LMFDB - Embedded newform 4641.2.a.w.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4641.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4641 = 3 \cdot 7 \cdot 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4641.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

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

Embedding invariants

Embedding label			1.12
Root			$-1.98662$ 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)

$f(q)$	$=$	$q+1.98662 q^{2} -1.00000 q^{3} +1.94664 q^{4} -1.69822 q^{5} -1.98662 q^{6} +1.00000 q^{7} -0.106000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.98662 q^{2} -1.00000 q^{3} +1.94664 q^{4} -1.69822 q^{5} -1.98662 q^{6} +1.00000 q^{7} -0.106000 q^{8} +1.00000 q^{9} -3.37371 q^{10} +0.449673 q^{11} -1.94664 q^{12} +1.00000 q^{13} +1.98662 q^{14} +1.69822 q^{15} -4.10387 q^{16} +1.00000 q^{17} +1.98662 q^{18} +4.75881 q^{19} -3.30583 q^{20} -1.00000 q^{21} +0.893328 q^{22} +5.83945 q^{23} +0.106000 q^{24} -2.11605 q^{25} +1.98662 q^{26} -1.00000 q^{27} +1.94664 q^{28} -9.68110 q^{29} +3.37371 q^{30} -1.96396 q^{31} -7.94081 q^{32} -0.449673 q^{33} +1.98662 q^{34} -1.69822 q^{35} +1.94664 q^{36} +9.74675 q^{37} +9.45393 q^{38} -1.00000 q^{39} +0.180011 q^{40} +2.27141 q^{41} -1.98662 q^{42} -5.71362 q^{43} +0.875353 q^{44} -1.69822 q^{45} +11.6007 q^{46} +5.36809 q^{47} +4.10387 q^{48} +1.00000 q^{49} -4.20377 q^{50} -1.00000 q^{51} +1.94664 q^{52} +2.00123 q^{53} -1.98662 q^{54} -0.763644 q^{55} -0.106000 q^{56} -4.75881 q^{57} -19.2326 q^{58} -0.670760 q^{59} +3.30583 q^{60} +8.22174 q^{61} -3.90163 q^{62} +1.00000 q^{63} -7.56760 q^{64} -1.69822 q^{65} -0.893328 q^{66} +7.51834 q^{67} +1.94664 q^{68} -5.83945 q^{69} -3.37371 q^{70} +7.79790 q^{71} -0.106000 q^{72} +11.8708 q^{73} +19.3631 q^{74} +2.11605 q^{75} +9.26371 q^{76} +0.449673 q^{77} -1.98662 q^{78} -4.46814 q^{79} +6.96927 q^{80} +1.00000 q^{81} +4.51241 q^{82} +5.59406 q^{83} -1.94664 q^{84} -1.69822 q^{85} -11.3508 q^{86} +9.68110 q^{87} -0.0476652 q^{88} +7.23859 q^{89} -3.37371 q^{90} +1.00000 q^{91} +11.3673 q^{92} +1.96396 q^{93} +10.6643 q^{94} -8.08151 q^{95} +7.94081 q^{96} +11.5484 q^{97} +1.98662 q^{98} +0.449673 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - q^{2} - 14 q^{3} + 17 q^{4} - q^{5} + q^{6} + 14 q^{7} - 6 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q - q^2 - 14 * q^3 + 17 * q^4 - q^5 + q^6 + 14 * q^7 - 6 * q^8 + 14 * q^9	\( 14 q - q^{2} - 14 q^{3} + 17 q^{4} - q^{5} + q^{6} + 14 q^{7} - 6 q^{8} + 14 q^{9} + 11 q^{10} - 4 q^{11} - 17 q^{12} + 14 q^{13} - q^{14} + q^{15} + 19 q^{16} + 14 q^{17} - q^{18} + 6 q^{19} + q^{20} - 14 q^{21} + 12 q^{22} + 7 q^{23} + 6 q^{24} + 19 q^{25} - q^{26} - 14 q^{27} + 17 q^{28} - 4 q^{29} - 11 q^{30} + 31 q^{31} - 18 q^{32} + 4 q^{33} - q^{34} - q^{35} + 17 q^{36} + 2 q^{37} + 9 q^{38} - 14 q^{39} + 50 q^{40} + 4 q^{41} + q^{42} + 14 q^{43} - 8 q^{44} - q^{45} - 17 q^{46} - q^{47} - 19 q^{48} + 14 q^{49} - 3 q^{50} - 14 q^{51} + 17 q^{52} - 43 q^{53} + q^{54} + 23 q^{55} - 6 q^{56} - 6 q^{57} - 10 q^{58} + 11 q^{59} - q^{60} + 25 q^{61} - 3 q^{62} + 14 q^{63} + 36 q^{64} - q^{65} - 12 q^{66} + 11 q^{67} + 17 q^{68} - 7 q^{69} + 11 q^{70} + 20 q^{71} - 6 q^{72} + 14 q^{73} - 24 q^{74} - 19 q^{75} + 9 q^{76} - 4 q^{77} + q^{78} + 42 q^{79} + 13 q^{80} + 14 q^{81} + 2 q^{82} + 15 q^{83} - 17 q^{84} - q^{85} - 11 q^{86} + 4 q^{87} + 63 q^{88} + 21 q^{89} + 11 q^{90} + 14 q^{91} + 30 q^{92} - 31 q^{93} - 29 q^{94} + 16 q^{95} + 18 q^{96} + 15 q^{97} - q^{98} - 4 q^{99}+O(q^{100}) \) 14 * q - q^2 - 14 * q^3 + 17 * q^4 - q^5 + q^6 + 14 * q^7 - 6 * q^8 + 14 * q^9 + 11 * q^10 - 4 * q^11 - 17 * q^12 + 14 * q^13 - q^14 + q^15 + 19 * q^16 + 14 * q^17 - q^18 + 6 * q^19 + q^20 - 14 * q^21 + 12 * q^22 + 7 * q^23 + 6 * q^24 + 19 * q^25 - q^26 - 14 * q^27 + 17 * q^28 - 4 * q^29 - 11 * q^30 + 31 * q^31 - 18 * q^32 + 4 * q^33 - q^34 - q^35 + 17 * q^36 + 2 * q^37 + 9 * q^38 - 14 * q^39 + 50 * q^40 + 4 * q^41 + q^42 + 14 * q^43 - 8 * q^44 - q^45 - 17 * q^46 - q^47 - 19 * q^48 + 14 * q^49 - 3 * q^50 - 14 * q^51 + 17 * q^52 - 43 * q^53 + q^54 + 23 * q^55 - 6 * q^56 - 6 * q^57 - 10 * q^58 + 11 * q^59 - q^60 + 25 * q^61 - 3 * q^62 + 14 * q^63 + 36 * q^64 - q^65 - 12 * q^66 + 11 * q^67 + 17 * q^68 - 7 * q^69 + 11 * q^70 + 20 * q^71 - 6 * q^72 + 14 * q^73 - 24 * q^74 - 19 * q^75 + 9 * q^76 - 4 * q^77 + q^78 + 42 * q^79 + 13 * q^80 + 14 * q^81 + 2 * q^82 + 15 * q^83 - 17 * q^84 - q^85 - 11 * q^86 + 4 * q^87 + 63 * q^88 + 21 * q^89 + 11 * q^90 + 14 * q^91 + 30 * q^92 - 31 * q^93 - 29 * q^94 + 16 * q^95 + 18 * q^96 + 15 * q^97 - q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.98662	1.40475	0.702375	−	0.711807i	$-0.252123\pi$
$2$	1.98662	1.40475	0.702375	+	0.711807i	$0.252123\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.94664	0.973322
$5$	−1.69822	−0.759467	−0.379734	−	0.925096i	$-0.623984\pi$
$5$	−1.69822	−0.759467	−0.379734	+	0.925096i	$0.623984\pi$
$6$	−1.98662	−0.811033
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−0.106000	−0.0374766
$9$	1.00000	0.333333
$10$	−3.37371	−1.06686
$11$	0.449673	0.135582	0.0677908	−	0.997700i	$-0.478405\pi$
$11$	0.449673	0.135582	0.0677908	+	0.997700i	$0.478405\pi$
$12$	−1.94664	−0.561947
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	1.98662	0.530945
$15$	1.69822	0.438479
$16$	−4.10387	−1.02597
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.98662	0.468250
$19$	4.75881	1.09175	0.545873	−	0.837868i	$-0.316198\pi$
$19$	4.75881	1.09175	0.545873	+	0.837868i	$0.316198\pi$
$20$	−3.30583	−0.739206
$21$	−1.00000	−0.218218
$22$	0.893328	0.190458
$23$	5.83945	1.21761	0.608804	−	0.793320i	$-0.291649\pi$
$23$	5.83945	1.21761	0.608804	+	0.793320i	$0.291649\pi$
$24$	0.106000	0.0216371
$25$	−2.11605	−0.423209
$26$	1.98662	0.389607
$27$	−1.00000	−0.192450
$28$	1.94664	0.367881
$29$	−9.68110	−1.79774	−0.898868	−	0.438219i	$-0.855609\pi$
$29$	−9.68110	−1.79774	−0.898868	+	0.438219i	$0.855609\pi$
$30$	3.37371	0.615953
$31$	−1.96396	−0.352737	−0.176368	−	0.984324i	$-0.556435\pi$
$31$	−1.96396	−0.352737	−0.176368	+	0.984324i	$0.556435\pi$
$32$	−7.94081	−1.40375
$33$	−0.449673	−0.0782781
