LMFDB - Embedded newform 6033.2.a.b.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6033,2,Mod(1,6033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6033, 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("6033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6033 = 3 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6033.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:	$48.1737475394$
Analytic rank:	$1$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	6033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.62301 q^{2} +1.00000 q^{3} +0.634165 q^{4} -2.89779 q^{5} -1.62301 q^{6} -2.91247 q^{7} +2.21677 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.62301 q^{2} +1.00000 q^{3} +0.634165 q^{4} -2.89779 q^{5} -1.62301 q^{6} -2.91247 q^{7} +2.21677 q^{8} +1.00000 q^{9} +4.70315 q^{10} +1.00321 q^{11} +0.634165 q^{12} -3.80044 q^{13} +4.72697 q^{14} -2.89779 q^{15} -4.86616 q^{16} -0.747105 q^{17} -1.62301 q^{18} +6.85913 q^{19} -1.83768 q^{20} -2.91247 q^{21} -1.62822 q^{22} -1.71574 q^{23} +2.21677 q^{24} +3.39719 q^{25} +6.16816 q^{26} +1.00000 q^{27} -1.84698 q^{28} -2.76438 q^{29} +4.70315 q^{30} +0.873258 q^{31} +3.46431 q^{32} +1.00321 q^{33} +1.21256 q^{34} +8.43972 q^{35} +0.634165 q^{36} -0.351922 q^{37} -11.1324 q^{38} -3.80044 q^{39} -6.42372 q^{40} -6.72576 q^{41} +4.72697 q^{42} +8.48914 q^{43} +0.636199 q^{44} -2.89779 q^{45} +2.78467 q^{46} +7.23090 q^{47} -4.86616 q^{48} +1.48247 q^{49} -5.51367 q^{50} -0.747105 q^{51} -2.41011 q^{52} +8.24099 q^{53} -1.62301 q^{54} -2.90708 q^{55} -6.45626 q^{56} +6.85913 q^{57} +4.48662 q^{58} +8.99518 q^{59} -1.83768 q^{60} -2.09436 q^{61} -1.41731 q^{62} -2.91247 q^{63} +4.10972 q^{64} +11.0129 q^{65} -1.62822 q^{66} -10.9480 q^{67} -0.473787 q^{68} -1.71574 q^{69} -13.6978 q^{70} +0.824016 q^{71} +2.21677 q^{72} +15.7349 q^{73} +0.571173 q^{74} +3.39719 q^{75} +4.34982 q^{76} -2.92181 q^{77} +6.16816 q^{78} -10.3047 q^{79} +14.1011 q^{80} +1.00000 q^{81} +10.9160 q^{82} -11.6910 q^{83} -1.84698 q^{84} +2.16495 q^{85} -13.7780 q^{86} -2.76438 q^{87} +2.22388 q^{88} +10.8274 q^{89} +4.70315 q^{90} +11.0687 q^{91} -1.08806 q^{92} +0.873258 q^{93} -11.7358 q^{94} -19.8763 q^{95} +3.46431 q^{96} -13.0070 q^{97} -2.40606 q^{98} +1.00321 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q - 11 q^{2} + 71 q^{3} + 53 q^{4} - 8 q^{5} - 11 q^{6} - 46 q^{7} - 33 q^{8} + 71 q^{9}+O(q^{10}) $ 71 * q - 11 * q^2 + 71 * q^3 + 53 * q^4 - 8 * q^5 - 11 * q^6 - 46 * q^7 - 33 * q^8 + 71 * q^9	\( 71 q - 11 q^{2} + 71 q^{3} + 53 q^{4} - 8 q^{5} - 11 q^{6} - 46 q^{7} - 33 q^{8} + 71 q^{9} - 41 q^{10} - 18 q^{11} + 53 q^{12} - 67 q^{13} - 7 q^{14} - 8 q^{15} + 21 q^{16} - 25 q^{17} - 11 q^{18} - 43 q^{19} - 8 q^{20} - 46 q^{21} - 49 q^{22} - 75 q^{23} - 33 q^{24} + 19 q^{25} + 71 q^{27} - 89 q^{28} - 35 q^{29} - 41 q^{30} - 82 q^{31} - 62 q^{32} - 18 q^{33} - 28 q^{34} - 51 q^{35} + 53 q^{36} - 66 q^{37} - 29 q^{38} - 67 q^{39} - 102 q^{40} + q^{41} - 7 q^{42} - 112 q^{43} - 25 q^{44} - 8 q^{45} - 36 q^{46} - 67 q^{47} + 21 q^{48} + 7 q^{49} - 24 q^{50} - 25 q^{51} - 134 q^{52} - 40 q^{53} - 11 q^{54} - 112 q^{55} + 9 q^{56} - 43 q^{57} - 47 q^{58} - 18 q^{59} - 8 q^{60} - 144 q^{61} - 19 q^{62} - 46 q^{63} - 17 q^{64} - 31 q^{65} - 49 q^{66} - 85 q^{67} - 22 q^{68} - 75 q^{69} - 11 q^{70} - 44 q^{71} - 33 q^{72} - 98 q^{73} + 6 q^{74} + 19 q^{75} - 85 q^{76} - 39 q^{77} - 126 q^{79} + 21 q^{80} + 71 q^{81} - 69 q^{82} - 43 q^{83} - 89 q^{84} - 112 q^{85} + 32 q^{86} - 35 q^{87} - 85 q^{88} + 8 q^{89} - 41 q^{90} - 40 q^{91} - 96 q^{92} - 82 q^{93} - 99 q^{94} - 103 q^{95} - 62 q^{96} - 67 q^{97} - 11 q^{98} - 18 q^{99}+O(q^{100}) \) 71 * q - 11 * q^2 + 71 * q^3 + 53 * q^4 - 8 * q^5 - 11 * q^6 - 46 * q^7 - 33 * q^8 + 71 * q^9 - 41 * q^10 - 18 * q^11 + 53 * q^12 - 67 * q^13 - 7 * q^14 - 8 * q^15 + 21 * q^16 - 25 * q^17 - 11 * q^18 - 43 * q^19 - 8 * q^20 - 46 * q^21 - 49 * q^22 - 75 * q^23 - 33 * q^24 + 19 * q^25 + 71 * q^27 - 89 * q^28 - 35 * q^29 - 41 * q^30 - 82 * q^31 - 62 * q^32 - 18 * q^33 - 28 * q^34 - 51 * q^35 + 53 * q^36 - 66 * q^37 - 29 * q^38 - 67 * q^39 - 102 * q^40 + q^41 - 7 * q^42 - 112 * q^43 - 25 * q^44 - 8 * q^45 - 36 * q^46 - 67 * q^47 + 21 * q^48 + 7 * q^49 - 24 * q^50 - 25 * q^51 - 134 * q^52 - 40 * q^53 - 11 * q^54 - 112 * q^55 + 9 * q^56 - 43 * q^57 - 47 * q^58 - 18 * q^59 - 8 * q^60 - 144 * q^61 - 19 * q^62 - 46 * q^63 - 17 * q^64 - 31 * q^65 - 49 * q^66 - 85 * q^67 - 22 * q^68 - 75 * q^69 - 11 * q^70 - 44 * q^71 - 33 * q^72 - 98 * q^73 + 6 * q^74 + 19 * q^75 - 85 * q^76 - 39 * q^77 - 126 * q^79 + 21 * q^80 + 71 * q^81 - 69 * q^82 - 43 * q^83 - 89 * q^84 - 112 * q^85 + 32 * q^86 - 35 * q^87 - 85 * q^88 + 8 * q^89 - 41 * q^90 - 40 * q^91 - 96 * q^92 - 82 * q^93 - 99 * q^94 - 103 * q^95 - 62 * q^96 - 67 * q^97 - 11 * q^98 - 18 * 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 $

$2$	−1.62301	−1.14764	−0.573821	−	0.818981i	$-0.694540\pi$
$2$	−1.62301	−1.14764	−0.573821	+	0.818981i	$0.694540\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.634165	0.317082
$5$	−2.89779	−1.29593	−0.647966	−	0.761670i	$-0.724380\pi$
$5$	−2.89779	−1.29593	−0.647966	+	0.761670i	$0.724380\pi$
$6$	−1.62301	−0.662591
$7$	−2.91247	−1.10081	−0.550405	−	0.834898i	$-0.685527\pi$
$7$	−2.91247	−1.10081	−0.550405	+	0.834898i	$0.685527\pi$
$8$	2.21677	0.783745
$9$	1.00000	0.333333
$10$	4.70315	1.48727
$11$	1.00321	0.302478	0.151239	−	0.988497i	$-0.451674\pi$
$11$	1.00321	0.302478	0.151239	+	0.988497i	$0.451674\pi$
$12$	0.634165	0.183068
$13$	−3.80044	−1.05405	−0.527027	−	0.849849i	$-0.676693\pi$
$13$	−3.80044	−1.05405	−0.527027	+	0.849849i	$0.676693\pi$
$14$	4.72697	1.26334
$15$	−2.89779	−0.748206
$16$	−4.86616	−1.21654
$17$	−0.747105	−0.181199	−0.0905997	−	0.995887i	$-0.528878\pi$
$17$	−0.747105	−0.181199	−0.0905997	+	0.995887i	$0.528878\pi$
$18$	−1.62301	−0.382547
$19$	6.85913	1.57359	0.786796	−	0.617213i	$-0.211739\pi$
$19$	6.85913	1.57359	0.786796	+	0.617213i	$0.211739\pi$
$20$	−1.83768	−0.410917
$21$	−2.91247	−0.635553
$22$	−1.62822	−0.347137
$23$	−1.71574	−0.357757	−0.178879	−	0.983871i	$-0.557247\pi$
$23$	−1.71574	−0.357757	−0.178879	+	0.983871i	$0.557247\pi$
$24$	2.21677	0.452495
