LMFDB - Embedded newform 9280.2.a.bt.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9280,2,Mod(1,9280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9280, 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("9280.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9280 = 2^{6} \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9280.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:	$74.1011730757$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 580)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.311108$ of defining polynomial
Character	$\chi$	$=$	9280.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.90321 q^{3} -1.00000 q^{5} +1.52543 q^{7} +5.42864 q^{9} +O(q^{10})$	$q+2.90321 q^{3} -1.00000 q^{5} +1.52543 q^{7} +5.42864 q^{9} -1.52543 q^{11} -0.622216 q^{13} -2.90321 q^{15} +5.52543 q^{17} +2.90321 q^{19} +4.42864 q^{21} +2.90321 q^{23} +1.00000 q^{25} +7.05086 q^{27} -1.00000 q^{29} +2.90321 q^{31} -4.42864 q^{33} -1.52543 q^{35} -2.47457 q^{37} -1.80642 q^{39} -8.23506 q^{41} -5.65878 q^{43} -5.42864 q^{45} +4.70964 q^{47} -4.67307 q^{49} +16.0415 q^{51} +11.2859 q^{53} +1.52543 q^{55} +8.42864 q^{57} +10.2351 q^{59} +7.93978 q^{61} +8.28100 q^{63} +0.622216 q^{65} -2.90321 q^{67} +8.42864 q^{69} -7.47949 q^{71} +2.90321 q^{73} +2.90321 q^{75} -2.32693 q^{77} +16.5763 q^{79} +4.18421 q^{81} -6.76986 q^{83} -5.52543 q^{85} -2.90321 q^{87} +13.9081 q^{89} -0.949145 q^{91} +8.42864 q^{93} -2.90321 q^{95} +17.5669 q^{97} -8.28100 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 2 q^{3} - 3 q^{5} - 2 q^{7} + 3 q^{9}+O(q^{10}) $ 3 * q + 2 * q^3 - 3 * q^5 - 2 * q^7 + 3 * q^9	$ 3 q + 2 q^{3} - 3 q^{5} - 2 q^{7} + 3 q^{9} + 2 q^{11} - 2 q^{13} - 2 q^{15} + 10 q^{17} + 2 q^{19} + 2 q^{23} + 3 q^{25} + 8 q^{27} - 3 q^{29} + 2 q^{31} + 2 q^{35} - 14 q^{37} + 8 q^{39} + 2 q^{41} - 10 q^{43} - 3 q^{45} - 6 q^{47} - q^{49} + 8 q^{51} - 6 q^{53} - 2 q^{55} + 12 q^{57} + 4 q^{59} + 10 q^{61} + 18 q^{63} + 2 q^{65} - 2 q^{67} + 12 q^{69} + 4 q^{71} + 2 q^{73} + 2 q^{75} - 20 q^{77} + 30 q^{79} - q^{81} - 14 q^{83} - 10 q^{85} - 2 q^{87} + 2 q^{89} - 16 q^{91} + 12 q^{93} - 2 q^{95} + 6 q^{97} - 18 q^{99}+O(q^{100}) $ 3 * q + 2 * q^3 - 3 * q^5 - 2 * q^7 + 3 * q^9 + 2 * q^11 - 2 * q^13 - 2 * q^15 + 10 * q^17 + 2 * q^19 + 2 * q^23 + 3 * q^25 + 8 * q^27 - 3 * q^29 + 2 * q^31 + 2 * q^35 - 14 * q^37 + 8 * q^39 + 2 * q^41 - 10 * q^43 - 3 * q^45 - 6 * q^47 - q^49 + 8 * q^51 - 6 * q^53 - 2 * q^55 + 12 * q^57 + 4 * q^59 + 10 * q^61 + 18 * q^63 + 2 * q^65 - 2 * q^67 + 12 * q^69 + 4 * q^71 + 2 * q^73 + 2 * q^75 - 20 * q^77 + 30 * q^79 - q^81 - 14 * q^83 - 10 * q^85 - 2 * q^87 + 2 * q^89 - 16 * q^91 + 12 * q^93 - 2 * q^95 + 6 * q^97 - 18 * 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
$3$	2.90321	1.67617	0.838085	−	0.545540i	$-0.183675\pi$
$3$	2.90321	1.67617	0.838085	+	0.545540i	$0.183675\pi$
$4$	0	0
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0	0
$7$	1.52543	0.576557	0.288279	−	0.957547i	$-0.406917\pi$
$7$	1.52543	0.576557	0.288279	+	0.957547i	$0.406917\pi$
$8$	0	0
$9$	5.42864	1.80955
$10$	0	0
$11$	−1.52543	−0.459934	−0.229967	−	0.973198i	$-0.573862\pi$
$11$	−1.52543	−0.459934	−0.229967	+	0.973198i	$0.573862\pi$
$12$	0	0
$13$	−0.622216	−0.172572	−0.0862858	−	0.996270i	$-0.527500\pi$
$13$	−0.622216	−0.172572	−0.0862858	+	0.996270i	$0.527500\pi$
$14$	0	0
$15$	−2.90321	−0.749606
$16$	0	0
$17$	5.52543	1.34011	0.670057	−	0.742310i	$-0.266270\pi$
$17$	5.52543	1.34011	0.670057	+	0.742310i	$0.266270\pi$
$18$	0	0
$19$	2.90321	0.666042	0.333021	−	0.942919i	$-0.391932\pi$
$19$	2.90321	0.666042	0.333021	+	0.942919i	$0.391932\pi$
$20$	0	0
$21$	4.42864	0.966408
$22$	0	0
$23$	2.90321	0.605362	0.302681	−	0.953092i	$-0.402118\pi$
$23$	2.90321	0.605362	0.302681	+	0.953092i	$0.402118\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	7.05086	1.35694
$28$	0	0
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	0	0
$31$	2.90321	0.521432	0.260716	−	0.965416i	$-0.416041\pi$
$31$	2.90321	0.521432	0.260716	+	0.965416i	$0.416041\pi$
$32$	0	0
$33$	−4.42864	−0.770927
$34$	0	0
$35$	−1.52543	−0.257844
$36$	0	0
$37$	−2.47457	−0.406817	−0.203409	−	0.979094i	$-0.565202\pi$
$37$	−2.47457	−0.406817	−0.203409	+	0.979094i	$0.565202\pi$
$38$	0	0
$39$	−1.80642	−0.289259
$40$	0	0
$41$	−8.23506	−1.28610	−0.643050	−	0.765824i	$-0.722331\pi$
$41$	−8.23506	−1.28610	−0.643050	+	0.765824i	$0.722331\pi$
$42$	0	0
$43$	−5.65878	−0.862956	−0.431478	−	0.902123i	$-0.642008\pi$
$43$	−5.65878	−0.862956	−0.431478	+	0.902123i	$0.642008\pi$
$44$	0	0
$45$	−5.42864	−0.809254
$46$	0	0
$47$	4.70964	0.686971	0.343485	−	0.939158i	$-0.388392\pi$
$47$	4.70964	0.686971	0.343485	+	0.939158i	$0.388392\pi$
$48$	0	0
$49$	−4.67307	−0.667582
$50$	0	0
$51$	16.0415	2.24626
$52$	0	0
$53$	11.2859	1.55024	0.775120	−	0.631814i	$-0.217689\pi$
