LMFDB - Embedded newform 1682.4.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1682,4,Mod(1,1682)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1682, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1682.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1682 = 2 \cdot 29^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1682.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:	$99.2412126297$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 58)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1682.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2.00000 q^{2} -7.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} -14.0000 q^{6} -2.00000 q^{7} +8.00000 q^{8} +22.0000 q^{9} +O(q^{10})$

\(q+2.00000 q^{2} -7.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} -14.0000 q^{6} -2.00000 q^{7} +8.00000 q^{8} +22.0000 q^{9} +10.0000 q^{10} -37.0000 q^{11} -28.0000 q^{12} +27.0000 q^{13} -4.00000 q^{14} -35.0000 q^{15} +16.0000 q^{16} -24.0000 q^{17} +44.0000 q^{18} +88.0000 q^{19} +20.0000 q^{20} +14.0000 q^{21} -74.0000 q^{22} -28.0000 q^{23} -56.0000 q^{24} -100.000 q^{25} +54.0000 q^{26} +35.0000 q^{27} -8.00000 q^{28} -70.0000 q^{30} +143.000 q^{31} +32.0000 q^{32} +259.000 q^{33} -48.0000 q^{34} -10.0000 q^{35} +88.0000 q^{36} +360.000 q^{37} +176.000 q^{38} -189.000 q^{39} +40.0000 q^{40} -386.000 q^{41} +28.0000 q^{42} -381.000 q^{43} -148.000 q^{44} +110.000 q^{45} -56.0000 q^{46} +103.000 q^{47} -112.000 q^{48} -339.000 q^{49} -200.000 q^{50} +168.000 q^{51} +108.000 q^{52} -431.000 q^{53} +70.0000 q^{54} -185.000 q^{55} -16.0000 q^{56} -616.000 q^{57} +288.000 q^{59} -140.000 q^{60} +840.000 q^{61} +286.000 q^{62} -44.0000 q^{63} +64.0000 q^{64} +135.000 q^{65} +518.000 q^{66} -180.000 q^{67} -96.0000 q^{68} +196.000 q^{69} -20.0000 q^{70} +706.000 q^{71} +176.000 q^{72} -716.000 q^{73} +720.000 q^{74} +700.000 q^{75} +352.000 q^{76} +74.0000 q^{77} -378.000 q^{78} -931.000 q^{79} +80.0000 q^{80} -839.000 q^{81} -772.000 q^{82} +1188.00 q^{83} +56.0000 q^{84} -120.000 q^{85} -762.000 q^{86} -296.000 q^{88} +642.000 q^{89} +220.000 q^{90} -54.0000 q^{91} -112.000 q^{92} -1001.00 q^{93} +206.000 q^{94} +440.000 q^{95} -224.000 q^{96} -486.000 q^{97} -678.000 q^{98} -814.000 q^{99} +O(q^{100})\)

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
$3$	−7.00000	−1.34715	−0.673575	−	0.739119i	$-0.735242\pi$
$3$	−7.00000	−1.34715	−0.673575	+	0.739119i	$0.735242\pi$
$4$	4.00000	0.500000
$5$	5.00000	0.447214	0.223607	−	0.974679i	$-0.428217\pi$
$5$	5.00000	0.447214	0.223607	+	0.974679i	$0.428217\pi$
$6$	−14.0000	−0.952579
$7$	−2.00000	−0.107990	−0.0539949	−	0.998541i	$-0.517195\pi$
$7$	−2.00000	−0.107990	−0.0539949	+	0.998541i	$0.517195\pi$
$8$	8.00000	0.353553
$9$	22.0000	0.814815
$10$	10.0000	0.316228
$11$	−37.0000	−1.01417	−0.507087	−	0.861895i	$-0.669278\pi$
$11$	−37.0000	−1.01417	−0.507087	+	0.861895i	$0.669278\pi$
$12$	−28.0000	−0.673575
$13$	27.0000	0.576035	0.288017	−	0.957625i	$-0.407004\pi$
$13$	27.0000	0.576035	0.288017	+	0.957625i	$0.407004\pi$
$14$	−4.00000	−0.0763604
$15$	−35.0000	−0.602464
$16$	16.0000	0.250000
$17$	−24.0000	−0.342403	−0.171202	−	0.985236i	$-0.554765\pi$
$17$	−24.0000	−0.342403	−0.171202	+	0.985236i	$0.554765\pi$
$18$	44.0000	0.576161
$19$	88.0000	1.06256	0.531279	−	0.847197i	$-0.321712\pi$
$19$	88.0000	1.06256	0.531279	+	0.847197i	$0.321712\pi$
$20$	20.0000	0.223607
$21$	14.0000	0.145479
$22$	−74.0000	−0.717130
$23$	−28.0000	−0.253844	−0.126922	−	0.991913i	$-0.540510\pi$
$23$	−28.0000	−0.253844	−0.126922	+	0.991913i	$0.540510\pi$
$24$	−56.0000	−0.476290
$25$	−100.000	−0.800000
$26$	54.0000	0.407318
$27$	35.0000	0.249472
$28$	−8.00000	−0.0539949
$29$	0	0
$29$	0	0
$30$	−70.0000	−0.426006
$31$	143.000	0.828502	0.414251	−	0.910163i	$-0.364044\pi$
$31$	143.000	0.828502	0.414251	+	0.910163i	$0.364044\pi$
$32$	32.0000	0.176777
$33$	259.000	1.36625
$34$	−48.0000	−0.242116
$35$	−10.0000	−0.0482945
$36$	88.0000	0.407407
$37$	360.000	1.59956	0.799779	−	0.600295i	$-0.204950\pi$
$37$	360.000	1.59956	0.799779	+	0.600295i	$0.204950\pi$
$38$	176.000	0.751341
$39$	−189.000	−0.776006
$40$	40.0000	0.158114
$41$	−386.000	−1.47032	−0.735159	−	0.677894i	$-0.762893\pi$
$41$	−386.000	−1.47032	−0.735159	+	0.677894i	$0.762893\pi$
$42$	28.0000	0.102869
$43$	−381.000	−1.35121	−0.675604	−	0.737265i	$-0.736117\pi$
$43$	−381.000	−1.35121	−0.675604	+	0.737265i	$0.736117\pi$
$44$	−148.000	−0.507087
$45$	110.000	0.364396
$46$	−56.0000	−0.179495
$47$	103.000	0.319662	0.159831	−	0.987144i	$-0.448905\pi$
$47$	103.000	0.319662	0.159831	+	0.987144i	$0.448905\pi$
$48$	−112.000	−0.336788
$49$	−339.000	−0.988338
$50$	−200.000	−0.565685
$51$	168.000	0.461269
$52$	108.000	0.288017
$53$	−431.000	−1.11703	−0.558513	−	0.829496i	$-0.688628\pi$
$53$	−431.000	−1.11703	−0.558513	+	0.829496i	$0.688628\pi$
$54$	70.0000	0.176404
$55$	−185.000	−0.453553
$56$	−16.0000	−0.0381802
$57$	−616.000	−1.43142
$58$	0	0
$59$	288.000	0.635498	0.317749	−	0.948175i	$-0.397073\pi$
$59$	288.000	0.635498	0.317749	+	0.948175i	$0.397073\pi$
$60$	−140.000	−0.301232
$61$	840.000	1.76313	0.881565	−	0.472062i	$-0.156490\pi$
$61$	840.000	1.76313	0.881565	+	0.472062i	$0.156490\pi$
$62$	286.000	0.585839
$63$	−44.0000	−0.0879917
$64$	64.0000	0.125000
$65$	135.000	0.257611
$66$	518.000	0.966082
