LMFDB - Embedded newform 4641.2.a.ba.1.13

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			1.13
Root			$1.63714$ 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)

$f(q)$	$=$	$q+1.63714 q^{2} -1.00000 q^{3} +0.680235 q^{4} -3.04998 q^{5} -1.63714 q^{6} -1.00000 q^{7} -2.16064 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.63714 q^{2} -1.00000 q^{3} +0.680235 q^{4} -3.04998 q^{5} -1.63714 q^{6} -1.00000 q^{7} -2.16064 q^{8} +1.00000 q^{9} -4.99325 q^{10} +5.04452 q^{11} -0.680235 q^{12} +1.00000 q^{13} -1.63714 q^{14} +3.04998 q^{15} -4.89775 q^{16} -1.00000 q^{17} +1.63714 q^{18} -4.72211 q^{19} -2.07470 q^{20} +1.00000 q^{21} +8.25860 q^{22} -0.791944 q^{23} +2.16064 q^{24} +4.30236 q^{25} +1.63714 q^{26} -1.00000 q^{27} -0.680235 q^{28} -8.14950 q^{29} +4.99325 q^{30} -9.70453 q^{31} -3.69703 q^{32} -5.04452 q^{33} -1.63714 q^{34} +3.04998 q^{35} +0.680235 q^{36} +4.08029 q^{37} -7.73077 q^{38} -1.00000 q^{39} +6.58991 q^{40} -2.26862 q^{41} +1.63714 q^{42} +4.97044 q^{43} +3.43146 q^{44} -3.04998 q^{45} -1.29653 q^{46} +7.65604 q^{47} +4.89775 q^{48} +1.00000 q^{49} +7.04358 q^{50} +1.00000 q^{51} +0.680235 q^{52} +1.60730 q^{53} -1.63714 q^{54} -15.3857 q^{55} +2.16064 q^{56} +4.72211 q^{57} -13.3419 q^{58} +8.90811 q^{59} +2.07470 q^{60} +8.93086 q^{61} -15.8877 q^{62} -1.00000 q^{63} +3.74294 q^{64} -3.04998 q^{65} -8.25860 q^{66} -2.44575 q^{67} -0.680235 q^{68} +0.791944 q^{69} +4.99325 q^{70} +5.56432 q^{71} -2.16064 q^{72} +7.88966 q^{73} +6.68001 q^{74} -4.30236 q^{75} -3.21215 q^{76} -5.04452 q^{77} -1.63714 q^{78} +15.2147 q^{79} +14.9380 q^{80} +1.00000 q^{81} -3.71405 q^{82} -7.33926 q^{83} +0.680235 q^{84} +3.04998 q^{85} +8.13731 q^{86} +8.14950 q^{87} -10.8994 q^{88} +0.462306 q^{89} -4.99325 q^{90} -1.00000 q^{91} -0.538708 q^{92} +9.70453 q^{93} +12.5340 q^{94} +14.4023 q^{95} +3.69703 q^{96} -11.4877 q^{97} +1.63714 q^{98} +5.04452 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.63714	1.15763	0.578817	−	0.815457i	$-0.303514\pi$
$2$	1.63714	1.15763	0.578817	+	0.815457i	$0.303514\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.680235	0.340118
$5$	−3.04998	−1.36399	−0.681996	−	0.731356i	$-0.738888\pi$
$5$	−3.04998	−1.36399	−0.681996	+	0.731356i	$0.738888\pi$
$6$	−1.63714	−0.668361
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.16064	−0.763903
$9$	1.00000	0.333333
$10$	−4.99325	−1.57900
$11$	5.04452	1.52098	0.760490	−	0.649350i	$-0.224959\pi$
$11$	5.04452	1.52098	0.760490	+	0.649350i	$0.224959\pi$
$12$	−0.680235	−0.196367
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−1.63714	−0.437545
$15$	3.04998	0.787501
$16$	−4.89775	−1.22444
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.63714	0.385878
$19$	−4.72211	−1.08333	−0.541663	−	0.840596i	$-0.682205\pi$
$19$	−4.72211	−1.08333	−0.541663	+	0.840596i	$0.682205\pi$
$20$	−2.07470	−0.463918
$21$	1.00000	0.218218
$22$	8.25860	1.76074
$23$	−0.791944	−0.165132	−0.0825659	−	0.996586i	$-0.526311\pi$
$23$	−0.791944	−0.165132	−0.0825659	+	0.996586i	$0.526311\pi$
$24$	2.16064	0.441039
$25$	4.30236	0.860472
$26$	1.63714	0.321070
$27$	−1.00000	−0.192450
$28$	−0.680235	−0.128552
$29$	−8.14950	−1.51332	−0.756662	−	0.653806i	$-0.773171\pi$
$29$	−8.14950	−1.51332	−0.756662	+	0.653806i	$0.773171\pi$
$30$	4.99325	0.911638
$31$	−9.70453	−1.74299	−0.871493	−	0.490409i	$-0.836848\pi$
$31$	−9.70453	−1.74299	−0.871493	+	0.490409i	$0.836848\pi$
$32$	−3.69703	−0.653549
$33$	−5.04452	−0.878138
$34$	−1.63714	−0.280768
$35$	3.04998	0.515540
$36$	0.680235	0.113373
$37$	4.08029	0.670795	0.335397	−	0.942077i	$-0.391129\pi$
$37$	4.08029	0.670795	0.335397	+	0.942077i	$0.391129\pi$
$38$	−7.73077	−1.25410
$39$	−1.00000	−0.160128
$40$	6.58991	1.04196
$41$	−2.26862	−0.354299	−0.177149	−	0.984184i	$-0.556688\pi$
$41$	−2.26862	−0.354299	−0.177149	+	0.984184i	$0.556688\pi$
$42$	1.63714	0.252617
$43$	4.97044	0.757984	0.378992	−	0.925400i	$-0.376271\pi$
$43$	4.97044	0.757984	0.378992	+	0.925400i	$0.376271\pi$
$44$	3.43146	0.517312
$45$	−3.04998	−0.454664
$46$	−1.29653	−0.191162
$47$	7.65604	1.11675	0.558374	−	0.829589i	$-0.311425\pi$
$47$	7.65604	1.11675	0.558374	+	0.829589i	$0.311425\pi$
$48$	4.89775	0.706929
$49$	1.00000	0.142857
$50$	7.04358	0.996112
$51$	1.00000	0.140028
$52$	0.680235	0.0943317
$53$	1.60730	0.220780	0.110390	−	0.993888i	$-0.464790\pi$
$53$	1.60730	0.220780	0.110390	+	0.993888i	$0.464790\pi$
$54$	−1.63714	−0.222787
$55$	−15.3857	−2.07460
$56$	2.16064	0.288728
$57$	4.72211	0.625459
$58$	−13.3419	−1.75188
$59$	8.90811	1.15974	0.579869	−	0.814710i	$-0.303104\pi$
$59$	8.90811	1.15974	0.579869	+	0.814710i	$0.303104\pi$
$60$	2.07470	0.267843
$61$	8.93086	1.14348	0.571740	−	0.820435i	$-0.306269\pi$
$61$	8.93086	1.14348	0.571740	+	0.820435i	$0.306269\pi$
$62$	−15.8877	−2.01774
$63$	−1.00000	−0.125988
$64$	3.74294	0.467867
$65$	−3.04998	−0.378303
$66$	−8.25860	−1.01656
$67$	−2.44575	−0.298796	−0.149398	−	0.988777i	$-0.547734\pi$
$67$	−2.44575	−0.298796	−0.149398	+	0.988777i	$0.547734\pi$
$68$	−0.680235	−0.0824907
$69$	0.791944	0.0953388
$70$	4.99325	0.596807
$71$	5.56432	0.660363	0.330181	−	0.943917i	$-0.392890\pi$
$71$	5.56432	0.660363	0.330181	+	0.943917i	$0.392890\pi$
$72$	−2.16064	−0.254634
$73$	7.88966	0.923415	0.461708	−	0.887032i	$-0.347237\pi$
$73$	7.88966	0.923415	0.461708	+	0.887032i	$0.347237\pi$
$74$	6.68001	0.776535
$75$	−4.30236	−0.496794
$76$	−3.21215	−0.368458
$77$	−5.04452	−0.574876
$78$	−1.63714	−0.185370
$79$	15.2147	1.71179	0.855895	−	0.517149i	$-0.173007\pi$
