LMFDB - Embedded newform 5733.2.a.bl.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:	$1$
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			1.4
Root			$1.19566$ 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)

$f(q)$	$=$	$q+0.195656 q^{2} -1.96172 q^{4} -3.93251 q^{5} -0.775135 q^{8} +O(q^{10})$	$q+0.195656 q^{2} -1.96172 q^{4} -3.93251 q^{5} -0.775135 q^{8} -0.769420 q^{10} -4.50627 q^{11} +1.00000 q^{13} +3.77178 q^{16} +2.28141 q^{17} -1.78768 q^{19} +7.71448 q^{20} -0.881681 q^{22} -1.74021 q^{23} +10.4646 q^{25} +0.195656 q^{26} -1.65110 q^{29} +5.60523 q^{31} +2.28824 q^{32} +0.446372 q^{34} +7.14407 q^{37} -0.349771 q^{38} +3.04823 q^{40} +8.11574 q^{41} +6.81353 q^{43} +8.84004 q^{44} -0.340483 q^{46} -3.54543 q^{47} +2.04747 q^{50} -1.96172 q^{52} -3.28965 q^{53} +17.7210 q^{55} -0.323048 q^{58} -4.50627 q^{59} +7.54467 q^{61} +1.09670 q^{62} -7.09585 q^{64} -3.93251 q^{65} -12.6653 q^{67} -4.47548 q^{68} -9.54869 q^{71} +1.08004 q^{73} +1.39778 q^{74} +3.50693 q^{76} +0.791698 q^{79} -14.8326 q^{80} +1.58789 q^{82} +7.14643 q^{83} -8.97166 q^{85} +1.33311 q^{86} +3.49297 q^{88} +11.2656 q^{89} +3.41381 q^{92} -0.693685 q^{94} +7.03008 q^{95} -8.81353 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.195656	0.138350	0.0691749	−	0.997605i	$-0.477963\pi$
$2$	0.195656	0.138350	0.0691749	+	0.997605i	$0.477963\pi$
$3$	0	0
$3$	0	0
$4$	−1.96172	−0.980859
$5$	−3.93251	−1.75867	−0.879336	−	0.476202i	$-0.842013\pi$
$5$	−3.93251	−1.75867	−0.879336	+	0.476202i	$0.842013\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	−0.775135	−0.274052
$9$	0	0
$10$	−0.769420	−0.243312
$11$	−4.50627	−1.35869	−0.679346	−	0.733818i	$-0.737737\pi$
$11$	−4.50627	−1.35869	−0.679346	+	0.733818i	$0.737737\pi$
$12$	0	0
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0	0
$15$	0	0
$16$	3.77178	0.942944
$17$	2.28141	0.553323	0.276661	−	0.960967i	$-0.410772\pi$
$17$	2.28141	0.553323	0.276661	+	0.960967i	$0.410772\pi$
$18$	0	0
$19$	−1.78768	−0.410123	−0.205061	−	0.978749i	$-0.565739\pi$
$19$	−1.78768	−0.410123	−0.205061	+	0.978749i	$0.565739\pi$
$20$	7.71448	1.72501
$21$	0	0
$22$	−0.881681	−0.187975
$23$	−1.74021	−0.362859	−0.181430	−	0.983404i	$-0.558072\pi$
$23$	−1.74021	−0.362859	−0.181430	+	0.983404i	$0.558072\pi$
$24$	0	0
$25$	10.4646	2.09293
$26$	0.195656	0.0383714
$27$	0	0
$28$	0	0
$29$	−1.65110	−0.306602	−0.153301	−	0.988180i	$-0.548990\pi$
$29$	−1.65110	−0.306602	−0.153301	+	0.988180i	$0.548990\pi$
$30$	0	0
$31$	5.60523	1.00673	0.503365	−	0.864074i	$-0.332095\pi$
$31$	5.60523	1.00673	0.503365	+	0.864074i	$0.332095\pi$
$32$	2.28824	0.404508
$33$	0	0
$34$	0.446372	0.0765522
$35$	0	0
$36$	0	0
$37$	7.14407	1.17448	0.587239	−	0.809414i	$-0.300215\pi$
$37$	7.14407	1.17448	0.587239	+	0.809414i	$0.300215\pi$
$38$	−0.349771	−0.0567404
$39$	0	0
$40$	3.04823	0.481967
$41$	8.11574	1.26746	0.633732	−	0.773552i	$-0.281522\pi$
$41$	8.11574	1.26746	0.633732	+	0.773552i	$0.281522\pi$
$42$	0	0
$43$	6.81353	1.03905	0.519527	−	0.854454i	$-0.326108\pi$
$43$	6.81353	1.03905	0.519527	+	0.854454i	$0.326108\pi$
$44$	8.84004	1.33269
$45$	0	0
$46$	−0.340483	−0.0502015
$47$	−3.54543	−0.517154	−0.258577	−	0.965991i	$-0.583254\pi$
$47$	−3.54543	−0.517154	−0.258577	+	0.965991i	$0.583254\pi$
$48$	0	0
$49$	0	0
$50$	2.04747	0.289556
$51$	0	0
$52$	−1.96172	−0.272041
$53$	−3.28965	−0.451869	−0.225934	−	0.974143i	$-0.572543\pi$
$53$	−3.28965	−0.451869	−0.225934	+	0.974143i	$0.572543\pi$
$54$	0	0
$55$	17.7210	2.38949
$56$	0	0
$57$	0	0
$58$	−0.323048	−0.0424183
$59$	−4.50627	−0.586667	−0.293333	−	0.956010i	$-0.594765\pi$
$59$	−4.50627	−0.586667	−0.293333	+	0.956010i	$0.594765\pi$
$60$	0	0
$61$	7.54467	0.965996	0.482998	−	0.875621i	$-0.339548\pi$
$61$	7.54467	0.965996	0.482998	+	0.875621i	$0.339548\pi$
$62$	1.09670	0.139281
$63$	0	0
$64$	−7.09585	−0.886981
$65$	−3.93251	−0.487768
$66$	0	0
$67$	−12.6653	−1.54731	−0.773653	−	0.633609i	$-0.781573\pi$
$67$	−12.6653	−1.54731	−0.773653	+	0.633609i	$0.781573\pi$
$68$	−4.47548	−0.542732
$69$	0	0
$70$	0	0
$71$	−9.54869	−1.13322	−0.566610	−	0.823986i	$-0.691746\pi$
$71$	−9.54869	−1.13322	−0.566610	+	0.823986i	$0.691746\pi$
$72$	0	0
$73$	1.08004	0.126409	0.0632044	−	0.998001i	$-0.479868\pi$
$73$	1.08004	0.126409	0.0632044	+	0.998001i	$0.479868\pi$
$74$	1.39778	0.162489
$75$	0	0
$76$	3.50693	0.402273
$77$	0	0
$78$	0	0
$79$	0.791698	0.0890730	0.0445365	−	0.999008i	$-0.485819\pi$
$79$	0.791698	0.0890730	0.0445365	+	0.999008i	$0.485819\pi$
$80$	−14.8326	−1.65833
$81$	0	0
$82$	1.58789	0.175354
$83$	7.14643	0.784422	0.392211	−	0.919875i	$-0.371710\pi$
$83$	7.14643	0.784422	0.392211	+	0.919875i	$0.371710\pi$
$84$	0	0
$85$	−8.97166	−0.973114
$86$	1.33311	0.143753
$87$	0	0
