LMFDB - Embedded newform 7605.2.a.bw.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7605,2,Mod(1,7605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7605, 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("7605.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7605 = 3^{2} \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7605.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:	$60.7262307372$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.756.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 6x - 2 $ x^3 - 6*x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 195)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.60168$ of defining polynomial
Character	$\chi$	$=$	7605.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.60168 q^{2} +4.76873 q^{4} +1.00000 q^{5} -3.60168 q^{7} +7.20336 q^{8} +O(q^{10})$	$q+2.60168 q^{2} +4.76873 q^{4} +1.00000 q^{5} -3.60168 q^{7} +7.20336 q^{8} +2.60168 q^{10} -5.20336 q^{11} -9.37041 q^{14} +9.20336 q^{16} +2.93579 q^{17} -6.76873 q^{19} +4.76873 q^{20} -13.5375 q^{22} -5.53747 q^{23} +1.00000 q^{25} -17.1755 q^{28} -1.83294 q^{29} -4.10284 q^{31} +9.53747 q^{32} +7.63798 q^{34} -3.60168 q^{35} +3.53747 q^{37} -17.6101 q^{38} +7.20336 q^{40} -5.37041 q^{41} +3.16706 q^{43} -24.8134 q^{44} -14.4067 q^{46} +3.80504 q^{47} +5.97209 q^{49} +2.60168 q^{50} +5.20336 q^{53} -5.20336 q^{55} -25.9442 q^{56} -4.76873 q^{58} -7.37041 q^{59} -3.43462 q^{61} -10.6743 q^{62} +6.40672 q^{64} -3.50117 q^{67} +14.0000 q^{68} -9.37041 q^{70} -9.70452 q^{71} +0.805037 q^{73} +9.20336 q^{74} -32.2783 q^{76} +18.7408 q^{77} -4.10284 q^{79} +9.20336 q^{80} -13.9721 q^{82} -11.5375 q^{83} +2.93579 q^{85} +8.23966 q^{86} -37.4817 q^{88} +9.83294 q^{89} -26.4067 q^{92} +9.89949 q^{94} -6.76873 q^{95} +5.57377 q^{97} +15.5375 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 6 q^{4} + 3 q^{5} - 3 q^{7} + 6 q^{8}+O(q^{10}) $ 3 * q + 6 * q^4 + 3 * q^5 - 3 * q^7 + 6 * q^8	$ 3 q + 6 q^{4} + 3 q^{5} - 3 q^{7} + 6 q^{8} - 12 q^{14} + 12 q^{16} - 12 q^{19} + 6 q^{20} - 24 q^{22} + 3 q^{25} - 12 q^{28} - 6 q^{29} - 3 q^{31} + 12 q^{32} - 3 q^{35} - 6 q^{37} - 6 q^{38} + 6 q^{40} + 9 q^{43} - 12 q^{44} - 12 q^{46} - 12 q^{47} - 6 q^{49} - 30 q^{56} - 6 q^{58} - 6 q^{59} - 3 q^{61} + 6 q^{62} - 12 q^{64} - 9 q^{67} + 42 q^{68} - 12 q^{70} - 12 q^{71} - 21 q^{73} + 12 q^{74} - 48 q^{76} + 24 q^{77} - 3 q^{79} + 12 q^{80} - 18 q^{82} - 18 q^{83} - 6 q^{86} - 48 q^{88} + 30 q^{89} - 48 q^{92} + 36 q^{94} - 12 q^{95} - 15 q^{97} + 30 q^{98}+O(q^{100}) $ 3 * q + 6 * q^4 + 3 * q^5 - 3 * q^7 + 6 * q^8 - 12 * q^14 + 12 * q^16 - 12 * q^19 + 6 * q^20 - 24 * q^22 + 3 * q^25 - 12 * q^28 - 6 * q^29 - 3 * q^31 + 12 * q^32 - 3 * q^35 - 6 * q^37 - 6 * q^38 + 6 * q^40 + 9 * q^43 - 12 * q^44 - 12 * q^46 - 12 * q^47 - 6 * q^49 - 30 * q^56 - 6 * q^58 - 6 * q^59 - 3 * q^61 + 6 * q^62 - 12 * q^64 - 9 * q^67 + 42 * q^68 - 12 * q^70 - 12 * q^71 - 21 * q^73 + 12 * q^74 - 48 * q^76 + 24 * q^77 - 3 * q^79 + 12 * q^80 - 18 * q^82 - 18 * q^83 - 6 * q^86 - 48 * q^88 + 30 * q^89 - 48 * q^92 + 36 * q^94 - 12 * q^95 - 15 * q^97 + 30 * 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 $

$2$	2.60168	1.83966	0.919832	−	0.392311i	$-0.128324\pi$
$2$	2.60168	1.83966	0.919832	+	0.392311i	$0.128324\pi$
$3$	0	0
$3$	0	0
$4$	4.76873	2.38437
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0	0
$7$	−3.60168	−1.36131	−0.680653	−	0.732606i	$-0.738304\pi$
$7$	−3.60168	−1.36131	−0.680653	+	0.732606i	$0.738304\pi$
$8$	7.20336	2.54677
$9$	0	0
$10$	2.60168	0.822723
$11$	−5.20336	−1.56887	−0.784436	−	0.620210i	$-0.787047\pi$
$11$	−5.20336	−1.56887	−0.784436	+	0.620210i	$0.787047\pi$
$12$	0	0
$13$	0	0
$13$	0	0
$14$	−9.37041	−2.50435
$15$	0	0
$16$	9.20336	2.30084
$17$	2.93579	0.712034	0.356017	−	0.934480i	$-0.384135\pi$
$17$	2.93579	0.712034	0.356017	+	0.934480i	$0.384135\pi$
$18$	0	0
$19$	−6.76873	−1.55285	−0.776427	−	0.630207i	$-0.782970\pi$
$19$	−6.76873	−1.55285	−0.776427	+	0.630207i	$0.782970\pi$
$20$	4.76873	1.06632
$21$	0	0
$22$	−13.5375	−2.88620
$23$	−5.53747	−1.15464	−0.577321	−	0.816517i	$-0.695902\pi$
$23$	−5.53747	−1.15464	−0.577321	+	0.816517i	$0.695902\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	0	0
$28$	−17.1755	−3.24586
$29$	−1.83294	−0.340369	−0.170185	−	0.985412i	$-0.554436\pi$
$29$	−1.83294	−0.340369	−0.170185	+	0.985412i	$0.554436\pi$
$30$	0	0
$31$	−4.10284	−0.736893	−0.368446	−	0.929649i	$-0.620110\pi$
$31$	−4.10284	−0.736893	−0.368446	+	0.929649i	$0.620110\pi$
$32$	9.53747	1.68600
$33$	0	0
$34$	7.63798	1.30990
$35$	−3.60168	−0.608795
$36$	0	0
$37$	3.53747	0.581556	0.290778	−	0.956791i	$-0.406086\pi$
$37$	3.53747	0.581556	0.290778	+	0.956791i	$0.406086\pi$
$38$	−17.6101	−2.85673
$39$	0	0
$40$	7.20336	1.13895
$41$	−5.37041	−0.838718	−0.419359	−	0.907821i	$-0.637745\pi$
$41$	−5.37041	−0.838718	−0.419359	+	0.907821i	$0.637745\pi$
$42$	0	0
$43$	3.16706	0.482971	0.241486	−	0.970404i	$-0.422365\pi$
$43$	3.16706	0.482971	0.241486	+	0.970404i	$0.422365\pi$
$44$	−24.8134	−3.74077
$45$	0	0
$46$	−14.4067	−2.12415
$47$	3.80504	0.555022	0.277511	−	0.960722i	$-0.410491\pi$
