LMFDB - Embedded newform 119.4.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [119,4,Mod(1,119)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(119, 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("119.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 119 = 7 \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	119.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:	$7.02122729068$
Analytic rank:	$0$
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	$\chi$	$=$	119.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} -6.00000 q^{3} -7.00000 q^{4} -20.0000 q^{5} +6.00000 q^{6} -7.00000 q^{7} +15.0000 q^{8} +9.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} -6.00000 q^{3} -7.00000 q^{4} -20.0000 q^{5} +6.00000 q^{6} -7.00000 q^{7} +15.0000 q^{8} +9.00000 q^{9} +20.0000 q^{10} +60.0000 q^{11} +42.0000 q^{12} -68.0000 q^{13} +7.00000 q^{14} +120.000 q^{15} +41.0000 q^{16} -17.0000 q^{17} -9.00000 q^{18} -70.0000 q^{19} +140.000 q^{20} +42.0000 q^{21} -60.0000 q^{22} -176.000 q^{23} -90.0000 q^{24} +275.000 q^{25} +68.0000 q^{26} +108.000 q^{27} +49.0000 q^{28} -90.0000 q^{29} -120.000 q^{30} +196.000 q^{31} -161.000 q^{32} -360.000 q^{33} +17.0000 q^{34} +140.000 q^{35} -63.0000 q^{36} +22.0000 q^{37} +70.0000 q^{38} +408.000 q^{39} -300.000 q^{40} -138.000 q^{41} -42.0000 q^{42} +328.000 q^{43} -420.000 q^{44} -180.000 q^{45} +176.000 q^{46} -12.0000 q^{47} -246.000 q^{48} +49.0000 q^{49} -275.000 q^{50} +102.000 q^{51} +476.000 q^{52} -234.000 q^{53} -108.000 q^{54} -1200.00 q^{55} -105.000 q^{56} +420.000 q^{57} +90.0000 q^{58} -54.0000 q^{59} -840.000 q^{60} +44.0000 q^{61} -196.000 q^{62} -63.0000 q^{63} -167.000 q^{64} +1360.00 q^{65} +360.000 q^{66} -596.000 q^{67} +119.000 q^{68} +1056.00 q^{69} -140.000 q^{70} +200.000 q^{71} +135.000 q^{72} +1122.00 q^{73} -22.0000 q^{74} -1650.00 q^{75} +490.000 q^{76} -420.000 q^{77} -408.000 q^{78} +480.000 q^{79} -820.000 q^{80} -891.000 q^{81} +138.000 q^{82} -838.000 q^{83} -294.000 q^{84} +340.000 q^{85} -328.000 q^{86} +540.000 q^{87} +900.000 q^{88} +778.000 q^{89} +180.000 q^{90} +476.000 q^{91} +1232.00 q^{92} -1176.00 q^{93} +12.0000 q^{94} +1400.00 q^{95} +966.000 q^{96} +1142.00 q^{97} -49.0000 q^{98} +540.000 q^{99} +O(q^{100})\)

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 $

$2$	−1.00000	−0.353553	−0.176777	−	0.984251i	$-0.556567\pi$
$2$	−1.00000	−0.353553	−0.176777	+	0.984251i	$0.556567\pi$
$3$	−6.00000	−1.15470	−0.577350	−	0.816497i	$-0.695913\pi$
$3$	−6.00000	−1.15470	−0.577350	+	0.816497i	$0.695913\pi$
$4$	−7.00000	−0.875000
$5$	−20.0000	−1.78885	−0.894427	−	0.447214i	$-0.852416\pi$
$5$	−20.0000	−1.78885	−0.894427	+	0.447214i	$0.852416\pi$
$6$	6.00000	0.408248
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	15.0000	0.662913
$9$	9.00000	0.333333
$10$	20.0000	0.632456
$11$	60.0000	1.64461	0.822304	−	0.569049i	$-0.192689\pi$
$11$	60.0000	1.64461	0.822304	+	0.569049i	$0.192689\pi$
$12$	42.0000	1.01036
$13$	−68.0000	−1.45075	−0.725377	−	0.688352i	$-0.758335\pi$
$13$	−68.0000	−1.45075	−0.725377	+	0.688352i	$0.758335\pi$
$14$	7.00000	0.133631
$15$	120.000	2.06559
$16$	41.0000	0.640625
$17$	−17.0000	−0.242536
$17$	−17.0000	−0.242536
$18$	−9.00000	−0.117851
$19$	−70.0000	−0.845216	−0.422608	−	0.906313i	$-0.638885\pi$
$19$	−70.0000	−0.845216	−0.422608	+	0.906313i	$0.638885\pi$
$20$	140.000	1.56525
$21$	42.0000	0.436436
$22$	−60.0000	−0.581456
$23$	−176.000	−1.59559	−0.797794	−	0.602930i	$-0.794000\pi$
$23$	−176.000	−1.59559	−0.797794	+	0.602930i	$0.794000\pi$
$24$	−90.0000	−0.765466
$25$	275.000	2.20000
$26$	68.0000	0.512919
$27$	108.000	0.769800
$28$	49.0000	0.330719
$29$	−90.0000	−0.576296	−0.288148	−	0.957586i	$-0.593039\pi$
$29$	−90.0000	−0.576296	−0.288148	+	0.957586i	$0.593039\pi$
$30$	−120.000	−0.730297
$31$	196.000	1.13557	0.567785	−	0.823177i	$-0.307801\pi$
$31$	196.000	1.13557	0.567785	+	0.823177i	$0.307801\pi$
$32$	−161.000	−0.889408
$33$	−360.000	−1.89903
$34$	17.0000	0.0857493
$35$	140.000	0.676123
$36$	−63.0000	−0.291667
$37$	22.0000	0.0977507	0.0488754	−	0.998805i	$-0.484436\pi$
$37$	22.0000	0.0977507	0.0488754	+	0.998805i	$0.484436\pi$
$38$	70.0000	0.298829
$39$	408.000	1.67519
$40$	−300.000	−1.18585
$41$	−138.000	−0.525658	−0.262829	−	0.964842i	$-0.584656\pi$
$41$	−138.000	−0.525658	−0.262829	+	0.964842i	$0.584656\pi$
$42$	−42.0000	−0.154303
$43$	328.000	1.16324	0.581622	−	0.813459i	$-0.302418\pi$
$43$	328.000	1.16324	0.581622	+	0.813459i	$0.302418\pi$
$44$	−420.000	−1.43903
$45$	−180.000	−0.596285
$46$	176.000	0.564126
$47$	−12.0000	−0.0372421	−0.0186211	−	0.999827i	$-0.505928\pi$
$47$	−12.0000	−0.0372421	−0.0186211	+	0.999827i	$0.505928\pi$
$48$	−246.000	−0.739730
$49$	49.0000	0.142857
$50$	−275.000	−0.777817
$51$	102.000	0.280056
$52$	476.000	1.26941
$53$	−234.000	−0.606460	−0.303230	−	0.952917i	$-0.598065\pi$
$53$	−234.000	−0.606460	−0.303230	+	0.952917i	$0.598065\pi$
$54$	−108.000	−0.272166
$55$	−1200.00	−2.94196
$56$	−105.000	−0.250557
$57$	420.000	0.975971
$58$	90.0000	0.203751
$59$	−54.0000	−0.119156	−0.0595780	−	0.998224i	$-0.518975\pi$
$59$	−54.0000	−0.119156	−0.0595780	+	0.998224i	$0.518975\pi$
$60$	−840.000	−1.80739
$61$	44.0000	0.0923545	0.0461772	−	0.998933i	$-0.485296\pi$
$61$	44.0000	0.0923545	0.0461772	+	0.998933i	$0.485296\pi$
$62$	−196.000	−0.401484
$63$	−63.0000	−0.125988
