LMFDB - Embedded newform 819.4.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,4,Mod(1,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, 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("819.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	819.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:	$48.3225642947$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	819.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q+1.00000 q^{2} -7.00000 q^{4} -9.00000 q^{5} -7.00000 q^{7} -15.0000 q^{8} -9.00000 q^{10} +57.0000 q^{11} -13.0000 q^{13} -7.00000 q^{14} +41.0000 q^{16} +37.0000 q^{17} +107.000 q^{19} +63.0000 q^{20} +57.0000 q^{22} +183.000 q^{23} -44.0000 q^{25} -13.0000 q^{26} +49.0000 q^{28} -191.000 q^{29} -240.000 q^{31} +161.000 q^{32} +37.0000 q^{34} +63.0000 q^{35} -379.000 q^{37} +107.000 q^{38} +135.000 q^{40} +84.0000 q^{41} -313.000 q^{43} -399.000 q^{44} +183.000 q^{46} -296.000 q^{47} +49.0000 q^{49} -44.0000 q^{50} +91.0000 q^{52} +414.000 q^{53} -513.000 q^{55} +105.000 q^{56} -191.000 q^{58} -40.0000 q^{59} +65.0000 q^{61} -240.000 q^{62} -167.000 q^{64} +117.000 q^{65} -1086.00 q^{67} -259.000 q^{68} +63.0000 q^{70} +208.000 q^{71} +635.000 q^{73} -379.000 q^{74} -749.000 q^{76} -399.000 q^{77} -582.000 q^{79} -369.000 q^{80} +84.0000 q^{82} -798.000 q^{83} -333.000 q^{85} -313.000 q^{86} -855.000 q^{88} +726.000 q^{89} +91.0000 q^{91} -1281.00 q^{92} -296.000 q^{94} -963.000 q^{95} +1498.00 q^{97} +49.0000 q^{98} +O(q^{100})\)

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	$-0.443433\pi$
$2$	1.00000	0.353553	0.176777	+	0.984251i	$0.443433\pi$
$3$	0	0
$3$	0	0
$4$	−7.00000	−0.875000
$5$	−9.00000	−0.804984	−0.402492	−	0.915423i	$-0.631856\pi$
$5$	−9.00000	−0.804984	−0.402492	+	0.915423i	$0.631856\pi$
$6$	0	0
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	−15.0000	−0.662913
$9$	0	0
$10$	−9.00000	−0.284605
$11$	57.0000	1.56238	0.781188	−	0.624295i	$-0.214614\pi$
$11$	57.0000	1.56238	0.781188	+	0.624295i	$0.214614\pi$
$12$	0	0
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	−7.00000	−0.133631
$15$	0	0
$16$	41.0000	0.640625
$17$	37.0000	0.527872	0.263936	−	0.964540i	$-0.414979\pi$
$17$	37.0000	0.527872	0.263936	+	0.964540i	$0.414979\pi$
$18$	0	0
$19$	107.000	1.29197	0.645986	−	0.763349i	$-0.276446\pi$
$19$	107.000	1.29197	0.645986	+	0.763349i	$0.276446\pi$
$20$	63.0000	0.704361
$21$	0	0
$22$	57.0000	0.552384
$23$	183.000	1.65905	0.829525	−	0.558470i	$-0.188611\pi$
$23$	183.000	1.65905	0.829525	+	0.558470i	$0.188611\pi$
$24$	0	0
$25$	−44.0000	−0.352000
$26$	−13.0000	−0.0980581
$27$	0	0
$28$	49.0000	0.330719
$29$	−191.000	−1.22303	−0.611514	−	0.791234i	$-0.709439\pi$
$29$	−191.000	−1.22303	−0.611514	+	0.791234i	$0.709439\pi$
$30$	0	0
$31$	−240.000	−1.39049	−0.695246	−	0.718772i	$-0.744705\pi$
$31$	−240.000	−1.39049	−0.695246	+	0.718772i	$0.744705\pi$
$32$	161.000	0.889408
$33$	0	0
$34$	37.0000	0.186631
$35$	63.0000	0.304256
$36$	0	0
$37$	−379.000	−1.68398	−0.841989	−	0.539494i	$-0.818616\pi$
$37$	−379.000	−1.68398	−0.841989	+	0.539494i	$0.818616\pi$
$38$	107.000	0.456781
$39$	0	0
$40$	135.000	0.533634
$41$	84.0000	0.319966	0.159983	−	0.987120i	$-0.448856\pi$
$41$	84.0000	0.319966	0.159983	+	0.987120i	$0.448856\pi$
$42$	0	0
$43$	−313.000	−1.11005	−0.555024	−	0.831834i	$-0.687291\pi$
$43$	−313.000	−1.11005	−0.555024	+	0.831834i	$0.687291\pi$
$44$	−399.000	−1.36708
$45$	0	0
$46$	183.000	0.586563
$47$	−296.000	−0.918639	−0.459320	−	0.888271i	$-0.651907\pi$
$47$	−296.000	−0.918639	−0.459320	+	0.888271i	$0.651907\pi$
$48$	0	0
$49$	49.0000	0.142857
$50$	−44.0000	−0.124451
$51$	0	0
$52$	91.0000	0.242681
$53$	414.000	1.07297	0.536484	−	0.843911i	$-0.319752\pi$
$53$	414.000	1.07297	0.536484	+	0.843911i	$0.319752\pi$
$54$	0	0
$55$	−513.000	−1.25769
$56$	105.000	0.250557
$57$	0	0
$58$	−191.000	−0.432406
$59$	−40.0000	−0.0882637	−0.0441318	−	0.999026i	$-0.514052\pi$
$59$	−40.0000	−0.0882637	−0.0441318	+	0.999026i	$0.514052\pi$
$60$	0	0
$61$	65.0000	0.136433	0.0682164	−	0.997671i	$-0.478269\pi$
$61$	65.0000	0.136433	0.0682164	+	0.997671i	$0.478269\pi$
$62$	−240.000	−0.491613
$63$	0	0
$64$	−167.000	−0.326172
$65$	117.000	0.223263
$66$	0	0
$67$	−1086.00	−1.98024	−0.990120	−	0.140226i	$-0.955217\pi$
$67$	−1086.00	−1.98024	−0.990120	+	0.140226i	$0.955217\pi$
$68$	−259.000	−0.461888
$69$	0	0
$70$	63.0000	0.107571
$71$	208.000	0.347677	0.173838	−	0.984774i	$-0.444383\pi$
$71$	208.000	0.347677	0.173838	+	0.984774i	$0.444383\pi$
$72$	0	0
$73$	635.000	1.01810	0.509049	−	0.860738i	$-0.329997\pi$
$73$	635.000	1.01810	0.509049	+	0.860738i	$0.329997\pi$
$74$	−379.000	−0.595376
$75$	0	0
$76$	−749.000	−1.13048
