LMFDB - Embedded newform 430.2.a.h.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(1,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("430.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.316.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 2 $ x^3 - x^2 - 4*x + 2
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			1.2
Root			$2.34292$ of defining polynomial
Character	$\chi$	$=$	430.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.14637 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.14637 q^{6} -4.48929 q^{7} -1.00000 q^{8} -1.68585 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.14637 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.14637 q^{6} -4.48929 q^{7} -1.00000 q^{8} -1.68585 q^{9} +1.00000 q^{10} +5.53948 q^{11} -1.14637 q^{12} +5.17513 q^{13} +4.48929 q^{14} +1.14637 q^{15} +1.00000 q^{16} -1.83221 q^{17} +1.68585 q^{18} +2.19656 q^{19} -1.00000 q^{20} +5.14637 q^{21} -5.53948 q^{22} +0.167788 q^{23} +1.14637 q^{24} +1.00000 q^{25} -5.17513 q^{26} +5.37169 q^{27} -4.48929 q^{28} +5.92839 q^{29} -1.14637 q^{30} -6.02877 q^{31} -1.00000 q^{32} -6.35027 q^{33} +1.83221 q^{34} +4.48929 q^{35} -1.68585 q^{36} +6.81079 q^{37} -2.19656 q^{38} -5.93260 q^{39} +1.00000 q^{40} +10.8824 q^{41} -5.14637 q^{42} +1.00000 q^{43} +5.53948 q^{44} +1.68585 q^{45} -0.167788 q^{46} -1.14637 q^{47} -1.14637 q^{48} +13.1537 q^{49} -1.00000 q^{50} +2.10038 q^{51} +5.17513 q^{52} +13.2713 q^{53} -5.37169 q^{54} -5.53948 q^{55} +4.48929 q^{56} -2.51806 q^{57} -5.92839 q^{58} -3.66442 q^{59} +1.14637 q^{60} -8.61423 q^{61} +6.02877 q^{62} +7.56825 q^{63} +1.00000 q^{64} -5.17513 q^{65} +6.35027 q^{66} -9.05019 q^{67} -1.83221 q^{68} -0.192347 q^{69} -4.48929 q^{70} +1.53948 q^{71} +1.68585 q^{72} -12.4219 q^{73} -6.81079 q^{74} -1.14637 q^{75} +2.19656 q^{76} -24.8683 q^{77} +5.93260 q^{78} -8.32150 q^{79} -1.00000 q^{80} -1.10038 q^{81} -10.8824 q^{82} +7.27131 q^{83} +5.14637 q^{84} +1.83221 q^{85} -1.00000 q^{86} -6.79610 q^{87} -5.53948 q^{88} +12.1825 q^{89} -1.68585 q^{90} -23.2327 q^{91} +0.167788 q^{92} +6.91117 q^{93} +1.14637 q^{94} -2.19656 q^{95} +1.14637 q^{96} +6.81079 q^{97} -13.1537 q^{98} -9.33871 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - 2 q^{3} + 3 q^{4} - 3 q^{5} + 2 q^{6} - 6 q^{7} - 3 q^{8} + 7 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 - 2 * q^3 + 3 * q^4 - 3 * q^5 + 2 * q^6 - 6 * q^7 - 3 * q^8 + 7 * q^9	\( 3 q - 3 q^{2} - 2 q^{3} + 3 q^{4} - 3 q^{5} + 2 q^{6} - 6 q^{7} - 3 q^{8} + 7 q^{9} + 3 q^{10} + 6 q^{11} - 2 q^{12} - 4 q^{13} + 6 q^{14} + 2 q^{15} + 3 q^{16} + 8 q^{17} - 7 q^{18} + 2 q^{19} - 3 q^{20} + 14 q^{21} - 6 q^{22} + 14 q^{23} + 2 q^{24} + 3 q^{25} + 4 q^{26} - 8 q^{27} - 6 q^{28} + 6 q^{29} - 2 q^{30} - 3 q^{32} + 20 q^{33} - 8 q^{34} + 6 q^{35} + 7 q^{36} - 8 q^{37} - 2 q^{38} + 2 q^{39} + 3 q^{40} + 16 q^{41} - 14 q^{42} + 3 q^{43} + 6 q^{44} - 7 q^{45} - 14 q^{46} - 2 q^{47} - 2 q^{48} + 5 q^{49} - 3 q^{50} - 4 q^{52} + 22 q^{53} + 8 q^{54} - 6 q^{55} + 6 q^{56} + 18 q^{57} - 6 q^{58} + 16 q^{59} + 2 q^{60} - 2 q^{61} - 6 q^{63} + 3 q^{64} + 4 q^{65} - 20 q^{66} - 24 q^{67} + 8 q^{68} - 4 q^{69} - 6 q^{70} - 6 q^{71} - 7 q^{72} - 10 q^{73} + 8 q^{74} - 2 q^{75} + 2 q^{76} - 10 q^{77} - 2 q^{78} - 4 q^{79} - 3 q^{80} + 3 q^{81} - 16 q^{82} + 4 q^{83} + 14 q^{84} - 8 q^{85} - 3 q^{86} - 58 q^{87} - 6 q^{88} - 16 q^{89} + 7 q^{90} - 14 q^{91} + 14 q^{92} - 14 q^{93} + 2 q^{94} - 2 q^{95} + 2 q^{96} - 8 q^{97} - 5 q^{98} - 30 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 2 * q^3 + 3 * q^4 - 3 * q^5 + 2 * q^6 - 6 * q^7 - 3 * q^8 + 7 * q^9 + 3 * q^10 + 6 * q^11 - 2 * q^12 - 4 * q^13 + 6 * q^14 + 2 * q^15 + 3 * q^16 + 8 * q^17 - 7 * q^18 + 2 * q^19 - 3 * q^20 + 14 * q^21 - 6 * q^22 + 14 * q^23 + 2 * q^24 + 3 * q^25 + 4 * q^26 - 8 * q^27 - 6 * q^28 + 6 * q^29 - 2 * q^30 - 3 * q^32 + 20 * q^33 - 8 * q^34 + 6 * q^35 + 7 * q^36 - 8 * q^37 - 2 * q^38 + 2 * q^39 + 3 * q^40 + 16 * q^41 - 14 * q^42 + 3 * q^43 + 6 * q^44 - 7 * q^45 - 14 * q^46 - 2 * q^47 - 2 * q^48 + 5 * q^49 - 3 * q^50 - 4 * q^52 + 22 * q^53 + 8 * q^54 - 6 * q^55 + 6 * q^56 + 18 * q^57 - 6 * q^58 + 16 * q^59 + 2 * q^60 - 2 * q^61 - 6 * q^63 + 3 * q^64 + 4 * q^65 - 20 * q^66 - 24 * q^67 + 8 * q^68 - 4 * q^69 - 6 * q^70 - 6 * q^71 - 7 * q^72 - 10 * q^73 + 8 * q^74 - 2 * q^75 + 2 * q^76 - 10 * q^77 - 2 * q^78 - 4 * q^79 - 3 * q^80 + 3 * q^81 - 16 * q^82 + 4 * q^83 + 14 * q^84 - 8 * q^85 - 3 * q^86 - 58 * q^87 - 6 * q^88 - 16 * q^89 + 7 * q^90 - 14 * q^91 + 14 * q^92 - 14 * q^93 + 2 * q^94 - 2 * q^95 + 2 * q^96 - 8 * q^97 - 5 * q^98 - 30 * 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
$3$	−1.14637	−0.661854	−0.330927	−	0.943656i	$-0.607361\pi$
$3$	−1.14637	−0.661854	−0.330927	+	0.943656i	$0.607361\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.14637	0.468002
$7$	−4.48929	−1.69679	−0.848396	−	0.529362i	$-0.822431\pi$
$7$	−4.48929	−1.69679	−0.848396	+	0.529362i	$0.822431\pi$
$8$	−1.00000	−0.353553
$9$	−1.68585	−0.561949
$10$	1.00000	0.316228
$11$	5.53948	1.67022	0.835108	−	0.550086i	$-0.185405\pi$
$11$	5.53948	1.67022	0.835108	+	0.550086i	$0.185405\pi$
$12$	−1.14637	−0.330927
$13$	5.17513	1.43532	0.717662	−	0.696392i	$-0.245212\pi$
$13$	5.17513	1.43532	0.717662	+	0.696392i	$0.245212\pi$
$14$	4.48929	1.19981
$15$	1.14637	0.295990
$16$	1.00000	0.250000
$17$	−1.83221	−0.444377	−0.222188	−	0.975004i	$-0.571320\pi$
$17$	−1.83221	−0.444377	−0.222188	+	0.975004i	$0.571320\pi$
$18$	1.68585	0.397358
$19$	2.19656	0.503925	0.251962	−	0.967737i	$-0.418924\pi$
$19$	2.19656	0.503925	0.251962	+	0.967737i	$0.418924\pi$
$20$	−1.00000	−0.223607
$21$	5.14637	1.12303
$22$	−5.53948	−1.18102
$23$	0.167788	0.0349863	0.0174931	−	0.999847i	$-0.494431\pi$
$23$	0.167788	0.0349863	0.0174931	+	0.999847i	$0.494431\pi$
$24$	1.14637	0.234001
$25$	1.00000	0.200000
$26$	−5.17513	−1.01493
$27$	5.37169	1.03378
$28$	−4.48929	−0.848396
$29$	5.92839	1.10087	0.550437	−	0.834877i	$-0.314461\pi$
$29$	5.92839	1.10087	0.550437	+	0.834877i	$0.314461\pi$
$30$	−1.14637	−0.209297
$31$	−6.02877	−1.08280	−0.541399	−	0.840765i	$-0.682105\pi$
$31$	−6.02877	−1.08280	−0.541399	+	0.840765i	$0.682105\pi$