$64$	−167.000	−0.326172
$65$	1360.00	2.59519
$66$	360.000	0.671408
$67$	−596.000	−1.08676	−0.543381	−	0.839487i	$-0.682856\pi$
$67$	−596.000	−1.08676	−0.543381	+	0.839487i	$0.682856\pi$
$68$	119.000	0.212219
$69$	1056.00	1.84243
$70$	−140.000	−0.239046
$71$	200.000	0.334305	0.167152	−	0.985931i	$-0.446543\pi$
$71$	200.000	0.334305	0.167152	+	0.985931i	$0.446543\pi$
$72$	135.000	0.220971
$73$	1122.00	1.79891	0.899453	−	0.437017i	$-0.143965\pi$
$73$	1122.00	1.79891	0.899453	+	0.437017i	$0.143965\pi$
$74$	−22.0000	−0.0345601
$75$	−1650.00	−2.54034
$76$	490.000	0.739564
$77$	−420.000	−0.621603
$78$	−408.000	−0.592268
$79$	480.000	0.683598	0.341799	−	0.939773i	$-0.388964\pi$
$79$	480.000	0.683598	0.341799	+	0.939773i	$0.388964\pi$
$80$	−820.000	−1.14598
$81$	−891.000	−1.22222
$82$	138.000	0.185848
$83$	−838.000	−1.10822	−0.554111	−	0.832443i	$-0.686942\pi$
$83$	−838.000	−1.10822	−0.554111	+	0.832443i	$0.686942\pi$
$84$	−294.000	−0.381881
$85$	340.000	0.433861
$86$	−328.000	−0.411269
$87$	540.000	0.665449
$88$	900.000	1.09023
$89$	778.000	0.926605	0.463302	−	0.886200i	$-0.346664\pi$
$89$	778.000	0.926605	0.463302	+	0.886200i	$0.346664\pi$
$90$	180.000	0.210819
$91$	476.000	0.548334
$92$	1232.00	1.39614
$93$	−1176.00	−1.31124
$94$	12.0000	0.0131671
$95$	1400.00	1.51197
$96$	966.000	1.02700
$97$	1142.00	1.19539	0.597693	−	0.801725i	$-0.296084\pi$
$97$	1142.00	1.19539	0.597693	+	0.801725i	$0.296084\pi$
$98$	−49.0000	−0.0505076
$99$	540.000	0.548202
$100$	−1925.00	−1.92500
$101$	32.0000	0.0315259	0.0157630	−	0.999876i	$-0.494982\pi$
$101$	32.0000	0.0315259	0.0157630	+	0.999876i	$0.494982\pi$
$102$	−102.000	−0.0990148
$103$	−1300.00	−1.24362	−0.621810	−	0.783168i	$-0.713602\pi$
$103$	−1300.00	−1.24362	−0.621810	+	0.783168i	$0.713602\pi$
$104$	−1020.00	−0.961723
$105$	−840.000	−0.780720
$106$	234.000	0.214416
$107$	−256.000	−0.231294	−0.115647	−	0.993290i	$-0.536894\pi$
$107$	−256.000	−0.231294	−0.115647	+	0.993290i	$0.536894\pi$
$108$	−756.000	−0.673575
$109$	318.000	0.279439	0.139720	−	0.990191i	$-0.455380\pi$
$109$	318.000	0.279439	0.139720	+	0.990191i	$0.455380\pi$
$110$	1200.00	1.04014
$111$	−132.000	−0.112873
$112$	−287.000	−0.242133
$113$	1918.00	1.59673	0.798364	−	0.602175i	$-0.205699\pi$
$113$	1918.00	1.59673	0.798364	+	0.602175i	$0.205699\pi$
$114$	−420.000	−0.345058
$115$	3520.00	2.85428
$116$	630.000	0.504259
$117$	−612.000	−0.483585
$118$	54.0000	0.0421280
$119$	119.000	0.0916698
$120$	1800.00	1.36931
$121$	2269.00	1.70473
$122$	−44.0000	−0.0326522
$123$	828.000	0.606978
$124$	−1372.00	−0.993623
$125$	−3000.00	−2.14663
$126$	63.0000	0.0445435
$127$	1832.00	1.28003	0.640015	−	0.768363i	$-0.278928\pi$
$127$	1832.00	1.28003	0.640015	+	0.768363i	$0.278928\pi$
$128$	1455.00	1.00473
$129$	−1968.00	−1.34320
$130$	−1360.00	−0.917538
$131$	262.000	0.174741	0.0873704	−	0.996176i	$-0.472154\pi$
$131$	262.000	0.174741	0.0873704	+	0.996176i	$0.472154\pi$
$132$	2520.00	1.66165
$133$	490.000	0.319462
$134$	596.000	0.384228
$135$	−2160.00	−1.37706
$136$	−255.000	−0.160780
$137$	−1902.00	−1.18612	−0.593061	−	0.805157i	$-0.702081\pi$
$137$	−1902.00	−1.18612	−0.593061	+	0.805157i	$0.702081\pi$
$138$	−1056.00	−0.651396
$139$	82.0000	0.0500370	0.0250185	−	0.999687i	$-0.492036\pi$
$139$	82.0000	0.0500370	0.0250185	+	0.999687i	$0.492036\pi$
$140$	−980.000	−0.591608
$141$	72.0000	0.0430035
$142$	−200.000	−0.118195
$143$	−4080.00	−2.38592
$144$	369.000	0.213542
$145$	1800.00	1.03091
$146$	−1122.00	−0.636009
$147$	−294.000	−0.164957
$148$	−154.000	−0.0855319
$149$	−1258.00	−0.691674	−0.345837	−	0.938295i	$-0.612405\pi$
$149$	−1258.00	−0.691674	−0.345837	+	0.938295i	$0.612405\pi$
$150$	1650.00	0.898146
$151$	−1840.00	−0.991636	−0.495818	−	0.868426i	$-0.665132\pi$
$151$	−1840.00	−0.991636	−0.495818	+	0.868426i	$0.665132\pi$
$152$	−1050.00	−0.560304
$153$	−153.000	−0.0808452
$154$	420.000	0.219770
$155$	−3920.00	−2.03137
$156$	−2856.00	−1.46579
$157$	−2156.00	−1.09597	−0.547986	−	0.836488i	$-0.684605\pi$
$157$	−2156.00	−1.09597	−0.547986	+	0.836488i	$0.684605\pi$
$158$	−480.000	−0.241688
$159$	1404.00	0.700280
$160$	3220.00	1.59102
$161$	1232.00	0.603076
$162$	891.000	0.432121
$163$	−1692.00	−0.813053	−0.406527	−	0.913639i	$-0.633260\pi$
$163$	−1692.00	−0.813053	−0.406527	+	0.913639i	$0.633260\pi$
$164$	966.000	0.459951
$165$	7200.00	3.39709
$166$	838.000	0.391816
$167$	−2644.00	−1.22514	−0.612571	−	0.790415i	$-0.709865\pi$
$167$	−2644.00	−1.22514	−0.612571	+	0.790415i	$0.709865\pi$
$168$	630.000	0.289319
$169$	2427.00	1.10469
$170$	−340.000	−0.153393
$171$	−630.000	−0.281739
$172$	−2296.00	−1.01784
$173$	−1808.00	−0.794565	−0.397282	−	0.917696i	$-0.630047\pi$
$173$	−1808.00	−0.794565	−0.397282	+	0.917696i	$0.630047\pi$
$174$	−540.000	−0.235272
$175$	−1925.00	−0.831522
$176$	2460.00	1.05358
$177$	324.000	0.137589
$178$	−778.000	−0.327604
$179$	−1716.00	−0.716536	−0.358268	−	0.933619i	$-0.616633\pi$
$179$	−1716.00	−0.716536	−0.358268	+	0.933619i	$0.616633\pi$
$180$	1260.00	0.521749
$181$	3304.00	1.35682	0.678410	−	0.734684i	$-0.262669\pi$
$181$	3304.00	1.35682	0.678410	+	0.734684i	$0.262669\pi$
$182$	−476.000	−0.193865
$183$	−264.000	−0.106642
$184$	−2640.00	−1.05774
$185$	−440.000	−0.174862
$186$	1176.00	0.463594
$187$	−1020.00	−0.398876
$188$	84.0000	0.0325869
$189$	−756.000	−0.290957
$190$	−1400.00	−0.534561
$191$	4088.00	1.54868	0.774338	−	0.632772i	$-0.218083\pi$
