LMFDB - Embedded newform 8049.2.a.a.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8049,2,Mod(1,8049)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8049, 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("8049.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8049 = 3 \cdot 2683 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8049.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:	$64.2715885869$
Analytic rank:	$1$
Dimension:	$95$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	8049.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.32680 q^{2} +1.00000 q^{3} +3.41399 q^{4} +0.167407 q^{5} -2.32680 q^{6} +5.19602 q^{7} -3.29007 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.32680 q^{2} +1.00000 q^{3} +3.41399 q^{4} +0.167407 q^{5} -2.32680 q^{6} +5.19602 q^{7} -3.29007 q^{8} +1.00000 q^{9} -0.389523 q^{10} +3.61380 q^{11} +3.41399 q^{12} -2.80992 q^{13} -12.0901 q^{14} +0.167407 q^{15} +0.827353 q^{16} -2.52559 q^{17} -2.32680 q^{18} -8.40780 q^{19} +0.571527 q^{20} +5.19602 q^{21} -8.40859 q^{22} +1.00288 q^{23} -3.29007 q^{24} -4.97197 q^{25} +6.53813 q^{26} +1.00000 q^{27} +17.7392 q^{28} -8.45877 q^{29} -0.389523 q^{30} -4.24666 q^{31} +4.65506 q^{32} +3.61380 q^{33} +5.87654 q^{34} +0.869852 q^{35} +3.41399 q^{36} +1.31429 q^{37} +19.5632 q^{38} -2.80992 q^{39} -0.550782 q^{40} +4.04858 q^{41} -12.0901 q^{42} -5.50209 q^{43} +12.3375 q^{44} +0.167407 q^{45} -2.33350 q^{46} +1.56151 q^{47} +0.827353 q^{48} +19.9987 q^{49} +11.5688 q^{50} -2.52559 q^{51} -9.59306 q^{52} +10.2335 q^{53} -2.32680 q^{54} +0.604977 q^{55} -17.0953 q^{56} -8.40780 q^{57} +19.6819 q^{58} -2.78684 q^{59} +0.571527 q^{60} -4.51039 q^{61} +9.88112 q^{62} +5.19602 q^{63} -12.4861 q^{64} -0.470402 q^{65} -8.40859 q^{66} -9.30062 q^{67} -8.62235 q^{68} +1.00288 q^{69} -2.02397 q^{70} -1.29253 q^{71} -3.29007 q^{72} -12.1020 q^{73} -3.05808 q^{74} -4.97197 q^{75} -28.7041 q^{76} +18.7774 q^{77} +6.53813 q^{78} -2.03278 q^{79} +0.138505 q^{80} +1.00000 q^{81} -9.42022 q^{82} -11.8585 q^{83} +17.7392 q^{84} -0.422802 q^{85} +12.8022 q^{86} -8.45877 q^{87} -11.8897 q^{88} -12.6090 q^{89} -0.389523 q^{90} -14.6004 q^{91} +3.42383 q^{92} -4.24666 q^{93} -3.63332 q^{94} -1.40753 q^{95} +4.65506 q^{96} +1.27585 q^{97} -46.5329 q^{98} +3.61380 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 95 q - 9 q^{2} + 95 q^{3} + 65 q^{4} - 15 q^{5} - 9 q^{6} - 36 q^{7} - 27 q^{8} + 95 q^{9}+O(q^{10}) $ 95 * q - 9 * q^2 + 95 * q^3 + 65 * q^4 - 15 * q^5 - 9 * q^6 - 36 * q^7 - 27 * q^8 + 95 * q^9	\( 95 q - 9 q^{2} + 95 q^{3} + 65 q^{4} - 15 q^{5} - 9 q^{6} - 36 q^{7} - 27 q^{8} + 95 q^{9} - 36 q^{10} - 48 q^{11} + 65 q^{12} - 73 q^{13} - 17 q^{14} - 15 q^{15} + 13 q^{16} - 9 q^{17} - 9 q^{18} - 66 q^{19} - 35 q^{20} - 36 q^{21} - 37 q^{22} - 58 q^{23} - 27 q^{24} + 24 q^{25} - 25 q^{26} + 95 q^{27} - 75 q^{28} - 31 q^{29} - 36 q^{30} - 129 q^{31} - 53 q^{32} - 48 q^{33} - 61 q^{34} - 38 q^{35} + 65 q^{36} - 127 q^{37} + q^{38} - 73 q^{39} - 74 q^{40} - 31 q^{41} - 17 q^{42} - 62 q^{43} - 76 q^{44} - 15 q^{45} - 60 q^{46} - 75 q^{47} + 13 q^{48} + 5 q^{49} - 30 q^{50} - 9 q^{51} - 137 q^{52} - 28 q^{53} - 9 q^{54} - 117 q^{55} - 23 q^{56} - 66 q^{57} - 90 q^{58} - 60 q^{59} - 35 q^{60} - 96 q^{61} + 10 q^{62} - 36 q^{63} - 75 q^{64} - 28 q^{65} - 37 q^{66} - 116 q^{67} + 3 q^{68} - 58 q^{69} - 73 q^{70} - 144 q^{71} - 27 q^{72} - 121 q^{73} - 16 q^{74} + 24 q^{75} - 118 q^{76} - 3 q^{77} - 25 q^{78} - 135 q^{79} - 36 q^{80} + 95 q^{81} - 102 q^{82} - 21 q^{83} - 75 q^{84} - 129 q^{85} - 46 q^{86} - 31 q^{87} - 77 q^{88} - 63 q^{89} - 36 q^{90} - 123 q^{91} - 42 q^{92} - 129 q^{93} - 44 q^{94} - 80 q^{95} - 53 q^{96} - 144 q^{97} + 10 q^{98} - 48 q^{99}+O(q^{100}) \) 95 * q - 9 * q^2 + 95 * q^3 + 65 * q^4 - 15 * q^5 - 9 * q^6 - 36 * q^7 - 27 * q^8 + 95 * q^9 - 36 * q^10 - 48 * q^11 + 65 * q^12 - 73 * q^13 - 17 * q^14 - 15 * q^15 + 13 * q^16 - 9 * q^17 - 9 * q^18 - 66 * q^19 - 35 * q^20 - 36 * q^21 - 37 * q^22 - 58 * q^23 - 27 * q^24 + 24 * q^25 - 25 * q^26 + 95 * q^27 - 75 * q^28 - 31 * q^29 - 36 * q^30 - 129 * q^31 - 53 * q^32 - 48 * q^33 - 61 * q^34 - 38 * q^35 + 65 * q^36 - 127 * q^37 + q^38 - 73 * q^39 - 74 * q^40 - 31 * q^41 - 17 * q^42 - 62 * q^43 - 76 * q^44 - 15 * q^45 - 60 * q^46 - 75 * q^47 + 13 * q^48 + 5 * q^49 - 30 * q^50 - 9 * q^51 - 137 * q^52 - 28 * q^53 - 9 * q^54 - 117 * q^55 - 23 * q^56 - 66 * q^57 - 90 * q^58 - 60 * q^59 - 35 * q^60 - 96 * q^61 + 10 * q^62 - 36 * q^63 - 75 * q^64 - 28 * q^65 - 37 * q^66 - 116 * q^67 + 3 * q^68 - 58 * q^69 - 73 * q^70 - 144 * q^71 - 27 * q^72 - 121 * q^73 - 16 * q^74 + 24 * q^75 - 118 * q^76 - 3 * q^77 - 25 * q^78 - 135 * q^79 - 36 * q^80 + 95 * q^81 - 102 * q^82 - 21 * q^83 - 75 * q^84 - 129 * q^85 - 46 * q^86 - 31 * q^87 - 77 * q^88 - 63 * q^89 - 36 * q^90 - 123 * q^91 - 42 * q^92 - 129 * q^93 - 44 * q^94 - 80 * q^95 - 53 * q^96 - 144 * q^97 + 10 * q^98 - 48 * 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 $

$2$	−2.32680	−1.64529	−0.822647	−	0.568552i	$-0.807504\pi$
$2$	−2.32680	−1.64529	−0.822647	+	0.568552i	$0.807504\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.41399	1.70700
$5$	0.167407	0.0748668	0.0374334	−	0.999299i	$-0.488082\pi$
$5$	0.167407	0.0748668	0.0374334	+	0.999299i	$0.488082\pi$
$6$	−2.32680	−0.949911
$7$	5.19602	1.96391	0.981956	−	0.189108i	$-0.0605595\pi$
$7$	5.19602	1.96391	0.981956	+	0.189108i	$0.0605595\pi$
$8$	−3.29007	−1.16322
$9$	1.00000	0.333333
$10$	−0.389523	−0.123178
$11$	3.61380	1.08960	0.544801	−	0.838565i	$-0.316605\pi$
$11$	3.61380	1.08960	0.544801	+	0.838565i	$0.316605\pi$
$12$	3.41399	0.985534
$13$	−2.80992	−0.779333	−0.389666	−	0.920956i	$-0.627410\pi$
$13$	−2.80992	−0.779333	−0.389666	+	0.920956i	$0.627410\pi$
$14$	−12.0901	−3.23122
$15$	0.167407	0.0432244
$16$	0.827353	0.206838
$17$	−2.52559	−0.612546	−0.306273	−	0.951944i	$-0.599082\pi$
$17$	−2.52559	−0.612546	−0.306273	+	0.951944i	$0.599082\pi$
$18$	−2.32680	−0.548432
$19$	−8.40780	−1.92888	−0.964440	−	0.264301i	$-0.914859\pi$
$19$	−8.40780	−1.92888	−0.964440	+	0.264301i	$0.914859\pi$
$20$	0.571527	0.127797
$21$	5.19602	1.13387
$22$	−8.40859	−1.79272
$23$	1.00288	0.209115	0.104558	−	0.994519i	$-0.466657\pi$
