LMFDB - Embedded newform 4030.2.a.f.1.5

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:	$1$
Dimension:	$6$
Coefficient field:	6.6.4418197.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 7x^{4} - x^{3} + 12x^{2} + 3x - 1 $ x^6 - 7x^4 - x^3 + 12x^2 + 3*x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.467757$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +0.300926 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.300926 q^{6} +3.15038 q^{7} +1.00000 q^{8} -2.90944 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.300926 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.300926 q^{6} +3.15038 q^{7} +1.00000 q^{8} -2.90944 q^{9} -1.00000 q^{10} -4.96352 q^{11} +0.300926 q^{12} +1.00000 q^{13} +3.15038 q^{14} -0.300926 q^{15} +1.00000 q^{16} +1.88940 q^{17} -2.90944 q^{18} -4.66561 q^{19} -1.00000 q^{20} +0.948034 q^{21} -4.96352 q^{22} -4.45581 q^{23} +0.300926 q^{24} +1.00000 q^{25} +1.00000 q^{26} -1.77831 q^{27} +3.15038 q^{28} -2.08163 q^{29} -0.300926 q^{30} -1.00000 q^{31} +1.00000 q^{32} -1.49365 q^{33} +1.88940 q^{34} -3.15038 q^{35} -2.90944 q^{36} -5.70317 q^{37} -4.66561 q^{38} +0.300926 q^{39} -1.00000 q^{40} +6.80470 q^{41} +0.948034 q^{42} -0.777730 q^{43} -4.96352 q^{44} +2.90944 q^{45} -4.45581 q^{46} -6.80921 q^{47} +0.300926 q^{48} +2.92492 q^{49} +1.00000 q^{50} +0.568571 q^{51} +1.00000 q^{52} -3.39123 q^{53} -1.77831 q^{54} +4.96352 q^{55} +3.15038 q^{56} -1.40400 q^{57} -2.08163 q^{58} -13.2811 q^{59} -0.300926 q^{60} -3.23767 q^{61} -1.00000 q^{62} -9.16587 q^{63} +1.00000 q^{64} -1.00000 q^{65} -1.49365 q^{66} -8.44633 q^{67} +1.88940 q^{68} -1.34087 q^{69} -3.15038 q^{70} +13.1139 q^{71} -2.90944 q^{72} +11.3045 q^{73} -5.70317 q^{74} +0.300926 q^{75} -4.66561 q^{76} -15.6370 q^{77} +0.300926 q^{78} -2.47892 q^{79} -1.00000 q^{80} +8.19319 q^{81} +6.80470 q^{82} -2.94456 q^{83} +0.948034 q^{84} -1.88940 q^{85} -0.777730 q^{86} -0.626417 q^{87} -4.96352 q^{88} +8.26456 q^{89} +2.90944 q^{90} +3.15038 q^{91} -4.45581 q^{92} -0.300926 q^{93} -6.80921 q^{94} +4.66561 q^{95} +0.300926 q^{96} -10.2891 q^{97} +2.92492 q^{98} +14.4411 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} - 3 q^{3} + 6 q^{4} - 6 q^{5} - 3 q^{6} - 2 q^{7} + 6 q^{8} - q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 - 3 * q^3 + 6 * q^4 - 6 * q^5 - 3 * q^6 - 2 * q^7 + 6 * q^8 - q^9	\( 6 q + 6 q^{2} - 3 q^{3} + 6 q^{4} - 6 q^{5} - 3 q^{6} - 2 q^{7} + 6 q^{8} - q^{9} - 6 q^{10} - 4 q^{11} - 3 q^{12} + 6 q^{13} - 2 q^{14} + 3 q^{15} + 6 q^{16} - 8 q^{17} - q^{18} - 9 q^{19} - 6 q^{20} - 5 q^{21} - 4 q^{22} - 7 q^{23} - 3 q^{24} + 6 q^{25} + 6 q^{26} + 9 q^{27} - 2 q^{28} - 14 q^{29} + 3 q^{30} - 6 q^{31} + 6 q^{32} - 6 q^{33} - 8 q^{34} + 2 q^{35} - q^{36} - 9 q^{38} - 3 q^{39} - 6 q^{40} + 2 q^{41} - 5 q^{42} - 7 q^{43} - 4 q^{44} + q^{45} - 7 q^{46} - 8 q^{47} - 3 q^{48} - 14 q^{49} + 6 q^{50} - 5 q^{51} + 6 q^{52} - 24 q^{53} + 9 q^{54} + 4 q^{55} - 2 q^{56} - 15 q^{57} - 14 q^{58} - 5 q^{59} + 3 q^{60} - 5 q^{61} - 6 q^{62} - 19 q^{63} + 6 q^{64} - 6 q^{65} - 6 q^{66} - 12 q^{67} - 8 q^{68} + 2 q^{70} - 10 q^{71} - q^{72} + 5 q^{73} - 3 q^{75} - 9 q^{76} - q^{77} - 3 q^{78} - 16 q^{79} - 6 q^{80} - 10 q^{81} + 2 q^{82} - 22 q^{83} - 5 q^{84} + 8 q^{85} - 7 q^{86} - 31 q^{87} - 4 q^{88} + 14 q^{89} + q^{90} - 2 q^{91} - 7 q^{92} + 3 q^{93} - 8 q^{94} + 9 q^{95} - 3 q^{96} - 9 q^{97} - 14 q^{98} - 21 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 - 3 * q^3 + 6 * q^4 - 6 * q^5 - 3 * q^6 - 2 * q^7 + 6 * q^8 - q^9 - 6 * q^10 - 4 * q^11 - 3 * q^12 + 6 * q^13 - 2 * q^14 + 3 * q^15 + 6 * q^16 - 8 * q^17 - q^18 - 9 * q^19 - 6 * q^20 - 5 * q^21 - 4 * q^22 - 7 * q^23 - 3 * q^24 + 6 * q^25 + 6 * q^26 + 9 * q^27 - 2 * q^28 - 14 * q^29 + 3 * q^30 - 6 * q^31 + 6 * q^32 - 6 * q^33 - 8 * q^34 + 2 * q^35 - q^36 - 9 * q^38 - 3 * q^39 - 6 * q^40 + 2 * q^41 - 5 * q^42 - 7 * q^43 - 4 * q^44 + q^45 - 7 * q^46 - 8 * q^47 - 3 * q^48 - 14 * q^49 + 6 * q^50 - 5 * q^51 + 6 * q^52 - 24 * q^53 + 9 * q^54 + 4 * q^55 - 2 * q^56 - 15 * q^57 - 14 * q^58 - 5 * q^59 + 3 * q^60 - 5 * q^61 - 6 * q^62 - 19 * q^63 + 6 * q^64 - 6 * q^65 - 6 * q^66 - 12 * q^67 - 8 * q^68 + 2 * q^70 - 10 * q^71 - q^72 + 5 * q^73 - 3 * q^75 - 9 * q^76 - q^77 - 3 * q^78 - 16 * q^79 - 6 * q^80 - 10 * q^81 + 2 * q^82 - 22 * q^83 - 5 * q^84 + 8 * q^85 - 7 * q^86 - 31 * q^87 - 4 * q^88 + 14 * q^89 + q^90 - 2 * q^91 - 7 * q^92 + 3 * q^93 - 8 * q^94 + 9 * q^95 - 3 * q^96 - 9 * q^97 - 14 * 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
$3$	0.300926	0.173740	0.0868700	−	0.996220i	$-0.472314\pi$
$3$	0.300926	0.173740	0.0868700	+	0.996220i	$0.472314\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.300926	0.122853
$7$	3.15038	1.19073	0.595367	−	0.803454i	$-0.297007\pi$
$7$	3.15038	1.19073	0.595367	+	0.803454i	$0.297007\pi$
$8$	1.00000	0.353553
$9$	−2.90944	−0.969814
$10$	−1.00000	−0.316228
$11$	−4.96352	−1.49656	−0.748278	−	0.663385i	$-0.769119\pi$
$11$	−4.96352	−1.49656	−0.748278	+	0.663385i	$0.769119\pi$
$12$	0.300926	0.0868700
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	3.15038	0.841976
$15$	−0.300926	−0.0776989
$16$	1.00000	0.250000
$17$	1.88940	0.458248	0.229124	−	0.973397i	$-0.426414\pi$
$17$	1.88940	0.458248	0.229124	+	0.973397i	$0.426414\pi$
$18$	−2.90944	−0.685762
$19$	−4.66561	−1.07036	−0.535182	−	0.844737i	$-0.679757\pi$
$19$	−4.66561	−1.07036	−0.535182	+	0.844737i	$0.679757\pi$
$20$	−1.00000	−0.223607
$21$	0.948034	0.206878
$22$	−4.96352	−1.05822
$23$	−4.45581	−0.929101	−0.464551	−	0.885547i	$-0.653784\pi$
$23$	−4.45581	−0.929101	−0.464551	+	0.885547i	$0.653784\pi$
$24$	0.300926	0.0614263
$25$	1.00000	0.200000
$26$	1.00000	0.196116
$27$	−1.77831	−0.342235
$28$	3.15038	0.595367
$29$	−2.08163	−0.386549	−0.193274	−	0.981145i	$-0.561911\pi$
$29$	−2.08163	−0.386549	−0.193274	+	0.981145i	$0.561911\pi$
$30$	−0.300926	−0.0549414
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	1.00000	0.176777
$33$	−1.49365	−0.260012
$34$	1.88940	0.324030
$35$	−3.15038	−0.532512
$36$	−2.90944	−0.484907
$37$	−5.70317	−0.937595	−0.468798	−	0.883306i	$-0.655313\pi$
$37$	−5.70317	−0.937595	−0.468798	+	0.883306i	$0.655313\pi$
