LMFDB - Embedded newform 1089.4.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1089,4,Mod(1,1089)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1089, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1089.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1089 = 3^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1089.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:	$64.2530799963$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 363)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1089.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} -7.00000 q^{4} -7.00000 q^{5} -4.00000 q^{7} -15.0000 q^{8} +O(q^{10})$

$q+1.00000 q^{2} -7.00000 q^{4} -7.00000 q^{5} -4.00000 q^{7} -15.0000 q^{8} -7.00000 q^{10} -43.0000 q^{13} -4.00000 q^{14} +41.0000 q^{16} -41.0000 q^{17} +72.0000 q^{19} +49.0000 q^{20} -104.000 q^{23} -76.0000 q^{25} -43.0000 q^{26} +28.0000 q^{28} -273.000 q^{29} -272.000 q^{31} +161.000 q^{32} -41.0000 q^{34} +28.0000 q^{35} -165.000 q^{37} +72.0000 q^{38} +105.000 q^{40} +403.000 q^{41} -120.000 q^{43} -104.000 q^{46} +220.000 q^{47} -327.000 q^{49} -76.0000 q^{50} +301.000 q^{52} +741.000 q^{53} +60.0000 q^{56} -273.000 q^{58} +112.000 q^{59} +858.000 q^{61} -272.000 q^{62} -167.000 q^{64} +301.000 q^{65} +284.000 q^{67} +287.000 q^{68} +28.0000 q^{70} +624.000 q^{71} -586.000 q^{73} -165.000 q^{74} -504.000 q^{76} -308.000 q^{79} -287.000 q^{80} +403.000 q^{82} +287.000 q^{85} -120.000 q^{86} +321.000 q^{89} +172.000 q^{91} +728.000 q^{92} +220.000 q^{94} -504.000 q^{95} +179.000 q^{97} -327.000 q^{98} +O(q^{100})$

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
$5$	−7.00000	−0.626099	−0.313050	−	0.949737i	$-0.601351\pi$
$5$	−7.00000	−0.626099	−0.313050	+	0.949737i	$0.601351\pi$
$6$	0	0
$7$	−4.00000	−0.215980	−0.107990	−	0.994152i	$-0.534441\pi$
$7$	−4.00000	−0.215980	−0.107990	+	0.994152i	$0.534441\pi$
$8$	−15.0000	−0.662913
$9$	0	0
$10$	−7.00000	−0.221359
$11$	0	0
$11$	0	0
$12$	0	0
$13$	−43.0000	−0.917389	−0.458694	−	0.888594i	$-0.651683\pi$
$13$	−43.0000	−0.917389	−0.458694	+	0.888594i	$0.651683\pi$
$14$	−4.00000	−0.0763604
$15$	0	0
$16$	41.0000	0.640625
$17$	−41.0000	−0.584939	−0.292469	−	0.956275i	$-0.594477\pi$
$17$	−41.0000	−0.584939	−0.292469	+	0.956275i	$0.594477\pi$
$18$	0	0
$19$	72.0000	0.869365	0.434682	−	0.900584i	$-0.356861\pi$
$19$	72.0000	0.869365	0.434682	+	0.900584i	$0.356861\pi$
$20$	49.0000	0.547837
$21$	0	0
$22$	0	0
$23$	−104.000	−0.942848	−0.471424	−	0.881907i	$-0.656260\pi$
$23$	−104.000	−0.942848	−0.471424	+	0.881907i	$0.656260\pi$
$24$	0	0
$25$	−76.0000	−0.608000
$26$	−43.0000	−0.324346
$27$	0	0
$28$	28.0000	0.188982
$29$	−273.000	−1.74810	−0.874049	−	0.485838i	$-0.838514\pi$
$29$	−273.000	−1.74810	−0.874049	+	0.485838i	$0.838514\pi$
$30$	0	0
$31$	−272.000	−1.57589	−0.787946	−	0.615745i	$-0.788855\pi$
$31$	−272.000	−1.57589	−0.787946	+	0.615745i	$0.788855\pi$
$32$	161.000	0.889408
$33$	0	0
$34$	−41.0000	−0.206807
$35$	28.0000	0.135225
$36$	0	0
$37$	−165.000	−0.733131	−0.366565	−	0.930392i	$-0.619466\pi$
$37$	−165.000	−0.733131	−0.366565	+	0.930392i	$0.619466\pi$
$38$	72.0000	0.307367
$39$	0	0
$40$	105.000	0.415049
$41$	403.000	1.53507	0.767537	−	0.641005i	$-0.221482\pi$
$41$	403.000	1.53507	0.767537	+	0.641005i	$0.221482\pi$
$42$	0	0
$43$	−120.000	−0.425577	−0.212789	−	0.977098i	$-0.568255\pi$
$43$	−120.000	−0.425577	−0.212789	+	0.977098i	$0.568255\pi$
$44$	0	0
$45$	0	0
$46$	−104.000	−0.333347
$47$	220.000	0.682772	0.341386	−	0.939923i	$-0.389104\pi$
$47$	220.000	0.682772	0.341386	+	0.939923i	$0.389104\pi$
$48$	0	0
$49$	−327.000	−0.953353
$50$	−76.0000	−0.214960
$51$	0	0
$52$	301.000	0.802715
$53$	741.000	1.92046	0.960228	−	0.279217i	$-0.0900748\pi$
$53$	741.000	1.92046	0.960228	+	0.279217i	$0.0900748\pi$
$54$	0	0
$55$	0	0
$56$	60.0000	0.143176
$57$	0	0
$58$	−273.000	−0.618046
$59$	112.000	0.247138	0.123569	−	0.992336i	$-0.460566\pi$
$59$	112.000	0.247138	0.123569	+	0.992336i	$0.460566\pi$
$60$	0	0
$61$	858.000	1.80091	0.900456	−	0.434947i	$-0.143233\pi$
$61$	858.000	1.80091	0.900456	+	0.434947i	$0.143233\pi$
$62$	−272.000	−0.557162
$63$	0	0
$64$	−167.000	−0.326172
$65$	301.000	0.574376
$66$	0	0
$67$	284.000	0.517853	0.258926	−	0.965897i	$-0.416631\pi$
$67$	284.000	0.517853	0.258926	+	0.965897i	$0.416631\pi$
$68$	287.000	0.511822
$69$	0	0
$70$	28.0000	0.0478091
$71$	624.000	1.04303	0.521515	−	0.853242i	$-0.325367\pi$
$71$	624.000	1.04303	0.521515	+	0.853242i	$0.325367\pi$
$72$	0	0
$73$	−586.000	−0.939536	−0.469768	−	0.882790i	$-0.655662\pi$
