LMFDB - Embedded newform 8030.2.a.q.1.1

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:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
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			1.1
Root			$-1.56155$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.56155 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.56155 q^{6} -0.438447 q^{7} +1.00000 q^{8} -0.561553 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.56155 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.56155 q^{6} -0.438447 q^{7} +1.00000 q^{8} -0.561553 q^{9} -1.00000 q^{10} +1.00000 q^{11} -1.56155 q^{12} -2.00000 q^{13} -0.438447 q^{14} +1.56155 q^{15} +1.00000 q^{16} -4.12311 q^{17} -0.561553 q^{18} +1.00000 q^{19} -1.00000 q^{20} +0.684658 q^{21} +1.00000 q^{22} +5.68466 q^{23} -1.56155 q^{24} +1.00000 q^{25} -2.00000 q^{26} +5.56155 q^{27} -0.438447 q^{28} -7.00000 q^{29} +1.56155 q^{30} +6.12311 q^{31} +1.00000 q^{32} -1.56155 q^{33} -4.12311 q^{34} +0.438447 q^{35} -0.561553 q^{36} +4.12311 q^{37} +1.00000 q^{38} +3.12311 q^{39} -1.00000 q^{40} +7.68466 q^{41} +0.684658 q^{42} +4.56155 q^{43} +1.00000 q^{44} +0.561553 q^{45} +5.68466 q^{46} +11.1231 q^{47} -1.56155 q^{48} -6.80776 q^{49} +1.00000 q^{50} +6.43845 q^{51} -2.00000 q^{52} -11.8078 q^{53} +5.56155 q^{54} -1.00000 q^{55} -0.438447 q^{56} -1.56155 q^{57} -7.00000 q^{58} -9.12311 q^{59} +1.56155 q^{60} -9.56155 q^{61} +6.12311 q^{62} +0.246211 q^{63} +1.00000 q^{64} +2.00000 q^{65} -1.56155 q^{66} -12.0000 q^{67} -4.12311 q^{68} -8.87689 q^{69} +0.438447 q^{70} +14.9309 q^{71} -0.561553 q^{72} -1.00000 q^{73} +4.12311 q^{74} -1.56155 q^{75} +1.00000 q^{76} -0.438447 q^{77} +3.12311 q^{78} -2.00000 q^{79} -1.00000 q^{80} -7.00000 q^{81} +7.68466 q^{82} +4.00000 q^{83} +0.684658 q^{84} +4.12311 q^{85} +4.56155 q^{86} +10.9309 q^{87} +1.00000 q^{88} +1.00000 q^{89} +0.561553 q^{90} +0.876894 q^{91} +5.68466 q^{92} -9.56155 q^{93} +11.1231 q^{94} -1.00000 q^{95} -1.56155 q^{96} -4.87689 q^{97} -6.80776 q^{98} -0.561553 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{5} + q^{6} - 5 q^{7} + 2 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + q^3 + 2 * q^4 - 2 * q^5 + q^6 - 5 * q^7 + 2 * q^8 + 3 * q^9	$ 2 q + 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{5} + q^{6} - 5 q^{7} + 2 q^{8} + 3 q^{9} - 2 q^{10} + 2 q^{11} + q^{12} - 4 q^{13} - 5 q^{14} - q^{15} + 2 q^{16} + 3 q^{18} + 2 q^{19} - 2 q^{20} - 11 q^{21} + 2 q^{22} - q^{23} + q^{24} + 2 q^{25} - 4 q^{26} + 7 q^{27} - 5 q^{28} - 14 q^{29} - q^{30} + 4 q^{31} + 2 q^{32} + q^{33} + 5 q^{35} + 3 q^{36} + 2 q^{38} - 2 q^{39} - 2 q^{40} + 3 q^{41} - 11 q^{42} + 5 q^{43} + 2 q^{44} - 3 q^{45} - q^{46} + 14 q^{47} + q^{48} + 7 q^{49} + 2 q^{50} + 17 q^{51} - 4 q^{52} - 3 q^{53} + 7 q^{54} - 2 q^{55} - 5 q^{56} + q^{57} - 14 q^{58} - 10 q^{59} - q^{60} - 15 q^{61} + 4 q^{62} - 16 q^{63} + 2 q^{64} + 4 q^{65} + q^{66} - 24 q^{67} - 26 q^{69} + 5 q^{70} + q^{71} + 3 q^{72} - 2 q^{73} + q^{75} + 2 q^{76} - 5 q^{77} - 2 q^{78} - 4 q^{79} - 2 q^{80} - 14 q^{81} + 3 q^{82} + 8 q^{83} - 11 q^{84} + 5 q^{86} - 7 q^{87} + 2 q^{88} + 2 q^{89} - 3 q^{90} + 10 q^{91} - q^{92} - 15 q^{93} + 14 q^{94} - 2 q^{95} + q^{96} - 18 q^{97} + 7 q^{98} + 3 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + q^3 + 2 * q^4 - 2 * q^5 + q^6 - 5 * q^7 + 2 * q^8 + 3 * q^9 - 2 * q^10 + 2 * q^11 + q^12 - 4 * q^13 - 5 * q^14 - q^15 + 2 * q^16 + 3 * q^18 + 2 * q^19 - 2 * q^20 - 11 * q^21 + 2 * q^22 - q^23 + q^24 + 2 * q^25 - 4 * q^26 + 7 * q^27 - 5 * q^28 - 14 * q^29 - q^30 + 4 * q^31 + 2 * q^32 + q^33 + 5 * q^35 + 3 * q^36 + 2 * q^38 - 2 * q^39 - 2 * q^40 + 3 * q^41 - 11 * q^42 + 5 * q^43 + 2 * q^44 - 3 * q^45 - q^46 + 14 * q^47 + q^48 + 7 * q^49 + 2 * q^50 + 17 * q^51 - 4 * q^52 - 3 * q^53 + 7 * q^54 - 2 * q^55 - 5 * q^56 + q^57 - 14 * q^58 - 10 * q^59 - q^60 - 15 * q^61 + 4 * q^62 - 16 * q^63 + 2 * q^64 + 4 * q^65 + q^66 - 24 * q^67 - 26 * q^69 + 5 * q^70 + q^71 + 3 * q^72 - 2 * q^73 + q^75 + 2 * q^76 - 5 * q^77 - 2 * q^78 - 4 * q^79 - 2 * q^80 - 14 * q^81 + 3 * q^82 + 8 * q^83 - 11 * q^84 + 5 * q^86 - 7 * q^87 + 2 * q^88 + 2 * q^89 - 3 * q^90 + 10 * q^91 - q^92 - 15 * q^93 + 14 * q^94 - 2 * q^95 + q^96 - 18 * q^97 + 7 * q^98 + 3 * 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
$3$	−1.56155	−0.901563	−0.450781	−	0.892634i	$-0.648855\pi$
$3$	−1.56155	−0.901563	−0.450781	+	0.892634i	$0.648855\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.56155	−0.637501
$7$	−0.438447	−0.165717	−0.0828587	−	0.996561i	$-0.526405\pi$
$7$	−0.438447	−0.165717	−0.0828587	+	0.996561i	$0.526405\pi$
$8$	1.00000	0.353553
$9$	−0.561553	−0.187184
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.56155	−0.450781
$13$	−2.00000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	−0.438447	−0.117180
$15$	1.56155	0.403191
$16$	1.00000	0.250000
$17$	−4.12311	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$17$	−4.12311	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$18$	−0.561553	−0.132359
$19$	1.00000	0.229416	0.114708	−	0.993399i	$-0.463407\pi$
$19$	1.00000	0.229416	0.114708	+	0.993399i	$0.463407\pi$
$20$	−1.00000	−0.223607
$21$	0.684658	0.149405
$22$	1.00000	0.213201
$23$	5.68466	1.18533	0.592667	−	0.805448i	$-0.298075\pi$
$23$	5.68466	1.18533	0.592667	+	0.805448i	$0.298075\pi$
$24$	−1.56155	−0.318751
$25$	1.00000	0.200000
$26$	−2.00000	−0.392232
$27$	5.56155	1.07032
$28$	−0.438447	−0.0828587
$29$	−7.00000	−1.29987	−0.649934	−	0.759991i	$-0.725203\pi$
$29$	−7.00000	−1.29987	−0.649934	+	0.759991i	$0.725203\pi$
$30$	1.56155	0.285099
$31$	6.12311	1.09974	0.549871	−	0.835250i	$-0.314677\pi$
$31$	6.12311	1.09974	0.549871	+	0.835250i	$0.314677\pi$
$32$	1.00000	0.176777
$33$	−1.56155	−0.271831
$34$	−4.12311	−0.707107
$35$	0.438447	0.0741111
$36$	−0.561553	−0.0935921
$37$	4.12311	0.677834	0.338917	−	0.940816i	$-0.389939\pi$
$37$	4.12311	0.677834	0.338917	+	0.940816i	$0.389939\pi$
$38$	1.00000	0.162221
$39$	3.12311	0.500097
$40$	−1.00000	−0.158114
$41$	7.68466	1.20014	0.600071	−	0.799947i	$-0.295139\pi$
