LMFDB - Embedded newform 7105.2.a.s.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [7105,2,Mod(1,7105)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("7105.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7105, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 7105 = 5 \cdot 7^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7105.a (trivial)

Newform invariants

comment:select newform

sage:traces = [7,3,-1,7,7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$56.7337106361$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 6x^{5} + 21x^{4} + 3x^{3} - 31x^{2} + 14x - 1 $ x^7 - 3x^6 - 6x^5 + 21x^4 + 3x^3 - 31x^2 + 14x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1015)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.51361$ of defining polynomial
Character	$\chi$	$=$	7105.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.51361 q^{2} -1.54354 q^{3} +0.291015 q^{4} +1.00000 q^{5} +2.33632 q^{6} +2.58674 q^{8} -0.617478 q^{9} -1.51361 q^{10} +4.01366 q^{11} -0.449194 q^{12} -3.87986 q^{13} -1.54354 q^{15} -4.49734 q^{16} +2.19526 q^{17} +0.934621 q^{18} +0.543142 q^{19} +0.291015 q^{20} -6.07512 q^{22} -2.32906 q^{23} -3.99274 q^{24} +1.00000 q^{25} +5.87260 q^{26} +5.58373 q^{27} +1.00000 q^{29} +2.33632 q^{30} -4.43667 q^{31} +1.63375 q^{32} -6.19526 q^{33} -3.32276 q^{34} -0.179696 q^{36} +1.53781 q^{37} -0.822105 q^{38} +5.98873 q^{39} +2.58674 q^{40} -7.60470 q^{41} +3.90509 q^{43} +1.16804 q^{44} -0.617478 q^{45} +3.52528 q^{46} -8.46445 q^{47} +6.94183 q^{48} -1.51361 q^{50} -3.38847 q^{51} -1.12910 q^{52} +12.7660 q^{53} -8.45159 q^{54} +4.01366 q^{55} -0.838362 q^{57} -1.51361 q^{58} +4.04841 q^{59} -0.449194 q^{60} +2.69060 q^{61} +6.71538 q^{62} +6.52183 q^{64} -3.87986 q^{65} +9.37720 q^{66} +15.4043 q^{67} +0.638853 q^{68} +3.59500 q^{69} +1.69141 q^{71} -1.59725 q^{72} +3.30606 q^{73} -2.32765 q^{74} -1.54354 q^{75} +0.158063 q^{76} -9.06460 q^{78} -8.45062 q^{79} -4.49734 q^{80} -6.76629 q^{81} +11.5106 q^{82} -16.9746 q^{83} +2.19526 q^{85} -5.91078 q^{86} -1.54354 q^{87} +10.3823 q^{88} -8.41174 q^{89} +0.934621 q^{90} -0.677791 q^{92} +6.84818 q^{93} +12.8119 q^{94} +0.543142 q^{95} -2.52176 q^{96} +9.95498 q^{97} -2.47835 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 3 q^{2} - q^{3} + 7 q^{4} + 7 q^{5} + 4 q^{6} + 6 q^{8} + 12 q^{9} + 3 q^{10} + 7 q^{11} + 3 q^{12} - 5 q^{13} - q^{15} + 7 q^{16} - 14 q^{17} + 29 q^{18} + 9 q^{19} + 7 q^{20} + 9 q^{22} + 12 q^{23}+ \cdots - 7 q^{99}+O(q^{100}) $ 7 * q + 3 * q^2 - q^3 + 7 * q^4 + 7 * q^5 + 4 * q^6 + 6 * q^8 + 12 * q^9 + 3 * q^10 + 7 * q^11 + 3 * q^12 - 5 * q^13 - q^15 + 7 * q^16 - 14 * q^17 + 29 * q^18 + 9 * q^19 + 7 * q^20 + 9 * q^22 + 12 * q^23 - 12 * q^24 + 7 * q^25 + 3 * q^26 - 4 * q^27 + 7 * q^29 + 4 * q^30 + 7 * q^31 + 20 * q^32 - 14 * q^33 - 17 * q^34 + 15 * q^36 + 23 * q^37 + q^38 - 5 * q^39 + 6 * q^40 - 13 * q^41 + 31 * q^43 + 6 * q^44 + 12 * q^45 + 5 * q^46 + 6 * q^47 - 12 * q^48 + 3 * q^50 - 10 * q^51 + 7 * q^52 + 23 * q^53 + 15 * q^54 + 7 * q^55 + 29 * q^57 + 3 * q^58 - 4 * q^59 + 3 * q^60 + 4 * q^61 + 5 * q^62 - 20 * q^64 - 5 * q^65 + 5 * q^66 + 13 * q^67 - 24 * q^68 + 29 * q^69 - 11 * q^71 + 53 * q^72 - 8 * q^73 + 50 * q^74 - q^75 + 43 * q^76 - 64 * q^78 + 7 * q^80 + 19 * q^81 - 32 * q^82 + 6 * q^83 - 14 * q^85 + 23 * q^86 - q^87 + 13 * q^88 + 5 * q^89 + 29 * q^90 + 11 * q^92 - 24 * q^93 + 44 * q^94 + 9 * q^95 - 13 * q^96 - 4 * q^97 - 7 * 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 $

$2$	−1.51361	−1.07028	−0.535142	−	0.844762i	$-0.679742\pi$
$2$	−1.51361	−1.07028	−0.535142	+	0.844762i	$0.679742\pi$
$3$	−1.54354	−0.891164	−0.445582	−	0.895241i	$-0.647003\pi$
$3$	−1.54354	−0.891164	−0.445582	+	0.895241i	$0.647003\pi$
$4$	0.291015	0.145508
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.33632	0.953799
$7$	0	0
$7$	0	0
$8$	2.58674	0.914549
$9$	−0.617478	−0.205826
$10$	−1.51361	−0.478646
$11$	4.01366	1.21016	0.605082	−	0.796163i	$-0.293140\pi$
$11$	4.01366	1.21016	0.605082	+	0.796163i	$0.293140\pi$
$12$	−0.449194	−0.129671
$13$	−3.87986	−1.07608	−0.538040	−	0.842919i	$-0.680835\pi$
$13$	−3.87986	−1.07608	−0.538040	+	0.842919i	$0.680835\pi$
$14$	0	0
$15$	−1.54354	−0.398541
$16$	−4.49734	−1.12434
$17$	2.19526	0.532428	0.266214	−	0.963914i	$-0.414227\pi$
$17$	2.19526	0.532428	0.266214	+	0.963914i	$0.414227\pi$
$18$	0.934621	0.220292
$19$	0.543142	0.124605	0.0623026	−	0.998057i	$-0.480156\pi$
$19$	0.543142	0.124605	0.0623026	+	0.998057i	$0.480156\pi$
$20$	0.291015	0.0650730
$21$	0	0
$22$	−6.07512	−1.29522
$23$	−2.32906	−0.485642	−0.242821	−	0.970071i	$-0.578073\pi$
$23$	−2.32906	−0.485642	−0.242821	+	0.970071i	$0.578073\pi$
$24$	−3.99274	−0.815014
$25$	1.00000	0.200000
$26$	5.87260	1.15171
$27$	5.58373	1.07459
$28$	0	0
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	2.33632	0.426552
$31$	−4.43667	−0.796849	−0.398424	−	0.917201i	$-0.630443\pi$
$31$	−4.43667	−0.796849	−0.398424	+	0.917201i	$0.630443\pi$
$32$	1.63375	0.288808
$33$	−6.19526	−1.07846
$34$	−3.32276	−0.569849
$35$	0	0
$36$	−0.179696	−0.0299493
$37$	1.53781	0.252815	0.126407	−	0.991978i	$-0.459655\pi$
$37$	1.53781	0.252815	0.126407	+	0.991978i	$0.459655\pi$
$38$	−0.822105	−0.133363
$39$	5.98873	0.958965
$40$	2.58674	0.408999
$41$	−7.60470	−1.18766	−0.593828	−	0.804592i	$-0.702384\pi$
$41$	−7.60470	−1.18766	−0.593828	+	0.804592i	$0.702384\pi$
$42$	0	0
$43$	3.90509	0.595521	0.297760	−	0.954641i	$-0.403760\pi$
$43$	3.90509	0.595521	0.297760	+	0.954641i	$0.403760\pi$
$44$	1.16804	0.176088
$45$	−0.617478	−0.0920482
$46$	3.52528	0.519775
