LMFDB - Embedded newform 3025.2.a.p.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3025,2,Mod(1,3025)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3025, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3025.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 3025 = 5^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3025.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3,-1,-1,9,0,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	yes
Analytic conductor:	$24.1547466114$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.404.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 5x - 1 $ x^3 - x^2 - 5*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 605)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.210756$ of defining polynomial
Character	$\chi$	$=$	3025.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.74483 q^{2} +0.210756 q^{3} +5.53407 q^{4} +0.578488 q^{6} +2.32331 q^{7} +9.70041 q^{8} -2.95558 q^{9} +1.16634 q^{12} +0.534070 q^{13} +6.37709 q^{14} +15.5578 q^{16} -2.42151 q^{17} -8.11256 q^{18} +4.95558 q^{19} +0.489652 q^{21} +4.53407 q^{23} +2.04442 q^{24} +1.46593 q^{26} -1.25517 q^{27} +12.8574 q^{28} -5.48965 q^{29} +1.04442 q^{31} +23.3026 q^{32} -6.64663 q^{34} -16.3564 q^{36} -7.48965 q^{37} +13.6022 q^{38} +0.112558 q^{39} +10.6022 q^{41} +1.34401 q^{42} -4.32331 q^{43} +12.4452 q^{46} -6.76855 q^{47} +3.27890 q^{48} -1.60221 q^{49} -0.510348 q^{51} +2.95558 q^{52} +4.53407 q^{53} -3.44523 q^{54} +22.5371 q^{56} +1.04442 q^{57} -15.0681 q^{58} -6.44523 q^{59} +6.79861 q^{61} +2.86675 q^{62} -6.86675 q^{63} +32.8461 q^{64} -0.721104 q^{67} -13.4008 q^{68} +0.955582 q^{69} +4.53407 q^{71} -28.6704 q^{72} -1.06814 q^{73} -20.5578 q^{74} +27.4245 q^{76} +0.308953 q^{78} +4.64663 q^{79} +8.60221 q^{81} +29.1012 q^{82} -13.6022 q^{83} +2.70977 q^{84} -11.8667 q^{86} -1.15698 q^{87} +12.7148 q^{89} +1.24081 q^{91} +25.0919 q^{92} +0.220117 q^{93} -18.5785 q^{94} +4.91116 q^{96} -4.75919 q^{97} -4.39779 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{2} - q^{3} + 9 q^{4} + 5 q^{6} + q^{7} + 9 q^{8} + 2 q^{9} - 9 q^{12} - 6 q^{13} + 5 q^{14} + 13 q^{16} - 4 q^{17} - 20 q^{18} + 4 q^{19} - 17 q^{21} + 6 q^{23} + 17 q^{24} + 12 q^{26} - 13 q^{27}+ \cdots - 36 q^{98}+O(q^{100}) $ 3 * q - q^2 - q^3 + 9 * q^4 + 5 * q^6 + q^7 + 9 * q^8 + 2 * q^9 - 9 * q^12 - 6 * q^13 + 5 * q^14 + 13 * q^16 - 4 * q^17 - 20 * q^18 + 4 * q^19 - 17 * q^21 + 6 * q^23 + 17 * q^24 + 12 * q^26 - 13 * q^27 + 25 * q^28 + 2 * q^29 + 14 * q^31 + 27 * q^32 - 8 * q^34 + 2 * q^36 - 4 * q^37 + 18 * q^38 - 4 * q^39 + 9 * q^41 + 35 * q^42 - 7 * q^43 + 8 * q^46 + 15 * q^47 - 7 * q^48 + 18 * q^49 - 20 * q^51 - 2 * q^52 + 6 * q^53 + 19 * q^54 - 3 * q^56 + 14 * q^57 - 30 * q^58 + 10 * q^59 + 3 * q^61 - 24 * q^62 + 12 * q^63 + 29 * q^64 - 19 * q^67 - 8 * q^69 + 6 * q^71 - 48 * q^72 + 12 * q^73 - 28 * q^74 + 16 * q^76 + 2 * q^78 + 2 * q^79 + 3 * q^81 + 27 * q^82 - 18 * q^83 - 31 * q^84 - 3 * q^86 - 10 * q^87 + 11 * q^89 + 20 * q^91 + 34 * q^92 - 20 * q^93 - 59 * q^94 - 7 * q^96 + 2 * q^97 - 36 * q^98

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 $

$2$	2.74483	1.94089	0.970443	−	0.241332i	$-0.0775843\pi$
$2$	2.74483	1.94089	0.970443	+	0.241332i	$0.0775843\pi$
$3$	0.210756	0.121680	0.0608400	−	0.998148i	$-0.480622\pi$
$3$	0.210756	0.121680	0.0608400	+	0.998148i	$0.480622\pi$
$4$	5.53407	2.76704
$5$	0	0
$5$	0	0
$6$	0.578488	0.236167
$7$	2.32331	0.878130	0.439065	−	0.898455i	$-0.355310\pi$
$7$	2.32331	0.878130	0.439065	+	0.898455i	$0.355310\pi$
$8$	9.70041	3.42961
$9$	−2.95558	−0.985194
$10$	0	0
$11$	0	0
$11$	0	0
$12$	1.16634	0.336693
$13$	0.534070	0.148124	0.0740622	−	0.997254i	$-0.476404\pi$
$13$	0.534070	0.148124	0.0740622	+	0.997254i	$0.476404\pi$
$14$	6.37709	1.70435
$15$	0	0
$16$	15.5578	3.88945
$17$	−2.42151	−0.587303	−0.293651	−	0.955913i	$-0.594870\pi$
$17$	−2.42151	−0.587303	−0.293651	+	0.955913i	$0.594870\pi$
$18$	−8.11256	−1.91215
$19$	4.95558	1.13689	0.568444	−	0.822722i	$-0.307546\pi$
$19$	4.95558	1.13689	0.568444	+	0.822722i	$0.307546\pi$
$20$	0	0
$21$	0.489652	0.106851
$22$	0	0
$23$	4.53407	0.945419	0.472709	−	0.881218i	$-0.343276\pi$
$23$	4.53407	0.945419	0.472709	+	0.881218i	$0.343276\pi$
$24$	2.04442	0.417315
$25$	0	0
$26$	1.46593	0.287492
$27$	−1.25517	−0.241558
$28$	12.8574	2.42982
$29$	−5.48965	−1.01940	−0.509701	−	0.860351i	$-0.670244\pi$
$29$	−5.48965	−1.01940	−0.509701	+	0.860351i	$0.670244\pi$
$30$	0	0
$31$	1.04442	0.187583	0.0937915	−	0.995592i	$-0.470101\pi$
$31$	1.04442	0.187583	0.0937915	+	0.995592i	$0.470101\pi$
$32$	23.3026	4.11936
$33$	0	0
$34$	−6.64663	−1.13989
$35$	0	0
$36$	−16.3564	−2.72607
$37$	−7.48965	−1.23129	−0.615646	−	0.788023i	$-0.711105\pi$
$37$	−7.48965	−1.23129	−0.615646	+	0.788023i	$0.711105\pi$
$38$	13.6022	2.20657
$39$	0.112558	0.0180238
$40$	0	0
$41$	10.6022	1.65579	0.827894	−	0.560885i	$-0.189539\pi$
$41$	10.6022	1.65579	0.827894	+	0.560885i	$0.189539\pi$
$42$	1.34401	0.207385
$43$	−4.32331	−0.659299	−0.329650	−	0.944103i	$-0.606931\pi$
$43$	−4.32331	−0.659299	−0.329650	+	0.944103i	$0.606931\pi$
$44$	0	0
$45$	0	0
$46$	12.4452	1.83495
$47$	−6.76855	−0.987294	−0.493647	−	0.869662i	$-0.664337\pi$
$47$	−6.76855	−0.987294	−0.493647	+	0.869662i	$0.664337\pi$
$48$	3.27890	0.473268
$49$	−1.60221	−0.228887
$50$	0	0
$51$	−0.510348	−0.0714630
