LMFDB - Embedded newform 5780.2.a.q.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5780,2,Mod(1,5780)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5780, 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("5780.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5780 = 2^{2} \cdot 5 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5780.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:	$46.1535323683$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 24x^{10} + 206x^{8} - 16x^{7} - 776x^{6} + 152x^{5} + 1226x^{4} - 384x^{3} - 588x^{2} + 200x + 34 $ x^12 - 24x^10 + 206x^8 - 16x^7 - 776x^6 + 152x^5 + 1226x^4 - 384x^3 - 588x^2 + 200*x + 34
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 340)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$0.567193$ of defining polynomial
Character	$\chi$	$=$	5780.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.567193 q^{3} -1.00000 q^{5} -2.93861 q^{7} -2.67829 q^{9} +O(q^{10})$	$q+0.567193 q^{3} -1.00000 q^{5} -2.93861 q^{7} -2.67829 q^{9} +4.64331 q^{11} -0.911081 q^{13} -0.567193 q^{15} +3.78507 q^{19} -1.66676 q^{21} -2.25065 q^{23} +1.00000 q^{25} -3.22069 q^{27} +1.11005 q^{29} +0.114502 q^{31} +2.63366 q^{33} +2.93861 q^{35} +10.1080 q^{37} -0.516759 q^{39} -0.709367 q^{41} -1.49508 q^{43} +2.67829 q^{45} +4.65244 q^{47} +1.63545 q^{49} +4.81340 q^{53} -4.64331 q^{55} +2.14686 q^{57} -2.55759 q^{59} -15.5516 q^{61} +7.87047 q^{63} +0.911081 q^{65} +2.81415 q^{67} -1.27655 q^{69} -15.8992 q^{71} -8.34895 q^{73} +0.567193 q^{75} -13.6449 q^{77} -10.8713 q^{79} +6.20812 q^{81} -12.6595 q^{83} +0.629611 q^{87} +6.76828 q^{89} +2.67732 q^{91} +0.0649448 q^{93} -3.78507 q^{95} +12.9638 q^{97} -12.4362 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{5} - 8 q^{7} + 12 q^{9}+O(q^{10}) $ 12 * q - 12 * q^5 - 8 * q^7 + 12 * q^9	$ 12 q - 12 q^{5} - 8 q^{7} + 12 q^{9} + 8 q^{13} - 16 q^{21} - 8 q^{23} + 12 q^{25} - 16 q^{29} - 24 q^{31} + 8 q^{35} - 24 q^{37} + 8 q^{39} - 24 q^{41} + 8 q^{43} - 12 q^{45} + 8 q^{47} + 20 q^{49} + 16 q^{53} - 32 q^{57} + 8 q^{59} - 40 q^{61} - 24 q^{63} - 8 q^{65} + 16 q^{67} - 16 q^{69} - 16 q^{71} - 32 q^{73} + 24 q^{77} - 8 q^{79} + 4 q^{81} + 32 q^{83} + 16 q^{87} - 8 q^{89} - 8 q^{91} - 8 q^{93} - 32 q^{97} - 24 q^{99}+O(q^{100}) $ 12 * q - 12 * q^5 - 8 * q^7 + 12 * q^9 + 8 * q^13 - 16 * q^21 - 8 * q^23 + 12 * q^25 - 16 * q^29 - 24 * q^31 + 8 * q^35 - 24 * q^37 + 8 * q^39 - 24 * q^41 + 8 * q^43 - 12 * q^45 + 8 * q^47 + 20 * q^49 + 16 * q^53 - 32 * q^57 + 8 * q^59 - 40 * q^61 - 24 * q^63 - 8 * q^65 + 16 * q^67 - 16 * q^69 - 16 * q^71 - 32 * q^73 + 24 * q^77 - 8 * q^79 + 4 * q^81 + 32 * q^83 + 16 * q^87 - 8 * q^89 - 8 * q^91 - 8 * q^93 - 32 * q^97 - 24 * q^99

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	0
$2$	0	0
$3$	0.567193	0.327469	0.163735	−	0.986504i	$-0.447646\pi$
$3$	0.567193	0.327469	0.163735	+	0.986504i	$0.447646\pi$
$4$	0	0
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0	0
$7$	−2.93861	−1.11069	−0.555346	−	0.831619i	$-0.687414\pi$
$7$	−2.93861	−1.11069	−0.555346	+	0.831619i	$0.687414\pi$
$8$	0	0
$9$	−2.67829	−0.892764
$10$	0	0
$11$	4.64331	1.40001	0.700006	−	0.714137i	$-0.253181\pi$
$11$	4.64331	1.40001	0.700006	+	0.714137i	$0.253181\pi$
$12$	0	0
$13$	−0.911081	−0.252689	−0.126344	−	0.991986i	$-0.540324\pi$
$13$	−0.911081	−0.252689	−0.126344	+	0.991986i	$0.540324\pi$
$14$	0	0
$15$	−0.567193	−0.146449
$16$	0	0
$17$	0	0
$17$	0	0
$18$	0	0
$19$	3.78507	0.868354	0.434177	−	0.900827i	$-0.357039\pi$
$19$	3.78507	0.868354	0.434177	+	0.900827i	$0.357039\pi$
$20$	0	0
$21$	−1.66676	−0.363717
$22$	0	0
$23$	−2.25065	−0.469293	−0.234647	−	0.972081i	$-0.575393\pi$
$23$	−2.25065	−0.469293	−0.234647	+	0.972081i	$0.575393\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	−3.22069	−0.619822
$28$	0	0
$29$	1.11005	0.206131	0.103065	−	0.994675i	$-0.467135\pi$
$29$	1.11005	0.206131	0.103065	+	0.994675i	$0.467135\pi$
$30$	0	0
$31$	0.114502	0.0205652	0.0102826	−	0.999947i	$-0.496727\pi$
$31$	0.114502	0.0205652	0.0102826	+	0.999947i	$0.496727\pi$
$32$	0	0
$33$	2.63366	0.458461
$34$	0	0
$35$	2.93861	0.496716
$36$	0	0
$37$	10.1080	1.66174	0.830871	−	0.556466i	$-0.187843\pi$
$37$	10.1080	1.66174	0.830871	+	0.556466i	$0.187843\pi$
$38$	0	0
$39$	−0.516759	−0.0827477
$40$	0	0
$41$	−0.709367	−0.110784	−0.0553922	−	0.998465i	$-0.517641\pi$
$41$	−0.709367	−0.110784	−0.0553922	+	0.998465i	$0.517641\pi$
$42$	0	0
$43$	−1.49508	−0.227997	−0.113999	−	0.993481i	$-0.536366\pi$
$43$	−1.49508	−0.227997	−0.113999	+	0.993481i	$0.536366\pi$
$44$	0	0
$45$	2.67829	0.399256
$46$	0	0
$47$	4.65244	0.678629	0.339314	−	0.940673i	$-0.389805\pi$
$47$	4.65244	0.678629	0.339314	+	0.940673i	$0.389805\pi$
$48$	0	0
$49$	1.63545	0.233636
$50$	0	0
$51$	0	0
$52$	0	0
