LMFDB - Embedded newform 4830.2.a.ce.1.4

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:	4.4.6809.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} - x + 1 $ x^4 - 5*x^2 - x + 1
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			1.4
Root			$2.29041$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +4.58082 q^{11} +1.00000 q^{12} -3.70762 q^{13} +1.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} -0.873206 q^{17} +1.00000 q^{18} +1.12679 q^{19} +1.00000 q^{20} +1.00000 q^{21} +4.58082 q^{22} +1.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} -3.70762 q^{26} +1.00000 q^{27} +1.00000 q^{28} +9.36517 q^{29} +1.00000 q^{30} -0.0888596 q^{31} +1.00000 q^{32} +4.58082 q^{33} -0.873206 q^{34} +1.00000 q^{35} +1.00000 q^{36} +0.962065 q^{37} +1.12679 q^{38} -3.70762 q^{39} +1.00000 q^{40} -10.9839 q^{41} +1.00000 q^{42} +5.79647 q^{43} +4.58082 q^{44} +1.00000 q^{45} +1.00000 q^{46} -6.28844 q^{47} +1.00000 q^{48} +1.00000 q^{49} +1.00000 q^{50} -0.873206 q^{51} -3.70762 q^{52} +3.03793 q^{53} +1.00000 q^{54} +4.58082 q^{55} +1.00000 q^{56} +1.12679 q^{57} +9.36517 q^{58} -6.19958 q^{59} +1.00000 q^{60} +9.41523 q^{61} -0.0888596 q^{62} +1.00000 q^{63} +1.00000 q^{64} -3.70762 q^{65} +4.58082 q^{66} +3.36517 q^{67} -0.873206 q^{68} +1.00000 q^{69} +1.00000 q^{70} -1.61876 q^{71} +1.00000 q^{72} +8.19958 q^{73} +0.962065 q^{74} +1.00000 q^{75} +1.12679 q^{76} +4.58082 q^{77} -3.70762 q^{78} -1.03793 q^{79} +1.00000 q^{80} +1.00000 q^{81} -10.9839 q^{82} -8.03485 q^{83} +1.00000 q^{84} -0.873206 q^{85} +5.79647 q^{86} +9.36517 q^{87} +4.58082 q^{88} -14.0849 q^{89} +1.00000 q^{90} -3.70762 q^{91} +1.00000 q^{92} -0.0888596 q^{93} -6.28844 q^{94} +1.12679 q^{95} +1.00000 q^{96} +8.23837 q^{97} +1.00000 q^{98} +4.58082 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 4 q^{12} + 2 q^{13} + 4 q^{14} + 4 q^{15} + 4 q^{16} - 2 q^{17} + 4 q^{18} + 6 q^{19} + 4 q^{20} + 4 q^{21} + 4 q^{23} + 4 q^{24} + 4 q^{25} + 2 q^{26} + 4 q^{27} + 4 q^{28} + 14 q^{29} + 4 q^{30} - 4 q^{31} + 4 q^{32} - 2 q^{34} + 4 q^{35} + 4 q^{36} + 6 q^{37} + 6 q^{38} + 2 q^{39} + 4 q^{40} + 4 q^{42} + 10 q^{43} + 4 q^{45} + 4 q^{46} + 10 q^{47} + 4 q^{48} + 4 q^{49} + 4 q^{50} - 2 q^{51} + 2 q^{52} + 10 q^{53} + 4 q^{54} + 4 q^{56} + 6 q^{57} + 14 q^{58} + 14 q^{59} + 4 q^{60} + 4 q^{61} - 4 q^{62} + 4 q^{63} + 4 q^{64} + 2 q^{65} - 10 q^{67} - 2 q^{68} + 4 q^{69} + 4 q^{70} + 14 q^{71} + 4 q^{72} - 6 q^{73} + 6 q^{74} + 4 q^{75} + 6 q^{76} + 2 q^{78} - 2 q^{79} + 4 q^{80} + 4 q^{81} + 6 q^{83} + 4 q^{84} - 2 q^{85} + 10 q^{86} + 14 q^{87} - 8 q^{89} + 4 q^{90} + 2 q^{91} + 4 q^{92} - 4 q^{93} + 10 q^{94} + 6 q^{95} + 4 q^{96} + 8 q^{97} + 4 q^{98}+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 + 4 * q^12 + 2 * q^13 + 4 * q^14 + 4 * q^15 + 4 * q^16 - 2 * q^17 + 4 * q^18 + 6 * q^19 + 4 * q^20 + 4 * q^21 + 4 * q^23 + 4 * q^24 + 4 * q^25 + 2 * q^26 + 4 * q^27 + 4 * q^28 + 14 * q^29 + 4 * q^30 - 4 * q^31 + 4 * q^32 - 2 * q^34 + 4 * q^35 + 4 * q^36 + 6 * q^37 + 6 * q^38 + 2 * q^39 + 4 * q^40 + 4 * q^42 + 10 * q^43 + 4 * q^45 + 4 * q^46 + 10 * q^47 + 4 * q^48 + 4 * q^49 + 4 * q^50 - 2 * q^51 + 2 * q^52 + 10 * q^53 + 4 * q^54 + 4 * q^56 + 6 * q^57 + 14 * q^58 + 14 * q^59 + 4 * q^60 + 4 * q^61 - 4 * q^62 + 4 * q^63 + 4 * q^64 + 2 * q^65 - 10 * q^67 - 2 * q^68 + 4 * q^69 + 4 * q^70 + 14 * q^71 + 4 * q^72 - 6 * q^73 + 6 * q^74 + 4 * q^75 + 6 * q^76 + 2 * q^78 - 2 * q^79 + 4 * q^80 + 4 * q^81 + 6 * q^83 + 4 * q^84 - 2 * q^85 + 10 * q^86 + 14 * q^87 - 8 * q^89 + 4 * q^90 + 2 * q^91 + 4 * q^92 - 4 * q^93 + 10 * q^94 + 6 * q^95 + 4 * q^96 + 8 * q^97 + 4 * q^98

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
$11$	4.58082	1.38117	0.690585	−	0.723251i	$-0.257353\pi$
$11$	4.58082	1.38117	0.690585	+	0.723251i	$0.257353\pi$
$12$	1.00000	0.288675
$13$	−3.70762	−1.02831	−0.514154	−	0.857698i	$-0.671894\pi$
$13$	−3.70762	−1.02831	−0.514154	+	0.857698i	$0.671894\pi$
$14$	1.00000	0.267261
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	−0.873206	−0.211784	−0.105892	−	0.994378i	$-0.533770\pi$
$17$	−0.873206	−0.211784	−0.105892	+	0.994378i	$0.533770\pi$
$18$	1.00000	0.235702
$19$	1.12679	0.258504	0.129252	−	0.991612i	$-0.458742\pi$
$19$	1.12679	0.258504	0.129252	+	0.991612i	$0.458742\pi$
$20$	1.00000	0.223607
$21$	1.00000	0.218218
$22$	4.58082	0.976634
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	−3.70762	−0.727123
$27$	1.00000	0.192450
$28$	1.00000	0.188982
$29$	9.36517	1.73907	0.869534	−	0.493873i	$-0.164419\pi$
$29$	9.36517	1.73907	0.869534	+	0.493873i	$0.164419\pi$
$30$	1.00000	0.182574
$31$	−0.0888596	−0.0159597	−0.00797983	−	0.999968i	$-0.502540\pi$
$31$	−0.0888596	−0.0159597	−0.00797983	+	0.999968i	$0.502540\pi$
$32$	1.00000	0.176777
$33$	4.58082	0.797419
$34$	−0.873206	−0.149754
$35$	1.00000	0.169031
$36$	1.00000	0.166667
$37$	0.962065	0.158163	0.0790813	−	0.996868i	$-0.474801\pi$
$37$	0.962065	0.158163	0.0790813	+	0.996868i	$0.474801\pi$
$38$	1.12679	0.182790
$39$	−3.70762	−0.593694
$40$	1.00000	0.158114
$41$	−10.9839	−1.71540	−0.857700	−	0.514150i	$-0.828107\pi$
$41$	−10.9839	−1.71540	−0.857700	+	0.514150i	$0.828107\pi$
$42$	1.00000	0.154303
$43$	5.79647	0.883954	0.441977	−	0.897026i	$-0.354277\pi$
$43$	5.79647	0.883954	0.441977	+	0.897026i	$0.354277\pi$
$44$	4.58082	0.690585
$45$	1.00000	0.149071
$46$	1.00000	0.147442
$47$	−6.28844	−0.917263	−0.458631	−	0.888627i	$-0.651660\pi$
$47$	−6.28844	−0.917263	−0.458631	+	0.888627i	$0.651660\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	−0.873206	−0.122273
$52$	−3.70762	−0.514154
$53$	3.03793	0.417292	0.208646	−	0.977991i	$-0.433094\pi$
$53$	3.03793	0.417292	0.208646	+	0.977991i	$0.433094\pi$
$54$	1.00000	0.136083
$55$	4.58082	0.617678
$56$	1.00000	0.133631
$57$	1.12679	0.149248
$58$	9.36517	1.22971
$59$	−6.19958	−0.807116	−0.403558	−	0.914954i	$-0.632227\pi$
$59$	−6.19958	−0.807116	−0.403558	+	0.914954i	$0.632227\pi$
