1.23686	0.618430	−	0.785840i	$-0.287769\pi$
$367$	8696.00	1.23686	0.618430	+	0.785840i	$0.287769\pi$
$368$	1152.00	0.163185
$369$	−13986.0	−1.97312
$370$	−860.000	−0.120836
$371$	−468.000	−0.0654915
$372$	6656.00	0.927682
$373$	−12928.0	−1.79460	−0.897301	−	0.441419i	$-0.854475\pi$
$373$	−12928.0	−1.79460	−0.897301	+	0.441419i	$0.854475\pi$
$374$	−1848.00	−0.255502
$375$	1000.00	0.137706
$376$	1728.00	0.237007
$377$	−2760.00	−0.377048
$378$	−4160.00	−0.566051
$379$	−10060.0	−1.36345	−0.681725	−	0.731609i	$-0.738770\pi$
$379$	−10060.0	−1.36345	−0.681725	+	0.731609i	$0.738770\pi$
$380$	−1600.00	−0.215995
$381$	4112.00	0.552924
$382$	−4656.00	−0.623617
$383$	6012.00	0.802086	0.401043	−	0.916059i	$-0.368648\pi$
$383$	6012.00	0.802086	0.401043	+	0.916059i	$0.368648\pi$
$384$	−1024.00	−0.136083
$385$	−1430.00	−0.189298
$386$	−1976.00	−0.260559
$387$	20054.0	2.63411
$388$	1784.00	0.233425
$389$	8670.00	1.13004	0.565021	−	0.825076i	$-0.308868\pi$
$389$	8670.00	1.13004	0.565021	+	0.825076i	$0.308868\pi$
$390$	7360.00	0.955610
$391$	−6048.00	−0.782252
$392$	2664.00	0.343246
$393$	22464.0	2.88336
$394$	−2928.00	−0.374392
$395$	4700.00	0.598690
$396$	1628.00	0.206591
$397$	8186.00	1.03487	0.517435	−	0.855722i	$-0.326887\pi$
$397$	8186.00	1.03487	0.517435	+	0.855722i	$0.326887\pi$
$398$	1600.00	0.201509
$399$	−16640.0	−2.08782
$400$	400.000	0.0500000
$401$	−5298.00	−0.659774	−0.329887	−	0.944020i	$-0.607011\pi$
$401$	−5298.00	−0.659774	−0.329887	+	0.944020i	$0.607011\pi$
$402$	1984.00	0.246152
$403$	−19136.0	−2.36534
$404$	−1992.00	−0.245311
$405$	1795.00	0.220233
$406$	−1560.00	−0.190693
$407$	946.000	0.115212
$408$	5376.00	0.652332
$409$	−12190.0	−1.47373	−0.736866	−	0.676038i	$-0.763695\pi$
$409$	−12190.0	−1.47373	−0.736866	+	0.676038i	$0.763695\pi$
$410$	3780.00	0.455319
$411$	9552.00	1.14639
$412$	−3952.00	−0.472575
$413$	10920.0	1.30106
$414$	5328.00	0.632505
$415$	2490.00	0.294528
$416$	2944.00	0.346975
$417$	−14560.0	−1.70985
$418$	1760.00	0.205944
$419$	4500.00	0.524676	0.262338	−	0.964976i	$-0.415506\pi$
$419$	4500.00	0.524676	0.262338	+	0.964976i	$0.415506\pi$
$420$	4160.00	0.483303
$421$	12962.0	1.50054	0.750272	−	0.661129i	$-0.229922\pi$
$421$	12962.0	1.50054	0.750272	+	0.661129i	$0.229922\pi$
$422$	6064.00	0.699505
$423$	7992.00	0.918639
$424$	−144.000	−0.0164935
$425$	−2100.00	−0.239682
$426$	−14592.0	−1.65959
$427$	−18668.0	−2.11571
$428$	6744.00	0.761644
$429$	−8096.00	−0.911139
$430$	−5420.00	−0.607850
$431$	792.000	0.0885135	0.0442567	−	0.999020i	$-0.485908\pi$
$431$	792.000	0.0885135	0.0442567	+	0.999020i	$0.485908\pi$
$432$	−1280.00	−0.142556
$433$	12542.0	1.39199	0.695993	−	0.718048i	$-0.254964\pi$
$433$	12542.0	1.39199	0.695993	+	0.718048i	$0.254964\pi$
$434$	−10816.0	−1.19628
$435$	−1200.00	−0.132266
$436$	1400.00	0.153779
$437$	5760.00	0.630522
$438$	4288.00	0.467782
$439$	−1600.00	−0.173950	−0.0869748	−	0.996211i	$-0.527720\pi$
$439$	−1600.00	−0.173950	−0.0869748	+	0.996211i	$0.527720\pi$
$440$	−440.000	−0.0476731
$441$	12321.0	1.33042
$442$	−15456.0	−1.66327
$443$	432.000	0.0463317	0.0231658	−	0.999732i	$-0.492625\pi$
$443$	432.000	0.0463317	0.0231658	+	0.999732i	$0.492625\pi$
