LMFDB - Embedded newform 8030.2.a.s.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8030,2,Mod(1,8030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8030, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8030 = 2 \cdot 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8030.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:	$64.1198728231$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.229.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 4x - 1 $ x^3 - 4*x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.11491$ of defining polynomial
Character	$\chi$	$=$	8030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.11491 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.11491 q^{6} -3.58774 q^{7} -1.00000 q^{8} +1.47283 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.11491 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.11491 q^{6} -3.58774 q^{7} -1.00000 q^{8} +1.47283 q^{9} +1.00000 q^{10} -1.00000 q^{11} +2.11491 q^{12} +5.70265 q^{13} +3.58774 q^{14} -2.11491 q^{15} +1.00000 q^{16} -1.35793 q^{17} -1.47283 q^{18} -0.243019 q^{19} -1.00000 q^{20} -7.58774 q^{21} +1.00000 q^{22} +6.22982 q^{23} -2.11491 q^{24} +1.00000 q^{25} -5.70265 q^{26} -3.22982 q^{27} -3.58774 q^{28} -9.10170 q^{29} +2.11491 q^{30} +5.58774 q^{31} -1.00000 q^{32} -2.11491 q^{33} +1.35793 q^{34} +3.58774 q^{35} +1.47283 q^{36} -5.58774 q^{37} +0.243019 q^{38} +12.0606 q^{39} +1.00000 q^{40} +3.05433 q^{41} +7.58774 q^{42} +1.60095 q^{43} -1.00000 q^{44} -1.47283 q^{45} -6.22982 q^{46} +3.60095 q^{47} +2.11491 q^{48} +5.87189 q^{49} -1.00000 q^{50} -2.87189 q^{51} +5.70265 q^{52} +0.0737791 q^{53} +3.22982 q^{54} +1.00000 q^{55} +3.58774 q^{56} -0.513962 q^{57} +9.10170 q^{58} +5.32528 q^{59} -2.11491 q^{60} -13.2904 q^{61} -5.58774 q^{62} -5.28415 q^{63} +1.00000 q^{64} -5.70265 q^{65} +2.11491 q^{66} -14.1623 q^{67} -1.35793 q^{68} +13.1755 q^{69} -3.58774 q^{70} +10.7026 q^{71} -1.47283 q^{72} -1.00000 q^{73} +5.58774 q^{74} +2.11491 q^{75} -0.243019 q^{76} +3.58774 q^{77} -12.0606 q^{78} -10.0000 q^{79} -1.00000 q^{80} -11.2493 q^{81} -3.05433 q^{82} -16.4185 q^{83} -7.58774 q^{84} +1.35793 q^{85} -1.60095 q^{86} -19.2493 q^{87} +1.00000 q^{88} -2.22357 q^{89} +1.47283 q^{90} -20.4596 q^{91} +6.22982 q^{92} +11.8176 q^{93} -3.60095 q^{94} +0.243019 q^{95} -2.11491 q^{96} +16.5808 q^{97} -5.87189 q^{98} -1.47283 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 3 q^{4} - 3 q^{5} + q^{7} - 3 q^{8} - q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 3 * q^4 - 3 * q^5 + q^7 - 3 * q^8 - q^9	$ 3 q - 3 q^{2} + 3 q^{4} - 3 q^{5} + q^{7} - 3 q^{8} - q^{9} + 3 q^{10} - 3 q^{11} - q^{13} - q^{14} + 3 q^{16} - 5 q^{17} + q^{18} - 8 q^{19} - 3 q^{20} - 11 q^{21} + 3 q^{22} + 6 q^{23} + 3 q^{25} + q^{26} + 3 q^{27} + q^{28} - q^{29} + 5 q^{31} - 3 q^{32} + 5 q^{34} - q^{35} - q^{36} - 5 q^{37} + 8 q^{38} + 19 q^{39} + 3 q^{40} + 20 q^{41} + 11 q^{42} + 13 q^{43} - 3 q^{44} + q^{45} - 6 q^{46} + 19 q^{47} + 4 q^{49} - 3 q^{50} + 5 q^{51} - q^{52} + 3 q^{53} - 3 q^{54} + 3 q^{55} - q^{56} + 13 q^{57} + q^{58} + 5 q^{59} - 10 q^{61} - 5 q^{62} - 14 q^{63} + 3 q^{64} + q^{65} + q^{67} - 5 q^{68} + 16 q^{69} + q^{70} + 14 q^{71} + q^{72} - 3 q^{73} + 5 q^{74} - 8 q^{76} - q^{77} - 19 q^{78} - 30 q^{79} - 3 q^{80} - 13 q^{81} - 20 q^{82} - 33 q^{83} - 11 q^{84} + 5 q^{85} - 13 q^{86} - 37 q^{87} + 3 q^{88} - 22 q^{89} - q^{90} - 36 q^{91} + 6 q^{92} + 11 q^{93} - 19 q^{94} + 8 q^{95} - 10 q^{97} - 4 q^{98} + q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 + 3 * q^4 - 3 * q^5 + q^7 - 3 * q^8 - q^9 + 3 * q^10 - 3 * q^11 - q^13 - q^14 + 3 * q^16 - 5 * q^17 + q^18 - 8 * q^19 - 3 * q^20 - 11 * q^21 + 3 * q^22 + 6 * q^23 + 3 * q^25 + q^26 + 3 * q^27 + q^28 - q^29 + 5 * q^31 - 3 * q^32 + 5 * q^34 - q^35 - q^36 - 5 * q^37 + 8 * q^38 + 19 * q^39 + 3 * q^40 + 20 * q^41 + 11 * q^42 + 13 * q^43 - 3 * q^44 + q^45 - 6 * q^46 + 19 * q^47 + 4 * q^49 - 3 * q^50 + 5 * q^51 - q^52 + 3 * q^53 - 3 * q^54 + 3 * q^55 - q^56 + 13 * q^57 + q^58 + 5 * q^59 - 10 * q^61 - 5 * q^62 - 14 * q^63 + 3 * q^64 + q^65 + q^67 - 5 * q^68 + 16 * q^69 + q^70 + 14 * q^71 + q^72 - 3 * q^73 + 5 * q^74 - 8 * q^76 - q^77 - 19 * q^78 - 30 * q^79 - 3 * q^80 - 13 * q^81 - 20 * q^82 - 33 * q^83 - 11 * q^84 + 5 * q^85 - 13 * q^86 - 37 * q^87 + 3 * q^88 - 22 * q^89 - q^90 - 36 * q^91 + 6 * q^92 + 11 * q^93 - 19 * q^94 + 8 * q^95 - 10 * q^97 - 4 * q^98 + 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.11491	1.22104	0.610521	−	0.792000i	$-0.290960\pi$
$3$	2.11491	1.22104	0.610521	+	0.792000i	$0.290960\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.11491	−0.863407
$7$	−3.58774	−1.35604	−0.678019	−	0.735044i	$-0.737161\pi$
$7$	−3.58774	−1.35604	−0.678019	+	0.735044i	$0.737161\pi$
$8$	−1.00000	−0.353553
$9$	1.47283	0.490945
$10$	1.00000	0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	2.11491	0.610521
$13$	5.70265	1.58163	0.790815	−	0.612055i	$-0.209657\pi$
$13$	5.70265	1.58163	0.790815	+	0.612055i	$0.209657\pi$
$14$	3.58774	0.958864
$15$	−2.11491	−0.546067
$16$	1.00000	0.250000
$17$	−1.35793	−0.329346	−0.164673	−	0.986348i	$-0.552657\pi$
$17$	−1.35793	−0.329346	−0.164673	+	0.986348i	$0.552657\pi$
$18$	−1.47283	−0.347150
$19$	−0.243019	−0.0557523	−0.0278762	−	0.999611i	$-0.508874\pi$
$19$	−0.243019	−0.0557523	−0.0278762	+	0.999611i	$0.508874\pi$
$20$	−1.00000	−0.223607
$21$	−7.58774	−1.65578
$22$	1.00000	0.213201
$23$	6.22982	1.29901	0.649503	−	0.760359i	$-0.274977\pi$
$23$	6.22982	1.29901	0.649503	+	0.760359i	$0.274977\pi$
$24$	−2.11491	−0.431704
$25$	1.00000	0.200000
$26$	−5.70265	−1.11838
$27$	−3.22982	−0.621578
$28$	−3.58774	−0.678019
$29$	−9.10170	−1.69014	−0.845072	−	0.534653i	$-0.820442\pi$
$29$	−9.10170	−1.69014	−0.845072	+	0.534653i	$0.820442\pi$
$30$	2.11491	0.386128
$31$	5.58774	1.00359	0.501794	−	0.864987i	$-0.332674\pi$
$31$	5.58774	1.00359	0.501794	+	0.864987i	$0.332674\pi$
$32$	−1.00000	−0.176777
$33$	−2.11491	−0.368158
$34$	1.35793	0.232882
$35$	3.58774	0.606439
$36$	1.47283	0.245472
$37$	−5.58774	−0.918619	−0.459310	−	0.888276i	$-0.651903\pi$
