LMFDB - Embedded newform 5733.2.a.bl.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5733,2,Mod(1,5733)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5733, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("5733.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5733 = 3^{2} \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5733.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:	$45.7782354788$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.746052.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 7x^{3} + 8x + 2 $ x^5 - x^4 - 7x^3 + 8x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$3.00852$ of defining polynomial
Character	$\chi$	$=$	5733.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00852 q^{2} +2.03417 q^{4} -0.905722 q^{5} +0.0686323 q^{8} +O(q^{10})$	$q+2.00852 q^{2} +2.03417 q^{4} -0.905722 q^{5} +0.0686323 q^{8} -1.81916 q^{10} -0.716361 q^{11} +1.00000 q^{13} -3.93049 q^{16} -2.35227 q^{17} +6.63591 q^{19} -1.84239 q^{20} -1.43883 q^{22} -3.75906 q^{23} -4.17967 q^{25} +2.00852 q^{26} -3.25799 q^{29} +1.57050 q^{31} -8.03175 q^{32} -4.72459 q^{34} +5.20883 q^{37} +13.3284 q^{38} -0.0621618 q^{40} -4.92168 q^{41} -9.43766 q^{43} -1.45720 q^{44} -7.55016 q^{46} +8.31986 q^{47} -8.39497 q^{50} +2.03417 q^{52} -14.0833 q^{53} +0.648824 q^{55} -6.54376 q^{58} -0.716361 q^{59} -11.6527 q^{61} +3.15439 q^{62} -8.27099 q^{64} -0.905722 q^{65} +9.39174 q^{67} -4.78492 q^{68} -10.9914 q^{71} -3.47300 q^{73} +10.4621 q^{74} +13.4986 q^{76} +13.0082 q^{79} +3.55993 q^{80} -9.88531 q^{82} -3.54083 q^{83} +2.13050 q^{85} -18.9558 q^{86} -0.0491655 q^{88} -12.0501 q^{89} -7.64656 q^{92} +16.7106 q^{94} -6.01029 q^{95} +7.43766 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 4 q^{2} + 8 q^{4} - 2 q^{5} - 9 q^{8}+O(q^{10}) $ 5 * q - 4 * q^2 + 8 * q^4 - 2 * q^5 - 9 * q^8	$ 5 q - 4 q^{2} + 8 q^{4} - 2 q^{5} - 9 q^{8} - 5 q^{10} - 11 q^{11} + 5 q^{13} + 10 q^{16} + 5 q^{17} + 9 q^{19} - q^{20} + 8 q^{22} - 10 q^{23} + 9 q^{25} - 4 q^{26} + 3 q^{29} - 6 q^{31} - 22 q^{32} - 22 q^{34} + 4 q^{37} + 10 q^{38} + 28 q^{40} - 14 q^{41} + 2 q^{43} + 3 q^{46} - q^{47} - 9 q^{50} + 8 q^{52} - 17 q^{53} - 27 q^{58} - 11 q^{59} - 11 q^{61} + 23 q^{62} + 9 q^{64} - 2 q^{65} + 13 q^{67} + 32 q^{68} - 15 q^{71} + 33 q^{74} + 8 q^{76} + 2 q^{79} - 55 q^{80} + 34 q^{82} - 6 q^{83} - 22 q^{85} - 28 q^{86} - 3 q^{88} + 4 q^{89} - 21 q^{92} + 20 q^{94} + 12 q^{95} - 12 q^{97}+O(q^{100}) $ 5 * q - 4 * q^2 + 8 * q^4 - 2 * q^5 - 9 * q^8 - 5 * q^10 - 11 * q^11 + 5 * q^13 + 10 * q^16 + 5 * q^17 + 9 * q^19 - q^20 + 8 * q^22 - 10 * q^23 + 9 * q^25 - 4 * q^26 + 3 * q^29 - 6 * q^31 - 22 * q^32 - 22 * q^34 + 4 * q^37 + 10 * q^38 + 28 * q^40 - 14 * q^41 + 2 * q^43 + 3 * q^46 - q^47 - 9 * q^50 + 8 * q^52 - 17 * q^53 - 27 * q^58 - 11 * q^59 - 11 * q^61 + 23 * q^62 + 9 * q^64 - 2 * q^65 + 13 * q^67 + 32 * q^68 - 15 * q^71 + 33 * q^74 + 8 * q^76 + 2 * q^79 - 55 * q^80 + 34 * q^82 - 6 * q^83 - 22 * q^85 - 28 * q^86 - 3 * q^88 + 4 * q^89 - 21 * q^92 + 20 * q^94 + 12 * q^95 - 12 * q^97

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.00852	1.42024	0.710121	−	0.704080i	$-0.248640\pi$
$2$	2.00852	1.42024	0.710121	+	0.704080i	$0.248640\pi$
$3$	0	0
$3$	0	0
$4$	2.03417	1.01709
$5$	−0.905722	−0.405051	−0.202526	−	0.979277i	$-0.564915\pi$
$5$	−0.905722	−0.405051	−0.202526	+	0.979277i	$0.564915\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0.0686323	0.0242652
$9$	0	0
$10$	−1.81916	−0.575270
$11$	−0.716361	−0.215991	−0.107996	−	0.994151i	$-0.534443\pi$
$11$	−0.716361	−0.215991	−0.107996	+	0.994151i	$0.534443\pi$
$12$	0	0
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0	0
$15$	0	0
$16$	−3.93049	−0.982623
$17$	−2.35227	−0.570510	−0.285255	−	0.958452i	$-0.592078\pi$
$17$	−2.35227	−0.570510	−0.285255	+	0.958452i	$0.592078\pi$
$18$	0	0
$19$	6.63591	1.52238	0.761191	−	0.648528i	$-0.224615\pi$
$19$	6.63591	1.52238	0.761191	+	0.648528i	$0.224615\pi$
$20$	−1.84239	−0.411971
$21$	0	0
$22$	−1.43883	−0.306759
$23$	−3.75906	−0.783817	−0.391909	−	0.920004i	$-0.628185\pi$
$23$	−3.75906	−0.783817	−0.391909	+	0.920004i	$0.628185\pi$
$24$	0	0
$25$	−4.17967	−0.835934
$26$	2.00852	0.393904
$27$	0	0
$28$	0	0
$29$	−3.25799	−0.604994	−0.302497	−	0.953150i	$-0.597820\pi$
$29$	−3.25799	−0.604994	−0.302497	+	0.953150i	$0.597820\pi$
$30$	0	0
$31$	1.57050	0.282070	0.141035	−	0.990005i	$-0.454957\pi$
$31$	1.57050	0.282070	0.141035	+	0.990005i	$0.454957\pi$
$32$	−8.03175	−1.41983
$33$	0	0
$34$	−4.72459	−0.810261
$35$	0	0
$36$	0	0
$37$	5.20883	0.856326	0.428163	−	0.903702i	$-0.359161\pi$
$37$	5.20883	0.856326	0.428163	+	0.903702i	$0.359161\pi$
$38$	13.3284	2.16215
$39$	0	0
$40$	−0.0621618	−0.00982864
$41$	−4.92168	−0.768637	−0.384318	−	0.923201i	$-0.625563\pi$
$41$	−4.92168	−0.768637	−0.384318	+	0.923201i	$0.625563\pi$
$42$	0	0
$43$	−9.43766	−1.43923	−0.719615	−	0.694373i	$-0.755682\pi$
$43$	−9.43766	−1.43923	−0.719615	+	0.694373i	$0.755682\pi$
$44$	−1.45720	−0.219681
$45$	0	0
$46$	−7.55016	−1.11321
$47$	8.31986	1.21358	0.606788	−	0.794863i	$-0.292458\pi$
$47$	8.31986	1.21358	0.606788	+	0.794863i	$0.292458\pi$
