LMFDB - Embedded newform 4030.2.a.q.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4030,2,Mod(1,4030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4030, 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("4030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4030 = 2 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4030.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:	$32.1797120146$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 16x^{7} + 48x^{6} + 66x^{5} - 202x^{4} - 75x^{3} + 210x^{2} + 68x - 16 $ x^9 - 3x^8 - 16x^7 + 48x^6 + 66x^5 - 202x^4 - 75x^3 + 210x^2 + 68x - 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.15368$ of defining polynomial
Character	$\chi$	$=$	4030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.15368 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.15368 q^{6} +1.26985 q^{7} +1.00000 q^{8} +1.63833 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.15368 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.15368 q^{6} +1.26985 q^{7} +1.00000 q^{8} +1.63833 q^{9} -1.00000 q^{10} -4.08514 q^{11} -2.15368 q^{12} +1.00000 q^{13} +1.26985 q^{14} +2.15368 q^{15} +1.00000 q^{16} -6.01995 q^{17} +1.63833 q^{18} -7.72382 q^{19} -1.00000 q^{20} -2.73485 q^{21} -4.08514 q^{22} +4.31046 q^{23} -2.15368 q^{24} +1.00000 q^{25} +1.00000 q^{26} +2.93260 q^{27} +1.26985 q^{28} +4.40569 q^{29} +2.15368 q^{30} +1.00000 q^{31} +1.00000 q^{32} +8.79808 q^{33} -6.01995 q^{34} -1.26985 q^{35} +1.63833 q^{36} +2.67971 q^{37} -7.72382 q^{38} -2.15368 q^{39} -1.00000 q^{40} +1.77095 q^{41} -2.73485 q^{42} +8.08794 q^{43} -4.08514 q^{44} -1.63833 q^{45} +4.31046 q^{46} +4.46936 q^{47} -2.15368 q^{48} -5.38748 q^{49} +1.00000 q^{50} +12.9650 q^{51} +1.00000 q^{52} -0.464054 q^{53} +2.93260 q^{54} +4.08514 q^{55} +1.26985 q^{56} +16.6346 q^{57} +4.40569 q^{58} +0.0503486 q^{59} +2.15368 q^{60} -3.67885 q^{61} +1.00000 q^{62} +2.08044 q^{63} +1.00000 q^{64} -1.00000 q^{65} +8.79808 q^{66} -1.82982 q^{67} -6.01995 q^{68} -9.28335 q^{69} -1.26985 q^{70} +0.514493 q^{71} +1.63833 q^{72} -9.88312 q^{73} +2.67971 q^{74} -2.15368 q^{75} -7.72382 q^{76} -5.18752 q^{77} -2.15368 q^{78} +5.65383 q^{79} -1.00000 q^{80} -11.2309 q^{81} +1.77095 q^{82} +5.62212 q^{83} -2.73485 q^{84} +6.01995 q^{85} +8.08794 q^{86} -9.48844 q^{87} -4.08514 q^{88} +9.51562 q^{89} -1.63833 q^{90} +1.26985 q^{91} +4.31046 q^{92} -2.15368 q^{93} +4.46936 q^{94} +7.72382 q^{95} -2.15368 q^{96} -1.64249 q^{97} -5.38748 q^{98} -6.69280 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} - 9 q^{5} + 3 q^{6} + 3 q^{7} + 9 q^{8} + 14 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 - 9 * q^5 + 3 * q^6 + 3 * q^7 + 9 * q^8 + 14 * q^9	\( 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} - 9 q^{5} + 3 q^{6} + 3 q^{7} + 9 q^{8} + 14 q^{9} - 9 q^{10} + 6 q^{11} + 3 q^{12} + 9 q^{13} + 3 q^{14} - 3 q^{15} + 9 q^{16} + 3 q^{17} + 14 q^{18} + 6 q^{19} - 9 q^{20} - q^{21} + 6 q^{22} + 14 q^{23} + 3 q^{24} + 9 q^{25} + 9 q^{26} + 9 q^{27} + 3 q^{28} + 17 q^{29} - 3 q^{30} + 9 q^{31} + 9 q^{32} - 8 q^{33} + 3 q^{34} - 3 q^{35} + 14 q^{36} - 3 q^{37} + 6 q^{38} + 3 q^{39} - 9 q^{40} + 4 q^{41} - q^{42} + 5 q^{43} + 6 q^{44} - 14 q^{45} + 14 q^{46} + 25 q^{47} + 3 q^{48} + 8 q^{49} + 9 q^{50} + 15 q^{51} + 9 q^{52} + 18 q^{53} + 9 q^{54} - 6 q^{55} + 3 q^{56} + 13 q^{57} + 17 q^{58} - 6 q^{59} - 3 q^{60} + 26 q^{61} + 9 q^{62} + 8 q^{63} + 9 q^{64} - 9 q^{65} - 8 q^{66} - 2 q^{67} + 3 q^{68} + 8 q^{69} - 3 q^{70} + 18 q^{71} + 14 q^{72} - 5 q^{73} - 3 q^{74} + 3 q^{75} + 6 q^{76} + 19 q^{77} + 3 q^{78} + 18 q^{79} - 9 q^{80} + 41 q^{81} + 4 q^{82} + 13 q^{83} - q^{84} - 3 q^{85} + 5 q^{86} + 19 q^{87} + 6 q^{88} + 9 q^{89} - 14 q^{90} + 3 q^{91} + 14 q^{92} + 3 q^{93} + 25 q^{94} - 6 q^{95} + 3 q^{96} - 18 q^{97} + 8 q^{98} + 21 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 - 9 * q^5 + 3 * q^6 + 3 * q^7 + 9 * q^8 + 14 * q^9 - 9 * q^10 + 6 * q^11 + 3 * q^12 + 9 * q^13 + 3 * q^14 - 3 * q^15 + 9 * q^16 + 3 * q^17 + 14 * q^18 + 6 * q^19 - 9 * q^20 - q^21 + 6 * q^22 + 14 * q^23 + 3 * q^24 + 9 * q^25 + 9 * q^26 + 9 * q^27 + 3 * q^28 + 17 * q^29 - 3 * q^30 + 9 * q^31 + 9 * q^32 - 8 * q^33 + 3 * q^34 - 3 * q^35 + 14 * q^36 - 3 * q^37 + 6 * q^38 + 3 * q^39 - 9 * q^40 + 4 * q^41 - q^42 + 5 * q^43 + 6 * q^44 - 14 * q^45 + 14 * q^46 + 25 * q^47 + 3 * q^48 + 8 * q^49 + 9 * q^50 + 15 * q^51 + 9 * q^52 + 18 * q^53 + 9 * q^54 - 6 * q^55 + 3 * q^56 + 13 * q^57 + 17 * q^58 - 6 * q^59 - 3 * q^60 + 26 * q^61 + 9 * q^62 + 8 * q^63 + 9 * q^64 - 9 * q^65 - 8 * q^66 - 2 * q^67 + 3 * q^68 + 8 * q^69 - 3 * q^70 + 18 * q^71 + 14 * q^72 - 5 * q^73 - 3 * q^74 + 3 * q^75 + 6 * q^76 + 19 * q^77 + 3 * q^78 + 18 * q^79 - 9 * q^80 + 41 * q^81 + 4 * q^82 + 13 * q^83 - q^84 - 3 * q^85 + 5 * q^86 + 19 * q^87 + 6 * q^88 + 9 * q^89 - 14 * q^90 + 3 * q^91 + 14 * q^92 + 3 * q^93 + 25 * q^94 - 6 * q^95 + 3 * q^96 - 18 * q^97 + 8 * q^98 + 21 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.15368	−1.24343	−0.621713	−	0.783245i	$-0.713563\pi$
$3$	−2.15368	−1.24343	−0.621713	+	0.783245i	$0.713563\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.15368	−0.879235
$7$	1.26985	0.479959	0.239979	−	0.970778i	$-0.422859\pi$
$7$	1.26985	0.479959	0.239979	+	0.970778i	$0.422859\pi$
$8$	1.00000	0.353553
$9$	1.63833	0.546110
$10$	−1.00000	−0.316228
$11$	−4.08514	−1.23172	−0.615858	−	0.787857i	$-0.711191\pi$
$11$	−4.08514	−1.23172	−0.615858	+	0.787857i	$0.711191\pi$
$12$	−2.15368	−0.621713
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	1.26985	0.339382
$15$	2.15368	0.556077
$16$	1.00000	0.250000
$17$	−6.01995	−1.46005	−0.730026	−	0.683420i	$-0.760492\pi$
$17$	−6.01995	−1.46005	−0.730026	+	0.683420i	$0.760492\pi$
$18$	1.63833	0.386158
$19$	−7.72382	−1.77196	−0.885982	−	0.463719i	$-0.846515\pi$
$19$	−7.72382	−1.77196	−0.885982	+	0.463719i	$0.846515\pi$
$20$	−1.00000	−0.223607
$21$	−2.73485	−0.596794
$22$	−4.08514	−0.870955
$23$	4.31046	0.898793	0.449397	−	0.893332i	$-0.351639\pi$
$23$	4.31046	0.898793	0.449397	+	0.893332i	$0.351639\pi$
$24$	−2.15368	−0.439618
$25$	1.00000	0.200000
$26$	1.00000	0.196116
$27$	2.93260	0.564379
$28$	1.26985	0.239979