$34$	1.98662	0.340702
$35$	−1.69822	−0.287052
$36$	1.94664	0.324441
$37$	9.74675	1.60236	0.801178	−	0.598426i	$-0.204207\pi$
$37$	9.74675	1.60236	0.801178	+	0.598426i	$0.204207\pi$
$38$	9.45393	1.53363
$39$	−1.00000	−0.160128
$40$	0.180011	0.0284622
$41$	2.27141	0.354734	0.177367	−	0.984145i	$-0.443242\pi$
$41$	2.27141	0.354734	0.177367	+	0.984145i	$0.443242\pi$
$42$	−1.98662	−0.306542
$43$	−5.71362	−0.871318	−0.435659	−	0.900112i	$-0.643485\pi$
$43$	−5.71362	−0.871318	−0.435659	+	0.900112i	$0.643485\pi$
$44$	0.875353	0.131964
$45$	−1.69822	−0.253156
$46$	11.6007	1.71044
$47$	5.36809	0.783017	0.391508	−	0.920175i	$-0.371953\pi$
$47$	5.36809	0.783017	0.391508	+	0.920175i	$0.371953\pi$
$48$	4.10387	0.592342
$49$	1.00000	0.142857
$50$	−4.20377	−0.594503
$51$	−1.00000	−0.140028
$52$	1.94664	0.269951
$53$	2.00123	0.274890	0.137445	−	0.990509i	$-0.456111\pi$
$53$	2.00123	0.274890	0.137445	+	0.990509i	$0.456111\pi$
$54$	−1.98662	−0.270344
$55$	−0.763644	−0.102970
$56$	−0.106000	−0.0141648
$57$	−4.75881	−0.630320
$58$	−19.2326	−2.52537
$59$	−0.670760	−0.0873255	−0.0436627	−	0.999046i	$-0.513903\pi$
$59$	−0.670760	−0.0873255	−0.0436627	+	0.999046i	$0.513903\pi$
$60$	3.30583	0.426781
$61$	8.22174	1.05269	0.526343	−	0.850272i	$-0.323563\pi$
$61$	8.22174	1.05269	0.526343	+	0.850272i	$0.323563\pi$
$62$	−3.90163	−0.495507
$63$	1.00000	0.125988
$64$	−7.56760	−0.945950
$65$	−1.69822	−0.210638
$66$	−0.893328	−0.109961
$67$	7.51834	0.918512	0.459256	−	0.888304i	$-0.348116\pi$
$67$	7.51834	0.918512	0.459256	+	0.888304i	$0.348116\pi$
$68$	1.94664	0.236065
$69$	−5.83945	−0.702987
$70$	−3.37371	−0.403236
$71$	7.79790	0.925441	0.462720	−	0.886504i	$-0.346873\pi$
$71$	7.79790	0.925441	0.462720	+	0.886504i	$0.346873\pi$
$72$	−0.106000	−0.0124922
$73$	11.8708	1.38938	0.694688	−	0.719311i	$-0.255542\pi$
$73$	11.8708	1.38938	0.694688	+	0.719311i	$0.255542\pi$
$74$	19.3631	2.25091
$75$	2.11605	0.244340
$76$	9.26371	1.06262
$77$	0.449673	0.0512450
$78$	−1.98662	−0.224940
$79$	−4.46814	−0.502706	−0.251353	−	0.967896i	$-0.580875\pi$
$79$	−4.46814	−0.502706	−0.251353	+	0.967896i	$0.580875\pi$
$80$	6.96927	0.779188
$81$	1.00000	0.111111
$82$	4.51241	0.498313
$83$	5.59406	0.614028	0.307014	−	0.951705i	$-0.400670\pi$
$83$	5.59406	0.614028	0.307014	+	0.951705i	$0.400670\pi$
$84$	−1.94664	−0.212396
$85$	−1.69822	−0.184198
$86$	−11.3508	−1.22398
$87$	9.68110	1.03792
$88$	−0.0476652	−0.00508113
$89$	7.23859	0.767289	0.383645	−	0.923481i	$-0.374669\pi$
$89$	7.23859	0.767289	0.383645	+	0.923481i	$0.374669\pi$
$90$	−3.37371	−0.355621
$91$	1.00000	0.104828
$92$	11.3673	1.18512
$93$	1.96396	0.203653
$94$	10.6643	1.09994
$95$	−8.08151	−0.829146
$96$	7.94081	0.810455
$97$	11.5484	1.17257	0.586283	−	0.810106i	$-0.300591\pi$
$97$	11.5484	1.17257	0.586283	+	0.810106i	$0.300591\pi$
$98$	1.98662	0.200679
$99$	0.449673	0.0451939
$100$	−4.11919	−0.411919
$101$	3.77784	0.375909	0.187954	−	0.982178i	$-0.439814\pi$
$101$	3.77784	0.375909	0.187954	+	0.982178i	$0.439814\pi$
$102$	−1.98662	−0.196704
$103$	−5.11826	−0.504317	−0.252158	−	0.967686i	$-0.581140\pi$
$103$	−5.11826	−0.504317	−0.252158	+	0.967686i	$0.581140\pi$
$104$	−0.106000	−0.0103941
$105$	1.69822	0.165729
$106$	3.97567	0.386151
$107$	−3.82645	−0.369917	−0.184958	−	0.982746i	$-0.559215\pi$
$107$	−3.82645	−0.369917	−0.184958	+	0.982746i	$0.559215\pi$
$108$	−1.94664	−0.187316
$109$	10.9811	1.05180	0.525900	−	0.850547i	$-0.323729\pi$
$109$	10.9811	1.05180	0.525900	+	0.850547i	$0.323729\pi$
$110$	−1.51707	−0.144647
$111$	−9.74675	−0.925121
$112$	−4.10387	−0.387779
$113$	9.77832	0.919867	0.459934	−	0.887953i	$-0.347873\pi$
$113$	9.77832	0.919867	0.459934	+	0.887953i	$0.347873\pi$
$114$	−9.45393	−0.885442
$115$	−9.91667	−0.924734
$116$	−18.8457	−1.74978
$117$	1.00000	0.0924500
$118$	−1.33254	−0.122670
$119$	1.00000	0.0916698
$120$	−0.180011	−0.0164327
$121$	−10.7978	−0.981618
$122$	16.3334	1.47876
$123$	−2.27141	−0.204806
$124$	−3.82312	−0.343326
$125$	12.0846	1.08088
$126$	1.98662	0.176982
$127$	−3.72804	−0.330810	−0.165405	−	0.986226i	$-0.552893\pi$
$127$	−3.72804	−0.330810	−0.165405	+	0.986226i	$0.552893\pi$
$128$	0.847696	0.0749264
$129$	5.71362	0.503056
$130$	−3.37371	−0.295894
$131$	−0.500894	−0.0437633	−0.0218816	−	0.999761i	$-0.506966\pi$
$131$	−0.500894	−0.0437633	−0.0218816	+	0.999761i	$0.506966\pi$
$132$	−0.875353	−0.0761897
$133$	4.75881	0.412641
$134$	14.9361	1.29028
$135$	1.69822	0.146160
$136$	−0.106000	−0.00908940
$137$	−12.5759	−1.07443	−0.537216	−	0.843445i	$-0.680524\pi$
$137$	−12.5759	−1.07443	−0.537216	+	0.843445i	$0.680524\pi$
$138$	−11.6007	−0.987520
$139$	17.8580	1.51470	0.757350	−	0.653010i	$-0.226494\pi$
$139$	17.8580	1.51470	0.757350	+	0.653010i	$0.226494\pi$
$140$	−3.30583	−0.279394
$141$	−5.36809	−0.452075
$142$	15.4914	1.30001
$143$	0.449673	0.0376036
$144$	−4.10387	−0.341989
$145$	16.4407	1.36532
$146$	23.5828	1.95173
$147$	−1.00000	−0.0824786
$148$	18.9735	1.55961
$149$	5.92364	0.485283	0.242642	−	0.970116i	$-0.421986\pi$
$149$	5.92364	0.485283	0.242642	+	0.970116i	$0.421986\pi$
$150$	4.20377	0.343236
$151$	11.2824	0.918150	0.459075	−	0.888398i	$-0.348181\pi$
$151$	11.2824	0.918150	0.459075	+	0.888398i	$0.348181\pi$
$152$	−0.504433	−0.0409149
$153$	1.00000	0.0808452
$154$	0.893328	0.0719864
$155$	3.33523	0.267892
$156$	−1.94664	−0.155856
$157$	15.9090	1.26967	0.634836	−	0.772647i	$-0.281068\pi$
$157$	15.9090	1.26967	0.634836	+	0.772647i	$0.281068\pi$
$158$	−8.87649	−0.706175
$159$	−2.00123	−0.158708
$160$	13.4852	1.06610
$161$	5.83945	0.460213
$162$	1.98662	0.156083
$163$	11.8251	0.926214	0.463107	−	0.886302i	$-0.346735\pi$
$163$	11.8251	0.926214	0.463107	+	0.886302i	$0.346735\pi$
$164$	4.42162	0.345270
$165$	0.763644	0.0594496
$166$	11.1132	0.862555
$167$	−7.18024	−0.555623	−0.277812	−	0.960636i	$-0.589609\pi$
$167$	−7.18024	−0.555623	−0.277812	+	0.960636i	$0.589609\pi$
$168$	0.106000	0.00817806
$169$	1.00000	0.0769231
$170$	−3.37371	−0.258752
$171$	4.75881	0.363915
$172$	−11.1224	−0.848073
$173$	11.3290	0.861328	0.430664	−	0.902512i	$-0.358279\pi$
$173$	11.3290	0.861328	0.430664	+	0.902512i	$0.358279\pi$
$174$	19.2326	1.45802
$175$	−2.11605	−0.159958