$48$	0	0
$49$	0	0
$50$	−8.39497	−1.18723
$51$	0	0
$52$	2.03417	0.282089
$53$	−14.0833	−1.93449	−0.967243	−	0.253854i	$-0.918302\pi$
$53$	−14.0833	−1.93449	−0.967243	+	0.253854i	$0.918302\pi$
$54$	0	0
$55$	0.648824	0.0874874
$56$	0	0
$57$	0	0
$58$	−6.54376	−0.859238
$59$	−0.716361	−0.0932623	−0.0466311	−	0.998912i	$-0.514849\pi$
$59$	−0.716361	−0.0932623	−0.0466311	+	0.998912i	$0.514849\pi$
$60$	0	0
$61$	−11.6527	−1.49197	−0.745986	−	0.665962i	$-0.768021\pi$
$61$	−11.6527	−1.49197	−0.745986	+	0.665962i	$0.768021\pi$
$62$	3.15439	0.400607
$63$	0	0
$64$	−8.27099	−1.03387
$65$	−0.905722	−0.112341
$66$	0	0
$67$	9.39174	1.14738	0.573692	−	0.819071i	$-0.305511\pi$
$67$	9.39174	1.14738	0.573692	+	0.819071i	$0.305511\pi$
$68$	−4.78492	−0.580257
$69$	0	0
$70$	0	0
$71$	−10.9914	−1.30444	−0.652220	−	0.758030i	$-0.726162\pi$
$71$	−10.9914	−1.30444	−0.652220	+	0.758030i	$0.726162\pi$
$72$	0	0
$73$	−3.47300	−0.406484	−0.203242	−	0.979129i	$-0.565148\pi$
$73$	−3.47300	−0.406484	−0.203242	+	0.979129i	$0.565148\pi$
$74$	10.4621	1.21619
$75$	0	0
$76$	13.4986	1.54839
$77$	0	0
$78$	0	0
$79$	13.0082	1.46353	0.731766	−	0.681556i	$-0.238696\pi$
$79$	13.0082	1.46353	0.731766	+	0.681556i	$0.238696\pi$
$80$	3.55993	0.398012
$81$	0	0
$82$	−9.88531	−1.09165
$83$	−3.54083	−0.388656	−0.194328	−	0.980937i	$-0.562253\pi$
$83$	−3.54083	−0.388656	−0.194328	+	0.980937i	$0.562253\pi$
$84$	0	0
$85$	2.13050	0.231085
$86$	−18.9558	−2.04405
$87$	0	0
$88$	−0.0491655	−0.00524106
$89$	−12.0501	−1.27730	−0.638651	−	0.769496i	$-0.720507\pi$
$89$	−12.0501	−1.27730	−0.638651	+	0.769496i	$0.720507\pi$
$90$	0	0
$91$	0	0
$92$	−7.64656	−0.797209
$93$	0	0
$94$	16.7106	1.72357
$95$	−6.01029	−0.616642
$96$	0	0
$97$	7.43766	0.755180	0.377590	−	0.925973i	$-0.376753\pi$
$97$	7.43766	0.755180	0.377590	+	0.925973i	$0.376753\pi$
$98$	0	0
$99$	0	0
$100$	−8.50216	−0.850216
$101$	1.19905	0.119310	0.0596551	−	0.998219i	$-0.481000\pi$
$101$	1.19905	0.119310	0.0596551	+	0.998219i	$0.481000\pi$
$102$	0	0
$103$	−14.4123	−1.42009	−0.710043	−	0.704158i	$-0.751325\pi$
$103$	−14.4123	−1.42009	−0.710043	+	0.704158i	$0.751325\pi$
$104$	0.0686323	0.00672995
$105$	0	0
$106$	−28.2866	−2.74744
$107$	−13.5932	−1.31411	−0.657053	−	0.753845i	$-0.728197\pi$
$107$	−13.5932	−1.31411	−0.657053	+	0.753845i	$0.728197\pi$
$108$	0	0
$109$	−13.7248	−1.31460	−0.657299	−	0.753630i	$-0.728301\pi$
$109$	−13.7248	−1.31460	−0.657299	+	0.753630i	$0.728301\pi$
$110$	1.30318	0.124253
$111$	0	0
$112$	0	0
$113$	3.25799	0.306486	0.153243	−	0.988189i	$-0.451028\pi$
$113$	3.25799	0.306486	0.153243	+	0.988189i	$0.451028\pi$
$114$	0	0
$115$	3.40466	0.317486
$116$	−6.62731	−0.615331
$117$	0	0
$118$	−1.43883	−0.132455
$119$	0	0
$120$	0	0
$121$	−10.4868	−0.953348
$122$	−23.4047	−2.11896
$123$	0	0
$124$	3.19466	0.286889
$125$	8.31422	0.743647
$126$	0	0
$127$	−0.950834	−0.0843729	−0.0421865	−	0.999110i	$-0.513432\pi$
$127$	−0.950834	−0.0843729	−0.0421865	+	0.999110i	$0.513432\pi$
$128$	−0.548979	−0.0485233
$129$	0	0
$130$	−1.81916	−0.159551
$131$	18.8196	1.64428	0.822138	−	0.569288i	$-0.192781\pi$
$131$	18.8196	1.64428	0.822138	+	0.569288i	$0.192781\pi$
$132$	0	0
$133$	0	0
$134$	18.8635	1.62956
$135$	0	0
$136$	−0.161442	−0.0138435
$137$	−6.18179	−0.528146	−0.264073	−	0.964503i	$-0.585066\pi$
$137$	−6.18179	−0.528146	−0.264073	+	0.964503i	$0.585066\pi$
$138$	0	0
$139$	−4.00000	−0.339276	−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000	−0.339276	−0.169638	+	0.985506i	$0.554260\pi$
$140$	0	0
$141$	0	0
$142$	−22.0765	−1.85262
$143$	−0.716361	−0.0599051
$144$	0	0
$145$	2.95083	0.245053
$146$	−6.97560	−0.577305
$147$	0	0
$148$	10.5956	0.870956
$149$	21.0771	1.72670	0.863351	−	0.504604i	$-0.168361\pi$
$149$	21.0771	1.72670	0.863351	+	0.504604i	$0.168361\pi$
$150$	0	0
$151$	−15.7234	−1.27955	−0.639777	−	0.768560i	$-0.720973\pi$
$151$	−15.7234	−1.27955	−0.639777	+	0.768560i	$0.720973\pi$
$152$	0.455438	0.0369409
$153$	0	0
$154$	0	0
$155$	−1.42244	−0.114253
$156$	0	0
$157$	−7.78499	−0.621310	−0.310655	−	0.950523i	$-0.600548\pi$
$157$	−7.78499	−0.621310	−0.310655	+	0.950523i	$0.600548\pi$
$158$	26.1272	2.07857
$159$	0	0
$160$	7.27453	0.575102
$161$	0	0
$162$	0	0
$163$	1.68991	0.132364	0.0661820	−	0.997808i	$-0.478918\pi$
$163$	1.68991	0.132364	0.0661820	+	0.997808i	$0.478918\pi$
$164$	−10.0115	−0.781769
$165$	0	0
$166$	−7.11184	−0.551986
$167$	21.8667	1.69210	0.846049	−	0.533105i	$-0.178975\pi$
$167$	21.8667	1.69210	0.846049	+	0.533105i	$0.178975\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	4.27917	0.328197
$171$	0	0
$172$	−19.1978	−1.46382
$173$	−5.84122	−0.444100	−0.222050	−	0.975035i	$-0.571275\pi$
$173$	−5.84122	−0.444100	−0.222050	+	0.975035i	$0.571275\pi$
$174$	0	0
$175$	0	0
$176$	2.81565	0.212238
$177$	0	0
$178$	−24.2028	−1.81408
$179$	−2.53427	−0.189421	−0.0947103	−	0.995505i	$-0.530192\pi$
$179$	−2.53427	−0.189421	−0.0947103	+	0.995505i	$0.530192\pi$
$180$	0	0
$181$	−10.7248	−0.797169	−0.398585	−	0.917132i	$-0.630498\pi$
$181$	−10.7248	−0.797169	−0.398585	+	0.917132i	$0.630498\pi$
$182$	0	0
$183$	0	0
$184$	−0.257993	−0.0190195
$185$	−4.71775	−0.346856