$38$	−4.66561	−0.756861
$39$	0.300926	0.0481868
$40$	−1.00000	−0.158114
$41$	6.80470	1.06272	0.531358	−	0.847147i	$-0.321682\pi$
$41$	6.80470	1.06272	0.531358	+	0.847147i	$0.321682\pi$
$42$	0.948034	0.146285
$43$	−0.777730	−0.118603	−0.0593014	−	0.998240i	$-0.518887\pi$
$43$	−0.777730	−0.118603	−0.0593014	+	0.998240i	$0.518887\pi$
$44$	−4.96352	−0.748278
$45$	2.90944	0.433714
$46$	−4.45581	−0.656974
$47$	−6.80921	−0.993225	−0.496612	−	0.867972i	$-0.665423\pi$
$47$	−6.80921	−0.993225	−0.496612	+	0.867972i	$0.665423\pi$
$48$	0.300926	0.0434350
$49$	2.92492	0.417846
$50$	1.00000	0.141421
$51$	0.568571	0.0796159
$52$	1.00000	0.138675
$53$	−3.39123	−0.465822	−0.232911	−	0.972498i	$-0.574825\pi$
$53$	−3.39123	−0.465822	−0.232911	+	0.972498i	$0.574825\pi$
$54$	−1.77831	−0.241997
$55$	4.96352	0.669280
$56$	3.15038	0.420988
$57$	−1.40400	−0.185965
$58$	−2.08163	−0.273331
$59$	−13.2811	−1.72905	−0.864523	−	0.502593i	$-0.832379\pi$
$59$	−13.2811	−1.72905	−0.864523	+	0.502593i	$0.832379\pi$
$60$	−0.300926	−0.0388494
$61$	−3.23767	−0.414542	−0.207271	−	0.978284i	$-0.566458\pi$
$61$	−3.23767	−0.414542	−0.207271	+	0.978284i	$0.566458\pi$
$62$	−1.00000	−0.127000
$63$	−9.16587	−1.15479
$64$	1.00000	0.125000
$65$	−1.00000	−0.124035
$66$	−1.49365	−0.183856
$67$	−8.44633	−1.03188	−0.515941	−	0.856624i	$-0.672558\pi$
$67$	−8.44633	−1.03188	−0.515941	+	0.856624i	$0.672558\pi$
$68$	1.88940	0.229124
$69$	−1.34087	−0.161422
$70$	−3.15038	−0.376543
$71$	13.1139	1.55633	0.778165	−	0.628060i	$-0.216151\pi$
$71$	13.1139	1.55633	0.778165	+	0.628060i	$0.216151\pi$
$72$	−2.90944	−0.342881
$73$	11.3045	1.32309	0.661545	−	0.749906i	$-0.269901\pi$
$73$	11.3045	1.32309	0.661545	+	0.749906i	$0.269901\pi$
$74$	−5.70317	−0.662980
$75$	0.300926	0.0347480
$76$	−4.66561	−0.535182
$77$	−15.6370	−1.78200
$78$	0.300926	0.0340732
$79$	−2.47892	−0.278901	−0.139450	−	0.990229i	$-0.544534\pi$
$79$	−2.47892	−0.278901	−0.139450	+	0.990229i	$0.544534\pi$
$80$	−1.00000	−0.111803
$81$	8.19319	0.910354
$82$	6.80470	0.751454
$83$	−2.94456	−0.323207	−0.161604	−	0.986856i	$-0.551667\pi$
$83$	−2.94456	−0.323207	−0.161604	+	0.986856i	$0.551667\pi$
$84$	0.948034	0.103439
$85$	−1.88940	−0.204935
$86$	−0.777730	−0.0838648
$87$	−0.626417	−0.0671590
$88$	−4.96352	−0.529112
$89$	8.26456	0.876042	0.438021	−	0.898965i	$-0.355680\pi$
$89$	8.26456	0.876042	0.438021	+	0.898965i	$0.355680\pi$
$90$	2.90944	0.306682
$91$	3.15038	0.330250
$92$	−4.45581	−0.464551
$93$	−0.300926	−0.0312046
$94$	−6.80921	−0.702316
$95$	4.66561	0.478681
$96$	0.300926	0.0307132
$97$	−10.2891	−1.04470	−0.522351	−	0.852731i	$-0.674945\pi$
$97$	−10.2891	−1.04470	−0.522351	+	0.852731i	$0.674945\pi$
$98$	2.92492	0.295462
$99$	14.4411	1.45138
$100$	1.00000	0.100000
$101$	−14.3862	−1.43148	−0.715739	−	0.698368i	$-0.753910\pi$
$101$	−14.3862	−1.43148	−0.715739	+	0.698368i	$0.753910\pi$
$102$	0.568571	0.0562970
$103$	−5.54509	−0.546374	−0.273187	−	0.961961i	$-0.588078\pi$
$103$	−5.54509	−0.546374	−0.273187	+	0.961961i	$0.588078\pi$
$104$	1.00000	0.0980581
$105$	−0.948034	−0.0925186
$106$	−3.39123	−0.329386
$107$	−11.4428	−1.10621	−0.553107	−	0.833110i	$-0.686558\pi$
$107$	−11.4428	−1.10621	−0.553107	+	0.833110i	$0.686558\pi$
$108$	−1.77831	−0.171118
$109$	−1.00382	−0.0961489	−0.0480745	−	0.998844i	$-0.515308\pi$
$109$	−1.00382	−0.0961489	−0.0480745	+	0.998844i	$0.515308\pi$
$110$	4.96352	0.473253
$111$	−1.71623	−0.162898
$112$	3.15038	0.297683
$113$	14.6751	1.38052	0.690261	−	0.723561i	$-0.257496\pi$
$113$	14.6751	1.38052	0.690261	+	0.723561i	$0.257496\pi$
$114$	−1.40400	−0.131497
$115$	4.45581	0.415507
$116$	−2.08163	−0.193274
$117$	−2.90944	−0.268978
$118$	−13.2811	−1.22262
$119$	5.95235	0.545651
$120$	−0.300926	−0.0274707
$121$	13.6365	1.23968
$122$	−3.23767	−0.293125
$123$	2.04772	0.184636
$124$	−1.00000	−0.0898027
$125$	−1.00000	−0.0894427
$126$	−9.16587	−0.816560
$127$	−0.378647	−0.0335995	−0.0167998	−	0.999859i	$-0.505348\pi$
$127$	−0.378647	−0.0335995	−0.0167998	+	0.999859i	$0.505348\pi$
$128$	1.00000	0.0883883
$129$	−0.234040	−0.0206060
$130$	−1.00000	−0.0877058
$131$	−18.5959	−1.62473	−0.812366	−	0.583148i	$-0.801821\pi$
$131$	−18.5959	−1.62473	−0.812366	+	0.583148i	$0.801821\pi$
$132$	−1.49365	−0.130006
$133$	−14.6985	−1.27452
$134$	−8.44633	−0.729651
$135$	1.77831	0.153052
$136$	1.88940	0.162015
$137$	−2.27913	−0.194719	−0.0973594	−	0.995249i	$-0.531040\pi$
$137$	−2.27913	−0.194719	−0.0973594	+	0.995249i	$0.531040\pi$
$138$	−1.34087	−0.114143
$139$	9.01897	0.764979	0.382490	−	0.923960i	$-0.375067\pi$
$139$	9.01897	0.764979	0.382490	+	0.923960i	$0.375067\pi$
$140$	−3.15038	−0.266256
$141$	−2.04907	−0.172563
$142$	13.1139	1.10049
$143$	−4.96352	−0.415070
$144$	−2.90944	−0.242454
$145$	2.08163	0.172870
$146$	11.3045	0.935566
$147$	0.880187	0.0725966
$148$	−5.70317	−0.468798
$149$	−4.37620	−0.358512	−0.179256	−	0.983802i	$-0.557369\pi$
$149$	−4.37620	−0.358512	−0.179256	+	0.983802i	$0.557369\pi$
$150$	0.300926	0.0245705
$151$	19.7761	1.60935	0.804677	−	0.593712i	$-0.202338\pi$
$151$	19.7761	1.60935	0.804677	+	0.593712i	$0.202338\pi$
$152$	−4.66561	−0.378431
$153$	−5.49711	−0.444415
$154$	−15.6370	−1.26006
$155$	1.00000	0.0803219
$156$	0.300926	0.0240934
$157$	0.100858	0.00804936	0.00402468	−	0.999992i	$-0.498719\pi$
$157$	0.100858	0.00804936	0.00402468	+	0.999992i	$0.498719\pi$
$158$	−2.47892	−0.197212
$159$	−1.02051	−0.0809318
$160$	−1.00000	−0.0790569
$161$	−14.0375	−1.10631
$162$	8.19319	0.643718
$163$	2.69300	0.210932	0.105466	−	0.994423i	$-0.466367\pi$
$163$	2.69300	0.210932	0.105466	+	0.994423i	$0.466367\pi$
$164$	6.80470	0.531358
$165$	1.49365	0.116281
$166$	−2.94456	−0.228542
$167$	0.159566	0.0123476	0.00617378	−	0.999981i	$-0.498035\pi$
$167$	0.159566	0.0123476	0.00617378	+	0.999981i	$0.498035\pi$
$168$	0.948034	0.0731424
$169$	1.00000	0.0769231
$170$	−1.88940	−0.144911
$171$	13.5743	1.03805
$172$	−0.777730	−0.0593014
$173$	−4.88183	−0.371159	−0.185579	−	0.982629i	$-0.559416\pi$
$173$	−4.88183	−0.371159	−0.185579	+	0.982629i	$0.559416\pi$
$174$	−0.626417	−0.0474886
$175$	3.15038	0.238147
$176$	−4.96352	−0.374139
$177$	−3.99662	−0.300404
