LMFDB - Embedded newform 170.4.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,4,Mod(1,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, 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("170.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	170.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:	$10.0303247010$
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	$\chi$	$=$	170.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q-2.00000 q^{2} +4.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} -8.00000 q^{6} -4.00000 q^{7} -8.00000 q^{8} -11.0000 q^{9} +10.0000 q^{10} -12.0000 q^{11} +16.0000 q^{12} -58.0000 q^{13} +8.00000 q^{14} -20.0000 q^{15} +16.0000 q^{16} +17.0000 q^{17} +22.0000 q^{18} -52.0000 q^{19} -20.0000 q^{20} -16.0000 q^{21} +24.0000 q^{22} +84.0000 q^{23} -32.0000 q^{24} +25.0000 q^{25} +116.000 q^{26} -152.000 q^{27} -16.0000 q^{28} -246.000 q^{29} +40.0000 q^{30} +68.0000 q^{31} -32.0000 q^{32} -48.0000 q^{33} -34.0000 q^{34} +20.0000 q^{35} -44.0000 q^{36} -358.000 q^{37} +104.000 q^{38} -232.000 q^{39} +40.0000 q^{40} -78.0000 q^{41} +32.0000 q^{42} -412.000 q^{43} -48.0000 q^{44} +55.0000 q^{45} -168.000 q^{46} +408.000 q^{47} +64.0000 q^{48} -327.000 q^{49} -50.0000 q^{50} +68.0000 q^{51} -232.000 q^{52} +750.000 q^{53} +304.000 q^{54} +60.0000 q^{55} +32.0000 q^{56} -208.000 q^{57} +492.000 q^{58} -420.000 q^{59} -80.0000 q^{60} -190.000 q^{61} -136.000 q^{62} +44.0000 q^{63} +64.0000 q^{64} +290.000 q^{65} +96.0000 q^{66} +596.000 q^{67} +68.0000 q^{68} +336.000 q^{69} -40.0000 q^{70} +324.000 q^{71} +88.0000 q^{72} +1010.00 q^{73} +716.000 q^{74} +100.000 q^{75} -208.000 q^{76} +48.0000 q^{77} +464.000 q^{78} +164.000 q^{79} -80.0000 q^{80} -311.000 q^{81} +156.000 q^{82} +588.000 q^{83} -64.0000 q^{84} -85.0000 q^{85} +824.000 q^{86} -984.000 q^{87} +96.0000 q^{88} -486.000 q^{89} -110.000 q^{90} +232.000 q^{91} +336.000 q^{92} +272.000 q^{93} -816.000 q^{94} +260.000 q^{95} -128.000 q^{96} -718.000 q^{97} +654.000 q^{98} +132.000 q^{99} +O(q^{100})\)

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
$7$	−4.00000	−0.215980	−0.107990	−	0.994152i	$-0.534441\pi$
$7$	−4.00000	−0.215980	−0.107990	+	0.994152i	$0.534441\pi$
$8$	−8.00000	−0.353553
$9$	−11.0000	−0.407407
$10$	10.0000	0.316228
$11$	−12.0000	−0.328921	−0.164461	−	0.986384i	$-0.552588\pi$
$11$	−12.0000	−0.328921	−0.164461	+	0.986384i	$0.552588\pi$
$12$	16.0000	0.384900
$13$	−58.0000	−1.23741	−0.618704	−	0.785624i	$-0.712342\pi$
$13$	−58.0000	−1.23741	−0.618704	+	0.785624i	$0.712342\pi$
$14$	8.00000	0.152721
$15$	−20.0000	−0.344265
$16$	16.0000	0.250000
$17$	17.0000	0.242536
$17$	17.0000	0.242536
$18$	22.0000	0.288081
$19$	−52.0000	−0.627875	−0.313937	−	0.949444i	$-0.601648\pi$
$19$	−52.0000	−0.627875	−0.313937	+	0.949444i	$0.601648\pi$
$20$	−20.0000	−0.223607
$21$	−16.0000	−0.166261
$22$	24.0000	0.232583
$23$	84.0000	0.761531	0.380765	−	0.924672i	$-0.375661\pi$
$23$	84.0000	0.761531	0.380765	+	0.924672i	$0.375661\pi$
$24$	−32.0000	−0.272166
$25$	25.0000	0.200000
$26$	116.000	0.874980
$27$	−152.000	−1.08342
$28$	−16.0000	−0.107990
$29$	−246.000	−1.57521	−0.787604	−	0.616181i	$-0.788679\pi$
$29$	−246.000	−1.57521	−0.787604	+	0.616181i	$0.788679\pi$
$30$	40.0000	0.243432
$31$	68.0000	0.393973	0.196986	−	0.980406i	$-0.436884\pi$
$31$	68.0000	0.393973	0.196986	+	0.980406i	$0.436884\pi$
$32$	−32.0000	−0.176777
$33$	−48.0000	−0.253204
$34$	−34.0000	−0.171499
$35$	20.0000	0.0965891
$36$	−44.0000	−0.203704
$37$	−358.000	−1.59067	−0.795336	−	0.606169i	$-0.792705\pi$
$37$	−358.000	−1.59067	−0.795336	+	0.606169i	$0.792705\pi$
$38$	104.000	0.443974
$39$	−232.000	−0.952557
$40$	40.0000	0.158114
$41$	−78.0000	−0.297111	−0.148556	−	0.988904i	$-0.547462\pi$
$41$	−78.0000	−0.297111	−0.148556	+	0.988904i	$0.547462\pi$
$42$	32.0000	0.117564
$43$	−412.000	−1.46115	−0.730575	−	0.682833i	$-0.760748\pi$
$43$	−412.000	−1.46115	−0.730575	+	0.682833i	$0.760748\pi$
$44$	−48.0000	−0.164461
$45$	55.0000	0.182198
$46$	−168.000	−0.538484
$47$	408.000	1.26623	0.633116	−	0.774057i	$-0.281776\pi$
$47$	408.000	1.26623	0.633116	+	0.774057i	$0.281776\pi$
$48$	64.0000	0.192450
$49$	−327.000	−0.953353
$50$	−50.0000	−0.141421
$51$	68.0000	0.186704
$52$	−232.000	−0.618704
$53$	750.000	1.94378	0.971891	−	0.235432i	$-0.0756506\pi$
$53$	750.000	1.94378	0.971891	+	0.235432i	$0.0756506\pi$
$54$	304.000	0.766096
$55$	60.0000	0.147098
$56$	32.0000	0.0763604
$57$	−208.000	−0.483338
$58$	492.000	1.11384
$59$	−420.000	−0.926769	−0.463384	−	0.886157i	$-0.653365\pi$
$59$	−420.000	−0.926769	−0.463384	+	0.886157i	$0.653365\pi$
$60$	−80.0000	−0.172133
$61$	−190.000	−0.398803	−0.199402	−	0.979918i	$-0.563900\pi$
$61$	−190.000	−0.398803	−0.199402	+	0.979918i	$0.563900\pi$
$62$	−136.000	−0.278581
$63$	44.0000	0.0879917
$64$	64.0000	0.125000
$65$	290.000	0.553386
$66$	96.0000	0.179042
$67$	596.000	1.08676	0.543381	−	0.839487i	$-0.317144\pi$
$67$	596.000	1.08676	0.543381	+	0.839487i	$0.317144\pi$
$68$	68.0000	0.121268
$69$	336.000	0.586227
$70$	−40.0000	−0.0682988
$71$	324.000	0.541574	0.270787	−	0.962639i	$-0.412716\pi$
$71$	324.000	0.541574	0.270787	+	0.962639i	$0.412716\pi$
$72$	88.0000	0.144040
$73$	1010.00	1.61934	0.809668	−	0.586888i	$-0.199647\pi$
$73$	1010.00	1.61934	0.809668	+	0.586888i	$0.199647\pi$
$74$	716.000	1.12477
