LMFDB - Embedded newform 9065.2.a.s.1.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [9065,2,Mod(1,9065)] 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("9065.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9065, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 9065 = 5 \cdot 7^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9065.a (trivial)

Newform invariants

comment:select newform

sage:traces = [19,-3,1,11,-19,4,0,-9,12,3,-13] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	yes
Analytic conductor:	$72.3843894323$
Analytic rank:	$1$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 3 x^{18} - 20 x^{17} + 62 x^{16} + 161 x^{15} - 522 x^{14} - 670 x^{13} + 2318 x^{12} + \cdots + 9 $ x^19 - 3x^18 - 20x^17 + 62x^16 + 161x^15 - 522x^14 - 670x^13 + 2318x^12 + 1529x^11 - 5872x^10 - 1822x^9 + 8582x^8 + 804x^7 - 6991x^6 + 383x^5 + 2893x^4 - 460x^3 - 477x^2 + 102x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1295)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.60289$ of defining polynomial
Character	$\chi$	$=$	9065.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.60289 q^{2} -2.23948 q^{3} +0.569269 q^{4} -1.00000 q^{5} +3.58964 q^{6} +2.29331 q^{8} +2.01526 q^{9} +1.60289 q^{10} +2.85907 q^{11} -1.27486 q^{12} +3.48980 q^{13} +2.23948 q^{15} -4.81447 q^{16} +2.03875 q^{17} -3.23025 q^{18} +6.37906 q^{19} -0.569269 q^{20} -4.58279 q^{22} +3.61345 q^{23} -5.13582 q^{24} +1.00000 q^{25} -5.59379 q^{26} +2.20531 q^{27} -3.33608 q^{29} -3.58964 q^{30} -3.73108 q^{31} +3.13047 q^{32} -6.40282 q^{33} -3.26791 q^{34} +1.14722 q^{36} +1.00000 q^{37} -10.2250 q^{38} -7.81534 q^{39} -2.29331 q^{40} +4.95006 q^{41} -0.192899 q^{43} +1.62758 q^{44} -2.01526 q^{45} -5.79197 q^{46} -4.68499 q^{47} +10.7819 q^{48} -1.60289 q^{50} -4.56574 q^{51} +1.98664 q^{52} -13.8145 q^{53} -3.53487 q^{54} -2.85907 q^{55} -14.2858 q^{57} +5.34738 q^{58} -8.43775 q^{59} +1.27486 q^{60} -4.40293 q^{61} +5.98052 q^{62} +4.61114 q^{64} -3.48980 q^{65} +10.2630 q^{66} -0.386831 q^{67} +1.16060 q^{68} -8.09223 q^{69} +9.77799 q^{71} +4.62161 q^{72} -8.06134 q^{73} -1.60289 q^{74} -2.23948 q^{75} +3.63140 q^{76} +12.5272 q^{78} -11.9221 q^{79} +4.81447 q^{80} -10.9845 q^{81} -7.93442 q^{82} +5.18099 q^{83} -2.03875 q^{85} +0.309197 q^{86} +7.47108 q^{87} +6.55673 q^{88} +15.3052 q^{89} +3.23025 q^{90} +2.05702 q^{92} +8.35566 q^{93} +7.50953 q^{94} -6.37906 q^{95} -7.01061 q^{96} +4.92715 q^{97} +5.76176 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q - 3 q^{2} + q^{3} + 11 q^{4} - 19 q^{5} + 4 q^{6} - 9 q^{8} + 12 q^{9} + 3 q^{10} - 13 q^{11} + 4 q^{12} + 3 q^{13} - q^{15} - 5 q^{16} + 2 q^{17} - 11 q^{18} + 12 q^{19} - 11 q^{20} - 10 q^{22}+ \cdots - 71 q^{99}+O(q^{100}) $ 19 * q - 3 * q^2 + q^3 + 11 * q^4 - 19 * q^5 + 4 * q^6 - 9 * q^8 + 12 * q^9 + 3 * q^10 - 13 * q^11 + 4 * q^12 + 3 * q^13 - q^15 - 5 * q^16 + 2 * q^17 - 11 * q^18 + 12 * q^19 - 11 * q^20 - 10 * q^22 - 16 * q^23 - 15 * q^24 + 19 * q^25 + 3 * q^26 + 7 * q^27 - q^29 - 4 * q^30 + 8 * q^31 - 16 * q^32 + 2 * q^33 + 14 * q^34 + 5 * q^36 + 19 * q^37 - 2 * q^38 - 45 * q^39 + 9 * q^40 + 18 * q^41 - 37 * q^43 + q^44 - 12 * q^45 - 29 * q^46 - 2 * q^47 + 35 * q^48 - 3 * q^50 - 43 * q^51 - 40 * q^52 - 10 * q^53 + 38 * q^54 + 13 * q^55 + 12 * q^57 - 13 * q^58 + 28 * q^59 - 4 * q^60 - 22 * q^61 + 10 * q^62 - 7 * q^64 - 3 * q^65 - 34 * q^66 - 61 * q^67 + 17 * q^68 + 20 * q^69 - 17 * q^71 + 17 * q^72 - 16 * q^73 - 3 * q^74 + q^75 + 45 * q^76 + 53 * q^78 - 63 * q^79 + 5 * q^80 - 5 * q^81 - 37 * q^82 + 24 * q^83 - 2 * q^85 - 19 * q^86 - 32 * q^87 - 58 * q^88 + 16 * q^89 + 11 * q^90 + 7 * q^92 - 31 * q^93 - 12 * q^95 - 40 * q^96 + 24 * q^97 - 71 * 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 $

$2$	−1.60289	−1.13342	−0.566709	−	0.823918i	$-0.691783\pi$
$2$	−1.60289	−1.13342	−0.566709	+	0.823918i	$0.691783\pi$
$3$	−2.23948	−1.29296	−0.646481	−	0.762930i	$-0.723760\pi$
$3$	−2.23948	−1.29296	−0.646481	+	0.762930i	$0.723760\pi$
$4$	0.569269	0.284634
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	3.58964	1.46547
$7$	0	0
$7$	0	0
$8$	2.29331	0.810808
$9$	2.01526	0.671753
$10$	1.60289	0.506880
$11$	2.85907	0.862042	0.431021	−	0.902342i	$-0.358153\pi$
$11$	2.85907	0.862042	0.431021	+	0.902342i	$0.358153\pi$
$12$	−1.27486	−0.368022
$13$	3.48980	0.967897	0.483949	−	0.875096i	$-0.339202\pi$
$13$	3.48980	0.967897	0.483949	+	0.875096i	$0.339202\pi$
$14$	0	0
$15$	2.23948	0.578231
$16$	−4.81447	−1.20362
$17$	2.03875	0.494470	0.247235	−	0.968955i	$-0.420478\pi$
$17$	2.03875	0.494470	0.247235	+	0.968955i	$0.420478\pi$
$18$	−3.23025	−0.761376
$19$	6.37906	1.46346	0.731729	−	0.681596i	$-0.238714\pi$
$19$	6.37906	1.46346	0.731729	+	0.681596i	$0.238714\pi$
$20$	−0.569269	−0.127292
$21$	0	0
$22$	−4.58279	−0.977053
$23$	3.61345	0.753456	0.376728	−	0.926324i	$-0.377049\pi$
$23$	3.61345	0.753456	0.376728	+	0.926324i	$0.377049\pi$
$24$	−5.13582	−1.04834
$25$	1.00000	0.200000
$26$	−5.59379	−1.09703
$27$	2.20531	0.424411
$28$	0	0
$29$	−3.33608	−0.619495	−0.309747	−	0.950819i	$-0.600244\pi$
$29$	−3.33608	−0.619495	−0.309747	+	0.950819i	$0.600244\pi$
$30$	−3.58964	−0.655376
$31$	−3.73108	−0.670121	−0.335061	−	0.942197i	$-0.608757\pi$
$31$	−3.73108	−0.670121	−0.335061	+	0.942197i	$0.608757\pi$
$32$	3.13047	0.553393
$33$	−6.40282	−1.11459
$34$	−3.26791	−0.560441
$35$	0	0
$36$	1.14722	0.191204
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	−10.2250	−1.65871
$39$	−7.81534	−1.25146
$40$	−2.29331	−0.362604
$41$	4.95006	0.773070	0.386535	−	0.922275i	$-0.373672\pi$
$41$	4.95006	0.773070	0.386535	+	0.922275i	$0.373672\pi$