$37$	−5.58774	−0.918619	−0.459310	+	0.888276i	$0.651903\pi$
$38$	0.243019	0.0394229
$39$	12.0606	1.93124
$40$	1.00000	0.158114
$41$	3.05433	0.477007	0.238503	−	0.971142i	$-0.423343\pi$
$41$	3.05433	0.477007	0.238503	+	0.971142i	$0.423343\pi$
$42$	7.58774	1.17081
$43$	1.60095	0.244142	0.122071	−	0.992521i	$-0.461046\pi$
$43$	1.60095	0.244142	0.122071	+	0.992521i	$0.461046\pi$
$44$	−1.00000	−0.150756
$45$	−1.47283	−0.219557
$46$	−6.22982	−0.918536
$47$	3.60095	0.525252	0.262626	−	0.964898i	$-0.415411\pi$
$47$	3.60095	0.525252	0.262626	+	0.964898i	$0.415411\pi$
$48$	2.11491	0.305261
$49$	5.87189	0.838841
$50$	−1.00000	−0.141421
$51$	−2.87189	−0.402145
$52$	5.70265	0.790815
$53$	0.0737791	0.0101343	0.00506717	−	0.999987i	$-0.498387\pi$
$53$	0.0737791	0.0101343	0.00506717	+	0.999987i	$0.498387\pi$
$54$	3.22982	0.439522
$55$	1.00000	0.134840
$56$	3.58774	0.479432
$57$	−0.513962	−0.0680760
$58$	9.10170	1.19511
$59$	5.32528	0.693292	0.346646	−	0.937996i	$-0.387321\pi$
$59$	5.32528	0.693292	0.346646	+	0.937996i	$0.387321\pi$
$60$	−2.11491	−0.273033
$61$	−13.2904	−1.70166	−0.850830	−	0.525441i	$-0.823900\pi$
$61$	−13.2904	−1.70166	−0.850830	+	0.525441i	$0.823900\pi$
$62$	−5.58774	−0.709644
$63$	−5.28415	−0.665740
$64$	1.00000	0.125000
$65$	−5.70265	−0.707327
$66$	2.11491	0.260327
$67$	−14.1623	−1.73020	−0.865099	−	0.501601i	$-0.832744\pi$
$67$	−14.1623	−1.73020	−0.865099	+	0.501601i	$0.832744\pi$
$68$	−1.35793	−0.164673
$69$	13.1755	1.58614
$70$	−3.58774	−0.428817
$71$	10.7026	1.27017	0.635085	−	0.772442i	$-0.280965\pi$
$71$	10.7026	1.27017	0.635085	+	0.772442i	$0.280965\pi$
$72$	−1.47283	−0.173575
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	5.58774	0.649562
$75$	2.11491	0.244208
$76$	−0.243019	−0.0278762
$77$	3.58774	0.408861
$78$	−12.0606	−1.36559
$79$	−10.0000	−1.12509	−0.562544	−	0.826767i	$-0.690177\pi$
$79$	−10.0000	−1.12509	−0.562544	+	0.826767i	$0.690177\pi$
$80$	−1.00000	−0.111803
$81$	−11.2493	−1.24992
$82$	−3.05433	−0.337295
$83$	−16.4185	−1.80216	−0.901082	−	0.433648i	$-0.857226\pi$
$83$	−16.4185	−1.80216	−0.901082	+	0.433648i	$0.857226\pi$
$84$	−7.58774	−0.827890
$85$	1.35793	0.147288
$86$	−1.60095	−0.172634
$87$	−19.2493	−2.06374
$88$	1.00000	0.106600
$89$	−2.22357	−0.235698	−0.117849	−	0.993032i	$-0.537600\pi$
$89$	−2.22357	−0.235698	−0.117849	+	0.993032i	$0.537600\pi$
$90$	1.47283	0.155250
$91$	−20.4596	−2.14475
$92$	6.22982	0.649503
$93$	11.8176	1.22542
$94$	−3.60095	−0.371409
$95$	0.243019	0.0249332
$96$	−2.11491	−0.215852
$97$	16.5808	1.68352	0.841762	−	0.539849i	$-0.181519\pi$
$97$	16.5808	1.68352	0.841762	+	0.539849i	$0.181519\pi$
$98$	−5.87189	−0.593150
$99$	−1.47283	−0.148025
$100$	1.00000	0.100000
$101$	10.7981	1.07445	0.537226	−	0.843438i	$-0.319472\pi$
$101$	10.7981	1.07445	0.537226	+	0.843438i	$0.319472\pi$
$102$	2.87189	0.284359
$103$	−9.74378	−0.960083	−0.480041	−	0.877246i	$-0.659378\pi$
$103$	−9.74378	−0.960083	−0.480041	+	0.877246i	$0.659378\pi$
$104$	−5.70265	−0.559191
$105$	7.58774	0.740488
$106$	−0.0737791	−0.00716606
$107$	−7.49228	−0.724306	−0.362153	−	0.932119i	$-0.617958\pi$
$107$	−7.49228	−0.724306	−0.362153	+	0.932119i	$0.617958\pi$
$108$	−3.22982	−0.310789
$109$	7.43171	0.711828	0.355914	−	0.934519i	$-0.384170\pi$
$109$	7.43171	0.711828	0.355914	+	0.934519i	$0.384170\pi$
$110$	−1.00000	−0.0953463
$111$	−11.8176	−1.12167
$112$	−3.58774	−0.339010
$113$	15.3447	1.44351	0.721755	−	0.692149i	$-0.243336\pi$
$113$	15.3447	1.44351	0.721755	+	0.692149i	$0.243336\pi$
$114$	0.513962	0.0481370
$115$	−6.22982	−0.580933
$116$	−9.10170	−0.845072
$117$	8.39905	0.776493
$118$	−5.32528	−0.490231
$119$	4.87189	0.446605
$120$	2.11491	0.193064
$121$	1.00000	0.0909091
$122$	13.2904	1.20326
$123$	6.45963	0.582445
$124$	5.58774	0.501794
$125$	−1.00000	−0.0894427
$126$	5.28415	0.470749
$127$	−15.9325	−1.41378	−0.706889	−	0.707325i	$-0.749902\pi$
$127$	−15.9325	−1.41378	−0.706889	+	0.707325i	$0.749902\pi$
$128$	−1.00000	−0.0883883
$129$	3.38585	0.298108
$130$	5.70265	0.500155
$131$	14.9108	1.30276	0.651381	−	0.758751i	$-0.274190\pi$
$131$	14.9108	1.30276	0.651381	+	0.758751i	$0.274190\pi$
$132$	−2.11491	−0.184079
$133$	0.871889	0.0756023
$134$	14.1623	1.22343
$135$	3.22982	0.277978
$136$	1.35793	0.116441
$137$	−15.2577	−1.30356	−0.651778	−	0.758410i	$-0.725977\pi$
$137$	−15.2577	−1.30356	−0.651778	+	0.758410i	$0.725977\pi$
$138$	−13.1755	−1.12157
$139$	15.4053	1.30666	0.653330	−	0.757073i	$-0.273371\pi$
$139$	15.4053	1.30666	0.653330	+	0.757073i	$0.273371\pi$
$140$	3.58774	0.303219
$141$	7.61567	0.641355
$142$	−10.7026	−0.898146
$143$	−5.70265	−0.476879
$144$	1.47283	0.122736
$145$	9.10170	0.755855
$146$	1.00000	0.0827606
$147$	12.4185	1.02426
$148$	−5.58774	−0.459310
$149$	7.04113	0.576832	0.288416	−	0.957505i	$-0.406871\pi$
$149$	7.04113	0.576832	0.288416	+	0.957505i	$0.406871\pi$
$150$	−2.11491	−0.172681
$151$	−4.37961	−0.356407	−0.178204	−	0.983994i	$-0.557029\pi$
$151$	−4.37961	−0.356407	−0.178204	+	0.983994i	$0.557029\pi$
$152$	0.243019	0.0197114
$153$	−2.00000	−0.161690
$154$	−3.58774	−0.289108
$155$	−5.58774	−0.448818
$156$	12.0606	0.965619
$157$	1.12811	0.0900331	0.0450165	−	0.998986i	$-0.485666\pi$
$157$	1.12811	0.0900331	0.0450165	+	0.998986i	$0.485666\pi$
$158$	10.0000	0.795557
$159$	0.156036	0.0123745
$160$	1.00000	0.0790569
$161$	−22.3510	−1.76150
$162$	11.2493	0.883825
$163$	5.73530	0.449223	0.224612	−	0.974448i	$-0.427889\pi$
$163$	5.73530	0.449223	0.224612	+	0.974448i	$0.427889\pi$
$164$	3.05433	0.238503
$165$	2.11491	0.164645
$166$	16.4185	1.27432
$167$	−3.84396	−0.297455	−0.148727	−	0.988878i	$-0.547518\pi$
$167$	−3.84396	−0.297455	−0.148727	+	0.988878i	$0.547518\pi$
$168$	7.58774	0.585407
$169$	19.5202	1.50155
$170$	−1.35793	−0.104148
$171$	−0.357926	−0.0273713
$172$	1.60095	0.122071
$173$	10.3510	0.786969	0.393485	−	0.919331i	$-0.371269\pi$
$173$	10.3510	0.786969	0.393485	+	0.919331i	$0.371269\pi$
$174$	19.2493	1.45928
$175$	−3.58774	−0.271208
$176$	−1.00000	−0.0753778
$177$	11.2625	0.846539
$178$	2.22357	0.166664
$179$	−26.3726	−1.97118	−0.985592	−	0.169140i	$-0.945901\pi$
