LMFDB - Embedded newform 6046.2.a.e.1.2

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:	$56$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
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)

$f(q)$	$=$	$q+1.00000 q^{2} -3.31079 q^{3} +1.00000 q^{4} -3.14984 q^{5} -3.31079 q^{6} -0.324393 q^{7} +1.00000 q^{8} +7.96133 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.31079 q^{3} +1.00000 q^{4} -3.14984 q^{5} -3.31079 q^{6} -0.324393 q^{7} +1.00000 q^{8} +7.96133 q^{9} -3.14984 q^{10} -2.55668 q^{11} -3.31079 q^{12} +4.20519 q^{13} -0.324393 q^{14} +10.4285 q^{15} +1.00000 q^{16} -5.55370 q^{17} +7.96133 q^{18} +0.186799 q^{19} -3.14984 q^{20} +1.07400 q^{21} -2.55668 q^{22} -4.54459 q^{23} -3.31079 q^{24} +4.92152 q^{25} +4.20519 q^{26} -16.4259 q^{27} -0.324393 q^{28} -3.86544 q^{29} +10.4285 q^{30} +5.24725 q^{31} +1.00000 q^{32} +8.46462 q^{33} -5.55370 q^{34} +1.02179 q^{35} +7.96133 q^{36} -3.27004 q^{37} +0.186799 q^{38} -13.9225 q^{39} -3.14984 q^{40} +8.81058 q^{41} +1.07400 q^{42} +9.34626 q^{43} -2.55668 q^{44} -25.0769 q^{45} -4.54459 q^{46} +10.5821 q^{47} -3.31079 q^{48} -6.89477 q^{49} +4.92152 q^{50} +18.3871 q^{51} +4.20519 q^{52} +3.25192 q^{53} -16.4259 q^{54} +8.05314 q^{55} -0.324393 q^{56} -0.618453 q^{57} -3.86544 q^{58} +7.38527 q^{59} +10.4285 q^{60} +0.0821010 q^{61} +5.24725 q^{62} -2.58260 q^{63} +1.00000 q^{64} -13.2457 q^{65} +8.46462 q^{66} +8.18224 q^{67} -5.55370 q^{68} +15.0462 q^{69} +1.02179 q^{70} -10.9054 q^{71} +7.96133 q^{72} +13.1352 q^{73} -3.27004 q^{74} -16.2941 q^{75} +0.186799 q^{76} +0.829368 q^{77} -13.9225 q^{78} -5.63151 q^{79} -3.14984 q^{80} +30.4988 q^{81} +8.81058 q^{82} -15.6390 q^{83} +1.07400 q^{84} +17.4933 q^{85} +9.34626 q^{86} +12.7977 q^{87} -2.55668 q^{88} +8.20418 q^{89} -25.0769 q^{90} -1.36413 q^{91} -4.54459 q^{92} -17.3726 q^{93} +10.5821 q^{94} -0.588389 q^{95} -3.31079 q^{96} +15.3859 q^{97} -6.89477 q^{98} -20.3546 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 56 q^{2} - 18 q^{3} + 56 q^{4} - 17 q^{5} - 18 q^{6} - 35 q^{7} + 56 q^{8} + 34 q^{9}+O(q^{10}) $ 56 * q + 56 * q^2 - 18 * q^3 + 56 * q^4 - 17 * q^5 - 18 * q^6 - 35 * q^7 + 56 * q^8 + 34 * q^9	\( 56 q + 56 q^{2} - 18 q^{3} + 56 q^{4} - 17 q^{5} - 18 q^{6} - 35 q^{7} + 56 q^{8} + 34 q^{9} - 17 q^{10} - 53 q^{11} - 18 q^{12} - 21 q^{13} - 35 q^{14} - 36 q^{15} + 56 q^{16} - 22 q^{17} + 34 q^{18} - 31 q^{19} - 17 q^{20} - 23 q^{21} - 53 q^{22} - 59 q^{23} - 18 q^{24} + 41 q^{25} - 21 q^{26} - 63 q^{27} - 35 q^{28} - 88 q^{29} - 36 q^{30} - 44 q^{31} + 56 q^{32} + 4 q^{33} - 22 q^{34} - 51 q^{35} + 34 q^{36} - 60 q^{37} - 31 q^{38} - 62 q^{39} - 17 q^{40} - 39 q^{41} - 23 q^{42} - 66 q^{43} - 53 q^{44} - 34 q^{45} - 59 q^{46} - 51 q^{47} - 18 q^{48} + 41 q^{49} + 41 q^{50} - 48 q^{51} - 21 q^{52} - 75 q^{53} - 63 q^{54} - 41 q^{55} - 35 q^{56} - 12 q^{57} - 88 q^{58} - 77 q^{59} - 36 q^{60} - 43 q^{61} - 44 q^{62} - 88 q^{63} + 56 q^{64} - 54 q^{65} + 4 q^{66} - 62 q^{67} - 22 q^{68} - 48 q^{69} - 51 q^{70} - 122 q^{71} + 34 q^{72} - 7 q^{73} - 60 q^{74} - 63 q^{75} - 31 q^{76} - 39 q^{77} - 62 q^{78} - 91 q^{79} - 17 q^{80} + 8 q^{81} - 39 q^{82} - 51 q^{83} - 23 q^{84} - 72 q^{85} - 66 q^{86} - 19 q^{87} - 53 q^{88} - 62 q^{89} - 34 q^{90} - 48 q^{91} - 59 q^{92} - 41 q^{93} - 51 q^{94} - 120 q^{95} - 18 q^{96} + 6 q^{97} + 41 q^{98} - 128 q^{99}+O(q^{100}) \) 56 * q + 56 * q^2 - 18 * q^3 + 56 * q^4 - 17 * q^5 - 18 * q^6 - 35 * q^7 + 56 * q^8 + 34 * q^9 - 17 * q^10 - 53 * q^11 - 18 * q^12 - 21 * q^13 - 35 * q^14 - 36 * q^15 + 56 * q^16 - 22 * q^17 + 34 * q^18 - 31 * q^19 - 17 * q^20 - 23 * q^21 - 53 * q^22 - 59 * q^23 - 18 * q^24 + 41 * q^25 - 21 * q^26 - 63 * q^27 - 35 * q^28 - 88 * q^29 - 36 * q^30 - 44 * q^31 + 56 * q^32 + 4 * q^33 - 22 * q^34 - 51 * q^35 + 34 * q^36 - 60 * q^37 - 31 * q^38 - 62 * q^39 - 17 * q^40 - 39 * q^41 - 23 * q^42 - 66 * q^43 - 53 * q^44 - 34 * q^45 - 59 * q^46 - 51 * q^47 - 18 * q^48 + 41 * q^49 + 41 * q^50 - 48 * q^51 - 21 * q^52 - 75 * q^53 - 63 * q^54 - 41 * q^55 - 35 * q^56 - 12 * q^57 - 88 * q^58 - 77 * q^59 - 36 * q^60 - 43 * q^61 - 44 * q^62 - 88 * q^63 + 56 * q^64 - 54 * q^65 + 4 * q^66 - 62 * q^67 - 22 * q^68 - 48 * q^69 - 51 * q^70 - 122 * q^71 + 34 * q^72 - 7 * q^73 - 60 * q^74 - 63 * q^75 - 31 * q^76 - 39 * q^77 - 62 * q^78 - 91 * q^79 - 17 * q^80 + 8 * q^81 - 39 * q^82 - 51 * q^83 - 23 * q^84 - 72 * q^85 - 66 * q^86 - 19 * q^87 - 53 * q^88 - 62 * q^89 - 34 * q^90 - 48 * q^91 - 59 * q^92 - 41 * q^93 - 51 * q^94 - 120 * q^95 - 18 * q^96 + 6 * q^97 + 41 * q^98 - 128 * 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
$3$	−3.31079	−1.91149	−0.955743	−	0.294204i	$-0.904945\pi$
$3$	−3.31079	−1.91149	−0.955743	+	0.294204i	$0.904945\pi$
$4$	1.00000	0.500000
$5$	−3.14984	−1.40865	−0.704326	−	0.709876i	$-0.748751\pi$
$5$	−3.14984	−1.40865	−0.704326	+	0.709876i	$0.748751\pi$
$6$	−3.31079	−1.35162
$7$	−0.324393	−0.122609	−0.0613045	−	0.998119i	$-0.519526\pi$
$7$	−0.324393	−0.122609	−0.0613045	+	0.998119i	$0.519526\pi$
$8$	1.00000	0.353553
$9$	7.96133	2.65378
$10$	−3.14984	−0.996068
$11$	−2.55668	−0.770868	−0.385434	−	0.922735i	$-0.625948\pi$
$11$	−2.55668	−0.770868	−0.385434	+	0.922735i	$0.625948\pi$
$12$	−3.31079	−0.955743
$13$	4.20519	1.16631	0.583154	−	0.812361i	$-0.301818\pi$
$13$	4.20519	1.16631	0.583154	+	0.812361i	$0.301818\pi$
$14$	−0.324393	−0.0866976
$15$	10.4285	2.69262
$16$	1.00000	0.250000
$17$	−5.55370	−1.34697	−0.673486	−	0.739200i	$-0.735204\pi$
$17$	−5.55370	−1.34697	−0.673486	+	0.739200i	$0.735204\pi$
$18$	7.96133	1.87650
$19$	0.186799	0.0428547	0.0214274	−	0.999770i	$-0.493179\pi$
$19$	0.186799	0.0428547	0.0214274	+	0.999770i	$0.493179\pi$
$20$	−3.14984	−0.704326
$21$	1.07400	0.234365
$22$	−2.55668	−0.545086
$23$	−4.54459	−0.947612	−0.473806	−	0.880629i	$-0.657120\pi$
$23$	−4.54459	−0.947612	−0.473806	+	0.880629i	$0.657120\pi$
$24$	−3.31079	−0.675812
$25$	4.92152	0.984303
$26$	4.20519	0.824705
$27$	−16.4259	−3.16117
$28$	−0.324393	−0.0613045
$29$	−3.86544	−0.717794	−0.358897	−	0.933377i	$-0.616847\pi$
$29$	−3.86544	−0.717794	−0.358897	+	0.933377i	$0.616847\pi$
$30$	10.4285	1.90397
$31$	5.24725	0.942435	0.471217	−	0.882017i	$-0.343815\pi$
$31$	5.24725	0.942435	0.471217	+	0.882017i	$0.343815\pi$
$32$	1.00000	0.176777
$33$	8.46462	1.47350
$34$	−5.55370	−0.952453
$35$	1.02179	0.172713
$36$	7.96133	1.32689
$37$	−3.27004	−0.537592	−0.268796	−	0.963197i	$-0.586626\pi$
$37$	−3.27004	−0.537592	−0.268796	+	0.963197i	$0.586626\pi$
$38$	0.186799	0.0303029
$39$	−13.9225	−2.22938
$40$	−3.14984	−0.498034
$41$	8.81058	1.37598	0.687990	−	0.725720i	$-0.258493\pi$
$41$	8.81058	1.37598	0.687990	+	0.725720i	$0.258493\pi$
$42$	1.07400	0.165721
$43$	9.34626	1.42529	0.712645	−	0.701524i	$-0.247497\pi$
$43$	9.34626	1.42529	0.712645	+	0.701524i	$0.247497\pi$
$44$	−2.55668	−0.385434
$45$	−25.0769	−3.73825
$46$	−4.54459	−0.670063
$47$	10.5821	1.54356	0.771780	−	0.635889i	$-0.219367\pi$
$47$	10.5821	1.54356	0.771780	+	0.635889i	$0.219367\pi$
$48$	−3.31079	−0.477871
$49$	−6.89477	−0.984967
$50$	4.92152	0.696008
$51$	18.3871	2.57472
$52$	4.20519	0.583154
$53$	3.25192	0.446686	0.223343	−	0.974740i	$-0.428303\pi$
$53$	3.25192	0.446686	0.223343	+	0.974740i	$0.428303\pi$
$54$	−16.4259	−2.23528
$55$	8.05314	1.08588
$56$	−0.324393	−0.0433488
$57$	−0.618453	−0.0819161
$58$	−3.86544	−0.507557
$59$	7.38527	0.961480	0.480740	−	0.876863i	$-0.340368\pi$
$59$	7.38527	0.961480	0.480740	+	0.876863i	$0.340368\pi$
$60$	10.4285	1.34631
$61$	0.0821010	0.0105120	0.00525598	−	0.999986i	$-0.498327\pi$
$61$	0.0821010	0.0105120	0.00525598	+	0.999986i	$0.498327\pi$
$62$	5.24725	0.666402
$63$	−2.58260	−0.325377
$64$	1.00000	0.125000
$65$	−13.2457	−1.64292
$66$	8.46462	1.04192
$67$	8.18224	0.999619	0.499810	−	0.866135i	$-0.333403\pi$
$67$	8.18224	0.999619	0.499810	+	0.866135i	$0.333403\pi$
$68$	−5.55370	−0.673486
