LMFDB - Embedded newform 950.6.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,6,Mod(1,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("950.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	950.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:	$152.364628822$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	950.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+4.00000 q^{2} +16.0000 q^{3} +16.0000 q^{4} +64.0000 q^{6} +44.0000 q^{7} +64.0000 q^{8} +13.0000 q^{9} +O(q^{10})$

\(q+4.00000 q^{2} +16.0000 q^{3} +16.0000 q^{4} +64.0000 q^{6} +44.0000 q^{7} +64.0000 q^{8} +13.0000 q^{9} -236.000 q^{11} +256.000 q^{12} -1110.00 q^{13} +176.000 q^{14} +256.000 q^{16} +1358.00 q^{17} +52.0000 q^{18} +361.000 q^{19} +704.000 q^{21} -944.000 q^{22} -3292.00 q^{23} +1024.00 q^{24} -4440.00 q^{26} -3680.00 q^{27} +704.000 q^{28} -66.0000 q^{29} +6696.00 q^{31} +1024.00 q^{32} -3776.00 q^{33} +5432.00 q^{34} +208.000 q^{36} +5282.00 q^{37} +1444.00 q^{38} -17760.0 q^{39} -21110.0 q^{41} +2816.00 q^{42} +7728.00 q^{43} -3776.00 q^{44} -13168.0 q^{46} -20860.0 q^{47} +4096.00 q^{48} -14871.0 q^{49} +21728.0 q^{51} -17760.0 q^{52} +32722.0 q^{53} -14720.0 q^{54} +2816.00 q^{56} +5776.00 q^{57} -264.000 q^{58} -17636.0 q^{59} -53170.0 q^{61} +26784.0 q^{62} +572.000 q^{63} +4096.00 q^{64} -15104.0 q^{66} -17400.0 q^{67} +21728.0 q^{68} -52672.0 q^{69} -49456.0 q^{71} +832.000 q^{72} -61162.0 q^{73} +21128.0 q^{74} +5776.00 q^{76} -10384.0 q^{77} -71040.0 q^{78} -71600.0 q^{79} -62039.0 q^{81} -84440.0 q^{82} +10504.0 q^{83} +11264.0 q^{84} +30912.0 q^{86} -1056.00 q^{87} -15104.0 q^{88} +114058. q^{89} -48840.0 q^{91} -52672.0 q^{92} +107136. q^{93} -83440.0 q^{94} +16384.0 q^{96} +81430.0 q^{97} -59484.0 q^{98} -3068.00 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	4.00000	0.707107
$2$	4.00000	0.707107
$3$	16.0000	1.02640	0.513200	−	0.858269i	$-0.328460\pi$
$3$	16.0000	1.02640	0.513200	+	0.858269i	$0.328460\pi$
$4$	16.0000	0.500000
$5$	0	0
$5$	0	0
$6$	64.0000	0.725775
$7$	44.0000	0.339397	0.169698	−	0.985496i	$-0.445721\pi$
$7$	44.0000	0.339397	0.169698	+	0.985496i	$0.445721\pi$
$8$	64.0000	0.353553
$9$	13.0000	0.0534979
$10$	0	0
$11$	−236.000	−0.588072	−0.294036	−	0.955794i	$-0.594999\pi$
$11$	−236.000	−0.588072	−0.294036	+	0.955794i	$0.594999\pi$
$12$	256.000	0.513200
$13$	−1110.00	−1.82165	−0.910824	−	0.412794i	$-0.864553\pi$
$13$	−1110.00	−1.82165	−0.910824	+	0.412794i	$0.864553\pi$
$14$	176.000	0.239990
$15$	0	0
$16$	256.000	0.250000
$17$	1358.00	1.13967	0.569833	−	0.821761i	$-0.307008\pi$
$17$	1358.00	1.13967	0.569833	+	0.821761i	$0.307008\pi$
$18$	52.0000	0.0378288
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	0	0
$21$	704.000	0.348357
$22$	−944.000	−0.415829
$23$	−3292.00	−1.29760	−0.648799	−	0.760960i	$-0.724728\pi$
$23$	−3292.00	−1.29760	−0.648799	+	0.760960i	$0.724728\pi$
$24$	1024.00	0.362887
$25$	0	0
$26$	−4440.00	−1.28810
$27$	−3680.00	−0.971490
$28$	704.000	0.169698
$29$	−66.0000	−0.0145730	−0.00728650	−	0.999973i	$-0.502319\pi$
$29$	−66.0000	−0.0145730	−0.00728650	+	0.999973i	$0.502319\pi$
$30$	0	0
$31$	6696.00	1.25144	0.625722	−	0.780046i	$-0.284805\pi$
$31$	6696.00	1.25144	0.625722	+	0.780046i	$0.284805\pi$
$32$	1024.00	0.176777
$33$	−3776.00	−0.603597
$34$	5432.00	0.805865
$35$	0	0
$36$	208.000	0.0267490
$37$	5282.00	0.634299	0.317150	−	0.948376i	$-0.397274\pi$
$37$	5282.00	0.634299	0.317150	+	0.948376i	$0.397274\pi$
$38$	1444.00	0.162221
$39$	−17760.0	−1.86974
$40$	0	0
$41$	−21110.0	−1.96123	−0.980615	−	0.195944i	$-0.937223\pi$
$41$	−21110.0	−1.96123	−0.980615	+	0.195944i	$0.937223\pi$
$42$	2816.00	0.246326
$43$	7728.00	0.637376	0.318688	−	0.947860i	$-0.396758\pi$
$43$	7728.00	0.637376	0.318688	+	0.947860i	$0.396758\pi$
$44$	−3776.00	−0.294036
$45$	0	0
$46$	−13168.0	−0.917540
$47$	−20860.0	−1.37743	−0.688715	−	0.725032i	$-0.741825\pi$
$47$	−20860.0	−1.37743	−0.688715	+	0.725032i	$0.741825\pi$
$48$	4096.00	0.256600
$49$	−14871.0	−0.884810
$50$	0	0
$51$	21728.0	1.16975
$52$	−17760.0	−0.910824
$53$	32722.0	1.60011	0.800056	−	0.599926i	$-0.204803\pi$
$53$	32722.0	1.60011	0.800056	+	0.599926i	$0.204803\pi$
$54$	−14720.0	−0.686947
$55$	0	0
$56$	2816.00	0.119995
$57$	5776.00	0.235472
$58$	−264.000	−0.0103047
$59$	−17636.0	−0.659584	−0.329792	−	0.944054i	$-0.606979\pi$
$59$	−17636.0	−0.659584	−0.329792	+	0.944054i	$0.606979\pi$
$60$	0	0
$61$	−53170.0	−1.82954	−0.914770	−	0.403974i	$-0.867629\pi$
$61$	−53170.0	−1.82954	−0.914770	+	0.403974i	$0.867629\pi$
$62$	26784.0	0.884904
$63$	572.000	0.0181570
$64$	4096.00	0.125000
$65$	0	0
$66$	−15104.0	−0.426808
$67$	−17400.0	−0.473546	−0.236773	−	0.971565i	$-0.576090\pi$
$67$	−17400.0	−0.473546	−0.236773	+	0.971565i	$0.576090\pi$
$68$	21728.0	0.569833
$69$	−52672.0	−1.33186
$70$	0	0
$71$	−49456.0	−1.16432	−0.582161	−	0.813074i	$-0.697793\pi$
$71$	−49456.0	−1.16432	−0.582161	+	0.813074i	$0.697793\pi$
$72$	832.000	0.0189144
$73$	−61162.0	−1.34330	−0.671652	−	0.740866i	$-0.734415\pi$
$73$	−61162.0	−1.34330	−0.671652	+	0.740866i	$0.734415\pi$
$74$	21128.0	0.448517
$75$	0	0
