LMFDB - Embedded newform 6018.2.a.ba.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6018,2,Mod(1,6018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6018, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6018 = 2 \cdot 3 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6018.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:	$48.0539719364$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} - 31 x^{10} + 111 x^{9} + 381 x^{8} - 1101 x^{7} - 2301 x^{6} + 4690 x^{5} + \cdots + 5653 $ x^12 - 4x^11 - 31x^10 + 111x^9 + 381x^8 - 1101x^7 - 2301x^6 + 4690x^5 + 6915x^4 - 8325x^3 - 10082x^2 + 5149*x + 5653
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$2.01103$ of defining polynomial
Character	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.01103 q^{5} +1.00000 q^{6} -2.46588 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.01103 q^{5} +1.00000 q^{6} -2.46588 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.01103 q^{10} -4.82988 q^{11} +1.00000 q^{12} +2.72504 q^{13} -2.46588 q^{14} -1.01103 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +2.53639 q^{19} -1.01103 q^{20} -2.46588 q^{21} -4.82988 q^{22} -2.05846 q^{23} +1.00000 q^{24} -3.97781 q^{25} +2.72504 q^{26} +1.00000 q^{27} -2.46588 q^{28} +8.41813 q^{29} -1.01103 q^{30} +6.58040 q^{31} +1.00000 q^{32} -4.82988 q^{33} -1.00000 q^{34} +2.49308 q^{35} +1.00000 q^{36} +5.59003 q^{37} +2.53639 q^{38} +2.72504 q^{39} -1.01103 q^{40} +6.08586 q^{41} -2.46588 q^{42} -8.91632 q^{43} -4.82988 q^{44} -1.01103 q^{45} -2.05846 q^{46} +6.21538 q^{47} +1.00000 q^{48} -0.919455 q^{49} -3.97781 q^{50} -1.00000 q^{51} +2.72504 q^{52} +3.60753 q^{53} +1.00000 q^{54} +4.88317 q^{55} -2.46588 q^{56} +2.53639 q^{57} +8.41813 q^{58} +1.00000 q^{59} -1.01103 q^{60} +12.2799 q^{61} +6.58040 q^{62} -2.46588 q^{63} +1.00000 q^{64} -2.75510 q^{65} -4.82988 q^{66} -4.45438 q^{67} -1.00000 q^{68} -2.05846 q^{69} +2.49308 q^{70} +13.5336 q^{71} +1.00000 q^{72} -1.79164 q^{73} +5.59003 q^{74} -3.97781 q^{75} +2.53639 q^{76} +11.9099 q^{77} +2.72504 q^{78} -0.511565 q^{79} -1.01103 q^{80} +1.00000 q^{81} +6.08586 q^{82} +5.01616 q^{83} -2.46588 q^{84} +1.01103 q^{85} -8.91632 q^{86} +8.41813 q^{87} -4.82988 q^{88} +6.59546 q^{89} -1.01103 q^{90} -6.71960 q^{91} -2.05846 q^{92} +6.58040 q^{93} +6.21538 q^{94} -2.56437 q^{95} +1.00000 q^{96} +4.95915 q^{97} -0.919455 q^{98} -4.82988 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 q^{5} + 12 q^{6} + 5 q^{7} + 12 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 8 * q^5 + 12 * q^6 + 5 * q^7 + 12 * q^8 + 12 * q^9	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 q^{5} + 12 q^{6} + 5 q^{7} + 12 q^{8} + 12 q^{9} + 8 q^{10} + 11 q^{11} + 12 q^{12} + 6 q^{13} + 5 q^{14} + 8 q^{15} + 12 q^{16} - 12 q^{17} + 12 q^{18} + 3 q^{19} + 8 q^{20} + 5 q^{21} + 11 q^{22} + 22 q^{23} + 12 q^{24} + 22 q^{25} + 6 q^{26} + 12 q^{27} + 5 q^{28} + 26 q^{29} + 8 q^{30} + q^{31} + 12 q^{32} + 11 q^{33} - 12 q^{34} + 24 q^{35} + 12 q^{36} + 10 q^{37} + 3 q^{38} + 6 q^{39} + 8 q^{40} + 16 q^{41} + 5 q^{42} + 23 q^{43} + 11 q^{44} + 8 q^{45} + 22 q^{46} + 6 q^{47} + 12 q^{48} + 11 q^{49} + 22 q^{50} - 12 q^{51} + 6 q^{52} + 10 q^{53} + 12 q^{54} + 15 q^{55} + 5 q^{56} + 3 q^{57} + 26 q^{58} + 12 q^{59} + 8 q^{60} + 15 q^{61} + q^{62} + 5 q^{63} + 12 q^{64} + 4 q^{65} + 11 q^{66} + 4 q^{67} - 12 q^{68} + 22 q^{69} + 24 q^{70} + 10 q^{71} + 12 q^{72} + 24 q^{73} + 10 q^{74} + 22 q^{75} + 3 q^{76} + 24 q^{77} + 6 q^{78} + 23 q^{79} + 8 q^{80} + 12 q^{81} + 16 q^{82} + 5 q^{84} - 8 q^{85} + 23 q^{86} + 26 q^{87} + 11 q^{88} + 13 q^{89} + 8 q^{90} + 3 q^{91} + 22 q^{92} + q^{93} + 6 q^{94} + 11 q^{95} + 12 q^{96} + 13 q^{97} + 11 q^{98} + 11 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 8 * q^5 + 12 * q^6 + 5 * q^7 + 12 * q^8 + 12 * q^9 + 8 * q^10 + 11 * q^11 + 12 * q^12 + 6 * q^13 + 5 * q^14 + 8 * q^15 + 12 * q^16 - 12 * q^17 + 12 * q^18 + 3 * q^19 + 8 * q^20 + 5 * q^21 + 11 * q^22 + 22 * q^23 + 12 * q^24 + 22 * q^25 + 6 * q^26 + 12 * q^27 + 5 * q^28 + 26 * q^29 + 8 * q^30 + q^31 + 12 * q^32 + 11 * q^33 - 12 * q^34 + 24 * q^35 + 12 * q^36 + 10 * q^37 + 3 * q^38 + 6 * q^39 + 8 * q^40 + 16 * q^41 + 5 * q^42 + 23 * q^43 + 11 * q^44 + 8 * q^45 + 22 * q^46 + 6 * q^47 + 12 * q^48 + 11 * q^49 + 22 * q^50 - 12 * q^51 + 6 * q^52 + 10 * q^53 + 12 * q^54 + 15 * q^55 + 5 * q^56 + 3 * q^57 + 26 * q^58 + 12 * q^59 + 8 * q^60 + 15 * q^61 + q^62 + 5 * q^63 + 12 * q^64 + 4 * q^65 + 11 * q^66 + 4 * q^67 - 12 * q^68 + 22 * q^69 + 24 * q^70 + 10 * q^71 + 12 * q^72 + 24 * q^73 + 10 * q^74 + 22 * q^75 + 3 * q^76 + 24 * q^77 + 6 * q^78 + 23 * q^79 + 8 * q^80 + 12 * q^81 + 16 * q^82 + 5 * q^84 - 8 * q^85 + 23 * q^86 + 26 * q^87 + 11 * q^88 + 13 * q^89 + 8 * q^90 + 3 * q^91 + 22 * q^92 + q^93 + 6 * q^94 + 11 * q^95 + 12 * q^96 + 13 * q^97 + 11 * q^98 + 11 * 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
$5$	−1.01103	−0.452148	−0.226074	−	0.974110i	$-0.572589\pi$
$5$	−1.01103	−0.452148	−0.226074	+	0.974110i	$0.572589\pi$
$6$	1.00000	0.408248
$7$	−2.46588	−0.932014	−0.466007	−	0.884781i	$-0.654308\pi$
$7$	−2.46588	−0.932014	−0.466007	+	0.884781i	$0.654308\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−1.01103	−0.319717
$11$	−4.82988	−1.45626	−0.728132	−	0.685437i	$-0.759611\pi$
$11$	−4.82988	−1.45626	−0.728132	+	0.685437i	$0.759611\pi$
$12$	1.00000	0.288675
$13$	2.72504	0.755789	0.377895	−	0.925849i	$-0.376648\pi$
$13$	2.72504	0.755789	0.377895	+	0.925849i	$0.376648\pi$
$14$	−2.46588	−0.659033
$15$	−1.01103	−0.261048
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	2.53639	0.581887	0.290943	−	0.956740i	$-0.406031\pi$
$19$	2.53639	0.581887	0.290943	+	0.956740i	$0.406031\pi$
$20$	−1.01103	−0.226074
$21$	−2.46588	−0.538098
$22$	−4.82988	−1.02973
$23$	−2.05846	−0.429220	−0.214610	−	0.976700i	$-0.568848\pi$
$23$	−2.05846	−0.429220	−0.214610	+	0.976700i	$0.568848\pi$
$24$	1.00000	0.204124
$25$	−3.97781	−0.795562
$26$	2.72504	0.534424
$27$	1.00000	0.192450
$28$	−2.46588	−0.466007
$29$	8.41813	1.56321	0.781604	−	0.623775i	$-0.214402\pi$
$29$	8.41813	1.56321	0.781604	+	0.623775i	$0.214402\pi$
