LMFDB - Embedded newform 5733.2.a.bx.1.4

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:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} - 10x^{8} + 52x^{7} + 16x^{6} - 212x^{5} + 64x^{4} + 300x^{3} - 159x^{2} - 80x + 46 $ x^10 - 4x^9 - 10x^8 + 52x^7 + 16x^6 - 212x^5 + 64x^4 + 300x^3 - 159x^2 - 80*x + 46
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1911)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.67947$ 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)

$f(q)$	$=$	$q-1.67947 q^{2} +0.820610 q^{4} -1.01562 q^{5} +1.98075 q^{8} +O(q^{10})$	$q-1.67947 q^{2} +0.820610 q^{4} -1.01562 q^{5} +1.98075 q^{8} +1.70571 q^{10} -4.05316 q^{11} -1.00000 q^{13} -4.96782 q^{16} -7.26007 q^{17} -2.90686 q^{19} -0.833432 q^{20} +6.80714 q^{22} -9.53118 q^{23} -3.96851 q^{25} +1.67947 q^{26} -6.53200 q^{29} -9.86851 q^{31} +4.38180 q^{32} +12.1930 q^{34} +4.24217 q^{37} +4.88198 q^{38} -2.01169 q^{40} -8.83058 q^{41} +0.566950 q^{43} -3.32606 q^{44} +16.0073 q^{46} +12.1032 q^{47} +6.66498 q^{50} -0.820610 q^{52} -8.89147 q^{53} +4.11648 q^{55} +10.9703 q^{58} +5.44378 q^{59} +5.51703 q^{61} +16.5738 q^{62} +2.57655 q^{64} +1.01562 q^{65} -3.03034 q^{67} -5.95769 q^{68} +6.18315 q^{71} -3.99200 q^{73} -7.12458 q^{74} -2.38540 q^{76} +1.06343 q^{79} +5.04544 q^{80} +14.8307 q^{82} -8.02803 q^{83} +7.37350 q^{85} -0.952174 q^{86} -8.02827 q^{88} +6.60402 q^{89} -7.82138 q^{92} -20.3269 q^{94} +2.95228 q^{95} -1.63178 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{2} + 16 q^{4} + 6 q^{5} - 12 q^{8}+O(q^{10}) $ 10 * q - 4 * q^2 + 16 * q^4 + 6 * q^5 - 12 * q^8	$ 10 q - 4 q^{2} + 16 q^{4} + 6 q^{5} - 12 q^{8} + 8 q^{10} - 12 q^{11} - 10 q^{13} + 24 q^{16} + 10 q^{19} + 16 q^{20} + 8 q^{22} - 14 q^{23} + 32 q^{25} + 4 q^{26} - 18 q^{29} + 14 q^{31} - 28 q^{32} + 4 q^{34} + 24 q^{37} + 4 q^{38} + 16 q^{40} + 24 q^{41} + 2 q^{43} - 48 q^{44} + 20 q^{46} + 18 q^{47} + 28 q^{50} - 16 q^{52} - 10 q^{53} + 12 q^{55} + 12 q^{58} + 12 q^{59} - 4 q^{61} - 4 q^{62} + 32 q^{64} - 6 q^{65} - 12 q^{67} + 40 q^{68} - 32 q^{71} - 18 q^{73} - 24 q^{74} + 32 q^{76} + 34 q^{79} + 32 q^{80} + 48 q^{82} + 30 q^{83} - 40 q^{86} + 32 q^{88} + 10 q^{89} + 40 q^{92} - 24 q^{94} + 30 q^{95} - 2 q^{97}+O(q^{100}) $ 10 * q - 4 * q^2 + 16 * q^4 + 6 * q^5 - 12 * q^8 + 8 * q^10 - 12 * q^11 - 10 * q^13 + 24 * q^16 + 10 * q^19 + 16 * q^20 + 8 * q^22 - 14 * q^23 + 32 * q^25 + 4 * q^26 - 18 * q^29 + 14 * q^31 - 28 * q^32 + 4 * q^34 + 24 * q^37 + 4 * q^38 + 16 * q^40 + 24 * q^41 + 2 * q^43 - 48 * q^44 + 20 * q^46 + 18 * q^47 + 28 * q^50 - 16 * q^52 - 10 * q^53 + 12 * q^55 + 12 * q^58 + 12 * q^59 - 4 * q^61 - 4 * q^62 + 32 * q^64 - 6 * q^65 - 12 * q^67 + 40 * q^68 - 32 * q^71 - 18 * q^73 - 24 * q^74 + 32 * q^76 + 34 * q^79 + 32 * q^80 + 48 * q^82 + 30 * q^83 - 40 * q^86 + 32 * q^88 + 10 * q^89 + 40 * q^92 - 24 * q^94 + 30 * q^95 - 2 * 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 $

$2$	−1.67947	−1.18756	−0.593781	−	0.804626i	$-0.702366\pi$
$2$	−1.67947	−1.18756	−0.593781	+	0.804626i	$0.702366\pi$
$3$	0	0
$3$	0	0
$4$	0.820610	0.410305
$5$	−1.01562	−0.454201	−0.227100	−	0.973871i	$-0.572925\pi$
$5$	−1.01562	−0.454201	−0.227100	+	0.973871i	$0.572925\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	1.98075	0.700300
$9$	0	0
$10$	1.70571	0.539392
$11$	−4.05316	−1.22207	−0.611036	−	0.791603i	$-0.709247\pi$
$11$	−4.05316	−1.22207	−0.611036	+	0.791603i	$0.709247\pi$
$12$	0	0
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	0	0
$16$	−4.96782	−1.24195
$17$	−7.26007	−1.76082	−0.880412	−	0.474209i	$-0.842734\pi$
$17$	−7.26007	−1.76082	−0.880412	+	0.474209i	$0.842734\pi$
$18$	0	0
$19$	−2.90686	−0.666879	−0.333440	−	0.942771i	$-0.608209\pi$
$19$	−2.90686	−0.666879	−0.333440	+	0.942771i	$0.608209\pi$
$20$	−0.833432	−0.186361
$21$	0	0
$22$	6.80714	1.45129
$23$	−9.53118	−1.98739	−0.993694	−	0.112127i	$-0.964234\pi$
$23$	−9.53118	−1.98739	−0.993694	+	0.112127i	$0.964234\pi$
$24$	0	0
$25$	−3.96851	−0.793702
$26$	1.67947	0.329371
$27$	0	0
$28$	0	0
$29$	−6.53200	−1.21296	−0.606481	−	0.795098i	$-0.707419\pi$
$29$	−6.53200	−1.21296	−0.606481	+	0.795098i	$0.707419\pi$
$30$	0	0
$31$	−9.86851	−1.77244	−0.886218	−	0.463268i	$-0.846677\pi$
$31$	−9.86851	−1.77244	−0.886218	+	0.463268i	$0.846677\pi$
$32$	4.38180	0.774600
$33$	0	0
$34$	12.1930	2.09109
$35$	0	0
$36$	0	0
$37$	4.24217	0.697408	0.348704	−	0.937233i	$-0.386622\pi$
$37$	4.24217	0.697408	0.348704	+	0.937233i	$0.386622\pi$
$38$	4.88198	0.791961
$39$	0	0
$40$	−2.01169	−0.318077
$41$	−8.83058	−1.37911	−0.689553	−	0.724236i	$-0.742193\pi$
$41$	−8.83058	−1.37911	−0.689553	+	0.724236i	$0.742193\pi$
$42$	0	0
$43$	0.566950	0.0864590	0.0432295	−	0.999065i	$-0.486235\pi$
$43$	0.566950	0.0864590	0.0432295	+	0.999065i	$0.486235\pi$
$44$	−3.32606	−0.501423
$45$	0	0
$46$	16.0073	2.36015
$47$	12.1032	1.76543	0.882717	−	0.469905i	$-0.155712\pi$
$47$	12.1032	1.76543	0.882717	+	0.469905i	$0.155712\pi$
$48$	0	0
$49$	0	0
$50$	6.66498	0.942570
$51$	0	0
