LMFDB - Embedded newform 5733.2.a.bd.1.3

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:	$3$
Coefficient field:	3.3.404.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 5x - 1 $ x^3 - x^2 - 5*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 637)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.65544$ 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)

$f(q)$	$=$	$q+2.65544 q^{2} +5.05137 q^{4} -3.65544 q^{5} +8.10275 q^{8} +O(q^{10})$	$q+2.65544 q^{2} +5.05137 q^{4} -3.65544 q^{5} +8.10275 q^{8} -9.70682 q^{10} -0.655442 q^{11} -1.00000 q^{13} +11.4136 q^{16} -2.39593 q^{17} -2.70682 q^{19} -18.4650 q^{20} -1.74049 q^{22} -7.36226 q^{23} +8.36226 q^{25} -2.65544 q^{26} +0.208136 q^{29} -1.13642 q^{31} +14.1027 q^{32} -6.36226 q^{34} -7.44731 q^{37} -7.18780 q^{38} -29.6191 q^{40} +10.2055 q^{41} -3.10275 q^{43} -3.31088 q^{44} -19.5501 q^{46} -4.60407 q^{47} +22.2055 q^{50} -5.05137 q^{52} -5.25951 q^{53} +2.39593 q^{55} +0.552694 q^{58} -8.25951 q^{59} -1.89725 q^{61} -3.01770 q^{62} +14.6218 q^{64} +3.65544 q^{65} -12.8946 q^{67} -12.1027 q^{68} +6.75819 q^{71} +12.5367 q^{73} -19.7759 q^{74} -13.6731 q^{76} -1.51902 q^{79} -41.7219 q^{80} +27.1001 q^{82} -15.7582 q^{83} +8.75819 q^{85} -8.23917 q^{86} -5.31088 q^{88} +14.8096 q^{89} -37.1895 q^{92} -12.2258 q^{94} +9.89461 q^{95} -10.0177 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 2 q^{2} + 6 q^{4} - 5 q^{5} + 6 q^{8}+O(q^{10}) $ 3 * q + 2 * q^2 + 6 * q^4 - 5 * q^5 + 6 * q^8	$ 3 q + 2 q^{2} + 6 q^{4} - 5 q^{5} + 6 q^{8} - 14 q^{10} + 4 q^{11} - 3 q^{13} + 4 q^{16} - 4 q^{17} + 7 q^{19} - 16 q^{20} - 8 q^{22} - q^{23} + 4 q^{25} - 2 q^{26} + 7 q^{29} - 3 q^{31} + 24 q^{32} + 2 q^{34} - 10 q^{37} - 12 q^{38} - 22 q^{40} - 6 q^{41} + 9 q^{43} + 2 q^{44} - 28 q^{46} - 17 q^{47} + 30 q^{50} - 6 q^{52} - 13 q^{53} + 4 q^{55} + 14 q^{58} - 22 q^{59} - 24 q^{61} + 18 q^{62} + 20 q^{64} + 5 q^{65} - 14 q^{67} - 18 q^{68} - 4 q^{71} + 5 q^{73} - 8 q^{74} - 8 q^{76} + q^{79} - 40 q^{80} + 20 q^{82} - 23 q^{83} + 2 q^{85} - 6 q^{86} - 4 q^{88} + 11 q^{89} - 30 q^{92} - 16 q^{94} + 5 q^{95} - 3 q^{97}+O(q^{100}) $ 3 * q + 2 * q^2 + 6 * q^4 - 5 * q^5 + 6 * q^8 - 14 * q^10 + 4 * q^11 - 3 * q^13 + 4 * q^16 - 4 * q^17 + 7 * q^19 - 16 * q^20 - 8 * q^22 - q^23 + 4 * q^25 - 2 * q^26 + 7 * q^29 - 3 * q^31 + 24 * q^32 + 2 * q^34 - 10 * q^37 - 12 * q^38 - 22 * q^40 - 6 * q^41 + 9 * q^43 + 2 * q^44 - 28 * q^46 - 17 * q^47 + 30 * q^50 - 6 * q^52 - 13 * q^53 + 4 * q^55 + 14 * q^58 - 22 * q^59 - 24 * q^61 + 18 * q^62 + 20 * q^64 + 5 * q^65 - 14 * q^67 - 18 * q^68 - 4 * q^71 + 5 * q^73 - 8 * q^74 - 8 * q^76 + q^79 - 40 * q^80 + 20 * q^82 - 23 * q^83 + 2 * q^85 - 6 * q^86 - 4 * q^88 + 11 * q^89 - 30 * q^92 - 16 * q^94 + 5 * q^95 - 3 * 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 $

$2$	2.65544	1.87768	0.938841	−	0.344352i	$-0.111901\pi$
$2$	2.65544	1.87768	0.938841	+	0.344352i	$0.111901\pi$
$3$	0	0
$3$	0	0
$4$	5.05137	2.52569
$5$	−3.65544	−1.63476	−0.817382	−	0.576096i	$-0.804575\pi$
$5$	−3.65544	−1.63476	−0.817382	+	0.576096i	$0.804575\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	8.10275	2.86475
$9$	0	0
$10$	−9.70682	−3.06956
$11$	−0.655442	−0.197623	−0.0988117	−	0.995106i	$-0.531504\pi$
$11$	−0.655442	−0.197623	−0.0988117	+	0.995106i	$0.531504\pi$
$12$	0	0
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	0	0
$16$	11.4136	2.85341
$17$	−2.39593	−0.581099	−0.290549	−	0.956860i	$-0.593838\pi$
$17$	−2.39593	−0.581099	−0.290549	+	0.956860i	$0.593838\pi$
$18$	0	0
$19$	−2.70682	−0.620986	−0.310493	−	0.950576i	$-0.600494\pi$
$19$	−2.70682	−0.620986	−0.310493	+	0.950576i	$0.600494\pi$
$20$	−18.4650	−4.12890
$21$	0	0
$22$	−1.74049	−0.371074
$23$	−7.36226	−1.53514	−0.767569	−	0.640967i	$-0.778534\pi$
$23$	−7.36226	−1.53514	−0.767569	+	0.640967i	$0.778534\pi$
$24$	0	0
$25$	8.36226	1.67245
$26$	−2.65544	−0.520775
$27$	0	0
$28$	0	0
$29$	0.208136	0.0386499	0.0193250	−	0.999813i	$-0.493848\pi$
$29$	0.208136	0.0386499	0.0193250	+	0.999813i	$0.493848\pi$
$30$	0	0
$31$	−1.13642	−0.204107	−0.102054	−	0.994779i	$-0.532541\pi$
$31$	−1.13642	−0.204107	−0.102054	+	0.994779i	$0.532541\pi$
$32$	14.1027	2.49304
$33$	0	0
$34$	−6.36226	−1.09112
$35$	0	0
$36$	0	0
$37$	−7.44731	−1.22433	−0.612165	−	0.790730i	$-0.709701\pi$
$37$	−7.44731	−1.22433	−0.612165	+	0.790730i	$0.709701\pi$
$38$	−7.18780	−1.16601
$39$	0	0
$40$	−29.6191	−4.68320
$41$	10.2055	1.59383	0.796915	−	0.604091i	$-0.206464\pi$
$41$	10.2055	1.59383	0.796915	+	0.604091i	$0.206464\pi$
$42$	0	0
$43$	−3.10275	−0.473165	−0.236582	−	0.971611i	$-0.576027\pi$
$43$	−3.10275	−0.473165	−0.236582	+	0.971611i	$0.576027\pi$
$44$	−3.31088	−0.499135
$45$	0	0
$46$	−19.5501	−2.88250
$47$	−4.60407	−0.671572	−0.335786	−	0.941938i	$-0.609002\pi$
$47$	−4.60407	−0.671572	−0.335786	+	0.941938i	$0.609002\pi$
$48$	0	0
$49$	0	0
$50$	22.2055	3.14033
$51$	0	0
$52$	−5.05137	−0.700500
$53$	−5.25951	−0.722449	−0.361225	−	0.932479i	$-0.617641\pi$
