LMFDB - Embedded newform 1950.4.a.p.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,4,Mod(1,1950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1950, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1950.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1950.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:	$115.053724511$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1950.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +6.00000 q^{6} -5.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$

\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +6.00000 q^{6} -5.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} -35.0000 q^{11} +12.0000 q^{12} +13.0000 q^{13} -10.0000 q^{14} +16.0000 q^{16} -23.0000 q^{17} +18.0000 q^{18} -30.0000 q^{19} -15.0000 q^{21} -70.0000 q^{22} -63.0000 q^{23} +24.0000 q^{24} +26.0000 q^{26} +27.0000 q^{27} -20.0000 q^{28} -190.000 q^{29} +330.000 q^{31} +32.0000 q^{32} -105.000 q^{33} -46.0000 q^{34} +36.0000 q^{36} -43.0000 q^{37} -60.0000 q^{38} +39.0000 q^{39} -473.000 q^{41} -30.0000 q^{42} +232.000 q^{43} -140.000 q^{44} -126.000 q^{46} -270.000 q^{47} +48.0000 q^{48} -318.000 q^{49} -69.0000 q^{51} +52.0000 q^{52} +193.000 q^{53} +54.0000 q^{54} -40.0000 q^{56} -90.0000 q^{57} -380.000 q^{58} -200.000 q^{59} -679.000 q^{61} +660.000 q^{62} -45.0000 q^{63} +64.0000 q^{64} -210.000 q^{66} +12.0000 q^{67} -92.0000 q^{68} -189.000 q^{69} -899.000 q^{71} +72.0000 q^{72} -154.000 q^{73} -86.0000 q^{74} -120.000 q^{76} +175.000 q^{77} +78.0000 q^{78} +215.000 q^{79} +81.0000 q^{81} -946.000 q^{82} +1308.00 q^{83} -60.0000 q^{84} +464.000 q^{86} -570.000 q^{87} -280.000 q^{88} -1019.00 q^{89} -65.0000 q^{91} -252.000 q^{92} +990.000 q^{93} -540.000 q^{94} +96.0000 q^{96} +427.000 q^{97} -636.000 q^{98} -315.000 q^{99} +O(q^{100})\)

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
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	4.00000	0.500000
$5$	0	0
$5$	0	0
$6$	6.00000	0.408248
$7$	−5.00000	−0.269975	−0.134987	−	0.990847i	$-0.543099\pi$
$7$	−5.00000	−0.269975	−0.134987	+	0.990847i	$0.543099\pi$
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	0	0
$11$	−35.0000	−0.959354	−0.479677	−	0.877445i	$-0.659246\pi$
$11$	−35.0000	−0.959354	−0.479677	+	0.877445i	$0.659246\pi$
$12$	12.0000	0.288675
$13$	13.0000	0.277350
$13$	13.0000	0.277350
$14$	−10.0000	−0.190901
$15$	0	0
$16$	16.0000	0.250000
$17$	−23.0000	−0.328136	−0.164068	−	0.986449i	$-0.552462\pi$
$17$	−23.0000	−0.328136	−0.164068	+	0.986449i	$0.552462\pi$
$18$	18.0000	0.235702
$19$	−30.0000	−0.362235	−0.181118	−	0.983461i	$-0.557971\pi$
$19$	−30.0000	−0.362235	−0.181118	+	0.983461i	$0.557971\pi$
$20$	0	0
$21$	−15.0000	−0.155870
$22$	−70.0000	−0.678366
$23$	−63.0000	−0.571148	−0.285574	−	0.958357i	$-0.592184\pi$
$23$	−63.0000	−0.571148	−0.285574	+	0.958357i	$0.592184\pi$
$24$	24.0000	0.204124
$25$	0	0
$26$	26.0000	0.196116
$27$	27.0000	0.192450
$28$	−20.0000	−0.134987
$29$	−190.000	−1.21662	−0.608312	−	0.793698i	$-0.708153\pi$
$29$	−190.000	−1.21662	−0.608312	+	0.793698i	$0.708153\pi$
$30$	0	0
$31$	330.000	1.91193	0.955964	−	0.293485i	$-0.0948150\pi$
$31$	330.000	1.91193	0.955964	+	0.293485i	$0.0948150\pi$
$32$	32.0000	0.176777
$33$	−105.000	−0.553883
$34$	−46.0000	−0.232027
$35$	0	0
$36$	36.0000	0.166667
$37$	−43.0000	−0.191058	−0.0955291	−	0.995427i	$-0.530454\pi$
$37$	−43.0000	−0.191058	−0.0955291	+	0.995427i	$0.530454\pi$
$38$	−60.0000	−0.256139
$39$	39.0000	0.160128
$40$	0	0
$41$	−473.000	−1.80171	−0.900856	−	0.434118i	$-0.857060\pi$
$41$	−473.000	−1.80171	−0.900856	+	0.434118i	$0.857060\pi$
$42$	−30.0000	−0.110217
$43$	232.000	0.822783	0.411391	−	0.911459i	$-0.365043\pi$
$43$	232.000	0.822783	0.411391	+	0.911459i	$0.365043\pi$
$44$	−140.000	−0.479677
$45$	0	0
$46$	−126.000	−0.403863
$47$	−270.000	−0.837948	−0.418974	−	0.907998i	$-0.637610\pi$
$47$	−270.000	−0.837948	−0.418974	+	0.907998i	$0.637610\pi$
$48$	48.0000	0.144338
$49$	−318.000	−0.927114
$50$	0	0
$51$	−69.0000	−0.189450
$52$	52.0000	0.138675
$53$	193.000	0.500200	0.250100	−	0.968220i	$-0.419537\pi$
$53$	193.000	0.500200	0.250100	+	0.968220i	$0.419537\pi$
$54$	54.0000	0.136083
$55$	0	0
$56$	−40.0000	−0.0954504
$57$	−90.0000	−0.209137
$58$	−380.000	−0.860284
$59$	−200.000	−0.441318	−0.220659	−	0.975351i	$-0.570821\pi$
$59$	−200.000	−0.441318	−0.220659	+	0.975351i	$0.570821\pi$
$60$	0	0
$61$	−679.000	−1.42520	−0.712599	−	0.701572i	$-0.752482\pi$
$61$	−679.000	−1.42520	−0.712599	+	0.701572i	$0.752482\pi$
$62$	660.000	1.35194
$63$	−45.0000	−0.0899915
$64$	64.0000	0.125000
$65$	0	0
$66$	−210.000	−0.391655
$67$	12.0000	0.0218811	0.0109405	−	0.999940i	$-0.496517\pi$
$67$	12.0000	0.0218811	0.0109405	+	0.999940i	$0.496517\pi$
$68$	−92.0000	−0.164068
$69$	−189.000	−0.329753
$70$	0	0
$71$	−899.000	−1.50270	−0.751350	−	0.659904i	$-0.770597\pi$
$71$	−899.000	−1.50270	−0.751350	+	0.659904i	$0.770597\pi$
$72$	72.0000	0.117851