$76$	5776.00	0.114708
$77$	−10384.0	−0.199590
$78$	−71040.0	−1.32211
$79$	−71600.0	−1.29076	−0.645380	−	0.763862i	$-0.723301\pi$
$79$	−71600.0	−1.29076	−0.645380	+	0.763862i	$0.723301\pi$
$80$	0	0
$81$	−62039.0	−1.05064
$82$	−84440.0	−1.38680
$83$	10504.0	0.167363	0.0836815	−	0.996493i	$-0.473332\pi$
$83$	10504.0	0.167363	0.0836815	+	0.996493i	$0.473332\pi$
$84$	11264.0	0.174178
$85$	0	0
$86$	30912.0	0.450693
$87$	−1056.00	−0.0149577
$88$	−15104.0	−0.207915
$89$	114058.	1.52634	0.763169	−	0.646199i	$-0.223642\pi$
$89$	114058.	1.52634	0.763169	+	0.646199i	$0.223642\pi$
$90$	0	0
$91$	−48840.0	−0.618261
$92$	−52672.0	−0.648799
$93$	107136.	1.28448
$94$	−83440.0	−0.973990
$95$	0	0
$96$	16384.0	0.181444
$97$	81430.0	0.878729	0.439365	−	0.898309i	$-0.355204\pi$
$97$	81430.0	0.878729	0.439365	+	0.898309i	$0.355204\pi$
$98$	−59484.0	−0.625655
$99$	−3068.00	−0.0314606
$100$	0	0
$101$	93398.0	0.911033	0.455517	−	0.890227i	$-0.349455\pi$
$101$	93398.0	0.911033	0.455517	+	0.890227i	$0.349455\pi$
$102$	86912.0	0.827141
$103$	−23316.0	−0.216551	−0.108276	−	0.994121i	$-0.534533\pi$
$103$	−23316.0	−0.216551	−0.108276	+	0.994121i	$0.534533\pi$
$104$	−71040.0	−0.644050
$105$	0	0
$106$	130888.	1.13145
$107$	83776.0	0.707392	0.353696	−	0.935360i	$-0.384925\pi$
$107$	83776.0	0.707392	0.353696	+	0.935360i	$0.384925\pi$
$108$	−58880.0	−0.485745
$109$	−69634.0	−0.561378	−0.280689	−	0.959799i	$-0.590563\pi$
$109$	−69634.0	−0.561378	−0.280689	+	0.959799i	$0.590563\pi$
$110$	0	0
$111$	84512.0	0.651045
$112$	11264.0	0.0848492
$113$	194006.	1.42929	0.714643	−	0.699490i	$-0.246589\pi$
$113$	194006.	1.42929	0.714643	+	0.699490i	$0.246589\pi$
$114$	23104.0	0.166504
$115$	0	0
$116$	−1056.00	−0.00728650
$117$	−14430.0	−0.0974545
$118$	−70544.0	−0.466396
$119$	59752.0	0.386799
$120$	0	0
$121$	−105355.	−0.654172
$122$	−212680.	−1.29368
$123$	−337760.	−2.01301
$124$	107136.	0.625722
$125$	0	0
$126$	2288.00	0.0128390
$127$	1532.00	0.00842848	0.00421424	−	0.999991i	$-0.498659\pi$
$127$	1532.00	0.00842848	0.00421424	+	0.999991i	$0.498659\pi$
$128$	16384.0	0.0883883
$129$	123648.	0.654203
$130$	0	0
$131$	−238260.	−1.21303	−0.606517	−	0.795071i	$-0.707434\pi$
$131$	−238260.	−1.21303	−0.606517	+	0.795071i	$0.707434\pi$
$132$	−60416.0	−0.301799
$133$	15884.0	0.0778629
$134$	−69600.0	−0.334848
$135$	0	0
$136$	86912.0	0.402933
$137$	−336954.	−1.53380	−0.766901	−	0.641766i	$-0.778202\pi$
$137$	−336954.	−1.53380	−0.766901	+	0.641766i	$0.778202\pi$
$138$	−210688.	−0.941764
$139$	−113524.	−0.498369	−0.249184	−	0.968456i	$-0.580162\pi$
$139$	−113524.	−0.498369	−0.249184	+	0.968456i	$0.580162\pi$
$140$	0	0
$141$	−333760.	−1.41380
$142$	−197824.	−0.823300
$143$	261960.	1.07126
$144$	3328.00	0.0133745
$145$	0	0
$146$	−244648.	−0.949860
$147$	−237936.	−0.908169
$148$	84512.0	0.317150
$149$	−510490.	−1.88374	−0.941871	−	0.335974i	$-0.890935\pi$
$149$	−510490.	−1.88374	−0.941871	+	0.335974i	$0.890935\pi$
$150$	0	0
$151$	381040.	1.35997	0.679983	−	0.733228i	$-0.261987\pi$
$151$	381040.	1.35997	0.679983	+	0.733228i	$0.261987\pi$
$152$	23104.0	0.0811107
$153$	17654.0	0.0609698
$154$	−41536.0	−0.141131
$155$	0	0
$156$	−284160.	−0.934870
$157$	−62142.0	−0.201204	−0.100602	−	0.994927i	$-0.532077\pi$
$157$	−62142.0	−0.201204	−0.100602	+	0.994927i	$0.532077\pi$
$158$	−286400.	−0.912705
$159$	523552.	1.64235
$160$	0	0
$161$	−144848.	−0.440401
$162$	−248156.	−0.742912
$163$	−454760.	−1.34064	−0.670322	−	0.742071i	$-0.733844\pi$
$163$	−454760.	−1.34064	−0.670322	+	0.742071i	$0.733844\pi$
$164$	−337760.	−0.980615
$165$	0	0
$166$	42016.0	0.118344
$167$	396852.	1.10113	0.550563	−	0.834793i	$-0.314413\pi$
$167$	396852.	1.10113	0.550563	+	0.834793i	$0.314413\pi$
$168$	45056.0	0.123163
$169$	860807.	2.31840
$170$	0	0
$171$	4693.00	0.0122733
$172$	123648.	0.318688
$173$	127626.	0.324208	0.162104	−	0.986774i	$-0.448172\pi$
$173$	127626.	0.324208	0.162104	+	0.986774i	$0.448172\pi$
$174$	−4224.00	−0.0105767
$175$	0	0
$176$	−60416.0	−0.147018
$177$	−282176.	−0.676997
$178$	456232.	1.07928
$179$	387220.	0.903286	0.451643	−	0.892199i	$-0.350838\pi$
$179$	387220.	0.903286	0.451643	+	0.892199i	$0.350838\pi$
$180$	0	0
$181$	−380538.	−0.863379	−0.431690	−	0.902022i	$-0.642082\pi$
$181$	−380538.	−0.863379	−0.431690	+	0.902022i	$0.642082\pi$
$182$	−195360.	−0.437177
$183$	−850720.	−1.87784
$184$	−210688.	−0.458770
$185$	0	0
$186$	428544.	0.908266
$187$	−320488.	−0.670205
$188$	−333760.	−0.688715
$189$	−161920.	−0.329721
$190$	0	0
$191$	−955112.	−1.89440	−0.947198	−	0.320649i	$-0.896099\pi$
$191$	−955112.	−1.89440	−0.947198	+	0.320649i	$0.896099\pi$
$192$	65536.0	0.128300
$193$	468694.	0.905725	0.452862	−	0.891580i	$-0.350403\pi$
$193$	468694.	0.905725	0.452862	+	0.891580i	$0.350403\pi$
$194$	325720.	0.621355
$195$	0	0
$196$	−237936.	−0.442405
$197$	493850.	0.906629	0.453314	−	0.891351i	$-0.350241\pi$
$197$	493850.	0.906629	0.453314	+	0.891351i	$0.350241\pi$
$198$	−12272.0	−0.0222460
$199$	955016.	1.70953	0.854767	−	0.519011i	$-0.173700\pi$
$199$	955016.	1.70953	0.854767	+	0.519011i	$0.173700\pi$
$200$	0	0
$201$	−278400.	−0.486048