$41$	7.68466	1.20014	0.600071	+	0.799947i	$0.295139\pi$
$42$	0.684658	0.105645
$43$	4.56155	0.695630	0.347815	−	0.937563i	$-0.386924\pi$
$43$	4.56155	0.695630	0.347815	+	0.937563i	$0.386924\pi$
$44$	1.00000	0.150756
$45$	0.561553	0.0837114
$46$	5.68466	0.838157
$47$	11.1231	1.62247	0.811236	−	0.584719i	$-0.198795\pi$
$47$	11.1231	1.62247	0.811236	+	0.584719i	$0.198795\pi$
$48$	−1.56155	−0.225391
$49$	−6.80776	−0.972538
$50$	1.00000	0.141421
$51$	6.43845	0.901563
$52$	−2.00000	−0.277350
$53$	−11.8078	−1.62192	−0.810961	−	0.585101i	$-0.801055\pi$
$53$	−11.8078	−1.62192	−0.810961	+	0.585101i	$0.801055\pi$
$54$	5.56155	0.756831
$55$	−1.00000	−0.134840
$56$	−0.438447	−0.0585900
$57$	−1.56155	−0.206833
$58$	−7.00000	−0.919145
$59$	−9.12311	−1.18773	−0.593864	−	0.804566i	$-0.702398\pi$
$59$	−9.12311	−1.18773	−0.593864	+	0.804566i	$0.702398\pi$
$60$	1.56155	0.201596
$61$	−9.56155	−1.22423	−0.612116	−	0.790768i	$-0.709681\pi$
$61$	−9.56155	−1.22423	−0.612116	+	0.790768i	$0.709681\pi$
$62$	6.12311	0.777635
$63$	0.246211	0.0310197
$64$	1.00000	0.125000
$65$	2.00000	0.248069
$66$	−1.56155	−0.192214
$67$	−12.0000	−1.46603	−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000	−1.46603	−0.733017	+	0.680211i	$0.761888\pi$
$68$	−4.12311	−0.500000
$69$	−8.87689	−1.06865
$70$	0.438447	0.0524045
$71$	14.9309	1.77197	0.885984	−	0.463716i	$-0.153484\pi$
$71$	14.9309	1.77197	0.885984	+	0.463716i	$0.153484\pi$
$72$	−0.561553	−0.0661796
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	4.12311	0.479301
$75$	−1.56155	−0.180313
$76$	1.00000	0.114708
$77$	−0.438447	−0.0499657
$78$	3.12311	0.353622
$79$	−2.00000	−0.225018	−0.112509	−	0.993651i	$-0.535889\pi$
$79$	−2.00000	−0.225018	−0.112509	+	0.993651i	$0.535889\pi$
$80$	−1.00000	−0.111803
$81$	−7.00000	−0.777778
$82$	7.68466	0.848629
$83$	4.00000	0.439057	0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000	0.439057	0.219529	+	0.975606i	$0.429548\pi$
$84$	0.684658	0.0747024
$85$	4.12311	0.447214
$86$	4.56155	0.491885
$87$	10.9309	1.17191
$88$	1.00000	0.106600
$89$	1.00000	0.106000	0.0529999	−	0.998595i	$-0.483122\pi$
$89$	1.00000	0.106000	0.0529999	+	0.998595i	$0.483122\pi$
$90$	0.561553	0.0591929
$91$	0.876894	0.0919235
$92$	5.68466	0.592667
$93$	−9.56155	−0.991487
$94$	11.1231	1.14726
$95$	−1.00000	−0.102598
$96$	−1.56155	−0.159375
$97$	−4.87689	−0.495174	−0.247587	−	0.968866i	$-0.579638\pi$
$97$	−4.87689	−0.495174	−0.247587	+	0.968866i	$0.579638\pi$
$98$	−6.80776	−0.687688
$99$	−0.561553	−0.0564382
$100$	1.00000	0.100000
$101$	−0.561553	−0.0558766	−0.0279383	−	0.999610i	$-0.508894\pi$
$101$	−0.561553	−0.0558766	−0.0279383	+	0.999610i	$0.508894\pi$
$102$	6.43845	0.637501
$103$	17.3693	1.71145	0.855725	−	0.517431i	$-0.173112\pi$
$103$	17.3693	1.71145	0.855725	+	0.517431i	$0.173112\pi$
$104$	−2.00000	−0.196116
$105$	−0.684658	−0.0668158
$106$	−11.8078	−1.14687
$107$	−11.6847	−1.12960	−0.564799	−	0.825228i	$-0.691046\pi$
$107$	−11.6847	−1.12960	−0.564799	+	0.825228i	$0.691046\pi$
$108$	5.56155	0.535161
$109$	2.00000	0.191565	0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000	0.191565	0.0957826	+	0.995402i	$0.469465\pi$
$110$	−1.00000	−0.0953463
$111$	−6.43845	−0.611110
$112$	−0.438447	−0.0414294
$113$	−10.0000	−0.940721	−0.470360	−	0.882474i	$-0.655876\pi$
$113$	−10.0000	−0.940721	−0.470360	+	0.882474i	$0.655876\pi$
$114$	−1.56155	−0.146253
$115$	−5.68466	−0.530097
$116$	−7.00000	−0.649934
$117$	1.12311	0.103831
$118$	−9.12311	−0.839850
$119$	1.80776	0.165717
$120$	1.56155	0.142550
$121$	1.00000	0.0909091
$122$	−9.56155	−0.865662
$123$	−12.0000	−1.08200
$124$	6.12311	0.549871
$125$	−1.00000	−0.0894427
$126$	0.246211	0.0219342
$127$	−13.9309	−1.23616	−0.618082	−	0.786113i	$-0.712090\pi$
$127$	−13.9309	−1.23616	−0.618082	+	0.786113i	$0.712090\pi$
$128$	1.00000	0.0883883
$129$	−7.12311	−0.627154
$130$	2.00000	0.175412
$131$	−20.6847	−1.80723	−0.903613	−	0.428349i	$-0.859095\pi$
$131$	−20.6847	−1.80723	−0.903613	+	0.428349i	$0.859095\pi$
$132$	−1.56155	−0.135916
$133$	−0.438447	−0.0380182
$134$	−12.0000	−1.03664
$135$	−5.56155	−0.478662
$136$	−4.12311	−0.353553
$137$	−18.0000	−1.53784	−0.768922	−	0.639343i	$-0.779207\pi$
$137$	−18.0000	−1.53784	−0.768922	+	0.639343i	$0.779207\pi$
$138$	−8.87689	−0.755651
$139$	−4.00000	−0.339276	−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000	−0.339276	−0.169638	+	0.985506i	$0.554260\pi$
$140$	0.438447	0.0370556
$141$	−17.3693	−1.46276
$142$	14.9309	1.25297
$143$	−2.00000	−0.167248
$144$	−0.561553	−0.0467961
$145$	7.00000	0.581318
$146$	−1.00000	−0.0827606
$147$	10.6307	0.876804
$148$	4.12311	0.338917
$149$	1.31534	0.107757	0.0538785	−	0.998547i	$-0.482842\pi$
$149$	1.31534	0.107757	0.0538785	+	0.998547i	$0.482842\pi$
$150$	−1.56155	−0.127500
$151$	0	0		−	1.00000i	$-0.5\pi$
$151$	0	0			1.00000i	$0.5\pi$
$152$	1.00000	0.0811107
$153$	2.31534	0.187184
$154$	−0.438447	−0.0353311
$155$	−6.12311	−0.491820
$156$	3.12311	0.250049
$157$	−14.6847	−1.17196	−0.585982	−	0.810324i	$-0.699291\pi$
$157$	−14.6847	−1.17196	−0.585982	+	0.810324i	$0.699291\pi$
$158$	−2.00000	−0.159111
$159$	18.4384	1.46226
$160$	−1.00000	−0.0790569
$161$	−2.49242	−0.196430
$162$	−7.00000	−0.549972
$163$	17.5616	1.37553	0.687763	−	0.725935i	$-0.258593\pi$
$163$	17.5616	1.37553	0.687763	+	0.725935i	$0.258593\pi$
$164$	7.68466	0.600071
$165$	1.56155	0.121567
$166$	4.00000	0.310460
$167$	−22.0540	−1.70659	−0.853294	−	0.521430i	$-0.825399\pi$
$167$	−22.0540	−1.70659	−0.853294	+	0.521430i	$0.825399\pi$
$168$	0.684658	0.0528225
$169$	−9.00000	−0.692308
$170$	4.12311	0.316228
$171$	−0.561553	−0.0429430
$172$	4.56155	0.347815
$173$	14.8078	1.12581	0.562907	−	0.826520i	$-0.309683\pi$
$173$	14.8078	1.12581	0.562907	+	0.826520i	$0.309683\pi$
$174$	10.9309	0.828667
$175$	−0.438447	−0.0331435
$176$	1.00000	0.0753778
$177$	14.2462	1.07081
$178$	1.00000	0.0749532
$179$	−2.00000	−0.149487	−0.0747435	−	0.997203i	$-0.523814\pi$
$179$	−2.00000	−0.149487	−0.0747435	+	0.997203i	$0.523814\pi$
$180$	0.561553	0.0418557
$181$	−10.2462	−0.761595	−0.380797	−	0.924658i	$-0.624350\pi$
