LMFDB - Embedded newform 770.4.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,4,Mod(1,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("770.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	770.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:	$45.4314707044$
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	$\chi$	$=$	770.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{2} +4.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} -8.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} -11.0000 q^{9} +O(q^{10})$

\(q-2.00000 q^{2} +4.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} -8.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} -11.0000 q^{9} +10.0000 q^{10} +11.0000 q^{11} +16.0000 q^{12} -10.0000 q^{13} +14.0000 q^{14} -20.0000 q^{15} +16.0000 q^{16} +70.0000 q^{17} +22.0000 q^{18} +40.0000 q^{19} -20.0000 q^{20} -28.0000 q^{21} -22.0000 q^{22} +88.0000 q^{23} -32.0000 q^{24} +25.0000 q^{25} +20.0000 q^{26} -152.000 q^{27} -28.0000 q^{28} -42.0000 q^{29} +40.0000 q^{30} +108.000 q^{31} -32.0000 q^{32} +44.0000 q^{33} -140.000 q^{34} +35.0000 q^{35} -44.0000 q^{36} -42.0000 q^{37} -80.0000 q^{38} -40.0000 q^{39} +40.0000 q^{40} -242.000 q^{41} +56.0000 q^{42} -356.000 q^{43} +44.0000 q^{44} +55.0000 q^{45} -176.000 q^{46} -252.000 q^{47} +64.0000 q^{48} +49.0000 q^{49} -50.0000 q^{50} +280.000 q^{51} -40.0000 q^{52} -578.000 q^{53} +304.000 q^{54} -55.0000 q^{55} +56.0000 q^{56} +160.000 q^{57} +84.0000 q^{58} -620.000 q^{59} -80.0000 q^{60} -394.000 q^{61} -216.000 q^{62} +77.0000 q^{63} +64.0000 q^{64} +50.0000 q^{65} -88.0000 q^{66} +764.000 q^{67} +280.000 q^{68} +352.000 q^{69} -70.0000 q^{70} -384.000 q^{71} +88.0000 q^{72} -322.000 q^{73} +84.0000 q^{74} +100.000 q^{75} +160.000 q^{76} -77.0000 q^{77} +80.0000 q^{78} -824.000 q^{79} -80.0000 q^{80} -311.000 q^{81} +484.000 q^{82} +680.000 q^{83} -112.000 q^{84} -350.000 q^{85} +712.000 q^{86} -168.000 q^{87} -88.0000 q^{88} -614.000 q^{89} -110.000 q^{90} +70.0000 q^{91} +352.000 q^{92} +432.000 q^{93} +504.000 q^{94} -200.000 q^{95} -128.000 q^{96} -1582.00 q^{97} -98.0000 q^{98} -121.000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	4.00000	0.769800	0.384900	−	0.922958i	$-0.374236\pi$
$3$	4.00000	0.769800	0.384900	+	0.922958i	$0.374236\pi$
$4$	4.00000	0.500000
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−8.00000	−0.544331
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	−8.00000	−0.353553
$9$	−11.0000	−0.407407
$10$	10.0000	0.316228
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	16.0000	0.384900
$13$	−10.0000	−0.213346	−0.106673	−	0.994294i	$-0.534020\pi$
$13$	−10.0000	−0.213346	−0.106673	+	0.994294i	$0.534020\pi$
$14$	14.0000	0.267261
$15$	−20.0000	−0.344265
$16$	16.0000	0.250000
$17$	70.0000	0.998676	0.499338	−	0.866407i	$-0.333577\pi$
$17$	70.0000	0.998676	0.499338	+	0.866407i	$0.333577\pi$
$18$	22.0000	0.288081
$19$	40.0000	0.482980	0.241490	−	0.970403i	$-0.422364\pi$
$19$	40.0000	0.482980	0.241490	+	0.970403i	$0.422364\pi$
$20$	−20.0000	−0.223607
$21$	−28.0000	−0.290957
$22$	−22.0000	−0.213201
$23$	88.0000	0.797794	0.398897	−	0.916996i	$-0.369393\pi$
$23$	88.0000	0.797794	0.398897	+	0.916996i	$0.369393\pi$
$24$	−32.0000	−0.272166
$25$	25.0000	0.200000
$26$	20.0000	0.150859
$27$	−152.000	−1.08342
$28$	−28.0000	−0.188982
$29$	−42.0000	−0.268938	−0.134469	−	0.990918i	$-0.542933\pi$
$29$	−42.0000	−0.268938	−0.134469	+	0.990918i	$0.542933\pi$
$30$	40.0000	0.243432
$31$	108.000	0.625722	0.312861	−	0.949799i	$-0.398713\pi$
$31$	108.000	0.625722	0.312861	+	0.949799i	$0.398713\pi$
$32$	−32.0000	−0.176777
$33$	44.0000	0.232104
$34$	−140.000	−0.706171
$35$	35.0000	0.169031
$36$	−44.0000	−0.203704
$37$	−42.0000	−0.186615	−0.0933075	−	0.995637i	$-0.529744\pi$
$37$	−42.0000	−0.186615	−0.0933075	+	0.995637i	$0.529744\pi$
$38$	−80.0000	−0.341519
$39$	−40.0000	−0.164234
$40$	40.0000	0.158114
$41$	−242.000	−0.921806	−0.460903	−	0.887450i	$-0.652474\pi$
$41$	−242.000	−0.921806	−0.460903	+	0.887450i	$0.652474\pi$
$42$	56.0000	0.205738
$43$	−356.000	−1.26255	−0.631273	−	0.775561i	$-0.717467\pi$
$43$	−356.000	−1.26255	−0.631273	+	0.775561i	$0.717467\pi$
$44$	44.0000	0.150756
$45$	55.0000	0.182198
$46$	−176.000	−0.564126
$47$	−252.000	−0.782085	−0.391042	−	0.920373i	$-0.627885\pi$
$47$	−252.000	−0.782085	−0.391042	+	0.920373i	$0.627885\pi$
$48$	64.0000	0.192450
$49$	49.0000	0.142857
$50$	−50.0000	−0.141421
$51$	280.000	0.768781
$52$	−40.0000	−0.106673
$53$	−578.000	−1.49801	−0.749004	−	0.662566i	$-0.769468\pi$
$53$	−578.000	−1.49801	−0.749004	+	0.662566i	$0.769468\pi$
$54$	304.000	0.766096
$55$	−55.0000	−0.134840
$56$	56.0000	0.133631
$57$	160.000	0.371799
$58$	84.0000	0.190168
$59$	−620.000	−1.36809	−0.684043	−	0.729441i	$-0.739780\pi$
$59$	−620.000	−1.36809	−0.684043	+	0.729441i	$0.739780\pi$
$60$	−80.0000	−0.172133
$61$	−394.000	−0.826992	−0.413496	−	0.910506i	$-0.635692\pi$
$61$	−394.000	−0.826992	−0.413496	+	0.910506i	$0.635692\pi$
$62$	−216.000	−0.442452
$63$	77.0000	0.153986
$64$	64.0000	0.125000
$65$	50.0000	0.0954113
$66$	−88.0000	−0.164122
$67$	764.000	1.39310	0.696548	−	0.717510i	$-0.254718\pi$
$67$	764.000	1.39310	0.696548	+	0.717510i	$0.254718\pi$
$68$	280.000	0.499338
$69$	352.000	0.614142
$70$	−70.0000	−0.119523
$71$	−384.000	−0.641865	−0.320933	−	0.947102i	$-0.603996\pi$
