LMFDB - Embedded newform 370.4.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,4,Mod(1,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("370.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	370.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:	$21.8307067021$
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	$\chi$	$=$	370.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2.00000 q^{2} -2.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} -4.00000 q^{6} +2.00000 q^{7} +8.00000 q^{8} -23.0000 q^{9} +O(q^{10})$

\(q+2.00000 q^{2} -2.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} -4.00000 q^{6} +2.00000 q^{7} +8.00000 q^{8} -23.0000 q^{9} +10.0000 q^{10} -72.0000 q^{11} -8.00000 q^{12} +2.00000 q^{13} +4.00000 q^{14} -10.0000 q^{15} +16.0000 q^{16} -66.0000 q^{17} -46.0000 q^{18} +38.0000 q^{19} +20.0000 q^{20} -4.00000 q^{21} -144.000 q^{22} -36.0000 q^{23} -16.0000 q^{24} +25.0000 q^{25} +4.00000 q^{26} +100.000 q^{27} +8.00000 q^{28} -90.0000 q^{29} -20.0000 q^{30} -70.0000 q^{31} +32.0000 q^{32} +144.000 q^{33} -132.000 q^{34} +10.0000 q^{35} -92.0000 q^{36} +37.0000 q^{37} +76.0000 q^{38} -4.00000 q^{39} +40.0000 q^{40} -438.000 q^{41} -8.00000 q^{42} +272.000 q^{43} -288.000 q^{44} -115.000 q^{45} -72.0000 q^{46} -198.000 q^{47} -32.0000 q^{48} -339.000 q^{49} +50.0000 q^{50} +132.000 q^{51} +8.00000 q^{52} -354.000 q^{53} +200.000 q^{54} -360.000 q^{55} +16.0000 q^{56} -76.0000 q^{57} -180.000 q^{58} -498.000 q^{59} -40.0000 q^{60} +542.000 q^{61} -140.000 q^{62} -46.0000 q^{63} +64.0000 q^{64} +10.0000 q^{65} +288.000 q^{66} +2.00000 q^{67} -264.000 q^{68} +72.0000 q^{69} +20.0000 q^{70} +408.000 q^{71} -184.000 q^{72} -358.000 q^{73} +74.0000 q^{74} -50.0000 q^{75} +152.000 q^{76} -144.000 q^{77} -8.00000 q^{78} +722.000 q^{79} +80.0000 q^{80} +421.000 q^{81} -876.000 q^{82} -174.000 q^{83} -16.0000 q^{84} -330.000 q^{85} +544.000 q^{86} +180.000 q^{87} -576.000 q^{88} -102.000 q^{89} -230.000 q^{90} +4.00000 q^{91} -144.000 q^{92} +140.000 q^{93} -396.000 q^{94} +190.000 q^{95} -64.0000 q^{96} -574.000 q^{97} -678.000 q^{98} +1656.00 q^{99} +O(q^{100})\)

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
$3$	−2.00000	−0.384900	−0.192450	−	0.981307i	$-0.561643\pi$
$3$	−2.00000	−0.384900	−0.192450	+	0.981307i	$0.561643\pi$
$4$	4.00000	0.500000
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	−4.00000	−0.272166
$7$	2.00000	0.107990	0.0539949	−	0.998541i	$-0.482805\pi$
$7$	2.00000	0.107990	0.0539949	+	0.998541i	$0.482805\pi$
$8$	8.00000	0.353553
$9$	−23.0000	−0.851852
$10$	10.0000	0.316228
$11$	−72.0000	−1.97353	−0.986764	−	0.162160i	$-0.948154\pi$
$11$	−72.0000	−1.97353	−0.986764	+	0.162160i	$0.948154\pi$
$12$	−8.00000	−0.192450
$13$	2.00000	0.0426692	0.0213346	−	0.999772i	$-0.493208\pi$
$13$	2.00000	0.0426692	0.0213346	+	0.999772i	$0.493208\pi$
$14$	4.00000	0.0763604
$15$	−10.0000	−0.172133
$16$	16.0000	0.250000
$17$	−66.0000	−0.941609	−0.470804	−	0.882238i	$-0.656036\pi$
$17$	−66.0000	−0.941609	−0.470804	+	0.882238i	$0.656036\pi$
$18$	−46.0000	−0.602350
$19$	38.0000	0.458831	0.229416	−	0.973329i	$-0.426318\pi$
$19$	38.0000	0.458831	0.229416	+	0.973329i	$0.426318\pi$
$20$	20.0000	0.223607
$21$	−4.00000	−0.0415653
$22$	−144.000	−1.39550
$23$	−36.0000	−0.326370	−0.163185	−	0.986595i	$-0.552177\pi$
$23$	−36.0000	−0.326370	−0.163185	+	0.986595i	$0.552177\pi$
$24$	−16.0000	−0.136083
$25$	25.0000	0.200000
$26$	4.00000	0.0301717
$27$	100.000	0.712778
$28$	8.00000	0.0539949
$29$	−90.0000	−0.576296	−0.288148	−	0.957586i	$-0.593039\pi$
$29$	−90.0000	−0.576296	−0.288148	+	0.957586i	$0.593039\pi$
$30$	−20.0000	−0.121716
$31$	−70.0000	−0.405560	−0.202780	−	0.979224i	$-0.564998\pi$
$31$	−70.0000	−0.405560	−0.202780	+	0.979224i	$0.564998\pi$
$32$	32.0000	0.176777
$33$	144.000	0.759612
$34$	−132.000	−0.665818
$35$	10.0000	0.0482945
$36$	−92.0000	−0.425926
$37$	37.0000	0.164399
$37$	37.0000	0.164399
$38$	76.0000	0.324443
$39$	−4.00000	−0.0164234
$40$	40.0000	0.158114
$41$	−438.000	−1.66839	−0.834196	−	0.551467i	$-0.814068\pi$
$41$	−438.000	−1.66839	−0.834196	+	0.551467i	$0.814068\pi$
$42$	−8.00000	−0.0293911
$43$	272.000	0.964642	0.482321	−	0.875995i	$-0.339794\pi$
$43$	272.000	0.964642	0.482321	+	0.875995i	$0.339794\pi$
$44$	−288.000	−0.986764
$45$	−115.000	−0.380960
$46$	−72.0000	−0.230779
$47$	−198.000	−0.614495	−0.307248	−	0.951630i	$-0.599408\pi$
$47$	−198.000	−0.614495	−0.307248	+	0.951630i	$0.599408\pi$
$48$	−32.0000	−0.0962250
$49$	−339.000	−0.988338
$50$	50.0000	0.141421
$51$	132.000	0.362425
$52$	8.00000	0.0213346
$53$	−354.000	−0.917465	−0.458732	−	0.888574i	$-0.651696\pi$
$53$	−354.000	−0.917465	−0.458732	+	0.888574i	$0.651696\pi$
$54$	200.000	0.504010
$55$	−360.000	−0.882589
$56$	16.0000	0.0381802
$57$	−76.0000	−0.176604
$58$	−180.000	−0.407503
$59$	−498.000	−1.09888	−0.549441	−	0.835532i	$-0.685159\pi$
$59$	−498.000	−1.09888	−0.549441	+	0.835532i	$0.685159\pi$
$60$	−40.0000	−0.0860663
$61$	542.000	1.13764	0.568820	−	0.822462i	$-0.307400\pi$
$61$	542.000	1.13764	0.568820	+	0.822462i	$0.307400\pi$
$62$	−140.000	−0.286774
$63$	−46.0000	−0.0919914
$64$	64.0000	0.125000
$65$	10.0000	0.0190823
$66$	288.000	0.537127
$67$	2.00000	0.00364685	0.00182342	−	0.999998i	$-0.499420\pi$
$67$	2.00000	0.00364685	0.00182342	+	0.999998i	$0.499420\pi$
$68$	−264.000	−0.470804
$69$	72.0000	0.125620
