LMFDB - Embedded newform 2310.4.a.f.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:	$0$
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	$\chi$	$=$	2310.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} -6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} -10.0000 q^{10} -11.0000 q^{11} -12.0000 q^{12} -46.0000 q^{13} +14.0000 q^{14} +15.0000 q^{15} +16.0000 q^{16} -126.000 q^{17} +18.0000 q^{18} +44.0000 q^{19} -20.0000 q^{20} -21.0000 q^{21} -22.0000 q^{22} -96.0000 q^{23} -24.0000 q^{24} +25.0000 q^{25} -92.0000 q^{26} -27.0000 q^{27} +28.0000 q^{28} +234.000 q^{29} +30.0000 q^{30} -172.000 q^{31} +32.0000 q^{32} +33.0000 q^{33} -252.000 q^{34} -35.0000 q^{35} +36.0000 q^{36} +386.000 q^{37} +88.0000 q^{38} +138.000 q^{39} -40.0000 q^{40} -198.000 q^{41} -42.0000 q^{42} -28.0000 q^{43} -44.0000 q^{44} -45.0000 q^{45} -192.000 q^{46} +456.000 q^{47} -48.0000 q^{48} +49.0000 q^{49} +50.0000 q^{50} +378.000 q^{51} -184.000 q^{52} -30.0000 q^{53} -54.0000 q^{54} +55.0000 q^{55} +56.0000 q^{56} -132.000 q^{57} +468.000 q^{58} -108.000 q^{59} +60.0000 q^{60} +398.000 q^{61} -344.000 q^{62} +63.0000 q^{63} +64.0000 q^{64} +230.000 q^{65} +66.0000 q^{66} +632.000 q^{67} -504.000 q^{68} +288.000 q^{69} -70.0000 q^{70} -1032.00 q^{71} +72.0000 q^{72} -934.000 q^{73} +772.000 q^{74} -75.0000 q^{75} +176.000 q^{76} -77.0000 q^{77} +276.000 q^{78} +764.000 q^{79} -80.0000 q^{80} +81.0000 q^{81} -396.000 q^{82} +648.000 q^{83} -84.0000 q^{84} +630.000 q^{85} -56.0000 q^{86} -702.000 q^{87} -88.0000 q^{88} -606.000 q^{89} -90.0000 q^{90} -322.000 q^{91} -384.000 q^{92} +516.000 q^{93} +912.000 q^{94} -220.000 q^{95} -96.0000 q^{96} +1550.00 q^{97} +98.0000 q^{98} -99.0000 q^{99} +O(q^{100})\)

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
$13$	−46.0000	−0.981393	−0.490696	−	0.871331i	$-0.663258\pi$
$13$	−46.0000	−0.981393	−0.490696	+	0.871331i	$0.663258\pi$
$14$	14.0000	0.267261
$15$	15.0000	0.258199
$16$	16.0000	0.250000
$17$	−126.000	−1.79762	−0.898808	−	0.438342i	$-0.855566\pi$
$17$	−126.000	−1.79762	−0.898808	+	0.438342i	$0.855566\pi$
$18$	18.0000	0.235702
$19$	44.0000	0.531279	0.265639	−	0.964072i	$-0.414417\pi$
$19$	44.0000	0.531279	0.265639	+	0.964072i	$0.414417\pi$
$20$	−20.0000	−0.223607
$21$	−21.0000	−0.218218
$22$	−22.0000	−0.213201
$23$	−96.0000	−0.870321	−0.435161	−	0.900353i	$-0.643308\pi$
$23$	−96.0000	−0.870321	−0.435161	+	0.900353i	$0.643308\pi$
$24$	−24.0000	−0.204124
$25$	25.0000	0.200000
$26$	−92.0000	−0.693949
$27$	−27.0000	−0.192450
$28$	28.0000	0.188982
$29$	234.000	1.49837	0.749185	−	0.662361i	$-0.230446\pi$
$29$	234.000	1.49837	0.749185	+	0.662361i	$0.230446\pi$
$30$	30.0000	0.182574
$31$	−172.000	−0.996520	−0.498260	−	0.867028i	$-0.666027\pi$
$31$	−172.000	−0.996520	−0.498260	+	0.867028i	$0.666027\pi$
$32$	32.0000	0.176777
$33$	33.0000	0.174078
$34$	−252.000	−1.27111
$35$	−35.0000	−0.169031
$36$	36.0000	0.166667
$37$	386.000	1.71508	0.857541	−	0.514416i	$-0.171991\pi$
$37$	386.000	1.71508	0.857541	+	0.514416i	$0.171991\pi$
$38$	88.0000	0.375671
$39$	138.000	0.566607
$40$	−40.0000	−0.158114
$41$	−198.000	−0.754205	−0.377102	−	0.926172i	$-0.623080\pi$
$41$	−198.000	−0.754205	−0.377102	+	0.926172i	$0.623080\pi$
$42$	−42.0000	−0.154303
$43$	−28.0000	−0.0993014	−0.0496507	−	0.998767i	$-0.515811\pi$
$43$	−28.0000	−0.0993014	−0.0496507	+	0.998767i	$0.515811\pi$
$44$	−44.0000	−0.150756
$45$	−45.0000	−0.149071
$46$	−192.000	−0.615410
$47$	456.000	1.41520	0.707600	−	0.706613i	$-0.249778\pi$
$47$	456.000	1.41520	0.707600	+	0.706613i	$0.249778\pi$
$48$	−48.0000	−0.144338
$49$	49.0000	0.142857
$50$	50.0000	0.141421
$51$	378.000	1.03785
$52$	−184.000	−0.490696
$53$	−30.0000	−0.0777513	−0.0388756	−	0.999244i	$-0.512378\pi$
$53$	−30.0000	−0.0777513	−0.0388756	+	0.999244i	$0.512378\pi$
$54$	−54.0000	−0.136083
$55$	55.0000	0.134840
$56$	56.0000	0.133631
$57$	−132.000	−0.306734
$58$	468.000	1.05951
$59$	−108.000	−0.238312	−0.119156	−	0.992876i	$-0.538019\pi$
$59$	−108.000	−0.238312	−0.119156	+	0.992876i	$0.538019\pi$
$60$	60.0000	0.129099
$61$	398.000	0.835388	0.417694	−	0.908588i	$-0.362838\pi$
$61$	398.000	0.835388	0.417694	+	0.908588i	$0.362838\pi$
$62$	−344.000	−0.704646
$63$	63.0000	0.125988
$64$	64.0000	0.125000
$65$	230.000	0.438892
$66$	66.0000	0.123091
$67$	632.000	1.15240	0.576202	−	0.817307i	$-0.304534\pi$
$67$	632.000	1.15240	0.576202	+	0.817307i	$0.304534\pi$
$68$	−504.000	−0.898808
$69$	288.000	0.502480
$70$	−70.0000	−0.119523
$71$	−1032.00	−1.72501	−0.862506	−	0.506047i	$-0.831106\pi$
$71$	−1032.00	−1.72501	−0.862506	+	0.506047i	$0.831106\pi$
$72$	72.0000	0.117851
$73$	−934.000	−1.49749	−0.748743	−	0.662861i	$-0.769342\pi$
$73$	−934.000	−1.49749	−0.748743	+	0.662861i	$0.769342\pi$
$74$	772.000	1.21275
$75$	−75.0000	−0.115470
$76$	176.000	0.265639
$77$	−77.0000	−0.113961
$78$	276.000	0.400652
$79$	764.000	1.08806	0.544030	−	0.839066i	$-0.316898\pi$
$79$	764.000	1.08806	0.544030	+	0.839066i	$0.316898\pi$
$80$	−80.0000	−0.111803
$81$	81.0000	0.111111
$82$	−396.000	−0.533303
$83$	648.000	0.856955	0.428477	−	0.903553i	$-0.359050\pi$
$83$	648.000	0.856955	0.428477	+	0.903553i	$0.359050\pi$
$84$	−84.0000	−0.109109
$85$	630.000	0.803919
