LMFDB - Embedded newform 671.2.a.c.1.14

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:	$0$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 5 x^{18} - 18 x^{17} + 122 x^{16} + 78 x^{15} - 1177 x^{14} + 387 x^{13} + 5755 x^{12} + \cdots - 43 $ x^19 - 5x^18 - 18x^17 + 122x^16 + 78x^15 - 1177x^14 + 387x^13 + 5755x^12 - 4673x^11 - 15053x^10 + 16875x^9 + 20141x^8 - 28019x^7 - 11589x^6 + 21077x^5 + 1674x^4 - 6404x^3 + 241x^2 + 643x - 43
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$1.98166$ 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)

$f(q)$	$=$	$q+1.98166 q^{2} +1.84905 q^{3} +1.92698 q^{4} +2.60057 q^{5} +3.66419 q^{6} -2.18138 q^{7} -0.144707 q^{8} +0.418993 q^{9} +O(q^{10})$	\(q+1.98166 q^{2} +1.84905 q^{3} +1.92698 q^{4} +2.60057 q^{5} +3.66419 q^{6} -2.18138 q^{7} -0.144707 q^{8} +0.418993 q^{9} +5.15344 q^{10} +1.00000 q^{11} +3.56308 q^{12} +0.444418 q^{13} -4.32276 q^{14} +4.80859 q^{15} -4.14071 q^{16} +6.05961 q^{17} +0.830301 q^{18} -1.92163 q^{19} +5.01124 q^{20} -4.03349 q^{21} +1.98166 q^{22} -9.17660 q^{23} -0.267571 q^{24} +1.76296 q^{25} +0.880686 q^{26} -4.77242 q^{27} -4.20348 q^{28} +10.5575 q^{29} +9.52898 q^{30} +3.13863 q^{31} -7.91607 q^{32} +1.84905 q^{33} +12.0081 q^{34} -5.67284 q^{35} +0.807389 q^{36} -1.07395 q^{37} -3.80802 q^{38} +0.821752 q^{39} -0.376321 q^{40} +1.30812 q^{41} -7.99301 q^{42} -12.5238 q^{43} +1.92698 q^{44} +1.08962 q^{45} -18.1849 q^{46} -1.08337 q^{47} -7.65639 q^{48} -2.24156 q^{49} +3.49358 q^{50} +11.2045 q^{51} +0.856384 q^{52} -4.16225 q^{53} -9.45731 q^{54} +2.60057 q^{55} +0.315662 q^{56} -3.55320 q^{57} +20.9213 q^{58} +8.24320 q^{59} +9.26603 q^{60} -1.00000 q^{61} +6.21970 q^{62} -0.913984 q^{63} -7.40554 q^{64} +1.15574 q^{65} +3.66419 q^{66} -10.2859 q^{67} +11.6767 q^{68} -16.9680 q^{69} -11.2416 q^{70} -5.20811 q^{71} -0.0606312 q^{72} -0.283380 q^{73} -2.12820 q^{74} +3.25980 q^{75} -3.70294 q^{76} -2.18138 q^{77} +1.62843 q^{78} +14.7634 q^{79} -10.7682 q^{80} -10.0814 q^{81} +2.59225 q^{82} +15.2641 q^{83} -7.77245 q^{84} +15.7584 q^{85} -24.8180 q^{86} +19.5213 q^{87} -0.144707 q^{88} +16.3022 q^{89} +2.15925 q^{90} -0.969447 q^{91} -17.6831 q^{92} +5.80349 q^{93} -2.14687 q^{94} -4.99733 q^{95} -14.6372 q^{96} +4.78591 q^{97} -4.44202 q^{98} +0.418993 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q + 5 q^{2} + 23 q^{4} + q^{6} + 9 q^{7} + 9 q^{8} + 29 q^{9}+O(q^{10}) $ 19 * q + 5 * q^2 + 23 * q^4 + q^6 + 9 * q^7 + 9 * q^8 + 29 * q^9	\( 19 q + 5 q^{2} + 23 q^{4} + q^{6} + 9 q^{7} + 9 q^{8} + 29 q^{9} + 7 q^{10} + 19 q^{11} - 4 q^{12} + 8 q^{13} - 11 q^{14} - 5 q^{15} + 31 q^{16} + 9 q^{17} + 10 q^{18} + 17 q^{19} - 6 q^{20} + 18 q^{21} + 5 q^{22} - 10 q^{23} + 26 q^{24} + 45 q^{25} + 5 q^{26} - 33 q^{27} + 36 q^{28} + 27 q^{29} - 30 q^{30} + 7 q^{31} + 8 q^{32} - 5 q^{34} + 17 q^{35} + 38 q^{36} + 20 q^{37} - 37 q^{38} + 24 q^{39} + 10 q^{40} + 19 q^{41} + 21 q^{42} + 20 q^{43} + 23 q^{44} - 32 q^{45} + 41 q^{46} - 19 q^{47} + 5 q^{48} + 42 q^{49} + 36 q^{50} + 47 q^{51} - 28 q^{52} + 3 q^{53} - 33 q^{54} - 44 q^{56} + 11 q^{57} + 23 q^{58} - 28 q^{59} - 96 q^{60} - 19 q^{61} - 11 q^{62} - 32 q^{63} + 47 q^{64} + 25 q^{65} + q^{66} + 3 q^{67} + 38 q^{68} + 3 q^{70} - 19 q^{71} + 34 q^{72} + 20 q^{73} - 22 q^{74} - 50 q^{75} - 25 q^{76} + 9 q^{77} - 94 q^{78} + 69 q^{79} - 36 q^{80} + 47 q^{81} - 61 q^{82} + q^{83} - 28 q^{84} + 24 q^{85} - 27 q^{86} - 58 q^{87} + 9 q^{88} + 36 q^{90} + 24 q^{91} - 67 q^{92} - 14 q^{93} + 64 q^{94} - 3 q^{95} - 26 q^{96} + 21 q^{97} - 87 q^{98} + 29 q^{99}+O(q^{100}) \) 19 * q + 5 * q^2 + 23 * q^4 + q^6 + 9 * q^7 + 9 * q^8 + 29 * q^9 + 7 * q^10 + 19 * q^11 - 4 * q^12 + 8 * q^13 - 11 * q^14 - 5 * q^15 + 31 * q^16 + 9 * q^17 + 10 * q^18 + 17 * q^19 - 6 * q^20 + 18 * q^21 + 5 * q^22 - 10 * q^23 + 26 * q^24 + 45 * q^25 + 5 * q^26 - 33 * q^27 + 36 * q^28 + 27 * q^29 - 30 * q^30 + 7 * q^31 + 8 * q^32 - 5 * q^34 + 17 * q^35 + 38 * q^36 + 20 * q^37 - 37 * q^38 + 24 * q^39 + 10 * q^40 + 19 * q^41 + 21 * q^42 + 20 * q^43 + 23 * q^44 - 32 * q^45 + 41 * q^46 - 19 * q^47 + 5 * q^48 + 42 * q^49 + 36 * q^50 + 47 * q^51 - 28 * q^52 + 3 * q^53 - 33 * q^54 - 44 * q^56 + 11 * q^57 + 23 * q^58 - 28 * q^59 - 96 * q^60 - 19 * q^61 - 11 * q^62 - 32 * q^63 + 47 * q^64 + 25 * q^65 + q^66 + 3 * q^67 + 38 * q^68 + 3 * q^70 - 19 * q^71 + 34 * q^72 + 20 * q^73 - 22 * q^74 - 50 * q^75 - 25 * q^76 + 9 * q^77 - 94 * q^78 + 69 * q^79 - 36 * q^80 + 47 * q^81 - 61 * q^82 + q^83 - 28 * q^84 + 24 * q^85 - 27 * q^86 - 58 * q^87 + 9 * q^88 + 36 * q^90 + 24 * q^91 - 67 * q^92 - 14 * q^93 + 64 * q^94 - 3 * q^95 - 26 * q^96 + 21 * q^97 - 87 * q^98 + 29 * 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 $

$2$	1.98166	1.40125	0.700623	−	0.713532i	$-0.252906\pi$
$2$	1.98166	1.40125	0.700623	+	0.713532i	$0.252906\pi$
$3$	1.84905	1.06755	0.533775	−	0.845626i	$-0.320773\pi$
$3$	1.84905	1.06755	0.533775	+	0.845626i	$0.320773\pi$
$4$	1.92698	0.963488
$5$	2.60057	1.16301	0.581505	−	0.813543i	$-0.302464\pi$
$5$	2.60057	1.16301	0.581505	+	0.813543i	$0.302464\pi$
$6$	3.66419	1.49590
$7$	−2.18138	−0.824486	−0.412243	−	0.911074i	$-0.635254\pi$
$7$	−2.18138	−0.824486	−0.412243	+	0.911074i	$0.635254\pi$
$8$	−0.144707	−0.0511617
$9$	0.418993	0.139664
$10$	5.15344	1.62966
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	3.56308	1.02857
$13$	0.444418	0.123259	0.0616297	−	0.998099i	$-0.480370\pi$
$13$	0.444418	0.123259	0.0616297	+	0.998099i	$0.480370\pi$
$14$	−4.32276	−1.15531
$15$	4.80859	1.24157
$16$	−4.14071	−1.03518
$17$	6.05961	1.46967	0.734836	−	0.678245i	$-0.237259\pi$
$17$	6.05961	1.46967	0.734836	+	0.678245i	$0.237259\pi$
$18$	0.830301	0.195704
$19$	−1.92163	−0.440852	−0.220426	−	0.975404i	$-0.570745\pi$
$19$	−1.92163	−0.440852	−0.220426	+	0.975404i	$0.570745\pi$
$20$	5.01124	1.12055
$21$	−4.03349	−0.880180
$22$	1.98166	0.422491
$23$	−9.17660	−1.91345	−0.956726	−	0.290990i	$-0.906015\pi$
$23$	−9.17660	−1.91345	−0.956726	+	0.290990i	$0.906015\pi$
$24$	−0.267571	−0.0546177
$25$	1.76296	0.352591
$26$	0.880686	0.172717
$27$	−4.77242	−0.918452
$28$	−4.20348	−0.794382
$29$	10.5575	1.96048	0.980238	−	0.197822i	$-0.0633868\pi$
