LMFDB - Embedded newform 4655.2.a.br.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4655,2,Mod(1,4655)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4655, 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("4655.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4655 = 5 \cdot 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4655.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:	$37.1703621409$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	4655.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.970750 q^{2} +1.67805 q^{3} -1.05764 q^{4} -1.00000 q^{5} -1.62896 q^{6} +2.96821 q^{8} -0.184157 q^{9} +0.970750 q^{10} -2.07210 q^{11} -1.77478 q^{12} +3.19041 q^{13} -1.67805 q^{15} -0.766099 q^{16} +6.41955 q^{17} +0.178770 q^{18} +1.00000 q^{19} +1.05764 q^{20} +2.01149 q^{22} -7.12724 q^{23} +4.98079 q^{24} +1.00000 q^{25} -3.09709 q^{26} -5.34317 q^{27} -7.42287 q^{29} +1.62896 q^{30} +4.12205 q^{31} -5.19273 q^{32} -3.47708 q^{33} -6.23178 q^{34} +0.194772 q^{36} +6.01740 q^{37} -0.970750 q^{38} +5.35366 q^{39} -2.96821 q^{40} +3.33345 q^{41} +10.7946 q^{43} +2.19155 q^{44} +0.184157 q^{45} +6.91877 q^{46} +2.74900 q^{47} -1.28555 q^{48} -0.970750 q^{50} +10.7723 q^{51} -3.37432 q^{52} -11.2500 q^{53} +5.18688 q^{54} +2.07210 q^{55} +1.67805 q^{57} +7.20575 q^{58} +2.95814 q^{59} +1.77478 q^{60} -8.10822 q^{61} -4.00148 q^{62} +6.57304 q^{64} -3.19041 q^{65} +3.37538 q^{66} +11.6881 q^{67} -6.78960 q^{68} -11.9598 q^{69} -7.73825 q^{71} -0.546615 q^{72} +13.5562 q^{73} -5.84139 q^{74} +1.67805 q^{75} -1.05764 q^{76} -5.19707 q^{78} -13.8798 q^{79} +0.766099 q^{80} -8.41362 q^{81} -3.23595 q^{82} +8.62082 q^{83} -6.41955 q^{85} -10.4788 q^{86} -12.4559 q^{87} -6.15043 q^{88} -14.2789 q^{89} -0.178770 q^{90} +7.53808 q^{92} +6.91699 q^{93} -2.66859 q^{94} -1.00000 q^{95} -8.71364 q^{96} +15.2038 q^{97} +0.381591 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q + 4 q^{2} - 6 q^{3} + 36 q^{4} - 26 q^{5} + 4 q^{6} + 12 q^{8} + 44 q^{9} - 4 q^{10} + 14 q^{11} - 20 q^{12} - 14 q^{13} + 6 q^{15} + 64 q^{16} - 18 q^{17} + 8 q^{18} + 26 q^{19} - 36 q^{20} + 36 q^{22}+ \cdots + 24 q^{99}+O(q^{100}) $ 26 * q + 4 * q^2 - 6 * q^3 + 36 * q^4 - 26 * q^5 + 4 * q^6 + 12 * q^8 + 44 * q^9 - 4 * q^10 + 14 * q^11 - 20 * q^12 - 14 * q^13 + 6 * q^15 + 64 * q^16 - 18 * q^17 + 8 * q^18 + 26 * q^19 - 36 * q^20 + 36 * q^22 + 44 * q^24 + 26 * q^25 + 8 * q^26 - 30 * q^27 + 22 * q^29 - 4 * q^30 + 28 * q^32 - 38 * q^33 + 68 * q^36 + 48 * q^37 + 4 * q^38 + 26 * q^39 - 12 * q^40 - 4 * q^41 + 16 * q^43 + 44 * q^44 - 44 * q^45 + 48 * q^46 - 22 * q^47 - 48 * q^48 + 4 * q^50 + 34 * q^51 - 32 * q^52 + 28 * q^53 + 28 * q^54 - 14 * q^55 - 6 * q^57 + 52 * q^58 + 8 * q^59 + 20 * q^60 + 28 * q^61 + 16 * q^62 + 52 * q^64 + 14 * q^65 + 24 * q^66 + 60 * q^67 - 52 * q^68 + 4 * q^69 + 8 * q^71 + 36 * q^72 + 4 * q^73 + 8 * q^74 - 6 * q^75 + 36 * q^76 - 76 * q^78 + 50 * q^79 - 64 * q^80 + 114 * q^81 + 36 * q^82 - 20 * q^83 + 18 * q^85 + 40 * q^86 - 18 * q^87 + 108 * q^88 + 20 * q^89 - 8 * q^90 - 48 * q^92 + 32 * q^93 + 80 * q^94 - 26 * q^95 + 140 * q^96 - 26 * q^97 + 24 * q^99

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 $

$2$	−0.970750	−0.686424	−0.343212	−	0.939258i	$-0.611515\pi$
$2$	−0.970750	−0.686424	−0.343212	+	0.939258i	$0.611515\pi$
$3$	1.67805	0.968821	0.484411	−	0.874841i	$-0.339034\pi$
$3$	1.67805	0.968821	0.484411	+	0.874841i	$0.339034\pi$
$4$	−1.05764	−0.528822
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.62896	−0.665022
$7$	0	0
$7$	0	0
$8$	2.96821	1.04942
$9$	−0.184157	−0.0613855
$10$	0.970750	0.306978
$11$	−2.07210	−0.624762	−0.312381	−	0.949957i	$-0.601127\pi$
$11$	−2.07210	−0.624762	−0.312381	+	0.949957i	$0.601127\pi$
$12$	−1.77478	−0.512334
$13$	3.19041	0.884861	0.442430	−	0.896803i	$-0.354116\pi$
$13$	3.19041	0.884861	0.442430	+	0.896803i	$0.354116\pi$
$14$	0	0
$15$	−1.67805	−0.433270
$16$	−0.766099	−0.191525
$17$	6.41955	1.55697	0.778485	−	0.627663i	$-0.215988\pi$
$17$	6.41955	1.55697	0.778485	+	0.627663i	$0.215988\pi$
$18$	0.178770	0.0421365
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	1.05764	0.236496
$21$	0	0
$22$	2.01149	0.428852
$23$	−7.12724	−1.48613	−0.743066	−	0.669218i	$-0.766629\pi$
$23$	−7.12724	−1.48613	−0.743066	+	0.669218i	$0.766629\pi$
$24$	4.98079	1.01670
$25$	1.00000	0.200000
$26$	−3.09709	−0.607390
$27$	−5.34317	−1.02829
$28$	0	0
$29$	−7.42287	−1.37839	−0.689197	−	0.724574i	$-0.742036\pi$
$29$	−7.42287	−1.37839	−0.689197	+	0.724574i	$0.742036\pi$
$30$	1.62896	0.297407
$31$	4.12205	0.740341	0.370171	−	0.928964i	$-0.379299\pi$
$31$	4.12205	0.740341	0.370171	+	0.928964i	$0.379299\pi$
$32$	−5.19273	−0.917953
$33$	−3.47708	−0.605283
$34$	−6.23178	−1.06874
$35$	0	0
$36$	0.194772	0.0324620
$37$	6.01740	0.989255	0.494627	−	0.869105i	$-0.335305\pi$
$37$	6.01740	0.989255	0.494627	+	0.869105i	$0.335305\pi$
$38$	−0.970750	−0.157476
$39$	5.35366	0.857272
$40$	−2.96821	−0.469315
$41$	3.33345	0.520598	0.260299	−	0.965528i	$-0.416179\pi$
$41$	3.33345	0.520598	0.260299	+	0.965528i	$0.416179\pi$
$42$	0	0
$43$	10.7946	1.64616	0.823078	−	0.567928i	$-0.192255\pi$
$43$	10.7946	1.64616	0.823078	+	0.567928i	$0.192255\pi$
$44$	2.19155	0.330388
$45$	0.184157	0.0274524
$46$	6.91877	1.02012
$47$	2.74900	0.400983	0.200491	−	0.979695i	$-0.435746\pi$
$47$	2.74900	0.400983	0.200491	+	0.979695i	$0.435746\pi$
$48$	−1.28555	−0.185553
$49$	0	0
$50$	−0.970750	−0.137285
$51$	10.7723	1.50843
$52$	−3.37432	−0.467934
$53$	−11.2500	−1.54531	−0.772656	−	0.634825i	$-0.781072\pi$
