LMFDB - Embedded newform 8034.2.a.y.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8034,2,Mod(1,8034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, 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("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8034 = 2 \cdot 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8034.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:	$64.1518129839$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 5 x^{12} - 25 x^{11} + 134 x^{10} + 196 x^{9} - 1151 x^{8} - 801 x^{7} + 4263 x^{6} + \cdots - 180 $ x^13 - 5x^12 - 25x^11 + 134x^10 + 196x^9 - 1151x^8 - 801x^7 + 4263x^6 + 2205x^5 - 6840x^4 - 3579x^3 + 3559x^2 + 1839x - 180
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$3.49310$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.90785 q^{5} -1.00000 q^{6} +3.49310 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.90785 q^{5} -1.00000 q^{6} +3.49310 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.90785 q^{10} +1.79833 q^{11} -1.00000 q^{12} +1.00000 q^{13} +3.49310 q^{14} -2.90785 q^{15} +1.00000 q^{16} +4.53539 q^{17} +1.00000 q^{18} -3.14319 q^{19} +2.90785 q^{20} -3.49310 q^{21} +1.79833 q^{22} -8.15990 q^{23} -1.00000 q^{24} +3.45560 q^{25} +1.00000 q^{26} -1.00000 q^{27} +3.49310 q^{28} +6.89230 q^{29} -2.90785 q^{30} -3.14319 q^{31} +1.00000 q^{32} -1.79833 q^{33} +4.53539 q^{34} +10.1574 q^{35} +1.00000 q^{36} -1.41950 q^{37} -3.14319 q^{38} -1.00000 q^{39} +2.90785 q^{40} +10.9765 q^{41} -3.49310 q^{42} -6.04702 q^{43} +1.79833 q^{44} +2.90785 q^{45} -8.15990 q^{46} +0.558583 q^{47} -1.00000 q^{48} +5.20177 q^{49} +3.45560 q^{50} -4.53539 q^{51} +1.00000 q^{52} +2.33974 q^{53} -1.00000 q^{54} +5.22929 q^{55} +3.49310 q^{56} +3.14319 q^{57} +6.89230 q^{58} +4.35763 q^{59} -2.90785 q^{60} +9.67466 q^{61} -3.14319 q^{62} +3.49310 q^{63} +1.00000 q^{64} +2.90785 q^{65} -1.79833 q^{66} -13.7869 q^{67} +4.53539 q^{68} +8.15990 q^{69} +10.1574 q^{70} +14.3734 q^{71} +1.00000 q^{72} +8.34259 q^{73} -1.41950 q^{74} -3.45560 q^{75} -3.14319 q^{76} +6.28176 q^{77} -1.00000 q^{78} +6.31274 q^{79} +2.90785 q^{80} +1.00000 q^{81} +10.9765 q^{82} -3.92641 q^{83} -3.49310 q^{84} +13.1882 q^{85} -6.04702 q^{86} -6.89230 q^{87} +1.79833 q^{88} +11.8670 q^{89} +2.90785 q^{90} +3.49310 q^{91} -8.15990 q^{92} +3.14319 q^{93} +0.558583 q^{94} -9.13992 q^{95} -1.00000 q^{96} -15.0206 q^{97} +5.20177 q^{98} +1.79833 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 13 q^{2} - 13 q^{3} + 13 q^{4} + 3 q^{5} - 13 q^{6} + 5 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q + 13 * q^2 - 13 * q^3 + 13 * q^4 + 3 * q^5 - 13 * q^6 + 5 * q^7 + 13 * q^8 + 13 * q^9	\( 13 q + 13 q^{2} - 13 q^{3} + 13 q^{4} + 3 q^{5} - 13 q^{6} + 5 q^{7} + 13 q^{8} + 13 q^{9} + 3 q^{10} + 8 q^{11} - 13 q^{12} + 13 q^{13} + 5 q^{14} - 3 q^{15} + 13 q^{16} - q^{17} + 13 q^{18} + 5 q^{19} + 3 q^{20} - 5 q^{21} + 8 q^{22} - 9 q^{23} - 13 q^{24} + 24 q^{25} + 13 q^{26} - 13 q^{27} + 5 q^{28} - q^{29} - 3 q^{30} + 5 q^{31} + 13 q^{32} - 8 q^{33} - q^{34} + 28 q^{35} + 13 q^{36} + 35 q^{37} + 5 q^{38} - 13 q^{39} + 3 q^{40} + 24 q^{41} - 5 q^{42} + 9 q^{43} + 8 q^{44} + 3 q^{45} - 9 q^{46} - 8 q^{47} - 13 q^{48} - 16 q^{49} + 24 q^{50} + q^{51} + 13 q^{52} + 32 q^{53} - 13 q^{54} - 4 q^{55} + 5 q^{56} - 5 q^{57} - q^{58} + 12 q^{59} - 3 q^{60} + 17 q^{61} + 5 q^{62} + 5 q^{63} + 13 q^{64} + 3 q^{65} - 8 q^{66} + 20 q^{67} - q^{68} + 9 q^{69} + 28 q^{70} + 16 q^{71} + 13 q^{72} + 46 q^{73} + 35 q^{74} - 24 q^{75} + 5 q^{76} - 7 q^{77} - 13 q^{78} + 17 q^{79} + 3 q^{80} + 13 q^{81} + 24 q^{82} + 13 q^{83} - 5 q^{84} + 11 q^{85} + 9 q^{86} + q^{87} + 8 q^{88} + 14 q^{89} + 3 q^{90} + 5 q^{91} - 9 q^{92} - 5 q^{93} - 8 q^{94} + 2 q^{95} - 13 q^{96} + 46 q^{97} - 16 q^{98} + 8 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 - 13 * q^3 + 13 * q^4 + 3 * q^5 - 13 * q^6 + 5 * q^7 + 13 * q^8 + 13 * q^9 + 3 * q^10 + 8 * q^11 - 13 * q^12 + 13 * q^13 + 5 * q^14 - 3 * q^15 + 13 * q^16 - q^17 + 13 * q^18 + 5 * q^19 + 3 * q^20 - 5 * q^21 + 8 * q^22 - 9 * q^23 - 13 * q^24 + 24 * q^25 + 13 * q^26 - 13 * q^27 + 5 * q^28 - q^29 - 3 * q^30 + 5 * q^31 + 13 * q^32 - 8 * q^33 - q^34 + 28 * q^35 + 13 * q^36 + 35 * q^37 + 5 * q^38 - 13 * q^39 + 3 * q^40 + 24 * q^41 - 5 * q^42 + 9 * q^43 + 8 * q^44 + 3 * q^45 - 9 * q^46 - 8 * q^47 - 13 * q^48 - 16 * q^49 + 24 * q^50 + q^51 + 13 * q^52 + 32 * q^53 - 13 * q^54 - 4 * q^55 + 5 * q^56 - 5 * q^57 - q^58 + 12 * q^59 - 3 * q^60 + 17 * q^61 + 5 * q^62 + 5 * q^63 + 13 * q^64 + 3 * q^65 - 8 * q^66 + 20 * q^67 - q^68 + 9 * q^69 + 28 * q^70 + 16 * q^71 + 13 * q^72 + 46 * q^73 + 35 * q^74 - 24 * q^75 + 5 * q^76 - 7 * q^77 - 13 * q^78 + 17 * q^79 + 3 * q^80 + 13 * q^81 + 24 * q^82 + 13 * q^83 - 5 * q^84 + 11 * q^85 + 9 * q^86 + q^87 + 8 * q^88 + 14 * q^89 + 3 * q^90 + 5 * q^91 - 9 * q^92 - 5 * q^93 - 8 * q^94 + 2 * q^95 - 13 * q^96 + 46 * q^97 - 16 * q^98 + 8 * 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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	2.90785	1.30043	0.650215	−	0.759750i	$-0.274679\pi$
$5$	2.90785	1.30043	0.650215	+	0.759750i	$0.274679\pi$
$6$	−1.00000	−0.408248
$7$	3.49310	1.32027	0.660134	−	0.751148i	$-0.270499\pi$
$7$	3.49310	1.32027	0.660134	+	0.751148i	$0.270499\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	2.90785	0.919543
$11$	1.79833	0.542218	0.271109	−	0.962549i	$-0.412610\pi$
$11$	1.79833	0.542218	0.271109	+	0.962549i	$0.412610\pi$
$12$	−1.00000	−0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	3.49310	0.933571
$15$	−2.90785	−0.750804
$16$	1.00000	0.250000
$17$	4.53539	1.09999	0.549996	−	0.835167i	$-0.314629\pi$
$17$	4.53539	1.09999	0.549996	+	0.835167i	$0.314629\pi$
$18$	1.00000	0.235702
$19$	−3.14319	−0.721096	−0.360548	−	0.932741i	$-0.617410\pi$
$19$	−3.14319	−0.721096	−0.360548	+	0.932741i	$0.617410\pi$
$20$	2.90785	0.650215
$21$	−3.49310	−0.762257
$22$	1.79833	0.383406
$23$	−8.15990	−1.70146	−0.850728	−	0.525605i	$-0.823839\pi$
$23$	−8.15990	−1.70146	−0.850728	+	0.525605i	$0.823839\pi$
$24$	−1.00000	−0.204124
$25$	3.45560	0.691120
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	3.49310	0.660134