$77$	−399.000	−0.590523
$78$	0	0
$79$	−582.000	−0.828862	−0.414431	−	0.910081i	$-0.636019\pi$
$79$	−582.000	−0.828862	−0.414431	+	0.910081i	$0.636019\pi$
$80$	−369.000	−0.515693
$81$	0	0
$82$	84.0000	0.113125
$83$	−798.000	−1.05532	−0.527662	−	0.849454i	$-0.676931\pi$
$83$	−798.000	−1.05532	−0.527662	+	0.849454i	$0.676931\pi$
$84$	0	0
$85$	−333.000	−0.424928
$86$	−313.000	−0.392461
$87$	0	0
$88$	−855.000	−1.03572
$89$	726.000	0.864672	0.432336	−	0.901712i	$-0.357689\pi$
$89$	726.000	0.864672	0.432336	+	0.901712i	$0.357689\pi$
$90$	0	0
$91$	91.0000	0.104828
$92$	−1281.00	−1.45167
$93$	0	0
$94$	−296.000	−0.324788
$95$	−963.000	−1.04002
$96$	0	0
$97$	1498.00	1.56803	0.784015	−	0.620742i	$-0.213169\pi$
$97$	1498.00	1.56803	0.784015	+	0.620742i	$0.213169\pi$
$98$	49.0000	0.0505076
$99$	0	0
$100$	308.000	0.308000
$101$	−1664.00	−1.63935	−0.819674	−	0.572830i	$-0.805846\pi$
$101$	−1664.00	−1.63935	−0.819674	+	0.572830i	$0.805846\pi$
$102$	0	0
$103$	821.000	0.785394	0.392697	−	0.919668i	$-0.371542\pi$
$103$	821.000	0.785394	0.392697	+	0.919668i	$0.371542\pi$
$104$	195.000	0.183859
$105$	0	0
$106$	414.000	0.379351
$107$	554.000	0.500535	0.250267	−	0.968177i	$-0.419482\pi$
$107$	554.000	0.500535	0.250267	+	0.968177i	$0.419482\pi$
$108$	0	0
$109$	727.000	0.638844	0.319422	−	0.947613i	$-0.396511\pi$
$109$	727.000	0.638844	0.319422	+	0.947613i	$0.396511\pi$
$110$	−513.000	−0.444660
$111$	0	0
$112$	−287.000	−0.242133
$113$	390.000	0.324674	0.162337	−	0.986735i	$-0.448097\pi$
$113$	390.000	0.324674	0.162337	+	0.986735i	$0.448097\pi$
$114$	0	0
$115$	−1647.00	−1.33551
$116$	1337.00	1.07015
$117$	0	0
$118$	−40.0000	−0.0312059
$119$	−259.000	−0.199517
$120$	0	0
$121$	1918.00	1.44102
$122$	65.0000	0.0482363
$123$	0	0
$124$	1680.00	1.21668
$125$	1521.00	1.08834
$126$	0	0
$127$	−922.000	−0.644207	−0.322103	−	0.946704i	$-0.604390\pi$
$127$	−922.000	−0.644207	−0.322103	+	0.946704i	$0.604390\pi$
$128$	−1455.00	−1.00473
$129$	0	0
$130$	117.000	0.0789352
$131$	−2599.00	−1.73340	−0.866701	−	0.498828i	$-0.833764\pi$
$131$	−2599.00	−1.73340	−0.866701	+	0.498828i	$0.833764\pi$
$132$	0	0
$133$	−749.000	−0.488320
$134$	−1086.00	−0.700120
$135$	0	0
$136$	−555.000	−0.349933
$137$	−2645.00	−1.64947	−0.824736	−	0.565518i	$-0.808676\pi$
$137$	−2645.00	−1.64947	−0.824736	+	0.565518i	$0.808676\pi$
$138$	0	0
$139$	−1092.00	−0.666347	−0.333173	−	0.942866i	$-0.608119\pi$
$139$	−1092.00	−0.666347	−0.333173	+	0.942866i	$0.608119\pi$
$140$	−441.000	−0.266224
$141$	0	0
$142$	208.000	0.122922
$143$	−741.000	−0.433325
$144$	0	0
$145$	1719.00	0.984518
$146$	635.000	0.359952
$147$	0	0
$148$	2653.00	1.47348
$149$	−972.000	−0.534425	−0.267213	−	0.963638i	$-0.586103\pi$
$149$	−972.000	−0.534425	−0.267213	+	0.963638i	$0.586103\pi$
$150$	0	0
$151$	69.0000	0.0371864	0.0185932	−	0.999827i	$-0.494081\pi$
$151$	69.0000	0.0371864	0.0185932	+	0.999827i	$0.494081\pi$
$152$	−1605.00	−0.856465
$153$	0	0
$154$	−399.000	−0.208781
$155$	2160.00	1.11933
$156$	0	0
$157$	1237.00	0.628811	0.314406	−	0.949289i	$-0.398195\pi$
$157$	1237.00	0.628811	0.314406	+	0.949289i	$0.398195\pi$
$158$	−582.000	−0.293047
$159$	0	0
$160$	−1449.00	−0.715959
$161$	−1281.00	−0.627062
$162$	0	0
$163$	−694.000	−0.333486	−0.166743	−	0.986000i	$-0.553325\pi$
$163$	−694.000	−0.333486	−0.166743	+	0.986000i	$0.553325\pi$
$164$	−588.000	−0.279970
$165$	0	0
$166$	−798.000	−0.373113
$167$	−721.000	−0.334088	−0.167044	−	0.985949i	$-0.553422\pi$
$167$	−721.000	−0.334088	−0.167044	+	0.985949i	$0.553422\pi$
$168$	0	0
$169$	169.000	0.0769231
$170$	−333.000	−0.150235
$171$	0	0
$172$	2191.00	0.971292
$173$	−674.000	−0.296204	−0.148102	−	0.988972i	$-0.547316\pi$
$173$	−674.000	−0.296204	−0.148102	+	0.988972i	$0.547316\pi$
$174$	0	0
$175$	308.000	0.133043
$176$	2337.00	1.00090
$177$	0	0
$178$	726.000	0.305708
$179$	2780.00	1.16082	0.580410	−	0.814324i	$-0.302892\pi$
$179$	2780.00	1.16082	0.580410	+	0.814324i	$0.302892\pi$
$180$	0	0
$181$	−2506.00	−1.02911	−0.514557	−	0.857456i	$-0.672043\pi$
$181$	−2506.00	−1.02911	−0.514557	+	0.857456i	$0.672043\pi$
$182$	91.0000	0.0370625
$183$	0	0
$184$	−2745.00	−1.09980
$185$	3411.00	1.35558
$186$	0	0
$187$	2109.00	0.824735
$188$	2072.00	0.803809
$189$	0	0
$190$	−963.000	−0.367702
$191$	−4409.00	−1.67028	−0.835141	−	0.550035i	$-0.814614\pi$
$191$	−4409.00	−1.67028	−0.835141	+	0.550035i	$0.814614\pi$
$192$	0	0
$193$	−4712.00	−1.75739	−0.878697	−	0.477379i	$-0.841587\pi$
$193$	−4712.00	−1.75739	−0.878697	+	0.477379i	$0.841587\pi$
$194$	1498.00	0.554382
$195$	0	0
$196$	−343.000	−0.125000
$197$	1328.00	0.480285	0.240142	−	0.970738i	$-0.422806\pi$
$197$	1328.00	0.480285	0.240142	+	0.970738i	$0.422806\pi$