$191$	4088.00	1.54868	0.774338	+	0.632772i	$0.218083\pi$
$192$	1002.00	0.376631
$193$	3038.00	1.13306	0.566529	−	0.824042i	$-0.308286\pi$
$193$	3038.00	1.13306	0.566529	+	0.824042i	$0.308286\pi$
$194$	−1142.00	−0.422633
$195$	−8160.00	−2.99667
$196$	−343.000	−0.125000
$197$	−1230.00	−0.444842	−0.222421	−	0.974951i	$-0.571396\pi$
$197$	−1230.00	−0.444842	−0.222421	+	0.974951i	$0.571396\pi$
$198$	−540.000	−0.193819
$199$	1276.00	0.454539	0.227269	−	0.973832i	$-0.427020\pi$
$199$	1276.00	0.454539	0.227269	+	0.973832i	$0.427020\pi$
$200$	4125.00	1.45841
$201$	3576.00	1.25488
$202$	−32.0000	−0.0111461
$203$	630.000	0.217819
$204$	−714.000	−0.245049
$205$	2760.00	0.940326
$206$	1300.00	0.439686
$207$	−1584.00	−0.531863
$208$	−2788.00	−0.929390
$209$	−4200.00	−1.39005
$210$	840.000	0.276026
$211$	632.000	0.206202	0.103101	−	0.994671i	$-0.467123\pi$
$211$	632.000	0.206202	0.103101	+	0.994671i	$0.467123\pi$
$212$	1638.00	0.530652
$213$	−1200.00	−0.386022
$214$	256.000	0.0817748
$215$	−6560.00	−2.08088
$216$	1620.00	0.510310
$217$	−1372.00	−0.429205
$218$	−318.000	−0.0987967
$219$	−6732.00	−2.07720
$220$	8400.00	2.57422
$221$	1156.00	0.351860
$222$	132.000	0.0399066
$223$	−840.000	−0.252245	−0.126122	−	0.992015i	$-0.540253\pi$
$223$	−840.000	−0.252245	−0.126122	+	0.992015i	$0.540253\pi$
$224$	1127.00	0.336165
$225$	2475.00	0.733333
$226$	−1918.00	−0.564529
$227$	4566.00	1.33505	0.667524	−	0.744588i	$-0.267354\pi$
$227$	4566.00	1.33505	0.667524	+	0.744588i	$0.267354\pi$
$228$	−2940.00	−0.853975
$229$	1236.00	0.356669	0.178334	−	0.983970i	$-0.442929\pi$
$229$	1236.00	0.356669	0.178334	+	0.983970i	$0.442929\pi$
$230$	−3520.00	−1.00914
$231$	2520.00	0.717765
$232$	−1350.00	−0.382034
$233$	1386.00	0.389699	0.194850	−	0.980833i	$-0.437578\pi$
$233$	1386.00	0.389699	0.194850	+	0.980833i	$0.437578\pi$
$234$	612.000	0.170973
$235$	240.000	0.0666207
$236$	378.000	0.104261
$237$	−2880.00	−0.789351
$238$	−119.000	−0.0324102
$239$	6392.00	1.72998	0.864988	−	0.501793i	$-0.167326\pi$
$239$	6392.00	1.72998	0.864988	+	0.501793i	$0.167326\pi$
$240$	4920.00	1.32327
$241$	990.000	0.264612	0.132306	−	0.991209i	$-0.457762\pi$
$241$	990.000	0.264612	0.132306	+	0.991209i	$0.457762\pi$
$242$	−2269.00	−0.602714
$243$	2430.00	0.641500
$244$	−308.000	−0.0808102
$245$	−980.000	−0.255551
$246$	−828.000	−0.214599
$247$	4760.00	1.22620
$248$	2940.00	0.752783
$249$	5028.00	1.27966
$250$	3000.00	0.758947
$251$	4398.00	1.10597	0.552987	−	0.833190i	$-0.313488\pi$
$251$	4398.00	1.10597	0.552987	+	0.833190i	$0.313488\pi$
$252$	441.000	0.110240
$253$	−10560.0	−2.62412
$254$	−1832.00	−0.452559
$255$	−2040.00	−0.500979
$256$	−119.000	−0.0290527
$257$	3018.00	0.732520	0.366260	−	0.930513i	$-0.380638\pi$
$257$	3018.00	0.732520	0.366260	+	0.930513i	$0.380638\pi$
$258$	1968.00	0.474893
$259$	−154.000	−0.0369463
$260$	−9520.00	−2.27079
$261$	−810.000	−0.192099
$262$	−262.000	−0.0617802
$263$	−7384.00	−1.73124	−0.865622	−	0.500699i	$-0.833076\pi$
$263$	−7384.00	−1.73124	−0.865622	+	0.500699i	$0.833076\pi$
$264$	−5400.00	−1.25889
$265$	4680.00	1.08487
$266$	−490.000	−0.112947
$267$	−4668.00	−1.06995
$268$	4172.00	0.950916
$269$	1408.00	0.319135	0.159567	−	0.987187i	$-0.448990\pi$
$269$	1408.00	0.319135	0.159567	+	0.987187i	$0.448990\pi$
$270$	2160.00	0.486864
$271$	1952.00	0.437548	0.218774	−	0.975776i	$-0.429794\pi$
$271$	1952.00	0.437548	0.218774	+	0.975776i	$0.429794\pi$
$272$	−697.000	−0.155374
$273$	−2856.00	−0.633161
$274$	1902.00	0.419358
$275$	16500.0	3.61814
$276$	−7392.00	−1.61212
$277$	4274.00	0.927075	0.463537	−	0.886077i	$-0.346580\pi$
$277$	4274.00	0.927075	0.463537	+	0.886077i	$0.346580\pi$
$278$	−82.0000	−0.0176908
$279$	1764.00	0.378523
$280$	2100.00	0.448211
$281$	−150.000	−0.0318443	−0.0159222	−	0.999873i	$-0.505068\pi$
$281$	−150.000	−0.0318443	−0.0159222	+	0.999873i	$0.505068\pi$
$282$	−72.0000	−0.0152040
$283$	−586.000	−0.123089	−0.0615443	−	0.998104i	$-0.519603\pi$
$283$	−586.000	−0.123089	−0.0615443	+	0.998104i	$0.519603\pi$
$284$	−1400.00	−0.292517
$285$	−8400.00	−1.74587
$286$	4080.00	0.843551
$287$	966.000	0.198680
$288$	−1449.00	−0.296469
$289$	289.000	0.0588235
$290$	−1800.00	−0.364482
$291$	−6852.00	−1.38031
$292$	−7854.00	−1.57404
$293$	1248.00	0.248836	0.124418	−	0.992230i	$-0.460294\pi$
$293$	1248.00	0.248836	0.124418	+	0.992230i	$0.460294\pi$
$294$	294.000	0.0583212
$295$	1080.00	0.213153
$296$	330.000	0.0648002
$297$	6480.00	1.26602
$298$	1258.00	0.244544
$299$	11968.0	2.31481
$300$	11550.0	2.22280
$301$	−2296.00	−0.439665
$302$	1840.00	0.350596
$303$	−192.000	−0.0364030
$304$	−2870.00	−0.541466
$305$	−880.000	−0.165209
$306$	153.000	0.0285831
$307$	−6390.00	−1.18794	−0.593968	−	0.804488i	$-0.702440\pi$
$307$	−6390.00	−1.18794	−0.593968	+	0.804488i	$0.702440\pi$
$308$	2940.00	0.543903
$309$	7800.00	1.43601
$310$	3920.00	0.718197
$311$	−3800.00	−0.692856	−0.346428	−	0.938077i	$-0.612606\pi$
$311$	−3800.00	−0.692856	−0.346428	+	0.938077i	$0.612606\pi$
$312$	6120.00	1.11050
$313$	−3274.00	−0.591238	−0.295619	−	0.955306i	$-0.595526\pi$
$313$	−3274.00	−0.591238	−0.295619	+	0.955306i	$0.595526\pi$
$314$	2156.00	0.387484
$315$	1260.00	0.225374
$316$	−3360.00	−0.598148
$317$	−6838.00	−1.21155	−0.605773	−	0.795637i	$-0.707136\pi$
$317$	−6838.00	−1.21155	−0.605773	+	0.795637i	$0.707136\pi$
$318$	−1404.00	−0.247586
$319$	−5400.00	−0.947780