$29$	6.89230	1.27987	0.639934	−	0.768430i	$-0.278962\pi$
$29$	6.89230	1.27987	0.639934	+	0.768430i	$0.278962\pi$
$30$	−2.90785	−0.530899
$31$	−3.14319	−0.564533	−0.282266	−	0.959336i	$-0.591086\pi$
$31$	−3.14319	−0.564533	−0.282266	+	0.959336i	$0.591086\pi$
$32$	1.00000	0.176777
$33$	−1.79833	−0.313050
$34$	4.53539	0.777812
$35$	10.1574	1.71692
$36$	1.00000	0.166667
$37$	−1.41950	−0.233365	−0.116682	−	0.993169i	$-0.537226\pi$
$37$	−1.41950	−0.233365	−0.116682	+	0.993169i	$0.537226\pi$
$38$	−3.14319	−0.509892
$39$	−1.00000	−0.160128
$40$	2.90785	0.459772
$41$	10.9765	1.71425	0.857124	−	0.515109i	$-0.172249\pi$
$41$	10.9765	1.71425	0.857124	+	0.515109i	$0.172249\pi$
$42$	−3.49310	−0.538997
$43$	−6.04702	−0.922162	−0.461081	−	0.887358i	$-0.652538\pi$
$43$	−6.04702	−0.922162	−0.461081	+	0.887358i	$0.652538\pi$
$44$	1.79833	0.271109
$45$	2.90785	0.433477
$46$	−8.15990	−1.20311
$47$	0.558583	0.0814777	0.0407388	−	0.999170i	$-0.487029\pi$
$47$	0.558583	0.0814777	0.0407388	+	0.999170i	$0.487029\pi$
$48$	−1.00000	−0.144338
$49$	5.20177	0.743109
$50$	3.45560	0.488695
$51$	−4.53539	−0.635081
$52$	1.00000	0.138675
$53$	2.33974	0.321388	0.160694	−	0.987004i	$-0.448627\pi$
$53$	2.33974	0.321388	0.160694	+	0.987004i	$0.448627\pi$
$54$	−1.00000	−0.136083
$55$	5.22929	0.705117
$56$	3.49310	0.466785
$57$	3.14319	0.416325
$58$	6.89230	0.905004
$59$	4.35763	0.567316	0.283658	−	0.958926i	$-0.408452\pi$
$59$	4.35763	0.567316	0.283658	+	0.958926i	$0.408452\pi$
$60$	−2.90785	−0.375402
$61$	9.67466	1.23871	0.619357	−	0.785110i	$-0.287393\pi$
$61$	9.67466	1.23871	0.619357	+	0.785110i	$0.287393\pi$
$62$	−3.14319	−0.399185
$63$	3.49310	0.440090
$64$	1.00000	0.125000
$65$	2.90785	0.360675
$66$	−1.79833	−0.221360
$67$	−13.7869	−1.68434	−0.842169	−	0.539213i	$-0.818722\pi$
$67$	−13.7869	−1.68434	−0.842169	+	0.539213i	$0.818722\pi$
$68$	4.53539	0.549996
$69$	8.15990	0.982337
$70$	10.1574	1.21404
$71$	14.3734	1.70581	0.852905	−	0.522065i	$-0.174838\pi$
$71$	14.3734	1.70581	0.852905	+	0.522065i	$0.174838\pi$
$72$	1.00000	0.117851
$73$	8.34259	0.976426	0.488213	−	0.872725i	$-0.337649\pi$
$73$	8.34259	0.976426	0.488213	+	0.872725i	$0.337649\pi$
$74$	−1.41950	−0.165014
$75$	−3.45560	−0.399018
$76$	−3.14319	−0.360548
$77$	6.28176	0.715873
$78$	−1.00000	−0.113228
$79$	6.31274	0.710238	0.355119	−	0.934821i	$-0.384440\pi$
$79$	6.31274	0.710238	0.355119	+	0.934821i	$0.384440\pi$
$80$	2.90785	0.325108
$81$	1.00000	0.111111
$82$	10.9765	1.21216
$83$	−3.92641	−0.430980	−0.215490	−	0.976506i	$-0.569135\pi$
$83$	−3.92641	−0.430980	−0.215490	+	0.976506i	$0.569135\pi$
$84$	−3.49310	−0.381129
$85$	13.1882	1.43046
$86$	−6.04702	−0.652067
$87$	−6.89230	−0.738932
$88$	1.79833	0.191703
$89$	11.8670	1.25790	0.628949	−	0.777447i	$-0.283485\pi$
$89$	11.8670	1.25790	0.628949	+	0.777447i	$0.283485\pi$
$90$	2.90785	0.306514
$91$	3.49310	0.366177
$92$	−8.15990	−0.850728
$93$	3.14319	0.325933
$94$	0.558583	0.0576134
$95$	−9.13992	−0.937736
$96$	−1.00000	−0.102062
$97$	−15.0206	−1.52511	−0.762554	−	0.646925i	$-0.776055\pi$
$97$	−15.0206	−1.52511	−0.762554	+	0.646925i	$0.776055\pi$
$98$	5.20177	0.525458
$99$	1.79833	0.180739
$100$	3.45560	0.345560
$101$	−19.4452	−1.93487	−0.967434	−	0.253123i	$-0.918542\pi$
$101$	−19.4452	−1.93487	−0.967434	+	0.253123i	$0.918542\pi$
$102$	−4.53539	−0.449070
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.00000	0.0980581
$105$	−10.1574	−0.991263
$106$	2.33974	0.227255
$107$	−11.3678	−1.09897	−0.549484	−	0.835504i	$-0.685176\pi$
$107$	−11.3678	−1.09897	−0.549484	+	0.835504i	$0.685176\pi$
$108$	−1.00000	−0.0962250
$109$	12.7751	1.22364	0.611818	−	0.790999i	$-0.290439\pi$
$109$	12.7751	1.22364	0.611818	+	0.790999i	$0.290439\pi$
$110$	5.22929	0.498593
$111$	1.41950	0.134733
$112$	3.49310	0.330067
$113$	−10.2482	−0.964066	−0.482033	−	0.876153i	$-0.660101\pi$
$113$	−10.2482	−0.964066	−0.482033	+	0.876153i	$0.660101\pi$
$114$	3.14319	0.294386
$115$	−23.7278	−2.21263
$116$	6.89230	0.639934
$117$	1.00000	0.0924500
$118$	4.35763	0.401153
$119$	15.8426	1.45229
$120$	−2.90785	−0.265449
$121$	−7.76600	−0.706000
$122$	9.67466	0.875903
$123$	−10.9765	−0.989722
$124$	−3.14319	−0.282266
$125$	−4.49089	−0.401677
$126$	3.49310	0.311190
$127$	−10.6730	−0.947072	−0.473536	−	0.880775i	$-0.657023\pi$
$127$	−10.6730	−0.947072	−0.473536	+	0.880775i	$0.657023\pi$
$128$	1.00000	0.0883883
$129$	6.04702	0.532410
$130$	2.90785	0.255035
$131$	6.12299	0.534968	0.267484	−	0.963562i	$-0.413808\pi$
$131$	6.12299	0.534968	0.267484	+	0.963562i	$0.413808\pi$
$132$	−1.79833	−0.156525
$133$	−10.9795	−0.952041
$134$	−13.7869	−1.19101
$135$	−2.90785	−0.250268
$136$	4.53539	0.388906
$137$	−19.7578	−1.68802	−0.844010	−	0.536328i	$-0.819811\pi$
$137$	−19.7578	−1.68802	−0.844010	+	0.536328i	$0.819811\pi$
$138$	8.15990	0.694617
$139$	19.8446	1.68320	0.841600	−	0.540101i	$-0.181614\pi$
$139$	19.8446	1.68320	0.841600	+	0.540101i	$0.181614\pi$
$140$	10.1574	0.858459
$141$	−0.558583	−0.0470411
$142$	14.3734	1.20619
$143$	1.79833	0.150384
$144$	1.00000	0.0833333
$145$	20.0418	1.66438
$146$	8.34259	0.690437
$147$	−5.20177	−0.429034
$148$	−1.41950	−0.116682
$149$	23.1420	1.89587	0.947933	−	0.318469i	$-0.103169\pi$
$149$	23.1420	1.89587	0.947933	+	0.318469i	$0.103169\pi$
$150$	−3.45560	−0.282148
$151$	−3.79961	−0.309208	−0.154604	−	0.987977i	$-0.549410\pi$
$151$	−3.79961	−0.309208	−0.154604	+	0.987977i	$0.549410\pi$
$152$	−3.14319	−0.254946
$153$	4.53539	0.366664
$154$	6.28176	0.506199
$155$	−9.13992	−0.734136
$156$	−1.00000	−0.0800641
$157$	0.143199	0.0114285	0.00571426	−	0.999984i	$-0.498181\pi$
$157$	0.143199	0.0114285	0.00571426	+	0.999984i	$0.498181\pi$
$158$	6.31274	0.502214
$159$	−2.33974	−0.185553
$160$	2.90785	0.229886
$161$	−28.5034	−2.24638
$162$	1.00000	0.0785674
$163$	−2.40513	−0.188385	−0.0941924	−	0.995554i	$-0.530027\pi$
$163$	−2.40513	−0.188385	−0.0941924	+	0.995554i	$0.530027\pi$
$164$	10.9765	0.857124
$165$	−5.22929	−0.407099
$166$	−3.92641	−0.304749
$167$	−14.8835	−1.15172	−0.575859	−	0.817549i	$-0.695332\pi$
$167$	−14.8835	−1.15172	−0.575859	+	0.817549i	$0.695332\pi$
$168$	−3.49310	−0.269499
$169$	1.00000	0.0769231
$170$	13.1882	1.01149