$198$	0	0
$199$	1279.00	0.455608	0.227804	−	0.973707i	$-0.426846\pi$
$199$	1279.00	0.455608	0.227804	+	0.973707i	$0.426846\pi$
$200$	660.000	0.233345
$201$	0	0
$202$	−1664.00	−0.579597
$203$	1337.00	0.462261
$204$	0	0
$205$	−756.000	−0.257567
$206$	821.000	0.277679
$207$	0	0
$208$	−533.000	−0.177677
$209$	6099.00	2.01855
$210$	0	0
$211$	1549.00	0.505391	0.252696	−	0.967546i	$-0.418683\pi$
$211$	1549.00	0.505391	0.252696	+	0.967546i	$0.418683\pi$
$212$	−2898.00	−0.938846
$213$	0	0
$214$	554.000	0.176966
$215$	2817.00	0.893571
$216$	0	0
$217$	1680.00	0.525557
$218$	727.000	0.225865
$219$	0	0
$220$	3591.00	1.10048
$221$	−481.000	−0.146405
$222$	0	0
$223$	−3906.00	−1.17294	−0.586469	−	0.809972i	$-0.699482\pi$
$223$	−3906.00	−1.17294	−0.586469	+	0.809972i	$0.699482\pi$
$224$	−1127.00	−0.336165
$225$	0	0
$226$	390.000	0.114789
$227$	4538.00	1.32686	0.663431	−	0.748238i	$-0.269100\pi$
$227$	4538.00	1.32686	0.663431	+	0.748238i	$0.269100\pi$
$228$	0	0
$229$	−6466.00	−1.86587	−0.932937	−	0.360039i	$-0.882763\pi$
$229$	−6466.00	−1.86587	−0.932937	+	0.360039i	$0.882763\pi$
$230$	−1647.00	−0.472174
$231$	0	0
$232$	2865.00	0.810761
$233$	−3408.00	−0.958221	−0.479111	−	0.877755i	$-0.659041\pi$
$233$	−3408.00	−0.958221	−0.479111	+	0.877755i	$0.659041\pi$
$234$	0	0
$235$	2664.00	0.739490
$236$	280.000	0.0772307
$237$	0	0
$238$	−259.000	−0.0705398
$239$	1916.00	0.518560	0.259280	−	0.965802i	$-0.416515\pi$
$239$	1916.00	0.518560	0.259280	+	0.965802i	$0.416515\pi$
$240$	0	0
$241$	−4790.00	−1.28029	−0.640147	−	0.768252i	$-0.721127\pi$
$241$	−4790.00	−1.28029	−0.640147	+	0.768252i	$0.721127\pi$
$242$	1918.00	0.509478
$243$	0	0
$244$	−455.000	−0.119379
$245$	−441.000	−0.114998
$246$	0	0
$247$	−1391.00	−0.358329
$248$	3600.00	0.921775
$249$	0	0
$250$	1521.00	0.384786
$251$	−5075.00	−1.27622	−0.638110	−	0.769945i	$-0.720283\pi$
$251$	−5075.00	−1.27622	−0.638110	+	0.769945i	$0.720283\pi$
$252$	0	0
$253$	10431.0	2.59206
$254$	−922.000	−0.227762
$255$	0	0
$256$	−119.000	−0.0290527
$257$	−1682.00	−0.408250	−0.204125	−	0.978945i	$-0.565435\pi$
$257$	−1682.00	−0.408250	−0.204125	+	0.978945i	$0.565435\pi$
$258$	0	0
$259$	2653.00	0.636484
$260$	−819.000	−0.195355
$261$	0	0
$262$	−2599.00	−0.612850
$263$	−2316.00	−0.543006	−0.271503	−	0.962438i	$-0.587521\pi$
$263$	−2316.00	−0.543006	−0.271503	+	0.962438i	$0.587521\pi$
$264$	0	0
$265$	−3726.00	−0.863722
$266$	−749.000	−0.172647
$267$	0	0
$268$	7602.00	1.73271
$269$	−1230.00	−0.278790	−0.139395	−	0.990237i	$-0.544516\pi$
$269$	−1230.00	−0.278790	−0.139395	+	0.990237i	$0.544516\pi$
$270$	0	0
$271$	−4030.00	−0.903340	−0.451670	−	0.892185i	$-0.649172\pi$
$271$	−4030.00	−0.903340	−0.451670	+	0.892185i	$0.649172\pi$
$272$	1517.00	0.338168
$273$	0	0
$274$	−2645.00	−0.583176
$275$	−2508.00	−0.549957
$276$	0	0
$277$	−7106.00	−1.54137	−0.770683	−	0.637219i	$-0.780085\pi$
$277$	−7106.00	−1.54137	−0.770683	+	0.637219i	$0.780085\pi$
$278$	−1092.00	−0.235589
$279$	0	0
$280$	−945.000	−0.201695
$281$	1062.00	0.225458	0.112729	−	0.993626i	$-0.464041\pi$
$281$	1062.00	0.225458	0.112729	+	0.993626i	$0.464041\pi$
$282$	0	0
$283$	3988.00	0.837675	0.418837	−	0.908061i	$-0.362438\pi$
$283$	3988.00	0.837675	0.418837	+	0.908061i	$0.362438\pi$
$284$	−1456.00	−0.304217
$285$	0	0
$286$	−741.000	−0.153204
$287$	−588.000	−0.120936
$288$	0	0
$289$	−3544.00	−0.721352
$290$	1719.00	0.348080
$291$	0	0
$292$	−4445.00	−0.890835
$293$	2366.00	0.471752	0.235876	−	0.971783i	$-0.424204\pi$
$293$	2366.00	0.471752	0.235876	+	0.971783i	$0.424204\pi$
$294$	0	0
$295$	360.000	0.0710509
$296$	5685.00	1.11633
$297$	0	0
$298$	−972.000	−0.188948
$299$	−2379.00	−0.460138
$300$	0	0
$301$	2191.00	0.419559
$302$	69.0000	0.0131474
$303$	0	0
$304$	4387.00	0.827670
$305$	−585.000	−0.109826
$306$	0	0
$307$	−5376.00	−0.999428	−0.499714	−	0.866190i	$-0.666562\pi$
$307$	−5376.00	−0.999428	−0.499714	+	0.866190i	$0.666562\pi$
$308$	2793.00	0.516708
$309$	0	0
$310$	2160.00	0.395741
$311$	−7782.00	−1.41890	−0.709448	−	0.704758i	$-0.751056\pi$
$311$	−7782.00	−1.41890	−0.709448	+	0.704758i	$0.751056\pi$
$312$	0	0
$313$	5980.00	1.07990	0.539951	−	0.841696i	$-0.318443\pi$
$313$	5980.00	1.07990	0.539951	+	0.841696i	$0.318443\pi$
$314$	1237.00	0.222318
$315$	0	0
$316$	4074.00	0.725254
$317$	−6180.00	−1.09496	−0.547482	−	0.836818i	$-0.684413\pi$
$317$	−6180.00	−1.09496	−0.547482	+	0.836818i	$0.684413\pi$
$318$	0	0
$319$	−10887.0	−1.91083
$320$	1503.00	0.262563
$321$	0	0
$322$	−1281.00	−0.221700
$323$	3959.00	0.681996
$324$	0	0
$325$	572.000	0.0976272
$326$	−694.000	−0.117905
$327$	0	0
$328$	−1260.00	−0.212109
$329$	2072.00	0.347213
$330$	0	0
$331$	−7190.00	−1.19395	−0.596976	−	0.802259i	$-0.703631\pi$
