LMFDB - Embedded newform 671.2.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [671,2,Mod(1,671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(671, 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("671.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 671 = 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	671.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:	$5.35796197563$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.24217.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 5x^{3} - x^{2} + 3x + 1 $ x^5 - 5x^3 - x^2 + 3x + 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			1.2
Root			$0.878095$ of defining polynomial
Character	$\chi$	$=$	671.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.26073 q^{2} +0.467546 q^{3} -0.410549 q^{4} -2.13883 q^{5} -0.589451 q^{6} +2.81011 q^{7} +3.03906 q^{8} -2.78140 q^{9} +O(q^{10})$	\(q-1.26073 q^{2} +0.467546 q^{3} -0.410549 q^{4} -2.13883 q^{5} -0.589451 q^{6} +2.81011 q^{7} +3.03906 q^{8} -2.78140 q^{9} +2.69649 q^{10} +1.00000 q^{11} -0.191951 q^{12} -2.46755 q^{13} -3.54280 q^{14} -1.00000 q^{15} -3.01035 q^{16} +1.13883 q^{17} +3.50661 q^{18} -0.0997671 q^{19} +0.878095 q^{20} +1.31386 q^{21} -1.26073 q^{22} -0.527240 q^{23} +1.42090 q^{24} -0.425410 q^{25} +3.11092 q^{26} -2.70307 q^{27} -1.15369 q^{28} +10.1773 q^{29} +1.26073 q^{30} -10.7246 q^{31} -2.28287 q^{32} +0.467546 q^{33} -1.43576 q^{34} -6.01035 q^{35} +1.14190 q^{36} -6.71035 q^{37} +0.125780 q^{38} -1.15369 q^{39} -6.50003 q^{40} -6.85746 q^{41} -1.65642 q^{42} -8.54567 q^{43} -0.410549 q^{44} +5.94894 q^{45} +0.664710 q^{46} -0.149815 q^{47} -1.40748 q^{48} +0.896733 q^{49} +0.536329 q^{50} +0.532454 q^{51} +1.01305 q^{52} -8.21867 q^{53} +3.40785 q^{54} -2.13883 q^{55} +8.54011 q^{56} -0.0466457 q^{57} -12.8308 q^{58} +0.568016 q^{59} +0.410549 q^{60} +1.00000 q^{61} +13.5208 q^{62} -7.81605 q^{63} +8.89880 q^{64} +5.27766 q^{65} -0.589451 q^{66} -2.87018 q^{67} -0.467546 q^{68} -0.246509 q^{69} +7.57745 q^{70} -0.962443 q^{71} -8.45285 q^{72} -2.78004 q^{73} +8.45996 q^{74} -0.198899 q^{75} +0.0409593 q^{76} +2.81011 q^{77} +1.45450 q^{78} -10.5915 q^{79} +6.43863 q^{80} +7.08040 q^{81} +8.64544 q^{82} -1.78392 q^{83} -0.539403 q^{84} -2.43576 q^{85} +10.7738 q^{86} +4.75833 q^{87} +3.03906 q^{88} +2.04042 q^{89} -7.50003 q^{90} -6.93408 q^{91} +0.216458 q^{92} -5.01423 q^{93} +0.188877 q^{94} +0.213385 q^{95} -1.06735 q^{96} +13.4528 q^{97} -1.13054 q^{98} -2.78140 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 2 q^{2} - 2 q^{5} - 5 q^{6} - q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) $ 5 * q - 2 * q^2 - 2 * q^5 - 5 * q^6 - q^7 - 6 * q^8 - 3 * q^9	$ 5 q - 2 q^{2} - 2 q^{5} - 5 q^{6} - q^{7} - 6 q^{8} - 3 q^{9} + 5 q^{10} + 5 q^{11} + 12 q^{12} - 10 q^{13} - 3 q^{14} - 5 q^{15} + 2 q^{16} - 3 q^{17} - 6 q^{18} - 13 q^{19} - 2 q^{21} - 2 q^{22} - 12 q^{24} - 15 q^{25} + 9 q^{26} - 9 q^{27} - 12 q^{28} - 7 q^{29} + 2 q^{30} - 13 q^{31} + q^{32} - 3 q^{34} - 13 q^{35} + 3 q^{36} - 6 q^{37} + 9 q^{38} - 12 q^{39} - 5 q^{40} - 9 q^{41} + 13 q^{42} + 2 q^{43} + 6 q^{45} - 7 q^{46} - 3 q^{47} + q^{48} - 6 q^{49} + 9 q^{50} + 5 q^{51} - 12 q^{52} + 3 q^{53} + 15 q^{54} - 2 q^{55} + 28 q^{56} - 17 q^{57} - 15 q^{58} - 14 q^{59} + 5 q^{61} + 31 q^{62} + 6 q^{64} + 9 q^{65} - 5 q^{66} - 5 q^{67} - 10 q^{69} - 5 q^{70} + 3 q^{71} + 5 q^{72} - 4 q^{73} + 2 q^{74} + 2 q^{75} - 19 q^{76} - q^{77} + 22 q^{78} - 27 q^{79} - 2 q^{80} + q^{81} + 11 q^{82} - 3 q^{83} - 15 q^{84} - 8 q^{85} + 5 q^{86} + 14 q^{87} - 6 q^{88} - 12 q^{89} - 10 q^{90} + 4 q^{91} + 13 q^{92} - 12 q^{93} - 18 q^{94} + 7 q^{95} + 12 q^{96} - 5 q^{97} + 14 q^{98} - 3 q^{99}+O(q^{100}) $ 5 * q - 2 * q^2 - 2 * q^5 - 5 * q^6 - q^7 - 6 * q^8 - 3 * q^9 + 5 * q^10 + 5 * q^11 + 12 * q^12 - 10 * q^13 - 3 * q^14 - 5 * q^15 + 2 * q^16 - 3 * q^17 - 6 * q^18 - 13 * q^19 - 2 * q^21 - 2 * q^22 - 12 * q^24 - 15 * q^25 + 9 * q^26 - 9 * q^27 - 12 * q^28 - 7 * q^29 + 2 * q^30 - 13 * q^31 + q^32 - 3 * q^34 - 13 * q^35 + 3 * q^36 - 6 * q^37 + 9 * q^38 - 12 * q^39 - 5 * q^40 - 9 * q^41 + 13 * q^42 + 2 * q^43 + 6 * q^45 - 7 * q^46 - 3 * q^47 + q^48 - 6 * q^49 + 9 * q^50 + 5 * q^51 - 12 * q^52 + 3 * q^53 + 15 * q^54 - 2 * q^55 + 28 * q^56 - 17 * q^57 - 15 * q^58 - 14 * q^59 + 5 * q^61 + 31 * q^62 + 6 * q^64 + 9 * q^65 - 5 * q^66 - 5 * q^67 - 10 * q^69 - 5 * q^70 + 3 * q^71 + 5 * q^72 - 4 * q^73 + 2 * q^74 + 2 * q^75 - 19 * q^76 - q^77 + 22 * q^78 - 27 * q^79 - 2 * q^80 + q^81 + 11 * q^82 - 3 * q^83 - 15 * q^84 - 8 * q^85 + 5 * q^86 + 14 * q^87 - 6 * q^88 - 12 * q^89 - 10 * q^90 + 4 * q^91 + 13 * q^92 - 12 * q^93 - 18 * q^94 + 7 * q^95 + 12 * q^96 - 5 * q^97 + 14 * q^98 - 3 * 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 $

$2$	−1.26073	−0.891474	−0.445737	−	0.895164i	$-0.647058\pi$
$2$	−1.26073	−0.891474	−0.445737	+	0.895164i	$0.647058\pi$
$3$	0.467546	0.269938	0.134969	−	0.990850i	$-0.456907\pi$
$3$	0.467546	0.269938	0.134969	+	0.990850i	$0.456907\pi$
$4$	−0.410549	−0.205275
$5$	−2.13883	−0.956513	−0.478257	−	0.878220i	$-0.658731\pi$
$5$	−2.13883	−0.956513	−0.478257	+	0.878220i	$0.658731\pi$
$6$	−0.589451	−0.240642
$7$	2.81011	1.06212	0.531061	−	0.847333i	$-0.321793\pi$
$7$	2.81011	1.06212	0.531061	+	0.847333i	$0.321793\pi$
$8$	3.03906	1.07447
$9$	−2.78140	−0.927134
$10$	2.69649	0.852707
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.191951	−0.0554113
$13$	−2.46755	−0.684374	−0.342187	−	0.939632i	$-0.611168\pi$
$13$	−2.46755	−0.684374	−0.342187	+	0.939632i	$0.611168\pi$
$14$	−3.54280	−0.946854
$15$	−1.00000	−0.258199
$16$	−3.01035	−0.752588
$17$	1.13883	0.276207	0.138103	−	0.990418i	$-0.455899\pi$
$17$	1.13883	0.276207	0.138103	+	0.990418i	$0.455899\pi$
$18$	3.50661	0.826515
$19$	−0.0997671	−0.0228881	−0.0114441	−	0.999935i	$-0.503643\pi$
$19$	−0.0997671	−0.0228881	−0.0114441	+	0.999935i	$0.503643\pi$
$20$	0.878095	0.196348
$21$	1.31386	0.286707
$22$	−1.26073	−0.268789
$23$	−0.527240	−0.109937	−0.0549686	−	0.998488i	$-0.517506\pi$
$23$	−0.527240	−0.109937	−0.0549686	+	0.998488i	$0.517506\pi$
$24$	1.42090	0.290040
$25$	−0.425410	−0.0850820
$26$	3.11092	0.610101
$27$	−2.70307	−0.520206
$28$	−1.15369	−0.218027