$171$	−3.14319	−0.240365
$172$	−6.04702	−0.461081
$173$	8.94263	0.679896	0.339948	−	0.940444i	$-0.389591\pi$
$173$	8.94263	0.679896	0.339948	+	0.940444i	$0.389591\pi$
$174$	−6.89230	−0.522504
$175$	12.0708	0.912464
$176$	1.79833	0.135555
$177$	−4.35763	−0.327540
$178$	11.8670	0.889468
$179$	−19.1748	−1.43319	−0.716596	−	0.697488i	$-0.754301\pi$
$179$	−19.1748	−1.43319	−0.716596	+	0.697488i	$0.754301\pi$
$180$	2.90785	0.216738
$181$	21.6597	1.60995	0.804977	−	0.593306i	$-0.202178\pi$
$181$	21.6597	1.60995	0.804977	+	0.593306i	$0.202178\pi$
$182$	3.49310	0.258926
$183$	−9.67466	−0.715172
$184$	−8.15990	−0.601556
$185$	−4.12770	−0.303475
$186$	3.14319	0.230470
$187$	8.15614	0.596436
$188$	0.558583	0.0407388
$189$	−3.49310	−0.254086
$190$	−9.13992	−0.663079
$191$	22.2109	1.60713	0.803563	−	0.595220i	$-0.202935\pi$
$191$	22.2109	1.60713	0.803563	+	0.595220i	$0.202935\pi$
$192$	−1.00000	−0.0721688
$193$	−13.9238	−1.00226	−0.501128	−	0.865373i	$-0.667081\pi$
$193$	−13.9238	−1.00226	−0.501128	+	0.865373i	$0.667081\pi$
$194$	−15.0206	−1.07841
$195$	−2.90785	−0.208236
$196$	5.20177	0.371555
$197$	4.65380	0.331570	0.165785	−	0.986162i	$-0.446984\pi$
$197$	4.65380	0.331570	0.165785	+	0.986162i	$0.446984\pi$
$198$	1.79833	0.127802
$199$	−6.09436	−0.432018	−0.216009	−	0.976391i	$-0.569304\pi$
$199$	−6.09436	−0.432018	−0.216009	+	0.976391i	$0.569304\pi$
$200$	3.45560	0.244348
$201$	13.7869	0.972453
$202$	−19.4452	−1.36816
$203$	24.0755	1.68977
$204$	−4.53539	−0.317541
$205$	31.9182	2.22926
$206$	1.00000	0.0696733
$207$	−8.15990	−0.567152
$208$	1.00000	0.0693375
$209$	−5.65250	−0.390991
$210$	−10.1574	−0.700929
$211$	18.8312	1.29639	0.648196	−	0.761473i	$-0.275524\pi$
$211$	18.8312	1.29639	0.648196	+	0.761473i	$0.275524\pi$
$212$	2.33974	0.160694
$213$	−14.3734	−0.984850
$214$	−11.3678	−0.777087
$215$	−17.5838	−1.19921
$216$	−1.00000	−0.0680414
$217$	−10.9795	−0.745335
$218$	12.7751	0.865241
$219$	−8.34259	−0.563740
$220$	5.22929	0.352558
$221$	4.53539	0.305083
$222$	1.41950	0.0952707
$223$	−11.2457	−0.753066	−0.376533	−	0.926403i	$-0.622884\pi$
$223$	−11.2457	−0.753066	−0.376533	+	0.926403i	$0.622884\pi$
$224$	3.49310	0.233393
$225$	3.45560	0.230373
$226$	−10.2482	−0.681697
$227$	−13.9457	−0.925606	−0.462803	−	0.886461i	$-0.653156\pi$
$227$	−13.9457	−0.925606	−0.462803	+	0.886461i	$0.653156\pi$
$228$	3.14319	0.208163
$229$	−11.5990	−0.766482	−0.383241	−	0.923648i	$-0.625192\pi$
$229$	−11.5990	−0.766482	−0.383241	+	0.923648i	$0.625192\pi$
$230$	−23.7278	−1.56456
$231$	−6.28176	−0.413310
$232$	6.89230	0.452502
$233$	−2.17875	−0.142734	−0.0713672	−	0.997450i	$-0.522736\pi$
$233$	−2.17875	−0.142734	−0.0713672	+	0.997450i	$0.522736\pi$
$234$	1.00000	0.0653720
$235$	1.62428	0.105956
$236$	4.35763	0.283658
$237$	−6.31274	−0.410056
$238$	15.8426	1.02692
$239$	−19.8260	−1.28244	−0.641219	−	0.767358i	$-0.721571\pi$
$239$	−19.8260	−1.28244	−0.641219	+	0.767358i	$0.721571\pi$
$240$	−2.90785	−0.187701
$241$	−15.6492	−1.00805	−0.504027	−	0.863688i	$-0.668149\pi$
$241$	−15.6492	−1.00805	−0.504027	+	0.863688i	$0.668149\pi$
$242$	−7.76600	−0.499217
$243$	−1.00000	−0.0641500
$244$	9.67466	0.619357
$245$	15.1260	0.966362
$246$	−10.9765	−0.699839
$247$	−3.14319	−0.199996
$248$	−3.14319	−0.199593
$249$	3.92641	0.248826
$250$	−4.49089	−0.284029
$251$	−1.98335	−0.125188	−0.0625940	−	0.998039i	$-0.519937\pi$
$251$	−1.98335	−0.125188	−0.0625940	+	0.998039i	$0.519937\pi$
$252$	3.49310	0.220045
$253$	−14.6742	−0.922561
$254$	−10.6730	−0.669681
$255$	−13.1882	−0.825879
$256$	1.00000	0.0625000
$257$	15.0855	0.941008	0.470504	−	0.882398i	$-0.344072\pi$
$257$	15.0855	0.941008	0.470504	+	0.882398i	$0.344072\pi$
$258$	6.04702	0.376471
$259$	−4.95847	−0.308104
$260$	2.90785	0.180337
$261$	6.89230	0.426623
$262$	6.12299	0.378279
$263$	25.5423	1.57501	0.787504	−	0.616310i	$-0.211373\pi$
$263$	25.5423	1.57501	0.787504	+	0.616310i	$0.211373\pi$
$264$	−1.79833	−0.110680
$265$	6.80361	0.417942
$266$	−10.9795	−0.673195
$267$	−11.8670	−0.726248
$268$	−13.7869	−0.842169
$269$	−8.31856	−0.507192	−0.253596	−	0.967310i	$-0.581613\pi$
$269$	−8.31856	−0.507192	−0.253596	+	0.967310i	$0.581613\pi$
$270$	−2.90785	−0.176966
$271$	2.30569	0.140061	0.0700304	−	0.997545i	$-0.477690\pi$
$271$	2.30569	0.140061	0.0700304	+	0.997545i	$0.477690\pi$
$272$	4.53539	0.274998
$273$	−3.49310	−0.211412
$274$	−19.7578	−1.19361
$275$	6.21432	0.374738
$276$	8.15990	0.491168
$277$	−24.0339	−1.44406	−0.722029	−	0.691863i	$-0.756790\pi$
$277$	−24.0339	−1.44406	−0.722029	+	0.691863i	$0.756790\pi$
$278$	19.8446	1.19020
$279$	−3.14319	−0.188178
$280$	10.1574	0.607022
$281$	−1.90124	−0.113419	−0.0567093	−	0.998391i	$-0.518061\pi$
$281$	−1.90124	−0.113419	−0.0567093	+	0.998391i	$0.518061\pi$
$282$	−0.558583	−0.0332631
$283$	1.92051	0.114162	0.0570812	−	0.998370i	$-0.481821\pi$
$283$	1.92051	0.114162	0.0570812	+	0.998370i	$0.481821\pi$
$284$	14.3734	0.852905
$285$	9.13992	0.541402
$286$	1.79833	0.106338
$287$	38.3422	2.26327
$288$	1.00000	0.0589256
$289$	3.56972	0.209984
$290$	20.0418	1.17689
$291$	15.0206	0.880521
$292$	8.34259	0.488213
$293$	−3.27006	−0.191039	−0.0955195	−	0.995428i	$-0.530451\pi$
$293$	−3.27006	−0.191039	−0.0955195	+	0.995428i	$0.530451\pi$
$294$	−5.20177	−0.303373
$295$	12.6713	0.737754
$296$	−1.41950	−0.0825069
$297$	−1.79833	−0.104350
$298$	23.1420	1.34058
$299$	−8.15990	−0.471899
$300$	−3.45560	−0.199509
$301$	−21.1229	−1.21750
$302$	−3.79961	−0.218643
$303$	19.4452	1.11710
$304$	−3.14319	−0.180274
$305$	28.1325	1.61086
$306$	4.53539	0.259271
$307$	29.6895	1.69447	0.847235	−	0.531218i	$-0.178265\pi$
$307$	29.6895	1.69447	0.847235	+	0.531218i	$0.178265\pi$
$308$	6.28176	0.357937
$309$	−1.00000	−0.0568880
$310$	−9.13992	−0.519112
$311$	−1.59335	−0.0903508	−0.0451754	−	0.998979i	$-0.514385\pi$
$311$	−1.59335	−0.0903508	−0.0451754	+	0.998979i	$0.514385\pi$
$312$	−1.00000	−0.0566139
$313$	1.15844	0.0654788	0.0327394	−	0.999464i	$-0.489577\pi$
$313$	1.15844	0.0654788	0.0327394	+	0.999464i	$0.489577\pi$
$314$	0.143199	0.00808118
$315$	10.1574	0.572306
$316$	6.31274	0.355119
$317$	−19.7969	−1.11191	−0.555953	−	0.831214i	$-0.687646\pi$