$53$	−5.25951	−0.722449	−0.361225	+	0.932479i	$0.617641\pi$
$54$	0	0
$55$	2.39593	0.323067
$56$	0	0
$57$	0	0
$58$	0.552694	0.0725723
$59$	−8.25951	−1.07530	−0.537648	−	0.843169i	$-0.680687\pi$
$59$	−8.25951	−1.07530	−0.537648	+	0.843169i	$0.680687\pi$
$60$	0	0
$61$	−1.89725	−0.242918	−0.121459	−	0.992596i	$-0.538757\pi$
$61$	−1.89725	−0.242918	−0.121459	+	0.992596i	$0.538757\pi$
$62$	−3.01770	−0.383248
$63$	0	0
$64$	14.6218	1.82772
$65$	3.65544	0.453402
$66$	0	0
$67$	−12.8946	−1.57533	−0.787664	−	0.616105i	$-0.788710\pi$
$67$	−12.8946	−1.57533	−0.787664	+	0.616105i	$0.788710\pi$
$68$	−12.1027	−1.46767
$69$	0	0
$70$	0	0
$71$	6.75819	0.802050	0.401025	−	0.916067i	$-0.368654\pi$
$71$	6.75819	0.802050	0.401025	+	0.916067i	$0.368654\pi$
$72$	0	0
$73$	12.5367	1.46731	0.733656	−	0.679521i	$-0.237812\pi$
$73$	12.5367	1.46731	0.733656	+	0.679521i	$0.237812\pi$
$74$	−19.7759	−2.29890
$75$	0	0
$76$	−13.6731	−1.56842
$77$	0	0
$78$	0	0
$79$	−1.51902	−0.170903	−0.0854516	−	0.996342i	$-0.527233\pi$
$79$	−1.51902	−0.170903	−0.0854516	+	0.996342i	$0.527233\pi$
$80$	−41.7219	−4.66465
$81$	0	0
$82$	27.1001	2.99271
$83$	−15.7582	−1.72969	−0.864843	−	0.502042i	$-0.832582\pi$
$83$	−15.7582	−1.72969	−0.864843	+	0.502042i	$0.832582\pi$
$84$	0	0
$85$	8.75819	0.949959
$86$	−8.23917	−0.888453
$87$	0	0
$88$	−5.31088	−0.566142
$89$	14.8096	1.56981	0.784905	−	0.619616i	$-0.212712\pi$
$89$	14.8096	1.56981	0.784905	+	0.619616i	$0.212712\pi$
$90$	0	0
$91$	0	0
$92$	−37.1895	−3.87728
$93$	0	0
$94$	−12.2258	−1.26100
$95$	9.89461	1.01517
$96$	0	0
$97$	−10.0177	−1.01714	−0.508572	−	0.861020i	$-0.669826\pi$
$97$	−10.0177	−1.01714	−0.508572	+	0.861020i	$0.669826\pi$
$98$	0	0
$99$	0	0
$100$	42.2409	4.22409
$101$	3.01770	0.300273	0.150136	−	0.988665i	$-0.452029\pi$
$101$	3.01770	0.300273	0.150136	+	0.988665i	$0.452029\pi$
$102$	0	0
$103$	−5.03804	−0.496413	−0.248207	−	0.968707i	$-0.579841\pi$
$103$	−5.03804	−0.496413	−0.248207	+	0.968707i	$0.579841\pi$
$104$	−8.10275	−0.794540
$105$	0	0
$106$	−13.9663	−1.35653
$107$	−11.8432	−1.14493	−0.572465	−	0.819929i	$-0.694013\pi$
$107$	−11.8432	−1.14493	−0.572465	+	0.819929i	$0.694013\pi$
$108$	0	0
$109$	3.55005	0.340034	0.170017	−	0.985441i	$-0.445618\pi$
$109$	3.55005	0.340034	0.170017	+	0.985441i	$0.445618\pi$
$110$	6.36226	0.606618
$111$	0	0
$112$	0	0
$113$	9.46501	0.890393	0.445197	−	0.895433i	$-0.353134\pi$
$113$	9.46501	0.890393	0.445197	+	0.895433i	$0.353134\pi$
$114$	0	0
$115$	26.9123	2.50959
$116$	1.05137	0.0976176
$117$	0	0
$118$	−21.9327	−2.01906
$119$	0	0
$120$	0	0
$121$	−10.5704	−0.960945
$122$	−5.03804	−0.456123
$123$	0	0
$124$	−5.74049	−0.515511
$125$	−12.2905	−1.09930
$126$	0	0
$127$	5.46765	0.485175	0.242588	−	0.970130i	$-0.422004\pi$
$127$	5.46765	0.485175	0.242588	+	0.970130i	$0.422004\pi$
$128$	10.6218	0.938841
$129$	0	0
$130$	9.70682	0.851344
$131$	−9.82991	−0.858843	−0.429421	−	0.903104i	$-0.641282\pi$
$131$	−9.82991	−0.858843	−0.429421	+	0.903104i	$0.641282\pi$
$132$	0	0
$133$	0	0
$134$	−34.2409	−2.95796
$135$	0	0
$136$	−19.4136	−1.66471
$137$	−17.5501	−1.49940	−0.749701	−	0.661777i	$-0.769803\pi$
$137$	−17.5501	−1.49940	−0.749701	+	0.661777i	$0.769803\pi$
$138$	0	0
$139$	−4.91495	−0.416881	−0.208440	−	0.978035i	$-0.566839\pi$
$139$	−4.91495	−0.416881	−0.208440	+	0.978035i	$0.566839\pi$
$140$	0	0
$141$	0	0
$142$	17.9460	1.50599
$143$	0.655442	0.0548108
$144$	0	0
$145$	−0.760830	−0.0631835
$146$	33.2905	2.75515
$147$	0	0
$148$	−37.6191	−3.09227
$149$	10.3419	0.847243	0.423621	−	0.905839i	$-0.360759\pi$
$149$	10.3419	0.847243	0.423621	+	0.905839i	$0.360759\pi$
$150$	0	0
$151$	5.07171	0.412730	0.206365	−	0.978475i	$-0.433837\pi$
$151$	5.07171	0.412730	0.206365	+	0.978475i	$0.433837\pi$
$152$	−21.9327	−1.77897
$153$	0	0
$154$	0	0
$155$	4.15412	0.333667
$156$	0	0
$157$	−12.6014	−1.00570	−0.502852	−	0.864373i	$-0.667716\pi$
$157$	−12.6014	−1.00570	−0.502852	+	0.864373i	$0.667716\pi$
$158$	−4.03367	−0.320902
$159$	0	0
$160$	−51.5518	−4.07553
$161$	0	0
$162$	0	0
$163$	3.20814	0.251281	0.125640	−	0.992076i	$-0.459901\pi$
$163$	3.20814	0.251281	0.125640	+	0.992076i	$0.459901\pi$
$164$	51.5518	4.02552
$165$	0	0
$166$	−41.8450	−3.24780
$167$	−8.12045	−0.628379	−0.314190	−	0.949360i	$-0.601733\pi$
$167$	−8.12045	−0.628379	−0.314190	+	0.949360i	$0.601733\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	23.2569	1.78372
$171$	0	0
$172$	−15.6731	−1.19507
$173$	10.3286	0.785268	0.392634	−	0.919695i	$-0.371564\pi$
$173$	10.3286	0.785268	0.392634	+	0.919695i	$0.371564\pi$
$174$	0	0
$175$	0	0
$176$	−7.48098	−0.563900
$177$	0	0
$178$	39.3259	2.94760
$179$	2.37823	0.177757	0.0888786	−	0.996042i	$-0.471672\pi$
$179$	2.37823	0.177757	0.0888786	+	0.996042i	$0.471672\pi$
$180$	0	0
$181$	21.8096	1.62109	0.810546	−	0.585675i	$-0.199170\pi$
$181$	21.8096	1.62109	0.810546	+	0.585675i	$0.199170\pi$
$182$	0	0
$183$	0	0
$184$	−59.6545	−4.39779
$185$	27.2232	2.00149
$186$	0	0
$187$	1.57040	0.114839
$188$	−23.2569	−1.69618
$189$	0	0
$190$	26.2746	1.90616
$191$	25.0868	1.81522	0.907608	−	0.419819i	$-0.137907\pi$