$60$	1.00000	0.129099
$61$	9.41523	1.20550	0.602748	−	0.797931i	$-0.294072\pi$
$61$	9.41523	1.20550	0.602748	+	0.797931i	$0.294072\pi$
$62$	−0.0888596	−0.0112852
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	−3.70762	−0.459873
$66$	4.58082	0.563860
$67$	3.36517	0.411121	0.205560	−	0.978644i	$-0.434098\pi$
$67$	3.36517	0.411121	0.205560	+	0.978644i	$0.434098\pi$
$68$	−0.873206	−0.105892
$69$	1.00000	0.120386
$70$	1.00000	0.119523
$71$	−1.61876	−0.192111	−0.0960555	−	0.995376i	$-0.530623\pi$
$71$	−1.61876	−0.192111	−0.0960555	+	0.995376i	$0.530623\pi$
$72$	1.00000	0.117851
$73$	8.19958	0.959688	0.479844	−	0.877354i	$-0.340693\pi$
$73$	8.19958	0.959688	0.479844	+	0.877354i	$0.340693\pi$
$74$	0.962065	0.111838
$75$	1.00000	0.115470
$76$	1.12679	0.129252
$77$	4.58082	0.522033
$78$	−3.70762	−0.419805
$79$	−1.03793	−0.116777	−0.0583884	−	0.998294i	$-0.518596\pi$
$79$	−1.03793	−0.116777	−0.0583884	+	0.998294i	$0.518596\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−10.9839	−1.21297
$83$	−8.03485	−0.881939	−0.440970	−	0.897522i	$-0.645365\pi$
$83$	−8.03485	−0.881939	−0.440970	+	0.897522i	$0.645365\pi$
$84$	1.00000	0.109109
$85$	−0.873206	−0.0947125
$86$	5.79647	0.625050
$87$	9.36517	1.00405
$88$	4.58082	0.488317
$89$	−14.0849	−1.49300	−0.746499	−	0.665387i	$-0.768267\pi$
$89$	−14.0849	−1.49300	−0.746499	+	0.665387i	$0.768267\pi$
$90$	1.00000	0.105409
$91$	−3.70762	−0.388664
$92$	1.00000	0.104257
$93$	−0.0888596	−0.00921431
$94$	−6.28844	−0.648603
$95$	1.12679	0.115607
$96$	1.00000	0.102062
$97$	8.23837	0.836480	0.418240	−	0.908337i	$-0.362647\pi$
$97$	8.23837	0.836480	0.418240	+	0.908337i	$0.362647\pi$
$98$	1.00000	0.101015
$99$	4.58082	0.460390
$100$	1.00000	0.100000
$101$	9.90719	0.985802	0.492901	−	0.870085i	$-0.335936\pi$
$101$	9.90719	0.985802	0.492901	+	0.870085i	$0.335936\pi$
$102$	−0.873206	−0.0864603
$103$	7.41523	0.730644	0.365322	−	0.930881i	$-0.380959\pi$
$103$	7.41523	0.730644	0.365322	+	0.930881i	$0.380959\pi$
$104$	−3.70762	−0.363562
$105$	1.00000	0.0975900
$106$	3.03793	0.295070
$107$	16.4767	1.59287	0.796434	−	0.604726i	$-0.206717\pi$
$107$	16.4767	1.59287	0.796434	+	0.604726i	$0.206717\pi$
$108$	1.00000	0.0962250
$109$	−18.4767	−1.76975	−0.884876	−	0.465827i	$-0.845757\pi$
$109$	−18.4767	−1.76975	−0.884876	+	0.465827i	$0.845757\pi$
$110$	4.58082	0.436764
$111$	0.962065	0.0913152
$112$	1.00000	0.0944911
$113$	10.4532	0.983351	0.491676	−	0.870778i	$-0.336385\pi$
$113$	10.4532	0.983351	0.491676	+	0.870778i	$0.336385\pi$
$114$	1.12679	0.105534
$115$	1.00000	0.0932505
$116$	9.36517	0.869534
$117$	−3.70762	−0.342769
$118$	−6.19958	−0.570717
$119$	−0.873206	−0.0800467
$120$	1.00000	0.0912871
$121$	9.98392	0.907629
$122$	9.41523	0.852415
$123$	−10.9839	−0.990387
$124$	−0.0888596	−0.00797983
$125$	1.00000	0.0894427
$126$	1.00000	0.0890871
$127$	−3.54289	−0.314380	−0.157190	−	0.987568i	$-0.550244\pi$
$127$	−3.54289	−0.314380	−0.157190	+	0.987568i	$0.550244\pi$
$128$	1.00000	0.0883883
$129$	5.79647	0.510351
$130$	−3.70762	−0.325179
$131$	−4.63088	−0.404602	−0.202301	−	0.979323i	$-0.564842\pi$
$131$	−4.63088	−0.404602	−0.202301	+	0.979323i	$0.564842\pi$
$132$	4.58082	0.398709
$133$	1.12679	0.0977054
$134$	3.36517	0.290706
$135$	1.00000	0.0860663
$136$	−0.873206	−0.0748768
$137$	10.6309	0.908258	0.454129	−	0.890936i	$-0.349951\pi$
$137$	10.6309	0.908258	0.454129	+	0.890936i	$0.349951\pi$
$138$	1.00000	0.0851257
$139$	−19.5389	−1.65727	−0.828636	−	0.559788i	$-0.810882\pi$
$139$	−19.5389	−1.65727	−0.828636	+	0.559788i	$0.810882\pi$
$140$	1.00000	0.0845154
$141$	−6.28844	−0.529582
$142$	−1.61876	−0.135843
$143$	−16.9839	−1.42027
$144$	1.00000	0.0833333
$145$	9.36517	0.777735
$146$	8.19958	0.678602
$147$	1.00000	0.0824786
$148$	0.962065	0.0790813
$149$	−11.1616	−0.914397	−0.457199	−	0.889365i	$-0.651147\pi$
$149$	−11.1616	−0.914397	−0.457199	+	0.889365i	$0.651147\pi$
$150$	1.00000	0.0816497
$151$	11.4152	0.928958	0.464479	−	0.885584i	$-0.346242\pi$
$151$	11.4152	0.928958	0.464479	+	0.885584i	$0.346242\pi$
$152$	1.12679	0.0913951
$153$	−0.873206	−0.0705945
$154$	4.58082	0.369133
$155$	−0.0888596	−0.00713738
$156$	−3.70762	−0.296847
$157$	−0.153462	−0.0122476	−0.00612379	−	0.999981i	$-0.501949\pi$
$157$	−0.153462	−0.0122476	−0.00612379	+	0.999981i	$0.501949\pi$
$158$	−1.03793	−0.0825736
$159$	3.03793	0.240924
$160$	1.00000	0.0790569
$161$	1.00000	0.0788110
$162$	1.00000	0.0785674
$163$	−20.9839	−1.64359	−0.821794	−	0.569785i	$-0.807027\pi$
$163$	−20.9839	−1.64359	−0.821794	+	0.569785i	$0.807027\pi$
$164$	−10.9839	−0.857700
$165$	4.58082	0.356616
$166$	−8.03485	−0.623625
$167$	−0.441898	−0.0341951	−0.0170976	−	0.999854i	$-0.505443\pi$
$167$	−0.441898	−0.0341951	−0.0170976	+	0.999854i	$0.505443\pi$
$168$	1.00000	0.0771517
$169$	0.746412	0.0574163
$170$	−0.873206	−0.0669718
$171$	1.12679	0.0861681
$172$	5.79647	0.441977
$173$	−5.32637	−0.404956	−0.202478	−	0.979287i	$-0.564900\pi$
$173$	−5.32637	−0.404956	−0.202478	+	0.979287i	$0.564900\pi$
$174$	9.36517	0.709972
$175$	1.00000	0.0755929
$176$	4.58082	0.345292
$177$	−6.19958	−0.465989
$178$	−14.0849	−1.05571
$179$	−7.59295	−0.567524	−0.283762	−	0.958895i	$-0.591583\pi$
$179$	−7.59295	−0.567524	−0.283762	+	0.958895i	$0.591583\pi$
$180$	1.00000	0.0745356
$181$	−15.4911	−1.15144	−0.575722	−	0.817645i	$-0.695279\pi$
$181$	−15.4911	−1.15144	−0.575722	+	0.817645i	$0.695279\pi$
$182$	−3.70762	−0.274827
$183$	9.41523	0.695994
$184$	1.00000	0.0737210
$185$	0.962065	0.0707325
$186$	−0.0888596	−0.00651550
$187$	−4.00000	−0.292509
$188$	−6.28844	−0.458631
$189$	1.00000	0.0727393
$190$	1.12679	0.0817462
$191$	−17.5147	−1.26732	−0.633659	−	0.773613i	$-0.718448\pi$
$191$	−17.5147	−1.26732	−0.633659	+	0.773613i	$0.718448\pi$
$192$	1.00000	0.0721688
$193$	19.8161	1.42639	0.713197	−	0.700963i	$-0.247246\pi$
$193$	19.8161	1.42639	0.713197	+	0.700963i	$0.247246\pi$
$194$	8.23837	0.591481
$195$	−3.70762	−0.265508