$53$	11.2859	1.55024	0.775120	+	0.631814i	$0.217689\pi$
$54$	0	0
$55$	1.52543	0.205689
$56$	0	0
$57$	8.42864	1.11640
$58$	0	0
$59$	10.2351	1.33249	0.666246	−	0.745732i	$-0.267900\pi$
$59$	10.2351	1.33249	0.666246	+	0.745732i	$0.267900\pi$
$60$	0	0
$61$	7.93978	1.01658	0.508292	−	0.861185i	$-0.330277\pi$
$61$	7.93978	1.01658	0.508292	+	0.861185i	$0.330277\pi$
$62$	0	0
$63$	8.28100	1.04331
$64$	0	0
$65$	0.622216	0.0771764
$66$	0	0
$67$	−2.90321	−0.354684	−0.177342	−	0.984149i	$-0.556750\pi$
$67$	−2.90321	−0.354684	−0.177342	+	0.984149i	$0.556750\pi$
$68$	0	0
$69$	8.42864	1.01469
$70$	0	0
$71$	−7.47949	−0.887653	−0.443826	−	0.896113i	$-0.646379\pi$
$71$	−7.47949	−0.887653	−0.443826	+	0.896113i	$0.646379\pi$
$72$	0	0
$73$	2.90321	0.339795	0.169898	−	0.985462i	$-0.445656\pi$
$73$	2.90321	0.339795	0.169898	+	0.985462i	$0.445656\pi$
$74$	0	0
$75$	2.90321	0.335234
$76$	0	0
$77$	−2.32693	−0.265178
$78$	0	0
$79$	16.5763	1.86498	0.932489	−	0.361199i	$-0.117632\pi$
$79$	16.5763	1.86498	0.932489	+	0.361199i	$0.117632\pi$
$80$	0	0
$81$	4.18421	0.464912
$82$	0	0
$83$	−6.76986	−0.743089	−0.371544	−	0.928415i	$-0.621172\pi$
$83$	−6.76986	−0.743089	−0.371544	+	0.928415i	$0.621172\pi$
$84$	0	0
$85$	−5.52543	−0.599317
$86$	0	0
$87$	−2.90321	−0.311257
$88$	0	0
$89$	13.9081	1.47426	0.737130	−	0.675751i	$-0.236181\pi$
$89$	13.9081	1.47426	0.737130	+	0.675751i	$0.236181\pi$
$90$	0	0
$91$	−0.949145	−0.0994974
$92$	0	0
$93$	8.42864	0.874009
$94$	0	0
$95$	−2.90321	−0.297863
$96$	0	0
$97$	17.5669	1.78365	0.891825	−	0.452381i	$-0.149425\pi$
$97$	17.5669	1.78365	0.891825	+	0.452381i	$0.149425\pi$
$98$	0	0
$99$	−8.28100	−0.832271
$100$	0	0
$101$	−5.05086	−0.502579	−0.251289	−	0.967912i	$-0.580855\pi$
$101$	−5.05086	−0.502579	−0.251289	+	0.967912i	$0.580855\pi$
$102$	0	0
$103$	−9.56691	−0.942656	−0.471328	−	0.881958i	$-0.656225\pi$
$103$	−9.56691	−0.942656	−0.471328	+	0.881958i	$0.656225\pi$
$104$	0	0
$105$	−4.42864	−0.432191
$106$	0	0
$107$	−0.576283	−0.0557113	−0.0278557	−	0.999612i	$-0.508868\pi$
$107$	−0.576283	−0.0557113	−0.0278557	+	0.999612i	$0.508868\pi$
$108$	0	0
$109$	−7.28592	−0.697864	−0.348932	−	0.937148i	$-0.613456\pi$
$109$	−7.28592	−0.697864	−0.348932	+	0.937148i	$0.613456\pi$
$110$	0	0
$111$	−7.18421	−0.681895
$112$	0	0
$113$	11.7605	1.10633	0.553167	−	0.833070i	$-0.313419\pi$
$113$	11.7605	1.10633	0.553167	+	0.833070i	$0.313419\pi$
$114$	0	0
$115$	−2.90321	−0.270726
$116$	0	0
$117$	−3.37778	−0.312276
$118$	0	0
$119$	8.42864	0.772652
$120$	0	0
$121$	−8.67307	−0.788461
$122$	0	0
$123$	−23.9081	−2.15572
$124$	0	0
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	14.5161	1.28809	0.644046	−	0.764987i	$-0.277255\pi$
$127$	14.5161	1.28809	0.644046	+	0.764987i	$0.277255\pi$
$128$	0	0
$129$	−16.4286	−1.44646
$130$	0	0
$131$	−15.7605	−1.37700	−0.688500	−	0.725236i	$-0.741731\pi$
$131$	−15.7605	−1.37700	−0.688500	+	0.725236i	$0.741731\pi$
$132$	0	0
$133$	4.42864	0.384012
$134$	0	0
$135$	−7.05086	−0.606841
$136$	0	0
$137$	5.52543	0.472069	0.236035	−	0.971745i	$-0.424152\pi$
$137$	5.52543	0.472069	0.236035	+	0.971745i	$0.424152\pi$
$138$	0	0
$139$	−17.4193	−1.47748	−0.738742	−	0.673989i	$-0.764580\pi$
$139$	−17.4193	−1.47748	−0.738742	+	0.673989i	$0.764580\pi$
$140$	0	0
$141$	13.6731	1.15148
$142$	0	0
$143$	0.949145	0.0793715
$144$	0	0
$145$	1.00000	0.0830455
$146$	0	0
$147$	−13.5669	−1.11898
$148$	0	0
$149$	−2.00000	−0.163846	−0.0819232	−	0.996639i	$-0.526106\pi$
$149$	−2.00000	−0.163846	−0.0819232	+	0.996639i	$0.526106\pi$
$150$	0	0
$151$	5.37778	0.437638	0.218819	−	0.975765i	$-0.429780\pi$
$151$	5.37778	0.437638	0.218819	+	0.975765i	$0.429780\pi$
$152$	0	0
$153$	29.9956	2.42500
$154$	0	0
$155$	−2.90321	−0.233192
$156$	0	0
$157$	1.39207	0.111100	0.0555498	−	0.998456i	$-0.482309\pi$
$157$	1.39207	0.111100	0.0555498	+	0.998456i	$0.482309\pi$
$158$	0	0
$159$	32.7654	2.59847
$160$	0	0
$161$	4.42864	0.349026
$162$	0	0
$163$	7.19850	0.563830	0.281915	−	0.959439i	$-0.409030\pi$
$163$	7.19850	0.563830	0.281915	+	0.959439i	$0.409030\pi$
$164$	0	0
$165$	4.42864	0.344769
$166$	0	0
$167$	−15.7605	−1.21958	−0.609792	−	0.792562i	$-0.708747\pi$
$167$	−15.7605	−1.21958	−0.609792	+	0.792562i	$0.708747\pi$
$168$	0	0
$169$	−12.6128	−0.970219
$170$	0	0
$171$	15.7605	1.20523
$172$	0	0
$173$	−13.4795	−1.02483	−0.512413	−	0.858739i	$-0.671248\pi$
$173$	−13.4795	−1.02483	−0.512413	+	0.858739i	$0.671248\pi$
$174$	0	0
$175$	1.52543	0.115311
$176$	0	0
$177$	29.7146	2.23348
$178$	0	0
$179$	−0.266706	−0.0199346	−0.00996728	−	0.999950i	$-0.503173\pi$
$179$	−0.266706	−0.0199346	−0.00996728	+	0.999950i	$0.503173\pi$
$180$	0	0
$181$	20.7971	1.54583	0.772916	−	0.634508i	$-0.218797\pi$
$181$	20.7971	1.54583	0.772916	+	0.634508i	$0.218797\pi$
$182$	0	0
$183$	23.0509	1.70397
$184$	0	0
$185$	2.47457	0.181934
$186$	0	0
$187$	−8.42864	−0.616363
$188$	0	0