$42$	0	0
$43$	−0.192899	−0.0294169	−0.0147084	−	0.999892i	$-0.504682\pi$
$43$	−0.192899	−0.0294169	−0.0147084	+	0.999892i	$0.504682\pi$
$44$	1.62758	0.245367
$45$	−2.01526	−0.300417
$46$	−5.79197	−0.853980
$47$	−4.68499	−0.683375	−0.341688	−	0.939814i	$-0.610998\pi$
$47$	−4.68499	−0.683375	−0.341688	+	0.939814i	$0.610998\pi$
$48$	10.7819	1.55623
$49$	0	0
$50$	−1.60289	−0.226683
$51$	−4.56574	−0.639332
$52$	1.98664	0.275497
$53$	−13.8145	−1.89756	−0.948782	−	0.315930i	$-0.897683\pi$
$53$	−13.8145	−1.89756	−0.948782	+	0.315930i	$0.897683\pi$
$54$	−3.53487	−0.481035
$55$	−2.85907	−0.385517
$56$	0	0
$57$	−14.2858	−1.89220
$58$	5.34738	0.702146
$59$	−8.43775	−1.09850	−0.549250	−	0.835658i	$-0.685087\pi$
$59$	−8.43775	−1.09850	−0.549250	+	0.835658i	$0.685087\pi$
$60$	1.27486	0.164584
$61$	−4.40293	−0.563738	−0.281869	−	0.959453i	$-0.590954\pi$
$61$	−4.40293	−0.563738	−0.281869	+	0.959453i	$0.590954\pi$
$62$	5.98052	0.759527
$63$	0	0
$64$	4.61114	0.576392
$65$	−3.48980	−0.432857
$66$	10.2630	1.26329
$67$	−0.386831	−0.0472589	−0.0236295	−	0.999721i	$-0.507522\pi$
$67$	−0.386831	−0.0472589	−0.0236295	+	0.999721i	$0.507522\pi$
$68$	1.16060	0.140743
$69$	−8.09223	−0.974191
$70$	0	0
$71$	9.77799	1.16043	0.580217	−	0.814462i	$-0.302968\pi$
$71$	9.77799	1.16043	0.580217	+	0.814462i	$0.302968\pi$
$72$	4.62161	0.544662
$73$	−8.06134	−0.943508	−0.471754	−	0.881730i	$-0.656379\pi$
$73$	−8.06134	−0.943508	−0.471754	+	0.881730i	$0.656379\pi$
$74$	−1.60289	−0.186333
$75$	−2.23948	−0.258593
$76$	3.63140	0.416550
$77$	0	0
$78$	12.5272	1.41842
$79$	−11.9221	−1.34134	−0.670670	−	0.741756i	$-0.733993\pi$
$79$	−11.9221	−1.34134	−0.670670	+	0.741756i	$0.733993\pi$
$80$	4.81447	0.538274
$81$	−10.9845	−1.22050
$82$	−7.93442	−0.876210
$83$	5.18099	0.568688	0.284344	−	0.958722i	$-0.408224\pi$
$83$	5.18099	0.568688	0.284344	+	0.958722i	$0.408224\pi$
$84$	0	0
$85$	−2.03875	−0.221134
$86$	0.309197	0.0333416
$87$	7.47108	0.800983
$88$	6.55673	0.698950
$89$	15.3052	1.62234	0.811172	−	0.584807i	$-0.198830\pi$
$89$	15.3052	1.62234	0.811172	+	0.584807i	$0.198830\pi$
$90$	3.23025	0.340498
$91$	0	0
$92$	2.05702	0.214460
$93$	8.35566	0.866442
$94$	7.50953	0.774549
$95$	−6.37906	−0.654478
$96$	−7.01061	−0.715517
$97$	4.92715	0.500277	0.250138	−	0.968210i	$-0.419524\pi$
$97$	4.92715	0.500277	0.250138	+	0.968210i	$0.419524\pi$
$98$	0	0
$99$	5.76176	0.579079
$100$	0.569269	0.0569269
$101$	1.77664	0.176783	0.0883913	−	0.996086i	$-0.471827\pi$
$101$	1.77664	0.176783	0.0883913	+	0.996086i	$0.471827\pi$
$102$	7.31840	0.724630
$103$	−17.9773	−1.77136	−0.885678	−	0.464300i	$-0.846306\pi$
$103$	−17.9773	−1.77136	−0.885678	+	0.464300i	$0.846306\pi$
$104$	8.00320	0.784779
$105$	0	0
$106$	22.1431	2.15073
$107$	−17.5742	−1.69897	−0.849483	−	0.527616i	$-0.823086\pi$
$107$	−17.5742	−1.69897	−0.849483	+	0.527616i	$0.823086\pi$
$108$	1.25541	0.120802
$109$	1.18692	0.113687	0.0568433	−	0.998383i	$-0.481896\pi$
$109$	1.18692	0.113687	0.0568433	+	0.998383i	$0.481896\pi$
$110$	4.58279	0.436951
$111$	−2.23948	−0.212562
$112$	0	0
$113$	−8.36114	−0.786550	−0.393275	−	0.919421i	$-0.628658\pi$
$113$	−8.36114	−0.786550	−0.393275	+	0.919421i	$0.628658\pi$
$114$	22.8986	2.14465
$115$	−3.61345	−0.336956
$116$	−1.89913	−0.176329
$117$	7.03286	0.650188
$118$	13.5248	1.24506
$119$	0	0
$120$	5.13582	0.468834
$121$	−2.82572	−0.256884
$122$	7.05744	0.638950
$123$	−11.0855	−0.999550
$124$	−2.12399	−0.190740
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	3.60437	0.319836	0.159918	−	0.987130i	$-0.448877\pi$
$127$	3.60437	0.319836	0.159918	+	0.987130i	$0.448877\pi$
$128$	−13.6521	−1.20669
$129$	0.431994	0.0380349
$130$	5.59379	0.490607
$131$	6.64904	0.580930	0.290465	−	0.956886i	$-0.406190\pi$
$131$	6.64904	0.580930	0.290465	+	0.956886i	$0.406190\pi$
$132$	−3.64493	−0.317250
$133$	0	0
$134$	0.620049	0.0535641
$135$	−2.20531	−0.189803
$136$	4.67550	0.400920
$137$	−11.9755	−1.02314	−0.511568	−	0.859243i	$-0.670935\pi$
$137$	−11.9755	−1.02314	−0.511568	+	0.859243i	$0.670935\pi$
$138$	12.9710	1.10416
$139$	5.73090	0.486088	0.243044	−	0.970015i	$-0.421854\pi$
$139$	5.73090	0.486088	0.243044	+	0.970015i	$0.421854\pi$
$140$	0	0
$141$	10.4919	0.883579
$142$	−15.6731	−1.31526
$143$	9.97759	0.834368
$144$	−9.70240	−0.808533
$145$	3.33608	0.277046
$146$	12.9215	1.06939
$147$	0	0
$148$	0.569269	0.0467936
$149$	−15.7548	−1.29069	−0.645343	−	0.763893i	$-0.723286\pi$
$149$	−15.7548	−1.29069	−0.645343	+	0.763893i	$0.723286\pi$
$150$	3.58964	0.293093
$151$	−4.84112	−0.393965	−0.196982	−	0.980407i	$-0.563114\pi$
$151$	−4.84112	−0.393965	−0.196982	+	0.980407i	$0.563114\pi$
$152$	14.6292	1.18658
$153$	4.10862	0.332162
$154$	0	0
$155$	3.73108	0.299687
$156$	−4.44903	−0.356207
$157$	−3.36089	−0.268228	−0.134114	−	0.990966i	$-0.542819\pi$
$157$	−3.36089	−0.268228	−0.134114	+	0.990966i	$0.542819\pi$
$158$	19.1099	1.52030
$159$	30.9372	2.45348
$160$	−3.13047	−0.247485
$161$	0	0
$162$	17.6070	1.38334
$163$	−21.6172	−1.69319	−0.846595	−	0.532238i	$-0.821351\pi$
$163$	−21.6172	−1.69319	−0.846595	+	0.532238i	$0.821351\pi$
$164$	2.81792	0.220042
$165$	6.40282	0.498459
$166$	−8.30458	−0.644560
$167$	−12.5724	−0.972883	−0.486442	−	0.873713i	$-0.661705\pi$
$167$	−12.5724	−0.972883	−0.486442	+	0.873713i	$0.661705\pi$
$168$	0	0
$169$	−0.821270	−0.0631746
$170$	3.26791	0.250637
$171$	12.8555	0.983081
$172$	−0.109812	−0.00837305
$173$	9.96158	0.757365	0.378682	−	0.925527i	$-0.376377\pi$
$173$	9.96158	0.757365	0.378682	+	0.925527i	$0.376377\pi$
$174$	−11.9753	−0.907848
$175$	0	0
$176$	−13.7649	−1.03757
$177$	18.8961	1.42032
$178$	−24.5326	−1.83879
$179$	18.9663	1.41761	0.708804	−	0.705405i	$-0.249235\pi$
