LMFDB - Embedded newform 6525.2.a.bx.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6525,2,Mod(1,6525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6525, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6525.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6525 = 3^{2} \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6525.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:	$52.1023873189$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 2x^{6} - 10x^{5} + 19x^{4} + 24x^{3} - 44x^{2} - 3x + 14 $ x^7 - 2x^6 - 10x^5 + 19x^4 + 24x^3 - 44x^2 - 3x + 14
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 2175)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$2.66356$ of defining polynomial
Character	$\chi$	$=$	6525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.66356 q^{2} +5.09453 q^{4} +0.0170416 q^{7} +8.24244 q^{8} +O(q^{10})$	$q+2.66356 q^{2} +5.09453 q^{4} +0.0170416 q^{7} +8.24244 q^{8} -1.70990 q^{11} +4.69566 q^{13} +0.0453913 q^{14} +11.7651 q^{16} -3.91494 q^{17} +6.02411 q^{19} -4.55440 q^{22} +4.82786 q^{23} +12.5071 q^{26} +0.0868190 q^{28} +1.00000 q^{29} +1.33709 q^{31} +14.8522 q^{32} -10.4277 q^{34} +8.18905 q^{37} +16.0455 q^{38} -8.36721 q^{41} -3.72560 q^{43} -8.71111 q^{44} +12.8593 q^{46} -5.36826 q^{47} -6.99971 q^{49} +23.9222 q^{52} -7.21637 q^{53} +0.140465 q^{56} +2.66356 q^{58} +8.65422 q^{59} +5.72637 q^{61} +3.56141 q^{62} +16.0294 q^{64} -3.87486 q^{67} -19.9448 q^{68} +4.32991 q^{71} +1.78245 q^{73} +21.8120 q^{74} +30.6900 q^{76} -0.0291394 q^{77} +0.233544 q^{79} -22.2865 q^{82} -6.15497 q^{83} -9.92334 q^{86} -14.0937 q^{88} +12.4053 q^{89} +0.0800217 q^{91} +24.5957 q^{92} -14.2986 q^{94} +19.2918 q^{97} -18.6441 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 2 q^{2} + 10 q^{4} + q^{7} + 3 q^{8}+O(q^{10}) $ 7 * q + 2 * q^2 + 10 * q^4 + q^7 + 3 * q^8	$ 7 q + 2 q^{2} + 10 q^{4} + q^{7} + 3 q^{8} - 4 q^{11} + q^{13} - 15 q^{14} + 12 q^{16} + 8 q^{17} + 15 q^{19} - 3 q^{22} + 14 q^{23} - 6 q^{26} + 24 q^{28} + 7 q^{29} + 5 q^{31} + 18 q^{32} + 7 q^{34} + 6 q^{37} - 18 q^{38} - 22 q^{41} + 19 q^{43} - 15 q^{44} - 4 q^{46} + 22 q^{47} + 12 q^{49} - 11 q^{52} + 10 q^{53} - 14 q^{56} + 2 q^{58} - 6 q^{59} + 23 q^{61} + 40 q^{62} + 5 q^{64} + 13 q^{67} - 7 q^{68} - 26 q^{71} + 24 q^{73} + 10 q^{74} + 46 q^{76} + 4 q^{77} + 14 q^{79} - 16 q^{82} + 10 q^{83} - 44 q^{86} + 66 q^{88} - 14 q^{89} + 13 q^{91} + 58 q^{92} - 3 q^{94} + 31 q^{97} - 59 q^{98}+O(q^{100}) $ 7 * q + 2 * q^2 + 10 * q^4 + q^7 + 3 * q^8 - 4 * q^11 + q^13 - 15 * q^14 + 12 * q^16 + 8 * q^17 + 15 * q^19 - 3 * q^22 + 14 * q^23 - 6 * q^26 + 24 * q^28 + 7 * q^29 + 5 * q^31 + 18 * q^32 + 7 * q^34 + 6 * q^37 - 18 * q^38 - 22 * q^41 + 19 * q^43 - 15 * q^44 - 4 * q^46 + 22 * q^47 + 12 * q^49 - 11 * q^52 + 10 * q^53 - 14 * q^56 + 2 * q^58 - 6 * q^59 + 23 * q^61 + 40 * q^62 + 5 * q^64 + 13 * q^67 - 7 * q^68 - 26 * q^71 + 24 * q^73 + 10 * q^74 + 46 * q^76 + 4 * q^77 + 14 * q^79 - 16 * q^82 + 10 * q^83 - 44 * q^86 + 66 * q^88 - 14 * q^89 + 13 * q^91 + 58 * q^92 - 3 * q^94 + 31 * q^97 - 59 * 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 $

$2$	2.66356	1.88342	0.941709	−	0.336429i	$-0.109219\pi$
$2$	2.66356	1.88342	0.941709	+	0.336429i	$0.109219\pi$
$3$	0	0
$3$	0	0
$4$	5.09453	2.54726
$5$	0	0
$5$	0	0
$6$	0	0
$7$	0.0170416	0.00644113	0.00322057	−	0.999995i	$-0.498975\pi$
$7$	0.0170416	0.00644113	0.00322057	+	0.999995i	$0.498975\pi$
$8$	8.24244	2.91414
$9$	0	0
$10$	0	0
$11$	−1.70990	−0.515553	−0.257777	−	0.966205i	$-0.582990\pi$
$11$	−1.70990	−0.515553	−0.257777	+	0.966205i	$0.582990\pi$
$12$	0	0
$13$	4.69566	1.30234	0.651171	−	0.758931i	$-0.274278\pi$
$13$	4.69566	1.30234	0.651171	+	0.758931i	$0.274278\pi$
$14$	0.0453913	0.0121313
$15$	0	0
$16$	11.7651	2.94129
$17$	−3.91494	−0.949513	−0.474757	−	0.880117i	$-0.657464\pi$
$17$	−3.91494	−0.949513	−0.474757	+	0.880117i	$0.657464\pi$
$18$	0	0
$19$	6.02411	1.38202	0.691012	−	0.722843i	$-0.257165\pi$
$19$	6.02411	1.38202	0.691012	+	0.722843i	$0.257165\pi$
$20$	0	0
$21$	0	0
$22$	−4.55440	−0.971002
$23$	4.82786	1.00668	0.503339	−	0.864089i	$-0.332105\pi$
$23$	4.82786	1.00668	0.503339	+	0.864089i	$0.332105\pi$
$24$	0	0
$25$	0	0
$26$	12.5071	2.45285
$27$	0	0
$28$	0.0868190	0.0164073
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0	0
$31$	1.33709	0.240148	0.120074	−	0.992765i	$-0.461687\pi$
$31$	1.33709	0.240148	0.120074	+	0.992765i	$0.461687\pi$
$32$	14.8522	2.62553
$33$	0	0
$34$	−10.4277	−1.78833
$35$	0	0
$36$	0	0
$37$	8.18905	1.34627	0.673136	−	0.739519i	$-0.264947\pi$
$37$	8.18905	1.34627	0.673136	+	0.739519i	$0.264947\pi$
$38$	16.0455	2.60293
$39$	0	0
$40$	0	0
$41$	−8.36721	−1.30674	−0.653369	−	0.757039i	$-0.726645\pi$
$41$	−8.36721	−1.30674	−0.653369	+	0.757039i	$0.726645\pi$
$42$	0	0
$43$	−3.72560	−0.568149	−0.284074	−	0.958802i	$-0.591686\pi$
$43$	−3.72560	−0.568149	−0.284074	+	0.958802i	$0.591686\pi$
$44$	−8.71111	−1.31325
