LMFDB - Embedded newform 2960.2.a.ba.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2960,2,Mod(1,2960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2960, 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("2960.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2960 = 2^{4} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2960.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:	$23.6357189983$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.368464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 6x^{3} + 6x^{2} + 6x - 4 $ x^5 - 2x^4 - 6x^3 + 6x^2 + 6x - 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 185)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.09027$ of defining polynomial
Character	$\chi$	$=$	2960.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.744131 q^{3} +1.00000 q^{5} -3.94357 q^{7} -2.44627 q^{9} +O(q^{10})$	$q-0.744131 q^{3} +1.00000 q^{5} -3.94357 q^{7} -2.44627 q^{9} +4.52210 q^{11} +1.36924 q^{13} -0.744131 q^{15} +2.29957 q^{17} -4.84765 q^{19} +2.93453 q^{21} +4.41859 q^{23} +1.00000 q^{25} +4.05274 q^{27} -9.55595 q^{29} +4.75908 q^{31} -3.36504 q^{33} -3.94357 q^{35} -1.00000 q^{37} -1.01889 q^{39} +5.21439 q^{41} +1.19485 q^{43} -2.44627 q^{45} -5.34785 q^{47} +8.55174 q^{49} -1.71118 q^{51} +1.03384 q^{53} +4.52210 q^{55} +3.60728 q^{57} -14.6197 q^{59} +1.30772 q^{61} +9.64703 q^{63} +1.36924 q^{65} -7.23975 q^{67} -3.28801 q^{69} -15.1787 q^{71} -4.81551 q^{73} -0.744131 q^{75} -17.8332 q^{77} -4.64520 q^{79} +4.32304 q^{81} +5.89279 q^{83} +2.29957 q^{85} +7.11087 q^{87} -10.3435 q^{89} -5.39969 q^{91} -3.54138 q^{93} -4.84765 q^{95} +6.37000 q^{97} -11.0623 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + q^{3} + 5 q^{5} - 7 q^{7} + 2 q^{9}+O(q^{10}) $ 5 * q + q^3 + 5 * q^5 - 7 * q^7 + 2 * q^9	$ 5 q + q^{3} + 5 q^{5} - 7 q^{7} + 2 q^{9} - 7 q^{11} + 2 q^{13} + q^{15} - 8 q^{17} - 14 q^{19} - 9 q^{21} - 2 q^{23} + 5 q^{25} + 7 q^{27} + 2 q^{29} - 8 q^{31} - 21 q^{33} - 7 q^{35} - 5 q^{37} - 12 q^{39} - 9 q^{41} - 14 q^{43} + 2 q^{45} + 5 q^{47} + 2 q^{49} - 10 q^{51} - 15 q^{53} - 7 q^{55} + 4 q^{57} - 12 q^{59} + 12 q^{61} - 24 q^{63} + 2 q^{65} + 2 q^{67} - 30 q^{69} - 13 q^{71} - 5 q^{73} + q^{75} - 7 q^{77} - 36 q^{79} + 21 q^{81} + 9 q^{83} - 8 q^{85} + 6 q^{87} - 16 q^{89} + 4 q^{91} - 16 q^{93} - 14 q^{95} - 18 q^{99}+O(q^{100}) $ 5 * q + q^3 + 5 * q^5 - 7 * q^7 + 2 * q^9 - 7 * q^11 + 2 * q^13 + q^15 - 8 * q^17 - 14 * q^19 - 9 * q^21 - 2 * q^23 + 5 * q^25 + 7 * q^27 + 2 * q^29 - 8 * q^31 - 21 * q^33 - 7 * q^35 - 5 * q^37 - 12 * q^39 - 9 * q^41 - 14 * q^43 + 2 * q^45 + 5 * q^47 + 2 * q^49 - 10 * q^51 - 15 * q^53 - 7 * q^55 + 4 * q^57 - 12 * q^59 + 12 * q^61 - 24 * q^63 + 2 * q^65 + 2 * q^67 - 30 * q^69 - 13 * q^71 - 5 * q^73 + q^75 - 7 * q^77 - 36 * q^79 + 21 * q^81 + 9 * q^83 - 8 * q^85 + 6 * q^87 - 16 * q^89 + 4 * q^91 - 16 * q^93 - 14 * q^95 - 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
$3$	−0.744131	−0.429624	−0.214812	−	0.976655i	$-0.568914\pi$
$3$	−0.744131	−0.429624	−0.214812	+	0.976655i	$0.568914\pi$
$4$	0	0
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0	0
$7$	−3.94357	−1.49053	−0.745265	−	0.666769i	$-0.767677\pi$
$7$	−3.94357	−1.49053	−0.745265	+	0.666769i	$0.767677\pi$
$8$	0	0
$9$	−2.44627	−0.815423
$10$	0	0
$11$	4.52210	1.36347	0.681733	−	0.731601i	$-0.261227\pi$
$11$	4.52210	1.36347	0.681733	+	0.731601i	$0.261227\pi$
$12$	0	0
$13$	1.36924	0.379759	0.189879	−	0.981807i	$-0.439190\pi$
$13$	1.36924	0.379759	0.189879	+	0.981807i	$0.439190\pi$
$14$	0	0
$15$	−0.744131	−0.192134
$16$	0	0
$17$	2.29957	0.557727	0.278863	−	0.960331i	$-0.410042\pi$
$17$	2.29957	0.557727	0.278863	+	0.960331i	$0.410042\pi$
$18$	0	0
$19$	−4.84765	−1.11213	−0.556063	−	0.831140i	$-0.687689\pi$
$19$	−4.84765	−1.11213	−0.556063	+	0.831140i	$0.687689\pi$
$20$	0	0
$21$	2.93453	0.640367
$22$	0	0
$23$	4.41859	0.921339	0.460670	−	0.887572i	$-0.347609\pi$
$23$	4.41859	0.921339	0.460670	+	0.887572i	$0.347609\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	4.05274	0.779949
$28$	0	0
$29$	−9.55595	−1.77449	−0.887247	−	0.461294i	$-0.847385\pi$
$29$	−9.55595	−1.77449	−0.887247	+	0.461294i	$0.847385\pi$
$30$	0	0
$31$	4.75908	0.854756	0.427378	−	0.904073i	$-0.359437\pi$
$31$	4.75908	0.854756	0.427378	+	0.904073i	$0.359437\pi$
$32$	0	0
$33$	−3.36504	−0.585778
$34$	0	0
$35$	−3.94357	−0.666585
$36$	0	0
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	0	0
$39$	−1.01889	−0.163154
$40$	0	0
$41$	5.21439	0.814351	0.407175	−	0.913350i	$-0.366514\pi$
$41$	5.21439	0.814351	0.407175	+	0.913350i	$0.366514\pi$
$42$	0	0
$43$	1.19485	0.182214	0.0911068	−	0.995841i	$-0.470960\pi$
$43$	1.19485	0.182214	0.0911068	+	0.995841i	$0.470960\pi$
$44$	0	0
$45$	−2.44627	−0.364668
$46$	0	0
$47$	−5.34785	−0.780064	−0.390032	−	0.920801i	$-0.627536\pi$
$47$	−5.34785	−0.780064	−0.390032	+	0.920801i	$0.627536\pi$
