LMFDB - Embedded newform 4030.2.a.r.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4030,2,Mod(1,4030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4030, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("4030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4030 = 2 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4030.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:	$32.1797120146$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 4x^{8} - 8x^{7} + 39x^{6} + 13x^{5} - 106x^{4} + 9x^{3} + 74x^{2} - 3x - 7 $ x^9 - 4x^8 - 8x^7 + 39x^6 + 13x^5 - 106x^4 + 9x^3 + 74x^2 - 3x - 7
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.72735$ of defining polynomial
Character	$\chi$	$=$	4030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.50823 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.50823 q^{6} -3.09594 q^{7} +1.00000 q^{8} -0.725248 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.50823 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.50823 q^{6} -3.09594 q^{7} +1.00000 q^{8} -0.725248 q^{9} +1.00000 q^{10} -0.743610 q^{11} -1.50823 q^{12} +1.00000 q^{13} -3.09594 q^{14} -1.50823 q^{15} +1.00000 q^{16} -2.93595 q^{17} -0.725248 q^{18} +2.92476 q^{19} +1.00000 q^{20} +4.66939 q^{21} -0.743610 q^{22} +1.11511 q^{23} -1.50823 q^{24} +1.00000 q^{25} +1.00000 q^{26} +5.61852 q^{27} -3.09594 q^{28} -3.98528 q^{29} -1.50823 q^{30} -1.00000 q^{31} +1.00000 q^{32} +1.12153 q^{33} -2.93595 q^{34} -3.09594 q^{35} -0.725248 q^{36} +6.05657 q^{37} +2.92476 q^{38} -1.50823 q^{39} +1.00000 q^{40} -0.863733 q^{41} +4.66939 q^{42} -5.41300 q^{43} -0.743610 q^{44} -0.725248 q^{45} +1.11511 q^{46} +4.92033 q^{47} -1.50823 q^{48} +2.58487 q^{49} +1.00000 q^{50} +4.42808 q^{51} +1.00000 q^{52} -1.91307 q^{53} +5.61852 q^{54} -0.743610 q^{55} -3.09594 q^{56} -4.41121 q^{57} -3.98528 q^{58} +4.13079 q^{59} -1.50823 q^{60} -7.58910 q^{61} -1.00000 q^{62} +2.24533 q^{63} +1.00000 q^{64} +1.00000 q^{65} +1.12153 q^{66} +13.4497 q^{67} -2.93595 q^{68} -1.68184 q^{69} -3.09594 q^{70} +14.1556 q^{71} -0.725248 q^{72} +11.0354 q^{73} +6.05657 q^{74} -1.50823 q^{75} +2.92476 q^{76} +2.30218 q^{77} -1.50823 q^{78} -1.10592 q^{79} +1.00000 q^{80} -6.29827 q^{81} -0.863733 q^{82} +18.0284 q^{83} +4.66939 q^{84} -2.93595 q^{85} -5.41300 q^{86} +6.01072 q^{87} -0.743610 q^{88} +0.791684 q^{89} -0.725248 q^{90} -3.09594 q^{91} +1.11511 q^{92} +1.50823 q^{93} +4.92033 q^{94} +2.92476 q^{95} -1.50823 q^{96} -6.19662 q^{97} +2.58487 q^{98} +0.539301 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} + 9 q^{5} + 3 q^{6} + 9 q^{7} + 9 q^{8} + 14 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 + 9 * q^5 + 3 * q^6 + 9 * q^7 + 9 * q^8 + 14 * q^9	\( 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} + 9 q^{5} + 3 q^{6} + 9 q^{7} + 9 q^{8} + 14 q^{9} + 9 q^{10} + 10 q^{11} + 3 q^{12} + 9 q^{13} + 9 q^{14} + 3 q^{15} + 9 q^{16} + q^{17} + 14 q^{18} + 10 q^{19} + 9 q^{20} + 3 q^{21} + 10 q^{22} + 8 q^{23} + 3 q^{24} + 9 q^{25} + 9 q^{26} + 15 q^{27} + 9 q^{28} + 9 q^{29} + 3 q^{30} - 9 q^{31} + 9 q^{32} + 4 q^{33} + q^{34} + 9 q^{35} + 14 q^{36} - 3 q^{37} + 10 q^{38} + 3 q^{39} + 9 q^{40} + 3 q^{42} + 7 q^{43} + 10 q^{44} + 14 q^{45} + 8 q^{46} + 7 q^{47} + 3 q^{48} + 8 q^{49} + 9 q^{50} - 3 q^{51} + 9 q^{52} + 8 q^{53} + 15 q^{54} + 10 q^{55} + 9 q^{56} - 7 q^{57} + 9 q^{58} + 2 q^{59} + 3 q^{60} - 2 q^{61} - 9 q^{62} + 10 q^{63} + 9 q^{64} + 9 q^{65} + 4 q^{66} + 18 q^{67} + q^{68} - 16 q^{69} + 9 q^{70} + 14 q^{71} + 14 q^{72} + q^{73} - 3 q^{74} + 3 q^{75} + 10 q^{76} - 5 q^{77} + 3 q^{78} + 6 q^{79} + 9 q^{80} + q^{81} + 7 q^{83} + 3 q^{84} + q^{85} + 7 q^{86} + 11 q^{87} + 10 q^{88} - 19 q^{89} + 14 q^{90} + 9 q^{91} + 8 q^{92} - 3 q^{93} + 7 q^{94} + 10 q^{95} + 3 q^{96} - 6 q^{97} + 8 q^{98} - 5 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 + 9 * q^5 + 3 * q^6 + 9 * q^7 + 9 * q^8 + 14 * q^9 + 9 * q^10 + 10 * q^11 + 3 * q^12 + 9 * q^13 + 9 * q^14 + 3 * q^15 + 9 * q^16 + q^17 + 14 * q^18 + 10 * q^19 + 9 * q^20 + 3 * q^21 + 10 * q^22 + 8 * q^23 + 3 * q^24 + 9 * q^25 + 9 * q^26 + 15 * q^27 + 9 * q^28 + 9 * q^29 + 3 * q^30 - 9 * q^31 + 9 * q^32 + 4 * q^33 + q^34 + 9 * q^35 + 14 * q^36 - 3 * q^37 + 10 * q^38 + 3 * q^39 + 9 * q^40 + 3 * q^42 + 7 * q^43 + 10 * q^44 + 14 * q^45 + 8 * q^46 + 7 * q^47 + 3 * q^48 + 8 * q^49 + 9 * q^50 - 3 * q^51 + 9 * q^52 + 8 * q^53 + 15 * q^54 + 10 * q^55 + 9 * q^56 - 7 * q^57 + 9 * q^58 + 2 * q^59 + 3 * q^60 - 2 * q^61 - 9 * q^62 + 10 * q^63 + 9 * q^64 + 9 * q^65 + 4 * q^66 + 18 * q^67 + q^68 - 16 * q^69 + 9 * q^70 + 14 * q^71 + 14 * q^72 + q^73 - 3 * q^74 + 3 * q^75 + 10 * q^76 - 5 * q^77 + 3 * q^78 + 6 * q^79 + 9 * q^80 + q^81 + 7 * q^83 + 3 * q^84 + q^85 + 7 * q^86 + 11 * q^87 + 10 * q^88 - 19 * q^89 + 14 * q^90 + 9 * q^91 + 8 * q^92 - 3 * q^93 + 7 * q^94 + 10 * q^95 + 3 * q^96 - 6 * q^97 + 8 * q^98 - 5 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.50823	−0.870776	−0.435388	−	0.900243i	$-0.643389\pi$
$3$	−1.50823	−0.870776	−0.435388	+	0.900243i	$0.643389\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.50823	−0.615732
$7$	−3.09594	−1.17016	−0.585079	−	0.810977i	$-0.698936\pi$
$7$	−3.09594	−1.17016	−0.585079	+	0.810977i	$0.698936\pi$
$8$	1.00000	0.353553
$9$	−0.725248	−0.241749
$10$	1.00000	0.316228
$11$	−0.743610	−0.224207	−0.112103	−	0.993697i	$-0.535759\pi$
$11$	−0.743610	−0.224207	−0.112103	+	0.993697i	$0.535759\pi$
$12$	−1.50823	−0.435388
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−3.09594	−0.827426
$15$	−1.50823	−0.389423
$16$	1.00000	0.250000
$17$	−2.93595	−0.712071	−0.356036	−	0.934472i	$-0.615872\pi$
$17$	−2.93595	−0.712071	−0.356036	+	0.934472i	$0.615872\pi$
$18$	−0.725248	−0.170943
$19$	2.92476	0.670987	0.335494	−	0.942043i	$-0.391097\pi$
$19$	2.92476	0.670987	0.335494	+	0.942043i	$0.391097\pi$
$20$	1.00000	0.223607
$21$	4.66939	1.01894
$22$	−0.743610	−0.158538
$23$	1.11511	0.232517	0.116258	−	0.993219i	$-0.462910\pi$
$23$	1.11511	0.232517	0.116258	+	0.993219i	$0.462910\pi$
$24$	−1.50823	−0.307866
$25$	1.00000	0.200000
$26$	1.00000	0.196116
$27$	5.61852	1.08129
$28$	−3.09594	−0.585079
$29$	−3.98528	−0.740049	−0.370024	−	0.929022i	$-0.620651\pi$