$67$	−180.000	−0.328216	−0.164108	−	0.986442i	$-0.552475\pi$
$67$	−180.000	−0.328216	−0.164108	+	0.986442i	$0.552475\pi$
$68$	−96.0000	−0.171202
$69$	196.000	0.341966
$70$	−20.0000	−0.0341494
$71$	706.000	1.18010	0.590048	−	0.807368i	$-0.299109\pi$
$71$	706.000	1.18010	0.590048	+	0.807368i	$0.299109\pi$
$72$	176.000	0.288081
$73$	−716.000	−1.14797	−0.573983	−	0.818867i	$-0.694602\pi$
$73$	−716.000	−1.14797	−0.573983	+	0.818867i	$0.694602\pi$
$74$	720.000	1.13106
$75$	700.000	1.07772
$76$	352.000	0.531279
$77$	74.0000	0.109521
$78$	−378.000	−0.548719
$79$	−931.000	−1.32589	−0.662947	−	0.748666i	$-0.730695\pi$
$79$	−931.000	−1.32589	−0.662947	+	0.748666i	$0.730695\pi$
$80$	80.0000	0.111803
$81$	−839.000	−1.15089
$82$	−772.000	−1.03967
$83$	1188.00	1.57108	0.785542	−	0.618809i	$-0.212384\pi$
$83$	1188.00	1.57108	0.785542	+	0.618809i	$0.212384\pi$
$84$	56.0000	0.0727393
$85$	−120.000	−0.153127
$86$	−762.000	−0.955449
$87$	0	0
$88$	−296.000	−0.358565
$89$	642.000	0.764628	0.382314	−	0.924033i	$-0.375127\pi$
$89$	642.000	0.764628	0.382314	+	0.924033i	$0.375127\pi$
$90$	220.000	0.257667
$91$	−54.0000	−0.0622059
$92$	−112.000	−0.126922
$93$	−1001.00	−1.11612
$94$	206.000	0.226035
$95$	440.000	0.475190
$96$	−224.000	−0.238145
$97$	−486.000	−0.508720	−0.254360	−	0.967110i	$-0.581865\pi$
$97$	−486.000	−0.508720	−0.254360	+	0.967110i	$0.581865\pi$
$98$	−678.000	−0.698861
$99$	−814.000	−0.826364
$100$	−400.000	−0.400000
$101$	−240.000	−0.236444	−0.118222	−	0.992987i	$-0.537720\pi$
$101$	−240.000	−0.236444	−0.118222	+	0.992987i	$0.537720\pi$
$102$	336.000	0.326166
$103$	542.000	0.518494	0.259247	−	0.965811i	$-0.416526\pi$
$103$	542.000	0.518494	0.259247	+	0.965811i	$0.416526\pi$
$104$	216.000	0.203659
$105$	70.0000	0.0650600
$106$	−862.000	−0.789857
$107$	374.000	0.337906	0.168953	−	0.985624i	$-0.445961\pi$
$107$	374.000	0.337906	0.168953	+	0.985624i	$0.445961\pi$
$108$	140.000	0.124736
$109$	449.000	0.394554	0.197277	−	0.980348i	$-0.436790\pi$
$109$	449.000	0.394554	0.197277	+	0.980348i	$0.436790\pi$
$110$	−370.000	−0.320710
$111$	−2520.00	−2.15485
$112$	−32.0000	−0.0269975
$113$	−898.000	−0.747582	−0.373791	−	0.927513i	$-0.621942\pi$
$113$	−898.000	−0.747582	−0.373791	+	0.927513i	$0.621942\pi$
$114$	−1232.00	−1.01217
$115$	−140.000	−0.113522
$116$	0	0
$117$	594.000	0.469362
$118$	576.000	0.449365
$119$	48.0000	0.0369761
$120$	−280.000	−0.213003
$121$	38.0000	0.0285500
$122$	1680.00	1.24672
$123$	2702.00	1.98074
$124$	572.000	0.414251
$125$	−1125.00	−0.804984
$126$	−88.0000	−0.0622195
$127$	−1280.00	−0.894344	−0.447172	−	0.894448i	$-0.647569\pi$
$127$	−1280.00	−0.894344	−0.447172	+	0.894448i	$0.647569\pi$
$128$	128.000	0.0883883
$129$	2667.00	1.82028
$130$	270.000	0.182158
$131$	1292.00	0.861699	0.430849	−	0.902424i	$-0.358214\pi$
$131$	1292.00	0.861699	0.430849	+	0.902424i	$0.358214\pi$
$132$	1036.00	0.683123
$133$	−176.000	−0.114745
$134$	−360.000	−0.232084
$135$	175.000	0.111567
$136$	−192.000	−0.121058
$137$	−1852.00	−1.15494	−0.577471	−	0.816411i	$-0.695960\pi$
$137$	−1852.00	−1.15494	−0.577471	+	0.816411i	$0.695960\pi$
$138$	392.000	0.241806
$139$	−1532.00	−0.934838	−0.467419	−	0.884036i	$-0.654816\pi$
$139$	−1532.00	−0.934838	−0.467419	+	0.884036i	$0.654816\pi$
$140$	−40.0000	−0.0241473
$141$	−721.000	−0.430632
$142$	1412.00	0.834454
$143$	−999.000	−0.584200
$144$	352.000	0.203704
$145$	0	0
$146$	−1432.00	−0.811734
$147$	2373.00	1.33144
$148$	1440.00	0.799779
$149$	−1357.00	−0.746106	−0.373053	−	0.927810i	$-0.621689\pi$
$149$	−1357.00	−0.746106	−0.373053	+	0.927810i	$0.621689\pi$
$150$	1400.00	0.762063
$151$	−2134.00	−1.15008	−0.575041	−	0.818124i	$-0.695014\pi$
$151$	−2134.00	−1.15008	−0.575041	+	0.818124i	$0.695014\pi$
$152$	704.000	0.375671
$153$	−528.000	−0.278995
$154$	148.000	0.0774427
$155$	715.000	0.370517
$156$	−756.000	−0.388003
$157$	−2386.00	−1.21289	−0.606444	−	0.795126i	$-0.707405\pi$
$157$	−2386.00	−1.21289	−0.606444	+	0.795126i	$0.707405\pi$
$158$	−1862.00	−0.937549
$159$	3017.00	1.50480
$160$	160.000	0.0790569
$161$	56.0000	0.0274125
$162$	−1678.00	−0.813803
$163$	−3937.00	−1.89184	−0.945919	−	0.324403i	$-0.894837\pi$
$163$	−3937.00	−1.89184	−0.945919	+	0.324403i	$0.894837\pi$
$164$	−1544.00	−0.735159
$165$	1295.00	0.611004
$166$	2376.00	1.11092
$167$	−2762.00	−1.27982	−0.639910	−	0.768450i	$-0.721028\pi$
$167$	−2762.00	−1.27982	−0.639910	+	0.768450i	$0.721028\pi$
$168$	112.000	0.0514344
$169$	−1468.00	−0.668184
$170$	−240.000	−0.108277
$171$	1936.00	0.865787
$172$	−1524.00	−0.675604
$173$	−3822.00	−1.67966	−0.839830	−	0.542849i	$-0.817346\pi$
$173$	−3822.00	−1.67966	−0.839830	+	0.542849i	$0.817346\pi$
$174$	0	0
$175$	200.000	0.0863919
$176$	−592.000	−0.253544
$177$	−2016.00	−0.856112
$178$	1284.00	0.540673
$179$	1430.00	0.597113	0.298556	−	0.954392i	$-0.403495\pi$
$179$	1430.00	0.597113	0.298556	+	0.954392i	$0.403495\pi$
$180$	440.000	0.182198
$181$	−525.000	−0.215596	−0.107798	−	0.994173i	$-0.534380\pi$
$181$	−525.000	−0.215596	−0.107798	+	0.994173i	$0.534380\pi$
$182$	−108.000	−0.0439862
$183$	−5880.00	−2.37520
$184$	−224.000	−0.0897473
$185$	1800.00	0.715344
$186$	−2002.00	−0.789214
$187$	888.000	0.347257
$188$	412.000	0.159831
$189$	−70.0000	−0.0269405
$190$	880.000	0.336010
$191$	−224.000	−0.0848590	−0.0424295	−	0.999099i	$-0.513510\pi$
$191$	−224.000	−0.0848590	−0.0424295	+	0.999099i	$0.513510\pi$