$48$	0	0
$49$	8.55174	1.22168
$50$	0	0
$51$	−1.71118	−0.239613
$52$	0	0
$53$	1.03384	0.142009	0.0710046	−	0.997476i	$-0.477380\pi$
$53$	1.03384	0.142009	0.0710046	+	0.997476i	$0.477380\pi$
$54$	0	0
$55$	4.52210	0.609760
$56$	0	0
$57$	3.60728	0.477796
$58$	0	0
$59$	−14.6197	−1.90333	−0.951664	−	0.307143i	$-0.900627\pi$
$59$	−14.6197	−1.90333	−0.951664	+	0.307143i	$0.900627\pi$
$60$	0	0
$61$	1.30772	0.167436	0.0837179	−	0.996489i	$-0.473321\pi$
$61$	1.30772	0.167436	0.0837179	+	0.996489i	$0.473321\pi$
$62$	0	0
$63$	9.64703	1.21541
$64$	0	0
$65$	1.36924	0.169833
$66$	0	0
$67$	−7.23975	−0.884476	−0.442238	−	0.896898i	$-0.645815\pi$
$67$	−7.23975	−0.884476	−0.442238	+	0.896898i	$0.645815\pi$
$68$	0	0
$69$	−3.28801	−0.395829
$70$	0	0
$71$	−15.1787	−1.80138	−0.900692	−	0.434458i	$-0.856940\pi$
$71$	−15.1787	−1.80138	−0.900692	+	0.434458i	$0.856940\pi$
$72$	0	0
$73$	−4.81551	−0.563613	−0.281806	−	0.959471i	$-0.590934\pi$
$73$	−4.81551	−0.563613	−0.281806	+	0.959471i	$0.590934\pi$
$74$	0	0
$75$	−0.744131	−0.0859248
$76$	0	0
$77$	−17.8332	−2.03229
$78$	0	0
$79$	−4.64520	−0.522626	−0.261313	−	0.965254i	$-0.584155\pi$
$79$	−4.64520	−0.522626	−0.261313	+	0.965254i	$0.584155\pi$
$80$	0	0
$81$	4.32304	0.480338
$82$	0	0
$83$	5.89279	0.646818	0.323409	−	0.946259i	$-0.395171\pi$
$83$	5.89279	0.646818	0.323409	+	0.946259i	$0.395171\pi$
$84$	0	0
$85$	2.29957	0.249423
$86$	0	0
$87$	7.11087	0.762365
$88$	0	0
$89$	−10.3435	−1.09641	−0.548205	−	0.836344i	$-0.684689\pi$
$89$	−10.3435	−1.09641	−0.548205	+	0.836344i	$0.684689\pi$
$90$	0	0
$91$	−5.39969	−0.566042
$92$	0	0
$93$	−3.54138	−0.367224
$94$	0	0
$95$	−4.84765	−0.497358
$96$	0	0
$97$	6.37000	0.646776	0.323388	−	0.946267i	$-0.395178\pi$
$97$	6.37000	0.646776	0.323388	+	0.946267i	$0.395178\pi$
$98$	0	0
$99$	−11.0623	−1.11180
$100$	0	0
$101$	−4.62142	−0.459848	−0.229924	−	0.973209i	$-0.573848\pi$
$101$	−4.62142	−0.459848	−0.229924	+	0.973209i	$0.573848\pi$
$102$	0	0
$103$	−18.3734	−1.81039	−0.905193	−	0.425001i	$-0.860274\pi$
$103$	−18.3734	−1.81039	−0.905193	+	0.425001i	$0.860274\pi$
$104$	0	0
$105$	2.93453	0.286381
$106$	0	0
$107$	17.8700	1.72755	0.863777	−	0.503875i	$-0.168093\pi$
$107$	17.8700	1.72755	0.863777	+	0.503875i	$0.168093\pi$
$108$	0	0
$109$	−3.03189	−0.290402	−0.145201	−	0.989402i	$-0.546383\pi$
$109$	−3.03189	−0.290402	−0.145201	+	0.989402i	$0.546383\pi$
$110$	0	0
$111$	0.744131	0.0706298
$112$	0	0
$113$	−20.1901	−1.89933	−0.949663	−	0.313273i	$-0.898575\pi$
$113$	−20.1901	−1.89933	−0.949663	+	0.313273i	$0.898575\pi$
$114$	0	0
$115$	4.41859	0.412035
$116$	0	0
$117$	−3.34953	−0.309664
$118$	0	0
$119$	−9.06850	−0.831308
$120$	0	0
$121$	9.44942	0.859038
$122$	0	0
$123$	−3.88019	−0.349865
$124$	0	0
$125$	1.00000	0.0894427
$126$	0	0
$127$	13.5915	1.20605	0.603025	−	0.797722i	$-0.293962\pi$
$127$	13.5915	1.20605	0.603025	+	0.797722i	$0.293962\pi$
$128$	0	0
$129$	−0.889128	−0.0782834
$130$	0	0
$131$	−21.1799	−1.85049	−0.925246	−	0.379367i	$-0.876142\pi$
$131$	−21.1799	−1.85049	−0.925246	+	0.379367i	$0.876142\pi$
$132$	0	0
$133$	19.1170	1.65766
$134$	0	0
$135$	4.05274	0.348804
$136$	0	0
$137$	7.17856	0.613305	0.306653	−	0.951821i	$-0.400791\pi$
$137$	7.17856	0.613305	0.306653	+	0.951821i	$0.400791\pi$
$138$	0	0
$139$	12.9602	1.09927	0.549636	−	0.835404i	$-0.314766\pi$
$139$	12.9602	1.09927	0.549636	+	0.835404i	$0.314766\pi$
$140$	0	0
$141$	3.97950	0.335134
$142$	0	0
$143$	6.19185	0.517788
$144$	0	0
$145$	−9.55595	−0.793578
$146$	0	0
$147$	−6.36361	−0.524862
$148$	0	0
$149$	−15.8451	−1.29809	−0.649043	−	0.760752i	$-0.724830\pi$
$149$	−15.8451	−1.29809	−0.649043	+	0.760752i	$0.724830\pi$
$150$	0	0
$151$	−14.2944	−1.16326	−0.581632	−	0.813452i	$-0.697586\pi$
$151$	−14.2944	−1.16326	−0.581632	+	0.813452i	$0.697586\pi$
$152$	0	0
$153$	−5.62536	−0.454783
$154$	0	0
$155$	4.75908	0.382258
$156$	0	0
$157$	−1.95398	−0.155945	−0.0779723	−	0.996956i	$-0.524845\pi$
$157$	−1.95398	−0.155945	−0.0779723	+	0.996956i	$0.524845\pi$
$158$	0	0
$159$	−0.769314	−0.0610105
$160$	0	0
$161$	−17.4250	−1.37328
$162$	0	0
$163$	−3.01431	−0.236099	−0.118049	−	0.993008i	$-0.537664\pi$
$163$	−3.01431	−0.236099	−0.118049	+	0.993008i	$0.537664\pi$
$164$	0	0
$165$	−3.36504	−0.261968
$166$	0	0
$167$	−4.16008	−0.321916	−0.160958	−	0.986961i	$-0.551458\pi$
$167$	−4.16008	−0.321916	−0.160958	+	0.986961i	$0.551458\pi$
$168$	0	0
$169$	−11.1252	−0.855783
$170$	0	0
$171$	11.8587	0.906854
$172$	0	0
$173$	−3.79279	−0.288361	−0.144180	−	0.989551i	$-0.546055\pi$
$173$	−3.79279	−0.288361	−0.144180	+	0.989551i	$0.546055\pi$
$174$	0	0
$175$	−3.94357	−0.298106
$176$	0	0
$177$	10.8790	0.817715
$178$	0	0
$179$	13.0017	0.971793	0.485897	−	0.874016i	$-0.338493\pi$
$179$	13.0017	0.971793	0.485897	+	0.874016i	$0.338493\pi$
$180$	0	0
$181$	−16.6739	−1.23936	−0.619681	−	0.784854i	$-0.712738\pi$
$181$	−16.6739	−1.23936	−0.619681	+	0.784854i	$0.712738\pi$