$73$	−154.000	−0.246909	−0.123454	−	0.992350i	$-0.539397\pi$
$73$	−154.000	−0.246909	−0.123454	+	0.992350i	$0.539397\pi$
$74$	−86.0000	−0.135099
$75$	0	0
$76$	−120.000	−0.181118
$77$	175.000	0.259001
$78$	78.0000	0.113228
$79$	215.000	0.306195	0.153097	−	0.988211i	$-0.451075\pi$
$79$	215.000	0.306195	0.153097	+	0.988211i	$0.451075\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	−946.000	−1.27400
$83$	1308.00	1.72978	0.864889	−	0.501962i	$-0.167388\pi$
$83$	1308.00	1.72978	0.864889	+	0.501962i	$0.167388\pi$
$84$	−60.0000	−0.0779350
$85$	0	0
$86$	464.000	0.581795
$87$	−570.000	−0.702419
$88$	−280.000	−0.339183
$89$	−1019.00	−1.21364	−0.606819	−	0.794840i	$-0.707555\pi$
$89$	−1019.00	−1.21364	−0.606819	+	0.794840i	$0.707555\pi$
$90$	0	0
$91$	−65.0000	−0.0748775
$92$	−252.000	−0.285574
$93$	990.000	1.10385
$94$	−540.000	−0.592519
$95$	0	0
$96$	96.0000	0.102062
$97$	427.000	0.446962	0.223481	−	0.974708i	$-0.428258\pi$
$97$	427.000	0.446962	0.223481	+	0.974708i	$0.428258\pi$
$98$	−636.000	−0.655568
$99$	−315.000	−0.319785
$100$	0	0
$101$	−1144.00	−1.12705	−0.563526	−	0.826098i	$-0.690556\pi$
$101$	−1144.00	−1.12705	−0.563526	+	0.826098i	$0.690556\pi$
$102$	−138.000	−0.133961
$103$	−696.000	−0.665815	−0.332907	−	0.942960i	$-0.608030\pi$
$103$	−696.000	−0.665815	−0.332907	+	0.942960i	$0.608030\pi$
$104$	104.000	0.0980581
$105$	0	0
$106$	386.000	0.353695
$107$	1353.00	1.22242	0.611212	−	0.791467i	$-0.290682\pi$
$107$	1353.00	1.22242	0.611212	+	0.791467i	$0.290682\pi$
$108$	108.000	0.0962250
$109$	504.000	0.442885	0.221442	−	0.975173i	$-0.428924\pi$
$109$	504.000	0.442885	0.221442	+	0.975173i	$0.428924\pi$
$110$	0	0
$111$	−129.000	−0.110308
$112$	−80.0000	−0.0674937
$113$	−1790.00	−1.49017	−0.745084	−	0.666970i	$-0.767591\pi$
$113$	−1790.00	−1.49017	−0.745084	+	0.666970i	$0.767591\pi$
$114$	−180.000	−0.147882
$115$	0	0
$116$	−760.000	−0.608312
$117$	117.000	0.0924500
$118$	−400.000	−0.312059
$119$	115.000	0.0885885
$120$	0	0
$121$	−106.000	−0.0796394
$122$	−1358.00	−1.00777
$123$	−1419.00	−1.04022
$124$	1320.00	0.955964
$125$	0	0
$126$	−90.0000	−0.0636336
$127$	−1306.00	−0.912510	−0.456255	−	0.889849i	$-0.650809\pi$
$127$	−1306.00	−0.912510	−0.456255	+	0.889849i	$0.650809\pi$
$128$	128.000	0.0883883
$129$	696.000	0.475034
$130$	0	0
$131$	−1718.00	−1.14582	−0.572910	−	0.819618i	$-0.694185\pi$
$131$	−1718.00	−1.14582	−0.572910	+	0.819618i	$0.694185\pi$
$132$	−420.000	−0.276942
$133$	150.000	0.0977944
$134$	24.0000	0.0154723
$135$	0	0
$136$	−184.000	−0.116014
$137$	438.000	0.273145	0.136573	−	0.990630i	$-0.456391\pi$
$137$	438.000	0.273145	0.136573	+	0.990630i	$0.456391\pi$
$138$	−378.000	−0.233170
$139$	721.000	0.439960	0.219980	−	0.975504i	$-0.429401\pi$
$139$	721.000	0.439960	0.219980	+	0.975504i	$0.429401\pi$
$140$	0	0
$141$	−810.000	−0.483789
$142$	−1798.00	−1.06257
$143$	−455.000	−0.266077
$144$	144.000	0.0833333
$145$	0	0
$146$	−308.000	−0.174591
$147$	−954.000	−0.535269
$148$	−172.000	−0.0955291
$149$	29.0000	0.0159448	0.00797239	−	0.999968i	$-0.497462\pi$
$149$	29.0000	0.0159448	0.00797239	+	0.999968i	$0.497462\pi$
$150$	0	0
$151$	−816.000	−0.439769	−0.219885	−	0.975526i	$-0.570568\pi$
$151$	−816.000	−0.439769	−0.219885	+	0.975526i	$0.570568\pi$
$152$	−240.000	−0.128070
$153$	−207.000	−0.109379
$154$	350.000	0.183142
$155$	0	0
$156$	156.000	0.0800641
$157$	1298.00	0.659820	0.329910	−	0.944012i	$-0.392982\pi$
$157$	1298.00	0.659820	0.329910	+	0.944012i	$0.392982\pi$
$158$	430.000	0.216512
$159$	579.000	0.288790
$160$	0	0
$161$	315.000	0.154196
$162$	162.000	0.0785674
$163$	−3113.00	−1.49588	−0.747942	−	0.663764i	$-0.768958\pi$
$163$	−3113.00	−1.49588	−0.747942	+	0.663764i	$0.768958\pi$
$164$	−1892.00	−0.900856
$165$	0	0
$166$	2616.00	1.22314
$167$	172.000	0.0796992	0.0398496	−	0.999206i	$-0.487312\pi$
$167$	172.000	0.0796992	0.0398496	+	0.999206i	$0.487312\pi$
$168$	−120.000	−0.0551083
$169$	169.000	0.0769231
$170$	0	0
$171$	−270.000	−0.120745
$172$	928.000	0.411391
$173$	1982.00	0.871033	0.435516	−	0.900181i	$-0.356566\pi$
$173$	1982.00	0.871033	0.435516	+	0.900181i	$0.356566\pi$
$174$	−1140.00	−0.496685
$175$	0	0
$176$	−560.000	−0.239839
$177$	−600.000	−0.254795
$178$	−2038.00	−0.858172
$179$	2990.00	1.24851	0.624254	−	0.781221i	$-0.285403\pi$
$179$	2990.00	1.24851	0.624254	+	0.781221i	$0.285403\pi$
$180$	0	0
$181$	1885.00	0.774094	0.387047	−	0.922060i	$-0.373495\pi$
$181$	1885.00	0.774094	0.387047	+	0.922060i	$0.373495\pi$
$182$	−130.000	−0.0529464
$183$	−2037.00	−0.822838
$184$	−504.000	−0.201931
$185$	0	0
$186$	1980.00	0.780541
$187$	805.000	0.314799
$188$	−1080.00	−0.418974
$189$	−135.000	−0.0519566
$190$	0	0
$191$	−516.000	−0.195479	−0.0977394	−	0.995212i	$-0.531161\pi$
$191$	−516.000	−0.195479	−0.0977394	+	0.995212i	$0.531161\pi$
$192$	192.000	0.0721688
$193$	2713.00	1.01184	0.505922	−	0.862579i	$-0.331152\pi$
$193$	2713.00	1.01184	0.505922	+	0.862579i	$0.331152\pi$
$194$	854.000	0.316050
$195$	0	0
$196$	−1272.00	−0.463557