$47$	−8.46445	−1.23467	−0.617333	−	0.786702i	$-0.711787\pi$
$47$	−8.46445	−1.23467	−0.617333	+	0.786702i	$0.711787\pi$
$48$	6.94183	1.00197
$49$	0	0
$50$	−1.51361	−0.214057
$51$	−3.38847	−0.474481
$52$	−1.12910	−0.156578
$53$	12.7660	1.75355	0.876774	−	0.480903i	$-0.159691\pi$
$53$	12.7660	1.75355	0.876774	+	0.480903i	$0.159691\pi$
$54$	−8.45159	−1.15012
$55$	4.01366	0.541202
$56$	0	0
$57$	−0.838362	−0.111044
$58$	−1.51361	−0.198747
$59$	4.04841	0.527059	0.263529	−	0.964651i	$-0.415113\pi$
$59$	4.04841	0.527059	0.263529	+	0.964651i	$0.415113\pi$
$60$	−0.449194	−0.0579907
$61$	2.69060	0.344497	0.172248	−	0.985054i	$-0.444897\pi$
$61$	2.69060	0.344497	0.172248	+	0.985054i	$0.444897\pi$
$62$	6.71538	0.852855
$63$	0	0
$64$	6.52183	0.815228
$65$	−3.87986	−0.481238
$66$	9.37720	1.15425
$67$	15.4043	1.88193	0.940966	−	0.338500i	$-0.109920\pi$
$67$	15.4043	1.88193	0.940966	+	0.338500i	$0.109920\pi$
$68$	0.638853	0.0774724
$69$	3.59500	0.432787
$70$	0	0
$71$	1.69141	0.200734	0.100367	−	0.994950i	$-0.467998\pi$
$71$	1.69141	0.200734	0.100367	+	0.994950i	$0.467998\pi$
$72$	−1.59725	−0.188238
$73$	3.30606	0.386945	0.193472	−	0.981106i	$-0.438025\pi$
$73$	3.30606	0.386945	0.193472	+	0.981106i	$0.438025\pi$
$74$	−2.32765	−0.270583
$75$	−1.54354	−0.178233
$76$	0.158063	0.0181310
$77$	0	0
$78$	−9.06460	−1.02636
$79$	−8.45062	−0.950770	−0.475385	−	0.879778i	$-0.657691\pi$
$79$	−8.45062	−0.950770	−0.475385	+	0.879778i	$0.657691\pi$
$80$	−4.49734	−0.502818
$81$	−6.76629	−0.751810
$82$	11.5106	1.27113
$83$	−16.9746	−1.86320	−0.931602	−	0.363480i	$-0.881588\pi$
$83$	−16.9746	−1.86320	−0.931602	+	0.363480i	$0.881588\pi$
$84$	0	0
$85$	2.19526	0.238109
$86$	−5.91078	−0.637376
$87$	−1.54354	−0.165485
$88$	10.3823	1.10676
$89$	−8.41174	−0.891642	−0.445821	−	0.895122i	$-0.647088\pi$
$89$	−8.41174	−0.891642	−0.445821	+	0.895122i	$0.647088\pi$
$90$	0.934621	0.0985177
$91$	0	0
$92$	−0.677791	−0.0706646
$93$	6.84818	0.710123
$94$	12.8119	1.32144
$95$	0.543142	0.0557252
$96$	−2.52176	−0.257376
$97$	9.95498	1.01078	0.505388	−	0.862892i	$-0.331349\pi$
$97$	9.95498	1.01078	0.505388	+	0.862892i	$0.331349\pi$
$98$	0	0
$99$	−2.47835	−0.249083
$100$	0.291015	0.0291015
$101$	0.451912	0.0449669	0.0224834	−	0.999747i	$-0.492843\pi$
$101$	0.451912	0.0449669	0.0224834	+	0.999747i	$0.492843\pi$
$102$	5.12883	0.507829
$103$	4.06105	0.400147	0.200073	−	0.979781i	$-0.435882\pi$
$103$	4.06105	0.400147	0.200073	+	0.979781i	$0.435882\pi$
$104$	−10.0362	−0.984129
$105$	0	0
$106$	−19.3228	−1.87679
$107$	4.59122	0.443850	0.221925	−	0.975064i	$-0.428766\pi$
$107$	4.59122	0.443850	0.221925	+	0.975064i	$0.428766\pi$
$108$	1.62495	0.156361
$109$	−4.49080	−0.430141	−0.215070	−	0.976599i	$-0.568998\pi$
$109$	−4.49080	−0.430141	−0.215070	+	0.976599i	$0.568998\pi$
$110$	−6.07512	−0.579240
$111$	−2.37368	−0.225299
$112$	0	0
$113$	4.72498	0.444489	0.222244	−	0.974991i	$-0.428662\pi$
$113$	4.72498	0.444489	0.222244	+	0.974991i	$0.428662\pi$
$114$	1.26895	0.118848
$115$	−2.32906	−0.217186
$116$	0.291015	0.0270201
$117$	2.39573	0.221485
$118$	−6.12772	−0.564102
$119$	0	0
$120$	−3.99274	−0.364485
$121$	5.10949	0.464499
$122$	−4.07253	−0.368709
$123$	11.7382	1.05840
$124$	−1.29114	−0.115948
$125$	1.00000	0.0894427
$126$	0	0
$127$	4.02682	0.357322	0.178661	−	0.983911i	$-0.442823\pi$
$127$	4.02682	0.357322	0.178661	+	0.983911i	$0.442823\pi$
$128$	−13.1390	−1.16133
$129$	−6.02767	−0.530707
$130$	5.87260	0.515061
$131$	1.44454	0.126210	0.0631051	−	0.998007i	$-0.479900\pi$
$131$	1.44454	0.126210	0.0631051	+	0.998007i	$0.479900\pi$
$132$	−1.80291	−0.156924
$133$	0	0
$134$	−23.3161	−2.01420
$135$	5.58373	0.480571
$136$	5.67855	0.486932
$137$	8.43645	0.720774	0.360387	−	0.932803i	$-0.382645\pi$
$137$	8.43645	0.720774	0.360387	+	0.932803i	$0.382645\pi$
$138$	−5.44142	−0.463205
$139$	−1.93454	−0.164085	−0.0820427	−	0.996629i	$-0.526144\pi$
$139$	−1.93454	−0.164085	−0.0820427	+	0.996629i	$0.526144\pi$
$140$	0	0
$141$	13.0652	1.10029
$142$	−2.56014	−0.214842
$143$	−15.5725	−1.30223
$144$	2.77701	0.231417
$145$	1.00000	0.0830455
$146$	−5.00408	−0.414141
$147$	0	0
$148$	0.447527	0.0367865
$149$	−2.86808	−0.234962	−0.117481	−	0.993075i	$-0.537482\pi$
$149$	−2.86808	−0.234962	−0.117481	+	0.993075i	$0.537482\pi$
$150$	2.33632	0.190760
$151$	3.74703	0.304929	0.152464	−	0.988309i	$-0.451279\pi$
$151$	3.74703	0.304929	0.152464	+	0.988309i	$0.451279\pi$
$152$	1.40496	0.113958
$153$	−1.35552	−0.109588
$154$	0	0
$155$	−4.43667	−0.356362
$156$	1.74281	0.139537
$157$	−1.81294	−0.144689	−0.0723444	−	0.997380i	$-0.523048\pi$
$157$	−1.81294	−0.144689	−0.0723444	+	0.997380i	$0.523048\pi$
$158$	12.7910	1.01759
$159$	−19.7049	−1.56270
$160$	1.63375	0.129159
$161$	0	0
$162$	10.2415	0.804650
$163$	−3.03090	−0.237398	−0.118699	−	0.992930i	$-0.537872\pi$
$163$	−3.03090	−0.237398	−0.118699	+	0.992930i	$0.537872\pi$
$164$	−2.21309	−0.172813
$165$	−6.19526	−0.482300
$166$	25.6929	1.99416
$167$	−3.51523	−0.272017	−0.136008	−	0.990708i	$-0.543427\pi$
$167$	−3.51523	−0.272017	−0.136008	+	0.990708i	$0.543427\pi$
$168$	0	0
$169$	2.05334	0.157949
$170$	−3.32276	−0.254844
$171$	−0.335378	−0.0256470
$172$	1.13644	0.0866528
$173$	−11.9184	−0.906141	−0.453071	−	0.891475i	$-0.649671\pi$
$173$	−11.9184	−0.906141	−0.453071	+	0.891475i	$0.649671\pi$
$174$	2.33632	0.177116
$175$	0	0
$176$	−18.0508	−1.36063
$177$	−6.24890	−0.469696
$178$	12.7321	0.954310
$179$	16.7535	1.25222	0.626109	−	0.779735i	$-0.284646\pi$
$179$	16.7535	1.25222	0.626109	+	0.779735i	$0.284646\pi$
$180$	−0.179696	−0.0133937
$181$	22.2119	1.65100	0.825500	−	0.564402i	$-0.190893\pi$
