LMFDB - Embedded newform 671.2.a.c.1.6

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			1.6
Root			$-0.976920$ 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)

$f(q)$	$=$	$q-0.976920 q^{2} +0.347298 q^{3} -1.04563 q^{4} -2.45987 q^{5} -0.339282 q^{6} -4.72156 q^{7} +2.97533 q^{8} -2.87938 q^{9} +O(q^{10})$	\(q-0.976920 q^{2} +0.347298 q^{3} -1.04563 q^{4} -2.45987 q^{5} -0.339282 q^{6} -4.72156 q^{7} +2.97533 q^{8} -2.87938 q^{9} +2.40309 q^{10} +1.00000 q^{11} -0.363144 q^{12} -3.64373 q^{13} +4.61259 q^{14} -0.854307 q^{15} -0.815413 q^{16} +7.55245 q^{17} +2.81293 q^{18} +3.11859 q^{19} +2.57210 q^{20} -1.63979 q^{21} -0.976920 q^{22} +6.22515 q^{23} +1.03333 q^{24} +1.05094 q^{25} +3.55963 q^{26} -2.04190 q^{27} +4.93698 q^{28} -9.00853 q^{29} +0.834590 q^{30} +6.83631 q^{31} -5.15408 q^{32} +0.347298 q^{33} -7.37814 q^{34} +11.6144 q^{35} +3.01076 q^{36} +1.37973 q^{37} -3.04662 q^{38} -1.26546 q^{39} -7.31893 q^{40} +7.01523 q^{41} +1.60194 q^{42} -2.05414 q^{43} -1.04563 q^{44} +7.08290 q^{45} -6.08148 q^{46} +0.462126 q^{47} -0.283191 q^{48} +15.2931 q^{49} -1.02669 q^{50} +2.62295 q^{51} +3.80998 q^{52} -8.75381 q^{53} +1.99477 q^{54} -2.45987 q^{55} -14.0482 q^{56} +1.08308 q^{57} +8.80062 q^{58} -13.1468 q^{59} +0.893285 q^{60} -1.00000 q^{61} -6.67853 q^{62} +13.5952 q^{63} +6.66595 q^{64} +8.96309 q^{65} -0.339282 q^{66} -2.33892 q^{67} -7.89704 q^{68} +2.16198 q^{69} -11.3463 q^{70} -3.19609 q^{71} -8.56713 q^{72} +6.46095 q^{73} -1.34788 q^{74} +0.364990 q^{75} -3.26088 q^{76} -4.72156 q^{77} +1.23625 q^{78} +7.48398 q^{79} +2.00581 q^{80} +7.92901 q^{81} -6.85332 q^{82} +7.42750 q^{83} +1.71460 q^{84} -18.5780 q^{85} +2.00673 q^{86} -3.12864 q^{87} +2.97533 q^{88} +2.62699 q^{89} -6.91943 q^{90} +17.2041 q^{91} -6.50918 q^{92} +2.37423 q^{93} -0.451460 q^{94} -7.67132 q^{95} -1.79000 q^{96} +14.0175 q^{97} -14.9401 q^{98} -2.87938 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.976920	−0.690787	−0.345394	−	0.938458i	$-0.612255\pi$
$2$	−0.976920	−0.690787	−0.345394	+	0.938458i	$0.612255\pi$
$3$	0.347298	0.200513	0.100256	−	0.994962i	$-0.468034\pi$
$3$	0.347298	0.200513	0.100256	+	0.994962i	$0.468034\pi$
$4$	−1.04563	−0.522813
$5$	−2.45987	−1.10009	−0.550043	−	0.835136i	$-0.685389\pi$
$5$	−2.45987	−1.10009	−0.550043	+	0.835136i	$0.685389\pi$
$6$	−0.339282	−0.138511
$7$	−4.72156	−1.78458	−0.892290	−	0.451462i	$-0.850903\pi$
$7$	−4.72156	−1.78458	−0.892290	+	0.451462i	$0.850903\pi$
$8$	2.97533	1.05194
$9$	−2.87938	−0.959795
$10$	2.40309	0.759925
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.363144	−0.104831
$13$	−3.64373	−1.01059	−0.505294	−	0.862947i	$-0.668616\pi$
$13$	−3.64373	−1.01059	−0.505294	+	0.862947i	$0.668616\pi$
$14$	4.61259	1.23277
$15$	−0.854307	−0.220581
$16$	−0.815413	−0.203853
$17$	7.55245	1.83174	0.915869	−	0.401477i	$-0.131503\pi$
$17$	7.55245	1.83174	0.915869	+	0.401477i	$0.131503\pi$
$18$	2.81293	0.663014
$19$	3.11859	0.715454	0.357727	−	0.933826i	$-0.383552\pi$
$19$	3.11859	0.715454	0.357727	+	0.933826i	$0.383552\pi$
$20$	2.57210	0.575139
$21$	−1.63979	−0.357831
$22$	−0.976920	−0.208280
$23$	6.22515	1.29803	0.649017	−	0.760774i	$-0.275181\pi$
$23$	6.22515	1.29803	0.649017	+	0.760774i	$0.275181\pi$
$24$	1.03333	0.210927
$25$	1.05094	0.210188
$26$	3.55963	0.698102
$27$	−2.04190	−0.392963
$28$	4.93698	0.933002
$29$	−9.00853	−1.67284	−0.836421	−	0.548087i	$-0.815356\pi$
$29$	−9.00853	−1.67284	−0.836421	+	0.548087i	$0.815356\pi$
$30$	0.834590	0.152375
$31$	6.83631	1.22784	0.613918	−	0.789370i	$-0.289592\pi$
$31$	6.83631	1.22784	0.613918	+	0.789370i	$0.289592\pi$
$32$	−5.15408	−0.911121
$33$	0.347298	0.0604568
$34$	−7.37814	−1.26534
$35$	11.6144	1.96319
$36$	3.01076	0.501793
$37$	1.37973	0.226825	0.113413	−	0.993548i	$-0.463822\pi$
$37$	1.37973	0.226825	0.113413	+	0.993548i	$0.463822\pi$
$38$	−3.04662	−0.494226
$39$	−1.26546	−0.202636
$40$	−7.31893	−1.15722
$41$	7.01523	1.09559	0.547797	−	0.836611i	$-0.315466\pi$
$41$	7.01523	1.09559	0.547797	+	0.836611i	$0.315466\pi$
$42$	1.60194	0.247185
$43$	−2.05414	−0.313253	−0.156626	−	0.987658i	$-0.550062\pi$
$43$	−2.05414	−0.313253	−0.156626	+	0.987658i	$0.550062\pi$
$44$	−1.04563	−0.157634
$45$	7.08290	1.05586
$46$	−6.08148	−0.896665
$47$	0.462126	0.0674080	0.0337040	−	0.999432i	$-0.489270\pi$
$47$	0.462126	0.0674080	0.0337040	+	0.999432i	$0.489270\pi$
$48$	−0.283191	−0.0408751
$49$	15.2931	2.18473
$50$	−1.02669	−0.145195
$51$	2.62295	0.367286
$52$	3.80998	0.528349
$53$	−8.75381	−1.20243	−0.601214	−	0.799088i	$-0.705316\pi$
$53$	−8.75381	−1.20243	−0.601214	+	0.799088i	$0.705316\pi$
$54$	1.99477	0.271454
$55$	−2.45987	−0.331688
$56$	−14.0482	−1.87727
$57$	1.08308	0.143458
$58$	8.80062	1.15558
$59$	−13.1468	−1.71157	−0.855786	−	0.517330i	$-0.826926\pi$
$59$	−13.1468	−1.71157	−0.855786	+	0.517330i	$0.826926\pi$
$60$	0.893285	0.115323
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	−6.67853	−0.848174
$63$	13.5952	1.71283
$64$	6.66595	0.833244
$65$	8.96309	1.11173
$66$	−0.339282	−0.0417628
$67$	−2.33892	−0.285744	−0.142872	−	0.989741i	$-0.545634\pi$
$67$	−2.33892	−0.285744	−0.142872	+	0.989741i	$0.545634\pi$
$68$	−7.89704	−0.957657
$69$	2.16198	0.260272
$70$	−11.3463	−1.35615
$71$	−3.19609	−0.379306	−0.189653	−	0.981851i	$-0.560736\pi$
$71$	−3.19609	−0.379306	−0.189653	+	0.981851i	$0.560736\pi$
$72$	−8.56713	−1.00965
$73$	6.46095	0.756198	0.378099	−	0.925765i	$-0.376578\pi$
$73$	6.46095	0.756198	0.378099	+	0.925765i	$0.376578\pi$
$74$	−1.34788	−0.156688
$75$	0.364990	0.0421454