$86$	−56.0000	−0.0702167
$87$	−702.000	−0.865084
$88$	−88.0000	−0.106600
$89$	−606.000	−0.721751	−0.360876	−	0.932614i	$-0.617522\pi$
$89$	−606.000	−0.721751	−0.360876	+	0.932614i	$0.617522\pi$
$90$	−90.0000	−0.105409
$91$	−322.000	−0.370932
$92$	−384.000	−0.435161
$93$	516.000	0.575341
$94$	912.000	1.00070
$95$	−220.000	−0.237595
$96$	−96.0000	−0.102062
$97$	1550.00	1.62246	0.811230	−	0.584727i	$-0.198798\pi$
$97$	1550.00	1.62246	0.811230	+	0.584727i	$0.198798\pi$
$98$	98.0000	0.101015
$99$	−99.0000	−0.100504
$100$	100.000	0.100000
$101$	−474.000	−0.466978	−0.233489	−	0.972359i	$-0.575014\pi$
$101$	−474.000	−0.466978	−0.233489	+	0.972359i	$0.575014\pi$
$102$	756.000	0.733874
$103$	−376.000	−0.359693	−0.179847	−	0.983695i	$-0.557560\pi$
$103$	−376.000	−0.359693	−0.179847	+	0.983695i	$0.557560\pi$
$104$	−368.000	−0.346975
$105$	105.000	0.0975900
$106$	−60.0000	−0.0549784
$107$	1644.00	1.48534	0.742670	−	0.669657i	$-0.233559\pi$
$107$	1644.00	1.48534	0.742670	+	0.669657i	$0.233559\pi$
$108$	−108.000	−0.0962250
$109$	−2014.00	−1.76978	−0.884891	−	0.465798i	$-0.845767\pi$
$109$	−2014.00	−1.76978	−0.884891	+	0.465798i	$0.845767\pi$
$110$	110.000	0.0953463
$111$	−1158.00	−0.990203
$112$	112.000	0.0944911
$113$	−342.000	−0.284714	−0.142357	−	0.989815i	$-0.545468\pi$
$113$	−342.000	−0.284714	−0.142357	+	0.989815i	$0.545468\pi$
$114$	−264.000	−0.216894
$115$	480.000	0.389219
$116$	936.000	0.749185
$117$	−414.000	−0.327131
$118$	−216.000	−0.168512
$119$	−882.000	−0.679435
$120$	120.000	0.0912871
$121$	121.000	0.0909091
$122$	796.000	0.590709
$123$	594.000	0.435440
$124$	−688.000	−0.498260
$125$	−125.000	−0.0894427
$126$	126.000	0.0890871
$127$	320.000	0.223586	0.111793	−	0.993732i	$-0.464341\pi$
$127$	320.000	0.223586	0.111793	+	0.993732i	$0.464341\pi$
$128$	128.000	0.0883883
$129$	84.0000	0.0573317
$130$	460.000	0.310344
$131$	−1068.00	−0.712302	−0.356151	−	0.934428i	$-0.615911\pi$
$131$	−1068.00	−0.712302	−0.356151	+	0.934428i	$0.615911\pi$
$132$	132.000	0.0870388
$133$	308.000	0.200804
$134$	1264.00	0.814873
$135$	135.000	0.0860663
$136$	−1008.00	−0.635554
$137$	3090.00	1.92698	0.963491	−	0.267741i	$-0.0862771\pi$
$137$	3090.00	1.92698	0.963491	+	0.267741i	$0.0862771\pi$
$138$	576.000	0.355307
$139$	812.000	0.495489	0.247744	−	0.968825i	$-0.420311\pi$
$139$	812.000	0.495489	0.247744	+	0.968825i	$0.420311\pi$
$140$	−140.000	−0.0845154
$141$	−1368.00	−0.817067
$142$	−2064.00	−1.21977
$143$	506.000	0.295901
$144$	144.000	0.0833333
$145$	−1170.00	−0.670091
$146$	−1868.00	−1.05888
$147$	−147.000	−0.0824786
$148$	1544.00	0.857541
$149$	1146.00	0.630094	0.315047	−	0.949076i	$-0.397980\pi$
$149$	1146.00	0.630094	0.315047	+	0.949076i	$0.397980\pi$
$150$	−150.000	−0.0816497
$151$	1604.00	0.864448	0.432224	−	0.901766i	$-0.357729\pi$
$151$	1604.00	0.864448	0.432224	+	0.901766i	$0.357729\pi$
$152$	352.000	0.187835
$153$	−1134.00	−0.599206
$154$	−154.000	−0.0805823
$155$	860.000	0.445657
$156$	552.000	0.283304
$157$	3434.00	1.74562	0.872812	−	0.488056i	$-0.162294\pi$
$157$	3434.00	1.74562	0.872812	+	0.488056i	$0.162294\pi$
$158$	1528.00	0.769374
$159$	90.0000	0.0448897
$160$	−160.000	−0.0790569
$161$	−672.000	−0.328950
$162$	162.000	0.0785674
$163$	−1792.00	−0.861106	−0.430553	−	0.902565i	$-0.641681\pi$
$163$	−1792.00	−0.861106	−0.430553	+	0.902565i	$0.641681\pi$
$164$	−792.000	−0.377102
$165$	−165.000	−0.0778499
$166$	1296.00	0.605958
$167$	−120.000	−0.0556041	−0.0278020	−	0.999613i	$-0.508851\pi$
$167$	−120.000	−0.0556041	−0.0278020	+	0.999613i	$0.508851\pi$
$168$	−168.000	−0.0771517
$169$	−81.0000	−0.0368685
$170$	1260.00	0.568456
$171$	396.000	0.177093
$172$	−112.000	−0.0496507
$173$	4026.00	1.76931	0.884656	−	0.466244i	$-0.154393\pi$
$173$	4026.00	1.76931	0.884656	+	0.466244i	$0.154393\pi$
$174$	−1404.00	−0.611707
$175$	175.000	0.0755929
$176$	−176.000	−0.0753778
$177$	324.000	0.137589
$178$	−1212.00	−0.510355
$179$	−1236.00	−0.516106	−0.258053	−	0.966131i	$-0.583081\pi$
$179$	−1236.00	−0.516106	−0.258053	+	0.966131i	$0.583081\pi$
$180$	−180.000	−0.0745356
$181$	962.000	0.395055	0.197527	−	0.980297i	$-0.436709\pi$
$181$	962.000	0.395055	0.197527	+	0.980297i	$0.436709\pi$
$182$	−644.000	−0.262288
$183$	−1194.00	−0.482312
$184$	−768.000	−0.307705
$185$	−1930.00	−0.767008
$186$	1032.00	0.406827
$187$	1386.00	0.542002
$188$	1824.00	0.707600
$189$	−189.000	−0.0727393
$190$	−440.000	−0.168005
$191$	24.0000	0.00909204	0.00454602	−	0.999990i	$-0.498553\pi$
$191$	24.0000	0.00909204	0.00454602	+	0.999990i	$0.498553\pi$
$192$	−192.000	−0.0721688
$193$	758.000	0.282705	0.141352	−	0.989959i	$-0.454855\pi$
$193$	758.000	0.282705	0.141352	+	0.989959i	$0.454855\pi$
$194$	3100.00	1.14725
$195$	−690.000	−0.253394
$196$	196.000	0.0714286
$197$	18.0000	0.00650988	0.00325494	−	0.999995i	$-0.498964\pi$
$197$	18.0000	0.00650988	0.00325494	+	0.999995i	$0.498964\pi$
$198$	−198.000	−0.0710669
$199$	−1780.00	−0.634075	−0.317037	−	0.948413i	$-0.602688\pi$
$199$	−1780.00	−0.634075	−0.317037	+	0.948413i	$0.602688\pi$
$200$	200.000	0.0707107
$201$	−1896.00	−0.665341
$202$	−948.000	−0.330203
$203$	1638.00	0.566330
$204$	1512.00	0.518927
$205$	990.000	0.337291
$206$	−752.000	−0.254341
$207$	−864.000	−0.290107
