LMFDB - Embedded newform 403.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(1,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("403.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 11x^{6} + 10x^{5} + 37x^{4} - 33x^{3} - 36x^{2} + 33x - 4 $ x^8 - x^7 - 11x^6 + 10x^5 + 37x^4 - 33x^3 - 36x^2 + 33x - 4
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			1.1
Root			$2.53815$ of defining polynomial
Character	$\chi$	$=$	403.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.53815 q^{2} +2.96968 q^{3} +4.44218 q^{4} +2.45818 q^{5} -7.53747 q^{6} -1.29216 q^{7} -6.19862 q^{8} +5.81898 q^{9} +O(q^{10})$	\(q-2.53815 q^{2} +2.96968 q^{3} +4.44218 q^{4} +2.45818 q^{5} -7.53747 q^{6} -1.29216 q^{7} -6.19862 q^{8} +5.81898 q^{9} -6.23922 q^{10} +2.24289 q^{11} +13.1918 q^{12} +1.00000 q^{13} +3.27969 q^{14} +7.30000 q^{15} +6.84863 q^{16} +5.05469 q^{17} -14.7694 q^{18} -8.18572 q^{19} +10.9197 q^{20} -3.83729 q^{21} -5.69279 q^{22} -5.34564 q^{23} -18.4079 q^{24} +1.04264 q^{25} -2.53815 q^{26} +8.37145 q^{27} -5.74001 q^{28} +0.275880 q^{29} -18.5285 q^{30} -1.00000 q^{31} -4.98558 q^{32} +6.66066 q^{33} -12.8295 q^{34} -3.17636 q^{35} +25.8490 q^{36} +1.51045 q^{37} +20.7765 q^{38} +2.96968 q^{39} -15.2373 q^{40} -5.14041 q^{41} +9.73961 q^{42} -8.74762 q^{43} +9.96334 q^{44} +14.3041 q^{45} +13.5680 q^{46} +7.82059 q^{47} +20.3382 q^{48} -5.33032 q^{49} -2.64638 q^{50} +15.0108 q^{51} +4.44218 q^{52} +13.4964 q^{53} -21.2480 q^{54} +5.51343 q^{55} +8.00960 q^{56} -24.3089 q^{57} -0.700224 q^{58} -14.1324 q^{59} +32.4279 q^{60} +8.79160 q^{61} +2.53815 q^{62} -7.51905 q^{63} -1.04313 q^{64} +2.45818 q^{65} -16.9057 q^{66} +9.93254 q^{67} +22.4539 q^{68} -15.8748 q^{69} +8.06206 q^{70} +3.29658 q^{71} -36.0696 q^{72} -0.353201 q^{73} -3.83374 q^{74} +3.09631 q^{75} -36.3625 q^{76} -2.89817 q^{77} -7.53747 q^{78} -6.60096 q^{79} +16.8352 q^{80} +7.40357 q^{81} +13.0471 q^{82} +3.38992 q^{83} -17.0460 q^{84} +12.4253 q^{85} +22.2027 q^{86} +0.819275 q^{87} -13.9028 q^{88} +13.9960 q^{89} -36.3059 q^{90} -1.29216 q^{91} -23.7463 q^{92} -2.96968 q^{93} -19.8498 q^{94} -20.1220 q^{95} -14.8056 q^{96} -12.7220 q^{97} +13.5291 q^{98} +13.0513 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} + 7 q^{3} + 7 q^{4} + 11 q^{5} - 2 q^{7} + 9 q^{9}+O(q^{10}) $ 8 * q - q^2 + 7 * q^3 + 7 * q^4 + 11 * q^5 - 2 * q^7 + 9 * q^9	\( 8 q - q^{2} + 7 q^{3} + 7 q^{4} + 11 q^{5} - 2 q^{7} + 9 q^{9} - 2 q^{10} - 2 q^{11} + 19 q^{12} + 8 q^{13} + 3 q^{14} + 6 q^{15} - 7 q^{16} + 7 q^{17} - 12 q^{18} - 5 q^{19} + 6 q^{20} + 8 q^{21} - 4 q^{22} + 14 q^{23} - 17 q^{24} + 17 q^{25} - q^{26} + 7 q^{27} - 9 q^{28} + 12 q^{29} - 9 q^{30} - 8 q^{31} - 21 q^{32} + 10 q^{33} - 12 q^{34} - q^{35} + 11 q^{36} + 2 q^{37} + 24 q^{38} + 7 q^{39} - 19 q^{40} + 13 q^{41} - 27 q^{42} - 5 q^{43} + 22 q^{44} + 19 q^{45} + 17 q^{46} + 23 q^{47} + 3 q^{48} + 26 q^{49} - 26 q^{50} + 18 q^{51} + 7 q^{52} + 25 q^{53} - 36 q^{54} - 17 q^{55} + 8 q^{56} - 35 q^{57} - 29 q^{58} - 5 q^{59} + 71 q^{60} - 9 q^{61} + q^{62} - 37 q^{63} - 14 q^{64} + 11 q^{65} - 41 q^{66} + 22 q^{67} - 6 q^{68} - 7 q^{69} - 29 q^{70} - 17 q^{71} - 34 q^{72} - 27 q^{73} + 14 q^{74} - 33 q^{75} - 36 q^{76} + 31 q^{77} - 23 q^{79} + 9 q^{80} - 12 q^{81} + 18 q^{82} - 25 q^{83} - 62 q^{84} + 13 q^{85} + 11 q^{86} + 26 q^{87} + 5 q^{88} + 2 q^{89} - 14 q^{90} - 2 q^{91} - 20 q^{92} - 7 q^{93} - 38 q^{94} + 3 q^{95} - 52 q^{96} - 15 q^{97} + 39 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q - q^2 + 7 * q^3 + 7 * q^4 + 11 * q^5 - 2 * q^7 + 9 * q^9 - 2 * q^10 - 2 * q^11 + 19 * q^12 + 8 * q^13 + 3 * q^14 + 6 * q^15 - 7 * q^16 + 7 * q^17 - 12 * q^18 - 5 * q^19 + 6 * q^20 + 8 * q^21 - 4 * q^22 + 14 * q^23 - 17 * q^24 + 17 * q^25 - q^26 + 7 * q^27 - 9 * q^28 + 12 * q^29 - 9 * q^30 - 8 * q^31 - 21 * q^32 + 10 * q^33 - 12 * q^34 - q^35 + 11 * q^36 + 2 * q^37 + 24 * q^38 + 7 * q^39 - 19 * q^40 + 13 * q^41 - 27 * q^42 - 5 * q^43 + 22 * q^44 + 19 * q^45 + 17 * q^46 + 23 * q^47 + 3 * q^48 + 26 * q^49 - 26 * q^50 + 18 * q^51 + 7 * q^52 + 25 * q^53 - 36 * q^54 - 17 * q^55 + 8 * q^56 - 35 * q^57 - 29 * q^58 - 5 * q^59 + 71 * q^60 - 9 * q^61 + q^62 - 37 * q^63 - 14 * q^64 + 11 * q^65 - 41 * q^66 + 22 * q^67 - 6 * q^68 - 7 * q^69 - 29 * q^70 - 17 * q^71 - 34 * q^72 - 27 * q^73 + 14 * q^74 - 33 * q^75 - 36 * q^76 + 31 * q^77 - 23 * q^79 + 9 * q^80 - 12 * q^81 + 18 * q^82 - 25 * q^83 - 62 * q^84 + 13 * q^85 + 11 * q^86 + 26 * q^87 + 5 * q^88 + 2 * q^89 - 14 * q^90 - 2 * q^91 - 20 * q^92 - 7 * q^93 - 38 * q^94 + 3 * q^95 - 52 * q^96 - 15 * q^97 + 39 * q^98 - 8 * q^99

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 $

$2$	−2.53815	−1.79474	−0.897370	−	0.441279i	$-0.854525\pi$
$2$	−2.53815	−1.79474	−0.897370	+	0.441279i	$0.854525\pi$
$3$	2.96968	1.71454	0.857272	−	0.514864i	$-0.172158\pi$
$3$	2.96968	1.71454	0.857272	+	0.514864i	$0.172158\pi$
$4$	4.44218	2.22109
$5$	2.45818	1.09933	0.549666	−	0.835385i	$-0.314755\pi$
$5$	2.45818	1.09933	0.549666	+	0.835385i	$0.314755\pi$
$6$	−7.53747	−3.07716
$7$	−1.29216	−0.488390	−0.244195	−	0.969726i	$-0.578524\pi$
$7$	−1.29216	−0.488390	−0.244195	+	0.969726i	$0.578524\pi$
$8$	−6.19862	−2.19154
$9$	5.81898	1.93966
$10$	−6.23922	−1.97301
$11$	2.24289	0.676257	0.338129	−	0.941100i	$-0.390206\pi$
$11$	2.24289	0.676257	0.338129	+	0.941100i	$0.390206\pi$
$12$	13.1918	3.80816
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	3.27969	0.876534
$15$	7.30000	1.88485
$16$	6.84863	1.71216
$17$	5.05469	1.22594	0.612971	−	0.790105i	$-0.289974\pi$
$17$	5.05469	1.22594	0.612971	+	0.790105i	$0.289974\pi$
$18$	−14.7694	−3.48118
$19$	−8.18572	−1.87793	−0.938966	−	0.344010i	$-0.888215\pi$
$19$	−8.18572	−1.87793	−0.938966	+	0.344010i	$0.888215\pi$
$20$	10.9197	2.44172
$21$	−3.83729	−0.837366
$22$	−5.69279	−1.21371
$23$	−5.34564	−1.11464	−0.557322	−	0.830297i	$-0.688171\pi$
$23$	−5.34564	−1.11464	−0.557322	+	0.830297i	$0.688171\pi$
$24$	−18.4079	−3.75749
$25$	1.04264	0.208529
$26$	−2.53815	−0.497771
$27$	8.37145	1.61109
$28$	−5.74001	−1.08476
$29$	0.275880	0.0512297	0.0256148	−	0.999672i	$-0.491846\pi$