$70$	20.0000	0.0341494
$71$	408.000	0.681982	0.340991	−	0.940067i	$-0.389238\pi$
$71$	408.000	0.681982	0.340991	+	0.940067i	$0.389238\pi$
$72$	−184.000	−0.301175
$73$	−358.000	−0.573983	−0.286991	−	0.957933i	$-0.592655\pi$
$73$	−358.000	−0.573983	−0.286991	+	0.957933i	$0.592655\pi$
$74$	74.0000	0.116248
$75$	−50.0000	−0.0769800
$76$	152.000	0.229416
$77$	−144.000	−0.213121
$78$	−8.00000	−0.0116131
$79$	722.000	1.02824	0.514122	−	0.857717i	$-0.328118\pi$
$79$	722.000	1.02824	0.514122	+	0.857717i	$0.328118\pi$
$80$	80.0000	0.111803
$81$	421.000	0.577503
$82$	−876.000	−1.17973
$83$	−174.000	−0.230108	−0.115054	−	0.993359i	$-0.536704\pi$
$83$	−174.000	−0.230108	−0.115054	+	0.993359i	$0.536704\pi$
$84$	−16.0000	−0.0207827
$85$	−330.000	−0.421100
$86$	544.000	0.682105
$87$	180.000	0.221816
$88$	−576.000	−0.697748
$89$	−102.000	−0.121483	−0.0607415	−	0.998154i	$-0.519347\pi$
$89$	−102.000	−0.121483	−0.0607415	+	0.998154i	$0.519347\pi$
$90$	−230.000	−0.269379
$91$	4.00000	0.00460785
$92$	−144.000	−0.163185
$93$	140.000	0.156100
$94$	−396.000	−0.434514
$95$	190.000	0.205196
$96$	−64.0000	−0.0680414
$97$	−574.000	−0.600834	−0.300417	−	0.953808i	$-0.597126\pi$
$97$	−574.000	−0.600834	−0.300417	+	0.953808i	$0.597126\pi$
$98$	−678.000	−0.698861
$99$	1656.00	1.68115
$100$	100.000	0.100000
$101$	810.000	0.798000	0.399000	−	0.916951i	$-0.369357\pi$
$101$	810.000	0.798000	0.399000	+	0.916951i	$0.369357\pi$
$102$	264.000	0.256273
$103$	848.000	0.811223	0.405611	−	0.914046i	$-0.367059\pi$
$103$	848.000	0.811223	0.405611	+	0.914046i	$0.367059\pi$
$104$	16.0000	0.0150859
$105$	−20.0000	−0.0185886
$106$	−708.000	−0.648746
$107$	462.000	0.417413	0.208707	−	0.977978i	$-0.433075\pi$
$107$	462.000	0.417413	0.208707	+	0.977978i	$0.433075\pi$
$108$	400.000	0.356389
$109$	−1258.00	−1.10545	−0.552727	−	0.833362i	$-0.686413\pi$
$109$	−1258.00	−1.10545	−0.552727	+	0.833362i	$0.686413\pi$
$110$	−720.000	−0.624085
$111$	−74.0000	−0.0632772
$112$	32.0000	0.0269975
$113$	1230.00	1.02397	0.511985	−	0.858994i	$-0.328910\pi$
$113$	1230.00	1.02397	0.511985	+	0.858994i	$0.328910\pi$
$114$	−152.000	−0.124878
$115$	−180.000	−0.145957
$116$	−360.000	−0.288148
$117$	−46.0000	−0.0363479
$118$	−996.000	−0.777027
$119$	−132.000	−0.101684
$120$	−80.0000	−0.0608581
$121$	3853.00	2.89482
$122$	1084.00	0.804432
$123$	876.000	0.642165
$124$	−280.000	−0.202780
$125$	125.000	0.0894427
$126$	−92.0000	−0.0650477
$127$	−1726.00	−1.20597	−0.602983	−	0.797754i	$-0.706021\pi$
$127$	−1726.00	−1.20597	−0.602983	+	0.797754i	$0.706021\pi$
$128$	128.000	0.0883883
$129$	−544.000	−0.371291
$130$	20.0000	0.0134932
$131$	1302.00	0.868368	0.434184	−	0.900824i	$-0.357037\pi$
$131$	1302.00	0.868368	0.434184	+	0.900824i	$0.357037\pi$
$132$	576.000	0.379806
$133$	76.0000	0.0495491
$134$	4.00000	0.00257871
$135$	500.000	0.318764
$136$	−528.000	−0.332909
$137$	2754.00	1.71745	0.858723	−	0.512440i	$-0.171258\pi$
$137$	2754.00	1.71745	0.858723	+	0.512440i	$0.171258\pi$
$138$	144.000	0.0888268
$139$	1172.00	0.715164	0.357582	−	0.933882i	$-0.383601\pi$
$139$	1172.00	0.715164	0.357582	+	0.933882i	$0.383601\pi$
$140$	40.0000	0.0241473
$141$	396.000	0.236519
$142$	816.000	0.482234
$143$	−144.000	−0.0842090
$144$	−368.000	−0.212963
$145$	−450.000	−0.257727
$146$	−716.000	−0.405867
$147$	678.000	0.380412
$148$	148.000	0.0821995
$149$	−2502.00	−1.37565	−0.687825	−	0.725877i	$-0.741434\pi$
$149$	−2502.00	−1.37565	−0.687825	+	0.725877i	$0.741434\pi$
$150$	−100.000	−0.0544331
$151$	−268.000	−0.144434	−0.0722170	−	0.997389i	$-0.523007\pi$
$151$	−268.000	−0.144434	−0.0722170	+	0.997389i	$0.523007\pi$
$152$	304.000	0.162221
$153$	1518.00	0.802111
$154$	−288.000	−0.150699
$155$	−350.000	−0.181372
$156$	−16.0000	−0.00821170
$157$	−1978.00	−1.00549	−0.502744	−	0.864435i	$-0.667676\pi$
$157$	−1978.00	−1.00549	−0.502744	+	0.864435i	$0.667676\pi$
$158$	1444.00	0.727079
$159$	708.000	0.353132
$160$	160.000	0.0790569
$161$	−72.0000	−0.0352447
$162$	842.000	0.408357
$163$	−1204.00	−0.578556	−0.289278	−	0.957245i	$-0.593415\pi$
$163$	−1204.00	−0.578556	−0.289278	+	0.957245i	$0.593415\pi$
$164$	−1752.00	−0.834196
$165$	720.000	0.339709
$166$	−348.000	−0.162711
$167$	−2184.00	−1.01199	−0.505997	−	0.862535i	$-0.668875\pi$
$167$	−2184.00	−1.01199	−0.505997	+	0.862535i	$0.668875\pi$
$168$	−32.0000	−0.0146956
$169$	−2193.00	−0.998179
$170$	−660.000	−0.297763
$171$	−874.000	−0.390856
$172$	1088.00	0.482321
$173$	−3522.00	−1.54782	−0.773910	−	0.633296i	$-0.781702\pi$
$173$	−3522.00	−1.54782	−0.773910	+	0.633296i	$0.781702\pi$
$174$	360.000	0.156848
$175$	50.0000	0.0215980
$176$	−1152.00	−0.493382
$177$	996.000	0.422960
$178$	−204.000	−0.0859014
$179$	2034.00	0.849320	0.424660	−	0.905353i	$-0.360394\pi$
$179$	2034.00	0.849320	0.424660	+	0.905353i	$0.360394\pi$
$180$	−460.000	−0.190480
$181$	1010.00	0.414766	0.207383	−	0.978260i	$-0.433505\pi$
$181$	1010.00	0.414766	0.207383	+	0.978260i	$0.433505\pi$
$182$	8.00000	0.00325824
$183$	−1084.00	−0.437878
$184$	−288.000	−0.115389
$185$	185.000	0.0735215
$186$	280.000	0.110380
$187$	4752.00	1.85829
$188$	−792.000	−0.307248
$189$	200.000	0.0769728
$190$	380.000	0.145095
$191$	4086.00	1.54792	0.773960	−	0.633235i	$-0.218273\pi$
$191$	4086.00	1.54792	0.773960	+	0.633235i	$0.218273\pi$
$192$	−128.000	−0.0481125
$193$	−1438.00	−0.536319	−0.268159	−	0.963375i	$-0.586415\pi$
