LMFDB - Embedded newform 4830.2.a.bn.1.1

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:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{13}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 3 $ x^2 - x - 3
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.30278$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -2.00000 q^{11} +1.00000 q^{12} -2.60555 q^{13} +1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} +4.60555 q^{17} -1.00000 q^{18} -2.60555 q^{19} -1.00000 q^{20} -1.00000 q^{21} +2.00000 q^{22} +1.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} +2.60555 q^{26} +1.00000 q^{27} -1.00000 q^{28} +5.21110 q^{29} +1.00000 q^{30} +2.60555 q^{31} -1.00000 q^{32} -2.00000 q^{33} -4.60555 q^{34} +1.00000 q^{35} +1.00000 q^{36} -6.00000 q^{37} +2.60555 q^{38} -2.60555 q^{39} +1.00000 q^{40} -6.00000 q^{41} +1.00000 q^{42} +11.2111 q^{43} -2.00000 q^{44} -1.00000 q^{45} -1.00000 q^{46} -1.39445 q^{47} +1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} +4.60555 q^{51} -2.60555 q^{52} -3.21110 q^{53} -1.00000 q^{54} +2.00000 q^{55} +1.00000 q^{56} -2.60555 q^{57} -5.21110 q^{58} -5.21110 q^{59} -1.00000 q^{60} +10.0000 q^{61} -2.60555 q^{62} -1.00000 q^{63} +1.00000 q^{64} +2.60555 q^{65} +2.00000 q^{66} +3.21110 q^{67} +4.60555 q^{68} +1.00000 q^{69} -1.00000 q^{70} -6.00000 q^{71} -1.00000 q^{72} -2.00000 q^{73} +6.00000 q^{74} +1.00000 q^{75} -2.60555 q^{76} +2.00000 q^{77} +2.60555 q^{78} -14.4222 q^{79} -1.00000 q^{80} +1.00000 q^{81} +6.00000 q^{82} -10.6056 q^{83} -1.00000 q^{84} -4.60555 q^{85} -11.2111 q^{86} +5.21110 q^{87} +2.00000 q^{88} -5.39445 q^{89} +1.00000 q^{90} +2.60555 q^{91} +1.00000 q^{92} +2.60555 q^{93} +1.39445 q^{94} +2.60555 q^{95} -1.00000 q^{96} -11.8167 q^{97} -1.00000 q^{98} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9} + 2 q^{10} - 4 q^{11} + 2 q^{12} + 2 q^{13} + 2 q^{14} - 2 q^{15} + 2 q^{16} + 2 q^{17} - 2 q^{18} + 2 q^{19} - 2 q^{20} - 2 q^{21} + 4 q^{22} + 2 q^{23} - 2 q^{24} + 2 q^{25} - 2 q^{26} + 2 q^{27} - 2 q^{28} - 4 q^{29} + 2 q^{30} - 2 q^{31} - 2 q^{32} - 4 q^{33} - 2 q^{34} + 2 q^{35} + 2 q^{36} - 12 q^{37} - 2 q^{38} + 2 q^{39} + 2 q^{40} - 12 q^{41} + 2 q^{42} + 8 q^{43} - 4 q^{44} - 2 q^{45} - 2 q^{46} - 10 q^{47} + 2 q^{48} + 2 q^{49} - 2 q^{50} + 2 q^{51} + 2 q^{52} + 8 q^{53} - 2 q^{54} + 4 q^{55} + 2 q^{56} + 2 q^{57} + 4 q^{58} + 4 q^{59} - 2 q^{60} + 20 q^{61} + 2 q^{62} - 2 q^{63} + 2 q^{64} - 2 q^{65} + 4 q^{66} - 8 q^{67} + 2 q^{68} + 2 q^{69} - 2 q^{70} - 12 q^{71} - 2 q^{72} - 4 q^{73} + 12 q^{74} + 2 q^{75} + 2 q^{76} + 4 q^{77} - 2 q^{78} - 2 q^{80} + 2 q^{81} + 12 q^{82} - 14 q^{83} - 2 q^{84} - 2 q^{85} - 8 q^{86} - 4 q^{87} + 4 q^{88} - 18 q^{89} + 2 q^{90} - 2 q^{91} + 2 q^{92} - 2 q^{93} + 10 q^{94} - 2 q^{95} - 2 q^{96} - 2 q^{97} - 2 q^{98} - 4 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9 + 2 * q^10 - 4 * q^11 + 2 * q^12 + 2 * q^13 + 2 * q^14 - 2 * q^15 + 2 * q^16 + 2 * q^17 - 2 * q^18 + 2 * q^19 - 2 * q^20 - 2 * q^21 + 4 * q^22 + 2 * q^23 - 2 * q^24 + 2 * q^25 - 2 * q^26 + 2 * q^27 - 2 * q^28 - 4 * q^29 + 2 * q^30 - 2 * q^31 - 2 * q^32 - 4 * q^33 - 2 * q^34 + 2 * q^35 + 2 * q^36 - 12 * q^37 - 2 * q^38 + 2 * q^39 + 2 * q^40 - 12 * q^41 + 2 * q^42 + 8 * q^43 - 4 * q^44 - 2 * q^45 - 2 * q^46 - 10 * q^47 + 2 * q^48 + 2 * q^49 - 2 * q^50 + 2 * q^51 + 2 * q^52 + 8 * q^53 - 2 * q^54 + 4 * q^55 + 2 * q^56 + 2 * q^57 + 4 * q^58 + 4 * q^59 - 2 * q^60 + 20 * q^61 + 2 * q^62 - 2 * q^63 + 2 * q^64 - 2 * q^65 + 4 * q^66 - 8 * q^67 + 2 * q^68 + 2 * q^69 - 2 * q^70 - 12 * q^71 - 2 * q^72 - 4 * q^73 + 12 * q^74 + 2 * q^75 + 2 * q^76 + 4 * q^77 - 2 * q^78 - 2 * q^80 + 2 * q^81 + 12 * q^82 - 14 * q^83 - 2 * q^84 - 2 * q^85 - 8 * q^86 - 4 * q^87 + 4 * q^88 - 18 * q^89 + 2 * q^90 - 2 * q^91 + 2 * q^92 - 2 * q^93 + 10 * q^94 - 2 * q^95 - 2 * q^96 - 2 * q^97 - 2 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−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
$11$	−2.00000	−0.603023	−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000	−0.603023	−0.301511	+	0.953463i	$0.597491\pi$
$12$	1.00000	0.288675
$13$	−2.60555	−0.722650	−0.361325	−	0.932440i	$-0.617675\pi$
$13$	−2.60555	−0.722650	−0.361325	+	0.932440i	$0.617675\pi$
$14$	1.00000	0.267261
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	4.60555	1.11701	0.558505	−	0.829501i	$-0.311375\pi$
$17$	4.60555	1.11701	0.558505	+	0.829501i	$0.311375\pi$
$18$	−1.00000	−0.235702
$19$	−2.60555	−0.597754	−0.298877	−	0.954292i	$-0.596612\pi$
$19$	−2.60555	−0.597754	−0.298877	+	0.954292i	$0.596612\pi$
$20$	−1.00000	−0.223607
$21$	−1.00000	−0.218218
$22$	2.00000	0.426401
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	2.60555	0.510991
$27$	1.00000	0.192450
$28$	−1.00000	−0.188982
$29$	5.21110	0.967677	0.483839	−	0.875157i	$-0.339242\pi$
$29$	5.21110	0.967677	0.483839	+	0.875157i	$0.339242\pi$
$30$	1.00000	0.182574
$31$	2.60555	0.467971	0.233985	−	0.972240i	$-0.424823\pi$
$31$	2.60555	0.467971	0.233985	+	0.972240i	$0.424823\pi$
$32$	−1.00000	−0.176777
$33$	−2.00000	−0.348155
$34$	−4.60555	−0.789846
$35$	1.00000	0.169031
$36$	1.00000	0.166667
$37$	−6.00000	−0.986394	−0.493197	−	0.869918i	$-0.664172\pi$
$37$	−6.00000	−0.986394	−0.493197	+	0.869918i	$0.664172\pi$
$38$	2.60555	0.422676
$39$	−2.60555	−0.417222
$40$	1.00000	0.158114
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	1.00000	0.154303
$43$	11.2111	1.70968	0.854839	−	0.518894i	$-0.173656\pi$
$43$	11.2111	1.70968	0.854839	+	0.518894i	$0.173656\pi$
$44$	−2.00000	−0.301511
$45$	−1.00000	−0.149071
$46$	−1.00000	−0.147442
$47$	−1.39445	−0.203401	−0.101701	−	0.994815i	$-0.532428\pi$
$47$	−1.39445	−0.203401	−0.101701	+	0.994815i	$0.532428\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	4.60555	0.644906
$52$	−2.60555	−0.361325
$53$	−3.21110	−0.441079	−0.220539	−	0.975378i	$-0.570782\pi$
$53$	−3.21110	−0.441079	−0.220539	+	0.975378i	$0.570782\pi$