$53$	4.81340	0.661171	0.330585	−	0.943776i	$-0.392754\pi$
$53$	4.81340	0.661171	0.330585	+	0.943776i	$0.392754\pi$
$54$	0	0
$55$	−4.64331	−0.626104
$56$	0	0
$57$	2.14686	0.284359
$58$	0	0
$59$	−2.55759	−0.332970	−0.166485	−	0.986044i	$-0.553242\pi$
$59$	−2.55759	−0.332970	−0.166485	+	0.986044i	$0.553242\pi$
$60$	0	0
$61$	−15.5516	−1.99118	−0.995592	−	0.0937934i	$-0.970101\pi$
$61$	−15.5516	−1.99118	−0.995592	+	0.0937934i	$0.970101\pi$
$62$	0	0
$63$	7.87047	0.991586
$64$	0	0
$65$	0.911081	0.113006
$66$	0	0
$67$	2.81415	0.343803	0.171902	−	0.985114i	$-0.445009\pi$
$67$	2.81415	0.343803	0.171902	+	0.985114i	$0.445009\pi$
$68$	0	0
$69$	−1.27655	−0.153679
$70$	0	0
$71$	−15.8992	−1.88689	−0.943443	−	0.331534i	$-0.892434\pi$
$71$	−15.8992	−1.88689	−0.943443	+	0.331534i	$0.892434\pi$
$72$	0	0
$73$	−8.34895	−0.977170	−0.488585	−	0.872516i	$-0.662487\pi$
$73$	−8.34895	−0.977170	−0.488585	+	0.872516i	$0.662487\pi$
$74$	0	0
$75$	0.567193	0.0654938
$76$	0	0
$77$	−13.6449	−1.55498
$78$	0	0
$79$	−10.8713	−1.22312	−0.611558	−	0.791199i	$-0.709457\pi$
$79$	−10.8713	−1.22312	−0.611558	+	0.791199i	$0.709457\pi$
$80$	0	0
$81$	6.20812	0.689792
$82$	0	0
$83$	−12.6595	−1.38956	−0.694779	−	0.719223i	$-0.744498\pi$
$83$	−12.6595	−1.38956	−0.694779	+	0.719223i	$0.744498\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	0.629611	0.0675014
$88$	0	0
$89$	6.76828	0.717436	0.358718	−	0.933446i	$-0.383214\pi$
$89$	6.76828	0.717436	0.358718	+	0.933446i	$0.383214\pi$
$90$	0	0
$91$	2.67732	0.280659
$92$	0	0
$93$	0.0649448	0.00673446
$94$	0	0
$95$	−3.78507	−0.388340
$96$	0	0
$97$	12.9638	1.31628	0.658139	−	0.752896i	$-0.271344\pi$
$97$	12.9638	1.31628	0.658139	+	0.752896i	$0.271344\pi$
$98$	0	0
$99$	−12.4362	−1.24988
$100$	0	0
$101$	−0.357798	−0.0356022	−0.0178011	−	0.999842i	$-0.505667\pi$
$101$	−0.357798	−0.0356022	−0.0178011	+	0.999842i	$0.505667\pi$
$102$	0	0
$103$	5.49801	0.541735	0.270868	−	0.962617i	$-0.412689\pi$
$103$	5.49801	0.541735	0.270868	+	0.962617i	$0.412689\pi$
$104$	0	0
$105$	1.66676	0.162659
$106$	0	0
$107$	13.2074	1.27680	0.638402	−	0.769703i	$-0.279596\pi$
$107$	13.2074	1.27680	0.638402	+	0.769703i	$0.279596\pi$
$108$	0	0
$109$	−1.30914	−0.125393	−0.0626965	−	0.998033i	$-0.519970\pi$
$109$	−1.30914	−0.125393	−0.0626965	+	0.998033i	$0.519970\pi$
$110$	0	0
$111$	5.73317	0.544169
$112$	0	0
$113$	−15.3358	−1.44267	−0.721335	−	0.692586i	$-0.756471\pi$
$113$	−15.3358	−1.44267	−0.721335	+	0.692586i	$0.756471\pi$
$114$	0	0
$115$	2.25065	0.209874
$116$	0	0
$117$	2.44014	0.225591
$118$	0	0
$119$	0	0
$120$	0	0
$121$	10.5604	0.960034
$122$	0	0
$123$	−0.402348	−0.0362785
$124$	0	0
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	5.63290	0.499839	0.249920	−	0.968267i	$-0.419596\pi$
$127$	5.63290	0.499839	0.249920	+	0.968267i	$0.419596\pi$
$128$	0	0
$129$	−0.847998	−0.0746620
$130$	0	0
$131$	−12.7883	−1.11732	−0.558661	−	0.829396i	$-0.688685\pi$
$131$	−12.7883	−1.11732	−0.558661	+	0.829396i	$0.688685\pi$
$132$	0	0
$133$	−11.1229	−0.964474
$134$	0	0
$135$	3.22069	0.277193
$136$	0	0
$137$	20.6055	1.76044	0.880222	−	0.474563i	$-0.157394\pi$
$137$	20.6055	1.76044	0.880222	+	0.474563i	$0.157394\pi$
$138$	0	0
$139$	−20.7481	−1.75983	−0.879914	−	0.475134i	$-0.842400\pi$
$139$	−20.7481	−1.75983	−0.879914	+	0.475134i	$0.842400\pi$
$140$	0	0
$141$	2.63883	0.222230
$142$	0	0
$143$	−4.23044	−0.353767
$144$	0	0
$145$	−1.11005	−0.0921844
$146$	0	0
$147$	0.927618	0.0765086
$148$	0	0
$149$	−18.6179	−1.52524	−0.762620	−	0.646847i	$-0.776087\pi$
$149$	−18.6179	−1.52524	−0.762620	+	0.646847i	$0.776087\pi$
$150$	0	0
$151$	−16.0963	−1.30990	−0.654949	−	0.755673i	$-0.727310\pi$
$151$	−16.0963	−1.30990	−0.654949	+	0.755673i	$0.727310\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	−0.114502	−0.00919703
$156$	0	0
$157$	3.54661	0.283050	0.141525	−	0.989935i	$-0.454799\pi$
$157$	3.54661	0.283050	0.141525	+	0.989935i	$0.454799\pi$
$158$	0	0
$159$	2.73013	0.216513
$160$	0	0
$161$	6.61380	0.521240
$162$	0	0
$163$	7.41041	0.580428	0.290214	−	0.956962i	$-0.406274\pi$
$163$	7.41041	0.580428	0.290214	+	0.956962i	$0.406274\pi$
$164$	0	0
$165$	−2.63366	−0.205030
$166$	0	0
$167$	−0.0751285	−0.00581362	−0.00290681	−	0.999996i	$-0.500925\pi$
$167$	−0.0751285	−0.00581362	−0.00290681	+	0.999996i	$0.500925\pi$
$168$	0	0
$169$	−12.1699	−0.936149
$170$	0	0
$171$	−10.1375	−0.775236
$172$	0	0
$173$	−9.64765	−0.733497	−0.366749	−	0.930320i	$-0.619529\pi$
$173$	−9.64765	−0.733497	−0.366749	+	0.930320i	$0.619529\pi$
$174$	0	0
$175$	−2.93861	−0.222138
$176$	0	0
$177$	−1.45065	−0.109037
$178$	0	0
$179$	−15.5693	−1.16371	−0.581853	−	0.813294i	$-0.697672\pi$
$179$	−15.5693	−1.16371	−0.581853	+	0.813294i	$0.697672\pi$
$180$	0	0
$181$	−17.4712	−1.29863	−0.649313	−	0.760522i	$-0.724943\pi$
$181$	−17.4712	−1.29863	−0.649313	+	0.760522i	$0.724943\pi$