$29$	−3.98528	−0.740049	−0.370024	+	0.929022i	$0.620651\pi$
$30$	−1.50823	−0.275364
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	1.00000	0.176777
$33$	1.12153	0.195234
$34$	−2.93595	−0.503511
$35$	−3.09594	−0.523310
$36$	−0.725248	−0.120875
$37$	6.05657	0.995695	0.497847	−	0.867265i	$-0.334124\pi$
$37$	6.05657	0.995695	0.497847	+	0.867265i	$0.334124\pi$
$38$	2.92476	0.474459
$39$	−1.50823	−0.241510
$40$	1.00000	0.158114
$41$	−0.863733	−0.134892	−0.0674462	−	0.997723i	$-0.521485\pi$
$41$	−0.863733	−0.134892	−0.0674462	+	0.997723i	$0.521485\pi$
$42$	4.66939	0.720503
$43$	−5.41300	−0.825475	−0.412737	−	0.910850i	$-0.635427\pi$
$43$	−5.41300	−0.825475	−0.412737	+	0.910850i	$0.635427\pi$
$44$	−0.743610	−0.112103
$45$	−0.725248	−0.108114
$46$	1.11511	0.164414
$47$	4.92033	0.717704	0.358852	−	0.933394i	$-0.383168\pi$
$47$	4.92033	0.717704	0.358852	+	0.933394i	$0.383168\pi$
$48$	−1.50823	−0.217694
$49$	2.58487	0.369268
$50$	1.00000	0.141421
$51$	4.42808	0.620055
$52$	1.00000	0.138675
$53$	−1.91307	−0.262780	−0.131390	−	0.991331i	$-0.541944\pi$
$53$	−1.91307	−0.262780	−0.131390	+	0.991331i	$0.541944\pi$
$54$	5.61852	0.764584
$55$	−0.743610	−0.100268
$56$	−3.09594	−0.413713
$57$	−4.41121	−0.584279
$58$	−3.98528	−0.523293
$59$	4.13079	0.537783	0.268892	−	0.963170i	$-0.413343\pi$
$59$	4.13079	0.537783	0.268892	+	0.963170i	$0.413343\pi$
$60$	−1.50823	−0.194711
$61$	−7.58910	−0.971684	−0.485842	−	0.874047i	$-0.661487\pi$
$61$	−7.58910	−0.971684	−0.485842	+	0.874047i	$0.661487\pi$
$62$	−1.00000	−0.127000
$63$	2.24533	0.282885
$64$	1.00000	0.125000
$65$	1.00000	0.124035
$66$	1.12153	0.138051
$67$	13.4497	1.64314	0.821569	−	0.570109i	$-0.193099\pi$
$67$	13.4497	1.64314	0.821569	+	0.570109i	$0.193099\pi$
$68$	−2.93595	−0.356036
$69$	−1.68184	−0.202470
$70$	−3.09594	−0.370036
$71$	14.1556	1.67996	0.839979	−	0.542618i	$-0.182567\pi$
$71$	14.1556	1.67996	0.839979	+	0.542618i	$0.182567\pi$
$72$	−0.725248	−0.0854713
$73$	11.0354	1.29159	0.645797	−	0.763509i	$-0.276525\pi$
$73$	11.0354	1.29159	0.645797	+	0.763509i	$0.276525\pi$
$74$	6.05657	0.704062
$75$	−1.50823	−0.174155
$76$	2.92476	0.335494
$77$	2.30218	0.262357
$78$	−1.50823	−0.170773
$79$	−1.10592	−0.124426	−0.0622128	−	0.998063i	$-0.519816\pi$
$79$	−1.10592	−0.124426	−0.0622128	+	0.998063i	$0.519816\pi$
$80$	1.00000	0.111803
$81$	−6.29827	−0.699808
$82$	−0.863733	−0.0953833
$83$	18.0284	1.97887	0.989435	−	0.144979i	$-0.0463115\pi$
$83$	18.0284	1.97887	0.989435	+	0.144979i	$0.0463115\pi$
$84$	4.66939	0.509472
$85$	−2.93595	−0.318448
$86$	−5.41300	−0.583699
$87$	6.01072	0.644417
$88$	−0.743610	−0.0792691
$89$	0.791684	0.0839184	0.0419592	−	0.999119i	$-0.486640\pi$
$89$	0.791684	0.0839184	0.0419592	+	0.999119i	$0.486640\pi$
$90$	−0.725248	−0.0764478
$91$	−3.09594	−0.324543
$92$	1.11511	0.116258
$93$	1.50823	0.156396
$94$	4.92033	0.507493
$95$	2.92476	0.300075
$96$	−1.50823	−0.153933
$97$	−6.19662	−0.629171	−0.314586	−	0.949229i	$-0.601866\pi$
$97$	−6.19662	−0.629171	−0.314586	+	0.949229i	$0.601866\pi$
$98$	2.58487	0.261112
$99$	0.539301	0.0542018
$100$	1.00000	0.100000
$101$	11.6154	1.15578	0.577888	−	0.816116i	$-0.303877\pi$
$101$	11.6154	1.15578	0.577888	+	0.816116i	$0.303877\pi$
$102$	4.42808	0.438445
$103$	1.63566	0.161166	0.0805831	−	0.996748i	$-0.474322\pi$
$103$	1.63566	0.161166	0.0805831	+	0.996748i	$0.474322\pi$
$104$	1.00000	0.0980581
$105$	4.66939	0.455686
$106$	−1.91307	−0.185814
$107$	1.60644	0.155301	0.0776504	−	0.996981i	$-0.475258\pi$
$107$	1.60644	0.155301	0.0776504	+	0.996981i	$0.475258\pi$
$108$	5.61852	0.540643
$109$	1.01397	0.0971211	0.0485606	−	0.998820i	$-0.484537\pi$
$109$	1.01397	0.0971211	0.0485606	+	0.998820i	$0.484537\pi$
$110$	−0.743610	−0.0709004
$111$	−9.13470	−0.867027
$112$	−3.09594	−0.292539
$113$	−0.905114	−0.0851460	−0.0425730	−	0.999093i	$-0.513555\pi$
$113$	−0.905114	−0.0851460	−0.0425730	+	0.999093i	$0.513555\pi$
$114$	−4.41121	−0.413148
$115$	1.11511	0.103985
$116$	−3.98528	−0.370024
$117$	−0.725248	−0.0670492
$118$	4.13079	0.380270
$119$	9.08953	0.833235
$120$	−1.50823	−0.137682
$121$	−10.4470	−0.949731
$122$	−7.58910	−0.687085
$123$	1.30271	0.117461
$124$	−1.00000	−0.0898027
$125$	1.00000	0.0894427
$126$	2.24533	0.200030
$127$	21.7624	1.93110	0.965549	−	0.260223i	$-0.0837961\pi$
$127$	21.7624	1.93110	0.965549	+	0.260223i	$0.0837961\pi$
$128$	1.00000	0.0883883
$129$	8.16404	0.718804
$130$	1.00000	0.0877058
$131$	−8.41365	−0.735104	−0.367552	−	0.930003i	$-0.619804\pi$
$131$	−8.41365	−0.735104	−0.367552	+	0.930003i	$0.619804\pi$
$132$	1.12153	0.0976170
$133$	−9.05491	−0.785160
$134$	13.4497	1.16187
$135$	5.61852	0.483566
$136$	−2.93595	−0.251755
$137$	10.1773	0.869510	0.434755	−	0.900549i	$-0.356835\pi$
$137$	10.1773	0.869510	0.434755	+	0.900549i	$0.356835\pi$
$138$	−1.68184	−0.143168
$139$	2.69388	0.228492	0.114246	−	0.993452i	$-0.463555\pi$
$139$	2.69388	0.228492	0.114246	+	0.993452i	$0.463555\pi$
$140$	−3.09594	−0.261655
$141$	−7.42098	−0.624959
$142$	14.1556	1.18791
$143$	−0.743610	−0.0621838
$144$	−0.725248	−0.0604373
$145$	−3.98528	−0.330960
$146$	11.0354	0.913295
$147$	−3.89858	−0.321549
$148$	6.05657	0.497847
$149$	−5.63486	−0.461626	−0.230813	−	0.972998i	$-0.574139\pi$
$149$	−5.63486	−0.461626	−0.230813	+	0.972998i	$0.574139\pi$
$150$	−1.50823	−0.123146
$151$	11.0158	0.896457	0.448228	−	0.893919i	$-0.352055\pi$
$151$	11.0158	0.896457	0.448228	+	0.893919i	$0.352055\pi$
$152$	2.92476	0.237230
$153$	2.12929	0.172143
$154$	2.30218	0.185515
$155$	−1.00000	−0.0803219
$156$	−1.50823	−0.120755
$157$	−2.45129	−0.195634	−0.0978172	−	0.995204i	$-0.531186\pi$
$157$	−2.45129	−0.195634	−0.0978172	+	0.995204i	$0.531186\pi$
$158$	−1.10592	−0.0879822
$159$	2.88535	0.228823
$160$	1.00000	0.0790569
$161$	−3.45232	−0.272081
$162$	−6.29827	−0.494839
$163$	−11.2841	−0.883840	−0.441920	−	0.897054i	$-0.645703\pi$
$163$	−11.2841	−0.883840	−0.441920	+	0.897054i	$0.645703\pi$
$164$	−0.863733	−0.0674462
$165$	1.12153	0.0873113
$166$	18.0284	1.39927
$167$	−3.14923	−0.243695	−0.121847	−	0.992549i	$-0.538882\pi$
$167$	−3.14923	−0.243695	−0.121847	+	0.992549i	$0.538882\pi$
$168$	4.66939	0.360251
$169$	1.00000	0.0769231
$170$	−2.93595	−0.225177
$171$	−2.12118	−0.162211
