LMFDB - Embedded newform 4830.2.a.cd.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4830,2,Mod(1,4830)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4830, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4830.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4830 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4830.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:	$38.5677441763$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.10273.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 5x^{2} + x + 2 $ x^4 - 2x^3 - 5x^2 + x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.673533$ of defining polynomial
Character	$\chi$	$=$	4830.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +1.19508 q^{11} -1.00000 q^{12} -5.78684 q^{13} -1.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} -7.28590 q^{17} -1.00000 q^{18} -2.59176 q^{19} -1.00000 q^{20} -1.00000 q^{21} -1.19508 q^{22} -1.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} +5.78684 q^{26} -1.00000 q^{27} +1.00000 q^{28} -6.74375 q^{29} -1.00000 q^{30} +4.65293 q^{31} -1.00000 q^{32} -1.19508 q^{33} +7.28590 q^{34} -1.00000 q^{35} +1.00000 q^{36} -5.24470 q^{37} +2.59176 q^{38} +5.78684 q^{39} +1.00000 q^{40} +0.694134 q^{41} +1.00000 q^{42} +8.43977 q^{43} +1.19508 q^{44} -1.00000 q^{45} +1.00000 q^{46} -8.98192 q^{47} -1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} +7.28590 q^{51} -5.78684 q^{52} +7.93883 q^{53} +1.00000 q^{54} -1.19508 q^{55} -1.00000 q^{56} +2.59176 q^{57} +6.74375 q^{58} +7.24470 q^{59} +1.00000 q^{60} -0.390153 q^{61} -4.65293 q^{62} +1.00000 q^{63} +1.00000 q^{64} +5.78684 q^{65} +1.19508 q^{66} -6.04962 q^{67} -7.28590 q^{68} +1.00000 q^{69} +1.00000 q^{70} +3.13391 q^{71} -1.00000 q^{72} +3.63485 q^{73} +5.24470 q^{74} -1.00000 q^{75} -2.59176 q^{76} +1.19508 q^{77} -5.78684 q^{78} +12.3290 q^{79} -1.00000 q^{80} +1.00000 q^{81} -0.694134 q^{82} -4.20161 q^{83} -1.00000 q^{84} +7.28590 q^{85} -8.43977 q^{86} +6.74375 q^{87} -1.19508 q^{88} +1.45786 q^{89} +1.00000 q^{90} -5.78684 q^{91} -1.00000 q^{92} -4.65293 q^{93} +8.98192 q^{94} +2.59176 q^{95} +1.00000 q^{96} +6.64138 q^{97} -1.00000 q^{98} +1.19508 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^7 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{8} + 4 q^{9} + 4 q^{10} + 2 q^{11} - 4 q^{12} + 4 q^{13} - 4 q^{14} + 4 q^{15} + 4 q^{16} - 2 q^{17} - 4 q^{18} + 14 q^{19} - 4 q^{20} - 4 q^{21} - 2 q^{22} - 4 q^{23} + 4 q^{24} + 4 q^{25} - 4 q^{26} - 4 q^{27} + 4 q^{28} - 4 q^{29} - 4 q^{30} + 20 q^{31} - 4 q^{32} - 2 q^{33} + 2 q^{34} - 4 q^{35} + 4 q^{36} + 2 q^{37} - 14 q^{38} - 4 q^{39} + 4 q^{40} + 4 q^{42} + 8 q^{43} + 2 q^{44} - 4 q^{45} + 4 q^{46} - 6 q^{47} - 4 q^{48} + 4 q^{49} - 4 q^{50} + 2 q^{51} + 4 q^{52} + 6 q^{53} + 4 q^{54} - 2 q^{55} - 4 q^{56} - 14 q^{57} + 4 q^{58} + 6 q^{59} + 4 q^{60} + 4 q^{61} - 20 q^{62} + 4 q^{63} + 4 q^{64} - 4 q^{65} + 2 q^{66} - 4 q^{67} - 2 q^{68} + 4 q^{69} + 4 q^{70} - 16 q^{71} - 4 q^{72} - 14 q^{73} - 2 q^{74} - 4 q^{75} + 14 q^{76} + 2 q^{77} + 4 q^{78} + 18 q^{79} - 4 q^{80} + 4 q^{81} + 2 q^{83} - 4 q^{84} + 2 q^{85} - 8 q^{86} + 4 q^{87} - 2 q^{88} + 10 q^{89} + 4 q^{90} + 4 q^{91} - 4 q^{92} - 20 q^{93} + 6 q^{94} - 14 q^{95} + 4 q^{96} - 18 q^{97} - 4 q^{98} + 2 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^7 - 4 * q^8 + 4 * q^9 + 4 * q^10 + 2 * q^11 - 4 * q^12 + 4 * q^13 - 4 * q^14 + 4 * q^15 + 4 * q^16 - 2 * q^17 - 4 * q^18 + 14 * q^19 - 4 * q^20 - 4 * q^21 - 2 * q^22 - 4 * q^23 + 4 * q^24 + 4 * q^25 - 4 * q^26 - 4 * q^27 + 4 * q^28 - 4 * q^29 - 4 * q^30 + 20 * q^31 - 4 * q^32 - 2 * q^33 + 2 * q^34 - 4 * q^35 + 4 * q^36 + 2 * q^37 - 14 * q^38 - 4 * q^39 + 4 * q^40 + 4 * q^42 + 8 * q^43 + 2 * q^44 - 4 * q^45 + 4 * q^46 - 6 * q^47 - 4 * q^48 + 4 * q^49 - 4 * q^50 + 2 * q^51 + 4 * q^52 + 6 * q^53 + 4 * q^54 - 2 * q^55 - 4 * q^56 - 14 * q^57 + 4 * q^58 + 6 * q^59 + 4 * q^60 + 4 * q^61 - 20 * q^62 + 4 * q^63 + 4 * q^64 - 4 * q^65 + 2 * q^66 - 4 * q^67 - 2 * q^68 + 4 * q^69 + 4 * q^70 - 16 * q^71 - 4 * q^72 - 14 * q^73 - 2 * q^74 - 4 * q^75 + 14 * q^76 + 2 * q^77 + 4 * q^78 + 18 * q^79 - 4 * q^80 + 4 * q^81 + 2 * q^83 - 4 * q^84 + 2 * q^85 - 8 * q^86 + 4 * q^87 - 2 * q^88 + 10 * q^89 + 4 * q^90 + 4 * q^91 - 4 * q^92 - 20 * q^93 + 6 * q^94 - 14 * q^95 + 4 * q^96 - 18 * q^97 - 4 * q^98 + 2 * 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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.00000	0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	1.19508	0.360329	0.180165	−	0.983636i	$-0.442337\pi$
$11$	1.19508	0.360329	0.180165	+	0.983636i	$0.442337\pi$
$12$	−1.00000	−0.288675
$13$	−5.78684	−1.60498	−0.802490	−	0.596665i	$-0.796492\pi$
$13$	−5.78684	−1.60498	−0.802490	+	0.596665i	$0.796492\pi$
$14$	−1.00000	−0.267261
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	−7.28590	−1.76709	−0.883545	−	0.468347i	$-0.844850\pi$
$17$	−7.28590	−1.76709	−0.883545	+	0.468347i	$0.844850\pi$
$18$	−1.00000	−0.235702
$19$	−2.59176	−0.594591	−0.297296	−	0.954785i	$-0.596085\pi$
$19$	−2.59176	−0.594591	−0.297296	+	0.954785i	$0.596085\pi$
$20$	−1.00000	−0.223607
$21$	−1.00000	−0.218218
$22$	−1.19508	−0.254791
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	5.78684	1.13489
$27$	−1.00000	−0.192450
$28$	1.00000	0.188982
$29$	−6.74375	−1.25228	−0.626142	−	0.779709i	$-0.715367\pi$
$29$	−6.74375	−1.25228	−0.626142	+	0.779709i	$0.715367\pi$
$30$	−1.00000	−0.182574
$31$	4.65293	0.835691	0.417846	−	0.908518i	$-0.362785\pi$
$31$	4.65293	0.835691	0.417846	+	0.908518i	$0.362785\pi$
$32$	−1.00000	−0.176777
$33$	−1.19508	−0.208036
$34$	7.28590	1.24952
$35$	−1.00000	−0.169031
$36$	1.00000	0.166667
$37$	−5.24470	−0.862223	−0.431111	−	0.902299i	$-0.641878\pi$
$37$	−5.24470	−0.862223	−0.431111	+	0.902299i	$0.641878\pi$
$38$	2.59176	0.420439
$39$	5.78684	0.926636
$40$	1.00000	0.158114
$41$	0.694134	0.108405	0.0542027	−	0.998530i	$-0.482738\pi$
$41$	0.694134	0.108405	0.0542027	+	0.998530i	$0.482738\pi$
$42$	1.00000	0.154303