$29$	10.1773	1.88987	0.944934	−	0.327260i	$-0.106125\pi$
$29$	10.1773	1.88987	0.944934	+	0.327260i	$0.106125\pi$
$30$	1.26073	0.230178
$31$	−10.7246	−1.92619	−0.963095	−	0.269162i	$-0.913253\pi$
$31$	−10.7246	−1.92619	−0.963095	+	0.269162i	$0.913253\pi$
$32$	−2.28287	−0.403559
$33$	0.467546	0.0813892
$34$	−1.43576	−0.246231
$35$	−6.01035	−1.01593
$36$	1.14190	0.190317
$37$	−6.71035	−1.10317	−0.551587	−	0.834117i	$-0.685978\pi$
$37$	−6.71035	−1.10317	−0.551587	+	0.834117i	$0.685978\pi$
$38$	0.125780	0.0204042
$39$	−1.15369	−0.184738
$40$	−6.50003	−1.02775
$41$	−6.85746	−1.07096	−0.535478	−	0.844549i	$-0.679868\pi$
$41$	−6.85746	−1.07096	−0.535478	+	0.844549i	$0.679868\pi$
$42$	−1.65642	−0.255592
$43$	−8.54567	−1.30320	−0.651601	−	0.758562i	$-0.725902\pi$
$43$	−8.54567	−1.30320	−0.651601	+	0.758562i	$0.725902\pi$
$44$	−0.410549	−0.0618926
$45$	5.94894	0.886816
$46$	0.664710	0.0980062
$47$	−0.149815	−0.0218528	−0.0109264	−	0.999940i	$-0.503478\pi$
$47$	−0.149815	−0.0218528	−0.0109264	+	0.999940i	$0.503478\pi$
$48$	−1.40748	−0.203152
$49$	0.896733	0.128105
$50$	0.536329	0.0758484
$51$	0.532454	0.0745585
$52$	1.01305	0.140485
$53$	−8.21867	−1.12892	−0.564460	−	0.825460i	$-0.690916\pi$
$53$	−8.21867	−1.12892	−0.564460	+	0.825460i	$0.690916\pi$
$54$	3.40785	0.463750
$55$	−2.13883	−0.288400
$56$	8.54011	1.14122
$57$	−0.0466457	−0.00617837
$58$	−12.8308	−1.68477
$59$	0.568016	0.0739494	0.0369747	−	0.999316i	$-0.488228\pi$
$59$	0.568016	0.0739494	0.0369747	+	0.999316i	$0.488228\pi$
$60$	0.410549	0.0530017
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	13.5208	1.71715
$63$	−7.81605	−0.984730
$64$	8.89880	1.11235
$65$	5.27766	0.654613
$66$	−0.589451	−0.0725564
$67$	−2.87018	−0.350649	−0.175324	−	0.984511i	$-0.556097\pi$
$67$	−2.87018	−0.350649	−0.175324	+	0.984511i	$0.556097\pi$
$68$	−0.467546	−0.0566982
$69$	−0.246509	−0.0296762
$70$	7.57745	0.905679
$71$	−0.962443	−0.114221	−0.0571105	−	0.998368i	$-0.518189\pi$
$71$	−0.962443	−0.114221	−0.0571105	+	0.998368i	$0.518189\pi$
$72$	−8.45285	−0.996178
$73$	−2.78004	−0.325379	−0.162690	−	0.986677i	$-0.552017\pi$
$73$	−2.78004	−0.325379	−0.162690	+	0.986677i	$0.552017\pi$
$74$	8.45996	0.983451
$75$	−0.198899	−0.0229668
$76$	0.0409593	0.00469836
$77$	2.81011	0.320242
$78$	1.45450	0.164689
$79$	−10.5915	−1.19164	−0.595819	−	0.803119i	$-0.703173\pi$
$79$	−10.5915	−1.19164	−0.595819	+	0.803119i	$0.703173\pi$
$80$	6.43863	0.719860
$81$	7.08040	0.786711
$82$	8.64544	0.954729
$83$	−1.78392	−0.195810	−0.0979051	−	0.995196i	$-0.531214\pi$
$83$	−1.78392	−0.195810	−0.0979051	+	0.995196i	$0.531214\pi$
$84$	−0.539403	−0.0588536
$85$	−2.43576	−0.264195
$86$	10.7738	1.16177
$87$	4.75833	0.510147
$88$	3.03906	0.323965
$89$	2.04042	0.216284	0.108142	−	0.994135i	$-0.465510\pi$
$89$	2.04042	0.216284	0.108142	+	0.994135i	$0.465510\pi$
$90$	−7.50003	−0.790573
$91$	−6.93408	−0.726889
$92$	0.216458	0.0225673
$93$	−5.01423	−0.519951
$94$	0.188877	0.0194812
$95$	0.213385	0.0218928
$96$	−1.06735	−0.108936
$97$	13.4528	1.36592	0.682960	−	0.730456i	$-0.260692\pi$
$97$	13.4528	1.36592	0.682960	+	0.730456i	$0.260692\pi$
$98$	−1.13054	−0.114202
$99$	−2.78140	−0.279541
$100$	0.174652	0.0174652
$101$	4.12341	0.410295	0.205147	−	0.978731i	$-0.434233\pi$
$101$	4.12341	0.410295	0.205147	+	0.978731i	$0.434233\pi$
$102$	−0.671284	−0.0664670
$103$	−9.47517	−0.933616	−0.466808	−	0.884359i	$-0.654596\pi$
$103$	−9.47517	−0.933616	−0.466808	+	0.884359i	$0.654596\pi$
$104$	−7.49902	−0.735340
$105$	−2.81011	−0.274239
$106$	10.3616	1.00640
$107$	−15.9839	−1.54522	−0.772609	−	0.634882i	$-0.781049\pi$
$107$	−15.9839	−1.54522	−0.772609	+	0.634882i	$0.781049\pi$
$108$	1.10974	0.106785
$109$	−7.62445	−0.730290	−0.365145	−	0.930951i	$-0.618981\pi$
$109$	−7.62445	−0.730290	−0.365145	+	0.930951i	$0.618981\pi$
$110$	2.69649	0.257101
$111$	−3.13739	−0.297788
$112$	−8.45942	−0.799340
$113$	2.30188	0.216543	0.108272	−	0.994121i	$-0.465468\pi$
$113$	2.30188	0.216543	0.108272	+	0.994121i	$0.465468\pi$
$114$	0.0588078	0.00550786
$115$	1.12768	0.105156
$116$	−4.17827	−0.387942
$117$	6.86323	0.634506
$118$	−0.716118	−0.0659240
$119$	3.20024	0.293365
$120$	−3.03906	−0.277427
$121$	1.00000	0.0909091
$122$	−1.26073	−0.114142
$123$	−3.20618	−0.289091
$124$	4.40297	0.395398
$125$	11.6040	1.03790
$126$	9.85396	0.877861
$127$	6.49573	0.576403	0.288202	−	0.957570i	$-0.406943\pi$
$127$	6.49573	0.576403	0.288202	+	0.957570i	$0.406943\pi$
$128$	−6.65327	−0.588072
$129$	−3.99549	−0.351783
$130$	−6.65372	−0.583570
$131$	2.26557	0.197944	0.0989720	−	0.995090i	$-0.468445\pi$
$131$	2.26557	0.197944	0.0989720	+	0.995090i	$0.468445\pi$
$132$	−0.191951	−0.0167071
$133$	−0.280357	−0.0243100
$134$	3.61854	0.312594
$135$	5.78140	0.497584
$136$	3.46097	0.296776
$137$	9.50651	0.812196	0.406098	−	0.913830i	$-0.366889\pi$
$137$	9.50651	0.812196	0.406098	+	0.913830i	$0.366889\pi$
$138$	0.310782	0.0264555
$139$	10.9570	0.929358	0.464679	−	0.885479i	$-0.346170\pi$
$139$	10.9570	0.929358	0.464679	+	0.885479i	$0.346170\pi$
$140$	2.46755	0.208546
$141$	−0.0700454	−0.00589889
$142$	1.21338	0.101825
$143$	−2.46755	−0.206347
$144$	8.37299	0.697749
$145$	−21.7674	−1.80768
$146$	3.50489	0.290067
$147$	0.419263	0.0345803
$148$	2.75493	0.226454
$149$	−17.5264	−1.43582	−0.717908	−	0.696138i	$-0.754900\pi$
$149$	−17.5264	−1.43582	−0.717908	+	0.696138i	$0.754900\pi$
$150$	0.250758	0.0204743
$151$	14.9684	1.21812	0.609058	−	0.793126i	$-0.291548\pi$
$151$	14.9684	1.21812	0.609058	+	0.793126i	$0.291548\pi$
$152$	−0.303198	−0.0245926
$153$	−3.16754	−0.256080
$154$	−3.54280	−0.285487
$155$	22.9380	1.84243
$156$	0.473647	0.0379221
$157$	4.23956	0.338354	0.169177	−	0.985586i	$-0.445889\pi$
$157$	4.23956	0.338354	0.169177	+	0.985586i	$0.445889\pi$
$158$	13.3531	1.06231
$159$	−3.84260	−0.304738
$160$	4.88267	0.386009
$161$	−1.48161	−0.116767
$162$	−8.92650	−0.701332
$163$	7.24308	0.567322	0.283661	−	0.958925i	$-0.408451\pi$
$163$	7.24308	0.567322	0.283661	+	0.958925i	$0.408451\pi$
$164$	2.81533	0.219840
$165$	−1.00000	−0.0778499
$166$	2.24904	0.174560
$167$	17.9394	1.38819	0.694096	−	0.719883i	$-0.255805\pi$
$167$	17.9394	1.38819	0.694096	+	0.719883i	$0.255805\pi$
$168$	3.99289	0.308058
$169$	−6.91122	−0.531632
