LMFDB - Embedded newform 403.2.a.b.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:	$1$
Dimension:	$6$
Coefficient field:	6.6.5748973.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 6x^{4} + 4x^{3} + 8x^{2} - 4x - 1 $ x^6 - x^5 - 6x^4 + 4x^3 + 8x^2 - 4x - 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			1.1
Root			$-0.187851$ 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)

$f(q)$	$=$	$q-2.61388 q^{2} -1.18785 q^{3} +4.83234 q^{4} +1.45573 q^{5} +3.10489 q^{6} -1.87247 q^{7} -7.40339 q^{8} -1.58901 q^{9} +O(q^{10})$	\(q-2.61388 q^{2} -1.18785 q^{3} +4.83234 q^{4} +1.45573 q^{5} +3.10489 q^{6} -1.87247 q^{7} -7.40339 q^{8} -1.58901 q^{9} -3.80510 q^{10} +0.473692 q^{11} -5.74010 q^{12} +1.00000 q^{13} +4.89441 q^{14} -1.72919 q^{15} +9.68686 q^{16} -2.22798 q^{17} +4.15347 q^{18} +8.23894 q^{19} +7.03459 q^{20} +2.22422 q^{21} -1.23817 q^{22} -5.80264 q^{23} +8.79413 q^{24} -2.88085 q^{25} -2.61388 q^{26} +5.45106 q^{27} -9.04843 q^{28} -7.13067 q^{29} +4.51989 q^{30} +1.00000 q^{31} -10.5134 q^{32} -0.562676 q^{33} +5.82366 q^{34} -2.72582 q^{35} -7.67864 q^{36} -7.25508 q^{37} -21.5356 q^{38} -1.18785 q^{39} -10.7774 q^{40} -6.30750 q^{41} -5.81383 q^{42} -0.625207 q^{43} +2.28904 q^{44} -2.31317 q^{45} +15.1674 q^{46} -1.34262 q^{47} -11.5065 q^{48} -3.49384 q^{49} +7.53017 q^{50} +2.64651 q^{51} +4.83234 q^{52} -8.52918 q^{53} -14.2484 q^{54} +0.689569 q^{55} +13.8627 q^{56} -9.78663 q^{57} +18.6387 q^{58} +3.34763 q^{59} -8.35605 q^{60} -1.87837 q^{61} -2.61388 q^{62} +2.97538 q^{63} +8.10713 q^{64} +1.45573 q^{65} +1.47077 q^{66} +4.97297 q^{67} -10.7664 q^{68} +6.89267 q^{69} +7.12495 q^{70} -16.3567 q^{71} +11.7641 q^{72} -2.60031 q^{73} +18.9639 q^{74} +3.42202 q^{75} +39.8134 q^{76} -0.886976 q^{77} +3.10489 q^{78} -9.16549 q^{79} +14.1015 q^{80} -1.70802 q^{81} +16.4870 q^{82} +2.73403 q^{83} +10.7482 q^{84} -3.24334 q^{85} +1.63421 q^{86} +8.47017 q^{87} -3.50693 q^{88} -4.04630 q^{89} +6.04634 q^{90} -1.87247 q^{91} -28.0403 q^{92} -1.18785 q^{93} +3.50944 q^{94} +11.9937 q^{95} +12.4884 q^{96} -0.222505 q^{97} +9.13247 q^{98} -0.752702 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 5 q^{3} + 6 q^{4} - 9 q^{5} - 3 q^{8} - q^{9}+O(q^{10}) $ 6 * q - 2 * q^2 - 5 * q^3 + 6 * q^4 - 9 * q^5 - 3 * q^8 - q^9	\( 6 q - 2 q^{2} - 5 q^{3} + 6 q^{4} - 9 q^{5} - 3 q^{8} - q^{9} - 8 q^{10} - 5 q^{11} - 13 q^{12} + 6 q^{13} - 17 q^{14} + 4 q^{15} + 14 q^{16} - 23 q^{17} + 9 q^{18} + 7 q^{19} - 10 q^{20} + 2 q^{21} + 2 q^{22} - 18 q^{23} - 13 q^{24} + 11 q^{25} - 2 q^{26} - 5 q^{27} - 25 q^{28} - 18 q^{29} + 25 q^{30} + 6 q^{31} + 2 q^{32} - 2 q^{33} - 16 q^{34} - q^{35} - 2 q^{36} - 13 q^{37} - 8 q^{38} - 5 q^{39} - 29 q^{40} - 5 q^{41} + 31 q^{42} - 7 q^{43} + 30 q^{44} - 5 q^{45} + 19 q^{46} - 9 q^{47} - 19 q^{48} + 16 q^{49} + 29 q^{50} + 26 q^{51} + 6 q^{52} - 31 q^{53} - 4 q^{54} + 7 q^{55} + 8 q^{56} - 5 q^{57} + 35 q^{58} - q^{59} + 33 q^{60} - 15 q^{61} - 2 q^{62} + 11 q^{63} - 5 q^{64} - 9 q^{65} - 29 q^{66} - 28 q^{67} - 12 q^{68} + 5 q^{69} + 73 q^{70} + q^{71} + 45 q^{72} - 20 q^{73} + 4 q^{74} + q^{75} + 38 q^{76} - 29 q^{77} - 15 q^{79} + 7 q^{80} + 2 q^{81} + 36 q^{82} + q^{83} + 68 q^{84} + 29 q^{85} + 3 q^{86} + 10 q^{87} + 9 q^{88} - q^{89} - 32 q^{90} - 60 q^{92} - 5 q^{93} + 54 q^{94} - 13 q^{95} + 36 q^{96} - 5 q^{97} + 20 q^{98} - 15 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 5 * q^3 + 6 * q^4 - 9 * q^5 - 3 * q^8 - q^9 - 8 * q^10 - 5 * q^11 - 13 * q^12 + 6 * q^13 - 17 * q^14 + 4 * q^15 + 14 * q^16 - 23 * q^17 + 9 * q^18 + 7 * q^19 - 10 * q^20 + 2 * q^21 + 2 * q^22 - 18 * q^23 - 13 * q^24 + 11 * q^25 - 2 * q^26 - 5 * q^27 - 25 * q^28 - 18 * q^29 + 25 * q^30 + 6 * q^31 + 2 * q^32 - 2 * q^33 - 16 * q^34 - q^35 - 2 * q^36 - 13 * q^37 - 8 * q^38 - 5 * q^39 - 29 * q^40 - 5 * q^41 + 31 * q^42 - 7 * q^43 + 30 * q^44 - 5 * q^45 + 19 * q^46 - 9 * q^47 - 19 * q^48 + 16 * q^49 + 29 * q^50 + 26 * q^51 + 6 * q^52 - 31 * q^53 - 4 * q^54 + 7 * q^55 + 8 * q^56 - 5 * q^57 + 35 * q^58 - q^59 + 33 * q^60 - 15 * q^61 - 2 * q^62 + 11 * q^63 - 5 * q^64 - 9 * q^65 - 29 * q^66 - 28 * q^67 - 12 * q^68 + 5 * q^69 + 73 * q^70 + q^71 + 45 * q^72 - 20 * q^73 + 4 * q^74 + q^75 + 38 * q^76 - 29 * q^77 - 15 * q^79 + 7 * q^80 + 2 * q^81 + 36 * q^82 + q^83 + 68 * q^84 + 29 * q^85 + 3 * q^86 + 10 * q^87 + 9 * q^88 - q^89 - 32 * q^90 - 60 * q^92 - 5 * q^93 + 54 * q^94 - 13 * q^95 + 36 * q^96 - 5 * q^97 + 20 * q^98 - 15 * 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 $

$2$	−2.61388	−1.84829	−0.924144	−	0.382043i	$-0.875221\pi$
$2$	−2.61388	−1.84829	−0.924144	+	0.382043i	$0.875221\pi$
$3$	−1.18785	−0.685806	−0.342903	−	0.939371i	$-0.611410\pi$
$3$	−1.18785	−0.685806	−0.342903	+	0.939371i	$0.611410\pi$
$4$	4.83234	2.41617
$5$	1.45573	0.651023	0.325511	−	0.945538i	$-0.394464\pi$
$5$	1.45573	0.651023	0.325511	+	0.945538i	$0.394464\pi$
$6$	3.10489	1.26757
$7$	−1.87247	−0.707728	−0.353864	−	0.935297i	$-0.615132\pi$
$7$	−1.87247	−0.707728	−0.353864	+	0.935297i	$0.615132\pi$
$8$	−7.40339	−2.61749
$9$	−1.58901	−0.529670
$10$	−3.80510	−1.20328
$11$	0.473692	0.142824	0.0714118	−	0.997447i	$-0.477250\pi$
$11$	0.473692	0.142824	0.0714118	+	0.997447i	$0.477250\pi$
$12$	−5.74010	−1.65703
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	4.89441	1.30809
$15$	−1.72919	−0.446476
$16$	9.68686	2.42171
$17$	−2.22798	−0.540365	−0.270182	−	0.962809i	$-0.587084\pi$
$17$	−2.22798	−0.540365	−0.270182	+	0.962809i	$0.587084\pi$
$18$	4.15347	0.978983
$19$	8.23894	1.89014	0.945071	−	0.326865i	$-0.105992\pi$
$19$	8.23894	1.89014	0.945071	+	0.326865i	$0.105992\pi$
$20$	7.03459	1.57298
$21$	2.22422	0.485365
$22$	−1.23817	−0.263979
$23$	−5.80264	−1.20993	−0.604967	−	0.796251i	$-0.706814\pi$
$23$	−5.80264	−1.20993	−0.604967	+	0.796251i	$0.706814\pi$
$24$	8.79413	1.79509
$25$	−2.88085	−0.576169
$26$	−2.61388	−0.512623
$27$	5.45106	1.04906
$28$	−9.04843	−1.70999
$29$	−7.13067	−1.32413	−0.662066	−	0.749445i	$-0.730320\pi$
$29$	−7.13067	−1.32413	−0.662066	+	0.749445i	$0.730320\pi$
$30$	4.51989	0.825216
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−10.5134	−1.85853
