LMFDB - Embedded newform 4641.2.a.ba.1.14

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:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - x^{16} - 29 x^{15} + 26 x^{14} + 339 x^{13} - 266 x^{12} - 2047 x^{11} + 1356 x^{10} + \cdots + 18 $ x^17 - x^16 - 29x^15 + 26x^14 + 339x^13 - 266x^12 - 2047x^11 + 1356x^10 + 6792x^9 - 3573x^8 - 12125x^7 + 4456x^6 + 10521x^5 - 1858x^4 - 3551x^3 + 34x^2 + 323*x + 18
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$2.10320$ 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)

$f(q)$	$=$	$q+2.10320 q^{2} -1.00000 q^{3} +2.42343 q^{4} +2.55731 q^{5} -2.10320 q^{6} -1.00000 q^{7} +0.890557 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.10320 q^{2} -1.00000 q^{3} +2.42343 q^{4} +2.55731 q^{5} -2.10320 q^{6} -1.00000 q^{7} +0.890557 q^{8} +1.00000 q^{9} +5.37851 q^{10} +0.862068 q^{11} -2.42343 q^{12} +1.00000 q^{13} -2.10320 q^{14} -2.55731 q^{15} -2.97385 q^{16} -1.00000 q^{17} +2.10320 q^{18} -0.0742374 q^{19} +6.19745 q^{20} +1.00000 q^{21} +1.81310 q^{22} +8.95378 q^{23} -0.890557 q^{24} +1.53981 q^{25} +2.10320 q^{26} -1.00000 q^{27} -2.42343 q^{28} +9.29539 q^{29} -5.37851 q^{30} +0.944878 q^{31} -8.03569 q^{32} -0.862068 q^{33} -2.10320 q^{34} -2.55731 q^{35} +2.42343 q^{36} -2.81108 q^{37} -0.156136 q^{38} -1.00000 q^{39} +2.27743 q^{40} +6.41627 q^{41} +2.10320 q^{42} -5.27755 q^{43} +2.08916 q^{44} +2.55731 q^{45} +18.8316 q^{46} +4.14936 q^{47} +2.97385 q^{48} +1.00000 q^{49} +3.23852 q^{50} +1.00000 q^{51} +2.42343 q^{52} +2.32094 q^{53} -2.10320 q^{54} +2.20457 q^{55} -0.890557 q^{56} +0.0742374 q^{57} +19.5500 q^{58} +7.00362 q^{59} -6.19745 q^{60} -5.43642 q^{61} +1.98726 q^{62} -1.00000 q^{63} -10.9529 q^{64} +2.55731 q^{65} -1.81310 q^{66} +3.33394 q^{67} -2.42343 q^{68} -8.95378 q^{69} -5.37851 q^{70} +7.00786 q^{71} +0.890557 q^{72} +5.51874 q^{73} -5.91226 q^{74} -1.53981 q^{75} -0.179909 q^{76} -0.862068 q^{77} -2.10320 q^{78} +14.8395 q^{79} -7.60503 q^{80} +1.00000 q^{81} +13.4947 q^{82} +15.6870 q^{83} +2.42343 q^{84} -2.55731 q^{85} -11.0997 q^{86} -9.29539 q^{87} +0.767721 q^{88} -3.30346 q^{89} +5.37851 q^{90} -1.00000 q^{91} +21.6989 q^{92} -0.944878 q^{93} +8.72692 q^{94} -0.189848 q^{95} +8.03569 q^{96} -18.5992 q^{97} +2.10320 q^{98} +0.862068 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + q^{2} - 17 q^{3} + 25 q^{4} - 4 q^{5} - q^{6} - 17 q^{7} + 6 q^{8} + 17 q^{9}+O(q^{10}) $ 17 * q + q^2 - 17 * q^3 + 25 * q^4 - 4 * q^5 - q^6 - 17 * q^7 + 6 * q^8 + 17 * q^9	\( 17 q + q^{2} - 17 q^{3} + 25 q^{4} - 4 q^{5} - q^{6} - 17 q^{7} + 6 q^{8} + 17 q^{9} - q^{10} + 4 q^{11} - 25 q^{12} + 17 q^{13} - q^{14} + 4 q^{15} + 53 q^{16} - 17 q^{17} + q^{18} + 13 q^{19} - 5 q^{20} + 17 q^{21} + 4 q^{22} + 8 q^{23} - 6 q^{24} + 37 q^{25} + q^{26} - 17 q^{27} - 25 q^{28} - 3 q^{29} + q^{30} + 10 q^{31} + 18 q^{32} - 4 q^{33} - q^{34} + 4 q^{35} + 25 q^{36} - 25 q^{38} - 17 q^{39} - 12 q^{41} + q^{42} + 29 q^{43} + 12 q^{44} - 4 q^{45} + 19 q^{46} - 4 q^{47} - 53 q^{48} + 17 q^{49} + 9 q^{50} + 17 q^{51} + 25 q^{52} - 8 q^{53} - q^{54} + 27 q^{55} - 6 q^{56} - 13 q^{57} + 2 q^{58} + 25 q^{59} + 5 q^{60} - 5 q^{61} - 37 q^{62} - 17 q^{63} + 94 q^{64} - 4 q^{65} - 4 q^{66} + 15 q^{67} - 25 q^{68} - 8 q^{69} + q^{70} + 32 q^{71} + 6 q^{72} - 15 q^{73} + 16 q^{74} - 37 q^{75} + 3 q^{76} - 4 q^{77} - q^{78} + 27 q^{79} + 41 q^{80} + 17 q^{81} - 8 q^{82} - 24 q^{83} + 25 q^{84} + 4 q^{85} + 53 q^{86} + 3 q^{87} - 9 q^{88} - 8 q^{89} - q^{90} - 17 q^{91} + 14 q^{92} - 10 q^{93} + 51 q^{94} - 9 q^{95} - 18 q^{96} - 22 q^{97} + q^{98} + 4 q^{99}+O(q^{100}) \) 17 * q + q^2 - 17 * q^3 + 25 * q^4 - 4 * q^5 - q^6 - 17 * q^7 + 6 * q^8 + 17 * q^9 - q^10 + 4 * q^11 - 25 * q^12 + 17 * q^13 - q^14 + 4 * q^15 + 53 * q^16 - 17 * q^17 + q^18 + 13 * q^19 - 5 * q^20 + 17 * q^21 + 4 * q^22 + 8 * q^23 - 6 * q^24 + 37 * q^25 + q^26 - 17 * q^27 - 25 * q^28 - 3 * q^29 + q^30 + 10 * q^31 + 18 * q^32 - 4 * q^33 - q^34 + 4 * q^35 + 25 * q^36 - 25 * q^38 - 17 * q^39 - 12 * q^41 + q^42 + 29 * q^43 + 12 * q^44 - 4 * q^45 + 19 * q^46 - 4 * q^47 - 53 * q^48 + 17 * q^49 + 9 * q^50 + 17 * q^51 + 25 * q^52 - 8 * q^53 - q^54 + 27 * q^55 - 6 * q^56 - 13 * q^57 + 2 * q^58 + 25 * q^59 + 5 * q^60 - 5 * q^61 - 37 * q^62 - 17 * q^63 + 94 * q^64 - 4 * q^65 - 4 * q^66 + 15 * q^67 - 25 * q^68 - 8 * q^69 + q^70 + 32 * q^71 + 6 * q^72 - 15 * q^73 + 16 * q^74 - 37 * q^75 + 3 * q^76 - 4 * q^77 - q^78 + 27 * q^79 + 41 * q^80 + 17 * q^81 - 8 * q^82 - 24 * q^83 + 25 * q^84 + 4 * q^85 + 53 * q^86 + 3 * q^87 - 9 * q^88 - 8 * q^89 - q^90 - 17 * q^91 + 14 * q^92 - 10 * q^93 + 51 * q^94 - 9 * q^95 - 18 * q^96 - 22 * 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 $

$2$	2.10320	1.48718	0.743592	−	0.668634i	$-0.233121\pi$
$2$	2.10320	1.48718	0.743592	+	0.668634i	$0.233121\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.42343	1.21172
$5$	2.55731	1.14366	0.571831	−	0.820372i	$-0.306233\pi$
$5$	2.55731	1.14366	0.571831	+	0.820372i	$0.306233\pi$
$6$	−2.10320	−0.858626
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0.890557	0.314860
$9$	1.00000	0.333333
$10$	5.37851	1.70083
$11$	0.862068	0.259923	0.129962	−	0.991519i	$-0.458515\pi$
$11$	0.862068	0.259923	0.129962	+	0.991519i	$0.458515\pi$
$12$	−2.42343	−0.699584
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−2.10320	−0.562103
$15$	−2.55731	−0.660293
$16$	−2.97385	−0.743461
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	2.10320	0.495728
$19$	−0.0742374	−0.0170312	−0.00851561	−	0.999964i	$-0.502711\pi$
$19$	−0.0742374	−0.0170312	−0.00851561	+	0.999964i	$0.502711\pi$
$20$	6.19745	1.38579
$21$	1.00000	0.218218
$22$	1.81310	0.386554
$23$	8.95378	1.86699	0.933496	−	0.358587i	$-0.116741\pi$
$23$	8.95378	1.86699	0.933496	+	0.358587i	$0.116741\pi$
$24$	−0.890557	−0.181784
$25$	1.53981	0.307962
$26$	2.10320	0.412471
$27$	−1.00000	−0.192450
$28$	−2.42343	−0.457985
$29$	9.29539	1.72611	0.863055	−	0.505110i	$-0.168548\pi$
$29$	9.29539	1.72611	0.863055	+	0.505110i	$0.168548\pi$
$30$	−5.37851	−0.981978
$31$	0.944878	0.169705	0.0848525	−	0.996394i	$-0.472958\pi$
$31$	0.944878	0.169705	0.0848525	+	0.996394i	$0.472958\pi$