$29$	4.40569	0.818117	0.409058	−	0.912508i	$-0.365857\pi$
$29$	4.40569	0.818117	0.409058	+	0.912508i	$0.365857\pi$
$30$	2.15368	0.393206
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	1.00000	0.176777
$33$	8.79808	1.53155
$34$	−6.01995	−1.03241
$35$	−1.26985	−0.214644
$36$	1.63833	0.273055
$37$	2.67971	0.440541	0.220271	−	0.975439i	$-0.429306\pi$
$37$	2.67971	0.440541	0.220271	+	0.975439i	$0.429306\pi$
$38$	−7.72382	−1.25297
$39$	−2.15368	−0.344864
$40$	−1.00000	−0.158114
$41$	1.77095	0.276576	0.138288	−	0.990392i	$-0.455840\pi$
$41$	1.77095	0.276576	0.138288	+	0.990392i	$0.455840\pi$
$42$	−2.73485	−0.421997
$43$	8.08794	1.23340	0.616699	−	0.787199i	$-0.288469\pi$
$43$	8.08794	1.23340	0.616699	+	0.787199i	$0.288469\pi$
$44$	−4.08514	−0.615858
$45$	−1.63833	−0.244228
$46$	4.31046	0.635543
$47$	4.46936	0.651923	0.325961	−	0.945383i	$-0.394312\pi$
$47$	4.46936	0.651923	0.325961	+	0.945383i	$0.394312\pi$
$48$	−2.15368	−0.310857
$49$	−5.38748	−0.769639
$50$	1.00000	0.141421
$51$	12.9650	1.81547
$52$	1.00000	0.138675
$53$	−0.464054	−0.0637427	−0.0318714	−	0.999492i	$-0.510147\pi$
$53$	−0.464054	−0.0637427	−0.0318714	+	0.999492i	$0.510147\pi$
$54$	2.93260	0.399076
$55$	4.08514	0.550840
$56$	1.26985	0.169691
$57$	16.6346	2.20331
$58$	4.40569	0.578496
$59$	0.0503486	0.00655483	0.00327742	−	0.999995i	$-0.498957\pi$
$59$	0.0503486	0.00655483	0.00327742	+	0.999995i	$0.498957\pi$
$60$	2.15368	0.278039
$61$	−3.67885	−0.471028	−0.235514	−	0.971871i	$-0.575677\pi$
$61$	−3.67885	−0.471028	−0.235514	+	0.971871i	$0.575677\pi$
$62$	1.00000	0.127000
$63$	2.08044	0.262110
$64$	1.00000	0.125000
$65$	−1.00000	−0.124035
$66$	8.79808	1.08297
$67$	−1.82982	−0.223548	−0.111774	−	0.993734i	$-0.535653\pi$
$67$	−1.82982	−0.223548	−0.111774	+	0.993734i	$0.535653\pi$
$68$	−6.01995	−0.730026
$69$	−9.28335	−1.11758
$70$	−1.26985	−0.151776
$71$	0.514493	0.0610591	0.0305296	−	0.999534i	$-0.490281\pi$
$71$	0.514493	0.0610591	0.0305296	+	0.999534i	$0.490281\pi$
$72$	1.63833	0.193079
$73$	−9.88312	−1.15673	−0.578366	−	0.815778i	$-0.696309\pi$
$73$	−9.88312	−1.15673	−0.578366	+	0.815778i	$0.696309\pi$
$74$	2.67971	0.311510
$75$	−2.15368	−0.248685
$76$	−7.72382	−0.885982
$77$	−5.18752	−0.591173
$78$	−2.15368	−0.243856
$79$	5.65383	0.636106	0.318053	−	0.948073i	$-0.396971\pi$
$79$	5.65383	0.636106	0.318053	+	0.948073i	$0.396971\pi$
$80$	−1.00000	−0.111803
$81$	−11.2309	−1.24787
$82$	1.77095	0.195569
$83$	5.62212	0.617107	0.308554	−	0.951207i	$-0.400155\pi$
$83$	5.62212	0.617107	0.308554	+	0.951207i	$0.400155\pi$
$84$	−2.73485	−0.298397
$85$	6.01995	0.652955
$86$	8.08794	0.872145
$87$	−9.48844	−1.01727
$88$	−4.08514	−0.435477
$89$	9.51562	1.00865	0.504327	−	0.863513i	$-0.331741\pi$
$89$	9.51562	1.00865	0.504327	+	0.863513i	$0.331741\pi$
$90$	−1.63833	−0.172695
$91$	1.26985	0.133117
$92$	4.31046	0.449397
$93$	−2.15368	−0.223326
$94$	4.46936	0.460979
$95$	7.72382	0.792447
$96$	−2.15368	−0.219809
$97$	−1.64249	−0.166770	−0.0833850	−	0.996517i	$-0.526573\pi$
$97$	−1.64249	−0.166770	−0.0833850	+	0.996517i	$0.526573\pi$
$98$	−5.38748	−0.544217
$99$	−6.69280	−0.672652
$100$	1.00000	0.100000
$101$	14.0908	1.40209	0.701045	−	0.713117i	$-0.252717\pi$
$101$	14.0908	1.40209	0.701045	+	0.713117i	$0.252717\pi$
$102$	12.9650	1.28373
$103$	−14.3924	−1.41812	−0.709062	−	0.705147i	$-0.750881\pi$
$103$	−14.3924	−1.41812	−0.709062	+	0.705147i	$0.750881\pi$
$104$	1.00000	0.0980581
$105$	2.73485	0.266894
$106$	−0.464054	−0.0450729
$107$	14.0952	1.36263	0.681315	−	0.731990i	$-0.261408\pi$
$107$	14.0952	1.36263	0.681315	+	0.731990i	$0.261408\pi$
$108$	2.93260	0.282190
$109$	10.2068	0.977636	0.488818	−	0.872386i	$-0.337428\pi$
$109$	10.2068	0.977636	0.488818	+	0.872386i	$0.337428\pi$
$110$	4.08514	0.389503
$111$	−5.77123	−0.547781
$112$	1.26985	0.119990
$113$	−10.5908	−0.996301	−0.498151	−	0.867091i	$-0.665987\pi$
$113$	−10.5908	−0.996301	−0.498151	+	0.867091i	$0.665987\pi$
$114$	16.6346	1.55797
$115$	−4.31046	−0.401953
$116$	4.40569	0.409058
$117$	1.63833	0.151464
$118$	0.0503486	0.00463497
$119$	−7.64444	−0.700765
$120$	2.15368	0.196603
$121$	5.68837	0.517124
$122$	−3.67885	−0.333067
$123$	−3.81406	−0.343902
$124$	1.00000	0.0898027
$125$	−1.00000	−0.0894427
$126$	2.08044	0.185340
$127$	6.52502	0.579002	0.289501	−	0.957178i	$-0.406511\pi$
$127$	6.52502	0.579002	0.289501	+	0.957178i	$0.406511\pi$
$128$	1.00000	0.0883883
$129$	−17.4188	−1.53364
$130$	−1.00000	−0.0877058
$131$	15.6603	1.36825	0.684123	−	0.729366i	$-0.260185\pi$
$131$	15.6603	1.36825	0.684123	+	0.729366i	$0.260185\pi$
$132$	8.79808	0.765774
$133$	−9.80810	−0.850470
$134$	−1.82982	−0.158072
$135$	−2.93260	−0.252398
$136$	−6.01995	−0.516206
$137$	−9.37298	−0.800788	−0.400394	−	0.916343i	$-0.631127\pi$
$137$	−9.37298	−0.800788	−0.400394	+	0.916343i	$0.631127\pi$
$138$	−9.28335	−0.790251
$139$	18.2263	1.54594	0.772968	−	0.634445i	$-0.218771\pi$
$139$	18.2263	1.54594	0.772968	+	0.634445i	$0.218771\pi$
$140$	−1.26985	−0.107322
$141$	−9.62556	−0.810618
$142$	0.514493	0.0431753
$143$	−4.08514	−0.341617
$144$	1.63833	0.136527
$145$	−4.40569	−0.365873
$146$	−9.88312	−0.817933
$147$	11.6029	0.956990
$148$	2.67971	0.220271
$149$	15.1585	1.24183	0.620916	−	0.783877i	$-0.286761\pi$
$149$	15.1585	1.24183	0.620916	+	0.783877i	$0.286761\pi$
$150$	−2.15368	−0.175847
$151$	−4.64154	−0.377723	−0.188861	−	0.982004i	$-0.560480\pi$
$151$	−4.64154	−0.377723	−0.188861	+	0.982004i	$0.560480\pi$
$152$	−7.72382	−0.626484
$153$	−9.86265	−0.797348
$154$	−5.18752	−0.418023
$155$	−1.00000	−0.0803219
$156$	−2.15368	−0.172432
$157$	9.77887	0.780439	0.390219	−	0.920722i	$-0.372399\pi$
$157$	9.77887	0.780439	0.390219	+	0.920722i	$0.372399\pi$
$158$	5.65383	0.449795
$159$	0.999423	0.0792594
$160$	−1.00000	−0.0790569
$161$	5.47365	0.431384
$162$	−11.2309	−0.882380
$163$	7.83895	0.613994	0.306997	−	0.951710i	$-0.400676\pi$
$163$	7.83895	0.613994	0.306997	+	0.951710i	$0.400676\pi$
$164$	1.77095	0.138288
$165$	−8.79808	−0.684929
$166$	5.62212	0.436361
$167$	−2.24810	−0.173964	−0.0869818	−	0.996210i	$-0.527722\pi$
$167$	−2.24810	−0.173964	−0.0869818	+	0.996210i	$0.527722\pi$
$168$	−2.73485	−0.210998
$169$	1.00000	0.0769231
$170$	6.01995	0.461709
$171$	−12.6542	−0.967687