$189$	10.7556	0.782353
$190$	0	0
$191$	9.43356	0.682589	0.341294	−	0.939956i	$-0.389135\pi$
$191$	9.43356	0.682589	0.341294	+	0.939956i	$0.389135\pi$
$192$	0	0
$193$	5.23014	0.376474	0.188237	−	0.982124i	$-0.439723\pi$
$193$	5.23014	0.376474	0.188237	+	0.982124i	$0.439723\pi$
$194$	0	0
$195$	1.80642	0.129361
$196$	0	0
$197$	−11.5397	−0.822171	−0.411085	−	0.911597i	$-0.634850\pi$
$197$	−11.5397	−0.822171	−0.411085	+	0.911597i	$0.634850\pi$
$198$	0	0
$199$	−8.33677	−0.590978	−0.295489	−	0.955346i	$-0.595483\pi$
$199$	−8.33677	−0.590978	−0.295489	+	0.955346i	$0.595483\pi$
$200$	0	0
$201$	−8.42864	−0.594510
$202$	0	0
$203$	−1.52543	−0.107064
$204$	0	0
$205$	8.23506	0.575162
$206$	0	0
$207$	15.7605	1.09543
$208$	0	0
$209$	−4.42864	−0.306335
$210$	0	0
$211$	9.79213	0.674118	0.337059	−	0.941483i	$-0.390568\pi$
$211$	9.79213	0.674118	0.337059	+	0.941483i	$0.390568\pi$
$212$	0	0
$213$	−21.7146	−1.48786
$214$	0	0
$215$	5.65878	0.385926
$216$	0	0
$217$	4.42864	0.300636
$218$	0	0
$219$	8.42864	0.569555
$220$	0	0
$221$	−3.43801	−0.231265
$222$	0	0
$223$	−16.0558	−1.07517	−0.537587	−	0.843208i	$-0.680664\pi$
$223$	−16.0558	−1.07517	−0.537587	+	0.843208i	$0.680664\pi$
$224$	0	0
$225$	5.42864	0.361909
$226$	0	0
$227$	19.1985	1.27425	0.637125	−	0.770761i	$-0.280124\pi$
$227$	19.1985	1.27425	0.637125	+	0.770761i	$0.280124\pi$
$228$	0	0
$229$	10.5906	0.699845	0.349922	−	0.936779i	$-0.386208\pi$
$229$	10.5906	0.699845	0.349922	+	0.936779i	$0.386208\pi$
$230$	0	0
$231$	−6.75557	−0.444484
$232$	0	0
$233$	23.1240	1.51490	0.757451	−	0.652892i	$-0.226444\pi$
$233$	23.1240	1.51490	0.757451	+	0.652892i	$0.226444\pi$
$234$	0	0
$235$	−4.70964	−0.307223
$236$	0	0
$237$	48.1245	3.12602
$238$	0	0
$239$	16.9906	1.09903	0.549516	−	0.835483i	$-0.314812\pi$
$239$	16.9906	1.09903	0.549516	+	0.835483i	$0.314812\pi$
$240$	0	0
$241$	0.368416	0.0237318	0.0118659	−	0.999930i	$-0.496223\pi$
$241$	0.368416	0.0237318	0.0118659	+	0.999930i	$0.496223\pi$
$242$	0	0
$243$	−9.00492	−0.577666
$244$	0	0
$245$	4.67307	0.298552
$246$	0	0
$247$	−1.80642	−0.114940
$248$	0	0
$249$	−19.6543	−1.24554
$250$	0	0
$251$	15.7190	0.992175	0.496087	−	0.868273i	$-0.334770\pi$
$251$	15.7190	0.992175	0.496087	+	0.868273i	$0.334770\pi$
$252$	0	0
$253$	−4.42864	−0.278426
$254$	0	0
$255$	−16.0415	−1.00456
$256$	0	0
$257$	18.6035	1.16045	0.580227	−	0.814455i	$-0.302964\pi$
$257$	18.6035	1.16045	0.580227	+	0.814455i	$0.302964\pi$
$258$	0	0
$259$	−3.77478	−0.234553
$260$	0	0
$261$	−5.42864	−0.336024
$262$	0	0
$263$	12.7096	0.783710	0.391855	−	0.920027i	$-0.371834\pi$
$263$	12.7096	0.783710	0.391855	+	0.920027i	$0.371834\pi$
$264$	0	0
$265$	−11.2859	−0.693288
$266$	0	0
$267$	40.3783	2.47111
$268$	0	0
$269$	−21.7462	−1.32589	−0.662945	−	0.748668i	$-0.730694\pi$
$269$	−21.7462	−1.32589	−0.662945	+	0.748668i	$0.730694\pi$
$270$	0	0
$271$	18.3827	1.11667	0.558335	−	0.829616i	$-0.311440\pi$
$271$	18.3827	1.11667	0.558335	+	0.829616i	$0.311440\pi$
$272$	0	0
$273$	−2.75557	−0.166775
$274$	0	0
$275$	−1.52543	−0.0919867
$276$	0	0
$277$	−12.7971	−0.768901	−0.384450	−	0.923146i	$-0.625609\pi$
$277$	−12.7971	−0.768901	−0.384450	+	0.923146i	$0.625609\pi$
$278$	0	0
$279$	15.7605	0.943556
$280$	0	0
$281$	21.1842	1.26374	0.631872	−	0.775073i	$-0.282287\pi$
$281$	21.1842	1.26374	0.631872	+	0.775073i	$0.282287\pi$
$282$	0	0
$283$	−5.68736	−0.338079	−0.169039	−	0.985609i	$-0.554066\pi$
$283$	−5.68736	−0.338079	−0.169039	+	0.985609i	$0.554066\pi$
$284$	0	0
$285$	−8.42864	−0.499270
$286$	0	0
$287$	−12.5620	−0.741511
$288$	0	0
$289$	13.5303	0.795903
$290$	0	0
$291$	51.0005	2.98970
$292$	0	0
$293$	25.0879	1.46565	0.732825	−	0.680417i	$-0.238201\pi$
$293$	25.0879	1.46565	0.732825	+	0.680417i	$0.238201\pi$
$294$	0	0
$295$	−10.2351	−0.595908
$296$	0	0
$297$	−10.7556	−0.624101
$298$	0	0
$299$	−1.80642	−0.104468
$300$	0	0
$301$	−8.63206	−0.497544
$302$	0	0
$303$	−14.6637	−0.842408
$304$	0	0
$305$	−7.93978	−0.454630
$306$	0	0
$307$	30.8113	1.75850	0.879248	−	0.476364i	$-0.158046\pi$
$307$	30.8113	1.75850	0.879248	+	0.476364i	$0.158046\pi$
$308$	0	0
$309$	−27.7748	−1.58005
$310$	0	0
$311$	−30.0370	−1.70324	−0.851622	−	0.524156i	$-0.824381\pi$
$311$	−30.0370	−1.70324	−0.851622	+	0.524156i	$0.824381\pi$
$312$	0	0
$313$	−18.3368	−1.03646	−0.518228	−	0.855243i	$-0.673408\pi$
$313$	−18.3368	−1.03646	−0.518228	+	0.855243i	$0.673408\pi$
$314$	0	0
$315$	−8.28100	−0.466581
$316$	0	0
$317$	−20.4558	−1.14891	−0.574457	−	0.818535i	$-0.694787\pi$
$317$	−20.4558	−1.14891	−0.574457	+	0.818535i	$0.694787\pi$
$318$	0	0
$319$	1.52543	0.0854075
$320$	0	0
$321$	−1.67307	−0.0933817
$322$	0	0
$323$	16.0415	0.892572
$324$	0	0
$325$	−0.622216	−0.0345143
$326$	0	0
$327$	−21.1526	−1.16974
$328$	0	0
$329$	7.18421	0.396078
$330$	0	0
$331$	−12.0272	−0.661075	−0.330537	−	0.943793i	$-0.607230\pi$
$331$	−12.0272	−0.661075	−0.330537	+	0.943793i	$0.607230\pi$