$52$	−0.820610	−0.113798
$53$	−8.89147	−1.22134	−0.610669	−	0.791886i	$-0.709099\pi$
$53$	−8.89147	−1.22134	−0.610669	+	0.791886i	$0.709099\pi$
$54$	0	0
$55$	4.11648	0.555066
$56$	0	0
$57$	0	0
$58$	10.9703	1.44047
$59$	5.44378	0.708720	0.354360	−	0.935109i	$-0.384699\pi$
$59$	5.44378	0.708720	0.354360	+	0.935109i	$0.384699\pi$
$60$	0	0
$61$	5.51703	0.706384	0.353192	−	0.935551i	$-0.385096\pi$
$61$	5.51703	0.706384	0.353192	+	0.935551i	$0.385096\pi$
$62$	16.5738	2.10488
$63$	0	0
$64$	2.57655	0.322069
$65$	1.01562	0.125973
$66$	0	0
$67$	−3.03034	−0.370214	−0.185107	−	0.982718i	$-0.559263\pi$
$67$	−3.03034	−0.370214	−0.185107	+	0.982718i	$0.559263\pi$
$68$	−5.95769	−0.722476
$69$	0	0
$70$	0	0
$71$	6.18315	0.733805	0.366902	−	0.930259i	$-0.380418\pi$
$71$	6.18315	0.733805	0.366902	+	0.930259i	$0.380418\pi$
$72$	0	0
$73$	−3.99200	−0.467229	−0.233614	−	0.972329i	$-0.575055\pi$
$73$	−3.99200	−0.467229	−0.233614	+	0.972329i	$0.575055\pi$
$74$	−7.12458	−0.828216
$75$	0	0
$76$	−2.38540	−0.273624
$77$	0	0
$78$	0	0
$79$	1.06343	0.119645	0.0598227	−	0.998209i	$-0.480946\pi$
$79$	1.06343	0.119645	0.0598227	+	0.998209i	$0.480946\pi$
$80$	5.04544	0.564097
$81$	0	0
$82$	14.8307	1.63777
$83$	−8.02803	−0.881191	−0.440596	−	0.897706i	$-0.645233\pi$
$83$	−8.02803	−0.881191	−0.440596	+	0.897706i	$0.645233\pi$
$84$	0	0
$85$	7.37350	0.799768
$86$	−0.952174	−0.102676
$87$	0	0
$88$	−8.02827	−0.855817
$89$	6.60402	0.700025	0.350013	−	0.936745i	$-0.386177\pi$
$89$	6.60402	0.700025	0.350013	+	0.936745i	$0.386177\pi$
$90$	0	0
$91$	0	0
$92$	−7.82138	−0.815436
$93$	0	0
$94$	−20.3269	−2.09656
$95$	2.95228	0.302897
$96$	0	0
$97$	−1.63178	−0.165682	−0.0828410	−	0.996563i	$-0.526399\pi$
$97$	−1.63178	−0.165682	−0.0828410	+	0.996563i	$0.526399\pi$
$98$	0	0
$99$	0	0
$100$	−3.25660	−0.325660
$101$	15.5527	1.54755	0.773774	−	0.633461i	$-0.218366\pi$
$101$	15.5527	1.54755	0.773774	+	0.633461i	$0.218366\pi$
$102$	0	0
$103$	−14.5504	−1.43369	−0.716847	−	0.697230i	$-0.754416\pi$
$103$	−14.5504	−1.43369	−0.716847	+	0.697230i	$0.754416\pi$
$104$	−1.98075	−0.194228
$105$	0	0
$106$	14.9329	1.45041
$107$	−18.7040	−1.80818	−0.904092	−	0.427338i	$-0.859452\pi$
$107$	−18.7040	−1.80818	−0.904092	+	0.427338i	$0.859452\pi$
$108$	0	0
$109$	−10.8252	−1.03687	−0.518433	−	0.855118i	$-0.673484\pi$
$109$	−10.8252	−1.03687	−0.518433	+	0.855118i	$0.673484\pi$
$110$	−6.91350	−0.659176
$111$	0	0
$112$	0	0
$113$	9.52791	0.896311	0.448155	−	0.893956i	$-0.352081\pi$
$113$	9.52791	0.896311	0.448155	+	0.893956i	$0.352081\pi$
$114$	0	0
$115$	9.68009	0.902673
$116$	−5.36023	−0.497685
$117$	0	0
$118$	−9.14265	−0.841649
$119$	0	0
$120$	0	0
$121$	5.42807	0.493461
$122$	−9.26568	−0.838875
$123$	0	0
$124$	−8.09820	−0.727240
$125$	9.10863	0.814701
$126$	0	0
$127$	10.8621	0.963854	0.481927	−	0.876211i	$-0.339937\pi$
$127$	10.8621	0.963854	0.481927	+	0.876211i	$0.339937\pi$
$128$	−13.0908	−1.15708
$129$	0	0
$130$	−1.70571	−0.149600
$131$	3.62137	0.316401	0.158200	−	0.987407i	$-0.449431\pi$
$131$	3.62137	0.316401	0.158200	+	0.987407i	$0.449431\pi$
$132$	0	0
$133$	0	0
$134$	5.08935	0.439653
$135$	0	0
$136$	−14.3804	−1.23310
$137$	14.6162	1.24874	0.624372	−	0.781127i	$-0.285355\pi$
$137$	14.6162	1.24874	0.624372	+	0.781127i	$0.285355\pi$
$138$	0	0
$139$	11.1222	0.943370	0.471685	−	0.881767i	$-0.343646\pi$
$139$	11.1222	0.943370	0.471685	+	0.881767i	$0.343646\pi$
$140$	0	0
$141$	0	0
$142$	−10.3844	−0.871439
$143$	4.05316	0.338942
$144$	0	0
$145$	6.63406	0.550928
$146$	6.70444	0.554863
$147$	0	0
$148$	3.48117	0.286150
$149$	−5.23259	−0.428671	−0.214335	−	0.976760i	$-0.568759\pi$
$149$	−5.23259	−0.428671	−0.214335	+	0.976760i	$0.568759\pi$
$150$	0	0
$151$	−15.0293	−1.22307	−0.611535	−	0.791217i	$-0.709448\pi$
$151$	−15.0293	−1.22307	−0.611535	+	0.791217i	$0.709448\pi$
$152$	−5.75775	−0.467015
$153$	0	0
$154$	0	0
$155$	10.0227	0.805042
$156$	0	0
$157$	−1.33422	−0.106482	−0.0532410	−	0.998582i	$-0.516955\pi$
$157$	−1.33422	−0.106482	−0.0532410	+	0.998582i	$0.516955\pi$
$158$	−1.78600	−0.142086
$159$	0	0
$160$	−4.45026	−0.351824
$161$	0	0
$162$	0	0
$163$	−23.6878	−1.85537	−0.927686	−	0.373361i	$-0.878205\pi$
$163$	−23.6878	−1.85537	−0.927686	+	0.373361i	$0.878205\pi$
$164$	−7.24647	−0.565854
$165$	0	0
$166$	13.4828	1.04647
$167$	−9.08825	−0.703270	−0.351635	−	0.936137i	$-0.614374\pi$
$167$	−9.08825	−0.703270	−0.351635	+	0.936137i	$0.614374\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	−12.3836	−0.949775
$171$	0	0
$172$	0.465245	0.0354746
$173$	−6.51688	−0.495469	−0.247735	−	0.968828i	$-0.579686\pi$
$173$	−6.51688	−0.495469	−0.247735	+	0.968828i	$0.579686\pi$
$174$	0	0
$175$	0	0
$176$	20.1353	1.51776
$177$	0	0
$178$	−11.0912	−0.831324
$179$	0.541948	0.0405071	0.0202536	−	0.999795i	$-0.493553\pi$
$179$	0.541948	0.0405071	0.0202536	+	0.999795i	$0.493553\pi$
$180$	0	0
$181$	−17.9887	−1.33709	−0.668543	−	0.743674i	$-0.733082\pi$
$181$	−17.9887	−1.33709	−0.668543	+	0.743674i	$0.733082\pi$
$182$	0	0
$183$	0	0
$184$	−18.8788	−1.39177
$185$	−4.30845	−0.316764
