LMFDB - Embedded newform 2601.2.a.be.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2601,2,Mod(1,2601)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2601, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2601.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2601 = 3^{2} \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2601.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$20.7690895657$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.7232.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 5x^{2} + 4x + 4 $ x^4 - 2x^3 - 5x^2 + 4*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 51)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.63640$ of defining polynomial
Character	$\chi$	$=$	2601.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.222191 q^{2} -1.95063 q^{4} +0.636405 q^{5} -1.72844 q^{7} +0.877796 q^{8} +O(q^{10})$	$q-0.222191 q^{2} -1.95063 q^{4} +0.636405 q^{5} -1.72844 q^{7} +0.877796 q^{8} -0.141404 q^{10} -4.95063 q^{11} +2.50625 q^{13} +0.384044 q^{14} +3.70622 q^{16} -0.950631 q^{19} -1.24139 q^{20} +1.09999 q^{22} +2.12220 q^{23} -4.59499 q^{25} -0.556867 q^{26} +3.37155 q^{28} -9.58704 q^{29} +5.27281 q^{31} -2.57908 q^{32} -1.09999 q^{35} +8.48705 q^{37} +0.211222 q^{38} +0.558634 q^{40} -6.92171 q^{41} +7.15061 q^{43} +9.65685 q^{44} -0.471535 q^{46} -8.10124 q^{47} -4.01250 q^{49} +1.02097 q^{50} -4.88877 q^{52} +6.44438 q^{53} -3.15061 q^{55} -1.51722 q^{56} +2.13016 q^{58} +10.1125 q^{59} +2.96983 q^{61} -1.17157 q^{62} -6.83940 q^{64} +1.59499 q^{65} +7.70129 q^{67} +0.244408 q^{70} +0.384044 q^{71} +6.51420 q^{73} -1.88575 q^{74} +1.85433 q^{76} +8.55687 q^{77} -2.37280 q^{79} +2.35866 q^{80} +1.53794 q^{82} +13.3581 q^{83} -1.58880 q^{86} -4.34564 q^{88} +1.98875 q^{89} -4.33190 q^{91} -4.13964 q^{92} +1.80002 q^{94} -0.604986 q^{95} +3.04142 q^{97} +0.891542 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 6 q^{4} - 6 q^{5} + 4 q^{7} + 6 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 + 6 * q^4 - 6 * q^5 + 4 * q^7 + 6 * q^8	$ 4 q + 2 q^{2} + 6 q^{4} - 6 q^{5} + 4 q^{7} + 6 q^{8} - 12 q^{10} - 6 q^{11} + 2 q^{13} - 4 q^{14} + 6 q^{16} + 10 q^{19} - 16 q^{20} + 4 q^{22} + 6 q^{23} + 2 q^{25} + 20 q^{26} + 24 q^{28} - 16 q^{29} + 4 q^{31} + 14 q^{32} - 4 q^{35} + 12 q^{37} + 12 q^{38} - 8 q^{40} + 14 q^{41} + 14 q^{43} + 16 q^{44} - 12 q^{46} - 4 q^{47} + 30 q^{50} - 8 q^{52} + 20 q^{53} + 2 q^{55} + 16 q^{56} + 8 q^{58} + 24 q^{59} + 12 q^{61} - 16 q^{62} - 2 q^{64} - 14 q^{65} + 4 q^{67} - 4 q^{70} - 4 q^{71} + 20 q^{73} - 12 q^{74} + 40 q^{76} + 12 q^{77} + 8 q^{79} - 4 q^{82} + 4 q^{83} + 4 q^{86} + 16 q^{88} - 4 q^{89} - 28 q^{91} - 16 q^{92} + 8 q^{94} - 22 q^{95} + 24 q^{97} - 38 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 + 6 * q^4 - 6 * q^5 + 4 * q^7 + 6 * q^8 - 12 * q^10 - 6 * q^11 + 2 * q^13 - 4 * q^14 + 6 * q^16 + 10 * q^19 - 16 * q^20 + 4 * q^22 + 6 * q^23 + 2 * q^25 + 20 * q^26 + 24 * q^28 - 16 * q^29 + 4 * q^31 + 14 * q^32 - 4 * q^35 + 12 * q^37 + 12 * q^38 - 8 * q^40 + 14 * q^41 + 14 * q^43 + 16 * q^44 - 12 * q^46 - 4 * q^47 + 30 * q^50 - 8 * q^52 + 20 * q^53 + 2 * q^55 + 16 * q^56 + 8 * q^58 + 24 * q^59 + 12 * q^61 - 16 * q^62 - 2 * q^64 - 14 * q^65 + 4 * q^67 - 4 * q^70 - 4 * q^71 + 20 * q^73 - 12 * q^74 + 40 * q^76 + 12 * q^77 + 8 * q^79 - 4 * q^82 + 4 * q^83 + 4 * q^86 + 16 * q^88 - 4 * q^89 - 28 * q^91 - 16 * q^92 + 8 * q^94 - 22 * q^95 + 24 * q^97 - 38 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−0.222191	−0.157113	−0.0785565	−	0.996910i	$-0.525031\pi$
$2$	−0.222191	−0.157113	−0.0785565	+	0.996910i	$0.525031\pi$
$3$	0	0
$3$	0	0
$4$	−1.95063	−0.975315
$5$	0.636405	0.284609	0.142304	−	0.989823i	$-0.454549\pi$
$5$	0.636405	0.284609	0.142304	+	0.989823i	$0.454549\pi$
$6$	0	0
$7$	−1.72844	−0.653289	−0.326644	−	0.945147i	$-0.605918\pi$
$7$	−1.72844	−0.653289	−0.326644	+	0.945147i	$0.605918\pi$
$8$	0.877796	0.310348
$9$	0	0
$10$	−0.141404	−0.0447158
$11$	−4.95063	−1.49267	−0.746336	−	0.665570i	$-0.768189\pi$
$11$	−4.95063	−1.49267	−0.746336	+	0.665570i	$0.768189\pi$
$12$	0	0
$13$	2.50625	0.695108	0.347554	−	0.937660i	$-0.387012\pi$
$13$	2.50625	0.695108	0.347554	+	0.937660i	$0.387012\pi$
$14$	0.384044	0.102640
$15$	0	0
$16$	3.70622	0.926556
$17$	0	0
$17$	0	0
$18$	0	0
$19$	−0.950631	−0.218090	−0.109045	−	0.994037i	$-0.534779\pi$
$19$	−0.950631	−0.218090	−0.109045	+	0.994037i	$0.534779\pi$
$20$	−1.24139	−0.277584
$21$	0	0
$22$	1.09999	0.234518
$23$	2.12220	0.442510	0.221255	−	0.975216i	$-0.428985\pi$
$23$	2.12220	0.442510	0.221255	+	0.975216i	$0.428985\pi$
$24$	0	0
$25$	−4.59499	−0.918998
$26$	−0.556867	−0.109211
$27$	0	0
$28$	3.37155	0.637163
$29$	−9.58704	−1.78027	−0.890134	−	0.455699i	$-0.849389\pi$
$29$	−9.58704	−1.78027	−0.890134	+	0.455699i	$0.849389\pi$
$30$	0	0
$31$	5.27281	0.947025	0.473512	−	0.880787i	$-0.342986\pi$
$31$	5.27281	0.947025	0.473512	+	0.880787i	$0.342986\pi$
$32$	−2.57908	−0.455922
$33$	0	0
$34$	0	0
$35$	−1.09999	−0.185932
$36$	0	0
$37$	8.48705	1.39526	0.697631	−	0.716457i	$-0.254237\pi$
$37$	8.48705	1.39526	0.697631	+	0.716457i	$0.254237\pi$
$38$	0.211222	0.0342647
$39$	0	0
$40$	0.558634	0.0883278
$41$	−6.92171	−1.08099	−0.540495	−	0.841347i	$-0.681763\pi$
$41$	−6.92171	−1.08099	−0.540495	+	0.841347i	$0.681763\pi$
$42$	0	0
$43$	7.15061	1.09046	0.545229	−	0.838287i	$-0.316443\pi$