$75$	100.000	0.153960
$76$	−208.000	−0.313937
$77$	48.0000	0.0710404
$78$	464.000	0.673560
$79$	164.000	0.233563	0.116781	−	0.993158i	$-0.462742\pi$
$79$	164.000	0.233563	0.116781	+	0.993158i	$0.462742\pi$
$80$	−80.0000	−0.111803
$81$	−311.000	−0.426612
$82$	156.000	0.210089
$83$	588.000	0.777607	0.388804	−	0.921321i	$-0.372888\pi$
$83$	588.000	0.777607	0.388804	+	0.921321i	$0.372888\pi$
$84$	−64.0000	−0.0831306
$85$	−85.0000	−0.108465
$86$	824.000	1.03319
$87$	−984.000	−1.21260
$88$	96.0000	0.116291
$89$	−486.000	−0.578830	−0.289415	−	0.957204i	$-0.593461\pi$
$89$	−486.000	−0.578830	−0.289415	+	0.957204i	$0.593461\pi$
$90$	−110.000	−0.128834
$91$	232.000	0.267255
$92$	336.000	0.380765
$93$	272.000	0.303280
$94$	−816.000	−0.895361
$95$	260.000	0.280794
$96$	−128.000	−0.136083
$97$	−718.000	−0.751566	−0.375783	−	0.926708i	$-0.622626\pi$
$97$	−718.000	−0.751566	−0.375783	+	0.926708i	$0.622626\pi$
$98$	654.000	0.674122
$99$	132.000	0.134005
$100$	100.000	0.100000
$101$	54.0000	0.0532000	0.0266000	−	0.999646i	$-0.491532\pi$
$101$	54.0000	0.0532000	0.0266000	+	0.999646i	$0.491532\pi$
$102$	−136.000	−0.132020
$103$	392.000	0.374999	0.187500	−	0.982265i	$-0.439962\pi$
$103$	392.000	0.374999	0.187500	+	0.982265i	$0.439962\pi$
$104$	464.000	0.437490
$105$	80.0000	0.0743543
$106$	−1500.00	−1.37446
$107$	−300.000	−0.271048	−0.135524	−	0.990774i	$-0.543272\pi$
$107$	−300.000	−0.271048	−0.135524	+	0.990774i	$0.543272\pi$
$108$	−608.000	−0.541711
$109$	362.000	0.318104	0.159052	−	0.987270i	$-0.449156\pi$
$109$	362.000	0.318104	0.159052	+	0.987270i	$0.449156\pi$
$110$	−120.000	−0.104014
$111$	−1432.00	−1.22450
$112$	−64.0000	−0.0539949
$113$	954.000	0.794202	0.397101	−	0.917775i	$-0.370016\pi$
$113$	954.000	0.794202	0.397101	+	0.917775i	$0.370016\pi$
$114$	416.000	0.341772
$115$	−420.000	−0.340567
$116$	−984.000	−0.787604
$117$	638.000	0.504129
$118$	840.000	0.655324
$119$	−68.0000	−0.0523828
$120$	160.000	0.121716
$121$	−1187.00	−0.891811
$122$	380.000	0.281997
$123$	−312.000	−0.228716
$124$	272.000	0.196986
$125$	−125.000	−0.0894427
$126$	−88.0000	−0.0622195
$127$	−1048.00	−0.732244	−0.366122	−	0.930567i	$-0.619315\pi$
$127$	−1048.00	−0.732244	−0.366122	+	0.930567i	$0.619315\pi$
$128$	−128.000	−0.0883883
$129$	−1648.00	−1.12479
$130$	−580.000	−0.391303
$131$	−1236.00	−0.824350	−0.412175	−	0.911105i	$-0.635231\pi$
$131$	−1236.00	−0.824350	−0.412175	+	0.911105i	$0.635231\pi$
$132$	−192.000	−0.126602
$133$	208.000	0.135608
$134$	−1192.00	−0.768456
$135$	760.000	0.484521
$136$	−136.000	−0.0857493
$137$	1674.00	1.04394	0.521969	−	0.852965i	$-0.325198\pi$
$137$	1674.00	1.04394	0.521969	+	0.852965i	$0.325198\pi$
$138$	−672.000	−0.414525
$139$	−1132.00	−0.690755	−0.345378	−	0.938464i	$-0.612249\pi$
$139$	−1132.00	−0.690755	−0.345378	+	0.938464i	$0.612249\pi$
$140$	80.0000	0.0482945
$141$	1632.00	0.974746
$142$	−648.000	−0.382950
$143$	696.000	0.407010
$144$	−176.000	−0.101852
$145$	1230.00	0.704455
$146$	−2020.00	−1.14504
$147$	−1308.00	−0.733891
$148$	−1432.00	−0.795336
$149$	1470.00	0.808236	0.404118	−	0.914707i	$-0.367579\pi$
$149$	1470.00	0.808236	0.404118	+	0.914707i	$0.367579\pi$
$150$	−200.000	−0.108866
$151$	−1840.00	−0.991636	−0.495818	−	0.868426i	$-0.665132\pi$
$151$	−1840.00	−0.991636	−0.495818	+	0.868426i	$0.665132\pi$
$152$	416.000	0.221987
$153$	−187.000	−0.0988108
$154$	−96.0000	−0.0502331
$155$	−340.000	−0.176190
$156$	−928.000	−0.476279
$157$	254.000	0.129117	0.0645586	−	0.997914i	$-0.479436\pi$
$157$	254.000	0.129117	0.0645586	+	0.997914i	$0.479436\pi$
$158$	−328.000	−0.165154
$159$	3000.00	1.49632
$160$	160.000	0.0790569
$161$	−336.000	−0.164475
$162$	622.000	0.301660
$163$	−2284.00	−1.09753	−0.548763	−	0.835978i	$-0.684901\pi$
$163$	−2284.00	−1.09753	−0.548763	+	0.835978i	$0.684901\pi$
$164$	−312.000	−0.148556
$165$	240.000	0.113236
$166$	−1176.00	−0.549851
$167$	1284.00	0.594963	0.297482	−	0.954728i	$-0.403853\pi$
$167$	1284.00	0.594963	0.297482	+	0.954728i	$0.403853\pi$
$168$	128.000	0.0587822
$169$	1167.00	0.531179
$170$	170.000	0.0766965
$171$	572.000	0.255801
$172$	−1648.00	−0.730575
$173$	2250.00	0.988811	0.494406	−	0.869231i	$-0.335386\pi$
$173$	2250.00	0.988811	0.494406	+	0.869231i	$0.335386\pi$
$174$	1968.00	0.857435
$175$	−100.000	−0.0431959
$176$	−192.000	−0.0822304
$177$	−1680.00	−0.713427
$178$	972.000	0.409295
$179$	−1764.00	−0.736578	−0.368289	−	0.929711i	$-0.620056\pi$
$179$	−1764.00	−0.736578	−0.368289	+	0.929711i	$0.620056\pi$
$180$	220.000	0.0910991
$181$	1994.00	0.818856	0.409428	−	0.912343i	$-0.365728\pi$
$181$	1994.00	0.818856	0.409428	+	0.912343i	$0.365728\pi$
$182$	−464.000	−0.188978
$183$	−760.000	−0.306999
$184$	−672.000	−0.269242
$185$	1790.00	0.711370
$186$	−544.000	−0.214452
$187$	−204.000	−0.0797752
$188$	1632.00	0.633116
$189$	608.000	0.233997
$190$	−520.000	−0.198551
$191$	−168.000	−0.0636443	−0.0318221	−	0.999494i	$-0.510131\pi$
$191$	−168.000	−0.0636443	−0.0318221	+	0.999494i	$0.510131\pi$
$192$	256.000	0.0962250
$193$	3218.00	1.20019	0.600095	−	0.799929i	$-0.295129\pi$
$193$	3218.00	1.20019	0.600095	+	0.799929i	$0.295129\pi$
$194$	1436.00	0.531437
$195$	1160.00	0.425997
$196$	−1308.00	−0.476676
$197$	−2118.00	−0.765996	−0.382998	−	0.923749i	$-0.625108\pi$
$197$	−2118.00	−0.765996	−0.382998	+	0.923749i	$0.625108\pi$
$198$	−264.000	−0.0947559