$23$	1.00288	0.209115	0.104558	+	0.994519i	$0.466657\pi$
$24$	−3.29007	−0.671583
$25$	−4.97197	−0.994395
$26$	6.53813	1.28223
$27$	1.00000	0.192450
$28$	17.7392	3.35239
$29$	−8.45877	−1.57075	−0.785377	−	0.619017i	$-0.787531\pi$
$29$	−8.45877	−1.57075	−0.785377	+	0.619017i	$0.787531\pi$
$30$	−0.389523	−0.0711169
$31$	−4.24666	−0.762723	−0.381361	−	0.924426i	$-0.624545\pi$
$31$	−4.24666	−0.762723	−0.381361	+	0.924426i	$0.624545\pi$
$32$	4.65506	0.822906
$33$	3.61380	0.629082
$34$	5.87654	1.00782
$35$	0.869852	0.147032
$36$	3.41399	0.568998
$37$	1.31429	0.216068	0.108034	−	0.994147i	$-0.465545\pi$
$37$	1.31429	0.216068	0.108034	+	0.994147i	$0.465545\pi$
$38$	19.5632	3.17358
$39$	−2.80992	−0.449948
$40$	−0.550782	−0.0870863
$41$	4.04858	0.632281	0.316141	−	0.948712i	$-0.397613\pi$
$41$	4.04858	0.632281	0.316141	+	0.948712i	$0.397613\pi$
$42$	−12.0901	−1.86554
$43$	−5.50209	−0.839060	−0.419530	−	0.907741i	$-0.637805\pi$
$43$	−5.50209	−0.839060	−0.419530	+	0.907741i	$0.637805\pi$
$44$	12.3375	1.85995
$45$	0.167407	0.0249556
$46$	−2.33350	−0.344056
$47$	1.56151	0.227769	0.113885	−	0.993494i	$-0.463671\pi$
$47$	1.56151	0.227769	0.113885	+	0.993494i	$0.463671\pi$
$48$	0.827353	0.119418
$49$	19.9987	2.85695
$50$	11.5688	1.63607
$51$	−2.52559	−0.353654
$52$	−9.59306	−1.33032
$53$	10.2335	1.40568	0.702841	−	0.711347i	$-0.251914\pi$
$53$	10.2335	1.40568	0.702841	+	0.711347i	$0.251914\pi$
$54$	−2.32680	−0.316637
$55$	0.604977	0.0815751
$56$	−17.0953	−2.28445
$57$	−8.40780	−1.11364
$58$	19.6819	2.58435
$59$	−2.78684	−0.362815	−0.181408	−	0.983408i	$-0.558065\pi$
$59$	−2.78684	−0.362815	−0.181408	+	0.983408i	$0.558065\pi$
$60$	0.571527	0.0737838
$61$	−4.51039	−0.577497	−0.288748	−	0.957405i	$-0.593239\pi$
$61$	−4.51039	−0.577497	−0.288748	+	0.957405i	$0.593239\pi$
$62$	9.88112	1.25490
$63$	5.19602	0.654638
$64$	−12.4861	−1.56076
$65$	−0.470402	−0.0583462
$66$	−8.40859	−1.03503
$67$	−9.30062	−1.13625	−0.568126	−	0.822942i	$-0.692331\pi$
$67$	−9.30062	−1.13625	−0.568126	+	0.822942i	$0.692331\pi$
$68$	−8.62235	−1.04561
$69$	1.00288	0.120733
$70$	−2.02397	−0.241911
$71$	−1.29253	−0.153395	−0.0766975	−	0.997054i	$-0.524438\pi$
$71$	−1.29253	−0.153395	−0.0766975	+	0.997054i	$0.524438\pi$
$72$	−3.29007	−0.387739
$73$	−12.1020	−1.41643	−0.708216	−	0.705996i	$-0.750500\pi$
$73$	−12.1020	−1.41643	−0.708216	+	0.705996i	$0.750500\pi$
$74$	−3.05808	−0.355495
$75$	−4.97197	−0.574114
$76$	−28.7041	−3.29259
$77$	18.7774	2.13988
$78$	6.53813	0.740297
$79$	−2.03278	−0.228705	−0.114353	−	0.993440i	$-0.536479\pi$
$79$	−2.03278	−0.228705	−0.114353	+	0.993440i	$0.536479\pi$
$80$	0.138505	0.0154853
$81$	1.00000	0.111111
$82$	−9.42022	−1.04029
$83$	−11.8585	−1.30164	−0.650822	−	0.759230i	$-0.725576\pi$
$83$	−11.8585	−1.30164	−0.650822	+	0.759230i	$0.725576\pi$
$84$	17.7392	1.93550
$85$	−0.422802	−0.0458594
$86$	12.8022	1.38050
$87$	−8.45877	−0.906876
$88$	−11.8897	−1.26744
$89$	−12.6090	−1.33655	−0.668277	−	0.743913i	$-0.732968\pi$
$89$	−12.6090	−1.33655	−0.668277	+	0.743913i	$0.732968\pi$
$90$	−0.389523	−0.0410593
$91$	−14.6004	−1.53054
$92$	3.42383	0.356959
$93$	−4.24666	−0.440358
$94$	−3.63332	−0.374748
$95$	−1.40753	−0.144409
$96$	4.65506	0.475105
$97$	1.27585	0.129543	0.0647714	−	0.997900i	$-0.479368\pi$
$97$	1.27585	0.129543	0.0647714	+	0.997900i	$0.479368\pi$
$98$	−46.5329	−4.70053
$99$	3.61380	0.363201
$100$	−16.9743	−1.69743
$101$	17.6601	1.75724	0.878621	−	0.477521i	$-0.158464\pi$
$101$	17.6601	1.75724	0.878621	+	0.477521i	$0.158464\pi$
$102$	5.87654	0.581864
$103$	−8.90875	−0.877805	−0.438903	−	0.898535i	$-0.644633\pi$
$103$	−8.90875	−0.877805	−0.438903	+	0.898535i	$0.644633\pi$
$104$	9.24485	0.906533
$105$	0.869852	0.0848889
$106$	−23.8114	−2.31276
$107$	−20.0426	−1.93759	−0.968795	−	0.247865i	$-0.920271\pi$
$107$	−20.0426	−1.93759	−0.968795	+	0.247865i	$0.920271\pi$
$108$	3.41399	0.328511
$109$	14.9439	1.43137	0.715685	−	0.698424i	$-0.246115\pi$
$109$	14.9439	1.43137	0.715685	+	0.698424i	$0.246115\pi$
$110$	−1.40766	−0.134215
$111$	1.31429	0.124747
$112$	4.29894	0.406212
$113$	−8.88993	−0.836294	−0.418147	−	0.908379i	$-0.637320\pi$
$113$	−8.88993	−0.836294	−0.418147	+	0.908379i	$0.637320\pi$
$114$	19.5632	1.83227
$115$	0.167890	0.0156558
$116$	−28.8782	−2.68127
$117$	−2.80992	−0.259778
$118$	6.48441	0.596938
$119$	−13.1230	−1.20299
$120$	−0.550782	−0.0502793
$121$	2.05957	0.187234
$122$	10.4948	0.950152
$123$	4.04858	0.365048
$124$	−14.4981	−1.30196
$125$	−1.66938	−0.149314
$126$	−12.0901	−1.07707
$127$	1.53540	0.136245	0.0681223	−	0.997677i	$-0.478299\pi$
$127$	1.53540	0.136245	0.0681223	+	0.997677i	$0.478299\pi$
$128$	19.7425	1.74501
$129$	−5.50209	−0.484432
$130$	1.09453	0.0959967
$131$	22.4302	1.95974	0.979870	−	0.199639i	$-0.0639768\pi$
$131$	22.4302	1.95974	0.979870	+	0.199639i	$0.0639768\pi$
$132$	12.3375	1.07384
$133$	−43.6871	−3.78815
$134$	21.6407	1.86947
$135$	0.167407	0.0144081
$136$	8.30938	0.712523
$137$	−20.3167	−1.73577	−0.867887	−	0.496762i	$-0.834522\pi$
$137$	−20.3167	−1.73577	−0.867887	+	0.496762i	$0.834522\pi$
$138$	−2.33350	−0.198641
$139$	−19.3734	−1.64323	−0.821615	−	0.570044i	$-0.806926\pi$
$139$	−19.3734	−1.64323	−0.821615	+	0.570044i	$0.806926\pi$
$140$	2.96967	0.250983
$141$	1.56151	0.131503
$142$	3.00746	0.252380
$143$	−10.1545	−0.849163
$144$	0.827353	0.0689460
$145$	−1.41606	−0.117597
$146$	28.1589	2.33045
$147$	19.9987	1.64946
$148$	4.48697	0.368826
$149$	−9.85997	−0.807760	−0.403880	−	0.914812i	$-0.632339\pi$
$149$	−9.85997	−0.807760	−0.403880	+	0.914812i	$0.632339\pi$
$150$	11.5688	0.944587
$151$	−1.51761	−0.123502	−0.0617508	−	0.998092i	$-0.519668\pi$
$151$	−1.51761	−0.123502	−0.0617508	+	0.998092i	$0.519668\pi$
$152$	27.6623	2.24371
$153$	−2.52559	−0.204182
$154$	−43.6912	−3.52074
$155$	−0.710922	−0.0571026
$156$	−9.59306	−0.768059
$157$	−22.4657	−1.79296	−0.896481	−	0.443083i	$-0.853885\pi$
$157$	−22.4657	−1.79296	−0.896481	+	0.443083i	$0.853885\pi$
$158$	4.72986	0.376288
$159$	10.2335	0.811571
$160$	0.779291	0.0616084
$161$	5.21100	0.410684
$162$	−2.32680	−0.182811
$163$	−10.7369	−0.840975	−0.420488	−	0.907298i	$-0.638141\pi$
$163$	−10.7369	−0.840975	−0.420488	+	0.907298i	$0.638141\pi$
$164$	13.8218	1.07930
$165$	0.604977	0.0470974
$166$	27.5924	2.14159