$73$	−586.000	−0.939536	−0.469768	+	0.882790i	$0.655662\pi$
$74$	−165.000	−0.259201
$75$	0	0
$76$	−504.000	−0.760694
$77$	0	0
$78$	0	0
$79$	−308.000	−0.438642	−0.219321	−	0.975653i	$-0.570384\pi$
$79$	−308.000	−0.438642	−0.219321	+	0.975653i	$0.570384\pi$
$80$	−287.000	−0.401095
$81$	0	0
$82$	403.000	0.542731
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	0	0
$85$	287.000	0.366230
$86$	−120.000	−0.150464
$87$	0	0
$88$	0	0
$89$	321.000	0.382314	0.191157	−	0.981559i	$-0.438776\pi$
$89$	321.000	0.382314	0.191157	+	0.981559i	$0.438776\pi$
$90$	0	0
$91$	172.000	0.198137
$92$	728.000	0.824992
$93$	0	0
$94$	220.000	0.241396
$95$	−504.000	−0.544309
$96$	0	0
$97$	179.000	0.187368	0.0936840	−	0.995602i	$-0.470136\pi$
$97$	179.000	0.187368	0.0936840	+	0.995602i	$0.470136\pi$
$98$	−327.000	−0.337061
$99$	0	0
$100$	532.000	0.532000
$101$	14.0000	0.0137926	0.00689630	−	0.999976i	$-0.497805\pi$
$101$	14.0000	0.0137926	0.00689630	+	0.999976i	$0.497805\pi$
$102$	0	0
$103$	1244.00	1.19005	0.595024	−	0.803708i	$-0.297143\pi$
$103$	1244.00	1.19005	0.595024	+	0.803708i	$0.297143\pi$
$104$	645.000	0.608149
$105$	0	0
$106$	741.000	0.678984
$107$	1416.00	1.27934	0.639672	−	0.768648i	$-0.279070\pi$
$107$	1416.00	1.27934	0.639672	+	0.768648i	$0.279070\pi$
$108$	0	0
$109$	329.000	0.289105	0.144553	−	0.989497i	$-0.453826\pi$
$109$	329.000	0.289105	0.144553	+	0.989497i	$0.453826\pi$
$110$	0	0
$111$	0	0
$112$	−164.000	−0.138362
$113$	−267.000	−0.222277	−0.111138	−	0.993805i	$-0.535450\pi$
$113$	−267.000	−0.222277	−0.111138	+	0.993805i	$0.535450\pi$
$114$	0	0
$115$	728.000	0.590316
$116$	1911.00	1.52959
$117$	0	0
$118$	112.000	0.0873766
$119$	164.000	0.126335
$120$	0	0
$121$	0	0
$122$	858.000	0.636719
$123$	0	0
$124$	1904.00	1.37891
$125$	1407.00	1.00677
$126$	0	0
$127$	−308.000	−0.215201	−0.107601	−	0.994194i	$-0.534317\pi$
$127$	−308.000	−0.215201	−0.107601	+	0.994194i	$0.534317\pi$
$128$	−1455.00	−1.00473
$129$	0	0
$130$	301.000	0.203073
$131$	−2580.00	−1.72073	−0.860365	−	0.509678i	$-0.829764\pi$
$131$	−2580.00	−1.72073	−0.860365	+	0.509678i	$0.829764\pi$
$132$	0	0
$133$	−288.000	−0.187765
$134$	284.000	0.183089
$135$	0	0
$136$	615.000	0.387763
$137$	2758.00	1.71994	0.859970	−	0.510344i	$-0.170482\pi$
$137$	2758.00	1.71994	0.859970	+	0.510344i	$0.170482\pi$
$138$	0	0
$139$	−2980.00	−1.81842	−0.909210	−	0.416338i	$-0.863313\pi$
$139$	−2980.00	−1.81842	−0.909210	+	0.416338i	$0.863313\pi$
$140$	−196.000	−0.118322
$141$	0	0
$142$	624.000	0.368767
$143$	0	0
$144$	0	0
$145$	1911.00	1.09448
$146$	−586.000	−0.332176
$147$	0	0
$148$	1155.00	0.641489
$149$	2663.00	1.46417	0.732085	−	0.681213i	$-0.238547\pi$
$149$	2663.00	1.46417	0.732085	+	0.681213i	$0.238547\pi$
$150$	0	0
$151$	100.000	0.0538933	0.0269466	−	0.999637i	$-0.491422\pi$
$151$	100.000	0.0538933	0.0269466	+	0.999637i	$0.491422\pi$
$152$	−1080.00	−0.576313
$153$	0	0
$154$	0	0
$155$	1904.00	0.986664
$156$	0	0
$157$	−2506.00	−1.27389	−0.636945	−	0.770910i	$-0.719802\pi$
$157$	−2506.00	−1.27389	−0.636945	+	0.770910i	$0.719802\pi$
$158$	−308.000	−0.155083
$159$	0	0
$160$	−1127.00	−0.556857
$161$	416.000	0.203636
$162$	0	0
$163$	2548.00	1.22439	0.612193	−	0.790709i	$-0.290288\pi$
$163$	2548.00	1.22439	0.612193	+	0.790709i	$0.290288\pi$
$164$	−2821.00	−1.34319
$165$	0	0
$166$	0	0
$167$	−3324.00	−1.54023	−0.770116	−	0.637904i	$-0.779802\pi$
$167$	−3324.00	−1.54023	−0.770116	+	0.637904i	$0.779802\pi$
$168$	0	0
$169$	−348.000	−0.158398
$170$	287.000	0.129482
$171$	0	0
$172$	840.000	0.372380
$173$	2358.00	1.03627	0.518137	−	0.855298i	$-0.326626\pi$
$173$	2358.00	1.03627	0.518137	+	0.855298i	$0.326626\pi$
$174$	0	0
$175$	304.000	0.131316
$176$	0	0
$177$	0	0
$178$	321.000	0.135168
$179$	−36.0000	−0.0150322	−0.00751611	−	0.999972i	$-0.502392\pi$
$179$	−36.0000	−0.0150322	−0.00751611	+	0.999972i	$0.502392\pi$
$180$	0	0
$181$	2407.00	0.988458	0.494229	−	0.869332i	$-0.335450\pi$
$181$	2407.00	0.988458	0.494229	+	0.869332i	$0.335450\pi$
$182$	172.000	0.0700521
$183$	0	0
$184$	1560.00	0.625026
$185$	1155.00	0.459012
$186$	0	0
$187$	0	0
$188$	−1540.00	−0.597426
$189$	0	0
$190$	−504.000	−0.192442
$191$	−2732.00	−1.03498	−0.517488	−	0.855690i	$-0.673133\pi$
$191$	−2732.00	−1.03498	−0.517488	+	0.855690i	$0.673133\pi$
$192$	0	0
$193$	317.000	0.118229	0.0591144	−	0.998251i	$-0.481172\pi$
$193$	317.000	0.118229	0.0591144	+	0.998251i	$0.481172\pi$
$194$	179.000	0.0662446
$195$	0	0
$196$	2289.00	0.834184
$197$	−209.000	−0.0755870	−0.0377935	−	0.999286i	$-0.512033\pi$
$197$	−209.000	−0.0755870	−0.0377935	+	0.999286i	$0.512033\pi$
$198$	0	0