$29$	10.5575	1.96048	0.980238	+	0.197822i	$0.0633868\pi$
$30$	9.52898	1.73975
$31$	3.13863	0.563715	0.281858	−	0.959456i	$-0.409049\pi$
$31$	3.13863	0.563715	0.281858	+	0.959456i	$0.409049\pi$
$32$	−7.91607	−1.39938
$33$	1.84905	0.321879
$34$	12.0081	2.05937
$35$	−5.67284	−0.958885
$36$	0.807389	0.134565
$37$	−1.07395	−0.176556	−0.0882780	−	0.996096i	$-0.528136\pi$
$37$	−1.07395	−0.176556	−0.0882780	+	0.996096i	$0.528136\pi$
$38$	−3.80802	−0.617742
$39$	0.821752	0.131586
$40$	−0.376321	−0.0595015
$41$	1.30812	0.204294	0.102147	−	0.994769i	$-0.467429\pi$
$41$	1.30812	0.204294	0.102147	+	0.994769i	$0.467429\pi$
$42$	−7.99301	−1.23335
$43$	−12.5238	−1.90987	−0.954934	−	0.296817i	$-0.904075\pi$
$43$	−12.5238	−1.90987	−0.954934	+	0.296817i	$0.904075\pi$
$44$	1.92698	0.290503
$45$	1.08962	0.162431
$46$	−18.1849	−2.68122
$47$	−1.08337	−0.158025	−0.0790127	−	0.996874i	$-0.525177\pi$
$47$	−1.08337	−0.158025	−0.0790127	+	0.996874i	$0.525177\pi$
$48$	−7.65639	−1.10511
$49$	−2.24156	−0.320223
$50$	3.49358	0.494067
$51$	11.2045	1.56895
$52$	0.856384	0.118759
$53$	−4.16225	−0.571729	−0.285864	−	0.958270i	$-0.592281\pi$
$53$	−4.16225	−0.571729	−0.285864	+	0.958270i	$0.592281\pi$
$54$	−9.45731	−1.28698
$55$	2.60057	0.350661
$56$	0.315662	0.0421821
$57$	−3.55320	−0.470632
$58$	20.9213	2.74711
$59$	8.24320	1.07317	0.536587	−	0.843845i	$-0.319713\pi$
$59$	8.24320	1.07317	0.536587	+	0.843845i	$0.319713\pi$
$60$	9.26603	1.19624
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	6.21970	0.789903
$63$	−0.913984	−0.115151
$64$	−7.40554	−0.925692
$65$	1.15574	0.143352
$66$	3.66419	0.451031
$67$	−10.2859	−1.25662	−0.628309	−	0.777964i	$-0.716253\pi$
$67$	−10.2859	−1.25662	−0.628309	+	0.777964i	$0.716253\pi$
$68$	11.6767	1.41601
$69$	−16.9680	−2.04271
$70$	−11.2416	−1.34363
$71$	−5.20811	−0.618089	−0.309044	−	0.951048i	$-0.600009\pi$
$71$	−5.20811	−0.618089	−0.309044	+	0.951048i	$0.600009\pi$
$72$	−0.0606312	−0.00714545
$73$	−0.283380	−0.0331671	−0.0165835	−	0.999862i	$-0.505279\pi$
$73$	−0.283380	−0.0331671	−0.0165835	+	0.999862i	$0.505279\pi$
$74$	−2.12820	−0.247398
$75$	3.25980	0.376409
$76$	−3.70294	−0.424756
$77$	−2.18138	−0.248592
$78$	1.62843	0.184384
$79$	14.7634	1.66101	0.830505	−	0.557012i	$-0.188052\pi$
$79$	14.7634	1.66101	0.830505	+	0.557012i	$0.188052\pi$
$80$	−10.7682	−1.20392
$81$	−10.0814	−1.12016
$82$	2.59225	0.286266
$83$	15.2641	1.67546	0.837728	−	0.546088i	$-0.183884\pi$
$83$	15.2641	1.67546	0.837728	+	0.546088i	$0.183884\pi$
$84$	−7.77245	−0.848043
$85$	15.7584	1.70924
$86$	−24.8180	−2.67619
$87$	19.5213	2.09291
$88$	−0.144707	−0.0154258
$89$	16.3022	1.72803	0.864015	−	0.503466i	$-0.167942\pi$
$89$	16.3022	1.72803	0.864015	+	0.503466i	$0.167942\pi$
$90$	2.15925	0.227605
$91$	−0.969447	−0.101626
$92$	−17.6831	−1.84359
$93$	5.80349	0.601794
$94$	−2.14687	−0.221432
$95$	−4.99733	−0.512716
$96$	−14.6372	−1.49391
$97$	4.78591	0.485935	0.242968	−	0.970034i	$-0.421879\pi$
$97$	4.78591	0.485935	0.242968	+	0.970034i	$0.421879\pi$
$98$	−4.44202	−0.448712
$99$	0.418993	0.0421103
$100$	3.39718	0.339718
$101$	3.67611	0.365786	0.182893	−	0.983133i	$-0.441454\pi$
$101$	3.67611	0.365786	0.182893	+	0.983133i	$0.441454\pi$
$102$	22.2036	2.19848
$103$	8.87836	0.874811	0.437405	−	0.899264i	$-0.355898\pi$
$103$	8.87836	0.874811	0.437405	+	0.899264i	$0.355898\pi$
$104$	−0.0643105	−0.00630616
$105$	−10.4894	−1.02366
$106$	−8.24816	−0.801132
$107$	3.89110	0.376167	0.188083	−	0.982153i	$-0.439772\pi$
$107$	3.89110	0.376167	0.188083	+	0.982153i	$0.439772\pi$
$108$	−9.19634	−0.884918
$109$	−8.52962	−0.816990	−0.408495	−	0.912761i	$-0.633946\pi$
$109$	−8.52962	−0.816990	−0.408495	+	0.912761i	$0.633946\pi$
$110$	5.15344	0.491362
$111$	−1.98579	−0.188483
$112$	9.03249	0.853490
$113$	9.75866	0.918018	0.459009	−	0.888432i	$-0.348205\pi$
$113$	9.75866	0.918018	0.459009	+	0.888432i	$0.348205\pi$
$114$	−7.04123	−0.659471
$115$	−23.8644	−2.22536
$116$	20.3440	1.88890
$117$	0.186208	0.0172149
$118$	16.3352	1.50378
$119$	−13.2183	−1.21172
$120$	−0.695836	−0.0635209
$121$	1.00000	0.0909091
$122$	−1.98166	−0.179411
$123$	2.41878	0.218094
$124$	6.04807	0.543133
$125$	−8.41815	−0.752942
$126$	−1.81120	−0.161355
$127$	−20.5051	−1.81953	−0.909765	−	0.415123i	$-0.863739\pi$
$127$	−20.5051	−1.81953	−0.909765	+	0.415123i	$0.863739\pi$
$128$	1.15688	0.102255
$129$	−23.1572	−2.03888
$130$	2.29028	0.200871
$131$	13.2639	1.15887	0.579437	−	0.815017i	$-0.303273\pi$
$131$	13.2639	1.15887	0.579437	+	0.815017i	$0.303273\pi$
$132$	3.56308	0.310126
$133$	4.19181	0.363476
$134$	−20.3831	−1.76083
$135$	−12.4110	−1.06817
$136$	−0.876869	−0.0751909
$137$	−9.00446	−0.769303	−0.384652	−	0.923062i	$-0.625678\pi$
$137$	−9.00446	−0.769303	−0.384652	+	0.923062i	$0.625678\pi$
$138$	−33.6248	−2.86233
$139$	15.4273	1.30852	0.654262	−	0.756268i	$-0.272979\pi$
$139$	15.4273	1.30852	0.654262	+	0.756268i	$0.272979\pi$
$140$	−10.9314	−0.923874
$141$	−2.00320	−0.168700
$142$	−10.3207	−0.866094
$143$	0.444418	0.0371641
$144$	−1.73493	−0.144577
$145$	27.4555	2.28005
$146$	−0.561562	−0.0464752
$147$	−4.14477	−0.341855
$148$	−2.06947	−0.170110
$149$	9.29642	0.761592	0.380796	−	0.924659i	$-0.375650\pi$
$149$	9.29642	0.761592	0.380796	+	0.924659i	$0.375650\pi$
$150$	6.45981	0.527442
$151$	−8.26936	−0.672951	−0.336475	−	0.941692i	$-0.609235\pi$
$151$	−8.26936	−0.672951	−0.336475	+	0.941692i	$0.609235\pi$
$152$	0.278074	0.0225547
$153$	2.53893	0.205261
$154$	−4.32276	−0.348338
$155$	8.16223	0.655606
$156$	1.58350	0.126781
$157$	−13.5257	−1.07946	−0.539732	−	0.841837i	$-0.681475\pi$
$157$	−13.5257	−1.07946	−0.539732	+	0.841837i	$0.681475\pi$
$158$	29.2560	2.32748
$159$	−7.69621	−0.610349
$160$	−20.5863	−1.62749
$161$	20.0177	1.57761
$162$	−19.9780	−1.56962
$163$	−12.9831	−1.01692	−0.508458	−	0.861087i	$-0.669784\pi$
$163$	−12.9831	−1.01692	−0.508458	+	0.861087i	$0.669784\pi$
$164$	2.52072	0.196835
$165$	4.80859	0.374348
$166$	30.2483	2.34772
$167$	−21.3647	−1.65325	−0.826624	−	0.562755i	$-0.809742\pi$
$167$	−21.3647	−1.65325	−0.826624	+	0.562755i	$0.809742\pi$
$168$	0.583675	0.0450315
$169$	−12.8025	−0.984807
$170$	31.2279	2.39507
$171$	−0.805149	−0.0615713
$172$	−24.1332	−1.84014