$167$	18.4664	1.42897	0.714487	−	0.699649i	$-0.246660\pi$
$167$	18.4664	1.42897	0.714487	+	0.699649i	$0.246660\pi$
$168$	−17.0953	−1.31893
$169$	−5.10432	−0.392640
$170$	0.983776	0.0754522
$171$	−8.40780	−0.642960
$172$	−18.7841	−1.43227
$173$	15.5400	1.18148	0.590741	−	0.806861i	$-0.298836\pi$
$173$	15.5400	1.18148	0.590741	+	0.806861i	$0.298836\pi$
$174$	19.6819	1.49208
$175$	−25.8345	−1.95290
$176$	2.98989	0.225371
$177$	−2.78684	−0.209472
$178$	29.3387	2.19903
$179$	4.23708	0.316694	0.158347	−	0.987384i	$-0.449384\pi$
$179$	4.23708	0.316694	0.158347	+	0.987384i	$0.449384\pi$
$180$	0.571527	0.0425991
$181$	19.2627	1.43178	0.715892	−	0.698211i	$-0.246020\pi$
$181$	19.2627	1.43178	0.715892	+	0.698211i	$0.246020\pi$
$182$	33.9723	2.51819
$183$	−4.51039	−0.333418
$184$	−3.29955	−0.243246
$185$	0.220021	0.0161763
$186$	9.88112	0.724519
$187$	−9.12699	−0.667432
$188$	5.33098	0.388802
$189$	5.19602	0.377955
$190$	3.27503	0.237596
$191$	8.95108	0.647677	0.323839	−	0.946112i	$-0.395026\pi$
$191$	8.95108	0.647677	0.323839	+	0.946112i	$0.395026\pi$
$192$	−12.4861	−0.901106
$193$	10.2458	0.737508	0.368754	−	0.929527i	$-0.379784\pi$
$193$	10.2458	0.737508	0.368754	+	0.929527i	$0.379784\pi$
$194$	−2.96864	−0.213136
$195$	−0.470402	−0.0336862
$196$	68.2753	4.87681
$197$	20.0954	1.43174	0.715868	−	0.698236i	$-0.246031\pi$
$197$	20.0954	1.43174	0.715868	+	0.698236i	$0.246031\pi$
$198$	−8.40859	−0.597573
$199$	−19.0044	−1.34719	−0.673593	−	0.739102i	$-0.735250\pi$
$199$	−19.0044	−1.34719	−0.673593	+	0.739102i	$0.735250\pi$
$200$	16.3582	1.15670
$201$	−9.30062	−0.656015
$202$	−41.0914	−2.89118
$203$	−43.9520	−3.08482
$204$	−8.62235	−0.603685
$205$	0.677761	0.0473369
$206$	20.7289	1.44425
$207$	1.00288	0.0697051
$208$	−2.32480	−0.161196
$209$	−30.3841	−2.10171
$210$	−2.02397	−0.139667
$211$	9.25805	0.637350	0.318675	−	0.947864i	$-0.396762\pi$
$211$	9.25805	0.637350	0.318675	+	0.947864i	$0.396762\pi$
$212$	34.9372	2.39949
$213$	−1.29253	−0.0885627
$214$	46.6350	3.18791
$215$	−0.921089	−0.0628178
$216$	−3.29007	−0.223861
$217$	−22.0658	−1.49792
$218$	−34.7715	−2.35502
$219$	−12.1020	−0.817778
$220$	2.06539	0.139248
$221$	7.09672	0.477377
$222$	−3.05808	−0.205245
$223$	21.1482	1.41619	0.708096	−	0.706116i	$-0.249554\pi$
$223$	21.1482	1.41619	0.708096	+	0.706116i	$0.249554\pi$
$224$	24.1878	1.61612
$225$	−4.97197	−0.331465
$226$	20.6851	1.37595
$227$	−7.90405	−0.524610	−0.262305	−	0.964985i	$-0.584483\pi$
$227$	−7.90405	−0.524610	−0.262305	+	0.964985i	$0.584483\pi$
$228$	−28.7041	−1.90098
$229$	8.74908	0.578155	0.289078	−	0.957306i	$-0.406651\pi$
$229$	8.74908	0.578155	0.289078	+	0.957306i	$0.406651\pi$
$230$	−0.390646	−0.0257584
$231$	18.7774	1.23546
$232$	27.8300	1.82713
$233$	14.1635	0.927883	0.463941	−	0.885866i	$-0.346435\pi$
$233$	14.1635	0.927883	0.463941	+	0.885866i	$0.346435\pi$
$234$	6.53813	0.427411
$235$	0.261408	0.0170524
$236$	−9.51424	−0.619324
$237$	−2.03278	−0.132043
$238$	30.5347	1.97927
$239$	−20.1276	−1.30195	−0.650974	−	0.759100i	$-0.725639\pi$
$239$	−20.1276	−1.30195	−0.650974	+	0.759100i	$0.725639\pi$
$240$	0.138505	0.00894045
$241$	−3.15818	−0.203436	−0.101718	−	0.994813i	$-0.532434\pi$
$241$	−3.15818	−0.203436	−0.101718	+	0.994813i	$0.532434\pi$
$242$	−4.79221	−0.308055
$243$	1.00000	0.0641500
$244$	−15.3984	−0.985784
$245$	3.34792	0.213891
$246$	−9.42022	−0.600611
$247$	23.6253	1.50324
$248$	13.9718	0.887211
$249$	−11.8585	−0.751505
$250$	3.88431	0.245666
$251$	3.75409	0.236956	0.118478	−	0.992957i	$-0.462198\pi$
$251$	3.75409	0.236956	0.118478	+	0.992957i	$0.462198\pi$
$252$	17.7392	1.11746
$253$	3.62422	0.227853
$254$	−3.57256	−0.224162
$255$	−0.422802	−0.0264769
$256$	−20.9646	−1.31029
$257$	−14.2715	−0.890232	−0.445116	−	0.895473i	$-0.646838\pi$
$257$	−14.2715	−0.890232	−0.445116	+	0.895473i	$0.646838\pi$
$258$	12.8022	0.797033
$259$	6.82907	0.424338
$260$	−1.60595	−0.0995967
$261$	−8.45877	−0.523585
$262$	−52.1906	−3.22435
$263$	18.6880	1.15235	0.576175	−	0.817326i	$-0.304545\pi$
$263$	18.6880	1.15235	0.576175	+	0.817326i	$0.304545\pi$
$264$	−11.8897	−0.731759
$265$	1.71317	0.105239
$266$	101.651	6.23263
$267$	−12.6090	−0.771660
$268$	−31.7522	−1.93958
$269$	3.16497	0.192972	0.0964859	−	0.995334i	$-0.469240\pi$
$269$	3.16497	0.192972	0.0964859	+	0.995334i	$0.469240\pi$
$270$	−0.389523	−0.0237056
$271$	26.1495	1.58847	0.794236	−	0.607610i	$-0.207871\pi$
$271$	26.1495	1.58847	0.794236	+	0.607610i	$0.207871\pi$
$272$	−2.08955	−0.126698
$273$	−14.6004	−0.883659
$274$	47.2729	2.85586
$275$	−17.9677	−1.08350
$276$	3.42383	0.206090
$277$	−30.5446	−1.83525	−0.917624	−	0.397450i	$-0.869895\pi$
$277$	−30.5446	−1.83525	−0.917624	+	0.397450i	$0.869895\pi$
$278$	45.0780	2.70360
$279$	−4.24666	−0.254241
$280$	−2.86188	−0.171030
$281$	−17.9660	−1.07176	−0.535880	−	0.844294i	$-0.680020\pi$
$281$	−17.9660	−1.07176	−0.535880	+	0.844294i	$0.680020\pi$
$282$	−3.63332	−0.216361
$283$	15.5837	0.926358	0.463179	−	0.886265i	$-0.346709\pi$
$283$	15.5837	0.926358	0.463179	+	0.886265i	$0.346709\pi$
$284$	−4.41269	−0.261845
$285$	−1.40753	−0.0833747
$286$	23.6275	1.39712
$287$	21.0365	1.24175
$288$	4.65506	0.274302
$289$	−10.6214	−0.624788
$290$	3.29489	0.193482
$291$	1.27585	0.0747915
$292$	−41.3161	−2.41784
$293$	10.6077	0.619706	0.309853	−	0.950785i	$-0.399720\pi$
$293$	10.6077	0.619706	0.309853	+	0.950785i	$0.399720\pi$
$294$	−46.5329	−2.71385
$295$	−0.466537	−0.0271628
$296$	−4.32410	−0.251333
$297$	3.61380	0.209694
$298$	22.9422	1.32900
$299$	−2.81802	−0.162970
$300$	−16.9743	−0.980010
$301$	−28.5890	−1.64784
$302$	3.53118	0.203197
$303$	17.6601	1.01454
$304$	−6.95621	−0.398966
$305$	−0.755073	−0.0432353
$306$	5.87654	0.335940
$307$	−0.835318	−0.0476741	−0.0238371	−	0.999716i	$-0.507588\pi$
$307$	−0.835318	−0.0476741	−0.0238371	+	0.999716i	$0.507588\pi$
$308$	64.1059	3.65277
$309$	−8.90875	−0.506801
$310$	1.65417	0.0939506
$311$	−33.2691	−1.88652	−0.943258	−	0.332061i	$-0.892256\pi$
$311$	−33.2691	−1.88652	−0.943258	+	0.332061i	$0.892256\pi$
$312$	9.24485	0.523387
$313$	−30.1380	−1.70350	−0.851751	−	0.523948i	$-0.824459\pi$
$313$	−30.1380	−1.70350	−0.851751	+	0.523948i	$0.824459\pi$
$314$	52.2732	2.94995
$315$	0.869852	0.0490106
$316$	−6.93988	−0.390399
$317$	12.9258	0.725984	0.362992	−	0.931792i	$-0.381755\pi$
