LMFDB - Embedded newform 1155.4.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,4,Mod(1,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, 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("1155.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1155.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:	$68.1472060566$
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	$\chi$	$=$	1155.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +3.00000 q^{3} -7.00000 q^{4} +5.00000 q^{5} +3.00000 q^{6} -7.00000 q^{7} -15.0000 q^{8} +9.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} +3.00000 q^{3} -7.00000 q^{4} +5.00000 q^{5} +3.00000 q^{6} -7.00000 q^{7} -15.0000 q^{8} +9.00000 q^{9} +5.00000 q^{10} +11.0000 q^{11} -21.0000 q^{12} +54.0000 q^{13} -7.00000 q^{14} +15.0000 q^{15} +41.0000 q^{16} -78.0000 q^{17} +9.00000 q^{18} -148.000 q^{19} -35.0000 q^{20} -21.0000 q^{21} +11.0000 q^{22} +200.000 q^{23} -45.0000 q^{24} +25.0000 q^{25} +54.0000 q^{26} +27.0000 q^{27} +49.0000 q^{28} -218.000 q^{29} +15.0000 q^{30} -304.000 q^{31} +161.000 q^{32} +33.0000 q^{33} -78.0000 q^{34} -35.0000 q^{35} -63.0000 q^{36} +126.000 q^{37} -148.000 q^{38} +162.000 q^{39} -75.0000 q^{40} +58.0000 q^{41} -21.0000 q^{42} +532.000 q^{43} -77.0000 q^{44} +45.0000 q^{45} +200.000 q^{46} -368.000 q^{47} +123.000 q^{48} +49.0000 q^{49} +25.0000 q^{50} -234.000 q^{51} -378.000 q^{52} +222.000 q^{53} +27.0000 q^{54} +55.0000 q^{55} +105.000 q^{56} -444.000 q^{57} -218.000 q^{58} -204.000 q^{59} -105.000 q^{60} -666.000 q^{61} -304.000 q^{62} -63.0000 q^{63} -167.000 q^{64} +270.000 q^{65} +33.0000 q^{66} -356.000 q^{67} +546.000 q^{68} +600.000 q^{69} -35.0000 q^{70} +312.000 q^{71} -135.000 q^{72} -726.000 q^{73} +126.000 q^{74} +75.0000 q^{75} +1036.00 q^{76} -77.0000 q^{77} +162.000 q^{78} -512.000 q^{79} +205.000 q^{80} +81.0000 q^{81} +58.0000 q^{82} -1332.00 q^{83} +147.000 q^{84} -390.000 q^{85} +532.000 q^{86} -654.000 q^{87} -165.000 q^{88} -742.000 q^{89} +45.0000 q^{90} -378.000 q^{91} -1400.00 q^{92} -912.000 q^{93} -368.000 q^{94} -740.000 q^{95} +483.000 q^{96} +514.000 q^{97} +49.0000 q^{98} +99.0000 q^{99} +O(q^{100})\)

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 $

$2$	1.00000	0.353553	0.176777	−	0.984251i	$-0.443433\pi$
$2$	1.00000	0.353553	0.176777	+	0.984251i	$0.443433\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−7.00000	−0.875000
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	3.00000	0.204124
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	−15.0000	−0.662913
$9$	9.00000	0.333333
$10$	5.00000	0.158114
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−21.0000	−0.505181
$13$	54.0000	1.15207	0.576035	−	0.817425i	$-0.304599\pi$
$13$	54.0000	1.15207	0.576035	+	0.817425i	$0.304599\pi$
$14$	−7.00000	−0.133631
$15$	15.0000	0.258199
$16$	41.0000	0.640625
$17$	−78.0000	−1.11281	−0.556405	−	0.830911i	$-0.687820\pi$
$17$	−78.0000	−1.11281	−0.556405	+	0.830911i	$0.687820\pi$
$18$	9.00000	0.117851
$19$	−148.000	−1.78703	−0.893514	−	0.449036i	$-0.851768\pi$
$19$	−148.000	−1.78703	−0.893514	+	0.449036i	$0.851768\pi$
$20$	−35.0000	−0.391312
$21$	−21.0000	−0.218218
$22$	11.0000	0.106600
$23$	200.000	1.81317	0.906584	−	0.422025i	$-0.138680\pi$
$23$	200.000	1.81317	0.906584	+	0.422025i	$0.138680\pi$
$24$	−45.0000	−0.382733
$25$	25.0000	0.200000
$26$	54.0000	0.407318
$27$	27.0000	0.192450
$28$	49.0000	0.330719
$29$	−218.000	−1.39592	−0.697958	−	0.716138i	$-0.745908\pi$
$29$	−218.000	−1.39592	−0.697958	+	0.716138i	$0.745908\pi$
$30$	15.0000	0.0912871
$31$	−304.000	−1.76129	−0.880645	−	0.473776i	$-0.842891\pi$
$31$	−304.000	−1.76129	−0.880645	+	0.473776i	$0.842891\pi$
$32$	161.000	0.889408
$33$	33.0000	0.174078
$34$	−78.0000	−0.393438
$35$	−35.0000	−0.169031
$36$	−63.0000	−0.291667
$37$	126.000	0.559845	0.279923	−	0.960023i	$-0.409691\pi$
$37$	126.000	0.559845	0.279923	+	0.960023i	$0.409691\pi$
$38$	−148.000	−0.631810
$39$	162.000	0.665148
$40$	−75.0000	−0.296464
$41$	58.0000	0.220929	0.110464	−	0.993880i	$-0.464766\pi$
$41$	58.0000	0.220929	0.110464	+	0.993880i	$0.464766\pi$
$42$	−21.0000	−0.0771517
$43$	532.000	1.88673	0.943363	−	0.331762i	$-0.107643\pi$
$43$	532.000	1.88673	0.943363	+	0.331762i	$0.107643\pi$
$44$	−77.0000	−0.263822
$45$	45.0000	0.149071
$46$	200.000	0.641052
$47$	−368.000	−1.14209	−0.571046	−	0.820918i	$-0.693462\pi$
$47$	−368.000	−1.14209	−0.571046	+	0.820918i	$0.693462\pi$
$48$	123.000	0.369865
$49$	49.0000	0.142857
$50$	25.0000	0.0707107
$51$	−234.000	−0.642481
$52$	−378.000	−1.00806
$53$	222.000	0.575359	0.287680	−	0.957727i	$-0.407116\pi$
$53$	222.000	0.575359	0.287680	+	0.957727i	$0.407116\pi$
$54$	27.0000	0.0680414
$55$	55.0000	0.134840
$56$	105.000	0.250557
$57$	−444.000	−1.03174
$58$	−218.000	−0.493531
$59$	−204.000	−0.450145	−0.225072	−	0.974342i	$-0.572262\pi$
$59$	−204.000	−0.450145	−0.225072	+	0.974342i	$0.572262\pi$
$60$	−105.000	−0.225924
$61$	−666.000	−1.39791	−0.698955	−	0.715165i	$-0.746351\pi$
$61$	−666.000	−1.39791	−0.698955	+	0.715165i	$0.746351\pi$
$62$	−304.000	−0.622710
$63$	−63.0000	−0.125988
$64$	−167.000	−0.326172
$65$	270.000	0.515221
$66$	33.0000	0.0615457
$67$	−356.000	−0.649139	−0.324570	−	0.945862i	$-0.605219\pi$
$67$	−356.000	−0.649139	−0.324570	+	0.945862i	$0.605219\pi$
$68$	546.000	0.973709
$69$	600.000	1.04683