$208$	−736.000	−0.245348
$209$	−484.000	−0.160187
$210$	210.000	0.0690066
$211$	3188.00	1.04015	0.520073	−	0.854122i	$-0.325905\pi$
$211$	3188.00	1.04015	0.520073	+	0.854122i	$0.325905\pi$
$212$	−120.000	−0.0388756
$213$	3096.00	0.995936
$214$	3288.00	1.05029
$215$	140.000	0.0444089
$216$	−216.000	−0.0680414
$217$	−1204.00	−0.376649
$218$	−4028.00	−1.25142
$219$	2802.00	0.864574
$220$	220.000	0.0674200
$221$	5796.00	1.76417
$222$	−2316.00	−0.700179
$223$	5120.00	1.53749	0.768746	−	0.639555i	$-0.220881\pi$
$223$	5120.00	1.53749	0.768746	+	0.639555i	$0.220881\pi$
$224$	224.000	0.0668153
$225$	225.000	0.0666667
$226$	−684.000	−0.201323
$227$	−5448.00	−1.59294	−0.796468	−	0.604681i	$-0.793301\pi$
$227$	−5448.00	−1.59294	−0.796468	+	0.604681i	$0.793301\pi$
$228$	−528.000	−0.153367
$229$	2354.00	0.679287	0.339643	−	0.940554i	$-0.389694\pi$
$229$	2354.00	0.679287	0.339643	+	0.940554i	$0.389694\pi$
$230$	960.000	0.275220
$231$	231.000	0.0657952
$232$	1872.00	0.529754
$233$	3150.00	0.885680	0.442840	−	0.896601i	$-0.353971\pi$
$233$	3150.00	0.885680	0.442840	+	0.896601i	$0.353971\pi$
$234$	−828.000	−0.231316
$235$	−2280.00	−0.632897
$236$	−432.000	−0.119156
$237$	−2292.00	−0.628192
$238$	−1764.00	−0.480433
$239$	4020.00	1.08800	0.544000	−	0.839085i	$-0.316909\pi$
$239$	4020.00	1.08800	0.544000	+	0.839085i	$0.316909\pi$
$240$	240.000	0.0645497
$241$	6242.00	1.66839	0.834196	−	0.551468i	$-0.185932\pi$
$241$	6242.00	1.66839	0.834196	+	0.551468i	$0.185932\pi$
$242$	242.000	0.0642824
$243$	−243.000	−0.0641500
$244$	1592.00	0.417694
$245$	−245.000	−0.0638877
$246$	1188.00	0.307903
$247$	−2024.00	−0.521393
$248$	−1376.00	−0.352323
$249$	−1944.00	−0.494763
$250$	−250.000	−0.0632456
$251$	1788.00	0.449632	0.224816	−	0.974401i	$-0.427822\pi$
$251$	1788.00	0.449632	0.224816	+	0.974401i	$0.427822\pi$
$252$	252.000	0.0629941
$253$	1056.00	0.262412
$254$	640.000	0.158099
$255$	−1890.00	−0.464143
$256$	256.000	0.0625000
$257$	2982.00	0.723782	0.361891	−	0.932220i	$-0.382131\pi$
$257$	2982.00	0.723782	0.361891	+	0.932220i	$0.382131\pi$
$258$	168.000	0.0405396
$259$	2702.00	0.648240
$260$	920.000	0.219446
$261$	2106.00	0.499456
$262$	−2136.00	−0.503674
$263$	−3024.00	−0.709003	−0.354502	−	0.935055i	$-0.615349\pi$
$263$	−3024.00	−0.709003	−0.354502	+	0.935055i	$0.615349\pi$
$264$	264.000	0.0615457
$265$	150.000	0.0347714
$266$	616.000	0.141990
$267$	1818.00	0.416703
$268$	2528.00	0.576202
$269$	4602.00	1.04308	0.521541	−	0.853226i	$-0.325357\pi$
$269$	4602.00	1.04308	0.521541	+	0.853226i	$0.325357\pi$
$270$	270.000	0.0608581
$271$	1712.00	0.383751	0.191876	−	0.981419i	$-0.438543\pi$
$271$	1712.00	0.383751	0.191876	+	0.981419i	$0.438543\pi$
$272$	−2016.00	−0.449404
$273$	966.000	0.214157
$274$	6180.00	1.36258
$275$	−275.000	−0.0603023
$276$	1152.00	0.251240
$277$	6866.00	1.48931	0.744653	−	0.667451i	$-0.232615\pi$
$277$	6866.00	1.48931	0.744653	+	0.667451i	$0.232615\pi$
$278$	1624.00	0.350363
$279$	−1548.00	−0.332173
$280$	−280.000	−0.0597614
$281$	−7662.00	−1.62661	−0.813304	−	0.581840i	$-0.802333\pi$
$281$	−7662.00	−1.62661	−0.813304	+	0.581840i	$0.802333\pi$
$282$	−2736.00	−0.577753
$283$	4112.00	0.863721	0.431860	−	0.901940i	$-0.357857\pi$
$283$	4112.00	0.863721	0.431860	+	0.901940i	$0.357857\pi$
$284$	−4128.00	−0.862506
$285$	660.000	0.137176
$286$	1012.00	0.209234
$287$	−1386.00	−0.285063
$288$	288.000	0.0589256
$289$	10963.0	2.23143
$290$	−2340.00	−0.473826
$291$	−4650.00	−0.936728
$292$	−3736.00	−0.748743
$293$	1002.00	0.199787	0.0998933	−	0.994998i	$-0.468150\pi$
$293$	1002.00	0.199787	0.0998933	+	0.994998i	$0.468150\pi$
$294$	−294.000	−0.0583212
$295$	540.000	0.106576
$296$	3088.00	0.606373
$297$	297.000	0.0580259
$298$	2292.00	0.445544
$299$	4416.00	0.854127
$300$	−300.000	−0.0577350
$301$	−196.000	−0.0375324
$302$	3208.00	0.611257
$303$	1422.00	0.269610
$304$	704.000	0.132820
$305$	−1990.00	−0.373597
$306$	−2268.00	−0.423702
$307$	−2680.00	−0.498227	−0.249113	−	0.968474i	$-0.580139\pi$
$307$	−2680.00	−0.498227	−0.249113	+	0.968474i	$0.580139\pi$
$308$	−308.000	−0.0569803
$309$	1128.00	0.207669
$310$	1720.00	0.315127
$311$	−3564.00	−0.649826	−0.324913	−	0.945744i	$-0.605335\pi$
$311$	−3564.00	−0.649826	−0.324913	+	0.945744i	$0.605335\pi$
$312$	1104.00	0.200326
$313$	−3370.00	−0.608574	−0.304287	−	0.952580i	$-0.598418\pi$
$313$	−3370.00	−0.608574	−0.304287	+	0.952580i	$0.598418\pi$
$314$	6868.00	1.23434
$315$	−315.000	−0.0563436
$316$	3056.00	0.544030
$317$	5370.00	0.951449	0.475724	−	0.879594i	$-0.342186\pi$
$317$	5370.00	0.951449	0.475724	+	0.879594i	$0.342186\pi$
$318$	180.000	0.0317418
$319$	−2574.00	−0.451775
$320$	−320.000	−0.0559017
$321$	−4932.00	−0.857562
$322$	−1344.00	−0.232603
$323$	−5544.00	−0.955035
$324$	324.000	0.0555556
$325$	−1150.00	−0.196279
$326$	−3584.00	−0.608894
$327$	6042.00	1.02178
$328$	−1584.00	−0.266652
$329$	3192.00	0.534896
$330$	−330.000	−0.0550482
$331$	−4492.00	−0.745929	−0.372965	−	0.927846i	$-0.621659\pi$
$331$	−4492.00	−0.745929	−0.372965	+	0.927846i	$0.621659\pi$
$332$	2592.00	0.428477
$333$	3474.00	0.571694
$334$	−240.000	−0.0393180
$335$	−3160.00	−0.515371
$336$	−336.000	−0.0545545
$337$	2414.00	0.390205	0.195102	−	0.980783i	$-0.437496\pi$