$332$	0	0
$333$	−13.4336	−0.736155
$334$	0	0
$335$	2.90321	0.158619
$336$	0	0
$337$	−32.2306	−1.75571	−0.877857	−	0.478923i	$-0.841027\pi$
$337$	−32.2306	−1.75571	−0.877857	+	0.478923i	$0.841027\pi$
$338$	0	0
$339$	34.1432	1.85440
$340$	0	0
$341$	−4.42864	−0.239824
$342$	0	0
$343$	−17.8064	−0.961457
$344$	0	0
$345$	−8.42864	−0.453783
$346$	0	0
$347$	−29.9037	−1.60531	−0.802657	−	0.596441i	$-0.796581\pi$
$347$	−29.9037	−1.60531	−0.802657	+	0.596441i	$0.796581\pi$
$348$	0	0
$349$	−29.8163	−1.59603	−0.798014	−	0.602639i	$-0.794116\pi$
$349$	−29.8163	−1.59603	−0.798014	+	0.602639i	$0.794116\pi$
$350$	0	0
$351$	−4.38715	−0.234169
$352$	0	0
$353$	21.1842	1.12752	0.563761	−	0.825938i	$-0.309354\pi$
$353$	21.1842	1.12752	0.563761	+	0.825938i	$0.309354\pi$
$354$	0	0
$355$	7.47949	0.396970
$356$	0	0
$357$	24.4701	1.29510
$358$	0	0
$359$	−11.1985	−0.591034	−0.295517	−	0.955337i	$-0.595492\pi$
$359$	−11.1985	−0.591034	−0.295517	+	0.955337i	$0.595492\pi$
$360$	0	0
$361$	−10.5714	−0.556387
$362$	0	0
$363$	−25.1798	−1.32159
$364$	0	0
$365$	−2.90321	−0.151961
$366$	0	0
$367$	9.95407	0.519598	0.259799	−	0.965663i	$-0.416344\pi$
$367$	9.95407	0.519598	0.259799	+	0.965663i	$0.416344\pi$
$368$	0	0
$369$	−44.7052	−2.32726
$370$	0	0
$371$	17.2159	0.893802
$372$	0	0
$373$	−2.29529	−0.118845	−0.0594227	−	0.998233i	$-0.518926\pi$
$373$	−2.29529	−0.118845	−0.0594227	+	0.998233i	$0.518926\pi$
$374$	0	0
$375$	−2.90321	−0.149921
$376$	0	0
$377$	0.622216	0.0320457
$378$	0	0
$379$	9.61729	0.494007	0.247004	−	0.969015i	$-0.420554\pi$
$379$	9.61729	0.494007	0.247004	+	0.969015i	$0.420554\pi$
$380$	0	0
$381$	42.1432	2.15906
$382$	0	0
$383$	6.86172	0.350618	0.175309	−	0.984513i	$-0.443908\pi$
$383$	6.86172	0.350618	0.175309	+	0.984513i	$0.443908\pi$
$384$	0	0
$385$	2.32693	0.118591
$386$	0	0
$387$	−30.7195	−1.56156
$388$	0	0
$389$	−25.3590	−1.28575	−0.642877	−	0.765969i	$-0.722260\pi$
$389$	−25.3590	−1.28575	−0.642877	+	0.765969i	$0.722260\pi$
$390$	0	0
$391$	16.0415	0.811253
$392$	0	0
$393$	−45.7560	−2.30809
$394$	0	0
$395$	−16.5763	−0.834043
$396$	0	0
$397$	−24.2766	−1.21841	−0.609203	−	0.793015i	$-0.708510\pi$
$397$	−24.2766	−1.21841	−0.609203	+	0.793015i	$0.708510\pi$
$398$	0	0
$399$	12.8573	0.643669
$400$	0	0
$401$	5.30465	0.264902	0.132451	−	0.991190i	$-0.457715\pi$
$401$	5.30465	0.264902	0.132451	+	0.991190i	$0.457715\pi$
$402$	0	0
$403$	−1.80642	−0.0899844
$404$	0	0
$405$	−4.18421	−0.207915
$406$	0	0
$407$	3.77478	0.187109
$408$	0	0
$409$	0.714082	0.0353091	0.0176545	−	0.999844i	$-0.494380\pi$
$409$	0.714082	0.0353091	0.0176545	+	0.999844i	$0.494380\pi$
$410$	0	0
$411$	16.0415	0.791268
$412$	0	0
$413$	15.6128	0.768258
$414$	0	0
$415$	6.76986	0.332319
$416$	0	0
$417$	−50.5718	−2.47651
$418$	0	0
$419$	−16.6321	−0.812529	−0.406265	−	0.913755i	$-0.633169\pi$
$419$	−16.6321	−0.812529	−0.406265	+	0.913755i	$0.633169\pi$
$420$	0	0
$421$	30.4286	1.48300	0.741501	−	0.670952i	$-0.234114\pi$
$421$	30.4286	1.48300	0.741501	+	0.670952i	$0.234114\pi$
$422$	0	0
$423$	25.5669	1.24311
$424$	0	0
$425$	5.52543	0.268023
$426$	0	0
$427$	12.1116	0.586119
$428$	0	0
$429$	2.75557	0.133040
$430$	0	0
$431$	31.2257	1.50409	0.752044	−	0.659112i	$-0.229068\pi$
$431$	31.2257	1.50409	0.752044	+	0.659112i	$0.229068\pi$
$432$	0	0
$433$	35.2400	1.69353	0.846763	−	0.531971i	$-0.178548\pi$
$433$	35.2400	1.69353	0.846763	+	0.531971i	$0.178548\pi$
$434$	0	0
$435$	2.90321	0.139198
$436$	0	0
$437$	8.42864	0.403197
$438$	0	0
$439$	−30.6133	−1.46109	−0.730547	−	0.682862i	$-0.760735\pi$
$439$	−30.6133	−1.46109	−0.730547	+	0.682862i	$0.760735\pi$
$440$	0	0
$441$	−25.3684	−1.20802
$442$	0	0
$443$	31.4938	1.49631	0.748157	−	0.663521i	$-0.230939\pi$
$443$	31.4938	1.49631	0.748157	+	0.663521i	$0.230939\pi$
$444$	0	0
$445$	−13.9081	−0.659309
$446$	0	0
$447$	−5.80642	−0.274634
$448$	0	0
$449$	−18.6321	−0.879301	−0.439651	−	0.898169i	$-0.644898\pi$
$449$	−18.6321	−0.879301	−0.439651	+	0.898169i	$0.644898\pi$
$450$	0	0
$451$	12.5620	0.591521
$452$	0	0
$453$	15.6128	0.733556
$454$	0	0
$455$	0.949145	0.0444966
$456$	0	0
$457$	−31.2859	−1.46349	−0.731747	−	0.681577i	$-0.761295\pi$
$457$	−31.2859	−1.46349	−0.731747	+	0.681577i	$0.761295\pi$
$458$	0	0
$459$	38.9590	1.81845
$460$	0	0
$461$	28.9304	1.34742	0.673712	−	0.738994i	$-0.264699\pi$
$461$	28.9304	1.34742	0.673712	+	0.738994i	$0.264699\pi$
$462$	0	0
$463$	14.1289	0.656626	0.328313	−	0.944569i	$-0.393520\pi$
$463$	14.1289	0.656626	0.328313	+	0.944569i	$0.393520\pi$
$464$	0	0
$465$	−8.42864	−0.390869
$466$	0	0
$467$	30.6909	1.42021	0.710103	−	0.704098i	$-0.248648\pi$
$467$	30.6909	1.42021	0.710103	+	0.704098i	$0.248648\pi$
$468$	0	0
$469$	−4.42864	−0.204496
$470$	0	0
$471$	4.04149	0.186222
$472$	0	0
$473$	8.63206	0.396903
$474$	0	0
$475$	2.90321	0.133208
$476$	0	0
$477$	61.2672	2.80523
$478$	0	0