$53$	−11.2500	−1.54531	−0.772656	+	0.634825i	$0.781072\pi$
$54$	5.18688	0.705845
$55$	2.07210	0.279402
$56$	0	0
$57$	1.67805	0.222263
$58$	7.20575	0.946162
$59$	2.95814	0.385117	0.192558	−	0.981285i	$-0.438321\pi$
$59$	2.95814	0.385117	0.192558	+	0.981285i	$0.438321\pi$
$60$	1.77478	0.229123
$61$	−8.10822	−1.03815	−0.519076	−	0.854728i	$-0.673724\pi$
$61$	−8.10822	−1.03815	−0.519076	+	0.854728i	$0.673724\pi$
$62$	−4.00148	−0.508188
$63$	0	0
$64$	6.57304	0.821630
$65$	−3.19041	−0.395722
$66$	3.37538	0.415481
$67$	11.6881	1.42792	0.713962	−	0.700184i	$-0.246899\pi$
$67$	11.6881	1.42792	0.713962	+	0.700184i	$0.246899\pi$
$68$	−6.78960	−0.823360
$69$	−11.9598	−1.43980
$70$	0	0
$71$	−7.73825	−0.918361	−0.459181	−	0.888343i	$-0.651857\pi$
$71$	−7.73825	−0.918361	−0.459181	+	0.888343i	$0.651857\pi$
$72$	−0.546615	−0.0644192
$73$	13.5562	1.58663	0.793314	−	0.608813i	$-0.208354\pi$
$73$	13.5562	1.58663	0.793314	+	0.608813i	$0.208354\pi$
$74$	−5.84139	−0.679048
$75$	1.67805	0.193764
$76$	−1.05764	−0.121320
$77$	0	0
$78$	−5.19707	−0.588452
$79$	−13.8798	−1.56160	−0.780802	−	0.624778i	$-0.785189\pi$
$79$	−13.8798	−1.56160	−0.780802	+	0.624778i	$0.785189\pi$
$80$	0.766099	0.0856525
$81$	−8.41362	−0.934846
$82$	−3.23595	−0.357351
$83$	8.62082	0.946258	0.473129	−	0.880993i	$-0.343124\pi$
$83$	8.62082	0.946258	0.473129	+	0.880993i	$0.343124\pi$
$84$	0	0
$85$	−6.41955	−0.696298
$86$	−10.4788	−1.12996
$87$	−12.4559	−1.33542
$88$	−6.15043	−0.655638
$89$	−14.2789	−1.51356	−0.756781	−	0.653669i	$-0.773229\pi$
$89$	−14.2789	−1.51356	−0.756781	+	0.653669i	$0.773229\pi$
$90$	−0.178770	−0.0188440
$91$	0	0
$92$	7.53808	0.785900
$93$	6.91699	0.717258
$94$	−2.66859	−0.275244
$95$	−1.00000	−0.102598
$96$	−8.71364	−0.889332
$97$	15.2038	1.54371	0.771856	−	0.635798i	$-0.219329\pi$
$97$	15.2038	1.54371	0.771856	+	0.635798i	$0.219329\pi$
$98$	0	0
$99$	0.381591	0.0383513
$100$	−1.05764	−0.105764
$101$	6.04404	0.601404	0.300702	−	0.953718i	$-0.402779\pi$
$101$	6.04404	0.601404	0.300702	+	0.953718i	$0.402779\pi$
$102$	−10.4572	−1.03542
$103$	2.03477	0.200492	0.100246	−	0.994963i	$-0.468037\pi$
$103$	2.03477	0.200492	0.100246	+	0.994963i	$0.468037\pi$
$104$	9.46980	0.928591
$105$	0	0
$106$	10.9210	1.06074
$107$	3.29869	0.318896	0.159448	−	0.987206i	$-0.449029\pi$
$107$	3.29869	0.318896	0.159448	+	0.987206i	$0.449029\pi$
$108$	5.65117	0.543784
$109$	−10.4674	−1.00260	−0.501299	−	0.865274i	$-0.667144\pi$
$109$	−10.4674	−1.00260	−0.501299	+	0.865274i	$0.667144\pi$
$110$	−2.01149	−0.191788
$111$	10.0975	0.958411
$112$	0	0
$113$	12.8634	1.21009	0.605044	−	0.796192i	$-0.293156\pi$
$113$	12.8634	1.21009	0.605044	+	0.796192i	$0.293156\pi$
$114$	−1.62896	−0.152567
$115$	7.12724	0.664618
$116$	7.85076	0.728925
$117$	−0.587535	−0.0543176
$118$	−2.87161	−0.264353
$119$	0	0
$120$	−4.98079	−0.454682
$121$	−6.70640	−0.609672
$122$	7.87106	0.712612
$123$	5.59370	0.504367
$124$	−4.35966	−0.391509
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	−16.1581	−1.43380	−0.716901	−	0.697175i	$-0.754440\pi$
$127$	−16.1581	−1.43380	−0.716901	+	0.697175i	$0.754440\pi$
$128$	4.00468	0.353967
$129$	18.1138	1.59483
$130$	3.09709	0.271633
$131$	13.9199	1.21618	0.608092	−	0.793867i	$-0.291935\pi$
$131$	13.9199	1.21618	0.608092	+	0.793867i	$0.291935\pi$
$132$	3.67752	0.320087
$133$	0	0
$134$	−11.3462	−0.980162
$135$	5.34317	0.459867
$136$	19.0546	1.63392
$137$	19.9430	1.70384	0.851922	−	0.523669i	$-0.175437\pi$
$137$	19.9430	1.70384	0.851922	+	0.523669i	$0.175437\pi$
$138$	11.6100	0.988310
$139$	−8.29025	−0.703170	−0.351585	−	0.936156i	$-0.614357\pi$
$139$	−8.29025	−0.703170	−0.351585	+	0.936156i	$0.614357\pi$
$140$	0	0
$141$	4.61295	0.388481
$142$	7.51191	0.630385
$143$	−6.61085	−0.552827
$144$	0.141082	0.0117569
$145$	7.42287	0.616436
$146$	−13.1596	−1.08910
$147$	0	0
$148$	−6.36427	−0.523140
$149$	5.87288	0.481125	0.240562	−	0.970634i	$-0.422668\pi$
$149$	5.87288	0.481125	0.240562	+	0.970634i	$0.422668\pi$
$150$	−1.62896	−0.133004
$151$	21.2147	1.72643	0.863215	−	0.504836i	$-0.168447\pi$
$151$	21.2147	1.72643	0.863215	+	0.504836i	$0.168447\pi$
$152$	2.96821	0.240753
$153$	−1.18220	−0.0955754
$154$	0	0
$155$	−4.12205	−0.331091
$156$	−5.66227	−0.453344
$157$	−6.52574	−0.520810	−0.260405	−	0.965499i	$-0.583856\pi$
$157$	−6.52574	−0.520810	−0.260405	+	0.965499i	$0.583856\pi$
$158$	13.4739	1.07192
$159$	−18.8781	−1.49713
$160$	5.19273	0.410521
$161$	0	0
$162$	8.16752	0.641701
$163$	5.51115	0.431666	0.215833	−	0.976430i	$-0.430753\pi$
$163$	5.51115	0.431666	0.215833	+	0.976430i	$0.430753\pi$
$164$	−3.52561	−0.275304
$165$	3.47708	0.270691
$166$	−8.36866	−0.649534
$167$	19.2401	1.48884	0.744421	−	0.667710i	$-0.232726\pi$
$167$	19.2401	1.48884	0.744421	+	0.667710i	$0.232726\pi$
$168$	0	0
$169$	−2.82128	−0.217022
$170$	6.23178	0.477956
$171$	−0.184157	−0.0140828
$172$	−11.4168	−0.870524
$173$	24.3872	1.85413	0.927064	−	0.374904i	$-0.122324\pi$
$173$	24.3872	1.85413	0.927064	+	0.374904i	$0.122324\pi$
$174$	12.0916	0.916662
$175$	0	0
$176$	1.58744	0.119657
$177$	4.96390	0.373109
$178$	13.8613	1.03895
$179$	−13.9786	−1.04481	−0.522404	−	0.852698i	$-0.674965\pi$
$179$	−13.9786	−1.04481	−0.522404	+	0.852698i	$0.674965\pi$
$180$	−0.194772	−0.0145175
$181$	−4.39177	−0.326438	−0.163219	−	0.986590i	$-0.552188\pi$
$181$	−4.39177	−0.326438	−0.163219	+	0.986590i	$0.552188\pi$
$182$	0	0
$183$	−13.6060	−1.00578
$184$	−21.1551	−1.55958
$185$	−6.01740	−0.442408
$186$	−6.71467	−0.492343
$187$	−13.3020	−0.972736
$188$	−2.90746	−0.212049
$189$	0	0
$190$	0.970750	0.0704256