$178$	8.26456	0.619455
$179$	−17.8316	−1.33279	−0.666397	−	0.745597i	$-0.732165\pi$
$179$	−17.8316	−1.33279	−0.666397	+	0.745597i	$0.732165\pi$
$180$	2.90944	0.216857
$181$	14.7311	1.09496	0.547478	−	0.836820i	$-0.315588\pi$
$181$	14.7311	1.09496	0.547478	+	0.836820i	$0.315588\pi$
$182$	3.15038	0.233522
$183$	−0.974302	−0.0720224
$184$	−4.45581	−0.328487
$185$	5.70317	0.419305
$186$	−0.300926	−0.0220650
$187$	−9.37808	−0.685793
$188$	−6.80921	−0.496612
$189$	−5.60235	−0.407511
$190$	4.66561	0.338479
$191$	21.2023	1.53415	0.767073	−	0.641560i	$-0.221712\pi$
$191$	21.2023	1.53415	0.767073	+	0.641560i	$0.221712\pi$
$192$	0.300926	0.0217175
$193$	−24.9474	−1.79576	−0.897878	−	0.440244i	$-0.854892\pi$
$193$	−24.9474	−1.79576	−0.897878	+	0.440244i	$0.854892\pi$
$194$	−10.2891	−0.738716
$195$	−0.300926	−0.0215498
$196$	2.92492	0.208923
$197$	12.9775	0.924612	0.462306	−	0.886720i	$-0.347022\pi$
$197$	12.9775	0.924612	0.462306	+	0.886720i	$0.347022\pi$
$198$	14.4411	1.02628
$199$	−7.29756	−0.517310	−0.258655	−	0.965970i	$-0.583279\pi$
$199$	−7.29756	−0.517310	−0.258655	+	0.965970i	$0.583279\pi$
$200$	1.00000	0.0707107
$201$	−2.54172	−0.179279
$202$	−14.3862	−1.01221
$203$	−6.55794	−0.460277
$204$	0.568571	0.0398080
$205$	−6.80470	−0.475261
$206$	−5.54509	−0.386345
$207$	12.9639	0.901056
$208$	1.00000	0.0693375
$209$	23.1578	1.60186
$210$	−0.948034	−0.0654206
$211$	7.95412	0.547584	0.273792	−	0.961789i	$-0.411722\pi$
$211$	7.95412	0.547584	0.273792	+	0.961789i	$0.411722\pi$
$212$	−3.39123	−0.232911
$213$	3.94631	0.270397
$214$	−11.4428	−0.782211
$215$	0.777730	0.0530408
$216$	−1.77831	−0.120998
$217$	−3.15038	−0.213862
$218$	−1.00382	−0.0679876
$219$	3.40182	0.229873
$220$	4.96352	0.334640
$221$	1.88940	0.127095
$222$	−1.71623	−0.115186
$223$	−8.84055	−0.592007	−0.296004	−	0.955187i	$-0.595654\pi$
$223$	−8.84055	−0.592007	−0.296004	+	0.955187i	$0.595654\pi$
$224$	3.15038	0.210494
$225$	−2.90944	−0.193963
$226$	14.6751	0.976176
$227$	−13.1740	−0.874388	−0.437194	−	0.899367i	$-0.644028\pi$
$227$	−13.1740	−0.874388	−0.437194	+	0.899367i	$0.644028\pi$
$228$	−1.40400	−0.0929824
$229$	24.5085	1.61957	0.809783	−	0.586730i	$-0.199585\pi$
$229$	24.5085	1.61957	0.809783	+	0.586730i	$0.199585\pi$
$230$	4.45581	0.293808
$231$	−4.70558	−0.309604
$232$	−2.08163	−0.136666
$233$	−4.33762	−0.284167	−0.142084	−	0.989855i	$-0.545380\pi$
$233$	−4.33762	−0.284167	−0.142084	+	0.989855i	$0.545380\pi$
$234$	−2.90944	−0.190196
$235$	6.80921	0.444184
$236$	−13.2811	−0.864523
$237$	−0.745973	−0.0484562
$238$	5.95235	0.385833
$239$	−0.415754	−0.0268929	−0.0134465	−	0.999910i	$-0.504280\pi$
$239$	−0.415754	−0.0268929	−0.0134465	+	0.999910i	$0.504280\pi$
$240$	−0.300926	−0.0194247
$241$	−24.1094	−1.55303	−0.776513	−	0.630102i	$-0.783013\pi$
$241$	−24.1094	−1.55303	−0.776513	+	0.630102i	$0.783013\pi$
$242$	13.6365	0.876586
$243$	7.80047	0.500400
$244$	−3.23767	−0.207271
$245$	−2.92492	−0.186867
$246$	2.04772	0.130558
$247$	−4.66561	−0.296865
$248$	−1.00000	−0.0635001
$249$	−0.886096	−0.0561540
$250$	−1.00000	−0.0632456
$251$	0.649253	0.0409805	0.0204902	−	0.999790i	$-0.493477\pi$
$251$	0.649253	0.0409805	0.0204902	+	0.999790i	$0.493477\pi$
$252$	−9.16587	−0.577395
$253$	22.1165	1.39045
$254$	−0.378647	−0.0237584
$255$	−0.568571	−0.0356053
$256$	1.00000	0.0625000
$257$	−18.8917	−1.17843	−0.589215	−	0.807977i	$-0.700563\pi$
$257$	−18.8917	−1.17843	−0.589215	+	0.807977i	$0.700563\pi$
$258$	−0.234040	−0.0145707
$259$	−17.9672	−1.11643
$260$	−1.00000	−0.0620174
$261$	6.05638	0.374881
$262$	−18.5959	−1.14886
$263$	1.96769	0.121333	0.0606666	−	0.998158i	$-0.480677\pi$
$263$	1.96769	0.121333	0.0606666	+	0.998158i	$0.480677\pi$
$264$	−1.49365	−0.0919280
$265$	3.39123	0.208322
$266$	−14.6985	−0.901220
$267$	2.48702	0.152203
$268$	−8.44633	−0.515941
$269$	−8.70926	−0.531013	−0.265507	−	0.964109i	$-0.585539\pi$
$269$	−8.70926	−0.531013	−0.265507	+	0.964109i	$0.585539\pi$
$270$	1.77831	0.108224
$271$	25.4247	1.54444	0.772221	−	0.635354i	$-0.219146\pi$
$271$	25.4247	1.54444	0.772221	+	0.635354i	$0.219146\pi$
$272$	1.88940	0.114562
$273$	0.948034	0.0573776
$274$	−2.27913	−0.137687
$275$	−4.96352	−0.299311
$276$	−1.34087	−0.0807110
$277$	14.1698	0.851380	0.425690	−	0.904869i	$-0.360031\pi$
$277$	14.1698	0.851380	0.425690	+	0.904869i	$0.360031\pi$
$278$	9.01897	0.540922
$279$	2.90944	0.174184
$280$	−3.15038	−0.188272
$281$	−7.09200	−0.423073	−0.211537	−	0.977370i	$-0.567847\pi$
$281$	−7.09200	−0.423073	−0.211537	+	0.977370i	$0.567847\pi$
$282$	−2.04907	−0.122020
$283$	29.6798	1.76428	0.882140	−	0.470987i	$-0.156102\pi$
$283$	29.6798	1.76428	0.882140	+	0.470987i	$0.156102\pi$
$284$	13.1139	0.778165
$285$	1.40400	0.0831660
$286$	−4.96352	−0.293499
$287$	21.4374	1.26541
$288$	−2.90944	−0.171441
$289$	−13.4302	−0.790009
$290$	2.08163	0.122238
$291$	−3.09627	−0.181506
$292$	11.3045	0.661545
$293$	15.1271	0.883733	0.441867	−	0.897081i	$-0.354316\pi$
$293$	15.1271	0.883733	0.441867	+	0.897081i	$0.354316\pi$
$294$	0.880187	0.0513335
$295$	13.2811	0.773253
$296$	−5.70317	−0.331490
$297$	8.82666	0.512175
$298$	−4.37620	−0.253506
$299$	−4.45581	−0.257686
$300$	0.300926	0.0173740
$301$	−2.45015	−0.141224
$302$	19.7761	1.13799
$303$	−4.32918	−0.248705
$304$	−4.66561	−0.267591
$305$	3.23767	0.185389
$306$	−5.49711	−0.314249
$307$	17.6312	1.00626	0.503132	−	0.864210i	$-0.332181\pi$
$307$	17.6312	1.00626	0.503132	+	0.864210i	$0.332181\pi$
$308$	−15.6370	−0.891000
$309$	−1.66866	−0.0949270
$310$	1.00000	0.0567962
$311$	−28.8907	−1.63824	−0.819120	−	0.573623i	$-0.805538\pi$
$311$	−28.8907	−1.63824	−0.819120	+	0.573623i	$0.805538\pi$
$312$	0.300926	0.0170366
$313$	−5.63644	−0.318590	−0.159295	−	0.987231i	$-0.550922\pi$
$313$	−5.63644	−0.318590	−0.159295	+	0.987231i	$0.550922\pi$
$314$	0.100858	0.00569176
$315$	9.16587	0.516438
$316$	−2.47892	−0.139450
$317$	−18.9402	−1.06379	−0.531893	−	0.846811i	$-0.678519\pi$
$317$	−18.9402	−1.06379	−0.531893	+	0.846811i	$0.678519\pi$
$318$	−1.02051	−0.0572274
$319$	10.3322	0.578492
$320$	−1.00000	−0.0559017
$321$	−3.44343	−0.192194
$322$	−14.0375	−0.782281
$323$	−8.81521	−0.490492
$324$	8.19319	0.455177
$325$	1.00000	0.0554700
