LMFDB - Embedded newform 841.2.a.i.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [841,2,Mod(1,841)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(841, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("841.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.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:	$6.71541880999$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	8.8.2841328125.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} - 3x^{6} + 23x^{5} - 43x^{3} + 2x^{2} + 24x + 1 $ x^8 - 4x^7 - 3x^6 + 23x^5 - 43x^3 + 2x^2 + 24x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.0419454$ of defining polynomial
Character	$\chi$	$=$	841.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.0419454 q^{2} -3.02773 q^{3} -1.99824 q^{4} -1.74204 q^{5} -0.126999 q^{6} +2.05366 q^{7} -0.167708 q^{8} +6.16716 q^{9} -0.0730704 q^{10} +1.85185 q^{11} +6.05014 q^{12} +2.57790 q^{13} +0.0861414 q^{14} +5.27442 q^{15} +3.98945 q^{16} -5.23359 q^{17} +0.258684 q^{18} -0.379040 q^{19} +3.48101 q^{20} -6.21792 q^{21} +0.0776766 q^{22} +3.63048 q^{23} +0.507774 q^{24} -1.96531 q^{25} +0.108131 q^{26} -9.58931 q^{27} -4.10370 q^{28} +0.221238 q^{30} -2.36562 q^{31} +0.502754 q^{32} -5.60691 q^{33} -0.219525 q^{34} -3.57754 q^{35} -12.3235 q^{36} +6.56734 q^{37} -0.0158990 q^{38} -7.80518 q^{39} +0.292153 q^{40} -9.44586 q^{41} -0.260813 q^{42} +0.995519 q^{43} -3.70044 q^{44} -10.7434 q^{45} +0.152282 q^{46} -10.1675 q^{47} -12.0790 q^{48} -2.78250 q^{49} -0.0824356 q^{50} +15.8459 q^{51} -5.15126 q^{52} +9.93002 q^{53} -0.402227 q^{54} -3.22599 q^{55} -0.344414 q^{56} +1.14763 q^{57} -6.24449 q^{59} -10.5396 q^{60} +7.98529 q^{61} -0.0992270 q^{62} +12.6652 q^{63} -7.95780 q^{64} -4.49079 q^{65} -0.235184 q^{66} -4.13822 q^{67} +10.4580 q^{68} -10.9921 q^{69} -0.150061 q^{70} -2.28290 q^{71} -1.03428 q^{72} +9.06401 q^{73} +0.275470 q^{74} +5.95042 q^{75} +0.757414 q^{76} +3.80306 q^{77} -0.327391 q^{78} -10.2768 q^{79} -6.94976 q^{80} +10.5324 q^{81} -0.396210 q^{82} -15.6206 q^{83} +12.4249 q^{84} +9.11711 q^{85} +0.0417574 q^{86} -0.310570 q^{88} +9.61689 q^{89} -0.450637 q^{90} +5.29411 q^{91} -7.25457 q^{92} +7.16248 q^{93} -0.426481 q^{94} +0.660302 q^{95} -1.52221 q^{96} -5.17777 q^{97} -0.116713 q^{98} +11.4207 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 6 q^{3} + 6 q^{4} - q^{5} + 3 q^{6} - 15 q^{8} + 8 q^{9} + 3 q^{10} - 5 q^{11} - 12 q^{12} - 4 q^{13} - 15 q^{14} + 7 q^{15} - 2 q^{16} - 9 q^{17} + 11 q^{18} - 17 q^{19} - 7 q^{20} - 25 q^{21}+ \cdots - 15 q^{99}+O(q^{100}) $ 8 * q - 4 * q^2 - 6 * q^3 + 6 * q^4 - q^5 + 3 * q^6 - 15 * q^8 + 8 * q^9 + 3 * q^10 - 5 * q^11 - 12 * q^12 - 4 * q^13 - 15 * q^14 + 7 * q^15 - 2 * q^16 - 9 * q^17 + 11 * q^18 - 17 * q^19 - 7 * q^20 - 25 * q^21 + 25 * q^22 - 7 * q^23 + 25 * q^24 - 13 * q^25 - 3 * q^26 - 18 * q^27 + 25 * q^28 - 26 * q^30 - q^31 + 6 * q^32 + 12 * q^34 - 5 * q^35 - 19 * q^36 - 6 * q^37 - 14 * q^38 - 27 * q^39 + 25 * q^40 - 6 * q^41 + 15 * q^42 + 5 * q^43 - 20 * q^44 - q^45 - 14 * q^46 - 31 * q^47 - 11 * q^48 + 4 * q^49 - 11 * q^50 + 23 * q^51 + 2 * q^52 + 19 * q^53 - 46 * q^54 - 20 * q^55 - 20 * q^56 - 6 * q^57 - q^59 + 9 * q^60 - 21 * q^61 - 12 * q^62 - 10 * q^63 + q^64 - 17 * q^65 - 5 * q^66 + 2 * q^67 - 8 * q^68 + 14 * q^69 + 5 * q^70 - 12 * q^71 + 34 * q^73 - 27 * q^74 - 4 * q^75 + 16 * q^76 + 10 * q^77 + 6 * q^78 - 29 * q^79 - 41 * q^80 + 12 * q^81 - 22 * q^82 - 3 * q^83 + 10 * q^84 - 2 * q^85 - 5 * q^86 - 15 * q^88 - 36 * q^89 + 38 * q^90 - 4 * q^92 + 2 * q^93 + 13 * q^94 - 11 * q^95 - 2 * q^96 + 18 * q^97 - 27 * q^98 - 15 * q^99

Coefficient data

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

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

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

$2$	0.0419454	0.0296599	0.0148299	−	0.999890i	$-0.495279\pi$
$2$	0.0419454	0.0296599	0.0148299	+	0.999890i	$0.495279\pi$
$3$	−3.02773	−1.74806	−0.874031	−	0.485870i	$-0.838503\pi$
$3$	−3.02773	−1.74806	−0.874031	+	0.485870i	$0.838503\pi$
$4$	−1.99824	−0.999120
$5$	−1.74204	−0.779063	−0.389531	−	0.921013i	$-0.627363\pi$
$5$	−1.74204	−0.779063	−0.389531	+	0.921013i	$0.627363\pi$
$6$	−0.126999	−0.0518473
$7$	2.05366	0.776209	0.388104	−	0.921615i	$-0.373130\pi$
$7$	2.05366	0.776209	0.388104	+	0.921615i	$0.373130\pi$
$8$	−0.167708	−0.0592936
$9$	6.16716	2.05572
$10$	−0.0730704	−0.0231069
$11$	1.85185	0.558354	0.279177	−	0.960240i	$-0.409938\pi$
$11$	1.85185	0.558354	0.279177	+	0.960240i	$0.409938\pi$
$12$	6.05014	1.74652
$13$	2.57790	0.714980	0.357490	−	0.933917i	$-0.383633\pi$
$13$	2.57790	0.714980	0.357490	+	0.933917i	$0.383633\pi$
$14$	0.0861414	0.0230222
$15$	5.27442	1.36185
$16$	3.98945	0.997362
$17$	−5.23359	−1.26933	−0.634666	−	0.772787i	$-0.718862\pi$
$17$	−5.23359	−1.26933	−0.634666	+	0.772787i	$0.718862\pi$
$18$	0.258684	0.0609724
$19$	−0.379040	−0.0869578	−0.0434789	−	0.999054i	$-0.513844\pi$
$19$	−0.379040	−0.0869578	−0.0434789	+	0.999054i	$0.513844\pi$
$20$	3.48101	0.778377
$21$	−6.21792	−1.35686
$22$	0.0776766	0.0165607
$23$	3.63048	0.757007	0.378504	−	0.925600i	$-0.376439\pi$
$23$	3.63048	0.757007	0.378504	+	0.925600i	$0.376439\pi$
$24$	0.507774	0.103649
$25$	−1.96531	−0.393061
$26$	0.108131	0.0212062
$27$	−9.58931	−1.84546
$28$	−4.10370	−0.775526
$29$	0	0
$29$	0	0
$30$	0.221238	0.0403923
$31$	−2.36562	−0.424879	−0.212439	−	0.977174i	$-0.568141\pi$
$31$	−2.36562	−0.424879	−0.212439	+	0.977174i	$0.568141\pi$
$32$	0.502754	0.0888752
$33$	−5.60691	−0.976038
$34$	−0.219525	−0.0376482
$35$	−3.57754	−0.604715
$36$	−12.3235	−2.05391
$37$	6.56734	1.07966	0.539832	−	0.841773i	$-0.318488\pi$
$37$	6.56734	1.07966	0.539832	+	0.841773i	$0.318488\pi$
$38$	−0.0158990	−0.00257916
$39$	−7.80518	−1.24983
$40$	0.292153	0.0461935
$41$	−9.44586	−1.47520	−0.737598	−	0.675240i	$-0.764040\pi$
$41$	−9.44586	−1.47520	−0.737598	+	0.675240i	$0.764040\pi$
$42$	−0.260813	−0.0402443
$43$	0.995519	0.151815	0.0759076	−	0.997115i	$-0.475815\pi$
$43$	0.995519	0.151815	0.0759076	+	0.997115i	$0.475815\pi$
$44$	−3.70044	−0.557863
$45$	−10.7434	−1.60153
$46$	0.152282	0.0224527