$173$	13.8496	1.05297	0.526483	−	0.850186i	$-0.323510\pi$
$173$	13.8496	1.05297	0.526483	+	0.850186i	$0.323510\pi$
$174$	38.6847	2.93268
$175$	−3.84569	−0.290707
$176$	−4.14071	−0.312118
$177$	15.2421	1.14567
$178$	32.3054	2.42139
$179$	−1.03648	−0.0774700	−0.0387350	−	0.999250i	$-0.512333\pi$
$179$	−1.03648	−0.0774700	−0.0387350	+	0.999250i	$0.512333\pi$
$180$	2.09967	0.156500
$181$	−13.2287	−0.983281	−0.491640	−	0.870798i	$-0.663603\pi$
$181$	−13.2287	−0.983281	−0.491640	+	0.870798i	$0.663603\pi$
$182$	−1.92111	−0.142402
$183$	−1.84905	−0.136686
$184$	1.32792	0.0978954
$185$	−2.79288	−0.205336
$186$	11.5006	0.843262
$187$	6.05961	0.443123
$188$	−2.08762	−0.152256
$189$	10.4105	0.757250
$190$	−9.90302	−0.718440
$191$	−8.86840	−0.641695	−0.320848	−	0.947131i	$-0.603968\pi$
$191$	−8.86840	−0.641695	−0.320848	+	0.947131i	$0.603968\pi$
$192$	−13.6932	−0.988223
$193$	3.17960	0.228872	0.114436	−	0.993431i	$-0.463494\pi$
$193$	3.17960	0.228872	0.114436	+	0.993431i	$0.463494\pi$
$194$	9.48404	0.680915
$195$	2.13702	0.153035
$196$	−4.31944	−0.308532
$197$	17.0357	1.21374	0.606871	−	0.794801i	$-0.292425\pi$
$197$	17.0357	1.21374	0.606871	+	0.794801i	$0.292425\pi$
$198$	0.830301	0.0590069
$199$	27.9216	1.97931	0.989656	−	0.143458i	$-0.0458221\pi$
$199$	27.9216	1.97931	0.989656	+	0.143458i	$0.0458221\pi$
$200$	−0.255112	−0.0180392
$201$	−19.0191	−1.34150
$202$	7.28480	0.512557
$203$	−23.0299	−1.61638
$204$	21.5909	1.51166
$205$	3.40185	0.237596
$206$	17.5939	1.22582
$207$	−3.84493	−0.267241
$208$	−1.84021	−0.127596
$209$	−1.92163	−0.132922
$210$	−20.7864	−1.43440
$211$	14.8812	1.02446	0.512232	−	0.858847i	$-0.328819\pi$
$211$	14.8812	1.02446	0.512232	+	0.858847i	$0.328819\pi$
$212$	−8.02056	−0.550854
$213$	−9.63006	−0.659841
$214$	7.71084	0.527102
$215$	−32.5691	−2.22120
$216$	0.690602	0.0469895
$217$	−6.84656	−0.464775
$218$	−16.9028	−1.14480
$219$	−0.523984	−0.0354076
$220$	5.01124	0.337857
$221$	2.69300	0.181151
$222$	−3.93515	−0.264110
$223$	24.3925	1.63344	0.816722	−	0.577032i	$-0.195789\pi$
$223$	24.3925	1.63344	0.816722	+	0.577032i	$0.195789\pi$
$224$	17.2680	1.15377
$225$	0.738666	0.0492444
$226$	19.3383	1.28637
$227$	−4.57809	−0.303859	−0.151929	−	0.988391i	$-0.548549\pi$
$227$	−4.57809	−0.303859	−0.151929	+	0.988391i	$0.548549\pi$
$228$	−6.84693	−0.453449
$229$	−16.3940	−1.08335	−0.541673	−	0.840589i	$-0.682209\pi$
$229$	−16.3940	−1.08335	−0.541673	+	0.840589i	$0.682209\pi$
$230$	−47.2911	−3.11828
$231$	−4.03349	−0.265384
$232$	−1.52774	−0.100301
$233$	10.0688	0.659626	0.329813	−	0.944046i	$-0.393014\pi$
$233$	10.0688	0.659626	0.329813	+	0.944046i	$0.393014\pi$
$234$	0.369001	0.0241223
$235$	−2.81737	−0.183785
$236$	15.8845	1.03399
$237$	27.2982	1.77321
$238$	−26.1943	−1.69792
$239$	8.26608	0.534688	0.267344	−	0.963601i	$-0.413854\pi$
$239$	8.26608	0.534688	0.267344	+	0.963601i	$0.413854\pi$
$240$	−19.9110	−1.28525
$241$	1.52656	0.0983343	0.0491672	−	0.998791i	$-0.484343\pi$
$241$	1.52656	0.0983343	0.0491672	+	0.998791i	$0.484343\pi$
$242$	1.98166	0.127386
$243$	−4.32382	−0.277373
$244$	−1.92698	−0.123362
$245$	−5.82934	−0.372423
$246$	4.79320	0.305603
$247$	−0.854008	−0.0543392
$248$	−0.454182	−0.0288406
$249$	28.2242	1.78863
$250$	−16.6819	−1.05506
$251$	21.1073	1.33228	0.666142	−	0.745825i	$-0.267945\pi$
$251$	21.1073	1.33228	0.666142	+	0.745825i	$0.267945\pi$
$252$	−1.76123	−0.110947
$253$	−9.17660	−0.576928
$254$	−40.6341	−2.54961
$255$	29.1382	1.82470
$256$	17.1036	1.06898
$257$	8.94976	0.558271	0.279135	−	0.960252i	$-0.409952\pi$
$257$	8.94976	0.558271	0.279135	+	0.960252i	$0.409952\pi$
$258$	−45.8898	−2.85697
$259$	2.34269	0.145568
$260$	2.22708	0.138118
$261$	4.42351	0.273808
$262$	26.2846	1.62387
$263$	−29.0355	−1.79041	−0.895204	−	0.445657i	$-0.852970\pi$
$263$	−29.0355	−1.79041	−0.895204	+	0.445657i	$0.852970\pi$
$264$	−0.267571	−0.0164678
$265$	−10.8242	−0.664926
$266$	8.30675	0.509320
$267$	30.1436	1.84476
$268$	−19.8206	−1.21074
$269$	−0.271779	−0.0165706	−0.00828532	−	0.999966i	$-0.502637\pi$
$269$	−0.271779	−0.0165706	−0.00828532	+	0.999966i	$0.502637\pi$
$270$	−24.5944	−1.49677
$271$	−9.91921	−0.602549	−0.301275	−	0.953537i	$-0.597412\pi$
$271$	−9.91921	−0.602549	−0.301275	+	0.953537i	$0.597412\pi$
$272$	−25.0911	−1.52137
$273$	−1.79256	−0.108491
$274$	−17.8438	−1.07798
$275$	1.76296	0.106310
$276$	−32.6969	−1.96812
$277$	−2.47418	−0.148659	−0.0743295	−	0.997234i	$-0.523682\pi$
$277$	−2.47418	−0.148659	−0.0743295	+	0.997234i	$0.523682\pi$
$278$	30.5716	1.83356
$279$	1.31506	0.0787308
$280$	0.820900	0.0490581
$281$	−12.2927	−0.733321	−0.366660	−	0.930355i	$-0.619499\pi$
$281$	−12.2927	−0.733321	−0.366660	+	0.930355i	$0.619499\pi$
$282$	−3.96967	−0.236390
$283$	12.7133	0.755725	0.377862	−	0.925862i	$-0.376659\pi$
$283$	12.7133	0.755725	0.377862	+	0.925862i	$0.376659\pi$
$284$	−10.0359	−0.595521
$285$	−9.24033	−0.547350
$286$	0.880686	0.0520761
$287$	−2.85351	−0.168437
$288$	−3.31678	−0.195443
$289$	19.7189	1.15994
$290$	54.4074	3.19491
$291$	8.84939	0.518760
$292$	−0.546066	−0.0319561
$293$	−10.1272	−0.591637	−0.295818	−	0.955244i	$-0.595592\pi$
$293$	−10.1272	−0.591637	−0.295818	+	0.955244i	$0.595592\pi$
$294$	−8.21352	−0.479022
$295$	21.4370	1.24811
$296$	0.155408	0.00903290
$297$	−4.77242	−0.276924
$298$	18.4223	1.06718
$299$	−4.07825	−0.235851
$300$	6.28156	0.362666
$301$	27.3193	1.57466
$302$	−16.3871	−0.942969
$303$	6.79731	0.390496
$304$	7.95692	0.456361
$305$	−2.60057	−0.148908
$306$	5.03130	0.287620
$307$	−4.15427	−0.237097	−0.118548	−	0.992948i	$-0.537824\pi$
$307$	−4.15427	−0.237097	−0.118548	+	0.992948i	$0.537824\pi$
$308$	−4.20348	−0.239515
$309$	16.4165	0.933904
$310$	16.1748	0.918665
$311$	10.2275	0.579948	0.289974	−	0.957035i	$-0.406353\pi$
$311$	10.2275	0.579948	0.289974	+	0.957035i	$0.406353\pi$
$312$	−0.118913	−0.00673214
$313$	−8.72686	−0.493271	−0.246636	−	0.969108i	$-0.579325\pi$
$313$	−8.72686	−0.493271	−0.246636	+	0.969108i	$0.579325\pi$
$314$	−26.8033	−1.51260
$315$	−2.37688	−0.133922
$316$	28.4487	1.60036
$317$	−0.569591	−0.0319914	−0.0159957	−	0.999872i	$-0.505092\pi$
$317$	−0.569591	−0.0319914	−0.0159957	+	0.999872i	$0.505092\pi$
$318$	−15.2513	−0.855249
$319$	10.5575	0.591106