$193$	−1438.00	−0.536319	−0.268159	+	0.963375i	$0.586415\pi$
$194$	−1148.00	−0.424854
$195$	−20.0000	−0.00734477
$196$	−1356.00	−0.494169
$197$	−354.000	−0.128028	−0.0640138	−	0.997949i	$-0.520390\pi$
$197$	−354.000	−0.128028	−0.0640138	+	0.997949i	$0.520390\pi$
$198$	3312.00	1.18876
$199$	2702.00	0.962511	0.481256	−	0.876580i	$-0.340181\pi$
$199$	2702.00	0.962511	0.481256	+	0.876580i	$0.340181\pi$
$200$	200.000	0.0707107
$201$	−4.00000	−0.00140367
$202$	1620.00	0.564271
$203$	−180.000	−0.0622341
$204$	528.000	0.181213
$205$	−2190.00	−0.746128
$206$	1696.00	0.573621
$207$	828.000	0.278019
$208$	32.0000	0.0106673
$209$	−2736.00	−0.905517
$210$	−40.0000	−0.0131441
$211$	3044.00	0.993164	0.496582	−	0.867990i	$-0.334588\pi$
$211$	3044.00	0.993164	0.496582	+	0.867990i	$0.334588\pi$
$212$	−1416.00	−0.458732
$213$	−816.000	−0.262495
$214$	924.000	0.295156
$215$	1360.00	0.431401
$216$	800.000	0.252005
$217$	−140.000	−0.0437964
$218$	−2516.00	−0.781674
$219$	716.000	0.220926
$220$	−1440.00	−0.441294
$221$	−132.000	−0.0401777
$222$	−148.000	−0.0447437
$223$	−5074.00	−1.52368	−0.761839	−	0.647766i	$-0.775703\pi$
$223$	−5074.00	−1.52368	−0.761839	+	0.647766i	$0.775703\pi$
$224$	64.0000	0.0190901
$225$	−575.000	−0.170370
$226$	2460.00	0.724056
$227$	4764.00	1.39294	0.696471	−	0.717585i	$-0.254753\pi$
$227$	4764.00	1.39294	0.696471	+	0.717585i	$0.254753\pi$
$228$	−304.000	−0.0883022
$229$	830.000	0.239511	0.119755	−	0.992803i	$-0.461789\pi$
$229$	830.000	0.239511	0.119755	+	0.992803i	$0.461789\pi$
$230$	−360.000	−0.103207
$231$	288.000	0.0820303
$232$	−720.000	−0.203751
$233$	−1062.00	−0.298601	−0.149300	−	0.988792i	$-0.547702\pi$
$233$	−1062.00	−0.298601	−0.149300	+	0.988792i	$0.547702\pi$
$234$	−92.0000	−0.0257018
$235$	−990.000	−0.274811
$236$	−1992.00	−0.549441
$237$	−1444.00	−0.395772
$238$	−264.000	−0.0719016
$239$	−1758.00	−0.475797	−0.237899	−	0.971290i	$-0.576459\pi$
$239$	−1758.00	−0.475797	−0.237899	+	0.971290i	$0.576459\pi$
$240$	−160.000	−0.0430331
$241$	4034.00	1.07823	0.539114	−	0.842233i	$-0.318759\pi$
$241$	4034.00	1.07823	0.539114	+	0.842233i	$0.318759\pi$
$242$	7706.00	2.04694
$243$	−3542.00	−0.935059
$244$	2168.00	0.568820
$245$	−1695.00	−0.441998
$246$	1752.00	0.454079
$247$	76.0000	0.0195780
$248$	−560.000	−0.143387
$249$	348.000	0.0885687
$250$	250.000	0.0632456
$251$	2286.00	0.574865	0.287432	−	0.957801i	$-0.407198\pi$
$251$	2286.00	0.574865	0.287432	+	0.957801i	$0.407198\pi$
$252$	−184.000	−0.0459957
$253$	2592.00	0.644101
$254$	−3452.00	−0.852747
$255$	660.000	0.162082
$256$	256.000	0.0625000
$257$	4254.00	1.03252	0.516259	−	0.856432i	$-0.327324\pi$
$257$	4254.00	1.03252	0.516259	+	0.856432i	$0.327324\pi$
$258$	−1088.00	−0.262542
$259$	74.0000	0.0177534
$260$	40.0000	0.00954113
$261$	2070.00	0.490919
$262$	2604.00	0.614029
$263$	−78.0000	−0.0182878	−0.00914389	−	0.999958i	$-0.502911\pi$
$263$	−78.0000	−0.0182878	−0.00914389	+	0.999958i	$0.502911\pi$
$264$	1152.00	0.268563
$265$	−1770.00	−0.410303
$266$	152.000	0.0350365
$267$	204.000	0.0467588
$268$	8.00000	0.00182342
$269$	−2862.00	−0.648696	−0.324348	−	0.945938i	$-0.605145\pi$
$269$	−2862.00	−0.648696	−0.324348	+	0.945938i	$0.605145\pi$
$270$	1000.00	0.225400
$271$	−808.000	−0.181116	−0.0905581	−	0.995891i	$-0.528865\pi$
$271$	−808.000	−0.181116	−0.0905581	+	0.995891i	$0.528865\pi$
$272$	−1056.00	−0.235402
$273$	−8.00000	−0.00177356
$274$	5508.00	1.21442
$275$	−1800.00	−0.394706
$276$	288.000	0.0628100
$277$	−2806.00	−0.608651	−0.304325	−	0.952568i	$-0.598431\pi$
$277$	−2806.00	−0.608651	−0.304325	+	0.952568i	$0.598431\pi$
$278$	2344.00	0.505697
$279$	1610.00	0.345477
$280$	80.0000	0.0170747
$281$	−5286.00	−1.12219	−0.561097	−	0.827750i	$-0.689620\pi$
$281$	−5286.00	−1.12219	−0.561097	+	0.827750i	$0.689620\pi$
$282$	792.000	0.167244
$283$	1244.00	0.261301	0.130650	−	0.991429i	$-0.458293\pi$
$283$	1244.00	0.261301	0.130650	+	0.991429i	$0.458293\pi$
$284$	1632.00	0.340991
$285$	−380.000	−0.0789799
$286$	−288.000	−0.0595447
$287$	−876.000	−0.180169
$288$	−736.000	−0.150588
$289$	−557.000	−0.113373
$290$	−900.000	−0.182241
$291$	1148.00	0.231261
$292$	−1432.00	−0.286991
$293$	−9186.00	−1.83158	−0.915788	−	0.401662i	$-0.868433\pi$
$293$	−9186.00	−1.83158	−0.915788	+	0.401662i	$0.868433\pi$
$294$	1356.00	0.268992
$295$	−2490.00	−0.491435
$296$	296.000	0.0581238
$297$	−7200.00	−1.40669
$298$	−5004.00	−0.972731
$299$	−72.0000	−0.0139260
$300$	−200.000	−0.0384900
$301$	544.000	0.104172
$302$	−536.000	−0.102130
$303$	−1620.00	−0.307150
$304$	608.000	0.114708
$305$	2710.00	0.508768
$306$	3036.00	0.567178
$307$	−502.000	−0.0933246	−0.0466623	−	0.998911i	$-0.514858\pi$
$307$	−502.000	−0.0933246	−0.0466623	+	0.998911i	$0.514858\pi$
$308$	−576.000	−0.106561
$309$	−1696.00	−0.312240
$310$	−700.000	−0.128249
$311$	−462.000	−0.0842367	−0.0421184	−	0.999113i	$-0.513411\pi$
$311$	−462.000	−0.0842367	−0.0421184	+	0.999113i	$0.513411\pi$
$312$	−32.0000	−0.00580655
$313$	6410.00	1.15755	0.578777	−	0.815486i	$-0.303530\pi$
$313$	6410.00	1.15755	0.578777	+	0.815486i	$0.303530\pi$
$314$	−3956.00	−0.710987
$315$	−230.000	−0.0411398
$316$	2888.00	0.514122
$317$	−5394.00	−0.955701	−0.477851	−	0.878441i	$-0.658584\pi$
$317$	−5394.00	−0.955701	−0.477851	+	0.878441i	$0.658584\pi$
$318$	1416.00	0.249702
$319$	6480.00	1.13734
$320$	320.000	0.0559017
$321$	−924.000	−0.160662
$322$	−144.000	−0.0249218
$323$	−2508.00	−0.432040