$45$	0	0
$46$	12.8593	1.89600
$47$	−5.36826	−0.783041	−0.391520	−	0.920169i	$-0.628051\pi$
$47$	−5.36826	−0.783041	−0.391520	+	0.920169i	$0.628051\pi$
$48$	0	0
$49$	−6.99971	−0.999959
$50$	0	0
$51$	0	0
$52$	23.9222	3.31741
$53$	−7.21637	−0.991245	−0.495622	−	0.868538i	$-0.665060\pi$
$53$	−7.21637	−0.991245	−0.495622	+	0.868538i	$0.665060\pi$
$54$	0	0
$55$	0	0
$56$	0.140465	0.0187704
$57$	0	0
$58$	2.66356	0.349742
$59$	8.65422	1.12668	0.563342	−	0.826224i	$-0.309515\pi$
$59$	8.65422	1.12668	0.563342	+	0.826224i	$0.309515\pi$
$60$	0	0
$61$	5.72637	0.733187	0.366594	−	0.930381i	$-0.380524\pi$
$61$	5.72637	0.733187	0.366594	+	0.930381i	$0.380524\pi$
$62$	3.56141	0.452299
$63$	0	0
$64$	16.0294	2.00368
$65$	0	0
$66$	0	0
$67$	−3.87486	−0.473390	−0.236695	−	0.971584i	$-0.576064\pi$
$67$	−3.87486	−0.473390	−0.236695	+	0.971584i	$0.576064\pi$
$68$	−19.9448	−2.41866
$69$	0	0
$70$	0	0
$71$	4.32991	0.513866	0.256933	−	0.966429i	$-0.417288\pi$
$71$	4.32991	0.513866	0.256933	+	0.966429i	$0.417288\pi$
$72$	0	0
$73$	1.78245	0.208620	0.104310	−	0.994545i	$-0.466737\pi$
$73$	1.78245	0.208620	0.104310	+	0.994545i	$0.466737\pi$
$74$	21.8120	2.53559
$75$	0	0
$76$	30.6900	3.52038
$77$	−0.0291394	−0.00332075
$78$	0	0
$79$	0.233544	0.0262757	0.0131379	−	0.999914i	$-0.495818\pi$
$79$	0.233544	0.0262757	0.0131379	+	0.999914i	$0.495818\pi$
$80$	0	0
$81$	0	0
$82$	−22.2865	−2.46114
$83$	−6.15497	−0.675596	−0.337798	−	0.941219i	$-0.609682\pi$
$83$	−6.15497	−0.675596	−0.337798	+	0.941219i	$0.609682\pi$
$84$	0	0
$85$	0	0
$86$	−9.92334	−1.07006
$87$	0	0
$88$	−14.0937	−1.50240
$89$	12.4053	1.31496	0.657478	−	0.753474i	$-0.271623\pi$
$89$	12.4053	1.31496	0.657478	+	0.753474i	$0.271623\pi$
$90$	0	0
$91$	0.0800217	0.00838855
$92$	24.5957	2.56427
$93$	0	0
$94$	−14.2986	−1.47479
$95$	0	0
$96$	0	0
$97$	19.2918	1.95879	0.979395	−	0.201954i	$-0.0647293\pi$
$97$	19.2918	1.95879	0.979395	+	0.201954i	$0.0647293\pi$
$98$	−18.6441	−1.88334
$99$	0	0
$100$	0	0
$101$	8.74987	0.870644	0.435322	−	0.900275i	$-0.356634\pi$
$101$	8.74987	0.870644	0.435322	+	0.900275i	$0.356634\pi$
$102$	0	0
$103$	−10.9615	−1.08007	−0.540036	−	0.841642i	$-0.681589\pi$
$103$	−10.9615	−1.08007	−0.540036	+	0.841642i	$0.681589\pi$
$104$	38.7037	3.79521
$105$	0	0
$106$	−19.2212	−1.86693
$107$	15.8139	1.52879	0.764393	−	0.644750i	$-0.223039\pi$
$107$	15.8139	1.52879	0.764393	+	0.644750i	$0.223039\pi$
$108$	0	0
$109$	−20.2768	−1.94216	−0.971082	−	0.238747i	$-0.923263\pi$
$109$	−20.2768	−1.94216	−0.971082	+	0.238747i	$0.923263\pi$
$110$	0	0
$111$	0	0
$112$	0.200497	0.0189452
$113$	8.86901	0.834326	0.417163	−	0.908832i	$-0.363024\pi$
$113$	8.86901	0.834326	0.417163	+	0.908832i	$0.363024\pi$
$114$	0	0
$115$	0	0
$116$	5.09453	0.473015
$117$	0	0
$118$	23.0510	2.12202
$119$	−0.0667170	−0.00611594
$120$	0	0
$121$	−8.07625	−0.734205
$122$	15.2525	1.38090
$123$	0	0
$124$	6.81183	0.611721
$125$	0	0
$126$	0	0
$127$	4.88854	0.433788	0.216894	−	0.976195i	$-0.430407\pi$
$127$	4.88854	0.433788	0.216894	+	0.976195i	$0.430407\pi$
$128$	12.9909	1.14824
$129$	0	0
$130$	0	0
$131$	−14.0971	−1.23167	−0.615833	−	0.787876i	$-0.711181\pi$
$131$	−14.0971	−1.23167	−0.615833	+	0.787876i	$0.711181\pi$
$132$	0	0
$133$	0.102661	0.00890180
$134$	−10.3209	−0.891591
$135$	0	0
$136$	−32.2687	−2.76702
$137$	3.57023	0.305025	0.152513	−	0.988302i	$-0.451264\pi$
$137$	3.57023	0.305025	0.152513	+	0.988302i	$0.451264\pi$
$138$	0	0
$139$	11.7235	0.994371	0.497185	−	0.867644i	$-0.334367\pi$
$139$	11.7235	0.994371	0.497185	+	0.867644i	$0.334367\pi$
$140$	0	0
$141$	0	0
$142$	11.5330	0.967825
$143$	−8.02909	−0.671426
$144$	0	0
$145$	0	0
$146$	4.74766	0.392919
$147$	0	0
$148$	41.7193	3.42931
$149$	0.672890	0.0551253	0.0275626	−	0.999620i	$-0.491225\pi$
$149$	0.672890	0.0551253	0.0275626	+	0.999620i	$0.491225\pi$
$150$	0	0
$151$	24.2619	1.97441	0.987203	−	0.159468i	$-0.0509779\pi$
$151$	24.2619	1.97441	0.987203	+	0.159468i	$0.0509779\pi$
$152$	49.6533	4.02742
$153$	0	0
$154$	−0.0776145	−0.00625435
$155$	0	0
$156$	0	0
$157$	14.0158	1.11859	0.559293	−	0.828970i	$-0.311073\pi$
$157$	14.0158	1.11859	0.559293	+	0.828970i	$0.311073\pi$
$158$	0.622057	0.0494882
$159$	0	0
$160$	0	0
$161$	0.0822746	0.00648415
$162$	0	0
$163$	−9.77061	−0.765293	−0.382646	−	0.923895i	$-0.624987\pi$
$163$	−9.77061	−0.765293	−0.382646	+	0.923895i	$0.624987\pi$
$164$	−42.6270	−3.32861
$165$	0	0
$166$	−16.3941	−1.27243
$167$	5.91586	0.457783	0.228891	−	0.973452i	$-0.426490\pi$
$167$	5.91586	0.457783	0.228891	+	0.973452i	$0.426490\pi$
$168$	0	0
$169$	9.04921	0.696093
$170$	0	0
$171$	0	0
$172$	−18.9802	−1.44722
$173$	−20.1704	−1.53353	−0.766763	−	0.641930i	$-0.778134\pi$
$173$	−20.1704	−1.53353	−0.766763	+	0.641930i	$0.778134\pi$
$174$	0	0
$175$	0	0
$176$	−20.1172	−1.51639
$177$	0	0
$178$	33.0421	2.47661
$179$	−15.4896	−1.15775	−0.578873	−	0.815418i	$-0.696507\pi$
$179$	−15.4896	−1.15775	−0.578873	+	0.815418i	$0.696507\pi$
$180$	0	0
$181$	17.2509	1.28225	0.641126	−	0.767436i	$-0.278468\pi$