$32$	−8.03569	−1.42052
$33$	−0.862068	−0.150067
$34$	−2.10320	−0.360695
$35$	−2.55731	−0.432263
$36$	2.42343	0.403905
$37$	−2.81108	−0.462139	−0.231070	−	0.972937i	$-0.574223\pi$
$37$	−2.81108	−0.462139	−0.231070	+	0.972937i	$0.574223\pi$
$38$	−0.156136	−0.0253286
$39$	−1.00000	−0.160128
$40$	2.27743	0.360093
$41$	6.41627	1.00205	0.501026	−	0.865432i	$-0.332956\pi$
$41$	6.41627	1.00205	0.501026	+	0.865432i	$0.332956\pi$
$42$	2.10320	0.324530
$43$	−5.27755	−0.804818	−0.402409	−	0.915460i	$-0.631827\pi$
$43$	−5.27755	−0.804818	−0.402409	+	0.915460i	$0.631827\pi$
$44$	2.08916	0.314953
$45$	2.55731	0.381221
$46$	18.8316	2.77656
$47$	4.14936	0.605247	0.302623	−	0.953110i	$-0.402138\pi$
$47$	4.14936	0.605247	0.302623	+	0.953110i	$0.402138\pi$
$48$	2.97385	0.429238
$49$	1.00000	0.142857
$50$	3.23852	0.457996
$51$	1.00000	0.140028
$52$	2.42343	0.336069
$53$	2.32094	0.318806	0.159403	−	0.987214i	$-0.449043\pi$
$53$	2.32094	0.318806	0.159403	+	0.987214i	$0.449043\pi$
$54$	−2.10320	−0.286209
$55$	2.20457	0.297264
$56$	−0.890557	−0.119006
$57$	0.0742374	0.00983298
$58$	19.5500	2.56704
$59$	7.00362	0.911794	0.455897	−	0.890033i	$-0.349319\pi$
$59$	7.00362	0.911794	0.455897	+	0.890033i	$0.349319\pi$
$60$	−6.19745	−0.800088
$61$	−5.43642	−0.696063	−0.348031	−	0.937483i	$-0.613150\pi$
$61$	−5.43642	−0.696063	−0.348031	+	0.937483i	$0.613150\pi$
$62$	1.98726	0.252383
$63$	−1.00000	−0.125988
$64$	−10.9529	−1.36912
$65$	2.55731	0.317195
$66$	−1.81310	−0.223177
$67$	3.33394	0.407306	0.203653	−	0.979043i	$-0.434719\pi$
$67$	3.33394	0.407306	0.203653	+	0.979043i	$0.434719\pi$
$68$	−2.42343	−0.293884
$69$	−8.95378	−1.07791
$70$	−5.37851	−0.642855
$71$	7.00786	0.831680	0.415840	−	0.909438i	$-0.363488\pi$
$71$	7.00786	0.831680	0.415840	+	0.909438i	$0.363488\pi$
$72$	0.890557	0.104953
$73$	5.51874	0.645920	0.322960	−	0.946413i	$-0.395322\pi$
$73$	5.51874	0.645920	0.322960	+	0.946413i	$0.395322\pi$
$74$	−5.91226	−0.687286
$75$	−1.53981	−0.177802
$76$	−0.179909	−0.0206370
$77$	−0.862068	−0.0982418
$78$	−2.10320	−0.238140
$79$	14.8395	1.66957	0.834784	−	0.550577i	$-0.185592\pi$
$79$	14.8395	1.66957	0.834784	+	0.550577i	$0.185592\pi$
$80$	−7.60503	−0.850268
$81$	1.00000	0.111111
$82$	13.4947	1.49024
$83$	15.6870	1.72187	0.860936	−	0.508713i	$-0.169879\pi$
$83$	15.6870	1.72187	0.860936	+	0.508713i	$0.169879\pi$
$84$	2.42343	0.264418
$85$	−2.55731	−0.277379
$86$	−11.0997	−1.19691
$87$	−9.29539	−0.996570
$88$	0.767721	0.0818394
$89$	−3.30346	−0.350166	−0.175083	−	0.984554i	$-0.556019\pi$
$89$	−3.30346	−0.350166	−0.175083	+	0.984554i	$0.556019\pi$
$90$	5.37851	0.566945
$91$	−1.00000	−0.104828
$92$	21.6989	2.26226
$93$	−0.944878	−0.0979793
$94$	8.72692	0.900113
$95$	−0.189848	−0.0194780
$96$	8.03569	0.820139
$97$	−18.5992	−1.88846	−0.944232	−	0.329282i	$-0.893193\pi$
$97$	−18.5992	−1.88846	−0.944232	+	0.329282i	$0.893193\pi$
$98$	2.10320	0.212455
$99$	0.862068	0.0866411
$100$	3.73162	0.373162
$101$	−4.74312	−0.471958	−0.235979	−	0.971758i	$-0.575830\pi$
$101$	−4.74312	−0.471958	−0.235979	+	0.971758i	$0.575830\pi$
$102$	2.10320	0.208247
$103$	−11.8215	−1.16481	−0.582404	−	0.812899i	$-0.697888\pi$
$103$	−11.8215	−1.16481	−0.582404	+	0.812899i	$0.697888\pi$
$104$	0.890557	0.0873263
$105$	2.55731	0.249567
$106$	4.88140	0.474123
$107$	−19.2418	−1.86018	−0.930089	−	0.367335i	$-0.880270\pi$
$107$	−19.2418	−1.86018	−0.930089	+	0.367335i	$0.880270\pi$
$108$	−2.42343	−0.233195
$109$	0.254347	0.0243620	0.0121810	−	0.999926i	$-0.496123\pi$
$109$	0.254347	0.0243620	0.0121810	+	0.999926i	$0.496123\pi$
$110$	4.63665	0.442087
$111$	2.81108	0.266816
$112$	2.97385	0.281002
$113$	7.20001	0.677320	0.338660	−	0.940909i	$-0.390026\pi$
$113$	7.20001	0.677320	0.338660	+	0.940909i	$0.390026\pi$
$114$	0.156136	0.0146235
$115$	22.8976	2.13521
$116$	22.5267	2.09155
$117$	1.00000	0.0924500
$118$	14.7300	1.35600
$119$	1.00000	0.0916698
$120$	−2.27743	−0.207900
$121$	−10.2568	−0.932440
$122$	−11.4339	−1.03517
$123$	−6.41627	−0.578535
$124$	2.28985	0.205634
$125$	−8.84876	−0.791457
$126$	−2.10320	−0.187368
$127$	12.0476	1.06905	0.534526	−	0.845152i	$-0.320490\pi$
$127$	12.0476	1.06905	0.534526	+	0.845152i	$0.320490\pi$
$128$	−6.96479	−0.615606
$129$	5.27755	0.464662
$130$	5.37851	0.471727
$131$	10.1863	0.889981	0.444991	−	0.895535i	$-0.353207\pi$
$131$	10.1863	0.889981	0.444991	+	0.895535i	$0.353207\pi$
$132$	−2.08916	−0.181838
$133$	0.0742374	0.00643720
$134$	7.01194	0.605739
$135$	−2.55731	−0.220098
$136$	−0.890557	−0.0763647
$137$	7.18969	0.614257	0.307129	−	0.951668i	$-0.400632\pi$
$137$	7.18969	0.614257	0.307129	+	0.951668i	$0.400632\pi$
$138$	−18.8316	−1.60305
$139$	12.7527	1.08167	0.540834	−	0.841129i	$-0.318109\pi$
$139$	12.7527	1.08167	0.540834	+	0.841129i	$0.318109\pi$
$140$	−6.19745	−0.523780
$141$	−4.14936	−0.349439
$142$	14.7389	1.23686
$143$	0.862068	0.0720898
$144$	−2.97385	−0.247820
$145$	23.7711	1.97409
$146$	11.6070	0.960601
$147$	−1.00000	−0.0824786
$148$	−6.81247	−0.559981
$149$	8.70255	0.712940	0.356470	−	0.934307i	$-0.383980\pi$
$149$	8.70255	0.712940	0.356470	+	0.934307i	$0.383980\pi$
$150$	−3.23852	−0.264424
$151$	5.80756	0.472612	0.236306	−	0.971679i	$-0.424063\pi$
$151$	5.80756	0.472612	0.236306	+	0.971679i	$0.424063\pi$
$152$	−0.0661127	−0.00536244
$153$	−1.00000	−0.0808452
$154$	−1.81310	−0.146104
$155$	2.41634	0.194085
$156$	−2.42343	−0.194030
$157$	−3.38277	−0.269974	−0.134987	−	0.990847i	$-0.543099\pi$
$157$	−3.38277	−0.269974	−0.134987	+	0.990847i	$0.543099\pi$
$158$	31.2103	2.48296
$159$	−2.32094	−0.184063
$160$	−20.5497	−1.62460
$161$	−8.95378	−0.705657
$162$	2.10320	0.165243
$163$	−13.5639	−1.06241	−0.531204	−	0.847244i	$-0.678260\pi$
$163$	−13.5639	−1.06241	−0.531204	+	0.847244i	$0.678260\pi$
$164$	15.5494	1.21420
$165$	−2.20457	−0.171626
$166$	32.9928	2.56074
$167$	7.51109	0.581226	0.290613	−	0.956841i	$-0.406141\pi$
$167$	7.51109	0.581226	0.290613	+	0.956841i	$0.406141\pi$
$168$	0.890557	0.0687080
$169$	1.00000	0.0769231
$170$	−5.37851	−0.412513
$171$	−0.0742374	−0.00567708
$172$	−12.7898	−0.975211
$173$	−16.3798	−1.24533	−0.622666	−	0.782488i	$-0.713950\pi$
$173$	−16.3798	−1.24533	−0.622666	+	0.782488i	$0.713950\pi$