$181$	22.2119	1.65100	0.825500	+	0.564402i	$0.190893\pi$
$182$	0	0
$183$	−4.15306	−0.307003
$184$	−6.02466	−0.444144
$185$	1.53781	0.113062
$186$	−10.3655	−0.760034
$187$	8.81102	0.644326
$188$	−2.46328	−0.179653
$189$	0	0
$190$	−0.822105	−0.0596417
$191$	−18.7134	−1.35406	−0.677028	−	0.735957i	$-0.736732\pi$
$191$	−18.7134	−1.35406	−0.677028	+	0.735957i	$0.736732\pi$
$192$	−10.0667	−0.726502
$193$	−26.7711	−1.92703	−0.963514	−	0.267657i	$-0.913751\pi$
$193$	−26.7711	−1.92703	−0.963514	+	0.267657i	$0.913751\pi$
$194$	−15.0680	−1.08182
$195$	5.98873	0.428862
$196$	0	0
$197$	17.2624	1.22990	0.614948	−	0.788568i	$-0.289177\pi$
$197$	17.2624	1.22990	0.614948	+	0.788568i	$0.289177\pi$
$198$	3.75125	0.266590
$199$	17.9541	1.27274	0.636368	−	0.771386i	$-0.280436\pi$
$199$	17.9541	1.27274	0.636368	+	0.771386i	$0.280436\pi$
$200$	2.58674	0.182910
$201$	−23.7772	−1.67711
$202$	−0.684018	−0.0481273
$203$	0	0
$204$	−0.986097	−0.0690406
$205$	−7.60470	−0.531136
$206$	−6.14684	−0.428271
$207$	1.43814	0.0999577
$208$	17.4491	1.20987
$209$	2.17999	0.150793
$210$	0	0
$211$	−9.57813	−0.659386	−0.329693	−	0.944088i	$-0.606945\pi$
$211$	−9.57813	−0.659386	−0.329693	+	0.944088i	$0.606945\pi$
$212$	3.71511	0.255155
$213$	−2.61077	−0.178887
$214$	−6.94932	−0.475046
$215$	3.90509	0.266325
$216$	14.4436	0.982765
$217$	0	0
$218$	6.79732	0.460373
$219$	−5.10304	−0.344832
$220$	1.16804	0.0787491
$221$	−8.51730	−0.572935
$222$	3.59282	0.241134
$223$	3.67337	0.245987	0.122993	−	0.992407i	$-0.460751\pi$
$223$	3.67337	0.245987	0.122993	+	0.992407i	$0.460751\pi$
$224$	0	0
$225$	−0.617478	−0.0411652
$226$	−7.15178	−0.475729
$227$	−14.3301	−0.951121	−0.475560	−	0.879683i	$-0.657755\pi$
$227$	−14.3301	−0.951121	−0.475560	+	0.879683i	$0.657755\pi$
$228$	−0.243976	−0.0161577
$229$	−13.3809	−0.884236	−0.442118	−	0.896957i	$-0.645773\pi$
$229$	−13.3809	−0.884236	−0.442118	+	0.896957i	$0.645773\pi$
$230$	3.52528	0.232450
$231$	0	0
$232$	2.58674	0.169828
$233$	1.21911	0.0798665	0.0399333	−	0.999202i	$-0.487285\pi$
$233$	1.21911	0.0798665	0.0399333	+	0.999202i	$0.487285\pi$
$234$	−3.62620	−0.237052
$235$	−8.46445	−0.552160
$236$	1.17815	0.0766911
$237$	13.0439	0.847292
$238$	0	0
$239$	−24.2979	−1.57170	−0.785852	−	0.618415i	$-0.787775\pi$
$239$	−24.2979	−1.57170	−0.785852	+	0.618415i	$0.787775\pi$
$240$	6.94183	0.448093
$241$	−3.46110	−0.222949	−0.111475	−	0.993767i	$-0.535557\pi$
$241$	−3.46110	−0.222949	−0.111475	+	0.993767i	$0.535557\pi$
$242$	−7.73377	−0.497146
$243$	−6.30714	−0.404603
$244$	0.783007	0.0501269
$245$	0	0
$246$	−17.7670	−1.13278
$247$	−2.10731	−0.134085
$248$	−11.4765	−0.728758
$249$	26.2010	1.66042
$250$	−1.51361	−0.0957291
$251$	14.5668	0.919449	0.459724	−	0.888062i	$-0.347948\pi$
$251$	14.5668	0.919449	0.459724	+	0.888062i	$0.347948\pi$
$252$	0	0
$253$	−9.34805	−0.587707
$254$	−6.09503	−0.382436
$255$	−3.38847	−0.212194
$256$	6.84366	0.427729
$257$	−10.7576	−0.671039	−0.335519	−	0.942033i	$-0.608912\pi$
$257$	−10.7576	−0.671039	−0.335519	+	0.942033i	$0.608912\pi$
$258$	9.12354	0.568007
$259$	0	0
$260$	−1.12910	−0.0700238
$261$	−0.617478	−0.0382209
$262$	−2.18647	−0.135081
$263$	−18.1652	−1.12011	−0.560057	−	0.828454i	$-0.689221\pi$
$263$	−18.1652	−1.12011	−0.560057	+	0.828454i	$0.689221\pi$
$264$	−16.0255	−0.986301
$265$	12.7660	0.784210
$266$	0	0
$267$	12.9839	0.794600
$268$	4.48288	0.273836
$269$	8.86941	0.540777	0.270389	−	0.962751i	$-0.412848\pi$
$269$	8.86941	0.540777	0.270389	+	0.962751i	$0.412848\pi$
$270$	−8.45159	−0.514347
$271$	0.783091	0.0475694	0.0237847	−	0.999717i	$-0.492428\pi$
$271$	0.783091	0.0475694	0.0237847	+	0.999717i	$0.492428\pi$
$272$	−9.87282	−0.598628
$273$	0	0
$274$	−12.7695	−0.771433
$275$	4.01366	0.242033
$276$	1.04620	0.0629738
$277$	−9.94817	−0.597728	−0.298864	−	0.954296i	$-0.596608\pi$
$277$	−9.94817	−0.597728	−0.298864	+	0.954296i	$0.596608\pi$
$278$	2.92814	0.175618
$279$	2.73954	0.164012
$280$	0	0
$281$	−31.5588	−1.88264	−0.941320	−	0.337516i	$-0.890413\pi$
$281$	−31.5588	−1.88264	−0.941320	+	0.337516i	$0.890413\pi$
$282$	−19.7757	−1.17762
$283$	−22.5123	−1.33822	−0.669109	−	0.743164i	$-0.733324\pi$
$283$	−22.5123	−1.33822	−0.669109	+	0.743164i	$0.733324\pi$
$284$	0.492227	0.0292083
$285$	−0.838362	−0.0496603
$286$	23.5706	1.39376
$287$	0	0
$288$	−1.00880	−0.0594443
$289$	−12.1808	−0.716520
$290$	−1.51361	−0.0888822
$291$	−15.3659	−0.900767
$292$	0.962114	0.0563035
$293$	24.6650	1.44094	0.720472	−	0.693484i	$-0.243925\pi$
$293$	24.6650	1.44094	0.720472	+	0.693484i	$0.243925\pi$
$294$	0	0
$295$	4.04841	0.235708
$296$	3.97791	0.231211
$297$	22.4112	1.30043
$298$	4.34115	0.251476
$299$	9.03642	0.522590
$300$	−0.449194	−0.0259342
$301$	0	0
$302$	−5.67154	−0.326360
$303$	−0.697545	−0.0400729
$304$	−2.44269	−0.140098
$305$	2.69060	0.154064
$306$	2.05173	0.117290
$307$	19.3233	1.10284	0.551420	−	0.834228i	$-0.314086\pi$
$307$	19.3233	1.10284	0.551420	+	0.834228i	$0.314086\pi$
$308$	0	0
$309$	−6.26840	−0.356597
$310$	6.71538	0.381408
$311$	−8.52865	−0.483616	−0.241808	−	0.970324i	$-0.577740\pi$
$311$	−8.52865	−0.483616	−0.241808	+	0.970324i	$0.577740\pi$
$312$	15.4913	0.877020
$313$	−5.20631	−0.294278	−0.147139	−	0.989116i	$-0.547006\pi$
$313$	−5.20631	−0.294278	−0.147139	+	0.989116i	$0.547006\pi$
$314$	2.74409	0.154858
$315$	0	0
$316$	−2.45926	−0.138344
$317$	32.2004	1.80855	0.904276	−	0.426947i	$-0.140411\pi$
$317$	32.2004	1.80855	0.904276	+	0.426947i	$0.140411\pi$
$318$	29.8255	1.67253
$319$	4.01366	0.224722
$320$	6.52183	0.364581
$321$	−7.08674	−0.395543
$322$	0	0
$323$	1.19234	0.0663433
$324$	−1.96909	−0.109394
$325$	−3.87986	−0.215216
$326$	4.58760	0.254084