$43$	8.43977	1.28705	0.643527	−	0.765424i	$-0.277471\pi$
$43$	8.43977	1.28705	0.643527	+	0.765424i	$0.277471\pi$
$44$	1.19508	0.180165
$45$	−1.00000	−0.149071
$46$	1.00000	0.147442
$47$	−8.98192	−1.31015	−0.655074	−	0.755565i	$-0.727362\pi$
$47$	−8.98192	−1.31015	−0.655074	+	0.755565i	$0.727362\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	7.28590	1.02023
$52$	−5.78684	−0.802490
$53$	7.93883	1.09048	0.545241	−	0.838279i	$-0.316438\pi$
$53$	7.93883	1.09048	0.545241	+	0.838279i	$0.316438\pi$
$54$	1.00000	0.136083
$55$	−1.19508	−0.161144
$56$	−1.00000	−0.133631
$57$	2.59176	0.343287
$58$	6.74375	0.885498
$59$	7.24470	0.943179	0.471590	−	0.881818i	$-0.343680\pi$
$59$	7.24470	0.943179	0.471590	+	0.881818i	$0.343680\pi$
$60$	1.00000	0.129099
$61$	−0.390153	−0.0499539	−0.0249770	−	0.999688i	$-0.507951\pi$
$61$	−0.390153	−0.0499539	−0.0249770	+	0.999688i	$0.507951\pi$
$62$	−4.65293	−0.590923
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	5.78684	0.717769
$66$	1.19508	0.147104
$67$	−6.04962	−0.739079	−0.369539	−	0.929215i	$-0.620485\pi$
$67$	−6.04962	−0.739079	−0.369539	+	0.929215i	$0.620485\pi$
$68$	−7.28590	−0.883545
$69$	1.00000	0.120386
$70$	1.00000	0.119523
$71$	3.13391	0.371926	0.185963	−	0.982557i	$-0.440460\pi$
$71$	3.13391	0.371926	0.185963	+	0.982557i	$0.440460\pi$
$72$	−1.00000	−0.117851
$73$	3.63485	0.425427	0.212713	−	0.977115i	$-0.431770\pi$
$73$	3.63485	0.425427	0.212713	+	0.977115i	$0.431770\pi$
$74$	5.24470	0.609684
$75$	−1.00000	−0.115470
$76$	−2.59176	−0.297296
$77$	1.19508	0.136192
$78$	−5.78684	−0.655231
$79$	12.3290	1.38712	0.693559	−	0.720399i	$-0.256041\pi$
$79$	12.3290	1.38712	0.693559	+	0.720399i	$0.256041\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−0.694134	−0.0766542
$83$	−4.20161	−0.461187	−0.230593	−	0.973050i	$-0.574067\pi$
$83$	−4.20161	−0.461187	−0.230593	+	0.973050i	$0.574067\pi$
$84$	−1.00000	−0.109109
$85$	7.28590	0.790266
$86$	−8.43977	−0.910084
$87$	6.74375	0.723006
$88$	−1.19508	−0.127396
$89$	1.45786	0.154533	0.0772663	−	0.997010i	$-0.475381\pi$
$89$	1.45786	0.154533	0.0772663	+	0.997010i	$0.475381\pi$
$90$	1.00000	0.105409
$91$	−5.78684	−0.606626
$92$	−1.00000	−0.104257
$93$	−4.65293	−0.482487
$94$	8.98192	0.926414
$95$	2.59176	0.265909
$96$	1.00000	0.102062
$97$	6.64138	0.674330	0.337165	−	0.941446i	$-0.390532\pi$
$97$	6.64138	0.674330	0.337165	+	0.941446i	$0.390532\pi$
$98$	−1.00000	−0.101015
$99$	1.19508	0.120110
$100$	1.00000	0.100000
$101$	−13.0315	−1.29669	−0.648343	−	0.761348i	$-0.724538\pi$
$101$	−13.0315	−1.29669	−0.648343	+	0.761348i	$0.724538\pi$
$102$	−7.28590	−0.721411
$103$	−5.30587	−0.522803	−0.261401	−	0.965230i	$-0.584185\pi$
$103$	−5.30587	−0.522803	−0.261401	+	0.965230i	$0.584185\pi$
$104$	5.78684	0.567446
$105$	1.00000	0.0975900
$106$	−7.93883	−0.771087
$107$	14.7934	1.43013	0.715065	−	0.699058i	$-0.246397\pi$
$107$	14.7934	1.43013	0.715065	+	0.699058i	$0.246397\pi$
$108$	−1.00000	−0.0962250
$109$	3.30587	0.316645	0.158322	−	0.987387i	$-0.449392\pi$
$109$	3.30587	0.316645	0.158322	+	0.987387i	$0.449392\pi$
$110$	1.19508	0.113946
$111$	5.24470	0.497805
$112$	1.00000	0.0944911
$113$	−10.3290	−0.971669	−0.485834	−	0.874051i	$-0.661484\pi$
$113$	−10.3290	−0.971669	−0.485834	+	0.874051i	$0.661484\pi$
$114$	−2.59176	−0.242741
$115$	1.00000	0.0932505
$116$	−6.74375	−0.626142
$117$	−5.78684	−0.534993
$118$	−7.24470	−0.666928
$119$	−7.28590	−0.667897
$120$	−1.00000	−0.0912871
$121$	−9.57179	−0.870163
$122$	0.390153	0.0353227
$123$	−0.694134	−0.0625879
$124$	4.65293	0.417846
$125$	−1.00000	−0.0894427
$126$	−1.00000	−0.0890871
$127$	4.43977	0.393966	0.196983	−	0.980407i	$-0.436886\pi$
$127$	4.43977	0.393966	0.196983	+	0.980407i	$0.436886\pi$
$128$	−1.00000	−0.0883883
$129$	−8.43977	−0.743081
$130$	−5.78684	−0.507539
$131$	6.24281	0.545437	0.272718	−	0.962094i	$-0.412077\pi$
$131$	6.24281	0.545437	0.272718	+	0.962094i	$0.412077\pi$
$132$	−1.19508	−0.104018
$133$	−2.59176	−0.224734
$134$	6.04962	0.522608
$135$	1.00000	0.0860663
$136$	7.28590	0.624760
$137$	−11.6348	−0.994032	−0.497016	−	0.867741i	$-0.665571\pi$
$137$	−11.6348	−0.994032	−0.497016	+	0.867741i	$0.665571\pi$
$138$	−1.00000	−0.0851257
$139$	7.24470	0.614487	0.307244	−	0.951631i	$-0.400593\pi$
$139$	7.24470	0.614487	0.307244	+	0.951631i	$0.400593\pi$
$140$	−1.00000	−0.0845154
$141$	8.98192	0.756414
$142$	−3.13391	−0.262992
$143$	−6.91571	−0.578321
$144$	1.00000	0.0833333
$145$	6.74375	0.560038
$146$	−3.63485	−0.300822
$147$	−1.00000	−0.0824786
$148$	−5.24470	−0.431111
$149$	−0.390153	−0.0319625	−0.0159813	−	0.999872i	$-0.505087\pi$
$149$	−0.390153	−0.0319625	−0.0159813	+	0.999872i	$0.505087\pi$
$150$	1.00000	0.0816497
$151$	−7.57368	−0.616337	−0.308169	−	0.951332i	$-0.599716\pi$
$151$	−7.57368	−0.616337	−0.308169	+	0.951332i	$0.599716\pi$
$152$	2.59176	0.210220
$153$	−7.28590	−0.589030
$154$	−1.19508	−0.0963020
$155$	−4.65293	−0.373733
$156$	5.78684	0.463318
$157$	−11.1835	−0.892543	−0.446271	−	0.894898i	$-0.647248\pi$
$157$	−11.1835	−0.892543	−0.446271	+	0.894898i	$0.647248\pi$
$158$	−12.3290	−0.980841
$159$	−7.93883	−0.629590
$160$	1.00000	0.0790569
$161$	−1.00000	−0.0788110
$162$	−1.00000	−0.0785674
$163$	23.5737	1.84643	0.923216	−	0.384280i	$-0.125550\pi$
$163$	23.5737	1.84643	0.923216	+	0.384280i	$0.125550\pi$
$164$	0.694134	0.0542027
$165$	1.19508	0.0930366
$166$	4.20161	0.326108
$167$	18.4694	1.42921	0.714603	−	0.699530i	$-0.246607\pi$
$167$	18.4694	1.42921	0.714603	+	0.699530i	$0.246607\pi$
$168$	1.00000	0.0771517
$169$	20.4875	1.57596
$170$	−7.28590	−0.558803
$171$	−2.59176	−0.198197
$172$	8.43977	0.643527
$173$	−8.92074	−0.678232	−0.339116	−	0.940745i	$-0.610128\pi$
$173$	−8.92074	−0.678232	−0.339116	+	0.940745i	$0.610128\pi$
$174$	−6.74375	−0.511243
$175$	1.00000	0.0755929
$176$	1.19508	0.0900823
$177$	−7.24470	−0.544545
$178$	−1.45786	−0.109271
$179$	3.77842	0.282412	0.141206	−	0.989980i	$-0.454902\pi$
$179$	3.77842	0.282412	0.141206	+	0.989980i	$0.454902\pi$
$180$	−1.00000	−0.0745356
$181$	−15.4875	−1.15118	−0.575589	−	0.817739i	$-0.695227\pi$