$444$	−2752.00	−0.294153
$445$	−750.000	−0.0798953
$446$	−6176.00	−0.655700
$447$	−3120.00	−0.330136
$448$	1664.00	0.175484
$449$	−9690.00	−1.01848	−0.509242	−	0.860623i	$-0.670074\pi$
$449$	−9690.00	−1.01848	−0.509242	+	0.860623i	$0.670074\pi$
$450$	1850.00	0.193800
$451$	−4158.00	−0.434130
$452$	−1992.00	−0.207292
$453$	10784.0	1.11849
$454$	−1068.00	−0.110405
$455$	−11960.0	−1.23229
$456$	−5120.00	−0.525803
$457$	14096.0	1.44285	0.721426	−	0.692492i	$-0.243487\pi$
$457$	14096.0	1.44285	0.721426	+	0.692492i	$0.243487\pi$
$458$	220.000	0.0224453
$459$	6720.00	0.683361
$460$	−1440.00	−0.145957
$461$	−6618.00	−0.668614	−0.334307	−	0.942464i	$-0.608502\pi$
$461$	−6618.00	−0.668614	−0.334307	+	0.942464i	$0.608502\pi$
$462$	−4576.00	−0.460811
$463$	−16288.0	−1.63492	−0.817460	−	0.575986i	$-0.804618\pi$
$463$	−16288.0	−1.63492	−0.817460	+	0.575986i	$0.804618\pi$
$464$	−480.000	−0.0480247
$465$	−8320.00	−0.829744
$466$	6624.00	0.658478
$467$	4116.00	0.407850	0.203925	−	0.978987i	$-0.434630\pi$
$467$	4116.00	0.407850	0.203925	+	0.978987i	$0.434630\pi$
$468$	13616.0	1.34487
$469$	−3224.00	−0.317421
$470$	−2160.00	−0.211986
$471$	20912.0	2.04580
$472$	3360.00	0.327662
$473$	5962.00	0.579562
$474$	15040.0	1.45741
$475$	2000.00	0.193192
$476$	−8736.00	−0.841206
$477$	−666.000	−0.0639288
$478$	7560.00	0.723402
$479$	−13860.0	−1.32209	−0.661043	−	0.750348i	$-0.729886\pi$
$479$	−13860.0	−1.32209	−0.661043	+	0.750348i	$0.729886\pi$
$480$	1280.00	0.121716
$481$	7912.00	0.750013
$482$	10444.0	0.986953
$483$	−14976.0	−1.41083
$484$	484.000	0.0454545
$485$	−2230.00	−0.208782
$486$	10064.0	0.939326
$487$	−9304.00	−0.865718	−0.432859	−	0.901462i	$-0.642495\pi$
$487$	−9304.00	−0.865718	−0.432859	+	0.901462i	$0.642495\pi$
$488$	−5744.00	−0.532825
$489$	1664.00	0.153883
$490$	−3330.00	−0.307008
$491$	12972.0	1.19230	0.596149	−	0.802874i	$-0.296697\pi$
$491$	12972.0	1.19230	0.596149	+	0.802874i	$0.296697\pi$
$492$	12096.0	1.10839
$493$	2520.00	0.230213
$494$	14720.0	1.34066
$495$	−2035.00	−0.184781
$496$	−3328.00	−0.301273
$497$	23712.0	2.14010
$498$	7968.00	0.716977
$499$	−8980.00	−0.805611	−0.402806	−	0.915286i	$-0.631965\pi$
$499$	−8980.00	−0.805611	−0.402806	+	0.915286i	$0.631965\pi$
$500$	−500.000	−0.0447214
$501$	29712.0	2.64957
$502$	−3096.00	−0.275261
$503$	−13458.0	−1.19297	−0.596484	−	0.802625i	$-0.703436\pi$
$503$	−13458.0	−1.19297	−0.596484	+	0.802625i	$0.703436\pi$
$504$	7696.00	0.680173
$505$	2490.00	0.219413
$506$	1584.00	0.139165
$507$	−50136.0	−4.39175
$508$	−2056.00	−0.179567
$509$	4230.00	0.368353	0.184176	−	0.982893i	$-0.441038\pi$
$509$	4230.00	0.368353	0.184176	+	0.982893i	$0.441038\pi$
$510$	−6720.00	−0.583464
$511$	−6968.00	−0.603221
$512$	512.000	0.0441942
$513$	−6400.00	−0.550813
$514$	9252.00	0.793946
$515$	4940.00	0.422684
$516$	−17344.0	−1.47970
$517$	2376.00	0.202121
$518$	4472.00	0.379321
$519$	−2496.00	−0.211103
$520$	−3680.00	−0.310344
$521$	−20538.0	−1.72704	−0.863518	−	0.504317i	$-0.831744\pi$
$521$	−20538.0	−1.72704	−0.863518	+	0.504317i	$0.831744\pi$
$522$	−2220.00	−0.186143
$523$	3242.00	0.271057	0.135528	−	0.990773i	$-0.456727\pi$