$191$	25.0868	1.81522	0.907608	+	0.419819i	$0.137907\pi$
$192$	0	0
$193$	11.3109	0.814175	0.407088	−	0.913389i	$-0.366544\pi$
$193$	11.3109	0.814175	0.407088	+	0.913389i	$0.366544\pi$
$194$	−26.6014	−1.90987
$195$	0	0
$196$	0	0
$197$	16.7919	1.19637	0.598185	−	0.801358i	$-0.295889\pi$
$197$	16.7919	1.19637	0.598185	+	0.801358i	$0.295889\pi$
$198$	0	0
$199$	20.5341	1.45562	0.727811	−	0.685777i	$-0.240538\pi$
$199$	20.5341	1.45562	0.727811	+	0.685777i	$0.240538\pi$
$200$	67.7573	4.79116
$201$	0	0
$202$	8.01333	0.563816
$203$	0	0
$204$	0	0
$205$	−37.3056	−2.60554
$206$	−13.3782	−0.932105
$207$	0	0
$208$	−11.4136	−0.791393
$209$	1.77416	0.122721
$210$	0	0
$211$	−15.7785	−1.08624	−0.543119	−	0.839655i	$-0.682757\pi$
$211$	−15.7785	−1.08624	−0.543119	+	0.839655i	$0.682757\pi$
$212$	−26.5678	−1.82468
$213$	0	0
$214$	−31.4490	−2.14981
$215$	11.3419	0.773512
$216$	0	0
$217$	0	0
$218$	9.42697	0.638475
$219$	0	0
$220$	12.1027	0.815967
$221$	2.39593	0.161168
$222$	0	0
$223$	−8.44731	−0.565673	−0.282837	−	0.959168i	$-0.591275\pi$
$223$	−8.44731	−0.565673	−0.282837	+	0.959168i	$0.591275\pi$
$224$	0	0
$225$	0	0
$226$	25.1338	1.67187
$227$	−6.68912	−0.443972	−0.221986	−	0.975050i	$-0.571254\pi$
$227$	−6.68912	−0.443972	−0.221986	+	0.975050i	$0.571254\pi$
$228$	0	0
$229$	8.63510	0.570624	0.285312	−	0.958435i	$-0.407903\pi$
$229$	8.63510	0.570624	0.285312	+	0.958435i	$0.407903\pi$
$230$	71.4641	4.71220
$231$	0	0
$232$	1.68648	0.110723
$233$	4.16745	0.273019	0.136510	−	0.990639i	$-0.456412\pi$
$233$	4.16745	0.273019	0.136510	+	0.990639i	$0.456412\pi$
$234$	0	0
$235$	16.8299	1.09786
$236$	−41.7219	−2.71586
$237$	0	0
$238$	0	0
$239$	1.79450	0.116077	0.0580384	−	0.998314i	$-0.481515\pi$
$239$	1.79450	0.116077	0.0580384	+	0.998314i	$0.481515\pi$
$240$	0	0
$241$	13.8609	0.892862	0.446431	−	0.894818i	$-0.352695\pi$
$241$	13.8609	0.892862	0.446431	+	0.894818i	$0.352695\pi$
$242$	−28.0691	−1.80435
$243$	0	0
$244$	−9.58373	−0.613535
$245$	0	0
$246$	0	0
$247$	2.70682	0.172231
$248$	−9.20814	−0.584717
$249$	0	0
$250$	−32.6368	−2.06413
$251$	−14.7449	−0.930687	−0.465344	−	0.885130i	$-0.654069\pi$
$251$	−14.7449	−0.930687	−0.465344	+	0.885130i	$0.654069\pi$
$252$	0	0
$253$	4.82554	0.303379
$254$	14.5190	0.911004
$255$	0	0
$256$	−1.03804	−0.0648776
$257$	−23.7068	−1.47879	−0.739395	−	0.673272i	$-0.764888\pi$
$257$	−23.7068	−1.47879	−0.739395	+	0.673272i	$0.764888\pi$
$258$	0	0
$259$	0	0
$260$	18.4650	1.14515
$261$	0	0
$262$	−26.1027	−1.61263
$263$	−11.3756	−0.701449	−0.350725	−	0.936479i	$-0.614065\pi$
$263$	−11.3756	−0.701449	−0.350725	+	0.936479i	$0.614065\pi$
$264$	0	0
$265$	19.2258	1.18103
$266$	0	0
$267$	0	0
$268$	−65.1355	−3.97878
$269$	11.1054	0.677107	0.338554	−	0.940947i	$-0.390062\pi$
$269$	11.1054	0.677107	0.338554	+	0.940947i	$0.390062\pi$
$270$	0	0
$271$	−12.7245	−0.772959	−0.386480	−	0.922298i	$-0.626309\pi$
$271$	−12.7245	−0.772959	−0.386480	+	0.922298i	$0.626309\pi$
$272$	−27.3463	−1.65811
$273$	0	0
$274$	−46.6032	−2.81540
$275$	−5.48098	−0.330515
$276$	0	0
$277$	−3.00000	−0.180253	−0.0901263	−	0.995930i	$-0.528727\pi$
$277$	−3.00000	−0.180253	−0.0901263	+	0.995930i	$0.528727\pi$
$278$	−13.0514	−0.782769
$279$	0	0
$280$	0	0
$281$	−3.44731	−0.205649	−0.102825	−	0.994700i	$-0.532788\pi$
$281$	−3.44731	−0.205649	−0.102825	+	0.994700i	$0.532788\pi$
$282$	0	0
$283$	−12.4783	−0.741760	−0.370880	−	0.928681i	$-0.620944\pi$
$283$	−12.4783	−0.741760	−0.370880	+	0.928681i	$0.620944\pi$
$284$	34.1382	2.02573
$285$	0	0
$286$	1.74049	0.102917
$287$	0	0
$288$	0	0
$289$	−11.2595	−0.662324
$290$	−2.02034	−0.118638
$291$	0	0
$292$	63.3277	3.70597
$293$	13.5341	0.790670	0.395335	−	0.918537i	$-0.370629\pi$
$293$	13.5341	0.790670	0.395335	+	0.918537i	$0.370629\pi$
$294$	0	0
$295$	30.1922	1.75786
$296$	−60.3436	−3.50740
$297$	0	0
$298$	27.4624	1.59085
$299$	7.36226	0.425770
$300$	0	0
$301$	0	0
$302$	13.4676	0.774976
$303$	0	0
$304$	−30.8946	−1.77193
$305$	6.93529	0.397114
$306$	0	0
$307$	28.2365	1.61154	0.805772	−	0.592226i	$-0.201751\pi$
$307$	28.2365	1.61154	0.805772	+	0.592226i	$0.201751\pi$
$308$	0	0
$309$	0	0
$310$	11.0310	0.626521
$311$	24.7042	1.40085	0.700423	−	0.713728i	$-0.252995\pi$
$311$	24.7042	1.40085	0.700423	+	0.713728i	$0.252995\pi$
$312$	0	0
$313$	−20.8122	−1.17638	−0.588188	−	0.808724i	$-0.700158\pi$
$313$	−20.8122	−1.17638	−0.588188	+	0.808724i	$0.700158\pi$
$314$	−33.4624	−1.88839
$315$	0	0
$316$	−7.67314	−0.431648
$317$	−26.1382	−1.46806	−0.734032	−	0.679114i	$-0.762364\pi$
$317$	−26.1382	−1.46806	−0.734032	+	0.679114i	$0.762364\pi$
$318$	0	0
$319$	−0.136421	−0.00763813
$320$	−53.4490	−2.98789
$321$	0	0
$322$	0	0
$323$	6.48535	0.360854
$324$	0	0
$325$	−8.36226	−0.463855
$326$	8.51902	0.471825
$327$	0	0
$328$	82.6926	4.56593
$329$	0	0
$330$	0	0
$331$	−24.1382	−1.32675	−0.663376	−	0.748286i	$-0.730877\pi$
$331$	−24.1382	−1.32675	−0.663376	+	0.748286i	$0.730877\pi$
$332$	−79.6005	−4.36865
$333$	0	0
$334$	−21.5634	−1.17990
$335$	47.1355	2.57529