$54$	−1.00000	−0.136083
$55$	2.00000	0.269680
$56$	1.00000	0.133631
$57$	−2.60555	−0.345114
$58$	−5.21110	−0.684251
$59$	−5.21110	−0.678428	−0.339214	−	0.940709i	$-0.610161\pi$
$59$	−5.21110	−0.678428	−0.339214	+	0.940709i	$0.610161\pi$
$60$	−1.00000	−0.129099
$61$	10.0000	1.28037	0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000	1.28037	0.640184	+	0.768221i	$0.278858\pi$
$62$	−2.60555	−0.330905
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	2.60555	0.323179
$66$	2.00000	0.246183
$67$	3.21110	0.392299	0.196149	−	0.980574i	$-0.437156\pi$
$67$	3.21110	0.392299	0.196149	+	0.980574i	$0.437156\pi$
$68$	4.60555	0.558505
$69$	1.00000	0.120386
$70$	−1.00000	−0.119523
$71$	−6.00000	−0.712069	−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000	−0.712069	−0.356034	+	0.934473i	$0.615871\pi$
$72$	−1.00000	−0.117851
$73$	−2.00000	−0.234082	−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000	−0.234082	−0.117041	+	0.993127i	$0.537341\pi$
$74$	6.00000	0.697486
$75$	1.00000	0.115470
$76$	−2.60555	−0.298877
$77$	2.00000	0.227921
$78$	2.60555	0.295021
$79$	−14.4222	−1.62262	−0.811312	−	0.584613i	$-0.801246\pi$
$79$	−14.4222	−1.62262	−0.811312	+	0.584613i	$0.801246\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	6.00000	0.662589
$83$	−10.6056	−1.16411	−0.582055	−	0.813149i	$-0.697751\pi$
$83$	−10.6056	−1.16411	−0.582055	+	0.813149i	$0.697751\pi$
$84$	−1.00000	−0.109109
$85$	−4.60555	−0.499542
$86$	−11.2111	−1.20892
$87$	5.21110	0.558689
$88$	2.00000	0.213201
$89$	−5.39445	−0.571810	−0.285905	−	0.958258i	$-0.592294\pi$
$89$	−5.39445	−0.571810	−0.285905	+	0.958258i	$0.592294\pi$
$90$	1.00000	0.105409
$91$	2.60555	0.273136
$92$	1.00000	0.104257
$93$	2.60555	0.270183
$94$	1.39445	0.143826
$95$	2.60555	0.267324
$96$	−1.00000	−0.102062
$97$	−11.8167	−1.19980	−0.599900	−	0.800075i	$-0.704793\pi$
$97$	−11.8167	−1.19980	−0.599900	+	0.800075i	$0.704793\pi$
$98$	−1.00000	−0.101015
$99$	−2.00000	−0.201008
$100$	1.00000	0.100000
$101$	−15.8167	−1.57382	−0.786908	−	0.617070i	$-0.788319\pi$
$101$	−15.8167	−1.57382	−0.786908	+	0.617070i	$0.788319\pi$
$102$	−4.60555	−0.456018
$103$	8.00000	0.788263	0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000	0.788263	0.394132	+	0.919054i	$0.371045\pi$
$104$	2.60555	0.255495
$105$	1.00000	0.0975900
$106$	3.21110	0.311890
$107$	−9.21110	−0.890471	−0.445235	−	0.895414i	$-0.646880\pi$
$107$	−9.21110	−0.890471	−0.445235	+	0.895414i	$0.646880\pi$
$108$	1.00000	0.0962250
$109$	16.4222	1.57296	0.786481	−	0.617614i	$-0.211901\pi$
$109$	16.4222	1.57296	0.786481	+	0.617614i	$0.211901\pi$
$110$	−2.00000	−0.190693
$111$	−6.00000	−0.569495
$112$	−1.00000	−0.0944911
$113$	0.788897	0.0742132	0.0371066	−	0.999311i	$-0.488186\pi$
$113$	0.788897	0.0742132	0.0371066	+	0.999311i	$0.488186\pi$
$114$	2.60555	0.244032
$115$	−1.00000	−0.0932505
$116$	5.21110	0.483839
$117$	−2.60555	−0.240883
$118$	5.21110	0.479721
$119$	−4.60555	−0.422190
$120$	1.00000	0.0912871
$121$	−7.00000	−0.636364
$122$	−10.0000	−0.905357
$123$	−6.00000	−0.541002
$124$	2.60555	0.233985
$125$	−1.00000	−0.0894427
$126$	1.00000	0.0890871
$127$	−2.00000	−0.177471	−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	−2.00000	−0.177471	−0.0887357	+	0.996055i	$0.528283\pi$
$128$	−1.00000	−0.0883883
$129$	11.2111	0.987083
$130$	−2.60555	−0.228522
$131$	−12.0000	−1.04844	−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000	−1.04844	−0.524222	+	0.851581i	$0.675644\pi$
$132$	−2.00000	−0.174078
$133$	2.60555	0.225930
$134$	−3.21110	−0.277397
$135$	−1.00000	−0.0860663
$136$	−4.60555	−0.394923
$137$	−18.0000	−1.53784	−0.768922	−	0.639343i	$-0.779207\pi$
$137$	−18.0000	−1.53784	−0.768922	+	0.639343i	$0.779207\pi$
$138$	−1.00000	−0.0851257
$139$	−12.0000	−1.01783	−0.508913	−	0.860818i	$-0.669953\pi$
$139$	−12.0000	−1.01783	−0.508913	+	0.860818i	$0.669953\pi$
$140$	1.00000	0.0845154
$141$	−1.39445	−0.117434
$142$	6.00000	0.503509
$143$	5.21110	0.435774
$144$	1.00000	0.0833333
$145$	−5.21110	−0.432759
$146$	2.00000	0.165521
$147$	1.00000	0.0824786
$148$	−6.00000	−0.493197
$149$	−14.0000	−1.14692	−0.573462	−	0.819232i	$-0.694400\pi$
$149$	−14.0000	−1.14692	−0.573462	+	0.819232i	$0.694400\pi$
$150$	−1.00000	−0.0816497
$151$	17.2111	1.40062	0.700310	−	0.713839i	$-0.253045\pi$
$151$	17.2111	1.40062	0.700310	+	0.713839i	$0.253045\pi$
$152$	2.60555	0.211338
$153$	4.60555	0.372337
$154$	−2.00000	−0.161165
$155$	−2.60555	−0.209283
$156$	−2.60555	−0.208611
$157$	8.42221	0.672165	0.336083	−	0.941833i	$-0.390898\pi$
$157$	8.42221	0.672165	0.336083	+	0.941833i	$0.390898\pi$
$158$	14.4222	1.14737
$159$	−3.21110	−0.254657
$160$	1.00000	0.0790569
$161$	−1.00000	−0.0788110
$162$	−1.00000	−0.0785674
$163$	19.6333	1.53780	0.768900	−	0.639369i	$-0.220805\pi$
$163$	19.6333	1.53780	0.768900	+	0.639369i	$0.220805\pi$
$164$	−6.00000	−0.468521
$165$	2.00000	0.155700
$166$	10.6056	0.823150
$167$	13.3944	1.03649	0.518247	−	0.855231i	$-0.326585\pi$
$167$	13.3944	1.03649	0.518247	+	0.855231i	$0.326585\pi$
$168$	1.00000	0.0771517
$169$	−6.21110	−0.477777
$170$	4.60555	0.353230
$171$	−2.60555	−0.199251
$172$	11.2111	0.854839
$173$	−19.0278	−1.44665	−0.723327	−	0.690506i	$-0.757388\pi$
$173$	−19.0278	−1.44665	−0.723327	+	0.690506i	$0.757388\pi$
$174$	−5.21110	−0.395053
$175$	−1.00000	−0.0755929
$176$	−2.00000	−0.150756
$177$	−5.21110	−0.391690
$178$	5.39445	0.404331
$179$	−18.4222	−1.37694	−0.688470	−	0.725265i	$-0.741717\pi$
$179$	−18.4222	−1.37694	−0.688470	+	0.725265i	$0.741717\pi$
$180$	−1.00000	−0.0745356
$181$	−14.0000	−1.04061	−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000	−1.04061	−0.520306	+	0.853980i	$0.674182\pi$
$182$	−2.60555	−0.193136
$183$	10.0000	0.739221
$184$	−1.00000	−0.0737210
$185$	6.00000	0.441129
$186$	−2.60555	−0.191048
$187$	−9.21110	−0.673583
$188$	−1.39445	−0.101701
$189$	−1.00000	−0.0727393
$190$	−2.60555	−0.189027
$191$	−6.78890	−0.491227	−0.245614	−	0.969368i	$-0.578989\pi$