$320$	−19.2586	−1.07659
$321$	7.19485	0.401577
$322$	39.6682	2.21062
$323$	−11.6443	−0.647908
$324$	−19.4267	−1.07926
$325$	0.783490	0.0434602
$326$	−25.7281	−1.42495
$327$	−15.7717	−0.872178
$328$	−0.189294	−0.0104520
$329$	2.36324	0.130290
$330$	9.52898	0.524553
$331$	−20.0001	−1.09930	−0.549652	−	0.835394i	$-0.685240\pi$
$331$	−20.0001	−1.09930	−0.549652	+	0.835394i	$0.685240\pi$
$332$	29.4136	1.61428
$333$	−0.449976	−0.0246586
$334$	−42.3375	−2.31661
$335$	−26.7491	−1.46146
$336$	16.7015	0.911143
$337$	27.7992	1.51432	0.757161	−	0.653229i	$-0.226586\pi$
$337$	27.7992	1.51432	0.757161	+	0.653229i	$0.226586\pi$
$338$	−25.3702	−1.37996
$339$	18.0443	0.980030
$340$	30.3661	1.64684
$341$	3.13863	0.169966
$342$	−1.59553	−0.0862765
$343$	20.1594	1.08851
$344$	1.81229	0.0977121
$345$	−44.1264	−2.37569
$346$	27.4452	1.47546
$347$	14.0784	0.755770	0.377885	−	0.925853i	$-0.376651\pi$
$347$	14.0784	0.755770	0.377885	+	0.925853i	$0.376651\pi$
$348$	37.6172	2.01649
$349$	26.9981	1.44517	0.722586	−	0.691281i	$-0.242953\pi$
$349$	26.9981	1.44517	0.722586	+	0.691281i	$0.242953\pi$
$350$	−7.62084	−0.407351
$351$	−2.12095	−0.113208
$352$	−7.91607	−0.421928
$353$	−7.06670	−0.376122	−0.188061	−	0.982157i	$-0.560220\pi$
$353$	−7.06670	−0.376122	−0.188061	+	0.982157i	$0.560220\pi$
$354$	30.2047	1.60536
$355$	−13.5440	−0.718843
$356$	31.4140	1.66494
$357$	−24.4414	−1.29358
$358$	−2.05395	−0.108554
$359$	−1.11238	−0.0587090	−0.0293545	−	0.999569i	$-0.509345\pi$
$359$	−1.11238	−0.0587090	−0.0293545	+	0.999569i	$0.509345\pi$
$360$	−0.157676	−0.00831023
$361$	−15.3073	−0.805649
$362$	−26.2148	−1.37782
$363$	1.84905	0.0970501
$364$	−1.86810	−0.0979151
$365$	−0.736949	−0.0385737
$366$	−3.66419	−0.191530
$367$	−15.6511	−0.816979	−0.408489	−	0.912763i	$-0.633944\pi$
$367$	−15.6511	−0.816979	−0.408489	+	0.912763i	$0.633944\pi$
$368$	37.9977	1.98076
$369$	0.548092	0.0285325
$370$	−5.53453	−0.287727
$371$	9.07946	0.471382
$372$	11.1832	0.579822
$373$	−8.11997	−0.420436	−0.210218	−	0.977655i	$-0.567417\pi$
$373$	−8.11997	−0.420436	−0.210218	+	0.977655i	$0.567417\pi$
$374$	12.0081	0.620924
$375$	−15.5656	−0.803804
$376$	0.156771	0.00808484
$377$	4.69194	0.241647
$378$	20.6300	1.06109
$379$	35.5452	1.82583	0.912917	−	0.408145i	$-0.133824\pi$
$379$	35.5452	1.82583	0.912917	+	0.408145i	$0.133824\pi$
$380$	−9.62975	−0.493996
$381$	−37.9149	−1.94244
$382$	−17.5742	−0.899172
$383$	25.4279	1.29931	0.649653	−	0.760231i	$-0.274914\pi$
$383$	25.4279	1.29931	0.649653	+	0.760231i	$0.274914\pi$
$384$	2.13914	0.109163
$385$	−5.67284	−0.289115
$386$	6.30088	0.320706
$387$	−5.24740	−0.266740
$388$	9.22233	0.468193
$389$	−2.40965	−0.122174	−0.0610872	−	0.998132i	$-0.519457\pi$
$389$	−2.40965	−0.122174	−0.0610872	+	0.998132i	$0.519457\pi$
$390$	4.23485	0.214440
$391$	−55.6066	−2.81215
$392$	0.324370	0.0163832
$393$	24.5257	1.23716
$394$	33.7589	1.70075
$395$	38.3932	1.93177
$396$	0.807389	0.0405728
$397$	8.86157	0.444750	0.222375	−	0.974961i	$-0.428619\pi$
$397$	8.86157	0.444750	0.222375	+	0.974961i	$0.428619\pi$
$398$	55.3312	2.77350
$399$	7.75088	0.388029
$400$	−7.29990	−0.364995
$401$	−23.3978	−1.16843	−0.584214	−	0.811600i	$-0.698597\pi$
$401$	−23.3978	−1.16843	−0.584214	+	0.811600i	$0.698597\pi$
$402$	−37.6894	−1.87978
$403$	1.39487	0.0694832
$404$	7.08378	0.352431
$405$	−26.2174	−1.30275
$406$	−45.6375	−2.26495
$407$	−1.07395	−0.0532337
$408$	−1.62138	−0.0802700
$409$	−18.4508	−0.912336	−0.456168	−	0.889894i	$-0.650778\pi$
$409$	−18.4508	−0.912336	−0.456168	+	0.889894i	$0.650778\pi$
$410$	6.74132	0.332930
$411$	−16.6497	−0.821270
$412$	17.1084	0.842870
$413$	−17.9816	−0.884816
$414$	−7.61933	−0.374470
$415$	39.6954	1.94857
$416$	−3.51805	−0.172486
$417$	28.5258	1.39692
$418$	−3.80802	−0.186256
$419$	−22.7893	−1.11333	−0.556665	−	0.830737i	$-0.687919\pi$
$419$	−22.7893	−1.11333	−0.556665	+	0.830737i	$0.687919\pi$
$420$	−20.2128	−0.986283
$421$	16.9851	0.827802	0.413901	−	0.910322i	$-0.364166\pi$
$421$	16.9851	0.827802	0.413901	+	0.910322i	$0.364166\pi$
$422$	29.4895	1.43553
$423$	−0.453923	−0.0220705
$424$	0.602307	0.0292506
$425$	10.6828	0.518194
$426$	−19.0835	−0.924599
$427$	2.18138	0.105565
$428$	7.49806	0.362432
$429$	0.821752	0.0396746
$430$	−64.5409	−3.11244
$431$	−26.8912	−1.29531	−0.647653	−	0.761936i	$-0.724249\pi$
$431$	−26.8912	−1.29531	−0.647653	+	0.761936i	$0.724249\pi$
$432$	19.7612	0.950762
$433$	−4.94690	−0.237733	−0.118866	−	0.992910i	$-0.537926\pi$
$433$	−4.94690	−0.237733	−0.118866	+	0.992910i	$0.537926\pi$
$434$	−13.5676	−0.651264
$435$	50.7666	2.43407
$436$	−16.4364	−0.787160
$437$	17.6340	0.843550
$438$	−1.03836	−0.0496147
$439$	−16.1331	−0.769989	−0.384995	−	0.922919i	$-0.625797\pi$
$439$	−16.1331	−0.769989	−0.384995	+	0.922919i	$0.625797\pi$
$440$	−0.376321	−0.0179404
$441$	−0.939199	−0.0447237
$442$	5.33662	0.253837
$443$	19.9786	0.949213	0.474607	−	0.880198i	$-0.342590\pi$
$443$	19.9786	0.949213	0.474607	+	0.880198i	$0.342590\pi$
$444$	−3.82656	−0.181601
$445$	42.3950	2.00972
$446$	48.3377	2.28886
$447$	17.1896	0.813038
$448$	16.1543	0.763220
$449$	3.49232	0.164813	0.0824064	−	0.996599i	$-0.473739\pi$
$449$	3.49232	0.164813	0.0824064	+	0.996599i	$0.473739\pi$
$450$	1.46378	0.0690035
$451$	1.30812	0.0615969
$452$	18.8047	0.884499
$453$	−15.2905	−0.718409
$454$	−9.07222	−0.425780
$455$	−2.52111	−0.118192
$456$	0.514172	0.0240783
$457$	−8.64120	−0.404218	−0.202109	−	0.979363i	$-0.564780\pi$
$457$	−8.64120	−0.404218	−0.202109	+	0.979363i	$0.564780\pi$
$458$	−32.4873	−1.51803
$459$	−28.9190	−1.34982
$460$	−45.9861	−2.14411
$461$	3.04671	0.141899	0.0709497	−	0.997480i	$-0.477397\pi$
$461$	3.04671	0.141899	0.0709497	+	0.997480i	$0.477397\pi$
$462$	−7.99301	−0.371868
$463$	−8.03359	−0.373353	−0.186676	−	0.982421i	$-0.559772\pi$
$463$	−8.03359	−0.373353	−0.186676	+	0.982421i	$0.559772\pi$
$464$	−43.7155	−2.02944
$465$	15.0924	0.699893
$466$	19.9528	0.924298
$467$	12.0195	0.556195	0.278098	−	0.960553i	$-0.410296\pi$
$467$	12.0195	0.556195	0.278098	+	0.960553i	$0.410296\pi$
$468$	0.358818	0.0165864
$469$	22.4374	1.03606
$470$	−5.58307	−0.257528
$471$	−25.0096	−1.15238
$472$	−1.19285	−0.0549054
$473$	−12.5238	−0.575847
$474$	54.0958	2.48470