$79$	15.2147	1.71179	0.855895	+	0.517149i	$0.173007\pi$
$80$	14.9380	1.67012
$81$	1.00000	0.111111
$82$	−3.71405	−0.410148
$83$	−7.33926	−0.805588	−0.402794	−	0.915291i	$-0.631961\pi$
$83$	−7.33926	−0.805588	−0.402794	+	0.915291i	$0.631961\pi$
$84$	0.680235	0.0742198
$85$	3.04998	0.330816
$86$	8.13731	0.877469
$87$	8.14950	0.873718
$88$	−10.8994	−1.16188
$89$	0.462306	0.0490044	0.0245022	−	0.999700i	$-0.492200\pi$
$89$	0.462306	0.0490044	0.0245022	+	0.999700i	$0.492200\pi$
$90$	−4.99325	−0.526334
$91$	−1.00000	−0.104828
$92$	−0.538708	−0.0561642
$93$	9.70453	1.00631
$94$	12.5340	1.29279
$95$	14.4023	1.47765
$96$	3.69703	0.377327
$97$	−11.4877	−1.16640	−0.583198	−	0.812330i	$-0.698199\pi$
$97$	−11.4877	−1.16640	−0.583198	+	0.812330i	$0.698199\pi$
$98$	1.63714	0.165376
$99$	5.04452	0.506993
$100$	2.92662	0.292662
$101$	1.23285	0.122673	0.0613367	−	0.998117i	$-0.480464\pi$
$101$	1.23285	0.122673	0.0613367	+	0.998117i	$0.480464\pi$
$102$	1.63714	0.162101
$103$	−5.93380	−0.584674	−0.292337	−	0.956315i	$-0.594433\pi$
$103$	−5.93380	−0.584674	−0.292337	+	0.956315i	$0.594433\pi$
$104$	−2.16064	−0.211868
$105$	−3.04998	−0.297647
$106$	2.63138	0.255582
$107$	2.84409	0.274948	0.137474	−	0.990505i	$-0.456102\pi$
$107$	2.84409	0.274948	0.137474	+	0.990505i	$0.456102\pi$
$108$	−0.680235	−0.0654557
$109$	−2.08074	−0.199299	−0.0996495	−	0.995023i	$-0.531772\pi$
$109$	−2.08074	−0.199299	−0.0996495	+	0.995023i	$0.531772\pi$
$110$	−25.1885	−2.40163
$111$	−4.08029	−0.387284
$112$	4.89775	0.462794
$113$	11.5905	1.09035	0.545173	−	0.838324i	$-0.316464\pi$
$113$	11.5905	1.09035	0.545173	+	0.838324i	$0.316464\pi$
$114$	7.73077	0.724053
$115$	2.41541	0.225238
$116$	−5.54358	−0.514708
$117$	1.00000	0.0924500
$118$	14.5838	1.34255
$119$	1.00000	0.0916698
$120$	−6.58991	−0.601574
$121$	14.4472	1.31338
$122$	14.6211	1.32373
$123$	2.26862	0.204554
$124$	−6.60136	−0.592820
$125$	2.12779	0.190315
$126$	−1.63714	−0.145848
$127$	9.93391	0.881492	0.440746	−	0.897632i	$-0.354714\pi$
$127$	9.93391	0.881492	0.440746	+	0.897632i	$0.354714\pi$
$128$	13.5218	1.19517
$129$	−4.97044	−0.437622
$130$	−4.99325	−0.437937
$131$	−7.57144	−0.661520	−0.330760	−	0.943715i	$-0.607305\pi$
$131$	−7.57144	−0.661520	−0.330760	+	0.943715i	$0.607305\pi$
$132$	−3.43146	−0.298670
$133$	4.72211	0.409459
$134$	−4.00405	−0.345897
$135$	3.04998	0.262500
$136$	2.16064	0.185274
$137$	10.9175	0.932746	0.466373	−	0.884588i	$-0.345560\pi$
$137$	10.9175	0.932746	0.466373	+	0.884588i	$0.345560\pi$
$138$	1.29653	0.110368
$139$	−8.26601	−0.701114	−0.350557	−	0.936541i	$-0.614008\pi$
$139$	−8.26601	−0.701114	−0.350557	+	0.936541i	$0.614008\pi$
$140$	2.07470	0.175344
$141$	−7.65604	−0.644755
$142$	9.10958	0.764459
$143$	5.04452	0.421844
$144$	−4.89775	−0.408146
$145$	24.8558	2.06416
$146$	12.9165	1.06898
$147$	−1.00000	−0.0824786
$148$	2.77555	0.228149
$149$	18.7368	1.53498	0.767490	−	0.641061i	$-0.221505\pi$
$149$	18.7368	1.53498	0.767490	+	0.641061i	$0.221505\pi$
$150$	−7.04358	−0.575106
$151$	−2.12464	−0.172901	−0.0864505	−	0.996256i	$-0.527552\pi$
$151$	−2.12464	−0.172901	−0.0864505	+	0.996256i	$0.527552\pi$
$152$	10.2028	0.827556
$153$	−1.00000	−0.0808452
$154$	−8.25860	−0.665497
$155$	29.5986	2.37742
$156$	−0.680235	−0.0544624
$157$	17.8759	1.42665	0.713324	−	0.700834i	$-0.247189\pi$
$157$	17.8759	1.42665	0.713324	+	0.700834i	$0.247189\pi$
$158$	24.9087	1.98163
$159$	−1.60730	−0.127467
$160$	11.2759	0.891435
$161$	0.791944	0.0624139
$162$	1.63714	0.128626
$163$	−9.71531	−0.760962	−0.380481	−	0.924789i	$-0.624242\pi$
$163$	−9.71531	−0.760962	−0.380481	+	0.924789i	$0.624242\pi$
$164$	−1.54319	−0.120503
$165$	15.3857	1.19777
$166$	−12.0154	−0.932577
$167$	10.8727	0.841354	0.420677	−	0.907210i	$-0.361793\pi$
$167$	10.8727	0.841354	0.420677	+	0.907210i	$0.361793\pi$
$168$	−2.16064	−0.166697
$169$	1.00000	0.0769231
$170$	4.99325	0.382965
$171$	−4.72211	−0.361109
$172$	3.38107	0.257804
$173$	−20.9663	−1.59404	−0.797020	−	0.603953i	$-0.793592\pi$
$173$	−20.9663	−1.59404	−0.797020	+	0.603953i	$0.793592\pi$
$174$	13.3419	1.01145
$175$	−4.30236	−0.325228
$176$	−24.7068	−1.86235
$177$	−8.90811	−0.669574
$178$	0.756861	0.0567291
$179$	15.7650	1.17833	0.589166	−	0.808012i	$-0.299456\pi$
$179$	15.7650	1.17833	0.589166	+	0.808012i	$0.299456\pi$
$180$	−2.07470	−0.154639
$181$	19.7143	1.46535	0.732676	−	0.680578i	$-0.238271\pi$
$181$	19.7143	1.46535	0.732676	+	0.680578i	$0.238271\pi$
$182$	−1.63714	−0.121353
$183$	−8.93086	−0.660188
$184$	1.71111	0.126145
$185$	−12.4448	−0.914958
$186$	15.8877	1.16494
$187$	−5.04452	−0.368892
$188$	5.20791	0.379826
$189$	1.00000	0.0727393
$190$	23.5787	1.71058
$191$	−19.0873	−1.38111	−0.690553	−	0.723282i	$-0.742633\pi$
$191$	−19.0873	−1.38111	−0.690553	+	0.723282i	$0.742633\pi$
$192$	−3.74294	−0.270123
$193$	2.17511	0.156568	0.0782838	−	0.996931i	$-0.475056\pi$
$193$	2.17511	0.156568	0.0782838	+	0.996931i	$0.475056\pi$
$194$	−18.8070	−1.35026
$195$	3.04998	0.218413
$196$	0.680235	0.0485882
$197$	−15.2444	−1.08612	−0.543059	−	0.839695i	$-0.682734\pi$
$197$	−15.2444	−1.08612	−0.543059	+	0.839695i	$0.682734\pi$
$198$	8.25860	0.586913
$199$	21.7927	1.54484	0.772420	−	0.635112i	$-0.219046\pi$
$199$	21.7927	1.54484	0.772420	+	0.635112i	$0.219046\pi$
$200$	−9.29586	−0.657317
$201$	2.44575	0.172510
$202$	2.01835	0.142011
$203$	8.14950	0.571983
$204$	0.680235	0.0476260
$205$	6.91923	0.483260
$206$	−9.71447	−0.676839
$207$	−0.791944	−0.0550439
$208$	−4.89775	−0.339598
$209$	−23.8208	−1.64772
$210$	−4.99325	−0.344567