$196$	1.00000	0.0714286
$197$	−1.82228	−0.129832	−0.0649161	−	0.997891i	$-0.520678\pi$
$197$	−1.82228	−0.129832	−0.0649161	+	0.997891i	$0.520678\pi$
$198$	4.58082	0.325545
$199$	9.16164	0.649452	0.324726	−	0.945808i	$-0.394728\pi$
$199$	9.16164	0.649452	0.324726	+	0.945808i	$0.394728\pi$
$200$	1.00000	0.0707107
$201$	3.36517	0.237361
$202$	9.90719	0.697068
$203$	9.36517	0.657306
$204$	−0.873206	−0.0611366
$205$	−10.9839	−0.767150
$206$	7.41523	0.516644
$207$	1.00000	0.0695048
$208$	−3.70762	−0.257077
$209$	5.16164	0.357038
$210$	1.00000	0.0690066
$211$	−25.0536	−1.72476	−0.862381	−	0.506260i	$-0.831028\pi$
$211$	−25.0536	−1.72476	−0.862381	+	0.506260i	$0.831028\pi$
$212$	3.03793	0.208646
$213$	−1.61876	−0.110915
$214$	16.4767	1.12633
$215$	5.79647	0.395316
$216$	1.00000	0.0680414
$217$	−0.0888596	−0.00603218
$218$	−18.4767	−1.25140
$219$	8.19958	0.554076
$220$	4.58082	0.308839
$221$	3.23751	0.217779
$222$	0.962065	0.0645696
$223$	26.4598	1.77188	0.885940	−	0.463800i	$-0.153514\pi$
$223$	26.4598	1.77188	0.885940	+	0.463800i	$0.153514\pi$
$224$	1.00000	0.0668153
$225$	1.00000	0.0666667
$226$	10.4532	0.695334
$227$	14.7652	0.980000	0.490000	−	0.871723i	$-0.336997\pi$
$227$	14.7652	0.980000	0.490000	+	0.871723i	$0.336997\pi$
$228$	1.12679	0.0746238
$229$	−19.1616	−1.26624	−0.633118	−	0.774055i	$-0.718225\pi$
$229$	−19.1616	−1.26624	−0.633118	+	0.774055i	$0.718225\pi$
$230$	1.00000	0.0659380
$231$	4.58082	0.301396
$232$	9.36517	0.614853
$233$	10.4767	0.686354	0.343177	−	0.939271i	$-0.388497\pi$
$233$	10.4767	0.686354	0.343177	+	0.939271i	$0.388497\pi$
$234$	−3.70762	−0.242374
$235$	−6.28844	−0.410212
$236$	−6.19958	−0.403558
$237$	−1.03793	−0.0674211
$238$	−0.873206	−0.0566015
$239$	−9.61876	−0.622186	−0.311093	−	0.950380i	$-0.600695\pi$
$239$	−9.61876	−0.622186	−0.311093	+	0.950380i	$0.600695\pi$
$240$	1.00000	0.0645497
$241$	8.18831	0.527455	0.263728	−	0.964597i	$-0.415048\pi$
$241$	8.18831	0.527455	0.263728	+	0.964597i	$0.415048\pi$
$242$	9.98392	0.641791
$243$	1.00000	0.0641500
$244$	9.41523	0.602748
$245$	1.00000	0.0638877
$246$	−10.9839	−0.700309
$247$	−4.17772	−0.265822
$248$	−0.0888596	−0.00564259
$249$	−8.03485	−0.509188
$250$	1.00000	0.0632456
$251$	10.0607	0.635023	0.317511	−	0.948254i	$-0.397153\pi$
$251$	10.0607	0.635023	0.317511	+	0.948254i	$0.397153\pi$
$252$	1.00000	0.0629941
$253$	4.58082	0.287994
$254$	−3.54289	−0.222300
$255$	−0.873206	−0.0546823
$256$	1.00000	0.0625000
$257$	27.7925	1.73365	0.866825	−	0.498612i	$-0.166157\pi$
$257$	27.7925	1.73365	0.866825	+	0.498612i	$0.166157\pi$
$258$	5.79647	0.360873
$259$	0.962065	0.0597798
$260$	−3.70762	−0.229937
$261$	9.36517	0.579689
$262$	−4.63088	−0.286097
$263$	−6.25359	−0.385613	−0.192806	−	0.981237i	$-0.561759\pi$
$263$	−6.25359	−0.385613	−0.192806	+	0.981237i	$0.561759\pi$
$264$	4.58082	0.281930
$265$	3.03793	0.186619
$266$	1.12679	0.0690882
$267$	−14.0849	−0.861983
$268$	3.36517	0.205560
$269$	13.5001	0.823118	0.411559	−	0.911383i	$-0.364984\pi$
$269$	13.5001	0.823118	0.411559	+	0.911383i	$0.364984\pi$
$270$	1.00000	0.0608581
$271$	−6.91932	−0.420319	−0.210159	−	0.977667i	$-0.567398\pi$
$271$	−6.91932	−0.420319	−0.210159	+	0.977667i	$0.567398\pi$
$272$	−0.873206	−0.0529459
$273$	−3.70762	−0.224395
$274$	10.6309	0.642235
$275$	4.58082	0.276234
$276$	1.00000	0.0601929
$277$	−7.03399	−0.422631	−0.211316	−	0.977418i	$-0.567775\pi$
$277$	−7.03399	−0.422631	−0.211316	+	0.977418i	$0.567775\pi$
$278$	−19.5389	−1.17187
$279$	−0.0888596	−0.00531989
$280$	1.00000	0.0597614
$281$	14.9339	0.890879	0.445440	−	0.895312i	$-0.353047\pi$
$281$	14.9339	0.890879	0.445440	+	0.895312i	$0.353047\pi$
$282$	−6.28844	−0.374471
$283$	−19.9072	−1.18336	−0.591680	−	0.806173i	$-0.701535\pi$
$283$	−19.9072	−1.18336	−0.591680	+	0.806173i	$0.701535\pi$
$284$	−1.61876	−0.0960555
$285$	1.12679	0.0667455
$286$	−16.9839	−1.00428
$287$	−10.9839	−0.648360
$288$	1.00000	0.0589256
$289$	−16.2375	−0.955148
$290$	9.36517	0.549942
$291$	8.23837	0.482942
$292$	8.19958	0.479844
$293$	−7.74641	−0.452550	−0.226275	−	0.974063i	$-0.572655\pi$
$293$	−7.74641	−0.452550	−0.226275	+	0.974063i	$0.572655\pi$
$294$	1.00000	0.0583212
$295$	−6.19958	−0.360953
$296$	0.962065	0.0559189
$297$	4.58082	0.265806
$298$	−11.1616	−0.646577
$299$	−3.70762	−0.214417
$300$	1.00000	0.0577350
$301$	5.79647	0.334103
$302$	11.4152	0.656873
$303$	9.90719	0.569153
$304$	1.12679	0.0646261
$305$	9.41523	0.539115
$306$	−0.873206	−0.0499179
$307$	−22.9081	−1.30743	−0.653716	−	0.756740i	$-0.726791\pi$
$307$	−22.9081	−1.30743	−0.653716	+	0.756740i	$0.726791\pi$
$308$	4.58082	0.261017
$309$	7.41523	0.421838
$310$	−0.0888596	−0.00504689
$311$	6.47010	0.366886	0.183443	−	0.983030i	$-0.441276\pi$
$311$	6.47010	0.366886	0.183443	+	0.983030i	$0.441276\pi$
$312$	−3.70762	−0.209902
$313$	−22.3142	−1.26128	−0.630638	−	0.776077i	$-0.717207\pi$
$313$	−22.3142	−1.26128	−0.630638	+	0.776077i	$0.717207\pi$
$314$	−0.153462	−0.00866035
$315$	1.00000	0.0563436
$316$	−1.03793	−0.0583884
$317$	13.9224	0.781960	0.390980	−	0.920399i	$-0.372136\pi$
$317$	13.9224	0.781960	0.390980	+	0.920399i	$0.372136\pi$
$318$	3.03793	0.170359
$319$	42.9002	2.40195
$320$	1.00000	0.0559017
$321$	16.4767	0.919642
$322$	1.00000	0.0557278
$323$	−0.983923	−0.0547470
$324$	1.00000	0.0555556
$325$	−3.70762	−0.205661
$326$	−20.9839	−1.16219
$327$	−18.4767	−1.02177
$328$	−10.9839	−0.606486
$329$	−6.28844	−0.346693
$330$	4.58082	0.252166
$331$	0.177719	0.00976833	0.00488417	−	0.999988i	$-0.498445\pi$
$331$	0.177719	0.00976833	0.00488417	+	0.999988i	$0.498445\pi$
$332$	−8.03485	−0.440970
$333$	0.962065	0.0527209
$334$	−0.441898	−0.0241796
$335$	3.36517	0.183859
$336$	1.00000	0.0545545
$337$	−6.58082	−0.358480	−0.179240	−	0.983805i	$-0.557364\pi$
$337$	−6.58082	−0.358480	−0.179240	+	0.983805i	$0.557364\pi$
$338$	0.746412	0.0405994
$339$	10.4532	0.567738
$340$	−0.873206	−0.0473562
$341$	−0.407050	−0.0220430
$342$	1.12679	0.0609300