$181$	17.2509	1.28225	0.641126	+	0.767436i	$0.278468\pi$
$182$	0.213142	0.0157991
$183$	0	0
$184$	39.7933	2.93360
$185$	0	0
$186$	0	0
$187$	6.69415	0.489525
$188$	−27.3487	−1.99461
$189$	0	0
$190$	0	0
$191$	−11.5130	−0.833048	−0.416524	−	0.909125i	$-0.636752\pi$
$191$	−11.5130	−0.833048	−0.416524	+	0.909125i	$0.636752\pi$
$192$	0	0
$193$	−13.0261	−0.937642	−0.468821	−	0.883293i	$-0.655321\pi$
$193$	−13.0261	−0.937642	−0.468821	+	0.883293i	$0.655321\pi$
$194$	51.3849	3.68922
$195$	0	0
$196$	−35.6602	−2.54716
$197$	14.3280	1.02083	0.510415	−	0.859928i	$-0.329492\pi$
$197$	14.3280	1.02083	0.510415	+	0.859928i	$0.329492\pi$
$198$	0	0
$199$	−16.2728	−1.15355	−0.576775	−	0.816903i	$-0.695689\pi$
$199$	−16.2728	−1.15355	−0.576775	+	0.816903i	$0.695689\pi$
$200$	0	0
$201$	0	0
$202$	23.3058	1.63979
$203$	0.0170416	0.00119609
$204$	0	0
$205$	0	0
$206$	−29.1966	−2.03423
$207$	0	0
$208$	55.2451	3.83056
$209$	−10.3006	−0.712507
$210$	0	0
$211$	−24.3854	−1.67876	−0.839380	−	0.543544i	$-0.817082\pi$
$211$	−24.3854	−1.67876	−0.839380	+	0.543544i	$0.817082\pi$
$212$	−36.7640	−2.52496
$213$	0	0
$214$	42.1212	2.87934
$215$	0	0
$216$	0	0
$217$	0.0227862	0.00154683
$218$	−54.0083	−3.65791
$219$	0	0
$220$	0	0
$221$	−18.3832	−1.23659
$222$	0	0
$223$	−0.753555	−0.0504617	−0.0252309	−	0.999682i	$-0.508032\pi$
$223$	−0.753555	−0.0504617	−0.0252309	+	0.999682i	$0.508032\pi$
$224$	0.253106	0.0169114
$225$	0	0
$226$	23.6231	1.57138
$227$	−21.1711	−1.40518	−0.702589	−	0.711596i	$-0.747973\pi$
$227$	−21.1711	−1.40518	−0.702589	+	0.711596i	$0.747973\pi$
$228$	0	0
$229$	−7.97533	−0.527025	−0.263512	−	0.964656i	$-0.584881\pi$
$229$	−7.97533	−0.527025	−0.263512	+	0.964656i	$0.584881\pi$
$230$	0	0
$231$	0	0
$232$	8.24244	0.541143
$233$	14.0847	0.922718	0.461359	−	0.887214i	$-0.347362\pi$
$233$	14.0847	0.922718	0.461359	+	0.887214i	$0.347362\pi$
$234$	0	0
$235$	0	0
$236$	44.0892	2.86996
$237$	0	0
$238$	−0.177705	−0.0115189
$239$	−15.4813	−1.00140	−0.500701	−	0.865620i	$-0.666924\pi$
$239$	−15.4813	−1.00140	−0.500701	+	0.865620i	$0.666924\pi$
$240$	0	0
$241$	12.1294	0.781324	0.390662	−	0.920534i	$-0.372246\pi$
$241$	12.1294	0.781324	0.390662	+	0.920534i	$0.372246\pi$
$242$	−21.5115	−1.38281
$243$	0	0
$244$	29.1732	1.86762
$245$	0	0
$246$	0	0
$247$	28.2871	1.79987
$248$	11.0209	0.699826
$249$	0	0
$250$	0	0
$251$	−14.1090	−0.890550	−0.445275	−	0.895394i	$-0.646894\pi$
$251$	−14.1090	−0.890550	−0.445275	+	0.895394i	$0.646894\pi$
$252$	0	0
$253$	−8.25514	−0.518996
$254$	13.0209	0.817003
$255$	0	0
$256$	2.54296	0.158935
$257$	−26.6644	−1.66328	−0.831639	−	0.555317i	$-0.812597\pi$
$257$	−26.6644	−1.66328	−0.831639	+	0.555317i	$0.812597\pi$
$258$	0	0
$259$	0.139555	0.00867151
$260$	0	0
$261$	0	0
$262$	−37.5483	−2.31974
$263$	5.74517	0.354263	0.177131	−	0.984187i	$-0.443318\pi$
$263$	5.74517	0.354263	0.177131	+	0.984187i	$0.443318\pi$
$264$	0	0
$265$	0	0
$266$	0.273442	0.0167658
$267$	0	0
$268$	−19.7406	−1.20585
$269$	−19.3477	−1.17965	−0.589826	−	0.807530i	$-0.700804\pi$
$269$	−19.3477	−1.17965	−0.589826	+	0.807530i	$0.700804\pi$
$270$	0	0
$271$	−30.7485	−1.86784	−0.933920	−	0.357482i	$-0.883635\pi$
$271$	−30.7485	−1.86784	−0.933920	+	0.357482i	$0.883635\pi$
$272$	−46.0599	−2.79279
$273$	0	0
$274$	9.50950	0.574490
$275$	0	0
$276$	0	0
$277$	24.0737	1.44645	0.723225	−	0.690613i	$-0.242659\pi$
$277$	24.0737	1.44645	0.723225	+	0.690613i	$0.242659\pi$
$278$	31.2261	1.87282
$279$	0	0
$280$	0	0
$281$	−23.4067	−1.39633	−0.698164	−	0.715938i	$-0.745999\pi$
$281$	−23.4067	−1.39633	−0.698164	+	0.715938i	$0.745999\pi$
$282$	0	0
$283$	20.8589	1.23993	0.619967	−	0.784628i	$-0.287146\pi$
$283$	20.8589	1.23993	0.619967	+	0.784628i	$0.287146\pi$
$284$	22.0589	1.30895
$285$	0	0
$286$	−21.3859	−1.26458
$287$	−0.142591	−0.00841688
$288$	0	0
$289$	−1.67321	−0.0984242
$290$	0	0
$291$	0	0
$292$	9.08075	0.531410
$293$	−12.0727	−0.705294	−0.352647	−	0.935756i	$-0.614718\pi$
$293$	−12.0727	−0.705294	−0.352647	+	0.935756i	$0.614718\pi$
$294$	0	0
$295$	0	0
$296$	67.4978	3.92323
$297$	0	0
$298$	1.79228	0.103824
$299$	22.6700	1.31104
$300$	0	0
$301$	−0.0634903	−0.00365952
$302$	64.6229	3.71863
$303$	0	0
$304$	70.8745	4.06493
$305$	0	0
$306$	0	0
$307$	−20.4035	−1.16449	−0.582245	−	0.813013i	$-0.697826\pi$
$307$	−20.4035	−1.16449	−0.582245	+	0.813013i	$0.697826\pi$
$308$	−0.148452	−0.00845881
$309$	0	0
$310$	0	0
$311$	12.4159	0.704040	0.352020	−	0.935993i	$-0.385495\pi$
$311$	12.4159	0.704040	0.352020	+	0.935993i	$0.385495\pi$
$312$	0	0
$313$	−14.8518	−0.839473	−0.419737	−	0.907646i	$-0.637878\pi$
$313$	−14.8518	−0.839473	−0.419737	+	0.907646i	$0.637878\pi$
$314$	37.3320	2.10677
$315$	0	0
$316$	1.18980	0.0669312
$317$	−21.8783	−1.22881	−0.614404	−	0.788992i	$-0.710603\pi$
$317$	−21.8783	−1.22881	−0.614404	+	0.788992i	$0.710603\pi$
$318$	0	0
$319$	−1.70990	−0.0957358
$320$	0	0
$321$	0	0
$322$	0.219143	0.0122124
$323$	−23.5840	−1.31225
$324$	0	0
$325$	0	0