$172$	−5.41300	−0.412737
$173$	10.0247	0.762168	0.381084	−	0.924541i	$-0.375551\pi$
$173$	10.0247	0.762168	0.381084	+	0.924541i	$0.375551\pi$
$174$	6.01072	0.455671
$175$	−3.09594	−0.234031
$176$	−0.743610	−0.0560517
$177$	−6.23018	−0.468289
$178$	0.791684	0.0593392
$179$	−21.3859	−1.59846	−0.799230	−	0.601025i	$-0.794759\pi$
$179$	−21.3859	−1.59846	−0.799230	+	0.601025i	$0.794759\pi$
$180$	−0.725248	−0.0540568
$181$	−24.5580	−1.82538	−0.912692	−	0.408648i	$-0.866000\pi$
$181$	−24.5580	−1.82538	−0.912692	+	0.408648i	$0.866000\pi$
$182$	−3.09594	−0.229487
$183$	11.4461	0.846119
$184$	1.11511	0.0822071
$185$	6.05657	0.445288
$186$	1.50823	0.110589
$187$	2.18320	0.159651
$188$	4.92033	0.358852
$189$	−17.3946	−1.26527
$190$	2.92476	0.212185
$191$	19.0276	1.37679	0.688394	−	0.725337i	$-0.258316\pi$
$191$	19.0276	1.37679	0.688394	+	0.725337i	$0.258316\pi$
$192$	−1.50823	−0.108847
$193$	13.1680	0.947851	0.473926	−	0.880565i	$-0.342837\pi$
$193$	13.1680	0.947851	0.473926	+	0.880565i	$0.342837\pi$
$194$	−6.19662	−0.444891
$195$	−1.50823	−0.108006
$196$	2.58487	0.184634
$197$	−3.34129	−0.238057	−0.119029	−	0.992891i	$-0.537978\pi$
$197$	−3.34129	−0.238057	−0.119029	+	0.992891i	$0.537978\pi$
$198$	0.539301	0.0383265
$199$	−10.5967	−0.751182	−0.375591	−	0.926785i	$-0.622560\pi$
$199$	−10.5967	−0.751182	−0.375591	+	0.926785i	$0.622560\pi$
$200$	1.00000	0.0707107
$201$	−20.2852	−1.43080
$202$	11.6154	0.817257
$203$	12.3382	0.865973
$204$	4.42808	0.310027
$205$	−0.863733	−0.0603257
$206$	1.63566	0.113962
$207$	−0.808732	−0.0562108
$208$	1.00000	0.0693375
$209$	−2.17488	−0.150440
$210$	4.66939	0.322219
$211$	22.2507	1.53180	0.765902	−	0.642957i	$-0.222293\pi$
$211$	22.2507	1.53180	0.765902	+	0.642957i	$0.222293\pi$
$212$	−1.91307	−0.131390
$213$	−21.3499	−1.46287
$214$	1.60644	0.109814
$215$	−5.41300	−0.369164
$216$	5.61852	0.382292
$217$	3.09594	0.210166
$218$	1.01397	0.0686750
$219$	−16.6439	−1.12469
$220$	−0.743610	−0.0501342
$221$	−2.93595	−0.197493
$222$	−9.13470	−0.613081
$223$	29.7762	1.99396	0.996981	−	0.0776436i	$-0.0247396\pi$
$223$	29.7762	1.99396	0.996981	+	0.0776436i	$0.0247396\pi$
$224$	−3.09594	−0.206857
$225$	−0.725248	−0.0483498
$226$	−0.905114	−0.0602073
$227$	−18.2400	−1.21063	−0.605314	−	0.795987i	$-0.706953\pi$
$227$	−18.2400	−1.21063	−0.605314	+	0.795987i	$0.706953\pi$
$228$	−4.41121	−0.292140
$229$	12.2166	0.807298	0.403649	−	0.914914i	$-0.367742\pi$
$229$	12.2166	0.807298	0.403649	+	0.914914i	$0.367742\pi$
$230$	1.11511	0.0735283
$231$	−3.47221	−0.228454
$232$	−3.98528	−0.261647
$233$	21.7000	1.42161	0.710807	−	0.703387i	$-0.248330\pi$
$233$	21.7000	1.42161	0.710807	+	0.703387i	$0.248330\pi$
$234$	−0.725248	−0.0474109
$235$	4.92033	0.320967
$236$	4.13079	0.268892
$237$	1.66798	0.108347
$238$	9.08953	0.589186
$239$	−6.26304	−0.405122	−0.202561	−	0.979270i	$-0.564926\pi$
$239$	−6.26304	−0.405122	−0.202561	+	0.979270i	$0.564926\pi$
$240$	−1.50823	−0.0973557
$241$	18.5884	1.19739	0.598694	−	0.800978i	$-0.295687\pi$
$241$	18.5884	1.19739	0.598694	+	0.800978i	$0.295687\pi$
$242$	−10.4470	−0.671561
$243$	−7.35634	−0.471909
$244$	−7.58910	−0.485842
$245$	2.58487	0.165142
$246$	1.30271	0.0830575
$247$	2.92476	0.186098
$248$	−1.00000	−0.0635001
$249$	−27.1909	−1.72315
$250$	1.00000	0.0632456
$251$	20.2222	1.27641	0.638207	−	0.769865i	$-0.279676\pi$
$251$	20.2222	1.27641	0.638207	+	0.769865i	$0.279676\pi$
$252$	2.24533	0.141442
$253$	−0.829208	−0.0521319
$254$	21.7624	1.36549
$255$	4.42808	0.277297
$256$	1.00000	0.0625000
$257$	16.4786	1.02791	0.513955	−	0.857817i	$-0.328180\pi$
$257$	16.4786	1.02791	0.513955	+	0.857817i	$0.328180\pi$
$258$	8.16404	0.508271
$259$	−18.7508	−1.16512
$260$	1.00000	0.0620174
$261$	2.89032	0.178906
$262$	−8.41365	−0.519797
$263$	−17.4661	−1.07701	−0.538503	−	0.842623i	$-0.681010\pi$
$263$	−17.4661	−1.07701	−0.538503	+	0.842623i	$0.681010\pi$
$264$	1.12153	0.0690256
$265$	−1.91307	−0.117519
$266$	−9.05491	−0.555192
$267$	−1.19404	−0.0730741
$268$	13.4497	0.821569
$269$	26.7076	1.62839	0.814195	−	0.580592i	$-0.197179\pi$
$269$	26.7076	1.62839	0.814195	+	0.580592i	$0.197179\pi$
$270$	5.61852	0.341932
$271$	6.77005	0.411251	0.205626	−	0.978631i	$-0.434077\pi$
$271$	6.77005	0.411251	0.205626	+	0.978631i	$0.434077\pi$
$272$	−2.93595	−0.178018
$273$	4.66939	0.282604
$274$	10.1773	0.614836
$275$	−0.743610	−0.0448414
$276$	−1.68184	−0.101235
$277$	−6.41052	−0.385171	−0.192585	−	0.981280i	$-0.561687\pi$
$277$	−6.41052	−0.385171	−0.192585	+	0.981280i	$0.561687\pi$
$278$	2.69388	0.161568
$279$	0.725248	0.0434194
$280$	−3.09594	−0.185018
$281$	21.4973	1.28242	0.641211	−	0.767365i	$-0.278432\pi$
$281$	21.4973	1.28242	0.641211	+	0.767365i	$0.278432\pi$
$282$	−7.42098	−0.441913
$283$	18.9486	1.12638	0.563190	−	0.826328i	$-0.309574\pi$
$283$	18.9486	1.12638	0.563190	+	0.826328i	$0.309574\pi$
$284$	14.1556	0.839979
$285$	−4.41121	−0.261298
$286$	−0.743610	−0.0439706
$287$	2.67407	0.157845
$288$	−0.725248	−0.0427356
$289$	−8.38022	−0.492954
$290$	−3.98528	−0.234024
$291$	9.34592	0.547867
$292$	11.0354	0.645797
$293$	−18.8964	−1.10394	−0.551969	−	0.833864i	$-0.686123\pi$
$293$	−18.8964	−1.10394	−0.551969	+	0.833864i	$0.686123\pi$
$294$	−3.89858	−0.227370
$295$	4.13079	0.240504
$296$	6.05657	0.352031
$297$	−4.17799	−0.242432
$298$	−5.63486	−0.326419
$299$	1.11511	0.0644886
$300$	−1.50823	−0.0870776
$301$	16.7584	0.965935
$302$	11.0158	0.633891
$303$	−17.5187	−1.00642
$304$	2.92476	0.167747
$305$	−7.58910	−0.434550
$306$	2.12929	0.121723
$307$	25.8981	1.47808	0.739040	−	0.673662i	$-0.235279\pi$
$307$	25.8981	1.47808	0.739040	+	0.673662i	$0.235279\pi$
$308$	2.30218	0.131179
$309$	−2.46695	−0.140340
$310$	−1.00000	−0.0567962
$311$	−3.69195	−0.209351	−0.104676	−	0.994506i	$-0.533380\pi$
$311$	−3.69195	−0.209351	−0.104676	+	0.994506i	$0.533380\pi$
$312$	−1.50823	−0.0853866
$313$	−16.6538	−0.941330	−0.470665	−	0.882312i	$-0.655986\pi$
$313$	−16.6538	−0.941330	−0.470665	+	0.882312i	$0.655986\pi$
$314$	−2.45129	−0.138334
$315$	2.24533	0.126510
$316$	−1.10592	−0.0622128
$317$	1.93128	0.108471	0.0542356	−	0.998528i	$-0.482728\pi$
$317$	1.93128	0.108471	0.0542356	+	0.998528i	$0.482728\pi$
$318$	2.88535	0.161802
$319$	2.96350	0.165924
$320$	1.00000	0.0559017
