LMFDB - Embedded newform 6046.2.a.d.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6046,2,Mod(1,6046)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6046, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6046.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6046 = 2 \cdot 3023 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6046.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:	$48.2775530621$
Analytic rank:	$1$
Dimension:	$55$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6046.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.49688 q^{3} +1.00000 q^{4} +2.53302 q^{5} +1.49688 q^{6} -3.95759 q^{7} -1.00000 q^{8} -0.759363 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.49688 q^{3} +1.00000 q^{4} +2.53302 q^{5} +1.49688 q^{6} -3.95759 q^{7} -1.00000 q^{8} -0.759363 q^{9} -2.53302 q^{10} -1.23209 q^{11} -1.49688 q^{12} -0.312847 q^{13} +3.95759 q^{14} -3.79162 q^{15} +1.00000 q^{16} -0.335778 q^{17} +0.759363 q^{18} +5.16117 q^{19} +2.53302 q^{20} +5.92402 q^{21} +1.23209 q^{22} +0.900359 q^{23} +1.49688 q^{24} +1.41620 q^{25} +0.312847 q^{26} +5.62730 q^{27} -3.95759 q^{28} -9.67318 q^{29} +3.79162 q^{30} +0.418989 q^{31} -1.00000 q^{32} +1.84428 q^{33} +0.335778 q^{34} -10.0247 q^{35} -0.759363 q^{36} +1.74871 q^{37} -5.16117 q^{38} +0.468293 q^{39} -2.53302 q^{40} +4.13973 q^{41} -5.92402 q^{42} +2.48195 q^{43} -1.23209 q^{44} -1.92348 q^{45} -0.900359 q^{46} +9.44526 q^{47} -1.49688 q^{48} +8.66254 q^{49} -1.41620 q^{50} +0.502619 q^{51} -0.312847 q^{52} -2.11431 q^{53} -5.62730 q^{54} -3.12091 q^{55} +3.95759 q^{56} -7.72563 q^{57} +9.67318 q^{58} +14.6887 q^{59} -3.79162 q^{60} +5.15875 q^{61} -0.418989 q^{62} +3.00525 q^{63} +1.00000 q^{64} -0.792449 q^{65} -1.84428 q^{66} +8.25613 q^{67} -0.335778 q^{68} -1.34773 q^{69} +10.0247 q^{70} -12.9473 q^{71} +0.759363 q^{72} +6.19044 q^{73} -1.74871 q^{74} -2.11988 q^{75} +5.16117 q^{76} +4.87611 q^{77} -0.468293 q^{78} -1.30817 q^{79} +2.53302 q^{80} -6.14528 q^{81} -4.13973 q^{82} -5.91234 q^{83} +5.92402 q^{84} -0.850535 q^{85} -2.48195 q^{86} +14.4796 q^{87} +1.23209 q^{88} -17.9767 q^{89} +1.92348 q^{90} +1.23812 q^{91} +0.900359 q^{92} -0.627174 q^{93} -9.44526 q^{94} +13.0734 q^{95} +1.49688 q^{96} -17.4413 q^{97} -8.66254 q^{98} +0.935602 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 55 q - 55 q^{2} - 4 q^{3} + 55 q^{4} - 7 q^{5} + 4 q^{6} + 17 q^{7} - 55 q^{8} + 29 q^{9}+O(q^{10}) $ 55 * q - 55 * q^2 - 4 * q^3 + 55 * q^4 - 7 * q^5 + 4 * q^6 + 17 * q^7 - 55 * q^8 + 29 * q^9	\( 55 q - 55 q^{2} - 4 q^{3} + 55 q^{4} - 7 q^{5} + 4 q^{6} + 17 q^{7} - 55 q^{8} + 29 q^{9} + 7 q^{10} - 28 q^{11} - 4 q^{12} + q^{13} - 17 q^{14} - 8 q^{15} + 55 q^{16} - 32 q^{17} - 29 q^{18} - 3 q^{19} - 7 q^{20} - 25 q^{21} + 28 q^{22} - 27 q^{23} + 4 q^{24} + 30 q^{25} - q^{26} - q^{27} + 17 q^{28} - 69 q^{29} + 8 q^{30} - 13 q^{31} - 55 q^{32} - 18 q^{33} + 32 q^{34} - 23 q^{35} + 29 q^{36} + 3 q^{37} + 3 q^{38} - 28 q^{39} + 7 q^{40} - 51 q^{41} + 25 q^{42} + 23 q^{43} - 28 q^{44} - 28 q^{45} + 27 q^{46} - 27 q^{47} - 4 q^{48} + 8 q^{49} - 30 q^{50} - 42 q^{51} + q^{52} - 61 q^{53} + q^{54} + 5 q^{55} - 17 q^{56} - 52 q^{57} + 69 q^{58} - 71 q^{59} - 8 q^{60} - 16 q^{61} + 13 q^{62} + 14 q^{63} + 55 q^{64} - 82 q^{65} + 18 q^{66} + 32 q^{67} - 32 q^{68} - 44 q^{69} + 23 q^{70} - 84 q^{71} - 29 q^{72} - 43 q^{73} - 3 q^{74} - 37 q^{75} - 3 q^{76} - 47 q^{77} + 28 q^{78} - 20 q^{79} - 7 q^{80} - 33 q^{81} + 51 q^{82} + 17 q^{83} - 25 q^{84} + 10 q^{85} - 23 q^{86} - q^{87} + 28 q^{88} - 92 q^{89} + 28 q^{90} - 34 q^{91} - 27 q^{92} - 13 q^{93} + 27 q^{94} - 60 q^{95} + 4 q^{96} - 45 q^{97} - 8 q^{98} - 73 q^{99}+O(q^{100}) \) 55 * q - 55 * q^2 - 4 * q^3 + 55 * q^4 - 7 * q^5 + 4 * q^6 + 17 * q^7 - 55 * q^8 + 29 * q^9 + 7 * q^10 - 28 * q^11 - 4 * q^12 + q^13 - 17 * q^14 - 8 * q^15 + 55 * q^16 - 32 * q^17 - 29 * q^18 - 3 * q^19 - 7 * q^20 - 25 * q^21 + 28 * q^22 - 27 * q^23 + 4 * q^24 + 30 * q^25 - q^26 - q^27 + 17 * q^28 - 69 * q^29 + 8 * q^30 - 13 * q^31 - 55 * q^32 - 18 * q^33 + 32 * q^34 - 23 * q^35 + 29 * q^36 + 3 * q^37 + 3 * q^38 - 28 * q^39 + 7 * q^40 - 51 * q^41 + 25 * q^42 + 23 * q^43 - 28 * q^44 - 28 * q^45 + 27 * q^46 - 27 * q^47 - 4 * q^48 + 8 * q^49 - 30 * q^50 - 42 * q^51 + q^52 - 61 * q^53 + q^54 + 5 * q^55 - 17 * q^56 - 52 * q^57 + 69 * q^58 - 71 * q^59 - 8 * q^60 - 16 * q^61 + 13 * q^62 + 14 * q^63 + 55 * q^64 - 82 * q^65 + 18 * q^66 + 32 * q^67 - 32 * q^68 - 44 * q^69 + 23 * q^70 - 84 * q^71 - 29 * q^72 - 43 * q^73 - 3 * q^74 - 37 * q^75 - 3 * q^76 - 47 * q^77 + 28 * q^78 - 20 * q^79 - 7 * q^80 - 33 * q^81 + 51 * q^82 + 17 * q^83 - 25 * q^84 + 10 * q^85 - 23 * q^86 - q^87 + 28 * q^88 - 92 * q^89 + 28 * q^90 - 34 * q^91 - 27 * q^92 - 13 * q^93 + 27 * q^94 - 60 * q^95 + 4 * q^96 - 45 * q^97 - 8 * q^98 - 73 * 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
$3$	−1.49688	−0.864222	−0.432111	−	0.901820i	$-0.642231\pi$
$3$	−1.49688	−0.864222	−0.432111	+	0.901820i	$0.642231\pi$
$4$	1.00000	0.500000
$5$	2.53302	1.13280	0.566401	−	0.824130i	$-0.308335\pi$
$5$	2.53302	1.13280	0.566401	+	0.824130i	$0.308335\pi$
$6$	1.49688	0.611097
$7$	−3.95759	−1.49583	−0.747915	−	0.663795i	$-0.768945\pi$
$7$	−3.95759	−1.49583	−0.747915	+	0.663795i	$0.768945\pi$
$8$	−1.00000	−0.353553
$9$	−0.759363	−0.253121
$10$	−2.53302	−0.801012
$11$	−1.23209	−0.371489	−0.185744	−	0.982598i	$-0.559470\pi$
$11$	−1.23209	−0.371489	−0.185744	+	0.982598i	$0.559470\pi$
$12$	−1.49688	−0.432111
$13$	−0.312847	−0.0867682	−0.0433841	−	0.999058i	$-0.513814\pi$
$13$	−0.312847	−0.0867682	−0.0433841	+	0.999058i	$0.513814\pi$
$14$	3.95759	1.05771
$15$	−3.79162	−0.978992
$16$	1.00000	0.250000
$17$	−0.335778	−0.0814382	−0.0407191	−	0.999171i	$-0.512965\pi$
$17$	−0.335778	−0.0814382	−0.0407191	+	0.999171i	$0.512965\pi$
$18$	0.759363	0.178983
$19$	5.16117	1.18405	0.592027	−	0.805918i	$-0.298328\pi$
$19$	5.16117	1.18405	0.592027	+	0.805918i	$0.298328\pi$
$20$	2.53302	0.566401
$21$	5.92402	1.29273
$22$	1.23209	0.262682
$23$	0.900359	0.187738	0.0938689	−	0.995585i	$-0.470077\pi$
$23$	0.900359	0.187738	0.0938689	+	0.995585i	$0.470077\pi$
$24$	1.49688	0.305549
$25$	1.41620	0.283241
$26$	0.312847	0.0613544
$27$	5.62730	1.08297