$324$	1684.00	0.288752
$325$	50.0000	0.00853385
$326$	−2408.00	−0.409101
$327$	2516.00	0.425490
$328$	−3504.00	−0.589866
$329$	−396.000	−0.0663592
$330$	1440.00	0.240210
$331$	−11158.0	−1.85287	−0.926434	−	0.376458i	$-0.877142\pi$
$331$	−11158.0	−1.85287	−0.926434	+	0.376458i	$0.877142\pi$
$332$	−696.000	−0.115054
$333$	−851.000	−0.140044
$334$	−4368.00	−0.715588
$335$	10.0000	0.00163092
$336$	−64.0000	−0.0103913
$337$	218.000	0.0352380	0.0176190	−	0.999845i	$-0.494391\pi$
$337$	218.000	0.0352380	0.0176190	+	0.999845i	$0.494391\pi$
$338$	−4386.00	−0.705819
$339$	−2460.00	−0.394126
$340$	−1320.00	−0.210550
$341$	5040.00	0.800385
$342$	−1748.00	−0.276377
$343$	−1364.00	−0.214720
$344$	2176.00	0.341052
$345$	360.000	0.0561790
$346$	−7044.00	−1.09447
$347$	432.000	0.0668328	0.0334164	−	0.999442i	$-0.489361\pi$
$347$	432.000	0.0668328	0.0334164	+	0.999442i	$0.489361\pi$
$348$	720.000	0.110908
$349$	3026.00	0.464121	0.232060	−	0.972701i	$-0.425453\pi$
$349$	3026.00	0.464121	0.232060	+	0.972701i	$0.425453\pi$
$350$	100.000	0.0152721
$351$	200.000	0.0304137
$352$	−2304.00	−0.348874
$353$	−8958.00	−1.35067	−0.675335	−	0.737511i	$-0.736001\pi$
$353$	−8958.00	−1.35067	−0.675335	+	0.737511i	$0.736001\pi$
$354$	1992.00	0.299078
$355$	2040.00	0.304991
$356$	−408.000	−0.0607415
$357$	264.000	0.0391383
$358$	4068.00	0.600560
$359$	−6084.00	−0.894432	−0.447216	−	0.894426i	$-0.647585\pi$
$359$	−6084.00	−0.894432	−0.447216	+	0.894426i	$0.647585\pi$
$360$	−920.000	−0.134690
$361$	−5415.00	−0.789474
$362$	2020.00	0.293284
$363$	−7706.00	−1.11422
$364$	16.0000	0.00230392
$365$	−1790.00	−0.256693
$366$	−2168.00	−0.309626
$367$	−8206.00	−1.16717	−0.583583	−	0.812054i	$-0.698350\pi$
$367$	−8206.00	−1.16717	−0.583583	+	0.812054i	$0.698350\pi$
$368$	−576.000	−0.0815926
$369$	10074.0	1.42122
$370$	370.000	0.0519875
$371$	−708.000	−0.0990769
$372$	560.000	0.0780501
$373$	−2914.00	−0.404507	−0.202254	−	0.979333i	$-0.564827\pi$
$373$	−2914.00	−0.404507	−0.202254	+	0.979333i	$0.564827\pi$
$374$	9504.00	1.31401
$375$	−250.000	−0.0344265
$376$	−1584.00	−0.217257
$377$	−180.000	−0.0245901
$378$	400.000	0.0544280
$379$	−6496.00	−0.880415	−0.440207	−	0.897896i	$-0.645095\pi$
$379$	−6496.00	−0.880415	−0.440207	+	0.897896i	$0.645095\pi$
$380$	760.000	0.102598
$381$	3452.00	0.464177
$382$	8172.00	1.09454
$383$	8508.00	1.13509	0.567544	−	0.823343i	$-0.307894\pi$
$383$	8508.00	1.13509	0.567544	+	0.823343i	$0.307894\pi$
$384$	−256.000	−0.0340207
$385$	−720.000	−0.0953106
$386$	−2876.00	−0.379235
$387$	−6256.00	−0.821732
$388$	−2296.00	−0.300417
$389$	−8178.00	−1.06592	−0.532958	−	0.846142i	$-0.678920\pi$
$389$	−8178.00	−1.06592	−0.532958	+	0.846142i	$0.678920\pi$
$390$	−40.0000	−0.00519354
$391$	2376.00	0.307313
$392$	−2712.00	−0.349430
$393$	−2604.00	−0.334235
$394$	−708.000	−0.0905293
$395$	3610.00	0.459845
$396$	6624.00	0.840577
$397$	−5290.00	−0.668759	−0.334380	−	0.942438i	$-0.608527\pi$
$397$	−5290.00	−0.668759	−0.334380	+	0.942438i	$0.608527\pi$
$398$	5404.00	0.680598
$399$	−152.000	−0.0190715
$400$	400.000	0.0500000
$401$	810.000	0.100871	0.0504357	−	0.998727i	$-0.483939\pi$
$401$	810.000	0.100871	0.0504357	+	0.998727i	$0.483939\pi$
$402$	−8.00000	−0.000992547 0
$403$	−140.000	−0.0173050
$404$	3240.00	0.399000
$405$	2105.00	0.258267
$406$	−360.000	−0.0440062
$407$	−2664.00	−0.324446
$408$	1056.00	0.128137
$409$	−5830.00	−0.704829	−0.352414	−	0.935844i	$-0.614639\pi$
$409$	−5830.00	−0.704829	−0.352414	+	0.935844i	$0.614639\pi$
$410$	−4380.00	−0.527592
$411$	−5508.00	−0.661045
$412$	3392.00	0.405611
$413$	−996.000	−0.118668
$414$	1656.00	0.196589
$415$	−870.000	−0.102908
$416$	64.0000	0.00754293
$417$	−2344.00	−0.275267
$418$	−5472.00	−0.640297
$419$	3768.00	0.439329	0.219664	−	0.975575i	$-0.429504\pi$
$419$	3768.00	0.439329	0.219664	+	0.975575i	$0.429504\pi$
$420$	−80.0000	−0.00929429
$421$	15518.0	1.79644	0.898220	−	0.439547i	$-0.144861\pi$
$421$	15518.0	1.79644	0.898220	+	0.439547i	$0.144861\pi$
$422$	6088.00	0.702273
$423$	4554.00	0.523459
$424$	−2832.00	−0.324373
$425$	−1650.00	−0.188322
$426$	−1632.00	−0.185612
$427$	1084.00	0.122853
$428$	1848.00	0.208707
$429$	288.000	0.0324121
$430$	2720.00	0.305047
$431$	−798.000	−0.0891840	−0.0445920	−	0.999005i	$-0.514199\pi$
$431$	−798.000	−0.0891840	−0.0445920	+	0.999005i	$0.514199\pi$
$432$	1600.00	0.178195
$433$	−14470.0	−1.60597	−0.802984	−	0.596001i	$-0.796755\pi$
$433$	−14470.0	−1.60597	−0.802984	+	0.596001i	$0.796755\pi$
$434$	−280.000	−0.0309687
$435$	900.000	0.0991993
$436$	−5032.00	−0.552727
$437$	−1368.00	−0.149749
$438$	1432.00	0.156218
$439$	6734.00	0.732110	0.366055	−	0.930593i	$-0.380708\pi$
$439$	6734.00	0.732110	0.366055	+	0.930593i	$0.380708\pi$
$440$	−2880.00	−0.312042
$441$	7797.00	0.841918
$442$	−264.000	−0.0284100
$443$	−13770.0	−1.47682	−0.738411	−	0.674351i	$-0.764424\pi$
$443$	−13770.0	−1.47682	−0.738411	+	0.674351i	$0.764424\pi$
$444$	−296.000	−0.0316386
$445$	−510.000	−0.0543288
$446$	−10148.0	−1.07740
$447$	5004.00	0.529488
$448$	128.000	0.0134987
$449$	3882.00	0.408024	0.204012	−	0.978968i	$-0.434602\pi$
$449$	3882.00	0.408024	0.204012	+	0.978968i	$0.434602\pi$
$450$	−1150.00	−0.120470
$451$	31536.0	3.29262
$452$	4920.00	0.511985
$453$	536.000	0.0555927
$454$	9528.00	0.984959
$455$	20.0000	0.00206069
$456$	−608.000	−0.0624391
$457$	−4534.00	−0.464095	−0.232048	−	0.972704i	$-0.574543\pi$