$192$	−448.000	−0.168394
$193$	490.000	0.182751	0.0913756	−	0.995817i	$-0.470874\pi$
$193$	490.000	0.182751	0.0913756	+	0.995817i	$0.470874\pi$
$194$	−972.000	−0.359719
$195$	−945.000	−0.347040
$196$	−1356.00	−0.494169
$197$	106.000	0.0383360	0.0191680	−	0.999816i	$-0.493898\pi$
$197$	106.000	0.0383360	0.0191680	+	0.999816i	$0.493898\pi$
$198$	−1628.00	−0.584328
$199$	−2034.00	−0.724555	−0.362277	−	0.932070i	$-0.618001\pi$
$199$	−2034.00	−0.724555	−0.362277	+	0.932070i	$0.618001\pi$
$200$	−800.000	−0.282843
$201$	1260.00	0.442157
$202$	−480.000	−0.167191
$203$	0	0
$204$	672.000	0.230634
$205$	−1930.00	−0.657547
$206$	1084.00	0.366630
$207$	−616.000	−0.206836
$208$	432.000	0.144009
$209$	−3256.00	−1.07762
$210$	140.000	0.0460044
$211$	−5717.00	−1.86528	−0.932641	−	0.360806i	$-0.882502\pi$
$211$	−5717.00	−1.86528	−0.932641	+	0.360806i	$0.882502\pi$
$212$	−1724.00	−0.558513
$213$	−4942.00	−1.58977
$214$	748.000	0.238936
$215$	−1905.00	−0.604279
$216$	280.000	0.0882018
$217$	−286.000	−0.0894698
$218$	898.000	0.278992
$219$	5012.00	1.54648
$220$	−740.000	−0.226776
$221$	−648.000	−0.197236
$222$	−5040.00	−1.52371
$223$	3438.00	1.03240	0.516201	−	0.856468i	$-0.327346\pi$
$223$	3438.00	1.03240	0.516201	+	0.856468i	$0.327346\pi$
$224$	−64.0000	−0.0190901
$225$	−2200.00	−0.651852
$226$	−1796.00	−0.528620
$227$	5754.00	1.68241	0.841204	−	0.540719i	$-0.181848\pi$
$227$	5754.00	1.68241	0.841204	+	0.540719i	$0.181848\pi$
$228$	−2464.00	−0.715712
$229$	−2074.00	−0.598488	−0.299244	−	0.954177i	$-0.596734\pi$
$229$	−2074.00	−0.598488	−0.299244	+	0.954177i	$0.596734\pi$
$230$	−280.000	−0.0802724
$231$	−518.000	−0.147541
$232$	0	0
$233$	5063.00	1.42355	0.711777	−	0.702405i	$-0.247891\pi$
$233$	5063.00	1.42355	0.711777	+	0.702405i	$0.247891\pi$
$234$	1188.00	0.331889
$235$	515.000	0.142957
$236$	1152.00	0.317749
$237$	6517.00	1.78618
$238$	96.0000	0.0261460
$239$	−1624.00	−0.439531	−0.219765	−	0.975553i	$-0.570529\pi$
$239$	−1624.00	−0.439531	−0.219765	+	0.975553i	$0.570529\pi$
$240$	−560.000	−0.150616
$241$	−4463.00	−1.19289	−0.596446	−	0.802653i	$-0.703421\pi$
$241$	−4463.00	−1.19289	−0.596446	+	0.802653i	$0.703421\pi$
$242$	76.0000	0.0201879
$243$	4928.00	1.30095
$244$	3360.00	0.881565
$245$	−1695.00	−0.441998
$246$	5404.00	1.40060
$247$	2376.00	0.612070
$248$	1144.00	0.292920
$249$	−8316.00	−2.11649
$250$	−2250.00	−0.569210
$251$	2229.00	0.560531	0.280265	−	0.959923i	$-0.409578\pi$
$251$	2229.00	0.560531	0.280265	+	0.959923i	$0.409578\pi$
$252$	−176.000	−0.0439959
$253$	1036.00	0.257442
$254$	−2560.00	−0.632396
$255$	840.000	0.206286
$256$	256.000	0.0625000
$257$	−4187.00	−1.01626	−0.508128	−	0.861281i	$-0.669662\pi$
$257$	−4187.00	−1.01626	−0.508128	+	0.861281i	$0.669662\pi$
$258$	5334.00	1.28713
$259$	−720.000	−0.172736
$260$	540.000	0.128805
$261$	0	0
$262$	2584.00	0.609313
$263$	7611.00	1.78447	0.892233	−	0.451576i	$-0.149138\pi$
$263$	7611.00	1.78447	0.892233	+	0.451576i	$0.149138\pi$
$264$	2072.00	0.483041
$265$	−2155.00	−0.499549
$266$	−352.000	−0.0811372
$267$	−4494.00	−1.03007
$268$	−720.000	−0.164108
$269$	−5136.00	−1.16412	−0.582058	−	0.813147i	$-0.697753\pi$
$269$	−5136.00	−1.16412	−0.582058	+	0.813147i	$0.697753\pi$
$270$	350.000	0.0788901
$271$	−4015.00	−0.899977	−0.449989	−	0.893034i	$-0.648572\pi$
$271$	−4015.00	−0.899977	−0.449989	+	0.893034i	$0.648572\pi$
$272$	−384.000	−0.0856008
$273$	378.000	0.0838007
$274$	−3704.00	−0.816667
$275$	3700.00	0.811340
$276$	784.000	0.170983
$277$	2150.00	0.466357	0.233179	−	0.972434i	$-0.425087\pi$
$277$	2150.00	0.466357	0.233179	+	0.972434i	$0.425087\pi$
$278$	−3064.00	−0.661031
$279$	3146.00	0.675076
$280$	−80.0000	−0.0170747
$281$	−1965.00	−0.417160	−0.208580	−	0.978005i	$-0.566884\pi$
$281$	−1965.00	−0.417160	−0.208580	+	0.978005i	$0.566884\pi$
$282$	−1442.00	−0.304503
$283$	−2452.00	−0.515040	−0.257520	−	0.966273i	$-0.582905\pi$
$283$	−2452.00	−0.515040	−0.257520	+	0.966273i	$0.582905\pi$
$284$	2824.00	0.590048
$285$	−3080.00	−0.640152
$286$	−1998.00	−0.413092
$287$	772.000	0.158780
$288$	704.000	0.144040
$289$	−4337.00	−0.882760
$290$	0	0
$291$	3402.00	0.685322
$292$	−2864.00	−0.573983
$293$	−142.000	−0.0283131	−0.0141565	−	0.999900i	$-0.504506\pi$
$293$	−142.000	−0.0283131	−0.0141565	+	0.999900i	$0.504506\pi$
$294$	4746.00	0.941471
$295$	1440.00	0.284204
$296$	2880.00	0.565529
$297$	−1295.00	−0.253008
$298$	−2714.00	−0.527577
$299$	−756.000	−0.146223
$300$	2800.00	0.538860
$301$	762.000	0.145917
$302$	−4268.00	−0.813231
$303$	1680.00	0.318526
$304$	1408.00	0.265639
$305$	4200.00	0.788496
$306$	−1056.00	−0.197279
$307$	−9097.00	−1.69118	−0.845592	−	0.533830i	$-0.820752\pi$
$307$	−9097.00	−1.69118	−0.845592	+	0.533830i	$0.820752\pi$
$308$	296.000	0.0547603
$309$	−3794.00	−0.698489
$310$	1430.00	0.261995
$311$	4592.00	0.837262	0.418631	−	0.908156i	$-0.362510\pi$
$311$	4592.00	0.837262	0.418631	+	0.908156i	$0.362510\pi$
$312$	−1512.00	−0.274359
$313$	1225.00	0.221218	0.110609	−	0.993864i	$-0.464720\pi$
$313$	1225.00	0.221218	0.110609	+	0.993864i	$0.464720\pi$
$314$	−4772.00	−0.857642
$315$	−220.000	−0.0393511
$316$	−3724.00	−0.662947
$317$	−9852.00	−1.74556	−0.872781	−	0.488111i	$-0.837686\pi$
$317$	−9852.00	−1.74556	−0.872781	+	0.488111i	$0.837686\pi$
$318$	6034.00	1.06406
$319$	0	0
$320$	320.000	0.0559017
$321$	−2618.00	−0.455210
$322$	112.000	0.0193836