$326$	2.69300	0.149152
$327$	−0.302077	−0.0167049
$328$	6.80470	0.375727
$329$	−21.4516	−1.18267
$330$	1.49365	0.0822229
$331$	32.0008	1.75892	0.879462	−	0.475968i	$-0.157902\pi$
$331$	32.0008	1.75892	0.879462	+	0.475968i	$0.157902\pi$
$332$	−2.94456	−0.161604
$333$	16.5930	0.909293
$334$	0.159566	0.00873104
$335$	8.44633	0.461472
$336$	0.948034	0.0517195
$337$	24.8686	1.35468	0.677339	−	0.735671i	$-0.263133\pi$
$337$	24.8686	1.35468	0.677339	+	0.735671i	$0.263133\pi$
$338$	1.00000	0.0543928
$339$	4.41614	0.239852
$340$	−1.88940	−0.102467
$341$	4.96352	0.268789
$342$	13.5743	0.734015
$343$	−12.8381	−0.693190
$344$	−0.777730	−0.0419324
$345$	1.34087	0.0721901
$346$	−4.88183	−0.262449
$347$	−25.6965	−1.37946	−0.689729	−	0.724067i	$-0.742271\pi$
$347$	−25.6965	−1.37946	−0.689729	+	0.724067i	$0.742271\pi$
$348$	−0.626417	−0.0335795
$349$	−15.7290	−0.841952	−0.420976	−	0.907072i	$-0.638312\pi$
$349$	−15.7290	−0.841952	−0.420976	+	0.907072i	$0.638312\pi$
$350$	3.15038	0.168395
$351$	−1.77831	−0.0949190
$352$	−4.96352	−0.264556
$353$	−16.3575	−0.870621	−0.435311	−	0.900280i	$-0.643361\pi$
$353$	−16.3575	−0.870621	−0.435311	+	0.900280i	$0.643361\pi$
$354$	−3.99662	−0.212418
$355$	−13.1139	−0.696012
$356$	8.26456	0.438021
$357$	1.79122	0.0948014
$358$	−17.8316	−0.942428
$359$	17.3047	0.913308	0.456654	−	0.889644i	$-0.349048\pi$
$359$	17.3047	0.913308	0.456654	+	0.889644i	$0.349048\pi$
$360$	2.90944	0.153341
$361$	2.76787	0.145678
$362$	14.7311	0.774250
$363$	4.10358	0.215382
$364$	3.15038	0.165125
$365$	−11.3045	−0.591704
$366$	−0.974302	−0.0509276
$367$	−19.3654	−1.01086	−0.505432	−	0.862866i	$-0.668667\pi$
$367$	−19.3654	−1.01086	−0.505432	+	0.862866i	$0.668667\pi$
$368$	−4.45581	−0.232275
$369$	−19.7979	−1.03064
$370$	5.70317	0.296494
$371$	−10.6837	−0.554669
$372$	−0.300926	−0.0156023
$373$	13.0357	0.674965	0.337483	−	0.941332i	$-0.390425\pi$
$373$	13.0357	0.674965	0.337483	+	0.941332i	$0.390425\pi$
$374$	−9.37808	−0.484929
$375$	−0.300926	−0.0155398
$376$	−6.80921	−0.351158
$377$	−2.08163	−0.107209
$378$	−5.60235	−0.288154
$379$	−21.3118	−1.09471	−0.547357	−	0.836899i	$-0.684366\pi$
$379$	−21.3118	−1.09471	−0.547357	+	0.836899i	$0.684366\pi$
$380$	4.66561	0.239341
$381$	−0.113945	−0.00583758
$382$	21.2023	1.08480
$383$	−19.3110	−0.986745	−0.493372	−	0.869818i	$-0.664236\pi$
$383$	−19.3110	−0.986745	−0.493372	+	0.869818i	$0.664236\pi$
$384$	0.300926	0.0153566
$385$	15.6370	0.796934
$386$	−24.9474	−1.26979
$387$	2.26276	0.115023
$388$	−10.2891	−0.522351
$389$	−9.71130	−0.492382	−0.246191	−	0.969221i	$-0.579179\pi$
$389$	−9.71130	−0.492382	−0.246191	+	0.969221i	$0.579179\pi$
$390$	−0.300926	−0.0152380
$391$	−8.41883	−0.425759
$392$	2.92492	0.147731
$393$	−5.59600	−0.282281
$394$	12.9775	0.653799
$395$	2.47892	0.124728
$396$	14.4411	0.725691
$397$	20.9972	1.05382	0.526910	−	0.849921i	$-0.323350\pi$
$397$	20.9972	1.05382	0.526910	+	0.849921i	$0.323350\pi$
$398$	−7.29756	−0.365794
$399$	−4.42315	−0.221435
$400$	1.00000	0.0500000
$401$	−34.9041	−1.74303	−0.871515	−	0.490369i	$-0.836862\pi$
$401$	−34.9041	−1.74303	−0.871515	+	0.490369i	$0.836862\pi$
$402$	−2.54172	−0.126770
$403$	−1.00000	−0.0498135
$404$	−14.3862	−0.715739
$405$	−8.19319	−0.407123
$406$	−6.55794	−0.325465
$407$	28.3078	1.40316
$408$	0.568571	0.0281485
$409$	−23.7803	−1.17586	−0.587930	−	0.808912i	$-0.700057\pi$
$409$	−23.7803	−1.17586	−0.587930	+	0.808912i	$0.700057\pi$
$410$	−6.80470	−0.336060
$411$	−0.685849	−0.0338304
$412$	−5.54509	−0.273187
$413$	−41.8404	−2.05883
$414$	12.9639	0.637143
$415$	2.94456	0.144543
$416$	1.00000	0.0490290
$417$	2.71405	0.132907
$418$	23.1578	1.13269
$419$	−27.3830	−1.33775	−0.668873	−	0.743377i	$-0.733223\pi$
$419$	−27.3830	−1.33775	−0.668873	+	0.743377i	$0.733223\pi$
$420$	−0.948034	−0.0462593
$421$	26.3343	1.28346	0.641728	−	0.766933i	$-0.278218\pi$
$421$	26.3343	1.28346	0.641728	+	0.766933i	$0.278218\pi$
$422$	7.95412	0.387200
$423$	19.8110	0.963244
$424$	−3.39123	−0.164693
$425$	1.88940	0.0916495
$426$	3.94631	0.191199
$427$	−10.1999	−0.493609
$428$	−11.4428	−0.553107
$429$	−1.49365	−0.0721142
$430$	0.777730	0.0375055
$431$	29.5386	1.42283	0.711413	−	0.702775i	$-0.248056\pi$
$431$	29.5386	1.42283	0.711413	+	0.702775i	$0.248056\pi$
$432$	−1.77831	−0.0855589
$433$	24.3047	1.16801	0.584004	−	0.811751i	$-0.301485\pi$
$433$	24.3047	1.16801	0.584004	+	0.811751i	$0.301485\pi$
$434$	−3.15038	−0.151223
$435$	0.626417	0.0300344
$436$	−1.00382	−0.0480745
$437$	20.7891	0.994476
$438$	3.40182	0.162545
$439$	12.1983	0.582194	0.291097	−	0.956694i	$-0.405980\pi$
$439$	12.1983	0.582194	0.291097	+	0.956694i	$0.405980\pi$
$440$	4.96352	0.236626
$441$	−8.50990	−0.405233
$442$	1.88940	0.0898698
$443$	−32.0859	−1.52445	−0.762223	−	0.647315i	$-0.775892\pi$
$443$	−32.0859	−1.52445	−0.762223	+	0.647315i	$0.775892\pi$
$444$	−1.71623	−0.0814489
$445$	−8.26456	−0.391778
$446$	−8.84055	−0.418612
$447$	−1.31691	−0.0622879
$448$	3.15038	0.148842
$449$	9.39473	0.443365	0.221682	−	0.975119i	$-0.428845\pi$
$449$	9.39473	0.443365	0.221682	+	0.975119i	$0.428845\pi$
$450$	−2.90944	−0.137152
$451$	−33.7753	−1.59041
$452$	14.6751	0.690261
$453$	5.95114	0.279609
$454$	−13.1740	−0.618285
$455$	−3.15038	−0.147692
$456$	−1.40400	−0.0657485
$457$	−3.32286	−0.155437	−0.0777185	−	0.996975i	$-0.524764\pi$
$457$	−3.32286	−0.155437	−0.0777185	+	0.996975i	$0.524764\pi$
$458$	24.5085	1.14521
$459$	−3.35994	−0.156829
$460$	4.45581	0.207753
$461$	−8.51704	−0.396678	−0.198339	−	0.980133i	$-0.563555\pi$
$461$	−8.51704	−0.396678	−0.198339	+	0.980133i	$0.563555\pi$
$462$	−4.70558	−0.218923
$463$	20.7368	0.963721	0.481861	−	0.876248i	$-0.339961\pi$
$463$	20.7368	0.963721	0.481861	+	0.876248i	$0.339961\pi$
$464$	−2.08163	−0.0966372
$465$	0.300926	0.0139551
$466$	−4.33762	−0.200937
$467$	11.5796	0.535838	0.267919	−	0.963441i	$-0.413664\pi$
$467$	11.5796	0.535838	0.267919	+	0.963441i	$0.413664\pi$
$468$	−2.90944	−0.134489
$469$	−26.6092	−1.22870
$470$	6.80921	0.314085
$471$	0.0303509	0.00139850
$472$	−13.2811	−0.611310
$473$	3.86028	0.177496
$474$	−0.745973	−0.0342637
$475$	−4.66561	−0.214073
$476$	5.95235	0.272825
$477$	9.86660	0.451760