$331$	−7190.00	−1.19395	−0.596976	+	0.802259i	$0.703631\pi$
$332$	5586.00	0.923408
$333$	0	0
$334$	−721.000	−0.118118
$335$	9774.00	1.59406
$336$	0	0
$337$	4307.00	0.696194	0.348097	−	0.937459i	$-0.386828\pi$
$337$	4307.00	0.696194	0.348097	+	0.937459i	$0.386828\pi$
$338$	169.000	0.0271964
$339$	0	0
$340$	2331.00	0.371812
$341$	−13680.0	−2.17247
$342$	0	0
$343$	−343.000	−0.0539949
$344$	4695.00	0.735865
$345$	0	0
$346$	−674.000	−0.104724
$347$	9808.00	1.51735	0.758676	−	0.651468i	$-0.225847\pi$
$347$	9808.00	1.51735	0.758676	+	0.651468i	$0.225847\pi$
$348$	0	0
$349$	10850.0	1.66415	0.832073	−	0.554666i	$-0.187154\pi$
$349$	10850.0	1.66415	0.832073	+	0.554666i	$0.187154\pi$
$350$	308.000	0.0470380
$351$	0	0
$352$	9177.00	1.38959
$353$	10418.0	1.57081	0.785403	−	0.618985i	$-0.212456\pi$
$353$	10418.0	1.57081	0.785403	+	0.618985i	$0.212456\pi$
$354$	0	0
$355$	−1872.00	−0.279874
$356$	−5082.00	−0.756588
$357$	0	0
$358$	2780.00	0.410412
$359$	3872.00	0.569238	0.284619	−	0.958641i	$-0.408133\pi$
$359$	3872.00	0.569238	0.284619	+	0.958641i	$0.408133\pi$
$360$	0	0
$361$	4590.00	0.669194
$362$	−2506.00	−0.363847
$363$	0	0
$364$	−637.000	−0.0917249
$365$	−5715.00	−0.819553
$366$	0	0
$367$	7040.00	1.00132	0.500661	−	0.865644i	$-0.333090\pi$
$367$	7040.00	1.00132	0.500661	+	0.865644i	$0.333090\pi$
$368$	7503.00	1.06283
$369$	0	0
$370$	3411.00	0.479269
$371$	−2898.00	−0.405544
$372$	0	0
$373$	1896.00	0.263193	0.131597	−	0.991303i	$-0.457990\pi$
$373$	1896.00	0.263193	0.131597	+	0.991303i	$0.457990\pi$
$374$	2109.00	0.291588
$375$	0	0
$376$	4440.00	0.608977
$377$	2483.00	0.339207
$378$	0	0
$379$	828.000	0.112220	0.0561102	−	0.998425i	$-0.482130\pi$
$379$	828.000	0.112220	0.0561102	+	0.998425i	$0.482130\pi$
$380$	6741.00	0.910016
$381$	0	0
$382$	−4409.00	−0.590534
$383$	7383.00	0.984997	0.492498	−	0.870313i	$-0.336084\pi$
$383$	7383.00	0.984997	0.492498	+	0.870313i	$0.336084\pi$
$384$	0	0
$385$	3591.00	0.475362
$386$	−4712.00	−0.621333
$387$	0	0
$388$	−10486.0	−1.37203
$389$	−10506.0	−1.36935	−0.684673	−	0.728851i	$-0.740055\pi$
$389$	−10506.0	−1.36935	−0.684673	+	0.728851i	$0.740055\pi$
$390$	0	0
$391$	6771.00	0.875765
$392$	−735.000	−0.0947018
$393$	0	0
$394$	1328.00	0.169806
$395$	5238.00	0.667221
$396$	0	0
$397$	12098.0	1.52942	0.764712	−	0.644372i	$-0.222881\pi$
$397$	12098.0	1.52942	0.764712	+	0.644372i	$0.222881\pi$
$398$	1279.00	0.161082
$399$	0	0
$400$	−1804.00	−0.225500
$401$	−13250.0	−1.65006	−0.825029	−	0.565090i	$-0.808841\pi$
$401$	−13250.0	−1.65006	−0.825029	+	0.565090i	$0.808841\pi$
$402$	0	0
$403$	3120.00	0.385653
$404$	11648.0	1.43443
$405$	0	0
$406$	1337.00	0.163434
$407$	−21603.0	−2.63101
$408$	0	0
$409$	−919.000	−0.111104	−0.0555521	−	0.998456i	$-0.517692\pi$
$409$	−919.000	−0.111104	−0.0555521	+	0.998456i	$0.517692\pi$
$410$	−756.000	−0.0910639
$411$	0	0
$412$	−5747.00	−0.687219
$413$	280.000	0.0333605
$414$	0	0
$415$	7182.00	0.849519
$416$	−2093.00	−0.246677
$417$	0	0
$418$	6099.00	0.713665
$419$	3563.00	0.415427	0.207714	−	0.978190i	$-0.433398\pi$
$419$	3563.00	0.415427	0.207714	+	0.978190i	$0.433398\pi$
$420$	0	0
$421$	−4170.00	−0.482740	−0.241370	−	0.970433i	$-0.577597\pi$
$421$	−4170.00	−0.482740	−0.241370	+	0.970433i	$0.577597\pi$
$422$	1549.00	0.178683
$423$	0	0
$424$	−6210.00	−0.711284
$425$	−1628.00	−0.185811
$426$	0	0
$427$	−455.000	−0.0515667
$428$	−3878.00	−0.437968
$429$	0	0
$430$	2817.00	0.315925
$431$	1590.00	0.177697	0.0888487	−	0.996045i	$-0.471681\pi$
$431$	1590.00	0.177697	0.0888487	+	0.996045i	$0.471681\pi$
$432$	0	0
$433$	12264.0	1.36113	0.680566	−	0.732687i	$-0.261734\pi$
$433$	12264.0	1.36113	0.680566	+	0.732687i	$0.261734\pi$
$434$	1680.00	0.185812
$435$	0	0
$436$	−5089.00	−0.558988
$437$	19581.0	2.14345
$438$	0	0
$439$	−5311.00	−0.577404	−0.288702	−	0.957419i	$-0.593224\pi$
$439$	−5311.00	−0.577404	−0.288702	+	0.957419i	$0.593224\pi$
$440$	7695.00	0.833738
$441$	0	0
$442$	−481.000	−0.0517621
$443$	11614.0	1.24559	0.622797	−	0.782384i	$-0.285996\pi$
$443$	11614.0	1.24559	0.622797	+	0.782384i	$0.285996\pi$
$444$	0	0
$445$	−6534.00	−0.696048
$446$	−3906.00	−0.414696
$447$	0	0
$448$	1169.00	0.123281
$449$	5031.00	0.528792	0.264396	−	0.964414i	$-0.414827\pi$
$449$	5031.00	0.528792	0.264396	+	0.964414i	$0.414827\pi$
$450$	0	0
$451$	4788.00	0.499907
$452$	−2730.00	−0.284089
$453$	0	0
$454$	4538.00	0.469117
$455$	−819.000	−0.0843853
$456$	0	0
$457$	−11376.0	−1.16444	−0.582218	−	0.813033i	$-0.697815\pi$
$457$	−11376.0	−1.16444	−0.582218	+	0.813033i	$0.697815\pi$
$458$	−6466.00	−0.659686
$459$	0	0
$460$	11529.0	1.16857
$461$	7637.00	0.771563	0.385782	−	0.922590i	$-0.373932\pi$