$76$	−3.26088	−0.374049
$77$	−4.72156	−0.538071
$78$	1.23625	0.139978
$79$	7.48398	0.842014	0.421007	−	0.907057i	$-0.361677\pi$
$79$	7.48398	0.842014	0.421007	+	0.907057i	$0.361677\pi$
$80$	2.00581	0.224256
$81$	7.92901	0.881001
$82$	−6.85332	−0.756823
$83$	7.42750	0.815274	0.407637	−	0.913144i	$-0.366353\pi$
$83$	7.42750	0.815274	0.407637	+	0.913144i	$0.366353\pi$
$84$	1.71460	0.187079
$85$	−18.5780	−2.01507
$86$	2.00673	0.216391
$87$	−3.12864	−0.335426
$88$	2.97533	0.317172
$89$	2.62699	0.278461	0.139230	−	0.990260i	$-0.455537\pi$
$89$	2.62699	0.278461	0.139230	+	0.990260i	$0.455537\pi$
$90$	−6.91943	−0.729372
$91$	17.2041	1.80348
$92$	−6.50918	−0.678629
$93$	2.37423	0.246197
$94$	−0.451460	−0.0465645
$95$	−7.67132	−0.787061
$96$	−1.79000	−0.182691
$97$	14.0175	1.42326	0.711629	−	0.702556i	$-0.247958\pi$
$97$	14.0175	1.42326	0.711629	+	0.702556i	$0.247958\pi$
$98$	−14.9401	−1.50918
$99$	−2.87938	−0.289389
$100$	−1.09889	−0.109889
$101$	14.0501	1.39804	0.699019	−	0.715103i	$-0.253620\pi$
$101$	14.0501	1.39804	0.699019	+	0.715103i	$0.253620\pi$
$102$	−2.56241	−0.253717
$103$	5.18315	0.510711	0.255356	−	0.966847i	$-0.417807\pi$
$103$	5.18315	0.510711	0.255356	+	0.966847i	$0.417807\pi$
$104$	−10.8413	−1.06308
$105$	4.03366	0.393645
$106$	8.55178	0.830622
$107$	7.13382	0.689653	0.344826	−	0.938666i	$-0.387938\pi$
$107$	7.13382	0.689653	0.344826	+	0.938666i	$0.387938\pi$
$108$	2.13506	0.205446
$109$	13.7939	1.32122	0.660608	−	0.750731i	$-0.270298\pi$
$109$	13.7939	1.32122	0.660608	+	0.750731i	$0.270298\pi$
$110$	2.40309	0.229126
$111$	0.479176	0.0454813
$112$	3.85002	0.363793
$113$	−9.02749	−0.849235	−0.424617	−	0.905373i	$-0.639591\pi$
$113$	−9.02749	−0.849235	−0.424617	+	0.905373i	$0.639591\pi$
$114$	−1.05808	−0.0990986
$115$	−15.3130	−1.42795
$116$	9.41956	0.874584
$117$	10.4917	0.969958
$118$	12.8434	1.18233
$119$	−35.6593	−3.26888
$120$	−2.54185	−0.232038
$121$	1.00000	0.0909091
$122$	0.976920	0.0884462
$123$	2.43637	0.219681
$124$	−7.14822	−0.641929
$125$	9.71415	0.868860
$126$	−13.2814	−1.18320
$127$	−11.5367	−1.02372	−0.511858	−	0.859070i	$-0.671042\pi$
$127$	−11.5367	−1.02372	−0.511858	+	0.859070i	$0.671042\pi$
$128$	3.79605	0.335527
$129$	−0.713397	−0.0628111
$130$	−8.75622	−0.767972
$131$	12.3015	1.07479	0.537395	−	0.843331i	$-0.319408\pi$
$131$	12.3015	1.07479	0.537395	+	0.843331i	$0.319408\pi$
$132$	−0.363144	−0.0316076
$133$	−14.7246	−1.27679
$134$	2.28494	0.197389
$135$	5.02280	0.432293
$136$	22.4711	1.92688
$137$	−18.4305	−1.57463	−0.787313	−	0.616554i	$-0.788528\pi$
$137$	−18.4305	−1.57463	−0.787313	+	0.616554i	$0.788528\pi$
$138$	−2.11208	−0.179793
$139$	−4.71002	−0.399498	−0.199749	−	0.979847i	$-0.564013\pi$
$139$	−4.71002	−0.399498	−0.199749	+	0.979847i	$0.564013\pi$
$140$	−12.1443	−1.02638
$141$	0.160495	0.0135161
$142$	3.12233	0.262020
$143$	−3.64373	−0.304704
$144$	2.34789	0.195657
$145$	22.1598	1.84027
$146$	−6.31184	−0.522372
$147$	5.31126	0.438066
$148$	−1.44268	−0.118587
$149$	−3.70127	−0.303220	−0.151610	−	0.988440i	$-0.548446\pi$
$149$	−3.70127	−0.303220	−0.151610	+	0.988440i	$0.548446\pi$
$150$	−0.356566	−0.0291135
$151$	0.680484	0.0553770	0.0276885	−	0.999617i	$-0.491185\pi$
$151$	0.680484	0.0553770	0.0276885	+	0.999617i	$0.491185\pi$
$152$	9.27886	0.752615
$153$	−21.7464	−1.75809
$154$	4.61259	0.371693
$155$	−16.8164	−1.35073
$156$	1.32320	0.105941
$157$	−15.1246	−1.20707	−0.603536	−	0.797336i	$-0.706242\pi$
$157$	−15.1246	−1.20707	−0.603536	+	0.797336i	$0.706242\pi$
$158$	−7.31126	−0.581652
$159$	−3.04018	−0.241102
$160$	12.6783	1.00231
$161$	−29.3924	−2.31645
$162$	−7.74601	−0.608584
$163$	−1.68174	−0.131724	−0.0658621	−	0.997829i	$-0.520980\pi$
$163$	−1.68174	−0.131724	−0.0658621	+	0.997829i	$0.520980\pi$
$164$	−7.33531	−0.572791
$165$	−0.854307	−0.0665077
$166$	−7.25608	−0.563181
$167$	−8.21081	−0.635372	−0.317686	−	0.948196i	$-0.602906\pi$
$167$	−8.21081	−0.635372	−0.317686	+	0.948196i	$0.602906\pi$
$168$	−4.87892	−0.376417
$169$	0.276763	0.0212895
$170$	18.1492	1.39198
$171$	−8.97962	−0.686689
$172$	2.14786	0.163773
$173$	−10.1127	−0.768853	−0.384427	−	0.923156i	$-0.625601\pi$
$173$	−10.1127	−0.768853	−0.384427	+	0.923156i	$0.625601\pi$
$174$	3.05644	0.231708
$175$	−4.96208	−0.375098
$176$	−0.815413	−0.0614641
$177$	−4.56587	−0.343192
$178$	−2.56636	−0.192357
$179$	9.88089	0.738532	0.369266	−	0.929324i	$-0.379609\pi$
$179$	9.88089	0.738532	0.369266	+	0.929324i	$0.379609\pi$
$180$	−7.40607	−0.552016
$181$	14.1305	1.05031	0.525157	−	0.851005i	$-0.324007\pi$
$181$	14.1305	1.05031	0.525157	+	0.851005i	$0.324007\pi$
$182$	−16.8070	−1.24582
$183$	−0.347298	−0.0256730
$184$	18.5219	1.36545
$185$	−3.39394	−0.249527
$186$	−2.31944	−0.170070
$187$	7.55245	0.552290
$188$	−0.483211	−0.0352418
$189$	9.64094	0.701275
$190$	7.49427	0.543691
$191$	14.6519	1.06017	0.530086	−	0.847944i	$-0.322160\pi$
$191$	14.6519	1.06017	0.530086	+	0.847944i	$0.322160\pi$
$192$	2.31507	0.167076
$193$	22.1162	1.59196	0.795979	−	0.605324i	$-0.206957\pi$
$193$	22.1162	1.59196	0.795979	+	0.605324i	$0.206957\pi$
$194$	−13.6939	−0.983168
$195$	3.11286	0.222917
$196$	−15.9909	−1.14220
$197$	12.5323	0.892887	0.446444	−	0.894812i	$-0.352690\pi$
$197$	12.5323	0.892887	0.446444	+	0.894812i	$0.352690\pi$
$198$	2.81293	0.199906
$199$	−14.6887	−1.04126	−0.520628	−	0.853783i	$-0.674302\pi$
$199$	−14.6887	−1.04126	−0.520628	+	0.853783i	$0.674302\pi$
$200$	3.12690	0.221106
$201$	−0.812302	−0.0572953
$202$	−13.7258	−0.965747
$203$	42.5343	2.98532
$204$	−2.74263	−0.192022
$205$	−17.2565	−1.20525