$317$	−19.7969	−1.11191	−0.555953	+	0.831214i	$0.687646\pi$
$318$	−2.33974	−0.131206
$319$	12.3947	0.693968
$320$	2.90785	0.162554
$321$	11.3678	0.634489
$322$	−28.5034	−1.58843
$323$	−14.2556	−0.793201
$324$	1.00000	0.0555556
$325$	3.45560	0.191682
$326$	−2.40513	−0.133208
$327$	−12.7751	−0.706467
$328$	10.9765	0.606078
$329$	1.95119	0.107572
$330$	−5.22929	−0.287863
$331$	14.6807	0.806925	0.403463	−	0.914996i	$-0.367807\pi$
$331$	14.6807	0.806925	0.403463	+	0.914996i	$0.367807\pi$
$332$	−3.92641	−0.215490
$333$	−1.41950	−0.0777882
$334$	−14.8835	−0.814387
$335$	−40.0903	−2.19037
$336$	−3.49310	−0.190564
$337$	−4.04408	−0.220295	−0.110148	−	0.993915i	$-0.535132\pi$
$337$	−4.04408	−0.220295	−0.110148	+	0.993915i	$0.535132\pi$
$338$	1.00000	0.0543928
$339$	10.2482	0.556604
$340$	13.1882	0.715232
$341$	−5.65250	−0.306100
$342$	−3.14319	−0.169964
$343$	−6.28142	−0.339165
$344$	−6.04702	−0.326033
$345$	23.7278	1.27746
$346$	8.94263	0.480759
$347$	8.16490	0.438315	0.219157	−	0.975689i	$-0.429669\pi$
$347$	8.16490	0.438315	0.219157	+	0.975689i	$0.429669\pi$
$348$	−6.89230	−0.369466
$349$	−8.50322	−0.455167	−0.227584	−	0.973759i	$-0.573082\pi$
$349$	−8.50322	−0.455167	−0.227584	+	0.973759i	$0.573082\pi$
$350$	12.0708	0.645209
$351$	−1.00000	−0.0533761
$352$	1.79833	0.0958515
$353$	15.4329	0.821410	0.410705	−	0.911768i	$-0.365283\pi$
$353$	15.4329	0.821410	0.410705	+	0.911768i	$0.365283\pi$
$354$	−4.35763	−0.231606
$355$	41.7958	2.21829
$356$	11.8670	0.628949
$357$	−15.8426	−0.838478
$358$	−19.1748	−1.01342
$359$	−27.0391	−1.42707	−0.713535	−	0.700619i	$-0.752907\pi$
$359$	−27.0391	−1.42707	−0.713535	+	0.700619i	$0.752907\pi$
$360$	2.90785	0.153257
$361$	−9.12038	−0.480020
$362$	21.6597	1.13841
$363$	7.76600	0.407609
$364$	3.49310	0.183088
$365$	24.2590	1.26977
$366$	−9.67466	−0.505703
$367$	−3.53590	−0.184572	−0.0922862	−	0.995733i	$-0.529417\pi$
$367$	−3.53590	−0.184572	−0.0922862	+	0.995733i	$0.529417\pi$
$368$	−8.15990	−0.425364
$369$	10.9765	0.571416
$370$	−4.12770	−0.214589
$371$	8.17294	0.424318
$372$	3.14319	0.162967
$373$	−21.9175	−1.13485	−0.567423	−	0.823427i	$-0.692059\pi$
$373$	−21.9175	−1.13485	−0.567423	+	0.823427i	$0.692059\pi$
$374$	8.15614	0.421744
$375$	4.49089	0.231908
$376$	0.558583	0.0288067
$377$	6.89230	0.354972
$378$	−3.49310	−0.179666
$379$	26.9792	1.38583	0.692914	−	0.721020i	$-0.256326\pi$
$379$	26.9792	1.38583	0.692914	+	0.721020i	$0.256326\pi$
$380$	−9.13992	−0.468868
$381$	10.6730	0.546792
$382$	22.2109	1.13641
$383$	10.7986	0.551782	0.275891	−	0.961189i	$-0.411027\pi$
$383$	10.7986	0.551782	0.275891	+	0.961189i	$0.411027\pi$
$384$	−1.00000	−0.0510310
$385$	18.2664	0.930944
$386$	−13.9238	−0.708702
$387$	−6.04702	−0.307387
$388$	−15.0206	−0.762554
$389$	−3.52475	−0.178712	−0.0893560	−	0.996000i	$-0.528481\pi$
$389$	−3.52475	−0.178712	−0.0893560	+	0.996000i	$0.528481\pi$
$390$	−2.90785	−0.147245
$391$	−37.0083	−1.87159
$392$	5.20177	0.262729
$393$	−6.12299	−0.308864
$394$	4.65380	0.234455
$395$	18.3565	0.923616
$396$	1.79833	0.0903697
$397$	13.5683	0.680975	0.340488	−	0.940249i	$-0.389408\pi$
$397$	13.5683	0.680975	0.340488	+	0.940249i	$0.389408\pi$
$398$	−6.09436	−0.305483
$399$	10.9795	0.549661
$400$	3.45560	0.172780
$401$	−9.23409	−0.461128	−0.230564	−	0.973057i	$-0.574057\pi$
$401$	−9.23409	−0.461128	−0.230564	+	0.973057i	$0.574057\pi$
$402$	13.7869	0.687628
$403$	−3.14319	−0.156573
$404$	−19.4452	−0.967434
$405$	2.90785	0.144492
$406$	24.0755	1.19485
$407$	−2.55274	−0.126535
$408$	−4.53539	−0.224535
$409$	22.5133	1.11321	0.556604	−	0.830778i	$-0.312104\pi$
$409$	22.5133	1.11321	0.556604	+	0.830778i	$0.312104\pi$
$410$	31.9182	1.57633
$411$	19.7578	0.974579
$412$	1.00000	0.0492665
$413$	15.2217	0.749009
$414$	−8.15990	−0.401037
$415$	−11.4174	−0.560459
$416$	1.00000	0.0490290
$417$	−19.8446	−0.971796
$418$	−5.65250	−0.276473
$419$	−30.6902	−1.49931	−0.749657	−	0.661827i	$-0.769782\pi$
$419$	−30.6902	−1.49931	−0.749657	+	0.661827i	$0.769782\pi$
$420$	−10.1574	−0.495631
$421$	7.15677	0.348800	0.174400	−	0.984675i	$-0.444202\pi$
$421$	7.15677	0.348800	0.174400	+	0.984675i	$0.444202\pi$
$422$	18.8312	0.916688
$423$	0.558583	0.0271592
$424$	2.33974	0.113628
$425$	15.6725	0.760227
$426$	−14.3734	−0.696394
$427$	33.7946	1.63544
$428$	−11.3678	−0.549484
$429$	−1.79833	−0.0868244
$430$	−17.5838	−0.847967
$431$	−21.0737	−1.01508	−0.507542	−	0.861627i	$-0.669446\pi$
$431$	−21.0737	−1.01508	−0.507542	+	0.861627i	$0.669446\pi$
$432$	−1.00000	−0.0481125
$433$	36.0851	1.73414	0.867069	−	0.498189i	$-0.166001\pi$
$433$	36.0851	1.73414	0.867069	+	0.498189i	$0.166001\pi$
$434$	−10.9795	−0.527031
$435$	−20.0418	−0.960930
$436$	12.7751	0.611818
$437$	25.6481	1.22691
$438$	−8.34259	−0.398624
$439$	−17.8298	−0.850970	−0.425485	−	0.904965i	$-0.639897\pi$
$439$	−17.8298	−0.850970	−0.425485	+	0.904965i	$0.639897\pi$
$440$	5.22929	0.249296
$441$	5.20177	0.247703
$442$	4.53539	0.215726
$443$	−10.0280	−0.476443	−0.238222	−	0.971211i	$-0.576564\pi$
$443$	−10.0280	−0.476443	−0.238222	+	0.971211i	$0.576564\pi$
$444$	1.41950	0.0673666
$445$	34.5074	1.63581
$446$	−11.2457	−0.532498
$447$	−23.1420	−1.09458
$448$	3.49310	0.165034
$449$	−20.4947	−0.967206	−0.483603	−	0.875287i	$-0.660672\pi$
$449$	−20.4947	−0.967206	−0.483603	+	0.875287i	$0.660672\pi$
$450$	3.45560	0.162898
$451$	19.7395	0.929497
$452$	−10.2482	−0.482033
$453$	3.79961	0.178521
$454$	−13.9457	−0.654503
$455$	10.1574	0.476187
$456$	3.14319	0.147193
$457$	25.5979	1.19742	0.598709	−	0.800966i	$-0.295680\pi$
$457$	25.5979	1.19742	0.598709	+	0.800966i	$0.295680\pi$
$458$	−11.5990	−0.541985
$459$	−4.53539	−0.211694
$460$	−23.7278	−1.10631
$461$	20.2014	0.940874	0.470437	−	0.882434i	$-0.344096\pi$
$461$	20.2014	0.940874	0.470437	+	0.882434i	$0.344096\pi$
$462$	−6.28176	−0.292254
$463$	39.0830	1.81634	0.908170	−	0.418601i	$-0.137479\pi$
$463$	39.0830	1.81634	0.908170	+	0.418601i	$0.137479\pi$
$464$	6.89230	0.319967
$465$	9.13992	0.423854
$466$	−2.17875	−0.100928
$467$	−8.41853	−0.389563	−0.194782	−	0.980847i	$-0.562400\pi$
$467$	−8.41853	−0.389563	−0.194782	+	0.980847i	$0.562400\pi$
$468$	1.00000	0.0462250
$469$	−48.1591	−2.22378
$470$	1.62428	0.0749222
$471$	−0.143199	−0.00659826