$181$	−15.4875	−1.15118	−0.575589	+	0.817739i	$0.695227\pi$
$182$	5.78684	0.428949
$183$	0.390153	0.0288409
$184$	1.00000	0.0737210
$185$	5.24470	0.385598
$186$	4.65293	0.341170
$187$	−8.70720	−0.636734
$188$	−8.98192	−0.655074
$189$	−1.00000	−0.0727393
$190$	−2.59176	−0.188026
$191$	−10.8184	−0.782790	−0.391395	−	0.920223i	$-0.628007\pi$
$191$	−10.8184	−0.782790	−0.391395	+	0.920223i	$0.628007\pi$
$192$	−1.00000	−0.0721688
$193$	7.08429	0.509938	0.254969	−	0.966949i	$-0.417935\pi$
$193$	7.08429	0.509938	0.254969	+	0.966949i	$0.417935\pi$
$194$	−6.64138	−0.476823
$195$	−5.78684	−0.414404
$196$	1.00000	0.0714286
$197$	−7.30587	−0.520521	−0.260261	−	0.965538i	$-0.583809\pi$
$197$	−7.30587	−0.520521	−0.260261	+	0.965538i	$0.583809\pi$
$198$	−1.19508	−0.0849304
$199$	16.8795	1.19656	0.598280	−	0.801287i	$-0.295851\pi$
$199$	16.8795	1.19656	0.598280	+	0.801287i	$0.295851\pi$
$200$	−1.00000	−0.0707107
$201$	6.04962	0.426707
$202$	13.0315	0.916896
$203$	−6.74375	−0.473319
$204$	7.28590	0.510115
$205$	−0.694134	−0.0484804
$206$	5.30587	0.369677
$207$	−1.00000	−0.0695048
$208$	−5.78684	−0.401245
$209$	−3.09735	−0.214248
$210$	−1.00000	−0.0690066
$211$	5.18353	0.356849	0.178424	−	0.983954i	$-0.442900\pi$
$211$	5.18353	0.356849	0.178424	+	0.983954i	$0.442900\pi$
$212$	7.93883	0.545241
$213$	−3.13391	−0.214732
$214$	−14.7934	−1.01125
$215$	−8.43977	−0.575588
$216$	1.00000	0.0680414
$217$	4.65293	0.315862
$218$	−3.30587	−0.223902
$219$	−3.63485	−0.245620
$220$	−1.19508	−0.0805720
$221$	42.1623	2.83614
$222$	−5.24470	−0.352001
$223$	18.7276	1.25409	0.627045	−	0.778983i	$-0.284264\pi$
$223$	18.7276	1.25409	0.627045	+	0.778983i	$0.284264\pi$
$224$	−1.00000	−0.0668153
$225$	1.00000	0.0666667
$226$	10.3290	0.687074
$227$	−21.2859	−1.41279	−0.706397	−	0.707816i	$-0.749681\pi$
$227$	−21.2859	−1.41279	−0.706397	+	0.707816i	$0.749681\pi$
$228$	2.59176	0.171644
$229$	18.1816	1.20148	0.600738	−	0.799446i	$-0.294873\pi$
$229$	18.1816	1.20148	0.600738	+	0.799446i	$0.294873\pi$
$230$	−1.00000	−0.0659380
$231$	−1.19508	−0.0786302
$232$	6.74375	0.442749
$233$	19.9638	1.30787	0.653937	−	0.756549i	$-0.273116\pi$
$233$	19.9638	1.30787	0.653937	+	0.756549i	$0.273116\pi$
$234$	5.78684	0.378298
$235$	8.98192	0.585916
$236$	7.24470	0.471590
$237$	−12.3290	−0.800853
$238$	7.28590	0.472275
$239$	−24.7938	−1.60377	−0.801887	−	0.597475i	$-0.796171\pi$
$239$	−24.7938	−1.60377	−0.801887	+	0.597475i	$0.796171\pi$
$240$	1.00000	0.0645497
$241$	20.5918	1.32643	0.663216	−	0.748428i	$-0.269191\pi$
$241$	20.5918	1.32643	0.663216	+	0.748428i	$0.269191\pi$
$242$	9.57179	0.615298
$243$	−1.00000	−0.0641500
$244$	−0.390153	−0.0249770
$245$	−1.00000	−0.0638877
$246$	0.694134	0.0442563
$247$	14.9981	0.954307
$248$	−4.65293	−0.295462
$249$	4.20161	0.266266
$250$	1.00000	0.0632456
$251$	−17.9472	−1.13282	−0.566410	−	0.824123i	$-0.691668\pi$
$251$	−17.9472	−1.13282	−0.566410	+	0.824123i	$0.691668\pi$
$252$	1.00000	0.0629941
$253$	−1.19508	−0.0751338
$254$	−4.43977	−0.278576
$255$	−7.28590	−0.456261
$256$	1.00000	0.0625000
$257$	−9.32710	−0.581808	−0.290904	−	0.956752i	$-0.593956\pi$
$257$	−9.32710	−0.581808	−0.290904	+	0.956752i	$0.593956\pi$
$258$	8.43977	0.525437
$259$	−5.24470	−0.325890
$260$	5.78684	0.358885
$261$	−6.74375	−0.417428
$262$	−6.24281	−0.385682
$263$	16.3040	1.00535	0.502673	−	0.864476i	$-0.332350\pi$
$263$	16.3040	1.00535	0.502673	+	0.864476i	$0.332350\pi$
$264$	1.19508	0.0735519
$265$	−7.93883	−0.487678
$266$	2.59176	0.158911
$267$	−1.45786	−0.0892194
$268$	−6.04962	−0.369539
$269$	4.45597	0.271685	0.135843	−	0.990730i	$-0.456626\pi$
$269$	4.45597	0.271685	0.135843	+	0.990730i	$0.456626\pi$
$270$	−1.00000	−0.0608581
$271$	23.0200	1.39836	0.699182	−	0.714943i	$-0.253548\pi$
$271$	23.0200	1.39836	0.699182	+	0.714943i	$0.253548\pi$
$272$	−7.28590	−0.441772
$273$	5.78684	0.350235
$274$	11.6348	0.702887
$275$	1.19508	0.0720658
$276$	1.00000	0.0601929
$277$	19.7057	1.18400	0.592000	−	0.805938i	$-0.298338\pi$
$277$	19.7057	1.18400	0.592000	+	0.805938i	$0.298338\pi$
$278$	−7.24470	−0.434508
$279$	4.65293	0.278564
$280$	1.00000	0.0597614
$281$	22.5390	1.34456	0.672282	−	0.740295i	$-0.265314\pi$
$281$	22.5390	1.34456	0.672282	+	0.740295i	$0.265314\pi$
$282$	−8.98192	−0.534865
$283$	2.45597	0.145992	0.0729962	−	0.997332i	$-0.476744\pi$
$283$	2.45597	0.145992	0.0729962	+	0.997332i	$0.476744\pi$
$284$	3.13391	0.185963
$285$	−2.59176	−0.153523
$286$	6.91571	0.408935
$287$	0.694134	0.0409734
$288$	−1.00000	−0.0589256
$289$	36.0843	2.12261
$290$	−6.74375	−0.396007
$291$	−6.64138	−0.389325
$292$	3.63485	0.212713
$293$	−15.9638	−0.932617	−0.466308	−	0.884622i	$-0.654416\pi$
$293$	−15.9638	−0.932617	−0.466308	+	0.884622i	$0.654416\pi$
$294$	1.00000	0.0583212
$295$	−7.24470	−0.421803
$296$	5.24470	0.304842
$297$	−1.19508	−0.0693454
$298$	0.390153	0.0226009
$299$	5.78684	0.334662
$300$	−1.00000	−0.0577350
$301$	8.43977	0.486460
$302$	7.57368	0.435816
$303$	13.0315	0.748642
$304$	−2.59176	−0.148648
$305$	0.390153	0.0223401
$306$	7.28590	0.416507
$307$	−32.4532	−1.85220	−0.926102	−	0.377274i	$-0.876861\pi$
$307$	−32.4532	−1.85220	−0.926102	+	0.377274i	$0.876861\pi$
$308$	1.19508	0.0680958
$309$	5.30587	0.301840
$310$	4.65293	0.264269
$311$	−9.39669	−0.532837	−0.266419	−	0.963857i	$-0.585840\pi$
$311$	−9.39669	−0.532837	−0.266419	+	0.963857i	$0.585840\pi$
$312$	−5.78684	−0.327615
$313$	30.8230	1.74222	0.871110	−	0.491088i	$-0.163401\pi$
$313$	30.8230	1.74222	0.871110	+	0.491088i	$0.163401\pi$
$314$	11.1835	0.631123
$315$	−1.00000	−0.0563436
$316$	12.3290	0.693559
$317$	20.1854	1.13373	0.566863	−	0.823812i	$-0.308157\pi$
$317$	20.1854	1.13373	0.566863	+	0.823812i	$0.308157\pi$
$318$	7.93883	0.445187
$319$	−8.05930	−0.451234
$320$	−1.00000	−0.0559017
$321$	−14.7934	−0.825686
$322$	1.00000	0.0557278
$323$	18.8833	1.05070
$324$	1.00000	0.0555556
$325$	−5.78684	−0.320996
$326$	−23.5737	−1.30563
$327$	−3.30587	−0.182815
$328$	−0.694134	−0.0383271
$329$	−8.98192	−0.495189
$330$	−1.19508	−0.0657868
$331$	−4.96195	−0.272733	−0.136367	−	0.990658i	$-0.543543\pi$