$69$	15.0462	1.81135
$70$	1.02179	0.122127
$71$	−10.9054	−1.29423	−0.647117	−	0.762391i	$-0.724025\pi$
$71$	−10.9054	−1.29423	−0.647117	+	0.762391i	$0.724025\pi$
$72$	7.96133	0.938251
$73$	13.1352	1.53736	0.768678	−	0.639636i	$-0.220915\pi$
$73$	13.1352	1.53736	0.768678	+	0.639636i	$0.220915\pi$
$74$	−3.27004	−0.380135
$75$	−16.2941	−1.88148
$76$	0.186799	0.0214274
$77$	0.829368	0.0945152
$78$	−13.9225	−1.57641
$79$	−5.63151	−0.633595	−0.316797	−	0.948493i	$-0.602607\pi$
$79$	−5.63151	−0.633595	−0.316797	+	0.948493i	$0.602607\pi$
$80$	−3.14984	−0.352163
$81$	30.4988	3.38875
$82$	8.81058	0.972965
$83$	−15.6390	−1.71660	−0.858300	−	0.513148i	$-0.828479\pi$
$83$	−15.6390	−1.71660	−0.858300	+	0.513148i	$0.828479\pi$
$84$	1.07400	0.117183
$85$	17.4933	1.89742
$86$	9.34626	1.00783
$87$	12.7977	1.37205
$88$	−2.55668	−0.272543
$89$	8.20418	0.869641	0.434820	−	0.900517i	$-0.356812\pi$
$89$	8.20418	0.869641	0.434820	+	0.900517i	$0.356812\pi$
$90$	−25.0769	−2.64334
$91$	−1.36413	−0.143000
$92$	−4.54459	−0.473806
$93$	−17.3726	−1.80145
$94$	10.5821	1.09146
$95$	−0.588389	−0.0603674
$96$	−3.31079	−0.337906
$97$	15.3859	1.56220	0.781102	−	0.624404i	$-0.214658\pi$
$97$	15.3859	1.56220	0.781102	+	0.624404i	$0.214658\pi$
$98$	−6.89477	−0.696477
$99$	−20.3546	−2.04571
$100$	4.92152	0.492152
$101$	10.5432	1.04909	0.524544	−	0.851383i	$-0.324236\pi$
$101$	10.5432	1.04909	0.524544	+	0.851383i	$0.324236\pi$
$102$	18.3871	1.82060
$103$	3.26338	0.321550	0.160775	−	0.986991i	$-0.448601\pi$
$103$	3.26338	0.321550	0.160775	+	0.986991i	$0.448601\pi$
$104$	4.20519	0.412352
$105$	−3.38292	−0.330139
$106$	3.25192	0.315855
$107$	−5.67217	−0.548349	−0.274174	−	0.961680i	$-0.588405\pi$
$107$	−5.67217	−0.548349	−0.274174	+	0.961680i	$0.588405\pi$
$108$	−16.4259	−1.58058
$109$	−17.2838	−1.65548	−0.827742	−	0.561109i	$-0.810375\pi$
$109$	−17.2838	−1.65548	−0.827742	+	0.561109i	$0.810375\pi$
$110$	8.05314	0.767837
$111$	10.8264	1.02760
$112$	−0.324393	−0.0306522
$113$	−0.217100	−0.0204231	−0.0102115	−	0.999948i	$-0.503250\pi$
$113$	−0.217100	−0.0204231	−0.0102115	+	0.999948i	$0.503250\pi$
$114$	−0.618453	−0.0579235
$115$	14.3147	1.33486
$116$	−3.86544	−0.358897
$117$	33.4789	3.09512
$118$	7.38527	0.679869
$119$	1.80158	0.165151
$120$	10.4285	0.951985
$121$	−4.46340	−0.405763
$122$	0.0821010	0.00743308
$123$	−29.1700	−2.63017
$124$	5.24725	0.471217
$125$	0.247211	0.0221113
$126$	−2.58260	−0.230076
$127$	−17.3575	−1.54023	−0.770113	−	0.637907i	$-0.779800\pi$
$127$	−17.3575	−1.54023	−0.770113	+	0.637907i	$0.779800\pi$
$128$	1.00000	0.0883883
$129$	−30.9435	−2.72442
$130$	−13.2457	−1.16172
$131$	6.37075	0.556615	0.278308	−	0.960492i	$-0.410227\pi$
$131$	6.37075	0.556615	0.278308	+	0.960492i	$0.410227\pi$
$132$	8.46462	0.736751
$133$	−0.0605963	−0.00525437
$134$	8.18224	0.706838
$135$	51.7391	4.45299
$136$	−5.55370	−0.476226
$137$	14.4867	1.23769	0.618843	−	0.785514i	$-0.287602\pi$
$137$	14.4867	1.23769	0.618843	+	0.785514i	$0.287602\pi$
$138$	15.0462	1.28082
$139$	−14.1273	−1.19826	−0.599129	−	0.800653i	$-0.704486\pi$
$139$	−14.1273	−1.19826	−0.599129	+	0.800653i	$0.704486\pi$
$140$	1.02179	0.0863567
$141$	−35.0352	−2.95049
$142$	−10.9054	−0.915161
$143$	−10.7513	−0.899069
$144$	7.96133	0.663444
$145$	12.1755	1.01112
$146$	13.1352	1.08707
$147$	22.8271	1.88275
$148$	−3.27004	−0.268796
$149$	−12.8600	−1.05353	−0.526765	−	0.850011i	$-0.676595\pi$
$149$	−12.8600	−1.05353	−0.526765	+	0.850011i	$0.676595\pi$
$150$	−16.2941	−1.33041
$151$	−19.0173	−1.54761	−0.773804	−	0.633425i	$-0.781649\pi$
$151$	−19.0173	−1.54761	−0.773804	+	0.633425i	$0.781649\pi$
$152$	0.186799	0.0151514
$153$	−44.2149	−3.57456
$154$	0.829368	0.0668324
$155$	−16.5280	−1.32756
$156$	−13.9225	−1.11469
$157$	17.6588	1.40932	0.704661	−	0.709544i	$-0.251099\pi$
$157$	17.6588	1.40932	0.704661	+	0.709544i	$0.251099\pi$
$158$	−5.63151	−0.448019
$159$	−10.7664	−0.853834
$160$	−3.14984	−0.249017
$161$	1.47423	0.116186