$176$	−1.84540	−0.139102
$177$	0.670760	0.0504174
$178$	14.3803	1.07785
$179$	−17.7042	−1.32327	−0.661637	−	0.749824i	$-0.730138\pi$
$179$	−17.7042	−1.32327	−0.661637	+	0.749824i	$0.730138\pi$
$180$	−3.30583	−0.246402
$181$	−6.91439	−0.513942	−0.256971	−	0.966419i	$-0.582725\pi$
$181$	−6.91439	−0.513942	−0.256971	+	0.966419i	$0.582725\pi$
$182$	1.98662	0.147258
$183$	−8.22174	−0.607768
$184$	−0.618980	−0.0456318
$185$	−16.5521	−1.21694
$186$	3.90163	0.286081
$187$	0.449673	0.0328834
$188$	10.4498	0.762127
$189$	−1.00000	−0.0727393
$190$	−16.0549	−1.16474
$191$	11.8918	0.860461	0.430230	−	0.902719i	$-0.358432\pi$
$191$	11.8918	0.860461	0.430230	+	0.902719i	$0.358432\pi$
$192$	7.56760	0.546145
$193$	17.4650	1.25716	0.628579	−	0.777746i	$-0.283637\pi$
$193$	17.4650	1.25716	0.628579	+	0.777746i	$0.283637\pi$
$194$	22.9423	1.64716
$195$	1.69822	0.121612
$196$	1.94664	0.139046
$197$	−13.1283	−0.935351	−0.467676	−	0.883900i	$-0.654908\pi$
$197$	−13.1283	−0.935351	−0.467676	+	0.883900i	$0.654908\pi$
$198$	0.893328	0.0634861
$199$	−10.5433	−0.747397	−0.373699	−	0.927550i	$-0.621911\pi$
$199$	−10.5433	−0.747397	−0.373699	+	0.927550i	$0.621911\pi$
$200$	0.224300	0.0158604
$201$	−7.51834	−0.530303
$202$	7.50511	0.528058
$203$	−9.68110	−0.679480
$204$	−1.94664	−0.136292
$205$	−3.85735	−0.269409
$206$	−10.1680	−0.708439
$207$	5.83945	0.405870
$208$	−4.10387	−0.284552
$209$	2.13991	0.148021
$210$	3.37371	0.232808
$211$	−27.8138	−1.91478	−0.957390	−	0.288797i	$-0.906745\pi$
$211$	−27.8138	−1.91478	−0.957390	+	0.288797i	$0.906745\pi$
$212$	3.89567	0.267556
$213$	−7.79790	−0.534303
$214$	−7.60168	−0.519640
$215$	9.70298	0.661738
$216$	0.106000	0.00721237
$217$	−1.96396	−0.133322
$218$	21.8152	1.47751
$219$	−11.8708	−0.802157
$220$	−1.48654	−0.100223
$221$	1.00000	0.0672673
$222$	−19.3631	−1.29956
$223$	7.44460	0.498527	0.249263	−	0.968436i	$-0.419811\pi$
$223$	7.44460	0.498527	0.249263	+	0.968436i	$0.419811\pi$
$224$	−7.94081	−0.530568
$225$	−2.11605	−0.141070
$226$	19.4258	1.29218
$227$	2.54857	0.169154	0.0845772	−	0.996417i	$-0.473046\pi$
$227$	2.54857	0.169154	0.0845772	+	0.996417i	$0.473046\pi$
$228$	−9.26371	−0.613504
$229$	−9.45282	−0.624660	−0.312330	−	0.949974i	$-0.601109\pi$
$229$	−9.45282	−0.624660	−0.312330	+	0.949974i	$0.601109\pi$
$230$	−19.7006	−1.29902
$231$	−0.449673	−0.0295863
$232$	1.02619	0.0673730
$233$	8.75498	0.573558	0.286779	−	0.957997i	$-0.407415\pi$
$233$	8.75498	0.573558	0.286779	+	0.957997i	$0.407415\pi$
$234$	1.98662	0.129869
$235$	−9.11621	−0.594676
$236$	−1.30573	−0.0849957
$237$	4.46814	0.290237
$238$	1.98662	0.128773
$239$	−24.7971	−1.60399	−0.801996	−	0.597329i	$-0.796229\pi$
$239$	−24.7971	−1.60399	−0.801996	+	0.597329i	$0.796229\pi$
$240$	−6.96927	−0.449865
$241$	16.1673	1.04143	0.520715	−	0.853731i	$-0.325666\pi$
$241$	16.1673	1.04143	0.520715	+	0.853731i	$0.325666\pi$
$242$	−21.4511	−1.37893
$243$	−1.00000	−0.0641500
$244$	16.0048	1.02460
$245$	−1.69822	−0.108495
$246$	−4.51241	−0.287701
$247$	4.75881	0.302796
$248$	0.208179	0.0132194
$249$	−5.59406	−0.354509
$250$	24.0075	1.51837
$251$	13.9725	0.881936	0.440968	−	0.897523i	$-0.354635\pi$
$251$	13.9725	0.881936	0.440968	+	0.897523i	$0.354635\pi$
$252$	1.94664	0.122627
$253$	2.62584	0.165085
$254$	−7.40618	−0.464705
$255$	1.69822	0.106347
$256$	16.8193	1.05120
$257$	−20.7125	−1.29201	−0.646005	−	0.763333i	$-0.723562\pi$
$257$	−20.7125	−1.29201	−0.646005	+	0.763333i	$0.723562\pi$
$258$	11.3508	0.706667
$259$	9.74675	0.605634
$260$	−3.30583	−0.205019
$261$	−9.68110	−0.599245
$262$	−0.995084	−0.0614765
$263$	−28.4679	−1.75541	−0.877704	−	0.479204i	$-0.840925\pi$
$263$	−28.4679	−1.75541	−0.877704	+	0.479204i	$0.840925\pi$
$264$	0.0476652	0.00293359
$265$	−3.39853	−0.208770
$266$	9.45393	0.579658
$267$	−7.23859	−0.442995
$268$	14.6355	0.894007
$269$	−30.1644	−1.83916	−0.919579	−	0.392905i	$-0.871470\pi$
$269$	−30.1644	−1.83916	−0.919579	+	0.392905i	$0.871470\pi$
$270$	3.37371	0.205318
$271$	26.2797	1.59638	0.798190	−	0.602406i	$-0.205791\pi$
$271$	26.2797	1.59638	0.798190	+	0.602406i	$0.205791\pi$
$272$	−4.10387	−0.248833
$273$	−1.00000	−0.0605228
$274$	−24.9835	−1.50931
$275$	−0.951529	−0.0573794
$276$	−11.3673	−0.684232
$277$	5.15867	0.309955	0.154977	−	0.987918i	$-0.450470\pi$
$277$	5.15867	0.309955	0.154977	+	0.987918i	$0.450470\pi$
$278$	35.4771	2.12777
$279$	−1.96396	−0.117579
$280$	0.180011	0.0107577
$281$	−16.9301	−1.00997	−0.504983	−	0.863129i	$-0.668501\pi$
$281$	−16.9301	−1.00997	−0.504983	+	0.863129i	$0.668501\pi$
$282$	−10.6643	−0.635052
$283$	−29.2739	−1.74015	−0.870075	−	0.492919i	$-0.835930\pi$
$283$	−29.2739	−1.74015	−0.870075	+	0.492919i	$0.835930\pi$
$284$	15.1797	0.900751
$285$	8.08151	0.478708
$286$	0.893328	0.0528236
$287$	2.27141	0.134077
$288$	−7.94081	−0.467917
$289$	1.00000	0.0588235
$290$	32.6613	1.91794
$291$	−11.5484	−0.676981
$292$	23.1083	1.35231
$293$	−25.8442	−1.50983	−0.754916	−	0.655822i	$-0.772322\pi$
$293$	−25.8442	−1.50983	−0.754916	+	0.655822i	$0.772322\pi$
$294$	−1.98662	−0.115862
$295$	1.13910	0.0663208
$296$	−1.03315	−0.0600508
$297$	−0.449673	−0.0260927
$298$	11.7680	0.681702
$299$	5.83945	0.337704
$300$	4.11919	0.237821
$301$	−5.71362	−0.329327
$302$	22.4138	1.28977
$303$	−3.77784	−0.217031
$304$	−19.5295	−1.12010
$305$	−13.9623	−0.799480
$306$	1.98662	0.113567
$307$	26.7883	1.52889	0.764444	−	0.644690i	$-0.223013\pi$
$307$	26.7883	1.52889	0.764444	+	0.644690i	$0.223013\pi$
$308$	0.875353	0.0498779
$309$	5.11826	0.291167
$310$	6.62582	0.376321
$311$	25.2681	1.43282	0.716411	−	0.697678i	$-0.245783\pi$
$311$	25.2681	1.43282	0.716411	+	0.697678i	$0.245783\pi$
$312$	0.106000	0.00600105
$313$	−21.6249	−1.22231	−0.611155	−	0.791511i	$-0.709295\pi$
$313$	−21.6249	−1.22231	−0.611155	+	0.791511i	$0.709295\pi$
$314$	31.6050	1.78357
$315$	−1.69822	−0.0956839
$316$	−8.69788	−0.489294
$317$	1.53562	0.0862489	0.0431245	−	0.999070i	$-0.486269\pi$
$317$	1.53562	0.0862489	0.0431245	+	0.999070i	$0.486269\pi$
$318$	−3.97567	−0.222944
$319$	−4.35333	−0.243740
$320$	12.8515	0.718418
$321$	3.82645	0.213571
$322$	11.6007	0.646484
$323$	4.75881	0.264787
$324$	1.94664	0.108147
$325$	−2.11605	−0.117377
$326$	23.4920	1.30110