$179$	18.9663	1.41761	0.708804	+	0.705405i	$0.249235\pi$
$180$	−1.14722	−0.0855090
$181$	7.20783	0.535754	0.267877	−	0.963453i	$-0.413678\pi$
$181$	7.20783	0.535754	0.267877	+	0.963453i	$0.413678\pi$
$182$	0	0
$183$	9.86027	0.728892
$184$	8.28676	0.610908
$185$	−1.00000	−0.0735215
$186$	−13.3932	−0.982040
$187$	5.82894	0.426254
$188$	−2.66702	−0.194512
$189$	0	0
$190$	10.2250	0.741797
$191$	13.3183	0.963678	0.481839	−	0.876260i	$-0.339969\pi$
$191$	13.3183	0.963678	0.481839	+	0.876260i	$0.339969\pi$
$192$	−10.3265	−0.745254
$193$	−2.35578	−0.169573	−0.0847864	−	0.996399i	$-0.527021\pi$
$193$	−2.35578	−0.169573	−0.0847864	+	0.996399i	$0.527021\pi$
$194$	−7.89771	−0.567022
$195$	7.81534	0.559668
$196$	0	0
$197$	−6.23870	−0.444489	−0.222244	−	0.974991i	$-0.571338\pi$
$197$	−6.23870	−0.444489	−0.222244	+	0.974991i	$0.571338\pi$
$198$	−9.23550	−0.656338
$199$	0.842027	0.0596897	0.0298449	−	0.999555i	$-0.490499\pi$
$199$	0.842027	0.0596897	0.0298449	+	0.999555i	$0.490499\pi$
$200$	2.29331	0.162162
$201$	0.866299	0.0611040
$202$	−2.84777	−0.200368
$203$	0	0
$204$	−2.59914	−0.181976
$205$	−4.95006	−0.345727
$206$	28.8157	2.00769
$207$	7.28203	0.506136
$208$	−16.8016	−1.16498
$209$	18.2382	1.26156
$210$	0	0
$211$	4.55754	0.313754	0.156877	−	0.987618i	$-0.449857\pi$
$211$	4.55754	0.313754	0.156877	+	0.987618i	$0.449857\pi$
$212$	−7.86415	−0.540112
$213$	−21.8976	−1.50040
$214$	28.1696	1.92564
$215$	0.192899	0.0131556
$216$	5.05745	0.344116
$217$	0	0
$218$	−1.90251	−0.128854
$219$	18.0532	1.21992
$220$	−1.62758	−0.109731
$221$	7.11485	0.478597
$222$	3.58964	0.240921
$223$	−13.6964	−0.917178	−0.458589	−	0.888649i	$-0.651645\pi$
$223$	−13.6964	−0.917178	−0.458589	+	0.888649i	$0.651645\pi$
$224$	0	0
$225$	2.01526	0.134351
$226$	13.4020	0.891489
$227$	15.9331	1.05752	0.528759	−	0.848772i	$-0.322657\pi$
$227$	15.9331	1.05752	0.528759	+	0.848772i	$0.322657\pi$
$228$	−8.13244	−0.538584
$229$	12.9268	0.854230	0.427115	−	0.904197i	$-0.359530\pi$
$229$	12.9268	0.854230	0.427115	+	0.904197i	$0.359530\pi$
$230$	5.79197	0.381911
$231$	0	0
$232$	−7.65067	−0.502291
$233$	−15.5125	−1.01625	−0.508127	−	0.861282i	$-0.669662\pi$
$233$	−15.5125	−1.01625	−0.508127	+	0.861282i	$0.669662\pi$
$234$	−11.2729	−0.736934
$235$	4.68499	0.305615
$236$	−4.80335	−0.312671
$237$	26.6993	1.73430
$238$	0	0
$239$	−20.4475	−1.32264	−0.661318	−	0.750106i	$-0.730003\pi$
$239$	−20.4475	−1.32264	−0.661318	+	0.750106i	$0.730003\pi$
$240$	−10.7819	−0.695968
$241$	13.0544	0.840909	0.420454	−	0.907314i	$-0.361871\pi$
$241$	13.0544	0.840909	0.420454	+	0.907314i	$0.361871\pi$
$242$	4.52933	0.291156
$243$	17.9836	1.15365
$244$	−2.50645	−0.160459
$245$	0	0
$246$	17.7690	1.13291
$247$	22.2617	1.41648
$248$	−8.55651	−0.543339
$249$	−11.6027	−0.735292
$250$	1.60289	0.101376
$251$	−8.50092	−0.536573	−0.268287	−	0.963339i	$-0.586457\pi$
$251$	−8.50092	−0.536573	−0.268287	+	0.963339i	$0.586457\pi$
$252$	0	0
$253$	10.3311	0.649511
$254$	−5.77742	−0.362508
$255$	4.56574	0.285918
$256$	12.6606	0.791287
$257$	−7.24488	−0.451923	−0.225962	−	0.974136i	$-0.572552\pi$
$257$	−7.24488	−0.451923	−0.225962	+	0.974136i	$0.572552\pi$
$258$	−0.692440	−0.0431094
$259$	0	0
$260$	−1.98664	−0.123206
$261$	−6.72306	−0.416147
$262$	−10.6577	−0.658436
$263$	28.4112	1.75191	0.875955	−	0.482394i	$-0.160233\pi$
$263$	28.4112	1.75191	0.875955	+	0.482394i	$0.160233\pi$
$264$	−14.6837	−0.903717
$265$	13.8145	0.848617
$266$	0	0
$267$	−34.2756	−2.09763
$268$	−0.220211	−0.0134515
$269$	−23.1812	−1.41338	−0.706690	−	0.707523i	$-0.749812\pi$
$269$	−23.1812	−1.41338	−0.706690	+	0.707523i	$0.749812\pi$
$270$	3.53487	0.215125
$271$	12.4396	0.755653	0.377826	−	0.925877i	$-0.376672\pi$
$271$	12.4396	0.755653	0.377826	+	0.925877i	$0.376672\pi$
$272$	−9.81552	−0.595153
$273$	0	0
$274$	19.1954	1.15964
$275$	2.85907	0.172408
$276$	−4.60666	−0.277288
$277$	14.3135	0.860017	0.430009	−	0.902825i	$-0.358511\pi$
$277$	14.3135	0.860017	0.430009	+	0.902825i	$0.358511\pi$
$278$	−9.18602	−0.550941
$279$	−7.51908	−0.450156
$280$	0	0
$281$	2.65928	0.158639	0.0793197	−	0.996849i	$-0.474725\pi$
$281$	2.65928	0.158639	0.0793197	+	0.996849i	$0.474725\pi$
$282$	−16.8174	−1.00146
$283$	−24.2458	−1.44126	−0.720632	−	0.693318i	$-0.756148\pi$
$283$	−24.2458	−1.44126	−0.720632	+	0.693318i	$0.756148\pi$
$284$	5.56630	0.330299
$285$	14.2858	0.846216
$286$	−15.9930	−0.945687
$287$	0	0
$288$	6.30870	0.371743
$289$	−12.8435	−0.755499
$290$	−5.34738	−0.314009
$291$	−11.0342	−0.646839
$292$	−4.58907	−0.268555
$293$	−7.56345	−0.441861	−0.220931	−	0.975290i	$-0.570909\pi$
$293$	−7.56345	−0.441861	−0.220931	+	0.975290i	$0.570909\pi$
$294$	0	0
$295$	8.43775	0.491265
$296$	2.29331	0.133296
$297$	6.30513	0.365861
$298$	25.2533	1.46289
$299$	12.6102	0.729268
$300$	−1.27486	−0.0736043
$301$	0	0
$302$	7.75980	0.446526
$303$	−3.97875	−0.228573
$304$	−30.7118	−1.76144
$305$	4.40293	0.252111
$306$	−6.58567	−0.376478
$307$	−1.32000	−0.0753365	−0.0376682	−	0.999290i	$-0.511993\pi$
$307$	−1.32000	−0.0753365	−0.0376682	+	0.999290i	$0.511993\pi$
$308$	0	0
$309$	40.2598	2.29030
$310$	−5.98052	−0.339671
$311$	−9.23174	−0.523484	−0.261742	−	0.965138i	$-0.584297\pi$
$311$	−9.23174	−0.523484	−0.261742	+	0.965138i	$0.584297\pi$
$312$	−17.9230	−1.01469
$313$	−6.04079	−0.341446	−0.170723	−	0.985319i	$-0.554610\pi$
$313$	−6.04079	−0.341446	−0.170723	+	0.985319i	$0.554610\pi$
$314$	5.38715	0.304014
$315$	0	0
$316$	−6.78688	−0.381792
$317$	−30.7175	−1.72527	−0.862633	−	0.505830i	$-0.831186\pi$
$317$	−30.7175	−1.72527	−0.862633	+	0.505830i	$0.831186\pi$
$318$	−49.5891	−2.78082
$319$	−9.53809	−0.534030
$320$	−4.61114	−0.257770