$33$	−0.562676	−0.0979493
$34$	5.82366	0.998750
$35$	−2.72582	−0.460747
$36$	−7.67864	−1.27977
$37$	−7.25508	−1.19273	−0.596364	−	0.802714i	$-0.703388\pi$
$37$	−7.25508	−1.19273	−0.596364	+	0.802714i	$0.703388\pi$
$38$	−21.5356	−3.49353
$39$	−1.18785	−0.190208
$40$	−10.7774	−1.70405
$41$	−6.30750	−0.985067	−0.492533	−	0.870294i	$-0.663929\pi$
$41$	−6.30750	−0.985067	−0.492533	+	0.870294i	$0.663929\pi$
$42$	−5.81383	−0.897094
$43$	−0.625207	−0.0953432	−0.0476716	−	0.998863i	$-0.515180\pi$
$43$	−0.625207	−0.0953432	−0.0476716	+	0.998863i	$0.515180\pi$
$44$	2.28904	0.345086
$45$	−2.31317	−0.344827
$46$	15.1674	2.23631
$47$	−1.34262	−0.195841	−0.0979207	−	0.995194i	$-0.531219\pi$
$47$	−1.34262	−0.195841	−0.0979207	+	0.995194i	$0.531219\pi$
$48$	−11.5065	−1.66083
$49$	−3.49384	−0.499121
$50$	7.53017	1.06493
$51$	2.64651	0.370586
$52$	4.83234	0.670125
$53$	−8.52918	−1.17157	−0.585786	−	0.810466i	$-0.699214\pi$
$53$	−8.52918	−1.17157	−0.585786	+	0.810466i	$0.699214\pi$
$54$	−14.2484	−1.93896
$55$	0.689569	0.0929815
$56$	13.8627	1.85248
$57$	−9.78663	−1.29627
$58$	18.6387	2.44738
$59$	3.34763	0.435825	0.217912	−	0.975968i	$-0.430075\pi$
$59$	3.34763	0.435825	0.217912	+	0.975968i	$0.430075\pi$
$60$	−8.35605	−1.07876
$61$	−1.87837	−0.240501	−0.120251	−	0.992744i	$-0.538370\pi$
$61$	−1.87837	−0.240501	−0.120251	+	0.992744i	$0.538370\pi$
$62$	−2.61388	−0.331962
$63$	2.97538	0.374862
$64$	8.10713	1.01339
$65$	1.45573	0.180561
$66$	1.47077	0.181039
$67$	4.97297	0.607545	0.303773	−	0.952745i	$-0.401754\pi$
$67$	4.97297	0.607545	0.303773	+	0.952745i	$0.401754\pi$
$68$	−10.7664	−1.30561
$69$	6.89267	0.829780
$70$	7.12495	0.851594
$71$	−16.3567	−1.94118	−0.970589	−	0.240742i	$-0.922609\pi$
$71$	−16.3567	−1.94118	−0.970589	+	0.240742i	$0.922609\pi$
$72$	11.7641	1.38641
$73$	−2.60031	−0.304343	−0.152172	−	0.988354i	$-0.548627\pi$
$73$	−2.60031	−0.304343	−0.152172	+	0.988354i	$0.548627\pi$
$74$	18.9639	2.20451
$75$	3.42202	0.395140
$76$	39.8134	4.56691
$77$	−0.886976	−0.101080
$78$	3.10489	0.351560
$79$	−9.16549	−1.03120	−0.515599	−	0.856830i	$-0.672431\pi$
$79$	−9.16549	−1.03120	−0.515599	+	0.856830i	$0.672431\pi$
$80$	14.1015	1.57659
$81$	−1.70802	−0.189780
$82$	16.4870	1.82069
$83$	2.73403	0.300099	0.150050	−	0.988678i	$-0.452057\pi$
$83$	2.73403	0.300099	0.150050	+	0.988678i	$0.452057\pi$
$84$	10.7482	1.17272
$85$	−3.24334	−0.351790
$86$	1.63421	0.176222
$87$	8.47017	0.908098
$88$	−3.50693	−0.373840
$89$	−4.04630	−0.428907	−0.214453	−	0.976734i	$-0.568797\pi$
$89$	−4.04630	−0.428907	−0.214453	+	0.976734i	$0.568797\pi$
$90$	6.04634	0.637340
$91$	−1.87247	−0.196289
$92$	−28.0403	−2.92341
$93$	−1.18785	−0.123174
$94$	3.50944	0.361971
$95$	11.9937	1.23053
$96$	12.4884	1.27459
$97$	−0.222505	−0.0225920	−0.0112960	−	0.999936i	$-0.503596\pi$
$97$	−0.222505	−0.0225920	−0.0112960	+	0.999936i	$0.503596\pi$
$98$	9.13247	0.922519
$99$	−0.752702	−0.0756494
$100$	−13.9212	−1.39212
$101$	12.1753	1.21148	0.605742	−	0.795661i	$-0.292876\pi$
$101$	12.1753	1.21148	0.605742	+	0.795661i	$0.292876\pi$
$102$	−6.91765	−0.684949
$103$	3.87961	0.382269	0.191135	−	0.981564i	$-0.438783\pi$
$103$	3.87961	0.382269	0.191135	+	0.981564i	$0.438783\pi$
$104$	−7.40339	−0.725962
$105$	3.23787	0.315983
$106$	22.2942	2.16540
$107$	−2.09178	−0.202220	−0.101110	−	0.994875i	$-0.532239\pi$
$107$	−2.09178	−0.202220	−0.101110	+	0.994875i	$0.532239\pi$
$108$	26.3414	2.53470
$109$	0.270456	0.0259050	0.0129525	−	0.999916i	$-0.495877\pi$
$109$	0.270456	0.0259050	0.0129525	+	0.999916i	$0.495877\pi$
$110$	−1.80245	−0.171857
$111$	8.61796	0.817980
$112$	−18.1384	−1.71392
$113$	−13.5568	−1.27532	−0.637660	−	0.770318i	$-0.720097\pi$
$113$	−13.5568	−1.27532	−0.637660	+	0.770318i	$0.720097\pi$
$114$	25.5810	2.39588
$115$	−8.44708	−0.787694
$116$	−34.4578	−3.19933
$117$	−1.58901	−0.146904
$118$	−8.75030	−0.805530
$119$	4.17184	0.382432
$120$	12.8019	1.16865
$121$	−10.7756	−0.979601
$122$	4.90983	0.444515
$123$	7.49238	0.675565
$124$	4.83234	0.433957
$125$	−11.4724	−1.02612
$126$	−7.77727	−0.692854
$127$	−10.4805	−0.929993	−0.464996	−	0.885313i	$-0.653944\pi$
$127$	−10.4805	−0.929993	−0.464996	+	0.885313i	$0.653944\pi$
$128$	−0.164126	−0.0145068
$129$	0.742653	0.0653870
$130$	−3.80510	−0.333729
$131$	3.03271	0.264969	0.132485	−	0.991185i	$-0.457704\pi$
$131$	3.03271	0.264969	0.132485	+	0.991185i	$0.457704\pi$
$132$	−2.71904	−0.236662
$133$	−15.4272	−1.33771
$134$	−12.9987	−1.12292
$135$	7.93528	0.682960
$136$	16.4946	1.41440
$137$	18.8521	1.61064	0.805321	−	0.592839i	$-0.201993\pi$
$137$	18.8521	1.61064	0.805321	+	0.592839i	$0.201993\pi$
$138$	−18.0166	−1.53367
$139$	18.3851	1.55940	0.779702	−	0.626151i	$-0.215371\pi$
$139$	18.3851	1.55940	0.779702	+	0.626151i	$0.215371\pi$
$140$	−13.1721	−1.11324
$141$	1.59483	0.134309
$142$	42.7543	3.58786
$143$	0.473692	0.0396121
$144$	−15.3925	−1.28271
$145$	−10.3803	−0.862040
$146$	6.79688	0.562514
$147$	4.15017	0.342300
$148$	−35.0590	−2.88184
$149$	21.1706	1.73436	0.867181	−	0.497992i	$-0.165929\pi$
$149$	21.1706	1.73436	0.867181	+	0.497992i	$0.165929\pi$
$150$	−8.94472	−0.730334
$151$	5.03135	0.409446	0.204723	−	0.978820i	$-0.434371\pi$
$151$	5.03135	0.409446	0.204723	+	0.978820i	$0.434371\pi$
$152$	−60.9961	−4.94744
$153$	3.54028	0.286215
$154$	2.31845	0.186826
$155$	1.45573	0.116927
$156$	−5.74010	−0.459576
$157$	18.2044	1.45287	0.726433	−	0.687237i	$-0.241177\pi$
$157$	18.2044	1.45287	0.726433	+	0.687237i	$0.241177\pi$
$158$	23.9575	1.90595
$159$	10.1314	0.803472
$160$	−15.3048	−1.20995
$161$	10.8653	0.856304
$162$	4.46455	0.350768
$163$	−16.8075	−1.31646	−0.658231	−	0.752816i	$-0.728695\pi$
$163$	−16.8075	−1.31646	−0.658231	+	0.752816i	$0.728695\pi$
$164$	−30.4800	−2.38009
$165$	−0.819105	−0.0637673
$166$	−7.14642	−0.554670
$167$	−6.43956	−0.498308	−0.249154	−	0.968464i	$-0.580153\pi$
$167$	−6.43956	−0.498308	−0.249154	+	0.968464i	$0.580153\pi$
$168$	−16.4668	−1.27044
$169$	1.00000	0.0769231
$170$	8.47769	0.650209
$171$	−13.0918	−1.00115
$172$	−3.02122	−0.230366
$173$	0.195286	0.0148473	0.00742367	−	0.999972i	$-0.497637\pi$
$173$	0.195286	0.0148473	0.00742367	+	0.999972i	$0.497637\pi$