$182$	0	0
$183$	−0.973111	−0.0719345
$184$	0	0
$185$	−1.00000	−0.0735215
$186$	0	0
$187$	10.3989	0.760441
$188$	0	0
$189$	−15.9822	−1.16254
$190$	0	0
$191$	−8.73937	−0.632359	−0.316179	−	0.948699i	$-0.602400\pi$
$191$	−8.73937	−0.632359	−0.316179	+	0.948699i	$0.602400\pi$
$192$	0	0
$193$	21.6457	1.55809	0.779047	−	0.626966i	$-0.215703\pi$
$193$	21.6457	1.55809	0.779047	+	0.626966i	$0.215703\pi$
$194$	0	0
$195$	−1.01889	−0.0729645
$196$	0	0
$197$	−2.60609	−0.185676	−0.0928380	−	0.995681i	$-0.529594\pi$
$197$	−2.60609	−0.185676	−0.0928380	+	0.995681i	$0.529594\pi$
$198$	0	0
$199$	6.57573	0.466141	0.233071	−	0.972460i	$-0.425123\pi$
$199$	6.57573	0.466141	0.233071	+	0.972460i	$0.425123\pi$
$200$	0	0
$201$	5.38732	0.379992
$202$	0	0
$203$	37.6845	2.64494
$204$	0	0
$205$	5.21439	0.364189
$206$	0	0
$207$	−10.8091	−0.751281
$208$	0	0
$209$	−21.9216	−1.51635
$210$	0	0
$211$	2.00196	0.137820	0.0689102	−	0.997623i	$-0.478048\pi$
$211$	2.00196	0.137820	0.0689102	+	0.997623i	$0.478048\pi$
$212$	0	0
$213$	11.2950	0.773918
$214$	0	0
$215$	1.19485	0.0814884
$216$	0	0
$217$	−18.7678	−1.27404
$218$	0	0
$219$	3.58337	0.242142
$220$	0	0
$221$	3.14866	0.211802
$222$	0	0
$223$	7.43402	0.497819	0.248910	−	0.968527i	$-0.419928\pi$
$223$	7.43402	0.497819	0.248910	+	0.968527i	$0.419928\pi$
$224$	0	0
$225$	−2.44627	−0.163085
$226$	0	0
$227$	0.633009	0.0420143	0.0210071	−	0.999779i	$-0.493313\pi$
$227$	0.633009	0.0420143	0.0210071	+	0.999779i	$0.493313\pi$
$228$	0	0
$229$	15.9122	1.05151	0.525754	−	0.850636i	$-0.323783\pi$
$229$	15.9122	1.05151	0.525754	+	0.850636i	$0.323783\pi$
$230$	0	0
$231$	13.2703	0.873119
$232$	0	0
$233$	−8.89467	−0.582709	−0.291355	−	0.956615i	$-0.594106\pi$
$233$	−8.89467	−0.582709	−0.291355	+	0.956615i	$0.594106\pi$
$234$	0	0
$235$	−5.34785	−0.348855
$236$	0	0
$237$	3.45663	0.224533
$238$	0	0
$239$	0.0826797	0.00534810	0.00267405	−	0.999996i	$-0.499149\pi$
$239$	0.0826797	0.00534810	0.00267405	+	0.999996i	$0.499149\pi$
$240$	0	0
$241$	−19.6320	−1.26461	−0.632305	−	0.774719i	$-0.717891\pi$
$241$	−19.6320	−1.26461	−0.632305	+	0.774719i	$0.717891\pi$
$242$	0	0
$243$	−15.3751	−0.986314
$244$	0	0
$245$	8.55174	0.546351
$246$	0	0
$247$	−6.63759	−0.422340
$248$	0	0
$249$	−4.38501	−0.277888
$250$	0	0
$251$	3.16254	0.199618	0.0998089	−	0.995007i	$-0.468177\pi$
$251$	3.16254	0.199618	0.0998089	+	0.995007i	$0.468177\pi$
$252$	0	0
$253$	19.9813	1.25621
$254$	0	0
$255$	−1.71118	−0.107158
$256$	0	0
$257$	−11.7279	−0.731569	−0.365784	−	0.930700i	$-0.619199\pi$
$257$	−11.7279	−0.731569	−0.365784	+	0.930700i	$0.619199\pi$
$258$	0	0
$259$	3.94357	0.245041
$260$	0	0
$261$	23.3764	1.44696
$262$	0	0
$263$	−0.755431	−0.0465819	−0.0232909	−	0.999729i	$-0.507414\pi$
$263$	−0.755431	−0.0465819	−0.0232909	+	0.999729i	$0.507414\pi$
$264$	0	0
$265$	1.03384	0.0635084
$266$	0	0
$267$	7.69693	0.471044
$268$	0	0
$269$	13.4542	0.820320	0.410160	−	0.912014i	$-0.365473\pi$
$269$	13.4542	0.820320	0.410160	+	0.912014i	$0.365473\pi$
$270$	0	0
$271$	−7.94268	−0.482483	−0.241242	−	0.970465i	$-0.577555\pi$
$271$	−7.94268	−0.482483	−0.241242	+	0.970465i	$0.577555\pi$
$272$	0	0
$273$	4.01808	0.243185
$274$	0	0
$275$	4.52210	0.272693
$276$	0	0
$277$	6.88638	0.413762	0.206881	−	0.978366i	$-0.433669\pi$
$277$	6.88638	0.413762	0.206881	+	0.978366i	$0.433669\pi$
$278$	0	0
$279$	−11.6420	−0.696988
$280$	0	0
$281$	16.0874	0.959693	0.479847	−	0.877352i	$-0.340692\pi$
$281$	16.0874	0.959693	0.479847	+	0.877352i	$0.340692\pi$
$282$	0	0
$283$	−24.9263	−1.48172	−0.740859	−	0.671661i	$-0.765581\pi$
$283$	−24.9263	−1.48172	−0.740859	+	0.671661i	$0.765581\pi$
$284$	0	0
$285$	3.60728	0.213677
$286$	0	0
$287$	−20.5633	−1.21381
$288$	0	0
$289$	−11.7120	−0.688941
$290$	0	0
$291$	−4.74011	−0.277870
$292$	0	0
$293$	26.0732	1.52321	0.761607	−	0.648039i	$-0.224411\pi$
$293$	26.0732	1.52321	0.761607	+	0.648039i	$0.224411\pi$
$294$	0	0
$295$	−14.6197	−0.851194
$296$	0	0
$297$	18.3269	1.06343
$298$	0	0
$299$	6.05011	0.349887
$300$	0	0
$301$	−4.71199	−0.271595
$302$	0	0
$303$	3.43894	0.197562
$304$	0	0
$305$	1.30772	0.0748796
$306$	0	0
$307$	18.2979	1.04432	0.522158	−	0.852849i	$-0.325127\pi$
$307$	18.2979	1.04432	0.522158	+	0.852849i	$0.325127\pi$
$308$	0	0
$309$	13.6722	0.777785
$310$	0	0
$311$	1.44118	0.0817216	0.0408608	−	0.999165i	$-0.486990\pi$
$311$	1.44118	0.0817216	0.0408608	+	0.999165i	$0.486990\pi$
$312$	0	0
$313$	−18.5015	−1.04576	−0.522882	−	0.852405i	$-0.675143\pi$
$313$	−18.5015	−1.04576	−0.522882	+	0.852405i	$0.675143\pi$
$314$	0	0
$315$	9.64703	0.543549
$316$	0	0
$317$	−24.1703	−1.35754	−0.678769	−	0.734352i	$-0.737486\pi$
$317$	−24.1703	−1.35754	−0.678769	+	0.734352i	$0.737486\pi$
$318$	0	0
$319$	−43.2130	−2.41946
$320$	0	0
$321$	−13.2976	−0.742198
$322$	0	0
$323$	−11.1475	−0.620263
$324$	0	0
$325$	1.36924	0.0759518
$326$	0	0
$327$	2.25612	0.124764
$328$	0	0
$329$	21.0896	1.16271