$191$	−2.80252	−0.202783	−0.101392	−	0.994847i	$-0.532330\pi$
$191$	−2.80252	−0.202783	−0.101392	+	0.994847i	$0.532330\pi$
$192$	11.0299	0.796012
$193$	18.5878	1.33798	0.668989	−	0.743272i	$-0.266727\pi$
$193$	18.5878	1.33798	0.668989	+	0.743272i	$0.266727\pi$
$194$	−14.7591	−1.05964
$195$	−5.35366	−0.383384
$196$	0	0
$197$	22.3562	1.59282	0.796408	−	0.604760i	$-0.206731\pi$
$197$	22.3562	1.59282	0.796408	+	0.604760i	$0.206731\pi$
$198$	−0.370430	−0.0263253
$199$	14.5247	1.02963	0.514813	−	0.857302i	$-0.327861\pi$
$199$	14.5247	1.02963	0.514813	+	0.857302i	$0.327861\pi$
$200$	2.96821	0.209884
$201$	19.6131	1.38340
$202$	−5.86725	−0.412818
$203$	0	0
$204$	−11.3933	−0.797689
$205$	−3.33345	−0.232819
$206$	−1.97526	−0.137623
$207$	1.31253	0.0912270
$208$	−2.44417	−0.169473
$209$	−2.07210	−0.143330
$210$	0	0
$211$	13.2163	0.909846	0.454923	−	0.890531i	$-0.349667\pi$
$211$	13.2163	0.909846	0.454923	+	0.890531i	$0.349667\pi$
$212$	11.8985	0.817195
$213$	−12.9852	−0.889728
$214$	−3.20220	−0.218898
$215$	−10.7946	−0.736183
$216$	−15.8596	−1.07911
$217$	0	0
$218$	10.1613	0.688207
$219$	22.7479	1.53716
$220$	−2.19155	−0.147754
$221$	20.4810	1.37770
$222$	−9.80214	−0.657876
$223$	−4.30067	−0.287994	−0.143997	−	0.989578i	$-0.545996\pi$
$223$	−4.30067	−0.287994	−0.143997	+	0.989578i	$0.545996\pi$
$224$	0	0
$225$	−0.184157	−0.0122771
$226$	−12.4872	−0.830633
$227$	−18.3520	−1.21807	−0.609034	−	0.793144i	$-0.708443\pi$
$227$	−18.3520	−1.21807	−0.609034	+	0.793144i	$0.708443\pi$
$228$	−1.77478	−0.117538
$229$	15.3348	1.01335	0.506677	−	0.862136i	$-0.330874\pi$
$229$	15.3348	1.01335	0.506677	+	0.862136i	$0.330874\pi$
$230$	−6.91877	−0.456210
$231$	0	0
$232$	−22.0326	−1.44651
$233$	16.8166	1.10169	0.550845	−	0.834608i	$-0.314306\pi$
$233$	16.8166	1.10169	0.550845	+	0.834608i	$0.314306\pi$
$234$	0.570350	0.0372849
$235$	−2.74900	−0.179325
$236$	−3.12866	−0.203658
$237$	−23.2910	−1.51292
$238$	0	0
$239$	−3.41154	−0.220674	−0.110337	−	0.993894i	$-0.535193\pi$
$239$	−3.41154	−0.220674	−0.110337	+	0.993894i	$0.535193\pi$
$240$	1.28555	0.0829820
$241$	18.3852	1.18429	0.592146	−	0.805831i	$-0.298281\pi$
$241$	18.3852	1.18429	0.592146	+	0.805831i	$0.298281\pi$
$242$	6.51023	0.418494
$243$	1.91105	0.122594
$244$	8.57562	0.548997
$245$	0	0
$246$	−5.43008	−0.346209
$247$	3.19041	0.203001
$248$	12.2351	0.776929
$249$	14.4661	0.916755
$250$	0.970750	0.0613956
$251$	−0.157387	−0.00993418	−0.00496709	−	0.999988i	$-0.501581\pi$
$251$	−0.157387	−0.00993418	−0.00496709	+	0.999988i	$0.501581\pi$
$252$	0	0
$253$	14.7684	0.928479
$254$	15.6855	0.984196
$255$	−10.7723	−0.674588
$256$	−17.0336	−1.06460
$257$	−22.1753	−1.38326	−0.691628	−	0.722254i	$-0.743106\pi$
$257$	−22.1753	−1.38326	−0.691628	+	0.722254i	$0.743106\pi$
$258$	−17.5840	−1.09473
$259$	0	0
$260$	3.37432	0.209266
$261$	1.36697	0.0846134
$262$	−13.5127	−0.834817
$263$	−18.8373	−1.16156	−0.580778	−	0.814062i	$-0.697251\pi$
$263$	−18.8373	−1.16156	−0.580778	+	0.814062i	$0.697251\pi$
$264$	−10.3207	−0.635196
$265$	11.2500	0.691085
$266$	0	0
$267$	−23.9607	−1.46637
$268$	−12.3618	−0.755118
$269$	−7.88556	−0.480791	−0.240396	−	0.970675i	$-0.577277\pi$
$269$	−7.88556	−0.480791	−0.240396	+	0.970675i	$0.577277\pi$
$270$	−5.18688	−0.315663
$271$	24.4398	1.48461	0.742305	−	0.670062i	$-0.233733\pi$
$271$	24.4398	1.48461	0.742305	+	0.670062i	$0.233733\pi$
$272$	−4.91802	−0.298198
$273$	0	0
$274$	−19.3596	−1.16956
$275$	−2.07210	−0.124952
$276$	12.6493	0.761396
$277$	7.32569	0.440158	0.220079	−	0.975482i	$-0.429369\pi$
$277$	7.32569	0.440158	0.220079	+	0.975482i	$0.429369\pi$
$278$	8.04776	0.482673
$279$	−0.759102	−0.0454462
$280$	0	0
$281$	2.34019	0.139604	0.0698020	−	0.997561i	$-0.477763\pi$
$281$	2.34019	0.139604	0.0698020	+	0.997561i	$0.477763\pi$
$282$	−4.47802	−0.266662
$283$	13.1857	0.783806	0.391903	−	0.920007i	$-0.371817\pi$
$283$	13.1857	0.783806	0.391903	+	0.920007i	$0.371817\pi$
$284$	8.18432	0.485650
$285$	−1.67805	−0.0993990
$286$	6.41749	0.379474
$287$	0	0
$288$	0.956274	0.0563490
$289$	24.2107	1.42416
$290$	−7.20575	−0.423137
$291$	25.5127	1.49558
$292$	−14.3376	−0.839044
$293$	17.2826	1.00966	0.504831	−	0.863218i	$-0.331555\pi$
$293$	17.2826	1.00966	0.504831	+	0.863218i	$0.331555\pi$
$294$	0	0
$295$	−2.95814	−0.172230
$296$	17.8609	1.03814
$297$	11.0716	0.642438
$298$	−5.70110	−0.330256
$299$	−22.7388	−1.31502
$300$	−1.77478	−0.102467
$301$	0	0
$302$	−20.5942	−1.18506
$303$	10.1422	0.582653
$304$	−0.766099	−0.0439388
$305$	8.10822	0.464275
$306$	1.14762	0.0656053
$307$	−20.6155	−1.17659	−0.588295	−	0.808646i	$-0.700201\pi$
$307$	−20.6155	−1.17659	−0.588295	+	0.808646i	$0.700201\pi$
$308$	0	0
$309$	3.41445	0.194241
$310$	4.00148	0.227269
$311$	4.84409	0.274683	0.137342	−	0.990524i	$-0.456144\pi$
$311$	4.84409	0.274683	0.137342	+	0.990524i	$0.456144\pi$
$312$	15.8908	0.899638
$313$	−23.3798	−1.32151	−0.660753	−	0.750603i	$-0.729763\pi$
$313$	−23.3798	−1.32151	−0.660753	+	0.750603i	$0.729763\pi$
$314$	6.33486	0.357497
$315$	0	0
$316$	14.6799	0.825811
$317$	6.39331	0.359084	0.179542	−	0.983750i	$-0.442538\pi$
$317$	6.39331	0.359084	0.179542	+	0.983750i	$0.442538\pi$
$318$	18.3259	1.02767
$319$	15.3809	0.861168
$320$	−6.57304	−0.367444
$321$	5.53536	0.308954
$322$	0	0
$323$	6.41955	0.357193
$324$	8.89861	0.494367
$325$	3.19041	0.176972
$326$	−5.34995	−0.296306
$327$	−17.5649	−0.971338
$328$	9.89439	0.546326
$329$	0	0
$330$	−3.37538	−0.185809
$331$	29.7538	1.63542	0.817710	−	0.575631i	$-0.195243\pi$
$331$	29.7538	1.63542	0.817710	+	0.575631i	$0.195243\pi$
$332$	−9.11776	−0.500402