$321$	−2.42289	−0.135232
$322$	−3.45232	−0.192391
$323$	−8.58695	−0.477791
$324$	−6.29827	−0.349904
$325$	1.00000	0.0554700
$326$	−11.2841	−0.624969
$327$	−1.52930	−0.0845708
$328$	−0.863733	−0.0476917
$329$	−15.2331	−0.839827
$330$	1.12153	0.0617384
$331$	−5.81205	−0.319459	−0.159730	−	0.987161i	$-0.551062\pi$
$331$	−5.81205	−0.319459	−0.159730	+	0.987161i	$0.551062\pi$
$332$	18.0284	0.989435
$333$	−4.39252	−0.240708
$334$	−3.14923	−0.172318
$335$	13.4497	0.734833
$336$	4.66939	0.254736
$337$	−32.0699	−1.74696	−0.873479	−	0.486861i	$-0.838142\pi$
$337$	−32.0699	−1.74696	−0.873479	+	0.486861i	$0.838142\pi$
$338$	1.00000	0.0543928
$339$	1.36512	0.0741431
$340$	−2.93595	−0.159224
$341$	0.743610	0.0402687
$342$	−2.12118	−0.114700
$343$	13.6690	0.738056
$344$	−5.41300	−0.291849
$345$	−1.68184	−0.0905474
$346$	10.0247	0.538934
$347$	−12.7223	−0.682967	−0.341483	−	0.939888i	$-0.610929\pi$
$347$	−12.7223	−0.682967	−0.341483	+	0.939888i	$0.610929\pi$
$348$	6.01072	0.322208
$349$	−20.7984	−1.11331	−0.556656	−	0.830743i	$-0.687916\pi$
$349$	−20.7984	−1.11331	−0.556656	+	0.830743i	$0.687916\pi$
$350$	−3.09594	−0.165485
$351$	5.61852	0.299895
$352$	−0.743610	−0.0396345
$353$	−19.5797	−1.04212	−0.521060	−	0.853520i	$-0.674463\pi$
$353$	−19.5797	−1.04212	−0.521060	+	0.853520i	$0.674463\pi$
$354$	−6.23018	−0.331130
$355$	14.1556	0.751300
$356$	0.791684	0.0419592
$357$	−13.7091	−0.725561
$358$	−21.3859	−1.13028
$359$	−18.5761	−0.980411	−0.490206	−	0.871607i	$-0.663078\pi$
$359$	−18.5761	−0.980411	−0.490206	+	0.871607i	$0.663078\pi$
$360$	−0.725248	−0.0382239
$361$	−10.4458	−0.549776
$362$	−24.5580	−1.29074
$363$	15.7565	0.827003
$364$	−3.09594	−0.162272
$365$	11.0354	0.577619
$366$	11.4461	0.598297
$367$	11.0847	0.578619	0.289309	−	0.957236i	$-0.406574\pi$
$367$	11.0847	0.578619	0.289309	+	0.957236i	$0.406574\pi$
$368$	1.11511	0.0581292
$369$	0.626420	0.0326101
$370$	6.05657	0.314866
$371$	5.92276	0.307494
$372$	1.50823	0.0781980
$373$	8.73064	0.452056	0.226028	−	0.974121i	$-0.427426\pi$
$373$	8.73064	0.452056	0.226028	+	0.974121i	$0.427426\pi$
$374$	2.18320	0.112890
$375$	−1.50823	−0.0778846
$376$	4.92033	0.253747
$377$	−3.98528	−0.205253
$378$	−17.3946	−0.894684
$379$	−19.4966	−1.00147	−0.500737	−	0.865600i	$-0.666938\pi$
$379$	−19.4966	−1.00147	−0.500737	+	0.865600i	$0.666938\pi$
$380$	2.92476	0.150037
$381$	−32.8226	−1.68155
$382$	19.0276	0.973535
$383$	4.66664	0.238454	0.119227	−	0.992867i	$-0.461958\pi$
$383$	4.66664	0.238454	0.119227	+	0.992867i	$0.461958\pi$
$384$	−1.50823	−0.0769664
$385$	2.30218	0.117330
$386$	13.1680	0.670232
$387$	3.92577	0.199558
$388$	−6.19662	−0.314586
$389$	−28.8676	−1.46364	−0.731822	−	0.681496i	$-0.761330\pi$
$389$	−28.8676	−1.46364	−0.731822	+	0.681496i	$0.761330\pi$
$390$	−1.50823	−0.0763721
$391$	−3.27391	−0.165569
$392$	2.58487	0.130556
$393$	12.6897	0.640111
$394$	−3.34129	−0.168332
$395$	−1.10592	−0.0556448
$396$	0.539301	0.0271009
$397$	26.7821	1.34415	0.672077	−	0.740481i	$-0.265402\pi$
$397$	26.7821	1.34415	0.672077	+	0.740481i	$0.265402\pi$
$398$	−10.5967	−0.531166
$399$	13.6569	0.683699
$400$	1.00000	0.0500000
$401$	22.0565	1.10145	0.550725	−	0.834687i	$-0.314351\pi$
$401$	22.0565	1.10145	0.550725	+	0.834687i	$0.314351\pi$
$402$	−20.2852	−1.01173
$403$	−1.00000	−0.0498135
$404$	11.6154	0.577888
$405$	−6.29827	−0.312964
$406$	12.3382	0.612336
$407$	−4.50373	−0.223242
$408$	4.42808	0.219222
$409$	−19.9854	−0.988215	−0.494108	−	0.869401i	$-0.664505\pi$
$409$	−19.9854	−0.988215	−0.494108	+	0.869401i	$0.664505\pi$
$410$	−0.863733	−0.0426567
$411$	−15.3498	−0.757148
$412$	1.63566	0.0805831
$413$	−12.7887	−0.629291
$414$	−0.808732	−0.0397470
$415$	18.0284	0.884977
$416$	1.00000	0.0490290
$417$	−4.06299	−0.198965
$418$	−2.17488	−0.106377
$419$	−6.75951	−0.330224	−0.165112	−	0.986275i	$-0.552799\pi$
$419$	−6.75951	−0.330224	−0.165112	+	0.986275i	$0.552799\pi$
$420$	4.66939	0.227843
$421$	7.78473	0.379404	0.189702	−	0.981842i	$-0.439248\pi$
$421$	7.78473	0.379404	0.189702	+	0.981842i	$0.439248\pi$
$422$	22.2507	1.08315
$423$	−3.56846	−0.173504
$424$	−1.91307	−0.0929069
$425$	−2.93595	−0.142414
$426$	−21.3499	−1.03440
$427$	23.4954	1.13702
$428$	1.60644	0.0776504
$429$	1.12153	0.0541481
$430$	−5.41300	−0.261038
$431$	−16.3830	−0.789142	−0.394571	−	0.918865i	$-0.629107\pi$
$431$	−16.3830	−0.789142	−0.394571	+	0.918865i	$0.629107\pi$
$432$	5.61852	0.270321
$433$	−7.17007	−0.344571	−0.172286	−	0.985047i	$-0.555115\pi$
$433$	−7.17007	−0.344571	−0.172286	+	0.985047i	$0.555115\pi$
$434$	3.09594	0.148610
$435$	6.01072	0.288192
$436$	1.01397	0.0485606
$437$	3.26144	0.156016
$438$	−16.6439	−0.795276
$439$	13.8855	0.662720	0.331360	−	0.943504i	$-0.392493\pi$
$439$	13.8855	0.662720	0.331360	+	0.943504i	$0.392493\pi$
$440$	−0.743610	−0.0354502
$441$	−1.87467	−0.0892702
$442$	−2.93595	−0.139649
$443$	38.4315	1.82593	0.912967	−	0.408034i	$-0.133785\pi$
$443$	38.4315	1.82593	0.912967	+	0.408034i	$0.133785\pi$
$444$	−9.13470	−0.433513
$445$	0.791684	0.0375294
$446$	29.7762	1.40994
$447$	8.49866	0.401973
$448$	−3.09594	−0.146270
$449$	−11.5687	−0.545961	−0.272981	−	0.962020i	$-0.588009\pi$
$449$	−11.5687	−0.545961	−0.272981	+	0.962020i	$0.588009\pi$
$450$	−0.725248	−0.0341885
$451$	0.642280	0.0302438
$452$	−0.905114	−0.0425730
$453$	−16.6144	−0.780613
$454$	−18.2400	−0.856044
$455$	−3.09594	−0.145140
$456$	−4.41121	−0.206574
$457$	−20.9968	−0.982187	−0.491093	−	0.871107i	$-0.663403\pi$
$457$	−20.9968	−0.982187	−0.491093	+	0.871107i	$0.663403\pi$
$458$	12.2166	0.570846
$459$	−16.4957	−0.769952
$460$	1.11511	0.0519924
$461$	−25.5563	−1.19028	−0.595139	−	0.803623i	$-0.702903\pi$
$461$	−25.5563	−1.19028	−0.595139	+	0.803623i	$0.702903\pi$
$462$	−3.47221	−0.161542
$463$	40.1684	1.86678	0.933391	−	0.358862i	$-0.116835\pi$
$463$	40.1684	1.86678	0.933391	+	0.358862i	$0.116835\pi$
$464$	−3.98528	−0.185012
$465$	1.50823	0.0699424
$466$	21.7000	1.00523
$467$	−12.3666	−0.572257	−0.286128	−	0.958191i	$-0.592368\pi$
$467$	−12.3666	−0.572257	−0.286128	+	0.958191i	$0.592368\pi$
$468$	−0.725248	−0.0335246
$469$	−41.6394	−1.92273
$470$	4.92033	0.226958
$471$	3.69711	0.170354
$472$	4.13079	0.190135
$473$	4.02516	0.185077
$474$	1.66798	0.0766128