$47$	3.80504	0.555022	0.277511	+	0.960722i	$0.410491\pi$
$48$	0	0
$49$	5.97209	0.853156
$50$	2.60168	0.367933
$51$	0	0
$52$	0	0
$53$	5.20336	0.714736	0.357368	−	0.933964i	$-0.383674\pi$
$53$	5.20336	0.714736	0.357368	+	0.933964i	$0.383674\pi$
$54$	0	0
$55$	−5.20336	−0.701621
$56$	−25.9442	−3.46694
$57$	0	0
$58$	−4.76873	−0.626165
$59$	−7.37041	−0.959546	−0.479773	−	0.877393i	$-0.659281\pi$
$59$	−7.37041	−0.959546	−0.479773	+	0.877393i	$0.659281\pi$
$60$	0	0
$61$	−3.43462	−0.439759	−0.219879	−	0.975527i	$-0.570566\pi$
$61$	−3.43462	−0.439759	−0.219879	+	0.975527i	$0.570566\pi$
$62$	−10.6743	−1.35564
$63$	0	0
$64$	6.40672	0.800840
$65$	0	0
$66$	0	0
$67$	−3.50117	−0.427735	−0.213868	−	0.976863i	$-0.568606\pi$
$67$	−3.50117	−0.427735	−0.213868	+	0.976863i	$0.568606\pi$
$68$	14.0000	1.69775
$69$	0	0
$70$	−9.37041	−1.11998
$71$	−9.70452	−1.15172	−0.575858	−	0.817550i	$-0.695332\pi$
$71$	−9.70452	−1.15172	−0.575858	+	0.817550i	$0.695332\pi$
$72$	0	0
$73$	0.805037	0.0942225	0.0471113	−	0.998890i	$-0.484998\pi$
$73$	0.805037	0.0942225	0.0471113	+	0.998890i	$0.484998\pi$
$74$	9.20336	1.06987
$75$	0	0
$76$	−32.2783	−3.70257
$77$	18.7408	2.13572
$78$	0	0
$79$	−4.10284	−0.461606	−0.230803	−	0.973000i	$-0.574135\pi$
$79$	−4.10284	−0.461606	−0.230803	+	0.973000i	$0.574135\pi$
$80$	9.20336	1.02897
$81$	0	0
$82$	−13.9721	−1.54296
$83$	−11.5375	−1.26640	−0.633201	−	0.773988i	$-0.718259\pi$
$83$	−11.5375	−1.26640	−0.633201	+	0.773988i	$0.718259\pi$
$84$	0	0
$85$	2.93579	0.318431
$86$	8.23966	0.888506
$87$	0	0
$88$	−37.4817	−3.99556
$89$	9.83294	1.04229	0.521145	−	0.853468i	$-0.325505\pi$
$89$	9.83294	1.04229	0.521145	+	0.853468i	$0.325505\pi$
$90$	0	0
$91$	0	0
$92$	−26.4067	−2.75309
$93$	0	0
$94$	9.89949	1.02105
$95$	−6.76873	−0.694457
$96$	0	0
$97$	5.57377	0.565931	0.282965	−	0.959130i	$-0.408682\pi$
$97$	5.57377	0.565931	0.282965	+	0.959130i	$0.408682\pi$
$98$	15.5375	1.56952
$99$	0	0
$100$	4.76873	0.476873
$101$	−2.40672	−0.239477	−0.119739	−	0.992805i	$-0.538206\pi$
$101$	−2.40672	−0.239477	−0.119739	+	0.992805i	$0.538206\pi$
$102$	0	0
$103$	18.4430	1.81724	0.908622	−	0.417619i	$-0.137135\pi$
$103$	18.4430	1.81724	0.908622	+	0.417619i	$0.137135\pi$
$104$	0	0
$105$	0	0
$106$	13.5375	1.31488
$107$	−10.9358	−1.05720	−0.528601	−	0.848870i	$-0.677283\pi$
$107$	−10.9358	−1.05720	−0.528601	+	0.848870i	$0.677283\pi$
$108$	0	0
$109$	−13.8692	−1.32843	−0.664217	−	0.747540i	$-0.731235\pi$
$109$	−13.8692	−1.32843	−0.664217	+	0.747540i	$0.731235\pi$
$110$	−13.5375	−1.29075
$111$	0	0
$112$	−33.1475	−3.13215
$113$	11.2034	1.05392	0.526962	−	0.849889i	$-0.323331\pi$
$113$	11.2034	1.05392	0.526962	+	0.849889i	$0.323331\pi$
$114$	0	0
$115$	−5.53747	−0.516372
$116$	−8.74083	−0.811565
$117$	0	0
$118$	−19.1755	−1.76524
$119$	−10.5738	−0.969296
$120$	0	0
$121$	16.0749	1.46136
$122$	−8.93579	−0.809008
$123$	0	0
$124$	−19.5654	−1.75702
$125$	1.00000	0.0894427
$126$	0	0
$127$	−3.19496	−0.283507	−0.141754	−	0.989902i	$-0.545274\pi$
$127$	−3.19496	−0.283507	−0.141754	+	0.989902i	$0.545274\pi$
$128$	−2.40672	−0.212726
$129$	0	0
$130$	0	0
$131$	4.57377	0.399612	0.199806	−	0.979835i	$-0.435969\pi$
$131$	4.57377	0.399612	0.199806	+	0.979835i	$0.435969\pi$
$132$	0	0
$133$	24.3788	2.11391
$134$	−9.10891	−0.786890
$135$	0	0
$136$	21.1475	1.81339
$137$	10.6743	0.911966	0.455983	−	0.889989i	$-0.349288\pi$
$137$	10.6743	0.911966	0.455983	+	0.889989i	$0.349288\pi$
$138$	0	0
$139$	−16.1475	−1.36962	−0.684808	−	0.728723i	$-0.740114\pi$
$139$	−16.1475	−1.36962	−0.684808	+	0.728723i	$0.740114\pi$
$140$	−17.1755	−1.45159
$141$	0	0
$142$	−25.2481	−2.11877
$143$	0	0
$144$	0	0
$145$	−1.83294	−0.152218
$146$	2.09445	0.173338
$147$	0	0
$148$	16.8692	1.38664
$149$	−9.66589	−0.791861	−0.395930	−	0.918281i	$-0.629578\pi$
$149$	−9.66589	−0.791861	−0.395930	+	0.918281i	$0.629578\pi$
$150$	0	0
$151$	18.7129	1.52284	0.761418	−	0.648261i	$-0.224504\pi$
$151$	18.7129	1.52284	0.761418	+	0.648261i	$0.224504\pi$
$152$	−48.7576	−3.95477
$153$	0	0
$154$	48.7576	3.92900
$155$	−4.10284	−0.329548
$156$	0	0
$157$	−10.3704	−0.827649	−0.413825	−	0.910357i	$-0.635807\pi$
$157$	−10.3704	−0.827649	−0.413825	+	0.910357i	$0.635807\pi$
$158$	−10.6743	−0.849201
$159$	0	0
$160$	9.53747	0.754003
$161$	19.9442	1.57182
$162$	0	0
$163$	11.4733	0.898655	0.449327	−	0.893367i	$-0.351664\pi$
$163$	11.4733	0.898655	0.449327	+	0.893367i	$0.351664\pi$
$164$	−25.6101	−1.99981
$165$	0	0
$166$	−30.0168	−2.32975
$167$	−3.13075	−0.242265	−0.121132	−	0.992636i	$-0.538653\pi$
$167$	−3.13075	−0.242265	−0.121132	+	0.992636i	$0.538653\pi$
$168$	0	0
$169$	0	0
$170$	7.63798	0.585806
$171$	0	0
$172$	15.1028	1.15158
$173$	−8.26757	−0.628572	−0.314286	−	0.949328i	$-0.601765\pi$
$173$	−8.26757	−0.628572	−0.314286	+	0.949328i	$0.601765\pi$
$174$	0	0
$175$	−3.60168	−0.272261
$176$	−47.8884	−3.60972
$177$	0	0
$178$	25.5822	1.91746
$179$	18.4454	1.37867	0.689335	−	0.724443i	$-0.257903\pi$
$179$	18.4454	1.37867	0.689335	+	0.724443i	$0.257903\pi$
$180$	0	0
$181$	21.1028	1.56856	0.784281	−	0.620406i	$-0.213032\pi$
$181$	21.1028	1.56856	0.784281	+	0.620406i	$0.213032\pi$
$182$	0	0
$183$	0	0
$184$	−39.8884	−2.94061
$185$	3.53747	0.260080
$186$	0	0