$30$	−1.01103	−0.184589
$31$	6.58040	1.18187	0.590937	−	0.806718i	$-0.298758\pi$
$31$	6.58040	1.18187	0.590937	+	0.806718i	$0.298758\pi$
$32$	1.00000	0.176777
$33$	−4.82988	−0.840774
$34$	−1.00000	−0.171499
$35$	2.49308	0.421408
$36$	1.00000	0.166667
$37$	5.59003	0.918996	0.459498	−	0.888179i	$-0.348029\pi$
$37$	5.59003	0.918996	0.459498	+	0.888179i	$0.348029\pi$
$38$	2.53639	0.411456
$39$	2.72504	0.436355
$40$	−1.01103	−0.159858
$41$	6.08586	0.950452	0.475226	−	0.879864i	$-0.342366\pi$
$41$	6.08586	0.950452	0.475226	+	0.879864i	$0.342366\pi$
$42$	−2.46588	−0.380493
$43$	−8.91632	−1.35973	−0.679863	−	0.733339i	$-0.737961\pi$
$43$	−8.91632	−1.35973	−0.679863	+	0.733339i	$0.737961\pi$
$44$	−4.82988	−0.728132
$45$	−1.01103	−0.150716
$46$	−2.05846	−0.303504
$47$	6.21538	0.906607	0.453303	−	0.891356i	$-0.350245\pi$
$47$	6.21538	0.906607	0.453303	+	0.891356i	$0.350245\pi$
$48$	1.00000	0.144338
$49$	−0.919455	−0.131351
$50$	−3.97781	−0.562548
$51$	−1.00000	−0.140028
$52$	2.72504	0.377895
$53$	3.60753	0.495533	0.247766	−	0.968820i	$-0.420303\pi$
$53$	3.60753	0.495533	0.247766	+	0.968820i	$0.420303\pi$
$54$	1.00000	0.136083
$55$	4.88317	0.658446
$56$	−2.46588	−0.329517
$57$	2.53639	0.335953
$58$	8.41813	1.10536
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	−1.01103	−0.130524
$61$	12.2799	1.57228	0.786140	−	0.618048i	$-0.212076\pi$
$61$	12.2799	1.57228	0.786140	+	0.618048i	$0.212076\pi$
$62$	6.58040	0.835711
$63$	−2.46588	−0.310671
$64$	1.00000	0.125000
$65$	−2.75510	−0.341728
$66$	−4.82988	−0.594517
$67$	−4.45438	−0.544189	−0.272094	−	0.962271i	$-0.587716\pi$
$67$	−4.45438	−0.544189	−0.272094	+	0.962271i	$0.587716\pi$
$68$	−1.00000	−0.121268
$69$	−2.05846	−0.247810
$70$	2.49308	0.297980
$71$	13.5336	1.60614	0.803071	−	0.595884i	$-0.203198\pi$
$71$	13.5336	1.60614	0.803071	+	0.595884i	$0.203198\pi$
$72$	1.00000	0.117851
$73$	−1.79164	−0.209695	−0.104848	−	0.994488i	$-0.533435\pi$
$73$	−1.79164	−0.209695	−0.104848	+	0.994488i	$0.533435\pi$
$74$	5.59003	0.649828
$75$	−3.97781	−0.459318
$76$	2.53639	0.290943
$77$	11.9099	1.35726
$78$	2.72504	0.308550
$79$	−0.511565	−0.0575555	−0.0287778	−	0.999586i	$-0.509162\pi$
$79$	−0.511565	−0.0575555	−0.0287778	+	0.999586i	$0.509162\pi$
$80$	−1.01103	−0.113037
$81$	1.00000	0.111111
$82$	6.08586	0.672071
$83$	5.01616	0.550595	0.275298	−	0.961359i	$-0.411224\pi$
$83$	5.01616	0.550595	0.275298	+	0.961359i	$0.411224\pi$
$84$	−2.46588	−0.269049
$85$	1.01103	0.109662
$86$	−8.91632	−0.961472
$87$	8.41813	0.902519
$88$	−4.82988	−0.514867
$89$	6.59546	0.699118	0.349559	−	0.936914i	$-0.386331\pi$
$89$	6.59546	0.699118	0.349559	+	0.936914i	$0.386331\pi$
$90$	−1.01103	−0.106572
$91$	−6.71960	−0.704406
$92$	−2.05846	−0.214610
$93$	6.58040	0.682355
$94$	6.21538	0.641068
$95$	−2.56437	−0.263099
$96$	1.00000	0.102062
$97$	4.95915	0.503526	0.251763	−	0.967789i	$-0.418990\pi$
$97$	4.95915	0.503526	0.251763	+	0.967789i	$0.418990\pi$
$98$	−0.919455	−0.0928790
$99$	−4.82988	−0.485421
$100$	−3.97781	−0.397781
$101$	−5.86448	−0.583538	−0.291769	−	0.956489i	$-0.594244\pi$
$101$	−5.86448	−0.583538	−0.291769	+	0.956489i	$0.594244\pi$
$102$	−1.00000	−0.0990148
$103$	0.508146	0.0500691	0.0250346	−	0.999687i	$-0.492030\pi$
$103$	0.508146	0.0500691	0.0250346	+	0.999687i	$0.492030\pi$
$104$	2.72504	0.267212
$105$	2.49308	0.243300
$106$	3.60753	0.350395
$107$	8.67276	0.838428	0.419214	−	0.907887i	$-0.362306\pi$
$107$	8.67276	0.838428	0.419214	+	0.907887i	$0.362306\pi$
$108$	1.00000	0.0962250
$109$	−9.38988	−0.899387	−0.449693	−	0.893183i	$-0.648467\pi$
$109$	−9.38988	−0.899387	−0.449693	+	0.893183i	$0.648467\pi$
$110$	4.88317	0.465592
$111$	5.59003	0.530582
$112$	−2.46588	−0.233003
$113$	6.52754	0.614059	0.307030	−	0.951700i	$-0.400665\pi$
$113$	6.52754	0.614059	0.307030	+	0.951700i	$0.400665\pi$
$114$	2.53639	0.237554
$115$	2.08118	0.194071
$116$	8.41813	0.781604
$117$	2.72504	0.251930
$118$	1.00000	0.0920575
$119$	2.46588	0.226046
$120$	−1.01103	−0.0922943
$121$	12.3277	1.12070
$122$	12.2799	1.11177
$123$	6.08586	0.548744
$124$	6.58040	0.590937
$125$	9.07687	0.811860
$126$	−2.46588	−0.219678
$127$	2.45086	0.217479	0.108739	−	0.994070i	$-0.465319\pi$
$127$	2.45086	0.217479	0.108739	+	0.994070i	$0.465319\pi$
$128$	1.00000	0.0883883
$129$	−8.91632	−0.785038
$130$	−2.75510	−0.241639
$131$	9.72371	0.849564	0.424782	−	0.905296i	$-0.360351\pi$
$131$	9.72371	0.849564	0.424782	+	0.905296i	$0.360351\pi$
$132$	−4.82988	−0.420387
$133$	−6.25441	−0.542326
$134$	−4.45438	−0.384799
$135$	−1.01103	−0.0870159
$136$	−1.00000	−0.0857493
$137$	2.85042	0.243527	0.121764	−	0.992559i	$-0.461145\pi$
$137$	2.85042	0.243527	0.121764	+	0.992559i	$0.461145\pi$
$138$	−2.05846	−0.175228
$139$	−4.72362	−0.400652	−0.200326	−	0.979729i	$-0.564200\pi$
$139$	−4.72362	−0.400652	−0.200326	+	0.979729i	$0.564200\pi$
$140$	2.49308	0.210704
$141$	6.21538	0.523430
$142$	13.5336	1.13571
$143$	−13.1616	−1.10063
$144$	1.00000	0.0833333
$145$	−8.51101	−0.706801
$146$	−1.79164	−0.148277
$147$	−0.919455	−0.0758354
$148$	5.59003	0.459498
$149$	10.1105	0.828281	0.414141	−	0.910213i	$-0.364082\pi$
$149$	10.1105	0.828281	0.414141	+	0.910213i	$0.364082\pi$
$150$	−3.97781	−0.324787
$151$	−19.8017	−1.61144	−0.805721	−	0.592296i	$-0.798222\pi$
$151$	−19.8017	−1.61144	−0.805721	+	0.592296i	$0.798222\pi$
$152$	2.53639	0.205728
$153$	−1.00000	−0.0808452
$154$	11.9099	0.959726
$155$	−6.65300	−0.534382
$156$	2.72504	0.218178
$157$	−2.88744	−0.230443	−0.115221	−	0.993340i	$-0.536758\pi$
$157$	−2.88744	−0.230443	−0.115221	+	0.993340i	$0.536758\pi$
$158$	−0.511565	−0.0406979
$159$	3.60753	0.286096
$160$	−1.01103	−0.0799292
$161$	5.07592	0.400039
$162$	1.00000	0.0785674
$163$	12.4150	0.972420	0.486210	−	0.873842i	$-0.338379\pi$
$163$	12.4150	0.972420	0.486210	+	0.873842i	$0.338379\pi$
$164$	6.08586	0.475226
$165$	4.88317	0.380154
$166$	5.01616	0.389330
$167$	7.04334	0.545030	0.272515	−	0.962152i	$-0.412145\pi$
$167$	7.04334	0.545030	0.272515	+	0.962152i	$0.412145\pi$
$168$	−2.46588	−0.190246
$169$	−5.57418	−0.428783
$170$	1.01103	0.0775427
$171$	2.53639	0.193962
$172$	−8.91632	−0.679863
$173$	8.33797	0.633924	0.316962	−	0.948438i	$-0.397337\pi$
