LMFDB - Embedded newform 9405.2.a.bv.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9405,2,Mod(1,9405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9405, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("9405.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9405 = 3^{2} \cdot 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9405.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:	$75.0993031010$
Analytic rank:	$0$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 3 x^{18} - 27 x^{17} + 83 x^{16} + 294 x^{15} - 935 x^{14} - 1658 x^{13} + 5548 x^{12} + \cdots - 6 $ x^19 - 3x^18 - 27x^17 + 83x^16 + 294x^15 - 935x^14 - 1658x^13 + 5548x^12 + 5125x^11 - 18696x^10 - 8186x^9 + 35807x^8 + 4532x^7 - 36401x^6 + 3472x^5 + 15888x^4 - 4220x^3 - 997x^2 + 171x - 6
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Root			$2.79030$ of defining polynomial
Character	$\chi$	$=$	9405.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.79030 q^{2} +5.78575 q^{4} +1.00000 q^{5} +0.0343818 q^{7} +10.5634 q^{8} +O(q^{10})$	\(q+2.79030 q^{2} +5.78575 q^{4} +1.00000 q^{5} +0.0343818 q^{7} +10.5634 q^{8} +2.79030 q^{10} +1.00000 q^{11} -6.14793 q^{13} +0.0959355 q^{14} +17.9034 q^{16} +7.20966 q^{17} +1.00000 q^{19} +5.78575 q^{20} +2.79030 q^{22} +2.63929 q^{23} +1.00000 q^{25} -17.1545 q^{26} +0.198925 q^{28} -4.15811 q^{29} +1.13375 q^{31} +28.8291 q^{32} +20.1171 q^{34} +0.0343818 q^{35} +1.24663 q^{37} +2.79030 q^{38} +10.5634 q^{40} -0.237916 q^{41} +6.65040 q^{43} +5.78575 q^{44} +7.36441 q^{46} -2.23067 q^{47} -6.99882 q^{49} +2.79030 q^{50} -35.5704 q^{52} +3.35161 q^{53} +1.00000 q^{55} +0.363188 q^{56} -11.6023 q^{58} +3.09444 q^{59} +1.25542 q^{61} +3.16350 q^{62} +44.6348 q^{64} -6.14793 q^{65} -10.9722 q^{67} +41.7133 q^{68} +0.0959355 q^{70} -9.07612 q^{71} -1.27858 q^{73} +3.47846 q^{74} +5.78575 q^{76} +0.0343818 q^{77} -9.41403 q^{79} +17.9034 q^{80} -0.663857 q^{82} +6.01905 q^{83} +7.20966 q^{85} +18.5566 q^{86} +10.5634 q^{88} +9.21426 q^{89} -0.211377 q^{91} +15.2703 q^{92} -6.22422 q^{94} +1.00000 q^{95} -0.698924 q^{97} -19.5288 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q + 3 q^{2} + 25 q^{4} + 19 q^{5} + 12 q^{7} + 9 q^{8}+O(q^{10}) $ 19 * q + 3 * q^2 + 25 * q^4 + 19 * q^5 + 12 * q^7 + 9 * q^8	$ 19 q + 3 q^{2} + 25 q^{4} + 19 q^{5} + 12 q^{7} + 9 q^{8} + 3 q^{10} + 19 q^{11} + 13 q^{13} + 37 q^{16} + 23 q^{17} + 19 q^{19} + 25 q^{20} + 3 q^{22} + 28 q^{23} + 19 q^{25} - 6 q^{26} + 27 q^{28} + 6 q^{29} + 16 q^{31} + 16 q^{32} + 8 q^{34} + 12 q^{35} + 6 q^{37} + 3 q^{38} + 9 q^{40} + 14 q^{41} + 32 q^{43} + 25 q^{44} + 9 q^{46} + 14 q^{47} + 47 q^{49} + 3 q^{50} + 32 q^{52} + 5 q^{53} + 19 q^{55} - 43 q^{56} + 5 q^{59} + 30 q^{61} - 2 q^{62} + 55 q^{64} + 13 q^{65} + 26 q^{67} + 42 q^{68} - 7 q^{71} + 28 q^{73} - q^{74} + 25 q^{76} + 12 q^{77} + 13 q^{79} + 37 q^{80} + 8 q^{82} + 23 q^{83} + 23 q^{85} - 31 q^{86} + 9 q^{88} - 7 q^{89} + 38 q^{91} + 68 q^{92} + 28 q^{94} + 19 q^{95} + 16 q^{97} - 46 q^{98}+O(q^{100}) $ 19 * q + 3 * q^2 + 25 * q^4 + 19 * q^5 + 12 * q^7 + 9 * q^8 + 3 * q^10 + 19 * q^11 + 13 * q^13 + 37 * q^16 + 23 * q^17 + 19 * q^19 + 25 * q^20 + 3 * q^22 + 28 * q^23 + 19 * q^25 - 6 * q^26 + 27 * q^28 + 6 * q^29 + 16 * q^31 + 16 * q^32 + 8 * q^34 + 12 * q^35 + 6 * q^37 + 3 * q^38 + 9 * q^40 + 14 * q^41 + 32 * q^43 + 25 * q^44 + 9 * q^46 + 14 * q^47 + 47 * q^49 + 3 * q^50 + 32 * q^52 + 5 * q^53 + 19 * q^55 - 43 * q^56 + 5 * q^59 + 30 * q^61 - 2 * q^62 + 55 * q^64 + 13 * q^65 + 26 * q^67 + 42 * q^68 - 7 * q^71 + 28 * q^73 - q^74 + 25 * q^76 + 12 * q^77 + 13 * q^79 + 37 * q^80 + 8 * q^82 + 23 * q^83 + 23 * q^85 - 31 * q^86 + 9 * q^88 - 7 * q^89 + 38 * q^91 + 68 * q^92 + 28 * q^94 + 19 * q^95 + 16 * q^97 - 46 * q^98

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 $

$2$	2.79030	1.97304	0.986519	−	0.163650i	$-0.0523267\pi$
$2$	2.79030	1.97304	0.986519	+	0.163650i	$0.0523267\pi$
$3$	0	0
$3$	0	0
$4$	5.78575	2.89288
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0	0
$7$	0.0343818	0.0129951	0.00649756	−	0.999979i	$-0.497932\pi$
$7$	0.0343818	0.0129951	0.00649756	+	0.999979i	$0.497932\pi$
$8$	10.5634	3.73471
$9$	0	0
$10$	2.79030	0.882369
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0	0
$13$	−6.14793	−1.70513	−0.852565	−	0.522622i	$-0.824954\pi$
$13$	−6.14793	−1.70513	−0.852565	+	0.522622i	$0.824954\pi$
$14$	0.0959355	0.0256398
$15$	0	0
$16$	17.9034	4.47585
$17$	7.20966	1.74860	0.874300	−	0.485385i	$-0.161321\pi$
$17$	7.20966	1.74860	0.874300	+	0.485385i	$0.161321\pi$
$18$	0	0
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	5.78575	1.29373
$21$	0	0
$22$	2.79030	0.594893
$23$	2.63929	0.550330	0.275165	−	0.961397i	$-0.411267\pi$
$23$	2.63929	0.550330	0.275165	+	0.961397i	$0.411267\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	−17.1545	−3.36428
$27$	0	0
$28$	0.198925	0.0375932
$29$	−4.15811	−0.772141	−0.386070	−	0.922469i	$-0.626168\pi$
$29$	−4.15811	−0.772141	−0.386070	+	0.922469i	$0.626168\pi$
$30$	0	0
$31$	1.13375	0.203627	0.101814	−	0.994803i	$-0.467535\pi$
$31$	1.13375	0.203627	0.101814	+	0.994803i	$0.467535\pi$
$32$	28.8291	5.09631
$33$	0	0
$34$	20.1171	3.45005
$35$	0.0343818	0.00581159
$36$	0	0
$37$	1.24663	0.204944	0.102472	−	0.994736i	$-0.467325\pi$
