LMFDB - Embedded newform 2310.4.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2310,4,Mod(1,2310)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2310, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("2310.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2310 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2310.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:	$136.294412113$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2310.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} -6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$

\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} -6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} -10.0000 q^{10} +11.0000 q^{11} -12.0000 q^{12} +2.00000 q^{13} +14.0000 q^{14} +15.0000 q^{15} +16.0000 q^{16} -42.0000 q^{17} +18.0000 q^{18} +32.0000 q^{19} -20.0000 q^{20} -21.0000 q^{21} +22.0000 q^{22} -60.0000 q^{23} -24.0000 q^{24} +25.0000 q^{25} +4.00000 q^{26} -27.0000 q^{27} +28.0000 q^{28} -198.000 q^{29} +30.0000 q^{30} -160.000 q^{31} +32.0000 q^{32} -33.0000 q^{33} -84.0000 q^{34} -35.0000 q^{35} +36.0000 q^{36} +350.000 q^{37} +64.0000 q^{38} -6.00000 q^{39} -40.0000 q^{40} +438.000 q^{41} -42.0000 q^{42} -520.000 q^{43} +44.0000 q^{44} -45.0000 q^{45} -120.000 q^{46} +12.0000 q^{47} -48.0000 q^{48} +49.0000 q^{49} +50.0000 q^{50} +126.000 q^{51} +8.00000 q^{52} -246.000 q^{53} -54.0000 q^{54} -55.0000 q^{55} +56.0000 q^{56} -96.0000 q^{57} -396.000 q^{58} +492.000 q^{59} +60.0000 q^{60} -574.000 q^{61} -320.000 q^{62} +63.0000 q^{63} +64.0000 q^{64} -10.0000 q^{65} -66.0000 q^{66} -388.000 q^{67} -168.000 q^{68} +180.000 q^{69} -70.0000 q^{70} +492.000 q^{71} +72.0000 q^{72} +530.000 q^{73} +700.000 q^{74} -75.0000 q^{75} +128.000 q^{76} +77.0000 q^{77} -12.0000 q^{78} -424.000 q^{79} -80.0000 q^{80} +81.0000 q^{81} +876.000 q^{82} +1308.00 q^{83} -84.0000 q^{84} +210.000 q^{85} -1040.00 q^{86} +594.000 q^{87} +88.0000 q^{88} -1542.00 q^{89} -90.0000 q^{90} +14.0000 q^{91} -240.000 q^{92} +480.000 q^{93} +24.0000 q^{94} -160.000 q^{95} -96.0000 q^{96} +50.0000 q^{97} +98.0000 q^{98} +99.0000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	4.00000	0.500000
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−6.00000	−0.408248
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	−10.0000	−0.316228
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−12.0000	−0.288675
$13$	2.00000	0.0426692	0.0213346	−	0.999772i	$-0.493208\pi$
$13$	2.00000	0.0426692	0.0213346	+	0.999772i	$0.493208\pi$
$14$	14.0000	0.267261
$15$	15.0000	0.258199
$16$	16.0000	0.250000
$17$	−42.0000	−0.599206	−0.299603	−	0.954064i	$-0.596854\pi$
$17$	−42.0000	−0.599206	−0.299603	+	0.954064i	$0.596854\pi$
$18$	18.0000	0.235702
$19$	32.0000	0.386384	0.193192	−	0.981161i	$-0.438116\pi$
$19$	32.0000	0.386384	0.193192	+	0.981161i	$0.438116\pi$
$20$	−20.0000	−0.223607
$21$	−21.0000	−0.218218
$22$	22.0000	0.213201
$23$	−60.0000	−0.543951	−0.271975	−	0.962304i	$-0.587677\pi$
$23$	−60.0000	−0.543951	−0.271975	+	0.962304i	$0.587677\pi$
$24$	−24.0000	−0.204124
$25$	25.0000	0.200000
$26$	4.00000	0.0301717
$27$	−27.0000	−0.192450
$28$	28.0000	0.188982
$29$	−198.000	−1.26785	−0.633925	−	0.773394i	$-0.718557\pi$
$29$	−198.000	−1.26785	−0.633925	+	0.773394i	$0.718557\pi$
$30$	30.0000	0.182574
$31$	−160.000	−0.926995	−0.463498	−	0.886098i	$-0.653406\pi$
$31$	−160.000	−0.926995	−0.463498	+	0.886098i	$0.653406\pi$
$32$	32.0000	0.176777
$33$	−33.0000	−0.174078
$34$	−84.0000	−0.423702
$35$	−35.0000	−0.169031
$36$	36.0000	0.166667
$37$	350.000	1.55513	0.777563	−	0.628805i	$-0.216456\pi$
$37$	350.000	1.55513	0.777563	+	0.628805i	$0.216456\pi$
$38$	64.0000	0.273215
$39$	−6.00000	−0.0246351
$40$	−40.0000	−0.158114
$41$	438.000	1.66839	0.834196	−	0.551467i	$-0.185932\pi$
$41$	438.000	1.66839	0.834196	+	0.551467i	$0.185932\pi$
$42$	−42.0000	−0.154303
$43$	−520.000	−1.84417	−0.922084	−	0.386989i	$-0.873515\pi$
$43$	−520.000	−1.84417	−0.922084	+	0.386989i	$0.873515\pi$
$44$	44.0000	0.150756
$45$	−45.0000	−0.149071
$46$	−120.000	−0.384631
$47$	12.0000	0.0372421	0.0186211	−	0.999827i	$-0.494072\pi$
$47$	12.0000	0.0372421	0.0186211	+	0.999827i	$0.494072\pi$
$48$	−48.0000	−0.144338
$49$	49.0000	0.142857
$50$	50.0000	0.141421
$51$	126.000	0.345952
$52$	8.00000	0.0213346
$53$	−246.000	−0.637560	−0.318780	−	0.947829i	$-0.603273\pi$
$53$	−246.000	−0.637560	−0.318780	+	0.947829i	$0.603273\pi$
$54$	−54.0000	−0.136083
$55$	−55.0000	−0.134840
$56$	56.0000	0.133631
$57$	−96.0000	−0.223079
$58$	−396.000	−0.896506
$59$	492.000	1.08564	0.542822	−	0.839848i	$-0.317356\pi$
$59$	492.000	1.08564	0.542822	+	0.839848i	$0.317356\pi$
$60$	60.0000	0.129099
$61$	−574.000	−1.20481	−0.602403	−	0.798192i	$-0.705790\pi$
$61$	−574.000	−1.20481	−0.602403	+	0.798192i	$0.705790\pi$
$62$	−320.000	−0.655485
$63$	63.0000	0.125988
$64$	64.0000	0.125000
$65$	−10.0000	−0.0190823
$66$	−66.0000	−0.123091
$67$	−388.000	−0.707489	−0.353744	−	0.935342i	$-0.615092\pi$
$67$	−388.000	−0.707489	−0.353744	+	0.935342i	$0.615092\pi$
$68$	−168.000	−0.299603
$69$	180.000	0.314050
$70$	−70.0000	−0.119523
$71$	492.000	0.822390	0.411195	−	0.911548i	$-0.365112\pi$
$71$	492.000	0.822390	0.411195	+	0.911548i	$0.365112\pi$
$72$	72.0000	0.117851
$73$	530.000	0.849751	0.424875	−	0.905252i	$-0.360318\pi$