$461$	7637.00	0.771563	0.385782	+	0.922590i	$0.373932\pi$
$462$	0	0
$463$	−14747.0	−1.48024	−0.740120	−	0.672475i	$-0.765231\pi$
$463$	−14747.0	−1.48024	−0.740120	+	0.672475i	$0.765231\pi$
$464$	−7831.00	−0.783502
$465$	0	0
$466$	−3408.00	−0.338782
$467$	−7051.00	−0.698675	−0.349338	−	0.936997i	$-0.613593\pi$
$467$	−7051.00	−0.698675	−0.349338	+	0.936997i	$0.613593\pi$
$468$	0	0
$469$	7602.00	0.748460
$470$	2664.00	0.261449
$471$	0	0
$472$	600.000	0.0585111
$473$	−17841.0	−1.73431
$474$	0	0
$475$	−4708.00	−0.454774
$476$	1813.00	0.174577
$477$	0	0
$478$	1916.00	0.183338
$479$	4909.00	0.468263	0.234131	−	0.972205i	$-0.424775\pi$
$479$	4909.00	0.468263	0.234131	+	0.972205i	$0.424775\pi$
$480$	0	0
$481$	4927.00	0.467052
$482$	−4790.00	−0.452653
$483$	0	0
$484$	−13426.0	−1.26089
$485$	−13482.0	−1.26224
$486$	0	0
$487$	6376.00	0.593273	0.296637	−	0.954990i	$-0.404135\pi$
$487$	6376.00	0.593273	0.296637	+	0.954990i	$0.404135\pi$
$488$	−975.000	−0.0904430
$489$	0	0
$490$	−441.000	−0.0406579
$491$	10386.0	0.954610	0.477305	−	0.878738i	$-0.341614\pi$
$491$	10386.0	0.954610	0.477305	+	0.878738i	$0.341614\pi$
$492$	0	0
$493$	−7067.00	−0.645602
$494$	−1391.00	−0.126688
$495$	0	0
$496$	−9840.00	−0.890784
$497$	−1456.00	−0.131410
$498$	0	0
$499$	2876.00	0.258011	0.129005	−	0.991644i	$-0.458822\pi$
$499$	2876.00	0.258011	0.129005	+	0.991644i	$0.458822\pi$
$500$	−10647.0	−0.952297
$501$	0	0
$502$	−5075.00	−0.451212
$503$	11102.0	0.984123	0.492061	−	0.870561i	$-0.336244\pi$
$503$	11102.0	0.984123	0.492061	+	0.870561i	$0.336244\pi$
$504$	0	0
$505$	14976.0	1.31965
$506$	10431.0	0.916432
$507$	0	0
$508$	6454.00	0.563681
$509$	13613.0	1.18543	0.592717	−	0.805411i	$-0.298055\pi$
$509$	13613.0	1.18543	0.592717	+	0.805411i	$0.298055\pi$
$510$	0	0
$511$	−4445.00	−0.384805
$512$	11521.0	0.994455
$513$	0	0
$514$	−1682.00	−0.144338
$515$	−7389.00	−0.632230
$516$	0	0
$517$	−16872.0	−1.43526
$518$	2653.00	0.225031
$519$	0	0
$520$	−1755.00	−0.148004
$521$	9655.00	0.811887	0.405944	−	0.913898i	$-0.366943\pi$
$521$	9655.00	0.811887	0.405944	+	0.913898i	$0.366943\pi$
$522$	0	0
$523$	−21908.0	−1.83168	−0.915841	−	0.401541i	$-0.868475\pi$
$523$	−21908.0	−1.83168	−0.915841	+	0.401541i	$0.868475\pi$
$524$	18193.0	1.51673
$525$	0	0
$526$	−2316.00	−0.191982
$527$	−8880.00	−0.734002
$528$	0	0
$529$	21322.0	1.75245
$530$	−3726.00	−0.305372
$531$	0	0
$532$	5243.00	0.427280
$533$	−1092.00	−0.0887425
$534$	0	0
$535$	−4986.00	−0.402923
$536$	16290.0	1.31273
$537$	0	0
$538$	−1230.00	−0.0985670
$539$	2793.00	0.223197
$540$	0	0
$541$	−23353.0	−1.85587	−0.927933	−	0.372746i	$-0.878416\pi$
$541$	−23353.0	−1.85587	−0.927933	+	0.372746i	$0.878416\pi$
$542$	−4030.00	−0.319379
$543$	0	0
$544$	5957.00	0.469493
$545$	−6543.00	−0.514259
$546$	0	0
$547$	14660.0	1.14592	0.572958	−	0.819585i	$-0.305796\pi$
$547$	14660.0	1.14592	0.572958	+	0.819585i	$0.305796\pi$
$548$	18515.0	1.44329
$549$	0	0
$550$	−2508.00	−0.194439
$551$	−20437.0	−1.58012
$552$	0	0
$553$	4074.00	0.313280
$554$	−7106.00	−0.544955
$555$	0	0
$556$	7644.00	0.583054
$557$	−17184.0	−1.30720	−0.653599	−	0.756841i	$-0.726742\pi$
$557$	−17184.0	−1.30720	−0.653599	+	0.756841i	$0.726742\pi$
$558$	0	0
$559$	4069.00	0.307872
$560$	2583.00	0.194914
$561$	0	0
$562$	1062.00	0.0797113
$563$	8185.00	0.612712	0.306356	−	0.951917i	$-0.400890\pi$
$563$	8185.00	0.612712	0.306356	+	0.951917i	$0.400890\pi$
$564$	0	0
$565$	−3510.00	−0.261357
$566$	3988.00	0.296163
$567$	0	0
$568$	−3120.00	−0.230479
$569$	−1574.00	−0.115968	−0.0579838	−	0.998318i	$-0.518467\pi$
$569$	−1574.00	−0.115968	−0.0579838	+	0.998318i	$0.518467\pi$
$570$	0	0
$571$	7384.00	0.541175	0.270587	−	0.962695i	$-0.412782\pi$
$571$	7384.00	0.541175	0.270587	+	0.962695i	$0.412782\pi$
$572$	5187.00	0.379160
$573$	0	0
$574$	−588.000	−0.0427572
$575$	−8052.00	−0.583985
$576$	0	0
$577$	13298.0	0.959451	0.479725	−	0.877419i	$-0.340736\pi$
$577$	13298.0	0.959451	0.479725	+	0.877419i	$0.340736\pi$
$578$	−3544.00	−0.255036
$579$	0	0
$580$	−12033.0	−0.861454
$581$	5586.00	0.398875
$582$	0	0
$583$	23598.0	1.67638
$584$	−9525.00	−0.674910
$585$	0	0
$586$	2366.00	0.166789
$587$	−714.000	−0.0502043	−0.0251022	−	0.999685i	$-0.507991\pi$
$587$	−714.000	−0.0502043	−0.0251022	+	0.999685i	$0.507991\pi$
$588$	0	0
$589$	−25680.0	−1.79648
$590$	360.000	0.0251203
$591$	0	0
$592$	−15539.0	−1.07880
$593$	−20526.0	−1.42142	−0.710710	−	0.703485i	$-0.751626\pi$
$593$	−20526.0	−1.42142	−0.710710	+	0.703485i	$0.751626\pi$
$594$	0	0
$595$	2331.00	0.160608
$596$	6804.00	0.467622
$597$	0	0
$598$	−2379.00	−0.162683
$599$	−4255.00	−0.290241	−0.145121	−	0.989414i	$-0.546357\pi$
$599$	−4255.00	−0.290241	−0.145121	+	0.989414i	$0.546357\pi$
