LMFDB - Embedded newform 6005.2.a.e.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6005,2,Mod(1,6005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6005, 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("6005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6005 = 5 \cdot 1201 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6005.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:	$47.9501664138$
Analytic rank:	$1$
Dimension:	$88$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	6005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.93565 q^{2} -2.84784 q^{3} +1.74674 q^{4} +1.00000 q^{5} +5.51242 q^{6} -0.215804 q^{7} +0.490231 q^{8} +5.11019 q^{9} +O(q^{10})$	\(q-1.93565 q^{2} -2.84784 q^{3} +1.74674 q^{4} +1.00000 q^{5} +5.51242 q^{6} -0.215804 q^{7} +0.490231 q^{8} +5.11019 q^{9} -1.93565 q^{10} +4.79032 q^{11} -4.97442 q^{12} -1.79292 q^{13} +0.417720 q^{14} -2.84784 q^{15} -4.44239 q^{16} -1.46000 q^{17} -9.89154 q^{18} +4.27100 q^{19} +1.74674 q^{20} +0.614574 q^{21} -9.27237 q^{22} +6.50882 q^{23} -1.39610 q^{24} +1.00000 q^{25} +3.47046 q^{26} -6.00949 q^{27} -0.376952 q^{28} -6.21201 q^{29} +5.51242 q^{30} +9.10977 q^{31} +7.61844 q^{32} -13.6421 q^{33} +2.82605 q^{34} -0.215804 q^{35} +8.92615 q^{36} -6.93995 q^{37} -8.26716 q^{38} +5.10594 q^{39} +0.490231 q^{40} +5.72983 q^{41} -1.18960 q^{42} +10.4530 q^{43} +8.36742 q^{44} +5.11019 q^{45} -12.5988 q^{46} -12.4130 q^{47} +12.6512 q^{48} -6.95343 q^{49} -1.93565 q^{50} +4.15785 q^{51} -3.13175 q^{52} -6.10927 q^{53} +11.6323 q^{54} +4.79032 q^{55} -0.105794 q^{56} -12.1631 q^{57} +12.0243 q^{58} -11.0340 q^{59} -4.97442 q^{60} +0.228681 q^{61} -17.6333 q^{62} -1.10280 q^{63} -5.86184 q^{64} -1.79292 q^{65} +26.4062 q^{66} -6.11430 q^{67} -2.55023 q^{68} -18.5361 q^{69} +0.417720 q^{70} -11.7331 q^{71} +2.50518 q^{72} -15.3318 q^{73} +13.4333 q^{74} -2.84784 q^{75} +7.46031 q^{76} -1.03377 q^{77} -9.88331 q^{78} -9.30846 q^{79} -4.44239 q^{80} +1.78349 q^{81} -11.0909 q^{82} -8.04431 q^{83} +1.07350 q^{84} -1.46000 q^{85} -20.2334 q^{86} +17.6908 q^{87} +2.34836 q^{88} +13.9776 q^{89} -9.89154 q^{90} +0.386918 q^{91} +11.3692 q^{92} -25.9432 q^{93} +24.0272 q^{94} +4.27100 q^{95} -21.6961 q^{96} +1.98578 q^{97} +13.4594 q^{98} +24.4795 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 14 q^{2} - 34 q^{3} + 66 q^{4} + 88 q^{5} - q^{6} - 35 q^{7} - 39 q^{8} + 72 q^{9}+O(q^{10}) $ 88 * q - 14 * q^2 - 34 * q^3 + 66 * q^4 + 88 * q^5 - q^6 - 35 * q^7 - 39 * q^8 + 72 * q^9	\( 88 q - 14 q^{2} - 34 q^{3} + 66 q^{4} + 88 q^{5} - q^{6} - 35 q^{7} - 39 q^{8} + 72 q^{9} - 14 q^{10} - 26 q^{11} - 64 q^{12} - 31 q^{13} - 17 q^{14} - 34 q^{15} + 34 q^{16} - 31 q^{17} - 42 q^{18} - 56 q^{19} + 66 q^{20} - q^{21} - 49 q^{22} - 74 q^{23} - 3 q^{24} + 88 q^{25} - q^{26} - 130 q^{27} - 57 q^{28} - 6 q^{29} - q^{30} - 37 q^{31} - 87 q^{32} - 43 q^{33} - 35 q^{34} - 35 q^{35} + 53 q^{36} - 67 q^{37} - 40 q^{38} - 21 q^{39} - 39 q^{40} + 2 q^{41} - 15 q^{42} - 136 q^{43} - 15 q^{44} + 72 q^{45} - 16 q^{46} - 139 q^{47} - 71 q^{48} + 41 q^{49} - 14 q^{50} - 71 q^{51} - 71 q^{52} - 75 q^{53} + 26 q^{54} - 26 q^{55} - 22 q^{56} - 34 q^{57} - 65 q^{58} - 41 q^{59} - 64 q^{60} - 11 q^{61} - 30 q^{62} - 114 q^{63} - 33 q^{64} - 31 q^{65} + 24 q^{66} - 209 q^{67} - 42 q^{68} - 22 q^{69} - 17 q^{70} - 43 q^{71} - 80 q^{72} - 50 q^{73} + 9 q^{74} - 34 q^{75} - 62 q^{76} - 49 q^{77} - 19 q^{78} - 77 q^{79} + 34 q^{80} + 72 q^{81} - 107 q^{82} - 113 q^{83} + 19 q^{84} - 31 q^{85} + 14 q^{86} - 87 q^{87} - 107 q^{88} - 5 q^{89} - 42 q^{90} - 159 q^{91} - 100 q^{92} - 82 q^{93} - 31 q^{94} - 56 q^{95} + 58 q^{96} - 105 q^{97} - 29 q^{98} - 68 q^{99}+O(q^{100}) \) 88 * q - 14 * q^2 - 34 * q^3 + 66 * q^4 + 88 * q^5 - q^6 - 35 * q^7 - 39 * q^8 + 72 * q^9 - 14 * q^10 - 26 * q^11 - 64 * q^12 - 31 * q^13 - 17 * q^14 - 34 * q^15 + 34 * q^16 - 31 * q^17 - 42 * q^18 - 56 * q^19 + 66 * q^20 - q^21 - 49 * q^22 - 74 * q^23 - 3 * q^24 + 88 * q^25 - q^26 - 130 * q^27 - 57 * q^28 - 6 * q^29 - q^30 - 37 * q^31 - 87 * q^32 - 43 * q^33 - 35 * q^34 - 35 * q^35 + 53 * q^36 - 67 * q^37 - 40 * q^38 - 21 * q^39 - 39 * q^40 + 2 * q^41 - 15 * q^42 - 136 * q^43 - 15 * q^44 + 72 * q^45 - 16 * q^46 - 139 * q^47 - 71 * q^48 + 41 * q^49 - 14 * q^50 - 71 * q^51 - 71 * q^52 - 75 * q^53 + 26 * q^54 - 26 * q^55 - 22 * q^56 - 34 * q^57 - 65 * q^58 - 41 * q^59 - 64 * q^60 - 11 * q^61 - 30 * q^62 - 114 * q^63 - 33 * q^64 - 31 * q^65 + 24 * q^66 - 209 * q^67 - 42 * q^68 - 22 * q^69 - 17 * q^70 - 43 * q^71 - 80 * q^72 - 50 * q^73 + 9 * q^74 - 34 * q^75 - 62 * q^76 - 49 * q^77 - 19 * q^78 - 77 * q^79 + 34 * q^80 + 72 * q^81 - 107 * q^82 - 113 * q^83 + 19 * q^84 - 31 * q^85 + 14 * q^86 - 87 * q^87 - 107 * q^88 - 5 * q^89 - 42 * q^90 - 159 * q^91 - 100 * q^92 - 82 * q^93 - 31 * q^94 - 56 * q^95 + 58 * q^96 - 105 * q^97 - 29 * q^98 - 68 * 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 $

$2$	−1.93565	−1.36871	−0.684355	−	0.729149i	$-0.739916\pi$
$2$	−1.93565	−1.36871	−0.684355	+	0.729149i	$0.739916\pi$
$3$	−2.84784	−1.64420	−0.822101	−	0.569342i	$-0.807198\pi$
$3$	−2.84784	−1.64420	−0.822101	+	0.569342i	$0.807198\pi$
$4$	1.74674	0.873368
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	5.51242	2.25044
$7$	−0.215804	−0.0815661	−0.0407830	−	0.999168i	$-0.512985\pi$
$7$	−0.215804	−0.0815661	−0.0407830	+	0.999168i	$0.512985\pi$
$8$	0.490231	0.173323
$9$	5.11019	1.70340
$10$	−1.93565	−0.612106
$11$	4.79032	1.44434	0.722168	−	0.691718i	$-0.243146\pi$
$11$	4.79032	1.44434	0.722168	+	0.691718i	$0.243146\pi$
$12$	−4.97442	−1.43599
$13$	−1.79292	−0.497266	−0.248633	−	0.968598i	$-0.579981\pi$
$13$	−1.79292	−0.497266	−0.248633	+	0.968598i	$0.579981\pi$
$14$	0.417720	0.111640
$15$	−2.84784	−0.735309
$16$	−4.44239	−1.11060
$17$	−1.46000	−0.354102	−0.177051	−	0.984202i	$-0.556656\pi$
$17$	−1.46000	−0.354102	−0.177051	+	0.984202i	$0.556656\pi$
$18$	−9.89154	−2.33146
$19$	4.27100	0.979835	0.489917	−	0.871769i	$-0.337027\pi$
$19$	4.27100	0.979835	0.489917	+	0.871769i	$0.337027\pi$
$20$	1.74674	0.390582
$21$	0.614574	0.134111
$22$	−9.27237	−1.97688
$23$	6.50882	1.35718	0.678591	−	0.734516i	$-0.262591\pi$
$23$	6.50882	1.35718	0.678591	+	0.734516i	$0.262591\pi$