$73$	530.000	0.849751	0.424875	+	0.905252i	$0.360318\pi$
$74$	700.000	1.09964
$75$	−75.0000	−0.115470
$76$	128.000	0.193192
$77$	77.0000	0.113961
$78$	−12.0000	−0.0174196
$79$	−424.000	−0.603845	−0.301922	−	0.953333i	$-0.597628\pi$
$79$	−424.000	−0.603845	−0.301922	+	0.953333i	$0.597628\pi$
$80$	−80.0000	−0.111803
$81$	81.0000	0.111111
$82$	876.000	1.17973
$83$	1308.00	1.72978	0.864889	−	0.501962i	$-0.167388\pi$
$83$	1308.00	1.72978	0.864889	+	0.501962i	$0.167388\pi$
$84$	−84.0000	−0.109109
$85$	210.000	0.267973
$86$	−1040.00	−1.30402
$87$	594.000	0.731994
$88$	88.0000	0.106600
$89$	−1542.00	−1.83654	−0.918268	−	0.395960i	$-0.870412\pi$
$89$	−1542.00	−1.83654	−0.918268	+	0.395960i	$0.870412\pi$
$90$	−90.0000	−0.105409
$91$	14.0000	0.0161275
$92$	−240.000	−0.271975
$93$	480.000	0.535201
$94$	24.0000	0.0263342
$95$	−160.000	−0.172796
$96$	−96.0000	−0.102062
$97$	50.0000	0.0523374	0.0261687	−	0.999658i	$-0.491669\pi$
$97$	50.0000	0.0523374	0.0261687	+	0.999658i	$0.491669\pi$
$98$	98.0000	0.101015
$99$	99.0000	0.100504
$100$	100.000	0.100000
$101$	642.000	0.632489	0.316244	−	0.948678i	$-0.397578\pi$
$101$	642.000	0.632489	0.316244	+	0.948678i	$0.397578\pi$
$102$	252.000	0.244625
$103$	−760.000	−0.727039	−0.363520	−	0.931587i	$-0.618425\pi$
$103$	−760.000	−0.727039	−0.363520	+	0.931587i	$0.618425\pi$
$104$	16.0000	0.0150859
$105$	105.000	0.0975900
$106$	−492.000	−0.450823
$107$	−1140.00	−1.02998	−0.514990	−	0.857196i	$-0.672205\pi$
$107$	−1140.00	−1.02998	−0.514990	+	0.857196i	$0.672205\pi$
$108$	−108.000	−0.0962250
$109$	50.0000	0.0439370	0.0219685	−	0.999759i	$-0.493007\pi$
$109$	50.0000	0.0439370	0.0219685	+	0.999759i	$0.493007\pi$
$110$	−110.000	−0.0953463
$111$	−1050.00	−0.897852
$112$	112.000	0.0944911
$113$	330.000	0.274724	0.137362	−	0.990521i	$-0.456138\pi$
$113$	330.000	0.274724	0.137362	+	0.990521i	$0.456138\pi$
$114$	−192.000	−0.157741
$115$	300.000	0.243262
$116$	−792.000	−0.633925
$117$	18.0000	0.0142231
$118$	984.000	0.767666
$119$	−294.000	−0.226478
$120$	120.000	0.0912871
$121$	121.000	0.0909091
$122$	−1148.00	−0.851927
$123$	−1314.00	−0.963247
$124$	−640.000	−0.463498
$125$	−125.000	−0.0894427
$126$	126.000	0.0890871
$127$	−1720.00	−1.20177	−0.600887	−	0.799334i	$-0.705186\pi$
$127$	−1720.00	−1.20177	−0.600887	+	0.799334i	$0.705186\pi$
$128$	128.000	0.0883883
$129$	1560.00	1.06473
$130$	−20.0000	−0.0134932
$131$	516.000	0.344146	0.172073	−	0.985084i	$-0.444953\pi$
$131$	516.000	0.344146	0.172073	+	0.985084i	$0.444953\pi$
$132$	−132.000	−0.0870388
$133$	224.000	0.146040
$134$	−776.000	−0.500270
$135$	135.000	0.0860663
$136$	−336.000	−0.211851
$137$	−3126.00	−1.94943	−0.974716	−	0.223447i	$-0.928269\pi$
$137$	−3126.00	−1.94943	−0.974716	+	0.223447i	$0.928269\pi$
$138$	360.000	0.222067
$139$	−1624.00	−0.990978	−0.495489	−	0.868614i	$-0.665011\pi$
$139$	−1624.00	−0.990978	−0.495489	+	0.868614i	$0.665011\pi$
$140$	−140.000	−0.0845154
$141$	−36.0000	−0.0215018
$142$	984.000	0.581517
$143$	22.0000	0.0128653
$144$	144.000	0.0833333
$145$	990.000	0.567000
$146$	1060.00	0.600865
$147$	−147.000	−0.0824786
$148$	1400.00	0.777563
$149$	−750.000	−0.412365	−0.206183	−	0.978514i	$-0.566104\pi$
$149$	−750.000	−0.412365	−0.206183	+	0.978514i	$0.566104\pi$
$150$	−150.000	−0.0816497
$151$	752.000	0.405277	0.202639	−	0.979254i	$-0.435048\pi$
$151$	752.000	0.405277	0.202639	+	0.979254i	$0.435048\pi$
$152$	256.000	0.136608
$153$	−378.000	−0.199735
$154$	154.000	0.0805823
$155$	800.000	0.414565
$156$	−24.0000	−0.0123176
$157$	686.000	0.348718	0.174359	−	0.984682i	$-0.444215\pi$
$157$	686.000	0.348718	0.174359	+	0.984682i	$0.444215\pi$
$158$	−848.000	−0.426983
$159$	738.000	0.368096
$160$	−160.000	−0.0790569
$161$	−420.000	−0.205594
$162$	162.000	0.0785674
$163$	−1924.00	−0.924536	−0.462268	−	0.886740i	$-0.652964\pi$
$163$	−1924.00	−0.924536	−0.462268	+	0.886740i	$0.652964\pi$
$164$	1752.00	0.834196
$165$	165.000	0.0778499
$166$	2616.00	1.22314
$167$	−648.000	−0.300262	−0.150131	−	0.988666i	$-0.547970\pi$
$167$	−648.000	−0.300262	−0.150131	+	0.988666i	$0.547970\pi$
$168$	−168.000	−0.0771517
$169$	−2193.00	−0.998179
$170$	420.000	0.189485
$171$	288.000	0.128795
$172$	−2080.00	−0.922084
$173$	522.000	0.229404	0.114702	−	0.993400i	$-0.463409\pi$
$173$	522.000	0.229404	0.114702	+	0.993400i	$0.463409\pi$
$174$	1188.00	0.517598
$175$	175.000	0.0755929
$176$	176.000	0.0753778
$177$	−1476.00	−0.626796
$178$	−3084.00	−1.29863
$179$	−2100.00	−0.876879	−0.438440	−	0.898761i	$-0.644469\pi$
$179$	−2100.00	−0.876879	−0.438440	+	0.898761i	$0.644469\pi$
$180$	−180.000	−0.0745356
$181$	−3130.00	−1.28537	−0.642683	−	0.766133i	$-0.722179\pi$
$181$	−3130.00	−1.28537	−0.642683	+	0.766133i	$0.722179\pi$
$182$	28.0000	0.0114038
$183$	1722.00	0.695595
$184$	−480.000	−0.192316
$185$	−1750.00	−0.695473
$186$	960.000	0.378444
$187$	−462.000	−0.180667
$188$	48.0000	0.0186211
$189$	−189.000	−0.0727393
$190$	−320.000	−0.122185
$191$	3756.00	1.42290	0.711452	−	0.702735i	$-0.248038\pi$
$191$	3756.00	1.42290	0.711452	+	0.702735i	$0.248038\pi$
$192$	−192.000	−0.0721688
$193$	−1798.00	−0.670585	−0.335292	−	0.942114i	$-0.608835\pi$
$193$	−1798.00	−0.670585	−0.335292	+	0.942114i	$0.608835\pi$
$194$	100.000	0.0370082
$195$	30.0000	0.0110172
$196$	196.000	0.0714286
$197$	−4542.00	−1.64266	−0.821330	−	0.570453i	$-0.806768\pi$
$197$	−4542.00	−1.64266	−0.821330	+	0.570453i	$0.806768\pi$
