LMFDB - Embedded newform 4030.2.a.n.1.3

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:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 16x^{6} + 18x^{5} + 64x^{4} - 84x^{3} - 19x^{2} + 22x + 4 $ x^8 - x^7 - 16x^6 + 18x^5 + 64x^4 - 84x^3 - 19x^2 + 22x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.54913$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.54913 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.54913 q^{6} -2.44745 q^{7} +1.00000 q^{8} -0.600186 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.54913 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.54913 q^{6} -2.44745 q^{7} +1.00000 q^{8} -0.600186 q^{9} -1.00000 q^{10} -5.54556 q^{11} -1.54913 q^{12} -1.00000 q^{13} -2.44745 q^{14} +1.54913 q^{15} +1.00000 q^{16} +2.34210 q^{17} -0.600186 q^{18} +4.05227 q^{19} -1.00000 q^{20} +3.79143 q^{21} -5.54556 q^{22} -9.12289 q^{23} -1.54913 q^{24} +1.00000 q^{25} -1.00000 q^{26} +5.57717 q^{27} -2.44745 q^{28} -6.24163 q^{29} +1.54913 q^{30} -1.00000 q^{31} +1.00000 q^{32} +8.59082 q^{33} +2.34210 q^{34} +2.44745 q^{35} -0.600186 q^{36} -5.94196 q^{37} +4.05227 q^{38} +1.54913 q^{39} -1.00000 q^{40} +7.55244 q^{41} +3.79143 q^{42} +1.44624 q^{43} -5.54556 q^{44} +0.600186 q^{45} -9.12289 q^{46} +10.0998 q^{47} -1.54913 q^{48} -1.00997 q^{49} +1.00000 q^{50} -3.62822 q^{51} -1.00000 q^{52} -4.83126 q^{53} +5.57717 q^{54} +5.54556 q^{55} -2.44745 q^{56} -6.27750 q^{57} -6.24163 q^{58} +3.28367 q^{59} +1.54913 q^{60} -0.864407 q^{61} -1.00000 q^{62} +1.46893 q^{63} +1.00000 q^{64} +1.00000 q^{65} +8.59082 q^{66} -1.53132 q^{67} +2.34210 q^{68} +14.1326 q^{69} +2.44745 q^{70} +12.8137 q^{71} -0.600186 q^{72} -3.86412 q^{73} -5.94196 q^{74} -1.54913 q^{75} +4.05227 q^{76} +13.5725 q^{77} +1.54913 q^{78} +12.9284 q^{79} -1.00000 q^{80} -6.83922 q^{81} +7.55244 q^{82} +15.0039 q^{83} +3.79143 q^{84} -2.34210 q^{85} +1.44624 q^{86} +9.66912 q^{87} -5.54556 q^{88} -17.7702 q^{89} +0.600186 q^{90} +2.44745 q^{91} -9.12289 q^{92} +1.54913 q^{93} +10.0998 q^{94} -4.05227 q^{95} -1.54913 q^{96} -15.2244 q^{97} -1.00997 q^{98} +3.32837 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} - q^{3} + 8 q^{4} - 8 q^{5} - q^{6} + q^{7} + 8 q^{8} + 9 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 - q^3 + 8 * q^4 - 8 * q^5 - q^6 + q^7 + 8 * q^8 + 9 * q^9	\( 8 q + 8 q^{2} - q^{3} + 8 q^{4} - 8 q^{5} - q^{6} + q^{7} + 8 q^{8} + 9 q^{9} - 8 q^{10} + 4 q^{11} - q^{12} - 8 q^{13} + q^{14} + q^{15} + 8 q^{16} - 5 q^{17} + 9 q^{18} + 2 q^{19} - 8 q^{20} + 17 q^{21} + 4 q^{22} + 4 q^{23} - q^{24} + 8 q^{25} - 8 q^{26} + 11 q^{27} + q^{28} + 11 q^{29} + q^{30} - 8 q^{31} + 8 q^{32} + 10 q^{33} - 5 q^{34} - q^{35} + 9 q^{36} + 19 q^{37} + 2 q^{38} + q^{39} - 8 q^{40} + 10 q^{41} + 17 q^{42} + 19 q^{43} + 4 q^{44} - 9 q^{45} + 4 q^{46} + 11 q^{47} - q^{48} + 11 q^{49} + 8 q^{50} + 7 q^{51} - 8 q^{52} + 8 q^{53} + 11 q^{54} - 4 q^{55} + q^{56} - 11 q^{57} + 11 q^{58} + 28 q^{59} + q^{60} - 12 q^{61} - 8 q^{62} + 20 q^{63} + 8 q^{64} + 8 q^{65} + 10 q^{66} + 24 q^{67} - 5 q^{68} + 30 q^{69} - q^{70} + 18 q^{71} + 9 q^{72} - 3 q^{73} + 19 q^{74} - q^{75} + 2 q^{76} - 7 q^{77} + q^{78} + 22 q^{79} - 8 q^{80} + 24 q^{81} + 10 q^{82} + 17 q^{83} + 17 q^{84} + 5 q^{85} + 19 q^{86} + 11 q^{87} + 4 q^{88} + 17 q^{89} - 9 q^{90} - q^{91} + 4 q^{92} + q^{93} + 11 q^{94} - 2 q^{95} - q^{96} - 24 q^{97} + 11 q^{98} + 23 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 - q^3 + 8 * q^4 - 8 * q^5 - q^6 + q^7 + 8 * q^8 + 9 * q^9 - 8 * q^10 + 4 * q^11 - q^12 - 8 * q^13 + q^14 + q^15 + 8 * q^16 - 5 * q^17 + 9 * q^18 + 2 * q^19 - 8 * q^20 + 17 * q^21 + 4 * q^22 + 4 * q^23 - q^24 + 8 * q^25 - 8 * q^26 + 11 * q^27 + q^28 + 11 * q^29 + q^30 - 8 * q^31 + 8 * q^32 + 10 * q^33 - 5 * q^34 - q^35 + 9 * q^36 + 19 * q^37 + 2 * q^38 + q^39 - 8 * q^40 + 10 * q^41 + 17 * q^42 + 19 * q^43 + 4 * q^44 - 9 * q^45 + 4 * q^46 + 11 * q^47 - q^48 + 11 * q^49 + 8 * q^50 + 7 * q^51 - 8 * q^52 + 8 * q^53 + 11 * q^54 - 4 * q^55 + q^56 - 11 * q^57 + 11 * q^58 + 28 * q^59 + q^60 - 12 * q^61 - 8 * q^62 + 20 * q^63 + 8 * q^64 + 8 * q^65 + 10 * q^66 + 24 * q^67 - 5 * q^68 + 30 * q^69 - q^70 + 18 * q^71 + 9 * q^72 - 3 * q^73 + 19 * q^74 - q^75 + 2 * q^76 - 7 * q^77 + q^78 + 22 * q^79 - 8 * q^80 + 24 * q^81 + 10 * q^82 + 17 * q^83 + 17 * q^84 + 5 * q^85 + 19 * q^86 + 11 * q^87 + 4 * q^88 + 17 * q^89 - 9 * q^90 - q^91 + 4 * q^92 + q^93 + 11 * q^94 - 2 * q^95 - q^96 - 24 * q^97 + 11 * q^98 + 23 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.54913	−0.894392	−0.447196	−	0.894436i	$-0.647577\pi$
$3$	−1.54913	−0.894392	−0.447196	+	0.894436i	$0.647577\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.54913	−0.632431
$7$	−2.44745	−0.925050	−0.462525	−	0.886606i	$-0.653056\pi$
$7$	−2.44745	−0.925050	−0.462525	+	0.886606i	$0.653056\pi$
$8$	1.00000	0.353553
$9$	−0.600186	−0.200062
$10$	−1.00000	−0.316228
$11$	−5.54556	−1.67205	−0.836025	−	0.548691i	$-0.815126\pi$
$11$	−5.54556	−1.67205	−0.836025	+	0.548691i	$0.815126\pi$
$12$	−1.54913	−0.447196
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−2.44745	−0.654109
$15$	1.54913	0.399984
$16$	1.00000	0.250000
$17$	2.34210	0.568042	0.284021	−	0.958818i	$-0.408331\pi$
$17$	2.34210	0.568042	0.284021	+	0.958818i	$0.408331\pi$
$18$	−0.600186	−0.141465
$19$	4.05227	0.929654	0.464827	−	0.885402i	$-0.346117\pi$
$19$	4.05227	0.929654	0.464827	+	0.885402i	$0.346117\pi$
$20$	−1.00000	−0.223607
$21$	3.79143	0.827358
$22$	−5.54556	−1.18232
$23$	−9.12289	−1.90225	−0.951127	−	0.308801i	$-0.900072\pi$
$23$	−9.12289	−1.90225	−0.951127	+	0.308801i	$0.900072\pi$
$24$	−1.54913	−0.316215
$25$	1.00000	0.200000
$26$	−1.00000	−0.196116
$27$	5.57717	1.07333
$28$	−2.44745	−0.462525
$29$	−6.24163	−1.15904	−0.579521	−	0.814957i	$-0.696760\pi$
$29$	−6.24163	−1.15904	−0.579521	+	0.814957i	$0.696760\pi$
$30$	1.54913	0.282832
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	1.00000	0.176777
$33$	8.59082	1.49547
$34$	2.34210	0.401666
$35$	2.44745	0.413695
$36$	−0.600186	−0.100031
$37$	−5.94196	−0.976853	−0.488426	−	0.872605i	$-0.662429\pi$