$331$	−4.96195	−0.272733	−0.136367	+	0.990658i	$0.543543\pi$
$332$	−4.20161	−0.230593
$333$	−5.24470	−0.287408
$334$	−18.4694	−1.01060
$335$	6.04962	0.330526
$336$	−1.00000	−0.0545545
$337$	4.58334	0.249671	0.124835	−	0.992177i	$-0.460160\pi$
$337$	4.58334	0.249671	0.124835	+	0.992177i	$0.460160\pi$
$338$	−20.4875	−1.11437
$339$	10.3290	0.560993
$340$	7.28590	0.395133
$341$	5.56061	0.301124
$342$	2.59176	0.140146
$343$	1.00000	0.0539949
$344$	−8.43977	−0.455042
$345$	−1.00000	−0.0538382
$346$	8.92074	0.479582
$347$	10.2678	0.551205	0.275603	−	0.961272i	$-0.411123\pi$
$347$	10.2678	0.551205	0.275603	+	0.961272i	$0.411123\pi$
$348$	6.74375	0.361503
$349$	−14.6779	−0.785692	−0.392846	−	0.919604i	$-0.628509\pi$
$349$	−14.6779	−0.785692	−0.392846	+	0.919604i	$0.628509\pi$
$350$	−1.00000	−0.0534522
$351$	5.78684	0.308879
$352$	−1.19508	−0.0636978
$353$	8.54679	0.454900	0.227450	−	0.973790i	$-0.426961\pi$
$353$	8.54679	0.454900	0.227450	+	0.973790i	$0.426961\pi$
$354$	7.24470	0.385051
$355$	−3.13391	−0.166330
$356$	1.45786	0.0772663
$357$	7.28590	0.385611
$358$	−3.77842	−0.199696
$359$	16.4513	0.868268	0.434134	−	0.900848i	$-0.357055\pi$
$359$	16.4513	0.868268	0.434134	+	0.900848i	$0.357055\pi$
$360$	1.00000	0.0527046
$361$	−12.2828	−0.646461
$362$	15.4875	0.814005
$363$	9.57179	0.502389
$364$	−5.78684	−0.303313
$365$	−3.63485	−0.190257
$366$	−0.390153	−0.0203936
$367$	−10.6941	−0.558229	−0.279115	−	0.960258i	$-0.590041\pi$
$367$	−10.6941	−0.558229	−0.279115	+	0.960258i	$0.590041\pi$
$368$	−1.00000	−0.0521286
$369$	0.694134	0.0361351
$370$	−5.24470	−0.272659
$371$	7.93883	0.412163
$372$	−4.65293	−0.241243
$373$	26.5106	1.37267	0.686334	−	0.727286i	$-0.259219\pi$
$373$	26.5106	1.37267	0.686334	+	0.727286i	$0.259219\pi$
$374$	8.70720	0.450239
$375$	1.00000	0.0516398
$376$	8.98192	0.463207
$377$	39.0250	2.00989
$378$	1.00000	0.0514344
$379$	6.71913	0.345139	0.172569	−	0.984997i	$-0.444793\pi$
$379$	6.71913	0.345139	0.172569	+	0.984997i	$0.444793\pi$
$380$	2.59176	0.132955
$381$	−4.43977	−0.227456
$382$	10.8184	0.553516
$383$	−35.3290	−1.80523	−0.902614	−	0.430452i	$-0.858354\pi$
$383$	−35.3290	−1.80523	−0.902614	+	0.430452i	$0.858354\pi$
$384$	1.00000	0.0510310
$385$	−1.19508	−0.0609067
$386$	−7.08429	−0.360581
$387$	8.43977	0.429018
$388$	6.64138	0.337165
$389$	4.91571	0.249237	0.124618	−	0.992205i	$-0.460229\pi$
$389$	4.91571	0.249237	0.124618	+	0.992205i	$0.460229\pi$
$390$	5.78684	0.293028
$391$	7.28590	0.368464
$392$	−1.00000	−0.0505076
$393$	−6.24281	−0.314908
$394$	7.30587	0.368064
$395$	−12.3290	−0.620338
$396$	1.19508	0.0600548
$397$	13.4829	0.676685	0.338343	−	0.941023i	$-0.390134\pi$
$397$	13.4829	0.676685	0.338343	+	0.941023i	$0.390134\pi$
$398$	−16.8795	−0.846095
$399$	2.59176	0.129750
$400$	1.00000	0.0500000
$401$	14.5621	0.727197	0.363599	−	0.931556i	$-0.381548\pi$
$401$	14.5621	0.727197	0.363599	+	0.931556i	$0.381548\pi$
$402$	−6.04962	−0.301728
$403$	−26.9258	−1.34127
$404$	−13.0315	−0.648343
$405$	−1.00000	−0.0496904
$406$	6.74375	0.334687
$407$	−6.26781	−0.310684
$408$	−7.28590	−0.360706
$409$	12.8165	0.633734	0.316867	−	0.948470i	$-0.397369\pi$
$409$	12.8165	0.633734	0.316867	+	0.948470i	$0.397369\pi$
$410$	0.694134	0.0342808
$411$	11.6348	0.573905
$412$	−5.30587	−0.261401
$413$	7.24470	0.356488
$414$	1.00000	0.0491473
$415$	4.20161	0.206249
$416$	5.78684	0.283723
$417$	−7.24470	−0.354774
$418$	3.09735	0.151497
$419$	0.641383	0.0313336	0.0156668	−	0.999877i	$-0.495013\pi$
$419$	0.641383	0.0313336	0.0156668	+	0.999877i	$0.495013\pi$
$420$	1.00000	0.0487950
$421$	−37.0250	−1.80449	−0.902244	−	0.431225i	$-0.858082\pi$
$421$	−37.0250	−1.80449	−0.902244	+	0.431225i	$0.858082\pi$
$422$	−5.18353	−0.252330
$423$	−8.98192	−0.436716
$424$	−7.93883	−0.385544
$425$	−7.28590	−0.353418
$426$	3.13391	0.151838
$427$	−0.390153	−0.0188808
$428$	14.7934	0.715065
$429$	6.91571	0.333894
$430$	8.43977	0.407002
$431$	29.0362	1.39862	0.699312	−	0.714817i	$-0.253490\pi$
$431$	29.0362	1.39862	0.699312	+	0.714817i	$0.253490\pi$
$432$	−1.00000	−0.0481125
$433$	4.27433	0.205411	0.102706	−	0.994712i	$-0.467250\pi$
$433$	4.27433	0.205411	0.102706	+	0.994712i	$0.467250\pi$
$434$	−4.65293	−0.223348
$435$	−6.74375	−0.323338
$436$	3.30587	0.158322
$437$	2.59176	0.123981
$438$	3.63485	0.173680
$439$	20.2266	0.965363	0.482682	−	0.875796i	$-0.339663\pi$
$439$	20.2266	0.965363	0.482682	+	0.875796i	$0.339663\pi$
$440$	1.19508	0.0569730
$441$	1.00000	0.0476190
$442$	−42.1623	−2.00546
$443$	−8.09924	−0.384806	−0.192403	−	0.981316i	$-0.561628\pi$
$443$	−8.09924	−0.384806	−0.192403	+	0.981316i	$0.561628\pi$
$444$	5.24470	0.248902
$445$	−1.45786	−0.0691090
$446$	−18.7276	−0.886775
$447$	0.390153	0.0184536
$448$	1.00000	0.0472456
$449$	−22.3309	−1.05386	−0.526930	−	0.849909i	$-0.676657\pi$
$449$	−22.3309	−1.05386	−0.526930	+	0.849909i	$0.676657\pi$
$450$	−1.00000	−0.0471405
$451$	0.829542	0.0390616
$452$	−10.3290	−0.485834
$453$	7.57368	0.355842
$454$	21.2859	0.998997
$455$	5.78684	0.271291
$456$	−2.59176	−0.121370
$457$	12.6002	0.589412	0.294706	−	0.955588i	$-0.404778\pi$
$457$	12.6002	0.589412	0.294706	+	0.955588i	$0.404778\pi$
$458$	−18.1816	−0.849572
$459$	7.28590	0.340077
$460$	1.00000	0.0466252
$461$	−5.63950	−0.262658	−0.131329	−	0.991339i	$-0.541924\pi$
$461$	−5.63950	−0.262658	−0.131329	+	0.991339i	$0.541924\pi$
$462$	1.19508	0.0556000
$463$	−22.4036	−1.04118	−0.520592	−	0.853806i	$-0.674289\pi$
$463$	−22.4036	−1.04118	−0.520592	+	0.853806i	$0.674289\pi$
$464$	−6.74375	−0.313071
$465$	4.65293	0.215775
$466$	−19.9638	−0.924807
$467$	6.37018	0.294777	0.147388	−	0.989079i	$-0.452913\pi$
$467$	6.37018	0.294777	0.147388	+	0.989079i	$0.452913\pi$
$468$	−5.78684	−0.267497
$469$	−6.04962	−0.279345
$470$	−8.98192	−0.414305
$471$	11.1835	0.515310
$472$	−7.24470	−0.333464
$473$	10.0862	0.463763
$474$	12.3290	0.566289
$475$	−2.59176	−0.118918
$476$	−7.28590	−0.333949
$477$	7.93883	0.363494
$478$	24.7938	1.13404
$479$	38.7703	1.77146	0.885729	−	0.464202i	$-0.153659\pi$