$25$	3.39719	0.679437
$26$	6.16816	1.20968
$27$	1.00000	0.192450
$28$	−1.84698	−0.349047
$29$	−2.76438	−0.513333	−0.256666	−	0.966500i	$-0.582624\pi$
$29$	−2.76438	−0.513333	−0.256666	+	0.966500i	$0.582624\pi$
$30$	4.70315	0.858673
$31$	0.873258	0.156842	0.0784209	−	0.996920i	$-0.475012\pi$
$31$	0.873258	0.156842	0.0784209	+	0.996920i	$0.475012\pi$
$32$	3.46431	0.612409
$33$	1.00321	0.174636
$34$	1.21256	0.207952
$35$	8.43972	1.42657
$36$	0.634165	0.105694
$37$	−0.351922	−0.0578555	−0.0289278	−	0.999582i	$-0.509209\pi$
$37$	−0.351922	−0.0578555	−0.0289278	+	0.999582i	$0.509209\pi$
$38$	−11.1324	−1.80592
$39$	−3.80044	−0.608558
$40$	−6.42372	−1.01568
$41$	−6.72576	−1.05039	−0.525193	−	0.850983i	$-0.676007\pi$
$41$	−6.72576	−1.05039	−0.525193	+	0.850983i	$0.676007\pi$
$42$	4.72697	0.729387
$43$	8.48914	1.29458	0.647291	−	0.762243i	$-0.275902\pi$
$43$	8.48914	1.29458	0.647291	+	0.762243i	$0.275902\pi$
$44$	0.636199	0.0959106
$45$	−2.89779	−0.431977
$46$	2.78467	0.410577
$47$	7.23090	1.05474	0.527368	−	0.849637i	$-0.323179\pi$
$47$	7.23090	1.05474	0.527368	+	0.849637i	$0.323179\pi$
$48$	−4.86616	−0.702370
$49$	1.48247	0.211781
$50$	−5.51367	−0.779751
$51$	−0.747105	−0.104616
$52$	−2.41011	−0.334222
$53$	8.24099	1.13199	0.565993	−	0.824410i	$-0.308493\pi$
$53$	8.24099	1.13199	0.565993	+	0.824410i	$0.308493\pi$
$54$	−1.62301	−0.220864
$55$	−2.90708	−0.391991
$56$	−6.45626	−0.862754
$57$	6.85913	0.908513
$58$	4.48662	0.589122
$59$	8.99518	1.17107	0.585536	−	0.810646i	$-0.300884\pi$
$59$	8.99518	1.17107	0.585536	+	0.810646i	$0.300884\pi$
$60$	−1.83768	−0.237243
$61$	−2.09436	−0.268155	−0.134077	−	0.990971i	$-0.542807\pi$
$61$	−2.09436	−0.268155	−0.134077	+	0.990971i	$0.542807\pi$
$62$	−1.41731	−0.179998
$63$	−2.91247	−0.366936
$64$	4.10972	0.513715
$65$	11.0129	1.36598
$66$	−1.62822	−0.200420
$67$	−10.9480	−1.33752	−0.668758	−	0.743480i	$-0.733174\pi$
$67$	−10.9480	−1.33752	−0.668758	+	0.743480i	$0.733174\pi$
$68$	−0.473787	−0.0574552
$69$	−1.71574	−0.206551
$70$	−13.6978	−1.63720
$71$	0.824016	0.0977927	0.0488964	−	0.998804i	$-0.484430\pi$
$71$	0.824016	0.0977927	0.0488964	+	0.998804i	$0.484430\pi$
$72$	2.21677	0.261248
$73$	15.7349	1.84163	0.920814	−	0.390003i	$-0.127526\pi$
$73$	15.7349	1.84163	0.920814	+	0.390003i	$0.127526\pi$
$74$	0.571173	0.0663975
$75$	3.39719	0.392273
$76$	4.34982	0.498958
$77$	−2.92181	−0.332971
$78$	6.16816	0.698407
$79$	−10.3047	−1.15937	−0.579687	−	0.814839i	$-0.696825\pi$
$79$	−10.3047	−1.15937	−0.579687	+	0.814839i	$0.696825\pi$
$80$	14.1011	1.57655
$81$	1.00000	0.111111
$82$	10.9160	1.20547
$83$	−11.6910	−1.28326	−0.641628	−	0.767016i	$-0.721741\pi$
$83$	−11.6910	−1.28326	−0.641628	+	0.767016i	$0.721741\pi$
$84$	−1.84698	−0.201523
$85$	2.16495	0.234822
$86$	−13.7780	−1.48572
$87$	−2.76438	−0.296373
$88$	2.22388	0.237066
$89$	10.8274	1.14770	0.573851	−	0.818960i	$-0.305449\pi$
$89$	10.8274	1.14770	0.573851	+	0.818960i	$0.305449\pi$
$90$	4.70315	0.495755
$91$	11.0687	1.16031
$92$	−1.08806	−0.113439
$93$	0.873258	0.0905526
$94$	−11.7358	−1.21046
$95$	−19.8763	−2.03927
$96$	3.46431	0.353574
$97$	−13.0070	−1.32066	−0.660328	−	0.750977i	$-0.729583\pi$
$97$	−13.0070	−1.32066	−0.660328	+	0.750977i	$0.729583\pi$
$98$	−2.40606	−0.243049
$99$	1.00321	0.100826
$100$	2.15438	0.215438
$101$	−11.2259	−1.11702	−0.558510	−	0.829498i	$-0.688627\pi$
$101$	−11.2259	−1.11702	−0.558510	+	0.829498i	$0.688627\pi$
$102$	1.21256	0.120061
$103$	13.2526	1.30581	0.652907	−	0.757438i	$-0.273549\pi$
$103$	13.2526	1.30581	0.652907	+	0.757438i	$0.273549\pi$
$104$	−8.42469	−0.826109
$105$	8.43972	0.823632
$106$	−13.3752	−1.29912
$107$	16.7154	1.61593	0.807967	−	0.589227i	$-0.200568\pi$
$107$	16.7154	1.61593	0.807967	+	0.589227i	$0.200568\pi$
$108$	0.634165	0.0610225
$109$	−2.83059	−0.271121	−0.135561	−	0.990769i	$-0.543284\pi$
$109$	−2.83059	−0.271121	−0.135561	+	0.990769i	$0.543284\pi$
$110$	4.71823	0.449865
$111$	−0.351922	−0.0334029
$112$	14.1725	1.33918
$113$	18.5899	1.74879	0.874395	−	0.485215i	$-0.161259\pi$
$113$	18.5899	1.74879	0.874395	+	0.485215i	$0.161259\pi$
$114$	−11.1324	−1.04265
$115$	4.97187	0.463629
$116$	−1.75307	−0.162769
$117$	−3.80044	−0.351351
$118$	−14.5993	−1.34397
$119$	2.17592	0.199466
$120$	−6.42372	−0.586403
$121$	−9.99358	−0.908507
$122$	3.39916	0.307746
$123$	−6.72576	−0.606441
$124$	0.553789	0.0497317
$125$	4.64461	0.415427
$126$	4.72697	0.421112
$127$	−8.66811	−0.769170	−0.384585	−	0.923090i	$-0.625655\pi$
$127$	−8.66811	−0.769170	−0.384585	+	0.923090i	$0.625655\pi$
$128$	−13.5987	−1.20197
$129$	8.48914	0.747427
$130$	−17.8740	−1.56766
$131$	17.3114	1.51250	0.756250	−	0.654283i	$-0.227029\pi$
$131$	17.3114	1.51250	0.756250	+	0.654283i	$0.227029\pi$
$132$	0.636199	0.0553740
$133$	−19.9770	−1.73222
$134$	17.7688	1.53499
$135$	−2.89779	−0.249402
$136$	−1.65616	−0.142014
$137$	−6.17229	−0.527334	−0.263667	−	0.964614i	$-0.584932\pi$
$137$	−6.17229	−0.527334	−0.263667	+	0.964614i	$0.584932\pi$
$138$	2.78467	0.237047
$139$	14.8603	1.26043	0.630215	−	0.776420i	$-0.282967\pi$
$139$	14.8603	1.26043	0.630215	+	0.776420i	$0.282967\pi$
$140$	5.35217	0.452341
$141$	7.23090	0.608952
$142$	−1.33739	−0.112231
$143$	−3.81263	−0.318828
$144$	−4.86616	−0.405514
$145$	8.01060	0.665244
$146$	−25.5379	−2.11353
$147$	1.48247	0.122272
$148$	−0.223176	−0.0183450
$149$	−3.93543	−0.322403	−0.161201	−	0.986922i	$-0.551537\pi$
$149$	−3.93543	−0.322403	−0.161201	+	0.986922i	$0.551537\pi$
$150$	−5.51367	−0.450189
$151$	4.03523	0.328383	0.164191	−	0.986429i	$-0.447499\pi$
$151$	4.03523	0.328383	0.164191	+	0.986429i	$0.447499\pi$
$152$	15.2051	1.23329
$153$	−0.747105	−0.0603998
$154$	4.74213	0.382131
$155$	−2.53052	−0.203256
$156$	−2.41011	−0.192963
$157$	−14.8740	−1.18707	−0.593537	−	0.804807i	$-0.702269\pi$
$157$	−14.8740	−1.18707	−0.593537	+	0.804807i	$0.702269\pi$
$158$	16.7247	1.33055
$159$	8.24099	0.653553
$160$	−10.0388	−0.793640
$161$	4.99705	0.393823
$162$	−1.62301	−0.127516
$163$	4.72656	0.370213	0.185106	−	0.982718i	$-0.440737\pi$
$163$	4.72656	0.370213	0.185106	+	0.982718i	$0.440737\pi$
$164$	−4.26524	−0.333059
$165$	−2.90708	−0.226316
$166$	18.9747	1.47272
$167$	12.2166	0.945345	0.472673	−	0.881238i	$-0.343289\pi$
$167$	12.2166	0.945345	0.472673	+	0.881238i	$0.343289\pi$