$43$	7.15061	1.09046	0.545229	+	0.838287i	$0.316443\pi$
$44$	9.65685	1.45583
$45$	0	0
$46$	−0.471535	−0.0695241
$47$	−8.10124	−1.18169	−0.590843	−	0.806786i	$-0.701205\pi$
$47$	−8.10124	−1.18169	−0.590843	+	0.806786i	$0.701205\pi$
$48$	0	0
$49$	−4.01250	−0.573214
$50$	1.02097	0.144387
$51$	0	0
$52$	−4.88877	−0.677950
$53$	6.44438	0.885204	0.442602	−	0.896718i	$-0.354055\pi$
$53$	6.44438	0.885204	0.442602	+	0.896718i	$0.354055\pi$
$54$	0	0
$55$	−3.15061	−0.424828
$56$	−1.51722	−0.202747
$57$	0	0
$58$	2.13016	0.279703
$59$	10.1125	1.31653	0.658267	−	0.752785i	$-0.271290\pi$
$59$	10.1125	1.31653	0.658267	+	0.752785i	$0.271290\pi$
$60$	0	0
$61$	2.96983	0.380248	0.190124	−	0.981760i	$-0.439111\pi$
$61$	2.96983	0.380248	0.190124	+	0.981760i	$0.439111\pi$
$62$	−1.17157	−0.148790
$63$	0	0
$64$	−6.83940	−0.854925
$65$	1.59499	0.197834
$66$	0	0
$67$	7.70129	0.940862	0.470431	−	0.882437i	$-0.344098\pi$
$67$	7.70129	0.940862	0.470431	+	0.882437i	$0.344098\pi$
$68$	0	0
$69$	0	0
$70$	0.244408	0.0292123
$71$	0.384044	0.0455777	0.0227888	−	0.999740i	$-0.492745\pi$
$71$	0.384044	0.0455777	0.0227888	+	0.999740i	$0.492745\pi$
$72$	0	0
$73$	6.51420	0.762430	0.381215	−	0.924487i	$-0.375506\pi$
$73$	6.51420	0.762430	0.381215	+	0.924487i	$0.375506\pi$
$74$	−1.88575	−0.219214
$75$	0	0
$76$	1.85433	0.212706
$77$	8.55687	0.975145
$78$	0	0
$79$	−2.37280	−0.266961	−0.133480	−	0.991051i	$-0.542615\pi$
$79$	−2.37280	−0.266961	−0.133480	+	0.991051i	$0.542615\pi$
$80$	2.35866	0.263706
$81$	0	0
$82$	1.53794	0.169838
$83$	13.3581	1.46625	0.733123	−	0.680096i	$-0.238062\pi$
$83$	13.3581	1.46625	0.733123	+	0.680096i	$0.238062\pi$
$84$	0	0
$85$	0	0
$86$	−1.58880	−0.171325
$87$	0	0
$88$	−4.34564	−0.463247
$89$	1.98875	0.210807	0.105404	−	0.994430i	$-0.466387\pi$
$89$	1.98875	0.210807	0.105404	+	0.994430i	$0.466387\pi$
$90$	0	0
$91$	−4.33190	−0.454106
$92$	−4.13964	−0.431587
$93$	0	0
$94$	1.80002	0.185658
$95$	−0.604986	−0.0620703
$96$	0	0
$97$	3.04142	0.308809	0.154405	−	0.988008i	$-0.450654\pi$
$97$	3.04142	0.308809	0.154405	+	0.988008i	$0.450654\pi$
$98$	0.891542	0.0900594
$99$	0	0
$100$	8.96313	0.896313
$101$	18.5456	1.84536	0.922679	−	0.385569i	$-0.125995\pi$
$101$	18.5456	1.84536	0.922679	+	0.385569i	$0.125995\pi$
$102$	0	0
$103$	3.39501	0.334521	0.167260	−	0.985913i	$-0.446508\pi$
$103$	3.39501	0.334521	0.167260	+	0.985913i	$0.446508\pi$
$104$	2.19998	0.215725
$105$	0	0
$106$	−1.43189	−0.139077
$107$	13.1531	1.27156	0.635779	−	0.771871i	$-0.280679\pi$
$107$	13.1531	1.27156	0.635779	+	0.771871i	$0.280679\pi$
$108$	0	0
$109$	−17.3896	−1.66562	−0.832809	−	0.553561i	$-0.813269\pi$
$109$	−17.3896	−1.66562	−0.832809	+	0.553561i	$0.813269\pi$
$110$	0.700037	0.0667460
$111$	0	0
$112$	−6.40598	−0.605309
$113$	−0.776042	−0.0730039	−0.0365019	−	0.999334i	$-0.511622\pi$
$113$	−0.776042	−0.0730039	−0.0365019	+	0.999334i	$0.511622\pi$
$114$	0	0
$115$	1.35058	0.125942
$116$	18.7008	1.73632
$117$	0	0
$118$	−2.24691	−0.206845
$119$	0	0
$120$	0	0
$121$	13.5087	1.22807
$122$	−0.659871	−0.0597419
$123$	0	0
$124$	−10.2853	−0.923648
$125$	−6.10630	−0.546164
$126$	0	0
$127$	10.8519	0.962950	0.481475	−	0.876460i	$-0.340101\pi$
$127$	10.8519	0.962950	0.481475	+	0.876460i	$0.340101\pi$
$128$	6.67782	0.590242
$129$	0	0
$130$	−0.354393	−0.0310823
$131$	−0.706223	−0.0617030	−0.0308515	−	0.999524i	$-0.509822\pi$
$131$	−0.706223	−0.0617030	−0.0308515	+	0.999524i	$0.509822\pi$
$132$	0	0
$133$	1.64311	0.142476
$134$	−1.71116	−0.147822
$135$	0	0
$136$	0	0
$137$	−12.3125	−1.05192	−0.525962	−	0.850508i	$-0.676295\pi$
$137$	−12.3125	−1.05192	−0.525962	+	0.850508i	$0.676295\pi$
$138$	0	0
$139$	−13.3444	−1.13186	−0.565928	−	0.824454i	$-0.691482\pi$
$139$	−13.3444	−1.13186	−0.565928	+	0.824454i	$0.691482\pi$
$140$	2.14567	0.181342
$141$	0	0
$142$	−0.0853313	−0.00716085
$143$	−12.4075	−1.03757
$144$	0	0
$145$	−6.10124	−0.506680
$146$	−1.44740	−0.119788
$147$	0	0
$148$	−16.5551	−1.36082
$149$	−0.356892	−0.0292377	−0.0146189	−	0.999893i	$-0.504653\pi$
$149$	−0.356892	−0.0292377	−0.0146189	+	0.999893i	$0.504653\pi$
$150$	0	0
$151$	9.13317	0.743247	0.371624	−	0.928384i	$-0.378801\pi$
$151$	9.13317	0.743247	0.371624	+	0.928384i	$0.378801\pi$
$152$	−0.834460	−0.0676837
$153$	0	0
$154$	−1.90126	−0.153208
$155$	3.35564	0.269532
$156$	0	0
$157$	17.5975	1.40443	0.702216	−	0.711964i	$-0.252194\pi$
$157$	17.5975	1.40443	0.702216	+	0.711964i	$0.252194\pi$
$158$	0.527215	0.0419430
$159$	0	0
$160$	−1.64134	−0.129759
$161$	−3.66810	−0.289087
$162$	0	0
$163$	16.5901	1.29943	0.649717	−	0.760177i	$-0.274888\pi$
$163$	16.5901	1.29943	0.649717	+	0.760177i	$0.274888\pi$
$164$	13.5017	1.05431
$165$	0	0
$166$	−2.96806	−0.230366
$167$	14.2234	1.10064	0.550321	−	0.834953i	$-0.314505\pi$
$167$	14.2234	1.10064	0.550321	+	0.834953i	$0.314505\pi$
$168$	0	0
$169$	−6.71872	−0.516825
$170$	0	0
$171$	0	0
$172$	−13.9482	−1.06354
$173$	1.89331	0.143946	0.0719728	−	0.997407i	$-0.477071\pi$
$173$	1.89331	0.143946	0.0719728	+	0.997407i	$0.477071\pi$
$174$	0	0
$175$	7.94216	0.600371
$176$	−18.3481	−1.38304
$177$	0	0
$178$	−0.441884	−0.0331206
$179$	22.2469	1.66281	0.831406	−	0.555666i	$-0.187536\pi$
$179$	22.2469	1.66281	0.831406	+	0.555666i	$0.187536\pi$
$180$	0	0
$181$	−11.6142	−0.863276	−0.431638	−	0.902047i	$-0.642064\pi$
$181$	−11.6142	−0.863276	−0.431638	+	0.902047i	$0.642064\pi$
$182$	0.962511	0.0713460
$183$	0	0
$184$	1.86286	0.137332
$185$	5.40120	0.397104
