LMFDB - Embedded newform 1441.2.a.f.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1441,2,Mod(1,1441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1441, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1441.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1441 = 11 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1441.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:	$11.5064429313$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	1441.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.10874 q^{2} -1.73148 q^{3} +2.44680 q^{4} +1.13214 q^{5} +3.65125 q^{6} +3.68428 q^{7} -0.942192 q^{8} -0.00197058 q^{9} +O(q^{10})$	\(q-2.10874 q^{2} -1.73148 q^{3} +2.44680 q^{4} +1.13214 q^{5} +3.65125 q^{6} +3.68428 q^{7} -0.942192 q^{8} -0.00197058 q^{9} -2.38740 q^{10} -1.00000 q^{11} -4.23659 q^{12} +2.41557 q^{13} -7.76920 q^{14} -1.96029 q^{15} -2.90676 q^{16} +7.02104 q^{17} +0.00415546 q^{18} +6.50913 q^{19} +2.77013 q^{20} -6.37926 q^{21} +2.10874 q^{22} +7.04965 q^{23} +1.63139 q^{24} -3.71825 q^{25} -5.09383 q^{26} +5.19786 q^{27} +9.01470 q^{28} +9.17992 q^{29} +4.13374 q^{30} -8.98487 q^{31} +8.01400 q^{32} +1.73148 q^{33} -14.8056 q^{34} +4.17113 q^{35} -0.00482163 q^{36} +0.492153 q^{37} -13.7261 q^{38} -4.18252 q^{39} -1.06670 q^{40} -4.27499 q^{41} +13.4522 q^{42} -9.07898 q^{43} -2.44680 q^{44} -0.00223098 q^{45} -14.8659 q^{46} -1.94529 q^{47} +5.03301 q^{48} +6.57389 q^{49} +7.84084 q^{50} -12.1568 q^{51} +5.91043 q^{52} -11.4582 q^{53} -10.9610 q^{54} -1.13214 q^{55} -3.47130 q^{56} -11.2704 q^{57} -19.3581 q^{58} +9.76288 q^{59} -4.79643 q^{60} -1.61716 q^{61} +18.9468 q^{62} -0.00726018 q^{63} -11.0860 q^{64} +2.73478 q^{65} -3.65125 q^{66} -1.51808 q^{67} +17.1791 q^{68} -12.2063 q^{69} -8.79585 q^{70} +5.08694 q^{71} +0.00185667 q^{72} -13.5727 q^{73} -1.03782 q^{74} +6.43808 q^{75} +15.9266 q^{76} -3.68428 q^{77} +8.81987 q^{78} +7.55536 q^{79} -3.29087 q^{80} -8.99408 q^{81} +9.01487 q^{82} +8.41784 q^{83} -15.6088 q^{84} +7.94882 q^{85} +19.1452 q^{86} -15.8949 q^{87} +0.942192 q^{88} +7.35231 q^{89} +0.00470457 q^{90} +8.89964 q^{91} +17.2491 q^{92} +15.5571 q^{93} +4.10211 q^{94} +7.36927 q^{95} -13.8761 q^{96} +9.82474 q^{97} -13.8627 q^{98} +0.00197058 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9}+O(q^{10}) $ 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9	\( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9} - 8 q^{10} - 31 q^{11} + 10 q^{12} - 8 q^{13} + 29 q^{14} + 36 q^{15} + 52 q^{16} - q^{17} + 33 q^{18} - 2 q^{19} + 22 q^{20} - 13 q^{21} - 6 q^{22} + 45 q^{23} + 16 q^{24} + 41 q^{25} + 24 q^{26} + 22 q^{27} + 17 q^{28} + 5 q^{29} + 29 q^{30} + 28 q^{31} + 69 q^{32} - 4 q^{33} + 14 q^{34} + 36 q^{35} + 63 q^{36} - 3 q^{37} + 4 q^{38} + 40 q^{39} - 48 q^{40} + 21 q^{41} - 9 q^{42} - 20 q^{43} - 38 q^{44} + 28 q^{45} - 24 q^{46} + 57 q^{47} - 46 q^{48} + 37 q^{49} + 64 q^{50} + 17 q^{51} - 11 q^{52} + 32 q^{53} - 26 q^{54} - 8 q^{55} + 84 q^{56} + 10 q^{57} - 17 q^{58} + 70 q^{59} - 33 q^{60} - 51 q^{61} - 34 q^{62} + 32 q^{63} + 80 q^{64} - q^{65} - 7 q^{66} + 24 q^{67} - 13 q^{68} + 19 q^{69} - 9 q^{70} + 128 q^{71} + 118 q^{72} - 27 q^{73} - 23 q^{74} + 41 q^{75} - 34 q^{76} - 4 q^{77} + 9 q^{78} + 2 q^{79} - 45 q^{80} + 43 q^{81} - 18 q^{82} + 46 q^{83} - 103 q^{84} - 50 q^{85} + 78 q^{86} - 9 q^{87} - 24 q^{88} + 52 q^{89} - 46 q^{90} + 38 q^{91} + 54 q^{92} + 4 q^{93} + 3 q^{94} + 70 q^{95} - 21 q^{96} + 3 q^{97} - 120 q^{98} - 45 q^{99}+O(q^{100}) \) 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9 - 8 * q^10 - 31 * q^11 + 10 * q^12 - 8 * q^13 + 29 * q^14 + 36 * q^15 + 52 * q^16 - q^17 + 33 * q^18 - 2 * q^19 + 22 * q^20 - 13 * q^21 - 6 * q^22 + 45 * q^23 + 16 * q^24 + 41 * q^25 + 24 * q^26 + 22 * q^27 + 17 * q^28 + 5 * q^29 + 29 * q^30 + 28 * q^31 + 69 * q^32 - 4 * q^33 + 14 * q^34 + 36 * q^35 + 63 * q^36 - 3 * q^37 + 4 * q^38 + 40 * q^39 - 48 * q^40 + 21 * q^41 - 9 * q^42 - 20 * q^43 - 38 * q^44 + 28 * q^45 - 24 * q^46 + 57 * q^47 - 46 * q^48 + 37 * q^49 + 64 * q^50 + 17 * q^51 - 11 * q^52 + 32 * q^53 - 26 * q^54 - 8 * q^55 + 84 * q^56 + 10 * q^57 - 17 * q^58 + 70 * q^59 - 33 * q^60 - 51 * q^61 - 34 * q^62 + 32 * q^63 + 80 * q^64 - q^65 - 7 * q^66 + 24 * q^67 - 13 * q^68 + 19 * q^69 - 9 * q^70 + 128 * q^71 + 118 * q^72 - 27 * q^73 - 23 * q^74 + 41 * q^75 - 34 * q^76 - 4 * q^77 + 9 * q^78 + 2 * q^79 - 45 * q^80 + 43 * q^81 - 18 * q^82 + 46 * q^83 - 103 * q^84 - 50 * q^85 + 78 * q^86 - 9 * q^87 - 24 * q^88 + 52 * q^89 - 46 * q^90 + 38 * q^91 + 54 * q^92 + 4 * q^93 + 3 * q^94 + 70 * q^95 - 21 * q^96 + 3 * q^97 - 120 * q^98 - 45 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.10874	−1.49111	−0.745554	−	0.666446i	$-0.767815\pi$
$2$	−2.10874	−1.49111	−0.745554	+	0.666446i	$0.767815\pi$
$3$	−1.73148	−0.999672	−0.499836	−	0.866120i	$-0.666606\pi$
$3$	−1.73148	−0.999672	−0.499836	+	0.866120i	$0.666606\pi$
$4$	2.44680	1.22340
$5$	1.13214	0.506310	0.253155	−	0.967426i	$-0.418532\pi$
$5$	1.13214	0.506310	0.253155	+	0.967426i	$0.418532\pi$
$6$	3.65125	1.49062
$7$	3.68428	1.39253	0.696263	−	0.717787i	$-0.254845\pi$
$7$	3.68428	1.39253	0.696263	+	0.717787i	$0.254845\pi$
$8$	−0.942192	−0.333115
$9$	−0.00197058	−0.000656861 0
$10$	−2.38740	−0.754962
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−4.23659	−1.22300
$13$	2.41557	0.669960	0.334980	−	0.942225i	$-0.391270\pi$
$13$	2.41557	0.669960	0.334980	+	0.942225i	$0.391270\pi$
$14$	−7.76920	−2.07641
$15$	−1.96029	−0.506144
$16$	−2.90676	−0.726691
$17$	7.02104	1.70285	0.851426	−	0.524475i	$-0.175738\pi$
$17$	7.02104	1.70285	0.851426	+	0.524475i	$0.175738\pi$
$18$	0.00415546	0.000979451 0
$19$	6.50913	1.49330	0.746648	−	0.665219i	$-0.231662\pi$
$19$	6.50913	1.49330	0.746648	+	0.665219i	$0.231662\pi$
$20$	2.77013	0.619420
$21$	−6.37926	−1.39207
$22$	2.10874	0.449586
$23$	7.04965	1.46995	0.734977	−	0.678092i	$-0.237193\pi$
$23$	7.04965	1.46995	0.734977	+	0.678092i	$0.237193\pi$
$24$	1.63139	0.333006
$25$	−3.71825	−0.743650
$26$	−5.09383	−0.998982
$27$	5.19786	1.00033
$28$	9.01470	1.70362
$29$	9.17992	1.70467	0.852334	−	0.522997i	$-0.175186\pi$
$29$	9.17992	1.70467	0.852334	+	0.522997i	$0.175186\pi$