$47$	−10.1675	−1.48309	−0.741543	−	0.670905i	$-0.765906\pi$
$47$	−10.1675	−1.48309	−0.741543	+	0.670905i	$0.765906\pi$
$48$	−12.0790	−1.74345
$49$	−2.78250	−0.397500
$50$	−0.0824356	−0.0116582
$51$	15.8459	2.21887
$52$	−5.15126	−0.714351
$53$	9.93002	1.36399	0.681997	−	0.731355i	$-0.261112\pi$
$53$	9.93002	1.36399	0.681997	+	0.731355i	$0.261112\pi$
$54$	−0.402227	−0.0547362
$55$	−3.22599	−0.434993
$56$	−0.344414	−0.0460242
$57$	1.14763	0.152008
$58$	0	0
$59$	−6.24449	−0.812963	−0.406482	−	0.913659i	$-0.633244\pi$
$59$	−6.24449	−0.812963	−0.406482	+	0.913659i	$0.633244\pi$
$60$	−10.5396	−1.36065
$61$	7.98529	1.02241	0.511206	−	0.859458i	$-0.329199\pi$
$61$	7.98529	1.02241	0.511206	+	0.859458i	$0.329199\pi$
$62$	−0.0992270	−0.0126018
$63$	12.6652	1.59567
$64$	−7.95780	−0.994726
$65$	−4.49079	−0.557014
$66$	−0.235184	−0.0289491
$67$	−4.13822	−0.505565	−0.252782	−	0.967523i	$-0.581346\pi$
$67$	−4.13822	−0.505565	−0.252782	+	0.967523i	$0.581346\pi$
$68$	10.4580	1.26822
$69$	−10.9921	−1.32330
$70$	−0.150061	−0.0179358
$71$	−2.28290	−0.270930	−0.135465	−	0.990782i	$-0.543253\pi$
$71$	−2.28290	−0.270930	−0.135465	+	0.990782i	$0.543253\pi$
$72$	−1.03428	−0.121891
$73$	9.06401	1.06086	0.530431	−	0.847728i	$-0.322030\pi$
$73$	9.06401	1.06086	0.530431	+	0.847728i	$0.322030\pi$
$74$	0.275470	0.0320227
$75$	5.95042	0.687096
$76$	0.757414	0.0868813
$77$	3.80306	0.433399
$78$	−0.327391	−0.0370698
$79$	−10.2768	−1.15622	−0.578112	−	0.815957i	$-0.696210\pi$
$79$	−10.2768	−1.15622	−0.578112	+	0.815957i	$0.696210\pi$
$80$	−6.94976	−0.777007
$81$	10.5324	1.17027
$82$	−0.396210	−0.0437541
$83$	−15.6206	−1.71459	−0.857294	−	0.514827i	$-0.827856\pi$
$83$	−15.6206	−1.71459	−0.857294	+	0.514827i	$0.827856\pi$
$84$	12.4249	1.35567
$85$	9.11711	0.988889
$86$	0.0417574	0.00450282
$87$	0	0
$88$	−0.310570	−0.0331069
$89$	9.61689	1.01939	0.509694	−	0.860356i	$-0.329758\pi$
$89$	9.61689	1.01939	0.509694	+	0.860356i	$0.329758\pi$
$90$	−0.450637	−0.0475013
$91$	5.29411	0.554974
$92$	−7.25457	−0.756341
$93$	7.16248	0.742714
$94$	−0.426481	−0.0439881
$95$	0.660302	0.0677456
$96$	−1.52221	−0.155359
$97$	−5.17777	−0.525723	−0.262862	−	0.964834i	$-0.584666\pi$
$97$	−5.17777	−0.525723	−0.262862	+	0.964834i	$0.584666\pi$
$98$	−0.116713	−0.0117898
$99$	11.4207	1.14782
$100$	3.92716	0.392716
$101$	8.46144	0.841945	0.420973	−	0.907073i	$-0.361689\pi$
$101$	8.46144	0.841945	0.420973	+	0.907073i	$0.361689\pi$
$102$	0.664663	0.0658114
$103$	3.51409	0.346254	0.173127	−	0.984900i	$-0.444613\pi$
$103$	3.51409	0.346254	0.173127	+	0.984900i	$0.444613\pi$
$104$	−0.432333	−0.0423938
$105$	10.8318	1.05708
$106$	0.416519	0.0404559
$107$	−4.44378	−0.429596	−0.214798	−	0.976658i	$-0.568909\pi$
$107$	−4.44378	−0.429596	−0.214798	+	0.976658i	$0.568909\pi$
$108$	19.1618	1.84384
$109$	−11.7628	−1.12667	−0.563335	−	0.826229i	$-0.690482\pi$
$109$	−11.7628	−1.12667	−0.563335	+	0.826229i	$0.690482\pi$
$110$	−0.135316	−0.0129018
$111$	−19.8842	−1.88732
$112$	8.19295	0.774161
$113$	−11.4197	−1.07428	−0.537139	−	0.843494i	$-0.680495\pi$
$113$	−11.4197	−1.07428	−0.537139	+	0.843494i	$0.680495\pi$
$114$	0.0481379	0.00450853
$115$	−6.32443	−0.589756
$116$	0	0
$117$	15.8983	1.46980
$118$	−0.261927	−0.0241124
$119$	−10.7480	−0.985267
$120$	−0.884561	−0.0807490
$121$	−7.57065	−0.688241
$122$	0.334946	0.0303246
$123$	28.5995	2.57873
$124$	4.72709	0.424505
$125$	12.1338	1.08528
$126$	0.531248	0.0473273
$127$	12.0462	1.06893	0.534466	−	0.845190i	$-0.320513\pi$
$127$	12.0462	1.06893	0.534466	+	0.845190i	$0.320513\pi$
$128$	−1.33930	−0.118379
$129$	−3.01417	−0.265383
$130$	−0.188368	−0.0165210
$131$	−14.5943	−1.27511	−0.637556	−	0.770404i	$-0.720054\pi$
$131$	−14.5943	−1.27511	−0.637556	+	0.770404i	$0.720054\pi$
$132$	11.2040	0.975179
$133$	−0.778418	−0.0674974
$134$	−0.173579	−0.0149950
$135$	16.7049	1.43773
$136$	0.877713	0.0752633
$137$	2.86241	0.244552	0.122276	−	0.992496i	$-0.460981\pi$
$137$	2.86241	0.244552	0.122276	+	0.992496i	$0.460981\pi$
$138$	−0.461069	−0.0392488
$139$	−22.2683	−1.88877	−0.944387	−	0.328835i	$-0.893344\pi$
$139$	−22.2683	−1.88877	−0.944387	+	0.328835i	$0.893344\pi$
$140$	7.14879	0.604183
$141$	30.7846	2.59253
$142$	−0.0957570	−0.00803575
$143$	4.77388	0.399212
$144$	24.6036	2.05030
$145$	0	0
$146$	0.380194	0.0314650
$147$	8.42466	0.694854
$148$	−13.1231	−1.07871
$149$	4.23624	0.347046	0.173523	−	0.984830i	$-0.444485\pi$
$149$	4.23624	0.347046	0.173523	+	0.984830i	$0.444485\pi$
$150$	0.249593	0.0203792
$151$	7.79459	0.634315	0.317158	−	0.948373i	$-0.397272\pi$
$151$	7.79459	0.634315	0.317158	+	0.948373i	$0.397272\pi$
$152$	0.0635680	0.00515604
$153$	−32.2764	−2.60939
$154$	0.159521	0.0128546
$155$	4.12101	0.331007
$156$	15.5966	1.24873
$157$	−6.32741	−0.504982	−0.252491	−	0.967599i	$-0.581250\pi$
$157$	−6.32741	−0.504982	−0.252491	+	0.967599i	$0.581250\pi$
$158$	−0.431062	−0.0342935
$159$	−30.0654	−2.38434
$160$	−0.875817	−0.0692394
$161$	7.45575	0.587596
$162$	0.441785	0.0347099
$163$	1.75944	0.137810	0.0689051	−	0.997623i	$-0.478049\pi$
$163$	1.75944	0.137810	0.0689051	+	0.997623i	$0.478049\pi$
$164$	18.8751	1.47390
$165$	9.76744	0.760394
$166$	−0.655214	−0.0508545
$167$	−13.9203	−1.07718	−0.538592	−	0.842567i	$-0.681044\pi$
$167$	−13.9203	−1.07718	−0.538592	+	0.842567i	$0.681044\pi$
$168$	1.04279	0.0804532
$169$	−6.35445	−0.488804
$170$	0.382421	0.0293303
$171$	−2.33760	−0.178761
$172$	−1.98929	−0.151682
$173$	−8.38553	−0.637540	−0.318770	−	0.947832i	$-0.603270\pi$
$173$	−8.38553	−0.637540	−0.318770	+	0.947832i	$0.603270\pi$
$174$	0	0
$175$	−4.03606	−0.305098
$176$	7.38786	0.556881
$177$	18.9066	1.42111
$178$	0.403384	0.0302349
$179$	−19.6755	−1.47062	−0.735308	−	0.677733i	$-0.762963\pi$
$179$	−19.6755	−1.47062	−0.735308	+	0.677733i	$0.762963\pi$
$180$	21.4679	1.60013
$181$	12.0535	0.895932	0.447966	−	0.894051i	$-0.352149\pi$
$181$	12.0535	0.895932	0.447966	+	0.894051i	$0.352149\pi$
$182$	0.222064	0.0164604
$183$	−24.1773	−1.78724
$184$	−0.608859	−0.0448857
$185$	−11.4406	−0.841126
$186$	0.300433	0.0220288
$187$	−9.69183	−0.708737
$188$	20.3172	1.48178
$189$	−19.6931	−1.43247
$190$	0.0276966	0.00200932
$191$	−11.6202	−0.840810	−0.420405	−	0.907337i	$-0.638112\pi$