$24$	−1.39610	−0.284978
$25$	1.00000	0.200000
$26$	3.47046	0.680613
$27$	−6.00949	−1.15653
$28$	−0.376952	−0.0712372
$29$	−6.21201	−1.15354	−0.576771	−	0.816906i	$-0.695687\pi$
$29$	−6.21201	−1.15354	−0.576771	+	0.816906i	$0.695687\pi$
$30$	5.51242	1.00643
$31$	9.10977	1.63616	0.818082	−	0.575102i	$-0.195038\pi$
$31$	9.10977	1.63616	0.818082	+	0.575102i	$0.195038\pi$
$32$	7.61844	1.34676
$33$	−13.6421	−2.37478
$34$	2.82605	0.484663
$35$	−0.215804	−0.0364775
$36$	8.92615	1.48769
$37$	−6.93995	−1.14092	−0.570460	−	0.821325i	$-0.693235\pi$
$37$	−6.93995	−1.14092	−0.570460	+	0.821325i	$0.693235\pi$
$38$	−8.26716	−1.34111
$39$	5.10594	0.817605
$40$	0.490231	0.0775124
$41$	5.72983	0.894850	0.447425	−	0.894322i	$-0.352341\pi$
$41$	5.72983	0.894850	0.447425	+	0.894322i	$0.352341\pi$
$42$	−1.18960	−0.183559
$43$	10.4530	1.59407	0.797036	−	0.603932i	$-0.206400\pi$
$43$	10.4530	1.59407	0.797036	+	0.603932i	$0.206400\pi$
$44$	8.36742	1.26144
$45$	5.11019	0.761783
$46$	−12.5988	−1.85759
$47$	−12.4130	−1.81062	−0.905309	−	0.424753i	$-0.860361\pi$
$47$	−12.4130	−1.81062	−0.905309	+	0.424753i	$0.860361\pi$
$48$	12.6512	1.82604
$49$	−6.95343	−0.993347
$50$	−1.93565	−0.273742
$51$	4.15785	0.582215
$52$	−3.13175	−0.434296
$53$	−6.10927	−0.839172	−0.419586	−	0.907715i	$-0.637825\pi$
$53$	−6.10927	−0.839172	−0.419586	+	0.907715i	$0.637825\pi$
$54$	11.6323	1.58295
$55$	4.79032	0.645926
$56$	−0.105794	−0.0141373
$57$	−12.1631	−1.61105
$58$	12.0243	1.57886
$59$	−11.0340	−1.43650	−0.718251	−	0.695784i	$-0.755057\pi$
$59$	−11.0340	−1.43650	−0.718251	+	0.695784i	$0.755057\pi$
$60$	−4.97442	−0.642195
$61$	0.228681	0.0292796	0.0146398	−	0.999893i	$-0.495340\pi$
$61$	0.228681	0.0292796	0.0146398	+	0.999893i	$0.495340\pi$
$62$	−17.6333	−2.23943
$63$	−1.10280	−0.138939
$64$	−5.86184	−0.732730
$65$	−1.79292	−0.222384
$66$	26.4062	3.25038
$67$	−6.11430	−0.746980	−0.373490	−	0.927634i	$-0.621839\pi$
$67$	−6.11430	−0.746980	−0.373490	+	0.927634i	$0.621839\pi$
$68$	−2.55023	−0.309261
$69$	−18.5361	−2.23148
$70$	0.417720	0.0499271
$71$	−11.7331	−1.39247	−0.696233	−	0.717815i	$-0.745142\pi$
$71$	−11.7331	−1.39247	−0.696233	+	0.717815i	$0.745142\pi$
$72$	2.50518	0.295238
$73$	−15.3318	−1.79446	−0.897228	−	0.441568i	$-0.854422\pi$
$73$	−15.3318	−1.79446	−0.897228	+	0.441568i	$0.854422\pi$
$74$	13.4333	1.56159
$75$	−2.84784	−0.328840
$76$	7.46031	0.855756
$77$	−1.03377	−0.117809
$78$	−9.88331	−1.11906
$79$	−9.30846	−1.04728	−0.523642	−	0.851939i	$-0.675427\pi$
$79$	−9.30846	−1.04728	−0.523642	+	0.851939i	$0.675427\pi$
$80$	−4.44239	−0.496674
$81$	1.78349	0.198166
$82$	−11.0909	−1.22479
$83$	−8.04431	−0.882978	−0.441489	−	0.897267i	$-0.645550\pi$
$83$	−8.04431	−0.882978	−0.441489	+	0.897267i	$0.645550\pi$
$84$	1.07350	0.117128
$85$	−1.46000	−0.158359
$86$	−20.2334	−2.18182
$87$	17.6908	1.89665
$88$	2.34836	0.250336
$89$	13.9776	1.48162	0.740810	−	0.671715i	$-0.234442\pi$
$89$	13.9776	1.48162	0.740810	+	0.671715i	$0.234442\pi$
$90$	−9.89154	−1.04266
$91$	0.386918	0.0405600
$92$	11.3692	1.18532
$93$	−25.9432	−2.69018
$94$	24.0272	2.47821
$95$	4.27100	0.438195
$96$	−21.6961	−2.21435
$97$	1.98578	0.201625	0.100813	−	0.994905i	$-0.467856\pi$
$97$	1.98578	0.201625	0.100813	+	0.994905i	$0.467856\pi$
$98$	13.4594	1.35960
$99$	24.4795	2.46028
$100$	1.74674	0.174674
$101$	−7.76800	−0.772944	−0.386472	−	0.922301i	$-0.626306\pi$
$101$	−7.76800	−0.772944	−0.386472	+	0.922301i	$0.626306\pi$
$102$	−8.04813	−0.796883
$103$	−6.74763	−0.664863	−0.332432	−	0.943127i	$-0.607869\pi$
$103$	−6.74763	−0.664863	−0.332432	+	0.943127i	$0.607869\pi$
$104$	−0.878944	−0.0861876
$105$	0.614574	0.0599763
$106$	11.8254	1.14858
$107$	−9.42839	−0.911477	−0.455738	−	0.890114i	$-0.650625\pi$
$107$	−9.42839	−0.911477	−0.455738	+	0.890114i	$0.650625\pi$
$108$	−10.4970	−1.01007
$109$	18.2880	1.75168	0.875838	−	0.482605i	$-0.160309\pi$
$109$	18.2880	1.75168	0.875838	+	0.482605i	$0.160309\pi$
$110$	−9.27237	−0.884086
$111$	19.7639	1.87590
$112$	0.958683	0.0905870
$113$	7.24711	0.681750	0.340875	−	0.940109i	$-0.389277\pi$
$113$	7.24711	0.681750	0.340875	+	0.940109i	$0.389277\pi$
$114$	23.5435	2.20505
$115$	6.50882	0.606951
$116$	−10.8507	−1.00747
$117$	−9.16215	−0.847041
$118$	21.3579	1.96615
$119$	0.315073	0.0288827
$120$	−1.39610	−0.127446
$121$	11.9472	1.08610
$122$	−0.442647	−0.0400753
$123$	−16.3176	−1.47131
$124$	15.9124	1.42897
$125$	1.00000	0.0894427
$126$	2.13463	0.190168
$127$	−0.815627	−0.0723752	−0.0361876	−	0.999345i	$-0.511521\pi$
$127$	−0.815627	−0.0723752	−0.0361876	+	0.999345i	$0.511521\pi$
$128$	−3.89041	−0.343866
$129$	−29.7686	−2.62098
$130$	3.47046	0.304379
$131$	4.08288	0.356723	0.178361	−	0.983965i	$-0.442920\pi$
$131$	4.08288	0.356723	0.178361	+	0.983965i	$0.442920\pi$
$132$	−23.8291	−2.07405
$133$	−0.921697	−0.0799213
$134$	11.8351	1.02240
$135$	−6.00949	−0.517215
$136$	−0.715737	−0.0613740
$137$	7.18715	0.614040	0.307020	−	0.951703i	$-0.400668\pi$
$137$	7.18715	0.614040	0.307020	+	0.951703i	$0.400668\pi$
$138$	35.8793	3.05425
$139$	6.17665	0.523897	0.261948	−	0.965082i	$-0.415635\pi$
$139$	6.17665	0.523897	0.261948	+	0.965082i	$0.415635\pi$
$140$	−0.376952	−0.0318582
$141$	35.3502	2.97702
$142$	22.7112	1.90588
$143$	−8.58865	−0.718219
$144$	−22.7015	−1.89179
$145$	−6.21201	−0.515880
$146$	29.6770	2.45609
$147$	19.8023	1.63326
$148$	−12.1223	−0.996443
$149$	15.0227	1.23071	0.615355	−	0.788250i	$-0.289013\pi$
$149$	15.0227	1.23071	0.615355	+	0.788250i	$0.289013\pi$
$150$	5.51242	0.450087
$151$	−14.1613	−1.15243	−0.576216	−	0.817297i	$-0.695471\pi$
$151$	−14.1613	−1.15243	−0.576216	+	0.817297i	$0.695471\pi$
$152$	2.09378	0.169828
$153$	−7.46088	−0.603176
$154$	2.00101	0.161246
$155$	9.10977	0.731715
$156$	8.91873	0.714070
$157$	−5.82286	−0.464715	−0.232358	−	0.972630i	$-0.574644\pi$
$157$	−5.82286	−0.464715	−0.232358	+	0.972630i	$0.574644\pi$
$158$	18.0179	1.43343
$159$	17.3982	1.37977
$160$	7.61844	0.602290
$161$	−1.40463	−0.110700
$162$	−3.45221	−0.271232
$163$	−11.7684	−0.921773	−0.460886	−	0.887459i	$-0.652468\pi$
$163$	−11.7684	−0.921773	−0.460886	+	0.887459i	$0.652468\pi$
$164$	10.0085	0.781533
$165$	−13.6421	−1.06203
$166$	15.5710	1.20854
$167$	−2.83341	−0.219256	−0.109628	−	0.993973i	$-0.534966\pi$