$320$	3340.00	0.583474
$321$	1536.00	0.267075
$322$	−1232.00	−0.213219
$323$	1190.00	0.204995
$324$	6237.00	1.06944
$325$	−18700.0	−3.19166
$326$	1692.00	0.287458
$327$	−1908.00	−0.322669
$328$	−2070.00	−0.348465
$329$	84.0000	0.0140762
$330$	−7200.00	−1.20105
$331$	−6104.00	−1.01361	−0.506807	−	0.862060i	$-0.669174\pi$
$331$	−6104.00	−1.01361	−0.506807	+	0.862060i	$0.669174\pi$
$332$	5866.00	0.969695
$333$	198.000	0.0325836
$334$	2644.00	0.433153
$335$	11920.0	1.94406
$336$	1722.00	0.279592
$337$	4678.00	0.756163	0.378081	−	0.925772i	$-0.376584\pi$
$337$	4678.00	0.756163	0.378081	+	0.925772i	$0.376584\pi$
$338$	−2427.00	−0.390566
$339$	−11508.0	−1.84374
$340$	−2380.00	−0.379628
$341$	11760.0	1.86757
$342$	630.000	0.0996096
$343$	−343.000	−0.0539949
$344$	4920.00	0.771130
$345$	−21120.0	−3.29583
$346$	1808.00	0.280921
$347$	−7396.00	−1.14420	−0.572101	−	0.820183i	$-0.693871\pi$
$347$	−7396.00	−1.14420	−0.572101	+	0.820183i	$0.693871\pi$
$348$	−3780.00	−0.582268
$349$	4020.00	0.616578	0.308289	−	0.951293i	$-0.400244\pi$
$349$	4020.00	0.616578	0.308289	+	0.951293i	$0.400244\pi$
$350$	1925.00	0.293987
$351$	−7344.00	−1.11679
$352$	−9660.00	−1.46273
$353$	−5622.00	−0.847674	−0.423837	−	0.905739i	$-0.639317\pi$
$353$	−5622.00	−0.847674	−0.423837	+	0.905739i	$0.639317\pi$
$354$	−324.000	−0.0486452
$355$	−4000.00	−0.598022
$356$	−5446.00	−0.810779
$357$	−714.000	−0.105851
$358$	1716.00	0.253334
$359$	7368.00	1.08320	0.541599	−	0.840637i	$-0.317819\pi$
$359$	7368.00	1.08320	0.541599	+	0.840637i	$0.317819\pi$
$360$	−2700.00	−0.395285
$361$	−1959.00	−0.285610
$362$	−3304.00	−0.479708
$363$	−13614.0	−1.96846
$364$	−3332.00	−0.479792
$365$	−22440.0	−3.21798
$366$	264.000	0.0377036
$367$	11080.0	1.57594	0.787972	−	0.615711i	$-0.211131\pi$
$367$	11080.0	1.57594	0.787972	+	0.615711i	$0.211131\pi$
$368$	−7216.00	−1.02217
$369$	−1242.00	−0.175219
$370$	440.000	0.0618230
$371$	1638.00	0.229220
$372$	8232.00	1.14734
$373$	2142.00	0.297342	0.148671	−	0.988887i	$-0.452500\pi$
$373$	2142.00	0.297342	0.148671	+	0.988887i	$0.452500\pi$
$374$	1020.00	0.141024
$375$	18000.0	2.47871
$376$	−180.000	−0.0246883
$377$	6120.00	0.836064
$378$	756.000	0.102869
$379$	7612.00	1.03167	0.515834	−	0.856689i	$-0.327482\pi$
$379$	7612.00	1.03167	0.515834	+	0.856689i	$0.327482\pi$
$380$	−9800.00	−1.32297
$381$	−10992.0	−1.47805
$382$	−4088.00	−0.547540
$383$	7572.00	1.01021	0.505106	−	0.863057i	$-0.331453\pi$
$383$	7572.00	1.01021	0.505106	+	0.863057i	$0.331453\pi$
$384$	−8730.00	−1.16016
$385$	8400.00	1.11196
$386$	−3038.00	−0.400596
$387$	2952.00	0.387748
$388$	−7994.00	−1.04596
$389$	6858.00	0.893867	0.446934	−	0.894567i	$-0.352516\pi$
$389$	6858.00	0.893867	0.446934	+	0.894567i	$0.352516\pi$
$390$	8160.00	1.05948
$391$	2992.00	0.386987
$392$	735.000	0.0947018
$393$	−1572.00	−0.201773
$394$	1230.00	0.157275
$395$	−9600.00	−1.22286
$396$	−3780.00	−0.479677
$397$	10008.0	1.26521	0.632603	−	0.774476i	$-0.281986\pi$
$397$	10008.0	1.26521	0.632603	+	0.774476i	$0.281986\pi$
$398$	−1276.00	−0.160704
$399$	−2940.00	−0.368882
$400$	11275.0	1.40938
$401$	−8402.00	−1.04632	−0.523162	−	0.852233i	$-0.675248\pi$
$401$	−8402.00	−1.04632	−0.523162	+	0.852233i	$0.675248\pi$
$402$	−3576.00	−0.443668
$403$	−13328.0	−1.64743
$404$	−224.000	−0.0275852
$405$	17820.0	2.18638
$406$	−630.000	−0.0770108
$407$	1320.00	0.160762
$408$	1530.00	0.185653
$409$	13382.0	1.61784	0.808921	−	0.587917i	$-0.200052\pi$
$409$	13382.0	1.61784	0.808921	+	0.587917i	$0.200052\pi$
$410$	−2760.00	−0.332455
$411$	11412.0	1.36962
$412$	9100.00	1.08817
$413$	378.000	0.0450367
$414$	1584.00	0.188042
$415$	16760.0	1.98245
$416$	10948.0	1.29031
$417$	−492.000	−0.0577778
$418$	4200.00	0.491456
$419$	−14662.0	−1.70951	−0.854756	−	0.519030i	$-0.826293\pi$
$419$	−14662.0	−1.70951	−0.854756	+	0.519030i	$0.826293\pi$
$420$	5880.00	0.683130
$421$	−7370.00	−0.853187	−0.426594	−	0.904443i	$-0.640287\pi$
$421$	−7370.00	−0.853187	−0.426594	+	0.904443i	$0.640287\pi$
$422$	−632.000	−0.0729035
$423$	−108.000	−0.0124140
$424$	−3510.00	−0.402030
$425$	−4675.00	−0.533578
$426$	1200.00	0.136479
$427$	−308.000	−0.0349067
$428$	1792.00	0.202382
$429$	24480.0	2.75502
$430$	6560.00	0.735701
$431$	3480.00	0.388923	0.194461	−	0.980910i	$-0.437704\pi$
$431$	3480.00	0.388923	0.194461	+	0.980910i	$0.437704\pi$
$432$	4428.00	0.493153
$433$	13070.0	1.45059	0.725293	−	0.688440i	$-0.241704\pi$
$433$	13070.0	1.45059	0.725293	+	0.688440i	$0.241704\pi$
$434$	1372.00	0.151747
$435$	−10800.0	−1.19039
$436$	−2226.00	−0.244509
$437$	12320.0	1.34862
$438$	6732.00	0.734400
$439$	9352.00	1.01673	0.508367	−	0.861140i	$-0.330249\pi$
$439$	9352.00	1.01673	0.508367	+	0.861140i	$0.330249\pi$
$440$	−18000.0	−1.95026
$441$	441.000	0.0476190
$442$	−1156.00	−0.124401
$443$	1828.00	0.196052	0.0980258	−	0.995184i	$-0.468747\pi$
$443$	1828.00	0.196052	0.0980258	+	0.995184i	$0.468747\pi$
$444$	924.000	0.0987637
$445$	−15560.0	−1.65756
$446$	840.000	0.0891820
$447$	7548.00	0.798676
$448$	1169.00	0.123281
$449$	−7334.00	−0.770853	−0.385426	−	0.922739i	$-0.625946\pi$
$449$	−7334.00	−0.770853	−0.385426	+	0.922739i	$0.625946\pi$
$450$	−2475.00	−0.259272
$451$	−8280.00	−0.864501
$452$	−13426.0	−1.39714
$453$	11040.0	1.14504
$454$	−4566.00	−0.472011
$455$	−9520.00	−0.980889
$456$	6300.00	0.646984
$457$	−5370.00	−0.549667	−0.274834	−	0.961492i	$-0.588623\pi$
