LMFDB - Embedded newform 8021.2.a.a.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8021,2,Mod(1,8021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8021, 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("8021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8021 = 13 \cdot 617 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8021.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:	$64.0480074613$
Analytic rank:	$1$
Dimension:	$134$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	8021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.55271 q^{2} -2.07589 q^{3} +4.51632 q^{4} +1.36107 q^{5} +5.29914 q^{6} -3.73550 q^{7} -6.42344 q^{8} +1.30931 q^{9} +O(q^{10})$	\(q-2.55271 q^{2} -2.07589 q^{3} +4.51632 q^{4} +1.36107 q^{5} +5.29914 q^{6} -3.73550 q^{7} -6.42344 q^{8} +1.30931 q^{9} -3.47441 q^{10} -4.88732 q^{11} -9.37538 q^{12} +1.00000 q^{13} +9.53564 q^{14} -2.82543 q^{15} +7.36452 q^{16} +5.80287 q^{17} -3.34228 q^{18} +3.30043 q^{19} +6.14703 q^{20} +7.75447 q^{21} +12.4759 q^{22} -2.29061 q^{23} +13.3343 q^{24} -3.14749 q^{25} -2.55271 q^{26} +3.50968 q^{27} -16.8707 q^{28} -4.85362 q^{29} +7.21249 q^{30} -4.25817 q^{31} -5.95260 q^{32} +10.1455 q^{33} -14.8130 q^{34} -5.08427 q^{35} +5.91326 q^{36} +1.06475 q^{37} -8.42504 q^{38} -2.07589 q^{39} -8.74275 q^{40} +2.21441 q^{41} -19.7949 q^{42} -9.13392 q^{43} -22.0727 q^{44} +1.78206 q^{45} +5.84727 q^{46} +5.48436 q^{47} -15.2879 q^{48} +6.95394 q^{49} +8.03462 q^{50} -12.0461 q^{51} +4.51632 q^{52} -6.59148 q^{53} -8.95920 q^{54} -6.65198 q^{55} +23.9947 q^{56} -6.85132 q^{57} +12.3899 q^{58} +2.08444 q^{59} -12.7605 q^{60} +9.96838 q^{61} +10.8699 q^{62} -4.89092 q^{63} +0.466219 q^{64} +1.36107 q^{65} -25.8986 q^{66} +3.89134 q^{67} +26.2076 q^{68} +4.75506 q^{69} +12.9787 q^{70} -3.43870 q^{71} -8.41026 q^{72} +14.4044 q^{73} -2.71799 q^{74} +6.53383 q^{75} +14.9058 q^{76} +18.2566 q^{77} +5.29914 q^{78} -10.0130 q^{79} +10.0236 q^{80} -11.2136 q^{81} -5.65274 q^{82} -13.0394 q^{83} +35.0217 q^{84} +7.89811 q^{85} +23.3162 q^{86} +10.0756 q^{87} +31.3934 q^{88} +4.18128 q^{89} -4.54908 q^{90} -3.73550 q^{91} -10.3451 q^{92} +8.83948 q^{93} -14.0000 q^{94} +4.49212 q^{95} +12.3569 q^{96} +11.5663 q^{97} -17.7514 q^{98} -6.39901 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9}+O(q^{10}) $ 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9	\( 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9} - 33 q^{10} - 47 q^{11} - 53 q^{12} + 134 q^{13} - 28 q^{14} - 30 q^{15} + 30 q^{16} - 17 q^{17} - 14 q^{18} - 87 q^{19} - 12 q^{20} - 24 q^{21} - 52 q^{22} - 44 q^{23} - 36 q^{24} + 58 q^{25} - 6 q^{26} - 117 q^{27} - 71 q^{28} - 42 q^{29} - 21 q^{30} - 82 q^{31} - 31 q^{32} + 12 q^{33} - 30 q^{34} - 54 q^{35} + 32 q^{36} - 55 q^{37} - 12 q^{38} - 33 q^{39} - 86 q^{40} - 16 q^{41} + 6 q^{42} - 148 q^{43} - 54 q^{44} - 24 q^{45} - 57 q^{46} - 21 q^{47} - 82 q^{48} + 12 q^{49} - 17 q^{50} - 123 q^{51} + 98 q^{52} - 17 q^{53} - 10 q^{54} - 148 q^{55} - 47 q^{56} - q^{57} - 58 q^{58} - 64 q^{59} - 16 q^{60} - 112 q^{61} - 15 q^{62} - 58 q^{63} - 65 q^{64} - 8 q^{65} - 20 q^{66} - 110 q^{67} - 8 q^{68} - 57 q^{69} - 40 q^{70} - 78 q^{71} - 28 q^{72} - 43 q^{73} - 52 q^{74} - 150 q^{75} - 96 q^{76} - 24 q^{77} - 16 q^{78} - 228 q^{79} + 20 q^{80} + 54 q^{81} - 89 q^{82} - 12 q^{83} + 6 q^{84} - 77 q^{85} + 29 q^{86} - 77 q^{87} - 95 q^{88} - 32 q^{89} - 46 q^{90} - 32 q^{91} - 62 q^{92} - 9 q^{93} - 87 q^{94} - 61 q^{95} - 54 q^{96} - 38 q^{97} + 6 q^{98} - 193 q^{99}+O(q^{100}) \) 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9 - 33 * q^10 - 47 * q^11 - 53 * q^12 + 134 * q^13 - 28 * q^14 - 30 * q^15 + 30 * q^16 - 17 * q^17 - 14 * q^18 - 87 * q^19 - 12 * q^20 - 24 * q^21 - 52 * q^22 - 44 * q^23 - 36 * q^24 + 58 * q^25 - 6 * q^26 - 117 * q^27 - 71 * q^28 - 42 * q^29 - 21 * q^30 - 82 * q^31 - 31 * q^32 + 12 * q^33 - 30 * q^34 - 54 * q^35 + 32 * q^36 - 55 * q^37 - 12 * q^38 - 33 * q^39 - 86 * q^40 - 16 * q^41 + 6 * q^42 - 148 * q^43 - 54 * q^44 - 24 * q^45 - 57 * q^46 - 21 * q^47 - 82 * q^48 + 12 * q^49 - 17 * q^50 - 123 * q^51 + 98 * q^52 - 17 * q^53 - 10 * q^54 - 148 * q^55 - 47 * q^56 - q^57 - 58 * q^58 - 64 * q^59 - 16 * q^60 - 112 * q^61 - 15 * q^62 - 58 * q^63 - 65 * q^64 - 8 * q^65 - 20 * q^66 - 110 * q^67 - 8 * q^68 - 57 * q^69 - 40 * q^70 - 78 * q^71 - 28 * q^72 - 43 * q^73 - 52 * q^74 - 150 * q^75 - 96 * q^76 - 24 * q^77 - 16 * q^78 - 228 * q^79 + 20 * q^80 + 54 * q^81 - 89 * q^82 - 12 * q^83 + 6 * q^84 - 77 * q^85 + 29 * q^86 - 77 * q^87 - 95 * q^88 - 32 * q^89 - 46 * q^90 - 32 * q^91 - 62 * q^92 - 9 * q^93 - 87 * q^94 - 61 * q^95 - 54 * q^96 - 38 * q^97 + 6 * q^98 - 193 * 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 $

$2$	−2.55271	−1.80504	−0.902519	−	0.430650i	$-0.858284\pi$
$2$	−2.55271	−1.80504	−0.902519	+	0.430650i	$0.858284\pi$
$3$	−2.07589	−1.19851	−0.599257	−	0.800557i	$-0.704537\pi$
$3$	−2.07589	−1.19851	−0.599257	+	0.800557i	$0.704537\pi$
$4$	4.51632	2.25816
$5$	1.36107	0.608689	0.304344	−	0.952562i	$-0.401563\pi$
$5$	1.36107	0.608689	0.304344	+	0.952562i	$0.401563\pi$
$6$	5.29914	2.16336
$7$	−3.73550	−1.41189	−0.705943	−	0.708269i	$-0.749476\pi$
$7$	−3.73550	−1.41189	−0.705943	+	0.708269i	$0.749476\pi$
$8$	−6.42344	−2.27103
$9$	1.30931	0.436436
$10$	−3.47441	−1.09871
$11$	−4.88732	−1.47358	−0.736791	−	0.676121i	$-0.763660\pi$
$11$	−4.88732	−1.47358	−0.736791	+	0.676121i	$0.763660\pi$
$12$	−9.37538	−2.70644
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	9.53564	2.54851
$15$	−2.82543	−0.729522
$16$	7.36452	1.84113
$17$	5.80287	1.40740	0.703701	−	0.710496i	$-0.251529\pi$
$17$	5.80287	1.40740	0.703701	+	0.710496i	$0.251529\pi$
$18$	−3.34228	−0.787784
$19$	3.30043	0.757171	0.378585	−	0.925566i	$-0.376411\pi$
$19$	3.30043	0.757171	0.378585	+	0.925566i	$0.376411\pi$
$20$	6.14703	1.37452
$21$	7.75447	1.69216
$22$	12.4759	2.65987
$23$	−2.29061	−0.477626	−0.238813	−	0.971066i	$-0.576758\pi$
$23$	−2.29061	−0.477626	−0.238813	+	0.971066i	$0.576758\pi$
$24$	13.3343	2.72186
$25$	−3.14749	−0.629498
$26$	−2.55271	−0.500627