$174$	−22.1400	−1.67843
$175$	5.39431	0.407771
$176$	4.58859	0.345878
$177$	−3.97649	−0.298891
$178$	10.5765	0.792743
$179$	17.8105	1.33122	0.665610	−	0.746299i	$-0.268171\pi$
$179$	17.8105	1.33122	0.665610	+	0.746299i	$0.268171\pi$
$180$	−11.1780	−0.833162
$181$	0.625622	0.0465021	0.0232510	−	0.999730i	$-0.492598\pi$
$181$	0.625622	0.0465021	0.0232510	+	0.999730i	$0.492598\pi$
$182$	4.89441	0.362798
$183$	2.23123	0.164937
$184$	42.9592	3.16699
$185$	−10.5614	−0.776493
$186$	3.10489	0.227662
$187$	−1.05538	−0.0771769
$188$	−6.48801	−0.473186
$189$	−10.2070	−0.742447
$190$	−31.3500	−2.27437
$191$	8.32610	0.602456	0.301228	−	0.953552i	$-0.402604\pi$
$191$	8.32610	0.602456	0.301228	+	0.953552i	$0.402604\pi$
$192$	−9.63006	−0.694990
$193$	−12.9204	−0.930031	−0.465016	−	0.885302i	$-0.653951\pi$
$193$	−12.9204	−0.930031	−0.465016	+	0.885302i	$0.653951\pi$
$194$	0.581601	0.0417565
$195$	−1.72919	−0.123830
$196$	−16.8835	−1.20596
$197$	8.16174	0.581500	0.290750	−	0.956799i	$-0.406095\pi$
$197$	8.16174	0.581500	0.290750	+	0.956799i	$0.406095\pi$
$198$	1.96747	0.139822
$199$	−23.2350	−1.64708	−0.823542	−	0.567255i	$-0.808005\pi$
$199$	−23.2350	−1.64708	−0.823542	+	0.567255i	$0.808005\pi$
$200$	21.3280	1.50812
$201$	−5.90715	−0.416658
$202$	−31.8246	−2.23917
$203$	13.3520	0.937126
$204$	12.7888	0.895398
$205$	−9.18203	−0.641301
$206$	−10.1408	−0.706544
$207$	9.22044	0.640865
$208$	9.68686	0.671663
$209$	3.90272	0.269957
$210$	−8.46338	−0.584029
$211$	−18.9729	−1.30615	−0.653075	−	0.757293i	$-0.726521\pi$
$211$	−18.9729	−1.30615	−0.653075	+	0.757293i	$0.726521\pi$
$212$	−41.2159	−2.83072
$213$	19.4293	1.33127
$214$	5.46764	0.373760
$215$	−0.910134	−0.0620706
$216$	−40.3563	−2.74590
$217$	−1.87247	−0.127112
$218$	−0.706939	−0.0478800
$219$	3.08878	0.208720
$220$	3.33223	0.224659
$221$	−2.22798	−0.149870
$222$	−22.5263	−1.51186
$223$	5.28784	0.354100	0.177050	−	0.984202i	$-0.443345\pi$
$223$	5.28784	0.354100	0.177050	+	0.984202i	$0.443345\pi$
$224$	19.6862	1.31534
$225$	4.57769	0.305179
$226$	35.4359	2.35716
$227$	18.5099	1.22854	0.614272	−	0.789094i	$-0.289450\pi$
$227$	18.5099	1.22854	0.614272	+	0.789094i	$0.289450\pi$
$228$	−47.2924	−3.13201
$229$	−23.3154	−1.54072	−0.770361	−	0.637608i	$-0.779924\pi$
$229$	−23.3154	−1.54072	−0.770361	+	0.637608i	$0.779924\pi$
$230$	22.0796	1.45589
$231$	1.05360	0.0693215
$232$	52.7911	3.46591
$233$	−4.50768	−0.295308	−0.147654	−	0.989039i	$-0.547172\pi$
$233$	−4.50768	−0.295308	−0.147654	+	0.989039i	$0.547172\pi$
$234$	4.15347	0.271521
$235$	−1.95450	−0.127497
$236$	16.1769	1.05303
$237$	10.8872	0.707202
$238$	−10.9047	−0.706844
$239$	19.4290	1.25676	0.628379	−	0.777907i	$-0.283719\pi$
$239$	19.4290	1.25676	0.628379	+	0.777907i	$0.283719\pi$
$240$	−16.7504	−1.08124
$241$	24.7137	1.59195	0.795975	−	0.605329i	$-0.206958\pi$
$241$	24.7137	1.59195	0.795975	+	0.605329i	$0.206958\pi$
$242$	28.1661	1.81059
$243$	−14.3243	−0.918905
$244$	−9.07694	−0.581092
$245$	−5.08610	−0.324939
$246$	−19.5841	−1.24864
$247$	8.23894	0.524231
$248$	−7.40339	−0.470116
$249$	−3.24763	−0.205810
$250$	29.9874	1.89657
$251$	−23.6209	−1.49094	−0.745469	−	0.666541i	$-0.767774\pi$
$251$	−23.6209	−1.49094	−0.745469	+	0.666541i	$0.767774\pi$
$252$	14.3780	0.905732
$253$	−2.74866	−0.172807
$254$	27.3947	1.71890
$255$	3.85261	0.241260
$256$	−15.7853	−0.986578
$257$	28.1310	1.75476	0.877381	−	0.479794i	$-0.159288\pi$
$257$	28.1310	1.75476	0.877381	+	0.479794i	$0.159288\pi$
$258$	−1.94120	−0.120854
$259$	13.5849	0.844127
$260$	7.03459	0.436267
$261$	11.3307	0.701353
$262$	−7.92713	−0.489740
$263$	−8.74814	−0.539434	−0.269717	−	0.962940i	$-0.586930\pi$
$263$	−8.74814	−0.539434	−0.269717	+	0.962940i	$0.586930\pi$
$264$	4.16571	0.256382
$265$	−12.4162	−0.762720
$266$	40.3248	2.47247
$267$	4.80640	0.294147
$268$	24.0311	1.46793
$269$	−23.5756	−1.43743	−0.718714	−	0.695306i	$-0.755269\pi$
$269$	−23.5756	−1.43743	−0.718714	+	0.695306i	$0.755269\pi$
$270$	−20.7418	−1.26231
$271$	20.2744	1.23159	0.615793	−	0.787908i	$-0.288836\pi$
$271$	20.2744	1.23159	0.615793	+	0.787908i	$0.288836\pi$
$272$	−21.5821	−1.30861
$273$	2.22422	0.134616
$274$	−49.2770	−2.97693
$275$	−1.36463	−0.0822906
$276$	33.3077	2.00489
$277$	9.32738	0.560428	0.280214	−	0.959938i	$-0.409595\pi$
$277$	9.32738	0.560428	0.280214	+	0.959938i	$0.409595\pi$
$278$	−48.0563	−2.88223
$279$	−1.58901	−0.0951315
$280$	20.1803	1.20600
$281$	−2.25294	−0.134399	−0.0671994	−	0.997740i	$-0.521406\pi$
$281$	−2.25294	−0.134399	−0.0671994	+	0.997740i	$0.521406\pi$
$282$	−4.16870	−0.248242
$283$	14.9433	0.888289	0.444145	−	0.895955i	$-0.353508\pi$
$283$	14.9433	0.888289	0.444145	+	0.895955i	$0.353508\pi$
$284$	−79.0410	−4.69022
$285$	−14.2467	−0.843902
$286$	−1.23817	−0.0732147
$287$	11.8106	0.697160
$288$	16.7060	0.984409
$289$	−12.0361	−0.708006
$290$	27.1329	1.59330
$291$	0.264303	0.0154937
$292$	−12.5656	−0.735345
$293$	−3.65982	−0.213809	−0.106904	−	0.994269i	$-0.534094\pi$
$293$	−3.65982	−0.213809	−0.106904	+	0.994269i	$0.534094\pi$
$294$	−10.8480	−0.632669
$295$	4.87326	0.283732
$296$	53.7122	3.12196
$297$	2.58213	0.149830
$298$	−55.3373	−3.20560
$299$	−5.80264	−0.335575
$300$	16.5364	0.954727
$301$	1.17068	0.0674771
$302$	−13.1513	−0.756774
$303$	−14.4624	−0.830843
$304$	79.8094	4.57738
$305$	−2.73441	−0.156572
$306$	−9.25386	−0.529008
$307$	−12.9401	−0.738530	−0.369265	−	0.929324i	$-0.620391\pi$
$307$	−12.9401	−0.738530	−0.369265	+	0.929324i	$0.620391\pi$
$308$	−4.28617	−0.244227
$309$	−4.60840	−0.262163
$310$	−3.80510	−0.216115
$311$	27.7204	1.57188	0.785940	−	0.618302i	$-0.212179\pi$
$311$	27.7204	1.57188	0.785940	+	0.618302i	$0.212179\pi$
$312$	8.79413	0.497869
$313$	10.0937	0.570530	0.285265	−	0.958449i	$-0.407918\pi$
$313$	10.0937	0.570530	0.285265	+	0.958449i	$0.407918\pi$
$314$	−47.5839	−2.68532
$315$	4.33135	0.244044
$316$	−44.2908	−2.49155
$317$	6.71388	0.377089	0.188544	−	0.982065i	$-0.439623\pi$
$317$	6.71388	0.377089	0.188544	+	0.982065i	$0.439623\pi$
$318$	−26.4822	−1.48505
$319$	−3.37774	−0.189117
$320$	11.8018	0.659741
$321$	2.48472	0.138683
$322$	−28.4005	−1.58270
$323$	−18.3562	−1.02137
$324$	−8.25374	−0.458541