$28$	−3.95759	−0.747915
$29$	−9.67318	−1.79626	−0.898132	−	0.439725i	$-0.855076\pi$
$29$	−9.67318	−1.79626	−0.898132	+	0.439725i	$0.855076\pi$
$30$	3.79162	0.692252
$31$	0.418989	0.0752526	0.0376263	−	0.999292i	$-0.488020\pi$
$31$	0.418989	0.0752526	0.0376263	+	0.999292i	$0.488020\pi$
$32$	−1.00000	−0.176777
$33$	1.84428	0.321049
$34$	0.335778	0.0575855
$35$	−10.0247	−1.69448
$36$	−0.759363	−0.126560
$37$	1.74871	0.287487	0.143743	−	0.989615i	$-0.454086\pi$
$37$	1.74871	0.287487	0.143743	+	0.989615i	$0.454086\pi$
$38$	−5.16117	−0.837252
$39$	0.468293	0.0749870
$40$	−2.53302	−0.400506
$41$	4.13973	0.646518	0.323259	−	0.946311i	$-0.395222\pi$
$41$	4.13973	0.646518	0.323259	+	0.946311i	$0.395222\pi$
$42$	−5.92402	−0.914097
$43$	2.48195	0.378494	0.189247	−	0.981930i	$-0.439395\pi$
$43$	2.48195	0.378494	0.189247	+	0.981930i	$0.439395\pi$
$44$	−1.23209	−0.185744
$45$	−1.92348	−0.286736
$46$	−0.900359	−0.132751
$47$	9.44526	1.37773	0.688866	−	0.724888i	$-0.258109\pi$
$47$	9.44526	1.37773	0.688866	+	0.724888i	$0.258109\pi$
$48$	−1.49688	−0.216055
$49$	8.66254	1.23751
$50$	−1.41620	−0.200282
$51$	0.502619	0.0703807
$52$	−0.312847	−0.0433841
$53$	−2.11431	−0.290423	−0.145212	−	0.989401i	$-0.546386\pi$
$53$	−2.11431	−0.290423	−0.145212	+	0.989401i	$0.546386\pi$
$54$	−5.62730	−0.765778
$55$	−3.12091	−0.420823
$56$	3.95759	0.528856
$57$	−7.72563	−1.02328
$58$	9.67318	1.27015
$59$	14.6887	1.91231	0.956153	−	0.292869i	$-0.0946100\pi$
$59$	14.6887	1.91231	0.956153	+	0.292869i	$0.0946100\pi$
$60$	−3.79162	−0.489496
$61$	5.15875	0.660510	0.330255	−	0.943892i	$-0.392865\pi$
$61$	5.15875	0.660510	0.330255	+	0.943892i	$0.392865\pi$
$62$	−0.418989	−0.0532116
$63$	3.00525	0.378626
$64$	1.00000	0.125000
$65$	−0.792449	−0.0982912
$66$	−1.84428	−0.227016
$67$	8.25613	1.00865	0.504324	−	0.863515i	$-0.331742\pi$
$67$	8.25613	1.00865	0.504324	+	0.863515i	$0.331742\pi$
$68$	−0.335778	−0.0407191
$69$	−1.34773	−0.162247
$70$	10.0247	1.19818
$71$	−12.9473	−1.53656	−0.768278	−	0.640116i	$-0.778886\pi$
$71$	−12.9473	−1.53656	−0.768278	+	0.640116i	$0.778886\pi$
$72$	0.759363	0.0894917
$73$	6.19044	0.724537	0.362268	−	0.932074i	$-0.382002\pi$
$73$	6.19044	0.724537	0.362268	+	0.932074i	$0.382002\pi$
$74$	−1.74871	−0.203284
$75$	−2.11988	−0.244783
$76$	5.16117	0.592027
$77$	4.87611	0.555684
$78$	−0.468293	−0.0530238
$79$	−1.30817	−0.147180	−0.0735902	−	0.997289i	$-0.523446\pi$
$79$	−1.30817	−0.147180	−0.0735902	+	0.997289i	$0.523446\pi$
$80$	2.53302	0.283201
$81$	−6.14528	−0.682809
$82$	−4.13973	−0.457157
$83$	−5.91234	−0.648964	−0.324482	−	0.945892i	$-0.605190\pi$
$83$	−5.91234	−0.648964	−0.324482	+	0.945892i	$0.605190\pi$
$84$	5.92402	0.646364
$85$	−0.850535	−0.0922534
$86$	−2.48195	−0.267636
$87$	14.4796	1.55237
$88$	1.23209	0.131341
$89$	−17.9767	−1.90552	−0.952762	−	0.303718i	$-0.901772\pi$
$89$	−17.9767	−1.90552	−0.952762	+	0.303718i	$0.901772\pi$
$90$	1.92348	0.202753
$91$	1.23812	0.129790
$92$	0.900359	0.0938689
$93$	−0.627174	−0.0650349
$94$	−9.44526	−0.974204
$95$	13.0734	1.34130
$96$	1.49688	0.152774
$97$	−17.4413	−1.77090	−0.885448	−	0.464739i	$-0.846148\pi$
$97$	−17.4413	−1.77090	−0.885448	+	0.464739i	$0.846148\pi$
$98$	−8.66254	−0.875048
$99$	0.935602	0.0940316
$100$	1.41620	0.141620
$101$	−0.853923	−0.0849685	−0.0424842	−	0.999097i	$-0.513527\pi$
$101$	−0.853923	−0.0849685	−0.0424842	+	0.999097i	$0.513527\pi$
$102$	−0.502619	−0.0497667
$103$	10.4037	1.02510	0.512552	−	0.858656i	$-0.328700\pi$
$103$	10.4037	1.02510	0.512552	+	0.858656i	$0.328700\pi$
$104$	0.312847	0.0306772
$105$	15.0057	1.46441
$106$	2.11431	0.205360
$107$	−1.55379	−0.150211	−0.0751053	−	0.997176i	$-0.523929\pi$
$107$	−1.55379	−0.150211	−0.0751053	+	0.997176i	$0.523929\pi$
$108$	5.62730	0.541487
$109$	−5.47519	−0.524428	−0.262214	−	0.965010i	$-0.584453\pi$
$109$	−5.47519	−0.524428	−0.262214	+	0.965010i	$0.584453\pi$
$110$	3.12091	0.297567
$111$	−2.61761	−0.248452
$112$	−3.95759	−0.373957
$113$	5.79045	0.544720	0.272360	−	0.962195i	$-0.412196\pi$
$113$	5.79045	0.544720	0.272360	+	0.962195i	$0.412196\pi$
$114$	7.72563	0.723572
$115$	2.28063	0.212670
$116$	−9.67318	−0.898132
$117$	0.237564	0.0219628
$118$	−14.6887	−1.35220
$119$	1.32887	0.121818
$120$	3.79162	0.346126
$121$	−9.48196	−0.861996
$122$	−5.15875	−0.467051
$123$	−6.19667	−0.558735
$124$	0.418989	0.0376263
$125$	−9.07784	−0.811946
$126$	−3.00525	−0.267729
$127$	3.29947	0.292781	0.146390	−	0.989227i	$-0.453234\pi$
$127$	3.29947	0.292781	0.146390	+	0.989227i	$0.453234\pi$
$128$	−1.00000	−0.0883883
$129$	−3.71517	−0.327103
$130$	0.792449	0.0695024
$131$	2.79046	0.243804	0.121902	−	0.992542i	$-0.461101\pi$
$131$	2.79046	0.243804	0.121902	+	0.992542i	$0.461101\pi$
$132$	1.84428	0.160524
$133$	−20.4258	−1.77114
$134$	−8.25613	−0.713221
$135$	14.2541	1.22680
$136$	0.335778	0.0287928
$137$	12.6837	1.08364	0.541820	−	0.840494i	$-0.317735\pi$
$137$	12.6837	1.08364	0.541820	+	0.840494i	$0.317735\pi$
$138$	1.34773	0.114726
$139$	−3.72706	−0.316125	−0.158063	−	0.987429i	$-0.550525\pi$
$139$	−3.72706	−0.316125	−0.158063	+	0.987429i	$0.550525\pi$
$140$	−10.0247	−0.847239
$141$	−14.1384	−1.19067
$142$	12.9473	1.08651
$143$	0.385456	0.0322334
$144$	−0.759363	−0.0632802
$145$	−24.5024	−2.03481
$146$	−6.19044	−0.512325
$147$	−12.9667	−1.06948
$148$	1.74871	0.143743
$149$	−7.73667	−0.633813	−0.316906	−	0.948457i	$-0.602644\pi$
$149$	−7.73667	−0.633813	−0.316906	+	0.948457i	$0.602644\pi$
$150$	2.11988	0.173088
$151$	−13.0379	−1.06101	−0.530507	−	0.847681i	$-0.677998\pi$
$151$	−13.0379	−1.06101	−0.530507	+	0.847681i	$0.677998\pi$
$152$	−5.16117	−0.418626
$153$	0.254978	0.0206137
$154$	−4.87611	−0.392928
$155$	1.06131	0.0852463
$156$	0.468293	0.0374935
$157$	−12.5971	−1.00536	−0.502679	−	0.864473i	$-0.667652\pi$
$157$	−12.5971	−1.00536	−0.502679	+	0.864473i	$0.667652\pi$
$158$	1.30817	0.104072
$159$	3.16486	0.250990
$160$	−2.53302	−0.200253
$161$	−3.56325	−0.280824
$162$	6.14528	0.482819
$163$	−21.6672	−1.69711	−0.848553	−	0.529110i	$-0.822526\pi$
$163$	−21.6672	−1.69711	−0.848553	+	0.529110i	$0.822526\pi$
$164$	4.13973	0.323259
$165$	4.67161	0.363685
$166$	5.91234	0.458887
$167$	−5.15889	−0.399207	−0.199604	−	0.979877i	$-0.563965\pi$
$167$	−5.15889	−0.399207	−0.199604	+	0.979877i	$0.563965\pi$