$37$	−5.94196	−0.976853	−0.488426	+	0.872605i	$0.662429\pi$
$38$	4.05227	0.657364
$39$	1.54913	0.248060
$40$	−1.00000	−0.158114
$41$	7.55244	1.17949	0.589746	−	0.807588i	$-0.299228\pi$
$41$	7.55244	1.17949	0.589746	+	0.807588i	$0.299228\pi$
$42$	3.79143	0.585030
$43$	1.44624	0.220549	0.110275	−	0.993901i	$-0.464827\pi$
$43$	1.44624	0.220549	0.110275	+	0.993901i	$0.464827\pi$
$44$	−5.54556	−0.836025
$45$	0.600186	0.0894705
$46$	−9.12289	−1.34510
$47$	10.0998	1.47320	0.736600	−	0.676329i	$-0.236430\pi$
$47$	10.0998	1.47320	0.736600	+	0.676329i	$0.236430\pi$
$48$	−1.54913	−0.223598
$49$	−1.00997	−0.144282
$50$	1.00000	0.141421
$51$	−3.62822	−0.508053
$52$	−1.00000	−0.138675
$53$	−4.83126	−0.663625	−0.331812	−	0.943345i	$-0.607660\pi$
$53$	−4.83126	−0.663625	−0.331812	+	0.943345i	$0.607660\pi$
$54$	5.57717	0.758956
$55$	5.54556	0.747764
$56$	−2.44745	−0.327055
$57$	−6.27750	−0.831475
$58$	−6.24163	−0.819566
$59$	3.28367	0.427497	0.213749	−	0.976889i	$-0.431433\pi$
$59$	3.28367	0.427497	0.213749	+	0.976889i	$0.431433\pi$
$60$	1.54913	0.199992
$61$	−0.864407	−0.110676	−0.0553380	−	0.998468i	$-0.517624\pi$
$61$	−0.864407	−0.110676	−0.0553380	+	0.998468i	$0.517624\pi$
$62$	−1.00000	−0.127000
$63$	1.46893	0.185067
$64$	1.00000	0.125000
$65$	1.00000	0.124035
$66$	8.59082	1.05746
$67$	−1.53132	−0.187081	−0.0935405	−	0.995615i	$-0.529818\pi$
$67$	−1.53132	−0.187081	−0.0935405	+	0.995615i	$0.529818\pi$
$68$	2.34210	0.284021
$69$	14.1326	1.70136
$70$	2.44745	0.292527
$71$	12.8137	1.52071	0.760356	−	0.649507i	$-0.225025\pi$
$71$	12.8137	1.52071	0.760356	+	0.649507i	$0.225025\pi$
$72$	−0.600186	−0.0707326
$73$	−3.86412	−0.452261	−0.226130	−	0.974097i	$-0.572608\pi$
$73$	−3.86412	−0.452261	−0.226130	+	0.974097i	$0.572608\pi$
$74$	−5.94196	−0.690739
$75$	−1.54913	−0.178878
$76$	4.05227	0.464827
$77$	13.5725	1.54673
$78$	1.54913	0.175405
$79$	12.9284	1.45456	0.727282	−	0.686339i	$-0.240783\pi$
$79$	12.9284	1.45456	0.727282	+	0.686339i	$0.240783\pi$
$80$	−1.00000	−0.111803
$81$	−6.83922	−0.759913
$82$	7.55244	0.834027
$83$	15.0039	1.64689	0.823447	−	0.567394i	$-0.192048\pi$
$83$	15.0039	1.64689	0.823447	+	0.567394i	$0.192048\pi$
$84$	3.79143	0.413679
$85$	−2.34210	−0.254036
$86$	1.44624	0.155952
$87$	9.66912	1.03664
$88$	−5.54556	−0.591159
$89$	−17.7702	−1.88364	−0.941821	−	0.336116i	$-0.890887\pi$
$89$	−17.7702	−1.88364	−0.941821	+	0.336116i	$0.890887\pi$
$90$	0.600186	0.0632652
$91$	2.44745	0.256563
$92$	−9.12289	−0.951127
$93$	1.54913	0.160638
$94$	10.0998	1.04171
$95$	−4.05227	−0.415754
$96$	−1.54913	−0.158108
$97$	−15.2244	−1.54580	−0.772901	−	0.634527i	$-0.781195\pi$
$97$	−15.2244	−1.54580	−0.772901	+	0.634527i	$0.781195\pi$
$98$	−1.00997	−0.102023
$99$	3.32837	0.334514
$100$	1.00000	0.100000
$101$	5.00777	0.498292	0.249146	−	0.968466i	$-0.419850\pi$
$101$	5.00777	0.498292	0.249146	+	0.968466i	$0.419850\pi$
$102$	−3.62822	−0.359247
$103$	15.2753	1.50512	0.752560	−	0.658524i	$-0.228819\pi$
$103$	15.2753	1.50512	0.752560	+	0.658524i	$0.228819\pi$
$104$	−1.00000	−0.0980581
$105$	−3.79143	−0.370006
$106$	−4.83126	−0.469254
$107$	18.7916	1.81665	0.908327	−	0.418261i	$-0.137360\pi$
$107$	18.7916	1.81665	0.908327	+	0.418261i	$0.137360\pi$
$108$	5.57717	0.536663
$109$	−2.05689	−0.197015	−0.0985074	−	0.995136i	$-0.531407\pi$
$109$	−2.05689	−0.197015	−0.0985074	+	0.995136i	$0.531407\pi$
$110$	5.54556	0.528749
$111$	9.20489	0.873690
$112$	−2.44745	−0.231263
$113$	−16.9106	−1.59082	−0.795408	−	0.606074i	$-0.792744\pi$
$113$	−16.9106	−1.59082	−0.795408	+	0.606074i	$0.792744\pi$
$114$	−6.27750	−0.587942
$115$	9.12289	0.850714
$116$	−6.24163	−0.579521
$117$	0.600186	0.0554872
$118$	3.28367	0.302286
$119$	−5.73217	−0.525467
$120$	1.54913	0.141416
$121$	19.7533	1.79575
$122$	−0.864407	−0.0782597
$123$	−11.6997	−1.05493
$124$	−1.00000	−0.0898027
$125$	−1.00000	−0.0894427
$126$	1.46893	0.130862
$127$	−14.7356	−1.30757	−0.653787	−	0.756679i	$-0.726821\pi$
$127$	−14.7356	−1.30757	−0.653787	+	0.756679i	$0.726821\pi$
$128$	1.00000	0.0883883
$129$	−2.24042	−0.197258
$130$	1.00000	0.0877058
$131$	14.9000	1.30182	0.650910	−	0.759155i	$-0.274388\pi$
$131$	14.9000	1.30182	0.650910	+	0.759155i	$0.274388\pi$
$132$	8.59082	0.747735
$133$	−9.91773	−0.859976
$134$	−1.53132	−0.132286
$135$	−5.57717	−0.480006
$136$	2.34210	0.200833
$137$	15.7314	1.34402	0.672011	−	0.740541i	$-0.265431\pi$
$137$	15.7314	1.34402	0.672011	+	0.740541i	$0.265431\pi$
$138$	14.1326	1.20304
$139$	10.4165	0.883519	0.441759	−	0.897134i	$-0.354355\pi$
$139$	10.4165	0.883519	0.441759	+	0.897134i	$0.354355\pi$
$140$	2.44745	0.206848
$141$	−15.6459	−1.31762
$142$	12.8137	1.07531
$143$	5.54556	0.463743
$144$	−0.600186	−0.0500155
$145$	6.24163	0.518339
$146$	−3.86412	−0.319797
$147$	1.56458	0.129045
$148$	−5.94196	−0.488426
$149$	21.9458	1.79787	0.898934	−	0.438083i	$-0.144342\pi$
$149$	21.9458	1.79787	0.898934	+	0.438083i	$0.144342\pi$
$150$	−1.54913	−0.126486
$151$	−21.9433	−1.78572	−0.892862	−	0.450331i	$-0.851306\pi$
$151$	−21.9433	−1.78572	−0.892862	+	0.450331i	$0.851306\pi$
$152$	4.05227	0.328682
$153$	−1.40569	−0.113644
$154$	13.5725	1.09370
$155$	1.00000	0.0803219
$156$	1.54913	0.124030
$157$	5.98154	0.477379	0.238689	−	0.971096i	$-0.423282\pi$
$157$	5.98154	0.477379	0.238689	+	0.971096i	$0.423282\pi$
$158$	12.9284	1.02853
$159$	7.48427	0.593541
$160$	−1.00000	−0.0790569
$161$	22.3278	1.75968
$162$	−6.83922	−0.537340
$163$	−9.29991	−0.728425	−0.364213	−	0.931316i	$-0.618662\pi$
$163$	−9.29991	−0.728425	−0.364213	+	0.931316i	$0.618662\pi$
$164$	7.55244	0.589746
$165$	−8.59082	−0.668794
$166$	15.0039	1.16453
$167$	7.25922	0.561735	0.280868	−	0.959747i	$-0.409378\pi$
$167$	7.25922	0.561735	0.280868	+	0.959747i	$0.409378\pi$
$168$	3.79143	0.292515
$169$	1.00000	0.0769231
$170$	−2.34210	−0.179631
$171$	−2.43211	−0.185988
$172$	1.44624	0.110275
$173$	4.11152	0.312593	0.156296	−	0.987710i	$-0.450044\pi$
$173$	4.11152	0.312593	0.156296	+	0.987710i	$0.450044\pi$
$174$	9.66912	0.733014
$175$	−2.44745	−0.185010
$176$	−5.54556	−0.418013
$177$	−5.08684	−0.382350
$178$	−17.7702	−1.33194
$179$	1.25592	0.0938719	0.0469360	−	0.998898i	$-0.485054\pi$