$479$	−9.04641	−0.413341	−0.206670	−	0.978411i	$-0.566263\pi$
$479$	−9.04641	−0.413341	−0.206670	+	0.978411i	$0.566263\pi$
$480$	0	0
$481$	1.53972	0.0702051
$482$	0	0
$483$	12.8573	0.585026
$484$	0	0
$485$	−17.5669	−0.797673
$486$	0	0
$487$	14.6494	0.663828	0.331914	−	0.943310i	$-0.392306\pi$
$487$	14.6494	0.663828	0.331914	+	0.943310i	$0.392306\pi$
$488$	0	0
$489$	20.8988	0.945075
$490$	0	0
$491$	−22.1289	−0.998664	−0.499332	−	0.866411i	$-0.666421\pi$
$491$	−22.1289	−0.998664	−0.499332	+	0.866411i	$0.666421\pi$
$492$	0	0
$493$	−5.52543	−0.248853
$494$	0	0
$495$	8.28100	0.372203
$496$	0	0
$497$	−11.4094	−0.511783
$498$	0	0
$499$	29.9813	1.34215	0.671073	−	0.741391i	$-0.265834\pi$
$499$	29.9813	1.34215	0.671073	+	0.741391i	$0.265834\pi$
$500$	0	0
$501$	−45.7560	−2.04423
$502$	0	0
$503$	17.6874	0.788640	0.394320	−	0.918973i	$-0.370980\pi$
$503$	17.6874	0.788640	0.394320	+	0.918973i	$0.370980\pi$
$504$	0	0
$505$	5.05086	0.224760
$506$	0	0
$507$	−36.6178	−1.62625
$508$	0	0
$509$	−1.45091	−0.0643107	−0.0321553	−	0.999483i	$-0.510237\pi$
$509$	−1.45091	−0.0643107	−0.0321553	+	0.999483i	$0.510237\pi$
$510$	0	0
$511$	4.42864	0.195911
$512$	0	0
$513$	20.4701	0.903778
$514$	0	0
$515$	9.56691	0.421569
$516$	0	0
$517$	−7.18421	−0.315961
$518$	0	0
$519$	−39.1338	−1.71778
$520$	0	0
$521$	−31.8765	−1.39653	−0.698267	−	0.715837i	$-0.746045\pi$
$521$	−31.8765	−1.39653	−0.698267	+	0.715837i	$0.746045\pi$
$522$	0	0
$523$	14.9032	0.651672	0.325836	−	0.945426i	$-0.394354\pi$
$523$	14.9032	0.651672	0.325836	+	0.945426i	$0.394354\pi$
$524$	0	0
$525$	4.42864	0.193282
$526$	0	0
$527$	16.0415	0.698778
$528$	0	0
$529$	−14.5714	−0.633537
$530$	0	0
$531$	55.5625	2.41121
$532$	0	0
$533$	5.12399	0.221944
$534$	0	0
$535$	0.576283	0.0249149
$536$	0	0
$537$	−0.774305	−0.0334137
$538$	0	0
$539$	7.12843	0.307043
$540$	0	0
$541$	12.7841	0.549633	0.274817	−	0.961497i	$-0.411383\pi$
$541$	12.7841	0.549633	0.274817	+	0.961497i	$0.411383\pi$
$542$	0	0
$543$	60.3783	2.59108
$544$	0	0
$545$	7.28592	0.312094
$546$	0	0
$547$	−18.8617	−0.806469	−0.403235	−	0.915097i	$-0.632114\pi$
$547$	−18.8617	−0.806469	−0.403235	+	0.915097i	$0.632114\pi$
$548$	0	0
$549$	43.1022	1.83956
$550$	0	0
$551$	−2.90321	−0.123681
$552$	0	0
$553$	25.2859	1.07527
$554$	0	0
$555$	7.18421	0.304953
$556$	0	0
$557$	15.6316	0.662331	0.331166	−	0.943573i	$-0.392558\pi$
$557$	15.6316	0.662331	0.331166	+	0.943573i	$0.392558\pi$
$558$	0	0
$559$	3.52098	0.148922
$560$	0	0
$561$	−24.4701	−1.03313
$562$	0	0
$563$	−1.18865	−0.0500958	−0.0250479	−	0.999686i	$-0.507974\pi$
$563$	−1.18865	−0.0500958	−0.0250479	+	0.999686i	$0.507974\pi$
$564$	0	0
$565$	−11.7605	−0.494768
$566$	0	0
$567$	6.38271	0.268048
$568$	0	0
$569$	28.5303	1.19605	0.598027	−	0.801476i	$-0.295951\pi$
$569$	28.5303	1.19605	0.598027	+	0.801476i	$0.295951\pi$
$570$	0	0
$571$	−22.8385	−0.955763	−0.477882	−	0.878424i	$-0.658595\pi$
$571$	−22.8385	−0.955763	−0.477882	+	0.878424i	$0.658595\pi$
$572$	0	0
$573$	27.3876	1.14413
$574$	0	0
$575$	2.90321	0.121072
$576$	0	0
$577$	4.18913	0.174396	0.0871979	−	0.996191i	$-0.472209\pi$
$577$	4.18913	0.174396	0.0871979	+	0.996191i	$0.472209\pi$
$578$	0	0
$579$	15.1842	0.631034
$580$	0	0
$581$	−10.3269	−0.428433
$582$	0	0
$583$	−17.2159	−0.713008
$584$	0	0
$585$	3.37778	0.139654
$586$	0	0
$587$	39.2815	1.62132	0.810660	−	0.585517i	$-0.199109\pi$
$587$	39.2815	1.62132	0.810660	+	0.585517i	$0.199109\pi$
$588$	0	0
$589$	8.42864	0.347296
$590$	0	0
$591$	−33.5022	−1.37810
$592$	0	0
$593$	−21.4509	−0.880883	−0.440442	−	0.897781i	$-0.645178\pi$
$593$	−21.4509	−0.880883	−0.440442	+	0.897781i	$0.645178\pi$
$594$	0	0
$595$	−8.42864	−0.345541
$596$	0	0
$597$	−24.2034	−0.990580
$598$	0	0
$599$	−18.3827	−0.751097	−0.375549	−	0.926803i	$-0.622546\pi$
$599$	−18.3827	−0.751097	−0.375549	+	0.926803i	$0.622546\pi$
$600$	0	0
$601$	−12.3555	−0.503992	−0.251996	−	0.967728i	$-0.581087\pi$
$601$	−12.3555	−0.503992	−0.251996	+	0.967728i	$0.581087\pi$
$602$	0	0
$603$	−15.7605	−0.641817
$604$	0	0
$605$	8.67307	0.352610
$606$	0	0
$607$	−48.4340	−1.96588	−0.982938	−	0.183935i	$-0.941117\pi$
$607$	−48.4340	−1.96588	−0.982938	+	0.183935i	$0.941117\pi$
$608$	0	0
$609$	−4.42864	−0.179458
$610$	0	0
$611$	−2.93041	−0.118552
$612$	0	0
$613$	0.958989	0.0387332	0.0193666	−	0.999812i	$-0.493835\pi$
$613$	0.958989	0.0387332	0.0193666	+	0.999812i	$0.493835\pi$
$614$	0	0
$615$	23.9081	0.964069
$616$	0	0
$617$	5.09679	0.205189	0.102594	−	0.994723i	$-0.467286\pi$
$617$	5.09679	0.205189	0.102594	+	0.994723i	$0.467286\pi$
$618$	0	0
$619$	0.0142901	0.000574368 0	0.000287184	−	1.00000i	$-0.499909\pi$
$619$	0.0142901	0.000574368 0	0.000287184		1.00000i	$0.499909\pi$
$620$	0	0
$621$	20.4701	0.821438
$622$	0	0
$623$	21.2159	0.849995
$624$	0	0
$625$	1.00000	0.0400000
$626$	0	0
$627$	−12.8573	−0.513470
$628$	0	0
$629$	−13.6731	−0.545181
$630$	0	0