$326$	−26.0245	−1.44137
$327$	0	0
$328$	−68.9662	−3.80802
$329$	−0.0914839	−0.00504367
$330$	0	0
$331$	28.6380	1.57409	0.787043	−	0.616898i	$-0.211611\pi$
$331$	28.6380	1.57409	0.787043	+	0.616898i	$0.211611\pi$
$332$	−31.3567	−1.72092
$333$	0	0
$334$	15.7572	0.862196
$335$	0	0
$336$	0	0
$337$	−6.75074	−0.367736	−0.183868	−	0.982951i	$-0.558862\pi$
$337$	−6.75074	−0.367736	−0.183868	+	0.982951i	$0.558862\pi$
$338$	24.1031	1.31103
$339$	0	0
$340$	0	0
$341$	−2.28628	−0.123809
$342$	0	0
$343$	−0.238578	−0.0128820
$344$	−30.7081	−1.65567
$345$	0	0
$346$	−53.7249	−2.88827
$347$	−1.87591	−0.100704	−0.0503520	−	0.998732i	$-0.516034\pi$
$347$	−1.87591	−0.100704	−0.0503520	+	0.998732i	$0.516034\pi$
$348$	0	0
$349$	24.6359	1.31873	0.659364	−	0.751824i	$-0.270826\pi$
$349$	24.6359	1.31873	0.659364	+	0.751824i	$0.270826\pi$
$350$	0	0
$351$	0	0
$352$	−25.3958	−1.35360
$353$	−13.3468	−0.710379	−0.355189	−	0.934794i	$-0.615584\pi$
$353$	−13.3468	−0.710379	−0.355189	+	0.934794i	$0.615584\pi$
$354$	0	0
$355$	0	0
$356$	63.1989	3.34954
$357$	0	0
$358$	−41.2574	−2.18052
$359$	−21.5263	−1.13611	−0.568057	−	0.822990i	$-0.692305\pi$
$359$	−21.5263	−1.13611	−0.568057	+	0.822990i	$0.692305\pi$
$360$	0	0
$361$	17.2898	0.909992
$362$	45.9488	2.41502
$363$	0	0
$364$	0.407673	0.0213678
$365$	0	0
$366$	0	0
$367$	−9.36534	−0.488867	−0.244433	−	0.969666i	$-0.578602\pi$
$367$	−9.36534	−0.488867	−0.244433	+	0.969666i	$0.578602\pi$
$368$	56.8005	2.96093
$369$	0	0
$370$	0	0
$371$	−0.122979	−0.00638474
$372$	0	0
$373$	−19.3366	−1.00121	−0.500605	−	0.865676i	$-0.666889\pi$
$373$	−19.3366	−1.00121	−0.500605	+	0.865676i	$0.666889\pi$
$374$	17.8302	0.921980
$375$	0	0
$376$	−44.2475	−2.28189
$377$	4.69566	0.241839
$378$	0	0
$379$	−12.4163	−0.637783	−0.318891	−	0.947791i	$-0.603311\pi$
$379$	−12.4163	−0.637783	−0.318891	+	0.947791i	$0.603311\pi$
$380$	0	0
$381$	0	0
$382$	−30.6654	−1.56898
$383$	24.5909	1.25653	0.628267	−	0.777998i	$-0.283764\pi$
$383$	24.5909	1.25653	0.628267	+	0.777998i	$0.283764\pi$
$384$	0	0
$385$	0	0
$386$	−34.6958	−1.76597
$387$	0	0
$388$	98.2828	4.98955
$389$	−17.1567	−0.869880	−0.434940	−	0.900460i	$-0.643230\pi$
$389$	−17.1567	−0.869880	−0.434940	+	0.900460i	$0.643230\pi$
$390$	0	0
$391$	−18.9008	−0.955854
$392$	−57.6947	−2.91402
$393$	0	0
$394$	38.1635	1.92265
$395$	0	0
$396$	0	0
$397$	−2.90545	−0.145820	−0.0729102	−	0.997339i	$-0.523229\pi$
$397$	−2.90545	−0.145820	−0.0729102	+	0.997339i	$0.523229\pi$
$398$	−43.3436	−2.17262
$399$	0	0
$400$	0	0
$401$	−20.4427	−1.02086	−0.510431	−	0.859919i	$-0.670514\pi$
$401$	−20.4427	−1.02086	−0.510431	+	0.859919i	$0.670514\pi$
$402$	0	0
$403$	6.27851	0.312755
$404$	44.5764	2.21776
$405$	0	0
$406$	0.0453913	0.00225273
$407$	−14.0024	−0.694075
$408$	0	0
$409$	−3.13657	−0.155093	−0.0775467	−	0.996989i	$-0.524709\pi$
$409$	−3.13657	−0.155093	−0.0775467	+	0.996989i	$0.524709\pi$
$410$	0	0
$411$	0	0
$412$	−55.8438	−2.75123
$413$	0.147482	0.00725712
$414$	0	0
$415$	0	0
$416$	69.7410	3.41933
$417$	0	0
$418$	−27.4362	−1.34195
$419$	−36.6119	−1.78861	−0.894305	−	0.447458i	$-0.852330\pi$
$419$	−36.6119	−1.78861	−0.894305	+	0.447458i	$0.852330\pi$
$420$	0	0
$421$	−13.8706	−0.676012	−0.338006	−	0.941144i	$-0.609752\pi$
$421$	−13.8706	−0.676012	−0.338006	+	0.941144i	$0.609752\pi$
$422$	−64.9519	−3.16181
$423$	0	0
$424$	−59.4805	−2.88863
$425$	0	0
$426$	0	0
$427$	0.0975868	0.00472256
$428$	80.5643	3.89422
$429$	0	0
$430$	0	0
$431$	29.6786	1.42957	0.714785	−	0.699344i	$-0.246525\pi$
$431$	29.6786	1.42957	0.714785	+	0.699344i	$0.246525\pi$
$432$	0	0
$433$	32.1319	1.54416	0.772081	−	0.635525i	$-0.219216\pi$
$433$	32.1319	1.54416	0.772081	+	0.635525i	$0.219216\pi$
$434$	0.0606922	0.00291332
$435$	0	0
$436$	−103.301	−4.94720
$437$	29.0835	1.39125
$438$	0	0
$439$	34.9322	1.66722	0.833611	−	0.552352i	$-0.186269\pi$
$439$	34.9322	1.66722	0.833611	+	0.552352i	$0.186269\pi$
$440$	0	0
$441$	0	0
$442$	−48.9648	−2.32902
$443$	30.7938	1.46306	0.731528	−	0.681812i	$-0.238808\pi$
$443$	30.7938	1.46306	0.731528	+	0.681812i	$0.238808\pi$
$444$	0	0
$445$	0	0
$446$	−2.00713	−0.0950406
$447$	0	0
$448$	0.273168	0.0129060
$449$	−26.6304	−1.25677	−0.628383	−	0.777904i	$-0.716283\pi$
$449$	−26.6304	−1.25677	−0.628383	+	0.777904i	$0.716283\pi$
$450$	0	0
$451$	14.3071	0.673693
$452$	45.1834	2.12525
$453$	0	0
$454$	−56.3905	−2.64654
$455$	0	0
$456$	0	0
$457$	−9.03169	−0.422485	−0.211242	−	0.977434i	$-0.567751\pi$
$457$	−9.03169	−0.422485	−0.211242	+	0.977434i	$0.567751\pi$
$458$	−21.2427	−0.992608
$459$	0	0
$460$	0	0
$461$	17.6240	0.820832	0.410416	−	0.911898i	$-0.365384\pi$
$461$	17.6240	0.820832	0.410416	+	0.911898i	$0.365384\pi$
$462$	0	0
$463$	11.1431	0.517865	0.258933	−	0.965895i	$-0.416629\pi$
$463$	11.1431	0.517865	0.258933	+	0.965895i	$0.416629\pi$
$464$	11.7651	0.546183
$465$	0	0
$466$	37.5153	1.73786
$467$	−19.8932	−0.920548	−0.460274	−	0.887777i	$-0.652249\pi$
$467$	−19.8932	−0.920548	−0.460274	+	0.887777i	$0.652249\pi$