$167$	−2.83341	−0.219256	−0.109628	+	0.993973i	$0.534966\pi$
$168$	0.301283	0.0232445
$169$	−9.78545	−0.752727
$170$	2.82605	0.216748
$171$	21.8256	1.66905
$172$	18.2587	1.39221
$173$	4.71442	0.358431	0.179215	−	0.983810i	$-0.442644\pi$
$173$	4.71442	0.358431	0.179215	+	0.983810i	$0.442644\pi$
$174$	−34.2432	−2.59597
$175$	−0.215804	−0.0163132
$176$	−21.2804	−1.60407
$177$	31.4230	2.36190
$178$	−27.0557	−2.02791
$179$	0.112716	0.00842481	0.00421241	−	0.999991i	$-0.498659\pi$
$179$	0.112716	0.00842481	0.00421241	+	0.999991i	$0.498659\pi$
$180$	8.92615	0.665316
$181$	−9.12443	−0.678213	−0.339107	−	0.940748i	$-0.610125\pi$
$181$	−9.12443	−0.678213	−0.339107	+	0.940748i	$0.610125\pi$
$182$	−0.748937	−0.0555149
$183$	−0.651248	−0.0481416
$184$	3.19083	0.235231
$185$	−6.93995	−0.510235
$186$	50.2169	3.68208
$187$	−6.99386	−0.511442
$188$	−21.6822	−1.58134
$189$	1.29687	0.0943334
$190$	−8.26716	−0.599763
$191$	−3.75464	−0.271676	−0.135838	−	0.990731i	$-0.543373\pi$
$191$	−3.75464	−0.271676	−0.135838	+	0.990731i	$0.543373\pi$
$192$	16.6936	1.20476
$193$	16.1694	1.16390	0.581951	−	0.813224i	$-0.302290\pi$
$193$	16.1694	1.16390	0.581951	+	0.813224i	$0.302290\pi$
$194$	−3.84377	−0.275967
$195$	5.10594	0.365644
$196$	−12.1458	−0.867557
$197$	−21.6902	−1.54537	−0.772683	−	0.634792i	$-0.781086\pi$
$197$	−21.6902	−1.54537	−0.772683	+	0.634792i	$0.781086\pi$
$198$	−47.3836	−3.36741
$199$	9.77490	0.692924	0.346462	−	0.938064i	$-0.387383\pi$
$199$	9.77490	0.692924	0.346462	+	0.938064i	$0.387383\pi$
$200$	0.490231	0.0346646
$201$	17.4125	1.22819
$202$	15.0361	1.05794
$203$	1.34057	0.0940899
$204$	7.26266	0.508488
$205$	5.72983	0.400189
$206$	13.0610	0.910005
$207$	33.2613	2.31182
$208$	7.96483	0.552262
$209$	20.4595	1.41521
$210$	−1.18960	−0.0820902
$211$	−17.6815	−1.21725	−0.608624	−	0.793459i	$-0.708278\pi$
$211$	−17.6815	−1.21725	−0.608624	+	0.793459i	$0.708278\pi$
$212$	−10.6713	−0.732906
$213$	33.4141	2.28950
$214$	18.2500	1.24755
$215$	10.4530	0.712891
$216$	−2.94604	−0.200453
$217$	−1.96592	−0.133455
$218$	−35.3992	−2.39754
$219$	43.6626	2.95045
$220$	8.36742	0.564131
$221$	2.61766	0.176083
$222$	−38.2559	−2.56757
$223$	19.5267	1.30760	0.653802	−	0.756666i	$-0.273173\pi$
$223$	19.5267	1.30760	0.653802	+	0.756666i	$0.273173\pi$
$224$	−1.64409	−0.109850
$225$	5.11019	0.340680
$226$	−14.0278	−0.933119
$227$	−19.4724	−1.29243	−0.646215	−	0.763156i	$-0.723649\pi$
$227$	−19.4724	−1.29243	−0.646215	+	0.763156i	$0.723649\pi$
$228$	−21.2458	−1.40704
$229$	4.10009	0.270942	0.135471	−	0.990781i	$-0.456745\pi$
$229$	4.10009	0.270942	0.135471	+	0.990781i	$0.456745\pi$
$230$	−12.5988	−0.830740
$231$	2.94401	0.193701
$232$	−3.04532	−0.199935
$233$	−20.2133	−1.32421	−0.662107	−	0.749409i	$-0.730338\pi$
$233$	−20.2133	−1.32421	−0.662107	+	0.749409i	$0.730338\pi$
$234$	17.7347	1.15935
$235$	−12.4130	−0.809733
$236$	−19.2734	−1.25459
$237$	26.5090	1.72194
$238$	−0.609871	−0.0395321
$239$	−7.45987	−0.482539	−0.241270	−	0.970458i	$-0.577564\pi$
$239$	−7.45987	−0.482539	−0.241270	+	0.970458i	$0.577564\pi$
$240$	12.6512	0.816632
$241$	9.52362	0.613470	0.306735	−	0.951795i	$-0.400763\pi$
$241$	9.52362	0.613470	0.306735	+	0.951795i	$0.400763\pi$
$242$	−23.1255	−1.48656
$243$	12.9494	0.830703
$244$	0.399446	0.0255719
$245$	−6.95343	−0.444238
$246$	31.5852	2.01380
$247$	−7.65755	−0.487238
$248$	4.46590	0.283585
$249$	22.9089	1.45179
$250$	−1.93565	−0.122421
$251$	−25.1477	−1.58731	−0.793655	−	0.608368i	$-0.791825\pi$
$251$	−25.1477	−1.58731	−0.793655	+	0.608368i	$0.791825\pi$
$252$	−1.92630	−0.121345
$253$	31.1793	1.96023
$254$	1.57877	0.0990606
$255$	4.15785	0.260374
$256$	19.2541	1.20338
$257$	27.7907	1.73353	0.866767	−	0.498713i	$-0.166194\pi$
$257$	27.7907	1.73353	0.866767	+	0.498713i	$0.166194\pi$
$258$	57.6215	3.58736
$259$	1.49767	0.0930604
$260$	−3.13175	−0.194223
$261$	−31.7446	−1.96494
$262$	−7.90302	−0.488250
$263$	21.9191	1.35159	0.675793	−	0.737091i	$-0.263801\pi$
$263$	21.9191	1.35159	0.675793	+	0.737091i	$0.263801\pi$
$264$	−6.68777	−0.411603
$265$	−6.10927	−0.375289
$266$	1.78408	0.109389
$267$	−39.8059	−2.43608
$268$	−10.6801	−0.652388
$269$	−4.71290	−0.287351	−0.143675	−	0.989625i	$-0.545892\pi$
$269$	−4.71290	−0.287351	−0.143675	+	0.989625i	$0.545892\pi$
$270$	11.6323	0.707917
$271$	2.70638	0.164401	0.0822006	−	0.996616i	$-0.473805\pi$
$271$	2.70638	0.164401	0.0822006	+	0.996616i	$0.473805\pi$
$272$	6.48588	0.393264
$273$	−1.10188	−0.0666888
$274$	−13.9118	−0.840442
$275$	4.79032	0.288867
$276$	−32.3776	−1.94890
$277$	−5.21981	−0.313628	−0.156814	−	0.987628i	$-0.550122\pi$
$277$	−5.21981	−0.313628	−0.156814	+	0.987628i	$0.550122\pi$
$278$	−11.9558	−0.717063
$279$	46.5527	2.78704
$280$	−0.105794	−0.00632238
$281$	−14.5588	−0.868503	−0.434252	−	0.900792i	$-0.642987\pi$
$281$	−14.5588	−0.868503	−0.434252	+	0.900792i	$0.642987\pi$
$282$	−68.4255	−4.07468
$283$	−0.905513	−0.0538272	−0.0269136	−	0.999638i	$-0.508568\pi$
$283$	−0.905513	−0.0538272	−0.0269136	+	0.999638i	$0.508568\pi$
$284$	−20.4947	−1.21614
$285$	−12.1631	−0.720481
$286$	16.6246	0.983033
$287$	−1.23652	−0.0729894
$288$	38.9317	2.29407
$289$	−14.8684	−0.874612
$290$	12.0243	0.706090
$291$	−5.65519	−0.331513
$292$	−26.7807	−1.56722
$293$	22.7621	1.32977	0.664887	−	0.746944i	$-0.268480\pi$
$293$	22.7621	1.32977	0.664887	+	0.746944i	$0.268480\pi$
$294$	−38.3302	−2.23546
$295$	−11.0340	−0.642423
$296$	−3.40218	−0.197748
$297$	−28.7874	−1.67041
$298$	−29.0787	−1.68449
$299$	−11.6698	−0.674881
$300$	−4.97442	−0.287198
$301$	−2.25580	−0.130022
$302$	27.4114	1.57735
$303$	22.1220	1.27088
$304$	−18.9734	−1.08820
$305$	0.228681	0.0130943
$306$	14.4416	0.825574
$307$	10.0203	0.571891	0.285946	−	0.958246i	$-0.407692\pi$
$307$	10.0203	0.571891	0.285946	+	0.958246i	$0.407692\pi$
$308$	−1.80572	−0.102890
$309$	19.2162	1.09317
$310$	−17.6333	−1.00151
$311$	7.14617	0.405222	0.202611	−	0.979259i	$-0.435057\pi$
$311$	7.14617	0.405222	0.202611	+	0.979259i	$0.435057\pi$
$312$	2.50309	0.141710
$313$	14.6324	0.827073	0.413536	−	0.910488i	$-0.364293\pi$
$313$	14.6324	0.827073	0.413536	+	0.910488i	$0.364293\pi$
$314$	11.2710	0.636060
$315$	−1.10280	−0.0621356
$316$	−16.2594	−0.914663
$317$	7.63672	0.428921	0.214460	−	0.976733i	$-0.431201\pi$