$327$	−10.9811	−0.607256
$328$	−0.240768	−0.0132942
$329$	5.36809	0.295952
$330$	1.51707	0.0835119
$331$	−33.1025	−1.81948	−0.909740	−	0.415179i	$-0.863719\pi$
$331$	−33.1025	−1.81948	−0.909740	+	0.415179i	$0.863719\pi$
$332$	10.8896	0.597646
$333$	9.74675	0.534119
$334$	−14.2644	−0.780512
$335$	−12.7678	−0.697580
$336$	4.10387	0.223884
$337$	31.2951	1.70475	0.852376	−	0.522929i	$-0.175161\pi$
$337$	31.2951	1.70475	0.852376	+	0.522929i	$0.175161\pi$
$338$	1.98662	0.108058
$339$	−9.77832	−0.531086
$340$	−3.30583	−0.179284
$341$	−0.883138	−0.0478246
$342$	9.45393	0.511210
$343$	1.00000	0.0539949
$344$	0.605642	0.0326540
$345$	9.91667	0.533896
$346$	22.5064	1.20995
$347$	34.1540	1.83348	0.916741	−	0.399483i	$-0.130810\pi$
$347$	34.1540	1.83348	0.916741	+	0.399483i	$0.130810\pi$
$348$	18.8457	1.01023
$349$	9.19444	0.492167	0.246083	−	0.969249i	$-0.420856\pi$
$349$	9.19444	0.492167	0.246083	+	0.969249i	$0.420856\pi$
$350$	−4.20377	−0.224701
$351$	−1.00000	−0.0533761
$352$	−3.57077	−0.190323
$353$	4.09703	0.218063	0.109032	−	0.994038i	$-0.465225\pi$
$353$	4.09703	0.218063	0.109032	+	0.994038i	$0.465225\pi$
$354$	1.33254	0.0708238
$355$	−13.2426	−0.702842
$356$	14.0910	0.746819
$357$	−1.00000	−0.0529256
$358$	−35.1715	−1.85887
$359$	−9.48717	−0.500714	−0.250357	−	0.968154i	$-0.580548\pi$
$359$	−9.48717	−0.500714	−0.250357	+	0.968154i	$0.580548\pi$
$360$	0.180011	0.00948741
$361$	3.64629	0.191910
$362$	−13.7362	−0.721960
$363$	10.7978	0.566737
$364$	1.94664	0.102032
$365$	−20.1593	−1.05519
$366$	−16.3334	−0.853762
$367$	−1.22657	−0.0640263	−0.0320131	−	0.999487i	$-0.510192\pi$
$367$	−1.22657	−0.0640263	−0.0320131	+	0.999487i	$0.510192\pi$
$368$	−23.9643	−1.24923
$369$	2.27141	0.118245
$370$	−32.8827	−1.70949
$371$	2.00123	0.103899
$372$	3.82312	0.198220
$373$	−17.9176	−0.927736	−0.463868	−	0.885904i	$-0.653539\pi$
$373$	−17.9176	−0.927736	−0.463868	+	0.885904i	$0.653539\pi$
$374$	0.893328	0.0461929
$375$	−12.0846	−0.624047
$376$	−0.569016	−0.0293448
$377$	−9.68110	−0.498602
$378$	−1.98662	−0.102181
$379$	−17.7355	−0.911012	−0.455506	−	0.890233i	$-0.650542\pi$
$379$	−17.7355	−0.911012	−0.455506	+	0.890233i	$0.650542\pi$
$380$	−15.7318	−0.807026
$381$	3.72804	0.190993
$382$	23.6244	1.20873
$383$	27.6538	1.41304	0.706521	−	0.707692i	$-0.250263\pi$
$383$	27.6538	1.41304	0.706521	+	0.707692i	$0.250263\pi$
$384$	−0.847696	−0.0432588
$385$	−0.763644	−0.0389189
$386$	34.6962	1.76599
$387$	−5.71362	−0.290439
$388$	22.4807	1.14128
$389$	−12.3230	−0.624799	−0.312399	−	0.949951i	$-0.601133\pi$
$389$	−12.3230	−0.624799	−0.312399	+	0.949951i	$0.601133\pi$
$390$	3.37371	0.170835
$391$	5.83945	0.295314
$392$	−0.106000	−0.00535379
$393$	0.500894	0.0252667
$394$	−26.0808	−1.31393
$395$	7.58790	0.381788
$396$	0.875353	0.0439882
$397$	−10.1099	−0.507403	−0.253702	−	0.967283i	$-0.581648\pi$
$397$	−10.1099	−0.507403	−0.253702	+	0.967283i	$0.581648\pi$
$398$	−20.9456	−1.04991
$399$	−4.75881	−0.238239
$400$	8.68397	0.434199
$401$	−14.7762	−0.737890	−0.368945	−	0.929451i	$-0.620281\pi$
$401$	−14.7762	−0.737890	−0.368945	+	0.929451i	$0.620281\pi$
$402$	−14.9361	−0.744943
$403$	−1.96396	−0.0978316
$404$	7.35410	0.365880
$405$	−1.69822	−0.0843853
$406$	−19.2326	−0.954500
$407$	4.38285	0.217250
$408$	0.106000	0.00524777
$409$	−0.778856	−0.0385120	−0.0192560	−	0.999815i	$-0.506130\pi$
$409$	−0.778856	−0.0385120	−0.0192560	+	0.999815i	$0.506130\pi$
$410$	−7.66307	−0.378452
$411$	12.5759	0.620324
$412$	−9.96342	−0.490862
$413$	−0.670760	−0.0330059
$414$	11.6007	0.570145
$415$	−9.49995	−0.466334
$416$	−7.94081	−0.389330
$417$	−17.8580	−0.874512
$418$	4.25118	0.207932
$419$	−12.2176	−0.596871	−0.298435	−	0.954430i	$-0.596465\pi$
$419$	−12.2176	−0.596871	−0.298435	+	0.954430i	$0.596465\pi$
$420$	3.30583	0.161308
$421$	26.4102	1.28715	0.643576	−	0.765382i	$-0.277450\pi$
$421$	26.4102	1.28715	0.643576	+	0.765382i	$0.277450\pi$
$422$	−55.2553	−2.68979
$423$	5.36809	0.261006
$424$	−0.212129	−0.0103019
$425$	−2.11605	−0.102643
$426$	−15.4914	−0.750563
$427$	8.22174	0.397878
$428$	−7.44873	−0.360048
$429$	−0.449673	−0.0217104
$430$	19.2761	0.929576
$431$	−21.7701	−1.04863	−0.524315	−	0.851524i	$-0.675679\pi$
$431$	−21.7701	−1.04863	−0.524315	+	0.851524i	$0.675679\pi$
$432$	4.10387	0.197447
$433$	−5.49894	−0.264262	−0.132131	−	0.991232i	$-0.542182\pi$
$433$	−5.49894	−0.264262	−0.132131	+	0.991232i	$0.542182\pi$
$434$	−3.90163	−0.187284
$435$	−16.4407	−0.788269
$436$	21.3763	1.02374
$437$	27.7888	1.32932
$438$	−23.5828	−1.12683
$439$	26.1209	1.24668	0.623341	−	0.781950i	$-0.285775\pi$
$439$	26.1209	1.24668	0.623341	+	0.781950i	$0.285775\pi$
$440$	0.0809461	0.00385895
$441$	1.00000	0.0476190
$442$	1.98662	0.0944937
$443$	8.54112	0.405801	0.202900	−	0.979199i	$-0.434963\pi$
$443$	8.54112	0.405801	0.202900	+	0.979199i	$0.434963\pi$
$444$	−18.9735	−0.900440
$445$	−12.2927	−0.582731
$446$	14.7896	0.700306
$447$	−5.92364	−0.280178
$448$	−7.56760	−0.357536
$449$	13.6370	0.643571	0.321785	−	0.946813i	$-0.395717\pi$
$449$	13.6370	0.643571	0.321785	+	0.946813i	$0.395717\pi$
$450$	−4.20377	−0.198168
$451$	1.02139	0.0480954
$452$	19.0349	0.895327
$453$	−11.2824	−0.530094
$454$	5.06303	0.237620
$455$	−1.69822	−0.0796138
$456$	0.504433	0.0236222
$457$	11.5756	0.541482	0.270741	−	0.962652i	$-0.412731\pi$
$457$	11.5756	0.541482	0.270741	+	0.962652i	$0.412731\pi$
$458$	−18.7791	−0.877491
$459$	−1.00000	−0.0466760
$460$	−19.3042	−0.900064
$461$	−8.82870	−0.411194	−0.205597	−	0.978637i	$-0.565914\pi$
$461$	−8.82870	−0.411194	−0.205597	+	0.978637i	$0.565914\pi$
$462$	−0.893328	−0.0415614
$463$	−19.0275	−0.884281	−0.442140	−	0.896946i	$-0.645781\pi$
$463$	−19.0275	−0.884281	−0.442140	+	0.896946i	$0.645781\pi$
$464$	39.7300	1.84442
$465$	−3.33523	−0.154668
$466$	17.3928	0.805705
$467$	−18.7480	−0.867556	−0.433778	−	0.901020i	$-0.642820\pi$
$467$	−18.7480	−0.867556	−0.433778	+	0.901020i	$0.642820\pi$
$468$	1.94664	0.0899836
$469$	7.51834	0.347165
$470$	−18.1104	−0.835370
$471$	−15.9090	−0.733046
$472$	0.0711003	0.00327266
$473$	−2.56926	−0.118135
$474$	8.87649	0.407711
$475$	−10.0699	−0.462037
$476$	1.94664	0.0892242
$477$	2.00123	0.0916299
$478$	−49.2624	−2.25321