$323$	−2112.00	−0.363823
$324$	−3356.00	−0.575446
$325$	−2700.00	−0.460828
$326$	−7874.00	−1.33773
$327$	−3143.00	−0.531524
$328$	−3088.00	−0.519836
$329$	−206.000	−0.0345202
$330$	2590.00	0.432045
$331$	4183.00	0.694618	0.347309	−	0.937751i	$-0.387096\pi$
$331$	4183.00	0.694618	0.347309	+	0.937751i	$0.387096\pi$
$332$	4752.00	0.785542
$333$	7920.00	1.30334
$334$	−5524.00	−0.904970
$335$	−900.000	−0.146783
$336$	224.000	0.0363696
$337$	4480.00	0.724158	0.362079	−	0.932147i	$-0.382067\pi$
$337$	4480.00	0.724158	0.362079	+	0.932147i	$0.382067\pi$
$338$	−2936.00	−0.472477
$339$	6286.00	1.00711
$340$	−480.000	−0.0765637
$341$	−5291.00	−0.840245
$342$	3872.00	0.612204
$343$	1364.00	0.214720
$344$	−3048.00	−0.477724
$345$	980.000	0.152932
$346$	−7644.00	−1.18770
$347$	−5002.00	−0.773837	−0.386918	−	0.922114i	$-0.626461\pi$
$347$	−5002.00	−0.773837	−0.386918	+	0.922114i	$0.626461\pi$
$348$	0	0
$349$	−6427.00	−0.985758	−0.492879	−	0.870098i	$-0.664055\pi$
$349$	−6427.00	−0.985758	−0.492879	+	0.870098i	$0.664055\pi$
$350$	400.000	0.0610883
$351$	945.000	0.143705
$352$	−1184.00	−0.179282
$353$	9734.00	1.46767	0.733836	−	0.679326i	$-0.237728\pi$
$353$	9734.00	1.46767	0.733836	+	0.679326i	$0.237728\pi$
$354$	−4032.00	−0.605363
$355$	3530.00	0.527755
$356$	2568.00	0.382314
$357$	−336.000	−0.0498123
$358$	2860.00	0.422223
$359$	−5379.00	−0.790788	−0.395394	−	0.918512i	$-0.629392\pi$
$359$	−5379.00	−0.790788	−0.395394	+	0.918512i	$0.629392\pi$
$360$	880.000	0.128834
$361$	885.000	0.129028
$362$	−1050.00	−0.152450
$363$	−266.000	−0.0384611
$364$	−216.000	−0.0311030
$365$	−3580.00	−0.513386
$366$	−11760.0	−1.67952
$367$	9640.00	1.37113	0.685564	−	0.728012i	$-0.259556\pi$
$367$	9640.00	1.37113	0.685564	+	0.728012i	$0.259556\pi$
$368$	−448.000	−0.0634609
$369$	−8492.00	−1.19804
$370$	3600.00	0.505825
$371$	862.000	0.120628
$372$	−4004.00	−0.558058
$373$	7543.00	1.04708	0.523541	−	0.852000i	$-0.324611\pi$
$373$	7543.00	1.04708	0.523541	+	0.852000i	$0.324611\pi$
$374$	1776.00	0.245548
$375$	7875.00	1.08444
$376$	824.000	0.113017
$377$	0	0
$378$	−140.000	−0.0190498
$379$	−3804.00	−0.515563	−0.257781	−	0.966203i	$-0.582991\pi$
$379$	−3804.00	−0.515563	−0.257781	+	0.966203i	$0.582991\pi$
$380$	1760.00	0.237595
$381$	8960.00	1.20482
$382$	−448.000	−0.0600044
$383$	9174.00	1.22394	0.611971	−	0.790880i	$-0.290377\pi$
$383$	9174.00	1.22394	0.611971	+	0.790880i	$0.290377\pi$
$384$	−896.000	−0.119072
$385$	370.000	0.0489791
$386$	980.000	0.129225
$387$	−8382.00	−1.10098
$388$	−1944.00	−0.254360
$389$	4536.00	0.591219	0.295610	−	0.955309i	$-0.404477\pi$
$389$	4536.00	0.591219	0.295610	+	0.955309i	$0.404477\pi$
$390$	−1890.00	−0.245395
$391$	672.000	0.0869169
$392$	−2712.00	−0.349430
$393$	−9044.00	−1.16084
$394$	212.000	0.0271076
$395$	−4655.00	−0.592958
$396$	−3256.00	−0.413182
$397$	−9853.00	−1.24561	−0.622806	−	0.782376i	$-0.714007\pi$
$397$	−9853.00	−1.24561	−0.622806	+	0.782376i	$0.714007\pi$
$398$	−4068.00	−0.512338
$399$	1232.00	0.154579
$400$	−1600.00	−0.200000
$401$	−11429.0	−1.42328	−0.711642	−	0.702542i	$-0.752048\pi$
$401$	−11429.0	−1.42328	−0.711642	+	0.702542i	$0.752048\pi$
$402$	2520.00	0.312652
$403$	3861.00	0.477246
$404$	−960.000	−0.118222
$405$	−4195.00	−0.514694
$406$	0	0
$407$	−13320.0	−1.62223
$408$	1344.00	0.163083
$409$	−2662.00	−0.321827	−0.160914	−	0.986968i	$-0.551444\pi$
$409$	−2662.00	−0.321827	−0.160914	+	0.986968i	$0.551444\pi$
$410$	−3860.00	−0.464956
$411$	12964.0	1.55588
$412$	2168.00	0.259247
$413$	−576.000	−0.0686274
$414$	−1232.00	−0.146255
$415$	5940.00	0.702610
$416$	864.000	0.101830
$417$	10724.0	1.25937
$418$	−6512.00	−0.761991
$419$	5126.00	0.597665	0.298832	−	0.954306i	$-0.403403\pi$
$419$	5126.00	0.597665	0.298832	+	0.954306i	$0.403403\pi$
$420$	280.000	0.0325300
$421$	16200.0	1.87539	0.937696	−	0.347458i	$-0.112955\pi$
$421$	16200.0	1.87539	0.937696	+	0.347458i	$0.112955\pi$
$422$	−11434.0	−1.31895
$423$	2266.00	0.260465
$424$	−3448.00	−0.394928
$425$	2400.00	0.273923
$426$	−9884.00	−1.12413
$427$	−1680.00	−0.190400
$428$	1496.00	0.168953
$429$	6993.00	0.787005
$430$	−3810.00	−0.427290
$431$	12000.0	1.34111	0.670556	−	0.741859i	$-0.266055\pi$
$431$	12000.0	1.34111	0.670556	+	0.741859i	$0.266055\pi$
$432$	560.000	0.0623681
$433$	3736.00	0.414644	0.207322	−	0.978273i	$-0.433525\pi$
$433$	3736.00	0.414644	0.207322	+	0.978273i	$0.433525\pi$
$434$	−572.000	−0.0632647
$435$	0	0
$436$	1796.00	0.197277
$437$	−2464.00	−0.269723
$438$	10024.0	1.09353
$439$	3172.00	0.344855	0.172427	−	0.985022i	$-0.444839\pi$
$439$	3172.00	0.344855	0.172427	+	0.985022i	$0.444839\pi$
$440$	−1480.00	−0.160355
$441$	−7458.00	−0.805313
$442$	−1296.00	−0.139467
$443$	1540.00	0.165164	0.0825820	−	0.996584i	$-0.473683\pi$
$443$	1540.00	0.165164	0.0825820	+	0.996584i	$0.473683\pi$
$444$	−10080.0	−1.07742
$445$	3210.00	0.341952
$446$	6876.00	0.730018
$447$	9499.00	1.00512
$448$	−128.000	−0.0134987
$449$	−8358.00	−0.878482	−0.439241	−	0.898369i	$-0.644753\pi$
$449$	−8358.00	−0.878482	−0.439241	+	0.898369i	$0.644753\pi$
$450$	−4400.00	−0.460929
$451$	14282.0	1.49116
$452$	−3592.00	−0.373791
$453$	14938.0	1.54933
$454$	11508.0	1.18964
$455$	−270.000	−0.0278193
$456$	−4928.00	−0.506085
$457$	798.000	0.0816824	0.0408412	−	0.999166i	$-0.486996\pi$
$457$	798.000	0.0816824	0.0408412	+	0.999166i	$0.486996\pi$