$317$	7.63672	0.428921	0.214460	+	0.976733i	$0.431201\pi$
$318$	−33.6768	−1.88850
$319$	−29.7575	−1.66610
$320$	−5.86184	−0.327687
$321$	26.8505	1.49865
$322$	2.71886	0.151516
$323$	−6.23566	−0.346961
$324$	3.11529	0.173072
$325$	−1.79292	−0.0994532
$326$	22.7795	1.26164
$327$	−52.0814	−2.88011
$328$	2.80894	0.155098
$329$	2.67876	0.147685
$330$	26.4062	1.45362
$331$	−15.5648	−0.855518	−0.427759	−	0.903893i	$-0.640697\pi$
$331$	−15.5648	−0.855518	−0.427759	+	0.903893i	$0.640697\pi$
$332$	−14.0513	−0.771164
$333$	−35.4645	−1.94344
$334$	5.48449	0.300098
$335$	−6.11430	−0.334060
$336$	−2.73018	−0.148943
$337$	−34.2991	−1.86839	−0.934197	−	0.356759i	$-0.883882\pi$
$337$	−34.2991	−1.86839	−0.934197	+	0.356759i	$0.883882\pi$
$338$	18.9412	1.03026
$339$	−20.6386	−1.12093
$340$	−2.55023	−0.138306
$341$	43.6387	2.36317
$342$	−42.2468	−2.28444
$343$	3.01120	0.162590
$344$	5.12440	0.276289
$345$	−18.5361	−0.997949
$346$	−9.12546	−0.490588
$347$	−9.12691	−0.489958	−0.244979	−	0.969528i	$-0.578781\pi$
$347$	−9.12691	−0.489958	−0.244979	+	0.969528i	$0.578781\pi$
$348$	30.9012	1.65648
$349$	−32.4986	−1.73961	−0.869806	−	0.493394i	$-0.835756\pi$
$349$	−32.4986	−1.73961	−0.869806	+	0.493394i	$0.835756\pi$
$350$	0.417720	0.0223281
$351$	10.7745	0.575101
$352$	36.4947	1.94518
$353$	35.7485	1.90270	0.951350	−	0.308112i	$-0.0996971\pi$
$353$	35.7485	1.90270	0.951350	+	0.308112i	$0.0996971\pi$
$354$	−60.8239	−3.23275
$355$	−11.7331	−0.622730
$356$	24.4151	1.29400
$357$	−0.897278	−0.0474890
$358$	−0.218179	−0.0115311
$359$	30.6672	1.61855	0.809276	−	0.587429i	$-0.199860\pi$
$359$	30.6672	1.61855	0.809276	+	0.587429i	$0.199860\pi$
$360$	2.50518	0.132034
$361$	−0.758553	−0.0399239
$362$	17.6617	0.928277
$363$	−34.0236	−1.78577
$364$	0.675843	0.0354238
$365$	−15.3318	−0.802505
$366$	1.26059	0.0658919
$367$	−3.35908	−0.175342	−0.0876712	−	0.996149i	$-0.527942\pi$
$367$	−3.35908	−0.175342	−0.0876712	+	0.996149i	$0.527942\pi$
$368$	−28.9147	−1.50728
$369$	29.2805	1.52428
$370$	13.4333	0.698364
$371$	1.31840	0.0684480
$372$	−45.3159	−2.34952
$373$	−22.5049	−1.16526	−0.582631	−	0.812737i	$-0.697977\pi$
$373$	−22.5049	−1.16526	−0.582631	+	0.812737i	$0.697977\pi$
$374$	13.5377	0.700016
$375$	−2.84784	−0.147062
$376$	−6.08523	−0.313822
$377$	11.1376	0.573617
$378$	−2.51028	−0.129115
$379$	−9.99875	−0.513601	−0.256801	−	0.966464i	$-0.582668\pi$
$379$	−9.99875	−0.513601	−0.256801	+	0.966464i	$0.582668\pi$
$380$	7.46031	0.382706
$381$	2.32277	0.118999
$382$	7.26766	0.371846
$383$	−27.6418	−1.41243	−0.706214	−	0.707999i	$-0.749598\pi$
$383$	−27.6418	−1.41243	−0.706214	+	0.707999i	$0.749598\pi$
$384$	11.0793	0.565386
$385$	−1.03377	−0.0526857
$386$	−31.2983	−1.59304
$387$	53.4170	2.71534
$388$	3.46863	0.176093
$389$	−8.89996	−0.451246	−0.225623	−	0.974215i	$-0.572442\pi$
$389$	−8.89996	−0.451246	−0.225623	+	0.974215i	$0.572442\pi$
$390$	−9.88331	−0.500461
$391$	−9.50288	−0.480581
$392$	−3.40879	−0.172170
$393$	−11.6274	−0.586524
$394$	41.9847	2.11516
$395$	−9.30846	−0.468359
$396$	42.7591	2.14873
$397$	0.240075	0.0120490	0.00602452	−	0.999982i	$-0.498082\pi$
$397$	0.240075	0.0120490	0.00602452	+	0.999982i	$0.498082\pi$
$398$	−18.9208	−0.948413
$399$	2.62485	0.131407
$400$	−4.44239	−0.222119
$401$	−18.9996	−0.948793	−0.474397	−	0.880311i	$-0.657334\pi$
$401$	−18.9996	−0.948793	−0.474397	+	0.880311i	$0.657334\pi$
$402$	−33.7046	−1.68103
$403$	−16.3331	−0.813608
$404$	−13.5686	−0.675065
$405$	1.78349	0.0886224
$406$	−2.59488	−0.128782
$407$	−33.2446	−1.64787
$408$	2.03831	0.100911
$409$	−21.7513	−1.07553	−0.537765	−	0.843095i	$-0.680731\pi$
$409$	−21.7513	−1.07553	−0.537765	+	0.843095i	$0.680731\pi$
$410$	−11.0909	−0.547743
$411$	−20.4679	−1.00960
$412$	−11.7863	−0.580670
$413$	2.38117	0.117170
$414$	−64.3822	−3.16421
$415$	−8.04431	−0.394880
$416$	−13.6592	−0.669699
$417$	−17.5901	−0.861392
$418$	−39.6023	−1.93701
$419$	33.9313	1.65765	0.828827	−	0.559505i	$-0.189009\pi$
$419$	33.9313	1.65765	0.828827	+	0.559505i	$0.189009\pi$
$420$	1.07350	0.0523814
$421$	39.1509	1.90810	0.954048	−	0.299652i	$-0.0968707\pi$
$421$	39.1509	1.90810	0.954048	+	0.299652i	$0.0968707\pi$
$422$	34.2252	1.66606
$423$	−63.4327	−3.08420
$424$	−2.99495	−0.145448
$425$	−1.46000	−0.0708204
$426$	−64.6779	−3.13366
$427$	−0.0493502	−0.00238823
$428$	−16.4689	−0.796054
$429$	24.4591	1.18090
$430$	−20.2334	−0.975741
$431$	−8.32931	−0.401209	−0.200604	−	0.979672i	$-0.564291\pi$
$431$	−8.32931	−0.401209	−0.200604	+	0.979672i	$0.564291\pi$
$432$	26.6965	1.28444
$433$	−9.57797	−0.460288	−0.230144	−	0.973157i	$-0.573920\pi$
$433$	−9.57797	−0.460288	−0.230144	+	0.973157i	$0.573920\pi$
$434$	3.80533	0.182662
$435$	17.6908	0.848210
$436$	31.9444	1.52986
$437$	27.7992	1.32982
$438$	−84.5155	−4.03831
$439$	−34.4588	−1.64463	−0.822314	−	0.569034i	$-0.807317\pi$
$439$	−34.4588	−1.64463	−0.822314	+	0.569034i	$0.807317\pi$
$440$	2.34836	0.111954
$441$	−35.5334	−1.69206
$442$	−5.06687	−0.241006
$443$	21.6593	1.02907	0.514533	−	0.857471i	$-0.327965\pi$
$443$	21.6593	1.02907	0.514533	+	0.857471i	$0.327965\pi$
$444$	34.5222	1.63835
$445$	13.9776	0.662601
$446$	−37.7968	−1.78973
$447$	−42.7823	−2.02354
$448$	1.26501	0.0597659
$449$	−15.3581	−0.724795	−0.362398	−	0.932024i	$-0.618042\pi$
$449$	−15.3581	−0.724795	−0.362398	+	0.932024i	$0.618042\pi$
$450$	−9.89154	−0.466292
$451$	27.4477	1.29246
$452$	12.6588	0.595419
$453$	40.3292	1.89483
$454$	37.6918	1.76896
$455$	0.386918	0.0181390
$456$	−5.96275	−0.279231
$457$	−3.20173	−0.149771	−0.0748853	−	0.997192i	$-0.523859\pi$
$457$	−3.20173	−0.149771	−0.0748853	+	0.997192i	$0.523859\pi$
$458$	−7.93634	−0.370841
$459$	8.77386	0.409528
$460$	11.3692	0.530091
$461$	37.8330	1.76206	0.881029	−	0.473062i	$-0.156851\pi$
$461$	37.8330	1.76206	0.881029	+	0.473062i	$0.156851\pi$
$462$	−5.69856	−0.265121
$463$	−36.0194	−1.67396	−0.836981	−	0.547232i	$-0.815682\pi$
$463$	−36.0194	−1.67396	−0.836981	+	0.547232i	$0.815682\pi$
$464$	27.5962	1.28112
$465$	−25.9432	−1.20309
$466$	39.1258	1.81247
$467$	−9.67705	−0.447800	−0.223900	−	0.974612i	$-0.571879\pi$
$467$	−9.67705	−0.447800	−0.223900	+	0.974612i	$0.571879\pi$
$468$	−16.0039	−0.739779
$469$	1.31949	0.0609283
$470$	24.0272	1.10829
$471$	16.5826	0.764085
$472$	−5.40920	−0.248979