$70$	−35.0000	−0.0597614
$71$	312.000	0.521515	0.260758	−	0.965404i	$-0.416028\pi$
$71$	312.000	0.521515	0.260758	+	0.965404i	$0.416028\pi$
$72$	−135.000	−0.220971
$73$	−726.000	−1.16400	−0.581999	−	0.813189i	$-0.697729\pi$
$73$	−726.000	−1.16400	−0.581999	+	0.813189i	$0.697729\pi$
$74$	126.000	0.197935
$75$	75.0000	0.115470
$76$	1036.00	1.56365
$77$	−77.0000	−0.113961
$78$	162.000	0.235165
$79$	−512.000	−0.729171	−0.364585	−	0.931170i	$-0.618789\pi$
$79$	−512.000	−0.729171	−0.364585	+	0.931170i	$0.618789\pi$
$80$	205.000	0.286496
$81$	81.0000	0.111111
$82$	58.0000	0.0781101
$83$	−1332.00	−1.76152	−0.880759	−	0.473565i	$-0.842967\pi$
$83$	−1332.00	−1.76152	−0.880759	+	0.473565i	$0.842967\pi$
$84$	147.000	0.190941
$85$	−390.000	−0.497664
$86$	532.000	0.667059
$87$	−654.000	−0.805933
$88$	−165.000	−0.199876
$89$	−742.000	−0.883729	−0.441864	−	0.897082i	$-0.645683\pi$
$89$	−742.000	−0.883729	−0.441864	+	0.897082i	$0.645683\pi$
$90$	45.0000	0.0527046
$91$	−378.000	−0.435441
$92$	−1400.00	−1.58652
$93$	−912.000	−1.01688
$94$	−368.000	−0.403790
$95$	−740.000	−0.799183
$96$	483.000	0.513500
$97$	514.000	0.538029	0.269014	−	0.963136i	$-0.413302\pi$
$97$	514.000	0.538029	0.269014	+	0.963136i	$0.413302\pi$
$98$	49.0000	0.0505076
$99$	99.0000	0.100504
$100$	−175.000	−0.175000
$101$	−1954.00	−1.92505	−0.962526	−	0.271189i	$-0.912583\pi$
$101$	−1954.00	−1.92505	−0.962526	+	0.271189i	$0.912583\pi$
$102$	−234.000	−0.227151
$103$	1288.00	1.23214	0.616070	−	0.787691i	$-0.288724\pi$
$103$	1288.00	1.23214	0.616070	+	0.787691i	$0.288724\pi$
$104$	−810.000	−0.763721
$105$	−105.000	−0.0975900
$106$	222.000	0.203420
$107$	−892.000	−0.805915	−0.402957	−	0.915219i	$-0.632018\pi$
$107$	−892.000	−0.805915	−0.402957	+	0.915219i	$0.632018\pi$
$108$	−189.000	−0.168394
$109$	−442.000	−0.388403	−0.194201	−	0.980962i	$-0.562212\pi$
$109$	−442.000	−0.388403	−0.194201	+	0.980962i	$0.562212\pi$
$110$	55.0000	0.0476731
$111$	378.000	0.323227
$112$	−287.000	−0.242133
$113$	−1262.00	−1.05061	−0.525305	−	0.850914i	$-0.676049\pi$
$113$	−1262.00	−1.05061	−0.525305	+	0.850914i	$0.676049\pi$
$114$	−444.000	−0.364776
$115$	1000.00	0.810874
$116$	1526.00	1.22143
$117$	486.000	0.384023
$118$	−204.000	−0.159150
$119$	546.000	0.420603
$120$	−225.000	−0.171163
$121$	121.000	0.0909091
$122$	−666.000	−0.494236
$123$	174.000	0.127553
$124$	2128.00	1.54113
$125$	125.000	0.0894427
$126$	−63.0000	−0.0445435
$127$	1584.00	1.10675	0.553375	−	0.832932i	$-0.313340\pi$
$127$	1584.00	1.10675	0.553375	+	0.832932i	$0.313340\pi$
$128$	−1455.00	−1.00473
$129$	1596.00	1.08930
$130$	270.000	0.182158
$131$	−1348.00	−0.899048	−0.449524	−	0.893268i	$-0.648406\pi$
$131$	−1348.00	−0.899048	−0.449524	+	0.893268i	$0.648406\pi$
$132$	−231.000	−0.152318
$133$	1036.00	0.675433
$134$	−356.000	−0.229505
$135$	135.000	0.0860663
$136$	1170.00	0.737696
$137$	90.0000	0.0561257	0.0280628	−	0.999606i	$-0.491066\pi$
$137$	90.0000	0.0561257	0.0280628	+	0.999606i	$0.491066\pi$
$138$	600.000	0.370112
$139$	−2252.00	−1.37419	−0.687094	−	0.726568i	$-0.741114\pi$
$139$	−2252.00	−1.37419	−0.687094	+	0.726568i	$0.741114\pi$
$140$	245.000	0.147902
$141$	−1104.00	−0.659387
$142$	312.000	0.184384
$143$	594.000	0.347362
$144$	369.000	0.213542
$145$	−1090.00	−0.624273
$146$	−726.000	−0.411536
$147$	147.000	0.0824786
$148$	−882.000	−0.489865
$149$	2670.00	1.46802	0.734010	−	0.679139i	$-0.237647\pi$
$149$	2670.00	1.46802	0.734010	+	0.679139i	$0.237647\pi$
$150$	75.0000	0.0408248
$151$	−3208.00	−1.72890	−0.864448	−	0.502722i	$-0.832332\pi$
$151$	−3208.00	−1.72890	−0.864448	+	0.502722i	$0.832332\pi$
$152$	2220.00	1.18464
$153$	−702.000	−0.370937
$154$	−77.0000	−0.0402911
$155$	−1520.00	−0.787673
$156$	−1134.00	−0.582004
$157$	1766.00	0.897721	0.448860	−	0.893602i	$-0.351830\pi$
$157$	1766.00	0.897721	0.448860	+	0.893602i	$0.351830\pi$
$158$	−512.000	−0.257801
$159$	666.000	0.332184
$160$	805.000	0.397755
$161$	−1400.00	−0.685313
$162$	81.0000	0.0392837
$163$	924.000	0.444008	0.222004	−	0.975046i	$-0.428740\pi$
$163$	924.000	0.444008	0.222004	+	0.975046i	$0.428740\pi$
$164$	−406.000	−0.193313
$165$	165.000	0.0778499
$166$	−1332.00	−0.622791
$167$	792.000	0.366987	0.183493	−	0.983021i	$-0.441259\pi$
$167$	792.000	0.366987	0.183493	+	0.983021i	$0.441259\pi$
$168$	315.000	0.144659
$169$	719.000	0.327264
$170$	−390.000	−0.175951
$171$	−1332.00	−0.595676
$172$	−3724.00	−1.65089
$173$	−2634.00	−1.15757	−0.578784	−	0.815481i	$-0.696473\pi$
$173$	−2634.00	−1.15757	−0.578784	+	0.815481i	$0.696473\pi$
$174$	−654.000	−0.284940
$175$	−175.000	−0.0755929
$176$	451.000	0.193156
$177$	−612.000	−0.259891
$178$	−742.000	−0.312445
$179$	−516.000	−0.215462	−0.107731	−	0.994180i	$-0.534358\pi$
$179$	−516.000	−0.215462	−0.107731	+	0.994180i	$0.534358\pi$
$180$	−315.000	−0.130437
$181$	110.000	0.0451726	0.0225863	−	0.999745i	$-0.492810\pi$
$181$	110.000	0.0451726	0.0225863	+	0.999745i	$0.492810\pi$
$182$	−378.000	−0.153952
$183$	−1998.00	−0.807084
$184$	−3000.00	−1.20197
$185$	630.000	0.250370
$186$	−912.000	−0.359522
$187$	−858.000	−0.335525
$188$	2576.00	0.999330
$189$	−189.000	−0.0727393
$190$	−740.000	−0.282554
$191$	−3296.00	−1.24864	−0.624320	−	0.781169i	$-0.714624\pi$
$191$	−3296.00	−1.24864	−0.624320	+	0.781169i	$0.714624\pi$
$192$	−501.000	−0.188315
$193$	418.000	0.155898	0.0779490	−	0.996957i	$-0.475163\pi$