$181$	−10.2462	−0.761595	−0.380797	+	0.924658i	$0.624350\pi$
$182$	0.876894	0.0649997
$183$	14.9309	1.10372
$184$	5.68466	0.419079
$185$	−4.12311	−0.303137
$186$	−9.56155	−0.701087
$187$	−4.12311	−0.301511
$188$	11.1231	0.811236
$189$	−2.43845	−0.177371
$190$	−1.00000	−0.0725476
$191$	12.4924	0.903920	0.451960	−	0.892038i	$-0.350725\pi$
$191$	12.4924	0.903920	0.451960	+	0.892038i	$0.350725\pi$
$192$	−1.56155	−0.112695
$193$	13.0000	0.935760	0.467880	−	0.883792i	$-0.345018\pi$
$193$	13.0000	0.935760	0.467880	+	0.883792i	$0.345018\pi$
$194$	−4.87689	−0.350141
$195$	−3.12311	−0.223650
$196$	−6.80776	−0.486269
$197$	23.1231	1.64745	0.823727	−	0.566987i	$-0.191891\pi$
$197$	23.1231	1.64745	0.823727	+	0.566987i	$0.191891\pi$
$198$	−0.561553	−0.0399078
$199$	−1.00000	−0.0708881	−0.0354441	−	0.999372i	$-0.511285\pi$
$199$	−1.00000	−0.0708881	−0.0354441	+	0.999372i	$0.511285\pi$
$200$	1.00000	0.0707107
$201$	18.7386	1.32172
$202$	−0.561553	−0.0395107
$203$	3.06913	0.215411
$204$	6.43845	0.450781
$205$	−7.68466	−0.536720
$206$	17.3693	1.21018
$207$	−3.19224	−0.221876
$208$	−2.00000	−0.138675
$209$	1.00000	0.0691714
$210$	−0.684658	−0.0472459
$211$	−16.1231	−1.10996	−0.554980	−	0.831864i	$-0.687274\pi$
$211$	−16.1231	−1.10996	−0.554980	+	0.831864i	$0.687274\pi$
$212$	−11.8078	−0.810961
$213$	−23.3153	−1.59754
$214$	−11.6847	−0.798747
$215$	−4.56155	−0.311095
$216$	5.56155	0.378416
$217$	−2.68466	−0.182246
$218$	2.00000	0.135457
$219$	1.56155	0.105520
$220$	−1.00000	−0.0674200
$221$	8.24621	0.554700
$222$	−6.43845	−0.432120
$223$	−17.6847	−1.18425	−0.592126	−	0.805845i	$-0.701711\pi$
$223$	−17.6847	−1.18425	−0.592126	+	0.805845i	$0.701711\pi$
$224$	−0.438447	−0.0292950
$225$	−0.561553	−0.0374369
$226$	−10.0000	−0.665190
$227$	12.0000	0.796468	0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000	0.796468	0.398234	+	0.917284i	$0.369623\pi$
$228$	−1.56155	−0.103416
$229$	0.315342	0.0208384	0.0104192	−	0.999946i	$-0.496683\pi$
$229$	0.315342	0.0208384	0.0104192	+	0.999946i	$0.496683\pi$
$230$	−5.68466	−0.374835
$231$	0.684658	0.0450472
$232$	−7.00000	−0.459573
$233$	16.0540	1.05173	0.525865	−	0.850568i	$-0.323742\pi$
$233$	16.0540	1.05173	0.525865	+	0.850568i	$0.323742\pi$
$234$	1.12311	0.0734197
$235$	−11.1231	−0.725591
$236$	−9.12311	−0.593864
$237$	3.12311	0.202868
$238$	1.80776	0.117180
$239$	4.56155	0.295062	0.147531	−	0.989057i	$-0.452867\pi$
$239$	4.56155	0.295062	0.147531	+	0.989057i	$0.452867\pi$
$240$	1.56155	0.100798
$241$	−9.36932	−0.603531	−0.301765	−	0.953382i	$-0.597576\pi$
$241$	−9.36932	−0.603531	−0.301765	+	0.953382i	$0.597576\pi$
$242$	1.00000	0.0642824
$243$	−5.75379	−0.369106
$244$	−9.56155	−0.612116
$245$	6.80776	0.434932
$246$	−12.0000	−0.765092
$247$	−2.00000	−0.127257
$248$	6.12311	0.388818
$249$	−6.24621	−0.395838
$250$	−1.00000	−0.0632456
$251$	−22.5616	−1.42407	−0.712036	−	0.702143i	$-0.752227\pi$
$251$	−22.5616	−1.42407	−0.712036	+	0.702143i	$0.752227\pi$
$252$	0.246211	0.0155099
$253$	5.68466	0.357391
$254$	−13.9309	−0.874101
$255$	−6.43845	−0.403191
$256$	1.00000	0.0625000
$257$	0.876894	0.0546992	0.0273496	−	0.999626i	$-0.491293\pi$
$257$	0.876894	0.0546992	0.0273496	+	0.999626i	$0.491293\pi$
$258$	−7.12311	−0.443465
$259$	−1.80776	−0.112329
$260$	2.00000	0.124035
$261$	3.93087	0.243315
$262$	−20.6847	−1.27790
$263$	7.80776	0.481447	0.240724	−	0.970594i	$-0.422615\pi$
$263$	7.80776	0.481447	0.240724	+	0.970594i	$0.422615\pi$
$264$	−1.56155	−0.0961069
$265$	11.8078	0.725345
$266$	−0.438447	−0.0268829
$267$	−1.56155	−0.0955655
$268$	−12.0000	−0.733017
$269$	−24.0000	−1.46331	−0.731653	−	0.681677i	$-0.761251\pi$
$269$	−24.0000	−1.46331	−0.731653	+	0.681677i	$0.761251\pi$
$270$	−5.56155	−0.338465
$271$	14.2462	0.865396	0.432698	−	0.901539i	$-0.357562\pi$
$271$	14.2462	0.865396	0.432698	+	0.901539i	$0.357562\pi$
$272$	−4.12311	−0.250000
$273$	−1.36932	−0.0828748
$274$	−18.0000	−1.08742
$275$	1.00000	0.0603023
$276$	−8.87689	−0.534326
$277$	−6.87689	−0.413193	−0.206596	−	0.978426i	$-0.566239\pi$
$277$	−6.87689	−0.413193	−0.206596	+	0.978426i	$0.566239\pi$
$278$	−4.00000	−0.239904
$279$	−3.43845	−0.205854
$280$	0.438447	0.0262022
$281$	−20.7386	−1.23716	−0.618582	−	0.785721i	$-0.712292\pi$
$281$	−20.7386	−1.23716	−0.618582	+	0.785721i	$0.712292\pi$
$282$	−17.3693	−1.03433
$283$	−2.87689	−0.171014	−0.0855068	−	0.996338i	$-0.527251\pi$
$283$	−2.87689	−0.171014	−0.0855068	+	0.996338i	$0.527251\pi$
$284$	14.9309	0.885984
$285$	1.56155	0.0924984
$286$	−2.00000	−0.118262
$287$	−3.36932	−0.198884
$288$	−0.561553	−0.0330898
$289$	0	0
$290$	7.00000	0.411054
$291$	7.61553	0.446430
$292$	−1.00000	−0.0585206
$293$	25.9309	1.51490	0.757449	−	0.652895i	$-0.226446\pi$
$293$	25.9309	1.51490	0.757449	+	0.652895i	$0.226446\pi$
$294$	10.6307	0.619994
$295$	9.12311	0.531168
$296$	4.12311	0.239651
$297$	5.56155	0.322714
$298$	1.31534	0.0761957
$299$	−11.3693	−0.657505
$300$	−1.56155	−0.0901563
$301$	−2.00000	−0.115278
$302$	0	0
$303$	0.876894	0.0503763
$304$	1.00000	0.0573539
$305$	9.56155	0.547493
$306$	2.31534	0.132359
$307$	−2.56155	−0.146196	−0.0730978	−	0.997325i	$-0.523289\pi$
$307$	−2.56155	−0.146196	−0.0730978	+	0.997325i	$0.523289\pi$
$308$	−0.438447	−0.0249828
$309$	−27.1231	−1.54298
$310$	−6.12311	−0.347769
$311$	−21.8078	−1.23660	−0.618302	−	0.785940i	$-0.712179\pi$
$311$	−21.8078	−1.23660	−0.618302	+	0.785940i	$0.712179\pi$
$312$	3.12311	0.176811
$313$	−27.3002	−1.54310	−0.771549	−	0.636170i	$-0.780518\pi$
$313$	−27.3002	−1.54310	−0.771549	+	0.636170i	$0.780518\pi$
$314$	−14.6847	−0.828703
$315$	−0.246211	−0.0138724
$316$	−2.00000	−0.112509
$317$	10.7538	0.603993	0.301996	−	0.953309i	$-0.402347\pi$
$317$	10.7538	0.603993	0.301996	+	0.953309i	$0.402347\pi$
$318$	18.4384	1.03398
$319$	−7.00000	−0.391925
$320$	−1.00000	−0.0559017
$321$	18.2462	1.01840
$322$	−2.49242	−0.138897
$323$	−4.12311	−0.229416
$324$	−7.00000	−0.388889
$325$	−2.00000	−0.110940
$326$	17.5616	0.972644
$327$	−3.12311	−0.172708
$328$	7.68466	0.424314
$329$	−4.87689	−0.268872
$330$	1.56155	0.0859607