$27$	3.50968	0.675439
$28$	−16.8707	−3.18826
$29$	−4.85362	−0.901294	−0.450647	−	0.892702i	$-0.648807\pi$
$29$	−4.85362	−0.901294	−0.450647	+	0.892702i	$0.648807\pi$
$30$	7.21249	1.31682
$31$	−4.25817	−0.764790	−0.382395	−	0.923999i	$-0.624901\pi$
$31$	−4.25817	−0.764790	−0.382395	+	0.923999i	$0.624901\pi$
$32$	−5.95260	−1.05228
$33$	10.1455	1.76611
$34$	−14.8130	−2.54041
$35$	−5.08427	−0.859399
$36$	5.91326	0.985543
$37$	1.06475	0.175044	0.0875219	−	0.996163i	$-0.472105\pi$
$37$	1.06475	0.175044	0.0875219	+	0.996163i	$0.472105\pi$
$38$	−8.42504	−1.36672
$39$	−2.07589	−0.332408
$40$	−8.74275	−1.38235
$41$	2.21441	0.345833	0.172916	−	0.984937i	$-0.444681\pi$
$41$	2.21441	0.345833	0.172916	+	0.984937i	$0.444681\pi$
$42$	−19.7949	−3.05442
$43$	−9.13392	−1.39291	−0.696455	−	0.717600i	$-0.745240\pi$
$43$	−9.13392	−1.39291	−0.696455	+	0.717600i	$0.745240\pi$
$44$	−22.0727	−3.32758
$45$	1.78206	0.265654
$46$	5.84727	0.862133
$47$	5.48436	0.799976	0.399988	−	0.916520i	$-0.369014\pi$
$47$	5.48436	0.799976	0.399988	+	0.916520i	$0.369014\pi$
$48$	−15.2879	−2.20662
$49$	6.95394	0.993420
$50$	8.03462	1.13627
$51$	−12.0461	−1.68679
$52$	4.51632	0.626301
$53$	−6.59148	−0.905409	−0.452704	−	0.891661i	$-0.649541\pi$
$53$	−6.59148	−0.905409	−0.452704	+	0.891661i	$0.649541\pi$
$54$	−8.95920	−1.21919
$55$	−6.65198	−0.896952
$56$	23.9947	3.20643
$57$	−6.85132	−0.907480
$58$	12.3899	1.62687
$59$	2.08444	0.271371	0.135685	−	0.990752i	$-0.456676\pi$
$59$	2.08444	0.271371	0.135685	+	0.990752i	$0.456676\pi$
$60$	−12.7605	−1.64738
$61$	9.96838	1.27632	0.638160	−	0.769904i	$-0.279696\pi$
$61$	9.96838	1.27632	0.638160	+	0.769904i	$0.279696\pi$
$62$	10.8699	1.38047
$63$	−4.89092	−0.616198
$64$	0.466219	0.0582773
$65$	1.36107	0.168820
$66$	−25.8986	−3.18789
$67$	3.89134	0.475403	0.237702	−	0.971338i	$-0.423606\pi$
$67$	3.89134	0.475403	0.237702	+	0.971338i	$0.423606\pi$
$68$	26.2076	3.17814
$69$	4.75506	0.572441
$70$	12.9787	1.55125
$71$	−3.43870	−0.408099	−0.204050	−	0.978961i	$-0.565410\pi$
$71$	−3.43870	−0.408099	−0.204050	+	0.978961i	$0.565410\pi$
$72$	−8.41026	−0.991159
$73$	14.4044	1.68590	0.842952	−	0.537989i	$-0.180816\pi$
$73$	14.4044	1.68590	0.842952	+	0.537989i	$0.180816\pi$
$74$	−2.71799	−0.315960
$75$	6.53383	0.754462
$76$	14.9058	1.70981
$77$	18.2566	2.08053
$78$	5.29914	0.600009
$79$	−10.0130	−1.12656	−0.563278	−	0.826268i	$-0.690460\pi$
$79$	−10.0130	−1.12656	−0.563278	+	0.826268i	$0.690460\pi$
$80$	10.0236	1.12068
$81$	−11.2136	−1.24596
$82$	−5.65274	−0.624241
$83$	−13.0394	−1.43126	−0.715631	−	0.698479i	$-0.753861\pi$
$83$	−13.0394	−1.43126	−0.715631	+	0.698479i	$0.753861\pi$
$84$	35.0217	3.82118
$85$	7.89811	0.856670
$86$	23.3162	2.51426
$87$	10.0756	1.08021
$88$	31.3934	3.34654
$89$	4.18128	0.443215	0.221608	−	0.975136i	$-0.428870\pi$
$89$	4.18128	0.443215	0.221608	+	0.975136i	$0.428870\pi$
$90$	−4.54908	−0.479515
$91$	−3.73550	−0.391587
$92$	−10.3451	−1.07856
$93$	8.83948	0.916611
$94$	−14.0000	−1.44399
$95$	4.49212	0.460881
$96$	12.3569	1.26117
$97$	11.5663	1.17438	0.587189	−	0.809450i	$-0.300235\pi$
$97$	11.5663	1.17438	0.587189	+	0.809450i	$0.300235\pi$
$98$	−17.7514	−1.79316
$99$	−6.39901	−0.643124
$100$	−14.2151	−1.42151
$101$	8.60246	0.855977	0.427988	−	0.903784i	$-0.359222\pi$
$101$	8.60246	0.855977	0.427988	+	0.903784i	$0.359222\pi$
$102$	30.7502	3.04472
$103$	0.650032	0.0640495	0.0320248	−	0.999487i	$-0.489804\pi$
$103$	0.650032	0.0640495	0.0320248	+	0.999487i	$0.489804\pi$
$104$	−6.42344	−0.629870
$105$	10.5544	1.03000
$106$	16.8261	1.63430
$107$	14.3528	1.38753	0.693766	−	0.720200i	$-0.255950\pi$
$107$	14.3528	1.38753	0.693766	+	0.720200i	$0.255950\pi$
$108$	15.8509	1.52525
$109$	−8.21938	−0.787274	−0.393637	−	0.919266i	$-0.628783\pi$
$109$	−8.21938	−0.787274	−0.393637	+	0.919266i	$0.628783\pi$
$110$	16.9806	1.61903
$111$	−2.21030	−0.209792
$112$	−27.5102	−2.59946
$113$	10.3605	0.974632	0.487316	−	0.873226i	$-0.337976\pi$
$113$	10.3605	0.974632	0.487316	+	0.873226i	$0.337976\pi$
$114$	17.4894	1.63804
$115$	−3.11768	−0.290726
$116$	−21.9205	−2.03527
$117$	1.30931	0.121046
$118$	−5.32097	−0.489835
$119$	−21.6766	−1.98709
$120$	18.1490	1.65677
$121$	12.8859	1.17144
$122$	−25.4464	−2.30381
$123$	−4.59687	−0.414485
$124$	−19.2313	−1.72702
$125$	−11.0893	−0.991857
$126$	12.4851	1.11226
$127$	−2.48293	−0.220324	−0.110162	−	0.993914i	$-0.535137\pi$
$127$	−2.48293	−0.220324	−0.110162	+	0.993914i	$0.535137\pi$
$128$	10.7151	0.947089
$129$	18.9610	1.66942
$130$	−3.47441	−0.304726
$131$	−3.92300	−0.342754	−0.171377	−	0.985206i	$-0.554822\pi$
$131$	−3.92300	−0.342754	−0.171377	+	0.985206i	$0.554822\pi$
$132$	45.8204	3.98816
$133$	−12.3288	−1.06904
$134$	−9.93347	−0.858121
$135$	4.77693	0.411132
$136$	−37.2744	−3.19625
$137$	16.5088	1.41044	0.705221	−	0.708988i	$-0.250848\pi$
$137$	16.5088	1.41044	0.705221	+	0.708988i	$0.250848\pi$
$138$	−12.1383	−1.03328
$139$	−15.4693	−1.31209	−0.656046	−	0.754721i	$-0.727772\pi$
$139$	−15.4693	−1.31209	−0.656046	+	0.754721i	$0.727772\pi$
$140$	−22.9622	−1.94066
$141$	−11.3849	−0.958782
$142$	8.77801	0.736634
$143$	−4.88732	−0.408698
$144$	9.64243	0.803536
$145$	−6.60611	−0.548608
$146$	−36.7702	−3.04312
$147$	−14.4356	−1.19063
$148$	4.80875	0.395277
$149$	−3.36452	−0.275632	−0.137816	−	0.990458i	$-0.544008\pi$
$149$	−3.36452	−0.275632	−0.137816	+	0.990458i	$0.544008\pi$
$150$	−16.6790	−1.36183
$151$	2.57118	0.209240	0.104620	−	0.994512i	$-0.466637\pi$
$151$	2.57118	0.209240	0.104620	+	0.994512i	$0.466637\pi$
$152$	−21.2001	−1.71956
$153$	7.59775	0.614241
$154$	−46.6037	−3.75543
$155$	−5.79566	−0.465519
$156$	−9.37538	−0.750631
$157$	−1.72677	−0.137811	−0.0689054	−	0.997623i	$-0.521951\pi$
$157$	−1.72677	−0.137811	−0.0689054	+	0.997623i	$0.521951\pi$
$158$	25.5604	2.03347
$159$	13.6832	1.08515
$160$	−8.10191	−0.640512
$161$	8.55658	0.674353
$162$	28.6251	2.24900
$163$	−1.42754	−0.111814	−0.0559069	−	0.998436i	$-0.517805\pi$
$163$	−1.42754	−0.111814	−0.0559069	+	0.998436i	$0.517805\pi$
$164$	10.0010	0.780946
$165$	13.8088	1.07501
$166$	33.2858	2.58348
$167$	23.7322	1.83646	0.918228	−	0.396053i	$-0.129620\pi$