$199$	−1728.00	−0.615551	−0.307776	−	0.951459i	$-0.599585\pi$
$199$	−1728.00	−0.615551	−0.307776	+	0.951459i	$0.599585\pi$
$200$	1140.00	0.403051
$201$	0	0
$202$	14.0000	0.00487642
$203$	1092.00	0.377554
$204$	0	0
$205$	−2821.00	−0.961108
$206$	1244.00	0.420746
$207$	0	0
$208$	−1763.00	−0.587702
$209$	0	0
$210$	0	0
$211$	3552.00	1.15891	0.579454	−	0.815005i	$-0.303266\pi$
$211$	3552.00	1.15891	0.579454	+	0.815005i	$0.303266\pi$
$212$	−5187.00	−1.68040
$213$	0	0
$214$	1416.00	0.452317
$215$	840.000	0.266454
$216$	0	0
$217$	1088.00	0.340361
$218$	329.000	0.102214
$219$	0	0
$220$	0	0
$221$	1763.00	0.536616
$222$	0	0
$223$	940.000	0.282274	0.141137	−	0.989990i	$-0.454924\pi$
$223$	940.000	0.282274	0.141137	+	0.989990i	$0.454924\pi$
$224$	−644.000	−0.192094
$225$	0	0
$226$	−267.000	−0.0785866
$227$	−4944.00	−1.44557	−0.722786	−	0.691072i	$-0.757139\pi$
$227$	−4944.00	−1.44557	−0.722786	+	0.691072i	$0.757139\pi$
$228$	0	0
$229$	1179.00	0.340221	0.170110	−	0.985425i	$-0.445588\pi$
$229$	1179.00	0.340221	0.170110	+	0.985425i	$0.445588\pi$
$230$	728.000	0.208708
$231$	0	0
$232$	4095.00	1.15884
$233$	−1545.00	−0.434405	−0.217202	−	0.976127i	$-0.569693\pi$
$233$	−1545.00	−0.434405	−0.217202	+	0.976127i	$0.569693\pi$
$234$	0	0
$235$	−1540.00	−0.427483
$236$	−784.000	−0.216246
$237$	0	0
$238$	164.000	0.0446661
$239$	3636.00	0.984072	0.492036	−	0.870575i	$-0.336253\pi$
$239$	3636.00	0.984072	0.492036	+	0.870575i	$0.336253\pi$
$240$	0	0
$241$	−1810.00	−0.483786	−0.241893	−	0.970303i	$-0.577768\pi$
$241$	−1810.00	−0.483786	−0.241893	+	0.970303i	$0.577768\pi$
$242$	0	0
$243$	0	0
$244$	−6006.00	−1.57580
$245$	2289.00	0.596893
$246$	0	0
$247$	−3096.00	−0.797546
$248$	4080.00	1.04468
$249$	0	0
$250$	1407.00	0.355946
$251$	5576.00	1.40221	0.701104	−	0.713059i	$-0.252691\pi$
$251$	5576.00	1.40221	0.701104	+	0.713059i	$0.252691\pi$
$252$	0	0
$253$	0	0
$254$	−308.000	−0.0760852
$255$	0	0
$256$	−119.000	−0.0290527
$257$	2549.00	0.618686	0.309343	−	0.950951i	$-0.399891\pi$
$257$	2549.00	0.618686	0.309343	+	0.950951i	$0.399891\pi$
$258$	0	0
$259$	660.000	0.158341
$260$	−2107.00	−0.502579
$261$	0	0
$262$	−2580.00	−0.608370
$263$	3824.00	0.896570	0.448285	−	0.893891i	$-0.352035\pi$
$263$	3824.00	0.896570	0.448285	+	0.893891i	$0.352035\pi$
$264$	0	0
$265$	−5187.00	−1.20240
$266$	−288.000	−0.0663850
$267$	0	0
$268$	−1988.00	−0.453121
$269$	5429.00	1.23053	0.615264	−	0.788321i	$-0.289049\pi$
$269$	5429.00	1.23053	0.615264	+	0.788321i	$0.289049\pi$
$270$	0	0
$271$	1624.00	0.364026	0.182013	−	0.983296i	$-0.441739\pi$
$271$	1624.00	0.364026	0.182013	+	0.983296i	$0.441739\pi$
$272$	−1681.00	−0.374726
$273$	0	0
$274$	2758.00	0.608091
$275$	0	0
$276$	0	0
$277$	−7279.00	−1.57889	−0.789445	−	0.613821i	$-0.789632\pi$
$277$	−7279.00	−1.57889	−0.789445	+	0.613821i	$0.789632\pi$
$278$	−2980.00	−0.642908
$279$	0	0
$280$	−420.000	−0.0896421
$281$	−5094.00	−1.08143	−0.540716	−	0.841205i	$-0.681847\pi$
$281$	−5094.00	−1.08143	−0.540716	+	0.841205i	$0.681847\pi$
$282$	0	0
$283$	−8332.00	−1.75013	−0.875064	−	0.484008i	$-0.839181\pi$
$283$	−8332.00	−1.75013	−0.875064	+	0.484008i	$0.839181\pi$
$284$	−4368.00	−0.912652
$285$	0	0
$286$	0	0
$287$	−1612.00	−0.331545
$288$	0	0
$289$	−3232.00	−0.657847
$290$	1911.00	0.386958
$291$	0	0
$292$	4102.00	0.822094
$293$	−1617.00	−0.322410	−0.161205	−	0.986921i	$-0.551538\pi$
$293$	−1617.00	−0.322410	−0.161205	+	0.986921i	$0.551538\pi$
$294$	0	0
$295$	−784.000	−0.154733
$296$	2475.00	0.486002
$297$	0	0
$298$	2663.00	0.517663
$299$	4472.00	0.864958
$300$	0	0
$301$	480.000	0.0919161
$302$	100.000	0.0190542
$303$	0	0
$304$	2952.00	0.556937
$305$	−6006.00	−1.12755
$306$	0	0
$307$	−3728.00	−0.693056	−0.346528	−	0.938040i	$-0.612639\pi$
$307$	−3728.00	−0.693056	−0.346528	+	0.938040i	$0.612639\pi$
$308$	0	0
$309$	0	0
$310$	1904.00	0.348838
$311$	5508.00	1.00428	0.502138	−	0.864787i	$-0.332547\pi$
$311$	5508.00	1.00428	0.502138	+	0.864787i	$0.332547\pi$
$312$	0	0
$313$	695.000	0.125507	0.0627536	−	0.998029i	$-0.480012\pi$
$313$	695.000	0.125507	0.0627536	+	0.998029i	$0.480012\pi$
$314$	−2506.00	−0.450388
$315$	0	0
$316$	2156.00	0.383812
$317$	9626.00	1.70552	0.852760	−	0.522302i	$-0.174927\pi$
$317$	9626.00	1.70552	0.852760	+	0.522302i	$0.174927\pi$
$318$	0	0
$319$	0	0
$320$	1169.00	0.204216
$321$	0	0
$322$	416.000	0.0719962
$323$	−2952.00	−0.508525
$324$	0	0
$325$	3268.00	0.557772
$326$	2548.00	0.432885
$327$	0	0
$328$	−6045.00	−1.01762
$329$	−880.000	−0.147465
$330$	0	0
$331$	7984.00	1.32580	0.662901	−	0.748707i	$-0.269325\pi$