$211$	18.4960	1.27332	0.636658	−	0.771146i	$-0.280316\pi$
$211$	18.4960	1.27332	0.636658	+	0.771146i	$0.280316\pi$
$212$	1.09334	0.0750911
$213$	−5.56432	−0.381261
$214$	4.65617	0.318289
$215$	−15.1597	−1.03388
$216$	2.16064	0.147013
$217$	9.70453	0.658786
$218$	−3.40647	−0.230715
$219$	−7.88966	−0.533134
$220$	−10.4659	−0.705609
$221$	−1.00000	−0.0672673
$222$	−6.68001	−0.448333
$223$	−0.527733	−0.0353396	−0.0176698	−	0.999844i	$-0.505625\pi$
$223$	−0.527733	−0.0353396	−0.0176698	+	0.999844i	$0.505625\pi$
$224$	3.69703	0.247018
$225$	4.30236	0.286824
$226$	18.9754	1.26222
$227$	−16.7604	−1.11243	−0.556214	−	0.831039i	$-0.687747\pi$
$227$	−16.7604	−1.11243	−0.556214	+	0.831039i	$0.687747\pi$
$228$	3.21215	0.212730
$229$	7.56242	0.499739	0.249869	−	0.968280i	$-0.419612\pi$
$229$	7.56242	0.499739	0.249869	+	0.968280i	$0.419612\pi$
$230$	3.95437	0.260744
$231$	5.04452	0.331905
$232$	17.6082	1.15603
$233$	−19.2984	−1.26428	−0.632140	−	0.774854i	$-0.717823\pi$
$233$	−19.2984	−1.26428	−0.632140	+	0.774854i	$0.717823\pi$
$234$	1.63714	0.107023
$235$	−23.3507	−1.52323
$236$	6.05961	0.394447
$237$	−15.2147	−0.988303
$238$	1.63714	0.106120
$239$	16.0919	1.04090	0.520448	−	0.853893i	$-0.325765\pi$
$239$	16.0919	1.04090	0.520448	+	0.853893i	$0.325765\pi$
$240$	−14.9380	−0.964245
$241$	−16.0523	−1.03402	−0.517010	−	0.855980i	$-0.672955\pi$
$241$	−16.0523	−1.03402	−0.517010	+	0.855980i	$0.672955\pi$
$242$	23.6521	1.52041
$243$	−1.00000	−0.0641500
$244$	6.07509	0.388918
$245$	−3.04998	−0.194856
$246$	3.71405	0.236799
$247$	−4.72211	−0.300461
$248$	20.9680	1.33147
$249$	7.33926	0.465107
$250$	3.48349	0.220315
$251$	−27.3847	−1.72851	−0.864253	−	0.503058i	$-0.832208\pi$
$251$	−27.3847	−1.72851	−0.864253	+	0.503058i	$0.832208\pi$
$252$	−0.680235	−0.0428508
$253$	−3.99498	−0.251162
$254$	16.2632	1.02045
$255$	−3.04998	−0.190997
$256$	14.6512	0.915700
$257$	19.2063	1.19806	0.599029	−	0.800728i	$-0.295554\pi$
$257$	19.2063	1.19806	0.599029	+	0.800728i	$0.295554\pi$
$258$	−8.13731	−0.506607
$259$	−4.08029	−0.253537
$260$	−2.07470	−0.128668
$261$	−8.14950	−0.504441
$262$	−12.3955	−0.765798
$263$	6.55183	0.404003	0.202002	−	0.979385i	$-0.435255\pi$
$263$	6.55183	0.404003	0.202002	+	0.979385i	$0.435255\pi$
$264$	10.8994	0.670812
$265$	−4.90223	−0.301142
$266$	7.73077	0.474004
$267$	−0.462306	−0.0282927
$268$	−1.66369	−0.101626
$269$	18.4867	1.12715	0.563577	−	0.826064i	$-0.309425\pi$
$269$	18.4867	1.12715	0.563577	+	0.826064i	$0.309425\pi$
$270$	4.99325	0.303879
$271$	32.2534	1.95926	0.979628	−	0.200820i	$-0.0643606\pi$
$271$	32.2534	1.95926	0.979628	+	0.200820i	$0.0643606\pi$
$272$	4.89775	0.296970
$273$	1.00000	0.0605228
$274$	17.8735	1.07978
$275$	21.7033	1.30876
$276$	0.538708	0.0324264
$277$	−17.2172	−1.03448	−0.517240	−	0.855840i	$-0.673041\pi$
$277$	−17.2172	−1.03448	−0.517240	+	0.855840i	$0.673041\pi$
$278$	−13.5326	−0.811633
$279$	−9.70453	−0.580995
$280$	−6.58991	−0.393822
$281$	−17.2749	−1.03053	−0.515267	−	0.857029i	$-0.672307\pi$
$281$	−17.2749	−1.03053	−0.515267	+	0.857029i	$0.672307\pi$
$282$	−12.5340	−0.746391
$283$	6.21741	0.369587	0.184793	−	0.982777i	$-0.440838\pi$
$283$	6.21741	0.369587	0.184793	+	0.982777i	$0.440838\pi$
$284$	3.78504	0.224601
$285$	−14.4023	−0.853120
$286$	8.25860	0.488341
$287$	2.26862	0.133912
$288$	−3.69703	−0.217850
$289$	1.00000	0.0588235
$290$	40.6925	2.38954
$291$	11.4877	0.673419
$292$	5.36683	0.314070
$293$	1.66195	0.0970920	0.0485460	−	0.998821i	$-0.484541\pi$
$293$	1.66195	0.0970920	0.0485460	+	0.998821i	$0.484541\pi$
$294$	−1.63714	−0.0954801
$295$	−27.1695	−1.58187
$296$	−8.81604	−0.512422
$297$	−5.04452	−0.292713
$298$	30.6748	1.77695
$299$	−0.791944	−0.0457993
$300$	−2.92662	−0.168968
$301$	−4.97044	−0.286491
$302$	−3.47834	−0.200156
$303$	−1.23285	−0.0708255
$304$	23.1277	1.32647
$305$	−27.2389	−1.55970
$306$	−1.63714	−0.0935892
$307$	13.3075	0.759496	0.379748	−	0.925090i	$-0.376011\pi$
$307$	13.3075	0.759496	0.379748	+	0.925090i	$0.376011\pi$
$308$	−3.43146	−0.195526
$309$	5.93380	0.337562
$310$	48.4571	2.75218
$311$	−15.0516	−0.853495	−0.426748	−	0.904371i	$-0.640341\pi$
$311$	−15.0516	−0.853495	−0.426748	+	0.904371i	$0.640341\pi$
$312$	2.16064	0.122322
$313$	24.4970	1.38465	0.692325	−	0.721586i	$-0.256586\pi$
$313$	24.4970	1.38465	0.692325	+	0.721586i	$0.256586\pi$
$314$	29.2653	1.65154
$315$	3.04998	0.171847
$316$	10.3496	0.582210
$317$	16.9501	0.952012	0.476006	−	0.879442i	$-0.342084\pi$
$317$	16.9501	0.952012	0.476006	+	0.879442i	$0.342084\pi$
$318$	−2.63138	−0.147560
$319$	−41.1103	−2.30174
$320$	−11.4159	−0.638167
$321$	−2.84409	−0.158741
$322$	1.29653	0.0722525
$323$	4.72211	0.262745
$324$	0.680235	0.0377909
$325$	4.30236	0.238652
$326$	−15.9054	−0.880916
$327$	2.08074	0.115065
$328$	4.90167	0.270650
$329$	−7.65604	−0.422091
$330$	25.1885	1.38658
$331$	5.46650	0.300466	0.150233	−	0.988651i	$-0.451998\pi$
$331$	5.46650	0.300466	0.150233	+	0.988651i	$0.451998\pi$
$332$	−4.99242	−0.273995
$333$	4.08029	0.223598
$334$	17.8001	0.973980
$335$	7.45949	0.407556
$336$	−4.89775	−0.267194
$337$	20.7187	1.12862	0.564309	−	0.825564i	$-0.309143\pi$
$337$	20.7187	1.12862	0.564309	+	0.825564i	$0.309143\pi$
$338$	1.63714	0.0890488
$339$	−11.5905	−0.629512
$340$	2.07470	0.112517
$341$	−48.9547	−2.65105
$342$	−7.73077	−0.418032
$343$	−1.00000	−0.0539949
$344$	−10.7393	−0.579026
$345$	−2.41541	−0.130041
$346$	−34.3249	−1.84532
$347$	−9.44260	−0.506905	−0.253453	−	0.967348i	$-0.581566\pi$
$347$	−9.44260	−0.506905	−0.253453	+	0.967348i	$0.581566\pi$