$197$	−1116.00	−0.403613	−0.201806	−	0.979425i	$-0.564681\pi$
$197$	−1116.00	−0.403613	−0.201806	+	0.979425i	$0.564681\pi$
$198$	−630.000	−0.226122
$199$	−1164.00	−0.414642	−0.207321	−	0.978273i	$-0.566474\pi$
$199$	−1164.00	−0.414642	−0.207321	+	0.978273i	$0.566474\pi$
$200$	0	0
$201$	36.0000	0.0126331
$202$	−2288.00	−0.796946
$203$	950.000	0.328458
$204$	−276.000	−0.0947248
$205$	0	0
$206$	−1392.00	−0.470802
$207$	−567.000	−0.190383
$208$	208.000	0.0693375
$209$	1050.00	0.347512
$210$	0	0
$211$	−3572.00	−1.16543	−0.582717	−	0.812675i	$-0.698010\pi$
$211$	−3572.00	−1.16543	−0.582717	+	0.812675i	$0.698010\pi$
$212$	772.000	0.250100
$213$	−2697.00	−0.867584
$214$	2706.00	0.864385
$215$	0	0
$216$	216.000	0.0680414
$217$	−1650.00	−0.516172
$218$	1008.00	0.313167
$219$	−462.000	−0.142553
$220$	0	0
$221$	−299.000	−0.0910087
$222$	−258.000	−0.0779992
$223$	−5248.00	−1.57593	−0.787964	−	0.615721i	$-0.788865\pi$
$223$	−5248.00	−1.57593	−0.787964	+	0.615721i	$0.788865\pi$
$224$	−160.000	−0.0477252
$225$	0	0
$226$	−3580.00	−1.05371
$227$	−5810.00	−1.69878	−0.849390	−	0.527765i	$-0.823030\pi$
$227$	−5810.00	−1.69878	−0.849390	+	0.527765i	$0.823030\pi$
$228$	−360.000	−0.104568
$229$	5278.00	1.52306	0.761529	−	0.648131i	$-0.224449\pi$
$229$	5278.00	1.52306	0.761529	+	0.648131i	$0.224449\pi$
$230$	0	0
$231$	525.000	0.149534
$232$	−1520.00	−0.430142
$233$	5091.00	1.43143	0.715714	−	0.698394i	$-0.246102\pi$
$233$	5091.00	1.43143	0.715714	+	0.698394i	$0.246102\pi$
$234$	234.000	0.0653720
$235$	0	0
$236$	−800.000	−0.220659
$237$	645.000	0.176782
$238$	230.000	0.0626415
$239$	4549.00	1.23117	0.615587	−	0.788069i	$-0.288919\pi$
$239$	4549.00	1.23117	0.615587	+	0.788069i	$0.288919\pi$
$240$	0	0
$241$	−4534.00	−1.21187	−0.605935	−	0.795514i	$-0.707201\pi$
$241$	−4534.00	−1.21187	−0.605935	+	0.795514i	$0.707201\pi$
$242$	−212.000	−0.0563135
$243$	243.000	0.0641500
$244$	−2716.00	−0.712599
$245$	0	0
$246$	−2838.00	−0.735546
$247$	−390.000	−0.100466
$248$	2640.00	0.675968
$249$	3924.00	0.998688
$250$	0	0
$251$	−6144.00	−1.54504	−0.772522	−	0.634988i	$-0.781005\pi$
$251$	−6144.00	−1.54504	−0.772522	+	0.634988i	$0.781005\pi$
$252$	−180.000	−0.0449958
$253$	2205.00	0.547933
$254$	−2612.00	−0.645242
$255$	0	0
$256$	256.000	0.0625000
$257$	282.000	0.0684462	0.0342231	−	0.999414i	$-0.489104\pi$
$257$	282.000	0.0684462	0.0342231	+	0.999414i	$0.489104\pi$
$258$	1392.00	0.335900
$259$	215.000	0.0515809
$260$	0	0
$261$	−1710.00	−0.405542
$262$	−3436.00	−0.810217
$263$	−1736.00	−0.407020	−0.203510	−	0.979073i	$-0.565235\pi$
$263$	−1736.00	−0.407020	−0.203510	+	0.979073i	$0.565235\pi$
$264$	−840.000	−0.195827
$265$	0	0
$266$	300.000	0.0691511
$267$	−3057.00	−0.700694
$268$	48.0000	0.0109405
$269$	6636.00	1.50410	0.752052	−	0.659104i	$-0.229064\pi$
$269$	6636.00	1.50410	0.752052	+	0.659104i	$0.229064\pi$
$270$	0	0
$271$	106.000	0.0237603	0.0118802	−	0.999929i	$-0.496218\pi$
$271$	106.000	0.0237603	0.0118802	+	0.999929i	$0.496218\pi$
$272$	−368.000	−0.0820341
$273$	−195.000	−0.0432305
$274$	876.000	0.193143
$275$	0	0
$276$	−756.000	−0.164876
$277$	4366.00	0.947031	0.473515	−	0.880786i	$-0.342985\pi$
$277$	4366.00	0.947031	0.473515	+	0.880786i	$0.342985\pi$
$278$	1442.00	0.311099
$279$	2970.00	0.637309
$280$	0	0
$281$	−4266.00	−0.905652	−0.452826	−	0.891599i	$-0.649584\pi$
$281$	−4266.00	−0.905652	−0.452826	+	0.891599i	$0.649584\pi$
$282$	−1620.00	−0.342091
$283$	3076.00	0.646110	0.323055	−	0.946380i	$-0.395290\pi$
$283$	3076.00	0.646110	0.323055	+	0.946380i	$0.395290\pi$
$284$	−3596.00	−0.751350
$285$	0	0
$286$	−910.000	−0.188145
$287$	2365.00	0.486417
$288$	288.000	0.0589256
$289$	−4384.00	−0.892326
$290$	0	0
$291$	1281.00	0.258053
$292$	−616.000	−0.123454
$293$	−7048.00	−1.40529	−0.702643	−	0.711543i	$-0.747997\pi$
$293$	−7048.00	−1.40529	−0.702643	+	0.711543i	$0.747997\pi$
$294$	−1908.00	−0.378493
$295$	0	0
$296$	−344.000	−0.0675493
$297$	−945.000	−0.184628
$298$	58.0000	0.0112747
$299$	−819.000	−0.158408
$300$	0	0
$301$	−1160.00	−0.222131
$302$	−1632.00	−0.310964
$303$	−3432.00	−0.650704
$304$	−480.000	−0.0905588
$305$	0	0
$306$	−414.000	−0.0773425
$307$	4263.00	0.792516	0.396258	−	0.918139i	$-0.370309\pi$
$307$	4263.00	0.792516	0.396258	+	0.918139i	$0.370309\pi$
$308$	700.000	0.129501
$309$	−2088.00	−0.384408
$310$	0	0
$311$	444.000	0.0809548	0.0404774	−	0.999180i	$-0.487112\pi$
$311$	444.000	0.0809548	0.0404774	+	0.999180i	$0.487112\pi$
$312$	312.000	0.0566139
$313$	4242.00	0.766045	0.383022	−	0.923739i	$-0.374883\pi$
$313$	4242.00	0.766045	0.383022	+	0.923739i	$0.374883\pi$
$314$	2596.00	0.466563
$315$	0	0
$316$	860.000	0.153097
$317$	2736.00	0.484760	0.242380	−	0.970181i	$-0.422072\pi$
$317$	2736.00	0.484760	0.242380	+	0.970181i	$0.422072\pi$
$318$	1158.00	0.204206
$319$	6650.00	1.16717
$320$	0	0
$321$	4059.00	0.705767
$322$	630.000	0.109033
$323$	690.000	0.118863
$324$	324.000	0.0555556
$325$	0	0
$326$	−6226.00	−1.05775
$327$	1512.00	0.255700