$327$	6.93174	0.383326
$328$	−19.6714	−1.08617
$329$	0	0
$330$	9.37720	0.516198
$331$	1.93012	0.106089	0.0530446	−	0.998592i	$-0.483107\pi$
$331$	1.93012	0.106089	0.0530446	+	0.998592i	$0.483107\pi$
$332$	−4.93987	−0.271110
$333$	−0.949565	−0.0520358
$334$	5.32069	0.291135
$335$	15.4043	0.841626
$336$	0	0
$337$	32.3370	1.76151	0.880755	−	0.473573i	$-0.157036\pi$
$337$	32.3370	1.76151	0.880755	+	0.473573i	$0.157036\pi$
$338$	−3.10795	−0.169050
$339$	−7.29321	−0.396113
$340$	0.638853	0.0346467
$341$	−17.8073	−0.964319
$342$	0.507631	0.0274496
$343$	0	0
$344$	10.1014	0.544633
$345$	3.59500	0.193548
$346$	18.0399	0.969828
$347$	27.2411	1.46238	0.731189	−	0.682175i	$-0.238966\pi$
$347$	27.2411	1.46238	0.731189	+	0.682175i	$0.238966\pi$
$348$	−0.449194	−0.0240793
$349$	15.3222	0.820178	0.410089	−	0.912045i	$-0.365498\pi$
$349$	15.3222	0.820178	0.410089	+	0.912045i	$0.365498\pi$
$350$	0	0
$351$	−21.6641	−1.15634
$352$	6.55731	0.349506
$353$	25.1417	1.33816	0.669080	−	0.743190i	$-0.266688\pi$
$353$	25.1417	1.33816	0.669080	+	0.743190i	$0.266688\pi$
$354$	9.45839	0.502708
$355$	1.69141	0.0897709
$356$	−2.44794	−0.129741
$357$	0	0
$358$	−25.3583	−1.34023
$359$	−18.0018	−0.950099	−0.475049	−	0.879959i	$-0.657570\pi$
$359$	−18.0018	−0.950099	−0.475049	+	0.879959i	$0.657570\pi$
$360$	−1.59725	−0.0841826
$361$	−18.7050	−0.984474
$362$	−33.6202	−1.76704
$363$	−7.88671	−0.413945
$364$	0	0
$365$	3.30606	0.173047
$366$	6.28611	0.328580
$367$	26.7468	1.39617	0.698085	−	0.716015i	$-0.254036\pi$
$367$	26.7468	1.39617	0.698085	+	0.716015i	$0.254036\pi$
$368$	10.4746	0.546024
$369$	4.69574	0.244450
$370$	−2.32765	−0.121009
$371$	0	0
$372$	1.99293	0.103328
$373$	13.1888	0.682889	0.341444	−	0.939902i	$-0.389084\pi$
$373$	13.1888	0.682889	0.341444	+	0.939902i	$0.389084\pi$
$374$	−13.3365	−0.689612
$375$	−1.54354	−0.0797082
$376$	−21.8953	−1.12916
$377$	−3.87986	−0.199823
$378$	0	0
$379$	26.5034	1.36139	0.680693	−	0.732568i	$-0.261679\pi$
$379$	26.5034	1.36139	0.680693	+	0.732568i	$0.261679\pi$
$380$	0.158063	0.00810844
$381$	−6.21557	−0.318433
$382$	28.3248	1.44922
$383$	17.9532	0.917363	0.458682	−	0.888601i	$-0.348322\pi$
$383$	17.9532	0.917363	0.458682	+	0.888601i	$0.348322\pi$
$384$	20.2806	1.03494
$385$	0	0
$386$	40.5211	2.06247
$387$	−2.41131	−0.122574
$388$	2.89705	0.147076
$389$	−0.578580	−0.0293352	−0.0146676	−	0.999892i	$-0.504669\pi$
$389$	−0.578580	−0.0293352	−0.0146676	+	0.999892i	$0.504669\pi$
$390$	−9.06460	−0.459004
$391$	−5.11288	−0.258569
$392$	0	0
$393$	−2.22971	−0.112474
$394$	−26.1286	−1.31634
$395$	−8.45062	−0.425197
$396$	−0.721237	−0.0362435
$397$	27.1768	1.36397	0.681983	−	0.731368i	$-0.261118\pi$
$397$	27.1768	1.36397	0.681983	+	0.731368i	$0.261118\pi$
$398$	−27.1756	−1.36219
$399$	0	0
$400$	−4.49734	−0.224867
$401$	37.6744	1.88137	0.940685	−	0.339282i	$-0.110184\pi$
$401$	37.6744	1.88137	0.940685	+	0.339282i	$0.110184\pi$
$402$	35.9893	1.79499
$403$	17.2137	0.857473
$404$	0.131513	0.00654303
$405$	−6.76629	−0.336220
$406$	0	0
$407$	6.17226	0.305947
$408$	−8.76508	−0.433936
$409$	−21.4613	−1.06119	−0.530595	−	0.847625i	$-0.678032\pi$
$409$	−21.4613	−1.06119	−0.530595	+	0.847625i	$0.678032\pi$
$410$	11.5106	0.568466
$411$	−13.0220	−0.642328
$412$	1.18183	0.0582244
$413$	0	0
$414$	−2.17679	−0.106983
$415$	−16.9746	−0.833250
$416$	−6.33872	−0.310781
$417$	2.98604	0.146227
$418$	−3.29965	−0.161391
$419$	−15.8618	−0.774902	−0.387451	−	0.921890i	$-0.626644\pi$
$419$	−15.8618	−0.774902	−0.387451	+	0.921890i	$0.626644\pi$
$420$	0	0
$421$	1.62638	0.0792650	0.0396325	−	0.999214i	$-0.487381\pi$
$421$	1.62638	0.0792650	0.0396325	+	0.999214i	$0.487381\pi$
$422$	14.4976	0.705730
$423$	5.22661	0.254127
$424$	33.0223	1.60371
$425$	2.19526	0.106486
$426$	3.95168	0.191460
$427$	0	0
$428$	1.33612	0.0645836
$429$	24.0367	1.16051
$430$	−5.91078	−0.285043
$431$	6.38754	0.307677	0.153838	−	0.988096i	$-0.450836\pi$
$431$	6.38754	0.307677	0.153838	+	0.988096i	$0.450836\pi$
$432$	−25.1119	−1.20820
$433$	−34.4468	−1.65541	−0.827703	−	0.561166i	$-0.810353\pi$
$433$	−34.4468	−1.65541	−0.827703	+	0.561166i	$0.810353\pi$
$434$	0	0
$435$	−1.54354	−0.0740072
$436$	−1.30689	−0.0625888
$437$	−1.26501	−0.0605135
$438$	7.72402	0.369068
$439$	6.43845	0.307290	0.153645	−	0.988126i	$-0.450899\pi$
$439$	6.43845	0.307290	0.153645	+	0.988126i	$0.450899\pi$
$440$	10.3823	0.494956
$441$	0	0
$442$	12.8919	0.613204
$443$	10.1112	0.480397	0.240198	−	0.970724i	$-0.422788\pi$
$443$	10.1112	0.480397	0.240198	+	0.970724i	$0.422788\pi$
$444$	−0.690776	−0.0327828
$445$	−8.41174	−0.398755
$446$	−5.56004	−0.263276
$447$	4.42700	0.209390
$448$	0	0
$449$	−9.33097	−0.440356	−0.220178	−	0.975460i	$-0.570664\pi$
$449$	−9.33097	−0.440356	−0.220178	+	0.975460i	$0.570664\pi$
$450$	0.934621	0.0440584
$451$	−30.5227	−1.43726
$452$	1.37504	0.0646765
$453$	−5.78369	−0.271742
$454$	21.6902	1.01797
$455$	0	0
$456$	−2.16862	−0.101555
$457$	−13.9718	−0.653574	−0.326787	−	0.945098i	$-0.605966\pi$
$457$	−13.9718	−0.653574	−0.326787	+	0.945098i	$0.605966\pi$
$458$	20.2535	0.946384
$459$	12.2577	0.572141
$460$	−0.677791	−0.0316022
$461$	−36.2775	−1.68961	−0.844805	−	0.535074i	$-0.820284\pi$
$461$	−36.2775	−1.68961	−0.844805	+	0.535074i	$0.820284\pi$
$462$	0	0
$463$	−20.5066	−0.953021	−0.476510	−	0.879169i	$-0.658099\pi$
$463$	−20.5066	−0.953021	−0.476510	+	0.879169i	$0.658099\pi$
$464$	−4.49734	−0.208784
$465$	6.84818	0.317577
$466$	−1.84526	−0.0854799
$467$	33.5085	1.55059	0.775294	−	0.631601i	$-0.217602\pi$
$467$	33.5085	1.55059	0.775294	+	0.631601i	$0.217602\pi$
$468$	0.697194	0.0322278
$469$	0	0
$470$	12.8119	0.590968