$473$	50.0733	2.30238
$474$	−51.3121	−2.35684
$475$	4.27100	0.195967
$476$	0.550349	0.0252252
$477$	−31.2195	−1.42944
$478$	14.4397	0.660456
$479$	29.9442	1.36818	0.684092	−	0.729395i	$-0.260199\pi$
$479$	29.9442	1.36818	0.684092	+	0.729395i	$0.260199\pi$
$480$	−21.6961	−0.990286
$481$	12.4428	0.567341
$482$	−18.4344	−0.839663
$483$	4.00015	0.182013
$484$	20.8685	0.948569
$485$	1.98578	0.0901697
$486$	−25.0654	−1.13699
$487$	10.5512	0.478119	0.239060	−	0.971005i	$-0.423161\pi$
$487$	10.5512	0.478119	0.239060	+	0.971005i	$0.423161\pi$
$488$	0.112107	0.00507483
$489$	33.5145	1.51558
$490$	13.4594	0.608033
$491$	−7.39740	−0.333840	−0.166920	−	0.985970i	$-0.553382\pi$
$491$	−7.39740	−0.333840	−0.166920	+	0.985970i	$0.553382\pi$
$492$	−28.5026	−1.28500
$493$	9.06954	0.408471
$494$	14.8223	0.666888
$495$	24.4795	1.10027
$496$	−40.4691	−1.81712
$497$	2.53205	0.113578
$498$	−44.3436	−1.98708
$499$	11.7505	0.526024	0.263012	−	0.964793i	$-0.415284\pi$
$499$	11.7505	0.526024	0.263012	+	0.964793i	$0.415284\pi$
$500$	1.74674	0.0781164
$501$	8.06911	0.360501
$502$	48.6772	2.17257
$503$	−7.22208	−0.322017	−0.161008	−	0.986953i	$-0.551475\pi$
$503$	−7.22208	−0.322017	−0.161008	+	0.986953i	$0.551475\pi$
$504$	−0.540626	−0.0240814
$505$	−7.76800	−0.345671
$506$	−60.3522	−2.68298
$507$	27.8674	1.23763
$508$	−1.42468	−0.0632101
$509$	21.9678	0.973705	0.486852	−	0.873484i	$-0.338145\pi$
$509$	21.9678	0.973705	0.486852	+	0.873484i	$0.338145\pi$
$510$	−8.04813	−0.356377
$511$	3.30866	0.146367
$512$	−29.4884	−1.30322
$513$	−25.6665	−1.13321
$514$	−53.7930	−2.37271
$515$	−6.74763	−0.297336
$516$	−51.9978	−2.28908
$517$	−59.4621	−2.61514
$518$	−2.89896	−0.127373
$519$	−13.4259	−0.589332
$520$	−0.878944	−0.0385443
$521$	−26.2328	−1.14928	−0.574641	−	0.818406i	$-0.694858\pi$
$521$	−26.2328	−1.14928	−0.574641	+	0.818406i	$0.694858\pi$
$522$	61.4464	2.68943
$523$	−2.14026	−0.0935870	−0.0467935	−	0.998905i	$-0.514900\pi$
$523$	−2.14026	−0.0935870	−0.0467935	+	0.998905i	$0.514900\pi$
$524$	7.13171	0.311550
$525$	0.614574	0.0268222
$526$	−42.4276	−1.84993
$527$	−13.3003	−0.579369
$528$	60.6033	2.63742
$529$	19.3648	0.841946
$530$	11.8254	0.513662
$531$	−56.3858	−2.44693
$532$	−1.60996	−0.0698007
$533$	−10.2731	−0.444978
$534$	77.0502	3.33429
$535$	−9.42839	−0.407625
$536$	−2.99742	−0.129469
$537$	−0.320998	−0.0138521
$538$	9.12252	0.393300
$539$	−33.3091	−1.43473
$540$	−10.4970	−0.451719
$541$	0.707346	0.0304112	0.0152056	−	0.999884i	$-0.495160\pi$
$541$	0.707346	0.0304112	0.0152056	+	0.999884i	$0.495160\pi$
$542$	−5.23861	−0.225017
$543$	25.9849	1.11512
$544$	−11.1229	−0.476891
$545$	18.2880	0.783373
$546$	2.13285	0.0912777
$547$	−2.94760	−0.126030	−0.0630151	−	0.998013i	$-0.520072\pi$
$547$	−2.94760	−0.126030	−0.0630151	+	0.998013i	$0.520072\pi$
$548$	12.5541	0.536282
$549$	1.16861	0.0498749
$550$	−9.27237	−0.395375
$551$	−26.5315	−1.13028
$552$	−9.08697	−0.386767
$553$	2.00880	0.0854228
$554$	10.1037	0.429266
$555$	19.7639	0.838929
$556$	10.7890	0.457555
$557$	−19.1319	−0.810644	−0.405322	−	0.914174i	$-0.632841\pi$
$557$	−19.1319	−0.810644	−0.405322	+	0.914174i	$0.632841\pi$
$558$	−90.1097	−3.81465
$559$	−18.7414	−0.792678
$560$	0.958683	0.0405117
$561$	19.9174	0.840913
$562$	28.1807	1.18873
$563$	−16.9241	−0.713266	−0.356633	−	0.934245i	$-0.616075\pi$
$563$	−16.9241	−0.713266	−0.356633	+	0.934245i	$0.616075\pi$
$564$	61.7474	2.60003
$565$	7.24711	0.304888
$566$	1.75275	0.0736738
$567$	−0.384884	−0.0161636
$568$	−5.75195	−0.241346
$569$	−19.4137	−0.813865	−0.406933	−	0.913458i	$-0.633402\pi$
$569$	−19.4137	−0.813865	−0.406933	+	0.913458i	$0.633402\pi$
$570$	23.5435	0.986130
$571$	4.70299	0.196814	0.0984069	−	0.995146i	$-0.468625\pi$
$571$	4.70299	0.196814	0.0984069	+	0.995146i	$0.468625\pi$
$572$	−15.0021	−0.627269
$573$	10.6926	0.446690
$574$	2.39347	0.0999013
$575$	6.50882	0.271437
$576$	−29.9551	−1.24813
$577$	32.6924	1.36100	0.680501	−	0.732748i	$-0.261762\pi$
$577$	32.6924	1.36100	0.680501	+	0.732748i	$0.261762\pi$
$578$	28.7800	1.19709
$579$	−46.0480	−1.91369
$580$	−10.8507	−0.450553
$581$	1.73599	0.0720210
$582$	10.9465	0.453745
$583$	−29.2653	−1.21205
$584$	−7.51614	−0.311020
$585$	−9.16215	−0.378808
$586$	−44.0594	−1.82008
$587$	−35.6972	−1.47338	−0.736690	−	0.676231i	$-0.763612\pi$
$587$	−35.6972	−1.47338	−0.736690	+	0.676231i	$0.763612\pi$
$588$	34.5893	1.42644
$589$	38.9079	1.60317
$590$	21.3579	0.879291
$591$	61.7703	2.54089
$592$	30.8299	1.26710
$593$	33.4989	1.37563	0.687817	−	0.725884i	$-0.258569\pi$
$593$	33.4989	1.37563	0.687817	+	0.725884i	$0.258569\pi$
$594$	55.7223	2.28631
$595$	0.315073	0.0129167
$596$	26.2407	1.07486
$597$	−27.8374	−1.13931
$598$	22.5886	0.923716
$599$	2.07934	0.0849597	0.0424798	−	0.999097i	$-0.486474\pi$
$599$	2.07934	0.0849597	0.0424798	+	0.999097i	$0.486474\pi$
$600$	−1.39610	−0.0569956
$601$	−11.6694	−0.476005	−0.238003	−	0.971265i	$-0.576493\pi$
$601$	−11.6694	−0.476005	−0.238003	+	0.971265i	$0.576493\pi$
$602$	4.36644	0.177963
$603$	−31.2452	−1.27240
$604$	−24.7361	−1.00650
$605$	11.9472	0.485721
$606$	−42.8204	−1.73946
$607$	0.394767	0.0160231	0.00801155	−	0.999968i	$-0.497450\pi$
$607$	0.394767	0.0160231	0.00801155	+	0.999968i	$0.497450\pi$
$608$	32.5383	1.31960
$609$	−3.81774	−0.154703
$610$	−0.442647	−0.0179222
$611$	22.2554	0.900359
$612$	−13.0322	−0.526795
$613$	−36.7954	−1.48615	−0.743075	−	0.669208i	$-0.766634\pi$
$613$	−36.7954	−1.48615	−0.743075	+	0.669208i	$0.766634\pi$
$614$	−19.3959	−0.782754
$615$	−16.3176	−0.657991
$616$	−0.506785	−0.0204190
$617$	24.2164	0.974916	0.487458	−	0.873146i	$-0.337924\pi$
$617$	24.2164	0.974916	0.487458	+	0.873146i	$0.337924\pi$
$618$	−37.1957	−1.49623
$619$	−16.5533	−0.665335	−0.332667	−	0.943044i	$-0.607949\pi$
$619$	−16.5533	−0.665335	−0.332667	+	0.943044i	$0.607949\pi$
$620$	15.9124	0.639056
$621$	−39.1147	−1.56962
$622$	−13.8325	−0.554632
$623$	−3.01641	−0.120850
$624$	−22.6826	−0.908029
$625$	1.00000	0.0400000
$626$	−28.3232	−1.13202
$627$	−58.2653	−2.32689
$628$	−10.1710	−0.405867
$629$	10.1323	0.404002
$630$	2.13463	0.0850457
$631$	29.3019	1.16649	0.583246	−	0.812296i	$-0.301782\pi$
$631$	29.3019	1.16649	0.583246	+	0.812296i	$0.301782\pi$
$632$	−4.56330	−0.181518
$633$	50.3542	2.00140