$30$	4.13374	0.754714
$31$	−8.98487	−1.61373	−0.806866	−	0.590735i	$-0.798838\pi$
$31$	−8.98487	−1.61373	−0.806866	+	0.590735i	$0.798838\pi$
$32$	8.01400	1.41669
$33$	1.73148	0.301412
$34$	−14.8056	−2.53914
$35$	4.17113	0.705050
$36$	−0.00482163	−0.000803605 0
$37$	0.492153	0.0809095	0.0404547	−	0.999181i	$-0.487119\pi$
$37$	0.492153	0.0809095	0.0404547	+	0.999181i	$0.487119\pi$
$38$	−13.7261	−2.22667
$39$	−4.18252	−0.669740
$40$	−1.06670	−0.168660
$41$	−4.27499	−0.667642	−0.333821	−	0.942636i	$-0.608338\pi$
$41$	−4.27499	−0.667642	−0.333821	+	0.942636i	$0.608338\pi$
$42$	13.4522	2.07572
$43$	−9.07898	−1.38453	−0.692266	−	0.721643i	$-0.743387\pi$
$43$	−9.07898	−1.38453	−0.692266	+	0.721643i	$0.743387\pi$
$44$	−2.44680	−0.368869
$45$	−0.00223098	−0.000332575 0
$46$	−14.8659	−2.19186
$47$	−1.94529	−0.283749	−0.141875	−	0.989885i	$-0.545313\pi$
$47$	−1.94529	−0.283749	−0.141875	+	0.989885i	$0.545313\pi$
$48$	5.03301	0.726452
$49$	6.57389	0.939128
$50$	7.84084	1.10886
$51$	−12.1568	−1.70229
$52$	5.91043	0.819629
$53$	−11.4582	−1.57390	−0.786951	−	0.617016i	$-0.788341\pi$
$53$	−11.4582	−1.57390	−0.786951	+	0.617016i	$0.788341\pi$
$54$	−10.9610	−1.49160
$55$	−1.13214	−0.152658
$56$	−3.47130	−0.463871
$57$	−11.2704	−1.49281
$58$	−19.3581	−2.54184
$59$	9.76288	1.27102	0.635509	−	0.772093i	$-0.280790\pi$
$59$	9.76288	1.27102	0.635509	+	0.772093i	$0.280790\pi$
$60$	−4.79643	−0.619217
$61$	−1.61716	−0.207057	−0.103528	−	0.994627i	$-0.533013\pi$
$61$	−1.61716	−0.207057	−0.103528	+	0.994627i	$0.533013\pi$
$62$	18.9468	2.40625
$63$	−0.00726018	−0.000914696 0
$64$	−11.0860	−1.38574
$65$	2.73478	0.339207
$66$	−3.65125	−0.449438
$67$	−1.51808	−0.185463	−0.0927314	−	0.995691i	$-0.529560\pi$
$67$	−1.51808	−0.185463	−0.0927314	+	0.995691i	$0.529560\pi$
$68$	17.1791	2.08327
$69$	−12.2063	−1.46947
$70$	−8.79585	−1.05130
$71$	5.08694	0.603709	0.301854	−	0.953354i	$-0.402394\pi$
$71$	5.08694	0.603709	0.301854	+	0.953354i	$0.402394\pi$
$72$	0.00185667	0.000218810 0
$73$	−13.5727	−1.58857	−0.794285	−	0.607545i	$-0.792154\pi$
$73$	−13.5727	−1.58857	−0.794285	+	0.607545i	$0.792154\pi$
$74$	−1.03782	−0.120645
$75$	6.43808	0.743406
$76$	15.9266	1.82690
$77$	−3.68428	−0.419862
$78$	8.81987	0.998654
$79$	7.55536	0.850044	0.425022	−	0.905183i	$-0.360266\pi$
$79$	7.55536	0.850044	0.425022	+	0.905183i	$0.360266\pi$
$80$	−3.29087	−0.367931
$81$	−8.99408	−0.999343
$82$	9.01487	0.995526
$83$	8.41784	0.923977	0.461989	−	0.886886i	$-0.347136\pi$
$83$	8.41784	0.923977	0.461989	+	0.886886i	$0.347136\pi$
$84$	−15.6088	−1.70306
$85$	7.94882	0.862171
$86$	19.1452	2.06448
$87$	−15.8949	−1.70411
$88$	0.942192	0.100438
$89$	7.35231	0.779343	0.389671	−	0.920954i	$-0.372589\pi$
$89$	7.35231	0.779343	0.389671	+	0.920954i	$0.372589\pi$
$90$	0.00470457	0.000495906 0
$91$	8.89964	0.932936
$92$	17.2491	1.79834
$93$	15.5571	1.61320
$94$	4.10211	0.423100
$95$	7.36927	0.756071
$96$	−13.8761	−1.41622
$97$	9.82474	0.997552	0.498776	−	0.866731i	$-0.333783\pi$
$97$	9.82474	0.997552	0.498776	+	0.866731i	$0.333783\pi$
$98$	−13.8627	−1.40034
$99$	0.00197058	0.000198051 0
$100$	−9.09783	−0.909783
$101$	10.3599	1.03085	0.515425	−	0.856935i	$-0.327634\pi$
$101$	10.3599	1.03085	0.515425	+	0.856935i	$0.327634\pi$
$102$	25.6356	2.53830
$103$	2.49768	0.246104	0.123052	−	0.992400i	$-0.460732\pi$
$103$	2.49768	0.246104	0.123052	+	0.992400i	$0.460732\pi$
$104$	−2.27593	−0.223174
$105$	−7.22224	−0.704818
$106$	24.1624	2.34686
$107$	−13.8213	−1.33616	−0.668078	−	0.744092i	$-0.732883\pi$
$107$	−13.8213	−1.33616	−0.668078	+	0.744092i	$0.732883\pi$
$108$	12.7181	1.22380
$109$	−0.758690	−0.0726693	−0.0363347	−	0.999340i	$-0.511568\pi$
$109$	−0.758690	−0.0726693	−0.0363347	+	0.999340i	$0.511568\pi$
$110$	2.38740	0.227630
$111$	−0.852154	−0.0808829
$112$	−10.7093	−1.01194
$113$	−4.56576	−0.429510	−0.214755	−	0.976668i	$-0.568895\pi$
$113$	−4.56576	−0.429510	−0.214755	+	0.976668i	$0.568895\pi$
$114$	23.7665	2.22593
$115$	7.98121	0.744252
$116$	22.4615	2.08549
$117$	−0.00476009	−0.000440071 0
$118$	−20.5874	−1.89523
$119$	25.8675	2.37127
$120$	1.84697	0.168604
$121$	1.00000	0.0909091
$122$	3.41018	0.308743
$123$	7.40208	0.667423
$124$	−21.9842	−1.97424
$125$	−9.87031	−0.882827
$126$	0.0153099	0.00136391
$127$	−3.64680	−0.323601	−0.161801	−	0.986823i	$-0.551730\pi$
$127$	−3.64680	−0.323601	−0.161801	+	0.986823i	$0.551730\pi$
$128$	7.34944	0.649605
$129$	15.7201	1.38408
$130$	−5.76694	−0.505794
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	4.23659	0.368748
$133$	23.9814	2.07945
$134$	3.20124	0.276545
$135$	5.88472	0.506476
$136$	−6.61517	−0.567246
$137$	−4.89456	−0.418170	−0.209085	−	0.977897i	$-0.567049\pi$
$137$	−4.89456	−0.418170	−0.209085	+	0.977897i	$0.567049\pi$
$138$	25.7401	2.19114
$139$	−4.23928	−0.359571	−0.179786	−	0.983706i	$-0.557540\pi$
$139$	−4.23928	−0.359571	−0.179786	+	0.983706i	$0.557540\pi$
$140$	10.2059	0.862558
$141$	3.36823	0.283656
$142$	−10.7271	−0.900195
$143$	−2.41557	−0.202000
$144$	0.00572802	0.000477335 0
$145$	10.3930	0.863091
$146$	28.6215	2.36873
$147$	−11.3826	−0.938819
$148$	1.20420	0.0989847
$149$	−10.4266	−0.854179	−0.427090	−	0.904209i	$-0.640461\pi$
$149$	−10.4266	−0.854179	−0.427090	+	0.904209i	$0.640461\pi$
$150$	−13.5763	−1.10850
$151$	20.7703	1.69026	0.845130	−	0.534561i	$-0.179523\pi$
$151$	20.7703	1.69026	0.845130	+	0.534561i	$0.179523\pi$
$152$	−6.13285	−0.497440
$153$	−0.0138355	−0.00111854
$154$	7.76920	0.626060
$155$	−10.1722	−0.817048
$156$	−10.2338	−0.819360
$157$	5.48235	0.437539	0.218769	−	0.975777i	$-0.429796\pi$
$157$	5.48235	0.437539	0.218769	+	0.975777i	$0.429796\pi$
$158$	−15.9323	−1.26751
$159$	19.8396	1.57338
$160$	9.07300	0.717284
$161$	25.9729	2.04695
$162$	18.9662	1.49013
$163$	−4.22879	−0.331224	−0.165612	−	0.986191i	$-0.552960\pi$
$163$	−4.22879	−0.331224	−0.165612	+	0.986191i	$0.552960\pi$
$164$	−10.4601	−0.816794
$165$	1.96029	0.152608
$166$	−17.7511	−1.37775
$167$	−1.45787	−0.112813	−0.0564066	−	0.998408i	$-0.517964\pi$
$167$	−1.45787	−0.112813	−0.0564066	+	0.998408i	$0.517964\pi$
$168$	6.01049	0.463719
$169$	−7.16500	−0.551154
$170$	−16.7620	−1.28559
$171$	−0.0128268	−0.000980889 0
$172$	−22.2145	−1.69384