$348$	5.54358	0.297167
$349$	7.89241	0.422471	0.211236	−	0.977435i	$-0.432251\pi$
$349$	7.89241	0.422471	0.211236	+	0.977435i	$0.432251\pi$
$350$	−7.04358	−0.376495
$351$	−1.00000	−0.0533761
$352$	−18.6497	−0.994034
$353$	−30.2560	−1.61036	−0.805181	−	0.593028i	$-0.797932\pi$
$353$	−30.2560	−1.61036	−0.805181	+	0.593028i	$0.797932\pi$
$354$	−14.5838	−0.775123
$355$	−16.9710	−0.900729
$356$	0.314477	0.0166672
$357$	−1.00000	−0.0529256
$358$	25.8096	1.36408
$359$	7.61351	0.401826	0.200913	−	0.979609i	$-0.435609\pi$
$359$	7.61351	0.401826	0.200913	+	0.979609i	$0.435609\pi$
$360$	6.58991	0.347319
$361$	3.29832	0.173596
$362$	32.2751	1.69634
$363$	−14.4472	−0.758280
$364$	−0.680235	−0.0356540
$365$	−24.0633	−1.25953
$366$	−14.6211	−0.764257
$367$	−30.2060	−1.57674	−0.788371	−	0.615200i	$-0.789075\pi$
$367$	−30.2060	−1.57674	−0.788371	+	0.615200i	$0.789075\pi$
$368$	3.87874	0.202193
$369$	−2.26862	−0.118100
$370$	−20.3739	−1.05919
$371$	−1.60730	−0.0834469
$372$	6.60136	0.342265
$373$	7.47109	0.386838	0.193419	−	0.981116i	$-0.438042\pi$
$373$	7.47109	0.386838	0.193419	+	0.981116i	$0.438042\pi$
$374$	−8.25860	−0.427042
$375$	−2.12779	−0.109878
$376$	−16.5420	−0.853087
$377$	−8.14950	−0.419721
$378$	1.63714	0.0842055
$379$	−21.3257	−1.09543	−0.547714	−	0.836665i	$-0.684502\pi$
$379$	−21.3257	−1.09543	−0.547714	+	0.836665i	$0.684502\pi$
$380$	9.79697	0.502574
$381$	−9.93391	−0.508930
$382$	−31.2486	−1.59882
$383$	24.7777	1.26608	0.633039	−	0.774120i	$-0.281807\pi$
$383$	24.7777	1.26608	0.633039	+	0.774120i	$0.281807\pi$
$384$	−13.5218	−0.690030
$385$	15.3857	0.784126
$386$	3.56096	0.181248
$387$	4.97044	0.252661
$388$	−7.81432	−0.396712
$389$	−11.3671	−0.576333	−0.288166	−	0.957580i	$-0.593046\pi$
$389$	−11.3671	−0.576333	−0.288166	+	0.957580i	$0.593046\pi$
$390$	4.99325	0.252843
$391$	0.791944	0.0400503
$392$	−2.16064	−0.109129
$393$	7.57144	0.381929
$394$	−24.9572	−1.25733
$395$	−46.4046	−2.33487
$396$	3.43146	0.172437
$397$	18.6321	0.935117	0.467558	−	0.883962i	$-0.345134\pi$
$397$	18.6321	0.935117	0.467558	+	0.883962i	$0.345134\pi$
$398$	35.6777	1.78836
$399$	−4.72211	−0.236401
$400$	−21.0719	−1.05359
$401$	−3.58860	−0.179206	−0.0896031	−	0.995978i	$-0.528560\pi$
$401$	−3.58860	−0.179206	−0.0896031	+	0.995978i	$0.528560\pi$
$402$	4.00405	0.199704
$403$	−9.70453	−0.483417
$404$	0.838629	0.0417234
$405$	−3.04998	−0.151555
$406$	13.3419	0.662147
$407$	20.5831	1.02027
$408$	−2.16064	−0.106968
$409$	−0.617903	−0.0305533	−0.0152767	−	0.999883i	$-0.504863\pi$
$409$	−0.617903	−0.0305533	−0.0152767	+	0.999883i	$0.504863\pi$
$410$	11.3278	0.559439
$411$	−10.9175	−0.538521
$412$	−4.03638	−0.198858
$413$	−8.90811	−0.438339
$414$	−1.29653	−0.0637207
$415$	22.3846	1.09882
$416$	−3.69703	−0.181262
$417$	8.26601	0.404788
$418$	−38.9980	−1.90745
$419$	−16.4521	−0.803736	−0.401868	−	0.915698i	$-0.631639\pi$
$419$	−16.4521	−0.803736	−0.401868	+	0.915698i	$0.631639\pi$
$420$	−2.07470	−0.101235
$421$	−15.9312	−0.776440	−0.388220	−	0.921567i	$-0.626910\pi$
$421$	−15.9312	−0.776440	−0.388220	+	0.921567i	$0.626910\pi$
$422$	30.2806	1.47404
$423$	7.65604	0.372249
$424$	−3.47280	−0.168654
$425$	−4.30236	−0.208695
$426$	−9.10958	−0.441361
$427$	−8.93086	−0.432195
$428$	1.93465	0.0935147
$429$	−5.04452	−0.243552
$430$	−24.8186	−1.19686
$431$	−28.5430	−1.37487	−0.687433	−	0.726248i	$-0.741263\pi$
$431$	−28.5430	−1.37487	−0.687433	+	0.726248i	$0.741263\pi$
$432$	4.89775	0.235643
$433$	−32.4705	−1.56043	−0.780216	−	0.625511i	$-0.784891\pi$
$433$	−32.4705	−1.56043	−0.780216	+	0.625511i	$0.784891\pi$
$434$	15.8877	0.762634
$435$	−24.8558	−1.19174
$436$	−1.41540	−0.0677851
$437$	3.73965	0.178892
$438$	−12.9165	−0.617174
$439$	−19.3796	−0.924936	−0.462468	−	0.886636i	$-0.653036\pi$
$439$	−19.3796	−0.924936	−0.462468	+	0.886636i	$0.653036\pi$
$440$	33.2429	1.58479
$441$	1.00000	0.0476190
$442$	−1.63714	−0.0778709
$443$	24.3255	1.15574	0.577869	−	0.816130i	$-0.303885\pi$
$443$	24.3255	1.15574	0.577869	+	0.816130i	$0.303885\pi$
$444$	−2.77555	−0.131722
$445$	−1.41002	−0.0668415
$446$	−0.863975	−0.0409104
$447$	−18.7368	−0.886221
$448$	−3.74294	−0.176837
$449$	−34.9743	−1.65054	−0.825269	−	0.564740i	$-0.808976\pi$
$449$	−34.9743	−1.65054	−0.825269	+	0.564740i	$0.808976\pi$
$450$	7.04358	0.332037
$451$	−11.4441	−0.538881
$452$	7.88429	0.370846
$453$	2.12464	0.0998245
$454$	−27.4392	−1.28779
$455$	3.04998	0.142985
$456$	−10.2028	−0.477789
$457$	9.19452	0.430101	0.215051	−	0.976603i	$-0.431008\pi$
$457$	9.19452	0.430101	0.215051	+	0.976603i	$0.431008\pi$
$458$	12.3808	0.578515
$459$	1.00000	0.0466760
$460$	1.64305	0.0766075
$461$	18.6790	0.869970	0.434985	−	0.900438i	$-0.356754\pi$
$461$	18.6790	0.869970	0.434985	+	0.900438i	$0.356754\pi$
$462$	8.25860	0.384225
$463$	26.0200	1.20925	0.604627	−	0.796509i	$-0.293322\pi$
$463$	26.0200	1.20925	0.604627	+	0.796509i	$0.293322\pi$
$464$	39.9142	1.85297
$465$	−29.5986	−1.37260
$466$	−31.5942	−1.46357
$467$	11.5244	0.533288	0.266644	−	0.963795i	$-0.414085\pi$
$467$	11.5244	0.533288	0.266644	+	0.963795i	$0.414085\pi$
$468$	0.680235	0.0314439
$469$	2.44575	0.112934
$470$	−38.2285	−1.76335
$471$	−17.8759	−0.823676
$472$	−19.2472	−0.885926
$473$	25.0735	1.15288
$474$	−24.9087	−1.14409
$475$	−20.3162	−0.932172
$476$	0.680235	0.0311785
$477$	1.60730	0.0735932
$478$	26.3447	1.20498
$479$	−15.1875	−0.693932	−0.346966	−	0.937878i	$-0.612788\pi$
$479$	−15.1875	−0.693932	−0.346966	+	0.937878i	$0.612788\pi$
$480$	−11.2759	−0.514670
$481$	4.08029	0.186045
$482$	−26.2799	−1.19702