$472$	4.35763	0.200576
$473$	−10.8746	−0.500013
$474$	−6.31274	−0.289954
$475$	−10.8616	−0.498364
$476$	15.8426	0.726143
$477$	2.33974	0.107129
$478$	−19.8260	−0.906821
$479$	5.69263	0.260103	0.130052	−	0.991507i	$-0.458486\pi$
$479$	5.69263	0.260103	0.130052	+	0.991507i	$0.458486\pi$
$480$	−2.90785	−0.132725
$481$	−1.41950	−0.0647237
$482$	−15.6492	−0.712802
$483$	28.5034	1.29695
$484$	−7.76600	−0.353000
$485$	−43.6776	−1.98330
$486$	−1.00000	−0.0453609
$487$	11.6499	0.527906	0.263953	−	0.964536i	$-0.414974\pi$
$487$	11.6499	0.527906	0.263953	+	0.964536i	$0.414974\pi$
$488$	9.67466	0.437951
$489$	2.40513	0.108764
$490$	15.1260	0.683321
$491$	10.6236	0.479438	0.239719	−	0.970842i	$-0.422945\pi$
$491$	10.6236	0.479438	0.239719	+	0.970842i	$0.422945\pi$
$492$	−10.9765	−0.494861
$493$	31.2592	1.40785
$494$	−3.14319	−0.141419
$495$	5.22929	0.235039
$496$	−3.14319	−0.141133
$497$	50.2078	2.25213
$498$	3.92641	0.175947
$499$	−32.6298	−1.46071	−0.730356	−	0.683067i	$-0.760646\pi$
$499$	−32.6298	−1.46071	−0.730356	+	0.683067i	$0.760646\pi$
$500$	−4.49089	−0.200839
$501$	14.8835	0.664945
$502$	−1.98335	−0.0885212
$503$	−1.75786	−0.0783791	−0.0391896	−	0.999232i	$-0.512478\pi$
$503$	−1.75786	−0.0783791	−0.0391896	+	0.999232i	$0.512478\pi$
$504$	3.49310	0.155595
$505$	−56.5437	−2.51616
$506$	−14.6742	−0.652349
$507$	−1.00000	−0.0444116
$508$	−10.6730	−0.473536
$509$	14.6010	0.647178	0.323589	−	0.946198i	$-0.395111\pi$
$509$	14.6010	0.647178	0.323589	+	0.946198i	$0.395111\pi$
$510$	−13.1882	−0.583984
$511$	29.1415	1.28914
$512$	1.00000	0.0441942
$513$	3.14319	0.138775
$514$	15.0855	0.665393
$515$	2.90785	0.128135
$516$	6.04702	0.266205
$517$	1.00452	0.0441787
$518$	−4.95847	−0.217862
$519$	−8.94263	−0.392538
$520$	2.90785	0.127518
$521$	−21.6496	−0.948487	−0.474244	−	0.880394i	$-0.657278\pi$
$521$	−21.6496	−0.948487	−0.474244	+	0.880394i	$0.657278\pi$
$522$	6.89230	0.301668
$523$	−27.8648	−1.21844	−0.609221	−	0.793001i	$-0.708518\pi$
$523$	−27.8648	−1.21844	−0.609221	+	0.793001i	$0.708518\pi$
$524$	6.12299	0.267484
$525$	−12.0708	−0.526811
$526$	25.5423	1.11370
$527$	−14.2556	−0.620982
$528$	−1.79833	−0.0782624
$529$	43.5840	1.89496
$530$	6.80361	0.295530
$531$	4.35763	0.189105
$532$	−10.9795	−0.476020
$533$	10.9765	0.475447
$534$	−11.8670	−0.513535
$535$	−33.0559	−1.42913
$536$	−13.7869	−0.595504
$537$	19.1748	0.827454
$538$	−8.31856	−0.358639
$539$	9.35451	0.402927
$540$	−2.90785	−0.125134
$541$	−3.67417	−0.157965	−0.0789824	−	0.996876i	$-0.525167\pi$
$541$	−3.67417	−0.157965	−0.0789824	+	0.996876i	$0.525167\pi$
$542$	2.30569	0.0990379
$543$	−21.6597	−0.929508
$544$	4.53539	0.194453
$545$	37.1482	1.59125
$546$	−3.49310	−0.149491
$547$	−11.8829	−0.508074	−0.254037	−	0.967194i	$-0.581759\pi$
$547$	−11.8829	−0.508074	−0.254037	+	0.967194i	$0.581759\pi$
$548$	−19.7578	−0.844010
$549$	9.67466	0.412905
$550$	6.21432	0.264979
$551$	−21.6638	−0.922908
$552$	8.15990	0.347308
$553$	22.0510	0.937705
$554$	−24.0339	−1.02110
$555$	4.12770	0.175211
$556$	19.8446	0.841600
$557$	−29.0827	−1.23227	−0.616137	−	0.787639i	$-0.711303\pi$
$557$	−29.0827	−1.23227	−0.616137	+	0.787639i	$0.711303\pi$
$558$	−3.14319	−0.133062
$559$	−6.04702	−0.255762
$560$	10.1574	0.429229
$561$	−8.15614	−0.344352
$562$	−1.90124	−0.0801990
$563$	21.4484	0.903942	0.451971	−	0.892033i	$-0.350721\pi$
$563$	21.4484	0.903942	0.451971	+	0.892033i	$0.350721\pi$
$564$	−0.558583	−0.0235206
$565$	−29.8001	−1.25370
$566$	1.92051	0.0807251
$567$	3.49310	0.146697
$568$	14.3734	0.603095
$569$	−24.6033	−1.03142	−0.515711	−	0.856763i	$-0.672472\pi$
$569$	−24.6033	−1.03142	−0.515711	+	0.856763i	$0.672472\pi$
$570$	9.13992	0.382829
$571$	32.2080	1.34786	0.673932	−	0.738793i	$-0.264604\pi$
$571$	32.2080	1.34786	0.673932	+	0.738793i	$0.264604\pi$
$572$	1.79833	0.0751921
$573$	−22.2109	−0.927875
$574$	38.3422	1.60037
$575$	−28.1973	−1.17591
$576$	1.00000	0.0416667
$577$	−32.2351	−1.34196	−0.670982	−	0.741474i	$-0.734127\pi$
$577$	−32.2351	−1.34196	−0.670982	+	0.741474i	$0.734127\pi$
$578$	3.56972	0.148481
$579$	13.9238	0.578653
$580$	20.0418	0.832190
$581$	−13.7154	−0.569009
$582$	15.0206	0.622622
$583$	4.20763	0.174262
$584$	8.34259	0.345219
$585$	2.90785	0.120225
$586$	−3.27006	−0.135085
$587$	−6.38743	−0.263637	−0.131819	−	0.991274i	$-0.542082\pi$
$587$	−6.38743	−0.263637	−0.131819	+	0.991274i	$0.542082\pi$
$588$	−5.20177	−0.214517
$589$	9.87962	0.407083
$590$	12.6713	0.521671
$591$	−4.65380	−0.191432
$592$	−1.41950	−0.0583412
$593$	29.0886	1.19452	0.597262	−	0.802046i	$-0.296255\pi$
$593$	29.0886	1.19452	0.597262	+	0.802046i	$0.296255\pi$
$594$	−1.79833	−0.0737865
$595$	46.0678	1.88860
$596$	23.1420	0.947933
$597$	6.09436	0.249426
$598$	−8.15990	−0.333683
$599$	36.3783	1.48638	0.743188	−	0.669082i	$-0.233313\pi$
$599$	36.3783	1.48638	0.743188	+	0.669082i	$0.233313\pi$
$600$	−3.45560	−0.141074
$601$	−25.5654	−1.04283	−0.521417	−	0.853302i	$-0.674596\pi$
$601$	−25.5654	−1.04283	−0.521417	+	0.853302i	$0.674596\pi$
$602$	−21.1229	−0.860903
$603$	−13.7869	−0.561446
$604$	−3.79961	−0.154604
$605$	−22.5824	−0.918104
$606$	19.4452	0.789907
$607$	−3.59408	−0.145879	−0.0729396	−	0.997336i	$-0.523238\pi$
$607$	−3.59408	−0.145879	−0.0729396	+	0.997336i	$0.523238\pi$
$608$	−3.14319	−0.127473
$609$	−24.0755	−0.975589
$610$	28.1325	1.13905
$611$	0.558583	0.0225978
$612$	4.53539	0.183332
$613$	−23.7740	−0.960224	−0.480112	−	0.877207i	$-0.659404\pi$
$613$	−23.7740	−0.960224	−0.480112	+	0.877207i	$0.659404\pi$
$614$	29.6895	1.19817
$615$	−31.9182	−1.28706
$616$	6.28176	0.253099
$617$	15.7608	0.634507	0.317253	−	0.948341i	$-0.397239\pi$
$617$	15.7608	0.634507	0.317253	+	0.948341i	$0.397239\pi$
$618$	−1.00000	−0.0402259
$619$	−40.2594	−1.61816	−0.809080	−	0.587698i	$-0.800034\pi$
$619$	−40.2594	−1.61816	−0.809080	+	0.587698i	$0.800034\pi$
$620$	−9.13992	−0.367068
$621$	8.15990	0.327446
$622$	−1.59335	−0.0638877
$623$	41.4526	1.66076
$624$	−1.00000	−0.0400320
$625$	−30.3368	−1.21347
$626$	1.15844	0.0463005
$627$	5.65250	0.225739
$628$	0.143199	0.00571426
$629$	−6.43799	−0.256699
$630$	10.1574	0.404681
$631$	−18.7031	−0.744560	−0.372280	−	0.928121i	$-0.621424\pi$