$331$	7984.00	1.32580	0.662901	+	0.748707i	$0.269325\pi$
$332$	0	0
$333$	0	0
$334$	−3324.00	−0.544554
$335$	−1988.00	−0.324227
$336$	0	0
$337$	−1631.00	−0.263639	−0.131819	−	0.991274i	$-0.542082\pi$
$337$	−1631.00	−0.263639	−0.131819	+	0.991274i	$0.542082\pi$
$338$	−348.000	−0.0560021
$339$	0	0
$340$	−2009.00	−0.320451
$341$	0	0
$342$	0	0
$343$	2680.00	0.421885
$344$	1800.00	0.282121
$345$	0	0
$346$	2358.00	0.366378
$347$	−10952.0	−1.69433	−0.847167	−	0.531326i	$-0.821694\pi$
$347$	−10952.0	−1.69433	−0.847167	+	0.531326i	$0.821694\pi$
$348$	0	0
$349$	1137.00	0.174390	0.0871951	−	0.996191i	$-0.472210\pi$
$349$	1137.00	0.174390	0.0871951	+	0.996191i	$0.472210\pi$
$350$	304.000	0.0464271
$351$	0	0
$352$	0	0
$353$	−2067.00	−0.311658	−0.155829	−	0.987784i	$-0.549805\pi$
$353$	−2067.00	−0.311658	−0.155829	+	0.987784i	$0.549805\pi$
$354$	0	0
$355$	−4368.00	−0.653040
$356$	−2247.00	−0.334525
$357$	0	0
$358$	−36.0000	−0.00531469
$359$	5860.00	0.861501	0.430751	−	0.902471i	$-0.358249\pi$
$359$	5860.00	0.861501	0.430751	+	0.902471i	$0.358249\pi$
$360$	0	0
$361$	−1675.00	−0.244205
$362$	2407.00	0.349473
$363$	0	0
$364$	−1204.00	−0.173370
$365$	4102.00	0.588242
$366$	0	0
$367$	7936.00	1.12876	0.564381	−	0.825514i	$-0.309115\pi$
$367$	7936.00	1.12876	0.564381	+	0.825514i	$0.309115\pi$
$368$	−4264.00	−0.604012
$369$	0	0
$370$	1155.00	0.162285
$371$	−2964.00	−0.414780
$372$	0	0
$373$	−3118.00	−0.432826	−0.216413	−	0.976302i	$-0.569436\pi$
$373$	−3118.00	−0.432826	−0.216413	+	0.976302i	$0.569436\pi$
$374$	0	0
$375$	0	0
$376$	−3300.00	−0.452618
$377$	11739.0	1.60369
$378$	0	0
$379$	−4748.00	−0.643505	−0.321752	−	0.946824i	$-0.604272\pi$
$379$	−4748.00	−0.643505	−0.321752	+	0.946824i	$0.604272\pi$
$380$	3528.00	0.476270
$381$	0	0
$382$	−2732.00	−0.365920
$383$	−4916.00	−0.655864	−0.327932	−	0.944701i	$-0.606352\pi$
$383$	−4916.00	−0.655864	−0.327932	+	0.944701i	$0.606352\pi$
$384$	0	0
$385$	0	0
$386$	317.000	0.0418002
$387$	0	0
$388$	−1253.00	−0.163947
$389$	9645.00	1.25712	0.628562	−	0.777760i	$-0.283644\pi$
$389$	9645.00	1.25712	0.628562	+	0.777760i	$0.283644\pi$
$390$	0	0
$391$	4264.00	0.551508
$392$	4905.00	0.631990
$393$	0	0
$394$	−209.000	−0.0267240
$395$	2156.00	0.274633
$396$	0	0
$397$	−5093.00	−0.643855	−0.321927	−	0.946764i	$-0.604331\pi$
$397$	−5093.00	−0.643855	−0.321927	+	0.946764i	$0.604331\pi$
$398$	−1728.00	−0.217630
$399$	0	0
$400$	−3116.00	−0.389500
$401$	−10223.0	−1.27310	−0.636549	−	0.771236i	$-0.719639\pi$
$401$	−10223.0	−1.27310	−0.636549	+	0.771236i	$0.719639\pi$
$402$	0	0
$403$	11696.0	1.44571
$404$	−98.0000	−0.0120685
$405$	0	0
$406$	1092.00	0.133485
$407$	0	0
$408$	0	0
$409$	11505.0	1.39092	0.695459	−	0.718566i	$-0.255201\pi$
$409$	11505.0	1.39092	0.695459	+	0.718566i	$0.255201\pi$
$410$	−2821.00	−0.339803
$411$	0	0
$412$	−8708.00	−1.04129
$413$	−448.000	−0.0533768
$414$	0	0
$415$	0	0
$416$	−6923.00	−0.815933
$417$	0	0
$418$	0	0
$419$	−6680.00	−0.778853	−0.389426	−	0.921058i	$-0.627327\pi$
$419$	−6680.00	−0.778853	−0.389426	+	0.921058i	$0.627327\pi$
$420$	0	0
$421$	12055.0	1.39555	0.697773	−	0.716319i	$-0.254174\pi$
$421$	12055.0	1.39555	0.697773	+	0.716319i	$0.254174\pi$
$422$	3552.00	0.409736
$423$	0	0
$424$	−11115.0	−1.27309
$425$	3116.00	0.355643
$426$	0	0
$427$	−3432.00	−0.388960
$428$	−9912.00	−1.11943
$429$	0	0
$430$	840.000	0.0942056
$431$	12156.0	1.35855	0.679274	−	0.733885i	$-0.262295\pi$
$431$	12156.0	1.35855	0.679274	+	0.733885i	$0.262295\pi$
$432$	0	0
$433$	−989.000	−0.109765	−0.0548826	−	0.998493i	$-0.517478\pi$
$433$	−989.000	−0.109765	−0.0548826	+	0.998493i	$0.517478\pi$
$434$	1088.00	0.120336
$435$	0	0
$436$	−2303.00	−0.252967
$437$	−7488.00	−0.819679
$438$	0	0
$439$	15464.0	1.68122	0.840611	−	0.541639i	$-0.182196\pi$
$439$	15464.0	1.68122	0.840611	+	0.541639i	$0.182196\pi$
$440$	0	0
$441$	0	0
$442$	1763.00	0.189723
$443$	−2476.00	−0.265549	−0.132775	−	0.991146i	$-0.542389\pi$
$443$	−2476.00	−0.265549	−0.132775	+	0.991146i	$0.542389\pi$
$444$	0	0
$445$	−2247.00	−0.239366
$446$	940.000	0.0997989
$447$	0	0
$448$	668.000	0.0704465
$449$	−10991.0	−1.15523	−0.577614	−	0.816310i	$-0.696016\pi$
$449$	−10991.0	−1.15523	−0.577614	+	0.816310i	$0.696016\pi$
$450$	0	0
$451$	0	0
$452$	1869.00	0.194492
$453$	0	0
$454$	−4944.00	−0.511087
$455$	−1204.00	−0.124054
$456$	0	0
$457$	−14271.0	−1.46076	−0.730382	−	0.683039i	$-0.760658\pi$
$457$	−14271.0	−1.46076	−0.730382	+	0.683039i	$0.760658\pi$
$458$	1179.00	0.120286
$459$	0	0
$460$	−5096.00	−0.516527
$461$	6423.00	0.648913	0.324457	−	0.945901i	$-0.394819\pi$
$461$	6423.00	0.648913	0.324457	+	0.945901i	$0.394819\pi$