$458$	−4148.00	−0.423195
$459$	−840.000	−0.0854201
$460$	−560.000	−0.0567612
$461$	−15330.0	−1.54878	−0.774392	−	0.632706i	$-0.781944\pi$
$461$	−15330.0	−1.54878	−0.774392	+	0.632706i	$0.781944\pi$
$462$	−1036.00	−0.104327
$463$	−6020.00	−0.604262	−0.302131	−	0.953266i	$-0.597698\pi$
$463$	−6020.00	−0.604262	−0.302131	+	0.953266i	$0.597698\pi$
$464$	0	0
$465$	−5005.00	−0.499143
$466$	10126.0	1.00660
$467$	3275.00	0.324516	0.162258	−	0.986748i	$-0.448122\pi$
$467$	3275.00	0.324516	0.162258	+	0.986748i	$0.448122\pi$
$468$	2376.00	0.234681
$469$	360.000	0.0354440
$470$	1030.00	0.101086
$471$	16702.0	1.63394
$472$	2304.00	0.224683
$473$	14097.0	1.37036
$474$	13034.0	1.26302
$475$	−8800.00	−0.850046
$476$	192.000	0.0184880
$477$	−9482.00	−0.910170
$478$	−3248.00	−0.310795
$479$	−13463.0	−1.28422	−0.642109	−	0.766614i	$-0.721940\pi$
$479$	−13463.0	−1.28422	−0.642109	+	0.766614i	$0.721940\pi$
$480$	−1120.00	−0.106502
$481$	9720.00	0.921401
$482$	−8926.00	−0.843502
$483$	−392.000	−0.0369288
$484$	152.000	0.0142750
$485$	−2430.00	−0.227506
$486$	9856.00	0.919912
$487$	−12358.0	−1.14989	−0.574943	−	0.818194i	$-0.694976\pi$
$487$	−12358.0	−1.14989	−0.574943	+	0.818194i	$0.694976\pi$
$488$	6720.00	0.623361
$489$	27559.0	2.54859
$490$	−3390.00	−0.312540
$491$	−407.000	−0.0374087	−0.0187043	−	0.999825i	$-0.505954\pi$
$491$	−407.000	−0.0374087	−0.0187043	+	0.999825i	$0.505954\pi$
$492$	10808.0	0.990370
$493$	0	0
$494$	4752.00	0.432799
$495$	−4070.00	−0.369561
$496$	2288.00	0.207125
$497$	−1412.00	−0.127438
$498$	−16632.0	−1.49658
$499$	14084.0	1.26350	0.631750	−	0.775172i	$-0.282337\pi$
$499$	14084.0	1.26350	0.631750	+	0.775172i	$0.282337\pi$
$500$	−4500.00	−0.402492
$501$	19334.0	1.72411
$502$	4458.00	0.396355
$503$	−13767.0	−1.22036	−0.610179	−	0.792263i	$-0.708903\pi$
$503$	−13767.0	−1.22036	−0.610179	+	0.792263i	$0.708903\pi$
$504$	−352.000	−0.0311098
$505$	−1200.00	−0.105741
$506$	2072.00	0.182039
$507$	10276.0	0.900144
$508$	−5120.00	−0.447172
$509$	21381.0	1.86188	0.930939	−	0.365174i	$-0.118991\pi$
$509$	21381.0	1.86188	0.930939	+	0.365174i	$0.118991\pi$
$510$	1680.00	0.145866
$511$	1432.00	0.123969
$512$	512.000	0.0441942
$513$	3080.00	0.265079
$514$	−8374.00	−0.718602
$515$	2710.00	0.231877
$516$	10668.0	0.910141
$517$	−3811.00	−0.324193
$518$	−1440.00	−0.122143
$519$	26754.0	2.26276
$520$	1080.00	0.0910791
$521$	10243.0	0.861332	0.430666	−	0.902511i	$-0.358279\pi$
$521$	10243.0	0.861332	0.430666	+	0.902511i	$0.358279\pi$
$522$	0	0
$523$	−10568.0	−0.883569	−0.441784	−	0.897121i	$-0.645654\pi$
$523$	−10568.0	−0.883569	−0.441784	+	0.897121i	$0.645654\pi$
$524$	5168.00	0.430849
$525$	−1400.00	−0.116383
$526$	15222.0	1.26181
$527$	−3432.00	−0.283682
$528$	4144.00	0.341561
$529$	−11383.0	−0.935563
$530$	−4310.00	−0.353235
$531$	6336.00	0.517814
$532$	−704.000	−0.0573727
$533$	−10422.0	−0.846955
$534$	−8988.00	−0.728369
$535$	1870.00	0.151116
$536$	−1440.00	−0.116042
$537$	−10010.0	−0.804401
$538$	−10272.0	−0.823155
$539$	12543.0	1.00235
$540$	700.000	0.0557837
$541$	15720.0	1.24927	0.624635	−	0.780916i	$-0.285248\pi$
$541$	15720.0	1.24927	0.624635	+	0.780916i	$0.285248\pi$
$542$	−8030.00	−0.636380
$543$	3675.00	0.290441
$544$	−768.000	−0.0605289
$545$	2245.00	0.176450
$546$	756.000	0.0592561
$547$	−18106.0	−1.41528	−0.707639	−	0.706575i	$-0.750240\pi$
$547$	−18106.0	−1.41528	−0.707639	+	0.706575i	$0.750240\pi$
$548$	−7408.00	−0.577471
$549$	18480.0	1.43663
$550$	7400.00	0.573704
$551$	0	0
$552$	1568.00	0.120903
$553$	1862.00	0.143183
$554$	4300.00	0.329764
$555$	−12600.0	−0.963676
$556$	−6128.00	−0.467419
$557$	−2346.00	−0.178462	−0.0892309	−	0.996011i	$-0.528441\pi$
$557$	−2346.00	−0.178462	−0.0892309	+	0.996011i	$0.528441\pi$
$558$	6292.00	0.477351
$559$	−10287.0	−0.778343
$560$	−160.000	−0.0120736
$561$	−6216.00	−0.467807
$562$	−3930.00	−0.294977
$563$	691.000	0.0517268	0.0258634	−	0.999665i	$-0.491767\pi$
$563$	691.000	0.0517268	0.0258634	+	0.999665i	$0.491767\pi$
$564$	−2884.00	−0.215316
$565$	−4490.00	−0.334329
$566$	−4904.00	−0.364188
$567$	1678.00	0.124285
$568$	5648.00	0.417227
$569$	15542.0	1.14509	0.572544	−	0.819874i	$-0.305957\pi$
$569$	15542.0	1.14509	0.572544	+	0.819874i	$0.305957\pi$
$570$	−6160.00	−0.452656
$571$	12124.0	0.888570	0.444285	−	0.895885i	$-0.353458\pi$
$571$	12124.0	0.888570	0.444285	+	0.895885i	$0.353458\pi$
$572$	−3996.00	−0.292100
$573$	1568.00	0.114318
$574$	1544.00	0.112274
$575$	2800.00	0.203075
$576$	1408.00	0.101852
$577$	−15808.0	−1.14055	−0.570274	−	0.821455i	$-0.693163\pi$
$577$	−15808.0	−1.14055	−0.570274	+	0.821455i	$0.693163\pi$
$578$	−8674.00	−0.624206
$579$	−3430.00	−0.246193
$580$	0	0
$581$	−2376.00	−0.169661
$582$	6804.00	0.484596
$583$	15947.0	1.13286
$584$	−5728.00	−0.405867
$585$	2970.00	0.209905
$586$	−284.000	−0.0200204
$587$	−6516.00	−0.458167	−0.229084	−	0.973407i	$-0.573573\pi$
$587$	−6516.00	−0.458167	−0.229084	+	0.973407i	$0.573573\pi$
$588$	9492.00	0.665720
$589$	12584.0	0.880331
$590$	2880.00	0.200962
$591$	−742.000	−0.0516443
$592$	5760.00	0.399889
$593$	14751.0	1.02150	0.510751	−	0.859729i	$-0.329367\pi$
$593$	14751.0	1.02150	0.510751	+	0.859729i	$0.329367\pi$
$594$	−2590.00	−0.178904
$595$	240.000	0.0165362
$596$	−5428.00	−0.373053
$597$	14238.0	0.976085
$598$	−1512.00	−0.103395
$599$	18681.0	1.27427	0.637133	−	0.770754i	$-0.280120\pi$