$186$	0	0
$187$	1.68508	0.123225
$188$	16.9240	1.23431
$189$	0	0
$190$	−12.0718	−0.875781
$191$	1.67861	0.121460	0.0607298	−	0.998154i	$-0.480657\pi$
$191$	1.67861	0.121460	0.0607298	+	0.998154i	$0.480657\pi$
$192$	0	0
$193$	−6.44816	−0.464148	−0.232074	−	0.972698i	$-0.574551\pi$
$193$	−6.44816	−0.464148	−0.232074	+	0.972698i	$0.574551\pi$
$194$	14.9387	1.07254
$195$	0	0
$196$	0	0
$197$	−1.87251	−0.133411	−0.0667054	−	0.997773i	$-0.521249\pi$
$197$	−1.87251	−0.133411	−0.0667054	+	0.997773i	$0.521249\pi$
$198$	0	0
$199$	−11.3967	−0.807888	−0.403944	−	0.914784i	$-0.632361\pi$
$199$	−11.3967	−0.807888	−0.403944	+	0.914784i	$0.632361\pi$
$200$	−0.286860	−0.0202841
$201$	0	0
$202$	2.40833	0.169449
$203$	0	0
$204$	0	0
$205$	4.45767	0.311337
$206$	−28.9475	−2.01687
$207$	0	0
$208$	−3.93049	−0.272531
$209$	−4.75371	−0.328821
$210$	0	0
$211$	7.53599	0.518799	0.259400	−	0.965770i	$-0.416475\pi$
$211$	7.53599	0.518799	0.259400	+	0.965770i	$0.416475\pi$
$212$	−28.6478	−1.96754
$213$	0	0
$214$	−27.3023	−1.86635
$215$	8.54789	0.582962
$216$	0	0
$217$	0	0
$218$	−27.5666	−1.86705
$219$	0	0
$220$	1.31982	0.0889821
$221$	−2.35227	−0.158231
$222$	0	0
$223$	17.6349	1.18092	0.590459	−	0.807067i	$-0.298947\pi$
$223$	17.6349	1.18092	0.590459	+	0.807067i	$0.298947\pi$
$224$	0	0
$225$	0	0
$226$	6.54376	0.435284
$227$	5.32904	0.353701	0.176851	−	0.984238i	$-0.443409\pi$
$227$	5.32904	0.353701	0.176851	+	0.984238i	$0.443409\pi$
$228$	0	0
$229$	−8.51900	−0.562951	−0.281476	−	0.959568i	$-0.590824\pi$
$229$	−8.51900	−0.562951	−0.281476	+	0.959568i	$0.590824\pi$
$230$	6.83834	0.450907
$231$	0	0
$232$	−0.223604	−0.0146803
$233$	−4.75371	−0.311426	−0.155713	−	0.987802i	$-0.549767\pi$
$233$	−4.75371	−0.311426	−0.155713	+	0.987802i	$0.549767\pi$
$234$	0	0
$235$	−7.53548	−0.491561
$236$	−1.45720	−0.0948557
$237$	0	0
$238$	0	0
$239$	−14.8314	−0.959365	−0.479682	−	0.877442i	$-0.659248\pi$
$239$	−14.8314	−0.959365	−0.479682	+	0.877442i	$0.659248\pi$
$240$	0	0
$241$	−6.12131	−0.394308	−0.197154	−	0.980373i	$-0.563170\pi$
$241$	−6.12131	−0.394308	−0.197154	+	0.980373i	$0.563170\pi$
$242$	−21.0630	−1.35398
$243$	0	0
$244$	−23.7035	−1.51746
$245$	0	0
$246$	0	0
$247$	6.63591	0.422233
$248$	0.107787	0.00684448
$249$	0	0
$250$	16.6993	1.05616
$251$	13.9708	0.881832	0.440916	−	0.897548i	$-0.354654\pi$
$251$	13.9708	0.881832	0.440916	+	0.897548i	$0.354654\pi$
$252$	0	0
$253$	2.69284	0.169298
$254$	−1.90977	−0.119830
$255$	0	0
$256$	15.4393	0.964959
$257$	−17.2651	−1.07696	−0.538482	−	0.842637i	$-0.681002\pi$
$257$	−17.2651	−1.07696	−0.538482	+	0.842637i	$0.681002\pi$
$258$	0	0
$259$	0	0
$260$	−1.84239	−0.114260
$261$	0	0
$262$	37.7996	2.33527
$263$	2.60672	0.160737	0.0803687	−	0.996765i	$-0.474390\pi$
$263$	2.60672	0.160737	0.0803687	+	0.996765i	$0.474390\pi$
$264$	0	0
$265$	12.7555	0.783565
$266$	0	0
$267$	0	0
$268$	19.1044	1.16699
$269$	14.4895	0.883443	0.441721	−	0.897152i	$-0.354368\pi$
$269$	14.4895	0.883443	0.441721	+	0.897152i	$0.354368\pi$
$270$	0	0
$271$	−8.63591	−0.524594	−0.262297	−	0.964987i	$-0.584480\pi$
$271$	−8.63591	−0.524594	−0.262297	+	0.964987i	$0.584480\pi$
$272$	9.24558	0.560596
$273$	0	0
$274$	−12.4163	−0.750095
$275$	2.99415	0.180554
$276$	0	0
$277$	12.2270	0.734647	0.367324	−	0.930093i	$-0.380274\pi$
$277$	12.2270	0.734647	0.367324	+	0.930093i	$0.380274\pi$
$278$	−8.03410	−0.481853
$279$	0	0
$280$	0	0
$281$	24.1822	1.44259	0.721293	−	0.692630i	$-0.243548\pi$
$281$	24.1822	1.44259	0.721293	+	0.692630i	$0.243548\pi$
$282$	0	0
$283$	−30.7683	−1.82899	−0.914493	−	0.404601i	$-0.867410\pi$
$283$	−30.7683	−1.82899	−0.914493	+	0.404601i	$0.867410\pi$
$284$	−22.3584	−1.32673
$285$	0	0
$286$	−1.43883	−0.0850797
$287$	0	0
$288$	0	0
$289$	−11.4668	−0.674519
$290$	5.92682	0.348035
$291$	0	0
$292$	−7.06467	−0.413429
$293$	31.8295	1.85950	0.929749	−	0.368193i	$-0.120024\pi$
$293$	31.8295	1.85950	0.929749	+	0.368193i	$0.120024\pi$
$294$	0	0
$295$	0.648824	0.0377760
$296$	0.357494	0.0207789
$297$	0	0
$298$	42.3338	2.45233
$299$	−3.75906	−0.217392
$300$	0	0
$301$	0	0
$302$	−31.5809	−1.81728
$303$	0	0
$304$	−26.0824	−1.49593
$305$	10.5541	0.604324
$306$	0	0
$307$	28.7884	1.64304	0.821520	−	0.570179i	$-0.193126\pi$
$307$	28.7884	1.64304	0.821520	+	0.570179i	$0.193126\pi$
$308$	0	0
$309$	0	0
$310$	−2.85700	−0.162266
$311$	−5.51862	−0.312932	−0.156466	−	0.987683i	$-0.550010\pi$
$311$	−5.51862	−0.312932	−0.156466	+	0.987683i	$0.550010\pi$
$312$	0	0
$313$	−4.84799	−0.274024	−0.137012	−	0.990569i	$-0.543750\pi$
$313$	−4.84799	−0.274024	−0.137012	+	0.990569i	$0.543750\pi$
$314$	−15.6363	−0.882410
$315$	0	0
$316$	26.4608	1.48854
$317$	7.65511	0.429954	0.214977	−	0.976619i	$-0.431032\pi$
$317$	7.65511	0.429954	0.214977	+	0.976619i	$0.431032\pi$
$318$	0	0
$319$	2.33390	0.130673
$320$	7.49121	0.418772
$321$	0	0
$322$	0	0
$323$	−15.6095	−0.868534
$324$	0	0
$325$	−4.17967	−0.231846
$326$	3.39423	0.187989
$327$	0	0
$328$	−0.337786	−0.0186511
$329$	0	0
$330$	0	0
$331$	11.3432	0.623477	0.311739	−	0.950168i	$-0.399089\pi$
$331$	11.3432	0.623477	0.311739	+	0.950168i	$0.399089\pi$
$332$	−7.20265	−0.395297
$333$	0	0