$457$	−5370.00	−0.549667	−0.274834	+	0.961492i	$0.588623\pi$
$458$	−1236.00	−0.126102
$459$	−1836.00	−0.186704
$460$	−24640.0	−2.49749
$461$	14284.0	1.44311	0.721553	−	0.692359i	$-0.243428\pi$
$461$	14284.0	1.44311	0.721553	+	0.692359i	$0.243428\pi$
$462$	−2520.00	−0.253768
$463$	−11272.0	−1.13143	−0.565717	−	0.824599i	$-0.691401\pi$
$463$	−11272.0	−1.13143	−0.565717	+	0.824599i	$0.691401\pi$
$464$	−3690.00	−0.369190
$465$	23520.0	2.34562
$466$	−1386.00	−0.137779
$467$	16722.0	1.65696	0.828482	−	0.560016i	$-0.189205\pi$
$467$	16722.0	1.65696	0.828482	+	0.560016i	$0.189205\pi$
$468$	4284.00	0.423137
$469$	4172.00	0.410757
$470$	−240.000	−0.0235540
$471$	12936.0	1.26552
$472$	−810.000	−0.0789900
$473$	19680.0	1.91308
$474$	2880.00	0.279078
$475$	−19250.0	−1.85947
$476$	−833.000	−0.0802111
$477$	−2106.00	−0.202153
$478$	−6392.00	−0.611639
$479$	−6972.00	−0.665050	−0.332525	−	0.943094i	$-0.607901\pi$
$479$	−6972.00	−0.665050	−0.332525	+	0.943094i	$0.607901\pi$
$480$	−19320.0	−1.83715
$481$	−1496.00	−0.141812
$482$	−990.000	−0.0935545
$483$	−7392.00	−0.696372
$484$	−15883.0	−1.49164
$485$	−22840.0	−2.13837
$486$	−2430.00	−0.226805
$487$	17936.0	1.66891	0.834454	−	0.551078i	$-0.185783\pi$
$487$	17936.0	1.66891	0.834454	+	0.551078i	$0.185783\pi$
$488$	660.000	0.0612229
$489$	10152.0	0.938833
$490$	980.000	0.0903508
$491$	8780.00	0.806998	0.403499	−	0.914980i	$-0.367794\pi$
$491$	8780.00	0.806998	0.403499	+	0.914980i	$0.367794\pi$
$492$	−5796.00	−0.531105
$493$	1530.00	0.139772
$494$	−4760.00	−0.433527
$495$	−10800.0	−0.980654
$496$	8036.00	0.727474
$497$	−1400.00	−0.126355
$498$	−5028.00	−0.452430
$499$	−5080.00	−0.455736	−0.227868	−	0.973692i	$-0.573175\pi$
$499$	−5080.00	−0.455736	−0.227868	+	0.973692i	$0.573175\pi$
$500$	21000.0	1.87830
$501$	15864.0	1.41467
$502$	−4398.00	−0.391021
$503$	−1392.00	−0.123392	−0.0616960	−	0.998095i	$-0.519651\pi$
$503$	−1392.00	−0.123392	−0.0616960	+	0.998095i	$0.519651\pi$
$504$	−945.000	−0.0835191
$505$	−640.000	−0.0563953
$506$	10560.0	0.927765
$507$	−14562.0	−1.27558
$508$	−12824.0	−1.12003
$509$	−11204.0	−0.975655	−0.487828	−	0.872940i	$-0.662211\pi$
$509$	−11204.0	−0.975655	−0.487828	+	0.872940i	$0.662211\pi$
$510$	2040.00	0.177123
$511$	−7854.00	−0.679923
$512$	−11521.0	−0.994455
$513$	−7560.00	−0.650647
$514$	−3018.00	−0.258985
$515$	26000.0	2.22465
$516$	13776.0	1.17530
$517$	−720.000	−0.0612487
$518$	154.000	0.0130625
$519$	10848.0	0.917484
$520$	20400.0	1.72038
$521$	−2962.00	−0.249074	−0.124537	−	0.992215i	$-0.539745\pi$
$521$	−2962.00	−0.249074	−0.124537	+	0.992215i	$0.539745\pi$
$522$	810.000	0.0679171
$523$	−4014.00	−0.335602	−0.167801	−	0.985821i	$-0.553667\pi$
$523$	−4014.00	−0.335602	−0.167801	+	0.985821i	$0.553667\pi$
$524$	−1834.00	−0.152898
$525$	11550.0	0.960159
$526$	7384.00	0.612087
$527$	−3332.00	−0.275416
$528$	−14760.0	−1.21657
$529$	18809.0	1.54590
$530$	−4680.00	−0.383559
$531$	−486.000	−0.0397187
$532$	−3430.00	−0.279529
$533$	9384.00	0.762601
$534$	4668.00	0.378285
$535$	5120.00	0.413751
$536$	−8940.00	−0.720428
$537$	10296.0	0.827384
$538$	−1408.00	−0.112831
$539$	2940.00	0.234944
$540$	15120.0	1.20493
$541$	19866.0	1.57875	0.789377	−	0.613909i	$-0.210404\pi$
$541$	19866.0	1.57875	0.789377	+	0.613909i	$0.210404\pi$
$542$	−1952.00	−0.154697
$543$	−19824.0	−1.56672
$544$	2737.00	0.215713
$545$	−6360.00	−0.499876
$546$	2856.00	0.223856
$547$	−14084.0	−1.10089	−0.550446	−	0.834871i	$-0.685542\pi$
$547$	−14084.0	−1.10089	−0.550446	+	0.834871i	$0.685542\pi$
$548$	13314.0	1.03786
$549$	396.000	0.0307848
$550$	−16500.0	−1.27920
$551$	6300.00	0.487094
$552$	15840.0	1.22137
$553$	−3360.00	−0.258376
$554$	−4274.00	−0.327771
$555$	2640.00	0.201913
$556$	−574.000	−0.0437824
$557$	5382.00	0.409412	0.204706	−	0.978823i	$-0.434376\pi$
$557$	5382.00	0.409412	0.204706	+	0.978823i	$0.434376\pi$
$558$	−1764.00	−0.133828
$559$	−22304.0	−1.68758
$560$	5740.00	0.433142
$561$	6120.00	0.460582
$562$	150.000	0.0112587
$563$	3662.00	0.274129	0.137065	−	0.990562i	$-0.456233\pi$
$563$	3662.00	0.274129	0.137065	+	0.990562i	$0.456233\pi$
$564$	−504.000	−0.0376281
$565$	−38360.0	−2.85631
$566$	586.000	0.0435184
$567$	6237.00	0.461957
$568$	3000.00	0.221615
$569$	−22154.0	−1.63224	−0.816120	−	0.577883i	$-0.803879\pi$
$569$	−22154.0	−1.63224	−0.816120	+	0.577883i	$0.803879\pi$
$570$	8400.00	0.617258
$571$	−6764.00	−0.495735	−0.247867	−	0.968794i	$-0.579730\pi$
$571$	−6764.00	−0.495735	−0.247867	+	0.968794i	$0.579730\pi$
$572$	28560.0	2.08768
$573$	−24528.0	−1.78826
$574$	−966.000	−0.0702440
$575$	−48400.0	−3.51029
$576$	−1503.00	−0.108724
$577$	7738.00	0.558297	0.279148	−	0.960248i	$-0.409948\pi$
$577$	7738.00	0.558297	0.279148	+	0.960248i	$0.409948\pi$
$578$	−289.000	−0.0207973
$579$	−18228.0	−1.30834
$580$	−12600.0	−0.902046
$581$	5866.00	0.418869
$582$	6852.00	0.488015
$583$	−14040.0	−0.997388
$584$	16830.0	1.19252
$585$	12240.0	0.865063
$586$	−1248.00	−0.0879768
$587$	18334.0	1.28914	0.644570	−	0.764545i	$-0.277036\pi$
$587$	18334.0	1.28914	0.644570	+	0.764545i	$0.277036\pi$
$588$	2058.00	0.144338
$589$	−13720.0	−0.959801
$590$	−1080.00	−0.0753608
$591$	7380.00	0.513659
$592$	902.000	0.0626216
$593$	−7206.00	−0.499013	−0.249507	−	0.968373i	$-0.580268\pi$
$593$	−7206.00	−0.499013	−0.249507	+	0.968373i	$0.580268\pi$
$594$	−6480.00	−0.447605
$595$	−2380.00	−0.163984
$596$	8806.00	0.605214
$597$	−7656.00	−0.524856