$337$	2414.00	0.390205	0.195102	+	0.980783i	$0.437496\pi$
$338$	−162.000	−0.0260699
$339$	1026.00	0.164380
$340$	2520.00	0.401959
$341$	1892.00	0.300462
$342$	792.000	0.125224
$343$	343.000	0.0539949
$344$	−224.000	−0.0351083
$345$	−1440.00	−0.224716
$346$	8052.00	1.25109
$347$	−7716.00	−1.19371	−0.596854	−	0.802350i	$-0.703583\pi$
$347$	−7716.00	−1.19371	−0.596854	+	0.802350i	$0.703583\pi$
$348$	−2808.00	−0.432542
$349$	2942.00	0.451237	0.225618	−	0.974216i	$-0.427560\pi$
$349$	2942.00	0.451237	0.225618	+	0.974216i	$0.427560\pi$
$350$	350.000	0.0534522
$351$	1242.00	0.188869
$352$	−352.000	−0.0533002
$353$	3510.00	0.529231	0.264615	−	0.964354i	$-0.414755\pi$
$353$	3510.00	0.529231	0.264615	+	0.964354i	$0.414755\pi$
$354$	648.000	0.0972904
$355$	5160.00	0.771449
$356$	−2424.00	−0.360876
$357$	2646.00	0.392272
$358$	−2472.00	−0.364942
$359$	11772.0	1.73065	0.865324	−	0.501213i	$-0.167113\pi$
$359$	11772.0	1.73065	0.865324	+	0.501213i	$0.167113\pi$
$360$	−360.000	−0.0527046
$361$	−4923.00	−0.717743
$362$	1924.00	0.279346
$363$	−363.000	−0.0524864
$364$	−1288.00	−0.185466
$365$	4670.00	0.669696
$366$	−2388.00	−0.341046
$367$	−1960.00	−0.278777	−0.139389	−	0.990238i	$-0.544514\pi$
$367$	−1960.00	−0.278777	−0.139389	+	0.990238i	$0.544514\pi$
$368$	−1536.00	−0.217580
$369$	−1782.00	−0.251402
$370$	−3860.00	−0.542356
$371$	−210.000	−0.0293872
$372$	2064.00	0.287670
$373$	11810.0	1.63941	0.819703	−	0.572788i	$-0.194138\pi$
$373$	11810.0	1.63941	0.819703	+	0.572788i	$0.194138\pi$
$374$	2772.00	0.383253
$375$	375.000	0.0516398
$376$	3648.00	0.500349
$377$	−10764.0	−1.47049
$378$	−378.000	−0.0514344
$379$	−7708.00	−1.04468	−0.522340	−	0.852738i	$-0.674941\pi$
$379$	−7708.00	−1.04468	−0.522340	+	0.852738i	$0.674941\pi$
$380$	−880.000	−0.118797
$381$	−960.000	−0.129087
$382$	48.0000	0.00642904
$383$	−5352.00	−0.714032	−0.357016	−	0.934098i	$-0.616206\pi$
$383$	−5352.00	−0.714032	−0.357016	+	0.934098i	$0.616206\pi$
$384$	−384.000	−0.0510310
$385$	385.000	0.0509647
$386$	1516.00	0.199903
$387$	−252.000	−0.0331005
$388$	6200.00	0.811230
$389$	−3378.00	−0.440286	−0.220143	−	0.975468i	$-0.570652\pi$
$389$	−3378.00	−0.440286	−0.220143	+	0.975468i	$0.570652\pi$
$390$	−1380.00	−0.179177
$391$	12096.0	1.56450
$392$	392.000	0.0505076
$393$	3204.00	0.411248
$394$	36.0000	0.00460318
$395$	−3820.00	−0.486595
$396$	−396.000	−0.0502519
$397$	−15190.0	−1.92031	−0.960156	−	0.279463i	$-0.909844\pi$
$397$	−15190.0	−1.92031	−0.960156	+	0.279463i	$0.909844\pi$
$398$	−3560.00	−0.448358
$399$	−924.000	−0.115934
$400$	400.000	0.0500000
$401$	−11742.0	−1.46226	−0.731132	−	0.682237i	$-0.761007\pi$
$401$	−11742.0	−1.46226	−0.731132	+	0.682237i	$0.761007\pi$
$402$	−3792.00	−0.470467
$403$	7912.00	0.977977
$404$	−1896.00	−0.233489
$405$	−405.000	−0.0496904
$406$	3276.00	0.400456
$407$	−4246.00	−0.517116
$408$	3024.00	0.366937
$409$	−8566.00	−1.03560	−0.517801	−	0.855501i	$-0.673249\pi$
$409$	−8566.00	−1.03560	−0.517801	+	0.855501i	$0.673249\pi$
$410$	1980.00	0.238501
$411$	−9270.00	−1.11254
$412$	−1504.00	−0.179847
$413$	−756.000	−0.0900734
$414$	−1728.00	−0.205137
$415$	−3240.00	−0.383242
$416$	−1472.00	−0.173487
$417$	−2436.00	−0.286071
$418$	−968.000	−0.113269
$419$	4044.00	0.471509	0.235755	−	0.971813i	$-0.424244\pi$
$419$	4044.00	0.471509	0.235755	+	0.971813i	$0.424244\pi$
$420$	420.000	0.0487950
$421$	3134.00	0.362807	0.181404	−	0.983409i	$-0.441936\pi$
$421$	3134.00	0.362807	0.181404	+	0.983409i	$0.441936\pi$
$422$	6376.00	0.735495
$423$	4104.00	0.471734
$424$	−240.000	−0.0274892
$425$	−3150.00	−0.359523
$426$	6192.00	0.704233
$427$	2786.00	0.315747
$428$	6576.00	0.742670
$429$	−1518.00	−0.170839
$430$	280.000	0.0314019
$431$	15156.0	1.69383	0.846913	−	0.531732i	$-0.178459\pi$
$431$	15156.0	1.69383	0.846913	+	0.531732i	$0.178459\pi$
$432$	−432.000	−0.0481125
$433$	−3514.00	−0.390005	−0.195002	−	0.980803i	$-0.562471\pi$
$433$	−3514.00	−0.390005	−0.195002	+	0.980803i	$0.562471\pi$
$434$	−2408.00	−0.266331
$435$	3510.00	0.386877
$436$	−8056.00	−0.884891
$437$	−4224.00	−0.462383
$438$	5604.00	0.611346
$439$	−12616.0	−1.37159	−0.685796	−	0.727794i	$-0.740546\pi$
$439$	−12616.0	−1.37159	−0.685796	+	0.727794i	$0.740546\pi$
$440$	440.000	0.0476731
$441$	441.000	0.0476190
$442$	11592.0	1.24746
$443$	−10968.0	−1.17631	−0.588155	−	0.808748i	$-0.700146\pi$
$443$	−10968.0	−1.17631	−0.588155	+	0.808748i	$0.700146\pi$
$444$	−4632.00	−0.495101
$445$	3030.00	0.322777
$446$	10240.0	1.08717
$447$	−3438.00	−0.363785
$448$	448.000	0.0472456
$449$	11682.0	1.22786	0.613928	−	0.789362i	$-0.289588\pi$
$449$	11682.0	1.22786	0.613928	+	0.789362i	$0.289588\pi$
$450$	450.000	0.0471405
$451$	2178.00	0.227401
$452$	−1368.00	−0.142357
$453$	−4812.00	−0.499089
$454$	−10896.0	−1.12638
$455$	1610.00	0.165886
$456$	−1056.00	−0.108447
$457$	1334.00	0.136547	0.0682734	−	0.997667i	$-0.478251\pi$
$457$	1334.00	0.136547	0.0682734	+	0.997667i	$0.478251\pi$
$458$	4708.00	0.480328
$459$	3402.00	0.345952
$460$	1920.00	0.194610
$461$	−9354.00	−0.945031	−0.472515	−	0.881322i	$-0.656654\pi$
$461$	−9354.00	−0.945031	−0.472515	+	0.881322i	$0.656654\pi$
$462$	462.000	0.0465242
$463$	9344.00	0.937910	0.468955	−	0.883222i	$-0.344631\pi$