$198$	198.000	0.0710669
$199$	2624.00	0.934726	0.467363	−	0.884066i	$-0.345204\pi$
$199$	2624.00	0.934726	0.467363	+	0.884066i	$0.345204\pi$
$200$	200.000	0.0707107
$201$	1164.00	0.408469
$202$	1284.00	0.447237
$203$	−1386.00	−0.479203
$204$	504.000	0.172976
$205$	−2190.00	−0.746128
$206$	−1520.00	−0.514094
$207$	−540.000	−0.181317
$208$	32.0000	0.0106673
$209$	352.000	0.116499
$210$	210.000	0.0690066
$211$	2696.00	0.879622	0.439811	−	0.898090i	$-0.355045\pi$
$211$	2696.00	0.879622	0.439811	+	0.898090i	$0.355045\pi$
$212$	−984.000	−0.318780
$213$	−1476.00	−0.474807
$214$	−2280.00	−0.728307
$215$	2600.00	0.824737
$216$	−216.000	−0.0680414
$217$	−1120.00	−0.350371
$218$	100.000	0.0310681
$219$	−1590.00	−0.490604
$220$	−220.000	−0.0674200
$221$	−84.0000	−0.0255677
$222$	−2100.00	−0.634877
$223$	−4072.00	−1.22279	−0.611393	−	0.791327i	$-0.709391\pi$
$223$	−4072.00	−1.22279	−0.611393	+	0.791327i	$0.709391\pi$
$224$	224.000	0.0668153
$225$	225.000	0.0666667
$226$	660.000	0.194259
$227$	3444.00	1.00699	0.503494	−	0.863999i	$-0.332048\pi$
$227$	3444.00	1.00699	0.503494	+	0.863999i	$0.332048\pi$
$228$	−384.000	−0.111540
$229$	−634.000	−0.182952	−0.0914758	−	0.995807i	$-0.529158\pi$
$229$	−634.000	−0.182952	−0.0914758	+	0.995807i	$0.529158\pi$
$230$	600.000	0.172012
$231$	−231.000	−0.0657952
$232$	−1584.00	−0.448253
$233$	−5418.00	−1.52337	−0.761685	−	0.647948i	$-0.775627\pi$
$233$	−5418.00	−1.52337	−0.761685	+	0.647948i	$0.775627\pi$
$234$	36.0000	0.0100572
$235$	−60.0000	−0.0166552
$236$	1968.00	0.542822
$237$	1272.00	0.348630
$238$	−588.000	−0.160144
$239$	384.000	0.103928	0.0519642	−	0.998649i	$-0.483452\pi$
$239$	384.000	0.103928	0.0519642	+	0.998649i	$0.483452\pi$
$240$	240.000	0.0645497
$241$	−4702.00	−1.25677	−0.628387	−	0.777901i	$-0.716284\pi$
$241$	−4702.00	−1.25677	−0.628387	+	0.777901i	$0.716284\pi$
$242$	242.000	0.0642824
$243$	−243.000	−0.0641500
$244$	−2296.00	−0.602403
$245$	−245.000	−0.0638877
$246$	−2628.00	−0.681119
$247$	64.0000	0.0164867
$248$	−1280.00	−0.327742
$249$	−3924.00	−0.998688
$250$	−250.000	−0.0632456
$251$	−2796.00	−0.703115	−0.351558	−	0.936166i	$-0.614348\pi$
$251$	−2796.00	−0.703115	−0.351558	+	0.936166i	$0.614348\pi$
$252$	252.000	0.0629941
$253$	−660.000	−0.164007
$254$	−3440.00	−0.849783
$255$	−630.000	−0.154714
$256$	256.000	0.0625000
$257$	3906.00	0.948053	0.474026	−	0.880511i	$-0.342800\pi$
$257$	3906.00	0.948053	0.474026	+	0.880511i	$0.342800\pi$
$258$	3120.00	0.752879
$259$	2450.00	0.587782
$260$	−40.0000	−0.00954113
$261$	−1782.00	−0.422617
$262$	1032.00	0.243348
$263$	−48.0000	−0.0112540	−0.00562701	−	0.999984i	$-0.501791\pi$
$263$	−48.0000	−0.0112540	−0.00562701	+	0.999984i	$0.501791\pi$
$264$	−264.000	−0.0615457
$265$	1230.00	0.285126
$266$	448.000	0.103266
$267$	4626.00	1.06032
$268$	−1552.00	−0.353744
$269$	−3486.00	−0.790131	−0.395065	−	0.918653i	$-0.629278\pi$
$269$	−3486.00	−0.790131	−0.395065	+	0.918653i	$0.629278\pi$
$270$	270.000	0.0608581
$271$	−5560.00	−1.24630	−0.623148	−	0.782104i	$-0.714146\pi$
$271$	−5560.00	−1.24630	−0.623148	+	0.782104i	$0.714146\pi$
$272$	−672.000	−0.149801
$273$	−42.0000	−0.00931119
$274$	−6252.00	−1.37846
$275$	275.000	0.0603023
$276$	720.000	0.157025
$277$	4562.00	0.989545	0.494773	−	0.869022i	$-0.335251\pi$
$277$	4562.00	0.989545	0.494773	+	0.869022i	$0.335251\pi$
$278$	−3248.00	−0.700727
$279$	−1440.00	−0.308998
$280$	−280.000	−0.0597614
$281$	−6186.00	−1.31326	−0.656630	−	0.754213i	$-0.728018\pi$
$281$	−6186.00	−1.31326	−0.656630	+	0.754213i	$0.728018\pi$
$282$	−72.0000	−0.0152040
$283$	−5032.00	−1.05697	−0.528483	−	0.848944i	$-0.677239\pi$
$283$	−5032.00	−1.05697	−0.528483	+	0.848944i	$0.677239\pi$
$284$	1968.00	0.411195
$285$	480.000	0.0997640
$286$	44.0000	0.00909711
$287$	3066.00	0.630593
$288$	288.000	0.0589256
$289$	−3149.00	−0.640953
$290$	1980.00	0.400930
$291$	−150.000	−0.0302170
$292$	2120.00	0.424875
$293$	8946.00	1.78372	0.891862	−	0.452308i	$-0.149399\pi$
$293$	8946.00	1.78372	0.891862	+	0.452308i	$0.149399\pi$
$294$	−294.000	−0.0583212
$295$	−2460.00	−0.485514
$296$	2800.00	0.549820
$297$	−297.000	−0.0580259
$298$	−1500.00	−0.291586
$299$	−120.000	−0.0232100
$300$	−300.000	−0.0577350
$301$	−3640.00	−0.697030
$302$	1504.00	0.286574
$303$	−1926.00	−0.365168
$304$	512.000	0.0965961
$305$	2870.00	0.538806
$306$	−756.000	−0.141234
$307$	−1024.00	−0.190367	−0.0951837	−	0.995460i	$-0.530344\pi$
$307$	−1024.00	−0.190367	−0.0951837	+	0.995460i	$0.530344\pi$
$308$	308.000	0.0569803
$309$	2280.00	0.419756
$310$	1600.00	0.293142
$311$	−684.000	−0.124714	−0.0623570	−	0.998054i	$-0.519862\pi$
$311$	−684.000	−0.124714	−0.0623570	+	0.998054i	$0.519862\pi$
$312$	−48.0000	−0.00870982
$313$	−2662.00	−0.480719	−0.240360	−	0.970684i	$-0.577265\pi$
$313$	−2662.00	−0.480719	−0.240360	+	0.970684i	$0.577265\pi$
$314$	1372.00	0.246581
$315$	−315.000	−0.0563436
$316$	−1696.00	−0.301922
$317$	114.000	0.0201984	0.0100992	−	0.999949i	$-0.496785\pi$
$317$	114.000	0.0201984	0.0100992	+	0.999949i	$0.496785\pi$
$318$	1476.00	0.260283
$319$	−2178.00	−0.382271
$320$	−320.000	−0.0559017
$321$	3420.00	0.594660
$322$	−840.000	−0.145377
$323$	−1344.00	−0.231524
$324$	324.000	0.0555556
$325$	50.0000	0.00853385
$326$	−3848.00	−0.653745
$327$	−150.000	−0.0253670
$328$	3504.00	0.589866
$329$	84.0000	0.0140762
$330$	330.000	0.0550482
