LMFDB - Embedded newform 4641.2.a.w.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4641,2,Mod(1,4641)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4641, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4641.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4641 = 3 \cdot 7 \cdot 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4641.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:	$37.0585715781$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 22 x^{12} + 19 x^{11} + 187 x^{10} - 135 x^{9} - 776 x^{8} + 443 x^{7} + 1636 x^{6} + \cdots - 19 $ x^14 - x^13 - 22x^12 + 19x^11 + 187x^10 - 135x^9 - 776x^8 + 443x^7 + 1636x^6 - 648x^5 - 1635x^4 + 306x^3 + 604x^2 + 8x - 19
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.63791$ of defining polynomial
Character	$\chi$	$=$	4641.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.63791 q^{2} -1.00000 q^{3} +4.95855 q^{4} -0.496275 q^{5} +2.63791 q^{6} +1.00000 q^{7} -7.80439 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.63791 q^{2} -1.00000 q^{3} +4.95855 q^{4} -0.496275 q^{5} +2.63791 q^{6} +1.00000 q^{7} -7.80439 q^{8} +1.00000 q^{9} +1.30913 q^{10} +2.94372 q^{11} -4.95855 q^{12} +1.00000 q^{13} -2.63791 q^{14} +0.496275 q^{15} +10.6701 q^{16} +1.00000 q^{17} -2.63791 q^{18} +3.33739 q^{19} -2.46081 q^{20} -1.00000 q^{21} -7.76527 q^{22} -4.96288 q^{23} +7.80439 q^{24} -4.75371 q^{25} -2.63791 q^{26} -1.00000 q^{27} +4.95855 q^{28} +6.05542 q^{29} -1.30913 q^{30} +5.44633 q^{31} -12.5381 q^{32} -2.94372 q^{33} -2.63791 q^{34} -0.496275 q^{35} +4.95855 q^{36} +2.79747 q^{37} -8.80371 q^{38} -1.00000 q^{39} +3.87313 q^{40} -2.20266 q^{41} +2.63791 q^{42} +6.80262 q^{43} +14.5966 q^{44} -0.496275 q^{45} +13.0916 q^{46} +4.20399 q^{47} -10.6701 q^{48} +1.00000 q^{49} +12.5398 q^{50} -1.00000 q^{51} +4.95855 q^{52} -2.03579 q^{53} +2.63791 q^{54} -1.46090 q^{55} -7.80439 q^{56} -3.33739 q^{57} -15.9736 q^{58} -9.59572 q^{59} +2.46081 q^{60} +9.95911 q^{61} -14.3669 q^{62} +1.00000 q^{63} +11.7340 q^{64} -0.496275 q^{65} +7.76527 q^{66} +8.02766 q^{67} +4.95855 q^{68} +4.96288 q^{69} +1.30913 q^{70} -15.0507 q^{71} -7.80439 q^{72} -1.91488 q^{73} -7.37947 q^{74} +4.75371 q^{75} +16.5486 q^{76} +2.94372 q^{77} +2.63791 q^{78} +10.6642 q^{79} -5.29533 q^{80} +1.00000 q^{81} +5.81041 q^{82} -2.93693 q^{83} -4.95855 q^{84} -0.496275 q^{85} -17.9447 q^{86} -6.05542 q^{87} -22.9739 q^{88} +10.7125 q^{89} +1.30913 q^{90} +1.00000 q^{91} -24.6087 q^{92} -5.44633 q^{93} -11.0897 q^{94} -1.65626 q^{95} +12.5381 q^{96} -11.4020 q^{97} -2.63791 q^{98} +2.94372 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - q^{2} - 14 q^{3} + 17 q^{4} - q^{5} + q^{6} + 14 q^{7} - 6 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q - q^2 - 14 * q^3 + 17 * q^4 - q^5 + q^6 + 14 * q^7 - 6 * q^8 + 14 * q^9	\( 14 q - q^{2} - 14 q^{3} + 17 q^{4} - q^{5} + q^{6} + 14 q^{7} - 6 q^{8} + 14 q^{9} + 11 q^{10} - 4 q^{11} - 17 q^{12} + 14 q^{13} - q^{14} + q^{15} + 19 q^{16} + 14 q^{17} - q^{18} + 6 q^{19} + q^{20} - 14 q^{21} + 12 q^{22} + 7 q^{23} + 6 q^{24} + 19 q^{25} - q^{26} - 14 q^{27} + 17 q^{28} - 4 q^{29} - 11 q^{30} + 31 q^{31} - 18 q^{32} + 4 q^{33} - q^{34} - q^{35} + 17 q^{36} + 2 q^{37} + 9 q^{38} - 14 q^{39} + 50 q^{40} + 4 q^{41} + q^{42} + 14 q^{43} - 8 q^{44} - q^{45} - 17 q^{46} - q^{47} - 19 q^{48} + 14 q^{49} - 3 q^{50} - 14 q^{51} + 17 q^{52} - 43 q^{53} + q^{54} + 23 q^{55} - 6 q^{56} - 6 q^{57} - 10 q^{58} + 11 q^{59} - q^{60} + 25 q^{61} - 3 q^{62} + 14 q^{63} + 36 q^{64} - q^{65} - 12 q^{66} + 11 q^{67} + 17 q^{68} - 7 q^{69} + 11 q^{70} + 20 q^{71} - 6 q^{72} + 14 q^{73} - 24 q^{74} - 19 q^{75} + 9 q^{76} - 4 q^{77} + q^{78} + 42 q^{79} + 13 q^{80} + 14 q^{81} + 2 q^{82} + 15 q^{83} - 17 q^{84} - q^{85} - 11 q^{86} + 4 q^{87} + 63 q^{88} + 21 q^{89} + 11 q^{90} + 14 q^{91} + 30 q^{92} - 31 q^{93} - 29 q^{94} + 16 q^{95} + 18 q^{96} + 15 q^{97} - q^{98} - 4 q^{99}+O(q^{100}) \) 14 * q - q^2 - 14 * q^3 + 17 * q^4 - q^5 + q^6 + 14 * q^7 - 6 * q^8 + 14 * q^9 + 11 * q^10 - 4 * q^11 - 17 * q^12 + 14 * q^13 - q^14 + q^15 + 19 * q^16 + 14 * q^17 - q^18 + 6 * q^19 + q^20 - 14 * q^21 + 12 * q^22 + 7 * q^23 + 6 * q^24 + 19 * q^25 - q^26 - 14 * q^27 + 17 * q^28 - 4 * q^29 - 11 * q^30 + 31 * q^31 - 18 * q^32 + 4 * q^33 - q^34 - q^35 + 17 * q^36 + 2 * q^37 + 9 * q^38 - 14 * q^39 + 50 * q^40 + 4 * q^41 + q^42 + 14 * q^43 - 8 * q^44 - q^45 - 17 * q^46 - q^47 - 19 * q^48 + 14 * q^49 - 3 * q^50 - 14 * q^51 + 17 * q^52 - 43 * q^53 + q^54 + 23 * q^55 - 6 * q^56 - 6 * q^57 - 10 * q^58 + 11 * q^59 - q^60 + 25 * q^61 - 3 * q^62 + 14 * q^63 + 36 * q^64 - q^65 - 12 * q^66 + 11 * q^67 + 17 * q^68 - 7 * q^69 + 11 * q^70 + 20 * q^71 - 6 * q^72 + 14 * q^73 - 24 * q^74 - 19 * q^75 + 9 * q^76 - 4 * q^77 + q^78 + 42 * q^79 + 13 * q^80 + 14 * q^81 + 2 * q^82 + 15 * q^83 - 17 * q^84 - q^85 - 11 * q^86 + 4 * q^87 + 63 * q^88 + 21 * q^89 + 11 * q^90 + 14 * q^91 + 30 * q^92 - 31 * q^93 - 29 * q^94 + 16 * q^95 + 18 * q^96 + 15 * q^97 - q^98 - 4 * 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 $

$2$	−2.63791	−1.86528	−0.932641	−	0.360806i	$-0.882502\pi$
$2$	−2.63791	−1.86528	−0.932641	+	0.360806i	$0.882502\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.95855	2.47928
$5$	−0.496275	−0.221941	−0.110971	−	0.993824i	$-0.535396\pi$
$5$	−0.496275	−0.221941	−0.110971	+	0.993824i	$0.535396\pi$
$6$	2.63791	1.07692
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−7.80439	−2.75927
$9$	1.00000	0.333333
$10$	1.30913	0.413983
$11$	2.94372	0.887566	0.443783	−	0.896134i	$-0.353636\pi$
$11$	2.94372	0.887566	0.443783	+	0.896134i	$0.353636\pi$
$12$	−4.95855	−1.43141
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−2.63791	−0.705010
$15$	0.496275	0.128138
$16$	10.6701	2.66753
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.63791	−0.621761
$19$	3.33739	0.765649	0.382824	−	0.923821i	$-0.374951\pi$
$19$	3.33739	0.765649	0.382824	+	0.923821i	$0.374951\pi$
$20$	−2.46081	−0.550253
$21$	−1.00000	−0.218218
$22$	−7.76527	−1.65556
$23$	−4.96288	−1.03483	−0.517416	−	0.855734i	$-0.673106\pi$
$23$	−4.96288	−1.03483	−0.517416	+	0.855734i	$0.673106\pi$
$24$	7.80439	1.59306