$32$	−1.00000	−0.176777
$33$	−6.35027	−1.10544
$34$	1.83221	0.314222
$35$	4.48929	0.758828
$36$	−1.68585	−0.280974
$37$	6.81079	1.11969	0.559843	−	0.828598i	$-0.310861\pi$
$37$	6.81079	1.11969	0.559843	+	0.828598i	$0.310861\pi$
$38$	−2.19656	−0.356329
$39$	−5.93260	−0.949976
$40$	1.00000	0.158114
$41$	10.8824	1.69955	0.849773	−	0.527149i	$-0.176739\pi$
$41$	10.8824	1.69955	0.849773	+	0.527149i	$0.176739\pi$
$42$	−5.14637	−0.794101
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	5.53948	0.835108
$45$	1.68585	0.251311
$46$	−0.167788	−0.0247390
$47$	−1.14637	−0.167215	−0.0836073	−	0.996499i	$-0.526644\pi$
$47$	−1.14637	−0.167215	−0.0836073	+	0.996499i	$0.526644\pi$
$48$	−1.14637	−0.165464
$49$	13.1537	1.87910
$50$	−1.00000	−0.141421
$51$	2.10038	0.294113
$52$	5.17513	0.717662
$53$	13.2713	1.82295	0.911477	−	0.411351i	$-0.134943\pi$
$53$	13.2713	1.82295	0.911477	+	0.411351i	$0.134943\pi$
$54$	−5.37169	−0.730995
$55$	−5.53948	−0.746943
$56$	4.48929	0.599906
$57$	−2.51806	−0.333525
$58$	−5.92839	−0.778435
$59$	−3.66442	−0.477067	−0.238534	−	0.971134i	$-0.576667\pi$
$59$	−3.66442	−0.477067	−0.238534	+	0.971134i	$0.576667\pi$
$60$	1.14637	0.147995
$61$	−8.61423	−1.10294	−0.551470	−	0.834195i	$-0.685933\pi$
$61$	−8.61423	−1.10294	−0.551470	+	0.834195i	$0.685933\pi$
$62$	6.02877	0.765654
$63$	7.56825	0.953510
$64$	1.00000	0.125000
$65$	−5.17513	−0.641896
$66$	6.35027	0.781664
$67$	−9.05019	−1.10566	−0.552828	−	0.833295i	$-0.686452\pi$
$67$	−9.05019	−1.10566	−0.552828	+	0.833295i	$0.686452\pi$
$68$	−1.83221	−0.222188
$69$	−0.192347	−0.0231558
$70$	−4.48929	−0.536573
$71$	1.53948	0.182703	0.0913514	−	0.995819i	$-0.470881\pi$
$71$	1.53948	0.182703	0.0913514	+	0.995819i	$0.470881\pi$
$72$	1.68585	0.198679
$73$	−12.4219	−1.45387	−0.726936	−	0.686705i	$-0.759056\pi$
$73$	−12.4219	−1.45387	−0.726936	+	0.686705i	$0.759056\pi$
$74$	−6.81079	−0.791738
$75$	−1.14637	−0.132371
$76$	2.19656	0.251962
$77$	−24.8683	−2.83401
$78$	5.93260	0.671734
$79$	−8.32150	−0.936242	−0.468121	−	0.883664i	$-0.655069\pi$
$79$	−8.32150	−0.936242	−0.468121	+	0.883664i	$0.655069\pi$
$80$	−1.00000	−0.111803
$81$	−1.10038	−0.122265
$82$	−10.8824	−1.20176
$83$	7.27131	0.798130	0.399065	−	0.916923i	$-0.369335\pi$
$83$	7.27131	0.798130	0.399065	+	0.916923i	$0.369335\pi$
$84$	5.14637	0.561515
$85$	1.83221	0.198731
$86$	−1.00000	−0.107833
$87$	−6.79610	−0.728618
$88$	−5.53948	−0.590511
$89$	12.1825	1.29134	0.645670	−	0.763616i	$-0.276578\pi$
$89$	12.1825	1.29134	0.645670	+	0.763616i	$0.276578\pi$
$90$	−1.68585	−0.177704
$91$	−23.2327	−2.43545
$92$	0.167788	0.0174931
$93$	6.91117	0.716655
$94$	1.14637	0.118239
$95$	−2.19656	−0.225362
$96$	1.14637	0.117000
$97$	6.81079	0.691531	0.345765	−	0.938321i	$-0.387619\pi$
$97$	6.81079	0.691531	0.345765	+	0.938321i	$0.387619\pi$
$98$	−13.1537	−1.32873
$99$	−9.33871	−0.938576
$100$	1.00000	0.100000
$101$	−0.460519	−0.0458234	−0.0229117	−	0.999737i	$-0.507294\pi$
$101$	−0.460519	−0.0458234	−0.0229117	+	0.999737i	$0.507294\pi$
$102$	−2.10038	−0.207969
$103$	2.68585	0.264644	0.132322	−	0.991207i	$-0.457757\pi$
$103$	2.68585	0.264644	0.132322	+	0.991207i	$0.457757\pi$
$104$	−5.17513	−0.507464
$105$	−5.14637	−0.502234
$106$	−13.2713	−1.28902
$107$	13.3001	1.28577	0.642884	−	0.765964i	$-0.277738\pi$
$107$	13.3001	1.28577	0.642884	+	0.765964i	$0.277738\pi$
$108$	5.37169	0.516891
$109$	−0.685846	−0.0656921	−0.0328461	−	0.999460i	$-0.510457\pi$
$109$	−0.685846	−0.0656921	−0.0328461	+	0.999460i	$0.510457\pi$
$110$	5.53948	0.528169
$111$	−7.80765	−0.741070
$112$	−4.48929	−0.424198
$113$	14.3215	1.34725	0.673627	−	0.739072i	$-0.264736\pi$
$113$	14.3215	1.34725	0.673627	+	0.739072i	$0.264736\pi$
$114$	2.51806	0.235838
$115$	−0.167788	−0.0156463
$116$	5.92839	0.550437
$117$	−8.72448	−0.806579
$118$	3.66442	0.337338
$119$	8.22533	0.754014
$120$	−1.14637	−0.104648
$121$	19.6858	1.78962
$122$	8.61423	0.779896
$123$	−12.4752	−1.12485
$124$	−6.02877	−0.541399
$125$	−1.00000	−0.0894427
$126$	−7.56825	−0.674233
$127$	−11.6644	−1.03505	−0.517525	−	0.855668i	$-0.673147\pi$
$127$	−11.6644	−1.03505	−0.517525	+	0.855668i	$0.673147\pi$
$128$	−1.00000	−0.0883883
$129$	−1.14637	−0.100932
$130$	5.17513	0.453889
$131$	5.89962	0.515452	0.257726	−	0.966218i	$-0.417027\pi$
$131$	5.89962	0.515452	0.257726	+	0.966218i	$0.417027\pi$
$132$	−6.35027	−0.552720
$133$	−9.86098	−0.855055
$134$	9.05019	0.781818
$135$	−5.37169	−0.462322
$136$	1.83221	0.157111
$137$	−17.0073	−1.45304	−0.726518	−	0.687148i	$-0.758863\pi$
$137$	−17.0073	−1.45304	−0.726518	+	0.687148i	$0.758863\pi$
$138$	0.192347	0.0163736
$139$	2.46052	0.208699	0.104349	−	0.994541i	$-0.466724\pi$
$139$	2.46052	0.208699	0.104349	+	0.994541i	$0.466724\pi$
$140$	4.48929	0.379414
$141$	1.31415	0.110672
$142$	−1.53948	−0.129190
$143$	28.6676	2.39730
$144$	−1.68585	−0.140487
$145$	−5.92839	−0.492326
$146$	12.4219	1.02804
$147$	−15.0790	−1.24369
$148$	6.81079	0.559843
$149$	−12.8150	−1.04985	−0.524923	−	0.851150i	$-0.675906\pi$
$149$	−12.8150	−1.04985	−0.524923	+	0.851150i	$0.675906\pi$
$150$	1.14637	0.0936004
$151$	−1.31415	−0.106944	−0.0534722	−	0.998569i	$-0.517029\pi$
$151$	−1.31415	−0.106944	−0.0534722	+	0.998569i	$0.517029\pi$
$152$	−2.19656	−0.178164
$153$	3.08883	0.249717
$154$	24.8683	2.00395
$155$	6.02877	0.484242
$156$	−5.93260	−0.474988
$157$	−5.10352	−0.407305	−0.203653	−	0.979043i	$-0.565281\pi$
$157$	−5.10352	−0.407305	−0.203653	+	0.979043i	$0.565281\pi$
$158$	8.32150	0.662023
$159$	−15.2138	−1.20653
$160$	1.00000	0.0790569
$161$	−0.753250	−0.0593644
$162$	1.10038	0.0864543
$163$	11.3288	0.887344	0.443672	−	0.896189i	$-0.353676\pi$
$163$	11.3288	0.887344	0.443672	+	0.896189i	$0.353676\pi$
$164$	10.8824	0.849773
$165$	6.35027	0.494368
$166$	−7.27131	−0.564363
$167$	2.12494	0.164433	0.0822165	−	0.996614i	$-0.473800\pi$
$167$	2.12494	0.164433	0.0822165	+	0.996614i	$0.473800\pi$
$168$	−5.14637	−0.397051
$169$	13.7820	1.06016
$170$	−1.83221	−0.140524
$171$	−3.70306	−0.283180
$172$	1.00000	0.0762493
$173$	−18.1537	−1.38020	−0.690101	−	0.723713i	$-0.742434\pi$
$173$	−18.1537	−1.38020	−0.690101	+	0.723713i	$0.742434\pi$
$174$	6.79610	0.515211
$175$	−4.48929	−0.339358
$176$	5.53948	0.417554
$177$	4.20077	0.315749