$483$	−0.791944	−0.0360347
$484$	9.82748	0.446704
$485$	35.0371	1.59095
$486$	−1.63714	−0.0742623
$487$	12.4150	0.562580	0.281290	−	0.959623i	$-0.409238\pi$
$487$	12.4150	0.562580	0.281290	+	0.959623i	$0.409238\pi$
$488$	−19.2964	−0.873507
$489$	9.71531	0.439342
$490$	−4.99325	−0.225572
$491$	−17.3284	−0.782022	−0.391011	−	0.920386i	$-0.627874\pi$
$491$	−17.3284	−0.782022	−0.391011	+	0.920386i	$0.627874\pi$
$492$	1.54319	0.0695726
$493$	8.14950	0.367035
$494$	−7.73077	−0.347824
$495$	−15.3857	−0.691534
$496$	47.5304	2.13418
$497$	−5.56432	−0.249594
$498$	12.0154	0.538424
$499$	41.6090	1.86267	0.931336	−	0.364160i	$-0.118644\pi$
$499$	41.6090	1.86267	0.931336	+	0.364160i	$0.118644\pi$
$500$	1.44739	0.0647295
$501$	−10.8727	−0.485756
$502$	−44.8326	−2.00098
$503$	−9.20726	−0.410532	−0.205266	−	0.978706i	$-0.565806\pi$
$503$	−9.20726	−0.410532	−0.205266	+	0.978706i	$0.565806\pi$
$504$	2.16064	0.0962427
$505$	−3.76017	−0.167325
$506$	−6.54035	−0.290754
$507$	−1.00000	−0.0444116
$508$	6.75740	0.299811
$509$	27.8691	1.23528	0.617639	−	0.786462i	$-0.288089\pi$
$509$	27.8691	1.23528	0.617639	+	0.786462i	$0.288089\pi$
$510$	−4.99325	−0.221105
$511$	−7.88966	−0.349018
$512$	−3.05745	−0.135121
$513$	4.72211	0.208486
$514$	31.4435	1.38691
$515$	18.0979	0.797491
$516$	−3.38107	−0.148843
$517$	38.6210	1.69855
$518$	−6.68001	−0.293503
$519$	20.9663	0.920320
$520$	6.58991	0.288987
$521$	−29.9599	−1.31257	−0.656284	−	0.754514i	$-0.727873\pi$
$521$	−29.9599	−1.31257	−0.656284	+	0.754514i	$0.727873\pi$
$522$	−13.3419	−0.583959
$523$	−20.1619	−0.881616	−0.440808	−	0.897601i	$-0.645308\pi$
$523$	−20.1619	−0.881616	−0.440808	+	0.897601i	$0.645308\pi$
$524$	−5.15036	−0.224995
$525$	4.30236	0.187770
$526$	10.7263	0.467688
$527$	9.70453	0.422736
$528$	24.7068	1.07523
$529$	−22.3728	−0.972732
$530$	−8.02565	−0.348612
$531$	8.90811	0.386579
$532$	3.21215	0.139264
$533$	−2.26862	−0.0982647
$534$	−0.756861	−0.0327526
$535$	−8.67440	−0.375027
$536$	5.28440	0.228251
$537$	−15.7650	−0.680311
$538$	30.2654	1.30483
$539$	5.04452	0.217283
$540$	2.07470	0.0892810
$541$	19.9373	0.857173	0.428586	−	0.903501i	$-0.359012\pi$
$541$	19.9373	0.857173	0.428586	+	0.903501i	$0.359012\pi$
$542$	52.8035	2.26810
$543$	−19.7143	−0.846021
$544$	3.69703	0.158509
$545$	6.34622	0.271842
$546$	1.63714	0.0700632
$547$	−9.40906	−0.402302	−0.201151	−	0.979560i	$-0.564468\pi$
$547$	−9.40906	−0.402302	−0.201151	+	0.979560i	$0.564468\pi$
$548$	7.42648	0.317243
$549$	8.93086	0.381160
$550$	35.5315	1.51507
$551$	38.4828	1.63942
$552$	−1.71111	−0.0728296
$553$	−15.2147	−0.646996
$554$	−28.1870	−1.19755
$555$	12.4448	0.528251
$556$	−5.62283	−0.238461
$557$	9.21725	0.390548	0.195274	−	0.980749i	$-0.437440\pi$
$557$	9.21725	0.390548	0.195274	+	0.980749i	$0.437440\pi$
$558$	−15.8877	−0.672580
$559$	4.97044	0.210227
$560$	−14.9380	−0.631247
$561$	5.04452	0.212980
$562$	−28.2815	−1.19298
$563$	28.7743	1.21269	0.606346	−	0.795201i	$-0.292635\pi$
$563$	28.7743	1.21269	0.606346	+	0.795201i	$0.292635\pi$
$564$	−5.20791	−0.219293
$565$	−35.3509	−1.48722
$566$	10.1788	0.427846
$567$	−1.00000	−0.0419961
$568$	−12.0225	−0.504453
$569$	1.92956	0.0808913	0.0404457	−	0.999182i	$-0.487122\pi$
$569$	1.92956	0.0808913	0.0404457	+	0.999182i	$0.487122\pi$
$570$	−23.5787	−0.987601
$571$	−8.52963	−0.356954	−0.178477	−	0.983944i	$-0.557117\pi$
$571$	−8.52963	−0.356954	−0.178477	+	0.983944i	$0.557117\pi$
$572$	3.43146	0.143477
$573$	19.0873	0.797382
$574$	3.71405	0.155021
$575$	−3.40723	−0.142091
$576$	3.74294	0.155956
$577$	26.0657	1.08513	0.542564	−	0.840015i	$-0.317454\pi$
$577$	26.0657	1.08513	0.542564	+	0.840015i	$0.317454\pi$
$578$	1.63714	0.0680961
$579$	−2.17511	−0.0903943
$580$	16.9078	0.702058
$581$	7.33926	0.304484
$582$	18.8070	0.779573
$583$	8.10806	0.335802
$584$	−17.0467	−0.705399
$585$	−3.04998	−0.126101
$586$	2.72084	0.112397
$587$	−25.0292	−1.03307	−0.516534	−	0.856267i	$-0.672778\pi$
$587$	−25.0292	−1.03307	−0.516534	+	0.856267i	$0.672778\pi$
$588$	−0.680235	−0.0280524
$589$	45.8259	1.88822
$590$	−44.4804	−1.83123
$591$	15.2444	0.627070
$592$	−19.9842	−0.821346
$593$	−36.1707	−1.48535	−0.742677	−	0.669650i	$-0.766444\pi$
$593$	−36.1707	−1.48535	−0.742677	+	0.669650i	$0.766444\pi$
$594$	−8.25860	−0.338854
$595$	−3.04998	−0.125037
$596$	12.7454	0.522074
$597$	−21.7927	−0.891914
$598$	−1.29653	−0.0530189
$599$	−0.858625	−0.0350825	−0.0175412	−	0.999846i	$-0.505584\pi$
$599$	−0.858625	−0.0350825	−0.0175412	+	0.999846i	$0.505584\pi$
$600$	9.29586	0.379502
$601$	37.9385	1.54754	0.773771	−	0.633465i	$-0.218368\pi$
$601$	37.9385	1.54754	0.773771	+	0.633465i	$0.218368\pi$
$602$	−8.13731	−0.331652
$603$	−2.44575	−0.0995988
$604$	−1.44526	−0.0588067
$605$	−44.0636	−1.79144
$606$	−2.01835	−0.0819900
$607$	3.83083	0.155489	0.0777443	−	0.996973i	$-0.475228\pi$
$607$	3.83083	0.155489	0.0777443	+	0.996973i	$0.475228\pi$
$608$	17.4578	0.708006
$609$	−8.14950	−0.330234
$610$	−44.5940	−1.80556
$611$	7.65604	0.309730
$612$	−0.680235	−0.0274969
$613$	−9.02518	−0.364524	−0.182262	−	0.983250i	$-0.558342\pi$
$613$	−9.02518	−0.364524	−0.182262	+	0.983250i	$0.558342\pi$
$614$	21.7862	0.879219
$615$	−6.91923	−0.279010
$616$	10.8994	0.439150
$617$	22.6733	0.912793	0.456396	−	0.889777i	$-0.349140\pi$
$617$	22.6733	0.912793	0.456396	+	0.889777i	$0.349140\pi$
$618$	9.71447	0.390773
$619$	−33.6373	−1.35200	−0.675999	−	0.736903i	$-0.736287\pi$
$619$	−33.6373	−1.35200	−0.675999	+	0.736903i	$0.736287\pi$
$620$	20.1340	0.808601
$621$	0.791944	0.0317796
$622$	−24.6415	−0.988035