$162$	30.4988	2.39621
$163$	−2.06967	−0.162109	−0.0810545	−	0.996710i	$-0.525829\pi$
$163$	−2.06967	−0.162109	−0.0810545	+	0.996710i	$0.525829\pi$
$164$	8.81058	0.687990
$165$	−26.6622	−2.07565
$166$	−15.6390	−1.21382
$167$	−5.84623	−0.452395	−0.226197	−	0.974081i	$-0.572629\pi$
$167$	−5.84623	−0.452395	−0.226197	+	0.974081i	$0.572629\pi$
$168$	1.07400	0.0828606
$169$	4.68358	0.360276
$170$	17.4933	1.34168
$171$	1.48717	0.113727
$172$	9.34626	0.712645
$173$	−12.8602	−0.977746	−0.488873	−	0.872355i	$-0.662592\pi$
$173$	−12.8602	−0.977746	−0.488873	+	0.872355i	$0.662592\pi$
$174$	12.7977	0.970188
$175$	−1.59650	−0.120684
$176$	−2.55668	−0.192717
$177$	−24.4511	−1.83785
$178$	8.20418	0.614929
$179$	−14.2717	−1.06672	−0.533360	−	0.845888i	$-0.679071\pi$
$179$	−14.2717	−1.06672	−0.533360	+	0.845888i	$0.679071\pi$
$180$	−25.0769	−1.86912
$181$	15.7941	1.17397	0.586983	−	0.809599i	$-0.300316\pi$
$181$	15.7941	1.17397	0.586983	+	0.809599i	$0.300316\pi$
$182$	−1.36413	−0.101116
$183$	−0.271819	−0.0200935
$184$	−4.54459	−0.335031
$185$	10.3001	0.757280
$186$	−17.3726	−1.27382
$187$	14.1990	1.03834
$188$	10.5821	0.771780
$189$	5.32845	0.387587
$190$	−0.588389	−0.0426862
$191$	6.22779	0.450627	0.225314	−	0.974286i	$-0.427659\pi$
$191$	6.22779	0.450627	0.225314	+	0.974286i	$0.427659\pi$
$192$	−3.31079	−0.238936
$193$	25.4199	1.82976	0.914882	−	0.403720i	$-0.132283\pi$
$193$	25.4199	1.82976	0.914882	+	0.403720i	$0.132283\pi$
$194$	15.3859	1.10464
$195$	43.8536	3.14042
$196$	−6.89477	−0.492484
$197$	−22.8101	−1.62515	−0.812576	−	0.582855i	$-0.801935\pi$
$197$	−22.8101	−1.62515	−0.812576	+	0.582855i	$0.801935\pi$
$198$	−20.3546	−1.44654
$199$	15.3368	1.08720	0.543598	−	0.839346i	$-0.317062\pi$
$199$	15.3368	1.08720	0.543598	+	0.839346i	$0.317062\pi$
$200$	4.92152	0.348004
$201$	−27.0897	−1.91076
$202$	10.5432	0.741817
$203$	1.25392	0.0880080
$204$	18.3871	1.28736
$205$	−27.7519	−1.93828
$206$	3.26338	0.227370
$207$	−36.1810	−2.51475
$208$	4.20519	0.291577
$209$	−0.477586	−0.0330353
$210$	−3.38292	−0.233444
$211$	−14.6365	−1.00762	−0.503811	−	0.863814i	$-0.668069\pi$
$211$	−14.6365	−1.00762	−0.503811	+	0.863814i	$0.668069\pi$
$212$	3.25192	0.223343
$213$	36.1055	2.47391
$214$	−5.67217	−0.387741
$215$	−29.4393	−2.00774
$216$	−16.4259	−1.11764
$217$	−1.70217	−0.115551
$218$	−17.2838	−1.17060
$219$	−43.4878	−2.93863
$220$	8.05314	0.542942
$221$	−23.3544	−1.57098
$222$	10.8264	0.726622
$223$	−7.39331	−0.495093	−0.247546	−	0.968876i	$-0.579624\pi$
$223$	−7.39331	−0.495093	−0.247546	+	0.968876i	$0.579624\pi$
$224$	−0.324393	−0.0216744
$225$	39.1818	2.61212
$226$	−0.217100	−0.0144413
$227$	−19.0087	−1.26165	−0.630826	−	0.775925i	$-0.717284\pi$
$227$	−19.0087	−1.26165	−0.630826	+	0.775925i	$0.717284\pi$
$228$	−0.618453	−0.0409581
$229$	−24.8430	−1.64167	−0.820836	−	0.571164i	$-0.806492\pi$
$229$	−24.8430	−1.64167	−0.820836	+	0.571164i	$0.806492\pi$
$230$	14.3147	0.943886
$231$	−2.74586	−0.180664
$232$	−3.86544	−0.253779
$233$	−3.25571	−0.213289	−0.106644	−	0.994297i	$-0.534011\pi$
$233$	−3.25571	−0.213289	−0.106644	+	0.994297i	$0.534011\pi$
$234$	33.4789	2.18858
$235$	−33.3320	−2.17434
$236$	7.38527	0.480740
$237$	18.6447	1.21111
$238$	1.80158	0.116779
$239$	−12.6295	−0.816935	−0.408468	−	0.912773i	$-0.633937\pi$
$239$	−12.6295	−0.816935	−0.408468	+	0.912773i	$0.633937\pi$
$240$	10.4285	0.673155
$241$	−13.8511	−0.892230	−0.446115	−	0.894976i	$-0.647193\pi$
$241$	−13.8511	−0.892230	−0.446115	+	0.894976i	$0.647193\pi$
$242$	−4.46340	−0.286918
$243$	−51.6972	−3.31638
$244$	0.0821010	0.00525598
$245$	21.7174	1.38748
$246$	−29.1700	−1.85981
$247$	0.785526	0.0499818
$248$	5.24725	0.333201
$249$	51.7773	3.28126
$250$	0.247211	0.0156350
$251$	−22.8002	−1.43914	−0.719568	−	0.694422i	$-0.755660\pi$
$251$	−22.8002	−1.43914	−0.719568	+	0.694422i	$0.755660\pi$
$252$	−2.58260	−0.162688
$253$	11.6191	0.730483
$254$	−17.3575	−1.08910
$255$	−57.9166	−3.62688