$598$	−11968.0	−0.818408
$599$	4176.00	0.284853	0.142426	−	0.989805i	$-0.454510\pi$
$599$	4176.00	0.284853	0.142426	+	0.989805i	$0.454510\pi$
$600$	−24750.0	−1.68402
$601$	−18158.0	−1.23241	−0.616207	−	0.787585i	$-0.711331\pi$
$601$	−18158.0	−1.23241	−0.616207	+	0.787585i	$0.711331\pi$
$602$	2296.00	0.155445
$603$	−5364.00	−0.362254
$604$	12880.0	0.867682
$605$	−45380.0	−3.04952
$606$	192.000	0.0128704
$607$	−2896.00	−0.193649	−0.0968246	−	0.995301i	$-0.530869\pi$
$607$	−2896.00	−0.193649	−0.0968246	+	0.995301i	$0.530869\pi$
$608$	11270.0	0.751742
$609$	−3780.00	−0.251516
$610$	880.000	0.0584101
$611$	816.000	0.0540292
$612$	1071.00	0.0707396
$613$	4762.00	0.313761	0.156880	−	0.987618i	$-0.449856\pi$
$613$	4762.00	0.313761	0.156880	+	0.987618i	$0.449856\pi$
$614$	6390.00	0.419999
$615$	−16560.0	−1.08579
$616$	−6300.00	−0.412069
$617$	10158.0	0.662797	0.331398	−	0.943491i	$-0.392480\pi$
$617$	10158.0	0.662797	0.331398	+	0.943491i	$0.392480\pi$
$618$	−7800.00	−0.507706
$619$	−10050.0	−0.652574	−0.326287	−	0.945271i	$-0.605798\pi$
$619$	−10050.0	−0.652574	−0.326287	+	0.945271i	$0.605798\pi$
$620$	27440.0	1.77745
$621$	−19008.0	−1.22828
$622$	3800.00	0.244962
$623$	−5446.00	−0.350224
$624$	16728.0	1.07317
$625$	25625.0	1.64000
$626$	3274.00	0.209034
$627$	25200.0	1.60509
$628$	15092.0	0.958975
$629$	−374.000	−0.0237080
$630$	−1260.00	−0.0796819
$631$	6352.00	0.400743	0.200372	−	0.979720i	$-0.435785\pi$
$631$	6352.00	0.400743	0.200372	+	0.979720i	$0.435785\pi$
$632$	7200.00	0.453166
$633$	−3792.00	−0.238102
$634$	6838.00	0.428346
$635$	−36640.0	−2.28979
$636$	−9828.00	−0.612745
$637$	−3332.00	−0.207251
$638$	5400.00	0.335091
$639$	1800.00	0.111435
$640$	−29100.0	−1.79731
$641$	8334.00	0.513531	0.256765	−	0.966474i	$-0.417343\pi$
$641$	8334.00	0.513531	0.256765	+	0.966474i	$0.417343\pi$
$642$	−1536.00	−0.0944254
$643$	4634.00	0.284210	0.142105	−	0.989852i	$-0.454613\pi$
$643$	4634.00	0.284210	0.142105	+	0.989852i	$0.454613\pi$
$644$	−8624.00	−0.527691
$645$	39360.0	2.40279
$646$	−1190.00	−0.0724767
$647$	6164.00	0.374547	0.187273	−	0.982308i	$-0.440035\pi$
$647$	6164.00	0.374547	0.187273	+	0.982308i	$0.440035\pi$
$648$	−13365.0	−0.810227
$649$	−3240.00	−0.195965
$650$	18700.0	1.12842
$651$	8232.00	0.495603
$652$	11844.0	0.711422
$653$	31566.0	1.89169	0.945845	−	0.324620i	$-0.105236\pi$
$653$	31566.0	1.89169	0.945845	+	0.324620i	$0.105236\pi$
$654$	1908.00	0.114081
$655$	−5240.00	−0.312586
$656$	−5658.00	−0.336750
$657$	10098.0	0.599635
$658$	−84.0000	−0.00497669
$659$	18352.0	1.08481	0.542407	−	0.840116i	$-0.317513\pi$
$659$	18352.0	1.08481	0.542407	+	0.840116i	$0.317513\pi$
$660$	−50400.0	−2.97245
$661$	296.000	0.0174176	0.00870882	−	0.999962i	$-0.497228\pi$
$661$	296.000	0.0174176	0.00870882	+	0.999962i	$0.497228\pi$
$662$	6104.00	0.358367
$663$	−6936.00	−0.406292
$664$	−12570.0	−0.734655
$665$	−9800.00	−0.571470
$666$	−198.000	−0.0115200
$667$	15840.0	0.919531
$668$	18508.0	1.07200
$669$	5040.00	0.291267
$670$	−11920.0	−0.687328
$671$	2640.00	0.151887
$672$	−6762.00	−0.388169
$673$	15794.0	0.904627	0.452313	−	0.891859i	$-0.350599\pi$
$673$	15794.0	0.904627	0.452313	+	0.891859i	$0.350599\pi$
$674$	−4678.00	−0.267344
$675$	29700.0	1.69356
$676$	−16989.0	−0.966602
$677$	−16392.0	−0.930570	−0.465285	−	0.885161i	$-0.654048\pi$
$677$	−16392.0	−0.930570	−0.465285	+	0.885161i	$0.654048\pi$
$678$	11508.0	0.651861
$679$	−7994.00	−0.451814
$680$	5100.00	0.287612
$681$	−27396.0	−1.54158
$682$	−11760.0	−0.660284
$683$	10880.0	0.609534	0.304767	−	0.952427i	$-0.401421\pi$
$683$	10880.0	0.609534	0.304767	+	0.952427i	$0.401421\pi$
$684$	4410.00	0.246521
$685$	38040.0	2.12180
$686$	343.000	0.0190901
$687$	−7416.00	−0.411846
$688$	13448.0	0.745204
$689$	15912.0	0.879824
$690$	21120.0	1.16525
$691$	−10130.0	−0.557689	−0.278845	−	0.960336i	$-0.589951\pi$
$691$	−10130.0	−0.557689	−0.278845	+	0.960336i	$0.589951\pi$
$692$	12656.0	0.695244
$693$	−3780.00	−0.207201
$694$	7396.00	0.404536
$695$	−1640.00	−0.0895090
$696$	8100.00	0.441135
$697$	2346.00	0.127491
$698$	−4020.00	−0.217993
$699$	−8316.00	−0.449986
$700$	13475.0	0.727582
$701$	−12558.0	−0.676618	−0.338309	−	0.941035i	$-0.609855\pi$
$701$	−12558.0	−0.676618	−0.338309	+	0.941035i	$0.609855\pi$
$702$	7344.00	0.394845
$703$	−1540.00	−0.0826205
$704$	−10020.0	−0.536425
$705$	−1440.00	−0.0769270
$706$	5622.00	0.299698
$707$	−224.000	−0.0119157
$708$	−2268.00	−0.120391
$709$	−19282.0	−1.02137	−0.510685	−	0.859768i	$-0.670608\pi$
$709$	−19282.0	−1.02137	−0.510685	+	0.859768i	$0.670608\pi$
$710$	4000.00	0.211433
$711$	4320.00	0.227866
$712$	11670.0	0.614258
$713$	−34496.0	−1.81190
$714$	714.000	0.0374241
$715$	81600.0	4.26807
$716$	12012.0	0.626969
$717$	−38352.0	−1.99760
$718$	−7368.00	−0.382968
$719$	19012.0	0.986131	0.493065	−	0.869992i	$-0.335876\pi$
$719$	19012.0	0.986131	0.493065	+	0.869992i	$0.335876\pi$
$720$	−7380.00	−0.381995
$721$	9100.00	0.470044
$722$	1959.00	0.100978
$723$	−5940.00	−0.305548
$724$	−23128.0	−1.18722
$725$	−24750.0	−1.26785
$726$	13614.0	0.695954
$727$	−32228.0	−1.64411	−0.822057	−	0.569406i	$-0.807173\pi$
$727$	−32228.0	−1.64411	−0.822057	+	0.569406i	$0.807173\pi$
$728$	7140.00	0.363497
$729$	9477.00	0.481481
$730$	22440.0	1.13773
$731$	−5576.00	−0.282128
$732$	1848.00	0.0933115
$733$	31096.0	1.56693	0.783463	−	0.621438i	$-0.213451\pi$