$172$	8.08794	0.616699
$173$	−0.994252	−0.0755916	−0.0377958	−	0.999285i	$-0.512034\pi$
$173$	−0.994252	−0.0755916	−0.0377958	+	0.999285i	$0.512034\pi$
$174$	−9.48844	−0.719317
$175$	1.26985	0.0959918
$176$	−4.08514	−0.307929
$177$	−0.108435	−0.00815045
$178$	9.51562	0.713226
$179$	26.0281	1.94543	0.972716	−	0.232001i	$-0.0745273\pi$
$179$	26.0281	1.94543	0.972716	+	0.232001i	$0.0745273\pi$
$180$	−1.63833	−0.122114
$181$	−1.64104	−0.121978	−0.0609888	−	0.998138i	$-0.519425\pi$
$181$	−1.64104	−0.121978	−0.0609888	+	0.998138i	$0.519425\pi$
$182$	1.26985	0.0941277
$183$	7.92306	0.585689
$184$	4.31046	0.317771
$185$	−2.67971	−0.197016
$186$	−2.15368	−0.157915
$187$	24.5923	1.79837
$188$	4.46936	0.325961
$189$	3.72397	0.270879
$190$	7.72382	0.560345
$191$	15.7124	1.13691	0.568456	−	0.822714i	$-0.307541\pi$
$191$	15.7124	1.13691	0.568456	+	0.822714i	$0.307541\pi$
$192$	−2.15368	−0.155428
$193$	−6.79521	−0.489130	−0.244565	−	0.969633i	$-0.578645\pi$
$193$	−6.79521	−0.489130	−0.244565	+	0.969633i	$0.578645\pi$
$194$	−1.64249	−0.117924
$195$	2.15368	0.154228
$196$	−5.38748	−0.384820
$197$	21.3206	1.51903	0.759513	−	0.650492i	$-0.225437\pi$
$197$	21.3206	1.51903	0.759513	+	0.650492i	$0.225437\pi$
$198$	−6.69280	−0.475637
$199$	2.44230	0.173130	0.0865649	−	0.996246i	$-0.472411\pi$
$199$	2.44230	0.173130	0.0865649	+	0.996246i	$0.472411\pi$
$200$	1.00000	0.0707107
$201$	3.94085	0.277966
$202$	14.0908	0.991428
$203$	5.59458	0.392662
$204$	12.9650	0.907733
$205$	−1.77095	−0.123689
$206$	−14.3924	−1.00276
$207$	7.06196	0.490840
$208$	1.00000	0.0693375
$209$	31.5529	2.18256
$210$	2.73485	0.188723
$211$	8.01904	0.552053	0.276027	−	0.961150i	$-0.410982\pi$
$211$	8.01904	0.552053	0.276027	+	0.961150i	$0.410982\pi$
$212$	−0.464054	−0.0318714
$213$	−1.10805	−0.0759226
$214$	14.0952	0.963525
$215$	−8.08794	−0.551593
$216$	2.93260	0.199538
$217$	1.26985	0.0862032
$218$	10.2068	0.691293
$219$	21.2851	1.43831
$220$	4.08514	0.275420
$221$	−6.01995	−0.404945
$222$	−5.77123	−0.387340
$223$	2.15328	0.144194	0.0720972	−	0.997398i	$-0.477031\pi$
$223$	2.15328	0.144194	0.0720972	+	0.997398i	$0.477031\pi$
$224$	1.26985	0.0848456
$225$	1.63833	0.109222
$226$	−10.5908	−0.704491
$227$	−19.7374	−1.31002	−0.655009	−	0.755621i	$-0.727335\pi$
$227$	−19.7374	−1.31002	−0.655009	+	0.755621i	$0.727335\pi$
$228$	16.6346	1.10165
$229$	22.8707	1.51134	0.755669	−	0.654954i	$-0.227312\pi$
$229$	22.8707	1.51134	0.755669	+	0.654954i	$0.227312\pi$
$230$	−4.31046	−0.284223
$231$	11.1723	0.735080
$232$	4.40569	0.289248
$233$	8.10578	0.531027	0.265514	−	0.964107i	$-0.414458\pi$
$233$	8.10578	0.531027	0.265514	+	0.964107i	$0.414458\pi$
$234$	1.63833	0.107101
$235$	−4.46936	−0.291549
$236$	0.0503486	0.00327742
$237$	−12.1765	−0.790951
$238$	−7.64444	−0.495515
$239$	0.812589	0.0525620	0.0262810	−	0.999655i	$-0.491634\pi$
$239$	0.812589	0.0525620	0.0262810	+	0.999655i	$0.491634\pi$
$240$	2.15368	0.139019
$241$	−4.51481	−0.290824	−0.145412	−	0.989371i	$-0.546451\pi$
$241$	−4.51481	−0.290824	−0.145412	+	0.989371i	$0.546451\pi$
$242$	5.68837	0.365662
$243$	15.3899	0.987260
$244$	−3.67885	−0.235514
$245$	5.38748	0.344193
$246$	−3.81406	−0.243175
$247$	−7.72382	−0.491455
$248$	1.00000	0.0635001
$249$	−12.1082	−0.767328
$250$	−1.00000	−0.0632456
$251$	4.12005	0.260055	0.130028	−	0.991510i	$-0.458493\pi$
$251$	4.12005	0.260055	0.130028	+	0.991510i	$0.458493\pi$
$252$	2.08044	0.131055
$253$	−17.6088	−1.10706
$254$	6.52502	0.409416
$255$	−12.9650	−0.811901
$256$	1.00000	0.0625000
$257$	16.0831	1.00324	0.501618	−	0.865089i	$-0.332738\pi$
$257$	16.0831	1.00324	0.501618	+	0.865089i	$0.332738\pi$
$258$	−17.4188	−1.08445
$259$	3.40283	0.211442
$260$	−1.00000	−0.0620174
$261$	7.21797	0.446781
$262$	15.6603	0.967497
$263$	4.48132	0.276330	0.138165	−	0.990409i	$-0.455880\pi$
$263$	4.48132	0.276330	0.138165	+	0.990409i	$0.455880\pi$
$264$	8.79808	0.541484
$265$	0.464054	0.0285066
$266$	−9.80810	−0.601373
$267$	−20.4936	−1.25419
$268$	−1.82982	−0.111774
$269$	10.3018	0.628112	0.314056	−	0.949405i	$-0.398312\pi$
$269$	10.3018	0.628112	0.314056	+	0.949405i	$0.398312\pi$
$270$	−2.93260	−0.178472
$271$	−23.0577	−1.40065	−0.700327	−	0.713822i	$-0.746963\pi$
$271$	−23.0577	−1.40065	−0.700327	+	0.713822i	$0.746963\pi$
$272$	−6.01995	−0.365013
$273$	−2.73485	−0.165521
$274$	−9.37298	−0.566243
$275$	−4.08514	−0.246343
$276$	−9.28335	−0.558792
$277$	7.90607	0.475030	0.237515	−	0.971384i	$-0.423667\pi$
$277$	7.90607	0.475030	0.237515	+	0.971384i	$0.423667\pi$
$278$	18.2263	1.09314
$279$	1.63833	0.0980842
$280$	−1.26985	−0.0758882
$281$	−17.5978	−1.04980	−0.524900	−	0.851164i	$-0.675897\pi$
$281$	−17.5978	−1.04980	−0.524900	+	0.851164i	$0.675897\pi$
$282$	−9.62556	−0.573194
$283$	−18.8226	−1.11889	−0.559444	−	0.828868i	$-0.688985\pi$
$283$	−18.8226	−1.11889	−0.559444	+	0.828868i	$0.688985\pi$
$284$	0.514493	0.0305296
$285$	−16.6346	−0.985349
$286$	−4.08514	−0.241559
$287$	2.24885	0.132745
$288$	1.63833	0.0965395
$289$	19.2397	1.13175
$290$	−4.40569	−0.258711
$291$	3.53740	0.207366
$292$	−9.88312	−0.578366
$293$	−6.11199	−0.357066	−0.178533	−	0.983934i	$-0.557135\pi$
$293$	−6.11199	−0.357066	−0.178533	+	0.983934i	$0.557135\pi$
$294$	11.6029	0.676694
$295$	−0.0503486	−0.00293141
$296$	2.67971	0.155755
$297$	−11.9801	−0.695155
$298$	15.1585	0.878108
$299$	4.31046	0.249280
$300$	−2.15368	−0.124343
$301$	10.2705	0.591981
$302$	−4.64154	−0.267090
$303$	−30.3471	−1.74340
$304$	−7.72382	−0.442991
$305$	3.67885	0.210650
$306$	−9.86265	−0.563810
$307$	18.6087	1.06205	0.531027	−	0.847355i	$-0.321806\pi$
$307$	18.6087	1.06205	0.531027	+	0.847355i	$0.321806\pi$
$308$	−5.18752	−0.295587
$309$	30.9965	1.76333
$310$	−1.00000	−0.0567962
$311$	−18.1267	−1.02787	−0.513936	−	0.857829i	$-0.671813\pi$
$311$	−18.1267	−1.02787	−0.513936	+	0.857829i	$0.671813\pi$
$312$	−2.15368	−0.121928
$313$	−32.6580	−1.84594	−0.922971	−	0.384870i	$-0.874246\pi$
$313$	−32.6580	−1.84594	−0.922971	+	0.384870i	$0.874246\pi$
$314$	9.77887	0.551854
$315$	−2.08044	−0.117219
$316$	5.65383	0.318053
$317$	11.7286	0.658742	0.329371	−	0.944201i	$-0.393163\pi$
$317$	11.7286	0.658742	0.329371	+	0.944201i	$0.393163\pi$
$318$	0.999423	0.0560449