$168$	−6.45626	−0.498111
$169$	1.44336	0.111028
$170$	−3.51374	−0.269492
$171$	6.85913	0.524530
$172$	5.38351	0.410489
$173$	−17.9157	−1.36211	−0.681053	−	0.732235i	$-0.738477\pi$
$173$	−17.9157	−1.36211	−0.681053	+	0.732235i	$0.738477\pi$
$174$	4.48662	0.340130
$175$	−9.89420	−0.747931
$176$	−4.88177	−0.367977
$177$	8.99518	0.676119
$178$	−17.5730	−1.31715
$179$	2.31160	0.172777	0.0863885	−	0.996262i	$-0.472467\pi$
$179$	2.31160	0.172777	0.0863885	+	0.996262i	$0.472467\pi$
$180$	−1.83768	−0.136972
$181$	−26.0257	−1.93447	−0.967237	−	0.253876i	$-0.918295\pi$
$181$	−26.0257	−1.93447	−0.967237	+	0.253876i	$0.918295\pi$
$182$	−17.9646	−1.33162
$183$	−2.09436	−0.154819
$184$	−3.80340	−0.280391
$185$	1.01979	0.0749768
$186$	−1.41731	−0.103922
$187$	−0.749501	−0.0548089
$188$	4.58558	0.334438
$189$	−2.91247	−0.211851
$190$	32.2595	2.34035
$191$	23.0497	1.66782	0.833909	−	0.551902i	$-0.186098\pi$
$191$	23.0497	1.66782	0.833909	+	0.551902i	$0.186098\pi$
$192$	4.10972	0.296593
$193$	−2.76073	−0.198722	−0.0993608	−	0.995051i	$-0.531680\pi$
$193$	−2.76073	−0.198722	−0.0993608	+	0.995051i	$0.531680\pi$
$194$	21.1104	1.51564
$195$	11.0129	0.788649
$196$	0.940128	0.0671520
$197$	−4.96240	−0.353556	−0.176778	−	0.984251i	$-0.556567\pi$
$197$	−4.96240	−0.353556	−0.176778	+	0.984251i	$0.556567\pi$
$198$	−1.62822	−0.115712
$199$	−8.83341	−0.626184	−0.313092	−	0.949723i	$-0.601365\pi$
$199$	−8.83341	−0.626184	−0.313092	+	0.949723i	$0.601365\pi$
$200$	7.53077	0.532506
$201$	−10.9480	−0.772215
$202$	18.2198	1.28194
$203$	8.05117	0.565081
$204$	−0.473787	−0.0331718
$205$	19.4898	1.36123
$206$	−21.5091	−1.49861
$207$	−1.71574	−0.119252
$208$	18.4936	1.28230
$209$	6.88112	0.475977
$210$	−13.6978	−0.945235
$211$	6.92960	0.477053	0.238527	−	0.971136i	$-0.423336\pi$
$211$	6.92960	0.477053	0.238527	+	0.971136i	$0.423336\pi$
$212$	5.22614	0.358933
$213$	0.824016	0.0564607
$214$	−27.1292	−1.85451
$215$	−24.5997	−1.67769
$216$	2.21677	0.150832
$217$	−2.54333	−0.172653
$218$	4.59408	0.311150
$219$	15.7349	1.06326
$220$	−1.84357	−0.124293
$221$	2.83933	0.190994
$222$	0.571173	0.0383346
$223$	−15.2596	−1.02186	−0.510929	−	0.859623i	$-0.670699\pi$
$223$	−15.2596	−1.02186	−0.510929	+	0.859623i	$0.670699\pi$
$224$	−10.0897	−0.674145
$225$	3.39719	0.226479
$226$	−30.1716	−2.00698
$227$	−20.5532	−1.36416	−0.682081	−	0.731277i	$-0.738925\pi$
$227$	−20.5532	−1.36416	−0.682081	+	0.731277i	$0.738925\pi$
$228$	4.34982	0.288074
$229$	15.7497	1.04077	0.520386	−	0.853931i	$-0.325788\pi$
$229$	15.7497	1.04077	0.520386	+	0.853931i	$0.325788\pi$
$230$	−8.06939	−0.532080
$231$	−2.92181	−0.192241
$232$	−6.12799	−0.402322
$233$	−2.59089	−0.169735	−0.0848674	−	0.996392i	$-0.527047\pi$
$233$	−2.59089	−0.169735	−0.0848674	+	0.996392i	$0.527047\pi$
$234$	6.16816	0.403225
$235$	−20.9536	−1.36686
$236$	5.70443	0.371326
$237$	−10.3047	−0.669365
$238$	−3.53154	−0.228916
$239$	12.4289	0.803956	0.401978	−	0.915649i	$-0.368323\pi$
$239$	12.4289	0.803956	0.401978	+	0.915649i	$0.368323\pi$
$240$	14.1011	0.910224
$241$	−11.4386	−0.736826	−0.368413	−	0.929662i	$-0.620099\pi$
$241$	−11.4386	−0.736826	−0.368413	+	0.929662i	$0.620099\pi$
$242$	16.2197	1.04264
$243$	1.00000	0.0641500
$244$	−1.32817	−0.0850272
$245$	−4.29588	−0.274454
$246$	10.9160	0.695977
$247$	−26.0677	−1.65865
$248$	1.93581	0.122924
$249$	−11.6910	−0.740888
$250$	−7.53826	−0.476761
$251$	2.19330	0.138440	0.0692200	−	0.997601i	$-0.477949\pi$
$251$	2.19330	0.138440	0.0692200	+	0.997601i	$0.477949\pi$
$252$	−1.84698	−0.116349
$253$	−1.72125	−0.108214
$254$	14.0684	0.882732
$255$	2.16495	0.135575
$256$	13.8515	0.865716
$257$	0.614016	0.0383012	0.0191506	−	0.999817i	$-0.493904\pi$
$257$	0.614016	0.0383012	0.0191506	+	0.999817i	$0.493904\pi$
$258$	−13.7780	−0.857779
$259$	1.02496	0.0636879
$260$	6.98398	0.433128
$261$	−2.76438	−0.171111
$262$	−28.0965	−1.73581
$263$	−5.99528	−0.369685	−0.184842	−	0.982768i	$-0.559177\pi$
$263$	−5.99528	−0.369685	−0.184842	+	0.982768i	$0.559177\pi$
$264$	2.22388	0.136870
$265$	−23.8807	−1.46698
$266$	32.4229	1.98797
$267$	10.8274	0.662626
$268$	−6.94286	−0.424103
$269$	−8.14348	−0.496516	−0.248258	−	0.968694i	$-0.579858\pi$
$269$	−8.14348	−0.496516	−0.248258	+	0.968694i	$0.579858\pi$
$270$	4.70315	0.286224
$271$	−23.1457	−1.40600	−0.703000	−	0.711190i	$-0.748157\pi$
$271$	−23.1457	−1.40600	−0.703000	+	0.711190i	$0.748157\pi$
$272$	3.63553	0.220437
$273$	11.0687	0.669906
$274$	10.0177	0.605191
$275$	3.40808	0.205515
$276$	−1.08806	−0.0654938
$277$	−14.8151	−0.890151	−0.445075	−	0.895493i	$-0.646823\pi$
$277$	−14.8151	−0.890151	−0.445075	+	0.895493i	$0.646823\pi$
$278$	−24.1184	−1.44652
$279$	0.873258	0.0522806
$280$	18.7089	1.11807
$281$	7.12442	0.425007	0.212504	−	0.977160i	$-0.431838\pi$
$281$	7.12442	0.425007	0.212504	+	0.977160i	$0.431838\pi$
$282$	−11.7358	−0.698859
$283$	1.91334	0.113736	0.0568680	−	0.998382i	$-0.481889\pi$
$283$	1.91334	0.113736	0.0568680	+	0.998382i	$0.481889\pi$
$284$	0.522562	0.0310084
$285$	−19.8763	−1.17737
$286$	6.18794	0.365901
$287$	19.5885	1.15628
$288$	3.46431	0.204136
$289$	−16.4418	−0.967167
$290$	−13.0013	−0.763462
$291$	−13.0070	−0.762481
$292$	9.97850	0.583948
$293$	−11.2012	−0.654382	−0.327191	−	0.944958i	$-0.606102\pi$
$293$	−11.2012	−0.654382	−0.327191	+	0.944958i	$0.606102\pi$
$294$	−2.40606	−0.140324
$295$	−26.0661	−1.51763
$296$	−0.780128	−0.0453440
$297$	1.00321	0.0582120
$298$	6.38724	0.370003
$299$	6.52059	0.377095
$300$	2.15438	0.124383
$301$	−24.7243	−1.42509
$302$	−6.54923	−0.376866
$303$	−11.2259	−0.644912
$304$	−33.3776	−1.91434
$305$	6.06900	0.347510
$306$	1.21256	0.0693174
$307$	1.22292	0.0697956	0.0348978	−	0.999391i	$-0.488889\pi$
$307$	1.22292	0.0697956	0.0348978	+	0.999391i	$0.488889\pi$
$308$	−1.85291	−0.105579
$309$	13.2526	0.753912
$310$	4.10706	0.233265
$311$	2.47717	0.140467	0.0702336	−	0.997531i	$-0.477626\pi$
$311$	2.47717	0.140467	0.0702336	+	0.997531i	$0.477626\pi$
$312$	−8.42469	−0.476954
$313$	−26.3765	−1.49089	−0.745443	−	0.666569i	$-0.767762\pi$
$313$	−26.3765	−1.49089	−0.745443	+	0.666569i	$0.767762\pi$
$314$	24.1407	1.36234
$315$	8.43972	0.475524
$316$	−6.53490	−0.367617
$317$	−15.7852	−0.886584	−0.443292	−	0.896377i	$-0.646190\pi$