$599$	18681.0	1.27427	0.637133	+	0.770754i	$0.280120\pi$
$600$	5600.00	0.381032
$601$	22526.0	1.52888	0.764438	−	0.644697i	$-0.223016\pi$
$601$	22526.0	1.52888	0.764438	+	0.644697i	$0.223016\pi$
$602$	1524.00	0.103179
$603$	−3960.00	−0.267436
$604$	−8536.00	−0.575041
$605$	190.000	0.0127679
$606$	3360.00	0.225232
$607$	9329.00	0.623810	0.311905	−	0.950113i	$-0.399033\pi$
$607$	9329.00	0.623810	0.311905	+	0.950113i	$0.399033\pi$
$608$	2816.00	0.187835
$609$	0	0
$610$	8400.00	0.557551
$611$	2781.00	0.184136
$612$	−2112.00	−0.139498
$613$	19525.0	1.28647	0.643236	−	0.765668i	$-0.277591\pi$
$613$	19525.0	1.28647	0.643236	+	0.765668i	$0.277591\pi$
$614$	−18194.0	−1.19585
$615$	13510.0	0.885814
$616$	592.000	0.0387214
$617$	25332.0	1.65288	0.826441	−	0.563024i	$-0.190362\pi$
$617$	25332.0	1.65288	0.826441	+	0.563024i	$0.190362\pi$
$618$	−7588.00	−0.493906
$619$	21091.0	1.36950	0.684749	−	0.728779i	$-0.259912\pi$
$619$	21091.0	1.36950	0.684749	+	0.728779i	$0.259912\pi$
$620$	2860.00	0.185259
$621$	−980.000	−0.0633270
$622$	9184.00	0.592034
$623$	−1284.00	−0.0825720
$624$	−3024.00	−0.194001
$625$	6875.00	0.440000
$626$	2450.00	0.156424
$627$	22792.0	1.45171
$628$	−9544.00	−0.606444
$629$	−8640.00	−0.547694
$630$	−440.000	−0.0278254
$631$	6242.00	0.393804	0.196902	−	0.980423i	$-0.436912\pi$
$631$	6242.00	0.393804	0.196902	+	0.980423i	$0.436912\pi$
$632$	−7448.00	−0.468775
$633$	40019.0	2.51282
$634$	−19704.0	−1.23430
$635$	−6400.00	−0.399963
$636$	12068.0	0.752401
$637$	−9153.00	−0.569317
$638$	0	0
$639$	15532.0	0.961559
$640$	640.000	0.0395285
$641$	−15392.0	−0.948436	−0.474218	−	0.880407i	$-0.657269\pi$
$641$	−15392.0	−0.948436	−0.474218	+	0.880407i	$0.657269\pi$
$642$	−5236.00	−0.321882
$643$	−14870.0	−0.911999	−0.456000	−	0.889980i	$-0.650718\pi$
$643$	−14870.0	−0.911999	−0.456000	+	0.889980i	$0.650718\pi$
$644$	224.000	0.0137063
$645$	13335.0	0.814054
$646$	−4224.00	−0.257262
$647$	17016.0	1.03395	0.516977	−	0.855999i	$-0.327057\pi$
$647$	17016.0	1.03395	0.516977	+	0.855999i	$0.327057\pi$
$648$	−6712.00	−0.406902
$649$	−10656.0	−0.644506
$650$	−5400.00	−0.325855
$651$	2002.00	0.120529
$652$	−15748.0	−0.945919
$653$	24122.0	1.44558	0.722792	−	0.691065i	$-0.242858\pi$
$653$	24122.0	1.44558	0.722792	+	0.691065i	$0.242858\pi$
$654$	−6286.00	−0.375844
$655$	6460.00	0.385363
$656$	−6176.00	−0.367580
$657$	−15752.0	−0.935379
$658$	−412.000	−0.0244095
$659$	20217.0	1.19506	0.597528	−	0.801848i	$-0.296149\pi$
$659$	20217.0	1.19506	0.597528	+	0.801848i	$0.296149\pi$
$660$	5180.00	0.305502
$661$	3942.00	0.231961	0.115980	−	0.993252i	$-0.462999\pi$
$661$	3942.00	0.231961	0.115980	+	0.993252i	$0.462999\pi$
$662$	8366.00	0.491169
$663$	4536.00	0.265707
$664$	9504.00	0.555462
$665$	−880.000	−0.0513157
$666$	15840.0	0.921603
$667$	0	0
$668$	−11048.0	−0.639910
$669$	−24066.0	−1.39080
$670$	−1800.00	−0.103791
$671$	−31080.0	−1.78812
$672$	448.000	0.0257172
$673$	−6551.00	−0.375219	−0.187610	−	0.982244i	$-0.560074\pi$
$673$	−6551.00	−0.375219	−0.187610	+	0.982244i	$0.560074\pi$
$674$	8960.00	0.512057
$675$	−3500.00	−0.199578
$676$	−5872.00	−0.334092
$677$	−14958.0	−0.849162	−0.424581	−	0.905390i	$-0.639579\pi$
$677$	−14958.0	−0.849162	−0.424581	+	0.905390i	$0.639579\pi$
$678$	12572.0	0.712131
$679$	972.000	0.0549366
$680$	−960.000	−0.0541387
$681$	−40278.0	−2.26646
$682$	−10582.0	−0.594143
$683$	−27584.0	−1.54535	−0.772674	−	0.634803i	$-0.781081\pi$
$683$	−27584.0	−1.54535	−0.772674	+	0.634803i	$0.781081\pi$
$684$	7744.00	0.432894
$685$	−9260.00	−0.516506
$686$	2728.00	0.151830
$687$	14518.0	0.806254
$688$	−6096.00	−0.337802
$689$	−11637.0	−0.643446
$690$	1960.00	0.108139
$691$	24244.0	1.33471	0.667355	−	0.744739i	$-0.267426\pi$
$691$	24244.0	1.33471	0.667355	+	0.744739i	$0.267426\pi$
$692$	−15288.0	−0.839830
$693$	1628.00	0.0892390
$694$	−10004.0	−0.547185
$695$	−7660.00	−0.418072
$696$	0	0
$697$	9264.00	0.503442
$698$	−12854.0	−0.697036
$699$	−35441.0	−1.91774
$700$	800.000	0.0431959
$701$	7431.00	0.400378	0.200189	−	0.979757i	$-0.435844\pi$
$701$	7431.00	0.400378	0.200189	+	0.979757i	$0.435844\pi$
$702$	1890.00	0.101615
$703$	31680.0	1.69962
$704$	−2368.00	−0.126772
$705$	−3605.00	−0.192585
$706$	19468.0	1.03780
$707$	480.000	0.0255336
$708$	−8064.00	−0.428056
$709$	−28429.0	−1.50589	−0.752943	−	0.658085i	$-0.771367\pi$
$709$	−28429.0	−1.50589	−0.752943	+	0.658085i	$0.771367\pi$
$710$	7060.00	0.373179
$711$	−20482.0	−1.08036
$712$	5136.00	0.270337
$713$	−4004.00	−0.210310
$714$	−672.000	−0.0352226
$715$	−4995.00	−0.261262
$716$	5720.00	0.298556
$717$	11368.0	0.592114
$718$	−10758.0	−0.559171
$719$	−29890.0	−1.55036	−0.775180	−	0.631740i	$-0.782341\pi$
$719$	−29890.0	−1.55036	−0.775180	+	0.631740i	$0.782341\pi$
$720$	1760.00	0.0910991
$721$	−1084.00	−0.0559921
$722$	1770.00	0.0912363
$723$	31241.0	1.60701
$724$	−2100.00	−0.107798
$725$	0	0
$726$	−532.000	−0.0271961
$727$	−13072.0	−0.666869	−0.333434	−	0.942773i	$-0.608208\pi$
$727$	−13072.0	−0.666869	−0.333434	+	0.942773i	$0.608208\pi$
$728$	−432.000	−0.0219931
$729$	−11843.0	−0.601687
$730$	−7160.00	−0.363018
$731$	9144.00	0.462658
$732$	−23520.0	−1.18760
$733$	−13456.0	−0.678047	−0.339024	−	0.940778i	$-0.610097\pi$
$733$	−13456.0	−0.678047	−0.339024	+	0.940778i	$0.610097\pi$
$734$	19280.0	0.969534
$735$	11865.0	0.595438
$736$	−896.000	−0.0448736
$737$	6660.00	0.332869