$191$	−6.78890	−0.491227	−0.245614	+	0.969368i	$0.578989\pi$
$192$	1.00000	0.0721688
$193$	−12.4222	−0.894170	−0.447085	−	0.894492i	$-0.647538\pi$
$193$	−12.4222	−0.894170	−0.447085	+	0.894492i	$0.647538\pi$
$194$	11.8167	0.848386
$195$	2.60555	0.186587
$196$	1.00000	0.0714286
$197$	−8.78890	−0.626183	−0.313092	−	0.949723i	$-0.601365\pi$
$197$	−8.78890	−0.626183	−0.313092	+	0.949723i	$0.601365\pi$
$198$	2.00000	0.142134
$199$	26.4222	1.87302	0.936510	−	0.350640i	$-0.114036\pi$
$199$	26.4222	1.87302	0.936510	+	0.350640i	$0.114036\pi$
$200$	−1.00000	−0.0707107
$201$	3.21110	0.226494
$202$	15.8167	1.11286
$203$	−5.21110	−0.365748
$204$	4.60555	0.322453
$205$	6.00000	0.419058
$206$	−8.00000	−0.557386
$207$	1.00000	0.0695048
$208$	−2.60555	−0.180662
$209$	5.21110	0.360460
$210$	−1.00000	−0.0690066
$211$	10.4222	0.717494	0.358747	−	0.933435i	$-0.383204\pi$
$211$	10.4222	0.717494	0.358747	+	0.933435i	$0.383204\pi$
$212$	−3.21110	−0.220539
$213$	−6.00000	−0.411113
$214$	9.21110	0.629658
$215$	−11.2111	−0.764591
$216$	−1.00000	−0.0680414
$217$	−2.60555	−0.176876
$218$	−16.4222	−1.11225
$219$	−2.00000	−0.135147
$220$	2.00000	0.134840
$221$	−12.0000	−0.807207
$222$	6.00000	0.402694
$223$	−11.3944	−0.763029	−0.381514	−	0.924363i	$-0.624597\pi$
$223$	−11.3944	−0.763029	−0.381514	+	0.924363i	$0.624597\pi$
$224$	1.00000	0.0668153
$225$	1.00000	0.0666667
$226$	−0.788897	−0.0524767
$227$	22.6056	1.50038	0.750192	−	0.661221i	$-0.229961\pi$
$227$	22.6056	1.50038	0.750192	+	0.661221i	$0.229961\pi$
$228$	−2.60555	−0.172557
$229$	−23.2111	−1.53383	−0.766916	−	0.641747i	$-0.778210\pi$
$229$	−23.2111	−1.53383	−0.766916	+	0.641747i	$0.778210\pi$
$230$	1.00000	0.0659380
$231$	2.00000	0.131590
$232$	−5.21110	−0.342126
$233$	−22.0000	−1.44127	−0.720634	−	0.693316i	$-0.756149\pi$
$233$	−22.0000	−1.44127	−0.720634	+	0.693316i	$0.756149\pi$
$234$	2.60555	0.170330
$235$	1.39445	0.0909638
$236$	−5.21110	−0.339214
$237$	−14.4222	−0.936823
$238$	4.60555	0.298534
$239$	−6.00000	−0.388108	−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000	−0.388108	−0.194054	+	0.980991i	$0.562164\pi$
$240$	−1.00000	−0.0645497
$241$	−21.8167	−1.40533	−0.702667	−	0.711519i	$-0.748008\pi$
$241$	−21.8167	−1.40533	−0.702667	+	0.711519i	$0.748008\pi$
$242$	7.00000	0.449977
$243$	1.00000	0.0641500
$244$	10.0000	0.640184
$245$	−1.00000	−0.0638877
$246$	6.00000	0.382546
$247$	6.78890	0.431967
$248$	−2.60555	−0.165453
$249$	−10.6056	−0.672100
$250$	1.00000	0.0632456
$251$	−11.3944	−0.719211	−0.359606	−	0.933104i	$-0.617089\pi$
$251$	−11.3944	−0.719211	−0.359606	+	0.933104i	$0.617089\pi$
$252$	−1.00000	−0.0629941
$253$	−2.00000	−0.125739
$254$	2.00000	0.125491
$255$	−4.60555	−0.288411
$256$	1.00000	0.0625000
$257$	25.6333	1.59896	0.799481	−	0.600692i	$-0.205108\pi$
$257$	25.6333	1.59896	0.799481	+	0.600692i	$0.205108\pi$
$258$	−11.2111	−0.697973
$259$	6.00000	0.372822
$260$	2.60555	0.161589
$261$	5.21110	0.322559
$262$	12.0000	0.741362
$263$	10.4222	0.642661	0.321330	−	0.946967i	$-0.395870\pi$
$263$	10.4222	0.642661	0.321330	+	0.946967i	$0.395870\pi$
$264$	2.00000	0.123091
$265$	3.21110	0.197256
$266$	−2.60555	−0.159757
$267$	−5.39445	−0.330135
$268$	3.21110	0.196149
$269$	25.0278	1.52597	0.762985	−	0.646417i	$-0.223733\pi$
$269$	25.0278	1.52597	0.762985	+	0.646417i	$0.223733\pi$
$270$	1.00000	0.0608581
$271$	−23.8167	−1.44676	−0.723379	−	0.690451i	$-0.757412\pi$
$271$	−23.8167	−1.44676	−0.723379	+	0.690451i	$0.757412\pi$
$272$	4.60555	0.279253
$273$	2.60555	0.157695
$274$	18.0000	1.08742
$275$	−2.00000	−0.120605
$276$	1.00000	0.0601929
$277$	13.2111	0.793778	0.396889	−	0.917867i	$-0.370090\pi$
$277$	13.2111	0.793778	0.396889	+	0.917867i	$0.370090\pi$
$278$	12.0000	0.719712
$279$	2.60555	0.155990
$280$	−1.00000	−0.0597614
$281$	−10.7889	−0.643612	−0.321806	−	0.946806i	$-0.604290\pi$
$281$	−10.7889	−0.643612	−0.321806	+	0.946806i	$0.604290\pi$
$282$	1.39445	0.0830382
$283$	−24.2389	−1.44085	−0.720425	−	0.693533i	$-0.756053\pi$
$283$	−24.2389	−1.44085	−0.720425	+	0.693533i	$0.756053\pi$
$284$	−6.00000	−0.356034
$285$	2.60555	0.154340
$286$	−5.21110	−0.308139
$287$	6.00000	0.354169
$288$	−1.00000	−0.0589256
$289$	4.21110	0.247712
$290$	5.21110	0.306006
$291$	−11.8167	−0.692705
$292$	−2.00000	−0.117041
$293$	21.6333	1.26383	0.631916	−	0.775037i	$-0.282269\pi$
$293$	21.6333	1.26383	0.631916	+	0.775037i	$0.282269\pi$
$294$	−1.00000	−0.0583212
$295$	5.21110	0.303402
$296$	6.00000	0.348743
$297$	−2.00000	−0.116052
$298$	14.0000	0.810998
$299$	−2.60555	−0.150683
$300$	1.00000	0.0577350
$301$	−11.2111	−0.646197
$302$	−17.2111	−0.990388
$303$	−15.8167	−0.908643
$304$	−2.60555	−0.149439
$305$	−10.0000	−0.572598
$306$	−4.60555	−0.263282
$307$	−1.57779	−0.0900495	−0.0450248	−	0.998986i	$-0.514337\pi$
$307$	−1.57779	−0.0900495	−0.0450248	+	0.998986i	$0.514337\pi$
$308$	2.00000	0.113961
$309$	8.00000	0.455104
$310$	2.60555	0.147985
$311$	−11.0278	−0.625327	−0.312663	−	0.949864i	$-0.601221\pi$
$311$	−11.0278	−0.625327	−0.312663	+	0.949864i	$0.601221\pi$
$312$	2.60555	0.147510
$313$	13.3944	0.757099	0.378550	−	0.925581i	$-0.376423\pi$
$313$	13.3944	0.757099	0.378550	+	0.925581i	$0.376423\pi$
$314$	−8.42221	−0.475293
$315$	1.00000	0.0563436
$316$	−14.4222	−0.811312
$317$	8.78890	0.493634	0.246817	−	0.969062i	$-0.420615\pi$
$317$	8.78890	0.493634	0.246817	+	0.969062i	$0.420615\pi$
$318$	3.21110	0.180070
$319$	−10.4222	−0.583531
$320$	−1.00000	−0.0559017
$321$	−9.21110	−0.514114
$322$	1.00000	0.0557278
$323$	−12.0000	−0.667698
$324$	1.00000	0.0555556
$325$	−2.60555	−0.144530
$326$	−19.6333	−1.08739
$327$	16.4222	0.908150
$328$	6.00000	0.331295
$329$	1.39445	0.0768784
$330$	−2.00000	−0.110096
$331$	−14.4222	−0.792716	−0.396358	−	0.918096i	$-0.629726\pi$
$331$	−14.4222	−0.792716	−0.396358	+	0.918096i	$0.629726\pi$
$332$	−10.6056	−0.582055
$333$	−6.00000	−0.328798
$334$	−13.3944	−0.732912
$335$	−3.21110	−0.175441
$336$	−1.00000	−0.0545545
$337$	−10.4222	−0.567734	−0.283867	−	0.958864i	$-0.591617\pi$