$29$	0.275880	0.0512297	0.0256148	+	0.999672i	$0.491846\pi$
$30$	−18.5285	−3.38282
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−4.98558	−0.881334
$33$	6.66066	1.15947
$34$	−12.8295	−2.20025
$35$	−3.17636	−0.536903
$36$	25.8490	4.30816
$37$	1.51045	0.248316	0.124158	−	0.992262i	$-0.460377\pi$
$37$	1.51045	0.248316	0.124158	+	0.992262i	$0.460377\pi$
$38$	20.7765	3.37040
$39$	2.96968	0.475529
$40$	−15.2373	−2.40923
$41$	−5.14041	−0.802797	−0.401398	−	0.915904i	$-0.631476\pi$
$41$	−5.14041	−0.802797	−0.401398	+	0.915904i	$0.631476\pi$
$42$	9.73961	1.50285
$43$	−8.74762	−1.33400	−0.667000	−	0.745058i	$-0.732422\pi$
$43$	−8.74762	−1.33400	−0.667000	+	0.745058i	$0.732422\pi$
$44$	9.96334	1.50203
$45$	14.3041	2.13233
$46$	13.5680	2.00049
$47$	7.82059	1.14075	0.570375	−	0.821385i	$-0.306798\pi$
$47$	7.82059	1.14075	0.570375	+	0.821385i	$0.306798\pi$
$48$	20.3382	2.93557
$49$	−5.33032	−0.761475
$50$	−2.64638	−0.374255
$51$	15.0108	2.10193
$52$	4.44218	0.616020
$53$	13.4964	1.85387	0.926935	−	0.375221i	$-0.122433\pi$
$53$	13.4964	1.85387	0.926935	+	0.375221i	$0.122433\pi$
$54$	−21.2480	−2.89148
$55$	5.51343	0.743431
$56$	8.00960	1.07033
$57$	−24.3089	−3.21980
$58$	−0.700224	−0.0919439
$59$	−14.1324	−1.83989	−0.919944	−	0.392051i	$-0.871766\pi$
$59$	−14.1324	−1.83989	−0.919944	+	0.392051i	$0.871766\pi$
$60$	32.4279	4.18643
$61$	8.79160	1.12565	0.562825	−	0.826576i	$-0.309715\pi$
$61$	8.79160	1.12565	0.562825	+	0.826576i	$0.309715\pi$
$62$	2.53815	0.322345
$63$	−7.51905	−0.947311
$64$	−1.04313	−0.130391
$65$	2.45818	0.304900
$66$	−16.9057	−2.08095
$67$	9.93254	1.21345	0.606727	−	0.794911i	$-0.292482\pi$
$67$	9.93254	1.21345	0.606727	+	0.794911i	$0.292482\pi$
$68$	22.4539	2.72293
$69$	−15.8748	−1.91110
$70$	8.06206	0.963601
$71$	3.29658	0.391232	0.195616	−	0.980681i	$-0.437329\pi$
$71$	3.29658	0.391232	0.195616	+	0.980681i	$0.437329\pi$
$72$	−36.0696	−4.25085
$73$	−0.353201	−0.0413391	−0.0206695	−	0.999786i	$-0.506580\pi$
$73$	−0.353201	−0.0413391	−0.0206695	+	0.999786i	$0.506580\pi$
$74$	−3.83374	−0.445663
$75$	3.09631	0.357532
$76$	−36.3625	−4.17106
$77$	−2.89817	−0.330277
$78$	−7.53747	−0.853451
$79$	−6.60096	−0.742666	−0.371333	−	0.928500i	$-0.621099\pi$
$79$	−6.60096	−0.742666	−0.371333	+	0.928500i	$0.621099\pi$
$80$	16.8352	1.88223
$81$	7.40357	0.822619
$82$	13.0471	1.44081
$83$	3.38992	0.372093	0.186046	−	0.982541i	$-0.440433\pi$
$83$	3.38992	0.372093	0.186046	+	0.982541i	$0.440433\pi$
$84$	−17.0460	−1.85987
$85$	12.4253	1.34772
$86$	22.2027	2.39418
$87$	0.819275	0.0878355
$88$	−13.9028	−1.48205
$89$	13.9960	1.48357	0.741785	−	0.670638i	$-0.233980\pi$
$89$	13.9960	1.48357	0.741785	+	0.670638i	$0.233980\pi$
$90$	−36.3059	−3.82697
$91$	−1.29216	−0.135455
$92$	−23.7463	−2.47572
$93$	−2.96968	−0.307941
$94$	−19.8498	−2.04735
$95$	−20.1220	−2.06447
$96$	−14.8056	−1.51109
$97$	−12.7220	−1.29172	−0.645862	−	0.763454i	$-0.723502\pi$
$97$	−12.7220	−1.29172	−0.645862	+	0.763454i	$0.723502\pi$
$98$	13.5291	1.36665
$99$	13.0513	1.31171
$100$	4.63161	0.463161
$101$	−5.68113	−0.565293	−0.282647	−	0.959224i	$-0.591212\pi$
$101$	−5.68113	−0.565293	−0.282647	+	0.959224i	$0.591212\pi$
$102$	−38.0996	−3.77242
$103$	−4.02402	−0.396499	−0.198249	−	0.980152i	$-0.563526\pi$
$103$	−4.02402	−0.396499	−0.198249	+	0.980152i	$0.563526\pi$
$104$	−6.19862	−0.607824
$105$	−9.43276	−0.920543
$106$	−34.2558	−3.32722
$107$	−5.23843	−0.506418	−0.253209	−	0.967412i	$-0.581486\pi$
$107$	−5.23843	−0.506418	−0.253209	+	0.967412i	$0.581486\pi$
$108$	37.1875	3.57837
$109$	12.6676	1.21334	0.606670	−	0.794954i	$-0.292505\pi$
$109$	12.6676	1.21334	0.606670	+	0.794954i	$0.292505\pi$
$110$	−13.9939	−1.33426
$111$	4.48554	0.425749
$112$	−8.84952	−0.836201
$113$	−3.25915	−0.306595	−0.153298	−	0.988180i	$-0.548989\pi$
$113$	−3.25915	−0.306595	−0.153298	+	0.988180i	$0.548989\pi$
$114$	61.6996	5.77870
$115$	−13.1405	−1.22536
$116$	1.22551	0.113786
$117$	5.81898	0.537965
$118$	35.8702	3.30212
$119$	−6.53146	−0.598738
$120$	−45.2499	−4.13073
$121$	−5.96944	−0.542676
$122$	−22.3144	−2.02025
$123$	−15.2654	−1.37643
$124$	−4.44218	−0.398920
$125$	−9.72789	−0.870089
$126$	19.0844	1.70018
$127$	5.57636	0.494822	0.247411	−	0.968911i	$-0.420420\pi$
$127$	5.57636	0.494822	0.247411	+	0.968911i	$0.420420\pi$
$128$	12.6188	1.11535
$129$	−25.9776	−2.28720
$130$	−6.23922	−0.547215
$131$	9.51289	0.831145	0.415573	−	0.909560i	$-0.363581\pi$
$131$	9.51289	0.831145	0.415573	+	0.909560i	$0.363581\pi$
$132$	29.5879	2.57529
$133$	10.5772	0.917164
$134$	−25.2102	−2.17783
$135$	20.5785	1.77112
$136$	−31.3321	−2.68670
$137$	−12.8088	−1.09433	−0.547164	−	0.837026i	$-0.684293\pi$
$137$	−12.8088	−1.09433	−0.547164	+	0.837026i	$0.684293\pi$
$138$	40.2926	3.42993
$139$	−1.00991	−0.0856594	−0.0428297	−	0.999082i	$-0.513637\pi$
$139$	−1.00991	−0.0856594	−0.0428297	+	0.999082i	$0.513637\pi$
$140$	−14.1100	−1.19251
$141$	23.2246	1.95587
$142$	−8.36721	−0.702160
$143$	2.24289	0.187560
$144$	39.8520	3.32100
$145$	0.678163	0.0563183
$146$	0.896477	0.0741929
$147$	−15.8293	−1.30558
$148$	6.70968	0.551533
$149$	−20.5857	−1.68644	−0.843222	−	0.537565i	$-0.819344\pi$
$149$	−20.5857	−1.68644	−0.843222	+	0.537565i	$0.819344\pi$
$150$	−7.85890	−0.641676
$151$	21.4120	1.74248	0.871241	−	0.490856i	$-0.163316\pi$
$151$	21.4120	1.74248	0.871241	+	0.490856i	$0.163316\pi$
$152$	50.7401	4.11557
$153$	29.4131	2.37791
$154$	7.35599	0.592762
$155$	−2.45818	−0.197446
$156$	13.1918	1.05619
$157$	2.90959	0.232211	0.116105	−	0.993237i	$-0.462959\pi$
$157$	2.90959	0.232211	0.116105	+	0.993237i	$0.462959\pi$
$158$	16.7542	1.33289
$159$	40.0799	3.17854
$160$	−12.2554	−0.968878
$161$	6.90742	0.544381
$162$	−18.7913	−1.47639
$163$	4.38556	0.343504	0.171752	−	0.985140i	$-0.445057\pi$
$163$	4.38556	0.343504	0.171752	+	0.985140i	$0.445057\pi$
$164$	−22.8346	−1.78309
$165$	16.3731	1.27464
$166$	−8.60412	−0.667809
$167$	14.6189	1.13125	0.565624	−	0.824663i	$-0.308635\pi$
$167$	14.6189	1.13125	0.565624	+	0.824663i	$0.308635\pi$
$168$	23.7859	1.83512
$169$	1.00000	0.0769231
$170$	−31.5373	−2.41880
$171$	−47.6325	−3.64255
$172$	−38.8585	−2.96293
$173$	5.18326	0.394076	0.197038	−	0.980396i	$-0.436868\pi$