$174$	−19.5500	−1.48208
$175$	−1.53981	−0.116399
$176$	−2.56366	−0.193243
$177$	−7.00362	−0.526424
$178$	−6.94781	−0.520761
$179$	−3.33314	−0.249131	−0.124565	−	0.992211i	$-0.539754\pi$
$179$	−3.33314	−0.249131	−0.124565	+	0.992211i	$0.539754\pi$
$180$	6.19745	0.461931
$181$	−10.3674	−0.770606	−0.385303	−	0.922790i	$-0.625903\pi$
$181$	−10.3674	−0.770606	−0.385303	+	0.922790i	$0.625903\pi$
$182$	−2.10320	−0.155899
$183$	5.43642	0.401872
$184$	7.97386	0.587840
$185$	−7.18880	−0.528531
$186$	−1.98726	−0.145713
$187$	−0.862068	−0.0630407
$188$	10.0557	0.733387
$189$	1.00000	0.0727393
$190$	−0.399287	−0.0289673
$191$	4.14069	0.299610	0.149805	−	0.988716i	$-0.452135\pi$
$191$	4.14069	0.299610	0.149805	+	0.988716i	$0.452135\pi$
$192$	10.9529	0.790460
$193$	−6.73846	−0.485045	−0.242523	−	0.970146i	$-0.577975\pi$
$193$	−6.73846	−0.485045	−0.242523	+	0.970146i	$0.577975\pi$
$194$	−39.1178	−2.80849
$195$	−2.55731	−0.183132
$196$	2.42343	0.173102
$197$	−2.12700	−0.151543	−0.0757713	−	0.997125i	$-0.524142\pi$
$197$	−2.12700	−0.151543	−0.0757713	+	0.997125i	$0.524142\pi$
$198$	1.81310	0.128851
$199$	−18.2598	−1.29440	−0.647201	−	0.762319i	$-0.724061\pi$
$199$	−18.2598	−1.29440	−0.647201	+	0.762319i	$0.724061\pi$
$200$	1.37129	0.0969648
$201$	−3.33394	−0.235158
$202$	−9.97570	−0.701888
$203$	−9.29539	−0.652408
$204$	2.42343	0.169674
$205$	16.4084	1.14601
$206$	−24.8630	−1.73228
$207$	8.95378	0.622331
$208$	−2.97385	−0.206199
$209$	−0.0639977	−0.00442681
$210$	5.37851	0.371153
$211$	7.68689	0.529187	0.264594	−	0.964360i	$-0.414762\pi$
$211$	7.68689	0.529187	0.264594	+	0.964360i	$0.414762\pi$
$212$	5.62465	0.386302
$213$	−7.00786	−0.480171
$214$	−40.4693	−2.76643
$215$	−13.4963	−0.920440
$216$	−0.890557	−0.0605947
$217$	−0.944878	−0.0641425
$218$	0.534941	0.0362308
$219$	−5.51874	−0.372922
$220$	5.34263	0.360200
$221$	−1.00000	−0.0672673
$222$	5.91226	0.396805
$223$	15.9490	1.06802	0.534012	−	0.845477i	$-0.320684\pi$
$223$	15.9490	1.06802	0.534012	+	0.845477i	$0.320684\pi$
$224$	8.03569	0.536907
$225$	1.53981	0.102654
$226$	15.1430	1.00730
$227$	−6.52105	−0.432817	−0.216409	−	0.976303i	$-0.569434\pi$
$227$	−6.52105	−0.432817	−0.216409	+	0.976303i	$0.569434\pi$
$228$	0.179909	0.0119148
$229$	−24.3194	−1.60707	−0.803535	−	0.595258i	$-0.797050\pi$
$229$	−24.3194	−1.60707	−0.803535	+	0.595258i	$0.797050\pi$
$230$	48.1580	3.17545
$231$	0.862068	0.0567199
$232$	8.27807	0.543482
$233$	1.23740	0.0810645	0.0405323	−	0.999178i	$-0.487095\pi$
$233$	1.23740	0.0810645	0.0405323	+	0.999178i	$0.487095\pi$
$234$	2.10320	0.137490
$235$	10.6112	0.692198
$236$	16.9728	1.10483
$237$	−14.8395	−0.963926
$238$	2.10320	0.136330
$239$	3.74530	0.242263	0.121132	−	0.992636i	$-0.461348\pi$
$239$	3.74530	0.242263	0.121132	+	0.992636i	$0.461348\pi$
$240$	7.60503	0.490903
$241$	−29.8143	−1.92051	−0.960254	−	0.279129i	$-0.909954\pi$
$241$	−29.8143	−1.92051	−0.960254	+	0.279129i	$0.909954\pi$
$242$	−21.5721	−1.38671
$243$	−1.00000	−0.0641500
$244$	−13.1748	−0.843430
$245$	2.55731	0.163380
$246$	−13.4947	−0.860388
$247$	−0.0742374	−0.00472361
$248$	0.841468	0.0534333
$249$	−15.6870	−0.994123
$250$	−18.6107	−1.17704
$251$	25.2531	1.59396	0.796981	−	0.604004i	$-0.206429\pi$
$251$	25.2531	1.59396	0.796981	+	0.604004i	$0.206429\pi$
$252$	−2.42343	−0.152662
$253$	7.71877	0.485275
$254$	25.3385	1.58988
$255$	2.55731	0.160145
$256$	7.25757	0.453598
$257$	−19.8286	−1.23688	−0.618439	−	0.785833i	$-0.712234\pi$
$257$	−19.8286	−1.23688	−0.618439	+	0.785833i	$0.712234\pi$
$258$	11.0997	0.691038
$259$	2.81108	0.174672
$260$	6.19745	0.384350
$261$	9.29539	0.575370
$262$	21.4238	1.32357
$263$	29.6351	1.82738	0.913689	−	0.406415i	$-0.133221\pi$
$263$	29.6351	1.82738	0.913689	+	0.406415i	$0.133221\pi$
$264$	−0.767721	−0.0472500
$265$	5.93536	0.364606
$266$	0.156136	0.00957330
$267$	3.30346	0.202168
$268$	8.07958	0.493539
$269$	−3.43195	−0.209250	−0.104625	−	0.994512i	$-0.533364\pi$
$269$	−3.43195	−0.209250	−0.104625	+	0.994512i	$0.533364\pi$
$270$	−5.37851	−0.327326
$271$	0.527723	0.0320569	0.0160284	−	0.999872i	$-0.494898\pi$
$271$	0.527723	0.0320569	0.0160284	+	0.999872i	$0.494898\pi$
$272$	2.97385	0.180316
$273$	1.00000	0.0605228
$274$	15.1213	0.913513
$275$	1.32742	0.0800465
$276$	−21.6989	−1.30612
$277$	2.38511	0.143307	0.0716536	−	0.997430i	$-0.477172\pi$
$277$	2.38511	0.143307	0.0716536	+	0.997430i	$0.477172\pi$
$278$	26.8214	1.60864
$279$	0.944878	0.0565683
$280$	−2.27743	−0.136102
$281$	25.0457	1.49410	0.747052	−	0.664766i	$-0.231469\pi$
$281$	25.0457	1.49410	0.747052	+	0.664766i	$0.231469\pi$
$282$	−8.72692	−0.519681
$283$	−19.5691	−1.16326	−0.581632	−	0.813452i	$-0.697586\pi$
$283$	−19.5691	−1.16326	−0.581632	+	0.813452i	$0.697586\pi$
$284$	16.9831	1.00776
$285$	0.189848	0.0112456
$286$	1.81310	0.107211
$287$	−6.41627	−0.378740
$288$	−8.03569	−0.473508
$289$	1.00000	0.0588235
$290$	49.9953	2.93583
$291$	18.5992	1.09030
$292$	13.3743	0.782671
$293$	14.6347	0.854971	0.427485	−	0.904022i	$-0.359400\pi$
$293$	14.6347	0.854971	0.427485	+	0.904022i	$0.359400\pi$
$294$	−2.10320	−0.122661
$295$	17.9104	1.04278
$296$	−2.50343	−0.145509
$297$	−0.862068	−0.0500223
$298$	18.3032	1.06027
$299$	8.95378	0.517811
$300$	−3.73162	−0.215445
$301$	5.27755	0.304193
$302$	12.2144	0.702861
$303$	4.74312	0.272485
$304$	0.220771	0.0126621
$305$	−13.9026	−0.796060
$306$	−2.10320	−0.120232
$307$	−24.0751	−1.37404	−0.687021	−	0.726638i	$-0.741082\pi$
$307$	−24.0751	−1.37404	−0.687021	+	0.726638i	$0.741082\pi$
$308$	−2.08916	−0.119041
$309$	11.8215	0.672503
$310$	5.08204	0.288640
$311$	−9.55358	−0.541734	−0.270867	−	0.962617i	$-0.587310\pi$
$311$	−9.55358	−0.541734	−0.270867	+	0.962617i	$0.587310\pi$
$312$	−0.890557	−0.0504179
$313$	10.1783	0.575313	0.287657	−	0.957734i	$-0.407124\pi$
$313$	10.1783	0.575313	0.287657	+	0.957734i	$0.407124\pi$
$314$	−7.11462	−0.401501
$315$	−2.55731	−0.144088
$316$	35.9624	2.02304
$317$	−19.4270	−1.09113	−0.545565	−	0.838069i	$-0.683685\pi$
$317$	−19.4270	−1.09113	−0.545565	+	0.838069i	$0.683685\pi$
$318$	−4.88140	−0.273735
$319$	8.01326	0.448656
$320$	−28.0100	−1.56581
$321$	19.2418	1.07397
$322$	−18.8316	−1.04944
$323$	0.0742374	0.00413068