$71$	−384.000	−0.641865	−0.320933	+	0.947102i	$0.603996\pi$
$72$	88.0000	0.144040
$73$	−322.000	−0.516264	−0.258132	−	0.966110i	$-0.583107\pi$
$73$	−322.000	−0.516264	−0.258132	+	0.966110i	$0.583107\pi$
$74$	84.0000	0.131957
$75$	100.000	0.153960
$76$	160.000	0.241490
$77$	−77.0000	−0.113961
$78$	80.0000	0.116131
$79$	−824.000	−1.17351	−0.586755	−	0.809765i	$-0.699595\pi$
$79$	−824.000	−1.17351	−0.586755	+	0.809765i	$0.699595\pi$
$80$	−80.0000	−0.111803
$81$	−311.000	−0.426612
$82$	484.000	0.651815
$83$	680.000	0.899273	0.449637	−	0.893212i	$-0.351553\pi$
$83$	680.000	0.899273	0.449637	+	0.893212i	$0.351553\pi$
$84$	−112.000	−0.145479
$85$	−350.000	−0.446622
$86$	712.000	0.892755
$87$	−168.000	−0.207029
$88$	−88.0000	−0.106600
$89$	−614.000	−0.731279	−0.365640	−	0.930756i	$-0.619150\pi$
$89$	−614.000	−0.731279	−0.365640	+	0.930756i	$0.619150\pi$
$90$	−110.000	−0.128834
$91$	70.0000	0.0806373
$92$	352.000	0.398897
$93$	432.000	0.481681
$94$	504.000	0.553017
$95$	−200.000	−0.215995
$96$	−128.000	−0.136083
$97$	−1582.00	−1.65596	−0.827978	−	0.560760i	$-0.810509\pi$
$97$	−1582.00	−1.65596	−0.827978	+	0.560760i	$0.810509\pi$
$98$	−98.0000	−0.101015
$99$	−121.000	−0.122838
$100$	100.000	0.100000
$101$	710.000	0.699482	0.349741	−	0.936847i	$-0.386270\pi$
$101$	710.000	0.699482	0.349741	+	0.936847i	$0.386270\pi$
$102$	−560.000	−0.543610
$103$	−132.000	−0.126275	−0.0631376	−	0.998005i	$-0.520111\pi$
$103$	−132.000	−0.126275	−0.0631376	+	0.998005i	$0.520111\pi$
$104$	80.0000	0.0754293
$105$	140.000	0.130120
$106$	1156.00	1.05925
$107$	684.000	0.617989	0.308994	−	0.951064i	$-0.400008\pi$
$107$	684.000	0.617989	0.308994	+	0.951064i	$0.400008\pi$
$108$	−608.000	−0.541711
$109$	86.0000	0.0755716	0.0377858	−	0.999286i	$-0.487970\pi$
$109$	86.0000	0.0755716	0.0377858	+	0.999286i	$0.487970\pi$
$110$	110.000	0.0953463
$111$	−168.000	−0.143656
$112$	−112.000	−0.0944911
$113$	1506.00	1.25374	0.626870	−	0.779124i	$-0.284336\pi$
$113$	1506.00	1.25374	0.626870	+	0.779124i	$0.284336\pi$
$114$	−320.000	−0.262901
$115$	−440.000	−0.356784
$116$	−168.000	−0.134469
$117$	110.000	0.0869188
$118$	1240.00	0.967383
$119$	−490.000	−0.377464
$120$	160.000	0.121716
$121$	121.000	0.0909091
$122$	788.000	0.584772
$123$	−968.000	−0.709607
$124$	432.000	0.312861
$125$	−125.000	−0.0894427
$126$	−154.000	−0.108884
$127$	−1384.00	−0.967009	−0.483504	−	0.875342i	$-0.660636\pi$
$127$	−1384.00	−0.967009	−0.483504	+	0.875342i	$0.660636\pi$
$128$	−128.000	−0.0883883
$129$	−1424.00	−0.971909
$130$	−100.000	−0.0674660
$131$	2464.00	1.64336	0.821682	−	0.569946i	$-0.193036\pi$
$131$	2464.00	1.64336	0.821682	+	0.569946i	$0.193036\pi$
$132$	176.000	0.116052
$133$	−280.000	−0.182549
$134$	−1528.00	−0.985068
$135$	760.000	0.484521
$136$	−560.000	−0.353085
$137$	−2518.00	−1.57027	−0.785136	−	0.619323i	$-0.787407\pi$
$137$	−2518.00	−1.57027	−0.785136	+	0.619323i	$0.787407\pi$
$138$	−704.000	−0.434264
$139$	−2648.00	−1.61583	−0.807915	−	0.589299i	$-0.799404\pi$
$139$	−2648.00	−1.61583	−0.807915	+	0.589299i	$0.799404\pi$
$140$	140.000	0.0845154
$141$	−1008.00	−0.602049
$142$	768.000	0.453867
$143$	−110.000	−0.0643263
$144$	−176.000	−0.101852
$145$	210.000	0.120273
$146$	644.000	0.365054
$147$	196.000	0.109971
$148$	−168.000	−0.0933075
$149$	174.000	0.0956687	0.0478343	−	0.998855i	$-0.484768\pi$
$149$	174.000	0.0956687	0.0478343	+	0.998855i	$0.484768\pi$
$150$	−200.000	−0.108866
$151$	72.0000	0.0388032	0.0194016	−	0.999812i	$-0.493824\pi$
$151$	72.0000	0.0388032	0.0194016	+	0.999812i	$0.493824\pi$
$152$	−320.000	−0.170759
$153$	−770.000	−0.406868
$154$	154.000	0.0805823
$155$	−540.000	−0.279831
$156$	−160.000	−0.0821170
$157$	−1278.00	−0.649653	−0.324826	−	0.945774i	$-0.605306\pi$
$157$	−1278.00	−0.649653	−0.324826	+	0.945774i	$0.605306\pi$
$158$	1648.00	0.829796
$159$	−2312.00	−1.15317
$160$	160.000	0.0790569
$161$	−616.000	−0.301538
$162$	622.000	0.301660
$163$	916.000	0.440164	0.220082	−	0.975481i	$-0.429368\pi$
$163$	916.000	0.440164	0.220082	+	0.975481i	$0.429368\pi$
$164$	−968.000	−0.460903
$165$	−220.000	−0.103800
$166$	−1360.00	−0.635882
$167$	2112.00	0.978632	0.489316	−	0.872107i	$-0.337247\pi$
$167$	2112.00	0.978632	0.489316	+	0.872107i	$0.337247\pi$
$168$	224.000	0.102869
$169$	−2097.00	−0.954483
$170$	700.000	0.315809
$171$	−440.000	−0.196770
$172$	−1424.00	−0.631273
$173$	−2698.00	−1.18569	−0.592847	−	0.805315i	$-0.701996\pi$
$173$	−2698.00	−1.18569	−0.592847	+	0.805315i	$0.701996\pi$
$174$	336.000	0.146391
$175$	−175.000	−0.0755929
$176$	176.000	0.0753778
$177$	−2480.00	−1.05315
$178$	1228.00	0.517093
$179$	−3692.00	−1.54164	−0.770819	−	0.637055i	$-0.780152\pi$
$179$	−3692.00	−1.54164	−0.770819	+	0.637055i	$0.780152\pi$
$180$	220.000	0.0910991
$181$	754.000	0.309637	0.154819	−	0.987943i	$-0.450521\pi$
$181$	754.000	0.309637	0.154819	+	0.987943i	$0.450521\pi$
$182$	−140.000	−0.0570192
$183$	−1576.00	−0.636619
$184$	−704.000	−0.282063
$185$	210.000	0.0834568
$186$	−864.000	−0.340600
$187$	770.000	0.301112
$188$	−1008.00	−0.391042
$189$	1064.00	0.409495
$190$	400.000	0.152732
$191$	−1728.00	−0.654627	−0.327313	−	0.944916i	$-0.606143\pi$
$191$	−1728.00	−0.654627	−0.327313	+	0.944916i	$0.606143\pi$
$192$	256.000	0.0962250
$193$	−3566.00	−1.32998	−0.664990	−	0.746852i	$-0.731564\pi$
$193$	−3566.00	−1.32998	−0.664990	+	0.746852i	$0.731564\pi$