$523$	3242.00	0.271057	0.135528	+	0.990773i	$0.456727\pi$
$524$	−11232.0	−0.936397
$525$	−5200.00	−0.432279
$526$	9924.00	0.822637
$527$	17472.0	1.44420
$528$	−1408.00	−0.116052
$529$	−6983.00	−0.573929
$530$	180.000	0.0147523
$531$	15540.0	1.27002
$532$	8320.00	0.678041
$533$	−34776.0	−2.82611
$534$	−2400.00	−0.194491
$535$	−8430.00	−0.681235
$536$	−992.000	−0.0799401
$537$	32160.0	2.58437
$538$	3180.00	0.254832
$539$	3663.00	0.292721
$540$	1600.00	0.127506
$541$	−9178.00	−0.729377	−0.364689	−	0.931130i	$-0.618825\pi$
$541$	−9178.00	−0.729377	−0.364689	+	0.931130i	$0.618825\pi$
$542$	12424.0	0.984606
$543$	12464.0	0.985049
$544$	−2688.00	−0.211851
$545$	−1750.00	−0.137545
$546$	−38272.0	−2.99980
$547$	−15334.0	−1.19860	−0.599300	−	0.800524i	$-0.704554\pi$
$547$	−15334.0	−1.19860	−0.599300	+	0.800524i	$0.704554\pi$
$548$	−4776.00	−0.372300
$549$	−26566.0	−2.06523
$550$	550.000	0.0426401
$551$	−2400.00	−0.185560
$552$	−4608.00	−0.355307
$553$	−24440.0	−1.87938
$554$	3112.00	0.238657
$555$	3440.00	0.263099
$556$	7280.00	0.555289
$557$	−12024.0	−0.914674	−0.457337	−	0.889294i	$-0.651197\pi$
$557$	−12024.0	−0.914674	−0.457337	+	0.889294i	$0.651197\pi$
$558$	−15392.0	−1.16773
$559$	49864.0	3.77285
$560$	−2080.00	−0.156957
$561$	7392.00	0.556311
$562$	−6516.00	−0.489076
$563$	10242.0	0.766694	0.383347	−	0.923604i	$-0.374771\pi$
$563$	10242.0	0.766694	0.383347	+	0.923604i	$0.374771\pi$
$564$	−6912.00	−0.516042
$565$	2490.00	0.185407
$566$	4444.00	0.330027
$567$	−9334.00	−0.691342
$568$	7296.00	0.538967
$569$	−22470.0	−1.65552	−0.827760	−	0.561082i	$-0.810385\pi$
$569$	−22470.0	−1.65552	−0.827760	+	0.561082i	$0.810385\pi$
$570$	6400.00	0.470292
$571$	−5788.00	−0.424204	−0.212102	−	0.977248i	$-0.568031\pi$
$571$	−5788.00	−0.424204	−0.212102	+	0.977248i	$0.568031\pi$
$572$	4048.00	0.295901
$573$	18624.0	1.35782
$574$	−19656.0	−1.42931
$575$	1800.00	0.130548
$576$	2368.00	0.171296
$577$	−26314.0	−1.89855	−0.949277	−	0.314440i	$-0.898183\pi$
$577$	−26314.0	−1.89855	−0.949277	+	0.314440i	$0.898183\pi$
$578$	4286.00	0.308433
$579$	7904.00	0.567321
$580$	600.000	0.0429546
$581$	−12948.0	−0.924567
$582$	−7136.00	−0.508242
$583$	−198.000	−0.0140657
$584$	−2144.00	−0.151917
$585$	−17020.0	−1.20289
$586$	−7896.00	−0.556622
$587$	636.000	0.0447198	0.0223599	−	0.999750i	$-0.492882\pi$
$587$	636.000	0.0447198	0.0223599	+	0.999750i	$0.492882\pi$
$588$	−10656.0	−0.747357
$589$	−16640.0	−1.16407
$590$	−4200.00	−0.293070
$591$	11712.0	0.815173
$592$	1376.00	0.0955291
$593$	−20508.0	−1.42017	−0.710087	−	0.704114i	$-0.751344\pi$
$593$	−20508.0	−1.42017	−0.710087	+	0.704114i	$0.751344\pi$
$594$	−1760.00	−0.121572
$595$	10920.0	0.752397
$596$	1560.00	0.107215
$597$	−6400.00	−0.438751
$598$	13248.0	0.905938
$599$	24240.0	1.65346	0.826728	−	0.562603i	$-0.190200\pi$
$599$	24240.0	1.65346	0.826728	+	0.562603i	$0.190200\pi$
$600$	−1600.00	−0.108866
$601$	9302.00	0.631342	0.315671	−	0.948869i	$-0.397770\pi$
$601$	9302.00	0.631342	0.315671	+	0.948869i	$0.397770\pi$
$602$	28184.0	1.90813
$603$	−4588.00	−0.309847
$604$	−5392.00	−0.363241
$605$	−605.000	−0.0406558
$606$	7968.00	0.534122