$457$	−4534.00	−0.464095	−0.232048	+	0.972704i	$0.574543\pi$
$458$	1660.00	0.169360
$459$	−6600.00	−0.671158
$460$	−720.000	−0.0729786
$461$	−7770.00	−0.785000	−0.392500	−	0.919752i	$-0.628390\pi$
$461$	−7770.00	−0.785000	−0.392500	+	0.919752i	$0.628390\pi$
$462$	576.000	0.0580042
$463$	−13948.0	−1.40004	−0.700020	−	0.714123i	$-0.746826\pi$
$463$	−13948.0	−1.40004	−0.700020	+	0.714123i	$0.746826\pi$
$464$	−1440.00	−0.144074
$465$	700.000	0.0698102
$466$	−2124.00	−0.211142
$467$	−6444.00	−0.638528	−0.319264	−	0.947666i	$-0.603436\pi$
$467$	−6444.00	−0.638528	−0.319264	+	0.947666i	$0.603436\pi$
$468$	−184.000	−0.0181739
$469$	4.00000	0.000393823 0
$470$	−1980.00	−0.194320
$471$	3956.00	0.387012
$472$	−3984.00	−0.388514
$473$	−19584.0	−1.90375
$474$	−2888.00	−0.279853
$475$	950.000	0.0917663
$476$	−528.000	−0.0508421
$477$	8142.00	0.781544
$478$	−3516.00	−0.336440
$479$	474.000	0.0452142	0.0226071	−	0.999744i	$-0.492803\pi$
$479$	474.000	0.0452142	0.0226071	+	0.999744i	$0.492803\pi$
$480$	−320.000	−0.0304290
$481$	74.0000	0.00701478
$482$	8068.00	0.762422
$483$	144.000	0.0135657
$484$	15412.0	1.44741
$485$	−2870.00	−0.268701
$486$	−7084.00	−0.661187
$487$	17984.0	1.67337	0.836687	−	0.547682i	$-0.184490\pi$
$487$	17984.0	1.67337	0.836687	+	0.547682i	$0.184490\pi$
$488$	4336.00	0.402216
$489$	2408.00	0.222686
$490$	−3390.00	−0.312540
$491$	13140.0	1.20774	0.603870	−	0.797083i	$-0.293625\pi$
$491$	13140.0	1.20774	0.603870	+	0.797083i	$0.293625\pi$
$492$	3504.00	0.321082
$493$	5940.00	0.542645
$494$	152.000	0.0138437
$495$	8280.00	0.751835
$496$	−1120.00	−0.101390
$497$	816.000	0.0736471
$498$	696.000	0.0626275
$499$	11306.0	1.01428	0.507140	−	0.861863i	$-0.330703\pi$
$499$	11306.0	1.01428	0.507140	+	0.861863i	$0.330703\pi$
$500$	500.000	0.0447214
$501$	4368.00	0.389517
$502$	4572.00	0.406491
$503$	20076.0	1.77961	0.889806	−	0.456339i	$-0.150840\pi$
$503$	20076.0	1.77961	0.889806	+	0.456339i	$0.150840\pi$
$504$	−368.000	−0.0325239
$505$	4050.00	0.356877
$506$	5184.00	0.455448
$507$	4386.00	0.384199
$508$	−6904.00	−0.602983
$509$	−3450.00	−0.300429	−0.150215	−	0.988653i	$-0.547996\pi$
$509$	−3450.00	−0.300429	−0.150215	+	0.988653i	$0.547996\pi$
$510$	1320.00	0.114609
$511$	−716.000	−0.0619843
$512$	512.000	0.0441942
$513$	3800.00	0.327045
$514$	8508.00	0.730101
$515$	4240.00	0.362790
$516$	−2176.00	−0.185645
$517$	14256.0	1.21272
$518$	148.000	0.0125536
$519$	7044.00	0.595756
$520$	80.0000	0.00674660
$521$	−7026.00	−0.590815	−0.295408	−	0.955371i	$-0.595455\pi$
$521$	−7026.00	−0.590815	−0.295408	+	0.955371i	$0.595455\pi$
$522$	4140.00	0.347132
$523$	15104.0	1.26281	0.631407	−	0.775452i	$-0.282478\pi$
$523$	15104.0	1.26281	0.631407	+	0.775452i	$0.282478\pi$
$524$	5208.00	0.434184
$525$	−100.000	−0.00831306
$526$	−156.000	−0.0129314
$527$	4620.00	0.381879
$528$	2304.00	0.189903
$529$	−10871.0	−0.893482
$530$	−3540.00	−0.290128
$531$	11454.0	0.936085
$532$	304.000	0.0247746
$533$	−876.000	−0.0711891
$534$	408.000	0.0330635
$535$	2310.00	0.186673
$536$	16.0000	0.00128936
$537$	−4068.00	−0.326903
$538$	−5724.00	−0.458697
$539$	24408.0	1.95051
$540$	2000.00	0.159382
$541$	19118.0	1.51931	0.759655	−	0.650326i	$-0.225368\pi$
$541$	19118.0	1.51931	0.759655	+	0.650326i	$0.225368\pi$
$542$	−1616.00	−0.128069
$543$	−2020.00	−0.159644
$544$	−2112.00	−0.166455
$545$	−6290.00	−0.494374
$546$	−16.0000	−0.00125410
$547$	−19240.0	−1.50392	−0.751959	−	0.659210i	$-0.770891\pi$
$547$	−19240.0	−1.50392	−0.751959	+	0.659210i	$0.770891\pi$
$548$	11016.0	0.858723
$549$	−12466.0	−0.969100
$550$	−3600.00	−0.279099
$551$	−3420.00	−0.264423
$552$	576.000	0.0444134
$553$	1444.00	0.111040
$554$	−5612.00	−0.430381
$555$	−370.000	−0.0282984
$556$	4688.00	0.357582
$557$	−23214.0	−1.76590	−0.882952	−	0.469463i	$-0.844448\pi$
$557$	−23214.0	−1.76590	−0.882952	+	0.469463i	$0.844448\pi$
$558$	3220.00	0.244289
$559$	544.000	0.0411606
$560$	160.000	0.0120736
$561$	−9504.00	−0.715257
$562$	−10572.0	−0.793511
$563$	4968.00	0.371894	0.185947	−	0.982560i	$-0.440465\pi$
$563$	4968.00	0.371894	0.185947	+	0.982560i	$0.440465\pi$
$564$	1584.00	0.118260
$565$	6150.00	0.457934
$566$	2488.00	0.184768
$567$	842.000	0.0623645
$568$	3264.00	0.241117
$569$	8226.00	0.606067	0.303033	−	0.952980i	$-0.402001\pi$
$569$	8226.00	0.606067	0.303033	+	0.952980i	$0.402001\pi$
$570$	−760.000	−0.0558472
$571$	−844.000	−0.0618569	−0.0309285	−	0.999522i	$-0.509846\pi$
$571$	−844.000	−0.0618569	−0.0309285	+	0.999522i	$0.509846\pi$
$572$	−576.000	−0.0421045
$573$	−8172.00	−0.595794
$574$	−1752.00	−0.127399
$575$	−900.000	−0.0652741
$576$	−1472.00	−0.106481
$577$	−610.000	−0.0440115	−0.0220057	−	0.999758i	$-0.507005\pi$
$577$	−610.000	−0.0440115	−0.0220057	+	0.999758i	$0.507005\pi$
$578$	−1114.00	−0.0801666
$579$	2876.00	0.206429
$580$	−1800.00	−0.128864
$581$	−348.000	−0.0248494
$582$	2296.00	0.163526
$583$	25488.0	1.81064
$584$	−2864.00	−0.202933
$585$	−230.000	−0.0162553
$586$	−18372.0	−1.29512
$587$	−6504.00	−0.457323	−0.228662	−	0.973506i	$-0.573435\pi$
$587$	−6504.00	−0.457323	−0.228662	+	0.973506i	$0.573435\pi$
$588$	2712.00	0.190206
$589$	−2660.00	−0.186084
$590$	−4980.00	−0.347497
$591$	708.000	0.0492779
$592$	592.000	0.0410997
$593$	6282.00	0.435027	0.217513	−	0.976057i	$-0.430205\pi$
$593$	6282.00	0.435027	0.217513	+	0.976057i	$0.430205\pi$
$594$	−14400.0	−0.994679
$595$	−660.000	−0.0454746