$186$	0	0
$187$	29.4262	2.15186
$188$	9.93202	0.724367
$189$	0	0
$190$	−4.95825	−0.359709
$191$	15.9819	1.15641	0.578204	−	0.815892i	$-0.303754\pi$
$191$	15.9819	1.15641	0.578204	+	0.815892i	$0.303754\pi$
$192$	0	0
$193$	−8.62801	−0.621058	−0.310529	−	0.950564i	$-0.600506\pi$
$193$	−8.62801	−0.621058	−0.310529	+	0.950564i	$0.600506\pi$
$194$	2.74052	0.196758
$195$	0	0
$196$	0	0
$197$	0.179690	0.0128024	0.00640118	−	0.999980i	$-0.497962\pi$
$197$	0.179690	0.0128024	0.00640118	+	0.999980i	$0.497962\pi$
$198$	0	0
$199$	−0.414150	−0.0293583	−0.0146791	−	0.999892i	$-0.504673\pi$
$199$	−0.414150	−0.0293583	−0.0146791	+	0.999892i	$0.504673\pi$
$200$	−7.86061	−0.555829
$201$	0	0
$202$	−26.1202	−1.83781
$203$	0	0
$204$	0	0
$205$	8.96855	0.626391
$206$	24.4369	1.70260
$207$	0	0
$208$	4.96782	0.344456
$209$	11.7820	0.814975
$210$	0	0
$211$	−8.50902	−0.585785	−0.292893	−	0.956145i	$-0.594618\pi$
$211$	−8.50902	−0.585785	−0.292893	+	0.956145i	$0.594618\pi$
$212$	−7.29643	−0.501121
$213$	0	0
$214$	31.4128	2.14733
$215$	−0.575808	−0.0392698
$216$	0	0
$217$	0	0
$218$	18.1806	1.23134
$219$	0	0
$220$	3.37803	0.227747
$221$	7.26007	0.488365
$222$	0	0
$223$	22.6174	1.51457	0.757287	−	0.653083i	$-0.226525\pi$
$223$	22.6174	1.51457	0.757287	+	0.653083i	$0.226525\pi$
$224$	0	0
$225$	0	0
$226$	−16.0018	−1.06443
$227$	−2.15420	−0.142980	−0.0714898	−	0.997441i	$-0.522775\pi$
$227$	−2.15420	−0.142980	−0.0714898	+	0.997441i	$0.522775\pi$
$228$	0	0
$229$	−5.06718	−0.334849	−0.167424	−	0.985885i	$-0.553545\pi$
$229$	−5.06718	−0.334849	−0.167424	+	0.985885i	$0.553545\pi$
$230$	−16.2574	−1.07198
$231$	0	0
$232$	−12.9382	−0.849437
$233$	8.97668	0.588082	0.294041	−	0.955793i	$-0.405000\pi$
$233$	8.97668	0.588082	0.294041	+	0.955793i	$0.405000\pi$
$234$	0	0
$235$	−12.2923	−0.801862
$236$	4.46722	0.290791
$237$	0	0
$238$	0	0
$239$	−27.3970	−1.77216	−0.886081	−	0.463530i	$-0.846583\pi$
$239$	−27.3970	−1.77216	−0.886081	+	0.463530i	$0.846583\pi$
$240$	0	0
$241$	−1.42092	−0.0915295	−0.0457648	−	0.998952i	$-0.514572\pi$
$241$	−1.42092	−0.0915295	−0.0457648	+	0.998952i	$0.514572\pi$
$242$	−9.11627	−0.586016
$243$	0	0
$244$	4.52734	0.289833
$245$	0	0
$246$	0	0
$247$	2.90686	0.184959
$248$	−19.5470	−1.24124
$249$	0	0
$250$	−15.2977	−0.967508
$251$	12.7519	0.804895	0.402447	−	0.915443i	$-0.368160\pi$
$251$	12.7519	0.804895	0.402447	+	0.915443i	$0.368160\pi$
$252$	0	0
$253$	38.6313	2.42873
$254$	−18.2425	−1.14464
$255$	0	0
$256$	16.8325	1.05203
$257$	−12.7298	−0.794064	−0.397032	−	0.917805i	$-0.629960\pi$
$257$	−12.7298	−0.794064	−0.397032	+	0.917805i	$0.629960\pi$
$258$	0	0
$259$	0	0
$260$	0.833432	0.0516872
$261$	0	0
$262$	−6.08198	−0.375746
$263$	28.9952	1.78792	0.893961	−	0.448144i	$-0.147915\pi$
$263$	28.9952	1.78792	0.893961	+	0.448144i	$0.147915\pi$
$264$	0	0
$265$	9.03039	0.554733
$266$	0	0
$267$	0	0
$268$	−2.48673	−0.151901
$269$	−1.34213	−0.0818314	−0.0409157	−	0.999163i	$-0.513028\pi$
$269$	−1.34213	−0.0818314	−0.0409157	+	0.999163i	$0.513028\pi$
$270$	0	0
$271$	−11.3410	−0.688916	−0.344458	−	0.938802i	$-0.611937\pi$
$271$	−11.3410	−0.688916	−0.344458	+	0.938802i	$0.611937\pi$
$272$	36.0667	2.18687
$273$	0	0
$274$	−24.5474	−1.48296
$275$	16.0850	0.969961
$276$	0	0
$277$	13.0962	0.786875	0.393437	−	0.919351i	$-0.371286\pi$
$277$	13.0962	0.786875	0.393437	+	0.919351i	$0.371286\pi$
$278$	−18.6793	−1.12031
$279$	0	0
$280$	0	0
$281$	−2.93491	−0.175082	−0.0875410	−	0.996161i	$-0.527901\pi$
$281$	−2.93491	−0.175082	−0.0875410	+	0.996161i	$0.527901\pi$
$282$	0	0
$283$	21.2779	1.26484	0.632420	−	0.774626i	$-0.282062\pi$
$283$	21.2779	1.26484	0.632420	+	0.774626i	$0.282062\pi$
$284$	5.07396	0.301084
$285$	0	0
$286$	−6.80714	−0.402515
$287$	0	0
$288$	0	0
$289$	35.7086	2.10050
$290$	−11.1417	−0.654262
$291$	0	0
$292$	−3.27588	−0.191706
$293$	−7.81571	−0.456599	−0.228299	−	0.973591i	$-0.573317\pi$
$293$	−7.81571	−0.456599	−0.228299	+	0.973591i	$0.573317\pi$
$294$	0	0
$295$	−5.52883	−0.321901
$296$	8.40266	0.488395
$297$	0	0
$298$	8.78797	0.509073
$299$	9.53118	0.551202
$300$	0	0
$301$	0	0
$302$	25.2413	1.45247
$303$	0	0
$304$	14.4408	0.828234
$305$	−5.60323	−0.320840
$306$	0	0
$307$	−1.63049	−0.0930568	−0.0465284	−	0.998917i	$-0.514816\pi$
$307$	−1.63049	−0.0930568	−0.0465284	+	0.998917i	$0.514816\pi$
$308$	0	0
$309$	0	0
$310$	−16.8328	−0.956038
$311$	11.3479	0.643483	0.321741	−	0.946828i	$-0.395732\pi$
$311$	11.3479	0.643483	0.321741	+	0.946828i	$0.395732\pi$
$312$	0	0
$313$	−5.83580	−0.329859	−0.164930	−	0.986305i	$-0.552740\pi$
$313$	−5.83580	−0.329859	−0.164930	+	0.986305i	$0.552740\pi$
$314$	2.24077	0.126454
$315$	0	0
$316$	0.872664	0.0490912
$317$	−23.6802	−1.33001	−0.665006	−	0.746838i	$-0.731571\pi$
$317$	−23.6802	−1.33001	−0.665006	+	0.746838i	$0.731571\pi$
$318$	0	0
$319$	26.4752	1.48233
$320$	−2.61681	−0.146284
$321$	0	0
$322$	0	0
$323$	21.1040	1.17426
$324$	0	0
$325$	3.96851	0.220133
$326$	39.7829	2.20337
$327$	0	0
$328$	−17.4911	−0.965787
$329$	0	0
$330$	0	0
$331$	−19.2273	−1.05683	−0.528413	−	0.848987i	$-0.677213\pi$