$167$	23.7322	1.83646	0.918228	+	0.396053i	$0.129620\pi$
$168$	−49.8104	−3.84295
$169$	1.00000	0.0769231
$170$	−20.1616	−1.54632
$171$	4.32128	0.330457
$172$	−41.2517	−3.14542
$173$	−23.9529	−1.82111	−0.910553	−	0.413391i	$-0.864344\pi$
$173$	−23.9529	−1.82111	−0.910553	+	0.413391i	$0.864344\pi$
$174$	−25.7200	−1.94983
$175$	11.7574	0.888779
$176$	−35.9927	−2.71305
$177$	−4.32706	−0.325242
$178$	−10.6736	−0.800020
$179$	6.23682	0.466162	0.233081	−	0.972457i	$-0.425119\pi$
$179$	6.23682	0.466162	0.233081	+	0.972457i	$0.425119\pi$
$180$	8.04836	0.599889
$181$	−10.1627	−0.755384	−0.377692	−	0.925931i	$-0.623282\pi$
$181$	−10.1627	−0.755384	−0.377692	+	0.925931i	$0.623282\pi$
$182$	9.53564	0.706828
$183$	−20.6932	−1.52969
$184$	14.7136	1.08470
$185$	1.44920	0.106547
$186$	−22.5646	−1.65452
$187$	−28.3604	−2.07392
$188$	24.7691	1.80647
$189$	−13.1104	−0.953643
$190$	−11.4671	−0.831908
$191$	15.4706	1.11941	0.559707	−	0.828691i	$-0.310914\pi$
$191$	15.4706	1.11941	0.559707	+	0.828691i	$0.310914\pi$
$192$	−0.967817	−0.0698462
$193$	11.0404	0.794704	0.397352	−	0.917666i	$-0.369929\pi$
$193$	11.0404	0.794704	0.397352	+	0.917666i	$0.369929\pi$
$194$	−29.5253	−2.11980
$195$	−2.82543	−0.202333
$196$	31.4062	2.24330
$197$	21.9129	1.56123	0.780616	−	0.625011i	$-0.214905\pi$
$197$	21.9129	1.56123	0.780616	+	0.625011i	$0.214905\pi$
$198$	16.3348	1.16086
$199$	7.15543	0.507235	0.253617	−	0.967305i	$-0.418380\pi$
$199$	7.15543	0.507235	0.253617	+	0.967305i	$0.418380\pi$
$200$	20.2177	1.42961
$201$	−8.07799	−0.569778
$202$	−21.9596	−1.54507
$203$	18.1307	1.27252
$204$	−54.4041	−3.80905
$205$	3.01397	0.210505
$206$	−1.65934	−0.115612
$207$	−2.99912	−0.208453
$208$	7.36452	0.510638
$209$	−16.1303	−1.11575
$210$	−26.9423	−1.85919
$211$	−10.4315	−0.718133	−0.359067	−	0.933312i	$-0.616905\pi$
$211$	−10.4315	−0.718133	−0.359067	+	0.933312i	$0.616905\pi$
$212$	−29.7692	−2.04456
$213$	7.13836	0.489113
$214$	−36.6384	−2.50455
$215$	−12.4319	−0.847849
$216$	−22.5442	−1.53394
$217$	15.9064	1.07980
$218$	20.9817	1.42106
$219$	−29.9018	−2.02058
$220$	−30.0425	−2.02546
$221$	5.80287	0.390343
$222$	5.64225	0.378683
$223$	−6.92170	−0.463511	−0.231756	−	0.972774i	$-0.574447\pi$
$223$	−6.92170	−0.463511	−0.231756	+	0.972774i	$0.574447\pi$
$224$	22.2359	1.48570
$225$	−4.12104	−0.274736
$226$	−26.4473	−1.75925
$227$	20.0822	1.33290	0.666452	−	0.745548i	$-0.267812\pi$
$227$	20.0822	1.33290	0.666452	+	0.745548i	$0.267812\pi$
$228$	−30.9428	−2.04924
$229$	20.7822	1.37333	0.686664	−	0.726975i	$-0.259075\pi$
$229$	20.7822	1.37333	0.686664	+	0.726975i	$0.259075\pi$
$230$	7.95854	0.524771
$231$	−37.8986	−2.49354
$232$	31.1769	2.04687
$233$	−17.0089	−1.11429	−0.557144	−	0.830416i	$-0.688103\pi$
$233$	−17.0089	−1.11429	−0.557144	+	0.830416i	$0.688103\pi$
$234$	−3.34228	−0.218492
$235$	7.46459	0.486936
$236$	9.41400	0.612799
$237$	20.7859	1.35019
$238$	55.3340	3.58677
$239$	19.5527	1.26476	0.632379	−	0.774659i	$-0.282079\pi$
$239$	19.5527	1.26476	0.632379	+	0.774659i	$0.282079\pi$
$240$	−20.8079	−1.34315
$241$	−13.5152	−0.870591	−0.435296	−	0.900288i	$-0.643356\pi$
$241$	−13.5152	−0.870591	−0.435296	+	0.900288i	$0.643356\pi$
$242$	−32.8938	−2.11450
$243$	12.7492	0.817861
$244$	45.0204	2.88214
$245$	9.46480	0.604684
$246$	11.7345	0.748162
$247$	3.30043	0.210001
$248$	27.3521	1.73686
$249$	27.0684	1.71539
$250$	28.3078	1.79034
$251$	−4.47371	−0.282378	−0.141189	−	0.989983i	$-0.545093\pi$
$251$	−4.47371	−0.282378	−0.141189	+	0.989983i	$0.545093\pi$
$252$	−22.0890	−1.39147
$253$	11.1950	0.703821
$254$	6.33819	0.397694
$255$	−16.3956	−1.02673
$256$	−28.2849	−1.76781
$257$	−21.3628	−1.33257	−0.666286	−	0.745696i	$-0.732117\pi$
$257$	−21.3628	−1.33257	−0.666286	+	0.745696i	$0.732117\pi$
$258$	−48.4019	−3.01337
$259$	−3.97737	−0.247142
$260$	6.14703	0.381223
$261$	−6.35489	−0.393358
$262$	10.0143	0.618684
$263$	−19.1099	−1.17837	−0.589183	−	0.808000i	$-0.700550\pi$
$263$	−19.1099	−1.17837	−0.589183	+	0.808000i	$0.700550\pi$
$264$	−65.1691	−4.01088
$265$	−8.97146	−0.551112
$266$	31.4717	1.92965
$267$	−8.67987	−0.531200
$268$	17.5746	1.07354
$269$	−27.5063	−1.67709	−0.838545	−	0.544832i	$-0.816593\pi$
$269$	−27.5063	−1.67709	−0.838545	+	0.544832i	$0.816593\pi$
$270$	−12.1941	−0.742109
$271$	−4.34067	−0.263677	−0.131838	−	0.991271i	$-0.542088\pi$
$271$	−4.34067	−0.263677	−0.131838	+	0.991271i	$0.542088\pi$
$272$	42.7353	2.59121
$273$	7.75447	0.469322
$274$	−42.1421	−2.54590
$275$	15.3828	0.927616
$276$	21.4754	1.29267
$277$	21.7042	1.30408	0.652040	−	0.758185i	$-0.273913\pi$
$277$	21.7042	1.30408	0.652040	+	0.758185i	$0.273913\pi$
$278$	39.4887	2.36838
$279$	−5.57526	−0.333782
$280$	32.6585	1.95172
$281$	−2.73391	−0.163092	−0.0815458	−	0.996670i	$-0.525986\pi$
$281$	−2.73391	−0.163092	−0.0815458	+	0.996670i	$0.525986\pi$
$282$	29.0624	1.73064
$283$	−24.8911	−1.47962	−0.739810	−	0.672816i	$-0.765085\pi$
$283$	−24.8911	−1.47962	−0.739810	+	0.672816i	$0.765085\pi$
$284$	−15.5303	−0.921554
$285$	−9.32513	−0.552373
$286$	12.4759	0.737715
$287$	−8.27192	−0.488276
$288$	−7.79379	−0.459254
$289$	16.6733	0.980781
$290$	16.8635	0.990258
$291$	−24.0103	−1.40751
$292$	65.0548	3.80704
$293$	16.8027	0.981625	0.490813	−	0.871265i	$-0.336700\pi$
$293$	16.8027	0.981625	0.490813	+	0.871265i	$0.336700\pi$
$294$	36.8499	2.14913
$295$	2.83707	0.165181
$296$	−6.83935	−0.397529
$297$	−17.1529	−0.995314
$298$	8.58864	0.497526
$299$	−2.29061	−0.132470
$300$	29.5089	1.70370
$301$	34.1197	1.96663
$302$	−6.56347	−0.377685
$303$	−17.8577	−1.02590
$304$	24.3061	1.39405
$305$	13.5677	0.776882
$306$	−19.3948	−1.10873
$307$	19.7951	1.12977	0.564884	−	0.825170i	$-0.308921\pi$
$307$	19.7951	1.12977	0.564884	+	0.825170i	$0.308921\pi$
$308$	82.4525	4.69817
$309$	−1.34939	−0.0767642
$310$	14.7946	0.840279
$311$	30.9577	1.75545	0.877726	−	0.479162i	$-0.159060\pi$
$311$	30.9577	1.75545	0.877726	+	0.479162i	$0.159060\pi$
$312$	13.3343	0.754908
$313$	26.5276	1.49943	0.749715	−	0.661761i	$-0.230191\pi$
$313$	26.5276	1.49943	0.749715	+	0.661761i	$0.230191\pi$
$314$	4.40793	0.248754
$315$	−6.65688	−0.375073
$316$	−45.2221	−2.54394
$317$	18.5159	1.03996	0.519978	−	0.854179i	$-0.325940\pi$