$343$	1.00000	0.0539949
$344$	5.79647	0.312525
$345$	1.00000	0.0538382
$346$	−5.32637	−0.286347
$347$	4.98392	0.267551	0.133776	−	0.991012i	$-0.457290\pi$
$347$	4.98392	0.267551	0.133776	+	0.991012i	$0.457290\pi$
$348$	9.36517	0.502026
$349$	31.5956	1.69128	0.845638	−	0.533757i	$-0.179220\pi$
$349$	31.5956	1.69128	0.845638	+	0.533757i	$0.179220\pi$
$350$	1.00000	0.0534522
$351$	−3.70762	−0.197898
$352$	4.58082	0.244159
$353$	9.36122	0.498247	0.249124	−	0.968472i	$-0.419857\pi$
$353$	9.36122	0.498247	0.249124	+	0.968472i	$0.419857\pi$
$354$	−6.19958	−0.329504
$355$	−1.61876	−0.0859146
$356$	−14.0849	−0.746499
$357$	−0.873206	−0.0462150
$358$	−7.59295	−0.401300
$359$	24.3451	1.28489	0.642444	−	0.766333i	$-0.277921\pi$
$359$	24.3451	1.28489	0.642444	+	0.766333i	$0.277921\pi$
$360$	1.00000	0.0527046
$361$	−17.7303	−0.933176
$362$	−15.4911	−0.814194
$363$	9.98392	0.524020
$364$	−3.70762	−0.194332
$365$	8.19958	0.429185
$366$	9.41523	0.492142
$367$	−10.5526	−0.550842	−0.275421	−	0.961324i	$-0.588817\pi$
$367$	−10.5526	−0.550842	−0.275421	+	0.961324i	$0.588817\pi$
$368$	1.00000	0.0521286
$369$	−10.9839	−0.571800
$370$	0.962065	0.0500154
$371$	3.03793	0.157722
$372$	−0.0888596	−0.00460716
$373$	−25.7167	−1.33156	−0.665779	−	0.746149i	$-0.731901\pi$
$373$	−25.7167	−1.33156	−0.665779	+	0.746149i	$0.731901\pi$
$374$	−4.00000	−0.206835
$375$	1.00000	0.0516398
$376$	−6.28844	−0.324301
$377$	−34.7224	−1.78830
$378$	1.00000	0.0514344
$379$	0.860215	0.0441863	0.0220931	−	0.999756i	$-0.492967\pi$
$379$	0.860215	0.0441863	0.0220931	+	0.999756i	$0.492967\pi$
$380$	1.12679	0.0578033
$381$	−3.54289	−0.181508
$382$	−17.5147	−0.896129
$383$	26.4234	1.35017	0.675087	−	0.737738i	$-0.264106\pi$
$383$	26.4234	1.35017	0.675087	+	0.737738i	$0.264106\pi$
$384$	1.00000	0.0510310
$385$	4.58082	0.233460
$386$	19.8161	1.00861
$387$	5.79647	0.294651
$388$	8.23837	0.418240
$389$	−34.6466	−1.75665	−0.878325	−	0.478063i	$-0.841339\pi$
$389$	−34.6466	−1.75665	−0.878325	+	0.478063i	$0.841339\pi$
$390$	−3.70762	−0.187742
$391$	−0.873206	−0.0441599
$392$	1.00000	0.0505076
$393$	−4.63088	−0.233597
$394$	−1.82228	−0.0918052
$395$	−1.03793	−0.0522242
$396$	4.58082	0.230195
$397$	19.8289	0.995185	0.497593	−	0.867411i	$-0.334217\pi$
$397$	19.8289	0.995185	0.497593	+	0.867411i	$0.334217\pi$
$398$	9.16164	0.459232
$399$	1.12679	0.0564103
$400$	1.00000	0.0500000
$401$	−19.1813	−0.957867	−0.478934	−	0.877851i	$-0.658977\pi$
$401$	−19.1813	−0.957867	−0.478934	+	0.877851i	$0.658977\pi$
$402$	3.36517	0.167839
$403$	0.329457	0.0164114
$404$	9.90719	0.492901
$405$	1.00000	0.0496904
$406$	9.36517	0.464785
$407$	4.40705	0.218449
$408$	−0.873206	−0.0432301
$409$	−38.0697	−1.88243	−0.941213	−	0.337815i	$-0.890312\pi$
$409$	−38.0697	−1.88243	−0.941213	+	0.337815i	$0.890312\pi$
$410$	−10.9839	−0.542457
$411$	10.6309	0.524383
$412$	7.41523	0.365322
$413$	−6.19958	−0.305061
$414$	1.00000	0.0491473
$415$	−8.03485	−0.394415
$416$	−3.70762	−0.181781
$417$	−19.5389	−0.956826
$418$	5.16164	0.252464
$419$	22.9154	1.11949	0.559745	−	0.828665i	$-0.310899\pi$
$419$	22.9154	1.11949	0.559745	+	0.828665i	$0.310899\pi$
$420$	1.00000	0.0487950
$421$	35.6609	1.73801	0.869004	−	0.494806i	$-0.164761\pi$
$421$	35.6609	1.73801	0.869004	+	0.494806i	$0.164761\pi$
$422$	−25.0536	−1.21959
$423$	−6.28844	−0.305754
$424$	3.03793	0.147535
$425$	−0.873206	−0.0423567
$426$	−1.61876	−0.0784290
$427$	9.41523	0.455635
$428$	16.4767	0.796434
$429$	−16.9839	−0.819992
$430$	5.79647	0.279531
$431$	10.5550	0.508417	0.254209	−	0.967149i	$-0.418185\pi$
$431$	10.5550	0.508417	0.254209	+	0.967149i	$0.418185\pi$
$432$	1.00000	0.0481125
$433$	−25.7295	−1.23648	−0.618240	−	0.785990i	$-0.712154\pi$
$433$	−25.7295	−1.23648	−0.618240	+	0.785990i	$0.712154\pi$
$434$	−0.0888596	−0.00426540
$435$	9.36517	0.449025
$436$	−18.4767	−0.884876
$437$	1.12679	0.0539019
$438$	8.19958	0.391791
$439$	3.32637	0.158759	0.0793795	−	0.996844i	$-0.474706\pi$
$439$	3.32637	0.158759	0.0793795	+	0.996844i	$0.474706\pi$
$440$	4.58082	0.218382
$441$	1.00000	0.0476190
$442$	3.23751	0.153993
$443$	−4.98392	−0.236793	−0.118397	−	0.992966i	$-0.537775\pi$
$443$	−4.98392	−0.236793	−0.118397	+	0.992966i	$0.537775\pi$
$444$	0.962065	0.0456576
$445$	−14.0849	−0.667689
$446$	26.4598	1.25291
$447$	−11.1616	−0.527928
$448$	1.00000	0.0472456
$449$	−17.7447	−0.837424	−0.418712	−	0.908119i	$-0.637518\pi$
$449$	−17.7447	−0.837424	−0.418712	+	0.908119i	$0.637518\pi$
$450$	1.00000	0.0471405
$451$	−50.3154	−2.36926
$452$	10.4532	0.491676
$453$	11.4152	0.536334
$454$	14.7652	0.692964
$455$	−3.70762	−0.173816
$456$	1.12679	0.0527670
$457$	7.97179	0.372905	0.186452	−	0.982464i	$-0.440301\pi$
$457$	7.97179	0.372905	0.186452	+	0.982464i	$0.440301\pi$
$458$	−19.1616	−0.895365
$459$	−0.873206	−0.0407578
$460$	1.00000	0.0466252
$461$	5.40002	0.251504	0.125752	−	0.992062i	$-0.459866\pi$
$461$	5.40002	0.251504	0.125752	+	0.992062i	$0.459866\pi$
$462$	4.58082	0.213119
$463$	−16.0196	−0.744496	−0.372248	−	0.928133i	$-0.621413\pi$
$463$	−16.0196	−0.744496	−0.372248	+	0.928133i	$0.621413\pi$
$464$	9.36517	0.434767
$465$	−0.0888596	−0.00412077
$466$	10.4767	0.485326
$467$	−9.11890	−0.421972	−0.210986	−	0.977489i	$-0.567667\pi$
$467$	−9.11890	−0.421972	−0.210986	+	0.977489i	$0.567667\pi$
$468$	−3.70762	−0.171385
$469$	3.36517	0.155389
$470$	−6.28844	−0.290064
$471$	−0.153462	−0.00707114
$472$	−6.19958	−0.285359
$473$	26.5526	1.22089
$474$	−1.03793	−0.0476739
$475$	1.12679	0.0517009
$476$	−0.873206	−0.0400233
$477$	3.03793	0.139097
$478$	−9.61876	−0.439952
$479$	4.98392	0.227721	0.113861	−	0.993497i	$-0.463678\pi$
$479$	4.98392	0.227721	0.113861	+	0.993497i	$0.463678\pi$
$480$	1.00000	0.0456435
$481$	−3.56697	−0.162640
$482$	8.18831	0.372967
$483$	1.00000	0.0455016
$484$	9.98392	0.453815
$485$	8.23837	0.374085
$486$	1.00000	0.0453609
$487$	13.4410	0.609072	0.304536	−	0.952501i	$-0.401499\pi$