$634$	−14.7820	−0.587068
$635$	−0.815627	−0.0323672
$636$	30.3901	1.20505
$637$	12.4669	0.493957
$638$	57.6001	2.28041
$639$	−59.9586	−2.37192
$640$	−3.89041	−0.153782
$641$	30.4804	1.20390	0.601952	−	0.798533i	$-0.294390\pi$
$641$	30.4804	1.20390	0.601952	+	0.798533i	$0.294390\pi$
$642$	−51.9732	−2.05122
$643$	46.9107	1.84998	0.924990	−	0.379992i	$-0.124073\pi$
$643$	46.9107	1.84998	0.924990	+	0.379992i	$0.124073\pi$
$644$	−2.45351	−0.0966819
$645$	−29.7686	−1.17214
$646$	12.0700	0.474890
$647$	−7.76691	−0.305349	−0.152674	−	0.988277i	$-0.548789\pi$
$647$	−7.76691	−0.305349	−0.152674	+	0.988277i	$0.548789\pi$
$648$	0.874323	0.0343467
$649$	−52.8563	−2.07479
$650$	3.47046	0.136123
$651$	5.59863	0.219428
$652$	−20.5563	−0.805047
$653$	47.1570	1.84540	0.922698	−	0.385524i	$-0.125979\pi$
$653$	47.1570	1.84540	0.922698	+	0.385524i	$0.125979\pi$
$654$	100.811	3.94203
$655$	4.08288	0.159531
$656$	−25.4541	−0.993817
$657$	−78.3486	−3.05667
$658$	−5.18515	−0.202138
$659$	−11.2355	−0.437671	−0.218836	−	0.975762i	$-0.570226\pi$
$659$	−11.2355	−0.437671	−0.218836	+	0.975762i	$0.570226\pi$
$660$	−23.8291	−0.927545
$661$	−25.2005	−0.980188	−0.490094	−	0.871670i	$-0.663037\pi$
$661$	−25.2005	−0.980188	−0.490094	+	0.871670i	$0.663037\pi$
$662$	30.1280	1.17096
$663$	−7.45467	−0.289516
$664$	−3.94357	−0.153040
$665$	−0.921697	−0.0357419
$666$	68.6468	2.66001
$667$	−40.4329	−1.56557
$668$	−4.94922	−0.191491
$669$	−55.6089	−2.14996
$670$	11.8351	0.457231
$671$	1.09546	0.0422896
$672$	4.68209	0.180616
$673$	−35.4575	−1.36679	−0.683394	−	0.730050i	$-0.739497\pi$
$673$	−35.4575	−1.36679	−0.683394	+	0.730050i	$0.739497\pi$
$674$	66.3911	2.55729
$675$	−6.00949	−0.231305
$676$	−17.0926	−0.657407
$677$	−1.55538	−0.0597782	−0.0298891	−	0.999553i	$-0.509515\pi$
$677$	−1.55538	−0.0597782	−0.0298891	+	0.999553i	$0.509515\pi$
$678$	39.9491	1.53423
$679$	−0.428539	−0.0164458
$680$	−0.715737	−0.0274473
$681$	55.4543	2.12501
$682$	−84.4692	−3.23449
$683$	−16.7531	−0.641040	−0.320520	−	0.947242i	$-0.603858\pi$
$683$	−16.7531	−0.641040	−0.320520	+	0.947242i	$0.603858\pi$
$684$	38.1236	1.45769
$685$	7.18715	0.274607
$686$	−5.82862	−0.222538
$687$	−11.6764	−0.445483
$688$	−46.4364	−1.77037
$689$	10.9534	0.417292
$690$	35.8793	1.36590
$691$	−34.6186	−1.31695	−0.658477	−	0.752600i	$-0.728799\pi$
$691$	−34.6186	−1.31695	−0.658477	+	0.752600i	$0.728799\pi$
$692$	8.23484	0.313042
$693$	−5.28275	−0.200675
$694$	17.6665	0.670611
$695$	6.17665	0.234294
$696$	8.67259	0.328734
$697$	−8.36555	−0.316868
$698$	62.9059	2.38102
$699$	57.5641	2.17727
$700$	−0.376952	−0.0142474
$701$	24.6908	0.932559	0.466279	−	0.884638i	$-0.345594\pi$
$701$	24.6908	0.932559	0.466279	+	0.884638i	$0.345594\pi$
$702$	−20.8557	−0.787147
$703$	−29.6405	−1.11791
$704$	−28.0801	−1.05831
$705$	35.3502	1.33136
$706$	−69.1965	−2.60425
$707$	1.67636	0.0630461
$708$	54.8877	2.06281
$709$	−18.6237	−0.699429	−0.349715	−	0.936856i	$-0.613721\pi$
$709$	−18.6237	−0.699429	−0.349715	+	0.936856i	$0.613721\pi$
$710$	22.7112	0.852337
$711$	−47.5680	−1.78394
$712$	6.85224	0.256799
$713$	59.2939	2.22057
$714$	1.73681	0.0649987
$715$	−8.58865	−0.321197
$716$	0.196886	0.00735796
$717$	21.2445	0.793392
$718$	−59.3609	−2.21533
$719$	51.1481	1.90750	0.953752	−	0.300595i	$-0.0971851\pi$
$719$	51.1481	1.90750	0.953752	+	0.300595i	$0.0971851\pi$
$720$	−22.7015	−0.846033
$721$	1.45616	0.0542303
$722$	1.46829	0.0546442
$723$	−27.1218	−1.00867
$724$	−15.9380	−0.592329
$725$	−6.21201	−0.230708
$726$	65.8577	2.44421
$727$	−31.4385	−1.16599	−0.582994	−	0.812476i	$-0.698119\pi$
$727$	−31.4385	−1.16599	−0.582994	+	0.812476i	$0.698119\pi$
$728$	0.189679	0.00702998
$729$	−42.2282	−1.56401
$730$	29.6770	1.09840
$731$	−15.2614	−0.564464
$732$	−1.13756	−0.0420453
$733$	1.57686	0.0582428	0.0291214	−	0.999576i	$-0.490729\pi$
$733$	1.57686	0.0582428	0.0291214	+	0.999576i	$0.490729\pi$
$734$	6.50199	0.239993
$735$	19.8023	0.730417
$736$	49.5870	1.82780
$737$	−29.2894	−1.07889
$738$	−56.6769	−2.08630
$739$	−7.86238	−0.289222	−0.144611	−	0.989489i	$-0.546193\pi$
$739$	−7.86238	−0.289222	−0.144611	+	0.989489i	$0.546193\pi$
$740$	−12.1223	−0.445623
$741$	21.8075	0.801118
$742$	−2.55196	−0.0936855
$743$	−10.4729	−0.384213	−0.192106	−	0.981374i	$-0.561532\pi$
$743$	−10.4729	−0.384213	−0.192106	+	0.981374i	$0.561532\pi$
$744$	−12.7182	−0.466270
$745$	15.0227	0.550390
$746$	43.5616	1.59490
$747$	−41.1080	−1.50406
$748$	−12.2164	−0.446677
$749$	2.03468	0.0743456
$750$	5.51242	0.201285
$751$	−43.2721	−1.57902	−0.789511	−	0.613737i	$-0.789666\pi$
$751$	−43.2721	−1.57902	−0.789511	+	0.613737i	$0.789666\pi$
$752$	55.1432	2.01087
$753$	71.6167	2.60986
$754$	−21.5585	−0.785115
$755$	−14.1613	−0.515384
$756$	2.26529	0.0823877
$757$	14.5853	0.530112	0.265056	−	0.964233i	$-0.414610\pi$
$757$	14.5853	0.530112	0.265056	+	0.964233i	$0.414610\pi$
$758$	19.3541	0.702971
$759$	−88.7937	−3.22301
$760$	2.09378	0.0759493
$761$	−12.5238	−0.453988	−0.226994	−	0.973896i	$-0.572890\pi$
$761$	−12.5238	−0.453988	−0.226994	+	0.973896i	$0.572890\pi$
$762$	−4.49608	−0.162876
$763$	−3.94662	−0.142877
$764$	−6.55836	−0.237273
$765$	−7.46088	−0.269749
$766$	53.5047	1.93320
$767$	19.7830	0.714323
$768$	−54.8327	−1.97861
$769$	−37.0326	−1.33543	−0.667715	−	0.744417i	$-0.732727\pi$
$769$	−37.0326	−1.33543	−0.667715	+	0.744417i	$0.732727\pi$
$770$	2.00101	0.0721114
$771$	−79.1434	−2.85028
$772$	28.2437	1.01651
$773$	−0.729490	−0.0262379	−0.0131190	−	0.999914i	$-0.504176\pi$
$773$	−0.729490	−0.0262379	−0.0131190	+	0.999914i	$0.504176\pi$
$774$	−103.397	−3.71651
$775$	9.10977	0.327233
$776$	0.973492	0.0349463
$777$	−4.26511	−0.153010
$778$	17.2272	0.617625
$779$	24.4721	0.876805
$780$	8.91873	0.319342
$781$	−56.2055	−2.01119
$782$	18.3942	0.657776
$783$	37.3310	1.33410
$784$	30.8898	1.10321
$785$	−5.82286	−0.207827
$786$	22.5065	0.802782
$787$	−44.6796	−1.59266	−0.796328	−	0.604866i	$-0.793227\pi$
$787$	−44.6796	−1.59266	−0.796328	+	0.604866i	$0.793227\pi$
$788$	−37.8871	−1.34967
$789$	−62.4220	−2.22228
$790$	18.0179	0.641048
$791$	−1.56395	−0.0556077
$792$	12.0006	0.426423
$793$	−0.410007	−0.0145598
$794$	−0.464702	−0.0164916
$795$	17.3982	0.617051
$796$	17.0742	0.605178
$797$	−48.6062	−1.72172	−0.860859	−	0.508843i	$-0.830073\pi$