$179$	−26.3726	−1.97118	−0.985592	+	0.169140i	$0.945901\pi$
$180$	−1.47283	−0.109779
$181$	−21.7827	−1.61909	−0.809547	−	0.587056i	$-0.800287\pi$
$181$	−21.7827	−1.61909	−0.809547	+	0.587056i	$0.800287\pi$
$182$	20.4596	1.51657
$183$	−28.1079	−2.07780
$184$	−6.22982	−0.459268
$185$	5.58774	0.410819
$186$	−11.8176	−0.866505
$187$	1.35793	0.0993014
$188$	3.60095	0.262626
$189$	11.5877	0.842884
$190$	−0.243019	−0.0176304
$191$	−15.0668	−1.09020	−0.545098	−	0.838372i	$-0.683508\pi$
$191$	−15.0668	−1.09020	−0.545098	+	0.838372i	$0.683508\pi$
$192$	2.11491	0.152630
$193$	−11.2104	−0.806940	−0.403470	−	0.914993i	$-0.632196\pi$
$193$	−11.2104	−0.806940	−0.403470	+	0.914993i	$0.632196\pi$
$194$	−16.5808	−1.19043
$195$	−12.0606	−0.863676
$196$	5.87189	0.419421
$197$	−9.80435	−0.698531	−0.349266	−	0.937024i	$-0.613569\pi$
$197$	−9.80435	−0.698531	−0.349266	+	0.937024i	$0.613569\pi$
$198$	1.47283	0.104670
$199$	−15.6964	−1.11269	−0.556344	−	0.830952i	$-0.687796\pi$
$199$	−15.6964	−1.11269	−0.556344	+	0.830952i	$0.687796\pi$
$200$	−1.00000	−0.0707107
$201$	−29.9519	−2.11264
$202$	−10.7981	−0.759752
$203$	32.6546	2.29190
$204$	−2.87189	−0.201072
$205$	−3.05433	−0.213324
$206$	9.74378	0.678881
$207$	9.17548	0.637740
$208$	5.70265	0.395408
$209$	0.243019	0.0168100
$210$	−7.58774	−0.523604
$211$	−2.35168	−0.161897	−0.0809483	−	0.996718i	$-0.525795\pi$
$211$	−2.35168	−0.161897	−0.0809483	+	0.996718i	$0.525795\pi$
$212$	0.0737791	0.00506717
$213$	22.6351	1.55093
$214$	7.49228	0.512162
$215$	−1.60095	−0.109184
$216$	3.22982	0.219761
$217$	−20.0474	−1.36090
$218$	−7.43171	−0.503339
$219$	−2.11491	−0.142912
$220$	1.00000	0.0674200
$221$	−7.74378	−0.520903
$222$	11.8176	0.793142
$223$	−1.80908	−0.121145	−0.0605724	−	0.998164i	$-0.519293\pi$
$223$	−1.80908	−0.121145	−0.0605724	+	0.998164i	$0.519293\pi$
$224$	3.58774	0.239716
$225$	1.47283	0.0981889
$226$	−15.3447	−1.02072
$227$	22.3510	1.48349	0.741743	−	0.670684i	$-0.233999\pi$
$227$	22.3510	1.48349	0.741743	+	0.670684i	$0.233999\pi$
$228$	−0.513962	−0.0340380
$229$	−20.0606	−1.32564	−0.662820	−	0.748779i	$-0.730641\pi$
$229$	−20.0606	−1.32564	−0.662820	+	0.748779i	$0.730641\pi$
$230$	6.22982	0.410782
$231$	7.58774	0.499237
$232$	9.10170	0.597556
$233$	−8.98055	−0.588336	−0.294168	−	0.955754i	$-0.595042\pi$
$233$	−8.98055	−0.588336	−0.294168	+	0.955754i	$0.595042\pi$
$234$	−8.39905	−0.549063
$235$	−3.60095	−0.234900
$236$	5.32528	0.346646
$237$	−21.1491	−1.37378
$238$	−4.87189	−0.315798
$239$	10.7306	0.694103	0.347052	−	0.937846i	$-0.387183\pi$
$239$	10.7306	0.694103	0.347052	+	0.937846i	$0.387183\pi$
$240$	−2.11491	−0.136517
$241$	−12.3510	−0.795596	−0.397798	−	0.917473i	$-0.630225\pi$
$241$	−12.3510	−0.795596	−0.397798	+	0.917473i	$0.630225\pi$
$242$	−1.00000	−0.0642824
$243$	−14.1017	−0.904625
$244$	−13.2904	−0.850830
$245$	−5.87189	−0.375141
$246$	−6.45963	−0.411851
$247$	−1.38585	−0.0881796
$248$	−5.58774	−0.354822
$249$	−34.7236	−2.20052
$250$	1.00000	0.0632456
$251$	3.31055	0.208960	0.104480	−	0.994527i	$-0.466682\pi$
$251$	3.31055	0.208960	0.104480	+	0.994527i	$0.466682\pi$
$252$	−5.28415	−0.332870
$253$	−6.22982	−0.391665
$254$	15.9325	0.999692
$255$	2.87189	0.179845
$256$	1.00000	0.0625000
$257$	−3.40530	−0.212417	−0.106208	−	0.994344i	$-0.533871\pi$
$257$	−3.40530	−0.212417	−0.106208	+	0.994344i	$0.533871\pi$
$258$	−3.38585	−0.210794
$259$	20.0474	1.24568
$260$	−5.70265	−0.353663
$261$	−13.4053	−0.829767
$262$	−14.9108	−0.921191
$263$	18.5334	1.14282	0.571409	−	0.820665i	$-0.306397\pi$
$263$	18.5334	1.14282	0.571409	+	0.820665i	$0.306397\pi$
$264$	2.11491	0.130164
$265$	−0.0737791	−0.00453221
$266$	−0.871889	−0.0534589
$267$	−4.70265	−0.287797
$268$	−14.1623	−0.865099
$269$	0.837003	0.0510330	0.0255165	−	0.999674i	$-0.491877\pi$
$269$	0.837003	0.0510330	0.0255165	+	0.999674i	$0.491877\pi$
$270$	−3.22982	−0.196560
$271$	−29.3642	−1.78375	−0.891873	−	0.452286i	$-0.850609\pi$
$271$	−29.3642	−1.78375	−0.891873	+	0.452286i	$0.850609\pi$
$272$	−1.35793	−0.0823364
$273$	−43.2702	−2.61883
$274$	15.2577	0.921754
$275$	−1.00000	−0.0603023
$276$	13.1755	0.793071
$277$	−13.1538	−0.790335	−0.395168	−	0.918609i	$-0.629314\pi$
$277$	−13.1538	−0.790335	−0.395168	+	0.918609i	$0.629314\pi$
$278$	−15.4053	−0.923948
$279$	8.22982	0.492706
$280$	−3.58774	−0.214409
$281$	−25.0815	−1.49624	−0.748120	−	0.663564i	$-0.769043\pi$
$281$	−25.0815	−1.49624	−0.748120	+	0.663564i	$0.769043\pi$
$282$	−7.61567	−0.453506
$283$	−7.63511	−0.453860	−0.226930	−	0.973911i	$-0.572869\pi$
$283$	−7.63511	−0.453860	−0.226930	+	0.973911i	$0.572869\pi$
$284$	10.7026	0.635085
$285$	0.513962	0.0304445
$286$	5.70265	0.337205
$287$	−10.9582	−0.646839
$288$	−1.47283	−0.0867876
$289$	−15.1560	−0.891532
$290$	−9.10170	−0.534470
$291$	35.0668	2.05565
$292$	−1.00000	−0.0585206
$293$	−9.52645	−0.556541	−0.278271	−	0.960503i	$-0.589761\pi$
$293$	−9.52645	−0.556541	−0.278271	+	0.960503i	$0.589761\pi$
$294$	−12.4185	−0.724262
$295$	−5.32528	−0.310050
$296$	5.58774	0.324781
$297$	3.22982	0.187413
$298$	−7.04113	−0.407882
$299$	35.5264	2.05455
$300$	2.11491	0.122104
$301$	−5.74378	−0.331066
$302$	4.37961	0.252018
$303$	22.8370	1.31195
$304$	−0.243019	−0.0139381
$305$	13.2904	0.761006
$306$	2.00000	0.114332
$307$	−26.5202	−1.51359	−0.756794	−	0.653653i	$-0.773235\pi$
$307$	−26.5202	−1.51359	−0.756794	+	0.653653i	$0.773235\pi$
$308$	3.58774	0.204431
$309$	−20.6072	−1.17230
$310$	5.58774	0.317362
$311$	−14.4534	−0.819576	−0.409788	−	0.912181i	$-0.634397\pi$
$311$	−14.4534	−0.819576	−0.409788	+	0.912181i	$0.634397\pi$
$312$	−12.0606	−0.682796
$313$	19.6568	1.11107	0.555534	−	0.831494i	$-0.312514\pi$
$313$	19.6568	1.11107	0.555534	+	0.831494i	$0.312514\pi$
$314$	−1.12811	−0.0636630
$315$	5.28415	0.297728
$316$	−10.0000	−0.562544
$317$	19.6219	1.10208	0.551038	−	0.834480i	$-0.314232\pi$
$317$	19.6219	1.10208	0.551038	+	0.834480i	$0.314232\pi$
$318$	−0.156036	−0.00875006
$319$	9.10170	0.509598
$320$	−1.00000	−0.0559017
$321$	−15.8455	−0.884409
$322$	22.3510	1.24557
$323$	0.330002	0.0183618
$324$	−11.2493	−0.624959