$319$	−17.9979	−1.00769
$320$	−1.00000	−0.0559017
$321$	−30.3564	−1.69433
$322$	5.47365	0.305035
$323$	46.4969	2.58716
$324$	−11.2309	−0.623937
$325$	1.00000	0.0554700
$326$	7.83895	0.434159
$327$	−21.9822	−1.21562
$328$	1.77095	0.0977844
$329$	5.67542	0.312896
$330$	−8.79808	−0.484318
$331$	18.3118	1.00651	0.503254	−	0.864138i	$-0.332136\pi$
$331$	18.3118	1.00651	0.503254	+	0.864138i	$0.332136\pi$
$332$	5.62212	0.308554
$333$	4.39024	0.240584
$334$	−2.24810	−0.123011
$335$	1.82982	0.0999738
$336$	−2.73485	−0.149198
$337$	−18.7608	−1.02196	−0.510982	−	0.859591i	$-0.670718\pi$
$337$	−18.7608	−1.02196	−0.510982	+	0.859591i	$0.670718\pi$
$338$	1.00000	0.0543928
$339$	22.8092	1.23883
$340$	6.01995	0.326477
$341$	−4.08514	−0.221223
$342$	−12.6542	−0.684258
$343$	−15.7303	−0.849354
$344$	8.08794	0.436072
$345$	9.28335	0.499799
$346$	−0.994252	−0.0534513
$347$	9.84169	0.528329	0.264165	−	0.964478i	$-0.414904\pi$
$347$	9.84169	0.528329	0.264165	+	0.964478i	$0.414904\pi$
$348$	−9.48844	−0.508634
$349$	−29.0188	−1.55334	−0.776670	−	0.629908i	$-0.783093\pi$
$349$	−29.0188	−1.55334	−0.776670	+	0.629908i	$0.783093\pi$
$350$	1.26985	0.0678764
$351$	2.93260	0.156531
$352$	−4.08514	−0.217739
$353$	10.2563	0.545886	0.272943	−	0.962030i	$-0.412003\pi$
$353$	10.2563	0.545886	0.272943	+	0.962030i	$0.412003\pi$
$354$	−0.108435	−0.00576324
$355$	−0.514493	−0.0273065
$356$	9.51562	0.504327
$357$	16.4637	0.871349
$358$	26.0281	1.37563
$359$	−12.1640	−0.641989	−0.320995	−	0.947081i	$-0.604017\pi$
$359$	−12.1640	−0.641989	−0.320995	+	0.947081i	$0.604017\pi$
$360$	−1.63833	−0.0863475
$361$	40.6573	2.13986
$362$	−1.64104	−0.0862512
$363$	−12.2509	−0.643006
$364$	1.26985	0.0665583
$365$	9.88312	0.517306
$366$	7.92306	0.414145
$367$	28.8505	1.50599	0.752993	−	0.658029i	$-0.228610\pi$
$367$	28.8505	1.50599	0.752993	+	0.658029i	$0.228610\pi$
$368$	4.31046	0.224698
$369$	2.90140	0.151041
$370$	−2.67971	−0.139311
$371$	−0.589280	−0.0305939
$372$	−2.15368	−0.111663
$373$	−30.8764	−1.59872	−0.799359	−	0.600854i	$-0.794827\pi$
$373$	−30.8764	−1.59872	−0.799359	+	0.600854i	$0.794827\pi$
$374$	24.5923	1.27164
$375$	2.15368	0.111215
$376$	4.46936	0.230490
$377$	4.40569	0.226905
$378$	3.72397	0.191540
$379$	−31.9281	−1.64003	−0.820017	−	0.572339i	$-0.806036\pi$
$379$	−31.9281	−1.64003	−0.820017	+	0.572339i	$0.806036\pi$
$380$	7.72382	0.396223
$381$	−14.0528	−0.719947
$382$	15.7124	0.803918
$383$	26.6731	1.36293	0.681466	−	0.731850i	$-0.261343\pi$
$383$	26.6731	1.36293	0.681466	+	0.731850i	$0.261343\pi$
$384$	−2.15368	−0.109904
$385$	5.18752	0.264381
$386$	−6.79521	−0.345867
$387$	13.2507	0.673571
$388$	−1.64249	−0.0833850
$389$	−22.9749	−1.16487	−0.582436	−	0.812877i	$-0.697900\pi$
$389$	−22.9749	−1.16487	−0.582436	+	0.812877i	$0.697900\pi$
$390$	2.15368	0.109056
$391$	−25.9487	−1.31228
$392$	−5.38748	−0.272109
$393$	−33.7272	−1.70131
$394$	21.3206	1.07411
$395$	−5.65383	−0.284475
$396$	−6.69280	−0.336326
$397$	−24.2453	−1.21684	−0.608418	−	0.793617i	$-0.708195\pi$
$397$	−24.2453	−1.21684	−0.608418	+	0.793617i	$0.708195\pi$
$398$	2.44230	0.122421
$399$	21.1235	1.05750
$400$	1.00000	0.0500000
$401$	26.8108	1.33887	0.669433	−	0.742872i	$-0.266537\pi$
$401$	26.8108	1.33887	0.669433	+	0.742872i	$0.266537\pi$
$402$	3.94085	0.196552
$403$	1.00000	0.0498135
$404$	14.0908	0.701045
$405$	11.2309	0.558066
$406$	5.59458	0.277654
$407$	−10.9470	−0.542622
$408$	12.9650	0.641864
$409$	−14.6008	−0.721964	−0.360982	−	0.932573i	$-0.617558\pi$
$409$	−14.6008	−0.721964	−0.360982	+	0.932573i	$0.617558\pi$
$410$	−1.77095	−0.0874610
$411$	20.1864	0.995721
$412$	−14.3924	−0.709062
$413$	0.0639353	0.00314605
$414$	7.06196	0.347076
$415$	−5.62212	−0.275979
$416$	1.00000	0.0490290
$417$	−39.2536	−1.92226
$418$	31.5529	1.54330
$419$	20.0883	0.981377	0.490689	−	0.871335i	$-0.336745\pi$
$419$	20.0883	0.981377	0.490689	+	0.871335i	$0.336745\pi$
$420$	2.73485	0.133447
$421$	−37.6799	−1.83641	−0.918203	−	0.396109i	$-0.870360\pi$
$421$	−37.6799	−1.83641	−0.918203	+	0.396109i	$0.870360\pi$
$422$	8.01904	0.390361
$423$	7.32228	0.356021
$424$	−0.464054	−0.0225365
$425$	−6.01995	−0.292010
$426$	−1.10805	−0.0536854
$427$	−4.67159	−0.226074
$428$	14.0952	0.681315
$429$	8.79808	0.424775
$430$	−8.08794	−0.390035
$431$	−14.0630	−0.677393	−0.338696	−	0.940896i	$-0.609986\pi$
$431$	−14.0630	−0.677393	−0.338696	+	0.940896i	$0.609986\pi$
$432$	2.93260	0.141095
$433$	−21.3097	−1.02408	−0.512040	−	0.858961i	$-0.671110\pi$
$433$	−21.3097	−1.02408	−0.512040	+	0.858961i	$0.671110\pi$
$434$	1.26985	0.0609548
$435$	9.48844	0.454936
$436$	10.2068	0.488818
$437$	−33.2932	−1.59263
$438$	21.2851	1.01704
$439$	20.7464	0.990174	0.495087	−	0.868843i	$-0.335136\pi$
$439$	20.7464	0.990174	0.495087	+	0.868843i	$0.335136\pi$
$440$	4.08514	0.194751
$441$	−8.82646	−0.420308
$442$	−6.01995	−0.286340
$443$	−17.6119	−0.836765	−0.418383	−	0.908271i	$-0.637403\pi$
$443$	−17.6119	−0.836765	−0.418383	+	0.908271i	$0.637403\pi$
$444$	−5.77123	−0.273890
$445$	−9.51562	−0.451084
$446$	2.15328	0.101961
$447$	−32.6465	−1.54413
$448$	1.26985	0.0599949
$449$	20.7869	0.980994	0.490497	−	0.871443i	$-0.336815\pi$
$449$	20.7869	0.980994	0.490497	+	0.871443i	$0.336815\pi$
$450$	1.63833	0.0772316
$451$	−7.23458	−0.340663
$452$	−10.5908	−0.498151
$453$	9.99638	0.469671
$454$	−19.7374	−0.926323
$455$	−1.26985	−0.0595316
$456$	16.6346	0.778987
$457$	36.7730	1.72017	0.860085	−	0.510151i	$-0.170411\pi$
$457$	36.7730	1.72017	0.860085	+	0.510151i	$0.170411\pi$
$458$	22.8707	1.06868
$459$	−17.6541	−0.824023
$460$	−4.31046	−0.200976
$461$	−6.16451	−0.287110	−0.143555	−	0.989642i	$-0.545853\pi$
$461$	−6.16451	−0.287110	−0.143555	+	0.989642i	$0.545853\pi$
$462$	11.1723	0.519780
$463$	4.17218	0.193897	0.0969487	−	0.995289i	$-0.469092\pi$
$463$	4.17218	0.193897	0.0969487	+	0.995289i	$0.469092\pi$
$464$	4.40569	0.204529
$465$	2.15368	0.0998744
$466$	8.10578	0.375493
$467$	−2.73033	−0.126345	−0.0631724	−	0.998003i	$-0.520122\pi$
$467$	−2.73033	−0.126345	−0.0631724	+	0.998003i	$0.520122\pi$
$468$	1.63833	0.0757318
$469$	−2.32360	−0.107294
$470$	−4.46936	−0.206156
$471$	−21.0605	−0.970418
$472$	0.0503486	0.00231748
$473$	−33.0403	−1.51920
$474$	−12.1765	−0.559287