$462$	0	0
$463$	−5336.00	−0.535605	−0.267802	−	0.963474i	$-0.586297\pi$
$463$	−5336.00	−0.535605	−0.267802	+	0.963474i	$0.586297\pi$
$464$	−11193.0	−1.11987
$465$	0	0
$466$	−1545.00	−0.153585
$467$	−3540.00	−0.350774	−0.175387	−	0.984500i	$-0.556118\pi$
$467$	−3540.00	−0.350774	−0.175387	+	0.984500i	$0.556118\pi$
$468$	0	0
$469$	−1136.00	−0.111846
$470$	−1540.00	−0.151138
$471$	0	0
$472$	−1680.00	−0.163831
$473$	0	0
$474$	0	0
$475$	−5472.00	−0.528574
$476$	−1148.00	−0.110543
$477$	0	0
$478$	3636.00	0.347922
$479$	−11332.0	−1.08094	−0.540472	−	0.841362i	$-0.681754\pi$
$479$	−11332.0	−1.08094	−0.540472	+	0.841362i	$0.681754\pi$
$480$	0	0
$481$	7095.00	0.672566
$482$	−1810.00	−0.171044
$483$	0	0
$484$	0	0
$485$	−1253.00	−0.117311
$486$	0	0
$487$	19532.0	1.81741	0.908706	−	0.417437i	$-0.137072\pi$
$487$	19532.0	1.81741	0.908706	+	0.417437i	$0.137072\pi$
$488$	−12870.0	−1.19385
$489$	0	0
$490$	2289.00	0.211034
$491$	12916.0	1.18715	0.593575	−	0.804778i	$-0.297716\pi$
$491$	12916.0	1.18715	0.593575	+	0.804778i	$0.297716\pi$
$492$	0	0
$493$	11193.0	1.02253
$494$	−3096.00	−0.281975
$495$	0	0
$496$	−11152.0	−1.00956
$497$	−2496.00	−0.225273
$498$	0	0
$499$	4136.00	0.371048	0.185524	−	0.982640i	$-0.440602\pi$
$499$	4136.00	0.371048	0.185524	+	0.982640i	$0.440602\pi$
$500$	−9849.00	−0.880921
$501$	0	0
$502$	5576.00	0.495755
$503$	2008.00	0.177997	0.0889983	−	0.996032i	$-0.471633\pi$
$503$	2008.00	0.177997	0.0889983	+	0.996032i	$0.471633\pi$
$504$	0	0
$505$	−98.0000	−0.00863553
$506$	0	0
$507$	0	0
$508$	2156.00	0.188301
$509$	−12198.0	−1.06221	−0.531107	−	0.847305i	$-0.678224\pi$
$509$	−12198.0	−1.06221	−0.531107	+	0.847305i	$0.678224\pi$
$510$	0	0
$511$	2344.00	0.202921
$512$	11521.0	0.994455
$513$	0	0
$514$	2549.00	0.218738
$515$	−8708.00	−0.745088
$516$	0	0
$517$	0	0
$518$	660.000	0.0559821
$519$	0	0
$520$	−4515.00	−0.380761
$521$	−14346.0	−1.20635	−0.603176	−	0.797608i	$-0.706098\pi$
$521$	−14346.0	−1.20635	−0.603176	+	0.797608i	$0.706098\pi$
$522$	0	0
$523$	−17264.0	−1.44341	−0.721704	−	0.692202i	$-0.756641\pi$
$523$	−17264.0	−1.44341	−0.721704	+	0.692202i	$0.756641\pi$
$524$	18060.0	1.50564
$525$	0	0
$526$	3824.00	0.316985
$527$	11152.0	0.921800
$528$	0	0
$529$	−1351.00	−0.111038
$530$	−5187.00	−0.425111
$531$	0	0
$532$	2016.00	0.164295
$533$	−17329.0	−1.40826
$534$	0	0
$535$	−9912.00	−0.800997
$536$	−4260.00	−0.343291
$537$	0	0
$538$	5429.00	0.435057
$539$	0	0
$540$	0	0
$541$	12122.0	0.963337	0.481669	−	0.876353i	$-0.340031\pi$
$541$	12122.0	0.963337	0.481669	+	0.876353i	$0.340031\pi$
$542$	1624.00	0.128703
$543$	0	0
$544$	−6601.00	−0.520249
$545$	−2303.00	−0.181009
$546$	0	0
$547$	−17036.0	−1.33164	−0.665820	−	0.746113i	$-0.731918\pi$
$547$	−17036.0	−1.33164	−0.665820	+	0.746113i	$0.731918\pi$
$548$	−19306.0	−1.50495
$549$	0	0
$550$	0	0
$551$	−19656.0	−1.51973
$552$	0	0
$553$	1232.00	0.0947377
$554$	−7279.00	−0.558222
$555$	0	0
$556$	20860.0	1.59112
$557$	−8426.00	−0.640971	−0.320486	−	0.947253i	$-0.603846\pi$
$557$	−8426.00	−0.640971	−0.320486	+	0.947253i	$0.603846\pi$
$558$	0	0
$559$	5160.00	0.390420
$560$	1148.00	0.0866283
$561$	0	0
$562$	−5094.00	−0.382344
$563$	−4412.00	−0.330273	−0.165136	−	0.986271i	$-0.552806\pi$
$563$	−4412.00	−0.330273	−0.165136	+	0.986271i	$0.552806\pi$
$564$	0	0
$565$	1869.00	0.139167
$566$	−8332.00	−0.618763
$567$	0	0
$568$	−9360.00	−0.691438
$569$	−8886.00	−0.654693	−0.327347	−	0.944904i	$-0.606154\pi$
$569$	−8886.00	−0.654693	−0.327347	+	0.944904i	$0.606154\pi$
$570$	0	0
$571$	11848.0	0.868342	0.434171	−	0.900830i	$-0.357041\pi$
$571$	11848.0	0.868342	0.434171	+	0.900830i	$0.357041\pi$
$572$	0	0
$573$	0	0
$574$	−1612.00	−0.117219
$575$	7904.00	0.573251
$576$	0	0
$577$	−2025.00	−0.146104	−0.0730519	−	0.997328i	$-0.523274\pi$
$577$	−2025.00	−0.146104	−0.0730519	+	0.997328i	$0.523274\pi$
$578$	−3232.00	−0.232584
$579$	0	0
$580$	−13377.0	−0.957672
$581$	0	0
$582$	0	0
$583$	0	0
$584$	8790.00	0.622830
$585$	0	0
$586$	−1617.00	−0.113989
$587$	5900.00	0.414854	0.207427	−	0.978251i	$-0.433491\pi$
$587$	5900.00	0.414854	0.207427	+	0.978251i	$0.433491\pi$
$588$	0	0
$589$	−19584.0	−1.37002
$590$	−784.000	−0.0547064
$591$	0	0
$592$	−6765.00	−0.469662
$593$	17579.0	1.21734	0.608670	−	0.793423i	$-0.291703\pi$
$593$	17579.0	1.21734	0.608670	+	0.793423i	$0.291703\pi$
$594$	0	0
$595$	−1148.00	−0.0790982
$596$	−18641.0	−1.28115
$597$	0	0
$598$	4472.00	0.305809
$599$	−5092.00	−0.347335	−0.173667	−	0.984804i	$-0.555562\pi$
$599$	−5092.00	−0.347335	−0.173667	+	0.984804i	$0.555562\pi$
$600$	0	0