$324$	2.42343	0.134635
$325$	1.53981	0.0854133
$326$	−28.5276	−1.58000
$327$	−0.254347	−0.0140654
$328$	5.71405	0.315506
$329$	−4.14936	−0.228762
$330$	−4.63665	−0.255239
$331$	−25.1861	−1.38435	−0.692176	−	0.721729i	$-0.743348\pi$
$331$	−25.1861	−1.38435	−0.692176	+	0.721729i	$0.743348\pi$
$332$	38.0164	2.08642
$333$	−2.81108	−0.154046
$334$	15.7973	0.864390
$335$	8.52591	0.465820
$336$	−2.97385	−0.162237
$337$	21.0739	1.14797	0.573985	−	0.818866i	$-0.305397\pi$
$337$	21.0739	1.14797	0.573985	+	0.818866i	$0.305397\pi$
$338$	2.10320	0.114399
$339$	−7.20001	−0.391051
$340$	−6.19745	−0.336104
$341$	0.814549	0.0441103
$342$	−0.156136	−0.00844285
$343$	−1.00000	−0.0539949
$344$	−4.69996	−0.253405
$345$	−22.8976	−1.23276
$346$	−34.4499	−1.85204
$347$	30.8270	1.65488	0.827441	−	0.561553i	$-0.189796\pi$
$347$	30.8270	1.65488	0.827441	+	0.561553i	$0.189796\pi$
$348$	−22.5267	−1.20756
$349$	15.1882	0.813004	0.406502	−	0.913650i	$-0.366748\pi$
$349$	15.1882	0.813004	0.406502	+	0.913650i	$0.366748\pi$
$350$	−3.23852	−0.173106
$351$	−1.00000	−0.0533761
$352$	−6.92732	−0.369227
$353$	−8.47137	−0.450886	−0.225443	−	0.974256i	$-0.572383\pi$
$353$	−8.47137	−0.450886	−0.225443	+	0.974256i	$0.572383\pi$
$354$	−14.7300	−0.782890
$355$	17.9212	0.951161
$356$	−8.00570	−0.424301
$357$	−1.00000	−0.0529256
$358$	−7.01025	−0.370503
$359$	−16.0896	−0.849177	−0.424588	−	0.905386i	$-0.639581\pi$
$359$	−16.0896	−0.849177	−0.424588	+	0.905386i	$0.639581\pi$
$360$	2.27743	0.120031
$361$	−18.9945	−0.999710
$362$	−21.8048	−1.14603
$363$	10.2568	0.538344
$364$	−2.42343	−0.127022
$365$	14.1131	0.738714
$366$	11.4339	0.597657
$367$	−12.0724	−0.630174	−0.315087	−	0.949063i	$-0.602034\pi$
$367$	−12.0724	−0.630174	−0.315087	+	0.949063i	$0.602034\pi$
$368$	−26.6272	−1.38804
$369$	6.41627	0.334018
$370$	−15.1195	−0.786023
$371$	−2.32094	−0.120497
$372$	−2.28985	−0.118723
$373$	−1.96270	−0.101625	−0.0508125	−	0.998708i	$-0.516181\pi$
$373$	−1.96270	−0.101625	−0.0508125	+	0.998708i	$0.516181\pi$
$374$	−1.81310	−0.0937531
$375$	8.84876	0.456948
$376$	3.69525	0.190568
$377$	9.29539	0.478737
$378$	2.10320	0.108177
$379$	22.6014	1.16095	0.580477	−	0.814276i	$-0.302866\pi$
$379$	22.6014	1.16095	0.580477	+	0.814276i	$0.302866\pi$
$380$	−0.460083	−0.0236017
$381$	−12.0476	−0.617217
$382$	8.70869	0.445575
$383$	−6.94966	−0.355111	−0.177556	−	0.984111i	$-0.556819\pi$
$383$	−6.94966	−0.355111	−0.177556	+	0.984111i	$0.556819\pi$
$384$	6.96479	0.355420
$385$	−2.20457	−0.112355
$386$	−14.1723	−0.721351
$387$	−5.27755	−0.268273
$388$	−45.0739	−2.28828
$389$	2.40583	0.121980	0.0609901	−	0.998138i	$-0.480574\pi$
$389$	2.40583	0.121980	0.0609901	+	0.998138i	$0.480574\pi$
$390$	−5.37851	−0.272352
$391$	−8.95378	−0.452812
$392$	0.890557	0.0449799
$393$	−10.1863	−0.513831
$394$	−4.47350	−0.225372
$395$	37.9490	1.90942
$396$	2.08916	0.104984
$397$	−33.9492	−1.70386	−0.851931	−	0.523655i	$-0.824568\pi$
$397$	−33.9492	−1.70386	−0.851931	+	0.523655i	$0.824568\pi$
$398$	−38.4039	−1.92501
$399$	−0.0742374	−0.00371652
$400$	−4.57916	−0.228958
$401$	25.9963	1.29819	0.649097	−	0.760705i	$-0.275147\pi$
$401$	25.9963	1.29819	0.649097	+	0.760705i	$0.275147\pi$
$402$	−7.01194	−0.349724
$403$	0.944878	0.0470677
$404$	−11.4946	−0.571878
$405$	2.55731	0.127074
$406$	−19.5500	−0.970251
$407$	−2.42335	−0.120121
$408$	0.890557	0.0440892
$409$	21.3995	1.05814	0.529068	−	0.848579i	$-0.322542\pi$
$409$	21.3995	1.05814	0.529068	+	0.848579i	$0.322542\pi$
$410$	34.5100	1.70433
$411$	−7.18969	−0.354641
$412$	−28.6486	−1.41142
$413$	−7.00362	−0.344626
$414$	18.8316	0.925520
$415$	40.1165	1.96924
$416$	−8.03569	−0.393982
$417$	−12.7527	−0.624502
$418$	−0.134600	−0.00658349
$419$	−11.9038	−0.581538	−0.290769	−	0.956793i	$-0.593911\pi$
$419$	−11.9038	−0.581538	−0.290769	+	0.956793i	$0.593911\pi$
$420$	6.19745	0.302405
$421$	9.11906	0.444436	0.222218	−	0.974997i	$-0.428670\pi$
$421$	9.11906	0.444436	0.222218	+	0.974997i	$0.428670\pi$
$422$	16.1670	0.786999
$423$	4.14936	0.201749
$424$	2.06693	0.100379
$425$	−1.53981	−0.0746918
$426$	−14.7389	−0.714102
$427$	5.43642	0.263087
$428$	−46.6312	−2.25401
$429$	−0.862068	−0.0416211
$430$	−28.3854	−1.36886
$431$	−11.6531	−0.561310	−0.280655	−	0.959809i	$-0.590552\pi$
$431$	−11.6531	−0.561310	−0.280655	+	0.959809i	$0.590552\pi$
$432$	2.97385	0.143079
$433$	−26.4076	−1.26907	−0.634534	−	0.772895i	$-0.718808\pi$
$433$	−26.4076	−1.26907	−0.634534	+	0.772895i	$0.718808\pi$
$434$	−1.98726	−0.0953916
$435$	−23.7711	−1.13974
$436$	0.616392	0.0295198
$437$	−0.664706	−0.0317972
$438$	−11.6070	−0.554604
$439$	−1.11867	−0.0533910	−0.0266955	−	0.999644i	$-0.508498\pi$
$439$	−1.11867	−0.0533910	−0.0266955	+	0.999644i	$0.508498\pi$
$440$	1.96330	0.0935965
$441$	1.00000	0.0476190
$442$	−2.10320	−0.100039
$443$	−22.0067	−1.04557	−0.522786	−	0.852464i	$-0.675107\pi$
$443$	−22.0067	−1.04557	−0.522786	+	0.852464i	$0.675107\pi$
$444$	6.81247	0.323305
$445$	−8.44795	−0.400471
$446$	33.5439	1.58835
$447$	−8.70255	−0.411616
$448$	10.9529	0.517478
$449$	25.7364	1.21457	0.607287	−	0.794482i	$-0.292258\pi$
$449$	25.7364	1.21457	0.607287	+	0.794482i	$0.292258\pi$
$450$	3.23852	0.152665
$451$	5.53126	0.260457
$452$	17.4487	0.820719
$453$	−5.80756	−0.272863
$454$	−13.7150	−0.643679
$455$	−2.55731	−0.119888
$456$	0.0661127	0.00309601
$457$	25.0514	1.17185	0.585927	−	0.810364i	$-0.300730\pi$
$457$	25.0514	1.17185	0.585927	+	0.810364i	$0.300730\pi$
$458$	−51.1484	−2.39001
$459$	1.00000	0.0466760
$460$	55.4906	2.58726
$461$	0.166151	0.00773842	0.00386921	−	0.999993i	$-0.498768\pi$
$461$	0.166151	0.00773842	0.00386921	+	0.999993i	$0.498768\pi$
$462$	1.81310	0.0843530
$463$	−39.0096	−1.81293	−0.906466	−	0.422280i	$-0.861230\pi$
$463$	−39.0096	−1.81293	−0.906466	+	0.422280i	$0.861230\pi$
$464$	−27.6430	−1.28330
$465$	−2.41634	−0.112055
$466$	2.60249	0.120558
$467$	32.5153	1.50463	0.752314	−	0.658805i	$-0.228938\pi$
$467$	32.5153	1.50463	0.752314	+	0.658805i	$0.228938\pi$
$468$	2.42343	0.112023
$469$	−3.33394	−0.153947
$470$	22.3174	1.02943
$471$	3.38277	0.155870
$472$	6.23713	0.287087
$473$	−4.54961	−0.209191
$474$	−31.2103	−1.43354
$475$	−0.114312	−0.00524497
$476$	2.42343	0.111078