$596$	−10008.0	−0.687825
$597$	−5404.00	−0.370471
$598$	−144.000	−0.00984715
$599$	−924.000	−0.0630277	−0.0315139	−	0.999503i	$-0.510033\pi$
$599$	−924.000	−0.0630277	−0.0315139	+	0.999503i	$0.510033\pi$
$600$	−400.000	−0.0272166
$601$	1622.00	0.110088	0.0550439	−	0.998484i	$-0.482470\pi$
$601$	1622.00	0.110088	0.0550439	+	0.998484i	$0.482470\pi$
$602$	1088.00	0.0736604
$603$	−46.0000	−0.00310658
$604$	−1072.00	−0.0722170
$605$	19265.0	1.29460
$606$	−3240.00	−0.217188
$607$	−1708.00	−0.114210	−0.0571051	−	0.998368i	$-0.518187\pi$
$607$	−1708.00	−0.114210	−0.0571051	+	0.998368i	$0.518187\pi$
$608$	1216.00	0.0811107
$609$	360.000	0.0239539
$610$	5420.00	0.359753
$611$	−396.000	−0.0262200
$612$	6072.00	0.401056
$613$	2198.00	0.144823	0.0724114	−	0.997375i	$-0.476931\pi$
$613$	2198.00	0.144823	0.0724114	+	0.997375i	$0.476931\pi$
$614$	−1004.00	−0.0659905
$615$	4380.00	0.287185
$616$	−1152.00	−0.0753497
$617$	1554.00	0.101397	0.0506983	−	0.998714i	$-0.483855\pi$
$617$	1554.00	0.101397	0.0506983	+	0.998714i	$0.483855\pi$
$618$	−3392.00	−0.220787
$619$	−27484.0	−1.78461	−0.892306	−	0.451430i	$-0.850914\pi$
$619$	−27484.0	−1.78461	−0.892306	+	0.451430i	$0.850914\pi$
$620$	−1400.00	−0.0906861
$621$	−3600.00	−0.232630
$622$	−924.000	−0.0595643
$623$	−204.000	−0.0131189
$624$	−64.0000	−0.00410585
$625$	625.000	0.0400000
$626$	12820.0	0.818515
$627$	5472.00	0.348534
$628$	−7912.00	−0.502744
$629$	−2442.00	−0.154800
$630$	−460.000	−0.0290902
$631$	18722.0	1.18116	0.590579	−	0.806980i	$-0.298899\pi$
$631$	18722.0	1.18116	0.590579	+	0.806980i	$0.298899\pi$
$632$	5776.00	0.363539
$633$	−6088.00	−0.382269
$634$	−10788.0	−0.675783
$635$	−8630.00	−0.539325
$636$	2832.00	0.176566
$637$	−678.000	−0.0421716
$638$	12960.0	0.804218
$639$	−9384.00	−0.580947
$640$	640.000	0.0395285
$641$	−27426.0	−1.68996	−0.844978	−	0.534801i	$-0.820387\pi$
$641$	−27426.0	−1.68996	−0.844978	+	0.534801i	$0.820387\pi$
$642$	−1848.00	−0.113606
$643$	28460.0	1.74549	0.872747	−	0.488173i	$-0.162336\pi$
$643$	28460.0	1.74549	0.872747	+	0.488173i	$0.162336\pi$
$644$	−288.000	−0.0176223
$645$	−2720.00	−0.166046
$646$	−5016.00	−0.305498
$647$	−7404.00	−0.449894	−0.224947	−	0.974371i	$-0.572221\pi$
$647$	−7404.00	−0.449894	−0.224947	+	0.974371i	$0.572221\pi$
$648$	3368.00	0.204178
$649$	35856.0	2.16868
$650$	100.000	0.00603434
$651$	280.000	0.0168572
$652$	−4816.00	−0.289278
$653$	12342.0	0.739632	0.369816	−	0.929105i	$-0.379421\pi$
$653$	12342.0	0.739632	0.369816	+	0.929105i	$0.379421\pi$
$654$	5032.00	0.300867
$655$	6510.00	0.388346
$656$	−7008.00	−0.417098
$657$	8234.00	0.488948
$658$	−792.000	−0.0469231
$659$	−18924.0	−1.11863	−0.559313	−	0.828957i	$-0.688935\pi$
$659$	−18924.0	−1.11863	−0.559313	+	0.828957i	$0.688935\pi$
$660$	2880.00	0.169854
$661$	29414.0	1.73082	0.865410	−	0.501064i	$-0.167058\pi$
$661$	29414.0	1.73082	0.865410	+	0.501064i	$0.167058\pi$
$662$	−22316.0	−1.31018
$663$	264.000	0.0154644
$664$	−1392.00	−0.0813555
$665$	380.000	0.0221590
$666$	−1702.00	−0.0990258
$667$	3240.00	0.188086
$668$	−8736.00	−0.505997
$669$	10148.0	0.586464
$670$	20.0000	0.00115323
$671$	−39024.0	−2.24516
$672$	−128.000	−0.00734778
$673$	27002.0	1.54658	0.773292	−	0.634050i	$-0.218609\pi$
$673$	27002.0	1.54658	0.773292	+	0.634050i	$0.218609\pi$
$674$	436.000	0.0249171
$675$	2500.00	0.142556
$676$	−8772.00	−0.499090
$677$	−34074.0	−1.93437	−0.967186	−	0.254068i	$-0.918231\pi$
$677$	−34074.0	−1.93437	−0.967186	+	0.254068i	$0.918231\pi$
$678$	−4920.00	−0.278689
$679$	−1148.00	−0.0648839
$680$	−2640.00	−0.148881
$681$	−9528.00	−0.536144
$682$	10080.0	0.565958
$683$	−7176.00	−0.402023	−0.201012	−	0.979589i	$-0.564423\pi$
$683$	−7176.00	−0.402023	−0.201012	+	0.979589i	$0.564423\pi$
$684$	−3496.00	−0.195428
$685$	13770.0	0.768065
$686$	−2728.00	−0.151830
$687$	−1660.00	−0.0921877
$688$	4352.00	0.241161
$689$	−708.000	−0.0391475
$690$	720.000	0.0397245
$691$	16544.0	0.910801	0.455400	−	0.890287i	$-0.349496\pi$
$691$	16544.0	0.910801	0.455400	+	0.890287i	$0.349496\pi$
$692$	−14088.0	−0.773910
$693$	3312.00	0.181548
$694$	864.000	0.0472579
$695$	5860.00	0.319831
$696$	1440.00	0.0784239
$697$	28908.0	1.57097
$698$	6052.00	0.328183
$699$	2124.00	0.114931
$700$	200.000	0.0107990
$701$	−25770.0	−1.38847	−0.694236	−	0.719747i	$-0.744258\pi$
$701$	−25770.0	−1.38847	−0.694236	+	0.719747i	$0.744258\pi$
$702$	400.000	0.0215057
$703$	1406.00	0.0754314
$704$	−4608.00	−0.246691
$705$	1980.00	0.105775
$706$	−17916.0	−0.955067
$707$	1620.00	0.0861759
$708$	3984.00	0.211480
$709$	−26602.0	−1.40911	−0.704555	−	0.709649i	$-0.748853\pi$
$709$	−26602.0	−1.40911	−0.704555	+	0.709649i	$0.748853\pi$
$710$	4080.00	0.215662
$711$	−16606.0	−0.875912
$712$	−816.000	−0.0429507
$713$	2520.00	0.132363
$714$	528.000	0.0276749
$715$	−720.000	−0.0376594
$716$	8136.00	0.424660
$717$	3516.00	0.183134
$718$	−12168.0	−0.632459
$719$	−2604.00	−0.135066	−0.0675332	−	0.997717i	$-0.521513\pi$
$719$	−2604.00	−0.135066	−0.0675332	+	0.997717i	$0.521513\pi$
$720$	−1840.00	−0.0952399
$721$	1696.00	0.0876038
$722$	−10830.0	−0.558242
$723$	−8068.00	−0.415010
$724$	4040.00	0.207383
$725$	−2250.00	−0.115259
$726$	−15412.0	−0.787869
$727$	2468.00	0.125905	0.0629526	−	0.998017i	$-0.479948\pi$
$727$	2468.00	0.125905	0.0629526	+	0.998017i	$0.479948\pi$
$728$	32.0000	0.00162912
$729$	−4283.00	−0.217599
$730$	−3580.00	−0.181509