$206$	−5.06353	−0.352793
$207$	−17.9246	−1.24585
$208$	2.97114	0.206012
$209$	3.11859	0.215718
$210$	−3.94056	−0.271925
$211$	13.4080	0.923047	0.461524	−	0.887128i	$-0.347303\pi$
$211$	13.4080	0.923047	0.461524	+	0.887128i	$0.347303\pi$
$212$	9.15322	0.628646
$213$	−1.11000	−0.0760557
$214$	−6.96918	−0.476403
$215$	5.05290	0.344605
$216$	−6.07533	−0.413374
$217$	−32.2780	−2.19117
$218$	−13.4756	−0.912679
$219$	2.24388	0.151627
$220$	2.57210	0.173411
$221$	−27.5191	−1.85113
$222$	−0.468117	−0.0314179
$223$	−3.05622	−0.204660	−0.102330	−	0.994751i	$-0.532630\pi$
$223$	−3.05622	−0.204660	−0.102330	+	0.994751i	$0.532630\pi$
$224$	24.3353	1.62597
$225$	−3.02607	−0.201738
$226$	8.81914	0.586640
$227$	−9.78960	−0.649759	−0.324879	−	0.945755i	$-0.605324\pi$
$227$	−9.78960	−0.649759	−0.324879	+	0.945755i	$0.605324\pi$
$228$	−1.13250	−0.0750015
$229$	−7.49245	−0.495115	−0.247557	−	0.968873i	$-0.579628\pi$
$229$	−7.49245	−0.495115	−0.247557	+	0.968873i	$0.579628\pi$
$230$	14.9596	0.986408
$231$	−1.63979	−0.107890
$232$	−26.8034	−1.75973
$233$	15.2128	0.996626	0.498313	−	0.866997i	$-0.333953\pi$
$233$	15.2128	0.996626	0.498313	+	0.866997i	$0.333953\pi$
$234$	−10.2496	−0.670034
$235$	−1.13677	−0.0741545
$236$	13.7467	0.894832
$237$	2.59917	0.168834
$238$	34.8363	2.25810
$239$	28.5870	1.84914	0.924569	−	0.381015i	$-0.124425\pi$
$239$	28.5870	1.84914	0.924569	+	0.381015i	$0.124425\pi$
$240$	0.696612	0.0449661
$241$	−1.87641	−0.120870	−0.0604350	−	0.998172i	$-0.519249\pi$
$241$	−1.87641	−0.120870	−0.0604350	+	0.998172i	$0.519249\pi$
$242$	−0.976920	−0.0627988
$243$	8.87942	0.569615
$244$	1.04563	0.0669394
$245$	−37.6190	−2.40339
$246$	−2.38014	−0.151752
$247$	−11.3633	−0.723030
$248$	20.3403	1.29161
$249$	2.57956	0.163473
$250$	−9.48996	−0.600198
$251$	−13.8777	−0.875956	−0.437978	−	0.898986i	$-0.644305\pi$
$251$	−13.8777	−0.875956	−0.437978	+	0.898986i	$0.644305\pi$
$252$	−14.2155	−0.895491
$253$	6.22515	0.391372
$254$	11.2704	0.707169
$255$	−6.45211	−0.404047
$256$	−17.0403	−1.06502
$257$	8.83137	0.550886	0.275443	−	0.961317i	$-0.411175\pi$
$257$	8.83137	0.550886	0.275443	+	0.961317i	$0.411175\pi$
$258$	0.696932	0.0433891
$259$	−6.51445	−0.404788
$260$	−9.37204	−0.581229
$261$	25.9390	1.60559
$262$	−12.0176	−0.742451
$263$	−27.0329	−1.66692	−0.833461	−	0.552578i	$-0.813644\pi$
$263$	−27.0329	−1.66692	−0.833461	+	0.552578i	$0.813644\pi$
$264$	1.03333	0.0635969
$265$	21.5332	1.32277
$266$	14.3848	0.881987
$267$	0.912349	0.0558349
$268$	2.44564	0.149391
$269$	3.25490	0.198455	0.0992273	−	0.995065i	$-0.468363\pi$
$269$	3.25490	0.198455	0.0992273	+	0.995065i	$0.468363\pi$
$270$	−4.90687	−0.298623
$271$	1.51697	0.0921492	0.0460746	−	0.998938i	$-0.485329\pi$
$271$	1.51697	0.0921492	0.0460746	+	0.998938i	$0.485329\pi$
$272$	−6.15836	−0.373406
$273$	5.97494	0.361620
$274$	18.0052	1.08773
$275$	1.05094	0.0633742
$276$	−2.26062	−0.136074
$277$	32.1804	1.93353	0.966766	−	0.255663i	$-0.0822937\pi$
$277$	32.1804	1.93353	0.966766	+	0.255663i	$0.0822937\pi$
$278$	4.60131	0.275968
$279$	−19.6843	−1.17847
$280$	34.5567	2.06516
$281$	16.1157	0.961380	0.480690	−	0.876890i	$-0.340386\pi$
$281$	16.1157	0.961380	0.480690	+	0.876890i	$0.340386\pi$
$282$	−0.156791	−0.00933678
$283$	−4.12258	−0.245062	−0.122531	−	0.992465i	$-0.539101\pi$
$283$	−4.12258	−0.245062	−0.122531	+	0.992465i	$0.539101\pi$
$284$	3.34192	0.198306
$285$	−2.66423	−0.157816
$286$	3.55963	0.210486
$287$	−33.1228	−1.95518
$288$	14.8406	0.874489
$289$	40.0395	2.35526
$290$	−21.6483	−1.27123
$291$	4.86824	0.285381
$292$	−6.75574	−0.395350
$293$	11.6904	0.682961	0.341480	−	0.939889i	$-0.389072\pi$
$293$	11.6904	0.682961	0.341480	+	0.939889i	$0.389072\pi$
$294$	−5.18868	−0.302610
$295$	32.3394	1.88288
$296$	4.10514	0.238607
$297$	−2.04190	−0.118483
$298$	3.61585	0.209460
$299$	−22.6828	−1.31178
$300$	−0.381643	−0.0220342
$301$	9.69872	0.559025
$302$	−0.664779	−0.0382537
$303$	4.87957	0.280324
$304$	−2.54294	−0.145848
$305$	2.45987	0.140852
$306$	21.2445	1.21447
$307$	−2.76858	−0.158011	−0.0790055	−	0.996874i	$-0.525174\pi$
$307$	−2.76858	−0.158011	−0.0790055	+	0.996874i	$0.525174\pi$
$308$	4.93698	0.281311
$309$	1.80010	0.102404
$310$	16.4283	0.933064
$311$	−10.5903	−0.600518	−0.300259	−	0.953858i	$-0.597073\pi$
$311$	−10.5903	−0.600518	−0.300259	+	0.953858i	$0.597073\pi$
$312$	−3.76517	−0.213161
$313$	−7.33658	−0.414688	−0.207344	−	0.978268i	$-0.566482\pi$
$313$	−7.33658	−0.414688	−0.207344	+	0.978268i	$0.566482\pi$
$314$	14.7755	0.833829
$315$	−33.4423	−1.88426
$316$	−7.82545	−0.440216
$317$	−22.2305	−1.24859	−0.624296	−	0.781188i	$-0.714614\pi$
$317$	−22.2305	−1.24859	−0.624296	+	0.781188i	$0.714614\pi$
$318$	2.97002	0.166550
$319$	−9.00853	−0.504381
$320$	−16.3973	−0.916639
$321$	2.47756	0.138284
$322$	28.7140	1.60017
$323$	23.5530	1.31052
$324$	−8.29078	−0.460599
$325$	−3.82935	−0.212414
$326$	1.64293	0.0909934
$327$	4.79060	0.264921
$328$	20.8727	1.15250
$329$	−2.18195	−0.120295
$330$	0.834590	0.0459426
$331$	26.5447	1.45903	0.729515	−	0.683965i	$-0.239746\pi$
$331$	26.5447	1.45903	0.729515	+	0.683965i	$0.239746\pi$
$332$	−7.76639	−0.426236
$333$	−3.97276	−0.217706
$334$	8.02131	0.438907
$335$	5.75343	0.314343
$336$	1.33710	0.0729450
$337$	20.7624	1.13100	0.565501	−	0.824748i	$-0.308683\pi$
$337$	20.7624	1.13100	0.565501	+	0.824748i	$0.308683\pi$
$338$	−0.270376	−0.0147065
$339$	−3.13523	−0.170282
$340$	19.4257	1.05350
$341$	6.83631	0.370207
$342$	8.77238	0.474356
$343$	−39.1563	−2.11424
$344$	−6.11174	−0.329523
$345$	−5.31818	−0.286321