$607$	−34.0000	−0.00227350	−0.00113675	−	0.999999i	$-0.500362\pi$
$607$	−34.0000	−0.00227350	−0.00113675	+	0.999999i	$0.500362\pi$
$608$	2560.00	0.170759
$609$	6240.00	0.415201
$610$	7180.00	0.476573
$611$	19872.0	1.31577
$612$	−12432.0	−0.821134
$613$	21152.0	1.39367	0.696836	−	0.717230i	$-0.254590\pi$
$613$	21152.0	1.39367	0.696836	+	0.717230i	$0.254590\pi$
$614$	2812.00	0.184826
$615$	−15120.0	−0.991378
$616$	2288.00	0.149653
$617$	23526.0	1.53504	0.767521	−	0.641024i	$-0.221490\pi$
$617$	23526.0	1.53504	0.767521	+	0.641024i	$0.221490\pi$
$618$	15808.0	1.02895
$619$	−5020.00	−0.325963	−0.162981	−	0.986629i	$-0.552111\pi$
$619$	−5020.00	−0.325963	−0.162981	+	0.986629i	$0.552111\pi$
$620$	4160.00	0.269467
$621$	−5760.00	−0.372207
$622$	−1536.00	−0.0990161
$623$	3900.00	0.250803
$624$	−11776.0	−0.755476
$625$	625.000	0.0400000
$626$	2164.00	0.138164
$627$	−7040.00	−0.448406
$628$	−10456.0	−0.664395
$629$	−7224.00	−0.457933
$630$	−9620.00	−0.608365
$631$	−6208.00	−0.391659	−0.195829	−	0.980638i	$-0.562740\pi$
$631$	−6208.00	−0.391659	−0.195829	+	0.980638i	$0.562740\pi$
$632$	−7520.00	−0.473306
$633$	−24256.0	−1.52305
$634$	6372.00	0.399155
$635$	2570.00	0.160610
$636$	576.000	0.0359118
$637$	30636.0	1.90556
$638$	−660.000	−0.0409556
$639$	33744.0	2.08903
$640$	−640.000	−0.0395285
$641$	−21378.0	−1.31729	−0.658643	−	0.752456i	$-0.728869\pi$
$641$	−21378.0	−1.31729	−0.658643	+	0.752456i	$0.728869\pi$
$642$	−26976.0	−1.65835
$643$	−16288.0	−0.998967	−0.499484	−	0.866323i	$-0.666477\pi$
$643$	−16288.0	−0.998967	−0.499484	+	0.866323i	$0.666477\pi$
$644$	7488.00	0.458181
$645$	21680.0	1.32349
$646$	−13440.0	−0.818560
$647$	1596.00	0.0969787	0.0484894	−	0.998824i	$-0.484559\pi$
$647$	1596.00	0.0969787	0.0484894	+	0.998824i	$0.484559\pi$
$648$	−2872.00	−0.174109
$649$	4620.00	0.279431
$650$	4600.00	0.277580
$651$	43264.0	2.60468
$652$	−832.000	−0.0499749
$653$	23262.0	1.39405	0.697023	−	0.717048i	$-0.254507\pi$
$653$	23262.0	1.39405	0.697023	+	0.717048i	$0.254507\pi$
$654$	−5600.00	−0.334828
$655$	14040.0	0.837539
$656$	−6048.00	−0.359961
$657$	−9916.00	−0.588828
$658$	11232.0	0.665454
$659$	29100.0	1.72014	0.860072	−	0.510172i	$-0.170418\pi$
$659$	29100.0	1.72014	0.860072	+	0.510172i	$0.170418\pi$
$660$	1760.00	0.103800
$661$	18182.0	1.06989	0.534945	−	0.844887i	$-0.320332\pi$
$661$	18182.0	1.06989	0.534945	+	0.844887i	$0.320332\pi$
$662$	−11816.0	−0.693719
$663$	61824.0	3.62149
$664$	−3984.00	−0.232845
$665$	−10400.0	−0.606458
$666$	6364.00	0.370270
$667$	−2160.00	−0.125391
$668$	−14856.0	−0.860473
$669$	24704.0	1.42767
$670$	1240.00	0.0715006
$671$	−7898.00	−0.454395
$672$	−6656.00	−0.382084
$673$	5252.00	0.300817	0.150408	−	0.988624i	$-0.451941\pi$
$673$	5252.00	0.300817	0.150408	+	0.988624i	$0.451941\pi$
$674$	−18728.0	−1.07029
$675$	−2000.00	−0.114044
$676$	25068.0	1.42626
$677$	−3564.00	−0.202327	−0.101164	−	0.994870i	$-0.532257\pi$
$677$	−3564.00	−0.202327	−0.101164	+	0.994870i	$0.532257\pi$
$678$	7968.00	0.451341
$679$	11596.0	0.655396
$680$	3360.00	0.189485
$681$	4272.00	0.240387
$682$	−4576.00	−0.256927
$683$	9132.00	0.511605	0.255803	−	0.966729i	$-0.417660\pi$