$168$	−5.92402	−0.457048
$169$	−12.9021	−0.992471
$170$	0.850535	0.0652330
$171$	−3.91920	−0.299709
$172$	2.48195	0.189247
$173$	13.8006	1.04924	0.524618	−	0.851338i	$-0.324208\pi$
$173$	13.8006	1.04924	0.524618	+	0.851338i	$0.324208\pi$
$174$	−14.4796	−1.09769
$175$	−5.60476	−0.423680
$176$	−1.23209	−0.0928722
$177$	−21.9872	−1.65266
$178$	17.9767	1.34741
$179$	5.11840	0.382567	0.191283	−	0.981535i	$-0.438735\pi$
$179$	5.11840	0.382567	0.191283	+	0.981535i	$0.438735\pi$
$180$	−1.92348	−0.143368
$181$	−7.88031	−0.585739	−0.292870	−	0.956152i	$-0.594610\pi$
$181$	−7.88031	−0.585739	−0.292870	+	0.956152i	$0.594610\pi$
$182$	−1.23812	−0.0917757
$183$	−7.72201	−0.570827
$184$	−0.900359	−0.0663753
$185$	4.42953	0.325666
$186$	0.627174	0.0459866
$187$	0.413709	0.0302534
$188$	9.44526	0.688866
$189$	−22.2706	−1.61994
$190$	−13.0734	−0.948441
$191$	20.7179	1.49910	0.749548	−	0.661949i	$-0.230271\pi$
$191$	20.7179	1.49910	0.749548	+	0.661949i	$0.230271\pi$
$192$	−1.49688	−0.108028
$193$	26.0225	1.87314	0.936569	−	0.350483i	$-0.113983\pi$
$193$	26.0225	1.87314	0.936569	+	0.350483i	$0.113983\pi$
$194$	17.4413	1.25221
$195$	1.18620	0.0849454
$196$	8.66254	0.618753
$197$	12.2324	0.871519	0.435760	−	0.900063i	$-0.356480\pi$
$197$	12.2324	0.871519	0.435760	+	0.900063i	$0.356480\pi$
$198$	−0.935602	−0.0664904
$199$	−15.9164	−1.12828	−0.564140	−	0.825679i	$-0.690792\pi$
$199$	−15.9164	−1.12828	−0.564140	+	0.825679i	$0.690792\pi$
$200$	−1.41620	−0.100141
$201$	−12.3584	−0.871695
$202$	0.853923	0.0600818
$203$	38.2825	2.68691
$204$	0.502619	0.0351903
$205$	10.4860	0.732377
$206$	−10.4037	−0.724858
$207$	−0.683699	−0.0475204
$208$	−0.312847	−0.0216920
$209$	−6.35902	−0.439863
$210$	−15.0057	−1.03549
$211$	6.41358	0.441529	0.220764	−	0.975327i	$-0.429145\pi$
$211$	6.41358	0.441529	0.220764	+	0.975327i	$0.429145\pi$
$212$	−2.11431	−0.145212
$213$	19.3804	1.32793
$214$	1.55379	0.106215
$215$	6.28684	0.428759
$216$	−5.62730	−0.382889
$217$	−1.65819	−0.112565
$218$	5.47519	0.370827
$219$	−9.26632	−0.626160
$220$	−3.12091	−0.210412
$221$	0.105047	0.00706625
$222$	2.61761	0.175682
$223$	−2.57141	−0.172195	−0.0860973	−	0.996287i	$-0.527440\pi$
$223$	−2.57141	−0.172195	−0.0860973	+	0.996287i	$0.527440\pi$
$224$	3.95759	0.264428
$225$	−1.07541	−0.0716942
$226$	−5.79045	−0.385175
$227$	−0.604951	−0.0401520	−0.0200760	−	0.999798i	$-0.506391\pi$
$227$	−0.604951	−0.0401520	−0.0200760	+	0.999798i	$0.506391\pi$
$228$	−7.72563	−0.511642
$229$	5.07471	0.335346	0.167673	−	0.985843i	$-0.446375\pi$
$229$	5.07471	0.335346	0.167673	+	0.985843i	$0.446375\pi$
$230$	−2.28063	−0.150380
$231$	−7.29893	−0.480234
$232$	9.67318	0.635075
$233$	5.19150	0.340107	0.170053	−	0.985435i	$-0.445606\pi$
$233$	5.19150	0.340107	0.170053	+	0.985435i	$0.445606\pi$
$234$	−0.237564	−0.0155301
$235$	23.9251	1.56070
$236$	14.6887	0.956153
$237$	1.95816	0.127196
$238$	−1.32887	−0.0861381
$239$	5.37190	0.347480	0.173740	−	0.984792i	$-0.444415\pi$
$239$	5.37190	0.347480	0.173740	+	0.984792i	$0.444415\pi$
$240$	−3.79162	−0.244748
$241$	−11.8123	−0.760898	−0.380449	−	0.924802i	$-0.624231\pi$
$241$	−11.8123	−0.760898	−0.380449	+	0.924802i	$0.624231\pi$
$242$	9.48196	0.609523
$243$	−7.68317	−0.492876
$244$	5.15875	0.330255
$245$	21.9424	1.40185
$246$	6.19667	0.395085
$247$	−1.61466	−0.102738
$248$	−0.418989	−0.0266058
$249$	8.85005	0.560849
$250$	9.07784	0.574133
$251$	−29.9094	−1.88787	−0.943933	−	0.330137i	$-0.892905\pi$
$251$	−29.9094	−1.88787	−0.943933	+	0.330137i	$0.892905\pi$
$252$	3.00525	0.189313
$253$	−1.10932	−0.0697425
$254$	−3.29947	−0.207027
$255$	1.27314	0.0797274
$256$	1.00000	0.0625000
$257$	5.10265	0.318294	0.159147	−	0.987255i	$-0.449126\pi$
$257$	5.10265	0.318294	0.159147	+	0.987255i	$0.449126\pi$
$258$	3.71517	0.231297
$259$	−6.92069	−0.430031
$260$	−0.792449	−0.0491456
$261$	7.34545	0.454672
$262$	−2.79046	−0.172395
$263$	15.7555	0.971524	0.485762	−	0.874091i	$-0.338542\pi$
$263$	15.7555	0.971524	0.485762	+	0.874091i	$0.338542\pi$
$264$	−1.84428	−0.113508
$265$	−5.35560	−0.328992
$266$	20.4258	1.25239
$267$	26.9089	1.64680
$268$	8.25613	0.504324
$269$	−29.8313	−1.81885	−0.909424	−	0.415870i	$-0.863477\pi$
$269$	−29.8313	−1.81885	−0.909424	+	0.415870i	$0.863477\pi$
$270$	−14.2541	−0.867476
$271$	29.8659	1.81423	0.907113	−	0.420886i	$-0.138281\pi$
$271$	29.8659	1.81423	0.907113	+	0.420886i	$0.138281\pi$
$272$	−0.335778	−0.0203596
$273$	−1.85331	−0.112168
$274$	−12.6837	−0.766249
$275$	−1.74489	−0.105221
$276$	−1.34773	−0.0811236
$277$	30.7889	1.84993	0.924964	−	0.380054i	$-0.124095\pi$
$277$	30.7889	1.84993	0.924964	+	0.380054i	$0.124095\pi$
$278$	3.72706	0.223534
$279$	−0.318164	−0.0190480
$280$	10.0247	0.599089
$281$	−15.9763	−0.953066	−0.476533	−	0.879157i	$-0.658107\pi$
$281$	−15.9763	−0.953066	−0.476533	+	0.879157i	$0.658107\pi$
$282$	14.1384	0.841928
$283$	−14.1708	−0.842368	−0.421184	−	0.906975i	$-0.638385\pi$
$283$	−14.1708	−0.842368	−0.421184	+	0.906975i	$0.638385\pi$
$284$	−12.9473	−0.768278
$285$	−19.5692	−1.15918
$286$	−0.385456	−0.0227925
$287$	−16.3834	−0.967080
$288$	0.759363	0.0447459
$289$	−16.8873	−0.993368
$290$	24.5024	1.43883
$291$	26.1075	1.53045
$292$	6.19044	0.362268
$293$	−15.0085	−0.876808	−0.438404	−	0.898778i	$-0.644456\pi$
$293$	−15.0085	−0.876808	−0.438404	+	0.898778i	$0.644456\pi$
$294$	12.9667	0.756236
$295$	37.2068	2.16626
$296$	−1.74871	−0.101642
$297$	−6.93333	−0.402313
$298$	7.73667	0.448173
$299$	−0.281675	−0.0162897
$300$	−2.11988	−0.122391
$301$	−9.82255	−0.566162
$302$	13.0379	0.750250
$303$	1.27822	0.0734316
$304$	5.16117	0.296013
$305$	13.0672	0.748228
$306$	−0.254978	−0.0145761
$307$	−9.93173	−0.566834	−0.283417	−	0.958997i	$-0.591468\pi$
$307$	−9.93173	−0.566834	−0.283417	+	0.958997i	$0.591468\pi$
$308$	4.87611	0.277842
$309$	−15.5730	−0.885917
$310$	−1.06131	−0.0602783
$311$	−18.2556	−1.03518	−0.517589	−	0.855630i	$-0.673170\pi$
$311$	−18.2556	−1.03518	−0.517589	+	0.855630i	$0.673170\pi$
$312$	−0.468293	−0.0265119
$313$	−26.9328	−1.52233	−0.761166	−	0.648558i	$-0.775373\pi$
$313$	−26.9328	−1.52233	−0.761166	+	0.648558i	$0.775373\pi$
$314$	12.5971	0.710895
$315$	7.61236	0.428908
$316$	−1.30817	−0.0735902
$317$	10.6629	0.598887	0.299444	−	0.954114i	$-0.403199\pi$