$88$	3.49297	0.372352
$89$	11.2656	1.19415	0.597077	−	0.802184i	$-0.296329\pi$
$89$	11.2656	1.19415	0.597077	+	0.802184i	$0.296329\pi$
$90$	0	0
$91$	0	0
$92$	3.41381	0.355914
$93$	0	0
$94$	−0.693685	−0.0715482
$95$	7.03008	0.721271
$96$	0	0
$97$	−8.81353	−0.894879	−0.447439	−	0.894314i	$-0.647664\pi$
$97$	−8.81353	−0.894879	−0.447439	+	0.894314i	$0.647664\pi$
$98$	0	0
$99$	0	0
$100$	−20.5287	−2.05287
$101$	14.3171	1.42461	0.712303	−	0.701872i	$-0.247652\pi$
$101$	14.3171	1.42461	0.712303	+	0.701872i	$0.247652\pi$
$102$	0	0
$103$	−7.49214	−0.738223	−0.369111	−	0.929385i	$-0.620338\pi$
$103$	−7.49214	−0.738223	−0.369111	+	0.929385i	$0.620338\pi$
$104$	−0.775135	−0.0760082
$105$	0	0
$106$	−0.643641	−0.0625160
$107$	−10.9784	−1.06132	−0.530660	−	0.847585i	$-0.678056\pi$
$107$	−10.9784	−1.06132	−0.530660	+	0.847585i	$0.678056\pi$
$108$	0	0
$109$	−12.4463	−1.19214	−0.596068	−	0.802934i	$-0.703271\pi$
$109$	−12.4463	−1.19214	−0.596068	+	0.802934i	$0.703271\pi$
$110$	3.46722	0.330586
$111$	0	0
$112$	0	0
$113$	1.65110	0.155323	0.0776613	−	0.996980i	$-0.475255\pi$
$113$	1.65110	0.155323	0.0776613	+	0.996980i	$0.475255\pi$
$114$	0	0
$115$	6.84340	0.638150
$116$	3.23900	0.300733
$117$	0	0
$118$	−0.881681	−0.0811653
$119$	0	0
$120$	0	0
$121$	9.30650	0.846046
$122$	1.47616	0.133645
$123$	0	0
$124$	−10.9959	−0.987460
$125$	−21.4897	−1.92210
$126$	0	0
$127$	−4.49297	−0.398687	−0.199343	−	0.979930i	$-0.563881\pi$
$127$	−4.49297	−0.398687	−0.199343	+	0.979930i	$0.563881\pi$
$128$	−5.96483	−0.527222
$129$	0	0
$130$	−0.769420	−0.0674826
$131$	12.6567	1.10582	0.552911	−	0.833240i	$-0.313517\pi$
$131$	12.6567	1.10582	0.552911	+	0.833240i	$0.313517\pi$
$132$	0	0
$133$	0	0
$134$	−2.47804	−0.214070
$135$	0	0
$136$	−1.76840	−0.151639
$137$	9.28641	0.793392	0.396696	−	0.917950i	$-0.370157\pi$
$137$	9.28641	0.793392	0.396696	+	0.917950i	$0.370157\pi$
$138$	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
$142$	−1.86826	−0.156781
$143$	−4.50627	−0.376834
$144$	0	0
$145$	6.49297	0.539212
$146$	0.211316	0.0174887
$147$	0	0
$148$	−14.0147	−1.15200
$149$	15.1649	1.24235	0.621177	−	0.783670i	$-0.286655\pi$
$149$	15.1649	1.24235	0.621177	+	0.783670i	$0.286655\pi$
$150$	0	0
$151$	5.14159	0.418416	0.209208	−	0.977871i	$-0.432911\pi$
$151$	5.14159	0.418416	0.209208	+	0.977871i	$0.432911\pi$
$152$	1.38570	0.112395
$153$	0	0
$154$	0	0
$155$	−22.0426	−1.77051
$156$	0	0
$157$	−10.7311	−0.856438	−0.428219	−	0.903675i	$-0.640859\pi$
$157$	−10.7311	−0.856438	−0.428219	+	0.903675i	$0.640859\pi$
$158$	0.154901	0.0123232
$159$	0	0
$160$	−8.99853	−0.711397
$161$	0	0
$162$	0	0
$163$	2.37239	0.185820	0.0929101	−	0.995675i	$-0.470383\pi$
$163$	2.37239	0.185820	0.0929101	+	0.995675i	$0.470383\pi$
$164$	−15.9208	−1.24320
$165$	0	0
$166$	1.39824	0.108525
$167$	−12.0784	−0.934653	−0.467327	−	0.884085i	$-0.654783\pi$
$167$	−12.0784	−0.934653	−0.467327	+	0.884085i	$0.654783\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	−1.75536	−0.134630
$171$	0	0
$172$	−13.3662	−1.01917
$173$	19.4097	1.47569	0.737846	−	0.674969i	$-0.235843\pi$
$173$	19.4097	1.47569	0.737846	+	0.674969i	$0.235843\pi$
$174$	0	0
$175$	0	0
$176$	−16.9967	−1.28117
$177$	0	0
$178$	2.20419	0.165211
$179$	−14.6444	−1.09457	−0.547286	−	0.836945i	$-0.684339\pi$
$179$	−14.6444	−1.09457	−0.547286	+	0.836945i	$0.684339\pi$
$180$	0	0
$181$	−9.44627	−0.702136	−0.351068	−	0.936350i	$-0.614181\pi$
$181$	−9.44627	−0.702136	−0.351068	+	0.936350i	$0.614181\pi$
$182$	0	0
$183$	0	0
$184$	1.34890	0.0994422
$185$	−28.0941	−2.06552
$186$	0	0
$187$	−10.2807	−0.751796
$188$	6.95513	0.507255
$189$	0	0
$190$	1.37548	0.0997878
$191$	−12.5537	−0.908357	−0.454179	−	0.890911i	$-0.650067\pi$
$191$	−12.5537	−0.908357	−0.454179	+	0.890911i	$0.650067\pi$
$192$	0	0
$193$	−9.36859	−0.674366	−0.337183	−	0.941439i	$-0.609474\pi$
$193$	−9.36859	−0.674366	−0.337183	+	0.941439i	$0.609474\pi$
$194$	−1.72442	−0.123806
$195$	0	0
$196$	0	0
$197$	7.62276	0.543099	0.271550	−	0.962424i	$-0.412464\pi$
$197$	7.62276	0.543099	0.271550	+	0.962424i	$0.412464\pi$
$198$	0	0
$199$	13.5289	0.959036	0.479518	−	0.877532i	$-0.340812\pi$
$199$	13.5289	0.959036	0.479518	+	0.877532i	$0.340812\pi$
$200$	−8.11151	−0.573570
$201$	0	0
$202$	2.80123	0.197094
$203$	0	0
$204$	0	0
$205$	−31.9152	−2.22906
$206$	−1.46588	−0.102133
$207$	0	0
$208$	3.77178	0.261526
$209$	8.05579	0.557231
$210$	0	0
$211$	−15.7995	−1.08768	−0.543840	−	0.839189i	$-0.683030\pi$
$211$	−15.7995	−1.08768	−0.543840	+	0.839189i	$0.683030\pi$
$212$	6.45338	0.443220
$213$	0	0
$214$	−2.14799	−0.146833
$215$	−26.7943	−1.82736
$216$	0	0
$217$	0	0
$218$	−2.43519	−0.164932
$219$	0	0
$220$	−34.7636	−2.34376
$221$	2.28141	0.153464
$222$	0	0