$173$	17.7169	1.34699	0.673497	−	0.739190i	$-0.264791\pi$
$173$	17.7169	1.34699	0.673497	+	0.739190i	$0.264791\pi$
$174$	33.5182	2.54101
$175$	−13.6991	−1.03555
$176$	2.90676	0.219106
$177$	−16.9042	−1.27060
$178$	−15.5041	−1.16208
$179$	1.25603	0.0938803	0.0469402	−	0.998898i	$-0.485053\pi$
$179$	1.25603	0.0938803	0.0469402	+	0.998898i	$0.485053\pi$
$180$	−0.00545878	−0.000406873 0
$181$	−2.24057	−0.166540	−0.0832700	−	0.996527i	$-0.526536\pi$
$181$	−2.24057	−0.166540	−0.0832700	+	0.996527i	$0.526536\pi$
$182$	−18.7671	−1.39111
$183$	2.80009	0.206988
$184$	−6.64212	−0.489664
$185$	0.557188	0.0409653
$186$	−32.8060	−2.40546
$187$	−7.02104	−0.513429
$188$	−4.75973	−0.347139
$189$	19.1503	1.39298
$190$	−15.5399	−1.12738
$191$	6.93919	0.502102	0.251051	−	0.967974i	$-0.419224\pi$
$191$	6.93919	0.502102	0.251051	+	0.967974i	$0.419224\pi$
$192$	19.1951	1.38529
$193$	0.920937	0.0662905	0.0331453	−	0.999451i	$-0.489448\pi$
$193$	0.920937	0.0662905	0.0331453	+	0.999451i	$0.489448\pi$
$194$	−20.7179	−1.48746
$195$	−4.73522	−0.339096
$196$	16.0850	1.14893
$197$	−19.8978	−1.41766	−0.708828	−	0.705381i	$-0.750776\pi$
$197$	−19.8978	−1.41766	−0.708828	+	0.705381i	$0.750776\pi$
$198$	−0.00415546	−0.000295316 0
$199$	−7.71364	−0.546806	−0.273403	−	0.961900i	$-0.588149\pi$
$199$	−7.71364	−0.546806	−0.273403	+	0.961900i	$0.588149\pi$
$200$	3.50331	0.247721
$201$	2.62853	0.185402
$202$	−21.8464	−1.53711
$203$	33.8214	2.37379
$204$	−29.7453	−2.08259
$205$	−4.83991	−0.338034
$206$	−5.26697	−0.366967
$207$	−0.0138919	−0.000965556 0
$208$	−7.02150	−0.486853
$209$	−6.50913	−0.450246
$210$	15.2298	1.05096
$211$	−2.64884	−0.182354	−0.0911768	−	0.995835i	$-0.529063\pi$
$211$	−2.64884	−0.182354	−0.0911768	+	0.995835i	$0.529063\pi$
$212$	−28.0359	−1.92551
$213$	−8.80795	−0.603511
$214$	29.1456	1.99235
$215$	−10.2787	−0.701002
$216$	−4.89738	−0.333224
$217$	−33.1028	−2.24716
$218$	1.59988	0.108358
$219$	23.5010	1.58805
$220$	−2.77013	−0.186762
$221$	16.9598	1.14084
$222$	1.79697	0.120605
$223$	20.3014	1.35949	0.679743	−	0.733451i	$-0.262091\pi$
$223$	20.3014	1.35949	0.679743	+	0.733451i	$0.262091\pi$
$224$	29.5258	1.97278
$225$	0.00732713	0.000488475 0
$226$	9.62801	0.640446
$227$	19.1663	1.27211	0.636055	−	0.771644i	$-0.280565\pi$
$227$	19.1663	1.27211	0.636055	+	0.771644i	$0.280565\pi$
$228$	−27.5765	−1.82630
$229$	16.9775	1.12191	0.560954	−	0.827847i	$-0.310435\pi$
$229$	16.9775	1.12191	0.560954	+	0.827847i	$0.310435\pi$
$230$	−16.8303	−1.10976
$231$	6.37926	0.419724
$232$	−8.64925	−0.567851
$233$	10.1922	0.667712	0.333856	−	0.942624i	$-0.391650\pi$
$233$	10.1922	0.667712	0.333856	+	0.942624i	$0.391650\pi$
$234$	0.0100378	0.000656192 0
$235$	−2.20234	−0.143665
$236$	23.8878	1.55497
$237$	−13.0820	−0.849765
$238$	−54.5478	−3.53581
$239$	13.9108	0.899816	0.449908	−	0.893075i	$-0.351457\pi$
$239$	13.9108	0.899816	0.449908	+	0.893075i	$0.351457\pi$
$240$	5.69809	0.367810
$241$	9.96404	0.641840	0.320920	−	0.947106i	$-0.396008\pi$
$241$	9.96404	0.641840	0.320920	+	0.947106i	$0.396008\pi$
$242$	−2.10874	−0.135555
$243$	−0.0204789	−0.00131372
$244$	−3.95688	−0.253313
$245$	7.44259	0.475490
$246$	−15.6091	−0.995199
$247$	15.7233	1.00045
$248$	8.46548	0.537558
$249$	−14.5753	−0.923674
$250$	20.8140	1.31639
$251$	−9.15810	−0.578054	−0.289027	−	0.957321i	$-0.593332\pi$
$251$	−9.15810	−0.578054	−0.289027	+	0.957321i	$0.593332\pi$
$252$	−0.0177642	−0.00111904
$253$	−7.04965	−0.443208
$254$	7.69017	0.482524
$255$	−13.7632	−0.861888
$256$	6.67382	0.417114
$257$	25.4602	1.58816	0.794082	−	0.607811i	$-0.207952\pi$
$257$	25.4602	1.58816	0.794082	+	0.607811i	$0.207952\pi$
$258$	−33.1496	−2.06381
$259$	1.81323	0.112668
$260$	6.69146	0.414987
$261$	−0.0180898	−0.00111973
$262$	−2.10874	−0.130279
$263$	0.361773	0.0223078	0.0111539	−	0.999938i	$-0.496450\pi$
$263$	0.361773	0.0223078	0.0111539	+	0.999938i	$0.496450\pi$
$264$	−1.63139	−0.100405
$265$	−12.9723	−0.796882
$266$	−50.5707	−3.10069
$267$	−12.7304	−0.779087
$268$	−3.71444	−0.226895
$269$	−30.7691	−1.87603	−0.938014	−	0.346597i	$-0.887337\pi$
$269$	−30.7691	−1.87603	−0.938014	+	0.346597i	$0.887337\pi$
$270$	−12.4094	−0.755210
$271$	29.9619	1.82006	0.910028	−	0.414547i	$-0.136060\pi$
$271$	29.9619	1.82006	0.910028	+	0.414547i	$0.136060\pi$
$272$	−20.4085	−1.23745
$273$	−15.4096	−0.932630
$274$	10.3214	0.623537
$275$	3.71825	0.224219
$276$	−29.8665	−1.79775
$277$	−13.0682	−0.785192	−0.392596	−	0.919711i	$-0.628423\pi$
$277$	−13.0682	−0.785192	−0.392596	+	0.919711i	$0.628423\pi$
$278$	8.93956	0.536159
$279$	0.0177054	0.00106000
$280$	−3.93000	−0.234863
$281$	−2.18974	−0.130629	−0.0653145	−	0.997865i	$-0.520805\pi$
$281$	−2.18974	−0.130629	−0.0653145	+	0.997865i	$0.520805\pi$
$282$	−7.10273	−0.422961
$283$	21.0408	1.25075	0.625374	−	0.780325i	$-0.284946\pi$
$283$	21.0408	1.25075	0.625374	+	0.780325i	$0.284946\pi$
$284$	12.4467	0.738578
$285$	−12.7598	−0.755823
$286$	5.09383	0.301204
$287$	−15.7503	−0.929709
$288$	−0.0157923	−0.000930568 0
$289$	32.2950	1.89971
$290$	−21.9162	−1.28696
$291$	−17.0114	−0.997224
$292$	−33.2098	−1.94346
$293$	2.61654	0.152860	0.0764300	−	0.997075i	$-0.475648\pi$
$293$	2.61654	0.152860	0.0764300	+	0.997075i	$0.475648\pi$
$294$	24.0029	1.39988
$295$	11.0530	0.643529
$296$	−0.463703	−0.0269522
$297$	−5.19786	−0.301610
$298$	21.9870	1.27367
$299$	17.0290	0.984810
$300$	15.7527	0.909484
$301$	−33.4495	−1.92800
$302$	−43.7992	−2.52036
$303$	−17.9380	−1.03051
$304$	−18.9205	−1.08516
$305$	−1.83086	−0.104835
$306$	0.0291756	0.00166786
$307$	−8.91144	−0.508603	−0.254301	−	0.967125i	$-0.581846\pi$
$307$	−8.91144	−0.508603	−0.254301	+	0.967125i	$0.581846\pi$
$308$	−9.01470	−0.513660
$309$	−4.32469	−0.246023
$310$	21.4505	1.21831
$311$	−17.4429	−0.989095	−0.494547	−	0.869151i	$-0.664666\pi$
$311$	−17.4429	−0.989095	−0.494547	+	0.869151i	$0.664666\pi$
$312$	3.94074	0.223100
$313$	−2.58404	−0.146059	−0.0730293	−	0.997330i	$-0.523267\pi$
$313$	−2.58404	−0.146059	−0.0730293	+	0.997330i	$0.523267\pi$
$314$	−11.5609	−0.652417
$315$	−0.00821956	−0.000463120 0
$316$	18.4865	1.03994
$317$	−10.9572	−0.615420	−0.307710	−	0.951480i	$-0.599563\pi$
$317$	−10.9572	−0.615420	−0.307710	+	0.951480i	$0.599563\pi$
$318$	−41.8367	−2.34609