$194$	3164.00	1.17094
$195$	200.000	0.0734477
$196$	196.000	0.0714286
$197$	1278.00	0.462202	0.231101	−	0.972930i	$-0.425767\pi$
$197$	1278.00	0.462202	0.231101	+	0.972930i	$0.425767\pi$
$198$	242.000	0.0868596
$199$	−164.000	−0.0584204	−0.0292102	−	0.999573i	$-0.509299\pi$
$199$	−164.000	−0.0584204	−0.0292102	+	0.999573i	$0.509299\pi$
$200$	−200.000	−0.0707107
$201$	3056.00	1.07241
$202$	−1420.00	−0.494608
$203$	294.000	0.101649
$204$	1120.00	0.384391
$205$	1210.00	0.412244
$206$	264.000	0.0892901
$207$	−968.000	−0.325027
$208$	−160.000	−0.0533366
$209$	440.000	0.145624
$210$	−280.000	−0.0920087
$211$	548.000	0.178796	0.0893978	−	0.995996i	$-0.471506\pi$
$211$	548.000	0.178796	0.0893978	+	0.995996i	$0.471506\pi$
$212$	−2312.00	−0.749004
$213$	−1536.00	−0.494108
$214$	−1368.00	−0.436984
$215$	1780.00	0.564628
$216$	1216.00	0.383048
$217$	−756.000	−0.236501
$218$	−172.000	−0.0534372
$219$	−1288.00	−0.397420
$220$	−220.000	−0.0674200
$221$	−700.000	−0.213064
$222$	336.000	0.101580
$223$	−2308.00	−0.693072	−0.346536	−	0.938037i	$-0.612642\pi$
$223$	−2308.00	−0.693072	−0.346536	+	0.938037i	$0.612642\pi$
$224$	224.000	0.0668153
$225$	−275.000	−0.0814815
$226$	−3012.00	−0.886528
$227$	5568.00	1.62802	0.814011	−	0.580849i	$-0.197279\pi$
$227$	5568.00	1.62802	0.814011	+	0.580849i	$0.197279\pi$
$228$	640.000	0.185899
$229$	−4862.00	−1.40301	−0.701507	−	0.712663i	$-0.747489\pi$
$229$	−4862.00	−1.40301	−0.701507	+	0.712663i	$0.747489\pi$
$230$	880.000	0.252285
$231$	−308.000	−0.0877269
$232$	336.000	0.0950840
$233$	6626.00	1.86302	0.931510	−	0.363716i	$-0.118492\pi$
$233$	6626.00	1.86302	0.931510	+	0.363716i	$0.118492\pi$
$234$	−220.000	−0.0614609
$235$	1260.00	0.349759
$236$	−2480.00	−0.684043
$237$	−3296.00	−0.903368
$238$	980.000	0.266907
$239$	2200.00	0.595423	0.297712	−	0.954656i	$-0.403777\pi$
$239$	2200.00	0.595423	0.297712	+	0.954656i	$0.403777\pi$
$240$	−320.000	−0.0860663
$241$	1094.00	0.292410	0.146205	−	0.989254i	$-0.453294\pi$
$241$	1094.00	0.292410	0.146205	+	0.989254i	$0.453294\pi$
$242$	−242.000	−0.0642824
$243$	2860.00	0.755017
$244$	−1576.00	−0.413496
$245$	−245.000	−0.0638877
$246$	1936.00	0.501768
$247$	−400.000	−0.103042
$248$	−864.000	−0.221226
$249$	2720.00	0.692261
$250$	250.000	0.0632456
$251$	−3580.00	−0.900269	−0.450135	−	0.892961i	$-0.648624\pi$
$251$	−3580.00	−0.900269	−0.450135	+	0.892961i	$0.648624\pi$
$252$	308.000	0.0769928
$253$	968.000	0.240544
$254$	2768.00	0.683779
$255$	−1400.00	−0.343809
$256$	256.000	0.0625000
$257$	−478.000	−0.116019	−0.0580094	−	0.998316i	$-0.518475\pi$
$257$	−478.000	−0.116019	−0.0580094	+	0.998316i	$0.518475\pi$
$258$	2848.00	0.687243
$259$	294.000	0.0705339
$260$	200.000	0.0477057
$261$	462.000	0.109567
$262$	−4928.00	−1.16203
$263$	5368.00	1.25857	0.629287	−	0.777173i	$-0.283347\pi$
$263$	5368.00	1.25857	0.629287	+	0.777173i	$0.283347\pi$
$264$	−352.000	−0.0820610
$265$	2890.00	0.669929
$266$	560.000	0.129082
$267$	−2456.00	−0.562939
$268$	3056.00	0.696548
$269$	−6790.00	−1.53901	−0.769505	−	0.638641i	$-0.779497\pi$
$269$	−6790.00	−1.53901	−0.769505	+	0.638641i	$0.779497\pi$
$270$	−1520.00	−0.342608
$271$	−1640.00	−0.367612	−0.183806	−	0.982963i	$-0.558842\pi$
$271$	−1640.00	−0.367612	−0.183806	+	0.982963i	$0.558842\pi$
$272$	1120.00	0.249669
$273$	280.000	0.0620746
$274$	5036.00	1.11035
$275$	275.000	0.0603023
$276$	1408.00	0.307071
$277$	−5234.00	−1.13531	−0.567654	−	0.823267i	$-0.692149\pi$
$277$	−5234.00	−1.13531	−0.567654	+	0.823267i	$0.692149\pi$
$278$	5296.00	1.14256
$279$	−1188.00	−0.254924
$280$	−280.000	−0.0597614
$281$	258.000	0.0547722	0.0273861	−	0.999625i	$-0.491282\pi$
$281$	258.000	0.0547722	0.0273861	+	0.999625i	$0.491282\pi$
$282$	2016.00	0.425713
$283$	−856.000	−0.179802	−0.0899009	−	0.995951i	$-0.528655\pi$
$283$	−856.000	−0.179802	−0.0899009	+	0.995951i	$0.528655\pi$
$284$	−1536.00	−0.320933
$285$	−800.000	−0.166273
$286$	220.000	0.0454856
$287$	1694.00	0.348410
$288$	352.000	0.0720201
$289$	−13.0000	−0.00264604
$290$	−420.000	−0.0850457
$291$	−6328.00	−1.27476
$292$	−1288.00	−0.258132
$293$	6158.00	1.22783	0.613915	−	0.789372i	$-0.289594\pi$
$293$	6158.00	1.22783	0.613915	+	0.789372i	$0.289594\pi$
$294$	−392.000	−0.0777616
$295$	3100.00	0.611827
$296$	336.000	0.0659784
$297$	−1672.00	−0.326664
$298$	−348.000	−0.0676480
$299$	−880.000	−0.170206
$300$	400.000	0.0769800
$301$	2492.00	0.477198
$302$	−144.000	−0.0274380
$303$	2840.00	0.538461
$304$	640.000	0.120745
$305$	1970.00	0.369842
$306$	1540.00	0.287699
$307$	4496.00	0.835832	0.417916	−	0.908486i	$-0.362761\pi$
$307$	4496.00	0.835832	0.417916	+	0.908486i	$0.362761\pi$
$308$	−308.000	−0.0569803
$309$	−528.000	−0.0972067
$310$	1080.00	0.197871
$311$	3044.00	0.555014	0.277507	−	0.960724i	$-0.410492\pi$
$311$	3044.00	0.555014	0.277507	+	0.960724i	$0.410492\pi$
$312$	320.000	0.0580655
$313$	7506.00	1.35548	0.677738	−	0.735303i	$-0.262960\pi$
$313$	7506.00	1.35548	0.677738	+	0.735303i	$0.262960\pi$
$314$	2556.00	0.459374
$315$	−385.000	−0.0688644
$316$	−3296.00	−0.586755
$317$	10166.0	1.80120	0.900598	−	0.434652i	$-0.143129\pi$
$317$	10166.0	1.80120	0.900598	+	0.434652i	$0.143129\pi$
$318$	4624.00	0.815412
$319$	−462.000	−0.0810879
$320$	−320.000	−0.0559017
$321$	2736.00	0.475728
$322$	1232.00	0.213219
$323$	2800.00	0.482341
$324$	−1244.00	−0.213306
$325$	−250.000	−0.0426692