$325$	5.70265	0.316326
$326$	−5.73530	−0.317649
$327$	15.7174	0.869173
$328$	−3.05433	−0.168647
$329$	−12.9193	−0.712262
$330$	−2.11491	−0.116422
$331$	−17.3253	−0.952283	−0.476142	−	0.879369i	$-0.657965\pi$
$331$	−17.3253	−0.952283	−0.476142	+	0.879369i	$0.657965\pi$
$332$	−16.4185	−0.901082
$333$	−8.22982	−0.450991
$334$	3.84396	0.210332
$335$	14.1623	0.773768
$336$	−7.58774	−0.413945
$337$	−21.2882	−1.15964	−0.579820	−	0.814745i	$-0.696877\pi$
$337$	−21.2882	−1.15964	−0.579820	+	0.814745i	$0.696877\pi$
$338$	−19.5202	−1.06176
$339$	32.4527	1.76259
$340$	1.35793	0.0736439
$341$	−5.58774	−0.302593
$342$	0.357926	0.0193544
$343$	4.04737	0.218538
$344$	−1.60095	−0.0863172
$345$	−13.1755	−0.709344
$346$	−10.3510	−0.556471
$347$	−35.7174	−1.91741	−0.958704	−	0.284404i	$-0.908204\pi$
$347$	−35.7174	−1.91741	−0.958704	+	0.284404i	$0.908204\pi$
$348$	−19.2493	−1.03187
$349$	−0.0869828	−0.00465608	−0.00232804	−	0.999997i	$-0.500741\pi$
$349$	−0.0869828	−0.00465608	−0.00232804	+	0.999997i	$0.500741\pi$
$350$	3.58774	0.191773
$351$	−18.4185	−0.983107
$352$	1.00000	0.0533002
$353$	2.90677	0.154712	0.0773560	−	0.997004i	$-0.475352\pi$
$353$	2.90677	0.154712	0.0773560	+	0.997004i	$0.475352\pi$
$354$	−11.2625	−0.598593
$355$	−10.7026	−0.568038
$356$	−2.22357	−0.117849
$357$	10.3036	0.545324
$358$	26.3726	1.39384
$359$	−30.8106	−1.62612	−0.813061	−	0.582179i	$-0.802200\pi$
$359$	−30.8106	−1.62612	−0.813061	+	0.582179i	$0.802200\pi$
$360$	1.47283	0.0776252
$361$	−18.9409	−0.996892
$362$	21.7827	1.14487
$363$	2.11491	0.111004
$364$	−20.4596	−1.07238
$365$	1.00000	0.0523424
$366$	28.1079	1.46923
$367$	−7.47507	−0.390195	−0.195098	−	0.980784i	$-0.562502\pi$
$367$	−7.47507	−0.390195	−0.195098	+	0.980784i	$0.562502\pi$
$368$	6.22982	0.324752
$369$	4.49852	0.234184
$370$	−5.58774	−0.290493
$371$	−0.264700	−0.0137426
$372$	11.8176	0.612712
$373$	−12.4163	−0.642890	−0.321445	−	0.946928i	$-0.604169\pi$
$373$	−12.4163	−0.642890	−0.321445	+	0.946928i	$0.604169\pi$
$374$	−1.35793	−0.0702167
$375$	−2.11491	−0.109213
$376$	−3.60095	−0.185705
$377$	−51.9038	−2.67318
$378$	−11.5877	−0.596009
$379$	2.25150	0.115652	0.0578258	−	0.998327i	$-0.481583\pi$
$379$	2.25150	0.115652	0.0578258	+	0.998327i	$0.481583\pi$
$380$	0.243019	0.0124666
$381$	−33.6957	−1.72628
$382$	15.0668	0.770885
$383$	−6.94567	−0.354907	−0.177454	−	0.984129i	$-0.556786\pi$
$383$	−6.94567	−0.354907	−0.177454	+	0.984129i	$0.556786\pi$
$384$	−2.11491	−0.107926
$385$	−3.58774	−0.182848
$386$	11.2104	0.570593
$387$	2.35793	0.119860
$388$	16.5808	0.841762
$389$	−15.0668	−0.763918	−0.381959	−	0.924179i	$-0.624750\pi$
$389$	−15.0668	−0.763918	−0.381959	+	0.924179i	$0.624750\pi$
$390$	12.0606	0.610711
$391$	−8.45963	−0.427822
$392$	−5.87189	−0.296575
$393$	31.5349	1.59073
$394$	9.80435	0.493936
$395$	10.0000	0.503155
$396$	−1.47283	−0.0740127
$397$	18.0995	0.908386	0.454193	−	0.890903i	$-0.349928\pi$
$397$	18.0995	0.908386	0.454193	+	0.890903i	$0.349928\pi$
$398$	15.6964	0.786790
$399$	1.84396	0.0923137
$400$	1.00000	0.0500000
$401$	−28.7221	−1.43431	−0.717157	−	0.696912i	$-0.754557\pi$
$401$	−28.7221	−1.43431	−0.717157	+	0.696912i	$0.754557\pi$
$402$	29.9519	1.49387
$403$	31.8649	1.58731
$404$	10.7981	0.537226
$405$	11.2493	0.558980
$406$	−32.6546	−1.62062
$407$	5.58774	0.276974
$408$	2.87189	0.142180
$409$	−28.1692	−1.39288	−0.696440	−	0.717615i	$-0.745234\pi$
$409$	−28.1692	−1.39288	−0.696440	+	0.717615i	$0.745234\pi$
$410$	3.05433	0.150843
$411$	−32.2687	−1.59170
$412$	−9.74378	−0.480041
$413$	−19.1057	−0.940131
$414$	−9.17548	−0.450950
$415$	16.4185	0.805953
$416$	−5.70265	−0.279595
$417$	32.5808	1.59549
$418$	−0.243019	−0.0118864
$419$	13.7827	0.673328	0.336664	−	0.941625i	$-0.390701\pi$
$419$	13.7827	0.673328	0.336664	+	0.941625i	$0.390701\pi$
$420$	7.58774	0.370244
$421$	20.5008	0.999146	0.499573	−	0.866272i	$-0.333490\pi$
$421$	20.5008	0.999146	0.499573	+	0.866272i	$0.333490\pi$
$422$	2.35168	0.114478
$423$	5.30359	0.257870
$424$	−0.0737791	−0.00358303
$425$	−1.35793	−0.0658691
$426$	−22.6351	−1.09667
$427$	47.6825	2.30752
$428$	−7.49228	−0.362153
$429$	−12.0606	−0.582290
$430$	1.60095	0.0772044
$431$	14.1887	0.683445	0.341722	−	0.939801i	$-0.388990\pi$
$431$	14.1887	0.683445	0.341722	+	0.939801i	$0.388990\pi$
$432$	−3.22982	−0.155395
$433$	33.0187	1.58678	0.793389	−	0.608714i	$-0.208314\pi$
$433$	33.0187	1.58678	0.793389	+	0.608714i	$0.208314\pi$
$434$	20.0474	0.962305
$435$	19.2493	0.922931
$436$	7.43171	0.355914
$437$	−1.51396	−0.0724226
$438$	2.11491	0.101054
$439$	−2.25622	−0.107684	−0.0538418	−	0.998549i	$-0.517147\pi$
$439$	−2.25622	−0.107684	−0.0538418	+	0.998549i	$0.517147\pi$
$440$	−1.00000	−0.0476731
$441$	8.64832	0.411825
$442$	7.74378	0.368334
$443$	−2.82452	−0.134197	−0.0670984	−	0.997746i	$-0.521374\pi$
$443$	−2.82452	−0.134197	−0.0670984	+	0.997746i	$0.521374\pi$
$444$	−11.8176	−0.560836
$445$	2.22357	0.105407
$446$	1.80908	0.0856624
$447$	14.8913	0.704336
$448$	−3.58774	−0.169505
$449$	−16.5683	−0.781906	−0.390953	−	0.920411i	$-0.627855\pi$
$449$	−16.5683	−0.781906	−0.390953	+	0.920411i	$0.627855\pi$
$450$	−1.47283	−0.0694301
$451$	−3.05433	−0.143823
$452$	15.3447	0.721755
$453$	−9.26247	−0.435189
$454$	−22.3510	−1.04898
$455$	20.4596	0.959162
$456$	0.513962	0.0240685
$457$	3.12339	0.146106	0.0730529	−	0.997328i	$-0.476726\pi$
$457$	3.12339	0.146106	0.0730529	+	0.997328i	$0.476726\pi$
$458$	20.0606	0.937369
$459$	4.38585	0.204714
$460$	−6.22982	−0.290467
$461$	−2.21661	−0.103238	−0.0516189	−	0.998667i	$-0.516438\pi$
$461$	−2.21661	−0.103238	−0.0516189	+	0.998667i	$0.516438\pi$
$462$	−7.58774	−0.353014
$463$	15.2144	0.707072	0.353536	−	0.935421i	$-0.384979\pi$
$463$	15.2144	0.707072	0.353536	+	0.935421i	$0.384979\pi$
$464$	−9.10170	−0.422536
$465$	−11.8176	−0.548026
$466$	8.98055	0.416016
$467$	20.7243	0.959008	0.479504	−	0.877540i	$-0.340817\pi$
$467$	20.7243	0.959008	0.479504	+	0.877540i	$0.340817\pi$
$468$	8.39905	0.388246
$469$	50.8106	2.34622
$470$	3.60095	0.166099
$471$	2.38585	0.109934
$472$	−5.32528	−0.245116
$473$	−1.60095	−0.0736115
$474$	21.1491	0.971409