$319$	−9.17992	−0.513977
$320$	−12.5509	−0.701616
$321$	23.9313	1.33572
$322$	−54.7701	−3.05222
$323$	45.7009	2.54286
$324$	−22.0067	−1.22260
$325$	−8.98171	−0.498216
$326$	8.91743	0.493891
$327$	1.31366	0.0726455
$328$	4.02787	0.222402
$329$	−7.16697	−0.395128
$330$	−4.13374	−0.227555
$331$	6.80337	0.373947	0.186973	−	0.982365i	$-0.440132\pi$
$331$	6.80337	0.373947	0.186973	+	0.982365i	$0.440132\pi$
$332$	20.5968	1.13040
$333$	−0.000969829 0	−5.31463e−5 0
$334$	3.07427	0.168216
$335$	−1.71868	−0.0939017
$336$	18.5430	1.01160
$337$	25.9713	1.41475	0.707374	−	0.706839i	$-0.249880\pi$
$337$	25.9713	1.41475	0.707374	+	0.706839i	$0.249880\pi$
$338$	15.1092	0.821830
$339$	7.90552	0.429369
$340$	19.4492	1.05478
$341$	8.98487	0.486558
$342$	0.0270484	0.00146261
$343$	−1.56989	−0.0847663
$344$	8.55414	0.461208
$345$	−13.8193	−0.744008
$346$	−37.3605	−2.00851
$347$	16.5238	0.887046	0.443523	−	0.896263i	$-0.353728\pi$
$347$	16.5238	0.887046	0.443523	+	0.896263i	$0.353728\pi$
$348$	−38.8916	−2.08481
$349$	−30.6766	−1.64208	−0.821039	−	0.570871i	$-0.806605\pi$
$349$	−30.6766	−1.64208	−0.821039	+	0.570871i	$0.806605\pi$
$350$	28.8878	1.54412
$351$	12.5558	0.670180
$352$	−8.01400	−0.427148
$353$	−35.6996	−1.90010	−0.950049	−	0.312100i	$-0.898968\pi$
$353$	−35.6996	−1.90010	−0.950049	+	0.312100i	$0.898968\pi$
$354$	35.6467	1.89460
$355$	5.75915	0.305664
$356$	17.9896	0.953449
$357$	−44.7890	−2.37049
$358$	−2.64865	−0.139986
$359$	−2.82897	−0.149308	−0.0746538	−	0.997210i	$-0.523785\pi$
$359$	−2.82897	−0.149308	−0.0746538	+	0.997210i	$0.523785\pi$
$360$	0.00210201	0.000110786 0
$361$	23.3688	1.22994
$362$	4.72478	0.248329
$363$	−1.73148	−0.0908792
$364$	21.7757	1.14136
$365$	−15.3663	−0.804309
$366$	−5.90467	−0.308642
$367$	−10.7791	−0.562662	−0.281331	−	0.959611i	$-0.590776\pi$
$367$	−10.7791	−0.562662	−0.281331	+	0.959611i	$0.590776\pi$
$368$	−20.4917	−1.06820
$369$	0.00842424	0.000438548 0
$370$	−1.17497	−0.0610836
$371$	−42.2151	−2.19170
$372$	38.0653	1.97359
$373$	−26.9967	−1.39784	−0.698918	−	0.715202i	$-0.746335\pi$
$373$	−26.9967	−1.39784	−0.698918	+	0.715202i	$0.746335\pi$
$374$	14.8056	0.765578
$375$	17.0903	0.882537
$376$	1.83283	0.0945211
$377$	22.1748	1.14206
$378$	−40.3832	−2.07709
$379$	−34.4088	−1.76746	−0.883730	−	0.467998i	$-0.844976\pi$
$379$	−34.4088	−1.76746	−0.883730	+	0.467998i	$0.844976\pi$
$380$	18.0311	0.924978
$381$	6.31437	0.323495
$382$	−14.6330	−0.748688
$383$	20.8419	1.06497	0.532485	−	0.846440i	$-0.321258\pi$
$383$	20.8419	1.06497	0.532485	+	0.846440i	$0.321258\pi$
$384$	−12.7254	−0.649392
$385$	−4.17113	−0.212580
$386$	−1.94202	−0.0988463
$387$	0.0178909	0.000909445 0
$388$	24.0392	1.22041
$389$	32.8406	1.66508	0.832542	−	0.553962i	$-0.186885\pi$
$389$	32.8406	1.66508	0.832542	+	0.553962i	$0.186885\pi$
$390$	9.98536	0.505628
$391$	49.4959	2.50311
$392$	−6.19387	−0.312838
$393$	−1.73148	−0.0873417
$394$	41.9593	2.11388
$395$	8.55375	0.430386
$396$	0.00482163	0.000242296 0
$397$	−20.5555	−1.03165	−0.515826	−	0.856693i	$-0.672515\pi$
$397$	−20.5555	−1.03165	−0.515826	+	0.856693i	$0.672515\pi$
$398$	16.2661	0.815346
$399$	−41.5234	−2.07877
$400$	10.8081	0.540404
$401$	0.569699	0.0284494	0.0142247	−	0.999899i	$-0.495472\pi$
$401$	0.569699	0.0284494	0.0142247	+	0.999899i	$0.495472\pi$
$402$	−5.54289	−0.276454
$403$	−21.7036	−1.08113
$404$	25.3487	1.26114
$405$	−10.1826	−0.505977
$406$	−71.3206	−3.53958
$407$	−0.492153	−0.0243951
$408$	11.4540	0.567060
$409$	−10.4435	−0.516398	−0.258199	−	0.966092i	$-0.583129\pi$
$409$	−10.4435	−0.516398	−0.258199	+	0.966092i	$0.583129\pi$
$410$	10.2061	0.504045
$411$	8.47484	0.418033
$412$	6.11133	0.301084
$413$	35.9691	1.76993
$414$	0.0292945	0.00143975
$415$	9.53020	0.467819
$416$	19.3584	0.949125
$417$	7.34024	0.359453
$418$	13.7261	0.671365
$419$	8.10257	0.395836	0.197918	−	0.980219i	$-0.436582\pi$
$419$	8.10257	0.395836	0.197918	+	0.980219i	$0.436582\pi$
$420$	−17.6714	−0.862275
$421$	−20.3841	−0.993459	−0.496730	−	0.867905i	$-0.665466\pi$
$421$	−20.3841	−0.993459	−0.496730	+	0.867905i	$0.665466\pi$
$422$	5.58572	0.271909
$423$	0.00383335	0.000186384 0
$424$	10.7958	0.524290
$425$	−26.1060	−1.26633
$426$	18.5737	0.899899
$427$	−5.95808	−0.288332
$428$	−33.8180	−1.63465
$429$	4.18252	0.201934
$430$	21.6752	1.04527
$431$	−8.15427	−0.392777	−0.196389	−	0.980526i	$-0.562921\pi$
$431$	−8.15427	−0.392777	−0.196389	+	0.980526i	$0.562921\pi$
$432$	−15.1089	−0.726929
$433$	−26.1341	−1.25592	−0.627961	−	0.778245i	$-0.716110\pi$
$433$	−26.1341	−1.25592	−0.627961	+	0.778245i	$0.716110\pi$
$434$	69.8053	3.35076
$435$	−17.9953	−0.862807
$436$	−1.85636	−0.0889037
$437$	45.8871	2.19508
$438$	−49.5575	−2.36795
$439$	12.3907	0.591376	0.295688	−	0.955285i	$-0.404451\pi$
$439$	12.3907	0.591376	0.295688	+	0.955285i	$0.404451\pi$
$440$	1.06670	0.0508528
$441$	−0.0129544	−0.000616877 0
$442$	−35.7640	−1.70112
$443$	−25.0434	−1.18985	−0.594925	−	0.803781i	$-0.702818\pi$
$443$	−25.0434	−1.18985	−0.594925	+	0.803781i	$0.702818\pi$
$444$	−2.08505	−0.0989522
$445$	8.32386	0.394589
$446$	−42.8106	−2.02714
$447$	18.0534	0.853899
$448$	−40.8437	−1.92969
$449$	31.0618	1.46590	0.732950	−	0.680283i	$-0.238143\pi$
$449$	31.0618	1.46590	0.732950	+	0.680283i	$0.238143\pi$
$450$	−0.0154510	−0.000728369 0
$451$	4.27499	0.201302
$452$	−11.1715	−0.525463
$453$	−35.9633	−1.68970
$454$	−40.4168	−1.89685
$455$	10.0757	0.472355
$456$	10.6189	0.497276
$457$	−41.6135	−1.94660	−0.973298	−	0.229546i	$-0.926276\pi$
$457$	−41.6135	−1.94660	−0.973298	+	0.229546i	$0.926276\pi$
$458$	−35.8013	−1.67288
$459$	36.4944	1.70341
$460$	19.5285	0.910519
$461$	−20.6752	−0.962940	−0.481470	−	0.876463i	$-0.659897\pi$
$461$	−20.6752	−0.962940	−0.481470	+	0.876463i	$0.659897\pi$
$462$	−13.4522	−0.625854
$463$	8.08535	0.375758	0.187879	−	0.982192i	$-0.439839\pi$
$463$	8.08535	0.375758	0.187879	+	0.982192i	$0.439839\pi$
$464$	−26.6839	−1.23877
$465$	17.6129	0.816780
$466$	−21.4927	−0.995630
$467$	12.1174	0.560725	0.280362	−	0.959894i	$-0.409545\pi$
$467$	12.1174	0.560725	0.280362	+	0.959894i	$0.409545\pi$
$468$	−0.0116470	−0.000538383 0
$469$	−5.59302	−0.258262
$470$	4.64418	0.214220
$471$	−9.49258	−0.437395
$472$	−9.19850	−0.423396
$473$	9.07898	0.417452