$346$	9.87929	0.531114
$347$	−13.6102	−0.730632	−0.365316	−	0.930884i	$-0.619039\pi$
$347$	−13.6102	−0.730632	−0.365316	+	0.930884i	$0.619039\pi$
$348$	3.27139	0.175365
$349$	13.0273	0.697334	0.348667	−	0.937247i	$-0.386634\pi$
$349$	13.0273	0.697334	0.348667	+	0.937247i	$0.386634\pi$
$350$	4.84756	0.259113
$351$	7.44012	0.397124
$352$	−5.15408	−0.274713
$353$	26.5517	1.41320	0.706602	−	0.707611i	$-0.250227\pi$
$353$	26.5517	1.41320	0.706602	+	0.707611i	$0.250227\pi$
$354$	4.46049	0.237072
$355$	7.86196	0.417269
$356$	−2.74685	−0.145583
$357$	−12.3844	−0.655452
$358$	−9.65284	−0.510169
$359$	34.9557	1.84489	0.922445	−	0.386128i	$-0.126188\pi$
$359$	34.9557	1.84489	0.922445	+	0.386128i	$0.126188\pi$
$360$	21.0740	1.11070
$361$	−9.27438	−0.488125
$362$	−13.8044	−0.725544
$363$	0.347298	0.0182284
$364$	−17.9890	−0.942882
$365$	−15.8931	−0.831882
$366$	0.339282	0.0177346
$367$	−8.20527	−0.428312	−0.214156	−	0.976799i	$-0.568700\pi$
$367$	−8.20527	−0.428312	−0.214156	+	0.976799i	$0.568700\pi$
$368$	−5.07607	−0.264608
$369$	−20.1995	−1.05155
$370$	3.31561	0.172370
$371$	41.3316	2.14583
$372$	−2.48256	−0.128715
$373$	33.1545	1.71667	0.858336	−	0.513087i	$-0.171498\pi$
$373$	33.1545	1.71667	0.858336	+	0.513087i	$0.171498\pi$
$374$	−7.37814	−0.381515
$375$	3.37371	0.174217
$376$	1.37498	0.0709091
$377$	32.8246	1.69056
$378$	−9.41843	−0.484432
$379$	−6.72850	−0.345620	−0.172810	−	0.984955i	$-0.555285\pi$
$379$	−6.72850	−0.345620	−0.172810	+	0.984955i	$0.555285\pi$
$380$	8.02133	0.411486
$381$	−4.00667	−0.205268
$382$	−14.3137	−0.732354
$383$	7.57720	0.387177	0.193589	−	0.981083i	$-0.437987\pi$
$383$	7.57720	0.387177	0.193589	+	0.981083i	$0.437987\pi$
$384$	1.31836	0.0672773
$385$	11.6144	0.591925
$386$	−21.6058	−1.09970
$387$	5.91465	0.300658
$388$	−14.6570	−0.744098
$389$	−28.4550	−1.44273	−0.721364	−	0.692556i	$-0.756484\pi$
$389$	−28.4550	−1.44273	−0.721364	+	0.692556i	$0.756484\pi$
$390$	−3.04102	−0.153988
$391$	47.0151	2.37766
$392$	45.5021	2.29820
$393$	4.27230	0.215509
$394$	−12.2430	−0.616795
$395$	−18.4096	−0.926287
$396$	3.01076	0.151296
$397$	11.5866	0.581517	0.290758	−	0.956797i	$-0.406092\pi$
$397$	11.5866	0.581517	0.290758	+	0.956797i	$0.406092\pi$
$398$	14.3497	0.719287
$399$	−5.11383	−0.256012
$400$	−0.856952	−0.0428476
$401$	−11.0846	−0.553537	−0.276768	−	0.960937i	$-0.589263\pi$
$401$	−11.0846	−0.553537	−0.276768	+	0.960937i	$0.589263\pi$
$402$	0.793554	0.0395789
$403$	−24.9096	−1.24084
$404$	−14.6912	−0.730913
$405$	−19.5043	−0.969176
$406$	−41.5526	−2.06222
$407$	1.37973	0.0683904
$408$	7.80415	0.386363
$409$	21.5998	1.06804	0.534020	−	0.845472i	$-0.320681\pi$
$409$	21.5998	1.06804	0.534020	+	0.845472i	$0.320681\pi$
$410$	16.8583	0.832570
$411$	−6.40088	−0.315732
$412$	−5.41964	−0.267006
$413$	62.0735	3.05444
$414$	17.5109	0.860614
$415$	−18.2707	−0.896871
$416$	18.7801	0.920768
$417$	−1.63578	−0.0801044
$418$	−3.04662	−0.149015
$419$	−17.4353	−0.851772	−0.425886	−	0.904777i	$-0.640038\pi$
$419$	−17.4353	−0.851772	−0.425886	+	0.904777i	$0.640038\pi$
$420$	−4.21770	−0.205803
$421$	4.84909	0.236330	0.118165	−	0.992994i	$-0.462299\pi$
$421$	4.84909	0.236330	0.118165	+	0.992994i	$0.462299\pi$
$422$	−13.0986	−0.637629
$423$	−1.33064	−0.0646978
$424$	−26.0455	−1.26488
$425$	7.93719	0.385010
$426$	1.08438	0.0525383
$427$	4.72156	0.228492
$428$	−7.45931	−0.360560
$429$	−1.26546	−0.0610970
$430$	−4.93628	−0.238049
$431$	−25.7815	−1.24185	−0.620925	−	0.783870i	$-0.713243\pi$
$431$	−25.7815	−1.24185	−0.620925	+	0.783870i	$0.713243\pi$
$432$	1.66499	0.0801069
$433$	−0.873678	−0.0419863	−0.0209932	−	0.999780i	$-0.506683\pi$
$433$	−0.873678	−0.0419863	−0.0209932	+	0.999780i	$0.506683\pi$
$434$	31.5330	1.51363
$435$	7.69605	0.368997
$436$	−14.4233	−0.690749
$437$	19.4137	0.928683
$438$	−2.19209	−0.104742
$439$	9.44647	0.450855	0.225428	−	0.974260i	$-0.427622\pi$
$439$	9.44647	0.450855	0.225428	+	0.974260i	$0.427622\pi$
$440$	−7.31893	−0.348916
$441$	−44.0347	−2.09689
$442$	26.8840	1.27874
$443$	−6.19118	−0.294152	−0.147076	−	0.989125i	$-0.546986\pi$
$443$	−6.19118	−0.294152	−0.147076	+	0.989125i	$0.546986\pi$
$444$	−0.501039	−0.0237782
$445$	−6.46205	−0.306331
$446$	2.98569	0.141376
$447$	−1.28544	−0.0607994
$448$	−31.4737	−1.48699
$449$	−2.22094	−0.104813	−0.0524063	−	0.998626i	$-0.516689\pi$
$449$	−2.22094	−0.104813	−0.0524063	+	0.998626i	$0.516689\pi$
$450$	2.95623	0.139358
$451$	7.01523	0.330334
$452$	9.43938	0.443991
$453$	0.236331	0.0111038
$454$	9.56366	0.448845
$455$	−42.3197	−1.98398
$456$	3.22253	0.150909
$457$	−2.54427	−0.119016	−0.0595081	−	0.998228i	$-0.518953\pi$
$457$	−2.54427	−0.119016	−0.0595081	+	0.998228i	$0.518953\pi$
$458$	7.31952	0.342019
$459$	−15.4213	−0.719806
$460$	16.0117	0.746550
$461$	−23.0730	−1.07462	−0.537309	−	0.843385i	$-0.680559\pi$
$461$	−23.0730	−1.07462	−0.537309	+	0.843385i	$0.680559\pi$
$462$	1.60194	0.0745291
$463$	−24.1373	−1.12176	−0.560879	−	0.827898i	$-0.689537\pi$
$463$	−24.1373	−1.12176	−0.560879	+	0.827898i	$0.689537\pi$
$464$	7.34567	0.341014
$465$	−5.84030	−0.270837
$466$	−14.8617	−0.688456
$467$	5.59507	0.258909	0.129454	−	0.991585i	$-0.458677\pi$
$467$	5.59507	0.258909	0.129454	+	0.991585i	$0.458677\pi$
$468$	−10.9704	−0.507107
$469$	11.0433	0.509934
$470$	1.11053	0.0512250
$471$	−5.25273	−0.242033
$472$	−39.1162	−1.80047
$473$	−2.05414	−0.0944493
$474$	−2.53918	−0.116629
$475$	3.27746	0.150380
$476$	37.2863	1.70902
$477$	25.2056	1.15408
$478$	−27.9272	−1.27736
$479$	27.8217	1.27121	0.635604	−	0.772015i	$-0.280751\pi$