$199$	−5164.00	−1.83953	−0.919764	−	0.392471i	$-0.871620\pi$
$199$	−5164.00	−1.83953	−0.919764	+	0.392471i	$0.871620\pi$
$200$	−200.000	−0.0707107
$201$	2384.00	0.836589
$202$	−108.000	−0.0376181
$203$	984.000	0.340213
$204$	272.000	0.0933520
$205$	390.000	0.132872
$206$	−784.000	−0.265164
$207$	−924.000	−0.310253
$208$	−928.000	−0.309352
$209$	624.000	0.206521
$210$	−160.000	−0.0525764
$211$	188.000	0.0613386	0.0306693	−	0.999530i	$-0.490236\pi$
$211$	188.000	0.0613386	0.0306693	+	0.999530i	$0.490236\pi$
$212$	3000.00	0.971891
$213$	1296.00	0.416904
$214$	600.000	0.191660
$215$	2060.00	0.653446
$216$	1216.00	0.383048
$217$	−272.000	−0.0850902
$218$	−724.000	−0.224933
$219$	4040.00	1.24657
$220$	240.000	0.0735491
$221$	−986.000	−0.300116
$222$	2864.00	0.865852
$223$	−3184.00	−0.956127	−0.478064	−	0.878325i	$-0.658661\pi$
$223$	−3184.00	−0.956127	−0.478064	+	0.878325i	$0.658661\pi$
$224$	128.000	0.0381802
$225$	−275.000	−0.0814815
$226$	−1908.00	−0.561585
$227$	−5100.00	−1.49118	−0.745592	−	0.666402i	$-0.767833\pi$
$227$	−5100.00	−1.49118	−0.745592	+	0.666402i	$0.767833\pi$
$228$	−832.000	−0.241669
$229$	−466.000	−0.134472	−0.0672361	−	0.997737i	$-0.521418\pi$
$229$	−466.000	−0.134472	−0.0672361	+	0.997737i	$0.521418\pi$
$230$	840.000	0.240817
$231$	192.000	0.0546869
$232$	1968.00	0.556920
$233$	−1950.00	−0.548278	−0.274139	−	0.961690i	$-0.588393\pi$
$233$	−1950.00	−0.548278	−0.274139	+	0.961690i	$0.588393\pi$
$234$	−1276.00	−0.356473
$235$	−2040.00	−0.566276
$236$	−1680.00	−0.463384
$237$	656.000	0.179797
$238$	136.000	0.0370402
$239$	−504.000	−0.136406	−0.0682030	−	0.997671i	$-0.521727\pi$
$239$	−504.000	−0.136406	−0.0682030	+	0.997671i	$0.521727\pi$
$240$	−320.000	−0.0860663
$241$	506.000	0.135246	0.0676231	−	0.997711i	$-0.478458\pi$
$241$	506.000	0.135246	0.0676231	+	0.997711i	$0.478458\pi$
$242$	2374.00	0.630605
$243$	2860.00	0.755017
$244$	−760.000	−0.199402
$245$	1635.00	0.426352
$246$	624.000	0.161727
$247$	3016.00	0.776937
$248$	−544.000	−0.139290
$249$	2352.00	0.598602
$250$	250.000	0.0632456
$251$	1620.00	0.407384	0.203692	−	0.979035i	$-0.434706\pi$
$251$	1620.00	0.407384	0.203692	+	0.979035i	$0.434706\pi$
$252$	176.000	0.0439959
$253$	−1008.00	−0.250484
$254$	2096.00	0.517775
$255$	−340.000	−0.0834966
$256$	256.000	0.0625000
$257$	−6846.00	−1.66164	−0.830821	−	0.556540i	$-0.812128\pi$
$257$	−6846.00	−1.66164	−0.830821	+	0.556540i	$0.812128\pi$
$258$	3296.00	0.795349
$259$	1432.00	0.343553
$260$	1160.00	0.276693
$261$	2706.00	0.641752
$262$	2472.00	0.582903
$263$	−5472.00	−1.28296	−0.641479	−	0.767141i	$-0.721679\pi$
$263$	−5472.00	−1.28296	−0.641479	+	0.767141i	$0.721679\pi$
$264$	384.000	0.0895211
$265$	−3750.00	−0.869286
$266$	−416.000	−0.0958895
$267$	−1944.00	−0.445584
$268$	2384.00	0.543381
$269$	618.000	0.140075	0.0700374	−	0.997544i	$-0.477688\pi$
$269$	618.000	0.140075	0.0700374	+	0.997544i	$0.477688\pi$
$270$	−1520.00	−0.342608
$271$	4856.00	1.08849	0.544245	−	0.838926i	$-0.316816\pi$
$271$	4856.00	1.08849	0.544245	+	0.838926i	$0.316816\pi$
$272$	272.000	0.0606339
$273$	928.000	0.205733
$274$	−3348.00	−0.738175
$275$	−300.000	−0.0657843
$276$	1344.00	0.293113
$277$	674.000	0.146198	0.0730988	−	0.997325i	$-0.476711\pi$
$277$	674.000	0.146198	0.0730988	+	0.997325i	$0.476711\pi$
$278$	2264.00	0.488438
$279$	−748.000	−0.160507
$280$	−160.000	−0.0341494
$281$	7098.00	1.50687	0.753436	−	0.657521i	$-0.228395\pi$
$281$	7098.00	1.50687	0.753436	+	0.657521i	$0.228395\pi$
$282$	−3264.00	−0.689250
$283$	−7516.00	−1.57873	−0.789364	−	0.613926i	$-0.789589\pi$
$283$	−7516.00	−1.57873	−0.789364	+	0.613926i	$0.789589\pi$
$284$	1296.00	0.270787
$285$	1040.00	0.216155
$286$	−1392.00	−0.287800
$287$	312.000	0.0641700
$288$	352.000	0.0720201
$289$	289.000	0.0588235
$290$	−2460.00	−0.498125
$291$	−2872.00	−0.578555
$292$	4040.00	0.809668
$293$	4998.00	0.996540	0.498270	−	0.867022i	$-0.333969\pi$
$293$	4998.00	0.996540	0.498270	+	0.867022i	$0.333969\pi$
$294$	2616.00	0.518940
$295$	2100.00	0.414463
$296$	2864.00	0.562387
$297$	1824.00	0.356361
$298$	−2940.00	−0.571509
$299$	−4872.00	−0.942325
$300$	400.000	0.0769800
$301$	1648.00	0.315579
$302$	3680.00	0.701193
$303$	216.000	0.0409534
$304$	−832.000	−0.156969
$305$	950.000	0.178350
$306$	374.000	0.0698698
$307$	−8692.00	−1.61589	−0.807946	−	0.589257i	$-0.799421\pi$
$307$	−8692.00	−1.61589	−0.807946	+	0.589257i	$0.799421\pi$
$308$	192.000	0.0355202
$309$	1568.00	0.288674
$310$	680.000	0.124585
$311$	7308.00	1.33247	0.666236	−	0.745741i	$-0.267904\pi$
$311$	7308.00	1.33247	0.666236	+	0.745741i	$0.267904\pi$
$312$	1856.00	0.336780
$313$	−6502.00	−1.17417	−0.587084	−	0.809526i	$-0.699724\pi$
$313$	−6502.00	−1.17417	−0.587084	+	0.809526i	$0.699724\pi$
$314$	−508.000	−0.0912997
$315$	−220.000	−0.0393511
$316$	656.000	0.116781
$317$	4290.00	0.760096	0.380048	−	0.924967i	$-0.375907\pi$
$317$	4290.00	0.760096	0.380048	+	0.924967i	$0.375907\pi$
$318$	−6000.00	−1.05806
$319$	2952.00	0.518120
$320$	−320.000	−0.0559017
$321$	−1200.00	−0.208653
$322$	672.000	0.116302
$323$	−884.000	−0.152282
$324$	−1244.00	−0.213306
$325$	−1450.00	−0.247482
$326$	4568.00	0.776068
$327$	1448.00	0.244876
$328$	624.000	0.105045
$329$	−1632.00	−0.273480
$330$	−480.000	−0.0800701
$331$	1724.00	0.286283	0.143141	−	0.989702i	$-0.454280\pi$
$331$	1724.00	0.286283	0.143141	+	0.989702i	$0.454280\pi$