$52$	2.95558	0.409865
$53$	4.53407	0.622802	0.311401	−	0.950279i	$-0.399202\pi$
$53$	4.53407	0.622802	0.311401	+	0.950279i	$0.399202\pi$
$54$	−3.44523	−0.468837
$55$	0	0
$56$	22.5371	3.01165
$57$	1.04442	0.138337
$58$	−15.0681	−1.97854
$59$	−6.44523	−0.839098	−0.419549	−	0.907733i	$-0.637812\pi$
$59$	−6.44523	−0.839098	−0.419549	+	0.907733i	$0.637812\pi$
$60$	0	0
$61$	6.79861	0.870472	0.435236	−	0.900316i	$-0.356665\pi$
$61$	6.79861	0.870472	0.435236	+	0.900316i	$0.356665\pi$
$62$	2.86675	0.364077
$63$	−6.86675	−0.865129
$64$	32.8461	4.10576
$65$	0	0
$66$	0	0
$67$	−0.721104	−0.0880968	−0.0440484	−	0.999029i	$-0.514026\pi$
$67$	−0.721104	−0.0880968	−0.0440484	+	0.999029i	$0.514026\pi$
$68$	−13.4008	−1.62509
$69$	0.955582	0.115039
$70$	0	0
$71$	4.53407	0.538095	0.269048	−	0.963127i	$-0.413291\pi$
$71$	4.53407	0.538095	0.269048	+	0.963127i	$0.413291\pi$
$72$	−28.6704	−3.37883
$73$	−1.06814	−0.125016	−0.0625082	−	0.998044i	$-0.519910\pi$
$73$	−1.06814	−0.125016	−0.0625082	+	0.998044i	$0.519910\pi$
$74$	−20.5578	−2.38979
$75$	0	0
$76$	27.4245	3.14581
$77$	0	0
$78$	0.308953	0.0349821
$79$	4.64663	0.522787	0.261393	−	0.965232i	$-0.415818\pi$
$79$	4.64663	0.522787	0.261393	+	0.965232i	$0.415818\pi$
$80$	0	0
$81$	8.60221	0.955801
$82$	29.1012	3.21369
$83$	−13.6022	−1.49304	−0.746518	−	0.665365i	$-0.768276\pi$
$83$	−13.6022	−1.49304	−0.746518	+	0.665365i	$0.768276\pi$
$84$	2.70977	0.295660
$85$	0	0
$86$	−11.8667	−1.27962
$87$	−1.15698	−0.124041
$88$	0	0
$89$	12.7148	1.34776	0.673881	−	0.738840i	$-0.264626\pi$
$89$	12.7148	1.34776	0.673881	+	0.738840i	$0.264626\pi$
$90$	0	0
$91$	1.24081	0.130073
$92$	25.0919	2.61601
$93$	0.220117	0.0228251
$94$	−18.5785	−1.91622
$95$	0	0
$96$	4.91116	0.501244
$97$	−4.75919	−0.483222	−0.241611	−	0.970373i	$-0.577676\pi$
$97$	−4.75919	−0.483222	−0.241611	+	0.970373i	$0.577676\pi$
$98$	−4.39779	−0.444244
$99$	0	0
$100$	0	0
$101$	−6.57849	−0.654584	−0.327292	−	0.944923i	$-0.606136\pi$
$101$	−6.57849	−0.654584	−0.327292	+	0.944923i	$0.606136\pi$
$102$	−1.40082	−0.138701
$103$	−16.3564	−1.61164	−0.805822	−	0.592158i	$-0.798276\pi$
$103$	−16.3564	−1.61164	−0.805822	+	0.592158i	$0.798276\pi$
$104$	5.18070	0.508009
$105$	0	0
$106$	12.4452	1.20879
$107$	−10.2108	−0.987111	−0.493556	−	0.869714i	$-0.664303\pi$
$107$	−10.2108	−0.987111	−0.493556	+	0.869714i	$0.664303\pi$
$108$	−6.94622	−0.668400
$109$	−12.0919	−1.15819	−0.579095	−	0.815260i	$-0.696594\pi$
$109$	−12.0919	−1.15819	−0.579095	+	0.815260i	$0.696594\pi$
$110$	0	0
$111$	−1.57849	−0.149823
$112$	36.1456	3.41544
$113$	10.8430	1.02003	0.510013	−	0.860167i	$-0.329641\pi$
$113$	10.8430	1.02003	0.510013	+	0.860167i	$0.329641\pi$
$114$	2.86675	0.268495
$115$	0	0
$116$	−30.3801	−2.82072
$117$	−1.57849	−0.145931
$118$	−17.6910	−1.62859
$119$	−5.62593	−0.515728
$120$	0	0
$121$	0	0
$122$	18.6610	1.68949
$123$	2.23448	0.201476
$124$	5.77988	0.519049
$125$	0	0
$126$	−18.8480	−1.67912
$127$	8.12192	0.720704	0.360352	−	0.932816i	$-0.382657\pi$
$127$	8.12192	0.720704	0.360352	+	0.932816i	$0.382657\pi$
$128$	43.5515	3.84944
$129$	−0.911164	−0.0802235
$130$	0	0
$131$	5.79861	0.506627	0.253313	−	0.967384i	$-0.418480\pi$
$131$	5.79861	0.506627	0.253313	+	0.967384i	$0.418480\pi$
$132$	0	0
$133$	11.5134	0.998336
$134$	−1.97930	−0.170986
$135$	0	0
$136$	−23.4897	−2.01422
$137$	−8.86675	−0.757537	−0.378769	−	0.925491i	$-0.623652\pi$
$137$	−8.86675	−0.757537	−0.378769	+	0.925491i	$0.623652\pi$
$138$	2.62291	0.223277
$139$	−16.8667	−1.43062	−0.715309	−	0.698808i	$-0.753714\pi$
$139$	−16.8667	−1.43062	−0.715309	+	0.698808i	$0.753714\pi$
$140$	0	0
$141$	−1.42651	−0.120134
$142$	12.4452	1.04438
$143$	0	0
$144$	−45.9823	−3.83186
$145$	0	0
$146$	−2.93186	−0.242642
$147$	−0.337675	−0.0278510
$148$	−41.4483	−3.40703
$149$	4.46593	0.365863	0.182932	−	0.983126i	$-0.441441\pi$
$149$	4.46593	0.365863	0.182932	+	0.983126i	$0.441441\pi$
$150$	0	0
$151$	−11.5134	−0.936945	−0.468473	−	0.883478i	$-0.655196\pi$
$151$	−11.5134	−0.936945	−0.468473	+	0.883478i	$0.655196\pi$
$152$	48.0712	3.89909
$153$	7.15698	0.578607
$154$	0	0
$155$	0	0
$156$	0.622906	0.0498724
$157$	5.91116	0.471762	0.235881	−	0.971782i	$-0.424202\pi$
$157$	5.91116	0.471762	0.235881	+	0.971782i	$0.424202\pi$
$158$	12.7542	1.01467
$159$	0.955582	0.0757826
$160$	0	0
$161$	10.5341	0.830201
$162$	23.6116	1.85510
$163$	−23.4990	−1.84058	−0.920292	−	0.391231i	$-0.872049\pi$
$163$	−23.4990	−1.84058	−0.920292	+	0.391231i	$0.872049\pi$
$164$	58.6734	4.58162
$165$	0	0
$166$	−37.3357	−2.89781
$167$	−14.2345	−1.10150	−0.550748	−	0.834671i	$-0.685658\pi$
$167$	−14.2345	−1.10150	−0.550748	+	0.834671i	$0.685658\pi$
$168$	4.74983	0.366457
$169$	−12.7148	−0.978059
$170$	0	0
$171$	−14.6466	−1.12006
$172$	−23.9255	−1.82430
$173$	6.44523	0.490022	0.245011	−	0.969520i	$-0.421208\pi$
$173$	6.44523	0.490022	0.245011	+	0.969520i	$0.421208\pi$
$174$	−3.17570	−0.240749
$175$	0	0
$176$	0	0
$177$	−1.35837	−0.102101
$178$	34.8998	2.61585
$179$	16.9793	1.26909	0.634546	−	0.772885i	$-0.281187\pi$
$179$	16.9793	1.26909	0.634546	+	0.772885i	$0.281187\pi$
$180$	0	0
$181$	4.48965	0.333713	0.166857	−	0.985981i	$-0.446638\pi$
$181$	4.48965	0.333713	0.166857	+	0.985981i	$0.446638\pi$
$182$	3.40582	0.252456
$183$	1.43285	0.105919
$184$	43.9823	3.24242
$185$	0	0
$186$	0.604184	0.0443009
$187$	0	0
$188$	−37.4576	−2.73188
$189$	−2.91616	−0.212120
$190$	0	0