$317$	18.5159	1.03996	0.519978	+	0.854179i	$0.325940\pi$
$318$	−34.9291	−1.95873
$319$	23.7212	1.32813
$320$	0.634556	0.0354728
$321$	−29.7947	−1.66298
$322$	−21.8425	−1.21723
$323$	19.1520	1.06564
$324$	−50.6444	−2.81358
$325$	−3.14749	−0.174591
$326$	3.64410	0.201828
$327$	17.0625	0.943559
$328$	−14.2241	−0.785396
$329$	−20.4868	−1.12947
$330$	−35.2497	−1.94043
$331$	31.3284	1.72196	0.860982	−	0.508636i	$-0.169850\pi$
$331$	31.3284	1.72196	0.860982	+	0.508636i	$0.169850\pi$
$332$	−58.8902	−3.23202
$333$	1.39409	0.0763954
$334$	−60.5815	−3.31487
$335$	5.29639	0.289373
$336$	57.1080	3.11550
$337$	−21.0246	−1.14528	−0.572641	−	0.819806i	$-0.694081\pi$
$337$	−21.0246	−1.14528	−0.572641	+	0.819806i	$0.694081\pi$
$338$	−2.55271	−0.138849
$339$	−21.5072	−1.16811
$340$	35.6704	1.93450
$341$	20.8110	1.12698
$342$	−11.0310	−0.596487
$343$	0.172047	0.00928966
$344$	58.6712	3.16334
$345$	6.47196	0.348439
$346$	61.1448	3.28717
$347$	25.6493	1.37692	0.688462	−	0.725272i	$-0.258286\pi$
$347$	25.6493	1.37692	0.688462	+	0.725272i	$0.258286\pi$
$348$	45.5045	2.43930
$349$	−26.8489	−1.43719	−0.718594	−	0.695430i	$-0.755214\pi$
$349$	−26.8489	−1.43719	−0.718594	+	0.695430i	$0.755214\pi$
$350$	−30.0133	−1.60428
$351$	3.50968	0.187333
$352$	29.0922	1.55062
$353$	9.48184	0.504667	0.252334	−	0.967640i	$-0.418802\pi$
$353$	9.48184	0.504667	0.252334	+	0.967640i	$0.418802\pi$
$354$	11.0457	0.587074
$355$	−4.68032	−0.248405
$356$	18.8840	1.00085
$357$	44.9982	2.38156
$358$	−15.9208	−0.841440
$359$	−8.05040	−0.424884	−0.212442	−	0.977174i	$-0.568142\pi$
$359$	−8.05040	−0.424884	−0.212442	+	0.977174i	$0.568142\pi$
$360$	−11.4470	−0.603307
$361$	−8.10715	−0.426692
$362$	25.9423	1.36350
$363$	−26.7496	−1.40399
$364$	−16.8707	−0.884266
$365$	19.6053	1.02619
$366$	52.8238	2.76114
$367$	16.1764	0.844402	0.422201	−	0.906502i	$-0.361258\pi$
$367$	16.1764	0.844402	0.422201	+	0.906502i	$0.361258\pi$
$368$	−16.8693	−0.879372
$369$	2.89935	0.150934
$370$	−3.69938	−0.192322
$371$	24.6224	1.27833
$372$	39.9219	2.06986
$373$	6.89791	0.357160	0.178580	−	0.983925i	$-0.442850\pi$
$373$	6.89791	0.357160	0.178580	+	0.983925i	$0.442850\pi$
$374$	72.3960	3.74351
$375$	23.0201	1.18875
$376$	−35.2284	−1.81677
$377$	−4.85362	−0.249974
$378$	33.4671	1.72136
$379$	−25.2251	−1.29573	−0.647864	−	0.761756i	$-0.724338\pi$
$379$	−25.2251	−1.29573	−0.647864	+	0.761756i	$0.724338\pi$
$380$	20.2878	1.04074
$381$	5.15428	0.264062
$382$	−39.4919	−2.02058
$383$	27.1912	1.38940	0.694701	−	0.719298i	$-0.255536\pi$
$383$	27.1912	1.38940	0.694701	+	0.719298i	$0.255536\pi$
$384$	−22.2433	−1.13510
$385$	24.8484	1.26639
$386$	−28.1829	−1.43447
$387$	−11.9591	−0.607916
$388$	52.2371	2.65193
$389$	2.30112	0.116672	0.0583358	−	0.998297i	$-0.481421\pi$
$389$	2.30112	0.116672	0.0583358	+	0.998297i	$0.481421\pi$
$390$	7.21249	0.365219
$391$	−13.2921	−0.672212
$392$	−44.6682	−2.25609
$393$	8.14370	0.410795
$394$	−55.9374	−2.81808
$395$	−13.6284	−0.685722
$396$	−28.9000	−1.45228
$397$	11.1675	0.560481	0.280240	−	0.959930i	$-0.409586\pi$
$397$	11.1675	0.560481	0.280240	+	0.959930i	$0.409586\pi$
$398$	−18.2657	−0.915578
$399$	25.5931	1.28126
$400$	−23.1798	−1.15899
$401$	−35.3692	−1.76625	−0.883127	−	0.469133i	$-0.844566\pi$
$401$	−35.3692	−1.76625	−0.883127	+	0.469133i	$0.844566\pi$
$402$	20.6208	1.02847
$403$	−4.25817	−0.212114
$404$	38.8515	1.93293
$405$	−15.2625	−0.758402
$406$	−46.2824	−2.29695
$407$	−5.20377	−0.257941
$408$	77.3774	3.83075
$409$	11.2279	0.555182	0.277591	−	0.960699i	$-0.410464\pi$
$409$	11.2279	0.555182	0.277591	+	0.960699i	$0.410464\pi$
$410$	−7.69378	−0.379969
$411$	−34.2704	−1.69043
$412$	2.93575	0.144634
$413$	−7.78642	−0.383145
$414$	7.65588	0.376266
$415$	−17.7475	−0.871193
$416$	−5.95260	−0.291850
$417$	32.1126	1.57256
$418$	41.1758	2.01398
$419$	25.2443	1.23326	0.616631	−	0.787252i	$-0.288497\pi$
$419$	25.2443	1.23326	0.616631	+	0.787252i	$0.288497\pi$
$420$	47.6670	2.32591
$421$	−20.9770	−1.02236	−0.511179	−	0.859474i	$-0.670791\pi$
$421$	−20.9770	−1.02236	−0.511179	+	0.859474i	$0.670791\pi$
$422$	26.6286	1.29626
$423$	7.18072	0.349138
$424$	42.3399	2.05621
$425$	−18.2645	−0.885957
$426$	−18.2222	−0.882867
$427$	−37.2369	−1.80202
$428$	64.8216	3.13327
$429$	10.1455	0.489830
$430$	31.7350	1.53040
$431$	18.4094	0.886751	0.443375	−	0.896336i	$-0.353781\pi$
$431$	18.4094	0.886751	0.443375	+	0.896336i	$0.353781\pi$
$432$	25.8471	1.24357
$433$	4.44301	0.213517	0.106759	−	0.994285i	$-0.465953\pi$
$433$	4.44301	0.213517	0.106759	+	0.994285i	$0.465953\pi$
$434$	−40.6044	−1.94907
$435$	13.7135	0.657514
$436$	−37.1214	−1.77779
$437$	−7.56001	−0.361644
$438$	76.3307	3.64722
$439$	7.39785	0.353080	0.176540	−	0.984293i	$-0.443510\pi$
$439$	7.39785	0.353080	0.176540	+	0.984293i	$0.443510\pi$
$440$	42.7286	2.03700
$441$	9.10486	0.433565
$442$	−14.8130	−0.704584
$443$	−21.1177	−1.00333	−0.501667	−	0.865061i	$-0.667280\pi$
$443$	−21.1177	−1.00333	−0.501667	+	0.865061i	$0.667280\pi$
$444$	−9.98243	−0.473745
$445$	5.69102	0.269780
$446$	17.6691	0.836655
$447$	6.98436	0.330349
$448$	−1.74156	−0.0822809
$449$	−5.25241	−0.247876	−0.123938	−	0.992290i	$-0.539552\pi$
$449$	−5.25241	−0.247876	−0.123938	+	0.992290i	$0.539552\pi$
$450$	10.5198	0.495908
$451$	−10.8225	−0.509613
$452$	46.7913	2.20088
$453$	−5.33748	−0.250777
$454$	−51.2641	−2.40594
$455$	−5.08427	−0.238354
$456$	44.0091	2.06091
$457$	−24.7501	−1.15776	−0.578881	−	0.815412i	$-0.696510\pi$
$457$	−24.7501	−1.15776	−0.578881	+	0.815412i	$0.696510\pi$
$458$	−53.0509	−2.47891
$459$	20.3662	0.950614
$460$	−14.0805	−0.656505
$461$	8.69173	0.404814	0.202407	−	0.979301i	$-0.435124\pi$
$461$	8.69173	0.404814	0.202407	+	0.979301i	$0.435124\pi$
$462$	96.7440	4.50094
$463$	−3.42601	−0.159220	−0.0796101	−	0.996826i	$-0.525368\pi$
$463$	−3.42601	−0.159220	−0.0796101	+	0.996826i	$0.525368\pi$
$464$	−35.7446	−1.65940
$465$	12.0311	0.557931
$466$	43.4187	2.01133
$467$	−22.0391	−1.01985	−0.509924	−	0.860220i	$-0.670326\pi$
$467$	−22.0391	−1.01985	−0.509924	+	0.860220i	$0.670326\pi$
$468$	5.91326	0.273341
$469$	−14.5361	−0.671215
$470$	−19.0549	−0.878938