$477$	2.32094	0.106269
$478$	7.87709	0.360290
$479$	1.44736	0.0661317	0.0330659	−	0.999453i	$-0.489473\pi$
$479$	1.44736	0.0661317	0.0330659	+	0.999453i	$0.489473\pi$
$480$	20.5497	0.937962
$481$	−2.81108	−0.128174
$482$	−62.7053	−2.85615
$483$	8.95378	0.407411
$484$	−24.8567	−1.12985
$485$	−47.5639	−2.15976
$486$	−2.10320	−0.0954029
$487$	−18.1541	−0.822640	−0.411320	−	0.911491i	$-0.634932\pi$
$487$	−18.1541	−0.822640	−0.411320	+	0.911491i	$0.634932\pi$
$488$	−4.84145	−0.219162
$489$	13.5639	0.613382
$490$	5.37851	0.242976
$491$	−17.0176	−0.767991	−0.383996	−	0.923335i	$-0.625452\pi$
$491$	−17.0176	−0.767991	−0.383996	+	0.923335i	$0.625452\pi$
$492$	−15.5494	−0.701020
$493$	−9.29539	−0.418643
$494$	−0.156136	−0.00702488
$495$	2.20457	0.0990881
$496$	−2.80992	−0.126169
$497$	−7.00786	−0.314346
$498$	−32.9928	−1.47844
$499$	−36.2702	−1.62368	−0.811839	−	0.583881i	$-0.801533\pi$
$499$	−36.2702	−1.62368	−0.811839	+	0.583881i	$0.801533\pi$
$500$	−21.4444	−0.959021
$501$	−7.51109	−0.335571
$502$	53.1122	2.37052
$503$	−29.2525	−1.30430	−0.652152	−	0.758088i	$-0.726134\pi$
$503$	−29.2525	−1.30430	−0.652152	+	0.758088i	$0.726134\pi$
$504$	−0.890557	−0.0396686
$505$	−12.1296	−0.539760
$506$	16.2341	0.721693
$507$	−1.00000	−0.0444116
$508$	29.1965	1.29539
$509$	−38.3660	−1.70054	−0.850272	−	0.526344i	$-0.823562\pi$
$509$	−38.3660	−1.70054	−0.850272	+	0.526344i	$0.823562\pi$
$510$	5.37851	0.238165
$511$	−5.51874	−0.244135
$512$	29.1937	1.29019
$513$	0.0742374	0.00327766
$514$	−41.7035	−1.83946
$515$	−30.2312	−1.33215
$516$	12.7898	0.563038
$517$	3.57704	0.157318
$518$	5.91226	0.259770
$519$	16.3798	0.718993
$520$	2.27743	0.0998718
$521$	−9.71358	−0.425560	−0.212780	−	0.977100i	$-0.568252\pi$
$521$	−9.71358	−0.425560	−0.212780	+	0.977100i	$0.568252\pi$
$522$	19.5500	0.855681
$523$	22.3778	0.978512	0.489256	−	0.872140i	$-0.337268\pi$
$523$	22.3778	0.978512	0.489256	+	0.872140i	$0.337268\pi$
$524$	24.6858	1.07840
$525$	1.53981	0.0672028
$526$	62.3284	2.71765
$527$	−0.944878	−0.0411595
$528$	2.56366	0.111569
$529$	57.1702	2.48566
$530$	12.4832	0.542237
$531$	7.00362	0.303931
$532$	0.179909	0.00780005
$533$	6.41627	0.277919
$534$	6.94781	0.300661
$535$	−49.2072	−2.12741
$536$	2.96907	0.128244
$537$	3.33314	0.143836
$538$	−7.21807	−0.311193
$539$	0.862068	0.0371319
$540$	−6.19745	−0.266696
$541$	10.1099	0.434656	0.217328	−	0.976099i	$-0.430266\pi$
$541$	10.1099	0.434656	0.217328	+	0.976099i	$0.430266\pi$
$542$	1.10990	0.0476745
$543$	10.3674	0.444909
$544$	8.03569	0.344527
$545$	0.650442	0.0278619
$546$	2.10320	0.0900085
$547$	−18.0352	−0.771129	−0.385565	−	0.922681i	$-0.625993\pi$
$547$	−18.0352	−0.771129	−0.385565	+	0.922681i	$0.625993\pi$
$548$	17.4237	0.744305
$549$	−5.43642	−0.232021
$550$	2.79183	0.119044
$551$	−0.690065	−0.0293978
$552$	−7.97386	−0.339390
$553$	−14.8395	−0.631038
$554$	5.01635	0.213124
$555$	7.18880	0.305148
$556$	30.9053	1.31067
$557$	−26.0104	−1.10209	−0.551047	−	0.834474i	$-0.685772\pi$
$557$	−26.0104	−1.10209	−0.551047	+	0.834474i	$0.685772\pi$
$558$	1.98726	0.0841275
$559$	−5.27755	−0.223216
$560$	7.60503	0.321371
$561$	0.862068	0.0363966
$562$	52.6761	2.22201
$563$	−40.5220	−1.70780	−0.853899	−	0.520440i	$-0.825768\pi$
$563$	−40.5220	−1.70780	−0.853899	+	0.520440i	$0.825768\pi$
$564$	−10.0557	−0.423421
$565$	18.4126	0.774625
$566$	−41.1577	−1.72999
$567$	−1.00000	−0.0419961
$568$	6.24090	0.261862
$569$	−21.7940	−0.913651	−0.456825	−	0.889556i	$-0.651014\pi$
$569$	−21.7940	−0.913651	−0.456825	+	0.889556i	$0.651014\pi$
$570$	0.399287	0.0167243
$571$	9.19317	0.384722	0.192361	−	0.981324i	$-0.438385\pi$
$571$	9.19317	0.384722	0.192361	+	0.981324i	$0.438385\pi$
$572$	2.08916	0.0873523
$573$	−4.14069	−0.172980
$574$	−13.4947	−0.563256
$575$	13.7871	0.574963
$576$	−10.9529	−0.456372
$577$	−15.8494	−0.659821	−0.329911	−	0.944012i	$-0.607019\pi$
$577$	−15.8494	−0.659821	−0.329911	+	0.944012i	$0.607019\pi$
$578$	2.10320	0.0874814
$579$	6.73846	0.280041
$580$	57.6077	2.39203
$581$	−15.6870	−0.650807
$582$	39.1178	1.62148
$583$	2.00081	0.0828652
$584$	4.91476	0.203374
$585$	2.55731	0.105732
$586$	30.7797	1.27150
$587$	34.7796	1.43551	0.717755	−	0.696296i	$-0.245170\pi$
$587$	34.7796	1.43551	0.717755	+	0.696296i	$0.245170\pi$
$588$	−2.42343	−0.0999406
$589$	−0.0701453	−0.00289029
$590$	37.6691	1.55081
$591$	2.12700	0.0874932
$592$	8.35973	0.343583
$593$	2.31691	0.0951440	0.0475720	−	0.998868i	$-0.484852\pi$
$593$	2.31691	0.0951440	0.0475720	+	0.998868i	$0.484852\pi$
$594$	−1.81310	−0.0743923
$595$	2.55731	0.104839
$596$	21.0900	0.863881
$597$	18.2598	0.747324
$598$	18.8316	0.770079
$599$	−33.3363	−1.36208	−0.681042	−	0.732244i	$-0.738473\pi$
$599$	−33.3363	−1.36208	−0.681042	+	0.732244i	$0.738473\pi$
$600$	−1.37129	−0.0559826
$601$	−27.9150	−1.13868	−0.569338	−	0.822104i	$-0.692800\pi$
$601$	−27.9150	−1.13868	−0.569338	+	0.822104i	$0.692800\pi$
$602$	11.0997	0.452390
$603$	3.33394	0.135769
$604$	14.0742	0.572671
$605$	−26.2299	−1.06640
$606$	9.97570	0.405235
$607$	−6.27334	−0.254627	−0.127314	−	0.991863i	$-0.540635\pi$
$607$	−6.27334	−0.254627	−0.127314	+	0.991863i	$0.540635\pi$
$608$	0.596549	0.0241933
$609$	9.29539	0.376668
$610$	−29.2399	−1.18389
$611$	4.14936	0.167865
$612$	−2.42343	−0.0979614
$613$	12.2323	0.494058	0.247029	−	0.969008i	$-0.420546\pi$
$613$	12.2323	0.494058	0.247029	+	0.969008i	$0.420546\pi$
$614$	−50.6347	−2.04345
$615$	−16.4084	−0.661649
$616$	−0.767721	−0.0309324
$617$	8.75606	0.352506	0.176253	−	0.984345i	$-0.443602\pi$
$617$	8.75606	0.352506	0.176253	+	0.984345i	$0.443602\pi$
$618$	24.8630	1.00013
$619$	−33.2149	−1.33502	−0.667509	−	0.744601i	$-0.732640\pi$
$619$	−33.2149	−1.33502	−0.667509	+	0.744601i	$0.732640\pi$
$620$	5.85583	0.235176
$621$	−8.95378	−0.359303
$622$	−20.0930	−0.805657
$623$	3.30346	0.132350
$624$	2.97385	0.119049
$625$	−30.3280	−1.21312
$626$	21.4070	0.855596
$627$	0.0639977	0.00255582
$628$	−8.19790	−0.327132
$629$	2.81108	0.112085
$630$	−5.37851	−0.214285
$631$	−21.5858	−0.859319	−0.429659	−	0.902991i	$-0.641366\pi$
$631$	−21.5858	−0.859319	−0.429659	+	0.902991i	$0.641366\pi$
$632$	13.2154	0.525680
$633$	−7.68689	−0.305526
$634$	−40.8588	−1.62271