$202$	373592.	0.644198
$203$	−2904.00	−0.00494603
$204$	347648.	0.584877
$205$	0	0
$206$	−93264.0	−0.153125
$207$	−42796.0	−0.0694188
$208$	−284160.	−0.455412
$209$	−85196.0	−0.134913
$210$	0	0
$211$	−342740.	−0.529979	−0.264989	−	0.964251i	$-0.585368\pi$
$211$	−342740.	−0.529979	−0.264989	+	0.964251i	$0.585368\pi$
$212$	523552.	0.800056
$213$	−791296.	−1.19506
$214$	335104.	0.500202
$215$	0	0
$216$	−235520.	−0.343474
$217$	294624.	0.424736
$218$	−278536.	−0.396954
$219$	−978592.	−1.37877
$220$	0	0
$221$	−1.50738e6	−2.07607
$222$	338048.	0.460358
$223$	1.29004e6	1.73716	0.868580	−	0.495549i	$-0.165033\pi$
$223$	1.29004e6	1.73716	0.868580	+	0.495549i	$0.165033\pi$
$224$	45056.0	0.0599974
$225$	0	0
$226$	776024.	1.01066
$227$	662680.	0.853570	0.426785	−	0.904353i	$-0.359646\pi$
$227$	662680.	0.853570	0.426785	+	0.904353i	$0.359646\pi$
$228$	92416.0	0.117736
$229$	1.34268e6	1.69193	0.845967	−	0.533236i	$-0.179024\pi$
$229$	1.34268e6	1.69193	0.845967	+	0.533236i	$0.179024\pi$
$230$	0	0
$231$	−166144.	−0.204859
$232$	−4224.00	−0.00515233
$233$	−419226.	−0.505893	−0.252946	−	0.967480i	$-0.581400\pi$
$233$	−419226.	−0.505893	−0.252946	+	0.967480i	$0.581400\pi$
$234$	−57720.0	−0.0689107
$235$	0	0
$236$	−282176.	−0.329792
$237$	−1.14560e6	−1.32484
$238$	239008.	0.273508
$239$	−302016.	−0.342007	−0.171004	−	0.985270i	$-0.554701\pi$
$239$	−302016.	−0.342007	−0.171004	+	0.985270i	$0.554701\pi$
$240$	0	0
$241$	−944942.	−1.04800	−0.524002	−	0.851717i	$-0.675561\pi$
$241$	−944942.	−1.04800	−0.524002	+	0.851717i	$0.675561\pi$
$242$	−421420.	−0.462569
$243$	−98384.0	−0.106883
$244$	−850720.	−0.914770
$245$	0	0
$246$	−1.35104e6	−1.42341
$247$	−400710.	−0.417915
$248$	428544.	0.442452
$249$	168064.	0.171781
$250$	0	0
$251$	518196.	0.519170	0.259585	−	0.965720i	$-0.416414\pi$
$251$	518196.	0.519170	0.259585	+	0.965720i	$0.416414\pi$
$252$	9152.00	0.00907851
$253$	776912.	0.763081
$254$	6128.00	0.00595984
$255$	0	0
$256$	65536.0	0.0625000
$257$	462102.	0.436420	0.218210	−	0.975902i	$-0.429978\pi$
$257$	462102.	0.436420	0.218210	+	0.975902i	$0.429978\pi$
$258$	494592.	0.462592
$259$	232408.	0.215279
$260$	0	0
$261$	−858.000	−0.000779625 0
$262$	−953040.	−0.857744
$263$	823764.	0.734367	0.367184	−	0.930148i	$-0.380322\pi$
$263$	823764.	0.734367	0.367184	+	0.930148i	$0.380322\pi$
$264$	−241664.	−0.213404
$265$	0	0
$266$	63536.0	0.0550574
$267$	1.82493e6	1.56663
$268$	−278400.	−0.236773
$269$	1.34473e6	1.13307	0.566534	−	0.824039i	$-0.308284\pi$
$269$	1.34473e6	1.13307	0.566534	+	0.824039i	$0.308284\pi$
$270$	0	0
$271$	1.47126e6	1.21693	0.608464	−	0.793581i	$-0.291786\pi$
$271$	1.47126e6	1.21693	0.608464	+	0.793581i	$0.291786\pi$
$272$	347648.	0.284916
$273$	−781440.	−0.634584
$274$	−1.34782e6	−1.08456
$275$	0	0
$276$	−842752.	−0.665928
$277$	−1.03154e6	−0.807770	−0.403885	−	0.914810i	$-0.632340\pi$
$277$	−1.03154e6	−0.807770	−0.403885	+	0.914810i	$0.632340\pi$
$278$	−454096.	−0.352400
$279$	87048.0	0.0669496
$280$	0	0
$281$	−1.15655e6	−0.873773	−0.436886	−	0.899517i	$-0.643919\pi$
$281$	−1.15655e6	−0.873773	−0.436886	+	0.899517i	$0.643919\pi$
$282$	−1.33504e6	−0.999704
$283$	−1.40507e6	−1.04288	−0.521438	−	0.853289i	$-0.674604\pi$
$283$	−1.40507e6	−1.04288	−0.521438	+	0.853289i	$0.674604\pi$
$284$	−791296.	−0.582161
$285$	0	0
$286$	1.04784e6	0.757495
$287$	−928840.	−0.665635
$288$	13312.0	0.00945719
$289$	424307.	0.298838
$290$	0	0
$291$	1.30288e6	0.901928
$292$	−978592.	−0.671652
$293$	−1.17381e6	−0.798780	−0.399390	−	0.916781i	$-0.630778\pi$
$293$	−1.17381e6	−0.798780	−0.399390	+	0.916781i	$0.630778\pi$
$294$	−951744.	−0.642173
$295$	0	0
$296$	338048.	0.224259
$297$	868480.	0.571306
$298$	−2.04196e6	−1.33201
$299$	3.65412e6	2.36377
$300$	0	0
$301$	340032.	0.216323
$302$	1.52416e6	0.961642
$303$	1.49437e6	0.935085
$304$	92416.0	0.0573539
$305$	0	0
$306$	70616.0	0.0431121
$307$	−2.16204e6	−1.30924	−0.654618	−	0.755960i	$-0.727170\pi$
$307$	−2.16204e6	−1.30924	−0.654618	+	0.755960i	$0.727170\pi$
$308$	−166144.	−0.0997948
$309$	−373056.	−0.222268
$310$	0	0
$311$	−2.52954e6	−1.48300	−0.741498	−	0.670955i	$-0.765884\pi$
$311$	−2.52954e6	−1.48300	−0.741498	+	0.670955i	$0.765884\pi$
$312$	−1.13664e6	−0.661053
$313$	2.45569e6	1.41681	0.708406	−	0.705806i	$-0.249415\pi$
$313$	2.45569e6	1.41681	0.708406	+	0.705806i	$0.249415\pi$
$314$	−248568.	−0.142273
$315$	0	0
$316$	−1.14560e6	−0.645380
$317$	−1.32653e6	−0.741430	−0.370715	−	0.928747i	$-0.620887\pi$
$317$	−1.32653e6	−0.741430	−0.370715	+	0.928747i	$0.620887\pi$
$318$	2.09421e6	1.16132
$319$	15576.0	0.00856997
$320$	0	0
$321$	1.34042e6	0.726068
$322$	−579392.	−0.311410
$323$	490238.	0.261457
$324$	−992624.	−0.525318
$325$	0	0
$326$	−1.81904e6	−0.947978
$327$	−1.11414e6	−0.576198
$328$	−1.35104e6	−0.693400
$329$	−917840.	−0.467495
$330$	0	0
$331$	−593436.	−0.297717	−0.148859	−	0.988858i	$-0.547560\pi$
$331$	−593436.	−0.297717	−0.148859	+	0.988858i	$0.547560\pi$
$332$	168064.	0.0836815
$333$	68666.0	0.0339337
$334$	1.58741e6	0.778614
$335$	0	0
$336$	180224.	0.0870892
$337$	−1.02295e6	−0.490661	−0.245330	−	0.969440i	$-0.578896\pi$