$191$	−2.75919	−0.199648	−0.0998239	−	0.995005i	$-0.531828\pi$
$191$	−2.75919	−0.199648	−0.0998239	+	0.995005i	$0.531828\pi$
$192$	6.92250	0.499588
$193$	−11.8036	−0.849642	−0.424821	−	0.905277i	$-0.639663\pi$
$193$	−11.8036	−0.849642	−0.424821	+	0.905277i	$0.639663\pi$
$194$	−13.0631	−0.937879
$195$	0	0
$196$	−8.86675	−0.633339
$197$	6.51035	0.463843	0.231922	−	0.972734i	$-0.425499\pi$
$197$	6.51035	0.463843	0.231922	+	0.972734i	$0.425499\pi$
$198$	0	0
$199$	23.9586	1.69838	0.849190	−	0.528087i	$-0.177090\pi$
$199$	23.9586	1.69838	0.849190	+	0.528087i	$0.177090\pi$
$200$	0	0
$201$	−0.151977	−0.0107196
$202$	−18.0568	−1.27047
$203$	−12.7542	−0.895168
$204$	−2.82430	−0.197741
$205$	0	0
$206$	−44.8955	−3.12802
$207$	−13.4008	−0.931421
$208$	8.30895	0.576122
$209$	0	0
$210$	0	0
$211$	−16.8667	−1.16115	−0.580577	−	0.814205i	$-0.697173\pi$
$211$	−16.8667	−1.16115	−0.580577	+	0.814205i	$0.697173\pi$
$212$	25.0919	1.72332
$213$	0.955582	0.0654754
$214$	−28.0267	−1.91587
$215$	0	0
$216$	−12.1757	−0.828451
$217$	2.42651	0.164722
$218$	−33.1901	−2.24791
$219$	−0.225117	−0.0152120
$220$	0	0
$221$	−1.29326	−0.0869939
$222$	−4.33268	−0.290790
$223$	25.0174	1.67529	0.837644	−	0.546216i	$-0.183932\pi$
$223$	25.0174	1.67529	0.837644	+	0.546216i	$0.183932\pi$
$224$	54.1393	3.61733
$225$	0	0
$226$	29.7622	1.97975
$227$	−4.00936	−0.266111	−0.133055	−	0.991109i	$-0.542479\pi$
$227$	−4.00936	−0.266111	−0.133055	+	0.991109i	$0.542479\pi$
$228$	5.77988	0.382782
$229$	−17.3327	−1.14538	−0.572688	−	0.819774i	$-0.694099\pi$
$229$	−17.3327	−1.14538	−0.572688	+	0.819774i	$0.694099\pi$
$230$	0	0
$231$	0	0
$232$	−53.2519	−3.49616
$233$	−2.11256	−0.138398	−0.0691992	−	0.997603i	$-0.522044\pi$
$233$	−2.11256	−0.138398	−0.0691992	+	0.997603i	$0.522044\pi$
$234$	−4.33268	−0.283236
$235$	0	0
$236$	−35.6684	−2.32181
$237$	0.979304	0.0636127
$238$	−15.4422	−1.00097
$239$	−23.9349	−1.54822	−0.774110	−	0.633052i	$-0.781802\pi$
$239$	−23.9349	−1.54822	−0.774110	+	0.633052i	$0.781802\pi$
$240$	0	0
$241$	−14.5134	−0.934889	−0.467444	−	0.884023i	$-0.654825\pi$
$241$	−14.5134	−0.934889	−0.467444	+	0.884023i	$0.654825\pi$
$242$	0	0
$243$	5.57849	0.357860
$244$	37.6240	2.40863
$245$	0	0
$246$	6.13325	0.391042
$247$	2.64663	0.168401
$248$	10.1313	0.643337
$249$	−2.86675	−0.181673
$250$	0	0
$251$	28.8066	1.81826	0.909129	−	0.416514i	$-0.136748\pi$
$251$	28.8066	1.81826	0.909129	+	0.416514i	$0.136748\pi$
$252$	−38.0011	−2.39384
$253$	0	0
$254$	22.2933	1.39880
$255$	0	0
$256$	53.8491	3.36557
$257$	27.6497	1.72474	0.862369	−	0.506280i	$-0.168980\pi$
$257$	27.6497	1.72474	0.862369	+	0.506280i	$0.168980\pi$
$258$	−2.50099	−0.155705
$259$	−17.4008	−1.08123
$260$	0	0
$261$	16.2251	1.00431
$262$	15.9162	0.983304
$263$	−3.13325	−0.193205	−0.0966024	−	0.995323i	$-0.530798\pi$
$263$	−3.13325	−0.193205	−0.0966024	+	0.995323i	$0.530798\pi$
$264$	0	0
$265$	0	0
$266$	31.6022	1.93766
$267$	2.67971	0.163996
$268$	−3.99064	−0.243767
$269$	18.0030	1.09766	0.548832	−	0.835933i	$-0.315073\pi$
$269$	18.0030	1.09766	0.548832	+	0.835933i	$0.315073\pi$
$270$	0	0
$271$	20.3327	1.23512	0.617561	−	0.786523i	$-0.288121\pi$
$271$	20.3327	1.23512	0.617561	+	0.786523i	$0.288121\pi$
$272$	−37.6734	−2.28428
$273$	0.261509	0.0158272
$274$	−24.3377	−1.47029
$275$	0	0
$276$	5.28826	0.318316
$277$	25.4897	1.53152	0.765762	−	0.643124i	$-0.222362\pi$
$277$	25.4897	1.53152	0.765762	+	0.643124i	$0.222362\pi$
$278$	−46.2963	−2.77667
$279$	−3.08686	−0.184806
$280$	0	0
$281$	18.2726	1.09005	0.545025	−	0.838420i	$-0.316520\pi$
$281$	18.2726	1.09005	0.545025	+	0.838420i	$0.316520\pi$
$282$	−3.91553	−0.233166
$283$	11.0538	0.657079	0.328539	−	0.944490i	$-0.393444\pi$
$283$	11.0538	0.657079	0.328539	+	0.944490i	$0.393444\pi$
$284$	25.0919	1.48893
$285$	0	0
$286$	0	0
$287$	24.6323	1.45400
$288$	−68.8728	−4.05837
$289$	−11.1363	−0.655075
$290$	0	0
$291$	−1.00303	−0.0587985
$292$	−5.91116	−0.345925
$293$	−27.1393	−1.58550	−0.792748	−	0.609550i	$-0.791350\pi$
$293$	−27.1393	−1.58550	−0.792748	+	0.609550i	$0.791350\pi$
$294$	−0.926860	−0.0540556
$295$	0	0
$296$	−72.6527	−4.22285
$297$	0	0
$298$	12.2582	0.710098
$299$	2.42151	0.140040
$300$	0	0
$301$	−10.0444	−0.578951
$302$	−31.6022	−1.81850
$303$	−1.38646	−0.0796498
$304$	77.0979	4.42187
$305$	0	0
$306$	19.6447	1.12301
$307$	−11.7385	−0.669951	−0.334976	−	0.942227i	$-0.608728\pi$
$307$	−11.7385	−0.669951	−0.334976	+	0.942227i	$0.608728\pi$
$308$	0	0
$309$	−3.44721	−0.196105
$310$	0	0
$311$	10.6416	0.603431	0.301716	−	0.953398i	$-0.402441\pi$
$311$	10.6416	0.603431	0.301716	+	0.953398i	$0.402441\pi$
$312$	1.09186	0.0618146
$313$	27.1807	1.53634	0.768172	−	0.640244i	$-0.221167\pi$
$313$	27.1807	1.53634	0.768172	+	0.640244i	$0.221167\pi$
$314$	16.2251	0.915636
$315$	0	0
$316$	25.7148	1.44657
$317$	−4.97930	−0.279666	−0.139833	−	0.990175i	$-0.544657\pi$
$317$	−4.97930	−0.279666	−0.139833	+	0.990175i	$0.544657\pi$
$318$	2.62291	0.147085
$319$	0	0
$320$	0	0
$321$	−2.15198	−0.120112
$322$	28.9142	1.61132
$323$	−12.0000	−0.667698
$324$	47.6052	2.64474
$325$	0	0
$326$	−64.5007	−3.57236
$327$	−2.54843	−0.140929
$328$	102.846	5.67871
$329$	−15.7255	−0.866973
$330$	0	0
$331$	7.55477	0.415247	0.207624	−	0.978209i	$-0.433427\pi$
$331$	7.55477	0.415247	0.207624	+	0.978209i	$0.433427\pi$
$332$	−75.2756	−4.13128
$333$	22.1363	1.21306
$334$	−39.0712	−2.13788
$335$	0	0
$336$	7.61791	0.415591