$178$	−12.1825	−0.913116
$179$	−1.07475	−0.0803306	−0.0401653	−	0.999193i	$-0.512788\pi$
$179$	−1.07475	−0.0803306	−0.0401653	+	0.999193i	$0.512788\pi$
$180$	1.68585	0.125656
$181$	17.1611	1.27557	0.637786	−	0.770214i	$-0.279851\pi$
$181$	17.1611	1.27557	0.637786	+	0.770214i	$0.279851\pi$
$182$	23.2327	1.72212
$183$	9.87506	0.729985
$184$	−0.167788	−0.0123695
$185$	−6.81079	−0.500739
$186$	−6.91117	−0.506752
$187$	−10.1495	−0.742205
$188$	−1.14637	−0.0836073
$189$	−24.1151	−1.75411
$190$	2.19656	0.159355
$191$	−13.7894	−0.997764	−0.498882	−	0.866670i	$-0.666256\pi$
$191$	−13.7894	−0.997764	−0.498882	+	0.866670i	$0.666256\pi$
$192$	−1.14637	−0.0827318
$193$	24.6858	1.77693	0.888463	−	0.458948i	$-0.151774\pi$
$193$	24.6858	1.77693	0.888463	+	0.458948i	$0.151774\pi$
$194$	−6.81079	−0.488986
$195$	5.93260	0.424842
$196$	13.1537	0.939551
$197$	14.4893	1.03232	0.516160	−	0.856492i	$-0.327361\pi$
$197$	14.4893	1.03232	0.516160	+	0.856492i	$0.327361\pi$
$198$	9.33871	0.663673
$199$	−7.24675	−0.513708	−0.256854	−	0.966450i	$-0.582686\pi$
$199$	−7.24675	−0.513708	−0.256854	+	0.966450i	$0.582686\pi$
$200$	−1.00000	−0.0707107
$201$	10.3748	0.731784
$202$	0.460519	0.0324020
$203$	−26.6142	−1.86795
$204$	2.10038	0.147056
$205$	−10.8824	−0.760060
$206$	−2.68585	−0.187132
$207$	−0.282865	−0.0196605
$208$	5.17513	0.358831
$209$	12.1678	0.841664
$210$	5.14637	0.355133
$211$	25.9572	1.78696	0.893482	−	0.449099i	$-0.148255\pi$
$211$	25.9572	1.78696	0.893482	+	0.449099i	$0.148255\pi$
$212$	13.2713	0.911477
$213$	−1.76481	−0.120923
$214$	−13.3001	−0.909175
$215$	−1.00000	−0.0681994
$216$	−5.37169	−0.365497
$217$	27.0649	1.83728
$218$	0.685846	0.0464514
$219$	14.2400	0.962251
$220$	−5.53948	−0.373472
$221$	−9.48194	−0.637824
$222$	7.80765	0.524015
$223$	−7.02142	−0.470189	−0.235095	−	0.971972i	$-0.575540\pi$
$223$	−7.02142	−0.470189	−0.235095	+	0.971972i	$0.575540\pi$
$224$	4.48929	0.299953
$225$	−1.68585	−0.112390
$226$	−14.3215	−0.952652
$227$	24.2499	1.60952	0.804761	−	0.593599i	$-0.202294\pi$
$227$	24.2499	1.60952	0.804761	+	0.593599i	$0.202294\pi$
$228$	−2.51806	−0.166762
$229$	27.0361	1.78660	0.893298	−	0.449464i	$-0.148385\pi$
$229$	27.0361	1.78660	0.893298	+	0.449464i	$0.148385\pi$
$230$	0.167788	0.0110636
$231$	28.5082	1.87570
$232$	−5.92839	−0.389218
$233$	−4.93573	−0.323351	−0.161675	−	0.986844i	$-0.551690\pi$
$233$	−4.93573	−0.323351	−0.161675	+	0.986844i	$0.551690\pi$
$234$	8.72448	0.570337
$235$	1.14637	0.0747806
$236$	−3.66442	−0.238534
$237$	9.53948	0.619656
$238$	−8.22533	−0.533169
$239$	−13.6932	−0.885739	−0.442869	−	0.896586i	$-0.646040\pi$
$239$	−13.6932	−0.885739	−0.442869	+	0.896586i	$0.646040\pi$
$240$	1.14637	0.0739976
$241$	−9.49663	−0.611732	−0.305866	−	0.952075i	$-0.598946\pi$
$241$	−9.49663	−0.611732	−0.305866	+	0.952075i	$0.598946\pi$
$242$	−19.6858	−1.26545
$243$	−14.8536	−0.952861
$244$	−8.61423	−0.551470
$245$	−13.1537	−0.840360
$246$	12.4752	0.795390
$247$	11.3675	0.723296
$248$	6.02877	0.382827
$249$	−8.33558	−0.528246
$250$	1.00000	0.0632456
$251$	−19.1365	−1.20789	−0.603943	−	0.797028i	$-0.706404\pi$
$251$	−19.1365	−1.20789	−0.603943	+	0.797028i	$0.706404\pi$
$252$	7.56825	0.476755
$253$	0.929460	0.0584347
$254$	11.6644	0.731891
$255$	−2.10038	−0.131531
$256$	1.00000	0.0625000
$257$	11.6932	0.729401	0.364701	−	0.931125i	$-0.381171\pi$
$257$	11.6932	0.729401	0.364701	+	0.931125i	$0.381171\pi$
$258$	1.14637	0.0713696
$259$	−30.5756	−1.89988
$260$	−5.17513	−0.320948
$261$	−9.99435	−0.618634
$262$	−5.89962	−0.364479
$263$	32.2113	1.98623	0.993115	−	0.117140i	$-0.0373727\pi$
$263$	32.2113	1.98623	0.993115	+	0.117140i	$0.0373727\pi$
$264$	6.35027	0.390832
$265$	−13.2713	−0.815250
$266$	9.86098	0.604616
$267$	−13.9656	−0.854679
$268$	−9.05019	−0.552828
$269$	−9.85677	−0.600978	−0.300489	−	0.953785i	$-0.597150\pi$
$269$	−9.85677	−0.600978	−0.300489	+	0.953785i	$0.597150\pi$
$270$	5.37169	0.326911
$271$	7.15058	0.434367	0.217183	−	0.976131i	$-0.430313\pi$
$271$	7.15058	0.434367	0.217183	+	0.976131i	$0.430313\pi$
$272$	−1.83221	−0.111094
$273$	26.6331	1.61191
$274$	17.0073	1.02745
$275$	5.53948	0.334043
$276$	−0.192347	−0.0115779
$277$	24.6858	1.48323	0.741614	−	0.670826i	$-0.234060\pi$
$277$	24.6858	1.48323	0.741614	+	0.670826i	$0.234060\pi$
$278$	−2.46052	−0.147572
$279$	10.1636	0.608477
$280$	−4.48929	−0.268286
$281$	−19.3246	−1.15281	−0.576406	−	0.817164i	$-0.695545\pi$
$281$	−19.3246	−1.15281	−0.576406	+	0.817164i	$0.695545\pi$
$282$	−1.31415	−0.0782567
$283$	−13.3001	−0.790608	−0.395304	−	0.918550i	$-0.629361\pi$
$283$	−13.3001	−0.790608	−0.395304	+	0.918550i	$0.629361\pi$
$284$	1.53948	0.0913514
$285$	2.51806	0.149157
$286$	−28.6676	−1.69515
$287$	−48.8543	−2.88378
$288$	1.68585	0.0993394
$289$	−13.6430	−0.802529
$290$	5.92839	0.348127
$291$	−7.80765	−0.457693
$292$	−12.4219	−0.726936
$293$	6.58546	0.384727	0.192363	−	0.981324i	$-0.438385\pi$
$293$	6.58546	0.384727	0.192363	+	0.981324i	$0.438385\pi$
$294$	15.0790	0.879423
$295$	3.66442	0.213351
$296$	−6.81079	−0.395869
$297$	29.7564	1.72664
$298$	12.8150	0.742353
$299$	0.868327	0.0502167
$300$	−1.14637	−0.0661854
$301$	−4.48929	−0.258758
$302$	1.31415	0.0756211
$303$	0.527923	0.0303284
$304$	2.19656	0.125981
$305$	8.61423	0.493249
$306$	−3.08883	−0.176576
$307$	−2.17200	−0.123963	−0.0619813	−	0.998077i	$-0.519742\pi$
$307$	−2.17200	−0.123963	−0.0619813	+	0.998077i	$0.519742\pi$
$308$	−24.8683	−1.41700
$309$	−3.07896	−0.175156
$310$	−6.02877	−0.342411
$311$	19.4005	1.10010	0.550050	−	0.835132i	$-0.314609\pi$
$311$	19.4005	1.10010	0.550050	+	0.835132i	$0.314609\pi$
$312$	5.93260	0.335867
$313$	2.58546	0.146139	0.0730695	−	0.997327i	$-0.476721\pi$
$313$	2.58546	0.146139	0.0730695	+	0.997327i	$0.476721\pi$
$314$	5.10352	0.288008
$315$	−7.56825	−0.426423
$316$	−8.32150	−0.468121
$317$	7.27552	0.408634	0.204317	−	0.978905i	$-0.434503\pi$
$317$	7.27552	0.408634	0.204317	+	0.978905i	$0.434503\pi$
$318$	15.2138	0.853146
$319$	32.8402	1.83870
$320$	−1.00000	−0.0559017
$321$	−15.2467	−0.850991
$322$	0.753250	0.0419770
$323$	−4.02456	−0.223932
$324$	−1.10038	−0.0611325
$325$	5.17513	0.287065
$326$	−11.3288	−0.627447
$327$	0.786230	0.0434786
$328$	−10.8824	−0.600880