$331$	6404.00	1.06343	0.531716	−	0.846923i	$-0.321548\pi$
$331$	6404.00	1.06343	0.531716	+	0.846923i	$0.321548\pi$
$332$	5232.00	0.864889
$333$	3150.00	0.518375
$334$	−1296.00	−0.212317
$335$	1940.00	0.316399
$336$	−336.000	−0.0545545
$337$	−6694.00	−1.08203	−0.541017	−	0.841012i	$-0.681961\pi$
$337$	−6694.00	−1.08203	−0.541017	+	0.841012i	$0.681961\pi$
$338$	−4386.00	−0.705819
$339$	−990.000	−0.158612
$340$	840.000	0.133986
$341$	−1760.00	−0.279500
$342$	576.000	0.0910717
$343$	343.000	0.0539949
$344$	−4160.00	−0.652012
$345$	−900.000	−0.140447
$346$	1044.00	0.162213
$347$	−3948.00	−0.610777	−0.305389	−	0.952228i	$-0.598786\pi$
$347$	−3948.00	−0.610777	−0.305389	+	0.952228i	$0.598786\pi$
$348$	2376.00	0.365997
$349$	5546.00	0.850632	0.425316	−	0.905045i	$-0.360163\pi$
$349$	5546.00	0.850632	0.425316	+	0.905045i	$0.360163\pi$
$350$	350.000	0.0534522
$351$	−54.0000	−0.00821170
$352$	352.000	0.0533002
$353$	402.000	0.0606128	0.0303064	−	0.999541i	$-0.490352\pi$
$353$	402.000	0.0606128	0.0303064	+	0.999541i	$0.490352\pi$
$354$	−2952.00	−0.443212
$355$	−2460.00	−0.367784
$356$	−6168.00	−0.918268
$357$	882.000	0.130757
$358$	−4200.00	−0.620047
$359$	−7680.00	−1.12907	−0.564533	−	0.825410i	$-0.690944\pi$
$359$	−7680.00	−1.12907	−0.564533	+	0.825410i	$0.690944\pi$
$360$	−360.000	−0.0527046
$361$	−5835.00	−0.850707
$362$	−6260.00	−0.908890
$363$	−363.000	−0.0524864
$364$	56.0000	0.00806373
$365$	−2650.00	−0.380020
$366$	3444.00	0.491860
$367$	−7432.00	−1.05708	−0.528538	−	0.848909i	$-0.677260\pi$
$367$	−7432.00	−1.05708	−0.528538	+	0.848909i	$0.677260\pi$
$368$	−960.000	−0.135988
$369$	3942.00	0.556131
$370$	−3500.00	−0.491774
$371$	−1722.00	−0.240975
$372$	1920.00	0.267600
$373$	6722.00	0.933115	0.466558	−	0.884491i	$-0.345494\pi$
$373$	6722.00	0.933115	0.466558	+	0.884491i	$0.345494\pi$
$374$	−924.000	−0.127751
$375$	375.000	0.0516398
$376$	96.0000	0.0131671
$377$	−396.000	−0.0540982
$378$	−378.000	−0.0514344
$379$	−1468.00	−0.198961	−0.0994803	−	0.995040i	$-0.531718\pi$
$379$	−1468.00	−0.198961	−0.0994803	+	0.995040i	$0.531718\pi$
$380$	−640.000	−0.0863982
$381$	5160.00	0.693845
$382$	7512.00	1.00614
$383$	−8292.00	−1.10627	−0.553135	−	0.833092i	$-0.686569\pi$
$383$	−8292.00	−1.10627	−0.553135	+	0.833092i	$0.686569\pi$
$384$	−384.000	−0.0510310
$385$	−385.000	−0.0509647
$386$	−3596.00	−0.474175
$387$	−4680.00	−0.614723
$388$	200.000	0.0261687
$389$	−10014.0	−1.30522	−0.652609	−	0.757695i	$-0.726326\pi$
$389$	−10014.0	−1.30522	−0.652609	+	0.757695i	$0.726326\pi$
$390$	60.0000	0.00779030
$391$	2520.00	0.325938
$392$	392.000	0.0505076
$393$	−1548.00	−0.198693
$394$	−9084.00	−1.16154
$395$	2120.00	0.270048
$396$	396.000	0.0502519
$397$	−4930.00	−0.623248	−0.311624	−	0.950205i	$-0.600873\pi$
$397$	−4930.00	−0.623248	−0.311624	+	0.950205i	$0.600873\pi$
$398$	5248.00	0.660951
$399$	−672.000	−0.0843160
$400$	400.000	0.0500000
$401$	13938.0	1.73574	0.867868	−	0.496794i	$-0.165490\pi$
$401$	13938.0	1.73574	0.867868	+	0.496794i	$0.165490\pi$
$402$	2328.00	0.288831
$403$	−320.000	−0.0395542
$404$	2568.00	0.316244
$405$	−405.000	−0.0496904
$406$	−2772.00	−0.338847
$407$	3850.00	0.468888
$408$	1008.00	0.122312
$409$	3866.00	0.467387	0.233694	−	0.972310i	$-0.424919\pi$
$409$	3866.00	0.467387	0.233694	+	0.972310i	$0.424919\pi$
$410$	−4380.00	−0.527592
$411$	9378.00	1.12551
$412$	−3040.00	−0.363520
$413$	3444.00	0.410335
$414$	−1080.00	−0.128210
$415$	−6540.00	−0.773581
$416$	64.0000	0.00754293
$417$	4872.00	0.572141
$418$	704.000	0.0823774
$419$	3708.00	0.432333	0.216167	−	0.976356i	$-0.430645\pi$
$419$	3708.00	0.432333	0.216167	+	0.976356i	$0.430645\pi$
$420$	420.000	0.0487950
$421$	11438.0	1.32412	0.662059	−	0.749451i	$-0.269683\pi$
$421$	11438.0	1.32412	0.662059	+	0.749451i	$0.269683\pi$
$422$	5392.00	0.621987
$423$	108.000	0.0124140
$424$	−1968.00	−0.225412
$425$	−1050.00	−0.119841
$426$	−2952.00	−0.335739
$427$	−4018.00	−0.455374
$428$	−4560.00	−0.514990
$429$	−66.0000	−0.00742776
$430$	5200.00	0.583177
$431$	7224.00	0.807350	0.403675	−	0.914902i	$-0.367733\pi$
$431$	7224.00	0.807350	0.403675	+	0.914902i	$0.367733\pi$
$432$	−432.000	−0.0481125
$433$	−3886.00	−0.431292	−0.215646	−	0.976472i	$-0.569186\pi$
$433$	−3886.00	−0.431292	−0.215646	+	0.976472i	$0.569186\pi$
$434$	−2240.00	−0.247750
$435$	−2970.00	−0.327358
$436$	200.000	0.0219685
$437$	−1920.00	−0.210174
$438$	−3180.00	−0.346909
$439$	5720.00	0.621869	0.310935	−	0.950431i	$-0.399358\pi$
$439$	5720.00	0.621869	0.310935	+	0.950431i	$0.399358\pi$
$440$	−440.000	−0.0476731
$441$	441.000	0.0476190
$442$	−168.000	−0.0180791
$443$	−4404.00	−0.472326	−0.236163	−	0.971713i	$-0.575890\pi$
$443$	−4404.00	−0.472326	−0.236163	+	0.971713i	$0.575890\pi$
$444$	−4200.00	−0.448926
$445$	7710.00	0.821324
$446$	−8144.00	−0.864640
$447$	2250.00	0.238079
$448$	448.000	0.0472456
$449$	6762.00	0.710732	0.355366	−	0.934727i	$-0.384356\pi$
$449$	6762.00	0.710732	0.355366	+	0.934727i	$0.384356\pi$
$450$	450.000	0.0471405
$451$	4818.00	0.503039
$452$	1320.00	0.137362
$453$	−2256.00	−0.233987
$454$	6888.00	0.712048
$455$	−70.0000	−0.00721242
$456$	−768.000	−0.0788704
$457$	8810.00	0.901782	0.450891	−	0.892579i	$-0.351106\pi$
$457$	8810.00	0.901782	0.450891	+	0.892579i	$0.351106\pi$
$458$	−1268.00	−0.129366
$459$	1134.00	0.115317
$460$	1200.00	0.121631