$601$	−10091.0	−0.684893	−0.342446	−	0.939537i	$-0.611255\pi$
$601$	−10091.0	−0.684893	−0.342446	+	0.939537i	$0.611255\pi$
$602$	480.000	0.0324972
$603$	0	0
$604$	−700.000	−0.0471566
$605$	0	0
$606$	0	0
$607$	−12464.0	−0.833440	−0.416720	−	0.909035i	$-0.636820\pi$
$607$	−12464.0	−0.833440	−0.416720	+	0.909035i	$0.636820\pi$
$608$	11592.0	0.773220
$609$	0	0
$610$	−6006.00	−0.398649
$611$	−9460.00	−0.626368
$612$	0	0
$613$	18337.0	1.20820	0.604098	−	0.796910i	$-0.293533\pi$
$613$	18337.0	1.20820	0.604098	+	0.796910i	$0.293533\pi$
$614$	−3728.00	−0.245032
$615$	0	0
$616$	0	0
$617$	19545.0	1.27529	0.637643	−	0.770332i	$-0.279909\pi$
$617$	19545.0	1.27529	0.637643	+	0.770332i	$0.279909\pi$
$618$	0	0
$619$	16580.0	1.07659	0.538293	−	0.842758i	$-0.319069\pi$
$619$	16580.0	1.07659	0.538293	+	0.842758i	$0.319069\pi$
$620$	−13328.0	−0.863331
$621$	0	0
$622$	5508.00	0.355065
$623$	−1284.00	−0.0825720
$624$	0	0
$625$	−349.000	−0.0223360
$626$	695.000	0.0443735
$627$	0	0
$628$	17542.0	1.11465
$629$	6765.00	0.428837
$630$	0	0
$631$	−10880.0	−0.686412	−0.343206	−	0.939260i	$-0.611513\pi$
$631$	−10880.0	−0.686412	−0.343206	+	0.939260i	$0.611513\pi$
$632$	4620.00	0.290781
$633$	0	0
$634$	9626.00	0.602993
$635$	2156.00	0.134737
$636$	0	0
$637$	14061.0	0.874595
$638$	0	0
$639$	0	0
$640$	10185.0	0.629059
$641$	−4575.00	−0.281906	−0.140953	−	0.990016i	$-0.545017\pi$
$641$	−4575.00	−0.281906	−0.140953	+	0.990016i	$0.545017\pi$
$642$	0	0
$643$	−15832.0	−0.971000	−0.485500	−	0.874237i	$-0.661362\pi$
$643$	−15832.0	−0.971000	−0.485500	+	0.874237i	$0.661362\pi$
$644$	−2912.00	−0.178181
$645$	0	0
$646$	−2952.00	−0.179791
$647$	24220.0	1.47169	0.735847	−	0.677147i	$-0.236784\pi$
$647$	24220.0	1.47169	0.735847	+	0.677147i	$0.236784\pi$
$648$	0	0
$649$	0	0
$650$	3268.00	0.197202
$651$	0	0
$652$	−17836.0	−1.07134
$653$	19898.0	1.19245	0.596224	−	0.802818i	$-0.296667\pi$
$653$	19898.0	1.19245	0.596224	+	0.802818i	$0.296667\pi$
$654$	0	0
$655$	18060.0	1.07735
$656$	16523.0	0.983407
$657$	0	0
$658$	−880.000	−0.0521367
$659$	−12500.0	−0.738894	−0.369447	−	0.929252i	$-0.620453\pi$
$659$	−12500.0	−0.738894	−0.369447	+	0.929252i	$0.620453\pi$
$660$	0	0
$661$	2863.00	0.168469	0.0842343	−	0.996446i	$-0.473156\pi$
$661$	2863.00	0.168469	0.0842343	+	0.996446i	$0.473156\pi$
$662$	7984.00	0.468742
$663$	0	0
$664$	0	0
$665$	2016.00	0.117560
$666$	0	0
$667$	28392.0	1.64819
$668$	23268.0	1.34770
$669$	0	0
$670$	−1988.00	−0.114632
$671$	0	0
$672$	0	0
$673$	−5378.00	−0.308034	−0.154017	−	0.988068i	$-0.549221\pi$
$673$	−5378.00	−0.308034	−0.154017	+	0.988068i	$0.549221\pi$
$674$	−1631.00	−0.0932103
$675$	0	0
$676$	2436.00	0.138598
$677$	22431.0	1.27340	0.636701	−	0.771111i	$-0.280298\pi$
$677$	22431.0	1.27340	0.636701	+	0.771111i	$0.280298\pi$
$678$	0	0
$679$	−716.000	−0.0404677
$680$	−4305.00	−0.242778
$681$	0	0
$682$	0	0
$683$	−21884.0	−1.22601	−0.613007	−	0.790077i	$-0.710040\pi$
$683$	−21884.0	−1.22601	−0.613007	+	0.790077i	$0.710040\pi$
$684$	0	0
$685$	−19306.0	−1.07685
$686$	2680.00	0.149159
$687$	0	0
$688$	−4920.00	−0.272636
$689$	−31863.0	−1.76180
$690$	0	0
$691$	9260.00	0.509793	0.254897	−	0.966968i	$-0.417959\pi$
$691$	9260.00	0.509793	0.254897	+	0.966968i	$0.417959\pi$
$692$	−16506.0	−0.906740
$693$	0	0
$694$	−10952.0	−0.599038
$695$	20860.0	1.13851
$696$	0	0
$697$	−16523.0	−0.897924
$698$	1137.00	0.0616563
$699$	0	0
$700$	−2128.00	−0.114901
$701$	−35017.0	−1.88670	−0.943348	−	0.331805i	$-0.892342\pi$
$701$	−35017.0	−1.88670	−0.943348	+	0.331805i	$0.892342\pi$
$702$	0	0
$703$	−11880.0	−0.637358
$704$	0	0
$705$	0	0
$706$	−2067.00	−0.110188
$707$	−56.0000	−0.00297892
$708$	0	0
$709$	13310.0	0.705032	0.352516	−	0.935806i	$-0.385326\pi$
$709$	13310.0	0.705032	0.352516	+	0.935806i	$0.385326\pi$
$710$	−4368.00	−0.230885
$711$	0	0
$712$	−4815.00	−0.253441
$713$	28288.0	1.48583
$714$	0	0
$715$	0	0
$716$	252.000	0.0131532
$717$	0	0
$718$	5860.00	0.304587
$719$	−6084.00	−0.315570	−0.157785	−	0.987473i	$-0.550435\pi$
$719$	−6084.00	−0.315570	−0.157785	+	0.987473i	$0.550435\pi$
$720$	0	0
$721$	−4976.00	−0.257026
$722$	−1675.00	−0.0863394
$723$	0	0
$724$	−16849.0	−0.864901
$725$	20748.0	1.06284
$726$	0	0
$727$	36012.0	1.83715	0.918577	−	0.395242i	$-0.129339\pi$
$727$	36012.0	1.83715	0.918577	+	0.395242i	$0.129339\pi$
$728$	−2580.00	−0.131348
$729$	0	0
$730$	4102.00	0.207975
$731$	4920.00	0.248937
$732$	0	0
$733$	13881.0	0.699463	0.349732	−	0.936850i	$-0.386273\pi$
$733$	13881.0	0.699463	0.349732	+	0.936850i	$0.386273\pi$
$734$	7936.00	0.399078
$735$	0	0
$736$	−16744.0	−0.838576
$737$	0	0