$332$	2352.00	0.388804
$333$	3938.00	0.648051
$334$	−2568.00	−0.420703
$335$	−2980.00	−0.486014
$336$	−256.000	−0.0415653
$337$	−9286.00	−1.50101	−0.750505	−	0.660864i	$-0.770190\pi$
$337$	−9286.00	−1.50101	−0.750505	+	0.660864i	$0.770190\pi$
$338$	−2334.00	−0.375600
$339$	3816.00	0.611377
$340$	−340.000	−0.0542326
$341$	−816.000	−0.129586
$342$	−1144.00	−0.180878
$343$	2680.00	0.421885
$344$	3296.00	0.516594
$345$	−1680.00	−0.262169
$346$	−4500.00	−0.699195
$347$	−8100.00	−1.25311	−0.626557	−	0.779375i	$-0.715537\pi$
$347$	−8100.00	−1.25311	−0.626557	+	0.779375i	$0.715537\pi$
$348$	−3936.00	−0.606298
$349$	−10258.0	−1.57335	−0.786674	−	0.617369i	$-0.788198\pi$
$349$	−10258.0	−1.57335	−0.786674	+	0.617369i	$0.788198\pi$
$350$	200.000	0.0305441
$351$	8816.00	1.34064
$352$	384.000	0.0581456
$353$	−8430.00	−1.27106	−0.635529	−	0.772077i	$-0.719218\pi$
$353$	−8430.00	−1.27106	−0.635529	+	0.772077i	$0.719218\pi$
$354$	3360.00	0.504469
$355$	−1620.00	−0.242199
$356$	−1944.00	−0.289415
$357$	−272.000	−0.0403243
$358$	3528.00	0.520840
$359$	−12120.0	−1.78181	−0.890904	−	0.454191i	$-0.849928\pi$
$359$	−12120.0	−1.78181	−0.890904	+	0.454191i	$0.849928\pi$
$360$	−440.000	−0.0644168
$361$	−4155.00	−0.605773
$362$	−3988.00	−0.579018
$363$	−4748.00	−0.686516
$364$	928.000	0.133628
$365$	−5050.00	−0.724189
$366$	1520.00	0.217081
$367$	1244.00	0.176938	0.0884690	−	0.996079i	$-0.471803\pi$
$367$	1244.00	0.176938	0.0884690	+	0.996079i	$0.471803\pi$
$368$	1344.00	0.190383
$369$	858.000	0.121045
$370$	−3580.00	−0.503014
$371$	−3000.00	−0.419817
$372$	1088.00	0.151640
$373$	5870.00	0.814845	0.407422	−	0.913240i	$-0.366428\pi$
$373$	5870.00	0.814845	0.407422	+	0.913240i	$0.366428\pi$
$374$	408.000	0.0564096
$375$	−500.000	−0.0688530
$376$	−3264.00	−0.447681
$377$	14268.0	1.94918
$378$	−1216.00	−0.165461
$379$	6764.00	0.916737	0.458369	−	0.888762i	$-0.348434\pi$
$379$	6764.00	0.916737	0.458369	+	0.888762i	$0.348434\pi$
$380$	1040.00	0.140397
$381$	−4192.00	−0.563682
$382$	336.000	0.0450033
$383$	−2856.00	−0.381031	−0.190515	−	0.981684i	$-0.561016\pi$
$383$	−2856.00	−0.381031	−0.190515	+	0.981684i	$0.561016\pi$
$384$	−512.000	−0.0680414
$385$	−240.000	−0.0317702
$386$	−6436.00	−0.848663
$387$	4532.00	0.595283
$388$	−2872.00	−0.375783
$389$	−13458.0	−1.75411	−0.877054	−	0.480393i	$-0.840494\pi$
$389$	−13458.0	−1.75411	−0.877054	+	0.480393i	$0.840494\pi$
$390$	−2320.00	−0.301225
$391$	1428.00	0.184698
$392$	2616.00	0.337061
$393$	−4944.00	−0.634585
$394$	4236.00	0.541641
$395$	−820.000	−0.104452
$396$	528.000	0.0670025
$397$	13394.0	1.69326	0.846632	−	0.532179i	$-0.178627\pi$
$397$	13394.0	1.69326	0.846632	+	0.532179i	$0.178627\pi$
$398$	10328.0	1.30074
$399$	832.000	0.104391
$400$	400.000	0.0500000
$401$	−6534.00	−0.813697	−0.406848	−	0.913496i	$-0.633372\pi$
$401$	−6534.00	−0.813697	−0.406848	+	0.913496i	$0.633372\pi$
$402$	−4768.00	−0.591558
$403$	−3944.00	−0.487505
$404$	216.000	0.0266000
$405$	1555.00	0.190787
$406$	−1968.00	−0.240567
$407$	4296.00	0.523206
$408$	−544.000	−0.0660098
$409$	−5350.00	−0.646798	−0.323399	−	0.946263i	$-0.604826\pi$
$409$	−5350.00	−0.646798	−0.323399	+	0.946263i	$0.604826\pi$
$410$	−780.000	−0.0939548
$411$	6696.00	0.803624
$412$	1568.00	0.187500
$413$	1680.00	0.200163
$414$	1848.00	0.219382
$415$	−2940.00	−0.347756
$416$	1856.00	0.218745
$417$	−4528.00	−0.531744
$418$	−1248.00	−0.146033
$419$	3300.00	0.384763	0.192381	−	0.981320i	$-0.438379\pi$
$419$	3300.00	0.384763	0.192381	+	0.981320i	$0.438379\pi$
$420$	320.000	0.0371771
$421$	−9754.00	−1.12917	−0.564585	−	0.825375i	$-0.690964\pi$
$421$	−9754.00	−1.12917	−0.564585	+	0.825375i	$0.690964\pi$
$422$	−376.000	−0.0433730
$423$	−4488.00	−0.515872
$424$	−6000.00	−0.687231
$425$	425.000	0.0485071
$426$	−2592.00	−0.294795
$427$	760.000	0.0861334
$428$	−1200.00	−0.135524
$429$	2784.00	0.313317
$430$	−4120.00	−0.462056
$431$	9300.00	1.03936	0.519681	−	0.854360i	$-0.326051\pi$
$431$	9300.00	1.03936	0.519681	+	0.854360i	$0.326051\pi$
$432$	−2432.00	−0.270856
$433$	17426.0	1.93404	0.967021	−	0.254697i	$-0.0819757\pi$
$433$	17426.0	1.93404	0.967021	+	0.254697i	$0.0819757\pi$
$434$	544.000	0.0601678
$435$	4920.00	0.542290
$436$	1448.00	0.159052
$437$	−4368.00	−0.478146
$438$	−8080.00	−0.881455
$439$	15620.0	1.69818	0.849091	−	0.528247i	$-0.177150\pi$
$439$	15620.0	1.69818	0.849091	+	0.528247i	$0.177150\pi$
$440$	−480.000	−0.0520071
$441$	3597.00	0.388403
$442$	1972.00	0.212214
$443$	−16452.0	−1.76447	−0.882233	−	0.470814i	$-0.843960\pi$
$443$	−16452.0	−1.76447	−0.882233	+	0.470814i	$0.843960\pi$
$444$	−5728.00	−0.612250
$445$	2430.00	0.258861
$446$	6368.00	0.676084
$447$	5880.00	0.622180
$448$	−256.000	−0.0269975
$449$	4026.00	0.423160	0.211580	−	0.977361i	$-0.432139\pi$
$449$	4026.00	0.423160	0.211580	+	0.977361i	$0.432139\pi$
$450$	550.000	0.0576161
$451$	936.000	0.0977262
$452$	3816.00	0.397101
$453$	−7360.00	−0.763362
$454$	10200.0	1.05443
$455$	−1160.00	−0.119520
$456$	1664.00	0.170886
$457$	1946.00	0.199190	0.0995952	−	0.995028i	$-0.468245\pi$
$457$	1946.00	0.199190	0.0995952	+	0.995028i	$0.468245\pi$
$458$	932.000	0.0950862
$459$	−2584.00	−0.262769
$460$	−1680.00	−0.170283
$461$	8430.00	0.851679	0.425840	−	0.904799i	$-0.359979\pi$
$461$	8430.00	0.851679	0.425840	+	0.904799i	$0.359979\pi$
$462$	−384.000	−0.0386695