$337$	−10.4222	−0.567734	−0.283867	+	0.958864i	$0.591617\pi$
$338$	6.21110	0.337839
$339$	0.788897	0.0428470
$340$	−4.60555	−0.249771
$341$	−5.21110	−0.282197
$342$	2.60555	0.140892
$343$	−1.00000	−0.0539949
$344$	−11.2111	−0.604462
$345$	−1.00000	−0.0538382
$346$	19.0278	1.02294
$347$	18.4222	0.988956	0.494478	−	0.869190i	$-0.335359\pi$
$347$	18.4222	0.988956	0.494478	+	0.869190i	$0.335359\pi$
$348$	5.21110	0.279344
$349$	28.2389	1.51159	0.755796	−	0.654807i	$-0.227250\pi$
$349$	28.2389	1.51159	0.755796	+	0.654807i	$0.227250\pi$
$350$	1.00000	0.0534522
$351$	−2.60555	−0.139074
$352$	2.00000	0.106600
$353$	−7.21110	−0.383808	−0.191904	−	0.981414i	$-0.561466\pi$
$353$	−7.21110	−0.383808	−0.191904	+	0.981414i	$0.561466\pi$
$354$	5.21110	0.276967
$355$	6.00000	0.318447
$356$	−5.39445	−0.285905
$357$	−4.60555	−0.243752
$358$	18.4222	0.973644
$359$	14.7889	0.780528	0.390264	−	0.920703i	$-0.372384\pi$
$359$	14.7889	0.780528	0.390264	+	0.920703i	$0.372384\pi$
$360$	1.00000	0.0527046
$361$	−12.2111	−0.642690
$362$	14.0000	0.735824
$363$	−7.00000	−0.367405
$364$	2.60555	0.136568
$365$	2.00000	0.104685
$366$	−10.0000	−0.522708
$367$	5.57779	0.291159	0.145579	−	0.989347i	$-0.453495\pi$
$367$	5.57779	0.291159	0.145579	+	0.989347i	$0.453495\pi$
$368$	1.00000	0.0521286
$369$	−6.00000	−0.312348
$370$	−6.00000	−0.311925
$371$	3.21110	0.166712
$372$	2.60555	0.135092
$373$	20.4222	1.05742	0.528711	−	0.848802i	$-0.322676\pi$
$373$	20.4222	1.05742	0.528711	+	0.848802i	$0.322676\pi$
$374$	9.21110	0.476295
$375$	−1.00000	−0.0516398
$376$	1.39445	0.0719132
$377$	−13.5778	−0.699292
$378$	1.00000	0.0514344
$379$	35.6333	1.83036	0.915180	−	0.403045i	$-0.132048\pi$
$379$	35.6333	1.83036	0.915180	+	0.403045i	$0.132048\pi$
$380$	2.60555	0.133662
$381$	−2.00000	−0.102463
$382$	6.78890	0.347350
$383$	−5.21110	−0.266275	−0.133137	−	0.991098i	$-0.542505\pi$
$383$	−5.21110	−0.266275	−0.133137	+	0.991098i	$0.542505\pi$
$384$	−1.00000	−0.0510310
$385$	−2.00000	−0.101929
$386$	12.4222	0.632274
$387$	11.2111	0.569892
$388$	−11.8167	−0.599900
$389$	28.4222	1.44106	0.720532	−	0.693422i	$-0.243898\pi$
$389$	28.4222	1.44106	0.720532	+	0.693422i	$0.243898\pi$
$390$	−2.60555	−0.131937
$391$	4.60555	0.232913
$392$	−1.00000	−0.0505076
$393$	−12.0000	−0.605320
$394$	8.78890	0.442778
$395$	14.4222	0.725660
$396$	−2.00000	−0.100504
$397$	13.3944	0.672248	0.336124	−	0.941818i	$-0.390884\pi$
$397$	13.3944	0.672248	0.336124	+	0.941818i	$0.390884\pi$
$398$	−26.4222	−1.32443
$399$	2.60555	0.130441
$400$	1.00000	0.0500000
$401$	1.21110	0.0604796	0.0302398	−	0.999543i	$-0.490373\pi$
$401$	1.21110	0.0604796	0.0302398	+	0.999543i	$0.490373\pi$
$402$	−3.21110	−0.160155
$403$	−6.78890	−0.338179
$404$	−15.8167	−0.786908
$405$	−1.00000	−0.0496904
$406$	5.21110	0.258623
$407$	12.0000	0.594818
$408$	−4.60555	−0.228009
$409$	−17.6333	−0.871911	−0.435955	−	0.899968i	$-0.643589\pi$
$409$	−17.6333	−0.871911	−0.435955	+	0.899968i	$0.643589\pi$
$410$	−6.00000	−0.296319
$411$	−18.0000	−0.887875
$412$	8.00000	0.394132
$413$	5.21110	0.256422
$414$	−1.00000	−0.0491473
$415$	10.6056	0.520606
$416$	2.60555	0.127748
$417$	−12.0000	−0.587643
$418$	−5.21110	−0.254883
$419$	−31.3944	−1.53372	−0.766860	−	0.641815i	$-0.778182\pi$
$419$	−31.3944	−1.53372	−0.766860	+	0.641815i	$0.778182\pi$
$420$	1.00000	0.0487950
$421$	18.0000	0.877266	0.438633	−	0.898666i	$-0.355463\pi$
$421$	18.0000	0.877266	0.438633	+	0.898666i	$0.355463\pi$
$422$	−10.4222	−0.507345
$423$	−1.39445	−0.0678004
$424$	3.21110	0.155945
$425$	4.60555	0.223402
$426$	6.00000	0.290701
$427$	−10.0000	−0.483934
$428$	−9.21110	−0.445235
$429$	5.21110	0.251594
$430$	11.2111	0.540647
$431$	−10.4222	−0.502020	−0.251010	−	0.967984i	$-0.580763\pi$
$431$	−10.4222	−0.502020	−0.251010	+	0.967984i	$0.580763\pi$
$432$	1.00000	0.0481125
$433$	−35.8167	−1.72124	−0.860619	−	0.509249i	$-0.829923\pi$
$433$	−35.8167	−1.72124	−0.860619	+	0.509249i	$0.829923\pi$
$434$	2.60555	0.125070
$435$	−5.21110	−0.249853
$436$	16.4222	0.786481
$437$	−2.60555	−0.124640
$438$	2.00000	0.0955637
$439$	14.2389	0.679584	0.339792	−	0.940501i	$-0.389643\pi$
$439$	14.2389	0.679584	0.339792	+	0.940501i	$0.389643\pi$
$440$	−2.00000	−0.0953463
$441$	1.00000	0.0476190
$442$	12.0000	0.570782
$443$	5.57779	0.265009	0.132505	−	0.991182i	$-0.457698\pi$
$443$	5.57779	0.265009	0.132505	+	0.991182i	$0.457698\pi$
$444$	−6.00000	−0.284747
$445$	5.39445	0.255721
$446$	11.3944	0.539543
$447$	−14.0000	−0.662177
$448$	−1.00000	−0.0472456
$449$	−6.00000	−0.283158	−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000	−0.283158	−0.141579	+	0.989927i	$0.545218\pi$
$450$	−1.00000	−0.0471405
$451$	12.0000	0.565058
$452$	0.788897	0.0371066
$453$	17.2111	0.808648
$454$	−22.6056	−1.06093
$455$	−2.60555	−0.122150
$456$	2.60555	0.122016
$457$	27.6333	1.29263	0.646316	−	0.763070i	$-0.276309\pi$
$457$	27.6333	1.29263	0.646316	+	0.763070i	$0.276309\pi$
$458$	23.2111	1.08458
$459$	4.60555	0.214969
$460$	−1.00000	−0.0466252
$461$	−23.8167	−1.10925	−0.554626	−	0.832100i	$-0.687139\pi$
$461$	−23.8167	−1.10925	−0.554626	+	0.832100i	$0.687139\pi$
$462$	−2.00000	−0.0930484
$463$	−29.6333	−1.37718	−0.688588	−	0.725153i	$-0.741769\pi$
$463$	−29.6333	−1.37718	−0.688588	+	0.725153i	$0.741769\pi$
$464$	5.21110	0.241919
$465$	−2.60555	−0.120830
$466$	22.0000	1.01913
$467$	29.0278	1.34324	0.671622	−	0.740894i	$-0.265598\pi$
$467$	29.0278	1.34324	0.671622	+	0.740894i	$0.265598\pi$
$468$	−2.60555	−0.120442
$469$	−3.21110	−0.148275
$470$	−1.39445	−0.0643211
$471$	8.42221	0.388075
$472$	5.21110	0.239860
$473$	−22.4222	−1.03097
$474$	14.4222	0.662434
$475$	−2.60555	−0.119551
$476$	−4.60555	−0.211095
$477$	−3.21110	−0.147026
$478$	6.00000	0.274434
$479$	−24.0000	−1.09659	−0.548294	−	0.836286i	$-0.684723\pi$
$479$	−24.0000	−1.09659	−0.548294	+	0.836286i	$0.684723\pi$
$480$	1.00000	0.0456435
$481$	15.6333	0.712817
$482$	21.8167	0.993721
$483$	−1.00000	−0.0455016