$738$	0	0
$739$	−14900.0	−0.741685	−0.370843	−	0.928696i	$-0.620931\pi$
$739$	−14900.0	−0.741685	−0.370843	+	0.928696i	$0.620931\pi$
$740$	−8085.00	−0.401636
$741$	0	0
$742$	−2964.00	−0.146647
$743$	−32936.0	−1.62625	−0.813126	−	0.582088i	$-0.802236\pi$
$743$	−32936.0	−1.62625	−0.813126	+	0.582088i	$0.802236\pi$
$744$	0	0
$745$	−18641.0	−0.916716
$746$	−3118.00	−0.153027
$747$	0	0
$748$	0	0
$749$	−5664.00	−0.276312
$750$	0	0
$751$	3712.00	0.180363	0.0901816	−	0.995925i	$-0.471255\pi$
$751$	3712.00	0.180363	0.0901816	+	0.995925i	$0.471255\pi$
$752$	9020.00	0.437401
$753$	0	0
$754$	11739.0	0.566988
$755$	−700.000	−0.0337425
$756$	0	0
$757$	−20569.0	−0.987573	−0.493787	−	0.869583i	$-0.664388\pi$
$757$	−20569.0	−0.987573	−0.493787	+	0.869583i	$0.664388\pi$
$758$	−4748.00	−0.227513
$759$	0	0
$760$	7560.00	0.360829
$761$	17619.0	0.839275	0.419637	−	0.907692i	$-0.362157\pi$
$761$	17619.0	0.839275	0.419637	+	0.907692i	$0.362157\pi$
$762$	0	0
$763$	−1316.00	−0.0624409
$764$	19124.0	0.905605
$765$	0	0
$766$	−4916.00	−0.231883
$767$	−4816.00	−0.226722
$768$	0	0
$769$	−41435.0	−1.94302	−0.971511	−	0.236993i	$-0.923838\pi$
$769$	−41435.0	−1.94302	−0.971511	+	0.236993i	$0.923838\pi$
$770$	0	0
$771$	0	0
$772$	−2219.00	−0.103450
$773$	11298.0	0.525693	0.262847	−	0.964838i	$-0.415339\pi$
$773$	11298.0	0.525693	0.262847	+	0.964838i	$0.415339\pi$
$774$	0	0
$775$	20672.0	0.958142
$776$	−2685.00	−0.124209
$777$	0	0
$778$	9645.00	0.444460
$779$	29016.0	1.33454
$780$	0	0
$781$	0	0
$782$	4264.00	0.194988
$783$	0	0
$784$	−13407.0	−0.610742
$785$	17542.0	0.797581
$786$	0	0
$787$	1508.00	0.0683029	0.0341515	−	0.999417i	$-0.489127\pi$
$787$	1508.00	0.0683029	0.0341515	+	0.999417i	$0.489127\pi$
$788$	1463.00	0.0661386
$789$	0	0
$790$	2156.00	0.0970975
$791$	1068.00	0.0480072
$792$	0	0
$793$	−36894.0	−1.65214
$794$	−5093.00	−0.227637
$795$	0	0
$796$	12096.0	0.538607
$797$	25114.0	1.11617	0.558083	−	0.829785i	$-0.311537\pi$
$797$	25114.0	1.11617	0.558083	+	0.829785i	$0.311537\pi$
$798$	0	0
$799$	−9020.00	−0.399380
$800$	−12236.0	−0.540760
$801$	0	0
$802$	−10223.0	−0.450108
$803$	0	0
$804$	0	0
$805$	−2912.00	−0.127496
$806$	11696.0	0.511134
$807$	0	0
$808$	−210.000	−0.00914328
$809$	6570.00	0.285524	0.142762	−	0.989757i	$-0.454402\pi$
$809$	6570.00	0.285524	0.142762	+	0.989757i	$0.454402\pi$
$810$	0	0
$811$	36584.0	1.58402	0.792009	−	0.610510i	$-0.209035\pi$
$811$	36584.0	1.58402	0.792009	+	0.610510i	$0.209035\pi$
$812$	−7644.00	−0.330359
$813$	0	0
$814$	0	0
$815$	−17836.0	−0.766586
$816$	0	0
$817$	−8640.00	−0.369982
$818$	11505.0	0.491764
$819$	0	0
$820$	19747.0	0.840970
$821$	−5234.00	−0.222494	−0.111247	−	0.993793i	$-0.535485\pi$
$821$	−5234.00	−0.222494	−0.111247	+	0.993793i	$0.535485\pi$
$822$	0	0
$823$	22632.0	0.958569	0.479284	−	0.877660i	$-0.340896\pi$
$823$	22632.0	0.958569	0.479284	+	0.877660i	$0.340896\pi$
$824$	−18660.0	−0.788898
$825$	0	0
$826$	−448.000	−0.0188716
$827$	8492.00	0.357069	0.178534	−	0.983934i	$-0.442864\pi$
$827$	8492.00	0.357069	0.178534	+	0.983934i	$0.442864\pi$
$828$	0	0
$829$	−9317.00	−0.390341	−0.195171	−	0.980769i	$-0.562526\pi$
$829$	−9317.00	−0.390341	−0.195171	+	0.980769i	$0.562526\pi$
$830$	0	0
$831$	0	0
$832$	7181.00	0.299226
$833$	13407.0	0.557653
$834$	0	0
$835$	23268.0	0.964338
$836$	0	0
$837$	0	0
$838$	−6680.00	−0.275366
$839$	−424.000	−0.0174471	−0.00872354	−	0.999962i	$-0.502777\pi$
$839$	−424.000	−0.0174471	−0.00872354	+	0.999962i	$0.502777\pi$
$840$	0	0
$841$	50140.0	2.05584
$842$	12055.0	0.493400
$843$	0	0
$844$	−24864.0	−1.01405
$845$	2436.00	0.0991727
$846$	0	0
$847$	0	0
$848$	30381.0	1.23029
$849$	0	0
$850$	3116.00	0.125739
$851$	17160.0	0.691231
$852$	0	0
$853$	21589.0	0.866581	0.433290	−	0.901254i	$-0.357352\pi$
$853$	21589.0	0.866581	0.433290	+	0.901254i	$0.357352\pi$
$854$	−3432.00	−0.137518
$855$	0	0
$856$	−21240.0	−0.848094
$857$	7754.00	0.309068	0.154534	−	0.987987i	$-0.450612\pi$
$857$	7754.00	0.309068	0.154534	+	0.987987i	$0.450612\pi$
$858$	0	0
$859$	5448.00	0.216395	0.108198	−	0.994129i	$-0.465492\pi$
$859$	5448.00	0.216395	0.108198	+	0.994129i	$0.465492\pi$
$860$	−5880.00	−0.233147
$861$	0	0
$862$	12156.0	0.480319
$863$	41748.0	1.64672	0.823359	−	0.567520i	$-0.192097\pi$
$863$	41748.0	1.64672	0.823359	+	0.567520i	$0.192097\pi$
$864$	0	0
$865$	−16506.0	−0.648810
$866$	−989.000	−0.0388078
$867$	0	0
$868$	−7616.00	−0.297816
$869$	0	0
$870$	0	0
$871$	−12212.0	−0.475072
$872$	−4935.00	−0.191652
$873$	0	0
$874$	−7488.00	−0.289800
$875$	−5628.00	−0.217441
$876$	0	0
$877$	22869.0	0.880537	0.440269	−	0.897866i	$-0.354883\pi$