$256$	1.00000	0.0625000
$257$	−22.4595	−1.40099	−0.700493	−	0.713659i	$-0.747037\pi$
$257$	−22.4595	−1.40099	−0.700493	+	0.713659i	$0.747037\pi$
$258$	−30.9435	−1.92646
$259$	1.06078	0.0659135
$260$	−13.2457	−0.821462
$261$	−30.7740	−1.90486
$262$	6.37075	0.393587
$263$	21.4599	1.32328	0.661638	−	0.749824i	$-0.269862\pi$
$263$	21.4599	1.32328	0.661638	+	0.749824i	$0.269862\pi$
$264$	8.46462	0.520962
$265$	−10.2431	−0.629226
$266$	−0.0605963	−0.00371540
$267$	−27.1623	−1.66231
$268$	8.18224	0.499810
$269$	−20.3119	−1.23844	−0.619219	−	0.785218i	$-0.712551\pi$
$269$	−20.3119	−1.23844	−0.619219	+	0.785218i	$0.712551\pi$
$270$	51.7391	3.14874
$271$	−25.5834	−1.55408	−0.777040	−	0.629452i	$-0.783280\pi$
$271$	−25.5834	−1.55408	−0.777040	+	0.629452i	$0.783280\pi$
$272$	−5.55370	−0.336743
$273$	4.51635	0.273342
$274$	14.4867	0.875177
$275$	−12.5827	−0.758767
$276$	15.0462	0.905673
$277$	25.3535	1.52334	0.761672	−	0.647963i	$-0.224379\pi$
$277$	25.3535	1.52334	0.761672	+	0.647963i	$0.224379\pi$
$278$	−14.1273	−0.847296
$279$	41.7751	2.50101
$280$	1.02179	0.0610634
$281$	25.7161	1.53410	0.767048	−	0.641590i	$-0.221725\pi$
$281$	25.7161	1.53410	0.767048	+	0.641590i	$0.221725\pi$
$282$	−35.0352	−2.08631
$283$	23.2820	1.38397	0.691986	−	0.721910i	$-0.256736\pi$
$283$	23.2820	1.38397	0.691986	+	0.721910i	$0.256736\pi$
$284$	−10.9054	−0.647117
$285$	1.94803	0.115391
$286$	−10.7513	−0.635738
$287$	−2.85809	−0.168708
$288$	7.96133	0.469126
$289$	13.8436	0.814332
$290$	12.1755	0.714972
$291$	−50.9395	−2.98613
$292$	13.1352	0.768678
$293$	−21.8715	−1.27775	−0.638874	−	0.769311i	$-0.720599\pi$
$293$	−21.8715	−1.27775	−0.638874	+	0.769311i	$0.720599\pi$
$294$	22.8271	1.33131
$295$	−23.2624	−1.35439
$296$	−3.27004	−0.190067
$297$	41.9958	2.43684
$298$	−12.8600	−0.744959
$299$	−19.1108	−1.10521
$300$	−16.2941	−0.940741
$301$	−3.03186	−0.174753
$302$	−19.0173	−1.09432
$303$	−34.9063	−2.00532
$304$	0.186799	0.0107137
$305$	−0.258605	−0.0148077
$306$	−44.2149	−2.52760
$307$	−8.02848	−0.458210	−0.229105	−	0.973402i	$-0.573580\pi$
$307$	−8.02848	−0.458210	−0.229105	+	0.973402i	$0.573580\pi$
$308$	0.829368	0.0472576
$309$	−10.8044	−0.614639
$310$	−16.5280	−0.938729
$311$	−22.5718	−1.27993	−0.639965	−	0.768404i	$-0.721051\pi$
$311$	−22.5718	−1.27993	−0.639965	+	0.768404i	$0.721051\pi$
$312$	−13.9225	−0.788205
$313$	29.2731	1.65461	0.827306	−	0.561752i	$-0.189872\pi$
$313$	29.2731	1.65461	0.827306	+	0.561752i	$0.189872\pi$
$314$	17.6588	0.996541
$315$	8.13478	0.458343
$316$	−5.63151	−0.316797
$317$	5.15743	0.289670	0.144835	−	0.989456i	$-0.453735\pi$
$317$	5.15743	0.289670	0.144835	+	0.989456i	$0.453735\pi$
$318$	−10.7664	−0.603752
$319$	9.88269	0.553324
$320$	−3.14984	−0.176082
$321$	18.7793	1.04816
$322$	1.47423	0.0821557
$323$	−1.03743	−0.0577241
$324$	30.4988	1.69438
$325$	20.6959	1.14800
$326$	−2.06967	−0.114628
$327$	57.2229	3.16443
$328$	8.81058	0.486483
$329$	−3.43276	−0.189254
$330$	−26.6622	−1.46771
$331$	8.65592	0.475772	0.237886	−	0.971293i	$-0.423545\pi$
$331$	8.65592	0.475772	0.237886	+	0.971293i	$0.423545\pi$
$332$	−15.6390	−0.858300
$333$	−26.0339	−1.42665
$334$	−5.84623	−0.319892
$335$	−25.7728	−1.40812
$336$	1.07400	0.0585913
$337$	17.7777	0.968412	0.484206	−	0.874954i	$-0.339109\pi$
$337$	17.7777	0.968412	0.484206	+	0.874954i	$0.339109\pi$
$338$	4.68358	0.254753
$339$	0.718773	0.0390384
$340$	17.4933	0.948708
$341$	−13.4155	−0.726492
$342$	1.48717	0.0804170
$343$	4.50736	0.243375
$344$	9.34626	0.503916
$345$	−47.3931	−2.55156
$346$	−12.8602	−0.691371
$347$	−7.21325	−0.387227	−0.193614	−	0.981078i	$-0.562021\pi$
$347$	−7.21325	−0.387227	−0.193614	+	0.981078i	$0.562021\pi$
$348$	12.7977	0.686026
$349$	16.9363	0.906578	0.453289	−	0.891364i	$-0.350251\pi$
$349$	16.9363	0.906578	0.453289	+	0.891364i	$0.350251\pi$
$350$	−1.59650	−0.0853367
$351$	−69.0740	−3.68690
$352$	−2.55668	−0.136271
$353$	2.37733	0.126532	0.0632661	−	0.997997i	$-0.479848\pi$