$331$	−19.2273	−1.05683	−0.528413	+	0.848987i	$0.677213\pi$
$332$	−6.58789	−0.361557
$333$	0	0
$334$	15.2634	0.835177
$335$	3.07768	0.168152
$336$	0	0
$337$	−19.8950	−1.08375	−0.541875	−	0.840459i	$-0.682285\pi$
$337$	−19.8950	−1.08375	−0.541875	+	0.840459i	$0.682285\pi$
$338$	−1.67947	−0.0913510
$339$	0	0
$340$	6.05077	0.328149
$341$	39.9986	2.16605
$342$	0	0
$343$	0	0
$344$	1.12298	0.0605472
$345$	0	0
$346$	10.9449	0.588401
$347$	−16.6933	−0.896145	−0.448072	−	0.893997i	$-0.647889\pi$
$347$	−16.6933	−0.896145	−0.448072	+	0.893997i	$0.647889\pi$
$348$	0	0
$349$	−11.9128	−0.637676	−0.318838	−	0.947809i	$-0.603293\pi$
$349$	−11.9128	−0.637676	−0.318838	+	0.947809i	$0.603293\pi$
$350$	0	0
$351$	0	0
$352$	−17.7601	−0.946617
$353$	−11.9997	−0.638681	−0.319340	−	0.947640i	$-0.603461\pi$
$353$	−11.9997	−0.638681	−0.319340	+	0.947640i	$0.603461\pi$
$354$	0	0
$355$	−6.27976	−0.333295
$356$	5.41933	0.287224
$357$	0	0
$358$	−0.910184	−0.0481047
$359$	6.50164	0.343143	0.171572	−	0.985172i	$-0.445116\pi$
$359$	6.50164	0.343143	0.171572	+	0.985172i	$0.445116\pi$
$360$	0	0
$361$	−10.5502	−0.555272
$362$	30.2113	1.58787
$363$	0	0
$364$	0	0
$365$	4.05437	0.212216
$366$	0	0
$367$	−11.2963	−0.589660	−0.294830	−	0.955550i	$-0.595263\pi$
$367$	−11.2963	−0.589660	−0.294830	+	0.955550i	$0.595263\pi$
$368$	47.3492	2.46825
$369$	0	0
$370$	7.23590	0.376177
$371$	0	0
$372$	0	0
$373$	−30.2400	−1.56577	−0.782884	−	0.622167i	$-0.786252\pi$
$373$	−30.2400	−1.56577	−0.782884	+	0.622167i	$0.786252\pi$
$374$	−49.4203	−2.55546
$375$	0	0
$376$	23.9734	1.23633
$377$	6.53200	0.336415
$378$	0	0
$379$	−2.33348	−0.119863	−0.0599313	−	0.998203i	$-0.519088\pi$
$379$	−2.33348	−0.119863	−0.0599313	+	0.998203i	$0.519088\pi$
$380$	2.42267	0.124280
$381$	0	0
$382$	−26.8411	−1.37331
$383$	25.4474	1.30030	0.650151	−	0.759805i	$-0.274705\pi$
$383$	25.4474	1.30030	0.650151	+	0.759805i	$0.274705\pi$
$384$	0	0
$385$	0	0
$386$	14.4905	0.737545
$387$	0	0
$388$	−1.33905	−0.0679802
$389$	7.31939	0.371108	0.185554	−	0.982634i	$-0.440592\pi$
$389$	7.31939	0.371108	0.185554	+	0.982634i	$0.440592\pi$
$390$	0	0
$391$	69.1970	3.49944
$392$	0	0
$393$	0	0
$394$	−0.301783	−0.0152036
$395$	−1.08005	−0.0543431
$396$	0	0
$397$	−9.01082	−0.452240	−0.226120	−	0.974099i	$-0.572604\pi$
$397$	−9.01082	−0.452240	−0.226120	+	0.974099i	$0.572604\pi$
$398$	0.695551	0.0348648
$399$	0	0
$400$	19.7148	0.985741
$401$	−34.9597	−1.74580	−0.872902	−	0.487895i	$-0.837765\pi$
$401$	−34.9597	−1.74580	−0.872902	+	0.487895i	$0.837765\pi$
$402$	0	0
$403$	9.86851	0.491585
$404$	12.7627	0.634967
$405$	0	0
$406$	0	0
$407$	−17.1942	−0.852283
$408$	0	0
$409$	4.05390	0.200452	0.100226	−	0.994965i	$-0.468043\pi$
$409$	4.05390	0.200452	0.100226	+	0.994965i	$0.468043\pi$
$410$	−15.0624	−0.743879
$411$	0	0
$412$	−11.9402	−0.588252
$413$	0	0
$414$	0	0
$415$	8.15346	0.400238
$416$	−4.38180	−0.214835
$417$	0	0
$418$	−19.7874	−0.967834
$419$	20.7873	1.01552	0.507762	−	0.861497i	$-0.330473\pi$
$419$	20.7873	1.01552	0.507762	+	0.861497i	$0.330473\pi$
$420$	0	0
$421$	19.7027	0.960249	0.480125	−	0.877200i	$-0.340591\pi$
$421$	19.7027	0.960249	0.480125	+	0.877200i	$0.340591\pi$
$422$	14.2906	0.695657
$423$	0	0
$424$	−17.6117	−0.855302
$425$	28.8116	1.39757
$426$	0	0
$427$	0	0
$428$	−15.3487	−0.741907
$429$	0	0
$430$	0.967051	0.0466353
$431$	−3.54528	−0.170770	−0.0853850	−	0.996348i	$-0.527212\pi$
$431$	−3.54528	−0.170770	−0.0853850	+	0.996348i	$0.527212\pi$
$432$	0	0
$433$	10.2828	0.494159	0.247079	−	0.968995i	$-0.420529\pi$
$433$	10.2828	0.494159	0.247079	+	0.968995i	$0.420529\pi$
$434$	0	0
$435$	0	0
$436$	−8.88327	−0.425431
$437$	27.7058	1.32535
$438$	0	0
$439$	−13.7824	−0.657800	−0.328900	−	0.944365i	$-0.606678\pi$
$439$	−13.7824	−0.657800	−0.328900	+	0.944365i	$0.606678\pi$
$440$	8.15371	0.388713
$441$	0	0
$442$	−12.1930	−0.579964
$443$	−16.2294	−0.771082	−0.385541	−	0.922691i	$-0.625985\pi$
$443$	−16.2294	−0.771082	−0.385541	+	0.922691i	$0.625985\pi$
$444$	0	0
$445$	−6.70721	−0.317952
$446$	−37.9852	−1.79865
$447$	0	0
$448$	0	0
$449$	−39.8213	−1.87928	−0.939642	−	0.342159i	$-0.888842\pi$
$449$	−39.8213	−1.87928	−0.939642	+	0.342159i	$0.888842\pi$
$450$	0	0
$451$	35.7917	1.68537
$452$	7.81871	0.367761
$453$	0	0
$454$	3.61792	0.169797
$455$	0	0
$456$	0	0
$457$	−3.04965	−0.142656	−0.0713282	−	0.997453i	$-0.522724\pi$
$457$	−3.04965	−0.142656	−0.0713282	+	0.997453i	$0.522724\pi$
$458$	8.51016	0.397654
$459$	0	0
$460$	7.94359	0.370372
$461$	14.0689	0.655252	0.327626	−	0.944808i	$-0.393751\pi$
$461$	14.0689	0.655252	0.327626	+	0.944808i	$0.393751\pi$
$462$	0	0
$463$	26.2561	1.22022	0.610112	−	0.792315i	$-0.291125\pi$
$463$	26.2561	1.22022	0.610112	+	0.792315i	$0.291125\pi$
$464$	32.4498	1.50644
$465$	0	0
$466$	−15.0760	−0.698384
$467$	0.631924	0.0292419	0.0146210	−	0.999893i	$-0.495346\pi$
$467$	0.631924	0.0292419	0.0146210	+	0.999893i	$0.495346\pi$
$468$	0	0
$469$	0	0
$470$	20.6445	0.952261
$471$	0	0
$472$	10.7827	0.496316
$473$	−2.29794	−0.105659
$474$	0	0