$179$	1.25592	0.0938719	0.0469360	+	0.998898i	$0.485054\pi$
$180$	0.600186	0.0447352
$181$	15.0542	1.11897	0.559484	−	0.828841i	$-0.310999\pi$
$181$	15.0542	1.11897	0.559484	+	0.828841i	$0.310999\pi$
$182$	2.44745	0.181417
$183$	1.33908	0.0989878
$184$	−9.12289	−0.672548
$185$	5.94196	0.436862
$186$	1.54913	0.113588
$187$	−12.9883	−0.949795
$188$	10.0998	0.736600
$189$	−13.6499	−0.992881
$190$	−4.05227	−0.293982
$191$	11.3609	0.822043	0.411022	−	0.911626i	$-0.365172\pi$
$191$	11.3609	0.822043	0.411022	+	0.911626i	$0.365172\pi$
$192$	−1.54913	−0.111799
$193$	−21.2055	−1.52640	−0.763202	−	0.646161i	$-0.776374\pi$
$193$	−21.2055	−1.52640	−0.763202	+	0.646161i	$0.776374\pi$
$194$	−15.2244	−1.09305
$195$	−1.54913	−0.110936
$196$	−1.00997	−0.0721410
$197$	17.0707	1.21624	0.608119	−	0.793846i	$-0.291924\pi$
$197$	17.0707	1.21624	0.608119	+	0.793846i	$0.291924\pi$
$198$	3.32837	0.236537
$199$	2.56114	0.181555	0.0907773	−	0.995871i	$-0.471065\pi$
$199$	2.56114	0.181555	0.0907773	+	0.995871i	$0.471065\pi$
$200$	1.00000	0.0707107
$201$	2.37222	0.167324
$202$	5.00777	0.352346
$203$	15.2761	1.07217
$204$	−3.62822	−0.254026
$205$	−7.55244	−0.527485
$206$	15.2753	1.06428
$207$	5.47543	0.380569
$208$	−1.00000	−0.0693375
$209$	−22.4721	−1.55443
$210$	−3.79143	−0.261634
$211$	−14.2991	−0.984390	−0.492195	−	0.870485i	$-0.663805\pi$
$211$	−14.2991	−0.984390	−0.492195	+	0.870485i	$0.663805\pi$
$212$	−4.83126	−0.331812
$213$	−19.8502	−1.36011
$214$	18.7916	1.28457
$215$	−1.44624	−0.0986327
$216$	5.57717	0.379478
$217$	2.44745	0.166144
$218$	−2.05689	−0.139310
$219$	5.98603	0.404498
$220$	5.54556	0.373882
$221$	−2.34210	−0.157547
$222$	9.20489	0.617792
$223$	−2.46758	−0.165242	−0.0826208	−	0.996581i	$-0.526329\pi$
$223$	−2.46758	−0.165242	−0.0826208	+	0.996581i	$0.526329\pi$
$224$	−2.44745	−0.163527
$225$	−0.600186	−0.0400124
$226$	−16.9106	−1.12488
$227$	−26.1082	−1.73287	−0.866433	−	0.499294i	$-0.833593\pi$
$227$	−26.1082	−1.73287	−0.866433	+	0.499294i	$0.833593\pi$
$228$	−6.27750	−0.415738
$229$	−6.36309	−0.420485	−0.210243	−	0.977649i	$-0.567425\pi$
$229$	−6.36309	−0.420485	−0.210243	+	0.977649i	$0.567425\pi$
$230$	9.12289	0.601545
$231$	−21.0256	−1.38338
$232$	−6.24163	−0.409783
$233$	−13.3530	−0.874786	−0.437393	−	0.899271i	$-0.644098\pi$
$233$	−13.3530	−0.874786	−0.437393	+	0.899271i	$0.644098\pi$
$234$	0.600186	0.0392354
$235$	−10.0998	−0.658835
$236$	3.28367	0.213749
$237$	−20.0279	−1.30095
$238$	−5.73217	−0.371562
$239$	14.8652	0.961551	0.480776	−	0.876844i	$-0.340355\pi$
$239$	14.8652	0.961551	0.480776	+	0.876844i	$0.340355\pi$
$240$	1.54913	0.0999961
$241$	−10.7130	−0.690086	−0.345043	−	0.938587i	$-0.612136\pi$
$241$	−10.7130	−0.690086	−0.345043	+	0.938587i	$0.612136\pi$
$242$	19.7533	1.26979
$243$	−6.13664	−0.393666
$244$	−0.864407	−0.0553380
$245$	1.00997	0.0645249
$246$	−11.6997	−0.745948
$247$	−4.05227	−0.257840
$248$	−1.00000	−0.0635001
$249$	−23.2431	−1.47297
$250$	−1.00000	−0.0632456
$251$	−24.9380	−1.57407	−0.787036	−	0.616908i	$-0.788385\pi$
$251$	−24.9380	−1.57407	−0.787036	+	0.616908i	$0.788385\pi$
$252$	1.46893	0.0925337
$253$	50.5916	3.18066
$254$	−14.7356	−0.924594
$255$	3.62822	0.227208
$256$	1.00000	0.0625000
$257$	10.7059	0.667816	0.333908	−	0.942606i	$-0.391633\pi$
$257$	10.7059	0.667816	0.333908	+	0.942606i	$0.391633\pi$
$258$	−2.24042	−0.139482
$259$	14.5427	0.903638
$260$	1.00000	0.0620174
$261$	3.74614	0.231880
$262$	14.9000	0.920525
$263$	7.82206	0.482329	0.241165	−	0.970484i	$-0.422471\pi$
$263$	7.82206	0.482329	0.241165	+	0.970484i	$0.422471\pi$
$264$	8.59082	0.528728
$265$	4.83126	0.296782
$266$	−9.91773	−0.608095
$267$	27.5285	1.68471
$268$	−1.53132	−0.0935405
$269$	8.95435	0.545956	0.272978	−	0.962020i	$-0.411991\pi$
$269$	8.95435	0.545956	0.272978	+	0.962020i	$0.411991\pi$
$270$	−5.57717	−0.339416
$271$	−5.63277	−0.342167	−0.171083	−	0.985257i	$-0.554727\pi$
$271$	−5.63277	−0.342167	−0.171083	+	0.985257i	$0.554727\pi$
$272$	2.34210	0.142011
$273$	−3.79143	−0.229468
$274$	15.7314	0.950367
$275$	−5.54556	−0.334410
$276$	14.1326	0.850681
$277$	24.6756	1.48261	0.741305	−	0.671168i	$-0.234207\pi$
$277$	24.6756	1.48261	0.741305	+	0.671168i	$0.234207\pi$
$278$	10.4165	0.624742
$279$	0.600186	0.0359322
$280$	2.44745	0.146263
$281$	3.10065	0.184969	0.0924845	−	0.995714i	$-0.470519\pi$
$281$	3.10065	0.184969	0.0924845	+	0.995714i	$0.470519\pi$
$282$	−15.6459	−0.931697
$283$	3.09939	0.184240	0.0921199	−	0.995748i	$-0.470636\pi$
$283$	3.09939	0.184240	0.0921199	+	0.995748i	$0.470636\pi$
$284$	12.8137	0.760356
$285$	6.27750	0.371847
$286$	5.54556	0.327916
$287$	−18.4842	−1.09109
$288$	−0.600186	−0.0353663
$289$	−11.5146	−0.677328
$290$	6.24163	0.366521
$291$	23.5846	1.38255
$292$	−3.86412	−0.226130
$293$	−12.9052	−0.753932	−0.376966	−	0.926227i	$-0.623033\pi$
$293$	−12.9052	−0.753932	−0.376966	+	0.926227i	$0.623033\pi$
$294$	1.56458	0.0912484
$295$	−3.28367	−0.191183
$296$	−5.94196	−0.345370
$297$	−30.9285	−1.79466
$298$	21.9458	1.27129
$299$	9.12289	0.527590
$300$	−1.54913	−0.0894392
$301$	−3.53960	−0.204019
$302$	−21.9433	−1.26270
$303$	−7.75771	−0.445669
$304$	4.05227	0.232413
$305$	0.864407	0.0494958
$306$	−1.40569	−0.0803582
$307$	−27.1174	−1.54767	−0.773835	−	0.633387i	$-0.781664\pi$
$307$	−27.1174	−1.54767	−0.773835	+	0.633387i	$0.781664\pi$
$308$	13.5725	0.773365
$309$	−23.6635	−1.34617
$310$	1.00000	0.0567962
$311$	15.0204	0.851729	0.425865	−	0.904787i	$-0.359970\pi$
$311$	15.0204	0.851729	0.425865	+	0.904787i	$0.359970\pi$
$312$	1.54913	0.0877024
$313$	22.4506	1.26898	0.634492	−	0.772929i	$-0.281209\pi$
$313$	22.4506	1.26898	0.634492	+	0.772929i	$0.281209\pi$
$314$	5.98154	0.337558
$315$	−1.46893	−0.0827647
$316$	12.9284	0.727282
$317$	−20.4469	−1.14841	−0.574207	−	0.818710i	$-0.694690\pi$
$317$	−20.4469	−1.14841	−0.574207	+	0.818710i	$0.694690\pi$
$318$	7.48427	0.419697
$319$	34.6134	1.93798
$320$	−1.00000	−0.0559017
$321$	−29.1107	−1.62480
$322$	22.3278	1.24428
$323$	9.49080	0.528082
$324$	−6.83922	−0.379957
$325$	−1.00000	−0.0554700
$326$	−9.29991	−0.515074
$327$	3.18640	0.176209
$328$	7.55244	0.417014
$329$	−24.7187	−1.36278