$461$	17898.0	1.80823	0.904114	−	0.427292i	$-0.140532\pi$
$461$	17898.0	1.80823	0.904114	+	0.427292i	$0.140532\pi$
$462$	−462.000	−0.0465242
$463$	−1888.00	−0.189509	−0.0947546	−	0.995501i	$-0.530207\pi$
$463$	−1888.00	−0.189509	−0.0947546	+	0.995501i	$0.530207\pi$
$464$	−3168.00	−0.316963
$465$	−2400.00	−0.239349
$466$	−10836.0	−1.07718
$467$	14652.0	1.45185	0.725925	−	0.687774i	$-0.241412\pi$
$467$	14652.0	1.45185	0.725925	+	0.687774i	$0.241412\pi$
$468$	72.0000	0.00711154
$469$	−2716.00	−0.267406
$470$	−120.000	−0.0117770
$471$	−2058.00	−0.201333
$472$	3936.00	0.383833
$473$	−5720.00	−0.556038
$474$	2544.00	0.246519
$475$	800.000	0.0772769
$476$	−1176.00	−0.113239
$477$	−2214.00	−0.212520
$478$	768.000	0.0734885
$479$	−792.000	−0.0755478	−0.0377739	−	0.999286i	$-0.512027\pi$
$479$	−792.000	−0.0755478	−0.0377739	+	0.999286i	$0.512027\pi$
$480$	480.000	0.0456435
$481$	700.000	0.0663560
$482$	−9404.00	−0.888673
$483$	1260.00	0.118700
$484$	484.000	0.0454545
$485$	−250.000	−0.0234060
$486$	−486.000	−0.0453609
$487$	1712.00	0.159298	0.0796490	−	0.996823i	$-0.474620\pi$
$487$	1712.00	0.159298	0.0796490	+	0.996823i	$0.474620\pi$
$488$	−4592.00	−0.425963
$489$	5772.00	0.533781
$490$	−490.000	−0.0451754
$491$	−8484.00	−0.779791	−0.389896	−	0.920859i	$-0.627489\pi$
$491$	−8484.00	−0.779791	−0.389896	+	0.920859i	$0.627489\pi$
$492$	−5256.00	−0.481624
$493$	8316.00	0.759703
$494$	128.000	0.0116579
$495$	−495.000	−0.0449467
$496$	−2560.00	−0.231749
$497$	3444.00	0.310834
$498$	−7848.00	−0.706179
$499$	−17164.0	−1.53981	−0.769906	−	0.638157i	$-0.779697\pi$
$499$	−17164.0	−1.53981	−0.769906	+	0.638157i	$0.779697\pi$
$500$	−500.000	−0.0447214
$501$	1944.00	0.173356
$502$	−5592.00	−0.497178
$503$	−7656.00	−0.678656	−0.339328	−	0.940668i	$-0.610200\pi$
$503$	−7656.00	−0.678656	−0.339328	+	0.940668i	$0.610200\pi$
$504$	504.000	0.0445435
$505$	−3210.00	−0.282858
$506$	−1320.00	−0.115971
$507$	6579.00	0.576299
$508$	−6880.00	−0.600887
$509$	−3870.00	−0.337003	−0.168502	−	0.985701i	$-0.553893\pi$
$509$	−3870.00	−0.337003	−0.168502	+	0.985701i	$0.553893\pi$
$510$	−1260.00	−0.109399
$511$	3710.00	0.321176
$512$	512.000	0.0441942
$513$	−864.000	−0.0743597
$514$	7812.00	0.670375
$515$	3800.00	0.325142
$516$	6240.00	0.532366
$517$	132.000	0.0112289
$518$	4900.00	0.415625
$519$	−1566.00	−0.132447
$520$	−80.0000	−0.00674660
$521$	426.000	0.0358223	0.0179111	−	0.999840i	$-0.494298\pi$
$521$	426.000	0.0358223	0.0179111	+	0.999840i	$0.494298\pi$
$522$	−3564.00	−0.298835
$523$	1064.00	0.0889588	0.0444794	−	0.999010i	$-0.485837\pi$
$523$	1064.00	0.0889588	0.0444794	+	0.999010i	$0.485837\pi$
$524$	2064.00	0.172073
$525$	−525.000	−0.0436436
$526$	−96.0000	−0.00795779
$527$	6720.00	0.555461
$528$	−528.000	−0.0435194
$529$	−8567.00	−0.704118
$530$	2460.00	0.201614
$531$	4428.00	0.361881
$532$	896.000	0.0730198
$533$	876.000	0.0711891
$534$	9252.00	0.749763
$535$	5700.00	0.460621
$536$	−3104.00	−0.250135
$537$	6300.00	0.506266
$538$	−6972.00	−0.558707
$539$	539.000	0.0430730
$540$	540.000	0.0430331
$541$	−12622.0	−1.00307	−0.501536	−	0.865137i	$-0.667232\pi$
$541$	−12622.0	−1.00307	−0.501536	+	0.865137i	$0.667232\pi$
$542$	−11120.0	−0.881264
$543$	9390.00	0.742106
$544$	−1344.00	−0.105926
$545$	−250.000	−0.0196492
$546$	−84.0000	−0.00658401
$547$	−12040.0	−0.941121	−0.470561	−	0.882368i	$-0.655948\pi$
$547$	−12040.0	−0.941121	−0.470561	+	0.882368i	$0.655948\pi$
$548$	−12504.0	−0.974716
$549$	−5166.00	−0.401602
$550$	550.000	0.0426401
$551$	−6336.00	−0.489878
$552$	1440.00	0.111033
$553$	−2968.00	−0.228232
$554$	9124.00	0.699714
$555$	5250.00	0.401532
$556$	−6496.00	−0.495489
$557$	−918.000	−0.0698329	−0.0349164	−	0.999390i	$-0.511117\pi$
$557$	−918.000	−0.0698329	−0.0349164	+	0.999390i	$0.511117\pi$
$558$	−2880.00	−0.218495
$559$	−1040.00	−0.0786893
$560$	−560.000	−0.0422577
$561$	1386.00	0.104308
$562$	−12372.0	−0.928614
$563$	−20436.0	−1.52980	−0.764898	−	0.644152i	$-0.777210\pi$
$563$	−20436.0	−1.52980	−0.764898	+	0.644152i	$0.777210\pi$
$564$	−144.000	−0.0107509
$565$	−1650.00	−0.122860
$566$	−10064.0	−0.747388
$567$	567.000	0.0419961
$568$	3936.00	0.290759
$569$	−930.000	−0.0685196	−0.0342598	−	0.999413i	$-0.510907\pi$
$569$	−930.000	−0.0685196	−0.0342598	+	0.999413i	$0.510907\pi$
$570$	960.000	0.0705438
$571$	−14704.0	−1.07766	−0.538829	−	0.842415i	$-0.681133\pi$
$571$	−14704.0	−1.07766	−0.538829	+	0.842415i	$0.681133\pi$
$572$	88.0000	0.00643263
$573$	−11268.0	−0.821514
$574$	6132.00	0.445897
$575$	−1500.00	−0.108790
$576$	576.000	0.0416667
$577$	20882.0	1.50664	0.753318	−	0.657656i	$-0.228452\pi$
$577$	20882.0	1.50664	0.753318	+	0.657656i	$0.228452\pi$
$578$	−6298.00	−0.453222
$579$	5394.00	0.387162
$580$	3960.00	0.283500
$581$	9156.00	0.653795
$582$	−300.000	−0.0213667
$583$	−2706.00	−0.192232
$584$	4240.00	0.300432
$585$	−90.0000	−0.00636076
$586$	17892.0	1.26128
$587$	−11604.0	−0.815926	−0.407963	−	0.912999i	$-0.633761\pi$
$587$	−11604.0	−0.815926	−0.407963	+	0.912999i	$0.633761\pi$
$588$	−588.000	−0.0412393
$589$	−5120.00	−0.358176
$590$	−4920.00	−0.343310
$591$	13626.0	0.948390
$592$	5600.00	0.388781
$593$	6270.00	0.434196	0.217098	−	0.976150i	$-0.430341\pi$
$593$	6270.00	0.434196	0.217098	+	0.976150i	$0.430341\pi$
$594$	−594.000	−0.0410305
$595$	1470.00	0.101284
$596$	−3000.00	−0.206183
$597$	−7872.00	−0.539664
$598$	−240.000	−0.0164119