$337$	−1.02295e6	−0.490661	−0.245330	+	0.969440i	$0.578896\pi$
$338$	3.44323e6	1.63936
$339$	3.10410e6	1.46702
$340$	0	0
$341$	−1.58026e6	−0.735938
$342$	18772.0	0.00867851
$343$	−1.39383e6	−0.639698
$344$	494592.	0.225347
$345$	0	0
$346$	510504.	0.229250
$347$	1.66921e6	0.744195	0.372098	−	0.928194i	$-0.378639\pi$
$347$	1.66921e6	0.744195	0.372098	+	0.928194i	$0.378639\pi$
$348$	−16896.0	−0.00747887
$349$	−874610.	−0.384371	−0.192186	−	0.981359i	$-0.561558\pi$
$349$	−874610.	−0.384371	−0.192186	+	0.981359i	$0.561558\pi$
$350$	0	0
$351$	4.08480e6	1.76971
$352$	−241664.	−0.103957
$353$	−2.64981e6	−1.13182	−0.565911	−	0.824466i	$-0.691475\pi$
$353$	−2.64981e6	−1.13182	−0.565911	+	0.824466i	$0.691475\pi$
$354$	−1.12870e6	−0.478709
$355$	0	0
$356$	1.82493e6	0.763169
$357$	956032.	0.397010
$358$	1.54888e6	0.638720
$359$	−264.000	−0.000108110 0	−5.40552e−5	−	1.00000i	$-0.500017\pi$
$359$	−264.000	−0.000108110 0	−5.40552e−5		1.00000i	$0.500017\pi$
$360$	0	0
$361$	130321.	0.0526316
$362$	−1.52215e6	−0.610501
$363$	−1.68568e6	−0.671442
$364$	−781440.	−0.309131
$365$	0	0
$366$	−3.40288e6	−1.32783
$367$	−2.79547e6	−1.08340	−0.541701	−	0.840571i	$-0.682219\pi$
$367$	−2.79547e6	−1.08340	−0.541701	+	0.840571i	$0.682219\pi$
$368$	−842752.	−0.324400
$369$	−274430.	−0.104922
$370$	0	0
$371$	1.43977e6	0.543072
$372$	1.71418e6	0.642241
$373$	3.01002e6	1.12020	0.560102	−	0.828424i	$-0.310762\pi$
$373$	3.01002e6	1.12020	0.560102	+	0.828424i	$0.310762\pi$
$374$	−1.28195e6	−0.473907
$375$	0	0
$376$	−1.33504e6	−0.486995
$377$	73260.0	0.0265469
$378$	−647680.	−0.233148
$379$	−1.09421e6	−0.391294	−0.195647	−	0.980674i	$-0.562681\pi$
$379$	−1.09421e6	−0.391294	−0.195647	+	0.980674i	$0.562681\pi$
$380$	0	0
$381$	24512.0	0.00865100
$382$	−3.82045e6	−1.33954
$383$	2.20359e6	0.767597	0.383799	−	0.923417i	$-0.374616\pi$
$383$	2.20359e6	0.767597	0.383799	+	0.923417i	$0.374616\pi$
$384$	262144.	0.0907218
$385$	0	0
$386$	1.87478e6	0.640444
$387$	100464.	0.0340983
$388$	1.30288e6	0.439365
$389$	−3.75716e6	−1.25888	−0.629442	−	0.777047i	$-0.716717\pi$
$389$	−3.75716e6	−1.25888	−0.629442	+	0.777047i	$0.716717\pi$
$390$	0	0
$391$	−4.47054e6	−1.47883
$392$	−951744.	−0.312828
$393$	−3.81216e6	−1.24506
$394$	1.97540e6	0.641083
$395$	0	0
$396$	−49088.0	−0.0157303
$397$	1.08189e6	0.344514	0.172257	−	0.985052i	$-0.444894\pi$
$397$	1.08189e6	0.344514	0.172257	+	0.985052i	$0.444894\pi$
$398$	3.82006e6	1.20882
$399$	254144.	0.0799186
$400$	0	0
$401$	2.82741e6	0.878067	0.439034	−	0.898471i	$-0.355321\pi$
$401$	2.82741e6	0.878067	0.439034	+	0.898471i	$0.355321\pi$
$402$	−1.11360e6	−0.343688
$403$	−7.43256e6	−2.27969
$404$	1.49437e6	0.455517
$405$	0	0
$406$	−11616.0	−0.00349737
$407$	−1.24655e6	−0.373013
$408$	1.39059e6	0.413570
$409$	−703158.	−0.207847	−0.103924	−	0.994585i	$-0.533140\pi$
$409$	−703158.	−0.207847	−0.103924	+	0.994585i	$0.533140\pi$
$410$	0	0
$411$	−5.39126e6	−1.57429
$412$	−373056.	−0.108276
$413$	−775984.	−0.223861
$414$	−171184.	−0.0490865
$415$	0	0
$416$	−1.13664e6	−0.322025
$417$	−1.81638e6	−0.511526
$418$	−340784.	−0.0953978
$419$	−696972.	−0.193946	−0.0969729	−	0.995287i	$-0.530916\pi$
$419$	−696972.	−0.193946	−0.0969729	+	0.995287i	$0.530916\pi$
$420$	0	0
$421$	4.46906e6	1.22888	0.614442	−	0.788962i	$-0.289381\pi$
$421$	4.46906e6	1.22888	0.614442	+	0.788962i	$0.289381\pi$
$422$	−1.37096e6	−0.374752
$423$	−271180.	−0.0736897
$424$	2.09421e6	0.565725
$425$	0	0
$426$	−3.16518e6	−0.845036
$427$	−2.33948e6	−0.620940
$428$	1.34042e6	0.353696
$429$	4.19136e6	1.09954
$430$	0	0
$431$	−5.32026e6	−1.37956	−0.689779	−	0.724020i	$-0.742292\pi$
$431$	−5.32026e6	−1.37956	−0.689779	+	0.724020i	$0.742292\pi$
$432$	−942080.	−0.242873
$433$	−49338.0	−0.0126463	−0.00632313	−	0.999980i	$-0.502013\pi$
$433$	−49338.0	−0.0126463	−0.00632313	+	0.999980i	$0.502013\pi$
$434$	1.17850e6	0.300334
$435$	0	0
$436$	−1.11414e6	−0.280689
$437$	−1.18841e6	−0.297689
$438$	−3.91437e6	−0.974937
$439$	4.37879e6	1.08441	0.542204	−	0.840247i	$-0.317590\pi$
$439$	4.37879e6	1.08441	0.542204	+	0.840247i	$0.317590\pi$
$440$	0	0
$441$	−193323.	−0.0473355
$442$	−6.02952e6	−1.46800
$443$	4.02787e6	0.975139	0.487569	−	0.873084i	$-0.337884\pi$
$443$	4.02787e6	0.975139	0.487569	+	0.873084i	$0.337884\pi$
$444$	1.35219e6	0.325522
$445$	0	0
$446$	5.16014e6	1.22836
$447$	−8.16784e6	−1.93347
$448$	180224.	0.0424246
$449$	−673038.	−0.157552	−0.0787760	−	0.996892i	$-0.525101\pi$
$449$	−673038.	−0.157552	−0.0787760	+	0.996892i	$0.525101\pi$
$450$	0	0
$451$	4.98196e6	1.15334
$452$	3.10410e6	0.714643
$453$	6.09664e6	1.39587
$454$	2.65072e6	0.603565
$455$	0	0
$456$	369664.	0.0832521
$457$	2.18114e6	0.488532	0.244266	−	0.969708i	$-0.421453\pi$
$457$	2.18114e6	0.488532	0.244266	+	0.969708i	$0.421453\pi$
$458$	5.37071e6	1.19638
$459$	−4.99744e6	−1.10717
$460$	0	0
$461$	−1.76608e6	−0.387042	−0.193521	−	0.981096i	$-0.561991\pi$
$461$	−1.76608e6	−0.387042	−0.193521	+	0.981096i	$0.561991\pi$
$462$	−664576.	−0.144857
$463$	5.86576e6	1.27166	0.635831	−	0.771829i	$-0.280658\pi$
$463$	5.86576e6	1.27166	0.635831	+	0.771829i	$0.280658\pi$