$353$	2.37733	0.126532	0.0632661	+	0.997997i	$0.479848\pi$
$354$	−24.4511	−1.29956
$355$	34.3503	1.82313
$356$	8.20418	0.434820
$357$	−5.96466	−0.315683
$358$	−14.2717	−0.754285
$359$	18.0119	0.950630	0.475315	−	0.879816i	$-0.342334\pi$
$359$	18.0119	0.950630	0.475315	+	0.879816i	$0.342334\pi$
$360$	−25.0769	−1.32167
$361$	−18.9651	−0.998163
$362$	15.7941	0.830119
$363$	14.7774	0.775610
$364$	−1.36413	−0.0714999
$365$	−41.3738	−2.16560
$366$	−0.271819	−0.0142082
$367$	−1.86969	−0.0975971	−0.0487986	−	0.998809i	$-0.515539\pi$
$367$	−1.86969	−0.0975971	−0.0487986	+	0.998809i	$0.515539\pi$
$368$	−4.54459	−0.236903
$369$	70.1439	3.65154
$370$	10.3001	0.535478
$371$	−1.05490	−0.0547677
$372$	−17.3726	−0.900725
$373$	−25.5755	−1.32425	−0.662125	−	0.749393i	$-0.730345\pi$
$373$	−25.5755	−1.32425	−0.662125	+	0.749393i	$0.730345\pi$
$374$	14.1990	0.734215
$375$	−0.818465	−0.0422653
$376$	10.5821	0.545731
$377$	−16.2549	−0.837169
$378$	5.32845	0.274066
$379$	3.11206	0.159856	0.0799278	−	0.996801i	$-0.474531\pi$
$379$	3.11206	0.159856	0.0799278	+	0.996801i	$0.474531\pi$
$380$	−0.588389	−0.0301837
$381$	57.4669	2.94412
$382$	6.22779	0.318642
$383$	−31.2186	−1.59520	−0.797598	−	0.603189i	$-0.793896\pi$
$383$	−31.2186	−1.59520	−0.797598	+	0.603189i	$0.793896\pi$
$384$	−3.31079	−0.168953
$385$	−2.61238	−0.133139
$386$	25.4199	1.29384
$387$	74.4086	3.78240
$388$	15.3859	0.781102
$389$	32.6819	1.65704	0.828519	−	0.559961i	$-0.189184\pi$
$389$	32.6819	1.65704	0.828519	+	0.559961i	$0.189184\pi$
$390$	43.8536	2.22062
$391$	25.2393	1.27641
$392$	−6.89477	−0.348238
$393$	−21.0922	−1.06396
$394$	−22.8101	−1.14916
$395$	17.7384	0.892515
$396$	−20.3546	−1.02285
$397$	−19.8313	−0.995306	−0.497653	−	0.867376i	$-0.665805\pi$
$397$	−19.8313	−0.995306	−0.497653	+	0.867376i	$0.665805\pi$
$398$	15.3368	0.768764
$399$	0.200622	0.0100437
$400$	4.92152	0.246076
$401$	25.8535	1.29106	0.645531	−	0.763734i	$-0.276636\pi$
$401$	25.8535	1.29106	0.645531	+	0.763734i	$0.276636\pi$
$402$	−27.0897	−1.35111
$403$	22.0657	1.09917
$404$	10.5432	0.524544
$405$	−96.0663	−4.77357
$406$	1.25392	0.0622310
$407$	8.36045	0.414412
$408$	18.3871	0.910299
$409$	13.6379	0.674351	0.337176	−	0.941442i	$-0.390528\pi$
$409$	13.6379	0.674351	0.337176	+	0.941442i	$0.390528\pi$
$410$	−27.7519	−1.37057
$411$	−47.9626	−2.36582
$412$	3.26338	0.160775
$413$	−2.39573	−0.117886
$414$	−36.1810	−1.77820
$415$	49.2603	2.41809
$416$	4.20519	0.206176
$417$	46.7724	2.29045
$418$	−0.477586	−0.0233595
$419$	−14.6236	−0.714412	−0.357206	−	0.934026i	$-0.616271\pi$
$419$	−14.6236	−0.714412	−0.357206	+	0.934026i	$0.616271\pi$
$420$	−3.38292	−0.165070
$421$	−20.0651	−0.977912	−0.488956	−	0.872308i	$-0.662622\pi$
$421$	−20.0651	−0.977912	−0.488956	+	0.872308i	$0.662622\pi$
$422$	−14.6365	−0.712496
$423$	84.2477	4.09626
$424$	3.25192	0.157927
$425$	−27.3326	−1.32583
$426$	36.1055	1.74932
$427$	−0.0266330	−0.00128886
$428$	−5.67217	−0.274174
$429$	35.5953	1.71856
$430$	−29.4393	−1.41969
$431$	28.2115	1.35890	0.679450	−	0.733722i	$-0.262218\pi$
$431$	28.2115	1.35890	0.679450	+	0.733722i	$0.262218\pi$
$432$	−16.4259	−0.790292
$433$	12.4218	0.596953	0.298477	−	0.954417i	$-0.403522\pi$
$433$	12.4218	0.596953	0.298477	+	0.954417i	$0.403522\pi$
$434$	−1.70217	−0.0817068
$435$	−40.3106	−1.93275
$436$	−17.2838	−0.827742
$437$	−0.848926	−0.0406096
$438$	−43.4878	−2.07793
$439$	23.5543	1.12418	0.562092	−	0.827075i	$-0.309997\pi$
$439$	23.5543	1.12418	0.562092	+	0.827075i	$0.309997\pi$
$440$	8.05314	0.383918
$441$	−54.8915	−2.61388
$442$	−23.3544	−1.11085
$443$	−2.92417	−0.138932	−0.0694658	−	0.997584i	$-0.522129\pi$
$443$	−2.92417	−0.138932	−0.0694658	+	0.997584i	$0.522129\pi$
$444$	10.8264	0.513799
$445$	−25.8419	−1.22502
$446$	−7.39331	−0.350083
$447$	42.5767	2.01381
$448$	−0.324393	−0.0153261
$449$	−17.8403	−0.841936	−0.420968	−	0.907075i	$-0.638310\pi$
$449$	−17.8403	−0.841936	−0.420968	+	0.907075i	$0.638310\pi$