$336$	0	0
$337$	−30.5297	−1.66306	−0.831530	−	0.555480i	$-0.812534\pi$
$337$	−30.5297	−1.66306	−0.831530	+	0.555480i	$0.812534\pi$
$338$	2.65544	0.144437
$339$	0	0
$340$	44.2409	2.39930
$341$	0.744859	0.0403364
$342$	0	0
$343$	0	0
$344$	−25.1408	−1.35550
$345$	0	0
$346$	27.4270	1.47448
$347$	24.9974	1.34193	0.670964	−	0.741490i	$-0.265880\pi$
$347$	24.9974	1.34193	0.670964	+	0.741490i	$0.265880\pi$
$348$	0	0
$349$	−1.83887	−0.0984324	−0.0492162	−	0.998788i	$-0.515672\pi$
$349$	−1.83887	−0.0984324	−0.0492162	+	0.998788i	$0.515672\pi$
$350$	0	0
$351$	0	0
$352$	−9.24354	−0.492682
$353$	23.2569	1.23784	0.618919	−	0.785455i	$-0.287571\pi$
$353$	23.2569	1.23784	0.618919	+	0.785455i	$0.287571\pi$
$354$	0	0
$355$	−24.7042	−1.31116
$356$	74.8087	3.96485
$357$	0	0
$358$	6.31525	0.333772
$359$	21.4473	1.13195	0.565973	−	0.824424i	$-0.308501\pi$
$359$	21.4473	1.13195	0.565973	+	0.824424i	$0.308501\pi$
$360$	0	0
$361$	−11.6731	−0.614376
$362$	57.9140	3.04389
$363$	0	0
$364$	0	0
$365$	−45.8273	−2.39871
$366$	0	0
$367$	−1.12045	−0.0584870	−0.0292435	−	0.999572i	$-0.509310\pi$
$367$	−1.12045	−0.0584870	−0.0292435	+	0.999572i	$0.509310\pi$
$368$	−84.0301	−4.38037
$369$	0	0
$370$	72.2896	3.75816
$371$	0	0
$372$	0	0
$373$	15.6058	0.808038	0.404019	−	0.914751i	$-0.367613\pi$
$373$	15.6058	0.808038	0.404019	+	0.914751i	$0.367613\pi$
$374$	4.17009	0.215630
$375$	0	0
$376$	−37.3056	−1.92389
$377$	−0.208136	−0.0107196
$378$	0	0
$379$	12.7849	0.656714	0.328357	−	0.944554i	$-0.393505\pi$
$379$	12.7849	0.656714	0.328357	+	0.944554i	$0.393505\pi$
$380$	49.9814	2.56399
$381$	0	0
$382$	66.6165	3.40840
$383$	−34.0354	−1.73913	−0.869564	−	0.493820i	$-0.835600\pi$
$383$	−34.0354	−1.73913	−0.869564	+	0.493820i	$0.835600\pi$
$384$	0	0
$385$	0	0
$386$	30.0354	1.52876
$387$	0	0
$388$	−50.6032	−2.56899
$389$	24.6705	1.25084	0.625422	−	0.780287i	$-0.284927\pi$
$389$	24.6705	1.25084	0.625422	+	0.780287i	$0.284927\pi$
$390$	0	0
$391$	17.6395	0.892066
$392$	0	0
$393$	0	0
$394$	44.5898	2.24640
$395$	5.55269	0.279386
$396$	0	0
$397$	−4.97966	−0.249922	−0.124961	−	0.992162i	$-0.539881\pi$
$397$	−4.97966	−0.249922	−0.124961	+	0.992162i	$0.539881\pi$
$398$	54.5271	2.73320
$399$	0	0
$400$	95.4438	4.77219
$401$	−0.689115	−0.0344128	−0.0172064	−	0.999852i	$-0.505477\pi$
$401$	−0.689115	−0.0344128	−0.0172064	+	0.999852i	$0.505477\pi$
$402$	0	0
$403$	1.13642	0.0566092
$404$	15.2435	0.758394
$405$	0	0
$406$	0	0
$407$	4.88128	0.241956
$408$	0	0
$409$	19.9770	0.987800	0.493900	−	0.869519i	$-0.335571\pi$
$409$	19.9770	0.987800	0.493900	+	0.869519i	$0.335571\pi$
$410$	−99.0629	−4.89237
$411$	0	0
$412$	−25.4490	−1.25378
$413$	0	0
$414$	0	0
$415$	57.6032	2.82763
$416$	−14.1027	−0.691444
$417$	0	0
$418$	4.71119	0.230432
$419$	−19.6661	−0.960754	−0.480377	−	0.877062i	$-0.659500\pi$
$419$	−19.6661	−0.960754	−0.480377	+	0.877062i	$0.659500\pi$
$420$	0	0
$421$	14.9283	0.727560	0.363780	−	0.931485i	$-0.381486\pi$
$421$	14.9283	0.727560	0.363780	+	0.931485i	$0.381486\pi$
$422$	−41.8990	−2.03961
$423$	0	0
$424$	−42.6165	−2.06964
$425$	−20.0354	−0.971860
$426$	0	0
$427$	0	0
$428$	−59.8246	−2.89173
$429$	0	0
$430$	30.1178	1.45241
$431$	32.6838	1.57433	0.787163	−	0.616746i	$-0.211549\pi$
$431$	32.6838	1.57433	0.787163	+	0.616746i	$0.211549\pi$
$432$	0	0
$433$	−8.96196	−0.430684	−0.215342	−	0.976539i	$-0.569087\pi$
$433$	−8.96196	−0.430684	−0.215342	+	0.976539i	$0.569087\pi$
$434$	0	0
$435$	0	0
$436$	17.9327	0.858818
$437$	19.9283	0.953299
$438$	0	0
$439$	−7.93265	−0.378605	−0.189302	−	0.981919i	$-0.560623\pi$
$439$	−7.93265	−0.378605	−0.189302	+	0.981919i	$0.560623\pi$
$440$	19.4136	0.925509
$441$	0	0
$442$	6.36226	0.302622
$443$	8.91058	0.423355	0.211677	−	0.977340i	$-0.432107\pi$
$443$	8.91058	0.423355	0.211677	+	0.977340i	$0.432107\pi$
$444$	0	0
$445$	−54.1355	−2.56627
$446$	−22.4313	−1.06215
$447$	0	0
$448$	0	0
$449$	8.45168	0.398859	0.199430	−	0.979912i	$-0.436091\pi$
$449$	8.45168	0.398859	0.199430	+	0.979912i	$0.436091\pi$
$450$	0	0
$451$	−6.68912	−0.314978
$452$	47.8113	2.24885
$453$	0	0
$454$	−17.7626	−0.833638
$455$	0	0
$456$	0	0
$457$	23.1692	1.08381	0.541904	−	0.840440i	$-0.317703\pi$
$457$	23.1692	1.08381	0.541904	+	0.840440i	$0.317703\pi$
$458$	22.9300	1.07145
$459$	0	0
$460$	135.944	6.33843
$461$	−2.27284	−0.105857	−0.0529284	−	0.998598i	$-0.516856\pi$
$461$	−2.27284	−0.105857	−0.0529284	+	0.998598i	$0.516856\pi$
$462$	0	0
$463$	−4.10976	−0.190997	−0.0954983	−	0.995430i	$-0.530444\pi$
$463$	−4.10976	−0.190997	−0.0954983	+	0.995430i	$0.530444\pi$
$464$	2.37559	0.110284
$465$	0	0
$466$	11.0664	0.512643
$467$	−32.9150	−1.52312	−0.761561	−	0.648093i	$-0.775567\pi$
$467$	−32.9150	−1.52312	−0.761561	+	0.648093i	$0.775567\pi$
$468$	0	0
$469$	0	0
$470$	44.6908	2.06143
$471$	0	0
$472$	−66.9247	−3.08046
$473$	2.03367	0.0935084
$474$	0	0
$475$	−22.6351	−1.03857
$476$	0	0
$477$	0	0
$478$	4.76520	0.217955
$479$	9.31525	0.425625	0.212812	−	0.977093i	$-0.431738\pi$
$479$	9.31525	0.425625	0.212812	+	0.977093i	$0.431738\pi$