$317$	12.9258	0.725984	0.362992	+	0.931792i	$0.381755\pi$
$318$	−23.8114	−1.33527
$319$	−30.5683	−1.71150
$320$	−2.09026	−0.116849
$321$	−20.0426	−1.11867
$322$	−12.1249	−0.675697
$323$	21.2347	1.18153
$324$	3.41399	0.189666
$325$	13.9709	0.774965
$326$	24.9825	1.38365
$327$	14.9439	0.826401
$328$	−13.3201	−0.735480
$329$	8.11364	0.447319
$330$	−1.40766	−0.0774891
$331$	14.5582	0.800192	0.400096	−	0.916473i	$-0.368977\pi$
$331$	14.5582	0.800192	0.400096	+	0.916473i	$0.368977\pi$
$332$	−40.4850	−2.22190
$333$	1.31429	0.0720225
$334$	−42.9676	−2.35108
$335$	−1.55699	−0.0850676
$336$	4.29894	0.234527
$337$	−30.1947	−1.64481	−0.822405	−	0.568903i	$-0.807368\pi$
$337$	−30.1947	−1.64481	−0.822405	+	0.568903i	$0.807368\pi$
$338$	11.8767	0.646009
$339$	−8.88993	−0.482835
$340$	−1.44344	−0.0782817
$341$	−15.3466	−0.831065
$342$	19.5632	1.05786
$343$	67.5414	3.64689
$344$	18.1023	0.976008
$345$	0.167890	0.00903888
$346$	−36.1584	−1.94389
$347$	−23.4852	−1.26075	−0.630375	−	0.776291i	$-0.717099\pi$
$347$	−23.4852	−1.26075	−0.630375	+	0.776291i	$0.717099\pi$
$348$	−28.8782	−1.54803
$349$	13.1900	0.706045	0.353022	−	0.935615i	$-0.385154\pi$
$349$	13.1900	0.706045	0.353022	+	0.935615i	$0.385154\pi$
$350$	60.1117	3.21310
$351$	−2.80992	−0.149983
$352$	16.8225	0.896641
$353$	−1.12308	−0.0597754	−0.0298877	−	0.999553i	$-0.509515\pi$
$353$	−1.12308	−0.0597754	−0.0298877	+	0.999553i	$0.509515\pi$
$354$	6.48441	0.344642
$355$	−0.216379	−0.0114842
$356$	−43.0471	−2.28149
$357$	−13.1230	−0.694545
$358$	−9.85883	−0.521055
$359$	1.98058	0.104531	0.0522655	−	0.998633i	$-0.483356\pi$
$359$	1.98058	0.104531	0.0522655	+	0.998633i	$0.483356\pi$
$360$	−0.550782	−0.0290288
$361$	51.6910	2.72058
$362$	−44.8204	−2.35571
$363$	2.05957	0.108100
$364$	−49.8458	−2.61263
$365$	−2.02596	−0.106044
$366$	10.4948	0.548571
$367$	−4.00137	−0.208870	−0.104435	−	0.994532i	$-0.533303\pi$
$367$	−4.00137	−0.208870	−0.104435	+	0.994532i	$0.533303\pi$
$368$	0.829737	0.0432530
$369$	4.04858	0.210760
$370$	−0.511945	−0.0266148
$371$	53.1737	2.76064
$372$	−14.4981	−0.751689
$373$	3.39955	0.176022	0.0880111	−	0.996119i	$-0.471949\pi$
$373$	3.39955	0.176022	0.0880111	+	0.996119i	$0.471949\pi$
$374$	21.2367	1.09812
$375$	−1.66938	−0.0862065
$376$	−5.13748	−0.264945
$377$	23.7685	1.22414
$378$	−12.0901	−0.621848
$379$	14.1907	0.728928	0.364464	−	0.931217i	$-0.381252\pi$
$379$	14.1907	0.728928	0.364464	+	0.931217i	$0.381252\pi$
$380$	−4.80528	−0.246506
$381$	1.53540	0.0786608
$382$	−20.8274	−1.06562
$383$	−0.262402	−0.0134081	−0.00670407	−	0.999978i	$-0.502134\pi$
$383$	−0.262402	−0.0134081	−0.00670407	+	0.999978i	$0.502134\pi$
$384$	19.7425	1.00748
$385$	3.14348	0.160206
$386$	−23.8399	−1.21342
$387$	−5.50209	−0.279687
$388$	4.35573	0.221129
$389$	2.67625	0.135691	0.0678456	−	0.997696i	$-0.478387\pi$
$389$	2.67625	0.135691	0.0678456	+	0.997696i	$0.478387\pi$
$390$	1.09453	0.0554237
$391$	−2.53287	−0.128093
$392$	−65.7971	−3.32325
$393$	22.4302	1.13146
$394$	−46.7579	−2.35563
$395$	−0.340302	−0.0171224
$396$	12.3375	0.619982
$397$	−27.0952	−1.35987	−0.679935	−	0.733273i	$-0.737992\pi$
$397$	−27.0952	−1.35987	−0.679935	+	0.733273i	$0.737992\pi$
$398$	44.2194	2.21652
$399$	−43.6871	−2.18709
$400$	−4.11358	−0.205679
$401$	4.98731	0.249054	0.124527	−	0.992216i	$-0.460259\pi$
$401$	4.98731	0.249054	0.124527	+	0.992216i	$0.460259\pi$
$402$	21.6407	1.07934
$403$	11.9328	0.594415
$404$	60.2913	2.99960
$405$	0.167407	0.00831854
$406$	102.267	5.07545
$407$	4.74958	0.235428
$408$	8.30938	0.411376
$409$	2.17474	0.107534	0.0537670	−	0.998554i	$-0.482877\pi$
$409$	2.17474	0.107534	0.0537670	+	0.998554i	$0.482877\pi$
$410$	−1.57701	−0.0778832
$411$	−20.3167	−1.00215
$412$	−30.4144	−1.49841
$413$	−14.4805	−0.712538
$414$	−2.33350	−0.114685
$415$	−1.98521	−0.0974500
$416$	−13.0804	−0.641318
$417$	−19.3734	−0.948719
$418$	70.6977	3.45794
$419$	−31.5816	−1.54286	−0.771431	−	0.636313i	$-0.780459\pi$
$419$	−31.5816	−1.54286	−0.771431	+	0.636313i	$0.780459\pi$
$420$	2.96967	0.144905
$421$	−22.7682	−1.10965	−0.554827	−	0.831965i	$-0.687216\pi$
$421$	−22.7682	−1.10965	−0.554827	+	0.831965i	$0.687216\pi$
$422$	−21.5416	−1.04863
$423$	1.56151	0.0759232
$424$	−33.6690	−1.63511
$425$	12.5572	0.609113
$426$	3.00746	0.145712
$427$	−23.4361	−1.13415
$428$	−68.4252	−3.30746
$429$	−10.1545	−0.490265
$430$	2.14319	0.103354
$431$	−23.1157	−1.11344	−0.556721	−	0.830699i	$-0.687941\pi$
$431$	−23.1157	−1.11344	−0.556721	+	0.830699i	$0.687941\pi$
$432$	0.827353	0.0398060
$433$	−8.89953	−0.427684	−0.213842	−	0.976868i	$-0.568598\pi$
$433$	−8.89953	−0.427684	−0.213842	+	0.976868i	$0.568598\pi$
$434$	51.3426	2.46452
$435$	−1.41606	−0.0678949
$436$	51.0185	2.44334
$437$	−8.43203	−0.403359
$438$	28.1589	1.34549
$439$	13.6870	0.653245	0.326622	−	0.945155i	$-0.394089\pi$
$439$	13.6870	0.653245	0.326622	+	0.945155i	$0.394089\pi$
$440$	−1.99042	−0.0948894
$441$	19.9987	0.952318
$442$	−16.5126	−0.785426
$443$	−6.26469	−0.297645	−0.148822	−	0.988864i	$-0.547548\pi$
$443$	−6.26469	−0.297645	−0.148822	+	0.988864i	$0.547548\pi$
$444$	4.48697	0.212942
$445$	−2.11084	−0.100064
$446$	−49.2077	−2.33005
$447$	−9.85997	−0.466361
$448$	−64.8781	−3.06520
$449$	−11.3938	−0.537706	−0.268853	−	0.963181i	$-0.586645\pi$
$449$	−11.3938	−0.537706	−0.268853	+	0.963181i	$0.586645\pi$
$450$	11.5688	0.545358
$451$	14.6308	0.688935
$452$	−30.3501	−1.42755
$453$	−1.51761	−0.0713037
$454$	18.3911	0.863138
$455$	−2.44422	−0.114587
$456$	27.6623	1.29540
$457$	15.5123	0.725637	0.362818	−	0.931860i	$-0.381815\pi$
$457$	15.5123	0.725637	0.362818	+	0.931860i	$0.381815\pi$
$458$	−20.3573	−0.951236
$459$	−2.52559	−0.117885
$460$	0.573174	0.0267244
$461$	−25.3710	−1.18165	−0.590823	−	0.806801i	$-0.701197\pi$
$461$	−25.3710	−1.18165	−0.590823	+	0.806801i	$0.701197\pi$
$462$	−43.6912	−2.03270
$463$	−19.2538	−0.894799	−0.447399	−	0.894334i	$-0.647650\pi$
$463$	−19.2538	−0.894799	−0.447399	+	0.894334i	$0.647650\pi$
$464$	−6.99839	−0.324892
$465$	−0.710922	−0.0329682
$466$	−32.9556	−1.52664
$467$	24.8679	1.15075	0.575374	−	0.817891i	$-0.304857\pi$
$467$	24.8679	1.15075	0.575374	+	0.817891i	$0.304857\pi$
$468$	−9.59306	−0.443439
$469$	−48.3263	−2.23150
$470$	−0.608244	−0.0280562
$471$	−22.4657	−1.03517