$484$	−7.00000	−0.318182
$485$	11.8167	0.536567
$486$	−1.00000	−0.0453609
$487$	−40.0555	−1.81509	−0.907544	−	0.419956i	$-0.862045\pi$
$487$	−40.0555	−1.81509	−0.907544	+	0.419956i	$0.862045\pi$
$488$	−10.0000	−0.452679
$489$	19.6333	0.887849
$490$	1.00000	0.0451754
$491$	−18.7889	−0.847931	−0.423966	−	0.905678i	$-0.639362\pi$
$491$	−18.7889	−0.847931	−0.423966	+	0.905678i	$0.639362\pi$
$492$	−6.00000	−0.270501
$493$	24.0000	1.08091
$494$	−6.78890	−0.305447
$495$	2.00000	0.0898933
$496$	2.60555	0.116993
$497$	6.00000	0.269137
$498$	10.6056	0.475246
$499$	−28.8444	−1.29125	−0.645627	−	0.763653i	$-0.723404\pi$
$499$	−28.8444	−1.29125	−0.645627	+	0.763653i	$0.723404\pi$
$500$	−1.00000	−0.0447214
$501$	13.3944	0.598420
$502$	11.3944	0.508559
$503$	−34.4222	−1.53481	−0.767405	−	0.641163i	$-0.778452\pi$
$503$	−34.4222	−1.53481	−0.767405	+	0.641163i	$0.778452\pi$
$504$	1.00000	0.0445435
$505$	15.8167	0.703832
$506$	2.00000	0.0889108
$507$	−6.21110	−0.275845
$508$	−2.00000	−0.0887357
$509$	−23.8167	−1.05565	−0.527827	−	0.849352i	$-0.676993\pi$
$509$	−23.8167	−1.05565	−0.527827	+	0.849352i	$0.676993\pi$
$510$	4.60555	0.203937
$511$	2.00000	0.0884748
$512$	−1.00000	−0.0441942
$513$	−2.60555	−0.115038
$514$	−25.6333	−1.13064
$515$	−8.00000	−0.352522
$516$	11.2111	0.493541
$517$	2.78890	0.122656
$518$	−6.00000	−0.263625
$519$	−19.0278	−0.835226
$520$	−2.60555	−0.114261
$521$	−7.81665	−0.342454	−0.171227	−	0.985232i	$-0.554773\pi$
$521$	−7.81665	−0.342454	−0.171227	+	0.985232i	$0.554773\pi$
$522$	−5.21110	−0.228084
$523$	−24.2389	−1.05989	−0.529946	−	0.848032i	$-0.677788\pi$
$523$	−24.2389	−1.05989	−0.529946	+	0.848032i	$0.677788\pi$
$524$	−12.0000	−0.524222
$525$	−1.00000	−0.0436436
$526$	−10.4222	−0.454430
$527$	12.0000	0.522728
$528$	−2.00000	−0.0870388
$529$	1.00000	0.0434783
$530$	−3.21110	−0.139481
$531$	−5.21110	−0.226143
$532$	2.60555	0.112965
$533$	15.6333	0.677154
$534$	5.39445	0.233441
$535$	9.21110	0.398231
$536$	−3.21110	−0.138699
$537$	−18.4222	−0.794977
$538$	−25.0278	−1.07902
$539$	−2.00000	−0.0861461
$540$	−1.00000	−0.0430331
$541$	−18.8444	−0.810184	−0.405092	−	0.914276i	$-0.632761\pi$
$541$	−18.8444	−0.810184	−0.405092	+	0.914276i	$0.632761\pi$
$542$	23.8167	1.02301
$543$	−14.0000	−0.600798
$544$	−4.60555	−0.197461
$545$	−16.4222	−0.703450
$546$	−2.60555	−0.111507
$547$	14.4222	0.616649	0.308324	−	0.951281i	$-0.400232\pi$
$547$	14.4222	0.616649	0.308324	+	0.951281i	$0.400232\pi$
$548$	−18.0000	−0.768922
$549$	10.0000	0.426790
$550$	2.00000	0.0852803
$551$	−13.5778	−0.578434
$552$	−1.00000	−0.0425628
$553$	14.4222	0.613295
$554$	−13.2111	−0.561286
$555$	6.00000	0.254686
$556$	−12.0000	−0.508913
$557$	−16.4222	−0.695831	−0.347916	−	0.937526i	$-0.613110\pi$
$557$	−16.4222	−0.695831	−0.347916	+	0.937526i	$0.613110\pi$
$558$	−2.60555	−0.110302
$559$	−29.2111	−1.23550
$560$	1.00000	0.0422577
$561$	−9.21110	−0.388893
$562$	10.7889	0.455102
$563$	31.8167	1.34091	0.670456	−	0.741949i	$-0.266098\pi$
$563$	31.8167	1.34091	0.670456	+	0.741949i	$0.266098\pi$
$564$	−1.39445	−0.0587169
$565$	−0.788897	−0.0331892
$566$	24.2389	1.01884
$567$	−1.00000	−0.0419961
$568$	6.00000	0.251754
$569$	14.7889	0.619983	0.309991	−	0.950739i	$-0.399674\pi$
$569$	14.7889	0.619983	0.309991	+	0.950739i	$0.399674\pi$
$570$	−2.60555	−0.109135
$571$	4.00000	0.167395	0.0836974	−	0.996491i	$-0.473327\pi$
$571$	4.00000	0.167395	0.0836974	+	0.996491i	$0.473327\pi$
$572$	5.21110	0.217887
$573$	−6.78890	−0.283610
$574$	−6.00000	−0.250435
$575$	1.00000	0.0417029
$576$	1.00000	0.0416667
$577$	0.788897	0.0328422	0.0164211	−	0.999865i	$-0.494773\pi$
$577$	0.788897	0.0328422	0.0164211	+	0.999865i	$0.494773\pi$
$578$	−4.21110	−0.175159
$579$	−12.4222	−0.516249
$580$	−5.21110	−0.216379
$581$	10.6056	0.439992
$582$	11.8167	0.489816
$583$	6.42221	0.265981
$584$	2.00000	0.0827606
$585$	2.60555	0.107726
$586$	−21.6333	−0.893664
$587$	12.0000	0.495293	0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000	0.495293	0.247647	+	0.968850i	$0.420343\pi$
$588$	1.00000	0.0412393
$589$	−6.78890	−0.279732
$590$	−5.21110	−0.214538
$591$	−8.78890	−0.361527
$592$	−6.00000	−0.246598
$593$	28.0555	1.15210	0.576051	−	0.817414i	$-0.304593\pi$
$593$	28.0555	1.15210	0.576051	+	0.817414i	$0.304593\pi$
$594$	2.00000	0.0820610
$595$	4.60555	0.188809
$596$	−14.0000	−0.573462
$597$	26.4222	1.08139
$598$	2.60555	0.106549
$599$	−15.2111	−0.621509	−0.310754	−	0.950490i	$-0.600582\pi$
$599$	−15.2111	−0.621509	−0.310754	+	0.950490i	$0.600582\pi$
$600$	−1.00000	−0.0408248
$601$	−34.0000	−1.38689	−0.693444	−	0.720510i	$-0.743908\pi$
$601$	−34.0000	−1.38689	−0.693444	+	0.720510i	$0.743908\pi$
$602$	11.2111	0.456930
$603$	3.21110	0.130766
$604$	17.2111	0.700310
$605$	7.00000	0.284590
$606$	15.8167	0.642508
$607$	1.81665	0.0737357	0.0368679	−	0.999320i	$-0.488262\pi$
$607$	1.81665	0.0737357	0.0368679	+	0.999320i	$0.488262\pi$
$608$	2.60555	0.105669
$609$	−5.21110	−0.211165
$610$	10.0000	0.404888
$611$	3.63331	0.146988
$612$	4.60555	0.186168
$613$	41.2666	1.66674	0.833371	−	0.552713i	$-0.186408\pi$
$613$	41.2666	1.66674	0.833371	+	0.552713i	$0.186408\pi$
$614$	1.57779	0.0636746
$615$	6.00000	0.241943
$616$	−2.00000	−0.0805823
$617$	−26.8444	−1.08072	−0.540358	−	0.841435i	$-0.681711\pi$
$617$	−26.8444	−1.08072	−0.540358	+	0.841435i	$0.681711\pi$
$618$	−8.00000	−0.321807
$619$	31.4500	1.26408	0.632040	−	0.774935i	$-0.282218\pi$
$619$	31.4500	1.26408	0.632040	+	0.774935i	$0.282218\pi$
$620$	−2.60555	−0.104641
$621$	1.00000	0.0401286
$622$	11.0278	0.442173
$623$	5.39445	0.216124
$624$	−2.60555	−0.104306
$625$	1.00000	0.0400000
$626$	−13.3944	−0.535350
$627$	5.21110	0.208111
$628$	8.42221	0.336083
$629$	−27.6333	−1.10181
$630$	−1.00000	−0.0398410
$631$	−9.57779	−0.381286	−0.190643	−	0.981659i	$-0.561057\pi$
$631$	−9.57779	−0.381286	−0.190643	+	0.981659i	$0.561057\pi$
$632$	14.4222	0.573685
$633$	10.4222	0.414245
$634$	−8.78890	−0.349052
$635$	2.00000	0.0793676