$479$	15.3735	0.702431	0.351216	−	0.936295i	$-0.385768\pi$
$479$	15.3735	0.702431	0.351216	+	0.936295i	$0.385768\pi$
$480$	−13.4852	−0.615514
$481$	9.74675	0.444414
$482$	32.1183	1.46295
$483$	−5.83945	−0.265704
$484$	−21.0195	−0.955430
$485$	−19.6118	−0.890526
$486$	−1.98662	−0.0901147
$487$	34.4153	1.55951	0.779753	−	0.626087i	$-0.215344\pi$
$487$	34.4153	1.55951	0.779753	+	0.626087i	$0.215344\pi$
$488$	−0.871502	−0.0394510
$489$	−11.8251	−0.534750
$490$	−3.37371	−0.152409
$491$	23.0450	1.04001	0.520003	−	0.854164i	$-0.325931\pi$
$491$	23.0450	1.04001	0.520003	+	0.854164i	$0.325931\pi$
$492$	−4.42162	−0.199342
$493$	−9.68110	−0.436015
$494$	9.45393	0.425353
$495$	−0.763644	−0.0343233
$496$	8.05981	0.361896
$497$	7.79790	0.349784
$498$	−11.1132	−0.497996
$499$	−34.0294	−1.52336	−0.761682	−	0.647951i	$-0.775626\pi$
$499$	−34.0294	−1.52336	−0.761682	+	0.647951i	$0.775626\pi$
$500$	23.5244	1.05204
$501$	7.18024	0.320789
$502$	27.7580	1.23890
$503$	8.58367	0.382727	0.191364	−	0.981519i	$-0.438709\pi$
$503$	8.58367	0.382727	0.191364	+	0.981519i	$0.438709\pi$
$504$	−0.106000	−0.00472160
$505$	−6.41560	−0.285490
$506$	5.21654	0.231904
$507$	−1.00000	−0.0444116
$508$	−7.25716	−0.321984
$509$	−10.3866	−0.460378	−0.230189	−	0.973146i	$-0.573935\pi$
$509$	−10.3866	−0.460378	−0.230189	+	0.973146i	$0.573935\pi$
$510$	3.37371	0.149391
$511$	11.8708	0.525135
$512$	31.7180	1.40175
$513$	−4.75881	−0.210107
$514$	−41.1478	−1.81495
$515$	8.69193	0.383012
$516$	11.1224	0.489635
$517$	2.41389	0.106163
$518$	19.3631	0.850764
$519$	−11.3290	−0.497288
$520$	0.180011	0.00789400
$521$	−7.91707	−0.346853	−0.173427	−	0.984847i	$-0.555484\pi$
$521$	−7.91707	−0.346853	−0.173427	+	0.984847i	$0.555484\pi$
$522$	−19.2326	−0.841790
$523$	24.4849	1.07065	0.535324	−	0.844647i	$-0.320189\pi$
$523$	24.4849	1.07065	0.535324	+	0.844647i	$0.320189\pi$
$524$	−0.975061	−0.0425958
$525$	2.11605	0.0923518
$526$	−56.5548	−2.46591
$527$	−1.96396	−0.0855513
$528$	1.84540	0.0803107
$529$	11.0991	0.482571
$530$	−6.75156	−0.293269
$531$	−0.670760	−0.0291085
$532$	9.26371	0.401633
$533$	2.27141	0.0983855
$534$	−14.3803	−0.622297
$535$	6.49815	0.280940
$536$	−0.796942	−0.0344227
$537$	17.7042	0.763993
$538$	−59.9252	−2.58356
$539$	0.449673	0.0193688
$540$	3.30583	0.142260
$541$	−15.0001	−0.644903	−0.322452	−	0.946586i	$-0.604507\pi$
$541$	−15.0001	−0.644903	−0.322452	+	0.946586i	$0.604507\pi$
$542$	52.2077	2.24251
$543$	6.91439	0.296725
$544$	−7.94081	−0.340459
$545$	−18.6483	−0.798807
$546$	−1.98662	−0.0850193
$547$	35.6287	1.52337	0.761686	−	0.647947i	$-0.224372\pi$
$547$	35.6287	1.52337	0.761686	+	0.647947i	$0.224372\pi$
$548$	−24.4808	−1.04577
$549$	8.22174	0.350895
$550$	−1.89032	−0.0806037
$551$	−46.0706	−1.96267
$552$	0.618980	0.0263455
$553$	−4.46814	−0.190005
$554$	10.2483	0.435409
$555$	16.5521	0.702599
$556$	34.7632	1.47429
$557$	3.49662	0.148156	0.0740782	−	0.997252i	$-0.476399\pi$
$557$	3.49662	0.148156	0.0740782	+	0.997252i	$0.476399\pi$
$558$	−3.90163	−0.165169
$559$	−5.71362	−0.241660
$560$	6.96927	0.294506
$561$	−0.449673	−0.0189852
$562$	−33.6336	−1.41875
$563$	−18.5920	−0.783558	−0.391779	−	0.920059i	$-0.628140\pi$
$563$	−18.5920	−0.783558	−0.391779	+	0.920059i	$0.628140\pi$
$564$	−10.4498	−0.440014
$565$	−16.6058	−0.698609
$566$	−58.1559	−2.44448
$567$	1.00000	0.0419961
$568$	−0.826575	−0.0346823
$569$	−6.77453	−0.284003	−0.142001	−	0.989866i	$-0.545354\pi$
$569$	−6.77453	−0.284003	−0.142001	+	0.989866i	$0.545354\pi$
$570$	16.0549	0.672464
$571$	27.7189	1.16000	0.580001	−	0.814616i	$-0.303052\pi$
$571$	27.7189	1.16000	0.580001	+	0.814616i	$0.303052\pi$
$572$	0.875353	0.0366004
$573$	−11.8918	−0.496787
$574$	4.51241	0.188344
$575$	−12.3565	−0.515303
$576$	−7.56760	−0.315317
$577$	34.0076	1.41576	0.707878	−	0.706334i	$-0.249653\pi$
$577$	34.0076	1.41576	0.707878	+	0.706334i	$0.249653\pi$
$578$	1.98662	0.0826323
$579$	−17.4650	−0.725820
$580$	32.0041	1.32890
$581$	5.59406	0.232081
$582$	−22.9423	−0.950989
$583$	0.899898	0.0372700
$584$	−1.25830	−0.0520690
$585$	−1.69822	−0.0702128
$586$	−51.3424	−2.12094
$587$	−19.0603	−0.786701	−0.393351	−	0.919389i	$-0.628684\pi$
$587$	−19.0603	−0.786701	−0.393351	+	0.919389i	$0.628684\pi$
$588$	−1.94664	−0.0802782
$589$	−9.34610	−0.385099
$590$	2.26295	0.0931642
$591$	13.1283	0.540025
$592$	−39.9994	−1.64396
$593$	−28.5699	−1.17322	−0.586612	−	0.809868i	$-0.699539\pi$
$593$	−28.5699	−1.17322	−0.586612	+	0.809868i	$0.699539\pi$
$594$	−0.893328	−0.0366537
$595$	−1.69822	−0.0696203
$596$	11.5312	0.472337
$597$	10.5433	0.431510
$598$	11.6007	0.474389
$599$	27.5952	1.12751	0.563754	−	0.825943i	$-0.309357\pi$
$599$	27.5952	1.12751	0.563754	+	0.825943i	$0.309357\pi$
$600$	−0.224300	−0.00915702
$601$	−28.2733	−1.15329	−0.576647	−	0.816994i	$-0.695639\pi$
$601$	−28.2733	−1.15329	−0.576647	+	0.816994i	$0.695639\pi$
$602$	−11.3508	−0.462622
$603$	7.51834	0.306171
$604$	21.9628	0.893655
$605$	18.3370	0.745507
$606$	−7.50511	−0.304874
$607$	12.7224	0.516386	0.258193	−	0.966093i	$-0.416873\pi$
$607$	12.7224	0.516386	0.258193	+	0.966093i	$0.416873\pi$
$608$	−37.7888	−1.53254
$609$	9.68110	0.392298
$610$	−27.7378	−1.12307
$611$	5.36809	0.217170
$612$	1.94664	0.0786884
$613$	−40.9466	−1.65382	−0.826910	−	0.562335i	$-0.809903\pi$
$613$	−40.9466	−1.65382	−0.826910	+	0.562335i	$0.809903\pi$
$614$	53.2181	2.14771
$615$	3.85735	0.155543
$616$	−0.0476652	−0.00192049
$617$	42.6672	1.71772	0.858858	−	0.512214i	$-0.171174\pi$
$617$	42.6672	1.71772	0.858858	+	0.512214i	$0.171174\pi$
$618$	10.1680	0.409017
$619$	−23.7892	−0.956169	−0.478084	−	0.878314i	$-0.658669\pi$
$619$	−23.7892	−0.956169	−0.478084	+	0.878314i	$0.658669\pi$
$620$	6.49250	0.260745
$621$	−5.83945	−0.234329
$622$	50.1980	2.01276
$623$	7.23859	0.290008
$624$	4.10387	0.164286
$625$	−9.94212	−0.397685
$626$	−42.9603	−1.71704
$627$	−2.13991	−0.0854598
$628$	30.9691	1.23580
$629$	9.74675	0.388629
$630$	−3.37371	−0.134412
$631$	11.8231	0.470671	0.235335	−	0.971914i	$-0.424381\pi$
$631$	11.8231	0.470671	0.235335	+	0.971914i	$0.424381\pi$
$632$	0.473622	0.0188397
$633$	27.8138	1.10550
$634$	3.05068	0.121158
$635$	6.33103	0.251239
$636$	−3.89567	−0.154474
$637$	1.00000	0.0396214