$472$	9.16889	0.422033
$473$	−19.8835	−0.914242
$474$	4.72986	0.217250
$475$	41.8034	1.91807
$476$	−44.8019	−2.05349
$477$	10.2335	0.468561
$478$	46.8329	2.14209
$479$	7.93672	0.362638	0.181319	−	0.983424i	$-0.441963\pi$
$479$	7.93672	0.362638	0.181319	+	0.983424i	$0.441963\pi$
$480$	0.779291	0.0355696
$481$	−3.69305	−0.168389
$482$	7.34844	0.334712
$483$	5.21100	0.237109
$484$	7.03136	0.319607
$485$	0.213586	0.00969845
$486$	−2.32680	−0.105546
$487$	−5.58291	−0.252986	−0.126493	−	0.991968i	$-0.540372\pi$
$487$	−5.58291	−0.252986	−0.126493	+	0.991968i	$0.540372\pi$
$488$	14.8395	0.671753
$489$	−10.7369	−0.485537
$490$	−7.78994	−0.351914
$491$	8.07938	0.364617	0.182309	−	0.983241i	$-0.441643\pi$
$491$	8.07938	0.364617	0.182309	+	0.983241i	$0.441643\pi$
$492$	13.8218	0.623135
$493$	21.3634	0.962159
$494$	−54.9712	−2.47327
$495$	0.604977	0.0271917
$496$	−3.51348	−0.157760
$497$	−6.71602	−0.301255
$498$	27.5924	1.23645
$499$	42.5524	1.90491	0.952455	−	0.304681i	$-0.0985497\pi$
$499$	42.5524	1.90491	0.952455	+	0.304681i	$0.0985497\pi$
$500$	−5.69925	−0.254878
$501$	18.4664	0.825018
$502$	−8.73502	−0.389863
$503$	10.2997	0.459243	0.229622	−	0.973280i	$-0.426251\pi$
$503$	10.2997	0.459243	0.229622	+	0.973280i	$0.426251\pi$
$504$	−17.0953	−0.761485
$505$	2.95642	0.131559
$506$	−8.43283	−0.374885
$507$	−5.10432	−0.226691
$508$	5.24183	0.232569
$509$	23.2368	1.02995	0.514976	−	0.857204i	$-0.327801\pi$
$509$	23.2368	1.02995	0.514976	+	0.857204i	$0.327801\pi$
$510$	0.983776	0.0435623
$511$	−62.8823	−2.78175
$512$	9.29548	0.410806
$513$	−8.40780	−0.371213
$514$	33.2069	1.46469
$515$	−1.49139	−0.0657185
$516$	−18.7841	−0.826923
$517$	5.64299	0.248178
$518$	−15.8899	−0.698161
$519$	15.5400	0.682129
$520$	1.54766	0.0678692
$521$	−14.8077	−0.648738	−0.324369	−	0.945931i	$-0.605152\pi$
$521$	−14.8077	−0.648738	−0.324369	+	0.945931i	$0.605152\pi$
$522$	19.6819	0.861452
$523$	20.9040	0.914067	0.457034	−	0.889449i	$-0.348912\pi$
$523$	20.9040	0.914067	0.457034	+	0.889449i	$0.348912\pi$
$524$	76.5766	3.34527
$525$	−25.8345	−1.12751
$526$	−43.4832	−1.89596
$527$	10.7253	0.467203
$528$	2.98989	0.130118
$529$	−21.9942	−0.956271
$530$	−3.98619	−0.173149
$531$	−2.78684	−0.120938
$532$	−149.147	−6.46636
$533$	−11.3762	−0.492758
$534$	29.3387	1.26961
$535$	−3.35527	−0.145061
$536$	30.5997	1.32171
$537$	4.23708	0.182843
$538$	−7.36425	−0.317496
$539$	72.2713	3.11294
$540$	0.571527	0.0245946
$541$	−5.40090	−0.232203	−0.116102	−	0.993237i	$-0.537040\pi$
$541$	−5.40090	−0.232203	−0.116102	+	0.993237i	$0.537040\pi$
$542$	−60.8447	−2.61350
$543$	19.2627	0.826641
$544$	−11.7568	−0.504068
$545$	2.50172	0.107162
$546$	33.9723	1.45388
$547$	19.2913	0.824836	0.412418	−	0.910995i	$-0.364684\pi$
$547$	19.2913	0.824836	0.412418	+	0.910995i	$0.364684\pi$
$548$	−69.3611	−2.96296
$549$	−4.51039	−0.192499
$550$	41.8073	1.78267
$551$	71.1196	3.02980
$552$	−3.29955	−0.140438
$553$	−10.5624	−0.449157
$554$	71.0712	3.01952
$555$	0.220021	0.00933938
$556$	−66.1406	−2.80498
$557$	28.4039	1.20351	0.601756	−	0.798680i	$-0.294468\pi$
$557$	28.4039	1.20351	0.601756	+	0.798680i	$0.294468\pi$
$558$	9.88112	0.418301
$559$	15.4604	0.653907
$560$	0.719675	0.0304118
$561$	−9.12699	−0.385342
$562$	41.8032	1.76336
$563$	20.4883	0.863477	0.431738	−	0.901999i	$-0.357900\pi$
$563$	20.4883	0.863477	0.431738	+	0.901999i	$0.357900\pi$
$564$	5.33098	0.224475
$565$	−1.48824	−0.0626107
$566$	−36.2602	−1.52413
$567$	5.19602	0.218213
$568$	4.25252	0.178432
$569$	17.8317	0.747546	0.373773	−	0.927520i	$-0.378064\pi$
$569$	17.8317	0.747546	0.373773	+	0.927520i	$0.378064\pi$
$570$	3.27503	0.137176
$571$	−29.9968	−1.25533	−0.627664	−	0.778485i	$-0.715989\pi$
$571$	−29.9968	−1.25533	−0.627664	+	0.778485i	$0.715989\pi$
$572$	−34.6674	−1.44952
$573$	8.95108	0.373937
$574$	−48.9477	−2.04304
$575$	−4.98630	−0.207943
$576$	−12.4861	−0.520254
$577$	37.7858	1.57304	0.786522	−	0.617563i	$-0.211880\pi$
$577$	37.7858	1.57304	0.786522	+	0.617563i	$0.211880\pi$
$578$	24.7138	1.02796
$579$	10.2458	0.425800
$580$	−4.83442	−0.200738
$581$	−61.6173	−2.55632
$582$	−2.96864	−0.123054
$583$	36.9819	1.53164
$584$	39.8165	1.64762
$585$	−0.470402	−0.0194487
$586$	−24.6819	−1.01960
$587$	25.0808	1.03520	0.517598	−	0.855624i	$-0.326826\pi$
$587$	25.0808	1.03520	0.517598	+	0.855624i	$0.326826\pi$
$588$	68.2753	2.81563
$589$	35.7051	1.47120
$590$	1.08554	0.0446909
$591$	20.0954	0.826613
$592$	1.08738	0.0446910
$593$	8.09288	0.332335	0.166167	−	0.986098i	$-0.446861\pi$
$593$	8.09288	0.332335	0.166167	+	0.986098i	$0.446861\pi$
$594$	−8.40859	−0.345009
$595$	−2.19689	−0.0900638
$596$	−33.6618	−1.37884
$597$	−19.0044	−0.777798
$598$	6.55697	0.268135
$599$	−41.7773	−1.70697	−0.853487	−	0.521115i	$-0.825516\pi$
$599$	−41.7773	−1.70697	−0.853487	+	0.521115i	$0.825516\pi$
$600$	16.3582	0.667819
$601$	18.5272	0.755741	0.377871	−	0.925858i	$-0.376656\pi$
$601$	18.5272	0.755741	0.377871	+	0.925858i	$0.376656\pi$
$602$	66.5208	2.71118
$603$	−9.30062	−0.378751
$604$	−5.18112	−0.210817
$605$	0.344787	0.0140176
$606$	−41.0914	−1.66922
$607$	47.0948	1.91152	0.955759	−	0.294152i	$-0.0950372\pi$
$607$	47.0948	1.91152	0.955759	+	0.294152i	$0.0950372\pi$
$608$	−39.1388	−1.58729
$609$	−43.9520	−1.78102
$610$	1.75690	0.0711349
$611$	−4.38772	−0.177508
$612$	−8.62235	−0.348538
$613$	20.6273	0.833130	0.416565	−	0.909106i	$-0.363234\pi$
$613$	20.6273	0.833130	0.416565	+	0.909106i	$0.363234\pi$
$614$	1.94362	0.0784380
$615$	0.677761	0.0273300
$616$	−61.7790	−2.48915
$617$	−13.2363	−0.532873	−0.266437	−	0.963852i	$-0.585846\pi$
$617$	−13.2363	−0.532873	−0.266437	+	0.963852i	$0.585846\pi$
$618$	20.7289	0.833837
$619$	−5.53661	−0.222535	−0.111267	−	0.993790i	$-0.535491\pi$
$619$	−5.53661	−0.222535	−0.111267	+	0.993790i	$0.535491\pi$
$620$	−2.42708	−0.0974739
$621$	1.00288	0.0402443
$622$	77.4104	3.10387
$623$	−65.5168	−2.62488
$624$	−2.32480	−0.0930664
$625$	24.5804	0.983216
$626$	70.1251	2.80276
$627$	−30.3841	−1.21342
$628$	−76.6978	−3.06058
$629$	−3.31935	−0.132351
$630$	−2.02397	−0.0806369
$631$	−44.1441	−1.75735	−0.878675	−	0.477420i	$-0.841572\pi$
$631$	−44.1441	−1.75735	−0.878675	+	0.477420i	$0.841572\pi$
$632$	6.68798	0.266034
$633$	9.25805	0.367974
$634$	−30.0757	−1.19446
$635$	0.257037	0.0102002