$317$	−15.7852	−0.886584	−0.443292	+	0.896377i	$0.646190\pi$
$318$	−13.3752	−0.750045
$319$	−2.77325	−0.155272
$320$	−11.9091	−0.665739
$321$	16.7154	0.932960
$322$	−8.11026	−0.451967
$323$	−5.12448	−0.285134
$324$	0.634165	0.0352314
$325$	−12.9108	−0.716163
$326$	−7.67126	−0.424872
$327$	−2.83059	−0.156532
$328$	−14.9094	−0.823235
$329$	−21.0598	−1.16106
$330$	4.71823	0.259730
$331$	−26.7746	−1.47166	−0.735832	−	0.677164i	$-0.763209\pi$
$331$	−26.7746	−1.47166	−0.735832	+	0.677164i	$0.763209\pi$
$332$	−7.41403	−0.406898
$333$	−0.351922	−0.0192852
$334$	−19.8276	−1.08492
$335$	31.7251	1.73333
$336$	14.1725	0.773176
$337$	−31.2339	−1.70142	−0.850711	−	0.525634i	$-0.823828\pi$
$337$	−31.2339	−1.70142	−0.850711	+	0.525634i	$0.823828\pi$
$338$	−2.34260	−0.127420
$339$	18.5899	1.00966
$340$	1.37294	0.0744579
$341$	0.876058	0.0474412
$342$	−11.1324	−0.601973
$343$	16.0696	0.867679
$344$	18.8184	1.01462
$345$	4.97187	0.267676
$346$	29.0774	1.56321
$347$	2.97353	0.159627	0.0798137	−	0.996810i	$-0.474567\pi$
$347$	2.97353	0.159627	0.0798137	+	0.996810i	$0.474567\pi$
$348$	−1.75307	−0.0939746
$349$	0.484357	0.0259271	0.0129635	−	0.999916i	$-0.495873\pi$
$349$	0.484357	0.0259271	0.0129635	+	0.999916i	$0.495873\pi$
$350$	16.0584	0.858357
$351$	−3.80044	−0.202853
$352$	3.47542	0.185240
$353$	0.125651	0.00668774	0.00334387	−	0.999994i	$-0.498936\pi$
$353$	0.125651	0.00668774	0.00334387	+	0.999994i	$0.498936\pi$
$354$	−14.5993	−0.775943
$355$	−2.38783	−0.126733
$356$	6.86635	0.363916
$357$	2.17592	0.115162
$358$	−3.75175	−0.198286
$359$	−27.7068	−1.46231	−0.731155	−	0.682211i	$-0.761019\pi$
$359$	−27.7068	−1.46231	−0.731155	+	0.682211i	$0.761019\pi$
$360$	−6.42372	−0.338560
$361$	28.0476	1.47619
$362$	42.2400	2.22008
$363$	−9.99358	−0.524527
$364$	7.01936	0.367914
$365$	−45.5964	−2.38662
$366$	3.39916	0.177677
$367$	17.9328	0.936087	0.468043	−	0.883705i	$-0.344959\pi$
$367$	17.9328	0.936087	0.468043	+	0.883705i	$0.344959\pi$
$368$	8.34909	0.435227
$369$	−6.72576	−0.350129
$370$	−1.65514	−0.0860465
$371$	−24.0016	−1.24610
$372$	0.553789	0.0287126
$373$	−31.7697	−1.64497	−0.822486	−	0.568786i	$-0.807413\pi$
$373$	−31.7697	−1.64497	−0.822486	+	0.568786i	$0.807413\pi$
$374$	1.21645	0.0629010
$375$	4.64461	0.239847
$376$	16.0292	0.826644
$377$	10.5059	0.541080
$378$	4.72697	0.243129
$379$	6.32979	0.325140	0.162570	−	0.986697i	$-0.448022\pi$
$379$	6.32979	0.325140	0.162570	+	0.986697i	$0.448022\pi$
$380$	−12.6049	−0.646615
$381$	−8.66811	−0.444081
$382$	−37.4099	−1.91406
$383$	−25.4881	−1.30238	−0.651190	−	0.758915i	$-0.725730\pi$
$383$	−25.4881	−1.30238	−0.651190	+	0.758915i	$0.725730\pi$
$384$	−13.5987	−0.693958
$385$	8.46679	0.431507
$386$	4.48069	0.228061
$387$	8.48914	0.431527
$388$	−8.24855	−0.418757
$389$	32.0847	1.62676	0.813380	−	0.581732i	$-0.197625\pi$
$389$	32.0847	1.62676	0.813380	+	0.581732i	$0.197625\pi$
$390$	−17.8740	−0.905087
$391$	1.28184	0.0648254
$392$	3.28628	0.165982
$393$	17.3114	0.873242
$394$	8.05402	0.405756
$395$	29.8610	1.50247
$396$	0.636199	0.0319702
$397$	−22.5571	−1.13211	−0.566055	−	0.824367i	$-0.691531\pi$
$397$	−22.5571	−1.13211	−0.566055	+	0.824367i	$0.691531\pi$
$398$	14.3367	0.718635
$399$	−19.9770	−1.00010
$400$	−16.5313	−0.826564
$401$	−32.4403	−1.61999	−0.809997	−	0.586435i	$-0.800531\pi$
$401$	−32.4403	−1.61999	−0.809997	+	0.586435i	$0.800531\pi$
$402$	17.7688	0.886227
$403$	−3.31877	−0.165320
$404$	−7.11908	−0.354187
$405$	−2.89779	−0.143992
$406$	−13.0671	−0.648511
$407$	−0.353050	−0.0175000
$408$	−1.65616	−0.0819919
$409$	−0.0323912	−0.00160164	−0.000800822	−	1.00000i	$-0.500255\pi$
$409$	−0.0323912	−0.00160164	−0.000800822		1.00000i	$0.500255\pi$
$410$	−31.6322	−1.56220
$411$	−6.17229	−0.304457
$412$	8.40431	0.414051
$413$	−26.1982	−1.28913
$414$	2.78467	0.136859
$415$	33.8781	1.66301
$416$	−13.1659	−0.645511
$417$	14.8603	0.727710
$418$	−11.1681	−0.546252
$419$	22.6069	1.10442	0.552210	−	0.833705i	$-0.313785\pi$
$419$	22.6069	1.10442	0.552210	+	0.833705i	$0.313785\pi$
$420$	5.35217	0.261159
$421$	−13.6642	−0.665951	−0.332975	−	0.942935i	$-0.608053\pi$
$421$	−13.6642	−0.665951	−0.332975	+	0.942935i	$0.608053\pi$
$422$	−11.2468	−0.547486
$423$	7.23090	0.351579
$424$	18.2683	0.887189
$425$	−2.53805	−0.123114
$426$	−1.33739	−0.0647966
$427$	6.09974	0.295187
$428$	10.6003	0.512384
$429$	−3.81263	−0.184076
$430$	39.9257	1.92539
$431$	33.5670	1.61687	0.808433	−	0.588589i	$-0.200316\pi$
$431$	33.5670	1.61687	0.808433	+	0.588589i	$0.200316\pi$
$432$	−4.86616	−0.234123
$433$	−8.67905	−0.417089	−0.208544	−	0.978013i	$-0.566873\pi$
$433$	−8.67905	−0.417089	−0.208544	+	0.978013i	$0.566873\pi$
$434$	4.12786	0.198144
$435$	8.01060	0.384079
$436$	−1.79506	−0.0859678
$437$	−11.7685	−0.562964
$438$	−25.5379	−1.22025
$439$	24.3754	1.16338	0.581688	−	0.813412i	$-0.302393\pi$
$439$	24.3754	1.16338	0.581688	+	0.813412i	$0.302393\pi$
$440$	−6.44432	−0.307221
$441$	1.48247	0.0705937
$442$	−4.60826	−0.219193
$443$	24.2252	1.15098	0.575488	−	0.817810i	$-0.304812\pi$
$443$	24.2252	1.15098	0.575488	+	0.817810i	$0.304812\pi$
$444$	−0.223176	−0.0105915
$445$	−31.3755	−1.48734
$446$	24.7665	1.17273
$447$	−3.93543	−0.186139
$448$	−11.9694	−0.565502
$449$	39.6207	1.86982	0.934908	−	0.354890i	$-0.115482\pi$
$449$	39.6207	1.86982	0.934908	+	0.354890i	$0.115482\pi$
$450$	−5.51367	−0.259917
$451$	−6.74733	−0.317719
$452$	11.7890	0.554510
$453$	4.03523	0.189592
$454$	33.3580	1.56557
$455$	−32.0747	−1.50368
$456$	15.2051	0.712043
$457$	−6.70446	−0.313621	−0.156811	−	0.987629i	$-0.550121\pi$
$457$	−6.70446	−0.313621	−0.156811	+	0.987629i	$0.550121\pi$
$458$	−25.5620	−1.19443
$459$	−0.747105	−0.0348719
$460$	3.15298	0.147009
$461$	12.8916	0.600422	0.300211	−	0.953873i	$-0.402943\pi$
$461$	12.8916	0.600422	0.300211	+	0.953873i	$0.402943\pi$
$462$	4.74213	0.220624
$463$	12.2745	0.570442	0.285221	−	0.958462i	$-0.407933\pi$
$463$	12.2745	0.570442	0.285221	+	0.958462i	$0.407933\pi$
$464$	13.4519	0.624490
$465$	−2.53052	−0.117350
$466$	4.20504	0.194795
$467$	−25.9695	−1.20173	−0.600863	−	0.799352i	$-0.705176\pi$
$467$	−25.9695	−1.20173	−0.600863	+	0.799352i	$0.705176\pi$
$468$	−2.41011	−0.111407
$469$	31.8858	1.47235
$470$	34.0080	1.56867
$471$	−14.8740	−0.685357
$472$	19.9402	0.917822