$479$	27.8217	1.27121	0.635604	+	0.772015i	$0.280751\pi$
$480$	4.40316	0.200976
$481$	−5.02734	−0.229227
$482$	1.83310	0.0834954
$483$	−10.2079	−0.464476
$484$	−1.04563	−0.0475285
$485$	−34.4811	−1.56571
$486$	−8.67449	−0.393483
$487$	28.2998	1.28238	0.641192	−	0.767380i	$-0.278440\pi$
$487$	28.2998	1.28238	0.641192	+	0.767380i	$0.278440\pi$
$488$	−2.97533	−0.134687
$489$	−0.584066	−0.0264124
$490$	36.7508	1.66023
$491$	−3.70645	−0.167270	−0.0836348	−	0.996496i	$-0.526653\pi$
$491$	−3.70645	−0.167270	−0.0836348	+	0.996496i	$0.526653\pi$
$492$	−2.54754	−0.114852
$493$	−68.0365	−3.06421
$494$	11.1010	0.499460
$495$	7.08290	0.318353
$496$	−5.57441	−0.250298
$497$	15.0905	0.676903
$498$	−2.52002	−0.112925
$499$	12.4246	0.556203	0.278102	−	0.960552i	$-0.410295\pi$
$499$	12.4246	0.556203	0.278102	+	0.960552i	$0.410295\pi$
$500$	−10.1574	−0.454252
$501$	−2.85160	−0.127400
$502$	13.5575	0.605099
$503$	−39.4627	−1.75955	−0.879777	−	0.475387i	$-0.842308\pi$
$503$	−39.4627	−1.75955	−0.879777	+	0.475387i	$0.842308\pi$
$504$	40.4502	1.80180
$505$	−34.5614	−1.53796
$506$	−6.08148	−0.270355
$507$	0.0961193	0.00426881
$508$	12.0631	0.535212
$509$	38.9460	1.72625	0.863125	−	0.504991i	$-0.168504\pi$
$509$	38.9460	1.72625	0.863125	+	0.504991i	$0.168504\pi$
$510$	6.30319	0.279110
$511$	−30.5058	−1.34950
$512$	9.05495	0.400176
$513$	−6.36785	−0.281147
$514$	−8.62755	−0.380545
$515$	−12.7499	−0.561826
$516$	0.745947	0.0328385
$517$	0.462126	0.0203243
$518$	6.36410	0.279623
$519$	−3.51212	−0.154165
$520$	26.6682	1.16948
$521$	−6.44332	−0.282287	−0.141143	−	0.989989i	$-0.545078\pi$
$521$	−6.44332	−0.282287	−0.141143	+	0.989989i	$0.545078\pi$
$522$	−25.3404	−1.10912
$523$	−31.6099	−1.38220	−0.691101	−	0.722758i	$-0.742874\pi$
$523$	−31.6099	−1.38220	−0.691101	+	0.722758i	$0.742874\pi$
$524$	−12.8628	−0.561914
$525$	−1.72332	−0.0752119
$526$	26.4090	1.15149
$527$	51.6308	2.24908
$528$	−0.283191	−0.0123243
$529$	15.7525	0.684890
$530$	−21.0362	−0.913756
$531$	37.8548	1.64276
$532$	15.3964	0.667520
$533$	−25.5616	−1.10720
$534$	−0.891293	−0.0385700
$535$	−17.5483	−0.758677
$536$	−6.95907	−0.300586
$537$	3.43161	0.148085
$538$	−3.17977	−0.137090
$539$	15.2931	0.658720
$540$	−5.25197	−0.226009
$541$	−0.190222	−0.00817828	−0.00408914	−	0.999992i	$-0.501302\pi$
$541$	−0.190222	−0.00817828	−0.00408914	+	0.999992i	$0.501302\pi$
$542$	−1.48196	−0.0636555
$543$	4.90751	0.210601
$544$	−38.9259	−1.66893
$545$	−33.9312	−1.45345
$546$	−5.83704	−0.249802
$547$	−11.5701	−0.494702	−0.247351	−	0.968926i	$-0.579560\pi$
$547$	−11.5701	−0.494702	−0.247351	+	0.968926i	$0.579560\pi$
$548$	19.2714	0.823235
$549$	2.87938	0.122889
$550$	−1.02669	−0.0437781
$551$	−28.0939	−1.19684
$552$	6.43262	0.273790
$553$	−35.3361	−1.50264
$554$	−31.4377	−1.33566
$555$	−1.17871	−0.0500334
$556$	4.92492	0.208863
$557$	0.363924	0.0154199	0.00770997	−	0.999970i	$-0.497546\pi$
$557$	0.363924	0.0154199	0.00770997	+	0.999970i	$0.497546\pi$
$558$	19.2300	0.814073
$559$	7.48472	0.316570
$560$	−9.47053	−0.400203
$561$	2.62295	0.110741
$562$	−15.7437	−0.664109
$563$	−27.7077	−1.16774	−0.583871	−	0.811847i	$-0.698463\pi$
$563$	−27.7077	−1.16774	−0.583871	+	0.811847i	$0.698463\pi$
$564$	−0.167818	−0.00706642
$565$	22.2064	0.934231
$566$	4.02743	0.169286
$567$	−37.4373	−1.57222
$568$	−9.50944	−0.399007
$569$	39.0534	1.63720	0.818602	−	0.574361i	$-0.194749\pi$
$569$	39.0534	1.63720	0.818602	+	0.574361i	$0.194749\pi$
$570$	2.60274	0.109017
$571$	27.8561	1.16574	0.582871	−	0.812564i	$-0.301929\pi$
$571$	27.8561	1.16574	0.582871	+	0.812564i	$0.301929\pi$
$572$	3.80998	0.159303
$573$	5.08857	0.212578
$574$	32.3583	1.35061
$575$	6.54227	0.272831
$576$	−19.1938	−0.799743
$577$	−15.7908	−0.657381	−0.328691	−	0.944438i	$-0.606607\pi$
$577$	−15.7908	−0.657381	−0.328691	+	0.944438i	$0.606607\pi$
$578$	−39.1154	−1.62699
$579$	7.68091	0.319208
$580$	−23.1708	−0.962117
$581$	−35.0694	−1.45492
$582$	−4.75588	−0.197138
$583$	−8.75381	−0.362546
$584$	19.2235	0.795474
$585$	−25.8082	−1.06704
$586$	−11.4206	−0.471780
$587$	−32.5907	−1.34516	−0.672581	−	0.740024i	$-0.734814\pi$
$587$	−32.5907	−1.34516	−0.672581	+	0.740024i	$0.734814\pi$
$588$	−5.55360	−0.229026
$589$	21.3196	0.878461
$590$	−31.5931	−1.30067
$591$	4.35243	0.179035
$592$	−1.12505	−0.0462391
$593$	4.80499	0.197317	0.0986586	−	0.995121i	$-0.468545\pi$
$593$	4.80499	0.197317	0.0986586	+	0.995121i	$0.468545\pi$
$594$	1.99477	0.0818465
$595$	87.7172	3.59605
$596$	3.87015	0.158527
$597$	−5.10137	−0.208785
$598$	22.1592	0.906159
$599$	−3.29562	−0.134655	−0.0673277	−	0.997731i	$-0.521447\pi$
$599$	−3.29562	−0.134655	−0.0673277	+	0.997731i	$0.521447\pi$
$600$	1.08597	0.0443344
$601$	22.3621	0.912170	0.456085	−	0.889936i	$-0.349251\pi$
$601$	22.3621	0.912170	0.456085	+	0.889936i	$0.349251\pi$
$602$	−9.47488	−0.386167
$603$	6.73465	0.274256
$604$	−0.711532	−0.0289518
$605$	−2.45987	−0.100008
$606$	−4.76696	−0.193644
$607$	−20.9391	−0.849893	−0.424947	−	0.905218i	$-0.639707\pi$
$607$	−20.9391	−0.849893	−0.424947	+	0.905218i	$0.639707\pi$
$608$	−16.0735	−0.651865
$609$	14.7721	0.598595
$610$	−2.40309	−0.0972984
$611$	−1.68386	−0.0681217
$612$	22.7386	0.919154
$613$	31.0793	1.25528	0.627640	−	0.778504i	$-0.284021\pi$
$613$	31.0793	1.25528	0.627640	+	0.778504i	$0.284021\pi$
$614$	2.70468	0.109152
$615$	−5.99316	−0.241667
$616$	−14.0482	−0.566019
$617$	27.3936	1.10282	0.551412	−	0.834233i	$-0.314089\pi$
$617$	27.3936	1.10282	0.551412	+	0.834233i	$0.314089\pi$
$618$	−1.75855	−0.0707393
$619$	11.3488	0.456145	0.228073	−	0.973644i	$-0.426758\pi$