$471$	2.79836	0.128941
$472$	10.4722	0.482021
$473$	15.6737	0.720678
$474$	−19.7434	−0.906843
$475$	0.543142	0.0249210
$476$	0	0
$477$	−7.88273	−0.360926
$478$	36.7776	1.68217
$479$	21.7118	0.992039	0.496020	−	0.868311i	$-0.334794\pi$
$479$	21.7118	0.992039	0.496020	+	0.868311i	$0.334794\pi$
$480$	−2.52176	−0.115102
$481$	−5.96650	−0.272049
$482$	5.23876	0.238619
$483$	0	0
$484$	1.48694	0.0675881
$485$	9.95498	0.452032
$486$	9.54655	0.433040
$487$	−10.9121	−0.494473	−0.247236	−	0.968955i	$-0.579522\pi$
$487$	−10.9121	−0.494473	−0.247236	+	0.968955i	$0.579522\pi$
$488$	6.95988	0.315059
$489$	4.67832	0.211561
$490$	0	0
$491$	11.6055	0.523748	0.261874	−	0.965102i	$-0.415660\pi$
$491$	11.6055	0.523748	0.261874	+	0.965102i	$0.415660\pi$
$492$	3.41599	0.154005
$493$	2.19526	0.0988694
$494$	3.18965	0.143509
$495$	−2.47835	−0.111393
$496$	19.9532	0.895925
$497$	0	0
$498$	−39.6581	−1.77712
$499$	35.1975	1.57566	0.787829	−	0.615894i	$-0.211205\pi$
$499$	35.1975	1.57566	0.787829	+	0.615894i	$0.211205\pi$
$500$	0.291015	0.0130146
$501$	5.42590	0.242412
$502$	−22.0485	−0.984071
$503$	42.2115	1.88212	0.941059	−	0.338241i	$-0.109832\pi$
$503$	42.2115	1.88212	0.941059	+	0.338241i	$0.109832\pi$
$504$	0	0
$505$	0.451912	0.0201098
$506$	14.1493	0.629013
$507$	−3.16941	−0.140758
$508$	1.17187	0.0519932
$509$	14.5528	0.645042	0.322521	−	0.946562i	$-0.395470\pi$
$509$	14.5528	0.645042	0.322521	+	0.946562i	$0.395470\pi$
$510$	5.12883	0.227108
$511$	0	0
$512$	15.9194	0.703543
$513$	3.03276	0.133899
$514$	16.2828	0.718202
$515$	4.06105	0.178951
$516$	−1.75414	−0.0772219
$517$	−33.9734	−1.49415
$518$	0	0
$519$	18.3966	0.807521
$520$	−10.0362	−0.440116
$521$	−13.7260	−0.601348	−0.300674	−	0.953727i	$-0.597212\pi$
$521$	−13.7260	−0.601348	−0.300674	+	0.953727i	$0.597212\pi$
$522$	0.934621	0.0409072
$523$	21.6646	0.947325	0.473662	−	0.880706i	$-0.342932\pi$
$523$	21.6646	0.947325	0.473662	+	0.880706i	$0.342932\pi$
$524$	0.420384	0.0183646
$525$	0	0
$526$	27.4950	1.19884
$527$	−9.73963	−0.424265
$528$	27.8622	1.21255
$529$	−17.5755	−0.764152
$530$	−19.3228	−0.839328
$531$	−2.49981	−0.108482
$532$	0	0
$533$	29.5052	1.27801
$534$	−19.6525	−0.850447
$535$	4.59122	0.198496
$536$	39.8468	1.72112
$537$	−25.8598	−1.11593
$538$	−13.4248	−0.578785
$539$	0	0
$540$	1.62495	0.0699267
$541$	23.0289	0.990090	0.495045	−	0.868867i	$-0.335152\pi$
$541$	23.0289	0.990090	0.495045	+	0.868867i	$0.335152\pi$
$542$	−1.18529	−0.0509127
$543$	−34.2851	−1.47131
$544$	3.58650	0.153770
$545$	−4.49080	−0.192365
$546$	0	0
$547$	3.66452	0.156684	0.0783418	−	0.996927i	$-0.475037\pi$
$547$	3.66452	0.156684	0.0783418	+	0.996927i	$0.475037\pi$
$548$	2.45513	0.104878
$549$	−1.66139	−0.0709063
$550$	−6.07512	−0.259044
$551$	0.543142	0.0231386
$552$	9.29931	0.395805
$553$	0	0
$554$	15.0577	0.639739
$555$	−2.37368	−0.100757
$556$	−0.562980	−0.0238757
$557$	16.9085	0.716437	0.358218	−	0.933638i	$-0.383384\pi$
$557$	16.9085	0.716437	0.358218	+	0.933638i	$0.383384\pi$
$558$	−4.14660	−0.175540
$559$	−15.1512	−0.640828
$560$	0	0
$561$	−13.6002	−0.574200
$562$	47.7677	2.01496
$563$	5.25354	0.221410	0.110705	−	0.993853i	$-0.464689\pi$
$563$	5.25354	0.221410	0.110705	+	0.993853i	$0.464689\pi$
$564$	3.80218	0.160101
$565$	4.72498	0.198782
$566$	34.0748	1.43227
$567$	0	0
$568$	4.37524	0.183581
$569$	11.1578	0.467759	0.233879	−	0.972266i	$-0.424858\pi$
$569$	11.1578	0.467759	0.233879	+	0.972266i	$0.424858\pi$
$570$	1.26895	0.0531506
$571$	−0.860773	−0.0360222	−0.0180111	−	0.999838i	$-0.505733\pi$
$571$	−0.860773	−0.0360222	−0.0180111	+	0.999838i	$0.505733\pi$
$572$	−4.53182	−0.189485
$573$	28.8850	1.20669
$574$	0	0
$575$	−2.32906	−0.0971284
$576$	−4.02708	−0.167795
$577$	21.2358	0.884058	0.442029	−	0.897001i	$-0.354259\pi$
$577$	21.2358	0.884058	0.442029	+	0.897001i	$0.354259\pi$
$578$	18.4370	0.766880
$579$	41.3224	1.71730
$580$	0.291015	0.0120838
$581$	0	0
$582$	23.2580	0.964076
$583$	51.2385	2.12208
$584$	8.55190	0.353880
$585$	2.39573	0.0990512
$586$	−37.3332	−1.54222
$587$	14.7082	0.607071	0.303536	−	0.952820i	$-0.401833\pi$
$587$	14.7082	0.607071	0.303536	+	0.952820i	$0.401833\pi$
$588$	0	0
$589$	−2.40974	−0.0992915
$590$	−6.12772	−0.252274
$591$	−26.6453	−1.09604
$592$	−6.91606	−0.284248
$593$	7.04719	0.289394	0.144697	−	0.989476i	$-0.453779\pi$
$593$	7.04719	0.289394	0.144697	+	0.989476i	$0.453779\pi$
$594$	−33.9218	−1.39183
$595$	0	0
$596$	−0.834655	−0.0341888
$597$	−27.7130	−1.13422
$598$	−13.6776	−0.559319
$599$	20.0349	0.818606	0.409303	−	0.912399i	$-0.365772\pi$
$599$	20.0349	0.818606	0.409303	+	0.912399i	$0.365772\pi$
$600$	−3.99274	−0.163003
$601$	−6.45008	−0.263104	−0.131552	−	0.991309i	$-0.541996\pi$
$601$	−6.45008	−0.263104	−0.131552	+	0.991309i	$0.541996\pi$
$602$	0	0
$603$	−9.51180	−0.387351
$604$	1.09044	0.0443695
$605$	5.10949	0.207730
$606$	1.05581	0.0428894
$607$	−29.1491	−1.18313	−0.591563	−	0.806259i	$-0.701489\pi$
$607$	−29.1491	−1.18313	−0.591563	+	0.806259i	$0.701489\pi$
$608$	0.887356	0.0359870
$609$	0	0
$610$	−4.07253	−0.164892
$611$	32.8409	1.32860
$612$	−0.394478	−0.0159458
$613$	25.3312	1.02312	0.511559	−	0.859248i	$-0.329068\pi$
$613$	25.3312	1.02312	0.511559	+	0.859248i	$0.329068\pi$
$614$	−29.2480	−1.18035
$615$	11.7382	0.473329
$616$	0	0
$617$	24.0388	0.967768	0.483884	−	0.875132i	$-0.339226\pi$
$617$	24.0388	0.967768	0.483884	+	0.875132i	$0.339226\pi$
$618$	9.48791	0.381660
$619$	7.81559	0.314135	0.157067	−	0.987588i	$-0.449796\pi$
$619$	7.81559	0.314135	0.157067	+	0.987588i	$0.449796\pi$
$620$	−1.29114	−0.0518534
$621$	−13.0048	−0.521866
$622$	12.9091	0.517606
$623$	0	0