$334$	43.9199	2.40319
$335$	−8.50631	−0.464749
$336$	0	0
$337$	1.74149	0.0948649	0.0474324	−	0.998874i	$-0.484896\pi$
$337$	1.74149	0.0948649	0.0474324	+	0.998874i	$0.484896\pi$
$338$	2.00852	0.109249
$339$	0	0
$340$	4.33381	0.235034
$341$	−1.12504	−0.0609246
$342$	0	0
$343$	0	0
$344$	−0.647729	−0.0349232
$345$	0	0
$346$	−11.7322	−0.630729
$347$	−21.0503	−1.13004	−0.565019	−	0.825078i	$-0.691131\pi$
$347$	−21.0503	−1.13004	−0.565019	+	0.825078i	$0.691131\pi$
$348$	0	0
$349$	−8.35601	−0.447287	−0.223643	−	0.974671i	$-0.571795\pi$
$349$	−8.35601	−0.447287	−0.223643	+	0.974671i	$0.571795\pi$
$350$	0	0
$351$	0	0
$352$	5.75364	0.306670
$353$	8.53355	0.454195	0.227097	−	0.973872i	$-0.427076\pi$
$353$	8.53355	0.454195	0.227097	+	0.973872i	$0.427076\pi$
$354$	0	0
$355$	9.95515	0.528365
$356$	−24.5119	−1.29913
$357$	0	0
$358$	−5.09015	−0.269023
$359$	16.1713	0.853488	0.426744	−	0.904372i	$-0.359661\pi$
$359$	16.1713	0.853488	0.426744	+	0.904372i	$0.359661\pi$
$360$	0	0
$361$	25.0353	1.31765
$362$	−21.5410	−1.13217
$363$	0	0
$364$	0	0
$365$	3.14557	0.164647
$366$	0	0
$367$	28.1540	1.46963	0.734813	−	0.678269i	$-0.237270\pi$
$367$	28.1540	1.46963	0.734813	+	0.678269i	$0.237270\pi$
$368$	14.7749	0.770197
$369$	0	0
$370$	−9.47571	−0.492619
$371$	0	0
$372$	0	0
$373$	−28.5037	−1.47586	−0.737932	−	0.674875i	$-0.764197\pi$
$373$	−28.5037	−1.47586	−0.737932	+	0.674875i	$0.764197\pi$
$374$	3.38452	0.175009
$375$	0	0
$376$	0.571012	0.0294477
$377$	−3.25799	−0.167795
$378$	0	0
$379$	−7.26263	−0.373056	−0.186528	−	0.982450i	$-0.559724\pi$
$379$	−7.26263	−0.373056	−0.186528	+	0.982450i	$0.559724\pi$
$380$	−12.2259	−0.627178
$381$	0	0
$382$	3.37152	0.172502
$383$	−12.9325	−0.660822	−0.330411	−	0.943837i	$-0.607187\pi$
$383$	−12.9325	−0.660822	−0.330411	+	0.943837i	$0.607187\pi$
$384$	0	0
$385$	0	0
$386$	−12.9513	−0.659203
$387$	0	0
$388$	15.1295	0.768083
$389$	21.1357	1.07162	0.535811	−	0.844338i	$-0.320006\pi$
$389$	21.1357	1.07162	0.535811	+	0.844338i	$0.320006\pi$
$390$	0	0
$391$	8.84232	0.447175
$392$	0	0
$393$	0	0
$394$	−3.76098	−0.189476
$395$	−11.7818	−0.592805
$396$	0	0
$397$	19.2073	0.963988	0.481994	−	0.876175i	$-0.339913\pi$
$397$	19.2073	0.963988	0.481994	+	0.876175i	$0.339913\pi$
$398$	−22.8905	−1.14740
$399$	0	0
$400$	16.4282	0.821408
$401$	−16.6692	−0.832420	−0.416210	−	0.909268i	$-0.636642\pi$
$401$	−16.6692	−0.832420	−0.416210	+	0.909268i	$0.636642\pi$
$402$	0	0
$403$	1.57050	0.0782321
$404$	2.43908	0.121349
$405$	0	0
$406$	0	0
$407$	−3.73140	−0.184959
$408$	0	0
$409$	12.3483	0.610585	0.305293	−	0.952259i	$-0.401246\pi$
$409$	12.3483	0.610585	0.305293	+	0.952259i	$0.401246\pi$
$410$	8.95333	0.442174
$411$	0	0
$412$	−29.3171	−1.44435
$413$	0	0
$414$	0	0
$415$	3.20700	0.157426
$416$	−8.03175	−0.393789
$417$	0	0
$418$	−9.54794	−0.467005
$419$	−4.35934	−0.212968	−0.106484	−	0.994314i	$-0.533959\pi$
$419$	−4.35934	−0.212968	−0.106484	+	0.994314i	$0.533959\pi$
$420$	0	0
$421$	−10.0000	−0.487370	−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000	−0.487370	−0.243685	+	0.969854i	$0.578356\pi$
$422$	15.1362	0.736820
$423$	0	0
$424$	−0.966567	−0.0469407
$425$	9.83171	0.476908
$426$	0	0
$427$	0	0
$428$	−27.6509	−1.33656
$429$	0	0
$430$	17.1687	0.827946
$431$	23.3626	1.12533	0.562667	−	0.826683i	$-0.309775\pi$
$431$	23.3626	1.12533	0.562667	+	0.826683i	$0.309775\pi$
$432$	0	0
$433$	−2.71285	−0.130371	−0.0651856	−	0.997873i	$-0.520764\pi$
$433$	−2.71285	−0.130371	−0.0651856	+	0.997873i	$0.520764\pi$
$434$	0	0
$435$	0	0
$436$	−27.9186	−1.33706
$437$	−24.9448	−1.19327
$438$	0	0
$439$	−8.83519	−0.421681	−0.210840	−	0.977521i	$-0.567620\pi$
$439$	−8.83519	−0.421681	−0.210840	+	0.977521i	$0.567620\pi$
$440$	0.0445303	0.00212290
$441$	0	0
$442$	−4.72459	−0.224726
$443$	2.90558	0.138048	0.0690240	−	0.997615i	$-0.478011\pi$
$443$	2.90558	0.138048	0.0690240	+	0.997615i	$0.478011\pi$
$444$	0	0
$445$	10.9140	0.517373
$446$	35.4201	1.67719
$447$	0	0
$448$	0	0
$449$	15.2777	0.720998	0.360499	−	0.932760i	$-0.382606\pi$
$449$	15.2777	0.720998	0.360499	+	0.932760i	$0.382606\pi$
$450$	0	0
$451$	3.52570	0.166019
$452$	6.62731	0.311723
$453$	0	0
$454$	10.7035	0.502341
$455$	0	0
$456$	0	0
$457$	23.6600	1.10677	0.553384	−	0.832926i	$-0.313336\pi$
$457$	23.6600	1.10677	0.553384	+	0.832926i	$0.313336\pi$
$458$	−17.1106	−0.799527
$459$	0	0
$460$	6.92566	0.322910
$461$	26.6170	1.23968	0.619839	−	0.784729i	$-0.287198\pi$
$461$	26.6170	1.23968	0.619839	+	0.784729i	$0.287198\pi$
$462$	0	0
$463$	−1.44250	−0.0670385	−0.0335193	−	0.999438i	$-0.510672\pi$
$463$	−1.44250	−0.0670385	−0.0335193	+	0.999438i	$0.510672\pi$
$464$	12.8055	0.594481
$465$	0	0
$466$	−9.54794	−0.442300
$467$	8.38959	0.388224	0.194112	−	0.980979i	$-0.437817\pi$
$467$	8.38959	0.388224	0.194112	+	0.980979i	$0.437817\pi$
$468$	0	0
$469$	0	0
$470$	−15.1352	−0.698135
$471$	0	0
$472$	−0.0491655	−0.00226303
$473$	6.76077	0.310861
$474$	0	0
$475$	−27.7359	−1.27261
$476$	0	0
$477$	0	0
$478$	−29.7893	−1.36253
$479$	−12.6122	−0.576265	−0.288132	−	0.957591i	$-0.593034\pi$
$479$	−12.6122	−0.576265	−0.288132	+	0.957591i	$0.593034\pi$
$480$	0	0
$481$	5.20883	0.237502