$480$	0	0
$481$	7.44731	0.339568
$482$	36.8069	1.67651
$483$	0	0
$484$	−53.3950	−2.42705
$485$	36.6191	1.66279
$486$	0	0
$487$	20.2409	0.917203	0.458601	−	0.888642i	$-0.348351\pi$
$487$	20.2409	0.917203	0.458601	+	0.888642i	$0.348351\pi$
$488$	−15.3730	−0.695901
$489$	0	0
$490$	0	0
$491$	4.36226	0.196866	0.0984330	−	0.995144i	$-0.468617\pi$
$491$	4.36226	0.196866	0.0984330	+	0.995144i	$0.468617\pi$
$492$	0	0
$493$	−0.498680	−0.0224594
$494$	7.18780	0.323394
$495$	0	0
$496$	−12.9707	−0.582401
$497$	0	0
$498$	0	0
$499$	9.69348	0.433940	0.216970	−	0.976178i	$-0.430383\pi$
$499$	9.69348	0.433940	0.216970	+	0.976178i	$0.430383\pi$
$500$	−62.0841	−2.77649
$501$	0	0
$502$	−39.1541	−1.74753
$503$	−2.64843	−0.118088	−0.0590439	−	0.998255i	$-0.518805\pi$
$503$	−2.64843	−0.118088	−0.0590439	+	0.998255i	$0.518805\pi$
$504$	0	0
$505$	−11.0310	−0.490875
$506$	12.8139	0.569649
$507$	0	0
$508$	27.6191	1.22540
$509$	13.9416	0.617951	0.308976	−	0.951070i	$-0.400014\pi$
$509$	13.9416	0.617951	0.308976	+	0.951070i	$0.400014\pi$
$510$	0	0
$511$	0	0
$512$	−24.0000	−1.06066
$513$	0	0
$514$	−62.9521	−2.77670
$515$	18.4163	0.811518
$516$	0	0
$517$	3.01770	0.132718
$518$	0	0
$519$	0	0
$520$	29.6191	1.29888
$521$	14.6218	0.640591	0.320296	−	0.947318i	$-0.396218\pi$
$521$	14.6218	0.640591	0.320296	+	0.947318i	$0.396218\pi$
$522$	0	0
$523$	16.5190	0.722326	0.361163	−	0.932503i	$-0.382380\pi$
$523$	16.5190	0.722326	0.361163	+	0.932503i	$0.382380\pi$
$524$	−49.6545	−2.16917
$525$	0	0
$526$	−30.2072	−1.31710
$527$	2.72279	0.118607
$528$	0	0
$529$	31.2029	1.35665
$530$	51.0531	2.21761
$531$	0	0
$532$	0	0
$533$	−10.2055	−0.442049
$534$	0	0
$535$	43.2923	1.87169
$536$	−104.482	−4.51293
$537$	0	0
$538$	29.4897	1.27139
$539$	0	0
$540$	0	0
$541$	−43.1018	−1.85309	−0.926546	−	0.376181i	$-0.877237\pi$
$541$	−43.1018	−1.85309	−0.926546	+	0.376181i	$0.877237\pi$
$542$	−33.7892	−1.45137
$543$	0	0
$544$	−33.7892	−1.44870
$545$	−12.9770	−0.555874
$546$	0	0
$547$	−13.5057	−0.577462	−0.288731	−	0.957410i	$-0.593233\pi$
$547$	−13.5057	−0.577462	−0.288731	+	0.957410i	$0.593233\pi$
$548$	−88.6519	−3.78702
$549$	0	0
$550$	−14.5544	−0.620603
$551$	−0.563387	−0.0240011
$552$	0	0
$553$	0	0
$554$	−7.96633	−0.338457
$555$	0	0
$556$	−24.8273	−1.05291
$557$	−1.35157	−0.0572677	−0.0286338	−	0.999590i	$-0.509116\pi$
$557$	−1.35157	−0.0572677	−0.0286338	+	0.999590i	$0.509116\pi$
$558$	0	0
$559$	3.10275	0.131232
$560$	0	0
$561$	0	0
$562$	−9.15412	−0.386143
$563$	−31.7626	−1.33863	−0.669316	−	0.742978i	$-0.733413\pi$
$563$	−31.7626	−1.33863	−0.669316	+	0.742978i	$0.733413\pi$
$564$	0	0
$565$	−34.5988	−1.45558
$566$	−33.1355	−1.39279
$567$	0	0
$568$	54.7599	2.29768
$569$	−30.3730	−1.27330	−0.636650	−	0.771153i	$-0.719680\pi$
$569$	−30.3730	−1.27330	−0.636650	+	0.771153i	$0.719680\pi$
$570$	0	0
$571$	−0.432244	−0.0180888	−0.00904442	−	0.999959i	$-0.502879\pi$
$571$	−0.432244	−0.0180888	−0.00904442	+	0.999959i	$0.502879\pi$
$572$	3.31088	0.138435
$573$	0	0
$574$	0	0
$575$	−61.5651	−2.56744
$576$	0	0
$577$	18.1382	0.755101	0.377551	−	0.925989i	$-0.376766\pi$
$577$	18.1382	0.755101	0.377551	+	0.925989i	$0.376766\pi$
$578$	−29.8990	−1.24363
$579$	0	0
$580$	−3.84324	−0.159582
$581$	0	0
$582$	0	0
$583$	3.44731	0.142773
$584$	101.582	4.20349
$585$	0	0
$586$	35.9390	1.48463
$587$	−19.3065	−0.796865	−0.398433	−	0.917198i	$-0.630446\pi$
$587$	−19.3065	−0.796865	−0.398433	+	0.917198i	$0.630446\pi$
$588$	0	0
$589$	3.07608	0.126748
$590$	80.1736	3.30069
$591$	0	0
$592$	−85.0008	−3.49351
$593$	−8.20113	−0.336780	−0.168390	−	0.985720i	$-0.553857\pi$
$593$	−8.20113	−0.336780	−0.168390	+	0.985720i	$0.553857\pi$
$594$	0	0
$595$	0	0
$596$	52.2409	2.13987
$597$	0	0
$598$	19.5501	0.799461
$599$	−23.4783	−0.959299	−0.479649	−	0.877460i	$-0.659236\pi$
$599$	−23.4783	−0.959299	−0.479649	+	0.877460i	$0.659236\pi$
$600$	0	0
$601$	−8.96196	−0.365566	−0.182783	−	0.983153i	$-0.558511\pi$
$601$	−8.96196	−0.365566	−0.182783	+	0.983153i	$0.558511\pi$
$602$	0	0
$603$	0	0
$604$	25.6191	1.04243
$605$	38.6395	1.57092
$606$	0	0
$607$	43.4641	1.76415	0.882077	−	0.471106i	$-0.156145\pi$
$607$	43.4641	1.76415	0.882077	+	0.471106i	$0.156145\pi$
$608$	−38.1736	−1.54814
$609$	0	0
$610$	18.4163	0.745653
$611$	4.60407	0.186261
$612$	0	0
$613$	−21.4490	−0.866318	−0.433159	−	0.901317i	$-0.642601\pi$
$613$	−21.4490	−0.866318	−0.433159	+	0.901317i	$0.642601\pi$
$614$	74.9805	3.02597
$615$	0	0
$616$	0	0
$617$	12.1294	0.488312	0.244156	−	0.969736i	$-0.421489\pi$
$617$	12.1294	0.488312	0.244156	+	0.969736i	$0.421489\pi$
$618$	0	0
$619$	12.7245	0.511442	0.255721	−	0.966751i	$-0.417687\pi$
$619$	12.7245	0.511442	0.255721	+	0.966751i	$0.417687\pi$
$620$	20.9840	0.842739
$621$	0	0
$622$	65.6005	2.63034
$623$	0	0
$624$	0	0
$625$	3.11608	0.124643
$626$	−55.2656	−2.20886
$627$	0	0
$628$	−63.6545	−2.54009
$629$	17.8432	0.711456
$630$	0	0
$631$	−11.7538	−0.467912	−0.233956	−	0.972247i	$-0.575167\pi$
$631$	−11.7538	−0.467912	−0.233956	+	0.972247i	$0.575167\pi$
$632$	−12.3082	−0.489596