$487$	13.4410	0.609072	0.304536	+	0.952501i	$0.401499\pi$
$488$	9.41523	0.426207
$489$	−20.9839	−0.948926
$490$	1.00000	0.0451754
$491$	−3.31510	−0.149609	−0.0748043	−	0.997198i	$-0.523833\pi$
$491$	−3.31510	−0.149609	−0.0748043	+	0.997198i	$0.523833\pi$
$492$	−10.9839	−0.495194
$493$	−8.17772	−0.368306
$494$	−4.17772	−0.187964
$495$	4.58082	0.205893
$496$	−0.0888596	−0.00398991
$497$	−1.61876	−0.0726111
$498$	−8.03485	−0.360050
$499$	−30.7303	−1.37568	−0.687839	−	0.725863i	$-0.741441\pi$
$499$	−30.7303	−1.37568	−0.687839	+	0.725863i	$0.741441\pi$
$500$	1.00000	0.0447214
$501$	−0.441898	−0.0197426
$502$	10.0607	0.449029
$503$	−39.9145	−1.77970	−0.889850	−	0.456253i	$-0.849191\pi$
$503$	−39.9145	−1.77970	−0.889850	+	0.456253i	$0.849191\pi$
$504$	1.00000	0.0445435
$505$	9.90719	0.440864
$506$	4.58082	0.203642
$507$	0.746412	0.0331493
$508$	−3.54289	−0.157190
$509$	−24.3081	−1.07744	−0.538718	−	0.842486i	$-0.681091\pi$
$509$	−24.3081	−1.07744	−0.538718	+	0.842486i	$0.681091\pi$
$510$	−0.873206	−0.0386662
$511$	8.19958	0.362728
$512$	1.00000	0.0441942
$513$	1.12679	0.0497492
$514$	27.7925	1.22588
$515$	7.41523	0.326754
$516$	5.79647	0.255176
$517$	−28.8062	−1.26690
$518$	0.962065	0.0422707
$519$	−5.32637	−0.233802
$520$	−3.70762	−0.162590
$521$	−4.11707	−0.180372	−0.0901859	−	0.995925i	$-0.528746\pi$
$521$	−4.11707	−0.180372	−0.0901859	+	0.995925i	$0.528746\pi$
$522$	9.36517	0.409902
$523$	9.75373	0.426501	0.213250	−	0.976998i	$-0.431595\pi$
$523$	9.75373	0.426501	0.213250	+	0.976998i	$0.431595\pi$
$524$	−4.63088	−0.202301
$525$	1.00000	0.0436436
$526$	−6.25359	−0.272669
$527$	0.0775927	0.00337999
$528$	4.58082	0.199355
$529$	1.00000	0.0434783
$530$	3.03793	0.131959
$531$	−6.19958	−0.269039
$532$	1.12679	0.0488527
$533$	40.7242	1.76396
$534$	−14.0849	−0.609514
$535$	16.4767	0.712352
$536$	3.36517	0.145353
$537$	−7.59295	−0.327660
$538$	13.5001	0.582032
$539$	4.58082	0.197310
$540$	1.00000	0.0430331
$541$	29.6367	1.27418	0.637090	−	0.770790i	$-0.280138\pi$
$541$	29.6367	1.27418	0.637090	+	0.770790i	$0.280138\pi$
$542$	−6.91932	−0.297210
$543$	−15.4911	−0.664787
$544$	−0.873206	−0.0374384
$545$	−18.4767	−0.791457
$546$	−3.70762	−0.158671
$547$	−28.0437	−1.19906	−0.599531	−	0.800351i	$-0.704646\pi$
$547$	−28.0437	−1.19906	−0.599531	+	0.800351i	$0.704646\pi$
$548$	10.6309	0.454129
$549$	9.41523	0.401832
$550$	4.58082	0.195327
$551$	10.5526	0.449557
$552$	1.00000	0.0425628
$553$	−1.03793	−0.0441375
$554$	−7.03399	−0.298845
$555$	0.962065	0.0408374
$556$	−19.5389	−0.828636
$557$	−18.7522	−0.794556	−0.397278	−	0.917698i	$-0.630045\pi$
$557$	−18.7522	−0.794556	−0.397278	+	0.917698i	$0.630045\pi$
$558$	−0.0888596	−0.00376173
$559$	−21.4911	−0.908977
$560$	1.00000	0.0422577
$561$	−4.00000	−0.168880
$562$	14.9339	0.629947
$563$	−20.8975	−0.880723	−0.440362	−	0.897821i	$-0.645150\pi$
$563$	−20.8975	−0.880723	−0.440362	+	0.897821i	$0.645150\pi$
$564$	−6.28844	−0.264791
$565$	10.4532	0.439768
$566$	−19.9072	−0.836762
$567$	1.00000	0.0419961
$568$	−1.61876	−0.0679215
$569$	−6.37952	−0.267443	−0.133722	−	0.991019i	$-0.542693\pi$
$569$	−6.37952	−0.267443	−0.133722	+	0.991019i	$0.542693\pi$
$570$	1.12679	0.0471962
$571$	6.96207	0.291353	0.145677	−	0.989332i	$-0.453464\pi$
$571$	6.96207	0.291353	0.145677	+	0.989332i	$0.453464\pi$
$572$	−16.9839	−0.710134
$573$	−17.5147	−0.731686
$574$	−10.9839	−0.458460
$575$	1.00000	0.0417029
$576$	1.00000	0.0416667
$577$	−27.7925	−1.15702	−0.578509	−	0.815676i	$-0.696365\pi$
$577$	−27.7925	−1.15702	−0.578509	+	0.815676i	$0.696365\pi$
$578$	−16.2375	−0.675391
$579$	19.8161	0.823529
$580$	9.36517	0.388867
$581$	−8.03485	−0.333342
$582$	8.23837	0.341492
$583$	13.9162	0.576352
$584$	8.19958	0.339301
$585$	−3.70762	−0.153291
$586$	−7.74641	−0.320001
$587$	8.60730	0.355261	0.177631	−	0.984097i	$-0.443157\pi$
$587$	8.60730	0.355261	0.177631	+	0.984097i	$0.443157\pi$
$588$	1.00000	0.0412393
$589$	−0.100126	−0.00412564
$590$	−6.19958	−0.255233
$591$	−1.82228	−0.0749586
$592$	0.962065	0.0395406
$593$	15.0379	0.617534	0.308767	−	0.951138i	$-0.400084\pi$
$593$	15.0379	0.617534	0.308767	+	0.951138i	$0.400084\pi$
$594$	4.58082	0.187953
$595$	−0.873206	−0.0357980
$596$	−11.1616	−0.457199
$597$	9.16164	0.374961
$598$	−3.70762	−0.151616
$599$	−42.4947	−1.73628	−0.868142	−	0.496315i	$-0.834686\pi$
$599$	−42.4947	−1.73628	−0.868142	+	0.496315i	$0.834686\pi$
$600$	1.00000	0.0408248
$601$	−33.3848	−1.36179	−0.680897	−	0.732379i	$-0.738410\pi$
$601$	−33.3848	−1.36179	−0.680897	+	0.732379i	$0.738410\pi$
$602$	5.79647	0.236247
$603$	3.36517	0.137040
$604$	11.4152	0.464479
$605$	9.98392	0.405904
$606$	9.90719	0.402452
$607$	45.3163	1.83933	0.919665	−	0.392704i	$-0.128460\pi$
$607$	45.3163	1.83933	0.919665	+	0.392704i	$0.128460\pi$
$608$	1.12679	0.0456975
$609$	9.36517	0.379496
$610$	9.41523	0.381212
$611$	23.3151	0.943228
$612$	−0.873206	−0.0352973
$613$	−24.5987	−0.993533	−0.496767	−	0.867884i	$-0.665480\pi$
$613$	−24.5987	−0.993533	−0.496767	+	0.867884i	$0.665480\pi$
$614$	−22.9081	−0.924494
$615$	−10.9839	−0.442915
$616$	4.58082	0.184567
$617$	12.6066	0.507524	0.253762	−	0.967267i	$-0.418332\pi$
$617$	12.6066	0.507524	0.253762	+	0.967267i	$0.418332\pi$
$618$	7.41523	0.298284
$619$	39.0126	1.56805	0.784024	−	0.620730i	$-0.213164\pi$
$619$	39.0126	1.56805	0.784024	+	0.620730i	$0.213164\pi$
$620$	−0.0888596	−0.00356869
$621$	1.00000	0.0401286
$622$	6.47010	0.259428
$623$	−14.0849	−0.564300
$624$	−3.70762	−0.148423
$625$	1.00000	0.0400000
$626$	−22.3142	−0.891856
$627$	5.16164	0.206136
$628$	−0.153462	−0.00612379
$629$	−0.840081	−0.0334962
$630$	1.00000	0.0398410
$631$	−12.7310	−0.506814	−0.253407	−	0.967360i	$-0.581551\pi$
$631$	−12.7310	−0.506814	−0.253407	+	0.967360i	$0.581551\pi$
$632$	−1.03793	−0.0412868
$633$	−25.0536	−0.995792
$634$	13.9224	0.552929
$635$	−3.54289	−0.140595
$636$	3.03793	0.120462
$637$	−3.70762	−0.146901
$638$	42.9002	1.69843
$639$	−1.61876	−0.0640370
$640$	1.00000	0.0395285