$328$	−3784.00	−0.637001
$329$	1350.00	0.226225
$330$	0	0
$331$	6148.00	1.02092	0.510460	−	0.859901i	$-0.329475\pi$
$331$	6148.00	1.02092	0.510460	+	0.859901i	$0.329475\pi$
$332$	5232.00	0.864889
$333$	−387.000	−0.0636861
$334$	344.000	0.0563558
$335$	0	0
$336$	−240.000	−0.0389675
$337$	−4016.00	−0.649156	−0.324578	−	0.945859i	$-0.605222\pi$
$337$	−4016.00	−0.649156	−0.324578	+	0.945859i	$0.605222\pi$
$338$	338.000	0.0543928
$339$	−5370.00	−0.860349
$340$	0	0
$341$	−11550.0	−1.83422
$342$	−540.000	−0.0853797
$343$	3305.00	0.520272
$344$	1856.00	0.290898
$345$	0	0
$346$	3964.00	0.615913
$347$	−7299.00	−1.12920	−0.564598	−	0.825366i	$-0.690969\pi$
$347$	−7299.00	−1.12920	−0.564598	+	0.825366i	$0.690969\pi$
$348$	−2280.00	−0.351209
$349$	116.000	0.0177918	0.00889590	−	0.999960i	$-0.497168\pi$
$349$	116.000	0.0177918	0.00889590	+	0.999960i	$0.497168\pi$
$350$	0	0
$351$	351.000	0.0533761
$352$	−1120.00	−0.169591
$353$	6878.00	1.03705	0.518525	−	0.855062i	$-0.326481\pi$
$353$	6878.00	1.03705	0.518525	+	0.855062i	$0.326481\pi$
$354$	−1200.00	−0.180167
$355$	0	0
$356$	−4076.00	−0.606819
$357$	345.000	0.0511466
$358$	5980.00	0.882829
$359$	4656.00	0.684497	0.342248	−	0.939610i	$-0.388812\pi$
$359$	4656.00	0.684497	0.342248	+	0.939610i	$0.388812\pi$
$360$	0	0
$361$	−5959.00	−0.868786
$362$	3770.00	0.547367
$363$	−318.000	−0.0459798
$364$	−260.000	−0.0374387
$365$	0	0
$366$	−4074.00	−0.581834
$367$	5640.00	0.802195	0.401098	−	0.916035i	$-0.368629\pi$
$367$	5640.00	0.802195	0.401098	+	0.916035i	$0.368629\pi$
$368$	−1008.00	−0.142787
$369$	−4257.00	−0.600571
$370$	0	0
$371$	−965.000	−0.135041
$372$	3960.00	0.551926
$373$	4160.00	0.577471	0.288735	−	0.957409i	$-0.406765\pi$
$373$	4160.00	0.577471	0.288735	+	0.957409i	$0.406765\pi$
$374$	1610.00	0.222597
$375$	0	0
$376$	−2160.00	−0.296259
$377$	−2470.00	−0.337431
$378$	−270.000	−0.0367389
$379$	−7854.00	−1.06447	−0.532233	−	0.846598i	$-0.678647\pi$
$379$	−7854.00	−1.06447	−0.532233	+	0.846598i	$0.678647\pi$
$380$	0	0
$381$	−3918.00	−0.526838
$382$	−1032.00	−0.138224
$383$	−1206.00	−0.160897	−0.0804487	−	0.996759i	$-0.525635\pi$
$383$	−1206.00	−0.160897	−0.0804487	+	0.996759i	$0.525635\pi$
$384$	384.000	0.0510310
$385$	0	0
$386$	5426.00	0.715482
$387$	2088.00	0.274261
$388$	1708.00	0.223481
$389$	−952.000	−0.124083	−0.0620415	−	0.998074i	$-0.519761\pi$
$389$	−952.000	−0.124083	−0.0620415	+	0.998074i	$0.519761\pi$
$390$	0	0
$391$	1449.00	0.187415
$392$	−2544.00	−0.327784
$393$	−5154.00	−0.661539
$394$	−2232.00	−0.285397
$395$	0	0
$396$	−1260.00	−0.159892
$397$	−5747.00	−0.726533	−0.363267	−	0.931685i	$-0.618339\pi$
$397$	−5747.00	−0.726533	−0.363267	+	0.931685i	$0.618339\pi$
$398$	−2328.00	−0.293196
$399$	450.000	0.0564616
$400$	0	0
$401$	11958.0	1.48916	0.744581	−	0.667532i	$-0.232649\pi$
$401$	11958.0	1.48916	0.744581	+	0.667532i	$0.232649\pi$
$402$	72.0000	0.00893292
$403$	4290.00	0.530273
$404$	−4576.00	−0.563526
$405$	0	0
$406$	1900.00	0.232255
$407$	1505.00	0.183293
$408$	−552.000	−0.0669806
$409$	14878.0	1.79870	0.899352	−	0.437226i	$-0.144039\pi$
$409$	14878.0	1.79870	0.899352	+	0.437226i	$0.144039\pi$
$410$	0	0
$411$	1314.00	0.157700
$412$	−2784.00	−0.332907
$413$	1000.00	0.119145
$414$	−1134.00	−0.134621
$415$	0	0
$416$	416.000	0.0490290
$417$	2163.00	0.254011
$418$	2100.00	0.245728
$419$	3178.00	0.370538	0.185269	−	0.982688i	$-0.440684\pi$
$419$	3178.00	0.370538	0.185269	+	0.982688i	$0.440684\pi$
$420$	0	0
$421$	−4412.00	−0.510755	−0.255377	−	0.966841i	$-0.582200\pi$
$421$	−4412.00	−0.510755	−0.255377	+	0.966841i	$0.582200\pi$
$422$	−7144.00	−0.824086
$423$	−2430.00	−0.279316
$424$	1544.00	0.176847
$425$	0	0
$426$	−5394.00	−0.613475
$427$	3395.00	0.384767
$428$	5412.00	0.611212
$429$	−1365.00	−0.153620
$430$	0	0
$431$	9216.00	1.02997	0.514987	−	0.857198i	$-0.327797\pi$
$431$	9216.00	1.02997	0.514987	+	0.857198i	$0.327797\pi$
$432$	432.000	0.0481125
$433$	−2536.00	−0.281460	−0.140730	−	0.990048i	$-0.544945\pi$
$433$	−2536.00	−0.281460	−0.140730	+	0.990048i	$0.544945\pi$
$434$	−3300.00	−0.364989
$435$	0	0
$436$	2016.00	0.221442
$437$	1890.00	0.206890
$438$	−924.000	−0.100800
$439$	−1811.00	−0.196889	−0.0984445	−	0.995143i	$-0.531387\pi$
$439$	−1811.00	−0.196889	−0.0984445	+	0.995143i	$0.531387\pi$
$440$	0	0
$441$	−2862.00	−0.309038
$442$	−598.000	−0.0643528
$443$	−14743.0	−1.58118	−0.790588	−	0.612348i	$-0.790225\pi$
$443$	−14743.0	−1.58118	−0.790588	+	0.612348i	$0.790225\pi$
$444$	−516.000	−0.0551538
$445$	0	0
$446$	−10496.0	−1.11435
$447$	87.0000	0.00920572
$448$	−320.000	−0.0337468
$449$	999.000	0.105002	0.0525008	−	0.998621i	$-0.483281\pi$
$449$	999.000	0.105002	0.0525008	+	0.998621i	$0.483281\pi$
$450$	0	0
$451$	16555.0	1.72848
$452$	−7160.00	−0.745084
$453$	−2448.00	−0.253901
$454$	−11620.0	−1.20122
$455$	0	0
$456$	−720.000	−0.0739410
$457$	−18497.0	−1.89333	−0.946666	−	0.322215i	$-0.895573\pi$
$457$	−18497.0	−1.89333	−0.946666	+	0.322215i	$0.895573\pi$