$683$	9132.00	0.511605	0.255803	+	0.966729i	$0.417660\pi$
$684$	11840.0	0.661862
$685$	5970.00	0.332996
$686$	−520.000	−0.0289412
$687$	−880.000	−0.0488706
$688$	8672.00	0.480548
$689$	−1656.00	−0.0915654
$690$	5760.00	0.317796
$691$	−1828.00	−0.100637	−0.0503187	−	0.998733i	$-0.516024\pi$
$691$	−1828.00	−0.100637	−0.0503187	+	0.998733i	$0.516024\pi$
$692$	1248.00	0.0685576
$693$	10582.0	0.580053
$694$	−16548.0	−0.905120
$695$	−9100.00	−0.496666
$696$	1920.00	0.104565
$697$	31752.0	1.72553
$698$	−4940.00	−0.267882
$699$	−26496.0	−1.43372
$700$	2600.00	0.140387
$701$	23802.0	1.28244	0.641219	−	0.767358i	$-0.278429\pi$
$701$	23802.0	1.28244	0.641219	+	0.767358i	$0.278429\pi$
$702$	−14720.0	−0.791411
$703$	6880.00	0.369110
$704$	704.000	0.0376889
$705$	8640.00	0.461562
$706$	6804.00	0.362708
$707$	−12948.0	−0.688769
$708$	−13440.0	−0.713427
$709$	−10510.0	−0.556716	−0.278358	−	0.960477i	$-0.589790\pi$
$709$	−10510.0	−0.556716	−0.278358	+	0.960477i	$0.589790\pi$
$710$	−9120.00	−0.482067
$711$	−34780.0	−1.83453
$712$	1200.00	0.0631628
$713$	−14976.0	−0.786614
$714$	34944.0	1.83158
$715$	−5060.00	−0.264662
$716$	−16080.0	−0.839299
$717$	−30240.0	−1.57508
$718$	16440.0	0.854506
$719$	8520.00	0.441923	0.220961	−	0.975283i	$-0.429081\pi$
$719$	8520.00	0.441923	0.220961	+	0.975283i	$0.429081\pi$
$720$	−2960.00	−0.153212
$721$	−25688.0	−1.32687
$722$	−918.000	−0.0473191
$723$	−41776.0	−2.14892
$724$	−6232.00	−0.319904
$725$	−750.000	−0.0384197
$726$	−1936.00	−0.0989693
$727$	29396.0	1.49964	0.749819	−	0.661643i	$-0.230140\pi$
$727$	29396.0	1.49964	0.749819	+	0.661643i	$0.230140\pi$
$728$	19136.0	0.974213
$729$	−30563.0	−1.55276
$730$	2680.00	0.135878
$731$	−45528.0	−2.30358
$732$	22976.0	1.16013
$733$	24392.0	1.22911	0.614556	−	0.788873i	$-0.289335\pi$
$733$	24392.0	1.22911	0.614556	+	0.788873i	$0.289335\pi$
$734$	17392.0	0.874592
$735$	13320.0	0.668457
$736$	2304.00	0.115389
$737$	−1364.00	−0.0681731
$738$	−27972.0	−1.39521
$739$	−13540.0	−0.673988	−0.336994	−	0.941507i	$-0.609410\pi$
$739$	−13540.0	−0.673988	−0.336994	+	0.941507i	$0.609410\pi$
$740$	−1720.00	−0.0854439
$741$	−58880.0	−2.91904
$742$	−936.000	−0.0463095
$743$	−8238.00	−0.406760	−0.203380	−	0.979100i	$-0.565193\pi$
$743$	−8238.00	−0.406760	−0.203380	+	0.979100i	$0.565193\pi$
$744$	13312.0	0.655970
$745$	−1950.00	−0.0958959
$746$	−25856.0	−1.26898
$747$	−18426.0	−0.902506
$748$	−3696.00	−0.180667
$749$	43836.0	2.13849
$750$	2000.00	0.0973729
$751$	−16048.0	−0.779760	−0.389880	−	0.920866i	$-0.627484\pi$
$751$	−16048.0	−0.779760	−0.389880	+	0.920866i	$0.627484\pi$
$752$	3456.00	0.167590
$753$	12384.0	0.599333
$754$	−5520.00	−0.266613
$755$	6740.00	0.324892
$756$	−8320.00	−0.400259
$757$	−33334.0	−1.60046	−0.800228	−	0.599696i	$-0.795288\pi$
$757$	−33334.0	−1.60046	−0.800228	+	0.599696i	$0.795288\pi$
$758$	−20120.0	−0.964105
$759$	−6336.00	−0.303007
$760$	−3200.00	−0.152732
$761$	17682.0	0.842276	0.421138	−	0.906997i	$-0.361631\pi$
$761$	17682.0	0.842276	0.421138	+	0.906997i	$0.361631\pi$
$762$	8224.00	0.390976
$763$	9100.00	0.431772
$764$	−9312.00	−0.440964
$765$	15540.0	0.734444
$766$	12024.0	0.567160
$767$	38640.0	1.81905