$631$	−18.7031	−0.744560	−0.372280	+	0.928121i	$0.621424\pi$
$632$	6.31274	0.251107
$633$	−18.8312	−0.748473
$634$	−19.7969	−0.786236
$635$	−31.0354	−1.23160
$636$	−2.33974	−0.0927766
$637$	5.20177	0.206101
$638$	12.3947	0.490709
$639$	14.3734	0.568604
$640$	2.90785	0.114943
$641$	7.56221	0.298689	0.149345	−	0.988785i	$-0.452284\pi$
$641$	7.56221	0.298689	0.149345	+	0.988785i	$0.452284\pi$
$642$	11.3678	0.448652
$643$	25.4871	1.00511	0.502557	−	0.864544i	$-0.332393\pi$
$643$	25.4871	1.00511	0.502557	+	0.864544i	$0.332393\pi$
$644$	−28.5034	−1.12319
$645$	17.5838	0.692363
$646$	−14.2556	−0.560878
$647$	23.1933	0.911822	0.455911	−	0.890025i	$-0.349314\pi$
$647$	23.1933	0.911822	0.455911	+	0.890025i	$0.349314\pi$
$648$	1.00000	0.0392837
$649$	7.83648	0.307609
$650$	3.45560	0.135540
$651$	10.9795	0.430319
$652$	−2.40513	−0.0941924
$653$	40.4380	1.58246	0.791231	−	0.611518i	$-0.209441\pi$
$653$	40.4380	1.58246	0.791231	+	0.611518i	$0.209441\pi$
$654$	−12.7751	−0.499547
$655$	17.8047	0.695689
$656$	10.9765	0.428562
$657$	8.34259	0.325475
$658$	1.95119	0.0760652
$659$	−26.2945	−1.02429	−0.512143	−	0.858900i	$-0.671148\pi$
$659$	−26.2945	−1.02429	−0.512143	+	0.858900i	$0.671148\pi$
$660$	−5.22929	−0.203550
$661$	34.6344	1.34712	0.673561	−	0.739132i	$-0.264764\pi$
$661$	34.6344	1.34712	0.673561	+	0.739132i	$0.264764\pi$
$662$	14.6807	0.570582
$663$	−4.53539	−0.176140
$664$	−3.92641	−0.152374
$665$	−31.9267	−1.23806
$666$	−1.41950	−0.0550046
$667$	−56.2405	−2.17764
$668$	−14.8835	−0.575859
$669$	11.2457	0.434783
$670$	−40.0903	−1.54882
$671$	17.3983	0.671653
$672$	−3.49310	−0.134749
$673$	−28.7792	−1.10936	−0.554678	−	0.832065i	$-0.687159\pi$
$673$	−28.7792	−1.10936	−0.554678	+	0.832065i	$0.687159\pi$
$674$	−4.04408	−0.155772
$675$	−3.45560	−0.133006
$676$	1.00000	0.0384615
$677$	−45.4887	−1.74827	−0.874135	−	0.485682i	$-0.838571\pi$
$677$	−45.4887	−1.74827	−0.874135	+	0.485682i	$0.838571\pi$
$678$	10.2482	0.393578
$679$	−52.4684	−2.01355
$680$	13.1882	0.505745
$681$	13.9457	0.534399
$682$	−5.65250	−0.216445
$683$	−1.38956	−0.0531702	−0.0265851	−	0.999647i	$-0.508463\pi$
$683$	−1.38956	−0.0531702	−0.0265851	+	0.999647i	$0.508463\pi$
$684$	−3.14319	−0.120183
$685$	−57.4526	−2.19515
$686$	−6.28142	−0.239826
$687$	11.5990	0.442529
$688$	−6.04702	−0.230540
$689$	2.33974	0.0891369
$690$	23.7278	0.903301
$691$	46.8541	1.78241	0.891207	−	0.453596i	$-0.149859\pi$
$691$	46.8541	1.78241	0.891207	+	0.453596i	$0.149859\pi$
$692$	8.94263	0.339948
$693$	6.28176	0.238624
$694$	8.16490	0.309935
$695$	57.7053	2.18889
$696$	−6.89230	−0.261252
$697$	49.7829	1.88566
$698$	−8.50322	−0.321852
$699$	2.17875	0.0824077
$700$	12.0708	0.456232
$701$	37.3510	1.41073	0.705363	−	0.708846i	$-0.250784\pi$
$701$	37.3510	1.41073	0.705363	+	0.708846i	$0.250784\pi$
$702$	−1.00000	−0.0377426
$703$	4.46176	0.168278
$704$	1.79833	0.0677773
$705$	−1.62428	−0.0611737
$706$	15.4329	0.580824
$707$	−67.9240	−2.55455
$708$	−4.35763	−0.163770
$709$	45.7643	1.71872	0.859358	−	0.511375i	$-0.170864\pi$
$709$	45.7643	1.71872	0.859358	+	0.511375i	$0.170864\pi$
$710$	41.7958	1.56857
$711$	6.31274	0.236746
$712$	11.8670	0.444734
$713$	25.6481	0.960528
$714$	−15.8426	−0.592893
$715$	5.22929	0.195564
$716$	−19.1748	−0.716596
$717$	19.8260	0.740416
$718$	−27.0391	−1.00909
$719$	−5.12560	−0.191152	−0.0955762	−	0.995422i	$-0.530469\pi$
$719$	−5.12560	−0.191152	−0.0955762	+	0.995422i	$0.530469\pi$
$720$	2.90785	0.108369
$721$	3.49310	0.130090
$722$	−9.12038	−0.339425
$723$	15.6492	0.582000
$724$	21.6597	0.804977
$725$	23.8170	0.884542
$726$	7.76600	0.288223
$727$	26.3019	0.975484	0.487742	−	0.872988i	$-0.337821\pi$
$727$	26.3019	0.975484	0.487742	+	0.872988i	$0.337821\pi$
$728$	3.49310	0.129463
$729$	1.00000	0.0370370
$730$	24.2590	0.897866
$731$	−27.4256	−1.01437
$732$	−9.67466	−0.357586
$733$	−31.6940	−1.17064	−0.585322	−	0.810801i	$-0.699032\pi$
$733$	−31.6940	−1.17064	−0.585322	+	0.810801i	$0.699032\pi$
$734$	−3.53590	−0.130512
$735$	−15.1260	−0.557929
$736$	−8.15990	−0.300778
$737$	−24.7935	−0.913279
$738$	10.9765	0.404052
$739$	28.8759	1.06222	0.531108	−	0.847304i	$-0.321776\pi$
$739$	28.8759	1.06222	0.531108	+	0.847304i	$0.321776\pi$
$740$	−4.12770	−0.151737
$741$	3.14319	0.115468
$742$	8.17294	0.300038
$743$	25.2310	0.925634	0.462817	−	0.886454i	$-0.346839\pi$
$743$	25.2310	0.925634	0.462817	+	0.886454i	$0.346839\pi$
$744$	3.14319	0.115235
$745$	67.2935	2.46544
$746$	−21.9175	−0.802457
$747$	−3.92641	−0.143660
$748$	8.15614	0.298218
$749$	−39.7089	−1.45093
$750$	4.49089	0.163984
$751$	37.8902	1.38263	0.691317	−	0.722552i	$-0.257031\pi$
$751$	37.8902	1.38263	0.691317	+	0.722552i	$0.257031\pi$
$752$	0.558583	0.0203694
$753$	1.98335	0.0722773
$754$	6.89230	0.251003
$755$	−11.0487	−0.402103
$756$	−3.49310	−0.127043
$757$	−24.2699	−0.882106	−0.441053	−	0.897481i	$-0.645395\pi$
$757$	−24.2699	−0.882106	−0.441053	+	0.897481i	$0.645395\pi$
$758$	26.9792	0.979929
$759$	14.6742	0.532641
$760$	−9.13992	−0.331540
$761$	−5.23581	−0.189798	−0.0948989	−	0.995487i	$-0.530253\pi$
$761$	−5.23581	−0.189798	−0.0948989	+	0.995487i	$0.530253\pi$
$762$	10.6730	0.386640
$763$	44.6249	1.61553
$764$	22.2109	0.803563
$765$	13.1882	0.476821
$766$	10.7986	0.390169
$767$	4.35763	0.157345
$768$	−1.00000	−0.0360844
$769$	−4.32489	−0.155959	−0.0779797	−	0.996955i	$-0.524847\pi$
$769$	−4.32489	−0.155959	−0.0779797	+	0.996955i	$0.524847\pi$
$770$	18.2664	0.658277
$771$	−15.0855	−0.543291
$772$	−13.9238	−0.501128
$773$	45.2804	1.62862	0.814311	−	0.580429i	$-0.197115\pi$
$773$	45.2804	1.62862	0.814311	+	0.580429i	$0.197115\pi$
$774$	−6.04702	−0.217356
$775$	−10.8616	−0.390160
$776$	−15.0206	−0.539207
$777$	4.95847	0.177884
$778$	−3.52475	−0.126368
$779$	−34.5013	−1.23614
$780$	−2.90785	−0.104118
$781$	25.8482	0.924921
$782$	−37.0083	−1.32341
$783$	−6.89230	−0.246311
$784$	5.20177	0.185777
$785$	0.416401	0.0148620
$786$	−6.12299	−0.218400
$787$	36.8200	1.31249	0.656245	−	0.754548i	$-0.272144\pi$
$787$	36.8200	1.31249	0.656245	+	0.754548i	$0.272144\pi$
$788$	4.65380	0.165785
$789$	−25.5423	−0.909331
$790$	18.3565	0.653095
$791$	−35.7979	−1.27283
$792$	1.79833	0.0639010
$793$	9.67466	0.343557