$182$	0	0
$183$	−8.82078	−0.652051
$184$	0	0
$185$	−10.1080	−0.743153
$186$	0	0
$187$	0	0
$188$	0	0
$189$	9.46436	0.688431
$190$	0	0
$191$	−17.3320	−1.25410	−0.627049	−	0.778980i	$-0.715737\pi$
$191$	−17.3320	−1.25410	−0.627049	+	0.778980i	$0.715737\pi$
$192$	0	0
$193$	−11.3026	−0.813577	−0.406789	−	0.913522i	$-0.633351\pi$
$193$	−11.3026	−0.813577	−0.406789	+	0.913522i	$0.633351\pi$
$194$	0	0
$195$	0.516759	0.0370059
$196$	0	0
$197$	−18.1238	−1.29127	−0.645634	−	0.763647i	$-0.723407\pi$
$197$	−18.1238	−1.29127	−0.645634	+	0.763647i	$0.723407\pi$
$198$	0	0
$199$	19.8734	1.40879	0.704394	−	0.709809i	$-0.251219\pi$
$199$	19.8734	1.40879	0.704394	+	0.709809i	$0.251219\pi$
$200$	0	0
$201$	1.59617	0.112585
$202$	0	0
$203$	−3.26200	−0.228947
$204$	0	0
$205$	0.709367	0.0495443
$206$	0	0
$207$	6.02790	0.418968
$208$	0	0
$209$	17.5753	1.21571
$210$	0	0
$211$	−20.5043	−1.41157	−0.705786	−	0.708425i	$-0.749406\pi$
$211$	−20.5043	−1.41157	−0.705786	+	0.708425i	$0.749406\pi$
$212$	0	0
$213$	−9.01791	−0.617897
$214$	0	0
$215$	1.49508	0.101963
$216$	0	0
$217$	−0.336478	−0.0228416
$218$	0	0
$219$	−4.73546	−0.319993
$220$	0	0
$221$	0	0
$222$	0	0
$223$	2.02374	0.135519	0.0677597	−	0.997702i	$-0.478415\pi$
$223$	2.02374	0.135519	0.0677597	+	0.997702i	$0.478415\pi$
$224$	0	0
$225$	−2.67829	−0.178553
$226$	0	0
$227$	−1.55247	−0.103041	−0.0515205	−	0.998672i	$-0.516407\pi$
$227$	−1.55247	−0.103041	−0.0515205	+	0.998672i	$0.516407\pi$
$228$	0	0
$229$	9.62923	0.636318	0.318159	−	0.948037i	$-0.396935\pi$
$229$	9.62923	0.636318	0.318159	+	0.948037i	$0.396935\pi$
$230$	0	0
$231$	−7.73930	−0.509208
$232$	0	0
$233$	−2.68210	−0.175710	−0.0878550	−	0.996133i	$-0.528001\pi$
$233$	−2.68210	−0.175710	−0.0878550	+	0.996133i	$0.528001\pi$
$234$	0	0
$235$	−4.65244	−0.303492
$236$	0	0
$237$	−6.16612	−0.400533
$238$	0	0
$239$	4.92375	0.318491	0.159245	−	0.987239i	$-0.449094\pi$
$239$	4.92375	0.318491	0.159245	+	0.987239i	$0.449094\pi$
$240$	0	0
$241$	−7.47841	−0.481727	−0.240864	−	0.970559i	$-0.577431\pi$
$241$	−7.47841	−0.481727	−0.240864	+	0.970559i	$0.577431\pi$
$242$	0	0
$243$	13.1833	0.845707
$244$	0	0
$245$	−1.63545	−0.104485
$246$	0	0
$247$	−3.44851	−0.219423
$248$	0	0
$249$	−7.18037	−0.455037
$250$	0	0
$251$	6.12708	0.386738	0.193369	−	0.981126i	$-0.438059\pi$
$251$	6.12708	0.386738	0.193369	+	0.981126i	$0.438059\pi$
$252$	0	0
$253$	−10.4505	−0.657016
$254$	0	0
$255$	0	0
$256$	0	0
$257$	8.09538	0.504976	0.252488	−	0.967600i	$-0.418751\pi$
$257$	8.09538	0.504976	0.252488	+	0.967600i	$0.418751\pi$
$258$	0	0
$259$	−29.7034	−1.84568
$260$	0	0
$261$	−2.97303	−0.184026
$262$	0	0
$263$	−23.8985	−1.47365	−0.736823	−	0.676085i	$-0.763675\pi$
$263$	−23.8985	−1.47365	−0.736823	+	0.676085i	$0.763675\pi$
$264$	0	0
$265$	−4.81340	−0.295685
$266$	0	0
$267$	3.83892	0.234938
$268$	0	0
$269$	19.0635	1.16232	0.581160	−	0.813790i	$-0.302599\pi$
$269$	19.0635	1.16232	0.581160	+	0.813790i	$0.302599\pi$
$270$	0	0
$271$	25.7649	1.56511	0.782554	−	0.622583i	$-0.213917\pi$
$271$	25.7649	1.56511	0.782554	+	0.622583i	$0.213917\pi$
$272$	0	0
$273$	1.51856	0.0919072
$274$	0	0
$275$	4.64331	0.280002
$276$	0	0
$277$	−21.4446	−1.28848	−0.644241	−	0.764822i	$-0.722827\pi$
$277$	−21.4446	−1.28848	−0.644241	+	0.764822i	$0.722827\pi$
$278$	0	0
$279$	−0.306670	−0.0183599
$280$	0	0
$281$	−19.8460	−1.18391	−0.591956	−	0.805971i	$-0.701644\pi$
$281$	−19.8460	−1.18391	−0.591956	+	0.805971i	$0.701644\pi$
$282$	0	0
$283$	−6.30248	−0.374643	−0.187322	−	0.982299i	$-0.559981\pi$
$283$	−6.30248	−0.374643	−0.187322	+	0.982299i	$0.559981\pi$
$284$	0	0
$285$	−2.14686	−0.127169
$286$	0	0
$287$	2.08456	0.123047
$288$	0	0
$289$	0	0
$290$	0	0
$291$	7.35300	0.431040
$292$	0	0
$293$	−29.7727	−1.73934	−0.869671	−	0.493631i	$-0.835669\pi$
$293$	−29.7727	−1.73934	−0.869671	+	0.493631i	$0.835669\pi$
$294$	0	0
$295$	2.55759	0.148909
$296$	0	0
$297$	−14.9547	−0.867758
$298$	0	0
$299$	2.05053	0.118585
$300$	0	0
$301$	4.39346	0.253235
$302$	0	0
$303$	−0.202940	−0.0116586
$304$	0	0
$305$	15.5516	0.890484
$306$	0	0
$307$	26.9312	1.53704	0.768521	−	0.639824i	$-0.220993\pi$
$307$	26.9312	1.53704	0.768521	+	0.639824i	$0.220993\pi$
$308$	0	0
$309$	3.11843	0.177402
$310$	0	0
$311$	4.78741	0.271469	0.135735	−	0.990745i	$-0.456661\pi$
$311$	4.78741	0.271469	0.135735	+	0.990745i	$0.456661\pi$
$312$	0	0
$313$	−13.6529	−0.771708	−0.385854	−	0.922560i	$-0.626093\pi$
$313$	−13.6529	−0.771708	−0.385854	+	0.922560i	$0.626093\pi$
$314$	0	0
$315$	−7.87047	−0.443451
$316$	0	0
$317$	−3.16144	−0.177564	−0.0887820	−	0.996051i	$-0.528297\pi$
$317$	−3.16144	−0.177564	−0.0887820	+	0.996051i	$0.528297\pi$
$318$	0	0
$319$	5.15430	0.288585
$320$	0	0
$321$	7.49113	0.418114
$322$	0	0
$323$	0	0
$324$	0	0
$325$	−0.911081	−0.0505377
$326$	0	0