$468$	0	0
$469$	−0.0660340	−0.00304917
$470$	0	0
$471$	0	0
$472$	71.3319	3.28332
$473$	6.37039	0.292911
$474$	0	0
$475$	0	0
$476$	−0.339892	−0.0155789
$477$	0	0
$478$	−41.2353	−1.88606
$479$	21.6917	0.991118	0.495559	−	0.868574i	$-0.334963\pi$
$479$	21.6917	0.991118	0.495559	+	0.868574i	$0.334963\pi$
$480$	0	0
$481$	38.4530	1.75331
$482$	32.3073	1.47156
$483$	0	0
$484$	−41.1447	−1.87021
$485$	0	0
$486$	0	0
$487$	−11.1364	−0.504639	−0.252320	−	0.967644i	$-0.581193\pi$
$487$	−11.1364	−0.504639	−0.252320	+	0.967644i	$0.581193\pi$
$488$	47.1993	2.13661
$489$	0	0
$490$	0	0
$491$	−27.7172	−1.25086	−0.625431	−	0.780280i	$-0.715077\pi$
$491$	−27.7172	−1.25086	−0.625431	+	0.780280i	$0.715077\pi$
$492$	0	0
$493$	−3.91494	−0.176320
$494$	75.3444	3.38990
$495$	0	0
$496$	15.7310	0.706344
$497$	0.0737888	0.00330988
$498$	0	0
$499$	−29.8657	−1.33697	−0.668485	−	0.743725i	$-0.733057\pi$
$499$	−29.8657	−1.33697	−0.668485	+	0.743725i	$0.733057\pi$
$500$	0	0
$501$	0	0
$502$	−37.5800	−1.67728
$503$	28.6721	1.27843	0.639213	−	0.769030i	$-0.279260\pi$
$503$	28.6721	1.27843	0.639213	+	0.769030i	$0.279260\pi$
$504$	0	0
$505$	0	0
$506$	−21.9880	−0.977487
$507$	0	0
$508$	24.9048	1.10497
$509$	22.7354	1.00773	0.503864	−	0.863783i	$-0.331911\pi$
$509$	22.7354	1.00773	0.503864	+	0.863783i	$0.331911\pi$
$510$	0	0
$511$	0.0303759	0.00134375
$512$	−19.2084	−0.848899
$513$	0	0
$514$	−71.0220	−3.13265
$515$	0	0
$516$	0	0
$517$	9.17916	0.403699
$518$	0.371712	0.0163321
$519$	0	0
$520$	0	0
$521$	−15.8392	−0.693926	−0.346963	−	0.937879i	$-0.612787\pi$
$521$	−15.8392	−0.693926	−0.346963	+	0.937879i	$0.612787\pi$
$522$	0	0
$523$	−28.1248	−1.22981	−0.614905	−	0.788601i	$-0.710806\pi$
$523$	−28.1248	−1.22981	−0.614905	+	0.788601i	$0.710806\pi$
$524$	−71.8179	−3.13738
$525$	0	0
$526$	15.3026	0.667224
$527$	−5.23463	−0.228024
$528$	0	0
$529$	0.308221	0.0134009
$530$	0	0
$531$	0	0
$532$	0.523007	0.0226752
$533$	−39.2896	−1.70182
$534$	0	0
$535$	0	0
$536$	−31.9383	−1.37953
$537$	0	0
$538$	−51.5338	−2.22178
$539$	11.9688	0.515532
$540$	0	0
$541$	−23.9993	−1.03181	−0.515906	−	0.856645i	$-0.672545\pi$
$541$	−23.9993	−1.03181	−0.515906	+	0.856645i	$0.672545\pi$
$542$	−81.9004	−3.51792
$543$	0	0
$544$	−58.1457	−2.49297
$545$	0	0
$546$	0	0
$547$	24.1285	1.03166	0.515831	−	0.856691i	$-0.327483\pi$
$547$	24.1285	1.03166	0.515831	+	0.856691i	$0.327483\pi$
$548$	18.1886	0.776980
$549$	0	0
$550$	0	0
$551$	6.02411	0.256636
$552$	0	0
$553$	0.00397997	0.000169245 0
$554$	64.1217	2.72427
$555$	0	0
$556$	59.7255	2.53292
$557$	29.8474	1.26467	0.632337	−	0.774693i	$-0.282096\pi$
$557$	29.8474	1.26467	0.632337	+	0.774693i	$0.282096\pi$
$558$	0	0
$559$	−17.4942	−0.739924
$560$	0	0
$561$	0	0
$562$	−62.3451	−2.62987
$563$	9.29980	0.391940	0.195970	−	0.980610i	$-0.437214\pi$
$563$	9.29980	0.391940	0.195970	+	0.980610i	$0.437214\pi$
$564$	0	0
$565$	0	0
$566$	55.5589	2.33531
$567$	0	0
$568$	35.6891	1.49748
$569$	10.7468	0.450529	0.225264	−	0.974298i	$-0.427675\pi$
$569$	10.7468	0.450529	0.225264	+	0.974298i	$0.427675\pi$
$570$	0	0
$571$	−22.3620	−0.935822	−0.467911	−	0.883776i	$-0.654993\pi$
$571$	−22.3620	−0.935822	−0.467911	+	0.883776i	$0.654993\pi$
$572$	−40.9044	−1.71030
$573$	0	0
$574$	−0.379799	−0.0158525
$575$	0	0
$576$	0	0
$577$	29.7336	1.23783	0.618913	−	0.785459i	$-0.287573\pi$
$577$	29.7336	1.23783	0.618913	+	0.785459i	$0.287573\pi$
$578$	−4.45669	−0.185374
$579$	0	0
$580$	0	0
$581$	−0.104891	−0.00435160
$582$	0	0
$583$	12.3392	0.511039
$584$	14.6918	0.607949
$585$	0	0
$586$	−32.1563	−1.32836
$587$	25.9770	1.07219	0.536093	−	0.844159i	$-0.319899\pi$
$587$	25.9770	1.07219	0.536093	+	0.844159i	$0.319899\pi$
$588$	0	0
$589$	8.05476	0.331891
$590$	0	0
$591$	0	0
$592$	96.3454	3.95977
$593$	−30.1217	−1.23695	−0.618476	−	0.785804i	$-0.712250\pi$
$593$	−30.1217	−1.23695	−0.618476	+	0.785804i	$0.712250\pi$
$594$	0	0
$595$	0	0
$596$	3.42805	0.140419
$597$	0	0
$598$	60.3827	2.46923
$599$	27.4666	1.12226	0.561128	−	0.827729i	$-0.310368\pi$
$599$	27.4666	1.12226	0.561128	+	0.827729i	$0.310368\pi$
$600$	0	0
$601$	−6.66716	−0.271959	−0.135980	−	0.990712i	$-0.543418\pi$
$601$	−6.66716	−0.271959	−0.135980	+	0.990712i	$0.543418\pi$
$602$	−0.169110	−0.00689241
$603$	0	0
$604$	123.603	5.02933
$605$	0	0
$606$	0	0
$607$	15.4510	0.627138	0.313569	−	0.949565i	$-0.398475\pi$
$607$	15.4510	0.627138	0.313569	+	0.949565i	$0.398475\pi$
$608$	89.4714	3.62854
$609$	0	0
$610$	0	0
$611$	−25.2075	−1.01979
$612$	0	0
$613$	−23.4474	−0.947031	−0.473516	−	0.880785i	$-0.657015\pi$
$613$	−23.4474	−0.947031	−0.473516	+	0.880785i	$0.657015\pi$
$614$	−54.3459	−2.19322
$615$	0	0
$616$	−0.240180	−0.00967713
$617$	36.8162	1.48216	0.741082	−	0.671415i	$-0.234313\pi$
$617$	36.8162	1.48216	0.741082	+	0.671415i	$0.234313\pi$
$618$	0	0
$619$	24.5202	0.985551	0.492776	−	0.870156i	$-0.335982\pi$
$619$	24.5202	0.985551	0.492776	+	0.870156i	$0.335982\pi$
$620$	0	0
$621$	0	0
$622$	33.0704	1.32600
$623$	0.211406	0.00846980