$186$	0	0
$187$	0	0
$188$	15.8025	1.15252
$189$	0	0
$190$	0.134423	0.00975205
$191$	−6.63311	−0.479955	−0.239978	−	0.970778i	$-0.577140\pi$
$191$	−6.63311	−0.479955	−0.239978	+	0.970778i	$0.577140\pi$
$192$	0	0
$193$	2.91769	0.210020	0.105010	−	0.994471i	$-0.466513\pi$
$193$	2.91769	0.210020	0.105010	+	0.994471i	$0.466513\pi$
$194$	−0.675776	−0.0485179
$195$	0	0
$196$	7.82690	0.559064
$197$	−4.53517	−0.323117	−0.161559	−	0.986863i	$-0.551652\pi$
$197$	−4.53517	−0.323117	−0.161559	+	0.986863i	$0.551652\pi$
$198$	0	0
$199$	2.46029	0.174405	0.0872026	−	0.996191i	$-0.472207\pi$
$199$	2.46029	0.174405	0.0872026	+	0.996191i	$0.472207\pi$
$200$	−4.03346	−0.285209
$201$	0	0
$202$	−4.12068	−0.289930
$203$	16.5706	1.16303
$204$	0	0
$205$	−4.40501	−0.307659
$206$	−0.754343	−0.0525576
$207$	0	0
$208$	9.28872	0.644057
$209$	4.70622	0.325536
$210$	0	0
$211$	19.9038	1.37023	0.685116	−	0.728434i	$-0.259752\pi$
$211$	19.9038	1.37023	0.685116	+	0.728434i	$0.259752\pi$
$212$	−12.5706	−0.863353
$213$	0	0
$214$	−2.92251	−0.199778
$215$	4.55068	0.310354
$216$	0	0
$217$	−9.11373	−0.618681
$218$	3.86381	0.261690
$219$	0	0
$220$	6.14567	0.414341
$221$	0	0
$222$	0	0
$223$	14.3631	0.961823	0.480911	−	0.876769i	$-0.340306\pi$
$223$	14.3631	0.961823	0.480911	+	0.876769i	$0.340306\pi$
$224$	4.45779	0.297849
$225$	0	0
$226$	0.172430	0.0114699
$227$	10.8744	0.721758	0.360879	−	0.932613i	$-0.382477\pi$
$227$	10.8744	0.721758	0.360879	+	0.932613i	$0.382477\pi$
$228$	0	0
$229$	18.9900	1.25489	0.627447	−	0.778659i	$-0.284100\pi$
$229$	18.9900	1.25489	0.627447	+	0.778659i	$0.284100\pi$
$230$	−0.300087	−0.0197872
$231$	0	0
$232$	−8.41546	−0.552502
$233$	−7.08079	−0.463878	−0.231939	−	0.972730i	$-0.574507\pi$
$233$	−7.08079	−0.463878	−0.231939	+	0.972730i	$0.574507\pi$
$234$	0	0
$235$	−5.15567	−0.336319
$236$	−19.7257	−1.28404
$237$	0	0
$238$	0	0
$239$	5.28872	0.342099	0.171049	−	0.985262i	$-0.445284\pi$
$239$	5.28872	0.342099	0.171049	+	0.985262i	$0.445284\pi$
$240$	0	0
$241$	5.79826	0.373499	0.186749	−	0.982408i	$-0.440205\pi$
$241$	5.79826	0.373499	0.186749	+	0.982408i	$0.440205\pi$
$242$	−3.00153	−0.192945
$243$	0	0
$244$	−5.79304	−0.370862
$245$	−2.55357	−0.163142
$246$	0	0
$247$	−2.38252	−0.151596
$248$	4.62845	0.293907
$249$	0	0
$250$	1.35677	0.0858095
$251$	8.33190	0.525905	0.262952	−	0.964809i	$-0.415304\pi$
$251$	8.33190	0.525905	0.262952	+	0.964809i	$0.415304\pi$
$252$	0	0
$253$	−10.5062	−0.660522
$254$	−2.41120	−0.151292
$255$	0	0
$256$	12.1950	0.762190
$257$	4.25565	0.265460	0.132730	−	0.991152i	$-0.457626\pi$
$257$	4.25565	0.265460	0.132730	+	0.991152i	$0.457626\pi$
$258$	0	0
$259$	−14.6694	−0.911509
$260$	−3.11123	−0.192951
$261$	0	0
$262$	0.156917	0.00969435
$263$	9.09999	0.561129	0.280565	−	0.959835i	$-0.409478\pi$
$263$	9.09999	0.561129	0.280565	+	0.959835i	$0.409478\pi$
$264$	0	0
$265$	4.10124	0.251937
$266$	−0.365084	−0.0223848
$267$	0	0
$268$	−15.0224	−0.917637
$269$	−21.3820	−1.30368	−0.651842	−	0.758355i	$-0.726003\pi$
$269$	−21.3820	−1.30368	−0.651842	+	0.758355i	$0.726003\pi$
$270$	0	0
$271$	−19.3213	−1.17368	−0.586842	−	0.809702i	$-0.699629\pi$
$271$	−19.3213	−1.17368	−0.586842	+	0.809702i	$0.699629\pi$
$272$	0	0
$273$	0	0
$274$	2.73572	0.165271
$275$	22.7481	1.37176
$276$	0	0
$277$	3.34013	0.200689	0.100344	−	0.994953i	$-0.468006\pi$
$277$	3.34013	0.200689	0.100344	+	0.994953i	$0.468006\pi$
$278$	2.96501	0.177829
$279$	0	0
$280$	−0.965565	−0.0577035
$281$	−4.67754	−0.279039	−0.139519	−	0.990219i	$-0.544556\pi$
$281$	−4.67754	−0.279039	−0.139519	+	0.990219i	$0.544556\pi$
$282$	0	0
$283$	10.0582	0.597897	0.298948	−	0.954269i	$-0.403364\pi$
$283$	10.0582	0.597897	0.298948	+	0.954269i	$0.403364\pi$
$284$	−0.749129	−0.0444526
$285$	0	0
$286$	2.75684	0.163015
$287$	11.9638	0.706198
$288$	0	0
$289$	0	0
$290$	1.35564	0.0796061
$291$	0	0
$292$	−12.7068	−0.743609
$293$	−5.76934	−0.337048	−0.168524	−	0.985698i	$-0.553900\pi$
$293$	−5.76934	−0.337048	−0.168524	+	0.985698i	$0.553900\pi$
$294$	0	0
$295$	6.43563	0.374697
$296$	7.44990	0.433017
$297$	0	0
$298$	0.0792983	0.00459363
$299$	5.31877	0.307592
$300$	0	0
$301$	−12.3594	−0.712383
$302$	−2.02931	−0.116774
$303$	0	0
$304$	−3.52325	−0.202072
$305$	1.89001	0.108222
$306$	0	0
$307$	−13.2375	−0.755502	−0.377751	−	0.925907i	$-0.623302\pi$
$307$	−13.2375	−0.755502	−0.377751	+	0.925907i	$0.623302\pi$
$308$	−16.6913	−0.951074
$309$	0	0
$310$	−0.745595	−0.0423469
$311$	1.29530	0.0734499	0.0367250	−	0.999325i	$-0.488307\pi$
$311$	1.29530	0.0734499	0.0367250	+	0.999325i	$0.488307\pi$
$312$	0	0
$313$	−19.1007	−1.07964	−0.539818	−	0.841782i	$-0.681507\pi$
$313$	−19.1007	−1.07964	−0.539818	+	0.841782i	$0.681507\pi$
$314$	−3.91001	−0.220655
$315$	0	0
$316$	4.62845	0.260371
$317$	−15.1043	−0.848339	−0.424170	−	0.905583i	$-0.639434\pi$
$317$	−15.1043	−0.848339	−0.424170	+	0.905583i	$0.639434\pi$
$318$	0	0
$319$	47.4619	2.65735
$320$	−4.35263	−0.243319
$321$	0	0
$322$	0.815020	0.0454193
$323$	0	0
$324$	0	0
$325$	−11.5162	−0.638803
$326$	−3.68617	−0.204158
$327$	0	0
$328$	−6.07585	−0.335483
$329$	14.0025	0.771983
$330$	0	0
$331$	−22.6769	−1.24644	−0.623218	−	0.782048i	$-0.714175\pi$
$331$	−22.6769	−1.24644	−0.623218	+	0.782048i	$0.714175\pi$
$332$	−26.0568	−1.43005
$333$	0	0
$334$	−3.16033	−0.172925
$335$	4.90114	0.267778
$336$	0	0
$337$	−1.61669	−0.0880666	−0.0440333	−	0.999030i	$-0.514021\pi$