$463$	9344.00	0.937910	0.468955	+	0.883222i	$0.344631\pi$
$464$	3744.00	0.374592
$465$	−2580.00	−0.257300
$466$	6300.00	0.626270
$467$	6204.00	0.614747	0.307374	−	0.951589i	$-0.400550\pi$
$467$	6204.00	0.614747	0.307374	+	0.951589i	$0.400550\pi$
$468$	−1656.00	−0.163565
$469$	4424.00	0.435568
$470$	−4560.00	−0.447526
$471$	−10302.0	−1.00784
$472$	−864.000	−0.0842560
$473$	308.000	0.0299405
$474$	−4584.00	−0.444199
$475$	1100.00	0.106256
$476$	−3528.00	−0.339718
$477$	−270.000	−0.0259171
$478$	8040.00	0.769333
$479$	9480.00	0.904284	0.452142	−	0.891946i	$-0.350660\pi$
$479$	9480.00	0.904284	0.452142	+	0.891946i	$0.350660\pi$
$480$	480.000	0.0456435
$481$	−17756.0	−1.68317
$482$	12484.0	1.17973
$483$	2016.00	0.189920
$484$	484.000	0.0454545
$485$	−7750.00	−0.725586
$486$	−486.000	−0.0453609
$487$	15848.0	1.47462	0.737312	−	0.675553i	$-0.236095\pi$
$487$	15848.0	1.47462	0.737312	+	0.675553i	$0.236095\pi$
$488$	3184.00	0.295354
$489$	5376.00	0.497160
$490$	−490.000	−0.0451754
$491$	20700.0	1.90260	0.951301	−	0.308262i	$-0.0997475\pi$
$491$	20700.0	1.90260	0.951301	+	0.308262i	$0.0997475\pi$
$492$	2376.00	0.217720
$493$	−29484.0	−2.69349
$494$	−4048.00	−0.368680
$495$	495.000	0.0449467
$496$	−2752.00	−0.249130
$497$	−7224.00	−0.651993
$498$	−3888.00	−0.349850
$499$	−7684.00	−0.689345	−0.344672	−	0.938723i	$-0.612010\pi$
$499$	−7684.00	−0.689345	−0.344672	+	0.938723i	$0.612010\pi$
$500$	−500.000	−0.0447214
$501$	360.000	0.0321030
$502$	3576.00	0.317938
$503$	−4320.00	−0.382941	−0.191470	−	0.981498i	$-0.561326\pi$
$503$	−4320.00	−0.382941	−0.191470	+	0.981498i	$0.561326\pi$
$504$	504.000	0.0445435
$505$	2370.00	0.208839
$506$	2112.00	0.185553
$507$	243.000	0.0212860
$508$	1280.00	0.111793
$509$	−1062.00	−0.0924800	−0.0462400	−	0.998930i	$-0.514724\pi$
$509$	−1062.00	−0.0924800	−0.0462400	+	0.998930i	$0.514724\pi$
$510$	−3780.00	−0.328198
$511$	−6538.00	−0.565996
$512$	512.000	0.0441942
$513$	−1188.00	−0.102245
$514$	5964.00	0.511791
$515$	1880.00	0.160860
$516$	336.000	0.0286658
$517$	−5016.00	−0.426699
$518$	5404.00	0.458375
$519$	−12078.0	−1.02151
$520$	1840.00	0.155172
$521$	−414.000	−0.0348132	−0.0174066	−	0.999848i	$-0.505541\pi$
$521$	−414.000	−0.0348132	−0.0174066	+	0.999848i	$0.505541\pi$
$522$	4212.00	0.353169
$523$	10064.0	0.841430	0.420715	−	0.907193i	$-0.361779\pi$
$523$	10064.0	0.841430	0.420715	+	0.907193i	$0.361779\pi$
$524$	−4272.00	−0.356151
$525$	−525.000	−0.0436436
$526$	−6048.00	−0.501341
$527$	21672.0	1.79136
$528$	528.000	0.0435194
$529$	−2951.00	−0.242541
$530$	300.000	0.0245871
$531$	−972.000	−0.0794373
$532$	1232.00	0.100402
$533$	9108.00	0.740171
$534$	3636.00	0.294654
$535$	−8220.00	−0.664265
$536$	5056.00	0.407436
$537$	3708.00	0.297974
$538$	9204.00	0.737570
$539$	−539.000	−0.0430730
$540$	540.000	0.0430331
$541$	−15382.0	−1.22241	−0.611205	−	0.791472i	$-0.709315\pi$
$541$	−15382.0	−1.22241	−0.611205	+	0.791472i	$0.709315\pi$
$542$	3424.00	0.271353
$543$	−2886.00	−0.228085
$544$	−4032.00	−0.317777
$545$	10070.0	0.791470
$546$	1932.00	0.151432
$547$	−9700.00	−0.758212	−0.379106	−	0.925353i	$-0.623768\pi$
$547$	−9700.00	−0.758212	−0.379106	+	0.925353i	$0.623768\pi$
$548$	12360.0	0.963491
$549$	3582.00	0.278463
$550$	−550.000	−0.0426401
$551$	10296.0	0.796051
$552$	2304.00	0.177654
$553$	5348.00	0.411248
$554$	13732.0	1.05310
$555$	5790.00	0.442832
$556$	3248.00	0.247744
$557$	−23814.0	−1.81155	−0.905773	−	0.423762i	$-0.860709\pi$
$557$	−23814.0	−1.81155	−0.905773	+	0.423762i	$0.860709\pi$
$558$	−3096.00	−0.234882
$559$	1288.00	0.0974537
$560$	−560.000	−0.0422577
$561$	−4158.00	−0.312925
$562$	−15324.0	−1.15018
$563$	15936.0	1.19293	0.596467	−	0.802637i	$-0.296570\pi$
$563$	15936.0	1.19293	0.596467	+	0.802637i	$0.296570\pi$
$564$	−5472.00	−0.408533
$565$	1710.00	0.127328
$566$	8224.00	0.610743
$567$	567.000	0.0419961
$568$	−8256.00	−0.609884
$569$	6498.00	0.478753	0.239376	−	0.970927i	$-0.423057\pi$
$569$	6498.00	0.478753	0.239376	+	0.970927i	$0.423057\pi$
$570$	1320.00	0.0969977
$571$	−4588.00	−0.336255	−0.168128	−	0.985765i	$-0.553772\pi$
$571$	−4588.00	−0.336255	−0.168128	+	0.985765i	$0.553772\pi$
$572$	2024.00	0.147951
$573$	−72.0000	−0.00524929
$574$	−2772.00	−0.201570
$575$	−2400.00	−0.174064
$576$	576.000	0.0416667
$577$	6518.00	0.470274	0.235137	−	0.971962i	$-0.424446\pi$
$577$	6518.00	0.470274	0.235137	+	0.971962i	$0.424446\pi$
$578$	21926.0	1.57786
$579$	−2274.00	−0.163220
$580$	−4680.00	−0.335046
$581$	4536.00	0.323898
$582$	−9300.00	−0.662367
$583$	330.000	0.0234429
$584$	−7472.00	−0.529441
$585$	2070.00	0.146297
$586$	2004.00	0.141270
$587$	10716.0	0.753487	0.376743	−	0.926318i	$-0.377044\pi$
$587$	10716.0	0.753487	0.376743	+	0.926318i	$0.377044\pi$
$588$	−588.000	−0.0412393
$589$	−7568.00	−0.529430
$590$	1080.00	0.0753608
$591$	−54.0000	−0.00375848
$592$	6176.00	0.428770
$593$	−8622.00	−0.597071	−0.298536	−	0.954399i	$-0.596498\pi$
$593$	−8622.00	−0.597071	−0.298536	+	0.954399i	$0.596498\pi$
$594$	594.000	0.0410305
$595$	4410.00	0.303853
$596$	4584.00	0.315047
$597$	5340.00	0.366083
$598$	8832.00	0.603959
$599$	−5496.00	−0.374892	−0.187446	−	0.982275i	$-0.560021\pi$
$599$	−5496.00	−0.374892	−0.187446	+	0.982275i	$0.560021\pi$
$600$	−600.000	−0.0408248