$337$	−3.69105	−0.201064	−0.100532	−	0.994934i	$-0.532054\pi$
$337$	−3.69105	−0.201064	−0.100532	+	0.994934i	$0.532054\pi$
$338$	−34.8998	−1.89830
$339$	2.28523	0.124117
$340$	0	0
$341$	0	0
$342$	−40.2024	−2.17390
$343$	−19.9856	−1.07912
$344$	−41.9379	−2.26114
$345$	0	0
$346$	17.6910	0.951077
$347$	15.7655	0.846338	0.423169	−	0.906051i	$-0.360918\pi$
$347$	15.7655	0.846338	0.423169	+	0.906051i	$0.360918\pi$
$348$	−6.40279	−0.343226
$349$	−10.5578	−0.565146	−0.282573	−	0.959246i	$-0.591188\pi$
$349$	−10.5578	−0.565146	−0.282573	+	0.959246i	$0.591188\pi$
$350$	0	0
$351$	−0.670351	−0.0357807
$352$	0	0
$353$	24.5528	1.30681	0.653407	−	0.757007i	$-0.273339\pi$
$353$	24.5528	1.30681	0.653407	+	0.757007i	$0.273339\pi$
$354$	−3.72849	−0.198167
$355$	0	0
$356$	70.3644	3.72931
$357$	−1.18570	−0.0627538
$358$	46.6052	2.46316
$359$	−16.6704	−0.879827	−0.439914	−	0.898040i	$-0.644991\pi$
$359$	−16.6704	−0.879827	−0.439914	+	0.898040i	$0.644991\pi$
$360$	0	0
$361$	5.55779	0.292515
$362$	12.3233	0.647699
$363$	0	0
$364$	6.86675	0.359915
$365$	0	0
$366$	3.93291	0.205577
$367$	−15.2789	−0.797552	−0.398776	−	0.917048i	$-0.630565\pi$
$367$	−15.2789	−0.797552	−0.398776	+	0.917048i	$0.630565\pi$
$368$	70.5401	3.67716
$369$	−31.3357	−1.63127
$370$	0	0
$371$	10.5341	0.546902
$372$	1.21814	0.0631578
$373$	−17.8461	−0.924033	−0.462017	−	0.886871i	$-0.652874\pi$
$373$	−17.8461	−0.924033	−0.462017	+	0.886871i	$0.652874\pi$
$374$	0	0
$375$	0	0
$376$	−65.6577	−3.38604
$377$	−2.93186	−0.150998
$378$	−8.00436	−0.411700
$379$	1.89244	0.0972082	0.0486041	−	0.998818i	$-0.484523\pi$
$379$	1.89244	0.0972082	0.0486041	+	0.998818i	$0.484523\pi$
$380$	0	0
$381$	1.71174	0.0876952
$382$	−7.57349	−0.387493
$383$	−5.31698	−0.271685	−0.135842	−	0.990730i	$-0.543374\pi$
$383$	−5.31698	−0.271685	−0.135842	+	0.990730i	$0.543374\pi$
$384$	9.17873	0.468400
$385$	0	0
$386$	−32.3988	−1.64906
$387$	12.7779	0.649538
$388$	−26.3377	−1.33709
$389$	−26.8273	−1.36020	−0.680100	−	0.733120i	$-0.738064\pi$
$389$	−26.8273	−1.36020	−0.680100	+	0.733120i	$0.738064\pi$
$390$	0	0
$391$	−10.9793	−0.555247
$392$	−15.5421	−0.784994
$393$	1.22209	0.0616463
$394$	17.8698	0.900266
$395$	0	0
$396$	0	0
$397$	−31.5972	−1.58582	−0.792909	−	0.609340i	$-0.791435\pi$
$397$	−31.5972	−1.58582	−0.792909	+	0.609340i	$0.791435\pi$
$398$	65.7622	3.29636
$399$	2.42651	0.121478
$400$	0	0
$401$	−3.13628	−0.156618	−0.0783092	−	0.996929i	$-0.524952\pi$
$401$	−3.13628	−0.156618	−0.0783092	+	0.996929i	$0.524952\pi$
$402$	−0.417150	−0.0208056
$403$	0.557793	0.0277856
$404$	−36.4058	−1.81126
$405$	0	0
$406$	−35.0080	−1.73742
$407$	0	0
$408$	−4.95058	−0.245090
$409$	0.424538	0.0209921	0.0104960	−	0.999945i	$-0.496659\pi$
$409$	0.424538	0.0209921	0.0104960	+	0.999945i	$0.496659\pi$
$410$	0	0
$411$	−1.86872	−0.0921771
$412$	−90.5175	−4.45947
$413$	−14.9743	−0.736837
$414$	−36.7829	−1.80778
$415$	0	0
$416$	12.4452	0.610178
$417$	−3.55477	−0.174078
$418$	0	0
$419$	6.71174	0.327890	0.163945	−	0.986469i	$-0.447578\pi$
$419$	6.71174	0.327890	0.163945	+	0.986469i	$0.447578\pi$
$420$	0	0
$421$	2.77988	0.135483	0.0677416	−	0.997703i	$-0.478421\pi$
$421$	2.77988	0.135483	0.0677416	+	0.997703i	$0.478421\pi$
$422$	−46.2963	−2.25367
$423$	20.0050	0.972676
$424$	43.9823	2.13597
$425$	0	0
$426$	2.62291	0.127080
$427$	15.7953	0.764388
$428$	−56.5070	−2.73137
$429$	0	0
$430$	0	0
$431$	16.1964	0.780153	0.390076	−	0.920782i	$-0.372449\pi$
$431$	16.1964	0.780153	0.390076	+	0.920782i	$0.372449\pi$
$432$	−19.5277	−0.939529
$433$	−7.82733	−0.376157	−0.188079	−	0.982154i	$-0.560226\pi$
$433$	−7.82733	−0.376157	−0.188079	+	0.982154i	$0.560226\pi$
$434$	6.66035	0.319707
$435$	0	0
$436$	−66.9172	−3.20475
$437$	22.4690	1.07484
$438$	−0.617907	−0.0295247
$439$	20.7355	0.989650	0.494825	−	0.868993i	$-0.335232\pi$
$439$	20.7355	0.989650	0.494825	+	0.868993i	$0.335232\pi$
$440$	0	0
$441$	4.73546	0.225498
$442$	−3.54977	−0.168845
$443$	−5.30262	−0.251935	−0.125968	−	0.992034i	$-0.540204\pi$
$443$	−5.30262	−0.251935	−0.125968	+	0.992034i	$0.540204\pi$
$444$	−8.73546	−0.414567
$445$	0	0
$446$	68.6684	3.25154
$447$	0.941221	0.0445182
$448$	76.3117	3.60539
$449$	−30.0030	−1.41593	−0.707965	−	0.706247i	$-0.750387\pi$
$449$	−30.0030	−1.41593	−0.707965	+	0.706247i	$0.750387\pi$
$450$	0	0
$451$	0	0
$452$	60.0061	2.82245
$453$	−2.42651	−0.114007
$454$	−11.0050	−0.516490
$455$	0	0
$456$	10.1313	0.474441
$457$	−37.5134	−1.75480	−0.877401	−	0.479758i	$-0.840724\pi$
$457$	−37.5134	−1.75480	−0.877401	+	0.479758i	$0.840724\pi$
$458$	−47.5752	−2.22304
$459$	3.03942	0.141868
$460$	0	0
$461$	15.7829	0.735083	0.367542	−	0.930007i	$-0.380200\pi$
$461$	15.7829	0.735083	0.367542	+	0.930007i	$0.380200\pi$
$462$	0	0
$463$	16.5672	0.769941	0.384970	−	0.922929i	$-0.374212\pi$
$463$	16.5672	0.769941	0.384970	+	0.922929i	$0.374212\pi$
$464$	−85.4069	−3.96491
$465$	0	0
$466$	−5.79861	−0.268615
$467$	−3.70041	−0.171234	−0.0856172	−	0.996328i	$-0.527286\pi$
$467$	−3.70041	−0.171234	−0.0856172	+	0.996328i	$0.527286\pi$
$468$	−8.73546	−0.403797
$469$	−1.67535	−0.0773605
$470$	0	0
$471$	1.24581	0.0574040
$472$	−62.5214	−2.87778
$473$	0	0
$474$	2.68802	0.123465
$475$	0	0
$476$	−31.1343	−1.42704
$477$	−13.4008	−0.613581
$478$	−65.6971	−3.00492
$479$	1.26454	0.0577781	0.0288890	−	0.999583i	$-0.490803\pi$
$479$	1.26454	0.0577781	0.0288890	+	0.999583i	$0.490803\pi$