$329$	5.14637	0.283728
$330$	−6.35027	−0.349571
$331$	30.0147	1.64976	0.824878	−	0.565310i	$-0.191244\pi$
$331$	30.0147	1.64976	0.824878	+	0.565310i	$0.191244\pi$
$332$	7.27131	0.399065
$333$	−11.4819	−0.629207
$334$	−2.12494	−0.116272
$335$	9.05019	0.494465
$336$	5.14637	0.280757
$337$	23.3717	1.27314	0.636569	−	0.771220i	$-0.280353\pi$
$337$	23.3717	1.27314	0.636569	+	0.771220i	$0.280353\pi$
$338$	−13.7820	−0.749643
$339$	−16.4177	−0.891686
$340$	1.83221	0.0993656
$341$	−33.3963	−1.80851
$342$	3.70306	0.200238
$343$	−27.6258	−1.49165
$344$	−1.00000	−0.0539164
$345$	0.192347	0.0103556
$346$	18.1537	0.975950
$347$	23.8322	1.27938	0.639690	−	0.768633i	$-0.279063\pi$
$347$	23.8322	1.27938	0.639690	+	0.768633i	$0.279063\pi$
$348$	−6.79610	−0.364309
$349$	−17.8652	−0.956302	−0.478151	−	0.878278i	$-0.658693\pi$
$349$	−17.8652	−0.956302	−0.478151	+	0.878278i	$0.658693\pi$
$350$	4.48929	0.239963
$351$	27.7992	1.48381
$352$	−5.53948	−0.295255
$353$	−13.7747	−0.733152	−0.366576	−	0.930388i	$-0.619470\pi$
$353$	−13.7747	−0.733152	−0.366576	+	0.930388i	$0.619470\pi$
$354$	−4.20077	−0.223268
$355$	−1.53948	−0.0817072
$356$	12.1825	0.645670
$357$	−9.42923	−0.499048
$358$	1.07475	0.0568023
$359$	13.2425	0.698914	0.349457	−	0.936952i	$-0.386366\pi$
$359$	13.2425	0.698914	0.349457	+	0.936952i	$0.386366\pi$
$360$	−1.68585	−0.0888519
$361$	−14.1751	−0.746060
$362$	−17.1611	−0.901965
$363$	−22.5672	−1.18447
$364$	−23.2327	−1.21772
$365$	12.4219	0.650191
$366$	−9.87506	−0.516178
$367$	−14.7434	−0.769598	−0.384799	−	0.923000i	$-0.625729\pi$
$367$	−14.7434	−0.769598	−0.384799	+	0.923000i	$0.625729\pi$
$368$	0.167788	0.00874657
$369$	−18.3461	−0.955058
$370$	6.81079	0.354076
$371$	−59.5787	−3.09317
$372$	6.91117	0.358328
$373$	−5.43910	−0.281626	−0.140813	−	0.990036i	$-0.544972\pi$
$373$	−5.43910	−0.281626	−0.140813	+	0.990036i	$0.544972\pi$
$374$	10.1495	0.524818
$375$	1.14637	0.0591981
$376$	1.14637	0.0591193
$377$	30.6802	1.58011
$378$	24.1151	1.24035
$379$	−18.0147	−0.925353	−0.462676	−	0.886527i	$-0.653111\pi$
$379$	−18.0147	−0.925353	−0.462676	+	0.886527i	$0.653111\pi$
$380$	−2.19656	−0.112681
$381$	13.3717	0.685053
$382$	13.7894	0.705525
$383$	2.19656	0.112239	0.0561194	−	0.998424i	$-0.482127\pi$
$383$	2.19656	0.112239	0.0561194	+	0.998424i	$0.482127\pi$
$384$	1.14637	0.0585002
$385$	24.8683	1.26741
$386$	−24.6858	−1.25648
$387$	−1.68585	−0.0856964
$388$	6.81079	0.345765
$389$	18.8353	0.954990	0.477495	−	0.878634i	$-0.341545\pi$
$389$	18.8353	0.954990	0.477495	+	0.878634i	$0.341545\pi$
$390$	−5.93260	−0.300409
$391$	−0.307424	−0.0155471
$392$	−13.1537	−0.664363
$393$	−6.76312	−0.341154
$394$	−14.4893	−0.729960
$395$	8.32150	0.418700
$396$	−9.33871	−0.469288
$397$	−33.7220	−1.69246	−0.846228	−	0.532820i	$-0.821132\pi$
$397$	−33.7220	−1.69246	−0.846228	+	0.532820i	$0.821132\pi$
$398$	7.24675	0.363247
$399$	11.3043	0.565922
$400$	1.00000	0.0500000
$401$	−19.0832	−0.952968	−0.476484	−	0.879183i	$-0.658089\pi$
$401$	−19.0832	−0.952968	−0.476484	+	0.879183i	$0.658089\pi$
$402$	−10.3748	−0.517449
$403$	−31.1997	−1.55417
$404$	−0.460519	−0.0229117
$405$	1.10038	0.0546785
$406$	26.6142	1.32084
$407$	37.7282	1.87012
$408$	−2.10038	−0.103985
$409$	31.9326	1.57897	0.789483	−	0.613773i	$-0.210349\pi$
$409$	31.9326	1.57897	0.789483	+	0.613773i	$0.210349\pi$
$410$	10.8824	0.537444
$411$	19.4966	0.961698
$412$	2.68585	0.132322
$413$	16.4507	0.809484
$414$	0.282865	0.0139021
$415$	−7.27131	−0.356934
$416$	−5.17513	−0.253732
$417$	−2.82065	−0.138128
$418$	−12.1678	−0.595146
$419$	−30.7539	−1.50242	−0.751212	−	0.660061i	$-0.770531\pi$
$419$	−30.7539	−1.50242	−0.751212	+	0.660061i	$0.770531\pi$
$420$	−5.14637	−0.251117
$421$	−15.8280	−0.771410	−0.385705	−	0.922622i	$-0.626042\pi$
$421$	−15.8280	−0.771410	−0.385705	+	0.922622i	$0.626042\pi$
$422$	−25.9572	−1.26357
$423$	1.93260	0.0939660
$424$	−13.2713	−0.644512
$425$	−1.83221	−0.0888753
$426$	1.76481	0.0855052
$427$	38.6718	1.87146
$428$	13.3001	0.642884
$429$	−32.8635	−1.58666
$430$	1.00000	0.0482243
$431$	−2.88661	−0.139043	−0.0695217	−	0.997580i	$-0.522147\pi$
$431$	−2.88661	−0.139043	−0.0695217	+	0.997580i	$0.522147\pi$
$432$	5.37169	0.258446
$433$	−33.4580	−1.60789	−0.803944	−	0.594704i	$-0.797269\pi$
$433$	−33.4580	−1.60789	−0.803944	+	0.594704i	$0.797269\pi$
$434$	−27.0649	−1.29916
$435$	6.79610	0.325848
$436$	−0.685846	−0.0328461
$437$	0.368557	0.0176305
$438$	−14.2400	−0.680414
$439$	−29.3717	−1.40183	−0.700917	−	0.713243i	$-0.747226\pi$
$439$	−29.3717	−1.40183	−0.700917	+	0.713243i	$0.747226\pi$
$440$	5.53948	0.264084
$441$	−22.1751	−1.05596
$442$	9.48194	0.451010
$443$	−1.88554	−0.0895847	−0.0447923	−	0.998996i	$-0.514263\pi$
$443$	−1.88554	−0.0895847	−0.0447923	+	0.998996i	$0.514263\pi$
$444$	−7.80765	−0.370535
$445$	−12.1825	−0.577505
$446$	7.02142	0.332474
$447$	14.6907	0.694845
$448$	−4.48929	−0.212099
$449$	2.61002	0.123174	0.0615872	−	0.998102i	$-0.480384\pi$
$449$	2.61002	0.123174	0.0615872	+	0.998102i	$0.480384\pi$
$450$	1.68585	0.0794716
$451$	60.2829	2.83861
$452$	14.3215	0.673627
$453$	1.50650	0.0707816
$454$	−24.2499	−1.13810
$455$	23.2327	1.08916
$456$	2.51806	0.117919
$457$	−5.46365	−0.255579	−0.127789	−	0.991801i	$-0.540788\pi$
$457$	−5.46365	−0.255579	−0.127789	+	0.991801i	$0.540788\pi$
$458$	−27.0361	−1.26331
$459$	−9.84208	−0.459389
$460$	−0.167788	−0.00782317
$461$	−26.7533	−1.24602	−0.623012	−	0.782213i	$-0.714091\pi$
$461$	−26.7533	−1.24602	−0.623012	+	0.782213i	$0.714091\pi$
$462$	−28.5082	−1.32632
$463$	−4.79671	−0.222922	−0.111461	−	0.993769i	$-0.535553\pi$
$463$	−4.79671	−0.222922	−0.111461	+	0.993769i	$0.535553\pi$
$464$	5.92839	0.275218
$465$	−6.91117	−0.320498
$466$	4.93573	0.228643
$467$	−24.4752	−1.13258	−0.566289	−	0.824207i	$-0.691621\pi$
$467$	−24.4752	−1.13258	−0.566289	+	0.824207i	$0.691621\pi$
$468$	−8.72448	−0.403289
$469$	40.6289	1.87607
$470$	−1.14637	−0.0528779
$471$	5.85050	0.269577
$472$	3.66442	0.168669
$473$	5.53948	0.254706
$474$	−9.53948	−0.438163
$475$	2.19656	0.100785
$476$	8.22533	0.377007
$477$	−22.3734	−1.02441
$478$	13.6932	0.626312
$479$	−21.8223	−0.997088	−0.498544	−	0.866864i	$-0.666132\pi$
$479$	−21.8223	−0.997088	−0.498544	+	0.866864i	$0.666132\pi$