$475$	2.92476	0.134197
$476$	9.08953	0.416618
$477$	1.38745	0.0635270
$478$	−6.26304	−0.286465
$479$	−23.6854	−1.08221	−0.541107	−	0.840954i	$-0.681995\pi$
$479$	−23.6854	−1.08221	−0.541107	+	0.840954i	$0.681995\pi$
$480$	−1.50823	−0.0688409
$481$	6.05657	0.276156
$482$	18.5884	0.846681
$483$	5.20689	0.236922
$484$	−10.4470	−0.474866
$485$	−6.19662	−0.281374
$486$	−7.35634	−0.333690
$487$	−36.1931	−1.64007	−0.820033	−	0.572316i	$-0.806045\pi$
$487$	−36.1931	−1.64007	−0.820033	+	0.572316i	$0.806045\pi$
$488$	−7.58910	−0.343542
$489$	17.0190	0.769627
$490$	2.58487	0.116773
$491$	33.3578	1.50542	0.752709	−	0.658354i	$-0.228747\pi$
$491$	33.3578	1.50542	0.752709	+	0.658354i	$0.228747\pi$
$492$	1.30271	0.0587305
$493$	11.7006	0.526967
$494$	2.92476	0.131591
$495$	0.539301	0.0242398
$496$	−1.00000	−0.0449013
$497$	−43.8249	−1.96582
$498$	−27.1909	−1.21845
$499$	−11.4656	−0.513270	−0.256635	−	0.966508i	$-0.582614\pi$
$499$	−11.4656	−0.513270	−0.256635	+	0.966508i	$0.582614\pi$
$500$	1.00000	0.0447214
$501$	4.74975	0.212203
$502$	20.2222	0.902561
$503$	−16.6728	−0.743405	−0.371703	−	0.928352i	$-0.621226\pi$
$503$	−16.6728	−0.743405	−0.371703	+	0.928352i	$0.621226\pi$
$504$	2.24533	0.100015
$505$	11.6154	0.516879
$506$	−0.829208	−0.0368628
$507$	−1.50823	−0.0669828
$508$	21.7624	0.965549
$509$	12.3017	0.545265	0.272632	−	0.962118i	$-0.412106\pi$
$509$	12.3017	0.545265	0.272632	+	0.962118i	$0.412106\pi$
$510$	4.42808	0.196079
$511$	−34.1650	−1.51137
$512$	1.00000	0.0441942
$513$	16.4329	0.725528
$514$	16.4786	0.726842
$515$	1.63566	0.0720757
$516$	8.16404	0.359402
$517$	−3.65881	−0.160914
$518$	−18.7508	−0.823864
$519$	−15.1196	−0.663677
$520$	1.00000	0.0438529
$521$	−0.277235	−0.0121459	−0.00607294	−	0.999982i	$-0.501933\pi$
$521$	−0.277235	−0.0121459	−0.00607294	+	0.999982i	$0.501933\pi$
$522$	2.89032	0.126506
$523$	−15.7567	−0.688990	−0.344495	−	0.938788i	$-0.611950\pi$
$523$	−15.7567	−0.688990	−0.344495	+	0.938788i	$0.611950\pi$
$524$	−8.41365	−0.367552
$525$	4.66939	0.203789
$526$	−17.4661	−0.761559
$527$	2.93595	0.127892
$528$	1.12153	0.0488085
$529$	−21.7565	−0.945936
$530$	−1.91307	−0.0830985
$531$	−2.99585	−0.130009
$532$	−9.05491	−0.392580
$533$	−0.863733	−0.0374124
$534$	−1.19404	−0.0516712
$535$	1.60644	0.0694527
$536$	13.4497	0.580937
$537$	32.2549	1.39190
$538$	26.7076	1.15144
$539$	−1.92214	−0.0827924
$540$	5.61852	0.241783
$541$	−10.7849	−0.463680	−0.231840	−	0.972754i	$-0.574475\pi$
$541$	−10.7849	−0.463680	−0.231840	+	0.972754i	$0.574475\pi$
$542$	6.77005	0.290799
$543$	37.0391	1.58950
$544$	−2.93595	−0.125878
$545$	1.01397	0.0434339
$546$	4.66939	0.199832
$547$	38.2762	1.63657	0.818285	−	0.574813i	$-0.194925\pi$
$547$	38.2762	1.63657	0.818285	+	0.574813i	$0.194925\pi$
$548$	10.1773	0.434755
$549$	5.50398	0.234904
$550$	−0.743610	−0.0317076
$551$	−11.6560	−0.496563
$552$	−1.68184	−0.0715840
$553$	3.42386	0.145598
$554$	−6.41052	−0.272357
$555$	−9.13470	−0.387746
$556$	2.69388	0.114246
$557$	2.66266	0.112821	0.0564103	−	0.998408i	$-0.482034\pi$
$557$	2.66266	0.112821	0.0564103	+	0.998408i	$0.482034\pi$
$558$	0.725248	0.0307022
$559$	−5.41300	−0.228946
$560$	−3.09594	−0.130828
$561$	−3.29276	−0.139020
$562$	21.4973	0.906809
$563$	7.72864	0.325723	0.162862	−	0.986649i	$-0.447928\pi$
$563$	7.72864	0.325723	0.162862	+	0.986649i	$0.447928\pi$
$564$	−7.42098	−0.312480
$565$	−0.905114	−0.0380784
$566$	18.9486	0.796471
$567$	19.4991	0.818885
$568$	14.1556	0.593955
$569$	30.0920	1.26152	0.630762	−	0.775977i	$-0.282743\pi$
$569$	30.0920	1.26152	0.630762	+	0.775977i	$0.282743\pi$
$570$	−4.41121	−0.184765
$571$	44.8718	1.87783	0.938913	−	0.344155i	$-0.111834\pi$
$571$	44.8718	1.87783	0.938913	+	0.344155i	$0.111834\pi$
$572$	−0.743610	−0.0310919
$573$	−28.6979	−1.19887
$574$	2.67407	0.111613
$575$	1.11511	0.0465034
$576$	−0.725248	−0.0302187
$577$	15.9414	0.663650	0.331825	−	0.943341i	$-0.392336\pi$
$577$	15.9414	0.663650	0.331825	+	0.943341i	$0.392336\pi$
$578$	−8.38022	−0.348571
$579$	−19.8603	−0.825366
$580$	−3.98528	−0.165480
$581$	−55.8148	−2.31559
$582$	9.34592	0.387401
$583$	1.42258	0.0589172
$584$	11.0354	0.456648
$585$	−0.725248	−0.0299853
$586$	−18.8964	−0.780602
$587$	−16.8497	−0.695460	−0.347730	−	0.937595i	$-0.613047\pi$
$587$	−16.8497	−0.695460	−0.347730	+	0.937595i	$0.613047\pi$
$588$	−3.89858	−0.160775
$589$	−2.92476	−0.120513
$590$	4.13079	0.170062
$591$	5.03943	0.207294
$592$	6.05657	0.248924
$593$	−0.0828472	−0.00340213	−0.00170106	−	0.999999i	$-0.500541\pi$
$593$	−0.0828472	−0.00340213	−0.00170106	+	0.999999i	$0.500541\pi$
$594$	−4.17799	−0.171425
$595$	9.08953	0.372634
$596$	−5.63486	−0.230813
$597$	15.9823	0.654111
$598$	1.11511	0.0456003
$599$	−8.56001	−0.349753	−0.174876	−	0.984590i	$-0.555953\pi$
$599$	−8.56001	−0.349753	−0.174876	+	0.984590i	$0.555953\pi$
$600$	−1.50823	−0.0615732
$601$	−18.3676	−0.749232	−0.374616	−	0.927180i	$-0.622225\pi$
$601$	−18.3676	−0.749232	−0.374616	+	0.927180i	$0.622225\pi$
$602$	16.7584	0.683019
$603$	−9.75434	−0.397227
$604$	11.0158	0.448228
$605$	−10.4470	−0.424733
$606$	−17.5187	−0.711648
$607$	27.8643	1.13098	0.565488	−	0.824756i	$-0.308688\pi$
$607$	27.8643	1.13098	0.565488	+	0.824756i	$0.308688\pi$
$608$	2.92476	0.118615
$609$	−18.6088	−0.754069
$610$	−7.58910	−0.307274
$611$	4.92033	0.199055
$612$	2.12929	0.0860714
$613$	0.557421	0.0225140	0.0112570	−	0.999937i	$-0.496417\pi$
$613$	0.557421	0.0225140	0.0112570	+	0.999937i	$0.496417\pi$
$614$	25.8981	1.04516
$615$	1.30271	0.0525302
$616$	2.30218	0.0927573
$617$	2.23912	0.0901435	0.0450718	−	0.998984i	$-0.485648\pi$
$617$	2.23912	0.0901435	0.0450718	+	0.998984i	$0.485648\pi$
$618$	−2.46695	−0.0992352
$619$	−30.5294	−1.22708	−0.613540	−	0.789663i	$-0.710255\pi$
$619$	−30.5294	−1.22708	−0.613540	+	0.789663i	$0.710255\pi$
$620$	−1.00000	−0.0401610
$621$	6.26528	0.251417
$622$	−3.69195	−0.148034
$623$	−2.45101	−0.0981977
$624$	−1.50823	−0.0603774
$625$	1.00000	0.0400000
$626$	−16.6538	−0.665621
$627$	3.28022	0.130999
$628$	−2.45129	−0.0978172
$629$	−17.7818	−0.709006
$630$	2.24533	0.0894560
$631$	47.7709	1.90173	0.950865	−	0.309607i	$-0.100197\pi$
$631$	47.7709	1.90173	0.950865	+	0.309607i	$0.100197\pi$
$632$	−1.10592	−0.0439911