$636$	34.9372	1.38535
$637$	−56.1948	−2.22652
$638$	71.1264	2.81592
$639$	−1.29253	−0.0511317
$640$	3.30504	0.130643
$641$	19.6375	0.775634	0.387817	−	0.921736i	$-0.373229\pi$
$641$	19.6375	0.775634	0.387817	+	0.921736i	$0.373229\pi$
$642$	46.6350	1.84054
$643$	48.4310	1.90993	0.954967	−	0.296713i	$-0.0958905\pi$
$643$	48.4310	1.90993	0.954967	+	0.296713i	$0.0958905\pi$
$644$	17.7903	0.701036
$645$	−0.921089	−0.0362679
$646$	−49.4088	−1.94396
$647$	−1.51380	−0.0595136	−0.0297568	−	0.999557i	$-0.509473\pi$
$647$	−1.51380	−0.0595136	−0.0297568	+	0.999557i	$0.509473\pi$
$648$	−3.29007	−0.129246
$649$	−10.0711	−0.395324
$650$	−32.5074	−1.27505
$651$	−22.0658	−0.864825
$652$	−36.6555	−1.43554
$653$	−3.59762	−0.140786	−0.0703929	−	0.997519i	$-0.522425\pi$
$653$	−3.59762	−0.140786	−0.0703929	+	0.997519i	$0.522425\pi$
$654$	−34.7715	−1.35967
$655$	3.75499	0.146719
$656$	3.34960	0.130780
$657$	−12.1020	−0.472144
$658$	−18.8788	−0.735972
$659$	−5.45984	−0.212685	−0.106343	−	0.994330i	$-0.533914\pi$
$659$	−5.45984	−0.212685	−0.106343	+	0.994330i	$0.533914\pi$
$660$	2.06539	0.0803950
$661$	17.6133	0.685077	0.342539	−	0.939504i	$-0.388713\pi$
$661$	17.6133	0.685077	0.342539	+	0.939504i	$0.388713\pi$
$662$	−33.8741	−1.31655
$663$	7.09672	0.275614
$664$	39.0155	1.51409
$665$	−7.31354	−0.283607
$666$	−3.05808	−0.118498
$667$	−8.48315	−0.328469
$668$	63.0442	2.43925
$669$	21.1482	0.817639
$670$	3.62281	0.139961
$671$	−16.2997	−0.629242
$672$	24.1878	0.933065
$673$	13.8969	0.535687	0.267843	−	0.963462i	$-0.413689\pi$
$673$	13.8969	0.535687	0.267843	+	0.963462i	$0.413689\pi$
$674$	70.2570	2.70620
$675$	−4.97197	−0.191371
$676$	−17.4261	−0.670235
$677$	20.0425	0.770294	0.385147	−	0.922855i	$-0.374151\pi$
$677$	20.0425	0.770294	0.385147	+	0.922855i	$0.374151\pi$
$678$	20.6851	0.794405
$679$	6.62934	0.254411
$680$	1.39105	0.0533444
$681$	−7.90405	−0.302884
$682$	35.7084	1.36735
$683$	11.9121	0.455803	0.227902	−	0.973684i	$-0.426814\pi$
$683$	11.9121	0.455803	0.227902	+	0.973684i	$0.426814\pi$
$684$	−28.7041	−1.09753
$685$	−3.40117	−0.129952
$686$	−157.155	−6.00022
$687$	8.74908	0.333798
$688$	−4.55216	−0.173550
$689$	−28.7554	−1.09549
$690$	−0.390646	−0.0148716
$691$	14.8310	0.564199	0.282099	−	0.959385i	$-0.408969\pi$
$691$	14.8310	0.564199	0.282099	+	0.959385i	$0.408969\pi$
$692$	53.0533	2.01678
$693$	18.7774	0.713295
$694$	54.6452	2.07430
$695$	−3.24325	−0.123023
$696$	27.8300	1.05489
$697$	−10.2250	−0.387301
$698$	−30.6905	−1.16165
$699$	14.1635	0.535713
$700$	−88.1988	−3.33360
$701$	31.2225	1.17926	0.589629	−	0.807674i	$-0.299274\pi$
$701$	31.2225	1.17926	0.589629	+	0.807674i	$0.299274\pi$
$702$	6.53813	0.246766
$703$	−11.0503	−0.416768
$704$	−45.1223	−1.70061
$705$	0.261408	0.00984519
$706$	2.61317	0.0983481
$707$	91.7621	3.45107
$708$	−9.51424	−0.357567
$709$	−7.16394	−0.269047	−0.134524	−	0.990910i	$-0.542950\pi$
$709$	−7.16394	−0.269047	−0.134524	+	0.990910i	$0.542950\pi$
$710$	0.503470	0.0188949
$711$	−2.03278	−0.0762351
$712$	41.4846	1.55470
$713$	−4.25890	−0.159497
$714$	30.5347	1.14273
$715$	−1.69994	−0.0635741
$716$	14.4654	0.540596
$717$	−20.1276	−0.751680
$718$	−4.60841	−0.171984
$719$	−3.87515	−0.144519	−0.0722594	−	0.997386i	$-0.523021\pi$
$719$	−3.87515	−0.144519	−0.0722594	+	0.997386i	$0.523021\pi$
$720$	0.138505	0.00516177
$721$	−46.2901	−1.72393
$722$	−120.275	−4.47616
$723$	−3.15818	−0.117454
$724$	65.7626	2.44405
$725$	42.0568	1.56195
$726$	−4.79221	−0.177856
$727$	−22.7312	−0.843052	−0.421526	−	0.906816i	$-0.638505\pi$
$727$	−22.7312	−0.843052	−0.421526	+	0.906816i	$0.638505\pi$
$728$	48.0365	1.78035
$729$	1.00000	0.0370370
$730$	4.71401	0.174473
$731$	13.8960	0.513963
$732$	−15.3984	−0.569143
$733$	−35.6903	−1.31825	−0.659125	−	0.752034i	$-0.729073\pi$
$733$	−35.6903	−1.31825	−0.659125	+	0.752034i	$0.729073\pi$
$734$	9.31038	0.343652
$735$	3.34792	0.123490
$736$	4.66848	0.172082
$737$	−33.6106	−1.23806
$738$	−9.42022	−0.346763
$739$	−2.23660	−0.0822745	−0.0411372	−	0.999154i	$-0.513098\pi$
$739$	−2.23660	−0.0822745	−0.0411372	+	0.999154i	$0.513098\pi$
$740$	0.751151	0.0276129
$741$	23.6253	0.867896
$742$	−123.724	−4.54206
$743$	27.7617	1.01848	0.509239	−	0.860625i	$-0.329927\pi$
$743$	27.7617	1.01848	0.509239	+	0.860625i	$0.329927\pi$
$744$	13.9718	0.512232
$745$	−1.65063	−0.0604744
$746$	−7.91008	−0.289609
$747$	−11.8585	−0.433882
$748$	−31.1595	−1.13930
$749$	−104.142	−3.80526
$750$	3.88431	0.141835
$751$	31.1909	1.13817	0.569086	−	0.822278i	$-0.307297\pi$
$751$	31.1909	1.13817	0.569086	+	0.822278i	$0.307297\pi$
$752$	1.29192	0.0471114
$753$	3.75409	0.136807
$754$	−55.3045	−2.01407
$755$	−0.254060	−0.00924618
$756$	17.7392	0.645168
$757$	−21.7853	−0.791800	−0.395900	−	0.918294i	$-0.629567\pi$
$757$	−21.7853	−0.791800	−0.395900	+	0.918294i	$0.629567\pi$
$758$	−33.0189	−1.19930
$759$	3.62422	0.131551
$760$	4.63086	0.167979
$761$	−24.2546	−0.879228	−0.439614	−	0.898187i	$-0.644885\pi$
$761$	−24.2546	−0.879228	−0.439614	+	0.898187i	$0.644885\pi$
$762$	−3.57256	−0.129420
$763$	77.6490	2.81108
$764$	30.5589	1.10558
$765$	−0.422802	−0.0152865
$766$	0.610557	0.0220603
$767$	7.83080	0.282754
$768$	−20.9646	−0.756496
$769$	0.146617	0.00528715	0.00264357	−	0.999997i	$-0.499159\pi$
$769$	0.146617	0.00528715	0.00264357	+	0.999997i	$0.499159\pi$
$770$	−7.31423	−0.263587
$771$	−14.2715	−0.513976
$772$	34.9790	1.25892
$773$	34.2583	1.23218	0.616092	−	0.787674i	$-0.288715\pi$
$773$	34.2583	1.23218	0.616092	+	0.787674i	$0.288715\pi$
$774$	12.8022	0.460167
$775$	21.1143	0.758448
$776$	−4.19763	−0.150686
$777$	6.82907	0.244992
$778$	−6.22709	−0.223252
$779$	−34.0396	−1.21960
$780$	−1.60595	−0.0575022
$781$	−4.67095	−0.167140
$782$	5.89348	0.210750
$783$	−8.45877	−0.302292
$784$	16.5460	0.590927
$785$	−3.76093	−0.134233
$786$	−52.1906	−1.86158
$787$	−28.6983	−1.02299	−0.511493	−	0.859288i	$-0.670907\pi$
$787$	−28.6983	−1.02299	−0.511493	+	0.859288i	$0.670907\pi$
$788$	68.6054	2.44397
$789$	18.6880	0.665310
$790$	0.791813	0.0281715
$791$	−46.1923	−1.64241
$792$	−11.8897	−0.422481
$793$	12.6739	0.450062
$794$	63.0451	2.23739
$795$	1.71317	0.0607598
$796$	−64.8808	−2.29964
$797$	−0.0882628	−0.00312643	−0.00156321	−	0.999999i	$-0.500498\pi$
$797$	−0.0882628	−0.00312643	−0.00156321	+	0.999999i	$0.500498\pi$