$327$	−0.742536	−0.0410623
$328$	0	0
$329$	−13.6717	−0.753747
$330$	0	0
$331$	32.2230	1.77114	0.885569	−	0.464509i	$-0.153769\pi$
$331$	32.2230	1.77114	0.885569	+	0.464509i	$0.153769\pi$
$332$	0	0
$333$	−27.0721	−1.48354
$334$	0	0
$335$	−2.81415	−0.153754
$336$	0	0
$337$	6.74718	0.367542	0.183771	−	0.982969i	$-0.441169\pi$
$337$	6.74718	0.367542	0.183771	+	0.982969i	$0.441169\pi$
$338$	0	0
$339$	−8.69836	−0.472430
$340$	0	0
$341$	0.531669	0.0287915
$342$	0	0
$343$	15.7643	0.851194
$344$	0	0
$345$	1.27655	0.0687274
$346$	0	0
$347$	30.2965	1.62640	0.813202	−	0.581982i	$-0.197723\pi$
$347$	30.2965	1.62640	0.813202	+	0.581982i	$0.197723\pi$
$348$	0	0
$349$	18.2473	0.976757	0.488379	−	0.872632i	$-0.337588\pi$
$349$	18.2473	0.976757	0.488379	+	0.872632i	$0.337588\pi$
$350$	0	0
$351$	2.93431	0.156622
$352$	0	0
$353$	28.7243	1.52884	0.764420	−	0.644719i	$-0.223025\pi$
$353$	28.7243	1.52884	0.764420	+	0.644719i	$0.223025\pi$
$354$	0	0
$355$	15.8992	0.843841
$356$	0	0
$357$	0	0
$358$	0	0
$359$	−11.7932	−0.622423	−0.311211	−	0.950341i	$-0.600735\pi$
$359$	−11.7932	−0.622423	−0.311211	+	0.950341i	$0.600735\pi$
$360$	0	0
$361$	−4.67325	−0.245960
$362$	0	0
$363$	5.98977	0.314381
$364$	0	0
$365$	8.34895	0.437004
$366$	0	0
$367$	−33.2306	−1.73462	−0.867311	−	0.497767i	$-0.834153\pi$
$367$	−33.2306	−1.73462	−0.867311	+	0.497767i	$0.834153\pi$
$368$	0	0
$369$	1.89989	0.0989044
$370$	0	0
$371$	−14.1447	−0.734357
$372$	0	0
$373$	−11.5286	−0.596929	−0.298465	−	0.954421i	$-0.596474\pi$
$373$	−11.5286	−0.596929	−0.298465	+	0.954421i	$0.596474\pi$
$374$	0	0
$375$	−0.567193	−0.0292897
$376$	0	0
$377$	−1.01134	−0.0520868
$378$	0	0
$379$	2.48418	0.127604	0.0638019	−	0.997963i	$-0.479677\pi$
$379$	2.48418	0.127604	0.0638019	+	0.997963i	$0.479677\pi$
$380$	0	0
$381$	3.19494	0.163682
$382$	0	0
$383$	−0.571205	−0.0291872	−0.0145936	−	0.999894i	$-0.504645\pi$
$383$	−0.571205	−0.0291872	−0.0145936	+	0.999894i	$0.504645\pi$
$384$	0	0
$385$	13.6449	0.695409
$386$	0	0
$387$	4.00425	0.203548
$388$	0	0
$389$	−12.7923	−0.648595	−0.324298	−	0.945955i	$-0.605128\pi$
$389$	−12.7923	−0.648595	−0.324298	+	0.945955i	$0.605128\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	−7.25345	−0.365888
$394$	0	0
$395$	10.8713	0.546994
$396$	0	0
$397$	−25.9684	−1.30331	−0.651657	−	0.758514i	$-0.725926\pi$
$397$	−25.9684	−1.30331	−0.651657	+	0.758514i	$0.725926\pi$
$398$	0	0
$399$	−6.30881	−0.315835
$400$	0	0
$401$	3.86483	0.193001	0.0965003	−	0.995333i	$-0.469235\pi$
$401$	3.86483	0.193001	0.0965003	+	0.995333i	$0.469235\pi$
$402$	0	0
$403$	−0.104321	−0.00519659
$404$	0	0
$405$	−6.20812	−0.308484
$406$	0	0
$407$	46.9345	2.32646
$408$	0	0
$409$	31.0395	1.53480	0.767402	−	0.641166i	$-0.221549\pi$
$409$	31.0395	1.53480	0.767402	+	0.641166i	$0.221549\pi$
$410$	0	0
$411$	11.6873	0.576491
$412$	0	0
$413$	7.51578	0.369827
$414$	0	0
$415$	12.6595	0.621429
$416$	0	0
$417$	−11.7682	−0.576289
$418$	0	0
$419$	−3.16156	−0.154452	−0.0772262	−	0.997014i	$-0.524606\pi$
$419$	−3.16156	−0.154452	−0.0772262	+	0.997014i	$0.524606\pi$
$420$	0	0
$421$	−21.8507	−1.06494	−0.532470	−	0.846449i	$-0.678736\pi$
$421$	−21.8507	−1.06494	−0.532470	+	0.846449i	$0.678736\pi$
$422$	0	0
$423$	−12.4606	−0.605855
$424$	0	0
$425$	0	0
$426$	0	0
$427$	45.7003	2.21159
$428$	0	0
$429$	−2.39947	−0.115848
$430$	0	0
$431$	13.5543	0.652890	0.326445	−	0.945216i	$-0.394149\pi$
$431$	13.5543	0.652890	0.326445	+	0.945216i	$0.394149\pi$
$432$	0	0
$433$	31.5631	1.51683	0.758413	−	0.651774i	$-0.225975\pi$
$433$	31.5631	1.51683	0.758413	+	0.651774i	$0.225975\pi$
$434$	0	0
$435$	−0.629611	−0.0301875
$436$	0	0
$437$	−8.51887	−0.407513
$438$	0	0
$439$	−17.4642	−0.833521	−0.416760	−	0.909016i	$-0.636835\pi$
$439$	−17.4642	−0.833521	−0.416760	+	0.909016i	$0.636835\pi$
$440$	0	0
$441$	−4.38022	−0.208582
$442$	0	0
$443$	10.2584	0.487390	0.243695	−	0.969852i	$-0.421640\pi$
$443$	10.2584	0.487390	0.243695	+	0.969852i	$0.421640\pi$
$444$	0	0
$445$	−6.76828	−0.320847
$446$	0	0
$447$	−10.5600	−0.499469
$448$	0	0
$449$	−31.9238	−1.50657	−0.753287	−	0.657691i	$-0.771533\pi$
$449$	−31.9238	−1.50657	−0.753287	+	0.657691i	$0.771533\pi$
$450$	0	0
$451$	−3.29381	−0.155100
$452$	0	0
$453$	−9.12971	−0.428951
$454$	0	0
$455$	−2.67732	−0.125515
$456$	0	0
$457$	−3.01515	−0.141043	−0.0705214	−	0.997510i	$-0.522466\pi$
$457$	−3.01515	−0.141043	−0.0705214	+	0.997510i	$0.522466\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	−4.81904	−0.224445	−0.112222	−	0.993683i	$-0.535797\pi$
$461$	−4.81904	−0.224445	−0.112222	+	0.993683i	$0.535797\pi$
$462$	0	0
$463$	23.7981	1.10599	0.552997	−	0.833183i	$-0.313484\pi$
$463$	23.7981	1.10599	0.552997	+	0.833183i	$0.313484\pi$
$464$	0	0
$465$	−0.0649448	−0.00301174
$466$	0	0
$467$	−24.7852	−1.14692	−0.573460	−	0.819233i	$-0.694399\pi$