$37$	1.24663	0.204944	0.102472	+	0.994736i	$0.467325\pi$
$38$	2.79030	0.452646
$39$	0	0
$40$	10.5634	1.67021
$41$	−0.237916	−0.0371563	−0.0185781	−	0.999827i	$-0.505914\pi$
$41$	−0.237916	−0.0371563	−0.0185781	+	0.999827i	$0.505914\pi$
$42$	0	0
$43$	6.65040	1.01418	0.507088	−	0.861894i	$-0.330722\pi$
$43$	6.65040	1.01418	0.507088	+	0.861894i	$0.330722\pi$
$44$	5.78575	0.872235
$45$	0	0
$46$	7.36441	1.08582
$47$	−2.23067	−0.325376	−0.162688	−	0.986678i	$-0.552016\pi$
$47$	−2.23067	−0.325376	−0.162688	+	0.986678i	$0.552016\pi$
$48$	0	0
$49$	−6.99882	−0.999831
$50$	2.79030	0.394607
$51$	0	0
$52$	−35.5704	−4.93273
$53$	3.35161	0.460379	0.230189	−	0.973146i	$-0.426065\pi$
$53$	3.35161	0.460379	0.230189	+	0.973146i	$0.426065\pi$
$54$	0	0
$55$	1.00000	0.134840
$56$	0.363188	0.0485330
$57$	0	0
$58$	−11.6023	−1.52346
$59$	3.09444	0.402861	0.201431	−	0.979503i	$-0.435441\pi$
$59$	3.09444	0.402861	0.201431	+	0.979503i	$0.435441\pi$
$60$	0	0
$61$	1.25542	0.160740	0.0803701	−	0.996765i	$-0.474390\pi$
$61$	1.25542	0.160740	0.0803701	+	0.996765i	$0.474390\pi$
$62$	3.16350	0.401764
$63$	0	0
$64$	44.6348	5.57935
$65$	−6.14793	−0.762557
$66$	0	0
$67$	−10.9722	−1.34047	−0.670235	−	0.742149i	$-0.733806\pi$
$67$	−10.9722	−1.34047	−0.670235	+	0.742149i	$0.733806\pi$
$68$	41.7133	5.05848
$69$	0	0
$70$	0.0959355	0.0114665
$71$	−9.07612	−1.07714	−0.538569	−	0.842581i	$-0.681035\pi$
$71$	−9.07612	−1.07714	−0.538569	+	0.842581i	$0.681035\pi$
$72$	0	0
$73$	−1.27858	−0.149646	−0.0748231	−	0.997197i	$-0.523839\pi$
$73$	−1.27858	−0.149646	−0.0748231	+	0.997197i	$0.523839\pi$
$74$	3.47846	0.404363
$75$	0	0
$76$	5.78575	0.663671
$77$	0.0343818	0.00391817
$78$	0	0
$79$	−9.41403	−1.05916	−0.529580	−	0.848260i	$-0.677651\pi$
$79$	−9.41403	−1.05916	−0.529580	+	0.848260i	$0.677651\pi$
$80$	17.9034	2.00166
$81$	0	0
$82$	−0.663857	−0.0733107
$83$	6.01905	0.660676	0.330338	−	0.943863i	$-0.392837\pi$
$83$	6.01905	0.660676	0.330338	+	0.943863i	$0.392837\pi$
$84$	0	0
$85$	7.20966	0.781998
$86$	18.5566	2.00101
$87$	0	0
$88$	10.5634	1.12606
$89$	9.21426	0.976709	0.488355	−	0.872645i	$-0.337597\pi$
$89$	9.21426	0.976709	0.488355	+	0.872645i	$0.337597\pi$
$90$	0	0
$91$	−0.211377	−0.0221584
$92$	15.2703	1.59204
$93$	0	0
$94$	−6.22422	−0.641980
$95$	1.00000	0.102598
$96$	0	0
$97$	−0.698924	−0.0709650	−0.0354825	−	0.999370i	$-0.511297\pi$
$97$	−0.698924	−0.0709650	−0.0354825	+	0.999370i	$0.511297\pi$
$98$	−19.5288	−1.97270
$99$	0	0
$100$	5.78575	0.578575
$101$	19.7265	1.96286	0.981428	−	0.191829i	$-0.0614418\pi$
$101$	19.7265	1.96286	0.981428	+	0.191829i	$0.0614418\pi$
$102$	0	0
$103$	2.03248	0.200266	0.100133	−	0.994974i	$-0.468073\pi$
$103$	2.03248	0.200266	0.100133	+	0.994974i	$0.468073\pi$
$104$	−64.9428	−6.36817
$105$	0	0
$106$	9.35198	0.908344
$107$	3.55989	0.344148	0.172074	−	0.985084i	$-0.444953\pi$
$107$	3.55989	0.344148	0.172074	+	0.985084i	$0.444953\pi$
$108$	0	0
$109$	−13.4728	−1.29046	−0.645228	−	0.763990i	$-0.723238\pi$
$109$	−13.4728	−1.29046	−0.645228	+	0.763990i	$0.723238\pi$
$110$	2.79030	0.266044
$111$	0	0
$112$	0.615552	0.0581642
$113$	1.28133	0.120537	0.0602687	−	0.998182i	$-0.480804\pi$
$113$	1.28133	0.120537	0.0602687	+	0.998182i	$0.480804\pi$
$114$	0	0
$115$	2.63929	0.246115
$116$	−24.0578	−2.23371
$117$	0	0
$118$	8.63440	0.794861
$119$	0.247882	0.0227233
$120$	0	0
$121$	1.00000	0.0909091
$122$	3.50300	0.317147
$123$	0	0
$124$	6.55959	0.589068
$125$	1.00000	0.0894427
$126$	0	0
$127$	−16.0139	−1.42100	−0.710501	−	0.703696i	$-0.751532\pi$
$127$	−16.0139	−1.42100	−0.710501	+	0.703696i	$0.751532\pi$
$128$	66.8862	5.91196
$129$	0	0
$130$	−17.1545	−1.50455
$131$	15.6162	1.36439	0.682195	−	0.731170i	$-0.261025\pi$
$131$	15.6162	1.36439	0.682195	+	0.731170i	$0.261025\pi$
$132$	0	0
$133$	0.0343818	0.00298128
$134$	−30.6157	−2.64480
$135$	0	0
$136$	76.1583	6.53052
$137$	−20.2272	−1.72813	−0.864064	−	0.503382i	$-0.832089\pi$
$137$	−20.2272	−1.72813	−0.864064	+	0.503382i	$0.832089\pi$
$138$	0	0
$139$	6.94140	0.588762	0.294381	−	0.955688i	$-0.404887\pi$
$139$	6.94140	0.588762	0.294381	+	0.955688i	$0.404887\pi$
$140$	0.198925	0.0168122
$141$	0	0
$142$	−25.3251	−2.12523
$143$	−6.14793	−0.514116
$144$	0	0
$145$	−4.15811	−0.345312
$146$	−3.56761	−0.295257
$147$	0	0
$148$	7.21267	0.592878
$149$	9.25712	0.758372	0.379186	−	0.925320i	$-0.376204\pi$
$149$	9.25712	0.758372	0.379186	+	0.925320i	$0.376204\pi$
$150$	0	0
$151$	−23.9439	−1.94852	−0.974262	−	0.225417i	$-0.927625\pi$
$151$	−23.9439	−1.94852	−0.974262	+	0.225417i	$0.927625\pi$
$152$	10.5634	0.856802
$153$	0	0
$154$	0.0959355	0.00773070
$155$	1.13375	0.0910649
$156$	0	0
$157$	4.47378	0.357047	0.178523	−	0.983936i	$-0.442868\pi$
$157$	4.47378	0.357047	0.178523	+	0.983936i	$0.442868\pi$
$158$	−26.2679	−2.08976
$159$	0	0
$160$	28.8291	2.27914
$161$	0.0907437	0.00715161
$162$	0	0
$163$	−2.18587	−0.171211	−0.0856053	−	0.996329i	$-0.527282\pi$
$163$	−2.18587	−0.171211	−0.0856053	+	0.996329i	$0.527282\pi$
$164$	−1.37652	−0.107489
$165$	0	0
$166$	16.7949	1.30354
$167$	13.9985	1.08324	0.541620	−	0.840623i	$-0.317811\pi$
$167$	13.9985	1.08324	0.541620	+	0.840623i	$0.317811\pi$
$168$	0	0
$169$	24.7971	1.90747
$170$	20.1171	1.54291
$171$	0	0
$172$	38.4776	2.93389
$173$	−20.6306	−1.56852	−0.784260	−	0.620433i	$-0.786957\pi$
$173$	−20.6306	−1.56852	−0.784260	+	0.620433i	$0.786957\pi$