$325$	−2.88085	−0.159801
$326$	43.9326	2.43320
$327$	−0.321262	−0.0177658
$328$	46.6969	2.57841
$329$	2.51402	0.138603
$330$	2.14104	0.117860
$331$	−11.4339	−0.628466	−0.314233	−	0.949346i	$-0.601747\pi$
$331$	−11.4339	−0.628466	−0.314233	+	0.949346i	$0.601747\pi$
$332$	13.2118	0.725091
$333$	11.5284	0.631752
$334$	16.8322	0.921017
$335$	7.23931	0.395526
$336$	21.5457	1.17541
$337$	32.3608	1.76280	0.881402	−	0.472368i	$-0.156601\pi$
$337$	32.3608	1.76280	0.881402	+	0.472368i	$0.156601\pi$
$338$	−2.61388	−0.142176
$339$	16.1035	0.874622
$340$	−15.6729	−0.849985
$341$	0.473692	0.0256519
$342$	34.2202	1.85042
$343$	19.6494	1.06097
$344$	4.62865	0.249560
$345$	10.0339	0.540206
$346$	−0.510454	−0.0274422
$347$	−35.7708	−1.92028	−0.960139	−	0.279524i	$-0.909823\pi$
$347$	−35.7708	−1.92028	−0.960139	+	0.279524i	$0.909823\pi$
$348$	40.9308	2.19412
$349$	−34.5463	−1.84922	−0.924611	−	0.380914i	$-0.875609\pi$
$349$	−34.5463	−1.84922	−0.924611	+	0.380914i	$0.875609\pi$
$350$	−14.1000	−0.753679
$351$	5.45106	0.290956
$352$	−4.98014	−0.265442
$353$	−3.23327	−0.172090	−0.0860448	−	0.996291i	$-0.527423\pi$
$353$	−3.23327	−0.172090	−0.0860448	+	0.996291i	$0.527423\pi$
$354$	10.3940	0.552438
$355$	−23.8109	−1.26375
$356$	−19.5531	−1.03631
$357$	−4.95552	−0.262274
$358$	−46.5545	−2.46048
$359$	18.1255	0.956628	0.478314	−	0.878189i	$-0.341248\pi$
$359$	18.1255	0.956628	0.478314	+	0.878189i	$0.341248\pi$
$360$	17.1253	0.902583
$361$	48.8801	2.57264
$362$	−1.63530	−0.0859493
$363$	12.7998	0.671817
$364$	−9.04843	−0.474267
$365$	−3.78535	−0.198134
$366$	−5.83215	−0.304851
$367$	−10.3219	−0.538798	−0.269399	−	0.963029i	$-0.586825\pi$
$367$	−10.3219	−0.538798	−0.269399	+	0.963029i	$0.586825\pi$
$368$	−56.2093	−2.93011
$369$	10.0227	0.521760
$370$	27.6063	1.43518
$371$	15.9707	0.829155
$372$	−5.74010	−0.297611
$373$	22.9385	1.18771	0.593856	−	0.804572i	$-0.297605\pi$
$373$	22.9385	1.18771	0.593856	+	0.804572i	$0.297605\pi$
$374$	2.75863	0.142645
$375$	13.6275	0.703721
$376$	9.93995	0.512614
$377$	−7.13067	−0.367248
$378$	26.6797	1.37226
$379$	−16.7886	−0.862374	−0.431187	−	0.902263i	$-0.641905\pi$
$379$	−16.7886	−0.862374	−0.431187	+	0.902263i	$0.641905\pi$
$380$	57.9576	2.97316
$381$	12.4493	0.637795
$382$	−21.7634	−1.11351
$383$	−15.6720	−0.800803	−0.400402	−	0.916340i	$-0.631129\pi$
$383$	−15.6720	−0.800803	−0.400402	+	0.916340i	$0.631129\pi$
$384$	0.194957	0.00994887
$385$	−1.29120	−0.0658056
$386$	33.7723	1.71897
$387$	0.993460	0.0505004
$388$	−1.07522	−0.0545862
$389$	−24.6996	−1.25232	−0.626161	−	0.779694i	$-0.715375\pi$
$389$	−24.6996	−1.25232	−0.626161	+	0.779694i	$0.715375\pi$
$390$	4.51989	0.228874
$391$	12.9282	0.653805
$392$	25.8663	1.30645
$393$	−3.60241	−0.181718
$394$	−21.3338	−1.07478
$395$	−13.3425	−0.671334
$396$	−3.63731	−0.182782
$397$	32.7794	1.64515	0.822577	−	0.568654i	$-0.192536\pi$
$397$	32.7794	1.64515	0.822577	+	0.568654i	$0.192536\pi$
$398$	60.7333	3.04429
$399$	18.3252	0.917408
$400$	−27.9063	−1.39532
$401$	0.730444	0.0364767	0.0182383	−	0.999834i	$-0.494194\pi$
$401$	0.730444	0.0364767	0.0182383	+	0.999834i	$0.494194\pi$
$402$	15.4406	0.770105
$403$	1.00000	0.0498135
$404$	58.8351	2.92715
$405$	−2.48642	−0.123551
$406$	−34.9004	−1.73208
$407$	−3.43668	−0.170350
$408$	−19.5932	−0.970006
$409$	−18.7575	−0.927501	−0.463750	−	0.885966i	$-0.653497\pi$
$409$	−18.7575	−0.927501	−0.463750	+	0.885966i	$0.653497\pi$
$410$	24.0007	1.18531
$411$	−22.3935	−1.10459
$412$	18.7476	0.923628
$413$	−6.26835	−0.308446
$414$	−24.1011	−1.18450
$415$	3.98002	0.195371
$416$	−10.5134	−0.515464
$417$	−21.8388	−1.06945
$418$	−10.2012	−0.498958
$419$	0.410476	0.0200530	0.0100265	−	0.999950i	$-0.496808\pi$
$419$	0.410476	0.0200530	0.0100265	+	0.999950i	$0.496808\pi$
$420$	15.6465	0.763470
$421$	−34.2921	−1.67130	−0.835648	−	0.549266i	$-0.814907\pi$
$421$	−34.2921	−1.67130	−0.835648	+	0.549266i	$0.814907\pi$
$422$	49.5928	2.41414
$423$	2.13344	0.103731
$424$	63.1448	3.06658
$425$	6.41847	0.311342
$426$	−50.7857	−2.46058
$427$	3.51720	0.170209
$428$	−10.1082	−0.488597
$429$	−0.562676	−0.0271663
$430$	2.37898	0.114724
$431$	−9.82120	−0.473071	−0.236535	−	0.971623i	$-0.576012\pi$
$431$	−9.82120	−0.473071	−0.236535	+	0.971623i	$0.576012\pi$
$432$	52.8036	2.54052
$433$	−38.6759	−1.85864	−0.929321	−	0.369272i	$-0.879607\pi$
$433$	−38.6759	−1.85864	−0.929321	+	0.369272i	$0.879607\pi$
$434$	4.89441	0.234939
$435$	12.3303	0.591193
$436$	1.30694	0.0625910
$437$	−47.8076	−2.28695
$438$	−8.07369	−0.385776
$439$	−1.26349	−0.0603032	−0.0301516	−	0.999545i	$-0.509599\pi$
$439$	−1.26349	−0.0603032	−0.0301516	+	0.999545i	$0.509599\pi$
$440$	−5.10515	−0.243378
$441$	5.55175	0.264369
$442$	5.82366	0.277003
$443$	7.74313	0.367887	0.183944	−	0.982937i	$-0.441114\pi$
$443$	7.74313	0.367887	0.183944	+	0.982937i	$0.441114\pi$
$444$	41.6449	1.97638
$445$	−5.89032	−0.279228
$446$	−13.8217	−0.654478
$447$	−25.1475	−1.18944
$448$	−15.1804	−0.717206
$449$	−26.5846	−1.25460	−0.627302	−	0.778776i	$-0.715841\pi$
$449$	−26.5846	−1.25460	−0.627302	+	0.778776i	$0.715841\pi$
$450$	−11.9655	−0.564060
$451$	−2.98782	−0.140691
$452$	−65.5113	−3.08139
$453$	−5.97650	−0.280800
$454$	−48.3826	−2.27071
$455$	−2.72582	−0.127788
$456$	72.4543	3.39298
$457$	−8.87208	−0.415018	−0.207509	−	0.978233i	$-0.566536\pi$
$457$	−8.87208	−0.415018	−0.207509	+	0.978233i	$0.566536\pi$
$458$	60.9434	2.84770
$459$	−12.1449	−0.566874
$460$	−40.8192	−1.90320
$461$	−13.3273	−0.620715	−0.310358	−	0.950620i	$-0.600449\pi$
$461$	−13.3273	−0.620715	−0.310358	+	0.950620i	$0.600449\pi$
$462$	−2.75397	−0.128126
$463$	−0.523451	−0.0243268	−0.0121634	−	0.999926i	$-0.503872\pi$
$463$	−0.523451	−0.0243268	−0.0121634	+	0.999926i	$0.503872\pi$
$464$	−69.0738	−3.20667
$465$	−1.72919	−0.0801894
$466$	11.7825	0.545815
$467$	35.0489	1.62187	0.810934	−	0.585137i	$-0.198959\pi$
$467$	35.0489	1.62187	0.810934	+	0.585137i	$0.198959\pi$
$468$	−7.67864	−0.354945
$469$	−9.31176	−0.429977
$470$	5.10881	0.235652
$471$	−21.6241	−0.996384
$472$	−24.7838	−1.14077
$473$	−0.296156	−0.0136173
$474$	−28.4579	−1.30711
$475$	−23.7351	−1.08904
$476$	20.1597	0.924020