$633$	0	0
$634$	−69.4084	−2.75656
$635$	−19.9867	−0.793147
$636$	0	0
$637$	0	0
$638$	−0.362259	−0.0143420
$639$	0	0
$640$	−38.8273	−1.53478
$641$	−4.68648	−0.185105	−0.0925523	−	0.995708i	$-0.529503\pi$
$641$	−4.68648	−0.185105	−0.0925523	+	0.995708i	$0.529503\pi$
$642$	0	0
$643$	−0.751182	−0.0296237	−0.0148119	−	0.999890i	$-0.504715\pi$
$643$	−0.751182	−0.0296237	−0.0148119	+	0.999890i	$0.504715\pi$
$644$	0	0
$645$	0	0
$646$	17.2215	0.677570
$647$	−40.8476	−1.60589	−0.802943	−	0.596056i	$-0.796733\pi$
$647$	−40.8476	−1.60589	−0.802943	+	0.596056i	$0.796733\pi$
$648$	0	0
$649$	5.41363	0.212504
$650$	−22.2055	−0.870971
$651$	0	0
$652$	16.2055	0.634656
$653$	46.4783	1.81884	0.909419	−	0.415881i	$-0.136527\pi$
$653$	46.4783	1.81884	0.909419	+	0.415881i	$0.136527\pi$
$654$	0	0
$655$	35.9327	1.40400
$656$	116.482	4.54785
$657$	0	0
$658$	0	0
$659$	−30.3596	−1.18264	−0.591321	−	0.806436i	$-0.701394\pi$
$659$	−30.3596	−1.18264	−0.591321	+	0.806436i	$0.701394\pi$
$660$	0	0
$661$	−0.107118	−0.00416640	−0.00208320	−	0.999998i	$-0.500663\pi$
$661$	−0.107118	−0.00416640	−0.00208320	+	0.999998i	$0.500663\pi$
$662$	−64.0975	−2.49122
$663$	0	0
$664$	−127.685	−4.95513
$665$	0	0
$666$	0	0
$667$	−1.53235	−0.0593330
$668$	−41.0194	−1.58709
$669$	0	0
$670$	125.166	4.83557
$671$	1.24354	0.0480063
$672$	0	0
$673$	38.5385	1.48555	0.742774	−	0.669542i	$-0.233510\pi$
$673$	38.5385	1.48555	0.742774	+	0.669542i	$0.233510\pi$
$674$	−81.0699	−3.12270
$675$	0	0
$676$	5.05137	0.194284
$677$	20.7803	0.798650	0.399325	−	0.916809i	$-0.369244\pi$
$677$	20.7803	0.798650	0.399325	+	0.916809i	$0.369244\pi$
$678$	0	0
$679$	0	0
$680$	70.9654	2.72140
$681$	0	0
$682$	1.97793	0.0757388
$683$	−27.5837	−1.05546	−0.527731	−	0.849412i	$-0.676957\pi$
$683$	−27.5837	−1.05546	−0.527731	+	0.849412i	$0.676957\pi$
$684$	0	0
$685$	64.1532	2.45117
$686$	0	0
$687$	0	0
$688$	−35.4136	−1.35013
$689$	5.25951	0.200371
$690$	0	0
$691$	43.6775	1.66157	0.830785	−	0.556593i	$-0.187892\pi$
$691$	43.6775	1.66157	0.830785	+	0.556593i	$0.187892\pi$
$692$	52.1736	1.98334
$693$	0	0
$694$	66.3791	2.51971
$695$	17.9663	0.681502
$696$	0	0
$697$	−24.4517	−0.926173
$698$	−4.88301	−0.184825
$699$	0	0
$700$	0	0
$701$	20.8973	0.789278	0.394639	−	0.918836i	$-0.370870\pi$
$701$	20.8973	0.789278	0.394639	+	0.918836i	$0.370870\pi$
$702$	0	0
$703$	20.1585	0.760292
$704$	−9.58373	−0.361200
$705$	0	0
$706$	61.7573	2.32427
$707$	0	0
$708$	0	0
$709$	9.93966	0.373292	0.186646	−	0.982427i	$-0.440238\pi$
$709$	9.93966	0.373292	0.186646	+	0.982427i	$0.440238\pi$
$710$	−65.6005	−2.46194
$711$	0	0
$712$	119.998	4.49712
$713$	8.36663	0.313333
$714$	0	0
$715$	−2.39593	−0.0896028
$716$	12.0133	0.448959
$717$	0	0
$718$	56.9521	2.12543
$719$	11.9797	0.446766	0.223383	−	0.974731i	$-0.428290\pi$
$719$	11.9797	0.446766	0.223383	+	0.974731i	$0.428290\pi$
$720$	0	0
$721$	0	0
$722$	−30.9974	−1.15360
$723$	0	0
$724$	110.168	4.09437
$725$	1.74049	0.0646402
$726$	0	0
$727$	24.1736	0.896547	0.448274	−	0.893896i	$-0.352039\pi$
$727$	24.1736	0.896547	0.448274	+	0.893896i	$0.352039\pi$
$728$	0	0
$729$	0	0
$730$	−121.692	−4.50401
$731$	7.43397	0.274955
$732$	0	0
$733$	−36.4473	−1.34621	−0.673106	−	0.739546i	$-0.735040\pi$
$733$	−36.4473	−1.34621	−0.673106	+	0.739546i	$0.735040\pi$
$734$	−2.97529	−0.109820
$735$	0	0
$736$	−103.828	−3.82715
$737$	8.45168	0.311321
$738$	0	0
$739$	43.2772	1.59198	0.795989	−	0.605311i	$-0.206951\pi$
$739$	43.2772	1.59198	0.795989	+	0.605311i	$0.206951\pi$
$740$	137.515	5.05514
$741$	0	0
$742$	0	0
$743$	−22.6572	−0.831211	−0.415606	−	0.909545i	$-0.636430\pi$
$743$	−22.6572	−0.831211	−0.415606	+	0.909545i	$0.636430\pi$
$744$	0	0
$745$	−37.8043	−1.38504
$746$	41.4403	1.51724
$747$	0	0
$748$	7.93265	0.290047
$749$	0	0
$750$	0	0
$751$	29.8679	1.08990	0.544948	−	0.838470i	$-0.316549\pi$
$751$	29.8679	1.08990	0.544948	+	0.838470i	$0.316549\pi$
$752$	−52.5491	−1.91627
$753$	0	0
$754$	−0.552694	−0.0201279
$755$	−18.5394	−0.674716
$756$	0	0
$757$	2.55706	0.0929380	0.0464690	−	0.998920i	$-0.485203\pi$
$757$	2.55706	0.0929380	0.0464690	+	0.998920i	$0.485203\pi$
$758$	33.9494	1.23310
$759$	0	0
$760$	80.1736	2.90820
$761$	−14.7289	−0.533922	−0.266961	−	0.963707i	$-0.586019\pi$
$761$	−14.7289	−0.533922	−0.266961	+	0.963707i	$0.586019\pi$
$762$	0	0
$763$	0	0
$764$	126.723	4.58467
$765$	0	0
$766$	−90.3791	−3.26553
$767$	8.25951	0.298234
$768$	0	0
$769$	−36.1692	−1.30429	−0.652147	−	0.758092i	$-0.726132\pi$
$769$	−36.1692	−1.30429	−0.652147	+	0.758092i	$0.726132\pi$
$770$	0	0
$771$	0	0
$772$	57.1355	2.05635
$773$	−38.9567	−1.40117	−0.700587	−	0.713567i	$-0.747079\pi$
$773$	−38.9567	−1.40117	−0.700587	+	0.713567i	$0.747079\pi$
$774$	0	0
$775$	−9.50305	−0.341360
$776$	−81.1709	−2.91387
$777$	0	0
$778$	65.5111	2.34869
$779$	−27.6244	−0.989747
$780$	0	0
$781$	−4.42960	−0.158504
$782$	46.8406	1.67502
$783$	0	0
$784$	0	0
$785$	46.0638	1.64409
$786$	0	0
$787$	29.1045	1.03746	0.518731	−	0.854937i	$-0.326405\pi$
$787$	29.1045	1.03746	0.518731	+	0.854937i	$0.326405\pi$