$333$	−1.10814	−0.0607259
$334$	−18.6773	−1.02198
$335$	−11.6881	−0.638587
$336$	0	0
$337$	29.3188	1.59710	0.798548	−	0.601931i	$-0.205602\pi$
$337$	29.3188	1.59710	0.798548	+	0.601931i	$0.205602\pi$
$338$	2.73876	0.148969
$339$	21.5854	1.17236
$340$	6.78960	0.368218
$341$	−8.54130	−0.462537
$342$	0.178770	0.00966677
$343$	0	0
$344$	32.0405	1.72751
$345$	11.9598	0.643896
$346$	−23.6739	−1.27272
$347$	18.1167	0.972556	0.486278	−	0.873804i	$-0.338354\pi$
$347$	18.1167	0.972556	0.486278	+	0.873804i	$0.338354\pi$
$348$	13.1740	0.706198
$349$	13.0008	0.695917	0.347959	−	0.937510i	$-0.386875\pi$
$349$	13.0008	0.695917	0.347959	+	0.937510i	$0.386875\pi$
$350$	0	0
$351$	−17.0469	−0.909896
$352$	10.7599	0.573502
$353$	6.34602	0.337765	0.168882	−	0.985636i	$-0.445984\pi$
$353$	6.34602	0.337765	0.168882	+	0.985636i	$0.445984\pi$
$354$	−4.81870	−0.256111
$355$	7.73825	0.410704
$356$	15.1020	0.800405
$357$	0	0
$358$	13.5697	0.717181
$359$	−30.1925	−1.59350	−0.796749	−	0.604310i	$-0.793449\pi$
$359$	−30.1925	−1.59350	−0.796749	+	0.604310i	$0.793449\pi$
$360$	0.546615	0.0288091
$361$	1.00000	0.0526316
$362$	4.26331	0.224075
$363$	−11.2537	−0.590663
$364$	0	0
$365$	−13.5562	−0.709561
$366$	13.2080	0.690394
$367$	−5.39305	−0.281515	−0.140758	−	0.990044i	$-0.544954\pi$
$367$	−5.39305	−0.281515	−0.140758	+	0.990044i	$0.544954\pi$
$368$	5.46017	0.284631
$369$	−0.613878	−0.0319572
$370$	5.84139	0.303680
$371$	0	0
$372$	−7.31571	−0.379302
$373$	27.2735	1.41217	0.706084	−	0.708128i	$-0.250460\pi$
$373$	27.2735	1.41217	0.706084	+	0.708128i	$0.250460\pi$
$374$	12.9129	0.667709
$375$	−1.67805	−0.0866540
$376$	8.15960	0.420799
$377$	−23.6820	−1.21969
$378$	0	0
$379$	12.6077	0.647614	0.323807	−	0.946123i	$-0.395037\pi$
$379$	12.6077	0.647614	0.323807	+	0.946123i	$0.395037\pi$
$380$	1.05764	0.0542560
$381$	−27.1141	−1.38910
$382$	2.72055	0.139195
$383$	5.22525	0.266998	0.133499	−	0.991049i	$-0.457379\pi$
$383$	5.22525	0.266998	0.133499	+	0.991049i	$0.457379\pi$
$384$	6.72004	0.342930
$385$	0	0
$386$	−18.0441	−0.918420
$387$	−1.98789	−0.101050
$388$	−16.0802	−0.816349
$389$	5.70078	0.289041	0.144521	−	0.989502i	$-0.453836\pi$
$389$	5.70078	0.289041	0.144521	+	0.989502i	$0.453836\pi$
$390$	5.19707	0.263164
$391$	−45.7537	−2.31386
$392$	0	0
$393$	23.3582	1.17826
$394$	−21.7023	−1.09335
$395$	13.8798	0.698371
$396$	−0.403588	−0.0202810
$397$	−22.0844	−1.10838	−0.554191	−	0.832389i	$-0.686972\pi$
$397$	−22.0844	−1.10838	−0.554191	+	0.832389i	$0.686972\pi$
$398$	−14.0998	−0.706760
$399$	0	0
$400$	−0.766099	−0.0383050
$401$	−8.48959	−0.423950	−0.211975	−	0.977275i	$-0.567990\pi$
$401$	−8.48959	−0.423950	−0.211975	+	0.977275i	$0.567990\pi$
$402$	−19.0394	−0.949601
$403$	13.1510	0.655099
$404$	−6.39244	−0.318036
$405$	8.41362	0.418076
$406$	0	0
$407$	−12.4687	−0.618049
$408$	31.9745	1.58297
$409$	1.02862	0.0508618	0.0254309	−	0.999677i	$-0.491904\pi$
$409$	1.02862	0.0508618	0.0254309	+	0.999677i	$0.491904\pi$
$410$	3.23595	0.159812
$411$	33.4653	1.65072
$412$	−2.15207	−0.106025
$413$	0	0
$414$	−1.27414	−0.0626204
$415$	−8.62082	−0.423179
$416$	−16.5669	−0.812260
$417$	−13.9114	−0.681246
$418$	2.01149	0.0983853
$419$	−17.3446	−0.847341	−0.423671	−	0.905816i	$-0.639259\pi$
$419$	−17.3446	−0.847341	−0.423671	+	0.905816i	$0.639259\pi$
$420$	0	0
$421$	2.42626	0.118249	0.0591243	−	0.998251i	$-0.481169\pi$
$421$	2.42626	0.118249	0.0591243	+	0.998251i	$0.481169\pi$
$422$	−12.8297	−0.624540
$423$	−0.506246	−0.0246145
$424$	−33.3925	−1.62168
$425$	6.41955	0.311394
$426$	12.6053	0.610731
$427$	0	0
$428$	−3.48884	−0.168639
$429$	−11.0933	−0.535591
$430$	10.4788	0.505334
$431$	−4.77955	−0.230223	−0.115112	−	0.993353i	$-0.536723\pi$
$431$	−4.77955	−0.230223	−0.115112	+	0.993353i	$0.536723\pi$
$432$	4.09340	0.196944
$433$	−10.6077	−0.509774	−0.254887	−	0.966971i	$-0.582038\pi$
$433$	−10.6077	−0.509774	−0.254887	+	0.966971i	$0.582038\pi$
$434$	0	0
$435$	12.4559	0.597216
$436$	11.0708	0.530196
$437$	−7.12724	−0.340942
$438$	−22.0825	−1.05514
$439$	−2.08988	−0.0997445	−0.0498722	−	0.998756i	$-0.515881\pi$
$439$	−2.08988	−0.0997445	−0.0498722	+	0.998756i	$0.515881\pi$
$440$	6.15043	0.293210
$441$	0	0
$442$	−19.8819	−0.945687
$443$	−18.0451	−0.857347	−0.428674	−	0.903459i	$-0.641019\pi$
$443$	−18.0451	−0.857347	−0.428674	+	0.903459i	$0.641019\pi$
$444$	−10.6796	−0.506829
$445$	14.2789	0.676885
$446$	4.17487	0.197686
$447$	9.85497	0.466124
$448$	0	0
$449$	4.44713	0.209873	0.104936	−	0.994479i	$-0.466536\pi$
$449$	4.44713	0.209873	0.104936	+	0.994479i	$0.466536\pi$
$450$	0.178770	0.00842730
$451$	−6.90726	−0.325250
$452$	−13.6049	−0.639921
$453$	35.5993	1.67260
$454$	17.8152	0.836111
$455$	0	0
$456$	4.98079	0.233247
$457$	27.9726	1.30850	0.654250	−	0.756278i	$-0.272984\pi$
$457$	27.9726	1.30850	0.654250	+	0.756278i	$0.272984\pi$
$458$	−14.8863	−0.695591
$459$	−34.3007	−1.60102
$460$	−7.53808	−0.351465
$461$	−26.7944	−1.24794	−0.623970	−	0.781448i	$-0.714481\pi$
$461$	−26.7944	−1.24794	−0.623970	+	0.781448i	$0.714481\pi$
$462$	0	0
$463$	−6.91134	−0.321197	−0.160599	−	0.987020i	$-0.551342\pi$
$463$	−6.91134	−0.321197	−0.160599	+	0.987020i	$0.551342\pi$
$464$	5.68666	0.263997
$465$	−6.91699	−0.320768
$466$	−16.3247	−0.756226
$467$	33.7690	1.56264	0.781322	−	0.624128i	$-0.214546\pi$
$467$	33.7690	1.56264	0.781322	+	0.624128i	$0.214546\pi$
$468$	0.621403	0.0287244
$469$	0	0
$470$	2.66859	0.123093
$471$	−10.9505	−0.504572
$472$	8.78037	0.404149
$473$	−22.3674	−1.02846
$474$	22.6098	1.03850
$475$	1.00000	0.0458831
$476$	0	0
$477$	2.07177	0.0948598
$478$	3.31175	0.151476