$601$	986.000	0.0669214	0.0334607	−	0.999440i	$-0.489347\pi$
$601$	986.000	0.0669214	0.0334607	+	0.999440i	$0.489347\pi$
$602$	−392.000	−0.0265394
$603$	5688.00	0.384135
$604$	6416.00	0.432224
$605$	−605.000	−0.0406558
$606$	2844.00	0.190643
$607$	10064.0	0.672957	0.336479	−	0.941691i	$-0.390764\pi$
$607$	10064.0	0.672957	0.336479	+	0.941691i	$0.390764\pi$
$608$	1408.00	0.0939177
$609$	−4914.00	−0.326971
$610$	−3980.00	−0.264173
$611$	−20976.0	−1.38887
$612$	−4536.00	−0.299603
$613$	3746.00	0.246818	0.123409	−	0.992356i	$-0.460617\pi$
$613$	3746.00	0.246818	0.123409	+	0.992356i	$0.460617\pi$
$614$	−5360.00	−0.352300
$615$	−2970.00	−0.194735
$616$	−616.000	−0.0402911
$617$	−14454.0	−0.943106	−0.471553	−	0.881838i	$-0.656306\pi$
$617$	−14454.0	−0.943106	−0.471553	+	0.881838i	$0.656306\pi$
$618$	2256.00	0.146844
$619$	9956.00	0.646471	0.323235	−	0.946319i	$-0.395229\pi$
$619$	9956.00	0.646471	0.323235	+	0.946319i	$0.395229\pi$
$620$	3440.00	0.222829
$621$	2592.00	0.167493
$622$	−7128.00	−0.459496
$623$	−4242.00	−0.272796
$624$	2208.00	0.141652
$625$	625.000	0.0400000
$626$	−6740.00	−0.430327
$627$	1452.00	0.0924837
$628$	13736.0	0.872812
$629$	−48636.0	−3.08306
$630$	−630.000	−0.0398410
$631$	−7960.00	−0.502191	−0.251096	−	0.967962i	$-0.580791\pi$
$631$	−7960.00	−0.502191	−0.251096	+	0.967962i	$0.580791\pi$
$632$	6112.00	0.384687
$633$	−9564.00	−0.600529
$634$	10740.0	0.672776
$635$	−1600.00	−0.0999907
$636$	360.000	0.0224449
$637$	−2254.00	−0.140199
$638$	−5148.00	−0.319453
$639$	−9288.00	−0.575004
$640$	−640.000	−0.0395285
$641$	−9390.00	−0.578600	−0.289300	−	0.957238i	$-0.593423\pi$
$641$	−9390.00	−0.578600	−0.289300	+	0.957238i	$0.593423\pi$
$642$	−9864.00	−0.606388
$643$	16076.0	0.985965	0.492983	−	0.870039i	$-0.335907\pi$
$643$	16076.0	0.985965	0.492983	+	0.870039i	$0.335907\pi$
$644$	−2688.00	−0.164475
$645$	−420.000	−0.0256395
$646$	−11088.0	−0.675312
$647$	−16824.0	−1.02229	−0.511144	−	0.859495i	$-0.670778\pi$
$647$	−16824.0	−1.02229	−0.511144	+	0.859495i	$0.670778\pi$
$648$	648.000	0.0392837
$649$	1188.00	0.0718537
$650$	−2300.00	−0.138790
$651$	3612.00	0.217458
$652$	−7168.00	−0.430553
$653$	−13518.0	−0.810108	−0.405054	−	0.914293i	$-0.632747\pi$
$653$	−13518.0	−0.810108	−0.405054	+	0.914293i	$0.632747\pi$
$654$	12084.0	0.722510
$655$	5340.00	0.318551
$656$	−3168.00	−0.188551
$657$	−8406.00	−0.499162
$658$	6384.00	0.378228
$659$	28428.0	1.68042	0.840211	−	0.542260i	$-0.182431\pi$
$659$	28428.0	1.68042	0.840211	+	0.542260i	$0.182431\pi$
$660$	−660.000	−0.0389249
$661$	−10798.0	−0.635391	−0.317696	−	0.948193i	$-0.602909\pi$
$661$	−10798.0	−0.635391	−0.317696	+	0.948193i	$0.602909\pi$
$662$	−8984.00	−0.527452
$663$	−17388.0	−1.01854
$664$	5184.00	0.302979
$665$	−1540.00	−0.0898025
$666$	6948.00	0.404249
$667$	−22464.0	−1.30406
$668$	−480.000	−0.0278020
$669$	−15360.0	−0.887671
$670$	−6320.00	−0.364422
$671$	−4378.00	−0.251879
$672$	−672.000	−0.0385758
$673$	23822.0	1.36444	0.682222	−	0.731145i	$-0.261014\pi$
$673$	23822.0	1.36444	0.682222	+	0.731145i	$0.261014\pi$
$674$	4828.00	0.275916
$675$	−675.000	−0.0384900
$676$	−324.000	−0.0184342
$677$	−7782.00	−0.441782	−0.220891	−	0.975298i	$-0.570897\pi$
$677$	−7782.00	−0.441782	−0.220891	+	0.975298i	$0.570897\pi$
$678$	2052.00	0.116234
$679$	10850.0	0.613232
$680$	5040.00	0.284228
$681$	16344.0	0.919682
$682$	3784.00	0.212459
$683$	6552.00	0.367065	0.183532	−	0.983014i	$-0.441247\pi$
$683$	6552.00	0.367065	0.183532	+	0.983014i	$0.441247\pi$
$684$	1584.00	0.0885464
$685$	−15450.0	−0.861772
$686$	686.000	0.0381802
$687$	−7062.00	−0.392186
$688$	−448.000	−0.0248253
$689$	1380.00	0.0763045
$690$	−2880.00	−0.158898
$691$	32108.0	1.76765	0.883825	−	0.467818i	$-0.154960\pi$
$691$	32108.0	1.76765	0.883825	+	0.467818i	$0.154960\pi$
$692$	16104.0	0.884656
$693$	−693.000	−0.0379869
$694$	−15432.0	−0.844079
$695$	−4060.00	−0.221589
$696$	−5616.00	−0.305853
$697$	24948.0	1.35577
$698$	5884.00	0.319073
$699$	−9450.00	−0.511347
$700$	700.000	0.0377964
$701$	−26142.0	−1.40852	−0.704258	−	0.709944i	$-0.748720\pi$
$701$	−26142.0	−1.40852	−0.704258	+	0.709944i	$0.748720\pi$
$702$	2484.00	0.133551
$703$	16984.0	0.911186
$704$	−704.000	−0.0376889
$705$	6840.00	0.365403
$706$	7020.00	0.374223
$707$	−3318.00	−0.176501
$708$	1296.00	0.0687947
$709$	27374.0	1.45000	0.725002	−	0.688747i	$-0.241839\pi$
$709$	27374.0	1.45000	0.725002	+	0.688747i	$0.241839\pi$
$710$	10320.0	0.545497
$711$	6876.00	0.362687
$712$	−4848.00	−0.255178
$713$	16512.0	0.867292
$714$	5292.00	0.277378
$715$	−2530.00	−0.132331
$716$	−4944.00	−0.258053
$717$	−12060.0	−0.628158
$718$	23544.0	1.22375
$719$	−1020.00	−0.0529062	−0.0264531	−	0.999650i	$-0.508421\pi$
$719$	−1020.00	−0.0529062	−0.0264531	+	0.999650i	$0.508421\pi$
$720$	−720.000	−0.0372678
$721$	−2632.00	−0.135951
$722$	−9846.00	−0.507521
$723$	−18726.0	−0.963247
$724$	3848.00	0.197527
$725$	5850.00	0.299674
$726$	−726.000	−0.0371135
$727$	11792.0	0.601570	0.300785	−	0.953692i	$-0.402751\pi$
$727$	11792.0	0.601570	0.300785	+	0.953692i	$0.402751\pi$
$728$	−2576.00	−0.131144
$729$	729.000	0.0370370
$730$	9340.00	0.473546
$731$	3528.00	0.178506
$732$	−4776.00	−0.241156
$733$	20234.0	1.01959	0.509795	−	0.860296i	$-0.329721\pi$