$480$	−1.14637	−0.0523242
$481$	35.2467	1.60711
$482$	9.49663	0.432560
$483$	0.863500	0.0392906
$484$	19.6858	0.894811
$485$	−6.81079	−0.309262
$486$	14.8536	0.673775
$487$	−12.2744	−0.556208	−0.278104	−	0.960551i	$-0.589706\pi$
$487$	−12.2744	−0.556208	−0.278104	+	0.960551i	$0.589706\pi$
$488$	8.61423	0.389948
$489$	−12.9870	−0.587292
$490$	13.1537	0.594224
$491$	17.4292	0.786570	0.393285	−	0.919417i	$-0.371339\pi$
$491$	17.4292	0.786570	0.393285	+	0.919417i	$0.371339\pi$
$492$	−12.4752	−0.562426
$493$	−10.8621	−0.489202
$494$	−11.3675	−0.511447
$495$	9.33871	0.419744
$496$	−6.02877	−0.270700
$497$	−6.91117	−0.310008
$498$	8.33558	0.373526
$499$	−6.92525	−0.310017	−0.155008	−	0.987913i	$-0.549540\pi$
$499$	−6.92525	−0.310017	−0.155008	+	0.987913i	$0.549540\pi$
$500$	−1.00000	−0.0447214
$501$	−2.43596	−0.108831
$502$	19.1365	0.854104
$503$	−7.85677	−0.350316	−0.175158	−	0.984540i	$-0.556044\pi$
$503$	−7.85677	−0.350316	−0.175158	+	0.984540i	$0.556044\pi$
$504$	−7.56825	−0.337117
$505$	0.460519	0.0204928
$506$	−0.929460	−0.0413196
$507$	−15.7992	−0.701669
$508$	−11.6644	−0.517525
$509$	−23.2285	−1.02958	−0.514792	−	0.857315i	$-0.672131\pi$
$509$	−23.2285	−1.02958	−0.514792	+	0.857315i	$0.672131\pi$
$510$	2.10038	0.0930066
$511$	55.7654	2.46692
$512$	−1.00000	−0.0441942
$513$	11.7992	0.520949
$514$	−11.6932	−0.515765
$515$	−2.68585	−0.118353
$516$	−1.14637	−0.0504659
$517$	−6.35027	−0.279285
$518$	30.5756	1.34341
$519$	20.8108	0.913492
$520$	5.17513	0.226945
$521$	41.0754	1.79954	0.899772	−	0.436360i	$-0.143733\pi$
$521$	41.0754	1.79954	0.899772	+	0.436360i	$0.143733\pi$
$522$	9.99435	0.437441
$523$	−14.7104	−0.643241	−0.321621	−	0.946869i	$-0.604228\pi$
$523$	−14.7104	−0.643241	−0.321621	+	0.946869i	$0.604228\pi$
$524$	5.89962	0.257726
$525$	5.14637	0.224606
$526$	−32.2113	−1.40448
$527$	11.0460	0.481171
$528$	−6.35027	−0.276360
$529$	−22.9718	−0.998776
$530$	13.2713	0.576469
$531$	6.17765	0.268087
$532$	−9.86098	−0.427528
$533$	56.3179	2.43940
$534$	13.9656	0.604350
$535$	−13.3001	−0.575012
$536$	9.05019	0.390909
$537$	1.23206	0.0531672
$538$	9.85677	0.424956
$539$	72.8647	3.13851
$540$	−5.37169	−0.231161
$541$	11.0361	0.474480	0.237240	−	0.971451i	$-0.423757\pi$
$541$	11.0361	0.474480	0.237240	+	0.971451i	$0.423757\pi$
$542$	−7.15058	−0.307144
$543$	−19.6728	−0.844243
$544$	1.83221	0.0785554
$545$	0.685846	0.0293784
$546$	−26.6331	−1.13979
$547$	22.7434	0.972437	0.486218	−	0.873837i	$-0.338376\pi$
$547$	22.7434	0.972437	0.486218	+	0.873837i	$0.338376\pi$
$548$	−17.0073	−0.726518
$549$	14.5223	0.619795
$550$	−5.53948	−0.236204
$551$	13.0220	0.554758
$552$	0.192347	0.00818682
$553$	37.3576	1.58861
$554$	−24.6858	−1.04880
$555$	7.80765	0.331416
$556$	2.46052	0.104349
$557$	−21.3759	−0.905726	−0.452863	−	0.891580i	$-0.649597\pi$
$557$	−21.3759	−0.905726	−0.452863	+	0.891580i	$0.649597\pi$
$558$	−10.1636	−0.430259
$559$	5.17513	0.218885
$560$	4.48929	0.189707
$561$	11.6350	0.491232
$562$	19.3246	0.815161
$563$	35.6503	1.50248	0.751241	−	0.660027i	$-0.229455\pi$
$563$	35.6503	1.50248	0.751241	+	0.660027i	$0.229455\pi$
$564$	1.31415	0.0553359
$565$	−14.3215	−0.602510
$566$	13.3001	0.559044
$567$	4.93994	0.207458
$568$	−1.53948	−0.0645952
$569$	6.03863	0.253153	0.126576	−	0.991957i	$-0.459601\pi$
$569$	6.03863	0.253153	0.126576	+	0.991957i	$0.459601\pi$
$570$	−2.51806	−0.105470
$571$	27.2243	1.13930	0.569650	−	0.821888i	$-0.307079\pi$
$571$	27.2243	1.13930	0.569650	+	0.821888i	$0.307079\pi$
$572$	28.6676	1.19865
$573$	15.8077	0.660374
$574$	48.8543	2.03914
$575$	0.167788	0.00699726
$576$	−1.68585	−0.0702436
$577$	−25.6012	−1.06579	−0.532897	−	0.846180i	$-0.678897\pi$
$577$	−25.6012	−1.06579	−0.532897	+	0.846180i	$0.678897\pi$
$578$	13.6430	0.567474
$579$	−28.2990	−1.17607
$580$	−5.92839	−0.246163
$581$	−32.6430	−1.35426
$582$	7.80765	0.323638
$583$	73.5162	3.04473
$584$	12.4219	0.514021
$585$	8.72448	0.360713
$586$	−6.58546	−0.272043
$587$	10.7679	0.444441	0.222220	−	0.974996i	$-0.428670\pi$
$587$	10.7679	0.444441	0.222220	+	0.974996i	$0.428670\pi$
$588$	−15.0790	−0.621846
$589$	−13.2425	−0.545649
$590$	−3.66442	−0.150862
$591$	−16.6100	−0.683245
$592$	6.81079	0.279922
$593$	−32.1438	−1.31999	−0.659995	−	0.751270i	$-0.729442\pi$
$593$	−32.1438	−1.31999	−0.659995	+	0.751270i	$0.729442\pi$
$594$	−29.7564	−1.22092
$595$	−8.22533	−0.337206
$596$	−12.8150	−0.524923
$597$	8.30742	0.340000
$598$	−0.868327	−0.0355085
$599$	−20.3650	−0.832090	−0.416045	−	0.909344i	$-0.636584\pi$
$599$	−20.3650	−0.832090	−0.416045	+	0.909344i	$0.636584\pi$
$600$	1.14637	0.0468002
$601$	−39.8799	−1.62673	−0.813367	−	0.581751i	$-0.802368\pi$
$601$	−39.8799	−1.62673	−0.813367	+	0.581751i	$0.802368\pi$
$602$	4.48929	0.182970
$603$	15.2572	0.621323
$604$	−1.31415	−0.0534722
$605$	−19.6858	−0.800343
$606$	−0.527923	−0.0214454
$607$	−15.8568	−0.643606	−0.321803	−	0.946807i	$-0.604289\pi$
$607$	−15.8568	−0.643606	−0.321803	+	0.946807i	$0.604289\pi$
$608$	−2.19656	−0.0890822
$609$	30.5096	1.23631
$610$	−8.61423	−0.348780
$611$	−5.93260	−0.240007
$612$	3.08883	0.124858
$613$	20.5040	0.828148	0.414074	−	0.910243i	$-0.364105\pi$
$613$	20.5040	0.828148	0.414074	+	0.910243i	$0.364105\pi$
$614$	2.17200	0.0876548
$615$	12.4752	0.503049
$616$	24.8683	1.00197
$617$	−10.1067	−0.406879	−0.203439	−	0.979088i	$-0.565212\pi$
$617$	−10.1067	−0.406879	−0.203439	+	0.979088i	$0.565212\pi$
$618$	3.07896	0.123854
$619$	−29.2039	−1.17380	−0.586902	−	0.809658i	$-0.699653\pi$
$619$	−29.2039	−1.17380	−0.586902	+	0.809658i	$0.699653\pi$
$620$	6.02877	0.242121
$621$	0.901307	0.0361682
$622$	−19.4005	−0.777888
$623$	−54.6907	−2.19114
$624$	−5.93260	−0.237494
$625$	1.00000	0.0400000
$626$	−2.58546	−0.103336
$627$	−13.9487	−0.557059
$628$	−5.10352	−0.203653
$629$	−12.4788	−0.497563
$630$	7.56825	0.301526
$631$	−23.5542	−0.937677	−0.468838	−	0.883284i	$-0.655327\pi$
$631$	−23.5542	−0.937677	−0.468838	+	0.883284i	$0.655327\pi$
$632$	8.32150	0.331012
$633$	−29.7564	−1.18271
$634$	−7.27552	−0.288948
$635$	11.6644	0.462889
$636$	−15.2138	−0.603265
$637$	68.0722	2.69712
$638$	−32.8402	−1.30015
$639$	−2.59533	−0.102670
$640$	1.00000	0.0395285
$641$	−21.6644	−0.855693	−0.427847	−	0.903851i	$-0.640728\pi$