$798$	101.651	3.59841
$799$	−3.94373	−0.139519
$800$	−23.1448	−0.818294
$801$	−12.6090	−0.445518
$802$	−11.6045	−0.409768
$803$	−43.7343	−1.54335
$804$	−31.7522	−1.11982
$805$	0.872359	0.0307466
$806$	−27.7652	−0.977988
$807$	3.16497	0.111412
$808$	−58.1029	−2.04405
$809$	−43.3323	−1.52348	−0.761740	−	0.647882i	$-0.775655\pi$
$809$	−43.3323	−1.52348	−0.761740	+	0.647882i	$0.775655\pi$
$810$	−0.389523	−0.0136864
$811$	17.2037	0.604103	0.302051	−	0.953292i	$-0.402329\pi$
$811$	17.2037	0.604103	0.302051	+	0.953292i	$0.402329\pi$
$812$	−150.052	−5.26578
$813$	26.1495	0.917104
$814$	−11.0513	−0.387348
$815$	−1.79743	−0.0629611
$816$	−2.08955	−0.0731490
$817$	46.2604	1.61845
$818$	−5.06018	−0.176925
$819$	−14.6004	−0.510181
$820$	2.31387	0.0808039
$821$	44.5996	1.55654	0.778269	−	0.627931i	$-0.216098\pi$
$821$	44.5996	1.55654	0.778269	+	0.627931i	$0.216098\pi$
$822$	47.2729	1.64883
$823$	−33.7065	−1.17493	−0.587467	−	0.809248i	$-0.699875\pi$
$823$	−33.7065	−1.17493	−0.587467	+	0.809248i	$0.699875\pi$
$824$	29.3104	1.02108
$825$	−17.9677	−0.625556
$826$	33.6931	1.17233
$827$	15.2705	0.531006	0.265503	−	0.964110i	$-0.414462\pi$
$827$	15.2705	0.531006	0.265503	+	0.964110i	$0.414462\pi$
$828$	3.42383	0.118986
$829$	−7.39966	−0.257001	−0.128500	−	0.991709i	$-0.541016\pi$
$829$	−7.39966	−0.257001	−0.128500	+	0.991709i	$0.541016\pi$
$830$	4.61918	0.160334
$831$	−30.5446	−1.05958
$832$	35.0850	1.21635
$833$	−50.5085	−1.75002
$834$	45.0780	1.56092
$835$	3.09141	0.106983
$836$	−103.731	−3.58762
$837$	−4.24666	−0.146786
$838$	73.4840	2.53846
$839$	39.4930	1.36345	0.681725	−	0.731609i	$-0.261230\pi$
$839$	39.4930	1.36345	0.681725	+	0.731609i	$0.261230\pi$
$840$	−2.86188	−0.0987441
$841$	42.5508	1.46727
$842$	52.9771	1.82571
$843$	−17.9660	−0.618781
$844$	31.6069	1.08795
$845$	−0.854501	−0.0293957
$846$	−3.63332	−0.124916
$847$	10.7016	0.367711
$848$	8.46673	0.290749
$849$	15.5837	0.534833
$850$	−29.2180	−1.00217
$851$	1.31808	0.0451830
$852$	−4.41269	−0.151176
$853$	30.6898	1.05080	0.525399	−	0.850856i	$-0.323916\pi$
$853$	30.6898	1.05080	0.525399	+	0.850856i	$0.323916\pi$
$854$	54.5311	1.86602
$855$	−1.40753	−0.0481364
$856$	65.9415	2.25384
$857$	−18.1287	−0.619265	−0.309633	−	0.950856i	$-0.600206\pi$
$857$	−18.1287	−0.619265	−0.309633	+	0.950856i	$0.600206\pi$
$858$	23.6275	0.806630
$859$	−18.3838	−0.627248	−0.313624	−	0.949547i	$-0.601543\pi$
$859$	−18.3838	−0.627248	−0.313624	+	0.949547i	$0.601543\pi$
$860$	−3.14459	−0.107230
$861$	21.0365	0.716922
$862$	53.7855	1.83194
$863$	−41.2880	−1.40546	−0.702730	−	0.711457i	$-0.748036\pi$
$863$	−41.2880	−1.40546	−0.702730	+	0.711457i	$0.748036\pi$
$864$	4.65506	0.158368
$865$	2.60150	0.0884538
$866$	20.7074	0.703666
$867$	−10.6214	−0.360721
$868$	−75.3323	−2.55694
$869$	−7.34605	−0.249198
$870$	3.29489	0.111707
$871$	26.1340	0.885518
$872$	−49.1666	−1.66499
$873$	1.27585	0.0431809
$874$	19.6196	0.663644
$875$	−8.67415	−0.293240
$876$	−41.3161	−1.39594
$877$	−27.1705	−0.917482	−0.458741	−	0.888570i	$-0.651699\pi$
$877$	−27.1705	−0.917482	−0.458741	+	0.888570i	$0.651699\pi$
$878$	−31.8469	−1.07478
$879$	10.6077	0.357787
$880$	0.500529	0.0168728
$881$	−36.2437	−1.22108	−0.610541	−	0.791985i	$-0.709048\pi$
$881$	−36.2437	−1.22108	−0.610541	+	0.791985i	$0.709048\pi$
$882$	−46.5329	−1.56684
$883$	12.0857	0.406716	0.203358	−	0.979104i	$-0.434814\pi$
$883$	12.0857	0.406716	0.203358	+	0.979104i	$0.434814\pi$
$884$	24.2281	0.814881
$885$	−0.466537	−0.0156825
$886$	14.5767	0.489713
$887$	−25.3840	−0.852312	−0.426156	−	0.904650i	$-0.640133\pi$
$887$	−25.3840	−0.852312	−0.426156	+	0.904650i	$0.640133\pi$
$888$	−4.32410	−0.145107
$889$	7.97797	0.267572
$890$	4.91151	0.164634
$891$	3.61380	0.121067
$892$	72.1999	2.41743
$893$	−13.1288	−0.439340
$894$	22.9422	0.767301
$895$	0.709318	0.0237099
$896$	102.583	3.42704
$897$	−2.81802	−0.0940910
$898$	26.5110	0.884685
$899$	35.9215	1.19805
$900$	−16.9743	−0.565809
$901$	−25.8457	−0.861045
$902$	−34.0428	−1.13350
$903$	−28.5890	−0.951381
$904$	29.2485	0.972791
$905$	3.22471	0.107193
$906$	3.53118	0.117316
$907$	−4.61095	−0.153104	−0.0765520	−	0.997066i	$-0.524391\pi$
$907$	−4.61095	−0.153104	−0.0765520	+	0.997066i	$0.524391\pi$
$908$	−26.9843	−0.895507
$909$	17.6601	0.585747
$910$	5.68721	0.188529
$911$	−54.8930	−1.81869	−0.909343	−	0.416047i	$-0.863415\pi$
$911$	−54.8930	−1.81869	−0.909343	+	0.416047i	$0.863415\pi$
$912$	−6.95621	−0.230343
$913$	−42.8545	−1.41828
$914$	−36.0941	−1.19389
$915$	−0.755073	−0.0249619
$916$	29.8693	0.986909
$917$	116.548	3.84876
$918$	5.87654	0.193955
$919$	−52.5073	−1.73205	−0.866027	−	0.499997i	$-0.833335\pi$
$919$	−52.5073	−1.73205	−0.866027	+	0.499997i	$0.833335\pi$
$920$	−0.552369	−0.0182111
$921$	−0.835318	−0.0275247
$922$	59.0332	1.94416
$923$	3.63191	0.119546
$924$	64.1059	2.10893
$925$	−6.53460	−0.214856
$926$	44.7997	1.47221
$927$	−8.90875	−0.292602
$928$	−39.3761	−1.29258
$929$	14.4132	0.472881	0.236441	−	0.971646i	$-0.424019\pi$
$929$	14.4132	0.472881	0.236441	+	0.971646i	$0.424019\pi$
$930$	1.65417	0.0542424
$931$	−168.145	−5.51072
$932$	48.3541	1.58389
$933$	−33.2691	−1.08918
$934$	−57.8625	−1.89332
$935$	−1.52792	−0.0499685
$936$	9.24485	0.302178
$937$	−38.7772	−1.26680	−0.633398	−	0.773826i	$-0.718340\pi$
$937$	−38.7772	−1.26680	−0.633398	+	0.773826i	$0.718340\pi$
$938$	112.445	3.67147
$939$	−30.1380	−0.983517
$940$	0.892445	0.0291083
$941$	−11.3977	−0.371553	−0.185777	−	0.982592i	$-0.559480\pi$
$941$	−11.3977	−0.371553	−0.185777	+	0.982592i	$0.559480\pi$
$942$	52.2732	1.70315
$943$	4.06024	0.132220
$944$	−2.30570	−0.0750440
$945$	0.869852	0.0282963
$946$	46.2648	1.50420
$947$	6.10017	0.198229	0.0991145	−	0.995076i	$-0.468399\pi$
$947$	6.10017	0.198229	0.0991145	+	0.995076i	$0.468399\pi$
$948$	−6.93988	−0.225397
$949$	34.0057	1.10387
$950$	−97.2680	−3.15579
$951$	12.9258	0.419147
$952$	43.1757	1.39933
$953$	12.4546	0.403444	0.201722	−	0.979443i	$-0.435346\pi$
$953$	12.4546	0.403444	0.201722	+	0.979443i	$0.435346\pi$
$954$	−23.8114	−0.770921
$955$	1.49848	0.0484895
$956$	−68.7155	−2.22242
$957$	−30.5683	−0.988134
$958$	−18.4672	−0.596647
$959$	−105.566	−3.40891
$960$	−2.09026	−0.0674630
$961$	−12.9659	−0.418254
$962$	8.59298	0.277049