$25$	−4.75371	−0.950742
$26$	−2.63791	−0.517336
$27$	−1.00000	−0.192450
$28$	4.95855	0.937078
$29$	6.05542	1.12446	0.562232	−	0.826980i	$-0.309943\pi$
$29$	6.05542	1.12446	0.562232	+	0.826980i	$0.309943\pi$
$30$	−1.30913	−0.239013
$31$	5.44633	0.978190	0.489095	−	0.872231i	$-0.337327\pi$
$31$	5.44633	0.978190	0.489095	+	0.872231i	$0.337327\pi$
$32$	−12.5381	−2.21644
$33$	−2.94372	−0.512436
$34$	−2.63791	−0.452397
$35$	−0.496275	−0.0838859
$36$	4.95855	0.826425
$37$	2.79747	0.459901	0.229951	−	0.973202i	$-0.426143\pi$
$37$	2.79747	0.459901	0.229951	+	0.973202i	$0.426143\pi$
$38$	−8.80371	−1.42815
$39$	−1.00000	−0.160128
$40$	3.87313	0.612395
$41$	−2.20266	−0.343997	−0.171999	−	0.985097i	$-0.555022\pi$
$41$	−2.20266	−0.343997	−0.171999	+	0.985097i	$0.555022\pi$
$42$	2.63791	0.407038
$43$	6.80262	1.03739	0.518695	−	0.854959i	$-0.326418\pi$
$43$	6.80262	1.03739	0.518695	+	0.854959i	$0.326418\pi$
$44$	14.5966	2.20052
$45$	−0.496275	−0.0739804
$46$	13.0916	1.93025
$47$	4.20399	0.613215	0.306607	−	0.951836i	$-0.400806\pi$
$47$	4.20399	0.613215	0.306607	+	0.951836i	$0.400806\pi$
$48$	−10.6701	−1.54010
$49$	1.00000	0.142857
$50$	12.5398	1.77340
$51$	−1.00000	−0.140028
$52$	4.95855	0.687628
$53$	−2.03579	−0.279638	−0.139819	−	0.990177i	$-0.544652\pi$
$53$	−2.03579	−0.279638	−0.139819	+	0.990177i	$0.544652\pi$
$54$	2.63791	0.358974
$55$	−1.46090	−0.196987
$56$	−7.80439	−1.04290
$57$	−3.33739	−0.442048
$58$	−15.9736	−2.09744
$59$	−9.59572	−1.24926	−0.624628	−	0.780922i	$-0.714750\pi$
$59$	−9.59572	−1.24926	−0.624628	+	0.780922i	$0.714750\pi$
$60$	2.46081	0.317689
$61$	9.95911	1.27513	0.637567	−	0.770395i	$-0.279941\pi$
$61$	9.95911	1.27513	0.637567	+	0.770395i	$0.279941\pi$
$62$	−14.3669	−1.82460
$63$	1.00000	0.125988
$64$	11.7340	1.46674
$65$	−0.496275	−0.0615554
$66$	7.76527	0.955838
$67$	8.02766	0.980734	0.490367	−	0.871516i	$-0.336863\pi$
$67$	8.02766	0.980734	0.490367	+	0.871516i	$0.336863\pi$
$68$	4.95855	0.601313
$69$	4.96288	0.597461
$70$	1.30913	0.156471
$71$	−15.0507	−1.78619	−0.893096	−	0.449866i	$-0.851472\pi$
$71$	−15.0507	−1.78619	−0.893096	+	0.449866i	$0.851472\pi$
$72$	−7.80439	−0.919756
$73$	−1.91488	−0.224120	−0.112060	−	0.993701i	$-0.535745\pi$
$73$	−1.91488	−0.224120	−0.112060	+	0.993701i	$0.535745\pi$
$74$	−7.37947	−0.857846
$75$	4.75371	0.548911
$76$	16.5486	1.89826
$77$	2.94372	0.335468
$78$	2.63791	0.298684
$79$	10.6642	1.19982	0.599909	−	0.800068i	$-0.295203\pi$
$79$	10.6642	1.19982	0.599909	+	0.800068i	$0.295203\pi$
$80$	−5.29533	−0.592036
$81$	1.00000	0.111111
$82$	5.81041	0.641652
$83$	−2.93693	−0.322369	−0.161185	−	0.986924i	$-0.551531\pi$
$83$	−2.93693	−0.322369	−0.161185	+	0.986924i	$0.551531\pi$
$84$	−4.95855	−0.541022
$85$	−0.496275	−0.0538286
$86$	−17.9447	−1.93503
$87$	−6.05542	−0.649209
$88$	−22.9739	−2.44903
$89$	10.7125	1.13552	0.567759	−	0.823195i	$-0.307810\pi$
$89$	10.7125	1.13552	0.567759	+	0.823195i	$0.307810\pi$
$90$	1.30913	0.137994
$91$	1.00000	0.104828
$92$	−24.6087	−2.56564
$93$	−5.44633	−0.564758
$94$	−11.0897	−1.14382
$95$	−1.65626	−0.169929
$96$	12.5381	1.27966
$97$	−11.4020	−1.15770	−0.578848	−	0.815435i	$-0.696498\pi$
$97$	−11.4020	−1.15770	−0.578848	+	0.815435i	$0.696498\pi$
$98$	−2.63791	−0.266469
$99$	2.94372	0.295855
$100$	−23.5715	−2.35715
$101$	7.06388	0.702882	0.351441	−	0.936210i	$-0.385692\pi$
$101$	7.06388	0.702882	0.351441	+	0.936210i	$0.385692\pi$
$102$	2.63791	0.261192
$103$	6.77040	0.667108	0.333554	−	0.942731i	$-0.391752\pi$
$103$	6.77040	0.667108	0.333554	+	0.942731i	$0.391752\pi$
$104$	−7.80439	−0.765283
$105$	0.496275	0.0484315
$106$	5.37023	0.521603
$107$	4.72761	0.457036	0.228518	−	0.973540i	$-0.426612\pi$
$107$	4.72761	0.457036	0.228518	+	0.973540i	$0.426612\pi$
$108$	−4.95855	−0.477137
$109$	19.8139	1.89783	0.948916	−	0.315530i	$-0.102182\pi$
$109$	19.8139	1.89783	0.948916	+	0.315530i	$0.102182\pi$
$110$	3.85371	0.367437
$111$	−2.79747	−0.265524
$112$	10.6701	1.00823
$113$	−2.77631	−0.261173	−0.130587	−	0.991437i	$-0.541686\pi$
$113$	−2.77631	−0.261173	−0.130587	+	0.991437i	$0.541686\pi$
$114$	8.80371	0.824543
$115$	2.46296	0.229672
$116$	30.0261	2.78785
$117$	1.00000	0.0924500
$118$	25.3126	2.33022
$119$	1.00000	0.0916698
$120$	−3.87313	−0.353566
$121$	−2.33450	−0.212227
$122$	−26.2712	−2.37848
$123$	2.20266	0.198607
$124$	27.0059	2.42520
$125$	4.84053	0.432950
$126$	−2.63791	−0.235003
$127$	−3.33832	−0.296228	−0.148114	−	0.988970i	$-0.547320\pi$
$127$	−3.33832	−0.296228	−0.148114	+	0.988970i	$0.547320\pi$
$128$	−5.87697	−0.519455
$129$	−6.80262	−0.598938
$130$	1.30913	0.114818
$131$	1.57976	0.138024	0.0690121	−	0.997616i	$-0.478015\pi$
$131$	1.57976	0.138024	0.0690121	+	0.997616i	$0.478015\pi$
$132$	−14.5966	−1.27047
$133$	3.33739	0.289388
$134$	−21.1762	−1.82935
$135$	0.496275	0.0427126
$136$	−7.80439	−0.669221
$137$	−2.75370	−0.235265	−0.117632	−	0.993057i	$-0.537530\pi$
$137$	−2.75370	−0.235265	−0.117632	+	0.993057i	$0.537530\pi$
$138$	−13.0916	−1.11443
$139$	9.36380	0.794227	0.397114	−	0.917769i	$-0.370012\pi$
$139$	9.36380	0.794227	0.397114	+	0.917769i	$0.370012\pi$
$140$	−2.46081	−0.207976
$141$	−4.20399	−0.354040
$142$	39.7024	3.33175
$143$	2.94372	0.246166
$144$	10.6701	0.889178
$145$	−3.00516	−0.249565
$146$	5.05129	0.418047
$147$	−1.00000	−0.0824786
$148$	13.8714	1.14022
$149$	10.6027	0.868610	0.434305	−	0.900766i	$-0.356994\pi$
$149$	10.6027	0.868610	0.434305	+	0.900766i	$0.356994\pi$
$150$	−12.5398	−1.02387
$151$	−8.10967	−0.659956	−0.329978	−	0.943989i	$-0.607041\pi$
$151$	−8.10967	−0.659956	−0.329978	+	0.943989i	$0.607041\pi$
$152$	−26.0462	−2.11263
$153$	1.00000	0.0808452
$154$	−7.76527	−0.625743
$155$	−2.70288	−0.217101
$156$	−4.95855	−0.397002
$157$	−13.2685	−1.05894	−0.529470	−	0.848329i	$-0.677609\pi$
$157$	−13.2685	−1.05894	−0.529470	+	0.848329i	$0.677609\pi$
$158$	−28.1312	−2.23800
$159$	2.03579	0.161449
$160$	6.22233	0.491919
$161$	−4.96288	−0.391130
$162$	−2.63791	−0.207254
$163$	−11.1430	−0.872785	−0.436392	−	0.899756i	$-0.643744\pi$
$163$	−11.1430	−0.872785	−0.436392	+	0.899756i	$0.643744\pi$
$164$	−10.9220	−0.852865
$165$	1.46090	0.113731
$166$	7.74734	0.601310
$167$	−21.7376	−1.68211	−0.841055	−	0.540950i	$-0.818065\pi$