$641$	−21.6644	−0.855693	−0.427847	+	0.903851i	$0.640728\pi$
$642$	15.2467	0.601741
$643$	−3.34292	−0.131832	−0.0659160	−	0.997825i	$-0.520997\pi$
$643$	−3.34292	−0.131832	−0.0659160	+	0.997825i	$0.520997\pi$
$644$	−0.753250	−0.0296822
$645$	1.14637	0.0451381
$646$	4.02456	0.158344
$647$	−5.77529	−0.227050	−0.113525	−	0.993535i	$-0.536214\pi$
$647$	−5.77529	−0.227050	−0.113525	+	0.993535i	$0.536214\pi$
$648$	1.10038	0.0432272
$649$	−20.2990	−0.796806
$650$	−5.17513	−0.202985
$651$	−31.0263	−1.21601
$652$	11.3288	0.443672
$653$	−27.0031	−1.05671	−0.528357	−	0.849022i	$-0.677192\pi$
$653$	−27.0031	−1.05671	−0.528357	+	0.849022i	$0.677192\pi$
$654$	−0.786230	−0.0307440
$655$	−5.89962	−0.230517
$656$	10.8824	0.424886
$657$	20.9414	0.817001
$658$	−5.14637	−0.200626
$659$	35.3618	1.37750	0.688751	−	0.724998i	$-0.258160\pi$
$659$	35.3618	1.37750	0.688751	+	0.724998i	$0.258160\pi$
$660$	6.35027	0.247184
$661$	−24.4324	−0.950309	−0.475154	−	0.879902i	$-0.657608\pi$
$661$	−24.4324	−0.950309	−0.475154	+	0.879902i	$0.657608\pi$
$662$	−30.0147	−1.16655
$663$	10.8698	0.422147
$664$	−7.27131	−0.282181
$665$	9.86098	0.382392
$666$	11.4819	0.444916
$667$	0.994714	0.0385155
$668$	2.12494	0.0822165
$669$	8.04912	0.311197
$670$	−9.05019	−0.349639
$671$	−47.7184	−1.84215
$672$	−5.14637	−0.198525
$673$	18.9070	0.728810	0.364405	−	0.931241i	$-0.381272\pi$
$673$	18.9070	0.728810	0.364405	+	0.931241i	$0.381272\pi$
$674$	−23.3717	−0.900244
$675$	5.37169	0.206757
$676$	13.7820	0.530078
$677$	1.66442	0.0639690	0.0319845	−	0.999488i	$-0.489817\pi$
$677$	1.66442	0.0639690	0.0319845	+	0.999488i	$0.489817\pi$
$678$	16.4177	0.630517
$679$	−30.5756	−1.17338
$680$	−1.83221	−0.0702621
$681$	−27.7992	−1.06527
$682$	33.3963	1.27881
$683$	−35.7795	−1.36906	−0.684532	−	0.728983i	$-0.739994\pi$
$683$	−35.7795	−1.36906	−0.684532	+	0.728983i	$0.739994\pi$
$684$	−3.70306	−0.141590
$685$	17.0073	0.649817
$686$	27.6258	1.05476
$687$	−30.9933	−1.18247
$688$	1.00000	0.0381246
$689$	68.6808	2.61653
$690$	−0.192347	−0.00732252
$691$	40.3074	1.53337	0.766683	−	0.642025i	$-0.221906\pi$
$691$	40.3074	1.53337	0.766683	+	0.642025i	$0.221906\pi$
$692$	−18.1537	−0.690101
$693$	41.9242	1.59257
$694$	−23.8322	−0.904658
$695$	−2.46052	−0.0933328
$696$	6.79610	0.257605
$697$	−19.9389	−0.755238
$698$	17.8652	0.676207
$699$	5.65815	0.214011
$700$	−4.48929	−0.169679
$701$	40.7764	1.54010	0.770051	−	0.637982i	$-0.220231\pi$
$701$	40.7764	1.54010	0.770051	+	0.637982i	$0.220231\pi$
$702$	−27.7992	−1.04921
$703$	14.9603	0.564238
$704$	5.53948	0.208777
$705$	−1.31415	−0.0494939
$706$	13.7747	0.518417
$707$	2.06740	0.0777527
$708$	4.20077	0.157875
$709$	1.18921	0.0446618	0.0223309	−	0.999751i	$-0.492891\pi$
$709$	1.18921	0.0446618	0.0223309	+	0.999751i	$0.492891\pi$
$710$	1.53948	0.0577757
$711$	14.0288	0.526120
$712$	−12.1825	−0.456558
$713$	−1.01156	−0.0378831
$714$	9.42923	0.352880
$715$	−28.6676	−1.07211
$716$	−1.07475	−0.0401653
$717$	15.6974	0.586230
$718$	−13.2425	−0.494207
$719$	2.60015	0.0969694	0.0484847	−	0.998824i	$-0.484561\pi$
$719$	2.60015	0.0969694	0.0484847	+	0.998824i	$0.484561\pi$
$720$	1.68585	0.0628278
$721$	−12.0575	−0.449046
$722$	14.1751	0.527544
$723$	10.8866	0.404878
$724$	17.1611	0.637786
$725$	5.92839	0.220175
$726$	22.5672	0.837546
$727$	26.1004	0.968010	0.484005	−	0.875065i	$-0.339182\pi$
$727$	26.1004	0.968010	0.484005	+	0.875065i	$0.339182\pi$
$728$	23.2327	0.861060
$729$	20.3288	0.752920
$730$	−12.4219	−0.459755
$731$	−1.83221	−0.0677668
$732$	9.87506	0.364993
$733$	−17.8322	−0.658648	−0.329324	−	0.944217i	$-0.606821\pi$
$733$	−17.8322	−0.658648	−0.329324	+	0.944217i	$0.606821\pi$
$734$	14.7434	0.544188
$735$	15.0790	0.556196
$736$	−0.167788	−0.00618476
$737$	−50.1334	−1.84669
$738$	18.3461	0.675328
$739$	−5.27552	−0.194063	−0.0970316	−	0.995281i	$-0.530935\pi$
$739$	−5.27552	−0.194063	−0.0970316	+	0.995281i	$0.530935\pi$
$740$	−6.81079	−0.250370
$741$	−13.0313	−0.478716
$742$	59.5787	2.18720
$743$	−19.5107	−0.715779	−0.357889	−	0.933764i	$-0.616503\pi$
$743$	−19.5107	−0.715779	−0.357889	+	0.933764i	$0.616503\pi$
$744$	−6.91117	−0.253376
$745$	12.8150	0.469505
$746$	5.43910	0.199139
$747$	−12.2583	−0.448508
$748$	−10.1495	−0.371103
$749$	−59.7079	−2.18168
$750$	−1.14637	−0.0418593
$751$	45.2614	1.65161	0.825807	−	0.563953i	$-0.190720\pi$
$751$	45.2614	1.65161	0.825807	+	0.563953i	$0.190720\pi$
$752$	−1.14637	−0.0418036
$753$	21.9374	0.799444
$754$	−30.6802	−1.11731
$755$	1.31415	0.0478270
$756$	−24.1151	−0.877057
$757$	33.3780	1.21314	0.606571	−	0.795029i	$-0.292544\pi$
$757$	33.3780	1.21314	0.606571	+	0.795029i	$0.292544\pi$
$758$	18.0147	0.654323
$759$	−1.06550	−0.0386752
$760$	2.19656	0.0796775
$761$	41.3780	1.49995	0.749975	−	0.661466i	$-0.230065\pi$
$761$	41.3780	1.49995	0.749975	+	0.661466i	$0.230065\pi$
$762$	−13.3717	−0.484405
$763$	3.07896	0.111466
$764$	−13.7894	−0.498882
$765$	−3.08883	−0.111677
$766$	−2.19656	−0.0793649
$767$	−18.9639	−0.684746
$768$	−1.14637	−0.0413659
$769$	−11.7753	−0.424628	−0.212314	−	0.977202i	$-0.568100\pi$
$769$	−11.7753	−0.424628	−0.212314	+	0.977202i	$0.568100\pi$
$770$	−24.8683	−0.896192
$771$	−13.4047	−0.482757
$772$	24.6858	0.888463
$773$	9.43910	0.339501	0.169750	−	0.985487i	$-0.445704\pi$
$773$	9.43910	0.339501	0.169750	+	0.985487i	$0.445704\pi$
$774$	1.68585	0.0605965
$775$	−6.02877	−0.216560
$776$	−6.81079	−0.244493
$777$	35.0508	1.25744
$778$	−18.8353	−0.675280
$779$	23.9038	0.856443
$780$	5.93260	0.212421
$781$	8.52792	0.305153
$782$	0.307424	0.0109935
$783$	31.8455	1.13806
$784$	13.1537	0.469775
$785$	5.10352	0.182152
$786$	6.76312	0.241232
$787$	44.4857	1.58574	0.792872	−	0.609388i	$-0.208585\pi$
$787$	44.4857	1.58574	0.792872	+	0.609388i	$0.208585\pi$
$788$	14.4893	0.516160
$789$	−36.9259	−1.31460
$790$	−8.32150	−0.296066
$791$	−64.2933	−2.28601
$792$	9.33871	0.331837
$793$	−44.5798	−1.58308
$794$	33.7220	1.19675
$795$	15.2138	0.539577
$796$	−7.24675	−0.256854
$797$	12.3116	0.436100	0.218050	−	0.975938i	$-0.430030\pi$
$797$	12.3116	0.436100	0.218050	+	0.975938i	$0.430030\pi$
$798$	−11.3043	−0.400167
$799$	2.10038	0.0743063
$800$	−1.00000	−0.0353553
$801$	−20.5378	−0.725667
$802$	19.0832	0.673850