$624$	0	0
$625$	0	0
$626$	−39.5586	−1.58108
$627$	0	0
$628$	71.4041	2.84933
$629$	−32.0597	−1.27830
$630$	0	0
$631$	11.1275	0.442978	0.221489	−	0.975163i	$-0.428908\pi$
$631$	11.1275	0.442978	0.221489	+	0.975163i	$0.428908\pi$
$632$	1.92497	0.0765712
$633$	0	0
$634$	−58.2740	−2.31436
$635$	0	0
$636$	0	0
$637$	−32.8682	−1.30229
$638$	−4.55440	−0.180311
$639$	0	0
$640$	0	0
$641$	−26.2776	−1.03790	−0.518951	−	0.854804i	$-0.673677\pi$
$641$	−26.2776	−1.03790	−0.518951	+	0.854804i	$0.673677\pi$
$642$	0	0
$643$	6.11885	0.241304	0.120652	−	0.992695i	$-0.461502\pi$
$643$	6.11885	0.241304	0.120652	+	0.992695i	$0.461502\pi$
$644$	0.419150	0.0165168
$645$	0	0
$646$	−62.8174	−2.47152
$647$	26.3758	1.03694	0.518470	−	0.855096i	$-0.326502\pi$
$647$	26.3758	1.03694	0.518470	+	0.855096i	$0.326502\pi$
$648$	0	0
$649$	−14.7978	−0.580865
$650$	0	0
$651$	0	0
$652$	−49.7766	−1.94940
$653$	−47.9227	−1.87536	−0.937679	−	0.347502i	$-0.887030\pi$
$653$	−47.9227	−1.87536	−0.937679	+	0.347502i	$0.887030\pi$
$654$	0	0
$655$	0	0
$656$	−98.4415	−3.84349
$657$	0	0
$658$	−0.243672	−0.00949934
$659$	−33.0636	−1.28798	−0.643988	−	0.765036i	$-0.722721\pi$
$659$	−33.0636	−1.28798	−0.643988	+	0.765036i	$0.722721\pi$
$660$	0	0
$661$	20.6186	0.801970	0.400985	−	0.916085i	$-0.368668\pi$
$661$	20.6186	0.801970	0.400985	+	0.916085i	$0.368668\pi$
$662$	76.2789	2.96466
$663$	0	0
$664$	−50.7320	−1.96878
$665$	0	0
$666$	0	0
$667$	4.82786	0.186935
$668$	30.1385	1.16609
$669$	0	0
$670$	0	0
$671$	−9.79151	−0.377997
$672$	0	0
$673$	−28.1489	−1.08506	−0.542529	−	0.840037i	$-0.682533\pi$
$673$	−28.1489	−1.08506	−0.542529	+	0.840037i	$0.682533\pi$
$674$	−17.9810	−0.692601
$675$	0	0
$676$	46.1014	1.77313
$677$	4.01689	0.154382	0.0771908	−	0.997016i	$-0.475405\pi$
$677$	4.01689	0.154382	0.0771908	+	0.997016i	$0.475405\pi$
$678$	0	0
$679$	0.328764	0.0126168
$680$	0	0
$681$	0	0
$682$	−6.08964	−0.233184
$683$	−2.61163	−0.0999312	−0.0499656	−	0.998751i	$-0.515911\pi$
$683$	−2.61163	−0.0999312	−0.0499656	+	0.998751i	$0.515911\pi$
$684$	0	0
$685$	0	0
$686$	−0.635465	−0.0242622
$687$	0	0
$688$	−43.8322	−1.67109
$689$	−33.8856	−1.29094
$690$	0	0
$691$	−19.9707	−0.759723	−0.379861	−	0.925043i	$-0.624028\pi$
$691$	−19.9707	−0.759723	−0.379861	+	0.925043i	$0.624028\pi$
$692$	−102.759	−3.90629
$693$	0	0
$694$	−4.99658	−0.189668
$695$	0	0
$696$	0	0
$697$	32.7572	1.24077
$698$	65.6190	2.48372
$699$	0	0
$700$	0	0
$701$	−17.4402	−0.658709	−0.329355	−	0.944206i	$-0.606831\pi$
$701$	−17.4402	−0.658709	−0.329355	+	0.944206i	$0.606831\pi$
$702$	0	0
$703$	49.3317	1.86058
$704$	−27.4087	−1.03300
$705$	0	0
$706$	−35.5500	−1.33794
$707$	0.149112	0.00560793
$708$	0	0
$709$	−27.8452	−1.04575	−0.522874	−	0.852410i	$-0.675140\pi$
$709$	−27.8452	−1.04575	−0.522874	+	0.852410i	$0.675140\pi$
$710$	0	0
$711$	0	0
$712$	102.250	3.83197
$713$	6.45527	0.241752
$714$	0	0
$715$	0	0
$716$	−78.9121	−2.94908
$717$	0	0
$718$	−57.3364	−2.13978
$719$	23.3574	0.871085	0.435542	−	0.900168i	$-0.356557\pi$
$719$	23.3574	0.871085	0.435542	+	0.900168i	$0.356557\pi$
$720$	0	0
$721$	−0.186802	−0.00695688
$722$	46.0525	1.71389
$723$	0	0
$724$	87.8854	3.26623
$725$	0	0
$726$	0	0
$727$	22.8360	0.846939	0.423470	−	0.905910i	$-0.360812\pi$
$727$	22.8360	0.846939	0.423470	+	0.905910i	$0.360812\pi$
$728$	0.659574	0.0244454
$729$	0	0
$730$	0	0
$731$	14.5855	0.539465
$732$	0	0
$733$	1.44837	0.0534967	0.0267484	−	0.999642i	$-0.491485\pi$
$733$	1.44837	0.0534967	0.0267484	+	0.999642i	$0.491485\pi$
$734$	−24.9451	−0.920741
$735$	0	0
$736$	71.7045	2.64306
$737$	6.62561	0.244058
$738$	0	0
$739$	−21.4167	−0.787824	−0.393912	−	0.919148i	$-0.628879\pi$
$739$	−21.4167	−0.787824	−0.393912	+	0.919148i	$0.628879\pi$
$740$	0	0
$741$	0	0
$742$	−0.327561	−0.0120251
$743$	−16.7848	−0.615776	−0.307888	−	0.951423i	$-0.599622\pi$
$743$	−16.7848	−0.615776	−0.307888	+	0.951423i	$0.599622\pi$
$744$	0	0
$745$	0	0
$746$	−51.5040	−1.88570
$747$	0	0
$748$	34.1035	1.24695
$749$	0.269495	0.00984712
$750$	0	0
$751$	−13.1194	−0.478733	−0.239366	−	0.970929i	$-0.576940\pi$
$751$	−13.1194	−0.478733	−0.239366	+	0.970929i	$0.576940\pi$
$752$	−63.1583	−2.30315
$753$	0	0
$754$	12.5071	0.455483
$755$	0	0
$756$	0	0
$757$	−15.3278	−0.557099	−0.278549	−	0.960422i	$-0.589854\pi$
$757$	−15.3278	−0.557099	−0.278549	+	0.960422i	$0.589854\pi$
$758$	−33.0715	−1.20121
$759$	0	0
$760$	0	0
$761$	−16.7398	−0.606818	−0.303409	−	0.952860i	$-0.598125\pi$
$761$	−16.7398	−0.606818	−0.303409	+	0.952860i	$0.598125\pi$
$762$	0	0
$763$	−0.345549	−0.0125097
$764$	−58.6531	−2.12199
$765$	0	0
$766$	65.4991	2.36658
$767$	40.6373	1.46733
$768$	0	0
$769$	−19.4502	−0.701391	−0.350696	−	0.936489i	$-0.614055\pi$
$769$	−19.4502	−0.701391	−0.350696	+	0.936489i	$0.614055\pi$
$770$	0	0
$771$	0	0
$772$	−66.3620	−2.38842
$773$	34.5781	1.24369	0.621844	−	0.783142i	$-0.286384\pi$
$773$	34.5781	1.24369	0.621844	+	0.783142i	$0.286384\pi$
$774$	0	0
$775$	0	0
$776$	159.012	5.70819
$777$	0	0