$731$	−17952.0	−0.908316
$732$	−4336.00	−0.218939
$733$	−16810.0	−0.847055	−0.423528	−	0.905883i	$-0.639208\pi$
$733$	−16810.0	−0.847055	−0.423528	+	0.905883i	$0.639208\pi$
$734$	−16412.0	−0.825311
$735$	3390.00	0.170125
$736$	−1152.00	−0.0576947
$737$	−144.000	−0.00719716
$738$	20148.0	1.00496
$739$	−20788.0	−1.03478	−0.517388	−	0.855751i	$-0.673095\pi$
$739$	−20788.0	−1.03478	−0.517388	+	0.855751i	$0.673095\pi$
$740$	740.000	0.0367607
$741$	−152.000	−0.00753557
$742$	−1416.00	−0.0700579
$743$	2442.00	0.120576	0.0602882	−	0.998181i	$-0.480798\pi$
$743$	2442.00	0.120576	0.0602882	+	0.998181i	$0.480798\pi$
$744$	1120.00	0.0551898
$745$	−12510.0	−0.615209
$746$	−5828.00	−0.286030
$747$	4002.00	0.196018
$748$	19008.0	0.929146
$749$	924.000	0.0450764
$750$	−500.000	−0.0243432
$751$	37100.0	1.80266	0.901330	−	0.433132i	$-0.142592\pi$
$751$	37100.0	1.80266	0.901330	+	0.433132i	$0.142592\pi$
$752$	−3168.00	−0.153624
$753$	−4572.00	−0.221266
$754$	−360.000	−0.0173878
$755$	−1340.00	−0.0645928
$756$	800.000	0.0384864
$757$	−16882.0	−0.810550	−0.405275	−	0.914195i	$-0.632824\pi$
$757$	−16882.0	−0.810550	−0.405275	+	0.914195i	$0.632824\pi$
$758$	−12992.0	−0.622547
$759$	−5184.00	−0.247915
$760$	1520.00	0.0725476
$761$	−2550.00	−0.121468	−0.0607342	−	0.998154i	$-0.519344\pi$
$761$	−2550.00	−0.121468	−0.0607342	+	0.998154i	$0.519344\pi$
$762$	6904.00	0.328222
$763$	−2516.00	−0.119378
$764$	16344.0	0.773960
$765$	7590.00	0.358715
$766$	17016.0	0.802628
$767$	−996.000	−0.0468885
$768$	−512.000	−0.0240563
$769$	−19078.0	−0.894630	−0.447315	−	0.894377i	$-0.647620\pi$
$769$	−19078.0	−0.894630	−0.447315	+	0.894377i	$0.647620\pi$
$770$	−1440.00	−0.0673948
$771$	−8508.00	−0.397417
$772$	−5752.00	−0.268159
$773$	−11778.0	−0.548027	−0.274014	−	0.961726i	$-0.588351\pi$
$773$	−11778.0	−0.548027	−0.274014	+	0.961726i	$0.588351\pi$
$774$	−12512.0	−0.581052
$775$	−1750.00	−0.0811121
$776$	−4592.00	−0.212427
$777$	−148.000	−0.00683330
$778$	−16356.0	−0.753716
$779$	−16644.0	−0.765511
$780$	−80.0000	−0.00367238
$781$	−29376.0	−1.34591
$782$	4752.00	0.217303
$783$	−9000.00	−0.410771
$784$	−5424.00	−0.247085
$785$	−9890.00	−0.449668
$786$	−5208.00	−0.236340
$787$	686.000	0.0310715	0.0155357	−	0.999879i	$-0.495055\pi$
$787$	686.000	0.0310715	0.0155357	+	0.999879i	$0.495055\pi$
$788$	−1416.00	−0.0640138
$789$	156.000	0.00703897
$790$	7220.00	0.325160
$791$	2460.00	0.110578
$792$	13248.0	0.594378
$793$	1084.00	0.0485422
$794$	−10580.0	−0.472884
$795$	3540.00	0.157926
$796$	10808.0	0.481256
$797$	40578.0	1.80345	0.901723	−	0.432314i	$-0.142303\pi$
$797$	40578.0	1.80345	0.901723	+	0.432314i	$0.142303\pi$
$798$	−304.000	−0.0134856
$799$	13068.0	0.578614
$800$	800.000	0.0353553
$801$	2346.00	0.103485
$802$	1620.00	0.0713269
$803$	25776.0	1.13277
$804$	−16.0000	−0.000701836 0
$805$	−360.000	−0.0157619
$806$	−280.000	−0.0122365
$807$	5724.00	0.249683
$808$	6480.00	0.282136
$809$	−12822.0	−0.557228	−0.278614	−	0.960403i	$-0.589875\pi$
$809$	−12822.0	−0.557228	−0.278614	+	0.960403i	$0.589875\pi$
$810$	4210.00	0.182623
$811$	−12220.0	−0.529103	−0.264551	−	0.964372i	$-0.585224\pi$
$811$	−12220.0	−0.529103	−0.264551	+	0.964372i	$0.585224\pi$
$812$	−720.000	−0.0311171
$813$	1616.00	0.0697117
$814$	−5328.00	−0.229418
$815$	−6020.00	−0.258738
$816$	2112.00	0.0906064
$817$	10336.0	0.442608
$818$	−11660.0	−0.498389
$819$	−92.0000	−0.00392520
$820$	−8760.00	−0.373064
$821$	17166.0	0.729717	0.364858	−	0.931063i	$-0.381117\pi$
$821$	17166.0	0.729717	0.364858	+	0.931063i	$0.381117\pi$
$822$	−11016.0	−0.467430
$823$	22574.0	0.956112	0.478056	−	0.878329i	$-0.341342\pi$
$823$	22574.0	0.956112	0.478056	+	0.878329i	$0.341342\pi$
$824$	6784.00	0.286810
$825$	3600.00	0.151922
$826$	−1992.00	−0.0839111
$827$	−43764.0	−1.84017	−0.920087	−	0.391715i	$-0.871882\pi$
$827$	−43764.0	−1.84017	−0.920087	+	0.391715i	$0.871882\pi$
$828$	3312.00	0.139010
$829$	23654.0	0.990998	0.495499	−	0.868608i	$-0.334985\pi$
$829$	23654.0	0.990998	0.495499	+	0.868608i	$0.334985\pi$
$830$	−1740.00	−0.0727666
$831$	5612.00	0.234270
$832$	128.000	0.00533366
$833$	22374.0	0.930628
$834$	−4688.00	−0.194643
$835$	−10920.0	−0.452577
$836$	−10944.0	−0.452759
$837$	−7000.00	−0.289075
$838$	7536.00	0.310653
$839$	−7248.00	−0.298246	−0.149123	−	0.988819i	$-0.547645\pi$
$839$	−7248.00	−0.298246	−0.149123	+	0.988819i	$0.547645\pi$
$840$	−160.000	−0.00657205
$841$	−16289.0	−0.667883
$842$	31036.0	1.27027
$843$	10572.0	0.431932
$844$	12176.0	0.496582
$845$	−10965.0	−0.446399
$846$	9108.00	0.370141
$847$	7706.00	0.312611
$848$	−5664.00	−0.229366
$849$	−2488.00	−0.100575
$850$	−3300.00	−0.133164
$851$	−1332.00	−0.0536550
$852$	−3264.00	−0.131247
$853$	17390.0	0.698033	0.349017	−	0.937117i	$-0.386516\pi$
$853$	17390.0	0.698033	0.349017	+	0.937117i	$0.386516\pi$
$854$	2168.00	0.0868705
$855$	−4370.00	−0.174796
$856$	3696.00	0.147578
$857$	18954.0	0.755492	0.377746	−	0.925909i	$-0.376699\pi$
$857$	18954.0	0.755492	0.377746	+	0.925909i	$0.376699\pi$
$858$	576.000	0.0229188
$859$	−40714.0	−1.61716	−0.808582	−	0.588384i	$-0.799765\pi$
$859$	−40714.0	−1.61716	−0.808582	+	0.588384i	$0.799765\pi$
$860$	5440.00	0.215701
$861$	1752.00	0.0693473
$862$	−1596.00	−0.0630626
$863$	−2298.00	−0.0906429	−0.0453215	−	0.998972i	$-0.514431\pi$
$863$	−2298.00	−0.0906429	−0.0453215	+	0.998972i	$0.514431\pi$
$864$	3200.00	0.126003
$865$	−17610.0	−0.692206