$479$	16.9100	0.772638	0.386319	−	0.922365i	$-0.373746\pi$
$479$	16.9100	0.772638	0.386319	+	0.922365i	$0.373746\pi$
$480$	8.71364	0.397721
$481$	19.1980	0.875353
$482$	−17.8474	−0.812926
$483$	0	0
$484$	7.09298	0.322408
$485$	−15.2038	−0.690369
$486$	−1.85515	−0.0841514
$487$	−2.45737	−0.111354	−0.0556770	−	0.998449i	$-0.517732\pi$
$487$	−2.45737	−0.111354	−0.0556770	+	0.998449i	$0.517732\pi$
$488$	−24.0669	−1.08946
$489$	9.24797	0.418208
$490$	0	0
$491$	24.1806	1.09126	0.545628	−	0.838027i	$-0.316291\pi$
$491$	24.1806	1.09126	0.545628	+	0.838027i	$0.316291\pi$
$492$	−5.91614	−0.266720
$493$	−47.6515	−2.14612
$494$	−3.09709	−0.139345
$495$	−0.381591	−0.0171512
$496$	−3.15790	−0.141794
$497$	0	0
$498$	−14.0430	−0.629282
$499$	−28.4365	−1.27299	−0.636496	−	0.771280i	$-0.719617\pi$
$499$	−28.4365	−1.27299	−0.636496	+	0.771280i	$0.719617\pi$
$500$	1.05764	0.0472993
$501$	32.2858	1.44242
$502$	0.152783	0.00681906
$503$	20.8898	0.931430	0.465715	−	0.884935i	$-0.345797\pi$
$503$	20.8898	0.931430	0.465715	+	0.884935i	$0.345797\pi$
$504$	0	0
$505$	−6.04404	−0.268956
$506$	−14.3364	−0.637330
$507$	−4.73424	−0.210255
$508$	17.0895	0.758226
$509$	21.0796	0.934337	0.467168	−	0.884168i	$-0.345274\pi$
$509$	21.0796	0.934337	0.467168	+	0.884168i	$0.345274\pi$
$510$	10.4572	0.463054
$511$	0	0
$512$	8.52603	0.376801
$513$	−5.34317	−0.235907
$514$	21.5266	0.949500
$515$	−2.03477	−0.0896628
$516$	−19.1580	−0.843382
$517$	−5.69620	−0.250519
$518$	0	0
$519$	40.9229	1.79632
$520$	−9.46980	−0.415278
$521$	−29.0965	−1.27474	−0.637370	−	0.770558i	$-0.719978\pi$
$521$	−29.0965	−1.27474	−0.637370	+	0.770558i	$0.719978\pi$
$522$	−1.32699	−0.0580806
$523$	−11.2109	−0.490219	−0.245109	−	0.969495i	$-0.578824\pi$
$523$	−11.2109	−0.490219	−0.245109	+	0.969495i	$0.578824\pi$
$524$	−14.7223	−0.643145
$525$	0	0
$526$	18.2863	0.797319
$527$	26.4617	1.15269
$528$	2.66379	0.115927
$529$	27.7975	1.20859
$530$	−10.9210	−0.474377
$531$	−0.544761	−0.0236406
$532$	0	0
$533$	10.6351	0.460657
$534$	23.2598	1.00655
$535$	−3.29869	−0.142615
$536$	34.6926	1.49849
$537$	−23.4567	−1.01223
$538$	7.65491	0.330027
$539$	0	0
$540$	−5.65117	−0.243188
$541$	−45.7953	−1.96890	−0.984448	−	0.175677i	$-0.943788\pi$
$541$	−45.7953	−1.96890	−0.984448	+	0.175677i	$0.943788\pi$
$542$	−23.7249	−1.01907
$543$	−7.36960	−0.316260
$544$	−33.3350	−1.42923
$545$	10.4674	0.448376
$546$	0	0
$547$	−10.3490	−0.442490	−0.221245	−	0.975218i	$-0.571012\pi$
$547$	−10.3490	−0.442490	−0.221245	+	0.975218i	$0.571012\pi$
$548$	−21.0926	−0.901030
$549$	1.49318	0.0637275
$550$	2.01149	0.0857703
$551$	−7.42287	−0.316225
$552$	−35.4993	−1.51095
$553$	0	0
$554$	−7.11141	−0.302135
$555$	−10.0975	−0.428615
$556$	8.76814	0.371852
$557$	4.06046	0.172047	0.0860236	−	0.996293i	$-0.472584\pi$
$557$	4.06046	0.172047	0.0860236	+	0.996293i	$0.472584\pi$
$558$	0.736898	0.0311954
$559$	34.4391	1.45662
$560$	0	0
$561$	−22.3213	−0.942407
$562$	−2.27174	−0.0958275
$563$	−17.9643	−0.757106	−0.378553	−	0.925580i	$-0.623578\pi$
$563$	−17.9643	−0.757106	−0.378553	+	0.925580i	$0.623578\pi$
$564$	−4.87886	−0.205437
$565$	−12.8634	−0.541168
$566$	−12.8000	−0.538023
$567$	0	0
$568$	−22.9687	−0.963747
$569$	−13.3362	−0.559084	−0.279542	−	0.960133i	$-0.590183\pi$
$569$	−13.3362	−0.559084	−0.279542	+	0.960133i	$0.590183\pi$
$570$	1.62896	0.0682298
$571$	26.4036	1.10496	0.552478	−	0.833527i	$-0.313682\pi$
$571$	26.4036	1.10496	0.552478	+	0.833527i	$0.313682\pi$
$572$	6.99193	0.292347
$573$	−4.70277	−0.196461
$574$	0	0
$575$	−7.12724	−0.297226
$576$	−1.21047	−0.0504362
$577$	−33.9485	−1.41329	−0.706647	−	0.707566i	$-0.749793\pi$
$577$	−33.9485	−1.41329	−0.706647	+	0.707566i	$0.749793\pi$
$578$	−23.5025	−0.977575
$579$	31.1912	1.29626
$580$	−7.85076	−0.325985
$581$	0	0
$582$	−24.7664	−1.02660
$583$	23.3112	0.965452
$584$	40.2375	1.66504
$585$	0.587535	0.0242916
$586$	−16.7771	−0.693056
$587$	−41.2791	−1.70377	−0.851886	−	0.523727i	$-0.824541\pi$
$587$	−41.2791	−1.70377	−0.851886	+	0.523727i	$0.824541\pi$
$588$	0	0
$589$	4.12205	0.169846
$590$	2.87161	0.118222
$591$	37.5148	1.54315
$592$	−4.60993	−0.189467
$593$	19.7086	0.809336	0.404668	−	0.914464i	$-0.367387\pi$
$593$	19.7086	0.809336	0.404668	+	0.914464i	$0.367387\pi$
$594$	−10.7477	−0.440985
$595$	0	0
$596$	−6.21142	−0.254430
$597$	24.3731	0.997524
$598$	22.0737	0.902661
$599$	−9.79613	−0.400259	−0.200129	−	0.979769i	$-0.564136\pi$
$599$	−9.79613	−0.400259	−0.200129	+	0.979769i	$0.564136\pi$
$600$	4.98079	0.203340
$601$	8.29915	0.338530	0.169265	−	0.985571i	$-0.445861\pi$
$601$	8.29915	0.338530	0.169265	+	0.985571i	$0.445861\pi$
$602$	0	0
$603$	−2.15243	−0.0876539
$604$	−22.4376	−0.912975
$605$	6.70640	0.272654
$606$	−9.84552	−0.399947
$607$	41.2778	1.67542	0.837708	−	0.546119i	$-0.183895\pi$
$607$	41.2778	1.67542	0.837708	+	0.546119i	$0.183895\pi$
$608$	−5.19273	−0.210593
$609$	0	0
$610$	−7.87106	−0.318690
$611$	8.77043	0.354814
$612$	1.25035	0.0505424
$613$	19.3399	0.781132	0.390566	−	0.920575i	$-0.372279\pi$
$613$	19.3399	0.781132	0.390566	+	0.920575i	$0.372279\pi$
$614$	20.0125	0.807640
$615$	−5.59370	−0.225560
$616$	0	0
$617$	47.9842	1.93177	0.965886	−	0.258968i	$-0.0833824\pi$
$617$	47.9842	1.93177	0.965886	+	0.258968i	$0.0833824\pi$
$618$	−3.31457	−0.133332
$619$	−16.5649	−0.665800	−0.332900	−	0.942962i	$-0.608027\pi$
$619$	−16.5649	−0.665800	−0.332900	+	0.942962i	$0.608027\pi$
$620$	4.35966	0.175088
$621$	38.0820	1.52818
$622$	−4.70240	−0.188549
$623$	0	0
$624$	−4.10144	−0.164189
$625$	1.00000	0.0400000
$626$	22.6960	0.907114