$477$	13.5529	0.620547
$478$	−50.7850	−2.32285
$479$	25.6518	1.17206	0.586030	−	0.810289i	$-0.300690\pi$
$479$	25.6518	1.17206	0.586030	+	0.810289i	$0.300690\pi$
$480$	18.1798	0.829789
$481$	−7.25508	−0.330803
$482$	−64.5986	−2.94238
$483$	−12.9063	−0.587259
$484$	−52.0715	−2.36689
$485$	−0.323908	−0.0147079
$486$	37.4420	1.69840
$487$	12.3912	0.561501	0.280751	−	0.959781i	$-0.409417\pi$
$487$	12.3912	0.561501	0.280751	+	0.959781i	$0.409417\pi$
$488$	13.9063	0.629510
$489$	19.9648	0.902838
$490$	13.2944	0.600581
$491$	39.5596	1.78530	0.892649	−	0.450752i	$-0.148844\pi$
$491$	39.5596	1.78530	0.892649	+	0.450752i	$0.148844\pi$
$492$	36.2057	1.63228
$493$	15.8870	0.715514
$494$	−21.5356	−0.968931
$495$	−1.09573	−0.0492495
$496$	9.68686	0.434953
$497$	30.6274	1.37383
$498$	8.48889	0.380396
$499$	−21.9884	−0.984335	−0.492167	−	0.870501i	$-0.663795\pi$
$499$	−21.9884	−0.984335	−0.492167	+	0.870501i	$0.663795\pi$
$500$	−55.4386	−2.47929
$501$	7.64924	0.341743
$502$	61.7421	2.75568
$503$	−26.9747	−1.20274	−0.601370	−	0.798970i	$-0.705378\pi$
$503$	−26.9747	−1.20274	−0.601370	+	0.798970i	$0.705378\pi$
$504$	−22.0279	−0.981200
$505$	17.7239	0.788704
$506$	7.18467	0.319397
$507$	−1.18785	−0.0527543
$508$	−50.6453	−2.24702
$509$	−23.9429	−1.06125	−0.530626	−	0.847606i	$-0.678043\pi$
$509$	−23.9429	−1.06125	−0.530626	+	0.847606i	$0.678043\pi$
$510$	−10.0702	−0.445918
$511$	4.86901	0.215392
$512$	41.5889	1.83799
$513$	44.9110	1.98287
$514$	−73.5309	−3.24331
$515$	5.64767	0.248866
$516$	3.58875	0.157986
$517$	−0.635989	−0.0279708
$518$	−35.5093	−1.56019
$519$	−0.231971	−0.0101824
$520$	−10.7774	−0.472618
$521$	−19.7933	−0.867162	−0.433581	−	0.901115i	$-0.642750\pi$
$521$	−19.7933	−0.867162	−0.433581	+	0.901115i	$0.642750\pi$
$522$	−29.6170	−1.29630
$523$	−13.2335	−0.578663	−0.289331	−	0.957229i	$-0.593433\pi$
$523$	−13.2335	−0.578663	−0.289331	+	0.957229i	$0.593433\pi$
$524$	14.6551	0.640211
$525$	−6.40763	−0.279652
$526$	22.8666	0.997029
$527$	−2.22798	−0.0970524
$528$	−5.45056	−0.237205
$529$	10.6706	0.463938
$530$	32.4544	1.40973
$531$	−5.31942	−0.230843
$532$	−74.5495	−3.23213
$533$	−6.30750	−0.273208
$534$	−12.5633	−0.543668
$535$	−3.04506	−0.131650
$536$	−36.8169	−1.59025
$537$	−21.1562	−0.912960
$538$	61.6236	2.65678
$539$	−1.65501	−0.0712862
$540$	38.3460	1.65015
$541$	−40.8745	−1.75733	−0.878665	−	0.477438i	$-0.841565\pi$
$541$	−40.8745	−1.75733	−0.878665	+	0.477438i	$0.841565\pi$
$542$	−52.9949	−2.27633
$543$	−0.743145	−0.0318914
$544$	23.4238	1.00429
$545$	0.393712	0.0168648
$546$	−5.81383	−0.248809
$547$	9.72254	0.415706	0.207853	−	0.978160i	$-0.433352\pi$
$547$	9.72254	0.415706	0.207853	+	0.978160i	$0.433352\pi$
$548$	91.0997	3.89159
$549$	2.98475	0.127386
$550$	3.56699	0.152097
$551$	−58.7492	−2.50280
$552$	−51.0291	−2.17194
$553$	17.1621	0.729809
$554$	−24.3806	−1.03583
$555$	12.5454	0.532524
$556$	88.8431	3.76779
$557$	21.2819	0.901741	0.450871	−	0.892589i	$-0.351114\pi$
$557$	21.2819	0.901741	0.450871	+	0.892589i	$0.351114\pi$
$558$	4.15347	0.175831
$559$	−0.625207	−0.0264434
$560$	−26.4046	−1.11580
$561$	1.25363	0.0529284
$562$	5.88889	0.248408
$563$	16.1401	0.680222	0.340111	−	0.940385i	$-0.389535\pi$
$563$	16.1401	0.680222	0.340111	+	0.940385i	$0.389535\pi$
$564$	7.70678	0.324514
$565$	−19.7351	−0.830262
$566$	−39.0600	−1.64181
$567$	3.19822	0.134313
$568$	121.095	5.08102
$569$	−7.58871	−0.318135	−0.159068	−	0.987268i	$-0.550849\pi$
$569$	−7.58871	−0.318135	−0.159068	+	0.987268i	$0.550849\pi$
$570$	37.2391	1.55978
$571$	31.8961	1.33481	0.667405	−	0.744695i	$-0.267405\pi$
$571$	31.8961	1.33481	0.667405	+	0.744695i	$0.267405\pi$
$572$	2.28904	0.0957098
$573$	−9.89017	−0.413168
$574$	−30.8715	−1.28855
$575$	16.7165	0.697126
$576$	−12.8823	−0.536763
$577$	31.7439	1.32151	0.660757	−	0.750600i	$-0.270235\pi$
$577$	31.7439	1.32151	0.660757	+	0.750600i	$0.270235\pi$
$578$	31.4609	1.30860
$579$	15.3475	0.637821
$580$	−50.1614	−2.08284
$581$	−5.11941	−0.212389
$582$	−0.690856	−0.0286369
$583$	−4.04021	−0.167328
$584$	19.2511	0.796617
$585$	−2.31317	−0.0956379
$586$	9.56630	0.395180
$587$	−9.40171	−0.388050	−0.194025	−	0.980997i	$-0.562154\pi$
$587$	−9.40171	−0.388050	−0.194025	+	0.980997i	$0.562154\pi$
$588$	20.0550	0.827055
$589$	8.23894	0.339480
$590$	−12.7381	−0.524419
$591$	−9.69494	−0.398796
$592$	−70.2789	−2.88845
$593$	15.5339	0.637900	0.318950	−	0.947772i	$-0.396670\pi$
$593$	15.5339	0.637900	0.318950	+	0.947772i	$0.396670\pi$
$594$	−6.74935	−0.276929
$595$	6.07307	0.248972
$596$	102.304	4.19052
$597$	27.5997	1.12958
$598$	15.1674	0.620240
$599$	−32.0717	−1.31041	−0.655206	−	0.755450i	$-0.727418\pi$
$599$	−32.0717	−1.31041	−0.655206	+	0.755450i	$0.727418\pi$
$600$	−25.3345	−1.03428
$601$	−1.27453	−0.0519893	−0.0259946	−	0.999662i	$-0.508275\pi$
$601$	−1.27453	−0.0519893	−0.0259946	+	0.999662i	$0.508275\pi$
$602$	−3.06002	−0.124717
$603$	−7.90210	−0.321798
$604$	24.3132	0.989291
$605$	−15.6864	−0.637743
$606$	37.8029	1.53564
$607$	−4.88001	−0.198073	−0.0990367	−	0.995084i	$-0.531576\pi$
$607$	−4.88001	−0.198073	−0.0990367	+	0.995084i	$0.531576\pi$
$608$	−86.6196	−3.51289
$609$	−15.8602	−0.642687
$610$	7.14740	0.289390
$611$	−1.34262	−0.0543166
$612$	17.1079	0.691544
$613$	35.9018	1.45006	0.725030	−	0.688717i	$-0.241826\pi$
$613$	35.9018	1.45006	0.725030	+	0.688717i	$0.241826\pi$
$614$	33.8238	1.36502
$615$	10.9069	0.439808
$616$	6.56663	0.264577
$617$	0.484906	0.0195216	0.00976080	−	0.999952i	$-0.496893\pi$
$617$	0.484906	0.0195216	0.00976080	+	0.999952i	$0.496893\pi$
$618$	12.0458	0.484552
$619$	32.5604	1.30871	0.654356	−	0.756187i	$-0.272940\pi$
$619$	32.5604	1.30871	0.654356	+	0.756187i	$0.272940\pi$
$620$	7.03459	0.282516
$621$	−31.6305	−1.26929
$622$	−72.4577	−2.90529
$623$	7.57658	0.303549
$624$	−11.5065	−0.460630
$625$	−2.29650	−0.0918599
$626$	−26.3837	−1.05450
$627$	−4.63585	−0.185138
$628$	87.9697	3.51037
$629$	16.1642	0.644508
$630$	−11.3216	−0.451064
$631$	−39.4606	−1.57090	−0.785450	−	0.618925i	$-0.787568\pi$
$631$	−39.4606	−1.57090	−0.785450	+	0.618925i	$0.787568\pi$
$632$	67.8558	2.69916
$633$	22.5370	0.895765
$634$	−17.5492	−0.696969