$170$	3.07085	0.235523
$171$	0.277492	0.0212204
$172$	3.50842	0.267514
$173$	3.59638	0.273428	0.136714	−	0.990611i	$-0.456346\pi$
$173$	3.59638	0.273428	0.136714	+	0.990611i	$0.456346\pi$
$174$	−5.99899	−0.454782
$175$	−1.19545	−0.0903676
$176$	−3.01035	−0.226914
$177$	0.265574	0.0199617
$178$	−2.57243	−0.192812
$179$	8.91211	0.666122	0.333061	−	0.942905i	$-0.391918\pi$
$179$	8.91211	0.666122	0.333061	+	0.942905i	$0.391918\pi$
$180$	−2.44233	−0.182041
$181$	−11.8207	−0.878626	−0.439313	−	0.898334i	$-0.644778\pi$
$181$	−11.8207	−0.878626	−0.439313	+	0.898334i	$0.644778\pi$
$182$	8.74203	0.648003
$183$	0.467546	0.0345620
$184$	−1.60232	−0.118124
$185$	14.3523	1.05520
$186$	6.32161	0.463523
$187$	1.13883	0.0832794
$188$	0.0615065	0.00448582
$189$	−7.59593	−0.552522
$190$	−0.269022	−0.0195169
$191$	−24.2775	−1.75666	−0.878328	−	0.478059i	$-0.841341\pi$
$191$	−24.2775	−1.75666	−0.878328	+	0.478059i	$0.841341\pi$
$192$	4.16059	0.300265
$193$	−11.1856	−0.805159	−0.402579	−	0.915385i	$-0.631886\pi$
$193$	−11.1856	−0.805159	−0.402579	+	0.915385i	$0.631886\pi$
$194$	−16.9603	−1.21768
$195$	2.46755	0.176705
$196$	−0.368153	−0.0262966
$197$	20.6364	1.47028	0.735141	−	0.677915i	$-0.237116\pi$
$197$	20.6364	1.47028	0.735141	+	0.677915i	$0.237116\pi$
$198$	3.50661	0.249204
$199$	20.5560	1.45718	0.728590	−	0.684951i	$-0.240176\pi$
$199$	20.5560	1.45718	0.728590	+	0.684951i	$0.240176\pi$
$200$	−1.29285	−0.0914182
$201$	−1.34194	−0.0946532
$202$	−5.19852	−0.365767
$203$	28.5992	2.00727
$204$	−0.218599	−0.0153050
$205$	14.6669	1.02438
$206$	11.9457	0.832294
$207$	1.46647	0.101927
$208$	7.42818	0.515051
$209$	−0.0997671	−0.00690104
$210$	3.54280	0.244477
$211$	−2.33069	−0.160451	−0.0802257	−	0.996777i	$-0.525564\pi$
$211$	−2.33069	−0.160451	−0.0802257	+	0.996777i	$0.525564\pi$
$212$	3.37417	0.231739
$213$	−0.449986	−0.0308325
$214$	20.1514	1.37752
$215$	18.2777	1.24653
$216$	−8.21479	−0.558946
$217$	−30.1373	−2.04585
$218$	9.61241	0.651035
$219$	−1.29980	−0.0878321
$220$	0.878095	0.0592011
$221$	−2.81011	−0.189029
$222$	3.95542	0.265470
$223$	−11.3176	−0.757885	−0.378942	−	0.925420i	$-0.623712\pi$
$223$	−11.3176	−0.757885	−0.378942	+	0.925420i	$0.623712\pi$
$224$	−6.41513	−0.428629
$225$	1.18324	0.0788824
$226$	−2.90206	−0.193042
$227$	7.36337	0.488724	0.244362	−	0.969684i	$-0.421422\pi$
$227$	7.36337	0.488724	0.244362	+	0.969684i	$0.421422\pi$
$228$	0.0191504	0.00126826
$229$	26.0274	1.71994	0.859969	−	0.510346i	$-0.170483\pi$
$229$	26.0274	1.71994	0.859969	+	0.510346i	$0.170483\pi$
$230$	−1.42170	−0.0937442
$231$	1.31386	0.0864454
$232$	30.9293	2.03061
$233$	−4.82607	−0.316166	−0.158083	−	0.987426i	$-0.550531\pi$
$233$	−4.82607	−0.316166	−0.158083	+	0.987426i	$0.550531\pi$
$234$	−8.65271	−0.565646
$235$	0.320429	0.0209025
$236$	−0.233199	−0.0151799
$237$	−4.95202	−0.321668
$238$	−4.03465	−0.261527
$239$	9.68579	0.626521	0.313261	−	0.949667i	$-0.398579\pi$
$239$	9.68579	0.626521	0.313261	+	0.949667i	$0.398579\pi$
$240$	3.01035	0.194317
$241$	−21.8455	−1.40719	−0.703596	−	0.710600i	$-0.748423\pi$
$241$	−21.8455	−1.40719	−0.703596	+	0.710600i	$0.748423\pi$
$242$	−1.26073	−0.0810431
$243$	11.4196	0.732568
$244$	−0.410549	−0.0262827
$245$	−1.91796	−0.122534
$246$	4.04214	0.257717
$247$	0.246180	0.0156641
$248$	−32.5926	−2.06963
$249$	−0.834062	−0.0528565
$250$	−14.6296	−0.925257
$251$	7.70544	0.486363	0.243181	−	0.969981i	$-0.421809\pi$
$251$	7.70544	0.486363	0.243181	+	0.969981i	$0.421809\pi$
$252$	3.20887	0.202140
$253$	−0.527240	−0.0331473
$254$	−8.18939	−0.513848
$255$	−1.13883	−0.0713162
$256$	−9.40958	−0.588099
$257$	−19.8476	−1.23806	−0.619031	−	0.785367i	$-0.712474\pi$
$257$	−19.8476	−1.23806	−0.619031	+	0.785367i	$0.712474\pi$
$258$	5.03725	0.313606
$259$	−18.8568	−1.17171
$260$	−2.16674	−0.134375
$261$	−28.3070	−1.75216
$262$	−2.85629	−0.176462
$263$	4.77544	0.294466	0.147233	−	0.989102i	$-0.452963\pi$
$263$	4.77544	0.294466	0.147233	+	0.989102i	$0.452963\pi$
$264$	1.42090	0.0874503
$265$	17.5783	1.07983
$266$	0.353455	0.0216717
$267$	0.953990	0.0583832
$268$	1.17835	0.0719793
$269$	−0.667783	−0.0407155	−0.0203577	−	0.999793i	$-0.506481\pi$
$269$	−0.667783	−0.0407155	−0.0203577	+	0.999793i	$0.506481\pi$
$270$	−7.28881	−0.443583
$271$	−21.7513	−1.32130	−0.660648	−	0.750696i	$-0.729718\pi$
$271$	−21.7513	−1.32130	−0.660648	+	0.750696i	$0.729718\pi$
$272$	−3.42827	−0.207870
$273$	−3.24200	−0.196215
$274$	−11.9852	−0.724051
$275$	−0.425410	−0.0256532
$276$	0.101204	0.00609177
$277$	12.5361	0.753222	0.376611	−	0.926372i	$-0.377089\pi$
$277$	12.5361	0.753222	0.376611	+	0.926372i	$0.377089\pi$
$278$	−13.8138	−0.828498
$279$	29.8293	1.78584
$280$	−18.2658	−1.09159
$281$	−24.3318	−1.45151	−0.725755	−	0.687953i	$-0.758510\pi$
$281$	−24.3318	−1.45151	−0.725755	+	0.687953i	$0.758510\pi$
$282$	0.0883087	0.00525870
$283$	−26.2983	−1.56327	−0.781635	−	0.623736i	$-0.785614\pi$
$283$	−26.2983	−1.56327	−0.781635	+	0.623736i	$0.785614\pi$
$284$	0.395130	0.0234467
$285$	0.0997671	0.00590969
$286$	3.11092	0.183952
$287$	−19.2702	−1.13749
$288$	6.34958	0.374153
$289$	−15.7031	−0.923710
$290$	27.4429	1.61150
$291$	6.28977	0.368713
$292$	1.14134	0.0667921
$293$	−17.0971	−0.998824	−0.499412	−	0.866365i	$-0.666451\pi$
$293$	−17.0971	−0.998824	−0.499412	+	0.866365i	$0.666451\pi$
$294$	−0.528580	−0.0308274
$295$	−1.21489	−0.0707336
$296$	−20.3932	−1.18533
$297$	−2.70307	−0.156848
$298$	22.0961	1.27999
$299$	1.30099	0.0752382
$300$	0.0816577	0.00471451
$301$	−24.0143	−1.38416
$302$	−18.8712	−1.08592
$303$	1.92788	0.110754
$304$	0.300334	0.0172253
$305$	−2.13883	−0.122469
$306$	3.99343	0.228289
$307$	4.23325	0.241604	0.120802	−	0.992677i	$-0.461453\pi$
$307$	4.23325	0.241604	0.120802	+	0.992677i	$0.461453\pi$
$308$	−1.15369	−0.0657376
$309$	−4.43007	−0.252018
$310$	−28.9188	−1.64247
$311$	−4.53545	−0.257182	−0.128591	−	0.991698i	$-0.541045\pi$
$311$	−4.53545	−0.257182	−0.128591	+	0.991698i	$0.541045\pi$
$312$	−3.50614	−0.198496
$313$	−22.5638	−1.27538	−0.637690	−	0.770293i	$-0.720110\pi$
$313$	−22.5638	−1.27538	−0.637690	+	0.770293i	$0.720110\pi$
$314$	−5.34496	−0.301634
$315$	16.7172	0.941907
$316$	4.34834	0.244613
$317$	6.82983	0.383602	0.191801	−	0.981434i	$-0.438567\pi$