$187$	−15.2760	−1.11709
$188$	18.1452	1.32338
$189$	0	0
$190$	−17.6101	−1.27757
$191$	8.70219	0.629669	0.314834	−	0.949147i	$-0.398051\pi$
$191$	8.70219	0.629669	0.314834	+	0.949147i	$0.398051\pi$
$192$	0	0
$193$	−19.2676	−1.38691	−0.693455	−	0.720500i	$-0.743912\pi$
$193$	−19.2676	−1.38691	−0.693455	+	0.720500i	$0.743912\pi$
$194$	14.5012	1.04112
$195$	0	0
$196$	28.4793	2.03424
$197$	−15.1475	−1.07922	−0.539609	−	0.841916i	$-0.681428\pi$
$197$	−15.1475	−1.07922	−0.539609	+	0.841916i	$0.681428\pi$
$198$	0	0
$199$	−4.53747	−0.321653	−0.160826	−	0.986983i	$-0.551416\pi$
$199$	−4.53747	−0.321653	−0.160826	+	0.986983i	$0.551416\pi$
$200$	7.20336	0.509354
$201$	0	0
$202$	−6.26150	−0.440558
$203$	6.60168	0.463347
$204$	0	0
$205$	−5.37041	−0.375086
$206$	47.9828	3.34312
$207$	0	0
$208$	0	0
$209$	35.2201	2.43623
$210$	0	0
$211$	−22.1475	−1.52470	−0.762350	−	0.647165i	$-0.775954\pi$
$211$	−22.1475	−1.52470	−0.762350	+	0.647165i	$0.775954\pi$
$212$	24.8134	1.70419
$213$	0	0
$214$	−28.4514	−1.94490
$215$	3.16706	0.215991
$216$	0	0
$217$	14.7771	1.00314
$218$	−36.0833	−2.44387
$219$	0	0
$220$	−24.8134	−1.67292
$221$	0	0
$222$	0	0
$223$	7.61007	0.509608	0.254804	−	0.966993i	$-0.417989\pi$
$223$	7.61007	0.509608	0.254804	+	0.966993i	$0.417989\pi$
$224$	−34.3509	−2.29517
$225$	0	0
$226$	29.1475	1.93887
$227$	23.3425	1.54930	0.774648	−	0.632392i	$-0.217927\pi$
$227$	23.3425	1.54930	0.774648	+	0.632392i	$0.217927\pi$
$228$	0	0
$229$	−0.824549	−0.0544877	−0.0272439	−	0.999629i	$-0.508673\pi$
$229$	−0.824549	−0.0544877	−0.0272439	+	0.999629i	$0.508673\pi$
$230$	−14.4067	−0.949951
$231$	0	0
$232$	−13.2034	−0.866843
$233$	13.4044	0.878150	0.439075	−	0.898450i	$-0.355306\pi$
$233$	13.4044	0.878150	0.439075	+	0.898450i	$0.355306\pi$
$234$	0	0
$235$	3.80504	0.248213
$236$	−35.1475	−2.28791
$237$	0	0
$238$	−27.5096	−1.78318
$239$	12.7966	0.827746	0.413873	−	0.910335i	$-0.364176\pi$
$239$	12.7966	0.827746	0.413873	+	0.910335i	$0.364176\pi$
$240$	0	0
$241$	−12.7687	−0.822506	−0.411253	−	0.911521i	$-0.634909\pi$
$241$	−12.7687	−0.822506	−0.411253	+	0.911521i	$0.634909\pi$
$242$	41.8218	2.68841
$243$	0	0
$244$	−16.3788	−1.04855
$245$	5.97209	0.381543
$246$	0	0
$247$	0	0
$248$	−29.5543	−1.87670
$249$	0	0
$250$	2.60168	0.164545
$251$	8.40672	0.530627	0.265314	−	0.964162i	$-0.414525\pi$
$251$	8.40672	0.530627	0.265314	+	0.964162i	$0.414525\pi$
$252$	0	0
$253$	28.8134	1.81149
$254$	−8.31227	−0.521558
$255$	0	0
$256$	−19.0749	−1.19218
$257$	−6.13915	−0.382950	−0.191475	−	0.981498i	$-0.561327\pi$
$257$	−6.13915	−0.382950	−0.191475	+	0.981498i	$0.561327\pi$
$258$	0	0
$259$	−12.7408	−0.791676
$260$	0	0
$261$	0	0
$262$	11.8995	0.735153
$263$	4.73010	0.291670	0.145835	−	0.989309i	$-0.453413\pi$
$263$	4.73010	0.291670	0.145835	+	0.989309i	$0.453413\pi$
$264$	0	0
$265$	5.20336	0.319640
$266$	63.4258	3.88889
$267$	0	0
$268$	−16.6961	−1.01988
$269$	5.44302	0.331867	0.165933	−	0.986137i	$-0.446936\pi$
$269$	5.44302	0.331867	0.165933	+	0.986137i	$0.446936\pi$
$270$	0	0
$271$	−25.4793	−1.54776	−0.773879	−	0.633333i	$-0.781686\pi$
$271$	−25.4793	−1.54776	−0.773879	+	0.633333i	$0.781686\pi$
$272$	27.0191	1.63827
$273$	0	0
$274$	27.7711	1.67771
$275$	−5.20336	−0.313774
$276$	0	0
$277$	−22.8134	−1.37073	−0.685363	−	0.728201i	$-0.740357\pi$
$277$	−22.8134	−1.37073	−0.685363	+	0.728201i	$0.740357\pi$
$278$	−42.0107	−2.51964
$279$	0	0
$280$	−25.9442	−1.55046
$281$	−2.16706	−0.129276	−0.0646378	−	0.997909i	$-0.520589\pi$
$281$	−2.16706	−0.129276	−0.0646378	+	0.997909i	$0.520589\pi$
$282$	0	0
$283$	−29.7469	−1.76827	−0.884135	−	0.467232i	$-0.845251\pi$
$283$	−29.7469	−1.76827	−0.884135	+	0.467232i	$0.845251\pi$
$284$	−46.2783	−2.74611
$285$	0	0
$286$	0	0
$287$	19.3425	1.14175
$288$	0	0
$289$	−8.38114	−0.493008
$290$	−4.76873	−0.280030
$291$	0	0
$292$	3.83901	0.224661
$293$	33.0857	1.93289	0.966443	−	0.256883i	$-0.0826954\pi$
$293$	33.0857	1.93289	0.966443	+	0.256883i	$0.0826954\pi$
$294$	0	0
$295$	−7.37041	−0.429122
$296$	25.4817	1.48109
$297$	0	0
$298$	−25.1475	−1.45676
$299$	0	0
$300$	0	0
$301$	−11.4067	−0.657472
$302$	48.6850	2.80151
$303$	0	0
$304$	−62.2951	−3.57287
$305$	−3.43462	−0.196666
$306$	0	0
$307$	14.3704	0.820163	0.410081	−	0.912049i	$-0.365500\pi$
$307$	14.3704	0.820163	0.410081	+	0.912049i	$0.365500\pi$
$308$	89.3700	5.09233
$309$	0	0
$310$	−10.6743	−0.606259
$311$	8.70685	0.493720	0.246860	−	0.969051i	$-0.420601\pi$
$311$	8.70685	0.493720	0.246860	+	0.969051i	$0.420601\pi$
$312$	0	0
$313$	−8.16472	−0.461497	−0.230749	−	0.973013i	$-0.574118\pi$
$313$	−8.16472	−0.461497	−0.230749	+	0.973013i	$0.574118\pi$
$314$	−26.9805	−1.52260
$315$	0	0
$316$	−19.5654	−1.10064
$317$	13.4090	0.753127	0.376564	−	0.926391i	$-0.377106\pi$
$317$	13.4090	0.753127	0.376564	+	0.926391i	$0.377106\pi$
$318$	0	0
$319$	9.53747	0.533996
$320$	6.40672	0.358146
$321$	0	0
$322$	51.8884	2.89163
$323$	−19.8716	−1.10568
$324$	0	0
$325$	0	0
$326$	29.8497	1.65322
$327$	0	0
$328$	−38.6850	−2.13602
$329$	−13.7045	−0.755555
$330$	0	0
$331$	−21.4793	−1.18061	−0.590305	−	0.807180i	$-0.700993\pi$
$331$	−21.4793	−1.18061	−0.590305	+	0.807180i	$0.700993\pi$
$332$	−55.0191	−3.01957
$333$	0	0