$475$	11.5359	0.529303
$476$	0	0
$477$	0	0
$478$	46.0123	2.10455
$479$	17.2080	0.786253	0.393127	−	0.919484i	$-0.371393\pi$
$479$	17.2080	0.786253	0.393127	+	0.919484i	$0.371393\pi$
$480$	0	0
$481$	−4.24217	−0.193426
$482$	2.38639	0.108697
$483$	0	0
$484$	4.45433	0.202470
$485$	1.65727	0.0752529
$486$	0	0
$487$	−30.9293	−1.40154	−0.700770	−	0.713387i	$-0.747160\pi$
$487$	−30.9293	−1.40154	−0.700770	+	0.713387i	$0.747160\pi$
$488$	10.9278	0.494680
$489$	0	0
$490$	0	0
$491$	−23.0434	−1.03993	−0.519966	−	0.854187i	$-0.674056\pi$
$491$	−23.0434	−1.03993	−0.519966	+	0.854187i	$0.674056\pi$
$492$	0	0
$493$	47.4228	2.13581
$494$	−4.88198	−0.219650
$495$	0	0
$496$	49.0250	2.20129
$497$	0	0
$498$	0	0
$499$	−12.7385	−0.570252	−0.285126	−	0.958490i	$-0.592035\pi$
$499$	−12.7385	−0.570252	−0.285126	+	0.958490i	$0.592035\pi$
$500$	7.47464	0.334276
$501$	0	0
$502$	−21.4164	−0.955863
$503$	−12.7285	−0.567536	−0.283768	−	0.958893i	$-0.591584\pi$
$503$	−12.7285	−0.567536	−0.283768	+	0.958893i	$0.591584\pi$
$504$	0	0
$505$	−15.7957	−0.702898
$506$	−64.8801	−2.88427
$507$	0	0
$508$	8.91354	0.395474
$509$	−24.8747	−1.10255	−0.551276	−	0.834323i	$-0.685859\pi$
$509$	−24.8747	−1.10255	−0.551276	+	0.834323i	$0.685859\pi$
$510$	0	0
$511$	0	0
$512$	−2.08800	−0.0922776
$513$	0	0
$514$	21.3793	0.943001
$515$	14.7777	0.651185
$516$	0	0
$517$	−49.0562	−2.15749
$518$	0	0
$519$	0	0
$520$	2.01169	0.0882186
$521$	−36.7391	−1.60957	−0.804784	−	0.593568i	$-0.797719\pi$
$521$	−36.7391	−1.60957	−0.804784	+	0.593568i	$0.797719\pi$
$522$	0	0
$523$	19.5499	0.854858	0.427429	−	0.904049i	$-0.359419\pi$
$523$	19.5499	0.854858	0.427429	+	0.904049i	$0.359419\pi$
$524$	2.97174	0.129821
$525$	0	0
$526$	−48.6965	−2.12327
$527$	71.6460	3.12095
$528$	0	0
$529$	67.8433	2.94971
$530$	−15.1662	−0.658780
$531$	0	0
$532$	0	0
$533$	8.83058	0.382495
$534$	0	0
$535$	18.9962	0.821279
$536$	−6.00233	−0.259261
$537$	0	0
$538$	2.25407	0.0971799
$539$	0	0
$540$	0	0
$541$	−13.1112	−0.563695	−0.281847	−	0.959459i	$-0.590947\pi$
$541$	−13.1112	−0.563695	−0.281847	+	0.959459i	$0.590947\pi$
$542$	19.0468	0.818131
$543$	0	0
$544$	−31.8121	−1.36393
$545$	10.9943	0.470945
$546$	0	0
$547$	−28.5723	−1.22166	−0.610831	−	0.791761i	$-0.709165\pi$
$547$	−28.5723	−1.22166	−0.610831	+	0.791761i	$0.709165\pi$
$548$	11.9942	0.512366
$549$	0	0
$550$	−27.0142	−1.15189
$551$	18.9876	0.808899
$552$	0	0
$553$	0	0
$554$	−21.9946	−0.934463
$555$	0	0
$556$	9.12696	0.387069
$557$	−8.09164	−0.342854	−0.171427	−	0.985197i	$-0.554838\pi$
$557$	−8.09164	−0.342854	−0.171427	+	0.985197i	$0.554838\pi$
$558$	0	0
$559$	−0.566950	−0.0239794
$560$	0	0
$561$	0	0
$562$	4.92909	0.207921
$563$	12.0169	0.506450	0.253225	−	0.967407i	$-0.418509\pi$
$563$	12.0169	0.506450	0.253225	+	0.967407i	$0.418509\pi$
$564$	0	0
$565$	−9.67678	−0.407105
$566$	−35.7355	−1.50208
$567$	0	0
$568$	12.2472	0.513883
$569$	−33.6891	−1.41232	−0.706161	−	0.708051i	$-0.749574\pi$
$569$	−33.6891	−1.41232	−0.706161	+	0.708051i	$0.749574\pi$
$570$	0	0
$571$	−21.4169	−0.896269	−0.448135	−	0.893966i	$-0.647912\pi$
$571$	−21.4169	−0.896269	−0.448135	+	0.893966i	$0.647912\pi$
$572$	3.32606	0.139070
$573$	0	0
$574$	0	0
$575$	37.8245	1.57739
$576$	0	0
$577$	46.5340	1.93723	0.968617	−	0.248557i	$-0.0799565\pi$
$577$	46.5340	1.93723	0.968617	+	0.248557i	$0.0799565\pi$
$578$	−59.9714	−2.49448
$579$	0	0
$580$	5.44398	0.226049
$581$	0	0
$582$	0	0
$583$	36.0385	1.49256
$584$	−7.90714	−0.327200
$585$	0	0
$586$	13.1262	0.542240
$587$	−1.76869	−0.0730016	−0.0365008	−	0.999334i	$-0.511621\pi$
$587$	−1.76869	−0.0730016	−0.0365008	+	0.999334i	$0.511621\pi$
$588$	0	0
$589$	28.6864	1.18200
$590$	9.28550	0.382278
$591$	0	0
$592$	−21.0743	−0.866150
$593$	3.65783	0.150209	0.0751045	−	0.997176i	$-0.476071\pi$
$593$	3.65783	0.150209	0.0751045	+	0.997176i	$0.476071\pi$
$594$	0	0
$595$	0	0
$596$	−4.29392	−0.175886
$597$	0	0
$598$	−16.0073	−0.654587
$599$	−29.2941	−1.19692	−0.598461	−	0.801152i	$-0.704221\pi$
$599$	−29.2941	−1.19692	−0.598461	+	0.801152i	$0.704221\pi$
$600$	0	0
$601$	17.0717	0.696368	0.348184	−	0.937426i	$-0.386798\pi$
$601$	17.0717	0.696368	0.348184	+	0.937426i	$0.386798\pi$
$602$	0	0
$603$	0	0
$604$	−12.3332	−0.501832
$605$	−5.51288	−0.224130
$606$	0	0
$607$	26.4068	1.07182	0.535909	−	0.844276i	$-0.319969\pi$
$607$	26.4068	1.07182	0.535909	+	0.844276i	$0.319969\pi$
$608$	−12.7373	−0.516565
$609$	0	0
$610$	9.41045	0.381018
$611$	−12.1032	−0.489643
$612$	0	0
$613$	−27.9308	−1.12812	−0.564058	−	0.825735i	$-0.690760\pi$
$613$	−27.9308	−1.12812	−0.564058	+	0.825735i	$0.690760\pi$
$614$	2.73835	0.110511
$615$	0	0
$616$	0	0
$617$	−32.4751	−1.30740	−0.653699	−	0.756755i	$-0.726784\pi$
$617$	−32.4751	−1.30740	−0.653699	+	0.756755i	$0.726784\pi$
$618$	0	0
$619$	−7.57894	−0.304624	−0.152312	−	0.988332i	$-0.548672\pi$
$619$	−7.57894	−0.304624	−0.152312	+	0.988332i	$0.548672\pi$
$620$	8.22473	0.330313
$621$	0	0
$622$	−19.0585	−0.764176
$623$	0	0
$624$	0	0
$625$	10.5916	0.423664
$626$	9.80104	0.391728
$627$	0	0
$628$	−1.09487	−0.0436901