$321$	39.3571	2.19670
$322$	0	0
$323$	13.0053	0.723636
$324$	−6.25314	−0.347397
$325$	3.48980	0.193579
$326$	34.6501	1.91909
$327$	−2.65809	−0.146993
$328$	11.3520	0.626811
$329$	0	0
$330$	−10.2630	−0.564962
$331$	22.9595	1.26197	0.630985	−	0.775795i	$-0.282651\pi$
$331$	22.9595	1.26197	0.630985	+	0.775795i	$0.282651\pi$
$332$	2.94938	0.161868
$333$	2.01526	0.110435
$334$	20.1523	1.10268
$335$	0.386831	0.0211348
$336$	0	0
$337$	−11.7466	−0.639880	−0.319940	−	0.947438i	$-0.603663\pi$
$337$	−11.7466	−0.639880	−0.319940	+	0.947438i	$0.603663\pi$
$338$	1.31641	0.0716032
$339$	18.7246	1.01698
$340$	−1.16060	−0.0629423
$341$	−10.6674	−0.577672
$342$	−20.6059	−1.11424
$343$	0	0
$344$	−0.442378	−0.0238514
$345$	8.09223	0.435671
$346$	−15.9674	−0.858410
$347$	−23.8659	−1.28119	−0.640594	−	0.767880i	$-0.721312\pi$
$347$	−23.8659	−1.28119	−0.640594	+	0.767880i	$0.721312\pi$
$348$	4.25305	0.227987
$349$	7.11217	0.380706	0.190353	−	0.981716i	$-0.439037\pi$
$349$	7.11217	0.380706	0.190353	+	0.981716i	$0.439037\pi$
$350$	0	0
$351$	7.69609	0.410787
$352$	8.95022	0.477048
$353$	33.2898	1.77184	0.885920	−	0.463838i	$-0.153528\pi$
$353$	33.2898	1.77184	0.885920	+	0.463838i	$0.153528\pi$
$354$	−30.2885	−1.60982
$355$	−9.77799	−0.518962
$356$	8.71276	0.461775
$357$	0	0
$358$	−30.4010	−1.60674
$359$	0.210848	0.0111281	0.00556406	−	0.999985i	$-0.498229\pi$
$359$	0.210848	0.0111281	0.00556406	+	0.999985i	$0.498229\pi$
$360$	−4.62161	−0.243580
$361$	21.6924	1.14171
$362$	−11.5534	−0.607232
$363$	6.32814	0.332141
$364$	0	0
$365$	8.06134	0.421950
$366$	−15.8050	−0.826139
$367$	25.9454	1.35434	0.677168	−	0.735828i	$-0.263207\pi$
$367$	25.9454	1.35434	0.677168	+	0.735828i	$0.263207\pi$
$368$	−17.3968	−0.906873
$369$	9.97565	0.519312
$370$	1.60289	0.0833305
$371$	0	0
$372$	4.75662	0.246619
$373$	−26.2016	−1.35667	−0.678334	−	0.734754i	$-0.737298\pi$
$373$	−26.2016	−1.35667	−0.678334	+	0.734754i	$0.737298\pi$
$374$	−9.34317	−0.483124
$375$	2.23948	0.115646
$376$	−10.7441	−0.554086
$377$	−11.6423	−0.599607
$378$	0	0
$379$	−21.9297	−1.12645	−0.563227	−	0.826302i	$-0.690440\pi$
$379$	−21.9297	−1.12645	−0.563227	+	0.826302i	$0.690440\pi$
$380$	−3.63140	−0.186287
$381$	−8.07190	−0.413536
$382$	−21.3478	−1.09225
$383$	22.0037	1.12433	0.562167	−	0.827023i	$-0.309968\pi$
$383$	22.0037	1.12433	0.562167	+	0.827023i	$0.309968\pi$
$384$	30.5736	1.56020
$385$	0	0
$386$	3.77607	0.192197
$387$	−0.388742	−0.0197609
$388$	2.80488	0.142396
$389$	−25.7853	−1.30737	−0.653684	−	0.756768i	$-0.726777\pi$
$389$	−25.7853	−1.30737	−0.653684	+	0.756768i	$0.726777\pi$
$390$	−12.5272	−0.634337
$391$	7.36693	0.372562
$392$	0	0
$393$	−14.8904	−0.751120
$394$	9.99997	0.503791
$395$	11.9221	0.599866
$396$	3.27999	0.164826
$397$	15.4717	0.776503	0.388251	−	0.921554i	$-0.373079\pi$
$397$	15.4717	0.776503	0.388251	+	0.921554i	$0.373079\pi$
$398$	−1.34968	−0.0676533
$399$	0	0
$400$	−4.81447	−0.240724
$401$	22.2553	1.11138	0.555688	−	0.831391i	$-0.312455\pi$
$401$	22.2553	1.11138	0.555688	+	0.831391i	$0.312455\pi$
$402$	−1.38859	−0.0692563
$403$	−13.0207	−0.648608
$404$	1.01139	0.0503184
$405$	10.9845	0.545825
$406$	0	0
$407$	2.85907	0.141719
$408$	−10.4707	−0.518375
$409$	−20.7264	−1.02485	−0.512427	−	0.858731i	$-0.671254\pi$
$409$	−20.7264	−1.02485	−0.512427	+	0.858731i	$0.671254\pi$
$410$	7.93442	0.391853
$411$	26.8189	1.32288
$412$	−10.2339	−0.504189
$413$	0	0
$414$	−11.6723	−0.573663
$415$	−5.18099	−0.254325
$416$	10.9247	0.535628
$417$	−12.8342	−0.628494
$418$	−29.2339	−1.42988
$419$	−20.6748	−1.01003	−0.505016	−	0.863110i	$-0.668513\pi$
$419$	−20.6748	−1.01003	−0.505016	+	0.863110i	$0.668513\pi$
$420$	0	0
$421$	4.43614	0.216204	0.108102	−	0.994140i	$-0.465523\pi$
$421$	4.43614	0.216204	0.108102	+	0.994140i	$0.465523\pi$
$422$	−7.30526	−0.355615
$423$	−9.44145	−0.459059
$424$	−31.6809	−1.53856
$425$	2.03875	0.0988941
$426$	35.0995	1.70058
$427$	0	0
$428$	−10.0045	−0.483584
$429$	−22.3446	−1.07881
$430$	−0.309197	−0.0149108
$431$	−23.1769	−1.11639	−0.558195	−	0.829710i	$-0.688506\pi$
$431$	−23.1769	−1.11639	−0.558195	+	0.829710i	$0.688506\pi$
$432$	−10.6174	−0.510829
$433$	−14.2985	−0.687144	−0.343572	−	0.939126i	$-0.611637\pi$
$433$	−14.2985	−0.687144	−0.343572	+	0.939126i	$0.611637\pi$
$434$	0	0
$435$	−7.47108	−0.358211
$436$	0.675678	0.0323591
$437$	23.0504	1.10265
$438$	−28.9373	−1.38268
$439$	17.5275	0.836541	0.418271	−	0.908322i	$-0.362636\pi$
$439$	17.5275	0.836541	0.418271	+	0.908322i	$0.362636\pi$
$440$	−6.55673	−0.312580
$441$	0	0
$442$	−11.4044	−0.542450
$443$	38.2514	1.81738	0.908689	−	0.417473i	$-0.137084\pi$
$443$	38.2514	1.81738	0.908689	+	0.417473i	$0.137084\pi$
$444$	−1.27486	−0.0605024
$445$	−15.3052	−0.725535
$446$	21.9538	1.03954
$447$	35.2826	1.66881
$448$	0	0
$449$	32.4281	1.53038	0.765189	−	0.643805i	$-0.222645\pi$
$449$	32.4281	1.53038	0.765189	+	0.643805i	$0.222645\pi$
$450$	−3.23025	−0.152275
$451$	14.1526	0.666418
$452$	−4.75973	−0.223879
$453$	10.8416	0.509382
$454$	−25.5391	−1.19861
$455$	0	0
$456$	−32.7617	−1.53421
$457$	11.8807	0.555758	0.277879	−	0.960616i	$-0.410369\pi$
$457$	11.8807	0.555758	0.277879	+	0.960616i	$0.410369\pi$
$458$	−20.7204	−0.968199
$459$	4.49608	0.209859
$460$	−2.05702	−0.0959092
$461$	−34.9849	−1.62941	−0.814703	−	0.579878i	$-0.803100\pi$
$461$	−34.9849	−1.62941	−0.814703	+	0.579878i	$0.803100\pi$
$462$	0	0
$463$	3.31346	0.153989	0.0769947	−	0.997032i	$-0.475468\pi$
$463$	3.31346	0.153989	0.0769947	+	0.997032i	$0.475468\pi$
$464$	16.0615	0.745635
$465$	−8.35566	−0.387484
$466$	24.8648	1.15184
$467$	20.1826	0.933939	0.466970	−	0.884273i	$-0.345346\pi$
$467$	20.1826	0.933939	0.466970	+	0.884273i	$0.345346\pi$