$173$	5.18326	0.394076	0.197038	+	0.980396i	$0.436868\pi$
$174$	−2.07944	−0.157642
$175$	−1.34726	−0.101843
$176$	15.3607	1.15786
$177$	−41.9688	−3.15457
$178$	−35.5238	−2.66262
$179$	−12.8111	−0.957543	−0.478772	−	0.877940i	$-0.658918\pi$
$179$	−12.8111	−0.957543	−0.478772	+	0.877940i	$0.658918\pi$
$180$	63.5414	4.73610
$181$	−21.3744	−1.58874	−0.794372	−	0.607432i	$-0.792200\pi$
$181$	−21.3744	−1.58874	−0.794372	+	0.607432i	$0.792200\pi$
$182$	3.27969	0.243107
$183$	26.1082	1.92997
$184$	33.1356	2.44279
$185$	3.71295	0.272982
$186$	7.53747	0.552674
$187$	11.3371	0.829052
$188$	34.7405	2.53371
$189$	−10.8172	−0.786839
$190$	51.0725	3.70519
$191$	−18.5368	−1.34127	−0.670637	−	0.741785i	$-0.733979\pi$
$191$	−18.5368	−1.34127	−0.670637	+	0.741785i	$0.733979\pi$
$192$	−3.09776	−0.223562
$193$	−17.9712	−1.29359	−0.646797	−	0.762662i	$-0.723892\pi$
$193$	−17.9712	−1.29359	−0.646797	+	0.762662i	$0.723892\pi$
$194$	32.2903	2.31831
$195$	7.30000	0.522764
$196$	−23.6783	−1.69131
$197$	−5.96226	−0.424794	−0.212397	−	0.977184i	$-0.568127\pi$
$197$	−5.96226	−0.424794	−0.212397	+	0.977184i	$0.568127\pi$
$198$	−33.1262	−2.35418
$199$	−9.35882	−0.663429	−0.331715	−	0.943380i	$-0.607627\pi$
$199$	−9.35882	−0.663429	−0.331715	+	0.943380i	$0.607627\pi$
$200$	−6.46295	−0.457000
$201$	29.4964	2.08052
$202$	14.4195	1.01455
$203$	−0.356481	−0.0250201
$204$	66.6807	4.66858
$205$	−12.6360	−0.882540
$206$	10.2136	0.711612
$207$	−31.1062	−2.16203
$208$	6.84863	0.474867
$209$	−18.3597	−1.26997
$210$	23.9417	1.65214
$211$	−17.3475	−1.19425	−0.597126	−	0.802147i	$-0.703691\pi$
$211$	−17.3475	−1.19425	−0.597126	+	0.802147i	$0.703691\pi$
$212$	59.9534	4.11762
$213$	9.78978	0.670785
$214$	13.2959	0.908889
$215$	−21.5032	−1.46651
$216$	−51.8914	−3.53076
$217$	1.29216	0.0877175
$218$	−32.1523	−2.17763
$219$	−1.04889	−0.0708777
$220$	24.4917	1.65123
$221$	5.05469	0.340015
$222$	−11.3850	−0.764108
$223$	5.28678	0.354029	0.177014	−	0.984208i	$-0.443356\pi$
$223$	5.28678	0.354029	0.177014	+	0.984208i	$0.443356\pi$
$224$	6.44216	0.430435
$225$	6.06712	0.404475
$226$	8.27220	0.550259
$227$	2.99011	0.198461	0.0992304	−	0.995064i	$-0.468362\pi$
$227$	2.99011	0.198461	0.0992304	+	0.995064i	$0.468362\pi$
$228$	−107.985	−7.15146
$229$	−6.29502	−0.415986	−0.207993	−	0.978130i	$-0.566693\pi$
$229$	−6.29502	−0.415986	−0.207993	+	0.978130i	$0.566693\pi$
$230$	33.3526	2.19921
$231$	−8.60664	−0.566275
$232$	−1.71008	−0.112272
$233$	28.8505	1.89006	0.945029	−	0.326988i	$-0.106034\pi$
$233$	28.8505	1.89006	0.945029	+	0.326988i	$0.106034\pi$
$234$	−14.7694	−0.965507
$235$	19.2244	1.25406
$236$	−62.7789	−4.08656
$237$	−19.6027	−1.27333
$238$	16.5778	1.07458
$239$	−13.8008	−0.892697	−0.446349	−	0.894859i	$-0.647276\pi$
$239$	−13.8008	−0.892697	−0.446349	+	0.894859i	$0.647276\pi$
$240$	49.9949	3.22716
$241$	4.57470	0.294682	0.147341	−	0.989086i	$-0.452929\pi$
$241$	4.57470	0.294682	0.147341	+	0.989086i	$0.452929\pi$
$242$	15.1513	0.973963
$243$	−3.12815	−0.200671
$244$	39.0539	2.50017
$245$	−13.1029	−0.837113
$246$	38.7457	2.47033
$247$	−8.18572	−0.520845
$248$	6.19862	0.393613
$249$	10.0670	0.637969
$250$	24.6908	1.56158
$251$	14.3760	0.907407	0.453704	−	0.891153i	$-0.350102\pi$
$251$	14.3760	0.907407	0.453704	+	0.891153i	$0.350102\pi$
$252$	−33.4010	−2.10406
$253$	−11.9897	−0.753786
$254$	−14.1536	−0.888077
$255$	36.8992	2.31072
$256$	−29.9420	−1.87138
$257$	1.78911	0.111602	0.0558008	−	0.998442i	$-0.482229\pi$
$257$	1.78911	0.111602	0.0558008	+	0.998442i	$0.482229\pi$
$258$	65.9349	4.10493
$259$	−1.95174	−0.121275
$260$	10.9197	0.677210
$261$	1.60534	0.0993681
$262$	−24.1451	−1.49169
$263$	−13.4571	−0.829803	−0.414901	−	0.909866i	$-0.636184\pi$
$263$	−13.4571	−0.829803	−0.414901	+	0.909866i	$0.636184\pi$
$264$	−41.2869	−2.54103
$265$	33.1765	2.03802
$266$	−26.8466	−1.64607
$267$	41.5635	2.54364
$268$	44.1222	2.69519
$269$	10.8371	0.660747	0.330373	−	0.943850i	$-0.392825\pi$
$269$	10.8371	0.660747	0.330373	+	0.943850i	$0.392825\pi$
$270$	−52.2313	−3.17870
$271$	23.0216	1.39846	0.699230	−	0.714897i	$-0.253526\pi$
$271$	23.0216	1.39846	0.699230	+	0.714897i	$0.253526\pi$
$272$	34.6177	2.09901
$273$	−3.83729	−0.232244
$274$	32.5105	1.96403
$275$	2.33854	0.141019
$276$	−70.5189	−4.24474
$277$	7.80139	0.468740	0.234370	−	0.972147i	$-0.424697\pi$
$277$	7.80139	0.468740	0.234370	+	0.972147i	$0.424697\pi$
$278$	2.56330	0.153736
$279$	−5.81898	−0.348373
$280$	19.6890	1.17664
$281$	4.36973	0.260676	0.130338	−	0.991470i	$-0.458394\pi$
$281$	4.36973	0.260676	0.130338	+	0.991470i	$0.458394\pi$
$282$	−58.9474	−3.51027
$283$	−11.5845	−0.688628	−0.344314	−	0.938855i	$-0.611888\pi$
$283$	−11.5845	−0.688628	−0.344314	+	0.938855i	$0.611888\pi$
$284$	14.6440	0.868963
$285$	−59.7557	−3.53962
$286$	−5.69279	−0.336621
$287$	6.64223	0.392078
$288$	−29.0110	−1.70949
$289$	8.54988	0.502934
$290$	−1.72128	−0.101077
$291$	−37.7803	−2.21472
$292$	−1.56899	−0.0918179
$293$	0.502955	0.0293829	0.0146915	−	0.999892i	$-0.495323\pi$
$293$	0.502955	0.0293829	0.0146915	+	0.999892i	$0.495323\pi$
$294$	40.1772	2.34318
$295$	−34.7401	−2.02265
$296$	−9.36269	−0.544195
$297$	18.7763	1.08951
$298$	52.2494	3.02673
$299$	−5.34564	−0.309146
$300$	13.7544	0.794110
$301$	11.3033	0.651512
$302$	−54.3467	−3.12730
$303$	−16.8711	−0.969220
$304$	−56.0609	−3.21531
$305$	21.6113	1.23746
$306$	−74.6548	−4.26773
$307$	−0.983543	−0.0561338	−0.0280669	−	0.999606i	$-0.508935\pi$
$307$	−0.983543	−0.0561338	−0.0280669	+	0.999606i	$0.508935\pi$
$308$	−12.8742	−0.733577
$309$	−11.9500	−0.679814
$310$	6.23922	0.354364
$311$	13.8620	0.786040	0.393020	−	0.919530i	$-0.371430\pi$
$311$	13.8620	0.786040	0.393020	+	0.919530i	$0.371430\pi$
$312$	−18.4079	−1.04214
$313$	−7.46550	−0.421975	−0.210987	−	0.977489i	$-0.567668\pi$
$313$	−7.46550	−0.421975	−0.210987	+	0.977489i	$0.567668\pi$
$314$	−7.38496	−0.416758
$315$	−18.4832	−1.04141
$316$	−29.3227	−1.64953
$317$	28.3834	1.59417	0.797085	−	0.603868i	$-0.206374\pi$
$317$	28.3834	1.59417	0.797085	+	0.603868i	$0.206374\pi$
$318$	−101.729	−5.70466
$319$	0.618769	0.0346444
$320$	−2.56420	−0.143343
$321$	−15.5564	−0.868276