$467$	−24.7852	−1.14692	−0.573460	+	0.819233i	$0.694399\pi$
$468$	0	0
$469$	−8.26971	−0.381860
$470$	0	0
$471$	2.01161	0.0926901
$472$	0	0
$473$	−6.94212	−0.319199
$474$	0	0
$475$	3.78507	0.173671
$476$	0	0
$477$	−12.8917	−0.590270
$478$	0	0
$479$	−3.75217	−0.171441	−0.0857205	−	0.996319i	$-0.527319\pi$
$479$	−3.75217	−0.171441	−0.0857205	+	0.996319i	$0.527319\pi$
$480$	0	0
$481$	−9.20919	−0.419903
$482$	0	0
$483$	3.75130	0.170690
$484$	0	0
$485$	−12.9638	−0.588658
$486$	0	0
$487$	12.5306	0.567816	0.283908	−	0.958852i	$-0.408369\pi$
$487$	12.5306	0.567816	0.283908	+	0.958852i	$0.408369\pi$
$488$	0	0
$489$	4.20313	0.190072
$490$	0	0
$491$	−12.8534	−0.580066	−0.290033	−	0.957017i	$-0.593666\pi$
$491$	−12.8534	−0.580066	−0.290033	+	0.957017i	$0.593666\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	12.4362	0.558964
$496$	0	0
$497$	46.7216	2.09575
$498$	0	0
$499$	25.5667	1.14452	0.572261	−	0.820071i	$-0.306066\pi$
$499$	25.5667	1.14452	0.572261	+	0.820071i	$0.306066\pi$
$500$	0	0
$501$	−0.0426124	−0.00190378
$502$	0	0
$503$	−10.3748	−0.462588	−0.231294	−	0.972884i	$-0.574296\pi$
$503$	−10.3748	−0.462588	−0.231294	+	0.972884i	$0.574296\pi$
$504$	0	0
$505$	0.357798	0.0159218
$506$	0	0
$507$	−6.90270	−0.306560
$508$	0	0
$509$	−13.0874	−0.580089	−0.290045	−	0.957013i	$-0.593670\pi$
$509$	−13.0874	−0.580089	−0.290045	+	0.957013i	$0.593670\pi$
$510$	0	0
$511$	24.5343	1.08533
$512$	0	0
$513$	−12.1905	−0.538225
$514$	0	0
$515$	−5.49801	−0.242271
$516$	0	0
$517$	21.6028	0.950089
$518$	0	0
$519$	−5.47208	−0.240198
$520$	0	0
$521$	−18.3698	−0.804796	−0.402398	−	0.915465i	$-0.631823\pi$
$521$	−18.3698	−0.804796	−0.402398	+	0.915465i	$0.631823\pi$
$522$	0	0
$523$	−28.8990	−1.26366	−0.631831	−	0.775106i	$-0.717697\pi$
$523$	−28.8990	−1.26366	−0.631831	+	0.775106i	$0.717697\pi$
$524$	0	0
$525$	−1.66676	−0.0727434
$526$	0	0
$527$	0	0
$528$	0	0
$529$	−17.9346	−0.779764
$530$	0	0
$531$	6.84998	0.297264
$532$	0	0
$533$	0.646291	0.0279940
$534$	0	0
$535$	−13.2074	−0.571005
$536$	0	0
$537$	−8.83081	−0.381078
$538$	0	0
$539$	7.59392	0.327093
$540$	0	0
$541$	−24.8422	−1.06805	−0.534024	−	0.845469i	$-0.679321\pi$
$541$	−24.8422	−1.06805	−0.534024	+	0.845469i	$0.679321\pi$
$542$	0	0
$543$	−9.90955	−0.425260
$544$	0	0
$545$	1.30914	0.0560774
$546$	0	0
$547$	−11.0402	−0.472047	−0.236023	−	0.971747i	$-0.575844\pi$
$547$	−11.0402	−0.472047	−0.236023	+	0.971747i	$0.575844\pi$
$548$	0	0
$549$	41.6518	1.77766
$550$	0	0
$551$	4.20160	0.178994
$552$	0	0
$553$	31.9465	1.35851
$554$	0	0
$555$	−5.73317	−0.243360
$556$	0	0
$557$	12.9587	0.549078	0.274539	−	0.961576i	$-0.411475\pi$
$557$	12.9587	0.549078	0.274539	+	0.961576i	$0.411475\pi$
$558$	0	0
$559$	1.36214	0.0576123
$560$	0	0
$561$	0	0
$562$	0	0
$563$	32.7865	1.38178	0.690892	−	0.722958i	$-0.257218\pi$
$563$	32.7865	1.38178	0.690892	+	0.722958i	$0.257218\pi$
$564$	0	0
$565$	15.3358	0.645182
$566$	0	0
$567$	−18.2433	−0.766146
$568$	0	0
$569$	44.3438	1.85899	0.929494	−	0.368836i	$-0.120244\pi$
$569$	44.3438	1.85899	0.929494	+	0.368836i	$0.120244\pi$
$570$	0	0
$571$	9.82495	0.411161	0.205581	−	0.978640i	$-0.434092\pi$
$571$	9.82495	0.411161	0.205581	+	0.978640i	$0.434092\pi$
$572$	0	0
$573$	−9.83057	−0.410678
$574$	0	0
$575$	−2.25065	−0.0938587
$576$	0	0
$577$	27.9884	1.16517	0.582585	−	0.812769i	$-0.302041\pi$
$577$	27.9884	1.16517	0.582585	+	0.812769i	$0.302041\pi$
$578$	0	0
$579$	−6.41074	−0.266421
$580$	0	0
$581$	37.2013	1.54337
$582$	0	0
$583$	22.3501	0.925647
$584$	0	0
$585$	−2.44014	−0.100887
$586$	0	0
$587$	12.3851	0.511188	0.255594	−	0.966784i	$-0.417729\pi$
$587$	12.3851	0.511188	0.255594	+	0.966784i	$0.417729\pi$
$588$	0	0
$589$	0.433398	0.0178579
$590$	0	0
$591$	−10.2797	−0.422851
$592$	0	0
$593$	20.7954	0.853964	0.426982	−	0.904260i	$-0.359577\pi$
$593$	20.7954	0.853964	0.426982	+	0.904260i	$0.359577\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	11.2721	0.461334
$598$	0	0
$599$	−36.0571	−1.47325	−0.736626	−	0.676301i	$-0.763582\pi$
$599$	−36.0571	−1.47325	−0.736626	+	0.676301i	$0.763582\pi$
$600$	0	0
$601$	−27.9781	−1.14125	−0.570626	−	0.821210i	$-0.693299\pi$
$601$	−27.9781	−1.14125	−0.570626	+	0.821210i	$0.693299\pi$
$602$	0	0
$603$	−7.53712	−0.306935
$604$	0	0
$605$	−10.5604	−0.429340
$606$	0	0
$607$	−24.6062	−0.998737	−0.499368	−	0.866390i	$-0.666435\pi$
$607$	−24.6062	−0.998737	−0.499368	+	0.866390i	$0.666435\pi$
$608$	0	0
$609$	−1.85018	−0.0749732
$610$	0	0
$611$	−4.23876	−0.171482
$612$	0	0
$613$	−32.7899	−1.32437	−0.662186	−	0.749340i	$-0.730371\pi$
$613$	−32.7899	−1.32437	−0.662186	+	0.749340i	$0.730371\pi$
$614$	0	0
$615$	0.402348	0.0162242
$616$	0	0
$617$	−43.7234	−1.76024	−0.880119	−	0.474754i	$-0.842537\pi$
$617$	−43.7234	−1.76024	−0.880119	+	0.474754i	$0.842537\pi$
$618$	0	0