$468$	4.00359	0.185066
$469$	0	0
$470$	−7.50953	−0.346389
$471$	7.52663	0.346809
$472$	−19.3504	−0.890673
$473$	−0.551513	−0.0253586
$474$	−42.7961	−1.96569
$475$	6.37906	0.292691
$476$	0	0
$477$	−27.8397	−1.27469
$478$	32.7751	1.49910
$479$	12.6547	0.578210	0.289105	−	0.957297i	$-0.406642\pi$
$479$	12.6547	0.578210	0.289105	+	0.957297i	$0.406642\pi$
$480$	7.01061	0.319989
$481$	3.48980	0.159121
$482$	−20.9248	−0.953100
$483$	0	0
$484$	−1.60859	−0.0731179
$485$	−4.92715	−0.223731
$486$	−28.8259	−1.30757
$487$	−30.1404	−1.36579	−0.682895	−	0.730516i	$-0.739279\pi$
$487$	−30.1404	−1.36579	−0.682895	+	0.730516i	$0.739279\pi$
$488$	−10.0973	−0.457083
$489$	48.4112	2.18923
$490$	0	0
$491$	31.4494	1.41929	0.709647	−	0.704558i	$-0.248855\pi$
$491$	31.4494	1.41929	0.709647	+	0.704558i	$0.248855\pi$
$492$	−6.31066	−0.284506
$493$	−6.80145	−0.306322
$494$	−35.6831	−1.60546
$495$	−5.76176	−0.258972
$496$	17.9632	0.806570
$497$	0	0
$498$	18.5979	0.833392
$499$	−38.0575	−1.70369	−0.851843	−	0.523797i	$-0.824515\pi$
$499$	−38.0575	−1.70369	−0.851843	+	0.523797i	$0.824515\pi$
$500$	−0.569269	−0.0254585
$501$	28.1557	1.25790
$502$	13.6261	0.608161
$503$	−32.9900	−1.47095	−0.735476	−	0.677550i	$-0.763042\pi$
$503$	−32.9900	−1.47095	−0.735476	+	0.677550i	$0.763042\pi$
$504$	0	0
$505$	−1.77664	−0.0790595
$506$	−16.5597	−0.736167
$507$	1.83922	0.0816825
$508$	2.05186	0.0910364
$509$	−0.0354764	−0.00157246	−0.000786231	−	1.00000i	$-0.500250\pi$
$509$	−0.0354764	−0.00157246	−0.000786231		1.00000i	$0.500250\pi$
$510$	−7.31840	−0.324064
$511$	0	0
$512$	7.01062	0.309828
$513$	14.0678	0.621108
$514$	11.6128	0.512218
$515$	17.9773	0.792175
$516$	0.245921	0.0108260
$517$	−13.3947	−0.589098
$518$	0	0
$519$	−22.3087	−0.979244
$520$	−8.00320	−0.350964
$521$	32.0262	1.40310	0.701548	−	0.712623i	$-0.252493\pi$
$521$	32.0262	1.40310	0.701548	+	0.712623i	$0.252493\pi$
$522$	10.7764	0.471668
$523$	−41.6254	−1.82015	−0.910076	−	0.414441i	$-0.863977\pi$
$523$	−41.6254	−1.82015	−0.910076	+	0.414441i	$0.863977\pi$
$524$	3.78509	0.165353
$525$	0	0
$526$	−45.5401	−1.98564
$527$	−7.60675	−0.331355
$528$	30.8262	1.34154
$529$	−9.94300	−0.432304
$530$	−22.1431	−0.961837
$531$	−17.0042	−0.737921
$532$	0	0
$533$	17.2747	0.748252
$534$	54.9401	2.37749
$535$	17.5742	0.759801
$536$	−0.887123	−0.0383179
$537$	−42.4746	−1.83291
$538$	37.1569	1.60195
$539$	0	0
$540$	−1.25541	−0.0540243
$541$	10.6005	0.455753	0.227876	−	0.973690i	$-0.426822\pi$
$541$	10.6005	0.455753	0.227876	+	0.973690i	$0.426822\pi$
$542$	−19.9394	−0.856470
$543$	−16.1418	−0.692709
$544$	6.38225	0.273637
$545$	−1.18692	−0.0508422
$546$	0	0
$547$	−42.8221	−1.83094	−0.915471	−	0.402385i	$-0.868181\pi$
$547$	−42.8221	−1.83094	−0.915471	+	0.402385i	$0.868181\pi$
$548$	−6.81728	−0.291220
$549$	−8.87305	−0.378693
$550$	−4.58279	−0.195411
$551$	−21.2811	−0.906604
$552$	−18.5580	−0.789881
$553$	0	0
$554$	−22.9431	−0.974758
$555$	2.23948	0.0950605
$556$	3.26242	0.138357
$557$	−10.4032	−0.440797	−0.220399	−	0.975410i	$-0.570736\pi$
$557$	−10.4032	−0.440797	−0.220399	+	0.975410i	$0.570736\pi$
$558$	12.0523	0.510214
$559$	−0.673181	−0.0284725
$560$	0	0
$561$	−13.0538	−0.551131
$562$	−4.26254	−0.179805
$563$	0.921851	0.0388514	0.0194257	−	0.999811i	$-0.493816\pi$
$563$	0.921851	0.0388514	0.0194257	+	0.999811i	$0.493816\pi$
$564$	5.97272	0.251497
$565$	8.36114	0.351756
$566$	38.8635	1.63355
$567$	0	0
$568$	22.4240	0.940888
$569$	−10.4255	−0.437061	−0.218530	−	0.975830i	$-0.570126\pi$
$569$	−10.4255	−0.437061	−0.218530	+	0.975830i	$0.570126\pi$
$570$	−22.8986	−0.959115
$571$	33.0601	1.38352	0.691761	−	0.722126i	$-0.256835\pi$
$571$	33.0601	1.38352	0.691761	+	0.722126i	$0.256835\pi$
$572$	5.67993	0.237490
$573$	−29.8260	−1.24600
$574$	0	0
$575$	3.61345	0.150691
$576$	9.29263	0.387193
$577$	−37.7066	−1.56975	−0.784874	−	0.619656i	$-0.787272\pi$
$577$	−37.7066	−1.56975	−0.784874	+	0.619656i	$0.787272\pi$
$578$	20.5867	0.856296
$579$	5.27572	0.219251
$580$	1.89913	0.0788569
$581$	0	0
$582$	17.6867	0.733139
$583$	−39.4966	−1.63578
$584$	−18.4871	−0.765004
$585$	−7.03286	−0.290773
$586$	12.1234	0.500813
$587$	−43.2908	−1.78680	−0.893400	−	0.449261i	$-0.851687\pi$
$587$	−43.2908	−1.78680	−0.893400	+	0.449261i	$0.851687\pi$
$588$	0	0
$589$	−23.8008	−0.980693
$590$	−13.5248	−0.556808
$591$	13.9714	0.574707
$592$	−4.81447	−0.197874
$593$	4.24435	0.174295	0.0871473	−	0.996195i	$-0.472225\pi$
$593$	4.24435	0.174295	0.0871473	+	0.996195i	$0.472225\pi$
$594$	−10.1064	−0.414673
$595$	0	0
$596$	−8.96874	−0.367374
$597$	−1.88570	−0.0771766
$598$	−20.2129	−0.826565
$599$	−4.99932	−0.204267	−0.102133	−	0.994771i	$-0.532567\pi$
$599$	−4.99932	−0.204267	−0.102133	+	0.994771i	$0.532567\pi$
$600$	−5.13582	−0.209669
$601$	16.8399	0.686913	0.343456	−	0.939169i	$-0.388402\pi$
$601$	16.8399	0.686913	0.343456	+	0.939169i	$0.388402\pi$
$602$	0	0
$603$	−0.779564	−0.0317463
$604$	−2.75590	−0.112136
$605$	2.82572	0.114882
$606$	6.37751	0.259069
$607$	−16.2375	−0.659058	−0.329529	−	0.944145i	$-0.606890\pi$
$607$	−16.2375	−0.659058	−0.329529	+	0.944145i	$0.606890\pi$
$608$	19.9694	0.809867
$609$	0	0
$610$	−7.05744	−0.285747
$611$	−16.3497	−0.661437
$612$	2.33891	0.0945447
$613$	−22.6446	−0.914605	−0.457303	−	0.889311i	$-0.651184\pi$
$613$	−22.6446	−0.914605	−0.457303	+	0.889311i	$0.651184\pi$
$614$	2.11582	0.0853877
$615$	11.0855	0.447012
$616$	0	0
$617$	−1.88719	−0.0759756	−0.0379878	−	0.999278i	$-0.512095\pi$
$617$	−1.88719	−0.0759756	−0.0379878	+	0.999278i	$0.512095\pi$
$618$	−64.5321	−2.59586
$619$	−7.55489	−0.303657	−0.151828	−	0.988407i	$-0.548516\pi$