$317$	10.6629	0.598887	0.299444	+	0.954114i	$0.403199\pi$
$318$	−3.16486	−0.177477
$319$	11.9182	0.667292
$320$	2.53302	0.141600
$321$	2.32583	0.129815
$322$	3.56325	0.198572
$323$	−1.73301	−0.0964272
$324$	−6.14528	−0.341404
$325$	−0.443056	−0.0245763
$326$	21.6672	1.20004
$327$	8.19568	0.453222
$328$	−4.13973	−0.228579
$329$	−37.3805	−2.06085
$330$	−4.67161	−0.257164
$331$	−10.1378	−0.557222	−0.278611	−	0.960404i	$-0.589874\pi$
$331$	−10.1378	−0.557222	−0.278611	+	0.960404i	$0.589874\pi$
$332$	−5.91234	−0.324482
$333$	−1.32791	−0.0727689
$334$	5.15889	0.282282
$335$	20.9130	1.14260
$336$	5.92402	0.323182
$337$	27.0079	1.47121	0.735606	−	0.677410i	$-0.236897\pi$
$337$	27.0079	1.47121	0.735606	+	0.677410i	$0.236897\pi$
$338$	12.9021	0.701783
$339$	−8.66759	−0.470759
$340$	−0.850535	−0.0461267
$341$	−0.516232	−0.0279555
$342$	3.91920	0.211926
$343$	−6.57965	−0.355268
$344$	−2.48195	−0.133818
$345$	−3.41382	−0.183794
$346$	−13.8006	−0.741922
$347$	−28.2681	−1.51751	−0.758756	−	0.651375i	$-0.774192\pi$
$347$	−28.2681	−1.51751	−0.758756	+	0.651375i	$0.774192\pi$
$348$	14.4796	0.776185
$349$	9.32527	0.499170	0.249585	−	0.968353i	$-0.419706\pi$
$349$	9.32527	0.499170	0.249585	+	0.968353i	$0.419706\pi$
$350$	5.60476	0.299587
$351$	−1.76048	−0.0939677
$352$	1.23209	0.0656706
$353$	−29.9001	−1.59142	−0.795710	−	0.605678i	$-0.792902\pi$
$353$	−29.9001	−1.59142	−0.795710	+	0.605678i	$0.792902\pi$
$354$	21.9872	1.16860
$355$	−32.7957	−1.74061
$356$	−17.9767	−0.952762
$357$	−1.98916	−0.105278
$358$	−5.11840	−0.270516
$359$	−2.87062	−0.151506	−0.0757528	−	0.997127i	$-0.524136\pi$
$359$	−2.87062	−0.151506	−0.0757528	+	0.997127i	$0.524136\pi$
$360$	1.92348	0.101376
$361$	7.63767	0.401983
$362$	7.88031	0.414180
$363$	14.1933	0.744956
$364$	1.23812	0.0648952
$365$	15.6805	0.820757
$366$	7.72201	0.403636
$367$	24.5919	1.28369	0.641844	−	0.766835i	$-0.278170\pi$
$367$	24.5919	1.28369	0.641844	+	0.766835i	$0.278170\pi$
$368$	0.900359	0.0469345
$369$	−3.14356	−0.163647
$370$	−4.42953	−0.230280
$371$	8.36759	0.434423
$372$	−0.627174	−0.0325175
$373$	−35.7291	−1.84998	−0.924992	−	0.379987i	$-0.875929\pi$
$373$	−35.7291	−1.84998	−0.924992	+	0.379987i	$0.875929\pi$
$374$	−0.413709	−0.0213924
$375$	13.5884	0.701702
$376$	−9.44526	−0.487102
$377$	3.02623	0.155859
$378$	22.2706	1.14547
$379$	22.8695	1.17473	0.587363	−	0.809324i	$-0.300166\pi$
$379$	22.8695	1.17473	0.587363	+	0.809324i	$0.300166\pi$
$380$	13.0734	0.670649
$381$	−4.93890	−0.253027
$382$	−20.7179	−1.06002
$383$	−30.7530	−1.57140	−0.785702	−	0.618605i	$-0.787698\pi$
$383$	−30.7530	−1.57140	−0.785702	+	0.618605i	$0.787698\pi$
$384$	1.49688	0.0763871
$385$	12.3513	0.629480
$386$	−26.0225	−1.32451
$387$	−1.88470	−0.0958047
$388$	−17.4413	−0.885448
$389$	10.0731	0.510724	0.255362	−	0.966846i	$-0.417805\pi$
$389$	10.0731	0.510724	0.255362	+	0.966846i	$0.417805\pi$
$390$	−1.18620	−0.0600655
$391$	−0.302321	−0.0152890
$392$	−8.66254	−0.437524
$393$	−4.17698	−0.210701
$394$	−12.2324	−0.616257
$395$	−3.31362	−0.166726
$396$	0.935602	0.0470158
$397$	−30.3411	−1.52278	−0.761388	−	0.648296i	$-0.775482\pi$
$397$	−30.3411	−1.52278	−0.761388	+	0.648296i	$0.775482\pi$
$398$	15.9164	0.797815
$399$	30.5749	1.53066
$400$	1.41620	0.0708102
$401$	7.93710	0.396360	0.198180	−	0.980166i	$-0.436497\pi$
$401$	7.93710	0.396360	0.198180	+	0.980166i	$0.436497\pi$
$402$	12.3584	0.616381
$403$	−0.131079	−0.00652953
$404$	−0.853923	−0.0424842
$405$	−15.5661	−0.773488
$406$	−38.2825	−1.89993
$407$	−2.15457	−0.106798
$408$	−0.502619	−0.0248833
$409$	4.55882	0.225419	0.112710	−	0.993628i	$-0.464047\pi$
$409$	4.55882	0.225419	0.112710	+	0.993628i	$0.464047\pi$
$410$	−10.4860	−0.517869
$411$	−18.9859	−0.936505
$412$	10.4037	0.512552
$413$	−58.1319	−2.86048
$414$	0.683699	0.0336020
$415$	−14.9761	−0.735148
$416$	0.312847	0.0153386
$417$	5.57895	0.273202
$418$	6.35902	0.311030
$419$	38.0923	1.86093	0.930466	−	0.366377i	$-0.119402\pi$
$419$	38.0923	1.86093	0.930466	+	0.366377i	$0.119402\pi$
$420$	15.0057	0.732203
$421$	−19.5499	−0.952804	−0.476402	−	0.879228i	$-0.658059\pi$
$421$	−19.5499	−0.952804	−0.476402	+	0.879228i	$0.658059\pi$
$422$	−6.41358	−0.312208
$423$	−7.17238	−0.348733
$424$	2.11431	0.102680
$425$	−0.475531	−0.0230666
$426$	−19.3804	−0.938985
$427$	−20.4162	−0.988011
$428$	−1.55379	−0.0751053
$429$	−0.576979	−0.0278568
$430$	−6.28684	−0.303178
$431$	−2.97261	−0.143186	−0.0715928	−	0.997434i	$-0.522808\pi$
$431$	−2.97261	−0.143186	−0.0715928	+	0.997434i	$0.522808\pi$
$432$	5.62730	0.270744
$433$	−3.14718	−0.151244	−0.0756218	−	0.997137i	$-0.524094\pi$
$433$	−3.14718	−0.151244	−0.0756218	+	0.997137i	$0.524094\pi$
$434$	1.65819	0.0795955
$435$	36.6770	1.75853
$436$	−5.47519	−0.262214
$437$	4.64691	0.222292
$438$	9.26632	0.442762
$439$	−16.2138	−0.773841	−0.386921	−	0.922113i	$-0.626461\pi$
$439$	−16.2138	−0.773841	−0.386921	+	0.922113i	$0.626461\pi$
$440$	3.12091	0.148784
$441$	−6.57801	−0.313238
$442$	−0.105047	−0.00499659
$443$	−37.9174	−1.80151	−0.900754	−	0.434329i	$-0.856986\pi$
$443$	−37.9174	−1.80151	−0.900754	+	0.434329i	$0.856986\pi$
$444$	−2.61761	−0.124226
$445$	−45.5353	−2.15858
$446$	2.57141	0.121760
$447$	11.5808	0.547755
$448$	−3.95759	−0.186979
$449$	−17.9666	−0.847896	−0.423948	−	0.905687i	$-0.639356\pi$
$449$	−17.9666	−0.847896	−0.423948	+	0.905687i	$0.639356\pi$
$450$	1.07541	0.0506955
$451$	−5.10052	−0.240174
$452$	5.79045	0.272360
$453$	19.5162	0.916951
$454$	0.604951	0.0283918
$455$	3.13619	0.147027
$456$	7.72563	0.361786
$457$	−16.6098	−0.776975	−0.388488	−	0.921454i	$-0.627002\pi$
$457$	−16.6098	−0.776975	−0.388488	+	0.921454i	$0.627002\pi$
$458$	−5.07471	−0.237125
$459$	−1.88953	−0.0881955
$460$	2.28063	0.106335
$461$	−9.03350	−0.420732	−0.210366	−	0.977623i	$-0.567466\pi$
$461$	−9.03350	−0.420732	−0.210366	+	0.977623i	$0.567466\pi$
$462$	7.29893	0.339577
$463$	37.0149	1.72023	0.860114	−	0.510103i	$-0.170393\pi$
$463$	37.0149	1.72023	0.860114	+	0.510103i	$0.170393\pi$
$464$	−9.67318	−0.449066
$465$	−1.58865	−0.0736717
$466$	−5.19150	−0.240492
$467$	−29.7782	−1.37797	−0.688987	−	0.724774i	$-0.741944\pi$
$467$	−29.7782	−1.37797	−0.688987	+	0.724774i	$0.741944\pi$
$468$	0.237564	0.0109814
$469$	−32.6744	−1.50876
$470$	−23.9251	−1.10358
$471$	18.8563	0.868852