$474$	27.5865	1.26709
$475$	−24.2026	−1.11049
$476$	63.2925	2.90101
$477$	0.0225793	0.00103384
$478$	−29.3344	−1.34172
$479$	14.8902	0.680352	0.340176	−	0.940362i	$-0.389513\pi$
$479$	14.8902	0.680352	0.340176	+	0.940362i	$0.389513\pi$
$480$	−15.7097	−0.717048
$481$	1.18883	0.0542061
$482$	−21.0116	−0.957053
$483$	−44.9715	−2.04628
$484$	2.44680	0.111218
$485$	11.1230	0.505070
$486$	0.0431848	0.00195890
$487$	16.9083	0.766190	0.383095	−	0.923709i	$-0.374858\pi$
$487$	16.9083	0.766190	0.383095	+	0.923709i	$0.374858\pi$
$488$	1.52368	0.0689737
$489$	7.32207	0.331115
$490$	−15.6945	−0.709006
$491$	9.94997	0.449036	0.224518	−	0.974470i	$-0.427919\pi$
$491$	9.94997	0.449036	0.224518	+	0.974470i	$0.427919\pi$
$492$	18.1114	0.816526
$493$	64.4526	2.90280
$494$	−33.1564	−1.49178
$495$	0.00223098	0.000100275 0
$496$	26.1169	1.17268
$497$	18.7417	0.840680
$498$	30.7356	1.37730
$499$	−5.41885	−0.242581	−0.121291	−	0.992617i	$-0.538703\pi$
$499$	−5.41885	−0.242581	−0.121291	+	0.992617i	$0.538703\pi$
$500$	−24.1507	−1.08005
$501$	2.52427	0.112776
$502$	19.3121	0.861941
$503$	19.1868	0.855497	0.427748	−	0.903898i	$-0.359307\pi$
$503$	19.1868	0.855497	0.427748	+	0.903898i	$0.359307\pi$
$504$	0.00684048	0.000304699 0
$505$	11.7289	0.521929
$506$	14.8659	0.660870
$507$	12.4061	0.550973
$508$	−8.92300	−0.395894
$509$	27.6989	1.22773	0.613865	−	0.789411i	$-0.289614\pi$
$509$	27.6989	1.22773	0.613865	+	0.789411i	$0.289614\pi$
$510$	29.0232	1.28517
$511$	−50.0058	−2.21212
$512$	−28.7723	−1.27157
$513$	33.8335	1.49379
$514$	−53.6890	−2.36812
$515$	2.82773	0.124605
$516$	38.4639	1.69328
$517$	1.94529	0.0855536
$518$	−3.82363	−0.168001
$519$	−30.6766	−1.34655
$520$	−2.57668	−0.112995
$521$	−9.78474	−0.428677	−0.214339	−	0.976759i	$-0.568760\pi$
$521$	−9.78474	−0.428677	−0.214339	+	0.976759i	$0.568760\pi$
$522$	0.0381468	0.00166964
$523$	20.8043	0.909707	0.454853	−	0.890566i	$-0.349692\pi$
$523$	20.8043	0.909707	0.454853	+	0.890566i	$0.349692\pi$
$524$	2.44680	0.106889
$525$	23.7197	1.03521
$526$	−0.762886	−0.0332634
$527$	−63.0832	−2.74795
$528$	−5.03301	−0.219034
$529$	26.6976	1.16076
$530$	27.3553	1.18824
$531$	−0.0192386	−0.000834883 0
$532$	58.6778	2.54401
$533$	−10.3266	−0.447293
$534$	26.8451	1.16170
$535$	−15.6477	−0.676509
$536$	1.43032	0.0617805
$537$	−2.17480	−0.0938495
$538$	64.8843	2.79736
$539$	−6.57389	−0.283158
$540$	14.3987	0.619623
$541$	−26.5428	−1.14116	−0.570582	−	0.821241i	$-0.693282\pi$
$541$	−26.5428	−1.14116	−0.570582	+	0.821241i	$0.693282\pi$
$542$	−63.1820	−2.71390
$543$	3.87950	0.166485
$544$	56.2666	2.41241
$545$	−0.858946	−0.0367932
$546$	32.4948	1.39065
$547$	−32.1053	−1.37272	−0.686362	−	0.727260i	$-0.740793\pi$
$547$	−32.1053	−1.37272	−0.686362	+	0.727260i	$0.740793\pi$
$548$	−11.9760	−0.511590
$549$	0.00318676	0.000136007 0
$550$	−7.84084	−0.334335
$551$	59.7533	2.54558
$552$	11.5007	0.489503
$553$	27.8360	1.18371
$554$	27.5575	1.17081
$555$	−0.964761	−0.0409518
$556$	−10.3727	−0.439900
$557$	−39.7097	−1.68255	−0.841277	−	0.540604i	$-0.818196\pi$
$557$	−39.7097	−1.68255	−0.841277	+	0.540604i	$0.818196\pi$
$558$	−0.0373363	−0.00158057
$559$	−21.9309	−0.927580
$560$	−12.1245	−0.512353
$561$	12.1568	0.513261
$562$	4.61760	0.194782
$563$	−22.7689	−0.959594	−0.479797	−	0.877379i	$-0.659290\pi$
$563$	−22.7689	−0.959594	−0.479797	+	0.877379i	$0.659290\pi$
$564$	8.24139	0.347025
$565$	−5.16909	−0.217465
$566$	−44.3698	−1.86500
$567$	−33.1367	−1.39161
$568$	−4.79288	−0.201105
$569$	−17.3274	−0.726400	−0.363200	−	0.931711i	$-0.618316\pi$
$569$	−17.3274	−0.726400	−0.363200	+	0.931711i	$0.618316\pi$
$570$	26.9071	1.12701
$571$	11.0661	0.463101	0.231550	−	0.972823i	$-0.425620\pi$
$571$	11.0661	0.463101	0.231550	+	0.972823i	$0.425620\pi$
$572$	−5.91043	−0.247128
$573$	−12.0151	−0.501937
$574$	33.2133	1.38630
$575$	−26.2124	−1.09313
$576$	0.0218458	0.000910242 0
$577$	−7.86954	−0.327613	−0.163807	−	0.986492i	$-0.552377\pi$
$577$	−7.86954	−0.327613	−0.163807	+	0.986492i	$0.552377\pi$
$578$	−68.1019	−2.83266
$579$	−1.59459	−0.0662687
$580$	25.4296	1.05591
$581$	31.0136	1.28666
$582$	35.8726	1.48697
$583$	11.4582	0.474549
$584$	12.7881	0.529177
$585$	−0.00538911	−0.000222812 0
$586$	−5.51762	−0.227931
$587$	39.4832	1.62964	0.814822	−	0.579711i	$-0.196835\pi$
$587$	39.4832	1.62964	0.814822	+	0.579711i	$0.196835\pi$
$588$	−27.8509	−1.14855
$589$	−58.4837	−2.40978
$590$	−23.3079	−0.959571
$591$	34.4526	1.41719
$592$	−1.43057	−0.0587962
$593$	38.3597	1.57524	0.787621	−	0.616160i	$-0.211312\pi$
$593$	38.3597	1.57524	0.787621	+	0.616160i	$0.211312\pi$
$594$	10.9610	0.449733
$595$	29.2857	1.20060
$596$	−25.5118	−1.04500
$597$	13.3560	0.546626
$598$	−35.9097	−1.46846
$599$	−32.2769	−1.31880	−0.659399	−	0.751793i	$-0.729189\pi$
$599$	−32.2769	−1.31880	−0.659399	+	0.751793i	$0.729189\pi$
$600$	−6.06591	−0.247640
$601$	19.8556	0.809926	0.404963	−	0.914333i	$-0.367284\pi$
$601$	19.8556	0.809926	0.404963	+	0.914333i	$0.367284\pi$
$602$	70.5364	2.87485
$603$	0.00299150	0.000121823 0
$604$	50.8207	2.06787
$605$	1.13214	0.0460282
$606$	37.8266	1.53660
$607$	34.9946	1.42039	0.710193	−	0.704007i	$-0.248608\pi$
$607$	34.9946	1.42039	0.710193	+	0.704007i	$0.248608\pi$
$608$	52.1642	2.11554
$609$	−58.5611	−2.37302
$610$	3.86082	0.156320
$611$	−4.69898	−0.190100
$612$	−0.0338528	−0.00136842
$613$	−40.0866	−1.61908	−0.809540	−	0.587064i	$-0.800284\pi$
$613$	−40.0866	−1.61908	−0.809540	+	0.587064i	$0.800284\pi$
$614$	18.7919	0.758381
$615$	8.38021	0.337923
$616$	3.47130	0.139862
$617$	3.92681	0.158087	0.0790437	−	0.996871i	$-0.474813\pi$
$617$	3.92681	0.158087	0.0790437	+	0.996871i	$0.474813\pi$
$618$	9.11966	0.366847
$619$	−41.8530	−1.68221	−0.841107	−	0.540868i	$-0.818096\pi$
$619$	−41.8530	−1.68221	−0.841107	+	0.540868i	$0.818096\pi$
$620$	−24.8893	−0.999578
$621$	36.6431	1.47044
$622$	36.7826	1.47485
$623$	27.0879	1.08525
$624$	12.1576	0.486694
$625$	7.41665	0.296666
$626$	5.44908	0.217789
$627$	11.2704	0.450098
$628$	13.4142	0.535286
$629$	3.45543	0.137777
$630$	0.0173330	0.000690561 0
$631$	14.3445	0.571047	0.285524	−	0.958372i	$-0.407832\pi$
$631$	14.3445	0.571047	0.285524	+	0.958372i	$0.407832\pi$
$632$	−7.11859	−0.283162
$633$	4.58641	0.182294