$173$	8.33797	0.633924	0.316962	+	0.948438i	$0.397337\pi$
$174$	8.41813	0.638177
$175$	9.80879	0.741475
$176$	−4.82988	−0.364066
$177$	1.00000	0.0751646
$178$	6.59546	0.494351
$179$	−3.57592	−0.267277	−0.133638	−	0.991030i	$-0.542666\pi$
$179$	−3.57592	−0.267277	−0.133638	+	0.991030i	$0.542666\pi$
$180$	−1.01103	−0.0753580
$181$	−5.13191	−0.381452	−0.190726	−	0.981643i	$-0.561084\pi$
$181$	−5.13191	−0.381452	−0.190726	+	0.981643i	$0.561084\pi$
$182$	−6.71960	−0.498090
$183$	12.2799	0.907756
$184$	−2.05846	−0.151752
$185$	−5.65171	−0.415522
$186$	6.58040	0.482498
$187$	4.82988	0.353196
$188$	6.21538	0.453303
$189$	−2.46588	−0.179366
$190$	−2.56437	−0.186039
$191$	0.927663	0.0671233	0.0335617	−	0.999437i	$-0.489315\pi$
$191$	0.927663	0.0671233	0.0335617	+	0.999437i	$0.489315\pi$
$192$	1.00000	0.0721688
$193$	9.21873	0.663579	0.331789	−	0.943353i	$-0.392348\pi$
$193$	9.21873	0.663579	0.331789	+	0.943353i	$0.392348\pi$
$194$	4.95915	0.356046
$195$	−2.75510	−0.197297
$196$	−0.919455	−0.0656753
$197$	−8.96361	−0.638631	−0.319315	−	0.947649i	$-0.603453\pi$
$197$	−8.96361	−0.638631	−0.319315	+	0.947649i	$0.603453\pi$
$198$	−4.82988	−0.343245
$199$	−21.4978	−1.52394	−0.761968	−	0.647614i	$-0.775767\pi$
$199$	−21.4978	−1.52394	−0.761968	+	0.647614i	$0.775767\pi$
$200$	−3.97781	−0.281274
$201$	−4.45438	−0.314187
$202$	−5.86448	−0.412624
$203$	−20.7581	−1.45693
$204$	−1.00000	−0.0700140
$205$	−6.15301	−0.429745
$206$	0.508146	0.0354042
$207$	−2.05846	−0.143073
$208$	2.72504	0.188947
$209$	−12.2504	−0.847381
$210$	2.49308	0.172039
$211$	−15.2561	−1.05027	−0.525137	−	0.851018i	$-0.675986\pi$
$211$	−15.2561	−1.05027	−0.525137	+	0.851018i	$0.675986\pi$
$212$	3.60753	0.247766
$213$	13.5336	0.927306
$214$	8.67276	0.592858
$215$	9.01470	0.614797
$216$	1.00000	0.0680414
$217$	−16.2264	−1.10152
$218$	−9.38988	−0.635963
$219$	−1.79164	−0.121068
$220$	4.88317	0.329223
$221$	−2.72504	−0.183306
$222$	5.59003	0.375178
$223$	17.6441	1.18154	0.590769	−	0.806841i	$-0.298824\pi$
$223$	17.6441	1.18154	0.590769	+	0.806841i	$0.298824\pi$
$224$	−2.46588	−0.164758
$225$	−3.97781	−0.265187
$226$	6.52754	0.434205
$227$	−9.45280	−0.627404	−0.313702	−	0.949521i	$-0.601569\pi$
$227$	−9.45280	−0.627404	−0.313702	+	0.949521i	$0.601569\pi$
$228$	2.53639	0.167976
$229$	17.6028	1.16323	0.581613	−	0.813466i	$-0.302422\pi$
$229$	17.6028	1.16323	0.581613	+	0.813466i	$0.302422\pi$
$230$	2.08118	0.137229
$231$	11.9099	0.783613
$232$	8.41813	0.552678
$233$	7.82770	0.512810	0.256405	−	0.966569i	$-0.417462\pi$
$233$	7.82770	0.512810	0.256405	+	0.966569i	$0.417462\pi$
$234$	2.72504	0.178141
$235$	−6.28396	−0.409920
$236$	1.00000	0.0650945
$237$	−0.511565	−0.0332297
$238$	2.46588	0.159839
$239$	−5.04893	−0.326588	−0.163294	−	0.986577i	$-0.552212\pi$
$239$	−5.04893	−0.326588	−0.163294	+	0.986577i	$0.552212\pi$
$240$	−1.01103	−0.0652619
$241$	4.13567	0.266402	0.133201	−	0.991089i	$-0.457474\pi$
$241$	4.13567	0.266402	0.133201	+	0.991089i	$0.457474\pi$
$242$	12.3277	0.792457
$243$	1.00000	0.0641500
$244$	12.2799	0.786140
$245$	0.929600	0.0593899
$246$	6.08586	0.388021
$247$	6.91175	0.439784
$248$	6.58040	0.417856
$249$	5.01616	0.317886
$250$	9.07687	0.574071
$251$	−6.08121	−0.383843	−0.191921	−	0.981410i	$-0.561472\pi$
$251$	−6.08121	−0.383843	−0.191921	+	0.981410i	$0.561472\pi$
$252$	−2.46588	−0.155336
$253$	9.94214	0.625057
$254$	2.45086	0.153781
$255$	1.01103	0.0633134
$256$	1.00000	0.0625000
$257$	17.0981	1.06655	0.533275	−	0.845942i	$-0.320961\pi$
$257$	17.0981	1.06655	0.533275	+	0.845942i	$0.320961\pi$
$258$	−8.91632	−0.555106
$259$	−13.7843	−0.856516
$260$	−2.75510	−0.170864
$261$	8.41813	0.521069
$262$	9.72371	0.600733
$263$	−17.1024	−1.05458	−0.527291	−	0.849685i	$-0.676792\pi$
$263$	−17.1024	−1.05458	−0.527291	+	0.849685i	$0.676792\pi$
$264$	−4.82988	−0.297259
$265$	−3.64734	−0.224054
$266$	−6.25441	−0.383483
$267$	6.59546	0.403636
$268$	−4.45438	−0.272094
$269$	29.1672	1.77836	0.889179	−	0.457560i	$-0.151277\pi$
$269$	29.1672	1.77836	0.889179	+	0.457560i	$0.151277\pi$
$270$	−1.01103	−0.0615295
$271$	4.00225	0.243120	0.121560	−	0.992584i	$-0.461210\pi$
$271$	4.00225	0.243120	0.121560	+	0.992584i	$0.461210\pi$
$272$	−1.00000	−0.0606339
$273$	−6.71960	−0.406689
$274$	2.85042	0.172200
$275$	19.2123	1.15855
$276$	−2.05846	−0.123905
$277$	19.6619	1.18137	0.590683	−	0.806904i	$-0.298858\pi$
$277$	19.6619	1.18137	0.590683	+	0.806904i	$0.298858\pi$
$278$	−4.72362	−0.283304
$279$	6.58040	0.393958
$280$	2.49308	0.148990
$281$	−5.56905	−0.332221	−0.166111	−	0.986107i	$-0.553121\pi$
$281$	−5.56905	−0.332221	−0.166111	+	0.986107i	$0.553121\pi$
$282$	6.21538	0.370121
$283$	19.6454	1.16780	0.583899	−	0.811826i	$-0.301526\pi$
$283$	19.6454	1.16780	0.583899	+	0.811826i	$0.301526\pi$
$284$	13.5336	0.803071
$285$	−2.56437	−0.151900
$286$	−13.1616	−0.778262
$287$	−15.0070	−0.885834
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−8.51101	−0.499784
$291$	4.95915	0.290711
$292$	−1.79164	−0.104848
$293$	−6.74694	−0.394160	−0.197080	−	0.980387i	$-0.563146\pi$
$293$	−6.74694	−0.394160	−0.197080	+	0.980387i	$0.563146\pi$
$294$	−0.919455	−0.0536237
$295$	−1.01103	−0.0588646
$296$	5.59003	0.324914
$297$	−4.82988	−0.280258
$298$	10.1105	0.585683
$299$	−5.60939	−0.324400
$300$	−3.97781	−0.229659
$301$	21.9865	1.26728
$302$	−19.8017	−1.13946
$303$	−5.86448	−0.336906
$304$	2.53639	0.145472
$305$	−12.4154	−0.710903
$306$	−1.00000	−0.0571662
$307$	−12.7456	−0.727431	−0.363716	−	0.931510i	$-0.618492\pi$
$307$	−12.7456	−0.727431	−0.363716	+	0.931510i	$0.618492\pi$
$308$	11.9099	0.678629
$309$	0.508146	0.0289074
$310$	−6.65300	−0.377865
$311$	−1.93510	−0.109729	−0.0548647	−	0.998494i	$-0.517473\pi$
$311$	−1.93510	−0.109729	−0.0548647	+	0.998494i	$0.517473\pi$
$312$	2.72504	0.154275
$313$	5.31697	0.300533	0.150266	−	0.988646i	$-0.451987\pi$
$313$	5.31697	0.300533	0.150266	+	0.988646i	$0.451987\pi$
$314$	−2.88744	−0.162948
$315$	2.49308	0.140469
$316$	−0.511565	−0.0287778
$317$	−29.2529	−1.64301	−0.821503	−	0.570204i	$-0.806864\pi$
$317$	−29.2529	−1.64301	−0.821503	+	0.570204i	$0.806864\pi$
$318$	3.60753	0.202300
$319$	−40.6586	−2.27644
$320$	−1.01103	−0.0565185
$321$	8.67276	0.484067