$334$	−8.14521	−0.445686
$335$	−3.50117	−0.191289
$336$	0	0
$337$	−7.44535	−0.405574	−0.202787	−	0.979223i	$-0.565000\pi$
$337$	−7.44535	−0.405574	−0.202787	+	0.979223i	$0.565000\pi$
$338$	0	0
$339$	0	0
$340$	14.0000	0.759257
$341$	21.3486	1.15609
$342$	0	0
$343$	3.70219	0.199900
$344$	22.8134	1.23002
$345$	0	0
$346$	−21.5096	−1.15636
$347$	24.9465	1.33920	0.669600	−	0.742722i	$-0.266466\pi$
$347$	24.9465	1.33920	0.669600	+	0.742722i	$0.266466\pi$
$348$	0	0
$349$	−2.10284	−0.112563	−0.0562813	−	0.998415i	$-0.517924\pi$
$349$	−2.10284	−0.112563	−0.0562813	+	0.998415i	$0.517924\pi$
$350$	−9.37041	−0.500870
$351$	0	0
$352$	−49.6269	−2.64512
$353$	18.5398	0.986774	0.493387	−	0.869810i	$-0.335759\pi$
$353$	18.5398	0.986774	0.493387	+	0.869810i	$0.335759\pi$
$354$	0	0
$355$	−9.70452	−0.515063
$356$	46.8907	2.48520
$357$	0	0
$358$	47.9889	2.53629
$359$	−4.75801	−0.251118	−0.125559	−	0.992086i	$-0.540072\pi$
$359$	−4.75801	−0.251118	−0.125559	+	0.992086i	$0.540072\pi$
$360$	0	0
$361$	26.8158	1.41136
$362$	54.9028	2.88563
$363$	0	0
$364$	0	0
$365$	0.805037	0.0421376
$366$	0	0
$367$	−10.2420	−0.534628	−0.267314	−	0.963610i	$-0.586136\pi$
$367$	−10.2420	−0.534628	−0.267314	+	0.963610i	$0.586136\pi$
$368$	−50.9633	−2.65665
$369$	0	0
$370$	9.20336	0.478460
$371$	−18.7408	−0.972975
$372$	0	0
$373$	−23.3402	−1.20851	−0.604254	−	0.796792i	$-0.706529\pi$
$373$	−23.3402	−1.20851	−0.604254	+	0.796792i	$0.706529\pi$
$374$	−39.7432	−2.05507
$375$	0	0
$376$	27.4090	1.41351
$377$	0	0
$378$	0	0
$379$	35.6571	1.83158	0.915791	−	0.401655i	$-0.131565\pi$
$379$	35.6571	1.83158	0.915791	+	0.401655i	$0.131565\pi$
$380$	−32.2783	−1.65584
$381$	0	0
$382$	22.6403	1.15838
$383$	−30.6185	−1.56453	−0.782265	−	0.622945i	$-0.785936\pi$
$383$	−30.6185	−1.56453	−0.782265	+	0.622945i	$0.785936\pi$
$384$	0	0
$385$	18.7408	0.955121
$386$	−50.1280	−2.55145
$387$	0	0
$388$	26.5798	1.34939
$389$	−25.0191	−1.26852	−0.634260	−	0.773120i	$-0.718695\pi$
$389$	−25.0191	−1.26852	−0.634260	+	0.773120i	$0.718695\pi$
$390$	0	0
$391$	−16.2568	−0.822144
$392$	43.0191	2.17279
$393$	0	0
$394$	−39.4090	−1.98540
$395$	−4.10284	−0.206437
$396$	0	0
$397$	−10.8329	−0.543690	−0.271845	−	0.962341i	$-0.587634\pi$
$397$	−10.8329	−0.543690	−0.271845	+	0.962341i	$0.587634\pi$
$398$	−11.8050	−0.591733
$399$	0	0
$400$	9.20336	0.460168
$401$	−24.4793	−1.22244	−0.611220	−	0.791461i	$-0.709321\pi$
$401$	−24.4793	−1.22244	−0.611220	+	0.791461i	$0.709321\pi$
$402$	0	0
$403$	0	0
$404$	−11.4770	−0.571002
$405$	0	0
$406$	17.1755	0.852403
$407$	−18.4067	−0.912387
$408$	0	0
$409$	−26.7106	−1.32075	−0.660377	−	0.750934i	$-0.729603\pi$
$409$	−26.7106	−1.32075	−0.660377	+	0.750934i	$0.729603\pi$
$410$	−13.9721	−0.690032
$411$	0	0
$412$	87.9499	4.33298
$413$	26.5459	1.30624
$414$	0	0
$415$	−11.5375	−0.566352
$416$	0	0
$417$	0	0
$418$	91.6315	4.48184
$419$	−15.0363	−0.734571	−0.367286	−	0.930108i	$-0.619713\pi$
$419$	−15.0363	−0.734571	−0.367286	+	0.930108i	$0.619713\pi$
$420$	0	0
$421$	5.90182	0.287637	0.143818	−	0.989604i	$-0.454062\pi$
$421$	5.90182	0.287637	0.143818	+	0.989604i	$0.454062\pi$
$422$	−57.6208	−2.80494
$423$	0	0
$424$	37.4817	1.82027
$425$	2.93579	0.142407
$426$	0	0
$427$	12.3704	0.598646
$428$	−52.1499	−2.52076
$429$	0	0
$430$	8.23966	0.397352
$431$	39.3486	1.89535	0.947677	−	0.319231i	$-0.103425\pi$
$431$	39.3486	1.89535	0.947677	+	0.319231i	$0.103425\pi$
$432$	0	0
$433$	12.4151	0.596632	0.298316	−	0.954467i	$-0.403575\pi$
$433$	12.4151	0.596632	0.298316	+	0.954467i	$0.403575\pi$
$434$	38.4454	1.84544
$435$	0	0
$436$	−66.1388	−3.16747
$437$	37.4817	1.79299
$438$	0	0
$439$	31.8413	1.51970	0.759852	−	0.650096i	$-0.225271\pi$
$439$	31.8413	1.51970	0.759852	+	0.650096i	$0.225271\pi$
$440$	−37.4817	−1.78687
$441$	0	0
$442$	0	0
$443$	1.06421	0.0505622	0.0252811	−	0.999680i	$-0.491952\pi$
$443$	1.06421	0.0505622	0.0252811	+	0.999680i	$0.491952\pi$
$444$	0	0
$445$	9.83294	0.466126
$446$	19.7990	0.937509
$447$	0	0
$448$	−23.0749	−1.09019
$449$	15.4044	0.726978	0.363489	−	0.931599i	$-0.381585\pi$
$449$	15.4044	0.726978	0.363489	+	0.931599i	$0.381585\pi$
$450$	0	0
$451$	27.9442	1.31584
$452$	53.4258	2.51294
$453$	0	0
$454$	60.7297	2.85019
$455$	0	0
$456$	0	0
$457$	9.57377	0.447842	0.223921	−	0.974607i	$-0.428114\pi$
$457$	9.57377	0.447842	0.223921	+	0.974607i	$0.428114\pi$
$458$	−2.14521	−0.100239
$459$	0	0
$460$	−26.4067	−1.23122
$461$	16.3727	0.762555	0.381277	−	0.924461i	$-0.375484\pi$
$461$	16.3727	0.762555	0.381277	+	0.924461i	$0.375484\pi$
$462$	0	0
$463$	24.6487	1.14552	0.572761	−	0.819722i	$-0.305872\pi$
$463$	24.6487	1.14552	0.572761	+	0.819722i	$0.305872\pi$
$464$	−16.8692	−0.783135
$465$	0	0
$466$	34.8739	1.61550
$467$	20.3402	0.941231	0.470616	−	0.882338i	$-0.344032\pi$
$467$	20.3402	0.941231	0.470616	+	0.882338i	$0.344032\pi$
$468$	0	0
$469$	12.6101	0.582279
$470$	9.89949	0.456629
$471$	0	0
$472$	−53.0917	−2.44374
$473$	−16.4793	−0.757720
$474$	0	0
$475$	−6.76873	−0.310571
$476$	−50.4235	−2.31116
$477$	0	0
$478$	33.2928	1.52278
$479$	−0.162393	−0.00741993	−0.00370996	−	0.999993i	$-0.501181\pi$
$479$	−0.162393	−0.00741993	−0.00370996	+	0.999993i	$0.501181\pi$
$480$	0	0