$619$	7.94422	0.319305	0.159653	−	0.987173i	$-0.448963\pi$
$619$	7.94422	0.319305	0.159653	+	0.987173i	$0.448963\pi$
$620$	0	0
$621$	7.24865	0.290878
$622$	0	0
$623$	−19.8894	−0.796850
$624$	0	0
$625$	1.00000	0.0400000
$626$	0	0
$627$	9.96857	0.398106
$628$	0	0
$629$	0	0
$630$	0	0
$631$	−2.88918	−0.115017	−0.0575083	−	0.998345i	$-0.518316\pi$
$631$	−2.88918	−0.115017	−0.0575083	+	0.998345i	$0.518316\pi$
$632$	0	0
$633$	−11.6299	−0.462246
$634$	0	0
$635$	−5.63290	−0.223535
$636$	0	0
$637$	−1.49003	−0.0590372
$638$	0	0
$639$	42.5827	1.68454
$640$	0	0
$641$	14.8514	0.586595	0.293297	−	0.956021i	$-0.405247\pi$
$641$	14.8514	0.586595	0.293297	+	0.956021i	$0.405247\pi$
$642$	0	0
$643$	35.2346	1.38952	0.694759	−	0.719242i	$-0.255511\pi$
$643$	35.2346	1.38952	0.694759	+	0.719242i	$0.255511\pi$
$644$	0	0
$645$	0.847998	0.0333899
$646$	0	0
$647$	−23.7726	−0.934599	−0.467299	−	0.884099i	$-0.654773\pi$
$647$	−23.7726	−0.934599	−0.467299	+	0.884099i	$0.654773\pi$
$648$	0	0
$649$	−11.8757	−0.466162
$650$	0	0
$651$	−0.190848	−0.00747991
$652$	0	0
$653$	−21.2647	−0.832150	−0.416075	−	0.909330i	$-0.636595\pi$
$653$	−21.2647	−0.832150	−0.416075	+	0.909330i	$0.636595\pi$
$654$	0	0
$655$	12.7883	0.499682
$656$	0	0
$657$	22.3609	0.872382
$658$	0	0
$659$	17.2360	0.671420	0.335710	−	0.941965i	$-0.391024\pi$
$659$	17.2360	0.671420	0.335710	+	0.941965i	$0.391024\pi$
$660$	0	0
$661$	−4.83746	−0.188155	−0.0940776	−	0.995565i	$-0.529990\pi$
$661$	−4.83746	−0.188155	−0.0940776	+	0.995565i	$0.529990\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	11.1229	0.431326
$666$	0	0
$667$	−2.49833	−0.0967357
$668$	0	0
$669$	1.14785	0.0443784
$670$	0	0
$671$	−72.2112	−2.78768
$672$	0	0
$673$	35.8878	1.38337	0.691687	−	0.722198i	$-0.256868\pi$
$673$	35.8878	1.38337	0.691687	+	0.722198i	$0.256868\pi$
$674$	0	0
$675$	−3.22069	−0.123964
$676$	0	0
$677$	−20.6054	−0.791931	−0.395965	−	0.918265i	$-0.629590\pi$
$677$	−20.6054	−0.791931	−0.395965	+	0.918265i	$0.629590\pi$
$678$	0	0
$679$	−38.0957	−1.46198
$680$	0	0
$681$	−0.880550	−0.0337428
$682$	0	0
$683$	−11.2790	−0.431577	−0.215789	−	0.976440i	$-0.569232\pi$
$683$	−11.2790	−0.431577	−0.215789	+	0.976440i	$0.569232\pi$
$684$	0	0
$685$	−20.6055	−0.787294
$686$	0	0
$687$	5.46163	0.208374
$688$	0	0
$689$	−4.38540	−0.167070
$690$	0	0
$691$	−3.83982	−0.146074	−0.0730369	−	0.997329i	$-0.523269\pi$
$691$	−3.83982	−0.146074	−0.0730369	+	0.997329i	$0.523269\pi$
$692$	0	0
$693$	36.5451	1.38823
$694$	0	0
$695$	20.7481	0.787019
$696$	0	0
$697$	0	0
$698$	0	0
$699$	−1.52127	−0.0575396
$700$	0	0
$701$	11.0182	0.416152	0.208076	−	0.978113i	$-0.433280\pi$
$701$	11.0182	0.416152	0.208076	+	0.978113i	$0.433280\pi$
$702$	0	0
$703$	38.2594	1.44298
$704$	0	0
$705$	−2.63883	−0.0993842
$706$	0	0
$707$	1.05143	0.0395431
$708$	0	0
$709$	13.3790	0.502460	0.251230	−	0.967927i	$-0.419165\pi$
$709$	13.3790	0.502460	0.251230	+	0.967927i	$0.419165\pi$
$710$	0	0
$711$	29.1165	1.09195
$712$	0	0
$713$	−0.257704	−0.00965111
$714$	0	0
$715$	4.23044	0.158209
$716$	0	0
$717$	2.79272	0.104296
$718$	0	0
$719$	24.3282	0.907288	0.453644	−	0.891183i	$-0.350124\pi$
$719$	24.3282	0.907288	0.453644	+	0.891183i	$0.350124\pi$
$720$	0	0
$721$	−16.1565	−0.601701
$722$	0	0
$723$	−4.24170	−0.157751
$724$	0	0
$725$	1.11005	0.0412261
$726$	0	0
$727$	−41.1943	−1.52781	−0.763906	−	0.645328i	$-0.776721\pi$
$727$	−41.1943	−1.52781	−0.763906	+	0.645328i	$0.776721\pi$
$728$	0	0
$729$	−11.1469	−0.412849
$730$	0	0
$731$	0	0
$732$	0	0
$733$	−48.3713	−1.78663	−0.893317	−	0.449427i	$-0.851628\pi$
$733$	−48.3713	−1.78663	−0.893317	+	0.449427i	$0.851628\pi$
$734$	0	0
$735$	−0.927618	−0.0342157
$736$	0	0
$737$	13.0670	0.481329
$738$	0	0
$739$	8.46957	0.311558	0.155779	−	0.987792i	$-0.450211\pi$
$739$	8.46957	0.311558	0.155779	+	0.987792i	$0.450211\pi$
$740$	0	0
$741$	−1.95597	−0.0718543
$742$	0	0
$743$	47.5857	1.74575	0.872875	−	0.487943i	$-0.162253\pi$
$743$	47.5857	1.74575	0.872875	+	0.487943i	$0.162253\pi$
$744$	0	0
$745$	18.6179	0.682108
$746$	0	0
$747$	33.9058	1.24055
$748$	0	0
$749$	−38.8114	−1.41814
$750$	0	0
$751$	−21.3937	−0.780667	−0.390334	−	0.920674i	$-0.627640\pi$
$751$	−21.3937	−0.780667	−0.390334	+	0.920674i	$0.627640\pi$
$752$	0	0
$753$	3.47524	0.126645
$754$	0	0
$755$	16.0963	0.585805
$756$	0	0
$757$	−46.5900	−1.69334	−0.846670	−	0.532118i	$-0.821396\pi$
$757$	−46.5900	−1.69334	−0.846670	+	0.532118i	$0.821396\pi$
$758$	0	0
$759$	−5.92744	−0.215153
$760$	0	0
$761$	33.4282	1.21177	0.605885	−	0.795552i	$-0.292819\pi$
$761$	33.4282	1.21177	0.605885	+	0.795552i	$0.292819\pi$
$762$	0	0
$763$	3.84706	0.139273
$764$	0	0
$765$	0	0
$766$	0	0
$767$	2.33018	0.0841378
$768$	0	0
$769$	−28.7957	−1.03840	−0.519199	−	0.854653i	$-0.673770\pi$
$769$	−28.7957	−1.03840	−0.519199	+	0.854653i	$0.673770\pi$
$770$	0	0
$771$	4.59164	0.165364