$480$	0	0
$481$	−4.00000	−0.182384
$482$	−39.8367	−1.81451
$483$	2.22012	0.101019
$484$	0	0
$485$	0	0
$486$	15.3120	0.694566
$487$	−21.6022	−0.978890	−0.489445	−	0.872034i	$-0.662801\pi$
$487$	−21.6022	−0.978890	−0.489445	+	0.872034i	$0.662801\pi$
$488$	65.9492	2.98538
$489$	−4.95256	−0.223962
$490$	0	0
$491$	25.5371	1.15247	0.576237	−	0.817283i	$-0.304521\pi$
$491$	25.5371	1.15247	0.576237	+	0.817283i	$0.304521\pi$
$492$	12.3658	0.557491
$493$	13.2933	0.598698
$494$	7.26454	0.326847
$495$	0	0
$496$	16.2488	0.729594
$497$	10.5341	0.472518
$498$	−7.86872	−0.352606
$499$	24.3614	1.09057	0.545283	−	0.838252i	$-0.316422\pi$
$499$	24.3614	1.09057	0.545283	+	0.838252i	$0.316422\pi$
$500$	0	0
$501$	−3.00000	−0.134030
$502$	79.0692	3.52903
$503$	12.4960	0.557169	0.278584	−	0.960412i	$-0.410135\pi$
$503$	12.4960	0.557169	0.278584	+	0.960412i	$0.410135\pi$
$504$	−66.6102	−2.96706
$505$	0	0
$506$	0	0
$507$	−2.67971	−0.119010
$508$	44.9473	1.99421
$509$	24.4483	1.08365	0.541825	−	0.840491i	$-0.317734\pi$
$509$	24.4483	1.08365	0.541825	+	0.840491i	$0.317734\pi$
$510$	0	0
$511$	−2.48163	−0.109781
$512$	60.7034	2.68274
$513$	−6.22012	−0.274625
$514$	75.8935	3.34752
$515$	0	0
$516$	−5.04245	−0.221981
$517$	0	0
$518$	−47.7622	−2.09855
$519$	1.35837	0.0596259
$520$	0	0
$521$	−0.0394184	−0.00172695	−0.000863476	−	1.00000i	$-0.500275\pi$
$521$	−0.0394184	−0.00172695	−0.000863476		1.00000i	$0.500275\pi$
$522$	44.5351	1.94925
$523$	21.0919	0.922283	0.461141	−	0.887327i	$-0.347440\pi$
$523$	21.0919	0.922283	0.461141	+	0.887327i	$0.347440\pi$
$524$	32.0899	1.40185
$525$	0	0
$526$	−8.60024	−0.374988
$527$	−2.52907	−0.110168
$528$	0	0
$529$	−2.44221	−0.106183
$530$	0	0
$531$	19.0494	0.826674
$532$	63.7158	2.76243
$533$	5.66232	0.245263
$534$	7.35534	0.318297
$535$	0	0
$536$	−6.99500	−0.302138
$537$	3.57849	0.154423
$538$	49.4152	2.13044
$539$	0	0
$540$	0	0
$541$	−33.4402	−1.43771	−0.718854	−	0.695161i	$-0.755333\pi$
$541$	−33.4402	−1.43771	−0.718854	+	0.695161i	$0.755333\pi$
$542$	55.8097	2.39723
$543$	0.946221	0.0406062
$544$	−56.4276	−2.41931
$545$	0	0
$546$	0.717796	0.0307188
$547$	−32.8066	−1.40271	−0.701355	−	0.712812i	$-0.747421\pi$
$547$	−32.8066	−1.40271	−0.701355	+	0.712812i	$0.747421\pi$
$548$	−49.0692	−2.09613
$549$	−20.0938	−0.857584
$550$	0	0
$551$	−27.2044	−1.15895
$552$	9.26953	0.394538
$553$	10.7956	0.459075
$554$	69.9647	2.97251
$555$	0	0
$556$	−93.3418	−3.95857
$557$	−28.3327	−1.20049	−0.600247	−	0.799815i	$-0.704931\pi$
$557$	−28.3327	−1.20049	−0.600247	+	0.799815i	$0.704931\pi$
$558$	−8.47290	−0.358687
$559$	−2.30895	−0.0976583
$560$	0	0
$561$	0	0
$562$	50.1550	2.11566
$563$	−29.0361	−1.22373	−0.611863	−	0.790964i	$-0.709580\pi$
$563$	−29.0361	−1.22373	−0.611863	+	0.790964i	$0.709580\pi$
$564$	−7.89441	−0.332415
$565$	0	0
$566$	30.3407	1.27531
$567$	19.9856	0.839318
$568$	43.9823	1.84546
$569$	28.7098	1.20358	0.601788	−	0.798656i	$-0.294455\pi$
$569$	28.7098	1.20358	0.601788	+	0.798656i	$0.294455\pi$
$570$	0	0
$571$	0.824301	0.0344959	0.0172480	−	0.999851i	$-0.494510\pi$
$571$	0.824301	0.0344959	0.0172480	+	0.999851i	$0.494510\pi$
$572$	0	0
$573$	−0.581515	−0.0242931
$574$	67.6113	2.82204
$575$	0	0
$576$	−97.0792	−4.04497
$577$	31.5421	1.31311	0.656557	−	0.754276i	$-0.272012\pi$
$577$	31.5421	1.31311	0.656557	+	0.754276i	$0.272012\pi$
$578$	−30.5672	−1.27143
$579$	−2.48768	−0.103384
$580$	0	0
$581$	−31.6022	−1.31108
$582$	−2.75313	−0.114121
$583$	0	0
$584$	−10.3614	−0.428758
$585$	0	0
$586$	−74.4927	−3.07726
$587$	26.7735	1.10506	0.552531	−	0.833492i	$-0.313662\pi$
$587$	26.7735	1.10506	0.552531	+	0.833492i	$0.313662\pi$
$588$	−1.86872	−0.0770647
$589$	5.17570	0.213261
$590$	0	0
$591$	1.37209	0.0564404
$592$	−116.522	−4.78904
$593$	11.0731	0.454719	0.227360	−	0.973811i	$-0.426991\pi$
$593$	11.0731	0.454719	0.227360	+	0.973811i	$0.426991\pi$
$594$	0	0
$595$	0	0
$596$	24.7148	1.01236
$597$	5.04942	0.206659
$598$	6.64663	0.271801
$599$	−11.9349	−0.487646	−0.243823	−	0.969820i	$-0.578402\pi$
$599$	−11.9349	−0.487646	−0.243823	+	0.969820i	$0.578402\pi$
$600$	0	0
$601$	5.26454	0.214745	0.107372	−	0.994219i	$-0.465756\pi$
$601$	5.26454	0.214745	0.107372	+	0.994219i	$0.465756\pi$
$602$	−27.5702	−1.12368
$603$	2.13128	0.0867925
$604$	−63.7158	−2.59256
$605$	0	0
$606$	−3.80558	−0.154591
$607$	−35.8461	−1.45495	−0.727473	−	0.686136i	$-0.759305\pi$
$607$	−35.8461	−1.45495	−0.727473	+	0.686136i	$0.759305\pi$
$608$	115.478	4.68325
$609$	−2.68802	−0.108924
$610$	0	0
$611$	−3.61488	−0.146242
$612$	39.6072	1.60103
$613$	−6.55779	−0.264867	−0.132433	−	0.991192i	$-0.542279\pi$
$613$	−6.55779	−0.264867	−0.132433	+	0.991192i	$0.542279\pi$
$614$	−32.2201	−1.30030
$615$	0	0
$616$	0	0
$617$	−17.7986	−0.716545	−0.358272	−	0.933617i	$-0.616634\pi$
$617$	−17.7986	−0.716545	−0.358272	+	0.933617i	$0.616634\pi$
$618$	−9.46198	−0.380617
$619$	44.8905	1.80430	0.902150	−	0.431422i	$-0.141988\pi$
$619$	44.8905	1.80430	0.902150	+	0.431422i	$0.141988\pi$
$620$	0	0
$621$	−5.69105	−0.228374
$622$	29.2094	1.17119
$623$	29.5404	1.18351
$624$	1.75116	0.0701025
$625$	0	0
$626$	74.6063	2.98187
$627$	0	0
$628$	32.7128	1.30538
$629$	18.1363	0.723141
$630$	0	0
$631$	21.9112	0.872270	0.436135	−	0.899881i	$-0.356347\pi$
$631$	21.9112	0.872270	0.436135	+	0.899881i	$0.356347\pi$
$632$	45.0742	1.79296
$633$	−3.55477	−0.141289
$634$	−13.6673	−0.542799
$635$	0	0