$223$	22.4737	1.50495	0.752474	−	0.658622i	$-0.228861\pi$
$223$	22.4737	1.50495	0.752474	+	0.658622i	$0.228861\pi$
$224$	0	0
$225$	0	0
$226$	0.323048	0.0214889
$227$	9.20249	0.610791	0.305395	−	0.952226i	$-0.401211\pi$
$227$	9.20249	0.610791	0.305395	+	0.952226i	$0.401211\pi$
$228$	0	0
$229$	15.2922	1.01054	0.505269	−	0.862962i	$-0.331393\pi$
$229$	15.2922	1.01054	0.505269	+	0.862962i	$0.331393\pi$
$230$	1.33895	0.0882880
$231$	0	0
$232$	1.27983	0.0840247
$233$	8.05579	0.527752	0.263876	−	0.964557i	$-0.414999\pi$
$233$	8.05579	0.527752	0.263876	+	0.964557i	$0.414999\pi$
$234$	0	0
$235$	13.9424	0.909504
$236$	8.84004	0.575438
$237$	0	0
$238$	0	0
$239$	−21.7258	−1.40533	−0.702663	−	0.711523i	$-0.748006\pi$
$239$	−21.7258	−1.40533	−0.702663	+	0.711523i	$0.748006\pi$
$240$	0	0
$241$	−20.4980	−1.32039	−0.660195	−	0.751094i	$-0.729527\pi$
$241$	−20.4980	−1.32039	−0.660195	+	0.751094i	$0.729527\pi$
$242$	1.82088	0.117050
$243$	0	0
$244$	−14.8005	−0.947507
$245$	0	0
$246$	0	0
$247$	−1.78768	−0.113748
$248$	−4.34481	−0.275896
$249$	0	0
$250$	−4.20460	−0.265922
$251$	−2.60871	−0.164660	−0.0823301	−	0.996605i	$-0.526236\pi$
$251$	−2.60871	−0.164660	−0.0823301	+	0.996605i	$0.526236\pi$
$252$	0	0
$253$	7.84187	0.493014
$254$	−0.879078	−0.0551583
$255$	0	0
$256$	13.0246	0.814040
$257$	8.99676	0.561202	0.280601	−	0.959824i	$-0.409466\pi$
$257$	8.99676	0.561202	0.280601	+	0.959824i	$0.409466\pi$
$258$	0	0
$259$	0	0
$260$	7.71448	0.478432
$261$	0	0
$262$	2.47637	0.152990
$263$	−1.43392	−0.0884194	−0.0442097	−	0.999022i	$-0.514077\pi$
$263$	−1.43392	−0.0884194	−0.0442097	+	0.999022i	$0.514077\pi$
$264$	0	0
$265$	12.9366	0.794689
$266$	0	0
$267$	0	0
$268$	24.8457	1.51769
$269$	8.16832	0.498031	0.249016	−	0.968499i	$-0.419893\pi$
$269$	8.16832	0.498031	0.249016	+	0.968499i	$0.419893\pi$
$270$	0	0
$271$	−0.212317	−0.0128973	−0.00644867	−	0.999979i	$-0.502053\pi$
$271$	−0.212317	−0.0128973	−0.00644867	+	0.999979i	$0.502053\pi$
$272$	8.60497	0.521753
$273$	0	0
$274$	1.81695	0.109766
$275$	−47.1565	−2.84364
$276$	0	0
$277$	22.9749	1.38043	0.690215	−	0.723604i	$-0.257516\pi$
$277$	22.9749	1.38043	0.690215	+	0.723604i	$0.257516\pi$
$278$	−0.782625	−0.0469387
$279$	0	0
$280$	0	0
$281$	0.345228	0.0205946	0.0102973	−	0.999947i	$-0.496722\pi$
$281$	0.345228	0.0205946	0.0102973	+	0.999947i	$0.496722\pi$
$282$	0	0
$283$	−28.9715	−1.72217	−0.861087	−	0.508457i	$-0.830216\pi$
$283$	−28.9715	−1.72217	−0.861087	+	0.508457i	$0.830216\pi$
$284$	18.7318	1.11153
$285$	0	0
$286$	−0.881681	−0.0521349
$287$	0	0
$288$	0	0
$289$	−11.7952	−0.693834
$290$	1.27039	0.0745999
$291$	0	0
$292$	−2.11873	−0.123989
$293$	−31.5427	−1.84274	−0.921372	−	0.388682i	$-0.872930\pi$
$293$	−31.5427	−1.84274	−0.921372	+	0.388682i	$0.872930\pi$
$294$	0	0
$295$	17.7210	1.03175
$296$	−5.53762	−0.321868
$297$	0	0
$298$	2.96710	0.171880
$299$	−1.74021	−0.100639
$300$	0	0
$301$	0	0
$302$	1.00598	0.0578879
$303$	0	0
$304$	−6.74274	−0.386723
$305$	−29.6695	−1.69887
$306$	0	0
$307$	−18.1941	−1.03839	−0.519197	−	0.854655i	$-0.673769\pi$
$307$	−18.1941	−1.03839	−0.519197	+	0.854655i	$0.673769\pi$
$308$	0	0
$309$	0	0
$310$	−4.31278	−0.244949
$311$	0.376623	0.0213563	0.0106782	−	0.999943i	$-0.496601\pi$
$311$	0.376623	0.0213563	0.0106782	+	0.999943i	$0.496601\pi$
$312$	0	0
$313$	10.9883	0.621095	0.310548	−	0.950558i	$-0.399488\pi$
$313$	10.9883	0.621095	0.310548	+	0.950558i	$0.399488\pi$
$314$	−2.09961	−0.118488
$315$	0	0
$316$	−1.55309	−0.0873680
$317$	−26.1806	−1.47045	−0.735225	−	0.677823i	$-0.762923\pi$
$317$	−26.1806	−1.47045	−0.735225	+	0.677823i	$0.762923\pi$
$318$	0	0
$319$	7.44031	0.416578
$320$	27.9045	1.55991
$321$	0	0
$322$	0	0
$323$	−4.07844	−0.226930
$324$	0	0
$325$	10.4646	0.580473
$326$	0.464174	0.0257082
$327$	0	0
$328$	−6.29079	−0.347351
$329$	0	0
$330$	0	0
$331$	−34.0932	−1.87393	−0.936967	−	0.349419i	$-0.886379\pi$
$331$	−34.0932	−1.87393	−0.936967	+	0.349419i	$0.886379\pi$
$332$	−14.0193	−0.769408
$333$	0	0
$334$	−2.36321	−0.129309
$335$	49.8062	2.72120
$336$	0	0
$337$	14.7532	0.803657	0.401829	−	0.915715i	$-0.368375\pi$
$337$	14.7532	0.803657	0.401829	+	0.915715i	$0.368375\pi$
$338$	0.195656	0.0106423
$339$	0	0
$340$	17.5999	0.954487
$341$	−25.2587	−1.36784
$342$	0	0
$343$	0	0
$344$	−5.28141	−0.284754
$345$	0	0
$346$	3.79763	0.204162
$347$	−29.9466	−1.60762	−0.803809	−	0.594888i	$-0.797196\pi$
$347$	−29.9466	−1.60762	−0.803809	+	0.594888i	$0.797196\pi$
$348$	0	0
$349$	−13.4793	−0.721532	−0.360766	−	0.932656i	$-0.617485\pi$
$349$	−13.4793	−0.721532	−0.360766	+	0.932656i	$0.617485\pi$
$350$	0	0
$351$	0	0
$352$	−10.3114	−0.549602
$353$	−0.163532	−0.00870392	−0.00435196	−	0.999991i	$-0.501385\pi$
$353$	−0.163532	−0.00870392	−0.00435196	+	0.999991i	$0.501385\pi$