$331$	−22.4924	−1.23630	−0.618148	−	0.786062i	$-0.712117\pi$
$331$	−22.4924	−1.23630	−0.618148	+	0.786062i	$0.712117\pi$
$332$	4.00000	0.219529
$333$	−2.31534	−0.126880
$334$	−22.0540	−1.20674
$335$	12.0000	0.655630
$336$	0.684658	0.0373512
$337$	3.63068	0.197776	0.0988880	−	0.995099i	$-0.468471\pi$
$337$	3.63068	0.197776	0.0988880	+	0.995099i	$0.468471\pi$
$338$	−9.00000	−0.489535
$339$	15.6155	0.848119
$340$	4.12311	0.223607
$341$	6.12311	0.331585
$342$	−0.561553	−0.0303653
$343$	6.05398	0.326884
$344$	4.56155	0.245942
$345$	8.87689	0.477916
$346$	14.8078	0.796070
$347$	22.8769	1.22810	0.614048	−	0.789269i	$-0.289540\pi$
$347$	22.8769	1.22810	0.614048	+	0.789269i	$0.289540\pi$
$348$	10.9309	0.585956
$349$	−10.4924	−0.561646	−0.280823	−	0.959760i	$-0.590607\pi$
$349$	−10.4924	−0.561646	−0.280823	+	0.959760i	$0.590607\pi$
$350$	−0.438447	−0.0234360
$351$	−11.1231	−0.593707
$352$	1.00000	0.0533002
$353$	−7.36932	−0.392229	−0.196115	−	0.980581i	$-0.562832\pi$
$353$	−7.36932	−0.392229	−0.196115	+	0.980581i	$0.562832\pi$
$354$	14.2462	0.757178
$355$	−14.9309	−0.792448
$356$	1.00000	0.0529999
$357$	−2.82292	−0.149405
$358$	−2.00000	−0.105703
$359$	10.0000	0.527780	0.263890	−	0.964553i	$-0.414994\pi$
$359$	10.0000	0.527780	0.263890	+	0.964553i	$0.414994\pi$
$360$	0.561553	0.0295964
$361$	−18.0000	−0.947368
$362$	−10.2462	−0.538529
$363$	−1.56155	−0.0819603
$364$	0.876894	0.0459618
$365$	1.00000	0.0523424
$366$	14.9309	0.780449
$367$	1.36932	0.0714778	0.0357389	−	0.999361i	$-0.488622\pi$
$367$	1.36932	0.0714778	0.0357389	+	0.999361i	$0.488622\pi$
$368$	5.68466	0.296333
$369$	−4.31534	−0.224648
$370$	−4.12311	−0.214350
$371$	5.17708	0.268781
$372$	−9.56155	−0.495743
$373$	17.6155	0.912097	0.456049	−	0.889955i	$-0.349264\pi$
$373$	17.6155	0.912097	0.456049	+	0.889955i	$0.349264\pi$
$374$	−4.12311	−0.213201
$375$	1.56155	0.0806382
$376$	11.1231	0.573630
$377$	14.0000	0.721037
$378$	−2.43845	−0.125420
$379$	−23.6155	−1.21305	−0.606524	−	0.795065i	$-0.707437\pi$
$379$	−23.6155	−1.21305	−0.606524	+	0.795065i	$0.707437\pi$
$380$	−1.00000	−0.0512989
$381$	21.7538	1.11448
$382$	12.4924	0.639168
$383$	−32.0000	−1.63512	−0.817562	−	0.575841i	$-0.804675\pi$
$383$	−32.0000	−1.63512	−0.817562	+	0.575841i	$0.804675\pi$
$384$	−1.56155	−0.0796877
$385$	0.438447	0.0223453
$386$	13.0000	0.661683
$387$	−2.56155	−0.130211
$388$	−4.87689	−0.247587
$389$	−26.8769	−1.36271	−0.681356	−	0.731952i	$-0.738610\pi$
$389$	−26.8769	−1.36271	−0.681356	+	0.731952i	$0.738610\pi$
$390$	−3.12311	−0.158145
$391$	−23.4384	−1.18533
$392$	−6.80776	−0.343844
$393$	32.3002	1.62933
$394$	23.1231	1.16493
$395$	2.00000	0.100631
$396$	−0.561553	−0.0282191
$397$	−24.7386	−1.24160	−0.620798	−	0.783970i	$-0.713191\pi$
$397$	−24.7386	−1.24160	−0.620798	+	0.783970i	$0.713191\pi$
$398$	−1.00000	−0.0501255
$399$	0.684658	0.0342758
$400$	1.00000	0.0500000
$401$	−1.00000	−0.0499376	−0.0249688	−	0.999688i	$-0.507949\pi$
$401$	−1.00000	−0.0499376	−0.0249688	+	0.999688i	$0.507949\pi$
$402$	18.7386	0.934598
$403$	−12.2462	−0.610027
$404$	−0.561553	−0.0279383
$405$	7.00000	0.347833
$406$	3.06913	0.152318
$407$	4.12311	0.204375
$408$	6.43845	0.318751
$409$	19.1231	0.945577	0.472788	−	0.881176i	$-0.343248\pi$
$409$	19.1231	0.945577	0.472788	+	0.881176i	$0.343248\pi$
$410$	−7.68466	−0.379518
$411$	28.1080	1.38646
$412$	17.3693	0.855725
$413$	4.00000	0.196827
$414$	−3.19224	−0.156890
$415$	−4.00000	−0.196352
$416$	−2.00000	−0.0980581
$417$	6.24621	0.305878
$418$	1.00000	0.0489116
$419$	−21.0540	−1.02855	−0.514277	−	0.857624i	$-0.671940\pi$
$419$	−21.0540	−1.02855	−0.514277	+	0.857624i	$0.671940\pi$
$420$	−0.684658	−0.0334079
$421$	−9.43845	−0.460002	−0.230001	−	0.973190i	$-0.573873\pi$
$421$	−9.43845	−0.460002	−0.230001	+	0.973190i	$0.573873\pi$
$422$	−16.1231	−0.784861
$423$	−6.24621	−0.303701
$424$	−11.8078	−0.573436
$425$	−4.12311	−0.200000
$426$	−23.3153	−1.12963
$427$	4.19224	0.202877
$428$	−11.6847	−0.564799
$429$	3.12311	0.150785
$430$	−4.56155	−0.219978
$431$	−2.56155	−0.123386	−0.0616928	−	0.998095i	$-0.519650\pi$
$431$	−2.56155	−0.123386	−0.0616928	+	0.998095i	$0.519650\pi$
$432$	5.56155	0.267580
$433$	2.87689	0.138255	0.0691274	−	0.997608i	$-0.477979\pi$
$433$	2.87689	0.138255	0.0691274	+	0.997608i	$0.477979\pi$
$434$	−2.68466	−0.128868
$435$	−10.9309	−0.524095
$436$	2.00000	0.0957826
$437$	5.68466	0.271934
$438$	1.56155	0.0746139
$439$	18.7386	0.894346	0.447173	−	0.894447i	$-0.352431\pi$
$439$	18.7386	0.894346	0.447173	+	0.894447i	$0.352431\pi$
$440$	−1.00000	−0.0476731
$441$	3.82292	0.182044
$442$	8.24621	0.392232
$443$	15.0540	0.715236	0.357618	−	0.933868i	$-0.383589\pi$
$443$	15.0540	0.715236	0.357618	+	0.933868i	$0.383589\pi$
$444$	−6.43845	−0.305555
$445$	−1.00000	−0.0474045
$446$	−17.6847	−0.837393
$447$	−2.05398	−0.0971497
$448$	−0.438447	−0.0207147
$449$	35.6155	1.68080	0.840400	−	0.541966i	$-0.182320\pi$
$449$	35.6155	1.68080	0.840400	+	0.541966i	$0.182320\pi$
$450$	−0.561553	−0.0264719
$451$	7.68466	0.361856
$452$	−10.0000	−0.470360
$453$	0	0
$454$	12.0000	0.563188
$455$	−0.876894	−0.0411094
$456$	−1.56155	−0.0731264
$457$	−14.6847	−0.686919	−0.343460	−	0.939167i	$-0.611599\pi$
$457$	−14.6847	−0.686919	−0.343460	+	0.939167i	$0.611599\pi$
$458$	0.315342	0.0147349
$459$	−22.9309	−1.07032
$460$	−5.68466	−0.265049
$461$	−36.4384	−1.69711	−0.848554	−	0.529109i	$-0.822526\pi$
$461$	−36.4384	−1.69711	−0.848554	+	0.529109i	$0.822526\pi$
$462$	0.684658	0.0318532
$463$	−0.492423	−0.0228848	−0.0114424	−	0.999935i	$-0.503642\pi$
$463$	−0.492423	−0.0228848	−0.0114424	+	0.999935i	$0.503642\pi$
$464$	−7.00000	−0.324967
$465$	9.56155	0.443406
$466$	16.0540	0.743686
$467$	−19.7386	−0.913395	−0.456698	−	0.889622i	$-0.650968\pi$
$467$	−19.7386	−0.913395	−0.456698	+	0.889622i	$0.650968\pi$
$468$	1.12311	0.0519156
$469$	5.26137	0.242947
$470$	−11.1231	−0.513071
$471$	22.9309	1.05660
$472$	−9.12311	−0.419925
$473$	4.56155	0.209740
$474$	3.12311	0.143449
$475$	1.00000	0.0458831
$476$	1.80776	0.0828587
$477$	6.63068	0.303598
$478$	4.56155	0.208641