$638$	−8.64840	−0.342394
$639$	7.79790	0.308480
$640$	−1.43957	−0.0569042
$641$	45.5155	1.79776	0.898878	−	0.438200i	$-0.144384\pi$
$641$	45.5155	1.79776	0.898878	+	0.438200i	$0.144384\pi$
$642$	7.60168	0.300014
$643$	−10.7884	−0.425453	−0.212726	−	0.977112i	$-0.568234\pi$
$643$	−10.7884	−0.425453	−0.212726	+	0.977112i	$0.568234\pi$
$644$	11.3673	0.447935
$645$	−9.70298	−0.382055
$646$	9.45393	0.371960
$647$	23.2594	0.914423	0.457211	−	0.889358i	$-0.348848\pi$
$647$	23.2594	0.914423	0.457211	+	0.889358i	$0.348848\pi$
$648$	−0.106000	−0.00416406
$649$	−0.301623	−0.0118397
$650$	−4.20377	−0.164885
$651$	1.96396	0.0769735
$652$	23.0193	0.901504
$653$	−17.4165	−0.681558	−0.340779	−	0.940143i	$-0.610691\pi$
$653$	−17.4165	−0.681558	−0.340779	+	0.940143i	$0.610691\pi$
$654$	−21.8152	−0.853043
$655$	0.850628	0.0332368
$656$	−9.32155	−0.363945
$657$	11.8708	0.463125
$658$	10.6643	0.415739
$659$	−47.4111	−1.84687	−0.923437	−	0.383750i	$-0.874632\pi$
$659$	−47.4111	−1.84687	−0.923437	+	0.383750i	$0.874632\pi$
$660$	1.48654	0.0578636
$661$	−12.7655	−0.496522	−0.248261	−	0.968693i	$-0.579859\pi$
$661$	−12.7655	−0.496522	−0.248261	+	0.968693i	$0.579859\pi$
$662$	−65.7620	−2.55591
$663$	−1.00000	−0.0388368
$664$	−0.592969	−0.0230116
$665$	−8.08151	−0.313388
$666$	19.3631	0.750303
$667$	−56.5323	−2.18894
$668$	−13.9774	−0.540800
$669$	−7.44460	−0.287825
$670$	−25.3647	−0.979925
$671$	3.69710	0.142725
$672$	7.94081	0.306323
$673$	−2.35820	−0.0909020	−0.0454510	−	0.998967i	$-0.514472\pi$
$673$	−2.35820	−0.0909020	−0.0454510	+	0.998967i	$0.514472\pi$
$674$	62.1714	2.39475
$675$	2.11605	0.0814466
$676$	1.94664	0.0748709
$677$	−16.2801	−0.625696	−0.312848	−	0.949803i	$-0.601283\pi$
$677$	−16.2801	−0.625696	−0.312848	+	0.949803i	$0.601283\pi$
$678$	−19.4258	−0.746042
$679$	11.5484	0.443188
$680$	0.180011	0.00690310
$681$	−2.54857	−0.0976613
$682$	−1.75446	−0.0671816
$683$	25.3076	0.968369	0.484185	−	0.874966i	$-0.339116\pi$
$683$	25.3076	0.968369	0.484185	+	0.874966i	$0.339116\pi$
$684$	9.26371	0.354207
$685$	21.3567	0.815996
$686$	1.98662	0.0758494
$687$	9.45282	0.360648
$688$	23.4479	0.893944
$689$	2.00123	0.0762407
$690$	19.7006	0.749990
$691$	13.1160	0.498956	0.249478	−	0.968380i	$-0.419741\pi$
$691$	13.1160	0.498956	0.249478	+	0.968380i	$0.419741\pi$
$692$	22.0535	0.838350
$693$	0.449673	0.0170817
$694$	67.8508	2.57558
$695$	−30.3269	−1.15036
$696$	−1.02619	−0.0388978
$697$	2.27141	0.0860357
$698$	18.2658	0.691371
$699$	−8.75498	−0.331144
$700$	−4.11919	−0.155691
$701$	−45.2692	−1.70979	−0.854897	−	0.518798i	$-0.826380\pi$
$701$	−45.2692	−1.70979	−0.854897	+	0.518798i	$0.826380\pi$
$702$	−1.98662	−0.0749800
$703$	46.3830	1.74937
$704$	−3.40295	−0.128253
$705$	9.11621	0.343336
$706$	8.13923	0.306324
$707$	3.77784	0.142080
$708$	1.30573	0.0490723
$709$	−21.8793	−0.821695	−0.410848	−	0.911704i	$-0.634767\pi$
$709$	−21.8793	−0.821695	−0.410848	+	0.911704i	$0.634767\pi$
$710$	−26.3079	−0.987317
$711$	−4.46814	−0.167569
$712$	−0.767289	−0.0287554
$713$	−11.4684	−0.429496
$714$	−1.98662	−0.0743472
$715$	−0.763644	−0.0285587
$716$	−34.4638	−1.28797
$717$	24.7971	0.926065
$718$	−18.8474	−0.703378
$719$	14.0808	0.525125	0.262562	−	0.964915i	$-0.415432\pi$
$719$	14.0808	0.525125	0.262562	+	0.964915i	$0.415432\pi$
$720$	6.96927	0.259729
$721$	−5.11826	−0.190614
$722$	7.24379	0.269586
$723$	−16.1673	−0.601269
$724$	−13.4598	−0.500231
$725$	20.4857	0.760818
$726$	21.4511	0.796124
$727$	−3.56178	−0.132099	−0.0660496	−	0.997816i	$-0.521040\pi$
$727$	−3.56178	−0.132099	−0.0660496	+	0.997816i	$0.521040\pi$
$728$	−0.106000	−0.00392861
$729$	1.00000	0.0370370
$730$	−40.0488	−1.48227
$731$	−5.71362	−0.211326
$732$	−16.0048	−0.591554
$733$	−9.57878	−0.353800	−0.176900	−	0.984229i	$-0.556607\pi$
$733$	−9.57878	−0.353800	−0.176900	+	0.984229i	$0.556607\pi$
$734$	−2.43672	−0.0899409
$735$	1.69822	0.0626398
$736$	−46.3699	−1.70922
$737$	3.38080	0.124533
$738$	4.51241	0.166104
$739$	−10.4383	−0.383980	−0.191990	−	0.981397i	$-0.561494\pi$
$739$	−10.4383	−0.383980	−0.191990	+	0.981397i	$0.561494\pi$
$740$	−32.2211	−1.18447
$741$	−4.75881	−0.174819
$742$	3.97567	0.145951
$743$	3.98931	0.146354	0.0731768	−	0.997319i	$-0.476686\pi$
$743$	3.98931	0.146354	0.0731768	+	0.997319i	$0.476686\pi$
$744$	−0.208179	−0.00763220
$745$	−10.0596	−0.368557
$746$	−35.5953	−1.30324
$747$	5.59406	0.204676
$748$	0.875353	0.0320061
$749$	−3.82645	−0.139815
$750$	−24.0075	−0.876630
$751$	−30.2610	−1.10424	−0.552120	−	0.833765i	$-0.686181\pi$
$751$	−30.2610	−1.10424	−0.552120	+	0.833765i	$0.686181\pi$
$752$	−22.0299	−0.803349
$753$	−13.9725	−0.509186
$754$	−19.2326	−0.700411
$755$	−19.1600	−0.697305
$756$	−1.94664	−0.0707987
$757$	−49.9091	−1.81398	−0.906988	−	0.421156i	$-0.861624\pi$
$757$	−49.9091	−1.81398	−0.906988	+	0.421156i	$0.861624\pi$
$758$	−35.2337	−1.27974
$759$	−2.62584	−0.0953121
$760$	0.856638	0.0310735
$761$	−9.56227	−0.346632	−0.173316	−	0.984866i	$-0.555448\pi$
$761$	−9.56227	−0.346632	−0.173316	+	0.984866i	$0.555448\pi$
$762$	7.40618	0.268297
$763$	10.9811	0.397543
$764$	23.1491	0.837505
$765$	−1.69822	−0.0613993
$766$	54.9375	1.98497
$767$	−0.670760	−0.0242197
$768$	−16.8193	−0.606912
$769$	12.1453	0.437969	0.218985	−	0.975728i	$-0.429726\pi$
$769$	12.1453	0.437969	0.218985	+	0.975728i	$0.429726\pi$
$770$	−1.51707	−0.0546713
$771$	20.7125	0.745943
$772$	33.9981	1.22362
$773$	13.2371	0.476107	0.238053	−	0.971252i	$-0.423491\pi$
$773$	13.2371	0.476107	0.238053	+	0.971252i	$0.423491\pi$
$774$	−11.3508	−0.407995
$775$	4.15582	0.149282
$776$	−1.22413	−0.0439437
$777$	−9.74675	−0.349663
$778$	−24.4810	−0.877686
$779$	10.8092	0.387280
$780$	3.30583	0.118368
$781$	3.50651	0.125473
$782$	11.6007	0.414842
$783$	9.68110	0.345974
$784$	−4.10387	−0.146567
$785$	−27.0169	−0.964275
$786$	0.995084	0.0354935
$787$	−40.1072	−1.42967	−0.714834	−	0.699294i	$-0.753498\pi$
$787$	−40.1072	−1.42967	−0.714834	+	0.699294i	$0.753498\pi$
$788$	−25.5561	−0.910397
$789$	28.4679	1.01348
$790$	15.0742	0.536317
$791$	9.77832	0.347677
$792$	−0.0476652	−0.00169371
$793$	8.22174	0.291962
$794$	−20.0846	−0.712775
$795$	3.39853	0.120533
$796$	−20.5241	−0.727458