$193$	418.000	0.155898	0.0779490	+	0.996957i	$0.475163\pi$
$194$	514.000	0.190222
$195$	810.000	0.297463
$196$	−343.000	−0.125000
$197$	−1602.00	−0.579380	−0.289690	−	0.957121i	$-0.593552\pi$
$197$	−1602.00	−0.579380	−0.289690	+	0.957121i	$0.593552\pi$
$198$	99.0000	0.0355335
$199$	−2776.00	−0.988871	−0.494436	−	0.869214i	$-0.664625\pi$
$199$	−2776.00	−0.988871	−0.494436	+	0.869214i	$0.664625\pi$
$200$	−375.000	−0.132583
$201$	−1068.00	−0.374781
$202$	−1954.00	−0.680609
$203$	1526.00	0.527607
$204$	1638.00	0.562171
$205$	290.000	0.0988023
$206$	1288.00	0.435627
$207$	1800.00	0.604390
$208$	2214.00	0.738045
$209$	−1628.00	−0.538809
$210$	−105.000	−0.0345033
$211$	3980.00	1.29855	0.649276	−	0.760553i	$-0.275072\pi$
$211$	3980.00	1.29855	0.649276	+	0.760553i	$0.275072\pi$
$212$	−1554.00	−0.503439
$213$	936.000	0.301097
$214$	−892.000	−0.284934
$215$	2660.00	0.843770
$216$	−405.000	−0.127578
$217$	2128.00	0.665705
$218$	−442.000	−0.137321
$219$	−2178.00	−0.672035
$220$	−385.000	−0.117985
$221$	−4212.00	−1.28204
$222$	378.000	0.114278
$223$	3504.00	1.05222	0.526110	−	0.850416i	$-0.323650\pi$
$223$	3504.00	1.05222	0.526110	+	0.850416i	$0.323650\pi$
$224$	−1127.00	−0.336165
$225$	225.000	0.0666667
$226$	−1262.00	−0.371447
$227$	5532.00	1.61750	0.808748	−	0.588155i	$-0.200145\pi$
$227$	5532.00	1.61750	0.808748	+	0.588155i	$0.200145\pi$
$228$	3108.00	0.902773
$229$	−4354.00	−1.25642	−0.628211	−	0.778043i	$-0.716212\pi$
$229$	−4354.00	−1.25642	−0.628211	+	0.778043i	$0.716212\pi$
$230$	1000.00	0.286687
$231$	−231.000	−0.0657952
$232$	3270.00	0.925371
$233$	1722.00	0.484172	0.242086	−	0.970255i	$-0.422168\pi$
$233$	1722.00	0.484172	0.242086	+	0.970255i	$0.422168\pi$
$234$	486.000	0.135773
$235$	−1840.00	−0.510759
$236$	1428.00	0.393877
$237$	−1536.00	−0.420987
$238$	546.000	0.148706
$239$	2400.00	0.649553	0.324776	−	0.945791i	$-0.394711\pi$
$239$	2400.00	0.649553	0.324776	+	0.945791i	$0.394711\pi$
$240$	615.000	0.165409
$241$	−830.000	−0.221846	−0.110923	−	0.993829i	$-0.535381\pi$
$241$	−830.000	−0.221846	−0.110923	+	0.993829i	$0.535381\pi$
$242$	121.000	0.0321412
$243$	243.000	0.0641500
$244$	4662.00	1.22317
$245$	245.000	0.0638877
$246$	174.000	0.0450969
$247$	−7992.00	−2.05878
$248$	4560.00	1.16758
$249$	−3996.00	−1.01701
$250$	125.000	0.0316228
$251$	5588.00	1.40522	0.702612	−	0.711573i	$-0.252017\pi$
$251$	5588.00	1.40522	0.702612	+	0.711573i	$0.252017\pi$
$252$	441.000	0.110240
$253$	2200.00	0.546691
$254$	1584.00	0.391295
$255$	−1170.00	−0.287326
$256$	−119.000	−0.0290527
$257$	−5902.00	−1.43252	−0.716258	−	0.697836i	$-0.754147\pi$
$257$	−5902.00	−1.43252	−0.716258	+	0.697836i	$0.754147\pi$
$258$	1596.00	0.385126
$259$	−882.000	−0.211602
$260$	−1890.00	−0.450819
$261$	−1962.00	−0.465306
$262$	−1348.00	−0.317862
$263$	3912.00	0.917202	0.458601	−	0.888642i	$-0.348351\pi$
$263$	3912.00	0.917202	0.458601	+	0.888642i	$0.348351\pi$
$264$	−495.000	−0.115398
$265$	1110.00	0.257309
$266$	1036.00	0.238802
$267$	−2226.00	−0.510221
$268$	2492.00	0.567997
$269$	5590.00	1.26702	0.633510	−	0.773735i	$-0.281614\pi$
$269$	5590.00	1.26702	0.633510	+	0.773735i	$0.281614\pi$
$270$	135.000	0.0304290
$271$	5376.00	1.20505	0.602525	−	0.798100i	$-0.294161\pi$
$271$	5376.00	1.20505	0.602525	+	0.798100i	$0.294161\pi$
$272$	−3198.00	−0.712894
$273$	−1134.00	−0.251402
$274$	90.0000	0.0198434
$275$	275.000	0.0603023
$276$	−4200.00	−0.915979
$277$	−3170.00	−0.687606	−0.343803	−	0.939042i	$-0.611715\pi$
$277$	−3170.00	−0.687606	−0.343803	+	0.939042i	$0.611715\pi$
$278$	−2252.00	−0.485849
$279$	−2736.00	−0.587097
$280$	525.000	0.112053
$281$	−374.000	−0.0793985	−0.0396992	−	0.999212i	$-0.512640\pi$
$281$	−374.000	−0.0793985	−0.0396992	+	0.999212i	$0.512640\pi$
$282$	−1104.00	−0.233129
$283$	−5564.00	−1.16871	−0.584356	−	0.811497i	$-0.698653\pi$
$283$	−5564.00	−1.16871	−0.584356	+	0.811497i	$0.698653\pi$
$284$	−2184.00	−0.456326
$285$	−2220.00	−0.461409
$286$	594.000	0.122811
$287$	−406.000	−0.0835032
$288$	1449.00	0.296469
$289$	1171.00	0.238347
$290$	−1090.00	−0.220714
$291$	1542.00	0.310631
$292$	5082.00	1.01850
$293$	5470.00	1.09065	0.545326	−	0.838224i	$-0.316406\pi$
$293$	5470.00	1.09065	0.545326	+	0.838224i	$0.316406\pi$
$294$	147.000	0.0291606
$295$	−1020.00	−0.201311
$296$	−1890.00	−0.371128
$297$	297.000	0.0580259
$298$	2670.00	0.519023
$299$	10800.0	2.08890
$300$	−525.000	−0.101036
$301$	−3724.00	−0.713116
$302$	−3208.00	−0.611257
$303$	−5862.00	−1.11143
$304$	−6068.00	−1.14481
$305$	−3330.00	−0.625165
$306$	−702.000	−0.131146
$307$	−2132.00	−0.396351	−0.198175	−	0.980167i	$-0.563502\pi$
$307$	−2132.00	−0.396351	−0.198175	+	0.980167i	$0.563502\pi$
$308$	539.000	0.0997155
$309$	3864.00	0.711376
$310$	−1520.00	−0.278485
$311$	1832.00	0.334030	0.167015	−	0.985954i	$-0.446587\pi$
$311$	1832.00	0.334030	0.167015	+	0.985954i	$0.446587\pi$
$312$	−2430.00	−0.440935
$313$	−2038.00	−0.368034	−0.184017	−	0.982923i	$-0.558910\pi$
$313$	−2038.00	−0.368034	−0.184017	+	0.982923i	$0.558910\pi$
$314$	1766.00	0.317392
$315$	−315.000	−0.0563436
$316$	3584.00	0.638025
$317$	−618.000	−0.109496	−0.0547482	−	0.998500i	$-0.517436\pi$
$317$	−618.000	−0.109496	−0.0547482	+	0.998500i	$0.517436\pi$
$318$	666.000	0.117445
$319$	−2398.00	−0.420885
$320$	−835.000	−0.145868
$321$	−2676.00	−0.465295
$322$	−1400.00	−0.242295