$330$	−8.59082	−0.472909
$331$	16.0603	0.882755	0.441377	−	0.897322i	$-0.354490\pi$
$331$	16.0603	0.882755	0.441377	+	0.897322i	$0.354490\pi$
$332$	15.0039	0.823447
$333$	3.56628	0.195431
$334$	7.25922	0.397207
$335$	1.53132	0.0836652
$336$	3.79143	0.206840
$337$	−20.8945	−1.13820	−0.569098	−	0.822270i	$-0.692708\pi$
$337$	−20.8945	−1.13820	−0.569098	+	0.822270i	$0.692708\pi$
$338$	1.00000	0.0543928
$339$	26.1968	1.42281
$340$	−2.34210	−0.127018
$341$	5.54556	0.300309
$342$	−2.43211	−0.131514
$343$	19.6040	1.05852
$344$	1.44624	0.0779760
$345$	−14.1326	−0.760872
$346$	4.11152	0.221037
$347$	4.36732	0.234450	0.117225	−	0.993105i	$-0.462600\pi$
$347$	4.36732	0.234450	0.117225	+	0.993105i	$0.462600\pi$
$348$	9.66912	0.518319
$349$	27.9147	1.49424	0.747121	−	0.664688i	$-0.231436\pi$
$349$	27.9147	1.49424	0.747121	+	0.664688i	$0.231436\pi$
$350$	−2.44745	−0.130822
$351$	−5.57717	−0.297687
$352$	−5.54556	−0.295580
$353$	20.6711	1.10021	0.550107	−	0.835094i	$-0.314587\pi$
$353$	20.6711	1.10021	0.550107	+	0.835094i	$0.314587\pi$
$354$	−5.08684	−0.270363
$355$	−12.8137	−0.680083
$356$	−17.7702	−0.941821
$357$	8.87990	0.469974
$358$	1.25592	0.0663775
$359$	−3.07167	−0.162117	−0.0810583	−	0.996709i	$-0.525830\pi$
$359$	−3.07167	−0.162117	−0.0810583	+	0.996709i	$0.525830\pi$
$360$	0.600186	0.0316326
$361$	−2.57913	−0.135744
$362$	15.0542	0.791230
$363$	−30.6005	−1.60611
$364$	2.44745	0.128281
$365$	3.86412	0.202257
$366$	1.33908	0.0699949
$367$	1.81266	0.0946199	0.0473099	−	0.998880i	$-0.484935\pi$
$367$	1.81266	0.0946199	0.0473099	+	0.998880i	$0.484935\pi$
$368$	−9.12289	−0.475563
$369$	−4.53287	−0.235972
$370$	5.94196	0.308908
$371$	11.8243	0.613886
$372$	1.54913	0.0803188
$373$	−20.8441	−1.07927	−0.539633	−	0.841900i	$-0.681437\pi$
$373$	−20.8441	−1.07927	−0.539633	+	0.841900i	$0.681437\pi$
$374$	−12.9883	−0.671606
$375$	1.54913	0.0799969
$376$	10.0998	0.520855
$377$	6.24163	0.321460
$378$	−13.6499	−0.702073
$379$	32.8527	1.68753	0.843766	−	0.536711i	$-0.180334\pi$
$379$	32.8527	1.68753	0.843766	+	0.536711i	$0.180334\pi$
$380$	−4.05227	−0.207877
$381$	22.8274	1.16948
$382$	11.3609	0.581272
$383$	10.0122	0.511602	0.255801	−	0.966729i	$-0.417661\pi$
$383$	10.0122	0.511602	0.255801	+	0.966729i	$0.417661\pi$
$384$	−1.54913	−0.0790539
$385$	−13.5725	−0.691719
$386$	−21.2055	−1.07933
$387$	−0.868013	−0.0441236
$388$	−15.2244	−0.772901
$389$	35.4099	1.79535	0.897675	−	0.440657i	$-0.145255\pi$
$389$	35.4099	1.79535	0.897675	+	0.440657i	$0.145255\pi$
$390$	−1.54913	−0.0784434
$391$	−21.3667	−1.08056
$392$	−1.00997	−0.0510114
$393$	−23.0821	−1.16434
$394$	17.0707	0.860011
$395$	−12.9284	−0.650501
$396$	3.32837	0.167257
$397$	6.88727	0.345662	0.172831	−	0.984951i	$-0.444709\pi$
$397$	6.88727	0.345662	0.172831	+	0.984951i	$0.444709\pi$
$398$	2.56114	0.128379
$399$	15.3639	0.769156
$400$	1.00000	0.0500000
$401$	2.69010	0.134337	0.0671686	−	0.997742i	$-0.478603\pi$
$401$	2.69010	0.134337	0.0671686	+	0.997742i	$0.478603\pi$
$402$	2.37222	0.118316
$403$	1.00000	0.0498135
$404$	5.00777	0.249146
$405$	6.83922	0.339843
$406$	15.2761	0.758140
$407$	32.9515	1.63335
$408$	−3.62822	−0.179624
$409$	11.3839	0.562897	0.281449	−	0.959576i	$-0.409185\pi$
$409$	11.3839	0.562897	0.281449	+	0.959576i	$0.409185\pi$
$410$	−7.55244	−0.372988
$411$	−24.3700	−1.20208
$412$	15.2753	0.752560
$413$	−8.03663	−0.395457
$414$	5.47543	0.269103
$415$	−15.0039	−0.736513
$416$	−1.00000	−0.0490290
$417$	−16.1366	−0.790212
$418$	−22.4721	−1.09915
$419$	23.0761	1.12734	0.563670	−	0.826000i	$-0.309389\pi$
$419$	23.0761	1.12734	0.563670	+	0.826000i	$0.309389\pi$
$420$	−3.79143	−0.185003
$421$	29.0039	1.41357	0.706783	−	0.707431i	$-0.250146\pi$
$421$	29.0039	1.41357	0.706783	+	0.707431i	$0.250146\pi$
$422$	−14.2991	−0.696069
$423$	−6.06173	−0.294731
$424$	−4.83126	−0.234627
$425$	2.34210	0.113608
$426$	−19.8502	−0.961745
$427$	2.11560	0.102381
$428$	18.7916	0.908327
$429$	−8.59082	−0.414769
$430$	−1.44624	−0.0697438
$431$	10.1033	0.486661	0.243331	−	0.969943i	$-0.421760\pi$
$431$	10.1033	0.486661	0.243331	+	0.969943i	$0.421760\pi$
$432$	5.57717	0.268332
$433$	−26.3104	−1.26440	−0.632199	−	0.774806i	$-0.717847\pi$
$433$	−26.3104	−1.26440	−0.632199	+	0.774806i	$0.717847\pi$
$434$	2.44745	0.117482
$435$	−9.66912	−0.463599
$436$	−2.05689	−0.0985074
$437$	−36.9684	−1.76844
$438$	5.98603	0.286024
$439$	15.8154	0.754827	0.377414	−	0.926045i	$-0.376813\pi$
$439$	15.8154	0.754827	0.377414	+	0.926045i	$0.376813\pi$
$440$	5.54556	0.264374
$441$	0.606173	0.0288654
$442$	−2.34210	−0.111402
$443$	−10.2929	−0.489029	−0.244514	−	0.969646i	$-0.578629\pi$
$443$	−10.2929	−0.489029	−0.244514	+	0.969646i	$0.578629\pi$
$444$	9.20489	0.436845
$445$	17.7702	0.842390
$446$	−2.46758	−0.116843
$447$	−33.9969	−1.60800
$448$	−2.44745	−0.115631
$449$	−6.92180	−0.326660	−0.163330	−	0.986572i	$-0.552223\pi$
$449$	−6.92180	−0.326660	−0.163330	+	0.986572i	$0.552223\pi$
$450$	−0.600186	−0.0282930
$451$	−41.8825	−1.97217
$452$	−16.9106	−0.795408
$453$	33.9932	1.59714
$454$	−26.1082	−1.22532
$455$	−2.44745	−0.114738
$456$	−6.27750	−0.293971
$457$	12.2905	0.574925	0.287463	−	0.957792i	$-0.407188\pi$
$457$	12.2905	0.574925	0.287463	+	0.957792i	$0.407188\pi$
$458$	−6.36309	−0.297328
$459$	13.0623	0.609695
$460$	9.12289	0.425357
$461$	−13.7756	−0.641594	−0.320797	−	0.947148i	$-0.603951\pi$
$461$	−13.7756	−0.641594	−0.320797	+	0.947148i	$0.603951\pi$
$462$	−21.0256	−0.978200
$463$	−15.2867	−0.710434	−0.355217	−	0.934784i	$-0.615593\pi$
$463$	−15.2867	−0.710434	−0.355217	+	0.934784i	$0.615593\pi$
$464$	−6.24163	−0.289760
$465$	−1.54913	−0.0718393
$466$	−13.3530	−0.618567
$467$	−23.5599	−1.09022	−0.545110	−	0.838364i	$-0.683512\pi$
$467$	−23.5599	−1.09022	−0.545110	+	0.838364i	$0.683512\pi$
$468$	0.600186	0.0277436
$469$	3.74784	0.173059
$470$	−10.0998	−0.465867
$471$	−9.26620	−0.426964
$472$	3.28367	0.151143
$473$	−8.02021	−0.368770
$474$	−20.0279	−0.919911
$475$	4.05227	0.185931
$476$	−5.73217	−0.262734
$477$	2.89966	0.132766
$478$	14.8652	0.679919
$479$	25.1565	1.14943	0.574715	−	0.818353i	$-0.305113\pi$