$167$	−21.7376	−1.68211	−0.841055	+	0.540950i	$0.818065\pi$
$168$	7.80439	0.602121
$169$	1.00000	0.0769231
$170$	1.30913	0.100406
$171$	3.33739	0.255216
$172$	33.7312	2.57198
$173$	13.0849	0.994828	0.497414	−	0.867513i	$-0.334283\pi$
$173$	13.0849	0.994828	0.497414	+	0.867513i	$0.334283\pi$
$174$	15.9736	1.21096
$175$	−4.75371	−0.359347
$176$	31.4099	2.36761
$177$	9.59572	0.721259
$178$	−28.2585	−2.11806
$179$	10.8989	0.814621	0.407310	−	0.913290i	$-0.366467\pi$
$179$	10.8989	0.814621	0.407310	+	0.913290i	$0.366467\pi$
$180$	−2.46081	−0.183418
$181$	−4.37788	−0.325405	−0.162703	−	0.986675i	$-0.552021\pi$
$181$	−4.37788	−0.325405	−0.162703	+	0.986675i	$0.552021\pi$
$182$	−2.63791	−0.195535
$183$	−9.95911	−0.736199
$184$	38.7323	2.85538
$185$	−1.38832	−0.102071
$186$	14.3669	1.05343
$187$	2.94372	0.215266
$188$	20.8457	1.52033
$189$	−1.00000	−0.0727393
$190$	4.36907	0.316965
$191$	−6.83743	−0.494739	−0.247370	−	0.968921i	$-0.579566\pi$
$191$	−6.83743	−0.494739	−0.247370	+	0.968921i	$0.579566\pi$
$192$	−11.7340	−0.846825
$193$	−3.23954	−0.233187	−0.116593	−	0.993180i	$-0.537197\pi$
$193$	−3.23954	−0.233187	−0.116593	+	0.993180i	$0.537197\pi$
$194$	30.0774	2.15943
$195$	0.496275	0.0355390
$196$	4.95855	0.354182
$197$	−14.2611	−1.01606	−0.508030	−	0.861339i	$-0.669626\pi$
$197$	−14.2611	−1.01606	−0.508030	+	0.861339i	$0.669626\pi$
$198$	−7.76527	−0.551853
$199$	−24.6280	−1.74583	−0.872917	−	0.487868i	$-0.837775\pi$
$199$	−24.6280	−1.74583	−0.872917	+	0.487868i	$0.837775\pi$
$200$	37.0998	2.62335
$201$	−8.02766	−0.566227
$202$	−18.6339	−1.31107
$203$	6.05542	0.425007
$204$	−4.95855	−0.347168
$205$	1.09313	0.0763472
$206$	−17.8597	−1.24434
$207$	−4.96288	−0.344944
$208$	10.6701	0.739841
$209$	9.82434	0.679564
$210$	−1.30913	−0.0903384
$211$	19.1484	1.31823	0.659113	−	0.752044i	$-0.270932\pi$
$211$	19.1484	1.31823	0.659113	+	0.752044i	$0.270932\pi$
$212$	−10.0946	−0.693299
$213$	15.0507	1.03126
$214$	−12.4710	−0.852501
$215$	−3.37597	−0.230240
$216$	7.80439	0.531021
$217$	5.44633	0.369721
$218$	−52.2673	−3.53999
$219$	1.91488	0.129396
$220$	−7.24394	−0.488386
$221$	1.00000	0.0672673
$222$	7.37947	0.495278
$223$	−18.0785	−1.21063	−0.605313	−	0.795988i	$-0.706952\pi$
$223$	−18.0785	−1.21063	−0.605313	+	0.795988i	$0.706952\pi$
$224$	−12.5381	−0.837734
$225$	−4.75371	−0.316914
$226$	7.32364	0.487161
$227$	0.839115	0.0556940	0.0278470	−	0.999612i	$-0.491135\pi$
$227$	0.839115	0.0556940	0.0278470	+	0.999612i	$0.491135\pi$
$228$	−16.5486	−1.09596
$229$	−14.9573	−0.988409	−0.494205	−	0.869346i	$-0.664541\pi$
$229$	−14.9573	−0.988409	−0.494205	+	0.869346i	$0.664541\pi$
$230$	−6.49705	−0.428403
$231$	−2.94372	−0.193683
$232$	−47.2588	−3.10269
$233$	1.21736	0.0797516	0.0398758	−	0.999205i	$-0.487304\pi$
$233$	1.21736	0.0797516	0.0398758	+	0.999205i	$0.487304\pi$
$234$	−2.63791	−0.172445
$235$	−2.08634	−0.136098
$236$	−47.5809	−3.09725
$237$	−10.6642	−0.692715
$238$	−2.63791	−0.170990
$239$	−18.5823	−1.20199	−0.600994	−	0.799253i	$-0.705229\pi$
$239$	−18.5823	−1.20199	−0.600994	+	0.799253i	$0.705229\pi$
$240$	5.29533	0.341812
$241$	−20.0534	−1.29176	−0.645878	−	0.763441i	$-0.723509\pi$
$241$	−20.0534	−1.29176	−0.645878	+	0.763441i	$0.723509\pi$
$242$	6.15819	0.395863
$243$	−1.00000	−0.0641500
$244$	49.3828	3.16141
$245$	−0.496275	−0.0317059
$246$	−5.81041	−0.370458
$247$	3.33739	0.212353
$248$	−42.5053	−2.69909
$249$	2.93693	0.186120
$250$	−12.7689	−0.807574
$251$	25.7376	1.62455	0.812273	−	0.583278i	$-0.198230\pi$
$251$	25.7376	1.62455	0.812273	+	0.583278i	$0.198230\pi$
$252$	4.95855	0.312359
$253$	−14.6093	−0.918482
$254$	8.80618	0.552549
$255$	0.496275	0.0310780
$256$	−7.96502	−0.497814
$257$	3.35692	0.209399	0.104699	−	0.994504i	$-0.466612\pi$
$257$	3.35692	0.209399	0.104699	+	0.994504i	$0.466612\pi$
$258$	17.9447	1.11719
$259$	2.79747	0.173826
$260$	−2.46081	−0.152613
$261$	6.05542	0.374821
$262$	−4.16726	−0.257454
$263$	14.3036	0.881998	0.440999	−	0.897508i	$-0.354624\pi$
$263$	14.3036	0.881998	0.440999	+	0.897508i	$0.354624\pi$
$264$	22.9739	1.41395
$265$	1.01031	0.0620631
$266$	−8.80371	−0.539790
$267$	−10.7125	−0.655592
$268$	39.8056	2.43151
$269$	−11.2294	−0.684672	−0.342336	−	0.939578i	$-0.611218\pi$
$269$	−11.2294	−0.684672	−0.342336	+	0.939578i	$0.611218\pi$
$270$	−1.30913	−0.0796710
$271$	12.7964	0.777326	0.388663	−	0.921380i	$-0.372937\pi$
$271$	12.7964	0.777326	0.388663	+	0.921380i	$0.372937\pi$
$272$	10.6701	0.646972
$273$	−1.00000	−0.0605228
$274$	7.26402	0.438835
$275$	−13.9936	−0.843846
$276$	24.6087	1.48127
$277$	−21.3915	−1.28529	−0.642646	−	0.766163i	$-0.722164\pi$
$277$	−21.3915	−1.28529	−0.642646	+	0.766163i	$0.722164\pi$
$278$	−24.7008	−1.48146
$279$	5.44633	0.326063
$280$	3.87313	0.231464
$281$	−7.76403	−0.463163	−0.231581	−	0.972816i	$-0.574390\pi$
$281$	−7.76403	−0.463163	−0.231581	+	0.972816i	$0.574390\pi$
$282$	11.0897	0.660384
$283$	−4.91386	−0.292098	−0.146049	−	0.989277i	$-0.546656\pi$
$283$	−4.91386	−0.292098	−0.146049	+	0.989277i	$0.546656\pi$
$284$	−74.6298	−4.42847
$285$	1.65626	0.0981085
$286$	−7.76527	−0.459170
$287$	−2.20266	−0.130019
$288$	−12.5381	−0.738812
$289$	1.00000	0.0588235
$290$	7.92732	0.465508
$291$	11.4020	0.668396
$292$	−9.49505	−0.555656
$293$	9.72533	0.568160	0.284080	−	0.958801i	$-0.408312\pi$
$293$	9.72533	0.568160	0.284080	+	0.958801i	$0.408312\pi$
$294$	2.63791	0.153846
$295$	4.76212	0.277261
$296$	−21.8325	−1.26899
$297$	−2.94372	−0.170812
$298$	−27.9690	−1.62020
$299$	−4.96288	−0.287011
$300$	23.5715	1.36090
$301$	6.80262	0.392097
$302$	21.3926	1.23100
$303$	−7.06388	−0.405809
$304$	35.6104	2.04239
$305$	−4.94246	−0.283005
$306$	−2.63791	−0.150799
$307$	10.8984	0.622005	0.311003	−	0.950409i	$-0.399335\pi$
$307$	10.8984	0.622005	0.311003	+	0.950409i	$0.399335\pi$
$308$	14.5966	0.831719
$309$	−6.77040	−0.385155
$310$	7.12994	0.404954
$311$	28.0744	1.59195	0.795976	−	0.605328i	$-0.206958\pi$
$311$	28.0744	1.59195	0.795976	+	0.605328i	$0.206958\pi$
$312$	7.80439	0.441836
$313$	30.2988	1.71259	0.856295	−	0.516488i	$-0.172761\pi$
$313$	30.2988	1.71259	0.856295	+	0.516488i	$0.172761\pi$
$314$	35.0010	1.97522
$315$	−0.496275	−0.0279620
$316$	52.8791	2.97468