$323$	11544.0	1.98862
$324$	−567.000	−0.0972222
$325$	1350.00	0.230414
$326$	924.000	0.156980
$327$	−1326.00	−0.224245
$328$	−870.000	−0.146456
$329$	2576.00	0.431670
$330$	165.000	0.0275241
$331$	−10316.0	−1.71305	−0.856524	−	0.516108i	$-0.827380\pi$
$331$	−10316.0	−1.71305	−0.856524	+	0.516108i	$0.827380\pi$
$332$	9324.00	1.54133
$333$	1134.00	0.186615
$334$	792.000	0.129749
$335$	−1780.00	−0.290304
$336$	−861.000	−0.139796
$337$	11986.0	1.93745	0.968723	−	0.248146i	$-0.0798213\pi$
$337$	11986.0	1.93745	0.968723	+	0.248146i	$0.0798213\pi$
$338$	719.000	0.115705
$339$	−3786.00	−0.606570
$340$	2730.00	0.435456
$341$	−3344.00	−0.531049
$342$	−1332.00	−0.210603
$343$	−343.000	−0.0539949
$344$	−7980.00	−1.25073
$345$	3000.00	0.468158
$346$	−2634.00	−0.409262
$347$	−1612.00	−0.249385	−0.124693	−	0.992195i	$-0.539794\pi$
$347$	−1612.00	−0.249385	−0.124693	+	0.992195i	$0.539794\pi$
$348$	4578.00	0.705191
$349$	−8794.00	−1.34880	−0.674401	−	0.738365i	$-0.735598\pi$
$349$	−8794.00	−1.34880	−0.674401	+	0.738365i	$0.735598\pi$
$350$	−175.000	−0.0267261
$351$	1458.00	0.221716
$352$	1771.00	0.268167
$353$	−10318.0	−1.55573	−0.777864	−	0.628433i	$-0.783697\pi$
$353$	−10318.0	−1.55573	−0.777864	+	0.628433i	$0.783697\pi$
$354$	−612.000	−0.0918854
$355$	1560.00	0.233229
$356$	5194.00	0.773262
$357$	1638.00	0.242835
$358$	−516.000	−0.0761772
$359$	6600.00	0.970292	0.485146	−	0.874433i	$-0.338767\pi$
$359$	6600.00	0.970292	0.485146	+	0.874433i	$0.338767\pi$
$360$	−675.000	−0.0988212
$361$	15045.0	2.19347
$362$	110.000	0.0159709
$363$	363.000	0.0524864
$364$	2646.00	0.381011
$365$	−3630.00	−0.520556
$366$	−1998.00	−0.285347
$367$	5024.00	0.714579	0.357290	−	0.933994i	$-0.383701\pi$
$367$	5024.00	0.714579	0.357290	+	0.933994i	$0.383701\pi$
$368$	8200.00	1.16156
$369$	522.000	0.0736429
$370$	630.000	0.0885193
$371$	−1554.00	−0.217465
$372$	6384.00	0.889771
$373$	8990.00	1.24795	0.623974	−	0.781445i	$-0.285517\pi$
$373$	8990.00	1.24795	0.623974	+	0.781445i	$0.285517\pi$
$374$	−858.000	−0.118626
$375$	375.000	0.0516398
$376$	5520.00	0.757107
$377$	−11772.0	−1.60819
$378$	−189.000	−0.0257172
$379$	3108.00	0.421233	0.210616	−	0.977569i	$-0.432453\pi$
$379$	3108.00	0.421233	0.210616	+	0.977569i	$0.432453\pi$
$380$	5180.00	0.699285
$381$	4752.00	0.638983
$382$	−3296.00	−0.441461
$383$	7264.00	0.969120	0.484560	−	0.874758i	$-0.338980\pi$
$383$	7264.00	0.969120	0.484560	+	0.874758i	$0.338980\pi$
$384$	−4365.00	−0.580079
$385$	−385.000	−0.0509647
$386$	418.000	0.0551182
$387$	4788.00	0.628909
$388$	−3598.00	−0.470775
$389$	1934.00	0.252076	0.126038	−	0.992025i	$-0.459774\pi$
$389$	1934.00	0.252076	0.126038	+	0.992025i	$0.459774\pi$
$390$	810.000	0.105169
$391$	−15600.0	−2.01771
$392$	−735.000	−0.0947018
$393$	−4044.00	−0.519066
$394$	−1602.00	−0.204842
$395$	−2560.00	−0.326095
$396$	−693.000	−0.0879408
$397$	8118.00	1.02627	0.513137	−	0.858307i	$-0.328483\pi$
$397$	8118.00	1.02627	0.513137	+	0.858307i	$0.328483\pi$
$398$	−2776.00	−0.349619
$399$	3108.00	0.389961
$400$	1025.00	0.128125
$401$	−11214.0	−1.39651	−0.698255	−	0.715849i	$-0.746040\pi$
$401$	−11214.0	−1.39651	−0.698255	+	0.715849i	$0.746040\pi$
$402$	−1068.00	−0.132505
$403$	−16416.0	−2.02913
$404$	13678.0	1.68442
$405$	405.000	0.0496904
$406$	1526.00	0.186537
$407$	1386.00	0.168800
$408$	3510.00	0.425909
$409$	−3430.00	−0.414676	−0.207338	−	0.978269i	$-0.566480\pi$
$409$	−3430.00	−0.414676	−0.207338	+	0.978269i	$0.566480\pi$
$410$	290.000	0.0349319
$411$	270.000	0.0324042
$412$	−9016.00	−1.07812
$413$	1428.00	0.170139
$414$	1800.00	0.213684
$415$	−6660.00	−0.787775
$416$	8694.00	1.02466
$417$	−6756.00	−0.793388
$418$	−1628.00	−0.190498
$419$	−8340.00	−0.972400	−0.486200	−	0.873848i	$-0.661617\pi$
$419$	−8340.00	−0.972400	−0.486200	+	0.873848i	$0.661617\pi$
$420$	735.000	0.0853913
$421$	−14114.0	−1.63391	−0.816953	−	0.576705i	$-0.804338\pi$
$421$	−14114.0	−1.63391	−0.816953	+	0.576705i	$0.804338\pi$
$422$	3980.00	0.459108
$423$	−3312.00	−0.380697
$424$	−3330.00	−0.381413
$425$	−1950.00	−0.222562
$426$	936.000	0.106454
$427$	4662.00	0.528361
$428$	6244.00	0.705176
$429$	1782.00	0.200550
$430$	2660.00	0.298318
$431$	−6336.00	−0.708108	−0.354054	−	0.935225i	$-0.615197\pi$
$431$	−6336.00	−0.708108	−0.354054	+	0.935225i	$0.615197\pi$
$432$	1107.00	0.123288
$433$	−8878.00	−0.985334	−0.492667	−	0.870218i	$-0.663978\pi$
$433$	−8878.00	−0.985334	−0.492667	+	0.870218i	$0.663978\pi$
$434$	2128.00	0.235362
$435$	−3270.00	−0.360424
$436$	3094.00	0.339853
$437$	−29600.0	−3.24018
$438$	−2178.00	−0.237600
$439$	−5960.00	−0.647962	−0.323981	−	0.946064i	$-0.605021\pi$
$439$	−5960.00	−0.647962	−0.323981	+	0.946064i	$0.605021\pi$
$440$	−825.000	−0.0893871
$441$	441.000	0.0476190
$442$	−4212.00	−0.453268
$443$	15924.0	1.70784	0.853919	−	0.520406i	$-0.174219\pi$
$443$	15924.0	1.70784	0.853919	+	0.520406i	$0.174219\pi$
$444$	−2646.00	−0.282823
$445$	−3710.00	−0.395215
$446$	3504.00	0.372016
$447$	8010.00	0.847562
$448$	1169.00	0.123281
$449$	11490.0	1.20768	0.603838	−	0.797107i	$-0.293637\pi$
$449$	11490.0	1.20768	0.603838	+	0.797107i	$0.293637\pi$
$450$	225.000	0.0235702
$451$	638.000	0.0666125
$452$	8834.00	0.919284
$453$	−9624.00	−0.998179
$454$	5532.00	0.571871
$455$	−1890.00	−0.194735
$456$	6660.00	0.683954
$457$	−10054.0	−1.02912	−0.514558	−	0.857455i	$-0.672044\pi$