$478$	−0.415754	−0.0190162
$479$	7.74388	0.353827	0.176913	−	0.984226i	$-0.443389\pi$
$479$	7.74388	0.353827	0.176913	+	0.984226i	$0.443389\pi$
$480$	−0.300926	−0.0137353
$481$	−5.70317	−0.260042
$482$	−24.1094	−1.09815
$483$	−4.22426	−0.192211
$484$	13.6365	0.619840
$485$	10.2891	0.467205
$486$	7.80047	0.353836
$487$	2.14030	0.0969862	0.0484931	−	0.998824i	$-0.484558\pi$
$487$	2.14030	0.0969862	0.0484931	+	0.998824i	$0.484558\pi$
$488$	−3.23767	−0.146563
$489$	0.810396	0.0366474
$490$	−2.92492	−0.132135
$491$	15.5236	0.700570	0.350285	−	0.936643i	$-0.386085\pi$
$491$	15.5236	0.700570	0.350285	+	0.936643i	$0.386085\pi$
$492$	2.04772	0.0923181
$493$	−3.93304	−0.177135
$494$	−4.66561	−0.209916
$495$	−14.4411	−0.649078
$496$	−1.00000	−0.0449013
$497$	41.3137	1.85317
$498$	−0.886096	−0.0397069
$499$	22.9404	1.02695	0.513476	−	0.858104i	$-0.328357\pi$
$499$	22.9404	1.02695	0.513476	+	0.858104i	$0.328357\pi$
$500$	−1.00000	−0.0447214
$501$	0.0480175	0.00214526
$502$	0.649253	0.0289776
$503$	−10.8543	−0.483968	−0.241984	−	0.970280i	$-0.577798\pi$
$503$	−10.8543	−0.483968	−0.241984	+	0.970280i	$0.577798\pi$
$504$	−9.16587	−0.408280
$505$	14.3862	0.640176
$506$	22.1165	0.983198
$507$	0.300926	0.0133646
$508$	−0.378647	−0.0167998
$509$	16.8325	0.746087	0.373043	−	0.927814i	$-0.378314\pi$
$509$	16.8325	0.746087	0.373043	+	0.927814i	$0.378314\pi$
$510$	−0.568571	−0.0251768
$511$	35.6135	1.57545
$512$	1.00000	0.0441942
$513$	8.29688	0.366316
$514$	−18.8917	−0.833275
$515$	5.54509	0.244346
$516$	−0.234040	−0.0103030
$517$	33.7976	1.48642
$518$	−17.9672	−0.789432
$519$	−1.46907	−0.0644851
$520$	−1.00000	−0.0438529
$521$	33.3980	1.46319	0.731596	−	0.681738i	$-0.238776\pi$
$521$	33.3980	1.46319	0.731596	+	0.681738i	$0.238776\pi$
$522$	6.05638	0.265081
$523$	40.2347	1.75934	0.879669	−	0.475586i	$-0.157764\pi$
$523$	40.2347	1.75934	0.879669	+	0.475586i	$0.157764\pi$
$524$	−18.5959	−0.812366
$525$	0.948034	0.0413756
$526$	1.96769	0.0857955
$527$	−1.88940	−0.0823037
$528$	−1.49365	−0.0650029
$529$	−3.14573	−0.136771
$530$	3.39123	0.147306
$531$	38.6405	1.67685
$532$	−14.6985	−0.637259
$533$	6.80470	0.294744
$534$	2.48702	0.107624
$535$	11.4428	0.494714
$536$	−8.44633	−0.364826
$537$	−5.36599	−0.231560
$538$	−8.70926	−0.375483
$539$	−14.5179	−0.625331
$540$	1.77831	0.0765262
$541$	−36.7918	−1.58180	−0.790901	−	0.611945i	$-0.790388\pi$
$541$	−36.7918	−1.58180	−0.790901	+	0.611945i	$0.790388\pi$
$542$	25.4247	1.09209
$543$	4.43298	0.190237
$544$	1.88940	0.0810075
$545$	1.00382	0.0429991
$546$	0.948034	0.0405721
$547$	25.0106	1.06938	0.534688	−	0.845050i	$-0.320429\pi$
$547$	25.0106	1.06938	0.534688	+	0.845050i	$0.320429\pi$
$548$	−2.27913	−0.0973594
$549$	9.41983	0.402028
$550$	−4.96352	−0.211645
$551$	9.71206	0.413748
$552$	−1.34087	−0.0570713
$553$	−7.80956	−0.332096
$554$	14.1698	0.602017
$555$	1.71623	0.0728501
$556$	9.01897	0.382490
$557$	9.36989	0.397015	0.198507	−	0.980099i	$-0.436391\pi$
$557$	9.36989	0.397015	0.198507	+	0.980099i	$0.436391\pi$
$558$	2.90944	0.123167
$559$	−0.777730	−0.0328945
$560$	−3.15038	−0.133128
$561$	−2.82211	−0.119150
$562$	−7.09200	−0.299158
$563$	29.5032	1.24341	0.621705	−	0.783252i	$-0.286440\pi$
$563$	29.5032	1.24341	0.621705	+	0.783252i	$0.286440\pi$
$564$	−2.04907	−0.0862814
$565$	−14.6751	−0.617388
$566$	29.6798	1.24753
$567$	25.8117	1.08399
$568$	13.1139	0.550245
$569$	31.1992	1.30794	0.653969	−	0.756521i	$-0.273103\pi$
$569$	31.1992	1.30794	0.653969	+	0.756521i	$0.273103\pi$
$570$	1.40400	0.0588073
$571$	−9.14924	−0.382884	−0.191442	−	0.981504i	$-0.561316\pi$
$571$	−9.14924	−0.382884	−0.191442	+	0.981504i	$0.561316\pi$
$572$	−4.96352	−0.207535
$573$	6.38034	0.266542
$574$	21.4374	0.894781
$575$	−4.45581	−0.185820
$576$	−2.90944	−0.121227
$577$	27.5281	1.14601	0.573004	−	0.819553i	$-0.305778\pi$
$577$	27.5281	1.14601	0.573004	+	0.819553i	$0.305778\pi$
$578$	−13.4302	−0.558621
$579$	−7.50734	−0.311995
$580$	2.08163	0.0864350
$581$	−9.27650	−0.384854
$582$	−3.09627	−0.128344
$583$	16.8324	0.697128
$584$	11.3045	0.467783
$585$	2.90944	0.120291
$586$	15.1271	0.624894
$587$	29.6183	1.22248	0.611239	−	0.791446i	$-0.290671\pi$
$587$	29.6183	1.22248	0.611239	+	0.791446i	$0.290671\pi$
$588$	0.880187	0.0362983
$589$	4.66561	0.192243
$590$	13.2811	0.546772
$591$	3.90529	0.160642
$592$	−5.70317	−0.234399
$593$	−17.1957	−0.706141	−0.353071	−	0.935597i	$-0.614862\pi$
$593$	−17.1957	−0.706141	−0.353071	+	0.935597i	$0.614862\pi$
$594$	8.82666	0.362162
$595$	−5.95235	−0.244023
$596$	−4.37620	−0.179256
$597$	−2.19603	−0.0898774
$598$	−4.45581	−0.182212
$599$	−13.5475	−0.553538	−0.276769	−	0.960937i	$-0.589264\pi$
$599$	−13.5475	−0.553538	−0.276769	+	0.960937i	$0.589264\pi$
$600$	0.300926	0.0122853
$601$	−28.3499	−1.15642	−0.578209	−	0.815889i	$-0.696248\pi$
$601$	−28.3499	−1.15642	−0.578209	+	0.815889i	$0.696248\pi$
$602$	−2.45015	−0.0998606
$603$	24.5741	1.00073
$604$	19.7761	0.804677
$605$	−13.6365	−0.554402
$606$	−4.32918	−0.175861
$607$	21.5229	0.873587	0.436794	−	0.899562i	$-0.356114\pi$
$607$	21.5229	0.873587	0.436794	+	0.899562i	$0.356114\pi$
$608$	−4.66561	−0.189215
$609$	−1.97346	−0.0799685
$610$	3.23767	0.131090
$611$	−6.80921	−0.275471
$612$	−5.49711	−0.222208
$613$	13.9442	0.563202	0.281601	−	0.959532i	$-0.409135\pi$
$613$	13.9442	0.563202	0.281601	+	0.959532i	$0.409135\pi$
$614$	17.6312	0.711536
$615$	−2.04772	−0.0825718
$616$	−15.6370	−0.630032
$617$	20.3340	0.818616	0.409308	−	0.912396i	$-0.365770\pi$
$617$	20.3340	0.818616	0.409308	+	0.912396i	$0.365770\pi$
$618$	−1.66866	−0.0671235
$619$	−40.4260	−1.62486	−0.812428	−	0.583061i	$-0.801855\pi$
$619$	−40.4260	−1.62486	−0.812428	+	0.583061i	$0.801855\pi$
$620$	1.00000	0.0401610
$621$	7.92381	0.317971
$622$	−28.8907	−1.15841
$623$	26.0366	1.04313
$624$	0.300926	0.0120467
$625$	1.00000	0.0400000
$626$	−5.63644	−0.225277
$627$	6.96879	0.278307
$628$	0.100858	0.00402468
$629$	−10.7756	−0.429651
$630$	9.16587	0.365177
$631$	−2.10823	−0.0839273	−0.0419637	−	0.999119i	$-0.513361\pi$
$631$	−2.10823	−0.0839273	−0.0419637	+	0.999119i	$0.513361\pi$
$632$	−2.47892	−0.0986062
$633$	2.39360	0.0951372
$634$	−18.9402	−0.752211