$191$	−11.6202	−0.840810	−0.420405	+	0.907337i	$0.638112\pi$
$192$	24.0941	1.73884
$193$	−19.0525	−1.37143	−0.685715	−	0.727871i	$-0.740510\pi$
$193$	−19.0525	−1.37143	−0.685715	+	0.727871i	$0.740510\pi$
$194$	−0.217184	−0.0155929
$195$	13.5969	0.973695
$196$	5.56010	0.397150
$197$	16.7067	1.19030	0.595151	−	0.803614i	$-0.297092\pi$
$197$	16.7067	1.19030	0.595151	+	0.803614i	$0.297092\pi$
$198$	0.479044	0.0340442
$199$	−8.90853	−0.631509	−0.315754	−	0.948841i	$-0.602258\pi$
$199$	−8.90853	−0.631509	−0.315754	+	0.948841i	$0.602258\pi$
$200$	0.329597	0.0233060
$201$	12.5294	0.883758
$202$	0.354918	0.0249720
$203$	0	0
$204$	−31.6639	−2.21692
$205$	16.4550	1.14927
$206$	0.147400	0.0102698
$207$	22.3897	1.55619
$208$	10.2844	0.713094
$209$	−0.701926	−0.0485533
$210$	0.454346	0.0313528
$211$	−0.254216	−0.0175010	−0.00875049	−	0.999962i	$-0.502785\pi$
$211$	−0.254216	−0.0175010	−0.00875049	+	0.999962i	$0.502785\pi$
$212$	−19.8426	−1.36279
$213$	6.91200	0.473603
$214$	−0.186396	−0.0127418
$215$	−1.73423	−0.118274
$216$	1.60820	0.109424
$217$	−4.85818	−0.329795
$218$	−0.493394	−0.0334169
$219$	−27.4434	−1.85445
$220$	6.44631	0.434610
$221$	−13.4917	−0.907547
$222$	−0.834049	−0.0559777
$223$	9.15674	0.613180	0.306590	−	0.951842i	$-0.400812\pi$
$223$	9.15674	0.613180	0.306590	+	0.951842i	$0.400812\pi$
$224$	1.03248	0.0689858
$225$	−12.1204	−0.808024
$226$	−0.479005	−0.0318629
$227$	−4.81446	−0.319547	−0.159773	−	0.987154i	$-0.551076\pi$
$227$	−4.81446	−0.319547	−0.159773	+	0.987154i	$0.551076\pi$
$228$	−2.29325	−0.151874
$229$	6.86601	0.453719	0.226859	−	0.973928i	$-0.427154\pi$
$229$	6.86601	0.453719	0.226859	+	0.973928i	$0.427154\pi$
$230$	−0.265281	−0.0174921
$231$	−11.5147	−0.757609
$232$	0	0
$233$	17.2302	1.12879	0.564393	−	0.825507i	$-0.309110\pi$
$233$	17.2302	1.12879	0.564393	+	0.825507i	$0.309110\pi$
$234$	0.666860	0.0435940
$235$	17.7122	1.15542
$236$	12.4780	0.812248
$237$	31.1152	2.02115
$238$	−0.450829	−0.0292229
$239$	−21.3042	−1.37805	−0.689026	−	0.724737i	$-0.741961\pi$
$239$	−21.3042	−1.37805	−0.689026	+	0.724737i	$0.741961\pi$
$240$	21.0420	1.35826
$241$	−8.99312	−0.579298	−0.289649	−	0.957133i	$-0.593539\pi$
$241$	−8.99312	−0.579298	−0.289649	+	0.957133i	$0.593539\pi$
$242$	−0.317554	−0.0204131
$243$	−3.12130	−0.200232
$244$	−15.9565	−1.02151
$245$	4.84722	0.309677
$246$	1.19962	0.0764849
$247$	−0.977127	−0.0621731
$248$	0.396734	0.0251926
$249$	47.2951	2.99721
$250$	0.508958	0.0321893
$251$	6.50262	0.410442	0.205221	−	0.978716i	$-0.434209\pi$
$251$	6.50262	0.410442	0.205221	+	0.978716i	$0.434209\pi$
$252$	−25.3082	−1.59426
$253$	6.72311	0.422678
$254$	0.505284	0.0317044
$255$	−27.6042	−1.72864
$256$	15.8594	0.991215
$257$	−5.78756	−0.361018	−0.180509	−	0.983573i	$-0.557774\pi$
$257$	−5.78756	−0.361018	−0.180509	+	0.983573i	$0.557774\pi$
$258$	−0.126430	−0.00787121
$259$	13.4871	0.838045
$260$	8.97368	0.556524
$261$	0	0
$262$	−0.612164	−0.0378196
$263$	−30.2467	−1.86509	−0.932547	−	0.361048i	$-0.882419\pi$
$263$	−30.2467	−1.86509	−0.932547	+	0.361048i	$0.882419\pi$
$264$	0.940322	0.0578728
$265$	−17.2985	−1.06264
$266$	−0.0326510	−0.00200196
$267$	−29.1174	−1.78195
$268$	8.26917	0.505120
$269$	−11.9363	−0.727766	−0.363883	−	0.931445i	$-0.618549\pi$
$269$	−11.9363	−0.727766	−0.363883	+	0.931445i	$0.618549\pi$
$270$	0.700695	0.0426429
$271$	17.5571	1.06652	0.533260	−	0.845951i	$-0.320967\pi$
$271$	17.5571	1.06652	0.533260	+	0.845951i	$0.320967\pi$
$272$	−20.8791	−1.26598
$273$	−16.0292	−0.970128
$274$	0.120065	0.00725337
$275$	−3.63946	−0.219468
$276$	21.9649	1.32213
$277$	1.07477	0.0645765	0.0322882	−	0.999479i	$-0.489721\pi$
$277$	1.07477	0.0645765	0.0322882	+	0.999479i	$0.489721\pi$
$278$	−0.934053	−0.0560208
$279$	−14.5892	−0.873432
$280$	0.599982	0.0358558
$281$	−29.8865	−1.78288	−0.891441	−	0.453138i	$-0.850305\pi$
$281$	−29.8865	−1.78288	−0.891441	+	0.453138i	$0.850305\pi$
$282$	1.29127	0.0768940
$283$	26.7501	1.59013	0.795065	−	0.606524i	$-0.207436\pi$
$283$	26.7501	1.59013	0.795065	+	0.606524i	$0.207436\pi$
$284$	4.56178	0.270692
$285$	−1.99922	−0.118423
$286$	0.200242	0.0118406
$287$	−19.3986	−1.14506
$288$	3.10057	0.182703
$289$	10.3905	0.611204
$290$	0	0
$291$	15.6769	0.918996
$292$	−18.1121	−1.05993
$293$	5.81037	0.339446	0.169723	−	0.985492i	$-0.445713\pi$
$293$	5.81037	0.339446	0.169723	+	0.985492i	$0.445713\pi$
$294$	0.353376	0.0206093
$295$	10.8781	0.633349
$296$	−1.10139	−0.0640172
$297$	−17.7580	−1.03042
$298$	0.177691	0.0102933
$299$	9.35900	0.541245
$300$	−11.8904	−0.686491
$301$	2.04445	0.117840
$302$	0.326947	0.0188137
$303$	−25.6190	−1.47177
$304$	−1.51216	−0.0867284
$305$	−13.9107	−0.796522
$306$	−1.35385	−0.0773942
$307$	−5.15345	−0.294123	−0.147061	−	0.989127i	$-0.546982\pi$
$307$	−5.15345	−0.294123	−0.147061	+	0.989127i	$0.546982\pi$
$308$	−7.59944	−0.433018
$309$	−10.6397	−0.605273
$310$	0.172857	0.00981763
$311$	10.6244	0.602453	0.301227	−	0.953553i	$-0.402604\pi$
$311$	10.6244	0.602453	0.301227	+	0.953553i	$0.402604\pi$
$312$	1.30899	0.0741069
$313$	16.7104	0.944526	0.472263	−	0.881458i	$-0.343437\pi$
$313$	16.7104	0.944526	0.472263	+	0.881458i	$0.343437\pi$
$314$	−0.265405	−0.0149777
$315$	−22.0633	−1.24313
$316$	20.5354	1.15521
$317$	1.49124	0.0837563	0.0418782	−	0.999123i	$-0.486666\pi$
$317$	1.49124	0.0837563	0.0418782	+	0.999123i	$0.486666\pi$
$318$	−1.26111	−0.0707193
$319$	0	0
$320$	13.8628	0.774954
$321$	13.4546	0.750961
$322$	0.312734	0.0174280
$323$	1.98374	0.110378
$324$	−21.0462	−1.16924
$325$	−5.06636	−0.281031
$326$	0.0738005	0.00408743
$327$	35.6145	1.96949
$328$	1.58414	0.0874697
$329$	−20.8806	−1.15118
$330$	0.409699	0.0225532
$331$	29.8803	1.64237	0.821184	−	0.570663i	$-0.193314\pi$
$331$	29.8803	1.64237	0.821184	+	0.570663i	$0.193314\pi$
$332$	31.2138	1.71308
$333$	40.5019	2.21949
$334$	−0.583892	−0.0319491
$335$	7.20894	0.393866
$336$	−24.8061	−1.35328
$337$	0.941345	0.0512783	0.0256392	−	0.999671i	$-0.491838\pi$
$337$	0.941345	0.0512783	0.0256392	+	0.999671i	$0.491838\pi$
$338$	−0.266540	−0.0144979
$339$	34.5759	1.87790
$340$	−18.2182	−0.988019
$341$	−4.38079	−0.237233
$342$	−0.0980516	−0.00530202