$322$	5.07592	0.282870
$323$	−2.53639	−0.141128
$324$	1.00000	0.0555556
$325$	−10.8397	−0.601277
$326$	12.4150	0.687605
$327$	−9.38988	−0.519261
$328$	6.08586	0.336036
$329$	−15.3264	−0.844970
$330$	4.88317	0.268810
$331$	−26.2060	−1.44041	−0.720207	−	0.693759i	$-0.755953\pi$
$331$	−26.2060	−1.44041	−0.720207	+	0.693759i	$0.755953\pi$
$332$	5.01616	0.275298
$333$	5.59003	0.306332
$334$	7.04334	0.385395
$335$	4.50352	0.246054
$336$	−2.46588	−0.134525
$337$	20.5612	1.12004	0.560020	−	0.828479i	$-0.310793\pi$
$337$	20.5612	1.12004	0.560020	+	0.828479i	$0.310793\pi$
$338$	−5.57418	−0.303195
$339$	6.52754	0.354527
$340$	1.01103	0.0548310
$341$	−31.7825	−1.72112
$342$	2.53639	0.137152
$343$	19.5284	1.05443
$344$	−8.91632	−0.480736
$345$	2.08118	0.112047
$346$	8.33797	0.448252
$347$	−0.833503	−0.0447448	−0.0223724	−	0.999750i	$-0.507122\pi$
$347$	−0.833503	−0.0447448	−0.0223724	+	0.999750i	$0.507122\pi$
$348$	8.41813	0.451259
$349$	−14.5770	−0.780287	−0.390144	−	0.920754i	$-0.627575\pi$
$349$	−14.5770	−0.780287	−0.390144	+	0.920754i	$0.627575\pi$
$350$	9.80879	0.524302
$351$	2.72504	0.145452
$352$	−4.82988	−0.257433
$353$	15.1270	0.805129	0.402565	−	0.915392i	$-0.368119\pi$
$353$	15.1270	0.805129	0.402565	+	0.915392i	$0.368119\pi$
$354$	1.00000	0.0531494
$355$	−13.6829	−0.726213
$356$	6.59546	0.349559
$357$	2.46588	0.130508
$358$	−3.57592	−0.188993
$359$	11.1965	0.590929	0.295464	−	0.955354i	$-0.404526\pi$
$359$	11.1965	0.590929	0.295464	+	0.955354i	$0.404526\pi$
$360$	−1.01103	−0.0532861
$361$	−12.5667	−0.661408
$362$	−5.13191	−0.269727
$363$	12.3277	0.647038
$364$	−6.71960	−0.352203
$365$	1.81140	0.0948132
$366$	12.2799	0.641881
$367$	15.0827	0.787308	0.393654	−	0.919259i	$-0.371211\pi$
$367$	15.0827	0.787308	0.393654	+	0.919259i	$0.371211\pi$
$368$	−2.05846	−0.107305
$369$	6.08586	0.316817
$370$	−5.65171	−0.293818
$371$	−8.89573	−0.461843
$372$	6.58040	0.341178
$373$	17.8496	0.924219	0.462110	−	0.886823i	$-0.347093\pi$
$373$	17.8496	0.924219	0.462110	+	0.886823i	$0.347093\pi$
$374$	4.82988	0.249747
$375$	9.07687	0.468727
$376$	6.21538	0.320534
$377$	22.9397	1.18146
$378$	−2.46588	−0.126831
$379$	−29.0271	−1.49102	−0.745510	−	0.666494i	$-0.767794\pi$
$379$	−29.0271	−1.49102	−0.745510	+	0.666494i	$0.767794\pi$
$380$	−2.56437	−0.131549
$381$	2.45086	0.125561
$382$	0.927663	0.0474634
$383$	−11.5928	−0.592366	−0.296183	−	0.955131i	$-0.595714\pi$
$383$	−11.5928	−0.592366	−0.296183	+	0.955131i	$0.595714\pi$
$384$	1.00000	0.0510310
$385$	−12.0413	−0.613681
$386$	9.21873	0.469221
$387$	−8.91632	−0.453242
$388$	4.95915	0.251763
$389$	−8.26296	−0.418949	−0.209474	−	0.977814i	$-0.567175\pi$
$389$	−8.26296	−0.418949	−0.209474	+	0.977814i	$0.567175\pi$
$390$	−2.75510	−0.139510
$391$	2.05846	0.104101
$392$	−0.919455	−0.0464395
$393$	9.72371	0.490496
$394$	−8.96361	−0.451580
$395$	0.517209	0.0260236
$396$	−4.82988	−0.242711
$397$	1.94249	0.0974909	0.0487454	−	0.998811i	$-0.484478\pi$
$397$	1.94249	0.0974909	0.0487454	+	0.998811i	$0.484478\pi$
$398$	−21.4978	−1.07759
$399$	−6.25441	−0.313112
$400$	−3.97781	−0.198891
$401$	−28.4137	−1.41891	−0.709457	−	0.704748i	$-0.751060\pi$
$401$	−28.4137	−1.41891	−0.709457	+	0.704748i	$0.751060\pi$
$402$	−4.45438	−0.222164
$403$	17.9318	0.893248
$404$	−5.86448	−0.291769
$405$	−1.01103	−0.0502387
$406$	−20.7581	−1.03021
$407$	−26.9992	−1.33830
$408$	−1.00000	−0.0495074
$409$	12.4718	0.616691	0.308346	−	0.951274i	$-0.400225\pi$
$409$	12.4718	0.616691	0.308346	+	0.951274i	$0.400225\pi$
$410$	−6.15301	−0.303876
$411$	2.85042	0.140601
$412$	0.508146	0.0250346
$413$	−2.46588	−0.121338
$414$	−2.05846	−0.101168
$415$	−5.07151	−0.248950
$416$	2.72504	0.133606
$417$	−4.72362	−0.231317
$418$	−12.2504	−0.599189
$419$	−8.73685	−0.426823	−0.213411	−	0.976962i	$-0.568457\pi$
$419$	−8.73685	−0.426823	−0.213411	+	0.976962i	$0.568457\pi$
$420$	2.49308	0.121650
$421$	−34.4791	−1.68041	−0.840204	−	0.542271i	$-0.817565\pi$
$421$	−34.4791	−1.68041	−0.840204	+	0.542271i	$0.817565\pi$
$422$	−15.2561	−0.742655
$423$	6.21538	0.302202
$424$	3.60753	0.175197
$425$	3.97781	0.192952
$426$	13.5336	0.655704
$427$	−30.2807	−1.46539
$428$	8.67276	0.419214
$429$	−13.1616	−0.635448
$430$	9.01470	0.434727
$431$	16.4866	0.794131	0.397065	−	0.917790i	$-0.370029\pi$
$431$	16.4866	0.794131	0.397065	+	0.917790i	$0.370029\pi$
$432$	1.00000	0.0481125
$433$	4.13832	0.198875	0.0994374	−	0.995044i	$-0.468296\pi$
$433$	4.13832	0.198875	0.0994374	+	0.995044i	$0.468296\pi$
$434$	−16.2264	−0.778894
$435$	−8.51101	−0.408072
$436$	−9.38988	−0.449693
$437$	−5.22106	−0.249757
$438$	−1.79164	−0.0856077
$439$	6.45247	0.307960	0.153980	−	0.988074i	$-0.450791\pi$
$439$	6.45247	0.307960	0.153980	+	0.988074i	$0.450791\pi$
$440$	4.88317	0.232796
$441$	−0.919455	−0.0437836
$442$	−2.72504	−0.129617
$443$	−1.65783	−0.0787657	−0.0393829	−	0.999224i	$-0.512539\pi$
$443$	−1.65783	−0.0787657	−0.0393829	+	0.999224i	$0.512539\pi$
$444$	5.59003	0.265291
$445$	−6.66823	−0.316105
$446$	17.6441	0.835474
$447$	10.1105	0.478208
$448$	−2.46588	−0.116502
$449$	−22.9470	−1.08293	−0.541467	−	0.840722i	$-0.682131\pi$
$449$	−22.9470	−1.08293	−0.541467	+	0.840722i	$0.682131\pi$
$450$	−3.97781	−0.187516
$451$	−29.3940	−1.38411
$452$	6.52754	0.307030
$453$	−19.8017	−0.930366
$454$	−9.45280	−0.443642
$455$	6.79374	0.318496
$456$	2.53639	0.118777
$457$	−3.20684	−0.150010	−0.0750049	−	0.997183i	$-0.523897\pi$
$457$	−3.20684	−0.150010	−0.0750049	+	0.997183i	$0.523897\pi$
$458$	17.6028	0.822524
$459$	−1.00000	−0.0466760
$460$	2.08118	0.0970354
$461$	26.2219	1.22128	0.610639	−	0.791909i	$-0.290913\pi$
$461$	26.2219	1.22128	0.610639	+	0.791909i	$0.290913\pi$
$462$	11.9099	0.554098
$463$	−23.2202	−1.07914	−0.539568	−	0.841942i	$-0.681412\pi$
$463$	−23.2202	−1.07914	−0.539568	+	0.841942i	$0.681412\pi$
$464$	8.41813	0.390802
$465$	−6.65300	−0.308526
$466$	7.82770	0.362611
$467$	−16.1594	−0.747768	−0.373884	−	0.927475i	$-0.621974\pi$
$467$	−16.1594	−0.747768	−0.373884	+	0.927475i	$0.621974\pi$
$468$	2.72504	0.125965
$469$	10.9839	0.507191
$470$	−6.28396	−0.289857
$471$	−2.88744	−0.133046
$472$	1.00000	0.0460287
$473$	43.0648	1.98012
$474$	−0.511565	−0.0234969