$635$	30.8094	1.22263
$636$	−5.62465	−0.223032
$637$	1.00000	0.0396214
$638$	16.8534	0.667234
$639$	7.00786	0.277227
$640$	−17.8111	−0.704045
$641$	2.39094	0.0944364	0.0472182	−	0.998885i	$-0.484964\pi$
$641$	2.39094	0.0944364	0.0472182	+	0.998885i	$0.484964\pi$
$642$	40.4693	1.59720
$643$	19.5101	0.769402	0.384701	−	0.923041i	$-0.374305\pi$
$643$	19.5101	0.769402	0.384701	+	0.923041i	$0.374305\pi$
$644$	−21.6989	−0.855055
$645$	13.4963	0.531416
$646$	0.156136	0.00614308
$647$	−33.7235	−1.32581	−0.662903	−	0.748705i	$-0.730676\pi$
$647$	−33.7235	−1.32581	−0.662903	+	0.748705i	$0.730676\pi$
$648$	0.890557	0.0349844
$649$	6.03760	0.236997
$650$	3.23852	0.127025
$651$	0.944878	0.0370327
$652$	−32.8712	−1.28734
$653$	4.13161	0.161682	0.0808412	−	0.996727i	$-0.474239\pi$
$653$	4.13161	0.161682	0.0808412	+	0.996727i	$0.474239\pi$
$654$	−0.534941	−0.0209178
$655$	26.0495	1.01784
$656$	−19.0810	−0.744987
$657$	5.51874	0.215307
$658$	−8.72692	−0.340211
$659$	23.4585	0.913815	0.456908	−	0.889514i	$-0.348957\pi$
$659$	23.4585	0.913815	0.456908	+	0.889514i	$0.348957\pi$
$660$	−5.34263	−0.207961
$661$	13.2653	0.515961	0.257980	−	0.966150i	$-0.416943\pi$
$661$	13.2653	0.515961	0.257980	+	0.966150i	$0.416943\pi$
$662$	−52.9712	−2.05878
$663$	1.00000	0.0388368
$664$	13.9702	0.542148
$665$	0.189848	0.00736198
$666$	−5.91226	−0.229095
$667$	83.2289	3.22263
$668$	18.2026	0.704280
$669$	−15.9490	−0.616624
$670$	17.9317	0.692761
$671$	−4.68657	−0.180923
$672$	−8.03569	−0.309984
$673$	−22.0640	−0.850506	−0.425253	−	0.905075i	$-0.639815\pi$
$673$	−22.0640	−0.850506	−0.425253	+	0.905075i	$0.639815\pi$
$674$	44.3226	1.70724
$675$	−1.53981	−0.0592673
$676$	2.42343	0.0932089
$677$	−3.40612	−0.130908	−0.0654540	−	0.997856i	$-0.520850\pi$
$677$	−3.40612	−0.130908	−0.0654540	+	0.997856i	$0.520850\pi$
$678$	−15.1430	−0.581565
$679$	18.5992	0.713772
$680$	−2.27743	−0.0873353
$681$	6.52105	0.249887
$682$	1.71316	0.0656001
$683$	40.9406	1.56655	0.783275	−	0.621675i	$-0.213548\pi$
$683$	40.9406	1.56655	0.783275	+	0.621675i	$0.213548\pi$
$684$	−0.179909	−0.00687900
$685$	18.3862	0.702502
$686$	−2.10320	−0.0803004
$687$	24.3194	0.927842
$688$	15.6946	0.598351
$689$	2.32094	0.0884209
$690$	−48.1580	−1.83334
$691$	−8.57834	−0.326335	−0.163168	−	0.986598i	$-0.552171\pi$
$691$	−8.57834	−0.326335	−0.163168	+	0.986598i	$0.552171\pi$
$692$	−39.6953	−1.50899
$693$	−0.862068	−0.0327473
$694$	64.8352	2.46111
$695$	32.6125	1.23706
$696$	−8.27807	−0.313780
$697$	−6.41627	−0.243033
$698$	31.9437	1.20909
$699$	−1.23740	−0.0468026
$700$	−3.73162	−0.141042
$701$	−32.9388	−1.24408	−0.622041	−	0.782984i	$-0.713696\pi$
$701$	−32.9388	−1.24408	−0.622041	+	0.782984i	$0.713696\pi$
$702$	−2.10320	−0.0793800
$703$	0.208688	0.00787080
$704$	−9.44218	−0.355866
$705$	−10.6112	−0.399641
$706$	−17.8169	−0.670550
$707$	4.74312	0.178383
$708$	−16.9728	−0.637877
$709$	−42.3783	−1.59155	−0.795775	−	0.605592i	$-0.792936\pi$
$709$	−42.3783	−1.59155	−0.795775	+	0.605592i	$0.792936\pi$
$710$	37.6919	1.41455
$711$	14.8395	0.556523
$712$	−2.94192	−0.110253
$713$	8.46023	0.316838
$714$	−2.10320	−0.0787101
$715$	2.20457	0.0824463
$716$	−8.07764	−0.301876
$717$	−3.74530	−0.139871
$718$	−33.8396	−1.26288
$719$	13.4610	0.502009	0.251004	−	0.967986i	$-0.419239\pi$
$719$	13.4610	0.502009	0.251004	+	0.967986i	$0.419239\pi$
$720$	−7.60503	−0.283423
$721$	11.8215	0.440256
$722$	−39.9491	−1.48675
$723$	29.8143	1.10881
$724$	−25.1248	−0.933755
$725$	14.3131	0.531576
$726$	21.5721	0.800617
$727$	1.48581	0.0551056	0.0275528	−	0.999620i	$-0.491229\pi$
$727$	1.48581	0.0551056	0.0275528	+	0.999620i	$0.491229\pi$
$728$	−0.890557	−0.0330062
$729$	1.00000	0.0370370
$730$	29.6826	1.09860
$731$	5.27755	0.195197
$732$	13.1748	0.486954
$733$	−29.8443	−1.10232	−0.551162	−	0.834398i	$-0.685816\pi$
$733$	−29.8443	−1.10232	−0.551162	+	0.834398i	$0.685816\pi$
$734$	−25.3906	−0.937184
$735$	−2.55731	−0.0943276
$736$	−71.9498	−2.65211
$737$	2.87409	0.105868
$738$	13.4947	0.496745
$739$	−9.41601	−0.346373	−0.173187	−	0.984889i	$-0.555406\pi$
$739$	−9.41601	−0.346373	−0.173187	+	0.984889i	$0.555406\pi$
$740$	−17.4216	−0.640429
$741$	0.0742374	0.00272718
$742$	−4.88140	−0.179202
$743$	−33.9353	−1.24497	−0.622483	−	0.782633i	$-0.713876\pi$
$743$	−33.9353	−1.24497	−0.622483	+	0.782633i	$0.713876\pi$
$744$	−0.841468	−0.0308497
$745$	22.2551	0.815362
$746$	−4.12795	−0.151135
$747$	15.6870	0.573957
$748$	−2.08916	−0.0763874
$749$	19.2418	0.703081
$750$	18.6107	0.679566
$751$	49.9874	1.82406	0.912032	−	0.410118i	$-0.134512\pi$
$751$	49.9874	1.82406	0.912032	+	0.410118i	$0.134512\pi$
$752$	−12.3396	−0.449978
$753$	−25.2531	−0.920275
$754$	19.5500	0.711969
$755$	14.8517	0.540508
$756$	2.42343	0.0881393
$757$	32.4206	1.17835	0.589173	−	0.808007i	$-0.299454\pi$
$757$	32.4206	1.17835	0.589173	+	0.808007i	$0.299454\pi$
$758$	47.5351	1.72655
$759$	−7.71877	−0.280174
$760$	−0.169070	−0.00613282
$761$	−28.8778	−1.04682	−0.523410	−	0.852081i	$-0.675340\pi$
$761$	−28.8778	−1.04682	−0.523410	+	0.852081i	$0.675340\pi$
$762$	−25.3385	−0.917915
$763$	−0.254347	−0.00920797
$764$	10.0347	0.363042
$765$	−2.55731	−0.0924596
$766$	−14.6165	−0.528115
$767$	7.00362	0.252886
$768$	−7.25757	−0.261885
$769$	26.0181	0.938237	0.469119	−	0.883135i	$-0.344572\pi$
$769$	26.0181	0.938237	0.469119	+	0.883135i	$0.344572\pi$
$770$	−4.63665	−0.167093
$771$	19.8286	0.714111
$772$	−16.3302	−0.587737
$773$	−21.5760	−0.776033	−0.388017	−	0.921652i	$-0.626840\pi$
$773$	−21.5760	−0.776033	−0.388017	+	0.921652i	$0.626840\pi$
$774$	−11.0997	−0.398971
$775$	1.45493	0.0522627
$776$	−16.5637	−0.594601
$777$	−2.81108	−0.100847
$778$	5.05992	0.181407
$779$	−0.476327	−0.0170662
$780$	−6.19745	−0.221904
$781$	6.04126	0.216173
$782$	−18.8316	−0.673415
$783$	−9.29539	−0.332190
$784$	−2.97385	−0.106209
$785$	−8.65076	−0.308759
$786$	−21.4238	−0.764161
$787$	52.6638	1.87726	0.938632	−	0.344921i	$-0.112094\pi$
$787$	52.6638	1.87726	0.938632	+	0.344921i	$0.112094\pi$
$788$	−5.15464	−0.183627
$789$	−29.6351	−1.05504
$790$	79.8142	2.83966
$791$	−7.20001	−0.256003
$792$	0.767721	0.0272798
$793$	−5.43642	−0.193053
$794$	−71.4018	−2.53395
$795$	−5.93536	−0.210506
$796$	−44.2513	−1.56845