$479$	−41.3693	−1.89021	−0.945106	−	0.326763i	$-0.894042\pi$
$479$	−41.3693	−1.89021	−0.945106	+	0.326763i	$0.894042\pi$
$480$	1.56155	0.0712748
$481$	−8.24621	−0.375995
$482$	−9.36932	−0.426761
$483$	3.89205	0.177094
$484$	1.00000	0.0454545
$485$	4.87689	0.221448
$486$	−5.75379	−0.260997
$487$	−20.1771	−0.914311	−0.457155	−	0.889387i	$-0.651132\pi$
$487$	−20.1771	−0.914311	−0.457155	+	0.889387i	$0.651132\pi$
$488$	−9.56155	−0.432831
$489$	−27.4233	−1.24012
$490$	6.80776	0.307543
$491$	20.9309	0.944597	0.472298	−	0.881439i	$-0.343424\pi$
$491$	20.9309	0.944597	0.472298	+	0.881439i	$0.343424\pi$
$492$	−12.0000	−0.541002
$493$	28.8617	1.29987
$494$	−2.00000	−0.0899843
$495$	0.561553	0.0252399
$496$	6.12311	0.274936
$497$	−6.54640	−0.293646
$498$	−6.24621	−0.279899
$499$	−35.6847	−1.59746	−0.798732	−	0.601686i	$-0.794496\pi$
$499$	−35.6847	−1.59746	−0.798732	+	0.601686i	$0.794496\pi$
$500$	−1.00000	−0.0447214
$501$	34.4384	1.53860
$502$	−22.5616	−1.00697
$503$	17.4384	0.777542	0.388771	−	0.921334i	$-0.372900\pi$
$503$	17.4384	0.777542	0.388771	+	0.921334i	$0.372900\pi$
$504$	0.246211	0.0109671
$505$	0.561553	0.0249888
$506$	5.68466	0.252714
$507$	14.0540	0.624159
$508$	−13.9309	−0.618082
$509$	−33.3693	−1.47907	−0.739534	−	0.673119i	$-0.764954\pi$
$509$	−33.3693	−1.47907	−0.739534	+	0.673119i	$0.764954\pi$
$510$	−6.43845	−0.285099
$511$	0.438447	0.0193958
$512$	1.00000	0.0441942
$513$	5.56155	0.245549
$514$	0.876894	0.0386782
$515$	−17.3693	−0.765384
$516$	−7.12311	−0.313577
$517$	11.1231	0.489194
$518$	−1.80776	−0.0794286
$519$	−23.1231	−1.01499
$520$	2.00000	0.0877058
$521$	−8.24621	−0.361273	−0.180637	−	0.983550i	$-0.557816\pi$
$521$	−8.24621	−0.361273	−0.180637	+	0.983550i	$0.557816\pi$
$522$	3.93087	0.172049
$523$	3.75379	0.164142	0.0820709	−	0.996626i	$-0.473847\pi$
$523$	3.75379	0.164142	0.0820709	+	0.996626i	$0.473847\pi$
$524$	−20.6847	−0.903613
$525$	0.684658	0.0298809
$526$	7.80776	0.340435
$527$	−25.2462	−1.09974
$528$	−1.56155	−0.0679579
$529$	9.31534	0.405015
$530$	11.8078	0.512896
$531$	5.12311	0.222324
$532$	−0.438447	−0.0190091
$533$	−15.3693	−0.665719
$534$	−1.56155	−0.0675750
$535$	11.6847	0.505172
$536$	−12.0000	−0.518321
$537$	3.12311	0.134772
$538$	−24.0000	−1.03471
$539$	−6.80776	−0.293231
$540$	−5.56155	−0.239331
$541$	−0.753789	−0.0324079	−0.0162040	−	0.999869i	$-0.505158\pi$
$541$	−0.753789	−0.0324079	−0.0162040	+	0.999869i	$0.505158\pi$
$542$	14.2462	0.611927
$543$	16.0000	0.686626
$544$	−4.12311	−0.176777
$545$	−2.00000	−0.0856706
$546$	−1.36932	−0.0586014
$547$	24.2462	1.03669	0.518347	−	0.855171i	$-0.326548\pi$
$547$	24.2462	1.03669	0.518347	+	0.855171i	$0.326548\pi$
$548$	−18.0000	−0.768922
$549$	5.36932	0.229157
$550$	1.00000	0.0426401
$551$	−7.00000	−0.298210
$552$	−8.87689	−0.377826
$553$	0.876894	0.0372893
$554$	−6.87689	−0.292171
$555$	6.43845	0.273297
$556$	−4.00000	−0.169638
$557$	−29.9309	−1.26821	−0.634106	−	0.773246i	$-0.718632\pi$
$557$	−29.9309	−1.26821	−0.634106	+	0.773246i	$0.718632\pi$
$558$	−3.43845	−0.145561
$559$	−9.12311	−0.385866
$560$	0.438447	0.0185278
$561$	6.43845	0.271831
$562$	−20.7386	−0.874806
$563$	−6.63068	−0.279450	−0.139725	−	0.990190i	$-0.544622\pi$
$563$	−6.63068	−0.279450	−0.139725	+	0.990190i	$0.544622\pi$
$564$	−17.3693	−0.731380
$565$	10.0000	0.420703
$566$	−2.87689	−0.120925
$567$	3.06913	0.128891
$568$	14.9309	0.626485
$569$	30.2462	1.26799	0.633994	−	0.773338i	$-0.281415\pi$
$569$	30.2462	1.26799	0.633994	+	0.773338i	$0.281415\pi$
$570$	1.56155	0.0654062
$571$	42.7926	1.79081	0.895407	−	0.445248i	$-0.146884\pi$
$571$	42.7926	1.79081	0.895407	+	0.445248i	$0.146884\pi$
$572$	−2.00000	−0.0836242
$573$	−19.5076	−0.814941
$574$	−3.36932	−0.140633
$575$	5.68466	0.237067
$576$	−0.561553	−0.0233980
$577$	−20.4233	−0.850233	−0.425116	−	0.905139i	$-0.639767\pi$
$577$	−20.4233	−0.850233	−0.425116	+	0.905139i	$0.639767\pi$
$578$	0	0
$579$	−20.3002	−0.843647
$580$	7.00000	0.290659
$581$	−1.75379	−0.0727594
$582$	7.61553	0.315674
$583$	−11.8078	−0.489028
$584$	−1.00000	−0.0413803
$585$	−1.12311	−0.0464347
$586$	25.9309	1.07119
$587$	−26.3002	−1.08552	−0.542762	−	0.839886i	$-0.682622\pi$
$587$	−26.3002	−1.08552	−0.542762	+	0.839886i	$0.682622\pi$
$588$	10.6307	0.438402
$589$	6.12311	0.252298
$590$	9.12311	0.375592
$591$	−36.1080	−1.48528
$592$	4.12311	0.169459
$593$	−28.2462	−1.15993	−0.579966	−	0.814640i	$-0.696934\pi$
$593$	−28.2462	−1.15993	−0.579966	+	0.814640i	$0.696934\pi$
$594$	5.56155	0.228193
$595$	−1.80776	−0.0741111
$596$	1.31534	0.0538785
$597$	1.56155	0.0639101
$598$	−11.3693	−0.464926
$599$	−3.63068	−0.148346	−0.0741728	−	0.997245i	$-0.523632\pi$
$599$	−3.63068	−0.148346	−0.0741728	+	0.997245i	$0.523632\pi$
$600$	−1.56155	−0.0637501
$601$	−5.36932	−0.219019	−0.109510	−	0.993986i	$-0.534928\pi$
$601$	−5.36932	−0.219019	−0.109510	+	0.993986i	$0.534928\pi$
$602$	−2.00000	−0.0815139
$603$	6.73863	0.274418
$604$	0	0
$605$	−1.00000	−0.0406558
$606$	0.876894	0.0356214
$607$	22.9309	0.930735	0.465368	−	0.885117i	$-0.345922\pi$
$607$	22.9309	0.930735	0.465368	+	0.885117i	$0.345922\pi$
$608$	1.00000	0.0405554
$609$	−4.79261	−0.194206
$610$	9.56155	0.387136
$611$	−22.2462	−0.899985
$612$	2.31534	0.0935921
$613$	−0.492423	−0.0198888	−0.00994438	−	0.999951i	$-0.503165\pi$
$613$	−0.492423	−0.0198888	−0.00994438	+	0.999951i	$0.503165\pi$
$614$	−2.56155	−0.103376
$615$	12.0000	0.483887
$616$	−0.438447	−0.0176655
$617$	38.1771	1.53695	0.768476	−	0.639879i	$-0.221016\pi$
$617$	38.1771	1.53695	0.768476	+	0.639879i	$0.221016\pi$
$618$	−27.1231	−1.09105
$619$	9.19224	0.369467	0.184734	−	0.982789i	$-0.440858\pi$
$619$	9.19224	0.369467	0.184734	+	0.982789i	$0.440858\pi$
$620$	−6.12311	−0.245910
$621$	31.6155	1.26869
$622$	−21.8078	−0.874412
$623$	−0.438447	−0.0175660
$624$	3.12311	0.125024
$625$	1.00000	0.0400000
$626$	−27.3002	−1.09113
$627$	−1.56155	−0.0623624
$628$	−14.6847	−0.585982
$629$	−17.0000	−0.677834
$630$	−0.246211	−0.00980929
$631$	43.9848	1.75101	0.875505	−	0.483210i	$-0.160529\pi$
$631$	43.9848	1.75101	0.875505	+	0.483210i	$0.160529\pi$