$631$	12.8859	0.512978	0.256489	−	0.966547i	$-0.417434\pi$
$631$	12.8859	0.512978	0.256489	+	0.966547i	$0.417434\pi$
$632$	0	0
$633$	28.4286	1.12994
$634$	0	0
$635$	−14.5161	−0.576052
$636$	0	0
$637$	2.90766	0.115206
$638$	0	0
$639$	−40.6035	−1.60625
$640$	0	0
$641$	−46.6865	−1.84400	−0.922002	−	0.387185i	$-0.873447\pi$
$641$	−46.6865	−1.84400	−0.922002	+	0.387185i	$0.873447\pi$
$642$	0	0
$643$	−28.1388	−1.10968	−0.554842	−	0.831956i	$-0.687221\pi$
$643$	−28.1388	−1.10968	−0.554842	+	0.831956i	$0.687221\pi$
$644$	0	0
$645$	16.4286	0.646877
$646$	0	0
$647$	47.5067	1.86768	0.933840	−	0.357690i	$-0.116436\pi$
$647$	47.5067	1.86768	0.933840	+	0.357690i	$0.116436\pi$
$648$	0	0
$649$	−15.6128	−0.612858
$650$	0	0
$651$	12.8573	0.503916
$652$	0	0
$653$	−25.5383	−0.999392	−0.499696	−	0.866201i	$-0.666555\pi$
$653$	−25.5383	−0.999392	−0.499696	+	0.866201i	$0.666555\pi$
$654$	0	0
$655$	15.7605	0.615813
$656$	0	0
$657$	15.7605	0.614875
$658$	0	0
$659$	11.4938	0.447734	0.223867	−	0.974620i	$-0.428132\pi$
$659$	11.4938	0.447734	0.223867	+	0.974620i	$0.428132\pi$
$660$	0	0
$661$	−48.4929	−1.88615	−0.943077	−	0.332574i	$-0.892083\pi$
$661$	−48.4929	−1.88615	−0.943077	+	0.332574i	$0.892083\pi$
$662$	0	0
$663$	−9.98126	−0.387640
$664$	0	0
$665$	−4.42864	−0.171735
$666$	0	0
$667$	−2.90321	−0.112413
$668$	0	0
$669$	−46.6133	−1.80218
$670$	0	0
$671$	−12.1116	−0.467561
$672$	0	0
$673$	−15.1526	−0.584088	−0.292044	−	0.956405i	$-0.594335\pi$
$673$	−15.1526	−0.584088	−0.292044	+	0.956405i	$0.594335\pi$
$674$	0	0
$675$	7.05086	0.271388
$676$	0	0
$677$	−38.8943	−1.49483	−0.747415	−	0.664357i	$-0.768705\pi$
$677$	−38.8943	−1.49483	−0.747415	+	0.664357i	$0.768705\pi$
$678$	0	0
$679$	26.7971	1.02838
$680$	0	0
$681$	55.7373	2.13586
$682$	0	0
$683$	11.3733	0.435189	0.217594	−	0.976039i	$-0.430179\pi$
$683$	11.3733	0.435189	0.217594	+	0.976039i	$0.430179\pi$
$684$	0	0
$685$	−5.52543	−0.211116
$686$	0	0
$687$	30.7467	1.17306
$688$	0	0
$689$	−7.02227	−0.267527
$690$	0	0
$691$	−29.4893	−1.12183	−0.560914	−	0.827874i	$-0.689550\pi$
$691$	−29.4893	−1.12183	−0.560914	+	0.827874i	$0.689550\pi$
$692$	0	0
$693$	−12.6321	−0.479852
$694$	0	0
$695$	17.4193	0.660751
$696$	0	0
$697$	−45.5022	−1.72352
$698$	0	0
$699$	67.1338	2.53923
$700$	0	0
$701$	−52.2895	−1.97495	−0.987473	−	0.157789i	$-0.949563\pi$
$701$	−52.2895	−1.97495	−0.987473	+	0.157789i	$0.949563\pi$
$702$	0	0
$703$	−7.18421	−0.270958
$704$	0	0
$705$	−13.6731	−0.514958
$706$	0	0
$707$	−7.70471	−0.289766
$708$	0	0
$709$	−9.18421	−0.344920	−0.172460	−	0.985017i	$-0.555172\pi$
$709$	−9.18421	−0.344920	−0.172460	+	0.985017i	$0.555172\pi$
$710$	0	0
$711$	89.9867	3.37476
$712$	0	0
$713$	8.42864	0.315655
$714$	0	0
$715$	−0.949145	−0.0354960
$716$	0	0
$717$	49.3274	1.84217
$718$	0	0
$719$	7.74620	0.288885	0.144442	−	0.989513i	$-0.453861\pi$
$719$	7.74620	0.288885	0.144442	+	0.989513i	$0.453861\pi$
$720$	0	0
$721$	−14.5936	−0.543495
$722$	0	0
$723$	1.06959	0.0397785
$724$	0	0
$725$	−1.00000	−0.0371391
$726$	0	0
$727$	−5.06821	−0.187969	−0.0939847	−	0.995574i	$-0.529960\pi$
$727$	−5.06821	−0.187969	−0.0939847	+	0.995574i	$0.529960\pi$
$728$	0	0
$729$	−38.6958	−1.43318
$730$	0	0
$731$	−31.2672	−1.15646
$732$	0	0
$733$	0.659257	0.0243502	0.0121751	−	0.999926i	$-0.496124\pi$
$733$	0.659257	0.0243502	0.0121751	+	0.999926i	$0.496124\pi$
$734$	0	0
$735$	13.5669	0.500423
$736$	0	0
$737$	4.42864	0.163131
$738$	0	0
$739$	−7.07805	−0.260370	−0.130185	−	0.991490i	$-0.541557\pi$
$739$	−7.07805	−0.260370	−0.130185	+	0.991490i	$0.541557\pi$
$740$	0	0
$741$	−5.24443	−0.192659
$742$	0	0
$743$	26.3412	0.966366	0.483183	−	0.875519i	$-0.339481\pi$
$743$	26.3412	0.966366	0.483183	+	0.875519i	$0.339481\pi$
$744$	0	0
$745$	2.00000	0.0732743
$746$	0	0
$747$	−36.7511	−1.34465
$748$	0	0
$749$	−0.879077	−0.0321208
$750$	0	0
$751$	−4.92195	−0.179604	−0.0898022	−	0.995960i	$-0.528623\pi$
$751$	−4.92195	−0.179604	−0.0898022	+	0.995960i	$0.528623\pi$
$752$	0	0
$753$	45.6356	1.66305
$754$	0	0
$755$	−5.37778	−0.195718
$756$	0	0
$757$	−30.9032	−1.12320	−0.561598	−	0.827410i	$-0.689813\pi$
$757$	−30.9032	−1.12320	−0.561598	+	0.827410i	$0.689813\pi$
$758$	0	0
$759$	−12.8573	−0.466690
$760$	0	0
$761$	31.3274	1.13562	0.567809	−	0.823160i	$-0.307791\pi$
$761$	31.3274	1.13562	0.567809	+	0.823160i	$0.307791\pi$
$762$	0	0
$763$	−11.1141	−0.402359
$764$	0	0
$765$	−29.9956	−1.08449
$766$	0	0
$767$	−6.36842	−0.229950
$768$	0	0
$769$	−26.5620	−0.957850	−0.478925	−	0.877856i	$-0.658973\pi$
$769$	−26.5620	−0.957850	−0.478925	+	0.877856i	$0.658973\pi$
$770$	0	0
$771$	54.0098	1.94512
$772$	0	0
$773$	14.8528	0.534219	0.267110	−	0.963666i	$-0.413931\pi$
$773$	14.8528	0.534219	0.267110	+	0.963666i	$0.413931\pi$
$774$	0	0
$775$	2.90321	0.104286
$776$	0	0
$777$	−10.9590	−0.393152
$778$	0	0
$779$	−23.9081	−0.856598
$780$	0	0
$781$	11.4094	0.408261
$782$	0	0