$473$	8.51637	0.391583
$474$	16.7247	0.768191
$475$	23.3017	1.06916
$476$	1.37989	0.0632472
$477$	8.24099	0.377329
$478$	−20.1722	−0.922654
$479$	16.1135	0.736246	0.368123	−	0.929777i	$-0.380000\pi$
$479$	16.1135	0.736246	0.368123	+	0.929777i	$0.380000\pi$
$480$	−10.0388	−0.458208
$481$	1.33746	0.0609828
$482$	18.5650	0.845613
$483$	4.99705	0.227374
$484$	−6.33757	−0.288072
$485$	37.6914	1.71148
$486$	−1.62301	−0.0736213
$487$	10.1444	0.459689	0.229844	−	0.973227i	$-0.426178\pi$
$487$	10.1444	0.459689	0.229844	+	0.973227i	$0.426178\pi$
$488$	−4.64270	−0.210165
$489$	4.72656	0.213742
$490$	6.97226	0.314974
$491$	−43.0432	−1.94251	−0.971257	−	0.238034i	$-0.923497\pi$
$491$	−43.0432	−1.94251	−0.971257	+	0.238034i	$0.923497\pi$
$492$	−4.26524	−0.192292
$493$	2.06528	0.0930156
$494$	42.3082	1.90354
$495$	−2.90708	−0.130664
$496$	−4.24942	−0.190804
$497$	−2.39992	−0.107651
$498$	18.9747	0.850274
$499$	30.3891	1.36040	0.680201	−	0.733025i	$-0.261892\pi$
$499$	30.3891	1.36040	0.680201	+	0.733025i	$0.261892\pi$
$500$	2.94545	0.131725
$501$	12.2166	0.545795
$502$	−3.55975	−0.158880
$503$	−9.55613	−0.426087	−0.213043	−	0.977043i	$-0.568338\pi$
$503$	−9.55613	−0.426087	−0.213043	+	0.977043i	$0.568338\pi$
$504$	−6.45626	−0.287585
$505$	32.5303	1.44758
$506$	2.79360	0.124191
$507$	1.44336	0.0641020
$508$	−5.49701	−0.243890
$509$	17.8417	0.790820	0.395410	−	0.918505i	$-0.370602\pi$
$509$	17.8417	0.790820	0.395410	+	0.918505i	$0.370602\pi$
$510$	−3.51374	−0.155591
$511$	−45.8273	−2.02728
$512$	4.71640	0.208438
$513$	6.85913	0.302838
$514$	−0.996554	−0.0439561
$515$	−38.4032	−1.69225
$516$	5.38351	0.236996
$517$	7.25409	0.319035
$518$	−1.66352	−0.0730909
$519$	−17.9157	−0.786412
$520$	24.4130	1.07058
$521$	20.6469	0.904557	0.452278	−	0.891877i	$-0.350611\pi$
$521$	20.6469	0.904557	0.452278	+	0.891877i	$0.350611\pi$
$522$	4.48662	0.196374
$523$	5.29796	0.231663	0.115832	−	0.993269i	$-0.463047\pi$
$523$	5.29796	0.231663	0.115832	+	0.993269i	$0.463047\pi$
$524$	10.9782	0.479587
$525$	−9.89420	−0.431818
$526$	9.73041	0.424266
$527$	−0.652415	−0.0284196
$528$	−4.88177	−0.212452
$529$	−20.0562	−0.872010
$530$	38.7586	1.68356
$531$	8.99518	0.390358
$532$	−12.6687	−0.549258
$533$	25.5609	1.10716
$534$	−17.5730	−0.760457
$535$	−48.4376	−2.09414
$536$	−24.2692	−1.04827
$537$	2.31160	0.0997529
$538$	13.2170	0.569823
$539$	1.48722	0.0640592
$540$	−1.83768	−0.0790810
$541$	1.60826	0.0691443	0.0345722	−	0.999402i	$-0.488993\pi$
$541$	1.60826	0.0691443	0.0345722	+	0.999402i	$0.488993\pi$
$542$	37.5657	1.61358
$543$	−26.0257	−1.11687
$544$	−2.58820	−0.110968
$545$	8.20245	0.351354
$546$	−17.9646	−0.768812
$547$	−37.2900	−1.59441	−0.797203	−	0.603711i	$-0.793688\pi$
$547$	−37.2900	−1.59441	−0.797203	+	0.603711i	$0.793688\pi$
$548$	−3.91425	−0.167208
$549$	−2.09436	−0.0893849
$550$	−5.53136	−0.235858
$551$	−18.9612	−0.807776
$552$	−3.80340	−0.161884
$553$	30.0122	1.27625
$554$	24.0450	1.02157
$555$	1.01979	0.0432879
$556$	9.42385	0.399660
$557$	−36.4155	−1.54297	−0.771487	−	0.636245i	$-0.780487\pi$
$557$	−36.4155	−1.54297	−0.771487	+	0.636245i	$0.780487\pi$
$558$	−1.41731	−0.0599994
$559$	−32.2625	−1.36456
$560$	−41.0691	−1.73548
$561$	−0.749501	−0.0316439
$562$	−11.5630	−0.487756
$563$	−30.3085	−1.27735	−0.638676	−	0.769476i	$-0.720518\pi$
$563$	−30.3085	−1.27735	−0.638676	+	0.769476i	$0.720518\pi$
$564$	4.58558	0.193088
$565$	−53.8696	−2.26631
$566$	−3.10537	−0.130528
$567$	−2.91247	−0.122312
$568$	1.82665	0.0766446
$569$	8.17806	0.342842	0.171421	−	0.985198i	$-0.445164\pi$
$569$	8.17806	0.342842	0.171421	+	0.985198i	$0.445164\pi$
$570$	32.2595	1.35120
$571$	12.1080	0.506703	0.253351	−	0.967374i	$-0.418467\pi$
$571$	12.1080	0.506703	0.253351	+	0.967374i	$0.418467\pi$
$572$	−2.41784	−0.101095
$573$	23.0497	0.962915
$574$	−31.7924	−1.32699
$575$	−5.82870	−0.243074
$576$	4.10972	0.171238
$577$	−29.6430	−1.23405	−0.617026	−	0.786943i	$-0.711663\pi$
$577$	−29.6430	−1.23405	−0.617026	+	0.786943i	$0.711663\pi$
$578$	26.6853	1.10996
$579$	−2.76073	−0.114732
$580$	5.08004	0.210937
$581$	34.0497	1.41262
$582$	21.1104	0.875056
$583$	8.26742	0.342401
$584$	34.8805	1.44337
$585$	11.0129	0.455327
$586$	18.1797	0.750997
$587$	−2.34347	−0.0967254	−0.0483627	−	0.998830i	$-0.515400\pi$
$587$	−2.34347	−0.0967254	−0.0483627	+	0.998830i	$0.515400\pi$
$588$	0.940128	0.0387702
$589$	5.98978	0.246805
$590$	42.3056	1.74170
$591$	−4.96240	−0.204126
$592$	1.71251	0.0703836
$593$	−29.9533	−1.23004	−0.615018	−	0.788513i	$-0.710851\pi$
$593$	−29.9533	−1.23004	−0.615018	+	0.788513i	$0.710851\pi$
$594$	−1.62822	−0.0668065
$595$	−6.30535	−0.258494
$596$	−2.49571	−0.102228
$597$	−8.83341	−0.361527
$598$	−10.5830	−0.432770
$599$	−35.4752	−1.44948	−0.724739	−	0.689023i	$-0.758040\pi$
$599$	−35.4752	−1.44948	−0.724739	+	0.689023i	$0.758040\pi$
$600$	7.53077	0.307442
$601$	35.0041	1.42785	0.713923	−	0.700225i	$-0.246917\pi$
$601$	35.0041	1.42785	0.713923	+	0.700225i	$0.246917\pi$
$602$	40.1279	1.63549
$603$	−10.9480	−0.445839
$604$	2.55900	0.104124
$605$	28.9593	1.17736
$606$	18.2198	0.740128
$607$	32.6961	1.32709	0.663547	−	0.748135i	$-0.269050\pi$
$607$	32.6961	1.32709	0.663547	+	0.748135i	$0.269050\pi$
$608$	23.7621	0.963681
$609$	8.05117	0.326250
$610$	−9.85006	−0.398817
$611$	−27.4806	−1.11175
$612$	−0.473787	−0.0191517
$613$	−7.40837	−0.299221	−0.149611	−	0.988745i	$-0.547802\pi$
$613$	−7.40837	−0.299221	−0.149611	+	0.988745i	$0.547802\pi$
$614$	−1.98481	−0.0801004
$615$	19.4898	0.785906
$616$	−6.47696	−0.260964
$617$	−21.0157	−0.846058	−0.423029	−	0.906116i	$-0.639033\pi$
$617$	−21.0157	−0.846058	−0.423029	+	0.906116i	$0.639033\pi$
$618$	−21.5091	−0.865221
$619$	−34.1022	−1.37068	−0.685341	−	0.728223i	$-0.740347\pi$
$619$	−34.1022	−1.37068	−0.685341	+	0.728223i	$0.740347\pi$
$620$	−1.60477	−0.0644489
$621$	−1.71574	−0.0688504
$622$	−4.02047	−0.161206
$623$	−31.5344	−1.26340
$624$	18.4936	0.740336
$625$	−30.4451	−1.21780
$626$	42.8093	1.71100
$627$	6.88112	0.274806
$628$	−9.43256	−0.376400
$629$	0.262922	0.0104834
$630$	−13.6978	−0.545732
$631$	−11.5776	−0.460898	−0.230449	−	0.973084i	$-0.574019\pi$
$631$	−11.5776	−0.460898	−0.230449	+	0.973084i	$0.574019\pi$
$632$	−22.8432	−0.908654
$633$	6.92960	0.275427
$634$	25.6195	1.01748