$471$	3.58457	0.165168
$472$	−13.3893	−0.616291
$473$	44.6404	2.05257
$474$	−53.0605	−2.43715
$475$	−10.3881	−0.476637
$476$	−97.8985	−4.48717
$477$	−8.63028	−0.395153
$478$	−49.9123	−2.28293
$479$	−23.5978	−1.07821	−0.539106	−	0.842238i	$-0.681238\pi$
$479$	−23.5978	−1.07821	−0.539106	+	0.842238i	$0.681238\pi$
$480$	16.8186	0.767663
$481$	1.06475	0.0485484
$482$	34.5004	1.57145
$483$	−17.7625	−0.808222
$484$	58.1967	2.64530
$485$	15.7425	0.714831
$486$	−32.5450	−1.47627
$487$	−34.1718	−1.54847	−0.774237	−	0.632896i	$-0.781866\pi$
$487$	−34.1718	−1.54847	−0.774237	+	0.632896i	$0.781866\pi$
$488$	−64.0313	−2.89856
$489$	2.96342	0.134010
$490$	−24.1609	−1.09148
$491$	42.6421	1.92441	0.962205	−	0.272326i	$-0.0877929\pi$
$491$	42.6421	1.92441	0.962205	+	0.272326i	$0.0877929\pi$
$492$	−20.7609	−0.935975
$493$	−28.1649	−1.26848
$494$	−8.42504	−0.379060
$495$	−8.70949	−0.391463
$496$	−31.3594	−1.40808
$497$	12.8453	0.576189
$498$	−69.0976	−3.09634
$499$	0.703466	0.0314915	0.0157457	−	0.999876i	$-0.494988\pi$
$499$	0.703466	0.0314915	0.0157457	+	0.999876i	$0.494988\pi$
$500$	−50.0829	−2.23977
$501$	−49.2654	−2.20102
$502$	11.4201	0.509703
$503$	−10.7356	−0.478677	−0.239338	−	0.970936i	$-0.576930\pi$
$503$	−10.7356	−0.478677	−0.239338	+	0.970936i	$0.576930\pi$
$504$	31.4165	1.39940
$505$	11.7085	0.521024
$506$	−28.5775	−1.27042
$507$	−2.07589	−0.0921934
$508$	−11.2137	−0.497528
$509$	−4.60768	−0.204232	−0.102116	−	0.994772i	$-0.532561\pi$
$509$	−4.60768	−0.204232	−0.102116	+	0.994772i	$0.532561\pi$
$510$	41.8531	1.85329
$511$	−53.8075	−2.38030
$512$	50.7730	2.24387
$513$	11.5835	0.511423
$514$	54.5329	2.40534
$515$	0.884738	0.0389862
$516$	85.6340	3.76982
$517$	−26.8038	−1.17883
$518$	10.1531	0.446100
$519$	49.7236	2.18262
$520$	−8.74275	−0.383395
$521$	33.9789	1.48864	0.744320	−	0.667823i	$-0.232774\pi$
$521$	33.9789	1.48864	0.744320	+	0.667823i	$0.232774\pi$
$522$	16.2222	0.710025
$523$	−6.64383	−0.290515	−0.145257	−	0.989394i	$-0.546401\pi$
$523$	−6.64383	−0.290515	−0.145257	+	0.989394i	$0.546401\pi$
$524$	−17.7175	−0.773993
$525$	−24.4071	−1.06521
$526$	48.7820	2.12700
$527$	−24.7096	−1.07637
$528$	74.7169	3.25163
$529$	−17.7531	−0.771873
$530$	22.9015	0.994778
$531$	2.72918	0.118436
$532$	−55.6806	−2.41406
$533$	2.21441	0.0959167
$534$	22.1572	0.958835
$535$	19.5351	0.844576
$536$	−24.9958	−1.07965
$537$	−12.9469	−0.558702
$538$	70.2156	3.02721
$539$	−33.9861	−1.46389
$540$	21.5741	0.928403
$541$	−13.8517	−0.595530	−0.297765	−	0.954639i	$-0.596241\pi$
$541$	−13.8517	−0.595530	−0.297765	+	0.954639i	$0.596241\pi$
$542$	11.0805	0.475947
$543$	21.0965	0.905338
$544$	−34.5422	−1.48098
$545$	−11.1871	−0.479205
$546$	−19.7949	−0.847144
$547$	7.34951	0.314242	0.157121	−	0.987579i	$-0.449779\pi$
$547$	7.34951	0.314242	0.157121	+	0.987579i	$0.449779\pi$
$548$	74.5590	3.18500
$549$	13.0517	0.557032
$550$	−39.2677	−1.67438
$551$	−16.0190	−0.682434
$552$	−30.5438	−1.30003
$553$	37.4037	1.59057
$554$	−55.4045	−2.35391
$555$	−3.00837	−0.127698
$556$	−69.8645	−2.96291
$557$	25.2031	1.06789	0.533945	−	0.845519i	$-0.320709\pi$
$557$	25.2031	1.06789	0.533945	+	0.845519i	$0.320709\pi$
$558$	14.2320	0.602489
$559$	−9.13392	−0.386324
$560$	−37.4432	−1.58227
$561$	58.8731	2.48562
$562$	6.97888	0.294386
$563$	4.75109	0.200235	0.100117	−	0.994976i	$-0.468078\pi$
$563$	4.75109	0.200235	0.100117	+	0.994976i	$0.468078\pi$
$564$	−51.4179	−2.16508
$565$	14.1013	0.593247
$566$	63.5396	2.67077
$567$	41.8885	1.75915
$568$	22.0883	0.926805
$569$	−38.6353	−1.61968	−0.809838	−	0.586654i	$-0.800445\pi$
$569$	−38.6353	−1.61968	−0.809838	+	0.586654i	$0.800445\pi$
$570$	23.8043	0.997054
$571$	−2.44392	−0.102275	−0.0511374	−	0.998692i	$-0.516285\pi$
$571$	−2.44392	−0.102275	−0.0511374	+	0.998692i	$0.516285\pi$
$572$	−22.0727	−0.922906
$573$	−32.1152	−1.34163
$574$	21.1158	0.881357
$575$	7.20968	0.300665
$576$	0.610424	0.0254343
$577$	−24.4592	−1.01825	−0.509125	−	0.860692i	$-0.670031\pi$
$577$	−24.4592	−1.01825	−0.509125	+	0.860692i	$0.670031\pi$
$578$	−42.5620	−1.77035
$579$	−22.9186	−0.952464
$580$	−29.8353	−1.23885
$581$	48.7087	2.02078
$582$	61.2913	2.54061
$583$	32.2146	1.33419
$584$	−92.5255	−3.82873
$585$	1.78206	0.0736791
$586$	−42.8924	−1.77187
$587$	5.84639	0.241306	0.120653	−	0.992695i	$-0.461501\pi$
$587$	5.84639	0.241306	0.120653	+	0.992695i	$0.461501\pi$
$588$	−65.1958	−2.68863
$589$	−14.0538	−0.579076
$590$	−7.24221	−0.298157
$591$	−45.4888	−1.87116
$592$	7.84137	0.322278
$593$	−24.0382	−0.987131	−0.493565	−	0.869709i	$-0.664307\pi$
$593$	−24.0382	−0.987131	−0.493565	+	0.869709i	$0.664307\pi$
$594$	43.7865	1.79658
$595$	−29.5034	−1.20952
$596$	−15.1953	−0.622422
$597$	−14.8539	−0.607928
$598$	5.84727	0.239113
$599$	−15.1623	−0.619513	−0.309757	−	0.950816i	$-0.600248\pi$
$599$	−15.1623	−0.619513	−0.309757	+	0.950816i	$0.600248\pi$
$600$	−41.9697	−1.71340
$601$	27.9902	1.14174	0.570871	−	0.821040i	$-0.306606\pi$
$601$	27.9902	1.14174	0.570871	+	0.821040i	$0.306606\pi$
$602$	−87.0978	−3.54984
$603$	5.09497	0.207483
$604$	11.6123	0.472497
$605$	17.5385	0.713043
$606$	45.5856	1.85179
$607$	−34.2677	−1.39088	−0.695441	−	0.718583i	$-0.744791\pi$
$607$	−34.2677	−1.39088	−0.695441	+	0.718583i	$0.744791\pi$
$608$	−19.6462	−0.796757
$609$	−37.6373	−1.52514
$610$	−34.6343	−1.40230
$611$	5.48436	0.221873
$612$	34.3139	1.38706
$613$	5.33028	0.215288	0.107644	−	0.994189i	$-0.465669\pi$
$613$	5.33028	0.215288	0.107644	+	0.994189i	$0.465669\pi$
$614$	−50.5312	−2.03927
$615$	−6.25666	−0.252293
$616$	−117.270	−4.72494
$617$	1.00000	0.0402585
$617$	1.00000	0.0402585
$618$	3.44461	0.138562
$619$	−31.4298	−1.26327	−0.631634	−	0.775266i	$-0.717616\pi$
$619$	−31.4298	−1.26327	−0.631634	+	0.775266i	$0.717616\pi$
$620$	−26.1751	−1.05122
$621$	−8.03933	−0.322607
$622$	−79.0261	−3.16866
$623$	−15.6192	−0.625769
$624$	−15.2879	−0.612006
$625$	0.644135	0.0257654
$626$	−67.7173	−2.70653
$627$	33.4846	1.33725
$628$	−7.79863	−0.311199
$629$	6.17860	0.246357
$630$	16.9931	0.677021
$631$	3.86645	0.153921	0.0769604	−	0.997034i	$-0.475479\pi$
$631$	3.86645	0.153921	0.0769604	+	0.997034i	$0.475479\pi$
$632$	64.3181	2.55844