$330$	0	0
$331$	0.308401	0.0169513	0.00847563	−	0.999964i	$-0.497302\pi$
$331$	0.308401	0.0169513	0.00847563	+	0.999964i	$0.497302\pi$
$332$	0	0
$333$	2.44627	0.134055
$334$	0	0
$335$	−7.23975	−0.395550
$336$	0	0
$337$	−17.7374	−0.966219	−0.483110	−	0.875560i	$-0.660493\pi$
$337$	−17.7374	−0.966219	−0.483110	+	0.875560i	$0.660493\pi$
$338$	0	0
$339$	15.0241	0.815996
$340$	0	0
$341$	21.5211	1.16543
$342$	0	0
$343$	−6.11940	−0.330417
$344$	0	0
$345$	−3.28801	−0.177020
$346$	0	0
$347$	−13.4103	−0.719902	−0.359951	−	0.932971i	$-0.617207\pi$
$347$	−13.4103	−0.719902	−0.359951	+	0.932971i	$0.617207\pi$
$348$	0	0
$349$	−18.0187	−0.964521	−0.482261	−	0.876028i	$-0.660184\pi$
$349$	−18.0187	−0.964521	−0.482261	+	0.876028i	$0.660184\pi$
$350$	0	0
$351$	5.54917	0.296193
$352$	0	0
$353$	−16.5967	−0.883355	−0.441678	−	0.897174i	$-0.645617\pi$
$353$	−16.5967	−0.883355	−0.441678	+	0.897174i	$0.645617\pi$
$354$	0	0
$355$	−15.1787	−0.805604
$356$	0	0
$357$	6.74815	0.357150
$358$	0	0
$359$	−0.294342	−0.0155348	−0.00776739	−	0.999970i	$-0.502472\pi$
$359$	−0.294342	−0.0155348	−0.00776739	+	0.999970i	$0.502472\pi$
$360$	0	0
$361$	4.49968	0.236825
$362$	0	0
$363$	−7.03160	−0.369063
$364$	0	0
$365$	−4.81551	−0.252055
$366$	0	0
$367$	−23.2638	−1.21436	−0.607181	−	0.794563i	$-0.707700\pi$
$367$	−23.2638	−1.21436	−0.607181	+	0.794563i	$0.707700\pi$
$368$	0	0
$369$	−12.7558	−0.664040
$370$	0	0
$371$	−4.07703	−0.211669
$372$	0	0
$373$	−37.2311	−1.92776	−0.963878	−	0.266345i	$-0.914184\pi$
$373$	−37.2311	−1.92776	−0.963878	+	0.266345i	$0.914184\pi$
$374$	0	0
$375$	−0.744131	−0.0384267
$376$	0	0
$377$	−13.0844	−0.673880
$378$	0	0
$379$	23.0305	1.18300	0.591498	−	0.806306i	$-0.298537\pi$
$379$	23.0305	1.18300	0.591498	+	0.806306i	$0.298537\pi$
$380$	0	0
$381$	−10.1138	−0.518148
$382$	0	0
$383$	12.8637	0.657302	0.328651	−	0.944451i	$-0.393406\pi$
$383$	12.8637	0.657302	0.328651	+	0.944451i	$0.393406\pi$
$384$	0	0
$385$	−17.8332	−0.908866
$386$	0	0
$387$	−2.92294	−0.148581
$388$	0	0
$389$	−16.1194	−0.817287	−0.408644	−	0.912694i	$-0.633998\pi$
$389$	−16.1194	−0.817287	−0.408644	+	0.912694i	$0.633998\pi$
$390$	0	0
$391$	10.1608	0.513856
$392$	0	0
$393$	15.7606	0.795016
$394$	0	0
$395$	−4.64520	−0.233725
$396$	0	0
$397$	−12.9491	−0.649897	−0.324948	−	0.945732i	$-0.605347\pi$
$397$	−12.9491	−0.649897	−0.324948	+	0.945732i	$0.605347\pi$
$398$	0	0
$399$	−14.2256	−0.712169
$400$	0	0
$401$	−17.2452	−0.861185	−0.430593	−	0.902546i	$-0.641695\pi$
$401$	−17.2452	−0.861185	−0.430593	+	0.902546i	$0.641695\pi$
$402$	0	0
$403$	6.51632	0.324601
$404$	0	0
$405$	4.32304	0.214814
$406$	0	0
$407$	−4.52210	−0.224152
$408$	0	0
$409$	31.2920	1.54729	0.773644	−	0.633621i	$-0.218432\pi$
$409$	31.2920	1.54729	0.773644	+	0.633621i	$0.218432\pi$
$410$	0	0
$411$	−5.34178	−0.263491
$412$	0	0
$413$	57.6539	2.83696
$414$	0	0
$415$	5.89279	0.289266
$416$	0	0
$417$	−9.64410	−0.472274
$418$	0	0
$419$	11.8203	0.577459	0.288730	−	0.957411i	$-0.406767\pi$
$419$	11.8203	0.577459	0.288730	+	0.957411i	$0.406767\pi$
$420$	0	0
$421$	19.1673	0.934155	0.467077	−	0.884216i	$-0.345307\pi$
$421$	19.1673	0.934155	0.467077	+	0.884216i	$0.345307\pi$
$422$	0	0
$423$	13.0823	0.636082
$424$	0	0
$425$	2.29957	0.111545
$426$	0	0
$427$	−5.15707	−0.249568
$428$	0	0
$429$	−4.60754	−0.222454
$430$	0	0
$431$	−9.78469	−0.471312	−0.235656	−	0.971837i	$-0.575724\pi$
$431$	−9.78469	−0.471312	−0.235656	+	0.971837i	$0.575724\pi$
$432$	0	0
$433$	35.2661	1.69478	0.847391	−	0.530969i	$-0.178172\pi$
$433$	35.2661	1.69478	0.847391	+	0.530969i	$0.178172\pi$
$434$	0	0
$435$	7.11087	0.340940
$436$	0	0
$437$	−21.4198	−1.02465
$438$	0	0
$439$	−24.4934	−1.16901	−0.584503	−	0.811392i	$-0.698710\pi$
$439$	−24.4934	−1.16901	−0.584503	+	0.811392i	$0.698710\pi$
$440$	0	0
$441$	−20.9199	−0.996184
$442$	0	0
$443$	26.1850	1.24409	0.622044	−	0.782982i	$-0.286302\pi$
$443$	26.1850	1.24409	0.622044	+	0.782982i	$0.286302\pi$
$444$	0	0
$445$	−10.3435	−0.490330
$446$	0	0
$447$	11.7909	0.557689
$448$	0	0
$449$	39.6969	1.87341	0.936705	−	0.350119i	$-0.113859\pi$
$449$	39.6969	1.87341	0.936705	+	0.350119i	$0.113859\pi$
$450$	0	0
$451$	23.5800	1.11034
$452$	0	0
$453$	10.6369	0.499766
$454$	0	0
$455$	−5.39969	−0.253142
$456$	0	0
$457$	20.6802	0.967380	0.483690	−	0.875239i	$-0.339296\pi$
$457$	20.6802	0.967380	0.483690	+	0.875239i	$0.339296\pi$
$458$	0	0
$459$	9.31954	0.434999
$460$	0	0
$461$	−5.51764	−0.256982	−0.128491	−	0.991711i	$-0.541013\pi$
$461$	−5.51764	−0.256982	−0.128491	+	0.991711i	$0.541013\pi$
$462$	0	0
$463$	−20.9783	−0.974944	−0.487472	−	0.873139i	$-0.662081\pi$
$463$	−20.9783	−0.974944	−0.487472	+	0.873139i	$0.662081\pi$
$464$	0	0
$465$	−3.54138	−0.164227
$466$	0	0
$467$	7.62261	0.352732	0.176366	−	0.984325i	$-0.443566\pi$
$467$	7.62261	0.352732	0.176366	+	0.984325i	$0.443566\pi$
$468$	0	0
$469$	28.5504	1.31834
$470$	0	0
$471$	1.45402	0.0669976