$317$	6.82983	0.383602	0.191801	+	0.981434i	$0.438567\pi$
$318$	4.84450	0.271666
$319$	10.1773	0.569817
$320$	−19.0330	−1.06398
$321$	−7.47319	−0.417113
$322$	1.86791	0.104095
$323$	−0.113618	−0.00632186
$324$	−2.90685	−0.161492
$325$	1.04972	0.0582279
$326$	−9.13159	−0.505752
$327$	−3.56478	−0.197133
$328$	−20.8403	−1.15071
$329$	−0.420998	−0.0232103
$330$	1.26073	0.0694011
$331$	4.47787	0.246126	0.123063	−	0.992399i	$-0.460728\pi$
$331$	4.47787	0.246126	0.123063	+	0.992399i	$0.460728\pi$
$332$	0.732386	0.0401949
$333$	18.6642	1.02279
$334$	−22.6168	−1.23754
$335$	6.13883	0.335400
$336$	−3.95517	−0.215772
$337$	22.5821	1.23012	0.615062	−	0.788479i	$-0.289131\pi$
$337$	22.5821	1.23012	0.615062	+	0.788479i	$0.289131\pi$
$338$	8.71321	0.473936
$339$	1.07624	0.0584531
$340$	1.00000	0.0542326
$341$	−10.7246	−0.580768
$342$	−0.349844	−0.0189174
$343$	−17.1509	−0.926060
$344$	−25.9708	−1.40025
$345$	0.527240	0.0283857
$346$	−4.53408	−0.243754
$347$	−4.14311	−0.222414	−0.111207	−	0.993797i	$-0.535472\pi$
$347$	−4.14311	−0.222414	−0.111207	+	0.993797i	$0.535472\pi$
$348$	−1.95353	−0.104720
$349$	27.2400	1.45813	0.729063	−	0.684446i	$-0.239956\pi$
$349$	27.2400	1.45813	0.729063	+	0.684446i	$0.239956\pi$
$350$	1.50715	0.0805603
$351$	6.66994	0.356015
$352$	−2.28287	−0.121677
$353$	32.8030	1.74593	0.872963	−	0.487786i	$-0.162196\pi$
$353$	32.8030	1.74593	0.872963	+	0.487786i	$0.162196\pi$
$354$	−0.334818	−0.0177954
$355$	2.05850	0.109254
$356$	−0.837694	−0.0443977
$357$	1.49626	0.0791903
$358$	−11.2358	−0.593830
$359$	−10.6997	−0.564708	−0.282354	−	0.959310i	$-0.591115\pi$
$359$	−10.6997	−0.564708	−0.282354	+	0.959310i	$0.591115\pi$
$360$	18.0792	0.952858
$361$	−18.9900	−0.999476
$362$	14.9028	0.783272
$363$	0.467546	0.0245398
$364$	2.84678	0.149212
$365$	5.94603	0.311230
$366$	−0.589451	−0.0308111
$367$	15.0346	0.784801	0.392401	−	0.919794i	$-0.371645\pi$
$367$	15.0346	0.784801	0.392401	+	0.919794i	$0.371645\pi$
$368$	1.58718	0.0827374
$369$	19.0734	0.992919
$370$	−18.0944	−0.940684
$371$	−23.0954	−1.19905
$372$	2.05859	0.106733
$373$	30.3223	1.57003	0.785014	−	0.619478i	$-0.212656\pi$
$373$	30.3223	1.57003	0.785014	+	0.619478i	$0.212656\pi$
$374$	−1.43576	−0.0742414
$375$	5.42541	0.280167
$376$	−0.455298	−0.0234802
$377$	−25.1128	−1.29338
$378$	9.57644	0.492559
$379$	−35.0383	−1.79980	−0.899898	−	0.436100i	$-0.856359\pi$
$379$	−35.0383	−1.79980	−0.899898	+	0.436100i	$0.856359\pi$
$380$	−0.0876050	−0.00449404
$381$	3.03705	0.155593
$382$	30.6074	1.56601
$383$	25.2992	1.29273	0.646364	−	0.763029i	$-0.276289\pi$
$383$	25.2992	1.29273	0.646364	+	0.763029i	$0.276289\pi$
$384$	−3.11071	−0.158743
$385$	−6.01035	−0.306316
$386$	14.1021	0.717778
$387$	23.7689	1.20824
$388$	−5.52302	−0.280389
$389$	9.32728	0.472912	0.236456	−	0.971642i	$-0.424014\pi$
$389$	9.32728	0.472912	0.236456	+	0.971642i	$0.424014\pi$
$390$	−3.11092	−0.157528
$391$	−0.600437	−0.0303654
$392$	2.72523	0.137645
$393$	1.05926	0.0534325
$394$	−26.0170	−1.31072
$395$	22.6534	1.13982
$396$	1.14190	0.0573828
$397$	2.22535	0.111687	0.0558436	−	0.998440i	$-0.482215\pi$
$397$	2.22535	0.111687	0.0558436	+	0.998440i	$0.482215\pi$
$398$	−25.9157	−1.29904
$399$	−0.131080	−0.00656219
$400$	1.28063	0.0640317
$401$	−29.6235	−1.47933	−0.739664	−	0.672977i	$-0.765015\pi$
$401$	−29.6235	−1.47933	−0.739664	+	0.672977i	$0.765015\pi$
$402$	1.69183	0.0843808
$403$	26.4634	1.31823
$404$	−1.69286	−0.0842231
$405$	−15.1438	−0.752499
$406$	−36.0560	−1.78943
$407$	−6.71035	−0.332619
$408$	1.61816	0.0801110
$409$	−27.4237	−1.35602	−0.678008	−	0.735054i	$-0.737157\pi$
$409$	−27.4237	−1.35602	−0.678008	+	0.735054i	$0.737157\pi$
$410$	−18.4911	−0.913211
$411$	4.44473	0.219242
$412$	3.89003	0.191648
$413$	1.59619	0.0785434
$414$	−1.84883	−0.0908648
$415$	3.81549	0.187295
$416$	5.63309	0.276185
$417$	5.12288	0.250869
$418$	0.125780	0.00615209
$419$	6.32679	0.309084	0.154542	−	0.987986i	$-0.450610\pi$
$419$	6.32679	0.309084	0.154542	+	0.987986i	$0.450610\pi$
$420$	1.15369	0.0562943
$421$	−15.0824	−0.735071	−0.367535	−	0.930010i	$-0.619798\pi$
$421$	−15.0824	−0.735071	−0.367535	+	0.930010i	$0.619798\pi$
$422$	2.93838	0.143038
$423$	0.416696	0.0202605
$424$	−24.9770	−1.21299
$425$	−0.484470	−0.0235002
$426$	0.567313	0.0274864
$427$	2.81011	0.135991
$428$	6.56217	0.317194
$429$	−1.15369	−0.0557007
$430$	−23.0434	−1.11125
$431$	30.5783	1.47290	0.736452	−	0.676489i	$-0.236500\pi$
$431$	30.5783	1.47290	0.736452	+	0.676489i	$0.236500\pi$
$432$	8.13718	0.391500
$433$	7.53273	0.362000	0.181000	−	0.983483i	$-0.442067\pi$
$433$	7.53273	0.362000	0.181000	+	0.983483i	$0.442067\pi$
$434$	37.9951	1.82382
$435$	−10.1773	−0.487962
$436$	3.13021	0.149910
$437$	0.0526013	0.00251626
$438$	1.63870	0.0783000
$439$	26.5861	1.26889	0.634443	−	0.772970i	$-0.281230\pi$
$439$	26.5861	1.26889	0.634443	+	0.772970i	$0.281230\pi$
$440$	−6.50003	−0.309877
$441$	−2.49417	−0.118770
$442$	3.54280	0.168514
$443$	−0.836402	−0.0397387	−0.0198693	−	0.999803i	$-0.506325\pi$
$443$	−0.836402	−0.0397387	−0.0198693	+	0.999803i	$0.506325\pi$
$444$	1.28805	0.0611284
$445$	−4.36411	−0.206879
$446$	14.2685	0.675634
$447$	−8.19438	−0.387581
$448$	25.0066	1.18145
$449$	−4.11867	−0.194372	−0.0971860	−	0.995266i	$-0.530984\pi$
$449$	−4.11867	−0.194372	−0.0971860	+	0.995266i	$0.530984\pi$
$450$	−1.49175	−0.0703216
$451$	−6.85746	−0.322905
$452$	−0.945037	−0.0444508
$453$	6.99843	0.328815
$454$	−9.28325	−0.435684
$455$	14.8308	0.695279
$456$	−0.141759	−0.00663848
$457$	−14.6907	−0.687204	−0.343602	−	0.939115i	$-0.611647\pi$
$457$	−14.6907	−0.687204	−0.343602	+	0.939115i	$0.611647\pi$
$458$	−32.8136	−1.53328
$459$	−3.07833	−0.143684
$460$	−0.462967	−0.0215860
$461$	−5.84674	−0.272310	−0.136155	−	0.990688i	$-0.543474\pi$
$461$	−5.84674	−0.272310	−0.136155	+	0.990688i	$0.543474\pi$
$462$	−1.65642	−0.0770638
$463$	−23.7291	−1.10278	−0.551391	−	0.834247i	$-0.685903\pi$
$463$	−23.7291	−1.10278	−0.551391	+	0.834247i	$0.685903\pi$
$464$	−30.6371	−1.42229
$465$	10.7246	0.497340
$466$	6.08439	0.281854
$467$	34.6939	1.60544	0.802721	−	0.596355i	$-0.203385\pi$
$467$	34.6939	1.60544	0.802721	+	0.596355i	$0.203385\pi$
$468$	−2.81770	−0.130248
$469$	−8.06554	−0.372432
$470$	−0.403976	−0.0186340
$471$	1.98219	0.0913344