$633$	21.6546	0.860693
$634$	−47.2657	−1.87716
$635$	−3.37944	−0.134109
$636$	61.7976	2.45043
$637$	6.95394	0.275525
$638$	−60.5532	−2.39733
$639$	−4.50233	−0.178109
$640$	14.5840	0.576482
$641$	22.1898	0.876445	0.438223	−	0.898867i	$-0.355608\pi$
$641$	22.1898	0.876445	0.438223	+	0.898867i	$0.355608\pi$
$642$	76.0572	3.00174
$643$	−7.13709	−0.281459	−0.140730	−	0.990048i	$-0.544945\pi$
$643$	−7.13709	−0.281459	−0.140730	+	0.990048i	$0.544945\pi$
$644$	38.6443	1.52280
$645$	25.8072	1.01616
$646$	−48.8894	−1.92353
$647$	23.8764	0.938677	0.469339	−	0.883018i	$-0.344492\pi$
$647$	23.8764	0.938677	0.469339	+	0.883018i	$0.344492\pi$
$648$	72.0301	2.82961
$649$	−10.1873	−0.399887
$650$	8.03462	0.315144
$651$	−33.0199	−1.29415
$652$	−6.44724	−0.252493
$653$	20.6710	0.808918	0.404459	−	0.914556i	$-0.367460\pi$
$653$	20.6710	0.808918	0.404459	+	0.914556i	$0.367460\pi$
$654$	−43.5556	−1.70316
$655$	−5.33947	−0.208630
$656$	16.3081	0.636723
$657$	18.8598	0.735789
$658$	52.2968	2.03874
$659$	21.0827	0.821264	0.410632	−	0.911801i	$-0.365308\pi$
$659$	21.0827	0.821264	0.410632	+	0.911801i	$0.365308\pi$
$660$	62.3648	2.42755
$661$	−7.64481	−0.297349	−0.148674	−	0.988886i	$-0.547501\pi$
$661$	−7.64481	−0.297349	−0.148674	+	0.988886i	$0.547501\pi$
$662$	−79.9722	−3.10821
$663$	−12.0461	−0.467832
$664$	83.7579	3.25044
$665$	−16.7803	−0.650712
$666$	−3.55869	−0.137897
$667$	11.1178	0.430482
$668$	107.182	4.14701
$669$	14.3687	0.555525
$670$	−13.5201	−0.522329
$671$	−48.7186	−1.88076
$672$	−46.1593	−1.78063
$673$	−34.1328	−1.31572	−0.657862	−	0.753138i	$-0.728539\pi$
$673$	−34.1328	−1.31572	−0.657862	+	0.753138i	$0.728539\pi$
$674$	53.6697	2.06728
$675$	−11.0467	−0.425187
$676$	4.51632	0.173705
$677$	−29.7101	−1.14185	−0.570926	−	0.821001i	$-0.693416\pi$
$677$	−29.7101	−1.14185	−0.570926	+	0.821001i	$0.693416\pi$
$678$	54.9016	2.10848
$679$	−43.2058	−1.65809
$680$	−50.7330	−1.94552
$681$	−41.6884	−1.59750
$682$	−53.1245	−2.03424
$683$	−15.5337	−0.594382	−0.297191	−	0.954818i	$-0.596050\pi$
$683$	−15.5337	−0.594382	−0.297191	+	0.954818i	$0.596050\pi$
$684$	19.5163	0.746225
$685$	22.4696	0.858520
$686$	−0.439186	−0.0167682
$687$	−43.1415	−1.64595
$688$	−67.2670	−2.56453
$689$	−6.59148	−0.251115
$690$	−16.5210	−0.628945
$691$	−37.8103	−1.43837	−0.719186	−	0.694817i	$-0.755485\pi$
$691$	−37.8103	−1.43837	−0.719186	+	0.694817i	$0.755485\pi$
$692$	−108.179	−4.11235
$693$	23.9035	0.908018
$694$	−65.4751	−2.48540
$695$	−21.0548	−0.798656
$696$	−64.7198	−2.45320
$697$	12.8499	0.486726
$698$	68.5374	2.59418
$699$	35.3085	1.33549
$700$	53.1004	2.00701
$701$	45.7661	1.72856	0.864280	−	0.503011i	$-0.167775\pi$
$701$	45.7661	1.72856	0.864280	+	0.503011i	$0.167775\pi$
$702$	−8.95920	−0.338143
$703$	3.51413	0.132538
$704$	−2.27856	−0.0858764
$705$	−15.4957	−0.583600
$706$	−24.2044	−0.910944
$707$	−32.1345	−1.20854
$708$	−19.5424	−0.734449
$709$	−6.20926	−0.233194	−0.116597	−	0.993179i	$-0.537199\pi$
$709$	−6.20926	−0.233194	−0.116597	+	0.993179i	$0.537199\pi$
$710$	11.9475	0.448381
$711$	−13.1102	−0.491670
$712$	−26.8582	−1.00655
$713$	9.75382	0.365283
$714$	−114.867	−4.29880
$715$	−6.65198	−0.248770
$716$	28.1675	1.05267
$717$	−40.5892	−1.51583
$718$	20.5503	0.766931
$719$	−35.1400	−1.31050	−0.655250	−	0.755412i	$-0.727437\pi$
$719$	−35.1400	−1.31050	−0.655250	+	0.755412i	$0.727437\pi$
$720$	13.1240	0.489103
$721$	−2.42819	−0.0904306
$722$	20.6952	0.770196
$723$	28.0561	1.04342
$724$	−45.8978	−1.70578
$725$	15.2767	0.567363
$726$	68.2839	2.53425
$727$	−17.2991	−0.641587	−0.320794	−	0.947149i	$-0.603950\pi$
$727$	−17.2991	−0.641587	−0.320794	+	0.947149i	$0.603950\pi$
$728$	23.9947	0.889304
$729$	7.17502	0.265741
$730$	−50.0467	−1.85231
$731$	−53.0029	−1.96038
$732$	−93.4573	−3.45428
$733$	11.0049	0.406473	0.203237	−	0.979130i	$-0.434854\pi$
$733$	11.0049	0.406473	0.203237	+	0.979130i	$0.434854\pi$
$734$	−41.2937	−1.52418
$735$	−19.6479	−0.724722
$736$	13.6351	0.502597
$737$	−19.0182	−0.700546
$738$	−7.40119	−0.272441
$739$	−14.3816	−0.529034	−0.264517	−	0.964381i	$-0.585213\pi$
$739$	−14.3816	−0.529034	−0.264517	+	0.964381i	$0.585213\pi$
$740$	6.54505	0.240601
$741$	−6.85132	−0.251690
$742$	−62.8539	−2.30744
$743$	−28.5428	−1.04713	−0.523567	−	0.851984i	$-0.675399\pi$
$743$	−28.5428	−1.04713	−0.523567	+	0.851984i	$0.675399\pi$
$744$	−56.7798	−2.08165
$745$	−4.57935	−0.167774
$746$	−17.6083	−0.644687
$747$	−17.0726	−0.624654
$748$	−128.085	−4.68325
$749$	−53.6147	−1.95904
$750$	−58.7637	−2.14575
$751$	35.2304	1.28557	0.642787	−	0.766045i	$-0.277778\pi$
$751$	35.2304	1.28557	0.642787	+	0.766045i	$0.277778\pi$
$752$	40.3897	1.47286
$753$	9.28692	0.338434
$754$	12.3899	0.451213
$755$	3.49955	0.127362
$756$	−59.2109	−2.15348
$757$	−17.5013	−0.636095	−0.318047	−	0.948075i	$-0.603027\pi$
$757$	−17.5013	−0.636095	−0.318047	+	0.948075i	$0.603027\pi$
$758$	64.3924	2.33884
$759$	−23.2395	−0.843539
$760$	−28.8548	−1.04667
$761$	−26.5406	−0.962094	−0.481047	−	0.876695i	$-0.659743\pi$
$761$	−26.5406	−0.962094	−0.481047	+	0.876695i	$0.659743\pi$
$762$	−13.1574	−0.476641
$763$	30.7035	1.11154
$764$	69.8702	2.52782
$765$	10.3411	0.373882
$766$	−69.4111	−2.50792
$767$	2.08444	0.0752648
$768$	58.7163	2.11874
$769$	−26.3614	−0.950617	−0.475309	−	0.879819i	$-0.657664\pi$
$769$	−26.3614	−0.950617	−0.475309	+	0.879819i	$0.657664\pi$
$770$	−63.4308	−2.28589
$771$	44.3467	1.59711
$772$	49.8619	1.79457
$773$	−1.44656	−0.0520290	−0.0260145	−	0.999662i	$-0.508282\pi$
$773$	−1.44656	−0.0520290	−0.0260145	+	0.999662i	$0.508282\pi$
$774$	30.5282	1.09731
$775$	13.4025	0.481433
$776$	−74.2953	−2.66705
$777$	8.25657	0.296203
$778$	−5.87410	−0.210597
$779$	7.30851	0.261854
$780$	−12.7605	−0.456901
$781$	16.8060	0.601367
$782$	33.9309	1.21337
$783$	−17.0347	−0.608770
$784$	51.2125	1.82902
$785$	−2.35025	−0.0838839
$786$	−20.7885	−0.741501
$787$	−14.2075	−0.506444	−0.253222	−	0.967408i	$-0.581490\pi$
$787$	−14.2075	−0.506444	−0.253222	+	0.967408i	$0.581490\pi$
$788$	98.9659	3.52551
$789$	39.6700	1.41229
$790$	34.7895	1.23775
$791$	−38.7015	−1.37607
$792$	41.1036	1.46055
$793$	9.96838	0.353988
$794$	−28.5074	−1.01169