$623$	−0.462306	−0.0185219
$624$	4.89775	0.196067
$625$	−28.0015	−1.12006
$626$	40.1050	1.60292
$627$	23.8208	0.951310
$628$	12.1598	0.485228
$629$	−4.08029	−0.162692
$630$	4.99325	0.198936
$631$	27.4082	1.09110	0.545551	−	0.838077i	$-0.316320\pi$
$631$	27.4082	1.09110	0.545551	+	0.838077i	$0.316320\pi$
$632$	−32.8736	−1.30764
$633$	−18.4960	−0.735150
$634$	27.7497	1.10208
$635$	−30.2982	−1.20235
$636$	−1.09334	−0.0433539
$637$	1.00000	0.0396214
$638$	−67.3034	−2.66457
$639$	5.56432	0.220121
$640$	−41.2411	−1.63020
$641$	−11.7827	−0.465388	−0.232694	−	0.972550i	$-0.574754\pi$
$641$	−11.7827	−0.465388	−0.232694	+	0.972550i	$0.574754\pi$
$642$	−4.65617	−0.183765
$643$	−38.0620	−1.50102	−0.750509	−	0.660860i	$-0.770192\pi$
$643$	−38.0620	−1.50102	−0.750509	+	0.660860i	$0.770192\pi$
$644$	0.538708	0.0212281
$645$	15.1597	0.596913
$646$	7.73077	0.304163
$647$	14.7488	0.579836	0.289918	−	0.957051i	$-0.406372\pi$
$647$	14.7488	0.579836	0.289918	+	0.957051i	$0.406372\pi$
$648$	−2.16064	−0.0848781
$649$	44.9371	1.76394
$650$	7.04358	0.276272
$651$	−9.70453	−0.380351
$652$	−6.60870	−0.258817
$653$	17.1947	0.672880	0.336440	−	0.941705i	$-0.390777\pi$
$653$	17.1947	0.672880	0.336440	+	0.941705i	$0.390777\pi$
$654$	3.40647	0.133204
$655$	23.0927	0.902307
$656$	11.1111	0.433817
$657$	7.88966	0.307805
$658$	−12.5340	−0.488627
$659$	35.2938	1.37485	0.687426	−	0.726254i	$-0.258740\pi$
$659$	35.2938	1.37485	0.687426	+	0.726254i	$0.258740\pi$
$660$	10.4659	0.407384
$661$	30.8304	1.19916	0.599582	−	0.800313i	$-0.295334\pi$
$661$	30.8304	1.19916	0.599582	+	0.800313i	$0.295334\pi$
$662$	8.94944	0.347830
$663$	1.00000	0.0388368
$664$	15.8575	0.615391
$665$	−14.4023	−0.558498
$666$	6.68001	0.258845
$667$	6.45395	0.249898
$668$	7.39599	0.286159
$669$	0.527733	0.0204033
$670$	12.2123	0.471801
$671$	45.0519	1.73921
$672$	−3.69703	−0.142616
$673$	3.60074	0.138798	0.0693991	−	0.997589i	$-0.477892\pi$
$673$	3.60074	0.138798	0.0693991	+	0.997589i	$0.477892\pi$
$674$	33.9194	1.30653
$675$	−4.30236	−0.165598
$676$	0.680235	0.0261629
$677$	42.3986	1.62951	0.814755	−	0.579806i	$-0.196872\pi$
$677$	42.3986	1.62951	0.814755	+	0.579806i	$0.196872\pi$
$678$	−18.9754	−0.728744
$679$	11.4877	0.440856
$680$	−6.58991	−0.252712
$681$	16.7604	0.642261
$682$	−80.1458	−3.06894
$683$	12.3955	0.474300	0.237150	−	0.971473i	$-0.423787\pi$
$683$	12.3955	0.474300	0.237150	+	0.971473i	$0.423787\pi$
$684$	−3.21215	−0.122819
$685$	−33.2982	−1.27226
$686$	−1.63714	−0.0625064
$687$	−7.56242	−0.288524
$688$	−24.3440	−0.928105
$689$	1.60730	0.0612333
$690$	−3.95437	−0.150540
$691$	4.40203	0.167461	0.0837306	−	0.996488i	$-0.473316\pi$
$691$	4.40203	0.167461	0.0837306	+	0.996488i	$0.473316\pi$
$692$	−14.2620	−0.542161
$693$	−5.04452	−0.191625
$694$	−15.4589	−0.586811
$695$	25.2111	0.956313
$696$	−17.6082	−0.667436
$697$	2.26862	0.0859300
$698$	12.9210	0.489067
$699$	19.2984	0.729932
$700$	−2.92662	−0.110616
$701$	3.97561	0.150157	0.0750784	−	0.997178i	$-0.476079\pi$
$701$	3.97561	0.150157	0.0750784	+	0.997178i	$0.476079\pi$
$702$	−1.63714	−0.0617900
$703$	−19.2676	−0.726690
$704$	18.8813	0.711616
$705$	23.3507	0.879440
$706$	−49.5333	−1.86421
$707$	−1.23285	−0.0463662
$708$	−6.05961	−0.227734
$709$	−21.8383	−0.820155	−0.410078	−	0.912051i	$-0.634498\pi$
$709$	−21.8383	−0.820155	−0.410078	+	0.912051i	$0.634498\pi$
$710$	−27.7840	−1.04272
$711$	15.2147	0.570597
$712$	−0.998878	−0.0374346
$713$	7.68544	0.287822
$714$	−1.63714	−0.0612685
$715$	−15.3857	−0.575391
$716$	10.7239	0.400772
$717$	−16.0919	−0.600962
$718$	12.4644	0.465167
$719$	−33.3681	−1.24442	−0.622209	−	0.782851i	$-0.713765\pi$
$719$	−33.3681	−1.24442	−0.622209	+	0.782851i	$0.713765\pi$
$720$	14.9380	0.556707
$721$	5.93380	0.220986
$722$	5.39982	0.200960
$723$	16.0523	0.596991
$724$	13.4104	0.498392
$725$	−35.0621	−1.30217
$726$	−23.6521	−0.877811
$727$	31.9938	1.18658	0.593291	−	0.804988i	$-0.297828\pi$
$727$	31.9938	1.18658	0.593291	+	0.804988i	$0.297828\pi$
$728$	2.16064	0.0800787
$729$	1.00000	0.0370370
$730$	−39.3950	−1.45808
$731$	−4.97044	−0.183838
$732$	−6.07509	−0.224542
$733$	−13.9596	−0.515611	−0.257806	−	0.966197i	$-0.582999\pi$
$733$	−13.9596	−0.515611	−0.257806	+	0.966197i	$0.582999\pi$
$734$	−49.4516	−1.82529
$735$	3.04998	0.112500
$736$	2.92784	0.107922
$737$	−12.3377	−0.454463
$738$	−3.71405	−0.136716
$739$	19.0970	0.702496	0.351248	−	0.936282i	$-0.385757\pi$
$739$	19.0970	0.702496	0.351248	+	0.936282i	$0.385757\pi$
$740$	−8.46538	−0.311193
$741$	4.72211	0.173471
$742$	−2.63138	−0.0966010
$743$	−36.9948	−1.35721	−0.678604	−	0.734505i	$-0.737415\pi$
$743$	−36.9948	−1.35721	−0.678604	+	0.734505i	$0.737415\pi$
$744$	−20.9680	−0.768725
$745$	−57.1469	−2.09370
$746$	12.2312	0.447818
$747$	−7.33926	−0.268529
$748$	−3.43146	−0.125467
$749$	−2.84409	−0.103921
$750$	−3.48349	−0.127199
$751$	21.6688	0.790706	0.395353	−	0.918529i	$-0.370622\pi$
$751$	21.6688	0.790706	0.395353	+	0.918529i	$0.370622\pi$
$752$	−37.4974	−1.36739
$753$	27.3847	0.997953
$754$	−13.3419	−0.485883
$755$	6.48011	0.235835
$756$	0.680235	0.0247399
$757$	−19.5914	−0.712061	−0.356030	−	0.934474i	$-0.615870\pi$
$757$	−19.5914	−0.712061	−0.356030	+	0.934474i	$0.615870\pi$
$758$	−34.9132	−1.26811
$759$	3.99498	0.145008
$760$	−31.1183	−1.12878
$761$	24.0791	0.872867	0.436433	−	0.899737i	$-0.356241\pi$
$761$	24.0791	0.872867	0.436433	+	0.899737i	$0.356241\pi$
$762$	−16.2632	−0.589154
$763$	2.08074	0.0753280
$764$	−12.9838	−0.469739
$765$	3.04998	0.110272
$766$	40.5645	1.46566