$475$	−0.243019	−0.0111505
$476$	4.87189	0.223303
$477$	0.108664	0.00497540
$478$	−10.7306	−0.490805
$479$	−36.5419	−1.66964	−0.834821	−	0.550522i	$-0.814429\pi$
$479$	−36.5419	−1.66964	−0.834821	+	0.550522i	$0.814429\pi$
$480$	2.11491	0.0965319
$481$	−31.8649	−1.45292
$482$	12.3510	0.562571
$483$	−47.2702	−2.15087
$484$	1.00000	0.0454545
$485$	−16.5808	−0.752894
$486$	14.1017	0.639666
$487$	−30.4332	−1.37906	−0.689530	−	0.724257i	$-0.742183\pi$
$487$	−30.4332	−1.37906	−0.689530	+	0.724257i	$0.742183\pi$
$488$	13.2904	0.601628
$489$	12.1296	0.548521
$490$	5.87189	0.265265
$491$	26.3983	1.19134	0.595670	−	0.803229i	$-0.296887\pi$
$491$	26.3983	1.19134	0.595670	+	0.803229i	$0.296887\pi$
$492$	6.45963	0.291223
$493$	12.3594	0.556641
$494$	1.38585	0.0623524
$495$	1.47283	0.0661990
$496$	5.58774	0.250897
$497$	−38.3983	−1.72240
$498$	34.7236	1.55600
$499$	7.77018	0.347841	0.173921	−	0.984760i	$-0.444356\pi$
$499$	7.77018	0.347841	0.173921	+	0.984760i	$0.444356\pi$
$500$	−1.00000	−0.0447214
$501$	−8.12963	−0.363205
$502$	−3.31055	−0.147757
$503$	12.1817	0.543156	0.271578	−	0.962416i	$-0.412454\pi$
$503$	12.1817	0.543156	0.271578	+	0.962416i	$0.412454\pi$
$504$	5.28415	0.235375
$505$	−10.7981	−0.480510
$506$	6.22982	0.276949
$507$	41.2834	1.83346
$508$	−15.9325	−0.706889
$509$	−9.52645	−0.422252	−0.211126	−	0.977459i	$-0.567713\pi$
$509$	−9.52645	−0.422252	−0.211126	+	0.977459i	$0.567713\pi$
$510$	−2.87189	−0.127169
$511$	3.58774	0.158712
$512$	−1.00000	−0.0441942
$513$	0.784906	0.0346544
$514$	3.40530	0.150201
$515$	9.74378	0.429362
$516$	3.38585	0.149054
$517$	−3.60095	−0.158369
$518$	−20.0474	−0.880831
$519$	21.8913	0.960923
$520$	5.70265	0.250078
$521$	−7.47507	−0.327489	−0.163744	−	0.986503i	$-0.552357\pi$
$521$	−7.47507	−0.327489	−0.163744	+	0.986503i	$0.552357\pi$
$522$	13.4053	0.586734
$523$	−14.9582	−0.654074	−0.327037	−	0.945011i	$-0.606050\pi$
$523$	−14.9582	−0.654074	−0.327037	+	0.945011i	$0.606050\pi$
$524$	14.9108	0.651381
$525$	−7.58774	−0.331156
$526$	−18.5334	−0.808095
$527$	−7.58774	−0.330527
$528$	−2.11491	−0.0920395
$529$	15.8106	0.687417
$530$	0.0737791	0.00320476
$531$	7.84325	0.340368
$532$	0.871889	0.0378012
$533$	17.4178	0.754448
$534$	4.70265	0.203504
$535$	7.49228	0.323920
$536$	14.1623	0.611717
$537$	−55.7757	−2.40690
$538$	−0.837003	−0.0360858
$539$	−5.87189	−0.252920
$540$	3.22982	0.138989
$541$	16.0599	0.690467	0.345234	−	0.938517i	$-0.387800\pi$
$541$	16.0599	0.690467	0.345234	+	0.938517i	$0.387800\pi$
$542$	29.3642	1.26130
$543$	−46.0683	−1.97698
$544$	1.35793	0.0582206
$545$	−7.43171	−0.318339
$546$	43.2702	1.85179
$547$	30.9582	1.32368	0.661838	−	0.749647i	$-0.269777\pi$
$547$	30.9582	1.32368	0.661838	+	0.749647i	$0.269777\pi$
$548$	−15.2577	−0.651778
$549$	−19.5745	−0.835421
$550$	1.00000	0.0426401
$551$	2.21189	0.0942295
$552$	−13.1755	−0.560786
$553$	35.8774	1.52566
$554$	13.1538	0.558851
$555$	11.8176	0.501627
$556$	15.4053	0.653330
$557$	22.6072	0.957897	0.478949	−	0.877843i	$-0.341018\pi$
$557$	22.6072	0.957897	0.478949	+	0.877843i	$0.341018\pi$
$558$	−8.22982	−0.348396
$559$	9.12963	0.386142
$560$	3.58774	0.151610
$561$	2.87189	0.121251
$562$	25.0815	1.05800
$563$	−28.4068	−1.19720	−0.598602	−	0.801046i	$-0.704277\pi$
$563$	−28.4068	−1.19720	−0.598602	+	0.801046i	$0.704277\pi$
$564$	7.61567	0.320677
$565$	−15.3447	−0.645557
$566$	7.63511	0.320928
$567$	40.3594	1.69494
$568$	−10.7026	−0.449073
$569$	−30.0947	−1.26164	−0.630819	−	0.775930i	$-0.717281\pi$
$569$	−30.0947	−1.26164	−0.630819	+	0.775930i	$0.717281\pi$
$570$	−0.513962	−0.0215275
$571$	−43.1142	−1.80427	−0.902136	−	0.431451i	$-0.858002\pi$
$571$	−43.1142	−1.80427	−0.902136	+	0.431451i	$0.858002\pi$
$572$	−5.70265	−0.238440
$573$	−31.8649	−1.33118
$574$	10.9582	0.457385
$575$	6.22982	0.259801
$576$	1.47283	0.0613681
$577$	34.8781	1.45200	0.725998	−	0.687697i	$-0.241378\pi$
$577$	34.8781	1.45200	0.725998	+	0.687697i	$0.241378\pi$
$578$	15.1560	0.630408
$579$	−23.7089	−0.985308
$580$	9.10170	0.377928
$581$	58.9053	2.44381
$582$	−35.0668	−1.45357
$583$	−0.0737791	−0.00305562
$584$	1.00000	0.0413803
$585$	−8.39905	−0.347258
$586$	9.52645	0.393534
$587$	11.7523	0.485067	0.242534	−	0.970143i	$-0.422021\pi$
$587$	11.7523	0.485067	0.242534	+	0.970143i	$0.422021\pi$
$588$	12.4185	0.512130
$589$	−1.35793	−0.0559524
$590$	5.32528	0.219238
$591$	−20.7353	−0.852936
$592$	−5.58774	−0.229655
$593$	33.1663	1.36198	0.680988	−	0.732294i	$-0.261551\pi$
$593$	33.1663	1.36198	0.680988	+	0.732294i	$0.261551\pi$
$594$	−3.22982	−0.132521
$595$	−4.87189	−0.199728
$596$	7.04113	0.288416
$597$	−33.1964	−1.35864
$598$	−35.5264	−1.45278
$599$	12.1560	0.496682	0.248341	−	0.968673i	$-0.420115\pi$
$599$	12.1560	0.496682	0.248341	+	0.968673i	$0.420115\pi$
$600$	−2.11491	−0.0863407
$601$	−2.93095	−0.119556	−0.0597779	−	0.998212i	$-0.519039\pi$
$601$	−2.93095	−0.119556	−0.0597779	+	0.998212i	$0.519039\pi$
$602$	5.74378	0.234099
$603$	−20.8587	−0.849431
$604$	−4.37961	−0.178204
$605$	−1.00000	−0.0406558
$606$	−22.8370	−0.927690
$607$	17.2276	0.699246	0.349623	−	0.936890i	$-0.386310\pi$
$607$	17.2276	0.699246	0.349623	+	0.936890i	$0.386310\pi$
$608$	0.243019	0.00985571
$609$	69.0614	2.79851
$610$	−13.2904	−0.538112
$611$	20.5349	0.830754
$612$	−2.00000	−0.0808452
$613$	−9.78491	−0.395209	−0.197604	−	0.980282i	$-0.563316\pi$
$613$	−9.78491	−0.395209	−0.197604	+	0.980282i	$0.563316\pi$
$614$	26.5202	1.07027
$615$	−6.45963	−0.260477
$616$	−3.58774	−0.144554
$617$	−11.4075	−0.459250	−0.229625	−	0.973279i	$-0.573750\pi$
$617$	−11.4075	−0.459250	−0.229625	+	0.973279i	$0.573750\pi$
$618$	20.6072	0.828943
$619$	6.91926	0.278109	0.139054	−	0.990285i	$-0.455594\pi$
$619$	6.91926	0.278109	0.139054	+	0.990285i	$0.455594\pi$
$620$	−5.58774	−0.224409
$621$	−20.1212	−0.807434
$622$	14.4534	0.579528
$623$	7.97760	0.319616
$624$	12.0606	0.482809
$625$	1.00000	0.0400000
$626$	−19.6568	−0.785644
$627$	0.513962	0.0205257
$628$	1.12811	0.0450165
$629$	7.58774	0.302543
$630$	−5.28415	−0.210525
$631$	44.0335	1.75294	0.876472	−	0.481453i	$-0.159891\pi$
$631$	44.0335	1.75294	0.876472	+	0.481453i	$0.159891\pi$