$619$	11.3488	0.456145	0.228073	+	0.973644i	$0.426758\pi$
$620$	17.5837	0.706177
$621$	−12.7111	−0.510080
$622$	10.3458	0.414830
$623$	−12.4035	−0.496936
$624$	1.03187	0.0413079
$625$	−29.1502	−1.16601
$626$	7.16726	0.286461
$627$	1.08308	0.0432541
$628$	15.8146	0.631073
$629$	10.4203	0.415485
$630$	32.6705	1.30162
$631$	35.5391	1.41479	0.707394	−	0.706819i	$-0.249871\pi$
$631$	35.5391	1.41479	0.707394	+	0.706819i	$0.249871\pi$
$632$	22.2674	0.885748
$633$	4.65658	0.185083
$634$	21.7175	0.862511
$635$	28.3787	1.12617
$636$	3.17889	0.126051
$637$	−55.7239	−2.20786
$638$	8.80062	0.348420
$639$	9.20277	0.364056
$640$	−9.33778	−0.369108
$641$	−8.50764	−0.336032	−0.168016	−	0.985784i	$-0.553736\pi$
$641$	−8.50764	−0.336032	−0.168016	+	0.985784i	$0.553736\pi$
$642$	−2.42038	−0.0955248
$643$	−37.3113	−1.47141	−0.735707	−	0.677300i	$-0.763150\pi$
$643$	−37.3113	−1.47141	−0.735707	+	0.677300i	$0.763150\pi$
$644$	30.7335	1.21107
$645$	1.75486	0.0690976
$646$	−23.0094	−0.905293
$647$	7.30155	0.287053	0.143527	−	0.989646i	$-0.454156\pi$
$647$	7.30155	0.287053	0.143527	+	0.989646i	$0.454156\pi$
$648$	23.5914	0.926760
$649$	−13.1468	−0.516058
$650$	3.74097	0.146733
$651$	−11.2101	−0.439358
$652$	1.75847	0.0688672
$653$	−25.8048	−1.00982	−0.504910	−	0.863172i	$-0.668474\pi$
$653$	−25.8048	−1.00982	−0.504910	+	0.863172i	$0.668474\pi$
$654$	−4.68003	−0.183004
$655$	−30.2601	−1.18236
$656$	−5.72031	−0.223340
$657$	−18.6036	−0.725794
$658$	2.13159	0.0830982
$659$	−7.01770	−0.273371	−0.136685	−	0.990615i	$-0.543645\pi$
$659$	−7.01770	−0.273371	−0.136685	+	0.990615i	$0.543645\pi$
$660$	0.893285	0.0347711
$661$	25.9209	1.00821	0.504103	−	0.863644i	$-0.331823\pi$
$661$	25.9209	1.00821	0.504103	+	0.863644i	$0.331823\pi$
$662$	−25.9321	−1.00788
$663$	−9.55732	−0.371176
$664$	22.0993	0.857619
$665$	36.2206	1.40457
$666$	3.88107	0.150388
$667$	−56.0794	−2.17140
$668$	8.58544	0.332181
$669$	−1.06142	−0.0410369
$670$	−5.62064	−0.217144
$671$	−1.00000	−0.0386046
$672$	8.45159	0.326027
$673$	−17.3693	−0.669538	−0.334769	−	0.942300i	$-0.608658\pi$
$673$	−17.3693	−0.669538	−0.334769	+	0.942300i	$0.608658\pi$
$674$	−20.2833	−0.781282
$675$	−2.14592	−0.0825964
$676$	−0.289391	−0.0111304
$677$	−27.9109	−1.07270	−0.536351	−	0.843995i	$-0.680198\pi$
$677$	−27.9109	−1.07270	−0.536351	+	0.843995i	$0.680198\pi$
$678$	3.06287	0.117629
$679$	−66.1843	−2.53992
$680$	−55.2758	−2.11973
$681$	−3.39991	−0.130285
$682$	−6.67853	−0.255734
$683$	29.0389	1.11114	0.555572	−	0.831468i	$-0.312499\pi$
$683$	29.0389	1.11114	0.555572	+	0.831468i	$0.312499\pi$
$684$	9.38933	0.359010
$685$	45.3366	1.73222
$686$	38.2526	1.46049
$687$	−2.60211	−0.0992767
$688$	1.67497	0.0638576
$689$	31.8965	1.21516
$690$	5.19544	0.197787
$691$	35.9848	1.36893	0.684463	−	0.729048i	$-0.260037\pi$
$691$	35.9848	1.36893	0.684463	+	0.729048i	$0.260037\pi$
$692$	10.5741	0.401967
$693$	13.5952	0.516438
$694$	13.2960	0.504711
$695$	11.5860	0.439482
$696$	−9.30876	−0.352848
$697$	52.9822	2.00684
$698$	−12.7266	−0.481709
$699$	5.28338	0.199836
$700$	5.18848	0.196106
$701$	−7.79083	−0.294255	−0.147128	−	0.989117i	$-0.547003\pi$
$701$	−7.79083	−0.294255	−0.147128	+	0.989117i	$0.547003\pi$
$702$	−7.26841	−0.274328
$703$	4.30280	0.162283
$704$	6.66595	0.251232
$705$	−0.394797	−0.0148689
$706$	−25.9389	−0.976223
$707$	−66.3384	−2.49491
$708$	4.77419	0.179425
$709$	29.8202	1.11992	0.559960	−	0.828520i	$-0.310816\pi$
$709$	29.8202	1.11992	0.559960	+	0.828520i	$0.310816\pi$
$710$	−7.68051	−0.288244
$711$	−21.5493	−0.808161
$712$	7.81618	0.292924
$713$	42.5570	1.59377
$714$	12.0986	0.452778
$715$	8.96309	0.335200
$716$	−10.3317	−0.386115
$717$	9.92820	0.370775
$718$	−34.1489	−1.27443
$719$	−26.0584	−0.971816	−0.485908	−	0.874010i	$-0.661511\pi$
$719$	−26.0584	−0.971816	−0.485908	+	0.874010i	$0.661511\pi$
$720$	−5.77549	−0.215240
$721$	−24.4725	−0.911405
$722$	9.06034	0.337191
$723$	−0.651672	−0.0242360
$724$	−14.7753	−0.549118
$725$	−9.46744	−0.351612
$726$	−0.339282	−0.0125920
$727$	−1.87217	−0.0694349	−0.0347175	−	0.999397i	$-0.511053\pi$
$727$	−1.87217	−0.0694349	−0.0347175	+	0.999397i	$0.511053\pi$
$728$	51.1879	1.89715
$729$	−20.7032	−0.766786
$730$	15.5263	0.574653
$731$	−15.5138	−0.573797
$732$	0.363144	0.0134222
$733$	16.7809	0.619815	0.309908	−	0.950767i	$-0.399702\pi$
$733$	16.7809	0.619815	0.309908	+	0.950767i	$0.399702\pi$
$734$	8.01590	0.295872
$735$	−13.0650	−0.481910
$736$	−32.0849	−1.18266
$737$	−2.33892	−0.0861552
$738$	19.7333	0.726394
$739$	2.00232	0.0736567	0.0368283	−	0.999322i	$-0.488275\pi$
$739$	2.00232	0.0736567	0.0368283	+	0.999322i	$0.488275\pi$
$740$	3.54879	0.130456
$741$	−3.94645	−0.144977
$742$	−40.3777	−1.48231
$743$	−31.3472	−1.15002	−0.575008	−	0.818148i	$-0.695001\pi$
$743$	−31.3472	−1.15002	−0.575008	+	0.818148i	$0.695001\pi$
$744$	7.06414	0.258984
$745$	9.10463	0.333568
$746$	−32.3893	−1.18586
$747$	−21.3866	−0.782496
$748$	−7.89704	−0.288744
$749$	−33.6828	−1.23074
$750$	−3.29584	−0.120347
$751$	−0.559148	−0.0204036	−0.0102018	−	0.999948i	$-0.503247\pi$
$751$	−0.559148	−0.0204036	−0.0102018	+	0.999948i	$0.503247\pi$
$752$	−0.376823	−0.0137413
$753$	−4.81971	−0.175640
$754$	−32.0671	−1.16781
$755$	−1.67390	−0.0609195
$756$	−10.0808	−0.366636
$757$	−2.20187	−0.0800285	−0.0400142	−	0.999199i	$-0.512740\pi$
$757$	−2.20187	−0.0800285	−0.0400142	+	0.999199i	$0.512740\pi$
$758$	6.57321	0.238750
$759$	2.16198	0.0784750
$760$	−22.8247	−0.827940
$761$	−4.55252	−0.165029	−0.0825143	−	0.996590i	$-0.526295\pi$
$761$	−4.55252	−0.165029	−0.0825143	+	0.996590i	$0.526295\pi$