$472$	1.72624	0.0794565
$473$	−8.54567	−0.392930
$474$	6.24317	0.286759
$475$	0.0424420	0.00194737
$476$	−1.31386	−0.0602205
$477$	22.8594	1.04666
$478$	−12.2112	−0.558527
$479$	−5.63994	−0.257695	−0.128848	−	0.991664i	$-0.541128\pi$
$479$	−5.63994	−0.257695	−0.128848	+	0.991664i	$0.541128\pi$
$480$	2.28287	0.104198
$481$	16.5581	0.754984
$482$	27.5414	1.25447
$483$	−0.692718	−0.0315198
$484$	−0.410549	−0.0186613
$485$	−28.7731	−1.30652
$486$	−14.3971	−0.653066
$487$	−1.22628	−0.0555682	−0.0277841	−	0.999614i	$-0.508845\pi$
$487$	−1.22628	−0.0555682	−0.0277841	+	0.999614i	$0.508845\pi$
$488$	3.03906	0.137572
$489$	3.38647	0.153141
$490$	2.41804	0.109236
$491$	17.8263	0.804491	0.402246	−	0.915532i	$-0.368230\pi$
$491$	17.8263	0.804491	0.402246	+	0.915532i	$0.368230\pi$
$492$	1.31629	0.0593431
$493$	11.5902	0.521994
$494$	−0.310367	−0.0139641
$495$	5.94894	0.267385
$496$	32.2847	1.44963
$497$	−2.70457	−0.121317
$498$	1.05153	0.0471202
$499$	4.03680	0.180712	0.0903561	−	0.995910i	$-0.471199\pi$
$499$	4.03680	0.180712	0.0903561	+	0.995910i	$0.471199\pi$
$500$	−4.76403	−0.213054
$501$	8.38748	0.374725
$502$	−9.71451	−0.433580
$503$	−40.6187	−1.81110	−0.905548	−	0.424243i	$-0.860540\pi$
$503$	−40.6187	−1.81110	−0.905548	+	0.424243i	$0.860540\pi$
$504$	−23.7535	−1.05806
$505$	−8.81927	−0.392452
$506$	0.664710	0.0295500
$507$	−3.23131	−0.143507
$508$	−2.66682	−0.118321
$509$	−24.1238	−1.06927	−0.534635	−	0.845083i	$-0.679551\pi$
$509$	−24.1238	−1.06927	−0.534635	+	0.845083i	$0.679551\pi$
$510$	1.43576	0.0635766
$511$	−7.81223	−0.345593
$512$	25.1695	1.11235
$513$	0.269677	0.0119065
$514$	25.0226	1.10370
$515$	20.2658	0.893017
$516$	1.64035	0.0722122
$517$	−0.149815	−0.00658886
$518$	23.7734	1.04455
$519$	1.68147	0.0738084
$520$	16.0391	0.703362
$521$	1.27020	0.0556483	0.0278241	−	0.999613i	$-0.491142\pi$
$521$	1.27020	0.0556483	0.0278241	+	0.999613i	$0.491142\pi$
$522$	35.6876	1.56201
$523$	40.4719	1.76971	0.884857	−	0.465862i	$-0.154256\pi$
$523$	40.4719	1.76971	0.884857	+	0.465862i	$0.154256\pi$
$524$	−0.930130	−0.0406329
$525$	−0.558928	−0.0243936
$526$	−6.02056	−0.262509
$527$	−12.2135	−0.532026
$528$	−1.40748	−0.0612525
$529$	−22.7220	−0.987914
$530$	−22.1616	−0.962638
$531$	−1.57988	−0.0685610
$532$	0.115100	0.00499023
$533$	16.9211	0.732934
$534$	−1.20273	−0.0520471
$535$	34.1868	1.47802
$536$	−8.72266	−0.376762
$537$	4.16682	0.179811
$538$	0.841897	0.0362968
$539$	0.896733	0.0386250
$540$	−2.37355	−0.102141
$541$	7.51470	0.323082	0.161541	−	0.986866i	$-0.448354\pi$
$541$	7.51470	0.323082	0.161541	+	0.986866i	$0.448354\pi$
$542$	27.4226	1.17790
$543$	−5.52672	−0.237174
$544$	−2.59980	−0.111466
$545$	16.3074	0.698532
$546$	4.08730	0.174920
$547$	11.8177	0.505289	0.252645	−	0.967559i	$-0.418700\pi$
$547$	11.8177	0.505289	0.252645	+	0.967559i	$0.418700\pi$
$548$	−3.90289	−0.166723
$549$	−2.78140	−0.118707
$550$	0.536329	0.0228692
$551$	−1.01536	−0.0432556
$552$	−0.749156	−0.0318862
$553$	−29.7633	−1.26567
$554$	−15.8047	−0.671477
$555$	6.71035	0.284838
$556$	−4.49838	−0.190774
$557$	−3.17318	−0.134452	−0.0672261	−	0.997738i	$-0.521415\pi$
$557$	−3.17318	−0.134452	−0.0672261	+	0.997738i	$0.521415\pi$
$558$	−37.6069	−1.59203
$559$	21.0868	0.891878
$560$	18.0933	0.764580
$561$	0.532454	0.0224802
$562$	30.6759	1.29398
$563$	9.97412	0.420359	0.210180	−	0.977663i	$-0.432595\pi$
$563$	9.97412	0.420359	0.210180	+	0.977663i	$0.432595\pi$
$564$	0.0287571	0.00121089
$565$	−4.92334	−0.207126
$566$	33.1551	1.39361
$567$	19.8967	0.835583
$568$	−2.92492	−0.122727
$569$	46.6667	1.95637	0.978185	−	0.207737i	$-0.0666097\pi$
$569$	46.6667	1.95637	0.978185	+	0.207737i	$0.0666097\pi$
$570$	−0.125780	−0.00526834
$571$	7.45161	0.311840	0.155920	−	0.987770i	$-0.450166\pi$
$571$	7.45161	0.311840	0.155920	+	0.987770i	$0.450166\pi$
$572$	1.01305	0.0423577
$573$	−11.3508	−0.474187
$574$	24.2947	1.01404
$575$	0.224293	0.00935368
$576$	−24.7511	−1.03130
$577$	18.0260	0.750431	0.375216	−	0.926938i	$-0.377569\pi$
$577$	18.0260	0.750431	0.375216	+	0.926938i	$0.377569\pi$
$578$	19.7974	0.823463
$579$	−5.22979	−0.217343
$580$	8.93660	0.371072
$581$	−5.01301	−0.207975
$582$	−7.92973	−0.328698
$583$	−8.21867	−0.340382
$584$	−8.44872	−0.349610
$585$	−14.6793	−0.606914
$586$	21.5549	0.890425
$587$	−34.5695	−1.42684	−0.713418	−	0.700739i	$-0.752854\pi$
$587$	−34.5695	−1.42684	−0.713418	+	0.700739i	$0.752854\pi$
$588$	−0.172128	−0.00709845
$589$	1.06996	0.0440869
$590$	1.53165	0.0630572
$591$	9.64845	0.396884
$592$	20.2005	0.830235
$593$	18.3496	0.753526	0.376763	−	0.926310i	$-0.377037\pi$
$593$	18.3496	0.753526	0.376763	+	0.926310i	$0.377037\pi$
$594$	3.40785	0.139826
$595$	−6.84476	−0.280608
$596$	7.19544	0.294737
$597$	9.61088	0.393347
$598$	−1.64020	−0.0670729
$599$	−20.3653	−0.832103	−0.416051	−	0.909341i	$-0.636586\pi$
$599$	−20.3653	−0.832103	−0.416051	+	0.909341i	$0.636586\pi$
$600$	−0.604465	−0.0246772
$601$	−7.17037	−0.292486	−0.146243	−	0.989249i	$-0.546718\pi$
$601$	−7.17037	−0.292486	−0.146243	+	0.989249i	$0.546718\pi$
$602$	30.2756	1.23394
$603$	7.98313	0.325098
$604$	−6.14529	−0.250048
$605$	−2.13883	−0.0869558
$606$	−2.43055	−0.0987342
$607$	−10.6843	−0.433662	−0.216831	−	0.976209i	$-0.569572\pi$
$607$	−10.6843	−0.433662	−0.216831	+	0.976209i	$0.569572\pi$
$608$	0.227756	0.00923671
$609$	13.3714	0.541838
$610$	2.69649	0.109178
$611$	0.369676	0.0149555
$612$	1.30043	0.0525668
$613$	−23.1111	−0.933448	−0.466724	−	0.884403i	$-0.654566\pi$
$613$	−23.1111	−0.933448	−0.466724	+	0.884403i	$0.654566\pi$
$614$	−5.33700	−0.215384
$615$	6.85746	0.276520
$616$	8.54011	0.344091
$617$	1.44110	0.0580165	0.0290083	−	0.999579i	$-0.490765\pi$
$617$	1.44110	0.0580165	0.0290083	+	0.999579i	$0.490765\pi$
$618$	5.58515	0.224668
$619$	45.2355	1.81817	0.909085	−	0.416612i	$-0.136782\pi$
$619$	45.2355	1.81817	0.909085	+	0.416612i	$0.136782\pi$
$620$	−9.41719	−0.378203
$621$	1.42517	0.0571900
$622$	5.71800	0.229271
$623$	5.73381	0.229720
$624$	3.47301	0.139032
$625$	−22.6920	−0.907679
$626$	28.4469	1.13697
$627$	−0.0466457	−0.00186285
$628$	−1.74055	−0.0694555
$629$	−7.64194	−0.304704
$630$	−21.0759	−0.839686
$631$	−34.6464	−1.37925	−0.689626	−	0.724166i	$-0.742225\pi$