$322$	−17.5320	−0.977022
$323$	−41.3763	−2.30224
$324$	32.8880	1.82711
$325$	1.04264	0.0578355
$326$	−11.1312	−0.616500
$327$	37.6188	2.08032
$328$	31.8634	1.75936
$329$	−10.1054	−0.557131
$330$	−41.5573	−2.28765
$331$	17.1819	0.944405	0.472203	−	0.881490i	$-0.343459\pi$
$331$	17.1819	0.944405	0.472203	+	0.881490i	$0.343459\pi$
$332$	15.0587	0.826452
$333$	8.78926	0.481648
$334$	−37.1050	−2.03029
$335$	24.4160	1.33399
$336$	−26.2802	−1.43370
$337$	32.4338	1.76678	0.883391	−	0.468636i	$-0.155255\pi$
$337$	32.4338	1.76678	0.883391	+	0.468636i	$0.155255\pi$
$338$	−2.53815	−0.138057
$339$	−9.67863	−0.525671
$340$	55.1956	2.99340
$341$	−2.24289	−0.121459
$342$	120.898	6.53743
$343$	15.9327	0.860287
$344$	54.2231	2.92352
$345$	−39.0232	−2.10094
$346$	−13.1559	−0.707263
$347$	−2.08478	−0.111917	−0.0559584	−	0.998433i	$-0.517821\pi$
$347$	−2.08478	−0.111917	−0.0559584	+	0.998433i	$0.517821\pi$
$348$	3.63937	0.195091
$349$	−23.2310	−1.24353	−0.621764	−	0.783205i	$-0.713584\pi$
$349$	−23.2310	−1.24353	−0.621764	+	0.783205i	$0.713584\pi$
$350$	3.41955	0.182782
$351$	8.37145	0.446835
$352$	−11.1821	−0.596009
$353$	10.1830	0.541987	0.270994	−	0.962581i	$-0.412648\pi$
$353$	10.1830	0.541987	0.270994	+	0.962581i	$0.412648\pi$
$354$	106.523	5.66163
$355$	8.10359	0.430094
$356$	62.1727	3.29514
$357$	−19.3963	−1.02656
$358$	32.5163	1.71854
$359$	−5.00387	−0.264094	−0.132047	−	0.991243i	$-0.542155\pi$
$359$	−5.00387	−0.264094	−0.132047	+	0.991243i	$0.542155\pi$
$360$	−88.6656	−4.67309
$361$	48.0060	2.52663
$362$	54.2512	2.85138
$363$	−17.7273	−0.930442
$364$	−5.74001	−0.300858
$365$	−0.868232	−0.0454454
$366$	−66.2665	−3.46380
$367$	4.58031	0.239090	0.119545	−	0.992829i	$-0.461856\pi$
$367$	4.58031	0.239090	0.119545	+	0.992829i	$0.461856\pi$
$368$	−36.6103	−1.90844
$369$	−29.9119	−1.55715
$370$	−9.42401	−0.489931
$371$	−17.4395	−0.905413
$372$	−13.1918	−0.683965
$373$	−2.24519	−0.116252	−0.0581259	−	0.998309i	$-0.518512\pi$
$373$	−2.24519	−0.116252	−0.0581259	+	0.998309i	$0.518512\pi$
$374$	−28.7753	−1.48793
$375$	−28.8887	−1.49181
$376$	−48.4768	−2.50000
$377$	0.275880	0.0142085
$378$	27.4558	1.41217
$379$	−20.8172	−1.06931	−0.534655	−	0.845071i	$-0.679558\pi$
$379$	−20.8172	−1.06931	−0.534655	+	0.845071i	$0.679558\pi$
$380$	−89.3854	−4.58538
$381$	16.5600	0.848394
$382$	47.0491	2.40724
$383$	−8.13129	−0.415490	−0.207745	−	0.978183i	$-0.566612\pi$
$383$	−8.13129	−0.415490	−0.207745	+	0.978183i	$0.566612\pi$
$384$	37.4737	1.91232
$385$	−7.12423	−0.363084
$386$	45.6135	2.32166
$387$	−50.9022	−2.58750
$388$	−56.5135	−2.86904
$389$	−3.37271	−0.171003	−0.0855015	−	0.996338i	$-0.527249\pi$
$389$	−3.37271	−0.171003	−0.0855015	+	0.996338i	$0.527249\pi$
$390$	−18.5285	−0.938225
$391$	−27.0206	−1.36649
$392$	33.0406	1.66880
$393$	28.2502	1.42503
$394$	15.1331	0.762394
$395$	−16.2264	−0.816436
$396$	57.9764	2.91343
$397$	21.7128	1.08973	0.544866	−	0.838523i	$-0.316580\pi$
$397$	21.7128	1.08973	0.544866	+	0.838523i	$0.316580\pi$
$398$	23.7541	1.19068
$399$	31.4110	1.57252
$400$	7.14068	0.357034
$401$	−20.5171	−1.02458	−0.512288	−	0.858814i	$-0.671202\pi$
$401$	−20.5171	−1.02458	−0.512288	+	0.858814i	$0.671202\pi$
$402$	−74.8663	−3.73399
$403$	−1.00000	−0.0498135
$404$	−25.2366	−1.25557
$405$	18.1993	0.904330
$406$	0.904801	0.0449045
$407$	3.38777	0.167926
$408$	−93.0461	−4.60647
$409$	19.2479	0.951746	0.475873	−	0.879514i	$-0.342132\pi$
$409$	19.2479	0.951746	0.475873	+	0.879514i	$0.342132\pi$
$410$	32.0721	1.58393
$411$	−38.0379	−1.87627
$412$	−17.8754	−0.880660
$413$	18.2614	0.898583
$414$	78.9520	3.88028
$415$	8.33304	0.409053
$416$	−4.98558	−0.244438
$417$	−2.99910	−0.146867
$418$	46.5995	2.27926
$419$	35.8679	1.75226	0.876131	−	0.482072i	$-0.160116\pi$
$419$	35.8679	1.75226	0.876131	+	0.482072i	$0.160116\pi$
$420$	−41.9020	−2.04461
$421$	−5.95297	−0.290130	−0.145065	−	0.989422i	$-0.546339\pi$
$421$	−5.95297	−0.290130	−0.145065	+	0.989422i	$0.546339\pi$
$422$	44.0305	2.14337
$423$	45.5078	2.21267
$424$	−83.6589	−4.06284
$425$	5.27024	0.255644
$426$	−24.8479	−1.20388
$427$	−11.3602	−0.549756
$428$	−23.2701	−1.12480
$429$	6.66066	0.321580
$430$	54.5783	2.63200
$431$	30.6363	1.47570	0.737849	−	0.674966i	$-0.235842\pi$
$431$	30.6363	1.47570	0.737849	+	0.674966i	$0.235842\pi$
$432$	57.3329	2.75843
$433$	41.2455	1.98213	0.991065	−	0.133378i	$-0.0425825\pi$
$433$	41.2455	1.98213	0.991065	+	0.133378i	$0.0425825\pi$
$434$	−3.27969	−0.157430
$435$	2.01392	0.0965603
$436$	56.2720	2.69494
$437$	43.7579	2.09322
$438$	2.66225	0.127207
$439$	−11.0835	−0.528989	−0.264494	−	0.964387i	$-0.585205\pi$
$439$	−11.0835	−0.528989	−0.264494	+	0.964387i	$0.585205\pi$
$440$	−34.1756	−1.62926
$441$	−31.0170	−1.47700
$442$	−12.8295	−0.610239
$443$	7.45534	0.354214	0.177107	−	0.984192i	$-0.443326\pi$
$443$	7.45534	0.354214	0.177107	+	0.984192i	$0.443326\pi$
$444$	19.9256	0.945627
$445$	34.4046	1.63093
$446$	−13.4186	−0.635390
$447$	−61.1328	−2.89148
$448$	1.34789	0.0636819
$449$	−9.76866	−0.461012	−0.230506	−	0.973071i	$-0.574038\pi$
$449$	−9.76866	−0.461012	−0.230506	+	0.973071i	$0.574038\pi$
$450$	−15.3992	−0.725927
$451$	−11.5294	−0.542897
$452$	−14.4778	−0.680976
$453$	63.5866	2.98756
$454$	−7.58934	−0.356185
$455$	−3.17636	−0.148910
$456$	150.682	7.05632
$457$	23.1694	1.08382	0.541910	−	0.840437i	$-0.317702\pi$
$457$	23.1694	1.08382	0.541910	+	0.840437i	$0.317702\pi$
$458$	15.9777	0.746587
$459$	42.3151	1.97510
$460$	−58.3727	−2.72164
$461$	2.73491	0.127378	0.0636888	−	0.997970i	$-0.479714\pi$
$461$	2.73491	0.127378	0.0636888	+	0.997970i	$0.479714\pi$
$462$	21.8449	1.01632
$463$	25.3667	1.17889	0.589446	−	0.807808i	$-0.299346\pi$
$463$	25.3667	1.17889	0.589446	+	0.807808i	$0.299346\pi$
$464$	1.88940	0.0877132
$465$	−7.30000	−0.338529
$466$	−73.2267	−3.39216
$467$	−36.1504	−1.67284	−0.836421	−	0.548088i	$-0.815356\pi$
$467$	−36.1504	−1.67284	−0.836421	+	0.548088i	$0.815356\pi$
$468$	25.8490	1.19487
$469$	−12.8344	−0.592639
$470$	−48.7943	−2.25071
$471$	8.64054	0.398135
$472$	87.6016	4.03219
$473$	−19.6200	−0.902127
$474$	49.7546	2.28530
$475$	−8.53479	−0.391603
$476$	−29.0140	−1.32985
$477$	78.5352	3.59588
$478$	35.0284	1.60216