$174$	0	0
$175$	0.0343818	0.00259902
$176$	17.9034	1.34952
$177$	0	0
$178$	25.7105	1.92708
$179$	19.5863	1.46395	0.731973	−	0.681334i	$-0.238600\pi$
$179$	19.5863	1.46395	0.731973	+	0.681334i	$0.238600\pi$
$180$	0	0
$181$	−12.2829	−0.912977	−0.456489	−	0.889729i	$-0.650893\pi$
$181$	−12.2829	−0.912977	−0.456489	+	0.889729i	$0.650893\pi$
$182$	−0.589805	−0.0437193
$183$	0	0
$184$	27.8798	2.05533
$185$	1.24663	0.0916538
$186$	0	0
$187$	7.20966	0.527223
$188$	−12.9061	−0.941273
$189$	0	0
$190$	2.79030	0.202429
$191$	21.8138	1.57839	0.789197	−	0.614140i	$-0.210497\pi$
$191$	21.8138	1.57839	0.789197	+	0.614140i	$0.210497\pi$
$192$	0	0
$193$	13.7901	0.992630	0.496315	−	0.868143i	$-0.334686\pi$
$193$	13.7901	0.992630	0.496315	+	0.868143i	$0.334686\pi$
$194$	−1.95020	−0.140017
$195$	0	0
$196$	−40.4934	−2.89239
$197$	−7.67059	−0.546507	−0.273253	−	0.961942i	$-0.588100\pi$
$197$	−7.67059	−0.546507	−0.273253	+	0.961942i	$0.588100\pi$
$198$	0	0
$199$	8.29578	0.588072	0.294036	−	0.955794i	$-0.405001\pi$
$199$	8.29578	0.588072	0.294036	+	0.955794i	$0.405001\pi$
$200$	10.5634	0.746943
$201$	0	0
$202$	55.0427	3.87279
$203$	−0.142963	−0.0100341
$204$	0	0
$205$	−0.237916	−0.0166168
$206$	5.67121	0.395132
$207$	0	0
$208$	−110.069	−7.63191
$209$	1.00000	0.0691714
$210$	0	0
$211$	−9.84976	−0.678086	−0.339043	−	0.940771i	$-0.610103\pi$
$211$	−9.84976	−0.678086	−0.339043	+	0.940771i	$0.610103\pi$
$212$	19.3916	1.33182
$213$	0	0
$214$	9.93316	0.679017
$215$	6.65040	0.453554
$216$	0	0
$217$	0.0389804	0.00264616
$218$	−37.5930	−2.54612
$219$	0	0
$220$	5.78575	0.390075
$221$	−44.3245	−2.98159
$222$	0	0
$223$	−18.3366	−1.22791	−0.613956	−	0.789340i	$-0.710423\pi$
$223$	−18.3366	−1.22791	−0.613956	+	0.789340i	$0.710423\pi$
$224$	0.991197	0.0662271
$225$	0	0
$226$	3.57529	0.237825
$227$	−26.9887	−1.79130	−0.895650	−	0.444759i	$-0.853289\pi$
$227$	−26.9887	−1.79130	−0.895650	+	0.444759i	$0.853289\pi$
$228$	0	0
$229$	13.3585	0.882756	0.441378	−	0.897321i	$-0.354490\pi$
$229$	13.3585	0.882756	0.441378	+	0.897321i	$0.354490\pi$
$230$	7.36441	0.485595
$231$	0	0
$232$	−43.9236	−2.88372
$233$	18.3235	1.20041	0.600207	−	0.799845i	$-0.295085\pi$
$233$	18.3235	1.20041	0.600207	+	0.799845i	$0.295085\pi$
$234$	0	0
$235$	−2.23067	−0.145513
$236$	17.9036	1.16543
$237$	0	0
$238$	0.691663	0.0448338
$239$	−20.2708	−1.31121	−0.655605	−	0.755104i	$-0.727586\pi$
$239$	−20.2708	−1.31121	−0.655605	+	0.755104i	$0.727586\pi$
$240$	0	0
$241$	11.3979	0.734206	0.367103	−	0.930180i	$-0.380350\pi$
$241$	11.3979	0.734206	0.367103	+	0.930180i	$0.380350\pi$
$242$	2.79030	0.179367
$243$	0	0
$244$	7.26356	0.465002
$245$	−6.99882	−0.447138
$246$	0	0
$247$	−6.14793	−0.391184
$248$	11.9762	0.760490
$249$	0	0
$250$	2.79030	0.176474
$251$	−18.3097	−1.15570	−0.577848	−	0.816144i	$-0.696107\pi$
$251$	−18.3097	−1.15570	−0.577848	+	0.816144i	$0.696107\pi$
$252$	0	0
$253$	2.63929	0.165931
$254$	−44.6834	−2.80369
$255$	0	0
$256$	97.3627	6.08517
$257$	−17.9985	−1.12271	−0.561357	−	0.827574i	$-0.689721\pi$
$257$	−17.9985	−1.12271	−0.561357	+	0.827574i	$0.689721\pi$
$258$	0	0
$259$	0.0428613	0.00266327
$260$	−35.5704	−2.20598
$261$	0	0
$262$	43.5737	2.69199
$263$	−1.33942	−0.0825923	−0.0412962	−	0.999147i	$-0.513149\pi$
$263$	−1.33942	−0.0825923	−0.0412962	+	0.999147i	$0.513149\pi$
$264$	0	0
$265$	3.35161	0.205888
$266$	0.0959355	0.00588218
$267$	0	0
$268$	−63.4825	−3.87781
$269$	7.98372	0.486776	0.243388	−	0.969929i	$-0.421741\pi$
$269$	7.98372	0.486776	0.243388	+	0.969929i	$0.421741\pi$
$270$	0	0
$271$	4.92062	0.298907	0.149453	−	0.988769i	$-0.452249\pi$
$271$	4.92062	0.298907	0.149453	+	0.988769i	$0.452249\pi$
$272$	129.078	7.82648
$273$	0	0
$274$	−56.4399	−3.40966
$275$	1.00000	0.0603023
$276$	0	0
$277$	−23.4110	−1.40663	−0.703315	−	0.710878i	$-0.748298\pi$
$277$	−23.4110	−1.40663	−0.703315	+	0.710878i	$0.748298\pi$
$278$	19.3686	1.16165
$279$	0	0
$280$	0.363188	0.0217046
$281$	−12.5834	−0.750664	−0.375332	−	0.926891i	$-0.622471\pi$
$281$	−12.5834	−0.750664	−0.375332	+	0.926891i	$0.622471\pi$
$282$	0	0
$283$	3.46942	0.206235	0.103118	−	0.994669i	$-0.467118\pi$
$283$	3.46942	0.206235	0.103118	+	0.994669i	$0.467118\pi$
$284$	−52.5122	−3.11603
$285$	0	0
$286$	−17.1545	−1.01437
$287$	−0.00818000	−0.000482850 0
$288$	0	0
$289$	34.9793	2.05760
$290$	−11.6023	−0.681313
$291$	0	0
$292$	−7.39753	−0.432908
$293$	−10.3342	−0.603729	−0.301864	−	0.953351i	$-0.597609\pi$
$293$	−10.3342	−0.603729	−0.301864	+	0.953351i	$0.597609\pi$
$294$	0	0
$295$	3.09444	0.180165
$296$	13.1686	0.765408
$297$	0	0
$298$	25.8301	1.49630
$299$	−16.2262	−0.938385
$300$	0	0
$301$	0.228653	0.0131793
$302$	−66.8105	−3.84451
$303$	0	0
$304$	17.9034	1.02683
$305$	1.25542	0.0718852
$306$	0	0
$307$	11.7125	0.668465	0.334233	−	0.942491i	$-0.391523\pi$
$307$	11.7125	0.668465	0.334233	+	0.942491i	$0.391523\pi$
$308$	0.198925	0.0113348
$309$	0	0
$310$	3.16350	0.179674
$311$	−28.9128	−1.63950	−0.819748	−	0.572725i	$-0.805886\pi$
$311$	−28.9128	−1.63950	−0.819748	+	0.572725i	$0.805886\pi$
$312$	0	0
$313$	−6.52403	−0.368760	−0.184380	−	0.982855i	$-0.559028\pi$
$313$	−6.52403	−0.368760	−0.184380	+	0.982855i	$0.559028\pi$
$314$	12.4832	0.704466
$315$	0	0
$316$	−54.4672	−3.06402
$317$	−28.4569	−1.59830	−0.799149	−	0.601133i	$-0.794716\pi$