$482$	−12.2948	−0.560013
$483$	0	0
$484$	−21.3320	−0.969636
$485$	−6.73645	−0.305886
$486$	0	0
$487$	21.5680	0.977341	0.488671	−	0.872468i	$-0.337482\pi$
$487$	21.5680	0.977341	0.488671	+	0.872468i	$0.337482\pi$
$488$	−0.799750	−0.0362030
$489$	0	0
$490$	0	0
$491$	−39.2347	−1.77064	−0.885318	−	0.464987i	$-0.846059\pi$
$491$	−39.2347	−1.77064	−0.885318	+	0.464987i	$0.846059\pi$
$492$	0	0
$493$	7.66368	0.345155
$494$	13.3284	0.599673
$495$	0	0
$496$	−6.17283	−0.277168
$497$	0	0
$498$	0	0
$499$	9.16814	0.410422	0.205211	−	0.978718i	$-0.434212\pi$
$499$	9.16814	0.410422	0.205211	+	0.978718i	$0.434212\pi$
$500$	16.9125	0.756352
$501$	0	0
$502$	28.0608	1.25241
$503$	−24.9370	−1.11188	−0.555942	−	0.831221i	$-0.687642\pi$
$503$	−24.9370	−1.11188	−0.555942	+	0.831221i	$0.687642\pi$
$504$	0	0
$505$	−1.08601	−0.0483267
$506$	5.40864	0.240443
$507$	0	0
$508$	−1.93416	−0.0858144
$509$	−5.89807	−0.261428	−0.130714	−	0.991420i	$-0.541727\pi$
$509$	−5.89807	−0.261428	−0.130714	+	0.991420i	$0.541727\pi$
$510$	0	0
$511$	0	0
$512$	32.1083	1.41900
$513$	0	0
$514$	−34.6773	−1.52955
$515$	13.0535	0.575208
$516$	0	0
$517$	−5.96003	−0.262122
$518$	0	0
$519$	0	0
$520$	−0.0621618	−0.00272597
$521$	37.1895	1.62930	0.814652	−	0.579950i	$-0.196928\pi$
$521$	37.1895	1.62930	0.814652	+	0.579950i	$0.196928\pi$
$522$	0	0
$523$	−5.09080	−0.222605	−0.111303	−	0.993787i	$-0.535502\pi$
$523$	−5.09080	−0.222605	−0.111303	+	0.993787i	$0.535502\pi$
$524$	38.2823	1.67237
$525$	0	0
$526$	5.23567	0.228286
$527$	−3.69424	−0.160924
$528$	0	0
$529$	−8.86950	−0.385630
$530$	25.6198	1.11285
$531$	0	0
$532$	0	0
$533$	−4.92168	−0.213181
$534$	0	0
$535$	12.3117	0.532280
$536$	0.644577	0.0278415
$537$	0	0
$538$	29.1026	1.25470
$539$	0	0
$540$	0	0
$541$	−0.766850	−0.0329694	−0.0164847	−	0.999864i	$-0.505247\pi$
$541$	−0.766850	−0.0329694	−0.0164847	+	0.999864i	$0.505247\pi$
$542$	−17.3454	−0.745050
$543$	0	0
$544$	18.8929	0.810025
$545$	12.4309	0.532480
$546$	0	0
$547$	14.1428	0.604702	0.302351	−	0.953197i	$-0.402229\pi$
$547$	14.1428	0.604702	0.302351	+	0.953197i	$0.402229\pi$
$548$	−12.5748	−0.537170
$549$	0	0
$550$	6.01383	0.256430
$551$	−21.6197	−0.921032
$552$	0	0
$553$	0	0
$554$	24.5582	1.04338
$555$	0	0
$556$	−8.13668	−0.345072
$557$	24.8627	1.05347	0.526733	−	0.850031i	$-0.323417\pi$
$557$	24.8627	1.05347	0.526733	+	0.850031i	$0.323417\pi$
$558$	0	0
$559$	−9.43766	−0.399171
$560$	0	0
$561$	0	0
$562$	48.5705	2.04882
$563$	−44.0094	−1.85478	−0.927388	−	0.374101i	$-0.877951\pi$
$563$	−44.0094	−1.85478	−0.927388	+	0.374101i	$0.877951\pi$
$564$	0	0
$565$	−2.95083	−0.124143
$566$	−61.7989	−2.59760
$567$	0	0
$568$	−0.754366	−0.0316525
$569$	33.2616	1.39440	0.697199	−	0.716877i	$-0.254429\pi$
$569$	33.2616	1.39440	0.697199	+	0.716877i	$0.254429\pi$
$570$	0	0
$571$	−12.3540	−0.516998	−0.258499	−	0.966011i	$-0.583228\pi$
$571$	−12.3540	−0.516998	−0.258499	+	0.966011i	$0.583228\pi$
$572$	−1.45720	−0.0609286
$573$	0	0
$574$	0	0
$575$	15.7116	0.655219
$576$	0	0
$577$	−25.9659	−1.08097	−0.540486	−	0.841353i	$-0.681760\pi$
$577$	−25.9659	−1.08097	−0.540486	+	0.841353i	$0.681760\pi$
$578$	−23.0314	−0.957979
$579$	0	0
$580$	6.00250	0.249240
$581$	0	0
$582$	0	0
$583$	10.0887	0.417831
$584$	−0.238360	−0.00986341
$585$	0	0
$586$	63.9303	2.64094
$587$	23.9747	0.989543	0.494771	−	0.869023i	$-0.335252\pi$
$587$	23.9747	0.989543	0.494771	+	0.869023i	$0.335252\pi$
$588$	0	0
$589$	10.4217	0.429418
$590$	1.30318	0.0536510
$591$	0	0
$592$	−20.4733	−0.841445
$593$	−47.0480	−1.93203	−0.966015	−	0.258484i	$-0.916777\pi$
$593$	−47.0480	−1.93203	−0.966015	+	0.258484i	$0.916777\pi$
$594$	0	0
$595$	0	0
$596$	42.8744	1.75620
$597$	0	0
$598$	−7.55016	−0.308749
$599$	−20.1736	−0.824271	−0.412135	−	0.911123i	$-0.635217\pi$
$599$	−20.1736	−0.824271	−0.412135	+	0.911123i	$0.635217\pi$
$600$	0	0
$601$	29.5773	1.20648	0.603242	−	0.797558i	$-0.293875\pi$
$601$	29.5773	1.20648	0.603242	+	0.797558i	$0.293875\pi$
$602$	0	0
$603$	0	0
$604$	−31.9841	−1.30142
$605$	9.49815	0.386155
$606$	0	0
$607$	−15.4420	−0.626771	−0.313385	−	0.949626i	$-0.601463\pi$
$607$	−15.4420	−0.626771	−0.313385	+	0.949626i	$0.601463\pi$
$608$	−53.2980	−2.16152
$609$	0	0
$610$	21.1981	0.858287
$611$	8.31986	0.336586
$612$	0	0
$613$	1.99485	0.0805711	0.0402855	−	0.999188i	$-0.487173\pi$
$613$	1.99485	0.0805711	0.0402855	+	0.999188i	$0.487173\pi$
$614$	57.8222	2.33351
$615$	0	0
$616$	0	0
$617$	2.85584	0.114972	0.0574858	−	0.998346i	$-0.481692\pi$
$617$	2.85584	0.114972	0.0574858	+	0.998346i	$0.481692\pi$
$618$	0	0
$619$	31.9823	1.28548	0.642738	−	0.766086i	$-0.277798\pi$
$619$	31.9823	1.28548	0.642738	+	0.766086i	$0.277798\pi$
$620$	−2.89348	−0.116205
$621$	0	0
$622$	−11.0843	−0.444440
$623$	0	0
$624$	0	0
$625$	13.3680	0.534719
$626$	−9.73730	−0.389181
$627$	0	0
$628$	−15.8360	−0.631925
$629$	−12.2526	−0.488542
$630$	0	0
$631$	32.1115	1.27834	0.639169	−	0.769066i	$-0.279278\pi$
$631$	32.1115	1.27834	0.639169	+	0.769066i	$0.279278\pi$
$632$	0.892781	0.0355129
$633$	0	0
$634$	15.3755	0.610638
$635$	0.861191	0.0341753
$636$	0	0
$637$	0	0
$638$	4.68769	0.185588
$639$	0	0
$640$	0.497222	0.0196544