$624$	−26.9334	−1.07820
$625$	1.00000	0.0400000
$626$	7.88032	0.314961
$627$	−3.36490	−0.134381
$628$	−0.527595	−0.0210533
$629$	3.37589	0.134606
$630$	0	0
$631$	1.45953	0.0581029	0.0290515	−	0.999578i	$-0.490751\pi$
$631$	1.45953	0.0581029	0.0290515	+	0.999578i	$0.490751\pi$
$632$	−21.8595	−0.869526
$633$	14.7842	0.587621
$634$	−48.7388	−1.93567
$635$	4.02682	0.159799
$636$	−5.73442	−0.227385
$637$	0	0
$638$	−6.07512	−0.240516
$639$	−1.04441	−0.0413162
$640$	−13.1390	−0.519364
$641$	−23.0243	−0.909404	−0.454702	−	0.890644i	$-0.650254\pi$
$641$	−23.0243	−0.909404	−0.454702	+	0.890644i	$0.650254\pi$
$642$	10.7266	0.423344
$643$	−15.8307	−0.624300	−0.312150	−	0.950033i	$-0.601049\pi$
$643$	−15.8307	−0.624300	−0.312150	+	0.950033i	$0.601049\pi$
$644$	0	0
$645$	−6.02767	−0.237339
$646$	−1.80473	−0.0710062
$647$	40.2746	1.58336	0.791679	−	0.610938i	$-0.209207\pi$
$647$	40.2746	1.58336	0.791679	+	0.610938i	$0.209207\pi$
$648$	−17.5026	−0.687567
$649$	16.2490	0.637828
$650$	5.87260	0.230342
$651$	0	0
$652$	−0.882039	−0.0345433
$653$	12.2860	0.480788	0.240394	−	0.970675i	$-0.422723\pi$
$653$	12.2860	0.480788	0.240394	+	0.970675i	$0.422723\pi$
$654$	−10.4920	−0.410268
$655$	1.44454	0.0564430
$656$	34.2009	1.33532
$657$	−2.04142	−0.0796433
$658$	0	0
$659$	−1.22553	−0.0477399	−0.0238699	−	0.999715i	$-0.507599\pi$
$659$	−1.22553	−0.0477399	−0.0238699	+	0.999715i	$0.507599\pi$
$660$	−1.80291	−0.0701784
$661$	30.5844	1.18960	0.594798	−	0.803875i	$-0.297232\pi$
$661$	30.5844	1.18960	0.594798	+	0.803875i	$0.297232\pi$
$662$	−2.92145	−0.113546
$663$	13.1468	0.510580
$664$	−43.9088	−1.70399
$665$	0	0
$666$	1.43727	0.0556931
$667$	−2.32906	−0.0901815
$668$	−1.02299	−0.0395805
$669$	−5.66999	−0.219215
$670$	−23.3161	−0.900779
$671$	10.7992	0.416898
$672$	0	0
$673$	−10.9882	−0.423564	−0.211782	−	0.977317i	$-0.567927\pi$
$673$	−10.9882	−0.423564	−0.211782	+	0.977317i	$0.567927\pi$
$674$	−48.9456	−1.88532
$675$	5.58373	0.214918
$676$	0.597552	0.0229828
$677$	−28.1005	−1.07999	−0.539995	−	0.841668i	$-0.681574\pi$
$677$	−28.1005	−1.07999	−0.539995	+	0.841668i	$0.681574\pi$
$678$	11.0391	0.423953
$679$	0	0
$680$	5.67855	0.217763
$681$	22.1191	0.847605
$682$	26.9533	1.03209
$683$	−44.1584	−1.68968	−0.844838	−	0.535023i	$-0.820303\pi$
$683$	−44.1584	−1.68968	−0.844838	+	0.535023i	$0.820303\pi$
$684$	−0.0976001	−0.00373183
$685$	8.43645	0.322340
$686$	0	0
$687$	20.6540	0.788000
$688$	−17.5625	−0.669565
$689$	−49.5304	−1.88696
$690$	−5.44142	−0.207151
$691$	19.8338	0.754515	0.377257	−	0.926108i	$-0.376867\pi$
$691$	19.8338	0.754515	0.377257	+	0.926108i	$0.376867\pi$
$692$	−3.46844	−0.131850
$693$	0	0
$694$	−41.2323	−1.56516
$695$	−1.93454	−0.0733812
$696$	−3.99274	−0.151344
$697$	−16.6943	−0.632341
$698$	−23.1918	−0.877823
$699$	−1.88175	−0.0711742
$700$	0	0
$701$	−33.4644	−1.26393	−0.631966	−	0.774996i	$-0.717752\pi$
$701$	−33.4644	−1.26393	−0.631966	+	0.774996i	$0.717752\pi$
$702$	32.7910	1.23762
$703$	0.835249	0.0315020
$704$	26.1764	0.986560
$705$	13.0652	0.492065
$706$	−38.0548	−1.43221
$707$	0	0
$708$	−1.81852	−0.0683444
$709$	−34.1024	−1.28074	−0.640370	−	0.768066i	$-0.721219\pi$
$709$	−34.1024	−1.28074	−0.640370	+	0.768066i	$0.721219\pi$
$710$	−2.56014	−0.0960804
$711$	5.21807	0.195693
$712$	−21.7589	−0.815451
$713$	10.3333	0.386983
$714$	0	0
$715$	−15.5725	−0.582377
$716$	4.87554	0.182207
$717$	37.5049	1.40065
$718$	27.2477	1.01688
$719$	24.0233	0.895918	0.447959	−	0.894054i	$-0.352151\pi$
$719$	24.0233	0.895918	0.447959	+	0.894054i	$0.352151\pi$
$720$	2.77701	0.103493
$721$	0	0
$722$	28.3121	1.05367
$723$	5.34236	0.198684
$724$	6.46402	0.240233
$725$	1.00000	0.0371391
$726$	11.9374	0.443039
$727$	32.7287	1.21384	0.606920	−	0.794763i	$-0.292405\pi$
$727$	32.7287	1.21384	0.606920	+	0.794763i	$0.292405\pi$
$728$	0	0
$729$	30.0342	1.11238
$730$	−5.00408	−0.185209
$731$	8.57268	0.317072
$732$	−1.20860	−0.0446713
$733$	50.4174	1.86221	0.931105	−	0.364752i	$-0.118846\pi$
$733$	50.4174	1.86221	0.931105	+	0.364752i	$0.118846\pi$
$734$	−40.4842	−1.49430
$735$	0	0
$736$	−3.80509	−0.140258
$737$	61.8276	2.27745
$738$	−7.10751	−0.261631
$739$	3.35595	0.123451	0.0617253	−	0.998093i	$-0.480340\pi$
$739$	3.35595	0.123451	0.0617253	+	0.998093i	$0.480340\pi$
$740$	0.447527	0.0164514
$741$	3.25273	0.119492
$742$	0	0
$743$	52.9147	1.94125	0.970626	−	0.240594i	$-0.0773421\pi$
$743$	52.9147	1.94125	0.970626	+	0.240594i	$0.0773421\pi$
$744$	17.7144	0.649443
$745$	−2.86808	−0.105078
$746$	−19.9627	−0.730885
$747$	10.4814	0.383496
$748$	2.56414	0.0937543
$749$	0	0
$750$	2.33632	0.0853104
$751$	16.9904	0.619990	0.309995	−	0.950738i	$-0.399673\pi$
$751$	16.9904	0.619990	0.309995	+	0.950738i	$0.399673\pi$
$752$	38.0675	1.38818
$753$	−22.4845	−0.819380
$754$	5.87260	0.213867
$755$	3.74703	0.136368
$756$	0	0
$757$	35.0021	1.27217	0.636086	−	0.771618i	$-0.280552\pi$
$757$	35.0021	1.27217	0.636086	+	0.771618i	$0.280552\pi$
$758$	−40.1158	−1.45707
$759$	14.4291	0.523743
$760$	1.40496	0.0509634
$761$	20.8524	0.755900	0.377950	−	0.925826i	$-0.376629\pi$
$761$	20.8524	0.755900	0.377950	+	0.925826i	$0.376629\pi$
$762$	9.40794	0.340814
$763$	0	0
$764$	−5.44589	−0.197025
$765$	−1.35552	−0.0490090
$766$	−27.1741	−0.981839
$767$	−15.7073	−0.567157
$768$	−10.5635	−0.381177
$769$	−23.6475	−0.852749	−0.426375	−	0.904547i	$-0.640209\pi$
$769$	−23.6475	−0.852749	−0.426375	+	0.904547i	$0.640209\pi$
$770$	0	0
$771$	16.6048	0.598006
$772$	−7.79081	−0.280397
$773$	33.1049	1.19070	0.595351	−	0.803466i	$-0.297013\pi$
$773$	33.1049	1.19070	0.595351	+	0.803466i	$0.297013\pi$
$774$	3.64978	0.131189
$775$	−4.43667	−0.159370