$475$	−3.38775	−0.155441
$476$	−25.4714	−1.16748
$477$	−1.74395	−0.0798500
$478$	16.3806	0.749230
$479$	−21.3120	−0.973768	−0.486884	−	0.873467i	$-0.661867\pi$
$479$	−21.3120	−0.973768	−0.486884	+	0.873467i	$0.661867\pi$
$480$	−38.0651	−1.73743
$481$	−0.477282	−0.0217622
$482$	3.02512	0.137791
$483$	37.0137	1.68418
$484$	1.92698	0.0875899
$485$	12.4461	0.565147
$486$	−8.56835	−0.388668
$487$	−37.5771	−1.70278	−0.851391	−	0.524532i	$-0.824240\pi$
$487$	−37.5771	−1.70278	−0.851391	+	0.524532i	$0.824240\pi$
$488$	0.144707	0.00655058
$489$	−24.0064	−1.08561
$490$	−11.5518	−0.521856
$491$	−34.9908	−1.57911	−0.789557	−	0.613677i	$-0.789690\pi$
$491$	−34.9908	−1.57911	−0.789557	+	0.613677i	$0.789690\pi$
$492$	4.66093	0.210131
$493$	63.9743	2.88126
$494$	−1.69235	−0.0761426
$495$	1.08962	0.0489747
$496$	−12.9962	−0.583546
$497$	11.3609	0.509605
$498$	55.9307	2.50631
$499$	33.3039	1.49089	0.745445	−	0.666568i	$-0.232237\pi$
$499$	33.3039	1.49089	0.745445	+	0.666568i	$0.232237\pi$
$500$	−16.2216	−0.725451
$501$	−39.5044	−1.76493
$502$	41.8276	1.86686
$503$	5.22511	0.232976	0.116488	−	0.993192i	$-0.462836\pi$
$503$	5.22511	0.232976	0.116488	+	0.993192i	$0.462836\pi$
$504$	0.132260	0.00589132
$505$	9.55997	0.425413
$506$	−18.1849	−0.808417
$507$	−23.6725	−1.05133
$508$	−39.5128	−1.75310
$509$	−22.3134	−0.989026	−0.494513	−	0.869170i	$-0.664654\pi$
$509$	−22.3134	−0.989026	−0.494513	+	0.869170i	$0.664654\pi$
$510$	57.7419	2.55686
$511$	0.618160	0.0273458
$512$	31.5798	1.39564
$513$	9.17082	0.404902
$514$	17.7354	0.782274
$515$	23.0888	1.01741
$516$	−44.6235	−1.96444
$517$	−1.08337	−0.0476465
$518$	4.64242	0.203976
$519$	25.6086	1.12409
$520$	−0.167244	−0.00733412
$521$	6.24416	0.273562	0.136781	−	0.990601i	$-0.456324\pi$
$521$	6.24416	0.273562	0.136781	+	0.990601i	$0.456324\pi$
$522$	8.76589	0.383673
$523$	−12.1521	−0.531372	−0.265686	−	0.964060i	$-0.585598\pi$
$523$	−12.1521	−0.531372	−0.265686	+	0.964060i	$0.585598\pi$
$524$	25.5593	1.11656
$525$	−7.11087	−0.310344
$526$	−57.5386	−2.50880
$527$	19.0189	0.828476
$528$	−7.65639	−0.333202
$529$	61.2099	2.66130
$530$	−21.4499	−0.931725
$531$	3.45384	0.149884
$532$	8.07753	0.350205
$533$	0.581352	0.0251812
$534$	59.7344	2.58496
$535$	10.1191	0.437486
$536$	1.48844	0.0642907
$537$	−1.91650	−0.0827031
$538$	−0.538573	−0.0232195
$539$	−2.24156	−0.0965510
$540$	−23.9157	−1.02917
$541$	−16.4664	−0.707946	−0.353973	−	0.935256i	$-0.615170\pi$
$541$	−16.4664	−0.707946	−0.353973	+	0.935256i	$0.615170\pi$
$542$	−19.6565	−0.844319
$543$	−24.4605	−1.04970
$544$	−47.9683	−2.05663
$545$	−22.1819	−0.950167
$546$	−3.55224	−0.152022
$547$	5.93546	0.253782	0.126891	−	0.991917i	$-0.459500\pi$
$547$	5.93546	0.253782	0.126891	+	0.991917i	$0.459500\pi$
$548$	−17.3514	−0.741215
$549$	−0.418993	−0.0178822
$550$	3.49358	0.148967
$551$	−20.2876	−0.864281
$552$	2.45539	0.104508
$553$	−32.2046	−1.36948
$554$	−4.90298	−0.208308
$555$	−5.16417	−0.219207
$556$	29.7280	1.26075
$557$	11.3990	0.482990	0.241495	−	0.970402i	$-0.422362\pi$
$557$	11.3990	0.482990	0.241495	+	0.970402i	$0.422362\pi$
$558$	2.60601	0.110321
$559$	−5.56583	−0.235409
$560$	23.4896	0.992617
$561$	11.2045	0.473056
$562$	−24.3599	−1.02756
$563$	−26.2922	−1.10808	−0.554042	−	0.832489i	$-0.686915\pi$
$563$	−26.2922	−1.10808	−0.554042	+	0.832489i	$0.686915\pi$
$564$	−3.86013	−0.162541
$565$	25.3781	1.06766
$566$	25.1934	1.05896
$567$	21.9915	0.923554
$568$	0.753650	0.0316225
$569$	−40.8755	−1.71359	−0.856795	−	0.515658i	$-0.827548\pi$
$569$	−40.8755	−1.71359	−0.856795	+	0.515658i	$0.827548\pi$
$570$	−18.3112	−0.766971
$571$	3.13722	0.131288	0.0656442	−	0.997843i	$-0.479090\pi$
$571$	3.13722	0.131288	0.0656442	+	0.997843i	$0.479090\pi$
$572$	0.856384	0.0358072
$573$	−16.3981	−0.685042
$574$	−5.65469	−0.236022
$575$	−16.1779	−0.674667
$576$	−3.10287	−0.129286
$577$	35.1099	1.46164	0.730822	−	0.682569i	$-0.239137\pi$
$577$	35.1099	1.46164	0.730822	+	0.682569i	$0.239137\pi$
$578$	39.0762	1.62535
$579$	5.87924	0.244333
$580$	52.9060	2.19680
$581$	−33.2969	−1.38139
$582$	17.5365	0.726911
$583$	−4.16225	−0.172383
$584$	0.0410071	0.00169688
$585$	0.484247	0.0200211
$586$	−20.0686	−0.829028
$587$	−11.7853	−0.486430	−0.243215	−	0.969972i	$-0.578202\pi$
$587$	−11.7853	−0.486430	−0.243215	+	0.969972i	$0.578202\pi$
$588$	−7.98687	−0.329373
$589$	−6.03129	−0.248515
$590$	42.4809	1.74891
$591$	31.4998	1.29573
$592$	4.44691	0.182767
$593$	−14.0578	−0.577284	−0.288642	−	0.957437i	$-0.593204\pi$
$593$	−14.0578	−0.577284	−0.288642	+	0.957437i	$0.593204\pi$
$594$	−9.45731	−0.388038
$595$	−34.3752	−1.40925
$596$	17.9140	0.733785
$597$	51.6286	2.11302
$598$	−8.08170	−0.330485
$599$	−23.2077	−0.948243	−0.474121	−	0.880460i	$-0.657234\pi$
$599$	−23.2077	−0.948243	−0.474121	+	0.880460i	$0.657234\pi$
$600$	−0.471716	−0.0192577
$601$	−9.72040	−0.396503	−0.198252	−	0.980151i	$-0.563526\pi$
$601$	−9.72040	−0.396503	−0.198252	+	0.980151i	$0.563526\pi$
$602$	54.1376	2.20648
$603$	−4.30970	−0.175505
$604$	−15.9349	−0.648380
$605$	2.60057	0.105728
$606$	13.4700	0.547180
$607$	−26.1875	−1.06292	−0.531459	−	0.847084i	$-0.678356\pi$
$607$	−26.1875	−1.06292	−0.531459	+	0.847084i	$0.678356\pi$
$608$	15.2118	0.616919
$609$	−42.5835	−1.72557
$610$	−5.15344	−0.208657
$611$	−0.481468	−0.0194781
$612$	4.89246	0.197766
$613$	−1.59718	−0.0645094	−0.0322547	−	0.999480i	$-0.510269\pi$
$613$	−1.59718	−0.0645094	−0.0322547	+	0.999480i	$0.510269\pi$
$614$	−8.23234	−0.332230
$615$	6.29021	0.253646
$616$	0.315662	0.0127184
$617$	−4.95280	−0.199392	−0.0996962	−	0.995018i	$-0.531787\pi$
$617$	−4.95280	−0.199392	−0.0996962	+	0.995018i	$0.531787\pi$
$618$	32.5320	1.30863
$619$	19.6334	0.789132	0.394566	−	0.918868i	$-0.370895\pi$
$619$	19.6334	0.789132	0.394566	+	0.918868i	$0.370895\pi$
$620$	15.7284	0.631669
$621$	43.7945	1.75741
$622$	20.2674	0.812649
$623$	−35.5614	−1.42474
$624$	−3.40264	−0.136215
$625$	−30.7068	−1.22827
$626$	−17.2937	−0.691194
$627$	−3.55320	−0.141901
$628$	−26.0636	−1.04005
$629$	−6.50771	−0.259479
$630$	−4.71016	−0.187657
$631$	15.1352	0.602521	0.301261	−	0.953542i	$-0.402593\pi$
$631$	15.1352	0.602521	0.301261	+	0.953542i	$0.402593\pi$
$632$	−2.13636	−0.0849800