$797$	−48.6062	−1.72172	−0.860859	+	0.508843i	$0.830073\pi$
$798$	−5.08078	−0.179858
$799$	18.1229	0.641143
$800$	7.61844	0.269352
$801$	71.4281	2.52379
$802$	36.7765	1.29862
$803$	−73.4444	−2.59180
$804$	30.4151	1.07266
$805$	−1.40463	−0.0495066
$806$	31.6151	1.11359
$807$	13.4216	0.472462
$808$	−3.80811	−0.133969
$809$	−0.310991	−0.0109339	−0.00546693	−	0.999985i	$-0.501740\pi$
$809$	−0.310991	−0.0109339	−0.00546693	+	0.999985i	$0.501740\pi$
$810$	−3.45221	−0.121298
$811$	−15.7239	−0.552141	−0.276071	−	0.961137i	$-0.589032\pi$
$811$	−15.7239	−0.552141	−0.276071	+	0.961137i	$0.589032\pi$
$812$	2.34163	0.0821751
$813$	−7.70735	−0.270309
$814$	64.3498	2.25546
$815$	−11.7684	−0.412229
$816$	−18.4708	−0.646606
$817$	44.6449	1.56193
$818$	42.1028	1.47209
$819$	1.97723	0.0690899
$820$	10.0085	0.349512
$821$	26.1565	0.912866	0.456433	−	0.889758i	$-0.349127\pi$
$821$	26.1565	0.912866	0.456433	+	0.889758i	$0.349127\pi$
$822$	39.6186	1.38186
$823$	51.1523	1.78306	0.891529	−	0.452963i	$-0.149633\pi$
$823$	51.1523	1.78306	0.891529	+	0.452963i	$0.149633\pi$
$824$	−3.30790	−0.115236
$825$	−13.6421	−0.474956
$826$	−4.60911	−0.160372
$827$	0.835531	0.0290543	0.0145271	−	0.999894i	$-0.495376\pi$
$827$	0.835531	0.0290543	0.0145271	+	0.999894i	$0.495376\pi$
$828$	58.0987	2.01907
$829$	−6.16984	−0.214287	−0.107144	−	0.994244i	$-0.534170\pi$
$829$	−6.16984	−0.214287	−0.107144	+	0.994244i	$0.534170\pi$
$830$	15.5710	0.540476
$831$	14.8652	0.515668
$832$	10.5098	0.364362
$833$	10.1520	0.351746
$834$	34.0483	1.17900
$835$	−2.83341	−0.0980543
$836$	35.7373	1.23600
$837$	−54.7451	−1.89227
$838$	−65.6791	−2.26885
$839$	−27.0213	−0.932879	−0.466440	−	0.884553i	$-0.654463\pi$
$839$	−27.0213	−0.932879	−0.466440	+	0.884553i	$0.654463\pi$
$840$	0.301283	0.0103953
$841$	9.58910	0.330659
$842$	−75.7823	−2.61163
$843$	41.4610	1.42799
$844$	−30.8850	−1.06310
$845$	−9.78545	−0.336630
$846$	122.783	4.22138
$847$	−2.57824	−0.0885893
$848$	27.1397	0.931982
$849$	2.57876	0.0885027
$850$	2.82605	0.0969326
$851$	−45.1709	−1.54844
$852$	58.3656	1.99957
$853$	13.6849	0.468562	0.234281	−	0.972169i	$-0.424726\pi$
$853$	13.6849	0.468562	0.234281	+	0.972169i	$0.424726\pi$
$854$	0.0955247	0.00326879
$855$	21.8256	0.746421
$856$	−4.62209	−0.157980
$857$	−13.1581	−0.449474	−0.224737	−	0.974419i	$-0.572152\pi$
$857$	−13.1581	−0.449474	−0.224737	+	0.974419i	$0.572152\pi$
$858$	−47.3442	−1.61630
$859$	−11.4297	−0.389975	−0.194988	−	0.980806i	$-0.562467\pi$
$859$	−11.4297	−0.389975	−0.194988	+	0.980806i	$0.562467\pi$
$860$	18.2587	0.622616
$861$	3.52141	0.120009
$862$	16.1226	0.549138
$863$	−37.8285	−1.28770	−0.643849	−	0.765152i	$-0.722664\pi$
$863$	−37.8285	−1.28770	−0.643849	+	0.765152i	$0.722664\pi$
$864$	−45.7829	−1.55757
$865$	4.71442	0.160295
$866$	18.5396	0.630000
$867$	42.3428	1.43804
$868$	−3.43395	−0.116556
$869$	−44.5905	−1.51263
$870$	−34.2432	−1.16095
$871$	10.9624	0.371448
$872$	8.96537	0.303606
$873$	10.1477	0.343448
$874$	−53.8094	−1.82013
$875$	−0.215804	−0.00729549
$876$	76.2670	2.57682
$877$	2.35136	0.0793999	0.0396999	−	0.999212i	$-0.487360\pi$
$877$	2.35136	0.0793999	0.0396999	+	0.999212i	$0.487360\pi$
$878$	66.7001	2.25102
$879$	−64.8227	−2.18642
$880$	−21.2804	−0.717364
$881$	35.3916	1.19237	0.596187	−	0.802845i	$-0.296682\pi$
$881$	35.3916	1.19237	0.596187	+	0.802845i	$0.296682\pi$
$882$	68.7801	2.31595
$883$	−24.3160	−0.818300	−0.409150	−	0.912467i	$-0.634175\pi$
$883$	−24.3160	−0.818300	−0.409150	+	0.912467i	$0.634175\pi$
$884$	4.57236	0.153785
$885$	31.4230	1.05627
$886$	−41.9248	−1.40849
$887$	8.54840	0.287027	0.143514	−	0.989648i	$-0.454160\pi$
$887$	8.54840	0.287027	0.143514	+	0.989648i	$0.454160\pi$
$888$	9.68887	0.325137
$889$	0.176015	0.00590336
$890$	−27.0557	−0.906908
$891$	8.54349	0.286218
$892$	34.1080	1.14202
$893$	−53.0158	−1.77411
$894$	82.8116	2.76963
$895$	0.112716	0.00376769
$896$	0.839563	0.0280478
$897$	33.2337	1.10964
$898$	29.7280	0.992035
$899$	−56.5900	−1.88738
$900$	8.92615	0.297538
$901$	8.91953	0.297153
$902$	−53.1291	−1.76901
$903$	6.42416	0.213783
$904$	3.55276	0.118163
$905$	−9.12443	−0.303306
$906$	−78.0632	−2.59347
$907$	24.6209	0.817523	0.408761	−	0.912641i	$-0.365961\pi$
$907$	24.6209	0.817523	0.408761	+	0.912641i	$0.365961\pi$
$908$	−34.0132	−1.12877
$909$	−39.6960	−1.31663
$910$	−0.748937	−0.0248270
$911$	−11.9417	−0.395646	−0.197823	−	0.980238i	$-0.563387\pi$
$911$	−11.9417	−0.395646	−0.197823	+	0.980238i	$0.563387\pi$
$912$	54.0333	1.78922
$913$	−38.5348	−1.27532
$914$	6.19743	0.204993
$915$	−0.651248	−0.0215296
$916$	7.16178	0.236632
$917$	−0.881100	−0.0290965
$918$	−16.9831	−0.560526
$919$	−11.8716	−0.391607	−0.195804	−	0.980643i	$-0.562732\pi$
$919$	−11.8716	−0.391607	−0.195804	+	0.980643i	$0.562732\pi$
$920$	3.19083	0.105198
$921$	−28.5363	−0.940305
$922$	−73.2314	−2.41175
$923$	21.0365	0.692426
$924$	5.14240	0.169173
$925$	−6.93995	−0.228184
$926$	69.7209	2.29117
$927$	−34.4817	−1.13253
$928$	−47.3258	−1.55355
$929$	−40.8408	−1.33994	−0.669972	−	0.742386i	$-0.733694\pi$
$929$	−40.8408	−1.33994	−0.669972	+	0.742386i	$0.733694\pi$
$930$	50.2169	1.64668
$931$	−29.6981	−0.973316
$932$	−35.3072	−1.15653
$933$	−20.3512	−0.666267
$934$	18.7314	0.612909
$935$	−6.99386	−0.228724
$936$	−4.49157	−0.146812
$937$	40.1546	1.31179	0.655897	−	0.754851i	$-0.272291\pi$
$937$	40.1546	1.31179	0.655897	+	0.754851i	$0.272291\pi$
$938$	−2.55406	−0.0833931
$939$	−41.6708	−1.35987
$940$	−21.6822	−0.707195
$941$	16.4170	0.535178	0.267589	−	0.963533i	$-0.413773\pi$
$941$	16.4170	0.535178	0.267589	+	0.963533i	$0.413773\pi$
$942$	−32.0981	−1.04581
$943$	37.2945	1.21447
$944$	49.0172	1.59537
$945$	1.29687	0.0421872
$946$	−96.9244	−3.15128
$947$	56.8868	1.84857	0.924286	−	0.381700i	$-0.124661\pi$
$947$	56.8868	1.84857	0.924286	+	0.381700i	$0.124661\pi$
$948$	46.3042	1.50389
$949$	27.4887	0.892321
$950$	−8.26716	−0.268222
$951$	−21.7482	−0.705232
$952$	0.154459	0.00500604
$953$	−30.2437	−0.979690	−0.489845	−	0.871810i	$-0.662947\pi$
$953$	−30.2437	−0.979690	−0.489845	+	0.871810i	$0.662947\pi$
$954$	60.4301	1.95650
$955$	−3.75464	−0.121497
$956$	−13.0304	−0.421434
$957$	84.7447	2.73941
$958$	−57.9614	−1.87265
$959$	−1.55101	−0.0500848
$960$	16.6936	0.538783