$354$	0	0
$355$	37.5503	1.99296
$356$	−22.1000	−1.17130
$357$	0	0
$358$	−2.86527	−0.151434
$359$	−8.92130	−0.470848	−0.235424	−	0.971893i	$-0.575648\pi$
$359$	−8.92130	−0.470848	−0.235424	+	0.971893i	$0.575648\pi$
$360$	0	0
$361$	−15.8042	−0.831799
$362$	−1.84822	−0.0971404
$363$	0	0
$364$	0	0
$365$	−4.24726	−0.222312
$366$	0	0
$367$	36.6552	1.91339	0.956693	−	0.291098i	$-0.0940207\pi$
$367$	36.6552	1.91339	0.956693	+	0.291098i	$0.0940207\pi$
$368$	−6.56369	−0.342156
$369$	0	0
$370$	−5.49679	−0.285765
$371$	0	0
$372$	0	0
$373$	27.1274	1.40460	0.702302	−	0.711879i	$-0.252156\pi$
$373$	27.1274	1.40460	0.702302	+	0.711879i	$0.252156\pi$
$374$	−2.01147	−0.104011
$375$	0	0
$376$	2.74819	0.141727
$377$	−1.65110	−0.0850360
$378$	0	0
$379$	−15.8943	−0.816434	−0.408217	−	0.912885i	$-0.633849\pi$
$379$	−15.8943	−0.816434	−0.408217	+	0.912885i	$0.633849\pi$
$380$	−13.7910	−0.707465
$381$	0	0
$382$	−2.45622	−0.125671
$383$	−1.15079	−0.0588025	−0.0294013	−	0.999568i	$-0.509360\pi$
$383$	−1.15079	−0.0588025	−0.0294013	+	0.999568i	$0.509360\pi$
$384$	0	0
$385$	0	0
$386$	−1.83302	−0.0932985
$387$	0	0
$388$	17.2897	0.877750
$389$	14.3130	0.725699	0.362850	−	0.931848i	$-0.381804\pi$
$389$	14.3130	0.725699	0.362850	+	0.931848i	$0.381804\pi$
$390$	0	0
$391$	−3.97013	−0.200778
$392$	0	0
$393$	0	0
$394$	1.49144	0.0751377
$395$	−3.11336	−0.156650
$396$	0	0
$397$	−25.9176	−1.30077	−0.650383	−	0.759607i	$-0.725391\pi$
$397$	−25.9176	−1.30077	−0.650383	+	0.759607i	$0.725391\pi$
$398$	2.64701	0.132682
$399$	0	0
$400$	39.4703	1.97351
$401$	4.29631	0.214548	0.107274	−	0.994230i	$-0.465788\pi$
$401$	4.29631	0.214548	0.107274	+	0.994230i	$0.465788\pi$
$402$	0	0
$403$	5.60523	0.279216
$404$	−28.0861	−1.39734
$405$	0	0
$406$	0	0
$407$	−32.1931	−1.59575
$408$	0	0
$409$	−24.7071	−1.22169	−0.610844	−	0.791751i	$-0.709170\pi$
$409$	−24.7071	−1.22169	−0.610844	+	0.791751i	$0.709170\pi$
$410$	−6.24441	−0.308389
$411$	0	0
$412$	14.6975	0.724093
$413$	0	0
$414$	0	0
$415$	−28.1034	−1.37954
$416$	2.28824	0.112190
$417$	0	0
$418$	1.57617	0.0770928
$419$	24.9293	1.21787	0.608937	−	0.793218i	$-0.291596\pi$
$419$	24.9293	1.21787	0.608937	+	0.793218i	$0.291596\pi$
$420$	0	0
$421$	−10.0000	−0.487370	−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000	−0.487370	−0.243685	+	0.969854i	$0.578356\pi$
$422$	−3.09127	−0.150480
$423$	0	0
$424$	2.54993	0.123835
$425$	23.8741	1.15806
$426$	0	0
$427$	0	0
$428$	21.5365	1.04101
$429$	0	0
$430$	−5.24247	−0.252814
$431$	5.68851	0.274006	0.137003	−	0.990571i	$-0.456253\pi$
$431$	5.68851	0.274006	0.137003	+	0.990571i	$0.456253\pi$
$432$	0	0
$433$	12.2598	0.589169	0.294584	−	0.955625i	$-0.404819\pi$
$433$	12.2598	0.589169	0.294584	+	0.955625i	$0.404819\pi$
$434$	0	0
$435$	0	0
$436$	24.4161	1.16932
$437$	3.11095	0.148817
$438$	0	0
$439$	5.02317	0.239743	0.119871	−	0.992789i	$-0.461752\pi$
$439$	5.02317	0.239743	0.119871	+	0.992789i	$0.461752\pi$
$440$	−13.7361	−0.654845
$441$	0	0
$442$	0.446372	0.0212317
$443$	−0.578803	−0.0274997	−0.0137499	−	0.999905i	$-0.504377\pi$
$443$	−0.578803	−0.0274997	−0.0137499	+	0.999905i	$0.504377\pi$
$444$	0	0
$445$	−44.3022	−2.10012
$446$	4.39711	0.208209
$447$	0	0
$448$	0	0
$449$	7.36359	0.347509	0.173755	−	0.984789i	$-0.444410\pi$
$449$	7.36359	0.347509	0.173755	+	0.984789i	$0.444410\pi$
$450$	0	0
$451$	−36.5717	−1.72210
$452$	−3.23900	−0.152350
$453$	0	0
$454$	1.80052	0.0845028
$455$	0	0
$456$	0	0
$457$	7.91824	0.370399	0.185200	−	0.982701i	$-0.440707\pi$
$457$	7.91824	0.370399	0.185200	+	0.982701i	$0.440707\pi$
$458$	2.99202	0.139808
$459$	0	0
$460$	−13.4248	−0.625936
$461$	9.53600	0.444136	0.222068	−	0.975031i	$-0.428719\pi$
$461$	9.53600	0.444136	0.222068	+	0.975031i	$0.428719\pi$
$462$	0	0
$463$	2.16049	0.100406	0.0502032	−	0.998739i	$-0.484013\pi$
$463$	2.16049	0.100406	0.0502032	+	0.998739i	$0.484013\pi$
$464$	−6.22758	−0.289108
$465$	0	0
$466$	1.57617	0.0730145
$467$	8.11900	0.375702	0.187851	−	0.982198i	$-0.439848\pi$
$467$	8.11900	0.375702	0.187851	+	0.982198i	$0.439848\pi$
$468$	0	0
$469$	0	0
$470$	2.72792	0.125830
$471$	0	0
$472$	3.49297	0.160777
$473$	−30.7036	−1.41176
$474$	0	0
$475$	−18.7074	−0.858357
$476$	0	0
$477$	0	0
$478$	−4.25079	−0.194427
$479$	−14.5533	−0.664955	−0.332478	−	0.943111i	$-0.607885\pi$
$479$	−14.5533	−0.664955	−0.332478	+	0.943111i	$0.607885\pi$
$480$	0	0
$481$	7.14407	0.325742
$482$	−4.01056	−0.182676
$483$	0	0
$484$	−18.2567	−0.829852
$485$	34.6593	1.57380
$486$	0	0
$487$	−33.2590	−1.50711	−0.753554	−	0.657386i	$-0.771662\pi$
$487$	−33.2590	−1.50711	−0.753554	+	0.657386i	$0.771662\pi$
$488$	−5.84814	−0.264733
$489$	0	0
$490$	0	0
$491$	22.5563	1.01795	0.508977	−	0.860780i	$-0.330024\pi$