$337$	−1.61669	−0.0880666	−0.0440333	+	0.999030i	$0.514021\pi$
$338$	1.49284	0.0811999
$339$	0	0
$340$	0	0
$341$	−26.1037	−1.41360
$342$	0	0
$343$	19.0344	1.02776
$344$	6.27677	0.338421
$345$	0	0
$346$	−0.420677	−0.0226157
$347$	15.3606	0.824602	0.412301	−	0.911048i	$-0.364725\pi$
$347$	15.3606	0.824602	0.412301	+	0.911048i	$0.364725\pi$
$348$	0	0
$349$	−15.1087	−0.808749	−0.404374	−	0.914594i	$-0.632511\pi$
$349$	−15.1087	−0.808749	−0.404374	+	0.914594i	$0.632511\pi$
$350$	−1.76468	−0.0943261
$351$	0	0
$352$	12.7681	0.680541
$353$	31.2482	1.66317	0.831586	−	0.555396i	$-0.187433\pi$
$353$	31.2482	1.66317	0.831586	+	0.555396i	$0.187433\pi$
$354$	0	0
$355$	0.244408	0.0129718
$356$	−3.87932	−0.205604
$357$	0	0
$358$	−4.94307	−0.261249
$359$	−2.72503	−0.143822	−0.0719108	−	0.997411i	$-0.522910\pi$
$359$	−2.72503	−0.143822	−0.0719108	+	0.997411i	$0.522910\pi$
$360$	0	0
$361$	−18.0963	−0.952437
$362$	2.58057	0.135632
$363$	0	0
$364$	8.44994	0.442897
$365$	4.14567	0.216994
$366$	0	0
$367$	−18.4515	−0.963163	−0.481581	−	0.876401i	$-0.659937\pi$
$367$	−18.4515	−0.963163	−0.481581	+	0.876401i	$0.659937\pi$
$368$	7.86536	0.410010
$369$	0	0
$370$	−1.20010	−0.0623902
$371$	−11.1387	−0.578294
$372$	0	0
$373$	24.4049	1.26364	0.631820	−	0.775115i	$-0.282308\pi$
$373$	24.4049	1.26364	0.631820	+	0.775115i	$0.282308\pi$
$374$	0	0
$375$	0	0
$376$	−7.11123	−0.366734
$377$	−24.0275	−1.23748
$378$	0	0
$379$	−5.89057	−0.302578	−0.151289	−	0.988490i	$-0.548342\pi$
$379$	−5.89057	−0.302578	−0.151289	+	0.988490i	$0.548342\pi$
$380$	1.18010	0.0605381
$381$	0	0
$382$	1.47382	0.0754072
$383$	−30.7756	−1.57256	−0.786279	−	0.617871i	$-0.787995\pi$
$383$	−30.7756	−1.57256	−0.786279	+	0.617871i	$0.787995\pi$
$384$	0	0
$385$	5.44563	0.277535
$386$	−0.648284	−0.0329968
$387$	0	0
$388$	−5.93268	−0.301186
$389$	−19.5244	−0.989925	−0.494963	−	0.868914i	$-0.664818\pi$
$389$	−19.5244	−0.989925	−0.494963	+	0.868914i	$0.664818\pi$
$390$	0	0
$391$	0	0
$392$	−3.52215	−0.177896
$393$	0	0
$394$	1.00768	0.0507659
$395$	−1.51006	−0.0759794
$396$	0	0
$397$	−0.904279	−0.0453844	−0.0226922	−	0.999742i	$-0.507224\pi$
$397$	−0.904279	−0.0453844	−0.0226922	+	0.999742i	$0.507224\pi$
$398$	−0.546655	−0.0274013
$399$	0	0
$400$	−17.0301	−0.851503
$401$	−1.26486	−0.0631639	−0.0315820	−	0.999501i	$-0.510055\pi$
$401$	−1.26486	−0.0631639	−0.0315820	+	0.999501i	$0.510055\pi$
$402$	0	0
$403$	13.2150	0.658285
$404$	−36.1757	−1.79981
$405$	0	0
$406$	−3.68185	−0.182727
$407$	−42.0162	−2.08267
$408$	0	0
$409$	28.6350	1.41591	0.707954	−	0.706258i	$-0.249618\pi$
$409$	28.6350	1.41591	0.707954	+	0.706258i	$0.249618\pi$
$410$	0.978756	0.0483373
$411$	0	0
$412$	−6.62242	−0.326263
$413$	−17.4788	−0.860076
$414$	0	0
$415$	8.50119	0.417307
$416$	−6.46382	−0.316915
$417$	0	0
$418$	−1.04568	−0.0511460
$419$	−23.9581	−1.17043	−0.585214	−	0.810879i	$-0.698990\pi$
$419$	−23.9581	−1.17043	−0.585214	+	0.810879i	$0.698990\pi$
$420$	0	0
$421$	−12.5312	−0.610735	−0.305368	−	0.952235i	$-0.598779\pi$
$421$	−12.5312	−0.610735	−0.305368	+	0.952235i	$0.598779\pi$
$422$	−4.42244	−0.215281
$423$	0	0
$424$	5.65685	0.274721
$425$	0	0
$426$	0	0
$427$	−5.13317	−0.248412
$428$	−25.6569	−1.24017
$429$	0	0
$430$	−1.01112	−0.0487606
$431$	17.6728	0.851267	0.425633	−	0.904896i	$-0.360051\pi$
$431$	17.6728	0.851267	0.425633	+	0.904896i	$0.360051\pi$
$432$	0	0
$433$	−14.0076	−0.673160	−0.336580	−	0.941655i	$-0.609270\pi$
$433$	−14.0076	−0.673160	−0.336580	+	0.941655i	$0.609270\pi$
$434$	2.02499	0.0972028
$435$	0	0
$436$	33.9206	1.62450
$437$	−2.01743	−0.0965069
$438$	0	0
$439$	−11.5740	−0.552398	−0.276199	−	0.961100i	$-0.589075\pi$
$439$	−11.5740	−0.552398	−0.276199	+	0.961100i	$0.589075\pi$
$440$	−2.76559	−0.131844
$441$	0	0
$442$	0	0
$443$	35.6174	1.69223	0.846117	−	0.532997i	$-0.178934\pi$
$443$	35.6174	1.69223	0.846117	+	0.532997i	$0.178934\pi$
$444$	0	0
$445$	1.26565	0.0599977
$446$	−3.19135	−0.151115
$447$	0	0
$448$	11.8215	0.558513
$449$	22.1461	1.04514	0.522569	−	0.852597i	$-0.324974\pi$
$449$	22.1461	1.04514	0.522569	+	0.852597i	$0.324974\pi$
$450$	0	0
$451$	34.2668	1.61356
$452$	1.51377	0.0712018
$453$	0	0
$454$	−2.41619	−0.113398
$455$	−2.75684	−0.129243
$456$	0	0
$457$	9.90632	0.463398	0.231699	−	0.972787i	$-0.425572\pi$
$457$	9.90632	0.463398	0.231699	+	0.972787i	$0.425572\pi$
$458$	−4.21941	−0.197160
$459$	0	0
$460$	−2.63449	−0.122834
$461$	9.62367	0.448219	0.224109	−	0.974564i	$-0.428053\pi$
$461$	9.62367	0.448219	0.224109	+	0.974564i	$0.428053\pi$
$462$	0	0
$463$	15.3013	0.711113	0.355557	−	0.934655i	$-0.384291\pi$
$463$	15.3013	0.711113	0.355557	+	0.934655i	$0.384291\pi$
$464$	−35.5317	−1.64952
$465$	0	0
$466$	1.57329	0.0728812
$467$	22.3150	1.03261	0.516307	−	0.856404i	$-0.327307\pi$
$467$	22.3150	1.03261	0.516307	+	0.856404i	$0.327307\pi$
$468$	0	0
$469$	−13.3112	−0.614655
$470$	1.14554	0.0528400
$471$	0	0
$472$	8.87670	0.408583
$473$	−35.4000	−1.62769
$474$	0	0
$475$	4.36814	0.200424
$476$	0	0
$477$	0	0
$478$	−1.17511	−0.0537481
$479$	15.5571	0.710824	0.355412	−	0.934710i	$-0.384341\pi$
$479$	15.5571	0.710824	0.355412	+	0.934710i	$0.384341\pi$
$480$	0	0
$481$	21.2707	0.969858
$482$	−1.28832	−0.0586815
$483$	0	0
$484$	−26.3506	−1.19775
$485$	1.93557	0.0878898
$486$	0	0
$487$	−0.0296516	−0.00134364	−0.000671822	−	1.00000i	$-0.500214\pi$
$487$	−0.0296516	−0.00134364	−0.000671822		1.00000i	$0.500214\pi$
$488$	2.60691	0.118009
$489$	0	0
$490$	0.567382	0.0256317