$627$	−3.47708	−0.138861
$628$	6.90191	0.275416
$629$	38.6290	1.54024
$630$	0	0
$631$	−17.7855	−0.708028	−0.354014	−	0.935240i	$-0.615184\pi$
$631$	−17.7855	−0.708028	−0.354014	+	0.935240i	$0.615184\pi$
$632$	−41.1983	−1.63878
$633$	22.1775	0.881478
$634$	−6.20631	−0.246484
$635$	16.1581	0.641215
$636$	19.9663	0.791716
$637$	0	0
$638$	−14.9311	−0.591126
$639$	1.42505	0.0563741
$640$	−4.00468	−0.158299
$641$	−8.84041	−0.349175	−0.174588	−	0.984642i	$-0.555859\pi$
$641$	−8.84041	−0.349175	−0.174588	+	0.984642i	$0.555859\pi$
$642$	−5.37345	−0.212073
$643$	−19.7442	−0.778634	−0.389317	−	0.921104i	$-0.627289\pi$
$643$	−19.7442	−0.778634	−0.389317	+	0.921104i	$0.627289\pi$
$644$	0	0
$645$	−18.1138	−0.713230
$646$	−6.23178	−0.245186
$647$	−13.0319	−0.512335	−0.256168	−	0.966632i	$-0.582460\pi$
$647$	−13.0319	−0.512335	−0.256168	+	0.966632i	$0.582460\pi$
$648$	−24.9734	−0.981047
$649$	−6.12957	−0.240606
$650$	−3.09709	−0.121478
$651$	0	0
$652$	−5.82883	−0.228275
$653$	−28.5153	−1.11589	−0.557944	−	0.829878i	$-0.688410\pi$
$653$	−28.5153	−1.11589	−0.557944	+	0.829878i	$0.688410\pi$
$654$	17.0511	0.666750
$655$	−13.9199	−0.543894
$656$	−2.55376	−0.0997075
$657$	−2.49645	−0.0973960
$658$	0	0
$659$	46.3775	1.80661	0.903305	−	0.429000i	$-0.141134\pi$
$659$	46.3775	1.80661	0.903305	+	0.429000i	$0.141134\pi$
$660$	−3.67752	−0.143147
$661$	−0.769470	−0.0299289	−0.0149645	−	0.999888i	$-0.504764\pi$
$661$	−0.769470	−0.0299289	−0.0149645	+	0.999888i	$0.504764\pi$
$662$	−28.8835	−1.12259
$663$	34.3681	1.33475
$664$	25.5884	0.993022
$665$	0	0
$666$	1.07573	0.0416837
$667$	52.9046	2.04847
$668$	−20.3492	−0.787333
$669$	−7.21673	−0.279015
$670$	11.3462	0.438342
$671$	16.8011	0.648598
$672$	0	0
$673$	13.7171	0.528754	0.264377	−	0.964419i	$-0.414834\pi$
$673$	13.7171	0.528754	0.264377	+	0.964419i	$0.414834\pi$
$674$	−28.4612	−1.09629
$675$	−5.34317	−0.205659
$676$	2.98391	0.114766
$677$	−10.3540	−0.397936	−0.198968	−	0.980006i	$-0.563759\pi$
$677$	−10.3540	−0.397936	−0.198968	+	0.980006i	$0.563759\pi$
$678$	−20.9540	−0.804735
$679$	0	0
$680$	−19.0546	−0.730709
$681$	−30.7956	−1.18009
$682$	8.29146	0.317497
$683$	−28.7565	−1.10034	−0.550169	−	0.835054i	$-0.685437\pi$
$683$	−28.7565	−1.10034	−0.550169	+	0.835054i	$0.685437\pi$
$684$	0.194772	0.00744730
$685$	−19.9430	−0.761982
$686$	0	0
$687$	25.7326	0.981759
$688$	−8.26971	−0.315280
$689$	−35.8923	−1.36739
$690$	−11.6100	−0.441986
$691$	−0.561446	−0.0213584	−0.0106792	−	0.999943i	$-0.503399\pi$
$691$	−0.561446	−0.0213584	−0.0106792	+	0.999943i	$0.503399\pi$
$692$	−25.7930	−0.980504
$693$	0	0
$694$	−17.5868	−0.667586
$695$	8.29025	0.314467
$696$	−36.9718	−1.40141
$697$	21.3993	0.810556
$698$	−12.6205	−0.477694
$699$	28.2190	1.06734
$700$	0	0
$701$	−16.2803	−0.614898	−0.307449	−	0.951565i	$-0.599475\pi$
$701$	−16.2803	−0.614898	−0.307449	+	0.951565i	$0.599475\pi$
$702$	16.5483	0.624574
$703$	6.01740	0.226951
$704$	−13.6200	−0.513323
$705$	−4.61295	−0.173734
$706$	−6.16040	−0.231850
$707$	0	0
$708$	−5.25004	−0.197309
$709$	−10.5550	−0.396400	−0.198200	−	0.980162i	$-0.563509\pi$
$709$	−10.5550	−0.396400	−0.198200	+	0.980162i	$0.563509\pi$
$710$	−7.51191	−0.281917
$711$	2.55606	0.0958599
$712$	−42.3828	−1.58836
$713$	−29.3788	−1.10024
$714$	0	0
$715$	6.61085	0.247232
$716$	14.7844	0.552518
$717$	−5.72473	−0.213794
$718$	29.3093	1.09382
$719$	23.8110	0.888000	0.444000	−	0.896027i	$-0.353559\pi$
$719$	23.8110	0.888000	0.444000	+	0.896027i	$0.353559\pi$
$720$	−0.141082	−0.00525782
$721$	0	0
$722$	−0.970750	−0.0361276
$723$	30.8512	1.14737
$724$	4.64493	0.172627
$725$	−7.42287	−0.275679
$726$	10.9245	0.405446
$727$	19.2047	0.712265	0.356132	−	0.934436i	$-0.384095\pi$
$727$	19.2047	0.712265	0.356132	+	0.934436i	$0.384095\pi$
$728$	0	0
$729$	28.4477	1.05362
$730$	13.1596	0.487060
$731$	69.2963	2.56302
$732$	14.3903	0.531880
$733$	13.1013	0.483908	0.241954	−	0.970288i	$-0.422212\pi$
$733$	13.1013	0.483908	0.241954	+	0.970288i	$0.422212\pi$
$734$	5.23531	0.193239
$735$	0	0
$736$	37.0098	1.36420
$737$	−24.2189	−0.892113
$738$	0.595922	0.0219362
$739$	−45.2125	−1.66317	−0.831585	−	0.555397i	$-0.812566\pi$
$739$	−45.2125	−1.66317	−0.831585	+	0.555397i	$0.812566\pi$
$740$	6.36427	0.233955
$741$	5.35366	0.196672
$742$	0	0
$743$	41.4986	1.52244	0.761218	−	0.648496i	$-0.224602\pi$
$743$	41.4986	1.52244	0.761218	+	0.648496i	$0.224602\pi$
$744$	20.5311	0.752705
$745$	−5.87288	−0.215166
$746$	−26.4757	−0.969345
$747$	−1.58758	−0.0580865
$748$	14.0687	0.514404
$749$	0	0
$750$	1.62896	0.0594814
$751$	10.9707	0.400325	0.200163	−	0.979763i	$-0.435853\pi$
$751$	10.9707	0.400325	0.200163	+	0.979763i	$0.435853\pi$
$752$	−2.10601	−0.0767981
$753$	−0.264103	−0.00962444
$754$	22.9893	0.837222
$755$	−21.2147	−0.772083
$756$	0	0
$757$	−30.2169	−1.09825	−0.549126	−	0.835739i	$-0.685039\pi$
$757$	−30.2169	−1.09825	−0.549126	+	0.835739i	$0.685039\pi$
$758$	−12.2389	−0.444538
$759$	24.7820	0.899530
$760$	−2.96821	−0.107668
$761$	27.3668	0.992045	0.496022	−	0.868310i	$-0.334793\pi$
$761$	27.3668	0.992045	0.496022	+	0.868310i	$0.334793\pi$
$762$	26.3210	0.953509
$763$	0	0
$764$	2.96407	0.107236
$765$	1.18220	0.0427426
$766$	−5.07241	−0.183274
$767$	9.43768	0.340775
$768$	−28.5832	−1.03141
$769$	39.1499	1.41178	0.705890	−	0.708321i	$-0.250547\pi$
$769$	39.1499	1.41178	0.705890	+	0.708321i	$0.250547\pi$
$770$	0	0
$771$	−37.2112	−1.34013
$772$	−19.6593	−0.707552
$773$	−4.93336	−0.177441	−0.0887204	−	0.996057i	$-0.528278\pi$
$773$	−4.93336	−0.177441	−0.0887204	+	0.996057i	$0.528278\pi$
$774$	1.92974	0.0693632
$775$	4.12205	0.148068