$457$	−10054.0	−1.02912	−0.514558	+	0.857455i	$0.672044\pi$
$458$	−4354.00	−0.444212
$459$	−2106.00	−0.214160
$460$	−7000.00	−0.709515
$461$	13398.0	1.35359	0.676797	−	0.736169i	$-0.263367\pi$
$461$	13398.0	1.35359	0.676797	+	0.736169i	$0.263367\pi$
$462$	−231.000	−0.0232621
$463$	11888.0	1.19327	0.596633	−	0.802514i	$-0.296505\pi$
$463$	11888.0	1.19327	0.596633	+	0.802514i	$0.296505\pi$
$464$	−8938.00	−0.894259
$465$	−4560.00	−0.454763
$466$	1722.00	0.171180
$467$	6332.00	0.627430	0.313715	−	0.949517i	$-0.398426\pi$
$467$	6332.00	0.627430	0.313715	+	0.949517i	$0.398426\pi$
$468$	−3402.00	−0.336020
$469$	2492.00	0.245352
$470$	−1840.00	−0.180581
$471$	5298.00	0.518299
$472$	3060.00	0.298407
$473$	5852.00	0.568869
$474$	−1536.00	−0.148841
$475$	−3700.00	−0.357406
$476$	−3822.00	−0.368027
$477$	1998.00	0.191786
$478$	2400.00	0.229652
$479$	7968.00	0.760057	0.380028	−	0.924975i	$-0.375914\pi$
$479$	7968.00	0.760057	0.380028	+	0.924975i	$0.375914\pi$
$480$	2415.00	0.229644
$481$	6804.00	0.644981
$482$	−830.000	−0.0784346
$483$	−4200.00	−0.395666
$484$	−847.000	−0.0795455
$485$	2570.00	0.240614
$486$	243.000	0.0226805
$487$	−10472.0	−0.974398	−0.487199	−	0.873291i	$-0.661981\pi$
$487$	−10472.0	−0.974398	−0.487199	+	0.873291i	$0.661981\pi$
$488$	9990.00	0.926693
$489$	2772.00	0.256348
$490$	245.000	0.0225877
$491$	3108.00	0.285666	0.142833	−	0.989747i	$-0.454379\pi$
$491$	3108.00	0.285666	0.142833	+	0.989747i	$0.454379\pi$
$492$	−1218.00	−0.111609
$493$	17004.0	1.55339
$494$	−7992.00	−0.727889
$495$	495.000	0.0449467
$496$	−12464.0	−1.12833
$497$	−2184.00	−0.197114
$498$	−3996.00	−0.359568
$499$	−7540.00	−0.676426	−0.338213	−	0.941070i	$-0.609822\pi$
$499$	−7540.00	−0.676426	−0.338213	+	0.941070i	$0.609822\pi$
$500$	−875.000	−0.0782624
$501$	2376.00	0.211880
$502$	5588.00	0.496822
$503$	16840.0	1.49276	0.746380	−	0.665520i	$-0.231790\pi$
$503$	16840.0	1.49276	0.746380	+	0.665520i	$0.231790\pi$
$504$	945.000	0.0835191
$505$	−9770.00	−0.860909
$506$	2200.00	0.193284
$507$	2157.00	0.188946
$508$	−11088.0	−0.968406
$509$	10598.0	0.922884	0.461442	−	0.887170i	$-0.347332\pi$
$509$	10598.0	0.922884	0.461442	+	0.887170i	$0.347332\pi$
$510$	−1170.00	−0.101585
$511$	5082.00	0.439950
$512$	11521.0	0.994455
$513$	−3996.00	−0.343914
$514$	−5902.00	−0.506471
$515$	6440.00	0.551030
$516$	−11172.0	−0.953139
$517$	−4048.00	−0.344354
$518$	−882.000	−0.0748125
$519$	−7902.00	−0.668322
$520$	−4050.00	−0.341547
$521$	−2934.00	−0.246720	−0.123360	−	0.992362i	$-0.539367\pi$
$521$	−2934.00	−0.246720	−0.123360	+	0.992362i	$0.539367\pi$
$522$	−1962.00	−0.164510
$523$	−8524.00	−0.712674	−0.356337	−	0.934358i	$-0.615974\pi$
$523$	−8524.00	−0.712674	−0.356337	+	0.934358i	$0.615974\pi$
$524$	9436.00	0.786667
$525$	−525.000	−0.0436436
$526$	3912.00	0.324280
$527$	23712.0	1.95998
$528$	1353.00	0.111518
$529$	27833.0	2.28758
$530$	1110.00	0.0909723
$531$	−1836.00	−0.150048
$532$	−7252.00	−0.591004
$533$	3132.00	0.254525
$534$	−2226.00	−0.180390
$535$	−4460.00	−0.360416
$536$	5340.00	0.430323
$537$	−1548.00	−0.124397
$538$	5590.00	0.447959
$539$	539.000	0.0430730
$540$	−945.000	−0.0753080
$541$	12918.0	1.02660	0.513298	−	0.858211i	$-0.328424\pi$
$541$	12918.0	1.02660	0.513298	+	0.858211i	$0.328424\pi$
$542$	5376.00	0.426050
$543$	330.000	0.0260804
$544$	−12558.0	−0.989742
$545$	−2210.00	−0.173699
$546$	−1134.00	−0.0888841
$547$	−7716.00	−0.603130	−0.301565	−	0.953446i	$-0.597509\pi$
$547$	−7716.00	−0.603130	−0.301565	+	0.953446i	$0.597509\pi$
$548$	−630.000	−0.0491100
$549$	−5994.00	−0.465970
$550$	275.000	0.0213201
$551$	32264.0	2.49454
$552$	−9000.00	−0.693959
$553$	3584.00	0.275601
$554$	−3170.00	−0.243105
$555$	1890.00	0.144551
$556$	15764.0	1.20241
$557$	−2666.00	−0.202804	−0.101402	−	0.994846i	$-0.532333\pi$
$557$	−2666.00	−0.202804	−0.101402	+	0.994846i	$0.532333\pi$
$558$	−2736.00	−0.207570
$559$	28728.0	2.17364
$560$	−1435.00	−0.108285
$561$	−2574.00	−0.193715
$562$	−374.000	−0.0280716
$563$	−6036.00	−0.451842	−0.225921	−	0.974146i	$-0.572539\pi$
$563$	−6036.00	−0.451842	−0.225921	+	0.974146i	$0.572539\pi$
$564$	7728.00	0.576964
$565$	−6310.00	−0.469847
$566$	−5564.00	−0.413202
$567$	−567.000	−0.0419961
$568$	−4680.00	−0.345719
$569$	4458.00	0.328452	0.164226	−	0.986423i	$-0.447487\pi$
$569$	4458.00	0.328452	0.164226	+	0.986423i	$0.447487\pi$
$570$	−2220.00	−0.163133
$571$	2564.00	0.187916	0.0939580	−	0.995576i	$-0.470048\pi$
$571$	2564.00	0.187916	0.0939580	+	0.995576i	$0.470048\pi$
$572$	−4158.00	−0.303942
$573$	−9888.00	−0.720902
$574$	−406.000	−0.0295228
$575$	5000.00	0.362634
$576$	−1503.00	−0.108724
$577$	19586.0	1.41313	0.706565	−	0.707648i	$-0.250244\pi$
$577$	19586.0	1.41313	0.706565	+	0.707648i	$0.250244\pi$
$578$	1171.00	0.0842685
$579$	1254.00	0.0900077
$580$	7630.00	0.546239
$581$	9324.00	0.665791
$582$	1542.00	0.109825
$583$	2442.00	0.173477
$584$	10890.0	0.771629
$585$	2430.00	0.171740
$586$	5470.00	0.385603
$587$	14340.0	1.00831	0.504153	−	0.863615i	$-0.331805\pi$
$587$	14340.0	1.00831	0.504153	+	0.863615i	$0.331805\pi$
$588$	−1029.00	−0.0721688
$589$	44992.0	3.14748
$590$	−1020.00	−0.0711741
$591$	−4806.00	−0.334505
$592$	5166.00	0.358651
$593$	978.000	0.0677262	0.0338631	−	0.999426i	$-0.489219\pi$
$593$	978.000	0.0677262	0.0338631	+	0.999426i	$0.489219\pi$
$594$	297.000	0.0205152
$595$	2730.00	0.188099
$596$	−18690.0	−1.28452