$600$	0	0
$601$	22232.0	1.50892	0.754461	−	0.656345i	$-0.227898\pi$
$601$	22232.0	1.50892	0.754461	+	0.656345i	$0.227898\pi$
$602$	2191.00	0.148336
$603$	0	0
$604$	−483.000	−0.0325381
$605$	−17262.0	−1.16000
$606$	0	0
$607$	−20263.0	−1.35494	−0.677471	−	0.735549i	$-0.736924\pi$
$607$	−20263.0	−1.35494	−0.677471	+	0.735549i	$0.736924\pi$
$608$	17227.0	1.14909
$609$	0	0
$610$	−585.000	−0.0388294
$611$	3848.00	0.254785
$612$	0	0
$613$	−9409.00	−0.619944	−0.309972	−	0.950746i	$-0.600320\pi$
$613$	−9409.00	−0.619944	−0.309972	+	0.950746i	$0.600320\pi$
$614$	−5376.00	−0.353351
$615$	0	0
$616$	5985.00	0.391465
$617$	−1815.00	−0.118426	−0.0592132	−	0.998245i	$-0.518859\pi$
$617$	−1815.00	−0.118426	−0.0592132	+	0.998245i	$0.518859\pi$
$618$	0	0
$619$	7859.00	0.510307	0.255153	−	0.966901i	$-0.417874\pi$
$619$	7859.00	0.510307	0.255153	+	0.966901i	$0.417874\pi$
$620$	−15120.0	−0.979409
$621$	0	0
$622$	−7782.00	−0.501656
$623$	−5082.00	−0.326815
$624$	0	0
$625$	−8189.00	−0.524096
$626$	5980.00	0.381803
$627$	0	0
$628$	−8659.00	−0.550210
$629$	−14023.0	−0.888925
$630$	0	0
$631$	−15839.0	−0.999272	−0.499636	−	0.866235i	$-0.666533\pi$
$631$	−15839.0	−0.999272	−0.499636	+	0.866235i	$0.666533\pi$
$632$	8730.00	0.549463
$633$	0	0
$634$	−6180.00	−0.387128
$635$	8298.00	0.518577
$636$	0	0
$637$	−637.000	−0.0396214
$638$	−10887.0	−0.675581
$639$	0	0
$640$	13095.0	0.808790
$641$	−30246.0	−1.86372	−0.931861	−	0.362817i	$-0.881815\pi$
$641$	−30246.0	−1.86372	−0.931861	+	0.362817i	$0.881815\pi$
$642$	0	0
$643$	3941.00	0.241707	0.120854	−	0.992670i	$-0.461437\pi$
$643$	3941.00	0.241707	0.120854	+	0.992670i	$0.461437\pi$
$644$	8967.00	0.548679
$645$	0	0
$646$	3959.00	0.241122
$647$	9984.00	0.606664	0.303332	−	0.952885i	$-0.401901\pi$
$647$	9984.00	0.606664	0.303332	+	0.952885i	$0.401901\pi$
$648$	0	0
$649$	−2280.00	−0.137901
$650$	572.000	0.0345164
$651$	0	0
$652$	4858.00	0.291801
$653$	14967.0	0.896943	0.448472	−	0.893797i	$-0.351969\pi$
$653$	14967.0	0.896943	0.448472	+	0.893797i	$0.351969\pi$
$654$	0	0
$655$	23391.0	1.39536
$656$	3444.00	0.204978
$657$	0	0
$658$	2072.00	0.122758
$659$	−9718.00	−0.574445	−0.287223	−	0.957864i	$-0.592732\pi$
$659$	−9718.00	−0.574445	−0.287223	+	0.957864i	$0.592732\pi$
$660$	0	0
$661$	7194.00	0.423319	0.211660	−	0.977343i	$-0.432113\pi$
$661$	7194.00	0.423319	0.211660	+	0.977343i	$0.432113\pi$
$662$	−7190.00	−0.422126
$663$	0	0
$664$	11970.0	0.699587
$665$	6741.00	0.393090
$666$	0	0
$667$	−34953.0	−2.02906
$668$	5047.00	0.292327
$669$	0	0
$670$	9774.00	0.563586
$671$	3705.00	0.213159
$672$	0	0
$673$	−23441.0	−1.34262	−0.671311	−	0.741176i	$-0.734268\pi$
$673$	−23441.0	−1.34262	−0.671311	+	0.741176i	$0.734268\pi$
$674$	4307.00	0.246142
$675$	0	0
$676$	−1183.00	−0.0673077
$677$	−4958.00	−0.281464	−0.140732	−	0.990048i	$-0.544946\pi$
$677$	−4958.00	−0.281464	−0.140732	+	0.990048i	$0.544946\pi$
$678$	0	0
$679$	−10486.0	−0.592659
$680$	4995.00	0.281690
$681$	0	0
$682$	−13680.0	−0.768085
$683$	3459.00	0.193785	0.0968924	−	0.995295i	$-0.469110\pi$
$683$	3459.00	0.193785	0.0968924	+	0.995295i	$0.469110\pi$
$684$	0	0
$685$	23805.0	1.32780
$686$	−343.000	−0.0190901
$687$	0	0
$688$	−12833.0	−0.711124
$689$	−5382.00	−0.297588
$690$	0	0
$691$	2900.00	0.159654	0.0798272	−	0.996809i	$-0.474563\pi$
$691$	2900.00	0.159654	0.0798272	+	0.996809i	$0.474563\pi$
$692$	4718.00	0.259178
$693$	0	0
$694$	9808.00	0.536465
$695$	9828.00	0.536399
$696$	0	0
$697$	3108.00	0.168901
$698$	10850.0	0.588365
$699$	0	0
$700$	−2156.00	−0.116413
$701$	24162.0	1.30183	0.650917	−	0.759149i	$-0.274384\pi$
$701$	24162.0	1.30183	0.650917	+	0.759149i	$0.274384\pi$
$702$	0	0
$703$	−40553.0	−2.17565
$704$	−9519.00	−0.509603
$705$	0	0
$706$	10418.0	0.555363
$707$	11648.0	0.619615
$708$	0	0
$709$	11318.0	0.599515	0.299758	−	0.954015i	$-0.403094\pi$
$709$	11318.0	0.599515	0.299758	+	0.954015i	$0.403094\pi$
$710$	−1872.00	−0.0989506
$711$	0	0
$712$	−10890.0	−0.573202
$713$	−43920.0	−2.30690
$714$	0	0
$715$	6669.00	0.348820
$716$	−19460.0	−1.01572
$717$	0	0
$718$	3872.00	0.201256
$719$	−5994.00	−0.310902	−0.155451	−	0.987844i	$-0.549683\pi$
$719$	−5994.00	−0.310902	−0.155451	+	0.987844i	$0.549683\pi$
$720$	0	0
$721$	−5747.00	−0.296851
$722$	4590.00	0.236596
$723$	0	0
$724$	17542.0	0.900474
$725$	8404.00	0.430506
$726$	0	0
$727$	−15743.0	−0.803130	−0.401565	−	0.915831i	$-0.631534\pi$
$727$	−15743.0	−0.803130	−0.401565	+	0.915831i	$0.631534\pi$
$728$	−1365.00	−0.0694921
$729$	0	0
$730$	−5715.00	−0.289756
$731$	−11581.0	−0.585963
$732$	0	0
$733$	−16644.0	−0.838691	−0.419345	−	0.907827i	$-0.637740\pi$
$733$	−16644.0	−0.838691	−0.419345	+	0.907827i	$0.637740\pi$