$961$	51.9880	1.67703
$962$	−24.0848	−0.776525
$963$	−48.1809	−1.55261
$964$	16.6352	0.535785
$965$	16.1694	0.520512
$966$	−7.74289	−0.249123
$967$	−1.22693	−0.0394554	−0.0197277	−	0.999805i	$-0.506280\pi$
$967$	−1.22693	−0.0394554	−0.0197277	+	0.999805i	$0.506280\pi$
$968$	5.85687	0.188247
$969$	17.7582	0.570474
$970$	−3.84377	−0.123416
$971$	−4.01745	−0.128926	−0.0644630	−	0.997920i	$-0.520533\pi$
$971$	−4.01745	−0.128926	−0.0644630	+	0.997920i	$0.520533\pi$
$972$	22.6191	0.725509
$973$	−1.33294	−0.0427322
$974$	−20.4234	−0.654407
$975$	5.10594	0.163521
$976$	−1.01589	−0.0325179
$977$	−2.38761	−0.0763864	−0.0381932	−	0.999270i	$-0.512160\pi$
$977$	−2.38761	−0.0763864	−0.0381932	+	0.999270i	$0.512160\pi$
$978$	−64.8724	−2.07439
$979$	66.9570	2.13996
$980$	−12.1458	−0.387983
$981$	93.4554	2.98380
$982$	14.3188	0.456930
$983$	19.5790	0.624473	0.312236	−	0.950004i	$-0.398922\pi$
$983$	19.5790	0.624473	0.312236	+	0.950004i	$0.398922\pi$
$984$	−7.99942	−0.255012
$985$	−21.6902	−0.691109
$986$	−17.5554	−0.559079
$987$	−7.62869	−0.242824
$988$	−13.3757	−0.425538
$989$	68.0369	2.16345
$990$	−47.3836	−1.50595
$991$	41.0034	1.30252	0.651258	−	0.758856i	$-0.274242\pi$
$991$	41.0034	1.30252	0.651258	+	0.758856i	$0.274242\pi$
$992$	69.4022	2.20352
$993$	44.3260	1.40664
$994$	−4.90116	−0.155455
$995$	9.77490	0.309885
$996$	40.0158	1.26795
$997$	13.0449	0.413137	0.206569	−	0.978432i	$-0.433770\pi$
$997$	13.0449	0.413137	0.206569	+	0.978432i	$0.433770\pi$
$998$	−22.7448	−0.719974
$999$	41.7056	1.31951

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6005.2.a.e.1.19	✓	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6005.2.a.e.1.19	✓	88	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:	\( N \)	\(=\)	\( 6005 = 5 \cdot 1201 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6005.a (trivial)

\(f(q)\)	\(=\)	\(q-1.93565 q^{2} -2.84784 q^{3} +1.74674 q^{4} +1.00000 q^{5} +5.51242 q^{6} -0.215804 q^{7} +0.490231 q^{8} +5.11019 q^{9} +O(q^{10})\)	\(q-1.93565 q^{2} -2.84784 q^{3} +1.74674 q^{4} +1.00000 q^{5} +5.51242 q^{6} -0.215804 q^{7} +0.490231 q^{8} +5.11019 q^{9} -1.93565 q^{10} +4.79032 q^{11} -4.97442 q^{12} -1.79292 q^{13} +0.417720 q^{14} -2.84784 q^{15} -4.44239 q^{16} -1.46000 q^{17} -9.89154 q^{18} +4.27100 q^{19} +1.74674 q^{20} +0.614574 q^{21} -9.27237 q^{22} +6.50882 q^{23} -1.39610 q^{24} +1.00000 q^{25} +3.47046 q^{26} -6.00949 q^{27} -0.376952 q^{28} -6.21201 q^{29} +5.51242 q^{30} +9.10977 q^{31} +7.61844 q^{32} -13.6421 q^{33} +2.82605 q^{34} -0.215804 q^{35} +8.92615 q^{36} -6.93995 q^{37} -8.26716 q^{38} +5.10594 q^{39} +0.490231 q^{40} +5.72983 q^{41} -1.18960 q^{42} +10.4530 q^{43} +8.36742 q^{44} +5.11019 q^{45} -12.5988 q^{46} -12.4130 q^{47} +12.6512 q^{48} -6.95343 q^{49} -1.93565 q^{50} +4.15785 q^{51} -3.13175 q^{52} -6.10927 q^{53} +11.6323 q^{54} +4.79032 q^{55} -0.105794 q^{56} -12.1631 q^{57} +12.0243 q^{58} -11.0340 q^{59} -4.97442 q^{60} +0.228681 q^{61} -17.6333 q^{62} -1.10280 q^{63} -5.86184 q^{64} -1.79292 q^{65} +26.4062 q^{66} -6.11430 q^{67} -2.55023 q^{68} -18.5361 q^{69} +0.417720 q^{70} -11.7331 q^{71} +2.50518 q^{72} -15.3318 q^{73} +13.4333 q^{74} -2.84784 q^{75} +7.46031 q^{76} -1.03377 q^{77} -9.88331 q^{78} -9.30846 q^{79} -4.44239 q^{80} +1.78349 q^{81} -11.0909 q^{82} -8.04431 q^{83} +1.07350 q^{84} -1.46000 q^{85} -20.2334 q^{86} +17.6908 q^{87} +2.34836 q^{88} +13.9776 q^{89} -9.89154 q^{90} +0.386918 q^{91} +11.3692 q^{92} -25.9432 q^{93} +24.0272 q^{94} +4.27100 q^{95} -21.6961 q^{96} +1.98578 q^{97} +13.4594 q^{98} +24.4795 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 14 q^{2} - 34 q^{3} + 66 q^{4} + 88 q^{5} - q^{6} - 35 q^{7} - 39 q^{8} + 72 q^{9}+O(q^{10}) \) 88 * q - 14 * q^2 - 34 * q^3 + 66 * q^4 + 88 * q^5 - q^6 - 35 * q^7 - 39 * q^8 + 72 * q^9	\( 88 q - 14 q^{2} - 34 q^{3} + 66 q^{4} + 88 q^{5} - q^{6} - 35 q^{7} - 39 q^{8} + 72 q^{9} - 14 q^{10} - 26 q^{11} - 64 q^{12} - 31 q^{13} - 17 q^{14} - 34 q^{15} + 34 q^{16} - 31 q^{17} - 42 q^{18} - 56 q^{19} + 66 q^{20} - q^{21} - 49 q^{22} - 74 q^{23} - 3 q^{24} + 88 q^{25} - q^{26} - 130 q^{27} - 57 q^{28} - 6 q^{29} - q^{30} - 37 q^{31} - 87 q^{32} - 43 q^{33} - 35 q^{34} - 35 q^{35} + 53 q^{36} - 67 q^{37} - 40 q^{38} - 21 q^{39} - 39 q^{40} + 2 q^{41} - 15 q^{42} - 136 q^{43} - 15 q^{44} + 72 q^{45} - 16 q^{46} - 139 q^{47} - 71 q^{48} + 41 q^{49} - 14 q^{50} - 71 q^{51} - 71 q^{52} - 75 q^{53} + 26 q^{54} - 26 q^{55} - 22 q^{56} - 34 q^{57} - 65 q^{58} - 41 q^{59} - 64 q^{60} - 11 q^{61} - 30 q^{62} - 114 q^{63} - 33 q^{64} - 31 q^{65} + 24 q^{66} - 209 q^{67} - 42 q^{68} - 22 q^{69} - 17 q^{70} - 43 q^{71} - 80 q^{72} - 50 q^{73} + 9 q^{74} - 34 q^{75} - 62 q^{76} - 49 q^{77} - 19 q^{78} - 77 q^{79} + 34 q^{80} + 72 q^{81} - 107 q^{82} - 113 q^{83} + 19 q^{84} - 31 q^{85} + 14 q^{86} - 87 q^{87} - 107 q^{88} - 5 q^{89} - 42 q^{90} - 159 q^{91} - 100 q^{92} - 82 q^{93} - 31 q^{94} - 56 q^{95} + 58 q^{96} - 105 q^{97} - 29 q^{98} - 68 q^{99}+O(q^{100}) \) 88 * q - 14 * q^2 - 34 * q^3 + 66 * q^4 + 88 * q^5 - q^6 - 35 * q^7 - 39 * q^8 + 72 * q^9 - 14 * q^10 - 26 * q^11 - 64 * q^12 - 31 * q^13 - 17 * q^14 - 34 * q^15 + 34 * q^16 - 31 * q^17 - 42 * q^18 - 56 * q^19 + 66 * q^20 - q^21 - 49 * q^22 - 74 * q^23 - 3 * q^24 + 88 * q^25 - q^26 - 130 * q^27 - 57 * q^28 - 6 * q^29 - q^30 - 37 * q^31 - 87 * q^32 - 43 * q^33 - 35 * q^34 - 35 * q^35 + 53 * q^36 - 67 * q^37 - 40 * q^38 - 21 * q^39 - 39 * q^40 + 2 * q^41 - 15 * q^42 - 136 * q^43 - 15 * q^44 + 72 * q^45 - 16 * q^46 - 139 * q^47 - 71 * q^48 + 41 * q^49 - 14 * q^50 - 71 * q^51 - 71 * q^52 - 75 * q^53 + 26 * q^54 - 26 * q^55 - 22 * q^56 - 34 * q^57 - 65 * q^58 - 41 * q^59 - 64 * q^60 - 11 * q^61 - 30 * q^62 - 114 * q^63 - 33 * q^64 - 31 * q^65 + 24 * q^66 - 209 * q^67 - 42 * q^68 - 22 * q^69 - 17 * q^70 - 43 * q^71 - 80 * q^72 - 50 * q^73 + 9 * q^74 - 34 * q^75 - 62 * q^76 - 49 * q^77 - 19 * q^78 - 77 * q^79 + 34 * q^80 + 72 * q^81 - 107 * q^82 - 113 * q^83 + 19 * q^84 - 31 * q^85 + 14 * q^86 - 87 * q^87 - 107 * q^88 - 5 * q^89 - 42 * q^90 - 159 * q^91 - 100 * q^92 - 82 * q^93 - 31 * q^94 - 56 * q^95 + 58 * q^96 - 105 * q^97 - 29 * q^98 - 68 * q^99

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