$475$	−10.0893	−0.462927
$476$	2.46588	0.113023
$477$	3.60753	0.165178
$478$	−5.04893	−0.230933
$479$	−3.50745	−0.160260	−0.0801298	−	0.996784i	$-0.525533\pi$
$479$	−3.50745	−0.160260	−0.0801298	+	0.996784i	$0.525533\pi$
$480$	−1.01103	−0.0461471
$481$	15.2330	0.694567
$482$	4.13567	0.188374
$483$	5.07592	0.230962
$484$	12.3277	0.560351
$485$	−5.01387	−0.227668
$486$	1.00000	0.0453609
$487$	−32.0244	−1.45116	−0.725582	−	0.688136i	$-0.758429\pi$
$487$	−32.0244	−1.45116	−0.725582	+	0.688136i	$0.758429\pi$
$488$	12.2799	0.555885
$489$	12.4150	0.561427
$490$	0.929600	0.0419950
$491$	−9.86126	−0.445033	−0.222516	−	0.974929i	$-0.571427\pi$
$491$	−9.86126	−0.445033	−0.222516	+	0.974929i	$0.571427\pi$
$492$	6.08586	0.274372
$493$	−8.41813	−0.379134
$494$	6.91175	0.310974
$495$	4.88317	0.219482
$496$	6.58040	0.295469
$497$	−33.3721	−1.49695
$498$	5.01616	0.224780
$499$	29.5084	1.32098	0.660489	−	0.750836i	$-0.270349\pi$
$499$	29.5084	1.32098	0.660489	+	0.750836i	$0.270349\pi$
$500$	9.07687	0.405930
$501$	7.04334	0.314673
$502$	−6.08121	−0.271418
$503$	36.5719	1.63066	0.815330	−	0.578997i	$-0.196556\pi$
$503$	36.5719	1.63066	0.815330	+	0.578997i	$0.196556\pi$
$504$	−2.46588	−0.109839
$505$	5.92919	0.263845
$506$	9.94214	0.441982
$507$	−5.57418	−0.247558
$508$	2.45086	0.108739
$509$	4.97629	0.220570	0.110285	−	0.993900i	$-0.464824\pi$
$509$	4.97629	0.220570	0.110285	+	0.993900i	$0.464824\pi$
$510$	1.01103	0.0447693
$511$	4.41795	0.195439
$512$	1.00000	0.0441942
$513$	2.53639	0.111984
$514$	17.0981	0.754165
$515$	−0.513752	−0.0226386
$516$	−8.91632	−0.392519
$517$	−30.0195	−1.32026
$518$	−13.7843	−0.605649
$519$	8.33797	0.365996
$520$	−2.75510	−0.120819
$521$	−12.7941	−0.560522	−0.280261	−	0.959924i	$-0.590421\pi$
$521$	−12.7941	−0.560522	−0.280261	+	0.959924i	$0.590421\pi$
$522$	8.41813	0.368452
$523$	8.28564	0.362306	0.181153	−	0.983455i	$-0.442017\pi$
$523$	8.28564	0.362306	0.181153	+	0.983455i	$0.442017\pi$
$524$	9.72371	0.424782
$525$	9.80879	0.428091
$526$	−17.1024	−0.745702
$527$	−6.58040	−0.286647
$528$	−4.82988	−0.210194
$529$	−18.7627	−0.815771
$530$	−3.64734	−0.158430
$531$	1.00000	0.0433963
$532$	−6.25441	−0.271163
$533$	16.5842	0.718342
$534$	6.59546	0.285414
$535$	−8.76845	−0.379093
$536$	−4.45438	−0.192400
$537$	−3.57592	−0.154312
$538$	29.1672	1.25749
$539$	4.44086	0.191281
$540$	−1.01103	−0.0435079
$541$	14.7490	0.634110	0.317055	−	0.948407i	$-0.397306\pi$
$541$	14.7490	0.634110	0.317055	+	0.948407i	$0.397306\pi$
$542$	4.00225	0.171912
$543$	−5.13191	−0.220231
$544$	−1.00000	−0.0428746
$545$	9.49348	0.406656
$546$	−6.71960	−0.287572
$547$	3.44660	0.147366	0.0736831	−	0.997282i	$-0.476525\pi$
$547$	3.44660	0.147366	0.0736831	+	0.997282i	$0.476525\pi$
$548$	2.85042	0.121764
$549$	12.2799	0.524093
$550$	19.2123	0.819217
$551$	21.3516	0.909610
$552$	−2.05846	−0.0876141
$553$	1.26146	0.0536425
$554$	19.6619	0.835352
$555$	−5.65171	−0.239902
$556$	−4.72362	−0.200326
$557$	23.3602	0.989805	0.494903	−	0.868948i	$-0.335204\pi$
$557$	23.3602	0.989805	0.494903	+	0.868948i	$0.335204\pi$
$558$	6.58040	0.278570
$559$	−24.2973	−1.02767
$560$	2.49308	0.105352
$561$	4.82988	0.203918
$562$	−5.56905	−0.234916
$563$	−1.48721	−0.0626783	−0.0313391	−	0.999509i	$-0.509977\pi$
$563$	−1.48721	−0.0626783	−0.0313391	+	0.999509i	$0.509977\pi$
$564$	6.21538	0.261715
$565$	−6.59956	−0.277646
$566$	19.6454	0.825758
$567$	−2.46588	−0.103557
$568$	13.5336	0.567857
$569$	9.16013	0.384013	0.192006	−	0.981394i	$-0.438501\pi$
$569$	9.16013	0.384013	0.192006	+	0.981394i	$0.438501\pi$
$570$	−2.56437	−0.107410
$571$	−18.7629	−0.785204	−0.392602	−	0.919708i	$-0.628425\pi$
$571$	−18.7629	−0.785204	−0.392602	+	0.919708i	$0.628425\pi$
$572$	−13.1616	−0.550314
$573$	0.927663	0.0387537
$574$	−15.0070	−0.626380
$575$	8.18819	0.341471
$576$	1.00000	0.0416667
$577$	42.1954	1.75662	0.878310	−	0.478092i	$-0.158672\pi$
$577$	42.1954	1.75662	0.878310	+	0.478092i	$0.158672\pi$
$578$	1.00000	0.0415945
$579$	9.21873	0.383117
$580$	−8.51101	−0.353401
$581$	−12.3692	−0.513162
$582$	4.95915	0.205563
$583$	−17.4240	−0.721626
$584$	−1.79164	−0.0741384
$585$	−2.75510	−0.113909
$586$	−6.74694	−0.278713
$587$	0.290033	0.0119709	0.00598546	−	0.999982i	$-0.498095\pi$
$587$	0.290033	0.0119709	0.00598546	+	0.999982i	$0.498095\pi$
$588$	−0.919455	−0.0379177
$589$	16.6904	0.687717
$590$	−1.01103	−0.0416236
$591$	−8.96361	−0.368714
$592$	5.59003	0.229749
$593$	10.2090	0.419235	0.209618	−	0.977783i	$-0.432778\pi$
$593$	10.2090	0.419235	0.209618	+	0.977783i	$0.432778\pi$
$594$	−4.82988	−0.198172
$595$	−2.49308	−0.102206
$596$	10.1105	0.414141
$597$	−21.4978	−0.879845
$598$	−5.60939	−0.229385
$599$	36.4871	1.49082	0.745410	−	0.666606i	$-0.232254\pi$
$599$	36.4871	1.49082	0.745410	+	0.666606i	$0.232254\pi$
$600$	−3.97781	−0.162393
$601$	−25.8287	−1.05357	−0.526787	−	0.849997i	$-0.676604\pi$
$601$	−25.8287	−1.05357	−0.526787	+	0.849997i	$0.676604\pi$
$602$	21.9865	0.896105
$603$	−4.45438	−0.181396
$604$	−19.8017	−0.805721
$605$	−12.4637	−0.506723
$606$	−5.86448	−0.238228
$607$	4.13044	0.167649	0.0838247	−	0.996481i	$-0.473286\pi$
$607$	4.13044	0.167649	0.0838247	+	0.996481i	$0.473286\pi$
$608$	2.53639	0.102864
$609$	−20.7581	−0.841160
$610$	−12.4154	−0.502684
$611$	16.9371	0.685203
$612$	−1.00000	−0.0404226
$613$	−34.9703	−1.41244	−0.706219	−	0.707994i	$-0.749601\pi$
$613$	−34.9703	−1.41244	−0.706219	+	0.707994i	$0.749601\pi$
$614$	−12.7456	−0.514372
$615$	−6.15301	−0.248113
$616$	11.9099	0.479863
$617$	5.43465	0.218791	0.109395	−	0.993998i	$-0.465109\pi$
$617$	5.43465	0.218791	0.109395	+	0.993998i	$0.465109\pi$
$618$	0.508146	0.0204406
$619$	2.92857	0.117709	0.0588546	−	0.998267i	$-0.481255\pi$
$619$	2.92857	0.117709	0.0588546	+	0.998267i	$0.481255\pi$
$620$	−6.65300	−0.267191
$621$	−2.05846	−0.0826034
$622$	−1.93510	−0.0775905
$623$	−16.2636	−0.651587
$624$	2.72504	0.109089
$625$	10.7120	0.428482
$626$	5.31697	0.212509
$627$	−12.2504	−0.489235
$628$	−2.88744	−0.115221
$629$	−5.59003	−0.222889
$630$	2.49308	0.0993268
$631$	4.70305	0.187225	0.0936126	−	0.995609i	$-0.470158\pi$
$631$	4.70305	0.187225	0.0936126	+	0.995609i	$0.470158\pi$
$632$	−0.511565	−0.0203490