$778$	−45.6978	−1.63835
$779$	−50.4050	−1.80595
$780$	0	0
$781$	−7.40370	−0.264925
$782$	−50.3433	−1.80027
$783$	0	0
$784$	−82.3526	−2.94116
$785$	0	0
$786$	0	0
$787$	39.5669	1.41041	0.705204	−	0.709004i	$-0.250855\pi$
$787$	39.5669	1.41041	0.705204	+	0.709004i	$0.250855\pi$
$788$	72.9946	2.60033
$789$	0	0
$790$	0	0
$791$	0.151142	0.00537400
$792$	0	0
$793$	26.8891	0.954860
$794$	−7.73883	−0.274641
$795$	0	0
$796$	−82.9023	−2.93839
$797$	32.0055	1.13369	0.566847	−	0.823823i	$-0.308163\pi$
$797$	32.0055	1.13369	0.566847	+	0.823823i	$0.308163\pi$
$798$	0	0
$799$	21.0164	0.743508
$800$	0	0
$801$	0	0
$802$	−54.4504	−1.92271
$803$	−3.04781	−0.107555
$804$	0	0
$805$	0	0
$806$	16.7232	0.589048
$807$	0	0
$808$	72.1203	2.53718
$809$	−27.5627	−0.969052	−0.484526	−	0.874777i	$-0.661008\pi$
$809$	−27.5627	−0.969052	−0.484526	+	0.874777i	$0.661008\pi$
$810$	0	0
$811$	−25.3316	−0.889514	−0.444757	−	0.895651i	$-0.646710\pi$
$811$	−25.3316	−0.889514	−0.444757	+	0.895651i	$0.646710\pi$
$812$	0.0868190	0.00304675
$813$	0	0
$814$	−37.2963	−1.30723
$815$	0	0
$816$	0	0
$817$	−22.4434	−0.785196
$818$	−8.35442	−0.292106
$819$	0	0
$820$	0	0
$821$	46.4854	1.62235	0.811177	−	0.584801i	$-0.198827\pi$
$821$	46.4854	1.62235	0.811177	+	0.584801i	$0.198827\pi$
$822$	0	0
$823$	16.9991	0.592552	0.296276	−	0.955102i	$-0.404255\pi$
$823$	16.9991	0.592552	0.296276	+	0.955102i	$0.404255\pi$
$824$	−90.3497	−3.14748
$825$	0	0
$826$	0.392827	0.0136682
$827$	14.1835	0.493208	0.246604	−	0.969116i	$-0.420685\pi$
$827$	14.1835	0.493208	0.246604	+	0.969116i	$0.420685\pi$
$828$	0	0
$829$	28.9652	1.00600	0.503001	−	0.864286i	$-0.332229\pi$
$829$	28.9652	1.00600	0.503001	+	0.864286i	$0.332229\pi$
$830$	0	0
$831$	0	0
$832$	75.2688	2.60948
$833$	27.4035	0.949474
$834$	0	0
$835$	0	0
$836$	−52.4767	−1.81494
$837$	0	0
$838$	−97.5179	−3.36870
$839$	−22.6082	−0.780523	−0.390262	−	0.920704i	$-0.627615\pi$
$839$	−22.6082	−0.780523	−0.390262	+	0.920704i	$0.627615\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	−36.9451	−1.27321
$843$	0	0
$844$	−124.232	−4.27625
$845$	0	0
$846$	0	0
$847$	−0.137633	−0.00472911
$848$	−84.9017	−2.91554
$849$	0	0
$850$	0	0
$851$	39.5356	1.35526
$852$	0	0
$853$	−35.6577	−1.22090	−0.610448	−	0.792057i	$-0.709010\pi$
$853$	−35.6577	−1.22090	−0.610448	+	0.792057i	$0.709010\pi$
$854$	0.259928	0.00889455
$855$	0	0
$856$	130.345	4.45510
$857$	3.41032	0.116494	0.0582472	−	0.998302i	$-0.481449\pi$
$857$	3.41032	0.116494	0.0582472	+	0.998302i	$0.481449\pi$
$858$	0	0
$859$	−28.5267	−0.973318	−0.486659	−	0.873592i	$-0.661785\pi$
$859$	−28.5267	−0.973318	−0.486659	+	0.873592i	$0.661785\pi$
$860$	0	0
$861$	0	0
$862$	79.0507	2.69248
$863$	24.5873	0.836962	0.418481	−	0.908226i	$-0.362563\pi$
$863$	24.5873	0.836962	0.418481	+	0.908226i	$0.362563\pi$
$864$	0	0
$865$	0	0
$866$	85.5851	2.90830
$867$	0	0
$868$	0.116085	0.00394017
$869$	−0.399336	−0.0135465
$870$	0	0
$871$	−18.1950	−0.616515
$872$	−167.130	−5.65974
$873$	0	0
$874$	77.4656	2.62031
$875$	0	0
$876$	0	0
$877$	−58.0640	−1.96068	−0.980341	−	0.197310i	$-0.936780\pi$
$877$	−58.0640	−1.96068	−0.980341	+	0.197310i	$0.936780\pi$
$878$	93.0438	3.14008
$879$	0	0
$880$	0	0
$881$	−52.7466	−1.77708	−0.888538	−	0.458802i	$-0.848279\pi$
$881$	−52.7466	−1.77708	−0.888538	+	0.458802i	$0.848279\pi$
$882$	0	0
$883$	−38.1567	−1.28408	−0.642038	−	0.766672i	$-0.721911\pi$
$883$	−38.1567	−1.28408	−0.642038	+	0.766672i	$0.721911\pi$
$884$	−93.6539	−3.14992
$885$	0	0
$886$	82.0209	2.75555
$887$	22.8088	0.765845	0.382922	−	0.923781i	$-0.374918\pi$
$887$	22.8088	0.765845	0.382922	+	0.923781i	$0.374918\pi$
$888$	0	0
$889$	0.0833087	0.00279408
$890$	0	0
$891$	0	0
$892$	−3.83900	−0.128539
$893$	−32.3389	−1.08218
$894$	0	0
$895$	0	0
$896$	0.221385	0.00739596
$897$	0	0
$898$	−70.9316	−2.36702
$899$	1.33709	0.0445944
$900$	0	0
$901$	28.2517	0.941200
$902$	38.1077	1.26885
$903$	0	0
$904$	73.1023	2.43135
$905$	0	0
$906$	0	0
$907$	33.4371	1.11026	0.555131	−	0.831763i	$-0.312668\pi$
$907$	33.4371	1.11026	0.555131	+	0.831763i	$0.312668\pi$
$908$	−107.857	−3.57936
$909$	0	0
$910$	0	0
$911$	18.0752	0.598857	0.299428	−	0.954119i	$-0.403204\pi$
$911$	18.0752	0.598857	0.299428	+	0.954119i	$0.403204\pi$
$912$	0	0
$913$	10.5244	0.348305
$914$	−24.0564	−0.795715
$915$	0	0
$916$	−40.6305	−1.34247
$917$	−0.240237	−0.00793333
$918$	0	0
$919$	38.7798	1.27923	0.639614	−	0.768696i	$-0.279094\pi$
$919$	38.7798	1.27923	0.639614	+	0.768696i	$0.279094\pi$
$920$	0	0
$921$	0	0
$922$	46.9425	1.54597
$923$	20.3318	0.669229
$924$	0	0
$925$	0	0
$926$	29.6804	0.975357
$927$	0	0
$928$	14.8522	0.487548
$929$	−8.16319	−0.267826	−0.133913	−	0.990993i	$-0.542754\pi$
$929$	−8.16319	−0.267826	−0.133913	+	0.990993i	$0.542754\pi$
$930$	0	0
$931$	−42.1670	−1.38197
$932$	71.7547	2.35040
$933$	0	0
$934$	−52.9866	−1.73378
$935$	0	0
$936$	0	0
$937$	16.7498	0.547192	0.273596	−	0.961845i	$-0.411787\pi$
$937$	16.7498	0.547192	0.273596	+	0.961845i	$0.411787\pi$
$938$	−0.175885	−0.00574285