$472$	−14.6887	−0.676102
$473$	−3.05798	−0.140606
$474$	−1.95816	−0.0899415
$475$	7.30927	0.335372
$476$	1.32887	0.0609089
$477$	1.60553	0.0735121
$478$	−5.37190	−0.245705
$479$	4.15376	0.189790	0.0948951	−	0.995487i	$-0.469748\pi$
$479$	4.15376	0.189790	0.0948951	+	0.995487i	$0.469748\pi$
$480$	3.79162	0.173063
$481$	−0.547080	−0.0249447
$482$	11.8123	0.538036
$483$	5.33375	0.242694
$484$	−9.48196	−0.430998
$485$	−44.1792	−2.00607
$486$	7.68317	0.348516
$487$	15.5937	0.706617	0.353308	−	0.935507i	$-0.385057\pi$
$487$	15.5937	0.706617	0.353308	+	0.935507i	$0.385057\pi$
$488$	−5.15875	−0.233526
$489$	32.4331	1.46668
$490$	−21.9424	−0.991257
$491$	−32.8051	−1.48047	−0.740236	−	0.672347i	$-0.765286\pi$
$491$	−32.8051	−1.48047	−0.740236	+	0.672347i	$0.765286\pi$
$492$	−6.19667	−0.279367
$493$	3.24805	0.146285
$494$	1.61466	0.0726469
$495$	2.36990	0.106519
$496$	0.418989	0.0188132
$497$	51.2399	2.29843
$498$	−8.85005	−0.396580
$499$	16.1497	0.722961	0.361481	−	0.932380i	$-0.382271\pi$
$499$	16.1497	0.722961	0.361481	+	0.932380i	$0.382271\pi$
$500$	−9.07784	−0.405973
$501$	7.72222	0.345003
$502$	29.9094	1.33492
$503$	26.5744	1.18489	0.592447	−	0.805610i	$-0.298162\pi$
$503$	26.5744	1.18489	0.592447	+	0.805610i	$0.298162\pi$
$504$	−3.00525	−0.133864
$505$	−2.16301	−0.0962525
$506$	1.10932	0.0493154
$507$	19.3129	0.857715
$508$	3.29947	0.146390
$509$	4.86027	0.215428	0.107714	−	0.994182i	$-0.465647\pi$
$509$	4.86027	0.215428	0.107714	+	0.994182i	$0.465647\pi$
$510$	−1.27314	−0.0563758
$511$	−24.4992	−1.08378
$512$	−1.00000	−0.0441942
$513$	29.0434	1.28230
$514$	−5.10265	−0.225068
$515$	26.3527	1.16124
$516$	−3.71517	−0.163551
$517$	−11.6374	−0.511812
$518$	6.92069	0.304078
$519$	−20.6577	−0.906773
$520$	0.792449	0.0347512
$521$	−23.6235	−1.03496	−0.517482	−	0.855694i	$-0.673130\pi$
$521$	−23.6235	−1.03496	−0.517482	+	0.855694i	$0.673130\pi$
$522$	−7.34545	−0.321502
$523$	−24.7407	−1.08184	−0.540918	−	0.841075i	$-0.681923\pi$
$523$	−24.7407	−1.08184	−0.540918	+	0.841075i	$0.681923\pi$
$524$	2.79046	0.121902
$525$	8.38963	0.366154
$526$	−15.7555	−0.686972
$527$	−0.140687	−0.00612844
$528$	1.84428	0.0802622
$529$	−22.1894	−0.964755
$530$	5.35560	0.232632
$531$	−11.1540	−0.484044
$532$	−20.4258	−0.885571
$533$	−1.29510	−0.0560972
$534$	−26.9089	−1.16446
$535$	−3.93578	−0.170159
$536$	−8.25613	−0.356611
$537$	−7.66160	−0.330623
$538$	29.8313	1.28612
$539$	−10.6730	−0.459719
$540$	14.2541	0.613398
$541$	32.5688	1.40024	0.700120	−	0.714025i	$-0.253130\pi$
$541$	32.5688	1.40024	0.700120	+	0.714025i	$0.253130\pi$
$542$	−29.8659	−1.28285
$543$	11.7959	0.506209
$544$	0.335778	0.0143964
$545$	−13.8688	−0.594073
$546$	1.85331	0.0793145
$547$	−20.2391	−0.865361	−0.432680	−	0.901547i	$-0.642432\pi$
$547$	−20.2391	−0.865361	−0.432680	+	0.901547i	$0.642432\pi$
$548$	12.6837	0.541820
$549$	−3.91736	−0.167189
$550$	1.74489	0.0744024
$551$	−49.9249	−2.12687
$552$	1.34773	0.0573630
$553$	5.17719	0.220157
$554$	−30.7889	−1.30810
$555$	−6.63046	−0.281447
$556$	−3.72706	−0.158063
$557$	−9.31719	−0.394782	−0.197391	−	0.980325i	$-0.563247\pi$
$557$	−9.31719	−0.394782	−0.197391	+	0.980325i	$0.563247\pi$
$558$	0.318164	0.0134690
$559$	−0.776471	−0.0328412
$560$	−10.0247	−0.423620
$561$	−0.619271	−0.0261456
$562$	15.9763	0.673919
$563$	12.9665	0.546473	0.273237	−	0.961947i	$-0.411906\pi$
$563$	12.9665	0.546473	0.273237	+	0.961947i	$0.411906\pi$
$564$	−14.1384	−0.595333
$565$	14.6674	0.617060
$566$	14.1708	0.595644
$567$	24.3205	1.02137
$568$	12.9473	0.543255
$569$	−10.0246	−0.420255	−0.210127	−	0.977674i	$-0.567388\pi$
$569$	−10.0246	−0.420255	−0.210127	+	0.977674i	$0.567388\pi$
$570$	19.5692	0.819664
$571$	27.2540	1.14055	0.570273	−	0.821455i	$-0.306837\pi$
$571$	27.2540	1.14055	0.570273	+	0.821455i	$0.306837\pi$
$572$	0.385456	0.0161167
$573$	−31.0122	−1.29555
$574$	16.3834	0.683829
$575$	1.27509	0.0531750
$576$	−0.759363	−0.0316401
$577$	4.03621	0.168030	0.0840148	−	0.996465i	$-0.473226\pi$
$577$	4.03621	0.168030	0.0840148	+	0.996465i	$0.473226\pi$
$578$	16.8873	0.702417
$579$	−38.9524	−1.61881
$580$	−24.5024	−1.01741
$581$	23.3987	0.970740
$582$	−26.1075	−1.08219
$583$	2.60502	0.107889
$584$	−6.19044	−0.256162
$585$	0.601756	0.0248796
$586$	15.0085	0.619997
$587$	12.7609	0.526697	0.263349	−	0.964701i	$-0.415173\pi$
$587$	12.7609	0.526697	0.263349	+	0.964701i	$0.415173\pi$
$588$	−12.9667	−0.534740
$589$	2.16247	0.0891031
$590$	−37.2068	−1.53178
$591$	−18.3103	−0.753186
$592$	1.74871	0.0718717
$593$	33.5870	1.37925	0.689627	−	0.724165i	$-0.257775\pi$
$593$	33.5870	1.37925	0.689627	+	0.724165i	$0.257775\pi$
$594$	6.93333	0.284478
$595$	3.36607	0.137995
$596$	−7.73667	−0.316906
$597$	23.8248	0.975085
$598$	0.281675	0.0115185
$599$	2.28225	0.0932502	0.0466251	−	0.998912i	$-0.485153\pi$
$599$	2.28225	0.0932502	0.0466251	+	0.998912i	$0.485153\pi$
$600$	2.11988	0.0865439
$601$	−20.4131	−0.832667	−0.416334	−	0.909212i	$-0.636685\pi$
$601$	−20.4131	−0.832667	−0.416334	+	0.909212i	$0.636685\pi$
$602$	9.82255	0.400337
$603$	−6.26940	−0.255310
$604$	−13.0379	−0.530507
$605$	−24.0180	−0.976471
$606$	−1.27822	−0.0519240
$607$	8.95266	0.363377	0.181689	−	0.983356i	$-0.441844\pi$
$607$	8.95266	0.363377	0.181689	+	0.983356i	$0.441844\pi$
$608$	−5.16117	−0.209313
$609$	−57.3042	−2.32208
$610$	−13.0672	−0.529077
$611$	−2.95492	−0.119543
$612$	0.254978	0.0103069
$613$	20.9069	0.844424	0.422212	−	0.906497i	$-0.361254\pi$
$613$	20.9069	0.844424	0.422212	+	0.906497i	$0.361254\pi$
$614$	9.93173	0.400812
$615$	−15.6963	−0.632936
$616$	−4.87611	−0.196464
$617$	−40.7307	−1.63976	−0.819879	−	0.572537i	$-0.805959\pi$
$617$	−40.7307	−1.63976	−0.819879	+	0.572537i	$0.805959\pi$
$618$	15.5730	0.626438
$619$	−6.67535	−0.268305	−0.134153	−	0.990961i	$-0.542831\pi$
$619$	−6.67535	−0.268305	−0.134153	+	0.990961i	$0.542831\pi$
$620$	1.06131	0.0426232
$621$	5.06659	0.203315
$622$	18.2556	0.731981
$623$	71.1444	2.85034
$624$	0.468293	0.0187467
$625$	−30.0754	−1.20302
$626$	26.9328	1.07645
$627$	9.51867	0.380139
$628$	−12.5971	−0.502679
$629$	−0.587180	−0.0234124
$630$	−7.61236	−0.303284
$631$	−35.8132	−1.42570	−0.712850	−	0.701317i	$-0.752596\pi$
$631$	−35.8132	−1.42570	−0.712850	+	0.701317i	$0.752596\pi$
$632$	1.30817	0.0520361
$633$	−9.60033	−0.381579