$803$	−68.8108	−2.42828
$804$	10.3748	0.365892
$805$	0.753250	0.0265486
$806$	31.1997	1.09896
$807$	11.2995	0.397760
$808$	0.460519	0.0162010
$809$	43.1407	1.51675	0.758373	−	0.651820i	$-0.225994\pi$
$809$	43.1407	1.51675	0.758373	+	0.651820i	$0.225994\pi$
$810$	−1.10038	−0.0386636
$811$	18.9828	0.666576	0.333288	−	0.942825i	$-0.391842\pi$
$811$	18.9828	0.666576	0.333288	+	0.942825i	$0.391842\pi$
$812$	−26.6142	−0.933976
$813$	−8.19717	−0.287487
$814$	−37.7282	−1.32237
$815$	−11.3288	−0.396832
$816$	2.10038	0.0735282
$817$	2.19656	0.0768478
$818$	−31.9326	−1.11650
$819$	39.1667	1.36860
$820$	−10.8824	−0.380030
$821$	−9.16465	−0.319849	−0.159924	−	0.987129i	$-0.551125\pi$
$821$	−9.16465	−0.319849	−0.159924	+	0.987129i	$0.551125\pi$
$822$	−19.4966	−0.680023
$823$	−5.71569	−0.199236	−0.0996182	−	0.995026i	$-0.531762\pi$
$823$	−5.71569	−0.199236	−0.0996182	+	0.995026i	$0.531762\pi$
$824$	−2.68585	−0.0935659
$825$	−6.35027	−0.221088
$826$	−16.4507	−0.572391
$827$	36.9154	1.28367	0.641837	−	0.766841i	$-0.278173\pi$
$827$	36.9154	1.28367	0.641837	+	0.766841i	$0.278173\pi$
$828$	−0.282865	−0.00983025
$829$	13.8511	0.481069	0.240535	−	0.970641i	$-0.422677\pi$
$829$	13.8511	0.481069	0.240535	+	0.970641i	$0.422677\pi$
$830$	7.27131	0.252391
$831$	−28.2990	−0.981682
$832$	5.17513	0.179416
$833$	−24.1004	−0.835029
$834$	2.82065	0.0976713
$835$	−2.12494	−0.0735367
$836$	12.1678	0.420832
$837$	−32.3847	−1.11938
$838$	30.7539	1.06237
$839$	−19.1611	−0.661513	−0.330757	−	0.943716i	$-0.607304\pi$
$839$	−19.1611	−0.661513	−0.330757	+	0.943716i	$0.607304\pi$
$840$	5.14637	0.177566
$841$	6.14575	0.211922
$842$	15.8280	0.545469
$843$	22.1531	0.762993
$844$	25.9572	0.893482
$845$	−13.7820	−0.474116
$846$	−1.93260	−0.0664440
$847$	−88.3754	−3.03662
$848$	13.2713	0.455739
$849$	15.2467	0.523267
$850$	1.83221	0.0628443
$851$	1.14277	0.0391737
$852$	−1.76481	−0.0604613
$853$	−55.9572	−1.91594	−0.957968	−	0.286874i	$-0.907384\pi$
$853$	−55.9572	−1.91594	−0.957968	+	0.286874i	$0.907384\pi$
$854$	−38.6718	−1.32332
$855$	3.70306	0.126642
$856$	−13.3001	−0.454587
$857$	4.32571	0.147763	0.0738817	−	0.997267i	$-0.476461\pi$
$857$	4.32571	0.147763	0.0738817	+	0.997267i	$0.476461\pi$
$858$	32.8635	1.12194
$859$	−18.0042	−0.614296	−0.307148	−	0.951662i	$-0.599375\pi$
$859$	−18.0042	−0.614296	−0.307148	+	0.951662i	$0.599375\pi$
$860$	−1.00000	−0.0340997
$861$	56.0048	1.90864
$862$	2.88661	0.0983185
$863$	−29.1793	−0.993276	−0.496638	−	0.867958i	$-0.665432\pi$
$863$	−29.1793	−0.993276	−0.496638	+	0.867958i	$0.665432\pi$
$864$	−5.37169	−0.182749
$865$	18.1537	0.617245
$866$	33.4580	1.13695
$867$	15.6399	0.531158
$868$	27.0649	0.918642
$869$	−46.0968	−1.56373
$870$	−6.79610	−0.230409
$871$	−46.8360	−1.58698
$872$	0.685846	0.0232257
$873$	−11.4819	−0.388605
$874$	−0.368557	−0.0124666
$875$	4.48929	0.151766
$876$	14.2400	0.481126
$877$	−39.9290	−1.34831	−0.674153	−	0.738591i	$-0.735491\pi$
$877$	−39.9290	−1.34831	−0.674153	+	0.738591i	$0.735491\pi$
$878$	29.3717	0.991247
$879$	−7.54935	−0.254633
$880$	−5.53948	−0.186736
$881$	6.60437	0.222507	0.111253	−	0.993792i	$-0.464513\pi$
$881$	6.60437	0.222507	0.111253	+	0.993792i	$0.464513\pi$
$882$	22.1751	0.746676
$883$	24.8297	0.835586	0.417793	−	0.908542i	$-0.362804\pi$
$883$	24.8297	0.835586	0.417793	+	0.908542i	$0.362804\pi$
$884$	−9.48194	−0.318912
$885$	−4.20077	−0.141207
$886$	1.88554	0.0633459
$887$	−31.8097	−1.06807	−0.534033	−	0.845464i	$-0.679324\pi$
$887$	−31.8097	−1.06807	−0.534033	+	0.845464i	$0.679324\pi$
$888$	7.80765	0.262008
$889$	52.3650	1.75626
$890$	12.1825	0.408358
$891$	−6.09556	−0.204209
$892$	−7.02142	−0.235095
$893$	−2.51806	−0.0842636
$894$	−14.6907	−0.491330
$895$	1.07475	0.0359249
$896$	4.48929	0.149977
$897$	−0.995420	−0.0332361
$898$	−2.61002	−0.0870975
$899$	−35.7409	−1.19202
$900$	−1.68585	−0.0561949
$901$	−24.3158	−0.810078
$902$	−60.2829	−2.00720
$903$	5.14637	0.171260
$904$	−14.3215	−0.476326
$905$	−17.1611	−0.570453
$906$	−1.50650	−0.0500501
$907$	37.4643	1.24398	0.621990	−	0.783025i	$-0.286324\pi$
$907$	37.4643	1.24398	0.621990	+	0.783025i	$0.286324\pi$
$908$	24.2499	0.804761
$909$	0.776365	0.0257504
$910$	−23.2327	−0.770156
$911$	32.1972	1.06674	0.533370	−	0.845882i	$-0.320925\pi$
$911$	32.1972	1.06674	0.533370	+	0.845882i	$0.320925\pi$
$912$	−2.51806	−0.0833812
$913$	40.2793	1.33305
$914$	5.46365	0.180722
$915$	−9.87506	−0.326459
$916$	27.0361	0.893298
$917$	−26.4851	−0.874614
$918$	9.84208	0.324837
$919$	28.1867	0.929793	0.464897	−	0.885365i	$-0.346092\pi$
$919$	28.1867	0.929793	0.464897	+	0.885365i	$0.346092\pi$
$920$	0.167788	0.00553182
$921$	2.48990	0.0820452
$922$	26.7533	0.881071
$923$	7.96702	0.262238
$924$	28.5082	0.937851
$925$	6.81079	0.223937
$926$	4.79671	0.157630
$927$	−4.52792	−0.148717
$928$	−5.92839	−0.194609
$929$	−7.12181	−0.233659	−0.116829	−	0.993152i	$-0.537273\pi$
$929$	−7.12181	−0.233659	−0.116829	+	0.993152i	$0.537273\pi$
$930$	6.91117	0.226626
$931$	28.8929	0.946926
$932$	−4.93573	−0.161675
$933$	−22.2400	−0.728106
$934$	24.4752	0.800853
$935$	10.1495	0.331924
$936$	8.72448	0.285169
$937$	−14.2780	−0.466443	−0.233222	−	0.972424i	$-0.574927\pi$
$937$	−14.2780	−0.466443	−0.233222	+	0.972424i	$0.574927\pi$
$938$	−40.6289	−1.32658
$939$	−2.96388	−0.0967227
$940$	1.14637	0.0373903
$941$	−50.3895	−1.64265	−0.821326	−	0.570460i	$-0.806765\pi$
$941$	−50.3895	−1.64265	−0.821326	+	0.570460i	$0.806765\pi$
$942$	−5.85050	−0.190620
$943$	1.82594	0.0594608
$944$	−3.66442	−0.119267
$945$	24.1151	0.784464
$946$	−5.53948	−0.180104
$947$	−47.4496	−1.54190	−0.770952	−	0.636893i	$-0.780219\pi$
$947$	−47.4496	−1.54190	−0.770952	+	0.636893i	$0.780219\pi$
$948$	9.53948	0.309828
$949$	−64.2849	−2.08678
$950$	−2.19656	−0.0712657
$951$	−8.34040	−0.270456
$952$	−8.22533	−0.266584
$953$	−27.1568	−0.879697	−0.439848	−	0.898072i	$-0.644968\pi$
$953$	−27.1568	−0.879697	−0.439848	+	0.898072i	$0.644968\pi$
$954$	22.3734	0.724365
$955$	13.7894	0.446213
$956$	−13.6932	−0.442869
$957$	−37.6468	−1.21695
$958$	21.8223	0.705048
$959$	76.3509	2.46550
$960$	1.14637	0.0369988
$961$	5.34606	0.172454
$962$	−35.2467	−1.13640
$963$	−22.4219	−0.722535
$964$	−9.49663	−0.305866
$965$	−24.6858	−0.794666