$317$	−1.95507	−0.109808	−0.0549038	−	0.998492i	$-0.517485\pi$
$317$	−1.95507	−0.109808	−0.0549038	+	0.998492i	$0.517485\pi$
$318$	−5.37023	−0.301148
$319$	17.8255	0.998035
$320$	−5.82328	−0.325531
$321$	−4.72761	−0.263870
$322$	13.0916	0.729568
$323$	3.33739	0.185697
$324$	4.95855	0.275475
$325$	−4.75371	−0.263688
$326$	29.3941	1.62799
$327$	−19.8139	−1.09571
$328$	17.1904	0.949181
$329$	4.20399	0.231773
$330$	−3.85371	−0.212140
$331$	−0.198926	−0.0109339	−0.00546697	−	0.999985i	$-0.501740\pi$
$331$	−0.198926	−0.0109339	−0.00546697	+	0.999985i	$0.501740\pi$
$332$	−14.5629	−0.799243
$333$	2.79747	0.153300
$334$	57.3419	3.13761
$335$	−3.98393	−0.217665
$336$	−10.6701	−0.582104
$337$	29.5440	1.60936	0.804682	−	0.593706i	$-0.202336\pi$
$337$	29.5440	1.60936	0.804682	+	0.593706i	$0.202336\pi$
$338$	−2.63791	−0.143483
$339$	2.77631	0.150788
$340$	−2.46081	−0.133456
$341$	16.0325	0.868208
$342$	−8.80371	−0.476050
$343$	1.00000	0.0539949
$344$	−53.0903	−2.86244
$345$	−2.46296	−0.132601
$346$	−34.5168	−1.85563
$347$	−27.0987	−1.45473	−0.727366	−	0.686249i	$-0.759256\pi$
$347$	−27.0987	−1.45473	−0.727366	+	0.686249i	$0.759256\pi$
$348$	−30.0261	−1.60957
$349$	−19.3174	−1.03403	−0.517017	−	0.855975i	$-0.672958\pi$
$349$	−19.3174	−1.03403	−0.517017	+	0.855975i	$0.672958\pi$
$350$	12.5398	0.670283
$351$	−1.00000	−0.0533761
$352$	−36.9086	−1.96723
$353$	27.6820	1.47337	0.736683	−	0.676239i	$-0.236391\pi$
$353$	27.6820	1.47337	0.736683	+	0.676239i	$0.236391\pi$
$354$	−25.3126	−1.34535
$355$	7.46931	0.396430
$356$	53.1183	2.81526
$357$	−1.00000	−0.0529256
$358$	−28.7502	−1.51950
$359$	−4.97429	−0.262533	−0.131267	−	0.991347i	$-0.541904\pi$
$359$	−4.97429	−0.262533	−0.131267	+	0.991347i	$0.541904\pi$
$360$	3.87313	0.204132
$361$	−7.86186	−0.413782
$362$	11.5484	0.606972
$363$	2.33450	0.122529
$364$	4.95855	0.259899
$365$	0.950310	0.0497415
$366$	26.2712	1.37322
$367$	6.78999	0.354435	0.177217	−	0.984172i	$-0.443290\pi$
$367$	6.78999	0.354435	0.177217	+	0.984172i	$0.443290\pi$
$368$	−52.9546	−2.76045
$369$	−2.20266	−0.114666
$370$	3.66225	0.190391
$371$	−2.03579	−0.105693
$372$	−27.0059	−1.40019
$373$	0.0780783	0.00404274	0.00202137	−	0.999998i	$-0.499357\pi$
$373$	0.0780783	0.00404274	0.00202137	+	0.999998i	$0.499357\pi$
$374$	−7.76527	−0.401532
$375$	−4.84053	−0.249964
$376$	−32.8095	−1.69202
$377$	6.05542	0.311870
$378$	2.63791	0.135679
$379$	−15.8014	−0.811661	−0.405831	−	0.913948i	$-0.633018\pi$
$379$	−15.8014	−0.811661	−0.405831	+	0.913948i	$0.633018\pi$
$380$	−8.21267	−0.421301
$381$	3.33832	0.171027
$382$	18.0365	0.922828
$383$	15.8100	0.807855	0.403928	−	0.914791i	$-0.367645\pi$
$383$	15.8100	0.807855	0.403928	+	0.914791i	$0.367645\pi$
$384$	5.87697	0.299908
$385$	−1.46090	−0.0744542
$386$	8.54559	0.434959
$387$	6.80262	0.345797
$388$	−56.5373	−2.87025
$389$	23.0394	1.16814	0.584071	−	0.811703i	$-0.301459\pi$
$389$	23.0394	1.16814	0.584071	+	0.811703i	$0.301459\pi$
$390$	−1.30913	−0.0662903
$391$	−4.96288	−0.250984
$392$	−7.80439	−0.394181
$393$	−1.57976	−0.0796883
$394$	37.6194	1.89524
$395$	−5.29239	−0.266289
$396$	14.5966	0.733507
$397$	−12.8959	−0.647229	−0.323614	−	0.946189i	$-0.604898\pi$
$397$	−12.8959	−0.647229	−0.323614	+	0.946189i	$0.604898\pi$
$398$	64.9664	3.25647
$399$	−3.33739	−0.167078
$400$	−50.7228	−2.53614
$401$	14.3600	0.717104	0.358552	−	0.933510i	$-0.383271\pi$
$401$	14.3600	0.717104	0.358552	+	0.933510i	$0.383271\pi$
$402$	21.1762	1.05617
$403$	5.44633	0.271301
$404$	35.0266	1.74264
$405$	−0.496275	−0.0246601
$406$	−15.9736	−0.792758
$407$	8.23498	0.408193
$408$	7.80439	0.386375
$409$	19.3069	0.954663	0.477332	−	0.878723i	$-0.341604\pi$
$409$	19.3069	0.954663	0.477332	+	0.878723i	$0.341604\pi$
$410$	−2.88356	−0.142409
$411$	2.75370	0.135830
$412$	33.5714	1.65394
$413$	−9.59572	−0.472175
$414$	13.0916	0.643418
$415$	1.45752	0.0715470
$416$	−12.5381	−0.614729
$417$	−9.36380	−0.458547
$418$	−25.9157	−1.26758
$419$	34.9339	1.70663	0.853316	−	0.521394i	$-0.174588\pi$
$419$	34.9339	1.70663	0.853316	+	0.521394i	$0.174588\pi$
$420$	2.46081	0.120075
$421$	6.51080	0.317317	0.158658	−	0.987334i	$-0.449283\pi$
$421$	6.51080	0.317317	0.158658	+	0.987334i	$0.449283\pi$
$422$	−50.5116	−2.45886
$423$	4.20399	0.204405
$424$	15.8881	0.771595
$425$	−4.75371	−0.230589
$426$	−39.7024	−1.92359
$427$	9.95911	0.481955
$428$	23.4421	1.13312
$429$	−2.94372	−0.142124
$430$	8.90551	0.429462
$431$	26.7893	1.29039	0.645197	−	0.764016i	$-0.276775\pi$
$431$	26.7893	1.29039	0.645197	+	0.764016i	$0.276775\pi$
$432$	−10.6701	−0.513367
$433$	23.1374	1.11191	0.555957	−	0.831211i	$-0.312352\pi$
$433$	23.1374	1.11191	0.555957	+	0.831211i	$0.312352\pi$
$434$	−14.3669	−0.689634
$435$	3.00516	0.144086
$436$	98.2485	4.70525
$437$	−16.5631	−0.792318
$438$	−5.05129	−0.241360
$439$	15.1037	0.720859	0.360429	−	0.932787i	$-0.382630\pi$
$439$	15.1037	0.720859	0.360429	+	0.932787i	$0.382630\pi$
$440$	11.4014	0.543541
$441$	1.00000	0.0476190
$442$	−2.63791	−0.125472
$443$	−23.2475	−1.10452	−0.552262	−	0.833671i	$-0.686235\pi$
$443$	−23.2475	−1.10452	−0.552262	+	0.833671i	$0.686235\pi$
$444$	−13.8714	−0.658308
$445$	−5.31633	−0.252018
$446$	47.6894	2.25816
$447$	−10.6027	−0.501492
$448$	11.7340	0.554377
$449$	9.16392	0.432472	0.216236	−	0.976341i	$-0.430622\pi$
$449$	9.16392	0.432472	0.216236	+	0.976341i	$0.430622\pi$
$450$	12.5398	0.591134
$451$	−6.48401	−0.305320
$452$	−13.7665	−0.647520
$453$	8.10967	0.381025
$454$	−2.21351	−0.103885
$455$	−0.496275	−0.0232658
$456$	26.0462	1.21973
$457$	−21.2669	−0.994825	−0.497412	−	0.867514i	$-0.665716\pi$
$457$	−21.2669	−0.994825	−0.497412	+	0.867514i	$0.665716\pi$
$458$	39.4561	1.84366
$459$	−1.00000	−0.0466760
$460$	12.2127	0.569420
$461$	8.36939	0.389801	0.194901	−	0.980823i	$-0.437562\pi$
$461$	8.36939	0.389801	0.194901	+	0.980823i	$0.437562\pi$
$462$	7.76527	0.361273
$463$	22.1237	1.02818	0.514088	−	0.857737i	$-0.328130\pi$
$463$	22.1237	1.02818	0.514088	+	0.857737i	$0.328130\pi$
$464$	64.6122	2.99954
$465$	2.70288	0.125343
$466$	−3.21127	−0.148759
$467$	−0.489996	−0.0226743	−0.0113372	−	0.999936i	$-0.503609\pi$
$467$	−0.489996	−0.0226743	−0.0113372	+	0.999936i	$0.503609\pi$
$468$	4.95855	0.229209
$469$	8.02766	0.370683