$734$	7040.00	0.354021
$735$	0	0
$736$	29463.0	1.47557
$737$	−61902.0	−3.09388
$738$	0	0
$739$	−17858.0	−0.888927	−0.444464	−	0.895797i	$-0.646606\pi$
$739$	−17858.0	−0.888927	−0.444464	+	0.895797i	$0.646606\pi$
$740$	−23877.0	−1.18613
$741$	0	0
$742$	−2898.00	−0.143381
$743$	−20022.0	−0.988608	−0.494304	−	0.869289i	$-0.664577\pi$
$743$	−20022.0	−0.988608	−0.494304	+	0.869289i	$0.664577\pi$
$744$	0	0
$745$	8748.00	0.430204
$746$	1896.00	0.0930529
$747$	0	0
$748$	−14763.0	−0.721643
$749$	−3878.00	−0.189184
$750$	0	0
$751$	16960.0	0.824073	0.412037	−	0.911167i	$-0.364818\pi$
$751$	16960.0	0.824073	0.412037	+	0.911167i	$0.364818\pi$
$752$	−12136.0	−0.588503
$753$	0	0
$754$	2483.00	0.119928
$755$	−621.000	−0.0299344
$756$	0	0
$757$	−222.000	−0.0106588	−0.00532941	−	0.999986i	$-0.501696\pi$
$757$	−222.000	−0.0106588	−0.00532941	+	0.999986i	$0.501696\pi$
$758$	828.000	0.0396759
$759$	0	0
$760$	14445.0	0.689441
$761$	22020.0	1.04892	0.524458	−	0.851437i	$-0.324268\pi$
$761$	22020.0	1.04892	0.524458	+	0.851437i	$0.324268\pi$
$762$	0	0
$763$	−5089.00	−0.241460
$764$	30863.0	1.46150
$765$	0	0
$766$	7383.00	0.348249
$767$	520.000	0.0244799
$768$	0	0
$769$	16345.0	0.766470	0.383235	−	0.923651i	$-0.374810\pi$
$769$	16345.0	0.766470	0.383235	+	0.923651i	$0.374810\pi$
$770$	3591.00	0.168066
$771$	0	0
$772$	32984.0	1.53772
$773$	−75.0000	−0.00348973	−0.00174487	−	0.999998i	$-0.500555\pi$
$773$	−75.0000	−0.00348973	−0.00174487	+	0.999998i	$0.500555\pi$
$774$	0	0
$775$	10560.0	0.489453
$776$	−22470.0	−1.03947
$777$	0	0
$778$	−10506.0	−0.484137
$779$	8988.00	0.413387
$780$	0	0
$781$	11856.0	0.543202
$782$	6771.00	0.309630
$783$	0	0
$784$	2009.00	0.0915179
$785$	−11133.0	−0.506183
$786$	0	0
$787$	14635.0	0.662873	0.331437	−	0.943477i	$-0.392467\pi$
$787$	14635.0	0.662873	0.331437	+	0.943477i	$0.392467\pi$
$788$	−9296.00	−0.420249
$789$	0	0
$790$	5238.00	0.235898
$791$	−2730.00	−0.122715
$792$	0	0
$793$	−845.000	−0.0378396
$794$	12098.0	0.540733
$795$	0	0
$796$	−8953.00	−0.398657
$797$	11424.0	0.507728	0.253864	−	0.967240i	$-0.418299\pi$
$797$	11424.0	0.507728	0.253864	+	0.967240i	$0.418299\pi$
$798$	0	0
$799$	−10952.0	−0.484924
$800$	−7084.00	−0.313072
$801$	0	0
$802$	−13250.0	−0.583384
$803$	36195.0	1.59065
$804$	0	0
$805$	11529.0	0.504775
$806$	3120.00	0.136349
$807$	0	0
$808$	24960.0	1.08674
$809$	−7762.00	−0.337327	−0.168663	−	0.985674i	$-0.553945\pi$
$809$	−7762.00	−0.337327	−0.168663	+	0.985674i	$0.553945\pi$
$810$	0	0
$811$	6167.00	0.267019	0.133510	−	0.991048i	$-0.457375\pi$
$811$	6167.00	0.267019	0.133510	+	0.991048i	$0.457375\pi$
$812$	−9359.00	−0.404478
$813$	0	0
$814$	−21603.0	−0.930202
$815$	6246.00	0.268451
$816$	0	0
$817$	−33491.0	−1.43415
$818$	−919.000	−0.0392813
$819$	0	0
$820$	5292.00	0.225372
$821$	−18696.0	−0.794756	−0.397378	−	0.917655i	$-0.630080\pi$
$821$	−18696.0	−0.794756	−0.397378	+	0.917655i	$0.630080\pi$
$822$	0	0
$823$	−36380.0	−1.54086	−0.770430	−	0.637525i	$-0.779958\pi$
$823$	−36380.0	−1.54086	−0.770430	+	0.637525i	$0.779958\pi$
$824$	−12315.0	−0.520647
$825$	0	0
$826$	280.000	0.0117947
$827$	−5231.00	−0.219951	−0.109976	−	0.993934i	$-0.535077\pi$
$827$	−5231.00	−0.219951	−0.109976	+	0.993934i	$0.535077\pi$
$828$	0	0
$829$	6473.00	0.271190	0.135595	−	0.990764i	$-0.456705\pi$
$829$	6473.00	0.271190	0.135595	+	0.990764i	$0.456705\pi$
$830$	7182.00	0.300350
$831$	0	0
$832$	2171.00	0.0904638
$833$	1813.00	0.0754102
$834$	0	0
$835$	6489.00	0.268935
$836$	−42693.0	−1.76623
$837$	0	0
$838$	3563.00	0.146876
$839$	7420.00	0.305324	0.152662	−	0.988278i	$-0.451215\pi$
$839$	7420.00	0.305324	0.152662	+	0.988278i	$0.451215\pi$
$840$	0	0
$841$	12092.0	0.495797
$842$	−4170.00	−0.170674
$843$	0	0
$844$	−10843.0	−0.442217
$845$	−1521.00	−0.0619219
$846$	0	0
$847$	−13426.0	−0.544655
$848$	16974.0	0.687370
$849$	0	0
$850$	−1628.00	−0.0656940
$851$	−69357.0	−2.79380
$852$	0	0
$853$	6300.00	0.252881	0.126441	−	0.991974i	$-0.459645\pi$
$853$	6300.00	0.252881	0.126441	+	0.991974i	$0.459645\pi$
$854$	−455.000	−0.0182316
$855$	0	0
$856$	−8310.00	−0.331811
$857$	−12654.0	−0.504379	−0.252189	−	0.967678i	$-0.581151\pi$
$857$	−12654.0	−0.504379	−0.252189	+	0.967678i	$0.581151\pi$
$858$	0	0
$859$	−15524.0	−0.616615	−0.308307	−	0.951287i	$-0.599763\pi$
$859$	−15524.0	−0.616615	−0.308307	+	0.951287i	$0.599763\pi$
$860$	−19719.0	−0.781875
$861$	0	0
$862$	1590.00	0.0628255
$863$	34210.0	1.34939	0.674694	−	0.738098i	$-0.264276\pi$
$863$	34210.0	1.34939	0.674694	+	0.738098i	$0.264276\pi$
$864$	0	0
$865$	6066.00	0.238440
$866$	12264.0	0.481233
$867$	0	0
$868$	−11760.0	−0.459862
$869$	−33174.0	−1.29500
$870$	0	0
$871$	14118.0	0.549219