$599$	−4572.00	−0.311865	−0.155932	−	0.987768i	$-0.549838\pi$
$599$	−4572.00	−0.311865	−0.155932	+	0.987768i	$0.549838\pi$
$600$	−600.000	−0.0408248
$601$	15050.0	1.02147	0.510734	−	0.859739i	$-0.329374\pi$
$601$	15050.0	1.02147	0.510734	+	0.859739i	$0.329374\pi$
$602$	−7280.00	−0.492875
$603$	−3492.00	−0.235830
$604$	3008.00	0.202639
$605$	−605.000	−0.0406558
$606$	−3852.00	−0.258213
$607$	14264.0	0.953802	0.476901	−	0.878957i	$-0.341760\pi$
$607$	14264.0	0.953802	0.476901	+	0.878957i	$0.341760\pi$
$608$	1024.00	0.0683038
$609$	4158.00	0.276668
$610$	5740.00	0.380993
$611$	24.0000	0.00158909
$612$	−1512.00	−0.0998676
$613$	−1942.00	−0.127955	−0.0639777	−	0.997951i	$-0.520379\pi$
$613$	−1942.00	−0.127955	−0.0639777	+	0.997951i	$0.520379\pi$
$614$	−2048.00	−0.134610
$615$	6570.00	0.430777
$616$	616.000	0.0402911
$617$	−846.000	−0.0552004	−0.0276002	−	0.999619i	$-0.508787\pi$
$617$	−846.000	−0.0552004	−0.0276002	+	0.999619i	$0.508787\pi$
$618$	4560.00	0.296812
$619$	12332.0	0.800751	0.400376	−	0.916351i	$-0.368880\pi$
$619$	12332.0	0.800751	0.400376	+	0.916351i	$0.368880\pi$
$620$	3200.00	0.207282
$621$	1620.00	0.104683
$622$	−1368.00	−0.0881862
$623$	−10794.0	−0.694145
$624$	−96.0000	−0.00615878
$625$	625.000	0.0400000
$626$	−5324.00	−0.339920
$627$	−1056.00	−0.0672609
$628$	2744.00	0.174359
$629$	−14700.0	−0.931840
$630$	−630.000	−0.0398410
$631$	29480.0	1.85987	0.929937	−	0.367719i	$-0.119861\pi$
$631$	29480.0	1.85987	0.929937	+	0.367719i	$0.119861\pi$
$632$	−3392.00	−0.213491
$633$	−8088.00	−0.507850
$634$	228.000	0.0142824
$635$	8600.00	0.537450
$636$	2952.00	0.184048
$637$	98.0000	0.00609561
$638$	−4356.00	−0.270307
$639$	4428.00	0.274130
$640$	−640.000	−0.0395285
$641$	14298.0	0.881025	0.440513	−	0.897746i	$-0.354797\pi$
$641$	14298.0	0.881025	0.440513	+	0.897746i	$0.354797\pi$
$642$	6840.00	0.420488
$643$	−27292.0	−1.67386	−0.836930	−	0.547311i	$-0.815652\pi$
$643$	−27292.0	−1.67386	−0.836930	+	0.547311i	$0.815652\pi$
$644$	−1680.00	−0.102797
$645$	−7800.00	−0.476162
$646$	−2688.00	−0.163712
$647$	8676.00	0.527185	0.263593	−	0.964634i	$-0.415093\pi$
$647$	8676.00	0.527185	0.263593	+	0.964634i	$0.415093\pi$
$648$	648.000	0.0392837
$649$	5412.00	0.327334
$650$	100.000	0.00603434
$651$	3360.00	0.202287
$652$	−7696.00	−0.462268
$653$	17130.0	1.02657	0.513284	−	0.858219i	$-0.328429\pi$
$653$	17130.0	1.02657	0.513284	+	0.858219i	$0.328429\pi$
$654$	−300.000	−0.0179372
$655$	−2580.00	−0.153907
$656$	7008.00	0.417098
$657$	4770.00	0.283250
$658$	168.000	0.00995338
$659$	11436.0	0.675999	0.337999	−	0.941146i	$-0.390250\pi$
$659$	11436.0	0.675999	0.337999	+	0.941146i	$0.390250\pi$
$660$	660.000	0.0389249
$661$	−7354.00	−0.432734	−0.216367	−	0.976312i	$-0.569421\pi$
$661$	−7354.00	−0.432734	−0.216367	+	0.976312i	$0.569421\pi$
$662$	12808.0	0.751959
$663$	252.000	0.0147615
$664$	10464.0	0.611569
$665$	−1120.00	−0.0653109
$666$	6300.00	0.366547
$667$	11880.0	0.689648
$668$	−2592.00	−0.150131
$669$	12216.0	0.705976
$670$	3880.00	0.223728
$671$	−6314.00	−0.363263
$672$	−672.000	−0.0385758
$673$	−7798.00	−0.446643	−0.223322	−	0.974745i	$-0.571690\pi$
$673$	−7798.00	−0.446643	−0.223322	+	0.974745i	$0.571690\pi$
$674$	−13388.0	−0.765113
$675$	−675.000	−0.0384900
$676$	−8772.00	−0.499090
$677$	−13566.0	−0.770138	−0.385069	−	0.922888i	$-0.625822\pi$
$677$	−13566.0	−0.770138	−0.385069	+	0.922888i	$0.625822\pi$
$678$	−1980.00	−0.112156
$679$	350.000	0.0197817
$680$	1680.00	0.0947427
$681$	−10332.0	−0.581385
$682$	−3520.00	−0.197636
$683$	−6396.00	−0.358325	−0.179163	−	0.983819i	$-0.557339\pi$
$683$	−6396.00	−0.358325	−0.179163	+	0.983819i	$0.557339\pi$
$684$	1152.00	0.0643974
$685$	15630.0	0.871813
$686$	686.000	0.0381802
$687$	1902.00	0.105627
$688$	−8320.00	−0.461042
$689$	−492.000	−0.0272042
$690$	−1800.00	−0.0993113
$691$	−16924.0	−0.931721	−0.465861	−	0.884858i	$-0.654255\pi$
$691$	−16924.0	−0.931721	−0.465861	+	0.884858i	$0.654255\pi$
$692$	2088.00	0.114702
$693$	693.000	0.0379869
$694$	−7896.00	−0.431885
$695$	8120.00	0.443179
$696$	4752.00	0.258799
$697$	−18396.0	−0.999710
$698$	11092.0	0.601488
$699$	16254.0	0.879518
$700$	700.000	0.0377964
$701$	7530.00	0.405712	0.202856	−	0.979209i	$-0.434978\pi$
$701$	7530.00	0.405712	0.202856	+	0.979209i	$0.434978\pi$
$702$	−108.000	−0.00580655
$703$	11200.0	0.600876
$704$	704.000	0.0376889
$705$	180.000	0.00961588
$706$	804.000	0.0428597
$707$	4494.00	0.239058
$708$	−5904.00	−0.313398
$709$	27830.0	1.47416	0.737079	−	0.675807i	$-0.236205\pi$
$709$	27830.0	1.47416	0.737079	+	0.675807i	$0.236205\pi$
$710$	−4920.00	−0.260062
$711$	−3816.00	−0.201282
$712$	−12336.0	−0.649313
$713$	9600.00	0.504240
$714$	1764.00	0.0924594
$715$	−110.000	−0.00575352
$716$	−8400.00	−0.438440
$717$	−1152.00	−0.0600031
$718$	−15360.0	−0.798371
$719$	−8892.00	−0.461218	−0.230609	−	0.973047i	$-0.574072\pi$
$719$	−8892.00	−0.461218	−0.230609	+	0.973047i	$0.574072\pi$
$720$	−720.000	−0.0372678
$721$	−5320.00	−0.274795
$722$	−11670.0	−0.601541
$723$	14106.0	0.725599
$724$	−12520.0	−0.642683
$725$	−4950.00	−0.253570
$726$	−726.000	−0.0371135
$727$	22448.0	1.14519	0.572593	−	0.819840i	$-0.305938\pi$
$727$	22448.0	1.14519	0.572593	+	0.819840i	$0.305938\pi$
$728$	112.000	0.00570192
$729$	729.000	0.0370370
$730$	−5300.00	−0.268715
$731$	21840.0	1.10504
$732$	6888.00	0.347798