$491$	−6.66935	−0.300984	−0.150492	−	0.988611i	$-0.548086\pi$
$491$	−6.66935	−0.300984	−0.150492	+	0.988611i	$0.548086\pi$
$492$	0	0
$493$	0	0
$494$	0.529375	0.0238177
$495$	0	0
$496$	19.5422	0.877471
$497$	−0.663798	−0.0297754
$498$	0	0
$499$	−18.6469	−0.834748	−0.417374	−	0.908735i	$-0.637049\pi$
$499$	−18.6469	−0.834748	−0.417374	+	0.908735i	$0.637049\pi$
$500$	11.9111	0.532682
$501$	0	0
$502$	−1.85128	−0.0826265
$503$	−25.7396	−1.14767	−0.573837	−	0.818970i	$-0.694546\pi$
$503$	−25.7396	−1.14767	−0.573837	+	0.818970i	$0.694546\pi$
$504$	0	0
$505$	11.8025	0.525205
$506$	2.33440	0.103777
$507$	0	0
$508$	−21.1680	−0.939180
$509$	−41.1950	−1.82594	−0.912968	−	0.408032i	$-0.866215\pi$
$509$	−41.1950	−1.82594	−0.912968	+	0.408032i	$0.866215\pi$
$510$	0	0
$511$	−11.2594	−0.498087
$512$	−16.0653	−0.709992
$513$	0	0
$514$	−0.945570	−0.0417073
$515$	2.16060	0.0952076
$516$	0	0
$517$	40.1062	1.76387
$518$	3.25940	0.143210
$519$	0	0
$520$	1.40007	0.0613973
$521$	−8.98205	−0.393511	−0.196755	−	0.980453i	$-0.563040\pi$
$521$	−8.98205	−0.393511	−0.196755	+	0.980453i	$0.563040\pi$
$522$	0	0
$523$	−5.38995	−0.235686	−0.117843	−	0.993032i	$-0.537598\pi$
$523$	−5.38995	−0.235686	−0.117843	+	0.993032i	$0.537598\pi$
$524$	1.37758	0.0601799
$525$	0	0
$526$	−2.02194	−0.0881607
$527$	0	0
$528$	0	0
$529$	−18.4963	−0.804185
$530$	−0.911259	−0.0395826
$531$	0	0
$532$	−3.20510	−0.138959
$533$	−17.3475	−0.751405
$534$	0	0
$535$	8.37070	0.361897
$536$	6.76016	0.291994
$537$	0	0
$538$	4.75090	0.204826
$539$	19.8644	0.855620
$540$	0	0
$541$	1.22765	0.0527806	0.0263903	−	0.999652i	$-0.491599\pi$
$541$	1.22765	0.0527806	0.0263903	+	0.999652i	$0.491599\pi$
$542$	4.29302	0.184401
$543$	0	0
$544$	0	0
$545$	−11.0668	−0.474050
$546$	0	0
$547$	13.5274	0.578391	0.289196	−	0.957270i	$-0.406612\pi$
$547$	13.5274	0.578391	0.289196	+	0.957270i	$0.406612\pi$
$548$	24.0171	1.02596
$549$	0	0
$550$	−5.05443	−0.215522
$551$	9.11373	0.388258
$552$	0	0
$553$	4.10124	0.174402
$554$	−0.742148	−0.0315308
$555$	0	0
$556$	26.0300	1.10392
$557$	18.3599	0.777936	0.388968	−	0.921251i	$-0.372832\pi$
$557$	18.3599	0.777936	0.388968	+	0.921251i	$0.372832\pi$
$558$	0	0
$559$	17.9212	0.757986
$560$	−4.07680	−0.172276
$561$	0	0
$562$	1.03931	0.0438406
$563$	−3.33315	−0.140475	−0.0702377	−	0.997530i	$-0.522376\pi$
$563$	−3.33315	−0.140475	−0.0702377	+	0.997530i	$0.522376\pi$
$564$	0	0
$565$	−0.493877	−0.0207775
$566$	−2.23484	−0.0939374
$567$	0	0
$568$	0.337113	0.0141449
$569$	−29.4369	−1.23406	−0.617029	−	0.786940i	$-0.711664\pi$
$569$	−29.4369	−1.23406	−0.617029	+	0.786940i	$0.711664\pi$
$570$	0	0
$571$	−25.8275	−1.08085	−0.540424	−	0.841393i	$-0.681736\pi$
$571$	−25.8275	−1.08085	−0.540424	+	0.841393i	$0.681736\pi$
$572$	24.2025	1.01196
$573$	0	0
$574$	−2.65824	−0.110953
$575$	−9.75150	−0.406666
$576$	0	0
$577$	−22.1850	−0.923575	−0.461788	−	0.886990i	$-0.652792\pi$
$577$	−22.1850	−0.923575	−0.461788	+	0.886990i	$0.652792\pi$
$578$	0	0
$579$	0	0
$580$	11.9013	0.494173
$581$	−23.0887	−0.957882
$582$	0	0
$583$	−31.9038	−1.32132
$584$	5.71814	0.236618
$585$	0	0
$586$	1.28190	0.0529547
$587$	−32.1482	−1.32690	−0.663448	−	0.748222i	$-0.730908\pi$
$587$	−32.1482	−1.32690	−0.663448	+	0.748222i	$0.730908\pi$
$588$	0	0
$589$	−5.01250	−0.206536
$590$	−1.42994	−0.0588698
$591$	0	0
$592$	31.4549	1.29279
$593$	29.3406	1.20488	0.602438	−	0.798166i	$-0.294196\pi$
$593$	29.3406	1.20488	0.602438	+	0.798166i	$0.294196\pi$
$594$	0	0
$595$	0	0
$596$	0.696164	0.0285160
$597$	0	0
$598$	−1.18178	−0.0483268
$599$	36.2632	1.48167	0.740836	−	0.671686i	$-0.234430\pi$
$599$	36.2632	1.48167	0.740836	+	0.671686i	$0.234430\pi$
$600$	0	0
$601$	45.7383	1.86570	0.932851	−	0.360262i	$-0.117313\pi$
$601$	45.7383	1.86570	0.932851	+	0.360262i	$0.117313\pi$
$602$	2.74615	0.111925
$603$	0	0
$604$	−17.8155	−0.724900
$605$	8.59703	0.349519
$606$	0	0
$607$	−33.6640	−1.36638	−0.683190	−	0.730241i	$-0.739408\pi$
$607$	−33.6640	−1.36638	−0.683190	+	0.730241i	$0.739408\pi$
$608$	2.45176	0.0994318
$609$	0	0
$610$	−0.419945	−0.0170031
$611$	−20.3037	−0.821400
$612$	0	0
$613$	−5.89120	−0.237943	−0.118972	−	0.992898i	$-0.537960\pi$
$613$	−5.89120	−0.237943	−0.118972	+	0.992898i	$0.537960\pi$
$614$	2.94125	0.118699
$615$	0	0
$616$	7.51118	0.302634
$617$	35.2179	1.41782	0.708909	−	0.705300i	$-0.249188\pi$
$617$	35.2179	1.41782	0.708909	+	0.705300i	$0.249188\pi$
$618$	0	0
$619$	−32.8288	−1.31950	−0.659750	−	0.751485i	$-0.729338\pi$
$619$	−32.8288	−1.31950	−0.659750	+	0.751485i	$0.729338\pi$
$620$	−6.54562	−0.262878
$621$	0	0
$622$	−0.287805	−0.0115399
$623$	−3.43744	−0.137718
$624$	0	0
$625$	19.0889	0.763555
$626$	4.24402	0.169625
$627$	0	0
$628$	−34.3262	−1.36976
$629$	0	0
$630$	0	0
$631$	10.7057	0.426186	0.213093	−	0.977032i	$-0.431646\pi$
$631$	10.7057	0.426186	0.213093	+	0.977032i	$0.431646\pi$
$632$	−2.08283	−0.0828506
$633$	0	0
$634$	3.35603	0.133285
$635$	6.90620	0.274064
$636$	0	0
$637$	−10.0563	−0.398446
$638$	−10.5456	−0.417505
$639$	0	0
$640$	4.24980	0.167988
$641$	36.9437	1.45919	0.729593	−	0.683881i	$-0.239709\pi$
$641$	36.9437	1.45919	0.729593	+	0.683881i	$0.239709\pi$
$642$	0	0
$643$	−39.3137	−1.55038	−0.775191	−	0.631727i	$-0.782346\pi$
$643$	−39.3137	−1.55038	−0.775191	+	0.631727i	$0.782346\pi$
$644$	7.15511	0.281951
$645$	0	0
$646$	0	0
$647$	14.8806	0.585016	0.292508	−	0.956263i	$-0.405510\pi$