$776$	25.7509	0.924404
$777$	0	0
$778$	0.875745	0.0313970
$779$	−4.13043	−0.147988
$780$	1.74281	0.0624027
$781$	6.78876	0.242921
$782$	7.73891	0.276743
$783$	5.58373	0.199546
$784$	0	0
$785$	−1.81294	−0.0647068
$786$	3.37492	0.120379
$787$	20.8886	0.744599	0.372299	−	0.928113i	$-0.378569\pi$
$787$	20.8886	0.744599	0.372299	+	0.928113i	$0.378569\pi$
$788$	5.02363	0.178959
$789$	28.0388	0.998206
$790$	12.7910	0.455082
$791$	0	0
$792$	−6.41083	−0.227799
$793$	−10.4392	−0.370706
$794$	−41.1351	−1.45983
$795$	−19.7049	−0.698860
$796$	5.22493	0.185193
$797$	18.0880	0.640709	0.320355	−	0.947298i	$-0.396198\pi$
$797$	18.0880	0.640709	0.320355	+	0.947298i	$0.396198\pi$
$798$	0	0
$799$	−18.5816	−0.657371
$800$	1.63375	0.0577617
$801$	5.19406	0.183523
$802$	−57.0243	−2.01360
$803$	13.2694	0.468267
$804$	−6.91952	−0.244033
$805$	0	0
$806$	−26.0548	−0.917740
$807$	−13.6903	−0.481921
$808$	1.16898	0.0411244
$809$	53.1460	1.86851	0.934257	−	0.356599i	$-0.116064\pi$
$809$	53.1460	1.86851	0.934257	+	0.356599i	$0.116064\pi$
$810$	10.2415	0.359850
$811$	28.1968	0.990124	0.495062	−	0.868858i	$-0.335145\pi$
$811$	28.1968	0.990124	0.495062	+	0.868858i	$0.335145\pi$
$812$	0	0
$813$	−1.20873	−0.0423921
$814$	−9.34239	−0.327451
$815$	−3.03090	−0.106168
$816$	15.2391	0.533476
$817$	2.12102	0.0742050
$818$	32.4840	1.13578
$819$	0	0
$820$	−2.21309	−0.0772843
$821$	23.5223	0.820935	0.410467	−	0.911875i	$-0.365366\pi$
$821$	23.5223	0.820935	0.410467	+	0.911875i	$0.365366\pi$
$822$	19.7102	0.687474
$823$	29.1883	1.01744	0.508719	−	0.860932i	$-0.330119\pi$
$823$	29.1883	1.01744	0.508719	+	0.860932i	$0.330119\pi$
$824$	10.5049	0.365954
$825$	−6.19526	−0.215691
$826$	0	0
$827$	−23.9459	−0.832679	−0.416340	−	0.909209i	$-0.636687\pi$
$827$	−23.9459	−0.832679	−0.416340	+	0.909209i	$0.636687\pi$
$828$	0.418521	0.0145446
$829$	−1.39036	−0.0482894	−0.0241447	−	0.999708i	$-0.507686\pi$
$829$	−1.39036	−0.0482894	−0.0241447	+	0.999708i	$0.507686\pi$
$830$	25.6929	0.891814
$831$	15.3554	0.532674
$832$	−25.3038	−0.877251
$833$	0	0
$834$	−4.51970	−0.156504
$835$	−3.51523	−0.121650
$836$	0.634410	0.0219415
$837$	−24.7731	−0.856285
$838$	24.0086	0.829365
$839$	35.4906	1.22527	0.612635	−	0.790366i	$-0.290109\pi$
$839$	35.4906	1.22527	0.612635	+	0.790366i	$0.290109\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	−2.46171	−0.0848361
$843$	48.7123	1.67774
$844$	−2.78738	−0.0959457
$845$	2.05334	0.0706369
$846$	−7.91105	−0.271988
$847$	0	0
$848$	−57.4131	−1.97158
$849$	34.7487	1.19257
$850$	−3.32276	−0.113970
$851$	−3.58165	−0.122777
$852$	−0.759773	−0.0260294
$853$	−55.9098	−1.91432	−0.957158	−	0.289566i	$-0.906489\pi$
$853$	−55.9098	−1.91432	−0.957158	+	0.289566i	$0.906489\pi$
$854$	0	0
$855$	−0.335378	−0.0114697
$856$	11.8763	0.405923
$857$	−37.3195	−1.27481	−0.637405	−	0.770529i	$-0.719992\pi$
$857$	−37.3195	−1.27481	−0.637405	+	0.770529i	$0.719992\pi$
$858$	−36.3823	−1.24207
$859$	12.7092	0.433632	0.216816	−	0.976213i	$-0.430433\pi$
$859$	12.7092	0.433632	0.216816	+	0.976213i	$0.430433\pi$
$860$	1.13644	0.0387523
$861$	0	0
$862$	−9.66824	−0.329302
$863$	−15.7046	−0.534591	−0.267296	−	0.963615i	$-0.586130\pi$
$863$	−15.7046	−0.534591	−0.267296	+	0.963615i	$0.586130\pi$
$864$	9.12240	0.310350
$865$	−11.9184	−0.405239
$866$	52.1390	1.77176
$867$	18.8016	0.638537
$868$	0	0
$869$	−33.9180	−1.15059
$870$	2.33632	0.0792087
$871$	−59.7665	−2.02511
$872$	−11.6165	−0.393385
$873$	−6.14698	−0.208044
$874$	1.91473	0.0647667
$875$	0	0
$876$	−1.48506	−0.0501756
$877$	19.4357	0.656297	0.328148	−	0.944626i	$-0.393575\pi$
$877$	19.4357	0.656297	0.328148	+	0.944626i	$0.393575\pi$
$878$	−9.74530	−0.328888
$879$	−38.0714	−1.28412
$880$	−18.0508	−0.608493
$881$	−57.2502	−1.92881	−0.964405	−	0.264431i	$-0.914816\pi$
$881$	−57.2502	−1.92881	−0.964405	+	0.264431i	$0.914816\pi$
$882$	0	0
$883$	43.0117	1.44746	0.723730	−	0.690083i	$-0.242426\pi$
$883$	43.0117	1.44746	0.723730	+	0.690083i	$0.242426\pi$
$884$	−2.47866	−0.0833665
$885$	−6.24890	−0.210054
$886$	−15.3044	−0.514161
$887$	21.6506	0.726955	0.363478	−	0.931603i	$-0.381589\pi$
$887$	21.6506	0.726955	0.363478	+	0.931603i	$0.381589\pi$
$888$	−6.14008	−0.206047
$889$	0	0
$890$	12.7321	0.426781
$891$	−27.1576	−0.909814
$892$	1.06901	0.0357930
$893$	−4.59740	−0.153846
$894$	−6.70075	−0.224107
$895$	16.7535	0.560009
$896$	0	0
$897$	−13.9481	−0.465713
$898$	14.1234	0.471305
$899$	−4.43667	−0.147971
$900$	−0.179696	−0.00598985
$901$	28.0247	0.933638
$902$	46.1995	1.53827
$903$	0	0
$904$	12.2223	0.406507
$905$	22.2119	0.738350
$906$	8.75426	0.290841
$907$	−19.3136	−0.641297	−0.320648	−	0.947198i	$-0.603901\pi$
$907$	−19.3136	−0.641297	−0.320648	+	0.947198i	$0.603901\pi$
$908$	−4.17027	−0.138395
$909$	−0.279045	−0.00925535
$910$	0	0
$911$	−17.1622	−0.568608	−0.284304	−	0.958734i	$-0.591763\pi$
$911$	−17.1622	−0.568608	−0.284304	+	0.958734i	$0.591763\pi$
$912$	3.77040	0.124850
$913$	−68.1303	−2.25478
$914$	21.1479	0.699510
$915$	−4.15306	−0.137296
$916$	−3.89405	−0.128663
$917$	0	0
$918$	−18.5534	−0.612354
$919$	−40.7494	−1.34420	−0.672100	−	0.740461i	$-0.734607\pi$
$919$	−40.7494	−1.34420	−0.672100	+	0.740461i	$0.734607\pi$
$920$	−6.02466	−0.198627
$921$	−29.8264	−0.982812
$922$	54.9100	1.80836
$923$	−6.56245	−0.216006
$924$	0	0
$925$	1.53781	0.0505629
$926$	31.0389	1.02000
$927$	−2.50761	−0.0823606
$928$	1.63375	0.0536304
$929$	18.0356	0.591729	0.295865	−	0.955230i	$-0.404392\pi$
$929$	18.0356	0.591729	0.295865	+	0.955230i	$0.404392\pi$
$930$	−10.3655	−0.339897
$931$	0	0
$932$	0.354780	0.0116212
$933$	13.1643	0.430981
$934$	−50.7188	−1.65957
$935$	8.81102	0.288151