$738$	−16984.0	−0.847140
$739$	−16915.0	−0.841987	−0.420993	−	0.907064i	$-0.638318\pi$
$739$	−16915.0	−0.841987	−0.420993	+	0.907064i	$0.638318\pi$
$740$	7200.00	0.357672
$741$	−16632.0	−0.824550
$742$	1724.00	0.0852965
$743$	−10164.0	−0.501859	−0.250929	−	0.968005i	$-0.580736\pi$
$743$	−10164.0	−0.501859	−0.250929	+	0.968005i	$0.580736\pi$
$744$	−8008.00	−0.394607
$745$	−6785.00	−0.333669
$746$	15086.0	0.740399
$747$	26136.0	1.28014
$748$	3552.00	0.173628
$749$	−748.000	−0.0364904
$750$	15750.0	0.766812
$751$	−5816.00	−0.282595	−0.141298	−	0.989967i	$-0.545127\pi$
$751$	−5816.00	−0.282595	−0.141298	+	0.989967i	$0.545127\pi$
$752$	1648.00	0.0799154
$753$	−15603.0	−0.755119
$754$	0	0
$755$	−10670.0	−0.514333
$756$	−280.000	−0.0134702
$757$	−30496.0	−1.46420	−0.732098	−	0.681200i	$-0.761459\pi$
$757$	−30496.0	−1.46420	−0.732098	+	0.681200i	$0.761459\pi$
$758$	−7608.00	−0.364558
$759$	−7252.00	−0.346813
$760$	3520.00	0.168005
$761$	−25654.0	−1.22202	−0.611010	−	0.791623i	$-0.709236\pi$
$761$	−25654.0	−1.22202	−0.611010	+	0.791623i	$0.709236\pi$
$762$	17920.0	0.851933
$763$	−898.000	−0.0426078
$764$	−896.000	−0.0424295
$765$	−2640.00	−0.124770
$766$	18348.0	0.865457
$767$	7776.00	0.366069
$768$	−1792.00	−0.0841969
$769$	15348.0	0.719718	0.359859	−	0.933007i	$-0.382825\pi$
$769$	15348.0	0.719718	0.359859	+	0.933007i	$0.382825\pi$
$770$	740.000	0.0346334
$771$	29309.0	1.36905
$772$	1960.00	0.0913756
$773$	−22062.0	−1.02654	−0.513270	−	0.858227i	$-0.671566\pi$
$773$	−22062.0	−1.02654	−0.513270	+	0.858227i	$0.671566\pi$
$774$	−16764.0	−0.778514
$775$	−14300.0	−0.662802
$776$	−3888.00	−0.179860
$777$	5040.00	0.232701
$778$	9072.00	0.418055
$779$	−33968.0	−1.56230
$780$	−3780.00	−0.173520
$781$	−26122.0	−1.19682
$782$	1344.00	0.0614595
$783$	0	0
$784$	−5424.00	−0.247085
$785$	−11930.0	−0.542420
$786$	−18088.0	−0.820837
$787$	−14942.0	−0.676779	−0.338389	−	0.941006i	$-0.609882\pi$
$787$	−14942.0	−0.676779	−0.338389	+	0.941006i	$0.609882\pi$
$788$	424.000	0.0191680
$789$	−53277.0	−2.40394
$790$	−9310.00	−0.419285
$791$	1796.00	0.0807312
$792$	−6512.00	−0.292164
$793$	22680.0	1.01562
$794$	−19706.0	−0.880781
$795$	15085.0	0.672968
$796$	−8136.00	−0.362277
$797$	−13744.0	−0.610837	−0.305419	−	0.952218i	$-0.598796\pi$
$797$	−13744.0	−0.610837	−0.305419	+	0.952218i	$0.598796\pi$
$798$	2464.00	0.109304
$799$	−2472.00	−0.109453
$800$	−3200.00	−0.141421
$801$	14124.0	0.623030
$802$	−22858.0	−1.00641
$803$	26492.0	1.16424
$804$	5040.00	0.221078
$805$	280.000	0.0122593
$806$	7722.00	0.337464
$807$	35952.0	1.56824
$808$	−1920.00	−0.0835957
$809$	−19376.0	−0.842057	−0.421028	−	0.907047i	$-0.638331\pi$
$809$	−19376.0	−0.842057	−0.421028	+	0.907047i	$0.638331\pi$
$810$	−8390.00	−0.363944
$811$	38174.0	1.65286	0.826431	−	0.563039i	$-0.190368\pi$
$811$	38174.0	1.65286	0.826431	+	0.563039i	$0.190368\pi$
$812$	0	0
$813$	28105.0	1.21241
$814$	−26640.0	−1.14709
$815$	−19685.0	−0.846056
$816$	2688.00	0.115317
$817$	−33528.0	−1.43574
$818$	−5324.00	−0.227566
$819$	−1188.00	−0.0506863
$820$	−7720.00	−0.328773
$821$	−15533.0	−0.660299	−0.330149	−	0.943929i	$-0.607099\pi$
$821$	−15533.0	−0.660299	−0.330149	+	0.943929i	$0.607099\pi$
$822$	25928.0	1.10017
$823$	−13624.0	−0.577039	−0.288519	−	0.957474i	$-0.593163\pi$
$823$	−13624.0	−0.577039	−0.288519	+	0.957474i	$0.593163\pi$
$824$	4336.00	0.183315
$825$	−25900.0	−1.09300
$826$	−1152.00	−0.0485269
$827$	37475.0	1.57574	0.787868	−	0.615844i	$-0.211185\pi$
$827$	37475.0	1.57574	0.787868	+	0.615844i	$0.211185\pi$
$828$	−2464.00	−0.103418
$829$	−11600.0	−0.485989	−0.242994	−	0.970028i	$-0.578130\pi$
$829$	−11600.0	−0.485989	−0.242994	+	0.970028i	$0.578130\pi$
$830$	11880.0	0.496820
$831$	−15050.0	−0.628254
$832$	1728.00	0.0720044
$833$	8136.00	0.338410
$834$	21448.0	0.890508
$835$	−13810.0	−0.572353
$836$	−13024.0	−0.538809
$837$	5005.00	0.206688
$838$	10252.0	0.422613
$839$	10783.0	0.443707	0.221854	−	0.975080i	$-0.428789\pi$
$839$	10783.0	0.443707	0.221854	+	0.975080i	$0.428789\pi$
$840$	560.000	0.0230022
$841$	0	0
$842$	32400.0	1.32610
$843$	13755.0	0.561978
$844$	−22868.0	−0.932641
$845$	−7340.00	−0.298821
$846$	4532.00	0.184177
$847$	−76.0000	−0.00308311
$848$	−6896.00	−0.279257
$849$	17164.0	0.693836
$850$	4800.00	0.193693
$851$	−10080.0	−0.406038
$852$	−19768.0	−0.794883
$853$	20026.0	0.803842	0.401921	−	0.915674i	$-0.368343\pi$
$853$	20026.0	0.803842	0.401921	+	0.915674i	$0.368343\pi$
$854$	−3360.00	−0.134633
$855$	9680.00	0.387192
$856$	2992.00	0.119468
$857$	−37259.0	−1.48511	−0.742557	−	0.669783i	$-0.766387\pi$
$857$	−37259.0	−1.48511	−0.742557	+	0.669783i	$0.766387\pi$
$858$	13986.0	0.556497
$859$	19681.0	0.781731	0.390866	−	0.920448i	$-0.372176\pi$
$859$	19681.0	0.781731	0.390866	+	0.920448i	$0.372176\pi$
$860$	−7620.00	−0.302139
$861$	−5404.00	−0.213900
$862$	24000.0	0.948310
$863$	−12422.0	−0.489977	−0.244988	−	0.969526i	$-0.578784\pi$
$863$	−12422.0	−0.489977	−0.244988	+	0.969526i	$0.578784\pi$
$864$	1120.00	0.0441009
$865$	−19110.0	−0.751167
$866$	7472.00	0.293197
$867$	30359.0	1.18921
$868$	−1144.00	−0.0447349
$869$	34447.0	1.34469
$870$	0	0
$871$	−4860.00	−0.189064
$872$	3592.00	0.139496
$873$	−10692.0	−0.414512
$874$	−4928.00	−0.190723
$875$	2250.00	0.0869302
$876$	20048.0	0.773241
$877$	−6111.00	−0.235295	−0.117648	−	0.993055i	$-0.537535\pi$