$326$	−1832.00	−0.311243
$327$	344.000	0.0581751
$328$	1936.00	0.325908
$329$	1764.00	0.295600
$330$	440.000	0.0733976
$331$	7348.00	1.22019	0.610095	−	0.792329i	$-0.291131\pi$
$331$	7348.00	1.22019	0.610095	+	0.792329i	$0.291131\pi$
$332$	2720.00	0.449637
$333$	462.000	0.0760284
$334$	−4224.00	−0.691997
$335$	−3820.00	−0.623012
$336$	−448.000	−0.0727393
$337$	2138.00	0.345591	0.172796	−	0.984958i	$-0.444720\pi$
$337$	2138.00	0.345591	0.172796	+	0.984958i	$0.444720\pi$
$338$	4194.00	0.674922
$339$	6024.00	0.965129
$340$	−1400.00	−0.223311
$341$	1188.00	0.188662
$342$	880.000	0.139137
$343$	−343.000	−0.0539949
$344$	2848.00	0.446378
$345$	−1760.00	−0.274653
$346$	5396.00	0.838413
$347$	−1364.00	−0.211018	−0.105509	−	0.994418i	$-0.533647\pi$
$347$	−1364.00	−0.211018	−0.105509	+	0.994418i	$0.533647\pi$
$348$	−672.000	−0.103514
$349$	−530.000	−0.0812901	−0.0406451	−	0.999174i	$-0.512941\pi$
$349$	−530.000	−0.0812901	−0.0406451	+	0.999174i	$0.512941\pi$
$350$	350.000	0.0534522
$351$	1520.00	0.231144
$352$	−352.000	−0.0533002
$353$	9874.00	1.48878	0.744391	−	0.667744i	$-0.232740\pi$
$353$	9874.00	1.48878	0.744391	+	0.667744i	$0.232740\pi$
$354$	4960.00	0.744692
$355$	1920.00	0.287051
$356$	−2456.00	−0.365640
$357$	−1960.00	−0.290572
$358$	7384.00	1.09010
$359$	−1352.00	−0.198763	−0.0993814	−	0.995049i	$-0.531686\pi$
$359$	−1352.00	−0.198763	−0.0993814	+	0.995049i	$0.531686\pi$
$360$	−440.000	−0.0644168
$361$	−5259.00	−0.766730
$362$	−1508.00	−0.218947
$363$	484.000	0.0699819
$364$	280.000	0.0403186
$365$	1610.00	0.230880
$366$	3152.00	0.450158
$367$	−6884.00	−0.979133	−0.489567	−	0.871966i	$-0.662845\pi$
$367$	−6884.00	−0.979133	−0.489567	+	0.871966i	$0.662845\pi$
$368$	1408.00	0.199449
$369$	2662.00	0.375551
$370$	−420.000	−0.0590129
$371$	4046.00	0.566194
$372$	1728.00	0.240840
$373$	3022.00	0.419499	0.209750	−	0.977755i	$-0.432735\pi$
$373$	3022.00	0.419499	0.209750	+	0.977755i	$0.432735\pi$
$374$	−1540.00	−0.212918
$375$	−500.000	−0.0688530
$376$	2016.00	0.276509
$377$	420.000	0.0573769
$378$	−2128.00	−0.289557
$379$	−644.000	−0.0872825	−0.0436412	−	0.999047i	$-0.513896\pi$
$379$	−644.000	−0.0872825	−0.0436412	+	0.999047i	$0.513896\pi$
$380$	−800.000	−0.107998
$381$	−5536.00	−0.744404
$382$	3456.00	0.462891
$383$	−12036.0	−1.60577	−0.802886	−	0.596132i	$-0.796703\pi$
$383$	−12036.0	−1.60577	−0.802886	+	0.596132i	$0.796703\pi$
$384$	−512.000	−0.0680414
$385$	385.000	0.0509647
$386$	7132.00	0.940438
$387$	3916.00	0.514371
$388$	−6328.00	−0.827978
$389$	−3642.00	−0.474696	−0.237348	−	0.971425i	$-0.576278\pi$
$389$	−3642.00	−0.474696	−0.237348	+	0.971425i	$0.576278\pi$
$390$	−400.000	−0.0519354
$391$	6160.00	0.796738
$392$	−392.000	−0.0505076
$393$	9856.00	1.26506
$394$	−2556.00	−0.326826
$395$	4120.00	0.524809
$396$	−484.000	−0.0614190
$397$	−8558.00	−1.08190	−0.540949	−	0.841055i	$-0.681935\pi$
$397$	−8558.00	−1.08190	−0.540949	+	0.841055i	$0.681935\pi$
$398$	328.000	0.0413094
$399$	−1120.00	−0.140527
$400$	400.000	0.0500000
$401$	−5246.00	−0.653299	−0.326649	−	0.945146i	$-0.605920\pi$
$401$	−5246.00	−0.653299	−0.326649	+	0.945146i	$0.605920\pi$
$402$	−6112.00	−0.758306
$403$	−1080.00	−0.133495
$404$	2840.00	0.349741
$405$	1555.00	0.190787
$406$	−588.000	−0.0718767
$407$	−462.000	−0.0562666
$408$	−2240.00	−0.271805
$409$	4406.00	0.532672	0.266336	−	0.963880i	$-0.414187\pi$
$409$	4406.00	0.532672	0.266336	+	0.963880i	$0.414187\pi$
$410$	−2420.00	−0.291501
$411$	−10072.0	−1.20880
$412$	−528.000	−0.0631376
$413$	4340.00	0.517088
$414$	1936.00	0.229829
$415$	−3400.00	−0.402167
$416$	320.000	0.0377146
$417$	−10592.0	−1.24387
$418$	−880.000	−0.102972
$419$	9876.00	1.15149	0.575745	−	0.817629i	$-0.304712\pi$
$419$	9876.00	1.15149	0.575745	+	0.817629i	$0.304712\pi$
$420$	560.000	0.0650600
$421$	−14642.0	−1.69503	−0.847515	−	0.530772i	$-0.821902\pi$
$421$	−14642.0	−1.69503	−0.847515	+	0.530772i	$0.821902\pi$
$422$	−1096.00	−0.126428
$423$	2772.00	0.318627
$424$	4624.00	0.529626
$425$	1750.00	0.199735
$426$	3072.00	0.349387
$427$	2758.00	0.312574
$428$	2736.00	0.308994
$429$	−440.000	−0.0495184
$430$	−3560.00	−0.399252
$431$	1728.00	0.193120	0.0965601	−	0.995327i	$-0.469216\pi$
$431$	1728.00	0.193120	0.0965601	+	0.995327i	$0.469216\pi$
$432$	−2432.00	−0.270856
$433$	8482.00	0.941383	0.470692	−	0.882298i	$-0.344004\pi$
$433$	8482.00	0.941383	0.470692	+	0.882298i	$0.344004\pi$
$434$	1512.00	0.167231
$435$	840.000	0.0925860
$436$	344.000	0.0377858
$437$	3520.00	0.385319
$438$	2576.00	0.281018
$439$	−384.000	−0.0417479	−0.0208739	−	0.999782i	$-0.506645\pi$
$439$	−384.000	−0.0417479	−0.0208739	+	0.999782i	$0.506645\pi$
$440$	440.000	0.0476731
$441$	−539.000	−0.0582011
$442$	1400.00	0.150659
$443$	17580.0	1.88544	0.942721	−	0.333582i	$-0.108257\pi$
$443$	17580.0	1.88544	0.942721	+	0.333582i	$0.108257\pi$
$444$	−672.000	−0.0718282
$445$	3070.00	0.327038
$446$	4616.00	0.490076
$447$	696.000	0.0736458
$448$	−448.000	−0.0472456
$449$	5010.00	0.526585	0.263292	−	0.964716i	$-0.415192\pi$
$449$	5010.00	0.526585	0.263292	+	0.964716i	$0.415192\pi$
$450$	550.000	0.0576161
$451$	−2662.00	−0.277935
$452$	6024.00	0.626870
$453$	288.000	0.0298707
$454$	−11136.0	−1.15119
$455$	−350.000	−0.0360621
$456$	−1280.00	−0.131451
$457$	10602.0	1.08521	0.542605	−	0.839988i	$-0.317438\pi$
$457$	10602.0	1.08521	0.542605	+	0.839988i	$0.317438\pi$