$458$	10556.0	1.07696
$459$	−621.000	−0.0631499
$460$	0	0
$461$	3951.00	0.399168	0.199584	−	0.979881i	$-0.436041\pi$
$461$	3951.00	0.399168	0.199584	+	0.979881i	$0.436041\pi$
$462$	1050.00	0.105737
$463$	947.000	0.0950558	0.0475279	−	0.998870i	$-0.484866\pi$
$463$	947.000	0.0950558	0.0475279	+	0.998870i	$0.484866\pi$
$464$	−3040.00	−0.304156
$465$	0	0
$466$	10182.0	1.01217
$467$	−4159.00	−0.412110	−0.206055	−	0.978540i	$-0.566063\pi$
$467$	−4159.00	−0.412110	−0.206055	+	0.978540i	$0.566063\pi$
$468$	468.000	0.0462250
$469$	−60.0000	−0.00590734
$470$	0	0
$471$	3894.00	0.380947
$472$	−1600.00	−0.156030
$473$	−8120.00	−0.789340
$474$	1290.00	0.125004
$475$	0	0
$476$	460.000	0.0442943
$477$	1737.00	0.166733
$478$	9098.00	0.870571
$479$	14135.0	1.34832	0.674159	−	0.738586i	$-0.264506\pi$
$479$	14135.0	1.34832	0.674159	+	0.738586i	$0.264506\pi$
$480$	0	0
$481$	−559.000	−0.0529900
$482$	−9068.00	−0.856921
$483$	945.000	0.0890248
$484$	−424.000	−0.0398197
$485$	0	0
$486$	486.000	0.0453609
$487$	7609.00	0.708001	0.354001	−	0.935245i	$-0.384821\pi$
$487$	7609.00	0.708001	0.354001	+	0.935245i	$0.384821\pi$
$488$	−5432.00	−0.503883
$489$	−9339.00	−0.863649
$490$	0	0
$491$	−13320.0	−1.22428	−0.612142	−	0.790748i	$-0.709692\pi$
$491$	−13320.0	−1.22428	−0.612142	+	0.790748i	$0.709692\pi$
$492$	−5676.00	−0.520109
$493$	4370.00	0.399219
$494$	−780.000	−0.0710402
$495$	0	0
$496$	5280.00	0.477982
$497$	4495.00	0.405691
$498$	7848.00	0.706179
$499$	−3010.00	−0.270032	−0.135016	−	0.990843i	$-0.543109\pi$
$499$	−3010.00	−0.270032	−0.135016	+	0.990843i	$0.543109\pi$
$500$	0	0
$501$	516.000	0.0460143
$502$	−12288.0	−1.09251
$503$	−16252.0	−1.44064	−0.720319	−	0.693643i	$-0.756005\pi$
$503$	−16252.0	−1.44064	−0.720319	+	0.693643i	$0.756005\pi$
$504$	−360.000	−0.0318168
$505$	0	0
$506$	4410.00	0.387447
$507$	507.000	0.0444116
$508$	−5224.00	−0.456255
$509$	15873.0	1.38224	0.691118	−	0.722742i	$-0.257118\pi$
$509$	15873.0	1.38224	0.691118	+	0.722742i	$0.257118\pi$
$510$	0	0
$511$	770.000	0.0666591
$512$	512.000	0.0441942
$513$	−810.000	−0.0697122
$514$	564.000	0.0483988
$515$	0	0
$516$	2784.00	0.237517
$517$	9450.00	0.803889
$518$	430.000	0.0364732
$519$	5946.00	0.502891
$520$	0	0
$521$	−7910.00	−0.665150	−0.332575	−	0.943077i	$-0.607918\pi$
$521$	−7910.00	−0.665150	−0.332575	+	0.943077i	$0.607918\pi$
$522$	−3420.00	−0.286761
$523$	7020.00	0.586928	0.293464	−	0.955970i	$-0.405192\pi$
$523$	7020.00	0.586928	0.293464	+	0.955970i	$0.405192\pi$
$524$	−6872.00	−0.572910
$525$	0	0
$526$	−3472.00	−0.287807
$527$	−7590.00	−0.627373
$528$	−1680.00	−0.138471
$529$	−8198.00	−0.673790
$530$	0	0
$531$	−1800.00	−0.147106
$532$	600.000	0.0488972
$533$	−6149.00	−0.499705
$534$	−6114.00	−0.495466
$535$	0	0
$536$	96.0000	0.00773614
$537$	8970.00	0.720827
$538$	13272.0	1.06356
$539$	11130.0	0.889430
$540$	0	0
$541$	7018.00	0.557722	0.278861	−	0.960332i	$-0.410043\pi$
$541$	7018.00	0.557722	0.278861	+	0.960332i	$0.410043\pi$
$542$	212.000	0.0168011
$543$	5655.00	0.446923
$544$	−736.000	−0.0580069
$545$	0	0
$546$	−390.000	−0.0305686
$547$	−21136.0	−1.65212	−0.826060	−	0.563582i	$-0.809423\pi$
$547$	−21136.0	−1.65212	−0.826060	+	0.563582i	$0.809423\pi$
$548$	1752.00	0.136573
$549$	−6111.00	−0.475066
$550$	0	0
$551$	5700.00	0.440704
$552$	−1512.00	−0.116585
$553$	−1075.00	−0.0826648
$554$	8732.00	0.669652
$555$	0	0
$556$	2884.00	0.219980
$557$	−13070.0	−0.994244	−0.497122	−	0.867681i	$-0.665610\pi$
$557$	−13070.0	−0.994244	−0.497122	+	0.867681i	$0.665610\pi$
$558$	5940.00	0.450646
$559$	3016.00	0.228199
$560$	0	0
$561$	2415.00	0.181749
$562$	−8532.00	−0.640393
$563$	15669.0	1.17295	0.586474	−	0.809968i	$-0.300516\pi$
$563$	15669.0	1.17295	0.586474	+	0.809968i	$0.300516\pi$
$564$	−3240.00	−0.241895
$565$	0	0
$566$	6152.00	0.456869
$567$	−405.000	−0.0299972
$568$	−7192.00	−0.531285
$569$	−1404.00	−0.103442	−0.0517212	−	0.998662i	$-0.516471\pi$
$569$	−1404.00	−0.103442	−0.0517212	+	0.998662i	$0.516471\pi$
$570$	0	0
$571$	8791.00	0.644294	0.322147	−	0.946690i	$-0.395595\pi$
$571$	8791.00	0.644294	0.322147	+	0.946690i	$0.395595\pi$
$572$	−1820.00	−0.133039
$573$	−1548.00	−0.112860
$574$	4730.00	0.343948
$575$	0	0
$576$	576.000	0.0416667
$577$	8511.00	0.614069	0.307034	−	0.951698i	$-0.400663\pi$
$577$	8511.00	0.614069	0.307034	+	0.951698i	$0.400663\pi$
$578$	−8768.00	−0.630970
$579$	8139.00	0.584189
$580$	0	0
$581$	−6540.00	−0.466996
$582$	2562.00	0.182471
$583$	−6755.00	−0.479869
$584$	−1232.00	−0.0872954
$585$	0	0
$586$	−14096.0	−0.993687
$587$	10494.0	0.737877	0.368938	−	0.929454i	$-0.379721\pi$
$587$	10494.0	0.737877	0.368938	+	0.929454i	$0.379721\pi$
$588$	−3816.00	−0.267635
$589$	−9900.00	−0.692568
$590$	0	0
$591$	−3348.00	−0.233026
$592$	−688.000	−0.0477646
$593$	22052.0	1.52709	0.763547	−	0.645752i	$-0.223456\pi$
$593$	22052.0	1.52709	0.763547	+	0.645752i	$0.223456\pi$
$594$	−1890.00	−0.130552
$595$	0	0
$596$	116.000	0.00797239
$597$	−3492.00	−0.239394
$598$	−1638.00	−0.112011