$632$	−2.00000	−0.0795557
$633$	25.1771	1.00070
$634$	10.7538	0.427088
$635$	13.9309	0.552830
$636$	18.4384	0.731132
$637$	13.6155	0.539467
$638$	−7.00000	−0.277133
$639$	−8.38447	−0.331685
$640$	−1.00000	−0.0395285
$641$	1.38447	0.0546834	0.0273417	−	0.999626i	$-0.491296\pi$
$641$	1.38447	0.0546834	0.0273417	+	0.999626i	$0.491296\pi$
$642$	18.2462	0.720121
$643$	−7.24621	−0.285763	−0.142881	−	0.989740i	$-0.545637\pi$
$643$	−7.24621	−0.285763	−0.142881	+	0.989740i	$0.545637\pi$
$644$	−2.49242	−0.0982152
$645$	7.12311	0.280472
$646$	−4.12311	−0.162221
$647$	0.876894	0.0344743	0.0172371	−	0.999851i	$-0.494513\pi$
$647$	0.876894	0.0344743	0.0172371	+	0.999851i	$0.494513\pi$
$648$	−7.00000	−0.274986
$649$	−9.12311	−0.358113
$650$	−2.00000	−0.0784465
$651$	4.19224	0.164307
$652$	17.5616	0.687763
$653$	37.8078	1.47953	0.739766	−	0.672864i	$-0.234936\pi$
$653$	37.8078	1.47953	0.739766	+	0.672864i	$0.234936\pi$
$654$	−3.12311	−0.122123
$655$	20.6847	0.808216
$656$	7.68466	0.300036
$657$	0.561553	0.0219083
$658$	−4.87689	−0.190121
$659$	15.0000	0.584317	0.292159	−	0.956370i	$-0.405627\pi$
$659$	15.0000	0.584317	0.292159	+	0.956370i	$0.405627\pi$
$660$	1.56155	0.0607834
$661$	3.75379	0.146005	0.0730027	−	0.997332i	$-0.476742\pi$
$661$	3.75379	0.146005	0.0730027	+	0.997332i	$0.476742\pi$
$662$	−22.4924	−0.874193
$663$	−12.8769	−0.500097
$664$	4.00000	0.155230
$665$	0.438447	0.0170023
$666$	−2.31534	−0.0897177
$667$	−39.7926	−1.54078
$668$	−22.0540	−0.853294
$669$	27.6155	1.06768
$670$	12.0000	0.463600
$671$	−9.56155	−0.369120
$672$	0.684658	0.0264113
$673$	−28.1922	−1.08673	−0.543365	−	0.839496i	$-0.682850\pi$
$673$	−28.1922	−1.08673	−0.543365	+	0.839496i	$0.682850\pi$
$674$	3.63068	0.139849
$675$	5.56155	0.214064
$676$	−9.00000	−0.346154
$677$	28.8769	1.10983	0.554915	−	0.831907i	$-0.312751\pi$
$677$	28.8769	1.10983	0.554915	+	0.831907i	$0.312751\pi$
$678$	15.6155	0.599711
$679$	2.13826	0.0820589
$680$	4.12311	0.158114
$681$	−18.7386	−0.718066
$682$	6.12311	0.234466
$683$	36.2311	1.38634	0.693171	−	0.720773i	$-0.256213\pi$
$683$	36.2311	1.38634	0.693171	+	0.720773i	$0.256213\pi$
$684$	−0.561553	−0.0214715
$685$	18.0000	0.687745
$686$	6.05398	0.231142
$687$	−0.492423	−0.0187871
$688$	4.56155	0.173908
$689$	23.6155	0.899680
$690$	8.87689	0.337938
$691$	50.9848	1.93955	0.969777	−	0.243991i	$-0.0784568\pi$
$691$	50.9848	1.93955	0.969777	+	0.243991i	$0.0784568\pi$
$692$	14.8078	0.562907
$693$	0.246211	0.00935279
$694$	22.8769	0.868395
$695$	4.00000	0.151729
$696$	10.9309	0.414334
$697$	−31.6847	−1.20014
$698$	−10.4924	−0.397144
$699$	−25.0691	−0.948202
$700$	−0.438447	−0.0165717
$701$	23.9848	0.905895	0.452948	−	0.891537i	$-0.350372\pi$
$701$	23.9848	0.905895	0.452948	+	0.891537i	$0.350372\pi$
$702$	−11.1231	−0.419815
$703$	4.12311	0.155506
$704$	1.00000	0.0376889
$705$	17.3693	0.654166
$706$	−7.36932	−0.277348
$707$	0.246211	0.00925973
$708$	14.2462	0.535405
$709$	−18.0000	−0.676004	−0.338002	−	0.941145i	$-0.609751\pi$
$709$	−18.0000	−0.676004	−0.338002	+	0.941145i	$0.609751\pi$
$710$	−14.9309	−0.560346
$711$	1.12311	0.0421198
$712$	1.00000	0.0374766
$713$	34.8078	1.30356
$714$	−2.82292	−0.105645
$715$	2.00000	0.0747958
$716$	−2.00000	−0.0747435
$717$	−7.12311	−0.266017
$718$	10.0000	0.373197
$719$	−15.0000	−0.559406	−0.279703	−	0.960087i	$-0.590236\pi$
$719$	−15.0000	−0.559406	−0.279703	+	0.960087i	$0.590236\pi$
$720$	0.561553	0.0209278
$721$	−7.61553	−0.283617
$722$	−18.0000	−0.669891
$723$	14.6307	0.544121
$724$	−10.2462	−0.380797
$725$	−7.00000	−0.259973
$726$	−1.56155	−0.0579547
$727$	−31.9309	−1.18425	−0.592125	−	0.805846i	$-0.701711\pi$
$727$	−31.9309	−1.18425	−0.592125	+	0.805846i	$0.701711\pi$
$728$	0.876894	0.0324999
$729$	29.9848	1.11055
$730$	1.00000	0.0370117
$731$	−18.8078	−0.695630
$732$	14.9309	0.551861
$733$	−46.1771	−1.70559	−0.852795	−	0.522246i	$-0.825094\pi$
$733$	−46.1771	−1.70559	−0.852795	+	0.522246i	$0.825094\pi$
$734$	1.36932	0.0505424
$735$	−10.6307	−0.392119
$736$	5.68466	0.209539
$737$	−12.0000	−0.442026
$738$	−4.31534	−0.158850
$739$	25.7538	0.947368	0.473684	−	0.880695i	$-0.342924\pi$
$739$	25.7538	0.947368	0.473684	+	0.880695i	$0.342924\pi$
$740$	−4.12311	−0.151568
$741$	3.12311	0.114730
$742$	5.17708	0.190057
$743$	−44.3002	−1.62522	−0.812608	−	0.582810i	$-0.801953\pi$
$743$	−44.3002	−1.62522	−0.812608	+	0.582810i	$0.801953\pi$
$744$	−9.56155	−0.350544
$745$	−1.31534	−0.0481904
$746$	17.6155	0.644950
$747$	−2.24621	−0.0821846
$748$	−4.12311	−0.150756
$749$	5.12311	0.187194
$750$	1.56155	0.0570198
$751$	−5.56155	−0.202944	−0.101472	−	0.994838i	$-0.532355\pi$
$751$	−5.56155	−0.202944	−0.101472	+	0.994838i	$0.532355\pi$
$752$	11.1231	0.405618
$753$	35.2311	1.28389
$754$	14.0000	0.509850
$755$	0	0
$756$	−2.43845	−0.0886855
$757$	15.7538	0.572581	0.286291	−	0.958143i	$-0.407578\pi$
$757$	15.7538	0.572581	0.286291	+	0.958143i	$0.407578\pi$
$758$	−23.6155	−0.857755
$759$	−8.87689	−0.322211
$760$	−1.00000	−0.0362738
$761$	6.38447	0.231437	0.115718	−	0.993282i	$-0.463083\pi$
$761$	6.38447	0.231437	0.115718	+	0.993282i	$0.463083\pi$
$762$	21.7538	0.788057
$763$	−0.876894	−0.0317457
$764$	12.4924	0.451960
$765$	−2.31534	−0.0837114
$766$	−32.0000	−1.15621
$767$	18.2462	0.658833
$768$	−1.56155	−0.0563477
$769$	0	0		−	1.00000i	$-0.5\pi$
$769$	0	0			1.00000i	$0.5\pi$
$770$	0.438447	0.0158005
$771$	−1.36932	−0.0493147
$772$	13.0000	0.467880
$773$	18.9309	0.680896	0.340448	−	0.940263i	$-0.389421\pi$
$773$	18.9309	0.680896	0.340448	+	0.940263i	$0.389421\pi$
$774$	−2.56155	−0.0920731
$775$	6.12311	0.219948
$776$	−4.87689	−0.175070
$777$	2.82292	0.101272
$778$	−26.8769	−0.963583
$779$	7.68466	0.275331
$780$	−3.12311	−0.111825
$781$	14.9309	0.534269
$782$	−23.4384	−0.838157
$783$	−38.9309	−1.39128
$784$	−6.80776	−0.243134
$785$	14.6847	0.524118
$786$	32.3002	1.15211
$787$	−28.6307	−1.02057	−0.510287	−	0.860004i	$-0.670461\pi$
$787$	−28.6307	−1.02057	−0.510287	+	0.860004i	$0.670461\pi$
$788$	23.1231	0.823727
$789$	−12.1922	−0.434055
$790$	2.00000	0.0711568
$791$	4.38447	0.155894
$792$	−0.561553	−0.0199539