$343$	−20.0899	−1.08475
$344$	−0.166956	−0.00900168
$345$	19.1487	1.03093
$346$	−0.351734	−0.0189094
$347$	−8.65358	−0.464548	−0.232274	−	0.972650i	$-0.574617\pi$
$347$	−8.65358	−0.464548	−0.232274	+	0.972650i	$0.574617\pi$
$348$	0	0
$349$	−34.5616	−1.85004	−0.925021	−	0.379916i	$-0.875953\pi$
$349$	−34.5616	−1.85004	−0.925021	+	0.379916i	$0.875953\pi$
$350$	−0.169294	−0.00904916
$351$	−24.7203	−1.31947
$352$	0.931026	0.0496239
$353$	−14.4231	−0.767663	−0.383831	−	0.923403i	$-0.625396\pi$
$353$	−14.4231	−0.767663	−0.383831	+	0.923403i	$0.625396\pi$
$354$	0.793046	0.0421499
$355$	3.97689	0.211072
$356$	−19.2169	−1.01849
$357$	32.5420	1.72231
$358$	−0.825297	−0.0436183
$359$	−22.2909	−1.17647	−0.588235	−	0.808690i	$-0.700177\pi$
$359$	−22.2909	−1.17647	−0.588235	+	0.808690i	$0.700177\pi$
$360$	1.80175	0.0949608
$361$	−18.8563	−0.992438
$362$	0.505590	0.0265732
$363$	22.9219	1.20309
$364$	−10.5789	−0.554486
$365$	−15.7898	−0.826478
$366$	−1.01413	−0.0530092
$367$	5.08046	0.265198	0.132599	−	0.991170i	$-0.457668\pi$
$367$	5.08046	0.265198	0.132599	+	0.991170i	$0.457668\pi$
$368$	14.4836	0.755010
$369$	−58.2542	−3.03259
$370$	−0.479878	−0.0249477
$371$	20.3928	1.05874
$372$	−14.3124	−0.742061
$373$	25.5097	1.32084	0.660422	−	0.750894i	$-0.270377\pi$
$373$	25.5097	1.32084	0.660422	+	0.750894i	$0.270377\pi$
$374$	−0.406528	−0.0210210
$375$	−36.7380	−1.89714
$376$	1.70517	0.0879376
$377$	0	0
$378$	−0.826036	−0.0424867
$379$	8.31922	0.427330	0.213665	−	0.976907i	$-0.431460\pi$
$379$	8.31922	0.427330	0.213665	+	0.976907i	$0.431460\pi$
$380$	−1.31944	−0.0676860
$381$	−36.4728	−1.86856
$382$	−0.487415	−0.0249383
$383$	25.3223	1.29391	0.646956	−	0.762528i	$-0.276042\pi$
$383$	25.3223	1.29391	0.646956	+	0.762528i	$0.276042\pi$
$384$	4.05505	0.206933
$385$	−6.62508	−0.337645
$386$	−0.799165	−0.0406764
$387$	6.13953	0.312090
$388$	10.3464	0.525261
$389$	27.3249	1.38543	0.692714	−	0.721212i	$-0.256415\pi$
$389$	27.3249	1.38543	0.692714	+	0.721212i	$0.256415\pi$
$390$	0.570328	0.0288797
$391$	−19.0004	−0.960893
$392$	0.466647	0.0235692
$393$	44.1877	2.22897
$394$	0.700769	0.0353042
$395$	17.9025	0.900771
$396$	−22.8212	−1.14681
$397$	11.2253	0.563380	0.281690	−	0.959506i	$-0.409105\pi$
$397$	11.2253	0.563380	0.281690	+	0.959506i	$0.409105\pi$
$398$	−0.373672	−0.0187305
$399$	2.35684	0.117990
$400$	−7.84049	−0.392024
$401$	33.3016	1.66300	0.831500	−	0.555524i	$-0.187482\pi$
$401$	33.3016	1.66300	0.831500	+	0.555524i	$0.187482\pi$
$402$	0.525552	0.0262121
$403$	−6.09834	−0.303780
$404$	−16.9080	−0.841204
$405$	−18.3478	−0.911710
$406$	0	0
$407$	12.1617	0.602835
$408$	−2.65748	−0.131565
$409$	−16.0820	−0.795203	−0.397602	−	0.917558i	$-0.630157\pi$
$409$	−16.0820	−0.795203	−0.397602	+	0.917558i	$0.630157\pi$
$410$	0.690213	0.0340872
$411$	−8.66659	−0.427492
$412$	−7.02200	−0.345949
$413$	−12.8240	−0.631029
$414$	0.939146	0.0461565
$415$	27.2117	1.33577
$416$	1.29605	0.0635440
$417$	67.4225	3.30169
$418$	−0.0294426	−0.00144008
$419$	28.0762	1.37161	0.685806	−	0.727784i	$-0.259450\pi$
$419$	28.0762	1.37161	0.685806	+	0.727784i	$0.259450\pi$
$420$	−21.6446	−1.05615
$421$	30.4981	1.48638	0.743192	−	0.669078i	$-0.233311\pi$
$421$	30.4981	1.48638	0.743192	+	0.669078i	$0.233311\pi$
$422$	−0.0106632	−0.000519077 0
$423$	−62.7048	−3.04881
$424$	−1.66534	−0.0808761
$425$	10.2856	0.498925
$426$	0.289927	0.0140470
$427$	16.3990	0.793605
$428$	8.87974	0.429218
$429$	−14.4540	−0.697847
$430$	−0.0727430	−0.00350798
$431$	−9.72567	−0.468469	−0.234234	−	0.972180i	$-0.575258\pi$
$431$	−9.72567	−0.468469	−0.234234	+	0.972180i	$0.575258\pi$
$432$	−38.2560	−1.84060
$433$	−23.2297	−1.11635	−0.558174	−	0.829724i	$-0.688498\pi$
$433$	−23.2297	−1.11635	−0.558174	+	0.829724i	$0.688498\pi$
$434$	−0.203778	−0.00978166
$435$	0	0
$436$	23.5049	1.12568
$437$	−1.37610	−0.0658277
$438$	−1.15112	−0.0550028
$439$	−13.6277	−0.650414	−0.325207	−	0.945643i	$-0.605434\pi$
$439$	−13.6277	−0.650414	−0.325207	+	0.945643i	$0.605434\pi$
$440$	0.541024	0.0257923
$441$	−17.1601	−0.817148
$442$	−0.565913	−0.0269177
$443$	−9.17324	−0.435834	−0.217917	−	0.975967i	$-0.569926\pi$
$443$	−9.17324	−0.435834	−0.217917	+	0.975967i	$0.569926\pi$
$444$	39.7333	1.88566
$445$	−16.7530	−0.794168
$446$	0.384083	0.0181869
$447$	−12.8262	−0.606658
$448$	−16.3426	−0.772115
$449$	−17.7444	−0.837410	−0.418705	−	0.908122i	$-0.637516\pi$
$449$	−17.7444	−0.837410	−0.418705	+	0.908122i	$0.637516\pi$
$450$	−0.508393	−0.0239659
$451$	−17.4923	−0.823682
$452$	22.8194	1.07333
$453$	−23.5999	−1.10882
$454$	−0.201944	−0.00947772
$455$	−9.22254	−0.432359
$456$	−0.192467	−0.00901308
$457$	2.52347	0.118043	0.0590215	−	0.998257i	$-0.481202\pi$
$457$	2.52347	0.118043	0.0590215	+	0.998257i	$0.481202\pi$
$458$	0.287997	0.0134572
$459$	50.1865	2.34251
$460$	12.6377	0.589237
$461$	−10.0128	−0.466342	−0.233171	−	0.972436i	$-0.574910\pi$
$461$	−10.0128	−0.466342	−0.233171	+	0.972436i	$0.574910\pi$
$462$	−0.482987	−0.0224706
$463$	27.8485	1.29423	0.647115	−	0.762393i	$-0.275976\pi$
$463$	27.8485	1.29423	0.647115	+	0.762393i	$0.275976\pi$
$464$	0	0
$465$	−12.4773	−0.578621
$466$	0.722726	0.0334796
$467$	−20.3278	−0.940660	−0.470330	−	0.882491i	$-0.655865\pi$
$467$	−20.3278	−0.940660	−0.470330	+	0.882491i	$0.655865\pi$
$468$	−31.7686	−1.46851
$469$	−8.49849	−0.392424
$470$	0.742945	0.0342695
$471$	19.1577	0.882740
$472$	1.04725	0.0482035
$473$	1.84355	0.0847667
$474$	1.30514	0.0599471
$475$	0.744931	0.0341798
$476$	21.4771	0.984400
$477$	61.2400	2.80399
$478$	−0.893611	−0.0408728
$479$	−21.4510	−0.980119	−0.490060	−	0.871689i	$-0.663025\pi$
$479$	−21.4510	−0.980119	−0.490060	+	0.871689i	$0.663025\pi$
$480$	2.65174	0.121035
$481$	16.9299	0.771939
$482$	−0.377220	−0.0171819
$483$	−22.5740	−1.02715
$484$	15.1280	0.687635
$485$	9.01987	0.409571
$486$	−0.130924	−0.00593884
$487$	16.3963	0.742988	0.371494	−	0.928435i	$-0.378846\pi$
$487$	16.3963	0.742988	0.371494	+	0.928435i	$0.378846\pi$
$488$	−1.33919	−0.0606225
$489$	−5.32712	−0.240901
$490$	0.203318	0.00918499
$491$	−29.2747	−1.32115	−0.660575	−	0.750760i	$-0.729687\pi$
$491$	−29.2747	−1.32115	−0.660575	+	0.750760i	$0.729687\pi$