$633$	−15.2561	−0.606375
$634$	−29.2529	−1.16178
$635$	−2.47790	−0.0983325
$636$	3.60753	0.143048
$637$	−2.50555	−0.0992734
$638$	−40.6586	−1.60969
$639$	13.5336	0.535380
$640$	−1.01103	−0.0399646
$641$	44.0119	1.73836	0.869182	−	0.494493i	$-0.164646\pi$
$641$	44.0119	1.73836	0.869182	+	0.494493i	$0.164646\pi$
$642$	8.67276	0.342287
$643$	42.4278	1.67319	0.836595	−	0.547822i	$-0.184543\pi$
$643$	42.4278	1.67319	0.836595	+	0.547822i	$0.184543\pi$
$644$	5.07592	0.200019
$645$	9.01470	0.354953
$646$	−2.53639	−0.0997928
$647$	−4.46173	−0.175409	−0.0877044	−	0.996147i	$-0.527953\pi$
$647$	−4.46173	−0.175409	−0.0877044	+	0.996147i	$0.527953\pi$
$648$	1.00000	0.0392837
$649$	−4.82988	−0.189589
$650$	−10.8397	−0.425167
$651$	−16.2264	−0.635965
$652$	12.4150	0.486210
$653$	1.27103	0.0497391	0.0248696	−	0.999691i	$-0.492083\pi$
$653$	1.27103	0.0497391	0.0248696	+	0.999691i	$0.492083\pi$
$654$	−9.38988	−0.367173
$655$	−9.83099	−0.384129
$656$	6.08586	0.237613
$657$	−1.79164	−0.0698984
$658$	−15.3264	−0.597484
$659$	−3.90864	−0.152259	−0.0761296	−	0.997098i	$-0.524256\pi$
$659$	−3.90864	−0.152259	−0.0761296	+	0.997098i	$0.524256\pi$
$660$	4.88317	0.190077
$661$	−48.5603	−1.88878	−0.944389	−	0.328830i	$-0.893346\pi$
$661$	−48.5603	−1.88878	−0.944389	+	0.328830i	$0.893346\pi$
$662$	−26.2060	−1.01853
$663$	−2.72504	−0.105832
$664$	5.01616	0.194665
$665$	6.32342	0.245212
$666$	5.59003	0.216609
$667$	−17.3284	−0.670960
$668$	7.04334	0.272515
$669$	17.6441	0.682161
$670$	4.50352	0.173986
$671$	−59.3104	−2.28965
$672$	−2.46588	−0.0951232
$673$	−28.6359	−1.10383	−0.551916	−	0.833900i	$-0.686103\pi$
$673$	−28.6359	−1.10383	−0.551916	+	0.833900i	$0.686103\pi$
$674$	20.5612	0.791988
$675$	−3.97781	−0.153106
$676$	−5.57418	−0.214391
$677$	−41.9707	−1.61306	−0.806532	−	0.591190i	$-0.798658\pi$
$677$	−41.9707	−1.61306	−0.806532	+	0.591190i	$0.798658\pi$
$678$	6.52754	0.250689
$679$	−12.2287	−0.469293
$680$	1.01103	0.0387714
$681$	−9.45280	−0.362232
$682$	−31.7825	−1.21702
$683$	16.6629	0.637588	0.318794	−	0.947824i	$-0.396722\pi$
$683$	16.6629	0.637588	0.318794	+	0.947824i	$0.396722\pi$
$684$	2.53639	0.0969812
$685$	−2.88187	−0.110110
$686$	19.5284	0.745598
$687$	17.6028	0.671588
$688$	−8.91632	−0.339932
$689$	9.83066	0.374518
$690$	2.08118	0.0792290
$691$	30.8996	1.17548	0.587738	−	0.809051i	$-0.300018\pi$
$691$	30.8996	1.17548	0.587738	+	0.809051i	$0.300018\pi$
$692$	8.33797	0.316962
$693$	11.9099	0.452419
$694$	−0.833503	−0.0316393
$695$	4.77574	0.181154
$696$	8.41813	0.319089
$697$	−6.08586	−0.230519
$698$	−14.5770	−0.551746
$699$	7.82770	0.296071
$700$	9.80879	0.370737
$701$	−5.14665	−0.194386	−0.0971932	−	0.995266i	$-0.530986\pi$
$701$	−5.14665	−0.194386	−0.0971932	+	0.995266i	$0.530986\pi$
$702$	2.72504	0.102850
$703$	14.1785	0.534752
$704$	−4.82988	−0.182033
$705$	−6.28396	−0.236668
$706$	15.1270	0.569312
$707$	14.4611	0.543865
$708$	1.00000	0.0375823
$709$	20.3106	0.762780	0.381390	−	0.924414i	$-0.375445\pi$
$709$	20.3106	0.762780	0.381390	+	0.924414i	$0.375445\pi$
$710$	−13.6829	−0.513510
$711$	−0.511565	−0.0191852
$712$	6.59546	0.247175
$713$	−13.5455	−0.507284
$714$	2.46588	0.0922831
$715$	13.3068	0.497647
$716$	−3.57592	−0.133638
$717$	−5.04893	−0.188556
$718$	11.1965	0.417850
$719$	−48.6216	−1.81328	−0.906640	−	0.421906i	$-0.861361\pi$
$719$	−48.6216	−1.81328	−0.906640	+	0.421906i	$0.861361\pi$
$720$	−1.01103	−0.0376790
$721$	−1.25302	−0.0466651
$722$	−12.5667	−0.467686
$723$	4.13567	0.153807
$724$	−5.13191	−0.190726
$725$	−33.4857	−1.24363
$726$	12.3277	0.457525
$727$	−27.6184	−1.02431	−0.512155	−	0.858893i	$-0.671153\pi$
$727$	−27.6184	−1.02431	−0.512155	+	0.858893i	$0.671153\pi$
$728$	−6.71960	−0.249045
$729$	1.00000	0.0370370
$730$	1.81140	0.0670430
$731$	8.91632	0.329782
$732$	12.2799	0.453878
$733$	15.9286	0.588337	0.294169	−	0.955754i	$-0.404957\pi$
$733$	15.9286	0.588337	0.294169	+	0.955754i	$0.404957\pi$
$734$	15.0827	0.556711
$735$	0.929600	0.0342888
$736$	−2.05846	−0.0758760
$737$	21.5141	0.792482
$738$	6.08586	0.224024
$739$	−7.85347	−0.288894	−0.144447	−	0.989513i	$-0.546140\pi$
$739$	−7.85347	−0.288894	−0.144447	+	0.989513i	$0.546140\pi$
$740$	−5.65171	−0.207761
$741$	6.91175	0.253909
$742$	−8.89573	−0.326573
$743$	−28.7620	−1.05518	−0.527588	−	0.849501i	$-0.676903\pi$
$743$	−28.7620	−1.05518	−0.527588	+	0.849501i	$0.676903\pi$
$744$	6.58040	0.241249
$745$	−10.2220	−0.374506
$746$	17.8496	0.653522
$747$	5.01616	0.183532
$748$	4.82988	0.176598
$749$	−21.3860	−0.781426
$750$	9.07687	0.331440
$751$	23.5041	0.857676	0.428838	−	0.903381i	$-0.358923\pi$
$751$	23.5041	0.857676	0.428838	+	0.903381i	$0.358923\pi$
$752$	6.21538	0.226652
$753$	−6.08121	−0.221612
$754$	22.9397	0.835415
$755$	20.0202	0.728610
$756$	−2.46588	−0.0896830
$757$	−35.7294	−1.29861	−0.649303	−	0.760530i	$-0.724939\pi$
$757$	−35.7294	−1.29861	−0.649303	+	0.760530i	$0.724939\pi$
$758$	−29.0271	−1.05431
$759$	9.94214	0.360877
$760$	−2.56437	−0.0930195
$761$	23.7205	0.859869	0.429935	−	0.902860i	$-0.358537\pi$
$761$	23.7205	0.859869	0.429935	+	0.902860i	$0.358537\pi$
$762$	2.45086	0.0887853
$763$	23.1543	0.838241
$764$	0.927663	0.0335617
$765$	1.01103	0.0365540
$766$	−11.5928	−0.418866
$767$	2.72504	0.0983954
$768$	1.00000	0.0360844
$769$	−30.8441	−1.11227	−0.556133	−	0.831093i	$-0.687716\pi$
$769$	−30.8441	−1.11227	−0.556133	+	0.831093i	$0.687716\pi$
$770$	−12.0413	−0.433938
$771$	17.0981	0.615773
$772$	9.21873	0.331789
$773$	−28.4708	−1.02402	−0.512012	−	0.858978i	$-0.671100\pi$
$773$	−28.4708	−1.02402	−0.512012	+	0.858978i	$0.671100\pi$
$774$	−8.91632	−0.320491
$775$	−26.1756	−0.940255
$776$	4.95915	0.178023
$777$	−13.7843	−0.494510
$778$	−8.26296	−0.296242
$779$	15.4361	0.553056
$780$	−2.75510	−0.0986485
$781$	−65.3656	−2.33896
$782$	2.05846	0.0736106
$783$	8.41813	0.300840
$784$	−0.919455	−0.0328377
$785$	2.91930	0.104194
$786$	9.72371	0.346833
$787$	−13.0431	−0.464937	−0.232468	−	0.972604i	$-0.574680\pi$
$787$	−13.0431	−0.464937	−0.232468	+	0.972604i	$0.574680\pi$
$788$	−8.96361	−0.319315
$789$	−17.1024	−0.608863
$790$	0.517209	0.0184015
$791$	−16.0961	−0.572311
$792$	−4.82988	−0.171622
$793$	33.4632	1.18831