$635$	0.378647	0.0150262
$636$	−1.02051	−0.0404659
$637$	2.92492	0.115890
$638$	10.3322	0.409056
$639$	−38.1540	−1.50935
$640$	−1.00000	−0.0395285
$641$	−9.15240	−0.361498	−0.180749	−	0.983529i	$-0.557852\pi$
$641$	−9.15240	−0.361498	−0.180749	+	0.983529i	$0.557852\pi$
$642$	−3.44343	−0.135901
$643$	5.66423	0.223375	0.111688	−	0.993743i	$-0.464374\pi$
$643$	5.66423	0.223375	0.111688	+	0.993743i	$0.464374\pi$
$644$	−14.0375	−0.553156
$645$	0.234040	0.00921530
$646$	−8.81521	−0.346830
$647$	−35.4275	−1.39280	−0.696400	−	0.717654i	$-0.745216\pi$
$647$	−35.4275	−1.39280	−0.696400	+	0.717654i	$0.745216\pi$
$648$	8.19319	0.321859
$649$	65.9207	2.58761
$650$	1.00000	0.0392232
$651$	−0.948034	−0.0371564
$652$	2.69300	0.105466
$653$	−7.47777	−0.292628	−0.146314	−	0.989238i	$-0.546741\pi$
$653$	−7.47777	−0.292628	−0.146314	+	0.989238i	$0.546741\pi$
$654$	−0.302077	−0.0118122
$655$	18.5959	0.726602
$656$	6.80470	0.265679
$657$	−32.8897	−1.28315
$658$	−21.4516	−0.836271
$659$	−3.69306	−0.143861	−0.0719306	−	0.997410i	$-0.522916\pi$
$659$	−3.69306	−0.143861	−0.0719306	+	0.997410i	$0.522916\pi$
$660$	1.49365	0.0581404
$661$	36.4497	1.41773	0.708865	−	0.705344i	$-0.249207\pi$
$661$	36.4497	1.41773	0.708865	+	0.705344i	$0.249207\pi$
$662$	32.0008	1.24375
$663$	0.568571	0.0220815
$664$	−2.94456	−0.114271
$665$	14.6985	0.569982
$666$	16.5930	0.642967
$667$	9.27535	0.359143
$668$	0.159566	0.00617378
$669$	−2.66036	−0.102855
$670$	8.44633	0.326310
$671$	16.0702	0.620385
$672$	0.948034	0.0365712
$673$	29.3390	1.13093	0.565467	−	0.824771i	$-0.308696\pi$
$673$	29.3390	1.13093	0.565467	+	0.824771i	$0.308696\pi$
$674$	24.8686	0.957902
$675$	−1.77831	−0.0684471
$676$	1.00000	0.0384615
$677$	32.2186	1.23826	0.619130	−	0.785289i	$-0.287485\pi$
$677$	32.2186	1.23826	0.619130	+	0.785289i	$0.287485\pi$
$678$	4.41614	0.169601
$679$	−32.4147	−1.24396
$680$	−1.88940	−0.0724553
$681$	−3.96440	−0.151916
$682$	4.96352	0.190063
$683$	−17.1496	−0.656213	−0.328107	−	0.944641i	$-0.606410\pi$
$683$	−17.1496	−0.656213	−0.328107	+	0.944641i	$0.606410\pi$
$684$	13.5743	0.519027
$685$	2.27913	0.0870809
$686$	−12.8381	−0.490159
$687$	7.37525	0.281383
$688$	−0.777730	−0.0296507
$689$	−3.39123	−0.129196
$690$	1.34087	0.0510461
$691$	33.3329	1.26804	0.634022	−	0.773315i	$-0.281403\pi$
$691$	33.3329	1.26804	0.634022	+	0.773315i	$0.281403\pi$
$692$	−4.88183	−0.185579
$693$	45.4949	1.72821
$694$	−25.6965	−0.975425
$695$	−9.01897	−0.342109
$696$	−0.626417	−0.0237443
$697$	12.8568	0.486987
$698$	−15.7290	−0.595350
$699$	−1.30531	−0.0493712
$700$	3.15038	0.119073
$701$	13.2118	0.499003	0.249502	−	0.968374i	$-0.419733\pi$
$701$	13.2118	0.499003	0.249502	+	0.968374i	$0.419733\pi$
$702$	−1.77831	−0.0671179
$703$	26.6087	1.00357
$704$	−4.96352	−0.187070
$705$	2.04907	0.0771724
$706$	−16.3575	−0.615622
$707$	−45.3220	−1.70451
$708$	−3.99662	−0.150202
$709$	11.9859	0.450141	0.225070	−	0.974342i	$-0.427739\pi$
$709$	11.9859	0.450141	0.225070	+	0.974342i	$0.427739\pi$
$710$	−13.1139	−0.492155
$711$	7.21228	0.270482
$712$	8.26456	0.309728
$713$	4.45581	0.166872
$714$	1.79122	0.0670347
$715$	4.96352	0.185625
$716$	−17.8316	−0.666397
$717$	−0.125111	−0.00467237
$718$	17.3047	0.645806
$719$	−31.2726	−1.16627	−0.583136	−	0.812375i	$-0.698175\pi$
$719$	−31.2726	−1.16627	−0.583136	+	0.812375i	$0.698175\pi$
$720$	2.90944	0.108429
$721$	−17.4692	−0.650586
$722$	2.76787	0.103010
$723$	−7.25517	−0.269823
$724$	14.7311	0.547478
$725$	−2.08163	−0.0773098
$726$	4.10358	0.152298
$727$	−21.0644	−0.781237	−0.390618	−	0.920553i	$-0.627739\pi$
$727$	−21.0644	−0.781237	−0.390618	+	0.920553i	$0.627739\pi$
$728$	3.15038	0.116761
$729$	−22.2322	−0.823415
$730$	−11.3045	−0.418398
$731$	−1.46945	−0.0543494
$732$	−0.974302	−0.0360112
$733$	7.83389	0.289351	0.144676	−	0.989479i	$-0.453786\pi$
$733$	7.83389	0.289351	0.144676	+	0.989479i	$0.453786\pi$
$734$	−19.3654	−0.714789
$735$	−0.880187	−0.0324662
$736$	−4.45581	−0.164243
$737$	41.9235	1.54427
$738$	−19.7979	−0.728771
$739$	−19.2833	−0.709348	−0.354674	−	0.934990i	$-0.615408\pi$
$739$	−19.2833	−0.709348	−0.354674	+	0.934990i	$0.615408\pi$
$740$	5.70317	0.209653
$741$	−1.40400	−0.0515774
$742$	−10.6837	−0.392210
$743$	−48.4537	−1.77759	−0.888797	−	0.458302i	$-0.848458\pi$
$743$	−48.4537	−1.77759	−0.888797	+	0.458302i	$0.848458\pi$
$744$	−0.300926	−0.0110325
$745$	4.37620	0.160332
$746$	13.0357	0.477272
$747$	8.56703	0.313451
$748$	−9.37808	−0.342897
$749$	−36.0491	−1.31721
$750$	−0.300926	−0.0109883
$751$	−3.92584	−0.143256	−0.0716280	−	0.997431i	$-0.522819\pi$
$751$	−3.92584	−0.143256	−0.0716280	+	0.997431i	$0.522819\pi$
$752$	−6.80921	−0.248306
$753$	0.195377	0.00711994
$754$	−2.08163	−0.0758085
$755$	−19.7761	−0.719725
$756$	−5.60235	−0.203756
$757$	−42.7038	−1.55210	−0.776048	−	0.630674i	$-0.782779\pi$
$757$	−42.7038	−1.55210	−0.776048	+	0.630674i	$0.782779\pi$
$758$	−21.3118	−0.774080
$759$	6.65544	0.241577
$760$	4.66561	0.169239
$761$	30.0194	1.08820	0.544101	−	0.839020i	$-0.316871\pi$
$761$	30.0194	1.08820	0.544101	+	0.839020i	$0.316871\pi$
$762$	−0.113945	−0.00412779
$763$	−3.16243	−0.114488
$764$	21.2023	0.767073
$765$	5.49711	0.198749
$766$	−19.3110	−0.697734
$767$	−13.2811	−0.479551
$768$	0.300926	0.0108587
$769$	33.6907	1.21492	0.607459	−	0.794351i	$-0.292189\pi$
$769$	33.6907	1.21492	0.607459	+	0.794351i	$0.292189\pi$
$770$	15.6370	0.563518
$771$	−5.68500	−0.204740
$772$	−24.9474	−0.897878
$773$	−36.9590	−1.32932	−0.664662	−	0.747144i	$-0.731424\pi$
$773$	−36.9590	−1.32932	−0.664662	+	0.747144i	$0.731424\pi$
$774$	2.26276	0.0813333
$775$	−1.00000	−0.0359211
$776$	−10.2891	−0.369358
$777$	−5.40680	−0.193968
$778$	−9.71130	−0.348167
$779$	−31.7481	−1.13749
$780$	−0.300926	−0.0107749
$781$	−65.0909	−2.32913
$782$	−8.41883	−0.301057
$783$	3.70178	0.132291
$784$	2.92492	0.104462
$785$	−0.100858	−0.00359978
$786$	−5.59600	−0.199603
$787$	24.2241	0.863494	0.431747	−	0.901995i	$-0.357897\pi$
$787$	24.2241	0.863494	0.431747	+	0.901995i	$0.357897\pi$
$788$	12.9775	0.462306
$789$	0.592131	0.0210804
$790$	2.47892	0.0881961
$791$	46.2324	1.64383
$792$	14.4411	0.513141
$793$	−3.23767	−0.114973
$794$	20.9972	0.745164