$632$	10.0000	0.397779
$633$	−4.97359	−0.197683
$634$	−19.6219	−0.779286
$635$	15.9325	0.632261
$636$	0.156036	0.00618723
$637$	33.4853	1.32674
$638$	−9.10170	−0.360340
$639$	15.7632	0.623584
$640$	1.00000	0.0395285
$641$	−9.37041	−0.370109	−0.185055	−	0.982728i	$-0.559246\pi$
$641$	−9.37041	−0.370109	−0.185055	+	0.982728i	$0.559246\pi$
$642$	15.8455	0.625371
$643$	−28.0210	−1.10504	−0.552519	−	0.833500i	$-0.686334\pi$
$643$	−28.0210	−1.10504	−0.552519	+	0.833500i	$0.686334\pi$
$644$	−22.3510	−0.880751
$645$	−3.38585	−0.133318
$646$	−0.330002	−0.0129837
$647$	0.763942	0.0300336	0.0150168	−	0.999887i	$-0.495220\pi$
$647$	0.763942	0.0300336	0.0150168	+	0.999887i	$0.495220\pi$
$648$	11.2493	0.441913
$649$	−5.32528	−0.209035
$650$	−5.70265	−0.223676
$651$	−42.3983	−1.66172
$652$	5.73530	0.224612
$653$	8.30583	0.325032	0.162516	−	0.986706i	$-0.448039\pi$
$653$	8.30583	0.325032	0.162516	+	0.986706i	$0.448039\pi$
$654$	−15.7174	−0.614598
$655$	−14.9108	−0.582612
$656$	3.05433	0.119252
$657$	−1.47283	−0.0574607
$658$	12.9193	0.503645
$659$	−6.22910	−0.242651	−0.121326	−	0.992613i	$-0.538715\pi$
$659$	−6.22910	−0.242651	−0.121326	+	0.992613i	$0.538715\pi$
$660$	2.11491	0.0823227
$661$	29.8774	1.16210	0.581048	−	0.813869i	$-0.302643\pi$
$661$	29.8774	1.16210	0.581048	+	0.813869i	$0.302643\pi$
$662$	17.3253	0.673366
$663$	−16.3774	−0.636044
$664$	16.4185	0.637161
$665$	−0.871889	−0.0338104
$666$	8.22982	0.318899
$667$	−56.7019	−2.19551
$668$	−3.84396	−0.148727
$669$	−3.82603	−0.147923
$670$	−14.1623	−0.547137
$671$	13.2904	0.513070
$672$	7.58774	0.292703
$673$	−46.6957	−1.79999	−0.899993	−	0.435904i	$-0.856429\pi$
$673$	−46.6957	−1.79999	−0.899993	+	0.435904i	$0.856429\pi$
$674$	21.2882	0.819989
$675$	−3.22982	−0.124316
$676$	19.5202	0.750777
$677$	37.1010	1.42591	0.712953	−	0.701211i	$-0.247357\pi$
$677$	37.1010	1.42591	0.712953	+	0.701211i	$0.247357\pi$
$678$	−32.4527	−1.24634
$679$	−59.4876	−2.28292
$680$	−1.35793	−0.0520741
$681$	47.2702	1.81140
$682$	5.58774	0.213966
$683$	19.4791	0.745346	0.372673	−	0.927963i	$-0.378441\pi$
$683$	19.4791	0.745346	0.372673	+	0.927963i	$0.378441\pi$
$684$	−0.357926	−0.0136857
$685$	15.2577	0.582968
$686$	−4.04737	−0.154529
$687$	−42.4263	−1.61866
$688$	1.60095	0.0610355
$689$	0.420736	0.0160288
$690$	13.1755	0.501582
$691$	49.7849	1.89391	0.946954	−	0.321370i	$-0.104143\pi$
$691$	49.7849	1.89391	0.946954	+	0.321370i	$0.104143\pi$
$692$	10.3510	0.393485
$693$	5.28415	0.200728
$694$	35.7174	1.35581
$695$	−15.4053	−0.584356
$696$	19.2493	0.729641
$697$	−4.14756	−0.157100
$698$	0.0869828	0.00329235
$699$	−18.9930	−0.718383
$700$	−3.58774	−0.135604
$701$	2.95415	0.111577	0.0557883	−	0.998443i	$-0.482233\pi$
$701$	2.95415	0.111577	0.0557883	+	0.998443i	$0.482233\pi$
$702$	18.4185	0.695162
$703$	1.35793	0.0512152
$704$	−1.00000	−0.0376889
$705$	−7.61567	−0.286823
$706$	−2.90677	−0.109398
$707$	−38.7408	−1.45700
$708$	11.2625	0.423269
$709$	−33.4200	−1.25512	−0.627558	−	0.778570i	$-0.715945\pi$
$709$	−33.4200	−1.25512	−0.627558	+	0.778570i	$0.715945\pi$
$710$	10.7026	0.401663
$711$	−14.7283	−0.552356
$712$	2.22357	0.0833319
$713$	34.8106	1.30367
$714$	−10.3036	−0.385602
$715$	5.70265	0.213267
$716$	−26.3726	−0.985592
$717$	22.6942	0.847529
$718$	30.8106	1.14984
$719$	50.2074	1.87242	0.936210	−	0.351440i	$-0.114308\pi$
$719$	50.2074	1.87242	0.936210	+	0.351440i	$0.114308\pi$
$720$	−1.47283	−0.0548893
$721$	34.9582	1.30191
$722$	18.9409	0.704909
$723$	−26.1212	−0.971456
$724$	−21.7827	−0.809547
$725$	−9.10170	−0.338029
$726$	−2.11491	−0.0784916
$727$	28.1381	1.04358	0.521792	−	0.853073i	$-0.325264\pi$
$727$	28.1381	1.04358	0.521792	+	0.853073i	$0.325264\pi$
$728$	20.4596	0.758284
$729$	3.92399	0.145333
$730$	−1.00000	−0.0370117
$731$	−2.17397	−0.0804070
$732$	−28.1079	−1.03890
$733$	23.6087	0.872007	0.436004	−	0.899945i	$-0.356393\pi$
$733$	23.6087	0.872007	0.436004	+	0.899945i	$0.356393\pi$
$734$	7.47507	0.275910
$735$	−12.4185	−0.458063
$736$	−6.22982	−0.229634
$737$	14.1623	0.521674
$738$	−4.49852	−0.165593
$739$	−28.0000	−1.03000	−0.514998	−	0.857191i	$-0.672207\pi$
$739$	−28.0000	−1.03000	−0.514998	+	0.857191i	$0.672207\pi$
$740$	5.58774	0.205409
$741$	−2.93095	−0.107671
$742$	0.264700	0.00971746
$743$	29.2353	1.07254	0.536270	−	0.844046i	$-0.319833\pi$
$743$	29.2353	1.07254	0.536270	+	0.844046i	$0.319833\pi$
$744$	−11.8176	−0.433253
$745$	−7.04113	−0.257967
$746$	12.4163	0.454592
$747$	−24.1817	−0.884763
$748$	1.35793	0.0496507
$749$	26.8804	0.982187
$750$	2.11491	0.0772255
$751$	17.4093	0.635275	0.317637	−	0.948212i	$-0.397111\pi$
$751$	17.4093	0.635275	0.317637	+	0.948212i	$0.397111\pi$
$752$	3.60095	0.131313
$753$	7.00152	0.255149
$754$	51.9038	1.89023
$755$	4.37961	0.159390
$756$	11.5877	0.421442
$757$	47.5995	1.73003	0.865017	−	0.501743i	$-0.167308\pi$
$757$	47.5995	1.73003	0.865017	+	0.501743i	$0.167308\pi$
$758$	−2.25150	−0.0817780
$759$	−13.1755	−0.478240
$760$	−0.243019	−0.00881522
$761$	−19.5356	−0.708167	−0.354083	−	0.935214i	$-0.615207\pi$
$761$	−19.5356	−0.708167	−0.354083	+	0.935214i	$0.615207\pi$
$762$	33.6957	1.22067
$763$	−26.6630	−0.965267
$764$	−15.0668	−0.545098
$765$	2.00000	0.0723102
$766$	6.94567	0.250957
$767$	30.3682	1.09653
$768$	2.11491	0.0763152
$769$	−15.9519	−0.575241	−0.287620	−	0.957745i	$-0.592864\pi$
$769$	−15.9519	−0.575241	−0.287620	+	0.957745i	$0.592864\pi$
$770$	3.58774	0.129293
$771$	−7.20189	−0.259370
$772$	−11.2104	−0.403470
$773$	35.9776	1.29402	0.647012	−	0.762480i	$-0.276018\pi$
$773$	35.9776	1.29402	0.647012	+	0.762480i	$0.276018\pi$
$774$	−2.35793	−0.0847539
$775$	5.58774	0.200718
$776$	−16.5808	−0.595215
$777$	42.3983	1.52103
$778$	15.0668	0.540172
$779$	−0.742260	−0.0265942
$780$	−12.0606	−0.431838
$781$	−10.7026	−0.382971
$782$	8.45963	0.302516
$783$	29.3968	1.05056
$784$	5.87189	0.209710
$785$	−1.12811	−0.0402640
$786$	−31.5349	−1.12481
$787$	5.08074	0.181109	0.0905544	−	0.995892i	$-0.471136\pi$
$787$	5.08074	0.181109	0.0905544	+	0.995892i	$0.471136\pi$
$788$	−9.80435	−0.349266
$789$	39.1964	1.39543
$790$	−10.0000	−0.355784