$647$	14.8806	0.585016	0.292508	+	0.956263i	$0.405510\pi$
$648$	0	0
$649$	−50.0632	−1.96515
$650$	2.55880	0.100364
$651$	0	0
$652$	−32.3611	−1.26736
$653$	−24.2908	−0.950571	−0.475285	−	0.879832i	$-0.657655\pi$
$653$	−24.2908	−0.950571	−0.475285	+	0.879832i	$0.657655\pi$
$654$	0	0
$655$	−0.449444	−0.0175612
$656$	−25.6534	−1.00160
$657$	0	0
$658$	−3.11123	−0.121289
$659$	9.14192	0.356119	0.178059	−	0.984020i	$-0.443018\pi$
$659$	9.14192	0.356119	0.178059	+	0.984020i	$0.443018\pi$
$660$	0	0
$661$	−16.7951	−0.653253	−0.326627	−	0.945153i	$-0.605912\pi$
$661$	−16.7951	−0.653253	−0.326627	+	0.945153i	$0.605912\pi$
$662$	5.03861	0.195831
$663$	0	0
$664$	11.7257	0.455046
$665$	1.04568	0.0405498
$666$	0	0
$667$	−20.3456	−0.787787
$668$	−27.7447	−1.07347
$669$	0	0
$670$	−1.08899	−0.0420714
$671$	−14.7025	−0.567585
$672$	0	0
$673$	18.6313	0.718186	0.359093	−	0.933302i	$-0.383086\pi$
$673$	18.6313	0.718186	0.359093	+	0.933302i	$0.383086\pi$
$674$	0.359214	0.0138364
$675$	0	0
$676$	13.1057	0.504067
$677$	−10.8010	−0.415117	−0.207559	−	0.978223i	$-0.566552\pi$
$677$	−10.8010	−0.415117	−0.207559	+	0.978223i	$0.566552\pi$
$678$	0	0
$679$	−5.25690	−0.201741
$680$	0	0
$681$	0	0
$682$	5.80002	0.222094
$683$	22.2199	0.850221	0.425111	−	0.905141i	$-0.360235\pi$
$683$	22.2199	0.850221	0.425111	+	0.905141i	$0.360235\pi$
$684$	0	0
$685$	−7.83571	−0.299387
$686$	−4.22929	−0.161475
$687$	0	0
$688$	26.5017	1.01037
$689$	16.1512	0.615313
$690$	0	0
$691$	−38.5413	−1.46618	−0.733090	−	0.680132i	$-0.761923\pi$
$691$	−38.5413	−1.46618	−0.733090	+	0.680132i	$0.761923\pi$
$692$	−3.69315	−0.140392
$693$	0	0
$694$	−3.41300	−0.129556
$695$	−8.49244	−0.322137
$696$	0	0
$697$	0	0
$698$	3.35702	0.127065
$699$	0	0
$700$	−15.4922	−0.585551
$701$	−18.0843	−0.683034	−0.341517	−	0.939876i	$-0.610941\pi$
$701$	−18.0843	−0.683034	−0.341517	+	0.939876i	$0.610941\pi$
$702$	0	0
$703$	−8.06805	−0.304292
$704$	33.8593	1.27612
$705$	0	0
$706$	−6.94307	−0.261306
$707$	−32.0550	−1.20555
$708$	0	0
$709$	52.2614	1.96272	0.981359	−	0.192185i	$-0.0615573\pi$
$709$	52.2614	1.96272	0.981359	+	0.192185i	$0.0615573\pi$
$710$	−0.0543053	−0.00203804
$711$	0	0
$712$	1.74572	0.0654236
$713$	11.1900	0.419068
$714$	0	0
$715$	−7.89620	−0.295301
$716$	−43.3955	−1.62177
$717$	0	0
$718$	0.605478	0.0225962
$719$	−2.25831	−0.0842206	−0.0421103	−	0.999113i	$-0.513408\pi$
$719$	−2.25831	−0.0842206	−0.0421103	+	0.999113i	$0.513408\pi$
$720$	0	0
$721$	−5.86808	−0.218539
$722$	4.02084	0.149640
$723$	0	0
$724$	22.6550	0.841966
$725$	44.0523	1.63606
$726$	0	0
$727$	−39.5601	−1.46720	−0.733601	−	0.679581i	$-0.762162\pi$
$727$	−39.5601	−1.46720	−0.733601	+	0.679581i	$0.762162\pi$
$728$	−3.80252	−0.140931
$729$	0	0
$730$	−0.921132	−0.0340926
$731$	0	0
$732$	0	0
$733$	−13.5137	−0.499139	−0.249570	−	0.968357i	$-0.580289\pi$
$733$	−13.5137	−0.499139	−0.249570	+	0.968357i	$0.580289\pi$
$734$	4.09977	0.151325
$735$	0	0
$736$	−5.47334	−0.201750
$737$	−38.1262	−1.40440
$738$	0	0
$739$	−10.7282	−0.394642	−0.197321	−	0.980339i	$-0.563224\pi$
$739$	−10.7282	−0.394642	−0.197321	+	0.980339i	$0.563224\pi$
$740$	−10.5357	−0.387302
$741$	0	0
$742$	2.47493	0.0908575
$743$	43.9921	1.61392	0.806958	−	0.590609i	$-0.201113\pi$
$743$	43.9921	1.61392	0.806958	+	0.590609i	$0.201113\pi$
$744$	0	0
$745$	−0.227128	−0.00832131
$746$	−5.42257	−0.198534
$747$	0	0
$748$	0	0
$749$	−22.7343	−0.830695
$750$	0	0
$751$	−12.5047	−0.456304	−0.228152	−	0.973626i	$-0.573268\pi$
$751$	−12.5047	−0.456304	−0.228152	+	0.973626i	$0.573268\pi$
$752$	−30.0250	−1.09490
$753$	0	0
$754$	5.33870	0.194424
$755$	5.81240	0.211535
$756$	0	0
$757$	−35.8474	−1.30290	−0.651449	−	0.758693i	$-0.725838\pi$
$757$	−35.8474	−1.30290	−0.651449	+	0.758693i	$0.725838\pi$
$758$	1.30883	0.0475390
$759$	0	0
$760$	−0.531055	−0.0192634
$761$	23.4468	0.849944	0.424972	−	0.905206i	$-0.360284\pi$
$761$	23.4468	0.849944	0.424972	+	0.905206i	$0.360284\pi$
$762$	0	0
$763$	30.0568	1.08813
$764$	12.9388	0.468108
$765$	0	0
$766$	6.83807	0.247070
$767$	25.3444	0.915133
$768$	0	0
$769$	22.8938	0.825573	0.412786	−	0.910828i	$-0.364556\pi$
$769$	22.8938	0.825573	0.412786	+	0.910828i	$0.364556\pi$
$770$	−1.20997	−0.0436044
$771$	0	0
$772$	−5.69133	−0.204835
$773$	−34.1287	−1.22753	−0.613763	−	0.789491i	$-0.710345\pi$
$773$	−34.1287	−1.22753	−0.613763	+	0.789491i	$0.710345\pi$
$774$	0	0
$775$	−24.2285	−0.870313
$776$	2.66974	0.0958382
$777$	0	0
$778$	4.33815	0.155530
$779$	6.57999	0.235753
$780$	0	0
$781$	−1.90126	−0.0680325
$782$	0	0
$783$	0	0
$784$	−14.8712	−0.531115
$785$	11.1991	0.399714
$786$	0	0
$787$	13.1730	0.469568	0.234784	−	0.972048i	$-0.424562\pi$
$787$	13.1730	0.469568	0.234784	+	0.972048i	$0.424562\pi$
$788$	8.84644	0.315141
$789$	0	0
$790$	0.335522	0.0119373
$791$	1.34134	0.0476926
$792$	0	0
$793$	7.44313	0.264313
$794$	0.200923	0.00713049
$795$	0	0
$796$	−4.79911	−0.170100
$797$	−36.3506	−1.28761	−0.643803	−	0.765191i	$-0.722644\pi$
$797$	−36.3506	−1.28761	−0.643803	+	0.765191i	$0.722644\pi$
$798$	0	0
$799$	0	0
$800$	11.8509	0.418991
$801$	0	0
$802$	0.281040	0.00992388
$803$	−32.2494	−1.13806
$804$	0	0
$805$	−2.33440	−0.0822767
$806$	−2.93625	−0.103425
$807$	0	0
$808$	16.2793	0.572703
$809$	45.1267	1.58657	0.793285	−	0.608851i	$-0.208369\pi$
$809$	45.1267	1.58657	0.793285	+	0.608851i	$0.208369\pi$
$810$	0	0
$811$	−3.32815	−0.116867	−0.0584336	−	0.998291i	$-0.518611\pi$
$811$	−3.32815	−0.116867	−0.0584336	+	0.998291i	$0.518611\pi$