$475$	−7.72382	−0.354393
$476$	−7.64444	−0.350382
$477$	−0.760273	−0.0348105
$478$	0.812589	0.0371670
$479$	5.21289	0.238183	0.119091	−	0.992883i	$-0.462002\pi$
$479$	5.21289	0.238183	0.119091	+	0.992883i	$0.462002\pi$
$480$	2.15368	0.0983015
$481$	2.67971	0.122184
$482$	−4.51481	−0.205644
$483$	−11.7885	−0.536394
$484$	5.68837	0.258562
$485$	1.64249	0.0745818
$486$	15.3899	0.698098
$487$	11.4169	0.517351	0.258675	−	0.965964i	$-0.416714\pi$
$487$	11.4169	0.517351	0.258675	+	0.965964i	$0.416714\pi$
$488$	−3.67885	−0.166534
$489$	−16.8826	−0.763457
$490$	5.38748	0.243381
$491$	15.1799	0.685057	0.342529	−	0.939507i	$-0.388717\pi$
$491$	15.1799	0.685057	0.342529	+	0.939507i	$0.388717\pi$
$492$	−3.81406	−0.171951
$493$	−26.5220	−1.19449
$494$	−7.72382	−0.347511
$495$	6.69280	0.300819
$496$	1.00000	0.0449013
$497$	0.653331	0.0293059
$498$	−12.1082	−0.542583
$499$	37.9924	1.70078	0.850388	−	0.526157i	$-0.176368\pi$
$499$	37.9924	1.70078	0.850388	+	0.526157i	$0.176368\pi$
$500$	−1.00000	−0.0447214
$501$	4.84169	0.216311
$502$	4.12005	0.183887
$503$	4.42989	0.197519	0.0987595	−	0.995111i	$-0.468513\pi$
$503$	4.42989	0.197519	0.0987595	+	0.995111i	$0.468513\pi$
$504$	2.08044	0.0926700
$505$	−14.0908	−0.627034
$506$	−17.6088	−0.782808
$507$	−2.15368	−0.0956482
$508$	6.52502	0.289501
$509$	−1.50377	−0.0666532	−0.0333266	−	0.999445i	$-0.510610\pi$
$509$	−1.50377	−0.0666532	−0.0333266	+	0.999445i	$0.510610\pi$
$510$	−12.9650	−0.574101
$511$	−12.5501	−0.555184
$512$	1.00000	0.0441942
$513$	−22.6509	−1.00006
$514$	16.0831	0.709395
$515$	14.3924	0.634204
$516$	−17.4188	−0.766820
$517$	−18.2580	−0.802984
$518$	3.40283	0.149512
$519$	2.14130	0.0939926
$520$	−1.00000	−0.0438529
$521$	−10.8595	−0.475765	−0.237882	−	0.971294i	$-0.576453\pi$
$521$	−10.8595	−0.475765	−0.237882	+	0.971294i	$0.576453\pi$
$522$	7.21797	0.315922
$523$	27.9462	1.22200	0.611000	−	0.791630i	$-0.290767\pi$
$523$	27.9462	1.22200	0.611000	+	0.791630i	$0.290767\pi$
$524$	15.6603	0.684123
$525$	−2.73485	−0.119359
$526$	4.48132	0.195395
$527$	−6.01995	−0.262233
$528$	8.79808	0.382887
$529$	−4.41992	−0.192170
$530$	0.464054	0.0201572
$531$	0.0824876	0.00357966
$532$	−9.80810	−0.425235
$533$	1.77095	0.0767084
$534$	−20.4936	−0.886844
$535$	−14.0952	−0.609387
$536$	−1.82982	−0.0790362
$537$	−56.0561	−2.41900
$538$	10.3018	0.444142
$539$	22.0086	0.947977
$540$	−2.93260	−0.126199
$541$	−14.8441	−0.638199	−0.319100	−	0.947721i	$-0.603380\pi$
$541$	−14.8441	−0.638199	−0.319100	+	0.947721i	$0.603380\pi$
$542$	−23.0577	−0.990412
$543$	3.53428	0.151670
$544$	−6.01995	−0.258103
$545$	−10.2068	−0.437212
$546$	−2.73485	−0.117041
$547$	−20.9267	−0.894762	−0.447381	−	0.894343i	$-0.647643\pi$
$547$	−20.9267	−0.894762	−0.447381	+	0.894343i	$0.647643\pi$
$548$	−9.37298	−0.400394
$549$	−6.02716	−0.257233
$550$	−4.08514	−0.174191
$551$	−34.0288	−1.44967
$552$	−9.28335	−0.395126
$553$	7.17953	0.305305
$554$	7.90607	0.335897
$555$	5.77123	0.244975
$556$	18.2263	0.772968
$557$	−14.9154	−0.631986	−0.315993	−	0.948762i	$-0.602338\pi$
$557$	−14.9154	−0.631986	−0.315993	+	0.948762i	$0.602338\pi$
$558$	1.63833	0.0693560
$559$	8.08794	0.342083
$560$	−1.26985	−0.0536610
$561$	−52.9639	−2.23614
$562$	−17.5978	−0.742320
$563$	23.2274	0.978918	0.489459	−	0.872026i	$-0.337194\pi$
$563$	23.2274	0.978918	0.489459	+	0.872026i	$0.337194\pi$
$564$	−9.62556	−0.405309
$565$	10.5908	0.445559
$566$	−18.8226	−0.791173
$567$	−14.2615	−0.598928
$568$	0.514493	0.0215877
$569$	38.9596	1.63327	0.816637	−	0.577152i	$-0.195836\pi$
$569$	38.9596	1.63327	0.816637	+	0.577152i	$0.195836\pi$
$570$	−16.6346	−0.696747
$571$	−32.3171	−1.35243	−0.676214	−	0.736705i	$-0.736380\pi$
$571$	−32.3171	−1.35243	−0.676214	+	0.736705i	$0.736380\pi$
$572$	−4.08514	−0.170808
$573$	−33.8395	−1.41367
$574$	2.24885	0.0938650
$575$	4.31046	0.179759
$576$	1.63833	0.0682637
$577$	24.8116	1.03292	0.516460	−	0.856311i	$-0.327249\pi$
$577$	24.8116	1.03292	0.516460	+	0.856311i	$0.327249\pi$
$578$	19.2397	0.800268
$579$	14.6347	0.608197
$580$	−4.40569	−0.182936
$581$	7.13926	0.296186
$582$	3.53740	0.146630
$583$	1.89573	0.0785130
$584$	−9.88312	−0.408966
$585$	−1.63833	−0.0677366
$586$	−6.11199	−0.252484
$587$	−31.7984	−1.31246	−0.656231	−	0.754560i	$-0.727850\pi$
$587$	−31.7984	−1.31246	−0.656231	+	0.754560i	$0.727850\pi$
$588$	11.6029	0.478495
$589$	−7.72382	−0.318254
$590$	−0.0503486	−0.00207282
$591$	−45.9176	−1.88880
$592$	2.67971	0.110135
$593$	0.630523	0.0258925	0.0129462	−	0.999916i	$-0.495879\pi$
$593$	0.630523	0.0258925	0.0129462	+	0.999916i	$0.495879\pi$
$594$	−11.9801	−0.491549
$595$	7.64444	0.313391
$596$	15.1585	0.620916
$597$	−5.25992	−0.215274
$598$	4.31046	0.176268
$599$	−9.31288	−0.380514	−0.190257	−	0.981734i	$-0.560932\pi$
$599$	−9.31288	−0.380514	−0.190257	+	0.981734i	$0.560932\pi$
$600$	−2.15368	−0.0879235
$601$	45.5149	1.85659	0.928296	−	0.371842i	$-0.121274\pi$
$601$	45.5149	1.85659	0.928296	+	0.371842i	$0.121274\pi$
$602$	10.2705	0.418594
$603$	−2.99785	−0.122082
$604$	−4.64154	−0.188861
$605$	−5.68837	−0.231265
$606$	−30.3471	−1.23277
$607$	11.2520	0.456705	0.228352	−	0.973579i	$-0.426666\pi$
$607$	11.2520	0.456705	0.228352	+	0.973579i	$0.426666\pi$
$608$	−7.72382	−0.313242
$609$	−12.0489	−0.488247
$610$	3.67885	0.148952
$611$	4.46936	0.180811
$612$	−9.86265	−0.398674
$613$	−25.2179	−1.01854	−0.509271	−	0.860606i	$-0.670085\pi$
$613$	−25.2179	−1.01854	−0.509271	+	0.860606i	$0.670085\pi$
$614$	18.6087	0.750985
$615$	3.81406	0.153798
$616$	−5.18752	−0.209011
$617$	−13.6328	−0.548835	−0.274417	−	0.961611i	$-0.588485\pi$
$617$	−13.6328	−0.548835	−0.274417	+	0.961611i	$0.588485\pi$
$618$	30.9965	1.24686
$619$	−9.74726	−0.391775	−0.195888	−	0.980626i	$-0.562759\pi$
$619$	−9.74726	−0.391775	−0.195888	+	0.980626i	$0.562759\pi$
$620$	−1.00000	−0.0401610
$621$	12.6409	0.507260
$622$	−18.1267	−0.726815
$623$	12.0834	0.484112
$624$	−2.15368	−0.0862161
$625$	1.00000	0.0400000
$626$	−32.6580	−1.30528
$627$	−67.9547	−2.71385
$628$	9.77887	0.390219
$629$	−16.1317	−0.643213
$630$	−2.08044	−0.0828865
$631$	16.0903	0.640543	0.320272	−	0.947326i	$-0.396226\pi$
$631$	16.0903	0.640543	0.320272	+	0.947326i	$0.396226\pi$
$632$	5.65383	0.224897
$633$	−17.2704	−0.686438