$631$	−34.6464	−1.37925	−0.689626	+	0.724166i	$0.742225\pi$
$632$	−32.1883	−1.28038
$633$	−1.08970	−0.0433119
$634$	−8.61060	−0.341971
$635$	−13.8933	−0.551337
$636$	1.57758	0.0625550
$637$	−2.21273	−0.0876715
$638$	−12.8308	−0.507977
$639$	2.67694	0.105898
$640$	14.2302	0.562498
$641$	−49.0089	−1.93574	−0.967868	−	0.251459i	$-0.919090\pi$
$641$	−49.0089	−1.93574	−0.967868	+	0.251459i	$0.919090\pi$
$642$	9.42170	0.371845
$643$	−12.2010	−0.481160	−0.240580	−	0.970629i	$-0.577338\pi$
$643$	−12.2010	−0.481160	−0.240580	+	0.970629i	$0.577338\pi$
$644$	0.608272	0.0239693
$645$	8.54567	0.336485
$646$	0.143242	0.00563577
$647$	7.74682	0.304559	0.152280	−	0.988337i	$-0.451339\pi$
$647$	7.74682	0.304559	0.152280	+	0.988337i	$0.451339\pi$
$648$	21.5178	0.845298
$649$	0.568016	0.0222966
$650$	−1.32342	−0.0519087
$651$	−14.0905	−0.552252
$652$	−2.97364	−0.116457
$653$	16.5227	0.646583	0.323291	−	0.946299i	$-0.395211\pi$
$653$	16.5227	0.646583	0.323291	+	0.946299i	$0.395211\pi$
$654$	4.49424	0.175739
$655$	−4.84567	−0.189336
$656$	20.6434	0.805988
$657$	7.73241	0.301670
$658$	0.530766	0.0206914
$659$	−39.4353	−1.53618	−0.768091	−	0.640341i	$-0.778793\pi$
$659$	−39.4353	−1.53618	−0.768091	+	0.640341i	$0.778793\pi$
$660$	0.410549	0.0159806
$661$	5.64073	0.219399	0.109699	−	0.993965i	$-0.465011\pi$
$661$	5.64073	0.219399	0.109699	+	0.993965i	$0.465011\pi$
$662$	−5.64540	−0.219415
$663$	−1.31386	−0.0510259
$664$	−5.42143	−0.210392
$665$	0.599635	0.0232529
$666$	−23.5305	−0.911790
$667$	−5.36586	−0.207767
$668$	−7.36500	−0.284960
$669$	−5.29151	−0.204582
$670$	−7.73943	−0.299000
$671$	1.00000	0.0386046
$672$	−2.99936	−0.115703
$673$	−30.8060	−1.18748	−0.593742	−	0.804656i	$-0.702350\pi$
$673$	−30.8060	−1.18748	−0.593742	+	0.804656i	$0.702350\pi$
$674$	−28.4700	−1.09662
$675$	1.14991	0.0442602
$676$	2.83740	0.109131
$677$	9.30135	0.357480	0.178740	−	0.983896i	$-0.442798\pi$
$677$	9.30135	0.357480	0.178740	+	0.983896i	$0.442798\pi$
$678$	−1.35685	−0.0521094
$679$	37.8037	1.45077
$680$	−7.40243	−0.283870
$681$	3.44271	0.131925
$682$	13.5208	0.517739
$683$	24.1322	0.923394	0.461697	−	0.887038i	$-0.347241\pi$
$683$	24.1322	0.923394	0.461697	+	0.887038i	$0.347241\pi$
$684$	−0.113924	−0.00435601
$685$	−20.3328	−0.776876
$686$	21.6227	0.825558
$687$	12.1690	0.464276
$688$	25.7255	0.980774
$689$	20.2799	0.772604
$690$	−0.664710	−0.0253051
$691$	−13.2525	−0.504149	−0.252075	−	0.967708i	$-0.581113\pi$
$691$	−13.2525	−0.504149	−0.252075	+	0.967708i	$0.581113\pi$
$692$	−1.47649	−0.0561278
$693$	−7.81605	−0.296907
$694$	5.22336	0.198276
$695$	−23.4351	−0.888943
$696$	14.4609	0.548138
$697$	−7.80948	−0.295805
$698$	−34.3425	−1.29988
$699$	−2.25641	−0.0853452
$700$	0.490791	0.0185502
$701$	39.3038	1.48449	0.742243	−	0.670131i	$-0.233762\pi$
$701$	39.3038	1.48449	0.742243	+	0.670131i	$0.233762\pi$
$702$	−8.40903	−0.317378
$703$	0.669472	0.0252496
$704$	8.89880	0.335386
$705$	0.149815	0.00564237
$706$	−41.3558	−1.55645
$707$	11.5872	0.435783
$708$	−0.109031	−0.00409764
$709$	30.2178	1.13485	0.567427	−	0.823424i	$-0.307939\pi$
$709$	30.2178	1.13485	0.567427	+	0.823424i	$0.307939\pi$
$710$	−2.59522	−0.0973970
$711$	29.4592	1.10481
$712$	6.20097	0.232391
$713$	5.65443	0.211760
$714$	−1.88638	−0.0705961
$715$	5.27766	0.197373
$716$	−3.65886	−0.136738
$717$	4.52855	0.169122
$718$	13.4895	0.503422
$719$	0.320098	0.0119376	0.00596881	−	0.999982i	$-0.498100\pi$
$719$	0.320098	0.0119376	0.00596881	+	0.999982i	$0.498100\pi$
$720$	−17.9084	−0.667407
$721$	−26.6263	−0.991615
$722$	23.9414	0.891007
$723$	−10.2138	−0.379854
$724$	4.85298	0.180360
$725$	−4.32951	−0.160794
$726$	−0.589451	−0.0218766
$727$	−44.5279	−1.65145	−0.825725	−	0.564074i	$-0.809233\pi$
$727$	−44.5279	−1.65145	−0.825725	+	0.564074i	$0.809233\pi$
$728$	−21.0731	−0.781021
$729$	−15.9020	−0.588963
$730$	−7.49637	−0.277453
$731$	−9.73206	−0.359953
$732$	−0.191951	−0.00709470
$733$	29.4375	1.08730	0.543650	−	0.839312i	$-0.317042\pi$
$733$	29.4375	1.08730	0.543650	+	0.839312i	$0.317042\pi$
$734$	−18.9547	−0.699630
$735$	−0.896733	−0.0330765
$736$	1.20362	0.0443661
$737$	−2.87018	−0.105725
$738$	−24.0464	−0.885161
$739$	42.3554	1.55807	0.779034	−	0.626982i	$-0.215710\pi$
$739$	42.3554	1.55807	0.779034	+	0.626982i	$0.215710\pi$
$740$	−5.89232	−0.216606
$741$	0.115100	0.00422832
$742$	29.1171	1.06892
$743$	−1.89122	−0.0693822	−0.0346911	−	0.999398i	$-0.511045\pi$
$743$	−1.89122	−0.0693822	−0.0346911	+	0.999398i	$0.511045\pi$
$744$	−15.2385	−0.558672
$745$	37.4859	1.37338
$746$	−38.2283	−1.39964
$747$	4.96179	0.181542
$748$	−0.467546	−0.0170952
$749$	−44.9165	−1.64121
$750$	−6.84000	−0.249761
$751$	12.8427	0.468637	0.234318	−	0.972160i	$-0.424714\pi$
$751$	12.8427	0.468637	0.234318	+	0.972160i	$0.424714\pi$
$752$	0.450996	0.0164461
$753$	3.60264	0.131288
$754$	31.6606	1.15301
$755$	−32.0150	−1.16514
$756$	3.11850	0.113419
$757$	42.5686	1.54718	0.773592	−	0.633684i	$-0.218458\pi$
$757$	42.5686	1.54718	0.773592	+	0.633684i	$0.218458\pi$
$758$	44.1740	1.60447
$759$	−0.246509	−0.00894771
$760$	0.648490	0.0235232
$761$	10.6089	0.384571	0.192286	−	0.981339i	$-0.438410\pi$
$761$	10.6089	0.384571	0.192286	+	0.981339i	$0.438410\pi$
$762$	−3.82891	−0.138707
$763$	−21.4256	−0.775658
$764$	9.96710	0.360597
$765$	6.77483	0.244944
$766$	−31.8956	−1.15243
$767$	−1.40161	−0.0506091
$768$	−4.39941	−0.158750
$769$	−8.50270	−0.306615	−0.153308	−	0.988179i	$-0.548993\pi$
$769$	−8.50270	−0.306615	−0.153308	+	0.988179i	$0.548993\pi$
$770$	7.57745	0.273072
$771$	−9.27968	−0.334199
$772$	4.59225	0.165279
$773$	38.7310	1.39306	0.696528	−	0.717530i	$-0.254727\pi$
$773$	38.7310	1.39306	0.696528	+	0.717530i	$0.254727\pi$
$774$	−29.9663	−1.07712
$775$	4.56234	0.163884
$776$	40.8837	1.46764
$777$	−8.81643	−0.316287
$778$	−11.7592	−0.421588
$779$	0.684149	0.0245122
$780$	−1.01305	−0.0362730
$781$	−0.962443	−0.0344389
$782$	0.756991	0.0270699
$783$	−27.5098	−0.983121
$784$	−2.69948	−0.0964100
$785$	−9.06770	−0.323640
$786$	−1.33544	−0.0476337
$787$	1.04569	0.0372748	0.0186374	−	0.999826i	$-0.494067\pi$
$787$	1.04569	0.0372748	0.0186374	+	0.999826i	$0.494067\pi$
$788$	−8.47225	−0.301812
$789$	2.23273	0.0794875
$790$	−28.5600	−1.01612
$791$	6.46856	0.229995
$792$	−8.45285	−0.300359