$797$	17.1301	0.606779	0.303390	−	0.952867i	$-0.401882\pi$
$797$	17.1301	0.606779	0.303390	+	0.952867i	$0.401882\pi$
$798$	−0.156136	−0.00552715
$799$	−4.14936	−0.146794
$800$	−12.3734	−0.437467
$801$	−3.30346	−0.116722
$802$	54.6754	1.93065
$803$	4.75753	0.167890
$804$	−8.07958	−0.284945
$805$	−22.8976	−0.807033
$806$	1.98726	0.0699983
$807$	3.43195	0.120810
$808$	−4.22402	−0.148600
$809$	−16.6220	−0.584399	−0.292199	−	0.956357i	$-0.594387\pi$
$809$	−16.6220	−0.584399	−0.292199	+	0.956357i	$0.594387\pi$
$810$	5.37851	0.188982
$811$	−56.5317	−1.98510	−0.992549	−	0.121846i	$-0.961119\pi$
$811$	−56.5317	−1.98510	−0.992549	+	0.121846i	$0.961119\pi$
$812$	−22.5267	−0.790533
$813$	−0.527723	−0.0185080
$814$	−5.09677	−0.178642
$815$	−34.6871	−1.21504
$816$	−2.97385	−0.104105
$817$	0.391791	0.0137070
$818$	45.0073	1.57364
$819$	−1.00000	−0.0349428
$820$	39.7645	1.38864
$821$	33.8214	1.18037	0.590187	−	0.807267i	$-0.299054\pi$
$821$	33.8214	1.18037	0.590187	+	0.807267i	$0.299054\pi$
$822$	−15.1213	−0.527417
$823$	−9.64778	−0.336301	−0.168150	−	0.985761i	$-0.553779\pi$
$823$	−9.64778	−0.336301	−0.168150	+	0.985761i	$0.553779\pi$
$824$	−10.5277	−0.366751
$825$	−1.32742	−0.0462149
$826$	−14.7300	−0.512522
$827$	−28.5401	−0.992436	−0.496218	−	0.868198i	$-0.665278\pi$
$827$	−28.5401	−0.992436	−0.496218	+	0.868198i	$0.665278\pi$
$828$	21.6989	0.754088
$829$	5.08441	0.176589	0.0882943	−	0.996094i	$-0.471858\pi$
$829$	5.08441	0.176589	0.0882943	+	0.996094i	$0.471858\pi$
$830$	84.3727	2.92862
$831$	−2.38511	−0.0827384
$832$	−10.9529	−0.379725
$833$	−1.00000	−0.0346479
$834$	−26.8214	−0.928749
$835$	19.2082	0.664726
$836$	−0.155094	−0.00536404
$837$	−0.944878	−0.0326598
$838$	−25.0360	−0.864854
$839$	−14.7976	−0.510871	−0.255435	−	0.966826i	$-0.582219\pi$
$839$	−14.7976	−0.510871	−0.255435	+	0.966826i	$0.582219\pi$
$840$	2.27743	0.0785787
$841$	57.4042	1.97945
$842$	19.1792	0.660957
$843$	−25.0457	−0.862621
$844$	18.6286	0.641224
$845$	2.55731	0.0879740
$846$	8.72692	0.300038
$847$	10.2568	0.352429
$848$	−6.90213	−0.237020
$849$	19.5691	0.671610
$850$	−3.23852	−0.111080
$851$	−25.1698	−0.862811
$852$	−16.9831	−0.581830
$853$	−41.4801	−1.42025	−0.710125	−	0.704076i	$-0.751362\pi$
$853$	−41.4801	−1.42025	−0.710125	+	0.704076i	$0.751362\pi$
$854$	11.4339	0.391259
$855$	−0.189848	−0.00649265
$856$	−17.1359	−0.585695
$857$	18.9725	0.648087	0.324043	−	0.946042i	$-0.394958\pi$
$857$	18.9725	0.648087	0.324043	+	0.946042i	$0.394958\pi$
$858$	−1.81310	−0.0618982
$859$	−40.9398	−1.39685	−0.698424	−	0.715684i	$-0.746115\pi$
$859$	−40.9398	−1.39685	−0.698424	+	0.715684i	$0.746115\pi$
$860$	−32.7073	−1.11531
$861$	6.41627	0.218666
$862$	−24.5088	−0.834771
$863$	21.2993	0.725036	0.362518	−	0.931977i	$-0.381917\pi$
$863$	21.2993	0.725036	0.362518	+	0.931977i	$0.381917\pi$
$864$	8.03569	0.273380
$865$	−41.8881	−1.42424
$866$	−55.5404	−1.88734
$867$	−1.00000	−0.0339618
$868$	−2.28985	−0.0777224
$869$	12.7926	0.433960
$870$	−49.9953	−1.69500
$871$	3.33394	0.112966
$872$	0.226510	0.00767061
$873$	−18.5992	−0.629488
$874$	−1.39801	−0.0472882
$875$	8.84876	0.299143
$876$	−13.3743	−0.451875
$877$	−31.8060	−1.07401	−0.537006	−	0.843578i	$-0.680445\pi$
$877$	−31.8060	−1.07401	−0.537006	+	0.843578i	$0.680445\pi$
$878$	−2.35277	−0.0794022
$879$	−14.6347	−0.493617
$880$	−6.55606	−0.221005
$881$	−26.3663	−0.888305	−0.444152	−	0.895951i	$-0.646495\pi$
$881$	−26.3663	−0.888305	−0.444152	+	0.895951i	$0.646495\pi$
$882$	2.10320	0.0708183
$883$	2.64448	0.0889938	0.0444969	−	0.999010i	$-0.485832\pi$
$883$	2.64448	0.0889938	0.0444969	+	0.999010i	$0.485832\pi$
$884$	−2.42343	−0.0815088
$885$	−17.9104	−0.602051
$886$	−46.2844	−1.55496
$887$	13.9859	0.469601	0.234800	−	0.972044i	$-0.424556\pi$
$887$	13.9859	0.469601	0.234800	+	0.972044i	$0.424556\pi$
$888$	2.50343	0.0840097
$889$	−12.0476	−0.404064
$890$	−17.7677	−0.595574
$891$	0.862068	0.0288804
$892$	38.6513	1.29414
$893$	−0.308038	−0.0103081
$894$	−18.3032	−0.612149
$895$	−8.52387	−0.284921
$896$	6.96479	0.232677
$897$	−8.95378	−0.298958
$898$	54.1286	1.80630
$899$	8.78300	0.292930
$900$	3.73162	0.124387
$901$	−2.32094	−0.0773218
$902$	11.6333	0.387347
$903$	−5.27755	−0.175626
$904$	6.41202	0.213261
$905$	−26.5127	−0.881312
$906$	−12.2144	−0.405797
$907$	38.1328	1.26618	0.633090	−	0.774078i	$-0.281786\pi$
$907$	38.1328	1.26618	0.633090	+	0.774078i	$0.281786\pi$
$908$	−15.8033	−0.524451
$909$	−4.74312	−0.157319
$910$	−5.37851	−0.178296
$911$	43.3988	1.43786	0.718932	−	0.695080i	$-0.244631\pi$
$911$	43.3988	1.43786	0.718932	+	0.695080i	$0.244631\pi$
$912$	−0.220771	−0.00731044
$913$	13.5233	0.447555
$914$	52.6880	1.74276
$915$	13.9026	0.459606
$916$	−58.9363	−1.94731
$917$	−10.1863	−0.336381
$918$	2.10320	0.0694158
$919$	37.7534	1.24537	0.622685	−	0.782472i	$-0.286042\pi$
$919$	37.7534	1.24537	0.622685	+	0.782472i	$0.286042\pi$
$920$	20.3916	0.672291
$921$	24.0751	0.793303
$922$	0.349448	0.0115085
$923$	7.00786	0.230667
$924$	2.08916	0.0687284
$925$	−4.32854	−0.142321
$926$	−82.0449	−2.69616
$927$	−11.8215	−0.388270
$928$	−74.6949	−2.45198
$929$	17.7132	0.581151	0.290576	−	0.956852i	$-0.406153\pi$
$929$	17.7132	0.581151	0.290576	+	0.956852i	$0.406153\pi$
$930$	−5.08204	−0.166647
$931$	−0.0742374	−0.00243303
$932$	2.99874	0.0982271
$933$	9.55358	0.312770
$934$	68.3860	2.23766
$935$	−2.20457	−0.0720972
$936$	0.890557	0.0291088
$937$	−20.2128	−0.660323	−0.330161	−	0.943924i	$-0.607103\pi$
$937$	−20.2128	−0.660323	−0.330161	+	0.943924i	$0.607103\pi$
$938$	−7.01194	−0.228948
$939$	−10.1783	−0.332157
$940$	25.7155	0.838747
$941$	−21.2612	−0.693096	−0.346548	−	0.938032i	$-0.612646\pi$
$941$	−21.2612	−0.693096	−0.346548	+	0.938032i	$0.612646\pi$
$942$	7.11462	0.231807
$943$	57.4499	1.87083
$944$	−20.8277	−0.677883
$945$	2.55731	0.0831891
$946$	−9.56871	−0.311106
$947$	−2.84633	−0.0924934	−0.0462467	−	0.998930i	$-0.514726\pi$
$947$	−2.84633	−0.0924934	−0.0462467	+	0.998930i	$0.514726\pi$
$948$	−35.9624	−1.16800
$949$	5.51874	0.179146
$950$	−0.240419	−0.00780024
$951$	19.4270	0.629964
$952$	0.890557	0.0288631
$953$	−37.0943	−1.20160	−0.600801	−	0.799399i	$-0.705151\pi$