$317$	−28.4569	−1.59830	−0.799149	+	0.601133i	$0.794716\pi$
$318$	0	0
$319$	−4.15811	−0.232809
$320$	44.6348	2.49516
$321$	0	0
$322$	0.253202	0.0141104
$323$	7.20966	0.401156
$324$	0	0
$325$	−6.14793	−0.341026
$326$	−6.09923	−0.337805
$327$	0	0
$328$	−2.51320	−0.138768
$329$	−0.0766945	−0.00422830
$330$	0	0
$331$	−28.1303	−1.54618	−0.773091	−	0.634295i	$-0.781291\pi$
$331$	−28.1303	−1.54618	−0.773091	+	0.634295i	$0.781291\pi$
$332$	34.8247	1.91125
$333$	0	0
$334$	39.0601	2.13727
$335$	−10.9722	−0.599476
$336$	0	0
$337$	−20.2886	−1.10519	−0.552594	−	0.833451i	$-0.686362\pi$
$337$	−20.2886	−1.10519	−0.552594	+	0.833451i	$0.686362\pi$
$338$	69.1911	3.76350
$339$	0	0
$340$	41.7133	2.26222
$341$	1.13375	0.0613960
$342$	0	0
$343$	−0.481305	−0.0259880
$344$	70.2506	3.78766
$345$	0	0
$346$	−57.5656	−3.09475
$347$	−23.4966	−1.26136	−0.630682	−	0.776041i	$-0.717225\pi$
$347$	−23.4966	−1.26136	−0.630682	+	0.776041i	$0.717225\pi$
$348$	0	0
$349$	−14.0214	−0.750547	−0.375274	−	0.926914i	$-0.622451\pi$
$349$	−14.0214	−0.750547	−0.375274	+	0.926914i	$0.622451\pi$
$350$	0.0959355	0.00512797
$351$	0	0
$352$	28.8291	1.53659
$353$	34.4808	1.83523	0.917615	−	0.397470i	$-0.130112\pi$
$353$	34.4808	1.83523	0.917615	+	0.397470i	$0.130112\pi$
$354$	0	0
$355$	−9.07612	−0.481711
$356$	53.3114	2.82550
$357$	0	0
$358$	54.6514	2.88842
$359$	−23.9126	−1.26206	−0.631030	−	0.775759i	$-0.717367\pi$
$359$	−23.9126	−1.26206	−0.631030	+	0.775759i	$0.717367\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	−34.2728	−1.80134
$363$	0	0
$364$	−1.22298	−0.0641014
$365$	−1.27858	−0.0669238
$366$	0	0
$367$	31.0756	1.62213	0.811067	−	0.584954i	$-0.198887\pi$
$367$	31.0756	1.62213	0.811067	+	0.584954i	$0.198887\pi$
$368$	47.2523	2.46320
$369$	0	0
$370$	3.47846	0.180836
$371$	0.115234	0.00598268
$372$	0	0
$373$	29.7388	1.53982	0.769908	−	0.638155i	$-0.220302\pi$
$373$	29.7388	1.53982	0.769908	+	0.638155i	$0.220302\pi$
$374$	20.1171	1.04023
$375$	0	0
$376$	−23.5634	−1.21519
$377$	25.5637	1.31660
$378$	0	0
$379$	18.3329	0.941696	0.470848	−	0.882214i	$-0.343948\pi$
$379$	18.3329	0.941696	0.470848	+	0.882214i	$0.343948\pi$
$380$	5.78575	0.296803
$381$	0	0
$382$	60.8671	3.11423
$383$	28.2900	1.44555	0.722775	−	0.691083i	$-0.242866\pi$
$383$	28.2900	1.44555	0.722775	+	0.691083i	$0.242866\pi$
$384$	0	0
$385$	0.0343818	0.00175226
$386$	38.4783	1.95849
$387$	0	0
$388$	−4.04380	−0.205293
$389$	−17.2408	−0.874143	−0.437072	−	0.899427i	$-0.643984\pi$
$389$	−17.2408	−0.874143	−0.437072	+	0.899427i	$0.643984\pi$
$390$	0	0
$391$	19.0284	0.962308
$392$	−73.9311	−3.73408
$393$	0	0
$394$	−21.4032	−1.07828
$395$	−9.41403	−0.473671
$396$	0	0
$397$	24.7434	1.24184	0.620919	−	0.783875i	$-0.286760\pi$
$397$	24.7434	1.24184	0.620919	+	0.783875i	$0.286760\pi$
$398$	23.1477	1.16029
$399$	0	0
$400$	17.9034	0.895170
$401$	−28.0934	−1.40292	−0.701458	−	0.712711i	$-0.747467\pi$
$401$	−28.0934	−1.40292	−0.701458	+	0.712711i	$0.747467\pi$
$402$	0	0
$403$	−6.97021	−0.347211
$404$	114.132	5.67830
$405$	0	0
$406$	−0.398910	−0.0197976
$407$	1.24663	0.0617930
$408$	0	0
$409$	15.0242	0.742900	0.371450	−	0.928453i	$-0.378861\pi$
$409$	15.0242	0.742900	0.371450	+	0.928453i	$0.378861\pi$
$410$	−0.663857	−0.0327856
$411$	0	0
$412$	11.7594	0.579344
$413$	0.106392	0.00523523
$414$	0	0
$415$	6.01905	0.295463
$416$	−177.239	−8.68986
$417$	0	0
$418$	2.79030	0.136478
$419$	4.37409	0.213688	0.106844	−	0.994276i	$-0.465925\pi$
$419$	4.37409	0.213688	0.106844	+	0.994276i	$0.465925\pi$
$420$	0	0
$421$	−15.5806	−0.759351	−0.379675	−	0.925120i	$-0.623964\pi$
$421$	−15.5806	−0.759351	−0.379675	+	0.925120i	$0.623964\pi$
$422$	−27.4838	−1.33789
$423$	0	0
$424$	35.4043	1.71938
$425$	7.20966	0.349720
$426$	0	0
$427$	0.0431637	0.00208884
$428$	20.5967	0.995577
$429$	0	0
$430$	18.5566	0.894878
$431$	35.8579	1.72721	0.863606	−	0.504167i	$-0.168200\pi$
$431$	35.8579	1.72721	0.863606	+	0.504167i	$0.168200\pi$
$432$	0	0
$433$	10.8368	0.520783	0.260392	−	0.965503i	$-0.416148\pi$
$433$	10.8368	0.520783	0.260392	+	0.965503i	$0.416148\pi$
$434$	0.108767	0.00522097
$435$	0	0
$436$	−77.9500	−3.73313
$437$	2.63929	0.126254
$438$	0	0
$439$	7.30473	0.348636	0.174318	−	0.984689i	$-0.444228\pi$
$439$	7.30473	0.348636	0.174318	+	0.984689i	$0.444228\pi$
$440$	10.5634	0.503589
$441$	0	0
$442$	−123.679	−5.88279
$443$	−34.1342	−1.62176	−0.810882	−	0.585210i	$-0.801012\pi$
$443$	−34.1342	−1.62176	−0.810882	+	0.585210i	$0.801012\pi$
$444$	0	0
$445$	9.21426	0.436798
$446$	−51.1647	−2.42272
$447$	0	0
$448$	1.53463	0.0725043
$449$	16.3406	0.771163	0.385581	−	0.922674i	$-0.374001\pi$
$449$	16.3406	0.771163	0.385581	+	0.922674i	$0.374001\pi$
$450$	0	0
$451$	−0.237916	−0.0112030
$452$	7.41346	0.348700
$453$	0	0
$454$	−75.3063	−3.53430
$455$	−0.211377	−0.00990952
$456$	0	0
$457$	−3.26382	−0.152675	−0.0763374	−	0.997082i	$-0.524323\pi$
$457$	−3.26382	−0.152675	−0.0763374	+	0.997082i	$0.524323\pi$
$458$	37.2742	1.74171
$459$	0	0
$460$	15.2703	0.711981
$461$	−20.4055	−0.950379	−0.475190	−	0.879883i	$-0.657621\pi$
$461$	−20.4055	−0.950379	−0.475190	+	0.879883i	$0.657621\pi$
$462$	0	0
$463$	4.35981	0.202617	0.101309	−	0.994855i	$-0.467697\pi$
$463$	4.35981	0.202617	0.101309	+	0.994855i	$0.467697\pi$
$464$	−74.4442	−3.45599
$465$	0	0
$466$	51.1280	2.36846
$467$	−7.38173	−0.341586	−0.170793	−	0.985307i	$-0.554633\pi$