$634$	−10.6629	−0.423477
$635$	8.35763	0.331663
$636$	3.16486	0.125495
$637$	−2.71005	−0.107376
$638$	−11.9182	−0.471847
$639$	9.83166	0.388934
$640$	−2.53302	−0.100127
$641$	−29.9266	−1.18203	−0.591016	−	0.806660i	$-0.701273\pi$
$641$	−29.9266	−1.18203	−0.591016	+	0.806660i	$0.701273\pi$
$642$	−2.32583	−0.0917932
$643$	21.0345	0.829518	0.414759	−	0.909931i	$-0.363866\pi$
$643$	21.0345	0.829518	0.414759	+	0.909931i	$0.363866\pi$
$644$	−3.56325	−0.140412
$645$	−9.41062	−0.370543
$646$	1.73301	0.0681844
$647$	−0.135921	−0.00534362	−0.00267181	−	0.999996i	$-0.500850\pi$
$647$	−0.135921	−0.00534362	−0.00267181	+	0.999996i	$0.500850\pi$
$648$	6.14528	0.241409
$649$	−18.0978	−0.710400
$650$	0.443056	0.0173781
$651$	2.48210	0.0972812
$652$	−21.6672	−0.848553
$653$	0.485308	0.0189916	0.00949579	−	0.999955i	$-0.496977\pi$
$653$	0.485308	0.0189916	0.00949579	+	0.999955i	$0.496977\pi$
$654$	−8.19568	−0.320476
$655$	7.06831	0.276182
$656$	4.13973	0.161629
$657$	−4.70079	−0.183395
$658$	37.3805	1.45724
$659$	0.571956	0.0222802	0.0111401	−	0.999938i	$-0.496454\pi$
$659$	0.571956	0.0222802	0.0111401	+	0.999938i	$0.496454\pi$
$660$	4.67161	0.181842
$661$	−3.20363	−0.124607	−0.0623033	−	0.998057i	$-0.519845\pi$
$661$	−3.20363	−0.124607	−0.0623033	+	0.998057i	$0.519845\pi$
$662$	10.1378	0.394016
$663$	−0.157243	−0.00610681
$664$	5.91234	0.229443
$665$	−51.7390	−2.00635
$666$	1.32791	0.0514554
$667$	−8.70933	−0.337227
$668$	−5.15889	−0.199604
$669$	3.84909	0.148814
$670$	−20.9130	−0.807939
$671$	−6.35604	−0.245372
$672$	−5.92402	−0.228524
$673$	−22.3583	−0.861848	−0.430924	−	0.902388i	$-0.641812\pi$
$673$	−22.3583	−0.861848	−0.430924	+	0.902388i	$0.641812\pi$
$674$	−27.0079	−1.04030
$675$	7.96941	0.306743
$676$	−12.9021	−0.496236
$677$	18.4341	0.708479	0.354240	−	0.935155i	$-0.384740\pi$
$677$	18.4341	0.708479	0.354240	+	0.935155i	$0.384740\pi$
$678$	8.66759	0.332877
$679$	69.0256	2.64896
$680$	0.850535	0.0326165
$681$	0.905537	0.0347002
$682$	0.516232	0.0197675
$683$	8.86753	0.339307	0.169653	−	0.985504i	$-0.445735\pi$
$683$	8.86753	0.339307	0.169653	+	0.985504i	$0.445735\pi$
$684$	−3.91920	−0.149854
$685$	32.1281	1.22755
$686$	6.57965	0.251212
$687$	−7.59621	−0.289813
$688$	2.48195	0.0946235
$689$	0.661457	0.0251995
$690$	3.41382	0.129962
$691$	−50.1526	−1.90789	−0.953947	−	0.299976i	$-0.903021\pi$
$691$	−50.1526	−1.90789	−0.953947	+	0.299976i	$0.903021\pi$
$692$	13.8006	0.524618
$693$	−3.70273	−0.140655
$694$	28.2681	1.07304
$695$	−9.44074	−0.358107
$696$	−14.4796	−0.548846
$697$	−1.39003	−0.0526513
$698$	−9.32527	−0.352967
$699$	−7.77103	−0.293927
$700$	−5.60476	−0.211840
$701$	2.47193	0.0933634	0.0466817	−	0.998910i	$-0.485135\pi$
$701$	2.47193	0.0933634	0.0466817	+	0.998910i	$0.485135\pi$
$702$	1.76048	0.0664452
$703$	9.02541	0.340400
$704$	−1.23209	−0.0464361
$705$	−35.8128	−1.34879
$706$	29.9001	1.12530
$707$	3.37948	0.127098
$708$	−21.9872	−0.826328
$709$	15.1743	0.569884	0.284942	−	0.958545i	$-0.408026\pi$
$709$	15.1743	0.569884	0.284942	+	0.958545i	$0.408026\pi$
$710$	32.7957	1.23080
$711$	0.993373	0.0372544
$712$	17.9767	0.673705
$713$	0.377240	0.0141278
$714$	1.98916	0.0744424
$715$	0.976368	0.0365141
$716$	5.11840	0.191283
$717$	−8.04107	−0.300299
$718$	2.87062	0.107131
$719$	−39.6353	−1.47815	−0.739074	−	0.673625i	$-0.764736\pi$
$719$	−39.6353	−1.47815	−0.739074	+	0.673625i	$0.764736\pi$
$720$	−1.92348	−0.0716840
$721$	−41.1735	−1.53338
$722$	−7.63767	−0.284245
$723$	17.6816	0.657584
$724$	−7.88031	−0.292870
$725$	−13.6992	−0.508776
$726$	−14.1933	−0.526763
$727$	−1.39483	−0.0517315	−0.0258658	−	0.999665i	$-0.508234\pi$
$727$	−1.39483	−0.0517315	−0.0258658	+	0.999665i	$0.508234\pi$
$728$	−1.23812	−0.0458878
$729$	29.9366	1.10876
$730$	−15.6805	−0.580363
$731$	−0.833386	−0.0308239
$732$	−7.72201	−0.285414
$733$	−16.0583	−0.593126	−0.296563	−	0.955013i	$-0.595840\pi$
$733$	−16.0583	−0.593126	−0.296563	+	0.955013i	$0.595840\pi$
$734$	−24.5919	−0.907704
$735$	−32.8451	−1.21151
$736$	−0.900359	−0.0331877
$737$	−10.1723	−0.374701
$738$	3.14356	0.115716
$739$	3.76951	0.138664	0.0693318	−	0.997594i	$-0.477913\pi$
$739$	3.76951	0.138664	0.0693318	+	0.997594i	$0.477913\pi$
$740$	4.42953	0.162833
$741$	2.41694	0.0887886
$742$	−8.36759	−0.307184
$743$	5.92964	0.217537	0.108769	−	0.994067i	$-0.465309\pi$
$743$	5.92964	0.217537	0.108769	+	0.994067i	$0.465309\pi$
$744$	0.627174	0.0229933
$745$	−19.5972	−0.717984
$746$	35.7291	1.30814
$747$	4.48961	0.164266
$748$	0.413709	0.0151267
$749$	6.14927	0.224689
$750$	−13.5884	−0.496178
$751$	27.3979	0.999763	0.499882	−	0.866094i	$-0.333377\pi$
$751$	27.3979	0.999763	0.499882	+	0.866094i	$0.333377\pi$
$752$	9.44526	0.344433
$753$	44.7707	1.63154
$754$	−3.02623	−0.110209
$755$	−33.0254	−1.20192
$756$	−22.2706	−0.809972
$757$	31.1448	1.13198	0.565988	−	0.824414i	$-0.308495\pi$
$757$	31.1448	1.13198	0.565988	+	0.824414i	$0.308495\pi$
$758$	−22.8695	−0.830656
$759$	1.66052	0.0602730
$760$	−13.0734	−0.474221
$761$	39.7274	1.44012	0.720058	−	0.693914i	$-0.244115\pi$
$761$	39.7274	1.44012	0.720058	+	0.693914i	$0.244115\pi$
$762$	4.93890	0.178917
$763$	21.6686	0.784455
$764$	20.7179	0.749548
$765$	0.645864	0.0233513
$766$	30.7530	1.11115
$767$	−4.59532	−0.165927
$768$	−1.49688	−0.0540139
$769$	−6.23002	−0.224660	−0.112330	−	0.993671i	$-0.535831\pi$
$769$	−6.23002	−0.224660	−0.112330	+	0.993671i	$0.535831\pi$
$770$	−12.3513	−0.445110
$771$	−7.63803	−0.275077
$772$	26.0225	0.936569
$773$	−20.3023	−0.730225	−0.365112	−	0.930963i	$-0.618969\pi$
$773$	−20.3023	−0.730225	−0.365112	+	0.930963i	$0.618969\pi$
$774$	1.88470	0.0677442
$775$	0.593374	0.0213146
$776$	17.4413	0.626106
$777$	10.3594	0.371642
$778$	−10.0731	−0.361136
$779$	21.3659	0.765512
$780$	1.18620	0.0424727
$781$	15.9522	0.570813
$782$	0.302321	0.0108110
$783$	−54.4339	−1.94531
$784$	8.66254	0.309376
$785$	−31.9087	−1.13887
$786$	4.17698	0.148988
$787$	−35.4381	−1.26323	−0.631616	−	0.775281i	$-0.717608\pi$
$787$	−35.4381	−1.26323	−0.631616	+	0.775281i	$0.717608\pi$
$788$	12.2324	0.435760
$789$	−23.5840	−0.839612
$790$	3.31362	0.117893
$791$	−22.9163	−0.814808
$792$	−0.935602	−0.0332452
$793$	−1.61390	−0.0573113
$794$	30.3411	1.07677
$795$	8.01667	0.284322
$796$	−15.9164	−0.564140