$633$	27.5161	1.09367
$634$	−1.12874	−0.0448278
$635$	−53.3248	−2.11613
$636$	−14.8304	−0.588065
$637$	−0.996192	−0.0394706
$638$	20.9213	0.828284
$639$	−2.18216	−0.0863249
$640$	3.00856	0.118924
$641$	−40.4127	−1.59621	−0.798104	−	0.602520i	$-0.794163\pi$
$641$	−40.4127	−1.59621	−0.798104	+	0.602520i	$0.794163\pi$
$642$	14.2577	0.562708
$643$	−16.3198	−0.643589	−0.321794	−	0.946810i	$-0.604286\pi$
$643$	−16.3198	−0.643589	−0.321794	+	0.946810i	$0.604286\pi$
$644$	38.5736	1.52001
$645$	−60.2220	−2.37124
$646$	−23.0751	−0.907878
$647$	−22.2041	−0.872933	−0.436466	−	0.899721i	$-0.643770\pi$
$647$	−22.2041	−0.872933	−0.436466	+	0.899721i	$0.643770\pi$
$648$	1.45885	0.0573092
$649$	8.24320	0.323574
$650$	1.55261	0.0608984
$651$	−12.6596	−0.496171
$652$	−25.0182	−0.979787
$653$	15.9029	0.622327	0.311163	−	0.950356i	$-0.399281\pi$
$653$	15.9029	0.622327	0.311163	+	0.950356i	$0.399281\pi$
$654$	−31.2542	−1.22214
$655$	34.4937	1.34778
$656$	−5.41655	−0.211481
$657$	−0.118734	−0.00463226
$658$	4.68314	0.182568
$659$	2.35249	0.0916402	0.0458201	−	0.998950i	$-0.485410\pi$
$659$	2.35249	0.0916402	0.0458201	+	0.998950i	$0.485410\pi$
$660$	9.26603	0.360680
$661$	−31.3644	−1.21994	−0.609968	−	0.792426i	$-0.708818\pi$
$661$	−31.3644	−1.21994	−0.609968	+	0.792426i	$0.708818\pi$
$662$	−39.6333	−1.54039
$663$	4.97950	0.193388
$664$	−2.20883	−0.0857191
$665$	10.9011	0.422727
$666$	−0.891700	−0.0345527
$667$	−96.8818	−3.75128
$668$	−41.1692	−1.59289
$669$	45.1030	1.74378
$670$	−53.0076	−2.04786
$671$	−1.00000	−0.0386046
$672$	31.9294	1.23170
$673$	−33.8125	−1.30338	−0.651688	−	0.758487i	$-0.725939\pi$
$673$	−33.8125	−1.30338	−0.651688	+	0.758487i	$0.725939\pi$
$674$	55.0886	2.12194
$675$	−8.41357	−0.323838
$676$	−24.6701	−0.948850
$677$	19.5191	0.750180	0.375090	−	0.926988i	$-0.377612\pi$
$677$	19.5191	0.750180	0.375090	+	0.926988i	$0.377612\pi$
$678$	35.7576	1.37326
$679$	−10.4399	−0.400647
$680$	−2.28036	−0.0874477
$681$	−8.46513	−0.324384
$682$	6.21970	0.238165
$683$	−34.3022	−1.31254	−0.656268	−	0.754528i	$-0.727866\pi$
$683$	−34.3022	−1.31254	−0.656268	+	0.754528i	$0.727866\pi$
$684$	−1.55150	−0.0593232
$685$	−23.4167	−0.894707
$686$	39.9491	1.52526
$687$	−30.3133	−1.15653
$688$	51.8577	1.97705
$689$	−1.84978	−0.0704710
$690$	−87.4436	−3.32892
$691$	−11.5937	−0.441046	−0.220523	−	0.975382i	$-0.570776\pi$
$691$	−11.5937	−0.441046	−0.220523	+	0.975382i	$0.570776\pi$
$692$	26.6879	1.01452
$693$	−0.913984	−0.0347194
$694$	27.8987	1.05902
$695$	40.1197	1.52183
$696$	−2.82488	−0.107077
$697$	7.92670	0.300245
$698$	53.5010	2.02504
$699$	18.6176	0.704184
$700$	−7.41055	−0.280092
$701$	6.50743	0.245782	0.122891	−	0.992420i	$-0.460783\pi$
$701$	6.50743	0.245782	0.122891	+	0.992420i	$0.460783\pi$
$702$	−4.20300	−0.158632
$703$	2.06373	0.0778352
$704$	−7.40554	−0.279107
$705$	−5.20947	−0.196200
$706$	−14.0038	−0.527040
$707$	−8.01900	−0.301586
$708$	29.3712	1.10384
$709$	3.54453	0.133118	0.0665588	−	0.997783i	$-0.478798\pi$
$709$	3.54453	0.133118	0.0665588	+	0.997783i	$0.478798\pi$
$710$	−26.8397	−1.00728
$711$	6.18574	0.231984
$712$	−2.35904	−0.0884089
$713$	−28.8020	−1.07864
$714$	−48.4345	−1.81262
$715$	1.15574	0.0432222
$716$	−1.99727	−0.0746414
$717$	15.2844	0.570807
$718$	−2.20435	−0.0822657
$719$	−40.7391	−1.51931	−0.759656	−	0.650325i	$-0.774633\pi$
$719$	−40.7391	−1.51931	−0.759656	+	0.650325i	$0.774633\pi$
$720$	−4.51180	−0.168145
$721$	−19.3671	−0.721269
$722$	−30.3339	−1.12891
$723$	2.82269	0.104977
$724$	−25.4914	−0.947380
$725$	18.6124	0.691247
$726$	3.66419	0.135991
$727$	−34.3861	−1.27531	−0.637654	−	0.770323i	$-0.720095\pi$
$727$	−34.3861	−1.27531	−0.637654	+	0.770323i	$0.720095\pi$
$728$	0.140286	0.00519934
$729$	22.2493	0.824048
$730$	−1.46038	−0.0540512
$731$	−75.8897	−2.80688
$732$	−3.56308	−0.131695
$733$	24.0134	0.886956	0.443478	−	0.896285i	$-0.353744\pi$
$733$	24.0134	0.886956	0.443478	+	0.896285i	$0.353744\pi$
$734$	−31.0151	−1.14479
$735$	−10.7788	−0.397580
$736$	72.6426	2.67764
$737$	−10.2859	−0.378885
$738$	1.08613	0.0399811
$739$	49.5917	1.82426	0.912131	−	0.409899i	$-0.134436\pi$
$739$	49.5917	1.82426	0.912131	+	0.409899i	$0.134436\pi$
$740$	−5.38181	−0.197839
$741$	−1.57910	−0.0580099
$742$	17.9924	0.660522
$743$	−13.9582	−0.512075	−0.256038	−	0.966667i	$-0.582417\pi$
$743$	−13.9582	−0.512075	−0.256038	+	0.966667i	$0.582417\pi$
$744$	−0.839807	−0.0307888
$745$	24.1760	0.885739
$746$	−16.0910	−0.589134
$747$	6.39555	0.234001
$748$	11.6767	0.426944
$749$	−8.48799	−0.310144
$750$	−30.8457	−1.12633
$751$	6.81173	0.248564	0.124282	−	0.992247i	$-0.460337\pi$
$751$	6.81173	0.248564	0.124282	+	0.992247i	$0.460337\pi$
$752$	4.48592	0.163584
$753$	39.0286	1.42228
$754$	9.29783	0.338607
$755$	−21.5050	−0.782648
$756$	20.0607	0.729602
$757$	21.4347	0.779057	0.389529	−	0.921014i	$-0.372638\pi$
$757$	21.4347	0.779057	0.389529	+	0.921014i	$0.372638\pi$
$758$	70.4385	2.55844
$759$	−16.9680	−0.615899
$760$	0.723149	0.0262314
$761$	25.6533	0.929931	0.464965	−	0.885329i	$-0.346067\pi$
$761$	25.6533	0.929931	0.464965	+	0.885329i	$0.346067\pi$
$762$	−75.1345	−2.72184
$763$	18.6064	0.673596
$764$	−17.0892	−0.618266
$765$	6.60267	0.238720
$766$	50.3895	1.82065
$767$	3.66343	0.132279
$768$	31.6255	1.14119
$769$	46.6407	1.68191	0.840953	−	0.541108i	$-0.181995\pi$
$769$	46.6407	1.68191	0.840953	+	0.541108i	$0.181995\pi$
$770$	−11.2416	−0.405121
$771$	16.5486	0.595982
$772$	6.12701	0.220516
$773$	−25.4354	−0.914849	−0.457425	−	0.889248i	$-0.651228\pi$
$773$	−25.4354	−0.914849	−0.457425	+	0.889248i	$0.651228\pi$
$774$	−10.3986	−0.373769
$775$	5.53328	0.198761
$776$	−0.692555	−0.0248613
$777$	4.33176	0.155401
$778$	−4.77512	−0.171196
$779$	−2.51372	−0.0900635
$780$	4.11799	0.147448
$781$	−5.20811	−0.186361
$782$	−110.193	−3.94051
$783$	−50.3847	−1.80060
$784$	9.28168	0.331488
$785$	−35.1744	−1.25543
$786$	48.6015	1.73356
$787$	3.14255	0.112020	0.0560099	−	0.998430i	$-0.482162\pi$
$787$	3.14255	0.112020	0.0560099	+	0.998430i	$0.482162\pi$
$788$	32.8273	1.16943
$789$	−53.6882	−1.91135
$790$	76.0822	2.70688
$791$	−21.2874	−0.756892
$792$	−0.0606312	−0.00215444
$793$	−0.444418	−0.0157818
$794$	17.5606	0.623203
$795$	−20.0145	−0.709842