$458$	9724.00	0.992080
$459$	−10640.0	−1.08199
$460$	−1760.00	−0.178392
$461$	−6610.00	−0.667806	−0.333903	−	0.942608i	$-0.608366\pi$
$461$	−6610.00	−0.667806	−0.333903	+	0.942608i	$0.608366\pi$
$462$	616.000	0.0620323
$463$	7592.00	0.762052	0.381026	−	0.924564i	$-0.375571\pi$
$463$	7592.00	0.762052	0.381026	+	0.924564i	$0.375571\pi$
$464$	−672.000	−0.0672345
$465$	−2160.00	−0.215414
$466$	−13252.0	−1.31735
$467$	−15500.0	−1.53588	−0.767938	−	0.640524i	$-0.778717\pi$
$467$	−15500.0	−1.53588	−0.767938	+	0.640524i	$0.778717\pi$
$468$	440.000	0.0434594
$469$	−5348.00	−0.526541
$470$	−2520.00	−0.247317
$471$	−5112.00	−0.500103
$472$	4960.00	0.483692
$473$	−3916.00	−0.380672
$474$	6592.00	0.638778
$475$	1000.00	0.0965961
$476$	−1960.00	−0.188732
$477$	6358.00	0.610299
$478$	−4400.00	−0.421028
$479$	−4400.00	−0.419710	−0.209855	−	0.977733i	$-0.567299\pi$
$479$	−4400.00	−0.419710	−0.209855	+	0.977733i	$0.567299\pi$
$480$	640.000	0.0608581
$481$	420.000	0.0398136
$482$	−2188.00	−0.206765
$483$	−2464.00	−0.232124
$484$	484.000	0.0454545
$485$	7910.00	0.740566
$486$	−5720.00	−0.533878
$487$	680.000	0.0632726	0.0316363	−	0.999499i	$-0.489928\pi$
$487$	680.000	0.0632726	0.0316363	+	0.999499i	$0.489928\pi$
$488$	3152.00	0.292386
$489$	3664.00	0.338838
$490$	490.000	0.0451754
$491$	−13084.0	−1.20259	−0.601296	−	0.799026i	$-0.705349\pi$
$491$	−13084.0	−1.20259	−0.601296	+	0.799026i	$0.705349\pi$
$492$	−3872.00	−0.354803
$493$	−2940.00	−0.268582
$494$	800.000	0.0728617
$495$	605.000	0.0549348
$496$	1728.00	0.156430
$497$	2688.00	0.242602
$498$	−5440.00	−0.489502
$499$	−12020.0	−1.07833	−0.539167	−	0.842199i	$-0.681261\pi$
$499$	−12020.0	−1.07833	−0.539167	+	0.842199i	$0.681261\pi$
$500$	−500.000	−0.0447214
$501$	8448.00	0.753351
$502$	7160.00	0.636587
$503$	3216.00	0.285078	0.142539	−	0.989789i	$-0.454473\pi$
$503$	3216.00	0.285078	0.142539	+	0.989789i	$0.454473\pi$
$504$	−616.000	−0.0544421
$505$	−3550.00	−0.312818
$506$	−1936.00	−0.170090
$507$	−8388.00	−0.734762
$508$	−5536.00	−0.483504
$509$	−2278.00	−0.198370	−0.0991852	−	0.995069i	$-0.531624\pi$
$509$	−2278.00	−0.198370	−0.0991852	+	0.995069i	$0.531624\pi$
$510$	2800.00	0.243110
$511$	2254.00	0.195129
$512$	−512.000	−0.0441942
$513$	−6080.00	−0.523272
$514$	956.000	0.0820377
$515$	660.000	0.0564720
$516$	−5696.00	−0.485954
$517$	−2772.00	−0.235807
$518$	−588.000	−0.0498750
$519$	−10792.0	−0.912748
$520$	−400.000	−0.0337330
$521$	1626.00	0.136730	0.0683650	−	0.997660i	$-0.478222\pi$
$521$	1626.00	0.136730	0.0683650	+	0.997660i	$0.478222\pi$
$522$	−924.000	−0.0774758
$523$	−9816.00	−0.820695	−0.410348	−	0.911929i	$-0.634593\pi$
$523$	−9816.00	−0.820695	−0.410348	+	0.911929i	$0.634593\pi$
$524$	9856.00	0.821682
$525$	−700.000	−0.0581914
$526$	−10736.0	−0.889946
$527$	7560.00	0.624893
$528$	704.000	0.0580259
$529$	−4423.00	−0.363524
$530$	−5780.00	−0.473712
$531$	6820.00	0.557369
$532$	−1120.00	−0.0912747
$533$	2420.00	0.196664
$534$	4912.00	0.398058
$535$	−3420.00	−0.276373
$536$	−6112.00	−0.492534
$537$	−14768.0	−1.18675
$538$	13580.0	1.08824
$539$	539.000	0.0430730
$540$	3040.00	0.242261
$541$	3110.00	0.247152	0.123576	−	0.992335i	$-0.460564\pi$
$541$	3110.00	0.247152	0.123576	+	0.992335i	$0.460564\pi$
$542$	3280.00	0.259941
$543$	3016.00	0.238359
$544$	−2240.00	−0.176543
$545$	−430.000	−0.0337967
$546$	−560.000	−0.0438934
$547$	6812.00	0.532468	0.266234	−	0.963908i	$-0.414221\pi$
$547$	6812.00	0.532468	0.266234	+	0.963908i	$0.414221\pi$
$548$	−10072.0	−0.785136
$549$	4334.00	0.336923
$550$	−550.000	−0.0426401
$551$	−1680.00	−0.129892
$552$	−2816.00	−0.217132
$553$	5768.00	0.443545
$554$	10468.0	0.802785
$555$	840.000	0.0642451
$556$	−10592.0	−0.807915
$557$	−16746.0	−1.27388	−0.636940	−	0.770914i	$-0.719800\pi$
$557$	−16746.0	−1.27388	−0.636940	+	0.770914i	$0.719800\pi$
$558$	2376.00	0.180258
$559$	3560.00	0.269359
$560$	560.000	0.0422577
$561$	3080.00	0.231796
$562$	−516.000	−0.0387298
$563$	15216.0	1.13904	0.569519	−	0.821978i	$-0.307130\pi$
$563$	15216.0	1.13904	0.569519	+	0.821978i	$0.307130\pi$
$564$	−4032.00	−0.301025
$565$	−7530.00	−0.560689
$566$	1712.00	0.127139
$567$	2177.00	0.161244
$568$	3072.00	0.226934
$569$	−286.000	−0.0210716	−0.0105358	−	0.999944i	$-0.503354\pi$
$569$	−286.000	−0.0210716	−0.0105358	+	0.999944i	$0.503354\pi$
$570$	1600.00	0.117573
$571$	−21980.0	−1.61092	−0.805459	−	0.592651i	$-0.798081\pi$
$571$	−21980.0	−1.61092	−0.805459	+	0.592651i	$0.798081\pi$
$572$	−440.000	−0.0321632
$573$	−6912.00	−0.503932
$574$	−3388.00	−0.246363
$575$	2200.00	0.159559
$576$	−704.000	−0.0509259
$577$	−3222.00	−0.232467	−0.116234	−	0.993222i	$-0.537082\pi$
$577$	−3222.00	−0.232467	−0.116234	+	0.993222i	$0.537082\pi$
$578$	26.0000	0.00187103
$579$	−14264.0	−1.02382
$580$	840.000	0.0601364
$581$	−4760.00	−0.339893
$582$	12656.0	0.901388
$583$	−6358.00	−0.451666
$584$	2576.00	0.182527
$585$	−550.000	−0.0388713
$586$	−12316.0	−0.868207
$587$	−6556.00	−0.460980	−0.230490	−	0.973075i	$-0.574033\pi$
$587$	−6556.00	−0.460980	−0.230490	+	0.973075i	$0.574033\pi$
$588$	784.000	0.0549857
$589$	4320.00	0.302211
$590$	−6200.00	−0.432627
$591$	5112.00	0.355803
$592$	−672.000	−0.0466538
$593$	−8186.00	−0.566878	−0.283439	−	0.958990i	$-0.591475\pi$
$593$	−8186.00	−0.566878	−0.283439	+	0.958990i	$0.591475\pi$
$594$	3344.00	0.230987
$595$	2450.00	0.168807