$635$	−15.2568	−0.605447
$636$	48.9584	1.94133
$637$	−3.49384	−0.138431
$638$	8.82900	0.349544
$639$	25.9909	1.02818
$640$	−0.238923	−0.00944427
$641$	8.69482	0.343425	0.171712	−	0.985147i	$-0.445070\pi$
$641$	8.69482	0.343425	0.171712	+	0.985147i	$0.445070\pi$
$642$	−6.49474	−0.256327
$643$	23.8382	0.940088	0.470044	−	0.882643i	$-0.344238\pi$
$643$	23.8382	0.940088	0.470044	+	0.882643i	$0.344238\pi$
$644$	52.5048	2.06898
$645$	1.08110	0.0425684
$646$	47.9808	1.88778
$647$	−2.62805	−0.103319	−0.0516596	−	0.998665i	$-0.516451\pi$
$647$	−2.62805	−0.103319	−0.0516596	+	0.998665i	$0.516451\pi$
$648$	12.6451	0.496748
$649$	1.58575	0.0622461
$650$	7.53017	0.295358
$651$	2.22422	0.0871740
$652$	−81.2194	−3.18080
$653$	11.6330	0.455234	0.227617	−	0.973751i	$-0.426907\pi$
$653$	11.6330	0.455234	0.227617	+	0.973751i	$0.426907\pi$
$654$	0.839739	0.0328364
$655$	4.41481	0.172501
$656$	−61.0999	−2.38555
$657$	4.13192	0.161201
$658$	−6.57134	−0.256177
$659$	−12.4112	−0.483470	−0.241735	−	0.970342i	$-0.577716\pi$
$659$	−12.4112	−0.483470	−0.241735	+	0.970342i	$0.577716\pi$
$660$	−3.95820	−0.154073
$661$	14.7402	0.573327	0.286663	−	0.958031i	$-0.407454\pi$
$661$	14.7402	0.573327	0.286663	+	0.958031i	$0.407454\pi$
$662$	29.8869	1.16159
$663$	2.64651	0.102782
$664$	−20.2411	−0.785508
$665$	−22.4578	−0.870878
$666$	−30.1338	−1.16766
$667$	41.3767	1.60211
$668$	−31.1182	−1.20400
$669$	−6.28116	−0.242844
$670$	−18.9227	−0.731046
$671$	−0.889771	−0.0343492
$672$	−23.3842	−0.902066
$673$	−40.4261	−1.55831	−0.779156	−	0.626830i	$-0.784352\pi$
$673$	−40.4261	−1.55831	−0.779156	+	0.626830i	$0.784352\pi$
$674$	−84.5870	−3.25817
$675$	−15.7037	−0.604434
$676$	4.83234	0.185859
$677$	−38.1075	−1.46459	−0.732296	−	0.680987i	$-0.761551\pi$
$677$	−38.1075	−1.46459	−0.732296	+	0.680987i	$0.761551\pi$
$678$	−42.0925	−1.61655
$679$	0.416635	0.0159890
$680$	24.0117	0.920808
$681$	−21.9870	−0.842544
$682$	−1.23817	−0.0474121
$683$	34.2087	1.30896	0.654479	−	0.756080i	$-0.272888\pi$
$683$	34.2087	1.30896	0.654479	+	0.756080i	$0.272888\pi$
$684$	−63.2638	−2.41895
$685$	27.4436	1.04856
$686$	−51.3612	−1.96098
$687$	27.6952	1.05664
$688$	−6.05629	−0.230894
$689$	−8.52918	−0.324936
$690$	−26.2273	−0.998456
$691$	21.2293	0.807599	0.403800	−	0.914847i	$-0.367689\pi$
$691$	21.2293	0.807599	0.403800	+	0.914847i	$0.367689\pi$
$692$	0.943691	0.0358737
$693$	1.40941	0.0535392
$694$	93.5004	3.54923
$695$	26.7638	1.01521
$696$	−62.7080	−2.37694
$697$	14.0530	0.532295
$698$	90.2997	3.41789
$699$	5.35446	0.202524
$700$	26.0671	0.985245
$701$	12.6202	0.476658	0.238329	−	0.971184i	$-0.423400\pi$
$701$	12.6202	0.476658	0.238329	+	0.971184i	$0.423400\pi$
$702$	−14.2484	−0.537771
$703$	−59.7742	−2.25443
$704$	3.84029	0.144736
$705$	2.32165	0.0874384
$706$	8.45136	0.318071
$707$	−22.7979	−0.857402
$708$	−19.2158	−0.722173
$709$	−32.8068	−1.23209	−0.616043	−	0.787712i	$-0.711265\pi$
$709$	−32.8068	−1.23209	−0.616043	+	0.787712i	$0.711265\pi$
$710$	62.2387	2.33578
$711$	14.5641	0.546195
$712$	29.9563	1.12266
$713$	−5.80264	−0.217310
$714$	12.9531	0.484758
$715$	0.689569	0.0257884
$716$	86.0666	3.21646
$717$	−23.0788	−0.861893
$718$	−47.3778	−1.76812
$719$	40.8388	1.52303	0.761514	−	0.648148i	$-0.224456\pi$
$719$	40.8388	1.52303	0.761514	+	0.648148i	$0.224456\pi$
$720$	−22.4074	−0.835073
$721$	−7.26446	−0.270543
$722$	−127.767	−4.75498
$723$	−29.3562	−1.09177
$724$	3.02322	0.112357
$725$	20.5424	0.762924
$726$	−33.4572	−1.24171
$727$	27.6544	1.02565	0.512823	−	0.858494i	$-0.328600\pi$
$727$	27.6544	1.02565	0.512823	+	0.858494i	$0.328600\pi$
$728$	13.8627	0.513784
$729$	22.1392	0.819971
$730$	9.89444	0.366210
$731$	1.39295	0.0515201
$732$	10.7821	0.398516
$733$	12.0887	0.446505	0.223253	−	0.974761i	$-0.428332\pi$
$733$	12.0887	0.446505	0.223253	+	0.974761i	$0.428332\pi$
$734$	26.9801	0.995855
$735$	6.04153	0.222845
$736$	61.0057	2.24870
$737$	2.35566	0.0867718
$738$	−26.1980	−0.964363
$739$	−2.55438	−0.0939645	−0.0469822	−	0.998896i	$-0.514960\pi$
$739$	−2.55438	−0.0939645	−0.0469822	+	0.998896i	$0.514960\pi$
$740$	−51.0365	−1.87614
$741$	−9.78663	−0.359521
$742$	−41.7453	−1.53252
$743$	−2.72082	−0.0998171	−0.0499086	−	0.998754i	$-0.515893\pi$
$743$	−2.72082	−0.0998171	−0.0499086	+	0.998754i	$0.515893\pi$
$744$	8.79413	0.322408
$745$	30.8187	1.12911
$746$	−59.9584	−2.19523
$747$	−4.34441	−0.158954
$748$	−5.09995	−0.186473
$749$	3.91679	0.143117
$750$	−35.6206	−1.30068
$751$	49.1103	1.79206	0.896030	−	0.443993i	$-0.146439\pi$
$751$	49.1103	1.79206	0.896030	+	0.443993i	$0.146439\pi$
$752$	−13.0058	−0.474272
$753$	28.0581	1.02249
$754$	18.6387	0.678781
$755$	7.32430	0.266558
$756$	−49.3236	−1.79388
$757$	18.5379	0.673770	0.336885	−	0.941546i	$-0.390627\pi$
$757$	18.5379	0.673770	0.336885	+	0.941546i	$0.390627\pi$
$758$	43.8834	1.59392
$759$	3.26500	0.118512
$760$	−88.7939	−3.22089
$761$	−8.01385	−0.290502	−0.145251	−	0.989395i	$-0.546399\pi$
$761$	−8.01385	−0.290502	−0.145251	+	0.989395i	$0.546399\pi$
$762$	−32.5408	−1.17883
$763$	−0.506423	−0.0183337
$764$	40.2346	1.45564
$765$	5.15370	0.186332
$766$	40.9647	1.48012
$767$	3.34763	0.120876
$768$	18.7505	0.676601
$769$	22.7932	0.821944	0.410972	−	0.911648i	$-0.365189\pi$
$769$	22.7932	0.821944	0.410972	+	0.911648i	$0.365189\pi$
$770$	3.37503	0.121628
$771$	−33.4154	−1.20343
$772$	−62.4359	−2.24712
$773$	−8.23733	−0.296276	−0.148138	−	0.988967i	$-0.547328\pi$
$773$	−8.23733	−0.296276	−0.148138	+	0.988967i	$0.547328\pi$
$774$	−2.59678	−0.0933394
$775$	−2.88085	−0.103483
$776$	1.64729	0.0591344
$777$	−16.1369	−0.578908
$778$	64.5618	2.31465
$779$	−51.9671	−1.86192
$780$	−8.35605	−0.299195
$781$	−7.74803	−0.277246
$782$	−33.7926	−1.20842
$783$	−38.8697	−1.38909
$784$	−33.8444	−1.20873
$785$	26.5007	0.945849
$786$	9.41625	0.335867
$787$	−33.4806	−1.19346	−0.596728	−	0.802444i	$-0.703533\pi$
$787$	−33.4806	−1.19346	−0.596728	+	0.802444i	$0.703533\pi$
$788$	39.4404	1.40500
$789$	10.3915	0.369947
$790$	34.8756	1.24082
$791$	25.3848	0.902580
$792$	5.57255	0.198012
$793$	−1.87837	−0.0667030
$794$	−85.6814	−3.04072
$795$	14.7486	0.523078
$796$	−112.279	−3.97964
$797$	−38.1906	−1.35278	−0.676390	−	0.736544i	$-0.736457\pi$