$479$	−34.8111	−1.59056	−0.795280	−	0.606243i	$-0.792676\pi$
$479$	−34.8111	−1.59056	−0.795280	+	0.606243i	$0.792676\pi$
$480$	−36.3947	−1.66118
$481$	1.51045	0.0688705
$482$	−11.6112	−0.528878
$483$	20.5128	0.933365
$484$	−26.5173	−1.20533
$485$	−31.2730	−1.42003
$486$	7.93971	0.360152
$487$	5.71137	0.258807	0.129403	−	0.991592i	$-0.458694\pi$
$487$	5.71137	0.258807	0.129403	+	0.991592i	$0.458694\pi$
$488$	−54.4958	−2.46691
$489$	13.0237	0.588952
$490$	33.2570	1.50240
$491$	−0.725912	−0.0327600	−0.0163800	−	0.999866i	$-0.505214\pi$
$491$	−0.725912	−0.0327600	−0.0163800	+	0.999866i	$0.505214\pi$
$492$	−67.8115	−3.05718
$493$	1.39449	0.0628046
$494$	20.7765	0.934781
$495$	32.0825	1.44200
$496$	−6.84863	−0.307512
$497$	−4.25971	−0.191074
$498$	−25.5515	−1.14499
$499$	−10.0875	−0.451576	−0.225788	−	0.974176i	$-0.572496\pi$
$499$	−10.0875	−0.451576	−0.225788	+	0.974176i	$0.572496\pi$
$500$	−43.2131	−1.93255
$501$	43.4135	1.93957
$502$	−36.4885	−1.62856
$503$	−7.66375	−0.341710	−0.170855	−	0.985296i	$-0.554653\pi$
$503$	−7.66375	−0.341710	−0.170855	+	0.985296i	$0.554653\pi$
$504$	46.6077	2.07607
$505$	−13.9652	−0.621444
$506$	30.4316	1.35285
$507$	2.96968	0.131888
$508$	24.7712	1.09905
$509$	16.8624	0.747414	0.373707	−	0.927547i	$-0.378087\pi$
$509$	16.8624	0.747414	0.373707	+	0.927547i	$0.378087\pi$
$510$	−93.6556	−4.14714
$511$	0.456392	0.0201896
$512$	50.7597	2.24328
$513$	−68.5263	−3.02551
$514$	−4.54102	−0.200296
$515$	−9.89177	−0.435883
$516$	−115.397	−5.08008
$517$	17.5407	0.771440
$518$	4.95380	0.217657
$519$	15.3926	0.675660
$520$	−15.2373	−0.668200
$521$	21.0597	0.922644	0.461322	−	0.887233i	$-0.347375\pi$
$521$	21.0597	0.922644	0.461322	+	0.887233i	$0.347375\pi$
$522$	−4.07459	−0.178340
$523$	−22.4371	−0.981108	−0.490554	−	0.871411i	$-0.663206\pi$
$523$	−22.4371	−0.981108	−0.490554	+	0.871411i	$0.663206\pi$
$524$	42.2580	1.84605
$525$	−4.00093	−0.174615
$526$	34.1562	1.48928
$527$	−5.05469	−0.220186
$528$	45.6164	1.98520
$529$	5.57587	0.242429
$530$	−84.2069	−3.65771
$531$	−82.2364	−3.56875
$532$	46.9861	2.03711
$533$	−5.14041	−0.222656
$534$	−105.494	−4.56518
$535$	−12.8770	−0.556721
$536$	−61.5680	−2.65933
$537$	−38.0447	−1.64175
$538$	−27.5060	−1.18587
$539$	−11.9553	−0.514953
$540$	91.4136	3.93381
$541$	−2.41191	−0.103696	−0.0518480	−	0.998655i	$-0.516511\pi$
$541$	−2.41191	−0.103696	−0.0518480	+	0.998655i	$0.516511\pi$
$542$	−58.4321	−2.50987
$543$	−63.4749	−2.72397
$544$	−25.2005	−1.08046
$545$	31.1393	1.33386
$546$	9.73961	0.416817
$547$	−7.85488	−0.335851	−0.167925	−	0.985800i	$-0.553707\pi$
$547$	−7.85488	−0.335851	−0.167925	+	0.985800i	$0.553707\pi$
$548$	−56.8989	−2.43060
$549$	51.1581	2.18338
$550$	−5.93555	−0.253093
$551$	−2.25828	−0.0962058
$552$	98.4020	4.18827
$553$	8.52950	0.362711
$554$	−19.8011	−0.841267
$555$	11.0263	0.468039
$556$	−4.48620	−0.190257
$557$	27.2675	1.15536	0.577681	−	0.816262i	$-0.303958\pi$
$557$	27.2675	1.15536	0.577681	+	0.816262i	$0.303958\pi$
$558$	14.7694	0.625239
$559$	−8.74762	−0.369985
$560$	−21.7537	−0.919261
$561$	33.6676	1.42145
$562$	−11.0910	−0.467846
$563$	36.9243	1.55617	0.778087	−	0.628156i	$-0.216190\pi$
$563$	36.9243	1.55617	0.778087	+	0.628156i	$0.216190\pi$
$564$	103.168	4.34416
$565$	−8.01158	−0.337050
$566$	29.4032	1.23591
$567$	−9.56659	−0.401759
$568$	−20.4343	−0.857402
$569$	22.1887	0.930200	0.465100	−	0.885258i	$-0.346018\pi$
$569$	22.1887	0.930200	0.465100	+	0.885258i	$0.346018\pi$
$570$	151.669	6.35270
$571$	−37.4416	−1.56688	−0.783440	−	0.621467i	$-0.786537\pi$
$571$	−37.4416	−1.56688	−0.783440	+	0.621467i	$0.786537\pi$
$572$	9.96334	0.416588
$573$	−55.0483	−2.29967
$574$	−16.8589	−0.703679
$575$	−5.57360	−0.232435
$576$	−6.06995	−0.252915
$577$	−22.2734	−0.927256	−0.463628	−	0.886030i	$-0.653452\pi$
$577$	−22.2734	−0.927256	−0.463628	+	0.886030i	$0.653452\pi$
$578$	−21.7008	−0.902636
$579$	−53.3686	−2.21792
$580$	3.01252	0.125088
$581$	−4.38032	−0.181726
$582$	95.8918	3.97484
$583$	30.2709	1.25369
$584$	2.18936	0.0905964
$585$	14.3041	0.591401
$586$	−1.27657	−0.0527347
$587$	7.17996	0.296349	0.148174	−	0.988961i	$-0.452660\pi$
$587$	7.17996	0.296349	0.148174	+	0.988961i	$0.452660\pi$
$588$	−70.3168	−2.89982
$589$	8.18572	0.337287
$590$	88.1754	3.63012
$591$	−17.7060	−0.728327
$592$	10.3445	0.425156
$593$	−28.2688	−1.16086	−0.580430	−	0.814310i	$-0.697115\pi$
$593$	−28.2688	−1.16086	−0.580430	+	0.814310i	$0.697115\pi$
$594$	−47.6569	−1.95539
$595$	−16.0555	−0.658212
$596$	−91.4453	−3.74575
$597$	−27.7927	−1.13748
$598$	13.5680	0.554837
$599$	1.35800	0.0554864	0.0277432	−	0.999615i	$-0.491168\pi$
$599$	1.35800	0.0554864	0.0277432	+	0.999615i	$0.491168\pi$
$600$	−19.1929	−0.783546
$601$	7.27227	0.296642	0.148321	−	0.988939i	$-0.452613\pi$
$601$	7.27227	0.296642	0.148321	+	0.988939i	$0.452613\pi$
$602$	−28.6895	−1.16930
$603$	57.7972	2.35369
$604$	95.1159	3.87021
$605$	−14.6739	−0.596581
$606$	42.8213	1.73950
$607$	12.0965	0.490981	0.245490	−	0.969399i	$-0.421051\pi$
$607$	12.0965	0.490981	0.245490	+	0.969399i	$0.421051\pi$
$608$	40.8105	1.65509
$609$	−1.05863	−0.0428980
$610$	−54.8527	−2.22092
$611$	7.82059	0.316387
$612$	130.658	5.28156
$613$	−24.1004	−0.973407	−0.486704	−	0.873567i	$-0.661801\pi$
$613$	−24.1004	−0.973407	−0.486704	+	0.873567i	$0.661801\pi$
$614$	2.49638	0.100746
$615$	−37.5250	−1.51315
$616$	17.9647	0.723817
$617$	−4.90967	−0.197656	−0.0988280	−	0.995105i	$-0.531509\pi$
$617$	−4.90967	−0.197656	−0.0988280	+	0.995105i	$0.531509\pi$
$618$	30.3310	1.22009
$619$	−18.0267	−0.724553	−0.362277	−	0.932071i	$-0.618000\pi$
$619$	−18.0267	−0.724553	−0.362277	+	0.932071i	$0.618000\pi$
$620$	−10.9197	−0.438545
$621$	−44.7508	−1.79579
$622$	−35.1837	−1.41074
$623$	−18.0850	−0.724561
$624$	20.3382	0.814180
$625$	−29.1261	−1.16504
$626$	18.9485	0.757335
$627$	−54.5223	−2.17741
$628$	12.9249	0.515761
$629$	7.63484	0.304421
$630$	46.9130	1.86906
$631$	25.0336	0.996571	0.498286	−	0.867013i	$-0.333963\pi$
$631$	25.0336	0.996571	0.498286	+	0.867013i	$0.333963\pi$
$632$	40.9168	1.62758
$633$	−51.5165	−2.04760
$634$	−72.0411	−2.86112
$635$	13.7077	0.543973
$636$	178.042	7.05983