$481$	0	0
$482$	−33.2201	−1.51314
$483$	0	0
$484$	76.6571	3.48441
$485$	5.57377	0.253092
$486$	0	0
$487$	−2.56305	−0.116143	−0.0580713	−	0.998312i	$-0.518495\pi$
$487$	−2.56305	−0.116143	−0.0580713	+	0.998312i	$0.518495\pi$
$488$	−24.7408	−1.11996
$489$	0	0
$490$	15.5375	0.701911
$491$	−28.4407	−1.28351	−0.641755	−	0.766910i	$-0.721793\pi$
$491$	−28.4407	−1.28351	−0.641755	+	0.766910i	$0.721793\pi$
$492$	0	0
$493$	−5.38114	−0.242354
$494$	0	0
$495$	0	0
$496$	−37.7599	−1.69547
$497$	34.9526	1.56784
$498$	0	0
$499$	27.8605	1.24721	0.623603	−	0.781741i	$-0.285668\pi$
$499$	27.8605	1.24721	0.623603	+	0.781741i	$0.285668\pi$
$500$	4.76873	0.213264
$501$	0	0
$502$	21.8716	0.976176
$503$	−31.4258	−1.40121	−0.700604	−	0.713550i	$-0.747086\pi$
$503$	−31.4258	−1.40121	−0.700604	+	0.713550i	$0.747086\pi$
$504$	0	0
$505$	−2.40672	−0.107097
$506$	74.9633	3.33253
$507$	0	0
$508$	−15.2359	−0.675985
$509$	16.2225	0.719049	0.359524	−	0.933136i	$-0.382939\pi$
$509$	16.2225	0.719049	0.359524	+	0.933136i	$0.382939\pi$
$510$	0	0
$511$	−2.89949	−0.128266
$512$	−44.8134	−1.98049
$513$	0	0
$514$	−15.9721	−0.704499
$515$	18.4430	0.812697
$516$	0	0
$517$	−19.7990	−0.870758
$518$	−33.1475	−1.45642
$519$	0	0
$520$	0	0
$521$	20.0386	0.877909	0.438954	−	0.898509i	$-0.355349\pi$
$521$	20.0386	0.877909	0.438954	+	0.898509i	$0.355349\pi$
$522$	0	0
$523$	−13.2592	−0.579783	−0.289892	−	0.957059i	$-0.593619\pi$
$523$	−13.2592	−0.579783	−0.289892	+	0.957059i	$0.593619\pi$
$524$	21.8111	0.952822
$525$	0	0
$526$	12.3062	0.536576
$527$	−12.0451	−0.524692
$528$	0	0
$529$	7.66356	0.333198
$530$	13.5375	0.588030
$531$	0	0
$532$	116.256	5.04034
$533$	0	0
$534$	0	0
$535$	−10.9358	−0.472795
$536$	−25.2201	−1.08934
$537$	0	0
$538$	14.1610	0.610524
$539$	−31.0749	−1.33849
$540$	0	0
$541$	−35.6850	−1.53422	−0.767109	−	0.641516i	$-0.778306\pi$
$541$	−35.6850	−1.53422	−0.767109	+	0.641516i	$0.778306\pi$
$542$	−66.2890	−2.84736
$543$	0	0
$544$	28.0000	1.20049
$545$	−13.8692	−0.594093
$546$	0	0
$547$	−0.627256	−0.0268195	−0.0134098	−	0.999910i	$-0.504269\pi$
$547$	−0.627256	−0.0268195	−0.0134098	+	0.999910i	$0.504269\pi$
$548$	50.9028	2.17446
$549$	0	0
$550$	−13.5375	−0.577240
$551$	12.4067	0.528544
$552$	0	0
$553$	14.7771	0.628387
$554$	−59.3532	−2.52168
$555$	0	0
$556$	−77.0033	−3.26567
$557$	9.20802	0.390156	0.195078	−	0.980788i	$-0.437504\pi$
$557$	9.20802	0.390156	0.195078	+	0.980788i	$0.437504\pi$
$558$	0	0
$559$	0	0
$560$	−33.1475	−1.40074
$561$	0	0
$562$	−5.63798	−0.237824
$563$	−2.66822	−0.112452	−0.0562260	−	0.998418i	$-0.517907\pi$
$563$	−2.66822	−0.112452	−0.0562260	+	0.998418i	$0.517907\pi$
$564$	0	0
$565$	11.2034	0.471329
$566$	−77.3919	−3.25302
$567$	0	0
$568$	−69.9052	−2.93316
$569$	26.1838	1.09768	0.548842	−	0.835926i	$-0.315069\pi$
$569$	26.1838	1.09768	0.548842	+	0.835926i	$0.315069\pi$
$570$	0	0
$571$	−19.2481	−0.805506	−0.402753	−	0.915309i	$-0.631947\pi$
$571$	−19.2481	−0.805506	−0.402753	+	0.915309i	$0.631947\pi$
$572$	0	0
$573$	0	0
$574$	50.3230	2.10044
$575$	−5.53747	−0.230928
$576$	0	0
$577$	−23.8716	−0.993787	−0.496893	−	0.867812i	$-0.665526\pi$
$577$	−23.8716	−0.993787	−0.496893	+	0.867812i	$0.665526\pi$
$578$	−21.8050	−0.906970
$579$	0	0
$580$	−8.74083	−0.362943
$581$	41.5543	1.72396
$582$	0	0
$583$	−27.0749	−1.12133
$584$	5.79897	0.239963
$585$	0	0
$586$	86.0783	3.55586
$587$	28.8753	1.19181	0.595906	−	0.803054i	$-0.296793\pi$
$587$	28.8753	1.19181	0.595906	+	0.803054i	$0.296793\pi$
$588$	0	0
$589$	27.7711	1.14429
$590$	−19.1755	−0.789441
$591$	0	0
$592$	32.5566	1.33807
$593$	−8.74083	−0.358943	−0.179471	−	0.983763i	$-0.557439\pi$
$593$	−8.74083	−0.358943	−0.179471	+	0.983763i	$0.557439\pi$
$594$	0	0
$595$	−10.5738	−0.433482
$596$	−46.0941	−1.88809
$597$	0	0
$598$	0	0
$599$	−21.5929	−0.882262	−0.441131	−	0.897443i	$-0.645423\pi$
$599$	−21.5929	−0.882262	−0.441131	+	0.897443i	$0.645423\pi$
$600$	0	0
$601$	30.2504	1.23394	0.616970	−	0.786987i	$-0.288360\pi$
$601$	30.2504	1.23394	0.616970	+	0.786987i	$0.288360\pi$
$602$	−29.6766	−1.20953
$603$	0	0
$604$	89.2369	3.63100
$605$	16.0749	0.653539
$606$	0	0
$607$	−22.5072	−0.913540	−0.456770	−	0.889585i	$-0.650994\pi$
$607$	−22.5072	−0.913540	−0.456770	+	0.889585i	$0.650994\pi$
$608$	−64.5566	−2.61812
$609$	0	0
$610$	−8.93579	−0.361800
$611$	0	0
$612$	0	0
$613$	−18.7771	−0.758401	−0.379201	−	0.925315i	$-0.623801\pi$
$613$	−18.7771	−0.758401	−0.379201	+	0.925315i	$0.623801\pi$
$614$	37.3872	1.50882
$615$	0	0
$616$	134.997	5.43918
$617$	−3.61007	−0.145336	−0.0726681	−	0.997356i	$-0.523151\pi$
$617$	−3.61007	−0.145336	−0.0726681	+	0.997356i	$0.523151\pi$
$618$	0	0
$619$	−2.87158	−0.115419	−0.0577093	−	0.998333i	$-0.518380\pi$
$619$	−2.87158	−0.115419	−0.0577093	+	0.998333i	$0.518380\pi$
$620$	−19.5654	−0.785764
$621$	0	0
$622$	22.6524	0.908280
$623$	−35.4151	−1.41888
$624$	0	0
$625$	1.00000	0.0400000
$626$	−21.2420	−0.849001
$627$	0	0
$628$	−49.4537	−1.97342
$629$	10.3853	0.414088
$630$	0	0
$631$	−16.9889	−0.676317	−0.338158	−	0.941089i	$-0.609804\pi$
$631$	−16.9889	−0.676317	−0.338158	+	0.941089i	$0.609804\pi$
$632$	−29.5543	−1.17561
$633$	0	0
$634$	34.8860	1.38550
$635$	−3.19496	−0.126788