$619$	−7.55489	−0.303657	−0.151828	+	0.988407i	$0.548516\pi$
$620$	2.12399	0.0853013
$621$	7.96876	0.319775
$622$	14.7975	0.593326
$623$	0	0
$624$	37.6267	1.50627
$625$	1.00000	0.0400000
$626$	9.68275	0.387000
$627$	−40.8440	−1.63115
$628$	−1.91325	−0.0763469
$629$	2.03875	0.0812904
$630$	0	0
$631$	−27.3098	−1.08718	−0.543592	−	0.839349i	$-0.682936\pi$
$631$	−27.3098	−1.08718	−0.543592	+	0.839349i	$0.682936\pi$
$632$	−27.3411	−1.08757
$633$	−10.2065	−0.405673
$634$	49.2369	1.95545
$635$	−3.60437	−0.143035
$636$	17.6116	0.698345
$637$	0	0
$638$	15.2885	0.605279
$639$	19.7052	0.779525
$640$	13.6521	0.539646
$641$	−9.50094	−0.375265	−0.187632	−	0.982239i	$-0.560081\pi$
$641$	−9.50094	−0.375265	−0.187632	+	0.982239i	$0.560081\pi$
$642$	−63.0853	−2.48978
$643$	−23.4592	−0.925142	−0.462571	−	0.886582i	$-0.653073\pi$
$643$	−23.4592	−0.925142	−0.462571	+	0.886582i	$0.653073\pi$
$644$	0	0
$645$	−0.431994	−0.0170097
$646$	−20.8462	−0.820182
$647$	−26.3195	−1.03473	−0.517363	−	0.855766i	$-0.673086\pi$
$647$	−26.3195	−1.03473	−0.517363	+	0.855766i	$0.673086\pi$
$648$	−25.1909	−0.989591
$649$	−24.1241	−0.946954
$650$	−5.59379	−0.219406
$651$	0	0
$652$	−12.3060	−0.481940
$653$	32.1357	1.25757	0.628784	−	0.777580i	$-0.283553\pi$
$653$	32.1357	1.25757	0.628784	+	0.777580i	$0.283553\pi$
$654$	4.26063	0.166604
$655$	−6.64904	−0.259800
$656$	−23.8319	−0.930480
$657$	−16.2457	−0.633804
$658$	0	0
$659$	0.428155	0.0166785	0.00833927	−	0.999965i	$-0.497345\pi$
$659$	0.428155	0.0166785	0.00833927	+	0.999965i	$0.497345\pi$
$660$	3.64493	0.141879
$661$	30.2319	1.17589	0.587943	−	0.808903i	$-0.299938\pi$
$661$	30.2319	1.17589	0.587943	+	0.808903i	$0.299938\pi$
$662$	−36.8017	−1.43034
$663$	−15.9335	−0.618808
$664$	11.8816	0.461096
$665$	0	0
$666$	−3.23025	−0.125169
$667$	−12.0548	−0.466762
$668$	−7.15709	−0.276916
$669$	30.6727	1.18588
$670$	−0.620049	−0.0239546
$671$	−12.5883	−0.485966
$672$	0	0
$673$	35.7646	1.37862	0.689311	−	0.724465i	$-0.257913\pi$
$673$	35.7646	1.37862	0.689311	+	0.724465i	$0.257913\pi$
$674$	18.8286	0.725251
$675$	2.20531	0.0848823
$676$	−0.467524	−0.0179817
$677$	31.7418	1.21994	0.609969	−	0.792425i	$-0.291182\pi$
$677$	31.7418	1.21994	0.609969	+	0.792425i	$0.291182\pi$
$678$	−30.0135	−1.15266
$679$	0	0
$680$	−4.67550	−0.179297
$681$	−35.6819	−1.36733
$682$	17.0987	0.654744
$683$	32.7872	1.25457	0.627284	−	0.778790i	$-0.284166\pi$
$683$	32.7872	1.25457	0.627284	+	0.778790i	$0.284166\pi$
$684$	7.31821	0.279819
$685$	11.9755	0.457560
$686$	0	0
$687$	−28.9494	−1.10449
$688$	0.928708	0.0354067
$689$	−48.2098	−1.83665
$690$	−12.9710	−0.493797
$691$	−21.8484	−0.831151	−0.415576	−	0.909559i	$-0.636420\pi$
$691$	−21.8484	−0.831151	−0.415576	+	0.909559i	$0.636420\pi$
$692$	5.67082	0.215572
$693$	0	0
$694$	38.2545	1.45212
$695$	−5.73090	−0.217385
$696$	17.1335	0.649443
$697$	10.0920	0.382260
$698$	−11.4001	−0.431499
$699$	34.7398	1.31398
$700$	0	0
$701$	−32.6578	−1.23347	−0.616734	−	0.787172i	$-0.711544\pi$
$701$	−32.6578	−1.23347	−0.616734	+	0.787172i	$0.711544\pi$
$702$	−12.3360	−0.465593
$703$	6.37906	0.240591
$704$	13.1836	0.496874
$705$	−10.4919	−0.395148
$706$	−53.3601	−2.00823
$707$	0	0
$708$	10.7570	0.404272
$709$	27.5489	1.03462	0.517310	−	0.855798i	$-0.326933\pi$
$709$	27.5489	1.03462	0.517310	+	0.855798i	$0.326933\pi$
$710$	15.6731	0.588200
$711$	−24.0261	−0.901049
$712$	35.0995	1.31541
$713$	−13.4820	−0.504907
$714$	0	0
$715$	−9.97759	−0.373141
$716$	10.7969	0.403500
$717$	45.7916	1.71012
$718$	−0.337967	−0.0126128
$719$	−28.1569	−1.05007	−0.525037	−	0.851079i	$-0.675949\pi$
$719$	−28.1569	−1.05007	−0.525037	+	0.851079i	$0.675949\pi$
$720$	9.70240	0.361587
$721$	0	0
$722$	−34.7707	−1.29403
$723$	−29.2351	−1.08726
$724$	4.10319	0.152494
$725$	−3.33608	−0.123899
$726$	−10.1433	−0.376454
$727$	−0.418224	−0.0155111	−0.00775553	−	0.999970i	$-0.502469\pi$
$727$	−0.418224	−0.0155111	−0.00775553	+	0.999970i	$0.502469\pi$
$728$	0	0
$729$	−7.32042	−0.271127
$730$	−12.9215	−0.478245
$731$	−0.393274	−0.0145458
$732$	5.61314	0.207468
$733$	−8.62347	−0.318515	−0.159258	−	0.987237i	$-0.550910\pi$
$733$	−8.62347	−0.318515	−0.159258	+	0.987237i	$0.550910\pi$
$734$	−41.5876	−1.53503
$735$	0	0
$736$	11.3118	0.416957
$737$	−1.10598	−0.0407392
$738$	−15.9899	−0.588597
$739$	−13.9653	−0.513723	−0.256861	−	0.966448i	$-0.582688\pi$
$739$	−13.9653	−0.513723	−0.256861	+	0.966448i	$0.582688\pi$
$740$	−0.569269	−0.0209267
$741$	−49.8545	−1.83145
$742$	0	0
$743$	−48.7950	−1.79012	−0.895058	−	0.445951i	$-0.852866\pi$
$743$	−48.7950	−1.79012	−0.895058	+	0.445951i	$0.852866\pi$
$744$	19.1621	0.702517
$745$	15.7548	0.577213
$746$	41.9984	1.53767
$747$	10.4410	0.382017
$748$	3.31823	0.121327
$749$	0	0
$750$	−3.58964	−0.131075
$751$	−1.11789	−0.0407924	−0.0203962	−	0.999792i	$-0.506493\pi$
$751$	−1.11789	−0.0407924	−0.0203962	+	0.999792i	$0.506493\pi$
$752$	22.5557	0.822523
$753$	19.0376	0.693769
$754$	18.6613	0.679605
$755$	4.84112	0.176186
$756$	0	0
$757$	−33.7927	−1.22822	−0.614108	−	0.789222i	$-0.710484\pi$
$757$	−33.7927	−1.22822	−0.614108	+	0.789222i	$0.710484\pi$
$758$	35.1510	1.27674
$759$	−23.1363	−0.839793
$760$	−14.6292	−0.530656
$761$	50.6643	1.83658	0.918289	−	0.395910i	$-0.129571\pi$
$761$	50.6643	1.83658	0.918289	+	0.395910i	$0.129571\pi$
$762$	12.9384	0.468709
$763$	0	0
$764$	7.58169	0.274296
$765$	−4.10862	−0.148547
$766$	−35.2695	−1.27434
$767$	−29.4461	−1.06324
$768$	−28.3531	−1.02310
$769$	12.1028	0.436437	0.218219	−	0.975900i	$-0.429975\pi$
$769$	12.1028	0.436437	0.218219	+	0.975900i	$0.429975\pi$
$770$	0	0
$771$	16.2247	0.584320
$772$	−1.34107	−0.0482663
$773$	28.9009	1.03949	0.519747	−	0.854320i	$-0.326026\pi$