$794$	1.94249	0.0689365
$795$	−3.64734	−0.129358
$796$	−21.4978	−0.761968
$797$	29.5757	1.04762	0.523812	−	0.851834i	$-0.324509\pi$
$797$	29.5757	1.04762	0.523812	+	0.851834i	$0.324509\pi$
$798$	−6.25441	−0.221404
$799$	−6.21538	−0.219884
$800$	−3.97781	−0.140637
$801$	6.59546	0.233039
$802$	−28.4137	−1.00332
$803$	8.65338	0.305371
$804$	−4.45438	−0.157094
$805$	−5.13192	−0.180877
$806$	17.9318	0.631622
$807$	29.1672	1.02674
$808$	−5.86448	−0.206312
$809$	49.8586	1.75293	0.876467	−	0.481462i	$-0.159894\pi$
$809$	49.8586	1.75293	0.876467	+	0.481462i	$0.159894\pi$
$810$	−1.01103	−0.0355241
$811$	27.7455	0.974277	0.487138	−	0.873325i	$-0.338041\pi$
$811$	27.7455	0.974277	0.487138	+	0.873325i	$0.338041\pi$
$812$	−20.7581	−0.728466
$813$	4.00225	0.140365
$814$	−26.9992	−0.946321
$815$	−12.5520	−0.439678
$816$	−1.00000	−0.0350070
$817$	−22.6152	−0.791207
$818$	12.4718	0.436067
$819$	−6.71960	−0.234802
$820$	−6.15301	−0.214872
$821$	17.1100	0.597145	0.298572	−	0.954387i	$-0.403490\pi$
$821$	17.1100	0.597145	0.298572	+	0.954387i	$0.403490\pi$
$822$	2.85042	0.0994197
$823$	28.3732	0.989026	0.494513	−	0.869170i	$-0.335346\pi$
$823$	28.3732	0.989026	0.494513	+	0.869170i	$0.335346\pi$
$824$	0.508146	0.0177021
$825$	19.2123	0.668888
$826$	−2.46588	−0.0857988
$827$	14.4715	0.503222	0.251611	−	0.967828i	$-0.419040\pi$
$827$	14.4715	0.503222	0.251611	+	0.967828i	$0.419040\pi$
$828$	−2.05846	−0.0715366
$829$	9.38055	0.325800	0.162900	−	0.986643i	$-0.447915\pi$
$829$	9.38055	0.325800	0.162900	+	0.986643i	$0.447915\pi$
$830$	−5.07151	−0.176035
$831$	19.6619	0.682062
$832$	2.72504	0.0944736
$833$	0.919455	0.0318572
$834$	−4.72362	−0.163566
$835$	−7.12105	−0.246434
$836$	−12.2504	−0.423690
$837$	6.58040	0.227452
$838$	−8.73685	−0.301809
$839$	−6.06962	−0.209546	−0.104773	−	0.994496i	$-0.533412\pi$
$839$	−6.06962	−0.209546	−0.104773	+	0.994496i	$0.533412\pi$
$840$	2.49308	0.0860195
$841$	41.8650	1.44362
$842$	−34.4791	−1.18823
$843$	−5.56905	−0.191808
$844$	−15.2561	−0.525137
$845$	5.63568	0.193873
$846$	6.21538	0.213689
$847$	−30.3987	−1.04451
$848$	3.60753	0.123883
$849$	19.6454	0.674228
$850$	3.97781	0.136438
$851$	−11.5069	−0.394451
$852$	13.5336	0.463653
$853$	−20.6420	−0.706770	−0.353385	−	0.935478i	$-0.614969\pi$
$853$	−20.6420	−0.706770	−0.353385	+	0.935478i	$0.614969\pi$
$854$	−30.2807	−1.03618
$855$	−2.56437	−0.0876996
$856$	8.67276	0.296429
$857$	22.8406	0.780221	0.390110	−	0.920768i	$-0.372437\pi$
$857$	22.8406	0.780221	0.390110	+	0.920768i	$0.372437\pi$
$858$	−13.1616	−0.449330
$859$	18.9324	0.645964	0.322982	−	0.946405i	$-0.395315\pi$
$859$	18.9324	0.645964	0.322982	+	0.946405i	$0.395315\pi$
$860$	9.01470	0.307399
$861$	−15.0070	−0.511437
$862$	16.4866	0.561535
$863$	8.95418	0.304804	0.152402	−	0.988319i	$-0.451299\pi$
$863$	8.95418	0.304804	0.152402	+	0.988319i	$0.451299\pi$
$864$	1.00000	0.0340207
$865$	−8.42997	−0.286628
$866$	4.13832	0.140626
$867$	1.00000	0.0339618
$868$	−16.2264	−0.550761
$869$	2.47080	0.0838160
$870$	−8.51101	−0.288550
$871$	−12.1383	−0.411292
$872$	−9.38988	−0.317981
$873$	4.95915	0.167842
$874$	−5.22106	−0.176605
$875$	−22.3824	−0.756664
$876$	−1.79164	−0.0605338
$877$	−12.7122	−0.429261	−0.214631	−	0.976695i	$-0.568855\pi$
$877$	−12.7122	−0.429261	−0.214631	+	0.976695i	$0.568855\pi$
$878$	6.45247	0.217760
$879$	−6.74694	−0.227569
$880$	4.88317	0.164612
$881$	−3.02717	−0.101988	−0.0509939	−	0.998699i	$-0.516239\pi$
$881$	−3.02717	−0.101988	−0.0509939	+	0.998699i	$0.516239\pi$
$882$	−0.919455	−0.0309597
$883$	18.1428	0.610553	0.305277	−	0.952264i	$-0.401251\pi$
$883$	18.1428	0.610553	0.305277	+	0.952264i	$0.401251\pi$
$884$	−2.72504	−0.0916529
$885$	−1.01103	−0.0339855
$886$	−1.65783	−0.0556958
$887$	10.9672	0.368243	0.184122	−	0.982903i	$-0.441056\pi$
$887$	10.9672	0.368243	0.184122	+	0.982903i	$0.441056\pi$
$888$	5.59003	0.187589
$889$	−6.04352	−0.202693
$890$	−6.66823	−0.223520
$891$	−4.82988	−0.161807
$892$	17.6441	0.590769
$893$	15.7646	0.527542
$894$	10.1105	0.338144
$895$	3.61537	0.120849
$896$	−2.46588	−0.0823791
$897$	−5.60939	−0.187292
$898$	−22.9470	−0.765750
$899$	55.3947	1.84752
$900$	−3.97781	−0.132594
$901$	−3.60753	−0.120184
$902$	−29.3940	−0.978713
$903$	21.9865	0.731666
$904$	6.52754	0.217103
$905$	5.18853	0.172473
$906$	−19.8017	−0.657868
$907$	−7.26652	−0.241281	−0.120640	−	0.992696i	$-0.538495\pi$
$907$	−7.26652	−0.241281	−0.120640	+	0.992696i	$0.538495\pi$
$908$	−9.45280	−0.313702
$909$	−5.86448	−0.194513
$910$	6.79374	0.225210
$911$	−23.2449	−0.770137	−0.385069	−	0.922888i	$-0.625822\pi$
$911$	−23.2449	−0.770137	−0.385069	+	0.922888i	$0.625822\pi$
$912$	2.53639	0.0839881
$913$	−24.2274	−0.801811
$914$	−3.20684	−0.106073
$915$	−12.4154	−0.410440
$916$	17.6028	0.581613
$917$	−23.9775	−0.791806
$918$	−1.00000	−0.0330049
$919$	4.97690	0.164173	0.0820865	−	0.996625i	$-0.473842\pi$
$919$	4.97690	0.164173	0.0820865	+	0.996625i	$0.473842\pi$
$920$	2.08118	0.0686144
$921$	−12.7456	−0.419983
$922$	26.2219	0.863574
$923$	36.8795	1.21390
$924$	11.9099	0.391806
$925$	−22.2361	−0.731118
$926$	−23.2202	−0.763064
$927$	0.508146	0.0166897
$928$	8.41813	0.276339
$929$	12.3672	0.405753	0.202877	−	0.979204i	$-0.434971\pi$
$929$	12.3672	0.405753	0.202877	+	0.979204i	$0.434971\pi$
$930$	−6.65300	−0.218161
$931$	−2.33209	−0.0764312
$932$	7.82770	0.256405
$933$	−1.93510	−0.0633523
$934$	−16.1594	−0.528752
$935$	−4.88317	−0.159697
$936$	2.72504	0.0890706
$937$	−36.8141	−1.20266	−0.601332	−	0.798999i	$-0.705363\pi$
$937$	−36.8141	−1.20266	−0.601332	+	0.798999i	$0.705363\pi$
$938$	10.9839	0.358638
$939$	5.31697	0.173513
$940$	−6.28396	−0.204960
$941$	−2.47156	−0.0805706	−0.0402853	−	0.999188i	$-0.512827\pi$
$941$	−2.47156	−0.0805706	−0.0402853	+	0.999188i	$0.512827\pi$
$942$	−2.88744	−0.0940779
$943$	−12.5275	−0.407953
$944$	1.00000	0.0325472
$945$	2.49308	0.0811000
$946$	43.0648	1.40016
$947$	17.9914	0.584643	0.292321	−	0.956320i	$-0.405572\pi$
$947$	17.9914	0.584643	0.292321	+	0.956320i	$0.405572\pi$
$948$	−0.511565	−0.0166149
$949$	−4.88227	−0.158485
$950$	−10.0893	−0.327339
$951$	−29.2529	−0.948590
$952$	2.46588	0.0799195
$953$	17.2598	0.559101	0.279551	−	0.960131i	$-0.409815\pi$