$733$	31096.0	1.56693	0.783463	+	0.621438i	$0.213451\pi$
$734$	−11080.0	−0.557180
$735$	5880.00	0.295084
$736$	28336.0	1.41913
$737$	−35760.0	−1.78730
$738$	1242.00	0.0619494
$739$	−7928.00	−0.394636	−0.197318	−	0.980340i	$-0.563223\pi$
$739$	−7928.00	−0.394636	−0.197318	+	0.980340i	$0.563223\pi$
$740$	3080.00	0.153004
$741$	−28560.0	−1.41589
$742$	−1638.00	−0.0810416
$743$	−26640.0	−1.31538	−0.657690	−	0.753289i	$-0.728466\pi$
$743$	−26640.0	−1.31538	−0.657690	+	0.753289i	$0.728466\pi$
$744$	−17640.0	−0.869239
$745$	25160.0	1.23730
$746$	−2142.00	−0.105126
$747$	−7542.00	−0.369407
$748$	7140.00	0.349016
$749$	1792.00	0.0874209
$750$	−18000.0	−0.876356
$751$	10904.0	0.529817	0.264909	−	0.964274i	$-0.414658\pi$
$751$	10904.0	0.529817	0.264909	+	0.964274i	$0.414658\pi$
$752$	−492.000	−0.0238582
$753$	−26388.0	−1.27707
$754$	−6120.00	−0.295593
$755$	36800.0	1.77389
$756$	5292.00	0.254588
$757$	−28406.0	−1.36385	−0.681924	−	0.731423i	$-0.738857\pi$
$757$	−28406.0	−1.36385	−0.681924	+	0.731423i	$0.738857\pi$
$758$	−7612.00	−0.364750
$759$	63360.0	3.03007
$760$	21000.0	1.00230
$761$	9590.00	0.456816	0.228408	−	0.973565i	$-0.426648\pi$
$761$	9590.00	0.456816	0.228408	+	0.973565i	$0.426648\pi$
$762$	10992.0	0.522570
$763$	−2226.00	−0.105618
$764$	−28616.0	−1.35509
$765$	3060.00	0.144620
$766$	−7572.00	−0.357164
$767$	3672.00	0.172866
$768$	714.000	0.0335472
$769$	−33338.0	−1.56333	−0.781664	−	0.623700i	$-0.785629\pi$
$769$	−33338.0	−1.56333	−0.781664	+	0.623700i	$0.785629\pi$
$770$	−8400.00	−0.393136
$771$	−18108.0	−0.845841
$772$	−21266.0	−0.991425
$773$	−34496.0	−1.60509	−0.802545	−	0.596591i	$-0.796521\pi$
$773$	−34496.0	−1.60509	−0.802545	+	0.596591i	$0.796521\pi$
$774$	−2952.00	−0.137090
$775$	53900.0	2.49825
$776$	17130.0	0.792437
$777$	924.000	0.0426619
$778$	−6858.00	−0.316030
$779$	9660.00	0.444295
$780$	57120.0	2.62208
$781$	12000.0	0.549800
$782$	−2992.00	−0.136821
$783$	−9720.00	−0.443633
$784$	2009.00	0.0915179
$785$	43120.0	1.96053
$786$	1572.00	0.0713376
$787$	13582.0	0.615179	0.307590	−	0.951519i	$-0.400478\pi$
$787$	13582.0	0.615179	0.307590	+	0.951519i	$0.400478\pi$
$788$	8610.00	0.389237
$789$	44304.0	1.99907
$790$	9600.00	0.432345
$791$	−13426.0	−0.603506
$792$	8100.00	0.363410
$793$	−2992.00	−0.133984
$794$	−10008.0	−0.447318
$795$	−28080.0	−1.25270
$796$	−8932.00	−0.397722
$797$	30244.0	1.34416	0.672081	−	0.740477i	$-0.265401\pi$
$797$	30244.0	1.34416	0.672081	+	0.740477i	$0.265401\pi$
$798$	2940.00	0.130420
$799$	204.000	0.00903254
$800$	−44275.0	−1.95670
$801$	7002.00	0.308868
$802$	8402.00	0.369931
$803$	67320.0	2.95849
$804$	−25032.0	−1.09802
$805$	−24640.0	−1.07881
$806$	13328.0	0.582455
$807$	−8448.00	−0.368505
$808$	480.000	0.0208989
$809$	−28906.0	−1.25622	−0.628109	−	0.778125i	$-0.716171\pi$
$809$	−28906.0	−1.25622	−0.628109	+	0.778125i	$0.716171\pi$
$810$	−17820.0	−0.773001
$811$	−5906.00	−0.255719	−0.127859	−	0.991792i	$-0.540811\pi$
$811$	−5906.00	−0.255719	−0.127859	+	0.991792i	$0.540811\pi$
$812$	−4410.00	−0.190592
$813$	−11712.0	−0.505237
$814$	−1320.00	−0.0568378
$815$	33840.0	1.45443
$816$	4182.00	0.179411
$817$	−22960.0	−0.983193
$818$	−13382.0	−0.571993
$819$	4284.00	0.182778
$820$	−19320.0	−0.822785
$821$	−11430.0	−0.485883	−0.242941	−	0.970041i	$-0.578112\pi$
$821$	−11430.0	−0.485883	−0.242941	+	0.970041i	$0.578112\pi$
$822$	−11412.0	−0.484233
$823$	−13168.0	−0.557725	−0.278862	−	0.960331i	$-0.589957\pi$
$823$	−13168.0	−0.557725	−0.278862	+	0.960331i	$0.589957\pi$
$824$	−19500.0	−0.824411
$825$	−99000.0	−4.17786
$826$	−378.000	−0.0159229
$827$	−24600.0	−1.03437	−0.517186	−	0.855873i	$-0.673020\pi$
$827$	−24600.0	−1.03437	−0.517186	+	0.855873i	$0.673020\pi$
$828$	11088.0	0.465380
$829$	25328.0	1.06113	0.530566	−	0.847644i	$-0.321980\pi$
$829$	25328.0	1.06113	0.530566	+	0.847644i	$0.321980\pi$
$830$	−16760.0	−0.700901
$831$	−25644.0	−1.07049
$832$	11356.0	0.473195
$833$	−833.000	−0.0346479
$834$	492.000	0.0204275
$835$	52880.0	2.19160
$836$	29400.0	1.21629
$837$	21168.0	0.874161
$838$	14662.0	0.604404
$839$	−11596.0	−0.477161	−0.238581	−	0.971123i	$-0.576682\pi$
$839$	−11596.0	−0.477161	−0.238581	+	0.971123i	$0.576682\pi$
$840$	−12600.0	−0.517549
$841$	−16289.0	−0.667883
$842$	7370.00	0.301647
$843$	900.000	0.0367706
$844$	−4424.00	−0.180427
$845$	−48540.0	−1.97613
$846$	108.000	0.00438903
$847$	−15883.0	−0.644329
$848$	−9594.00	−0.388513
$849$	3516.00	0.142131
$850$	4675.00	0.188648
$851$	−3872.00	−0.155970
$852$	8400.00	0.337769
$853$	39176.0	1.57252	0.786261	−	0.617895i	$-0.212014\pi$
$853$	39176.0	1.57252	0.786261	+	0.617895i	$0.212014\pi$
$854$	308.000	0.0123414
$855$	12600.0	0.503989
$856$	−3840.00	−0.153328
$857$	−25106.0	−1.00071	−0.500353	−	0.865822i	$-0.666796\pi$
$857$	−25106.0	−1.00071	−0.500353	+	0.865822i	$0.666796\pi$
$858$	−24480.0	−0.974048
$859$	9406.00	0.373607	0.186804	−	0.982397i	$-0.440187\pi$
$859$	9406.00	0.373607	0.186804	+	0.982397i	$0.440187\pi$
$860$	45920.0	1.82077
$861$	−5796.00	−0.229416
$862$	−3480.00	−0.137505
$863$	−32240.0	−1.27168	−0.635841	−	0.771820i	$-0.719347\pi$
$863$	−32240.0	−1.27168	−0.635841	+	0.771820i	$0.719347\pi$
$864$	−17388.0	−0.684666
$865$	36160.0	1.42136
$866$	−13070.0	−0.512860
$867$	−1734.00	−0.0679236
$868$	9604.00	0.375554
$869$	28800.0	1.12425
$870$	10800.0	0.420867
$871$	40528.0	1.57662
$872$	4770.00	0.185244
$873$	10278.0	0.398462
$874$	−12320.0	−0.476808