$762$	3.91419	0.141796
$763$	−65.1287	−2.35782
$764$	−15.3204	−0.554272
$765$	53.4932	1.93405
$766$	−7.40233	−0.267457
$767$	47.9035	1.72969
$768$	−5.91807	−0.213550
$769$	15.0961	0.544380	0.272190	−	0.962243i	$-0.412252\pi$
$769$	15.0961	0.544380	0.272190	+	0.962243i	$0.412252\pi$
$770$	−11.3463	−0.408894
$771$	3.06712	0.110460
$772$	−23.1253	−0.832297
$773$	−35.0842	−1.26189	−0.630945	−	0.775828i	$-0.717333\pi$
$773$	−35.0842	−1.26189	−0.630945	+	0.775828i	$0.717333\pi$
$774$	−5.77814	−0.207691
$775$	7.18456	0.258077
$776$	41.7066	1.49718
$777$	−2.26246	−0.0811651
$778$	27.7983	0.996618
$779$	21.8776	0.783848
$780$	−3.25489	−0.116544
$781$	−3.19609	−0.114365
$782$	−45.9300	−1.64245
$783$	18.3945	0.657366
$784$	−12.4702	−0.445364
$785$	37.2044	1.32788
$786$	−4.17369	−0.148871
$787$	−43.7479	−1.55944	−0.779722	−	0.626125i	$-0.784640\pi$
$787$	−43.7479	−1.55944	−0.779722	+	0.626125i	$0.784640\pi$
$788$	−13.1041	−0.466813
$789$	−9.38848	−0.334239
$790$	17.9847	0.639867
$791$	42.6238	1.51553
$792$	−8.56713	−0.304420
$793$	3.64373	0.129393
$794$	−11.3192	−0.401704
$795$	7.47844	0.265233
$796$	15.3589	0.544383
$797$	−4.04978	−0.143450	−0.0717252	−	0.997424i	$-0.522850\pi$
$797$	−4.04978	−0.143450	−0.0717252	+	0.997424i	$0.522850\pi$
$798$	4.99580	0.176849
$799$	3.49018	0.123474
$800$	−5.41663	−0.191507
$801$	−7.56412	−0.267265
$802$	10.8287	0.382376
$803$	6.46095	0.228002
$804$	0.849364	0.0299548
$805$	72.3014	2.54829
$806$	24.3347	0.857155
$807$	1.13042	0.0397926
$808$	41.8038	1.47065
$809$	49.8548	1.75280	0.876401	−	0.481582i	$-0.159938\pi$
$809$	49.8548	1.75280	0.876401	+	0.481582i	$0.159938\pi$
$810$	19.0541	0.669494
$811$	−18.2786	−0.641850	−0.320925	−	0.947105i	$-0.603994\pi$
$811$	−18.2786	−0.641850	−0.320925	+	0.947105i	$0.603994\pi$
$812$	−44.4750	−1.56077
$813$	0.526840	0.0184771
$814$	−1.34788	−0.0472432
$815$	4.13686	0.144908
$816$	−2.13879	−0.0748725
$817$	−6.40601	−0.224118
$818$	−21.1013	−0.737788
$819$	−49.5371	−1.73097
$820$	18.0439	0.630120
$821$	−45.7437	−1.59646	−0.798232	−	0.602350i	$-0.794231\pi$
$821$	−45.7437	−1.59646	−0.798232	+	0.602350i	$0.794231\pi$
$822$	6.25315	0.218104
$823$	−10.5923	−0.369225	−0.184613	−	0.982811i	$-0.559103\pi$
$823$	−10.5923	−0.369225	−0.184613	+	0.982811i	$0.559103\pi$
$824$	15.4216	0.537237
$825$	0.364990	0.0127073
$826$	−60.6409	−2.10997
$827$	−8.50237	−0.295656	−0.147828	−	0.989013i	$-0.547228\pi$
$827$	−8.50237	−0.295656	−0.147828	+	0.989013i	$0.547228\pi$
$828$	18.7424	0.651344
$829$	41.9221	1.45602	0.728008	−	0.685569i	$-0.240447\pi$
$829$	41.9221	1.45602	0.728008	+	0.685569i	$0.240447\pi$
$830$	17.8490	0.619547
$831$	11.1762	0.387697
$832$	−24.2889	−0.842066
$833$	115.500	4.00185
$834$	1.59803	0.0553351
$835$	20.1975	0.698963
$836$	−3.26088	−0.112780
$837$	−13.9590	−0.482495
$838$	17.0329	0.588393
$839$	49.2667	1.70087	0.850437	−	0.526077i	$-0.176338\pi$
$839$	49.2667	1.70087	0.850437	+	0.526077i	$0.176338\pi$
$840$	12.0015	0.414090
$841$	52.1536	1.79840
$842$	−4.73718	−0.163254
$843$	5.59694	0.192769
$844$	−14.0198	−0.482581
$845$	−0.680801	−0.0234203
$846$	1.29993	0.0446924
$847$	−4.72156	−0.162235
$848$	7.13797	0.245119
$849$	−1.43176	−0.0491380
$850$	−7.75400	−0.265960
$851$	8.58899	0.294427
$852$	1.16064	0.0397629
$853$	−16.1055	−0.551442	−0.275721	−	0.961238i	$-0.588917\pi$
$853$	−16.1055	−0.551442	−0.275721	+	0.961238i	$0.588917\pi$
$854$	−4.61259	−0.157839
$855$	22.0887	0.755417
$856$	21.2255	0.725473
$857$	−54.7150	−1.86903	−0.934515	−	0.355925i	$-0.884166\pi$
$857$	−54.7150	−1.86903	−0.934515	+	0.355925i	$0.884166\pi$
$858$	1.23625	0.0422050
$859$	46.3457	1.58130	0.790648	−	0.612271i	$-0.209744\pi$
$859$	46.3457	1.58130	0.790648	+	0.612271i	$0.209744\pi$
$860$	−5.28345	−0.180164
$861$	−11.5035	−0.392038
$862$	25.1865	0.857854
$863$	23.7776	0.809398	0.404699	−	0.914450i	$-0.367376\pi$
$863$	23.7776	0.809398	0.404699	+	0.914450i	$0.367376\pi$
$864$	10.5241	0.358037
$865$	24.8759	0.845805
$866$	0.853514	0.0290036
$867$	13.9056	0.472260
$868$	33.7507	1.14557
$869$	7.48398	0.253877
$870$	−7.51843	−0.254898
$871$	8.52239	0.288770
$872$	41.0415	1.38984
$873$	−40.3617	−1.36604
$874$	−18.9656	−0.641522
$875$	−45.8659	−1.55055
$876$	−2.34626	−0.0792727
$877$	12.3722	0.417781	0.208890	−	0.977939i	$-0.433015\pi$
$877$	12.3722	0.417781	0.208890	+	0.977939i	$0.433015\pi$
$878$	−9.22845	−0.311445
$879$	4.06005	0.136942
$880$	2.00581	0.0676157
$881$	48.3684	1.62957	0.814786	−	0.579761i	$-0.196854\pi$
$881$	48.3684	1.62957	0.814786	+	0.579761i	$0.196854\pi$
$882$	43.0184	1.44851
$883$	−18.0643	−0.607913	−0.303957	−	0.952686i	$-0.598308\pi$
$883$	−18.0643	−0.607913	−0.303957	+	0.952686i	$0.598308\pi$
$884$	28.7747	0.967797
$885$	11.2314	0.377540
$886$	6.04829	0.203196
$887$	6.81182	0.228718	0.114359	−	0.993439i	$-0.463519\pi$
$887$	6.81182	0.228718	0.114359	+	0.993439i	$0.463519\pi$
$888$	1.42571	0.0478436
$889$	54.4711	1.82690
$890$	6.31291	0.211609
$891$	7.92901	0.265632
$892$	3.19567	0.106999
$893$	1.44118	0.0482273
$894$	1.25578	0.0419995
$895$	−24.3057	−0.812449
$896$	−17.9233	−0.598774
$897$	−7.87767	−0.263028
$898$	2.16968	0.0724031
$899$	−61.5851	−2.05398
$900$	3.16413	0.105471
$901$	−66.1127	−2.20253
$902$	−6.85332	−0.228191
$903$	3.36835	0.112092
$904$	−26.8598	−0.893344
$905$	−34.7592	−1.15544
$906$	−0.230876	−0.00767036
$907$	−18.3398	−0.608963	−0.304481	−	0.952518i	$-0.598483\pi$
$907$	−18.3398	−0.608963	−0.304481	+	0.952518i	$0.598483\pi$
$908$	10.2363	0.339702
$909$	−40.4557	−1.34183