$634$	23.1060	0.917657
$635$	−4.12870	−0.163843
$636$	48.5436	1.92488
$637$	15.8797	0.629178
$638$	19.3581	0.766395
$639$	−0.0100242	−0.000396553 0
$640$	8.32062	0.328902
$641$	8.47261	0.334648	0.167324	−	0.985902i	$-0.446487\pi$
$641$	8.47261	0.334648	0.167324	+	0.985902i	$0.446487\pi$
$642$	−50.4650	−1.99170
$643$	18.1935	0.717481	0.358740	−	0.933437i	$-0.383206\pi$
$643$	18.1935	0.717481	0.358740	+	0.933437i	$0.383206\pi$
$644$	63.5505	2.50424
$645$	17.7974	0.700772
$646$	−96.3714	−3.79168
$647$	−12.2354	−0.481021	−0.240511	−	0.970646i	$-0.577315\pi$
$647$	−12.2354	−0.481021	−0.240511	+	0.970646i	$0.577315\pi$
$648$	8.47415	0.332896
$649$	−9.76288	−0.383226
$650$	18.9401	0.742893
$651$	57.3168	2.24642
$652$	−10.3470	−0.405220
$653$	5.11948	0.200341	0.100170	−	0.994970i	$-0.468061\pi$
$653$	5.11948	0.200341	0.100170	+	0.994970i	$0.468061\pi$
$654$	−2.77017	−0.108322
$655$	1.13214	0.0442365
$656$	12.4264	0.485169
$657$	0.0267462	0.00104347
$658$	15.1133	0.589178
$659$	18.5500	0.722606	0.361303	−	0.932448i	$-0.382332\pi$
$659$	18.5500	0.722606	0.361303	+	0.932448i	$0.382332\pi$
$660$	4.79643	0.186701
$661$	−38.3046	−1.48987	−0.744937	−	0.667134i	$-0.767521\pi$
$661$	−38.3046	−1.48987	−0.744937	+	0.667134i	$0.767521\pi$
$662$	−14.3466	−0.557595
$663$	−29.3657	−1.14047
$664$	−7.93122	−0.307791
$665$	27.1504	1.05285
$666$	0.00204512	7.92468e−5 0
$667$	64.7152	2.50578
$668$	−3.56711	−0.138016
$669$	−35.1516	−1.35904
$670$	3.62426	0.140017
$671$	1.61716	0.0624299
$672$	−51.1234	−1.97213
$673$	32.4486	1.25080	0.625401	−	0.780304i	$-0.284936\pi$
$673$	32.4486	1.25080	0.625401	+	0.780304i	$0.284936\pi$
$674$	−54.7669	−2.10954
$675$	−19.3269	−0.743894
$676$	−17.5313	−0.674283
$677$	20.8047	0.799588	0.399794	−	0.916605i	$-0.369082\pi$
$677$	20.8047	0.799588	0.399794	+	0.916605i	$0.369082\pi$
$678$	−16.6707	−0.640235
$679$	36.1971	1.38912
$680$	−7.48932	−0.287202
$681$	−33.1861	−1.27169
$682$	−18.9468	−0.725511
$683$	25.4579	0.974120	0.487060	−	0.873369i	$-0.338069\pi$
$683$	25.4579	0.974120	0.487060	+	0.873369i	$0.338069\pi$
$684$	−0.0313846	−0.00120002
$685$	−5.54134	−0.211724
$686$	3.31050	0.126396
$687$	−29.3963	−1.12154
$688$	26.3904	1.00613
$689$	−27.6781	−1.05445
$690$	29.1414	1.10940
$691$	13.5419	0.515160	0.257580	−	0.966257i	$-0.417075\pi$
$691$	13.5419	0.515160	0.257580	+	0.966257i	$0.417075\pi$
$692$	43.3499	1.64791
$693$	0.00726018	0.000275791 0
$694$	−34.8446	−1.32268
$695$	−4.79948	−0.182055
$696$	14.9760	0.567664
$697$	−30.0149	−1.13690
$698$	64.6890	2.44852
$699$	−17.6476	−0.667492
$700$	−33.5189	−1.26690
$701$	−7.16688	−0.270689	−0.135345	−	0.990799i	$-0.543214\pi$
$701$	−7.16688	−0.270689	−0.135345	+	0.990799i	$0.543214\pi$
$702$	−26.4770	−0.999310
$703$	3.20349	0.120822
$704$	11.0860	0.417818
$705$	3.81332	0.143618
$706$	75.2814	2.83325
$707$	38.1688	1.43548
$708$	−41.3613	−1.55445
$709$	−15.9432	−0.598759	−0.299379	−	0.954134i	$-0.596780\pi$
$709$	−15.9432	−0.598759	−0.299379	+	0.954134i	$0.596780\pi$
$710$	−12.1446	−0.455778
$711$	−0.0148885	−0.000558361 0
$712$	−6.92728	−0.259611
$713$	−63.3402	−2.37211
$714$	94.4486	3.53465
$715$	−2.73478	−0.102275
$716$	3.07327	0.114853
$717$	−24.0863	−0.899520
$718$	5.96558	0.222634
$719$	16.1750	0.603226	0.301613	−	0.953430i	$-0.402475\pi$
$719$	16.1750	0.603226	0.301613	+	0.953430i	$0.402475\pi$
$720$	0.00648494	0.000241679 0
$721$	9.20214	0.342706
$722$	−49.2788	−1.83397
$723$	−17.2526	−0.641629
$724$	−5.48223	−0.203745
$725$	−34.1333	−1.26768
$726$	3.65125	0.135511
$727$	−22.3319	−0.828245	−0.414123	−	0.910221i	$-0.635912\pi$
$727$	−22.3319	−0.828245	−0.414123	+	0.910221i	$0.635912\pi$
$728$	−8.38517	−0.310775
$729$	27.0177	1.00066
$730$	32.4036	1.19931
$731$	−63.7439	−2.35765
$732$	6.85126	0.253230
$733$	0.576875	0.0213074	0.0106537	−	0.999943i	$-0.496609\pi$
$733$	0.576875	0.0213074	0.0106537	+	0.999943i	$0.496609\pi$
$734$	22.7303	0.838989
$735$	−12.8867	−0.475333
$736$	56.4959	2.08247
$737$	1.51808	0.0559191
$738$	−0.0177646	−0.000653922 0
$739$	13.0682	0.480723	0.240362	−	0.970683i	$-0.422734\pi$
$739$	13.0682	0.480723	0.240362	+	0.970683i	$0.422734\pi$
$740$	1.36333	0.0501169
$741$	−27.2246	−1.00012
$742$	89.0208	3.26806
$743$	−20.8792	−0.765985	−0.382992	−	0.923752i	$-0.625106\pi$
$743$	−20.8792	−0.765985	−0.382992	+	0.923752i	$0.625106\pi$
$744$	−14.6578	−0.537382
$745$	−11.8044	−0.432479
$746$	56.9291	2.08432
$747$	−0.0165881	−0.000606925 0
$748$	−17.1791	−0.628130
$749$	−50.9215	−1.86063
$750$	−36.0390	−1.31596
$751$	30.1558	1.10040	0.550200	−	0.835033i	$-0.314552\pi$
$751$	30.1558	1.10040	0.550200	+	0.835033i	$0.314552\pi$
$752$	5.65449	0.206198
$753$	15.8571	0.577865
$754$	−46.7609	−1.70293
$755$	23.5149	0.855795
$756$	46.8571	1.70418
$757$	−51.5466	−1.87349	−0.936747	−	0.350008i	$-0.886179\pi$
$757$	−51.5466	−1.87349	−0.936747	+	0.350008i	$0.886179\pi$
$758$	72.5593	2.63547
$759$	12.2063	0.443062
$760$	−6.94326	−0.251859
$761$	−7.41519	−0.268800	−0.134400	−	0.990927i	$-0.542911\pi$
$761$	−7.41519	−0.268800	−0.134400	+	0.990927i	$0.542911\pi$
$762$	−13.3154	−0.482366
$763$	−2.79522	−0.101194
$764$	16.9788	0.614272
$765$	−0.0156638	−0.000566327 0
$766$	−43.9501	−1.58798
$767$	23.5830	0.851531
$768$	−11.5556	−0.416977
$769$	−4.06312	−0.146520	−0.0732599	−	0.997313i	$-0.523340\pi$
$769$	−4.06312	−0.146520	−0.0732599	+	0.997313i	$0.523340\pi$
$770$	8.79585	0.316980
$771$	−44.0839	−1.58764
$772$	2.25335	0.0810999
$773$	25.3895	0.913197	0.456599	−	0.889673i	$-0.349068\pi$
$773$	25.3895	0.913197	0.456599	+	0.889673i	$0.349068\pi$
$774$	−0.0377273	−0.00135608
$775$	33.4080	1.20005
$776$	−9.25679	−0.332300
$777$	−3.13957	−0.112631
$778$	−69.2524	−2.48282
$779$	−27.8265	−0.996988
$780$	−11.5861	−0.414850
$781$	−5.08694	−0.182025
$782$	−104.374	−3.73241
$783$	47.7159	1.70523
$784$	−19.1088	−0.682455
$785$	6.20680	0.221530
$786$	3.65125	0.130236
$787$	31.5113	1.12326	0.561628	−	0.827390i	$-0.310175\pi$
$787$	31.5113	1.12326	0.561628	+	0.827390i	$0.310175\pi$
$788$	−48.6859	−1.73436
$789$	−0.626403	−0.0223005
$790$	−18.0377	−0.641751
$791$	−16.8215	−0.598104
$792$	−0.00185667	−6.59738e−5 0
$793$	−3.90638	−0.138720
$794$	43.3463	1.53830
$795$	22.4613	0.796620
$796$	−18.8738	−0.668963