$797$	−38.1906	−1.35278	−0.676390	+	0.736544i	$0.736457\pi$
$798$	−47.8998	−1.69563
$799$	2.99133	0.105826
$800$	30.2876	1.07083
$801$	6.42960	0.227179
$802$	−1.90929	−0.0674194
$803$	−1.23175	−0.0434674
$804$	−28.5454	−1.00672
$805$	15.8169	0.557474
$806$	−2.61388	−0.0920698
$807$	28.0043	0.985797
$808$	−90.1383	−3.17105
$809$	−43.7291	−1.53743	−0.768716	−	0.639590i	$-0.779104\pi$
$809$	−43.7291	−1.53743	−0.768716	+	0.639590i	$0.779104\pi$
$810$	6.49919	0.228358
$811$	−39.6857	−1.39355	−0.696776	−	0.717288i	$-0.745383\pi$
$811$	−39.6857	−1.39355	−0.696776	+	0.717288i	$0.745383\pi$
$812$	64.5214	2.26426
$813$	−24.0830	−0.844629
$814$	8.98304	0.314856
$815$	−24.4672	−0.857047
$816$	25.6364	0.897452
$817$	−5.15104	−0.180212
$818$	49.0299	1.71429
$819$	2.97538	0.103968
$820$	−44.3707	−1.54949
$821$	−13.3871	−0.467215	−0.233607	−	0.972331i	$-0.575053\pi$
$821$	−13.3871	−0.467215	−0.233607	+	0.972331i	$0.575053\pi$
$822$	58.5337	2.04160
$823$	−29.7474	−1.03693	−0.518464	−	0.855099i	$-0.673496\pi$
$823$	−29.7474	−1.03693	−0.518464	+	0.855099i	$0.673496\pi$
$824$	−28.7223	−1.00059
$825$	1.62098	0.0564354
$826$	16.3847	0.570097
$827$	20.1838	0.701859	0.350930	−	0.936402i	$-0.385866\pi$
$827$	20.1838	0.701859	0.350930	+	0.936402i	$0.385866\pi$
$828$	44.5564	1.54844
$829$	−4.30943	−0.149673	−0.0748364	−	0.997196i	$-0.523843\pi$
$829$	−4.30943	−0.149673	−0.0748364	+	0.997196i	$0.523843\pi$
$830$	−10.4033	−0.361103
$831$	−11.0795	−0.384345
$832$	8.10713	0.281064
$833$	7.78422	0.269707
$834$	57.0838	1.97665
$835$	−9.37427	−0.324410
$836$	18.8593	0.652262
$837$	5.45106	0.188416
$838$	−1.07293	−0.0370638
$839$	27.3661	0.944784	0.472392	−	0.881389i	$-0.343391\pi$
$839$	27.3661	0.944784	0.472392	+	0.881389i	$0.343391\pi$
$840$	−23.9712	−0.827085
$841$	21.8465	0.753326
$842$	89.6353	3.08904
$843$	2.67615	0.0921716
$844$	−91.6837	−3.15588
$845$	1.45573	0.0500787
$846$	−5.57654	−0.191725
$847$	20.1771	0.693292
$848$	−82.6209	−2.83721
$849$	−17.7505	−0.609194
$850$	−16.7771	−0.575449
$851$	42.0986	1.44312
$852$	93.8889	3.21658
$853$	−0.854965	−0.0292734	−0.0146367	−	0.999893i	$-0.504659\pi$
$853$	−0.854965	−0.0292734	−0.0146367	+	0.999893i	$0.504659\pi$
$854$	−9.19353	−0.314596
$855$	−19.0581	−0.651772
$856$	15.4862	0.529309
$857$	−6.02461	−0.205797	−0.102898	−	0.994692i	$-0.532812\pi$
$857$	−6.02461	−0.205797	−0.102898	+	0.994692i	$0.532812\pi$
$858$	1.47077	0.0502111
$859$	21.1063	0.720138	0.360069	−	0.932926i	$-0.382753\pi$
$859$	21.1063	0.720138	0.360069	+	0.932926i	$0.382753\pi$
$860$	−4.39808	−0.149973
$861$	−14.0293	−0.478116
$862$	25.6714	0.874371
$863$	11.3584	0.386645	0.193323	−	0.981135i	$-0.438074\pi$
$863$	11.3584	0.386645	0.193323	+	0.981135i	$0.438074\pi$
$864$	−57.3094	−1.94971
$865$	0.284284	0.00966596
$866$	101.094	3.43531
$867$	14.2971	0.485555
$868$	−9.04843	−0.307124
$869$	−4.34163	−0.147280
$870$	−32.2299	−1.09269
$871$	4.97297	0.168503
$872$	−2.00230	−0.0678063
$873$	0.353563	0.0119663
$874$	124.963	4.22694
$875$	21.4818	0.726216
$876$	14.9260	0.504304
$877$	23.5475	0.795144	0.397572	−	0.917571i	$-0.369853\pi$
$877$	23.5475	0.795144	0.397572	+	0.917571i	$0.369853\pi$
$878$	3.30261	0.111458
$879$	4.34732	0.146631
$880$	6.67975	0.225174
$881$	−8.60545	−0.289925	−0.144962	−	0.989437i	$-0.546306\pi$
$881$	−8.60545	−0.289925	−0.144962	+	0.989437i	$0.546306\pi$
$882$	−14.5116	−0.488630
$883$	−6.41790	−0.215979	−0.107990	−	0.994152i	$-0.534441\pi$
$883$	−6.41790	−0.215979	−0.107990	+	0.994152i	$0.534441\pi$
$884$	−10.7664	−0.362112
$885$	−5.78870	−0.194585
$886$	−20.2396	−0.679962
$887$	−10.6502	−0.357599	−0.178799	−	0.983886i	$-0.557221\pi$
$887$	−10.6502	−0.357599	−0.178799	+	0.983886i	$0.557221\pi$
$888$	−63.8021	−2.14106
$889$	19.6244	0.658182
$890$	15.3966	0.516094
$891$	−0.809076	−0.0271051
$892$	25.5526	0.855566
$893$	−11.0618	−0.370168
$894$	65.7325	2.19842
$895$	25.9273	0.866655
$896$	0.307321	0.0102669
$897$	6.89267	0.230139
$898$	69.4888	2.31887
$899$	−7.13067	−0.237821
$900$	22.1210	0.737366
$901$	19.0028	0.633076
$902$	7.80978	0.260037
$903$	−1.39060	−0.0462762
$904$	100.367	3.33814
$905$	0.910737	0.0302739
$906$	15.6218	0.519000
$907$	−28.2417	−0.937749	−0.468874	−	0.883265i	$-0.655340\pi$
$907$	−28.2417	−0.937749	−0.468874	+	0.883265i	$0.655340\pi$
$908$	89.4462	2.96838
$909$	−19.3466	−0.641687
$910$	7.12495	0.236190
$911$	39.9672	1.32417	0.662087	−	0.749427i	$-0.269671\pi$
$911$	39.9672	1.32417	0.662087	+	0.749427i	$0.269671\pi$
$912$	−94.8017	−3.13920
$913$	1.29509	0.0428613
$914$	23.1905	0.767074
$915$	3.24807	0.107378
$916$	−112.668	−3.72265
$917$	−5.67867	−0.187526
$918$	31.7451	1.04775
$919$	−48.9399	−1.61438	−0.807189	−	0.590292i	$-0.799012\pi$
$919$	−48.9399	−1.61438	−0.807189	+	0.590292i	$0.799012\pi$
$920$	62.5370	2.06179
$921$	15.3709	0.506488
$922$	34.8359	1.14726
$923$	−16.3567	−0.538386
$924$	5.09134	0.167493
$925$	20.9008	0.687213
$926$	1.36823	0.0449630
$927$	−6.16474	−0.202476
$928$	74.9679	2.46094
$929$	24.7320	0.811429	0.405715	−	0.914000i	$-0.367023\pi$
$929$	24.7320	0.811429	0.405715	+	0.914000i	$0.367023\pi$
$930$	4.51989	0.148213
$931$	−28.7856	−0.943409
$932$	−21.7827	−0.713515
$933$	−32.9277	−1.07801
$934$	−91.6134	−2.99768
$935$	−1.53635	−0.0502439
$936$	11.7641	0.384520
$937$	22.8030	0.744941	0.372471	−	0.928044i	$-0.378511\pi$
$937$	22.8030	0.744941	0.372471	+	0.928044i	$0.378511\pi$
$938$	24.3398	0.794722
$939$	−11.9898	−0.391273
$940$	−9.44479	−0.308055
$941$	44.8916	1.46343	0.731713	−	0.681613i	$-0.238721\pi$
$941$	44.8916	1.46343	0.731713	+	0.681613i	$0.238721\pi$
$942$	56.5226	1.84161
$943$	36.6001	1.19186
$944$	32.4280	1.05544
$945$	−14.8586	−0.483350
$946$	0.774115	0.0251686
$947$	40.0472	1.30136	0.650680	−	0.759352i	$-0.274484\pi$
$947$	40.0472	1.30136	0.650680	+	0.759352i	$0.274484\pi$
$948$	52.6109	1.70872
$949$	−2.60031	−0.0844096
$950$	62.0406	2.01286
$951$	−7.97508	−0.258610
$952$	−30.8857	−1.00101
$953$	−19.7952	−0.641230	−0.320615	−	0.947210i	$-0.603890\pi$
$953$	−19.7952	−0.641230	−0.320615	+	0.947210i	$0.603890\pi$
$954$	−35.4257	−1.14695
$955$	12.1206	0.392213
$956$	93.8877	3.03654