$636$	−3.21110	−0.127328
$637$	−2.60555	−0.103236
$638$	10.4222	0.412619
$639$	−6.00000	−0.237356
$640$	1.00000	0.0395285
$641$	15.6333	0.617479	0.308739	−	0.951147i	$-0.400093\pi$
$641$	15.6333	0.617479	0.308739	+	0.951147i	$0.400093\pi$
$642$	9.21110	0.363533
$643$	−37.4500	−1.47688	−0.738441	−	0.674318i	$-0.764438\pi$
$643$	−37.4500	−1.47688	−0.738441	+	0.674318i	$0.764438\pi$
$644$	−1.00000	−0.0394055
$645$	−11.2111	−0.441437
$646$	12.0000	0.472134
$647$	6.23886	0.245275	0.122637	−	0.992452i	$-0.460865\pi$
$647$	6.23886	0.245275	0.122637	+	0.992452i	$0.460865\pi$
$648$	−1.00000	−0.0392837
$649$	10.4222	0.409107
$650$	2.60555	0.102198
$651$	−2.60555	−0.102120
$652$	19.6333	0.768900
$653$	−26.0000	−1.01746	−0.508729	−	0.860927i	$-0.669885\pi$
$653$	−26.0000	−1.01746	−0.508729	+	0.860927i	$0.669885\pi$
$654$	−16.4222	−0.642159
$655$	12.0000	0.468879
$656$	−6.00000	−0.234261
$657$	−2.00000	−0.0780274
$658$	−1.39445	−0.0543613
$659$	24.7889	0.965638	0.482819	−	0.875720i	$-0.339613\pi$
$659$	24.7889	0.965638	0.482819	+	0.875720i	$0.339613\pi$
$660$	2.00000	0.0778499
$661$	−7.21110	−0.280479	−0.140240	−	0.990118i	$-0.544787\pi$
$661$	−7.21110	−0.280479	−0.140240	+	0.990118i	$0.544787\pi$
$662$	14.4222	0.560535
$663$	−12.0000	−0.466041
$664$	10.6056	0.411575
$665$	−2.60555	−0.101039
$666$	6.00000	0.232495
$667$	5.21110	0.201775
$668$	13.3944	0.518247
$669$	−11.3944	−0.440535
$670$	3.21110	0.124056
$671$	−20.0000	−0.772091
$672$	1.00000	0.0385758
$673$	−14.0000	−0.539660	−0.269830	−	0.962908i	$-0.586968\pi$
$673$	−14.0000	−0.539660	−0.269830	+	0.962908i	$0.586968\pi$
$674$	10.4222	0.401448
$675$	1.00000	0.0384900
$676$	−6.21110	−0.238889
$677$	−0.422205	−0.0162267	−0.00811333	−	0.999967i	$-0.502583\pi$
$677$	−0.422205	−0.0162267	−0.00811333	+	0.999967i	$0.502583\pi$
$678$	−0.788897	−0.0302974
$679$	11.8167	0.453482
$680$	4.60555	0.176615
$681$	22.6056	0.866247
$682$	5.21110	0.199543
$683$	18.4222	0.704906	0.352453	−	0.935829i	$-0.385348\pi$
$683$	18.4222	0.704906	0.352453	+	0.935829i	$0.385348\pi$
$684$	−2.60555	−0.0996257
$685$	18.0000	0.687745
$686$	1.00000	0.0381802
$687$	−23.2111	−0.885559
$688$	11.2111	0.427419
$689$	8.36669	0.318746
$690$	1.00000	0.0380693
$691$	19.6333	0.746886	0.373443	−	0.927653i	$-0.378177\pi$
$691$	19.6333	0.746886	0.373443	+	0.927653i	$0.378177\pi$
$692$	−19.0278	−0.723327
$693$	2.00000	0.0759737
$694$	−18.4222	−0.699297
$695$	12.0000	0.455186
$696$	−5.21110	−0.197526
$697$	−27.6333	−1.04669
$698$	−28.2389	−1.06886
$699$	−22.0000	−0.832116
$700$	−1.00000	−0.0377964
$701$	6.00000	0.226617	0.113308	−	0.993560i	$-0.463855\pi$
$701$	6.00000	0.226617	0.113308	+	0.993560i	$0.463855\pi$
$702$	2.60555	0.0983402
$703$	15.6333	0.589621
$704$	−2.00000	−0.0753778
$705$	1.39445	0.0525180
$706$	7.21110	0.271393
$707$	15.8167	0.594846
$708$	−5.21110	−0.195845
$709$	20.7889	0.780743	0.390372	−	0.920657i	$-0.372346\pi$
$709$	20.7889	0.780743	0.390372	+	0.920657i	$0.372346\pi$
$710$	−6.00000	−0.225176
$711$	−14.4222	−0.540875
$712$	5.39445	0.202166
$713$	2.60555	0.0975787
$714$	4.60555	0.172358
$715$	−5.21110	−0.194884
$716$	−18.4222	−0.688470
$717$	−6.00000	−0.224074
$718$	−14.7889	−0.551917
$719$	−7.39445	−0.275766	−0.137883	−	0.990448i	$-0.544030\pi$
$719$	−7.39445	−0.275766	−0.137883	+	0.990448i	$0.544030\pi$
$720$	−1.00000	−0.0372678
$721$	−8.00000	−0.297936
$722$	12.2111	0.454450
$723$	−21.8167	−0.811370
$724$	−14.0000	−0.520306
$725$	5.21110	0.193535
$726$	7.00000	0.259794
$727$	33.2111	1.23173	0.615866	−	0.787851i	$-0.288806\pi$
$727$	33.2111	1.23173	0.615866	+	0.787851i	$0.288806\pi$
$728$	−2.60555	−0.0965682
$729$	1.00000	0.0370370
$730$	−2.00000	−0.0740233
$731$	51.6333	1.90973
$732$	10.0000	0.369611
$733$	−1.63331	−0.0603276	−0.0301638	−	0.999545i	$-0.509603\pi$
$733$	−1.63331	−0.0603276	−0.0301638	+	0.999545i	$0.509603\pi$
$734$	−5.57779	−0.205880
$735$	−1.00000	−0.0368856
$736$	−1.00000	−0.0368605
$737$	−6.42221	−0.236565
$738$	6.00000	0.220863
$739$	−16.0000	−0.588570	−0.294285	−	0.955718i	$-0.595081\pi$
$739$	−16.0000	−0.588570	−0.294285	+	0.955718i	$0.595081\pi$
$740$	6.00000	0.220564
$741$	6.78890	0.249396
$742$	−3.21110	−0.117883
$743$	−30.4222	−1.11608	−0.558041	−	0.829813i	$-0.688447\pi$
$743$	−30.4222	−1.11608	−0.558041	+	0.829813i	$0.688447\pi$
$744$	−2.60555	−0.0955241
$745$	14.0000	0.512920
$746$	−20.4222	−0.747710
$747$	−10.6056	−0.388037
$748$	−9.21110	−0.336791
$749$	9.21110	0.336566
$750$	1.00000	0.0365148
$751$	21.5778	0.787385	0.393692	−	0.919242i	$-0.371197\pi$
$751$	21.5778	0.787385	0.393692	+	0.919242i	$0.371197\pi$
$752$	−1.39445	−0.0508503
$753$	−11.3944	−0.415237
$754$	13.5778	0.494474
$755$	−17.2111	−0.626376
$756$	−1.00000	−0.0363696
$757$	−18.8444	−0.684912	−0.342456	−	0.939534i	$-0.611259\pi$
$757$	−18.8444	−0.684912	−0.342456	+	0.939534i	$0.611259\pi$
$758$	−35.6333	−1.29426
$759$	−2.00000	−0.0725954
$760$	−2.60555	−0.0945133
$761$	−18.0000	−0.652499	−0.326250	−	0.945284i	$-0.605785\pi$
$761$	−18.0000	−0.652499	−0.326250	+	0.945284i	$0.605785\pi$
$762$	2.00000	0.0724524
$763$	−16.4222	−0.594524
$764$	−6.78890	−0.245614
$765$	−4.60555	−0.166514
$766$	5.21110	0.188285
$767$	13.5778	0.490266
$768$	1.00000	0.0360844
$769$	47.8722	1.72631	0.863157	−	0.504935i	$-0.168484\pi$
$769$	47.8722	1.72631	0.863157	+	0.504935i	$0.168484\pi$
$770$	2.00000	0.0720750
$771$	25.6333	0.923161
$772$	−12.4222	−0.447085
$773$	−46.8444	−1.68488	−0.842438	−	0.538793i	$-0.818880\pi$
$773$	−46.8444	−1.68488	−0.842438	+	0.538793i	$0.818880\pi$
$774$	−11.2111	−0.402975
$775$	2.60555	0.0935942
$776$	11.8167	0.424193
$777$	6.00000	0.215249
$778$	−28.4222	−1.01899
$779$	15.6333	0.560121
$780$	2.60555	0.0932937
$781$	12.0000	0.429394
$782$	−4.60555	−0.164694
$783$	5.21110	0.186230
$784$	1.00000	0.0357143
$785$	−8.42221	−0.300601
$786$	12.0000	0.428026
$787$	−11.0278	−0.393097	−0.196549	−	0.980494i	$-0.562973\pi$
$787$	−11.0278	−0.393097	−0.196549	+	0.980494i	$0.562973\pi$