$492$	−57.1488	−2.57647
$493$	0	0
$494$	−0.0409860	−0.00184405
$495$	−19.8952	−0.894224
$496$	−9.43753	−0.423758
$497$	−4.68829	−0.210298
$498$	1.98381	0.0888968
$499$	−4.67402	−0.209238	−0.104619	−	0.994512i	$-0.533362\pi$
$499$	−4.67402	−0.209238	−0.104619	+	0.994512i	$0.533362\pi$
$500$	−24.2463	−1.08433
$501$	42.1469	1.88298
$502$	0.272755	0.0121737
$503$	−11.1073	−0.495248	−0.247624	−	0.968856i	$-0.579650\pi$
$503$	−11.1073	−0.495248	−0.247624	+	0.968856i	$0.579650\pi$
$504$	−2.12406	−0.0946130
$505$	−14.7401	−0.655928
$506$	0.282003	0.0125366
$507$	19.2396	0.854459
$508$	−24.0713	−1.06799
$509$	−33.2518	−1.47386	−0.736930	−	0.675969i	$-0.763726\pi$
$509$	−33.2518	−1.47386	−0.736930	+	0.675969i	$0.763726\pi$
$510$	−1.15787	−0.0512712
$511$	18.6144	0.823451
$512$	3.34383	0.147778
$513$	3.63474	0.160477
$514$	−0.242761	−0.0107077
$515$	−6.12168	−0.269753
$516$	6.02303	0.265149
$517$	−18.8288	−0.828088
$518$	0.565720	0.0248563
$519$	25.3891	1.11446
$520$	0.753140	0.0330274
$521$	−11.6310	−0.509565	−0.254783	−	0.966998i	$-0.582004\pi$
$521$	−11.6310	−0.509565	−0.254783	+	0.966998i	$0.582004\pi$
$522$	0	0
$523$	−0.747202	−0.0326728	−0.0163364	−	0.999867i	$-0.505200\pi$
$523$	−0.747202	−0.0326728	−0.0163364	+	0.999867i	$0.505200\pi$
$524$	29.1630	1.27399
$525$	12.2201	0.533330
$526$	−1.26871	−0.0553184
$527$	12.3807	0.539312
$528$	−22.3685	−0.973463
$529$	−9.81963	−0.426940
$530$	−0.725591	−0.0315176
$531$	−38.5108	−1.67122
$532$	1.55547	0.0674380
$533$	−24.3505	−1.05474
$534$	−1.22134	−0.0528525
$535$	7.74122	0.334682
$536$	0.694012	0.0299768
$537$	59.5722	2.57073
$538$	−0.500671	−0.0215854
$539$	−5.15277	−0.221946
$540$	−33.3805	−1.43647
$541$	−19.2472	−0.827500	−0.413750	−	0.910391i	$-0.635781\pi$
$541$	−19.2472	−0.827500	−0.413750	+	0.910391i	$0.635781\pi$
$542$	0.736441	0.0316328
$543$	−36.4949	−1.56614
$544$	−2.63121	−0.112812
$545$	20.4912	0.877747
$546$	−0.672349	−0.0287739
$547$	−25.2969	−1.08162	−0.540809	−	0.841146i	$-0.681882\pi$
$547$	−25.2969	−1.08162	−0.540809	+	0.841146i	$0.681882\pi$
$548$	−5.71977	−0.244337
$549$	49.2465	2.10179
$550$	−0.152658	−0.00650938
$551$	0	0
$552$	1.84346	0.0784630
$553$	−21.1049	−0.897472
$554$	0.0450815	0.00191533
$555$	34.6389	1.47034
$556$	44.4975	1.88711
$557$	36.1438	1.53146	0.765731	−	0.643161i	$-0.222377\pi$
$557$	36.1438	1.53146	0.765731	+	0.643161i	$0.222377\pi$
$558$	−0.611949	−0.0259059
$559$	2.56635	0.108545
$560$	−14.2724	−0.603120
$561$	29.3443	1.23892
$562$	−1.25360	−0.0528800
$563$	−8.84332	−0.372701	−0.186351	−	0.982483i	$-0.559666\pi$
$563$	−8.84332	−0.372701	−0.186351	+	0.982483i	$0.559666\pi$
$564$	−61.5149	−2.59025
$565$	19.8936	0.836929
$566$	1.12204	0.0471631
$567$	21.6299	0.908370
$568$	0.382860	0.0160644
$569$	16.4900	0.691297	0.345648	−	0.938364i	$-0.387659\pi$
$569$	16.4900	0.691297	0.345648	+	0.938364i	$0.387659\pi$
$570$	−0.0838580	−0.00351242
$571$	−22.6312	−0.947086	−0.473543	−	0.880771i	$-0.657025\pi$
$571$	−22.6312	−0.947086	−0.473543	+	0.880771i	$0.657025\pi$
$572$	−9.53936	−0.398861
$573$	35.1829	1.46979
$574$	−0.813680	−0.0339623
$575$	−7.13501	−0.297550
$576$	−49.0771	−2.04488
$577$	41.1401	1.71268	0.856342	−	0.516408i	$-0.172731\pi$
$577$	41.1401	1.71268	0.856342	+	0.516408i	$0.172731\pi$
$578$	0.435832	0.0181282
$579$	57.6859	2.39734
$580$	0	0
$581$	−32.0794	−1.33088
$582$	0.657574	0.0272573
$583$	18.3889	0.761591
$584$	−1.52011	−0.0629024
$585$	−27.6954	−1.14507
$586$	0.243718	0.0100679
$587$	−26.1878	−1.08089	−0.540443	−	0.841381i	$-0.681743\pi$
$587$	−26.1878	−1.08089	−0.540443	+	0.841381i	$0.681743\pi$
$588$	−16.8345	−0.694243
$589$	0.896667	0.0369465
$590$	0.456287	0.0187851
$591$	−50.5834	−2.08072
$592$	26.2001	1.07682
$593$	−31.4857	−1.29296	−0.646482	−	0.762929i	$-0.723760\pi$
$593$	−31.4857	−1.29296	−0.646482	+	0.762929i	$0.723760\pi$
$594$	−0.744865	−0.0305622
$595$	18.7234	0.767584
$596$	−8.46502	−0.346741
$597$	26.9726	1.10392
$598$	0.392567	0.0160533
$599$	−14.1791	−0.579342	−0.289671	−	0.957126i	$-0.593546\pi$
$599$	−14.1791	−0.579342	−0.289671	+	0.957126i	$0.593546\pi$
$600$	−0.997932	−0.0407404
$601$	14.0233	0.572021	0.286010	−	0.958227i	$-0.407671\pi$
$601$	14.0233	0.572021	0.286010	+	0.958227i	$0.407671\pi$
$602$	0.0857554	0.00349513
$603$	−25.5211	−1.03930
$604$	−15.5755	−0.633757
$605$	13.1883	0.536183
$606$	−1.07460	−0.0436526
$607$	−18.3000	−0.742776	−0.371388	−	0.928478i	$-0.621118\pi$
$607$	−18.3000	−0.742776	−0.371388	+	0.928478i	$0.621118\pi$
$608$	−0.190564	−0.00772840
$609$	0	0
$610$	−0.583488	−0.0236247
$611$	−26.2108	−1.06038
$612$	64.4960	2.60710
$613$	29.8490	1.20559	0.602795	−	0.797896i	$-0.294054\pi$
$613$	29.8490	1.20559	0.602795	+	0.797896i	$0.294054\pi$
$614$	−0.216163	−0.00872365
$615$	−49.8215	−2.00900
$616$	−0.637803	−0.0256978
$617$	−4.59374	−0.184937	−0.0924685	−	0.995716i	$-0.529476\pi$
$617$	−4.59374	−0.184937	−0.0924685	+	0.995716i	$0.529476\pi$
$618$	−0.446288	−0.0179523
$619$	−6.28557	−0.252638	−0.126319	−	0.991990i	$-0.540316\pi$
$619$	−6.28557	−0.252638	−0.126319	+	0.991990i	$0.540316\pi$
$620$	−8.23476	−0.330716
$621$	−34.8138	−1.39703
$622$	0.445644	0.0178687
$623$	19.7498	0.791258
$624$	−31.1384	−1.24653
$625$	−11.3110	−0.452441
$626$	0.700923	0.0280145
$627$	2.12524	0.0848741
$628$	12.6437	0.504538
$629$	−34.3708	−1.37045
$630$	−0.925453	−0.0368709
$631$	9.68689	0.385629	0.192815	−	0.981235i	$-0.438238\pi$
$631$	9.68689	0.385629	0.192815	+	0.981235i	$0.438238\pi$
$632$	1.72349	0.0685568
$633$	0.769699	0.0305928
$634$	0.0625506	0.00248420
$635$	−20.9850	−0.832765
$636$	60.0780	2.38225
$637$	−7.17299	−0.284204
$638$	0	0
$639$	−14.0790	−0.556956
$640$	2.33311	0.0922244
$641$	4.79880	0.189541	0.0947707	−	0.995499i	$-0.469788\pi$
$641$	4.79880	0.189541	0.0947707	+	0.995499i	$0.469788\pi$
$642$	0.564357	0.0222734
$643$	12.2717	0.483948	0.241974	−	0.970283i	$-0.422205\pi$
$643$	12.2717	0.483948	0.241974	+	0.970283i	$0.422205\pi$
$644$	−14.8984	−0.587079
$645$	5.25079	0.206750
$646$	0.0832088	0.00327381
$647$	−10.6295	−0.417888	−0.208944	−	0.977928i	$-0.567003\pi$
$647$	−10.6295	−0.417888	−0.208944	+	0.977928i	$0.567003\pi$