$636$	5.28826	0.209693
$637$	−0.855693	−0.0339038
$638$	0	0
$639$	−13.4008	−0.530128
$640$	0	0
$641$	35.7335	1.41139	0.705694	−	0.708517i	$-0.250635\pi$
$641$	35.7335	1.41139	0.705694	+	0.708517i	$0.250635\pi$
$642$	−5.90680	−0.233123
$643$	−0.412150	−0.0162536	−0.00812681	−	0.999967i	$-0.502587\pi$
$643$	−0.412150	−0.0162536	−0.00812681	+	0.999967i	$0.502587\pi$
$644$	58.2963	2.29720
$645$	0	0
$646$	−32.9379	−1.29592
$647$	16.5484	0.650586	0.325293	−	0.945613i	$-0.394537\pi$
$647$	16.5484	0.650586	0.325293	+	0.945613i	$0.394537\pi$
$648$	83.4450	3.27803
$649$	0	0
$650$	0	0
$651$	0.511402	0.0200434
$652$	−130.045	−5.09296
$653$	−11.0080	−0.430777	−0.215389	−	0.976528i	$-0.569102\pi$
$653$	−11.0080	−0.430777	−0.215389	+	0.976528i	$0.569102\pi$
$654$	−6.99500	−0.273526
$655$	0	0
$656$	164.947	6.44010
$657$	3.15698	0.123165
$658$	−43.1637	−1.68269
$659$	42.9980	1.67497	0.837483	−	0.546464i	$-0.184026\pi$
$659$	42.9980	1.67497	0.837483	+	0.546464i	$0.184026\pi$
$660$	0	0
$661$	19.4927	0.758177	0.379089	−	0.925360i	$-0.376238\pi$
$661$	19.4927	0.758177	0.379089	+	0.925360i	$0.376238\pi$
$662$	20.7365	0.805948
$663$	−0.272562	−0.0105854
$664$	−131.947	−5.12054
$665$	0	0
$666$	60.7602	2.35441
$667$	−24.8905	−0.963763
$668$	−78.7746	−3.04788
$669$	5.27256	0.203849
$670$	0	0
$671$	0	0
$672$	11.4102	0.440157
$673$	6.80663	0.262376	0.131188	−	0.991357i	$-0.458121\pi$
$673$	6.80663	0.262376	0.131188	+	0.991357i	$0.458121\pi$
$674$	−10.1313	−0.390242
$675$	0	0
$676$	−70.3644	−2.70632
$677$	1.02070	0.0392285	0.0196143	−	0.999808i	$-0.493756\pi$
$677$	1.02070	0.0392285	0.0196143	+	0.999808i	$0.493756\pi$
$678$	6.27256	0.240896
$679$	−11.0571	−0.424332
$680$	0	0
$681$	−0.844996	−0.0323803
$682$	0	0
$683$	−2.09820	−0.0802853	−0.0401426	−	0.999194i	$-0.512781\pi$
$683$	−2.09820	−0.0802853	−0.0401426	+	0.999194i	$0.512781\pi$
$684$	−81.0555	−3.09923
$685$	0	0
$686$	−54.8571	−2.09445
$687$	−3.65296	−0.139369
$688$	−67.2612	−2.56431
$689$	2.42151	0.0922523
$690$	0	0
$691$	11.9950	0.456311	0.228156	−	0.973625i	$-0.426730\pi$
$691$	11.9950	0.456311	0.228156	+	0.973625i	$0.426730\pi$
$692$	35.6684	1.35591
$693$	0	0
$694$	43.2736	1.64264
$695$	0	0
$696$	−11.2231	−0.425412
$697$	−25.6734	−0.972449
$698$	−28.9793	−1.09688
$699$	−0.445234	−0.0168403
$700$	0	0
$701$	29.3594	1.10889	0.554445	−	0.832220i	$-0.312931\pi$
$701$	29.3594	1.10889	0.554445	+	0.832220i	$0.312931\pi$
$702$	−1.84000	−0.0694462
$703$	−37.1156	−1.39984
$704$	0	0
$705$	0	0
$706$	67.3931	2.53637
$707$	−15.2839	−0.574810
$708$	−7.51732	−0.282518
$709$	−37.5451	−1.41004	−0.705018	−	0.709189i	$-0.749061\pi$
$709$	−37.5451	−1.41004	−0.705018	+	0.709189i	$0.749061\pi$
$710$	0	0
$711$	−13.7335	−0.515046
$712$	123.338	4.62230
$713$	4.73546	0.177345
$714$	−3.25454	−0.121798
$715$	0	0
$716$	93.9647	3.51162
$717$	−5.04442	−0.188387
$718$	−45.7572	−1.70764
$719$	−3.99500	−0.148988	−0.0744942	−	0.997221i	$-0.523734\pi$
$719$	−3.99500	−0.148988	−0.0744942	+	0.997221i	$0.523734\pi$
$720$	0	0
$721$	−38.0011	−1.41523
$722$	15.2552	0.567739
$723$	−3.05878	−0.113757
$724$	24.8461	0.923396
$725$	0	0
$726$	0	0
$727$	25.4990	0.945706	0.472853	−	0.881141i	$-0.343224\pi$
$727$	25.4990	0.945706	0.472853	+	0.881141i	$0.343224\pi$
$728$	12.0364	0.446098
$729$	−24.6309	−0.912257
$730$	0	0
$731$	10.4690	0.387208
$732$	7.92947	0.293082
$733$	36.2024	1.33717	0.668584	−	0.743637i	$-0.266901\pi$
$733$	36.2024	1.33717	0.668584	+	0.743637i	$0.266901\pi$
$734$	−41.9379	−1.54796
$735$	0	0
$736$	105.656	3.89452
$737$	0	0
$738$	−86.0111	−3.16611
$739$	−6.06011	−0.222925	−0.111462	−	0.993769i	$-0.535553\pi$
$739$	−6.06011	−0.222925	−0.111462	+	0.993769i	$0.535553\pi$
$740$	0	0
$741$	0.557793	0.0204910
$742$	28.9142	1.06147
$743$	−36.2869	−1.33124	−0.665619	−	0.746292i	$-0.731832\pi$
$743$	−36.2869	−1.33124	−0.665619	+	0.746292i	$0.731832\pi$
$744$	2.13523	0.0782812
$745$	0	0
$746$	−48.9843	−1.79344
$747$	40.2024	1.47093
$748$	0	0
$749$	−23.7228	−0.866812
$750$	0	0
$751$	−15.7335	−0.574123	−0.287062	−	0.957912i	$-0.592678\pi$
$751$	−15.7335	−0.574123	−0.287062	+	0.957912i	$0.592678\pi$
$752$	−105.304	−3.84003
$753$	6.07117	0.221246
$754$	−8.04744	−0.293071
$755$	0	0
$756$	−16.1383	−0.586943
$757$	25.1393	0.913704	0.456852	−	0.889543i	$-0.348977\pi$
$757$	25.1393	0.913704	0.456852	+	0.889543i	$0.348977\pi$
$758$	5.19442	0.188670
$759$	0	0
$760$	0	0
$761$	−15.4709	−0.560821	−0.280410	−	0.959880i	$-0.590471\pi$
$761$	−15.4709	−0.560821	−0.280410	+	0.959880i	$0.590471\pi$
$762$	4.69844	0.170206
$763$	−28.0932	−1.01704
$764$	−15.2695	−0.552432
$765$	0	0
$766$	−14.5942	−0.527309
$767$	−3.44221	−0.124291
$768$	11.3490	0.409522
$769$	17.3220	0.624647	0.312323	−	0.949976i	$-0.398893\pi$
$769$	17.3220	0.624647	0.312323	+	0.949976i	$0.398893\pi$
$770$	0	0
$771$	5.82733	0.209866
$772$	−65.3220	−2.35099
$773$	22.6991	0.816429	0.408214	−	0.912886i	$-0.366152\pi$
$773$	22.6991	0.816429	0.408214	+	0.912886i	$0.366152\pi$
$774$	35.0731	1.26068
$775$	0	0
$776$	−46.1661	−1.65726
$777$	−3.66732	−0.131565
$778$	−73.6363	−2.63999
$779$	52.5401	1.88245
$780$	0	0
$781$	0	0
$782$	−30.1363	−1.07767
$783$	6.89047	0.246245
$784$	−24.9269	−0.890245
$785$	0	0
$786$	3.35443	0.119648
$787$	−3.10122	−0.110547	−0.0552734	−	0.998471i	$-0.517603\pi$
$787$	−3.10122	−0.110547	−0.0552734	+	0.998471i	$0.517603\pi$
$788$	36.0287	1.28347
$789$	−0.660352	−0.0235091