$491$	22.5563	1.01795	0.508977	+	0.860780i	$0.330024\pi$
$492$	0	0
$493$	−3.76684	−0.169650
$494$	−0.349771	−0.0157370
$495$	0	0
$496$	21.1417	0.949290
$497$	0	0
$498$	0	0
$499$	−11.3854	−0.509682	−0.254841	−	0.966983i	$-0.582023\pi$
$499$	−11.3854	−0.509682	−0.254841	+	0.966983i	$0.582023\pi$
$500$	42.1568	1.88531
$501$	0	0
$502$	−0.510410	−0.0227807
$503$	8.81825	0.393186	0.196593	−	0.980485i	$-0.437012\pi$
$503$	8.81825	0.393186	0.196593	+	0.980485i	$0.437012\pi$
$504$	0	0
$505$	−56.3022	−2.50541
$506$	1.53431	0.0682084
$507$	0	0
$508$	8.81394	0.391056
$509$	−19.2838	−0.854738	−0.427369	−	0.904077i	$-0.640559\pi$
$509$	−19.2838	−0.854738	−0.427369	+	0.904077i	$0.640559\pi$
$510$	0	0
$511$	0	0
$512$	14.4780	0.639844
$513$	0	0
$514$	1.76027	0.0776423
$515$	29.4629	1.29829
$516$	0	0
$517$	15.9767	0.702653
$518$	0	0
$519$	0	0
$520$	3.04823	0.133674
$521$	−25.1168	−1.10039	−0.550193	−	0.835037i	$-0.685446\pi$
$521$	−25.1168	−1.10039	−0.550193	+	0.835037i	$0.685446\pi$
$522$	0	0
$523$	−29.9648	−1.31027	−0.655134	−	0.755513i	$-0.727388\pi$
$523$	−29.9648	−1.31027	−0.655134	+	0.755513i	$0.727388\pi$
$524$	−24.8289	−1.08466
$525$	0	0
$526$	−0.280556	−0.0122328
$527$	12.7878	0.557046
$528$	0	0
$529$	−19.9717	−0.868333
$530$	2.53113	0.109945
$531$	0	0
$532$	0	0
$533$	8.11574	0.351532
$534$	0	0
$535$	43.1726	1.86651
$536$	9.81728	0.424042
$537$	0	0
$538$	1.59818	0.0689026
$539$	0	0
$540$	0	0
$541$	5.09973	0.219255	0.109627	−	0.993973i	$-0.465034\pi$
$541$	5.09973	0.219255	0.109627	+	0.993973i	$0.465034\pi$
$542$	−0.0415412	−0.00178435
$543$	0	0
$544$	5.22042	0.223823
$545$	48.9451	2.09658
$546$	0	0
$547$	2.92025	0.124861	0.0624305	−	0.998049i	$-0.480115\pi$
$547$	2.92025	0.124861	0.0624305	+	0.998049i	$0.480115\pi$
$548$	−18.2173	−0.778206
$549$	0	0
$550$	−9.22647	−0.393418
$551$	2.95165	0.125744
$552$	0	0
$553$	0	0
$554$	4.49519	0.190982
$555$	0	0
$556$	7.84687	0.332782
$557$	−25.9874	−1.10112	−0.550561	−	0.834795i	$-0.685586\pi$
$557$	−25.9874	−1.10112	−0.550561	+	0.834795i	$0.685586\pi$
$558$	0	0
$559$	6.81353	0.288182
$560$	0	0
$561$	0	0
$562$	0.0675460	0.00284925
$563$	−3.65069	−0.153858	−0.0769291	−	0.997037i	$-0.524512\pi$
$563$	−3.65069	−0.153858	−0.0769291	+	0.997037i	$0.524512\pi$
$564$	0	0
$565$	−6.49297	−0.273161
$566$	−5.66845	−0.238263
$567$	0	0
$568$	7.40152	0.310561
$569$	25.3533	1.06286	0.531432	−	0.847101i	$-0.321654\pi$
$569$	25.3533	1.06286	0.531432	+	0.847101i	$0.321654\pi$
$570$	0	0
$571$	27.7253	1.16027	0.580133	−	0.814522i	$-0.303000\pi$
$571$	27.7253	1.16027	0.580133	+	0.814522i	$0.303000\pi$
$572$	8.84004	0.369621
$573$	0	0
$574$	0	0
$575$	−18.2107	−0.759438
$576$	0	0
$577$	39.5754	1.64755	0.823773	−	0.566920i	$-0.191865\pi$
$577$	39.5754	1.64755	0.823773	+	0.566920i	$0.191865\pi$
$578$	−2.30780	−0.0959918
$579$	0	0
$580$	−12.7374	−0.528891
$581$	0	0
$582$	0	0
$583$	14.8241	0.613951
$584$	−0.837175	−0.0346426
$585$	0	0
$586$	−6.17153	−0.254943
$587$	8.24177	0.340174	0.170087	−	0.985429i	$-0.445595\pi$
$587$	8.24177	0.340174	0.170087	+	0.985429i	$0.445595\pi$
$588$	0	0
$589$	−10.0204	−0.412882
$590$	3.46722	0.142743
$591$	0	0
$592$	26.9458	1.10747
$593$	11.9230	0.489618	0.244809	−	0.969571i	$-0.421275\pi$
$593$	11.9230	0.489618	0.244809	+	0.969571i	$0.421275\pi$
$594$	0	0
$595$	0	0
$596$	−29.7492	−1.21857
$597$	0	0
$598$	−0.340483	−0.0139234
$599$	35.6158	1.45522	0.727611	−	0.685990i	$-0.240631\pi$
$599$	35.6158	1.45522	0.727611	+	0.685990i	$0.240631\pi$
$600$	0	0
$601$	38.9252	1.58779	0.793896	−	0.608054i	$-0.208050\pi$
$601$	38.9252	1.58779	0.793896	+	0.608054i	$0.208050\pi$
$602$	0	0
$603$	0	0
$604$	−10.0863	−0.410408
$605$	−36.5979	−1.48792
$606$	0	0
$607$	−13.6966	−0.555926	−0.277963	−	0.960592i	$-0.589659\pi$
$607$	−13.6966	−0.555926	−0.277963	+	0.960592i	$0.589659\pi$
$608$	−4.09065	−0.165898
$609$	0	0
$610$	−5.80502	−0.235039
$611$	−3.54543	−0.143433
$612$	0	0
$613$	3.16112	0.127676	0.0638382	−	0.997960i	$-0.479666\pi$
$613$	3.16112	0.127676	0.0638382	+	0.997960i	$0.479666\pi$
$614$	−3.55979	−0.143662
$615$	0	0
$616$	0	0
$617$	−20.9297	−0.842597	−0.421299	−	0.906922i	$-0.638426\pi$
$617$	−20.9297	−0.842597	−0.421299	+	0.906922i	$0.638426\pi$
$618$	0	0
$619$	30.9544	1.24416	0.622082	−	0.782952i	$-0.286287\pi$
$619$	30.9544	1.24416	0.622082	+	0.782952i	$0.286287\pi$
$620$	43.2414	1.73662
$621$	0	0
$622$	0.0736887	0.00295465
$623$	0	0
$624$	0	0
$625$	32.1854	1.28742
$626$	2.14993	0.0859285
$627$	0	0
$628$	21.0515	0.840045
$629$	16.2986	0.649866
$630$	0	0
$631$	−15.1218	−0.601988	−0.300994	−	0.953626i	$-0.597318\pi$
$631$	−15.1218	−0.601988	−0.300994	+	0.953626i	$0.597318\pi$
$632$	−0.613673	−0.0244106
$633$	0	0
$634$	−5.12240	−0.203437
$635$	17.6687	0.701159
$636$	0	0