$636$	0	0
$637$	0	0
$638$	24.8134	0.982373
$639$	0	0
$640$	−2.40672	−0.0951338
$641$	16.6124	0.656151	0.328075	−	0.944652i	$-0.393600\pi$
$641$	16.6124	0.656151	0.328075	+	0.944652i	$0.393600\pi$
$642$	0	0
$643$	−45.3402	−1.78804	−0.894021	−	0.448025i	$-0.852128\pi$
$643$	−45.3402	−1.78804	−0.894021	+	0.448025i	$0.852128\pi$
$644$	95.1085	3.74780
$645$	0	0
$646$	−51.6995	−2.03409
$647$	−4.86925	−0.191430	−0.0957149	−	0.995409i	$-0.530514\pi$
$647$	−4.86925	−0.191430	−0.0957149	+	0.995409i	$0.530514\pi$
$648$	0	0
$649$	38.3509	1.50540
$650$	0	0
$651$	0	0
$652$	54.7129	2.14272
$653$	−19.2699	−0.754089	−0.377045	−	0.926195i	$-0.623060\pi$
$653$	−19.2699	−0.754089	−0.377045	+	0.926195i	$0.623060\pi$
$654$	0	0
$655$	4.57377	0.178712
$656$	−49.4258	−1.92975
$657$	0	0
$658$	−35.6548	−1.38997
$659$	−0.334110	−0.0130151	−0.00650755	−	0.999979i	$-0.502071\pi$
$659$	−0.334110	−0.0130151	−0.00650755	+	0.999979i	$0.502071\pi$
$660$	0	0
$661$	13.6682	0.531632	0.265816	−	0.964024i	$-0.414359\pi$
$661$	13.6682	0.531632	0.265816	+	0.964024i	$0.414359\pi$
$662$	−55.8823	−2.17193
$663$	0	0
$664$	−83.1085	−3.22524
$665$	24.3788	0.945370
$666$	0	0
$667$	10.1499	0.393005
$668$	−14.9297	−0.577648
$669$	0	0
$670$	−9.10891	−0.351908
$671$	17.8716	0.689925
$672$	0	0
$673$	−21.8800	−0.843411	−0.421706	−	0.906733i	$-0.638568\pi$
$673$	−21.8800	−0.843411	−0.421706	+	0.906733i	$0.638568\pi$
$674$	−19.3704	−0.746120
$675$	0	0
$676$	0	0
$677$	17.0749	0.656243	0.328122	−	0.944636i	$-0.393584\pi$
$677$	17.0749	0.656243	0.328122	+	0.944636i	$0.393584\pi$
$678$	0	0
$679$	−20.0749	−0.770405
$680$	21.1475	0.810971
$681$	0	0
$682$	55.5421	2.12682
$683$	−26.7301	−1.02280	−0.511399	−	0.859343i	$-0.670873\pi$
$683$	−26.7301	−1.02280	−0.511399	+	0.859343i	$0.670873\pi$
$684$	0	0
$685$	10.6743	0.407843
$686$	9.63192	0.367748
$687$	0	0
$688$	29.1475	1.11124
$689$	0	0
$690$	0	0
$691$	−48.7153	−1.85322	−0.926608	−	0.376029i	$-0.877289\pi$
$691$	−48.7153	−1.85322	−0.926608	+	0.376029i	$0.877289\pi$
$692$	−39.4258	−1.49875
$693$	0	0
$694$	64.9028	2.46368
$695$	−16.1475	−0.612511
$696$	0	0
$697$	−15.7664	−0.597195
$698$	−5.47093	−0.207078
$699$	0	0
$700$	−17.1755	−0.649171
$701$	−22.9419	−0.866502	−0.433251	−	0.901273i	$-0.642634\pi$
$701$	−22.9419	−0.866502	−0.433251	+	0.901273i	$0.642634\pi$
$702$	0	0
$703$	−23.9442	−0.903072
$704$	−33.3364	−1.25641
$705$	0	0
$706$	48.2346	1.81533
$707$	8.66822	0.326002
$708$	0	0
$709$	7.14521	0.268344	0.134172	−	0.990958i	$-0.457163\pi$
$709$	7.14521	0.268344	0.134172	+	0.990958i	$0.457163\pi$
$710$	−25.2481	−0.947543
$711$	0	0
$712$	70.8302	2.65447
$713$	22.7194	0.850847
$714$	0	0
$715$	0	0
$716$	87.9610	3.28726
$717$	0	0
$718$	−12.3788	−0.461973
$719$	−41.9782	−1.56552	−0.782761	−	0.622323i	$-0.786189\pi$
$719$	−41.9782	−1.56552	−0.782761	+	0.622323i	$0.786189\pi$
$720$	0	0
$721$	−66.4258	−2.47383
$722$	69.7660	2.59642
$723$	0	0
$724$	100.634	3.74003
$725$	−1.83294	−0.0680739
$726$	0	0
$727$	−11.4965	−0.426382	−0.213191	−	0.977011i	$-0.568386\pi$
$727$	−11.4965	−0.426382	−0.213191	+	0.977011i	$0.568386\pi$
$728$	0	0
$729$	0	0
$730$	2.09445	0.0775190
$731$	9.29781	0.343892
$732$	0	0
$733$	−46.1136	−1.70324	−0.851622	−	0.524157i	$-0.824381\pi$
$733$	−46.1136	−1.70324	−0.851622	+	0.524157i	$0.824381\pi$
$734$	−26.6464	−0.983536
$735$	0	0
$736$	−52.8134	−1.94673
$737$	18.2178	0.671062
$738$	0	0
$739$	11.6101	0.427084	0.213542	−	0.976934i	$-0.431500\pi$
$739$	11.6101	0.427084	0.213542	+	0.976934i	$0.431500\pi$
$740$	16.8692	0.620126
$741$	0	0
$742$	−48.7576	−1.78995
$743$	13.4151	0.492153	0.246076	−	0.969250i	$-0.420859\pi$
$743$	13.4151	0.492153	0.246076	+	0.969250i	$0.420859\pi$
$744$	0	0
$745$	−9.66589	−0.354131
$746$	−60.7236	−2.22325
$747$	0	0
$748$	−72.8470	−2.66355
$749$	39.3872	1.43918
$750$	0	0
$751$	44.1731	1.61190	0.805950	−	0.591984i	$-0.201655\pi$
$751$	44.1731	1.61190	0.805950	+	0.591984i	$0.201655\pi$
$752$	35.0191	1.27702
$753$	0	0
$754$	0	0
$755$	18.7129	0.681033
$756$	0	0
$757$	7.97209	0.289751	0.144875	−	0.989450i	$-0.453722\pi$
$757$	7.97209	0.289751	0.144875	+	0.989450i	$0.453722\pi$
$758$	92.7683	3.36950
$759$	0	0
$760$	−48.7576	−1.76862
$761$	13.6659	0.495388	0.247694	−	0.968838i	$-0.420327\pi$
$761$	13.6659	0.495388	0.247694	+	0.968838i	$0.420327\pi$
$762$	0	0
$763$	49.9526	1.80840
$764$	41.4984	1.50136
$765$	0	0
$766$	−79.6594	−2.87821
$767$	0	0
$768$	0	0
$769$	−16.4904	−0.594660	−0.297330	−	0.954775i	$-0.596096\pi$
$769$	−16.4904	−0.594660	−0.297330	+	0.954775i	$0.596096\pi$
$770$	48.7576	1.75710
$771$	0	0
$772$	−91.8819	−3.30690
$773$	−45.7041	−1.64386	−0.821932	−	0.569586i	$-0.807104\pi$
$773$	−45.7041	−1.64386	−0.821932	+	0.569586i	$0.807104\pi$
$774$	0	0
$775$	−4.10284	−0.147379
$776$	40.1499	1.44130
$777$	0	0
$778$	−65.0917	−2.33365
$779$	36.3509	1.30241
$780$	0	0
$781$	50.4961	1.80689
$782$	−42.2951	−1.51247
$783$	0	0
$784$	54.9633	1.96298
$785$	−10.3704	−0.370136
$786$	0	0
$787$	48.8218	1.74031	0.870155	−	0.492778i	$-0.164018\pi$
$787$	48.8218	1.74031	0.870155	+	0.492778i	$0.164018\pi$
$788$	−72.2346	−2.57325
$789$	0	0
$790$	−10.6743	−0.379774
$791$	−40.3509	−1.43471
$792$	0	0
$793$	0	0