$467$	−7.38173	−0.341586	−0.170793	+	0.985307i	$0.554633\pi$
$468$	0	0
$469$	−0.377245	−0.0174196
$470$	−6.22422	−0.287102
$471$	0	0
$472$	32.6877	1.50457
$473$	6.65040	0.305786
$474$	0	0
$475$	1.00000	0.0458831
$476$	1.43418	0.0657356
$477$	0	0
$478$	−56.5616	−2.58707
$479$	−16.5815	−0.757629	−0.378815	−	0.925473i	$-0.623668\pi$
$479$	−16.5815	−0.757629	−0.378815	+	0.925473i	$0.623668\pi$
$480$	0	0
$481$	−7.66418	−0.349456
$482$	31.8036	1.44862
$483$	0	0
$484$	5.78575	0.262989
$485$	−0.698924	−0.0317365
$486$	0	0
$487$	−36.8825	−1.67130	−0.835652	−	0.549259i	$-0.814910\pi$
$487$	−36.8825	−1.67130	−0.835652	+	0.549259i	$0.814910\pi$
$488$	13.2615	0.600319
$489$	0	0
$490$	−19.5288	−0.882220
$491$	−27.1390	−1.22477	−0.612384	−	0.790561i	$-0.709789\pi$
$491$	−27.1390	−1.22477	−0.612384	+	0.790561i	$0.709789\pi$
$492$	0	0
$493$	−29.9785	−1.35017
$494$	−17.1545	−0.771820
$495$	0	0
$496$	20.2980	0.911406
$497$	−0.312054	−0.0139975
$498$	0	0
$499$	−43.4584	−1.94547	−0.972734	−	0.231925i	$-0.925497\pi$
$499$	−43.4584	−1.94547	−0.972734	+	0.231925i	$0.925497\pi$
$500$	5.78575	0.258747
$501$	0	0
$502$	−51.0894	−2.28023
$503$	0.979831	0.0436885	0.0218443	−	0.999761i	$-0.493046\pi$
$503$	0.979831	0.0436885	0.0218443	+	0.999761i	$0.493046\pi$
$504$	0	0
$505$	19.7265	0.877816
$506$	7.36441	0.327388
$507$	0	0
$508$	−92.6523	−4.11078
$509$	9.33102	0.413590	0.206795	−	0.978384i	$-0.433697\pi$
$509$	9.33102	0.413590	0.206795	+	0.978384i	$0.433697\pi$
$510$	0	0
$511$	−0.0439598	−0.00194467
$512$	137.898	6.09430
$513$	0	0
$514$	−50.2211	−2.21516
$515$	2.03248	0.0895616
$516$	0	0
$517$	−2.23067	−0.0981047
$518$	0.119596	0.00525474
$519$	0	0
$520$	−64.9428	−2.84793
$521$	−5.27691	−0.231186	−0.115593	−	0.993297i	$-0.536877\pi$
$521$	−5.27691	−0.231186	−0.115593	+	0.993297i	$0.536877\pi$
$522$	0	0
$523$	7.73032	0.338023	0.169012	−	0.985614i	$-0.445942\pi$
$523$	7.73032	0.338023	0.169012	+	0.985614i	$0.445942\pi$
$524$	90.3512	3.94701
$525$	0	0
$526$	−3.73738	−0.162958
$527$	8.17395	0.356063
$528$	0	0
$529$	−16.0341	−0.697136
$530$	9.35198	0.406224
$531$	0	0
$532$	0.198925	0.00862448
$533$	1.46269	0.0633563
$534$	0	0
$535$	3.55989	0.153908
$536$	−115.903	−5.00627
$537$	0	0
$538$	22.2769	0.960427
$539$	−6.99882	−0.301460
$540$	0	0
$541$	−16.2559	−0.698894	−0.349447	−	0.936956i	$-0.613631\pi$
$541$	−16.2559	−0.698894	−0.349447	+	0.936956i	$0.613631\pi$
$542$	13.7300	0.589754
$543$	0	0
$544$	207.848	8.91141
$545$	−13.4728	−0.577110
$546$	0	0
$547$	−5.84956	−0.250109	−0.125055	−	0.992150i	$-0.539911\pi$
$547$	−5.84956	−0.250109	−0.125055	+	0.992150i	$0.539911\pi$
$548$	−117.030	−4.99926
$549$	0	0
$550$	2.79030	0.118979
$551$	−4.15811	−0.177141
$552$	0	0
$553$	−0.323672	−0.0137639
$554$	−65.3236	−2.77533
$555$	0	0
$556$	40.1612	1.70321
$557$	24.5808	1.04152	0.520760	−	0.853703i	$-0.325649\pi$
$557$	24.5808	1.04152	0.520760	+	0.853703i	$0.325649\pi$
$558$	0	0
$559$	−40.8862	−1.72930
$560$	0.615552	0.0260118
$561$	0	0
$562$	−35.1115	−1.48109
$563$	12.7482	0.537271	0.268636	−	0.963242i	$-0.413427\pi$
$563$	12.7482	0.537271	0.268636	+	0.963242i	$0.413427\pi$
$564$	0	0
$565$	1.28133	0.0539060
$566$	9.68070	0.406910
$567$	0	0
$568$	−95.8744	−4.02280
$569$	33.2759	1.39500	0.697499	−	0.716585i	$-0.254296\pi$
$569$	33.2759	1.39500	0.697499	+	0.716585i	$0.254296\pi$
$570$	0	0
$571$	−0.184704	−0.00772964	−0.00386482	−	0.999993i	$-0.501230\pi$
$571$	−0.184704	−0.00772964	−0.00386482	+	0.999993i	$0.501230\pi$
$572$	−35.5704	−1.48727
$573$	0	0
$574$	−0.0228246	−0.000952681 0
$575$	2.63929	0.110066
$576$	0	0
$577$	−31.7122	−1.32020	−0.660098	−	0.751180i	$-0.729485\pi$
$577$	−31.7122	−1.32020	−0.660098	+	0.751180i	$0.729485\pi$
$578$	97.6025	4.05973
$579$	0	0
$580$	−24.0578	−0.998944
$581$	0.206946	0.00858556
$582$	0	0
$583$	3.35161	0.138809
$584$	−13.5061	−0.558885
$585$	0	0
$586$	−28.8354	−1.19118
$587$	6.80709	0.280959	0.140479	−	0.990084i	$-0.455136\pi$
$587$	6.80709	0.280959	0.140479	+	0.990084i	$0.455136\pi$
$588$	0	0
$589$	1.13375	0.0467153
$590$	8.63440	0.355472
$591$	0	0
$592$	22.3189	0.917300
$593$	−42.9387	−1.76328	−0.881640	−	0.471922i	$-0.843560\pi$
$593$	−42.9387	−1.76328	−0.881640	+	0.471922i	$0.843560\pi$
$594$	0	0
$595$	0.247882	0.0101622
$596$	53.5594	2.19388
$597$	0	0
$598$	−45.2759	−1.85147
$599$	4.96785	0.202981	0.101490	−	0.994837i	$-0.467639\pi$
$599$	4.96785	0.202981	0.101490	+	0.994837i	$0.467639\pi$
$600$	0	0
$601$	−40.7039	−1.66035	−0.830174	−	0.557504i	$-0.811759\pi$
$601$	−40.7039	−1.66035	−0.830174	+	0.557504i	$0.811759\pi$
$602$	0.638010	0.0260033
$603$	0	0
$604$	−138.533	−5.63684
$605$	1.00000	0.0406558
$606$	0	0
$607$	−9.39723	−0.381422	−0.190711	−	0.981646i	$-0.561079\pi$
$607$	−9.39723	−0.381422	−0.190711	+	0.981646i	$0.561079\pi$
$608$	28.8291	1.16917
$609$	0	0
$610$	3.50300	0.141832
$611$	13.7140	0.554809
$612$	0	0
$613$	16.2734	0.657277	0.328638	−	0.944456i	$-0.393410\pi$
$613$	16.2734	0.657277	0.328638	+	0.944456i	$0.393410\pi$
$614$	32.6812	1.31891
$615$	0	0
$616$	0.363188	0.0146333
$617$	7.15505	0.288052	0.144026	−	0.989574i	$-0.453995\pi$
$617$	7.15505	0.288052	0.144026	+	0.989574i	$0.453995\pi$
$618$	0	0
$619$	17.2450	0.693137	0.346568	−	0.938025i	$-0.387347\pi$
$619$	17.2450	0.693137	0.346568	+	0.938025i	$0.387347\pi$
$620$	6.55959	0.263439