$634$	11.7286	0.465801
$635$	−6.52502	−0.258938
$636$	0.999423	0.0396297
$637$	−5.38748	−0.213460
$638$	−17.9979	−0.712542
$639$	0.842910	0.0333450
$640$	−1.00000	−0.0395285
$641$	35.9522	1.42003	0.710014	−	0.704187i	$-0.248688\pi$
$641$	35.9522	1.42003	0.710014	+	0.704187i	$0.248688\pi$
$642$	−30.3564	−1.19807
$643$	29.3603	1.15786	0.578929	−	0.815378i	$-0.303471\pi$
$643$	29.3603	1.15786	0.578929	+	0.815378i	$0.303471\pi$
$644$	5.47365	0.215692
$645$	17.4188	0.685865
$646$	46.4969	1.82940
$647$	7.62634	0.299822	0.149911	−	0.988699i	$-0.452101\pi$
$647$	7.62634	0.299822	0.149911	+	0.988699i	$0.452101\pi$
$648$	−11.2309	−0.441190
$649$	−0.205681	−0.00807369
$650$	1.00000	0.0392232
$651$	−2.73485	−0.107187
$652$	7.83895	0.306997
$653$	−45.6078	−1.78477	−0.892386	−	0.451273i	$-0.850970\pi$
$653$	−45.6078	−1.78477	−0.892386	+	0.451273i	$0.850970\pi$
$654$	−21.9822	−0.859572
$655$	−15.6603	−0.611899
$656$	1.77095	0.0691440
$657$	−16.1918	−0.631702
$658$	5.67542	0.221251
$659$	0.948105	0.0369329	0.0184665	−	0.999829i	$-0.494122\pi$
$659$	0.948105	0.0369329	0.0184665	+	0.999829i	$0.494122\pi$
$660$	−8.79808	−0.342465
$661$	18.6181	0.724158	0.362079	−	0.932147i	$-0.382067\pi$
$661$	18.6181	0.724158	0.362079	+	0.932147i	$0.382067\pi$
$662$	18.3118	0.711709
$663$	12.9650	0.503520
$664$	5.62212	0.218180
$665$	9.80810	0.380342
$666$	4.39024	0.170119
$667$	18.9906	0.735318
$668$	−2.24810	−0.0869818
$669$	−4.63748	−0.179295
$670$	1.82982	0.0706922
$671$	15.0286	0.580173
$672$	−2.73485	−0.105499
$673$	18.7376	0.722281	0.361140	−	0.932511i	$-0.382388\pi$
$673$	18.7376	0.722281	0.361140	+	0.932511i	$0.382388\pi$
$674$	−18.7608	−0.722638
$675$	2.93260	0.112876
$676$	1.00000	0.0384615
$677$	−41.4022	−1.59121	−0.795607	−	0.605813i	$-0.792848\pi$
$677$	−41.4022	−1.59121	−0.795607	+	0.605813i	$0.792848\pi$
$678$	22.8092	0.875983
$679$	−2.08572	−0.0800427
$680$	6.01995	0.230854
$681$	42.5080	1.62891
$682$	−4.08514	−0.156428
$683$	19.7621	0.756178	0.378089	−	0.925769i	$-0.376581\pi$
$683$	19.7621	0.756178	0.378089	+	0.925769i	$0.376581\pi$
$684$	−12.6542	−0.483844
$685$	9.37298	0.358123
$686$	−15.7303	−0.600584
$687$	−49.2561	−1.87924
$688$	8.08794	0.308350
$689$	−0.464054	−0.0176791
$690$	9.28335	0.353411
$691$	8.78414	0.334165	0.167082	−	0.985943i	$-0.446565\pi$
$691$	8.78414	0.334165	0.167082	+	0.985943i	$0.446565\pi$
$692$	−0.994252	−0.0377958
$693$	−8.49887	−0.322845
$694$	9.84169	0.373585
$695$	−18.2263	−0.691364
$696$	−9.48844	−0.359658
$697$	−10.6610	−0.403815
$698$	−29.0188	−1.09838
$699$	−17.4572	−0.660293
$700$	1.26985	0.0479959
$701$	41.3700	1.56252	0.781261	−	0.624204i	$-0.214577\pi$
$701$	41.3700	1.56252	0.781261	+	0.624204i	$0.214577\pi$
$702$	2.93260	0.110684
$703$	−20.6976	−0.780624
$704$	−4.08514	−0.153965
$705$	9.62556	0.362519
$706$	10.2563	0.386000
$707$	17.8933	0.672946
$708$	−0.108435	−0.00407523
$709$	19.3794	0.727807	0.363904	−	0.931437i	$-0.381444\pi$
$709$	19.3794	0.727807	0.363904	+	0.931437i	$0.381444\pi$
$710$	−0.514493	−0.0193086
$711$	9.26284	0.347383
$712$	9.51562	0.356613
$713$	4.31046	0.161428
$714$	16.4637	0.616137
$715$	4.08514	0.152776
$716$	26.0281	0.972716
$717$	−1.75006	−0.0653570
$718$	−12.1640	−0.453955
$719$	10.5843	0.394727	0.197364	−	0.980330i	$-0.436762\pi$
$719$	10.5843	0.394727	0.197364	+	0.980330i	$0.436762\pi$
$720$	−1.63833	−0.0610569
$721$	−18.2762	−0.680641
$722$	40.6573	1.51311
$723$	9.72344	0.361619
$724$	−1.64104	−0.0609888
$725$	4.40569	0.163623
$726$	−12.2509	−0.454674
$727$	−2.72924	−0.101222	−0.0506110	−	0.998718i	$-0.516117\pi$
$727$	−2.72924	−0.101222	−0.0506110	+	0.998718i	$0.516117\pi$
$728$	1.26985	0.0470638
$729$	0.547782	0.0202882
$730$	9.88312	0.365791
$731$	−48.6889	−1.80083
$732$	7.92306	0.292845
$733$	−37.8994	−1.39985	−0.699923	−	0.714219i	$-0.746782\pi$
$733$	−37.8994	−1.39985	−0.699923	+	0.714219i	$0.746782\pi$
$734$	28.8505	1.06489
$735$	−11.6029	−0.427979
$736$	4.31046	0.158886
$737$	7.47508	0.275348
$738$	2.90140	0.106802
$739$	17.1868	0.632228	0.316114	−	0.948721i	$-0.397622\pi$
$739$	17.1868	0.632228	0.316114	+	0.948721i	$0.397622\pi$
$740$	−2.67971	−0.0985081
$741$	16.6346	0.611088
$742$	−0.589280	−0.0216332
$743$	1.10199	0.0404280	0.0202140	−	0.999796i	$-0.493565\pi$
$743$	1.10199	0.0404280	0.0202140	+	0.999796i	$0.493565\pi$
$744$	−2.15368	−0.0789577
$745$	−15.1585	−0.555364
$746$	−30.8764	−1.13046
$747$	9.21088	0.337008
$748$	24.5923	0.899184
$749$	17.8988	0.654007
$750$	2.15368	0.0786412
$751$	−8.21332	−0.299708	−0.149854	−	0.988708i	$-0.547880\pi$
$751$	−8.21332	−0.299708	−0.149854	+	0.988708i	$0.547880\pi$
$752$	4.46936	0.162981
$753$	−8.87327	−0.323360
$754$	4.40569	0.160446
$755$	4.64154	0.168923
$756$	3.72397	0.135439
$757$	−11.2623	−0.409334	−0.204667	−	0.978832i	$-0.565611\pi$
$757$	−11.2623	−0.409334	−0.204667	+	0.978832i	$0.565611\pi$
$758$	−31.9281	−1.15968
$759$	37.9238	1.37655
$760$	7.72382	0.280172
$761$	−28.3135	−1.02636	−0.513181	−	0.858280i	$-0.671533\pi$
$761$	−28.3135	−1.02636	−0.513181	+	0.858280i	$0.671533\pi$
$762$	−14.0528	−0.509079
$763$	12.9612	0.469225
$764$	15.7124	0.568456
$765$	9.86265	0.356585
$766$	26.6731	0.963738
$767$	0.0503486	0.00181798
$768$	−2.15368	−0.0777142
$769$	17.6583	0.636775	0.318387	−	0.947961i	$-0.396859\pi$
$769$	17.6583	0.636775	0.318387	+	0.947961i	$0.396859\pi$
$770$	5.18752	0.186945
$771$	−34.6378	−1.24745
$772$	−6.79521	−0.244565
$773$	21.1896	0.762136	0.381068	−	0.924547i	$-0.375556\pi$
$773$	21.1896	0.762136	0.381068	+	0.924547i	$0.375556\pi$
$774$	13.2507	0.476287
$775$	1.00000	0.0359211
$776$	−1.64249	−0.0589621
$777$	−7.32861	−0.262912
$778$	−22.9749	−0.823688
$779$	−13.6785	−0.490083
$780$	2.15368	0.0771140
$781$	−2.10178	−0.0752075
$782$	−25.9487	−0.927925
$783$	12.9201	0.461728
$784$	−5.38748	−0.192410
$785$	−9.77887	−0.349023
$786$	−33.7272	−1.20301
$787$	7.37451	0.262873	0.131436	−	0.991325i	$-0.458041\pi$
$787$	7.37451	0.262873	0.131436	+	0.991325i	$0.458041\pi$
$788$	21.3206	0.759513
$789$	−9.65132	−0.343596
$790$	−5.65383	−0.201154
$791$	−13.4488	−0.478184
$792$	−6.69280	−0.237818
$793$	−3.67885	−0.130640
$794$	−24.2453	−0.860432
$795$	−0.999423	−0.0354459
$796$	2.44230	0.0865649