$953$	−37.0943	−1.20160	−0.600801	+	0.799399i	$0.705151\pi$
$954$	4.88140	0.158041
$955$	10.5890	0.342653
$956$	9.07647	0.293554
$957$	−8.01326	−0.259032
$958$	3.04409	0.0983500
$959$	−7.18969	−0.232167
$960$	28.0100	0.904019
$961$	−30.1072	−0.971200
$962$	−5.91226	−0.190619
$963$	−19.2418	−0.620059
$964$	−72.2529	−2.32711
$965$	−17.2323	−0.554728
$966$	18.8316	0.605895
$967$	24.1491	0.776583	0.388291	−	0.921537i	$-0.373065\pi$
$967$	24.1491	0.776583	0.388291	+	0.921537i	$0.373065\pi$
$968$	−9.13430	−0.293588
$969$	−0.0742374	−0.00238485
$970$	−100.036	−3.21196
$971$	−13.1445	−0.421827	−0.210913	−	0.977505i	$-0.567644\pi$
$971$	−13.1445	−0.421827	−0.210913	+	0.977505i	$0.567644\pi$
$972$	−2.42343	−0.0777316
$973$	−12.7527	−0.408832
$974$	−38.1816	−1.22342
$975$	−1.53981	−0.0493134
$976$	16.1671	0.517496
$977$	54.3934	1.74020	0.870099	−	0.492877i	$-0.164055\pi$
$977$	54.3934	1.74020	0.870099	+	0.492877i	$0.164055\pi$
$978$	28.5276	0.912211
$979$	−2.84781	−0.0910162
$980$	6.19745	0.197970
$981$	0.254347	0.00812066
$982$	−35.7912	−1.14214
$983$	−0.264802	−0.00844588	−0.00422294	−	0.999991i	$-0.501344\pi$
$983$	−0.264802	−0.00844588	−0.00422294	+	0.999991i	$0.501344\pi$
$984$	−5.71405	−0.182157
$985$	−5.43940	−0.173314
$986$	−19.5500	−0.622599
$987$	4.14936	0.132076
$988$	−0.179909	−0.00572367
$989$	−47.2540	−1.50259
$990$	4.63665	0.147362
$991$	−48.6826	−1.54645	−0.773227	−	0.634130i	$-0.781358\pi$
$991$	−48.6826	−1.54645	−0.773227	+	0.634130i	$0.781358\pi$
$992$	−7.59275	−0.241070
$993$	25.1861	0.799256
$994$	−14.7389	−0.467490
$995$	−46.6959	−1.48036
$996$	−38.0164	−1.20459
$997$	−12.1655	−0.385284	−0.192642	−	0.981269i	$-0.561706\pi$
$997$	−12.1655	−0.385284	−0.192642	+	0.981269i	$0.561706\pi$
$998$	−76.2834	−2.41471
$999$	2.81108	0.0889388

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4641.2.a.ba.1.14	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4641.2.a.ba.1.14	✓	17	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)

\(f(q)\)	\(=\)	\(q+2.10320 q^{2} -1.00000 q^{3} +2.42343 q^{4} +2.55731 q^{5} -2.10320 q^{6} -1.00000 q^{7} +0.890557 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.10320 q^{2} -1.00000 q^{3} +2.42343 q^{4} +2.55731 q^{5} -2.10320 q^{6} -1.00000 q^{7} +0.890557 q^{8} +1.00000 q^{9} +5.37851 q^{10} +0.862068 q^{11} -2.42343 q^{12} +1.00000 q^{13} -2.10320 q^{14} -2.55731 q^{15} -2.97385 q^{16} -1.00000 q^{17} +2.10320 q^{18} -0.0742374 q^{19} +6.19745 q^{20} +1.00000 q^{21} +1.81310 q^{22} +8.95378 q^{23} -0.890557 q^{24} +1.53981 q^{25} +2.10320 q^{26} -1.00000 q^{27} -2.42343 q^{28} +9.29539 q^{29} -5.37851 q^{30} +0.944878 q^{31} -8.03569 q^{32} -0.862068 q^{33} -2.10320 q^{34} -2.55731 q^{35} +2.42343 q^{36} -2.81108 q^{37} -0.156136 q^{38} -1.00000 q^{39} +2.27743 q^{40} +6.41627 q^{41} +2.10320 q^{42} -5.27755 q^{43} +2.08916 q^{44} +2.55731 q^{45} +18.8316 q^{46} +4.14936 q^{47} +2.97385 q^{48} +1.00000 q^{49} +3.23852 q^{50} +1.00000 q^{51} +2.42343 q^{52} +2.32094 q^{53} -2.10320 q^{54} +2.20457 q^{55} -0.890557 q^{56} +0.0742374 q^{57} +19.5500 q^{58} +7.00362 q^{59} -6.19745 q^{60} -5.43642 q^{61} +1.98726 q^{62} -1.00000 q^{63} -10.9529 q^{64} +2.55731 q^{65} -1.81310 q^{66} +3.33394 q^{67} -2.42343 q^{68} -8.95378 q^{69} -5.37851 q^{70} +7.00786 q^{71} +0.890557 q^{72} +5.51874 q^{73} -5.91226 q^{74} -1.53981 q^{75} -0.179909 q^{76} -0.862068 q^{77} -2.10320 q^{78} +14.8395 q^{79} -7.60503 q^{80} +1.00000 q^{81} +13.4947 q^{82} +15.6870 q^{83} +2.42343 q^{84} -2.55731 q^{85} -11.0997 q^{86} -9.29539 q^{87} +0.767721 q^{88} -3.30346 q^{89} +5.37851 q^{90} -1.00000 q^{91} +21.6989 q^{92} -0.944878 q^{93} +8.72692 q^{94} -0.189848 q^{95} +8.03569 q^{96} -18.5992 q^{97} +2.10320 q^{98} +0.862068 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + q^{2} - 17 q^{3} + 25 q^{4} - 4 q^{5} - q^{6} - 17 q^{7} + 6 q^{8} + 17 q^{9}+O(q^{10}) \) 17 * q + q^2 - 17 * q^3 + 25 * q^4 - 4 * q^5 - q^6 - 17 * q^7 + 6 * q^8 + 17 * q^9	\( 17 q + q^{2} - 17 q^{3} + 25 q^{4} - 4 q^{5} - q^{6} - 17 q^{7} + 6 q^{8} + 17 q^{9} - q^{10} + 4 q^{11} - 25 q^{12} + 17 q^{13} - q^{14} + 4 q^{15} + 53 q^{16} - 17 q^{17} + q^{18} + 13 q^{19} - 5 q^{20} + 17 q^{21} + 4 q^{22} + 8 q^{23} - 6 q^{24} + 37 q^{25} + q^{26} - 17 q^{27} - 25 q^{28} - 3 q^{29} + q^{30} + 10 q^{31} + 18 q^{32} - 4 q^{33} - q^{34} + 4 q^{35} + 25 q^{36} - 25 q^{38} - 17 q^{39} - 12 q^{41} + q^{42} + 29 q^{43} + 12 q^{44} - 4 q^{45} + 19 q^{46} - 4 q^{47} - 53 q^{48} + 17 q^{49} + 9 q^{50} + 17 q^{51} + 25 q^{52} - 8 q^{53} - q^{54} + 27 q^{55} - 6 q^{56} - 13 q^{57} + 2 q^{58} + 25 q^{59} + 5 q^{60} - 5 q^{61} - 37 q^{62} - 17 q^{63} + 94 q^{64} - 4 q^{65} - 4 q^{66} + 15 q^{67} - 25 q^{68} - 8 q^{69} + q^{70} + 32 q^{71} + 6 q^{72} - 15 q^{73} + 16 q^{74} - 37 q^{75} + 3 q^{76} - 4 q^{77} - q^{78} + 27 q^{79} + 41 q^{80} + 17 q^{81} - 8 q^{82} - 24 q^{83} + 25 q^{84} + 4 q^{85} + 53 q^{86} + 3 q^{87} - 9 q^{88} - 8 q^{89} - q^{90} - 17 q^{91} + 14 q^{92} - 10 q^{93} + 51 q^{94} - 9 q^{95} - 18 q^{96} - 22 q^{97} + q^{98} + 4 q^{99}+O(q^{100}) \) 17 * q + q^2 - 17 * q^3 + 25 * q^4 - 4 * q^5 - q^6 - 17 * q^7 + 6 * q^8 + 17 * q^9 - q^10 + 4 * q^11 - 25 * q^12 + 17 * q^13 - q^14 + 4 * q^15 + 53 * q^16 - 17 * q^17 + q^18 + 13 * q^19 - 5 * q^20 + 17 * q^21 + 4 * q^22 + 8 * q^23 - 6 * q^24 + 37 * q^25 + q^26 - 17 * q^27 - 25 * q^28 - 3 * q^29 + q^30 + 10 * q^31 + 18 * q^32 - 4 * q^33 - q^34 + 4 * q^35 + 25 * q^36 - 25 * q^38 - 17 * q^39 - 12 * q^41 + q^42 + 29 * q^43 + 12 * q^44 - 4 * q^45 + 19 * q^46 - 4 * q^47 - 53 * q^48 + 17 * q^49 + 9 * q^50 + 17 * q^51 + 25 * q^52 - 8 * q^53 - q^54 + 27 * q^55 - 6 * q^56 - 13 * q^57 + 2 * q^58 + 25 * q^59 + 5 * q^60 - 5 * q^61 - 37 * q^62 - 17 * q^63 + 94 * q^64 - 4 * q^65 - 4 * q^66 + 15 * q^67 - 25 * q^68 - 8 * q^69 + q^70 + 32 * q^71 + 6 * q^72 - 15 * q^73 + 16 * q^74 - 37 * q^75 + 3 * q^76 - 4 * q^77 - q^78 + 27 * q^79 + 41 * q^80 + 17 * q^81 - 8 * q^82 - 24 * q^83 + 25 * q^84 + 4 * q^85 + 53 * q^86 + 3 * q^87 - 9 * q^88 - 8 * q^89 - q^90 - 17 * q^91 + 14 * q^92 - 10 * q^93 + 51 * q^94 - 9 * q^95 - 18 * q^96 - 22 * q^97 + q^98 + 4 * q^99

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