$479$	25.1565	1.14943	0.574715	+	0.818353i	$0.305113\pi$
$480$	1.54913	0.0707079
$481$	5.94196	0.270930
$482$	−10.7130	−0.487965
$483$	−34.5888	−1.57384
$484$	19.7533	0.897876
$485$	15.2244	0.691303
$486$	−6.13664	−0.278364
$487$	0.268264	0.0121562	0.00607809	−	0.999982i	$-0.498065\pi$
$487$	0.268264	0.0121562	0.00607809	+	0.999982i	$0.498065\pi$
$488$	−0.864407	−0.0391299
$489$	14.4068	0.651498
$490$	1.00997	0.0456260
$491$	−26.8444	−1.21147	−0.605736	−	0.795666i	$-0.707121\pi$
$491$	−26.8444	−1.21147	−0.605736	+	0.795666i	$0.707121\pi$
$492$	−11.6997	−0.527465
$493$	−14.6185	−0.658384
$494$	−4.05227	−0.182320
$495$	−3.32837	−0.149599
$496$	−1.00000	−0.0449013
$497$	−31.3610	−1.40673
$498$	−23.2431	−1.04155
$499$	11.7989	0.528190	0.264095	−	0.964497i	$-0.414927\pi$
$499$	11.7989	0.528190	0.264095	+	0.964497i	$0.414927\pi$
$500$	−1.00000	−0.0447214
$501$	−11.2455	−0.502412
$502$	−24.9380	−1.11304
$503$	−7.35983	−0.328159	−0.164079	−	0.986447i	$-0.552465\pi$
$503$	−7.35983	−0.328159	−0.164079	+	0.986447i	$0.552465\pi$
$504$	1.46893	0.0654312
$505$	−5.00777	−0.222843
$506$	50.5916	2.24907
$507$	−1.54913	−0.0687994
$508$	−14.7356	−0.653787
$509$	25.4475	1.12794	0.563971	−	0.825794i	$-0.309273\pi$
$509$	25.4475	1.12794	0.563971	+	0.825794i	$0.309273\pi$
$510$	3.62822	0.160660
$511$	9.45724	0.418364
$512$	1.00000	0.0441942
$513$	22.6002	0.997822
$514$	10.7059	0.472217
$515$	−15.2753	−0.673110
$516$	−2.24042	−0.0986289
$517$	−56.0088	−2.46326
$518$	14.5427	0.638969
$519$	−6.36929	−0.279581
$520$	1.00000	0.0438529
$521$	−24.5340	−1.07486	−0.537428	−	0.843310i	$-0.680604\pi$
$521$	−24.5340	−1.07486	−0.537428	+	0.843310i	$0.680604\pi$
$522$	3.74614	0.163964
$523$	−3.66146	−0.160105	−0.0800523	−	0.996791i	$-0.525509\pi$
$523$	−3.66146	−0.160105	−0.0800523	+	0.996791i	$0.525509\pi$
$524$	14.9000	0.650910
$525$	3.79143	0.165472
$526$	7.82206	0.341058
$527$	−2.34210	−0.102023
$528$	8.59082	0.373867
$529$	60.2271	2.61857
$530$	4.83126	0.209857
$531$	−1.97081	−0.0855260
$532$	−9.91773	−0.429988
$533$	−7.55244	−0.327132
$534$	27.5285	1.19127
$535$	−18.7916	−0.812432
$536$	−1.53132	−0.0661431
$537$	−1.94559	−0.0839583
$538$	8.95435	0.386049
$539$	5.60088	0.241247
$540$	−5.57717	−0.240003
$541$	−32.2617	−1.38704	−0.693519	−	0.720439i	$-0.743940\pi$
$541$	−32.2617	−1.38704	−0.693519	+	0.720439i	$0.743940\pi$
$542$	−5.63277	−0.241948
$543$	−23.3209	−1.00080
$544$	2.34210	0.100417
$545$	2.05689	0.0881077
$546$	−3.79143	−0.162258
$547$	−38.0510	−1.62694	−0.813471	−	0.581605i	$-0.802425\pi$
$547$	−38.0510	−1.62694	−0.813471	+	0.581605i	$0.802425\pi$
$548$	15.7314	0.672011
$549$	0.518805	0.0221421
$550$	−5.54556	−0.236464
$551$	−25.2928	−1.07751
$552$	14.1326	0.601522
$553$	−31.6418	−1.34554
$554$	24.6756	1.04836
$555$	−9.20489	−0.390726
$556$	10.4165	0.441759
$557$	0.793849	0.0336365	0.0168182	−	0.999859i	$-0.494646\pi$
$557$	0.793849	0.0336365	0.0168182	+	0.999859i	$0.494646\pi$
$558$	0.600186	0.0254079
$559$	−1.44624	−0.0611694
$560$	2.44745	0.103424
$561$	20.1205	0.849490
$562$	3.10065	0.130793
$563$	−26.3962	−1.11247	−0.556234	−	0.831026i	$-0.687754\pi$
$563$	−26.3962	−1.11247	−0.556234	+	0.831026i	$0.687754\pi$
$564$	−15.6459	−0.658810
$565$	16.9106	0.711435
$566$	3.09939	0.130277
$567$	16.7387	0.702958
$568$	12.8137	0.537653
$569$	−10.5573	−0.442585	−0.221293	−	0.975207i	$-0.571028\pi$
$569$	−10.5573	−0.442585	−0.221293	+	0.975207i	$0.571028\pi$
$570$	6.27750	0.262936
$571$	−5.29402	−0.221548	−0.110774	−	0.993846i	$-0.535333\pi$
$571$	−5.29402	−0.221548	−0.110774	+	0.993846i	$0.535333\pi$
$572$	5.54556	0.231872
$573$	−17.5995	−0.735229
$574$	−18.4842	−0.771517
$575$	−9.12289	−0.380451
$576$	−0.600186	−0.0250078
$577$	−19.0055	−0.791208	−0.395604	−	0.918421i	$-0.629465\pi$
$577$	−19.0055	−0.791208	−0.395604	+	0.918421i	$0.629465\pi$
$578$	−11.5146	−0.478943
$579$	32.8501	1.36520
$580$	6.24163	0.259170
$581$	−36.7214	−1.52346
$582$	23.5846	0.977613
$583$	26.7921	1.10961
$584$	−3.86412	−0.159898
$585$	−0.600186	−0.0248146
$586$	−12.9052	−0.533110
$587$	13.8163	0.570260	0.285130	−	0.958489i	$-0.407963\pi$
$587$	13.8163	0.570260	0.285130	+	0.958489i	$0.407963\pi$
$588$	1.56458	0.0645224
$589$	−4.05227	−0.166971
$590$	−3.28367	−0.135187
$591$	−26.4448	−1.08779
$592$	−5.94196	−0.244213
$593$	−6.01761	−0.247114	−0.123557	−	0.992337i	$-0.539430\pi$
$593$	−6.01761	−0.247114	−0.123557	+	0.992337i	$0.539430\pi$
$594$	−30.9285	−1.26901
$595$	5.73217	0.234996
$596$	21.9458	0.898934
$597$	−3.96755	−0.162381
$598$	9.12289	0.373063
$599$	20.8331	0.851217	0.425609	−	0.904907i	$-0.360060\pi$
$599$	20.8331	0.851217	0.425609	+	0.904907i	$0.360060\pi$
$600$	−1.54913	−0.0632431
$601$	5.12603	0.209095	0.104547	−	0.994520i	$-0.466661\pi$
$601$	5.12603	0.209095	0.104547	+	0.994520i	$0.466661\pi$
$602$	−3.53960	−0.144263
$603$	0.919079	0.0374278
$604$	−21.9433	−0.892862
$605$	−19.7533	−0.803085
$606$	−7.75771	−0.315135
$607$	13.4816	0.547202	0.273601	−	0.961843i	$-0.411785\pi$
$607$	13.4816	0.547202	0.273601	+	0.961843i	$0.411785\pi$
$608$	4.05227	0.164341
$609$	−23.6647	−0.958942
$610$	0.864407	0.0349988
$611$	−10.0998	−0.408592
$612$	−1.40569	−0.0568218
$613$	−26.0503	−1.05216	−0.526081	−	0.850435i	$-0.676339\pi$
$613$	−26.0503	−1.05216	−0.526081	+	0.850435i	$0.676339\pi$
$614$	−27.1174	−1.09437
$615$	11.6997	0.471779
$616$	13.5725	0.546852
$617$	6.49390	0.261435	0.130717	−	0.991420i	$-0.458272\pi$
$617$	6.49390	0.261435	0.130717	+	0.991420i	$0.458272\pi$
$618$	−23.6635	−0.951885
$619$	6.55089	0.263303	0.131651	−	0.991296i	$-0.457972\pi$
$619$	6.55089	0.263303	0.131651	+	0.991296i	$0.457972\pi$
$620$	1.00000	0.0401610
$621$	−50.8799	−2.04174
$622$	15.0204	0.602264
$623$	43.4918	1.74246
$624$	1.54913	0.0620150
$625$	1.00000	0.0400000
$626$	22.4506	0.897307
$627$	34.8123	1.39027
$628$	5.98154	0.238689
$629$	−13.9167	−0.554894
$630$	−1.46893	−0.0585235
$631$	48.2402	1.92041	0.960205	−	0.279296i	$-0.0901011\pi$
$631$	48.2402	1.92041	0.960205	+	0.279296i	$0.0901011\pi$
$632$	12.9284	0.514266
$633$	22.1512	0.880431
$634$	−20.4469	−0.812051
$635$	14.7356	0.584765
$636$	7.48427	0.296771
$637$	1.00997	0.0400166