$633$	−33.5592	−1.33386
$634$	1.93128	0.0767008
$635$	21.7624	0.863613
$636$	2.88535	0.114411
$637$	2.58487	0.102416
$638$	2.96350	0.117326
$639$	−10.2663	−0.406129
$640$	1.00000	0.0395285
$641$	7.18859	0.283932	0.141966	−	0.989872i	$-0.454658\pi$
$641$	7.18859	0.283932	0.141966	+	0.989872i	$0.454658\pi$
$642$	−2.42289	−0.0956236
$643$	−22.1773	−0.874588	−0.437294	−	0.899319i	$-0.644063\pi$
$643$	−22.1773	−0.874588	−0.437294	+	0.899319i	$0.644063\pi$
$644$	−3.45232	−0.136041
$645$	8.16404	0.321459
$646$	−8.58695	−0.337849
$647$	−29.7454	−1.16941	−0.584706	−	0.811245i	$-0.698790\pi$
$647$	−29.7454	−1.16941	−0.584706	+	0.811245i	$0.698790\pi$
$648$	−6.29827	−0.247420
$649$	−3.07170	−0.120575
$650$	1.00000	0.0392232
$651$	−4.66939	−0.183008
$652$	−11.2841	−0.441920
$653$	10.7368	0.420162	0.210081	−	0.977684i	$-0.432627\pi$
$653$	10.7368	0.420162	0.210081	+	0.977684i	$0.432627\pi$
$654$	−1.52930	−0.0598006
$655$	−8.41365	−0.328749
$656$	−0.863733	−0.0337231
$657$	−8.00339	−0.312242
$658$	−15.2331	−0.593847
$659$	−4.42084	−0.172211	−0.0861057	−	0.996286i	$-0.527442\pi$
$659$	−4.42084	−0.172211	−0.0861057	+	0.996286i	$0.527442\pi$
$660$	1.12153	0.0436556
$661$	−27.8910	−1.08483	−0.542417	−	0.840109i	$-0.682491\pi$
$661$	−27.8910	−1.08483	−0.542417	+	0.840109i	$0.682491\pi$
$662$	−5.81205	−0.225892
$663$	4.42808	0.171972
$664$	18.0284	0.699636
$665$	−9.05491	−0.351134
$666$	−4.39252	−0.170207
$667$	−4.44404	−0.172074
$668$	−3.14923	−0.121847
$669$	−44.9093	−1.73629
$670$	13.4497	0.519606
$671$	5.64333	0.217858
$672$	4.66939	0.180126
$673$	31.2108	1.20309	0.601543	−	0.798840i	$-0.294553\pi$
$673$	31.2108	1.20309	0.601543	+	0.798840i	$0.294553\pi$
$674$	−32.0699	−1.23529
$675$	5.61852	0.216257
$676$	1.00000	0.0384615
$677$	17.9812	0.691075	0.345538	−	0.938405i	$-0.387697\pi$
$677$	17.9812	0.691075	0.345538	+	0.938405i	$0.387697\pi$
$678$	1.36512	0.0524271
$679$	19.1844	0.736230
$680$	−2.93595	−0.112588
$681$	27.5100	1.05419
$682$	0.743610	0.0284743
$683$	0.851126	0.0325674	0.0162837	−	0.999867i	$-0.494817\pi$
$683$	0.851126	0.0325674	0.0162837	+	0.999867i	$0.494817\pi$
$684$	−2.12118	−0.0811053
$685$	10.1773	0.388856
$686$	13.6690	0.521884
$687$	−18.4255	−0.702975
$688$	−5.41300	−0.206369
$689$	−1.91307	−0.0728822
$690$	−1.68184	−0.0640267
$691$	−34.1490	−1.29909	−0.649545	−	0.760324i	$-0.725040\pi$
$691$	−34.1490	−1.29909	−0.649545	+	0.760324i	$0.725040\pi$
$692$	10.0247	0.381084
$693$	−1.66965	−0.0634247
$694$	−12.7223	−0.482930
$695$	2.69388	0.102185
$696$	6.01072	0.227836
$697$	2.53587	0.0960530
$698$	−20.7984	−0.787231
$699$	−32.7286	−1.23791
$700$	−3.09594	−0.117016
$701$	20.8199	0.786357	0.393179	−	0.919462i	$-0.371375\pi$
$701$	20.8199	0.786357	0.393179	+	0.919462i	$0.371375\pi$
$702$	5.61852	0.212058
$703$	17.7141	0.668098
$704$	−0.743610	−0.0280259
$705$	−7.42098	−0.279490
$706$	−19.5797	−0.736891
$707$	−35.9606	−1.35244
$708$	−6.23018	−0.234144
$709$	9.41504	0.353589	0.176795	−	0.984248i	$-0.443427\pi$
$709$	9.41504	0.353589	0.176795	+	0.984248i	$0.443427\pi$
$710$	14.1556	0.531250
$711$	0.802065	0.0300798
$712$	0.791684	0.0296696
$713$	−1.11511	−0.0417613
$714$	−13.7091	−0.513049
$715$	−0.743610	−0.0278094
$716$	−21.3859	−0.799230
$717$	9.44609	0.352771
$718$	−18.5761	−0.693256
$719$	−25.5862	−0.954203	−0.477102	−	0.878848i	$-0.658313\pi$
$719$	−25.5862	−0.954203	−0.477102	+	0.878848i	$0.658313\pi$
$720$	−0.725248	−0.0270284
$721$	−5.06391	−0.188590
$722$	−10.4458	−0.388751
$723$	−28.0356	−1.04266
$724$	−24.5580	−0.912692
$725$	−3.98528	−0.148010
$726$	15.7565	0.584780
$727$	−40.7354	−1.51079	−0.755397	−	0.655268i	$-0.772556\pi$
$727$	−40.7354	−1.51079	−0.755397	+	0.655268i	$0.772556\pi$
$728$	−3.09594	−0.114743
$729$	29.9899	1.11074
$730$	11.0354	0.408438
$731$	15.8923	0.587797
$732$	11.4461	0.423060
$733$	0.818449	0.0302301	0.0151150	−	0.999886i	$-0.495189\pi$
$733$	0.818449	0.0302301	0.0151150	+	0.999886i	$0.495189\pi$
$734$	11.0847	0.409145
$735$	−3.89858	−0.143801
$736$	1.11511	0.0411036
$737$	−10.0013	−0.368403
$738$	0.626420	0.0230588
$739$	−49.0064	−1.80273	−0.901364	−	0.433062i	$-0.857433\pi$
$739$	−49.0064	−1.80273	−0.901364	+	0.433062i	$0.857433\pi$
$740$	6.05657	0.222644
$741$	−4.41121	−0.162050
$742$	5.92276	0.217431
$743$	15.7274	0.576982	0.288491	−	0.957483i	$-0.406846\pi$
$743$	15.7274	0.576982	0.288491	+	0.957483i	$0.406846\pi$
$744$	1.50823	0.0552943
$745$	−5.63486	−0.206445
$746$	8.73064	0.319652
$747$	−13.0750	−0.478390
$748$	2.18320	0.0798256
$749$	−4.97346	−0.181726
$750$	−1.50823	−0.0550727
$751$	21.7312	0.792981	0.396491	−	0.918039i	$-0.370228\pi$
$751$	21.7312	0.792981	0.396491	+	0.918039i	$0.370228\pi$
$752$	4.92033	0.179426
$753$	−30.4997	−1.11147
$754$	−3.98528	−0.145135
$755$	11.0158	0.400908
$756$	−17.3946	−0.632637
$757$	16.6295	0.604409	0.302205	−	0.953243i	$-0.402277\pi$
$757$	16.6295	0.604409	0.302205	+	0.953243i	$0.402277\pi$
$758$	−19.4966	−0.708149
$759$	1.25064	0.0453952
$760$	2.92476	0.106092
$761$	18.4247	0.667894	0.333947	−	0.942592i	$-0.391619\pi$
$761$	18.4247	0.667894	0.333947	+	0.942592i	$0.391619\pi$
$762$	−32.8226	−1.18904
$763$	−3.13921	−0.113647
$764$	19.0276	0.688394
$765$	2.12929	0.0769846
$766$	4.66664	0.168613
$767$	4.13079	0.149154
$768$	−1.50823	−0.0544235
$769$	7.09021	0.255680	0.127840	−	0.991795i	$-0.459196\pi$
$769$	7.09021	0.255680	0.127840	+	0.991795i	$0.459196\pi$
$770$	2.30218	0.0829646
$771$	−24.8536	−0.895079
$772$	13.1680	0.473926
$773$	−41.2806	−1.48476	−0.742379	−	0.669980i	$-0.766303\pi$
$773$	−41.2806	−1.48476	−0.742379	+	0.669980i	$0.766303\pi$
$774$	3.92577	0.141109
$775$	−1.00000	−0.0359211
$776$	−6.19662	−0.222446
$777$	28.2805	1.01456
$778$	−28.8676	−1.03495
$779$	−2.52621	−0.0905110
$780$	−1.50823	−0.0540032
$781$	−10.5262	−0.376658
$782$	−3.27391	−0.117075
$783$	−22.3914	−0.800204
$784$	2.58487	0.0923169
$785$	−2.45129	−0.0874904
$786$	12.6897	0.452627
$787$	−33.2829	−1.18641	−0.593203	−	0.805053i	$-0.702137\pi$
$787$	−33.2829	−1.18641	−0.593203	+	0.805053i	$0.702137\pi$
$788$	−3.34129	−0.119029
$789$	26.3429	0.937832
$790$	−1.10592	−0.0393468
$791$	2.80218	0.0996342
$792$	0.539301	0.0191632
$793$	−7.58910	−0.269497
$794$	26.7821	0.950460
$795$	2.88535	0.102333