$596$	696.000	0.0478343
$597$	−656.000	−0.0449720
$598$	1760.00	0.120354
$599$	5840.00	0.398357	0.199179	−	0.979963i	$-0.436173\pi$
$599$	5840.00	0.398357	0.199179	+	0.979963i	$0.436173\pi$
$600$	−800.000	−0.0544331
$601$	14102.0	0.957126	0.478563	−	0.878053i	$-0.341158\pi$
$601$	14102.0	0.957126	0.478563	+	0.878053i	$0.341158\pi$
$602$	−4984.00	−0.337430
$603$	−8404.00	−0.567558
$604$	288.000	0.0194016
$605$	−605.000	−0.0406558
$606$	−5680.00	−0.380750
$607$	−5312.00	−0.355202	−0.177601	−	0.984103i	$-0.556834\pi$
$607$	−5312.00	−0.355202	−0.177601	+	0.984103i	$0.556834\pi$
$608$	−1280.00	−0.0853797
$609$	1176.00	0.0782495
$610$	−3940.00	−0.261518
$611$	2520.00	0.166855
$612$	−3080.00	−0.203434
$613$	26302.0	1.73300	0.866499	−	0.499179i	$-0.166365\pi$
$613$	26302.0	1.73300	0.866499	+	0.499179i	$0.166365\pi$
$614$	−8992.00	−0.591022
$615$	4840.00	0.317346
$616$	616.000	0.0402911
$617$	26186.0	1.70860	0.854302	−	0.519777i	$-0.173985\pi$
$617$	26186.0	1.70860	0.854302	+	0.519777i	$0.173985\pi$
$618$	1056.00	0.0687355
$619$	−68.0000	−0.00441543	−0.00220771	−	0.999998i	$-0.500703\pi$
$619$	−68.0000	−0.00441543	−0.00220771	+	0.999998i	$0.500703\pi$
$620$	−2160.00	−0.139916
$621$	−13376.0	−0.864348
$622$	−6088.00	−0.392454
$623$	4298.00	0.276398
$624$	−640.000	−0.0410585
$625$	625.000	0.0400000
$626$	−15012.0	−0.958467
$627$	1760.00	0.112101
$628$	−5112.00	−0.324826
$629$	−2940.00	−0.186368
$630$	770.000	0.0486945
$631$	−15848.0	−0.999840	−0.499920	−	0.866072i	$-0.666637\pi$
$631$	−15848.0	−0.999840	−0.499920	+	0.866072i	$0.666637\pi$
$632$	6592.00	0.414898
$633$	2192.00	0.137637
$634$	−20332.0	−1.27364
$635$	6920.00	0.432460
$636$	−9248.00	−0.576583
$637$	−490.000	−0.0304780
$638$	924.000	0.0573378
$639$	4224.00	0.261501
$640$	640.000	0.0395285
$641$	−8494.00	−0.523390	−0.261695	−	0.965151i	$-0.584281\pi$
$641$	−8494.00	−0.523390	−0.261695	+	0.965151i	$0.584281\pi$
$642$	−5472.00	−0.336390
$643$	−16868.0	−1.03454	−0.517270	−	0.855822i	$-0.673052\pi$
$643$	−16868.0	−1.03454	−0.517270	+	0.855822i	$0.673052\pi$
$644$	−2464.00	−0.150769
$645$	7120.00	0.434651
$646$	−5600.00	−0.341067
$647$	1236.00	0.0751038	0.0375519	−	0.999295i	$-0.488044\pi$
$647$	1236.00	0.0751038	0.0375519	+	0.999295i	$0.488044\pi$
$648$	2488.00	0.150830
$649$	−6820.00	−0.412494
$650$	500.000	0.0301717
$651$	−3024.00	−0.182058
$652$	3664.00	0.220082
$653$	−19234.0	−1.15266	−0.576328	−	0.817218i	$-0.695515\pi$
$653$	−19234.0	−1.15266	−0.576328	+	0.817218i	$0.695515\pi$
$654$	−688.000	−0.0411360
$655$	−12320.0	−0.734935
$656$	−3872.00	−0.230452
$657$	3542.00	0.210330
$658$	−3528.00	−0.209021
$659$	−2380.00	−0.140685	−0.0703427	−	0.997523i	$-0.522409\pi$
$659$	−2380.00	−0.140685	−0.0703427	+	0.997523i	$0.522409\pi$
$660$	−880.000	−0.0518999
$661$	12386.0	0.728834	0.364417	−	0.931236i	$-0.381268\pi$
$661$	12386.0	0.728834	0.364417	+	0.931236i	$0.381268\pi$
$662$	−14696.0	−0.862804
$663$	−2800.00	−0.164017
$664$	−5440.00	−0.317941
$665$	1400.00	0.0816386
$666$	−924.000	−0.0537602
$667$	−3696.00	−0.214557
$668$	8448.00	0.489316
$669$	−9232.00	−0.533527
$670$	7640.00	0.440536
$671$	−4334.00	−0.249348
$672$	896.000	0.0514344
$673$	4922.00	0.281916	0.140958	−	0.990016i	$-0.454982\pi$
$673$	4922.00	0.281916	0.140958	+	0.990016i	$0.454982\pi$
$674$	−4276.00	−0.244370
$675$	−3800.00	−0.216685
$676$	−8388.00	−0.477242
$677$	12910.0	0.732897	0.366449	−	0.930438i	$-0.380574\pi$
$677$	12910.0	0.732897	0.366449	+	0.930438i	$0.380574\pi$
$678$	−12048.0	−0.682449
$679$	11074.0	0.625893
$680$	2800.00	0.157905
$681$	22272.0	1.25325
$682$	−2376.00	−0.133404
$683$	14220.0	0.796652	0.398326	−	0.917244i	$-0.369591\pi$
$683$	14220.0	0.796652	0.398326	+	0.917244i	$0.369591\pi$
$684$	−1760.00	−0.0983849
$685$	12590.0	0.702247
$686$	686.000	0.0381802
$687$	−19448.0	−1.08004
$688$	−5696.00	−0.315637
$689$	5780.00	0.319594
$690$	3520.00	0.194209
$691$	7996.00	0.440206	0.220103	−	0.975477i	$-0.429361\pi$
$691$	7996.00	0.440206	0.220103	+	0.975477i	$0.429361\pi$
$692$	−10792.0	−0.592847
$693$	847.000	0.0464284
$694$	2728.00	0.149212
$695$	13240.0	0.722621
$696$	1344.00	0.0731957
$697$	−16940.0	−0.920586
$698$	1060.00	0.0574808
$699$	26504.0	1.43415
$700$	−700.000	−0.0377964
$701$	1766.00	0.0951511	0.0475755	−	0.998868i	$-0.484851\pi$
$701$	1766.00	0.0951511	0.0475755	+	0.998868i	$0.484851\pi$
$702$	−3040.00	−0.163444
$703$	−1680.00	−0.0901314
$704$	704.000	0.0376889
$705$	5040.00	0.269245
$706$	−19748.0	−1.05273
$707$	−4970.00	−0.264379
$708$	−9920.00	−0.526577
$709$	−16010.0	−0.848051	−0.424026	−	0.905650i	$-0.639383\pi$
$709$	−16010.0	−0.848051	−0.424026	+	0.905650i	$0.639383\pi$
$710$	−3840.00	−0.202976
$711$	9064.00	0.478096
$712$	4912.00	0.258546
$713$	9504.00	0.499197
$714$	3920.00	0.205465
$715$	550.000	0.0287676
$716$	−14768.0	−0.770819
$717$	8800.00	0.458357
$718$	2704.00	0.140546
$719$	6684.00	0.346691	0.173346	−	0.984861i	$-0.444542\pi$
$719$	6684.00	0.346691	0.173346	+	0.984861i	$0.444542\pi$
$720$	880.000	0.0455495
$721$	924.000	0.0477275
$722$	10518.0	0.542160
$723$	4376.00	0.225097
$724$	3016.00	0.154819
$725$	−1050.00	−0.0537876
$726$	−968.000	−0.0494846
$727$	−1772.00	−0.0903987	−0.0451993	−	0.998978i	$-0.514392\pi$
$727$	−1772.00	−0.0903987	−0.0451993	+	0.998978i	$0.514392\pi$
$728$	−560.000	−0.0285096
$729$	19837.0	1.00782
$730$	−3220.00	−0.163257