$635$	25.1184	0.996792
$636$	5.22614	0.207230
$637$	−5.63403	−0.223228
$638$	4.50101	0.178197
$639$	0.824016	0.0325976
$640$	39.4063	1.55767
$641$	9.19401	0.363142	0.181571	−	0.983378i	$-0.441882\pi$
$641$	9.19401	0.363142	0.181571	+	0.983378i	$0.441882\pi$
$642$	−27.1292	−1.07070
$643$	−2.14294	−0.0845093	−0.0422546	−	0.999107i	$-0.513454\pi$
$643$	−2.14294	−0.0845093	−0.0422546	+	0.999107i	$0.513454\pi$
$644$	3.16895	0.124874
$645$	−24.5997	−0.968614
$646$	8.31709	0.327232
$647$	−12.7304	−0.500485	−0.250243	−	0.968183i	$-0.580510\pi$
$647$	−12.7304	−0.500485	−0.250243	+	0.968183i	$0.580510\pi$
$648$	2.21677	0.0870828
$649$	9.02403	0.354224
$650$	20.9544	0.821899
$651$	−2.54333	−0.0996811
$652$	2.99742	0.117388
$653$	−1.08652	−0.0425187	−0.0212593	−	0.999774i	$-0.506768\pi$
$653$	−1.08652	−0.0425187	−0.0212593	+	0.999774i	$0.506768\pi$
$654$	4.59408	0.179643
$655$	−50.1647	−1.96010
$656$	32.7286	1.27784
$657$	15.7349	0.613876
$658$	34.1802	1.33248
$659$	1.76607	0.0687964	0.0343982	−	0.999408i	$-0.489049\pi$
$659$	1.76607	0.0687964	0.0343982	+	0.999408i	$0.489049\pi$
$660$	−1.84357	−0.0717609
$661$	30.3344	1.17987	0.589936	−	0.807450i	$-0.299153\pi$
$661$	30.3344	1.17987	0.589936	+	0.807450i	$0.299153\pi$
$662$	43.4554	1.68894
$663$	2.83933	0.110270
$664$	−25.9162	−1.00575
$665$	57.8891	2.24484
$666$	0.571173	0.0221325
$667$	4.74297	0.183649
$668$	7.74731	0.299752
$669$	−15.2596	−0.589970
$670$	−51.4902	−1.98924
$671$	−2.10107	−0.0811110
$672$	−10.0897	−0.389218
$673$	−41.6825	−1.60674	−0.803370	−	0.595480i	$-0.796962\pi$
$673$	−41.6825	−1.60674	−0.803370	+	0.595480i	$0.796962\pi$
$674$	50.6930	1.95262
$675$	3.39719	0.130758
$676$	0.915331	0.0352050
$677$	−26.8473	−1.03183	−0.515913	−	0.856641i	$-0.672547\pi$
$677$	−26.8473	−1.03183	−0.515913	+	0.856641i	$0.672547\pi$
$678$	−30.1716	−1.15873
$679$	37.8823	1.45379
$680$	4.79919	0.184041
$681$	−20.5532	−0.787599
$682$	−1.42185	−0.0544455
$683$	−47.1827	−1.80539	−0.902697	−	0.430277i	$-0.858416\pi$
$683$	−47.1827	−1.80539	−0.902697	+	0.430277i	$0.858416\pi$
$684$	4.34982	0.166319
$685$	17.8860	0.683389
$686$	−26.0812	−0.995785
$687$	15.7497	0.600890
$688$	−41.3096	−1.57491
$689$	−31.3194	−1.19317
$690$	−8.06939	−0.307197
$691$	34.7313	1.32124	0.660621	−	0.750720i	$-0.270293\pi$
$691$	34.7313	1.32124	0.660621	+	0.750720i	$0.270293\pi$
$692$	−11.3615	−0.431900
$693$	−2.92181	−0.110990
$694$	−4.82607	−0.183195
$695$	−43.0619	−1.63343
$696$	−6.12799	−0.232281
$697$	5.02484	0.190330
$698$	−0.786117	−0.0297550
$699$	−2.59089	−0.0979964
$700$	−6.27455	−0.237156
$701$	26.3182	0.994026	0.497013	−	0.867743i	$-0.334430\pi$
$701$	26.3182	0.994026	0.497013	+	0.867743i	$0.334430\pi$
$702$	6.16816	0.232802
$703$	−2.41387	−0.0910410
$704$	4.12290	0.155388
$705$	−20.9536	−0.789160
$706$	−0.203933	−0.00767513
$707$	32.6951	1.22963
$708$	5.70443	0.214385
$709$	−2.37433	−0.0891697	−0.0445849	−	0.999006i	$-0.514197\pi$
$709$	−2.37433	−0.0891697	−0.0445849	+	0.999006i	$0.514197\pi$
$710$	3.87547	0.145444
$711$	−10.3047	−0.386458
$712$	24.0018	0.899505
$713$	−1.49829	−0.0561113
$714$	−3.53154	−0.132164
$715$	11.0482	0.413179
$716$	1.46593	0.0547846
$717$	12.4289	0.464164
$718$	44.9685	1.67821
$719$	−6.52642	−0.243394	−0.121697	−	0.992567i	$-0.538834\pi$
$719$	−6.52642	−0.243394	−0.121697	+	0.992567i	$0.538834\pi$
$720$	14.1011	0.525518
$721$	−38.5977	−1.43745
$722$	−45.5216	−1.69414
$723$	−11.4386	−0.425407
$724$	−16.5046	−0.613388
$725$	−9.39112	−0.348778
$726$	16.2197	0.601969
$727$	26.3112	0.975830	0.487915	−	0.872891i	$-0.337758\pi$
$727$	26.3112	0.975830	0.487915	+	0.872891i	$0.337758\pi$
$728$	24.5366	0.909388
$729$	1.00000	0.0370370
$730$	74.0034	2.73899
$731$	−6.34228	−0.234578
$732$	−1.32817	−0.0490905
$733$	42.7257	1.57811	0.789055	−	0.614322i	$-0.210570\pi$
$733$	42.7257	1.57811	0.789055	+	0.614322i	$0.210570\pi$
$734$	−29.1052	−1.07429
$735$	−4.29588	−0.158456
$736$	−5.94386	−0.219094
$737$	−10.9832	−0.404570
$738$	10.9160	0.401823
$739$	−5.33712	−0.196329	−0.0981646	−	0.995170i	$-0.531297\pi$
$739$	−5.33712	−0.196329	−0.0981646	+	0.995170i	$0.531297\pi$
$740$	0.646718	0.0237738
$741$	−26.0677	−0.957621
$742$	38.9549	1.43008
$743$	17.2328	0.632210	0.316105	−	0.948724i	$-0.397625\pi$
$743$	17.2328	0.632210	0.316105	+	0.948724i	$0.397625\pi$
$744$	1.93581	0.0709702
$745$	11.4040	0.417812
$746$	51.5625	1.88784
$747$	−11.6910	−0.427752
$748$	−0.475307	−0.0173789
$749$	−48.6829	−1.77884
$750$	−7.53826	−0.275258
$751$	9.59957	0.350293	0.175147	−	0.984542i	$-0.443960\pi$
$751$	9.59957	0.350293	0.175147	+	0.984542i	$0.443960\pi$
$752$	−35.1868	−1.28313
$753$	2.19330	0.0799284
$754$	−17.0511	−0.620966
$755$	−11.6933	−0.425561
$756$	−1.84698	−0.0671742
$757$	36.7059	1.33410	0.667050	−	0.745013i	$-0.267557\pi$
$757$	36.7059	1.33410	0.667050	+	0.745013i	$0.267557\pi$
$758$	−10.2733	−0.373144
$759$	−1.72125	−0.0624773
$760$	−44.0611	−1.59826
$761$	−30.6745	−1.11195	−0.555975	−	0.831199i	$-0.687655\pi$
$761$	−30.6745	−1.11195	−0.555975	+	0.831199i	$0.687655\pi$
$762$	14.0684	0.509646
$763$	8.24400	0.298453
$764$	14.6173	0.528835
$765$	2.16495	0.0782740
$766$	41.3674	1.49467
$767$	−34.1857	−1.23437
$768$	13.8515	0.499821
$769$	8.46242	0.305163	0.152581	−	0.988291i	$-0.451241\pi$
$769$	8.46242	0.305163	0.152581	+	0.988291i	$0.451241\pi$
$770$	−13.7417	−0.495216
$771$	0.614016	0.0221132
$772$	−1.75076	−0.0630111
$773$	−12.4542	−0.447948	−0.223974	−	0.974595i	$-0.571903\pi$
$773$	−12.4542	−0.447948	−0.223974	+	0.974595i	$0.571903\pi$
$774$	−13.7780	−0.495239
$775$	2.96662	0.106564
$776$	−28.8334	−1.03506
$777$	1.02496	0.0367702
$778$	−52.0739	−1.86694
$779$	−46.1328	−1.65288
$780$	6.98398	0.250067
$781$	0.826659	0.0295802
$782$	−2.08044	−0.0743964
$783$	−2.76438	−0.0987909
$784$	−7.21393	−0.257640
$785$	43.1017	1.53837
$786$	−28.0965	−1.00217
$787$	−42.8279	−1.52665	−0.763325	−	0.646014i	$-0.776435\pi$
$787$	−42.8279	−1.52665	−0.763325	+	0.646014i	$0.776435\pi$
$788$	−3.14698	−0.112106
$789$	−5.99528	−0.213438
$790$	−48.4647	−1.72430
$791$	−54.1424	−1.92508
$792$	2.22388	0.0790220
$793$	7.95948	0.282649
$794$	36.6105	1.29926
$795$	−23.8807	−0.846959
$796$	−5.60184	−0.198552
$797$	−24.0907	−0.853337	−0.426668	−	0.904408i	$-0.640313\pi$