$463$	6416.00	0.644010	0.322005	−	0.946738i	$-0.395643\pi$
$463$	6416.00	0.644010	0.322005	+	0.946738i	$0.395643\pi$
$464$	−3936.00	−0.393802
$465$	−1360.00	−0.135631
$466$	3900.00	0.387691
$467$	14964.0	1.48277	0.741383	−	0.671083i	$-0.234170\pi$
$467$	14964.0	1.48277	0.741383	+	0.671083i	$0.234170\pi$
$468$	2552.00	0.252065
$469$	−2384.00	−0.234718
$470$	4080.00	0.400418
$471$	1016.00	0.0993945
$472$	3360.00	0.327662
$473$	4944.00	0.480603
$474$	−1312.00	−0.127135
$475$	−1300.00	−0.125575
$476$	−272.000	−0.0261914
$477$	−8250.00	−0.791911
$478$	1008.00	0.0964537
$479$	−16452.0	−1.56933	−0.784667	−	0.619917i	$-0.787166\pi$
$479$	−16452.0	−1.56933	−0.784667	+	0.619917i	$0.787166\pi$
$480$	640.000	0.0608581
$481$	20764.0	1.96831
$482$	−1012.00	−0.0956335
$483$	−1344.00	−0.126613
$484$	−4748.00	−0.445905
$485$	3590.00	0.336110
$486$	−5720.00	−0.533878
$487$	12884.0	1.19883	0.599415	−	0.800439i	$-0.295400\pi$
$487$	12884.0	1.19883	0.599415	+	0.800439i	$0.295400\pi$
$488$	1520.00	0.140998
$489$	−9136.00	−0.844876
$490$	−3270.00	−0.301477
$491$	−11676.0	−1.07318	−0.536589	−	0.843844i	$-0.680287\pi$
$491$	−11676.0	−1.07318	−0.536589	+	0.843844i	$0.680287\pi$
$492$	−1248.00	−0.114358
$493$	−4182.00	−0.382044
$494$	−6032.00	−0.549378
$495$	−660.000	−0.0599289
$496$	1088.00	0.0984932
$497$	−1296.00	−0.116969
$498$	−4704.00	−0.423276
$499$	15548.0	1.39484	0.697419	−	0.716664i	$-0.254332\pi$
$499$	15548.0	1.39484	0.697419	+	0.716664i	$0.254332\pi$
$500$	−500.000	−0.0447214
$501$	5136.00	0.458003
$502$	−3240.00	−0.288064
$503$	−828.000	−0.0733970	−0.0366985	−	0.999326i	$-0.511684\pi$
$503$	−828.000	−0.0733970	−0.0366985	+	0.999326i	$0.511684\pi$
$504$	−352.000	−0.0311098
$505$	−270.000	−0.0237918
$506$	2016.00	0.177119
$507$	4668.00	0.408902
$508$	−4192.00	−0.366122
$509$	4230.00	0.368353	0.184176	−	0.982893i	$-0.441038\pi$
$509$	4230.00	0.368353	0.184176	+	0.982893i	$0.441038\pi$
$510$	680.000	0.0590410
$511$	−4040.00	−0.349744
$512$	−512.000	−0.0441942
$513$	7904.00	0.680254
$514$	13692.0	1.17496
$515$	−1960.00	−0.167705
$516$	−6592.00	−0.562397
$517$	−4896.00	−0.416491
$518$	−2864.00	−0.242928
$519$	9000.00	0.761187
$520$	−2320.00	−0.195651
$521$	−606.000	−0.0509584	−0.0254792	−	0.999675i	$-0.508111\pi$
$521$	−606.000	−0.0509584	−0.0254792	+	0.999675i	$0.508111\pi$
$522$	−5412.00	−0.453787
$523$	−6820.00	−0.570206	−0.285103	−	0.958497i	$-0.592028\pi$
$523$	−6820.00	−0.570206	−0.285103	+	0.958497i	$0.592028\pi$
$524$	−4944.00	−0.412175
$525$	−400.000	−0.0332522
$526$	10944.0	0.907188
$527$	1156.00	0.0955525
$528$	−768.000	−0.0633010
$529$	−5111.00	−0.420071
$530$	7500.00	0.614678
$531$	4620.00	0.377572
$532$	832.000	0.0678041
$533$	4524.00	0.367648
$534$	3888.00	0.315075
$535$	1500.00	0.121216
$536$	−4768.00	−0.384228
$537$	−7056.00	−0.567018
$538$	−1236.00	−0.0990479
$539$	3924.00	0.313578
$540$	3040.00	0.242261
$541$	6626.00	0.526569	0.263285	−	0.964718i	$-0.415194\pi$
$541$	6626.00	0.526569	0.263285	+	0.964718i	$0.415194\pi$
$542$	−9712.00	−0.769679
$543$	7976.00	0.630355
$544$	−544.000	−0.0428746
$545$	−1810.00	−0.142260
$546$	−1856.00	−0.145475
$547$	17324.0	1.35415	0.677076	−	0.735913i	$-0.263247\pi$
$547$	17324.0	1.35415	0.677076	+	0.735913i	$0.263247\pi$
$548$	6696.00	0.521969
$549$	2090.00	0.162475
$550$	600.000	0.0465165
$551$	12792.0	0.989034
$552$	−2688.00	−0.207262
$553$	−656.000	−0.0504448
$554$	−1348.00	−0.103377
$555$	7160.00	0.547613
$556$	−4528.00	−0.345378
$557$	8598.00	0.654056	0.327028	−	0.945015i	$-0.393953\pi$
$557$	8598.00	0.654056	0.327028	+	0.945015i	$0.393953\pi$
$558$	1496.00	0.113496
$559$	23896.0	1.80804
$560$	320.000	0.0241473
$561$	−816.000	−0.0614110
$562$	−14196.0	−1.06552
$563$	3084.00	0.230862	0.115431	−	0.993316i	$-0.463175\pi$
$563$	3084.00	0.230862	0.115431	+	0.993316i	$0.463175\pi$
$564$	6528.00	0.487373
$565$	−4770.00	−0.355178
$566$	15032.0	1.11633
$567$	1244.00	0.0921395
$568$	−2592.00	−0.191475
$569$	−9030.00	−0.665303	−0.332651	−	0.943050i	$-0.607943\pi$
$569$	−9030.00	−0.665303	−0.332651	+	0.943050i	$0.607943\pi$
$570$	−2080.00	−0.152845
$571$	7820.00	0.573129	0.286565	−	0.958061i	$-0.407487\pi$
$571$	7820.00	0.573129	0.286565	+	0.958061i	$0.407487\pi$
$572$	2784.00	0.203505
$573$	−672.000	−0.0489934
$574$	−624.000	−0.0453750
$575$	2100.00	0.152306
$576$	−704.000	−0.0509259
$577$	−2254.00	−0.162626	−0.0813130	−	0.996689i	$-0.525911\pi$
$577$	−2254.00	−0.162626	−0.0813130	+	0.996689i	$0.525911\pi$
$578$	−578.000	−0.0415945
$579$	12872.0	0.923907
$580$	4920.00	0.352227
$581$	−2352.00	−0.167947
$582$	5744.00	0.409100
$583$	−9000.00	−0.639351
$584$	−8080.00	−0.572522
$585$	−3190.00	−0.225453
$586$	−9996.00	−0.704660
$587$	−17364.0	−1.22094	−0.610468	−	0.792041i	$-0.709018\pi$
$587$	−17364.0	−1.22094	−0.610468	+	0.792041i	$0.709018\pi$
$588$	−5232.00	−0.366946
$589$	−3536.00	−0.247366
$590$	−4200.00	−0.293070
$591$	−8472.00	−0.589664
$592$	−5728.00	−0.397668
$593$	−6942.00	−0.480731	−0.240366	−	0.970682i	$-0.577267\pi$
$593$	−6942.00	−0.480731	−0.240366	+	0.970682i	$0.577267\pi$
$594$	−3648.00	−0.251985
$595$	340.000	0.0234263
$596$	5880.00	0.404118
$597$	−20656.0	−1.41607
$598$	9744.00	0.666324
$599$	7080.00	0.482940	0.241470	−	0.970408i	$-0.422370\pi$
$599$	7080.00	0.482940	0.241470	+	0.970408i	$0.422370\pi$
$600$	−800.000	−0.0544331
$601$	−22102.0	−1.50010	−0.750049	−	0.661382i	$-0.769970\pi$