$794$	13.5683	0.481522
$795$	−6.80361	−0.241299
$796$	−6.09436	−0.216009
$797$	−52.0857	−1.84497	−0.922485	−	0.386032i	$-0.873845\pi$
$797$	−52.0857	−1.84497	−0.922485	+	0.386032i	$0.873845\pi$
$798$	10.9795	0.388669
$799$	2.53339	0.0896248
$800$	3.45560	0.122174
$801$	11.8670	0.419299
$802$	−9.23409	−0.326067
$803$	15.0028	0.529436
$804$	13.7869	0.486227
$805$	−82.8836	−2.92126
$806$	−3.14319	−0.110714
$807$	8.31856	0.292827
$808$	−19.4452	−0.684079
$809$	−16.6770	−0.586334	−0.293167	−	0.956061i	$-0.594709\pi$
$809$	−16.6770	−0.586334	−0.293167	+	0.956061i	$0.594709\pi$
$810$	2.90785	0.102171
$811$	−52.9218	−1.85834	−0.929168	−	0.369658i	$-0.879475\pi$
$811$	−52.9218	−1.85834	−0.929168	+	0.369658i	$0.879475\pi$
$812$	24.0755	0.844885
$813$	−2.30569	−0.0808641
$814$	−2.55274	−0.0894734
$815$	−6.99377	−0.244981
$816$	−4.53539	−0.158770
$817$	19.0069	0.664967
$818$	22.5133	0.787157
$819$	3.49310	0.122059
$820$	31.9182	1.11463
$821$	−16.6406	−0.580760	−0.290380	−	0.956911i	$-0.593782\pi$
$821$	−16.6406	−0.580760	−0.290380	+	0.956911i	$0.593782\pi$
$822$	19.7578	0.689131
$823$	−12.3821	−0.431613	−0.215806	−	0.976436i	$-0.569238\pi$
$823$	−12.3821	−0.431613	−0.215806	+	0.976436i	$0.569238\pi$
$824$	1.00000	0.0348367
$825$	−6.21432	−0.216355
$826$	15.2217	0.529629
$827$	−26.3501	−0.916283	−0.458141	−	0.888879i	$-0.651485\pi$
$827$	−26.3501	−0.916283	−0.458141	+	0.888879i	$0.651485\pi$
$828$	−8.15990	−0.283576
$829$	−34.2083	−1.18810	−0.594051	−	0.804427i	$-0.702472\pi$
$829$	−34.2083	−1.18810	−0.594051	+	0.804427i	$0.702472\pi$
$830$	−11.4174	−0.396304
$831$	24.0339	0.833727
$832$	1.00000	0.0346688
$833$	23.5920	0.817415
$834$	−19.8446	−0.687164
$835$	−43.2789	−1.49773
$836$	−5.65250	−0.195496
$837$	3.14319	0.108644
$838$	−30.6902	−1.06018
$839$	13.9322	0.480993	0.240496	−	0.970650i	$-0.422690\pi$
$839$	13.9322	0.480993	0.240496	+	0.970650i	$0.422690\pi$
$840$	−10.1574	−0.350464
$841$	18.5038	0.638063
$842$	7.15677	0.246638
$843$	1.90124	0.0654822
$844$	18.8312	0.648196
$845$	2.90785	0.100033
$846$	0.558583	0.0192045
$847$	−27.1274	−0.932109
$848$	2.33974	0.0803469
$849$	−1.92051	−0.0659117
$850$	15.6725	0.537561
$851$	11.5830	0.397060
$852$	−14.3734	−0.492425
$853$	31.0566	1.06336	0.531679	−	0.846946i	$-0.321561\pi$
$853$	31.0566	1.06336	0.531679	+	0.846946i	$0.321561\pi$
$854$	33.7946	1.15643
$855$	−9.13992	−0.312579
$856$	−11.3678	−0.388544
$857$	−40.1803	−1.37253	−0.686266	−	0.727351i	$-0.740751\pi$
$857$	−40.1803	−1.37253	−0.686266	+	0.727351i	$0.740751\pi$
$858$	−1.79833	−0.0613941
$859$	−1.99533	−0.0680799	−0.0340400	−	0.999420i	$-0.510837\pi$
$859$	−1.99533	−0.0680799	−0.0340400	+	0.999420i	$0.510837\pi$
$860$	−17.5838	−0.599604
$861$	−38.3422	−1.30670
$862$	−21.0737	−0.717773
$863$	51.4088	1.74998	0.874989	−	0.484143i	$-0.160869\pi$
$863$	51.4088	1.74998	0.874989	+	0.484143i	$0.160869\pi$
$864$	−1.00000	−0.0340207
$865$	26.0038	0.884157
$866$	36.0851	1.22622
$867$	−3.56972	−0.121234
$868$	−10.9795	−0.372668
$869$	11.3524	0.385104
$870$	−20.0418	−0.679480
$871$	−13.7869	−0.467152
$872$	12.7751	0.432621
$873$	−15.0206	−0.508369
$874$	25.6481	0.867559
$875$	−15.6871	−0.530322
$876$	−8.34259	−0.281870
$877$	−36.3338	−1.22690	−0.613452	−	0.789732i	$-0.710220\pi$
$877$	−36.3338	−1.22690	−0.613452	+	0.789732i	$0.710220\pi$
$878$	−17.8298	−0.601727
$879$	3.27006	0.110296
$880$	5.22929	0.176279
$881$	−29.0994	−0.980384	−0.490192	−	0.871615i	$-0.663073\pi$
$881$	−29.0994	−0.980384	−0.490192	+	0.871615i	$0.663073\pi$
$882$	5.20177	0.175153
$883$	11.0181	0.370789	0.185395	−	0.982664i	$-0.440644\pi$
$883$	11.0181	0.370789	0.185395	+	0.982664i	$0.440644\pi$
$884$	4.53539	0.152542
$885$	−12.6713	−0.425943
$886$	−10.0280	−0.336896
$887$	−27.3719	−0.919059	−0.459530	−	0.888162i	$-0.651982\pi$
$887$	−27.3719	−0.919059	−0.459530	+	0.888162i	$0.651982\pi$
$888$	1.41950	0.0476354
$889$	−37.2817	−1.25039
$890$	34.5074	1.15669
$891$	1.79833	0.0602464
$892$	−11.2457	−0.376533
$893$	−1.75573	−0.0587532
$894$	−23.1420	−0.773984
$895$	−55.7575	−1.86377
$896$	3.49310	0.116696
$897$	8.15990	0.272451
$898$	−20.4947	−0.683918
$899$	−21.6638	−0.722528
$900$	3.45560	0.115187
$901$	10.6116	0.353524
$902$	19.7395	0.657253
$903$	21.1229	0.702925
$904$	−10.2482	−0.340849
$905$	62.9832	2.09363
$906$	3.79961	0.126233
$907$	3.55483	0.118036	0.0590182	−	0.998257i	$-0.481203\pi$
$907$	3.55483	0.118036	0.0590182	+	0.998257i	$0.481203\pi$
$908$	−13.9457	−0.462803
$909$	−19.4452	−0.644956
$910$	10.1574	0.336715
$911$	21.3811	0.708386	0.354193	−	0.935172i	$-0.384756\pi$
$911$	21.3811	0.708386	0.354193	+	0.935172i	$0.384756\pi$
$912$	3.14319	0.104081
$913$	−7.06100	−0.233685
$914$	25.5979	0.846703
$915$	−28.1325	−0.930031
$916$	−11.5990	−0.383241
$917$	21.3882	0.706301
$918$	−4.53539	−0.149690
$919$	30.6367	1.01061	0.505306	−	0.862940i	$-0.331380\pi$
$919$	30.6367	1.01061	0.505306	+	0.862940i	$0.331380\pi$
$920$	−23.7278	−0.782282
$921$	−29.6895	−0.978303
$922$	20.2014	0.665298
$923$	14.3734	0.473107
$924$	−6.28176	−0.206655
$925$	−4.90523	−0.161283
$926$	39.0830	1.28435
$927$	1.00000	0.0328443
$928$	6.89230	0.226251
$929$	36.7180	1.20468	0.602340	−	0.798240i	$-0.294235\pi$
$929$	36.7180	1.20468	0.602340	+	0.798240i	$0.294235\pi$
$930$	9.13992	0.299710
$931$	−16.3501	−0.535853
$932$	−2.17875	−0.0713672
$933$	1.59335	0.0521641
$934$	−8.41853	−0.275463
$935$	23.7168	0.775623
$936$	1.00000	0.0326860
$937$	−43.7189	−1.42824	−0.714118	−	0.700026i	$-0.753172\pi$
$937$	−43.7189	−1.42824	−0.714118	+	0.700026i	$0.753172\pi$
$938$	−48.1591	−1.57245
$939$	−1.15844	−0.0378042
$940$	1.62428	0.0529780
$941$	50.1572	1.63508	0.817539	−	0.575873i	$-0.195338\pi$
$941$	50.1572	1.63508	0.817539	+	0.575873i	$0.195338\pi$
$942$	−0.143199	−0.00466567
$943$	−89.5675	−2.91672
$944$	4.35763	0.141829
$945$	−10.1574	−0.330421
$946$	−10.8746	−0.353562
$947$	−49.3080	−1.60229	−0.801147	−	0.598468i	$-0.795776\pi$
$947$	−49.3080	−1.60229	−0.801147	+	0.598468i	$0.795776\pi$
$948$	−6.31274	−0.205028
$949$	8.34259	0.270812
$950$	−10.8616	−0.352397
$951$	19.7969	0.641959
$952$	15.8426	0.513461
$953$	38.5721	1.24947	0.624736	−	0.780836i	$-0.285207\pi$