$795$	18.6237	0.660516
$796$	32.3162	1.14542
$797$	2.33266	0.0826272	0.0413136	−	0.999146i	$-0.486846\pi$
$797$	2.33266	0.0826272	0.0413136	+	0.999146i	$0.486846\pi$
$798$	−65.3317	−2.31272
$799$	31.8250	1.12589
$800$	18.7358	0.662409
$801$	5.47459	0.193435
$802$	90.2873	3.18816
$803$	−70.3987	−2.48432
$804$	−36.4828	−1.28665
$805$	11.6461	0.410471
$806$	10.8699	0.382875
$807$	57.1000	2.01002
$808$	−55.2574	−1.94395
$809$	41.6494	1.46431	0.732157	−	0.681136i	$-0.238514\pi$
$809$	41.6494	1.46431	0.732157	+	0.681136i	$0.238514\pi$
$810$	38.9608	1.36894
$811$	9.19350	0.322828	0.161414	−	0.986887i	$-0.448395\pi$
$811$	9.19350	0.322828	0.161414	+	0.986887i	$0.448395\pi$
$812$	81.8840	2.87357
$813$	9.01074	0.316020
$814$	13.2837	0.465593
$815$	−1.94299	−0.0680598
$816$	−88.7138	−3.10560
$817$	−30.1459	−1.05467
$818$	−28.6615	−1.00213
$819$	−4.89092	−0.170903
$820$	13.6120	0.475353
$821$	49.0509	1.71189	0.855945	−	0.517068i	$-0.172976\pi$
$821$	49.0509	1.71189	0.855945	+	0.517068i	$0.172976\pi$
$822$	87.4824	3.05130
$823$	16.6587	0.580686	0.290343	−	0.956923i	$-0.406231\pi$
$823$	16.6587	0.580686	0.290343	+	0.956923i	$0.406231\pi$
$824$	−4.17544	−0.145458
$825$	−31.9329	−1.11176
$826$	19.8765	0.691591
$827$	−22.4839	−0.781841	−0.390920	−	0.920424i	$-0.627843\pi$
$827$	−22.4839	−0.781841	−0.390920	+	0.920424i	$0.627843\pi$
$828$	−13.5450	−0.470721
$829$	−3.29885	−0.114574	−0.0572870	−	0.998358i	$-0.518245\pi$
$829$	−3.29885	−0.114574	−0.0572870	+	0.998358i	$0.518245\pi$
$830$	45.3043	1.57254
$831$	−45.0555	−1.56296
$832$	0.466219	0.0161632
$833$	40.3528	1.39814
$834$	−81.9741	−2.83853
$835$	32.3012	1.11783
$836$	−72.8494	−2.51955
$837$	−14.9448	−0.516569
$838$	−64.4412	−2.22609
$839$	50.9527	1.75908	0.879542	−	0.475822i	$-0.157849\pi$
$839$	50.9527	1.75908	0.879542	+	0.475822i	$0.157849\pi$
$840$	−67.7954	−2.33916
$841$	−5.44238	−0.187668
$842$	53.5483	1.84539
$843$	5.67530	0.195468
$844$	−47.1120	−1.62166
$845$	1.36107	0.0468222
$846$	−18.3303	−0.630208
$847$	−48.1351	−1.65394
$848$	−48.5431	−1.66698
$849$	51.6710	1.77335
$850$	46.6239	1.59919
$851$	−2.43893	−0.0836054
$852$	32.2392	1.10450
$853$	12.3854	0.424069	0.212034	−	0.977262i	$-0.431991\pi$
$853$	12.3854	0.424069	0.212034	+	0.977262i	$0.431991\pi$
$854$	95.0549	3.25271
$855$	5.88157	0.201145
$856$	−92.1940	−3.15113
$857$	12.1022	0.413403	0.206702	−	0.978404i	$-0.433727\pi$
$857$	12.1022	0.413403	0.206702	+	0.978404i	$0.433727\pi$
$858$	−25.8986	−0.884162
$859$	−37.7943	−1.28952	−0.644762	−	0.764383i	$-0.723044\pi$
$859$	−37.7943	−1.28952	−0.644762	+	0.764383i	$0.723044\pi$
$860$	−56.1465	−1.91458
$861$	17.1716	0.585206
$862$	−46.9939	−1.60062
$863$	−4.44037	−0.151152	−0.0755760	−	0.997140i	$-0.524080\pi$
$863$	−4.44037	−0.151152	−0.0755760	+	0.997140i	$0.524080\pi$
$864$	−20.8918	−0.710752
$865$	−32.6016	−1.10849
$866$	−11.3417	−0.385407
$867$	−34.6118	−1.17548
$868$	71.8383	2.43835
$869$	48.9369	1.66007
$870$	−35.0067	−1.18684
$871$	3.89134	0.131853
$872$	52.7967	1.78792
$873$	15.1438	0.512541
$874$	19.2985	0.652782
$875$	41.4241	1.40039
$876$	−135.046	−4.56279
$877$	9.20474	0.310822	0.155411	−	0.987850i	$-0.450330\pi$
$877$	9.20474	0.310822	0.155411	+	0.987850i	$0.450330\pi$
$878$	−18.8846	−0.637323
$879$	−34.8805	−1.17649
$880$	−48.9886	−1.65141
$881$	9.42216	0.317441	0.158720	−	0.987324i	$-0.449263\pi$
$881$	9.42216	0.317441	0.158720	+	0.987324i	$0.449263\pi$
$882$	−23.2421	−0.782601
$883$	−16.4594	−0.553903	−0.276951	−	0.960884i	$-0.589324\pi$
$883$	−16.4594	−0.553903	−0.276951	+	0.960884i	$0.589324\pi$
$884$	26.2076	0.881458
$885$	−5.88943	−0.197971
$886$	53.9074	1.81105
$887$	−7.75556	−0.260406	−0.130203	−	0.991487i	$-0.541563\pi$
$887$	−7.75556	−0.260406	−0.130203	+	0.991487i	$0.541563\pi$
$888$	14.1977	0.476444
$889$	9.27497	0.311073
$890$	−14.5275	−0.486963
$891$	54.8046	1.83602
$892$	−31.2606	−1.04668
$893$	18.1007	0.605718
$894$	−17.8290	−0.596292
$895$	8.48875	0.283748
$896$	−40.0262	−1.33718
$897$	4.75506	0.158767
$898$	13.4079	0.447426
$899$	20.6675	0.689301
$900$	−18.6119	−0.620397
$901$	−38.2495	−1.27427
$902$	27.6267	0.919870
$903$	−70.8288	−2.35703
$904$	−66.5499	−2.21342
$905$	−13.8321	−0.459794
$906$	13.6250	0.452661
$907$	23.3230	0.774428	0.387214	−	0.921990i	$-0.373437\pi$
$907$	23.3230	0.774428	0.387214	+	0.921990i	$0.373437\pi$
$908$	90.6978	3.00991
$909$	11.2633	0.373579
$910$	12.9787	0.430239
$911$	−23.0399	−0.763346	−0.381673	−	0.924297i	$-0.624652\pi$
$911$	−23.0399	−0.763346	−0.381673	+	0.924297i	$0.624652\pi$
$912$	−50.4567	−1.67079
$913$	63.7277	2.10908
$914$	63.1798	2.08980
$915$	−28.1649	−0.931104
$916$	93.8592	3.10119
$917$	14.6543	0.483929
$918$	−51.9891	−1.71589
$919$	26.2708	0.866594	0.433297	−	0.901251i	$-0.357350\pi$
$919$	26.2708	0.866594	0.433297	+	0.901251i	$0.357350\pi$
$920$	20.0263	0.660246
$921$	−41.0925	−1.35404
$922$	−22.1874	−0.730705
$923$	−3.43870	−0.113186
$924$	−171.162	−5.63082
$925$	−3.35129	−0.110190
$926$	8.74560	0.287398
$927$	0.851092	0.0279535
$928$	28.8917	0.948415
$929$	−51.9540	−1.70456	−0.852278	−	0.523088i	$-0.824780\pi$
$929$	−51.9540	−1.70456	−0.852278	+	0.523088i	$0.824780\pi$
$930$	−30.7120	−1.00709
$931$	22.9510	0.752189
$932$	−76.8175	−2.51624
$933$	−64.2648	−2.10393
$934$	56.2594	1.84086
$935$	−38.6005	−1.26237
$936$	−8.41026	−0.274898
$937$	49.9266	1.63103	0.815515	−	0.578736i	$-0.196454\pi$
$937$	49.9266	1.63103	0.815515	+	0.578736i	$0.196454\pi$
$938$	37.1065	1.21157
$939$	−55.0684	−1.79709
$940$	33.7125	1.09958
$941$	−42.4897	−1.38513	−0.692563	−	0.721358i	$-0.743518\pi$
$941$	−42.4897	−1.38513	−0.692563	+	0.721358i	$0.743518\pi$
$942$	−9.15036	−0.298135
$943$	−5.07236	−0.165179
$944$	15.3509	0.499629
$945$	−17.8442	−0.580472
$946$	−113.954	−3.70496
$947$	−27.6213	−0.897571	−0.448785	−	0.893640i	$-0.648143\pi$
$947$	−27.6213	−0.897571	−0.448785	+	0.893640i	$0.648143\pi$
$948$	93.8760	3.04895
$949$	14.4044	0.467586
$950$	26.5177	0.860349
$951$	−38.4369	−1.24640
$952$	139.238	4.51274
$953$	9.71699	0.314764	0.157382	−	0.987538i	$-0.449695\pi$
$953$	9.71699	0.314764	0.157382	+	0.987538i	$0.449695\pi$
$954$	22.0306	0.713266