$966$	−0.863500	−0.0277827
$967$	−15.2383	−0.490032	−0.245016	−	0.969519i	$-0.578793\pi$
$967$	−15.2383	−0.490032	−0.245016	+	0.969519i	$0.578793\pi$
$968$	−19.6858	−0.632727
$969$	4.61361	0.148211
$970$	6.81079	0.218681
$971$	11.6314	0.373271	0.186635	−	0.982429i	$-0.440242\pi$
$971$	11.6314	0.373271	0.186635	+	0.982429i	$0.440242\pi$
$972$	−14.8536	−0.476431
$973$	−11.0460	−0.354118
$974$	12.2744	0.393299
$975$	−5.93260	−0.189995
$976$	−8.61423	−0.275735
$977$	−28.0477	−0.897325	−0.448662	−	0.893701i	$-0.648099\pi$
$977$	−28.0477	−0.897325	−0.448662	+	0.893701i	$0.648099\pi$
$978$	12.9870	0.415278
$979$	67.4846	2.15682
$980$	−13.1537	−0.420180
$981$	1.15623	0.0369156
$982$	−17.4292	−0.556189
$983$	−30.7539	−0.980896	−0.490448	−	0.871470i	$-0.663167\pi$
$983$	−30.7539	−0.980896	−0.490448	+	0.871470i	$0.663167\pi$
$984$	12.4752	0.397695
$985$	−14.4893	−0.461667
$986$	10.8621	0.345918
$987$	−5.89962	−0.187787
$988$	11.3675	0.361648
$989$	0.167788	0.00533536
$990$	−9.33871	−0.296804
$991$	41.4011	1.31515	0.657574	−	0.753390i	$-0.271583\pi$
$991$	41.4011	1.31515	0.657574	+	0.753390i	$0.271583\pi$
$992$	6.02877	0.191414
$993$	−34.4078	−1.09190
$994$	6.91117	0.219209
$995$	7.24675	0.229737
$996$	−8.33558	−0.264123
$997$	0.186076	0.00589307	0.00294654	−	0.999996i	$-0.499062\pi$
$997$	0.186076	0.00589307	0.00294654	+	0.999996i	$0.499062\pi$
$998$	6.92525	0.219215
$999$	36.5855	1.15751

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.a.h.1.2	✓	3
3.2	odd	2		3870.2.a.bn.1.1		3
4.3	odd	2		3440.2.a.n.1.2		3
5.2	odd	4		2150.2.b.t.1549.2		6
5.3	odd	4		2150.2.b.t.1549.5		6
5.4	even	2		2150.2.a.bf.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.a.h.1.2	✓	3	1.1	even	1	trivial
2150.2.a.bf.1.2		3	5.4	even	2
2150.2.b.t.1549.2		6	5.2	odd	4
2150.2.b.t.1549.5		6	5.3	odd	4
3440.2.a.n.1.2		3	4.3	odd	2
3870.2.a.bn.1.1		3	3.2	odd	2

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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.14637 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.14637 q^{6} -4.48929 q^{7} -1.00000 q^{8} -1.68585 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.14637 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.14637 q^{6} -4.48929 q^{7} -1.00000 q^{8} -1.68585 q^{9} +1.00000 q^{10} +5.53948 q^{11} -1.14637 q^{12} +5.17513 q^{13} +4.48929 q^{14} +1.14637 q^{15} +1.00000 q^{16} -1.83221 q^{17} +1.68585 q^{18} +2.19656 q^{19} -1.00000 q^{20} +5.14637 q^{21} -5.53948 q^{22} +0.167788 q^{23} +1.14637 q^{24} +1.00000 q^{25} -5.17513 q^{26} +5.37169 q^{27} -4.48929 q^{28} +5.92839 q^{29} -1.14637 q^{30} -6.02877 q^{31} -1.00000 q^{32} -6.35027 q^{33} +1.83221 q^{34} +4.48929 q^{35} -1.68585 q^{36} +6.81079 q^{37} -2.19656 q^{38} -5.93260 q^{39} +1.00000 q^{40} +10.8824 q^{41} -5.14637 q^{42} +1.00000 q^{43} +5.53948 q^{44} +1.68585 q^{45} -0.167788 q^{46} -1.14637 q^{47} -1.14637 q^{48} +13.1537 q^{49} -1.00000 q^{50} +2.10038 q^{51} +5.17513 q^{52} +13.2713 q^{53} -5.37169 q^{54} -5.53948 q^{55} +4.48929 q^{56} -2.51806 q^{57} -5.92839 q^{58} -3.66442 q^{59} +1.14637 q^{60} -8.61423 q^{61} +6.02877 q^{62} +7.56825 q^{63} +1.00000 q^{64} -5.17513 q^{65} +6.35027 q^{66} -9.05019 q^{67} -1.83221 q^{68} -0.192347 q^{69} -4.48929 q^{70} +1.53948 q^{71} +1.68585 q^{72} -12.4219 q^{73} -6.81079 q^{74} -1.14637 q^{75} +2.19656 q^{76} -24.8683 q^{77} +5.93260 q^{78} -8.32150 q^{79} -1.00000 q^{80} -1.10038 q^{81} -10.8824 q^{82} +7.27131 q^{83} +5.14637 q^{84} +1.83221 q^{85} -1.00000 q^{86} -6.79610 q^{87} -5.53948 q^{88} +12.1825 q^{89} -1.68585 q^{90} -23.2327 q^{91} +0.167788 q^{92} +6.91117 q^{93} +1.14637 q^{94} -2.19656 q^{95} +1.14637 q^{96} +6.81079 q^{97} -13.1537 q^{98} -9.33871 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - 2 q^{3} + 3 q^{4} - 3 q^{5} + 2 q^{6} - 6 q^{7} - 3 q^{8} + 7 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 - 2 * q^3 + 3 * q^4 - 3 * q^5 + 2 * q^6 - 6 * q^7 - 3 * q^8 + 7 * q^9	\( 3 q - 3 q^{2} - 2 q^{3} + 3 q^{4} - 3 q^{5} + 2 q^{6} - 6 q^{7} - 3 q^{8} + 7 q^{9} + 3 q^{10} + 6 q^{11} - 2 q^{12} - 4 q^{13} + 6 q^{14} + 2 q^{15} + 3 q^{16} + 8 q^{17} - 7 q^{18} + 2 q^{19} - 3 q^{20} + 14 q^{21} - 6 q^{22} + 14 q^{23} + 2 q^{24} + 3 q^{25} + 4 q^{26} - 8 q^{27} - 6 q^{28} + 6 q^{29} - 2 q^{30} - 3 q^{32} + 20 q^{33} - 8 q^{34} + 6 q^{35} + 7 q^{36} - 8 q^{37} - 2 q^{38} + 2 q^{39} + 3 q^{40} + 16 q^{41} - 14 q^{42} + 3 q^{43} + 6 q^{44} - 7 q^{45} - 14 q^{46} - 2 q^{47} - 2 q^{48} + 5 q^{49} - 3 q^{50} - 4 q^{52} + 22 q^{53} + 8 q^{54} - 6 q^{55} + 6 q^{56} + 18 q^{57} - 6 q^{58} + 16 q^{59} + 2 q^{60} - 2 q^{61} - 6 q^{63} + 3 q^{64} + 4 q^{65} - 20 q^{66} - 24 q^{67} + 8 q^{68} - 4 q^{69} - 6 q^{70} - 6 q^{71} - 7 q^{72} - 10 q^{73} + 8 q^{74} - 2 q^{75} + 2 q^{76} - 10 q^{77} - 2 q^{78} - 4 q^{79} - 3 q^{80} + 3 q^{81} - 16 q^{82} + 4 q^{83} + 14 q^{84} - 8 q^{85} - 3 q^{86} - 58 q^{87} - 6 q^{88} - 16 q^{89} + 7 q^{90} - 14 q^{91} + 14 q^{92} - 14 q^{93} + 2 q^{94} - 2 q^{95} + 2 q^{96} - 8 q^{97} - 5 q^{98} - 30 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 2 * q^3 + 3 * q^4 - 3 * q^5 + 2 * q^6 - 6 * q^7 - 3 * q^8 + 7 * q^9 + 3 * q^10 + 6 * q^11 - 2 * q^12 - 4 * q^13 + 6 * q^14 + 2 * q^15 + 3 * q^16 + 8 * q^17 - 7 * q^18 + 2 * q^19 - 3 * q^20 + 14 * q^21 - 6 * q^22 + 14 * q^23 + 2 * q^24 + 3 * q^25 + 4 * q^26 - 8 * q^27 - 6 * q^28 + 6 * q^29 - 2 * q^30 - 3 * q^32 + 20 * q^33 - 8 * q^34 + 6 * q^35 + 7 * q^36 - 8 * q^37 - 2 * q^38 + 2 * q^39 + 3 * q^40 + 16 * q^41 - 14 * q^42 + 3 * q^43 + 6 * q^44 - 7 * q^45 - 14 * q^46 - 2 * q^47 - 2 * q^48 + 5 * q^49 - 3 * q^50 - 4 * q^52 + 22 * q^53 + 8 * q^54 - 6 * q^55 + 6 * q^56 + 18 * q^57 - 6 * q^58 + 16 * q^59 + 2 * q^60 - 2 * q^61 - 6 * q^63 + 3 * q^64 + 4 * q^65 - 20 * q^66 - 24 * q^67 + 8 * q^68 - 4 * q^69 - 6 * q^70 - 6 * q^71 - 7 * q^72 - 10 * q^73 + 8 * q^74 - 2 * q^75 + 2 * q^76 - 10 * q^77 - 2 * q^78 - 4 * q^79 - 3 * q^80 + 3 * q^81 - 16 * q^82 + 4 * q^83 + 14 * q^84 - 8 * q^85 - 3 * q^86 - 58 * q^87 - 6 * q^88 - 16 * q^89 + 7 * q^90 - 14 * q^91 + 14 * q^92 - 14 * q^93 + 2 * q^94 - 2 * q^95 + 2 * q^96 - 8 * q^97 - 5 * q^98 - 30 * q^99

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