$641$	−24.7107	−0.976014	−0.488007	−	0.872840i	$-0.662276\pi$
$641$	−24.7107	−0.976014	−0.488007	+	0.872840i	$0.662276\pi$
$642$	16.4767	0.650285
$643$	−37.1464	−1.46491	−0.732456	−	0.680814i	$-0.761626\pi$
$643$	−37.1464	−1.46491	−0.732456	+	0.680814i	$0.761626\pi$
$644$	1.00000	0.0394055
$645$	5.79647	0.228236
$646$	−0.983923	−0.0387119
$647$	30.1804	1.18651	0.593257	−	0.805013i	$-0.297842\pi$
$647$	30.1804	1.18651	0.593257	+	0.805013i	$0.297842\pi$
$648$	1.00000	0.0392837
$649$	−28.3992	−1.11476
$650$	−3.70762	−0.145425
$651$	−0.0888596	−0.00348268
$652$	−20.9839	−0.821794
$653$	−40.6223	−1.58967	−0.794837	−	0.606823i	$-0.792444\pi$
$653$	−40.6223	−1.58967	−0.794837	+	0.606823i	$0.792444\pi$
$654$	−18.4767	−0.722498
$655$	−4.63088	−0.180944
$656$	−10.9839	−0.428850
$657$	8.19958	0.319896
$658$	−6.28844	−0.245149
$659$	−17.7165	−0.690136	−0.345068	−	0.938578i	$-0.612144\pi$
$659$	−17.7165	−0.690136	−0.345068	+	0.938578i	$0.612144\pi$
$660$	4.58082	0.178308
$661$	27.9162	1.08582	0.542908	−	0.839792i	$-0.317323\pi$
$661$	27.9162	1.08582	0.542908	+	0.839792i	$0.317323\pi$
$662$	0.177719	0.00690725
$663$	3.23751	0.125735
$664$	−8.03485	−0.311813
$665$	1.12679	0.0436952
$666$	0.962065	0.0372793
$667$	9.36517	0.362621
$668$	−0.441898	−0.0170976
$669$	26.4598	1.02300
$670$	3.36517	0.130008
$671$	43.1295	1.66500
$672$	1.00000	0.0385758
$673$	0.578597	0.0223033	0.0111516	−	0.999938i	$-0.496450\pi$
$673$	0.578597	0.0223033	0.0111516	+	0.999938i	$0.496450\pi$
$674$	−6.58082	−0.253484
$675$	1.00000	0.0384900
$676$	0.746412	0.0287081
$677$	18.3992	0.707137	0.353568	−	0.935409i	$-0.384968\pi$
$677$	18.3992	0.707137	0.353568	+	0.935409i	$0.384968\pi$
$678$	10.4532	0.401451
$679$	8.23837	0.316160
$680$	−0.873206	−0.0334859
$681$	14.7652	0.565803
$682$	−0.407050	−0.0155868
$683$	−16.4767	−0.630465	−0.315233	−	0.949014i	$-0.602083\pi$
$683$	−16.4767	−0.630465	−0.315233	+	0.949014i	$0.602083\pi$
$684$	1.12679	0.0430841
$685$	10.6309	0.406185
$686$	1.00000	0.0381802
$687$	−19.1616	−0.731062
$688$	5.79647	0.220989
$689$	−11.2635	−0.429105
$690$	1.00000	0.0380693
$691$	42.0916	1.60124	0.800619	−	0.599174i	$-0.204504\pi$
$691$	42.0916	1.60124	0.800619	+	0.599174i	$0.204504\pi$
$692$	−5.32637	−0.202478
$693$	4.58082	0.174011
$694$	4.98392	0.189187
$695$	−19.5389	−0.741154
$696$	9.36517	0.354986
$697$	9.59123	0.363294
$698$	31.5956	1.19591
$699$	10.4767	0.396267
$700$	1.00000	0.0377964
$701$	−30.6466	−1.15750	−0.578752	−	0.815503i	$-0.696460\pi$
$701$	−30.6466	−1.15750	−0.578752	+	0.815503i	$0.696460\pi$
$702$	−3.70762	−0.139935
$703$	1.08405	0.0408857
$704$	4.58082	0.172646
$705$	−6.28844	−0.236836
$706$	9.36122	0.352314
$707$	9.90719	0.372598
$708$	−6.19958	−0.232994
$709$	3.79013	0.142341	0.0711706	−	0.997464i	$-0.477327\pi$
$709$	3.79013	0.142341	0.0711706	+	0.997464i	$0.477327\pi$
$710$	−1.61876	−0.0607508
$711$	−1.03793	−0.0389256
$712$	−14.0849	−0.527854
$713$	−0.0888596	−0.00332782
$714$	−0.873206	−0.0326789
$715$	−16.9839	−0.635163
$716$	−7.59295	−0.283762
$717$	−9.61876	−0.359219
$718$	24.3451	0.908553
$719$	27.8532	1.03875	0.519374	−	0.854547i	$-0.326165\pi$
$719$	27.8532	1.03875	0.519374	+	0.854547i	$0.326165\pi$
$720$	1.00000	0.0372678
$721$	7.41523	0.276158
$722$	−17.7303	−0.659855
$723$	8.18831	0.304527
$724$	−15.4911	−0.575722
$725$	9.36517	0.347814
$726$	9.98392	0.370538
$727$	15.8144	0.586523	0.293262	−	0.956032i	$-0.405259\pi$
$727$	15.8144	0.586523	0.293262	+	0.956032i	$0.405259\pi$
$728$	−3.70762	−0.137413
$729$	1.00000	0.0370370
$730$	8.19958	0.303480
$731$	−5.06152	−0.187207
$732$	9.41523	0.347997
$733$	−30.9323	−1.14251	−0.571256	−	0.820772i	$-0.693543\pi$
$733$	−30.9323	−1.14251	−0.571256	+	0.820772i	$0.693543\pi$
$734$	−10.5526	−0.389504
$735$	1.00000	0.0368856
$736$	1.00000	0.0368605
$737$	15.4152	0.567827
$738$	−10.9839	−0.404324
$739$	18.5526	0.682469	0.341235	−	0.939978i	$-0.389155\pi$
$739$	18.5526	0.682469	0.341235	+	0.939978i	$0.389155\pi$
$740$	0.962065	0.0353662
$741$	−4.17772	−0.153472
$742$	3.03793	0.111526
$743$	28.8062	1.05680	0.528399	−	0.848996i	$-0.322793\pi$
$743$	28.8062	1.05680	0.528399	+	0.848996i	$0.322793\pi$
$744$	−0.0888596	−0.00325775
$745$	−11.1616	−0.408931
$746$	−25.7167	−0.941554
$747$	−8.03485	−0.293980
$748$	−4.00000	−0.146254
$749$	16.4767	0.602047
$750$	1.00000	0.0365148
$751$	−20.0157	−0.730383	−0.365191	−	0.930932i	$-0.618996\pi$
$751$	−20.0157	−0.730383	−0.365191	+	0.930932i	$0.618996\pi$
$752$	−6.28844	−0.229316
$753$	10.0607	0.366631
$754$	−34.7224	−1.26452
$755$	11.4152	0.415443
$756$	1.00000	0.0363696
$757$	14.2317	0.517261	0.258631	−	0.965976i	$-0.416729\pi$
$757$	14.2317	0.517261	0.258631	+	0.965976i	$0.416729\pi$
$758$	0.860215	0.0312444
$759$	4.58082	0.166273
$760$	1.12679	0.0408731
$761$	−23.8677	−0.865204	−0.432602	−	0.901585i	$-0.642404\pi$
$761$	−23.8677	−0.865204	−0.432602	+	0.901585i	$0.642404\pi$
$762$	−3.54289	−0.128345
$763$	−18.4767	−0.668903
$764$	−17.5147	−0.633659
$765$	−0.873206	−0.0315708
$766$	26.4234	0.954717
$767$	22.9856	0.829964
$768$	1.00000	0.0360844
$769$	−38.5420	−1.38986	−0.694930	−	0.719077i	$-0.744565\pi$
$769$	−38.5420	−1.38986	−0.694930	+	0.719077i	$0.744565\pi$
$770$	4.58082	0.165081
$771$	27.7925	1.00092
$772$	19.8161	0.713197
$773$	−34.5509	−1.24271	−0.621355	−	0.783529i	$-0.713417\pi$
$773$	−34.5509	−1.24271	−0.621355	+	0.783529i	$0.713417\pi$
$774$	5.79647	0.208350
$775$	−0.0888596	−0.00319193
$776$	8.23837	0.295740
$777$	0.962065	0.0345139
$778$	−34.6466	−1.24214
$779$	−12.3766	−0.443438
$780$	−3.70762	−0.132754
$781$	−7.41523	−0.265338
$782$	−0.873206	−0.0312258
$783$	9.36517	0.334684
$784$	1.00000	0.0357143
$785$	−0.153462	−0.00547729
$786$	−4.63088	−0.165178
$787$	−18.6680	−0.665441	−0.332720	−	0.943026i	$-0.607967\pi$
$787$	−18.6680	−0.665441	−0.332720	+	0.943026i	$0.607967\pi$
$788$	−1.82228	−0.0649161
$789$	−6.25359	−0.222634
$790$	−1.03793	−0.0369281
$791$	10.4532	0.371672