$772$	0	0
$773$	37.0530	1.33270	0.666352	−	0.745637i	$-0.267855\pi$
$773$	37.0530	1.33270	0.666352	+	0.745637i	$0.267855\pi$
$774$	0	0
$775$	0.114502	0.00411304
$776$	0	0
$777$	−16.8476	−0.604404
$778$	0	0
$779$	−2.68500	−0.0962002
$780$	0	0
$781$	−73.8249	−2.64166
$782$	0	0
$783$	−3.57511	−0.127764
$784$	0	0
$785$	−3.54661	−0.126584
$786$	0	0
$787$	−47.1362	−1.68022	−0.840112	−	0.542412i	$-0.817511\pi$
$787$	−47.1362	−1.68022	−0.840112	+	0.542412i	$0.817511\pi$
$788$	0	0
$789$	−13.5551	−0.482574
$790$	0	0
$791$	45.0660	1.60236
$792$	0	0
$793$	14.1688	0.503149
$794$	0	0
$795$	−2.73013	−0.0968276
$796$	0	0
$797$	25.0204	0.886267	0.443133	−	0.896456i	$-0.353867\pi$
$797$	25.0204	0.886267	0.443133	+	0.896456i	$0.353867\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	−18.1274	−0.640501
$802$	0	0
$803$	−38.7668	−1.36805
$804$	0	0
$805$	−6.61380	−0.233106
$806$	0	0
$807$	10.8127	0.380624
$808$	0	0
$809$	29.6747	1.04331	0.521653	−	0.853158i	$-0.325316\pi$
$809$	29.6747	1.04331	0.521653	+	0.853158i	$0.325316\pi$
$810$	0	0
$811$	21.5091	0.755286	0.377643	−	0.925951i	$-0.376735\pi$
$811$	21.5091	0.755286	0.377643	+	0.925951i	$0.376735\pi$
$812$	0	0
$813$	14.6137	0.512524
$814$	0	0
$815$	−7.41041	−0.259575
$816$	0	0
$817$	−5.65897	−0.197982
$818$	0	0
$819$	−7.17064	−0.250562
$820$	0	0
$821$	10.7932	0.376685	0.188343	−	0.982103i	$-0.439688\pi$
$821$	10.7932	0.376685	0.188343	+	0.982103i	$0.439688\pi$
$822$	0	0
$823$	−39.7222	−1.38463	−0.692314	−	0.721596i	$-0.743409\pi$
$823$	−39.7222	−1.38463	−0.692314	+	0.721596i	$0.743409\pi$
$824$	0	0
$825$	2.63366	0.0916921
$826$	0	0
$827$	53.1326	1.84760	0.923801	−	0.382872i	$-0.125065\pi$
$827$	53.1326	1.84760	0.923801	+	0.382872i	$0.125065\pi$
$828$	0	0
$829$	−24.5278	−0.851885	−0.425942	−	0.904750i	$-0.640057\pi$
$829$	−24.5278	−0.851885	−0.425942	+	0.904750i	$0.640057\pi$
$830$	0	0
$831$	−12.1632	−0.421938
$832$	0	0
$833$	0	0
$834$	0	0
$835$	0.0751285	0.00259993
$836$	0	0
$837$	−0.368776	−0.0127467
$838$	0	0
$839$	4.06585	0.140369	0.0701843	−	0.997534i	$-0.477641\pi$
$839$	4.06585	0.140369	0.0701843	+	0.997534i	$0.477641\pi$
$840$	0	0
$841$	−27.7678	−0.957510
$842$	0	0
$843$	−11.2565	−0.387694
$844$	0	0
$845$	12.1699	0.418658
$846$	0	0
$847$	−31.0329	−1.06630
$848$	0	0
$849$	−3.57472	−0.122684
$850$	0	0
$851$	−22.7495	−0.779844
$852$	0	0
$853$	−13.5923	−0.465393	−0.232696	−	0.972549i	$-0.574755\pi$
$853$	−13.5923	−0.465393	−0.232696	+	0.972549i	$0.574755\pi$
$854$	0	0
$855$	10.1375	0.346696
$856$	0	0
$857$	1.30562	0.0445990	0.0222995	−	0.999751i	$-0.492901\pi$
$857$	1.30562	0.0445990	0.0222995	+	0.999751i	$0.492901\pi$
$858$	0	0
$859$	46.1648	1.57512	0.787562	−	0.616235i	$-0.211343\pi$
$859$	46.1648	1.57512	0.787562	+	0.616235i	$0.211343\pi$
$860$	0	0
$861$	1.18235	0.0402942
$862$	0	0
$863$	−25.8151	−0.878755	−0.439377	−	0.898303i	$-0.644801\pi$
$863$	−25.8151	−0.878755	−0.439377	+	0.898303i	$0.644801\pi$
$864$	0	0
$865$	9.64765	0.328030
$866$	0	0
$867$	0	0
$868$	0	0
$869$	−50.4788	−1.71238
$870$	0	0
$871$	−2.56392	−0.0868752
$872$	0	0
$873$	−34.7209	−1.17513
$874$	0	0
$875$	2.93861	0.0993433
$876$	0	0
$877$	−14.0136	−0.473206	−0.236603	−	0.971606i	$-0.576034\pi$
$877$	−14.0136	−0.473206	−0.236603	+	0.971606i	$0.576034\pi$
$878$	0	0
$879$	−16.8869	−0.569581
$880$	0	0
$881$	31.1509	1.04950	0.524750	−	0.851256i	$-0.324159\pi$
$881$	31.1509	1.04950	0.524750	+	0.851256i	$0.324159\pi$
$882$	0	0
$883$	−41.5457	−1.39812	−0.699061	−	0.715062i	$-0.746399\pi$
$883$	−41.5457	−1.39812	−0.699061	+	0.715062i	$0.746399\pi$
$884$	0	0
$885$	1.45065	0.0487630
$886$	0	0
$887$	38.2415	1.28403	0.642013	−	0.766694i	$-0.278100\pi$
$887$	38.2415	1.28403	0.642013	+	0.766694i	$0.278100\pi$
$888$	0	0
$889$	−16.5529	−0.555167
$890$	0	0
$891$	28.8263	0.965717
$892$	0	0
$893$	17.6098	0.589290
$894$	0	0
$895$	15.5693	0.520425
$896$	0	0
$897$	1.16304	0.0388329
$898$	0	0
$899$	0.127103	0.00423911
$900$	0	0
$901$	0	0
$902$	0	0
$903$	2.49194	0.0829265
$904$	0	0
$905$	17.4712	0.580763
$906$	0	0
$907$	27.4628	0.911886	0.455943	−	0.890009i	$-0.349302\pi$
$907$	27.4628	0.911886	0.455943	+	0.890009i	$0.349302\pi$
$908$	0	0
$909$	0.958286	0.0317844
$910$	0	0
$911$	54.5123	1.80607	0.903036	−	0.429565i	$-0.141333\pi$
$911$	54.5123	1.80607	0.903036	+	0.429565i	$0.141333\pi$
$912$	0	0
$913$	−58.7819	−1.94540
$914$	0	0
$915$	8.82078	0.291606
$916$	0	0
$917$	37.5800	1.24100
$918$	0	0
$919$	−12.4407	−0.410382	−0.205191	−	0.978722i	$-0.565782\pi$
$919$	−12.4407	−0.410382	−0.205191	+	0.978722i	$0.565782\pi$
$920$	0	0
$921$	15.2752	0.503334
$922$	0	0
$923$	14.4855	0.476795
$924$	0	0
$925$	10.1080	0.332348
$926$	0	0
$927$	−14.7253	−0.483642
$928$	0	0
$929$	−23.5293	−0.771970	−0.385985	−	0.922505i	$-0.626138\pi$
$929$	−23.5293	−0.771970	−0.385985	+	0.922505i	$0.626138\pi$