$601$	−22102.0	−1.50010	−0.750049	+	0.661382i	$0.769970\pi$
$602$	−3296.00	−0.223148
$603$	−6556.00	−0.442754
$604$	−7360.00	−0.495818
$605$	5935.00	0.398830
$606$	−432.000	−0.0289584
$607$	−4228.00	−0.282717	−0.141359	−	0.989958i	$-0.545147\pi$
$607$	−4228.00	−0.282717	−0.141359	+	0.989958i	$0.545147\pi$
$608$	1664.00	0.110994
$609$	3936.00	0.261896
$610$	−1900.00	−0.126113
$611$	−23664.0	−1.56685
$612$	−748.000	−0.0494054
$613$	−2602.00	−0.171442	−0.0857209	−	0.996319i	$-0.527319\pi$
$613$	−2602.00	−0.171442	−0.0857209	+	0.996319i	$0.527319\pi$
$614$	17384.0	1.14261
$615$	1560.00	0.102285
$616$	−384.000	−0.0251166
$617$	4914.00	0.320632	0.160316	−	0.987066i	$-0.448749\pi$
$617$	4914.00	0.320632	0.160316	+	0.987066i	$0.448749\pi$
$618$	−3136.00	−0.204124
$619$	12764.0	0.828802	0.414401	−	0.910094i	$-0.363991\pi$
$619$	12764.0	0.828802	0.414401	+	0.910094i	$0.363991\pi$
$620$	−1360.00	−0.0880950
$621$	−12768.0	−0.825060
$622$	−14616.0	−0.942200
$623$	1944.00	0.125016
$624$	−3712.00	−0.238139
$625$	625.000	0.0400000
$626$	13004.0	0.830263
$627$	2496.00	0.158980
$628$	1016.00	0.0645586
$629$	−6086.00	−0.385794
$630$	440.000	0.0278254
$631$	−25336.0	−1.59843	−0.799216	−	0.601044i	$-0.794752\pi$
$631$	−25336.0	−1.59843	−0.799216	+	0.601044i	$0.794752\pi$
$632$	−1312.00	−0.0825768
$633$	752.000	0.0472185
$634$	−8580.00	−0.537469
$635$	5240.00	0.327469
$636$	12000.0	0.748162
$637$	18966.0	1.17969
$638$	−5904.00	−0.366366
$639$	−3564.00	−0.220641
$640$	640.000	0.0395285
$641$	5850.00	0.360470	0.180235	−	0.983624i	$-0.442314\pi$
$641$	5850.00	0.360470	0.180235	+	0.983624i	$0.442314\pi$
$642$	2400.00	0.147540
$643$	884.000	0.0542170	0.0271085	−	0.999632i	$-0.491370\pi$
$643$	884.000	0.0542170	0.0271085	+	0.999632i	$0.491370\pi$
$644$	−1344.00	−0.0822376
$645$	8240.00	0.503023
$646$	1768.00	0.107680
$647$	−19584.0	−1.18999	−0.594997	−	0.803728i	$-0.702847\pi$
$647$	−19584.0	−1.18999	−0.594997	+	0.803728i	$0.702847\pi$
$648$	2488.00	0.150830
$649$	5040.00	0.304834
$650$	2900.00	0.174996
$651$	−1088.00	−0.0655024
$652$	−9136.00	−0.548763
$653$	−12678.0	−0.759768	−0.379884	−	0.925034i	$-0.624036\pi$
$653$	−12678.0	−0.759768	−0.379884	+	0.925034i	$0.624036\pi$
$654$	−2896.00	−0.173154
$655$	6180.00	0.368660
$656$	−1248.00	−0.0742778
$657$	−11110.0	−0.659730
$658$	3264.00	0.193380
$659$	−32028.0	−1.89322	−0.946611	−	0.322377i	$-0.895518\pi$
$659$	−32028.0	−1.89322	−0.946611	+	0.322377i	$0.895518\pi$
$660$	960.000	0.0566181
$661$	−25354.0	−1.49192	−0.745958	−	0.665993i	$-0.768008\pi$
$661$	−25354.0	−1.49192	−0.745958	+	0.665993i	$0.768008\pi$
$662$	−3448.00	−0.202433
$663$	−3944.00	−0.231029
$664$	−4704.00	−0.274926
$665$	−1040.00	−0.0606458
$666$	−7876.00	−0.458241
$667$	−20664.0	−1.19957
$668$	5136.00	0.297482
$669$	−12736.0	−0.736027
$670$	5960.00	0.343664
$671$	2280.00	0.131175
$672$	512.000	0.0293911
$673$	26402.0	1.51222	0.756109	−	0.654446i	$-0.227098\pi$
$673$	26402.0	1.51222	0.756109	+	0.654446i	$0.227098\pi$
$674$	18572.0	1.06137
$675$	−3800.00	−0.216685
$676$	4668.00	0.265589
$677$	−2838.00	−0.161113	−0.0805563	−	0.996750i	$-0.525670\pi$
$677$	−2838.00	−0.161113	−0.0805563	+	0.996750i	$0.525670\pi$
$678$	−7632.00	−0.432309
$679$	2872.00	0.162323
$680$	680.000	0.0383482
$681$	−20400.0	−1.14791
$682$	1632.00	0.0916312
$683$	−4548.00	−0.254794	−0.127397	−	0.991852i	$-0.540662\pi$
$683$	−4548.00	−0.254794	−0.127397	+	0.991852i	$0.540662\pi$
$684$	2288.00	0.127900
$685$	−8370.00	−0.466863
$686$	−5360.00	−0.298317
$687$	−1864.00	−0.103517
$688$	−6592.00	−0.365287
$689$	−43500.0	−2.40525
$690$	3360.00	0.185381
$691$	6620.00	0.364452	0.182226	−	0.983257i	$-0.441670\pi$
$691$	6620.00	0.364452	0.182226	+	0.983257i	$0.441670\pi$
$692$	9000.00	0.494406
$693$	−528.000	−0.0289424
$694$	16200.0	0.886086
$695$	5660.00	0.308915
$696$	7872.00	0.428718
$697$	−1326.00	−0.0720600
$698$	20516.0	1.11252
$699$	−7800.00	−0.422065
$700$	−400.000	−0.0215980
$701$	−22626.0	−1.21908	−0.609538	−	0.792757i	$-0.708645\pi$
$701$	−22626.0	−1.21908	−0.609538	+	0.792757i	$0.708645\pi$
$702$	−17632.0	−0.947973
$703$	18616.0	0.998742
$704$	−768.000	−0.0411152
$705$	−8160.00	−0.435920
$706$	16860.0	0.898774
$707$	−216.000	−0.0114901
$708$	−6720.00	−0.356713
$709$	−4030.00	−0.213469	−0.106735	−	0.994288i	$-0.534040\pi$
$709$	−4030.00	−0.213469	−0.106735	+	0.994288i	$0.534040\pi$
$710$	3240.00	0.171261
$711$	−1804.00	−0.0951551
$712$	3888.00	0.204647
$713$	5712.00	0.300023
$714$	544.000	0.0285136
$715$	−3480.00	−0.182020
$716$	−7056.00	−0.368289
$717$	−2016.00	−0.105005
$718$	24240.0	1.25993
$719$	27804.0	1.44216	0.721081	−	0.692851i	$-0.243646\pi$
$719$	27804.0	1.44216	0.721081	+	0.692851i	$0.243646\pi$
$720$	880.000	0.0455495
$721$	−1568.00	−0.0809922
$722$	8310.00	0.428347
$723$	2024.00	0.104113
$724$	7976.00	0.409428
$725$	−6150.00	−0.315042
$726$	9496.00	0.485440
$727$	−1984.00	−0.101214	−0.0506069	−	0.998719i	$-0.516116\pi$
$727$	−1984.00	−0.101214	−0.0506069	+	0.998719i	$0.516116\pi$
$728$	−1856.00	−0.0944889
$729$	19837.0	1.00782
$730$	10100.0	0.512079
$731$	−7004.00	−0.354381
$732$	−3040.00	−0.153499
$733$	6614.00	0.333279	0.166640	−	0.986018i	$-0.446708\pi$
$733$	6614.00	0.333279	0.166640	+	0.986018i	$0.446708\pi$
$734$	−2488.00	−0.125114
$735$	6540.00	0.328206
$736$	−2688.00	−0.134621
$737$	−7152.00	−0.357459