$793$	19.1231	0.679081
$794$	−24.7386	−0.877941
$795$	−18.4384	−0.653944
$796$	−1.00000	−0.0354441
$797$	30.3153	1.07382	0.536912	−	0.843638i	$-0.319591\pi$
$797$	30.3153	1.07382	0.536912	+	0.843638i	$0.319591\pi$
$798$	0.684658	0.0242366
$799$	−45.8617	−1.62247
$800$	1.00000	0.0353553
$801$	−0.561553	−0.0198415
$802$	−1.00000	−0.0353112
$803$	−1.00000	−0.0352892
$804$	18.7386	0.660861
$805$	2.49242	0.0878464
$806$	−12.2462	−0.431354
$807$	37.4773	1.31926
$808$	−0.561553	−0.0197554
$809$	49.3002	1.73330	0.866651	−	0.498915i	$-0.166268\pi$
$809$	49.3002	1.73330	0.866651	+	0.498915i	$0.166268\pi$
$810$	7.00000	0.245955
$811$	−1.17708	−0.0413329	−0.0206665	−	0.999786i	$-0.506579\pi$
$811$	−1.17708	−0.0413329	−0.0206665	+	0.999786i	$0.506579\pi$
$812$	3.06913	0.107705
$813$	−22.2462	−0.780209
$814$	4.12311	0.144515
$815$	−17.5616	−0.615154
$816$	6.43845	0.225391
$817$	4.56155	0.159589
$818$	19.1231	0.668624
$819$	−0.492423	−0.0172066
$820$	−7.68466	−0.268360
$821$	15.1231	0.527800	0.263900	−	0.964550i	$-0.414991\pi$
$821$	15.1231	0.527800	0.263900	+	0.964550i	$0.414991\pi$
$822$	28.1080	0.980377
$823$	46.2462	1.61204	0.806021	−	0.591887i	$-0.201617\pi$
$823$	46.2462	1.61204	0.806021	+	0.591887i	$0.201617\pi$
$824$	17.3693	0.605089
$825$	−1.56155	−0.0543663
$826$	4.00000	0.139178
$827$	12.4924	0.434404	0.217202	−	0.976127i	$-0.430307\pi$
$827$	12.4924	0.434404	0.217202	+	0.976127i	$0.430307\pi$
$828$	−3.19224	−0.110938
$829$	−24.7386	−0.859208	−0.429604	−	0.903017i	$-0.641347\pi$
$829$	−24.7386	−0.859208	−0.429604	+	0.903017i	$0.641347\pi$
$830$	−4.00000	−0.138842
$831$	10.7386	0.372519
$832$	−2.00000	−0.0693375
$833$	28.0691	0.972538
$834$	6.24621	0.216289
$835$	22.0540	0.763209
$836$	1.00000	0.0345857
$837$	34.0540	1.17708
$838$	−21.0540	−0.727298
$839$	19.3693	0.668703	0.334352	−	0.942448i	$-0.391483\pi$
$839$	19.3693	0.668703	0.334352	+	0.942448i	$0.391483\pi$
$840$	−0.684658	−0.0236230
$841$	20.0000	0.689655
$842$	−9.43845	−0.325270
$843$	32.3845	1.11538
$844$	−16.1231	−0.554980
$845$	9.00000	0.309609
$846$	−6.24621	−0.214749
$847$	−0.438447	−0.0150652
$848$	−11.8078	−0.405480
$849$	4.49242	0.154180
$850$	−4.12311	−0.141421
$851$	23.4384	0.803460
$852$	−23.3153	−0.798770
$853$	−40.4233	−1.38407	−0.692034	−	0.721865i	$-0.743285\pi$
$853$	−40.4233	−1.38407	−0.692034	+	0.721865i	$0.743285\pi$
$854$	4.19224	0.143455
$855$	0.561553	0.0192047
$856$	−11.6847	−0.399373
$857$	−13.9460	−0.476387	−0.238194	−	0.971218i	$-0.576555\pi$
$857$	−13.9460	−0.476387	−0.238194	+	0.971218i	$0.576555\pi$
$858$	3.12311	0.106621
$859$	−10.2462	−0.349596	−0.174798	−	0.984604i	$-0.555927\pi$
$859$	−10.2462	−0.349596	−0.174798	+	0.984604i	$0.555927\pi$
$860$	−4.56155	−0.155548
$861$	5.26137	0.179307
$862$	−2.56155	−0.0872468
$863$	−35.1231	−1.19560	−0.597802	−	0.801644i	$-0.703959\pi$
$863$	−35.1231	−1.19560	−0.597802	+	0.801644i	$0.703959\pi$
$864$	5.56155	0.189208
$865$	−14.8078	−0.503479
$866$	2.87689	0.0977609
$867$	0	0
$868$	−2.68466	−0.0911232
$869$	−2.00000	−0.0678454
$870$	−10.9309	−0.370591
$871$	24.0000	0.813209
$872$	2.00000	0.0677285
$873$	2.73863	0.0926887
$874$	5.68466	0.192286
$875$	0.438447	0.0148222
$876$	1.56155	0.0527600
$877$	6.00000	0.202606	0.101303	−	0.994856i	$-0.467699\pi$
$877$	6.00000	0.202606	0.101303	+	0.994856i	$0.467699\pi$
$878$	18.7386	0.632398
$879$	−40.4924	−1.36578
$880$	−1.00000	−0.0337100
$881$	−17.8617	−0.601777	−0.300889	−	0.953659i	$-0.597283\pi$
$881$	−17.8617	−0.601777	−0.300889	+	0.953659i	$0.597283\pi$
$882$	3.82292	0.128724
$883$	−28.3002	−0.952377	−0.476189	−	0.879343i	$-0.657982\pi$
$883$	−28.3002	−0.952377	−0.476189	+	0.879343i	$0.657982\pi$
$884$	8.24621	0.277350
$885$	−14.2462	−0.478881
$886$	15.0540	0.505748
$887$	13.7538	0.461807	0.230904	−	0.972977i	$-0.425832\pi$
$887$	13.7538	0.461807	0.230904	+	0.972977i	$0.425832\pi$
$888$	−6.43845	−0.216060
$889$	6.10795	0.204854
$890$	−1.00000	−0.0335201
$891$	−7.00000	−0.234509
$892$	−17.6847	−0.592126
$893$	11.1231	0.372221
$894$	−2.05398	−0.0686952
$895$	2.00000	0.0668526
$896$	−0.438447	−0.0146475
$897$	17.7538	0.592782
$898$	35.6155	1.18851
$899$	−42.8617	−1.42952
$900$	−0.561553	−0.0187184
$901$	48.6847	1.62192
$902$	7.68466	0.255871
$903$	3.12311	0.103930
$904$	−10.0000	−0.332595
$905$	10.2462	0.340596
$906$	0	0
$907$	−45.1771	−1.50008	−0.750040	−	0.661392i	$-0.769966\pi$
$907$	−45.1771	−1.50008	−0.750040	+	0.661392i	$0.769966\pi$
$908$	12.0000	0.398234
$909$	0.315342	0.0104592
$910$	−0.876894	−0.0290688
$911$	−29.4233	−0.974837	−0.487419	−	0.873168i	$-0.662061\pi$
$911$	−29.4233	−0.974837	−0.487419	+	0.873168i	$0.662061\pi$
$912$	−1.56155	−0.0517082
$913$	4.00000	0.132381
$914$	−14.6847	−0.485725
$915$	−14.9309	−0.493599
$916$	0.315342	0.0104192
$917$	9.06913	0.299489
$918$	−22.9309	−0.756831
$919$	−33.6847	−1.11115	−0.555577	−	0.831465i	$-0.687503\pi$
$919$	−33.6847	−1.11115	−0.555577	+	0.831465i	$0.687503\pi$
$920$	−5.68466	−0.187418
$921$	4.00000	0.131804
$922$	−36.4384	−1.20004
$923$	−29.8617	−0.982911
$924$	0.684658	0.0225236
$925$	4.12311	0.135567
$926$	−0.492423	−0.0161820
$927$	−9.75379	−0.320356
$928$	−7.00000	−0.229786
$929$	−20.4384	−0.670564	−0.335282	−	0.942118i	$-0.608832\pi$
$929$	−20.4384	−0.670564	−0.335282	+	0.942118i	$0.608832\pi$
$930$	9.56155	0.313536
$931$	−6.80776	−0.223115
$932$	16.0540	0.525865
$933$	34.0540	1.11488
$934$	−19.7386	−0.645868
$935$	4.12311	0.134840
$936$	1.12311	0.0367099
$937$	−30.6307	−1.00066	−0.500330	−	0.865835i	$-0.666788\pi$
$937$	−30.6307	−1.00066	−0.500330	+	0.865835i	$0.666788\pi$
$938$	5.26137	0.171790
$939$	42.6307	1.39120
$940$	−11.1231	−0.362796
$941$	−41.6695	−1.35839	−0.679193	−	0.733959i	$-0.737670\pi$
$941$	−41.6695	−1.35839	−0.679193	+	0.733959i	$0.737670\pi$
$942$	22.9309	0.747128
$943$	43.6847	1.42257
$944$	−9.12311	−0.296932
$945$	2.43845	0.0793227
$946$	4.56155	0.148309
$947$	8.30019	0.269720	0.134860	−	0.990865i	$-0.456942\pi$
$947$	8.30019	0.269720	0.134860	+	0.990865i	$0.456942\pi$
$948$	3.12311	0.101434
$949$	2.00000	0.0649227
$950$	1.00000	0.0324443