$795$	1.02051	0.0361938
$796$	−7.29756	−0.258655
$797$	51.6621	1.82997	0.914983	−	0.403493i	$-0.132204\pi$
$797$	51.6621	1.82997	0.914983	+	0.403493i	$0.132204\pi$
$798$	−4.42315	−0.156578
$799$	−12.8653	−0.455143
$800$	1.00000	0.0353553
$801$	−24.0453	−0.849598
$802$	−34.9041	−1.23251
$803$	−56.1100	−1.98008
$804$	−2.54172	−0.0896396
$805$	14.0375	0.494758
$806$	−1.00000	−0.0352235
$807$	−2.62085	−0.0922582
$808$	−14.3862	−0.506104
$809$	−13.9235	−0.489526	−0.244763	−	0.969583i	$-0.578710\pi$
$809$	−13.9235	−0.489526	−0.244763	+	0.969583i	$0.578710\pi$
$810$	−8.19319	−0.287879
$811$	−48.2518	−1.69435	−0.847175	−	0.531313i	$-0.821699\pi$
$811$	−48.2518	−1.69435	−0.847175	+	0.531313i	$0.821699\pi$
$812$	−6.55794	−0.230138
$813$	7.65097	0.268331
$814$	28.3078	0.992186
$815$	−2.69300	−0.0943318
$816$	0.568571	0.0199040
$817$	3.62858	0.126948
$818$	−23.7803	−0.831458
$819$	−9.16587	−0.320281
$820$	−6.80470	−0.237631
$821$	15.3268	0.534910	0.267455	−	0.963570i	$-0.413817\pi$
$821$	15.3268	0.534910	0.267455	+	0.963570i	$0.413817\pi$
$822$	−0.685849	−0.0239217
$823$	11.5724	0.403388	0.201694	−	0.979449i	$-0.435355\pi$
$823$	11.5724	0.403388	0.201694	+	0.979449i	$0.435355\pi$
$824$	−5.54509	−0.193172
$825$	−1.49365	−0.0520023
$826$	−41.8404	−1.45582
$827$	−24.5182	−0.852580	−0.426290	−	0.904586i	$-0.640180\pi$
$827$	−24.5182	−0.852580	−0.426290	+	0.904586i	$0.640180\pi$
$828$	12.9639	0.450528
$829$	24.8568	0.863313	0.431656	−	0.902038i	$-0.357929\pi$
$829$	24.8568	0.863313	0.431656	+	0.902038i	$0.357929\pi$
$830$	2.94456	0.102207
$831$	4.26406	0.147919
$832$	1.00000	0.0346688
$833$	5.52636	0.191477
$834$	2.71405	0.0939798
$835$	−0.159566	−0.00552199
$836$	23.1578	0.800929
$837$	1.77831	0.0614673
$838$	−27.3830	−0.945930
$839$	−35.1576	−1.21377	−0.606887	−	0.794788i	$-0.707582\pi$
$839$	−35.1576	−1.21377	−0.606887	+	0.794788i	$0.707582\pi$
$840$	−0.948034	−0.0327103
$841$	−24.6668	−0.850580
$842$	26.3343	0.907540
$843$	−2.13417	−0.0735047
$844$	7.95412	0.273792
$845$	−1.00000	−0.0344010
$846$	19.8110	0.681116
$847$	42.9602	1.47613
$848$	−3.39123	−0.116455
$849$	8.93143	0.306526
$850$	1.88940	0.0648060
$851$	25.4123	0.871121
$852$	3.94631	0.135198
$853$	28.6515	0.981008	0.490504	−	0.871439i	$-0.336813\pi$
$853$	28.6515	0.981008	0.490504	+	0.871439i	$0.336813\pi$
$854$	−10.1999	−0.349034
$855$	−13.5743	−0.464232
$856$	−11.4428	−0.391106
$857$	53.8463	1.83935	0.919677	−	0.392675i	$-0.128450\pi$
$857$	53.8463	1.83935	0.919677	+	0.392675i	$0.128450\pi$
$858$	−1.49365	−0.0509925
$859$	−2.64326	−0.0901869	−0.0450934	−	0.998983i	$-0.514359\pi$
$859$	−2.64326	−0.0901869	−0.0450934	+	0.998983i	$0.514359\pi$
$860$	0.777730	0.0265204
$861$	6.45109	0.219853
$862$	29.5386	1.00609
$863$	−37.2858	−1.26922	−0.634612	−	0.772831i	$-0.718840\pi$
$863$	−37.2858	−1.26922	−0.634612	+	0.772831i	$0.718840\pi$
$864$	−1.77831	−0.0604992
$865$	4.88183	0.165987
$866$	24.3047	0.825907
$867$	−4.04149	−0.137256
$868$	−3.15038	−0.106931
$869$	12.3042	0.417390
$870$	0.626417	0.0212375
$871$	−8.44633	−0.286193
$872$	−1.00382	−0.0339938
$873$	29.9356	1.01317
$874$	20.7891	0.703201
$875$	−3.15038	−0.106502
$876$	3.40182	0.114937
$877$	−30.0955	−1.01625	−0.508127	−	0.861282i	$-0.669662\pi$
$877$	−30.0955	−1.01625	−0.508127	+	0.861282i	$0.669662\pi$
$878$	12.1983	0.411673
$879$	4.55214	0.153540
$880$	4.96352	0.167320
$881$	6.48049	0.218333	0.109167	−	0.994023i	$-0.465182\pi$
$881$	6.48049	0.218333	0.109167	+	0.994023i	$0.465182\pi$
$882$	−8.50990	−0.286543
$883$	−24.8652	−0.836781	−0.418390	−	0.908267i	$-0.637406\pi$
$883$	−24.8652	−0.836781	−0.418390	+	0.908267i	$0.637406\pi$
$884$	1.88940	0.0635475
$885$	3.99662	0.134345
$886$	−32.0859	−1.07795
$887$	−9.47569	−0.318163	−0.159081	−	0.987265i	$-0.550853\pi$
$887$	−9.47569	−0.318163	−0.159081	+	0.987265i	$0.550853\pi$
$888$	−1.71623	−0.0575930
$889$	−1.19288	−0.0400081
$890$	−8.26456	−0.277029
$891$	−40.6670	−1.36240
$892$	−8.84055	−0.296004
$893$	31.7691	1.06311
$894$	−1.31691	−0.0440442
$895$	17.8316	0.596044
$896$	3.15038	0.105247
$897$	−1.34087	−0.0447704
$898$	9.39473	0.313506
$899$	2.08163	0.0694262
$900$	−2.90944	−0.0969814
$901$	−6.40741	−0.213462
$902$	−33.7753	−1.12459
$903$	−0.737315	−0.0245363
$904$	14.6751	0.488088
$905$	−14.7311	−0.489679
$906$	5.95114	0.197714
$907$	−38.7436	−1.28646	−0.643231	−	0.765672i	$-0.722406\pi$
$907$	−38.7436	−1.28646	−0.643231	+	0.765672i	$0.722406\pi$
$908$	−13.1740	−0.437194
$909$	41.8557	1.38827
$910$	−3.15038	−0.104434
$911$	30.5601	1.01250	0.506251	−	0.862386i	$-0.331031\pi$
$911$	30.5601	1.01250	0.506251	+	0.862386i	$0.331031\pi$
$912$	−1.40400	−0.0464912
$913$	14.6154	0.483698
$914$	−3.32286	−0.109910
$915$	0.974302	0.0322094
$916$	24.5085	0.809783
$917$	−58.5843	−1.93462
$918$	−3.35994	−0.110895
$919$	42.6592	1.40720	0.703598	−	0.710598i	$-0.251575\pi$
$919$	42.6592	1.40720	0.703598	+	0.710598i	$0.251575\pi$
$920$	4.45581	0.146904
$921$	5.30568	0.174828
$922$	−8.51704	−0.280494
$923$	13.1139	0.431648
$924$	−4.70558	−0.154802
$925$	−5.70317	−0.187519
$926$	20.7368	0.681454
$927$	16.1331	0.529881
$928$	−2.08163	−0.0683329
$929$	−14.9660	−0.491018	−0.245509	−	0.969394i	$-0.578955\pi$
$929$	−14.9660	−0.491018	−0.245509	+	0.969394i	$0.578955\pi$
$930$	0.300926	0.00986777
$931$	−13.6465	−0.447247
$932$	−4.33762	−0.142084
$933$	−8.69397	−0.284628
$934$	11.5796	0.378894
$935$	9.37808	0.306696
$936$	−2.90944	−0.0950981
$937$	−2.06773	−0.0675496	−0.0337748	−	0.999429i	$-0.510753\pi$
$937$	−2.06773	−0.0675496	−0.0337748	+	0.999429i	$0.510753\pi$
$938$	−26.6092	−0.868820
$939$	−1.69615	−0.0553519
$940$	6.80921	0.222092
$941$	43.2291	1.40923	0.704615	−	0.709590i	$-0.251120\pi$
$941$	43.2291	1.40923	0.704615	+	0.709590i	$0.251120\pi$
$942$	0.0303509	0.000988886 0
$943$	−30.3205	−0.987371
$944$	−13.2811	−0.432262
$945$	5.60235	0.182245
$946$	3.86028	0.125508
$947$	17.5363	0.569852	0.284926	−	0.958550i	$-0.408031\pi$
$947$	17.5363	0.569852	0.284926	+	0.958550i	$0.408031\pi$
$948$	−0.745973	−0.0242281
$949$	11.3045	0.366959
$950$	−4.66561	−0.151372
$951$	−5.69960	−0.184822
$952$	5.95235	0.192917
$953$	−0.0617556	−0.00200046	−0.00100023	−	0.999999i	$-0.500318\pi$