$957$	4.01226	0.129698
$958$	−67.0506	−2.16631
$959$	−35.3000	−1.13990
$960$	−14.0188	−0.452454
$961$	1.00000	0.0322581
$962$	18.9639	0.611420
$963$	3.32385	0.107110
$964$	119.425	3.84643
$965$	−18.8086	−0.605472
$966$	33.7356	1.08542
$967$	−26.6660	−0.857521	−0.428760	−	0.903418i	$-0.641050\pi$
$967$	−26.6660	−0.857521	−0.428760	+	0.903418i	$0.641050\pi$
$968$	79.7761	2.56410
$969$	21.8044	0.700459
$970$	0.846656	0.0271845
$971$	35.4659	1.13816	0.569078	−	0.822283i	$-0.307300\pi$
$971$	35.4659	1.13816	0.569078	+	0.822283i	$0.307300\pi$
$972$	−69.2200	−2.22023
$973$	−34.4256	−1.10363
$974$	−32.3892	−1.03782
$975$	3.42202	0.109592
$976$	−18.1955	−0.582425
$977$	26.2636	0.840248	0.420124	−	0.907467i	$-0.361987\pi$
$977$	26.2636	0.840248	0.420124	+	0.907467i	$0.361987\pi$
$978$	−52.1854	−1.66871
$979$	−1.91670	−0.0612580
$980$	−24.5778	−0.785108
$981$	−0.429758	−0.0137211
$982$	−103.404	−3.29975
$983$	−48.8338	−1.55756	−0.778778	−	0.627300i	$-0.784160\pi$
$983$	−48.8338	−1.55756	−0.778778	+	0.627300i	$0.784160\pi$
$984$	−55.4690	−1.76829
$985$	11.8813	0.378570
$986$	−41.5266	−1.32248
$987$	−2.98628	−0.0950545
$988$	39.8134	1.26663
$989$	3.62785	0.115359
$990$	2.86411	0.0910273
$991$	−0.586724	−0.0186379	−0.00931895	−	0.999957i	$-0.502966\pi$
$991$	−0.586724	−0.0186379	−0.00931895	+	0.999957i	$0.502966\pi$
$992$	−10.5134	−0.333802
$993$	13.5818	0.431006
$994$	−80.0562	−2.53923
$995$	−33.8239	−1.07229
$996$	−15.6936	−0.497272
$997$	−37.5361	−1.18878	−0.594390	−	0.804177i	$-0.702606\pi$
$997$	−37.5361	−1.18878	−0.594390	+	0.804177i	$0.702606\pi$
$998$	57.4749	1.81934
$999$	−39.5479	−1.25124

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.a.b.1.1	✓	6
3.2	odd	2		3627.2.a.m.1.6		6
4.3	odd	2		6448.2.a.y.1.4		6
13.12	even	2		5239.2.a.g.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.a.b.1.1	✓	6	1.1	even	1	trivial
3627.2.a.m.1.6		6	3.2	odd	2
5239.2.a.g.1.6		6	13.12	even	2
6448.2.a.y.1.4		6	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)

\(f(q)\)	\(=\)	\(q-2.61388 q^{2} -1.18785 q^{3} +4.83234 q^{4} +1.45573 q^{5} +3.10489 q^{6} -1.87247 q^{7} -7.40339 q^{8} -1.58901 q^{9} +O(q^{10})\)	\(q-2.61388 q^{2} -1.18785 q^{3} +4.83234 q^{4} +1.45573 q^{5} +3.10489 q^{6} -1.87247 q^{7} -7.40339 q^{8} -1.58901 q^{9} -3.80510 q^{10} +0.473692 q^{11} -5.74010 q^{12} +1.00000 q^{13} +4.89441 q^{14} -1.72919 q^{15} +9.68686 q^{16} -2.22798 q^{17} +4.15347 q^{18} +8.23894 q^{19} +7.03459 q^{20} +2.22422 q^{21} -1.23817 q^{22} -5.80264 q^{23} +8.79413 q^{24} -2.88085 q^{25} -2.61388 q^{26} +5.45106 q^{27} -9.04843 q^{28} -7.13067 q^{29} +4.51989 q^{30} +1.00000 q^{31} -10.5134 q^{32} -0.562676 q^{33} +5.82366 q^{34} -2.72582 q^{35} -7.67864 q^{36} -7.25508 q^{37} -21.5356 q^{38} -1.18785 q^{39} -10.7774 q^{40} -6.30750 q^{41} -5.81383 q^{42} -0.625207 q^{43} +2.28904 q^{44} -2.31317 q^{45} +15.1674 q^{46} -1.34262 q^{47} -11.5065 q^{48} -3.49384 q^{49} +7.53017 q^{50} +2.64651 q^{51} +4.83234 q^{52} -8.52918 q^{53} -14.2484 q^{54} +0.689569 q^{55} +13.8627 q^{56} -9.78663 q^{57} +18.6387 q^{58} +3.34763 q^{59} -8.35605 q^{60} -1.87837 q^{61} -2.61388 q^{62} +2.97538 q^{63} +8.10713 q^{64} +1.45573 q^{65} +1.47077 q^{66} +4.97297 q^{67} -10.7664 q^{68} +6.89267 q^{69} +7.12495 q^{70} -16.3567 q^{71} +11.7641 q^{72} -2.60031 q^{73} +18.9639 q^{74} +3.42202 q^{75} +39.8134 q^{76} -0.886976 q^{77} +3.10489 q^{78} -9.16549 q^{79} +14.1015 q^{80} -1.70802 q^{81} +16.4870 q^{82} +2.73403 q^{83} +10.7482 q^{84} -3.24334 q^{85} +1.63421 q^{86} +8.47017 q^{87} -3.50693 q^{88} -4.04630 q^{89} +6.04634 q^{90} -1.87247 q^{91} -28.0403 q^{92} -1.18785 q^{93} +3.50944 q^{94} +11.9937 q^{95} +12.4884 q^{96} -0.222505 q^{97} +9.13247 q^{98} -0.752702 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 5 q^{3} + 6 q^{4} - 9 q^{5} - 3 q^{8} - q^{9}+O(q^{10}) \) 6 * q - 2 * q^2 - 5 * q^3 + 6 * q^4 - 9 * q^5 - 3 * q^8 - q^9	\( 6 q - 2 q^{2} - 5 q^{3} + 6 q^{4} - 9 q^{5} - 3 q^{8} - q^{9} - 8 q^{10} - 5 q^{11} - 13 q^{12} + 6 q^{13} - 17 q^{14} + 4 q^{15} + 14 q^{16} - 23 q^{17} + 9 q^{18} + 7 q^{19} - 10 q^{20} + 2 q^{21} + 2 q^{22} - 18 q^{23} - 13 q^{24} + 11 q^{25} - 2 q^{26} - 5 q^{27} - 25 q^{28} - 18 q^{29} + 25 q^{30} + 6 q^{31} + 2 q^{32} - 2 q^{33} - 16 q^{34} - q^{35} - 2 q^{36} - 13 q^{37} - 8 q^{38} - 5 q^{39} - 29 q^{40} - 5 q^{41} + 31 q^{42} - 7 q^{43} + 30 q^{44} - 5 q^{45} + 19 q^{46} - 9 q^{47} - 19 q^{48} + 16 q^{49} + 29 q^{50} + 26 q^{51} + 6 q^{52} - 31 q^{53} - 4 q^{54} + 7 q^{55} + 8 q^{56} - 5 q^{57} + 35 q^{58} - q^{59} + 33 q^{60} - 15 q^{61} - 2 q^{62} + 11 q^{63} - 5 q^{64} - 9 q^{65} - 29 q^{66} - 28 q^{67} - 12 q^{68} + 5 q^{69} + 73 q^{70} + q^{71} + 45 q^{72} - 20 q^{73} + 4 q^{74} + q^{75} + 38 q^{76} - 29 q^{77} - 15 q^{79} + 7 q^{80} + 2 q^{81} + 36 q^{82} + q^{83} + 68 q^{84} + 29 q^{85} + 3 q^{86} + 10 q^{87} + 9 q^{88} - q^{89} - 32 q^{90} - 60 q^{92} - 5 q^{93} + 54 q^{94} - 13 q^{95} + 36 q^{96} - 5 q^{97} + 20 q^{98} - 15 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 5 * q^3 + 6 * q^4 - 9 * q^5 - 3 * q^8 - q^9 - 8 * q^10 - 5 * q^11 - 13 * q^12 + 6 * q^13 - 17 * q^14 + 4 * q^15 + 14 * q^16 - 23 * q^17 + 9 * q^18 + 7 * q^19 - 10 * q^20 + 2 * q^21 + 2 * q^22 - 18 * q^23 - 13 * q^24 + 11 * q^25 - 2 * q^26 - 5 * q^27 - 25 * q^28 - 18 * q^29 + 25 * q^30 + 6 * q^31 + 2 * q^32 - 2 * q^33 - 16 * q^34 - q^35 - 2 * q^36 - 13 * q^37 - 8 * q^38 - 5 * q^39 - 29 * q^40 - 5 * q^41 + 31 * q^42 - 7 * q^43 + 30 * q^44 - 5 * q^45 + 19 * q^46 - 9 * q^47 - 19 * q^48 + 16 * q^49 + 29 * q^50 + 26 * q^51 + 6 * q^52 - 31 * q^53 - 4 * q^54 + 7 * q^55 + 8 * q^56 - 5 * q^57 + 35 * q^58 - q^59 + 33 * q^60 - 15 * q^61 - 2 * q^62 + 11 * q^63 - 5 * q^64 - 9 * q^65 - 29 * q^66 - 28 * q^67 - 12 * q^68 + 5 * q^69 + 73 * q^70 + q^71 + 45 * q^72 - 20 * q^73 + 4 * q^74 + q^75 + 38 * q^76 - 29 * q^77 - 15 * q^79 + 7 * q^80 + 2 * q^81 + 36 * q^82 + q^83 + 68 * q^84 + 29 * q^85 + 3 * q^86 + 10 * q^87 + 9 * q^88 - q^89 - 32 * q^90 - 60 * q^92 - 5 * q^93 + 54 * q^94 - 13 * q^95 + 36 * q^96 - 5 * q^97 + 20 * q^98 - 15 * q^99

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