$768$	−2048.00	−0.0962250
$769$	−15250.0	−0.715122	−0.357561	−	0.933890i	$-0.616392\pi$
$769$	−15250.0	−0.715122	−0.357561	+	0.933890i	$0.616392\pi$
$770$	−2860.00	−0.133854
$771$	−37008.0	−1.72868
$772$	−3952.00	−0.184243
$773$	−2538.00	−0.118093	−0.0590463	−	0.998255i	$-0.518806\pi$
$773$	−2538.00	−0.118093	−0.0590463	+	0.998255i	$0.518806\pi$
$774$	40108.0	1.86260
$775$	−5200.00	−0.241019
$776$	3568.00	0.165056
$777$	−17888.0	−0.825905
$778$	17340.0	0.799061
$779$	−30240.0	−1.39083
$780$	14720.0	0.675719
$781$	10032.0	0.459633
$782$	−12096.0	−0.553136
$783$	2400.00	0.109539
$784$	5328.00	0.242711
$785$	13070.0	0.594253
$786$	44928.0	2.03884
$787$	10406.0	0.471326	0.235663	−	0.971835i	$-0.424274\pi$
$787$	10406.0	0.471326	0.235663	+	0.971835i	$0.424274\pi$
$788$	−5856.00	−0.264735
$789$	−39696.0	−1.79115
$790$	9400.00	0.423338
$791$	−12948.0	−0.582020
$792$	3256.00	0.146082
$793$	−66056.0	−2.95803
$794$	16372.0	0.731764
$795$	−720.000	−0.0321205
$796$	3200.00	0.142489
$797$	32226.0	1.43225	0.716125	−	0.697972i	$-0.245914\pi$
$797$	32226.0	1.43225	0.716125	+	0.697972i	$0.245914\pi$
$798$	−33280.0	−1.47631
$799$	−18144.0	−0.803365
$800$	800.000	0.0353553
$801$	5550.00	0.244818
$802$	−10596.0	−0.466531
$803$	−2948.00	−0.129555
$804$	3968.00	0.174055
$805$	−9360.00	−0.409810
$806$	−38272.0	−1.67255
$807$	−12720.0	−0.554852
$808$	−3984.00	−0.173461
$809$	5190.00	0.225551	0.112775	−	0.993620i	$-0.464026\pi$
$809$	5190.00	0.225551	0.112775	+	0.993620i	$0.464026\pi$
$810$	3590.00	0.155728
$811$	20732.0	0.897656	0.448828	−	0.893618i	$-0.351842\pi$
$811$	20732.0	0.897656	0.448828	+	0.893618i	$0.351842\pi$
$812$	−3120.00	−0.134841
$813$	−49696.0	−2.14381
$814$	1892.00	0.0814675
$815$	1040.00	0.0446989
$816$	10752.0	0.461269
$817$	43360.0	1.85676
$818$	−24380.0	−1.04209
$819$	88504.0	3.77604
$820$	7560.00	0.321959
$821$	−16638.0	−0.707272	−0.353636	−	0.935383i	$-0.615055\pi$
$821$	−16638.0	−0.707272	−0.353636	+	0.935383i	$0.615055\pi$
$822$	19104.0	0.810619
$823$	−16948.0	−0.717825	−0.358913	−	0.933371i	$-0.616852\pi$
$823$	−16948.0	−0.717825	−0.358913	+	0.933371i	$0.616852\pi$
$824$	−7904.00	−0.334161
$825$	−2200.00	−0.0928414
$826$	21840.0	0.919989
$827$	−10194.0	−0.428634	−0.214317	−	0.976764i	$-0.568753\pi$
$827$	−10194.0	−0.428634	−0.214317	+	0.976764i	$0.568753\pi$
$828$	10656.0	0.447248
$829$	14570.0	0.610419	0.305209	−	0.952285i	$-0.401274\pi$
$829$	14570.0	0.610419	0.305209	+	0.952285i	$0.401274\pi$
$830$	4980.00	0.208263
$831$	−12448.0	−0.519635
$832$	5888.00	0.245348
$833$	−27972.0	−1.16347
$834$	−29120.0	−1.20904
$835$	18570.0	0.769630
$836$	3520.00	0.145624
$837$	16640.0	0.687171
$838$	9000.00	0.371002
$839$	11280.0	0.464158	0.232079	−	0.972697i	$-0.425447\pi$
$839$	11280.0	0.464158	0.232079	+	0.972697i	$0.425447\pi$
$840$	8320.00	0.341747
$841$	−23489.0	−0.963098
$842$	25924.0	1.06105
$843$	26064.0	1.06488
$844$	12128.0	0.494624
$845$	−31335.0	−1.27569
$846$	15984.0	0.649576
$847$	3146.00	0.127624
$848$	−288.000	−0.0116627
$849$	−17776.0	−0.718576
$850$	−4200.00	−0.169481
$851$	6192.00	0.249423
$852$	−29184.0	−1.17351
$853$	20072.0	0.805688	0.402844	−	0.915269i	$-0.368022\pi$