$936$	6.19712	0.202559
$937$	−19.4796	−0.636370	−0.318185	−	0.948029i	$-0.603073\pi$
$937$	−19.4796	−0.636370	−0.318185	+	0.948029i	$0.603073\pi$
$938$	0	0
$939$	8.03616	0.262250
$940$	−2.46328	−0.0803435
$941$	−36.6906	−1.19608	−0.598039	−	0.801467i	$-0.704053\pi$
$941$	−36.6906	−1.19608	−0.598039	+	0.801467i	$0.704053\pi$
$942$	−4.23562	−0.138004
$943$	17.7118	0.576775
$944$	−18.2071	−0.592591
$945$	0	0
$946$	−23.7239	−0.771330
$947$	−36.0543	−1.17161	−0.585804	−	0.810452i	$-0.699221\pi$
$947$	−36.0543	−1.17161	−0.585804	+	0.810452i	$0.699221\pi$
$948$	3.79597	0.123287
$949$	−12.8271	−0.416384
$950$	−0.822105	−0.0266726
$951$	−49.7026	−1.61172
$952$	0	0
$953$	55.3860	1.79413	0.897064	−	0.441900i	$-0.145695\pi$
$953$	55.3860	1.79413	0.897064	+	0.441900i	$0.145695\pi$
$954$	11.9314	0.386293
$955$	−18.7134	−0.605552
$956$	−7.07107	−0.228695
$957$	−6.19526	−0.200264
$958$	−32.8633	−1.06176
$959$	0	0
$960$	−10.0667	−0.324902
$961$	−11.3160	−0.365032
$962$	9.03095	0.291170
$963$	−2.83498	−0.0913559
$964$	−1.00723	−0.0324408
$965$	−26.7711	−0.861793
$966$	0	0
$967$	12.7237	0.409168	0.204584	−	0.978849i	$-0.434416\pi$
$967$	12.7237	0.409168	0.204584	+	0.978849i	$0.434416\pi$
$968$	13.2169	0.424807
$969$	−1.84042	−0.0591228
$970$	−15.0680	−0.483803
$971$	−27.3352	−0.877230	−0.438615	−	0.898675i	$-0.644531\pi$
$971$	−27.3352	−0.877230	−0.438615	+	0.898675i	$0.644531\pi$
$972$	−1.83547	−0.0588728
$973$	0	0
$974$	16.5166	0.529226
$975$	5.98873	0.191793
$976$	−12.1006	−0.387330
$977$	8.49649	0.271827	0.135913	−	0.990721i	$-0.456603\pi$
$977$	8.49649	0.271827	0.135913	+	0.990721i	$0.456603\pi$
$978$	−7.08116	−0.226430
$979$	−33.7619	−1.07903
$980$	0	0
$981$	2.77297	0.0885341
$982$	−17.5662	−0.560559
$983$	5.40600	0.172425	0.0862123	−	0.996277i	$-0.472524\pi$
$983$	5.40600	0.172425	0.0862123	+	0.996277i	$0.472524\pi$
$984$	30.3636	0.967956
$985$	17.2624	0.550026
$986$	−3.32276	−0.105818
$987$	0	0
$988$	−0.613261	−0.0195104
$989$	−9.09518	−0.289210
$990$	3.75125	0.119223
$991$	−30.2619	−0.961302	−0.480651	−	0.876912i	$-0.659600\pi$
$991$	−30.2619	−0.961302	−0.480651	+	0.876912i	$0.659600\pi$
$992$	−7.24839	−0.230137
$993$	−2.97923	−0.0945429
$994$	0	0
$995$	17.9541	0.569185
$996$	7.62489	0.241604
$997$	37.3747	1.18367	0.591834	−	0.806060i	$-0.298404\pi$
$997$	37.3747	1.18367	0.591834	+	0.806060i	$0.298404\pi$
$998$	−53.2753	−1.68640
$999$	8.58672	0.271672

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7105.2.a.s.1.2		7
7.6	odd	2		1015.2.a.k.1.2	✓	7
21.20	even	2		9135.2.a.be.1.6		7
35.34	odd	2		5075.2.a.y.1.6		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1015.2.a.k.1.2	✓	7	7.6	odd	2
5075.2.a.y.1.6		7	35.34	odd	2
7105.2.a.s.1.2		7	1.1	even	1	trivial
9135.2.a.be.1.6		7	21.20	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 7105 = 5 \cdot 7^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7105.a (trivial)

\(f(q)\)	\(=\)	\(q-1.51361 q^{2} -1.54354 q^{3} +0.291015 q^{4} +1.00000 q^{5} +2.33632 q^{6} +2.58674 q^{8} -0.617478 q^{9} -1.51361 q^{10} +4.01366 q^{11} -0.449194 q^{12} -3.87986 q^{13} -1.54354 q^{15} -4.49734 q^{16} +2.19526 q^{17} +0.934621 q^{18} +0.543142 q^{19} +0.291015 q^{20} -6.07512 q^{22} -2.32906 q^{23} -3.99274 q^{24} +1.00000 q^{25} +5.87260 q^{26} +5.58373 q^{27} +1.00000 q^{29} +2.33632 q^{30} -4.43667 q^{31} +1.63375 q^{32} -6.19526 q^{33} -3.32276 q^{34} -0.179696 q^{36} +1.53781 q^{37} -0.822105 q^{38} +5.98873 q^{39} +2.58674 q^{40} -7.60470 q^{41} +3.90509 q^{43} +1.16804 q^{44} -0.617478 q^{45} +3.52528 q^{46} -8.46445 q^{47} +6.94183 q^{48} -1.51361 q^{50} -3.38847 q^{51} -1.12910 q^{52} +12.7660 q^{53} -8.45159 q^{54} +4.01366 q^{55} -0.838362 q^{57} -1.51361 q^{58} +4.04841 q^{59} -0.449194 q^{60} +2.69060 q^{61} +6.71538 q^{62} +6.52183 q^{64} -3.87986 q^{65} +9.37720 q^{66} +15.4043 q^{67} +0.638853 q^{68} +3.59500 q^{69} +1.69141 q^{71} -1.59725 q^{72} +3.30606 q^{73} -2.32765 q^{74} -1.54354 q^{75} +0.158063 q^{76} -9.06460 q^{78} -8.45062 q^{79} -4.49734 q^{80} -6.76629 q^{81} +11.5106 q^{82} -16.9746 q^{83} +2.19526 q^{85} -5.91078 q^{86} -1.54354 q^{87} +10.3823 q^{88} -8.41174 q^{89} +0.934621 q^{90} -0.677791 q^{92} +6.84818 q^{93} +12.8119 q^{94} +0.543142 q^{95} -2.52176 q^{96} +9.95498 q^{97} -2.47835 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 3 q^{2} - q^{3} + 7 q^{4} + 7 q^{5} + 4 q^{6} + 6 q^{8} + 12 q^{9} + 3 q^{10} + 7 q^{11} + 3 q^{12} - 5 q^{13} - q^{15} + 7 q^{16} - 14 q^{17} + 29 q^{18} + 9 q^{19} + 7 q^{20} + 9 q^{22} + 12 q^{23}+ \cdots - 7 q^{99}+O(q^{100}) \) 7 * q + 3 * q^2 - q^3 + 7 * q^4 + 7 * q^5 + 4 * q^6 + 6 * q^8 + 12 * q^9 + 3 * q^10 + 7 * q^11 + 3 * q^12 - 5 * q^13 - q^15 + 7 * q^16 - 14 * q^17 + 29 * q^18 + 9 * q^19 + 7 * q^20 + 9 * q^22 + 12 * q^23 - 12 * q^24 + 7 * q^25 + 3 * q^26 - 4 * q^27 + 7 * q^29 + 4 * q^30 + 7 * q^31 + 20 * q^32 - 14 * q^33 - 17 * q^34 + 15 * q^36 + 23 * q^37 + q^38 - 5 * q^39 + 6 * q^40 - 13 * q^41 + 31 * q^43 + 6 * q^44 + 12 * q^45 + 5 * q^46 + 6 * q^47 - 12 * q^48 + 3 * q^50 - 10 * q^51 + 7 * q^52 + 23 * q^53 + 15 * q^54 + 7 * q^55 + 29 * q^57 + 3 * q^58 - 4 * q^59 + 3 * q^60 + 4 * q^61 + 5 * q^62 - 20 * q^64 - 5 * q^65 + 5 * q^66 + 13 * q^67 - 24 * q^68 + 29 * q^69 - 11 * q^71 + 53 * q^72 - 8 * q^73 + 50 * q^74 - q^75 + 43 * q^76 - 64 * q^78 + 7 * q^80 + 19 * q^81 - 32 * q^82 + 6 * q^83 - 14 * q^85 + 23 * q^86 - q^87 + 13 * q^88 + 5 * q^89 + 29 * q^90 + 11 * q^92 - 24 * q^93 + 44 * q^94 + 9 * q^95 - 13 * q^96 - 4 * q^97 - 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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