$797$	−24.0907	−0.853337	−0.426668	+	0.904408i	$0.640313\pi$
$798$	32.4229	1.14776
$799$	−5.40224	−0.191118
$800$	11.7689	0.416094
$801$	10.8274	0.382567
$802$	52.6510	1.85917
$803$	15.7853	0.557052
$804$	−6.94286	−0.244856
$805$	−14.4804	−0.510367
$806$	5.38639	0.189728
$807$	−8.14348	−0.286664
$808$	−24.8852	−0.875459
$809$	−35.6858	−1.25465	−0.627324	−	0.778759i	$-0.715850\pi$
$809$	−35.6858	−1.25465	−0.627324	+	0.778759i	$0.715850\pi$
$810$	4.70315	0.165252
$811$	26.6593	0.936134	0.468067	−	0.883693i	$-0.344951\pi$
$811$	26.6593	0.936134	0.468067	+	0.883693i	$0.344951\pi$
$812$	5.10577	0.179177
$813$	−23.1457	−0.811754
$814$	0.573004	0.0200838
$815$	−13.6966	−0.479770
$816$	3.63553	0.127269
$817$	58.2281	2.03714
$818$	0.0525713	0.00183811
$819$	11.0687	0.386770
$820$	12.3598	0.431622
$821$	−13.9634	−0.487325	−0.243663	−	0.969860i	$-0.578349\pi$
$821$	−13.9634	−0.487325	−0.243663	+	0.969860i	$0.578349\pi$
$822$	10.0177	0.349407
$823$	−29.6265	−1.03272	−0.516358	−	0.856373i	$-0.672713\pi$
$823$	−29.6265	−1.03272	−0.516358	+	0.856373i	$0.672713\pi$
$824$	29.3778	1.02343
$825$	3.40808	0.118654
$826$	42.5199	1.47946
$827$	−1.29524	−0.0450400	−0.0225200	−	0.999746i	$-0.507169\pi$
$827$	−1.29524	−0.0450400	−0.0225200	+	0.999746i	$0.507169\pi$
$828$	−1.08806	−0.0378128
$829$	−33.3091	−1.15687	−0.578436	−	0.815728i	$-0.696337\pi$
$829$	−33.3091	−1.15687	−0.578436	+	0.815728i	$0.696337\pi$
$830$	−54.9846	−1.90854
$831$	−14.8151	−0.513929
$832$	−15.6188	−0.541483
$833$	−1.10756	−0.0383746
$834$	−24.1184	−0.835151
$835$	−35.4010	−1.22510
$836$	4.36377	0.150924
$837$	0.873258	0.0301842
$838$	−36.6913	−1.26748
$839$	41.3993	1.42926	0.714632	−	0.699501i	$-0.246594\pi$
$839$	41.3993	1.42926	0.714632	+	0.699501i	$0.246594\pi$
$840$	18.7089	0.645518
$841$	−21.3582	−0.736490
$842$	22.1771	0.764273
$843$	7.12442	0.245378
$844$	4.39451	0.151265
$845$	−4.18257	−0.143885
$846$	−11.7358	−0.403486
$847$	29.1060	1.00009
$848$	−40.1020	−1.37711
$849$	1.91334	0.0656656
$850$	4.11929	0.141290
$851$	0.603807	0.0206982
$852$	0.522562	0.0179027
$853$	−35.5022	−1.21557	−0.607785	−	0.794101i	$-0.707942\pi$
$853$	−35.5022	−1.21557	−0.607785	+	0.794101i	$0.707942\pi$
$854$	−9.89995	−0.338769
$855$	−19.8763	−0.679755
$856$	37.0540	1.26648
$857$	0.516765	0.0176524	0.00882618	−	0.999961i	$-0.497191\pi$
$857$	0.516765	0.0176524	0.00882618	+	0.999961i	$0.497191\pi$
$858$	6.18794	0.211253
$859$	−21.7241	−0.741217	−0.370609	−	0.928789i	$-0.620851\pi$
$859$	−21.7241	−0.741217	−0.370609	+	0.928789i	$0.620851\pi$
$860$	−15.6003	−0.531966
$861$	19.5885	0.667576
$862$	−54.4796	−1.85558
$863$	27.6096	0.939843	0.469921	−	0.882708i	$-0.344282\pi$
$863$	27.6096	0.939843	0.469921	+	0.882708i	$0.344282\pi$
$864$	3.46431	0.117858
$865$	51.9159	1.76519
$866$	14.0862	0.478669
$867$	−16.4418	−0.558394
$868$	−1.61289	−0.0547452
$869$	−10.3378	−0.350685
$870$	−13.0013	−0.440785
$871$	41.6074	1.40981
$872$	−6.27475	−0.212490
$873$	−13.0070	−0.440219
$874$	19.1004	0.646081
$875$	−13.5273	−0.457306
$876$	9.97850	0.337142
$877$	−2.46730	−0.0833147	−0.0416573	−	0.999132i	$-0.513264\pi$
$877$	−2.46730	−0.0833147	−0.0416573	+	0.999132i	$0.513264\pi$
$878$	−39.5616	−1.33514
$879$	−11.2012	−0.377808
$880$	14.1463	0.476873
$881$	−36.7328	−1.23756	−0.618779	−	0.785565i	$-0.712372\pi$
$881$	−36.7328	−1.23756	−0.618779	+	0.785565i	$0.712372\pi$
$882$	−2.40606	−0.0810163
$883$	−34.8357	−1.17231	−0.586157	−	0.810197i	$-0.699360\pi$
$883$	−34.8357	−1.17231	−0.586157	+	0.810197i	$0.699360\pi$
$884$	1.80060	0.0605608
$885$	−26.0661	−0.876204
$886$	−39.3178	−1.32091
$887$	19.5838	0.657560	0.328780	−	0.944406i	$-0.393362\pi$
$887$	19.5838	0.657560	0.328780	+	0.944406i	$0.393362\pi$
$888$	−0.780128	−0.0261794
$889$	25.2456	0.846710
$890$	50.9228	1.70694
$891$	1.00321	0.0336087
$892$	−9.67710	−0.324013
$893$	49.5977	1.65972
$894$	6.38724	0.213621
$895$	−6.69853	−0.223907
$896$	39.6059	1.32314
$897$	6.52059	0.217716
$898$	−64.3048	−2.14588
$899$	−2.41402	−0.0805120
$900$	2.15438	0.0718126
$901$	−6.15688	−0.205115
$902$	10.9510	0.364628
$903$	−24.7243	−0.822775
$904$	41.2094	1.37060
$905$	75.4170	2.50694
$906$	−6.54923	−0.217584
$907$	30.3612	1.00813	0.504063	−	0.863667i	$-0.331838\pi$
$907$	30.3612	1.00813	0.504063	+	0.863667i	$0.331838\pi$
$908$	−13.0341	−0.432552
$909$	−11.2259	−0.372340
$910$	52.0575	1.72569
$911$	18.5010	0.612965	0.306483	−	0.951876i	$-0.400848\pi$
$911$	18.5010	0.612965	0.306483	+	0.951876i	$0.400848\pi$
$912$	−33.3776	−1.10524
$913$	−11.7285	−0.388157
$914$	10.8814	0.359925
$915$	6.06900	0.200635
$916$	9.98793	0.330010
$917$	−50.4187	−1.66497
$918$	1.21256	0.0400204
$919$	16.1139	0.531549	0.265775	−	0.964035i	$-0.414372\pi$
$919$	16.1139	0.531549	0.265775	+	0.964035i	$0.414372\pi$
$920$	11.0215	0.363367
$921$	1.22292	0.0402965
$922$	−20.9232	−0.689070
$923$	−3.13163	−0.103079
$924$	−1.85291	−0.0609562
$925$	−1.19554	−0.0393092
$926$	−19.9216	−0.654663
$927$	13.2526	0.435271
$928$	−9.57667	−0.314369
$929$	−14.9844	−0.491621	−0.245810	−	0.969318i	$-0.579054\pi$
$929$	−14.9844	−0.491621	−0.245810	+	0.969318i	$0.579054\pi$
$930$	4.10706	0.134676
$931$	10.1684	0.333257
$932$	−1.64305	−0.0538199
$933$	2.47717	0.0810988
$934$	42.1488	1.37915
$935$	2.17190	0.0710286
$936$	−8.42469	−0.275370
$937$	32.4480	1.06003	0.530016	−	0.847988i	$-0.322186\pi$
$937$	32.4480	1.06003	0.530016	+	0.847988i	$0.322186\pi$
$938$	−51.7510	−1.68973
$939$	−26.3765	−0.860763
$940$	−13.2881	−0.433409
$941$	46.4260	1.51345	0.756723	−	0.653736i	$-0.226799\pi$
$941$	46.4260	1.51345	0.756723	+	0.653736i	$0.226799\pi$
$942$	24.1407	0.786545
$943$	11.5397	0.375784
$944$	−43.7720	−1.42466
$945$	8.43972	0.274544
$946$	−13.8222	−0.449397
$947$	59.2628	1.92578	0.962892	−	0.269888i	$-0.0869868\pi$
$947$	59.2628	1.92578	0.962892	+	0.269888i	$0.0869868\pi$
$948$	−6.53490	−0.212244
$949$	−59.7995	−1.94117
$950$	−37.8190	−1.22701
$951$	−15.7852	−0.511870
$952$	4.82350	0.156331
$953$	−28.3942	−0.919777	−0.459889	−	0.887977i	$-0.652111\pi$
$953$	−28.3942	−0.919777	−0.459889	+	0.887977i	$0.652111\pi$
$954$	−13.3752	−0.433039
$955$	−66.7932	−2.16138
$956$	7.88195	0.254920
$957$	−2.77325	−0.0896463
$958$	−26.1524	−0.844947
$959$	17.9766	0.580495