$910$	41.3430	1.37051
$911$	21.7646	0.721092	0.360546	−	0.932741i	$-0.382590\pi$
$911$	21.7646	0.721092	0.360546	+	0.932741i	$0.382590\pi$
$912$	−0.883158	−0.0292443
$913$	7.42750	0.245814
$914$	2.48555	0.0822148
$915$	0.854307	0.0282425
$916$	7.83430	0.258853
$917$	−58.0824	−1.91805
$918$	15.0654	0.497233
$919$	−25.4171	−0.838433	−0.419217	−	0.907886i	$-0.637695\pi$
$919$	−25.4171	−0.838433	−0.419217	+	0.907886i	$0.637695\pi$
$920$	−45.5614	−1.50211
$921$	−0.961521	−0.0316832
$922$	22.5405	0.742333
$923$	11.6457	0.383323
$924$	1.71460	0.0564064
$925$	1.45001	0.0476761
$926$	23.5803	0.774896
$927$	−14.9243	−0.490178
$928$	46.4307	1.52416
$929$	−29.1102	−0.955076	−0.477538	−	0.878611i	$-0.658471\pi$
$929$	−29.1102	−0.955076	−0.477538	+	0.878611i	$0.658471\pi$
$930$	5.70551	0.187091
$931$	47.6929	1.56307
$932$	−15.9069	−0.521049
$933$	−3.67797	−0.120411
$934$	−5.46594	−0.178851
$935$	−18.5780	−0.607566
$936$	31.2163	1.02034
$937$	42.2703	1.38091	0.690455	−	0.723375i	$-0.257410\pi$
$937$	42.2703	1.38091	0.690455	+	0.723375i	$0.257410\pi$
$938$	−10.7885	−0.352256
$939$	−2.54798	−0.0831502
$940$	1.18863	0.0387690
$941$	44.2341	1.44199	0.720996	−	0.692940i	$-0.243685\pi$
$941$	44.2341	1.44199	0.720996	+	0.692940i	$0.243685\pi$
$942$	5.13150	0.167193
$943$	43.6708	1.42212
$944$	10.7201	0.348909
$945$	−23.7154	−0.771463
$946$	2.00673	0.0652443
$947$	−16.7129	−0.543096	−0.271548	−	0.962425i	$-0.587536\pi$
$947$	−16.7129	−0.543096	−0.271548	+	0.962425i	$0.587536\pi$
$948$	−2.71776	−0.0882688
$949$	−23.5420	−0.764205
$950$	−3.20182	−0.103881
$951$	−7.72062	−0.250358
$952$	−106.098	−3.43867
$953$	3.86490	0.125197	0.0625983	−	0.998039i	$-0.480061\pi$
$953$	3.86490	0.125197	0.0625983	+	0.998039i	$0.480061\pi$
$954$	−24.6239	−0.797227
$955$	−36.0417	−1.16628
$956$	−29.8913	−0.966753
$957$	−3.12864	−0.101135
$958$	−27.1796	−0.878134
$959$	87.0208	2.81005
$960$	−5.69476	−0.183798
$961$	15.7351	0.507583
$962$	4.91132	0.158347
$963$	−20.5410	−0.661925
$964$	1.96202	0.0631924
$965$	−54.4029	−1.75129
$966$	9.97232	0.320854
$967$	−22.8594	−0.735107	−0.367554	−	0.930002i	$-0.619805\pi$
$967$	−22.8594	−0.735107	−0.367554	+	0.930002i	$0.619805\pi$
$968$	2.97533	0.0956309
$969$	8.17991	0.262777
$970$	33.6853	1.08157
$971$	−15.7356	−0.504980	−0.252490	−	0.967600i	$-0.581249\pi$
$971$	−15.7356	−0.504980	−0.252490	+	0.967600i	$0.581249\pi$
$972$	−9.28456	−0.297802
$973$	22.2386	0.712937
$974$	−27.6466	−0.885855
$975$	−1.32992	−0.0425917
$976$	0.815413	0.0261007
$977$	1.70450	0.0545319	0.0272660	−	0.999628i	$-0.491320\pi$
$977$	1.70450	0.0545319	0.0272660	+	0.999628i	$0.491320\pi$
$978$	0.570586	0.0182453
$979$	2.62699	0.0839591
$980$	39.3354	1.25652
$981$	−39.7180	−1.26810
$982$	3.62090	0.115548
$983$	52.3102	1.66844	0.834218	−	0.551435i	$-0.185919\pi$
$983$	52.3102	1.66844	0.834218	+	0.551435i	$0.185919\pi$
$984$	7.24903	0.231091
$985$	−30.8277	−0.982252
$986$	66.4662	2.11672
$987$	−0.757788	−0.0241206
$988$	11.8818	0.378009
$989$	−12.7873	−0.406613
$990$	−6.91943	−0.219914
$991$	−11.8436	−0.376224	−0.188112	−	0.982148i	$-0.560237\pi$
$991$	−11.8436	−0.376224	−0.188112	+	0.982148i	$0.560237\pi$
$992$	−35.2348	−1.11871
$993$	9.21893	0.292554
$994$	−14.7422	−0.467596
$995$	36.1323	1.14547
$996$	−2.69725	−0.0854657
$997$	19.9226	0.630954	0.315477	−	0.948933i	$-0.397836\pi$
$997$	19.9226	0.630954	0.315477	+	0.948933i	$0.397836\pi$
$998$	−12.1379	−0.384218
$999$	−2.81726	−0.0891341

Twists

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

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

\(f(q)\)	\(=\)	\(q-0.976920 q^{2} +0.347298 q^{3} -1.04563 q^{4} -2.45987 q^{5} -0.339282 q^{6} -4.72156 q^{7} +2.97533 q^{8} -2.87938 q^{9} +O(q^{10})\)	\(q-0.976920 q^{2} +0.347298 q^{3} -1.04563 q^{4} -2.45987 q^{5} -0.339282 q^{6} -4.72156 q^{7} +2.97533 q^{8} -2.87938 q^{9} +2.40309 q^{10} +1.00000 q^{11} -0.363144 q^{12} -3.64373 q^{13} +4.61259 q^{14} -0.854307 q^{15} -0.815413 q^{16} +7.55245 q^{17} +2.81293 q^{18} +3.11859 q^{19} +2.57210 q^{20} -1.63979 q^{21} -0.976920 q^{22} +6.22515 q^{23} +1.03333 q^{24} +1.05094 q^{25} +3.55963 q^{26} -2.04190 q^{27} +4.93698 q^{28} -9.00853 q^{29} +0.834590 q^{30} +6.83631 q^{31} -5.15408 q^{32} +0.347298 q^{33} -7.37814 q^{34} +11.6144 q^{35} +3.01076 q^{36} +1.37973 q^{37} -3.04662 q^{38} -1.26546 q^{39} -7.31893 q^{40} +7.01523 q^{41} +1.60194 q^{42} -2.05414 q^{43} -1.04563 q^{44} +7.08290 q^{45} -6.08148 q^{46} +0.462126 q^{47} -0.283191 q^{48} +15.2931 q^{49} -1.02669 q^{50} +2.62295 q^{51} +3.80998 q^{52} -8.75381 q^{53} +1.99477 q^{54} -2.45987 q^{55} -14.0482 q^{56} +1.08308 q^{57} +8.80062 q^{58} -13.1468 q^{59} +0.893285 q^{60} -1.00000 q^{61} -6.67853 q^{62} +13.5952 q^{63} +6.66595 q^{64} +8.96309 q^{65} -0.339282 q^{66} -2.33892 q^{67} -7.89704 q^{68} +2.16198 q^{69} -11.3463 q^{70} -3.19609 q^{71} -8.56713 q^{72} +6.46095 q^{73} -1.34788 q^{74} +0.364990 q^{75} -3.26088 q^{76} -4.72156 q^{77} +1.23625 q^{78} +7.48398 q^{79} +2.00581 q^{80} +7.92901 q^{81} -6.85332 q^{82} +7.42750 q^{83} +1.71460 q^{84} -18.5780 q^{85} +2.00673 q^{86} -3.12864 q^{87} +2.97533 q^{88} +2.62699 q^{89} -6.91943 q^{90} +17.2041 q^{91} -6.50918 q^{92} +2.37423 q^{93} -0.451460 q^{94} -7.67132 q^{95} -1.79000 q^{96} +14.0175 q^{97} -14.9401 q^{98} -2.87938 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 5 q^{2} + 23 q^{4} + q^{6} + 9 q^{7} + 9 q^{8} + 29 q^{9}+O(q^{10}) \) 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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