$791$	−55.0529	−1.95746
$792$	1.47283	0.0523349
$793$	−75.7904	−2.69140
$794$	−18.0995	−0.642326
$795$	−0.156036	−0.00553403
$796$	−15.6964	−0.556344
$797$	12.2056	0.432346	0.216173	−	0.976355i	$-0.430642\pi$
$797$	12.2056	0.432346	0.216173	+	0.976355i	$0.430642\pi$
$798$	−1.84396	−0.0652756
$799$	−4.88982	−0.172989
$800$	−1.00000	−0.0353553
$801$	−3.27495	−0.115715
$802$	28.7221	1.01421
$803$	1.00000	0.0352892
$804$	−29.9519	−1.05632
$805$	22.3510	0.787768
$806$	−31.8649	−1.12239
$807$	1.77018	0.0623135
$808$	−10.7981	−0.379876
$809$	−31.4442	−1.10552	−0.552759	−	0.833341i	$-0.686425\pi$
$809$	−31.4442	−1.10552	−0.552759	+	0.833341i	$0.686425\pi$
$810$	−11.2493	−0.395259
$811$	22.3983	0.786512	0.393256	−	0.919429i	$-0.371349\pi$
$811$	22.3983	0.786512	0.393256	+	0.919429i	$0.371349\pi$
$812$	32.6546	1.14595
$813$	−62.1025	−2.17803
$814$	−5.58774	−0.195850
$815$	−5.73530	−0.200899
$816$	−2.87189	−0.100536
$817$	−0.389060	−0.0136115
$818$	28.1692	0.984914
$819$	−30.1336	−1.05295
$820$	−3.05433	−0.106662
$821$	−4.64279	−0.162035	−0.0810173	−	0.996713i	$-0.525817\pi$
$821$	−4.64279	−0.162035	−0.0810173	+	0.996713i	$0.525817\pi$
$822$	32.2687	1.12550
$823$	−31.6957	−1.10484	−0.552421	−	0.833565i	$-0.686296\pi$
$823$	−31.6957	−1.10484	−0.552421	+	0.833565i	$0.686296\pi$
$824$	9.74378	0.339441
$825$	−2.11491	−0.0736316
$826$	19.1057	0.664773
$827$	6.62111	0.230239	0.115119	−	0.993352i	$-0.463275\pi$
$827$	6.62111	0.230239	0.115119	+	0.993352i	$0.463275\pi$
$828$	9.17548	0.318870
$829$	48.3679	1.67989	0.839944	−	0.542674i	$-0.182588\pi$
$829$	48.3679	1.67989	0.839944	+	0.542674i	$0.182588\pi$
$830$	−16.4185	−0.569895
$831$	−27.8191	−0.965033
$832$	5.70265	0.197704
$833$	−7.97359	−0.276269
$834$	−32.5808	−1.12818
$835$	3.84396	0.133026
$836$	0.243019	0.00840498
$837$	−18.0474	−0.623808
$838$	−13.7827	−0.476114
$839$	10.2834	0.355023	0.177512	−	0.984119i	$-0.443195\pi$
$839$	10.2834	0.355023	0.177512	+	0.984119i	$0.443195\pi$
$840$	−7.58774	−0.261802
$841$	53.8410	1.85659
$842$	−20.5008	−0.706503
$843$	−53.0451	−1.82697
$844$	−2.35168	−0.0809483
$845$	−19.5202	−0.671515
$846$	−5.30359	−0.182341
$847$	−3.58774	−0.123276
$848$	0.0737791	0.00253358
$849$	−16.1476	−0.554183
$850$	1.35793	0.0465765
$851$	−34.8106	−1.19329
$852$	22.6351	0.775466
$853$	−52.3246	−1.79156	−0.895779	−	0.444499i	$-0.853382\pi$
$853$	−52.3246	−1.79156	−0.895779	+	0.444499i	$0.853382\pi$
$854$	−47.6825	−1.63166
$855$	0.357926	0.0122408
$856$	7.49228	0.256081
$857$	−19.9993	−0.683162	−0.341581	−	0.939852i	$-0.610962\pi$
$857$	−19.9993	−0.683162	−0.341581	+	0.939852i	$0.610962\pi$
$858$	12.0606	0.411741
$859$	−7.37113	−0.251500	−0.125750	−	0.992062i	$-0.540134\pi$
$859$	−7.37113	−0.251500	−0.125750	+	0.992062i	$0.540134\pi$
$860$	−1.60095	−0.0545918
$861$	−23.1755	−0.789818
$862$	−14.1887	−0.483269
$863$	49.3936	1.68138	0.840689	−	0.541518i	$-0.182150\pi$
$863$	49.3936	1.68138	0.840689	+	0.541518i	$0.182150\pi$
$864$	3.22982	0.109881
$865$	−10.3510	−0.351943
$866$	−33.0187	−1.12202
$867$	−32.0536	−1.08860
$868$	−20.0474	−0.680452
$869$	10.0000	0.339227
$870$	−19.2493	−0.652611
$871$	−80.7625	−2.73653
$872$	−7.43171	−0.251669
$873$	24.4207	0.826517
$874$	1.51396	0.0512105
$875$	3.58774	0.121288
$876$	−2.11491	−0.0714561
$877$	3.55286	0.119971	0.0599857	−	0.998199i	$-0.480894\pi$
$877$	3.55286	0.119971	0.0599857	+	0.998199i	$0.480894\pi$
$878$	2.25622	0.0761438
$879$	−20.1476	−0.679560
$880$	1.00000	0.0337100
$881$	−26.4985	−0.892758	−0.446379	−	0.894844i	$-0.647287\pi$
$881$	−26.4985	−0.892758	−0.446379	+	0.894844i	$0.647287\pi$
$882$	−8.64832	−0.291204
$883$	−21.1406	−0.711438	−0.355719	−	0.934593i	$-0.615764\pi$
$883$	−21.1406	−0.711438	−0.355719	+	0.934593i	$0.615764\pi$
$884$	−7.74378	−0.260451
$885$	−11.2625	−0.378584
$886$	2.82452	0.0948915
$887$	54.6755	1.83582	0.917912	−	0.396784i	$-0.129874\pi$
$887$	54.6755	1.83582	0.917912	+	0.396784i	$0.129874\pi$
$888$	11.8176	0.396571
$889$	57.1616	1.91714
$890$	−2.22357	−0.0745343
$891$	11.2493	0.376864
$892$	−1.80908	−0.0605724
$893$	−0.875097	−0.0292840
$894$	−14.8913	−0.498041
$895$	26.3726	0.881540
$896$	3.58774	0.119858
$897$	75.1352	2.50869
$898$	16.5683	0.552891
$899$	−50.8580	−1.69621
$900$	1.47283	0.0490945
$901$	−0.100187	−0.00333770
$902$	3.05433	0.101698
$903$	−12.1476	−0.404245
$904$	−15.3447	−0.510358
$905$	21.7827	0.724080
$906$	9.26247	0.307725
$907$	−4.23382	−0.140582	−0.0702909	−	0.997527i	$-0.522393\pi$
$907$	−4.23382	−0.140582	−0.0702909	+	0.997527i	$0.522393\pi$
$908$	22.3510	0.741743
$909$	15.9038	0.527496
$910$	−20.4596	−0.678230
$911$	54.7276	1.81321	0.906603	−	0.421984i	$-0.138666\pi$
$911$	54.7276	1.81321	0.906603	+	0.421984i	$0.138666\pi$
$912$	−0.513962	−0.0170190
$913$	16.4185	0.543373
$914$	−3.12339	−0.103312
$915$	28.1079	0.929220
$916$	−20.0606	−0.662820
$917$	−53.4960	−1.76659
$918$	−4.38585	−0.144755
$919$	14.1428	0.466529	0.233264	−	0.972413i	$-0.425059\pi$
$919$	14.1428	0.466529	0.233264	+	0.972413i	$0.425059\pi$
$920$	6.22982	0.205391
$921$	−56.0878	−1.84816
$922$	2.21661	0.0730002
$923$	61.0335	2.00894
$924$	7.58774	0.249618
$925$	−5.58774	−0.183724
$926$	−15.2144	−0.499975
$927$	−14.3510	−0.471348
$928$	9.10170	0.298778
$929$	28.9541	0.949955	0.474977	−	0.879998i	$-0.342456\pi$
$929$	28.9541	0.949955	0.474977	+	0.879998i	$0.342456\pi$
$930$	11.8176	0.387513
$931$	−1.42698	−0.0467674
$932$	−8.98055	−0.294168
$933$	−30.5676	−1.00074
$934$	−20.7243	−0.678121
$935$	−1.35793	−0.0444089
$936$	−8.39905	−0.274532
$937$	−47.7779	−1.56084	−0.780419	−	0.625257i	$-0.784994\pi$
$937$	−47.7779	−1.56084	−0.780419	+	0.625257i	$0.784994\pi$
$938$	−50.8106	−1.65902
$939$	41.5723	1.35666
$940$	−3.60095	−0.117450
$941$	60.7207	1.97944	0.989718	−	0.143029i	$-0.0456842\pi$
$941$	60.7207	1.97944	0.989718	+	0.143029i	$0.0456842\pi$
$942$	−2.38585	−0.0777352
$943$	19.0279	0.619634
$944$	5.32528	0.173323
$945$	−11.5877	−0.376949
$946$	1.60095	0.0520512
$947$	−9.44242	−0.306837	−0.153419	−	0.988161i	$-0.549028\pi$
$947$	−9.44242	−0.306837	−0.153419	+	0.988161i	$0.549028\pi$
$948$	−21.1491	−0.686890