$733$	−31774.0	−1.60109	−0.800545	−	0.599272i	$-0.795457\pi$
$733$	−31774.0	−1.60109	−0.800545	+	0.599272i	$0.795457\pi$
$734$	−14864.0	−0.747466
$735$	735.000	0.0368856
$736$	−1920.00	−0.0961578
$737$	−4268.00	−0.213316
$738$	7884.00	0.393244
$739$	−1744.00	−0.0868120	−0.0434060	−	0.999058i	$-0.513821\pi$
$739$	−1744.00	−0.0868120	−0.0434060	+	0.999058i	$0.513821\pi$
$740$	−7000.00	−0.347737
$741$	−192.000	−0.00951862
$742$	−3444.00	−0.170395
$743$	23376.0	1.15422	0.577108	−	0.816668i	$-0.304181\pi$
$743$	23376.0	1.15422	0.577108	+	0.816668i	$0.304181\pi$
$744$	3840.00	0.189222
$745$	3750.00	0.184415
$746$	13444.0	0.659812
$747$	11772.0	0.576593
$748$	−1848.00	−0.0903337
$749$	−7980.00	−0.389296
$750$	750.000	0.0365148
$751$	−12256.0	−0.595510	−0.297755	−	0.954642i	$-0.596238\pi$
$751$	−12256.0	−0.595510	−0.297755	+	0.954642i	$0.596238\pi$
$752$	192.000	0.00931053
$753$	8388.00	0.405944
$754$	−792.000	−0.0382532
$755$	−3760.00	−0.181246
$756$	−756.000	−0.0363696
$757$	36782.0	1.76600	0.883002	−	0.469370i	$-0.155519\pi$
$757$	36782.0	1.76600	0.883002	+	0.469370i	$0.155519\pi$
$758$	−2936.00	−0.140686
$759$	1980.00	0.0946897
$760$	−1280.00	−0.0610927
$761$	−2562.00	−0.122040	−0.0610200	−	0.998137i	$-0.519435\pi$
$761$	−2562.00	−0.122040	−0.0610200	+	0.998137i	$0.519435\pi$
$762$	10320.0	0.490622
$763$	350.000	0.0166066
$764$	15024.0	0.711452
$765$	1890.00	0.0893243
$766$	−16584.0	−0.782251
$767$	984.000	0.0463236
$768$	−768.000	−0.0360844
$769$	25850.0	1.21219	0.606095	−	0.795392i	$-0.292735\pi$
$769$	25850.0	1.21219	0.606095	+	0.795392i	$0.292735\pi$
$770$	−770.000	−0.0360375
$771$	−11718.0	−0.547359
$772$	−7192.00	−0.335292
$773$	34746.0	1.61672	0.808361	−	0.588687i	$-0.200355\pi$
$773$	34746.0	1.61672	0.808361	+	0.588687i	$0.200355\pi$
$774$	−9360.00	−0.434675
$775$	−4000.00	−0.185399
$776$	400.000	0.0185041
$777$	−7350.00	−0.339356
$778$	−20028.0	−0.922929
$779$	14016.0	0.644641
$780$	120.000	0.00550858
$781$	5412.00	0.247960
$782$	5040.00	0.230473
$783$	5346.00	0.243998
$784$	784.000	0.0357143
$785$	−3430.00	−0.155952
$786$	−3096.00	−0.140497
$787$	−21856.0	−0.989939	−0.494970	−	0.868910i	$-0.664821\pi$
$787$	−21856.0	−0.989939	−0.494970	+	0.868910i	$0.664821\pi$
$788$	−18168.0	−0.821330
$789$	144.000	0.00649751
$790$	4240.00	0.190952
$791$	2310.00	0.103836
$792$	792.000	0.0355335
$793$	−1148.00	−0.0514082
$794$	−9860.00	−0.440703
$795$	−3690.00	−0.164617
$796$	10496.0	0.467363
$797$	−9510.00	−0.422662	−0.211331	−	0.977415i	$-0.567780\pi$
$797$	−9510.00	−0.422662	−0.211331	+	0.977415i	$0.567780\pi$
$798$	−1344.00	−0.0596204
$799$	−504.000	−0.0223157
$800$	800.000	0.0353553
$801$	−13878.0	−0.612179
$802$	27876.0	1.22735
$803$	5830.00	0.256210
$804$	4656.00	0.204234
$805$	2100.00	0.0919444
$806$	−640.000	−0.0279690
$807$	10458.0	0.456182
$808$	5136.00	0.223619
$809$	21918.0	0.952529	0.476264	−	0.879302i	$-0.341991\pi$
$809$	21918.0	0.952529	0.476264	+	0.879302i	$0.341991\pi$
$810$	−810.000	−0.0351364
$811$	29792.0	1.28994	0.644968	−	0.764209i	$-0.276871\pi$
$811$	29792.0	1.28994	0.644968	+	0.764209i	$0.276871\pi$
$812$	−5544.00	−0.239601
$813$	16680.0	0.719549
$814$	7700.00	0.331554
$815$	9620.00	0.413465
$816$	2016.00	0.0864879
$817$	−16640.0	−0.712558
$818$	7732.00	0.330493
$819$	126.000	0.00537582
$820$	−8760.00	−0.373064
$821$	−5550.00	−0.235927	−0.117964	−	0.993018i	$-0.537637\pi$
$821$	−5550.00	−0.235927	−0.117964	+	0.993018i	$0.537637\pi$
$822$	18756.0	0.795852
$823$	−6304.00	−0.267003	−0.133502	−	0.991049i	$-0.542622\pi$
$823$	−6304.00	−0.267003	−0.133502	+	0.991049i	$0.542622\pi$
$824$	−6080.00	−0.257047
$825$	−825.000	−0.0348155
$826$	6888.00	0.290150
$827$	40356.0	1.69687	0.848437	−	0.529296i	$-0.177544\pi$
$827$	40356.0	1.69687	0.848437	+	0.529296i	$0.177544\pi$
$828$	−2160.00	−0.0906584
$829$	−15850.0	−0.664045	−0.332022	−	0.943271i	$-0.607731\pi$
$829$	−15850.0	−0.664045	−0.332022	+	0.943271i	$0.607731\pi$
$830$	−13080.0	−0.547004
$831$	−13686.0	−0.571314
$832$	128.000	0.00533366
$833$	−2058.00	−0.0856008
$834$	9744.00	0.404565
$835$	3240.00	0.134281
$836$	1408.00	0.0582496
$837$	4320.00	0.178400
$838$	7416.00	0.305706
$839$	3900.00	0.160480	0.0802401	−	0.996776i	$-0.474431\pi$
$839$	3900.00	0.160480	0.0802401	+	0.996776i	$0.474431\pi$
$840$	840.000	0.0345033
$841$	14815.0	0.607446
$842$	22876.0	0.936293
$843$	18558.0	0.758211
$844$	10784.0	0.439811
$845$	10965.0	0.446399
$846$	216.000	0.00877805
$847$	847.000	0.0343604
$848$	−3936.00	−0.159390
$849$	15096.0	0.610240
$850$	−2100.00	−0.0847405
$851$	−21000.0	−0.845912
$852$	−5904.00	−0.237403
$853$	−7126.00	−0.286037	−0.143019	−	0.989720i	$-0.545681\pi$
$853$	−7126.00	−0.286037	−0.143019	+	0.989720i	$0.545681\pi$
$854$	−8036.00	−0.321998
$855$	−1440.00	−0.0575988
$856$	−9120.00	−0.364153
$857$	17118.0	0.682310	0.341155	−	0.940007i	$-0.389182\pi$
$857$	17118.0	0.682310	0.341155	+	0.940007i	$0.389182\pi$
$858$	−132.000	−0.00525222
$859$	22340.0	0.887347	0.443673	−	0.896189i	$-0.353675\pi$
$859$	22340.0	0.887347	0.443673	+	0.896189i	$0.353675\pi$
$860$	10400.0	0.412369
$861$	−9198.00	−0.364073
$862$	14448.0	0.570883
$863$	−16860.0	−0.665030	−0.332515	−	0.943098i	$-0.607897\pi$
$863$	−16860.0	−0.665030	−0.332515	+	0.943098i	$0.607897\pi$
$864$	−864.000	−0.0340207
$865$	−2610.00	−0.102593
$866$	−7772.00	−0.304969
$867$	9447.00	0.370054
$868$	−4480.00	−0.175186