$637$	0	0
$638$	1.45574	0.0576335
$639$	0	0
$640$	23.4568	0.927210
$641$	47.2414	1.86592	0.932962	−	0.359976i	$-0.117215\pi$
$641$	47.2414	1.86592	0.932962	+	0.359976i	$0.117215\pi$
$642$	0	0
$643$	39.9249	1.57448	0.787241	−	0.616645i	$-0.211509\pi$
$643$	39.9249	1.57448	0.787241	+	0.616645i	$0.211509\pi$
$644$	0	0
$645$	0	0
$646$	−0.797972	−0.0313958
$647$	29.8278	1.17265	0.586327	−	0.810075i	$-0.300574\pi$
$647$	29.8278	1.17265	0.586327	+	0.810075i	$0.300574\pi$
$648$	0	0
$649$	20.3065	0.797100
$650$	2.04747	0.0803084
$651$	0	0
$652$	−4.65397	−0.182263
$653$	−25.1549	−0.984387	−0.492194	−	0.870486i	$-0.663805\pi$
$653$	−25.1549	−0.984387	−0.492194	+	0.870486i	$0.663805\pi$
$654$	0	0
$655$	−49.7727	−1.94478
$656$	30.6107	1.19515
$657$	0	0
$658$	0	0
$659$	−17.3155	−0.674517	−0.337258	−	0.941412i	$-0.609500\pi$
$659$	−17.3155	−0.674517	−0.337258	+	0.941412i	$0.609500\pi$
$660$	0	0
$661$	−9.20074	−0.357867	−0.178934	−	0.983861i	$-0.557265\pi$
$661$	−9.20074	−0.357867	−0.178934	+	0.983861i	$0.557265\pi$
$662$	−6.67055	−0.259258
$663$	0	0
$664$	−5.53945	−0.214972
$665$	0	0
$666$	0	0
$667$	2.87327	0.111253
$668$	23.6944	0.916763
$669$	0	0
$670$	9.74490	0.376478
$671$	−33.9984	−1.31249
$672$	0	0
$673$	17.3609	0.669212	0.334606	−	0.942358i	$-0.391397\pi$
$673$	17.3609	0.669212	0.334606	+	0.942358i	$0.391397\pi$
$674$	2.88655	0.111186
$675$	0	0
$676$	−1.96172	−0.0754507
$677$	−49.9825	−1.92098	−0.960492	−	0.278307i	$-0.910227\pi$
$677$	−49.9825	−1.92098	−0.960492	+	0.278307i	$0.910227\pi$
$678$	0	0
$679$	0	0
$680$	6.95425	0.266683
$681$	0	0
$682$	−4.94202	−0.189240
$683$	−33.6153	−1.28626	−0.643128	−	0.765759i	$-0.722364\pi$
$683$	−33.6153	−1.28626	−0.643128	+	0.765759i	$0.722364\pi$
$684$	0	0
$685$	−36.5189	−1.39532
$686$	0	0
$687$	0	0
$688$	25.6991	0.979770
$689$	−3.28965	−0.125326
$690$	0	0
$691$	−15.1309	−0.575607	−0.287803	−	0.957689i	$-0.592925\pi$
$691$	−15.1309	−0.575607	−0.287803	+	0.957689i	$0.592925\pi$
$692$	−38.0764	−1.44745
$693$	0	0
$694$	−5.85924	−0.222414
$695$	15.7300	0.596674
$696$	0	0
$697$	18.5153	0.701317
$698$	−2.63731	−0.0998238
$699$	0	0
$700$	0	0
$701$	−2.02467	−0.0764705	−0.0382353	−	0.999269i	$-0.512174\pi$
$701$	−2.02467	−0.0764705	−0.0382353	+	0.999269i	$0.512174\pi$
$702$	0	0
$703$	−12.7713	−0.481680
$704$	31.9758	1.20513
$705$	0	0
$706$	−0.0319960	−0.00120419
$707$	0	0
$708$	0	0
$709$	−30.4553	−1.14377	−0.571886	−	0.820333i	$-0.693788\pi$
$709$	−30.4553	−1.14377	−0.571886	+	0.820333i	$0.693788\pi$
$710$	7.34695	0.275726
$711$	0	0
$712$	−8.73238	−0.327260
$713$	−9.75429	−0.365301
$714$	0	0
$715$	17.7210	0.662727
$716$	28.7282	1.07362
$717$	0	0
$718$	−1.74551	−0.0651418
$719$	24.4246	0.910883	0.455442	−	0.890266i	$-0.349481\pi$
$719$	24.4246	0.910883	0.455442	+	0.890266i	$0.349481\pi$
$720$	0	0
$721$	0	0
$722$	−3.09219	−0.115079
$723$	0	0
$724$	18.5309	0.688697
$725$	−17.2782	−0.641695
$726$	0	0
$727$	−3.09307	−0.114716	−0.0573578	−	0.998354i	$-0.518268\pi$
$727$	−3.09307	−0.114716	−0.0573578	+	0.998354i	$0.518268\pi$
$728$	0	0
$729$	0	0
$730$	−0.831003	−0.0307568
$731$	15.5445	0.574933
$732$	0	0
$733$	−8.41427	−0.310788	−0.155394	−	0.987853i	$-0.549665\pi$
$733$	−8.41427	−0.310788	−0.155394	+	0.987853i	$0.549665\pi$
$734$	7.17182	0.264717
$735$	0	0
$736$	−3.98203	−0.146779
$737$	57.0731	2.10231
$738$	0	0
$739$	−7.22758	−0.265871	−0.132936	−	0.991125i	$-0.542440\pi$
$739$	−7.22758	−0.265871	−0.132936	+	0.991125i	$0.542440\pi$
$740$	55.1128	2.02599
$741$	0	0
$742$	0	0
$743$	53.9092	1.97774	0.988869	−	0.148791i	$-0.0475383\pi$
$743$	53.9092	1.97774	0.988869	+	0.148791i	$0.0475383\pi$
$744$	0	0
$745$	−59.6360	−2.18489
$746$	5.30765	0.194327
$747$	0	0
$748$	20.1678	0.737406
$749$	0	0
$750$	0	0
$751$	29.2442	1.06714	0.533568	−	0.845757i	$-0.320851\pi$
$751$	29.2442	1.06714	0.533568	+	0.845757i	$0.320851\pi$
$752$	−13.3726	−0.487647
$753$	0	0
$754$	−0.323048	−0.0117647
$755$	−20.2193	−0.735857
$756$	0	0
$757$	−22.0597	−0.801773	−0.400887	−	0.916128i	$-0.631298\pi$
$757$	−22.0597	−0.801773	−0.400887	+	0.916128i	$0.631298\pi$
$758$	−3.10981	−0.112954
$759$	0	0
$760$	−5.44926	−0.197666
$761$	−17.8161	−0.645833	−0.322917	−	0.946427i	$-0.604663\pi$
$761$	−17.8161	−0.645833	−0.322917	+	0.946427i	$0.604663\pi$
$762$	0	0
$763$	0	0
$764$	24.6269	0.890971
$765$	0	0
$766$	−0.225159	−0.00813532
$767$	−4.50627	−0.162712
$768$	0	0
$769$	−11.3069	−0.407738	−0.203869	−	0.978998i	$-0.565352\pi$
$769$	−11.3069	−0.407738	−0.203869	+	0.978998i	$0.565352\pi$
$770$	0	0
$771$	0	0
$772$	18.3785	0.661458
$773$	1.92821	0.0693528	0.0346764	−	0.999399i	$-0.488960\pi$
$773$	1.92821	0.0693528	0.0346764	+	0.999399i	$0.488960\pi$
$774$	0	0
$775$	58.6567	2.10701
$776$	6.83168	0.245243
$777$	0	0