$788$	−8.78890	−0.313092
$789$	10.4222	0.371040
$790$	−14.4222	−0.513119
$791$	−0.788897	−0.0280500
$792$	2.00000	0.0710669
$793$	−26.0555	−0.925258
$794$	−13.3944	−0.475351
$795$	3.21110	0.113886
$796$	26.4222	0.936510
$797$	31.2111	1.10555	0.552777	−	0.833329i	$-0.313568\pi$
$797$	31.2111	1.10555	0.552777	+	0.833329i	$0.313568\pi$
$798$	−2.60555	−0.0922355
$799$	−6.42221	−0.227201
$800$	−1.00000	−0.0353553
$801$	−5.39445	−0.190603
$802$	−1.21110	−0.0427655
$803$	4.00000	0.141157
$804$	3.21110	0.113247
$805$	1.00000	0.0352454
$806$	6.78890	0.239129
$807$	25.0278	0.881019
$808$	15.8167	0.556428
$809$	−54.8444	−1.92823	−0.964113	−	0.265491i	$-0.914466\pi$
$809$	−54.8444	−1.92823	−0.964113	+	0.265491i	$0.914466\pi$
$810$	1.00000	0.0351364
$811$	−46.4222	−1.63010	−0.815052	−	0.579388i	$-0.803292\pi$
$811$	−46.4222	−1.63010	−0.815052	+	0.579388i	$0.803292\pi$
$812$	−5.21110	−0.182874
$813$	−23.8167	−0.835287
$814$	−12.0000	−0.420600
$815$	−19.6333	−0.687725
$816$	4.60555	0.161227
$817$	−29.2111	−1.02197
$818$	17.6333	0.616534
$819$	2.60555	0.0910453
$820$	6.00000	0.209529
$821$	8.84441	0.308672	0.154336	−	0.988018i	$-0.450676\pi$
$821$	8.84441	0.308672	0.154336	+	0.988018i	$0.450676\pi$
$822$	18.0000	0.627822
$823$	11.5778	0.403577	0.201788	−	0.979429i	$-0.435325\pi$
$823$	11.5778	0.403577	0.201788	+	0.979429i	$0.435325\pi$
$824$	−8.00000	−0.278693
$825$	−2.00000	−0.0696311
$826$	−5.21110	−0.181317
$827$	−3.63331	−0.126342	−0.0631712	−	0.998003i	$-0.520121\pi$
$827$	−3.63331	−0.126342	−0.0631712	+	0.998003i	$0.520121\pi$
$828$	1.00000	0.0347524
$829$	−50.6611	−1.75953	−0.879766	−	0.475407i	$-0.842301\pi$
$829$	−50.6611	−1.75953	−0.879766	+	0.475407i	$0.842301\pi$
$830$	−10.6056	−0.368124
$831$	13.2111	0.458288
$832$	−2.60555	−0.0903312
$833$	4.60555	0.159573
$834$	12.0000	0.415526
$835$	−13.3944	−0.463534
$836$	5.21110	0.180230
$837$	2.60555	0.0900610
$838$	31.3944	1.08450
$839$	−27.6333	−0.954008	−0.477004	−	0.878901i	$-0.658277\pi$
$839$	−27.6333	−0.954008	−0.477004	+	0.878901i	$0.658277\pi$
$840$	−1.00000	−0.0345033
$841$	−1.84441	−0.0636004
$842$	−18.0000	−0.620321
$843$	−10.7889	−0.371589
$844$	10.4222	0.358747
$845$	6.21110	0.213668
$846$	1.39445	0.0479421
$847$	7.00000	0.240523
$848$	−3.21110	−0.110270
$849$	−24.2389	−0.831875
$850$	−4.60555	−0.157969
$851$	−6.00000	−0.205677
$852$	−6.00000	−0.205557
$853$	−21.0278	−0.719977	−0.359988	−	0.932957i	$-0.617219\pi$
$853$	−21.0278	−0.719977	−0.359988	+	0.932957i	$0.617219\pi$
$854$	10.0000	0.342193
$855$	2.60555	0.0891080
$856$	9.21110	0.314829
$857$	24.7889	0.846773	0.423386	−	0.905949i	$-0.360841\pi$
$857$	24.7889	0.846773	0.423386	+	0.905949i	$0.360841\pi$
$858$	−5.21110	−0.177904
$859$	43.6333	1.48875	0.744375	−	0.667762i	$-0.232748\pi$
$859$	43.6333	1.48875	0.744375	+	0.667762i	$0.232748\pi$
$860$	−11.2111	−0.382295
$861$	6.00000	0.204479
$862$	10.4222	0.354982
$863$	54.0555	1.84007	0.920036	−	0.391835i	$-0.128160\pi$
$863$	54.0555	1.84007	0.920036	+	0.391835i	$0.128160\pi$
$864$	−1.00000	−0.0340207
$865$	19.0278	0.646963
$866$	35.8167	1.21710
$867$	4.21110	0.143017
$868$	−2.60555	−0.0884382
$869$	28.8444	0.978480
$870$	5.21110	0.176673
$871$	−8.36669	−0.283495
$872$	−16.4222	−0.556126
$873$	−11.8167	−0.399933
$874$	2.60555	0.0881341
$875$	1.00000	0.0338062
$876$	−2.00000	−0.0675737
$877$	20.8444	0.703866	0.351933	−	0.936025i	$-0.385525\pi$
$877$	20.8444	0.703866	0.351933	+	0.936025i	$0.385525\pi$
$878$	−14.2389	−0.480538
$879$	21.6333	0.729673
$880$	2.00000	0.0674200
$881$	−16.1833	−0.545231	−0.272615	−	0.962123i	$-0.587889\pi$
$881$	−16.1833	−0.545231	−0.272615	+	0.962123i	$0.587889\pi$
$882$	−1.00000	−0.0336718
$883$	38.0555	1.28067	0.640335	−	0.768096i	$-0.278796\pi$
$883$	38.0555	1.28067	0.640335	+	0.768096i	$0.278796\pi$
$884$	−12.0000	−0.403604
$885$	5.21110	0.175169
$886$	−5.57779	−0.187390
$887$	−35.4500	−1.19029	−0.595147	−	0.803617i	$-0.702906\pi$
$887$	−35.4500	−1.19029	−0.595147	+	0.803617i	$0.702906\pi$
$888$	6.00000	0.201347
$889$	2.00000	0.0670778
$890$	−5.39445	−0.180822
$891$	−2.00000	−0.0670025
$892$	−11.3944	−0.381514
$893$	3.63331	0.121584
$894$	14.0000	0.468230
$895$	18.4222	0.615786
$896$	1.00000	0.0334077
$897$	−2.60555	−0.0869968
$898$	6.00000	0.200223
$899$	13.5778	0.452845
$900$	1.00000	0.0333333
$901$	−14.7889	−0.492690
$902$	−12.0000	−0.399556
$903$	−11.2111	−0.373082
$904$	−0.788897	−0.0262383
$905$	14.0000	0.465376
$906$	−17.2111	−0.571801
$907$	−2.00000	−0.0664089	−0.0332045	−	0.999449i	$-0.510571\pi$
$907$	−2.00000	−0.0664089	−0.0332045	+	0.999449i	$0.510571\pi$
$908$	22.6056	0.750192
$909$	−15.8167	−0.524605
$910$	2.60555	0.0863732
$911$	−7.63331	−0.252903	−0.126451	−	0.991973i	$-0.540359\pi$
$911$	−7.63331	−0.252903	−0.126451	+	0.991973i	$0.540359\pi$
$912$	−2.60555	−0.0862784
$913$	21.2111	0.701985
$914$	−27.6333	−0.914029
$915$	−10.0000	−0.330590
$916$	−23.2111	−0.766916
$917$	12.0000	0.396275
$918$	−4.60555	−0.152006
$919$	46.4222	1.53133	0.765664	−	0.643241i	$-0.222411\pi$
$919$	46.4222	1.53133	0.765664	+	0.643241i	$0.222411\pi$
$920$	1.00000	0.0329690
$921$	−1.57779	−0.0519901
$922$	23.8167	0.784360
$923$	15.6333	0.514577
$924$	2.00000	0.0657952
$925$	−6.00000	−0.197279
$926$	29.6333	0.973811
$927$	8.00000	0.262754
$928$	−5.21110	−0.171063
$929$	−21.6333	−0.709766	−0.354883	−	0.934911i	$-0.615479\pi$
$929$	−21.6333	−0.709766	−0.354883	+	0.934911i	$0.615479\pi$
$930$	2.60555	0.0854394
$931$	−2.60555	−0.0853935
$932$	−22.0000	−0.720634
$933$	−11.0278	−0.361033
$934$	−29.0278	−0.949817
$935$	9.21110	0.301235
$936$	2.60555	0.0851651
$937$	−12.1833	−0.398013	−0.199006	−	0.979998i	$-0.563771\pi$
$937$	−12.1833	−0.398013	−0.199006	+	0.979998i	$0.563771\pi$
$938$	3.21110	0.104846
$939$	13.3944	0.437111
$940$	1.39445	0.0454819
$941$	−37.2666	−1.21486	−0.607428	−	0.794374i	$-0.707799\pi$
$941$	−37.2666	−1.21486	−0.607428	+	0.794374i	$0.707799\pi$
$942$	−8.42221	−0.274410