$638$	34.6134	1.37036
$639$	−7.69063	−0.304237
$640$	−1.00000	−0.0395285
$641$	−37.7946	−1.49280	−0.746398	−	0.665499i	$-0.768219\pi$
$641$	−37.7946	−1.49280	−0.746398	+	0.665499i	$0.768219\pi$
$642$	−29.1107	−1.14891
$643$	−22.2650	−0.878044	−0.439022	−	0.898476i	$-0.644675\pi$
$643$	−22.2650	−0.878044	−0.439022	+	0.898476i	$0.644675\pi$
$644$	22.3278	0.879840
$645$	2.24042	0.0882163
$646$	9.49080	0.373411
$647$	−3.79210	−0.149083	−0.0745414	−	0.997218i	$-0.523749\pi$
$647$	−3.79210	−0.149083	−0.0745414	+	0.997218i	$0.523749\pi$
$648$	−6.83922	−0.268670
$649$	−18.2098	−0.714797
$650$	−1.00000	−0.0392232
$651$	−3.79143	−0.148598
$652$	−9.29991	−0.364213
$653$	23.8419	0.933005	0.466502	−	0.884520i	$-0.345514\pi$
$653$	23.8419	0.933005	0.466502	+	0.884520i	$0.345514\pi$
$654$	3.18640	0.124598
$655$	−14.9000	−0.582191
$656$	7.55244	0.294873
$657$	2.31919	0.0904802
$658$	−24.7187	−0.963634
$659$	15.2769	0.595102	0.297551	−	0.954706i	$-0.403830\pi$
$659$	15.2769	0.595102	0.297551	+	0.954706i	$0.403830\pi$
$660$	−8.59082	−0.334397
$661$	37.6856	1.46580	0.732901	−	0.680336i	$-0.238166\pi$
$661$	37.6856	1.46580	0.732901	+	0.680336i	$0.238166\pi$
$662$	16.0603	0.624202
$663$	3.62822	0.140908
$664$	15.0039	0.582265
$665$	9.91773	0.384593
$666$	3.56628	0.138191
$667$	56.9417	2.20479
$668$	7.25922	0.280868
$669$	3.82262	0.147791
$670$	1.53132	0.0591602
$671$	4.79362	0.185056
$672$	3.79143	0.146258
$673$	−44.6599	−1.72151	−0.860757	−	0.509016i	$-0.830009\pi$
$673$	−44.6599	−1.72151	−0.860757	+	0.509016i	$0.830009\pi$
$674$	−20.8945	−0.804826
$675$	5.57717	0.214665
$676$	1.00000	0.0384615
$677$	−10.0628	−0.386745	−0.193373	−	0.981125i	$-0.561943\pi$
$677$	−10.0628	−0.386745	−0.193373	+	0.981125i	$0.561943\pi$
$678$	26.1968	1.00608
$679$	37.2610	1.42994
$680$	−2.34210	−0.0898153
$681$	40.4452	1.54986
$682$	5.54556	0.212351
$683$	−24.7628	−0.947521	−0.473761	−	0.880654i	$-0.657104\pi$
$683$	−24.7628	−0.947521	−0.473761	+	0.880654i	$0.657104\pi$
$684$	−2.43211	−0.0929942
$685$	−15.7314	−0.601065
$686$	19.6040	0.748486
$687$	9.85728	0.376079
$688$	1.44624	0.0551374
$689$	4.83126	0.184056
$690$	−14.1326	−0.538018
$691$	−7.20138	−0.273954	−0.136977	−	0.990574i	$-0.543739\pi$
$691$	−7.20138	−0.273954	−0.136977	+	0.990574i	$0.543739\pi$
$692$	4.11152	0.156296
$693$	−8.14603	−0.309442
$694$	4.36732	0.165781
$695$	−10.4165	−0.395122
$696$	9.66912	0.366507
$697$	17.6885	0.670002
$698$	27.9147	1.05659
$699$	20.6856	0.782402
$700$	−2.44745	−0.0925050
$701$	−46.3871	−1.75202	−0.876008	−	0.482297i	$-0.839803\pi$
$701$	−46.3871	−1.75202	−0.876008	+	0.482297i	$0.839803\pi$
$702$	−5.57717	−0.210497
$703$	−24.0784	−0.908135
$704$	−5.54556	−0.209006
$705$	15.6459	0.589257
$706$	20.6711	0.777969
$707$	−12.2563	−0.460945
$708$	−5.08684	−0.191175
$709$	18.3704	0.689913	0.344957	−	0.938619i	$-0.387894\pi$
$709$	18.3704	0.689913	0.344957	+	0.938619i	$0.387894\pi$
$710$	−12.8137	−0.480891
$711$	−7.75947	−0.291003
$712$	−17.7702	−0.665968
$713$	9.12289	0.341655
$714$	8.87990	0.332322
$715$	−5.54556	−0.207392
$716$	1.25592	0.0469360
$717$	−23.0282	−0.860004
$718$	−3.07167	−0.114634
$719$	−30.9378	−1.15378	−0.576892	−	0.816820i	$-0.695735\pi$
$719$	−30.9378	−1.15378	−0.576892	+	0.816820i	$0.695735\pi$
$720$	0.600186	0.0223676
$721$	−37.3856	−1.39231
$722$	−2.57913	−0.0959854
$723$	16.5959	0.617208
$724$	15.0542	0.559484
$725$	−6.24163	−0.231808
$726$	−30.6005	−1.13569
$727$	−8.12584	−0.301371	−0.150685	−	0.988582i	$-0.548148\pi$
$727$	−8.12584	−0.301371	−0.150685	+	0.988582i	$0.548148\pi$
$728$	2.44745	0.0907086
$729$	30.0241	1.11200
$730$	3.86412	0.143017
$731$	3.38723	0.125281
$732$	1.33908	0.0494939
$733$	43.1005	1.59195	0.795977	−	0.605326i	$-0.206957\pi$
$733$	43.1005	1.59195	0.795977	+	0.605326i	$0.206957\pi$
$734$	1.81266	0.0669064
$735$	−1.56458	−0.0577106
$736$	−9.12289	−0.336274
$737$	8.49205	0.312809
$738$	−4.53287	−0.166857
$739$	−16.2253	−0.596858	−0.298429	−	0.954432i	$-0.596463\pi$
$739$	−16.2253	−0.596858	−0.298429	+	0.954432i	$0.596463\pi$
$740$	5.94196	0.218431
$741$	6.27750	0.230610
$742$	11.8243	0.434083
$743$	43.4806	1.59515	0.797573	−	0.603222i	$-0.206117\pi$
$743$	43.4806	1.59515	0.797573	+	0.603222i	$0.206117\pi$
$744$	1.54913	0.0567940
$745$	−21.9458	−0.804031
$746$	−20.8441	−0.763156
$747$	−9.00514	−0.329481
$748$	−12.9883	−0.474898
$749$	−45.9916	−1.68050
$750$	1.54913	0.0565663
$751$	−45.4236	−1.65753	−0.828765	−	0.559597i	$-0.810956\pi$
$751$	−45.4236	−1.65753	−0.828765	+	0.559597i	$0.810956\pi$
$752$	10.0998	0.368300
$753$	38.6323	1.40784
$754$	6.24163	0.227307
$755$	21.9433	0.798600
$756$	−13.6499	−0.496440
$757$	−2.00646	−0.0729260	−0.0364630	−	0.999335i	$-0.511609\pi$
$757$	−2.00646	−0.0729260	−0.0364630	+	0.999335i	$0.511609\pi$
$758$	32.8527	1.19327
$759$	−78.3731	−2.84476
$760$	−4.05227	−0.146991
$761$	12.2864	0.445382	0.222691	−	0.974889i	$-0.428516\pi$
$761$	12.2864	0.445382	0.222691	+	0.974889i	$0.428516\pi$
$762$	22.8274	0.826950
$763$	5.03415	0.182249
$764$	11.3609	0.411022
$765$	1.40569	0.0508230
$766$	10.0122	0.361757
$767$	−3.28367	−0.118566
$768$	−1.54913	−0.0558995
$769$	21.1263	0.761834	0.380917	−	0.924609i	$-0.375608\pi$
$769$	21.1263	0.761834	0.380917	+	0.924609i	$0.375608\pi$
$770$	−13.5725	−0.489119
$771$	−16.5849	−0.597290
$772$	−21.2055	−0.763202
$773$	−18.4904	−0.665054	−0.332527	−	0.943094i	$-0.607901\pi$
$773$	−18.4904	−0.665054	−0.332527	+	0.943094i	$0.607901\pi$
$774$	−0.868013	−0.0312001
$775$	−1.00000	−0.0359211
$776$	−15.2244	−0.546523
$777$	−22.5285	−0.808207
$778$	35.4099	1.26950
$779$	30.6045	1.09652
$780$	−1.54913	−0.0554679
$781$	−71.0594	−2.54271
$782$	−21.3667	−0.764071
$783$	−34.8106	−1.24403
$784$	−1.00997	−0.0360705
$785$	−5.98154	−0.213490
$786$	−23.0821	−0.823311
$787$	−25.0132	−0.891626	−0.445813	−	0.895126i	$-0.647085\pi$
$787$	−25.0132	−0.891626	−0.445813	+	0.895126i	$0.647085\pi$
$788$	17.0707	0.608119
$789$	−12.1174	−0.431392
$790$	−12.9284	−0.459973
$791$	41.3879	1.47159
$792$	3.32837	0.118269
$793$	0.864407	0.0306960
$794$	6.88727	0.244420
$795$	−7.48427	−0.265440
$796$	2.56114	0.0907773