$733$	20234.0	1.01959	0.509795	+	0.860296i	$0.329721\pi$
$734$	−3920.00	−0.197125
$735$	735.000	0.0368856
$736$	−3072.00	−0.153852
$737$	−6952.00	−0.347463
$738$	−3564.00	−0.177768
$739$	−6724.00	−0.334704	−0.167352	−	0.985897i	$-0.553522\pi$
$739$	−6724.00	−0.334704	−0.167352	+	0.985897i	$0.553522\pi$
$740$	−7720.00	−0.383504
$741$	6072.00	0.301026
$742$	−420.000	−0.0207799
$743$	−21144.0	−1.04401	−0.522004	−	0.852943i	$-0.674815\pi$
$743$	−21144.0	−1.04401	−0.522004	+	0.852943i	$0.674815\pi$
$744$	4128.00	0.203414
$745$	−5730.00	−0.281787
$746$	23620.0	1.15924
$747$	5832.00	0.285652
$748$	5544.00	0.271001
$749$	11508.0	0.561406
$750$	750.000	0.0365148
$751$	1112.00	0.0540312	0.0270156	−	0.999635i	$-0.491400\pi$
$751$	1112.00	0.0540312	0.0270156	+	0.999635i	$0.491400\pi$
$752$	7296.00	0.353800
$753$	−5364.00	−0.259595
$754$	−21528.0	−1.03979
$755$	−8020.00	−0.386593
$756$	−756.000	−0.0363696
$757$	31682.0	1.52114	0.760569	−	0.649257i	$-0.224920\pi$
$757$	31682.0	1.52114	0.760569	+	0.649257i	$0.224920\pi$
$758$	−15416.0	−0.738700
$759$	−3168.00	−0.151503
$760$	−1760.00	−0.0840025
$761$	−9990.00	−0.475870	−0.237935	−	0.971281i	$-0.576471\pi$
$761$	−9990.00	−0.475870	−0.237935	+	0.971281i	$0.576471\pi$
$762$	−1920.00	−0.0912786
$763$	−14098.0	−0.668915
$764$	96.0000	0.00454602
$765$	5670.00	0.267973
$766$	−10704.0	−0.504897
$767$	4968.00	0.233878
$768$	−768.000	−0.0360844
$769$	−38974.0	−1.82762	−0.913809	−	0.406144i	$-0.866873\pi$
$769$	−38974.0	−1.82762	−0.913809	+	0.406144i	$0.866873\pi$
$770$	770.000	0.0360375
$771$	−8946.00	−0.417876
$772$	3032.00	0.141352
$773$	1794.00	0.0834744	0.0417372	−	0.999129i	$-0.486711\pi$
$773$	1794.00	0.0834744	0.0417372	+	0.999129i	$0.486711\pi$
$774$	−504.000	−0.0234056
$775$	−4300.00	−0.199304
$776$	12400.0	0.573626
$777$	−8106.00	−0.374261
$778$	−6756.00	−0.311329
$779$	−8712.00	−0.400693
$780$	−2760.00	−0.126697
$781$	11352.0	0.520111
$782$	24192.0	1.10627
$783$	−6318.00	−0.288361
$784$	784.000	0.0357143
$785$	−17170.0	−0.780667
$786$	6408.00	0.290796
$787$	−29896.0	−1.35410	−0.677050	−	0.735937i	$-0.736742\pi$
$787$	−29896.0	−1.35410	−0.677050	+	0.735937i	$0.736742\pi$
$788$	72.0000	0.00325494
$789$	9072.00	0.409343
$790$	−7640.00	−0.344075
$791$	−2394.00	−0.107612
$792$	−792.000	−0.0355335
$793$	−18308.0	−0.819844
$794$	−30380.0	−1.35787
$795$	−450.000	−0.0200753
$796$	−7120.00	−0.317037
$797$	−1734.00	−0.0770658	−0.0385329	−	0.999257i	$-0.512268\pi$
$797$	−1734.00	−0.0770658	−0.0385329	+	0.999257i	$0.512268\pi$
$798$	−1848.00	−0.0819781
$799$	−57456.0	−2.54399
$800$	800.000	0.0353553
$801$	−5454.00	−0.240584
$802$	−23484.0	−1.03398
$803$	10274.0	0.451509
$804$	−7584.00	−0.332670
$805$	3360.00	0.147111
$806$	15824.0	0.691534
$807$	−13806.0	−0.602223
$808$	−3792.00	−0.165102
$809$	−12054.0	−0.523852	−0.261926	−	0.965088i	$-0.584358\pi$
$809$	−12054.0	−0.523852	−0.261926	+	0.965088i	$0.584358\pi$
$810$	−810.000	−0.0351364
$811$	−23308.0	−1.00919	−0.504596	−	0.863356i	$-0.668359\pi$
$811$	−23308.0	−1.00919	−0.504596	+	0.863356i	$0.668359\pi$
$812$	6552.00	0.283165
$813$	−5136.00	−0.221559
$814$	−8492.00	−0.365657
$815$	8960.00	0.385098
$816$	6048.00	0.259464
$817$	−1232.00	−0.0527567
$818$	−17132.0	−0.732282
$819$	−2898.00	−0.123644
$820$	3960.00	0.168645
$821$	−9558.00	−0.406305	−0.203153	−	0.979147i	$-0.565119\pi$
$821$	−9558.00	−0.406305	−0.203153	+	0.979147i	$0.565119\pi$
$822$	−18540.0	−0.786687
$823$	23960.0	1.01482	0.507408	−	0.861706i	$-0.330604\pi$
$823$	23960.0	1.01482	0.507408	+	0.861706i	$0.330604\pi$
$824$	−3008.00	−0.127171
$825$	825.000	0.0348155
$826$	−1512.00	−0.0636915
$827$	−4500.00	−0.189214	−0.0946072	−	0.995515i	$-0.530160\pi$
$827$	−4500.00	−0.189214	−0.0946072	+	0.995515i	$0.530160\pi$
$828$	−3456.00	−0.145054
$829$	−38038.0	−1.59362	−0.796812	−	0.604227i	$-0.793482\pi$
$829$	−38038.0	−1.59362	−0.796812	+	0.604227i	$0.793482\pi$
$830$	−6480.00	−0.270993
$831$	−20598.0	−0.859852
$832$	−2944.00	−0.122674
$833$	−6174.00	−0.256802
$834$	−4872.00	−0.202282
$835$	600.000	0.0248669
$836$	−1936.00	−0.0800933
$837$	4644.00	0.191780
$838$	8088.00	0.333407
$839$	−2436.00	−0.100238	−0.0501192	−	0.998743i	$-0.515960\pi$
$839$	−2436.00	−0.100238	−0.0501192	+	0.998743i	$0.515960\pi$
$840$	840.000	0.0345033
$841$	30367.0	1.24511
$842$	6268.00	0.256543
$843$	22986.0	0.939122
$844$	12752.0	0.520073
$845$	405.000	0.0164881
$846$	8208.00	0.333566
$847$	847.000	0.0343604
$848$	−480.000	−0.0194378
$849$	−12336.0	−0.498670
$850$	−6300.00	−0.254221
$851$	−37056.0	−1.49267
$852$	12384.0	0.497968
$853$	−2878.00	−0.115523	−0.0577613	−	0.998330i	$-0.518396\pi$
$853$	−2878.00	−0.115523	−0.0577613	+	0.998330i	$0.518396\pi$
$854$	5572.00	0.223267
$855$	−1980.00	−0.0791983
$856$	13152.0	0.525147
$857$	9234.00	0.368060	0.184030	−	0.982921i	$-0.441086\pi$
$857$	9234.00	0.368060	0.184030	+	0.982921i	$0.441086\pi$
$858$	−3036.00	−0.120801
$859$	12140.0	0.482202	0.241101	−	0.970500i	$-0.422492\pi$
$859$	12140.0	0.482202	0.241101	+	0.970500i	$0.422492\pi$
$860$	560.000	0.0222045
$861$	4158.00	0.164581
$862$	30312.0	1.19772
$863$	16368.0	0.645624	0.322812	−	0.946463i	$-0.395372\pi$
$863$	16368.0	0.645624	0.322812	+	0.946463i	$0.395372\pi$