$464$	−16896.0	−0.00364325
$465$	0	0
$466$	−1.67690e6	−0.357720
$467$	−3.43347e6	−0.728520	−0.364260	−	0.931297i	$-0.618678\pi$
$467$	−3.43347e6	−0.728520	−0.364260	+	0.931297i	$0.618678\pi$
$468$	−230880.	−0.0487272
$469$	−765600.	−0.160720
$470$	0	0
$471$	−994272.	−0.206516
$472$	−1.12870e6	−0.233198
$473$	−1.82381e6	−0.374823
$474$	−4.58240e6	−0.936801
$475$	0	0
$476$	956032.	0.193399
$477$	425386.	0.0856027
$478$	−1.20806e6	−0.241836
$479$	4.64218e6	0.924449	0.462224	−	0.886763i	$-0.347051\pi$
$479$	4.64218e6	0.924449	0.462224	+	0.886763i	$0.347051\pi$
$480$	0	0
$481$	−5.86302e6	−1.15547
$482$	−3.77977e6	−0.741050
$483$	−2.31757e6	−0.452027
$484$	−1.68568e6	−0.327086
$485$	0	0
$486$	−393536.	−0.0755777
$487$	5.23205e6	0.999654	0.499827	−	0.866125i	$-0.333397\pi$
$487$	5.23205e6	0.999654	0.499827	+	0.866125i	$0.333397\pi$
$488$	−3.40288e6	−0.646840
$489$	−7.27616e6	−1.37604
$490$	0	0
$491$	7.36592e6	1.37887	0.689435	−	0.724347i	$-0.257859\pi$
$491$	7.36592e6	1.37887	0.689435	+	0.724347i	$0.257859\pi$
$492$	−5.40416e6	−1.00650
$493$	−89628.0	−0.0166083
$494$	−1.60284e6	−0.295510
$495$	0	0
$496$	1.71418e6	0.312861
$497$	−2.17606e6	−0.395167
$498$	672256.	0.121468
$499$	−2.27004e6	−0.408115	−0.204058	−	0.978959i	$-0.565413\pi$
$499$	−2.27004e6	−0.408115	−0.204058	+	0.978959i	$0.565413\pi$
$500$	0	0
$501$	6.34963e6	1.13020
$502$	2.07278e6	0.367109
$503$	625364.	0.110208	0.0551040	−	0.998481i	$-0.482451\pi$
$503$	625364.	0.110208	0.0551040	+	0.998481i	$0.482451\pi$
$504$	36608.0	0.00641948
$505$	0	0
$506$	3.10765e6	0.539580
$507$	1.37729e7	2.37961
$508$	24512.0	0.00421424
$509$	226430.	0.0387382	0.0193691	−	0.999812i	$-0.493834\pi$
$509$	226430.	0.0387382	0.0193691	+	0.999812i	$0.493834\pi$
$510$	0	0
$511$	−2.69113e6	−0.455913
$512$	262144.	0.0441942
$513$	−1.32848e6	−0.222875
$514$	1.84841e6	0.308596
$515$	0	0
$516$	1.97837e6	0.327102
$517$	4.92296e6	0.810028
$518$	929632.	0.152225
$519$	2.04202e6	0.332767
$520$	0	0
$521$	−1.09782e7	−1.77188	−0.885942	−	0.463795i	$-0.846487\pi$
$521$	−1.09782e7	−1.77188	−0.885942	+	0.463795i	$0.846487\pi$
$522$	−3432.00	−0.000551278 0
$523$	−4.83090e6	−0.772279	−0.386139	−	0.922440i	$-0.626192\pi$
$523$	−4.83090e6	−0.772279	−0.386139	+	0.922440i	$0.626192\pi$
$524$	−3.81216e6	−0.606517
$525$	0	0
$526$	3.29506e6	0.519276
$527$	9.09317e6	1.42623
$528$	−966656.	−0.150899
$529$	4.40092e6	0.683761
$530$	0	0
$531$	−229268.	−0.0352864
$532$	254144.	0.0389315
$533$	2.34321e7	3.57267
$534$	7.29971e6	1.10778
$535$	0	0
$536$	−1.11360e6	−0.167424
$537$	6.19552e6	0.927133
$538$	5.37894e6	0.801200
$539$	3.50956e6	0.520332
$540$	0	0
$541$	−1.08458e7	−1.59319	−0.796595	−	0.604513i	$-0.793368\pi$
$541$	−1.08458e7	−1.59319	−0.796595	+	0.604513i	$0.793368\pi$
$542$	5.88502e6	0.860498
$543$	−6.08861e6	−0.886173
$544$	1.39059e6	0.201466
$545$	0	0
$546$	−3.12576e6	−0.448719
$547$	8.61762e6	1.23146	0.615728	−	0.787958i	$-0.288862\pi$
$547$	8.61762e6	1.23146	0.615728	+	0.787958i	$0.288862\pi$
$548$	−5.39126e6	−0.766901
$549$	−691210.	−0.0978767
$550$	0	0
$551$	−23826.0	−0.00334328
$552$	−3.37101e6	−0.470882
$553$	−3.15040e6	−0.438079
$554$	−4.12617e6	−0.571179
$555$	0	0
$556$	−1.81638e6	−0.249184
$557$	1.32556e7	1.81035	0.905175	−	0.425039i	$-0.139740\pi$
$557$	1.32556e7	1.81035	0.905175	+	0.425039i	$0.139740\pi$
$558$	348192.	0.0473405
$559$	−8.57808e6	−1.16108
$560$	0	0
$561$	−5.12781e6	−0.687899
$562$	−4.62620e6	−0.617851
$563$	−137232.	−0.0182467	−0.00912335	−	0.999958i	$-0.502904\pi$
$563$	−137232.	−0.0182467	−0.00912335	+	0.999958i	$0.502904\pi$
$564$	−5.34016e6	−0.706898
$565$	0	0
$566$	−5.62029e6	−0.737424
$567$	−2.72972e6	−0.356582
$568$	−3.16518e6	−0.411650
$569$	−3.34613e6	−0.433274	−0.216637	−	0.976252i	$-0.569509\pi$
$569$	−3.34613e6	−0.433274	−0.216637	+	0.976252i	$0.569509\pi$
$570$	0	0
$571$	4.16700e6	0.534851	0.267426	−	0.963579i	$-0.413827\pi$
$571$	4.16700e6	0.534851	0.267426	+	0.963579i	$0.413827\pi$
$572$	4.19136e6	0.535630
$573$	−1.52818e7	−1.94441
$574$	−3.71536e6	−0.470675
$575$	0	0
$576$	53248.0	0.00668724
$577$	2.68605e6	0.335872	0.167936	−	0.985798i	$-0.446290\pi$
$577$	2.68605e6	0.335872	0.167936	+	0.985798i	$0.446290\pi$
$578$	1.69723e6	0.211310
$579$	7.49910e6	0.929636
$580$	0	0
$581$	462176.	0.0568024
$582$	5.21152e6	0.637760
$583$	−7.72239e6	−0.940980
$584$	−3.91437e6	−0.474930
$585$	0	0
$586$	−4.69522e6	−0.564823
$587$	−7.14071e6	−0.855355	−0.427677	−	0.903931i	$-0.640668\pi$
$587$	−7.14071e6	−0.855355	−0.427677	+	0.903931i	$0.640668\pi$
$588$	−3.80698e6	−0.454085
$589$	2.41726e6	0.287101
$590$	0	0
$591$	7.90160e6	0.930564
$592$	1.35219e6	0.158575
$593$	2.67419e6	0.312288	0.156144	−	0.987734i	$-0.450094\pi$
$593$	2.67419e6	0.312288	0.156144	+	0.987734i	$0.450094\pi$
$594$	3.47392e6	0.403974
$595$	0	0
$596$	−8.16784e6	−0.941871
$597$	1.52803e7	1.75467
$598$	1.46165e7	1.67144
$599$	−1.01255e7	−1.15306	−0.576529	−	0.817077i	$-0.695593\pi$
$599$	−1.01255e7	−1.15306	−0.576529	+	0.817077i	$0.695593\pi$
$600$	0	0
$601$	1.63996e6	0.185203	0.0926014	−	0.995703i	$-0.470482\pi$
$601$	1.63996e6	0.185203	0.0926014	+	0.995703i	$0.470482\pi$