$450$	39.1818	1.84705
$451$	−22.5258	−1.06070
$452$	−0.217100	−0.0102115
$453$	62.9624	2.95823
$454$	−19.0087	−0.892122
$455$	4.29680	0.201437
$456$	−0.618453	−0.0289617
$457$	−19.4613	−0.910361	−0.455181	−	0.890399i	$-0.650425\pi$
$457$	−19.4613	−0.910361	−0.455181	+	0.890399i	$0.650425\pi$
$458$	−24.8430	−1.16084
$459$	91.2247	4.25800
$460$	14.3147	0.667428
$461$	−29.5434	−1.37597	−0.687987	−	0.725723i	$-0.741505\pi$
$461$	−29.5434	−1.37597	−0.687987	+	0.725723i	$0.741505\pi$
$462$	−2.74586	−0.127749
$463$	−12.8755	−0.598374	−0.299187	−	0.954194i	$-0.596716\pi$
$463$	−12.8755	−0.598374	−0.299187	+	0.954194i	$0.596716\pi$
$464$	−3.86544	−0.179449
$465$	54.7208	2.53762
$466$	−3.25571	−0.150818
$467$	18.2795	0.845875	0.422937	−	0.906159i	$-0.360999\pi$
$467$	18.2795	0.845875	0.422937	+	0.906159i	$0.360999\pi$
$468$	33.4789	1.54756
$469$	−2.65426	−0.122562
$470$	−33.3320	−1.53749
$471$	−58.4644	−2.69390
$472$	7.38527	0.339934
$473$	−23.8954	−1.09871
$474$	18.6447	0.856382
$475$	0.919336	0.0421820
$476$	1.80158	0.0825754
$477$	25.8896	1.18540
$478$	−12.6295	−0.577661
$479$	21.1560	0.966644	0.483322	−	0.875443i	$-0.339430\pi$
$479$	21.1560	0.966644	0.483322	+	0.875443i	$0.339430\pi$
$480$	10.4285	0.475992
$481$	−13.7511	−0.626998
$482$	−13.8511	−0.630902
$483$	−4.88087	−0.222087
$484$	−4.46340	−0.202882
$485$	−48.4632	−2.20060
$486$	−51.6972	−2.34503
$487$	−23.6842	−1.07323	−0.536617	−	0.843826i	$-0.680298\pi$
$487$	−23.6842	−1.07323	−0.536617	+	0.843826i	$0.680298\pi$
$488$	0.0821010	0.00371654
$489$	6.85224	0.309869
$490$	21.7174	0.981094
$491$	−22.9577	−1.03607	−0.518034	−	0.855360i	$-0.673336\pi$
$491$	−22.9577	−1.03607	−0.518034	+	0.855360i	$0.673336\pi$
$492$	−29.1700	−1.31508
$493$	21.4675	0.966848
$494$	0.785526	0.0353425
$495$	64.1137	2.88170
$496$	5.24725	0.235609
$497$	3.53763	0.158685
$498$	51.7773	2.32020
$499$	−14.8318	−0.663963	−0.331982	−	0.943286i	$-0.607717\pi$
$499$	−14.8318	−0.663963	−0.331982	+	0.943286i	$0.607717\pi$
$500$	0.247211	0.0110556
$501$	19.3556	0.864746
$502$	−22.8002	−1.01762
$503$	6.33848	0.282619	0.141309	−	0.989965i	$-0.454869\pi$
$503$	6.33848	0.282619	0.141309	+	0.989965i	$0.454869\pi$
$504$	−2.58260	−0.115038
$505$	−33.2095	−1.47780
$506$	11.6191	0.516530
$507$	−15.5064	−0.688661
$508$	−17.3575	−0.770113
$509$	−19.0845	−0.845904	−0.422952	−	0.906152i	$-0.639006\pi$
$509$	−19.0845	−0.845904	−0.422952	+	0.906152i	$0.639006\pi$
$510$	−57.9166	−2.56459
$511$	−4.26096	−0.188494
$512$	1.00000	0.0441942
$513$	−3.06835	−0.135471
$514$	−22.4595	−0.990647
$515$	−10.2791	−0.452953
$516$	−30.9435	−1.36221
$517$	−27.0551	−1.18988
$518$	1.06078	0.0466079
$519$	42.5775	1.86895
$520$	−13.2457	−0.580861
$521$	−9.26909	−0.406086	−0.203043	−	0.979170i	$-0.565083\pi$
$521$	−9.26909	−0.406086	−0.203043	+	0.979170i	$0.565083\pi$
$522$	−30.7740	−1.34694
$523$	−19.9592	−0.872756	−0.436378	−	0.899764i	$-0.643739\pi$
$523$	−19.9592	−0.872756	−0.436378	+	0.899764i	$0.643739\pi$
$524$	6.37075	0.278308
$525$	5.28569	0.230686
$526$	21.4599	0.935697
$527$	−29.1417	−1.26943
$528$	8.46462	0.368375
$529$	−2.34672	−0.102031
$530$	−10.2431	−0.444930
$531$	58.7965	2.55155
$532$	−0.0605963	−0.00262718
$533$	37.0501	1.60482
$534$	−27.1623	−1.17543
$535$	17.8664	0.772433
$536$	8.18224	0.353419
$537$	47.2507	2.03902
$538$	−20.3119	−0.875708
$539$	17.6277	0.759279
$540$	51.7391	2.22649
$541$	7.70544	0.331283	0.165641	−	0.986186i	$-0.447031\pi$
$541$	7.70544	0.331283	0.165641	+	0.986186i	$0.447031\pi$
$542$	−25.5834	−1.09890
$543$	−52.2909	−2.24402
$544$	−5.55370	−0.238113
$545$	54.4411	2.33200
$546$	4.51635	0.193282
$547$	−12.0524	−0.515322	−0.257661	−	0.966235i	$-0.582952\pi$
$547$	−12.0524	−0.515322	−0.257661	+	0.966235i	$0.582952\pi$
$548$	14.4867	0.618843
$549$	0.653633	0.0278964
$550$	−12.5827	−0.536530
$551$	−0.722061	−0.0307609
$552$	15.0462	0.640408
$553$	1.82682	0.0776843
$554$	25.3535	1.07717
$555$	−34.1015	−1.44753
$556$	−14.1273	−0.599129