$738$	−1716.00	−0.0855919
$739$	11852.0	0.589963	0.294982	−	0.955503i	$-0.404686\pi$
$739$	11852.0	0.589963	0.294982	+	0.955503i	$0.404686\pi$
$740$	7160.00	0.355685
$741$	12064.0	0.598087
$742$	6000.00	0.296856
$743$	564.000	0.0278481	0.0139241	−	0.999903i	$-0.495568\pi$
$743$	564.000	0.0278481	0.0139241	+	0.999903i	$0.495568\pi$
$744$	−2176.00	−0.107226
$745$	−7350.00	−0.361454
$746$	−11740.0	−0.576182
$747$	−6468.00	−0.316803
$748$	−816.000	−0.0398876
$749$	1200.00	0.0585408
$750$	1000.00	0.0486864
$751$	−16468.0	−0.800168	−0.400084	−	0.916479i	$-0.631019\pi$
$751$	−16468.0	−0.800168	−0.400084	+	0.916479i	$0.631019\pi$
$752$	6528.00	0.316558
$753$	6480.00	0.313605
$754$	−28536.0	−1.37828
$755$	9200.00	0.443473
$756$	2432.00	0.116999
$757$	25766.0	1.23710	0.618548	−	0.785747i	$-0.287721\pi$
$757$	25766.0	1.23710	0.618548	+	0.785747i	$0.287721\pi$
$758$	−13528.0	−0.648231
$759$	−4032.00	−0.192823
$760$	−2080.00	−0.0992757
$761$	25818.0	1.22983	0.614916	−	0.788593i	$-0.289190\pi$
$761$	25818.0	1.22983	0.614916	+	0.788593i	$0.289190\pi$
$762$	8384.00	0.398583
$763$	−1448.00	−0.0687040
$764$	−672.000	−0.0318221
$765$	935.000	0.0441895
$766$	5712.00	0.269429
$767$	24360.0	1.14679
$768$	1024.00	0.0481125
$769$	29810.0	1.39789	0.698944	−	0.715176i	$-0.253654\pi$
$769$	29810.0	1.39789	0.698944	+	0.715176i	$0.253654\pi$
$770$	480.000	0.0224649
$771$	−27384.0	−1.27913
$772$	12872.0	0.600095
$773$	21798.0	1.01426	0.507128	−	0.861871i	$-0.330707\pi$
$773$	21798.0	1.01426	0.507128	+	0.861871i	$0.330707\pi$
$774$	−9064.00	−0.420929
$775$	1700.00	0.0787946
$776$	5744.00	0.265719
$777$	5728.00	0.264467
$778$	26916.0	1.24034
$779$	4056.00	0.186548
$780$	4640.00	0.212998
$781$	−3888.00	−0.178135
$782$	−2856.00	−0.130601
$783$	37392.0	1.70662
$784$	−5232.00	−0.238338
$785$	−1270.00	−0.0577430
$786$	9888.00	0.448719
$787$	−34852.0	−1.57858	−0.789288	−	0.614023i	$-0.789550\pi$
$787$	−34852.0	−1.57858	−0.789288	+	0.614023i	$0.789550\pi$
$788$	−8472.00	−0.382998
$789$	−21888.0	−0.987622
$790$	1640.00	0.0738590
$791$	−3816.00	−0.171531
$792$	−1056.00	−0.0473779
$793$	11020.0	0.493483
$794$	−26788.0	−1.19732
$795$	−15000.0	−0.669176
$796$	−20656.0	−0.919764
$797$	30390.0	1.35065	0.675326	−	0.737520i	$-0.264003\pi$
$797$	30390.0	1.35065	0.675326	+	0.737520i	$0.264003\pi$
$798$	−1664.00	−0.0738157
$799$	6936.00	0.307106
$800$	−800.000	−0.0353553
$801$	5346.00	0.235820
$802$	13068.0	0.575370
$803$	−12120.0	−0.532635
$804$	9536.00	0.418295
$805$	1680.00	0.0735556
$806$	7888.00	0.344718
$807$	2472.00	0.107830
$808$	−432.000	−0.0188090
$809$	4002.00	0.173922	0.0869610	−	0.996212i	$-0.472284\pi$
$809$	4002.00	0.173922	0.0869610	+	0.996212i	$0.472284\pi$
$810$	−3110.00	−0.134906
$811$	−41764.0	−1.80830	−0.904151	−	0.427214i	$-0.859495\pi$
$811$	−41764.0	−1.80830	−0.904151	+	0.427214i	$0.859495\pi$
$812$	3936.00	0.170107
$813$	19424.0	0.837921
$814$	−8592.00	−0.369962
$815$	11420.0	0.490828
$816$	1088.00	0.0466760
$817$	21424.0	0.917418
$818$	10700.0	0.457355
$819$	−2552.00	−0.108882
$820$	1560.00	0.0664361
$821$	−20502.0	−0.871528	−0.435764	−	0.900061i	$-0.643522\pi$
$821$	−20502.0	−0.871528	−0.435764	+	0.900061i	$0.643522\pi$
$822$	−13392.0	−0.568248
$823$	40676.0	1.72281	0.861407	−	0.507915i	$-0.169584\pi$
$823$	40676.0	1.72281	0.861407	+	0.507915i	$0.169584\pi$
$824$	−3136.00	−0.132582
$825$	−1200.00	−0.0506408
$826$	−3360.00	−0.141537
$827$	33540.0	1.41028	0.705139	−	0.709069i	$-0.250885\pi$
$827$	33540.0	1.41028	0.705139	+	0.709069i	$0.250885\pi$
$828$	−3696.00	−0.155127
$829$	11222.0	0.470152	0.235076	−	0.971977i	$-0.424466\pi$
$829$	11222.0	0.470152	0.235076	+	0.971977i	$0.424466\pi$
$830$	5880.00	0.245901
$831$	2696.00	0.112543
$832$	−3712.00	−0.154676
$833$	−5559.00	−0.231222
$834$	9056.00	0.376000
$835$	−6420.00	−0.266076
$836$	2496.00	0.103261
$837$	−10336.0	−0.426839
$838$	−6600.00	−0.272068
$839$	37620.0	1.54802	0.774009	−	0.633175i	$-0.218249\pi$
$839$	37620.0	1.54802	0.774009	+	0.633175i	$0.218249\pi$
$840$	−640.000	−0.0262882
$841$	36127.0	1.48128
$842$	19508.0	0.798444
$843$	28392.0	1.15999
$844$	752.000	0.0306693
$845$	−5835.00	−0.237550
$846$	8976.00	0.364777
$847$	4748.00	0.192613
$848$	12000.0	0.485945
$849$	−30064.0	−1.21530
$850$	−850.000	−0.0342997
$851$	−30072.0	−1.21135
$852$	5184.00	0.208452
$853$	−21310.0	−0.855382	−0.427691	−	0.903925i	$-0.640673\pi$
$853$	−21310.0	−0.855382	−0.427691	+	0.903925i	$0.640673\pi$
$854$	−1520.00	−0.0609055
$855$	−2860.00	−0.114398
$856$	2400.00	0.0958298
$857$	−21990.0	−0.876504	−0.438252	−	0.898852i	$-0.644402\pi$
$857$	−21990.0	−0.876504	−0.438252	+	0.898852i	$0.644402\pi$
$858$	−5568.00	−0.221548
$859$	−5236.00	−0.207974	−0.103987	−	0.994579i	$-0.533160\pi$
$859$	−5236.00	−0.207974	−0.103987	+	0.994579i	$0.533160\pi$
$860$	8240.00	0.326723
$861$	1248.00	0.0493981
$862$	−18600.0	−0.734940
$863$	−32640.0	−1.28746	−0.643730	−	0.765252i	$-0.722614\pi$
$863$	−32640.0	−1.28746	−0.643730	+	0.765252i	$0.722614\pi$
$864$	4864.00	0.191524
$865$	−11250.0	−0.442210
$866$	−34852.0	−1.36757
$867$	1156.00	0.0452824
$868$	−1088.00	−0.0425451
$869$	−1968.00	−0.0768237
$870$	−9840.00	−0.383457
$871$	−34568.0	−1.34477
$872$	−2896.00	−0.112467
$873$	7898.00	0.306193
$874$	8736.00	0.338100
$875$	500.000	0.0193178
$876$	16160.0	0.623283
$877$	−18646.0	−0.717937	−0.358968	−	0.933350i	$-0.616871\pi$