$788$	84.8220	3.02166
$789$	0	0
$790$	14.7449	0.524599
$791$	0	0
$792$	0	0
$793$	1.89725	0.0673734
$794$	−13.2232	−0.469274
$795$	0	0
$796$	103.725	3.67645
$797$	17.8920	0.633766	0.316883	−	0.948465i	$-0.397364\pi$
$797$	17.8920	0.633766	0.316883	+	0.948465i	$0.397364\pi$
$798$	0	0
$799$	11.0310	0.390250
$800$	117.931	4.16948
$801$	0	0
$802$	−1.82991	−0.0646162
$803$	−8.21710	−0.289975
$804$	0	0
$805$	0	0
$806$	3.01770	0.106294
$807$	0	0
$808$	24.4517	0.860207
$809$	−20.4543	−0.719135	−0.359568	−	0.933119i	$-0.617076\pi$
$809$	−20.4543	−0.719135	−0.359568	+	0.933119i	$0.617076\pi$
$810$	0	0
$811$	−31.6458	−1.11123	−0.555617	−	0.831438i	$-0.687518\pi$
$811$	−31.6458	−1.11123	−0.555617	+	0.831438i	$0.687518\pi$
$812$	0	0
$813$	0	0
$814$	12.9620	0.454316
$815$	−11.7272	−0.410784
$816$	0	0
$817$	8.39857	0.293829
$818$	53.0478	1.85477
$819$	0	0
$820$	−188.445	−6.58077
$821$	−18.0761	−0.630860	−0.315430	−	0.948949i	$-0.602149\pi$
$821$	−18.0761	−0.630860	−0.315430	+	0.948949i	$0.602149\pi$
$822$	0	0
$823$	−23.0514	−0.803520	−0.401760	−	0.915745i	$-0.631601\pi$
$823$	−23.0514	−0.803520	−0.401760	+	0.915745i	$0.631601\pi$
$824$	−40.8220	−1.42210
$825$	0	0
$826$	0	0
$827$	26.3756	0.917169	0.458585	−	0.888651i	$-0.348357\pi$
$827$	26.3756	0.917169	0.458585	+	0.888651i	$0.348357\pi$
$828$	0	0
$829$	45.1152	1.56691	0.783457	−	0.621446i	$-0.213454\pi$
$829$	45.1152	1.56691	0.783457	+	0.621446i	$0.213454\pi$
$830$	152.962	5.30938
$831$	0	0
$832$	−14.6218	−0.506919
$833$	0	0
$834$	0	0
$835$	29.6838	1.02725
$836$	8.96196	0.309956
$837$	0	0
$838$	−52.2223	−1.80399
$839$	30.4871	1.05253	0.526265	−	0.850320i	$-0.323592\pi$
$839$	30.4871	1.05253	0.526265	+	0.850320i	$0.323592\pi$
$840$	0	0
$841$	−28.9567	−0.998506
$842$	39.6412	1.36613
$843$	0	0
$844$	−79.7033	−2.74350
$845$	−3.65544	−0.125751
$846$	0	0
$847$	0	0
$848$	−60.0301	−2.06144
$849$	0	0
$850$	−53.2029	−1.82484
$851$	54.8290	1.87951
$852$	0	0
$853$	−33.2746	−1.13930	−0.569650	−	0.821888i	$-0.692921\pi$
$853$	−33.2746	−1.13930	−0.569650	+	0.821888i	$0.692921\pi$
$854$	0	0
$855$	0	0
$856$	−95.9628	−3.27994
$857$	−45.6139	−1.55814	−0.779070	−	0.626937i	$-0.784308\pi$
$857$	−45.6139	−1.55814	−0.779070	+	0.626937i	$0.784308\pi$
$858$	0	0
$859$	20.9353	0.714303	0.357151	−	0.934046i	$-0.383748\pi$
$859$	20.9353	0.714303	0.357151	+	0.934046i	$0.383748\pi$
$860$	57.2923	1.95365
$861$	0	0
$862$	86.7900	2.95608
$863$	−2.96196	−0.100826	−0.0504131	−	0.998728i	$-0.516054\pi$
$863$	−2.96196	−0.100826	−0.0504131	+	0.998728i	$0.516054\pi$
$864$	0	0
$865$	−37.7556	−1.28373
$866$	−23.7980	−0.808688
$867$	0	0
$868$	0	0
$869$	0.995631	0.0337745
$870$	0	0
$871$	12.8946	0.436917
$872$	28.7652	0.974113
$873$	0	0
$874$	52.9184	1.78999
$875$	0	0
$876$	0	0
$877$	−36.9370	−1.24727	−0.623637	−	0.781714i	$-0.714346\pi$
$877$	−36.9370	−1.24727	−0.623637	+	0.781714i	$0.714346\pi$
$878$	−21.0647	−0.710899
$879$	0	0
$880$	27.3463	0.921843
$881$	−30.8946	−1.04087	−0.520433	−	0.853903i	$-0.674229\pi$
$881$	−30.8946	−1.04087	−0.520433	+	0.853903i	$0.674229\pi$
$882$	0	0
$883$	−9.64648	−0.324630	−0.162315	−	0.986739i	$-0.551896\pi$
$883$	−9.64648	−0.324630	−0.162315	+	0.986739i	$0.551896\pi$
$884$	12.1027	0.407059
$885$	0	0
$886$	23.6615	0.794925
$887$	51.3056	1.72267	0.861337	−	0.508034i	$-0.169628\pi$
$887$	51.3056	1.72267	0.861337	+	0.508034i	$0.169628\pi$
$888$	0	0
$889$	0	0
$890$	−143.754	−4.81864
$891$	0	0
$892$	−42.6705	−1.42871
$893$	12.4624	0.417037
$894$	0	0
$895$	−8.69348	−0.290591
$896$	0	0
$897$	0	0
$898$	22.4429	0.748931
$899$	−0.236531	−0.00788873
$900$	0	0
$901$	12.6014	0.419814
$902$	−17.7626	−0.591429
$903$	0	0
$904$	76.6926	2.55076
$905$	−79.7236	−2.65010
$906$	0	0
$907$	−18.5385	−0.615559	−0.307780	−	0.951458i	$-0.599586\pi$
$907$	−18.5385	−0.615559	−0.307780	+	0.951458i	$0.599586\pi$
$908$	−33.7892	−1.12133
$909$	0	0
$910$	0	0
$911$	−20.7272	−0.686721	−0.343361	−	0.939204i	$-0.611565\pi$
$911$	−20.7272	−0.686721	−0.343361	+	0.939204i	$0.611565\pi$
$912$	0	0
$913$	10.3286	0.341826
$914$	61.5244	2.03505
$915$	0	0
$916$	43.6191	1.44122
$917$	0	0
$918$	0	0
$919$	−5.13205	−0.169291	−0.0846454	−	0.996411i	$-0.526976\pi$
$919$	−5.13205	−0.169291	−0.0846454	+	0.996411i	$0.526976\pi$
$920$	218.064	7.18935
$921$	0	0
$922$	−6.03540	−0.198765
$923$	−6.75819	−0.222449
$924$	0	0
$925$	−62.2763	−2.04763
$926$	−10.9132	−0.358631
$927$	0	0
$928$	2.93529	0.0963557
$929$	−19.9283	−0.653826	−0.326913	−	0.945054i	$-0.606008\pi$
$929$	−19.9283	−0.653826	−0.326913	+	0.945054i	$0.606008\pi$
$930$	0	0
$931$	0	0
$932$	21.0514	0.689561
$933$	0	0
$934$	−87.4038	−2.85994
$935$	−5.74049	−0.187734
$936$	0	0
$937$	−1.64475	−0.0537316	−0.0268658	−	0.999639i	$-0.508553\pi$
$937$	−1.64475	−0.0537316	−0.0268658	+	0.999639i	$0.508553\pi$
$938$	0	0
$939$	0	0
$940$	85.0142	2.77286
$941$	17.7849	0.579770	0.289885	−	0.957062i	$-0.406383\pi$
$941$	17.7849	0.579770	0.289885	+	0.957062i	$0.406383\pi$
$942$	0	0
$943$	−75.1355	−2.44675
$944$	−94.2710	−3.06826