$872$	−10905.0	−0.423498
$873$	0	0
$874$	19581.0	0.757823
$875$	−10647.0	−0.411353
$876$	0	0
$877$	−44010.0	−1.69454	−0.847270	−	0.531162i	$-0.821756\pi$
$877$	−44010.0	−1.69454	−0.847270	+	0.531162i	$0.821756\pi$
$878$	−5311.00	−0.204143
$879$	0	0
$880$	−21033.0	−0.805707
$881$	−49035.0	−1.87518	−0.937589	−	0.347746i	$-0.886947\pi$
$881$	−49035.0	−1.87518	−0.937589	+	0.347746i	$0.886947\pi$
$882$	0	0
$883$	5735.00	0.218571	0.109285	−	0.994010i	$-0.465144\pi$
$883$	5735.00	0.218571	0.109285	+	0.994010i	$0.465144\pi$
$884$	3367.00	0.128105
$885$	0	0
$886$	11614.0	0.440384
$887$	10764.0	0.407463	0.203732	−	0.979027i	$-0.434693\pi$
$887$	10764.0	0.407463	0.203732	+	0.979027i	$0.434693\pi$
$888$	0	0
$889$	6454.00	0.243487
$890$	−6534.00	−0.246090
$891$	0	0
$892$	27342.0	1.02632
$893$	−31672.0	−1.18686
$894$	0	0
$895$	−25020.0	−0.934443
$896$	10185.0	0.379751
$897$	0	0
$898$	5031.00	0.186956
$899$	45840.0	1.70061
$900$	0	0
$901$	15318.0	0.566389
$902$	4788.00	0.176744
$903$	0	0
$904$	−5850.00	−0.215230
$905$	22554.0	0.828420
$906$	0	0
$907$	−32348.0	−1.18423	−0.592116	−	0.805853i	$-0.701707\pi$
$907$	−32348.0	−1.18423	−0.592116	+	0.805853i	$0.701707\pi$
$908$	−31766.0	−1.16100
$909$	0	0
$910$	−819.000	−0.0298347
$911$	46065.0	1.67530	0.837652	−	0.546205i	$-0.183928\pi$
$911$	46065.0	1.67530	0.837652	+	0.546205i	$0.183928\pi$
$912$	0	0
$913$	−45486.0	−1.64881
$914$	−11376.0	−0.411690
$915$	0	0
$916$	45262.0	1.63264
$917$	18193.0	0.655164
$918$	0	0
$919$	−26818.0	−0.962616	−0.481308	−	0.876552i	$-0.659838\pi$
$919$	−26818.0	−0.962616	−0.481308	+	0.876552i	$0.659838\pi$
$920$	24705.0	0.885326
$921$	0	0
$922$	7637.00	0.272789
$923$	−2704.00	−0.0964282
$924$	0	0
$925$	16676.0	0.592761
$926$	−14747.0	−0.523344
$927$	0	0
$928$	−30751.0	−1.08777
$929$	1076.00	0.0380004	0.0190002	−	0.999819i	$-0.493952\pi$
$929$	1076.00	0.0380004	0.0190002	+	0.999819i	$0.493952\pi$
$930$	0	0
$931$	5243.00	0.184568
$932$	23856.0	0.838443
$933$	0	0
$934$	−7051.00	−0.247019
$935$	−18981.0	−0.663898
$936$	0	0
$937$	31822.0	1.10948	0.554738	−	0.832025i	$-0.312818\pi$
$937$	31822.0	1.10948	0.554738	+	0.832025i	$0.312818\pi$
$938$	7602.00	0.264621
$939$	0	0
$940$	−18648.0	−0.647054
$941$	−7670.00	−0.265712	−0.132856	−	0.991135i	$-0.542415\pi$
$941$	−7670.00	−0.265712	−0.132856	+	0.991135i	$0.542415\pi$
$942$	0	0
$943$	15372.0	0.530839
$944$	−1640.00	−0.0565439
$945$	0	0
$946$	−17841.0	−0.613172
$947$	44661.0	1.53251	0.766255	−	0.642536i	$-0.222118\pi$
$947$	44661.0	1.53251	0.766255	+	0.642536i	$0.222118\pi$
$948$	0	0
$949$	−8255.00	−0.282369
$950$	−4708.00	−0.160787
$951$	0	0
$952$	3885.00	0.132262
$953$	50496.0	1.71640	0.858198	−	0.513318i	$-0.171584\pi$
$953$	50496.0	1.71640	0.858198	+	0.513318i	$0.171584\pi$
$954$	0	0
$955$	39681.0	1.34455
$956$	−13412.0	−0.453740
$957$	0	0
$958$	4909.00	0.165556
$959$	18515.0	0.623442
$960$	0	0
$961$	27809.0	0.933470
$962$	4927.00	0.165128
$963$	0	0
$964$	33530.0	1.12026
$965$	42408.0	1.41468
$966$	0	0
$967$	5287.00	0.175821	0.0879103	−	0.996128i	$-0.471981\pi$
$967$	5287.00	0.175821	0.0879103	+	0.996128i	$0.471981\pi$
$968$	−28770.0	−0.955272
$969$	0	0
$970$	−13482.0	−0.446269
$971$	2840.00	0.0938619	0.0469310	−	0.998898i	$-0.485056\pi$
$971$	2840.00	0.0938619	0.0469310	+	0.998898i	$0.485056\pi$
$972$	0	0
$973$	7644.00	0.251855
$974$	6376.00	0.209754
$975$	0	0
$976$	2665.00	0.0874022
$977$	8653.00	0.283351	0.141676	−	0.989913i	$-0.454751\pi$
$977$	8653.00	0.283351	0.141676	+	0.989913i	$0.454751\pi$
$978$	0	0
$979$	41382.0	1.35094
$980$	3087.00	0.100623
$981$	0	0
$982$	10386.0	0.337506
$983$	11069.0	0.359152	0.179576	−	0.983744i	$-0.442527\pi$
$983$	11069.0	0.359152	0.179576	+	0.983744i	$0.442527\pi$
$984$	0	0
$985$	−11952.0	−0.386622
$986$	−7067.00	−0.228255
$987$	0	0
$988$	9737.00	0.313538
$989$	−57279.0	−1.84162
$990$	0	0
$991$	6334.00	0.203033	0.101517	−	0.994834i	$-0.467630\pi$
$991$	6334.00	0.203033	0.101517	+	0.994834i	$0.467630\pi$
$992$	−38640.0	−1.23671
$993$	0	0
$994$	−1456.00	−0.0464603
$995$	−11511.0	−0.366757
$996$	0	0
$997$	−12154.0	−0.386079	−0.193040	−	0.981191i	$-0.561835\pi$
$997$	−12154.0	−0.386079	−0.193040	+	0.981191i	$0.561835\pi$
$998$	2876.00	0.0912206
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.4.a.a.1.1		1
3.2	odd	2		273.4.a.c.1.1	✓	1
21.20	even	2		1911.4.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.4.a.c.1.1	✓	1	3.2	odd	2
819.4.a.a.1.1		1	1.1	even	1	trivial
1911.4.a.d.1.1		1	21.20	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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	819.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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