$783$	−7.05086	−0.251977
$784$	0	0
$785$	−1.39207	−0.0496853
$786$	0	0
$787$	−25.5540	−0.910902	−0.455451	−	0.890261i	$-0.650522\pi$
$787$	−25.5540	−0.910902	−0.455451	+	0.890261i	$0.650522\pi$
$788$	0	0
$789$	36.8988	1.31363
$790$	0	0
$791$	17.9398	0.637865
$792$	0	0
$793$	−4.94025	−0.175434
$794$	0	0
$795$	−32.7654	−1.16207
$796$	0	0
$797$	10.2208	0.362038	0.181019	−	0.983480i	$-0.442060\pi$
$797$	10.2208	0.362038	0.181019	+	0.983480i	$0.442060\pi$
$798$	0	0
$799$	26.0228	0.920619
$800$	0	0
$801$	75.5022	2.66774
$802$	0	0
$803$	−4.42864	−0.156283
$804$	0	0
$805$	−4.42864	−0.156089
$806$	0	0
$807$	−63.1338	−2.22242
$808$	0	0
$809$	−2.44155	−0.0858402	−0.0429201	−	0.999079i	$-0.513666\pi$
$809$	−2.44155	−0.0858402	−0.0429201	+	0.999079i	$0.513666\pi$
$810$	0	0
$811$	−2.33984	−0.0821628	−0.0410814	−	0.999156i	$-0.513080\pi$
$811$	−2.33984	−0.0821628	−0.0410814	+	0.999156i	$0.513080\pi$
$812$	0	0
$813$	53.3689	1.87173
$814$	0	0
$815$	−7.19850	−0.252152
$816$	0	0
$817$	−16.4286	−0.574765
$818$	0	0
$819$	−5.15257	−0.180045
$820$	0	0
$821$	−14.6539	−0.511423	−0.255712	−	0.966753i	$-0.582310\pi$
$821$	−14.6539	−0.511423	−0.255712	+	0.966753i	$0.582310\pi$
$822$	0	0
$823$	−47.3733	−1.65133	−0.825665	−	0.564160i	$-0.809200\pi$
$823$	−47.3733	−1.65133	−0.825665	+	0.564160i	$0.809200\pi$
$824$	0	0
$825$	−4.42864	−0.154185
$826$	0	0
$827$	−18.3412	−0.637787	−0.318893	−	0.947791i	$-0.603311\pi$
$827$	−18.3412	−0.637787	−0.318893	+	0.947791i	$0.603311\pi$
$828$	0	0
$829$	−45.5625	−1.58245	−0.791225	−	0.611525i	$-0.790556\pi$
$829$	−45.5625	−1.58245	−0.791225	+	0.611525i	$0.790556\pi$
$830$	0	0
$831$	−37.1526	−1.28881
$832$	0	0
$833$	−25.8207	−0.894635
$834$	0	0
$835$	15.7605	0.545414
$836$	0	0
$837$	20.4701	0.707551
$838$	0	0
$839$	30.9733	1.06932	0.534658	−	0.845068i	$-0.320440\pi$
$839$	30.9733	1.06932	0.534658	+	0.845068i	$0.320440\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	0	0
$843$	61.5022	2.11825
$844$	0	0
$845$	12.6128	0.433895
$846$	0	0
$847$	−13.2301	−0.454593
$848$	0	0
$849$	−16.5116	−0.566677
$850$	0	0
$851$	−7.18421	−0.246271
$852$	0	0
$853$	−25.4050	−0.869850	−0.434925	−	0.900467i	$-0.643225\pi$
$853$	−25.4050	−0.869850	−0.434925	+	0.900467i	$0.643225\pi$
$854$	0	0
$855$	−15.7605	−0.538997
$856$	0	0
$857$	−19.2573	−0.657818	−0.328909	−	0.944362i	$-0.606681\pi$
$857$	−19.2573	−0.657818	−0.328909	+	0.944362i	$0.606681\pi$
$858$	0	0
$859$	42.2623	1.44197	0.720985	−	0.692951i	$-0.243690\pi$
$859$	42.2623	1.44197	0.720985	+	0.692951i	$0.243690\pi$
$860$	0	0
$861$	−36.4701	−1.24290
$862$	0	0
$863$	9.88400	0.336455	0.168228	−	0.985748i	$-0.446196\pi$
$863$	9.88400	0.336455	0.168228	+	0.985748i	$0.446196\pi$
$864$	0	0
$865$	13.4795	0.458317
$866$	0	0
$867$	39.2815	1.33407
$868$	0	0
$869$	−25.2859	−0.857766
$870$	0	0
$871$	1.80642	0.0612083
$872$	0	0
$873$	95.3644	3.22760
$874$	0	0
$875$	−1.52543	−0.0515689
$876$	0	0
$877$	12.6508	0.427187	0.213594	−	0.976923i	$-0.431483\pi$
$877$	12.6508	0.427187	0.213594	+	0.976923i	$0.431483\pi$
$878$	0	0
$879$	72.8355	2.45668
$880$	0	0
$881$	−0.0888033	−0.00299186	−0.00149593	−	0.999999i	$-0.500476\pi$
$881$	−0.0888033	−0.00299186	−0.00149593	+	0.999999i	$0.500476\pi$
$882$	0	0
$883$	57.3131	1.92874	0.964370	−	0.264557i	$-0.0852258\pi$
$883$	57.3131	1.92874	0.964370	+	0.264557i	$0.0852258\pi$
$884$	0	0
$885$	−29.7146	−0.998844
$886$	0	0
$887$	−27.0781	−0.909192	−0.454596	−	0.890698i	$-0.650216\pi$
$887$	−27.0781	−0.909192	−0.454596	+	0.890698i	$0.650216\pi$
$888$	0	0
$889$	22.1432	0.742659
$890$	0	0
$891$	−6.38271	−0.213829
$892$	0	0
$893$	13.6731	0.457552
$894$	0	0
$895$	0.266706	0.00891500
$896$	0	0
$897$	−5.24443	−0.175106
$898$	0	0
$899$	−2.90321	−0.0968275
$900$	0	0
$901$	62.3595	2.07750
$902$	0	0
$903$	−25.0607	−0.833968
$904$	0	0
$905$	−20.7971	−0.691318
$906$	0	0
$907$	−38.6276	−1.28261	−0.641304	−	0.767287i	$-0.721606\pi$
$907$	−38.6276	−1.28261	−0.641304	+	0.767287i	$0.721606\pi$
$908$	0	0
$909$	−27.4193	−0.909440
$910$	0	0
$911$	−5.27163	−0.174657	−0.0873284	−	0.996180i	$-0.527833\pi$
$911$	−5.27163	−0.174657	−0.0873284	+	0.996180i	$0.527833\pi$
$912$	0	0
$913$	10.3269	0.341771
$914$	0	0
$915$	−23.0509	−0.762038
$916$	0	0
$917$	−24.0415	−0.793920
$918$	0	0
$919$	−11.6632	−0.384734	−0.192367	−	0.981323i	$-0.561616\pi$
$919$	−11.6632	−0.384734	−0.192367	+	0.981323i	$0.561616\pi$
$920$	0	0
$921$	89.4519	2.94754
$922$	0	0
$923$	4.65386	0.153184
$924$	0	0
$925$	−2.47457	−0.0813634
$926$	0	0
$927$	−51.9353	−1.70578
$928$	0	0
$929$	−46.8198	−1.53611	−0.768054	−	0.640385i	$-0.778775\pi$
$929$	−46.8198	−1.53611	−0.768054	+	0.640385i	$0.778775\pi$
$930$	0	0
$931$	−13.5669	−0.444638
$932$	0	0
$933$	−87.2039	−2.85493
$934$	0	0
$935$	8.42864	0.275646
$936$	0	0
$937$	4.44738	0.145289	0.0726447	−	0.997358i	$-0.476856\pi$
$937$	4.44738	0.145289	0.0726447	+	0.997358i	$0.476856\pi$