$648$	−1.76636	−0.0693893
$649$	−11.5639	−0.453921
$650$	−0.212510	−0.00833534
$651$	14.7093	0.576501
$652$	−3.51579	−0.137689
$653$	−28.0426	−1.09739	−0.548695	−	0.836022i	$-0.684875\pi$
$653$	−28.0426	−1.09739	−0.548695	+	0.836022i	$0.684875\pi$
$654$	1.49387	0.0584148
$655$	25.4238	0.993391
$656$	−37.6838	−1.47130
$657$	55.8992	2.18084
$658$	−0.875845	−0.0341440
$659$	20.2814	0.790051	0.395026	−	0.918670i	$-0.370736\pi$
$659$	20.2814	0.790051	0.395026	+	0.918670i	$0.370736\pi$
$660$	−19.5177	−0.759725
$661$	−31.3294	−1.21857	−0.609287	−	0.792950i	$-0.708544\pi$
$661$	−31.3294	−1.21857	−0.609287	+	0.792950i	$0.708544\pi$
$662$	1.25334	0.0487124
$663$	40.8491	1.58645
$664$	2.61970	0.101664
$665$	1.35603	0.0525847
$666$	1.69887	0.0658297
$667$	0	0
$668$	27.8161	1.07624
$669$	−27.7241	−1.07188
$670$	0.302382	0.0116820
$671$	14.7876	0.570868
$672$	−3.12609	−0.120591
$673$	40.7084	1.56919	0.784597	−	0.620006i	$-0.212870\pi$
$673$	40.7084	1.56919	0.784597	+	0.620006i	$0.212870\pi$
$674$	0.0394851	0.00152091
$675$	18.8459	0.725381
$676$	12.6977	0.488374
$677$	−8.28145	−0.318282	−0.159141	−	0.987256i	$-0.550872\pi$
$677$	−8.28145	−0.318282	−0.159141	+	0.987256i	$0.550872\pi$
$678$	1.45030	0.0556984
$679$	−10.6334	−0.408071
$680$	−1.52901	−0.0586348
$681$	14.5769	0.558588
$682$	−0.183754	−0.00703629
$683$	3.36543	0.128775	0.0643874	−	0.997925i	$-0.479491\pi$
$683$	3.36543	0.128775	0.0643874	+	0.997925i	$0.479491\pi$
$684$	4.67109	0.178604
$685$	−4.98642	−0.190521
$686$	−0.842678	−0.0321736
$687$	−20.7884	−0.793128
$688$	3.97157	0.151415
$689$	25.5986	0.975228
$690$	0.803198	0.0305772
$691$	1.05513	0.0401391	0.0200696	−	0.999799i	$-0.493611\pi$
$691$	1.05513	0.0401391	0.0200696	+	0.999799i	$0.493611\pi$
$692$	16.7563	0.636979
$693$	23.4541	0.890948
$694$	−0.362978	−0.0137784
$695$	38.7922	1.47147
$696$	0	0
$697$	49.4358	1.87251
$698$	−1.44970	−0.0548720
$699$	−52.1683	−1.97319
$700$	8.06503	0.304829
$701$	14.0655	0.531247	0.265623	−	0.964077i	$-0.414422\pi$
$701$	14.0655	0.531247	0.265623	+	0.964077i	$0.414422\pi$
$702$	−1.03690	−0.0391353
$703$	−2.48929	−0.0938853
$704$	−14.7367	−0.555409
$705$	−53.6278	−2.01974
$706$	−0.604981	−0.0227688
$707$	17.3769	0.653525
$708$	−37.7800	−1.41986
$709$	4.07777	0.153144	0.0765720	−	0.997064i	$-0.475602\pi$
$709$	4.07777	0.153144	0.0765720	+	0.997064i	$0.475602\pi$
$710$	0.166812	0.00626035
$711$	−63.3784	−2.37687
$712$	−1.61283	−0.0604433
$713$	−8.58835	−0.321636
$714$	1.36499	0.0510834
$715$	−8.31628	−0.311011
$716$	39.3164	1.46932
$717$	64.5033	2.40892
$718$	−0.935002	−0.0348940
$719$	8.32542	0.310486	0.155243	−	0.987876i	$-0.450384\pi$
$719$	8.32542	0.310486	0.155243	+	0.987876i	$0.450384\pi$
$720$	−42.8603	−1.59731
$721$	7.21674	0.268765
$722$	−0.790936	−0.0294356
$723$	27.2288	1.01265
$724$	−24.0858	−0.895144
$725$	0	0
$726$	0.961467	0.0356834
$727$	36.8868	1.36806	0.684028	−	0.729456i	$-0.260227\pi$
$727$	36.8868	1.36806	0.684028	+	0.729456i	$0.260227\pi$
$728$	−0.887864	−0.0329064
$729$	−22.1467	−0.820248
$730$	−0.662311	−0.0245132
$731$	−5.21014	−0.192704
$732$	48.3121	1.78567
$733$	10.1401	0.374534	0.187267	−	0.982309i	$-0.440037\pi$
$733$	10.1401	0.374534	0.187267	+	0.982309i	$0.440037\pi$
$734$	0.213102	0.00786574
$735$	−14.6761	−0.541335
$736$	1.82524	0.0672792
$737$	−7.66338	−0.282284
$738$	−2.44349	−0.0899462
$739$	−12.1953	−0.448610	−0.224305	−	0.974519i	$-0.572011\pi$
$739$	−12.1953	−0.448610	−0.224305	+	0.974519i	$0.572011\pi$
$740$	22.8610	0.840386
$741$	2.95848	0.108682
$742$	0.855386	0.0314022
$743$	32.7458	1.20133	0.600664	−	0.799501i	$-0.294903\pi$
$743$	32.7458	1.20133	0.600664	+	0.799501i	$0.294903\pi$
$744$	−1.20120	−0.0440382
$745$	−7.37968	−0.270371
$746$	1.07002	0.0391761
$747$	−96.3350	−3.52471
$748$	19.3666	0.708113
$749$	−9.12599	−0.333456
$750$	−1.54099	−0.0562689
$751$	−47.8097	−1.74460	−0.872301	−	0.488970i	$-0.837373\pi$
$751$	−47.8097	−1.74460	−0.872301	+	0.488970i	$0.837373\pi$
$752$	−40.5628	−1.47917
$753$	−19.6882	−0.717478
$754$	0	0
$755$	−13.5785	−0.494171
$756$	39.3516	1.43121
$757$	14.8571	0.539989	0.269994	−	0.962862i	$-0.412978\pi$
$757$	14.8571	0.539989	0.269994	+	0.962862i	$0.412978\pi$
$758$	0.348953	0.0126745
$759$	−20.3558	−0.738867
$760$	−0.110738	−0.00401688
$761$	18.3548	0.665362	0.332681	−	0.943039i	$-0.392047\pi$
$761$	18.3548	0.665362	0.332681	+	0.943039i	$0.392047\pi$
$762$	−1.52987	−0.0554212
$763$	−24.1567	−0.874531
$764$	23.2200	0.840070
$765$	56.2267	2.03288
$766$	1.06216	0.0383772
$767$	−16.0976	−0.581252
$768$	−48.0181	−1.73270
$769$	13.0590	0.470920	0.235460	−	0.971884i	$-0.424340\pi$
$769$	13.0590	0.470920	0.235460	+	0.971884i	$0.424340\pi$
$770$	−0.277891	−0.0100145
$771$	17.5232	0.631082
$772$	38.0715	1.37022
$773$	30.2860	1.08931	0.544655	−	0.838660i	$-0.316660\pi$
$773$	30.2860	1.08931	0.544655	+	0.838660i	$0.316660\pi$
$774$	0.257525	0.00925654
$775$	4.64918	0.167003
$776$	0.868352	0.0311720
$777$	−40.8352	−1.46495
$778$	1.14615	0.0410916
$779$	3.58036	0.128280
$780$	−27.1699	−0.972839
$781$	−4.22759	−0.151275
$782$	−0.796981	−0.0285000
$783$	0	0
$784$	−11.1006	−0.396451
$785$	11.0226	0.393413
$786$	1.85347	0.0661110
$787$	−2.96391	−0.105652	−0.0528260	−	0.998604i	$-0.516823\pi$
$787$	−2.96391	−0.105652	−0.0528260	+	0.998604i	$0.516823\pi$
$788$	−33.3840	−1.18926
$789$	91.5790	3.26030
$790$	0.750926	0.0267168
$791$	−23.4522	−0.833864
$792$	−1.91533	−0.0680584
$793$	20.5852	0.731003
$794$	0.470848	0.0167098
$795$	52.3751	1.85755
$796$	17.8014	0.630953
$797$	−23.9622	−0.848786	−0.424393	−	0.905478i	$-0.639512\pi$
$797$	−23.9622	−0.848786	−0.424393	+	0.905478i	$0.639512\pi$
$798$	0.0988586	0.00349956
$799$	53.2127	1.88253
$800$	−0.988067	−0.0349334
$801$	59.3089	2.09558
$802$	1.39685	0.0493244
$803$	16.7852	0.592337
$804$	−25.0368	−0.882981
$805$	−12.9882	−0.457774
$806$	−0.255797	−0.00901007
$807$	36.1398	1.27218
$808$	−1.41905	−0.0499220
$809$	48.7622	1.71439	0.857194	−	0.514993i	$-0.172205\pi$
$809$	48.7622	1.71439	0.857194	+	0.514993i	$0.172205\pi$
$810$	−0.769606	−0.0270412
$811$	23.3346	0.819389	0.409695	−	0.912223i	$-0.365635\pi$
$811$	23.3346	0.819389	0.409695	+	0.912223i	$0.365635\pi$