$602$	1.36013e6	0.152964
$603$	−226200.	−0.0253337
$604$	6.09664e6	0.679983
$605$	0	0
$606$	5.97747e6	0.661205
$607$	4.21611e6	0.464451	0.232226	−	0.972662i	$-0.425399\pi$
$607$	4.21611e6	0.464451	0.232226	+	0.972662i	$0.425399\pi$
$608$	369664.	0.0405554
$609$	−46464.0	−0.00507660
$610$	0	0
$611$	2.31546e7	2.50919
$612$	282464.	0.0304849
$613$	−1.47536e7	−1.58579	−0.792895	−	0.609359i	$-0.791427\pi$
$613$	−1.47536e7	−1.58579	−0.792895	+	0.609359i	$0.791427\pi$
$614$	−8.64816e6	−0.925769
$615$	0	0
$616$	−664576.	−0.0705656
$617$	−5.22235e6	−0.552272	−0.276136	−	0.961119i	$-0.589054\pi$
$617$	−5.22235e6	−0.552272	−0.276136	+	0.961119i	$0.589054\pi$
$618$	−1.49222e6	−0.157168
$619$	1.73782e6	0.182296	0.0911482	−	0.995837i	$-0.470946\pi$
$619$	1.73782e6	0.182296	0.0911482	+	0.995837i	$0.470946\pi$
$620$	0	0
$621$	1.21146e7	1.26060
$622$	−1.01181e7	−1.04864
$623$	5.01855e6	0.518034
$624$	−4.54656e6	−0.467435
$625$	0	0
$626$	9.82274e6	1.00184
$627$	−1.36314e6	−0.138475
$628$	−994272.	−0.100602
$629$	7.17296e6	0.722889
$630$	0	0
$631$	−3.38978e6	−0.338920	−0.169460	−	0.985537i	$-0.554202\pi$
$631$	−3.38978e6	−0.338920	−0.169460	+	0.985537i	$0.554202\pi$
$632$	−4.58240e6	−0.456352
$633$	−5.48384e6	−0.543971
$634$	−5.30614e6	−0.524270
$635$	0	0
$636$	8.37683e6	0.821177
$637$	1.65068e7	1.61181
$638$	62304.0	0.00605988
$639$	−642928.	−0.0622888
$640$	0	0
$641$	−296414.	−0.0284940	−0.0142470	−	0.999899i	$-0.504535\pi$
$641$	−296414.	−0.0284940	−0.0142470	+	0.999899i	$0.504535\pi$
$642$	5.36166e6	0.513407
$643$	4.89217e6	0.466631	0.233316	−	0.972401i	$-0.425042\pi$
$643$	4.89217e6	0.466631	0.233316	+	0.972401i	$0.425042\pi$
$644$	−2.31757e6	−0.220200
$645$	0	0
$646$	1.96095e6	0.184878
$647$	1.22280e7	1.14841	0.574203	−	0.818713i	$-0.305312\pi$
$647$	1.22280e7	1.14841	0.574203	+	0.818713i	$0.305312\pi$
$648$	−3.97050e6	−0.371456
$649$	4.16210e6	0.387883
$650$	0	0
$651$	4.71398e6	0.435949
$652$	−7.27616e6	−0.670322
$653$	5.42771e6	0.498120	0.249060	−	0.968488i	$-0.419878\pi$
$653$	5.42771e6	0.498120	0.249060	+	0.968488i	$0.419878\pi$
$654$	−4.45658e6	−0.407434
$655$	0	0
$656$	−5.40416e6	−0.490308
$657$	−795106.	−0.0718640
$658$	−3.67136e6	−0.330569
$659$	8.24866e6	0.739895	0.369947	−	0.929053i	$-0.379376\pi$
$659$	8.24866e6	0.739895	0.369947	+	0.929053i	$0.379376\pi$
$660$	0	0
$661$	−1.13280e7	−1.00844	−0.504218	−	0.863576i	$-0.668219\pi$
$661$	−1.13280e7	−1.00844	−0.504218	+	0.863576i	$0.668219\pi$
$662$	−2.37374e6	−0.210518
$663$	−2.41181e7	−2.13088
$664$	672256.	0.0591718
$665$	0	0
$666$	274664.	0.0239947
$667$	217272.	0.0189099
$668$	6.34963e6	0.550563
$669$	2.06406e7	1.78302
$670$	0	0
$671$	1.25481e7	1.07590
$672$	720896.	0.0615814
$673$	−6.00051e6	−0.510682	−0.255341	−	0.966851i	$-0.582188\pi$
$673$	−6.00051e6	−0.510682	−0.255341	+	0.966851i	$0.582188\pi$
$674$	−4.09182e6	−0.346950
$675$	0	0
$676$	1.37729e7	1.15920
$677$	−3.63008e6	−0.304400	−0.152200	−	0.988350i	$-0.548636\pi$
$677$	−3.63008e6	−0.304400	−0.152200	+	0.988350i	$0.548636\pi$
$678$	1.24164e7	1.03734
$679$	3.58292e6	0.298238
$680$	0	0
$681$	1.06029e7	0.876105
$682$	−6.32102e6	−0.520387
$683$	−9.38930e6	−0.770161	−0.385081	−	0.922883i	$-0.625826\pi$
$683$	−9.38930e6	−0.770161	−0.385081	+	0.922883i	$0.625826\pi$
$684$	75088.0	0.00613663
$685$	0	0
$686$	−5.57533e6	−0.452335
$687$	2.14828e7	1.73660
$688$	1.97837e6	0.159344
$689$	−3.63214e7	−2.91484
$690$	0	0
$691$	2.01569e7	1.60593	0.802967	−	0.596023i	$-0.203253\pi$
$691$	2.01569e7	1.60593	0.802967	+	0.596023i	$0.203253\pi$
$692$	2.04202e6	0.162104
$693$	−134992.	−0.0106776
$694$	6.67683e6	0.526225
$695$	0	0
$696$	−67584.0	−0.00528836
$697$	−2.86674e7	−2.23515
$698$	−3.49844e6	−0.271792
$699$	−6.70762e6	−0.519249
$700$	0	0
$701$	−1.61355e7	−1.24019	−0.620095	−	0.784527i	$-0.712906\pi$
$701$	−1.61355e7	−1.24019	−0.620095	+	0.784527i	$0.712906\pi$
$702$	1.63392e7	1.25138
$703$	1.90680e6	0.145518
$704$	−966656.	−0.0735090
$705$	0	0
$706$	−1.05992e7	−0.800319
$707$	4.10951e6	0.309202
$708$	−4.51482e6	−0.338499
$709$	2.38589e7	1.78252	0.891260	−	0.453493i	$-0.149822\pi$
$709$	2.38589e7	1.78252	0.891260	+	0.453493i	$0.149822\pi$
$710$	0	0
$711$	−930800.	−0.0690530
$712$	7.29971e6	0.539642
$713$	−2.20432e7	−1.62387
$714$	3.82413e6	0.280729
$715$	0	0
$716$	6.19552e6	0.451643
$717$	−4.83226e6	−0.351036
$718$	−1056.00	−7.64457e−5 0
$719$	6.06270e6	0.437365	0.218683	−	0.975796i	$-0.429824\pi$
$719$	6.06270e6	0.437365	0.218683	+	0.975796i	$0.429824\pi$
$720$	0	0
$721$	−1.02590e6	−0.0734968
$722$	521284.	0.0372161
$723$	−1.51191e7	−1.07567
$724$	−6.08861e6	−0.431690
$725$	0	0
$726$	−6.74272e6	−0.474781
$727$	1.98663e7	1.39406	0.697028	−	0.717044i	$-0.254505\pi$
$727$	1.98663e7	1.39406	0.697028	+	0.717044i	$0.254505\pi$
$728$	−3.12576e6	−0.218588
$729$	1.35013e7	0.940931
$730$	0	0
$731$	1.04946e7	0.726396
$732$	−1.36115e7	−0.938921
$733$	3.45384e6	0.237434	0.118717	−	0.992928i	$-0.462122\pi$
$733$	3.45384e6	0.237434	0.118717	+	0.992928i	$0.462122\pi$
$734$	−1.11819e7	−0.766080
$735$	0	0
$736$	−3.37101e6	−0.229385
$737$	4.10640e6	0.278479