$951$	−16.7926	−0.544538
$952$	1.80776	0.0585900
$953$	26.9309	0.872376	0.436188	−	0.899855i	$-0.356328\pi$
$953$	26.9309	0.872376	0.436188	+	0.899855i	$0.356328\pi$
$954$	6.63068	0.214676
$955$	−12.4924	−0.404245
$956$	4.56155	0.147531
$957$	10.9309	0.353345
$958$	−41.3693	−1.33658
$959$	7.89205	0.254848
$960$	1.56155	0.0503989
$961$	6.49242	0.209433
$962$	−8.24621	−0.265869
$963$	6.56155	0.211443
$964$	−9.36932	−0.301765
$965$	−13.0000	−0.418485
$966$	3.89205	0.125225
$967$	10.2614	0.329983	0.164992	−	0.986295i	$-0.447240\pi$
$967$	10.2614	0.329983	0.164992	+	0.986295i	$0.447240\pi$
$968$	1.00000	0.0321412
$969$	6.43845	0.206833
$970$	4.87689	0.156588
$971$	7.12311	0.228591	0.114296	−	0.993447i	$-0.463539\pi$
$971$	7.12311	0.228591	0.114296	+	0.993447i	$0.463539\pi$
$972$	−5.75379	−0.184553
$973$	1.75379	0.0562239
$974$	−20.1771	−0.646515
$975$	3.12311	0.100019
$976$	−9.56155	−0.306058
$977$	0.561553	0.0179657	0.00898283	−	0.999960i	$-0.497141\pi$
$977$	0.561553	0.0179657	0.00898283	+	0.999960i	$0.497141\pi$
$978$	−27.4233	−0.876900
$979$	1.00000	0.0319601
$980$	6.80776	0.217466
$981$	−1.12311	−0.0358580
$982$	20.9309	0.667931
$983$	35.2311	1.12370	0.561848	−	0.827240i	$-0.310091\pi$
$983$	35.2311	1.12370	0.561848	+	0.827240i	$0.310091\pi$
$984$	−12.0000	−0.382546
$985$	−23.1231	−0.736763
$986$	28.8617	0.919145
$987$	7.61553	0.242405
$988$	−2.00000	−0.0636285
$989$	25.9309	0.824554
$990$	0.561553	0.0178473
$991$	16.0000	0.508257	0.254128	−	0.967170i	$-0.418211\pi$
$991$	16.0000	0.508257	0.254128	+	0.967170i	$0.418211\pi$
$992$	6.12311	0.194409
$993$	35.1231	1.11460
$994$	−6.54640	−0.207639
$995$	1.00000	0.0317021
$996$	−6.24621	−0.197919
$997$	24.1771	0.765696	0.382848	−	0.923811i	$-0.374943\pi$
$997$	24.1771	0.765696	0.382848	+	0.923811i	$0.374943\pi$
$998$	−35.6847	−1.12958
$999$	22.9309	0.725501

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.q.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.q.1.1	✓	2	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.56155 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.56155 q^{6} -0.438447 q^{7} +1.00000 q^{8} -0.561553 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.56155 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.56155 q^{6} -0.438447 q^{7} +1.00000 q^{8} -0.561553 q^{9} -1.00000 q^{10} +1.00000 q^{11} -1.56155 q^{12} -2.00000 q^{13} -0.438447 q^{14} +1.56155 q^{15} +1.00000 q^{16} -4.12311 q^{17} -0.561553 q^{18} +1.00000 q^{19} -1.00000 q^{20} +0.684658 q^{21} +1.00000 q^{22} +5.68466 q^{23} -1.56155 q^{24} +1.00000 q^{25} -2.00000 q^{26} +5.56155 q^{27} -0.438447 q^{28} -7.00000 q^{29} +1.56155 q^{30} +6.12311 q^{31} +1.00000 q^{32} -1.56155 q^{33} -4.12311 q^{34} +0.438447 q^{35} -0.561553 q^{36} +4.12311 q^{37} +1.00000 q^{38} +3.12311 q^{39} -1.00000 q^{40} +7.68466 q^{41} +0.684658 q^{42} +4.56155 q^{43} +1.00000 q^{44} +0.561553 q^{45} +5.68466 q^{46} +11.1231 q^{47} -1.56155 q^{48} -6.80776 q^{49} +1.00000 q^{50} +6.43845 q^{51} -2.00000 q^{52} -11.8078 q^{53} +5.56155 q^{54} -1.00000 q^{55} -0.438447 q^{56} -1.56155 q^{57} -7.00000 q^{58} -9.12311 q^{59} +1.56155 q^{60} -9.56155 q^{61} +6.12311 q^{62} +0.246211 q^{63} +1.00000 q^{64} +2.00000 q^{65} -1.56155 q^{66} -12.0000 q^{67} -4.12311 q^{68} -8.87689 q^{69} +0.438447 q^{70} +14.9309 q^{71} -0.561553 q^{72} -1.00000 q^{73} +4.12311 q^{74} -1.56155 q^{75} +1.00000 q^{76} -0.438447 q^{77} +3.12311 q^{78} -2.00000 q^{79} -1.00000 q^{80} -7.00000 q^{81} +7.68466 q^{82} +4.00000 q^{83} +0.684658 q^{84} +4.12311 q^{85} +4.56155 q^{86} +10.9309 q^{87} +1.00000 q^{88} +1.00000 q^{89} +0.561553 q^{90} +0.876894 q^{91} +5.68466 q^{92} -9.56155 q^{93} +11.1231 q^{94} -1.00000 q^{95} -1.56155 q^{96} -4.87689 q^{97} -6.80776 q^{98} -0.561553 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{5} + q^{6} - 5 q^{7} + 2 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + q^3 + 2 * q^4 - 2 * q^5 + q^6 - 5 * q^7 + 2 * q^8 + 3 * q^9	\( 2 q + 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{5} + q^{6} - 5 q^{7} + 2 q^{8} + 3 q^{9} - 2 q^{10} + 2 q^{11} + q^{12} - 4 q^{13} - 5 q^{14} - q^{15} + 2 q^{16} + 3 q^{18} + 2 q^{19} - 2 q^{20} - 11 q^{21} + 2 q^{22} - q^{23} + q^{24} + 2 q^{25} - 4 q^{26} + 7 q^{27} - 5 q^{28} - 14 q^{29} - q^{30} + 4 q^{31} + 2 q^{32} + q^{33} + 5 q^{35} + 3 q^{36} + 2 q^{38} - 2 q^{39} - 2 q^{40} + 3 q^{41} - 11 q^{42} + 5 q^{43} + 2 q^{44} - 3 q^{45} - q^{46} + 14 q^{47} + q^{48} + 7 q^{49} + 2 q^{50} + 17 q^{51} - 4 q^{52} - 3 q^{53} + 7 q^{54} - 2 q^{55} - 5 q^{56} + q^{57} - 14 q^{58} - 10 q^{59} - q^{60} - 15 q^{61} + 4 q^{62} - 16 q^{63} + 2 q^{64} + 4 q^{65} + q^{66} - 24 q^{67} - 26 q^{69} + 5 q^{70} + q^{71} + 3 q^{72} - 2 q^{73} + q^{75} + 2 q^{76} - 5 q^{77} - 2 q^{78} - 4 q^{79} - 2 q^{80} - 14 q^{81} + 3 q^{82} + 8 q^{83} - 11 q^{84} + 5 q^{86} - 7 q^{87} + 2 q^{88} + 2 q^{89} - 3 q^{90} + 10 q^{91} - q^{92} - 15 q^{93} + 14 q^{94} - 2 q^{95} + q^{96} - 18 q^{97} + 7 q^{98} + 3 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + q^3 + 2 * q^4 - 2 * q^5 + q^6 - 5 * q^7 + 2 * q^8 + 3 * q^9 - 2 * q^10 + 2 * q^11 + q^12 - 4 * q^13 - 5 * q^14 - q^15 + 2 * q^16 + 3 * q^18 + 2 * q^19 - 2 * q^20 - 11 * q^21 + 2 * q^22 - q^23 + q^24 + 2 * q^25 - 4 * q^26 + 7 * q^27 - 5 * q^28 - 14 * q^29 - q^30 + 4 * q^31 + 2 * q^32 + q^33 + 5 * q^35 + 3 * q^36 + 2 * q^38 - 2 * q^39 - 2 * q^40 + 3 * q^41 - 11 * q^42 + 5 * q^43 + 2 * q^44 - 3 * q^45 - q^46 + 14 * q^47 + q^48 + 7 * q^49 + 2 * q^50 + 17 * q^51 - 4 * q^52 - 3 * q^53 + 7 * q^54 - 2 * q^55 - 5 * q^56 + q^57 - 14 * q^58 - 10 * q^59 - q^60 - 15 * q^61 + 4 * q^62 - 16 * q^63 + 2 * q^64 + 4 * q^65 + q^66 - 24 * q^67 - 26 * q^69 + 5 * q^70 + q^71 + 3 * q^72 - 2 * q^73 + q^75 + 2 * q^76 - 5 * q^77 - 2 * q^78 - 4 * q^79 - 2 * q^80 - 14 * q^81 + 3 * q^82 + 8 * q^83 - 11 * q^84 + 5 * q^86 - 7 * q^87 + 2 * q^88 + 2 * q^89 - 3 * q^90 + 10 * q^91 - q^92 - 15 * q^93 + 14 * q^94 - 2 * q^95 + q^96 - 18 * q^97 + 7 * q^98 + 3 * q^99

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