$641$	−33.0248	−1.30440	−0.652200	−	0.758047i	$-0.726154\pi$
$641$	−33.0248	−1.30440	−0.652200	+	0.758047i	$0.726154\pi$
$642$	0	0
$643$	15.7942	0.622863	0.311432	−	0.950269i	$-0.399192\pi$
$643$	15.7942	0.622863	0.311432	+	0.950269i	$0.399192\pi$
$644$	0	0
$645$	0	0
$646$	−31.3520	−1.23353
$647$	4.64072	0.182445	0.0912227	−	0.995831i	$-0.470922\pi$
$647$	4.64072	0.182445	0.0912227	+	0.995831i	$0.470922\pi$
$648$	0	0
$649$	0.513173	0.0201438
$650$	−8.39497	−0.329278
$651$	0	0
$652$	3.43757	0.134626
$653$	−26.8285	−1.04988	−0.524941	−	0.851139i	$-0.675913\pi$
$653$	−26.8285	−1.04988	−0.524941	+	0.851139i	$0.675913\pi$
$654$	0	0
$655$	−17.0453	−0.666016
$656$	19.3446	0.755280
$657$	0	0
$658$	0	0
$659$	42.9889	1.67461	0.837306	−	0.546735i	$-0.184129\pi$
$659$	42.9889	1.67461	0.837306	+	0.546735i	$0.184129\pi$
$660$	0	0
$661$	−29.4698	−1.14624	−0.573122	−	0.819470i	$-0.694268\pi$
$661$	−29.4698	−1.14624	−0.573122	+	0.819470i	$0.694268\pi$
$662$	22.7830	0.885488
$663$	0	0
$664$	−0.243015	−0.00943082
$665$	0	0
$666$	0	0
$667$	12.2470	0.474205
$668$	44.4806	1.72101
$669$	0	0
$670$	−17.0851	−0.660056
$671$	8.34752	0.322252
$672$	0	0
$673$	−20.1702	−0.777504	−0.388752	−	0.921342i	$-0.627094\pi$
$673$	−20.1702	−0.777504	−0.388752	+	0.921342i	$0.627094\pi$
$674$	3.49782	0.134731
$675$	0	0
$676$	2.03417	0.0782373
$677$	6.20481	0.238470	0.119235	−	0.992866i	$-0.461956\pi$
$677$	6.20481	0.238470	0.119235	+	0.992866i	$0.461956\pi$
$678$	0	0
$679$	0	0
$680$	0.146221	0.00560733
$681$	0	0
$682$	−2.25968	−0.0865276
$683$	1.76952	0.0677087	0.0338543	−	0.999427i	$-0.489222\pi$
$683$	1.76952	0.0677087	0.0338543	+	0.999427i	$0.489222\pi$
$684$	0	0
$685$	5.59899	0.213926
$686$	0	0
$687$	0	0
$688$	37.0946	1.41422
$689$	−14.0833	−0.536530
$690$	0	0
$691$	44.9317	1.70928	0.854641	−	0.519219i	$-0.173777\pi$
$691$	44.9317	1.70928	0.854641	+	0.519219i	$0.173777\pi$
$692$	−11.8820	−0.451688
$693$	0	0
$694$	−42.2800	−1.60493
$695$	3.62289	0.137424
$696$	0	0
$697$	11.5771	0.438515
$698$	−16.7832	−0.635255
$699$	0	0
$700$	0	0
$701$	−38.5707	−1.45679	−0.728397	−	0.685156i	$-0.759734\pi$
$701$	−38.5707	−1.45679	−0.728397	+	0.685156i	$0.759734\pi$
$702$	0	0
$703$	34.5653	1.30366
$704$	5.92501	0.223307
$705$	0	0
$706$	17.1398	0.645066
$707$	0	0
$708$	0	0
$709$	8.77731	0.329639	0.164819	−	0.986324i	$-0.447296\pi$
$709$	8.77731	0.329639	0.164819	+	0.986324i	$0.447296\pi$
$710$	19.9952	0.750405
$711$	0	0
$712$	−0.827023	−0.0309940
$713$	−5.90360	−0.221091
$714$	0	0
$715$	0.648824	0.0242646
$716$	−5.15515	−0.192657
$717$	0	0
$718$	32.4804	1.21216
$719$	−4.20437	−0.156796	−0.0783982	−	0.996922i	$-0.524981\pi$
$719$	−4.20437	−0.156796	−0.0783982	+	0.996922i	$0.524981\pi$
$720$	0	0
$721$	0	0
$722$	50.2840	1.87138
$723$	0	0
$724$	−21.8161	−0.810789
$725$	13.6173	0.505735
$726$	0	0
$727$	−28.9856	−1.07502	−0.537509	−	0.843258i	$-0.680634\pi$
$727$	−28.9856	−1.07502	−0.537509	+	0.843258i	$0.680634\pi$
$728$	0	0
$729$	0	0
$730$	6.31796	0.233838
$731$	22.1999	0.821094
$732$	0	0
$733$	−24.0345	−0.887733	−0.443867	−	0.896093i	$-0.646394\pi$
$733$	−24.0345	−0.887733	−0.443867	+	0.896093i	$0.646394\pi$
$734$	56.5480	2.08722
$735$	0	0
$736$	30.1918	1.11288
$737$	−6.72788	−0.247825
$738$	0	0
$739$	11.8055	0.434273	0.217136	−	0.976141i	$-0.430328\pi$
$739$	11.8055	0.434273	0.217136	+	0.976141i	$0.430328\pi$
$740$	−9.59670	−0.352782
$741$	0	0
$742$	0	0
$743$	−47.2786	−1.73448	−0.867241	−	0.497888i	$-0.834109\pi$
$743$	−47.2786	−1.73448	−0.867241	+	0.497888i	$0.834109\pi$
$744$	0	0
$745$	−19.0900	−0.699402
$746$	−57.2503	−2.09608
$747$	0	0
$748$	3.42773	0.125330
$749$	0	0
$750$	0	0
$751$	5.47700	0.199859	0.0999294	−	0.994995i	$-0.468138\pi$
$751$	5.47700	0.199859	0.0999294	+	0.994995i	$0.468138\pi$
$752$	−32.7012	−1.19249
$753$	0	0
$754$	−6.54376	−0.238310
$755$	14.2410	0.518285
$756$	0	0
$757$	10.7453	0.390546	0.195273	−	0.980749i	$-0.437441\pi$
$757$	10.7453	0.390546	0.195273	+	0.980749i	$0.437441\pi$
$758$	−14.5872	−0.529830
$759$	0	0
$760$	−0.412500	−0.0149630
$761$	33.0399	1.19770	0.598848	−	0.800863i	$-0.295625\pi$
$761$	33.0399	1.19770	0.598848	+	0.800863i	$0.295625\pi$
$762$	0	0
$763$	0	0
$764$	3.41457	0.123535
$765$	0	0
$766$	−25.9753	−0.938527
$767$	−0.716361	−0.0258663
$768$	0	0
$769$	2.98332	0.107581	0.0537907	−	0.998552i	$-0.482870\pi$
$769$	2.98332	0.107581	0.0537907	+	0.998552i	$0.482870\pi$
$770$	0	0
$771$	0	0
$772$	−13.1167	−0.472079
$773$	21.9085	0.787995	0.393998	−	0.919111i	$-0.371092\pi$
$773$	21.9085	0.787995	0.393998	+	0.919111i	$0.371092\pi$
$774$	0	0
$775$	−6.56417	−0.235792
$776$	0.510464	0.0183246
$777$	0	0
$778$	42.4516	1.52196
$779$	−32.6598	−1.17016
$780$	0	0
$781$	7.87381	0.281747
$782$	17.7600	0.635097
$783$	0	0
$784$	0	0
$785$	7.05104	0.251662
$786$	0	0
$787$	−13.3632	−0.476347	−0.238174	−	0.971223i	$-0.576549\pi$
$787$	−13.3632	−0.476347	−0.238174	+	0.971223i	$0.576549\pi$
$788$	−3.80900	−0.135690
$789$	0	0
$790$	−23.6640	−0.841927
$791$	0	0
$792$	0	0
$793$	−11.6527	−0.413798
$794$	38.5784	1.36910
$795$	0	0
$796$	−23.1827	−0.821691
$797$	−32.5388	−1.15258	−0.576292	−	0.817244i	$-0.695501\pi$