$953$	17.2598	0.559101	0.279551	+	0.960131i	$0.409815\pi$
$954$	3.60753	0.116798
$955$	−0.937898	−0.0303497
$956$	−5.04893	−0.163294
$957$	−40.6586	−1.31430
$958$	−3.50745	−0.113321
$959$	−7.02877	−0.226971
$960$	−1.01103	−0.0326310
$961$	12.3016	0.396827
$962$	15.2330	0.491133
$963$	8.67276	0.279476
$964$	4.13567	0.133201
$965$	−9.32045	−0.300036
$966$	5.07592	0.163315
$967$	−14.9619	−0.481141	−0.240570	−	0.970632i	$-0.577334\pi$
$967$	−14.9619	−0.481141	−0.240570	+	0.970632i	$0.577334\pi$
$968$	12.3277	0.396228
$969$	−2.53639	−0.0814805
$970$	−5.01387	−0.160986
$971$	−29.8897	−0.959206	−0.479603	−	0.877486i	$-0.659219\pi$
$971$	−29.8897	−0.959206	−0.479603	+	0.877486i	$0.659219\pi$
$972$	1.00000	0.0320750
$973$	11.6479	0.373413
$974$	−32.0244	−1.02613
$975$	−10.8397	−0.347148
$976$	12.2799	0.393070
$977$	32.0060	1.02396	0.511981	−	0.858997i	$-0.328912\pi$
$977$	32.0060	1.02396	0.511981	+	0.858997i	$0.328912\pi$
$978$	12.4150	0.396989
$979$	−31.8553	−1.01810
$980$	0.929600	0.0296950
$981$	−9.38988	−0.299796
$982$	−9.86126	−0.314685
$983$	−7.61809	−0.242979	−0.121490	−	0.992593i	$-0.538767\pi$
$983$	−7.61809	−0.242979	−0.121490	+	0.992593i	$0.538767\pi$
$984$	6.08586	0.194010
$985$	9.06251	0.288755
$986$	−8.41813	−0.268088
$987$	−15.3264	−0.487843
$988$	6.91175	0.219892
$989$	18.3539	0.583621
$990$	4.88317	0.155197
$991$	−32.1201	−1.02033	−0.510164	−	0.860077i	$-0.670415\pi$
$991$	−32.1201	−1.02033	−0.510164	+	0.860077i	$0.670415\pi$
$992$	6.58040	0.208928
$993$	−26.2060	−0.831624
$994$	−33.3721	−1.05850
$995$	21.7350	0.689045
$996$	5.01616	0.158943
$997$	−35.5708	−1.12654	−0.563269	−	0.826274i	$-0.690457\pi$
$997$	−35.5708	−1.12654	−0.563269	+	0.826274i	$0.690457\pi$
$998$	29.5084	0.934072
$999$	5.59003	0.176861

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.ba.1.4	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.ba.1.4	✓	12	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:	\( N \)	\(=\)	\( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.01103 q^{5} +1.00000 q^{6} -2.46588 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.01103 q^{5} +1.00000 q^{6} -2.46588 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.01103 q^{10} -4.82988 q^{11} +1.00000 q^{12} +2.72504 q^{13} -2.46588 q^{14} -1.01103 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +2.53639 q^{19} -1.01103 q^{20} -2.46588 q^{21} -4.82988 q^{22} -2.05846 q^{23} +1.00000 q^{24} -3.97781 q^{25} +2.72504 q^{26} +1.00000 q^{27} -2.46588 q^{28} +8.41813 q^{29} -1.01103 q^{30} +6.58040 q^{31} +1.00000 q^{32} -4.82988 q^{33} -1.00000 q^{34} +2.49308 q^{35} +1.00000 q^{36} +5.59003 q^{37} +2.53639 q^{38} +2.72504 q^{39} -1.01103 q^{40} +6.08586 q^{41} -2.46588 q^{42} -8.91632 q^{43} -4.82988 q^{44} -1.01103 q^{45} -2.05846 q^{46} +6.21538 q^{47} +1.00000 q^{48} -0.919455 q^{49} -3.97781 q^{50} -1.00000 q^{51} +2.72504 q^{52} +3.60753 q^{53} +1.00000 q^{54} +4.88317 q^{55} -2.46588 q^{56} +2.53639 q^{57} +8.41813 q^{58} +1.00000 q^{59} -1.01103 q^{60} +12.2799 q^{61} +6.58040 q^{62} -2.46588 q^{63} +1.00000 q^{64} -2.75510 q^{65} -4.82988 q^{66} -4.45438 q^{67} -1.00000 q^{68} -2.05846 q^{69} +2.49308 q^{70} +13.5336 q^{71} +1.00000 q^{72} -1.79164 q^{73} +5.59003 q^{74} -3.97781 q^{75} +2.53639 q^{76} +11.9099 q^{77} +2.72504 q^{78} -0.511565 q^{79} -1.01103 q^{80} +1.00000 q^{81} +6.08586 q^{82} +5.01616 q^{83} -2.46588 q^{84} +1.01103 q^{85} -8.91632 q^{86} +8.41813 q^{87} -4.82988 q^{88} +6.59546 q^{89} -1.01103 q^{90} -6.71960 q^{91} -2.05846 q^{92} +6.58040 q^{93} +6.21538 q^{94} -2.56437 q^{95} +1.00000 q^{96} +4.95915 q^{97} -0.919455 q^{98} -4.82988 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 q^{5} + 12 q^{6} + 5 q^{7} + 12 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 8 * q^5 + 12 * q^6 + 5 * q^7 + 12 * q^8 + 12 * q^9	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 q^{5} + 12 q^{6} + 5 q^{7} + 12 q^{8} + 12 q^{9} + 8 q^{10} + 11 q^{11} + 12 q^{12} + 6 q^{13} + 5 q^{14} + 8 q^{15} + 12 q^{16} - 12 q^{17} + 12 q^{18} + 3 q^{19} + 8 q^{20} + 5 q^{21} + 11 q^{22} + 22 q^{23} + 12 q^{24} + 22 q^{25} + 6 q^{26} + 12 q^{27} + 5 q^{28} + 26 q^{29} + 8 q^{30} + q^{31} + 12 q^{32} + 11 q^{33} - 12 q^{34} + 24 q^{35} + 12 q^{36} + 10 q^{37} + 3 q^{38} + 6 q^{39} + 8 q^{40} + 16 q^{41} + 5 q^{42} + 23 q^{43} + 11 q^{44} + 8 q^{45} + 22 q^{46} + 6 q^{47} + 12 q^{48} + 11 q^{49} + 22 q^{50} - 12 q^{51} + 6 q^{52} + 10 q^{53} + 12 q^{54} + 15 q^{55} + 5 q^{56} + 3 q^{57} + 26 q^{58} + 12 q^{59} + 8 q^{60} + 15 q^{61} + q^{62} + 5 q^{63} + 12 q^{64} + 4 q^{65} + 11 q^{66} + 4 q^{67} - 12 q^{68} + 22 q^{69} + 24 q^{70} + 10 q^{71} + 12 q^{72} + 24 q^{73} + 10 q^{74} + 22 q^{75} + 3 q^{76} + 24 q^{77} + 6 q^{78} + 23 q^{79} + 8 q^{80} + 12 q^{81} + 16 q^{82} + 5 q^{84} - 8 q^{85} + 23 q^{86} + 26 q^{87} + 11 q^{88} + 13 q^{89} + 8 q^{90} + 3 q^{91} + 22 q^{92} + q^{93} + 6 q^{94} + 11 q^{95} + 12 q^{96} + 13 q^{97} + 11 q^{98} + 11 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 8 * q^5 + 12 * q^6 + 5 * q^7 + 12 * q^8 + 12 * q^9 + 8 * q^10 + 11 * q^11 + 12 * q^12 + 6 * q^13 + 5 * q^14 + 8 * q^15 + 12 * q^16 - 12 * q^17 + 12 * q^18 + 3 * q^19 + 8 * q^20 + 5 * q^21 + 11 * q^22 + 22 * q^23 + 12 * q^24 + 22 * q^25 + 6 * q^26 + 12 * q^27 + 5 * q^28 + 26 * q^29 + 8 * q^30 + q^31 + 12 * q^32 + 11 * q^33 - 12 * q^34 + 24 * q^35 + 12 * q^36 + 10 * q^37 + 3 * q^38 + 6 * q^39 + 8 * q^40 + 16 * q^41 + 5 * q^42 + 23 * q^43 + 11 * q^44 + 8 * q^45 + 22 * q^46 + 6 * q^47 + 12 * q^48 + 11 * q^49 + 22 * q^50 - 12 * q^51 + 6 * q^52 + 10 * q^53 + 12 * q^54 + 15 * q^55 + 5 * q^56 + 3 * q^57 + 26 * q^58 + 12 * q^59 + 8 * q^60 + 15 * q^61 + q^62 + 5 * q^63 + 12 * q^64 + 4 * q^65 + 11 * q^66 + 4 * q^67 - 12 * q^68 + 22 * q^69 + 24 * q^70 + 10 * q^71 + 12 * q^72 + 24 * q^73 + 10 * q^74 + 22 * q^75 + 3 * q^76 + 24 * q^77 + 6 * q^78 + 23 * q^79 + 8 * q^80 + 12 * q^81 + 16 * q^82 + 5 * q^84 - 8 * q^85 + 23 * q^86 + 26 * q^87 + 11 * q^88 + 13 * q^89 + 8 * q^90 + 3 * q^91 + 22 * q^92 + q^93 + 6 * q^94 + 11 * q^95 + 12 * q^96 + 13 * q^97 + 11 * q^98 + 11 * q^99

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