$796$	−10.5967	−0.375591
$797$	2.97848	0.105503	0.0527516	−	0.998608i	$-0.483201\pi$
$797$	2.97848	0.105503	0.0527516	+	0.998608i	$0.483201\pi$
$798$	13.6569	0.483448
$799$	−14.4458	−0.511057
$800$	1.00000	0.0353553
$801$	−0.574167	−0.0202872
$802$	22.0565	0.778842
$803$	−8.20602	−0.289584
$804$	−20.2852	−0.715402
$805$	−3.45232	−0.121678
$806$	−1.00000	−0.0352235
$807$	−40.2811	−1.41796
$808$	11.6154	0.408628
$809$	49.9488	1.75611	0.878053	−	0.478564i	$-0.158842\pi$
$809$	49.9488	1.75611	0.878053	+	0.478564i	$0.158842\pi$
$810$	−6.29827	−0.221299
$811$	34.5091	1.21178	0.605889	−	0.795549i	$-0.292818\pi$
$811$	34.5091	1.21178	0.605889	+	0.795549i	$0.292818\pi$
$812$	12.3382	0.432987
$813$	−10.2108	−0.358108
$814$	−4.50373	−0.157856
$815$	−11.2841	−0.395265
$816$	4.42808	0.155014
$817$	−15.8318	−0.553883
$818$	−19.9854	−0.698774
$819$	2.24533	0.0784581
$820$	−0.863733	−0.0301628
$821$	19.7980	0.690954	0.345477	−	0.938427i	$-0.387717\pi$
$821$	19.7980	0.690954	0.345477	+	0.938427i	$0.387717\pi$
$822$	−15.3498	−0.535384
$823$	−26.2004	−0.913288	−0.456644	−	0.889650i	$-0.650949\pi$
$823$	−26.2004	−0.913288	−0.456644	+	0.889650i	$0.650949\pi$
$824$	1.63566	0.0569809
$825$	1.12153	0.0390468
$826$	−12.7887	−0.444976
$827$	17.4376	0.606365	0.303183	−	0.952932i	$-0.401951\pi$
$827$	17.4376	0.606365	0.303183	+	0.952932i	$0.401951\pi$
$828$	−0.808732	−0.0281054
$829$	−19.3046	−0.670477	−0.335239	−	0.942133i	$-0.608817\pi$
$829$	−19.3046	−0.670477	−0.335239	+	0.942133i	$0.608817\pi$
$830$	18.0284	0.625773
$831$	9.66853	0.335397
$832$	1.00000	0.0346688
$833$	−7.58905	−0.262945
$834$	−4.06299	−0.140690
$835$	−3.14923	−0.108984
$836$	−2.17488	−0.0752199
$837$	−5.61852	−0.194205
$838$	−6.75951	−0.233504
$839$	8.36683	0.288855	0.144427	−	0.989515i	$-0.453866\pi$
$839$	8.36683	0.288855	0.144427	+	0.989515i	$0.453866\pi$
$840$	4.66939	0.161109
$841$	−13.1175	−0.452328
$842$	7.78473	0.268279
$843$	−32.4229	−1.11670
$844$	22.2507	0.765902
$845$	1.00000	0.0344010
$846$	−3.56846	−0.122686
$847$	32.3435	1.11133
$848$	−1.91307	−0.0656951
$849$	−28.5789	−0.980824
$850$	−2.93595	−0.100702
$851$	6.75376	0.231516
$852$	−21.3499	−0.731434
$853$	13.0653	0.447348	0.223674	−	0.974664i	$-0.428195\pi$
$853$	13.0653	0.447348	0.223674	+	0.974664i	$0.428195\pi$
$854$	23.4954	0.803997
$855$	−2.12118	−0.0725428
$856$	1.60644	0.0549071
$857$	−27.8227	−0.950407	−0.475203	−	0.879876i	$-0.657626\pi$
$857$	−27.8227	−0.950407	−0.475203	+	0.879876i	$0.657626\pi$
$858$	1.12153	0.0382885
$859$	−26.6108	−0.907947	−0.453974	−	0.891015i	$-0.649994\pi$
$859$	−26.6108	−0.907947	−0.453974	+	0.891015i	$0.649994\pi$
$860$	−5.41300	−0.184582
$861$	−4.03311	−0.137448
$862$	−16.3830	−0.558008
$863$	3.65213	0.124320	0.0621599	−	0.998066i	$-0.480201\pi$
$863$	3.65213	0.124320	0.0621599	+	0.998066i	$0.480201\pi$
$864$	5.61852	0.191146
$865$	10.0247	0.340852
$866$	−7.17007	−0.243649
$867$	12.6393	0.429253
$868$	3.09594	0.105083
$869$	0.822372	0.0278971
$870$	6.01072	0.203782
$871$	13.4497	0.455724
$872$	1.01397	0.0343375
$873$	4.49408	0.152102
$874$	3.26144	0.110320
$875$	−3.09594	−0.104662
$876$	−16.6439	−0.562345
$877$	−27.1223	−0.915854	−0.457927	−	0.888990i	$-0.651408\pi$
$877$	−27.1223	−0.915854	−0.457927	+	0.888990i	$0.651408\pi$
$878$	13.8855	0.468614
$879$	28.5001	0.961283
$880$	−0.743610	−0.0250671
$881$	−24.6399	−0.830140	−0.415070	−	0.909789i	$-0.636243\pi$
$881$	−24.6399	−0.830140	−0.415070	+	0.909789i	$0.636243\pi$
$882$	−1.87467	−0.0631236
$883$	−28.6740	−0.964959	−0.482479	−	0.875907i	$-0.660264\pi$
$883$	−28.6740	−0.964959	−0.482479	+	0.875907i	$0.660264\pi$
$884$	−2.93595	−0.0987465
$885$	−6.23018	−0.209425
$886$	38.4315	1.29113
$887$	53.0787	1.78221	0.891104	−	0.453799i	$-0.149932\pi$
$887$	53.0787	1.78221	0.891104	+	0.453799i	$0.149932\pi$
$888$	−9.13470	−0.306540
$889$	−67.3751	−2.25969
$890$	0.791684	0.0265373
$891$	4.68346	0.156902
$892$	29.7762	0.996981
$893$	14.3908	0.481570
$894$	8.49866	0.284238
$895$	−21.3859	−0.714853
$896$	−3.09594	−0.103428
$897$	−1.68184	−0.0561551
$898$	−11.5687	−0.386053
$899$	3.98528	0.132917
$900$	−0.725248	−0.0241749
$901$	5.61667	0.187118
$902$	0.642280	0.0213856
$903$	−25.2754	−0.841113
$904$	−0.905114	−0.0301036
$905$	−24.5580	−0.816336
$906$	−16.6144	−0.551977
$907$	21.7046	0.720688	0.360344	−	0.932819i	$-0.382659\pi$
$907$	21.7046	0.720688	0.360344	+	0.932819i	$0.382659\pi$
$908$	−18.2400	−0.605314
$909$	−8.42404	−0.279408
$910$	−3.09594	−0.102630
$911$	−12.3623	−0.409580	−0.204790	−	0.978806i	$-0.565651\pi$
$911$	−12.3623	−0.409580	−0.204790	+	0.978806i	$0.565651\pi$
$912$	−4.41121	−0.146070
$913$	−13.4061	−0.443676
$914$	−20.9968	−0.694511
$915$	11.4461	0.378396
$916$	12.2166	0.403649
$917$	26.0482	0.860188
$918$	−16.4957	−0.544439
$919$	−21.4683	−0.708175	−0.354088	−	0.935212i	$-0.615209\pi$
$919$	−21.4683	−0.708175	−0.354088	+	0.935212i	$0.615209\pi$
$920$	1.11511	0.0367641
$921$	−39.0602	−1.28708
$922$	−25.5563	−0.841653
$923$	14.1556	0.465937
$924$	−3.47221	−0.114227
$925$	6.05657	0.199139
$926$	40.1684	1.32001
$927$	−1.18626	−0.0389618
$928$	−3.98528	−0.130823
$929$	−7.22982	−0.237203	−0.118601	−	0.992942i	$-0.537841\pi$
$929$	−7.22982	−0.237203	−0.118601	+	0.992942i	$0.537841\pi$
$930$	1.50823	0.0494568
$931$	7.56015	0.247774
$932$	21.7000	0.710807
$933$	5.56830	0.182298
$934$	−12.3666	−0.404647
$935$	2.18320	0.0713982
$936$	−0.725248	−0.0237055
$937$	−45.3892	−1.48280	−0.741401	−	0.671063i	$-0.765838\pi$
$937$	−45.3892	−1.48280	−0.741401	+	0.671063i	$0.765838\pi$
$938$	−41.6394	−1.35957
$939$	25.1178	0.819687
$940$	4.92033	0.160484
$941$	−24.9609	−0.813704	−0.406852	−	0.913494i	$-0.633373\pi$
$941$	−24.9609	−0.813704	−0.406852	+	0.913494i	$0.633373\pi$
$942$	3.69711	0.120458
$943$	−0.963158	−0.0313648
$944$	4.13079	0.134446
$945$	−17.3946	−0.565848
$946$	4.02516	0.130869
$947$	−2.09326	−0.0680219	−0.0340110	−	0.999421i	$-0.510828\pi$
$947$	−2.09326	−0.0680219	−0.0340110	+	0.999421i	$0.510828\pi$
$948$	1.66798	0.0541734
$949$	11.0354	0.358224
$950$	2.92476	0.0948919
$951$	−2.91281	−0.0944542
$952$	9.08953	0.294593
$953$	−19.6386	−0.636157	−0.318078	−	0.948064i	$-0.603037\pi$
$953$	−19.6386	−0.636157	−0.318078	+	0.948064i	$0.603037\pi$