$790$	0	0
$791$	25.1918	0.895716
$792$	0	0
$793$	3.63093	0.128938
$794$	−86.7288	−3.07789
$795$	0	0
$796$	132.589	4.69948
$797$	19.0919	0.676268	0.338134	−	0.941098i	$-0.390204\pi$
$797$	19.0919	0.676268	0.338134	+	0.941098i	$0.390204\pi$
$798$	6.66035	0.235774
$799$	16.3901	0.579841
$800$	0	0
$801$	−37.5795	−1.32781
$802$	−8.60855	−0.303978
$803$	0	0
$804$	−0.841051	−0.0296616
$805$	0	0
$806$	1.53104	0.0539287
$807$	3.79424	0.133564
$808$	−63.8140	−2.24497
$809$	4.46896	0.157120	0.0785601	−	0.996909i	$-0.474968\pi$
$809$	4.46896	0.157120	0.0785601	+	0.996909i	$0.474968\pi$
$810$	0	0
$811$	−4.86675	−0.170895	−0.0854473	−	0.996343i	$-0.527232\pi$
$811$	−4.86675	−0.170895	−0.0854473	+	0.996343i	$0.527232\pi$
$812$	−70.5826	−2.47696
$813$	4.28523	0.150290
$814$	0	0
$815$	0	0
$816$	−7.93989	−0.277952
$817$	−21.4245	−0.749550
$818$	1.16528	0.0407432
$819$	−3.66732	−0.128147
$820$	0	0
$821$	17.0050	0.593479	0.296739	−	0.954959i	$-0.404101\pi$
$821$	17.0050	0.593479	0.296739	+	0.954959i	$0.404101\pi$
$822$	−5.12931	−0.178905
$823$	21.7479	0.758082	0.379041	−	0.925380i	$-0.376254\pi$
$823$	21.7479	0.758082	0.379041	+	0.925380i	$0.376254\pi$
$824$	−158.664	−5.52731
$825$	0	0
$826$	−41.1019	−1.43012
$827$	20.7084	0.720103	0.360051	−	0.932932i	$-0.382759\pi$
$827$	20.7084	0.720103	0.360051	+	0.932932i	$0.382759\pi$
$828$	−74.1611	−2.57727
$829$	11.3090	0.392776	0.196388	−	0.980526i	$-0.437079\pi$
$829$	11.3090	0.392776	0.196388	+	0.980526i	$0.437079\pi$
$830$	0	0
$831$	5.37209	0.186356
$832$	17.5421	0.608163
$833$	3.87977	0.134426
$834$	−9.75721	−0.337865
$835$	0	0
$836$	0	0
$837$	−1.31093	−0.0453122
$838$	18.4226	0.636397
$839$	−43.5084	−1.50208	−0.751038	−	0.660259i	$-0.770446\pi$
$839$	−43.5084	−1.50208	−0.751038	+	0.660259i	$0.770446\pi$
$840$	0	0
$841$	1.13628	0.0391821
$842$	7.63029	0.262957
$843$	3.85105	0.132637
$844$	−93.3418	−3.21296
$845$	0	0
$846$	54.9102	1.88785
$847$	0	0
$848$	70.5401	2.42236
$849$	2.32965	0.0799533
$850$	0	0
$851$	−33.9586	−1.16409
$852$	5.28826	0.181173
$853$	1.11559	0.0381969	0.0190985	−	0.999818i	$-0.493920\pi$
$853$	1.11559	0.0381969	0.0190985	+	0.999818i	$0.493920\pi$
$854$	43.3553	1.48359
$855$	0	0
$856$	−99.0485	−3.38541
$857$	−7.80361	−0.266566	−0.133283	−	0.991078i	$-0.542552\pi$
$857$	−7.80361	−0.266566	−0.133283	+	0.991078i	$0.542552\pi$
$858$	0	0
$859$	30.5341	1.04181	0.520905	−	0.853615i	$-0.325595\pi$
$859$	30.5341	1.04181	0.520905	+	0.853615i	$0.325595\pi$
$860$	0	0
$861$	5.19140	0.176922
$862$	44.4563	1.51419
$863$	4.28959	0.146019	0.0730097	−	0.997331i	$-0.476740\pi$
$863$	4.28959	0.146019	0.0730097	+	0.997331i	$0.476740\pi$
$864$	−29.2488	−0.995066
$865$	0	0
$866$	−21.4847	−0.730078
$867$	−2.34704	−0.0797095
$868$	13.4285	0.455792
$869$	0	0
$870$	0	0
$871$	−0.385120	−0.0130493
$872$	−117.296	−3.97214
$873$	14.0662	0.476068
$874$	61.6734	2.08613
$875$	0	0
$876$	−1.24581	−0.0420921
$877$	−11.3644	−0.383749	−0.191875	−	0.981419i	$-0.561457\pi$
$877$	−11.3644	−0.383749	−0.191875	+	0.981419i	$0.561457\pi$
$878$	56.9152	1.92080
$879$	−5.71977	−0.192923
$880$	0	0
$881$	−11.3277	−0.381639	−0.190820	−	0.981625i	$-0.561115\pi$
$881$	−11.3277	−0.381639	−0.190820	+	0.981625i	$0.561115\pi$
$882$	12.9980	0.437666
$883$	−31.2883	−1.05293	−0.526467	−	0.850196i	$-0.676484\pi$
$883$	−31.2883	−1.05293	−0.526467	+	0.850196i	$0.676484\pi$
$884$	−7.15698	−0.240715
$885$	0	0
$886$	−14.5548	−0.488977
$887$	28.2819	0.949614	0.474807	−	0.880090i	$-0.342518\pi$
$887$	28.2819	0.949614	0.474807	+	0.880090i	$0.342518\pi$
$888$	−15.3120	−0.513836
$889$	18.8698	0.632872
$890$	0	0
$891$	0	0
$892$	138.448	4.63558
$893$	−33.5421	−1.12244
$894$	2.58349	0.0864048
$895$	0	0
$896$	101.184	3.38031
$897$	0.510348	0.0170400
$898$	−82.3531	−2.74816
$899$	−5.73349	−0.191223
$900$	0	0
$901$	−10.9793	−0.365774
$902$	0	0
$903$	−2.11692	−0.0704467
$904$	105.182	3.49829
$905$	0	0
$906$	−6.66035	−0.221275
$907$	−33.6166	−1.11622	−0.558110	−	0.829767i	$-0.688473\pi$
$907$	−33.6166	−1.11622	−0.558110	+	0.829767i	$0.688473\pi$
$908$	−22.1881	−0.736338
$909$	19.4433	0.644892
$910$	0	0
$911$	7.53104	0.249515	0.124757	−	0.992187i	$-0.460185\pi$
$911$	7.53104	0.249515	0.124757	+	0.992187i	$0.460185\pi$
$912$	16.2488	0.538053
$913$	0	0
$914$	−102.968	−3.40587
$915$	0	0
$916$	−95.9202	−3.16929
$917$	13.4720	0.444884
$918$	8.34267	0.275349
$919$	40.0424	1.32088	0.660439	−	0.750880i	$-0.270370\pi$
$919$	40.0424	1.32088	0.660439	+	0.750880i	$0.270370\pi$
$920$	0	0
$921$	−2.47396	−0.0815196
$922$	43.3213	1.42671
$923$	2.42151	0.0797050
$924$	0	0
$925$	0	0
$926$	45.4740	1.49437
$927$	48.3427	1.58778
$928$	−127.923	−4.19929
$929$	51.3407	1.68443	0.842217	−	0.539139i	$-0.181250\pi$
$929$	51.3407	1.68443	0.842217	+	0.539139i	$0.181250\pi$
$930$	0	0
$931$	−7.93989	−0.260219
$932$	−11.6910	−0.382953
$933$	2.24279	0.0734255
$934$	−10.1570	−0.332346
$935$	0	0
$936$	−15.3120	−0.500488
$937$	35.8510	1.17120	0.585601	−	0.810599i	$-0.300858\pi$
$937$	35.8510	1.17120	0.585601	+	0.810599i	$0.300858\pi$
$938$	−4.59855	−0.150148
$939$	5.72849	0.186942
$940$	0	0
$941$	−0.607210	−0.0197945	−0.00989724	−	0.999951i	$-0.503150\pi$
$941$	−0.607210	−0.0197945	−0.00989724	+	0.999951i	$0.503150\pi$
$942$	3.41954	0.111415
$943$	48.0712	1.56541
$944$	−100.274	−3.26363
$945$	0	0
$946$	0	0
$947$	26.3851	0.857401	0.428701	−	0.903447i	$-0.358972\pi$