$629$	−30.7984	−1.22801
$630$	0	0
$631$	−16.5735	−0.659780	−0.329890	−	0.944019i	$-0.607012\pi$
$631$	−16.5735	−0.659780	−0.329890	+	0.944019i	$0.607012\pi$
$632$	2.10639	0.0837877
$633$	0	0
$634$	39.7701	1.57947
$635$	−11.0318	−0.437783
$636$	0	0
$637$	0	0
$638$	−44.4642	−1.76036
$639$	0	0
$640$	13.2954	0.525545
$641$	19.8649	0.784616	0.392308	−	0.919834i	$-0.371677\pi$
$641$	19.8649	0.784616	0.392308	+	0.919834i	$0.371677\pi$
$642$	0	0
$643$	9.68565	0.381965	0.190982	−	0.981593i	$-0.438833\pi$
$643$	9.68565	0.381965	0.190982	+	0.981593i	$0.438833\pi$
$644$	0	0
$645$	0	0
$646$	−35.4435	−1.39450
$647$	34.2542	1.34667	0.673337	−	0.739336i	$-0.264860\pi$
$647$	34.2542	1.34667	0.673337	+	0.739336i	$0.264860\pi$
$648$	0	0
$649$	−22.0645	−0.866107
$650$	−6.66498	−0.261422
$651$	0	0
$652$	−19.4385	−0.761269
$653$	37.5001	1.46749	0.733746	−	0.679424i	$-0.237770\pi$
$653$	37.5001	1.46749	0.733746	+	0.679424i	$0.237770\pi$
$654$	0	0
$655$	−3.67795	−0.143710
$656$	43.8687	1.71279
$657$	0	0
$658$	0	0
$659$	−40.1575	−1.56432	−0.782158	−	0.623081i	$-0.785881\pi$
$659$	−40.1575	−1.56432	−0.782158	+	0.623081i	$0.785881\pi$
$660$	0	0
$661$	−30.8232	−1.19888	−0.599441	−	0.800419i	$-0.704610\pi$
$661$	−30.8232	−1.19888	−0.599441	+	0.800419i	$0.704610\pi$
$662$	32.2916	1.25505
$663$	0	0
$664$	−15.9015	−0.617098
$665$	0	0
$666$	0	0
$667$	62.2576	2.41063
$668$	−7.45792	−0.288555
$669$	0	0
$670$	−5.16887	−0.199691
$671$	−22.3614	−0.863252
$672$	0	0
$673$	−27.2528	−1.05052	−0.525260	−	0.850942i	$-0.676032\pi$
$673$	−27.2528	−1.05052	−0.525260	+	0.850942i	$0.676032\pi$
$674$	33.4130	1.28702
$675$	0	0
$676$	0.820610	0.0315619
$677$	−0.689513	−0.0265001	−0.0132501	−	0.999912i	$-0.504218\pi$
$677$	−0.689513	−0.0265001	−0.0132501	+	0.999912i	$0.504218\pi$
$678$	0	0
$679$	0	0
$680$	14.6050	0.560077
$681$	0	0
$682$	−67.1763	−2.57231
$683$	0.746528	0.0285651	0.0142825	−	0.999898i	$-0.495454\pi$
$683$	0.746528	0.0285651	0.0142825	+	0.999898i	$0.495454\pi$
$684$	0	0
$685$	−14.8445	−0.567181
$686$	0	0
$687$	0	0
$688$	−2.81650	−0.107378
$689$	8.89147	0.338738
$690$	0	0
$691$	−36.8456	−1.40167	−0.700837	−	0.713321i	$-0.747190\pi$
$691$	−36.8456	−1.40167	−0.700837	+	0.713321i	$0.747190\pi$
$692$	−5.34782	−0.203294
$693$	0	0
$694$	28.0359	1.06423
$695$	−11.2959	−0.428479
$696$	0	0
$697$	64.1106	2.42836
$698$	20.0071	0.757280
$699$	0	0
$700$	0	0
$701$	19.8455	0.749556	0.374778	−	0.927115i	$-0.377719\pi$
$701$	19.8455	0.749556	0.374778	+	0.927115i	$0.377719\pi$
$702$	0	0
$703$	−12.3314	−0.465087
$704$	−10.4432	−0.393592
$705$	0	0
$706$	20.1531	0.758473
$707$	0	0
$708$	0	0
$709$	6.77166	0.254315	0.127157	−	0.991883i	$-0.459415\pi$
$709$	6.77166	0.254315	0.127157	+	0.991883i	$0.459415\pi$
$710$	10.5466	0.395808
$711$	0	0
$712$	13.0809	0.490227
$713$	94.0585	3.52252
$714$	0	0
$715$	−4.11648	−0.153948
$716$	0.444728	0.0166203
$717$	0	0
$718$	−10.9193	−0.407504
$719$	23.7828	0.886949	0.443475	−	0.896287i	$-0.353746\pi$
$719$	23.7828	0.886949	0.443475	+	0.896287i	$0.353746\pi$
$720$	0	0
$721$	0	0
$722$	17.7187	0.659420
$723$	0	0
$724$	−14.7617	−0.548613
$725$	25.9223	0.962730
$726$	0	0
$727$	−32.3712	−1.20058	−0.600290	−	0.799783i	$-0.704948\pi$
$727$	−32.3712	−1.20058	−0.600290	+	0.799783i	$0.704948\pi$
$728$	0	0
$729$	0	0
$730$	−6.80919	−0.252019
$731$	−4.11609	−0.152239
$732$	0	0
$733$	43.2848	1.59876	0.799379	−	0.600827i	$-0.205162\pi$
$733$	43.2848	1.59876	0.799379	+	0.600827i	$0.205162\pi$
$734$	18.9717	0.700258
$735$	0	0
$736$	−41.7637	−1.53943
$737$	12.2824	0.452429
$738$	0	0
$739$	23.2717	0.856063	0.428032	−	0.903764i	$-0.359207\pi$
$739$	23.2717	0.856063	0.428032	+	0.903764i	$0.359207\pi$
$740$	−3.53556	−0.129970
$741$	0	0
$742$	0	0
$743$	−30.9402	−1.13509	−0.567543	−	0.823344i	$-0.692106\pi$
$743$	−30.9402	−1.13509	−0.567543	+	0.823344i	$0.692106\pi$
$744$	0	0
$745$	5.31435	0.194703
$746$	50.7871	1.85945
$747$	0	0
$748$	24.1474	0.882918
$749$	0	0
$750$	0	0
$751$	13.4036	0.489106	0.244553	−	0.969636i	$-0.421359\pi$
$751$	13.4036	0.489106	0.244553	+	0.969636i	$0.421359\pi$
$752$	−60.1265	−2.19259
$753$	0	0
$754$	−10.9703	−0.399514
$755$	15.2642	0.555520
$756$	0	0
$757$	31.8271	1.15677	0.578387	−	0.815762i	$-0.303682\pi$
$757$	31.8271	1.15677	0.578387	+	0.815762i	$0.303682\pi$
$758$	3.91900	0.142344
$759$	0	0
$760$	5.84771	0.212119
$761$	3.91844	0.142043	0.0710216	−	0.997475i	$-0.477374\pi$
$761$	3.91844	0.142043	0.0710216	+	0.997475i	$0.477374\pi$
$762$	0	0
$763$	0	0
$764$	13.1149	0.474481
$765$	0	0
$766$	−42.7381	−1.54419
$767$	−5.44378	−0.196564
$768$	0	0
$769$	10.6889	0.385453	0.192727	−	0.981252i	$-0.438267\pi$
$769$	10.6889	0.385453	0.192727	+	0.981252i	$0.438267\pi$
$770$	0	0
$771$	0	0
$772$	−7.08023	−0.254823
$773$	−11.7012	−0.420862	−0.210431	−	0.977609i	$-0.567487\pi$
$773$	−11.7012	−0.420862	−0.210431	+	0.977609i	$0.567487\pi$
$774$	0	0
$775$	39.1632	1.40679
$776$	−3.23214	−0.116027
$777$	0	0
$778$	−12.2927	−0.440714
$779$	25.6693	0.919697
$780$	0	0
$781$	−25.0613	−0.896763
$782$	−116.214	−4.15581