$731$	−24920.0	−1.26087
$732$	−6304.00	−0.318309
$733$	9062.00	0.456634	0.228317	−	0.973587i	$-0.426678\pi$
$733$	9062.00	0.456634	0.228317	+	0.973587i	$0.426678\pi$
$734$	13768.0	0.692352
$735$	−980.000	−0.0491807
$736$	−2816.00	−0.141031
$737$	8404.00	0.420034
$738$	−5324.00	−0.265554
$739$	−28692.0	−1.42822	−0.714108	−	0.700035i	$-0.753168\pi$
$739$	−28692.0	−1.42822	−0.714108	+	0.700035i	$0.753168\pi$
$740$	840.000	0.0417284
$741$	−1600.00	−0.0793218
$742$	−8092.00	−0.400359
$743$	−4944.00	−0.244115	−0.122058	−	0.992523i	$-0.538949\pi$
$743$	−4944.00	−0.244115	−0.122058	+	0.992523i	$0.538949\pi$
$744$	−3456.00	−0.170300
$745$	−870.000	−0.0427843
$746$	−6044.00	−0.296631
$747$	−7480.00	−0.366371
$748$	3080.00	0.150556
$749$	−4788.00	−0.233578
$750$	1000.00	0.0486864
$751$	−9088.00	−0.441579	−0.220790	−	0.975321i	$-0.570863\pi$
$751$	−9088.00	−0.441579	−0.220790	+	0.975321i	$0.570863\pi$
$752$	−4032.00	−0.195521
$753$	−14320.0	−0.693028
$754$	−840.000	−0.0405716
$755$	−360.000	−0.0173533
$756$	4256.00	0.204748
$757$	−7562.00	−0.363072	−0.181536	−	0.983384i	$-0.558107\pi$
$757$	−7562.00	−0.363072	−0.181536	+	0.983384i	$0.558107\pi$
$758$	1288.00	0.0617180
$759$	3872.00	0.185171
$760$	1600.00	0.0763659
$761$	−7018.00	−0.334300	−0.167150	−	0.985931i	$-0.553456\pi$
$761$	−7018.00	−0.334300	−0.167150	+	0.985931i	$0.553456\pi$
$762$	11072.0	0.526373
$763$	−602.000	−0.0285634
$764$	−6912.00	−0.327313
$765$	3850.00	0.181957
$766$	24072.0	1.13545
$767$	6200.00	0.291876
$768$	1024.00	0.0481125
$769$	9758.00	0.457584	0.228792	−	0.973475i	$-0.426522\pi$
$769$	9758.00	0.457584	0.228792	+	0.973475i	$0.426522\pi$
$770$	−770.000	−0.0360375
$771$	−1912.00	−0.0893113
$772$	−14264.0	−0.664990
$773$	35114.0	1.63385	0.816923	−	0.576747i	$-0.195678\pi$
$773$	35114.0	1.63385	0.816923	+	0.576747i	$0.195678\pi$
$774$	−7832.00	−0.363715
$775$	2700.00	0.125144
$776$	12656.0	0.585469
$777$	1176.00	0.0542970
$778$	7284.00	0.335661
$779$	−9680.00	−0.445214
$780$	800.000	0.0367238
$781$	−4224.00	−0.193530
$782$	−12320.0	−0.563379
$783$	6384.00	0.291374
$784$	784.000	0.0357143
$785$	6390.00	0.290534
$786$	−19712.0	−0.894534
$787$	19896.0	0.901164	0.450582	−	0.892735i	$-0.351217\pi$
$787$	19896.0	0.901164	0.450582	+	0.892735i	$0.351217\pi$
$788$	5112.00	0.231101
$789$	21472.0	0.968851
$790$	−8240.00	−0.371096
$791$	−10542.0	−0.473869
$792$	968.000	0.0434298
$793$	3940.00	0.176436
$794$	17116.0	0.765018
$795$	11560.0	0.515712
$796$	−656.000	−0.0292102
$797$	42802.0	1.90229	0.951145	−	0.308746i	$-0.0999091\pi$
$797$	42802.0	1.90229	0.951145	+	0.308746i	$0.0999091\pi$
$798$	2240.00	0.0993673
$799$	−17640.0	−0.781049
$800$	−800.000	−0.0353553
$801$	6754.00	0.297929
$802$	10492.0	0.461952
$803$	−3542.00	−0.155659
$804$	12224.0	0.536203
$805$	3080.00	0.134852
$806$	2160.00	0.0943955
$807$	−27160.0	−1.18473
$808$	−5680.00	−0.247304
$809$	17322.0	0.752792	0.376396	−	0.926459i	$-0.377163\pi$
$809$	17322.0	0.752792	0.376396	+	0.926459i	$0.377163\pi$
$810$	−3110.00	−0.134906
$811$	6296.00	0.272605	0.136302	−	0.990667i	$-0.456478\pi$
$811$	6296.00	0.272605	0.136302	+	0.990667i	$0.456478\pi$
$812$	1176.00	0.0508245
$813$	−6560.00	−0.282988
$814$	924.000	0.0397865
$815$	−4580.00	−0.196847
$816$	4480.00	0.192195
$817$	−14240.0	−0.609785
$818$	−8812.00	−0.376656
$819$	−770.000	−0.0328522
$820$	4840.00	0.206122
$821$	9486.00	0.403244	0.201622	−	0.979463i	$-0.435379\pi$
$821$	9486.00	0.403244	0.201622	+	0.979463i	$0.435379\pi$
$822$	20144.0	0.854748
$823$	−32104.0	−1.35975	−0.679876	−	0.733328i	$-0.737966\pi$
$823$	−32104.0	−1.35975	−0.679876	+	0.733328i	$0.737966\pi$
$824$	1056.00	0.0446450
$825$	1100.00	0.0464207
$826$	−8680.00	−0.365637
$827$	−9772.00	−0.410890	−0.205445	−	0.978669i	$-0.565864\pi$
$827$	−9772.00	−0.410890	−0.205445	+	0.978669i	$0.565864\pi$
$828$	−3872.00	−0.162514
$829$	26010.0	1.08970	0.544852	−	0.838532i	$-0.316586\pi$
$829$	26010.0	1.08970	0.544852	+	0.838532i	$0.316586\pi$
$830$	6800.00	0.284375
$831$	−20936.0	−0.873961
$832$	−640.000	−0.0266683
$833$	3430.00	0.142668
$834$	21184.0	0.879547
$835$	−10560.0	−0.437657
$836$	1760.00	0.0728120
$837$	−16416.0	−0.677921
$838$	−19752.0	−0.814226
$839$	−26220.0	−1.07892	−0.539461	−	0.842011i	$-0.681372\pi$
$839$	−26220.0	−1.07892	−0.539461	+	0.842011i	$0.681372\pi$
$840$	−1120.00	−0.0460044
$841$	−22625.0	−0.927672
$842$	29284.0	1.19857
$843$	1032.00	0.0421637
$844$	2192.00	0.0893978
$845$	10485.0	0.426858
$846$	−5544.00	−0.225303
$847$	−847.000	−0.0343604
$848$	−9248.00	−0.374502
$849$	−3424.00	−0.138412
$850$	−3500.00	−0.141234
$851$	−3696.00	−0.148880
$852$	−6144.00	−0.247054
$853$	46846.0	1.88039	0.940197	−	0.340631i	$-0.110641\pi$
$853$	46846.0	1.88039	0.940197	+	0.340631i	$0.110641\pi$
$854$	−5516.00	−0.221023
$855$	2200.00	0.0879981
$856$	−5472.00	−0.218492
$857$	26454.0	1.05444	0.527218	−	0.849730i	$-0.323235\pi$
$857$	26454.0	1.05444	0.527218	+	0.849730i	$0.323235\pi$
$858$	880.000	0.0350148
$859$	27028.0	1.07355	0.536777	−	0.843724i	$-0.319642\pi$
$859$	27028.0	1.07355	0.536777	+	0.843724i	$0.319642\pi$
$860$	7120.00	0.282314
$861$	6776.00	0.268206
$862$	−3456.00	−0.136557
$863$	−21696.0	−0.855783	−0.427891	−	0.903830i	$-0.640743\pi$
$863$	−21696.0	−0.855783	−0.427891	+	0.903830i	$0.640743\pi$
$864$	4864.00	0.191524
$865$	13490.0	0.530259
$866$	−16964.0	−0.665658