$797$	−40.3021	−1.42757	−0.713787	−	0.700363i	$-0.753022\pi$
$797$	−40.3021	−1.42757	−0.713787	+	0.700363i	$0.753022\pi$
$798$	87.5623	3.09967
$799$	−13.6579	−0.483183
$800$	−29.7981	−1.05352
$801$	−0.0144883	−0.000511920 0
$802$	−1.20135	−0.0424212
$803$	13.5727	0.478972
$804$	6.43148	0.226821
$805$	29.4050	1.03639
$806$	45.7674	1.61209
$807$	53.2762	1.87541
$808$	−9.76102	−0.343392
$809$	−43.1321	−1.51644	−0.758221	−	0.651998i	$-0.773931\pi$
$809$	−43.1321	−1.51644	−0.758221	+	0.651998i	$0.773931\pi$
$810$	21.4725	0.754466
$811$	36.1044	1.26780	0.633898	−	0.773417i	$-0.281454\pi$
$811$	36.1044	1.26780	0.633898	+	0.773417i	$0.281454\pi$
$812$	82.7542	2.90410
$813$	−51.8785	−1.81946
$814$	1.03782	0.0363757
$815$	−4.78759	−0.167702
$816$	35.3369	1.23704
$817$	−59.0962	−2.06752
$818$	22.0227	0.770005
$819$	−0.0175375	−0.000612810 0
$820$	−11.8423	−0.413551
$821$	−10.2602	−0.358083	−0.179041	−	0.983842i	$-0.557300\pi$
$821$	−10.2602	−0.358083	−0.179041	+	0.983842i	$0.557300\pi$
$822$	−17.8713	−0.623332
$823$	13.3791	0.466366	0.233183	−	0.972433i	$-0.425086\pi$
$823$	13.3791	0.466366	0.233183	+	0.972433i	$0.425086\pi$
$824$	−2.35329	−0.0819809
$825$	−6.43808	−0.224145
$826$	−75.8497	−2.63915
$827$	−18.8417	−0.655189	−0.327594	−	0.944818i	$-0.606238\pi$
$827$	−18.8417	−0.655189	−0.327594	+	0.944818i	$0.606238\pi$
$828$	−0.0339908	−0.00118126
$829$	35.2096	1.22288	0.611440	−	0.791291i	$-0.290591\pi$
$829$	35.2096	1.22288	0.611440	+	0.791291i	$0.290591\pi$
$830$	−20.0967	−0.697568
$831$	22.6274	0.784934
$832$	−26.7790	−0.928393
$833$	46.1556	1.59920
$834$	−15.4787	−0.535983
$835$	−1.65051	−0.0571184
$836$	−15.9266	−0.550831
$837$	−46.7021	−1.61426
$838$	−17.0862	−0.590235
$839$	50.5200	1.74414	0.872072	−	0.489378i	$-0.162776\pi$
$839$	50.5200	1.74414	0.872072	+	0.489378i	$0.162776\pi$
$840$	6.80473	0.234786
$841$	55.2710	1.90590
$842$	42.9848	1.48135
$843$	3.79150	0.130586
$844$	−6.48118	−0.223092
$845$	−8.11181	−0.279055
$846$	−0.00808355	−0.000277918 0
$847$	3.68428	0.126593
$848$	33.3062	1.14374
$849$	−36.4318	−1.25034
$850$	55.0509	1.88823
$851$	3.46951	0.118933
$852$	−21.5513	−0.738336
$853$	−27.7221	−0.949187	−0.474594	−	0.880205i	$-0.657405\pi$
$853$	−27.7221	−0.949187	−0.474594	+	0.880205i	$0.657405\pi$
$854$	12.5641	0.429933
$855$	−0.0145218	−0.000496634 0
$856$	13.0223	0.445093
$857$	20.7564	0.709025	0.354513	−	0.935051i	$-0.384647\pi$
$857$	20.7564	0.709025	0.354513	+	0.935051i	$0.384647\pi$
$858$	−8.81987	−0.301105
$859$	1.20801	0.0412169	0.0206084	−	0.999788i	$-0.493440\pi$
$859$	1.20801	0.0412169	0.0206084	+	0.999788i	$0.493440\pi$
$860$	−25.1500	−0.857607
$861$	27.2713	0.929403
$862$	17.1953	0.585673
$863$	−17.3257	−0.589774	−0.294887	−	0.955532i	$-0.595282\pi$
$863$	−17.3257	−0.589774	−0.294887	+	0.955532i	$0.595282\pi$
$864$	41.6556	1.41715
$865$	20.0581	0.681997
$866$	55.1100	1.87272
$867$	−55.9182	−1.89908
$868$	−80.9959	−2.74918
$869$	−7.55536	−0.256298
$870$	37.9474	1.28654
$871$	−3.66703	−0.124253
$872$	0.714832	0.0242073
$873$	−0.0193605	−0.000655253 0
$874$	−96.7641	−3.27310
$875$	−36.3650	−1.22936
$876$	57.5022	1.94282
$877$	47.3156	1.59774	0.798868	−	0.601507i	$-0.205433\pi$
$877$	47.3156	1.59774	0.798868	+	0.601507i	$0.205433\pi$
$878$	−26.1288	−0.881805
$879$	−4.53050	−0.152810
$880$	3.29087	0.110935
$881$	−2.42783	−0.0817957	−0.0408978	−	0.999163i	$-0.513022\pi$
$881$	−2.42783	−0.0817957	−0.0408978	+	0.999163i	$0.513022\pi$
$882$	0.0273175	0.000919829 0
$883$	−38.2348	−1.28670	−0.643352	−	0.765570i	$-0.722457\pi$
$883$	−38.2348	−1.28670	−0.643352	+	0.765570i	$0.722457\pi$
$884$	41.4974	1.39571
$885$	−19.1380	−0.643318
$886$	52.8102	1.77419
$887$	−58.9768	−1.98025	−0.990124	−	0.140196i	$-0.955227\pi$
$887$	−58.9768	−1.98025	−0.990124	+	0.140196i	$0.955227\pi$
$888$	0.802893	0.0269433
$889$	−13.4358	−0.450623
$890$	−17.5529	−0.588375
$891$	8.99408	0.301313
$892$	49.6736	1.66320
$893$	−12.6621	−0.423722
$894$	−38.0701	−1.27325
$895$	1.42201	0.0475325
$896$	27.0774	0.904592
$897$	−29.4853	−0.984486
$898$	−65.5015	−2.18581
$899$	−82.4804	−2.75088
$900$	0.0179280	0.000597601 0
$901$	−80.4483	−2.68012
$902$	−9.01487	−0.300162
$903$	57.9171	1.92736
$904$	4.30182	0.143076
$905$	−2.53664	−0.0843209
$906$	75.8375	2.51953
$907$	1.84205	0.0611641	0.0305821	−	0.999532i	$-0.490264\pi$
$907$	1.84205	0.0611641	0.0305821	+	0.999532i	$0.490264\pi$
$908$	46.8961	1.55630
$909$	−0.0204151	−0.000677125 0
$910$	−21.2470	−0.704332
$911$	39.8340	1.31976	0.659880	−	0.751371i	$-0.270607\pi$
$911$	39.8340	1.31976	0.659880	+	0.751371i	$0.270607\pi$
$912$	32.7605	1.08481
$913$	−8.41784	−0.278590
$914$	87.7521	2.90258
$915$	3.17010	0.104800
$916$	41.5407	1.37254
$917$	3.68428	0.121666
$918$	−76.9573	−2.53997
$919$	−11.3519	−0.374464	−0.187232	−	0.982316i	$-0.559952\pi$
$919$	−11.3519	−0.374464	−0.187232	+	0.982316i	$0.559952\pi$
$920$	−7.51984	−0.247922
$921$	15.4300	0.508436
$922$	43.5987	1.43585
$923$	12.2879	0.404461
$924$	15.6088	0.513491
$925$	−1.82995	−0.0601683
$926$	−17.0499	−0.560295
$927$	−0.00492189	−0.000161656 0
$928$	73.5679	2.41499
$929$	29.5833	0.970596	0.485298	−	0.874349i	$-0.338711\pi$
$929$	29.5833	0.970596	0.485298	+	0.874349i	$0.338711\pi$
$930$	−37.1411	−1.21791
$931$	42.7903	1.40240
$932$	24.9382	0.816879
$933$	30.2020	0.988770
$934$	−25.5524	−0.836101
$935$	−7.94882	−0.259954
$936$	0.00448492	0.000146594 0
$937$	39.3344	1.28500	0.642499	−	0.766286i	$-0.277898\pi$
$937$	39.3344	1.28500	0.642499	+	0.766286i	$0.277898\pi$
$938$	11.7942	0.385096
$939$	4.47422	0.146011
$940$	−5.38870	−0.175760
$941$	−45.9548	−1.49808	−0.749042	−	0.662523i	$-0.769486\pi$
$941$	−45.9548	−1.49808	−0.749042	+	0.662523i	$0.769486\pi$
$942$	20.0174	0.652203
$943$	−30.1372	−0.981403
$944$	−28.3784	−0.923637
$945$	21.6809	0.705281
$946$	−19.1452	−0.622466
$947$	−3.89120	−0.126447	−0.0632234	−	0.997999i	$-0.520138\pi$
$947$	−3.89120	−0.126447	−0.0632234	+	0.997999i	$0.520138\pi$
$948$	−32.0090	−1.03960
$949$	−32.7860	−1.06428
$950$	51.0370	1.65586
$951$	18.9723	0.615217
$952$	−24.3721	−0.789904
$953$	−8.53220	−0.276385	−0.138193	−	0.990405i	$-0.544129\pi$
$953$	−8.53220	−0.276385	−0.138193	+	0.990405i	$0.544129\pi$