$943$	−6.00000	−0.195387
$944$	−5.21110	−0.169607
$945$	1.00000	0.0325300
$946$	22.4222	0.729009
$947$	21.5778	0.701184	0.350592	−	0.936528i	$-0.385980\pi$
$947$	21.5778	0.701184	0.350592	+	0.936528i	$0.385980\pi$
$948$	−14.4222	−0.468411
$949$	5.21110	0.169160
$950$	2.60555	0.0845352
$951$	8.78890	0.285000
$952$	4.60555	0.149267
$953$	−41.6333	−1.34864	−0.674318	−	0.738441i	$-0.735562\pi$
$953$	−41.6333	−1.34864	−0.674318	+	0.738441i	$0.735562\pi$
$954$	3.21110	0.103963
$955$	6.78890	0.219684
$956$	−6.00000	−0.194054
$957$	−10.4222	−0.336902
$958$	24.0000	0.775405
$959$	18.0000	0.581250
$960$	−1.00000	−0.0322749
$961$	−24.2111	−0.781003
$962$	−15.6333	−0.504038
$963$	−9.21110	−0.296824
$964$	−21.8167	−0.702667
$965$	12.4222	0.399885
$966$	1.00000	0.0321745
$967$	28.7889	0.925789	0.462894	−	0.886414i	$-0.346811\pi$
$967$	28.7889	0.925789	0.462894	+	0.886414i	$0.346811\pi$
$968$	7.00000	0.224989
$969$	−12.0000	−0.385496
$970$	−11.8167	−0.379410
$971$	10.1833	0.326799	0.163400	−	0.986560i	$-0.447754\pi$
$971$	10.1833	0.326799	0.163400	+	0.986560i	$0.447754\pi$
$972$	1.00000	0.0320750
$973$	12.0000	0.384702
$974$	40.0555	1.28346
$975$	−2.60555	−0.0834444
$976$	10.0000	0.320092
$977$	−24.4222	−0.781336	−0.390668	−	0.920532i	$-0.627756\pi$
$977$	−24.4222	−0.781336	−0.390668	+	0.920532i	$0.627756\pi$
$978$	−19.6333	−0.627804
$979$	10.7889	0.344815
$980$	−1.00000	−0.0319438
$981$	16.4222	0.524321
$982$	18.7889	0.599578
$983$	53.2111	1.69717	0.848585	−	0.529059i	$-0.177455\pi$
$983$	53.2111	1.69717	0.848585	+	0.529059i	$0.177455\pi$
$984$	6.00000	0.191273
$985$	8.78890	0.280038
$986$	−24.0000	−0.764316
$987$	1.39445	0.0443858
$988$	6.78890	0.215984
$989$	11.2111	0.356492
$990$	−2.00000	−0.0635642
$991$	17.2111	0.546729	0.273364	−	0.961911i	$-0.411864\pi$
$991$	17.2111	0.546729	0.273364	+	0.961911i	$0.411864\pi$
$992$	−2.60555	−0.0827263
$993$	−14.4222	−0.457675
$994$	−6.00000	−0.190308
$995$	−26.4222	−0.837640
$996$	−10.6056	−0.336050
$997$	36.6611	1.16107	0.580534	−	0.814236i	$-0.302844\pi$
$997$	36.6611	1.16107	0.580534	+	0.814236i	$0.302844\pi$
$998$	28.8444	0.913054
$999$	−6.00000	−0.189832

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4830.2.a.bn.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4830.2.a.bn.1.1	✓	2	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -2.00000 q^{11} +1.00000 q^{12} -2.60555 q^{13} +1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} +4.60555 q^{17} -1.00000 q^{18} -2.60555 q^{19} -1.00000 q^{20} -1.00000 q^{21} +2.00000 q^{22} +1.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} +2.60555 q^{26} +1.00000 q^{27} -1.00000 q^{28} +5.21110 q^{29} +1.00000 q^{30} +2.60555 q^{31} -1.00000 q^{32} -2.00000 q^{33} -4.60555 q^{34} +1.00000 q^{35} +1.00000 q^{36} -6.00000 q^{37} +2.60555 q^{38} -2.60555 q^{39} +1.00000 q^{40} -6.00000 q^{41} +1.00000 q^{42} +11.2111 q^{43} -2.00000 q^{44} -1.00000 q^{45} -1.00000 q^{46} -1.39445 q^{47} +1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} +4.60555 q^{51} -2.60555 q^{52} -3.21110 q^{53} -1.00000 q^{54} +2.00000 q^{55} +1.00000 q^{56} -2.60555 q^{57} -5.21110 q^{58} -5.21110 q^{59} -1.00000 q^{60} +10.0000 q^{61} -2.60555 q^{62} -1.00000 q^{63} +1.00000 q^{64} +2.60555 q^{65} +2.00000 q^{66} +3.21110 q^{67} +4.60555 q^{68} +1.00000 q^{69} -1.00000 q^{70} -6.00000 q^{71} -1.00000 q^{72} -2.00000 q^{73} +6.00000 q^{74} +1.00000 q^{75} -2.60555 q^{76} +2.00000 q^{77} +2.60555 q^{78} -14.4222 q^{79} -1.00000 q^{80} +1.00000 q^{81} +6.00000 q^{82} -10.6056 q^{83} -1.00000 q^{84} -4.60555 q^{85} -11.2111 q^{86} +5.21110 q^{87} +2.00000 q^{88} -5.39445 q^{89} +1.00000 q^{90} +2.60555 q^{91} +1.00000 q^{92} +2.60555 q^{93} +1.39445 q^{94} +2.60555 q^{95} -1.00000 q^{96} -11.8167 q^{97} -1.00000 q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9} + 2 q^{10} - 4 q^{11} + 2 q^{12} + 2 q^{13} + 2 q^{14} - 2 q^{15} + 2 q^{16} + 2 q^{17} - 2 q^{18} + 2 q^{19} - 2 q^{20} - 2 q^{21} + 4 q^{22} + 2 q^{23} - 2 q^{24} + 2 q^{25} - 2 q^{26} + 2 q^{27} - 2 q^{28} - 4 q^{29} + 2 q^{30} - 2 q^{31} - 2 q^{32} - 4 q^{33} - 2 q^{34} + 2 q^{35} + 2 q^{36} - 12 q^{37} - 2 q^{38} + 2 q^{39} + 2 q^{40} - 12 q^{41} + 2 q^{42} + 8 q^{43} - 4 q^{44} - 2 q^{45} - 2 q^{46} - 10 q^{47} + 2 q^{48} + 2 q^{49} - 2 q^{50} + 2 q^{51} + 2 q^{52} + 8 q^{53} - 2 q^{54} + 4 q^{55} + 2 q^{56} + 2 q^{57} + 4 q^{58} + 4 q^{59} - 2 q^{60} + 20 q^{61} + 2 q^{62} - 2 q^{63} + 2 q^{64} - 2 q^{65} + 4 q^{66} - 8 q^{67} + 2 q^{68} + 2 q^{69} - 2 q^{70} - 12 q^{71} - 2 q^{72} - 4 q^{73} + 12 q^{74} + 2 q^{75} + 2 q^{76} + 4 q^{77} - 2 q^{78} - 2 q^{80} + 2 q^{81} + 12 q^{82} - 14 q^{83} - 2 q^{84} - 2 q^{85} - 8 q^{86} - 4 q^{87} + 4 q^{88} - 18 q^{89} + 2 q^{90} - 2 q^{91} + 2 q^{92} - 2 q^{93} + 10 q^{94} - 2 q^{95} - 2 q^{96} - 2 q^{97} - 2 q^{98} - 4 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9 + 2 * q^10 - 4 * q^11 + 2 * q^12 + 2 * q^13 + 2 * q^14 - 2 * q^15 + 2 * q^16 + 2 * q^17 - 2 * q^18 + 2 * q^19 - 2 * q^20 - 2 * q^21 + 4 * q^22 + 2 * q^23 - 2 * q^24 + 2 * q^25 - 2 * q^26 + 2 * q^27 - 2 * q^28 - 4 * q^29 + 2 * q^30 - 2 * q^31 - 2 * q^32 - 4 * q^33 - 2 * q^34 + 2 * q^35 + 2 * q^36 - 12 * q^37 - 2 * q^38 + 2 * q^39 + 2 * q^40 - 12 * q^41 + 2 * q^42 + 8 * q^43 - 4 * q^44 - 2 * q^45 - 2 * q^46 - 10 * q^47 + 2 * q^48 + 2 * q^49 - 2 * q^50 + 2 * q^51 + 2 * q^52 + 8 * q^53 - 2 * q^54 + 4 * q^55 + 2 * q^56 + 2 * q^57 + 4 * q^58 + 4 * q^59 - 2 * q^60 + 20 * q^61 + 2 * q^62 - 2 * q^63 + 2 * q^64 - 2 * q^65 + 4 * q^66 - 8 * q^67 + 2 * q^68 + 2 * q^69 - 2 * q^70 - 12 * q^71 - 2 * q^72 - 4 * q^73 + 12 * q^74 + 2 * q^75 + 2 * q^76 + 4 * q^77 - 2 * q^78 - 2 * q^80 + 2 * q^81 + 12 * q^82 - 14 * q^83 - 2 * q^84 - 2 * q^85 - 8 * q^86 - 4 * q^87 + 4 * q^88 - 18 * q^89 + 2 * q^90 - 2 * q^91 + 2 * q^92 - 2 * q^93 + 10 * q^94 - 2 * q^95 - 2 * q^96 - 2 * q^97 - 2 * q^98 - 4 * q^99

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