$621$	0	0
$622$	−80.6753	−3.23478
$623$	0.316803	0.0126924
$624$	0	0
$625$	1.00000	0.0400000
$626$	−18.2040	−0.727577
$627$	0	0
$628$	25.8842	1.03289
$629$	8.98776	0.358366
$630$	0	0
$631$	38.9658	1.55121	0.775603	−	0.631221i	$-0.217446\pi$
$631$	38.9658	1.55121	0.775603	+	0.631221i	$0.217446\pi$
$632$	−99.4438	−3.95566
$633$	0	0
$634$	−79.4031	−3.15350
$635$	−16.0139	−0.635491
$636$	0	0
$637$	43.0283	1.70484
$638$	−11.6023	−0.459341
$639$	0	0
$640$	66.8862	2.64391
$641$	−43.2904	−1.70987	−0.854935	−	0.518736i	$-0.826403\pi$
$641$	−43.2904	−1.70987	−0.854935	+	0.518736i	$0.826403\pi$
$642$	0	0
$643$	15.5519	0.613309	0.306654	−	0.951821i	$-0.400790\pi$
$643$	15.5519	0.613309	0.306654	+	0.951821i	$0.400790\pi$
$644$	0.525021	0.0206887
$645$	0	0
$646$	20.1171	0.791497
$647$	−31.7327	−1.24754	−0.623771	−	0.781607i	$-0.714400\pi$
$647$	−31.7327	−1.24754	−0.623771	+	0.781607i	$0.714400\pi$
$648$	0	0
$649$	3.09444	0.121467
$650$	−17.1545	−0.672857
$651$	0	0
$652$	−12.6469	−0.495291
$653$	−12.9558	−0.506999	−0.253499	−	0.967336i	$-0.581582\pi$
$653$	−12.9558	−0.506999	−0.253499	+	0.967336i	$0.581582\pi$
$654$	0	0
$655$	15.6162	0.610174
$656$	−4.25951	−0.166306
$657$	0	0
$658$	−0.214000	−0.00834260
$659$	23.7133	0.923738	0.461869	−	0.886948i	$-0.347179\pi$
$659$	23.7133	0.923738	0.461869	+	0.886948i	$0.347179\pi$
$660$	0	0
$661$	28.8812	1.12335	0.561674	−	0.827358i	$-0.310157\pi$
$661$	28.8812	1.12335	0.561674	+	0.827358i	$0.310157\pi$
$662$	−78.4919	−3.05068
$663$	0	0
$664$	63.5814	2.46744
$665$	0.0343818	0.00133327
$666$	0	0
$667$	−10.9745	−0.424933
$668$	80.9921	3.13368
$669$	0	0
$670$	−30.6157	−1.18279
$671$	1.25542	0.0484650
$672$	0	0
$673$	25.0071	0.963953	0.481977	−	0.876184i	$-0.339919\pi$
$673$	25.0071	0.963953	0.481977	+	0.876184i	$0.339919\pi$
$674$	−56.6111	−2.18058
$675$	0	0
$676$	143.470	5.51806
$677$	8.93025	0.343217	0.171609	−	0.985165i	$-0.445104\pi$
$677$	8.93025	0.343217	0.171609	+	0.985165i	$0.445104\pi$
$678$	0	0
$679$	−0.0240303	−0.000922198 0
$680$	76.1583	2.92054
$681$	0	0
$682$	3.16350	0.121136
$683$	20.4143	0.781132	0.390566	−	0.920575i	$-0.372279\pi$
$683$	20.4143	0.781132	0.390566	+	0.920575i	$0.372279\pi$
$684$	0	0
$685$	−20.2272	−0.772843
$686$	−1.34298	−0.0512754
$687$	0	0
$688$	119.065	4.53930
$689$	−20.6055	−0.785005
$690$	0	0
$691$	−31.4003	−1.19453	−0.597263	−	0.802046i	$-0.703745\pi$
$691$	−31.4003	−1.19453	−0.597263	+	0.802046i	$0.703745\pi$
$692$	−119.364	−4.53753
$693$	0	0
$694$	−65.5625	−2.48872
$695$	6.94140	0.263302
$696$	0	0
$697$	−1.71530	−0.0649715
$698$	−39.1238	−1.48086
$699$	0	0
$700$	0.198925	0.00751865
$701$	−24.1473	−0.912033	−0.456016	−	0.889971i	$-0.650724\pi$
$701$	−24.1473	−0.912033	−0.456016	+	0.889971i	$0.650724\pi$
$702$	0	0
$703$	1.24663	0.0470174
$704$	44.6348	1.68224
$705$	0	0
$706$	96.2117	3.62098
$707$	0.678232	0.0255076
$708$	0	0
$709$	21.3742	0.802726	0.401363	−	0.915919i	$-0.368537\pi$
$709$	21.3742	0.802726	0.401363	+	0.915919i	$0.368537\pi$
$710$	−25.3251	−0.950433
$711$	0	0
$712$	97.3335	3.64773
$713$	2.99230	0.112062
$714$	0	0
$715$	−6.14793	−0.229920
$716$	113.321	4.23501
$717$	0	0
$718$	−66.7232	−2.49009
$719$	3.59917	0.134226	0.0671132	−	0.997745i	$-0.478621\pi$
$719$	3.59917	0.134226	0.0671132	+	0.997745i	$0.478621\pi$
$720$	0	0
$721$	0.0698803	0.00260248
$722$	2.79030	0.103844
$723$	0	0
$724$	−71.0655	−2.64113
$725$	−4.15811	−0.154428
$726$	0	0
$727$	−11.5404	−0.428009	−0.214005	−	0.976833i	$-0.568651\pi$
$727$	−11.5404	−0.428009	−0.214005	+	0.976833i	$0.568651\pi$
$728$	−2.23285	−0.0827551
$729$	0	0
$730$	−3.56761	−0.132043
$731$	47.9472	1.77339
$732$	0	0
$733$	40.1889	1.48441	0.742205	−	0.670173i	$-0.233780\pi$
$733$	40.1889	1.48441	0.742205	+	0.670173i	$0.233780\pi$
$734$	86.7101	3.20053
$735$	0	0
$736$	76.0883	2.80465
$737$	−10.9722	−0.404167
$738$	0	0
$739$	−3.29180	−0.121091	−0.0605453	−	0.998165i	$-0.519284\pi$
$739$	−3.29180	−0.121091	−0.0605453	+	0.998165i	$0.519284\pi$
$740$	7.21267	0.265143
$741$	0	0
$742$	0.321538	0.0118040
$743$	38.7088	1.42009	0.710045	−	0.704156i	$-0.248675\pi$
$743$	38.7088	1.42009	0.710045	+	0.704156i	$0.248675\pi$
$744$	0	0
$745$	9.25712	0.339154
$746$	82.9800	3.03811
$747$	0	0
$748$	41.7133	1.52519
$749$	0.122396	0.00447224
$750$	0	0
$751$	20.0164	0.730407	0.365204	−	0.930928i	$-0.380999\pi$
$751$	20.0164	0.730407	0.365204	+	0.930928i	$0.380999\pi$
$752$	−39.9366	−1.45634
$753$	0	0
$754$	71.3304	2.59770
$755$	−23.9439	−0.871407
$756$	0	0
$757$	−18.6378	−0.677404	−0.338702	−	0.940894i	$-0.609988\pi$
$757$	−18.6378	−0.677404	−0.338702	+	0.940894i	$0.609988\pi$
$758$	51.1541	1.85800
$759$	0	0
$760$	10.5634	0.383173
$761$	−37.2690	−1.35100	−0.675501	−	0.737359i	$-0.736072\pi$
$761$	−37.2690	−1.35100	−0.675501	+	0.737359i	$0.736072\pi$
$762$	0	0
$763$	−0.463218	−0.0167696
$764$	126.209	4.56610
$765$	0	0
$766$	78.9374	2.85212
$767$	−19.0244	−0.686931
$768$	0	0
$769$	34.6474	1.24942	0.624708	−	0.780858i	$-0.285218\pi$
$769$	34.6474	1.24942	0.624708	+	0.780858i	$0.285218\pi$
$770$	0.0959355	0.00345728
$771$	0	0
$772$	79.7858	2.87155
$773$	−3.33419	−0.119923	−0.0599613	−	0.998201i	$-0.519098\pi$
$773$	−3.33419	−0.119923	−0.0599613	+	0.998201i	$0.519098\pi$
$774$	0	0
$775$	1.13375	0.0407255
$776$	−7.38299	−0.265034
$777$	0	0
$778$	−48.1069	−1.72472