$599$	−6384.00	−0.435464	−0.217732	−	0.976009i	$-0.569866\pi$
$599$	−6384.00	−0.435464	−0.217732	+	0.976009i	$0.569866\pi$
$600$	0	0
$601$	10627.0	0.721272	0.360636	−	0.932707i	$-0.382560\pi$
$601$	10627.0	0.721272	0.360636	+	0.932707i	$0.382560\pi$
$602$	−2320.00	−0.157070
$603$	108.000	0.00729370
$604$	−3264.00	−0.219885
$605$	0	0
$606$	−6864.00	−0.460117
$607$	−12668.0	−0.847081	−0.423541	−	0.905877i	$-0.639213\pi$
$607$	−12668.0	−0.847081	−0.423541	+	0.905877i	$0.639213\pi$
$608$	−960.000	−0.0640348
$609$	2850.00	0.189635
$610$	0	0
$611$	−3510.00	−0.232405
$612$	−828.000	−0.0546894
$613$	11491.0	0.757124	0.378562	−	0.925576i	$-0.376419\pi$
$613$	11491.0	0.757124	0.378562	+	0.925576i	$0.376419\pi$
$614$	8526.00	0.560393
$615$	0	0
$616$	1400.00	0.0915708
$617$	23250.0	1.51703	0.758517	−	0.651653i	$-0.225924\pi$
$617$	23250.0	1.51703	0.758517	+	0.651653i	$0.225924\pi$
$618$	−4176.00	−0.271818
$619$	−20050.0	−1.30190	−0.650951	−	0.759120i	$-0.725630\pi$
$619$	−20050.0	−1.30190	−0.650951	+	0.759120i	$0.725630\pi$
$620$	0	0
$621$	−1701.00	−0.109918
$622$	888.000	0.0572437
$623$	5095.00	0.327651
$624$	624.000	0.0400320
$625$	0	0
$626$	8484.00	0.541675
$627$	3150.00	0.200636
$628$	5192.00	0.329910
$629$	989.000	0.0626932
$630$	0	0
$631$	−48.0000	−0.00302829	−0.00151414	−	0.999999i	$-0.500482\pi$
$631$	−48.0000	−0.00302829	−0.00151414	+	0.999999i	$0.500482\pi$
$632$	1720.00	0.108256
$633$	−10716.0	−0.672864
$634$	5472.00	0.342777
$635$	0	0
$636$	2316.00	0.144395
$637$	−4134.00	−0.257135
$638$	13300.0	0.825317
$639$	−8091.00	−0.500900
$640$	0	0
$641$	912.000	0.0561963	0.0280982	−	0.999605i	$-0.491055\pi$
$641$	912.000	0.0561963	0.0280982	+	0.999605i	$0.491055\pi$
$642$	8118.00	0.499053
$643$	−13877.0	−0.851097	−0.425549	−	0.904936i	$-0.639919\pi$
$643$	−13877.0	−0.851097	−0.425549	+	0.904936i	$0.639919\pi$
$644$	1260.00	0.0770978
$645$	0	0
$646$	1380.00	0.0840486
$647$	15987.0	0.971428	0.485714	−	0.874118i	$-0.338560\pi$
$647$	15987.0	0.971428	0.485714	+	0.874118i	$0.338560\pi$
$648$	648.000	0.0392837
$649$	7000.00	0.423381
$650$	0	0
$651$	−4950.00	−0.298012
$652$	−12452.0	−0.747942
$653$	−10542.0	−0.631762	−0.315881	−	0.948799i	$-0.602300\pi$
$653$	−10542.0	−0.631762	−0.315881	+	0.948799i	$0.602300\pi$
$654$	3024.00	0.180807
$655$	0	0
$656$	−7568.00	−0.450428
$657$	−1386.00	−0.0823029
$658$	2700.00	0.159965
$659$	22820.0	1.34892	0.674462	−	0.738310i	$-0.264376\pi$
$659$	22820.0	1.34892	0.674462	+	0.738310i	$0.264376\pi$
$660$	0	0
$661$	6360.00	0.374244	0.187122	−	0.982337i	$-0.440084\pi$
$661$	6360.00	0.374244	0.187122	+	0.982337i	$0.440084\pi$
$662$	12296.0	0.721900
$663$	−897.000	−0.0525439
$664$	10464.0	0.611569
$665$	0	0
$666$	−774.000	−0.0450329
$667$	11970.0	0.694873
$668$	688.000	0.0398496
$669$	−15744.0	−0.909863
$670$	0	0
$671$	23765.0	1.36727
$672$	−480.000	−0.0275542
$673$	32554.0	1.86458	0.932292	−	0.361708i	$-0.117806\pi$
$673$	32554.0	1.86458	0.932292	+	0.361708i	$0.117806\pi$
$674$	−8032.00	−0.459022
$675$	0	0
$676$	676.000	0.0384615
$677$	7065.00	0.401078	0.200539	−	0.979686i	$-0.435731\pi$
$677$	7065.00	0.401078	0.200539	+	0.979686i	$0.435731\pi$
$678$	−10740.0	−0.608359
$679$	−2135.00	−0.120668
$680$	0	0
$681$	−17430.0	−0.980792
$682$	−23100.0	−1.29699
$683$	−8236.00	−0.461408	−0.230704	−	0.973024i	$-0.574103\pi$
$683$	−8236.00	−0.461408	−0.230704	+	0.973024i	$0.574103\pi$
$684$	−1080.00	−0.0603726
$685$	0	0
$686$	6610.00	0.367888
$687$	15834.0	0.879337
$688$	3712.00	0.205696
$689$	2509.00	0.138730
$690$	0	0
$691$	23242.0	1.27955	0.639774	−	0.768563i	$-0.279028\pi$
$691$	23242.0	1.27955	0.639774	+	0.768563i	$0.279028\pi$
$692$	7928.00	0.435516
$693$	1575.00	0.0863338
$694$	−14598.0	−0.798462
$695$	0	0
$696$	−4560.00	−0.248342
$697$	10879.0	0.591207
$698$	232.000	0.0125807
$699$	15273.0	0.826435
$700$	0	0
$701$	−17308.0	−0.932545	−0.466273	−	0.884641i	$-0.654403\pi$
$701$	−17308.0	−0.932545	−0.466273	+	0.884641i	$0.654403\pi$
$702$	702.000	0.0377426
$703$	1290.00	0.0692081
$704$	−2240.00	−0.119919
$705$	0	0
$706$	13756.0	0.733306
$707$	5720.00	0.304275
$708$	−2400.00	−0.127398
$709$	−4252.00	−0.225229	−0.112614	−	0.993639i	$-0.535922\pi$
$709$	−4252.00	−0.225229	−0.112614	+	0.993639i	$0.535922\pi$
$710$	0	0
$711$	1935.00	0.102065
$712$	−8152.00	−0.429086
$713$	−20790.0	−1.09199
$714$	690.000	0.0361661
$715$	0	0
$716$	11960.0	0.624254
$717$	13647.0	0.710818
$718$	9312.00	0.484012
$719$	−35424.0	−1.83740	−0.918701	−	0.394953i	$-0.870761\pi$
$719$	−35424.0	−1.83740	−0.918701	+	0.394953i	$0.870761\pi$
$720$	0	0
$721$	3480.00	0.179753
$722$	−11918.0	−0.614324
$723$	−13602.0	−0.699673
$724$	7540.00	0.387047
$725$	0	0
$726$	−636.000	−0.0325126
$727$	−3754.00	−0.191511	−0.0957553	−	0.995405i	$-0.530527\pi$
$727$	−3754.00	−0.191511	−0.0957553	+	0.995405i	$0.530527\pi$
$728$	−520.000	−0.0264732
$729$	729.000	0.0370370
$730$	0	0
$731$	−5336.00	−0.269985
$732$	−8148.00	−0.411419