$853$	20072.0	0.805688	0.402844	+	0.915269i	$0.368022\pi$
$854$	−37336.0	−1.49603
$855$	−14800.0	−0.591988
$856$	13488.0	0.538563
$857$	14556.0	0.580191	0.290095	−	0.956998i	$-0.406313\pi$
$857$	14556.0	0.580191	0.290095	+	0.956998i	$0.406313\pi$
$858$	−16192.0	−0.644272
$859$	25700.0	1.02081	0.510403	−	0.859935i	$-0.329496\pi$
$859$	25700.0	1.02081	0.510403	+	0.859935i	$0.329496\pi$
$860$	−10840.0	−0.429815
$861$	78624.0	3.11208
$862$	1584.00	0.0625885
$863$	−22668.0	−0.894122	−0.447061	−	0.894503i	$-0.647529\pi$
$863$	−22668.0	−0.894122	−0.447061	+	0.894503i	$0.647529\pi$
$864$	−2560.00	−0.100802
$865$	−1560.00	−0.0613198
$866$	25084.0	0.984283
$867$	−17144.0	−0.671558
$868$	−21632.0	−0.845896
$869$	−10340.0	−0.403637
$870$	−2400.00	−0.0935260
$871$	−11408.0	−0.443795
$872$	2800.00	0.108738
$873$	16502.0	0.639757
$874$	11520.0	0.445846
$875$	−3250.00	−0.125566
$876$	8576.00	0.330772
$877$	23576.0	0.907759	0.453880	−	0.891063i	$-0.350040\pi$
$877$	23576.0	0.907759	0.453880	+	0.891063i	$0.350040\pi$
$878$	−3200.00	−0.123001
$879$	31584.0	1.21195
$880$	−880.000	−0.0337100
$881$	−15558.0	−0.594963	−0.297481	−	0.954728i	$-0.596147\pi$
$881$	−15558.0	−0.594963	−0.297481	+	0.954728i	$0.596147\pi$
$882$	24642.0	0.940748
$883$	19472.0	0.742112	0.371056	−	0.928610i	$-0.378996\pi$
$883$	19472.0	0.742112	0.371056	+	0.928610i	$0.378996\pi$
$884$	−30912.0	−1.17611
$885$	16800.0	0.638108
$886$	864.000	0.0327615
$887$	11886.0	0.449936	0.224968	−	0.974366i	$-0.427772\pi$
$887$	11886.0	0.449936	0.224968	+	0.974366i	$0.427772\pi$
$888$	−5504.00	−0.207998
$889$	−13364.0	−0.504178
$890$	−1500.00	−0.0564945
$891$	−3949.00	−0.148481
$892$	−12352.0	−0.463650
$893$	17280.0	0.647540
$894$	−6240.00	−0.233442
$895$	20100.0	0.750692
$896$	3328.00	0.124086
$897$	−52992.0	−1.97252
$898$	−19380.0	−0.720177
$899$	6240.00	0.231497
$900$	3700.00	0.137037
$901$	1512.00	0.0559068
$902$	−8316.00	−0.306976
$903$	−112736.	−4.15462
$904$	−3984.00	−0.146577
$905$	7790.00	0.286131
$906$	21568.0	0.790893
$907$	15596.0	0.570956	0.285478	−	0.958385i	$-0.407848\pi$
$907$	15596.0	0.570956	0.285478	+	0.958385i	$0.407848\pi$
$908$	−2136.00	−0.0780679
$909$	−18426.0	−0.672334
$910$	−23920.0	−0.871363
$911$	−30168.0	−1.09716	−0.548579	−	0.836099i	$-0.684831\pi$
$911$	−30168.0	−1.09716	−0.548579	+	0.836099i	$0.684831\pi$
$912$	−10240.0	−0.371799
$913$	−5478.00	−0.198571
$914$	28192.0	1.02025
$915$	−28720.0	−1.03765
$916$	440.000	0.0158712
$917$	−73008.0	−2.62916
$918$	13440.0	0.483209
$919$	28640.0	1.02802	0.514008	−	0.857785i	$-0.328160\pi$
$919$	28640.0	1.02802	0.514008	+	0.857785i	$0.328160\pi$
$920$	−2880.00	−0.103207
$921$	−11248.0	−0.402426
$922$	−13236.0	−0.472781
$923$	83904.0	2.99213
$924$	−9152.00	−0.325843
$925$	2150.00	0.0764233
$926$	−32576.0	−1.15606
$927$	−36556.0	−1.29521
$928$	−960.000	−0.0339586
$929$	23490.0	0.829582	0.414791	−	0.909917i	$-0.363855\pi$
$929$	23490.0	0.829582	0.414791	+	0.909917i	$0.363855\pi$
$930$	−16640.0	−0.586717
$931$	26640.0	0.937799
$932$	13248.0	0.465614
$933$	6144.00	0.215590
$934$	8232.00	0.288393
$935$	4620.00	0.161594
$936$	27232.0	0.950968