$793$	−2.46755	−0.0876251
$794$	−2.80558	−0.0995662
$795$	8.21867	0.291486
$796$	−8.43927	−0.299122
$797$	21.0518	0.745694	0.372847	−	0.927893i	$-0.378382\pi$
$797$	21.0518	0.745694	0.372847	+	0.927893i	$0.378382\pi$
$798$	0.165257	0.00585002
$799$	−0.170614	−0.00603589
$800$	0.971157	0.0343356
$801$	−5.67523	−0.200524
$802$	37.3474	1.31878
$803$	−2.78004	−0.0981055
$804$	0.550933	0.0194299
$805$	3.16890	0.111689
$806$	−33.3633	−1.17517
$807$	−0.312219	−0.0109906
$808$	12.5313	0.440850
$809$	−24.9182	−0.876078	−0.438039	−	0.898956i	$-0.644327\pi$
$809$	−24.9182	−0.876078	−0.438039	+	0.898956i	$0.644327\pi$
$810$	19.0923	0.670833
$811$	13.1312	0.461098	0.230549	−	0.973061i	$-0.425948\pi$
$811$	13.1312	0.461098	0.230549	+	0.973061i	$0.425948\pi$
$812$	−11.7414	−0.412042
$813$	−10.1697	−0.356667
$814$	8.45996	0.296522
$815$	−15.4917	−0.542651
$816$	−1.60287	−0.0561118
$817$	0.852577	0.0298279
$818$	34.5741	1.20885
$819$	19.2865	0.673923
$820$	−6.02150	−0.210280
$821$	−25.8217	−0.901183	−0.450592	−	0.892730i	$-0.648787\pi$
$821$	−25.8217	−0.901183	−0.450592	+	0.892730i	$0.648787\pi$
$822$	−5.60362	−0.195449
$823$	51.3184	1.78885	0.894423	−	0.447221i	$-0.147586\pi$
$823$	51.3184	1.78885	0.894423	+	0.447221i	$0.147586\pi$
$824$	−28.7956	−1.00314
$825$	−0.198899	−0.00692476
$826$	−2.01237	−0.0700193
$827$	25.1701	0.875249	0.437624	−	0.899158i	$-0.355820\pi$
$827$	25.1701	0.875249	0.437624	+	0.899158i	$0.355820\pi$
$828$	−0.602057	−0.0209229
$829$	−14.2404	−0.494589	−0.247294	−	0.968940i	$-0.579541\pi$
$829$	−14.2404	−0.494589	−0.247294	+	0.968940i	$0.579541\pi$
$830$	−4.81032	−0.166969
$831$	5.86120	0.203323
$832$	−21.9582	−0.761263
$833$	1.02123	0.0353834
$834$	−6.45859	−0.223643
$835$	−38.3693	−1.32782
$836$	0.0409593	0.00141661
$837$	28.9892	1.00201
$838$	−7.97640	−0.275540
$839$	50.0082	1.72647	0.863237	−	0.504799i	$-0.168434\pi$
$839$	50.0082	1.72647	0.863237	+	0.504799i	$0.168434\pi$
$840$	−8.54011	−0.294662
$841$	74.5765	2.57160
$842$	19.0149	0.655296
$843$	−11.3762	−0.391817
$844$	0.956864	0.0329366
$845$	14.7819	0.508513
$846$	−0.525343	−0.0180617
$847$	2.81011	0.0965566
$848$	24.7411	0.849612
$849$	−12.2956	−0.421985
$850$	0.610787	0.0209498
$851$	3.53797	0.121280
$852$	0.184741	0.00632914
$853$	−37.2981	−1.27706	−0.638531	−	0.769596i	$-0.720458\pi$
$853$	−37.2981	−1.27706	−0.638531	+	0.769596i	$0.720458\pi$
$854$	−3.54280	−0.121232
$855$	−0.593509	−0.0202976
$856$	−48.5760	−1.66029
$857$	9.21734	0.314858	0.157429	−	0.987530i	$-0.449679\pi$
$857$	9.21734	0.314858	0.157429	+	0.987530i	$0.449679\pi$
$858$	1.45450	0.0496557
$859$	−33.1072	−1.12960	−0.564801	−	0.825227i	$-0.691047\pi$
$859$	−33.1072	−1.12960	−0.564801	+	0.825227i	$0.691047\pi$
$860$	−7.50391	−0.255881
$861$	−9.00971	−0.307050
$862$	−38.5511	−1.31306
$863$	32.5545	1.10817	0.554084	−	0.832461i	$-0.313069\pi$
$863$	32.5545	1.10817	0.554084	+	0.832461i	$0.313069\pi$
$864$	6.17076	0.209933
$865$	−7.69204	−0.261537
$866$	−9.49677	−0.322713
$867$	−7.34190	−0.249344
$868$	12.3728	0.419961
$869$	−10.5915	−0.359292
$870$	12.8308	0.435005
$871$	7.08231	0.239975
$872$	−23.1712	−0.784675
$873$	−37.4175	−1.26639
$874$	−0.0663162	−0.00224318
$875$	32.6086	1.10237
$876$	0.533630	0.0180297
$877$	9.70859	0.327836	0.163918	−	0.986474i	$-0.447587\pi$
$877$	9.70859	0.327836	0.163918	+	0.986474i	$0.447587\pi$
$878$	−33.5180	−1.13118
$879$	−7.99368	−0.269620
$880$	6.43863	0.217046
$881$	2.50579	0.0844222	0.0422111	−	0.999109i	$-0.486560\pi$
$881$	2.50579	0.0844222	0.0422111	+	0.999109i	$0.486560\pi$
$882$	3.14449	0.105880
$883$	11.6673	0.392637	0.196318	−	0.980540i	$-0.437101\pi$
$883$	11.6673	0.392637	0.196318	+	0.980540i	$0.437101\pi$
$884$	1.15369	0.0388028
$885$	−0.568016	−0.0190937
$886$	1.05448	0.0354260
$887$	−58.7295	−1.97194	−0.985971	−	0.166914i	$-0.946620\pi$
$887$	−58.7295	−1.97194	−0.985971	+	0.166914i	$0.946620\pi$
$888$	−9.53473	−0.319965
$889$	18.2537	0.612211
$890$	5.50199	0.184427
$891$	7.08040	0.237202
$892$	4.64645	0.155575
$893$	0.0149466	0.000500170 0
$894$	10.3309	0.345518
$895$	−19.0615	−0.637155
$896$	−18.6964	−0.624604
$897$	0.608272	0.0203096
$898$	5.19255	0.173278
$899$	−109.147	−3.64025
$900$	−0.485777	−0.0161926
$901$	−9.35966	−0.311815
$902$	8.64544	0.287862
$903$	−11.2278	−0.373637
$904$	6.99557	0.232669
$905$	25.2825	0.840418
$906$	−8.82316	−0.293130
$907$	19.5525	0.649231	0.324615	−	0.945846i	$-0.394765\pi$
$907$	19.5525	0.649231	0.324615	+	0.945846i	$0.394765\pi$
$908$	−3.02303	−0.100323
$909$	−11.4689	−0.380398
$910$	−18.6977	−0.619823
$911$	15.6061	0.517053	0.258527	−	0.966004i	$-0.416763\pi$
$911$	15.6061	0.517053	0.258527	+	0.966004i	$0.416763\pi$
$912$	0.140420	0.00464977
$913$	−1.78392	−0.0590390
$914$	18.5211	0.612624
$915$	−1.00000	−0.0330590
$916$	−10.6855	−0.353060
$917$	6.36652	0.210241
$918$	3.88096	0.128091
$919$	−14.9336	−0.492614	−0.246307	−	0.969192i	$-0.579217\pi$
$919$	−14.9336	−0.492614	−0.246307	+	0.969192i	$0.579217\pi$
$920$	3.42708	0.112988
$921$	1.97924	0.0652181
$922$	7.37118	0.242757
$923$	2.37487	0.0781699
$924$	−0.539403	−0.0177450
$925$	2.85465	0.0938603
$926$	29.9160	0.983102
$927$	26.3543	0.865587
$928$	−23.2334	−0.762673
$929$	−42.9148	−1.40799	−0.703994	−	0.710206i	$-0.748602\pi$
$929$	−42.9148	−1.40799	−0.703994	+	0.710206i	$0.748602\pi$
$930$	−13.5208	−0.443366
$931$	−0.0894645	−0.00293208
$932$	1.98134	0.0649009
$933$	−2.12053	−0.0694230
$934$	−43.7398	−1.43121
$935$	−2.43576	−0.0796579
$936$	20.8578	0.681758
$937$	−10.5067	−0.343237	−0.171619	−	0.985163i	$-0.554900\pi$
$937$	−10.5067	−0.343237	−0.171619	+	0.985163i	$0.554900\pi$
$938$	10.1685	0.332013
$939$	−10.5496	−0.344273
$940$	−0.131552	−0.00429075
$941$	12.7160	0.414531	0.207265	−	0.978285i	$-0.433544\pi$
$941$	12.7160	0.414531	0.207265	+	0.978285i	$0.433544\pi$
$942$	−2.49901	−0.0814223
$943$	3.61553	0.117738
$944$	−1.70993	−0.0556534
$945$	16.2464	0.528495
$946$	10.7738	0.350287
$947$	−46.7842	−1.52028	−0.760141	−	0.649758i	$-0.774870\pi$
$947$	−46.7842	−1.52028	−0.760141	+	0.649758i	$0.774870\pi$
$948$	2.03305	0.0660303
$949$	6.85988	0.222681
$950$	−0.0535080	−0.00173603
$951$	3.19326	0.103548
$952$	9.72572	0.315212
$953$	−27.5607	−0.892778	−0.446389	−	0.894839i	$-0.647290\pi$