$869$	−4664.00	−0.182066
$870$	−5940.00	−0.231477
$871$	−776.000	−0.0301880
$872$	400.000	0.0155341
$873$	450.000	0.0174458
$874$	−3840.00	−0.148615
$875$	−875.000	−0.0338062
$876$	−6360.00	−0.245302
$877$	−6790.00	−0.261439	−0.130720	−	0.991419i	$-0.541729\pi$
$877$	−6790.00	−0.261439	−0.130720	+	0.991419i	$0.541729\pi$
$878$	11440.0	0.439728
$879$	−26838.0	−1.02983
$880$	−880.000	−0.0337100
$881$	32778.0	1.25348	0.626742	−	0.779227i	$-0.284388\pi$
$881$	32778.0	1.25348	0.626742	+	0.779227i	$0.284388\pi$
$882$	882.000	0.0336718
$883$	−39124.0	−1.49108	−0.745542	−	0.666458i	$-0.767809\pi$
$883$	−39124.0	−1.49108	−0.745542	+	0.666458i	$0.767809\pi$
$884$	−336.000	−0.0127838
$885$	7380.00	0.280312
$886$	−8808.00	−0.333985
$887$	23136.0	0.875796	0.437898	−	0.899025i	$-0.355723\pi$
$887$	23136.0	0.875796	0.437898	+	0.899025i	$0.355723\pi$
$888$	−8400.00	−0.317439
$889$	−12040.0	−0.454228
$890$	15420.0	0.580764
$891$	891.000	0.0335013
$892$	−16288.0	−0.611393
$893$	384.000	0.0143898
$894$	4500.00	0.168347
$895$	10500.0	0.392152
$896$	896.000	0.0334077
$897$	360.000	0.0134003
$898$	13524.0	0.502563
$899$	31680.0	1.17529
$900$	900.000	0.0333333
$901$	10332.0	0.382030
$902$	9636.00	0.355703
$903$	10920.0	0.402431
$904$	2640.00	0.0971295
$905$	15650.0	0.574833
$906$	−4512.00	−0.165454
$907$	−7924.00	−0.290091	−0.145045	−	0.989425i	$-0.546333\pi$
$907$	−7924.00	−0.290091	−0.145045	+	0.989425i	$0.546333\pi$
$908$	13776.0	0.503494
$909$	5778.00	0.210830
$910$	−140.000	−0.00509995
$911$	17412.0	0.633244	0.316622	−	0.948552i	$-0.397451\pi$
$911$	17412.0	0.633244	0.316622	+	0.948552i	$0.397451\pi$
$912$	−1536.00	−0.0557698
$913$	14388.0	0.521548
$914$	17620.0	0.637656
$915$	−8610.00	−0.311080
$916$	−2536.00	−0.0914758
$917$	3612.00	0.130075
$918$	2268.00	0.0815416
$919$	−9520.00	−0.341715	−0.170857	−	0.985296i	$-0.554654\pi$
$919$	−9520.00	−0.341715	−0.170857	+	0.985296i	$0.554654\pi$
$920$	2400.00	0.0860061
$921$	3072.00	0.109909
$922$	35796.0	1.27861
$923$	984.000	0.0350907
$924$	−924.000	−0.0328976
$925$	8750.00	0.311025
$926$	−3776.00	−0.134003
$927$	−6840.00	−0.242346
$928$	−6336.00	−0.224126
$929$	22386.0	0.790593	0.395296	−	0.918554i	$-0.370642\pi$
$929$	22386.0	0.790593	0.395296	+	0.918554i	$0.370642\pi$
$930$	−4800.00	−0.169245
$931$	1568.00	0.0551978
$932$	−21672.0	−0.761685
$933$	2052.00	0.0720037
$934$	29304.0	1.02661
$935$	2310.00	0.0807969
$936$	144.000	0.00502862
$937$	34058.0	1.18743	0.593717	−	0.804674i	$-0.297660\pi$
$937$	34058.0	1.18743	0.593717	+	0.804674i	$0.297660\pi$
$938$	−5432.00	−0.189084
$939$	7986.00	0.277543
$940$	−240.000	−0.00832759
$941$	1482.00	0.0513409	0.0256705	−	0.999670i	$-0.491828\pi$
$941$	1482.00	0.0513409	0.0256705	+	0.999670i	$0.491828\pi$
$942$	−4116.00	−0.142364
$943$	−26280.0	−0.907523
$944$	7872.00	0.271411
$945$	945.000	0.0325300
$946$	−11440.0	−0.393178
$947$	−45372.0	−1.55691	−0.778454	−	0.627702i	$-0.783996\pi$
$947$	−45372.0	−1.55691	−0.778454	+	0.627702i	$0.783996\pi$
$948$	5088.00	0.174315
$949$	1060.00	0.0362582
$950$	1600.00	0.0546430
$951$	−342.000	−0.0116615
$952$	−2352.00	−0.0800722
$953$	−39954.0	−1.35807	−0.679033	−	0.734108i	$-0.737601\pi$
$953$	−39954.0	−1.35807	−0.679033	+	0.734108i	$0.737601\pi$
$954$	−4428.00	−0.150274
$955$	−18780.0	−0.636342
$956$	1536.00	0.0519642
$957$	6534.00	0.220705
$958$	−1584.00	−0.0534204
$959$	−21882.0	−0.736816
$960$	960.000	0.0322749
$961$	−4191.00	−0.140680
$962$	1400.00	0.0469208
$963$	−10260.0	−0.343327
$964$	−18808.0	−0.628387
$965$	8990.00	0.299895
$966$	2520.00	0.0839334
$967$	−54160.0	−1.80110	−0.900552	−	0.434748i	$-0.856838\pi$
$967$	−54160.0	−1.80110	−0.900552	+	0.434748i	$0.856838\pi$
$968$	968.000	0.0321412
$969$	4032.00	0.133670
$970$	−500.000	−0.0165505
$971$	−26532.0	−0.876882	−0.438441	−	0.898760i	$-0.644469\pi$
$971$	−26532.0	−0.876882	−0.438441	+	0.898760i	$0.644469\pi$
$972$	−972.000	−0.0320750
$973$	−11368.0	−0.374554
$974$	3424.00	0.112641
$975$	−150.000	−0.00492702
$976$	−9184.00	−0.301202
$977$	44994.0	1.47337	0.736687	−	0.676234i	$-0.236389\pi$
$977$	44994.0	1.47337	0.736687	+	0.676234i	$0.236389\pi$
$978$	11544.0	0.377440
$979$	−16962.0	−0.553736
$980$	−980.000	−0.0319438
$981$	450.000	0.0146457
$982$	−16968.0	−0.551396
$983$	−56748.0	−1.84128	−0.920641	−	0.390410i	$-0.872333\pi$
$983$	−56748.0	−1.84128	−0.920641	+	0.390410i	$0.872333\pi$
$984$	−10512.0	−0.340559
$985$	22710.0	0.734620
$986$	16632.0	0.537191
$987$	−252.000	−0.00812690
$988$	256.000	0.00824337
$989$	31200.0	1.00314
$990$	−990.000	−0.0317821
$991$	−4768.00	−0.152836	−0.0764180	−	0.997076i	$-0.524348\pi$
$991$	−4768.00	−0.152836	−0.0764180	+	0.997076i	$0.524348\pi$
$992$	−5120.00	−0.163871
$993$	−19212.0	−0.613972
$994$	6888.00	0.219793
$995$	−13120.0	−0.418022
$996$	−15696.0	−0.499344
$997$	−18910.0	−0.600688	−0.300344	−	0.953831i	$-0.597101\pi$
$997$	−18910.0	−0.600688	−0.300344	+	0.953831i	$0.597101\pi$
$998$	−34328.0	−1.08881
$999$	−9450.00	−0.299284

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2310.4.a.h.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2310.4.a.h.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:	\( N \)	\(=\)	\( 2310 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2310.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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