$797$	−4.28489	−0.151779	−0.0758893	−	0.997116i	$-0.524180\pi$
$797$	−4.28489	−0.151779	−0.0758893	+	0.997116i	$0.524180\pi$
$798$	−9.45393	−0.334666
$799$	5.36809	0.189909
$800$	16.8031	0.594080
$801$	7.23859	0.255763
$802$	−29.3547	−1.03655
$803$	5.33800	0.188374
$804$	−14.6355	−0.516155
$805$	−9.91667	−0.349517
$806$	−3.90163	−0.137429
$807$	30.1644	1.06184
$808$	−0.400449	−0.0140878
$809$	11.8291	0.415890	0.207945	−	0.978141i	$-0.433322\pi$
$809$	11.8291	0.415890	0.207945	+	0.978141i	$0.433322\pi$
$810$	−3.37371	−0.118540
$811$	45.2169	1.58778	0.793890	−	0.608062i	$-0.208053\pi$
$811$	45.2169	1.58778	0.793890	+	0.608062i	$0.208053\pi$
$812$	−18.8457	−0.661353
$813$	−26.2797	−0.921670
$814$	8.70705	0.305182
$815$	−20.0817	−0.703430
$816$	4.10387	0.143664
$817$	−27.1900	−0.951259
$818$	−1.54729	−0.0540997
$819$	1.00000	0.0349428
$820$	−7.50888	−0.262222
$821$	30.3458	1.05907	0.529537	−	0.848287i	$-0.322366\pi$
$821$	30.3458	1.05907	0.529537	+	0.848287i	$0.322366\pi$
$822$	24.9835	0.871400
$823$	−4.75397	−0.165713	−0.0828565	−	0.996561i	$-0.526404\pi$
$823$	−4.75397	−0.165713	−0.0828565	+	0.996561i	$0.526404\pi$
$824$	0.542534	0.0189001
$825$	0.951529	0.0331280
$826$	−1.33254	−0.0463651
$827$	13.0545	0.453948	0.226974	−	0.973901i	$-0.427117\pi$
$827$	13.0545	0.453948	0.226974	+	0.973901i	$0.427117\pi$
$828$	11.3673	0.395042
$829$	50.0365	1.73784	0.868919	−	0.494954i	$-0.164815\pi$
$829$	50.0365	1.73784	0.868919	+	0.494954i	$0.164815\pi$
$830$	−18.8727	−0.655083
$831$	−5.15867	−0.178952
$832$	−7.56760	−0.262359
$833$	1.00000	0.0346479
$834$	−35.4771	−1.22847
$835$	12.1936	0.421978
$836$	4.16564	0.144072
$837$	1.96396	0.0678842
$838$	−24.2718	−0.838454
$839$	3.00108	0.103609	0.0518044	−	0.998657i	$-0.483503\pi$
$839$	3.00108	0.103609	0.0518044	+	0.998657i	$0.483503\pi$
$840$	−0.180011	−0.00621097
$841$	64.7238	2.23185
$842$	52.4669	1.80813
$843$	16.9301	0.583104
$844$	−54.1435	−1.86370
$845$	−1.69822	−0.0584206
$846$	10.6643	0.366647
$847$	−10.7978	−0.371017
$848$	−8.21277	−0.282028
$849$	29.2739	1.00468
$850$	−4.20377	−0.144188
$851$	56.9157	1.95104
$852$	−15.1797	−0.520049
$853$	−43.3342	−1.48373	−0.741867	−	0.670547i	$-0.766060\pi$
$853$	−43.3342	−1.48373	−0.741867	+	0.670547i	$0.766060\pi$
$854$	16.3334	0.558919
$855$	−8.08151	−0.276382
$856$	0.405602	0.0138632
$857$	−35.1122	−1.19941	−0.599704	−	0.800222i	$-0.704715\pi$
$857$	−35.1122	−1.19941	−0.599704	+	0.800222i	$0.704715\pi$
$858$	−0.893328	−0.0304977
$859$	−48.6308	−1.65926	−0.829631	−	0.558312i	$-0.811449\pi$
$859$	−48.6308	−1.65926	−0.829631	+	0.558312i	$0.811449\pi$
$860$	18.8882	0.644084
$861$	−2.27141	−0.0774093
$862$	−43.2489	−1.47306
$863$	−23.8003	−0.810172	−0.405086	−	0.914279i	$-0.632758\pi$
$863$	−23.8003	−0.810172	−0.405086	+	0.914279i	$0.632758\pi$
$864$	7.94081	0.270152
$865$	−19.2392	−0.654151
$866$	−10.9243	−0.371222
$867$	−1.00000	−0.0339618
$868$	−3.82312	−0.129765
$869$	−2.00920	−0.0681576
$870$	−32.6613	−1.10732
$871$	7.51834	0.254749
$872$	−1.16399	−0.0394178
$873$	11.5484	0.390855
$874$	55.2057	1.86736
$875$	12.0846	0.408535
$876$	−23.1083	−0.780756
$877$	−8.55827	−0.288992	−0.144496	−	0.989505i	$-0.546156\pi$
$877$	−8.55827	−0.288992	−0.144496	+	0.989505i	$0.546156\pi$
$878$	51.8922	1.75128
$879$	25.8442	0.871702
$880$	3.13390	0.105644
$881$	7.80947	0.263108	0.131554	−	0.991309i	$-0.458003\pi$
$881$	7.80947	0.263108	0.131554	+	0.991309i	$0.458003\pi$
$882$	1.98662	0.0668928
$883$	7.45909	0.251018	0.125509	−	0.992092i	$-0.459944\pi$
$883$	7.45909	0.251018	0.125509	+	0.992092i	$0.459944\pi$
$884$	1.94664	0.0654727
$885$	−1.13910	−0.0382904
$886$	16.9679	0.570049
$887$	−26.5002	−0.889790	−0.444895	−	0.895583i	$-0.646759\pi$
$887$	−26.5002	−0.889790	−0.444895	+	0.895583i	$0.646759\pi$
$888$	1.03315	0.0346704
$889$	−3.72804	−0.125034
$890$	−24.4209	−0.818591
$891$	0.449673	0.0150646
$892$	14.4920	0.485227
$893$	25.5457	0.854856
$894$	−11.7680	−0.393581
$895$	30.0657	1.00498
$896$	0.847696	0.0283195
$897$	−5.83945	−0.194973
$898$	27.0915	0.904056
$899$	19.0133	0.634128
$900$	−4.11919	−0.137306
$901$	2.00123	0.0666705
$902$	2.02911	0.0675620
$903$	5.71362	0.190137
$904$	−1.03650	−0.0344735
$905$	11.7422	0.390322
$906$	−22.4138	−0.744650
$907$	55.3568	1.83809	0.919046	−	0.394150i	$-0.128961\pi$
$907$	55.3568	1.83809	0.919046	+	0.394150i	$0.128961\pi$
$908$	4.96115	0.164642
$909$	3.77784	0.125303
$910$	−3.37371	−0.111837
$911$	9.77535	0.323872	0.161936	−	0.986801i	$-0.448226\pi$
$911$	9.77535	0.323872	0.161936	+	0.986801i	$0.448226\pi$
$912$	19.5295	0.646687
$913$	2.51550	0.0832508
$914$	22.9962	0.760647
$915$	13.9623	0.461580
$916$	−18.4013	−0.607995
$917$	−0.500894	−0.0165410
$918$	−1.98662	−0.0655681
$919$	35.8070	1.18116	0.590582	−	0.806978i	$-0.298898\pi$
$919$	35.8070	1.18116	0.590582	+	0.806978i	$0.298898\pi$
$920$	1.05116	0.0346559
$921$	−26.7883	−0.882704
$922$	−17.5392	−0.577624
$923$	7.79790	0.256671
$924$	−0.875353	−0.0287970
$925$	−20.6246	−0.678132
$926$	−37.8002	−1.24219
$927$	−5.11826	−0.168106
$928$	76.8758	2.52357
$929$	−39.9962	−1.31223	−0.656116	−	0.754660i	$-0.727802\pi$
$929$	−39.9962	−1.31223	−0.656116	+	0.754660i	$0.727802\pi$
$930$	−6.62582	−0.217269
$931$	4.75881	0.155964
$932$	17.0428	0.558256
$933$	−25.2681	−0.827241
$934$	−37.2452	−1.21870
$935$	−0.763644	−0.0249738
$936$	−0.106000	−0.00346471
$937$	23.8677	0.779722	0.389861	−	0.920874i	$-0.372523\pi$
$937$	23.8677	0.779722	0.389861	+	0.920874i	$0.372523\pi$
$938$	14.9361	0.487680
$939$	21.6249	0.705702
$940$	−17.7460	−0.578811
$941$	37.3084	1.21622	0.608109	−	0.793853i	$-0.291928\pi$
$941$	37.3084	1.21622	0.608109	+	0.793853i	$0.291928\pi$
$942$	−31.6050	−1.02975
$943$	13.2638	0.431927
$944$	2.75271	0.0895930
$945$	1.69822	0.0552431
$946$	−5.10413	−0.165950
$947$	53.0630	1.72432	0.862158	−	0.506639i	$-0.169112\pi$
$947$	53.0630	1.72432	0.862158	+	0.506639i	$0.169112\pi$
$948$	8.69788	0.282494
$949$	11.8708	0.385344
$950$	−20.0050	−0.649046
$951$	−1.53562	−0.0497958
$952$	−0.106000	−0.00343547
$953$	−25.1101	−0.813395	−0.406698	−	0.913563i	$-0.633320\pi$
$953$	−25.1101	−0.813395	−0.406698	+	0.913563i	$0.633320\pi$
$954$	3.97567	0.128717
$955$	−20.1949	−0.653492