$776$	45.1280	1.62000
$777$	0	0
$778$	−5.53403	−0.198405
$779$	3.33345	0.119433
$780$	5.66227	0.202742
$781$	16.0344	0.573757
$782$	44.4154	1.58829
$783$	39.6616	1.41739
$784$	0	0
$785$	6.52574	0.232914
$786$	−22.6749	−0.808789
$787$	−12.4757	−0.444710	−0.222355	−	0.974966i	$-0.571374\pi$
$787$	−12.4757	−0.444710	−0.222355	+	0.974966i	$0.571374\pi$
$788$	−23.6450	−0.842317
$789$	−31.6098	−1.12534
$790$	−13.4739	−0.479378
$791$	0	0
$792$	1.13264	0.0402467
$793$	−25.8686	−0.918619
$794$	21.4384	0.760820
$795$	18.8781	0.669537
$796$	−15.3619	−0.544489
$797$	−15.2294	−0.539452	−0.269726	−	0.962937i	$-0.586933\pi$
$797$	−15.2294	−0.539452	−0.269726	+	0.962937i	$0.586933\pi$
$798$	0	0
$799$	17.6473	0.624318
$800$	−5.19273	−0.183591
$801$	2.62956	0.0929108
$802$	8.24127	0.291010
$803$	−28.0897	−0.991265
$804$	−20.7437	−0.731575
$805$	0	0
$806$	−12.7663	−0.449675
$807$	−13.2324	−0.465801
$808$	17.9400	0.631126
$809$	−31.3685	−1.10286	−0.551428	−	0.834222i	$-0.685917\pi$
$809$	−31.3685	−1.10286	−0.551428	+	0.834222i	$0.685917\pi$
$810$	−8.16752	−0.286977
$811$	13.2401	0.464924	0.232462	−	0.972605i	$-0.425322\pi$
$811$	13.2401	0.464924	0.232462	+	0.972605i	$0.425322\pi$
$812$	0	0
$813$	41.0111	1.43832
$814$	12.1040	0.424244
$815$	−5.51115	−0.193047
$816$	−8.25266	−0.288901
$817$	10.7946	0.377654
$818$	−0.998530	−0.0349128
$819$	0	0
$820$	3.52561	0.123120
$821$	−32.5297	−1.13529	−0.567647	−	0.823272i	$-0.692146\pi$
$821$	−32.5297	−1.13529	−0.567647	+	0.823272i	$0.692146\pi$
$822$	−32.4864	−1.13309
$823$	46.4191	1.61807	0.809034	−	0.587762i	$-0.199991\pi$
$823$	46.4191	1.61807	0.809034	+	0.587762i	$0.199991\pi$
$824$	6.03963	0.210400
$825$	−3.47708	−0.121057
$826$	0	0
$827$	−24.7524	−0.860725	−0.430363	−	0.902656i	$-0.641614\pi$
$827$	−24.7524	−0.860725	−0.430363	+	0.902656i	$0.641614\pi$
$828$	−1.38819	−0.0482428
$829$	15.1949	0.527740	0.263870	−	0.964558i	$-0.415001\pi$
$829$	15.1949	0.527740	0.263870	+	0.964558i	$0.415001\pi$
$830$	8.36866	0.290480
$831$	12.2929	0.426434
$832$	20.9707	0.727028
$833$	0	0
$834$	13.5045	0.467624
$835$	−19.2401	−0.665831
$836$	2.19155	0.0757962
$837$	−22.0248	−0.761287
$838$	16.8373	0.581635
$839$	−34.7991	−1.20140	−0.600699	−	0.799475i	$-0.705111\pi$
$839$	−34.7991	−1.20140	−0.600699	+	0.799475i	$0.705111\pi$
$840$	0	0
$841$	26.0991	0.899968
$842$	−2.35529	−0.0811686
$843$	3.92695	0.135251
$844$	−13.9781	−0.481147
$845$	2.82128	0.0970550
$846$	0.491438	0.0168960
$847$	0	0
$848$	8.61865	0.295966
$849$	22.1262	0.759368
$850$	−6.23178	−0.213748
$851$	−42.8875	−1.47016
$852$	13.7337	0.470508
$853$	46.2090	1.58217	0.791084	−	0.611708i	$-0.209517\pi$
$853$	46.2090	1.58217	0.791084	+	0.611708i	$0.209517\pi$
$854$	0	0
$855$	0.184157	0.00629802
$856$	9.79120	0.334656
$857$	−43.9194	−1.50026	−0.750129	−	0.661292i	$-0.770009\pi$
$857$	−43.9194	−1.50026	−0.750129	+	0.661292i	$0.770009\pi$
$858$	10.7688	0.367642
$859$	30.1182	1.02762	0.513810	−	0.857904i	$-0.328234\pi$
$859$	30.1182	1.02762	0.513810	+	0.857904i	$0.328234\pi$
$860$	11.4168	0.389310
$861$	0	0
$862$	4.63975	0.158031
$863$	3.94149	0.134170	0.0670849	−	0.997747i	$-0.478630\pi$
$863$	3.94149	0.134170	0.0670849	+	0.997747i	$0.478630\pi$
$864$	27.7456	0.943924
$865$	−24.3872	−0.829191
$866$	10.2974	0.349921
$867$	40.6266	1.37975
$868$	0	0
$869$	28.7604	0.975631
$870$	−12.0916	−0.409944
$871$	37.2897	1.26351
$872$	−31.0695	−1.05215
$873$	−2.79988	−0.0947615
$874$	6.91877	0.234031
$875$	0	0
$876$	−24.0592	−0.812884
$877$	24.0531	0.812216	0.406108	−	0.913825i	$-0.366886\pi$
$877$	24.0531	0.812216	0.406108	+	0.913825i	$0.366886\pi$
$878$	2.02875	0.0684670
$879$	29.0011	0.978182
$880$	−1.58744	−0.0535124
$881$	6.22719	0.209799	0.104900	−	0.994483i	$-0.466548\pi$
$881$	6.22719	0.209799	0.104900	+	0.994483i	$0.466548\pi$
$882$	0	0
$883$	−17.6958	−0.595512	−0.297756	−	0.954642i	$-0.596238\pi$
$883$	−17.6958	−0.595512	−0.297756	+	0.954642i	$0.596238\pi$
$884$	−21.6616	−0.728559
$885$	−4.96390	−0.166860
$886$	17.5172	0.588503
$887$	33.5325	1.12591	0.562955	−	0.826487i	$-0.309664\pi$
$887$	33.5325	1.12591	0.562955	+	0.826487i	$0.309664\pi$
$888$	29.9714	1.00578
$889$	0	0
$890$	−13.8613	−0.464630
$891$	17.4339	0.584057
$892$	4.54858	0.152298
$893$	2.74900	0.0919917
$894$	−9.56671	−0.319959
$895$	13.9786	0.467252
$896$	0	0
$897$	−38.1568	−1.27402
$898$	−4.31705	−0.144062
$899$	−30.5974	−1.02048
$900$	0.194772	0.00649240
$901$	−72.2202	−2.40600
$902$	6.70522	0.223259
$903$	0	0
$904$	38.1813	1.26989
$905$	4.39177	0.145987
$906$	−34.5581	−1.14811
$907$	−21.7627	−0.722618	−0.361309	−	0.932446i	$-0.617670\pi$
$907$	−21.7627	−0.722618	−0.361309	+	0.932446i	$0.617670\pi$
$908$	19.4099	0.644141
$909$	−1.11305	−0.0369175
$910$	0	0
$911$	21.7326	0.720032	0.360016	−	0.932946i	$-0.382771\pi$
$911$	21.7326	0.720032	0.360016	+	0.932946i	$0.382771\pi$
$912$	−1.28555	−0.0425689
$913$	−17.8632	−0.591186
$914$	−27.1544	−0.898186
$915$	13.6060	0.449800
$916$	−16.2188	−0.535884
$917$	0	0
$918$	33.2974	1.09898
$919$	−14.5786	−0.480902	−0.240451	−	0.970661i	$-0.577295\pi$
$919$	−14.5786	−0.480902	−0.240451	+	0.970661i	$0.577295\pi$
$920$	21.1551	0.697464
$921$	−34.5938	−1.13991
$922$	26.0107	0.856616
$923$	−24.6882	−0.812622
$924$	0	0
$925$	6.01740	0.197851
$926$	6.70918	0.220477
$927$	−0.374717	−0.0123073
$928$	38.5449	1.26530
$929$	−57.4955	−1.88637	−0.943183	−	0.332273i	$-0.892184\pi$
$929$	−57.4955	−1.88637	−0.943183	+	0.332273i	$0.892184\pi$
$930$	6.71467	0.220183
$931$	0	0
$932$	−17.7859	−0.582598
$933$	8.12861	0.266119
$934$	−32.7813	−1.07264