$949$	−5.70265	−0.185116
$950$	0.243019	0.00788457
$951$	41.4985	1.34568
$952$	−4.87189	−0.157899
$953$	−44.4923	−1.44125	−0.720623	−	0.693327i	$-0.756144\pi$
$953$	−44.4923	−1.44125	−0.720623	+	0.693327i	$0.756144\pi$
$954$	−0.108664	−0.00351814
$955$	15.0668	0.487551
$956$	10.7306	0.347052
$957$	19.2493	0.622240
$958$	36.5419	1.18061
$959$	54.7408	1.76767
$960$	−2.11491	−0.0682583
$961$	0.222855	0.00718886
$962$	31.8649	1.02737
$963$	−11.0349	−0.355594
$964$	−12.3510	−0.397798
$965$	11.2104	0.360875
$966$	47.2702	1.52089
$967$	55.0731	1.77103	0.885515	−	0.464611i	$-0.153806\pi$
$967$	55.0731	1.77103	0.885515	+	0.464611i	$0.153806\pi$
$968$	−1.00000	−0.0321412
$969$	0.697923	0.0224205
$970$	16.5808	0.532377
$971$	−60.1414	−1.93003	−0.965015	−	0.262196i	$-0.915553\pi$
$971$	−60.1414	−1.93003	−0.965015	+	0.262196i	$0.915553\pi$
$972$	−14.1017	−0.452312
$973$	−55.2702	−1.77188
$974$	30.4332	0.975143
$975$	12.0606	0.386248
$976$	−13.2904	−0.425415
$977$	10.1234	0.323876	0.161938	−	0.986801i	$-0.448226\pi$
$977$	10.1234	0.323876	0.161938	+	0.986801i	$0.448226\pi$
$978$	−12.1296	−0.387863
$979$	2.22357	0.0710657
$980$	−5.87189	−0.187571
$981$	10.9457	0.349468
$982$	−26.3983	−0.842405
$983$	3.03712	0.0968691	0.0484345	−	0.998826i	$-0.484577\pi$
$983$	3.03712	0.0968691	0.0484345	+	0.998826i	$0.484577\pi$
$984$	−6.45963	−0.205925
$985$	9.80435	0.312393
$986$	−12.3594	−0.393605
$987$	−27.3230	−0.869702
$988$	−1.38585	−0.0440898
$989$	9.97359	0.317142
$990$	−1.47283	−0.0468097
$991$	−42.7672	−1.35855	−0.679273	−	0.733886i	$-0.737705\pi$
$991$	−42.7672	−1.35855	−0.679273	+	0.733886i	$0.737705\pi$
$992$	−5.58774	−0.177411
$993$	−36.6414	−1.16278
$994$	38.3983	1.21792
$995$	15.6964	0.497610
$996$	−34.7236	−1.10026
$997$	−14.6241	−0.463151	−0.231576	−	0.972817i	$-0.574388\pi$
$997$	−14.6241	−0.463151	−0.231576	+	0.972817i	$0.574388\pi$
$998$	−7.77018	−0.245961
$999$	18.0474	0.570994

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.s.1.3	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.s.1.3	✓	3	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:	\( N \)	\(=\)	\( 8030 = 2 \cdot 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8030.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.11491 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.11491 q^{6} -3.58774 q^{7} -1.00000 q^{8} +1.47283 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.11491 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.11491 q^{6} -3.58774 q^{7} -1.00000 q^{8} +1.47283 q^{9} +1.00000 q^{10} -1.00000 q^{11} +2.11491 q^{12} +5.70265 q^{13} +3.58774 q^{14} -2.11491 q^{15} +1.00000 q^{16} -1.35793 q^{17} -1.47283 q^{18} -0.243019 q^{19} -1.00000 q^{20} -7.58774 q^{21} +1.00000 q^{22} +6.22982 q^{23} -2.11491 q^{24} +1.00000 q^{25} -5.70265 q^{26} -3.22982 q^{27} -3.58774 q^{28} -9.10170 q^{29} +2.11491 q^{30} +5.58774 q^{31} -1.00000 q^{32} -2.11491 q^{33} +1.35793 q^{34} +3.58774 q^{35} +1.47283 q^{36} -5.58774 q^{37} +0.243019 q^{38} +12.0606 q^{39} +1.00000 q^{40} +3.05433 q^{41} +7.58774 q^{42} +1.60095 q^{43} -1.00000 q^{44} -1.47283 q^{45} -6.22982 q^{46} +3.60095 q^{47} +2.11491 q^{48} +5.87189 q^{49} -1.00000 q^{50} -2.87189 q^{51} +5.70265 q^{52} +0.0737791 q^{53} +3.22982 q^{54} +1.00000 q^{55} +3.58774 q^{56} -0.513962 q^{57} +9.10170 q^{58} +5.32528 q^{59} -2.11491 q^{60} -13.2904 q^{61} -5.58774 q^{62} -5.28415 q^{63} +1.00000 q^{64} -5.70265 q^{65} +2.11491 q^{66} -14.1623 q^{67} -1.35793 q^{68} +13.1755 q^{69} -3.58774 q^{70} +10.7026 q^{71} -1.47283 q^{72} -1.00000 q^{73} +5.58774 q^{74} +2.11491 q^{75} -0.243019 q^{76} +3.58774 q^{77} -12.0606 q^{78} -10.0000 q^{79} -1.00000 q^{80} -11.2493 q^{81} -3.05433 q^{82} -16.4185 q^{83} -7.58774 q^{84} +1.35793 q^{85} -1.60095 q^{86} -19.2493 q^{87} +1.00000 q^{88} -2.22357 q^{89} +1.47283 q^{90} -20.4596 q^{91} +6.22982 q^{92} +11.8176 q^{93} -3.60095 q^{94} +0.243019 q^{95} -2.11491 q^{96} +16.5808 q^{97} -5.87189 q^{98} -1.47283 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{4} - 3 q^{5} + q^{7} - 3 q^{8} - q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 3 * q^4 - 3 * q^5 + q^7 - 3 * q^8 - q^9	\( 3 q - 3 q^{2} + 3 q^{4} - 3 q^{5} + q^{7} - 3 q^{8} - q^{9} + 3 q^{10} - 3 q^{11} - q^{13} - q^{14} + 3 q^{16} - 5 q^{17} + q^{18} - 8 q^{19} - 3 q^{20} - 11 q^{21} + 3 q^{22} + 6 q^{23} + 3 q^{25} + q^{26} + 3 q^{27} + q^{28} - q^{29} + 5 q^{31} - 3 q^{32} + 5 q^{34} - q^{35} - q^{36} - 5 q^{37} + 8 q^{38} + 19 q^{39} + 3 q^{40} + 20 q^{41} + 11 q^{42} + 13 q^{43} - 3 q^{44} + q^{45} - 6 q^{46} + 19 q^{47} + 4 q^{49} - 3 q^{50} + 5 q^{51} - q^{52} + 3 q^{53} - 3 q^{54} + 3 q^{55} - q^{56} + 13 q^{57} + q^{58} + 5 q^{59} - 10 q^{61} - 5 q^{62} - 14 q^{63} + 3 q^{64} + q^{65} + q^{67} - 5 q^{68} + 16 q^{69} + q^{70} + 14 q^{71} + q^{72} - 3 q^{73} + 5 q^{74} - 8 q^{76} - q^{77} - 19 q^{78} - 30 q^{79} - 3 q^{80} - 13 q^{81} - 20 q^{82} - 33 q^{83} - 11 q^{84} + 5 q^{85} - 13 q^{86} - 37 q^{87} + 3 q^{88} - 22 q^{89} - q^{90} - 36 q^{91} + 6 q^{92} + 11 q^{93} - 19 q^{94} + 8 q^{95} - 10 q^{97} - 4 q^{98} + q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^4 - 3 * q^5 + q^7 - 3 * q^8 - q^9 + 3 * q^10 - 3 * q^11 - q^13 - q^14 + 3 * q^16 - 5 * q^17 + q^18 - 8 * q^19 - 3 * q^20 - 11 * q^21 + 3 * q^22 + 6 * q^23 + 3 * q^25 + q^26 + 3 * q^27 + q^28 - q^29 + 5 * q^31 - 3 * q^32 + 5 * q^34 - q^35 - q^36 - 5 * q^37 + 8 * q^38 + 19 * q^39 + 3 * q^40 + 20 * q^41 + 11 * q^42 + 13 * q^43 - 3 * q^44 + q^45 - 6 * q^46 + 19 * q^47 + 4 * q^49 - 3 * q^50 + 5 * q^51 - q^52 + 3 * q^53 - 3 * q^54 + 3 * q^55 - q^56 + 13 * q^57 + q^58 + 5 * q^59 - 10 * q^61 - 5 * q^62 - 14 * q^63 + 3 * q^64 + q^65 + q^67 - 5 * q^68 + 16 * q^69 + q^70 + 14 * q^71 + q^72 - 3 * q^73 + 5 * q^74 - 8 * q^76 - q^77 - 19 * q^78 - 30 * q^79 - 3 * q^80 - 13 * q^81 - 20 * q^82 - 33 * q^83 - 11 * q^84 + 5 * q^85 - 13 * q^86 - 37 * q^87 + 3 * q^88 - 22 * q^89 - q^90 - 36 * q^91 + 6 * q^92 + 11 * q^93 - 19 * q^94 + 8 * q^95 - 10 * q^97 - 4 * q^98 + q^99

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