$963$	−20.0426	−0.645863
$964$	−10.7820	−0.347265
$965$	1.71522	0.0552149
$966$	−12.1249	−0.390114
$967$	−12.4940	−0.401781	−0.200890	−	0.979614i	$-0.564384\pi$
$967$	−12.4940	−0.401781	−0.200890	+	0.979614i	$0.564384\pi$
$968$	−6.77614	−0.217793
$969$	21.2347	0.682156
$970$	−0.496972	−0.0159568
$971$	2.06439	0.0662494	0.0331247	−	0.999451i	$-0.489454\pi$
$971$	2.06439	0.0662494	0.0331247	+	0.999451i	$0.489454\pi$
$972$	3.41399	0.109504
$973$	−100.665	−3.22716
$974$	12.9903	0.416236
$975$	13.9709	0.447426
$976$	−3.73168	−0.119448
$977$	−11.5245	−0.368703	−0.184351	−	0.982860i	$-0.559018\pi$
$977$	−11.5245	−0.368703	−0.184351	+	0.982860i	$0.559018\pi$
$978$	24.9825	0.798852
$979$	−45.5665	−1.45631
$980$	11.4298	0.365111
$981$	14.9439	0.477123
$982$	−18.7991	−0.599903
$983$	−7.05192	−0.224921	−0.112461	−	0.993656i	$-0.535873\pi$
$983$	−7.05192	−0.224921	−0.112461	+	0.993656i	$0.535873\pi$
$984$	−13.3201	−0.424630
$985$	3.36411	0.107190
$986$	−49.7083	−1.58304
$987$	8.11364	0.258260
$988$	80.6565	2.56602
$989$	−5.51794	−0.175460
$990$	−1.40766	−0.0447384
$991$	42.2061	1.34072	0.670361	−	0.742035i	$-0.266139\pi$
$991$	42.2061	1.34072	0.670361	+	0.742035i	$0.266139\pi$
$992$	−19.7685	−0.627649
$993$	14.5582	0.461991
$994$	15.6268	0.495653
$995$	−3.18147	−0.100860
$996$	−40.4850	−1.28282
$997$	−16.1001	−0.509896	−0.254948	−	0.966955i	$-0.582058\pi$
$997$	−16.1001	−0.509896	−0.254948	+	0.966955i	$0.582058\pi$
$998$	−99.0110	−3.13414
$999$	1.31429	0.0415822

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8049.2.a.a.1.12	✓	95

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8049.2.a.a.1.12	✓	95	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:	\( N \)	\(=\)	\( 8049 = 3 \cdot 2683 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8049.a (trivial)

\(f(q)\)	\(=\)	\(q-2.32680 q^{2} +1.00000 q^{3} +3.41399 q^{4} +0.167407 q^{5} -2.32680 q^{6} +5.19602 q^{7} -3.29007 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.32680 q^{2} +1.00000 q^{3} +3.41399 q^{4} +0.167407 q^{5} -2.32680 q^{6} +5.19602 q^{7} -3.29007 q^{8} +1.00000 q^{9} -0.389523 q^{10} +3.61380 q^{11} +3.41399 q^{12} -2.80992 q^{13} -12.0901 q^{14} +0.167407 q^{15} +0.827353 q^{16} -2.52559 q^{17} -2.32680 q^{18} -8.40780 q^{19} +0.571527 q^{20} +5.19602 q^{21} -8.40859 q^{22} +1.00288 q^{23} -3.29007 q^{24} -4.97197 q^{25} +6.53813 q^{26} +1.00000 q^{27} +17.7392 q^{28} -8.45877 q^{29} -0.389523 q^{30} -4.24666 q^{31} +4.65506 q^{32} +3.61380 q^{33} +5.87654 q^{34} +0.869852 q^{35} +3.41399 q^{36} +1.31429 q^{37} +19.5632 q^{38} -2.80992 q^{39} -0.550782 q^{40} +4.04858 q^{41} -12.0901 q^{42} -5.50209 q^{43} +12.3375 q^{44} +0.167407 q^{45} -2.33350 q^{46} +1.56151 q^{47} +0.827353 q^{48} +19.9987 q^{49} +11.5688 q^{50} -2.52559 q^{51} -9.59306 q^{52} +10.2335 q^{53} -2.32680 q^{54} +0.604977 q^{55} -17.0953 q^{56} -8.40780 q^{57} +19.6819 q^{58} -2.78684 q^{59} +0.571527 q^{60} -4.51039 q^{61} +9.88112 q^{62} +5.19602 q^{63} -12.4861 q^{64} -0.470402 q^{65} -8.40859 q^{66} -9.30062 q^{67} -8.62235 q^{68} +1.00288 q^{69} -2.02397 q^{70} -1.29253 q^{71} -3.29007 q^{72} -12.1020 q^{73} -3.05808 q^{74} -4.97197 q^{75} -28.7041 q^{76} +18.7774 q^{77} +6.53813 q^{78} -2.03278 q^{79} +0.138505 q^{80} +1.00000 q^{81} -9.42022 q^{82} -11.8585 q^{83} +17.7392 q^{84} -0.422802 q^{85} +12.8022 q^{86} -8.45877 q^{87} -11.8897 q^{88} -12.6090 q^{89} -0.389523 q^{90} -14.6004 q^{91} +3.42383 q^{92} -4.24666 q^{93} -3.63332 q^{94} -1.40753 q^{95} +4.65506 q^{96} +1.27585 q^{97} -46.5329 q^{98} +3.61380 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 95 q - 9 q^{2} + 95 q^{3} + 65 q^{4} - 15 q^{5} - 9 q^{6} - 36 q^{7} - 27 q^{8} + 95 q^{9}+O(q^{10}) \) 95 * q - 9 * q^2 + 95 * q^3 + 65 * q^4 - 15 * q^5 - 9 * q^6 - 36 * q^7 - 27 * q^8 + 95 * q^9	\( 95 q - 9 q^{2} + 95 q^{3} + 65 q^{4} - 15 q^{5} - 9 q^{6} - 36 q^{7} - 27 q^{8} + 95 q^{9} - 36 q^{10} - 48 q^{11} + 65 q^{12} - 73 q^{13} - 17 q^{14} - 15 q^{15} + 13 q^{16} - 9 q^{17} - 9 q^{18} - 66 q^{19} - 35 q^{20} - 36 q^{21} - 37 q^{22} - 58 q^{23} - 27 q^{24} + 24 q^{25} - 25 q^{26} + 95 q^{27} - 75 q^{28} - 31 q^{29} - 36 q^{30} - 129 q^{31} - 53 q^{32} - 48 q^{33} - 61 q^{34} - 38 q^{35} + 65 q^{36} - 127 q^{37} + q^{38} - 73 q^{39} - 74 q^{40} - 31 q^{41} - 17 q^{42} - 62 q^{43} - 76 q^{44} - 15 q^{45} - 60 q^{46} - 75 q^{47} + 13 q^{48} + 5 q^{49} - 30 q^{50} - 9 q^{51} - 137 q^{52} - 28 q^{53} - 9 q^{54} - 117 q^{55} - 23 q^{56} - 66 q^{57} - 90 q^{58} - 60 q^{59} - 35 q^{60} - 96 q^{61} + 10 q^{62} - 36 q^{63} - 75 q^{64} - 28 q^{65} - 37 q^{66} - 116 q^{67} + 3 q^{68} - 58 q^{69} - 73 q^{70} - 144 q^{71} - 27 q^{72} - 121 q^{73} - 16 q^{74} + 24 q^{75} - 118 q^{76} - 3 q^{77} - 25 q^{78} - 135 q^{79} - 36 q^{80} + 95 q^{81} - 102 q^{82} - 21 q^{83} - 75 q^{84} - 129 q^{85} - 46 q^{86} - 31 q^{87} - 77 q^{88} - 63 q^{89} - 36 q^{90} - 123 q^{91} - 42 q^{92} - 129 q^{93} - 44 q^{94} - 80 q^{95} - 53 q^{96} - 144 q^{97} + 10 q^{98} - 48 q^{99}+O(q^{100}) \) 95 * q - 9 * q^2 + 95 * q^3 + 65 * q^4 - 15 * q^5 - 9 * q^6 - 36 * q^7 - 27 * q^8 + 95 * q^9 - 36 * q^10 - 48 * q^11 + 65 * q^12 - 73 * q^13 - 17 * q^14 - 15 * q^15 + 13 * q^16 - 9 * q^17 - 9 * q^18 - 66 * q^19 - 35 * q^20 - 36 * q^21 - 37 * q^22 - 58 * q^23 - 27 * q^24 + 24 * q^25 - 25 * q^26 + 95 * q^27 - 75 * q^28 - 31 * q^29 - 36 * q^30 - 129 * q^31 - 53 * q^32 - 48 * q^33 - 61 * q^34 - 38 * q^35 + 65 * q^36 - 127 * q^37 + q^38 - 73 * q^39 - 74 * q^40 - 31 * q^41 - 17 * q^42 - 62 * q^43 - 76 * q^44 - 15 * q^45 - 60 * q^46 - 75 * q^47 + 13 * q^48 + 5 * q^49 - 30 * q^50 - 9 * q^51 - 137 * q^52 - 28 * q^53 - 9 * q^54 - 117 * q^55 - 23 * q^56 - 66 * q^57 - 90 * q^58 - 60 * q^59 - 35 * q^60 - 96 * q^61 + 10 * q^62 - 36 * q^63 - 75 * q^64 - 28 * q^65 - 37 * q^66 - 116 * q^67 + 3 * q^68 - 58 * q^69 - 73 * q^70 - 144 * q^71 - 27 * q^72 - 121 * q^73 - 16 * q^74 + 24 * q^75 - 118 * q^76 - 3 * q^77 - 25 * q^78 - 135 * q^79 - 36 * q^80 + 95 * q^81 - 102 * q^82 - 21 * q^83 - 75 * q^84 - 129 * q^85 - 46 * q^86 - 31 * q^87 - 77 * q^88 - 63 * q^89 - 36 * q^90 - 123 * q^91 - 42 * q^92 - 129 * q^93 - 44 * q^94 - 80 * q^95 - 53 * q^96 - 144 * q^97 + 10 * q^98 - 48 * q^99

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