$877$	−18646.0	−0.717937	−0.358968	+	0.933350i	$0.616871\pi$
$878$	−31240.0	−1.20080
$879$	19992.0	0.767137
$880$	960.000	0.0367745
$881$	18978.0	0.725749	0.362875	−	0.931838i	$-0.381795\pi$
$881$	18978.0	0.725749	0.362875	+	0.931838i	$0.381795\pi$
$882$	−7194.00	−0.274642
$883$	28388.0	1.08192	0.540958	−	0.841049i	$-0.318062\pi$
$883$	28388.0	1.08192	0.540958	+	0.841049i	$0.318062\pi$
$884$	−3944.00	−0.150058
$885$	8400.00	0.319054
$886$	32904.0	1.24767
$887$	21420.0	0.810838	0.405419	−	0.914131i	$-0.367126\pi$
$887$	21420.0	0.810838	0.405419	+	0.914131i	$0.367126\pi$
$888$	11456.0	0.432926
$889$	4192.00	0.158150
$890$	−4860.00	−0.183042
$891$	3732.00	0.140322
$892$	−12736.0	−0.478064
$893$	−21216.0	−0.795035
$894$	−11760.0	−0.439948
$895$	8820.00	0.329408
$896$	512.000	0.0190901
$897$	−19488.0	−0.725402
$898$	−8052.00	−0.299219
$899$	−16728.0	−0.620590
$900$	−1100.00	−0.0407407
$901$	12750.0	0.471436
$902$	−1872.00	−0.0691029
$903$	6592.00	0.242932
$904$	−7632.00	−0.280793
$905$	−9970.00	−0.366203
$906$	14720.0	0.539778
$907$	−2908.00	−0.106459	−0.0532296	−	0.998582i	$-0.516952\pi$
$907$	−2908.00	−0.106459	−0.0532296	+	0.998582i	$0.516952\pi$
$908$	−20400.0	−0.745592
$909$	−594.000	−0.0216741
$910$	2320.00	0.0845135
$911$	36252.0	1.31842	0.659211	−	0.751958i	$-0.270890\pi$
$911$	36252.0	1.31842	0.659211	+	0.751958i	$0.270890\pi$
$912$	−3328.00	−0.120835
$913$	−7056.00	−0.255772
$914$	−3892.00	−0.140849
$915$	3800.00	0.137294
$916$	−1864.00	−0.0672361
$917$	4944.00	0.178043
$918$	5168.00	0.185805
$919$	13232.0	0.474955	0.237477	−	0.971393i	$-0.423679\pi$
$919$	13232.0	0.474955	0.237477	+	0.971393i	$0.423679\pi$
$920$	3360.00	0.120409
$921$	−34768.0	−1.24391
$922$	−16860.0	−0.602228
$923$	−18792.0	−0.670148
$924$	768.000	0.0273434
$925$	−8950.00	−0.318134
$926$	−12832.0	−0.455384
$927$	−4312.00	−0.152777
$928$	7872.00	0.278460
$929$	5946.00	0.209991	0.104996	−	0.994473i	$-0.466517\pi$
$929$	5946.00	0.209991	0.104996	+	0.994473i	$0.466517\pi$
$930$	2720.00	0.0959057
$931$	17004.0	0.598586
$932$	−7800.00	−0.274139
$933$	29232.0	1.02574
$934$	−29928.0	−1.04847
$935$	1020.00	0.0356765
$936$	−5104.00	−0.178237
$937$	−27046.0	−0.942961	−0.471480	−	0.881877i	$-0.656280\pi$
$937$	−27046.0	−0.942961	−0.471480	+	0.881877i	$0.656280\pi$
$938$	4768.00	0.165971
$939$	−26008.0	−0.903875
$940$	−8160.00	−0.283138
$941$	27378.0	0.948456	0.474228	−	0.880402i	$-0.342727\pi$
$941$	27378.0	0.948456	0.474228	+	0.880402i	$0.342727\pi$
$942$	−2032.00	−0.0702825
$943$	−6552.00	−0.226259
$944$	−6720.00	−0.231692
$945$	−3040.00	−0.104647
$946$	−9888.00	−0.339838
$947$	49164.0	1.68703	0.843514	−	0.537107i	$-0.180483\pi$
$947$	49164.0	1.68703	0.843514	+	0.537107i	$0.180483\pi$
$948$	2624.00	0.0898983
$949$	−58580.0	−2.00378
$950$	2600.00	0.0887949
$951$	17160.0	0.585122
$952$	544.000	0.0185201
$953$	9450.00	0.321213	0.160606	−	0.987019i	$-0.448655\pi$
$953$	9450.00	0.321213	0.160606	+	0.987019i	$0.448655\pi$
$954$	16500.0	0.559966
$955$	840.000	0.0284626
$956$	−2016.00	−0.0682030
$957$	11808.0	0.398849
$958$	32904.0	1.10969
$959$	−6696.00	−0.225469
$960$	−1280.00	−0.0430331
$961$	−25167.0	−0.844785
$962$	−41528.0	−1.39181
$963$	3300.00	0.110427
$964$	2024.00	0.0676231
$965$	−16090.0	−0.536741
$966$	2688.00	0.0895290
$967$	44264.0	1.47201	0.736005	−	0.676976i	$-0.236710\pi$
$967$	44264.0	1.47201	0.736005	+	0.676976i	$0.236710\pi$
$968$	9496.00	0.315303
$969$	−3536.00	−0.117227
$970$	−7180.00	−0.237666
$971$	−56868.0	−1.87949	−0.939743	−	0.341882i	$-0.888936\pi$
$971$	−56868.0	−1.87949	−0.939743	+	0.341882i	$0.888936\pi$
$972$	11440.0	0.377508
$973$	4528.00	0.149189
$974$	−25768.0	−0.847700
$975$	−5800.00	−0.190511
$976$	−3040.00	−0.0997008
$977$	52866.0	1.73115	0.865575	−	0.500780i	$-0.166953\pi$
$977$	52866.0	1.73115	0.865575	+	0.500780i	$0.166953\pi$
$978$	18272.0	0.597417
$979$	5832.00	0.190390
$980$	6540.00	0.213176
$981$	−3982.00	−0.129598
$982$	23352.0	0.758852
$983$	−47556.0	−1.54303	−0.771516	−	0.636210i	$-0.780501\pi$
$983$	−47556.0	−1.54303	−0.771516	+	0.636210i	$0.780501\pi$
$984$	2496.00	0.0808634
$985$	10590.0	0.342564
$986$	8364.00	0.270146
$987$	−6528.00	−0.210525
$988$	12064.0	0.388469
$989$	−34608.0	−1.11271
$990$	1320.00	0.0423761
$991$	42716.0	1.36924	0.684621	−	0.728899i	$-0.259968\pi$
$991$	42716.0	1.36924	0.684621	+	0.728899i	$0.259968\pi$
$992$	−2176.00	−0.0696452
$993$	6896.00	0.220381
$994$	2592.00	0.0827095
$995$	25820.0	0.822662
$996$	9408.00	0.299301
$997$	4538.00	0.144152	0.0720762	−	0.997399i	$-0.477038\pi$
$997$	4538.00	0.144152	0.0720762	+	0.997399i	$0.477038\pi$
$998$	−31096.0	−0.986299
$999$	54416.0	1.72337

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.4.a.a.1.1	✓	1
3.2	odd	2		1530.4.a.k.1.1		1
4.3	odd	2		1360.4.a.c.1.1		1
5.2	odd	4		850.4.c.a.749.1		2
5.3	odd	4		850.4.c.a.749.2		2
5.4	even	2		850.4.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.4.a.a.1.1	✓	1	1.1	even	1	trivial
850.4.a.b.1.1		1	5.4	even	2
850.4.c.a.749.1		2	5.2	odd	4
850.4.c.a.749.2		2	5.3	odd	4
1360.4.a.c.1.1		1	4.3	odd	2
1530.4.a.k.1.1		1	3.2	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:	\( N \)	\(=\)	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	170.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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