$812$	0	0
$813$	−53.1583	−1.86434
$814$	0.510129	0.0178800
$815$	−3.06501	−0.107363
$816$	63.2164	2.21302
$817$	−0.377342	−0.0132015
$818$	−0.674565	−0.0235856
$819$	32.6496	1.14087
$820$	−32.8811	−1.14826
$821$	36.6328	1.27849	0.639247	−	0.769001i	$-0.279246\pi$
$821$	36.6328	1.27849	0.639247	+	0.769001i	$0.279246\pi$
$822$	−0.363524	−0.0126793
$823$	26.8685	0.936578	0.468289	−	0.883575i	$-0.344871\pi$
$823$	26.8685	0.936578	0.468289	+	0.883575i	$0.344871\pi$
$824$	−0.589341	−0.0205307
$825$	11.0193	0.383643
$826$	−0.537909	−0.0187162
$827$	−2.55032	−0.0886834	−0.0443417	−	0.999016i	$-0.514119\pi$
$827$	−2.55032	−0.0886834	−0.0443417	+	0.999016i	$0.514119\pi$
$828$	−44.7401	−1.55483
$829$	−29.2663	−1.01646	−0.508230	−	0.861221i	$-0.669700\pi$
$829$	−29.2663	−1.01646	−0.508230	+	0.861221i	$0.669700\pi$
$830$	1.14141	0.0396188
$831$	−3.25410	−0.112884
$832$	−20.5144	−0.711209
$833$	14.5625	0.504559
$834$	2.82806	0.0979278
$835$	24.2496	0.839194
$836$	1.40262	0.0485105
$837$	22.6847	0.784098
$838$	1.17767	0.0406818
$839$	46.3868	1.60145	0.800725	−	0.599032i	$-0.204448\pi$
$839$	46.3868	1.60145	0.800725	+	0.599032i	$0.204448\pi$
$840$	−1.81658	−0.0626781
$841$	0	0
$842$	1.27925	0.0440860
$843$	90.4884	3.11659
$844$	0.507986	0.0174856
$845$	11.0697	0.380809
$846$	−2.63018	−0.0904273
$847$	−15.5475	−0.534218
$848$	39.6153	1.36039
$849$	−80.9923	−2.77965
$850$	0.431434	0.0147981
$851$	23.8426	0.817314
$852$	−13.8118	−0.473186
$853$	51.5353	1.76453	0.882267	−	0.470749i	$-0.156016\pi$
$853$	51.5353	1.76453	0.882267	+	0.470749i	$0.156016\pi$
$854$	0.687863	0.0235382
$855$	4.07219	0.139266
$856$	0.745256	0.0254723
$857$	17.2204	0.588236	0.294118	−	0.955769i	$-0.404974\pi$
$857$	17.2204	0.588236	0.294118	+	0.955769i	$0.404974\pi$
$858$	−0.606280	−0.0206981
$859$	−14.1463	−0.482665	−0.241332	−	0.970443i	$-0.577584\pi$
$859$	−14.1463	−0.482665	−0.241332	+	0.970443i	$0.577584\pi$
$860$	3.46541	0.118170
$861$	58.7336	2.00164
$862$	−0.407947	−0.0138947
$863$	−18.6105	−0.633508	−0.316754	−	0.948508i	$-0.602593\pi$
$863$	−18.6105	−0.633508	−0.316754	+	0.948508i	$0.602593\pi$
$864$	−4.82107	−0.164016
$865$	14.6079	0.496684
$866$	−0.974379	−0.0331107
$867$	−31.4595	−1.06842
$868$	9.70781	0.329504
$869$	−19.0310	−0.645583
$870$	0	0
$871$	−10.6679	−0.361469
$872$	1.97271	0.0668044
$873$	−31.9321	−1.08074
$874$	−0.0577209	−0.00195244
$875$	24.9187	0.842406
$876$	54.8385	1.85282
$877$	8.50645	0.287242	0.143621	−	0.989633i	$-0.454125\pi$
$877$	8.50645	0.287242	0.143621	+	0.989633i	$0.454125\pi$
$878$	−0.571618	−0.0192912
$879$	−17.5923	−0.593372
$880$	−12.8699	−0.433845
$881$	31.1664	1.05002	0.525011	−	0.851095i	$-0.324061\pi$
$881$	31.1664	1.05002	0.525011	+	0.851095i	$0.324061\pi$
$882$	−0.719788	−0.0242365
$883$	20.3483	0.684775	0.342387	−	0.939559i	$-0.388764\pi$
$883$	20.3483	0.684775	0.342387	+	0.939559i	$0.388764\pi$
$884$	26.9596	0.906748
$885$	−32.9361	−1.10713
$886$	−0.384775	−0.0129268
$887$	−11.2240	−0.376866	−0.188433	−	0.982086i	$-0.560341\pi$
$887$	−11.2240	−0.376866	−0.188433	+	0.982086i	$0.560341\pi$
$888$	3.33473	0.111906
$889$	24.7388	0.829714
$890$	−0.702710	−0.0235549
$891$	19.5044	0.653422
$892$	−18.2974	−0.612641
$893$	3.85390	0.128966
$894$	−0.538000	−0.0179934
$895$	34.2755	1.14570
$896$	−2.75046	−0.0918866
$897$	−28.3365	−0.946130
$898$	−0.744296	−0.0248375
$899$	0	0
$900$	24.2194	0.807314
$901$	−51.9697	−1.73136
$902$	−0.733723	−0.0244303
$903$	−6.19006	−0.205992
$904$	1.91518	0.0636978
$905$	−20.9977	−0.697987
$906$	−0.989908	−0.0328875
$907$	40.7943	1.35455	0.677276	−	0.735729i	$-0.263161\pi$
$907$	40.7943	1.35455	0.677276	+	0.735729i	$0.263161\pi$
$908$	9.62045	0.319266
$909$	52.1831	1.73080
$910$	−0.386843	−0.0128237
$911$	−30.2991	−1.00385	−0.501926	−	0.864910i	$-0.667375\pi$
$911$	−30.2991	−1.00385	−0.501926	+	0.864910i	$0.667375\pi$
$912$	4.57842	0.151607
$913$	−28.9271	−0.957348
$914$	0.105848	0.00350114
$915$	42.1178	1.39237
$916$	−13.7199	−0.453320
$917$	−29.9717	−0.989753
$918$	2.10509	0.0694784
$919$	26.5368	0.875369	0.437685	−	0.899129i	$-0.355799\pi$
$919$	26.5368	0.875369	0.437685	+	0.899129i	$0.355799\pi$
$920$	1.06066	0.0349688
$921$	15.6033	0.514145
$922$	−0.419990	−0.0138316
$923$	−5.88507	−0.193710
$924$	23.0091	0.756943
$925$	−12.9068	−0.424375
$926$	1.16812	0.0383867
$927$	21.6720	0.711801
$928$	0	0
$929$	4.73988	0.155510	0.0777551	−	0.996972i	$-0.475225\pi$
$929$	4.73988	0.155510	0.0777551	+	0.996972i	$0.475225\pi$
$930$	−0.523365	−0.0171618
$931$	1.05468	0.0345657
$932$	−34.4300	−1.12779
$933$	−32.1678	−1.05313
$934$	−0.852659	−0.0278999
$935$	16.8835	0.552150
$936$	−2.66627	−0.0871497
$937$	−18.6584	−0.609542	−0.304771	−	0.952426i	$-0.598580\pi$
$937$	−18.6584	−0.609542	−0.304771	+	0.952426i	$0.598580\pi$
$938$	−0.356472	−0.0116392
$939$	−50.5945	−1.65109
$940$	−35.3933	−1.15440
$941$	−22.5654	−0.735611	−0.367805	−	0.929903i	$-0.619891\pi$
$941$	−22.5654	−0.735611	−0.367805	+	0.929903i	$0.619891\pi$
$942$	0.803577	0.0261819
$943$	−34.2930	−1.11673
$944$	−24.9121	−0.810818
$945$	34.3062	1.11598
$946$	0.0773286	0.00251417
$947$	−27.6373	−0.898090	−0.449045	−	0.893509i	$-0.648236\pi$
$947$	−27.6373	−0.898090	−0.449045	+	0.893509i	$0.648236\pi$
$948$	−62.1757	−2.01937
$949$	23.3661	0.758496
$950$	0.0312464	0.00101377
$951$	−4.51507	−0.146411
$952$	1.80252	0.0584200
$953$	−37.3553	−1.21006	−0.605028	−	0.796204i	$-0.706838\pi$
$953$	−37.3553	−1.21006	−0.605028	+	0.796204i	$0.706838\pi$
$954$	2.56874	0.0831659
$955$	20.2429	0.655043
$956$	42.5708	1.37684
$957$	0	0
$958$	−0.899769	−0.0290702
$959$	5.87839	0.189823
$960$	−41.9728	−1.35467
$961$	−25.4038	−0.819478
$962$	0.710133	0.0228956
$963$	−27.4055	−0.883130
$964$	17.9704	0.578788
$965$	33.1902	1.06843
$966$	−0.946876	−0.0304652
$967$	−39.9522	−1.28478	−0.642389	−	0.766379i	$-0.722057\pi$
$967$	−39.9522	−1.28478	−0.642389	+	0.766379i	$0.722057\pi$
$968$	1.26966	0.0408083
$969$	−6.00624	−0.192948
$970$	0.378342	0.0121478
$971$	−14.7821	−0.474379	−0.237190	−	0.971463i	$-0.576226\pi$
$971$	−14.7821	−0.474379	−0.237190	+	0.971463i	$0.576226\pi$
$972$	6.23711	0.200056
$973$	−45.7315	−1.46608