$470$	5.50356	0.253860
$471$	13.2685	0.611379
$472$	74.8887	3.44703
$473$	20.0250	0.920752
$474$	28.1312	1.29211
$475$	−15.8650	−0.727935
$476$	4.95855	0.227275
$477$	−2.03579	−0.0932125
$478$	49.0184	2.24205
$479$	−15.7003	−0.717363	−0.358682	−	0.933460i	$-0.616774\pi$
$479$	−15.7003	−0.717363	−0.358682	+	0.933460i	$0.616774\pi$
$480$	−6.22233	−0.284009
$481$	2.79747	0.127554
$482$	52.8991	2.40949
$483$	4.96288	0.225819
$484$	−11.5757	−0.526170
$485$	5.65852	0.256940
$486$	2.63791	0.119658
$487$	7.18181	0.325439	0.162720	−	0.986672i	$-0.447973\pi$
$487$	7.18181	0.325439	0.162720	+	0.986672i	$0.447973\pi$
$488$	−77.7247	−3.51843
$489$	11.1430	0.503902
$490$	1.30913	0.0591404
$491$	7.34727	0.331578	0.165789	−	0.986161i	$-0.446983\pi$
$491$	7.34727	0.331578	0.165789	+	0.986161i	$0.446983\pi$
$492$	10.9220	0.492402
$493$	6.05542	0.272722
$494$	−8.80371	−0.396098
$495$	−1.46090	−0.0656624
$496$	58.1131	2.60935
$497$	−15.0507	−0.675117
$498$	−7.74734	−0.347166
$499$	26.0688	1.16700	0.583499	−	0.812114i	$-0.301683\pi$
$499$	26.0688	1.16700	0.583499	+	0.812114i	$0.301683\pi$
$500$	24.0020	1.07340
$501$	21.7376	0.971166
$502$	−67.8935	−3.03024
$503$	32.3204	1.44110	0.720548	−	0.693405i	$-0.243890\pi$
$503$	32.3204	1.44110	0.720548	+	0.693405i	$0.243890\pi$
$504$	−7.80439	−0.347635
$505$	−3.50563	−0.155998
$506$	38.5381	1.71323
$507$	−1.00000	−0.0444116
$508$	−16.5532	−0.734431
$509$	−4.97197	−0.220379	−0.110189	−	0.993911i	$-0.535146\pi$
$509$	−4.97197	−0.220379	−0.110189	+	0.993911i	$0.535146\pi$
$510$	−1.30913	−0.0579692
$511$	−1.91488	−0.0847095
$512$	32.7649	1.44802
$513$	−3.33739	−0.147349
$514$	−8.85523	−0.390587
$515$	−3.35999	−0.148059
$516$	−33.7312	−1.48493
$517$	12.3754	0.544268
$518$	−7.37947	−0.324235
$519$	−13.0849	−0.574364
$520$	3.87313	0.169848
$521$	8.88250	0.389149	0.194575	−	0.980888i	$-0.437667\pi$
$521$	8.88250	0.389149	0.194575	+	0.980888i	$0.437667\pi$
$522$	−15.9736	−0.699147
$523$	11.9867	0.524143	0.262072	−	0.965048i	$-0.415594\pi$
$523$	11.9867	0.524143	0.262072	+	0.965048i	$0.415594\pi$
$524$	7.83332	0.342200
$525$	4.75371	0.207469
$526$	−37.7316	−1.64518
$527$	5.44633	0.237246
$528$	−31.4099	−1.36694
$529$	1.63020	0.0708783
$530$	−2.66511	−0.115765
$531$	−9.59572	−0.416419
$532$	16.5486	0.717473
$533$	−2.20266	−0.0954077
$534$	28.2585	1.22286
$535$	−2.34620	−0.101435
$536$	−62.6509	−2.70611
$537$	−10.8989	−0.470321
$538$	29.6222	1.27711
$539$	2.94372	0.126795
$540$	2.46081	0.105896
$541$	−5.84669	−0.251369	−0.125684	−	0.992070i	$-0.540113\pi$
$541$	−5.84669	−0.251369	−0.125684	+	0.992070i	$0.540113\pi$
$542$	−33.7557	−1.44993
$543$	4.37788	0.187873
$544$	−12.5381	−0.537565
$545$	−9.83317	−0.421207
$546$	2.63791	0.112892
$547$	33.3310	1.42513	0.712565	−	0.701607i	$-0.247534\pi$
$547$	33.3310	1.42513	0.712565	+	0.701607i	$0.247534\pi$
$548$	−13.6544	−0.583287
$549$	9.95911	0.425044
$550$	36.9138	1.57401
$551$	20.2093	0.860944
$552$	−38.7323	−1.64855
$553$	10.6642	0.453489
$554$	56.4289	2.39743
$555$	1.38832	0.0589307
$556$	46.4309	1.96911
$557$	−45.3790	−1.92277	−0.961385	−	0.275207i	$-0.911254\pi$
$557$	−45.3790	−1.92277	−0.961385	+	0.275207i	$0.911254\pi$
$558$	−14.3669	−0.608200
$559$	6.80262	0.287720
$560$	−5.29533	−0.223768
$561$	−2.94372	−0.124284
$562$	20.4808	0.863930
$563$	5.50627	0.232062	0.116031	−	0.993246i	$-0.462983\pi$
$563$	5.50627	0.232062	0.116031	+	0.993246i	$0.462983\pi$
$564$	−20.8457	−0.877762
$565$	1.37781	0.0579650
$566$	12.9623	0.544846
$567$	1.00000	0.0419961
$568$	117.462	4.92858
$569$	−8.91121	−0.373577	−0.186789	−	0.982400i	$-0.559808\pi$
$569$	−8.91121	−0.373577	−0.186789	+	0.982400i	$0.559808\pi$
$570$	−4.36907	−0.183000
$571$	−21.2084	−0.887543	−0.443772	−	0.896140i	$-0.646360\pi$
$571$	−21.2084	−0.887543	−0.443772	+	0.896140i	$0.646360\pi$
$572$	14.5966	0.610315
$573$	6.83743	0.285638
$574$	5.81041	0.242522
$575$	23.5921	0.983859
$576$	11.7340	0.488915
$577$	16.2797	0.677734	0.338867	−	0.940834i	$-0.389956\pi$
$577$	16.2797	0.677734	0.338867	+	0.940834i	$0.389956\pi$
$578$	−2.63791	−0.109722
$579$	3.23954	0.134630
$580$	−14.9012	−0.618740
$581$	−2.93693	−0.121844
$582$	−30.0774	−1.24675
$583$	−5.99281	−0.248197
$584$	14.9445	0.618408
$585$	−0.496275	−0.0205185
$586$	−25.6545	−1.05978
$587$	34.8901	1.44007	0.720035	−	0.693938i	$-0.244126\pi$
$587$	34.8901	1.44007	0.720035	+	0.693938i	$0.244126\pi$
$588$	−4.95855	−0.204487
$589$	18.1765	0.748950
$590$	−12.5620	−0.517171
$591$	14.2611	0.586623
$592$	29.8494	1.22680
$593$	−21.9841	−0.902778	−0.451389	−	0.892327i	$-0.649071\pi$
$593$	−21.9841	−0.902778	−0.451389	+	0.892327i	$0.649071\pi$
$594$	7.76527	0.318613
$595$	−0.496275	−0.0203453
$596$	52.5742	2.15352
$597$	24.6280	1.00796
$598$	13.0916	0.535356
$599$	1.23059	0.0502807	0.0251404	−	0.999684i	$-0.491997\pi$
$599$	1.23059	0.0502807	0.0251404	+	0.999684i	$0.491997\pi$
$600$	−37.0998	−1.51459
$601$	−4.03175	−0.164459	−0.0822293	−	0.996613i	$-0.526204\pi$
$601$	−4.03175	−0.164459	−0.0822293	+	0.996613i	$0.526204\pi$
$602$	−17.9447	−0.731371
$603$	8.02766	0.326911
$604$	−40.2122	−1.63621
$605$	1.15855	0.0471019
$606$	18.6339	0.756949
$607$	23.9477	0.972006	0.486003	−	0.873957i	$-0.338454\pi$
$607$	23.9477	0.972006	0.486003	+	0.873957i	$0.338454\pi$
$608$	−41.8443	−1.69701
$609$	−6.05542	−0.245378
$610$	13.0378	0.527883
$611$	4.20399	0.170075
$612$	4.95855	0.200438
$613$	−11.2604	−0.454802	−0.227401	−	0.973801i	$-0.573023\pi$
$613$	−11.2604	−0.454802	−0.227401	+	0.973801i	$0.573023\pi$
$614$	−28.7490	−1.16022
$615$	−1.09313	−0.0440791
$616$	−22.9739	−0.925647
$617$	1.24415	0.0500874	0.0250437	−	0.999686i	$-0.492028\pi$
$617$	1.24415	0.0500874	0.0250437	+	0.999686i	$0.492028\pi$
$618$	17.8597	0.718422
$619$	−19.0358	−0.765114	−0.382557	−	0.923932i	$-0.624956\pi$
$619$	−19.0358	−0.765114	−0.382557	+	0.923932i	$0.624956\pi$
$620$	−13.4024	−0.538252
$621$	4.96288	0.199154
$622$	−74.0576	−2.96944
$623$	10.7125	0.429186
$624$	−10.6701	−0.427147
$625$	21.3663	0.854653
$626$	−79.9254	−3.19446
$627$	−9.82434	−0.392346
$628$	−65.7924	−2.62540
$629$	2.79747	0.111542
$630$	1.30913	0.0521569
$631$	24.9977	0.995142	0.497571	−	0.867423i	$-0.334225\pi$
$631$	24.9977	0.995142	0.497571	+	0.867423i	$0.334225\pi$