$796$	53.8044	1.90705
$797$	−24.9086	−0.882309	−0.441155	−	0.897431i	$-0.645431\pi$
$797$	−24.9086	−0.882309	−0.441155	+	0.897431i	$0.645431\pi$
$798$	15.3596	0.543725
$799$	−6.56479	−0.232245
$800$	−13.9557	−0.493408
$801$	6.83050	0.241344
$802$	−46.3664	−1.63725
$803$	−0.283380	−0.0100003
$804$	−36.6494	−1.29252
$805$	52.0573	1.83478
$806$	2.76415	0.0973630
$807$	−0.502533	−0.0176900
$808$	−0.531959	−0.0187142
$809$	−7.32785	−0.257634	−0.128817	−	0.991668i	$-0.541118\pi$
$809$	−7.32785	−0.257634	−0.128817	+	0.991668i	$0.541118\pi$
$810$	−51.9540	−1.82548
$811$	0.404969	0.0142204	0.00711019	−	0.999975i	$-0.497737\pi$
$811$	0.404969	0.0142204	0.00711019	+	0.999975i	$0.497737\pi$
$812$	−44.3781	−1.55737
$813$	−18.3411	−0.643252
$814$	−2.12820	−0.0745934
$815$	−33.7635	−1.18268
$816$	−46.3948	−1.62414
$817$	24.0662	0.841970
$818$	−36.5633	−1.27841
$819$	−0.406191	−0.0141935
$820$	6.55530	0.228921
$821$	−2.92173	−0.101969	−0.0509846	−	0.998699i	$-0.516236\pi$
$821$	−2.92173	−0.101969	−0.0509846	+	0.998699i	$0.516236\pi$
$822$	−32.9941	−1.15080
$823$	33.2014	1.15733	0.578665	−	0.815566i	$-0.303574\pi$
$823$	33.2014	1.15733	0.578665	+	0.815566i	$0.303574\pi$
$824$	−1.28476	−0.0447568
$825$	3.25980	0.113492
$826$	−35.6334	−1.23984
$827$	37.3203	1.29775	0.648877	−	0.760894i	$-0.275239\pi$
$827$	37.3203	1.29775	0.648877	+	0.760894i	$0.275239\pi$
$828$	−7.40908	−0.257483
$829$	−18.7158	−0.650027	−0.325014	−	0.945709i	$-0.605369\pi$
$829$	−18.7158	−0.650027	−0.325014	+	0.945709i	$0.605369\pi$
$830$	78.6628	2.73043
$831$	−4.57489	−0.158701
$832$	−3.29116	−0.114100
$833$	−13.5830	−0.470623
$834$	56.5285	1.95742
$835$	−55.5603	−1.92274
$836$	−3.70294	−0.128069
$837$	−14.9789	−0.517745
$838$	−45.1606	−1.56005
$839$	−0.337085	−0.0116375	−0.00581874	−	0.999983i	$-0.501852\pi$
$839$	−0.337085	−0.0116375	−0.00581874	+	0.999983i	$0.501852\pi$
$840$	1.51789	0.0523720
$841$	82.4605	2.84347
$842$	33.6587	1.15995
$843$	−22.7298	−0.782857
$844$	28.6758	0.987060
$845$	−33.2938	−1.14534
$846$	−0.899521	−0.0309262
$847$	−2.18138	−0.0749532
$848$	17.2347	0.591841
$849$	23.5075	0.806774
$850$	21.1698	0.726117
$851$	9.85519	0.337832
$852$	−18.5569	−0.635749
$853$	−3.30841	−0.113278	−0.0566389	−	0.998395i	$-0.518038\pi$
$853$	−3.30841	−0.113278	−0.0566389	+	0.998395i	$0.518038\pi$
$854$	4.32276	0.147922
$855$	−2.09385	−0.0716080
$856$	−0.563070	−0.0192453
$857$	10.2920	0.351568	0.175784	−	0.984429i	$-0.443754\pi$
$857$	10.2920	0.351568	0.175784	+	0.984429i	$0.443754\pi$
$858$	1.62843	0.0555938
$859$	34.1456	1.16503	0.582517	−	0.812819i	$-0.302068\pi$
$859$	34.1456	1.16503	0.582517	+	0.812819i	$0.302068\pi$
$860$	−62.7599	−2.14010
$861$	−5.27629	−0.179815
$862$	−53.2893	−1.81504
$863$	−40.4513	−1.37698	−0.688489	−	0.725247i	$-0.741726\pi$
$863$	−40.4513	−1.37698	−0.688489	+	0.725247i	$0.741726\pi$
$864$	37.7788	1.28526
$865$	36.0168	1.22461
$866$	−9.80307	−0.333122
$867$	36.4613	1.23829
$868$	−13.1932	−0.447805
$869$	14.7634	0.500813
$870$	100.602	3.41073
$871$	−4.57123	−0.154890
$872$	1.23430	0.0417986
$873$	2.00526	0.0678678
$874$	34.9447	1.18202
$875$	18.3632	0.620790
$876$	−1.00970	−0.0341148
$877$	52.6517	1.77792	0.888960	−	0.457984i	$-0.151428\pi$
$877$	52.6517	1.77792	0.888960	+	0.457984i	$0.151428\pi$
$878$	−31.9703	−1.07894
$879$	−18.7257	−0.631602
$880$	−10.7682	−0.362996
$881$	3.36425	0.113344	0.0566722	−	0.998393i	$-0.481951\pi$
$881$	3.36425	0.113344	0.0566722	+	0.998393i	$0.481951\pi$
$882$	−1.86117	−0.0626689
$883$	−7.82221	−0.263238	−0.131619	−	0.991300i	$-0.542018\pi$
$883$	−7.82221	−0.263238	−0.131619	+	0.991300i	$0.542018\pi$
$884$	5.18935	0.174537
$885$	39.6382	1.33242
$886$	39.5909	1.33008
$887$	26.2867	0.882619	0.441310	−	0.897355i	$-0.354514\pi$
$887$	26.2867	0.882619	0.441310	+	0.897355i	$0.354514\pi$
$888$	0.287357	0.00964308
$889$	44.7294	1.50018
$890$	84.0125	2.81611
$891$	−10.0814	−0.337740
$892$	47.0038	1.57380
$893$	2.08183	0.0696659
$894$	34.0639	1.13927
$895$	−2.69543	−0.0900983
$896$	−2.52361	−0.0843079
$897$	−7.54089	−0.251783
$898$	6.92059	0.230943
$899$	33.1361	1.10515
$900$	1.42339	0.0474464
$901$	−25.2216	−0.840254
$902$	2.59225	0.0863124
$903$	50.5148	1.68103
$904$	−1.41215	−0.0469673
$905$	−34.4021	−1.14356
$906$	−30.3005	−1.00667
$907$	20.4355	0.678551	0.339275	−	0.940687i	$-0.389818\pi$
$907$	20.4355	0.678551	0.339275	+	0.940687i	$0.389818\pi$
$908$	−8.82187	−0.292764
$909$	1.54026	0.0510873
$910$	−4.99599	−0.165615
$911$	−8.55567	−0.283462	−0.141731	−	0.989905i	$-0.545267\pi$
$911$	−8.55567	−0.283462	−0.141731	+	0.989905i	$0.545267\pi$
$912$	14.7128	0.487188
$913$	15.2641	0.505169
$914$	−17.1239	−0.566409
$915$	−4.80859	−0.158967
$916$	−31.5909	−1.04379
$917$	−28.9337	−0.955474
$918$	−57.3076	−1.89143
$919$	−48.6802	−1.60581	−0.802905	−	0.596106i	$-0.796714\pi$
$919$	−48.6802	−1.60581	−0.802905	+	0.596106i	$0.796714\pi$
$920$	3.45334	0.113853
$921$	−7.68145	−0.253113
$922$	6.03754	0.198836
$923$	−2.31458	−0.0761853
$924$	−7.77245	−0.255695
$925$	−1.89333	−0.0622522
$926$	−15.9198	−0.523159
$927$	3.71997	0.122180
$928$	−83.5738	−2.74345
$929$	10.0819	0.330778	0.165389	−	0.986228i	$-0.447112\pi$
$929$	10.0819	0.330778	0.165389	+	0.986228i	$0.447112\pi$
$930$	29.9080	0.980721
$931$	4.30746	0.141171
$932$	19.4023	0.635542
$933$	18.9112	0.619124
$934$	23.8185	0.779366
$935$	15.7584	0.515356
$936$	−0.0269456	−0.000880745 0
$937$	−4.03470	−0.131808	−0.0659039	−	0.997826i	$-0.520993\pi$
$937$	−4.03470	−0.131808	−0.0659039	+	0.997826i	$0.520993\pi$
$938$	44.4633	1.45178
$939$	−16.1364	−0.526592
$940$	−5.42901	−0.177075
$941$	−14.9304	−0.486716	−0.243358	−	0.969937i	$-0.578249\pi$
$941$	−14.9304	−0.486716	−0.243358	+	0.969937i	$0.578249\pi$
$942$	−49.5606	−1.61477
$943$	−12.0041	−0.390907
$944$	−34.1328	−1.11093
$945$	27.0731	0.880690
$946$	−24.8180	−0.806903
$947$	18.6683	0.606639	0.303319	−	0.952889i	$-0.401905\pi$
$947$	18.6683	0.606639	0.303319	+	0.952889i	$0.401905\pi$
$948$	52.6031	1.70847
$949$	−0.125939	−0.00408816
$950$	−6.71338	−0.217811
$951$	−1.05320	−0.0341525
$952$	1.91279	0.0619938
$953$	27.8528	0.902239	0.451120	−	0.892463i	$-0.351025\pi$
$953$	27.8528	0.902239	0.451120	+	0.892463i	$0.351025\pi$