$956$	−48.2711	−1.56120
$957$	4.35333	0.140723
$958$	30.5412	0.986740
$959$	−12.5759	−0.406097
$960$	−12.8515	−0.414779
$961$	−27.1429	−0.875577
$962$	19.3631	0.624290
$963$	−3.82645	−0.123306
$964$	31.4720	1.01365
$965$	−29.6594	−0.954770
$966$	−11.6007	−0.373248
$967$	27.5685	0.886542	0.443271	−	0.896388i	$-0.353818\pi$
$967$	27.5685	0.886542	0.443271	+	0.896388i	$0.353818\pi$
$968$	1.14456	0.0367877
$969$	−4.75881	−0.152875
$970$	−38.9611	−1.25097
$971$	8.65272	0.277679	0.138840	−	0.990315i	$-0.455663\pi$
$971$	8.65272	0.277679	0.138840	+	0.990315i	$0.455663\pi$
$972$	−1.94664	−0.0624386
$973$	17.8580	0.572503
$974$	68.3700	2.19072
$975$	2.11605	0.0677677
$976$	−33.7409	−1.08002
$977$	−25.1417	−0.804353	−0.402176	−	0.915562i	$-0.631746\pi$
$977$	−25.1417	−0.804353	−0.402176	+	0.915562i	$0.631746\pi$
$978$	−23.4920	−0.751190
$979$	3.25500	0.104030
$980$	−3.30583	−0.105601
$981$	10.9811	0.350600
$982$	45.7816	1.46095
$983$	−13.5863	−0.433336	−0.216668	−	0.976245i	$-0.569519\pi$
$983$	−13.5863	−0.433336	−0.216668	+	0.976245i	$0.569519\pi$
$984$	0.240768	0.00767542
$985$	22.2947	0.710369
$986$	−19.2326	−0.612492
$987$	−5.36809	−0.170868
$988$	9.26371	0.294718
$989$	−33.3644	−1.06092
$990$	−1.51707	−0.0482156
$991$	42.6952	1.35626	0.678128	−	0.734943i	$-0.262791\pi$
$991$	42.6952	1.35626	0.678128	+	0.734943i	$0.262791\pi$
$992$	15.5954	0.495154
$993$	33.1025	1.05048
$994$	15.4914	0.491359
$995$	17.9049	0.567624
$996$	−10.8896	−0.345051
$997$	−30.1217	−0.953965	−0.476982	−	0.878913i	$-0.658269\pi$
$997$	−30.1217	−0.953965	−0.476982	+	0.878913i	$0.658269\pi$
$998$	−67.6033	−2.13994
$999$	−9.74675	−0.308374

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4641.2.a.w.1.12	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4641.2.a.w.1.12	✓	14	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4641 = 3 \cdot 7 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4641.a (trivial)

\(f(q)\)	\(=\)	\(q+1.98662 q^{2} -1.00000 q^{3} +1.94664 q^{4} -1.69822 q^{5} -1.98662 q^{6} +1.00000 q^{7} -0.106000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.98662 q^{2} -1.00000 q^{3} +1.94664 q^{4} -1.69822 q^{5} -1.98662 q^{6} +1.00000 q^{7} -0.106000 q^{8} +1.00000 q^{9} -3.37371 q^{10} +0.449673 q^{11} -1.94664 q^{12} +1.00000 q^{13} +1.98662 q^{14} +1.69822 q^{15} -4.10387 q^{16} +1.00000 q^{17} +1.98662 q^{18} +4.75881 q^{19} -3.30583 q^{20} -1.00000 q^{21} +0.893328 q^{22} +5.83945 q^{23} +0.106000 q^{24} -2.11605 q^{25} +1.98662 q^{26} -1.00000 q^{27} +1.94664 q^{28} -9.68110 q^{29} +3.37371 q^{30} -1.96396 q^{31} -7.94081 q^{32} -0.449673 q^{33} +1.98662 q^{34} -1.69822 q^{35} +1.94664 q^{36} +9.74675 q^{37} +9.45393 q^{38} -1.00000 q^{39} +0.180011 q^{40} +2.27141 q^{41} -1.98662 q^{42} -5.71362 q^{43} +0.875353 q^{44} -1.69822 q^{45} +11.6007 q^{46} +5.36809 q^{47} +4.10387 q^{48} +1.00000 q^{49} -4.20377 q^{50} -1.00000 q^{51} +1.94664 q^{52} +2.00123 q^{53} -1.98662 q^{54} -0.763644 q^{55} -0.106000 q^{56} -4.75881 q^{57} -19.2326 q^{58} -0.670760 q^{59} +3.30583 q^{60} +8.22174 q^{61} -3.90163 q^{62} +1.00000 q^{63} -7.56760 q^{64} -1.69822 q^{65} -0.893328 q^{66} +7.51834 q^{67} +1.94664 q^{68} -5.83945 q^{69} -3.37371 q^{70} +7.79790 q^{71} -0.106000 q^{72} +11.8708 q^{73} +19.3631 q^{74} +2.11605 q^{75} +9.26371 q^{76} +0.449673 q^{77} -1.98662 q^{78} -4.46814 q^{79} +6.96927 q^{80} +1.00000 q^{81} +4.51241 q^{82} +5.59406 q^{83} -1.94664 q^{84} -1.69822 q^{85} -11.3508 q^{86} +9.68110 q^{87} -0.0476652 q^{88} +7.23859 q^{89} -3.37371 q^{90} +1.00000 q^{91} +11.3673 q^{92} +1.96396 q^{93} +10.6643 q^{94} -8.08151 q^{95} +7.94081 q^{96} +11.5484 q^{97} +1.98662 q^{98} +0.449673 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - q^{2} - 14 q^{3} + 17 q^{4} - q^{5} + q^{6} + 14 q^{7} - 6 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - q^2 - 14 * q^3 + 17 * q^4 - q^5 + q^6 + 14 * q^7 - 6 * q^8 + 14 * q^9	\( 14 q - q^{2} - 14 q^{3} + 17 q^{4} - q^{5} + q^{6} + 14 q^{7} - 6 q^{8} + 14 q^{9} + 11 q^{10} - 4 q^{11} - 17 q^{12} + 14 q^{13} - q^{14} + q^{15} + 19 q^{16} + 14 q^{17} - q^{18} + 6 q^{19} + q^{20} - 14 q^{21} + 12 q^{22} + 7 q^{23} + 6 q^{24} + 19 q^{25} - q^{26} - 14 q^{27} + 17 q^{28} - 4 q^{29} - 11 q^{30} + 31 q^{31} - 18 q^{32} + 4 q^{33} - q^{34} - q^{35} + 17 q^{36} + 2 q^{37} + 9 q^{38} - 14 q^{39} + 50 q^{40} + 4 q^{41} + q^{42} + 14 q^{43} - 8 q^{44} - q^{45} - 17 q^{46} - q^{47} - 19 q^{48} + 14 q^{49} - 3 q^{50} - 14 q^{51} + 17 q^{52} - 43 q^{53} + q^{54} + 23 q^{55} - 6 q^{56} - 6 q^{57} - 10 q^{58} + 11 q^{59} - q^{60} + 25 q^{61} - 3 q^{62} + 14 q^{63} + 36 q^{64} - q^{65} - 12 q^{66} + 11 q^{67} + 17 q^{68} - 7 q^{69} + 11 q^{70} + 20 q^{71} - 6 q^{72} + 14 q^{73} - 24 q^{74} - 19 q^{75} + 9 q^{76} - 4 q^{77} + q^{78} + 42 q^{79} + 13 q^{80} + 14 q^{81} + 2 q^{82} + 15 q^{83} - 17 q^{84} - q^{85} - 11 q^{86} + 4 q^{87} + 63 q^{88} + 21 q^{89} + 11 q^{90} + 14 q^{91} + 30 q^{92} - 31 q^{93} - 29 q^{94} + 16 q^{95} + 18 q^{96} + 15 q^{97} - q^{98} - 4 q^{99}+O(q^{100}) \) 14 * q - q^2 - 14 * q^3 + 17 * q^4 - q^5 + q^6 + 14 * q^7 - 6 * q^8 + 14 * q^9 + 11 * q^10 - 4 * q^11 - 17 * q^12 + 14 * q^13 - q^14 + q^15 + 19 * q^16 + 14 * q^17 - q^18 + 6 * q^19 + q^20 - 14 * q^21 + 12 * q^22 + 7 * q^23 + 6 * q^24 + 19 * q^25 - q^26 - 14 * q^27 + 17 * q^28 - 4 * q^29 - 11 * q^30 + 31 * q^31 - 18 * q^32 + 4 * q^33 - q^34 - q^35 + 17 * q^36 + 2 * q^37 + 9 * q^38 - 14 * q^39 + 50 * q^40 + 4 * q^41 + q^42 + 14 * q^43 - 8 * q^44 - q^45 - 17 * q^46 - q^47 - 19 * q^48 + 14 * q^49 - 3 * q^50 - 14 * q^51 + 17 * q^52 - 43 * q^53 + q^54 + 23 * q^55 - 6 * q^56 - 6 * q^57 - 10 * q^58 + 11 * q^59 - q^60 + 25 * q^61 - 3 * q^62 + 14 * q^63 + 36 * q^64 - q^65 - 12 * q^66 + 11 * q^67 + 17 * q^68 - 7 * q^69 + 11 * q^70 + 20 * q^71 - 6 * q^72 + 14 * q^73 - 24 * q^74 - 19 * q^75 + 9 * q^76 - 4 * q^77 + q^78 + 42 * q^79 + 13 * q^80 + 14 * q^81 + 2 * q^82 + 15 * q^83 - 17 * q^84 - q^85 - 11 * q^86 + 4 * q^87 + 63 * q^88 + 21 * q^89 + 11 * q^90 + 14 * q^91 + 30 * q^92 - 31 * q^93 - 29 * q^94 + 16 * q^95 + 18 * q^96 + 15 * q^97 - q^98 - 4 * q^99

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