$953$	−0.0617556	−0.00200046	−0.00100023	+	0.999999i	$0.500318\pi$
$954$	9.86660	0.319443
$955$	−21.2023	−0.686091
$956$	−0.415754	−0.0134465
$957$	3.10923	0.100507
$958$	7.74388	0.250193
$959$	−7.18012	−0.231858
$960$	−0.300926	−0.00971236
$961$	1.00000	0.0322581
$962$	−5.70317	−0.183878
$963$	33.2921	1.07282
$964$	−24.1094	−0.776513
$965$	24.9474	0.803087
$966$	−4.22426	−0.135913
$967$	−36.8990	−1.18659	−0.593296	−	0.804984i	$-0.702174\pi$
$967$	−36.8990	−1.18659	−0.593296	+	0.804984i	$0.702174\pi$
$968$	13.6365	0.438293
$969$	−2.65273	−0.0852180
$970$	10.2891	0.330364
$971$	−33.8502	−1.08631	−0.543153	−	0.839634i	$-0.682770\pi$
$971$	−33.8502	−1.08631	−0.543153	+	0.839634i	$0.682770\pi$
$972$	7.80047	0.250200
$973$	28.4132	0.910887
$974$	2.14030	0.0685796
$975$	0.300926	0.00963736
$976$	−3.23767	−0.103635
$977$	6.14025	0.196444	0.0982221	−	0.995165i	$-0.468684\pi$
$977$	6.14025	0.196444	0.0982221	+	0.995165i	$0.468684\pi$
$978$	0.810396	0.0259136
$979$	−41.0213	−1.31105
$980$	−2.92492	−0.0934333
$981$	2.92057	0.0932466
$982$	15.5236	0.495378
$983$	3.72011	0.118653	0.0593266	−	0.998239i	$-0.481105\pi$
$983$	3.72011	0.118653	0.0593266	+	0.998239i	$0.481105\pi$
$984$	2.04772	0.0652788
$985$	−12.9775	−0.413499
$986$	−3.93304	−0.125254
$987$	−6.45536	−0.205476
$988$	−4.66561	−0.148433
$989$	3.46542	0.110194
$990$	−14.4411	−0.458967
$991$	11.0600	0.351331	0.175665	−	0.984450i	$-0.443792\pi$
$991$	11.0600	0.351331	0.175665	+	0.984450i	$0.443792\pi$
$992$	−1.00000	−0.0317500
$993$	9.62989	0.305595
$994$	41.3137	1.31039
$995$	7.29756	0.231348
$996$	−0.886096	−0.0280770
$997$	−44.6240	−1.41326	−0.706629	−	0.707585i	$-0.749785\pi$
$997$	−44.6240	−1.41326	−0.706629	+	0.707585i	$0.749785\pi$
$998$	22.9404	0.726165
$999$	10.1420	0.320878

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4030.2.a.f.1.5	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4030.2.a.f.1.5	✓	6	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.300926 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.300926 q^{6} +3.15038 q^{7} +1.00000 q^{8} -2.90944 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.300926 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.300926 q^{6} +3.15038 q^{7} +1.00000 q^{8} -2.90944 q^{9} -1.00000 q^{10} -4.96352 q^{11} +0.300926 q^{12} +1.00000 q^{13} +3.15038 q^{14} -0.300926 q^{15} +1.00000 q^{16} +1.88940 q^{17} -2.90944 q^{18} -4.66561 q^{19} -1.00000 q^{20} +0.948034 q^{21} -4.96352 q^{22} -4.45581 q^{23} +0.300926 q^{24} +1.00000 q^{25} +1.00000 q^{26} -1.77831 q^{27} +3.15038 q^{28} -2.08163 q^{29} -0.300926 q^{30} -1.00000 q^{31} +1.00000 q^{32} -1.49365 q^{33} +1.88940 q^{34} -3.15038 q^{35} -2.90944 q^{36} -5.70317 q^{37} -4.66561 q^{38} +0.300926 q^{39} -1.00000 q^{40} +6.80470 q^{41} +0.948034 q^{42} -0.777730 q^{43} -4.96352 q^{44} +2.90944 q^{45} -4.45581 q^{46} -6.80921 q^{47} +0.300926 q^{48} +2.92492 q^{49} +1.00000 q^{50} +0.568571 q^{51} +1.00000 q^{52} -3.39123 q^{53} -1.77831 q^{54} +4.96352 q^{55} +3.15038 q^{56} -1.40400 q^{57} -2.08163 q^{58} -13.2811 q^{59} -0.300926 q^{60} -3.23767 q^{61} -1.00000 q^{62} -9.16587 q^{63} +1.00000 q^{64} -1.00000 q^{65} -1.49365 q^{66} -8.44633 q^{67} +1.88940 q^{68} -1.34087 q^{69} -3.15038 q^{70} +13.1139 q^{71} -2.90944 q^{72} +11.3045 q^{73} -5.70317 q^{74} +0.300926 q^{75} -4.66561 q^{76} -15.6370 q^{77} +0.300926 q^{78} -2.47892 q^{79} -1.00000 q^{80} +8.19319 q^{81} +6.80470 q^{82} -2.94456 q^{83} +0.948034 q^{84} -1.88940 q^{85} -0.777730 q^{86} -0.626417 q^{87} -4.96352 q^{88} +8.26456 q^{89} +2.90944 q^{90} +3.15038 q^{91} -4.45581 q^{92} -0.300926 q^{93} -6.80921 q^{94} +4.66561 q^{95} +0.300926 q^{96} -10.2891 q^{97} +2.92492 q^{98} +14.4411 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - 3 q^{3} + 6 q^{4} - 6 q^{5} - 3 q^{6} - 2 q^{7} + 6 q^{8} - q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 - 3 * q^3 + 6 * q^4 - 6 * q^5 - 3 * q^6 - 2 * q^7 + 6 * q^8 - q^9	\( 6 q + 6 q^{2} - 3 q^{3} + 6 q^{4} - 6 q^{5} - 3 q^{6} - 2 q^{7} + 6 q^{8} - q^{9} - 6 q^{10} - 4 q^{11} - 3 q^{12} + 6 q^{13} - 2 q^{14} + 3 q^{15} + 6 q^{16} - 8 q^{17} - q^{18} - 9 q^{19} - 6 q^{20} - 5 q^{21} - 4 q^{22} - 7 q^{23} - 3 q^{24} + 6 q^{25} + 6 q^{26} + 9 q^{27} - 2 q^{28} - 14 q^{29} + 3 q^{30} - 6 q^{31} + 6 q^{32} - 6 q^{33} - 8 q^{34} + 2 q^{35} - q^{36} - 9 q^{38} - 3 q^{39} - 6 q^{40} + 2 q^{41} - 5 q^{42} - 7 q^{43} - 4 q^{44} + q^{45} - 7 q^{46} - 8 q^{47} - 3 q^{48} - 14 q^{49} + 6 q^{50} - 5 q^{51} + 6 q^{52} - 24 q^{53} + 9 q^{54} + 4 q^{55} - 2 q^{56} - 15 q^{57} - 14 q^{58} - 5 q^{59} + 3 q^{60} - 5 q^{61} - 6 q^{62} - 19 q^{63} + 6 q^{64} - 6 q^{65} - 6 q^{66} - 12 q^{67} - 8 q^{68} + 2 q^{70} - 10 q^{71} - q^{72} + 5 q^{73} - 3 q^{75} - 9 q^{76} - q^{77} - 3 q^{78} - 16 q^{79} - 6 q^{80} - 10 q^{81} + 2 q^{82} - 22 q^{83} - 5 q^{84} + 8 q^{85} - 7 q^{86} - 31 q^{87} - 4 q^{88} + 14 q^{89} + q^{90} - 2 q^{91} - 7 q^{92} + 3 q^{93} - 8 q^{94} + 9 q^{95} - 3 q^{96} - 9 q^{97} - 14 q^{98} - 21 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 - 3 * q^3 + 6 * q^4 - 6 * q^5 - 3 * q^6 - 2 * q^7 + 6 * q^8 - q^9 - 6 * q^10 - 4 * q^11 - 3 * q^12 + 6 * q^13 - 2 * q^14 + 3 * q^15 + 6 * q^16 - 8 * q^17 - q^18 - 9 * q^19 - 6 * q^20 - 5 * q^21 - 4 * q^22 - 7 * q^23 - 3 * q^24 + 6 * q^25 + 6 * q^26 + 9 * q^27 - 2 * q^28 - 14 * q^29 + 3 * q^30 - 6 * q^31 + 6 * q^32 - 6 * q^33 - 8 * q^34 + 2 * q^35 - q^36 - 9 * q^38 - 3 * q^39 - 6 * q^40 + 2 * q^41 - 5 * q^42 - 7 * q^43 - 4 * q^44 + q^45 - 7 * q^46 - 8 * q^47 - 3 * q^48 - 14 * q^49 + 6 * q^50 - 5 * q^51 + 6 * q^52 - 24 * q^53 + 9 * q^54 + 4 * q^55 - 2 * q^56 - 15 * q^57 - 14 * q^58 - 5 * q^59 + 3 * q^60 - 5 * q^61 - 6 * q^62 - 19 * q^63 + 6 * q^64 - 6 * q^65 - 6 * q^66 - 12 * q^67 - 8 * q^68 + 2 * q^70 - 10 * q^71 - q^72 + 5 * q^73 - 3 * q^75 - 9 * q^76 - q^77 - 3 * q^78 - 16 * q^79 - 6 * q^80 - 10 * q^81 + 2 * q^82 - 22 * q^83 - 5 * q^84 + 8 * q^85 - 7 * q^86 - 31 * q^87 - 4 * q^88 + 14 * q^89 + q^90 - 2 * q^91 - 7 * q^92 + 3 * q^93 - 8 * q^94 + 9 * q^95 - 3 * q^96 - 9 * q^97 - 14 * q^98 - 21 * q^99

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