$935$	13.3020	0.435021
$936$	−1.74393	−0.0570020
$937$	−15.9686	−0.521673	−0.260836	−	0.965383i	$-0.583998\pi$
$937$	−15.9686	−0.521673	−0.260836	+	0.965383i	$0.583998\pi$
$938$	0	0
$939$	−39.2325	−1.28030
$940$	2.90746	0.0948310
$941$	−6.87171	−0.224011	−0.112006	−	0.993708i	$-0.535727\pi$
$941$	−6.87171	−0.224011	−0.112006	+	0.993708i	$0.535727\pi$
$942$	10.6302	0.346350
$943$	−23.7583	−0.773678
$944$	−2.26623	−0.0737595
$945$	0	0
$946$	21.7132	0.705957
$947$	19.2726	0.626275	0.313137	−	0.949708i	$-0.398620\pi$
$947$	19.2726	0.626275	0.313137	+	0.949708i	$0.398620\pi$
$948$	24.6336	0.800063
$949$	43.2497	1.40394
$950$	−0.970750	−0.0314953
$951$	10.7283	0.347888
$952$	0	0
$953$	22.5654	0.730964	0.365482	−	0.930818i	$-0.380904\pi$
$953$	22.5654	0.730964	0.365482	+	0.930818i	$0.380904\pi$
$954$	−2.01117	−0.0651140
$955$	2.80252	0.0906875
$956$	3.60820	0.116697
$957$	25.8100	0.834318
$958$	−16.4154	−0.530357
$959$	0	0
$960$	−11.0299	−0.355987
$961$	−14.0087	−0.451895
$962$	−18.6364	−0.600863
$963$	−0.607475	−0.0195756
$964$	−19.4450	−0.626280
$965$	−18.5878	−0.598362
$966$	0	0
$967$	−13.5956	−0.437207	−0.218603	−	0.975814i	$-0.570150\pi$
$967$	−13.5956	−0.437207	−0.218603	+	0.975814i	$0.570150\pi$
$968$	−19.9060	−0.639802
$969$	10.7723	0.346057
$970$	14.7591	0.473886
$971$	14.6314	0.469545	0.234772	−	0.972050i	$-0.424565\pi$
$971$	14.6314	0.469545	0.234772	+	0.972050i	$0.424565\pi$
$972$	−2.02121	−0.0648304
$973$	0	0
$974$	2.38549	0.0764361
$975$	5.35366	0.171454
$976$	6.21170	0.198832
$977$	−15.2720	−0.488596	−0.244298	−	0.969700i	$-0.578557\pi$
$977$	−15.2720	−0.488596	−0.244298	+	0.969700i	$0.578557\pi$
$978$	−8.97746	−0.287068
$979$	29.5874	0.945616
$980$	0	0
$981$	1.92765	0.0615450
$982$	−23.4733	−0.749065
$983$	−57.1459	−1.82267	−0.911335	−	0.411665i	$-0.864948\pi$
$983$	−57.1459	−1.82267	−0.911335	+	0.411665i	$0.864948\pi$
$984$	16.6033	0.529292
$985$	−22.3562	−0.712329
$986$	46.2577	1.47315
$987$	0	0
$988$	−3.37432	−0.107351
$989$	−76.9354	−2.44640
$990$	0.370430	0.0117730
$991$	−23.1236	−0.734544	−0.367272	−	0.930114i	$-0.619708\pi$
$991$	−23.1236	−0.734544	−0.367272	+	0.930114i	$0.619708\pi$
$992$	−21.4046	−0.679598
$993$	49.9284	1.58443
$994$	0	0
$995$	−14.5247	−0.460463
$996$	−15.3000	−0.484800
$997$	−25.4850	−0.807119	−0.403560	−	0.914953i	$-0.632227\pi$
$997$	−25.4850	−0.807119	−0.403560	+	0.914953i	$0.632227\pi$
$998$	27.6047	0.873812
$999$	−32.1520	−1.01724

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4655.2.a.br.1.9	✓	26
7.6	odd	2		4655.2.a.bs.1.9	yes	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4655.2.a.br.1.9	✓	26	1.1	even	1	trivial
4655.2.a.bs.1.9	yes	26	7.6	odd	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:	\( N \)	\(=\)	\( 4655 = 5 \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4655.a (trivial)

\(f(q)\)	\(=\)	\(q-0.970750 q^{2} +1.67805 q^{3} -1.05764 q^{4} -1.00000 q^{5} -1.62896 q^{6} +2.96821 q^{8} -0.184157 q^{9} +0.970750 q^{10} -2.07210 q^{11} -1.77478 q^{12} +3.19041 q^{13} -1.67805 q^{15} -0.766099 q^{16} +6.41955 q^{17} +0.178770 q^{18} +1.00000 q^{19} +1.05764 q^{20} +2.01149 q^{22} -7.12724 q^{23} +4.98079 q^{24} +1.00000 q^{25} -3.09709 q^{26} -5.34317 q^{27} -7.42287 q^{29} +1.62896 q^{30} +4.12205 q^{31} -5.19273 q^{32} -3.47708 q^{33} -6.23178 q^{34} +0.194772 q^{36} +6.01740 q^{37} -0.970750 q^{38} +5.35366 q^{39} -2.96821 q^{40} +3.33345 q^{41} +10.7946 q^{43} +2.19155 q^{44} +0.184157 q^{45} +6.91877 q^{46} +2.74900 q^{47} -1.28555 q^{48} -0.970750 q^{50} +10.7723 q^{51} -3.37432 q^{52} -11.2500 q^{53} +5.18688 q^{54} +2.07210 q^{55} +1.67805 q^{57} +7.20575 q^{58} +2.95814 q^{59} +1.77478 q^{60} -8.10822 q^{61} -4.00148 q^{62} +6.57304 q^{64} -3.19041 q^{65} +3.37538 q^{66} +11.6881 q^{67} -6.78960 q^{68} -11.9598 q^{69} -7.73825 q^{71} -0.546615 q^{72} +13.5562 q^{73} -5.84139 q^{74} +1.67805 q^{75} -1.05764 q^{76} -5.19707 q^{78} -13.8798 q^{79} +0.766099 q^{80} -8.41362 q^{81} -3.23595 q^{82} +8.62082 q^{83} -6.41955 q^{85} -10.4788 q^{86} -12.4559 q^{87} -6.15043 q^{88} -14.2789 q^{89} -0.178770 q^{90} +7.53808 q^{92} +6.91699 q^{93} -2.66859 q^{94} -1.00000 q^{95} -8.71364 q^{96} +15.2038 q^{97} +0.381591 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + 4 q^{2} - 6 q^{3} + 36 q^{4} - 26 q^{5} + 4 q^{6} + 12 q^{8} + 44 q^{9} - 4 q^{10} + 14 q^{11} - 20 q^{12} - 14 q^{13} + 6 q^{15} + 64 q^{16} - 18 q^{17} + 8 q^{18} + 26 q^{19} - 36 q^{20} + 36 q^{22}+ \cdots + 24 q^{99}+O(q^{100}) \) 26 * q + 4 * q^2 - 6 * q^3 + 36 * q^4 - 26 * q^5 + 4 * q^6 + 12 * q^8 + 44 * q^9 - 4 * q^10 + 14 * q^11 - 20 * q^12 - 14 * q^13 + 6 * q^15 + 64 * q^16 - 18 * q^17 + 8 * q^18 + 26 * q^19 - 36 * q^20 + 36 * q^22 + 44 * q^24 + 26 * q^25 + 8 * q^26 - 30 * q^27 + 22 * q^29 - 4 * q^30 + 28 * q^32 - 38 * q^33 + 68 * q^36 + 48 * q^37 + 4 * q^38 + 26 * q^39 - 12 * q^40 - 4 * q^41 + 16 * q^43 + 44 * q^44 - 44 * q^45 + 48 * q^46 - 22 * q^47 - 48 * q^48 + 4 * q^50 + 34 * q^51 - 32 * q^52 + 28 * q^53 + 28 * q^54 - 14 * q^55 - 6 * q^57 + 52 * q^58 + 8 * q^59 + 20 * q^60 + 28 * q^61 + 16 * q^62 + 52 * q^64 + 14 * q^65 + 24 * q^66 + 60 * q^67 - 52 * q^68 + 4 * q^69 + 8 * q^71 + 36 * q^72 + 4 * q^73 + 8 * q^74 - 6 * q^75 + 36 * q^76 - 76 * q^78 + 50 * q^79 - 64 * q^80 + 114 * q^81 + 36 * q^82 - 20 * q^83 + 18 * q^85 + 40 * q^86 - 18 * q^87 + 108 * q^88 + 20 * q^89 - 8 * q^90 - 48 * q^92 + 32 * q^93 + 80 * q^94 - 26 * q^95 + 140 * q^96 - 26 * q^97 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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