$797$	−2.22748	−0.0789015	−0.0394508	−	0.999222i	$-0.512561\pi$
$797$	−2.22748	−0.0789015	−0.0394508	+	0.999222i	$0.512561\pi$
$798$	21.1235	0.747764
$799$	−26.9053	−0.951841
$800$	1.00000	0.0353553
$801$	15.5897	0.550835
$802$	26.8108	0.946721
$803$	40.3739	1.42476
$804$	3.94085	0.138983
$805$	−5.47365	−0.192921
$806$	1.00000	0.0352235
$807$	−22.1868	−0.781011
$808$	14.0908	0.495714
$809$	−34.3023	−1.20600	−0.603002	−	0.797740i	$-0.706029\pi$
$809$	−34.3023	−1.20600	−0.603002	+	0.797740i	$0.706029\pi$
$810$	11.2309	0.394612
$811$	43.2229	1.51776	0.758881	−	0.651229i	$-0.225746\pi$
$811$	43.2229	1.51776	0.758881	+	0.651229i	$0.225746\pi$
$812$	5.59458	0.196331
$813$	49.6588	1.74161
$814$	−10.9470	−0.383692
$815$	−7.83895	−0.274586
$816$	12.9650	0.453867
$817$	−62.4697	−2.18554
$818$	−14.6008	−0.510506
$819$	2.08044	0.0726963
$820$	−1.77095	−0.0618443
$821$	22.3748	0.780884	0.390442	−	0.920627i	$-0.372322\pi$
$821$	22.3748	0.780884	0.390442	+	0.920627i	$0.372322\pi$
$822$	20.1864	0.704081
$823$	−42.0435	−1.46554	−0.732772	−	0.680474i	$-0.761774\pi$
$823$	−42.0435	−1.46554	−0.732772	+	0.680474i	$0.761774\pi$
$824$	−14.3924	−0.501382
$825$	8.79808	0.306310
$826$	0.0639353	0.00222459
$827$	13.0282	0.453034	0.226517	−	0.974007i	$-0.427266\pi$
$827$	13.0282	0.453034	0.226517	+	0.974007i	$0.427266\pi$
$828$	7.06196	0.245420
$829$	39.7810	1.38165	0.690826	−	0.723021i	$-0.257247\pi$
$829$	39.7810	1.38165	0.690826	+	0.723021i	$0.257247\pi$
$830$	−5.62212	−0.195147
$831$	−17.0271	−0.590665
$832$	1.00000	0.0346688
$833$	32.4323	1.12371
$834$	−39.2536	−1.35924
$835$	2.24810	0.0777989
$836$	31.5529	1.09128
$837$	2.93260	0.101366
$838$	20.0883	0.693938
$839$	16.9123	0.583879	0.291939	−	0.956437i	$-0.405699\pi$
$839$	16.9123	0.583879	0.291939	+	0.956437i	$0.405699\pi$
$840$	2.73485	0.0943614
$841$	−9.58988	−0.330685
$842$	−37.6799	−1.29854
$843$	37.9001	1.30535
$844$	8.01904	0.276027
$845$	−1.00000	−0.0344010
$846$	7.32228	0.251745
$847$	7.22338	0.248198
$848$	−0.464054	−0.0159357
$849$	40.5378	1.39125
$850$	−6.01995	−0.206482
$851$	11.5508	0.395956
$852$	−1.10805	−0.0379613
$853$	−53.2808	−1.82430	−0.912150	−	0.409856i	$-0.865579\pi$
$853$	−53.2808	−1.82430	−0.912150	+	0.409856i	$0.865579\pi$
$854$	−4.67159	−0.159859
$855$	12.6542	0.432763
$856$	14.0952	0.481763
$857$	51.7142	1.76652	0.883261	−	0.468881i	$-0.155343\pi$
$857$	51.7142	1.76652	0.883261	+	0.468881i	$0.155343\pi$
$858$	8.79808	0.300361
$859$	−5.48815	−0.187253	−0.0936267	−	0.995607i	$-0.529846\pi$
$859$	−5.48815	−0.187253	−0.0936267	+	0.995607i	$0.529846\pi$
$860$	−8.08794	−0.275796
$861$	−4.84329	−0.165059
$862$	−14.0630	−0.478989
$863$	−29.7708	−1.01341	−0.506705	−	0.862119i	$-0.669137\pi$
$863$	−29.7708	−1.01341	−0.506705	+	0.862119i	$0.669137\pi$
$864$	2.93260	0.0997691
$865$	0.994252	0.0338056
$866$	−21.3097	−0.724134
$867$	−41.4362	−1.40725
$868$	1.26985	0.0431016
$869$	−23.0967	−0.783502
$870$	9.48844	0.321688
$871$	−1.82982	−0.0620011
$872$	10.2068	0.345647
$873$	−2.69094	−0.0910747
$874$	−33.2932	−1.12616
$875$	−1.26985	−0.0429288
$876$	21.2851	0.719155
$877$	6.40857	0.216402	0.108201	−	0.994129i	$-0.465491\pi$
$877$	6.40857	0.216402	0.108201	+	0.994129i	$0.465491\pi$
$878$	20.7464	0.700159
$879$	13.1633	0.443986
$880$	4.08514	0.137710
$881$	−29.3196	−0.987802	−0.493901	−	0.869518i	$-0.664429\pi$
$881$	−29.3196	−0.987802	−0.493901	+	0.869518i	$0.664429\pi$
$882$	−8.82646	−0.297202
$883$	−19.7591	−0.664947	−0.332473	−	0.943113i	$-0.607883\pi$
$883$	−19.7591	−0.664947	−0.332473	+	0.943113i	$0.607883\pi$
$884$	−6.01995	−0.202473
$885$	0.108435	0.00364499
$886$	−17.6119	−0.591682
$887$	5.76874	0.193695	0.0968477	−	0.995299i	$-0.469124\pi$
$887$	5.76874	0.193695	0.0968477	+	0.995299i	$0.469124\pi$
$888$	−5.77123	−0.193670
$889$	8.28581	0.277897
$890$	−9.51562	−0.318964
$891$	45.8797	1.53703
$892$	2.15328	0.0720972
$893$	−34.5205	−1.15518
$894$	−32.6465	−1.09186
$895$	−26.0281	−0.870023
$896$	1.26985	0.0424228
$897$	−9.28335	−0.309962
$898$	20.7869	0.693668
$899$	4.40569	0.146938
$900$	1.63833	0.0546110
$901$	2.79358	0.0930677
$902$	−7.23458	−0.240885
$903$	−22.1193	−0.736085
$904$	−10.5908	−0.352246
$905$	1.64104	0.0545501
$906$	9.99638	0.332107
$907$	19.3502	0.642514	0.321257	−	0.946992i	$-0.395895\pi$
$907$	19.3502	0.642514	0.321257	+	0.946992i	$0.395895\pi$
$908$	−19.7374	−0.655009
$909$	23.0854	0.765695
$910$	−1.26985	−0.0420952
$911$	−27.2837	−0.903951	−0.451975	−	0.892030i	$-0.649281\pi$
$911$	−27.2837	−0.903951	−0.451975	+	0.892030i	$0.649281\pi$
$912$	16.6346	0.550827
$913$	−22.9671	−0.760101
$914$	36.7730	1.21634
$915$	−7.92306	−0.261928
$916$	22.8707	0.755669
$917$	19.8863	0.656702
$918$	−17.6541	−0.582672
$919$	36.6807	1.20999	0.604993	−	0.796231i	$-0.293176\pi$
$919$	36.6807	1.20999	0.604993	+	0.796231i	$0.293176\pi$
$920$	−4.31046	−0.142112
$921$	−40.0771	−1.32059
$922$	−6.16451	−0.203017
$923$	0.514493	0.0169348
$924$	11.1723	0.367540
$925$	2.67971	0.0881083
$926$	4.17218	0.137106
$927$	−23.5795	−0.774451
$928$	4.40569	0.144624
$929$	−52.7149	−1.72952	−0.864759	−	0.502187i	$-0.832529\pi$
$929$	−52.7149	−1.72952	−0.864759	+	0.502187i	$0.832529\pi$
$930$	2.15368	0.0706219
$931$	41.6119	1.36377
$932$	8.10578	0.265514
$933$	39.0391	1.27808
$934$	−2.73033	−0.0893392
$935$	−24.5923	−0.804255
$936$	1.63833	0.0535505
$937$	−24.8897	−0.813110	−0.406555	−	0.913626i	$-0.633270\pi$
$937$	−24.8897	−0.813110	−0.406555	+	0.913626i	$0.633270\pi$
$938$	−2.32360	−0.0758683
$939$	70.3349	2.29529
$940$	−4.46936	−0.145774
$941$	−48.6563	−1.58615	−0.793076	−	0.609123i	$-0.791522\pi$
$941$	−48.6563	−1.58615	−0.793076	+	0.609123i	$0.791522\pi$
$942$	−21.0605	−0.686189
$943$	7.63362	0.248585
$944$	0.0503486	0.00163871
$945$	−3.72397	−0.121141
$946$	−33.0403	−1.07423
$947$	19.8107	0.643760	0.321880	−	0.946781i	$-0.395685\pi$
$947$	19.8107	0.643760	0.321880	+	0.946781i	$0.395685\pi$
$948$	−12.1765	−0.395475
$949$	−9.88312	−0.320820
$950$	−7.72382	−0.250594
$951$	−25.2595	−0.819097
$952$	−7.64444	−0.247758
$953$	−23.7054	−0.767895	−0.383947	−	0.923355i	$-0.625436\pi$
$953$	−23.7054	−0.767895	−0.383947	+	0.923355i	$0.625436\pi$
$954$	−0.760273	−0.0246148
$955$	−15.7124	−0.508442