$767$	8.90811	0.321653
$768$	−14.6512	−0.528680
$769$	−7.49457	−0.270261	−0.135131	−	0.990828i	$-0.543145\pi$
$769$	−7.49457	−0.270261	−0.135131	+	0.990828i	$0.543145\pi$
$770$	25.1885	0.907732
$771$	−19.2063	−0.691699
$772$	1.47958	0.0532514
$773$	−33.5529	−1.20682	−0.603408	−	0.797433i	$-0.706191\pi$
$773$	−33.5529	−1.20682	−0.603408	+	0.797433i	$0.706191\pi$
$774$	8.13731	0.292490
$775$	−41.7524	−1.49979
$776$	24.8207	0.891013
$777$	4.08029	0.146379
$778$	−18.6095	−0.667182
$779$	10.7127	0.383821
$780$	2.07470	0.0742863
$781$	28.0693	1.00440
$782$	1.29653	0.0463636
$783$	8.14950	0.291239
$784$	−4.89775	−0.174920
$785$	−54.5210	−1.94594
$786$	12.3955	0.442134
$787$	25.8771	0.922418	0.461209	−	0.887292i	$-0.347416\pi$
$787$	25.8771	0.922418	0.461209	+	0.887292i	$0.347416\pi$
$788$	−10.3698	−0.369408
$789$	−6.55183	−0.233251
$790$	−75.9709	−2.70292
$791$	−11.5905	−0.412112
$792$	−10.8994	−0.387293
$793$	8.93086	0.317144
$794$	30.5033	1.08252
$795$	4.90223	0.173864
$796$	14.8241	0.525428
$797$	38.8681	1.37678	0.688390	−	0.725341i	$-0.258318\pi$
$797$	38.8681	1.37678	0.688390	+	0.725341i	$0.258318\pi$
$798$	−7.73077	−0.273666
$799$	−7.65604	−0.270851
$800$	−15.9060	−0.562360
$801$	0.462306	0.0163348
$802$	−5.87505	−0.207455
$803$	39.7996	1.40450
$804$	1.66369	0.0586738
$805$	−2.41541	−0.0851320
$806$	−15.8877	−0.559620
$807$	−18.4867	−0.650762
$808$	−2.66375	−0.0937105
$809$	34.3213	1.20667	0.603336	−	0.797487i	$-0.293838\pi$
$809$	34.3213	1.20667	0.603336	+	0.797487i	$0.293838\pi$
$810$	−4.99325	−0.175445
$811$	−11.8616	−0.416517	−0.208258	−	0.978074i	$-0.566779\pi$
$811$	−11.8616	−0.416517	−0.208258	+	0.978074i	$0.566779\pi$
$812$	5.54358	0.194541
$813$	−32.2534	−1.13118
$814$	33.6974	1.18109
$815$	29.6315	1.03795
$816$	−4.89775	−0.171456
$817$	−23.4709	−0.821144
$818$	−1.01159	−0.0353696
$819$	−1.00000	−0.0349428
$820$	4.70671	0.164365
$821$	−10.6980	−0.373363	−0.186682	−	0.982420i	$-0.559773\pi$
$821$	−10.6980	−0.373363	−0.186682	+	0.982420i	$0.559773\pi$
$822$	−17.8735	−0.623411
$823$	−8.43360	−0.293977	−0.146988	−	0.989138i	$-0.546958\pi$
$823$	−8.43360	−0.293977	−0.146988	+	0.989138i	$0.546958\pi$
$824$	12.8208	0.446634
$825$	−21.7033	−0.755613
$826$	−14.5838	−0.507437
$827$	−52.1039	−1.81183	−0.905914	−	0.423461i	$-0.860815\pi$
$827$	−52.1039	−1.81183	−0.905914	+	0.423461i	$0.860815\pi$
$828$	−0.538708	−0.0187214
$829$	23.2172	0.806366	0.403183	−	0.915119i	$-0.367904\pi$
$829$	23.2172	0.806366	0.403183	+	0.915119i	$0.367904\pi$
$830$	36.6467	1.27203
$831$	17.2172	0.597258
$832$	3.74294	0.129763
$833$	−1.00000	−0.0346479
$834$	13.5326	0.468597
$835$	−33.1615	−1.14760
$836$	−16.2037	−0.560418
$837$	9.70453	0.335438
$838$	−26.9344	−0.930433
$839$	8.79687	0.303702	0.151851	−	0.988403i	$-0.451477\pi$
$839$	8.79687	0.303702	0.151851	+	0.988403i	$0.451477\pi$
$840$	6.58991	0.227374
$841$	37.4144	1.29015
$842$	−26.0817	−0.898834
$843$	17.2749	0.594979
$844$	12.5816	0.433078
$845$	−3.04998	−0.104922
$846$	12.5340	0.430929
$847$	−14.4472	−0.496411
$848$	−7.87216	−0.270331
$849$	−6.21741	−0.213381
$850$	−7.04358	−0.241593
$851$	−3.23136	−0.110770
$852$	−3.78504	−0.129673
$853$	21.1962	0.725745	0.362873	−	0.931839i	$-0.381796\pi$
$853$	21.1962	0.725745	0.362873	+	0.931839i	$0.381796\pi$
$854$	−14.6211	−0.500323
$855$	14.4023	0.492549
$856$	−6.14505	−0.210034
$857$	0.162704	0.00555786	0.00277893	−	0.999996i	$-0.499115\pi$
$857$	0.162704	0.00555786	0.00277893	+	0.999996i	$0.499115\pi$
$858$	−8.25860	−0.281944
$859$	24.7913	0.845870	0.422935	−	0.906160i	$-0.361000\pi$
$859$	24.7913	0.845870	0.422935	+	0.906160i	$0.361000\pi$
$860$	−10.3122	−0.351642
$861$	−2.26862	−0.0773143
$862$	−46.7289	−1.59159
$863$	32.5434	1.10779	0.553894	−	0.832587i	$-0.313141\pi$
$863$	32.5434	1.10779	0.553894	+	0.832587i	$0.313141\pi$
$864$	3.69703	0.125776
$865$	63.9468	2.17426
$866$	−53.1588	−1.80641
$867$	−1.00000	−0.0339618
$868$	6.60136	0.224065
$869$	76.7510	2.60360
$870$	−40.6925	−1.37960
$871$	−2.44575	−0.0828712
$872$	4.49574	0.152245
$873$	−11.4877	−0.388799
$874$	6.12233	0.207091
$875$	−2.12779	−0.0719323
$876$	−5.36683	−0.181328
$877$	24.6304	0.831708	0.415854	−	0.909431i	$-0.363483\pi$
$877$	24.6304	0.831708	0.415854	+	0.909431i	$0.363483\pi$
$878$	−31.7271	−1.07074
$879$	−1.66195	−0.0560561
$880$	75.3552	2.54022
$881$	0.390624	0.0131605	0.00658023	−	0.999978i	$-0.497905\pi$
$881$	0.390624	0.0131605	0.00658023	+	0.999978i	$0.497905\pi$
$882$	1.63714	0.0551255
$883$	36.4740	1.22745	0.613725	−	0.789520i	$-0.289671\pi$
$883$	36.4740	1.22745	0.613725	+	0.789520i	$0.289671\pi$
$884$	−0.680235	−0.0228788
$885$	27.1695	0.913294
$886$	39.8242	1.33792
$887$	39.5990	1.32960	0.664802	−	0.747019i	$-0.268516\pi$
$887$	39.5990	1.32960	0.664802	+	0.747019i	$0.268516\pi$
$888$	8.81604	0.295847
$889$	−9.93391	−0.333173
$890$	−2.30841	−0.0773780
$891$	5.04452	0.168998
$892$	−0.358983	−0.0120196
$893$	−36.1527	−1.20980
$894$	−30.6748	−1.02592
$895$	−48.0829	−1.60724
$896$	−13.5218	−0.451731
$897$	0.791944	0.0264422
$898$	−57.2579	−1.91072
$899$	79.0871	2.63770
$900$	2.92662	0.0975539
$901$	−1.60730	−0.0535469
$902$	−18.7356	−0.623827
$903$	4.97044	0.165406
$904$	−25.0430	−0.832918
$905$	−60.1281	−1.99873
$906$	3.47834	0.115560
$907$	24.7662	0.822347	0.411173	−	0.911557i	$-0.365119\pi$
$907$	24.7662	0.822347	0.411173	+	0.911557i	$0.365119\pi$
$908$	−11.4010	−0.378357
$909$	1.23285	0.0408911
$910$	4.99325	0.165525
$911$	−21.5906	−0.715330	−0.357665	−	0.933850i	$-0.616427\pi$
$911$	−21.5906	−0.715330	−0.357665	+	0.933850i	$0.616427\pi$