$632$	−83.2277	−3.31062
$633$	−19.1484	−0.761079
$634$	5.15729	0.204822
$635$	1.65673	0.0657452
$636$	10.0946	0.400276
$637$	1.00000	0.0396214
$638$	−47.0219	−1.86162
$639$	−15.0507	−0.595398
$640$	2.91659	0.115289
$641$	6.76023	0.267013	0.133506	−	0.991048i	$-0.457376\pi$
$641$	6.76023	0.267013	0.133506	+	0.991048i	$0.457376\pi$
$642$	12.4710	0.492191
$643$	5.00340	0.197315	0.0986573	−	0.995121i	$-0.468545\pi$
$643$	5.00340	0.197315	0.0986573	+	0.995121i	$0.468545\pi$
$644$	−24.6087	−0.969719
$645$	3.37597	0.132929
$646$	−8.80371	−0.346377
$647$	21.8159	0.857670	0.428835	−	0.903383i	$-0.358924\pi$
$647$	21.8159	0.857670	0.428835	+	0.903383i	$0.358924\pi$
$648$	−7.80439	−0.306585
$649$	−28.2471	−1.10880
$650$	12.5398	0.491853
$651$	−5.44633	−0.213458
$652$	−55.2530	−2.16387
$653$	19.9863	0.782123	0.391061	−	0.920365i	$-0.372108\pi$
$653$	19.9863	0.782123	0.391061	+	0.920365i	$0.372108\pi$
$654$	52.2673	2.04381
$655$	−0.783996	−0.0306332
$656$	−23.5027	−0.917625
$657$	−1.91488	−0.0747067
$658$	−11.0897	−0.432323
$659$	46.4311	1.80870	0.904349	−	0.426793i	$-0.140357\pi$
$659$	46.4311	1.80870	0.904349	+	0.426793i	$0.140357\pi$
$660$	7.24394	0.281970
$661$	−40.7723	−1.58586	−0.792929	−	0.609313i	$-0.791445\pi$
$661$	−40.7723	−1.58586	−0.792929	+	0.609313i	$0.791445\pi$
$662$	0.524747	0.0203949
$663$	−1.00000	−0.0388368
$664$	22.9209	0.889503
$665$	−1.65626	−0.0642271
$666$	−7.37947	−0.285949
$667$	−30.0523	−1.16363
$668$	−107.787	−4.17041
$669$	18.0785	0.698955
$670$	10.5092	0.406007
$671$	29.3169	1.13176
$672$	12.5381	0.483666
$673$	−28.9402	−1.11556	−0.557782	−	0.829988i	$-0.688347\pi$
$673$	−28.9402	−1.11556	−0.557782	+	0.829988i	$0.688347\pi$
$674$	−77.9343	−3.00192
$675$	4.75371	0.182970
$676$	4.95855	0.190714
$677$	41.6246	1.59976	0.799881	−	0.600159i	$-0.204896\pi$
$677$	41.6246	1.59976	0.799881	+	0.600159i	$0.204896\pi$
$678$	−7.32364	−0.281263
$679$	−11.4020	−0.437568
$680$	3.87313	0.148528
$681$	−0.839115	−0.0321549
$682$	−42.2922	−1.61945
$683$	−6.66533	−0.255042	−0.127521	−	0.991836i	$-0.540702\pi$
$683$	−6.66533	−0.255042	−0.127521	+	0.991836i	$0.540702\pi$
$684$	16.5486	0.632752
$685$	1.36660	0.0522149
$686$	−2.63791	−0.100716
$687$	14.9573	0.570658
$688$	72.5849	2.76727
$689$	−2.03579	−0.0775575
$690$	6.49705	0.247338
$691$	5.93766	0.225879	0.112940	−	0.993602i	$-0.463973\pi$
$691$	5.93766	0.225879	0.112940	+	0.993602i	$0.463973\pi$
$692$	64.8822	2.46645
$693$	2.94372	0.111823
$694$	71.4838	2.71349
$695$	−4.64703	−0.176272
$696$	47.2588	1.79134
$697$	−2.20266	−0.0834316
$698$	50.9574	1.92877
$699$	−1.21736	−0.0460446
$700$	−23.5715	−0.890920
$701$	−29.3020	−1.10672	−0.553361	−	0.832942i	$-0.686655\pi$
$701$	−29.3020	−1.10672	−0.553361	+	0.832942i	$0.686655\pi$
$702$	2.63791	0.0995614
$703$	9.33624	0.352123
$704$	34.5415	1.30183
$705$	2.08634	0.0785759
$706$	−73.0226	−2.74824
$707$	7.06388	0.265665
$708$	47.5809	1.78820
$709$	33.2794	1.24983	0.624917	−	0.780691i	$-0.285133\pi$
$709$	33.2794	1.24983	0.624917	+	0.780691i	$0.285133\pi$
$710$	−19.7033	−0.739453
$711$	10.6642	0.399939
$712$	−83.6042	−3.13320
$713$	−27.0295	−1.01226
$714$	2.63791	0.0987212
$715$	−1.46090	−0.0546345
$716$	54.0427	2.01967
$717$	18.5823	0.693969
$718$	13.1217	0.489698
$719$	18.2994	0.682454	0.341227	−	0.939981i	$-0.389158\pi$
$719$	18.2994	0.682454	0.341227	+	0.939981i	$0.389158\pi$
$720$	−5.29533	−0.197345
$721$	6.77040	0.252143
$722$	20.7388	0.771820
$723$	20.0534	0.745796
$724$	−21.7079	−0.806769
$725$	−28.7857	−1.06907
$726$	−6.15819	−0.228552
$727$	−37.9837	−1.40874	−0.704370	−	0.709833i	$-0.748770\pi$
$727$	−37.9837	−1.40874	−0.704370	+	0.709833i	$0.748770\pi$
$728$	−7.80439	−0.289250
$729$	1.00000	0.0370370
$730$	−2.50683	−0.0927819
$731$	6.80262	0.251604
$732$	−49.3828	−1.82524
$733$	27.7193	1.02384	0.511918	−	0.859035i	$-0.328935\pi$
$733$	27.7193	1.02384	0.511918	+	0.859035i	$0.328935\pi$
$734$	−17.9114	−0.661121
$735$	0.496275	0.0183054
$736$	62.2249	2.29364
$737$	23.6312	0.870466
$738$	5.81041	0.213884
$739$	−8.08883	−0.297552	−0.148776	−	0.988871i	$-0.547533\pi$
$739$	−8.08883	−0.297552	−0.148776	+	0.988871i	$0.547533\pi$
$740$	−6.88404	−0.253062
$741$	−3.33739	−0.122602
$742$	5.37023	0.197147
$743$	−30.7106	−1.12666	−0.563331	−	0.826231i	$-0.690480\pi$
$743$	−30.7106	−1.12666	−0.563331	+	0.826231i	$0.690480\pi$
$744$	42.5053	1.55832
$745$	−5.26188	−0.192780
$746$	−0.205963	−0.00754085
$747$	−2.93693	−0.107456
$748$	14.5966	0.533705
$749$	4.72761	0.172743
$750$	12.7689	0.466253
$751$	17.0181	0.621000	0.310500	−	0.950573i	$-0.399503\pi$
$751$	17.0181	0.621000	0.310500	+	0.950573i	$0.399503\pi$
$752$	44.8571	1.63577
$753$	−25.7376	−0.937932
$754$	−15.9736	−0.581725
$755$	4.02463	0.146471
$756$	−4.95855	−0.180341
$757$	−25.4714	−0.925773	−0.462886	−	0.886418i	$-0.653186\pi$
$757$	−25.4714	−0.925773	−0.462886	+	0.886418i	$0.653186\pi$
$758$	41.6825	1.51398
$759$	14.6093	0.530286
$760$	12.9261	0.468879
$761$	18.5659	0.673012	0.336506	−	0.941681i	$-0.390755\pi$
$761$	18.5659	0.673012	0.336506	+	0.941681i	$0.390755\pi$
$762$	−8.80618	−0.319014
$763$	19.8139	0.717313
$764$	−33.9038	−1.22660
$765$	−0.496275	−0.0179429
$766$	−41.7054	−1.50688
$767$	−9.59572	−0.346482
$768$	7.96502	0.287413
$769$	45.9752	1.65791	0.828955	−	0.559316i	$-0.188936\pi$
$769$	45.9752	1.65791	0.828955	+	0.559316i	$0.188936\pi$
$770$	3.85371	0.138878
$771$	−3.35692	−0.120896
$772$	−16.0634	−0.578135
$773$	24.9669	0.897997	0.448999	−	0.893532i	$-0.351781\pi$
$773$	24.9669	0.897997	0.448999	+	0.893532i	$0.351781\pi$
$774$	−17.9447	−0.645008
$775$	−25.8903	−0.930006
$776$	88.9855	3.19439
$777$	−2.79747	−0.100359
$778$	−60.7757	−2.17891
$779$	−7.35112	−0.263381
$780$	2.46081	0.0881111
$781$	−44.3052	−1.58536
$782$	13.0916	0.468155
$783$	−6.05542	−0.216403
$784$	10.6701	0.381076
$785$	6.58482	0.235022
$786$	4.16726	0.148641
$787$	38.4090	1.36913	0.684566	−	0.728951i	$-0.259992\pi$
$787$	38.4090	1.36913	0.684566	+	0.728951i	$0.259992\pi$
$788$	−70.7143	−2.51909
$789$	−14.3036	−0.509222
$790$	13.9608	0.496704
$791$	−2.77631	−0.0987141
$792$	−22.9739	−0.816344
$793$	9.95911	0.353658
$794$	34.0183	1.20726
$795$	−1.01031	−0.0358321