$597$	−8328.00	−0.570925
$598$	10800.0	0.738537
$599$	1896.00	0.129330	0.0646648	−	0.997907i	$-0.479402\pi$
$599$	1896.00	0.129330	0.0646648	+	0.997907i	$0.479402\pi$
$600$	−1125.00	−0.0765466
$601$	1402.00	0.0951560	0.0475780	−	0.998868i	$-0.484850\pi$
$601$	1402.00	0.0951560	0.0475780	+	0.998868i	$0.484850\pi$
$602$	−3724.00	−0.252124
$603$	−3204.00	−0.216380
$604$	22456.0	1.51278
$605$	605.000	0.0406558
$606$	−5862.00	−0.392950
$607$	11504.0	0.769247	0.384624	−	0.923074i	$-0.374331\pi$
$607$	11504.0	0.769247	0.384624	+	0.923074i	$0.374331\pi$
$608$	−23828.0	−1.58940
$609$	4578.00	0.304614
$610$	−3330.00	−0.221029
$611$	−19872.0	−1.31577
$612$	4914.00	0.324570
$613$	−8146.00	−0.536727	−0.268364	−	0.963318i	$-0.586483\pi$
$613$	−8146.00	−0.536727	−0.268364	+	0.963318i	$0.586483\pi$
$614$	−2132.00	−0.140131
$615$	870.000	0.0570436
$616$	1155.00	0.0755459
$617$	−3238.00	−0.211275	−0.105638	−	0.994405i	$-0.533688\pi$
$617$	−3238.00	−0.211275	−0.105638	+	0.994405i	$0.533688\pi$
$618$	3864.00	0.251510
$619$	3268.00	0.212200	0.106100	−	0.994355i	$-0.466164\pi$
$619$	3268.00	0.212200	0.106100	+	0.994355i	$0.466164\pi$
$620$	10640.0	0.689214
$621$	5400.00	0.348945
$622$	1832.00	0.118097
$623$	5194.00	0.334018
$624$	6642.00	0.426110
$625$	625.000	0.0400000
$626$	−2038.00	−0.130120
$627$	−4884.00	−0.311082
$628$	−12362.0	−0.785506
$629$	−9828.00	−0.623002
$630$	−315.000	−0.0199205
$631$	−16024.0	−1.01094	−0.505472	−	0.862843i	$-0.668682\pi$
$631$	−16024.0	−1.01094	−0.505472	+	0.862843i	$0.668682\pi$
$632$	7680.00	0.483377
$633$	11940.0	0.749719
$634$	−618.000	−0.0387128
$635$	7920.00	0.494954
$636$	−4662.00	−0.290661
$637$	2646.00	0.164581
$638$	−2398.00	−0.148805
$639$	2808.00	0.173838
$640$	−7275.00	−0.449328
$641$	4674.00	0.288006	0.144003	−	0.989577i	$-0.454002\pi$
$641$	4674.00	0.288006	0.144003	+	0.989577i	$0.454002\pi$
$642$	−2676.00	−0.164507
$643$	7212.00	0.442323	0.221161	−	0.975237i	$-0.429015\pi$
$643$	7212.00	0.442323	0.221161	+	0.975237i	$0.429015\pi$
$644$	9800.00	0.599649
$645$	7980.00	0.487151
$646$	11544.0	0.703085
$647$	−7336.00	−0.445762	−0.222881	−	0.974846i	$-0.571546\pi$
$647$	−7336.00	−0.445762	−0.222881	+	0.974846i	$0.571546\pi$
$648$	−1215.00	−0.0736570
$649$	−2244.00	−0.135724
$650$	1350.00	0.0814636
$651$	6384.00	0.384345
$652$	−6468.00	−0.388507
$653$	18534.0	1.11071	0.555353	−	0.831614i	$-0.312583\pi$
$653$	18534.0	1.11071	0.555353	+	0.831614i	$0.312583\pi$
$654$	−1326.00	−0.0792824
$655$	−6740.00	−0.402067
$656$	2378.00	0.141532
$657$	−6534.00	−0.387999
$658$	2576.00	0.152618
$659$	−3716.00	−0.219658	−0.109829	−	0.993950i	$-0.535030\pi$
$659$	−3716.00	−0.219658	−0.109829	+	0.993950i	$0.535030\pi$
$660$	−1155.00	−0.0681187
$661$	−12786.0	−0.752372	−0.376186	−	0.926544i	$-0.622765\pi$
$661$	−12786.0	−0.752372	−0.376186	+	0.926544i	$0.622765\pi$
$662$	−10316.0	−0.605654
$663$	−12636.0	−0.740183
$664$	19980.0	1.16773
$665$	5180.00	0.302063
$666$	1134.00	0.0659784
$667$	−43600.0	−2.53103
$668$	−5544.00	−0.321113
$669$	10512.0	0.607500
$670$	−1780.00	−0.102638
$671$	−7326.00	−0.421486
$672$	−3381.00	−0.194085
$673$	11298.0	0.647111	0.323556	−	0.946209i	$-0.395122\pi$
$673$	11298.0	0.647111	0.323556	+	0.946209i	$0.395122\pi$
$674$	11986.0	0.684990
$675$	675.000	0.0384900
$676$	−5033.00	−0.286356
$677$	12190.0	0.692023	0.346012	−	0.938230i	$-0.387536\pi$
$677$	12190.0	0.692023	0.346012	+	0.938230i	$0.387536\pi$
$678$	−3786.00	−0.214455
$679$	−3598.00	−0.203356
$680$	5850.00	0.329908
$681$	16596.0	0.933862
$682$	−3344.00	−0.187754
$683$	−3708.00	−0.207735	−0.103867	−	0.994591i	$-0.533122\pi$
$683$	−3708.00	−0.207735	−0.103867	+	0.994591i	$0.533122\pi$
$684$	9324.00	0.521216
$685$	450.000	0.0251002
$686$	−343.000	−0.0190901
$687$	−13062.0	−0.725395
$688$	21812.0	1.20868
$689$	11988.0	0.662854
$690$	3000.00	0.165519
$691$	31292.0	1.72273	0.861363	−	0.507990i	$-0.169611\pi$
$691$	31292.0	1.72273	0.861363	+	0.507990i	$0.169611\pi$
$692$	18438.0	1.01287
$693$	−693.000	−0.0379869
$694$	−1612.00	−0.0881710
$695$	−11260.0	−0.614556
$696$	9810.00	0.534263
$697$	−4524.00	−0.245852
$698$	−8794.00	−0.476874
$699$	5166.00	0.279537
$700$	1225.00	0.0661438
$701$	−2010.00	−0.108298	−0.0541488	−	0.998533i	$-0.517245\pi$
$701$	−2010.00	−0.108298	−0.0541488	+	0.998533i	$0.517245\pi$
$702$	1458.00	0.0783884
$703$	−18648.0	−1.00046
$704$	−1837.00	−0.0983445
$705$	−5520.00	−0.294887
$706$	−10318.0	−0.550033
$707$	13678.0	0.727601
$708$	4284.00	0.227405
$709$	−29410.0	−1.55785	−0.778925	−	0.627117i	$-0.784235\pi$
$709$	−29410.0	−1.55785	−0.778925	+	0.627117i	$0.784235\pi$
$710$	1560.00	0.0824588
$711$	−4608.00	−0.243057
$712$	11130.0	0.585835
$713$	−60800.0	−3.19352
$714$	1638.00	0.0858552
$715$	2970.00	0.155345
$716$	3612.00	0.188529
$717$	7200.00	0.375019
$718$	6600.00	0.343050
$719$	13552.0	0.702927	0.351463	−	0.936202i	$-0.385684\pi$
$719$	13552.0	0.702927	0.351463	+	0.936202i	$0.385684\pi$
$720$	1845.00	0.0954987
$721$	−9016.00	−0.465705
$722$	15045.0	0.775508
$723$	−2490.00	−0.128083
$724$	−770.000	−0.0395260
$725$	−5450.00	−0.279183
$726$	363.000	0.0185567
$727$	−24456.0	−1.24762	−0.623812	−	0.781574i	$-0.714417\pi$
$727$	−24456.0	−1.24762	−0.623812	+	0.781574i	$0.714417\pi$
$728$	5670.00	0.288660
$729$	729.000	0.0370370
$730$	−3630.00	−0.184044
$731$	−41496.0	−2.09957