$783$	0	0
$784$	0	0
$785$	1.35506	0.0483642
$786$	0	0
$787$	−12.8318	−0.457403	−0.228702	−	0.973497i	$-0.573448\pi$
$787$	−12.8318	−0.457403	−0.228702	+	0.973497i	$0.573448\pi$
$788$	0.147455	0.00525287
$789$	0	0
$790$	1.81390	0.0645358
$791$	0	0
$792$	0	0
$793$	−5.51703	−0.195916
$794$	15.1334	0.537063
$795$	0	0
$796$	−0.339856	−0.0120459
$797$	−1.12352	−0.0397970	−0.0198985	−	0.999802i	$-0.506334\pi$
$797$	−1.12352	−0.0397970	−0.0198985	+	0.999802i	$0.506334\pi$
$798$	0	0
$799$	−87.8701	−3.10862
$800$	−17.3892	−0.614801
$801$	0	0
$802$	58.7137	2.07325
$803$	16.1802	0.570987
$804$	0	0
$805$	0	0
$806$	−16.5738	−0.583788
$807$	0	0
$808$	30.8059	1.08375
$809$	−7.84953	−0.275975	−0.137987	−	0.990434i	$-0.544063\pi$
$809$	−7.84953	−0.275975	−0.137987	+	0.990434i	$0.544063\pi$
$810$	0	0
$811$	7.38224	0.259225	0.129613	−	0.991565i	$-0.458627\pi$
$811$	7.38224	0.259225	0.129613	+	0.991565i	$0.458627\pi$
$812$	0	0
$813$	0	0
$814$	28.8771	1.01214
$815$	24.0579	0.842712
$816$	0	0
$817$	−1.64804	−0.0576577
$818$	−6.80839	−0.238050
$819$	0	0
$820$	7.35969	0.257011
$821$	27.7269	0.967674	0.483837	−	0.875158i	$-0.339243\pi$
$821$	27.7269	0.967674	0.483837	+	0.875158i	$0.339243\pi$
$822$	0	0
$823$	−8.41214	−0.293229	−0.146614	−	0.989194i	$-0.546838\pi$
$823$	−8.41214	−0.293229	−0.146614	+	0.989194i	$0.546838\pi$
$824$	−28.8207	−1.00402
$825$	0	0
$826$	0	0
$827$	6.80644	0.236683	0.118342	−	0.992973i	$-0.462242\pi$
$827$	6.80644	0.236683	0.118342	+	0.992973i	$0.462242\pi$
$828$	0	0
$829$	50.0143	1.73707	0.868534	−	0.495629i	$-0.165062\pi$
$829$	50.0143	1.73707	0.868534	+	0.495629i	$0.165062\pi$
$830$	−13.6935	−0.475308
$831$	0	0
$832$	−2.57655	−0.0893259
$833$	0	0
$834$	0	0
$835$	9.23025	0.319426
$836$	9.66840	0.334388
$837$	0	0
$838$	−34.9115	−1.20600
$839$	18.8435	0.650552	0.325276	−	0.945619i	$-0.394543\pi$
$839$	18.8435	0.650552	0.325276	+	0.945619i	$0.394543\pi$
$840$	0	0
$841$	13.6670	0.471276
$842$	−33.0900	−1.14036
$843$	0	0
$844$	−6.98259	−0.240351
$845$	−1.01562	−0.0349385
$846$	0	0
$847$	0	0
$848$	44.1712	1.51685
$849$	0	0
$850$	−48.3882	−1.65970
$851$	−40.4329	−1.38602
$852$	0	0
$853$	41.3669	1.41638	0.708189	−	0.706023i	$-0.249513\pi$
$853$	41.3669	1.41638	0.708189	+	0.706023i	$0.249513\pi$
$854$	0	0
$855$	0	0
$856$	−37.0479	−1.26627
$857$	29.5295	1.00871	0.504355	−	0.863497i	$-0.331730\pi$
$857$	29.5295	1.00871	0.504355	+	0.863497i	$0.331730\pi$
$858$	0	0
$859$	36.0619	1.23041	0.615207	−	0.788365i	$-0.289072\pi$
$859$	36.0619	1.23041	0.615207	+	0.788365i	$0.289072\pi$
$860$	−0.472514	−0.0161126
$861$	0	0
$862$	5.95418	0.202800
$863$	2.68662	0.0914537	0.0457269	−	0.998954i	$-0.485440\pi$
$863$	2.68662	0.0914537	0.0457269	+	0.998954i	$0.485440\pi$
$864$	0	0
$865$	6.61870	0.225043
$866$	−17.2696	−0.586844
$867$	0	0
$868$	0	0
$869$	−4.31026	−0.146215
$870$	0	0
$871$	3.03034	0.102679
$872$	−21.4420	−0.726116
$873$	0	0
$874$	−46.5310	−1.57393
$875$	0	0
$876$	0	0
$877$	−6.40742	−0.216363	−0.108182	−	0.994131i	$-0.534503\pi$
$877$	−6.40742	−0.216363	−0.108182	+	0.994131i	$0.534503\pi$
$878$	23.1472	0.781179
$879$	0	0
$880$	−20.4499	−0.689367
$881$	13.3454	0.449617	0.224808	−	0.974403i	$-0.427824\pi$
$881$	13.3454	0.449617	0.224808	+	0.974403i	$0.427824\pi$
$882$	0	0
$883$	−14.8329	−0.499167	−0.249584	−	0.968353i	$-0.580294\pi$
$883$	−14.8329	−0.499167	−0.249584	+	0.968353i	$0.580294\pi$
$884$	5.95769	0.200379
$885$	0	0
$886$	27.2568	0.915709
$887$	−32.8467	−1.10288	−0.551442	−	0.834213i	$-0.685922\pi$
$887$	−32.8467	−1.10288	−0.551442	+	0.834213i	$0.685922\pi$
$888$	0	0
$889$	0	0
$890$	11.2645	0.377588
$891$	0	0
$892$	18.5601	0.621437
$893$	−35.1823	−1.17733
$894$	0	0
$895$	−0.550416	−0.0183984
$896$	0	0
$897$	0	0
$898$	66.8786	2.23177
$899$	64.4611	2.14990
$900$	0	0
$901$	64.5527	2.15056
$902$	−60.1110	−2.00148
$903$	0	0
$904$	18.8724	0.627686
$905$	18.2697	0.607306
$906$	0	0
$907$	−6.78020	−0.225133	−0.112566	−	0.993644i	$-0.535907\pi$
$907$	−6.78020	−0.225133	−0.112566	+	0.993644i	$0.535907\pi$
$908$	−1.76776	−0.0586653
$909$	0	0
$910$	0	0
$911$	−19.2486	−0.637736	−0.318868	−	0.947799i	$-0.603303\pi$
$911$	−19.2486	−0.637736	−0.318868	+	0.947799i	$0.603303\pi$
$912$	0	0
$913$	32.5389	1.07688
$914$	5.12178	0.169413
$915$	0	0
$916$	−4.15818	−0.137390
$917$	0	0
$918$	0	0
$919$	23.6687	0.780757	0.390379	−	0.920654i	$-0.372344\pi$
$919$	23.6687	0.780757	0.390379	+	0.920654i	$0.372344\pi$
$920$	19.1738	0.632142
$921$	0	0
$922$	−23.6282	−0.778152
$923$	−6.18315	−0.203521
$924$	0	0
$925$	−16.8351	−0.553534
$926$	−44.0962	−1.44909
$927$	0	0
$928$	−28.6219	−0.939560
$929$	−18.2611	−0.599126	−0.299563	−	0.954076i	$-0.596841\pi$
$929$	−18.2611	−0.599126	−0.299563	+	0.954076i	$0.596841\pi$
$930$	0	0
$931$	0	0
$932$	7.36635	0.241293
$933$	0	0
$934$	−1.06129	−0.0347266
$935$	−29.8859	−0.977375
$936$	0	0
$937$	−2.02078	−0.0660159	−0.0330079	−	0.999455i	$-0.510509\pi$
$937$	−2.02078	−0.0660159	−0.0330079	+	0.999455i	$0.510509\pi$
$938$	0	0
$939$	0	0
$940$	−10.0872	−0.329008