$954$	1.38745	0.0449204
$955$	19.0276	0.615718
$956$	−6.26304	−0.202561
$957$	−4.46963	−0.144483
$958$	−23.6854	−0.765241
$959$	−31.5085	−1.01746
$960$	−1.50823	−0.0486779
$961$	1.00000	0.0322581
$962$	6.05657	0.195272
$963$	−1.16507	−0.0375439
$964$	18.5884	0.598694
$965$	13.1680	0.423892
$966$	5.20689	0.167529
$967$	−61.5747	−1.98011	−0.990054	−	0.140685i	$-0.955069\pi$
$967$	−61.5747	−1.98011	−0.990054	+	0.140685i	$0.955069\pi$
$968$	−10.4470	−0.335781
$969$	12.9511	0.416049
$970$	−6.19662	−0.198961
$971$	−29.0264	−0.931501	−0.465750	−	0.884916i	$-0.654216\pi$
$971$	−29.0264	−0.931501	−0.465750	+	0.884916i	$0.654216\pi$
$972$	−7.35634	−0.235955
$973$	−8.34011	−0.267372
$974$	−36.1931	−1.15970
$975$	−1.50823	−0.0483020
$976$	−7.58910	−0.242921
$977$	49.8131	1.59366	0.796831	−	0.604202i	$-0.206508\pi$
$977$	49.8131	1.59366	0.796831	+	0.604202i	$0.206508\pi$
$978$	17.0190	0.544208
$979$	−0.588704	−0.0188151
$980$	2.58487	0.0825708
$981$	−0.735383	−0.0234790
$982$	33.3578	1.06449
$983$	−3.59098	−0.114535	−0.0572673	−	0.998359i	$-0.518239\pi$
$983$	−3.59098	−0.114535	−0.0572673	+	0.998359i	$0.518239\pi$
$984$	1.30271	0.0415287
$985$	−3.34129	−0.106462
$986$	11.7006	0.372622
$987$	22.9750	0.731301
$988$	2.92476	0.0930492
$989$	−6.03610	−0.191937
$990$	0.539301	0.0171401
$991$	−54.3463	−1.72637	−0.863183	−	0.504891i	$-0.831533\pi$
$991$	−54.3463	−1.72637	−0.863183	+	0.504891i	$0.831533\pi$
$992$	−1.00000	−0.0317500
$993$	8.76590	0.278177
$994$	−43.8249	−1.39004
$995$	−10.5967	−0.335939
$996$	−27.1909	−0.861576
$997$	33.1135	1.04872	0.524358	−	0.851498i	$-0.324305\pi$
$997$	33.1135	1.04872	0.524358	+	0.851498i	$0.324305\pi$
$998$	−11.4656	−0.362937
$999$	34.0290	1.07663

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4030.2.a.r.1.3	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4030.2.a.r.1.3	✓	9	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:	\( N \)	\(=\)	\( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4030.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.50823 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.50823 q^{6} -3.09594 q^{7} +1.00000 q^{8} -0.725248 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.50823 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.50823 q^{6} -3.09594 q^{7} +1.00000 q^{8} -0.725248 q^{9} +1.00000 q^{10} -0.743610 q^{11} -1.50823 q^{12} +1.00000 q^{13} -3.09594 q^{14} -1.50823 q^{15} +1.00000 q^{16} -2.93595 q^{17} -0.725248 q^{18} +2.92476 q^{19} +1.00000 q^{20} +4.66939 q^{21} -0.743610 q^{22} +1.11511 q^{23} -1.50823 q^{24} +1.00000 q^{25} +1.00000 q^{26} +5.61852 q^{27} -3.09594 q^{28} -3.98528 q^{29} -1.50823 q^{30} -1.00000 q^{31} +1.00000 q^{32} +1.12153 q^{33} -2.93595 q^{34} -3.09594 q^{35} -0.725248 q^{36} +6.05657 q^{37} +2.92476 q^{38} -1.50823 q^{39} +1.00000 q^{40} -0.863733 q^{41} +4.66939 q^{42} -5.41300 q^{43} -0.743610 q^{44} -0.725248 q^{45} +1.11511 q^{46} +4.92033 q^{47} -1.50823 q^{48} +2.58487 q^{49} +1.00000 q^{50} +4.42808 q^{51} +1.00000 q^{52} -1.91307 q^{53} +5.61852 q^{54} -0.743610 q^{55} -3.09594 q^{56} -4.41121 q^{57} -3.98528 q^{58} +4.13079 q^{59} -1.50823 q^{60} -7.58910 q^{61} -1.00000 q^{62} +2.24533 q^{63} +1.00000 q^{64} +1.00000 q^{65} +1.12153 q^{66} +13.4497 q^{67} -2.93595 q^{68} -1.68184 q^{69} -3.09594 q^{70} +14.1556 q^{71} -0.725248 q^{72} +11.0354 q^{73} +6.05657 q^{74} -1.50823 q^{75} +2.92476 q^{76} +2.30218 q^{77} -1.50823 q^{78} -1.10592 q^{79} +1.00000 q^{80} -6.29827 q^{81} -0.863733 q^{82} +18.0284 q^{83} +4.66939 q^{84} -2.93595 q^{85} -5.41300 q^{86} +6.01072 q^{87} -0.743610 q^{88} +0.791684 q^{89} -0.725248 q^{90} -3.09594 q^{91} +1.11511 q^{92} +1.50823 q^{93} +4.92033 q^{94} +2.92476 q^{95} -1.50823 q^{96} -6.19662 q^{97} +2.58487 q^{98} +0.539301 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} + 9 q^{5} + 3 q^{6} + 9 q^{7} + 9 q^{8} + 14 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 + 9 * q^5 + 3 * q^6 + 9 * q^7 + 9 * q^8 + 14 * q^9	\( 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} + 9 q^{5} + 3 q^{6} + 9 q^{7} + 9 q^{8} + 14 q^{9} + 9 q^{10} + 10 q^{11} + 3 q^{12} + 9 q^{13} + 9 q^{14} + 3 q^{15} + 9 q^{16} + q^{17} + 14 q^{18} + 10 q^{19} + 9 q^{20} + 3 q^{21} + 10 q^{22} + 8 q^{23} + 3 q^{24} + 9 q^{25} + 9 q^{26} + 15 q^{27} + 9 q^{28} + 9 q^{29} + 3 q^{30} - 9 q^{31} + 9 q^{32} + 4 q^{33} + q^{34} + 9 q^{35} + 14 q^{36} - 3 q^{37} + 10 q^{38} + 3 q^{39} + 9 q^{40} + 3 q^{42} + 7 q^{43} + 10 q^{44} + 14 q^{45} + 8 q^{46} + 7 q^{47} + 3 q^{48} + 8 q^{49} + 9 q^{50} - 3 q^{51} + 9 q^{52} + 8 q^{53} + 15 q^{54} + 10 q^{55} + 9 q^{56} - 7 q^{57} + 9 q^{58} + 2 q^{59} + 3 q^{60} - 2 q^{61} - 9 q^{62} + 10 q^{63} + 9 q^{64} + 9 q^{65} + 4 q^{66} + 18 q^{67} + q^{68} - 16 q^{69} + 9 q^{70} + 14 q^{71} + 14 q^{72} + q^{73} - 3 q^{74} + 3 q^{75} + 10 q^{76} - 5 q^{77} + 3 q^{78} + 6 q^{79} + 9 q^{80} + q^{81} + 7 q^{83} + 3 q^{84} + q^{85} + 7 q^{86} + 11 q^{87} + 10 q^{88} - 19 q^{89} + 14 q^{90} + 9 q^{91} + 8 q^{92} - 3 q^{93} + 7 q^{94} + 10 q^{95} + 3 q^{96} - 6 q^{97} + 8 q^{98} - 5 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 + 9 * q^5 + 3 * q^6 + 9 * q^7 + 9 * q^8 + 14 * q^9 + 9 * q^10 + 10 * q^11 + 3 * q^12 + 9 * q^13 + 9 * q^14 + 3 * q^15 + 9 * q^16 + q^17 + 14 * q^18 + 10 * q^19 + 9 * q^20 + 3 * q^21 + 10 * q^22 + 8 * q^23 + 3 * q^24 + 9 * q^25 + 9 * q^26 + 15 * q^27 + 9 * q^28 + 9 * q^29 + 3 * q^30 - 9 * q^31 + 9 * q^32 + 4 * q^33 + q^34 + 9 * q^35 + 14 * q^36 - 3 * q^37 + 10 * q^38 + 3 * q^39 + 9 * q^40 + 3 * q^42 + 7 * q^43 + 10 * q^44 + 14 * q^45 + 8 * q^46 + 7 * q^47 + 3 * q^48 + 8 * q^49 + 9 * q^50 - 3 * q^51 + 9 * q^52 + 8 * q^53 + 15 * q^54 + 10 * q^55 + 9 * q^56 - 7 * q^57 + 9 * q^58 + 2 * q^59 + 3 * q^60 - 2 * q^61 - 9 * q^62 + 10 * q^63 + 9 * q^64 + 9 * q^65 + 4 * q^66 + 18 * q^67 + q^68 - 16 * q^69 + 9 * q^70 + 14 * q^71 + 14 * q^72 + q^73 - 3 * q^74 + 3 * q^75 + 10 * q^76 - 5 * q^77 + 3 * q^78 + 6 * q^79 + 9 * q^80 + q^81 + 7 * q^83 + 3 * q^84 + q^85 + 7 * q^86 + 11 * q^87 + 10 * q^88 - 19 * q^89 + 14 * q^90 + 9 * q^91 + 8 * q^92 - 3 * q^93 + 7 * q^94 + 10 * q^95 + 3 * q^96 - 6 * q^97 + 8 * q^98 - 5 * q^99

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