$779$	−0.237916	−0.00852424
$780$	0	0
$781$	−9.07612	−0.324769
$782$	53.0949	1.89867
$783$	0	0
$784$	−125.303	−4.47510
$785$	4.47378	0.159676
$786$	0	0
$787$	15.3798	0.548231	0.274116	−	0.961697i	$-0.411615\pi$
$787$	15.3798	0.548231	0.274116	+	0.961697i	$0.411615\pi$
$788$	−44.3801	−1.58098
$789$	0	0
$790$	−26.2679	−0.934571
$791$	0.0440545	0.00156640
$792$	0	0
$793$	−7.71825	−0.274083
$794$	69.0415	2.45019
$795$	0	0
$796$	47.9973	1.70122
$797$	−25.2733	−0.895227	−0.447614	−	0.894227i	$-0.647726\pi$
$797$	−25.2733	−0.895227	−0.447614	+	0.894227i	$0.647726\pi$
$798$	0	0
$799$	−16.0824	−0.568953
$800$	28.8291	1.01926
$801$	0	0
$802$	−78.3888	−2.76801
$803$	−1.27858	−0.0451200
$804$	0	0
$805$	0.0907437	0.00319830
$806$	−19.4490	−0.685060
$807$	0	0
$808$	208.378	7.33071
$809$	46.1986	1.62426	0.812129	−	0.583478i	$-0.198309\pi$
$809$	46.1986	1.62426	0.812129	+	0.583478i	$0.198309\pi$
$810$	0	0
$811$	56.9152	1.99856	0.999281	−	0.0379108i	$-0.0120703\pi$
$811$	56.9152	1.99856	0.999281	+	0.0379108i	$0.0120703\pi$
$812$	−0.827150	−0.0290273
$813$	0	0
$814$	3.47846	0.121920
$815$	−2.18587	−0.0765678
$816$	0	0
$817$	6.65040	0.232668
$818$	41.9220	1.46577
$819$	0	0
$820$	−1.37652	−0.0480703
$821$	−37.8716	−1.32173	−0.660865	−	0.750505i	$-0.729810\pi$
$821$	−37.8716	−1.32173	−0.660865	+	0.750505i	$0.729810\pi$
$822$	0	0
$823$	2.69506	0.0939437	0.0469719	−	0.998896i	$-0.485043\pi$
$823$	2.69506	0.0939437	0.0469719	+	0.998896i	$0.485043\pi$
$824$	21.4698	0.747936
$825$	0	0
$826$	0.296866	0.0103293
$827$	38.0500	1.32313	0.661564	−	0.749888i	$-0.269893\pi$
$827$	38.0500	1.32313	0.661564	+	0.749888i	$0.269893\pi$
$828$	0	0
$829$	−37.5351	−1.30365	−0.651824	−	0.758370i	$-0.725996\pi$
$829$	−37.5351	−1.30365	−0.651824	+	0.758370i	$0.725996\pi$
$830$	16.7949	0.582960
$831$	0	0
$832$	−274.412	−9.51352
$833$	−50.4591	−1.74831
$834$	0	0
$835$	13.9985	0.484440
$836$	5.78575	0.200104
$837$	0	0
$838$	12.2050	0.421615
$839$	−30.0563	−1.03766	−0.518829	−	0.854878i	$-0.673632\pi$
$839$	−30.0563	−1.03766	−0.518829	+	0.854878i	$0.673632\pi$
$840$	0	0
$841$	−11.7102	−0.403799
$842$	−43.4744	−1.49823
$843$	0	0
$844$	−56.9883	−1.96162
$845$	24.7971	0.853045
$846$	0	0
$847$	0.0343818	0.00118137
$848$	60.0052	2.06059
$849$	0	0
$850$	20.1171	0.690011
$851$	3.29021	0.112787
$852$	0	0
$853$	21.3714	0.731743	0.365871	−	0.930665i	$-0.380771\pi$
$853$	21.3714	0.731743	0.365871	+	0.930665i	$0.380771\pi$
$854$	0.120440	0.00412136
$855$	0	0
$856$	37.6044	1.28529
$857$	−7.03756	−0.240398	−0.120199	−	0.992750i	$-0.538353\pi$
$857$	−7.03756	−0.240398	−0.120199	+	0.992750i	$0.538353\pi$
$858$	0	0
$859$	1.28636	0.0438902	0.0219451	−	0.999759i	$-0.493014\pi$
$859$	1.28636	0.0438902	0.0219451	+	0.999759i	$0.493014\pi$
$860$	38.4776	1.31207
$861$	0	0
$862$	100.054	3.40785
$863$	−25.6311	−0.872491	−0.436246	−	0.899828i	$-0.643692\pi$
$863$	−25.6311	−0.872491	−0.436246	+	0.899828i	$0.643692\pi$
$864$	0	0
$865$	−20.6306	−0.701463
$866$	30.2379	1.02753
$867$	0	0
$868$	0.225531	0.00765501
$869$	−9.41403	−0.319349
$870$	0	0
$871$	67.4564	2.28567
$872$	−142.318	−4.81948
$873$	0	0
$874$	7.36441	0.249105
$875$	0.0343818	0.00116232
$876$	0	0
$877$	−9.53914	−0.322114	−0.161057	−	0.986945i	$-0.551490\pi$
$877$	−9.53914	−0.322114	−0.161057	+	0.986945i	$0.551490\pi$
$878$	20.3823	0.687871
$879$	0	0
$880$	17.9034	0.603524
$881$	6.74862	0.227367	0.113683	−	0.993517i	$-0.463735\pi$
$881$	6.74862	0.227367	0.113683	+	0.993517i	$0.463735\pi$
$882$	0	0
$883$	−7.39786	−0.248958	−0.124479	−	0.992222i	$-0.539726\pi$
$883$	−7.39786	−0.248958	−0.124479	+	0.992222i	$0.539726\pi$
$884$	−256.451	−8.62537
$885$	0	0
$886$	−95.2444	−3.19980
$887$	−1.86442	−0.0626010	−0.0313005	−	0.999510i	$-0.509965\pi$
$887$	−1.86442	−0.0626010	−0.0313005	+	0.999510i	$0.509965\pi$
$888$	0	0
$889$	−0.550587	−0.0184661
$890$	25.7105	0.861818
$891$	0	0
$892$	−106.091	−3.55220
$893$	−2.23067	−0.0746465
$894$	0	0
$895$	19.5863	0.654696
$896$	2.29967	0.0768266
$897$	0	0
$898$	45.5952	1.52153
$899$	−4.71425	−0.157229
$900$	0	0
$901$	24.1640	0.805019
$902$	−0.663857	−0.0221040
$903$	0	0
$904$	13.5352	0.450173
$905$	−12.2829	−0.408296
$906$	0	0
$907$	−20.3944	−0.677183	−0.338592	−	0.940933i	$-0.609951\pi$
$907$	−20.3944	−0.677183	−0.338592	+	0.940933i	$0.609951\pi$
$908$	−156.150	−5.18201
$909$	0	0
$910$	−0.589805	−0.0195518
$911$	−17.9899	−0.596031	−0.298015	−	0.954561i	$-0.596325\pi$
$911$	−17.9899	−0.596031	−0.298015	+	0.954561i	$0.596325\pi$
$912$	0	0
$913$	6.01905	0.199201
$914$	−9.10701	−0.301233
$915$	0	0
$916$	77.2891	2.55370
$917$	0.536913	0.0177304
$918$	0	0
$919$	−32.4913	−1.07179	−0.535894	−	0.844285i	$-0.680025\pi$
$919$	−32.4913	−1.07179	−0.535894	+	0.844285i	$0.680025\pi$
$920$	27.8798	0.919170
$921$	0	0
$922$	−56.9374	−1.87513
$923$	55.7994	1.83666
$924$	0	0
$925$	1.24663	0.0409888
$926$	12.1652	0.399772
$927$	0	0
$928$	−119.874	−3.93507
$929$	−56.1728	−1.84297	−0.921485	−	0.388414i	$-0.873023\pi$
$929$	−56.1728	−1.84297	−0.921485	+	0.388414i	$0.873023\pi$
$930$	0	0
$931$	−6.99882	−0.229377
$932$	106.015	3.47265
$933$	0	0
$934$	−20.5972	−0.673961
$935$	7.20966	0.235781
$936$	0	0
$937$	25.5031	0.833150	0.416575	−	0.909101i	$-0.363230\pi$
$937$	25.5031	0.833150	0.416575	+	0.909101i	$0.363230\pi$
$938$	−1.05262	−0.0343694
$939$	0	0
$940$	−12.9061	−0.420950