$472$	0	0
$473$	5.40326	0.248442
$474$	0	0
$475$	−4.84765	−0.222425
$476$	0	0
$477$	−2.52906	−0.115798
$478$	0	0
$479$	−32.7445	−1.49613	−0.748067	−	0.663623i	$-0.769018\pi$
$479$	−32.7445	−1.49613	−0.748067	+	0.663623i	$0.769018\pi$
$480$	0	0
$481$	−1.36924	−0.0624320
$482$	0	0
$483$	12.9665	0.589995
$484$	0	0
$485$	6.37000	0.289247
$486$	0	0
$487$	24.3487	1.10335	0.551673	−	0.834061i	$-0.313990\pi$
$487$	24.3487	1.10335	0.551673	+	0.834061i	$0.313990\pi$
$488$	0	0
$489$	2.24304	0.101434
$490$	0	0
$491$	−9.88214	−0.445975	−0.222987	−	0.974821i	$-0.571581\pi$
$491$	−9.88214	−0.445975	−0.222987	+	0.974821i	$0.571581\pi$
$492$	0	0
$493$	−21.9745	−0.989683
$494$	0	0
$495$	−11.0623	−0.497213
$496$	0	0
$497$	59.8584	2.68502
$498$	0	0
$499$	−38.4155	−1.71971	−0.859857	−	0.510535i	$-0.829447\pi$
$499$	−38.4155	−1.71971	−0.859857	+	0.510535i	$0.829447\pi$
$500$	0	0
$501$	3.09564	0.138303
$502$	0	0
$503$	14.2482	0.635297	0.317649	−	0.948209i	$-0.397107\pi$
$503$	14.2482	0.635297	0.317649	+	0.948209i	$0.397107\pi$
$504$	0	0
$505$	−4.62142	−0.205650
$506$	0	0
$507$	8.27859	0.367665
$508$	0	0
$509$	28.0410	1.24290	0.621448	−	0.783455i	$-0.286545\pi$
$509$	28.0410	1.24290	0.621448	+	0.783455i	$0.286545\pi$
$510$	0	0
$511$	18.9903	0.840081
$512$	0	0
$513$	−19.6462	−0.867402
$514$	0	0
$515$	−18.3734	−0.809629
$516$	0	0
$517$	−24.1835	−1.06359
$518$	0	0
$519$	2.82233	0.123887
$520$	0	0
$521$	31.3715	1.37441	0.687204	−	0.726464i	$-0.258838\pi$
$521$	31.3715	1.37441	0.687204	+	0.726464i	$0.258838\pi$
$522$	0	0
$523$	37.1439	1.62419	0.812095	−	0.583525i	$-0.198327\pi$
$523$	37.1439	1.62419	0.812095	+	0.583525i	$0.198327\pi$
$524$	0	0
$525$	2.93453	0.128073
$526$	0	0
$527$	10.9438	0.476720
$528$	0	0
$529$	−3.47608	−0.151134
$530$	0	0
$531$	35.7638	1.55202
$532$	0	0
$533$	7.13975	0.309257
$534$	0	0
$535$	17.8700	0.772585
$536$	0	0
$537$	−9.67497	−0.417506
$538$	0	0
$539$	38.6719	1.66571
$540$	0	0
$541$	−4.01732	−0.172718	−0.0863590	−	0.996264i	$-0.527523\pi$
$541$	−4.01732	−0.172718	−0.0863590	+	0.996264i	$0.527523\pi$
$542$	0	0
$543$	12.4076	0.532460
$544$	0	0
$545$	−3.03189	−0.129872
$546$	0	0
$547$	40.4991	1.73162	0.865809	−	0.500375i	$-0.166805\pi$
$547$	40.4991	1.73162	0.865809	+	0.500375i	$0.166805\pi$
$548$	0	0
$549$	−3.19903	−0.136531
$550$	0	0
$551$	46.3238	1.97346
$552$	0	0
$553$	18.3187	0.778989
$554$	0	0
$555$	0.744131	0.0315866
$556$	0	0
$557$	41.5078	1.75874	0.879370	−	0.476139i	$-0.157964\pi$
$557$	41.5078	1.75874	0.879370	+	0.476139i	$0.157964\pi$
$558$	0	0
$559$	1.63604	0.0691973
$560$	0	0
$561$	−7.73812	−0.326704
$562$	0	0
$563$	−8.82377	−0.371877	−0.185939	−	0.982561i	$-0.559533\pi$
$563$	−8.82377	−0.371877	−0.185939	+	0.982561i	$0.559533\pi$
$564$	0	0
$565$	−20.1901	−0.849405
$566$	0	0
$567$	−17.0482	−0.715958
$568$	0	0
$569$	−1.06707	−0.0447338	−0.0223669	−	0.999750i	$-0.507120\pi$
$569$	−1.06707	−0.0447338	−0.0223669	+	0.999750i	$0.507120\pi$
$570$	0	0
$571$	−3.43435	−0.143723	−0.0718616	−	0.997415i	$-0.522894\pi$
$571$	−3.43435	−0.143723	−0.0718616	+	0.997415i	$0.522894\pi$
$572$	0	0
$573$	6.50323	0.271676
$574$	0	0
$575$	4.41859	0.184268
$576$	0	0
$577$	30.2801	1.26058	0.630289	−	0.776361i	$-0.282936\pi$
$577$	30.2801	1.26058	0.630289	+	0.776361i	$0.282936\pi$
$578$	0	0
$579$	−16.1073	−0.669395
$580$	0	0
$581$	−23.2386	−0.964101
$582$	0	0
$583$	4.67514	0.193625
$584$	0	0
$585$	−3.34953	−0.138486
$586$	0	0
$587$	10.4265	0.430347	0.215173	−	0.976576i	$-0.430968\pi$
$587$	10.4265	0.430347	0.215173	+	0.976576i	$0.430968\pi$
$588$	0	0
$589$	−23.0703	−0.950597
$590$	0	0
$591$	1.93927	0.0797709
$592$	0	0
$593$	19.5382	0.802337	0.401169	−	0.916004i	$-0.368604\pi$
$593$	19.5382	0.802337	0.401169	+	0.916004i	$0.368604\pi$
$594$	0	0
$595$	−9.06850	−0.371772
$596$	0	0
$597$	−4.89320	−0.200265
$598$	0	0
$599$	9.95917	0.406921	0.203460	−	0.979083i	$-0.434781\pi$
$599$	9.95917	0.406921	0.203460	+	0.979083i	$0.434781\pi$
$600$	0	0
$601$	0.201892	0.00823534	0.00411767	−	0.999992i	$-0.498689\pi$
$601$	0.201892	0.00823534	0.00411767	+	0.999992i	$0.498689\pi$
$602$	0	0
$603$	17.7104	0.721222
$604$	0	0
$605$	9.44942	0.384174
$606$	0	0
$607$	−33.5993	−1.36375	−0.681876	−	0.731468i	$-0.738836\pi$
$607$	−33.5993	−1.36375	−0.681876	+	0.731468i	$0.738836\pi$
$608$	0	0
$609$	−28.0422	−1.13633
$610$	0	0
$611$	−7.32249	−0.296236
$612$	0	0
$613$	8.63736	0.348859	0.174430	−	0.984670i	$-0.444192\pi$
$613$	8.63736	0.348859	0.174430	+	0.984670i	$0.444192\pi$
$614$	0	0
$615$	−3.88019	−0.156464
$616$	0	0
$617$	8.37257	0.337067	0.168533	−	0.985696i	$-0.446097\pi$
$617$	8.37257	0.337067	0.168533	+	0.985696i	$0.446097\pi$
$618$	0	0
$619$	0.670360	0.0269441	0.0134720	−	0.999909i	$-0.495712\pi$
$619$	0.670360	0.0269441	0.0134720	+	0.999909i	$0.495712\pi$
$620$	0	0
$621$	17.9074	0.718598
$622$	0	0
$623$	40.7904	1.63423
$624$	0	0
$625$	1.00000	0.0400000
$626$	0	0
$627$	16.3125	0.651459