$637$	−5.33032	−0.211195
$638$	−1.57053	−0.0621777
$639$	19.1827	0.758858
$640$	31.0192	1.22614
$641$	10.0343	0.396330	0.198165	−	0.980169i	$-0.436502\pi$
$641$	10.0343	0.396330	0.198165	+	0.980169i	$0.436502\pi$
$642$	39.4845	1.55833
$643$	−36.0033	−1.41983	−0.709915	−	0.704288i	$-0.751267\pi$
$643$	−36.0033	−1.41983	−0.709915	+	0.704288i	$0.751267\pi$
$644$	30.6840	1.20912
$645$	−63.8576	−2.51439
$646$	105.019	4.13192
$647$	2.35595	0.0926221	0.0463111	−	0.998927i	$-0.485253\pi$
$647$	2.35595	0.0926221	0.0463111	+	0.998927i	$0.485253\pi$
$648$	−45.8919	−1.80280
$649$	−31.6975	−1.24424
$650$	−2.64638	−0.103800
$651$	3.83729	0.150395
$652$	19.4815	0.762953
$653$	26.8099	1.04915	0.524576	−	0.851364i	$-0.324224\pi$
$653$	26.8099	1.04915	0.524576	+	0.851364i	$0.324224\pi$
$654$	−95.4820	−3.73364
$655$	23.3844	0.913704
$656$	−35.2047	−1.37451
$657$	−2.05527	−0.0801838
$658$	25.6491	0.999905
$659$	46.6411	1.81688	0.908440	−	0.418016i	$-0.137274\pi$
$659$	46.6411	1.81688	0.908440	+	0.418016i	$0.137274\pi$
$660$	72.7323	2.83110
$661$	−28.3598	−1.10307	−0.551535	−	0.834152i	$-0.685958\pi$
$661$	−28.3598	−1.10307	−0.551535	+	0.834152i	$0.685958\pi$
$662$	−43.6103	−1.69496
$663$	15.0108	0.582971
$664$	−21.0128	−0.815456
$665$	26.0008	1.00827
$666$	−22.3084	−0.864434
$667$	−1.47476	−0.0571028
$668$	64.9400	2.51260
$669$	15.7000	0.606998
$670$	−61.9713	−2.39416
$671$	19.7186	0.761229
$672$	19.1311	0.737999
$673$	0.825811	0.0318327	0.0159163	−	0.999873i	$-0.494933\pi$
$673$	0.825811	0.0318327	0.0159163	+	0.999873i	$0.494933\pi$
$674$	−82.3217	−3.17091
$675$	8.72844	0.335958
$676$	4.44218	0.170853
$677$	−2.52240	−0.0969437	−0.0484719	−	0.998825i	$-0.515435\pi$
$677$	−2.52240	−0.0969437	−0.0484719	+	0.998825i	$0.515435\pi$
$678$	24.5658	0.943443
$679$	16.4389	0.630866
$680$	−77.0199	−2.95358
$681$	8.87967	0.340270
$682$	5.69279	0.217988
$683$	−3.11450	−0.119173	−0.0595865	−	0.998223i	$-0.518978\pi$
$683$	−3.11450	−0.119173	−0.0595865	+	0.998223i	$0.518978\pi$
$684$	−211.592	−8.09043
$685$	−31.4863	−1.20303
$686$	−40.4396	−1.54399
$687$	−18.6942	−0.713227
$688$	−59.9092	−2.28402
$689$	13.4964	0.514171
$690$	99.0465	3.77063
$691$	45.1330	1.71694	0.858470	−	0.512865i	$-0.171416\pi$
$691$	45.1330	1.71694	0.858470	+	0.512865i	$0.171416\pi$
$692$	23.0250	0.875278
$693$	−16.8644	−0.640626
$694$	5.29147	0.200862
$695$	−2.48254	−0.0941680
$696$	−5.07837	−0.192495
$697$	−25.9832	−0.984183
$698$	58.9637	2.23181
$699$	85.6766	3.24059
$700$	−5.98478	−0.226204
$701$	44.8769	1.69498	0.847488	−	0.530814i	$-0.178114\pi$
$701$	44.8769	1.69498	0.847488	+	0.530814i	$0.178114\pi$
$702$	−21.2480	−0.801953
$703$	−12.3641	−0.466321
$704$	−2.33963	−0.0881781
$705$	57.0902	2.15014
$706$	−25.8460	−0.972726
$707$	7.34092	0.276084
$708$	−186.433	−7.00658
$709$	−21.2715	−0.798869	−0.399434	−	0.916762i	$-0.630793\pi$
$709$	−21.2715	−0.798869	−0.399434	+	0.916762i	$0.630793\pi$
$710$	−20.5681	−0.771907
$711$	−38.4109	−1.44052
$712$	−86.7557	−3.25131
$713$	5.34564	0.200196
$714$	49.2307	1.84241
$715$	5.51343	0.206191
$716$	−56.9090	−2.12679
$717$	−40.9838	−1.53057
$718$	12.7006	0.473981
$719$	17.1155	0.638299	0.319149	−	0.947704i	$-0.396603\pi$
$719$	17.1155	0.638299	0.319149	+	0.947704i	$0.396603\pi$
$720$	97.9634	3.65088
$721$	5.19968	0.193646
$722$	−121.846	−4.53464
$723$	13.5854	0.505245
$724$	−94.9488	−3.52875
$725$	0.287645	0.0106829
$726$	44.9945	1.66990
$727$	−28.9004	−1.07186	−0.535929	−	0.844263i	$-0.680038\pi$
$727$	−28.9004	−1.07186	−0.535929	+	0.844263i	$0.680038\pi$
$728$	8.00960	0.296856
$729$	−31.5003	−1.16668
$730$	2.20370	0.0815626
$731$	−44.2165	−1.63541
$732$	115.977	4.28665
$733$	−25.5609	−0.944115	−0.472057	−	0.881568i	$-0.656489\pi$
$733$	−25.5609	−0.944115	−0.472057	+	0.881568i	$0.656489\pi$
$734$	−11.6255	−0.429105
$735$	−38.9113	−1.43527
$736$	26.6511	0.982373
$737$	22.2776	0.820607
$738$	75.9208	2.79468
$739$	14.7114	0.541169	0.270584	−	0.962696i	$-0.412783\pi$
$739$	14.7114	0.541169	0.270584	+	0.962696i	$0.412783\pi$
$740$	16.4936	0.606317
$741$	−24.3089	−0.893011
$742$	44.2639	1.62498
$743$	44.7872	1.64308	0.821541	−	0.570149i	$-0.193114\pi$
$743$	44.7872	1.64308	0.821541	+	0.570149i	$0.193114\pi$
$744$	18.4079	0.674866
$745$	−50.6033	−1.85396
$746$	5.69863	0.208642
$747$	19.7259	0.721733
$748$	50.3616	1.84140
$749$	6.76889	0.247330
$750$	73.3237	2.67740
$751$	12.4884	0.455709	0.227854	−	0.973695i	$-0.426829\pi$
$751$	12.4884	0.455709	0.227854	+	0.973695i	$0.426829\pi$
$752$	53.5603	1.95314
$753$	42.6922	1.55579
$754$	−0.700224	−0.0255007
$755$	52.6345	1.91556
$756$	−48.0522	−1.74764
$757$	26.1411	0.950116	0.475058	−	0.879955i	$-0.342427\pi$
$757$	26.1411	0.950116	0.475058	+	0.879955i	$0.342427\pi$
$758$	52.8372	1.91913
$759$	−35.6055	−1.29240
$760$	124.728	4.52437
$761$	−22.0498	−0.799304	−0.399652	−	0.916667i	$-0.630869\pi$
$761$	−22.0498	−0.799304	−0.399652	+	0.916667i	$0.630869\pi$
$762$	−42.0317	−1.52265
$763$	−16.3686	−0.592583
$764$	−82.3438	−2.97909
$765$	72.3027	2.61411
$766$	20.6384	0.745696
$767$	−14.1324	−0.510293
$768$	−88.9181	−3.20856
$769$	3.50705	0.126467	0.0632337	−	0.997999i	$-0.479859\pi$
$769$	3.50705	0.126467	0.0632337	+	0.997999i	$0.479859\pi$
$770$	18.0823	0.651642
$771$	5.31307	0.191346
$772$	−79.8313	−2.87319
$773$	17.7825	0.639592	0.319796	−	0.947486i	$-0.396386\pi$
$773$	17.7825	0.639592	0.319796	+	0.947486i	$0.396386\pi$
$774$	129.197	4.64390
$775$	−1.04264	−0.0374529
$776$	78.8589	2.83087
$777$	−5.79603	−0.207932
$778$	8.56042	0.306906
$779$	42.0779	1.50760
$780$	32.4279	1.16111
$781$	7.39388	0.264574
$782$	68.5821	2.45249
$783$	2.30952	0.0825354
$784$	−36.5054	−1.30376
$785$	7.15229	0.255276
$786$	−71.7031	−2.55757
$787$	−35.5318	−1.26657	−0.633287	−	0.773917i	$-0.718295\pi$
$787$	−35.5318	−1.26657	−0.633287	+	0.773917i	$0.718295\pi$
$788$	−26.4855	−0.943505
$789$	−39.9633	−1.42273
$790$	41.1848	1.46529
$791$	4.21134	0.149738
$792$	−80.9002	−2.87466
$793$	8.79160	0.312199
$794$	−55.1102	−1.95579
$795$	98.5235	3.49427
$796$	−41.5736	−1.47354
$797$	29.8387	1.05694	0.528470	−	0.848952i	$-0.322766\pi$
$797$	29.8387	1.05694	0.528470	+	0.848952i	$0.322766\pi$