$956$	0.812589	0.0262810
$957$	38.7616	1.25299
$958$	5.21289	0.168421
$959$	−11.9023	−0.384345
$960$	2.15368	0.0695097
$961$	1.00000	0.0322581
$962$	2.67971	0.0863973
$963$	23.0925	0.744146
$964$	−4.51481	−0.145412
$965$	6.79521	0.218746
$966$	−11.7885	−0.379288
$967$	37.8625	1.21758	0.608788	−	0.793333i	$-0.291656\pi$
$967$	37.8625	1.21758	0.608788	+	0.793333i	$0.291656\pi$
$968$	5.68837	0.182831
$969$	−100.139	−3.21694
$970$	1.64249	0.0527373
$971$	10.0272	0.321788	0.160894	−	0.986972i	$-0.448562\pi$
$971$	10.0272	0.321788	0.160894	+	0.986972i	$0.448562\pi$
$972$	15.3899	0.493630
$973$	23.1447	0.741986
$974$	11.4169	0.365822
$975$	−2.15368	−0.0689729
$976$	−3.67885	−0.117757
$977$	25.9529	0.830306	0.415153	−	0.909752i	$-0.363728\pi$
$977$	25.9529	0.830306	0.415153	+	0.909752i	$0.363728\pi$
$978$	−16.8826	−0.539845
$979$	−38.8726	−1.24237
$980$	5.38748	0.172097
$981$	16.7221	0.533897
$982$	15.1799	0.484409
$983$	−46.0757	−1.46959	−0.734794	−	0.678291i	$-0.762721\pi$
$983$	−46.0757	−1.46959	−0.734794	+	0.678291i	$0.762721\pi$
$984$	−3.81406	−0.121588
$985$	−21.3206	−0.679329
$986$	−26.5220	−0.844633
$987$	−12.2230	−0.389063
$988$	−7.72382	−0.245727
$989$	34.8627	1.10857
$990$	6.69280	0.212711
$991$	−1.25408	−0.0398370	−0.0199185	−	0.999802i	$-0.506341\pi$
$991$	−1.25408	−0.0398370	−0.0199185	+	0.999802i	$0.506341\pi$
$992$	1.00000	0.0317500
$993$	−39.4378	−1.25152
$994$	0.653331	0.0207224
$995$	−2.44230	−0.0774260
$996$	−12.1082	−0.383664
$997$	−47.6710	−1.50975	−0.754877	−	0.655866i	$-0.772304\pi$
$997$	−47.6710	−1.50975	−0.754877	+	0.655866i	$0.772304\pi$
$998$	37.9924	1.20263
$999$	7.85852	0.248632

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4030.2.a.q.1.2	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4030.2.a.q.1.2	✓	9	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:	\( N \)	\(=\)	\( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4030.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.15368 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.15368 q^{6} +1.26985 q^{7} +1.00000 q^{8} +1.63833 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.15368 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.15368 q^{6} +1.26985 q^{7} +1.00000 q^{8} +1.63833 q^{9} -1.00000 q^{10} -4.08514 q^{11} -2.15368 q^{12} +1.00000 q^{13} +1.26985 q^{14} +2.15368 q^{15} +1.00000 q^{16} -6.01995 q^{17} +1.63833 q^{18} -7.72382 q^{19} -1.00000 q^{20} -2.73485 q^{21} -4.08514 q^{22} +4.31046 q^{23} -2.15368 q^{24} +1.00000 q^{25} +1.00000 q^{26} +2.93260 q^{27} +1.26985 q^{28} +4.40569 q^{29} +2.15368 q^{30} +1.00000 q^{31} +1.00000 q^{32} +8.79808 q^{33} -6.01995 q^{34} -1.26985 q^{35} +1.63833 q^{36} +2.67971 q^{37} -7.72382 q^{38} -2.15368 q^{39} -1.00000 q^{40} +1.77095 q^{41} -2.73485 q^{42} +8.08794 q^{43} -4.08514 q^{44} -1.63833 q^{45} +4.31046 q^{46} +4.46936 q^{47} -2.15368 q^{48} -5.38748 q^{49} +1.00000 q^{50} +12.9650 q^{51} +1.00000 q^{52} -0.464054 q^{53} +2.93260 q^{54} +4.08514 q^{55} +1.26985 q^{56} +16.6346 q^{57} +4.40569 q^{58} +0.0503486 q^{59} +2.15368 q^{60} -3.67885 q^{61} +1.00000 q^{62} +2.08044 q^{63} +1.00000 q^{64} -1.00000 q^{65} +8.79808 q^{66} -1.82982 q^{67} -6.01995 q^{68} -9.28335 q^{69} -1.26985 q^{70} +0.514493 q^{71} +1.63833 q^{72} -9.88312 q^{73} +2.67971 q^{74} -2.15368 q^{75} -7.72382 q^{76} -5.18752 q^{77} -2.15368 q^{78} +5.65383 q^{79} -1.00000 q^{80} -11.2309 q^{81} +1.77095 q^{82} +5.62212 q^{83} -2.73485 q^{84} +6.01995 q^{85} +8.08794 q^{86} -9.48844 q^{87} -4.08514 q^{88} +9.51562 q^{89} -1.63833 q^{90} +1.26985 q^{91} +4.31046 q^{92} -2.15368 q^{93} +4.46936 q^{94} +7.72382 q^{95} -2.15368 q^{96} -1.64249 q^{97} -5.38748 q^{98} -6.69280 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} - 9 q^{5} + 3 q^{6} + 3 q^{7} + 9 q^{8} + 14 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 - 9 * q^5 + 3 * q^6 + 3 * q^7 + 9 * q^8 + 14 * q^9	\( 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} - 9 q^{5} + 3 q^{6} + 3 q^{7} + 9 q^{8} + 14 q^{9} - 9 q^{10} + 6 q^{11} + 3 q^{12} + 9 q^{13} + 3 q^{14} - 3 q^{15} + 9 q^{16} + 3 q^{17} + 14 q^{18} + 6 q^{19} - 9 q^{20} - q^{21} + 6 q^{22} + 14 q^{23} + 3 q^{24} + 9 q^{25} + 9 q^{26} + 9 q^{27} + 3 q^{28} + 17 q^{29} - 3 q^{30} + 9 q^{31} + 9 q^{32} - 8 q^{33} + 3 q^{34} - 3 q^{35} + 14 q^{36} - 3 q^{37} + 6 q^{38} + 3 q^{39} - 9 q^{40} + 4 q^{41} - q^{42} + 5 q^{43} + 6 q^{44} - 14 q^{45} + 14 q^{46} + 25 q^{47} + 3 q^{48} + 8 q^{49} + 9 q^{50} + 15 q^{51} + 9 q^{52} + 18 q^{53} + 9 q^{54} - 6 q^{55} + 3 q^{56} + 13 q^{57} + 17 q^{58} - 6 q^{59} - 3 q^{60} + 26 q^{61} + 9 q^{62} + 8 q^{63} + 9 q^{64} - 9 q^{65} - 8 q^{66} - 2 q^{67} + 3 q^{68} + 8 q^{69} - 3 q^{70} + 18 q^{71} + 14 q^{72} - 5 q^{73} - 3 q^{74} + 3 q^{75} + 6 q^{76} + 19 q^{77} + 3 q^{78} + 18 q^{79} - 9 q^{80} + 41 q^{81} + 4 q^{82} + 13 q^{83} - q^{84} - 3 q^{85} + 5 q^{86} + 19 q^{87} + 6 q^{88} + 9 q^{89} - 14 q^{90} + 3 q^{91} + 14 q^{92} + 3 q^{93} + 25 q^{94} - 6 q^{95} + 3 q^{96} - 18 q^{97} + 8 q^{98} + 21 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 - 9 * q^5 + 3 * q^6 + 3 * q^7 + 9 * q^8 + 14 * q^9 - 9 * q^10 + 6 * q^11 + 3 * q^12 + 9 * q^13 + 3 * q^14 - 3 * q^15 + 9 * q^16 + 3 * q^17 + 14 * q^18 + 6 * q^19 - 9 * q^20 - q^21 + 6 * q^22 + 14 * q^23 + 3 * q^24 + 9 * q^25 + 9 * q^26 + 9 * q^27 + 3 * q^28 + 17 * q^29 - 3 * q^30 + 9 * q^31 + 9 * q^32 - 8 * q^33 + 3 * q^34 - 3 * q^35 + 14 * q^36 - 3 * q^37 + 6 * q^38 + 3 * q^39 - 9 * q^40 + 4 * q^41 - q^42 + 5 * q^43 + 6 * q^44 - 14 * q^45 + 14 * q^46 + 25 * q^47 + 3 * q^48 + 8 * q^49 + 9 * q^50 + 15 * q^51 + 9 * q^52 + 18 * q^53 + 9 * q^54 - 6 * q^55 + 3 * q^56 + 13 * q^57 + 17 * q^58 - 6 * q^59 - 3 * q^60 + 26 * q^61 + 9 * q^62 + 8 * q^63 + 9 * q^64 - 9 * q^65 - 8 * q^66 - 2 * q^67 + 3 * q^68 + 8 * q^69 - 3 * q^70 + 18 * q^71 + 14 * q^72 - 5 * q^73 - 3 * q^74 + 3 * q^75 + 6 * q^76 + 19 * q^77 + 3 * q^78 + 18 * q^79 - 9 * q^80 + 41 * q^81 + 4 * q^82 + 13 * q^83 - q^84 - 3 * q^85 + 5 * q^86 + 19 * q^87 + 6 * q^88 + 9 * q^89 - 14 * q^90 + 3 * q^91 + 14 * q^92 + 3 * q^93 + 25 * q^94 - 6 * q^95 + 3 * q^96 - 18 * q^97 + 8 * q^98 + 21 * q^99

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