$812$	−32.3232	−1.13432
$813$	0	0
$814$	9.33565	0.327214
$815$	10.5580	0.369830
$816$	0	0
$817$	−6.79759	−0.237817
$818$	−6.36244	−0.222458
$819$	0	0
$820$	8.59255	0.300065
$821$	7.46983	0.260699	0.130349	−	0.991468i	$-0.458390\pi$
$821$	7.46983	0.260699	0.130349	+	0.991468i	$0.458390\pi$
$822$	0	0
$823$	54.1834	1.88871	0.944357	−	0.328923i	$-0.106686\pi$
$823$	54.1834	1.88871	0.944357	+	0.328923i	$0.106686\pi$
$824$	2.98013	0.103818
$825$	0	0
$826$	3.88364	0.135129
$827$	4.95063	0.172150	0.0860752	−	0.996289i	$-0.472567\pi$
$827$	4.95063	0.172150	0.0860752	+	0.996289i	$0.472567\pi$
$828$	0	0
$829$	−0.0762440	−0.00264806	−0.00132403	−	0.999999i	$-0.500421\pi$
$829$	−0.0762440	−0.00264806	−0.00132403	+	0.999999i	$0.500421\pi$
$830$	−1.88889	−0.0655643
$831$	0	0
$832$	−17.1412	−0.594265
$833$	0	0
$834$	0	0
$835$	9.05187	0.313253
$836$	−9.18010	−0.317501
$837$	0	0
$838$	5.32328	0.183890
$839$	36.4479	1.25832	0.629160	−	0.777276i	$-0.283399\pi$
$839$	36.4479	1.25832	0.629160	+	0.777276i	$0.283399\pi$
$840$	0	0
$841$	62.9113	2.16935
$842$	2.78433	0.0959545
$843$	0	0
$844$	−38.8249	−1.33641
$845$	−4.27583	−0.147093
$846$	0	0
$847$	−23.3491	−0.802283
$848$	23.8843	0.820191
$849$	0	0
$850$	0	0
$851$	18.0112	0.617418
$852$	0	0
$853$	39.9684	1.36849	0.684245	−	0.729252i	$-0.260132\pi$
$853$	39.9684	1.36849	0.684245	+	0.729252i	$0.260132\pi$
$854$	1.14055	0.0390287
$855$	0	0
$856$	11.5457	0.394625
$857$	2.95962	0.101099	0.0505493	−	0.998722i	$-0.483903\pi$
$857$	2.95962	0.101099	0.0505493	+	0.998722i	$0.483903\pi$
$858$	0	0
$859$	−22.4494	−0.765963	−0.382981	−	0.923756i	$-0.625103\pi$
$859$	−22.4494	−0.765963	−0.382981	+	0.923756i	$0.625103\pi$
$860$	−8.87670	−0.302693
$861$	0	0
$862$	−3.92673	−0.133745
$863$	27.8981	0.949661	0.474831	−	0.880077i	$-0.342509\pi$
$863$	27.8981	0.949661	0.474831	+	0.880077i	$0.342509\pi$
$864$	0	0
$865$	1.20491	0.0409682
$866$	3.11236	0.105762
$867$	0	0
$868$	17.7775	0.603409
$869$	11.7468	0.398484
$870$	0	0
$871$	19.3013	0.654001
$872$	−15.2645	−0.516921
$873$	0	0
$874$	0.448256	0.0151625
$875$	10.5544	0.356803
$876$	0	0
$877$	20.6961	0.698858	0.349429	−	0.936963i	$-0.386376\pi$
$877$	20.6961	0.698858	0.349429	+	0.936963i	$0.386376\pi$
$878$	2.57165	0.0867889
$879$	0	0
$880$	−11.6768	−0.393627
$881$	22.2399	0.749282	0.374641	−	0.927170i	$-0.377766\pi$
$881$	22.2399	0.749282	0.374641	+	0.927170i	$0.377766\pi$
$882$	0	0
$883$	4.23253	0.142436	0.0712180	−	0.997461i	$-0.477311\pi$
$883$	4.23253	0.142436	0.0712180	+	0.997461i	$0.477311\pi$
$884$	0	0
$885$	0	0
$886$	−7.91388	−0.265872
$887$	36.3047	1.21899	0.609496	−	0.792789i	$-0.291372\pi$
$887$	36.3047	1.21899	0.609496	+	0.792789i	$0.291372\pi$
$888$	0	0
$889$	−18.7568	−0.629084
$890$	−0.281217	−0.00942642
$891$	0	0
$892$	−28.0171	−0.938081
$893$	7.70129	0.257714
$894$	0	0
$895$	14.1580	0.473251
$896$	−11.5422	−0.385598
$897$	0	0
$898$	−4.92066	−0.164205
$899$	−50.5506	−1.68596
$900$	0	0
$901$	0	0
$902$	−7.61380	−0.253512
$903$	0	0
$904$	−0.681206	−0.0226566
$905$	−7.39133	−0.245696
$906$	0	0
$907$	24.3718	0.809251	0.404626	−	0.914482i	$-0.367402\pi$
$907$	24.3718	0.809251	0.404626	+	0.914482i	$0.367402\pi$
$908$	−21.2119	−0.703942
$909$	0	0
$910$	0.612546	0.0203057
$911$	−26.9178	−0.891826	−0.445913	−	0.895076i	$-0.647121\pi$
$911$	−26.9178	−0.891826	−0.445913	+	0.895076i	$0.647121\pi$
$912$	0	0
$913$	−66.1312	−2.18862
$914$	−2.20110	−0.0728059
$915$	0	0
$916$	−37.0425	−1.22392
$917$	1.22066	0.0403099
$918$	0	0
$919$	−23.8000	−0.785088	−0.392544	−	0.919733i	$-0.628405\pi$
$919$	−23.8000	−0.785088	−0.392544	+	0.919733i	$0.628405\pi$
$920$	1.18553	0.0390859
$921$	0	0
$922$	−2.13830	−0.0704210
$923$	0.962511	0.0316814
$924$	0	0
$925$	−38.9979	−1.28224
$926$	−3.39983	−0.111725
$927$	0	0
$928$	24.7258	0.811663
$929$	5.82742	0.191191	0.0955957	−	0.995420i	$-0.469524\pi$
$929$	5.82742	0.191191	0.0955957	+	0.995420i	$0.469524\pi$
$930$	0	0
$931$	3.81440	0.125012
$932$	13.8120	0.452427
$933$	0	0
$934$	−4.95819	−0.162237
$935$	0	0
$936$	0	0
$937$	55.4424	1.81123	0.905613	−	0.424106i	$-0.139411\pi$
$937$	55.4424	1.81123	0.905613	+	0.424106i	$0.139411\pi$
$938$	2.95764	0.0965702
$939$	0	0
$940$	10.0568	0.328017
$941$	21.1696	0.690109	0.345054	−	0.938583i	$-0.387860\pi$
$941$	21.1696	0.690109	0.345054	+	0.938583i	$0.387860\pi$
$942$	0	0
$943$	−14.6893	−0.478349
$944$	37.4791	1.21984
$945$	0	0
$946$	7.86558	0.255732
$947$	−37.5831	−1.22129	−0.610643	−	0.791906i	$-0.709089\pi$
$947$	−37.5831	−1.22129	−0.610643	+	0.791906i	$0.709089\pi$
$948$	0	0
$949$	16.3262	0.529971
$950$	−0.970563	−0.0314892
$951$	0	0
$952$	0	0
$953$	−21.2794	−0.689307	−0.344654	−	0.938730i	$-0.612004\pi$
$953$	−21.2794	−0.689307	−0.344654	+	0.938730i	$0.612004\pi$
$954$	0	0
$955$	−4.22134	−0.136599
$956$	−10.3163	−0.333654
$957$	0	0
$958$	−3.45666	−0.111680
$959$	21.2813	0.687210
$960$	0	0
$961$	−3.19748	−0.103144
$962$	−4.72616	−0.152377
$963$	0	0
$964$	−11.3103	−0.364279
$965$	1.85683	0.0597734
$966$	0	0
$967$	−26.2320	−0.843563	−0.421782	−	0.906697i	$-0.638595\pi$
$967$	−26.2320	−0.843563	−0.421782	+	0.906697i	$0.638595\pi$
$968$	11.8579	0.381128
$969$	0	0
$970$	−0.430067	−0.0138086
$971$	20.8243	0.668285	0.334142	−	0.942523i	$-0.391553\pi$
$971$	20.8243	0.668285	0.334142	+	0.942523i	$0.391553\pi$
$972$	0	0
$973$	23.0650	0.739429
$974$	0.00658834	0.000211104 0
$975$	0	0
$976$	11.0069	0.352321