$733$	35425.0	1.78506	0.892532	−	0.450984i	$-0.148927\pi$
$733$	35425.0	1.78506	0.892532	+	0.450984i	$0.148927\pi$
$734$	11280.0	0.567238
$735$	0	0
$736$	−2016.00	−0.100966
$737$	−420.000	−0.0209917
$738$	−8514.00	−0.424668
$739$	−7170.00	−0.356905	−0.178452	−	0.983949i	$-0.557109\pi$
$739$	−7170.00	−0.356905	−0.178452	+	0.983949i	$0.557109\pi$
$740$	0	0
$741$	−1170.00	−0.0580041
$742$	−1930.00	−0.0954886
$743$	−35946.0	−1.77487	−0.887437	−	0.460930i	$-0.847516\pi$
$743$	−35946.0	−1.77487	−0.887437	+	0.460930i	$0.847516\pi$
$744$	7920.00	0.390271
$745$	0	0
$746$	8320.00	0.408334
$747$	11772.0	0.576593
$748$	3220.00	0.157400
$749$	−6765.00	−0.330024
$750$	0	0
$751$	−20791.0	−1.01022	−0.505109	−	0.863055i	$-0.668548\pi$
$751$	−20791.0	−1.01022	−0.505109	+	0.863055i	$0.668548\pi$
$752$	−4320.00	−0.209487
$753$	−18432.0	−0.892031
$754$	−4940.00	−0.238600
$755$	0	0
$756$	−540.000	−0.0259783
$757$	10536.0	0.505862	0.252931	−	0.967484i	$-0.418605\pi$
$757$	10536.0	0.505862	0.252931	+	0.967484i	$0.418605\pi$
$758$	−15708.0	−0.752692
$759$	6615.00	0.316350
$760$	0	0
$761$	6778.00	0.322868	0.161434	−	0.986884i	$-0.448388\pi$
$761$	6778.00	0.322868	0.161434	+	0.986884i	$0.448388\pi$
$762$	−7836.00	−0.372531
$763$	−2520.00	−0.119568
$764$	−2064.00	−0.0977394
$765$	0	0
$766$	−2412.00	−0.113772
$767$	−2600.00	−0.122400
$768$	768.000	0.0360844
$769$	33436.0	1.56792	0.783962	−	0.620809i	$-0.213196\pi$
$769$	33436.0	1.56792	0.783962	+	0.620809i	$0.213196\pi$
$770$	0	0
$771$	846.000	0.0395174
$772$	10852.0	0.505922
$773$	13972.0	0.650114	0.325057	−	0.945694i	$-0.394617\pi$
$773$	13972.0	0.650114	0.325057	+	0.945694i	$0.394617\pi$
$774$	4176.00	0.193932
$775$	0	0
$776$	3416.00	0.158025
$777$	645.000	0.0297802
$778$	−1904.00	−0.0877400
$779$	14190.0	0.652644
$780$	0	0
$781$	31465.0	1.44162
$782$	2898.00	0.132522
$783$	−5130.00	−0.234140
$784$	−5088.00	−0.231778
$785$	0	0
$786$	−10308.0	−0.467779
$787$	38132.0	1.72714	0.863570	−	0.504229i	$-0.168223\pi$
$787$	38132.0	1.72714	0.863570	+	0.504229i	$0.168223\pi$
$788$	−4464.00	−0.201806
$789$	−5208.00	−0.234993
$790$	0	0
$791$	8950.00	0.402308
$792$	−2520.00	−0.113061
$793$	−8827.00	−0.395279
$794$	−11494.0	−0.513737
$795$	0	0
$796$	−4656.00	−0.207321
$797$	6259.00	0.278175	0.139087	−	0.990280i	$-0.455583\pi$
$797$	6259.00	0.278175	0.139087	+	0.990280i	$0.455583\pi$
$798$	900.000	0.0399244
$799$	6210.00	0.274961
$800$	0	0
$801$	−9171.00	−0.404546
$802$	23916.0	1.05300
$803$	5390.00	0.236873
$804$	144.000	0.00631653
$805$	0	0
$806$	8580.00	0.374960
$807$	19908.0	0.868395
$808$	−9152.00	−0.398473
$809$	−2026.00	−0.0880474	−0.0440237	−	0.999030i	$-0.514018\pi$
$809$	−2026.00	−0.0880474	−0.0440237	+	0.999030i	$0.514018\pi$
$810$	0	0
$811$	−5888.00	−0.254939	−0.127470	−	0.991842i	$-0.540686\pi$
$811$	−5888.00	−0.254939	−0.127470	+	0.991842i	$0.540686\pi$
$812$	3800.00	0.164229
$813$	318.000	0.0137180
$814$	3010.00	0.129607
$815$	0	0
$816$	−1104.00	−0.0473624
$817$	−6960.00	−0.298041
$818$	29756.0	1.27188
$819$	−585.000	−0.0249592
$820$	0	0
$821$	−31957.0	−1.35847	−0.679237	−	0.733919i	$-0.737689\pi$
$821$	−31957.0	−1.35847	−0.679237	+	0.733919i	$0.737689\pi$
$822$	2628.00	0.111511
$823$	40972.0	1.73535	0.867676	−	0.497131i	$-0.165613\pi$
$823$	40972.0	1.73535	0.867676	+	0.497131i	$0.165613\pi$
$824$	−5568.00	−0.235401
$825$	0	0
$826$	2000.00	0.0842481
$827$	20934.0	0.880226	0.440113	−	0.897943i	$-0.354938\pi$
$827$	20934.0	0.880226	0.440113	+	0.897943i	$0.354938\pi$
$828$	−2268.00	−0.0951914
$829$	−21994.0	−0.921451	−0.460726	−	0.887543i	$-0.652411\pi$
$829$	−21994.0	−0.921451	−0.460726	+	0.887543i	$0.652411\pi$
$830$	0	0
$831$	13098.0	0.546768
$832$	832.000	0.0346688
$833$	7314.00	0.304220
$834$	4326.00	0.179613
$835$	0	0
$836$	4200.00	0.173756
$837$	8910.00	0.367951
$838$	6356.00	0.262010
$839$	19925.0	0.819890	0.409945	−	0.912110i	$-0.365548\pi$
$839$	19925.0	0.819890	0.409945	+	0.912110i	$0.365548\pi$
$840$	0	0
$841$	11711.0	0.480175
$842$	−8824.00	−0.361158
$843$	−12798.0	−0.522878
$844$	−14288.0	−0.582717
$845$	0	0
$846$	−4860.00	−0.197506
$847$	530.000	0.0215006
$848$	3088.00	0.125050
$849$	9228.00	0.373032
$850$	0	0
$851$	2709.00	0.109123
$852$	−10788.0	−0.433792
$853$	−29821.0	−1.19701	−0.598506	−	0.801118i	$-0.704239\pi$
$853$	−29821.0	−1.19701	−0.598506	+	0.801118i	$0.704239\pi$
$854$	6790.00	0.272071
$855$	0	0
$856$	10824.0	0.432192
$857$	−469.000	−0.0186940	−0.00934699	−	0.999956i	$-0.502975\pi$
$857$	−469.000	−0.0186940	−0.00934699	+	0.999956i	$0.502975\pi$
$858$	−2730.00	−0.108625
$859$	−26595.0	−1.05636	−0.528178	−	0.849134i	$-0.677125\pi$
$859$	−26595.0	−1.05636	−0.528178	+	0.849134i	$0.677125\pi$
$860$	0	0
$861$	7095.00	0.280833
$862$	18432.0	0.728302
$863$	−174.000	−0.00686330	−0.00343165	−	0.999994i	$-0.501092\pi$
$863$	−174.000	−0.00686330	−0.00343165	+	0.999994i	$0.501092\pi$
$864$	864.000	0.0340207
$865$	0	0
$866$	−5072.00	−0.199023
$867$	−13152.0	−0.515185
$868$	−6600.00	−0.258086
$869$	−7525.00	−0.293749