$877$	−6111.00	−0.235295	−0.117648	+	0.993055i	$0.537535\pi$
$878$	6344.00	0.243849
$879$	994.000	0.0381420
$880$	−2960.00	−0.113388
$881$	33998.0	1.30014	0.650069	−	0.759875i	$-0.274740\pi$
$881$	33998.0	1.30014	0.650069	+	0.759875i	$0.274740\pi$
$882$	−14916.0	−0.569442
$883$	5214.00	0.198715	0.0993573	−	0.995052i	$-0.468321\pi$
$883$	5214.00	0.198715	0.0993573	+	0.995052i	$0.468321\pi$
$884$	−2592.00	−0.0986181
$885$	−10080.0	−0.382865
$886$	3080.00	0.116789
$887$	27507.0	1.04126	0.520628	−	0.853783i	$-0.325698\pi$
$887$	27507.0	1.04126	0.520628	+	0.853783i	$0.325698\pi$
$888$	−20160.0	−0.761853
$889$	2560.00	0.0965800
$890$	6420.00	0.241797
$891$	31043.0	1.16720
$892$	13752.0	0.516201
$893$	9064.00	0.339659
$894$	18998.0	0.710725
$895$	7150.00	0.267037
$896$	−256.000	−0.00954504
$897$	5292.00	0.196984
$898$	−16716.0	−0.621181
$899$	0	0
$900$	−8800.00	−0.325926
$901$	10344.0	0.382473
$902$	28564.0	1.05441
$903$	−5334.00	−0.196572
$904$	−7184.00	−0.264310
$905$	−2625.00	−0.0964176
$906$	29876.0	1.09554
$907$	−49012.0	−1.79429	−0.897143	−	0.441741i	$-0.854361\pi$
$907$	−49012.0	−1.79429	−0.897143	+	0.441741i	$0.854361\pi$
$908$	23016.0	0.841204
$909$	−5280.00	−0.192658
$910$	−540.000	−0.0196712
$911$	−38047.0	−1.38370	−0.691851	−	0.722040i	$-0.743205\pi$
$911$	−38047.0	−1.38370	−0.691851	+	0.722040i	$0.743205\pi$
$912$	−9856.00	−0.357856
$913$	−43956.0	−1.59335
$914$	1596.00	0.0577582
$915$	−29400.0	−1.06222
$916$	−8296.00	−0.299244
$917$	−2584.00	−0.0930547
$918$	−1680.00	−0.0604012
$919$	23214.0	0.833253	0.416626	−	0.909078i	$-0.363212\pi$
$919$	23214.0	0.833253	0.416626	+	0.909078i	$0.363212\pi$
$920$	−1120.00	−0.0401362
$921$	63679.0	2.27828
$922$	−30660.0	−1.09516
$923$	19062.0	0.679776
$924$	−2072.00	−0.0737703
$925$	−36000.0	−1.27965
$926$	−12040.0	−0.427277
$927$	11924.0	0.422476
$928$	0	0
$929$	13890.0	0.490545	0.245272	−	0.969454i	$-0.421123\pi$
$929$	13890.0	0.490545	0.245272	+	0.969454i	$0.421123\pi$
$930$	−10010.0	−0.352947
$931$	−29832.0	−1.05017
$932$	20252.0	0.711777
$933$	−32144.0	−1.12792
$934$	6550.00	0.229467
$935$	4440.00	0.155298
$936$	4752.00	0.165944
$937$	20830.0	0.726240	0.363120	−	0.931742i	$-0.381712\pi$
$937$	20830.0	0.726240	0.363120	+	0.931742i	$0.381712\pi$
$938$	720.000	0.0250627
$939$	−8575.00	−0.298013
$940$	2060.00	0.0714785
$941$	32305.0	1.11914	0.559571	−	0.828782i	$-0.310966\pi$
$941$	32305.0	1.11914	0.559571	+	0.828782i	$0.310966\pi$
$942$	33404.0	1.15537
$943$	10808.0	0.373231
$944$	4608.00	0.158875
$945$	−350.000	−0.0120481
$946$	28194.0	0.968992
$947$	35759.0	1.22704	0.613522	−	0.789677i	$-0.289752\pi$
$947$	35759.0	1.22704	0.613522	+	0.789677i	$0.289752\pi$
$948$	26068.0	0.893090
$949$	−19332.0	−0.661268
$950$	−17600.0	−0.601073
$951$	68964.0	2.35154
$952$	384.000	0.0130730
$953$	21847.0	0.742596	0.371298	−	0.928514i	$-0.378913\pi$
$953$	21847.0	0.742596	0.371298	+	0.928514i	$0.378913\pi$
$954$	−18964.0	−0.643587
$955$	−1120.00	−0.0379501
$956$	−6496.00	−0.219765
$957$	0	0
$958$	−26926.0	−0.908079
$959$	3704.00	0.124722
$960$	−2240.00	−0.0753080
$961$	−9342.00	−0.313585
$962$	19440.0	0.651529
$963$	8228.00	0.275331
$964$	−17852.0	−0.596446
$965$	2450.00	0.0817288
$966$	−784.000	−0.0261126
$967$	9151.00	0.304319	0.152159	−	0.988356i	$-0.451377\pi$
$967$	9151.00	0.304319	0.152159	+	0.988356i	$0.451377\pi$
$968$	304.000	0.0100939
$969$	14784.0	0.490124
$970$	−4860.00	−0.160871
$971$	26980.0	0.891688	0.445844	−	0.895111i	$-0.352904\pi$
$971$	26980.0	0.891688	0.445844	+	0.895111i	$0.352904\pi$
$972$	19712.0	0.650476
$973$	3064.00	0.100953
$974$	−24716.0	−0.813092
$975$	18900.0	0.620805
$976$	13440.0	0.440783
$977$	−25659.0	−0.840229	−0.420115	−	0.907471i	$-0.638010\pi$
$977$	−25659.0	−0.840229	−0.420115	+	0.907471i	$0.638010\pi$
$978$	55118.0	1.80213
$979$	−23754.0	−0.775466
$980$	−6780.00	−0.220999
$981$	9878.00	0.321489
$982$	−814.000	−0.0264519
$983$	−48693.0	−1.57992	−0.789962	−	0.613156i	$-0.789900\pi$
$983$	−48693.0	−1.57992	−0.789962	+	0.613156i	$0.789900\pi$
$984$	21616.0	0.700298
$985$	530.000	0.0171444
$986$	0	0
$987$	1442.00	0.0465039
$988$	9504.00	0.306035
$989$	10668.0	0.342996
$990$	−8140.00	−0.261319
$991$	−10898.0	−0.349330	−0.174665	−	0.984628i	$-0.555884\pi$
$991$	−10898.0	−0.349330	−0.174665	+	0.984628i	$0.555884\pi$
$992$	4576.00	0.146460
$993$	−29281.0	−0.935755
$994$	−2824.00	−0.0901125
$995$	−10170.0	−0.324031
$996$	−33264.0	−1.05824
$997$	41216.0	1.30925	0.654626	−	0.755953i	$-0.272826\pi$
$997$	41216.0	1.30925	0.654626	+	0.755953i	$0.272826\pi$
$998$	28168.0	0.893429
$999$	12600.0	0.399045

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1682.4.a.b.1.1		1
29.28	even	2		58.4.a.a.1.1	✓	1
87.86	odd	2		522.4.a.e.1.1		1
116.115	odd	2		464.4.a.a.1.1		1
145.144	even	2		1450.4.a.e.1.1		1
232.115	odd	2		1856.4.a.d.1.1		1
232.173	even	2		1856.4.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
58.4.a.a.1.1	✓	1	29.28	even	2
464.4.a.a.1.1		1	116.115	odd	2
522.4.a.e.1.1		1	87.86	odd	2
1450.4.a.e.1.1		1	145.144	even	2
1682.4.a.b.1.1		1	1.1	even	1	trivial
1856.4.a.a.1.1		1	232.173	even	2
1856.4.a.d.1.1		1	232.115	odd	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:	\( N \)	\(=\)	\( 1682 = 2 \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1682.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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