$941$	−54.1799	−1.76622	−0.883108	−	0.469171i	$-0.844553\pi$
$941$	−54.1799	−1.76622	−0.883108	+	0.469171i	$0.844553\pi$
$942$	0	0
$943$	−0.627931	−0.0204482
$944$	55.4010	1.80315
$945$	0	0
$946$	18.5566	0.603327
$947$	51.2517	1.66546	0.832728	−	0.553683i	$-0.186778\pi$
$947$	51.2517	1.66546	0.832728	+	0.553683i	$0.186778\pi$
$948$	0	0
$949$	7.86061	0.255166
$950$	2.79030	0.0905291
$951$	0	0
$952$	2.61846	0.0848649
$953$	44.6716	1.44705	0.723527	−	0.690296i	$-0.242520\pi$
$953$	44.6716	1.44705	0.723527	+	0.690296i	$0.242520\pi$
$954$	0	0
$955$	21.8138	0.705880
$956$	−117.282	−3.79317
$957$	0	0
$958$	−46.2674	−1.49483
$959$	−0.695449	−0.0224572
$960$	0	0
$961$	−29.7146	−0.958536
$962$	−21.3853	−0.689490
$963$	0	0
$964$	65.9457	2.12397
$965$	13.7901	0.443917
$966$	0	0
$967$	31.4814	1.01237	0.506187	−	0.862424i	$-0.331055\pi$
$967$	31.4814	1.01237	0.506187	+	0.862424i	$0.331055\pi$
$968$	10.5634	0.339519
$969$	0	0
$970$	−1.95020	−0.0626173
$971$	15.5131	0.497840	0.248920	−	0.968524i	$-0.419924\pi$
$971$	15.5131	0.497840	0.248920	+	0.968524i	$0.419924\pi$
$972$	0	0
$973$	0.238658	0.00765103
$974$	−102.913	−3.29755
$975$	0	0
$976$	22.4763	0.719450
$977$	−22.7362	−0.727396	−0.363698	−	0.931517i	$-0.618486\pi$
$977$	−22.7362	−0.727396	−0.363698	+	0.931517i	$0.618486\pi$
$978$	0	0
$979$	9.21426	0.294489
$980$	−40.4934	−1.29351
$981$	0	0
$982$	−75.7259	−2.41651
$983$	−14.5580	−0.464328	−0.232164	−	0.972677i	$-0.574581\pi$
$983$	−14.5580	−0.464328	−0.232164	+	0.972677i	$0.574581\pi$
$984$	0	0
$985$	−7.67059	−0.244405
$986$	−83.6490	−2.66393
$987$	0	0
$988$	−35.5704	−1.13165
$989$	17.5524	0.558132
$990$	0	0
$991$	−35.6591	−1.13275	−0.566374	−	0.824149i	$-0.691654\pi$
$991$	−35.6591	−1.13275	−0.566374	+	0.824149i	$0.691654\pi$
$992$	32.6849	1.03775
$993$	0	0
$994$	−0.870723	−0.0276176
$995$	8.29578	0.262994
$996$	0	0
$997$	33.1307	1.04926	0.524630	−	0.851330i	$-0.324204\pi$
$997$	33.1307	1.04926	0.524630	+	0.851330i	$0.324204\pi$
$998$	−121.262	−3.83848
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9405.2.a.bv.1.19	yes	19
3.2	odd	2		9405.2.a.bu.1.1	✓	19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9405.2.a.bu.1.1	✓	19	3.2	odd	2
9405.2.a.bv.1.19	yes	19	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:	\( N \)	\(=\)	\( 9405 = 3^{2} \cdot 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9405.a (trivial)

\(f(q)\)	\(=\)	\(q+2.79030 q^{2} +5.78575 q^{4} +1.00000 q^{5} +0.0343818 q^{7} +10.5634 q^{8} +O(q^{10})\)	\(q+2.79030 q^{2} +5.78575 q^{4} +1.00000 q^{5} +0.0343818 q^{7} +10.5634 q^{8} +2.79030 q^{10} +1.00000 q^{11} -6.14793 q^{13} +0.0959355 q^{14} +17.9034 q^{16} +7.20966 q^{17} +1.00000 q^{19} +5.78575 q^{20} +2.79030 q^{22} +2.63929 q^{23} +1.00000 q^{25} -17.1545 q^{26} +0.198925 q^{28} -4.15811 q^{29} +1.13375 q^{31} +28.8291 q^{32} +20.1171 q^{34} +0.0343818 q^{35} +1.24663 q^{37} +2.79030 q^{38} +10.5634 q^{40} -0.237916 q^{41} +6.65040 q^{43} +5.78575 q^{44} +7.36441 q^{46} -2.23067 q^{47} -6.99882 q^{49} +2.79030 q^{50} -35.5704 q^{52} +3.35161 q^{53} +1.00000 q^{55} +0.363188 q^{56} -11.6023 q^{58} +3.09444 q^{59} +1.25542 q^{61} +3.16350 q^{62} +44.6348 q^{64} -6.14793 q^{65} -10.9722 q^{67} +41.7133 q^{68} +0.0959355 q^{70} -9.07612 q^{71} -1.27858 q^{73} +3.47846 q^{74} +5.78575 q^{76} +0.0343818 q^{77} -9.41403 q^{79} +17.9034 q^{80} -0.663857 q^{82} +6.01905 q^{83} +7.20966 q^{85} +18.5566 q^{86} +10.5634 q^{88} +9.21426 q^{89} -0.211377 q^{91} +15.2703 q^{92} -6.22422 q^{94} +1.00000 q^{95} -0.698924 q^{97} -19.5288 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 3 q^{2} + 25 q^{4} + 19 q^{5} + 12 q^{7} + 9 q^{8}+O(q^{10}) \) 19 * q + 3 * q^2 + 25 * q^4 + 19 * q^5 + 12 * q^7 + 9 * q^8	\( 19 q + 3 q^{2} + 25 q^{4} + 19 q^{5} + 12 q^{7} + 9 q^{8} + 3 q^{10} + 19 q^{11} + 13 q^{13} + 37 q^{16} + 23 q^{17} + 19 q^{19} + 25 q^{20} + 3 q^{22} + 28 q^{23} + 19 q^{25} - 6 q^{26} + 27 q^{28} + 6 q^{29} + 16 q^{31} + 16 q^{32} + 8 q^{34} + 12 q^{35} + 6 q^{37} + 3 q^{38} + 9 q^{40} + 14 q^{41} + 32 q^{43} + 25 q^{44} + 9 q^{46} + 14 q^{47} + 47 q^{49} + 3 q^{50} + 32 q^{52} + 5 q^{53} + 19 q^{55} - 43 q^{56} + 5 q^{59} + 30 q^{61} - 2 q^{62} + 55 q^{64} + 13 q^{65} + 26 q^{67} + 42 q^{68} - 7 q^{71} + 28 q^{73} - q^{74} + 25 q^{76} + 12 q^{77} + 13 q^{79} + 37 q^{80} + 8 q^{82} + 23 q^{83} + 23 q^{85} - 31 q^{86} + 9 q^{88} - 7 q^{89} + 38 q^{91} + 68 q^{92} + 28 q^{94} + 19 q^{95} + 16 q^{97} - 46 q^{98}+O(q^{100}) \) 19 * q + 3 * q^2 + 25 * q^4 + 19 * q^5 + 12 * q^7 + 9 * q^8 + 3 * q^10 + 19 * q^11 + 13 * q^13 + 37 * q^16 + 23 * q^17 + 19 * q^19 + 25 * q^20 + 3 * q^22 + 28 * q^23 + 19 * q^25 - 6 * q^26 + 27 * q^28 + 6 * q^29 + 16 * q^31 + 16 * q^32 + 8 * q^34 + 12 * q^35 + 6 * q^37 + 3 * q^38 + 9 * q^40 + 14 * q^41 + 32 * q^43 + 25 * q^44 + 9 * q^46 + 14 * q^47 + 47 * q^49 + 3 * q^50 + 32 * q^52 + 5 * q^53 + 19 * q^55 - 43 * q^56 + 5 * q^59 + 30 * q^61 - 2 * q^62 + 55 * q^64 + 13 * q^65 + 26 * q^67 + 42 * q^68 - 7 * q^71 + 28 * q^73 - q^74 + 25 * q^76 + 12 * q^77 + 13 * q^79 + 37 * q^80 + 8 * q^82 + 23 * q^83 + 23 * q^85 - 31 * q^86 + 9 * q^88 - 7 * q^89 + 38 * q^91 + 68 * q^92 + 28 * q^94 + 19 * q^95 + 16 * q^97 - 46 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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