$864$	−864.000	−0.0340207
$865$	−20130.0	−0.791261
$866$	−7028.00	−0.275775
$867$	−32889.0	−1.28831
$868$	−4816.00	−0.188325
$869$	−8404.00	−0.328062
$870$	7020.00	0.273564
$871$	−29072.0	−1.13096
$872$	−16112.0	−0.625712
$873$	13950.0	0.540820
$874$	−8448.00	−0.326954
$875$	−875.000	−0.0338062
$876$	11208.0	0.432287
$877$	14666.0	0.564693	0.282346	−	0.959313i	$-0.408887\pi$
$877$	14666.0	0.564693	0.282346	+	0.959313i	$0.408887\pi$
$878$	−25232.0	−0.969862
$879$	−3006.00	−0.115347
$880$	880.000	0.0337100
$881$	−29958.0	−1.14564	−0.572821	−	0.819680i	$-0.694151\pi$
$881$	−29958.0	−1.14564	−0.572821	+	0.819680i	$0.694151\pi$
$882$	882.000	0.0336718
$883$	−9160.00	−0.349104	−0.174552	−	0.984648i	$-0.555848\pi$
$883$	−9160.00	−0.349104	−0.174552	+	0.984648i	$0.555848\pi$
$884$	23184.0	0.882084
$885$	−1620.00	−0.0615319
$886$	−21936.0	−0.831777
$887$	−50400.0	−1.90785	−0.953927	−	0.300039i	$-0.903000\pi$
$887$	−50400.0	−1.90785	−0.953927	+	0.300039i	$0.903000\pi$
$888$	−9264.00	−0.350090
$889$	2240.00	0.0845075
$890$	6060.00	0.228238
$891$	−891.000	−0.0335013
$892$	20480.0	0.768746
$893$	20064.0	0.751866
$894$	−6876.00	−0.257235
$895$	6180.00	0.230810
$896$	896.000	0.0334077
$897$	−13248.0	−0.493130
$898$	23364.0	0.868226
$899$	−40248.0	−1.49315
$900$	900.000	0.0333333
$901$	3780.00	0.139767
$902$	4356.00	0.160797
$903$	588.000	0.0216693
$904$	−2736.00	−0.100662
$905$	−4810.00	−0.176674
$906$	−9624.00	−0.352909
$907$	−40792.0	−1.49336	−0.746679	−	0.665184i	$-0.768353\pi$
$907$	−40792.0	−1.49336	−0.746679	+	0.665184i	$0.768353\pi$
$908$	−21792.0	−0.796468
$909$	−4266.00	−0.155659
$910$	3220.00	0.117299
$911$	5904.00	0.214718	0.107359	−	0.994220i	$-0.465761\pi$
$911$	5904.00	0.214718	0.107359	+	0.994220i	$0.465761\pi$
$912$	−2112.00	−0.0766835
$913$	−7128.00	−0.258382
$914$	2668.00	0.0965532
$915$	5970.00	0.215696
$916$	9416.00	0.339643
$917$	−7476.00	−0.269225
$918$	6804.00	0.244625
$919$	23204.0	0.832894	0.416447	−	0.909160i	$-0.363275\pi$
$919$	23204.0	0.832894	0.416447	+	0.909160i	$0.363275\pi$
$920$	3840.00	0.137610
$921$	8040.00	0.287651
$922$	−18708.0	−0.668238
$923$	47472.0	1.69291
$924$	924.000	0.0328976
$925$	9650.00	0.343016
$926$	18688.0	0.663203
$927$	−3384.00	−0.119898
$928$	7488.00	0.264877
$929$	15546.0	0.549029	0.274514	−	0.961583i	$-0.411483\pi$
$929$	15546.0	0.549029	0.274514	+	0.961583i	$0.411483\pi$
$930$	−5160.00	−0.181939
$931$	2156.00	0.0758969
$932$	12600.0	0.442840
$933$	10692.0	0.375177
$934$	12408.0	0.434692
$935$	−6930.00	−0.242391
$936$	−3312.00	−0.115658
$937$	18794.0	0.655254	0.327627	−	0.944807i	$-0.393751\pi$
$937$	18794.0	0.655254	0.327627	+	0.944807i	$0.393751\pi$
$938$	8848.00	0.307993
$939$	10110.0	0.351360
$940$	−9120.00	−0.316449
$941$	−36234.0	−1.25525	−0.627627	−	0.778514i	$-0.715974\pi$
$941$	−36234.0	−1.25525	−0.627627	+	0.778514i	$0.715974\pi$
$942$	−20604.0	−0.712648
$943$	19008.0	0.656400
$944$	−1728.00	−0.0595780
$945$	945.000	0.0325300
$946$	616.000	0.0211711
$947$	−16176.0	−0.555068	−0.277534	−	0.960716i	$-0.589517\pi$
$947$	−16176.0	−0.555068	−0.277534	+	0.960716i	$0.589517\pi$
$948$	−9168.00	−0.314096
$949$	42964.0	1.46962
$950$	2200.00	0.0751341
$951$	−16110.0	−0.549319
$952$	−7056.00	−0.240217
$953$	54342.0	1.84712	0.923562	−	0.383448i	$-0.125263\pi$
$953$	54342.0	1.84712	0.923562	+	0.383448i	$0.125263\pi$
$954$	−540.000	−0.0183261
$955$	−120.000	−0.00406608
$956$	16080.0	0.544000
$957$	7722.00	0.260833
$958$	18960.0	0.639426
$959$	21630.0	0.728331
$960$	960.000	0.0322749
$961$	−207.000	−0.00694841
$962$	−35512.0	−1.19018
$963$	14796.0	0.495114
$964$	24968.0	0.834196
$965$	−3790.00	−0.126429
$966$	4032.00	0.134293
$967$	−18880.0	−0.627859	−0.313930	−	0.949446i	$-0.601646\pi$
$967$	−18880.0	−0.627859	−0.313930	+	0.949446i	$0.601646\pi$
$968$	968.000	0.0321412
$969$	16632.0	0.551390
$970$	−15500.0	−0.513067
$971$	7788.00	0.257393	0.128697	−	0.991684i	$-0.458921\pi$
$971$	7788.00	0.257393	0.128697	+	0.991684i	$0.458921\pi$
$972$	−972.000	−0.0320750
$973$	5684.00	0.187277
$974$	31696.0	1.04272
$975$	3450.00	0.113321
$976$	6368.00	0.208847
$977$	39498.0	1.29340	0.646701	−	0.762744i	$-0.276148\pi$
$977$	39498.0	1.29340	0.646701	+	0.762744i	$0.276148\pi$
$978$	10752.0	0.351545
$979$	6666.00	0.217616
$980$	−980.000	−0.0319438
$981$	−18126.0	−0.589927
$982$	41400.0	1.34534
$983$	−1464.00	−0.0475019	−0.0237509	−	0.999718i	$-0.507561\pi$
$983$	−1464.00	−0.0475019	−0.0237509	+	0.999718i	$0.507561\pi$
$984$	4752.00	0.153951
$985$	−90.0000	−0.00291131
$986$	−58968.0	−1.90459
$987$	−9576.00	−0.308822
$988$	−8096.00	−0.260696
$989$	2688.00	0.0864241
$990$	990.000	0.0317821
$991$	31952.0	1.02421	0.512103	−	0.858924i	$-0.328866\pi$
$991$	31952.0	1.02421	0.512103	+	0.858924i	$0.328866\pi$
$992$	−5504.00	−0.176161
$993$	13476.0	0.430663
$994$	−14448.0	−0.461029
$995$	8900.00	0.283567
$996$	−7776.00	−0.247382
$997$	49754.0	1.58047	0.790233	−	0.612806i	$-0.209959\pi$
$997$	49754.0	1.58047	0.790233	+	0.612806i	$0.209959\pi$
$998$	−15368.0	−0.487440
$999$	−10422.0	−0.330068

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2310.4.a.f.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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