$732$	13986.0	0.706199
$733$	−6458.00	−0.325418	−0.162709	−	0.986674i	$-0.552023\pi$
$733$	−6458.00	−0.325418	−0.162709	+	0.986674i	$0.552023\pi$
$734$	5024.00	0.252642
$735$	735.000	0.0368856
$736$	32200.0	1.61265
$737$	−3916.00	−0.195723
$738$	522.000	0.0260367
$739$	−14692.0	−0.731331	−0.365666	−	0.930746i	$-0.619159\pi$
$739$	−14692.0	−0.731331	−0.365666	+	0.930746i	$0.619159\pi$
$740$	−4410.00	−0.219074
$741$	−23976.0	−1.18864
$742$	−1554.00	−0.0768856
$743$	8552.00	0.422264	0.211132	−	0.977458i	$-0.432285\pi$
$743$	8552.00	0.422264	0.211132	+	0.977458i	$0.432285\pi$
$744$	13680.0	0.674104
$745$	13350.0	0.656518
$746$	8990.00	0.441216
$747$	−11988.0	−0.587173
$748$	6006.00	0.293584
$749$	6244.00	0.304607
$750$	375.000	0.0182574
$751$	8080.00	0.392601	0.196301	−	0.980544i	$-0.437107\pi$
$751$	8080.00	0.392601	0.196301	+	0.980544i	$0.437107\pi$
$752$	−15088.0	−0.731653
$753$	16764.0	0.811307
$754$	−11772.0	−0.568582
$755$	−16040.0	−0.773186
$756$	1323.00	0.0636469
$757$	−27346.0	−1.31296	−0.656478	−	0.754345i	$-0.727954\pi$
$757$	−27346.0	−1.31296	−0.656478	+	0.754345i	$0.727954\pi$
$758$	3108.00	0.148928
$759$	6600.00	0.315632
$760$	11100.0	0.529789
$761$	38218.0	1.82050	0.910251	−	0.414058i	$-0.135889\pi$
$761$	38218.0	1.82050	0.910251	+	0.414058i	$0.135889\pi$
$762$	4752.00	0.225914
$763$	3094.00	0.146803
$764$	23072.0	1.09256
$765$	−3510.00	−0.165888
$766$	7264.00	0.342636
$767$	−11016.0	−0.518598
$768$	−357.000	−0.0167736
$769$	−33614.0	−1.57627	−0.788135	−	0.615502i	$-0.788953\pi$
$769$	−33614.0	−1.57627	−0.788135	+	0.615502i	$0.788953\pi$
$770$	−385.000	−0.0180187
$771$	−17706.0	−0.827064
$772$	−2926.00	−0.136411
$773$	−34722.0	−1.61561	−0.807803	−	0.589452i	$-0.799344\pi$
$773$	−34722.0	−1.61561	−0.807803	+	0.589452i	$0.799344\pi$
$774$	4788.00	0.222353
$775$	−7600.00	−0.352258
$776$	−7710.00	−0.356666
$777$	−2646.00	−0.122168
$778$	1934.00	0.0891224
$779$	−8584.00	−0.394806
$780$	−5670.00	−0.260280
$781$	3432.00	0.157243
$782$	−15600.0	−0.713369
$783$	−5886.00	−0.268644
$784$	2009.00	0.0915179
$785$	8830.00	0.401473
$786$	−4044.00	−0.183517
$787$	−27476.0	−1.24449	−0.622245	−	0.782823i	$-0.713779\pi$
$787$	−27476.0	−1.24449	−0.622245	+	0.782823i	$0.713779\pi$
$788$	11214.0	0.506957
$789$	11736.0	0.529547
$790$	−2560.00	−0.115292
$791$	8834.00	0.397093
$792$	−1485.00	−0.0666252
$793$	−35964.0	−1.61049
$794$	8118.00	0.362843
$795$	3330.00	0.148557
$796$	19432.0	0.865263
$797$	23814.0	1.05839	0.529194	−	0.848501i	$-0.322494\pi$
$797$	23814.0	1.05839	0.529194	+	0.848501i	$0.322494\pi$
$798$	3108.00	0.137872
$799$	28704.0	1.27093
$800$	4025.00	0.177882
$801$	−6678.00	−0.294576
$802$	−11214.0	−0.493741
$803$	−7986.00	−0.350959
$804$	7476.00	0.327933
$805$	−7000.00	−0.306481
$806$	−16416.0	−0.717406
$807$	16770.0	0.731514
$808$	29310.0	1.27614
$809$	34554.0	1.50167	0.750837	−	0.660488i	$-0.229650\pi$
$809$	34554.0	1.50167	0.750837	+	0.660488i	$0.229650\pi$
$810$	405.000	0.0175682
$811$	−17708.0	−0.766723	−0.383361	−	0.923598i	$-0.625234\pi$
$811$	−17708.0	−0.766723	−0.383361	+	0.923598i	$0.625234\pi$
$812$	−10682.0	−0.461656
$813$	16128.0	0.695736
$814$	1386.00	0.0596797
$815$	4620.00	0.198566
$816$	−9594.00	−0.411590
$817$	−78736.0	−3.37163
$818$	−3430.00	−0.146610
$819$	−3402.00	−0.145147
$820$	−2030.00	−0.0864520
$821$	−25042.0	−1.06452	−0.532261	−	0.846581i	$-0.678657\pi$
$821$	−25042.0	−1.06452	−0.532261	+	0.846581i	$0.678657\pi$
$822$	270.000	0.0114566
$823$	29224.0	1.23777	0.618885	−	0.785482i	$-0.287585\pi$
$823$	29224.0	1.23777	0.618885	+	0.785482i	$0.287585\pi$
$824$	−19320.0	−0.816801
$825$	825.000	0.0348155
$826$	1428.00	0.0601531
$827$	−36108.0	−1.51826	−0.759128	−	0.650941i	$-0.774374\pi$
$827$	−36108.0	−1.51826	−0.759128	+	0.650941i	$0.774374\pi$
$828$	−12600.0	−0.528841
$829$	−23482.0	−0.983792	−0.491896	−	0.870654i	$-0.663696\pi$
$829$	−23482.0	−0.983792	−0.491896	+	0.870654i	$0.663696\pi$
$830$	−6660.00	−0.278520
$831$	−9510.00	−0.396989
$832$	−9018.00	−0.375773
$833$	−3822.00	−0.158973
$834$	−6756.00	−0.280505
$835$	3960.00	0.164121
$836$	11396.0	0.471458
$837$	−8208.00	−0.338961
$838$	−8340.00	−0.343795
$839$	−232.000	−0.00954652	−0.00477326	−	0.999989i	$-0.501519\pi$
$839$	−232.000	−0.00954652	−0.00477326	+	0.999989i	$0.501519\pi$
$840$	1575.00	0.0646936
$841$	23135.0	0.948583
$842$	−14114.0	−0.577673
$843$	−1122.00	−0.0458407
$844$	−27860.0	−1.13623
$845$	3595.00	0.146357
$846$	−3312.00	−0.134597
$847$	−847.000	−0.0343604
$848$	9102.00	0.368590
$849$	−16692.0	−0.674756
$850$	−1950.00	−0.0786876
$851$	25200.0	1.01509
$852$	−6552.00	−0.263460
$853$	9934.00	0.398750	0.199375	−	0.979923i	$-0.436109\pi$
$853$	9934.00	0.398750	0.199375	+	0.979923i	$0.436109\pi$
$854$	4662.00	0.186804
$855$	−6660.00	−0.266394
$856$	13380.0	0.534251
$857$	−13750.0	−0.548064	−0.274032	−	0.961721i	$-0.588357\pi$
$857$	−13750.0	−0.548064	−0.274032	+	0.961721i	$0.588357\pi$
$858$	1782.00	0.0709050
$859$	−5228.00	−0.207657	−0.103828	−	0.994595i	$-0.533109\pi$
$859$	−5228.00	−0.207657	−0.103828	+	0.994595i	$0.533109\pi$
$860$	−18620.0	−0.738299
$861$	−1218.00	−0.0482106
$862$	−6336.00	−0.250354
$863$	−13152.0	−0.518771	−0.259385	−	0.965774i	$-0.583520\pi$
$863$	−13152.0	−0.518771	−0.259385	+	0.965774i	$0.583520\pi$
$864$	4347.00	0.171167
$865$	−13170.0	−0.517680
$866$	−8878.00	−0.348368
$867$	3513.00	0.137610