$955$	21.0566	0.681374
$956$	88.3062	2.85603
$957$	−49.2425	−1.59178
$958$	60.2384	1.94621
$959$	−61.6686	−1.99138
$960$	−1.31727	−0.0425146
$961$	−12.8680	−0.415097
$962$	−2.71799	−0.0876317
$963$	18.7922	0.605570
$964$	−61.0390	−1.96593
$965$	15.0267	0.483727
$966$	45.3425	1.45887
$967$	−33.7635	−1.08576	−0.542880	−	0.839810i	$-0.682666\pi$
$967$	−33.7635	−1.08576	−0.542880	+	0.839810i	$0.682666\pi$
$968$	−82.7715	−2.66038
$969$	−39.7573	−1.27719
$970$	−40.1861	−1.29030
$971$	14.3791	0.461448	0.230724	−	0.973019i	$-0.425891\pi$
$971$	14.3791	0.461448	0.230724	+	0.973019i	$0.425891\pi$
$972$	57.5795	1.84686
$973$	57.7857	1.85252
$974$	87.2308	2.79505
$975$	6.53383	0.209250
$976$	73.4123	2.34987
$977$	25.6326	0.820060	0.410030	−	0.912072i	$-0.365518\pi$
$977$	25.6326	0.820060	0.410030	+	0.912072i	$0.365518\pi$
$978$	−7.56474	−0.241894
$979$	−20.4352	−0.653113
$980$	42.7461	1.36547
$981$	−10.7617	−0.343595
$982$	−108.853	−3.47363
$983$	19.5646	0.624014	0.312007	−	0.950080i	$-0.398999\pi$
$983$	19.5646	0.624014	0.312007	+	0.950080i	$0.398999\pi$
$984$	29.5277	0.941308
$985$	29.8250	0.950305
$986$	71.8968	2.28966
$987$	42.5283	1.35369
$988$	14.9058	0.474217
$989$	20.9223	0.665290
$990$	22.2328	0.706605
$991$	−14.2308	−0.452055	−0.226028	−	0.974121i	$-0.572574\pi$
$991$	−14.2308	−0.452055	−0.226028	+	0.974121i	$0.572574\pi$
$992$	25.3472	0.804774
$993$	−65.0342	−2.06380
$994$	−32.7902	−1.04004
$995$	9.73904	0.308748
$996$	122.249	3.87362
$997$	−28.6632	−0.907772	−0.453886	−	0.891060i	$-0.649963\pi$
$997$	−28.6632	−0.907772	−0.453886	+	0.891060i	$0.649963\pi$
$998$	−1.79574	−0.0568433
$999$	3.73693	0.118231

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.a.1.6	✓	134

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.a.1.6	✓	134	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:	\( N \)	\(=\)	\( 8021 = 13 \cdot 617 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.55271 q^{2} -2.07589 q^{3} +4.51632 q^{4} +1.36107 q^{5} +5.29914 q^{6} -3.73550 q^{7} -6.42344 q^{8} +1.30931 q^{9} +O(q^{10})\)	\(q-2.55271 q^{2} -2.07589 q^{3} +4.51632 q^{4} +1.36107 q^{5} +5.29914 q^{6} -3.73550 q^{7} -6.42344 q^{8} +1.30931 q^{9} -3.47441 q^{10} -4.88732 q^{11} -9.37538 q^{12} +1.00000 q^{13} +9.53564 q^{14} -2.82543 q^{15} +7.36452 q^{16} +5.80287 q^{17} -3.34228 q^{18} +3.30043 q^{19} +6.14703 q^{20} +7.75447 q^{21} +12.4759 q^{22} -2.29061 q^{23} +13.3343 q^{24} -3.14749 q^{25} -2.55271 q^{26} +3.50968 q^{27} -16.8707 q^{28} -4.85362 q^{29} +7.21249 q^{30} -4.25817 q^{31} -5.95260 q^{32} +10.1455 q^{33} -14.8130 q^{34} -5.08427 q^{35} +5.91326 q^{36} +1.06475 q^{37} -8.42504 q^{38} -2.07589 q^{39} -8.74275 q^{40} +2.21441 q^{41} -19.7949 q^{42} -9.13392 q^{43} -22.0727 q^{44} +1.78206 q^{45} +5.84727 q^{46} +5.48436 q^{47} -15.2879 q^{48} +6.95394 q^{49} +8.03462 q^{50} -12.0461 q^{51} +4.51632 q^{52} -6.59148 q^{53} -8.95920 q^{54} -6.65198 q^{55} +23.9947 q^{56} -6.85132 q^{57} +12.3899 q^{58} +2.08444 q^{59} -12.7605 q^{60} +9.96838 q^{61} +10.8699 q^{62} -4.89092 q^{63} +0.466219 q^{64} +1.36107 q^{65} -25.8986 q^{66} +3.89134 q^{67} +26.2076 q^{68} +4.75506 q^{69} +12.9787 q^{70} -3.43870 q^{71} -8.41026 q^{72} +14.4044 q^{73} -2.71799 q^{74} +6.53383 q^{75} +14.9058 q^{76} +18.2566 q^{77} +5.29914 q^{78} -10.0130 q^{79} +10.0236 q^{80} -11.2136 q^{81} -5.65274 q^{82} -13.0394 q^{83} +35.0217 q^{84} +7.89811 q^{85} +23.3162 q^{86} +10.0756 q^{87} +31.3934 q^{88} +4.18128 q^{89} -4.54908 q^{90} -3.73550 q^{91} -10.3451 q^{92} +8.83948 q^{93} -14.0000 q^{94} +4.49212 q^{95} +12.3569 q^{96} +11.5663 q^{97} -17.7514 q^{98} -6.39901 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9}+O(q^{10}) \) 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9	\( 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9} - 33 q^{10} - 47 q^{11} - 53 q^{12} + 134 q^{13} - 28 q^{14} - 30 q^{15} + 30 q^{16} - 17 q^{17} - 14 q^{18} - 87 q^{19} - 12 q^{20} - 24 q^{21} - 52 q^{22} - 44 q^{23} - 36 q^{24} + 58 q^{25} - 6 q^{26} - 117 q^{27} - 71 q^{28} - 42 q^{29} - 21 q^{30} - 82 q^{31} - 31 q^{32} + 12 q^{33} - 30 q^{34} - 54 q^{35} + 32 q^{36} - 55 q^{37} - 12 q^{38} - 33 q^{39} - 86 q^{40} - 16 q^{41} + 6 q^{42} - 148 q^{43} - 54 q^{44} - 24 q^{45} - 57 q^{46} - 21 q^{47} - 82 q^{48} + 12 q^{49} - 17 q^{50} - 123 q^{51} + 98 q^{52} - 17 q^{53} - 10 q^{54} - 148 q^{55} - 47 q^{56} - q^{57} - 58 q^{58} - 64 q^{59} - 16 q^{60} - 112 q^{61} - 15 q^{62} - 58 q^{63} - 65 q^{64} - 8 q^{65} - 20 q^{66} - 110 q^{67} - 8 q^{68} - 57 q^{69} - 40 q^{70} - 78 q^{71} - 28 q^{72} - 43 q^{73} - 52 q^{74} - 150 q^{75} - 96 q^{76} - 24 q^{77} - 16 q^{78} - 228 q^{79} + 20 q^{80} + 54 q^{81} - 89 q^{82} - 12 q^{83} + 6 q^{84} - 77 q^{85} + 29 q^{86} - 77 q^{87} - 95 q^{88} - 32 q^{89} - 46 q^{90} - 32 q^{91} - 62 q^{92} - 9 q^{93} - 87 q^{94} - 61 q^{95} - 54 q^{96} - 38 q^{97} + 6 q^{98} - 193 q^{99}+O(q^{100}) \) 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9 - 33 * q^10 - 47 * q^11 - 53 * q^12 + 134 * q^13 - 28 * q^14 - 30 * q^15 + 30 * q^16 - 17 * q^17 - 14 * q^18 - 87 * q^19 - 12 * q^20 - 24 * q^21 - 52 * q^22 - 44 * q^23 - 36 * q^24 + 58 * q^25 - 6 * q^26 - 117 * q^27 - 71 * q^28 - 42 * q^29 - 21 * q^30 - 82 * q^31 - 31 * q^32 + 12 * q^33 - 30 * q^34 - 54 * q^35 + 32 * q^36 - 55 * q^37 - 12 * q^38 - 33 * q^39 - 86 * q^40 - 16 * q^41 + 6 * q^42 - 148 * q^43 - 54 * q^44 - 24 * q^45 - 57 * q^46 - 21 * q^47 - 82 * q^48 + 12 * q^49 - 17 * q^50 - 123 * q^51 + 98 * q^52 - 17 * q^53 - 10 * q^54 - 148 * q^55 - 47 * q^56 - q^57 - 58 * q^58 - 64 * q^59 - 16 * q^60 - 112 * q^61 - 15 * q^62 - 58 * q^63 - 65 * q^64 - 8 * q^65 - 20 * q^66 - 110 * q^67 - 8 * q^68 - 57 * q^69 - 40 * q^70 - 78 * q^71 - 28 * q^72 - 43 * q^73 - 52 * q^74 - 150 * q^75 - 96 * q^76 - 24 * q^77 - 16 * q^78 - 228 * q^79 + 20 * q^80 + 54 * q^81 - 89 * q^82 - 12 * q^83 + 6 * q^84 - 77 * q^85 + 29 * q^86 - 77 * q^87 - 95 * q^88 - 32 * q^89 - 46 * q^90 - 32 * q^91 - 62 * q^92 - 9 * q^93 - 87 * q^94 - 61 * q^95 - 54 * q^96 - 38 * q^97 + 6 * q^98 - 193 * q^99

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