$954$	−0.0476140	−0.00154156
$955$	7.85616	0.254219
$956$	34.0370	1.10084
$957$	15.8949	0.513808
$958$	−31.3997	−1.01448
$959$	−18.0329	−0.582313
$960$	21.7316	0.701386
$961$	49.7280	1.60413
$962$	−2.50694	−0.0808271
$963$	0.0272360	0.000877669 0
$964$	24.3800	0.785228
$965$	1.04263	0.0335635
$966$	94.8335	3.05122
$967$	−8.46616	−0.272253	−0.136127	−	0.990691i	$-0.543465\pi$
$967$	−8.46616	−0.272253	−0.136127	+	0.990691i	$0.543465\pi$
$968$	−0.942192	−0.0302832
$969$	−79.1302	−2.54203
$970$	−23.4556	−0.753114
$971$	−45.4264	−1.45780	−0.728901	−	0.684619i	$-0.759969\pi$
$971$	−45.4264	−1.45780	−0.728901	+	0.684619i	$0.759969\pi$
$972$	−0.0501078	−0.00160721
$973$	−15.6187	−0.500712
$974$	−35.6554	−1.14247
$975$	15.5517	0.498052
$976$	4.70071	0.150466
$977$	14.5324	0.464933	0.232466	−	0.972604i	$-0.425320\pi$
$977$	14.5324	0.464933	0.232466	+	0.972604i	$0.425320\pi$
$978$	−15.4404	−0.493729
$979$	−7.35231	−0.234981
$980$	18.2105	0.581715
$981$	0.00149506	4.77337e−5 0
$982$	−20.9819	−0.669560
$983$	−27.9447	−0.891296	−0.445648	−	0.895208i	$-0.647027\pi$
$983$	−27.9447	−0.891296	−0.445648	+	0.895208i	$0.647027\pi$
$984$	−6.97418	−0.222329
$985$	−22.5271	−0.717774
$986$	−135.914	−4.32838
$987$	12.4095	0.394998
$988$	38.4718	1.22395
$989$	−64.0036	−2.03520
$990$	−0.00470457	−0.000149521 0
$991$	25.3769	0.806125	0.403062	−	0.915173i	$-0.367946\pi$
$991$	25.3769	0.806125	0.403062	+	0.915173i	$0.367946\pi$
$992$	−72.0048	−2.28616
$993$	−11.7799	−0.373824
$994$	−39.5215	−1.25354
$995$	−8.73295	−0.276853
$996$	−35.6630	−1.13002
$997$	−2.96500	−0.0939024	−0.0469512	−	0.998897i	$-0.514951\pi$
$997$	−2.96500	−0.0939024	−0.0469512	+	0.998897i	$0.514951\pi$
$998$	11.4270	0.361714
$999$	2.55814	0.0809360

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.f.1.5	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.f.1.5	✓	31	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:	\( N \)	\(=\)	\( 1441 = 11 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1441.a (trivial)

\(f(q)\)	\(=\)	\(q-2.10874 q^{2} -1.73148 q^{3} +2.44680 q^{4} +1.13214 q^{5} +3.65125 q^{6} +3.68428 q^{7} -0.942192 q^{8} -0.00197058 q^{9} +O(q^{10})\)	\(q-2.10874 q^{2} -1.73148 q^{3} +2.44680 q^{4} +1.13214 q^{5} +3.65125 q^{6} +3.68428 q^{7} -0.942192 q^{8} -0.00197058 q^{9} -2.38740 q^{10} -1.00000 q^{11} -4.23659 q^{12} +2.41557 q^{13} -7.76920 q^{14} -1.96029 q^{15} -2.90676 q^{16} +7.02104 q^{17} +0.00415546 q^{18} +6.50913 q^{19} +2.77013 q^{20} -6.37926 q^{21} +2.10874 q^{22} +7.04965 q^{23} +1.63139 q^{24} -3.71825 q^{25} -5.09383 q^{26} +5.19786 q^{27} +9.01470 q^{28} +9.17992 q^{29} +4.13374 q^{30} -8.98487 q^{31} +8.01400 q^{32} +1.73148 q^{33} -14.8056 q^{34} +4.17113 q^{35} -0.00482163 q^{36} +0.492153 q^{37} -13.7261 q^{38} -4.18252 q^{39} -1.06670 q^{40} -4.27499 q^{41} +13.4522 q^{42} -9.07898 q^{43} -2.44680 q^{44} -0.00223098 q^{45} -14.8659 q^{46} -1.94529 q^{47} +5.03301 q^{48} +6.57389 q^{49} +7.84084 q^{50} -12.1568 q^{51} +5.91043 q^{52} -11.4582 q^{53} -10.9610 q^{54} -1.13214 q^{55} -3.47130 q^{56} -11.2704 q^{57} -19.3581 q^{58} +9.76288 q^{59} -4.79643 q^{60} -1.61716 q^{61} +18.9468 q^{62} -0.00726018 q^{63} -11.0860 q^{64} +2.73478 q^{65} -3.65125 q^{66} -1.51808 q^{67} +17.1791 q^{68} -12.2063 q^{69} -8.79585 q^{70} +5.08694 q^{71} +0.00185667 q^{72} -13.5727 q^{73} -1.03782 q^{74} +6.43808 q^{75} +15.9266 q^{76} -3.68428 q^{77} +8.81987 q^{78} +7.55536 q^{79} -3.29087 q^{80} -8.99408 q^{81} +9.01487 q^{82} +8.41784 q^{83} -15.6088 q^{84} +7.94882 q^{85} +19.1452 q^{86} -15.8949 q^{87} +0.942192 q^{88} +7.35231 q^{89} +0.00470457 q^{90} +8.89964 q^{91} +17.2491 q^{92} +15.5571 q^{93} +4.10211 q^{94} +7.36927 q^{95} -13.8761 q^{96} +9.82474 q^{97} -13.8627 q^{98} +0.00197058 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9}+O(q^{10}) \) 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9	\( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9} - 8 q^{10} - 31 q^{11} + 10 q^{12} - 8 q^{13} + 29 q^{14} + 36 q^{15} + 52 q^{16} - q^{17} + 33 q^{18} - 2 q^{19} + 22 q^{20} - 13 q^{21} - 6 q^{22} + 45 q^{23} + 16 q^{24} + 41 q^{25} + 24 q^{26} + 22 q^{27} + 17 q^{28} + 5 q^{29} + 29 q^{30} + 28 q^{31} + 69 q^{32} - 4 q^{33} + 14 q^{34} + 36 q^{35} + 63 q^{36} - 3 q^{37} + 4 q^{38} + 40 q^{39} - 48 q^{40} + 21 q^{41} - 9 q^{42} - 20 q^{43} - 38 q^{44} + 28 q^{45} - 24 q^{46} + 57 q^{47} - 46 q^{48} + 37 q^{49} + 64 q^{50} + 17 q^{51} - 11 q^{52} + 32 q^{53} - 26 q^{54} - 8 q^{55} + 84 q^{56} + 10 q^{57} - 17 q^{58} + 70 q^{59} - 33 q^{60} - 51 q^{61} - 34 q^{62} + 32 q^{63} + 80 q^{64} - q^{65} - 7 q^{66} + 24 q^{67} - 13 q^{68} + 19 q^{69} - 9 q^{70} + 128 q^{71} + 118 q^{72} - 27 q^{73} - 23 q^{74} + 41 q^{75} - 34 q^{76} - 4 q^{77} + 9 q^{78} + 2 q^{79} - 45 q^{80} + 43 q^{81} - 18 q^{82} + 46 q^{83} - 103 q^{84} - 50 q^{85} + 78 q^{86} - 9 q^{87} - 24 q^{88} + 52 q^{89} - 46 q^{90} + 38 q^{91} + 54 q^{92} + 4 q^{93} + 3 q^{94} + 70 q^{95} - 21 q^{96} + 3 q^{97} - 120 q^{98} - 45 q^{99}+O(q^{100}) \) 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9 - 8 * q^10 - 31 * q^11 + 10 * q^12 - 8 * q^13 + 29 * q^14 + 36 * q^15 + 52 * q^16 - q^17 + 33 * q^18 - 2 * q^19 + 22 * q^20 - 13 * q^21 - 6 * q^22 + 45 * q^23 + 16 * q^24 + 41 * q^25 + 24 * q^26 + 22 * q^27 + 17 * q^28 + 5 * q^29 + 29 * q^30 + 28 * q^31 + 69 * q^32 - 4 * q^33 + 14 * q^34 + 36 * q^35 + 63 * q^36 - 3 * q^37 + 4 * q^38 + 40 * q^39 - 48 * q^40 + 21 * q^41 - 9 * q^42 - 20 * q^43 - 38 * q^44 + 28 * q^45 - 24 * q^46 + 57 * q^47 - 46 * q^48 + 37 * q^49 + 64 * q^50 + 17 * q^51 - 11 * q^52 + 32 * q^53 - 26 * q^54 - 8 * q^55 + 84 * q^56 + 10 * q^57 - 17 * q^58 + 70 * q^59 - 33 * q^60 - 51 * q^61 - 34 * q^62 + 32 * q^63 + 80 * q^64 - q^65 - 7 * q^66 + 24 * q^67 - 13 * q^68 + 19 * q^69 - 9 * q^70 + 128 * q^71 + 118 * q^72 - 27 * q^73 - 23 * q^74 + 41 * q^75 - 34 * q^76 - 4 * q^77 + 9 * q^78 + 2 * q^79 - 45 * q^80 + 43 * q^81 - 18 * q^82 + 46 * q^83 - 103 * q^84 - 50 * q^85 + 78 * q^86 - 9 * q^87 - 24 * q^88 + 52 * q^89 - 46 * q^90 + 38 * q^91 + 54 * q^92 + 4 * q^93 + 3 * q^94 + 70 * q^95 - 21 * q^96 + 3 * q^97 - 120 * q^98 - 45 * q^99

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