$954$	−3.45592	−0.111890
$955$	−23.0629	−0.746298
$956$	15.9286	0.515166
$957$	19.5213	0.631035
$958$	−42.2331	−1.36449
$959$	19.6422	0.634279
$960$	−35.6102	−1.14931
$961$	−21.1490	−0.682225
$962$	−0.945811	−0.0304942
$963$	1.63034	0.0525370
$964$	2.94164	0.0947440
$965$	8.26876	0.266181
$966$	73.3486	2.35995
$967$	−46.3423	−1.49027	−0.745134	−	0.666915i	$-0.767614\pi$
$967$	−46.3423	−1.49027	−0.745134	+	0.666915i	$0.767614\pi$
$968$	−0.144707	−0.00465106
$969$	−21.5310	−0.691675
$970$	24.6639	0.791910
$971$	−15.7597	−0.505752	−0.252876	−	0.967499i	$-0.581377\pi$
$971$	−15.7597	−0.505752	−0.252876	+	0.967499i	$0.581377\pi$
$972$	−8.33191	−0.267246
$973$	−33.6528	−1.07886
$974$	−74.4650	−2.38601
$975$	1.44871	0.0463960
$976$	4.14071	0.132541
$977$	−10.4959	−0.335792	−0.167896	−	0.985805i	$-0.553697\pi$
$977$	−10.4959	−0.335792	−0.167896	+	0.985805i	$0.553697\pi$
$978$	−47.5726	−1.52120
$979$	16.3022	0.521021
$980$	−11.2330	−0.358825
$981$	−3.57385	−0.114104
$982$	−69.3400	−2.21273
$983$	36.0894	1.15107	0.575537	−	0.817776i	$-0.304793\pi$
$983$	36.0894	1.15107	0.575537	+	0.817776i	$0.304793\pi$
$984$	−0.350015	−0.0111581
$985$	44.3024	1.41159
$986$	126.775	4.03735
$987$	4.36975	0.139091
$988$	−1.64565	−0.0523552
$989$	114.926	3.65444
$990$	2.15925	0.0686256
$991$	11.9025	0.378094	0.189047	−	0.981968i	$-0.439460\pi$
$991$	11.9025	0.378094	0.189047	+	0.981968i	$0.439460\pi$
$992$	−24.8456	−0.788850
$993$	−36.9812	−1.17356
$994$	22.5134	0.714082
$995$	72.6122	2.30196
$996$	54.3873	1.72333
$997$	−20.2428	−0.641097	−0.320549	−	0.947232i	$-0.603867\pi$
$997$	−20.2428	−0.641097	−0.320549	+	0.947232i	$0.603867\pi$
$998$	65.9971	2.08910
$999$	5.12533	0.162158

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.a.c.1.14	✓	19
3.2	odd	2		6039.2.a.k.1.6		19
11.10	odd	2		7381.2.a.i.1.6		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.a.c.1.14	✓	19	1.1	even	1	trivial
6039.2.a.k.1.6		19	3.2	odd	2
7381.2.a.i.1.6		19	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)

\(f(q)\)	\(=\)	\(q+1.98166 q^{2} +1.84905 q^{3} +1.92698 q^{4} +2.60057 q^{5} +3.66419 q^{6} -2.18138 q^{7} -0.144707 q^{8} +0.418993 q^{9} +O(q^{10})\)	\(q+1.98166 q^{2} +1.84905 q^{3} +1.92698 q^{4} +2.60057 q^{5} +3.66419 q^{6} -2.18138 q^{7} -0.144707 q^{8} +0.418993 q^{9} +5.15344 q^{10} +1.00000 q^{11} +3.56308 q^{12} +0.444418 q^{13} -4.32276 q^{14} +4.80859 q^{15} -4.14071 q^{16} +6.05961 q^{17} +0.830301 q^{18} -1.92163 q^{19} +5.01124 q^{20} -4.03349 q^{21} +1.98166 q^{22} -9.17660 q^{23} -0.267571 q^{24} +1.76296 q^{25} +0.880686 q^{26} -4.77242 q^{27} -4.20348 q^{28} +10.5575 q^{29} +9.52898 q^{30} +3.13863 q^{31} -7.91607 q^{32} +1.84905 q^{33} +12.0081 q^{34} -5.67284 q^{35} +0.807389 q^{36} -1.07395 q^{37} -3.80802 q^{38} +0.821752 q^{39} -0.376321 q^{40} +1.30812 q^{41} -7.99301 q^{42} -12.5238 q^{43} +1.92698 q^{44} +1.08962 q^{45} -18.1849 q^{46} -1.08337 q^{47} -7.65639 q^{48} -2.24156 q^{49} +3.49358 q^{50} +11.2045 q^{51} +0.856384 q^{52} -4.16225 q^{53} -9.45731 q^{54} +2.60057 q^{55} +0.315662 q^{56} -3.55320 q^{57} +20.9213 q^{58} +8.24320 q^{59} +9.26603 q^{60} -1.00000 q^{61} +6.21970 q^{62} -0.913984 q^{63} -7.40554 q^{64} +1.15574 q^{65} +3.66419 q^{66} -10.2859 q^{67} +11.6767 q^{68} -16.9680 q^{69} -11.2416 q^{70} -5.20811 q^{71} -0.0606312 q^{72} -0.283380 q^{73} -2.12820 q^{74} +3.25980 q^{75} -3.70294 q^{76} -2.18138 q^{77} +1.62843 q^{78} +14.7634 q^{79} -10.7682 q^{80} -10.0814 q^{81} +2.59225 q^{82} +15.2641 q^{83} -7.77245 q^{84} +15.7584 q^{85} -24.8180 q^{86} +19.5213 q^{87} -0.144707 q^{88} +16.3022 q^{89} +2.15925 q^{90} -0.969447 q^{91} -17.6831 q^{92} +5.80349 q^{93} -2.14687 q^{94} -4.99733 q^{95} -14.6372 q^{96} +4.78591 q^{97} -4.44202 q^{98} +0.418993 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 5 q^{2} + 23 q^{4} + q^{6} + 9 q^{7} + 9 q^{8} + 29 q^{9}+O(q^{10}) \) 19 * q + 5 * q^2 + 23 * q^4 + q^6 + 9 * q^7 + 9 * q^8 + 29 * q^9	\( 19 q + 5 q^{2} + 23 q^{4} + q^{6} + 9 q^{7} + 9 q^{8} + 29 q^{9} + 7 q^{10} + 19 q^{11} - 4 q^{12} + 8 q^{13} - 11 q^{14} - 5 q^{15} + 31 q^{16} + 9 q^{17} + 10 q^{18} + 17 q^{19} - 6 q^{20} + 18 q^{21} + 5 q^{22} - 10 q^{23} + 26 q^{24} + 45 q^{25} + 5 q^{26} - 33 q^{27} + 36 q^{28} + 27 q^{29} - 30 q^{30} + 7 q^{31} + 8 q^{32} - 5 q^{34} + 17 q^{35} + 38 q^{36} + 20 q^{37} - 37 q^{38} + 24 q^{39} + 10 q^{40} + 19 q^{41} + 21 q^{42} + 20 q^{43} + 23 q^{44} - 32 q^{45} + 41 q^{46} - 19 q^{47} + 5 q^{48} + 42 q^{49} + 36 q^{50} + 47 q^{51} - 28 q^{52} + 3 q^{53} - 33 q^{54} - 44 q^{56} + 11 q^{57} + 23 q^{58} - 28 q^{59} - 96 q^{60} - 19 q^{61} - 11 q^{62} - 32 q^{63} + 47 q^{64} + 25 q^{65} + q^{66} + 3 q^{67} + 38 q^{68} + 3 q^{70} - 19 q^{71} + 34 q^{72} + 20 q^{73} - 22 q^{74} - 50 q^{75} - 25 q^{76} + 9 q^{77} - 94 q^{78} + 69 q^{79} - 36 q^{80} + 47 q^{81} - 61 q^{82} + q^{83} - 28 q^{84} + 24 q^{85} - 27 q^{86} - 58 q^{87} + 9 q^{88} + 36 q^{90} + 24 q^{91} - 67 q^{92} - 14 q^{93} + 64 q^{94} - 3 q^{95} - 26 q^{96} + 21 q^{97} - 87 q^{98} + 29 q^{99}+O(q^{100}) \) 19 * q + 5 * q^2 + 23 * q^4 + q^6 + 9 * q^7 + 9 * q^8 + 29 * q^9 + 7 * q^10 + 19 * q^11 - 4 * q^12 + 8 * q^13 - 11 * q^14 - 5 * q^15 + 31 * q^16 + 9 * q^17 + 10 * q^18 + 17 * q^19 - 6 * q^20 + 18 * q^21 + 5 * q^22 - 10 * q^23 + 26 * q^24 + 45 * q^25 + 5 * q^26 - 33 * q^27 + 36 * q^28 + 27 * q^29 - 30 * q^30 + 7 * q^31 + 8 * q^32 - 5 * q^34 + 17 * q^35 + 38 * q^36 + 20 * q^37 - 37 * q^38 + 24 * q^39 + 10 * q^40 + 19 * q^41 + 21 * q^42 + 20 * q^43 + 23 * q^44 - 32 * q^45 + 41 * q^46 - 19 * q^47 + 5 * q^48 + 42 * q^49 + 36 * q^50 + 47 * q^51 - 28 * q^52 + 3 * q^53 - 33 * q^54 - 44 * q^56 + 11 * q^57 + 23 * q^58 - 28 * q^59 - 96 * q^60 - 19 * q^61 - 11 * q^62 - 32 * q^63 + 47 * q^64 + 25 * q^65 + q^66 + 3 * q^67 + 38 * q^68 + 3 * q^70 - 19 * q^71 + 34 * q^72 + 20 * q^73 - 22 * q^74 - 50 * q^75 - 25 * q^76 + 9 * q^77 - 94 * q^78 + 69 * q^79 - 36 * q^80 + 47 * q^81 - 61 * q^82 + q^83 - 28 * q^84 + 24 * q^85 - 27 * q^86 - 58 * q^87 + 9 * q^88 + 36 * q^90 + 24 * q^91 - 67 * q^92 - 14 * q^93 + 64 * q^94 - 3 * q^95 - 26 * q^96 + 21 * q^97 - 87 * q^98 + 29 * q^99

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