$974$	0.687749	0.0220369
$975$	15.3396	0.491260
$976$	31.8569	1.01971
$977$	−9.82846	−0.314440	−0.157220	−	0.987564i	$-0.550253\pi$
$977$	−9.82846	−0.314440	−0.157220	+	0.987564i	$0.550253\pi$
$978$	−0.223448	−0.00714508
$979$	17.8091	0.569180
$980$	−9.68590	−0.309405
$981$	−72.5430	−2.31612
$982$	−1.22794	−0.0391851
$983$	47.3687	1.51083	0.755414	−	0.655248i	$-0.227436\pi$
$983$	47.3687	1.51083	0.755414	+	0.655248i	$0.227436\pi$
$984$	−4.79636	−0.152903
$985$	−29.1037	−0.927320
$986$	0	0
$987$	63.2209	2.01234
$988$	1.95253	0.0621184
$989$	3.61421	0.114925
$990$	−0.834513	−0.0265226
$991$	−48.9812	−1.55594	−0.777969	−	0.628303i	$-0.783750\pi$
$991$	−48.9812	−1.55594	−0.777969	+	0.628303i	$0.783750\pi$
$992$	−1.18933	−0.0377612
$993$	−90.4695	−2.87096
$994$	−0.196652	−0.00623742
$995$	15.5190	0.491985
$996$	−94.5070	−2.99457
$997$	1.16193	0.0367988	0.0183994	−	0.999831i	$-0.494143\pi$
$997$	1.16193	0.0367988	0.0183994	+	0.999831i	$0.494143\pi$
$998$	−0.196054	−0.00620597
$999$	−62.9763	−1.99248

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.a.i.1.5	✓	8
3.2	odd	2		7569.2.a.bi.1.4		8
29.2	odd	28		841.2.e.m.236.9		96
29.3	odd	28		841.2.e.m.270.9		96
29.4	even	14		841.2.d.p.190.5		48
29.5	even	14		841.2.d.p.605.5		48
29.6	even	14		841.2.d.p.645.5		48
29.7	even	7		841.2.d.q.571.4		48
29.8	odd	28		841.2.e.m.267.9		96
29.9	even	14		841.2.d.p.574.4		48
29.10	odd	28		841.2.e.m.651.9		96
29.11	odd	28		841.2.e.m.63.9		96
29.12	odd	4		841.2.b.f.840.9		16
29.13	even	14		841.2.d.p.778.4		48
29.14	odd	28		841.2.e.m.196.8		96
29.15	odd	28		841.2.e.m.196.9		96
29.16	even	7		841.2.d.q.778.5		48
29.17	odd	4		841.2.b.f.840.8		16
29.18	odd	28		841.2.e.m.63.8		96
29.19	odd	28		841.2.e.m.651.8		96
29.20	even	7		841.2.d.q.574.5		48
29.21	odd	28		841.2.e.m.267.8		96
29.22	even	14		841.2.d.p.571.5		48
29.23	even	7		841.2.d.q.645.4		48
29.24	even	7		841.2.d.q.605.4		48
29.25	even	7		841.2.d.q.190.4		48
29.26	odd	28		841.2.e.m.270.8		96
29.27	odd	28		841.2.e.m.236.8		96
29.28	even	2		841.2.a.j.1.4	yes	8
87.86	odd	2		7569.2.a.bd.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
841.2.a.i.1.5	✓	8	1.1	even	1	trivial
841.2.a.j.1.4	yes	8	29.28	even	2
841.2.b.f.840.8		16	29.17	odd	4
841.2.b.f.840.9		16	29.12	odd	4
841.2.d.p.190.5		48	29.4	even	14
841.2.d.p.571.5		48	29.22	even	14
841.2.d.p.574.4		48	29.9	even	14
841.2.d.p.605.5		48	29.5	even	14
841.2.d.p.645.5		48	29.6	even	14
841.2.d.p.778.4		48	29.13	even	14
841.2.d.q.190.4		48	29.25	even	7
841.2.d.q.571.4		48	29.7	even	7
841.2.d.q.574.5		48	29.20	even	7
841.2.d.q.605.4		48	29.24	even	7
841.2.d.q.645.4		48	29.23	even	7
841.2.d.q.778.5		48	29.16	even	7
841.2.e.m.63.8		96	29.18	odd	28
841.2.e.m.63.9		96	29.11	odd	28
841.2.e.m.196.8		96	29.14	odd	28
841.2.e.m.196.9		96	29.15	odd	28
841.2.e.m.236.8		96	29.27	odd	28
841.2.e.m.236.9		96	29.2	odd	28
841.2.e.m.267.8		96	29.21	odd	28
841.2.e.m.267.9		96	29.8	odd	28
841.2.e.m.270.8		96	29.26	odd	28
841.2.e.m.270.9		96	29.3	odd	28
841.2.e.m.651.8		96	29.19	odd	28
841.2.e.m.651.9		96	29.10	odd	28
7569.2.a.bd.1.5		8	87.86	odd	2
7569.2.a.bi.1.4		8	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.a (trivial)

\(f(q)\)	\(=\)	\(q+0.0419454 q^{2} -3.02773 q^{3} -1.99824 q^{4} -1.74204 q^{5} -0.126999 q^{6} +2.05366 q^{7} -0.167708 q^{8} +6.16716 q^{9} -0.0730704 q^{10} +1.85185 q^{11} +6.05014 q^{12} +2.57790 q^{13} +0.0861414 q^{14} +5.27442 q^{15} +3.98945 q^{16} -5.23359 q^{17} +0.258684 q^{18} -0.379040 q^{19} +3.48101 q^{20} -6.21792 q^{21} +0.0776766 q^{22} +3.63048 q^{23} +0.507774 q^{24} -1.96531 q^{25} +0.108131 q^{26} -9.58931 q^{27} -4.10370 q^{28} +0.221238 q^{30} -2.36562 q^{31} +0.502754 q^{32} -5.60691 q^{33} -0.219525 q^{34} -3.57754 q^{35} -12.3235 q^{36} +6.56734 q^{37} -0.0158990 q^{38} -7.80518 q^{39} +0.292153 q^{40} -9.44586 q^{41} -0.260813 q^{42} +0.995519 q^{43} -3.70044 q^{44} -10.7434 q^{45} +0.152282 q^{46} -10.1675 q^{47} -12.0790 q^{48} -2.78250 q^{49} -0.0824356 q^{50} +15.8459 q^{51} -5.15126 q^{52} +9.93002 q^{53} -0.402227 q^{54} -3.22599 q^{55} -0.344414 q^{56} +1.14763 q^{57} -6.24449 q^{59} -10.5396 q^{60} +7.98529 q^{61} -0.0992270 q^{62} +12.6652 q^{63} -7.95780 q^{64} -4.49079 q^{65} -0.235184 q^{66} -4.13822 q^{67} +10.4580 q^{68} -10.9921 q^{69} -0.150061 q^{70} -2.28290 q^{71} -1.03428 q^{72} +9.06401 q^{73} +0.275470 q^{74} +5.95042 q^{75} +0.757414 q^{76} +3.80306 q^{77} -0.327391 q^{78} -10.2768 q^{79} -6.94976 q^{80} +10.5324 q^{81} -0.396210 q^{82} -15.6206 q^{83} +12.4249 q^{84} +9.11711 q^{85} +0.0417574 q^{86} -0.310570 q^{88} +9.61689 q^{89} -0.450637 q^{90} +5.29411 q^{91} -7.25457 q^{92} +7.16248 q^{93} -0.426481 q^{94} +0.660302 q^{95} -1.52221 q^{96} -5.17777 q^{97} -0.116713 q^{98} +11.4207 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 6 q^{3} + 6 q^{4} - q^{5} + 3 q^{6} - 15 q^{8} + 8 q^{9} + 3 q^{10} - 5 q^{11} - 12 q^{12} - 4 q^{13} - 15 q^{14} + 7 q^{15} - 2 q^{16} - 9 q^{17} + 11 q^{18} - 17 q^{19} - 7 q^{20} - 25 q^{21}+ \cdots - 15 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 6 * q^3 + 6 * q^4 - q^5 + 3 * q^6 - 15 * q^8 + 8 * q^9 + 3 * q^10 - 5 * q^11 - 12 * q^12 - 4 * q^13 - 15 * q^14 + 7 * q^15 - 2 * q^16 - 9 * q^17 + 11 * q^18 - 17 * q^19 - 7 * q^20 - 25 * q^21 + 25 * q^22 - 7 * q^23 + 25 * q^24 - 13 * q^25 - 3 * q^26 - 18 * q^27 + 25 * q^28 - 26 * q^30 - q^31 + 6 * q^32 + 12 * q^34 - 5 * q^35 - 19 * q^36 - 6 * q^37 - 14 * q^38 - 27 * q^39 + 25 * q^40 - 6 * q^41 + 15 * q^42 + 5 * q^43 - 20 * q^44 - q^45 - 14 * q^46 - 31 * q^47 - 11 * q^48 + 4 * q^49 - 11 * q^50 + 23 * q^51 + 2 * q^52 + 19 * q^53 - 46 * q^54 - 20 * q^55 - 20 * q^56 - 6 * q^57 - q^59 + 9 * q^60 - 21 * q^61 - 12 * q^62 - 10 * q^63 + q^64 - 17 * q^65 - 5 * q^66 + 2 * q^67 - 8 * q^68 + 14 * q^69 + 5 * q^70 - 12 * q^71 + 34 * q^73 - 27 * q^74 - 4 * q^75 + 16 * q^76 + 10 * q^77 + 6 * q^78 - 29 * q^79 - 41 * q^80 + 12 * q^81 - 22 * q^82 - 3 * q^83 + 10 * q^84 - 2 * q^85 - 5 * q^86 - 15 * q^88 - 36 * q^89 + 38 * q^90 - 4 * q^92 + 2 * q^93 + 13 * q^94 - 11 * q^95 - 2 * q^96 + 18 * q^97 - 27 * q^98 - 15 * q^99

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