$792$	4.58082	0.162772
$793$	−34.9081	−1.23962
$794$	19.8289	0.703702
$795$	3.03793	0.107744
$796$	9.16164	0.324726
$797$	21.3588	0.756568	0.378284	−	0.925690i	$-0.376514\pi$
$797$	21.3588	0.756568	0.378284	+	0.925690i	$0.376514\pi$
$798$	1.12679	0.0398881
$799$	5.49110	0.194261
$800$	1.00000	0.0353553
$801$	−14.0849	−0.497666
$802$	−19.1813	−0.677314
$803$	37.5608	1.32549
$804$	3.36517	0.118680
$805$	1.00000	0.0352454
$806$	0.329457	0.0116046
$807$	13.5001	0.475228
$808$	9.90719	0.348534
$809$	−30.0437	−1.05628	−0.528140	−	0.849157i	$-0.677111\pi$
$809$	−30.0437	−1.05628	−0.528140	+	0.849157i	$0.677111\pi$
$810$	1.00000	0.0351364
$811$	13.7149	0.481596	0.240798	−	0.970575i	$-0.422591\pi$
$811$	13.7149	0.481596	0.240798	+	0.970575i	$0.422591\pi$
$812$	9.36517	0.328653
$813$	−6.91932	−0.242671
$814$	4.40705	0.154467
$815$	−20.9839	−0.735035
$816$	−0.873206	−0.0305683
$817$	6.53143	0.228506
$818$	−38.0697	−1.33108
$819$	−3.70762	−0.129555
$820$	−10.9839	−0.383575
$821$	19.7660	0.689840	0.344920	−	0.938632i	$-0.387906\pi$
$821$	19.7660	0.689840	0.344920	+	0.938632i	$0.387906\pi$
$822$	10.6309	0.370795
$823$	21.7660	0.758717	0.379358	−	0.925250i	$-0.376145\pi$
$823$	21.7660	0.758717	0.379358	+	0.925250i	$0.376145\pi$
$824$	7.41523	0.258322
$825$	4.58082	0.159484
$826$	−6.19958	−0.215711
$827$	27.8144	0.967201	0.483600	−	0.875289i	$-0.339329\pi$
$827$	27.8144	0.967201	0.483600	+	0.875289i	$0.339329\pi$
$828$	1.00000	0.0347524
$829$	1.95726	0.0679783	0.0339891	−	0.999422i	$-0.489179\pi$
$829$	1.95726	0.0679783	0.0339891	+	0.999422i	$0.489179\pi$
$830$	−8.03485	−0.278894
$831$	−7.03399	−0.244006
$832$	−3.70762	−0.128538
$833$	−0.873206	−0.0302548
$834$	−19.5389	−0.676578
$835$	−0.441898	−0.0152925
$836$	5.16164	0.178519
$837$	−0.0888596	−0.00307144
$838$	22.9154	0.791598
$839$	20.1394	0.695289	0.347645	−	0.937626i	$-0.386982\pi$
$839$	20.1394	0.695289	0.347645	+	0.937626i	$0.386982\pi$
$840$	1.00000	0.0345033
$841$	58.7064	2.02436
$842$	35.6609	1.22896
$843$	14.9339	0.514349
$844$	−25.0536	−0.862381
$845$	0.746412	0.0256773
$846$	−6.28844	−0.216201
$847$	9.98392	0.343052
$848$	3.03793	0.104323
$849$	−19.9072	−0.683213
$850$	−0.873206	−0.0299507
$851$	0.962065	0.0329792
$852$	−1.61876	−0.0554577
$853$	0.691539	0.0236778	0.0118389	−	0.999930i	$-0.496231\pi$
$853$	0.691539	0.0236778	0.0118389	+	0.999930i	$0.496231\pi$
$854$	9.41523	0.322183
$855$	1.12679	0.0385355
$856$	16.4767	0.563164
$857$	−48.7460	−1.66513	−0.832566	−	0.553926i	$-0.813129\pi$
$857$	−48.7460	−1.66513	−0.832566	+	0.553926i	$0.813129\pi$
$858$	−16.9839	−0.579822
$859$	−37.5372	−1.28075	−0.640377	−	0.768061i	$-0.721222\pi$
$859$	−37.5372	−1.28075	−0.640377	+	0.768061i	$0.721222\pi$
$860$	5.79647	0.197658
$861$	−10.9839	−0.374331
$862$	10.5550	0.359505
$863$	−12.4767	−0.424713	−0.212357	−	0.977192i	$-0.568114\pi$
$863$	−12.4767	−0.424713	−0.212357	+	0.977192i	$0.568114\pi$
$864$	1.00000	0.0340207
$865$	−5.32637	−0.181102
$866$	−25.7295	−0.874323
$867$	−16.2375	−0.551455
$868$	−0.0888596	−0.00301609
$869$	−4.75459	−0.161289
$870$	9.36517	0.317509
$871$	−12.4767	−0.422758
$872$	−18.4767	−0.625702
$873$	8.23837	0.278827
$874$	1.12679	0.0381144
$875$	1.00000	0.0338062
$876$	8.19958	0.277038
$877$	−17.1796	−0.580112	−0.290056	−	0.957010i	$-0.593674\pi$
$877$	−17.1796	−0.580112	−0.290056	+	0.957010i	$0.593674\pi$
$878$	3.32637	0.112260
$879$	−7.74641	−0.261280
$880$	4.58082	0.154419
$881$	−26.1983	−0.882644	−0.441322	−	0.897349i	$-0.645490\pi$
$881$	−26.1983	−0.882644	−0.441322	+	0.897349i	$0.645490\pi$
$882$	1.00000	0.0336718
$883$	30.9518	1.04161	0.520805	−	0.853676i	$-0.325632\pi$
$883$	30.9518	1.04161	0.520805	+	0.853676i	$0.325632\pi$
$884$	3.23751	0.108889
$885$	−6.19958	−0.208397
$886$	−4.98392	−0.167438
$887$	17.8893	0.600663	0.300332	−	0.953835i	$-0.402903\pi$
$887$	17.8893	0.600663	0.300332	+	0.953835i	$0.402903\pi$
$888$	0.962065	0.0322848
$889$	−3.54289	−0.118825
$890$	−14.0849	−0.472127
$891$	4.58082	0.153463
$892$	26.4598	0.885940
$893$	−7.08577	−0.237116
$894$	−11.1616	−0.373301
$895$	−7.59295	−0.253804
$896$	1.00000	0.0334077
$897$	−3.70762	−0.123794
$898$	−17.7447	−0.592148
$899$	−0.832185	−0.0277549
$900$	1.00000	0.0333333
$901$	−2.65274	−0.0883757
$902$	−50.3154	−1.67532
$903$	5.79647	0.192895
$904$	10.4532	0.347667
$905$	−15.4911	−0.514942
$906$	11.4152	0.379246
$907$	−26.1180	−0.867235	−0.433618	−	0.901097i	$-0.642763\pi$
$907$	−26.1180	−0.867235	−0.433618	+	0.901097i	$0.642763\pi$
$908$	14.7652	0.490000
$909$	9.90719	0.328601
$910$	−3.70762	−0.122906
$911$	−3.84586	−0.127419	−0.0637096	−	0.997968i	$-0.520293\pi$
$911$	−3.84586	−0.127419	−0.0637096	+	0.997968i	$0.520293\pi$
$912$	1.12679	0.0373119
$913$	−36.8062	−1.21811
$914$	7.97179	0.263684
$915$	9.41523	0.311258
$916$	−19.1616	−0.633118
$917$	−4.63088	−0.152925
$918$	−0.873206	−0.0288201
$919$	−12.1541	−0.400928	−0.200464	−	0.979701i	$-0.564245\pi$
$919$	−12.1541	−0.400928	−0.200464	+	0.979701i	$0.564245\pi$
$920$	1.00000	0.0329690
$921$	−22.9081	−0.754846
$922$	5.40002	0.177840
$923$	6.00172	0.197549
$924$	4.58082	0.150698
$925$	0.962065	0.0316325
$926$	−16.0196	−0.526438
$927$	7.41523	0.243548
$928$	9.36517	0.307427
$929$	10.4251	0.342038	0.171019	−	0.985268i	$-0.445294\pi$
$929$	10.4251	0.342038	0.171019	+	0.985268i	$0.445294\pi$
$930$	−0.0888596	−0.00291382
$931$	1.12679	0.0369292
$932$	10.4767	0.343177
$933$	6.47010	0.211822
$934$	−9.11890	−0.298379
$935$	−4.00000	−0.130814
$936$	−3.70762	−0.121187
$937$	−17.2011	−0.561936	−0.280968	−	0.959717i	$-0.590655\pi$
$937$	−17.2011	−0.561936	−0.280968	+	0.959717i	$0.590655\pi$
$938$	3.36517	0.109877
$939$	−22.3142	−0.728198
$940$	−6.28844	−0.205106
$941$	−30.0437	−0.979397	−0.489699	−	0.871892i	$-0.662893\pi$
$941$	−30.0437	−0.979397	−0.489699	+	0.871892i	$0.662893\pi$
$942$	−0.153462	−0.00500005
$943$	−10.9839	−0.357686
$944$	−6.19958	−0.201779
$945$	1.00000	0.0325300
$946$	26.5526	0.863300