$945$	0	0
$946$	5.40030	0.175579
$947$	−10.6484	−0.346028	−0.173014	−	0.984919i	$-0.555351\pi$
$947$	−10.6484	−0.346028	−0.173014	+	0.984919i	$0.555351\pi$
$948$	0	0
$949$	−12.5367	−0.406959
$950$	−60.1062	−1.95010
$951$	0	0
$952$	0	0
$953$	41.5544	1.34608	0.673040	−	0.739606i	$-0.264988\pi$
$953$	41.5544	1.34608	0.673040	+	0.739606i	$0.264988\pi$
$954$	0	0
$955$	−91.7033	−2.96745
$956$	9.06471	0.293174
$957$	0	0
$958$	24.7361	0.799188
$959$	0	0
$960$	0	0
$961$	−29.7085	−0.958340
$962$	19.7759	0.637600
$963$	0	0
$964$	70.0168	2.25509
$965$	−41.3463	−1.33098
$966$	0	0
$967$	−5.51465	−0.177339	−0.0886696	−	0.996061i	$-0.528262\pi$
$967$	−5.51465	−0.177339	−0.0886696	+	0.996061i	$0.528262\pi$
$968$	−85.6493	−2.75287
$969$	0	0
$970$	97.2400	3.12219
$971$	−39.8246	−1.27803	−0.639017	−	0.769193i	$-0.720658\pi$
$971$	−39.8246	−1.27803	−0.639017	+	0.769193i	$0.720658\pi$
$972$	0	0
$973$	0	0
$974$	53.7485	1.72221
$975$	0	0
$976$	−21.6545	−0.693145
$977$	−1.93092	−0.0617757	−0.0308879	−	0.999523i	$-0.509833\pi$
$977$	−1.93092	−0.0617757	−0.0308879	+	0.999523i	$0.509833\pi$
$978$	0	0
$979$	−9.70682	−0.310231
$980$	0	0
$981$	0	0
$982$	11.5837	0.369652
$983$	43.0238	1.37225	0.686123	−	0.727485i	$-0.259311\pi$
$983$	43.0238	1.37225	0.686123	+	0.727485i	$0.259311\pi$
$984$	0	0
$985$	−61.3817	−1.95578
$986$	−1.32422	−0.0421717
$987$	0	0
$988$	13.6731	0.435001
$989$	22.8432	0.726373
$990$	0	0
$991$	−17.6058	−0.559267	−0.279633	−	0.960107i	$-0.590213\pi$
$991$	−17.6058	−0.559267	−0.279633	+	0.960107i	$0.590213\pi$
$992$	−16.0267	−0.508847
$993$	0	0
$994$	0	0
$995$	−75.0612	−2.37960
$996$	0	0
$997$	−12.9707	−0.410786	−0.205393	−	0.978680i	$-0.565847\pi$
$997$	−12.9707	−0.410786	−0.205393	+	0.978680i	$0.565847\pi$
$998$	25.7405	0.814801
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5733.2.a.bd.1.3		3
3.2	odd	2		637.2.a.i.1.1	yes	3
7.6	odd	2		5733.2.a.be.1.3		3
21.2	odd	6		637.2.e.k.508.3		6
21.5	even	6		637.2.e.l.508.3		6
21.11	odd	6		637.2.e.k.79.3		6
21.17	even	6		637.2.e.l.79.3		6
21.20	even	2		637.2.a.h.1.1	✓	3
39.38	odd	2		8281.2.a.bk.1.3		3
273.272	even	2		8281.2.a.bh.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.a.h.1.1	✓	3	21.20	even	2
637.2.a.i.1.1	yes	3	3.2	odd	2
637.2.e.k.79.3		6	21.11	odd	6
637.2.e.k.508.3		6	21.2	odd	6
637.2.e.l.79.3		6	21.17	even	6
637.2.e.l.508.3		6	21.5	even	6
5733.2.a.bd.1.3		3	1.1	even	1	trivial
5733.2.a.be.1.3		3	7.6	odd	2
8281.2.a.bh.1.3		3	273.272	even	2
8281.2.a.bk.1.3		3	39.38	odd	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)

\(f(q)\)	\(=\)	\(q+2.65544 q^{2} +5.05137 q^{4} -3.65544 q^{5} +8.10275 q^{8} +O(q^{10})\)	\(q+2.65544 q^{2} +5.05137 q^{4} -3.65544 q^{5} +8.10275 q^{8} -9.70682 q^{10} -0.655442 q^{11} -1.00000 q^{13} +11.4136 q^{16} -2.39593 q^{17} -2.70682 q^{19} -18.4650 q^{20} -1.74049 q^{22} -7.36226 q^{23} +8.36226 q^{25} -2.65544 q^{26} +0.208136 q^{29} -1.13642 q^{31} +14.1027 q^{32} -6.36226 q^{34} -7.44731 q^{37} -7.18780 q^{38} -29.6191 q^{40} +10.2055 q^{41} -3.10275 q^{43} -3.31088 q^{44} -19.5501 q^{46} -4.60407 q^{47} +22.2055 q^{50} -5.05137 q^{52} -5.25951 q^{53} +2.39593 q^{55} +0.552694 q^{58} -8.25951 q^{59} -1.89725 q^{61} -3.01770 q^{62} +14.6218 q^{64} +3.65544 q^{65} -12.8946 q^{67} -12.1027 q^{68} +6.75819 q^{71} +12.5367 q^{73} -19.7759 q^{74} -13.6731 q^{76} -1.51902 q^{79} -41.7219 q^{80} +27.1001 q^{82} -15.7582 q^{83} +8.75819 q^{85} -8.23917 q^{86} -5.31088 q^{88} +14.8096 q^{89} -37.1895 q^{92} -12.2258 q^{94} +9.89461 q^{95} -10.0177 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 2 q^{2} + 6 q^{4} - 5 q^{5} + 6 q^{8}+O(q^{10}) \) 3 * q + 2 * q^2 + 6 * q^4 - 5 * q^5 + 6 * q^8	\( 3 q + 2 q^{2} + 6 q^{4} - 5 q^{5} + 6 q^{8} - 14 q^{10} + 4 q^{11} - 3 q^{13} + 4 q^{16} - 4 q^{17} + 7 q^{19} - 16 q^{20} - 8 q^{22} - q^{23} + 4 q^{25} - 2 q^{26} + 7 q^{29} - 3 q^{31} + 24 q^{32} + 2 q^{34} - 10 q^{37} - 12 q^{38} - 22 q^{40} - 6 q^{41} + 9 q^{43} + 2 q^{44} - 28 q^{46} - 17 q^{47} + 30 q^{50} - 6 q^{52} - 13 q^{53} + 4 q^{55} + 14 q^{58} - 22 q^{59} - 24 q^{61} + 18 q^{62} + 20 q^{64} + 5 q^{65} - 14 q^{67} - 18 q^{68} - 4 q^{71} + 5 q^{73} - 8 q^{74} - 8 q^{76} + q^{79} - 40 q^{80} + 20 q^{82} - 23 q^{83} + 2 q^{85} - 6 q^{86} - 4 q^{88} + 11 q^{89} - 30 q^{92} - 16 q^{94} + 5 q^{95} - 3 q^{97}+O(q^{100}) \) 3 * q + 2 * q^2 + 6 * q^4 - 5 * q^5 + 6 * q^8 - 14 * q^10 + 4 * q^11 - 3 * q^13 + 4 * q^16 - 4 * q^17 + 7 * q^19 - 16 * q^20 - 8 * q^22 - q^23 + 4 * q^25 - 2 * q^26 + 7 * q^29 - 3 * q^31 + 24 * q^32 + 2 * q^34 - 10 * q^37 - 12 * q^38 - 22 * q^40 - 6 * q^41 + 9 * q^43 + 2 * q^44 - 28 * q^46 - 17 * q^47 + 30 * q^50 - 6 * q^52 - 13 * q^53 + 4 * q^55 + 14 * q^58 - 22 * q^59 - 24 * q^61 + 18 * q^62 + 20 * q^64 + 5 * q^65 - 14 * q^67 - 18 * q^68 - 4 * q^71 + 5 * q^73 - 8 * q^74 - 8 * q^76 + q^79 - 40 * q^80 + 20 * q^82 - 23 * q^83 + 2 * q^85 - 6 * q^86 - 4 * q^88 + 11 * q^89 - 30 * q^92 - 16 * q^94 + 5 * q^95 - 3 * q^97

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