$796$	−122.119	−4.32841
$797$	49.4246	1.75071	0.875354	−	0.483483i	$-0.160628\pi$
$797$	49.4246	1.75071	0.875354	+	0.483483i	$0.160628\pi$
$798$	8.80371	0.311648
$799$	4.20399	0.148726
$800$	59.6023	2.10726
$801$	10.7125	0.378506
$802$	−37.8803	−1.33760
$803$	−5.63689	−0.198921
$804$	−39.8056	−1.40383
$805$	2.46296	0.0868078
$806$	−14.3669	−0.506053
$807$	11.2294	0.395295
$808$	−55.1292	−1.93944
$809$	−41.3639	−1.45428	−0.727138	−	0.686492i	$-0.759150\pi$
$809$	−41.3639	−1.45428	−0.727138	+	0.686492i	$0.759150\pi$
$810$	1.30913	0.0459981
$811$	13.0396	0.457882	0.228941	−	0.973440i	$-0.426474\pi$
$811$	13.0396	0.457882	0.228941	+	0.973440i	$0.426474\pi$
$812$	30.0261	1.05371
$813$	−12.7964	−0.448790
$814$	−21.7231	−0.761395
$815$	5.52998	0.193707
$816$	−10.6701	−0.373530
$817$	22.7030	0.794277
$818$	−50.9297	−1.78072
$819$	1.00000	0.0349428
$820$	5.42032	0.189286
$821$	49.1810	1.71643	0.858214	−	0.513292i	$-0.171574\pi$
$821$	49.1810	1.71643	0.858214	+	0.513292i	$0.171574\pi$
$822$	−7.26402	−0.253362
$823$	−4.18735	−0.145962	−0.0729809	−	0.997333i	$-0.523251\pi$
$823$	−4.18735	−0.145962	−0.0729809	+	0.997333i	$0.523251\pi$
$824$	−52.8388	−1.84073
$825$	13.9936	0.487195
$826$	25.3126	0.880739
$827$	−47.7513	−1.66048	−0.830238	−	0.557410i	$-0.811795\pi$
$827$	−47.7513	−1.66048	−0.830238	+	0.557410i	$0.811795\pi$
$828$	−24.6087	−0.855212
$829$	−29.3101	−1.01798	−0.508990	−	0.860772i	$-0.669981\pi$
$829$	−29.3101	−1.01798	−0.508990	+	0.860772i	$0.669981\pi$
$830$	−3.84481	−0.133455
$831$	21.3915	0.742064
$832$	11.7340	0.406802
$833$	1.00000	0.0346479
$834$	24.7008	0.855320
$835$	10.7879	0.373329
$836$	48.7145	1.68483
$837$	−5.44633	−0.188253
$838$	−92.1524	−3.18335
$839$	−4.28424	−0.147908	−0.0739542	−	0.997262i	$-0.523562\pi$
$839$	−4.28424	−0.147908	−0.0739542	+	0.997262i	$0.523562\pi$
$840$	−3.87313	−0.133636
$841$	7.66810	0.264417
$842$	−17.1749	−0.591885
$843$	7.76403	0.267407
$844$	94.9481	3.26825
$845$	−0.496275	−0.0170724
$846$	−11.0897	−0.381273
$847$	−2.33450	−0.0802143
$848$	−21.7222	−0.745943
$849$	4.91386	0.168643
$850$	12.5398	0.430113
$851$	−13.8835	−0.475921
$852$	74.6298	2.55678
$853$	42.2185	1.44553	0.722766	−	0.691092i	$-0.242870\pi$
$853$	42.2185	1.44553	0.722766	+	0.691092i	$0.242870\pi$
$854$	−26.2712	−0.898982
$855$	−1.65626	−0.0566430
$856$	−36.8961	−1.26108
$857$	20.3869	0.696403	0.348202	−	0.937420i	$-0.386792\pi$
$857$	20.3869	0.696403	0.348202	+	0.937420i	$0.386792\pi$
$858$	7.76527	0.265102
$859$	−3.02486	−0.103207	−0.0516034	−	0.998668i	$-0.516433\pi$
$859$	−3.02486	−0.103207	−0.0516034	+	0.998668i	$0.516433\pi$
$860$	−16.7399	−0.570828
$861$	2.20266	0.0750664
$862$	−70.6676	−2.40695
$863$	36.2041	1.23240	0.616200	−	0.787590i	$-0.288671\pi$
$863$	36.2041	1.23240	0.616200	+	0.787590i	$0.288671\pi$
$864$	12.5381	0.426553
$865$	−6.49372	−0.220793
$866$	−61.0344	−2.07403
$867$	−1.00000	−0.0339618
$868$	27.0059	0.916640
$869$	31.3925	1.06492
$870$	−7.92732	−0.268761
$871$	8.02766	0.272007
$872$	−154.636	−5.23662
$873$	−11.4020	−0.385899
$874$	43.6918	1.47790
$875$	4.84053	0.163640
$876$	9.49505	0.320808
$877$	49.3569	1.66666	0.833332	−	0.552773i	$-0.186431\pi$
$877$	49.3569	1.66666	0.833332	+	0.552773i	$0.186431\pi$
$878$	−39.8421	−1.34460
$879$	−9.72533	−0.328027
$880$	−15.5880	−0.525471
$881$	0.225765	0.00760622	0.00380311	−	0.999993i	$-0.498789\pi$
$881$	0.225765	0.00760622	0.00380311	+	0.999993i	$0.498789\pi$
$882$	−2.63791	−0.0888229
$883$	−54.1124	−1.82103	−0.910514	−	0.413478i	$-0.864314\pi$
$883$	−54.1124	−1.82103	−0.910514	+	0.413478i	$0.864314\pi$
$884$	4.95855	0.166774
$885$	−4.76212	−0.160077
$886$	61.3248	2.06025
$887$	34.8753	1.17100	0.585499	−	0.810673i	$-0.300899\pi$
$887$	34.8753	1.17100	0.585499	+	0.810673i	$0.300899\pi$
$888$	21.8325	0.732652
$889$	−3.33832	−0.111964
$890$	14.0240	0.470085
$891$	2.94372	0.0986184
$892$	−89.6432	−3.00147
$893$	14.0303	0.469507
$894$	27.9690	0.935424
$895$	−5.40885	−0.180798
$896$	−5.87697	−0.196336
$897$	4.96288	0.165706
$898$	−24.1736	−0.806683
$899$	32.9798	1.09994
$900$	−23.5715	−0.785717
$901$	−2.03579	−0.0678221
$902$	17.1042	0.569508
$903$	−6.80262	−0.226377
$904$	21.6674	0.720646
$905$	2.17263	0.0722208
$906$	−21.3926	−0.710720
$907$	17.1016	0.567851	0.283925	−	0.958846i	$-0.408363\pi$
$907$	17.1016	0.567851	0.283925	+	0.958846i	$0.408363\pi$
$908$	4.16079	0.138081
$909$	7.06388	0.234294
$910$	1.30913	0.0433972
$911$	−25.1344	−0.832739	−0.416370	−	0.909195i	$-0.636698\pi$
$911$	−25.1344	−0.832739	−0.416370	+	0.909195i	$0.636698\pi$
$912$	−35.6104	−1.17918
$913$	−8.64549	−0.286124
$914$	56.1002	1.85563
$915$	4.94246	0.163393
$916$	−74.1668	−2.45054
$917$	1.57976	0.0521682
$918$	2.63791	0.0870639
$919$	−19.8708	−0.655478	−0.327739	−	0.944768i	$-0.606287\pi$
$919$	−19.8708	−0.655478	−0.327739	+	0.944768i	$0.606287\pi$
$920$	−19.2219	−0.633726
$921$	−10.8984	−0.359115
$922$	−22.0777	−0.727089
$923$	−15.0507	−0.495401
$924$	−14.5966	−0.480193
$925$	−13.2984	−0.437248
$926$	−58.3603	−1.91784
$927$	6.77040	0.222369
$928$	−75.9232	−2.49230
$929$	−5.02887	−0.164992	−0.0824960	−	0.996591i	$-0.526289\pi$
$929$	−5.02887	−0.164992	−0.0824960	+	0.996591i	$0.526289\pi$
$930$	−7.12994	−0.233800
$931$	3.33739	0.109378
$932$	6.03632	0.197726
$933$	−28.0744	−0.919114
$934$	1.29256	0.0422940
$935$	−1.46090	−0.0477764
$936$	−7.80439	−0.255094
$937$	44.7185	1.46089	0.730445	−	0.682972i	$-0.239313\pi$
$937$	44.7185	1.46089	0.730445	+	0.682972i	$0.239313\pi$
$938$	−21.1762	−0.691428
$939$	−30.2988	−0.988764
$940$	−10.3452	−0.337423
$941$	53.5557	1.74587	0.872934	−	0.487839i	$-0.162215\pi$
$941$	53.5557	1.74587	0.872934	+	0.487839i	$0.162215\pi$
$942$	−35.0010	−1.14039
$943$	10.9315	0.355980
$944$	−102.388	−3.33244
$945$	0.496275	0.0161438
$946$	−52.8242	−1.71746
$947$	20.2457	0.657896	0.328948	−	0.944348i	$-0.393306\pi$
$947$	20.2457	0.657896	0.328948	+	0.944348i	$0.393306\pi$
$948$	−52.8791	−1.71743
$949$	−1.91488	−0.0621598
$950$	41.8503	1.35780
$951$	1.95507	0.0633975
$952$	−7.80439	−0.252942
$953$	−52.7402	−1.70842	−0.854212	−	0.519925i	$-0.825960\pi$
$953$	−52.7402	−1.70842	−0.854212	+	0.519925i	$0.825960\pi$
$954$	5.37023	0.173868
$955$	3.39325	0.109803