$773$	28.9009	1.03949	0.519747	+	0.854320i	$0.326026\pi$
$774$	0.623112	0.0223973
$775$	−3.73108	−0.134024
$776$	11.2995	0.405628
$777$	0	0
$778$	41.3311	1.48179
$779$	31.5767	1.13135
$780$	4.44903	0.159301
$781$	27.9560	1.00034
$782$	−11.8084	−0.422268
$783$	−7.35708	−0.262921
$784$	0	0
$785$	3.36089	0.119955
$786$	23.8677	0.851333
$787$	−46.5897	−1.66075	−0.830373	−	0.557209i	$-0.811872\pi$
$787$	−46.5897	−1.66075	−0.830373	+	0.557209i	$0.811872\pi$
$788$	−3.55149	−0.126517
$789$	−63.6262	−2.26515
$790$	−19.1099	−0.679898
$791$	0	0
$792$	13.2135	0.469522
$793$	−15.3654	−0.545640
$794$	−24.7995	−0.880101
$795$	−30.9372	−1.09723
$796$	0.479340	0.0169897
$797$	18.9933	0.672777	0.336389	−	0.941723i	$-0.390794\pi$
$797$	18.9933	0.672777	0.336389	+	0.941723i	$0.390794\pi$
$798$	0	0
$799$	−9.55153	−0.337909
$800$	3.13047	0.110679
$801$	30.8439	1.08981
$802$	−35.6729	−1.25965
$803$	−23.0479	−0.813344
$804$	0.493157	0.0173923
$805$	0	0
$806$	20.8708	0.735144
$807$	51.9137	1.82745
$808$	4.07439	0.143337
$809$	0.559396	0.0196673	0.00983366	−	0.999952i	$-0.496870\pi$
$809$	0.559396	0.0196673	0.00983366	+	0.999952i	$0.496870\pi$
$810$	−17.6070	−0.618647
$811$	−6.79271	−0.238524	−0.119262	−	0.992863i	$-0.538053\pi$
$811$	−6.79271	−0.238524	−0.119262	+	0.992863i	$0.538053\pi$
$812$	0	0
$813$	−27.8582	−0.977031
$814$	−4.58279	−0.160627
$815$	21.6172	0.757218
$816$	21.9816	0.769511
$817$	−1.23052	−0.0430503
$818$	33.2222	1.16159
$819$	0	0
$820$	−2.81792	−0.0984059
$821$	−6.54798	−0.228526	−0.114263	−	0.993451i	$-0.536451\pi$
$821$	−6.54798	−0.228526	−0.114263	+	0.993451i	$0.536451\pi$
$822$	−42.9878	−1.49937
$823$	4.98040	0.173606	0.0868029	−	0.996226i	$-0.472335\pi$
$823$	4.98040	0.173606	0.0868029	+	0.996226i	$0.472335\pi$
$824$	−41.2275	−1.43623
$825$	−6.40282	−0.222918
$826$	0	0
$827$	10.5604	0.367223	0.183611	−	0.982999i	$-0.441221\pi$
$827$	10.5604	0.367223	0.183611	+	0.982999i	$0.441221\pi$
$828$	4.14543	0.144064
$829$	−17.5093	−0.608125	−0.304062	−	0.952652i	$-0.598343\pi$
$829$	−17.5093	−0.608125	−0.304062	+	0.952652i	$0.598343\pi$
$830$	8.30458	0.288256
$831$	−32.0548	−1.11197
$832$	16.0920	0.557889
$833$	0	0
$834$	20.5719	0.712346
$835$	12.5724	0.435087
$836$	10.3824	0.359084
$837$	−8.22817	−0.284407
$838$	33.1395	1.14479
$839$	−13.8473	−0.478061	−0.239031	−	0.971012i	$-0.576830\pi$
$839$	−13.8473	−0.478061	−0.239031	+	0.971012i	$0.576830\pi$
$840$	0	0
$841$	−17.8706	−0.616226
$842$	−7.11065	−0.245049
$843$	−5.95540	−0.205115
$844$	2.59447	0.0893053
$845$	0.821270	0.0282526
$846$	15.1337	0.520306
$847$	0	0
$848$	66.5094	2.28394
$849$	54.2980	1.86350
$850$	−3.26791	−0.112088
$851$	3.61345	0.123867
$852$	−12.4656	−0.427065
$853$	47.1132	1.61312	0.806562	−	0.591149i	$-0.201325\pi$
$853$	47.1132	1.61312	0.806562	+	0.591149i	$0.201325\pi$
$854$	0	0
$855$	−12.8555	−0.439647
$856$	−40.3032	−1.37753
$857$	24.6386	0.841640	0.420820	−	0.907144i	$-0.361742\pi$
$857$	24.6386	0.841640	0.420820	+	0.907144i	$0.361742\pi$
$858$	35.8160	1.22274
$859$	−28.6614	−0.977915	−0.488958	−	0.872308i	$-0.662623\pi$
$859$	−28.6614	−0.977915	−0.488958	+	0.872308i	$0.662623\pi$
$860$	0.109812	0.00374454
$861$	0	0
$862$	37.1500	1.26534
$863$	45.8232	1.55984	0.779919	−	0.625880i	$-0.215260\pi$
$863$	45.8232	1.55984	0.779919	+	0.625880i	$0.215260\pi$
$864$	6.90364	0.234866
$865$	−9.96158	−0.338704
$866$	22.9190	0.778821
$867$	28.7627	0.976832
$868$	0	0
$869$	−34.0861	−1.15629
$870$	11.9753	0.406002
$871$	−1.34996	−0.0457418
$872$	2.72198	0.0921779
$873$	9.92949	0.336062
$874$	−36.9474	−1.24976
$875$	0	0
$876$	10.2771	0.347232
$877$	−10.1528	−0.342835	−0.171417	−	0.985198i	$-0.554835\pi$
$877$	−10.1528	−0.342835	−0.171417	+	0.985198i	$0.554835\pi$
$878$	−28.0947	−0.948150
$879$	16.9382	0.571310
$880$	13.7649	0.464015
$881$	57.9134	1.95115	0.975576	−	0.219662i	$-0.0704955\pi$
$881$	57.9134	1.95115	0.975576	+	0.219662i	$0.0704955\pi$
$882$	0	0
$883$	−21.7280	−0.731205	−0.365602	−	0.930771i	$-0.619137\pi$
$883$	−21.7280	−0.731205	−0.365602	+	0.930771i	$0.619137\pi$
$884$	4.05026	0.136225
$885$	−18.8961	−0.635187
$886$	−61.3129	−2.05985
$887$	8.42168	0.282772	0.141386	−	0.989955i	$-0.454844\pi$
$887$	8.42168	0.282772	0.141386	+	0.989955i	$0.454844\pi$
$888$	−5.13582	−0.172347
$889$	0	0
$890$	24.5326	0.822333
$891$	−31.4055	−1.05212
$892$	−7.79692	−0.261060
$893$	−29.8858	−1.00009
$894$	−56.5543	−1.89146
$895$	−18.9663	−0.633974
$896$	0	0
$897$	−28.2403	−0.942916
$898$	−51.9789	−1.73456
$899$	12.4472	0.415136
$900$	1.14722	0.0382408
$901$	−28.1643	−0.938290
$902$	−22.6851	−0.755330
$903$	0	0
$904$	−19.1747	−0.637740
$905$	−7.20783	−0.239596
$906$	−17.3779	−0.577342
$907$	45.4688	1.50977	0.754883	−	0.655859i	$-0.227694\pi$
$907$	45.4688	1.50977	0.754883	+	0.655859i	$0.227694\pi$
$908$	9.07023	0.301006
$909$	3.58039	0.118754
$910$	0	0
$911$	−14.8633	−0.492443	−0.246221	−	0.969214i	$-0.579189\pi$
$911$	−14.8633	−0.492443	−0.246221	+	0.969214i	$0.579189\pi$
$912$	68.7784	2.27748
$913$	14.8128	0.490233
$914$	−19.0436	−0.629905
$915$	−9.86027	−0.325970
$916$	7.35885	0.243143
$917$	0	0
$918$	−7.20674	−0.237858
$919$	−41.1517	−1.35747	−0.678734	−	0.734384i	$-0.737471\pi$
$919$	−41.1517	−1.35747	−0.678734	+	0.734384i	$0.737471\pi$
$920$	−8.28676	−0.273206
$921$	2.95611	0.0974073
$922$	56.0770	1.84680
$923$	34.1233	1.12318
$924$	0	0
$925$	1.00000	0.0328798
$926$	−5.31112	−0.174534
$927$	−36.2289	−1.18991
$928$	−10.4435	−0.342824
$929$	2.10190	0.0689610	0.0344805	−	0.999405i	$-0.489022\pi$
$929$	2.10190	0.0689610	0.0344805	+	0.999405i	$0.489022\pi$
$930$	13.3932	0.439182
$931$	0	0
$932$	−8.83076	−0.289261
$933$	20.6743	0.676845