$877$	22869.0	0.880537	0.440269	+	0.897866i	$0.354883\pi$
$878$	15464.0	0.594402
$879$	0	0
$880$	0	0
$881$	15013.0	0.574121	0.287061	−	0.957912i	$-0.407322\pi$
$881$	15013.0	0.574121	0.287061	+	0.957912i	$0.407322\pi$
$882$	0	0
$883$	−19172.0	−0.730679	−0.365339	−	0.930874i	$-0.619047\pi$
$883$	−19172.0	−0.730679	−0.365339	+	0.930874i	$0.619047\pi$
$884$	−12341.0	−0.469539
$885$	0	0
$886$	−2476.00	−0.0938858
$887$	−16756.0	−0.634286	−0.317143	−	0.948378i	$-0.602723\pi$
$887$	−16756.0	−0.634286	−0.317143	+	0.948378i	$0.602723\pi$
$888$	0	0
$889$	1232.00	0.0464791
$890$	−2247.00	−0.0846288
$891$	0	0
$892$	−6580.00	−0.246990
$893$	15840.0	0.593578
$894$	0	0
$895$	252.000	0.00941165
$896$	5820.00	0.217001
$897$	0	0
$898$	−10991.0	−0.408435
$899$	74256.0	2.75481
$900$	0	0
$901$	−30381.0	−1.12335
$902$	0	0
$903$	0	0
$904$	4005.00	0.147350
$905$	−16849.0	−0.618873
$906$	0	0
$907$	−48048.0	−1.75899	−0.879497	−	0.475904i	$-0.842121\pi$
$907$	−48048.0	−1.75899	−0.879497	+	0.475904i	$0.842121\pi$
$908$	34608.0	1.26488
$909$	0	0
$910$	−1204.00	−0.0438596
$911$	−26988.0	−0.981506	−0.490753	−	0.871299i	$-0.663278\pi$
$911$	−26988.0	−0.981506	−0.490753	+	0.871299i	$0.663278\pi$
$912$	0	0
$913$	0	0
$914$	−14271.0	−0.516458
$915$	0	0
$916$	−8253.00	−0.297693
$917$	10320.0	0.371643
$918$	0	0
$919$	−35356.0	−1.26908	−0.634541	−	0.772889i	$-0.718811\pi$
$919$	−35356.0	−1.26908	−0.634541	+	0.772889i	$0.718811\pi$
$920$	−10920.0	−0.391328
$921$	0	0
$922$	6423.00	0.229425
$923$	−26832.0	−0.956865
$924$	0	0
$925$	12540.0	0.445743
$926$	−5336.00	−0.189365
$927$	0	0
$928$	−43953.0	−1.55477
$929$	18681.0	0.659746	0.329873	−	0.944025i	$-0.392994\pi$
$929$	18681.0	0.659746	0.329873	+	0.944025i	$0.392994\pi$
$930$	0	0
$931$	−23544.0	−0.828811
$932$	10815.0	0.380104
$933$	0	0
$934$	−3540.00	−0.124017
$935$	0	0
$936$	0	0
$937$	46765.0	1.63047	0.815233	−	0.579134i	$-0.196609\pi$
$937$	46765.0	1.63047	0.815233	+	0.579134i	$0.196609\pi$
$938$	−1136.00	−0.0395434
$939$	0	0
$940$	10780.0	0.374048
$941$	−11433.0	−0.396073	−0.198037	−	0.980195i	$-0.563457\pi$
$941$	−11433.0	−0.396073	−0.198037	+	0.980195i	$0.563457\pi$
$942$	0	0
$943$	−41912.0	−1.44734
$944$	4592.00	0.158323
$945$	0	0
$946$	0	0
$947$	52284.0	1.79409	0.897044	−	0.441941i	$-0.145710\pi$
$947$	52284.0	1.79409	0.897044	+	0.441941i	$0.145710\pi$
$948$	0	0
$949$	25198.0	0.861920
$950$	−5472.00	−0.186879
$951$	0	0
$952$	−2460.00	−0.0837490
$953$	−25157.0	−0.855105	−0.427553	−	0.903990i	$-0.640624\pi$
$953$	−25157.0	−0.855105	−0.427553	+	0.903990i	$0.640624\pi$
$954$	0	0
$955$	19124.0	0.647998
$956$	−25452.0	−0.861063
$957$	0	0
$958$	−11332.0	−0.382172
$959$	−11032.0	−0.371472
$960$	0	0
$961$	44193.0	1.48343
$962$	7095.00	0.237788
$963$	0	0
$964$	12670.0	0.423312
$965$	−2219.00	−0.0740229
$966$	0	0
$967$	50240.0	1.67074	0.835372	−	0.549685i	$-0.185252\pi$
$967$	50240.0	1.67074	0.835372	+	0.549685i	$0.185252\pi$
$968$	0	0
$969$	0	0
$970$	−1253.00	−0.0414757
$971$	−5396.00	−0.178338	−0.0891688	−	0.996017i	$-0.528421\pi$
$971$	−5396.00	−0.178338	−0.0891688	+	0.996017i	$0.528421\pi$
$972$	0	0
$973$	11920.0	0.392742
$974$	19532.0	0.642552
$975$	0	0
$976$	35178.0	1.15371
$977$	42321.0	1.38584	0.692922	−	0.721013i	$-0.256323\pi$
$977$	42321.0	1.38584	0.692922	+	0.721013i	$0.256323\pi$
$978$	0	0
$979$	0	0
$980$	−16023.0	−0.522282
$981$	0	0
$982$	12916.0	0.419721
$983$	−43548.0	−1.41299	−0.706493	−	0.707720i	$-0.749724\pi$
$983$	−43548.0	−1.41299	−0.706493	+	0.707720i	$0.749724\pi$
$984$	0	0
$985$	1463.00	0.0473249
$986$	11193.0	0.361519
$987$	0	0
$988$	21672.0	0.697852
$989$	12480.0	0.401255
$990$	0	0
$991$	7540.00	0.241691	0.120846	−	0.992671i	$-0.461439\pi$
$991$	7540.00	0.241691	0.120846	+	0.992671i	$0.461439\pi$
$992$	−43792.0	−1.40161
$993$	0	0
$994$	−2496.00	−0.0796462
$995$	12096.0	0.385396
$996$	0	0
$997$	−9275.00	−0.294626	−0.147313	−	0.989090i	$-0.547062\pi$
$997$	−9275.00	−0.294626	−0.147313	+	0.989090i	$0.547062\pi$
$998$	4136.00	0.131185
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1089.4.a.h.1.1		1
3.2	odd	2		363.4.a.c.1.1	✓	1
11.10	odd	2		1089.4.a.d.1.1		1
33.32	even	2		363.4.a.e.1.1	yes	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
363.4.a.c.1.1	✓	1	3.2	odd	2
363.4.a.e.1.1	yes	1	33.32	even	2
1089.4.a.d.1.1		1	11.10	odd	2
1089.4.a.h.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:	\( N \)	\(=\)	\( 1089 = 3^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1089.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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