$794$	−28.1838	−1.00021
$795$	0	0
$796$	−21.6380	−0.766938
$797$	−13.7492	−0.487022	−0.243511	−	0.969898i	$-0.578299\pi$
$797$	−13.7492	−0.487022	−0.243511	+	0.969898i	$0.578299\pi$
$798$	0	0
$799$	11.1708	0.395194
$800$	9.53747	0.337200
$801$	0	0
$802$	−63.6873	−2.24888
$803$	−4.18890	−0.147823
$804$	0	0
$805$	19.9442	0.702940
$806$	0	0
$807$	0	0
$808$	−17.3364	−0.609894
$809$	−20.3341	−0.714909	−0.357455	−	0.933931i	$-0.616355\pi$
$809$	−20.3341	−0.714909	−0.357455	+	0.933931i	$0.616355\pi$
$810$	0	0
$811$	−22.4817	−0.789438	−0.394719	−	0.918802i	$-0.629158\pi$
$811$	−22.4817	−0.789438	−0.394719	+	0.918802i	$0.629158\pi$
$812$	31.4817	1.10479
$813$	0	0
$814$	−47.8884	−1.67849
$815$	11.4733	0.401891
$816$	0	0
$817$	−21.4370	−0.749984
$818$	−69.4924	−2.42974
$819$	0	0
$820$	−25.6101	−0.894343
$821$	−32.6077	−1.13802	−0.569009	−	0.822331i	$-0.692673\pi$
$821$	−32.6077	−1.13802	−0.569009	+	0.822331i	$0.692673\pi$
$822$	0	0
$823$	33.4817	1.16710	0.583549	−	0.812078i	$-0.301664\pi$
$823$	33.4817	1.16710	0.583549	+	0.812078i	$0.301664\pi$
$824$	132.852	4.62811
$825$	0	0
$826$	69.0638	2.40304
$827$	−51.0298	−1.77448	−0.887241	−	0.461306i	$-0.847381\pi$
$827$	−51.0298	−1.77448	−0.887241	+	0.461306i	$0.847381\pi$
$828$	0	0
$829$	21.1946	0.736118	0.368059	−	0.929802i	$-0.380022\pi$
$829$	21.1946	0.736118	0.368059	+	0.929802i	$0.380022\pi$
$830$	−30.0168	−1.04190
$831$	0	0
$832$	0	0
$833$	17.5328	0.607476
$834$	0	0
$835$	−3.13075	−0.108344
$836$	167.956	5.80886
$837$	0	0
$838$	−39.1196	−1.35137
$839$	53.8837	1.86027	0.930136	−	0.367215i	$-0.119689\pi$
$839$	53.8837	1.86027	0.930136	+	0.367215i	$0.119689\pi$
$840$	0	0
$841$	−25.6403	−0.884149
$842$	15.3546	0.529156
$843$	0	0
$844$	−105.616	−3.63544
$845$	0	0
$846$	0	0
$847$	−57.8968	−1.98936
$848$	47.8884	1.64449
$849$	0	0
$850$	7.63798	0.261981
$851$	−19.5886	−0.671489
$852$	0	0
$853$	4.06421	0.139156	0.0695780	−	0.997577i	$-0.477835\pi$
$853$	4.06421	0.139156	0.0695780	+	0.997577i	$0.477835\pi$
$854$	32.1838	1.10131
$855$	0	0
$856$	−78.7744	−2.69245
$857$	39.2141	1.33953	0.669764	−	0.742574i	$-0.266395\pi$
$857$	39.2141	1.33953	0.669764	+	0.742574i	$0.266395\pi$
$858$	0	0
$859$	−5.64031	−0.192445	−0.0962225	−	0.995360i	$-0.530676\pi$
$859$	−5.64031	−0.192445	−0.0962225	+	0.995360i	$0.530676\pi$
$860$	15.1028	0.515003
$861$	0	0
$862$	102.372	3.48682
$863$	−9.66589	−0.329031	−0.164515	−	0.986375i	$-0.552606\pi$
$863$	−9.66589	−0.329031	−0.164515	+	0.986375i	$0.552606\pi$
$864$	0	0
$865$	−8.26757	−0.281106
$866$	32.3001	1.09760
$867$	0	0
$868$	70.4682	2.39185
$869$	21.3486	0.724201
$870$	0	0
$871$	0	0
$872$	−99.9052	−3.38322
$873$	0	0
$874$	97.5152	3.29850
$875$	−3.60168	−0.121759
$876$	0	0
$877$	−15.8716	−0.535945	−0.267973	−	0.963427i	$-0.586354\pi$
$877$	−15.8716	−0.535945	−0.267973	+	0.963427i	$0.586354\pi$
$878$	82.8410	2.79575
$879$	0	0
$880$	−47.8884	−1.61432
$881$	29.2034	0.983886	0.491943	−	0.870627i	$-0.336287\pi$
$881$	29.2034	0.983886	0.491943	+	0.870627i	$0.336287\pi$
$882$	0	0
$883$	30.4598	1.02505	0.512527	−	0.858671i	$-0.328709\pi$
$883$	30.4598	1.02505	0.512527	+	0.858671i	$0.328709\pi$
$884$	0	0
$885$	0	0
$886$	2.76873	0.0930174
$887$	−11.5993	−0.389468	−0.194734	−	0.980856i	$-0.562384\pi$
$887$	−11.5993	−0.389468	−0.194734	+	0.980856i	$0.562384\pi$
$888$	0	0
$889$	11.5072	0.385940
$890$	25.5822	0.857516
$891$	0	0
$892$	36.2904	1.21509
$893$	−25.7553	−0.861868
$894$	0	0
$895$	18.4454	0.616560
$896$	8.66822	0.289585
$897$	0	0
$898$	40.0773	1.33740
$899$	7.52029	0.250816
$900$	0	0
$901$	15.2760	0.508916
$902$	72.7018	2.42071
$903$	0	0
$904$	80.7018	2.68410
$905$	21.1028	0.701482
$906$	0	0
$907$	42.9186	1.42509	0.712545	−	0.701627i	$-0.247543\pi$
$907$	42.9186	1.42509	0.712545	+	0.701627i	$0.247543\pi$
$908$	111.314	3.69409
$909$	0	0
$910$	0	0
$911$	−42.0726	−1.39393	−0.696964	−	0.717106i	$-0.745466\pi$
$911$	−42.0726	−1.39393	−0.696964	+	0.717106i	$0.745466\pi$
$912$	0	0
$913$	60.0336	1.98682
$914$	24.9079	0.823880
$915$	0	0
$916$	−3.93206	−0.129919
$917$	−16.4733	−0.543995
$918$	0	0
$919$	39.1150	1.29028	0.645142	−	0.764063i	$-0.276798\pi$
$919$	39.1150	1.29028	0.645142	+	0.764063i	$0.276798\pi$
$920$	−39.8884	−1.31508
$921$	0	0
$922$	42.5966	1.40285
$923$	0	0
$924$	0	0
$925$	3.53747	0.116311
$926$	64.1280	2.10738
$927$	0	0
$928$	−17.4817	−0.573863
$929$	10.4625	0.343265	0.171632	−	0.985161i	$-0.445096\pi$
$929$	10.4625	0.343265	0.171632	+	0.985161i	$0.445096\pi$
$930$	0	0
$931$	−40.4235	−1.32483
$932$	63.9220	2.09383
$933$	0	0
$934$	52.9186	1.73155
$935$	−15.2760	−0.499577
$936$	0	0
$937$	39.6269	1.29455	0.647277	−	0.762255i	$-0.275908\pi$
$937$	39.6269	1.29455	0.647277	+	0.762255i	$0.275908\pi$
$938$	32.8074	1.07120
$939$	0	0
$940$	18.1452	0.591832
$941$	15.3146	0.499242	0.249621	−	0.968344i	$-0.419694\pi$
$941$	15.3146	0.499242	0.249621	+	0.968344i	$0.419694\pi$
$942$	0	0
$943$	29.7385	0.968419
$944$	−67.8326	−2.20776
$945$	0	0
$946$	−42.8739	−1.39395
$947$	−33.2867	−1.08167	−0.540836	−	0.841128i	$-0.681892\pi$
$947$	−33.2867	−1.08167	−0.540836	+	0.841128i	$0.681892\pi$
$948$	0	0
$949$	0	0
$950$	−17.6101	−0.571346
$951$	0	0
$952$	−76.1667	−2.46858