$934$	−32.3506	−1.05854
$935$	−5.82894	−0.190627
$936$	16.1285	0.527177
$937$	26.0598	0.851335	0.425668	−	0.904880i	$-0.360039\pi$
$937$	26.0598	0.851335	0.425668	+	0.904880i	$0.360039\pi$
$938$	0	0
$939$	13.5282	0.441477
$940$	2.66702	0.0869885
$941$	−3.06990	−0.100076	−0.0500380	−	0.998747i	$-0.515934\pi$
$941$	−3.06990	−0.100076	−0.0500380	+	0.998747i	$0.515934\pi$
$942$	−12.0644	−0.393079
$943$	17.8868	0.582474
$944$	40.6233	1.32218
$945$	0	0
$946$	0.884016	0.0287418
$947$	48.6778	1.58182	0.790908	−	0.611935i	$-0.209608\pi$
$947$	48.6778	1.58182	0.790908	+	0.611935i	$0.209608\pi$
$948$	15.1991	0.493642
$949$	−28.1325	−0.913219
$950$	−10.2250	−0.331742
$951$	68.7911	2.23070
$952$	0	0
$953$	2.61312	0.0846472	0.0423236	−	0.999104i	$-0.486524\pi$
$953$	2.61312	0.0846472	0.0423236	+	0.999104i	$0.486524\pi$
$954$	44.6242	1.44476
$955$	−13.3183	−0.430970
$956$	−11.6401	−0.376468
$957$	21.3603	0.690481
$958$	−20.2842	−0.655353
$959$	0	0
$960$	10.3265	0.333288
$961$	−17.0791	−0.550938
$962$	−5.59379	−0.180351
$963$	−35.4166	−1.14129
$964$	7.43147	0.239352
$965$	2.35578	0.0758353
$966$	0	0
$967$	−30.5434	−0.982208	−0.491104	−	0.871101i	$-0.663407\pi$
$967$	−30.5434	−0.982208	−0.491104	+	0.871101i	$0.663407\pi$
$968$	−6.48025	−0.208283
$969$	−29.1252	−0.935635
$970$	7.89771	0.253580
$971$	36.7346	1.17887	0.589434	−	0.807816i	$-0.299351\pi$
$971$	36.7346	1.17887	0.589434	+	0.807816i	$0.299351\pi$
$972$	10.2375	0.328369
$973$	0	0
$974$	48.3118	1.54801
$975$	−7.81534	−0.250291
$976$	21.1978	0.678525
$977$	5.52528	0.176769	0.0883847	−	0.996086i	$-0.471830\pi$
$977$	5.52528	0.176769	0.0883847	+	0.996086i	$0.471830\pi$
$978$	−77.5981	−2.48131
$979$	43.7585	1.39853
$980$	0	0
$981$	2.39196	0.0763693
$982$	−50.4101	−1.60865
$983$	−49.0866	−1.56562	−0.782810	−	0.622260i	$-0.786214\pi$
$983$	−49.0866	−1.56562	−0.782810	+	0.622260i	$0.786214\pi$
$984$	−25.4226	−0.810443
$985$	6.23870	0.198781
$986$	10.9020	0.347190
$987$	0	0
$988$	12.6729	0.403178
$989$	−0.697032	−0.0221643
$990$	9.23550	0.293523
$991$	−44.3847	−1.40993	−0.704963	−	0.709244i	$-0.749037\pi$
$991$	−44.3847	−1.40993	−0.704963	+	0.709244i	$0.749037\pi$
$992$	−11.6800	−0.370840
$993$	−51.4173	−1.63168
$994$	0	0
$995$	−0.842027	−0.0266940
$996$	−6.60506	−0.209289
$997$	−22.1352	−0.701028	−0.350514	−	0.936557i	$-0.613993\pi$
$997$	−22.1352	−0.701028	−0.350514	+	0.936557i	$0.613993\pi$
$998$	61.0021	1.93099
$999$	2.20531	0.0697728

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9065.2.a.s.1.6		19
7.3	odd	6		1295.2.j.a.926.14	yes	38
7.5	odd	6		1295.2.j.a.186.14	✓	38
7.6	odd	2		9065.2.a.r.1.6		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1295.2.j.a.186.14	✓	38	7.5	odd	6
1295.2.j.a.926.14	yes	38	7.3	odd	6
9065.2.a.r.1.6		19	7.6	odd	2
9065.2.a.s.1.6		19	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 9065 = 5 \cdot 7^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9065.a (trivial)

\(f(q)\)	\(=\)	\(q-1.60289 q^{2} -2.23948 q^{3} +0.569269 q^{4} -1.00000 q^{5} +3.58964 q^{6} +2.29331 q^{8} +2.01526 q^{9} +1.60289 q^{10} +2.85907 q^{11} -1.27486 q^{12} +3.48980 q^{13} +2.23948 q^{15} -4.81447 q^{16} +2.03875 q^{17} -3.23025 q^{18} +6.37906 q^{19} -0.569269 q^{20} -4.58279 q^{22} +3.61345 q^{23} -5.13582 q^{24} +1.00000 q^{25} -5.59379 q^{26} +2.20531 q^{27} -3.33608 q^{29} -3.58964 q^{30} -3.73108 q^{31} +3.13047 q^{32} -6.40282 q^{33} -3.26791 q^{34} +1.14722 q^{36} +1.00000 q^{37} -10.2250 q^{38} -7.81534 q^{39} -2.29331 q^{40} +4.95006 q^{41} -0.192899 q^{43} +1.62758 q^{44} -2.01526 q^{45} -5.79197 q^{46} -4.68499 q^{47} +10.7819 q^{48} -1.60289 q^{50} -4.56574 q^{51} +1.98664 q^{52} -13.8145 q^{53} -3.53487 q^{54} -2.85907 q^{55} -14.2858 q^{57} +5.34738 q^{58} -8.43775 q^{59} +1.27486 q^{60} -4.40293 q^{61} +5.98052 q^{62} +4.61114 q^{64} -3.48980 q^{65} +10.2630 q^{66} -0.386831 q^{67} +1.16060 q^{68} -8.09223 q^{69} +9.77799 q^{71} +4.62161 q^{72} -8.06134 q^{73} -1.60289 q^{74} -2.23948 q^{75} +3.63140 q^{76} +12.5272 q^{78} -11.9221 q^{79} +4.81447 q^{80} -10.9845 q^{81} -7.93442 q^{82} +5.18099 q^{83} -2.03875 q^{85} +0.309197 q^{86} +7.47108 q^{87} +6.55673 q^{88} +15.3052 q^{89} +3.23025 q^{90} +2.05702 q^{92} +8.35566 q^{93} +7.50953 q^{94} -6.37906 q^{95} -7.01061 q^{96} +4.92715 q^{97} +5.76176 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q - 3 q^{2} + q^{3} + 11 q^{4} - 19 q^{5} + 4 q^{6} - 9 q^{8} + 12 q^{9} + 3 q^{10} - 13 q^{11} + 4 q^{12} + 3 q^{13} - q^{15} - 5 q^{16} + 2 q^{17} - 11 q^{18} + 12 q^{19} - 11 q^{20} - 10 q^{22}+ \cdots - 71 q^{99}+O(q^{100}) \) 19 * q - 3 * q^2 + q^3 + 11 * q^4 - 19 * q^5 + 4 * q^6 - 9 * q^8 + 12 * q^9 + 3 * q^10 - 13 * q^11 + 4 * q^12 + 3 * q^13 - q^15 - 5 * q^16 + 2 * q^17 - 11 * q^18 + 12 * q^19 - 11 * q^20 - 10 * q^22 - 16 * q^23 - 15 * q^24 + 19 * q^25 + 3 * q^26 + 7 * q^27 - q^29 - 4 * q^30 + 8 * q^31 - 16 * q^32 + 2 * q^33 + 14 * q^34 + 5 * q^36 + 19 * q^37 - 2 * q^38 - 45 * q^39 + 9 * q^40 + 18 * q^41 - 37 * q^43 + q^44 - 12 * q^45 - 29 * q^46 - 2 * q^47 + 35 * q^48 - 3 * q^50 - 43 * q^51 - 40 * q^52 - 10 * q^53 + 38 * q^54 + 13 * q^55 + 12 * q^57 - 13 * q^58 + 28 * q^59 - 4 * q^60 - 22 * q^61 + 10 * q^62 - 7 * q^64 - 3 * q^65 - 34 * q^66 - 61 * q^67 + 17 * q^68 + 20 * q^69 - 17 * q^71 + 17 * q^72 - 16 * q^73 - 3 * q^74 + q^75 + 45 * q^76 + 53 * q^78 - 63 * q^79 + 5 * q^80 - 5 * q^81 - 37 * q^82 + 24 * q^83 - 2 * q^85 - 19 * q^86 - 32 * q^87 - 58 * q^88 + 16 * q^89 + 11 * q^90 + 7 * q^92 - 31 * q^93 - 12 * q^95 - 40 * q^96 + 24 * q^97 - 71 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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