$938$	0	0
$939$	−53.2355	−1.73728
$940$	0	0
$941$	12.6726	0.413115	0.206557	−	0.978434i	$-0.433774\pi$
$941$	12.6726	0.413115	0.206557	+	0.978434i	$0.433774\pi$
$942$	0	0
$943$	−23.9081	−0.778556
$944$	0	0
$945$	−10.7556	−0.349879
$946$	0	0
$947$	−20.2306	−0.657407	−0.328703	−	0.944433i	$-0.606612\pi$
$947$	−20.2306	−0.657407	−0.328703	+	0.944433i	$0.606612\pi$
$948$	0	0
$949$	−1.80642	−0.0586390
$950$	0	0
$951$	−59.3876	−1.92578
$952$	0	0
$953$	−24.5718	−0.795960	−0.397980	−	0.917394i	$-0.630289\pi$
$953$	−24.5718	−0.795960	−0.397980	+	0.917394i	$0.630289\pi$
$954$	0	0
$955$	−9.43356	−0.305263
$956$	0	0
$957$	4.42864	0.143158
$958$	0	0
$959$	8.42864	0.272175
$960$	0	0
$961$	−22.5714	−0.728108
$962$	0	0
$963$	−3.12843	−0.100812
$964$	0	0
$965$	−5.23014	−0.168364
$966$	0	0
$967$	−52.9960	−1.70424	−0.852119	−	0.523349i	$-0.824683\pi$
$967$	−52.9960	−1.70424	−0.852119	+	0.523349i	$0.824683\pi$
$968$	0	0
$969$	46.5718	1.49610
$970$	0	0
$971$	4.02720	0.129239	0.0646195	−	0.997910i	$-0.479417\pi$
$971$	4.02720	0.129239	0.0646195	+	0.997910i	$0.479417\pi$
$972$	0	0
$973$	−26.5718	−0.851854
$974$	0	0
$975$	−1.80642	−0.0578519
$976$	0	0
$977$	13.2761	0.424739	0.212370	−	0.977189i	$-0.431882\pi$
$977$	13.2761	0.424739	0.212370	+	0.977189i	$0.431882\pi$
$978$	0	0
$979$	−21.2159	−0.678062
$980$	0	0
$981$	−39.5526	−1.26282
$982$	0	0
$983$	23.5857	0.752265	0.376133	−	0.926566i	$-0.377254\pi$
$983$	23.5857	0.752265	0.376133	+	0.926566i	$0.377254\pi$
$984$	0	0
$985$	11.5397	0.367686
$986$	0	0
$987$	20.8573	0.663895
$988$	0	0
$989$	−16.4286	−0.522400
$990$	0	0
$991$	−50.7882	−1.61334	−0.806670	−	0.591003i	$-0.798732\pi$
$991$	−50.7882	−1.61334	−0.806670	+	0.591003i	$0.798732\pi$
$992$	0	0
$993$	−34.9175	−1.10807
$994$	0	0
$995$	8.33677	0.264293
$996$	0	0
$997$	54.5705	1.72826	0.864132	−	0.503266i	$-0.167868\pi$
$997$	54.5705	1.72826	0.864132	+	0.503266i	$0.167868\pi$
$998$	0	0
$999$	−17.4479	−0.552026

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9280.2.a.bt.1.3		3
4.3	odd	2		9280.2.a.bh.1.1		3
8.3	odd	2		580.2.a.d.1.3	✓	3
8.5	even	2		2320.2.a.o.1.1		3
24.11	even	2		5220.2.a.w.1.1		3
40.3	even	4		2900.2.c.g.349.6		6
40.19	odd	2		2900.2.a.f.1.1		3
40.27	even	4		2900.2.c.g.349.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
580.2.a.d.1.3	✓	3	8.3	odd	2
2320.2.a.o.1.1		3	8.5	even	2
2900.2.a.f.1.1		3	40.19	odd	2
2900.2.c.g.349.1		6	40.27	even	4
2900.2.c.g.349.6		6	40.3	even	4
5220.2.a.w.1.1		3	24.11	even	2
9280.2.a.bh.1.1		3	4.3	odd	2
9280.2.a.bt.1.3		3	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:	\( N \)	\(=\)	\( 9280 = 2^{6} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9280.a (trivial)

\(f(q)\)	\(=\)	\(q+2.90321 q^{3} -1.00000 q^{5} +1.52543 q^{7} +5.42864 q^{9} +O(q^{10})\)	\(q+2.90321 q^{3} -1.00000 q^{5} +1.52543 q^{7} +5.42864 q^{9} -1.52543 q^{11} -0.622216 q^{13} -2.90321 q^{15} +5.52543 q^{17} +2.90321 q^{19} +4.42864 q^{21} +2.90321 q^{23} +1.00000 q^{25} +7.05086 q^{27} -1.00000 q^{29} +2.90321 q^{31} -4.42864 q^{33} -1.52543 q^{35} -2.47457 q^{37} -1.80642 q^{39} -8.23506 q^{41} -5.65878 q^{43} -5.42864 q^{45} +4.70964 q^{47} -4.67307 q^{49} +16.0415 q^{51} +11.2859 q^{53} +1.52543 q^{55} +8.42864 q^{57} +10.2351 q^{59} +7.93978 q^{61} +8.28100 q^{63} +0.622216 q^{65} -2.90321 q^{67} +8.42864 q^{69} -7.47949 q^{71} +2.90321 q^{73} +2.90321 q^{75} -2.32693 q^{77} +16.5763 q^{79} +4.18421 q^{81} -6.76986 q^{83} -5.52543 q^{85} -2.90321 q^{87} +13.9081 q^{89} -0.949145 q^{91} +8.42864 q^{93} -2.90321 q^{95} +17.5669 q^{97} -8.28100 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 2 q^{3} - 3 q^{5} - 2 q^{7} + 3 q^{9}+O(q^{10}) \) 3 * q + 2 * q^3 - 3 * q^5 - 2 * q^7 + 3 * q^9	\( 3 q + 2 q^{3} - 3 q^{5} - 2 q^{7} + 3 q^{9} + 2 q^{11} - 2 q^{13} - 2 q^{15} + 10 q^{17} + 2 q^{19} + 2 q^{23} + 3 q^{25} + 8 q^{27} - 3 q^{29} + 2 q^{31} + 2 q^{35} - 14 q^{37} + 8 q^{39} + 2 q^{41} - 10 q^{43} - 3 q^{45} - 6 q^{47} - q^{49} + 8 q^{51} - 6 q^{53} - 2 q^{55} + 12 q^{57} + 4 q^{59} + 10 q^{61} + 18 q^{63} + 2 q^{65} - 2 q^{67} + 12 q^{69} + 4 q^{71} + 2 q^{73} + 2 q^{75} - 20 q^{77} + 30 q^{79} - q^{81} - 14 q^{83} - 10 q^{85} - 2 q^{87} + 2 q^{89} - 16 q^{91} + 12 q^{93} - 2 q^{95} + 6 q^{97} - 18 q^{99}+O(q^{100}) \) 3 * q + 2 * q^3 - 3 * q^5 - 2 * q^7 + 3 * q^9 + 2 * q^11 - 2 * q^13 - 2 * q^15 + 10 * q^17 + 2 * q^19 + 2 * q^23 + 3 * q^25 + 8 * q^27 - 3 * q^29 + 2 * q^31 + 2 * q^35 - 14 * q^37 + 8 * q^39 + 2 * q^41 - 10 * q^43 - 3 * q^45 - 6 * q^47 - q^49 + 8 * q^51 - 6 * q^53 - 2 * q^55 + 12 * q^57 + 4 * q^59 + 10 * q^61 + 18 * q^63 + 2 * q^65 - 2 * q^67 + 12 * q^69 + 4 * q^71 + 2 * q^73 + 2 * q^75 - 20 * q^77 + 30 * q^79 - q^81 - 14 * q^83 - 10 * q^85 - 2 * q^87 + 2 * q^89 - 16 * q^91 + 12 * q^93 - 2 * q^95 + 6 * q^97 - 18 * q^99

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