$953$	−23.4090	−0.758293	−0.379147	−	0.925337i	$-0.623782\pi$
$953$	−23.4090	−0.758293	−0.379147	+	0.925337i	$0.623782\pi$
$954$	0	0
$955$	8.70219	0.281596
$956$	61.0238	1.97365
$957$	0	0
$958$	−0.422495	−0.0136502
$959$	−38.4454	−1.24147
$960$	0	0
$961$	−14.1667	−0.456989
$962$	0	0
$963$	0	0
$964$	−60.8907	−1.96116
$965$	−19.2676	−0.620245
$966$	0	0
$967$	−27.8669	−0.896140	−0.448070	−	0.893999i	$-0.647888\pi$
$967$	−27.8669	−0.896140	−0.448070	+	0.893999i	$0.647888\pi$
$968$	115.794	3.72175
$969$	0	0
$970$	14.5012	0.465604
$971$	4.51835	0.145001	0.0725003	−	0.997368i	$-0.476902\pi$
$971$	4.51835	0.145001	0.0725003	+	0.997368i	$0.476902\pi$
$972$	0	0
$973$	58.1583	1.86447
$974$	−6.66822	−0.213664
$975$	0	0
$976$	−31.6101	−1.01181
$977$	−42.4840	−1.35918	−0.679592	−	0.733591i	$-0.737843\pi$
$977$	−42.4840	−1.35918	−0.679592	+	0.733591i	$0.737843\pi$
$978$	0	0
$979$	−51.1643	−1.63522
$980$	28.4793	0.909739
$981$	0	0
$982$	−73.9935	−2.36123
$983$	9.87158	0.314854	0.157427	−	0.987531i	$-0.449680\pi$
$983$	9.87158	0.314854	0.157427	+	0.987531i	$0.449680\pi$
$984$	0	0
$985$	−15.1475	−0.482641
$986$	−14.0000	−0.445851
$987$	0	0
$988$	0	0
$989$	−17.5375	−0.557659
$990$	0	0
$991$	21.1196	0.670887	0.335444	−	0.942060i	$-0.391114\pi$
$991$	21.1196	0.670887	0.335444	+	0.942060i	$0.391114\pi$
$992$	−39.1308	−1.24240
$993$	0	0
$994$	90.9354	2.88430
$995$	−4.53747	−0.143847
$996$	0	0
$997$	17.0833	0.541035	0.270517	−	0.962715i	$-0.412805\pi$
$997$	17.0833	0.541035	0.270517	+	0.962715i	$0.412805\pi$
$998$	72.4840	2.29444
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7605.2.a.bw.1.3		3
3.2	odd	2		2535.2.a.ba.1.1		3
13.4	even	6		585.2.j.f.406.3		6
13.10	even	6		585.2.j.f.451.3		6
13.12	even	2		7605.2.a.bv.1.1		3
39.17	odd	6		195.2.i.d.16.1	✓	6
39.23	odd	6		195.2.i.d.61.1	yes	6
39.38	odd	2		2535.2.a.bb.1.3		3
195.17	even	12		975.2.bb.k.874.6		12
195.23	even	12		975.2.bb.k.724.6		12
195.62	even	12		975.2.bb.k.724.1		12
195.134	odd	6		975.2.i.l.601.3		6
195.173	even	12		975.2.bb.k.874.1		12
195.179	odd	6		975.2.i.l.451.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.i.d.16.1	✓	6	39.17	odd	6
195.2.i.d.61.1	yes	6	39.23	odd	6
585.2.j.f.406.3		6	13.4	even	6
585.2.j.f.451.3		6	13.10	even	6
975.2.i.l.451.3		6	195.179	odd	6
975.2.i.l.601.3		6	195.134	odd	6
975.2.bb.k.724.1		12	195.62	even	12
975.2.bb.k.724.6		12	195.23	even	12
975.2.bb.k.874.1		12	195.173	even	12
975.2.bb.k.874.6		12	195.17	even	12
2535.2.a.ba.1.1		3	3.2	odd	2
2535.2.a.bb.1.3		3	39.38	odd	2
7605.2.a.bv.1.1		3	13.12	even	2
7605.2.a.bw.1.3		3	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:	\( N \)	\(=\)	\( 7605 = 3^{2} \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7605.a (trivial)

\(f(q)\)	\(=\)	\(q+2.60168 q^{2} +4.76873 q^{4} +1.00000 q^{5} -3.60168 q^{7} +7.20336 q^{8} +O(q^{10})\)	\(q+2.60168 q^{2} +4.76873 q^{4} +1.00000 q^{5} -3.60168 q^{7} +7.20336 q^{8} +2.60168 q^{10} -5.20336 q^{11} -9.37041 q^{14} +9.20336 q^{16} +2.93579 q^{17} -6.76873 q^{19} +4.76873 q^{20} -13.5375 q^{22} -5.53747 q^{23} +1.00000 q^{25} -17.1755 q^{28} -1.83294 q^{29} -4.10284 q^{31} +9.53747 q^{32} +7.63798 q^{34} -3.60168 q^{35} +3.53747 q^{37} -17.6101 q^{38} +7.20336 q^{40} -5.37041 q^{41} +3.16706 q^{43} -24.8134 q^{44} -14.4067 q^{46} +3.80504 q^{47} +5.97209 q^{49} +2.60168 q^{50} +5.20336 q^{53} -5.20336 q^{55} -25.9442 q^{56} -4.76873 q^{58} -7.37041 q^{59} -3.43462 q^{61} -10.6743 q^{62} +6.40672 q^{64} -3.50117 q^{67} +14.0000 q^{68} -9.37041 q^{70} -9.70452 q^{71} +0.805037 q^{73} +9.20336 q^{74} -32.2783 q^{76} +18.7408 q^{77} -4.10284 q^{79} +9.20336 q^{80} -13.9721 q^{82} -11.5375 q^{83} +2.93579 q^{85} +8.23966 q^{86} -37.4817 q^{88} +9.83294 q^{89} -26.4067 q^{92} +9.89949 q^{94} -6.76873 q^{95} +5.57377 q^{97} +15.5375 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 6 q^{4} + 3 q^{5} - 3 q^{7} + 6 q^{8}+O(q^{10}) \) 3 * q + 6 * q^4 + 3 * q^5 - 3 * q^7 + 6 * q^8	\( 3 q + 6 q^{4} + 3 q^{5} - 3 q^{7} + 6 q^{8} - 12 q^{14} + 12 q^{16} - 12 q^{19} + 6 q^{20} - 24 q^{22} + 3 q^{25} - 12 q^{28} - 6 q^{29} - 3 q^{31} + 12 q^{32} - 3 q^{35} - 6 q^{37} - 6 q^{38} + 6 q^{40} + 9 q^{43} - 12 q^{44} - 12 q^{46} - 12 q^{47} - 6 q^{49} - 30 q^{56} - 6 q^{58} - 6 q^{59} - 3 q^{61} + 6 q^{62} - 12 q^{64} - 9 q^{67} + 42 q^{68} - 12 q^{70} - 12 q^{71} - 21 q^{73} + 12 q^{74} - 48 q^{76} + 24 q^{77} - 3 q^{79} + 12 q^{80} - 18 q^{82} - 18 q^{83} - 6 q^{86} - 48 q^{88} + 30 q^{89} - 48 q^{92} + 36 q^{94} - 12 q^{95} - 15 q^{97} + 30 q^{98}+O(q^{100}) \) 3 * q + 6 * q^4 + 3 * q^5 - 3 * q^7 + 6 * q^8 - 12 * q^14 + 12 * q^16 - 12 * q^19 + 6 * q^20 - 24 * q^22 + 3 * q^25 - 12 * q^28 - 6 * q^29 - 3 * q^31 + 12 * q^32 - 3 * q^35 - 6 * q^37 - 6 * q^38 + 6 * q^40 + 9 * q^43 - 12 * q^44 - 12 * q^46 - 12 * q^47 - 6 * q^49 - 30 * q^56 - 6 * q^58 - 6 * q^59 - 3 * q^61 + 6 * q^62 - 12 * q^64 - 9 * q^67 + 42 * q^68 - 12 * q^70 - 12 * q^71 - 21 * q^73 + 12 * q^74 - 48 * q^76 + 24 * q^77 - 3 * q^79 + 12 * q^80 - 18 * q^82 - 18 * q^83 - 6 * q^86 - 48 * q^88 + 30 * q^89 - 48 * q^92 + 36 * q^94 - 12 * q^95 - 15 * q^97 + 30 * q^98

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