$977$	−16.2900	−0.521162	−0.260581	−	0.965452i	$-0.583914\pi$
$977$	−16.2900	−0.521162	−0.260581	+	0.965452i	$0.583914\pi$
$978$	0	0
$979$	−9.84558	−0.314666
$980$	4.98108	0.159115
$981$	0	0
$982$	1.48187	0.0472884
$983$	−0.931671	−0.0297157	−0.0148578	−	0.999890i	$-0.504730\pi$
$983$	−0.931671	−0.0297157	−0.0148578	+	0.999890i	$0.504730\pi$
$984$	0	0
$985$	−2.88620	−0.0919621
$986$	0	0
$987$	0	0
$988$	4.64741	0.147854
$989$	15.1750	0.482538
$990$	0	0
$991$	−21.6972	−0.689234	−0.344617	−	0.938743i	$-0.611991\pi$
$991$	−21.6972	−0.689234	−0.344617	+	0.938743i	$0.611991\pi$
$992$	−13.5990	−0.431769
$993$	0	0
$994$	0.147490	0.00467810
$995$	1.56574	0.0496373
$996$	0	0
$997$	−3.22709	−0.102203	−0.0511015	−	0.998693i	$-0.516273\pi$
$997$	−3.22709	−0.102203	−0.0511015	+	0.998693i	$0.516273\pi$
$998$	4.14317	0.131150
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2601.2.a.be.1.2		4
3.2	odd	2		867.2.a.l.1.3		4
17.8	even	8		153.2.f.b.64.3		8
17.15	even	8		153.2.f.b.55.2		8
17.16	even	2		2601.2.a.bf.1.2		4
51.2	odd	8		867.2.e.g.616.3		8
51.5	even	16		867.2.h.k.688.1		16
51.8	odd	8		51.2.e.a.13.2	yes	8
51.11	even	16		867.2.h.i.733.3		16
51.14	even	16		867.2.h.i.757.3		16
51.20	even	16		867.2.h.i.757.4		16
51.23	even	16		867.2.h.i.733.4		16
51.26	odd	8		867.2.e.g.829.2		8
51.29	even	16		867.2.h.k.688.2		16
51.32	odd	8		51.2.e.a.4.3	✓	8
51.38	odd	4		867.2.d.f.577.3		8
51.41	even	16		867.2.h.k.712.1		16
51.44	even	16		867.2.h.k.712.2		16
51.47	odd	4		867.2.d.f.577.4		8
51.50	odd	2		867.2.a.k.1.3		4
68.15	odd	8		2448.2.be.x.1585.3		8
68.59	odd	8		2448.2.be.x.1441.3		8
204.59	even	8		816.2.bd.e.625.3		8
204.83	even	8		816.2.bd.e.769.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.e.a.4.3	✓	8	51.32	odd	8
51.2.e.a.13.2	yes	8	51.8	odd	8
153.2.f.b.55.2		8	17.15	even	8
153.2.f.b.64.3		8	17.8	even	8
816.2.bd.e.625.3		8	204.59	even	8
816.2.bd.e.769.3		8	204.83	even	8
867.2.a.k.1.3		4	51.50	odd	2
867.2.a.l.1.3		4	3.2	odd	2
867.2.d.f.577.3		8	51.38	odd	4
867.2.d.f.577.4		8	51.47	odd	4
867.2.e.g.616.3		8	51.2	odd	8
867.2.e.g.829.2		8	51.26	odd	8
867.2.h.i.733.3		16	51.11	even	16
867.2.h.i.733.4		16	51.23	even	16
867.2.h.i.757.3		16	51.14	even	16
867.2.h.i.757.4		16	51.20	even	16
867.2.h.k.688.1		16	51.5	even	16
867.2.h.k.688.2		16	51.29	even	16
867.2.h.k.712.1		16	51.41	even	16
867.2.h.k.712.2		16	51.44	even	16
2448.2.be.x.1441.3		8	68.59	odd	8
2448.2.be.x.1585.3		8	68.15	odd	8
2601.2.a.be.1.2		4	1.1	even	1	trivial
2601.2.a.bf.1.2		4	17.16	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2601 = 3^{2} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2601.a (trivial)

\(f(q)\)	\(=\)	\(q-0.222191 q^{2} -1.95063 q^{4} +0.636405 q^{5} -1.72844 q^{7} +0.877796 q^{8} +O(q^{10})\)	\(q-0.222191 q^{2} -1.95063 q^{4} +0.636405 q^{5} -1.72844 q^{7} +0.877796 q^{8} -0.141404 q^{10} -4.95063 q^{11} +2.50625 q^{13} +0.384044 q^{14} +3.70622 q^{16} -0.950631 q^{19} -1.24139 q^{20} +1.09999 q^{22} +2.12220 q^{23} -4.59499 q^{25} -0.556867 q^{26} +3.37155 q^{28} -9.58704 q^{29} +5.27281 q^{31} -2.57908 q^{32} -1.09999 q^{35} +8.48705 q^{37} +0.211222 q^{38} +0.558634 q^{40} -6.92171 q^{41} +7.15061 q^{43} +9.65685 q^{44} -0.471535 q^{46} -8.10124 q^{47} -4.01250 q^{49} +1.02097 q^{50} -4.88877 q^{52} +6.44438 q^{53} -3.15061 q^{55} -1.51722 q^{56} +2.13016 q^{58} +10.1125 q^{59} +2.96983 q^{61} -1.17157 q^{62} -6.83940 q^{64} +1.59499 q^{65} +7.70129 q^{67} +0.244408 q^{70} +0.384044 q^{71} +6.51420 q^{73} -1.88575 q^{74} +1.85433 q^{76} +8.55687 q^{77} -2.37280 q^{79} +2.35866 q^{80} +1.53794 q^{82} +13.3581 q^{83} -1.58880 q^{86} -4.34564 q^{88} +1.98875 q^{89} -4.33190 q^{91} -4.13964 q^{92} +1.80002 q^{94} -0.604986 q^{95} +3.04142 q^{97} +0.891542 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 6 q^{4} - 6 q^{5} + 4 q^{7} + 6 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 + 6 * q^4 - 6 * q^5 + 4 * q^7 + 6 * q^8	\( 4 q + 2 q^{2} + 6 q^{4} - 6 q^{5} + 4 q^{7} + 6 q^{8} - 12 q^{10} - 6 q^{11} + 2 q^{13} - 4 q^{14} + 6 q^{16} + 10 q^{19} - 16 q^{20} + 4 q^{22} + 6 q^{23} + 2 q^{25} + 20 q^{26} + 24 q^{28} - 16 q^{29} + 4 q^{31} + 14 q^{32} - 4 q^{35} + 12 q^{37} + 12 q^{38} - 8 q^{40} + 14 q^{41} + 14 q^{43} + 16 q^{44} - 12 q^{46} - 4 q^{47} + 30 q^{50} - 8 q^{52} + 20 q^{53} + 2 q^{55} + 16 q^{56} + 8 q^{58} + 24 q^{59} + 12 q^{61} - 16 q^{62} - 2 q^{64} - 14 q^{65} + 4 q^{67} - 4 q^{70} - 4 q^{71} + 20 q^{73} - 12 q^{74} + 40 q^{76} + 12 q^{77} + 8 q^{79} - 4 q^{82} + 4 q^{83} + 4 q^{86} + 16 q^{88} - 4 q^{89} - 28 q^{91} - 16 q^{92} + 8 q^{94} - 22 q^{95} + 24 q^{97} - 38 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 + 6 * q^4 - 6 * q^5 + 4 * q^7 + 6 * q^8 - 12 * q^10 - 6 * q^11 + 2 * q^13 - 4 * q^14 + 6 * q^16 + 10 * q^19 - 16 * q^20 + 4 * q^22 + 6 * q^23 + 2 * q^25 + 20 * q^26 + 24 * q^28 - 16 * q^29 + 4 * q^31 + 14 * q^32 - 4 * q^35 + 12 * q^37 + 12 * q^38 - 8 * q^40 + 14 * q^41 + 14 * q^43 + 16 * q^44 - 12 * q^46 - 4 * q^47 + 30 * q^50 - 8 * q^52 + 20 * q^53 + 2 * q^55 + 16 * q^56 + 8 * q^58 + 24 * q^59 + 12 * q^61 - 16 * q^62 - 2 * q^64 - 14 * q^65 + 4 * q^67 - 4 * q^70 - 4 * q^71 + 20 * q^73 - 12 * q^74 + 40 * q^76 + 12 * q^77 + 8 * q^79 - 4 * q^82 + 4 * q^83 + 4 * q^86 + 16 * q^88 - 4 * q^89 - 28 * q^91 - 16 * q^92 + 8 * q^94 - 22 * q^95 + 24 * q^97 - 38 * q^98

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