$867$	−52.0000	−0.00203692
$868$	−3024.00	−0.118250
$869$	−9064.00	−0.353826
$870$	−1680.00	−0.0654682
$871$	−7640.00	−0.297212
$872$	−688.000	−0.0267186
$873$	17402.0	0.674649
$874$	−7040.00	−0.272462
$875$	875.000	0.0338062
$876$	−5152.00	−0.198710
$877$	19430.0	0.748124	0.374062	−	0.927404i	$-0.377965\pi$
$877$	19430.0	0.748124	0.374062	+	0.927404i	$0.377965\pi$
$878$	768.000	0.0295202
$879$	24632.0	0.945184
$880$	−880.000	−0.0337100
$881$	42714.0	1.63345	0.816726	−	0.577026i	$-0.195787\pi$
$881$	42714.0	1.63345	0.816726	+	0.577026i	$0.195787\pi$
$882$	1078.00	0.0411544
$883$	27988.0	1.06667	0.533336	−	0.845904i	$-0.320938\pi$
$883$	27988.0	1.06667	0.533336	+	0.845904i	$0.320938\pi$
$884$	−2800.00	−0.106532
$885$	12400.0	0.470985
$886$	−35160.0	−1.33321
$887$	−34584.0	−1.30915	−0.654576	−	0.755997i	$-0.727153\pi$
$887$	−34584.0	−1.30915	−0.654576	+	0.755997i	$0.727153\pi$
$888$	1344.00	0.0507902
$889$	9688.00	0.365495
$890$	−6140.00	−0.231251
$891$	−3421.00	−0.128628
$892$	−9232.00	−0.346536
$893$	−10080.0	−0.377732
$894$	−1392.00	−0.0520754
$895$	18460.0	0.689441
$896$	896.000	0.0334077
$897$	−3520.00	−0.131025
$898$	−10020.0	−0.372352
$899$	−4536.00	−0.168280
$900$	−1100.00	−0.0407407
$901$	−40460.0	−1.49602
$902$	5324.00	0.196530
$903$	9968.00	0.367347
$904$	−12048.0	−0.443264
$905$	−3770.00	−0.138474
$906$	−576.000	−0.0211218
$907$	−12524.0	−0.458492	−0.229246	−	0.973368i	$-0.573626\pi$
$907$	−12524.0	−0.458492	−0.229246	+	0.973368i	$0.573626\pi$
$908$	22272.0	0.814011
$909$	−7810.00	−0.284974
$910$	700.000	0.0254998
$911$	−8032.00	−0.292110	−0.146055	−	0.989276i	$-0.546658\pi$
$911$	−8032.00	−0.292110	−0.146055	+	0.989276i	$0.546658\pi$
$912$	2560.00	0.0929496
$913$	7480.00	0.271141
$914$	−21204.0	−0.767359
$915$	7880.00	0.284705
$916$	−19448.0	−0.701507
$917$	−17248.0	−0.621133
$918$	21280.0	0.765081
$919$	−45272.0	−1.62501	−0.812506	−	0.582953i	$-0.801897\pi$
$919$	−45272.0	−1.62501	−0.812506	+	0.582953i	$0.801897\pi$
$920$	3520.00	0.126142
$921$	17984.0	0.643423
$922$	13220.0	0.472210
$923$	3840.00	0.136939
$924$	−1232.00	−0.0438634
$925$	−1050.00	−0.0373230
$926$	−15184.0	−0.538852
$927$	1452.00	0.0514455
$928$	1344.00	0.0475420
$929$	27650.0	0.976498	0.488249	−	0.872704i	$-0.337636\pi$
$929$	27650.0	0.976498	0.488249	+	0.872704i	$0.337636\pi$
$930$	4320.00	0.152321
$931$	1960.00	0.0689972
$932$	26504.0	0.931510
$933$	12176.0	0.427250
$934$	31000.0	1.08603
$935$	−3850.00	−0.134661
$936$	−880.000	−0.0307304
$937$	−16178.0	−0.564047	−0.282024	−	0.959407i	$-0.591006\pi$
$937$	−16178.0	−0.564047	−0.282024	+	0.959407i	$0.591006\pi$
$938$	10696.0	0.372321
$939$	30024.0	1.04345
$940$	5040.00	0.174879
$941$	52470.0	1.81772	0.908859	−	0.417103i	$-0.136955\pi$
$941$	52470.0	1.81772	0.908859	+	0.417103i	$0.136955\pi$
$942$	10224.0	0.353626
$943$	−21296.0	−0.735412
$944$	−9920.00	−0.342022
$945$	−5320.00	−0.183132
$946$	7832.00	0.269176
$947$	−33364.0	−1.14486	−0.572431	−	0.819953i	$-0.694000\pi$
$947$	−33364.0	−1.14486	−0.572431	+	0.819953i	$0.694000\pi$
$948$	−13184.0	−0.451684
$949$	3220.00	0.110143
$950$	−2000.00	−0.0683038
$951$	40664.0	1.38656
$952$	3920.00	0.133454
$953$	−38918.0	−1.32285	−0.661426	−	0.750011i	$-0.730048\pi$
$953$	−38918.0	−1.32285	−0.661426	+	0.750011i	$0.730048\pi$
$954$	−12716.0	−0.431547
$955$	8640.00	0.292758
$956$	8800.00	0.297712
$957$	−1848.00	−0.0624215
$958$	8800.00	0.296780
$959$	17626.0	0.593507
$960$	−1280.00	−0.0430331
$961$	−18127.0	−0.608472
$962$	−840.000	−0.0281525
$963$	−7524.00	−0.251773
$964$	4376.00	0.146205
$965$	17830.0	0.594786
$966$	4928.00	0.164136
$967$	−27416.0	−0.911726	−0.455863	−	0.890050i	$-0.650669\pi$
$967$	−27416.0	−0.911726	−0.455863	+	0.890050i	$0.650669\pi$
$968$	−968.000	−0.0321412
$969$	11200.0	0.371306
$970$	−15820.0	−0.523659
$971$	45036.0	1.48844	0.744219	−	0.667935i	$-0.232822\pi$
$971$	45036.0	1.48844	0.744219	+	0.667935i	$0.232822\pi$
$972$	11440.0	0.377508
$973$	18536.0	0.610726
$974$	−1360.00	−0.0447405
$975$	−1000.00	−0.0328468
$976$	−6304.00	−0.206748
$977$	−27726.0	−0.907915	−0.453958	−	0.891023i	$-0.649988\pi$
$977$	−27726.0	−0.907915	−0.453958	+	0.891023i	$0.649988\pi$
$978$	−7328.00	−0.239595
$979$	−6754.00	−0.220489
$980$	−980.000	−0.0319438
$981$	−946.000	−0.0307884
$982$	26168.0	0.850361
$983$	−30996.0	−1.00572	−0.502858	−	0.864369i	$-0.667718\pi$
$983$	−30996.0	−1.00572	−0.502858	+	0.864369i	$0.667718\pi$
$984$	7744.00	0.250884
$985$	−6390.00	−0.206703
$986$	5880.00	0.189916
$987$	7056.00	0.227553
$988$	−1600.00	−0.0515210
$989$	−31328.0	−1.00725
$990$	−1210.00	−0.0388448
$991$	−13384.0	−0.429018	−0.214509	−	0.976722i	$-0.568815\pi$
$991$	−13384.0	−0.429018	−0.214509	+	0.976722i	$0.568815\pi$
$992$	−3456.00	−0.110613
$993$	29392.0	0.939302
$994$	−5376.00	−0.171546
$995$	820.000	0.0261264
$996$	10880.0	0.346131
$997$	−16586.0	−0.526864	−0.263432	−	0.964678i	$-0.584855\pi$
$997$	−16586.0	−0.526864	−0.263432	+	0.964678i	$0.584855\pi$
$998$	24040.0	0.762498
$999$	6384.00	0.202183

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.4.a.c.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.4.a.c.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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	770.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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