$866$	−28940.0	−1.13559
$867$	1114.00	0.0436372
$868$	−560.000	−0.0218982
$869$	−51984.0	−2.02927
$870$	1800.00	0.0701445
$871$	4.00000	0.000155608 0
$872$	−10064.0	−0.390837
$873$	13202.0	0.511821
$874$	−2736.00	−0.105889
$875$	250.000	0.00965891
$876$	2864.00	0.110463
$877$	−47482.0	−1.82822	−0.914112	−	0.405461i	$-0.867111\pi$
$877$	−47482.0	−1.82822	−0.914112	+	0.405461i	$0.867111\pi$
$878$	13468.0	0.517680
$879$	18372.0	0.704974
$880$	−5760.00	−0.220647
$881$	36966.0	1.41364	0.706820	−	0.707394i	$-0.250129\pi$
$881$	36966.0	1.41364	0.706820	+	0.707394i	$0.250129\pi$
$882$	15594.0	0.595326
$883$	−10924.0	−0.416333	−0.208166	−	0.978093i	$-0.566750\pi$
$883$	−10924.0	−0.416333	−0.208166	+	0.978093i	$0.566750\pi$
$884$	−528.000	−0.0200889
$885$	4980.00	0.189154
$886$	−27540.0	−1.04427
$887$	702.000	0.0265737	0.0132868	−	0.999912i	$-0.495771\pi$
$887$	702.000	0.0265737	0.0132868	+	0.999912i	$0.495771\pi$
$888$	−592.000	−0.0223719
$889$	−3452.00	−0.130232
$890$	−1020.00	−0.0384163
$891$	−30312.0	−1.13972
$892$	−20296.0	−0.761839
$893$	−7524.00	−0.281950
$894$	10008.0	0.374404
$895$	10170.0	0.379827
$896$	256.000	0.00954504
$897$	144.000	0.00536011
$898$	7764.00	0.288517
$899$	6300.00	0.233723
$900$	−2300.00	−0.0851852
$901$	23364.0	0.863893
$902$	63072.0	2.32823
$903$	−1088.00	−0.0400957
$904$	9840.00	0.362028
$905$	5050.00	0.185489
$906$	1072.00	0.0393099
$907$	−53332.0	−1.95244	−0.976218	−	0.216790i	$-0.930441\pi$
$907$	−53332.0	−1.95244	−0.976218	+	0.216790i	$0.930441\pi$
$908$	19056.0	0.696471
$909$	−18630.0	−0.679778
$910$	40.0000	0.00145713
$911$	3438.00	0.125034	0.0625170	−	0.998044i	$-0.480087\pi$
$911$	3438.00	0.125034	0.0625170	+	0.998044i	$0.480087\pi$
$912$	−1216.00	−0.0441511
$913$	12528.0	0.454125
$914$	−9068.00	−0.328165
$915$	−5420.00	−0.195825
$916$	3320.00	0.119755
$917$	2604.00	0.0937750
$918$	−13200.0	−0.474581
$919$	51014.0	1.83112	0.915559	−	0.402185i	$-0.131749\pi$
$919$	51014.0	1.83112	0.915559	+	0.402185i	$0.131749\pi$
$920$	−1440.00	−0.0516037
$921$	1004.00	0.0359207
$922$	−15540.0	−0.555079
$923$	816.000	0.0290996
$924$	1152.00	0.0410152
$925$	925.000	0.0328798
$926$	−27896.0	−0.989978
$927$	−19504.0	−0.691041
$928$	−2880.00	−0.101876
$929$	31314.0	1.10590	0.552949	−	0.833215i	$-0.313502\pi$
$929$	31314.0	1.10590	0.552949	+	0.833215i	$0.313502\pi$
$930$	1400.00	0.0493632
$931$	−12882.0	−0.453481
$932$	−4248.00	−0.149300
$933$	924.000	0.0324227
$934$	−12888.0	−0.451508
$935$	23760.0	0.831054
$936$	−368.000	−0.0128509
$937$	21026.0	0.733073	0.366537	−	0.930404i	$-0.380543\pi$
$937$	21026.0	0.733073	0.366537	+	0.930404i	$0.380543\pi$
$938$	8.00000	0.000278475 0
$939$	−12820.0	−0.445543
$940$	−3960.00	−0.137405
$941$	−14790.0	−0.512370	−0.256185	−	0.966628i	$-0.582466\pi$
$941$	−14790.0	−0.512370	−0.256185	+	0.966628i	$0.582466\pi$
$942$	7912.00	0.273659
$943$	15768.0	0.544514
$944$	−7968.00	−0.274721
$945$	1000.00	0.0344233
$946$	−39168.0	−1.34615
$947$	−24492.0	−0.840426	−0.420213	−	0.907426i	$-0.638045\pi$
$947$	−24492.0	−0.840426	−0.420213	+	0.907426i	$0.638045\pi$
$948$	−5776.00	−0.197886
$949$	−716.000	−0.0244914
$950$	1900.00	0.0648886
$951$	10788.0	0.367849
$952$	−1056.00	−0.0359508
$953$	11706.0	0.397896	0.198948	−	0.980010i	$-0.436248\pi$
$953$	11706.0	0.397896	0.198948	+	0.980010i	$0.436248\pi$
$954$	16284.0	0.552635
$955$	20430.0	0.692251
$956$	−7032.00	−0.237899
$957$	−12960.0	−0.437761
$958$	948.000	0.0319713
$959$	5508.00	0.185467
$960$	−640.000	−0.0215166
$961$	−24891.0	−0.835521
$962$	148.000	0.00496020
$963$	−10626.0	−0.355574
$964$	16136.0	0.539114
$965$	−7190.00	−0.239849
$966$	288.000	0.00959239
$967$	18776.0	0.624401	0.312200	−	0.950016i	$-0.398934\pi$
$967$	18776.0	0.624401	0.312200	+	0.950016i	$0.398934\pi$
$968$	30824.0	1.02347
$969$	5016.00	0.166292
$970$	−5740.00	−0.190000
$971$	23388.0	0.772973	0.386486	−	0.922295i	$-0.373689\pi$
$971$	23388.0	0.772973	0.386486	+	0.922295i	$0.373689\pi$
$972$	−14168.0	−0.467530
$973$	2344.00	0.0772304
$974$	35968.0	1.18325
$975$	−100.000	−0.00328468
$976$	8672.00	0.284410
$977$	−12126.0	−0.397078	−0.198539	−	0.980093i	$-0.563620\pi$
$977$	−12126.0	−0.397078	−0.198539	+	0.980093i	$0.563620\pi$
$978$	4816.00	0.157463
$979$	7344.00	0.239750
$980$	−6780.00	−0.220999
$981$	28934.0	0.941684
$982$	26280.0	0.854001
$983$	−534.000	−0.0173265	−0.00866325	−	0.999962i	$-0.502758\pi$
$983$	−534.000	−0.0173265	−0.00866325	+	0.999962i	$0.502758\pi$
$984$	7008.00	0.227040
$985$	−1770.00	−0.0572557
$986$	11880.0	0.383708
$987$	792.000	0.0255417
$988$	304.000	0.00978900
$989$	−9792.00	−0.314831
$990$	16560.0	0.531628
$991$	3458.00	0.110845	0.0554223	−	0.998463i	$-0.482349\pi$
$991$	3458.00	0.110845	0.0554223	+	0.998463i	$0.482349\pi$
$992$	−2240.00	−0.0716936
$993$	22316.0	0.713169
$994$	1632.00	0.0520764
$995$	13510.0	0.430448
$996$	1392.00	0.0442843
$997$	27326.0	0.868027	0.434014	−	0.900906i	$-0.357097\pi$
$997$	27326.0	0.868027	0.434014	+	0.900906i	$0.357097\pi$
$998$	22612.0	0.717205
$999$	3700.00	0.117180

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.4.a.a.1.1	✓	1
5.4	even	2		1850.4.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.4.a.a.1.1	✓	1	1.1	even	1	trivial
1850.4.a.c.1.1		1	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	370.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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