$953$	38.5721	1.24947	0.624736	+	0.780836i	$0.285207\pi$
$954$	2.33974	0.0757518
$955$	64.5861	2.08996
$956$	−19.8260	−0.641219
$957$	−12.3947	−0.400662
$958$	5.69263	0.183921
$959$	−69.0159	−2.22864
$960$	−2.90785	−0.0938505
$961$	−21.1204	−0.681303
$962$	−1.41950	−0.0457666
$963$	−11.3678	−0.366322
$964$	−15.6492	−0.504027
$965$	−40.4883	−1.30336
$966$	28.5034	0.917081
$967$	−43.0306	−1.38377	−0.691886	−	0.722007i	$-0.743220\pi$
$967$	−43.0306	−1.38377	−0.691886	+	0.722007i	$0.743220\pi$
$968$	−7.76600	−0.249609
$969$	14.2556	0.457955
$970$	−43.6776	−1.40240
$971$	12.7501	0.409171	0.204586	−	0.978849i	$-0.434415\pi$
$971$	12.7501	0.409171	0.204586	+	0.978849i	$0.434415\pi$
$972$	−1.00000	−0.0320750
$973$	69.3194	2.22228
$974$	11.6499	0.373286
$975$	−3.45560	−0.110668
$976$	9.67466	0.309678
$977$	−21.1054	−0.675221	−0.337610	−	0.941286i	$-0.609619\pi$
$977$	−21.1054	−0.675221	−0.337610	+	0.941286i	$0.609619\pi$
$978$	2.40513	0.0769077
$979$	21.3408	0.682055
$980$	15.1260	0.483181
$981$	12.7751	0.407879
$982$	10.6236	0.339014
$983$	−16.1470	−0.515010	−0.257505	−	0.966277i	$-0.582900\pi$
$983$	−16.1470	−0.515010	−0.257505	+	0.966277i	$0.582900\pi$
$984$	−10.9765	−0.349920
$985$	13.5326	0.431184
$986$	31.2592	0.995497
$987$	−1.95119	−0.0621070
$988$	−3.14319	−0.0999981
$989$	49.3431	1.56902
$990$	5.22929	0.166198
$991$	12.1423	0.385714	0.192857	−	0.981227i	$-0.438225\pi$
$991$	12.1423	0.385714	0.192857	+	0.981227i	$0.438225\pi$
$992$	−3.14319	−0.0997963
$993$	−14.6807	−0.465879
$994$	50.2078	1.59250
$995$	−17.7215	−0.561809
$996$	3.92641	0.124413
$997$	−22.7262	−0.719747	−0.359873	−	0.933001i	$-0.617180\pi$
$997$	−22.7262	−0.719747	−0.359873	+	0.933001i	$0.617180\pi$
$998$	−32.6298	−1.03288
$999$	1.41950	0.0449111

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.y.1.10	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.y.1.10	✓	13	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:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.90785 q^{5} -1.00000 q^{6} +3.49310 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.90785 q^{5} -1.00000 q^{6} +3.49310 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.90785 q^{10} +1.79833 q^{11} -1.00000 q^{12} +1.00000 q^{13} +3.49310 q^{14} -2.90785 q^{15} +1.00000 q^{16} +4.53539 q^{17} +1.00000 q^{18} -3.14319 q^{19} +2.90785 q^{20} -3.49310 q^{21} +1.79833 q^{22} -8.15990 q^{23} -1.00000 q^{24} +3.45560 q^{25} +1.00000 q^{26} -1.00000 q^{27} +3.49310 q^{28} +6.89230 q^{29} -2.90785 q^{30} -3.14319 q^{31} +1.00000 q^{32} -1.79833 q^{33} +4.53539 q^{34} +10.1574 q^{35} +1.00000 q^{36} -1.41950 q^{37} -3.14319 q^{38} -1.00000 q^{39} +2.90785 q^{40} +10.9765 q^{41} -3.49310 q^{42} -6.04702 q^{43} +1.79833 q^{44} +2.90785 q^{45} -8.15990 q^{46} +0.558583 q^{47} -1.00000 q^{48} +5.20177 q^{49} +3.45560 q^{50} -4.53539 q^{51} +1.00000 q^{52} +2.33974 q^{53} -1.00000 q^{54} +5.22929 q^{55} +3.49310 q^{56} +3.14319 q^{57} +6.89230 q^{58} +4.35763 q^{59} -2.90785 q^{60} +9.67466 q^{61} -3.14319 q^{62} +3.49310 q^{63} +1.00000 q^{64} +2.90785 q^{65} -1.79833 q^{66} -13.7869 q^{67} +4.53539 q^{68} +8.15990 q^{69} +10.1574 q^{70} +14.3734 q^{71} +1.00000 q^{72} +8.34259 q^{73} -1.41950 q^{74} -3.45560 q^{75} -3.14319 q^{76} +6.28176 q^{77} -1.00000 q^{78} +6.31274 q^{79} +2.90785 q^{80} +1.00000 q^{81} +10.9765 q^{82} -3.92641 q^{83} -3.49310 q^{84} +13.1882 q^{85} -6.04702 q^{86} -6.89230 q^{87} +1.79833 q^{88} +11.8670 q^{89} +2.90785 q^{90} +3.49310 q^{91} -8.15990 q^{92} +3.14319 q^{93} +0.558583 q^{94} -9.13992 q^{95} -1.00000 q^{96} -15.0206 q^{97} +5.20177 q^{98} +1.79833 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 13 q^{2} - 13 q^{3} + 13 q^{4} + 3 q^{5} - 13 q^{6} + 5 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 13 * q^2 - 13 * q^3 + 13 * q^4 + 3 * q^5 - 13 * q^6 + 5 * q^7 + 13 * q^8 + 13 * q^9	\( 13 q + 13 q^{2} - 13 q^{3} + 13 q^{4} + 3 q^{5} - 13 q^{6} + 5 q^{7} + 13 q^{8} + 13 q^{9} + 3 q^{10} + 8 q^{11} - 13 q^{12} + 13 q^{13} + 5 q^{14} - 3 q^{15} + 13 q^{16} - q^{17} + 13 q^{18} + 5 q^{19} + 3 q^{20} - 5 q^{21} + 8 q^{22} - 9 q^{23} - 13 q^{24} + 24 q^{25} + 13 q^{26} - 13 q^{27} + 5 q^{28} - q^{29} - 3 q^{30} + 5 q^{31} + 13 q^{32} - 8 q^{33} - q^{34} + 28 q^{35} + 13 q^{36} + 35 q^{37} + 5 q^{38} - 13 q^{39} + 3 q^{40} + 24 q^{41} - 5 q^{42} + 9 q^{43} + 8 q^{44} + 3 q^{45} - 9 q^{46} - 8 q^{47} - 13 q^{48} - 16 q^{49} + 24 q^{50} + q^{51} + 13 q^{52} + 32 q^{53} - 13 q^{54} - 4 q^{55} + 5 q^{56} - 5 q^{57} - q^{58} + 12 q^{59} - 3 q^{60} + 17 q^{61} + 5 q^{62} + 5 q^{63} + 13 q^{64} + 3 q^{65} - 8 q^{66} + 20 q^{67} - q^{68} + 9 q^{69} + 28 q^{70} + 16 q^{71} + 13 q^{72} + 46 q^{73} + 35 q^{74} - 24 q^{75} + 5 q^{76} - 7 q^{77} - 13 q^{78} + 17 q^{79} + 3 q^{80} + 13 q^{81} + 24 q^{82} + 13 q^{83} - 5 q^{84} + 11 q^{85} + 9 q^{86} + q^{87} + 8 q^{88} + 14 q^{89} + 3 q^{90} + 5 q^{91} - 9 q^{92} - 5 q^{93} - 8 q^{94} + 2 q^{95} - 13 q^{96} + 46 q^{97} - 16 q^{98} + 8 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 - 13 * q^3 + 13 * q^4 + 3 * q^5 - 13 * q^6 + 5 * q^7 + 13 * q^8 + 13 * q^9 + 3 * q^10 + 8 * q^11 - 13 * q^12 + 13 * q^13 + 5 * q^14 - 3 * q^15 + 13 * q^16 - q^17 + 13 * q^18 + 5 * q^19 + 3 * q^20 - 5 * q^21 + 8 * q^22 - 9 * q^23 - 13 * q^24 + 24 * q^25 + 13 * q^26 - 13 * q^27 + 5 * q^28 - q^29 - 3 * q^30 + 5 * q^31 + 13 * q^32 - 8 * q^33 - q^34 + 28 * q^35 + 13 * q^36 + 35 * q^37 + 5 * q^38 - 13 * q^39 + 3 * q^40 + 24 * q^41 - 5 * q^42 + 9 * q^43 + 8 * q^44 + 3 * q^45 - 9 * q^46 - 8 * q^47 - 13 * q^48 - 16 * q^49 + 24 * q^50 + q^51 + 13 * q^52 + 32 * q^53 - 13 * q^54 - 4 * q^55 + 5 * q^56 - 5 * q^57 - q^58 + 12 * q^59 - 3 * q^60 + 17 * q^61 + 5 * q^62 + 5 * q^63 + 13 * q^64 + 3 * q^65 - 8 * q^66 + 20 * q^67 - q^68 + 9 * q^69 + 28 * q^70 + 16 * q^71 + 13 * q^72 + 46 * q^73 + 35 * q^74 - 24 * q^75 + 5 * q^76 - 7 * q^77 - 13 * q^78 + 17 * q^79 + 3 * q^80 + 13 * q^81 + 24 * q^82 + 13 * q^83 - 5 * q^84 + 11 * q^85 + 9 * q^86 + q^87 + 8 * q^88 + 14 * q^89 + 3 * q^90 + 5 * q^91 - 9 * q^92 - 5 * q^93 - 8 * q^94 + 2 * q^95 - 13 * q^96 + 46 * q^97 - 16 * q^98 + 8 * q^99

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