$797$	30.0470	1.06432	0.532160	−	0.846644i	$-0.321380\pi$
$797$	30.0470	1.06432	0.532160	+	0.846644i	$0.321380\pi$
$798$	15.3639	0.543876
$799$	23.6546	0.836840
$800$	1.00000	0.0353553
$801$	10.6655	0.376845
$802$	2.69010	0.0949907
$803$	21.4287	0.756203
$804$	2.37222	0.0836619
$805$	−22.3278	−0.786953
$806$	1.00000	0.0352235
$807$	−13.8715	−0.488299
$808$	5.00777	0.176173
$809$	11.2101	0.394127	0.197063	−	0.980391i	$-0.436860\pi$
$809$	11.2101	0.394127	0.197063	+	0.980391i	$0.436860\pi$
$810$	6.83922	0.240306
$811$	48.2767	1.69522	0.847611	−	0.530617i	$-0.178040\pi$
$811$	48.2767	1.69522	0.847611	+	0.530617i	$0.178040\pi$
$812$	15.2761	0.536086
$813$	8.72592	0.306031
$814$	32.9515	1.15495
$815$	9.29991	0.325762
$816$	−3.62822	−0.127013
$817$	5.86055	0.205035
$818$	11.3839	0.398028
$819$	−1.46893	−0.0513285
$820$	−7.55244	−0.263743
$821$	−23.6880	−0.826716	−0.413358	−	0.910569i	$-0.635644\pi$
$821$	−23.6880	−0.826716	−0.413358	+	0.910569i	$0.635644\pi$
$822$	−24.3700	−0.850001
$823$	−27.8310	−0.970127	−0.485063	−	0.874479i	$-0.661203\pi$
$823$	−27.8310	−0.970127	−0.485063	+	0.874479i	$0.661203\pi$
$824$	15.2753	0.532140
$825$	8.59082	0.299094
$826$	−8.03663	−0.279630
$827$	−22.4245	−0.779776	−0.389888	−	0.920862i	$-0.627486\pi$
$827$	−22.4245	−0.779776	−0.389888	+	0.920862i	$0.627486\pi$
$828$	5.47543	0.190284
$829$	−32.2365	−1.11962	−0.559810	−	0.828621i	$-0.689126\pi$
$829$	−32.2365	−1.11962	−0.559810	+	0.828621i	$0.689126\pi$
$830$	−15.0039	−0.520793
$831$	−38.2257	−1.32604
$832$	−1.00000	−0.0346688
$833$	−2.36546	−0.0819583
$834$	−16.1366	−0.558765
$835$	−7.25922	−0.251216
$836$	−22.4721	−0.777214
$837$	−5.57717	−0.192775
$838$	23.0761	0.797150
$839$	−26.2444	−0.906057	−0.453028	−	0.891496i	$-0.649656\pi$
$839$	−26.2444	−0.906057	−0.453028	+	0.891496i	$0.649656\pi$
$840$	−3.79143	−0.130817
$841$	9.95796	0.343378
$842$	29.0039	0.999542
$843$	−4.80331	−0.165435
$844$	−14.2991	−0.492195
$845$	−1.00000	−0.0344010
$846$	−6.06173	−0.208407
$847$	−48.3452	−1.66116
$848$	−4.83126	−0.165906
$849$	−4.80137	−0.164783
$850$	2.34210	0.0803333
$851$	54.2079	1.85822
$852$	−19.8502	−0.680057
$853$	14.8053	0.506923	0.253461	−	0.967345i	$-0.418431\pi$
$853$	14.8053	0.506923	0.253461	+	0.967345i	$0.418431\pi$
$854$	2.11560	0.0723942
$855$	2.43211	0.0831766
$856$	18.7916	0.642284
$857$	−2.42749	−0.0829214	−0.0414607	−	0.999140i	$-0.513201\pi$
$857$	−2.42749	−0.0829214	−0.0414607	+	0.999140i	$0.513201\pi$
$858$	−8.59082	−0.293286
$859$	9.65169	0.329312	0.164656	−	0.986351i	$-0.447349\pi$
$859$	9.65169	0.329312	0.164656	+	0.986351i	$0.447349\pi$
$860$	−1.44624	−0.0493163
$861$	28.6346	0.975863
$862$	10.1033	0.344121
$863$	35.2153	1.19874	0.599371	−	0.800471i	$-0.295417\pi$
$863$	35.2153	1.19874	0.599371	+	0.800471i	$0.295417\pi$
$864$	5.57717	0.189739
$865$	−4.11152	−0.139796
$866$	−26.3104	−0.894064
$867$	17.8376	0.605797
$868$	2.44745	0.0830720
$869$	−71.6955	−2.43210
$870$	−9.66912	−0.327814
$871$	1.53132	0.0518869
$872$	−2.05689	−0.0696552
$873$	9.13746	0.309256
$874$	−36.9684	−1.25047
$875$	2.44745	0.0827390
$876$	5.98603	0.202249
$877$	−35.2460	−1.19017	−0.595087	−	0.803662i	$-0.702882\pi$
$877$	−35.2460	−1.19017	−0.595087	+	0.803662i	$0.702882\pi$
$878$	15.8154	0.533744
$879$	19.9919	0.674311
$880$	5.54556	0.186941
$881$	0.188805	0.00636099	0.00318050	−	0.999995i	$-0.498988\pi$
$881$	0.188805	0.00636099	0.00318050	+	0.999995i	$0.498988\pi$
$882$	0.606173	0.0204109
$883$	−0.00355519	−0.000119642 0	−5.98209e−5	−	1.00000i	$-0.500019\pi$
$883$	−0.00355519	−0.000119642 0	−5.98209e−5		1.00000i	$0.500019\pi$
$884$	−2.34210	−0.0787733
$885$	5.08684	0.170992
$886$	−10.2929	−0.345796
$887$	−32.2186	−1.08180	−0.540898	−	0.841088i	$-0.681916\pi$
$887$	−32.2186	−1.08180	−0.540898	+	0.841088i	$0.681916\pi$
$888$	9.20489	0.308896
$889$	36.0647	1.20957
$890$	17.7702	0.595660
$891$	37.9273	1.27061
$892$	−2.46758	−0.0826208
$893$	40.9269	1.36957
$894$	−33.9969	−1.13703
$895$	−1.25592	−0.0419808
$896$	−2.44745	−0.0817637
$897$	−14.1326	−0.471873
$898$	−6.92180	−0.230983
$899$	6.24163	0.208170
$900$	−0.600186	−0.0200062
$901$	−11.3153	−0.376967
$902$	−41.8825	−1.39454
$903$	5.48332	0.182473
$904$	−16.9106	−0.562439
$905$	−15.0542	−0.500418
$906$	33.9932	1.12935
$907$	−7.35645	−0.244267	−0.122133	−	0.992514i	$-0.538974\pi$
$907$	−7.35645	−0.244267	−0.122133	+	0.992514i	$0.538974\pi$
$908$	−26.1082	−0.866433
$909$	−3.00560	−0.0996893
$910$	−2.44745	−0.0811323
$911$	−34.1287	−1.13073	−0.565367	−	0.824839i	$-0.691266\pi$
$911$	−34.1287	−1.13073	−0.565367	+	0.824839i	$0.691266\pi$
$912$	−6.27750	−0.207869
$913$	−83.2051	−2.75369
$914$	12.2905	0.406534
$915$	−1.33908	−0.0442687
$916$	−6.36309	−0.210243
$917$	−36.4671	−1.20425
$918$	13.0623	0.431119
$919$	−28.7039	−0.946853	−0.473426	−	0.880833i	$-0.656983\pi$
$919$	−28.7039	−0.946853	−0.473426	+	0.880833i	$0.656983\pi$
$920$	9.12289	0.300773
$921$	42.0084	1.38422
$922$	−13.7756	−0.453675
$923$	−12.8137	−0.421770
$924$	−21.0256	−0.691692
$925$	−5.94196	−0.195371
$926$	−15.2867	−0.502353
$927$	−9.16802	−0.301117
$928$	−6.24163	−0.204892
$929$	54.6399	1.79268	0.896339	−	0.443370i	$-0.146217\pi$
$929$	54.6399	1.79268	0.896339	+	0.443370i	$0.146217\pi$
$930$	−1.54913	−0.0507981
$931$	−4.09268	−0.134132
$932$	−13.3530	−0.437393
$933$	−23.2686	−0.761780
$934$	−23.5599	−0.770902
$935$	12.9883	0.424761
$936$	0.600186	0.0196177
$937$	57.9889	1.89441	0.947207	−	0.320622i	$-0.103892\pi$
$937$	57.9889	1.89441	0.947207	+	0.320622i	$0.103892\pi$
$938$	3.74784	0.122371
$939$	−34.7790	−1.13497
$940$	−10.0998	−0.329418
$941$	14.5839	0.475420	0.237710	−	0.971336i	$-0.423603\pi$
$941$	14.5839	0.475420	0.237710	+	0.971336i	$0.423603\pi$
$942$	−9.26620	−0.301909
$943$	−68.9001	−2.24369
$944$	3.28367	0.106874
$945$	13.6499	0.444030
$946$	−8.02021	−0.260760
$947$	37.8031	1.22843	0.614217	−	0.789137i	$-0.289472\pi$
$947$	37.8031	1.22843	0.614217	+	0.789137i	$0.289472\pi$
$948$	−20.0279	−0.650475
$949$	3.86412	0.125435
$950$	4.05227	0.131473
$951$	31.6750	1.02713
$952$	−5.73217	−0.185781
$953$	18.8531	0.610712	0.305356	−	0.952238i	$-0.401225\pi$
$953$	18.8531	0.610712	0.305356	+	0.952238i	$0.401225\pi$