$798$	−79.7257	−2.82226
$799$	39.5306	1.39849
$800$	−5.19818	−0.183783
$801$	81.4422	2.87762
$802$	52.0754	1.83885
$803$	−0.792192	−0.0279559
$804$	131.029	4.62102
$805$	16.9797	0.598455
$806$	2.53815	0.0894024
$807$	32.1825	1.13288
$808$	35.2151	1.23886
$809$	−18.0659	−0.635164	−0.317582	−	0.948231i	$-0.602871\pi$
$809$	−18.0659	−0.635164	−0.317582	+	0.948231i	$0.602871\pi$
$810$	−46.1925	−1.62304
$811$	−33.4411	−1.17427	−0.587137	−	0.809487i	$-0.699745\pi$
$811$	−33.4411	−1.17427	−0.587137	+	0.809487i	$0.699745\pi$
$812$	−1.58355	−0.0555719
$813$	68.3666	2.39772
$814$	−8.59865	−0.301383
$815$	10.7805	0.377624
$816$	102.803	3.59884
$817$	71.6055	2.50516
$818$	−48.8539	−1.70814
$819$	−7.51905	−0.262737
$820$	−56.1316	−1.96020
$821$	2.33271	0.0814120	0.0407060	−	0.999171i	$-0.487039\pi$
$821$	2.33271	0.0814120	0.0407060	+	0.999171i	$0.487039\pi$
$822$	96.5458	3.36742
$823$	17.1345	0.597270	0.298635	−	0.954367i	$-0.403469\pi$
$823$	17.1345	0.597270	0.298635	+	0.954367i	$0.403469\pi$
$824$	24.9434	0.868944
$825$	6.94470	0.241783
$826$	−46.3500	−1.61272
$827$	9.29835	0.323335	0.161668	−	0.986845i	$-0.448313\pi$
$827$	9.29835	0.323335	0.161668	+	0.986845i	$0.448313\pi$
$828$	−138.179	−4.80206
$829$	−25.5414	−0.887090	−0.443545	−	0.896252i	$-0.646279\pi$
$829$	−25.5414	−0.887090	−0.443545	+	0.896252i	$0.646279\pi$
$830$	−21.1505	−0.734144
$831$	23.1676	0.803676
$832$	−1.04313	−0.0361640
$833$	−26.9431	−0.933524
$834$	7.61216	0.263588
$835$	35.9360	1.24362
$836$	−81.5570	−2.82071
$837$	−8.37145	−0.289360
$838$	−91.0380	−3.14486
$839$	16.3591	0.564781	0.282390	−	0.959300i	$-0.408873\pi$
$839$	16.3591	0.564781	0.282390	+	0.959300i	$0.408873\pi$
$840$	58.4701	2.01741
$841$	−28.9239	−0.997376
$842$	15.1095	0.520708
$843$	12.9767	0.446941
$844$	−77.0608	−2.65254
$845$	2.45818	0.0845639
$846$	−115.505	−3.97116
$847$	7.71346	0.265038
$848$	92.4317	3.17412
$849$	−34.4022	−1.18068
$850$	−13.3766	−0.458815
$851$	−8.07431	−0.276784
$852$	43.4880	1.48987
$853$	31.9701	1.09463	0.547317	−	0.836925i	$-0.315649\pi$
$853$	31.9701	1.09463	0.547317	+	0.836925i	$0.315649\pi$
$854$	28.8337	0.986669
$855$	−117.089	−4.00437
$856$	32.4710	1.10984
$857$	−21.2660	−0.726432	−0.363216	−	0.931705i	$-0.618321\pi$
$857$	−21.2660	−0.726432	−0.363216	+	0.931705i	$0.618321\pi$
$858$	−16.9057	−0.577152
$859$	44.1120	1.50508	0.752542	−	0.658545i	$-0.228828\pi$
$859$	44.1120	1.50508	0.752542	+	0.658545i	$0.228828\pi$
$860$	−95.5212	−3.25725
$861$	19.7253	0.672235
$862$	−77.7593	−2.64849
$863$	−52.7045	−1.79408	−0.897041	−	0.441947i	$-0.854288\pi$
$863$	−52.7045	−1.79408	−0.897041	+	0.441947i	$0.854288\pi$
$864$	−41.7365	−1.41991
$865$	12.7414	0.433220
$866$	−104.687	−3.55741
$867$	25.3904	0.862302
$868$	5.74001	0.194829
$869$	−14.8052	−0.502234
$870$	−5.11163	−0.173301
$871$	9.93254	0.336551
$872$	−78.5219	−2.65909
$873$	−74.0291	−2.50551
$874$	−111.064	−3.75679
$875$	12.5700	0.424943
$876$	−4.65938	−0.157426
$877$	24.8028	0.837531	0.418766	−	0.908094i	$-0.362463\pi$
$877$	24.8028	0.837531	0.418766	+	0.908094i	$0.362463\pi$
$878$	28.1316	0.949397
$879$	1.49361	0.0503783
$880$	37.7594	1.27287
$881$	24.7276	0.833094	0.416547	−	0.909114i	$-0.363240\pi$
$881$	24.7276	0.833094	0.416547	+	0.909114i	$0.363240\pi$
$882$	78.7258	2.65083
$883$	−2.75118	−0.0925847	−0.0462924	−	0.998928i	$-0.514741\pi$
$883$	−2.75118	−0.0925847	−0.0462924	+	0.998928i	$0.514741\pi$
$884$	22.4539	0.755205
$885$	−103.167	−3.46791
$886$	−18.9227	−0.635722
$887$	−33.1672	−1.11364	−0.556822	−	0.830632i	$-0.687979\pi$
$887$	−33.1672	−1.11364	−0.556822	+	0.830632i	$0.687979\pi$
$888$	−27.8041	−0.933046
$889$	−7.20555	−0.241666
$890$	−87.3239	−2.92710
$891$	16.6054	0.556302
$892$	23.4848	0.786331
$893$	−64.0171	−2.14225
$894$	155.164	5.18946
$895$	−31.4919	−1.05266
$896$	−16.3055	−0.544727
$897$	−15.8748	−0.530045
$898$	24.7943	0.827396
$899$	−0.275880	−0.00920112
$900$	26.9513	0.898375
$901$	68.2200	2.27274
$902$	29.2632	0.974359
$903$	33.5672	1.11705
$904$	20.2022	0.671916
$905$	−52.5420	−1.74656
$906$	−161.392	−5.36189
$907$	32.5337	1.08026	0.540131	−	0.841581i	$-0.318375\pi$
$907$	32.5337	1.08026	0.540131	+	0.841581i	$0.318375\pi$
$908$	13.2826	0.440800
$909$	−33.0584	−1.09648
$910$	8.06206	0.267255
$911$	22.4875	0.745043	0.372522	−	0.928024i	$-0.378493\pi$
$911$	22.4875	0.745043	0.372522	+	0.928024i	$0.378493\pi$
$912$	−166.483	−5.51280
$913$	7.60323	0.251630
$914$	−58.8073	−1.94517
$915$	64.1787	2.12168
$916$	−27.9636	−0.923944
$917$	−12.2922	−0.405923
$918$	−107.402	−3.54479
$919$	14.6185	0.482221	0.241110	−	0.970498i	$-0.422488\pi$
$919$	14.6185	0.482221	0.241110	+	0.970498i	$0.422488\pi$
$920$	81.4532	2.68543
$921$	−2.92080	−0.0962438
$922$	−6.94161	−0.228610
$923$	3.29658	0.108508
$924$	−38.2323	−1.25775
$925$	1.57486	0.0517810
$926$	−64.3844	−2.11580
$927$	−23.4157	−0.769072
$928$	−1.37542	−0.0451504
$929$	−32.3931	−1.06278	−0.531391	−	0.847127i	$-0.678330\pi$
$929$	−32.3931	−1.06278	−0.531391	+	0.847127i	$0.678330\pi$
$930$	18.5285	0.607572
$931$	43.6325	1.43000
$932$	128.159	4.19799
$933$	41.1656	1.34770
$934$	91.7550	3.00231
$935$	27.8687	0.911403
$936$	−36.0696	−1.17897
$937$	0.353548	0.0115499	0.00577496	−	0.999983i	$-0.498162\pi$
$937$	0.353548	0.0115499	0.00577496	+	0.999983i	$0.498162\pi$
$938$	32.5756	1.06363
$939$	−22.1701	−0.723494
$940$	85.3983	2.78539
$941$	45.0771	1.46947	0.734736	−	0.678353i	$-0.237306\pi$
$941$	45.0771	1.46947	0.734736	+	0.678353i	$0.237306\pi$
$942$	−21.9309	−0.714549
$943$	27.4788	0.894832
$944$	−96.7878	−3.15018
$945$	−26.5907	−0.864997
$946$	49.7983	1.61908
$947$	−48.3735	−1.57193	−0.785964	−	0.618272i	$-0.787833\pi$
$947$	−48.3735	−1.57193	−0.785964	+	0.618272i	$0.787833\pi$
$948$	−87.0789	−2.82819
$949$	−0.353201	−0.0114654
$950$	21.6625	0.702825
$951$	84.2894	2.73327
$952$	40.4860	1.31216
$953$	42.3747	1.37265	0.686326	−	0.727294i	$-0.259222\pi$
$953$	42.3747	1.37265	0.686326	+	0.727294i	$0.259222\pi$
$954$	−199.334	−6.45367
$955$	−45.5667	−1.47450
$956$	−61.3055	−1.98276
$957$	1.83754	0.0593994
$958$	88.3556	2.85464
$959$	16.5510	0.534459
$960$	−7.61485	−0.245768
$961$	1.00000	0.0322581