$956$	−92.1413	−2.98006
$957$	−17.8255	−0.576216
$958$	41.4158	1.33808
$959$	−2.75370	−0.0889218
$960$	5.82328	0.187945
$961$	−1.33749	−0.0431450
$962$	−7.37947	−0.237924
$963$	4.72761	0.152345
$964$	−99.4361	−3.20262
$965$	1.60770	0.0517538
$966$	−13.0916	−0.421216
$967$	11.6470	0.374541	0.187270	−	0.982308i	$-0.440036\pi$
$967$	11.6470	0.374541	0.187270	+	0.982308i	$0.440036\pi$
$968$	18.2193	0.585591
$969$	−3.33739	−0.107212
$970$	−14.9267	−0.479266
$971$	21.6071	0.693405	0.346703	−	0.937975i	$-0.387301\pi$
$971$	21.6071	0.693405	0.346703	+	0.937975i	$0.387301\pi$
$972$	−4.95855	−0.159046
$973$	9.36380	0.300190
$974$	−18.9450	−0.607036
$975$	4.75371	0.152241
$976$	106.265	3.40146
$977$	−13.9591	−0.446591	−0.223296	−	0.974751i	$-0.571682\pi$
$977$	−13.9591	−0.446591	−0.223296	+	0.974751i	$0.571682\pi$
$978$	−29.3941	−0.939920
$979$	31.5345	1.00785
$980$	−2.46081	−0.0786076
$981$	19.8139	0.632610
$982$	−19.3814	−0.618486
$983$	6.66336	0.212528	0.106264	−	0.994338i	$-0.466111\pi$
$983$	6.66336	0.212528	0.106264	+	0.994338i	$0.466111\pi$
$984$	−17.1904	−0.548010
$985$	7.07743	0.225506
$986$	−15.9736	−0.508704
$987$	−4.20399	−0.133814
$988$	16.5486	0.526481
$989$	−33.7606	−1.07353
$990$	3.85371	0.122479
$991$	0.179691	0.00570808	0.00285404	−	0.999996i	$-0.499092\pi$
$991$	0.179691	0.00570808	0.00285404	+	0.999996i	$0.499092\pi$
$992$	−68.2864	−2.16810
$993$	0.198926	0.00631271
$994$	39.7024	1.25928
$995$	12.2223	0.387473
$996$	14.5629	0.461443
$997$	−19.2462	−0.609534	−0.304767	−	0.952427i	$-0.598579\pi$
$997$	−19.2462	−0.609534	−0.304767	+	0.952427i	$0.598579\pi$
$998$	−68.7670	−2.17678
$999$	−2.79747	−0.0885081

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4641.2.a.w.1.2	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4641.2.a.w.1.2	✓	14	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:	\( N \)	\(=\)	\( 4641 = 3 \cdot 7 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4641.a (trivial)

\(f(q)\)	\(=\)	\(q-2.63791 q^{2} -1.00000 q^{3} +4.95855 q^{4} -0.496275 q^{5} +2.63791 q^{6} +1.00000 q^{7} -7.80439 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.63791 q^{2} -1.00000 q^{3} +4.95855 q^{4} -0.496275 q^{5} +2.63791 q^{6} +1.00000 q^{7} -7.80439 q^{8} +1.00000 q^{9} +1.30913 q^{10} +2.94372 q^{11} -4.95855 q^{12} +1.00000 q^{13} -2.63791 q^{14} +0.496275 q^{15} +10.6701 q^{16} +1.00000 q^{17} -2.63791 q^{18} +3.33739 q^{19} -2.46081 q^{20} -1.00000 q^{21} -7.76527 q^{22} -4.96288 q^{23} +7.80439 q^{24} -4.75371 q^{25} -2.63791 q^{26} -1.00000 q^{27} +4.95855 q^{28} +6.05542 q^{29} -1.30913 q^{30} +5.44633 q^{31} -12.5381 q^{32} -2.94372 q^{33} -2.63791 q^{34} -0.496275 q^{35} +4.95855 q^{36} +2.79747 q^{37} -8.80371 q^{38} -1.00000 q^{39} +3.87313 q^{40} -2.20266 q^{41} +2.63791 q^{42} +6.80262 q^{43} +14.5966 q^{44} -0.496275 q^{45} +13.0916 q^{46} +4.20399 q^{47} -10.6701 q^{48} +1.00000 q^{49} +12.5398 q^{50} -1.00000 q^{51} +4.95855 q^{52} -2.03579 q^{53} +2.63791 q^{54} -1.46090 q^{55} -7.80439 q^{56} -3.33739 q^{57} -15.9736 q^{58} -9.59572 q^{59} +2.46081 q^{60} +9.95911 q^{61} -14.3669 q^{62} +1.00000 q^{63} +11.7340 q^{64} -0.496275 q^{65} +7.76527 q^{66} +8.02766 q^{67} +4.95855 q^{68} +4.96288 q^{69} +1.30913 q^{70} -15.0507 q^{71} -7.80439 q^{72} -1.91488 q^{73} -7.37947 q^{74} +4.75371 q^{75} +16.5486 q^{76} +2.94372 q^{77} +2.63791 q^{78} +10.6642 q^{79} -5.29533 q^{80} +1.00000 q^{81} +5.81041 q^{82} -2.93693 q^{83} -4.95855 q^{84} -0.496275 q^{85} -17.9447 q^{86} -6.05542 q^{87} -22.9739 q^{88} +10.7125 q^{89} +1.30913 q^{90} +1.00000 q^{91} -24.6087 q^{92} -5.44633 q^{93} -11.0897 q^{94} -1.65626 q^{95} +12.5381 q^{96} -11.4020 q^{97} -2.63791 q^{98} +2.94372 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - q^{2} - 14 q^{3} + 17 q^{4} - q^{5} + q^{6} + 14 q^{7} - 6 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - q^2 - 14 * q^3 + 17 * q^4 - q^5 + q^6 + 14 * q^7 - 6 * q^8 + 14 * q^9	\( 14 q - q^{2} - 14 q^{3} + 17 q^{4} - q^{5} + q^{6} + 14 q^{7} - 6 q^{8} + 14 q^{9} + 11 q^{10} - 4 q^{11} - 17 q^{12} + 14 q^{13} - q^{14} + q^{15} + 19 q^{16} + 14 q^{17} - q^{18} + 6 q^{19} + q^{20} - 14 q^{21} + 12 q^{22} + 7 q^{23} + 6 q^{24} + 19 q^{25} - q^{26} - 14 q^{27} + 17 q^{28} - 4 q^{29} - 11 q^{30} + 31 q^{31} - 18 q^{32} + 4 q^{33} - q^{34} - q^{35} + 17 q^{36} + 2 q^{37} + 9 q^{38} - 14 q^{39} + 50 q^{40} + 4 q^{41} + q^{42} + 14 q^{43} - 8 q^{44} - q^{45} - 17 q^{46} - q^{47} - 19 q^{48} + 14 q^{49} - 3 q^{50} - 14 q^{51} + 17 q^{52} - 43 q^{53} + q^{54} + 23 q^{55} - 6 q^{56} - 6 q^{57} - 10 q^{58} + 11 q^{59} - q^{60} + 25 q^{61} - 3 q^{62} + 14 q^{63} + 36 q^{64} - q^{65} - 12 q^{66} + 11 q^{67} + 17 q^{68} - 7 q^{69} + 11 q^{70} + 20 q^{71} - 6 q^{72} + 14 q^{73} - 24 q^{74} - 19 q^{75} + 9 q^{76} - 4 q^{77} + q^{78} + 42 q^{79} + 13 q^{80} + 14 q^{81} + 2 q^{82} + 15 q^{83} - 17 q^{84} - q^{85} - 11 q^{86} + 4 q^{87} + 63 q^{88} + 21 q^{89} + 11 q^{90} + 14 q^{91} + 30 q^{92} - 31 q^{93} - 29 q^{94} + 16 q^{95} + 18 q^{96} + 15 q^{97} - q^{98} - 4 q^{99}+O(q^{100}) \) 14 * q - q^2 - 14 * q^3 + 17 * q^4 - q^5 + q^6 + 14 * q^7 - 6 * q^8 + 14 * q^9 + 11 * q^10 - 4 * q^11 - 17 * q^12 + 14 * q^13 - q^14 + q^15 + 19 * q^16 + 14 * q^17 - q^18 + 6 * q^19 + q^20 - 14 * q^21 + 12 * q^22 + 7 * q^23 + 6 * q^24 + 19 * q^25 - q^26 - 14 * q^27 + 17 * q^28 - 4 * q^29 - 11 * q^30 + 31 * q^31 - 18 * q^32 + 4 * q^33 - q^34 - q^35 + 17 * q^36 + 2 * q^37 + 9 * q^38 - 14 * q^39 + 50 * q^40 + 4 * q^41 + q^42 + 14 * q^43 - 8 * q^44 - q^45 - 17 * q^46 - q^47 - 19 * q^48 + 14 * q^49 - 3 * q^50 - 14 * q^51 + 17 * q^52 - 43 * q^53 + q^54 + 23 * q^55 - 6 * q^56 - 6 * q^57 - 10 * q^58 + 11 * q^59 - q^60 + 25 * q^61 - 3 * q^62 + 14 * q^63 + 36 * q^64 - q^65 - 12 * q^66 + 11 * q^67 + 17 * q^68 - 7 * q^69 + 11 * q^70 + 20 * q^71 - 6 * q^72 + 14 * q^73 - 24 * q^74 - 19 * q^75 + 9 * q^76 - 4 * q^77 + q^78 + 42 * q^79 + 13 * q^80 + 14 * q^81 + 2 * q^82 + 15 * q^83 - 17 * q^84 - q^85 - 11 * q^86 + 4 * q^87 + 63 * q^88 + 21 * q^89 + 11 * q^90 + 14 * q^91 + 30 * q^92 - 31 * q^93 - 29 * q^94 + 16 * q^95 + 18 * q^96 + 15 * q^97 - q^98 - 4 * q^99

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