$960$	−11.9091	−0.384365
$961$	−30.2374	−0.975401
$962$	−2.17071	−0.0699864
$963$	16.7154	0.538645
$964$	−7.25397	−0.233635
$965$	8.00001	0.257529
$966$	−8.11026	−0.260943
$967$	4.90890	0.157860	0.0789298	−	0.996880i	$-0.474850\pi$
$967$	4.90890	0.157860	0.0789298	+	0.996880i	$0.474850\pi$
$968$	−22.1534	−0.712038
$969$	−5.12448	−0.164622
$970$	−61.1736	−1.96417
$971$	−45.2918	−1.45348	−0.726742	−	0.686910i	$-0.758966\pi$
$971$	−45.2918	−1.45348	−0.726742	+	0.686910i	$0.758966\pi$
$972$	0.634165	0.0203408
$973$	−43.2800	−1.38749
$974$	−16.4646	−0.527558
$975$	−12.9108	−0.413477
$976$	10.1915	0.326221
$977$	25.3338	0.810500	0.405250	−	0.914206i	$-0.367184\pi$
$977$	25.3338	0.810500	0.405250	+	0.914206i	$0.367184\pi$
$978$	−7.67126	−0.245300
$979$	10.8621	0.347155
$980$	−2.72429	−0.0870244
$981$	−2.83059	−0.0903737
$982$	69.8596	2.22931
$983$	−5.23923	−0.167106	−0.0835528	−	0.996503i	$-0.526627\pi$
$983$	−5.23923	−0.167106	−0.0835528	+	0.996503i	$0.526627\pi$
$984$	−14.9094	−0.475295
$985$	14.3800	0.458184
$986$	−3.35198	−0.106749
$987$	−21.0598	−0.670340
$988$	−16.5312	−0.525928
$989$	−14.5652	−0.463146
$990$	4.71823	0.149955
$991$	−0.981414	−0.0311756	−0.0155878	−	0.999879i	$-0.504962\pi$
$991$	−0.981414	−0.0311756	−0.0155878	+	0.999879i	$0.504962\pi$
$992$	3.02523	0.0960513
$993$	−26.7746	−0.849665
$994$	3.89510	0.123545
$995$	25.5974	0.811491
$996$	−7.41403	−0.234923
$997$	−29.1963	−0.924657	−0.462329	−	0.886709i	$-0.652986\pi$
$997$	−29.1963	−0.924657	−0.462329	+	0.886709i	$0.652986\pi$
$998$	−49.3218	−1.56126
$999$	−0.351922	−0.0111343

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6033.2.a.b.1.18	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6033.2.a.b.1.18	✓	71	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 6033 = 3 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6033.a (trivial)

\(f(q)\)	\(=\)	\(q-1.62301 q^{2} +1.00000 q^{3} +0.634165 q^{4} -2.89779 q^{5} -1.62301 q^{6} -2.91247 q^{7} +2.21677 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.62301 q^{2} +1.00000 q^{3} +0.634165 q^{4} -2.89779 q^{5} -1.62301 q^{6} -2.91247 q^{7} +2.21677 q^{8} +1.00000 q^{9} +4.70315 q^{10} +1.00321 q^{11} +0.634165 q^{12} -3.80044 q^{13} +4.72697 q^{14} -2.89779 q^{15} -4.86616 q^{16} -0.747105 q^{17} -1.62301 q^{18} +6.85913 q^{19} -1.83768 q^{20} -2.91247 q^{21} -1.62822 q^{22} -1.71574 q^{23} +2.21677 q^{24} +3.39719 q^{25} +6.16816 q^{26} +1.00000 q^{27} -1.84698 q^{28} -2.76438 q^{29} +4.70315 q^{30} +0.873258 q^{31} +3.46431 q^{32} +1.00321 q^{33} +1.21256 q^{34} +8.43972 q^{35} +0.634165 q^{36} -0.351922 q^{37} -11.1324 q^{38} -3.80044 q^{39} -6.42372 q^{40} -6.72576 q^{41} +4.72697 q^{42} +8.48914 q^{43} +0.636199 q^{44} -2.89779 q^{45} +2.78467 q^{46} +7.23090 q^{47} -4.86616 q^{48} +1.48247 q^{49} -5.51367 q^{50} -0.747105 q^{51} -2.41011 q^{52} +8.24099 q^{53} -1.62301 q^{54} -2.90708 q^{55} -6.45626 q^{56} +6.85913 q^{57} +4.48662 q^{58} +8.99518 q^{59} -1.83768 q^{60} -2.09436 q^{61} -1.41731 q^{62} -2.91247 q^{63} +4.10972 q^{64} +11.0129 q^{65} -1.62822 q^{66} -10.9480 q^{67} -0.473787 q^{68} -1.71574 q^{69} -13.6978 q^{70} +0.824016 q^{71} +2.21677 q^{72} +15.7349 q^{73} +0.571173 q^{74} +3.39719 q^{75} +4.34982 q^{76} -2.92181 q^{77} +6.16816 q^{78} -10.3047 q^{79} +14.1011 q^{80} +1.00000 q^{81} +10.9160 q^{82} -11.6910 q^{83} -1.84698 q^{84} +2.16495 q^{85} -13.7780 q^{86} -2.76438 q^{87} +2.22388 q^{88} +10.8274 q^{89} +4.70315 q^{90} +11.0687 q^{91} -1.08806 q^{92} +0.873258 q^{93} -11.7358 q^{94} -19.8763 q^{95} +3.46431 q^{96} -13.0070 q^{97} -2.40606 q^{98} +1.00321 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q - 11 q^{2} + 71 q^{3} + 53 q^{4} - 8 q^{5} - 11 q^{6} - 46 q^{7} - 33 q^{8} + 71 q^{9}+O(q^{10}) \) 71 * q - 11 * q^2 + 71 * q^3 + 53 * q^4 - 8 * q^5 - 11 * q^6 - 46 * q^7 - 33 * q^8 + 71 * q^9	\( 71 q - 11 q^{2} + 71 q^{3} + 53 q^{4} - 8 q^{5} - 11 q^{6} - 46 q^{7} - 33 q^{8} + 71 q^{9} - 41 q^{10} - 18 q^{11} + 53 q^{12} - 67 q^{13} - 7 q^{14} - 8 q^{15} + 21 q^{16} - 25 q^{17} - 11 q^{18} - 43 q^{19} - 8 q^{20} - 46 q^{21} - 49 q^{22} - 75 q^{23} - 33 q^{24} + 19 q^{25} + 71 q^{27} - 89 q^{28} - 35 q^{29} - 41 q^{30} - 82 q^{31} - 62 q^{32} - 18 q^{33} - 28 q^{34} - 51 q^{35} + 53 q^{36} - 66 q^{37} - 29 q^{38} - 67 q^{39} - 102 q^{40} + q^{41} - 7 q^{42} - 112 q^{43} - 25 q^{44} - 8 q^{45} - 36 q^{46} - 67 q^{47} + 21 q^{48} + 7 q^{49} - 24 q^{50} - 25 q^{51} - 134 q^{52} - 40 q^{53} - 11 q^{54} - 112 q^{55} + 9 q^{56} - 43 q^{57} - 47 q^{58} - 18 q^{59} - 8 q^{60} - 144 q^{61} - 19 q^{62} - 46 q^{63} - 17 q^{64} - 31 q^{65} - 49 q^{66} - 85 q^{67} - 22 q^{68} - 75 q^{69} - 11 q^{70} - 44 q^{71} - 33 q^{72} - 98 q^{73} + 6 q^{74} + 19 q^{75} - 85 q^{76} - 39 q^{77} - 126 q^{79} + 21 q^{80} + 71 q^{81} - 69 q^{82} - 43 q^{83} - 89 q^{84} - 112 q^{85} + 32 q^{86} - 35 q^{87} - 85 q^{88} + 8 q^{89} - 41 q^{90} - 40 q^{91} - 96 q^{92} - 82 q^{93} - 99 q^{94} - 103 q^{95} - 62 q^{96} - 67 q^{97} - 11 q^{98} - 18 q^{99}+O(q^{100}) \) 71 * q - 11 * q^2 + 71 * q^3 + 53 * q^4 - 8 * q^5 - 11 * q^6 - 46 * q^7 - 33 * q^8 + 71 * q^9 - 41 * q^10 - 18 * q^11 + 53 * q^12 - 67 * q^13 - 7 * q^14 - 8 * q^15 + 21 * q^16 - 25 * q^17 - 11 * q^18 - 43 * q^19 - 8 * q^20 - 46 * q^21 - 49 * q^22 - 75 * q^23 - 33 * q^24 + 19 * q^25 + 71 * q^27 - 89 * q^28 - 35 * q^29 - 41 * q^30 - 82 * q^31 - 62 * q^32 - 18 * q^33 - 28 * q^34 - 51 * q^35 + 53 * q^36 - 66 * q^37 - 29 * q^38 - 67 * q^39 - 102 * q^40 + q^41 - 7 * q^42 - 112 * q^43 - 25 * q^44 - 8 * q^45 - 36 * q^46 - 67 * q^47 + 21 * q^48 + 7 * q^49 - 24 * q^50 - 25 * q^51 - 134 * q^52 - 40 * q^53 - 11 * q^54 - 112 * q^55 + 9 * q^56 - 43 * q^57 - 47 * q^58 - 18 * q^59 - 8 * q^60 - 144 * q^61 - 19 * q^62 - 46 * q^63 - 17 * q^64 - 31 * q^65 - 49 * q^66 - 85 * q^67 - 22 * q^68 - 75 * q^69 - 11 * q^70 - 44 * q^71 - 33 * q^72 - 98 * q^73 + 6 * q^74 + 19 * q^75 - 85 * q^76 - 39 * q^77 - 126 * q^79 + 21 * q^80 + 71 * q^81 - 69 * q^82 - 43 * q^83 - 89 * q^84 - 112 * q^85 + 32 * q^86 - 35 * q^87 - 85 * q^88 + 8 * q^89 - 41 * q^90 - 40 * q^91 - 96 * q^92 - 82 * q^93 - 99 * q^94 - 103 * q^95 - 62 * q^96 - 67 * q^97 - 11 * q^98 - 18 * q^99

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