$868$	−14896.0	−0.582492
$869$	−5632.00	−0.219853
$870$	−3270.00	−0.127429
$871$	−19224.0	−0.747853
$872$	6630.00	0.257477
$873$	4626.00	0.179343
$874$	−29600.0	−1.14558
$875$	−875.000	−0.0338062
$876$	15246.0	0.588030
$877$	28262.0	1.08819	0.544093	−	0.839025i	$-0.316874\pi$
$877$	28262.0	1.08819	0.544093	+	0.839025i	$0.316874\pi$
$878$	−5960.00	−0.229089
$879$	16410.0	0.629688
$880$	2255.00	0.0863819
$881$	−34334.0	−1.31299	−0.656494	−	0.754332i	$-0.727961\pi$
$881$	−34334.0	−1.31299	−0.656494	+	0.754332i	$0.727961\pi$
$882$	441.000	0.0168359
$883$	−5780.00	−0.220286	−0.110143	−	0.993916i	$-0.535131\pi$
$883$	−5780.00	−0.220286	−0.110143	+	0.993916i	$0.535131\pi$
$884$	29484.0	1.12178
$885$	−3060.00	−0.116227
$886$	15924.0	0.603812
$887$	2472.00	0.0935757	0.0467878	−	0.998905i	$-0.485102\pi$
$887$	2472.00	0.0935757	0.0467878	+	0.998905i	$0.485102\pi$
$888$	−5670.00	−0.214271
$889$	−11088.0	−0.418312
$890$	−3710.00	−0.139730
$891$	891.000	0.0335013
$892$	−24528.0	−0.920693
$893$	54464.0	2.04095
$894$	8010.00	0.299658
$895$	−2580.00	−0.0963574
$896$	10185.0	0.379751
$897$	32400.0	1.20603
$898$	11490.0	0.426978
$899$	66272.0	2.45862
$900$	−1575.00	−0.0583333
$901$	−17316.0	−0.640266
$902$	638.000	0.0235511
$903$	−11172.0	−0.411717
$904$	18930.0	0.696463
$905$	550.000	0.0202018
$906$	−9624.00	−0.352909
$907$	16724.0	0.612251	0.306125	−	0.951991i	$-0.400967\pi$
$907$	16724.0	0.612251	0.306125	+	0.951991i	$0.400967\pi$
$908$	−38724.0	−1.41531
$909$	−17586.0	−0.641684
$910$	−1890.00	−0.0688493
$911$	4304.00	0.156529	0.0782645	−	0.996933i	$-0.475062\pi$
$911$	4304.00	0.156529	0.0782645	+	0.996933i	$0.475062\pi$
$912$	−18204.0	−0.660959
$913$	−14652.0	−0.531118
$914$	−10054.0	−0.363848
$915$	−9990.00	−0.360939
$916$	30478.0	1.09937
$917$	9436.00	0.339808
$918$	−2106.00	−0.0757172
$919$	7800.00	0.279976	0.139988	−	0.990153i	$-0.455294\pi$
$919$	7800.00	0.279976	0.139988	+	0.990153i	$0.455294\pi$
$920$	−15000.0	−0.537538
$921$	−6396.00	−0.228833
$922$	13398.0	0.478568
$923$	16848.0	0.600822
$924$	1617.00	0.0575708
$925$	3150.00	0.111969
$926$	11888.0	0.421883
$927$	11592.0	0.410713
$928$	−35098.0	−1.24154
$929$	−4814.00	−0.170013	−0.0850066	−	0.996380i	$-0.527091\pi$
$929$	−4814.00	−0.170013	−0.0850066	+	0.996380i	$0.527091\pi$
$930$	−4560.00	−0.160783
$931$	−7252.00	−0.255290
$932$	−12054.0	−0.423650
$933$	5496.00	0.192852
$934$	6332.00	0.221830
$935$	−4290.00	−0.150051
$936$	−7290.00	−0.254574
$937$	−342.000	−0.0119239	−0.00596193	−	0.999982i	$-0.501898\pi$
$937$	−342.000	−0.0119239	−0.00596193	+	0.999982i	$0.501898\pi$
$938$	2492.00	0.0867449
$939$	−6114.00	−0.212484
$940$	12880.0	0.446914
$941$	4662.00	0.161506	0.0807528	−	0.996734i	$-0.474268\pi$
$941$	4662.00	0.161506	0.0807528	+	0.996734i	$0.474268\pi$
$942$	5298.00	0.183246
$943$	11600.0	0.400581
$944$	−8364.00	−0.288374
$945$	−945.000	−0.0325300
$946$	5852.00	0.201126
$947$	18460.0	0.633442	0.316721	−	0.948519i	$-0.397418\pi$
$947$	18460.0	0.633442	0.316721	+	0.948519i	$0.397418\pi$
$948$	10752.0	0.368364
$949$	−39204.0	−1.34101
$950$	−3700.00	−0.126362
$951$	−1854.00	−0.0632177
$952$	−8190.00	−0.278823
$953$	−11158.0	−0.379269	−0.189634	−	0.981855i	$-0.560730\pi$
$953$	−11158.0	−0.379269	−0.189634	+	0.981855i	$0.560730\pi$
$954$	1998.00	0.0678067
$955$	−16480.0	−0.558409
$956$	−16800.0	−0.568359
$957$	−7194.00	−0.242998
$958$	7968.00	0.268721
$959$	−630.000	−0.0212135
$960$	−2505.00	−0.0842172
$961$	62625.0	2.10214
$962$	6804.00	0.228035
$963$	−8028.00	−0.268638
$964$	5810.00	0.194116
$965$	2090.00	0.0697197
$966$	−4200.00	−0.139889
$967$	−29400.0	−0.977705	−0.488852	−	0.872367i	$-0.662584\pi$
$967$	−29400.0	−0.977705	−0.488852	+	0.872367i	$0.662584\pi$
$968$	−1815.00	−0.0602648
$969$	34632.0	1.14813
$970$	2570.00	0.0850698
$971$	−6108.00	−0.201869	−0.100935	−	0.994893i	$-0.532183\pi$
$971$	−6108.00	−0.201869	−0.100935	+	0.994893i	$0.532183\pi$
$972$	−1701.00	−0.0561313
$973$	15764.0	0.519394
$974$	−10472.0	−0.344502
$975$	4050.00	0.133030
$976$	−27306.0	−0.895537
$977$	−21006.0	−0.687862	−0.343931	−	0.938995i	$-0.611759\pi$
$977$	−21006.0	−0.687862	−0.343931	+	0.938995i	$0.611759\pi$
$978$	2772.00	0.0906327
$979$	−8162.00	−0.266454
$980$	−1715.00	−0.0559017
$981$	−3978.00	−0.129468
$982$	3108.00	0.100998
$983$	−43704.0	−1.41805	−0.709024	−	0.705184i	$-0.750864\pi$
$983$	−43704.0	−1.41805	−0.709024	+	0.705184i	$0.750864\pi$
$984$	−2610.00	−0.0845567
$985$	−8010.00	−0.259106
$986$	17004.0	0.549207
$987$	7728.00	0.249225
$988$	55944.0	1.80143
$989$	106400.	3.42095
$990$	495.000	0.0158910
$991$	−17312.0	−0.554928	−0.277464	−	0.960736i	$-0.589494\pi$
$991$	−17312.0	−0.554928	−0.277464	+	0.960736i	$0.589494\pi$
$992$	−48944.0	−1.56651
$993$	−30948.0	−0.989028
$994$	−2184.00	−0.0696904
$995$	−13880.0	−0.442237
$996$	27972.0	0.889886
$997$	−10018.0	−0.318228	−0.159114	−	0.987260i	$-0.550864\pi$
$997$	−10018.0	−0.318228	−0.159114	+	0.987260i	$0.550864\pi$
$998$	−7540.00	−0.239153
$999$	3402.00	0.107742

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.4.a.d.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.4.a.d.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:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1155.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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