$962$	−3.83374	−0.123605
$963$	−30.4823	−0.982279
$964$	20.3216	0.654516
$965$	−44.1764	−1.42209
$966$	−52.0645	−1.67515
$967$	−40.1387	−1.29077	−0.645386	−	0.763856i	$-0.723304\pi$
$967$	−40.1387	−1.29077	−0.645386	+	0.763856i	$0.723304\pi$
$968$	37.0023	1.18930
$969$	−122.874	−3.94728
$970$	79.3754	2.54859
$971$	−9.24803	−0.296783	−0.148392	−	0.988929i	$-0.547410\pi$
$971$	−9.24803	−0.296783	−0.148392	+	0.988929i	$0.547410\pi$
$972$	−13.8958	−0.445709
$973$	1.30496	0.0418352
$974$	−14.4963	−0.464491
$975$	3.09631	0.0991614
$976$	60.2104	1.92729
$977$	27.3457	0.874865	0.437433	−	0.899251i	$-0.355888\pi$
$977$	27.3457	0.874865	0.437433	+	0.899251i	$0.355888\pi$
$978$	−33.0560	−1.05702
$979$	31.3914	1.00327
$980$	−58.2054	−1.85930
$981$	73.7127	2.35347
$982$	1.84247	0.0587956
$983$	−4.55237	−0.145198	−0.0725991	−	0.997361i	$-0.523129\pi$
$983$	−4.55237	−0.145198	−0.0725991	+	0.997361i	$0.523129\pi$
$984$	94.6241	3.01651
$985$	−14.6563	−0.466989
$986$	−3.53941	−0.112718
$987$	−30.0099	−0.955225
$988$	−36.3625	−1.15684
$989$	46.7616	1.48693
$990$	−81.4301	−2.58802
$991$	−1.42077	−0.0451324	−0.0225662	−	0.999745i	$-0.507184\pi$
$991$	−1.42077	−0.0451324	−0.0225662	+	0.999745i	$0.507184\pi$
$992$	4.98558	0.158292
$993$	51.0248	1.61922
$994$	10.8118	0.342928
$995$	−23.0057	−0.729329
$996$	44.7194	1.41699
$997$	−20.1107	−0.636913	−0.318456	−	0.947938i	$-0.603164\pi$
$997$	−20.1107	−0.636913	−0.318456	+	0.947938i	$0.603164\pi$
$998$	25.6034	0.810462
$999$	12.6446	0.400059

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.a.e.1.1	✓	8
3.2	odd	2		3627.2.a.p.1.8		8
4.3	odd	2		6448.2.a.bd.1.1		8
13.12	even	2		5239.2.a.i.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.a.e.1.1	✓	8	1.1	even	1	trivial
3627.2.a.p.1.8		8	3.2	odd	2
5239.2.a.i.1.8		8	13.12	even	2
6448.2.a.bd.1.1		8	4.3	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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.a (trivial)

\(f(q)\)	\(=\)	\(q-2.53815 q^{2} +2.96968 q^{3} +4.44218 q^{4} +2.45818 q^{5} -7.53747 q^{6} -1.29216 q^{7} -6.19862 q^{8} +5.81898 q^{9} +O(q^{10})\)	\(q-2.53815 q^{2} +2.96968 q^{3} +4.44218 q^{4} +2.45818 q^{5} -7.53747 q^{6} -1.29216 q^{7} -6.19862 q^{8} +5.81898 q^{9} -6.23922 q^{10} +2.24289 q^{11} +13.1918 q^{12} +1.00000 q^{13} +3.27969 q^{14} +7.30000 q^{15} +6.84863 q^{16} +5.05469 q^{17} -14.7694 q^{18} -8.18572 q^{19} +10.9197 q^{20} -3.83729 q^{21} -5.69279 q^{22} -5.34564 q^{23} -18.4079 q^{24} +1.04264 q^{25} -2.53815 q^{26} +8.37145 q^{27} -5.74001 q^{28} +0.275880 q^{29} -18.5285 q^{30} -1.00000 q^{31} -4.98558 q^{32} +6.66066 q^{33} -12.8295 q^{34} -3.17636 q^{35} +25.8490 q^{36} +1.51045 q^{37} +20.7765 q^{38} +2.96968 q^{39} -15.2373 q^{40} -5.14041 q^{41} +9.73961 q^{42} -8.74762 q^{43} +9.96334 q^{44} +14.3041 q^{45} +13.5680 q^{46} +7.82059 q^{47} +20.3382 q^{48} -5.33032 q^{49} -2.64638 q^{50} +15.0108 q^{51} +4.44218 q^{52} +13.4964 q^{53} -21.2480 q^{54} +5.51343 q^{55} +8.00960 q^{56} -24.3089 q^{57} -0.700224 q^{58} -14.1324 q^{59} +32.4279 q^{60} +8.79160 q^{61} +2.53815 q^{62} -7.51905 q^{63} -1.04313 q^{64} +2.45818 q^{65} -16.9057 q^{66} +9.93254 q^{67} +22.4539 q^{68} -15.8748 q^{69} +8.06206 q^{70} +3.29658 q^{71} -36.0696 q^{72} -0.353201 q^{73} -3.83374 q^{74} +3.09631 q^{75} -36.3625 q^{76} -2.89817 q^{77} -7.53747 q^{78} -6.60096 q^{79} +16.8352 q^{80} +7.40357 q^{81} +13.0471 q^{82} +3.38992 q^{83} -17.0460 q^{84} +12.4253 q^{85} +22.2027 q^{86} +0.819275 q^{87} -13.9028 q^{88} +13.9960 q^{89} -36.3059 q^{90} -1.29216 q^{91} -23.7463 q^{92} -2.96968 q^{93} -19.8498 q^{94} -20.1220 q^{95} -14.8056 q^{96} -12.7220 q^{97} +13.5291 q^{98} +13.0513 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} + 7 q^{3} + 7 q^{4} + 11 q^{5} - 2 q^{7} + 9 q^{9}+O(q^{10}) \) 8 * q - q^2 + 7 * q^3 + 7 * q^4 + 11 * q^5 - 2 * q^7 + 9 * q^9	\( 8 q - q^{2} + 7 q^{3} + 7 q^{4} + 11 q^{5} - 2 q^{7} + 9 q^{9} - 2 q^{10} - 2 q^{11} + 19 q^{12} + 8 q^{13} + 3 q^{14} + 6 q^{15} - 7 q^{16} + 7 q^{17} - 12 q^{18} - 5 q^{19} + 6 q^{20} + 8 q^{21} - 4 q^{22} + 14 q^{23} - 17 q^{24} + 17 q^{25} - q^{26} + 7 q^{27} - 9 q^{28} + 12 q^{29} - 9 q^{30} - 8 q^{31} - 21 q^{32} + 10 q^{33} - 12 q^{34} - q^{35} + 11 q^{36} + 2 q^{37} + 24 q^{38} + 7 q^{39} - 19 q^{40} + 13 q^{41} - 27 q^{42} - 5 q^{43} + 22 q^{44} + 19 q^{45} + 17 q^{46} + 23 q^{47} + 3 q^{48} + 26 q^{49} - 26 q^{50} + 18 q^{51} + 7 q^{52} + 25 q^{53} - 36 q^{54} - 17 q^{55} + 8 q^{56} - 35 q^{57} - 29 q^{58} - 5 q^{59} + 71 q^{60} - 9 q^{61} + q^{62} - 37 q^{63} - 14 q^{64} + 11 q^{65} - 41 q^{66} + 22 q^{67} - 6 q^{68} - 7 q^{69} - 29 q^{70} - 17 q^{71} - 34 q^{72} - 27 q^{73} + 14 q^{74} - 33 q^{75} - 36 q^{76} + 31 q^{77} - 23 q^{79} + 9 q^{80} - 12 q^{81} + 18 q^{82} - 25 q^{83} - 62 q^{84} + 13 q^{85} + 11 q^{86} + 26 q^{87} + 5 q^{88} + 2 q^{89} - 14 q^{90} - 2 q^{91} - 20 q^{92} - 7 q^{93} - 38 q^{94} + 3 q^{95} - 52 q^{96} - 15 q^{97} + 39 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q - q^2 + 7 * q^3 + 7 * q^4 + 11 * q^5 - 2 * q^7 + 9 * q^9 - 2 * q^10 - 2 * q^11 + 19 * q^12 + 8 * q^13 + 3 * q^14 + 6 * q^15 - 7 * q^16 + 7 * q^17 - 12 * q^18 - 5 * q^19 + 6 * q^20 + 8 * q^21 - 4 * q^22 + 14 * q^23 - 17 * q^24 + 17 * q^25 - q^26 + 7 * q^27 - 9 * q^28 + 12 * q^29 - 9 * q^30 - 8 * q^31 - 21 * q^32 + 10 * q^33 - 12 * q^34 - q^35 + 11 * q^36 + 2 * q^37 + 24 * q^38 + 7 * q^39 - 19 * q^40 + 13 * q^41 - 27 * q^42 - 5 * q^43 + 22 * q^44 + 19 * q^45 + 17 * q^46 + 23 * q^47 + 3 * q^48 + 26 * q^49 - 26 * q^50 + 18 * q^51 + 7 * q^52 + 25 * q^53 - 36 * q^54 - 17 * q^55 + 8 * q^56 - 35 * q^57 - 29 * q^58 - 5 * q^59 + 71 * q^60 - 9 * q^61 + q^62 - 37 * q^63 - 14 * q^64 + 11 * q^65 - 41 * q^66 + 22 * q^67 - 6 * q^68 - 7 * q^69 - 29 * q^70 - 17 * q^71 - 34 * q^72 - 27 * q^73 + 14 * q^74 - 33 * q^75 - 36 * q^76 + 31 * q^77 - 23 * q^79 + 9 * q^80 - 12 * q^81 + 18 * q^82 - 25 * q^83 - 62 * q^84 + 13 * q^85 + 11 * q^86 + 26 * q^87 + 5 * q^88 + 2 * q^89 - 14 * q^90 - 2 * q^91 - 20 * q^92 - 7 * q^93 - 38 * q^94 + 3 * q^95 - 52 * q^96 - 15 * q^97 + 39 * q^98 - 8 * q^99

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