$875$	21000.0	0.811348
$876$	47124.0	1.81755
$877$	−14394.0	−0.554220	−0.277110	−	0.960838i	$-0.589377\pi$
$877$	−14394.0	−0.554220	−0.277110	+	0.960838i	$0.589377\pi$
$878$	−9352.00	−0.359470
$879$	−7488.00	−0.287331
$880$	−49200.0	−1.88470
$881$	10754.0	0.411250	0.205625	−	0.978631i	$-0.434077\pi$
$881$	10754.0	0.411250	0.205625	+	0.978631i	$0.434077\pi$
$882$	−441.000	−0.0168359
$883$	37284.0	1.42096	0.710479	−	0.703718i	$-0.248478\pi$
$883$	37284.0	1.42096	0.710479	+	0.703718i	$0.248478\pi$
$884$	−8092.00	−0.307877
$885$	−6480.00	−0.246127
$886$	−1828.00	−0.0693147
$887$	−29388.0	−1.11246	−0.556230	−	0.831028i	$-0.687753\pi$
$887$	−29388.0	−1.11246	−0.556230	+	0.831028i	$0.687753\pi$
$888$	−1980.00	−0.0748248
$889$	−12824.0	−0.483806
$890$	15560.0	0.586036
$891$	−53460.0	−2.01008
$892$	5880.00	0.220714
$893$	840.000	0.0314776
$894$	−7548.00	−0.282375
$895$	34320.0	1.28178
$896$	−10185.0	−0.379751
$897$	−71808.0	−2.67291
$898$	7334.00	0.272538
$899$	−17640.0	−0.654424
$900$	−17325.0	−0.641667
$901$	3978.00	0.147088
$902$	8280.00	0.305647
$903$	13776.0	0.507682
$904$	28770.0	1.05849
$905$	−66080.0	−2.42715
$906$	−11040.0	−0.404834
$907$	−27544.0	−1.00836	−0.504181	−	0.863598i	$-0.668205\pi$
$907$	−27544.0	−1.00836	−0.504181	+	0.863598i	$0.668205\pi$
$908$	−31962.0	−1.16817
$909$	288.000	0.0105086
$910$	9520.00	0.346797
$911$	344.000	0.0125107	0.00625534	−	0.999980i	$-0.498009\pi$
$911$	344.000	0.0125107	0.00625534	+	0.999980i	$0.498009\pi$
$912$	17220.0	0.625232
$913$	−50280.0	−1.82259
$914$	5370.00	0.194337
$915$	5280.00	0.190767
$916$	−8652.00	−0.312085
$917$	−1834.00	−0.0660458
$918$	1836.00	0.0660098
$919$	16152.0	0.579766	0.289883	−	0.957062i	$-0.406384\pi$
$919$	16152.0	0.579766	0.289883	+	0.957062i	$0.406384\pi$
$920$	52800.0	1.89214
$921$	38340.0	1.37171
$922$	−14284.0	−0.510215
$923$	−13600.0	−0.484994
$924$	−17640.0	−0.628045
$925$	6050.00	0.215052
$926$	11272.0	0.400023
$927$	−11700.0	−0.414540
$928$	14490.0	0.512562
$929$	20910.0	0.738466	0.369233	−	0.929337i	$-0.379620\pi$
$929$	20910.0	0.738466	0.369233	+	0.929337i	$0.379620\pi$
$930$	−23520.0	−0.829302
$931$	−3430.00	−0.120745
$932$	−9702.00	−0.340987
$933$	22800.0	0.800041
$934$	−16722.0	−0.585825
$935$	20400.0	0.713531
$936$	−9180.00	−0.320574
$937$	26074.0	0.909072	0.454536	−	0.890728i	$-0.349805\pi$
$937$	26074.0	0.909072	0.454536	+	0.890728i	$0.349805\pi$
$938$	−4172.00	−0.145225
$939$	19644.0	0.682703
$940$	−1680.00	−0.0582931
$941$	36204.0	1.25422	0.627108	−	0.778933i	$-0.284239\pi$
$941$	36204.0	1.25422	0.627108	+	0.778933i	$0.284239\pi$
$942$	−12936.0	−0.447429
$943$	24288.0	0.838734
$944$	−2214.00	−0.0763343
$945$	15120.0	0.520480
$946$	−19680.0	−0.676376
$947$	12956.0	0.444576	0.222288	−	0.974981i	$-0.428647\pi$
$947$	12956.0	0.444576	0.222288	+	0.974981i	$0.428647\pi$
$948$	20160.0	0.690682
$949$	−76296.0	−2.60977
$950$	19250.0	0.657424
$951$	41028.0	1.39897
$952$	1785.00	0.0607691
$953$	51050.0	1.73523	0.867614	−	0.497239i	$-0.165653\pi$
$953$	51050.0	1.73523	0.867614	+	0.497239i	$0.165653\pi$
$954$	2106.00	0.0714720
$955$	−81760.0	−2.77036
$956$	−44744.0	−1.51373
$957$	32400.0	1.09440
$958$	6972.00	0.235131
$959$	13314.0	0.448312
$960$	−20040.0	−0.673738
$961$	8625.00	0.289517
$962$	1496.00	0.0501382
$963$	−2304.00	−0.0770980
$964$	−6930.00	−0.231536
$965$	−60760.0	−2.02687
$966$	7392.00	0.246205
$967$	28848.0	0.959348	0.479674	−	0.877447i	$-0.340755\pi$
$967$	28848.0	0.959348	0.479674	+	0.877447i	$0.340755\pi$
$968$	34035.0	1.13009
$969$	−7140.00	−0.236708
$970$	22840.0	0.756029
$971$	−24294.0	−0.802916	−0.401458	−	0.915877i	$-0.631496\pi$
$971$	−24294.0	−0.802916	−0.401458	+	0.915877i	$0.631496\pi$
$972$	−17010.0	−0.561313
$973$	−574.000	−0.0189122
$974$	−17936.0	−0.590048
$975$	112200.	3.68541
$976$	1804.00	0.0591646
$977$	18090.0	0.592375	0.296187	−	0.955130i	$-0.404285\pi$
$977$	18090.0	0.592375	0.296187	+	0.955130i	$0.404285\pi$
$978$	−10152.0	−0.331928
$979$	46680.0	1.52390
$980$	6860.00	0.223607
$981$	2862.00	0.0931464
$982$	−8780.00	−0.285317
$983$	−44988.0	−1.45971	−0.729855	−	0.683602i	$-0.760412\pi$
$983$	−44988.0	−1.45971	−0.729855	+	0.683602i	$0.760412\pi$
$984$	12420.0	0.402373
$985$	24600.0	0.795758
$986$	−1530.00	−0.0494170
$987$	−504.000	−0.0162538
$988$	−33320.0	−1.07293
$989$	−57728.0	−1.85606
$990$	10800.0	0.346714
$991$	22632.0	0.725458	0.362729	−	0.931895i	$-0.381845\pi$
$991$	22632.0	0.725458	0.362729	+	0.931895i	$0.381845\pi$
$992$	−31556.0	−1.00998
$993$	36624.0	1.17042
$994$	1400.00	0.0446733
$995$	−25520.0	−0.813104
$996$	−35196.0	−1.11971
$997$	−30788.0	−0.978000	−0.489000	−	0.872284i	$-0.662638\pi$
$997$	−30788.0	−0.978000	−0.489000	+	0.872284i	$0.662638\pi$
$998$	5080.00	0.161127
$999$	2376.00	0.0752486

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	119.4.a.a.1.1	✓	1
3.2	odd	2		1071.4.a.b.1.1		1
4.3	odd	2		1904.4.a.a.1.1		1
7.6	odd	2		833.4.a.b.1.1		1
17.16	even	2		2023.4.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.4.a.a.1.1	✓	1	1.1	even	1	trivial
833.4.a.b.1.1		1	7.6	odd	2
1071.4.a.b.1.1		1	3.2	odd	2
1904.4.a.a.1.1		1	4.3	odd	2
2023.4.a.b.1.1		1	17.16	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:	\( N \)	\(=\)	\( 119 = 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	119.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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