$912$	−23.1277	−0.765835
$913$	−37.0230	−1.22528
$914$	15.0527	0.497900
$915$	27.2389	0.900491
$916$	5.14423	0.169970
$917$	7.57144	0.250031
$918$	1.63714	0.0540338
$919$	28.5429	0.941543	0.470771	−	0.882255i	$-0.343976\pi$
$919$	28.5429	0.941543	0.470771	+	0.882255i	$0.343976\pi$
$920$	−5.21884	−0.172060
$921$	−13.3075	−0.438495
$922$	30.5803	1.00711
$923$	5.56432	0.183152
$924$	3.43146	0.112887
$925$	17.5549	0.577200
$926$	42.5985	1.39987
$927$	−5.93380	−0.194891
$928$	30.1289	0.989031
$929$	−24.6597	−0.809059	−0.404530	−	0.914525i	$-0.632565\pi$
$929$	−24.6597	−0.809059	−0.404530	+	0.914525i	$0.632565\pi$
$930$	−48.4571	−1.58897
$931$	−4.72211	−0.154761
$932$	−13.1274	−0.430004
$933$	15.0516	0.492766
$934$	18.8672	0.617352
$935$	15.3857	0.503165
$936$	−2.16064	−0.0706228
$937$	4.02770	0.131579	0.0657897	−	0.997834i	$-0.479043\pi$
$937$	4.02770	0.131579	0.0657897	+	0.997834i	$0.479043\pi$
$938$	4.00405	0.130737
$939$	−24.4970	−0.799428
$940$	−15.8840	−0.518079
$941$	−30.4691	−0.993265	−0.496632	−	0.867961i	$-0.665430\pi$
$941$	−30.4691	−0.993265	−0.496632	+	0.867961i	$0.665430\pi$
$942$	−29.2653	−0.953516
$943$	1.79662	0.0585059
$944$	−43.6297	−1.42003
$945$	−3.04998	−0.0992158
$946$	41.0488	1.33461
$947$	−28.1327	−0.914189	−0.457094	−	0.889418i	$-0.651110\pi$
$947$	−28.1327	−0.914189	−0.457094	+	0.889418i	$0.651110\pi$
$948$	−10.3496	−0.336139
$949$	7.88966	0.256109
$950$	−33.2605	−1.07911
$951$	−16.9501	−0.549644
$952$	−2.16064	−0.0700268
$953$	−24.6384	−0.798115	−0.399057	−	0.916926i	$-0.630663\pi$
$953$	−24.6384	−0.798115	−0.399057	+	0.916926i	$0.630663\pi$
$954$	2.63138	0.0851941
$955$	58.2157	1.88382
$956$	10.9463	0.354027
$957$	41.1103	1.32891
$958$	−24.8640	−0.803320
$959$	−10.9175	−0.352545
$960$	11.4159	0.368446
$961$	63.1779	2.03800
$962$	6.68001	0.215372
$963$	2.84409	0.0916494
$964$	−10.9193	−0.351688
$965$	−6.63402	−0.213557
$966$	−1.29653	−0.0417150
$967$	44.9309	1.44488	0.722440	−	0.691434i	$-0.243021\pi$
$967$	44.9309	1.44488	0.722440	+	0.691434i	$0.243021\pi$
$968$	−31.2152	−1.00329
$969$	−4.72211	−0.151696
$970$	57.3608	1.84174
$971$	52.9706	1.69991	0.849954	−	0.526856i	$-0.176629\pi$
$971$	52.9706	1.69991	0.849954	+	0.526856i	$0.176629\pi$
$972$	−0.680235	−0.0218186
$973$	8.26601	0.264996
$974$	20.3252	0.651261
$975$	−4.30236	−0.137786
$976$	−43.7411	−1.40012
$977$	25.9800	0.831175	0.415588	−	0.909553i	$-0.363576\pi$
$977$	25.9800	0.831175	0.415588	+	0.909553i	$0.363576\pi$
$978$	15.9054	0.508597
$979$	2.33211	0.0745346
$980$	−2.07470	−0.0662739
$981$	−2.08074	−0.0664330
$982$	−28.3691	−0.905295
$983$	−54.9214	−1.75172	−0.875861	−	0.482564i	$-0.839706\pi$
$983$	−54.9214	−1.75172	−0.875861	+	0.482564i	$0.839706\pi$
$984$	−4.90167	−0.156260
$985$	46.4950	1.48145
$986$	13.3419	0.424892
$987$	7.65604	0.243694
$988$	−3.21215	−0.102192
$989$	−3.93631	−0.125167
$990$	−25.1885	−0.800544
$991$	26.5483	0.843336	0.421668	−	0.906750i	$-0.361445\pi$
$991$	26.5483	0.843336	0.421668	+	0.906750i	$0.361445\pi$
$992$	35.8779	1.13913
$993$	−5.46650	−0.173474
$994$	−9.10958	−0.288938
$995$	−66.4671	−2.10715
$996$	4.99242	0.158191
$997$	5.84962	0.185259	0.0926296	−	0.995701i	$-0.470473\pi$
$997$	5.84962	0.185259	0.0926296	+	0.995701i	$0.470473\pi$
$998$	68.1198	2.15629
$999$	−4.08029	−0.129095

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4641.2.a.ba.1.13	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4641.2.a.ba.1.13	✓	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)

\(f(q)\)	\(=\)	\(q+1.63714 q^{2} -1.00000 q^{3} +0.680235 q^{4} -3.04998 q^{5} -1.63714 q^{6} -1.00000 q^{7} -2.16064 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.63714 q^{2} -1.00000 q^{3} +0.680235 q^{4} -3.04998 q^{5} -1.63714 q^{6} -1.00000 q^{7} -2.16064 q^{8} +1.00000 q^{9} -4.99325 q^{10} +5.04452 q^{11} -0.680235 q^{12} +1.00000 q^{13} -1.63714 q^{14} +3.04998 q^{15} -4.89775 q^{16} -1.00000 q^{17} +1.63714 q^{18} -4.72211 q^{19} -2.07470 q^{20} +1.00000 q^{21} +8.25860 q^{22} -0.791944 q^{23} +2.16064 q^{24} +4.30236 q^{25} +1.63714 q^{26} -1.00000 q^{27} -0.680235 q^{28} -8.14950 q^{29} +4.99325 q^{30} -9.70453 q^{31} -3.69703 q^{32} -5.04452 q^{33} -1.63714 q^{34} +3.04998 q^{35} +0.680235 q^{36} +4.08029 q^{37} -7.73077 q^{38} -1.00000 q^{39} +6.58991 q^{40} -2.26862 q^{41} +1.63714 q^{42} +4.97044 q^{43} +3.43146 q^{44} -3.04998 q^{45} -1.29653 q^{46} +7.65604 q^{47} +4.89775 q^{48} +1.00000 q^{49} +7.04358 q^{50} +1.00000 q^{51} +0.680235 q^{52} +1.60730 q^{53} -1.63714 q^{54} -15.3857 q^{55} +2.16064 q^{56} +4.72211 q^{57} -13.3419 q^{58} +8.90811 q^{59} +2.07470 q^{60} +8.93086 q^{61} -15.8877 q^{62} -1.00000 q^{63} +3.74294 q^{64} -3.04998 q^{65} -8.25860 q^{66} -2.44575 q^{67} -0.680235 q^{68} +0.791944 q^{69} +4.99325 q^{70} +5.56432 q^{71} -2.16064 q^{72} +7.88966 q^{73} +6.68001 q^{74} -4.30236 q^{75} -3.21215 q^{76} -5.04452 q^{77} -1.63714 q^{78} +15.2147 q^{79} +14.9380 q^{80} +1.00000 q^{81} -3.71405 q^{82} -7.33926 q^{83} +0.680235 q^{84} +3.04998 q^{85} +8.13731 q^{86} +8.14950 q^{87} -10.8994 q^{88} +0.462306 q^{89} -4.99325 q^{90} -1.00000 q^{91} -0.538708 q^{92} +9.70453 q^{93} +12.5340 q^{94} +14.4023 q^{95} +3.69703 q^{96} -11.4877 q^{97} +1.63714 q^{98} +5.04452 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + q^{2} - 17 q^{3} + 25 q^{4} - 4 q^{5} - q^{6} - 17 q^{7} + 6 q^{8} + 17 q^{9}+O(q^{10}) \) 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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