$738$	−1.09772e6	−0.0741909
$739$	1.73436e7	1.16823	0.584115	−	0.811671i	$-0.301442\pi$
$739$	1.73436e7	1.16823	0.584115	+	0.811671i	$0.301442\pi$
$740$	0	0
$741$	−6.41136e6	−0.428948
$742$	5.75907e6	0.384010
$743$	−3.26932e6	−0.217263	−0.108631	−	0.994082i	$-0.534647\pi$
$743$	−3.26932e6	−0.217263	−0.108631	+	0.994082i	$0.534647\pi$
$744$	6.85670e6	0.454133
$745$	0	0
$746$	1.20401e7	0.792104
$747$	136552.	0.00895358
$748$	−5.12781e6	−0.335103
$749$	3.68614e6	0.240087
$750$	0	0
$751$	2.58480e7	1.67235	0.836176	−	0.548461i	$-0.184786\pi$
$751$	2.58480e7	1.67235	0.836176	+	0.548461i	$0.184786\pi$
$752$	−5.34016e6	−0.344358
$753$	8.29114e6	0.532877
$754$	293040.	0.0187715
$755$	0	0
$756$	−2.59072e6	−0.164860
$757$	8.70668e6	0.552221	0.276111	−	0.961126i	$-0.410954\pi$
$757$	8.70668e6	0.552221	0.276111	+	0.961126i	$0.410954\pi$
$758$	−4.37685e6	−0.276687
$759$	1.24306e7	0.783226
$760$	0	0
$761$	−1.44971e7	−0.907445	−0.453722	−	0.891143i	$-0.649904\pi$
$761$	−1.44971e7	−0.907445	−0.453722	+	0.891143i	$0.649904\pi$
$762$	98048.0	0.00611718
$763$	−3.06390e6	−0.190530
$764$	−1.52818e7	−0.947198
$765$	0	0
$766$	8.81435e6	0.542773
$767$	1.95760e7	1.20153
$768$	1.04858e6	0.0641500
$769$	−1.44260e7	−0.879688	−0.439844	−	0.898074i	$-0.644966\pi$
$769$	−1.44260e7	−0.879688	−0.439844	+	0.898074i	$0.644966\pi$
$770$	0	0
$771$	7.39363e6	0.447942
$772$	7.49910e6	0.452862
$773$	1.40911e6	0.0848193	0.0424097	−	0.999100i	$-0.486497\pi$
$773$	1.40911e6	0.0848193	0.0424097	+	0.999100i	$0.486497\pi$
$774$	401856.	0.0241112
$775$	0	0
$776$	5.21152e6	0.310678
$777$	3.71853e6	0.220962
$778$	−1.50286e7	−0.890166
$779$	−7.62071e6	−0.449937
$780$	0	0
$781$	1.16716e7	0.684705
$782$	−1.78821e7	−1.04569
$783$	242880.	0.0141575
$784$	−3.80698e6	−0.221202
$785$	0	0
$786$	−1.52486e7	−0.880389
$787$	6.63490e6	0.381854	0.190927	−	0.981604i	$-0.438851\pi$
$787$	6.63490e6	0.381854	0.190927	+	0.981604i	$0.438851\pi$
$788$	7.90160e6	0.453314
$789$	1.31802e7	0.753755
$790$	0	0
$791$	8.53626e6	0.485095
$792$	−196352.	−0.0111230
$793$	5.90187e7	3.33278
$794$	4.32756e6	0.243608
$795$	0	0
$796$	1.52803e7	0.854767
$797$	−2.23377e7	−1.24564	−0.622819	−	0.782366i	$-0.714013\pi$
$797$	−2.23377e7	−1.24564	−0.622819	+	0.782366i	$0.714013\pi$
$798$	1.01658e6	0.0565110
$799$	−2.83279e7	−1.56981
$800$	0	0
$801$	1.48275e6	0.0816559
$802$	1.13096e7	0.620887
$803$	1.44342e7	0.789959
$804$	−4.45440e6	−0.243024
$805$	0	0
$806$	−2.97302e7	−1.61198
$807$	2.15157e7	1.16298
$808$	5.97747e6	0.322099
$809$	3.37121e7	1.81098	0.905491	−	0.424365i	$-0.139503\pi$
$809$	3.37121e7	1.81098	0.905491	+	0.424365i	$0.139503\pi$
$810$	0	0
$811$	−6.99340e6	−0.373367	−0.186684	−	0.982420i	$-0.559774\pi$
$811$	−6.99340e6	−0.373367	−0.186684	+	0.982420i	$0.559774\pi$
$812$	−46464.0	−0.00247301
$813$	2.35401e7	1.24906
$814$	−4.98621e6	−0.263760
$815$	0	0
$816$	5.56237e6	0.292438
$817$	2.78981e6	0.146224
$818$	−2.81263e6	−0.146970
$819$	−634920.	−0.0330757
$820$	0	0
$821$	1.43649e7	0.743779	0.371889	−	0.928277i	$-0.378710\pi$
$821$	1.43649e7	0.743779	0.371889	+	0.928277i	$0.378710\pi$
$822$	−2.15651e7	−1.11319
$823$	724436.	0.0372821	0.0186411	−	0.999826i	$-0.494066\pi$
$823$	724436.	0.0372821	0.0186411	+	0.999826i	$0.494066\pi$
$824$	−1.49222e6	−0.0765625
$825$	0	0
$826$	−3.10394e6	−0.158293
$827$	−1.62540e7	−0.826409	−0.413205	−	0.910638i	$-0.635591\pi$
$827$	−1.62540e7	−0.826409	−0.413205	+	0.910638i	$0.635591\pi$
$828$	−684736.	−0.0347094
$829$	−3.22107e7	−1.62785	−0.813923	−	0.580972i	$-0.802672\pi$
$829$	−3.22107e7	−1.62785	−0.813923	+	0.580972i	$0.802672\pi$
$830$	0	0
$831$	−1.65047e7	−0.829095
$832$	−4.54656e6	−0.227706
$833$	−2.01948e7	−1.00839
$834$	−7.26554e6	−0.361703
$835$	0	0
$836$	−1.36314e6	−0.0674565
$837$	−2.46413e7	−1.21576
$838$	−2.78789e6	−0.137140
$839$	3.18343e6	0.156132	0.0780658	−	0.996948i	$-0.475126\pi$
$839$	3.18343e6	0.156132	0.0780658	+	0.996948i	$0.475126\pi$
$840$	0	0
$841$	−2.05068e7	−0.999788
$842$	1.78762e7	0.868953
$843$	−1.85048e7	−0.896841
$844$	−5.48384e6	−0.264989
$845$	0	0
$846$	−1.08472e6	−0.0521065
$847$	−4.63562e6	−0.222024
$848$	8.37683e6	0.400028
$849$	−2.24812e7	−1.07041
$850$	0	0
$851$	−1.73883e7	−0.823065
$852$	−1.26607e7	−0.597530
$853$	1.99217e7	0.937461	0.468731	−	0.883341i	$-0.344712\pi$
$853$	1.99217e7	0.937461	0.468731	+	0.883341i	$0.344712\pi$
$854$	−9.35792e6	−0.439071
$855$	0	0
$856$	5.36166e6	0.250101
$857$	−2.81296e6	−0.130831	−0.0654157	−	0.997858i	$-0.520837\pi$
$857$	−2.81296e6	−0.130831	−0.0654157	+	0.997858i	$0.520837\pi$
$858$	1.67654e7	0.777493
$859$	−1.89673e7	−0.877047	−0.438524	−	0.898720i	$-0.644498\pi$
$859$	−1.89673e7	−0.877047	−0.438524	+	0.898720i	$0.644498\pi$
$860$	0	0
$861$	−1.48614e7	−0.683208
$862$	−2.12811e7	−0.975495
$863$	4.24282e7	1.93922	0.969611	−	0.244650i	$-0.0786730\pi$
$863$	4.24282e7	1.93922	0.969611	+	0.244650i	$0.0786730\pi$
$864$	−3.76832e6	−0.171737
$865$	0	0
$866$	−197352.	−0.00894225
$867$	6.78891e6	0.306727
$868$	4.71398e6	0.212368
$869$	1.68976e7	0.759059
$870$	0	0
$871$	1.93140e7	0.862635
$872$	−4.45658e6	−0.198477
$873$	1.05859e6	0.0470102