$797$	4.86049	0.172167	0.0860837	−	0.996288i	$-0.472565\pi$
$797$	4.86049	0.172167	0.0860837	+	0.996288i	$0.472565\pi$
$798$	−30.5749	−1.08234
$799$	−3.17152	−0.112200
$800$	−1.41620	−0.0500704
$801$	13.6508	0.482328
$802$	−7.93710	−0.280269
$803$	−7.62718	−0.269157
$804$	−12.3584	−0.435847
$805$	−9.02580	−0.318118
$806$	0.131079	0.00461708
$807$	44.6538	1.57189
$808$	0.853923	0.0300409
$809$	12.6045	0.443150	0.221575	−	0.975143i	$-0.428880\pi$
$809$	12.6045	0.443150	0.221575	+	0.975143i	$0.428880\pi$
$810$	15.5661	0.546938
$811$	−8.37261	−0.294002	−0.147001	−	0.989136i	$-0.546962\pi$
$811$	−8.37261	−0.294002	−0.147001	+	0.989136i	$0.546962\pi$
$812$	38.2825	1.34345
$813$	−44.7056	−1.56789
$814$	2.15457	0.0755177
$815$	−54.8835	−1.92249
$816$	0.502619	0.0175952
$817$	12.8098	0.448157
$818$	−4.55882	−0.159396
$819$	−0.940183	−0.0328527
$820$	10.4860	0.366188
$821$	−51.1659	−1.78570	−0.892852	−	0.450351i	$-0.851299\pi$
$821$	−51.1659	−1.78570	−0.892852	+	0.450351i	$0.851299\pi$
$822$	18.9859	0.662209
$823$	−28.7252	−1.00130	−0.500648	−	0.865651i	$-0.666905\pi$
$823$	−28.7252	−1.00130	−0.500648	+	0.865651i	$0.666905\pi$
$824$	−10.4037	−0.362429
$825$	2.61188	0.0909341
$826$	58.1319	2.02267
$827$	−25.5986	−0.890151	−0.445076	−	0.895493i	$-0.646823\pi$
$827$	−25.5986	−0.890151	−0.445076	+	0.895493i	$0.646823\pi$
$828$	−0.683699	−0.0237602
$829$	−15.9067	−0.552463	−0.276232	−	0.961091i	$-0.589086\pi$
$829$	−15.9067	−0.552463	−0.276232	+	0.961091i	$0.589086\pi$
$830$	14.9761	0.519828
$831$	−46.0872	−1.59875
$832$	−0.312847	−0.0108460
$833$	−2.90869	−0.100780
$834$	−5.57895	−0.193183
$835$	−13.0676	−0.452223
$836$	−6.35902	−0.219931
$837$	2.35778	0.0814966
$838$	−38.0923	−1.31588
$839$	−40.7059	−1.40532	−0.702662	−	0.711524i	$-0.748005\pi$
$839$	−40.7059	−1.40532	−0.702662	+	0.711524i	$0.748005\pi$
$840$	−15.0057	−0.517745
$841$	64.5704	2.22657
$842$	19.5499	0.673734
$843$	23.9145	0.823660
$844$	6.41358	0.220764
$845$	−32.6814	−1.12427
$846$	7.17238	0.246591
$847$	37.5257	1.28940
$848$	−2.11431	−0.0726058
$849$	21.2120	0.727993
$850$	0.475531	0.0163106
$851$	1.57447	0.0539721
$852$	19.3804	0.663963
$853$	−27.3386	−0.936055	−0.468028	−	0.883714i	$-0.655035\pi$
$853$	−27.3386	−0.936055	−0.468028	+	0.883714i	$0.655035\pi$
$854$	20.4162	0.698629
$855$	−9.92742	−0.339511
$856$	1.55379	0.0531074
$857$	4.44004	0.151669	0.0758344	−	0.997120i	$-0.475838\pi$
$857$	4.44004	0.151669	0.0758344	+	0.997120i	$0.475838\pi$
$858$	0.576979	0.0196977
$859$	32.8385	1.12043	0.560217	−	0.828346i	$-0.310718\pi$
$859$	32.8385	1.12043	0.560217	+	0.828346i	$0.310718\pi$
$860$	6.28684	0.214379
$861$	24.5239	0.835772
$862$	2.97261	0.101248
$863$	15.5974	0.530943	0.265472	−	0.964119i	$-0.414472\pi$
$863$	15.5974	0.530943	0.265472	+	0.964119i	$0.414472\pi$
$864$	−5.62730	−0.191445
$865$	34.9571	1.18858
$866$	3.14718	0.106945
$867$	25.2781	0.858490
$868$	−1.65819	−0.0562825
$869$	1.61178	0.0546759
$870$	−36.6770	−1.24347
$871$	−2.58291	−0.0875185
$872$	5.47519	0.185413
$873$	13.2443	0.448251
$874$	−4.64691	−0.157184
$875$	35.9264	1.21453
$876$	−9.26632	−0.313080
$877$	−43.6846	−1.47513	−0.737563	−	0.675279i	$-0.764023\pi$
$877$	−43.6846	−1.47513	−0.737563	+	0.675279i	$0.764023\pi$
$878$	16.2138	0.547188
$879$	22.4659	0.757757
$880$	−3.12091	−0.105206
$881$	25.5171	0.859694	0.429847	−	0.902902i	$-0.358568\pi$
$881$	25.5171	0.859694	0.429847	+	0.902902i	$0.358568\pi$
$882$	6.57801	0.221493
$883$	−18.2930	−0.615608	−0.307804	−	0.951450i	$-0.599594\pi$
$883$	−18.2930	−0.615608	−0.307804	+	0.951450i	$0.599594\pi$
$884$	0.105047	0.00353312
$885$	−55.6940	−1.87213
$886$	37.9174	1.27386
$887$	14.6820	0.492974	0.246487	−	0.969146i	$-0.420724\pi$
$887$	14.6820	0.492974	0.246487	+	0.969146i	$0.420724\pi$
$888$	2.61761	0.0878411
$889$	−13.0580	−0.437950
$890$	45.5353	1.52635
$891$	7.57153	0.253656
$892$	−2.57141	−0.0860973
$893$	48.7486	1.63131
$894$	−11.5808	−0.387321
$895$	12.9650	0.433373
$896$	3.95759	0.132214
$897$	0.421632	0.0140779
$898$	17.9666	0.599553
$899$	−4.05295	−0.135174
$900$	−1.07541	−0.0358471
$901$	0.709941	0.0236515
$902$	5.10052	0.169829
$903$	14.7031	0.489290
$904$	−5.79045	−0.192588
$905$	−19.9610	−0.663527
$906$	−19.5162	−0.648382
$907$	6.83943	0.227100	0.113550	−	0.993532i	$-0.463778\pi$
$907$	6.83943	0.227100	0.113550	+	0.993532i	$0.463778\pi$
$908$	−0.604951	−0.0200760
$909$	0.648437	0.0215073
$910$	−3.13619	−0.103964
$911$	−6.98391	−0.231387	−0.115694	−	0.993285i	$-0.536909\pi$
$911$	−6.98391	−0.231387	−0.115694	+	0.993285i	$0.536909\pi$
$912$	−7.72563	−0.255821
$913$	7.28454	0.241083
$914$	16.6098	0.549404
$915$	−19.5600	−0.646635
$916$	5.07471	0.167673
$917$	−11.0435	−0.364689
$918$	1.88953	0.0623637
$919$	40.4123	1.33308	0.666539	−	0.745470i	$-0.267775\pi$
$919$	40.4123	1.33308	0.666539	+	0.745470i	$0.267775\pi$
$920$	−2.28063	−0.0751901
$921$	14.8666	0.489870
$922$	9.03350	0.297502
$923$	4.05051	0.133324
$924$	−7.29893	−0.240117
$925$	2.47654	0.0814280
$926$	−37.0149	−1.21638
$927$	−7.90015	−0.259475
$928$	9.67318	0.317538
$929$	−53.0987	−1.74211	−0.871055	−	0.491185i	$-0.836564\pi$
$929$	−53.0987	−1.74211	−0.871055	+	0.491185i	$0.836564\pi$
$930$	1.58865	0.0520938
$931$	44.7088	1.46527
$932$	5.19150	0.170053
$933$	27.3263	0.894623
$934$	29.7782	0.974374
$935$	1.04793	0.0342711
$936$	−0.237564	−0.00776504
$937$	48.0941	1.57117	0.785583	−	0.618756i	$-0.212363\pi$
$937$	48.0941	1.57117	0.785583	+	0.618756i	$0.212363\pi$
$938$	32.6744	1.06686
$939$	40.3150	1.31563
$940$	23.9251	0.780349
$941$	−33.7054	−1.09876	−0.549382	−	0.835572i	$-0.685137\pi$
$941$	−33.7054	−1.09876	−0.549382	+	0.835572i	$0.685137\pi$
$942$	−18.8563	−0.614371
$943$	3.72725	0.121376
$944$	14.6887	0.478076
$945$	−56.4118	−1.83508
$946$	3.05798	0.0994237
$947$	−34.4160	−1.11837	−0.559185	−	0.829043i	$-0.688886\pi$
$947$	−34.4160	−1.11837	−0.559185	+	0.829043i	$0.688886\pi$
$948$	1.95816	0.0635982
$949$	−1.93666	−0.0628667
$950$	−7.30927	−0.237144
$951$	−15.9610	−0.517571
$952$	−1.32887	−0.0430691
$953$	27.2631	0.883139	0.441569	−	0.897227i	$-0.354422\pi$
$953$	27.2631	0.883139	0.441569	+	0.897227i	$0.354422\pi$
$954$	−1.60553	−0.0519809
$955$	52.4790	1.69818
$956$	5.37190	0.173740
$957$	−17.8401	−0.576688
$958$	−4.15376	−0.134202
$959$	−50.1969	−1.62094