$628$	0	0
$629$	−2.29957	−0.0916897
$630$	0	0
$631$	−15.0416	−0.598798	−0.299399	−	0.954128i	$-0.596786\pi$
$631$	−15.0416	−0.598798	−0.299399	+	0.954128i	$0.596786\pi$
$632$	0	0
$633$	−1.48972	−0.0592109
$634$	0	0
$635$	13.5915	0.539362
$636$	0	0
$637$	11.7094	0.463943
$638$	0	0
$639$	37.1313	1.46889
$640$	0	0
$641$	18.9440	0.748241	0.374121	−	0.927380i	$-0.377945\pi$
$641$	18.9440	0.748241	0.374121	+	0.927380i	$0.377945\pi$
$642$	0	0
$643$	27.9869	1.10369	0.551847	−	0.833945i	$-0.313923\pi$
$643$	27.9869	1.10369	0.551847	+	0.833945i	$0.313923\pi$
$644$	0	0
$645$	−0.889128	−0.0350094
$646$	0	0
$647$	−20.3334	−0.799387	−0.399694	−	0.916649i	$-0.630883\pi$
$647$	−20.3334	−0.799387	−0.399694	+	0.916649i	$0.630883\pi$
$648$	0	0
$649$	−66.1119	−2.59512
$650$	0	0
$651$	13.9657	0.547358
$652$	0	0
$653$	−12.5212	−0.489991	−0.244996	−	0.969524i	$-0.578787\pi$
$653$	−12.5212	−0.489991	−0.244996	+	0.969524i	$0.578787\pi$
$654$	0	0
$655$	−21.1799	−0.827566
$656$	0	0
$657$	11.7800	0.459583
$658$	0	0
$659$	10.5140	0.409565	0.204783	−	0.978807i	$-0.434351\pi$
$659$	10.5140	0.409565	0.204783	+	0.978807i	$0.434351\pi$
$660$	0	0
$661$	12.9804	0.504880	0.252440	−	0.967613i	$-0.418767\pi$
$661$	12.9804	0.504880	0.252440	+	0.967613i	$0.418767\pi$
$662$	0	0
$663$	−2.34301	−0.0909951
$664$	0	0
$665$	19.1170	0.741327
$666$	0	0
$667$	−42.2238	−1.63491
$668$	0	0
$669$	−5.53188	−0.213875
$670$	0	0
$671$	5.91363	0.228293
$672$	0	0
$673$	2.47979	0.0955890	0.0477945	−	0.998857i	$-0.484781\pi$
$673$	2.47979	0.0955890	0.0477945	+	0.998857i	$0.484781\pi$
$674$	0	0
$675$	4.05274	0.155990
$676$	0	0
$677$	−23.8883	−0.918103	−0.459052	−	0.888410i	$-0.651811\pi$
$677$	−23.8883	−0.918103	−0.459052	+	0.888410i	$0.651811\pi$
$678$	0	0
$679$	−25.1205	−0.964038
$680$	0	0
$681$	−0.471041	−0.0180503
$682$	0	0
$683$	36.3338	1.39028	0.695138	−	0.718876i	$-0.255343\pi$
$683$	36.3338	1.39028	0.695138	+	0.718876i	$0.255343\pi$
$684$	0	0
$685$	7.17856	0.274279
$686$	0	0
$687$	−11.8408	−0.451753
$688$	0	0
$689$	1.41558	0.0539292
$690$	0	0
$691$	−2.36561	−0.0899922	−0.0449961	−	0.998987i	$-0.514328\pi$
$691$	−2.36561	−0.0899922	−0.0449961	+	0.998987i	$0.514328\pi$
$692$	0	0
$693$	43.6249	1.65717
$694$	0	0
$695$	12.9602	0.491609
$696$	0	0
$697$	11.9908	0.454185
$698$	0	0
$699$	6.61880	0.250346
$700$	0	0
$701$	−36.1238	−1.36438	−0.682189	−	0.731176i	$-0.738972\pi$
$701$	−36.1238	−1.36438	−0.682189	+	0.731176i	$0.738972\pi$
$702$	0	0
$703$	4.84765	0.182832
$704$	0	0
$705$	3.97950	0.149877
$706$	0	0
$707$	18.2249	0.685417
$708$	0	0
$709$	24.4167	0.916989	0.458495	−	0.888697i	$-0.348389\pi$
$709$	24.4167	0.916989	0.458495	+	0.888697i	$0.348389\pi$
$710$	0	0
$711$	11.3634	0.426161
$712$	0	0
$713$	21.0284	0.787520
$714$	0	0
$715$	6.19185	0.231562
$716$	0	0
$717$	−0.0615245	−0.00229767
$718$	0	0
$719$	26.7224	0.996576	0.498288	−	0.867012i	$-0.333962\pi$
$719$	26.7224	0.996576	0.498288	+	0.867012i	$0.333962\pi$
$720$	0	0
$721$	72.4568	2.69843
$722$	0	0
$723$	14.6088	0.543307
$724$	0	0
$725$	−9.55595	−0.354899
$726$	0	0
$727$	−2.85449	−0.105867	−0.0529336	−	0.998598i	$-0.516857\pi$
$727$	−2.85449	−0.105867	−0.0529336	+	0.998598i	$0.516857\pi$
$728$	0	0
$729$	−1.52804	−0.0565940
$730$	0	0
$731$	2.74765	0.101625
$732$	0	0
$733$	−23.9471	−0.884507	−0.442253	−	0.896890i	$-0.645821\pi$
$733$	−23.9471	−0.884507	−0.442253	+	0.896890i	$0.645821\pi$
$734$	0	0
$735$	−6.36361	−0.234725
$736$	0	0
$737$	−32.7389	−1.20595
$738$	0	0
$739$	−27.0438	−0.994823	−0.497411	−	0.867515i	$-0.665716\pi$
$739$	−27.0438	−0.994823	−0.497411	+	0.867515i	$0.665716\pi$
$740$	0	0
$741$	4.93924	0.181447
$742$	0	0
$743$	−38.5442	−1.41405	−0.707026	−	0.707188i	$-0.749963\pi$
$743$	−38.5442	−1.41405	−0.707026	+	0.707188i	$0.749963\pi$
$744$	0	0
$745$	−15.8451	−0.580521
$746$	0	0
$747$	−14.4154	−0.527430
$748$	0	0
$749$	−70.4714	−2.57497
$750$	0	0
$751$	42.9011	1.56548	0.782741	−	0.622348i	$-0.213821\pi$
$751$	42.9011	1.56548	0.782741	+	0.622348i	$0.213821\pi$
$752$	0	0
$753$	−2.35334	−0.0857606
$754$	0	0
$755$	−14.2944	−0.520227
$756$	0	0
$757$	17.3376	0.630146	0.315073	−	0.949067i	$-0.397971\pi$
$757$	17.3376	0.630146	0.315073	+	0.949067i	$0.397971\pi$
$758$	0	0
$759$	−14.8687	−0.539700
$760$	0	0
$761$	41.5752	1.50710	0.753550	−	0.657390i	$-0.228340\pi$
$761$	41.5752	1.50710	0.753550	+	0.657390i	$0.228340\pi$
$762$	0	0
$763$	11.9565	0.432853
$764$	0	0
$765$	−5.62536	−0.203385
$766$	0	0
$767$	−20.0179	−0.722805
$768$	0	0
$769$	−10.1940	−0.367603	−0.183802	−	0.982963i	$-0.558840\pi$
$769$	−10.1940	−0.367603	−0.183802	+	0.982963i	$0.558840\pi$
$770$	0	0
$771$	8.72712	0.314300
$772$	0	0
$773$	−1.79833	−0.0646816	−0.0323408	−	0.999477i	$-0.510296\pi$
$773$	−1.79833	−0.0646816	−0.0323408	+	0.999477i	$0.510296\pi$
$774$	0	0
$775$	4.75908	0.170951
$776$	0	0
$777$	−2.93453	−0.105276
$778$	0	0
$779$	−25.2775	−0.905661
$780$	0	0
$781$	−68.6398	−2.45613