$954$	2.89966	0.0938799
$955$	−11.3609	−0.367629
$956$	14.8652	0.480776
$957$	−53.6207	−1.73331
$958$	25.1565	0.812770
$959$	−38.5018	−1.24329
$960$	1.54913	0.0499981
$961$	1.00000	0.0322581
$962$	5.94196	0.191577
$963$	−11.2785	−0.363443
$964$	−10.7130	−0.345043
$965$	21.2055	0.682628
$966$	−34.5888	−1.11288
$967$	53.9544	1.73506	0.867528	−	0.497388i	$-0.165707\pi$
$967$	53.9544	1.73506	0.867528	+	0.497388i	$0.165707\pi$
$968$	19.7533	0.634894
$969$	−14.7025	−0.472313
$970$	15.2244	0.488825
$971$	−0.904696	−0.0290331	−0.0145165	−	0.999895i	$-0.504621\pi$
$971$	−0.904696	−0.0290331	−0.0145165	+	0.999895i	$0.504621\pi$
$972$	−6.13664	−0.196833
$973$	−25.4940	−0.817299
$974$	0.268264	0.00859572
$975$	1.54913	0.0496120
$976$	−0.864407	−0.0276690
$977$	−32.9236	−1.05332	−0.526659	−	0.850076i	$-0.676556\pi$
$977$	−32.9236	−1.05332	−0.526659	+	0.850076i	$0.676556\pi$
$978$	14.4068	0.460679
$979$	98.5460	3.14954
$980$	1.00997	0.0322624
$981$	1.23452	0.0394152
$982$	−26.8444	−0.856640
$983$	−30.7336	−0.980250	−0.490125	−	0.871652i	$-0.663049\pi$
$983$	−30.7336	−0.980250	−0.490125	+	0.871652i	$0.663049\pi$
$984$	−11.6997	−0.372974
$985$	−17.0707	−0.543919
$986$	−14.6185	−0.465548
$987$	38.2925	1.21886
$988$	−4.05227	−0.128920
$989$	−13.1939	−0.419541
$990$	−3.32837	−0.105783
$991$	−7.36808	−0.234055	−0.117027	−	0.993129i	$-0.537337\pi$
$991$	−7.36808	−0.234055	−0.117027	+	0.993129i	$0.537337\pi$
$992$	−1.00000	−0.0317500
$993$	−24.8796	−0.789529
$994$	−31.3610	−0.994712
$995$	−2.56114	−0.0811937
$996$	−23.2431	−0.736484
$997$	−16.2999	−0.516223	−0.258111	−	0.966115i	$-0.583100\pi$
$997$	−16.2999	−0.516223	−0.258111	+	0.966115i	$0.583100\pi$
$998$	11.7989	0.373487
$999$	−33.1393	−1.04848

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4030.2.a.n.1.3	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4030.2.a.n.1.3	✓	8	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.54913 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.54913 q^{6} -2.44745 q^{7} +1.00000 q^{8} -0.600186 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.54913 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.54913 q^{6} -2.44745 q^{7} +1.00000 q^{8} -0.600186 q^{9} -1.00000 q^{10} -5.54556 q^{11} -1.54913 q^{12} -1.00000 q^{13} -2.44745 q^{14} +1.54913 q^{15} +1.00000 q^{16} +2.34210 q^{17} -0.600186 q^{18} +4.05227 q^{19} -1.00000 q^{20} +3.79143 q^{21} -5.54556 q^{22} -9.12289 q^{23} -1.54913 q^{24} +1.00000 q^{25} -1.00000 q^{26} +5.57717 q^{27} -2.44745 q^{28} -6.24163 q^{29} +1.54913 q^{30} -1.00000 q^{31} +1.00000 q^{32} +8.59082 q^{33} +2.34210 q^{34} +2.44745 q^{35} -0.600186 q^{36} -5.94196 q^{37} +4.05227 q^{38} +1.54913 q^{39} -1.00000 q^{40} +7.55244 q^{41} +3.79143 q^{42} +1.44624 q^{43} -5.54556 q^{44} +0.600186 q^{45} -9.12289 q^{46} +10.0998 q^{47} -1.54913 q^{48} -1.00997 q^{49} +1.00000 q^{50} -3.62822 q^{51} -1.00000 q^{52} -4.83126 q^{53} +5.57717 q^{54} +5.54556 q^{55} -2.44745 q^{56} -6.27750 q^{57} -6.24163 q^{58} +3.28367 q^{59} +1.54913 q^{60} -0.864407 q^{61} -1.00000 q^{62} +1.46893 q^{63} +1.00000 q^{64} +1.00000 q^{65} +8.59082 q^{66} -1.53132 q^{67} +2.34210 q^{68} +14.1326 q^{69} +2.44745 q^{70} +12.8137 q^{71} -0.600186 q^{72} -3.86412 q^{73} -5.94196 q^{74} -1.54913 q^{75} +4.05227 q^{76} +13.5725 q^{77} +1.54913 q^{78} +12.9284 q^{79} -1.00000 q^{80} -6.83922 q^{81} +7.55244 q^{82} +15.0039 q^{83} +3.79143 q^{84} -2.34210 q^{85} +1.44624 q^{86} +9.66912 q^{87} -5.54556 q^{88} -17.7702 q^{89} +0.600186 q^{90} +2.44745 q^{91} -9.12289 q^{92} +1.54913 q^{93} +10.0998 q^{94} -4.05227 q^{95} -1.54913 q^{96} -15.2244 q^{97} -1.00997 q^{98} +3.32837 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} - q^{3} + 8 q^{4} - 8 q^{5} - q^{6} + q^{7} + 8 q^{8} + 9 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 - q^3 + 8 * q^4 - 8 * q^5 - q^6 + q^7 + 8 * q^8 + 9 * q^9	\( 8 q + 8 q^{2} - q^{3} + 8 q^{4} - 8 q^{5} - q^{6} + q^{7} + 8 q^{8} + 9 q^{9} - 8 q^{10} + 4 q^{11} - q^{12} - 8 q^{13} + q^{14} + q^{15} + 8 q^{16} - 5 q^{17} + 9 q^{18} + 2 q^{19} - 8 q^{20} + 17 q^{21} + 4 q^{22} + 4 q^{23} - q^{24} + 8 q^{25} - 8 q^{26} + 11 q^{27} + q^{28} + 11 q^{29} + q^{30} - 8 q^{31} + 8 q^{32} + 10 q^{33} - 5 q^{34} - q^{35} + 9 q^{36} + 19 q^{37} + 2 q^{38} + q^{39} - 8 q^{40} + 10 q^{41} + 17 q^{42} + 19 q^{43} + 4 q^{44} - 9 q^{45} + 4 q^{46} + 11 q^{47} - q^{48} + 11 q^{49} + 8 q^{50} + 7 q^{51} - 8 q^{52} + 8 q^{53} + 11 q^{54} - 4 q^{55} + q^{56} - 11 q^{57} + 11 q^{58} + 28 q^{59} + q^{60} - 12 q^{61} - 8 q^{62} + 20 q^{63} + 8 q^{64} + 8 q^{65} + 10 q^{66} + 24 q^{67} - 5 q^{68} + 30 q^{69} - q^{70} + 18 q^{71} + 9 q^{72} - 3 q^{73} + 19 q^{74} - q^{75} + 2 q^{76} - 7 q^{77} + q^{78} + 22 q^{79} - 8 q^{80} + 24 q^{81} + 10 q^{82} + 17 q^{83} + 17 q^{84} + 5 q^{85} + 19 q^{86} + 11 q^{87} + 4 q^{88} + 17 q^{89} - 9 q^{90} - q^{91} + 4 q^{92} + q^{93} + 11 q^{94} - 2 q^{95} - q^{96} - 24 q^{97} + 11 q^{98} + 23 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 - q^3 + 8 * q^4 - 8 * q^5 - q^6 + q^7 + 8 * q^8 + 9 * q^9 - 8 * q^10 + 4 * q^11 - q^12 - 8 * q^13 + q^14 + q^15 + 8 * q^16 - 5 * q^17 + 9 * q^18 + 2 * q^19 - 8 * q^20 + 17 * q^21 + 4 * q^22 + 4 * q^23 - q^24 + 8 * q^25 - 8 * q^26 + 11 * q^27 + q^28 + 11 * q^29 + q^30 - 8 * q^31 + 8 * q^32 + 10 * q^33 - 5 * q^34 - q^35 + 9 * q^36 + 19 * q^37 + 2 * q^38 + q^39 - 8 * q^40 + 10 * q^41 + 17 * q^42 + 19 * q^43 + 4 * q^44 - 9 * q^45 + 4 * q^46 + 11 * q^47 - q^48 + 11 * q^49 + 8 * q^50 + 7 * q^51 - 8 * q^52 + 8 * q^53 + 11 * q^54 - 4 * q^55 + q^56 - 11 * q^57 + 11 * q^58 + 28 * q^59 + q^60 - 12 * q^61 - 8 * q^62 + 20 * q^63 + 8 * q^64 + 8 * q^65 + 10 * q^66 + 24 * q^67 - 5 * q^68 + 30 * q^69 - q^70 + 18 * q^71 + 9 * q^72 - 3 * q^73 + 19 * q^74 - q^75 + 2 * q^76 - 7 * q^77 + q^78 + 22 * q^79 - 8 * q^80 + 24 * q^81 + 10 * q^82 + 17 * q^83 + 17 * q^84 + 5 * q^85 + 19 * q^86 + 11 * q^87 + 4 * q^88 + 17 * q^89 - 9 * q^90 - q^91 + 4 * q^92 + q^93 + 11 * q^94 - 2 * q^95 - q^96 - 24 * q^97 + 11 * q^98 + 23 * q^99

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