$479$	38.7703	1.77146	0.885729	+	0.464202i	$0.153659\pi$
$480$	−1.00000	−0.0456435
$481$	30.3502	1.38385
$482$	−20.5918	−0.937929
$483$	1.00000	0.0455016
$484$	−9.57179	−0.435081
$485$	−6.64138	−0.301570
$486$	1.00000	0.0453609
$487$	−33.1801	−1.50354	−0.751768	−	0.659428i	$-0.770799\pi$
$487$	−33.1801	−1.50354	−0.751768	+	0.659428i	$0.770799\pi$
$488$	0.390153	0.0176614
$489$	−23.5737	−1.06604
$490$	1.00000	0.0451754
$491$	−14.8758	−0.671334	−0.335667	−	0.941981i	$-0.608962\pi$
$491$	−14.8758	−0.671334	−0.335667	+	0.941981i	$0.608962\pi$
$492$	−0.694134	−0.0312940
$493$	49.1343	2.21290
$494$	−14.9981	−0.674797
$495$	−1.19508	−0.0537147
$496$	4.65293	0.208923
$497$	3.13391	0.140575
$498$	−4.20161	−0.188279
$499$	13.1835	0.590176	0.295088	−	0.955470i	$-0.404651\pi$
$499$	13.1835	0.590176	0.295088	+	0.955470i	$0.404651\pi$
$500$	−1.00000	−0.0447214
$501$	−18.4694	−0.825153
$502$	17.9472	0.801025
$503$	18.2447	0.813491	0.406746	−	0.913541i	$-0.366664\pi$
$503$	18.2447	0.813491	0.406746	+	0.913541i	$0.366664\pi$
$504$	−1.00000	−0.0445435
$505$	13.0315	0.579896
$506$	1.19508	0.0531276
$507$	−20.4875	−0.909882
$508$	4.43977	0.196983
$509$	−5.93418	−0.263028	−0.131514	−	0.991314i	$-0.541984\pi$
$509$	−5.93418	−0.263028	−0.131514	+	0.991314i	$0.541984\pi$
$510$	7.28590	0.322625
$511$	3.63485	0.160796
$512$	−1.00000	−0.0441942
$513$	2.59176	0.114429
$514$	9.32710	0.411401
$515$	5.30587	0.233804
$516$	−8.43977	−0.371540
$517$	−10.7341	−0.472084
$518$	5.24470	0.230439
$519$	8.92074	0.391577
$520$	−5.78684	−0.253770
$521$	10.0658	0.440992	0.220496	−	0.975388i	$-0.429232\pi$
$521$	10.0658	0.440992	0.220496	+	0.975388i	$0.429232\pi$
$522$	6.74375	0.295166
$523$	−13.9073	−0.608124	−0.304062	−	0.952652i	$-0.598343\pi$
$523$	−13.9073	−0.608124	−0.304062	+	0.952652i	$0.598343\pi$
$524$	6.24281	0.272718
$525$	−1.00000	−0.0436436
$526$	−16.3040	−0.710887
$527$	−33.9008	−1.47674
$528$	−1.19508	−0.0520090
$529$	1.00000	0.0434783
$530$	7.93883	0.344841
$531$	7.24470	0.314393
$532$	−2.59176	−0.112367
$533$	−4.01684	−0.173989
$534$	1.45786	0.0630876
$535$	−14.7934	−0.639573
$536$	6.04962	0.261304
$537$	−3.77842	−0.163051
$538$	−4.45597	−0.192111
$539$	1.19508	0.0514756
$540$	1.00000	0.0430331
$541$	24.3902	1.04861	0.524307	−	0.851529i	$-0.324324\pi$
$541$	24.3902	1.04861	0.524307	+	0.851529i	$0.324324\pi$
$542$	−23.0200	−0.988793
$543$	15.4875	0.664633
$544$	7.28590	0.312380
$545$	−3.30587	−0.141608
$546$	−5.78684	−0.247654
$547$	−2.91571	−0.124667	−0.0623335	−	0.998055i	$-0.519854\pi$
$547$	−2.91571	−0.124667	−0.0623335	+	0.998055i	$0.519854\pi$
$548$	−11.6348	−0.497016
$549$	−0.390153	−0.0166513
$550$	−1.19508	−0.0509582
$551$	17.4782	0.744597
$552$	−1.00000	−0.0425628
$553$	12.3290	0.524282
$554$	−19.7057	−0.837215
$555$	−5.24470	−0.222625
$556$	7.24470	0.307244
$557$	−35.4301	−1.50122	−0.750611	−	0.660744i	$-0.770241\pi$
$557$	−35.4301	−1.50122	−0.750611	+	0.660744i	$0.770241\pi$
$558$	−4.65293	−0.196974
$559$	−48.8396	−2.06570
$560$	−1.00000	−0.0422577
$561$	8.70720	0.367618
$562$	−22.5390	−0.950751
$563$	35.7522	1.50678	0.753388	−	0.657577i	$-0.228418\pi$
$563$	35.7522	1.50678	0.753388	+	0.657577i	$0.228418\pi$
$564$	8.98192	0.378207
$565$	10.3290	0.434544
$566$	−2.45597	−0.103232
$567$	1.00000	0.0419961
$568$	−3.13391	−0.131496
$569$	40.4860	1.69726	0.848631	−	0.528986i	$-0.177427\pi$
$569$	40.4860	1.69726	0.848631	+	0.528986i	$0.177427\pi$
$570$	2.59176	0.108557
$571$	−2.63673	−0.110344	−0.0551719	−	0.998477i	$-0.517571\pi$
$571$	−2.63673	−0.110344	−0.0551719	+	0.998477i	$0.517571\pi$
$572$	−6.91571	−0.289161
$573$	10.8184	0.451944
$574$	−0.694134	−0.0289726
$575$	−1.00000	−0.0417029
$576$	1.00000	0.0416667
$577$	26.9045	1.12005	0.560025	−	0.828475i	$-0.310791\pi$
$577$	26.9045	1.12005	0.560025	+	0.828475i	$0.310791\pi$
$578$	−36.0843	−1.50091
$579$	−7.08429	−0.294413
$580$	6.74375	0.280019
$581$	−4.20161	−0.174312
$582$	6.64138	0.275294
$583$	9.48751	0.392932
$584$	−3.63485	−0.150411
$585$	5.78684	0.239256
$586$	15.9638	0.659460
$587$	17.6598	0.728900	0.364450	−	0.931223i	$-0.381257\pi$
$587$	17.6598	0.728900	0.364450	+	0.931223i	$0.381257\pi$
$588$	−1.00000	−0.0412393
$589$	−12.0593	−0.496895
$590$	7.24470	0.298259
$591$	7.30587	0.300523
$592$	−5.24470	−0.215556
$593$	16.5468	0.679495	0.339748	−	0.940517i	$-0.389658\pi$
$593$	16.5468	0.679495	0.339748	+	0.940517i	$0.389658\pi$
$594$	1.19508	0.0490346
$595$	7.28590	0.298693
$596$	−0.390153	−0.0159813
$597$	−16.8795	−0.690834
$598$	−5.78684	−0.236641
$599$	−2.27120	−0.0927987	−0.0463994	−	0.998923i	$-0.514775\pi$
$599$	−2.27120	−0.0927987	−0.0463994	+	0.998923i	$0.514775\pi$
$600$	1.00000	0.0408248
$601$	−9.87766	−0.402918	−0.201459	−	0.979497i	$-0.564568\pi$
$601$	−9.87766	−0.402918	−0.201459	+	0.979497i	$0.564568\pi$
$602$	−8.43977	−0.343979
$603$	−6.04962	−0.246360
$604$	−7.57368	−0.308169
$605$	9.57179	0.389149
$606$	−13.0315	−0.529370
$607$	−11.5571	−0.469088	−0.234544	−	0.972105i	$-0.575360\pi$
$607$	−11.5571	−0.469088	−0.234544	+	0.972105i	$0.575360\pi$
$608$	2.59176	0.105110
$609$	6.74375	0.273271
$610$	−0.390153	−0.0157968
$611$	51.9769	2.10276
$612$	−7.28590	−0.294515
$613$	38.9138	1.57172	0.785858	−	0.618407i	$-0.212222\pi$
$613$	38.9138	1.57172	0.785858	+	0.618407i	$0.212222\pi$
$614$	32.4532	1.30971
$615$	0.694134	0.0279902
$616$	−1.19508	−0.0481510
$617$	−43.6117	−1.75574	−0.877871	−	0.478896i	$-0.841037\pi$
$617$	−43.6117	−1.75574	−0.877871	+	0.478896i	$0.841037\pi$
$618$	−5.30587	−0.213433
$619$	16.1785	0.650269	0.325135	−	0.945668i	$-0.394590\pi$
$619$	16.1785	0.650269	0.325135	+	0.945668i	$0.394590\pi$
$620$	−4.65293	−0.186866
$621$	1.00000	0.0401286
$622$	9.39669	0.376773
$623$	1.45786	0.0584078
$624$	5.78684	0.231659
$625$	1.00000	0.0400000
$626$	−30.8230	−1.23194
$627$	3.09735	0.123696
$628$	−11.1835	−0.446271
$629$	38.2123	1.52362
$630$	1.00000	0.0398410
$631$	41.4726	1.65100	0.825498	−	0.564404i	$-0.190894\pi$
$631$	41.4726	1.65100	0.825498	+	0.564404i	$0.190894\pi$
$632$	−12.3290	−0.490421
$633$	−5.18353	−0.206027