$947$	39.6367	1.28802	0.644009	−	0.765018i	$-0.277270\pi$
$947$	39.6367	1.28802	0.644009	+	0.765018i	$0.277270\pi$
$948$	−1.03793	−0.0337105
$949$	−30.4009	−0.986854
$950$	1.12679	0.0365580
$951$	13.9224	0.451465
$952$	−0.873206	−0.0283008
$953$	50.5454	1.63733	0.818663	−	0.574274i	$-0.194716\pi$
$953$	50.5454	1.63733	0.818663	+	0.574274i	$0.194716\pi$
$954$	3.03793	0.0983568
$955$	−17.5147	−0.566762
$956$	−9.61876	−0.311093
$957$	42.9002	1.38677
$958$	4.98392	0.161023
$959$	10.6309	0.343289
$960$	1.00000	0.0322749
$961$	−30.9921	−0.999745
$962$	−3.56697	−0.115004
$963$	16.4767	0.530956
$964$	8.18831	0.263728
$965$	19.8161	0.637903
$966$	1.00000	0.0321745
$967$	−22.8501	−0.734810	−0.367405	−	0.930061i	$-0.619754\pi$
$967$	−22.8501	−0.734810	−0.367405	+	0.930061i	$0.619754\pi$
$968$	9.98392	0.320895
$969$	−0.983923	−0.0316082
$970$	8.23837	0.264518
$971$	−19.7555	−0.633983	−0.316991	−	0.948428i	$-0.602673\pi$
$971$	−19.7555	−0.633983	−0.316991	+	0.948428i	$0.602673\pi$
$972$	1.00000	0.0320750
$973$	−19.5389	−0.626390
$974$	13.4410	0.430679
$975$	−3.70762	−0.118739
$976$	9.41523	0.301374
$977$	−4.40773	−0.141016	−0.0705078	−	0.997511i	$-0.522462\pi$
$977$	−4.40773	−0.141016	−0.0705078	+	0.997511i	$0.522462\pi$
$978$	−20.9839	−0.670992
$979$	−64.5205	−2.06208
$980$	1.00000	0.0319438
$981$	−18.4767	−0.589917
$982$	−3.31510	−0.105789
$983$	−41.4091	−1.32074	−0.660372	−	0.750939i	$-0.729601\pi$
$983$	−41.4091	−1.32074	−0.660372	+	0.750939i	$0.729601\pi$
$984$	−10.9839	−0.350155
$985$	−1.82228	−0.0580627
$986$	−8.17772	−0.260432
$987$	−6.28844	−0.200163
$988$	−4.17772	−0.132911
$989$	5.79647	0.184317
$990$	4.58082	0.145588
$991$	6.55262	0.208151	0.104075	−	0.994569i	$-0.466812\pi$
$991$	6.55262	0.208151	0.104075	+	0.994569i	$0.466812\pi$
$992$	−0.0888596	−0.00282130
$993$	0.177719	0.00563975
$994$	−1.61876	−0.0513438
$995$	9.16164	0.290444
$996$	−8.03485	−0.254594
$997$	−46.0309	−1.45781	−0.728907	−	0.684613i	$-0.759971\pi$
$997$	−46.0309	−1.45781	−0.728907	+	0.684613i	$0.759971\pi$
$998$	−30.7303	−0.972752
$999$	0.962065	0.0304384

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4830.2.a.ce.1.4	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4830.2.a.ce.1.4	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +4.58082 q^{11} +1.00000 q^{12} -3.70762 q^{13} +1.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} -0.873206 q^{17} +1.00000 q^{18} +1.12679 q^{19} +1.00000 q^{20} +1.00000 q^{21} +4.58082 q^{22} +1.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} -3.70762 q^{26} +1.00000 q^{27} +1.00000 q^{28} +9.36517 q^{29} +1.00000 q^{30} -0.0888596 q^{31} +1.00000 q^{32} +4.58082 q^{33} -0.873206 q^{34} +1.00000 q^{35} +1.00000 q^{36} +0.962065 q^{37} +1.12679 q^{38} -3.70762 q^{39} +1.00000 q^{40} -10.9839 q^{41} +1.00000 q^{42} +5.79647 q^{43} +4.58082 q^{44} +1.00000 q^{45} +1.00000 q^{46} -6.28844 q^{47} +1.00000 q^{48} +1.00000 q^{49} +1.00000 q^{50} -0.873206 q^{51} -3.70762 q^{52} +3.03793 q^{53} +1.00000 q^{54} +4.58082 q^{55} +1.00000 q^{56} +1.12679 q^{57} +9.36517 q^{58} -6.19958 q^{59} +1.00000 q^{60} +9.41523 q^{61} -0.0888596 q^{62} +1.00000 q^{63} +1.00000 q^{64} -3.70762 q^{65} +4.58082 q^{66} +3.36517 q^{67} -0.873206 q^{68} +1.00000 q^{69} +1.00000 q^{70} -1.61876 q^{71} +1.00000 q^{72} +8.19958 q^{73} +0.962065 q^{74} +1.00000 q^{75} +1.12679 q^{76} +4.58082 q^{77} -3.70762 q^{78} -1.03793 q^{79} +1.00000 q^{80} +1.00000 q^{81} -10.9839 q^{82} -8.03485 q^{83} +1.00000 q^{84} -0.873206 q^{85} +5.79647 q^{86} +9.36517 q^{87} +4.58082 q^{88} -14.0849 q^{89} +1.00000 q^{90} -3.70762 q^{91} +1.00000 q^{92} -0.0888596 q^{93} -6.28844 q^{94} +1.12679 q^{95} +1.00000 q^{96} +8.23837 q^{97} +1.00000 q^{98} +4.58082 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{5} + 4 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 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	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{5} + 4 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9} + 4 q^{10} + 4 q^{12} + 2 q^{13} + 4 q^{14} + 4 q^{15} + 4 q^{16} - 2 q^{17} + 4 q^{18} + 6 q^{19} + 4 q^{20} + 4 q^{21} + 4 q^{23} + 4 q^{24} + 4 q^{25} + 2 q^{26} + 4 q^{27} + 4 q^{28} + 14 q^{29} + 4 q^{30} - 4 q^{31} + 4 q^{32} - 2 q^{34} + 4 q^{35} + 4 q^{36} + 6 q^{37} + 6 q^{38} + 2 q^{39} + 4 q^{40} + 4 q^{42} + 10 q^{43} + 4 q^{45} + 4 q^{46} + 10 q^{47} + 4 q^{48} + 4 q^{49} + 4 q^{50} - 2 q^{51} + 2 q^{52} + 10 q^{53} + 4 q^{54} + 4 q^{56} + 6 q^{57} + 14 q^{58} + 14 q^{59} + 4 q^{60} + 4 q^{61} - 4 q^{62} + 4 q^{63} + 4 q^{64} + 2 q^{65} - 10 q^{67} - 2 q^{68} + 4 q^{69} + 4 q^{70} + 14 q^{71} + 4 q^{72} - 6 q^{73} + 6 q^{74} + 4 q^{75} + 6 q^{76} + 2 q^{78} - 2 q^{79} + 4 q^{80} + 4 q^{81} + 6 q^{83} + 4 q^{84} - 2 q^{85} + 10 q^{86} + 14 q^{87} - 8 q^{89} + 4 q^{90} + 2 q^{91} + 4 q^{92} - 4 q^{93} + 10 q^{94} + 6 q^{95} + 4 q^{96} + 8 q^{97} + 4 q^{98}+O(q^{100}) \) 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 + 4 * q^12 + 2 * q^13 + 4 * q^14 + 4 * q^15 + 4 * q^16 - 2 * q^17 + 4 * q^18 + 6 * q^19 + 4 * q^20 + 4 * q^21 + 4 * q^23 + 4 * q^24 + 4 * q^25 + 2 * q^26 + 4 * q^27 + 4 * q^28 + 14 * q^29 + 4 * q^30 - 4 * q^31 + 4 * q^32 - 2 * q^34 + 4 * q^35 + 4 * q^36 + 6 * q^37 + 6 * q^38 + 2 * q^39 + 4 * q^40 + 4 * q^42 + 10 * q^43 + 4 * q^45 + 4 * q^46 + 10 * q^47 + 4 * q^48 + 4 * q^49 + 4 * q^50 - 2 * q^51 + 2 * q^52 + 10 * q^53 + 4 * q^54 + 4 * q^56 + 6 * q^57 + 14 * q^58 + 14 * q^59 + 4 * q^60 + 4 * q^61 - 4 * q^62 + 4 * q^63 + 4 * q^64 + 2 * q^65 - 10 * q^67 - 2 * q^68 + 4 * q^69 + 4 * q^70 + 14 * q^71 + 4 * q^72 - 6 * q^73 + 6 * q^74 + 4 * q^75 + 6 * q^76 + 2 * q^78 - 2 * q^79 + 4 * q^80 + 4 * q^81 + 6 * q^83 + 4 * q^84 - 2 * q^85 + 10 * q^86 + 14 * q^87 - 8 * q^89 + 4 * q^90 + 2 * q^91 + 4 * q^92 - 4 * q^93 + 10 * q^94 + 6 * q^95 + 4 * q^96 + 8 * q^97 + 4 * q^98

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