$930$	0	0
$931$	6.19030	0.202879
$932$	0	0
$933$	2.71539	0.0888978
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−35.8627	−1.17158	−0.585791	−	0.810462i	$-0.699216\pi$
$937$	−35.8627	−1.17158	−0.585791	+	0.810462i	$0.699216\pi$
$938$	0	0
$939$	−7.74383	−0.252710
$940$	0	0
$941$	−17.0799	−0.556788	−0.278394	−	0.960467i	$-0.589802\pi$
$941$	−17.0799	−0.556788	−0.278394	+	0.960467i	$0.589802\pi$
$942$	0	0
$943$	1.59654	0.0519904
$944$	0	0
$945$	−9.46436	−0.307876
$946$	0	0
$947$	−30.5137	−0.991562	−0.495781	−	0.868448i	$-0.665118\pi$
$947$	−30.5137	−0.991562	−0.495781	+	0.868448i	$0.665118\pi$
$948$	0	0
$949$	7.60657	0.246920
$950$	0	0
$951$	−1.79315	−0.0581467
$952$	0	0
$953$	4.78676	0.155058	0.0775292	−	0.996990i	$-0.475297\pi$
$953$	4.78676	0.155058	0.0775292	+	0.996990i	$0.475297\pi$
$954$	0	0
$955$	17.3320	0.560850
$956$	0	0
$957$	2.92348	0.0945027
$958$	0	0
$959$	−60.5515	−1.95531
$960$	0	0
$961$	−30.9869	−0.999577
$962$	0	0
$963$	−35.3732	−1.13989
$964$	0	0
$965$	11.3026	0.363843
$966$	0	0
$967$	−10.0468	−0.323084	−0.161542	−	0.986866i	$-0.551647\pi$
$967$	−10.0468	−0.323084	−0.161542	+	0.986866i	$0.551647\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	−12.2995	−0.394710	−0.197355	−	0.980332i	$-0.563235\pi$
$971$	−12.2995	−0.394710	−0.197355	+	0.980332i	$0.563235\pi$
$972$	0	0
$973$	60.9705	1.95463
$974$	0	0
$975$	−0.516759	−0.0165495
$976$	0	0
$977$	15.2749	0.488687	0.244344	−	0.969689i	$-0.421427\pi$
$977$	15.2749	0.488687	0.244344	+	0.969689i	$0.421427\pi$
$978$	0	0
$979$	31.4272	1.00442
$980$	0	0
$981$	3.50626	0.111946
$982$	0	0
$983$	10.8434	0.345852	0.172926	−	0.984935i	$-0.444678\pi$
$983$	10.8434	0.345852	0.172926	+	0.984935i	$0.444678\pi$
$984$	0	0
$985$	18.1238	0.577473
$986$	0	0
$987$	−7.75452	−0.246829
$988$	0	0
$989$	3.36490	0.106998
$990$	0	0
$991$	8.66986	0.275407	0.137704	−	0.990473i	$-0.456028\pi$
$991$	8.66986	0.275407	0.137704	+	0.990473i	$0.456028\pi$
$992$	0	0
$993$	18.2767	0.579993
$994$	0	0
$995$	−19.8734	−0.630029
$996$	0	0
$997$	35.1001	1.11163	0.555816	−	0.831306i	$-0.312406\pi$
$997$	35.1001	1.11163	0.555816	+	0.831306i	$0.312406\pi$
$998$	0	0
$999$	−32.5546	−1.02998

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5780.2.a.q.1.7		12
17.4	even	4		5780.2.c.j.5201.11		24
17.11	odd	16		340.2.u.a.121.4	✓	24
17.13	even	4		5780.2.c.j.5201.14		24
17.14	odd	16		340.2.u.a.281.4	yes	24
17.16	even	2		5780.2.a.r.1.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
340.2.u.a.121.4	✓	24	17.11	odd	16
340.2.u.a.281.4	yes	24	17.14	odd	16
5780.2.a.q.1.7		12	1.1	even	1	trivial
5780.2.a.r.1.6		12	17.16	even	2
5780.2.c.j.5201.11		24	17.4	even	4
5780.2.c.j.5201.14		24	17.13	even	4

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:	\( N \)	\(=\)	\( 5780 = 2^{2} \cdot 5 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5780.a (trivial)

\(f(q)\)	\(=\)	\(q+0.567193 q^{3} -1.00000 q^{5} -2.93861 q^{7} -2.67829 q^{9} +O(q^{10})\)	\(q+0.567193 q^{3} -1.00000 q^{5} -2.93861 q^{7} -2.67829 q^{9} +4.64331 q^{11} -0.911081 q^{13} -0.567193 q^{15} +3.78507 q^{19} -1.66676 q^{21} -2.25065 q^{23} +1.00000 q^{25} -3.22069 q^{27} +1.11005 q^{29} +0.114502 q^{31} +2.63366 q^{33} +2.93861 q^{35} +10.1080 q^{37} -0.516759 q^{39} -0.709367 q^{41} -1.49508 q^{43} +2.67829 q^{45} +4.65244 q^{47} +1.63545 q^{49} +4.81340 q^{53} -4.64331 q^{55} +2.14686 q^{57} -2.55759 q^{59} -15.5516 q^{61} +7.87047 q^{63} +0.911081 q^{65} +2.81415 q^{67} -1.27655 q^{69} -15.8992 q^{71} -8.34895 q^{73} +0.567193 q^{75} -13.6449 q^{77} -10.8713 q^{79} +6.20812 q^{81} -12.6595 q^{83} +0.629611 q^{87} +6.76828 q^{89} +2.67732 q^{91} +0.0649448 q^{93} -3.78507 q^{95} +12.9638 q^{97} -12.4362 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{5} - 8 q^{7} + 12 q^{9}+O(q^{10}) \) 12 * q - 12 * q^5 - 8 * q^7 + 12 * q^9	\( 12 q - 12 q^{5} - 8 q^{7} + 12 q^{9} + 8 q^{13} - 16 q^{21} - 8 q^{23} + 12 q^{25} - 16 q^{29} - 24 q^{31} + 8 q^{35} - 24 q^{37} + 8 q^{39} - 24 q^{41} + 8 q^{43} - 12 q^{45} + 8 q^{47} + 20 q^{49} + 16 q^{53} - 32 q^{57} + 8 q^{59} - 40 q^{61} - 24 q^{63} - 8 q^{65} + 16 q^{67} - 16 q^{69} - 16 q^{71} - 32 q^{73} + 24 q^{77} - 8 q^{79} + 4 q^{81} + 32 q^{83} + 16 q^{87} - 8 q^{89} - 8 q^{91} - 8 q^{93} - 32 q^{97} - 24 q^{99}+O(q^{100}) \) 12 * q - 12 * q^5 - 8 * q^7 + 12 * q^9 + 8 * q^13 - 16 * q^21 - 8 * q^23 + 12 * q^25 - 16 * q^29 - 24 * q^31 + 8 * q^35 - 24 * q^37 + 8 * q^39 - 24 * q^41 + 8 * q^43 - 12 * q^45 + 8 * q^47 + 20 * q^49 + 16 * q^53 - 32 * q^57 + 8 * q^59 - 40 * q^61 - 24 * q^63 - 8 * q^65 + 16 * q^67 - 16 * q^69 - 16 * q^71 - 32 * q^73 + 24 * q^77 - 8 * q^79 + 4 * q^81 + 32 * q^83 + 16 * q^87 - 8 * q^89 - 8 * q^91 - 8 * q^93 - 32 * q^97 - 24 * q^99

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