$953$	−27.5607	−0.892778	−0.446389	+	0.894839i	$0.647290\pi$
$954$	−28.8196	−0.933070
$955$	51.9253	1.68026
$956$	−3.97649	−0.128609
$957$	4.75833	0.153815
$958$	7.11046	0.229729
$959$	26.7144	0.862652
$960$	−8.89880	−0.287207
$961$	84.0164	2.71021
$962$	−20.8753	−0.673048
$963$	44.4575	1.43262
$964$	8.96865	0.288861
$965$	23.9241	0.770145
$966$	0.873333	0.0280990
$967$	50.4290	1.62169	0.810844	−	0.585263i	$-0.199009\pi$
$967$	50.4290	1.62169	0.810844	+	0.585263i	$0.199009\pi$
$968$	3.03906	0.0976792
$969$	−0.0531215	−0.00170651
$970$	36.2753	1.16473
$971$	−14.3527	−0.460601	−0.230301	−	0.973120i	$-0.573971\pi$
$971$	−14.3527	−0.460601	−0.230301	+	0.973120i	$0.573971\pi$
$972$	−4.68831	−0.150378
$973$	30.7903	0.987092
$974$	1.54602	0.0495376
$975$	0.490791	0.0157179
$976$	−3.01035	−0.0963590
$977$	3.84906	0.123142	0.0615711	−	0.998103i	$-0.480389\pi$
$977$	3.84906	0.123142	0.0615711	+	0.998103i	$0.480389\pi$
$978$	−4.26944	−0.136522
$979$	2.04042	0.0652122
$980$	0.787416	0.0251531
$981$	21.2067	0.677077
$982$	−22.4743	−0.717183
$983$	−0.334984	−0.0106843	−0.00534216	−	0.999986i	$-0.501700\pi$
$983$	−0.334984	−0.0106843	−0.00534216	+	0.999986i	$0.501700\pi$
$984$	−9.74377	−0.310620
$985$	−44.1377	−1.40634
$986$	−14.6121	−0.465344
$987$	−0.196836	−0.00626534
$988$	−0.101069	−0.00321543
$989$	4.50562	0.143270
$990$	−7.50003	−0.238367
$991$	−4.16046	−0.132161	−0.0660807	−	0.997814i	$-0.521049\pi$
$991$	−4.16046	−0.132161	−0.0660807	+	0.997814i	$0.521049\pi$
$992$	24.4828	0.777330
$993$	2.09361	0.0664387
$994$	3.40975	0.108151
$995$	−43.9659	−1.39381
$996$	0.342424	0.0108501
$997$	−12.4134	−0.393135	−0.196568	−	0.980490i	$-0.562979\pi$
$997$	−12.4134	−0.393135	−0.196568	+	0.980490i	$0.562979\pi$
$998$	−5.08934	−0.161100
$999$	18.1385	0.573877

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.a.a.1.2	✓	5
3.2	odd	2		6039.2.a.a.1.4		5
11.10	odd	2		7381.2.a.g.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.a.a.1.2	✓	5	1.1	even	1	trivial
6039.2.a.a.1.4		5	3.2	odd	2
7381.2.a.g.1.4		5	11.10	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:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.a (trivial)

\(f(q)\)	\(=\)	\(q-1.26073 q^{2} +0.467546 q^{3} -0.410549 q^{4} -2.13883 q^{5} -0.589451 q^{6} +2.81011 q^{7} +3.03906 q^{8} -2.78140 q^{9} +O(q^{10})\)	\(q-1.26073 q^{2} +0.467546 q^{3} -0.410549 q^{4} -2.13883 q^{5} -0.589451 q^{6} +2.81011 q^{7} +3.03906 q^{8} -2.78140 q^{9} +2.69649 q^{10} +1.00000 q^{11} -0.191951 q^{12} -2.46755 q^{13} -3.54280 q^{14} -1.00000 q^{15} -3.01035 q^{16} +1.13883 q^{17} +3.50661 q^{18} -0.0997671 q^{19} +0.878095 q^{20} +1.31386 q^{21} -1.26073 q^{22} -0.527240 q^{23} +1.42090 q^{24} -0.425410 q^{25} +3.11092 q^{26} -2.70307 q^{27} -1.15369 q^{28} +10.1773 q^{29} +1.26073 q^{30} -10.7246 q^{31} -2.28287 q^{32} +0.467546 q^{33} -1.43576 q^{34} -6.01035 q^{35} +1.14190 q^{36} -6.71035 q^{37} +0.125780 q^{38} -1.15369 q^{39} -6.50003 q^{40} -6.85746 q^{41} -1.65642 q^{42} -8.54567 q^{43} -0.410549 q^{44} +5.94894 q^{45} +0.664710 q^{46} -0.149815 q^{47} -1.40748 q^{48} +0.896733 q^{49} +0.536329 q^{50} +0.532454 q^{51} +1.01305 q^{52} -8.21867 q^{53} +3.40785 q^{54} -2.13883 q^{55} +8.54011 q^{56} -0.0466457 q^{57} -12.8308 q^{58} +0.568016 q^{59} +0.410549 q^{60} +1.00000 q^{61} +13.5208 q^{62} -7.81605 q^{63} +8.89880 q^{64} +5.27766 q^{65} -0.589451 q^{66} -2.87018 q^{67} -0.467546 q^{68} -0.246509 q^{69} +7.57745 q^{70} -0.962443 q^{71} -8.45285 q^{72} -2.78004 q^{73} +8.45996 q^{74} -0.198899 q^{75} +0.0409593 q^{76} +2.81011 q^{77} +1.45450 q^{78} -10.5915 q^{79} +6.43863 q^{80} +7.08040 q^{81} +8.64544 q^{82} -1.78392 q^{83} -0.539403 q^{84} -2.43576 q^{85} +10.7738 q^{86} +4.75833 q^{87} +3.03906 q^{88} +2.04042 q^{89} -7.50003 q^{90} -6.93408 q^{91} +0.216458 q^{92} -5.01423 q^{93} +0.188877 q^{94} +0.213385 q^{95} -1.06735 q^{96} +13.4528 q^{97} -1.13054 q^{98} -2.78140 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{2} - 2 q^{5} - 5 q^{6} - q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) 5 * q - 2 * q^2 - 2 * q^5 - 5 * q^6 - q^7 - 6 * q^8 - 3 * q^9	\( 5 q - 2 q^{2} - 2 q^{5} - 5 q^{6} - q^{7} - 6 q^{8} - 3 q^{9} + 5 q^{10} + 5 q^{11} + 12 q^{12} - 10 q^{13} - 3 q^{14} - 5 q^{15} + 2 q^{16} - 3 q^{17} - 6 q^{18} - 13 q^{19} - 2 q^{21} - 2 q^{22} - 12 q^{24} - 15 q^{25} + 9 q^{26} - 9 q^{27} - 12 q^{28} - 7 q^{29} + 2 q^{30} - 13 q^{31} + q^{32} - 3 q^{34} - 13 q^{35} + 3 q^{36} - 6 q^{37} + 9 q^{38} - 12 q^{39} - 5 q^{40} - 9 q^{41} + 13 q^{42} + 2 q^{43} + 6 q^{45} - 7 q^{46} - 3 q^{47} + q^{48} - 6 q^{49} + 9 q^{50} + 5 q^{51} - 12 q^{52} + 3 q^{53} + 15 q^{54} - 2 q^{55} + 28 q^{56} - 17 q^{57} - 15 q^{58} - 14 q^{59} + 5 q^{61} + 31 q^{62} + 6 q^{64} + 9 q^{65} - 5 q^{66} - 5 q^{67} - 10 q^{69} - 5 q^{70} + 3 q^{71} + 5 q^{72} - 4 q^{73} + 2 q^{74} + 2 q^{75} - 19 q^{76} - q^{77} + 22 q^{78} - 27 q^{79} - 2 q^{80} + q^{81} + 11 q^{82} - 3 q^{83} - 15 q^{84} - 8 q^{85} + 5 q^{86} + 14 q^{87} - 6 q^{88} - 12 q^{89} - 10 q^{90} + 4 q^{91} + 13 q^{92} - 12 q^{93} - 18 q^{94} + 7 q^{95} + 12 q^{96} - 5 q^{97} + 14 q^{98} - 3 q^{99}+O(q^{100}) \) 5 * q - 2 * q^2 - 2 * q^5 - 5 * q^6 - q^7 - 6 * q^8 - 3 * q^9 + 5 * q^10 + 5 * q^11 + 12 * q^12 - 10 * q^13 - 3 * q^14 - 5 * q^15 + 2 * q^16 - 3 * q^17 - 6 * q^18 - 13 * q^19 - 2 * q^21 - 2 * q^22 - 12 * q^24 - 15 * q^25 + 9 * q^26 - 9 * q^27 - 12 * q^28 - 7 * q^29 + 2 * q^30 - 13 * q^31 + q^32 - 3 * q^34 - 13 * q^35 + 3 * q^36 - 6 * q^37 + 9 * q^38 - 12 * q^39 - 5 * q^40 - 9 * q^41 + 13 * q^42 + 2 * q^43 + 6 * q^45 - 7 * q^46 - 3 * q^47 + q^48 - 6 * q^49 + 9 * q^50 + 5 * q^51 - 12 * q^52 + 3 * q^53 + 15 * q^54 - 2 * q^55 + 28 * q^56 - 17 * q^57 - 15 * q^58 - 14 * q^59 + 5 * q^61 + 31 * q^62 + 6 * q^64 + 9 * q^65 - 5 * q^66 - 5 * q^67 - 10 * q^69 - 5 * q^70 + 3 * q^71 + 5 * q^72 - 4 * q^73 + 2 * q^74 + 2 * q^75 - 19 * q^76 - q^77 + 22 * q^78 - 27 * q^79 - 2 * q^80 + q^81 + 11 * q^82 - 3 * q^83 - 15 * q^84 - 8 * q^85 + 5 * q^86 + 14 * q^87 - 6 * q^88 - 12 * q^89 - 10 * q^90 + 4 * q^91 + 13 * q^92 - 12 * q^93 - 18 * q^94 + 7 * q^95 + 12 * q^96 - 5 * q^97 + 14 * q^98 - 3 * q^99

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