$778$	2.80043	0.100400
$779$	−14.5084	−0.519816
$780$	0	0
$781$	43.0290	1.53970
$782$	−0.776782	−0.0277777
$783$	0	0
$784$	0	0
$785$	42.2003	1.50619
$786$	0	0
$787$	5.53155	0.197178	0.0985892	−	0.995128i	$-0.468567\pi$
$787$	5.53155	0.197178	0.0985892	+	0.995128i	$0.468567\pi$
$788$	−14.9537	−0.532704
$789$	0	0
$790$	−0.609148	−0.0216725
$791$	0	0
$792$	0	0
$793$	7.54467	0.267919
$794$	−5.07093	−0.179961
$795$	0	0
$796$	−26.5398	−0.940679
$797$	13.8038	0.488955	0.244477	−	0.969655i	$-0.421384\pi$
$797$	13.8038	0.488955	0.244477	+	0.969655i	$0.421384\pi$
$798$	0	0
$799$	−8.08857	−0.286153
$800$	23.9456	0.846605
$801$	0	0
$802$	0.840601	0.0296826
$803$	−4.86695	−0.171751
$804$	0	0
$805$	0	0
$806$	1.09670	0.0386296
$807$	0	0
$808$	−11.0977	−0.390415
$809$	−28.2996	−0.994961	−0.497480	−	0.867475i	$-0.665741\pi$
$809$	−28.2996	−0.994961	−0.497480	+	0.867475i	$0.665741\pi$
$810$	0	0
$811$	−12.2124	−0.428837	−0.214418	−	0.976742i	$-0.568786\pi$
$811$	−12.2124	−0.428837	−0.214418	+	0.976742i	$0.568786\pi$
$812$	0	0
$813$	0	0
$814$	−6.29879	−0.220772
$815$	−9.32946	−0.326797
$816$	0	0
$817$	−12.1804	−0.426140
$818$	−4.83410	−0.169020
$819$	0	0
$820$	62.6087	2.18639
$821$	41.4011	1.44491	0.722453	−	0.691420i	$-0.243014\pi$
$821$	41.4011	1.44491	0.722453	+	0.691420i	$0.243014\pi$
$822$	0	0
$823$	47.1752	1.64443	0.822213	−	0.569180i	$-0.192739\pi$
$823$	47.1752	1.64443	0.822213	+	0.569180i	$0.192739\pi$
$824$	5.80742	0.202311
$825$	0	0
$826$	0	0
$827$	−21.1124	−0.734150	−0.367075	−	0.930191i	$-0.619641\pi$
$827$	−21.1124	−0.734150	−0.367075	+	0.930191i	$0.619641\pi$
$828$	0	0
$829$	−0.636752	−0.0221153	−0.0110577	−	0.999939i	$-0.503520\pi$
$829$	−0.636752	−0.0221153	−0.0110577	+	0.999939i	$0.503520\pi$
$830$	−5.49861	−0.190859
$831$	0	0
$832$	−7.09585	−0.246004
$833$	0	0
$834$	0	0
$835$	47.4983	1.64375
$836$	−15.8032	−0.546565
$837$	0	0
$838$	4.87757	0.168493
$839$	26.9432	0.930183	0.465092	−	0.885263i	$-0.346021\pi$
$839$	26.9432	0.930183	0.465092	+	0.885263i	$0.346021\pi$
$840$	0	0
$841$	−26.2739	−0.905995
$842$	−1.95656	−0.0674276
$843$	0	0
$844$	30.9941	1.06686
$845$	−3.93251	−0.135282
$846$	0	0
$847$	0	0
$848$	−12.4078	−0.426087
$849$	0	0
$850$	4.67112	0.160218
$851$	−12.4322	−0.426170
$852$	0	0
$853$	6.74784	0.231042	0.115521	−	0.993305i	$-0.463146\pi$
$853$	6.74784	0.231042	0.115521	+	0.993305i	$0.463146\pi$
$854$	0	0
$855$	0	0
$856$	8.50973	0.290856
$857$	45.0268	1.53809	0.769043	−	0.639197i	$-0.220733\pi$
$857$	45.0268	1.53809	0.769043	+	0.639197i	$0.220733\pi$
$858$	0	0
$859$	−36.7270	−1.25311	−0.626554	−	0.779378i	$-0.715535\pi$
$859$	−36.7270	−1.25311	−0.626554	+	0.779378i	$0.715535\pi$
$860$	52.5629	1.79238
$861$	0	0
$862$	1.11299	0.0379087
$863$	43.4275	1.47829	0.739144	−	0.673547i	$-0.235230\pi$
$863$	43.4275	1.47829	0.739144	+	0.673547i	$0.235230\pi$
$864$	0	0
$865$	−76.3288	−2.59526
$866$	2.39871	0.0815114
$867$	0	0
$868$	0	0
$869$	−3.56761	−0.121023
$870$	0	0
$871$	−12.6653	−0.429146
$872$	9.64754	0.326707
$873$	0	0
$874$	0.608676	0.0205888
$875$	0	0
$876$	0	0
$877$	40.0081	1.35098	0.675488	−	0.737371i	$-0.263933\pi$
$877$	40.0081	1.35098	0.675488	+	0.737371i	$0.263933\pi$
$878$	0.982815	0.0331684
$879$	0	0
$880$	66.8395	2.25316
$881$	−35.4308	−1.19370	−0.596848	−	0.802355i	$-0.703580\pi$
$881$	−35.4308	−1.19370	−0.596848	+	0.802355i	$0.703580\pi$
$882$	0	0
$883$	22.6654	0.762751	0.381375	−	0.924420i	$-0.375451\pi$
$883$	22.6654	0.762751	0.381375	+	0.924420i	$0.375451\pi$
$884$	−4.47548	−0.150527
$885$	0	0
$886$	−0.113246	−0.00380459
$887$	−44.6881	−1.50048	−0.750240	−	0.661166i	$-0.770062\pi$
$887$	−44.6881	−1.50048	−0.750240	+	0.661166i	$0.770062\pi$
$888$	0	0
$889$	0	0
$890$	−8.66800	−0.290552
$891$	0	0
$892$	−44.0870	−1.47614
$893$	6.33810	0.212096
$894$	0	0
$895$	57.5892	1.92499
$896$	0	0
$897$	0	0
$898$	1.44073	0.0480779
$899$	−9.25480	−0.308665
$900$	0	0
$901$	−7.50505	−0.250029
$902$	−7.15549	−0.238252
$903$	0	0
$904$	−1.27983	−0.0425664
$905$	37.1476	1.23483
$906$	0	0
$907$	54.4748	1.80881	0.904403	−	0.426680i	$-0.140317\pi$
$907$	54.4748	1.80881	0.904403	+	0.426680i	$0.140317\pi$
$908$	−18.0527	−0.599100
$909$	0	0
$910$	0	0
$911$	27.4793	0.910431	0.455215	−	0.890381i	$-0.349562\pi$
$911$	27.4793	0.910431	0.455215	+	0.890381i	$0.349562\pi$
$912$	0	0
$913$	−32.2038	−1.06579
$914$	1.54925	0.0512447
$915$	0	0
$916$	−29.9990	−0.991196
$917$	0	0
$918$	0	0
$919$	−48.2880	−1.59287	−0.796437	−	0.604722i	$-0.793284\pi$
$919$	−48.2880	−1.59287	−0.796437	+	0.604722i	$0.793284\pi$
$920$	−5.30456	−0.174886
$921$	0	0
$922$	1.86578	0.0614461
$923$	−9.54869	−0.314299
$924$	0	0
$925$	74.7601	2.45810
$926$	0.422713	0.0138912
$927$	0	0
$928$	−3.77812	−0.124023