$797$	−32.5388	−1.15258	−0.576292	+	0.817244i	$0.695501\pi$
$798$	0	0
$799$	−19.5706	−0.692357
$800$	33.5701	1.18688
$801$	0	0
$802$	−33.4805	−1.18224
$803$	2.48792	0.0877969
$804$	0	0
$805$	0	0
$806$	3.15439	0.111109
$807$	0	0
$808$	0.0822938	0.00289509
$809$	−7.68827	−0.270305	−0.135153	−	0.990825i	$-0.543152\pi$
$809$	−7.68827	−0.270305	−0.135153	+	0.990825i	$0.543152\pi$
$810$	0	0
$811$	−48.3178	−1.69667	−0.848334	−	0.529461i	$-0.822394\pi$
$811$	−48.3178	−1.69667	−0.848334	+	0.529461i	$0.822394\pi$
$812$	0	0
$813$	0	0
$814$	−7.49461	−0.262686
$815$	−1.53059	−0.0536142
$816$	0	0
$817$	−62.6275	−2.19106
$818$	24.8019	0.867178
$819$	0	0
$820$	9.06766	0.316656
$821$	3.73442	0.130332	0.0651661	−	0.997874i	$-0.479242\pi$
$821$	3.73442	0.130332	0.0651661	+	0.997874i	$0.479242\pi$
$822$	0	0
$823$	14.2318	0.496089	0.248045	−	0.968749i	$-0.420212\pi$
$823$	14.2318	0.496089	0.248045	+	0.968749i	$0.420212\pi$
$824$	−0.989150	−0.0344587
$825$	0	0
$826$	0	0
$827$	−48.3016	−1.67961	−0.839805	−	0.542888i	$-0.817331\pi$
$827$	−48.3016	−1.67961	−0.839805	+	0.542888i	$0.817331\pi$
$828$	0	0
$829$	11.5101	0.399763	0.199882	−	0.979820i	$-0.435944\pi$
$829$	11.5101	0.399763	0.199882	+	0.979820i	$0.435944\pi$
$830$	6.44135	0.223582
$831$	0	0
$832$	−8.27099	−0.286745
$833$	0	0
$834$	0	0
$835$	−19.8052	−0.685386
$836$	−9.66985	−0.334439
$837$	0	0
$838$	−8.75583	−0.302465
$839$	−13.1103	−0.452616	−0.226308	−	0.974056i	$-0.572666\pi$
$839$	−13.1103	−0.452616	−0.226308	+	0.974056i	$0.572666\pi$
$840$	0	0
$841$	−18.3855	−0.633982
$842$	−20.0852	−0.692183
$843$	0	0
$844$	15.3295	0.527663
$845$	−0.905722	−0.0311578
$846$	0	0
$847$	0	0
$848$	55.3541	1.90087
$849$	0	0
$850$	19.7472	0.677325
$851$	−19.5803	−0.671203
$852$	0	0
$853$	8.80346	0.301425	0.150712	−	0.988578i	$-0.451843\pi$
$853$	8.80346	0.301425	0.150712	+	0.988578i	$0.451843\pi$
$854$	0	0
$855$	0	0
$856$	−0.932934	−0.0318870
$857$	−16.9651	−0.579516	−0.289758	−	0.957100i	$-0.593575\pi$
$857$	−16.9651	−0.579516	−0.289758	+	0.957100i	$0.593575\pi$
$858$	0	0
$859$	14.5410	0.496132	0.248066	−	0.968743i	$-0.420205\pi$
$859$	14.5410	0.496132	0.248066	+	0.968743i	$0.420205\pi$
$860$	17.3879	0.592922
$861$	0	0
$862$	46.9243	1.59825
$863$	−39.0444	−1.32909	−0.664544	−	0.747249i	$-0.731374\pi$
$863$	−39.0444	−1.32909	−0.664544	+	0.747249i	$0.731374\pi$
$864$	0	0
$865$	5.29052	0.179883
$866$	−5.44882	−0.185159
$867$	0	0
$868$	0	0
$869$	−9.31854	−0.316110
$870$	0	0
$871$	9.39174	0.318227
$872$	−0.941966	−0.0318990
$873$	0	0
$874$	−50.1022	−1.69473
$875$	0	0
$876$	0	0
$877$	32.5941	1.10062	0.550312	−	0.834959i	$-0.314509\pi$
$877$	32.5941	1.10062	0.550312	+	0.834959i	$0.314509\pi$
$878$	−17.7457	−0.598888
$879$	0	0
$880$	−2.55020	−0.0859671
$881$	43.4141	1.46266	0.731330	−	0.682024i	$-0.238900\pi$
$881$	43.4141	1.46266	0.731330	+	0.682024i	$0.238900\pi$
$882$	0	0
$883$	28.2902	0.952040	0.476020	−	0.879434i	$-0.342079\pi$
$883$	28.2902	0.952040	0.476020	+	0.879434i	$0.342079\pi$
$884$	−4.78492	−0.160934
$885$	0	0
$886$	5.83592	0.196062
$887$	50.2650	1.68773	0.843866	−	0.536554i	$-0.180274\pi$
$887$	50.2650	1.68773	0.843866	+	0.536554i	$0.180274\pi$
$888$	0	0
$889$	0	0
$890$	21.9210	0.734794
$891$	0	0
$892$	35.8724	1.20110
$893$	55.2099	1.84753
$894$	0	0
$895$	2.29535	0.0767250
$896$	0	0
$897$	0	0
$898$	30.6856	1.02399
$899$	−5.11668	−0.170651
$900$	0	0
$901$	33.1277	1.10364
$902$	7.08145	0.235786
$903$	0	0
$904$	0.223604	0.00743695
$905$	9.71369	0.322894
$906$	0	0
$907$	26.8277	0.890798	0.445399	−	0.895332i	$-0.353062\pi$
$907$	26.8277	0.890798	0.445399	+	0.895332i	$0.353062\pi$
$908$	10.8402	0.359744
$909$	0	0
$910$	0	0
$911$	22.3560	0.740687	0.370344	−	0.928895i	$-0.379240\pi$
$911$	22.3560	0.740687	0.370344	+	0.928895i	$0.379240\pi$
$912$	0	0
$913$	2.53651	0.0839463
$914$	47.5217	1.57188
$915$	0	0
$916$	−17.3291	−0.572569
$917$	0	0
$918$	0	0
$919$	−8.62244	−0.284428	−0.142214	−	0.989836i	$-0.545422\pi$
$919$	−8.62244	−0.284428	−0.142214	+	0.989836i	$0.545422\pi$
$920$	0.233670	0.00770386
$921$	0	0
$922$	53.4609	1.76064
$923$	−10.9914	−0.361786
$924$	0	0
$925$	−21.7712	−0.715832
$926$	−2.89729	−0.0952109
$927$	0	0
$928$	26.1674	0.858987
$929$	−41.3861	−1.35783	−0.678916	−	0.734216i	$-0.737550\pi$
$929$	−41.3861	−1.35783	−0.678916	+	0.734216i	$0.737550\pi$
$930$	0	0
$931$	0	0
$932$	−9.66985	−0.316747
$933$	0	0
$934$	16.8507	0.551372
$935$	−1.52621	−0.0499124
$936$	0	0
$937$	21.3818	0.698514	0.349257	−	0.937027i	$-0.386434\pi$
$937$	21.3818	0.698514	0.349257	+	0.937027i	$0.386434\pi$
$938$	0	0
$939$	0	0
$940$	−15.3285	−0.499959
$941$	53.1480	1.73258	0.866288	−	0.499545i	$-0.166499\pi$
$941$	53.1480	1.73258	0.866288	+	0.499545i	$0.166499\pi$
$942$	0	0
$943$	18.5009	0.602471
$944$	2.81565	0.0916416
$945$	0	0
$946$	13.5792	0.441497
$947$	8.86936	0.288216	0.144108	−	0.989562i	$-0.453969\pi$
$947$	8.86936	0.288216	0.144108	+	0.989562i	$0.453969\pi$
$948$	0	0
$949$	−3.47300	−0.112738
$950$	−55.7082	−1.80741
$951$	0	0
$952$	0	0
$953$	39.8167	1.28979	0.644894	−	0.764272i	$-0.276901\pi$
$953$	39.8167	1.28979	0.644894	+	0.764272i	$0.276901\pi$
$954$	0	0