$782$	0	0
$783$	−38.7277	−1.38402
$784$	0	0
$785$	−1.95398	−0.0697406
$786$	0	0
$787$	44.7062	1.59360	0.796802	−	0.604241i	$-0.206523\pi$
$787$	44.7062	1.59360	0.796802	+	0.604241i	$0.206523\pi$
$788$	0	0
$789$	0.562139	0.0200127
$790$	0	0
$791$	79.6211	2.83100
$792$	0	0
$793$	1.79058	0.0635852
$794$	0	0
$795$	−0.769314	−0.0272847
$796$	0	0
$797$	1.95203	0.0691444	0.0345722	−	0.999402i	$-0.488993\pi$
$797$	1.95203	0.0691444	0.0345722	+	0.999402i	$0.488993\pi$
$798$	0	0
$799$	−12.2977	−0.435062
$800$	0	0
$801$	25.3030	0.894038
$802$	0	0
$803$	−21.7762	−0.768467
$804$	0	0
$805$	−17.4250	−0.614151
$806$	0	0
$807$	−10.0117	−0.352429
$808$	0	0
$809$	32.1732	1.13115	0.565574	−	0.824698i	$-0.308655\pi$
$809$	32.1732	1.13115	0.565574	+	0.824698i	$0.308655\pi$
$810$	0	0
$811$	−43.5729	−1.53005	−0.765025	−	0.644000i	$-0.777274\pi$
$811$	−43.5729	−1.53005	−0.765025	+	0.644000i	$0.777274\pi$
$812$	0	0
$813$	5.91039	0.207286
$814$	0	0
$815$	−3.01431	−0.105587
$816$	0	0
$817$	−5.79223	−0.202645
$818$	0	0
$819$	13.2091	0.461564
$820$	0	0
$821$	−42.7990	−1.49370	−0.746848	−	0.664995i	$-0.768434\pi$
$821$	−42.7990	−1.49370	−0.746848	+	0.664995i	$0.768434\pi$
$822$	0	0
$823$	−52.9850	−1.84694	−0.923470	−	0.383670i	$-0.874660\pi$
$823$	−52.9850	−1.84694	−0.923470	+	0.383670i	$0.874660\pi$
$824$	0	0
$825$	−3.36504	−0.117156
$826$	0	0
$827$	−23.3945	−0.813508	−0.406754	−	0.913538i	$-0.633339\pi$
$827$	−23.3945	−0.813508	−0.406754	+	0.913538i	$0.633339\pi$
$828$	0	0
$829$	0.375803	0.0130522	0.00652608	−	0.999979i	$-0.497923\pi$
$829$	0.375803	0.0130522	0.00652608	+	0.999979i	$0.497923\pi$
$830$	0	0
$831$	−5.12437	−0.177762
$832$	0	0
$833$	19.6653	0.681362
$834$	0	0
$835$	−4.16008	−0.143965
$836$	0	0
$837$	19.2873	0.666666
$838$	0	0
$839$	−15.8320	−0.546583	−0.273291	−	0.961931i	$-0.588112\pi$
$839$	−15.8320	−0.546583	−0.273291	+	0.961931i	$0.588112\pi$
$840$	0	0
$841$	62.3161	2.14883
$842$	0	0
$843$	−11.9711	−0.412307
$844$	0	0
$845$	−11.1252	−0.382718
$846$	0	0
$847$	−37.2644	−1.28042
$848$	0	0
$849$	18.5485	0.636581
$850$	0	0
$851$	−4.41859	−0.151467
$852$	0	0
$853$	−9.32579	−0.319309	−0.159655	−	0.987173i	$-0.551038\pi$
$853$	−9.32579	−0.319309	−0.159655	+	0.987173i	$0.551038\pi$
$854$	0	0
$855$	11.8587	0.405557
$856$	0	0
$857$	−5.99313	−0.204721	−0.102361	−	0.994747i	$-0.532640\pi$
$857$	−5.99313	−0.204721	−0.102361	+	0.994747i	$0.532640\pi$
$858$	0	0
$859$	44.6541	1.52358	0.761788	−	0.647826i	$-0.224322\pi$
$859$	44.6541	1.52358	0.761788	+	0.647826i	$0.224322\pi$
$860$	0	0
$861$	15.3018	0.521483
$862$	0	0
$863$	21.8515	0.743832	0.371916	−	0.928266i	$-0.378701\pi$
$863$	21.8515	0.743832	0.371916	+	0.928266i	$0.378701\pi$
$864$	0	0
$865$	−3.79279	−0.128959
$866$	0	0
$867$	8.71525	0.295986
$868$	0	0
$869$	−21.0061	−0.712582
$870$	0	0
$871$	−9.91295	−0.335888
$872$	0	0
$873$	−15.5827	−0.527396
$874$	0	0
$875$	−3.94357	−0.133317
$876$	0	0
$877$	−11.3951	−0.384786	−0.192393	−	0.981318i	$-0.561625\pi$
$877$	−11.3951	−0.384786	−0.192393	+	0.981318i	$0.561625\pi$
$878$	0	0
$879$	−19.4019	−0.654409
$880$	0	0
$881$	−48.2087	−1.62419	−0.812096	−	0.583523i	$-0.801674\pi$
$881$	−48.2087	−1.62419	−0.812096	+	0.583523i	$0.801674\pi$
$882$	0	0
$883$	36.2461	1.21978	0.609890	−	0.792486i	$-0.291214\pi$
$883$	36.2461	1.21978	0.609890	+	0.792486i	$0.291214\pi$
$884$	0	0
$885$	10.8790	0.365693
$886$	0	0
$887$	23.8002	0.799134	0.399567	−	0.916704i	$-0.369160\pi$
$887$	23.8002	0.799134	0.399567	+	0.916704i	$0.369160\pi$
$888$	0	0
$889$	−53.5990	−1.79765
$890$	0	0
$891$	19.5493	0.654925
$892$	0	0
$893$	25.9245	0.867530
$894$	0	0
$895$	13.0017	0.434599
$896$	0	0
$897$	−4.50207	−0.150320
$898$	0	0
$899$	−45.4775	−1.51676
$900$	0	0
$901$	2.37739	0.0792023
$902$	0	0
$903$	3.50634	0.116684
$904$	0	0
$905$	−16.6739	−0.554260
$906$	0	0
$907$	9.82566	0.326256	0.163128	−	0.986605i	$-0.447842\pi$
$907$	9.82566	0.326256	0.163128	+	0.986605i	$0.447842\pi$
$908$	0	0
$909$	11.3052	0.374971
$910$	0	0
$911$	−31.2125	−1.03412	−0.517058	−	0.855950i	$-0.672973\pi$
$911$	−31.2125	−1.03412	−0.517058	+	0.855950i	$0.672973\pi$
$912$	0	0
$913$	26.6478	0.881914
$914$	0	0
$915$	−0.973111	−0.0321701
$916$	0	0
$917$	83.5243	2.75821
$918$	0	0
$919$	−28.5950	−0.943263	−0.471631	−	0.881796i	$-0.656335\pi$
$919$	−28.5950	−0.943263	−0.471631	+	0.881796i	$0.656335\pi$
$920$	0	0
$921$	−13.6160	−0.448663
$922$	0	0
$923$	−20.7833	−0.684092
$924$	0	0
$925$	−1.00000	−0.0328798
$926$	0	0
$927$	44.9463	1.47623
$928$	0	0
$929$	−45.3832	−1.48898	−0.744488	−	0.667636i	$-0.767306\pi$
$929$	−45.3832	−1.48898	−0.744488	+	0.667636i	$0.767306\pi$
$930$	0	0
$931$	−41.4558	−1.35866
$932$	0	0
$933$	−1.07242	−0.0351095
$934$	0	0
$935$	10.3989	0.340080
$936$	0	0
$937$	−27.0457	−0.883543	−0.441772	−	0.897128i	$-0.645650\pi$
$937$	−27.0457	−0.883543	−0.441772	+	0.897128i	$0.645650\pi$
$938$	0	0
$939$	13.7675	0.449285
$940$	0	0