$929$	−43.3154	−1.42113	−0.710566	−	0.703631i	$-0.751561\pi$
$929$	−43.3154	−1.42113	−0.710566	+	0.703631i	$0.751561\pi$
$930$	0	0
$931$	0	0
$932$	−15.8032	−0.517651
$933$	0	0
$934$	1.58853	0.0519784
$935$	40.4288	1.32216
$936$	0	0
$937$	−37.2211	−1.21596	−0.607980	−	0.793952i	$-0.708020\pi$
$937$	−37.2211	−1.21596	−0.607980	+	0.793952i	$0.708020\pi$
$938$	0	0
$939$	0	0
$940$	−27.3511	−0.892095
$941$	−15.9751	−0.520773	−0.260386	−	0.965504i	$-0.583850\pi$
$941$	−15.9751	−0.520773	−0.260386	+	0.965504i	$0.583850\pi$
$942$	0	0
$943$	−14.1231	−0.459911
$944$	−16.9967	−0.553194
$945$	0	0
$946$	−6.00736	−0.195316
$947$	−27.7572	−0.901988	−0.450994	−	0.892527i	$-0.648930\pi$
$947$	−27.7572	−0.901988	−0.450994	+	0.892527i	$0.648930\pi$
$948$	0	0
$949$	1.08004	0.0350595
$950$	−3.66023	−0.118754
$951$	0	0
$952$	0	0
$953$	−12.0303	−0.389700	−0.194850	−	0.980833i	$-0.562422\pi$
$953$	−12.0303	−0.389700	−0.194850	+	0.980833i	$0.562422\pi$
$954$	0	0
$955$	49.3677	1.59750
$956$	42.6199	1.37843
$957$	0	0
$958$	−2.84744	−0.0919965
$959$	0	0
$960$	0	0
$961$	0.418620	0.0135039
$962$	1.39778	0.0450663
$963$	0	0
$964$	40.2113	1.29512
$965$	36.8421	1.18599
$966$	0	0
$967$	5.40788	0.173906	0.0869528	−	0.996212i	$-0.472287\pi$
$967$	5.40788	0.173906	0.0869528	+	0.996212i	$0.472287\pi$
$968$	−7.21380	−0.231860
$969$	0	0
$970$	6.78131	0.217735
$971$	−42.2752	−1.35668	−0.678338	−	0.734750i	$-0.737300\pi$
$971$	−42.2752	−1.35668	−0.678338	+	0.734750i	$0.737300\pi$
$972$	0	0
$973$	0	0
$974$	−6.50733	−0.208508
$975$	0	0
$976$	28.4568	0.910881
$977$	10.8302	0.346488	0.173244	−	0.984879i	$-0.444575\pi$
$977$	10.8302	0.346488	0.173244	+	0.984879i	$0.444575\pi$
$978$	0	0
$979$	−50.7660	−1.62249
$980$	0	0
$981$	0	0
$982$	4.41329	0.140834
$983$	−21.5610	−0.687688	−0.343844	−	0.939027i	$-0.611729\pi$
$983$	−21.5610	−0.687688	−0.343844	+	0.939027i	$0.611729\pi$
$984$	0	0
$985$	−29.9766	−0.955134
$986$	−0.737005	−0.0234710
$987$	0	0
$988$	3.50693	0.111570
$989$	−11.8570	−0.377030
$990$	0	0
$991$	8.62624	0.274022	0.137011	−	0.990570i	$-0.456251\pi$
$991$	8.62624	0.274022	0.137011	+	0.990570i	$0.456251\pi$
$992$	12.8261	0.407230
$993$	0	0
$994$	0	0
$995$	−53.2024	−1.68663
$996$	0	0
$997$	21.6967	0.687142	0.343571	−	0.939127i	$-0.388363\pi$
$997$	21.6967	0.687142	0.343571	+	0.939127i	$0.388363\pi$
$998$	−2.22763	−0.0705144
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5733.2.a.bl.1.4		5
3.2	odd	2		637.2.a.l.1.2		5
7.2	even	3		819.2.j.h.235.2		10
7.4	even	3		819.2.j.h.352.2		10
7.6	odd	2		5733.2.a.bm.1.4		5
21.2	odd	6		91.2.e.c.53.4	✓	10
21.5	even	6		637.2.e.m.508.4		10
21.11	odd	6		91.2.e.c.79.4	yes	10
21.17	even	6		637.2.e.m.79.4		10
21.20	even	2		637.2.a.k.1.2		5
39.38	odd	2		8281.2.a.bw.1.4		5
84.11	even	6		1456.2.r.p.625.3		10
84.23	even	6		1456.2.r.p.417.3		10
273.116	odd	6		1183.2.e.f.170.2		10
273.233	odd	6		1183.2.e.f.508.2		10
273.272	even	2		8281.2.a.bx.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.e.c.53.4	✓	10	21.2	odd	6
91.2.e.c.79.4	yes	10	21.11	odd	6
637.2.a.k.1.2		5	21.20	even	2
637.2.a.l.1.2		5	3.2	odd	2
637.2.e.m.79.4		10	21.17	even	6
637.2.e.m.508.4		10	21.5	even	6
819.2.j.h.235.2		10	7.2	even	3
819.2.j.h.352.2		10	7.4	even	3
1183.2.e.f.170.2		10	273.116	odd	6
1183.2.e.f.508.2		10	273.233	odd	6
1456.2.r.p.417.3		10	84.23	even	6
1456.2.r.p.625.3		10	84.11	even	6
5733.2.a.bl.1.4		5	1.1	even	1	trivial
5733.2.a.bm.1.4		5	7.6	odd	2
8281.2.a.bw.1.4		5	39.38	odd	2
8281.2.a.bx.1.4		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)

\(f(q)\)	\(=\)	\(q+0.195656 q^{2} -1.96172 q^{4} -3.93251 q^{5} -0.775135 q^{8} +O(q^{10})\)	\(q+0.195656 q^{2} -1.96172 q^{4} -3.93251 q^{5} -0.775135 q^{8} -0.769420 q^{10} -4.50627 q^{11} +1.00000 q^{13} +3.77178 q^{16} +2.28141 q^{17} -1.78768 q^{19} +7.71448 q^{20} -0.881681 q^{22} -1.74021 q^{23} +10.4646 q^{25} +0.195656 q^{26} -1.65110 q^{29} +5.60523 q^{31} +2.28824 q^{32} +0.446372 q^{34} +7.14407 q^{37} -0.349771 q^{38} +3.04823 q^{40} +8.11574 q^{41} +6.81353 q^{43} +8.84004 q^{44} -0.340483 q^{46} -3.54543 q^{47} +2.04747 q^{50} -1.96172 q^{52} -3.28965 q^{53} +17.7210 q^{55} -0.323048 q^{58} -4.50627 q^{59} +7.54467 q^{61} +1.09670 q^{62} -7.09585 q^{64} -3.93251 q^{65} -12.6653 q^{67} -4.47548 q^{68} -9.54869 q^{71} +1.08004 q^{73} +1.39778 q^{74} +3.50693 q^{76} +0.791698 q^{79} -14.8326 q^{80} +1.58789 q^{82} +7.14643 q^{83} -8.97166 q^{85} +1.33311 q^{86} +3.49297 q^{88} +11.2656 q^{89} +3.41381 q^{92} -0.693685 q^{94} +7.03008 q^{95} -8.81353 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 4 q^{2} + 8 q^{4} - 2 q^{5} - 9 q^{8}+O(q^{10}) \) 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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