$634$	−20.1854	−0.801665
$635$	−4.43977	−0.176187
$636$	−7.93883	−0.314795
$637$	−5.78684	−0.229283
$638$	8.05930	0.319071
$639$	3.13391	0.123975
$640$	1.00000	0.0395285
$641$	−24.8068	−0.979811	−0.489905	−	0.871776i	$-0.662969\pi$
$641$	−24.8068	−0.979811	−0.489905	+	0.871776i	$0.662969\pi$
$642$	14.7934	0.583848
$643$	−18.7276	−0.738543	−0.369271	−	0.929322i	$-0.620393\pi$
$643$	−18.7276	−0.738543	−0.369271	+	0.929322i	$0.620393\pi$
$644$	−1.00000	−0.0394055
$645$	8.43977	0.332316
$646$	−18.8833	−0.742954
$647$	37.0581	1.45690	0.728451	−	0.685098i	$-0.240240\pi$
$647$	37.0581	1.45690	0.728451	+	0.685098i	$0.240240\pi$
$648$	−1.00000	−0.0392837
$649$	8.65796	0.339855
$650$	5.78684	0.226979
$651$	−4.65293	−0.182363
$652$	23.5737	0.923216
$653$	28.5886	1.11876	0.559380	−	0.828911i	$-0.311039\pi$
$653$	28.5886	1.11876	0.559380	+	0.828911i	$0.311039\pi$
$654$	3.30587	0.129270
$655$	−6.24281	−0.243927
$656$	0.694134	0.0271014
$657$	3.63485	0.141809
$658$	8.98192	0.350152
$659$	2.50094	0.0974229	0.0487114	−	0.998813i	$-0.484489\pi$
$659$	2.50094	0.0974229	0.0487114	+	0.998813i	$0.484489\pi$
$660$	1.19508	0.0465183
$661$	14.3040	0.556360	0.278180	−	0.960529i	$-0.410269\pi$
$661$	14.3040	0.556360	0.278180	+	0.960529i	$0.410269\pi$
$662$	4.96195	0.192851
$663$	−42.1623	−1.63745
$664$	4.20161	0.163054
$665$	2.59176	0.100504
$666$	5.24470	0.203228
$667$	6.74375	0.261119
$668$	18.4694	0.714603
$669$	−18.7276	−0.724049
$670$	−6.04962	−0.233717
$671$	−0.466262	−0.0179998
$672$	1.00000	0.0385758
$673$	−4.57179	−0.176230	−0.0881148	−	0.996110i	$-0.528084\pi$
$673$	−4.57179	−0.176230	−0.0881148	+	0.996110i	$0.528084\pi$
$674$	−4.58334	−0.176544
$675$	−1.00000	−0.0384900
$676$	20.4875	0.787981
$677$	13.2697	0.509996	0.254998	−	0.966942i	$-0.417925\pi$
$677$	13.2697	0.509996	0.254998	+	0.966942i	$0.417925\pi$
$678$	−10.3290	−0.396682
$679$	6.64138	0.254873
$680$	−7.28590	−0.279401
$681$	21.2859	0.815677
$682$	−5.56061	−0.212927
$683$	−10.8758	−0.416150	−0.208075	−	0.978113i	$-0.566720\pi$
$683$	−10.8758	−0.416150	−0.208075	+	0.978113i	$0.566720\pi$
$684$	−2.59176	−0.0990985
$685$	11.6348	0.444545
$686$	−1.00000	−0.0381802
$687$	−18.1816	−0.693673
$688$	8.43977	0.321763
$689$	−45.9407	−1.75020
$690$	1.00000	0.0380693
$691$	−4.45132	−0.169336	−0.0846682	−	0.996409i	$-0.526983\pi$
$691$	−4.45132	−0.169336	−0.0846682	+	0.996409i	$0.526983\pi$
$692$	−8.92074	−0.339116
$693$	1.19508	0.0453972
$694$	−10.2678	−0.389761
$695$	−7.24470	−0.274807
$696$	−6.74375	−0.255621
$697$	−5.05738	−0.191562
$698$	14.6779	0.555568
$699$	−19.9638	−0.755101
$700$	1.00000	0.0377964
$701$	4.16857	0.157445	0.0787224	−	0.996897i	$-0.474916\pi$
$701$	4.16857	0.157445	0.0787224	+	0.996897i	$0.474916\pi$
$702$	−5.78684	−0.218410
$703$	13.5930	0.512670
$704$	1.19508	0.0450411
$705$	−8.98192	−0.338279
$706$	−8.54679	−0.321663
$707$	−13.0315	−0.490101
$708$	−7.24470	−0.272272
$709$	−38.0269	−1.42813	−0.714065	−	0.700079i	$-0.753148\pi$
$709$	−38.0269	−1.42813	−0.714065	+	0.700079i	$0.753148\pi$
$710$	3.13391	0.117613
$711$	12.3290	0.462373
$712$	−1.45786	−0.0546355
$713$	−4.65293	−0.174254
$714$	−7.28590	−0.272668
$715$	6.91571	0.258633
$716$	3.77842	0.141206
$717$	24.7938	0.925940
$718$	−16.4513	−0.613958
$719$	2.95730	0.110289	0.0551443	−	0.998478i	$-0.482438\pi$
$719$	2.95730	0.110289	0.0551443	+	0.998478i	$0.482438\pi$
$720$	−1.00000	−0.0372678
$721$	−5.30587	−0.197601
$722$	12.2828	0.457117
$723$	−20.5918	−0.765816
$724$	−15.4875	−0.575589
$725$	−6.74375	−0.250457
$726$	−9.57179	−0.355243
$727$	−34.8434	−1.29227	−0.646135	−	0.763223i	$-0.723616\pi$
$727$	−34.8434	−1.29227	−0.646135	+	0.763223i	$0.723616\pi$
$728$	5.78684	0.214475
$729$	1.00000	0.0370370
$730$	3.63485	0.134532
$731$	−61.4913	−2.27434
$732$	0.390153	0.0144205
$733$	−1.59678	−0.0589784	−0.0294892	−	0.999565i	$-0.509388\pi$
$733$	−1.59678	−0.0589784	−0.0294892	+	0.999565i	$0.509388\pi$
$734$	10.6941	0.394728
$735$	1.00000	0.0368856
$736$	1.00000	0.0368605
$737$	−7.22976	−0.266312
$738$	−0.694134	−0.0255514
$739$	−49.3652	−1.81593	−0.907963	−	0.419049i	$-0.862363\pi$
$739$	−49.3652	−1.81593	−0.907963	+	0.419049i	$0.862363\pi$
$740$	5.24470	0.192799
$741$	−14.9981	−0.550970
$742$	−7.93883	−0.291444
$743$	4.86271	0.178395	0.0891977	−	0.996014i	$-0.471570\pi$
$743$	4.86271	0.178395	0.0891977	+	0.996014i	$0.471570\pi$
$744$	4.65293	0.170585
$745$	0.390153	0.0142941
$746$	−26.5106	−0.970623
$747$	−4.20161	−0.153729
$748$	−8.70720	−0.318367
$749$	14.7934	0.540538
$750$	−1.00000	−0.0365148
$751$	−22.1205	−0.807187	−0.403594	−	0.914938i	$-0.632239\pi$
$751$	−22.1205	−0.807187	−0.403594	+	0.914938i	$0.632239\pi$
$752$	−8.98192	−0.327537
$753$	17.9472	0.654034
$754$	−39.0250	−1.42121
$755$	7.57368	0.275634
$756$	−1.00000	−0.0363696
$757$	−31.9888	−1.16265	−0.581327	−	0.813670i	$-0.697466\pi$
$757$	−31.9888	−1.16265	−0.581327	+	0.813670i	$0.697466\pi$
$758$	−6.71913	−0.244050
$759$	1.19508	0.0433785
$760$	−2.59176	−0.0940131
$761$	50.5125	1.83108	0.915539	−	0.402230i	$-0.131765\pi$
$761$	50.5125	1.83108	0.915539	+	0.402230i	$0.131765\pi$
$762$	4.43977	0.160836
$763$	3.30587	0.119680
$764$	−10.8184	−0.391395
$765$	7.28590	0.263422
$766$	35.3290	1.27649
$767$	−41.9239	−1.51378
$768$	−1.00000	−0.0360844
$769$	50.8596	1.83404	0.917022	−	0.398838i	$-0.130586\pi$
$769$	50.8596	1.83404	0.917022	+	0.398838i	$0.130586\pi$
$770$	1.19508	0.0430676
$771$	9.32710	0.335907
$772$	7.08429	0.254969
$773$	31.4383	1.13076	0.565378	−	0.824832i	$-0.308730\pi$
$773$	31.4383	1.13076	0.565378	+	0.824832i	$0.308730\pi$
$774$	−8.43977	−0.303361
$775$	4.65293	0.167138
$776$	−6.64138	−0.238412
$777$	5.24470	0.188152
$778$	−4.91571	−0.176237
$779$	−1.79903	−0.0644569
$780$	−5.78684	−0.207202
$781$	3.74526	0.134016
$782$	−7.28590	−0.260543
$783$	6.74375	0.241002
$784$	1.00000	0.0357143
$785$	11.1835	0.399157
$786$	6.24281	0.222674
$787$	−18.8924	−0.673440	−0.336720	−	0.941605i	$-0.609318\pi$
$787$	−18.8924	−0.673440	−0.336720	+	0.941605i	$0.609318\pi$
$788$	−7.30587	−0.260261
$789$	−16.3040	−0.580437