$947$	26.3851	0.857401	0.428701	+	0.903447i	$0.358972\pi$
$948$	5.41954	0.176018
$949$	−0.570462	−0.0185180
$950$	0	0
$951$	−1.04942	−0.0340297
$952$	−54.5738	−1.76875
$953$	35.3594	1.14540	0.572702	−	0.819764i	$-0.305895\pi$
$953$	35.3594	1.14540	0.572702	+	0.819764i	$0.305895\pi$
$954$	−36.7829	−1.19089
$955$	0	0
$956$	−132.457	−4.28398
$957$	0	0
$958$	3.47093	0.112141
$959$	−20.6002	−0.665216
$960$	0	0
$961$	−29.9092	−0.964813
$962$	−10.9793	−0.353987
$963$	30.1787	0.972496
$964$	−80.3180	−2.58687
$965$	0	0
$966$	6.09384	0.196066
$967$	3.86872	0.124410	0.0622048	−	0.998063i	$-0.480187\pi$
$967$	3.86872	0.124410	0.0622048	+	0.998063i	$0.480187\pi$
$968$	0	0
$969$	−2.52907	−0.0812455
$970$	0	0
$971$	24.1076	0.773648	0.386824	−	0.922153i	$-0.373572\pi$
$971$	24.1076	0.773648	0.386824	+	0.922153i	$0.373572\pi$
$972$	30.8717	0.990212
$973$	−39.1868	−1.25627
$974$	−59.2943	−1.89991
$975$	0	0
$976$	105.771	3.38566
$977$	−10.8143	−0.345980	−0.172990	−	0.984924i	$-0.555343\pi$
$977$	−10.8143	−0.345980	−0.172990	+	0.984924i	$0.555343\pi$
$978$	−13.5939	−0.434685
$979$	0	0
$980$	0	0
$981$	35.7385	1.14104
$982$	70.0949	2.23682
$983$	38.7084	1.23461	0.617304	−	0.786725i	$-0.288225\pi$
$983$	38.7084	1.23461	0.617304	+	0.786725i	$0.288225\pi$
$984$	21.6754	0.690985
$985$	0	0
$986$	36.4877	1.16200
$987$	−3.31423	−0.105493
$988$	14.6466	0.465971
$989$	−19.6022	−0.623314
$990$	0	0
$991$	61.4533	1.95213	0.976064	−	0.217485i	$-0.0697854\pi$
$991$	61.4533	1.95213	0.976064	+	0.217485i	$0.0697854\pi$
$992$	24.3377	0.772722
$993$	1.59221	0.0505273
$994$	28.9142	0.917102
$995$	0	0
$996$	−15.8648	−0.502695
$997$	38.3377	1.21417	0.607083	−	0.794638i	$-0.292339\pi$
$997$	38.3377	1.21417	0.607083	+	0.794638i	$0.292339\pi$
$998$	66.8678	2.11666
$999$	9.40082	0.297429

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3025.2.a.p.1.3		3
5.4	even	2		605.2.a.h.1.1	yes	3
11.10	odd	2		3025.2.a.u.1.1		3
15.14	odd	2		5445.2.a.bb.1.3		3
20.19	odd	2		9680.2.a.cb.1.2		3
55.4	even	10		605.2.g.o.511.1		12
55.9	even	10		605.2.g.o.81.3		12
55.14	even	10		605.2.g.o.251.1		12
55.19	odd	10		605.2.g.p.251.3		12
55.24	odd	10		605.2.g.p.81.1		12
55.29	odd	10		605.2.g.p.511.3		12
55.39	odd	10		605.2.g.p.366.1		12
55.49	even	10		605.2.g.o.366.3		12
55.54	odd	2		605.2.a.g.1.3	✓	3
165.164	even	2		5445.2.a.bd.1.1		3
220.219	even	2		9680.2.a.bz.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.a.g.1.3	✓	3	55.54	odd	2
605.2.a.h.1.1	yes	3	5.4	even	2
605.2.g.o.81.3		12	55.9	even	10
605.2.g.o.251.1		12	55.14	even	10
605.2.g.o.366.3		12	55.49	even	10
605.2.g.o.511.1		12	55.4	even	10
605.2.g.p.81.1		12	55.24	odd	10
605.2.g.p.251.3		12	55.19	odd	10
605.2.g.p.366.1		12	55.39	odd	10
605.2.g.p.511.3		12	55.29	odd	10
3025.2.a.p.1.3		3	1.1	even	1	trivial
3025.2.a.u.1.1		3	11.10	odd	2
5445.2.a.bb.1.3		3	15.14	odd	2
5445.2.a.bd.1.1		3	165.164	even	2
9680.2.a.bz.1.2		3	220.219	even	2
9680.2.a.cb.1.2		3	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3025 = 5^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3025.a (trivial)

\(f(q)\)	\(=\)	\(q+2.74483 q^{2} +0.210756 q^{3} +5.53407 q^{4} +0.578488 q^{6} +2.32331 q^{7} +9.70041 q^{8} -2.95558 q^{9} +1.16634 q^{12} +0.534070 q^{13} +6.37709 q^{14} +15.5578 q^{16} -2.42151 q^{17} -8.11256 q^{18} +4.95558 q^{19} +0.489652 q^{21} +4.53407 q^{23} +2.04442 q^{24} +1.46593 q^{26} -1.25517 q^{27} +12.8574 q^{28} -5.48965 q^{29} +1.04442 q^{31} +23.3026 q^{32} -6.64663 q^{34} -16.3564 q^{36} -7.48965 q^{37} +13.6022 q^{38} +0.112558 q^{39} +10.6022 q^{41} +1.34401 q^{42} -4.32331 q^{43} +12.4452 q^{46} -6.76855 q^{47} +3.27890 q^{48} -1.60221 q^{49} -0.510348 q^{51} +2.95558 q^{52} +4.53407 q^{53} -3.44523 q^{54} +22.5371 q^{56} +1.04442 q^{57} -15.0681 q^{58} -6.44523 q^{59} +6.79861 q^{61} +2.86675 q^{62} -6.86675 q^{63} +32.8461 q^{64} -0.721104 q^{67} -13.4008 q^{68} +0.955582 q^{69} +4.53407 q^{71} -28.6704 q^{72} -1.06814 q^{73} -20.5578 q^{74} +27.4245 q^{76} +0.308953 q^{78} +4.64663 q^{79} +8.60221 q^{81} +29.1012 q^{82} -13.6022 q^{83} +2.70977 q^{84} -11.8667 q^{86} -1.15698 q^{87} +12.7148 q^{89} +1.24081 q^{91} +25.0919 q^{92} +0.220117 q^{93} -18.5785 q^{94} +4.91116 q^{96} -4.75919 q^{97} -4.39779 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{2} - q^{3} + 9 q^{4} + 5 q^{6} + q^{7} + 9 q^{8} + 2 q^{9} - 9 q^{12} - 6 q^{13} + 5 q^{14} + 13 q^{16} - 4 q^{17} - 20 q^{18} + 4 q^{19} - 17 q^{21} + 6 q^{23} + 17 q^{24} + 12 q^{26} - 13 q^{27}+ \cdots - 36 q^{98}+O(q^{100}) \) 3 * q - q^2 - q^3 + 9 * q^4 + 5 * q^6 + q^7 + 9 * q^8 + 2 * q^9 - 9 * q^12 - 6 * q^13 + 5 * q^14 + 13 * q^16 - 4 * q^17 - 20 * q^18 + 4 * q^19 - 17 * q^21 + 6 * q^23 + 17 * q^24 + 12 * q^26 - 13 * q^27 + 25 * q^28 + 2 * q^29 + 14 * q^31 + 27 * q^32 - 8 * q^34 + 2 * q^36 - 4 * q^37 + 18 * q^38 - 4 * q^39 + 9 * q^41 + 35 * q^42 - 7 * q^43 + 8 * q^46 + 15 * q^47 - 7 * q^48 + 18 * q^49 - 20 * q^51 - 2 * q^52 + 6 * q^53 + 19 * q^54 - 3 * q^56 + 14 * q^57 - 30 * q^58 + 10 * q^59 + 3 * q^61 - 24 * q^62 + 12 * q^63 + 29 * q^64 - 19 * q^67 - 8 * q^69 + 6 * q^71 - 48 * q^72 + 12 * q^73 - 28 * q^74 + 16 * q^76 + 2 * q^78 + 2 * q^79 + 3 * q^81 + 27 * q^82 - 18 * q^83 - 31 * q^84 - 3 * q^86 - 10 * q^87 + 11 * q^89 + 20 * q^91 + 34 * q^92 - 20 * q^93 - 59 * q^94 - 7 * q^96 + 2 * q^97 - 36 * q^98

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