$960$	−3.79162	−0.122374
$961$	−30.8244	−0.994337
$962$	0.547080	0.0176386
$963$	1.17989	0.0380214
$964$	−11.8123	−0.380449
$965$	65.9155	2.12190
$966$	−5.33375	−0.171611
$967$	−12.7889	−0.411263	−0.205631	−	0.978630i	$-0.565925\pi$
$967$	−12.7889	−0.411263	−0.205631	+	0.978630i	$0.565925\pi$
$968$	9.48196	0.304762
$969$	2.59410	0.0833345
$970$	44.1792	1.41851
$971$	7.88428	0.253019	0.126509	−	0.991965i	$-0.459623\pi$
$971$	7.88428	0.253019	0.126509	+	0.991965i	$0.459623\pi$
$972$	−7.68317	−0.246438
$973$	14.7502	0.472870
$974$	−15.5937	−0.499654
$975$	0.663199	0.0212394
$976$	5.15875	0.165128
$977$	−35.2627	−1.12815	−0.564076	−	0.825723i	$-0.690768\pi$
$977$	−35.2627	−1.12815	−0.564076	+	0.825723i	$0.690768\pi$
$978$	−32.4331	−1.03710
$979$	22.1489	0.707881
$980$	21.9424	0.700924
$981$	4.15765	0.132744
$982$	32.8051	1.04685
$983$	2.86771	0.0914656	0.0457328	−	0.998954i	$-0.485438\pi$
$983$	2.86771	0.0914656	0.0457328	+	0.998954i	$0.485438\pi$
$984$	6.19667	0.197543
$985$	30.9848	0.987259
$986$	−3.24805	−0.103439
$987$	55.9540	1.78103
$988$	−1.61466	−0.0513691
$989$	2.23465	0.0710576
$990$	−2.36990	−0.0753204
$991$	−37.5515	−1.19286	−0.596432	−	0.802664i	$-0.703415\pi$
$991$	−37.5515	−1.19286	−0.596432	+	0.802664i	$0.703415\pi$
$992$	−0.418989	−0.0133029
$993$	15.1750	0.481564
$994$	−51.2399	−1.62523
$995$	−40.3165	−1.27812
$996$	8.85005	0.280424
$997$	−49.8632	−1.57918	−0.789592	−	0.613632i	$-0.789708\pi$
$997$	−49.8632	−1.57918	−0.789592	+	0.613632i	$0.789708\pi$
$998$	−16.1497	−0.511211
$999$	9.84053	0.311341

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6046.2.a.d.1.16	✓	55

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6046.2.a.d.1.16	✓	55	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:	\( N \)	\(=\)	\( 6046 = 2 \cdot 3023 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6046.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.49688 q^{3} +1.00000 q^{4} +2.53302 q^{5} +1.49688 q^{6} -3.95759 q^{7} -1.00000 q^{8} -0.759363 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.49688 q^{3} +1.00000 q^{4} +2.53302 q^{5} +1.49688 q^{6} -3.95759 q^{7} -1.00000 q^{8} -0.759363 q^{9} -2.53302 q^{10} -1.23209 q^{11} -1.49688 q^{12} -0.312847 q^{13} +3.95759 q^{14} -3.79162 q^{15} +1.00000 q^{16} -0.335778 q^{17} +0.759363 q^{18} +5.16117 q^{19} +2.53302 q^{20} +5.92402 q^{21} +1.23209 q^{22} +0.900359 q^{23} +1.49688 q^{24} +1.41620 q^{25} +0.312847 q^{26} +5.62730 q^{27} -3.95759 q^{28} -9.67318 q^{29} +3.79162 q^{30} +0.418989 q^{31} -1.00000 q^{32} +1.84428 q^{33} +0.335778 q^{34} -10.0247 q^{35} -0.759363 q^{36} +1.74871 q^{37} -5.16117 q^{38} +0.468293 q^{39} -2.53302 q^{40} +4.13973 q^{41} -5.92402 q^{42} +2.48195 q^{43} -1.23209 q^{44} -1.92348 q^{45} -0.900359 q^{46} +9.44526 q^{47} -1.49688 q^{48} +8.66254 q^{49} -1.41620 q^{50} +0.502619 q^{51} -0.312847 q^{52} -2.11431 q^{53} -5.62730 q^{54} -3.12091 q^{55} +3.95759 q^{56} -7.72563 q^{57} +9.67318 q^{58} +14.6887 q^{59} -3.79162 q^{60} +5.15875 q^{61} -0.418989 q^{62} +3.00525 q^{63} +1.00000 q^{64} -0.792449 q^{65} -1.84428 q^{66} +8.25613 q^{67} -0.335778 q^{68} -1.34773 q^{69} +10.0247 q^{70} -12.9473 q^{71} +0.759363 q^{72} +6.19044 q^{73} -1.74871 q^{74} -2.11988 q^{75} +5.16117 q^{76} +4.87611 q^{77} -0.468293 q^{78} -1.30817 q^{79} +2.53302 q^{80} -6.14528 q^{81} -4.13973 q^{82} -5.91234 q^{83} +5.92402 q^{84} -0.850535 q^{85} -2.48195 q^{86} +14.4796 q^{87} +1.23209 q^{88} -17.9767 q^{89} +1.92348 q^{90} +1.23812 q^{91} +0.900359 q^{92} -0.627174 q^{93} -9.44526 q^{94} +13.0734 q^{95} +1.49688 q^{96} -17.4413 q^{97} -8.66254 q^{98} +0.935602 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 55 q - 55 q^{2} - 4 q^{3} + 55 q^{4} - 7 q^{5} + 4 q^{6} + 17 q^{7} - 55 q^{8} + 29 q^{9}+O(q^{10}) \) 55 * q - 55 * q^2 - 4 * q^3 + 55 * q^4 - 7 * q^5 + 4 * q^6 + 17 * q^7 - 55 * q^8 + 29 * q^9	\( 55 q - 55 q^{2} - 4 q^{3} + 55 q^{4} - 7 q^{5} + 4 q^{6} + 17 q^{7} - 55 q^{8} + 29 q^{9} + 7 q^{10} - 28 q^{11} - 4 q^{12} + q^{13} - 17 q^{14} - 8 q^{15} + 55 q^{16} - 32 q^{17} - 29 q^{18} - 3 q^{19} - 7 q^{20} - 25 q^{21} + 28 q^{22} - 27 q^{23} + 4 q^{24} + 30 q^{25} - q^{26} - q^{27} + 17 q^{28} - 69 q^{29} + 8 q^{30} - 13 q^{31} - 55 q^{32} - 18 q^{33} + 32 q^{34} - 23 q^{35} + 29 q^{36} + 3 q^{37} + 3 q^{38} - 28 q^{39} + 7 q^{40} - 51 q^{41} + 25 q^{42} + 23 q^{43} - 28 q^{44} - 28 q^{45} + 27 q^{46} - 27 q^{47} - 4 q^{48} + 8 q^{49} - 30 q^{50} - 42 q^{51} + q^{52} - 61 q^{53} + q^{54} + 5 q^{55} - 17 q^{56} - 52 q^{57} + 69 q^{58} - 71 q^{59} - 8 q^{60} - 16 q^{61} + 13 q^{62} + 14 q^{63} + 55 q^{64} - 82 q^{65} + 18 q^{66} + 32 q^{67} - 32 q^{68} - 44 q^{69} + 23 q^{70} - 84 q^{71} - 29 q^{72} - 43 q^{73} - 3 q^{74} - 37 q^{75} - 3 q^{76} - 47 q^{77} + 28 q^{78} - 20 q^{79} - 7 q^{80} - 33 q^{81} + 51 q^{82} + 17 q^{83} - 25 q^{84} + 10 q^{85} - 23 q^{86} - q^{87} + 28 q^{88} - 92 q^{89} + 28 q^{90} - 34 q^{91} - 27 q^{92} - 13 q^{93} + 27 q^{94} - 60 q^{95} + 4 q^{96} - 45 q^{97} - 8 q^{98} - 73 q^{99}+O(q^{100}) \) 55 * q - 55 * q^2 - 4 * q^3 + 55 * q^4 - 7 * q^5 + 4 * q^6 + 17 * q^7 - 55 * q^8 + 29 * q^9 + 7 * q^10 - 28 * q^11 - 4 * q^12 + q^13 - 17 * q^14 - 8 * q^15 + 55 * q^16 - 32 * q^17 - 29 * q^18 - 3 * q^19 - 7 * q^20 - 25 * q^21 + 28 * q^22 - 27 * q^23 + 4 * q^24 + 30 * q^25 - q^26 - q^27 + 17 * q^28 - 69 * q^29 + 8 * q^30 - 13 * q^31 - 55 * q^32 - 18 * q^33 + 32 * q^34 - 23 * q^35 + 29 * q^36 + 3 * q^37 + 3 * q^38 - 28 * q^39 + 7 * q^40 - 51 * q^41 + 25 * q^42 + 23 * q^43 - 28 * q^44 - 28 * q^45 + 27 * q^46 - 27 * q^47 - 4 * q^48 + 8 * q^49 - 30 * q^50 - 42 * q^51 + q^52 - 61 * q^53 + q^54 + 5 * q^55 - 17 * q^56 - 52 * q^57 + 69 * q^58 - 71 * q^59 - 8 * q^60 - 16 * q^61 + 13 * q^62 + 14 * q^63 + 55 * q^64 - 82 * q^65 + 18 * q^66 + 32 * q^67 - 32 * q^68 - 44 * q^69 + 23 * q^70 - 84 * q^71 - 29 * q^72 - 43 * q^73 - 3 * q^74 - 37 * q^75 - 3 * q^76 - 47 * q^77 + 28 * q^78 - 20 * q^79 - 7 * q^80 - 33 * q^81 + 51 * q^82 + 17 * q^83 - 25 * q^84 + 10 * q^85 - 23 * q^86 - q^87 + 28 * q^88 - 92 * q^89 + 28 * q^90 - 34 * q^91 - 27 * q^92 - 13 * q^93 + 27 * q^94 - 60 * q^95 + 4 * q^96 - 45 * q^97 - 8 * q^98 - 73 * q^99

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