$790$	12.3290	0.438645
$791$	−10.3290	−0.367256
$792$	−1.19508	−0.0424652
$793$	2.25775	0.0801750
$794$	−13.4829	−0.478489
$795$	7.93883	0.281561
$796$	16.8795	0.598280
$797$	−14.4032	−0.510188	−0.255094	−	0.966916i	$-0.582106\pi$
$797$	−14.4032	−0.510188	−0.255094	+	0.966916i	$0.582106\pi$
$798$	−2.59176	−0.0917474
$799$	65.4413	2.31515
$800$	−1.00000	−0.0353553
$801$	1.45786	0.0515108
$802$	−14.5621	−0.514206
$803$	4.34392	0.153294
$804$	6.04962	0.213354
$805$	1.00000	0.0352454
$806$	26.9258	0.948420
$807$	−4.45597	−0.156858
$808$	13.0315	0.458448
$809$	−10.7896	−0.379342	−0.189671	−	0.981848i	$-0.560742\pi$
$809$	−10.7896	−0.379342	−0.189671	+	0.981848i	$0.560742\pi$
$810$	1.00000	0.0351364
$811$	0.124241	0.00436268	0.00218134	−	0.999998i	$-0.499306\pi$
$811$	0.124241	0.00436268	0.00218134	+	0.999998i	$0.499306\pi$
$812$	−6.74375	−0.236659
$813$	−23.0200	−0.807346
$814$	6.26781	0.219687
$815$	−23.5737	−0.825750
$816$	7.28590	0.255057
$817$	−21.8739	−0.765270
$818$	−12.8165	−0.448118
$819$	−5.78684	−0.202209
$820$	−0.694134	−0.0242402
$821$	29.9735	1.04608	0.523041	−	0.852307i	$-0.324797\pi$
$821$	29.9735	1.04608	0.523041	+	0.852307i	$0.324797\pi$
$822$	−11.6348	−0.405812
$823$	9.66324	0.336839	0.168420	−	0.985715i	$-0.446134\pi$
$823$	9.66324	0.336839	0.168420	+	0.985715i	$0.446134\pi$
$824$	5.30587	0.184839
$825$	−1.19508	−0.0416072
$826$	−7.24470	−0.252075
$827$	33.1604	1.15310	0.576550	−	0.817062i	$-0.304398\pi$
$827$	33.1604	1.15310	0.576550	+	0.817062i	$0.304398\pi$
$828$	−1.00000	−0.0347524
$829$	4.79650	0.166589	0.0832947	−	0.996525i	$-0.473456\pi$
$829$	4.79650	0.166589	0.0832947	+	0.996525i	$0.473456\pi$
$830$	−4.20161	−0.145840
$831$	−19.7057	−0.683583
$832$	−5.78684	−0.200623
$833$	−7.28590	−0.252441
$834$	7.24470	0.250863
$835$	−18.4694	−0.639161
$836$	−3.09735	−0.107124
$837$	−4.65293	−0.160829
$838$	−0.641383	−0.0221562
$839$	−36.8795	−1.27322	−0.636612	−	0.771185i	$-0.719665\pi$
$839$	−36.8795	−1.27322	−0.636612	+	0.771185i	$0.719665\pi$
$840$	−1.00000	−0.0345033
$841$	16.4782	0.568214
$842$	37.0250	1.27597
$843$	−22.5390	−0.776285
$844$	5.18353	0.178424
$845$	−20.4875	−0.704792
$846$	8.98192	0.308805
$847$	−9.57179	−0.328891
$848$	7.93883	0.272621
$849$	−2.45597	−0.0842887
$850$	7.28590	0.249904
$851$	5.24470	0.179786
$852$	−3.13391	−0.107366
$853$	−4.27623	−0.146415	−0.0732077	−	0.997317i	$-0.523324\pi$
$853$	−4.27623	−0.146415	−0.0732077	+	0.997317i	$0.523324\pi$
$854$	0.390153	0.0133507
$855$	2.59176	0.0886364
$856$	−14.7934	−0.505627
$857$	−22.2559	−0.760246	−0.380123	−	0.924936i	$-0.624118\pi$
$857$	−22.2559	−0.760246	−0.380123	+	0.924936i	$0.624118\pi$
$858$	−6.91571	−0.236099
$859$	19.3040	0.658644	0.329322	−	0.944218i	$-0.393180\pi$
$859$	19.3040	0.658644	0.329322	+	0.944218i	$0.393180\pi$
$860$	−8.43977	−0.287794
$861$	−0.694134	−0.0236560
$862$	−29.0362	−0.988976
$863$	−47.9870	−1.63350	−0.816748	−	0.576995i	$-0.804225\pi$
$863$	−47.9870	−1.63350	−0.816748	+	0.576995i	$0.804225\pi$
$864$	1.00000	0.0340207
$865$	8.92074	0.303314
$866$	−4.27433	−0.145248
$867$	−36.0843	−1.22549
$868$	4.65293	0.157931
$869$	14.7341	0.499819
$870$	6.74375	0.228635
$871$	35.0082	1.18621
$872$	−3.30587	−0.111951
$873$	6.64138	0.224777
$874$	−2.59176	−0.0876677
$875$	−1.00000	−0.0338062
$876$	−3.63485	−0.122810
$877$	7.01534	0.236891	0.118446	−	0.992961i	$-0.462209\pi$
$877$	7.01534	0.236891	0.118446	+	0.992961i	$0.462209\pi$
$878$	−20.2266	−0.682615
$879$	15.9638	0.538447
$880$	−1.19508	−0.0402860
$881$	−18.0166	−0.606994	−0.303497	−	0.952832i	$-0.598154\pi$
$881$	−18.0166	−0.606994	−0.303497	+	0.952832i	$0.598154\pi$
$882$	−1.00000	−0.0336718
$883$	−42.5487	−1.43188	−0.715939	−	0.698163i	$-0.754001\pi$
$883$	−42.5487	−1.43188	−0.715939	+	0.698163i	$0.754001\pi$
$884$	42.1623	1.41807
$885$	7.24470	0.243528
$886$	8.09924	0.272099
$887$	−15.0681	−0.505937	−0.252968	−	0.967475i	$-0.581407\pi$
$887$	−15.0681	−0.505937	−0.252968	+	0.967475i	$0.581407\pi$
$888$	−5.24470	−0.176000
$889$	4.43977	0.148905
$890$	1.45786	0.0488675
$891$	1.19508	0.0400366
$892$	18.7276	0.627045
$893$	23.2790	0.779002
$894$	−0.390153	−0.0130487
$895$	−3.77842	−0.126299
$896$	−1.00000	−0.0334077
$897$	−5.78684	−0.193217
$898$	22.3309	0.745191
$899$	−31.3782	−1.04652
$900$	1.00000	0.0333333
$901$	−57.8415	−1.92698
$902$	−0.829542	−0.0276207
$903$	−8.43977	−0.280858
$904$	10.3290	0.343537
$905$	15.4875	0.514822
$906$	−7.57368	−0.251619
$907$	−36.1358	−1.19987	−0.599935	−	0.800049i	$-0.704807\pi$
$907$	−36.1358	−1.19987	−0.599935	+	0.800049i	$0.704807\pi$
$908$	−21.2859	−0.706397
$909$	−13.0315	−0.432229
$910$	−5.78684	−0.191832
$911$	52.9138	1.75311	0.876557	−	0.481298i	$-0.159835\pi$
$911$	52.9138	1.75311	0.876557	+	0.481298i	$0.159835\pi$
$912$	2.59176	0.0858218
$913$	−5.02124	−0.166179
$914$	−12.6002	−0.416777
$915$	−0.390153	−0.0128980
$916$	18.1816	0.600738
$917$	6.24281	0.206156
$918$	−7.28590	−0.240470
$919$	54.7553	1.80621	0.903106	−	0.429418i	$-0.141281\pi$
$919$	54.7553	1.80621	0.903106	+	0.429418i	$0.141281\pi$
$920$	−1.00000	−0.0329690
$921$	32.4532	1.06937
$922$	5.63950	0.185727
$923$	−18.1354	−0.596934
$924$	−1.19508	−0.0393151
$925$	−5.24470	−0.172445
$926$	22.4036	0.736228
$927$	−5.30587	−0.174268
$928$	6.74375	0.221375
$929$	50.9888	1.67289	0.836445	−	0.548051i	$-0.184630\pi$
$929$	50.9888	1.67289	0.836445	+	0.548051i	$0.184630\pi$
$930$	−4.65293	−0.152576
$931$	−2.59176	−0.0849416
$932$	19.9638	0.653937
$933$	9.39669	0.307634
$934$	−6.37018	−0.208439
$935$	8.70720	0.284756
$936$	5.78684	0.189149
$937$	27.2169	0.889139	0.444569	−	0.895744i	$-0.353357\pi$
$937$	27.2169	0.889139	0.444569	+	0.895744i	$0.353357\pi$
$938$	6.04962	0.197527
$939$	−30.8230	−1.00587
$940$	8.98192	0.292958
$941$	9.09735	0.296565	0.148283	−	0.988945i	$-0.452625\pi$
$941$	9.09735	0.296565	0.148283	+	0.988945i	$0.452625\pi$
$942$	−11.1835	−0.364379
$943$	−0.694134	−0.0226041
$944$	7.24470	0.235795
$945$	1.00000	0.0325300
$946$	−10.0862	−0.327930
$947$	6.25097	0.203129	0.101565	−	0.994829i	$-0.467615\pi$