$941$	−26.6332	−0.868217	−0.434108	−	0.900861i	$-0.642937\pi$
$941$	−26.6332	−0.868217	−0.434108	+	0.900861i	$0.642937\pi$
$942$	0	0
$943$	84.1658	2.74082
$944$	−27.0437	−0.880198
$945$	0	0
$946$	3.85931	0.125477
$947$	−3.57351	−0.116124	−0.0580618	−	0.998313i	$-0.518492\pi$
$947$	−3.57351	−0.116124	−0.0580618	+	0.998313i	$0.518492\pi$
$948$	0	0
$949$	3.99200	0.129586
$950$	−19.3742	−0.628581
$951$	0	0
$952$	0	0
$953$	5.18119	0.167835	0.0839176	−	0.996473i	$-0.473257\pi$
$953$	5.18119	0.167835	0.0839176	+	0.996473i	$0.473257\pi$
$954$	0	0
$955$	−16.2316	−0.525242
$956$	−22.4822	−0.727128
$957$	0	0
$958$	−28.9003	−0.933725
$959$	0	0
$960$	0	0
$961$	66.3874	2.14153
$962$	7.12458	0.229706
$963$	0	0
$964$	−1.16602	−0.0375551
$965$	8.76281	0.282085
$966$	0	0
$967$	−33.3558	−1.07265	−0.536325	−	0.844012i	$-0.680188\pi$
$967$	−33.3558	−1.07265	−0.536325	+	0.844012i	$0.680188\pi$
$968$	10.7516	0.345570
$969$	0	0
$970$	−2.78334	−0.0893676
$971$	−11.0917	−0.355949	−0.177975	−	0.984035i	$-0.556954\pi$
$971$	−11.0917	−0.355949	−0.177975	+	0.984035i	$0.556954\pi$
$972$	0	0
$973$	0	0
$974$	51.9447	1.66442
$975$	0	0
$976$	−27.4076	−0.877297
$977$	−31.3247	−1.00217	−0.501083	−	0.865399i	$-0.667065\pi$
$977$	−31.3247	−1.00217	−0.501083	+	0.865399i	$0.667065\pi$
$978$	0	0
$979$	−26.7671	−0.855481
$980$	0	0
$981$	0	0
$982$	38.7006	1.23499
$983$	−19.7083	−0.628596	−0.314298	−	0.949324i	$-0.601769\pi$
$983$	−19.7083	−0.628596	−0.314298	+	0.949324i	$0.601769\pi$
$984$	0	0
$985$	−0.182497	−0.00581484
$986$	−79.6450	−2.53641
$987$	0	0
$988$	2.38540	0.0758897
$989$	−5.40370	−0.171828
$990$	0	0
$991$	−36.9147	−1.17263	−0.586316	−	0.810082i	$-0.699422\pi$
$991$	−36.9147	−1.17263	−0.586316	+	0.810082i	$0.699422\pi$
$992$	−43.2418	−1.37293
$993$	0	0
$994$	0	0
$995$	0.420620	0.0133346
$996$	0	0
$997$	−1.04532	−0.0331057	−0.0165528	−	0.999863i	$-0.505269\pi$
$997$	−1.04532	−0.0331057	−0.0165528	+	0.999863i	$0.505269\pi$
$998$	21.3938	0.677210
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5733.2.a.bx.1.4		10
3.2	odd	2		1911.2.a.y.1.7	yes	10
7.6	odd	2		5733.2.a.bw.1.4		10
21.20	even	2		1911.2.a.x.1.7	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1911.2.a.x.1.7	✓	10	21.20	even	2
1911.2.a.y.1.7	yes	10	3.2	odd	2
5733.2.a.bw.1.4		10	7.6	odd	2
5733.2.a.bx.1.4		10	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:	\( N \)	\(=\)	\( 5733 = 3^{2} \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5733.a (trivial)

\(f(q)\)	\(=\)	\(q-1.67947 q^{2} +0.820610 q^{4} -1.01562 q^{5} +1.98075 q^{8} +O(q^{10})\)	\(q-1.67947 q^{2} +0.820610 q^{4} -1.01562 q^{5} +1.98075 q^{8} +1.70571 q^{10} -4.05316 q^{11} -1.00000 q^{13} -4.96782 q^{16} -7.26007 q^{17} -2.90686 q^{19} -0.833432 q^{20} +6.80714 q^{22} -9.53118 q^{23} -3.96851 q^{25} +1.67947 q^{26} -6.53200 q^{29} -9.86851 q^{31} +4.38180 q^{32} +12.1930 q^{34} +4.24217 q^{37} +4.88198 q^{38} -2.01169 q^{40} -8.83058 q^{41} +0.566950 q^{43} -3.32606 q^{44} +16.0073 q^{46} +12.1032 q^{47} +6.66498 q^{50} -0.820610 q^{52} -8.89147 q^{53} +4.11648 q^{55} +10.9703 q^{58} +5.44378 q^{59} +5.51703 q^{61} +16.5738 q^{62} +2.57655 q^{64} +1.01562 q^{65} -3.03034 q^{67} -5.95769 q^{68} +6.18315 q^{71} -3.99200 q^{73} -7.12458 q^{74} -2.38540 q^{76} +1.06343 q^{79} +5.04544 q^{80} +14.8307 q^{82} -8.02803 q^{83} +7.37350 q^{85} -0.952174 q^{86} -8.02827 q^{88} +6.60402 q^{89} -7.82138 q^{92} -20.3269 q^{94} +2.95228 q^{95} -1.63178 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} + 16 q^{4} + 6 q^{5} - 12 q^{8}+O(q^{10}) \) 10 * q - 4 * q^2 + 16 * q^4 + 6 * q^5 - 12 * q^8	\( 10 q - 4 q^{2} + 16 q^{4} + 6 q^{5} - 12 q^{8} + 8 q^{10} - 12 q^{11} - 10 q^{13} + 24 q^{16} + 10 q^{19} + 16 q^{20} + 8 q^{22} - 14 q^{23} + 32 q^{25} + 4 q^{26} - 18 q^{29} + 14 q^{31} - 28 q^{32} + 4 q^{34} + 24 q^{37} + 4 q^{38} + 16 q^{40} + 24 q^{41} + 2 q^{43} - 48 q^{44} + 20 q^{46} + 18 q^{47} + 28 q^{50} - 16 q^{52} - 10 q^{53} + 12 q^{55} + 12 q^{58} + 12 q^{59} - 4 q^{61} - 4 q^{62} + 32 q^{64} - 6 q^{65} - 12 q^{67} + 40 q^{68} - 32 q^{71} - 18 q^{73} - 24 q^{74} + 32 q^{76} + 34 q^{79} + 32 q^{80} + 48 q^{82} + 30 q^{83} - 40 q^{86} + 32 q^{88} + 10 q^{89} + 40 q^{92} - 24 q^{94} + 30 q^{95} - 2 q^{97}+O(q^{100}) \) 10 * q - 4 * q^2 + 16 * q^4 + 6 * q^5 - 12 * q^8 + 8 * q^10 - 12 * q^11 - 10 * q^13 + 24 * q^16 + 10 * q^19 + 16 * q^20 + 8 * q^22 - 14 * q^23 + 32 * q^25 + 4 * q^26 - 18 * q^29 + 14 * q^31 - 28 * q^32 + 4 * q^34 + 24 * q^37 + 4 * q^38 + 16 * q^40 + 24 * q^41 + 2 * q^43 - 48 * q^44 + 20 * q^46 + 18 * q^47 + 28 * q^50 - 16 * q^52 - 10 * q^53 + 12 * q^55 + 12 * q^58 + 12 * q^59 - 4 * q^61 - 4 * q^62 + 32 * q^64 - 6 * q^65 - 12 * q^67 + 40 * q^68 - 32 * q^71 - 18 * q^73 - 24 * q^74 + 32 * q^76 + 34 * q^79 + 32 * q^80 + 48 * q^82 + 30 * q^83 - 40 * q^86 + 32 * q^88 + 10 * q^89 + 40 * q^92 - 24 * q^94 + 30 * q^95 - 2 * q^97

Introduction

L-functions

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Database

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