$874$	−4.75365e6	−0.210498
$875$	0	0
$876$	−1.56575e7	−0.689384
$877$	−1.62443e7	−0.713187	−0.356593	−	0.934260i	$-0.616062\pi$
$877$	−1.62443e7	−0.713187	−0.356593	+	0.934260i	$0.616062\pi$
$878$	1.75152e7	0.766793
$879$	−1.87809e7	−0.819868
$880$	0	0
$881$	3.09750e7	1.34454	0.672268	−	0.740308i	$-0.265320\pi$
$881$	3.09750e7	1.34454	0.672268	+	0.740308i	$0.265320\pi$
$882$	−773292.	−0.0334713
$883$	−1.22844e7	−0.530216	−0.265108	−	0.964219i	$-0.585408\pi$
$883$	−1.22844e7	−0.530216	−0.265108	+	0.964219i	$0.585408\pi$
$884$	−2.41181e7	−1.03804
$885$	0	0
$886$	1.61115e7	0.689527
$887$	−9.16489e6	−0.391127	−0.195564	−	0.980691i	$-0.562654\pi$
$887$	−9.16489e6	−0.391127	−0.195564	+	0.980691i	$0.562654\pi$
$888$	5.40877e6	0.230179
$889$	67408.0	0.00286060
$890$	0	0
$891$	1.46412e7	0.617849
$892$	2.06406e7	0.868580
$893$	−7.53046e6	−0.316004
$894$	−3.26714e7	−1.36717
$895$	0	0
$896$	720896.	0.0299987
$897$	5.84659e7	2.42617
$898$	−2.69215e6	−0.111406
$899$	−441936.	−0.0182373
$900$	0	0
$901$	4.44365e7	1.82359
$902$	1.99278e7	0.815537
$903$	5.44051e6	0.222034
$904$	1.24164e7	0.505329
$905$	0	0
$906$	2.43866e7	0.987029
$907$	−8.14043e6	−0.328571	−0.164286	−	0.986413i	$-0.552532\pi$
$907$	−8.14043e6	−0.328571	−0.164286	+	0.986413i	$0.552532\pi$
$908$	1.06029e7	0.426785
$909$	1.21417e6	0.0487384
$910$	0	0
$911$	2.34933e7	0.937881	0.468941	−	0.883230i	$-0.344636\pi$
$911$	2.34933e7	0.937881	0.468941	+	0.883230i	$0.344636\pi$
$912$	1.47866e6	0.0588681
$913$	−2.47894e6	−0.0984215
$914$	8.72457e6	0.345445
$915$	0	0
$916$	2.14828e7	0.845967
$917$	−1.04834e7	−0.411700
$918$	−1.99898e7	−0.782890
$919$	−5.59887e6	−0.218681	−0.109341	−	0.994004i	$-0.534874\pi$
$919$	−5.59887e6	−0.218681	−0.109341	+	0.994004i	$0.534874\pi$
$920$	0	0
$921$	−3.45926e7	−1.34380
$922$	−7.06433e6	−0.273680
$923$	5.48962e7	2.12099
$924$	−2.65830e6	−0.102429
$925$	0	0
$926$	2.34630e7	0.899200
$927$	−303108.	−0.0115851
$928$	−67584.0	−0.00257617
$929$	1.50994e7	0.574010	0.287005	−	0.957929i	$-0.407340\pi$
$929$	1.50994e7	0.574010	0.287005	+	0.957929i	$0.407340\pi$
$930$	0	0
$931$	−5.36843e6	−0.202989
$932$	−6.70762e6	−0.252946
$933$	−4.04726e7	−1.52215
$934$	−1.37339e7	−0.515141
$935$	0	0
$936$	−923520.	−0.0344554
$937$	−3.28842e7	−1.22360	−0.611798	−	0.791014i	$-0.709554\pi$
$937$	−3.28842e7	−1.22360	−0.611798	+	0.791014i	$0.709554\pi$
$938$	−3.06240e6	−0.113646
$939$	3.92910e7	1.45422
$940$	0	0
$941$	1.75198e7	0.644993	0.322497	−	0.946571i	$-0.395478\pi$
$941$	1.75198e7	0.644993	0.322497	+	0.946571i	$0.395478\pi$
$942$	−3.97709e6	−0.146029
$943$	6.94941e7	2.54489
$944$	−4.51482e6	−0.164896
$945$	0	0
$946$	−7.29523e6	−0.265040
$947$	1.72088e7	0.623555	0.311777	−	0.950155i	$-0.399076\pi$
$947$	1.72088e7	0.623555	0.311777	+	0.950155i	$0.399076\pi$
$948$	−1.83296e7	−0.662418
$949$	6.78898e7	2.44703
$950$	0	0
$951$	−2.12245e7	−0.761004
$952$	3.82413e6	0.136754
$953$	3.46004e7	1.23409	0.617047	−	0.786926i	$-0.288329\pi$
$953$	3.46004e7	1.23409	0.617047	+	0.786926i	$0.288329\pi$
$954$	1.70154e6	0.0605302
$955$	0	0
$956$	−4.83226e6	−0.171004
$957$	249216.	0.00879622
$958$	1.85687e7	0.653684
$959$	−1.48260e7	−0.520567
$960$	0	0
$961$	1.62073e7	0.566111
$962$	−2.34521e7	−0.817041
$963$	1.08909e6	0.0378440
$964$	−1.51191e7	−0.524002
$965$	0	0
$966$	−9.27027e6	−0.319632
$967$	−2.22060e7	−0.763667	−0.381833	−	0.924231i	$-0.624707\pi$
$967$	−2.22060e7	−0.763667	−0.381833	+	0.924231i	$0.624707\pi$
$968$	−6.74272e6	−0.231285
$969$	7.84381e6	0.268360
$970$	0	0
$971$	−2.86350e7	−0.974651	−0.487325	−	0.873221i	$-0.662027\pi$
$971$	−2.86350e7	−0.974651	−0.487325	+	0.873221i	$0.662027\pi$
$972$	−1.57414e6	−0.0534415
$973$	−4.99506e6	−0.169145
$974$	2.09282e7	0.706862
$975$	0	0
$976$	−1.36115e7	−0.457385
$977$	1.16491e7	0.390441	0.195220	−	0.980759i	$-0.437458\pi$
$977$	1.16491e7	0.390441	0.195220	+	0.980759i	$0.437458\pi$
$978$	−2.91046e7	−0.973005
$979$	−2.69177e7	−0.897596
$980$	0	0
$981$	−905242.	−0.0300325
$982$	2.94637e7	0.975009
$983$	1.37607e7	0.454210	0.227105	−	0.973870i	$-0.427074\pi$
$983$	1.37607e7	0.454210	0.227105	+	0.973870i	$0.427074\pi$
$984$	−2.16166e7	−0.711706
$985$	0	0
$986$	−358512.	−0.0117439
$987$	−1.46854e7	−0.479837
$988$	−6.41136e6	−0.208957
$989$	−2.54406e7	−0.827058
$990$	0	0
$991$	−3.06640e7	−0.991848	−0.495924	−	0.868366i	$-0.665171\pi$
$991$	−3.06640e7	−0.991848	−0.495924	+	0.868366i	$0.665171\pi$
$992$	6.85670e6	0.221226
$993$	−9.49498e6	−0.305577
$994$	−8.70426e6	−0.279425
$995$	0	0
$996$	2.68902e6	0.0858907
$997$	7.78974e6	0.248190	0.124095	−	0.992270i	$-0.460397\pi$
$997$	7.78974e6	0.248190	0.124095	+	0.992270i	$0.460397\pi$
$998$	−9.08018e6	−0.288581
$999$	−1.94378e7	−0.616215

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.6.a.c.1.1		1
5.4	even	2		190.6.a.a.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.6.a.a.1.1	✓	1	5.4	even	2
950.6.a.c.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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	950.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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