$955$	−1.52035	−0.0491973
$956$	−30.1696	−0.975756
$957$	0	0
$958$	−25.3319	−0.818435
$959$	0	0
$960$	0	0
$961$	−28.5335	−0.920437
$962$	10.4621	0.337310
$963$	0	0
$964$	−12.4518	−0.401045
$965$	5.84024	0.188004
$966$	0	0
$967$	−22.1611	−0.712652	−0.356326	−	0.934362i	$-0.615971\pi$
$967$	−22.1611	−0.712652	−0.356326	+	0.934362i	$0.615971\pi$
$968$	−0.719735	−0.0231332
$969$	0	0
$970$	−13.5303	−0.434433
$971$	−36.0423	−1.15665	−0.578327	−	0.815805i	$-0.696294\pi$
$971$	−36.0423	−1.15665	−0.578327	+	0.815805i	$0.696294\pi$
$972$	0	0
$973$	0	0
$974$	43.3199	1.38806
$975$	0	0
$976$	45.8007	1.46604
$977$	−32.9416	−1.05389	−0.526947	−	0.849898i	$-0.676664\pi$
$977$	−32.9416	−1.05389	−0.526947	+	0.849898i	$0.676664\pi$
$978$	0	0
$979$	8.63219	0.275886
$980$	0	0
$981$	0	0
$982$	−78.8038	−2.51473
$983$	4.19945	0.133942	0.0669709	−	0.997755i	$-0.478667\pi$
$983$	4.19945	0.133942	0.0669709	+	0.997755i	$0.478667\pi$
$984$	0	0
$985$	1.69597	0.0540382
$986$	15.3927	0.490203
$987$	0	0
$988$	13.4986	0.429447
$989$	35.4767	1.12809
$990$	0	0
$991$	−13.4139	−0.426105	−0.213053	−	0.977041i	$-0.568341\pi$
$991$	−13.4139	−0.426105	−0.213053	+	0.977041i	$0.568341\pi$
$992$	−12.6139	−0.400491
$993$	0	0
$994$	0	0
$995$	10.3222	0.327236
$996$	0	0
$997$	−47.8868	−1.51659	−0.758295	−	0.651911i	$-0.773967\pi$
$997$	−47.8868	−1.51659	−0.758295	+	0.651911i	$0.773967\pi$
$998$	18.4144	0.582899
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5733.2.a.bl.1.5		5
3.2	odd	2		637.2.a.l.1.1		5
7.2	even	3		819.2.j.h.235.1		10
7.4	even	3		819.2.j.h.352.1		10
7.6	odd	2		5733.2.a.bm.1.5		5
21.2	odd	6		91.2.e.c.53.5	✓	10
21.5	even	6		637.2.e.m.508.5		10
21.11	odd	6		91.2.e.c.79.5	yes	10
21.17	even	6		637.2.e.m.79.5		10
21.20	even	2		637.2.a.k.1.1		5
39.38	odd	2		8281.2.a.bw.1.5		5
84.11	even	6		1456.2.r.p.625.4		10
84.23	even	6		1456.2.r.p.417.4		10
273.116	odd	6		1183.2.e.f.170.1		10
273.233	odd	6		1183.2.e.f.508.1		10
273.272	even	2		8281.2.a.bx.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.e.c.53.5	✓	10	21.2	odd	6
91.2.e.c.79.5	yes	10	21.11	odd	6
637.2.a.k.1.1		5	21.20	even	2
637.2.a.l.1.1		5	3.2	odd	2
637.2.e.m.79.5		10	21.17	even	6
637.2.e.m.508.5		10	21.5	even	6
819.2.j.h.235.1		10	7.2	even	3
819.2.j.h.352.1		10	7.4	even	3
1183.2.e.f.170.1		10	273.116	odd	6
1183.2.e.f.508.1		10	273.233	odd	6
1456.2.r.p.417.4		10	84.23	even	6
1456.2.r.p.625.4		10	84.11	even	6
5733.2.a.bl.1.5		5	1.1	even	1	trivial
5733.2.a.bm.1.5		5	7.6	odd	2
8281.2.a.bw.1.5		5	39.38	odd	2
8281.2.a.bx.1.5		5	273.272	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:	\( N \)	\(=\)	\( 5733 = 3^{2} \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5733.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00852 q^{2} +2.03417 q^{4} -0.905722 q^{5} +0.0686323 q^{8} +O(q^{10})\)	\(q+2.00852 q^{2} +2.03417 q^{4} -0.905722 q^{5} +0.0686323 q^{8} -1.81916 q^{10} -0.716361 q^{11} +1.00000 q^{13} -3.93049 q^{16} -2.35227 q^{17} +6.63591 q^{19} -1.84239 q^{20} -1.43883 q^{22} -3.75906 q^{23} -4.17967 q^{25} +2.00852 q^{26} -3.25799 q^{29} +1.57050 q^{31} -8.03175 q^{32} -4.72459 q^{34} +5.20883 q^{37} +13.3284 q^{38} -0.0621618 q^{40} -4.92168 q^{41} -9.43766 q^{43} -1.45720 q^{44} -7.55016 q^{46} +8.31986 q^{47} -8.39497 q^{50} +2.03417 q^{52} -14.0833 q^{53} +0.648824 q^{55} -6.54376 q^{58} -0.716361 q^{59} -11.6527 q^{61} +3.15439 q^{62} -8.27099 q^{64} -0.905722 q^{65} +9.39174 q^{67} -4.78492 q^{68} -10.9914 q^{71} -3.47300 q^{73} +10.4621 q^{74} +13.4986 q^{76} +13.0082 q^{79} +3.55993 q^{80} -9.88531 q^{82} -3.54083 q^{83} +2.13050 q^{85} -18.9558 q^{86} -0.0491655 q^{88} -12.0501 q^{89} -7.64656 q^{92} +16.7106 q^{94} -6.01029 q^{95} +7.43766 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 4 q^{2} + 8 q^{4} - 2 q^{5} - 9 q^{8}+O(q^{10}) \) 5 * q - 4 * q^2 + 8 * q^4 - 2 * q^5 - 9 * q^8	\( 5 q - 4 q^{2} + 8 q^{4} - 2 q^{5} - 9 q^{8} - 5 q^{10} - 11 q^{11} + 5 q^{13} + 10 q^{16} + 5 q^{17} + 9 q^{19} - q^{20} + 8 q^{22} - 10 q^{23} + 9 q^{25} - 4 q^{26} + 3 q^{29} - 6 q^{31} - 22 q^{32} - 22 q^{34} + 4 q^{37} + 10 q^{38} + 28 q^{40} - 14 q^{41} + 2 q^{43} + 3 q^{46} - q^{47} - 9 q^{50} + 8 q^{52} - 17 q^{53} - 27 q^{58} - 11 q^{59} - 11 q^{61} + 23 q^{62} + 9 q^{64} - 2 q^{65} + 13 q^{67} + 32 q^{68} - 15 q^{71} + 33 q^{74} + 8 q^{76} + 2 q^{79} - 55 q^{80} + 34 q^{82} - 6 q^{83} - 22 q^{85} - 28 q^{86} - 3 q^{88} + 4 q^{89} - 21 q^{92} + 20 q^{94} + 12 q^{95} - 12 q^{97}+O(q^{100}) \) 5 * q - 4 * q^2 + 8 * q^4 - 2 * q^5 - 9 * q^8 - 5 * q^10 - 11 * q^11 + 5 * q^13 + 10 * q^16 + 5 * q^17 + 9 * q^19 - q^20 + 8 * q^22 - 10 * q^23 + 9 * q^25 - 4 * q^26 + 3 * q^29 - 6 * q^31 - 22 * q^32 - 22 * q^34 + 4 * q^37 + 10 * q^38 + 28 * q^40 - 14 * q^41 + 2 * q^43 + 3 * q^46 - q^47 - 9 * q^50 + 8 * q^52 - 17 * q^53 - 27 * q^58 - 11 * q^59 - 11 * q^61 + 23 * q^62 + 9 * q^64 - 2 * q^65 + 13 * q^67 + 32 * q^68 - 15 * q^71 + 33 * q^74 + 8 * q^76 + 2 * q^79 - 55 * q^80 + 34 * q^82 - 6 * q^83 - 22 * q^85 - 28 * q^86 - 3 * q^88 + 4 * q^89 - 21 * q^92 + 20 * q^94 + 12 * q^95 - 12 * q^97

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