$870$	0	0
$871$	156.000	0.00606872
$872$	4032.00	0.156583
$873$	3843.00	0.148987
$874$	3780.00	0.146293
$875$	0	0
$876$	−1848.00	−0.0712764
$877$	18398.0	0.708388	0.354194	−	0.935172i	$-0.384755\pi$
$877$	18398.0	0.708388	0.354194	+	0.935172i	$0.384755\pi$
$878$	−3622.00	−0.139222
$879$	−21144.0	−0.811342
$880$	0	0
$881$	−17946.0	−0.686284	−0.343142	−	0.939284i	$-0.611491\pi$
$881$	−17946.0	−0.686284	−0.343142	+	0.939284i	$0.611491\pi$
$882$	−5724.00	−0.218523
$883$	27544.0	1.04975	0.524875	−	0.851179i	$-0.324112\pi$
$883$	27544.0	1.04975	0.524875	+	0.851179i	$0.324112\pi$
$884$	−1196.00	−0.0455043
$885$	0	0
$886$	−29486.0	−1.11806
$887$	10967.0	0.415147	0.207574	−	0.978219i	$-0.433443\pi$
$887$	10967.0	0.415147	0.207574	+	0.978219i	$0.433443\pi$
$888$	−1032.00	−0.0389996
$889$	6530.00	0.246355
$890$	0	0
$891$	−2835.00	−0.106595
$892$	−20992.0	−0.787964
$893$	8100.00	0.303534
$894$	174.000	0.00650943
$895$	0	0
$896$	−640.000	−0.0238626
$897$	−2457.00	−0.0914569
$898$	1998.00	0.0742474
$899$	−62700.0	−2.32610
$900$	0	0
$901$	−4439.00	−0.164134
$902$	33110.0	1.22222
$903$	−3480.00	−0.128247
$904$	−14320.0	−0.526854
$905$	0	0
$906$	−4896.00	−0.179535
$907$	23414.0	0.857166	0.428583	−	0.903503i	$-0.359013\pi$
$907$	23414.0	0.857166	0.428583	+	0.903503i	$0.359013\pi$
$908$	−23240.0	−0.849390
$909$	−10296.0	−0.375684
$910$	0	0
$911$	−14000.0	−0.509156	−0.254578	−	0.967052i	$-0.581936\pi$
$911$	−14000.0	−0.509156	−0.254578	+	0.967052i	$0.581936\pi$
$912$	−1440.00	−0.0522842
$913$	−45780.0	−1.65947
$914$	−36994.0	−1.33879
$915$	0	0
$916$	21112.0	0.761529
$917$	8590.00	0.309342
$918$	−1242.00	−0.0446537
$919$	7471.00	0.268167	0.134084	−	0.990970i	$-0.457191\pi$
$919$	7471.00	0.268167	0.134084	+	0.990970i	$0.457191\pi$
$920$	0	0
$921$	12789.0	0.457559
$922$	7902.00	0.282254
$923$	−11687.0	−0.416774
$924$	2100.00	0.0747672
$925$	0	0
$926$	1894.00	0.0672146
$927$	−6264.00	−0.221938
$928$	−6080.00	−0.215071
$929$	15861.0	0.560153	0.280077	−	0.959978i	$-0.409640\pi$
$929$	15861.0	0.560153	0.280077	+	0.959978i	$0.409640\pi$
$930$	0	0
$931$	9540.00	0.335833
$932$	20364.0	0.715714
$933$	1332.00	0.0467393
$934$	−8318.00	−0.291406
$935$	0	0
$936$	936.000	0.0326860
$937$	7494.00	0.261279	0.130639	−	0.991430i	$-0.458297\pi$
$937$	7494.00	0.261279	0.130639	+	0.991430i	$0.458297\pi$
$938$	−120.000	−0.00417712
$939$	12726.0	0.442276
$940$	0	0
$941$	−29995.0	−1.03912	−0.519558	−	0.854435i	$-0.673904\pi$
$941$	−29995.0	−1.03912	−0.519558	+	0.854435i	$0.673904\pi$
$942$	7788.00	0.269370
$943$	29799.0	1.02904
$944$	−3200.00	−0.110330
$945$	0	0
$946$	−16240.0	−0.558148
$947$	20792.0	0.713463	0.356731	−	0.934207i	$-0.383891\pi$
$947$	20792.0	0.713463	0.356731	+	0.934207i	$0.383891\pi$
$948$	2580.00	0.0883908
$949$	−2002.00	−0.0684802
$950$	0	0
$951$	8208.00	0.279877
$952$	920.000	0.0313208
$953$	−32895.0	−1.11813	−0.559063	−	0.829125i	$-0.688839\pi$
$953$	−32895.0	−1.11813	−0.559063	+	0.829125i	$0.688839\pi$
$954$	3474.00	0.117898
$955$	0	0
$956$	18196.0	0.615587
$957$	19950.0	0.673868
$958$	28270.0	0.953405
$959$	−2190.00	−0.0737422
$960$	0	0
$961$	79109.0	2.65547
$962$	−1118.00	−0.0374696
$963$	12177.0	0.407475
$964$	−18136.0	−0.605935
$965$	0	0
$966$	1890.00	0.0629501
$967$	37304.0	1.24055	0.620277	−	0.784383i	$-0.287020\pi$
$967$	37304.0	1.24055	0.620277	+	0.784383i	$0.287020\pi$
$968$	−848.000	−0.0281568
$969$	2070.00	0.0686254
$970$	0	0
$971$	−26248.0	−0.867496	−0.433748	−	0.901034i	$-0.642809\pi$
$971$	−26248.0	−0.867496	−0.433748	+	0.901034i	$0.642809\pi$
$972$	972.000	0.0320750
$973$	−3605.00	−0.118778
$974$	15218.0	0.500633
$975$	0	0
$976$	−10864.0	−0.356299
$977$	18804.0	0.615756	0.307878	−	0.951426i	$-0.400381\pi$
$977$	18804.0	0.615756	0.307878	+	0.951426i	$0.400381\pi$
$978$	−18678.0	−0.610692
$979$	35665.0	1.16431
$980$	0	0
$981$	4536.00	0.147628
$982$	−26640.0	−0.865699
$983$	−26228.0	−0.851010	−0.425505	−	0.904956i	$-0.639904\pi$
$983$	−26228.0	−0.851010	−0.425505	+	0.904956i	$0.639904\pi$
$984$	−11352.0	−0.367773
$985$	0	0
$986$	8740.00	0.282290
$987$	4050.00	0.130611
$988$	−1560.00	−0.0502330
$989$	−14616.0	−0.469931
$990$	0	0
$991$	23757.0	0.761520	0.380760	−	0.924674i	$-0.375662\pi$
$991$	23757.0	0.761520	0.380760	+	0.924674i	$0.375662\pi$
$992$	10560.0	0.337984
$993$	18444.0	0.589429
$994$	8990.00	0.286867
$995$	0	0
$996$	15696.0	0.499344
$997$	−38356.0	−1.21840	−0.609201	−	0.793016i	$-0.708510\pi$
$997$	−38356.0	−1.21840	−0.609201	+	0.793016i	$0.708510\pi$
$998$	−6020.00	−0.190942
$999$	−1161.00	−0.0367692

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.4.a.p.1.1		1
5.4	even	2		390.4.a.b.1.1	✓	1
15.14	odd	2		1170.4.a.j.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.4.a.b.1.1	✓	1	5.4	even	2
1170.4.a.j.1.1		1	15.14	odd	2
1950.4.a.p.1.1		1	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1950.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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