$947$	6.25097	0.203129	0.101565	+	0.994829i	$0.467615\pi$
$948$	−12.3290	−0.400427
$949$	−21.0343	−0.682802
$950$	2.59176	0.0840879
$951$	−20.1854	−0.654557
$952$	7.28590	0.236137
$953$	41.3040	1.33797	0.668984	−	0.743277i	$-0.266730\pi$
$953$	41.3040	1.33797	0.668984	+	0.743277i	$0.266730\pi$
$954$	−7.93883	−0.257029
$955$	10.8184	0.350074
$956$	−24.7938	−0.801887
$957$	8.05930	0.260520
$958$	−38.7703	−1.25261
$959$	−11.6348	−0.375709
$960$	1.00000	0.0322749
$961$	−9.35021	−0.301620
$962$	−30.3502	−0.978530
$963$	14.7934	0.476710
$964$	20.5918	0.663216
$965$	−7.08429	−0.228051
$966$	−1.00000	−0.0321745
$967$	5.27938	0.169773	0.0848867	−	0.996391i	$-0.472947\pi$
$967$	5.27938	0.169773	0.0848867	+	0.996391i	$0.472947\pi$
$968$	9.57179	0.307649
$969$	−18.8833	−0.606619
$970$	6.64138	0.213242
$971$	−46.2844	−1.48534	−0.742668	−	0.669659i	$-0.766440\pi$
$971$	−46.2844	−1.48534	−0.742668	+	0.669659i	$0.766440\pi$
$972$	−1.00000	−0.0320750
$973$	7.24470	0.232254
$974$	33.1801	1.06316
$975$	5.78684	0.185327
$976$	−0.390153	−0.0124885
$977$	−22.6330	−0.724093	−0.362046	−	0.932160i	$-0.617922\pi$
$977$	−22.6330	−0.724093	−0.362046	+	0.932160i	$0.617922\pi$
$978$	23.5737	0.753803
$979$	1.74225	0.0556826
$980$	−1.00000	−0.0319438
$981$	3.30587	0.105548
$982$	14.8758	0.474705
$983$	−9.56991	−0.305233	−0.152616	−	0.988286i	$-0.548770\pi$
$983$	−9.56991	−0.305233	−0.152616	+	0.988286i	$0.548770\pi$
$984$	0.694134	0.0221282
$985$	7.30587	0.232784
$986$	−49.1343	−1.56475
$987$	8.98192	0.285898
$988$	14.9981	0.477154
$989$	−8.43977	−0.268369
$990$	1.19508	0.0379820
$991$	−7.81836	−0.248358	−0.124179	−	0.992260i	$-0.539630\pi$
$991$	−7.81836	−0.248358	−0.124179	+	0.992260i	$0.539630\pi$
$992$	−4.65293	−0.147731
$993$	4.96195	0.157463
$994$	−3.13391	−0.0994015
$995$	−16.8795	−0.535118
$996$	4.20161	0.133133
$997$	−28.3262	−0.897101	−0.448550	−	0.893758i	$-0.648060\pi$
$997$	−28.3262	−0.897101	−0.448550	+	0.893758i	$0.648060\pi$
$998$	−13.1835	−0.417317
$999$	5.24470	0.165935

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4830.2.a.cd.1.3	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4830.2.a.cd.1.3	✓	4	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:	\( N \)	\(=\)	\( 4830 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4830.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +1.19508 q^{11} -1.00000 q^{12} -5.78684 q^{13} -1.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} -7.28590 q^{17} -1.00000 q^{18} -2.59176 q^{19} -1.00000 q^{20} -1.00000 q^{21} -1.19508 q^{22} -1.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} +5.78684 q^{26} -1.00000 q^{27} +1.00000 q^{28} -6.74375 q^{29} -1.00000 q^{30} +4.65293 q^{31} -1.00000 q^{32} -1.19508 q^{33} +7.28590 q^{34} -1.00000 q^{35} +1.00000 q^{36} -5.24470 q^{37} +2.59176 q^{38} +5.78684 q^{39} +1.00000 q^{40} +0.694134 q^{41} +1.00000 q^{42} +8.43977 q^{43} +1.19508 q^{44} -1.00000 q^{45} +1.00000 q^{46} -8.98192 q^{47} -1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} +7.28590 q^{51} -5.78684 q^{52} +7.93883 q^{53} +1.00000 q^{54} -1.19508 q^{55} -1.00000 q^{56} +2.59176 q^{57} +6.74375 q^{58} +7.24470 q^{59} +1.00000 q^{60} -0.390153 q^{61} -4.65293 q^{62} +1.00000 q^{63} +1.00000 q^{64} +5.78684 q^{65} +1.19508 q^{66} -6.04962 q^{67} -7.28590 q^{68} +1.00000 q^{69} +1.00000 q^{70} +3.13391 q^{71} -1.00000 q^{72} +3.63485 q^{73} +5.24470 q^{74} -1.00000 q^{75} -2.59176 q^{76} +1.19508 q^{77} -5.78684 q^{78} +12.3290 q^{79} -1.00000 q^{80} +1.00000 q^{81} -0.694134 q^{82} -4.20161 q^{83} -1.00000 q^{84} +7.28590 q^{85} -8.43977 q^{86} +6.74375 q^{87} -1.19508 q^{88} +1.45786 q^{89} +1.00000 q^{90} -5.78684 q^{91} -1.00000 q^{92} -4.65293 q^{93} +8.98192 q^{94} +2.59176 q^{95} +1.00000 q^{96} +6.64138 q^{97} -1.00000 q^{98} +1.19508 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^7 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{8} + 4 q^{9} + 4 q^{10} + 2 q^{11} - 4 q^{12} + 4 q^{13} - 4 q^{14} + 4 q^{15} + 4 q^{16} - 2 q^{17} - 4 q^{18} + 14 q^{19} - 4 q^{20} - 4 q^{21} - 2 q^{22} - 4 q^{23} + 4 q^{24} + 4 q^{25} - 4 q^{26} - 4 q^{27} + 4 q^{28} - 4 q^{29} - 4 q^{30} + 20 q^{31} - 4 q^{32} - 2 q^{33} + 2 q^{34} - 4 q^{35} + 4 q^{36} + 2 q^{37} - 14 q^{38} - 4 q^{39} + 4 q^{40} + 4 q^{42} + 8 q^{43} + 2 q^{44} - 4 q^{45} + 4 q^{46} - 6 q^{47} - 4 q^{48} + 4 q^{49} - 4 q^{50} + 2 q^{51} + 4 q^{52} + 6 q^{53} + 4 q^{54} - 2 q^{55} - 4 q^{56} - 14 q^{57} + 4 q^{58} + 6 q^{59} + 4 q^{60} + 4 q^{61} - 20 q^{62} + 4 q^{63} + 4 q^{64} - 4 q^{65} + 2 q^{66} - 4 q^{67} - 2 q^{68} + 4 q^{69} + 4 q^{70} - 16 q^{71} - 4 q^{72} - 14 q^{73} - 2 q^{74} - 4 q^{75} + 14 q^{76} + 2 q^{77} + 4 q^{78} + 18 q^{79} - 4 q^{80} + 4 q^{81} + 2 q^{83} - 4 q^{84} + 2 q^{85} - 8 q^{86} + 4 q^{87} - 2 q^{88} + 10 q^{89} + 4 q^{90} + 4 q^{91} - 4 q^{92} - 20 q^{93} + 6 q^{94} - 14 q^{95} + 4 q^{96} - 18 q^{97} - 4 q^{98} + 2 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^7 - 4 * q^8 + 4 * q^9 + 4 * q^10 + 2 * q^11 - 4 * q^12 + 4 * q^13 - 4 * q^14 + 4 * q^15 + 4 * q^16 - 2 * q^17 - 4 * q^18 + 14 * q^19 - 4 * q^20 - 4 * q^21 - 2 * q^22 - 4 * q^23 + 4 * q^24 + 4 * q^25 - 4 * q^26 - 4 * q^27 + 4 * q^28 - 4 * q^29 - 4 * q^30 + 20 * q^31 - 4 * q^32 - 2 * q^33 + 2 * q^34 - 4 * q^35 + 4 * q^36 + 2 * q^37 - 14 * q^38 - 4 * q^39 + 4 * q^40 + 4 * q^42 + 8 * q^43 + 2 * q^44 - 4 * q^45 + 4 * q^46 - 6 * q^47 - 4 * q^48 + 4 * q^49 - 4 * q^50 + 2 * q^51 + 4 * q^52 + 6 * q^53 + 4 * q^54 - 2 * q^55 - 4 * q^56 - 14 * q^57 + 4 * q^58 + 6 * q^59 + 4 * q^60 + 4 * q^61 - 20 * q^62 + 4 * q^63 + 4 * q^64 - 4 * q^65 + 2 * q^66 - 4 * q^67 - 2 * q^68 + 4 * q^69 + 4 * q^70 - 16 * q^71 - 4 * q^72 - 14 * q^73 - 2 * q^74 - 4 * q^75 + 14 * q^76 + 2 * q^77 + 4 * q^78 + 18 * q^79 - 4 * q^80 + 4 * q^81 + 2 * q^83 - 4 * q^84 + 2 * q^85 - 8 * q^86 + 4 * q^87 - 2 * q^88 + 10 * q^89 + 4 * q^90 + 4 * q^91 - 4 * q^92 - 20 * q^93 + 6 * q^94 - 14 * q^95 + 4 * q^96 - 18 * q^97 - 4 * q^98 + 2 * q^99

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