$939$	0	0
$940$	0	0
$941$	−1.27331	−0.0415088	−0.0207544	−	0.999785i	$-0.506607\pi$
$941$	−1.27331	−0.0415088	−0.0207544	+	0.999785i	$0.506607\pi$
$942$	0	0
$943$	−40.3957	−1.31547
$944$	101.818	3.31390
$945$	0	0
$946$	16.9679	0.551674
$947$	38.5681	1.25329	0.626647	−	0.779303i	$-0.284427\pi$
$947$	38.5681	1.25329	0.626647	+	0.779303i	$0.284427\pi$
$948$	0	0
$949$	8.36978	0.271695
$950$	0	0
$951$	0	0
$952$	−0.549911	−0.0178227
$953$	−47.2051	−1.52912	−0.764561	−	0.644551i	$-0.777044\pi$
$953$	−47.2051	−1.52912	−0.764561	+	0.644551i	$0.777044\pi$
$954$	0	0
$955$	0	0
$956$	−78.8699	−2.55084
$957$	0	0
$958$	57.7770	1.86669
$959$	0.0608425	0.00196471
$960$	0	0
$961$	−29.2122	−0.942329
$962$	102.422	3.30221
$963$	0	0
$964$	61.7936	1.99024
$965$	0	0
$966$	0	0
$967$	−14.9495	−0.480743	−0.240371	−	0.970681i	$-0.577269\pi$
$967$	−14.9495	−0.480743	−0.240371	+	0.970681i	$0.577269\pi$
$968$	−66.5680	−2.13958
$969$	0	0
$970$	0	0
$971$	−30.4517	−0.977240	−0.488620	−	0.872497i	$-0.662500\pi$
$971$	−30.4517	−0.977240	−0.488620	+	0.872497i	$0.662500\pi$
$972$	0	0
$973$	0.199787	0.00640487
$974$	−29.6625	−0.950447
$975$	0	0
$976$	67.3716	2.15651
$977$	−0.336322	−0.0107599	−0.00537995	−	0.999986i	$-0.501713\pi$
$977$	−0.336322	−0.0107599	−0.00537995	+	0.999986i	$0.501713\pi$
$978$	0	0
$979$	−21.2117	−0.677929
$980$	0	0
$981$	0	0
$982$	−73.8264	−2.35590
$983$	−1.44050	−0.0459449	−0.0229724	−	0.999736i	$-0.507313\pi$
$983$	−1.44050	−0.0459449	−0.0229724	+	0.999736i	$0.507313\pi$
$984$	0	0
$985$	0	0
$986$	−10.4277	−0.332085
$987$	0	0
$988$	144.110	4.58474
$989$	−17.9867	−0.571943
$990$	0	0
$991$	40.0507	1.27225	0.636126	−	0.771585i	$-0.280536\pi$
$991$	40.0507	1.27225	0.636126	+	0.771585i	$0.280536\pi$
$992$	19.8587	0.630516
$993$	0	0
$994$	0.196541	0.00623389
$995$	0	0
$996$	0	0
$997$	24.3419	0.770916	0.385458	−	0.922725i	$-0.374043\pi$
$997$	24.3419	0.770916	0.385458	+	0.922725i	$0.374043\pi$
$998$	−79.5488	−2.51807
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6525.2.a.bx.1.7		7
3.2	odd	2		2175.2.a.ba.1.1	✓	7
5.4	even	2		6525.2.a.bu.1.1		7
15.2	even	4		2175.2.c.o.349.1		14
15.8	even	4		2175.2.c.o.349.14		14
15.14	odd	2		2175.2.a.bb.1.7	yes	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2175.2.a.ba.1.1	✓	7	3.2	odd	2
2175.2.a.bb.1.7	yes	7	15.14	odd	2
2175.2.c.o.349.1		14	15.2	even	4
2175.2.c.o.349.14		14	15.8	even	4
6525.2.a.bu.1.1		7	5.4	even	2
6525.2.a.bx.1.7		7	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 6525 = 3^{2} \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6525.a (trivial)

\(f(q)\)	\(=\)	\(q+2.66356 q^{2} +5.09453 q^{4} +0.0170416 q^{7} +8.24244 q^{8} +O(q^{10})\)	\(q+2.66356 q^{2} +5.09453 q^{4} +0.0170416 q^{7} +8.24244 q^{8} -1.70990 q^{11} +4.69566 q^{13} +0.0453913 q^{14} +11.7651 q^{16} -3.91494 q^{17} +6.02411 q^{19} -4.55440 q^{22} +4.82786 q^{23} +12.5071 q^{26} +0.0868190 q^{28} +1.00000 q^{29} +1.33709 q^{31} +14.8522 q^{32} -10.4277 q^{34} +8.18905 q^{37} +16.0455 q^{38} -8.36721 q^{41} -3.72560 q^{43} -8.71111 q^{44} +12.8593 q^{46} -5.36826 q^{47} -6.99971 q^{49} +23.9222 q^{52} -7.21637 q^{53} +0.140465 q^{56} +2.66356 q^{58} +8.65422 q^{59} +5.72637 q^{61} +3.56141 q^{62} +16.0294 q^{64} -3.87486 q^{67} -19.9448 q^{68} +4.32991 q^{71} +1.78245 q^{73} +21.8120 q^{74} +30.6900 q^{76} -0.0291394 q^{77} +0.233544 q^{79} -22.2865 q^{82} -6.15497 q^{83} -9.92334 q^{86} -14.0937 q^{88} +12.4053 q^{89} +0.0800217 q^{91} +24.5957 q^{92} -14.2986 q^{94} +19.2918 q^{97} -18.6441 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 2 q^{2} + 10 q^{4} + q^{7} + 3 q^{8}+O(q^{10}) \) 7 * q + 2 * q^2 + 10 * q^4 + q^7 + 3 * q^8	\( 7 q + 2 q^{2} + 10 q^{4} + q^{7} + 3 q^{8} - 4 q^{11} + q^{13} - 15 q^{14} + 12 q^{16} + 8 q^{17} + 15 q^{19} - 3 q^{22} + 14 q^{23} - 6 q^{26} + 24 q^{28} + 7 q^{29} + 5 q^{31} + 18 q^{32} + 7 q^{34} + 6 q^{37} - 18 q^{38} - 22 q^{41} + 19 q^{43} - 15 q^{44} - 4 q^{46} + 22 q^{47} + 12 q^{49} - 11 q^{52} + 10 q^{53} - 14 q^{56} + 2 q^{58} - 6 q^{59} + 23 q^{61} + 40 q^{62} + 5 q^{64} + 13 q^{67} - 7 q^{68} - 26 q^{71} + 24 q^{73} + 10 q^{74} + 46 q^{76} + 4 q^{77} + 14 q^{79} - 16 q^{82} + 10 q^{83} - 44 q^{86} + 66 q^{88} - 14 q^{89} + 13 q^{91} + 58 q^{92} - 3 q^{94} + 31 q^{97} - 59 q^{98}+O(q^{100}) \) 7 * q + 2 * q^2 + 10 * q^4 + q^7 + 3 * q^8 - 4 * q^11 + q^13 - 15 * q^14 + 12 * q^16 + 8 * q^17 + 15 * q^19 - 3 * q^22 + 14 * q^23 - 6 * q^26 + 24 * q^28 + 7 * q^29 + 5 * q^31 + 18 * q^32 + 7 * q^34 + 6 * q^37 - 18 * q^38 - 22 * q^41 + 19 * q^43 - 15 * q^44 - 4 * q^46 + 22 * q^47 + 12 * q^49 - 11 * q^52 + 10 * q^53 - 14 * q^56 + 2 * q^58 - 6 * q^59 + 23 * q^61 + 40 * q^62 + 5 * q^64 + 13 * q^67 - 7 * q^68 - 26 * q^71 + 24 * q^73 + 10 * q^74 + 46 * q^76 + 4 * q^77 + 14 * q^79 - 16 * q^82 + 10 * q^83 - 44 * q^86 + 66 * q^88 - 14 * q^89 + 13 * q^91 + 58 * q^92 - 3 * q^94 + 31 * q^97 - 59 * q^98

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