$937$	51776.0	1.80517	0.902587	−	0.430507i	$-0.141665\pi$
$937$	51776.0	1.80517	0.902587	+	0.430507i	$0.141665\pi$
$938$	−6448.00	−0.224451
$939$	−8656.00	−0.300828
$940$	−4320.00	−0.149897
$941$	−32178.0	−1.11474	−0.557371	−	0.830263i	$-0.688190\pi$
$941$	−32178.0	−1.11474	−0.557371	+	0.830263i	$0.688190\pi$
$942$	41824.0	1.44660
$943$	−27216.0	−0.939846
$944$	6720.00	0.231692
$945$	10400.0	0.358002
$946$	11924.0	0.409813
$947$	19836.0	0.680658	0.340329	−	0.940306i	$-0.389462\pi$
$947$	19836.0	0.680658	0.340329	+	0.940306i	$0.389462\pi$
$948$	30080.0	1.03054
$949$	−24656.0	−0.843380
$950$	4000.00	0.136608
$951$	−25488.0	−0.869090
$952$	−17472.0	−0.594822
$953$	−15888.0	−0.540045	−0.270022	−	0.962854i	$-0.587031\pi$
$953$	−15888.0	−0.540045	−0.270022	+	0.962854i	$0.587031\pi$
$954$	−1332.00	−0.0452045
$955$	11640.0	0.394410
$956$	15120.0	0.511523
$957$	2640.00	0.0891735
$958$	−27720.0	−0.934857
$959$	−31044.0	−1.04532
$960$	2560.00	0.0860663
$961$	13473.0	0.452251
$962$	15824.0	0.530339
$963$	62382.0	2.08747
$964$	20888.0	0.697881
$965$	4940.00	0.164792
$966$	−29952.0	−0.997608
$967$	11126.0	0.369998	0.184999	−	0.982739i	$-0.440772\pi$
$967$	11126.0	0.369998	0.184999	+	0.982739i	$0.440772\pi$
$968$	968.000	0.0321412
$969$	53760.0	1.78227
$970$	−4460.00	−0.147631
$971$	−10188.0	−0.336713	−0.168357	−	0.985726i	$-0.553846\pi$
$971$	−10188.0	−0.336713	−0.168357	+	0.985726i	$0.553846\pi$
$972$	20128.0	0.664204
$973$	47320.0	1.55911
$974$	−18608.0	−0.612155
$975$	−18400.0	−0.604381
$976$	−11488.0	−0.376764
$977$	−10794.0	−0.353460	−0.176730	−	0.984259i	$-0.556552\pi$
$977$	−10794.0	−0.353460	−0.176730	+	0.984259i	$0.556552\pi$
$978$	3328.00	0.108812
$979$	1650.00	0.0538654
$980$	−6660.00	−0.217088
$981$	12950.0	0.421470
$982$	25944.0	0.843082
$983$	26892.0	0.872555	0.436278	−	0.899812i	$-0.356297\pi$
$983$	26892.0	0.872555	0.436278	+	0.899812i	$0.356297\pi$
$984$	24192.0	0.783753
$985$	7320.00	0.236786
$986$	5040.00	0.162785
$987$	−44928.0	−1.44891
$988$	29440.0	0.947987
$989$	39024.0	1.25469
$990$	−4070.00	−0.130660
$991$	41672.0	1.33578	0.667888	−	0.744261i	$-0.267198\pi$
$991$	41672.0	1.33578	0.667888	+	0.744261i	$0.267198\pi$
$992$	−6656.00	−0.213032
$993$	47264.0	1.51045
$994$	47424.0	1.51328
$995$	−4000.00	−0.127446
$996$	15936.0	0.506979
$997$	−5344.00	−0.169755	−0.0848777	−	0.996391i	$-0.527050\pi$
$997$	−5344.00	−0.169755	−0.0848777	+	0.996391i	$0.527050\pi$
$998$	−17960.0	−0.569653
$999$	−6880.00	−0.217891

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.4.a.d.1.1	✓	1
3.2	odd	2		990.4.a.j.1.1		1
4.3	odd	2		880.4.a.p.1.1		1
5.2	odd	4		550.4.b.a.199.2		2
5.3	odd	4		550.4.b.a.199.1		2
5.4	even	2		550.4.a.g.1.1		1
11.10	odd	2		1210.4.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.4.a.d.1.1	✓	1	1.1	even	1	trivial
550.4.a.g.1.1		1	5.4	even	2
550.4.b.a.199.1		2	5.3	odd	4
550.4.b.a.199.2		2	5.2	odd	4
880.4.a.p.1.1		1	4.3	odd	2
990.4.a.j.1.1		1	3.2	odd	2
1210.4.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:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	110.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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