$941$	31.3367	1.02155	0.510773	−	0.859716i	$-0.329359\pi$
$941$	31.3367	1.02155	0.510773	+	0.859716i	$0.329359\pi$
$942$	0	0
$943$	23.0402	0.750293
$944$	0	0
$945$	−15.9822	−0.519903
$946$	0	0
$947$	27.4446	0.891830	0.445915	−	0.895075i	$-0.352878\pi$
$947$	27.4446	0.891830	0.445915	+	0.895075i	$0.352878\pi$
$948$	0	0
$949$	−6.59359	−0.214037
$950$	0	0
$951$	17.9858	0.583231
$952$	0	0
$953$	−35.3324	−1.14453	−0.572265	−	0.820069i	$-0.693935\pi$
$953$	−35.3324	−1.14453	−0.572265	+	0.820069i	$0.693935\pi$
$954$	0	0
$955$	−8.73937	−0.282799
$956$	0	0
$957$	32.1561	1.03946
$958$	0	0
$959$	−28.3091	−0.914150
$960$	0	0
$961$	−8.35116	−0.269392
$962$	0	0
$963$	−43.7147	−1.40869
$964$	0	0
$965$	21.6457	0.696801
$966$	0	0
$967$	−31.4137	−1.01020	−0.505098	−	0.863062i	$-0.668544\pi$
$967$	−31.4137	−1.01020	−0.505098	+	0.863062i	$0.668544\pi$
$968$	0	0
$969$	8.29519	0.266480
$970$	0	0
$971$	−6.60982	−0.212119	−0.106060	−	0.994360i	$-0.533823\pi$
$971$	−6.60982	−0.212119	−0.106060	+	0.994360i	$0.533823\pi$
$972$	0	0
$973$	−51.1095	−1.63850
$974$	0	0
$975$	−1.01889	−0.0326307
$976$	0	0
$977$	−0.318781	−0.0101987	−0.00509935	−	0.999987i	$-0.501623\pi$
$977$	−0.318781	−0.0101987	−0.00509935	+	0.999987i	$0.501623\pi$
$978$	0	0
$979$	−46.7744	−1.49492
$980$	0	0
$981$	7.41681	0.236801
$982$	0	0
$983$	10.7688	0.343473	0.171736	−	0.985143i	$-0.445062\pi$
$983$	10.7688	0.343473	0.171736	+	0.985143i	$0.445062\pi$
$984$	0	0
$985$	−2.60609	−0.0830368
$986$	0	0
$987$	−15.6934	−0.499527
$988$	0	0
$989$	5.27957	0.167881
$990$	0	0
$991$	23.6638	0.751706	0.375853	−	0.926679i	$-0.377350\pi$
$991$	23.6638	0.751706	0.375853	+	0.926679i	$0.377350\pi$
$992$	0	0
$993$	−0.229491	−0.00728267
$994$	0	0
$995$	6.57573	0.208465
$996$	0	0
$997$	−4.48006	−0.141885	−0.0709425	−	0.997480i	$-0.522601\pi$
$997$	−4.48006	−0.141885	−0.0709425	+	0.997480i	$0.522601\pi$
$998$	0	0
$999$	−4.05274	−0.128223

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2960.2.a.ba.1.2		5
4.3	odd	2		185.2.a.d.1.4	✓	5
12.11	even	2		1665.2.a.q.1.2		5
20.3	even	4		925.2.b.g.149.3		10
20.7	even	4		925.2.b.g.149.8		10
20.19	odd	2		925.2.a.h.1.2		5
28.27	even	2		9065.2.a.j.1.4		5
60.59	even	2		8325.2.a.cc.1.4		5
148.147	odd	2		6845.2.a.g.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.a.d.1.4	✓	5	4.3	odd	2
925.2.a.h.1.2		5	20.19	odd	2
925.2.b.g.149.3		10	20.3	even	4
925.2.b.g.149.8		10	20.7	even	4
1665.2.a.q.1.2		5	12.11	even	2
2960.2.a.ba.1.2		5	1.1	even	1	trivial
6845.2.a.g.1.2		5	148.147	odd	2
8325.2.a.cc.1.4		5	60.59	even	2
9065.2.a.j.1.4		5	28.27	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2960 = 2^{4} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2960.a (trivial)

\(f(q)\)	\(=\)	\(q-0.744131 q^{3} +1.00000 q^{5} -3.94357 q^{7} -2.44627 q^{9} +O(q^{10})\)	\(q-0.744131 q^{3} +1.00000 q^{5} -3.94357 q^{7} -2.44627 q^{9} +4.52210 q^{11} +1.36924 q^{13} -0.744131 q^{15} +2.29957 q^{17} -4.84765 q^{19} +2.93453 q^{21} +4.41859 q^{23} +1.00000 q^{25} +4.05274 q^{27} -9.55595 q^{29} +4.75908 q^{31} -3.36504 q^{33} -3.94357 q^{35} -1.00000 q^{37} -1.01889 q^{39} +5.21439 q^{41} +1.19485 q^{43} -2.44627 q^{45} -5.34785 q^{47} +8.55174 q^{49} -1.71118 q^{51} +1.03384 q^{53} +4.52210 q^{55} +3.60728 q^{57} -14.6197 q^{59} +1.30772 q^{61} +9.64703 q^{63} +1.36924 q^{65} -7.23975 q^{67} -3.28801 q^{69} -15.1787 q^{71} -4.81551 q^{73} -0.744131 q^{75} -17.8332 q^{77} -4.64520 q^{79} +4.32304 q^{81} +5.89279 q^{83} +2.29957 q^{85} +7.11087 q^{87} -10.3435 q^{89} -5.39969 q^{91} -3.54138 q^{93} -4.84765 q^{95} +6.37000 q^{97} -11.0623 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{3} + 5 q^{5} - 7 q^{7} + 2 q^{9}+O(q^{10}) \) 5 * q + q^3 + 5 * q^5 - 7 * q^7 + 2 * q^9	\( 5 q + q^{3} + 5 q^{5} - 7 q^{7} + 2 q^{9} - 7 q^{11} + 2 q^{13} + q^{15} - 8 q^{17} - 14 q^{19} - 9 q^{21} - 2 q^{23} + 5 q^{25} + 7 q^{27} + 2 q^{29} - 8 q^{31} - 21 q^{33} - 7 q^{35} - 5 q^{37} - 12 q^{39} - 9 q^{41} - 14 q^{43} + 2 q^{45} + 5 q^{47} + 2 q^{49} - 10 q^{51} - 15 q^{53} - 7 q^{55} + 4 q^{57} - 12 q^{59} + 12 q^{61} - 24 q^{63} + 2 q^{65} + 2 q^{67} - 30 q^{69} - 13 q^{71} - 5 q^{73} + q^{75} - 7 q^{77} - 36 q^{79} + 21 q^{81} + 9 q^{83} - 8 q^{85} + 6 q^{87} - 16 q^{89} + 4 q^{91} - 16 q^{93} - 14 q^{95} - 18 q^{99}+O(q^{100}) \) 5 * q + q^3 + 5 * q^5 - 7 * q^7 + 2 * q^9 - 7 * q^11 + 2 * q^13 + q^15 - 8 * q^17 - 14 * q^19 - 9 * q^21 - 2 * q^23 + 5 * q^25 + 7 * q^27 + 2 * q^29 - 8 * q^31 - 21 * q^33 - 7 * q^35 - 5 * q^37 - 12 * q^39 - 9 * q^41 - 14 * q^43 + 2 * q^45 + 5 * q^47 + 2 * q^49 - 10 * q^51 - 15 * q^53 - 7 * q^55 + 4 * q^57 - 12 * q^59 + 12 * q^61 - 24 * q^63 + 2 * q^65 + 2 * q^67 - 30 * q^69 - 13 * q^71 - 5 * q^73 + q^75 - 7 * q^77 - 36 * q^79 + 21 * q^81 + 9 * q^83 - 8 * q^85 + 6 * q^87 - 16 * q^89 + 4 * q^91 - 16 * q^93 - 14 * q^95 - 18 * q^99

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