$557$	−11.5385	−0.488900	−0.244450	−	0.969662i	$-0.578607\pi$
$557$	−11.5385	−0.488900	−0.244450	+	0.969662i	$0.578607\pi$
$558$	41.7751	1.76848
$559$	39.3027	1.66233
$560$	1.02179	0.0431784
$561$	−47.0100	−1.98476
$562$	25.7161	1.08477
$563$	5.42062	0.228452	0.114226	−	0.993455i	$-0.463561\pi$
$563$	5.42062	0.228452	0.114226	+	0.993455i	$0.463561\pi$
$564$	−35.0352	−1.47525
$565$	0.683832	0.0287690
$566$	23.2820	0.978617
$567$	−9.89357	−0.415491
$568$	−10.9054	−0.457581
$569$	−24.6294	−1.03252	−0.516260	−	0.856432i	$-0.672676\pi$
$569$	−24.6294	−1.03252	−0.516260	+	0.856432i	$0.672676\pi$
$570$	1.94803	0.0815941
$571$	−23.7987	−0.995945	−0.497972	−	0.867193i	$-0.665922\pi$
$571$	−23.7987	−0.995945	−0.497972	+	0.867193i	$0.665922\pi$
$572$	−10.7513	−0.449535
$573$	−20.6189	−0.861367
$574$	−2.85809	−0.119294
$575$	−22.3663	−0.932738
$576$	7.96133	0.331722
$577$	−11.9760	−0.498567	−0.249284	−	0.968430i	$-0.580195\pi$
$577$	−11.9760	−0.498567	−0.249284	+	0.968430i	$0.580195\pi$
$578$	13.8436	0.575819
$579$	−84.1600	−3.49757
$580$	12.1755	0.505561
$581$	5.07317	0.210470
$582$	−50.9395	−2.11151
$583$	−8.31412	−0.344336
$584$	13.1352	0.543537
$585$	−105.453	−4.35995
$586$	−21.8715	−0.903504
$587$	4.12191	0.170129	0.0850647	−	0.996375i	$-0.472890\pi$
$587$	4.12191	0.170129	0.0850647	+	0.996375i	$0.472890\pi$
$588$	22.8271	0.941375
$589$	0.980184	0.0403878
$590$	−23.2624	−0.957699
$591$	75.5194	3.10645
$592$	−3.27004	−0.134398
$593$	7.58100	0.311314	0.155657	−	0.987811i	$-0.450250\pi$
$593$	7.58100	0.311314	0.155657	+	0.987811i	$0.450250\pi$
$594$	41.9958	1.72311
$595$	−5.67470	−0.232640
$596$	−12.8600	−0.526765
$597$	−50.7769	−2.07816
$598$	−19.1108	−0.781500
$599$	−2.49726	−0.102035	−0.0510176	−	0.998698i	$-0.516246\pi$
$599$	−2.49726	−0.102035	−0.0510176	+	0.998698i	$0.516246\pi$
$600$	−16.2941	−0.665204
$601$	19.3810	0.790567	0.395283	−	0.918559i	$-0.370646\pi$
$601$	19.3810	0.790567	0.395283	+	0.918559i	$0.370646\pi$
$602$	−3.03186	−0.123569
$603$	65.1415	2.65277
$604$	−19.0173	−0.773804
$605$	14.0590	0.571580
$606$	−34.9063	−1.41797
$607$	25.6620	1.04159	0.520795	−	0.853682i	$-0.325636\pi$
$607$	25.6620	1.04159	0.520795	+	0.853682i	$0.325636\pi$
$608$	0.186799	0.00757571
$609$	−4.15147	−0.168226
$610$	−0.258605	−0.0104706
$611$	44.4998	1.80027
$612$	−44.2149	−1.78728
$613$	−11.6485	−0.470478	−0.235239	−	0.971938i	$-0.575587\pi$
$613$	−11.6485	−0.470478	−0.235239	+	0.971938i	$0.575587\pi$
$614$	−8.02848	−0.324003
$615$	91.8808	3.70499
$616$	0.829368	0.0334162
$617$	−4.89410	−0.197029	−0.0985145	−	0.995136i	$-0.531409\pi$
$617$	−4.89410	−0.197029	−0.0985145	+	0.995136i	$0.531409\pi$
$618$	−10.8044	−0.434615
$619$	−17.2984	−0.695281	−0.347640	−	0.937628i	$-0.613017\pi$
$619$	−17.2984	−0.695281	−0.347640	+	0.937628i	$0.613017\pi$
$620$	−16.5280	−0.663782
$621$	74.6490	2.99556
$622$	−22.5718	−0.905047
$623$	−2.66137	−0.106626
$624$	−13.9225	−0.557345
$625$	−25.3863	−1.01545
$626$	29.2731	1.16999
$627$	1.58119	0.0631465
$628$	17.6588	0.704661
$629$	18.1609	0.724121
$630$	8.13478	0.324097
$631$	−10.9366	−0.435379	−0.217689	−	0.976018i	$-0.569852\pi$
$631$	−10.9366	−0.435379	−0.217689	+	0.976018i	$0.569852\pi$
$632$	−5.63151	−0.224009
$633$	48.4585	1.92605
$634$	5.15743	0.204828
$635$	54.6733	2.16964
$636$	−10.7664	−0.426917
$637$	−28.9938	−1.14878
$638$	9.88269	0.391259
$639$	−86.8215	−3.43461
$640$	−3.14984	−0.124509
$641$	35.9444	1.41972	0.709859	−	0.704344i	$-0.248759\pi$
$641$	35.9444	1.41972	0.709859	+	0.704344i	$0.248759\pi$
$642$	18.7793	0.741162
$643$	11.5567	0.455753	0.227877	−	0.973690i	$-0.426822\pi$
$643$	11.5567	0.455753	0.227877	+	0.973690i	$0.426822\pi$
$644$	1.47423	0.0580929
$645$	97.4672	3.83777
$646$	−1.03743	−0.0408171
$647$	39.4610	1.55137	0.775687	−	0.631118i	$-0.217404\pi$
$647$	39.4610	1.55137	0.775687	+	0.631118i	$0.217404\pi$
$648$	30.4988	1.19810
$649$	−18.8818	−0.741174
$650$	20.6959	0.811759
$651$	5.63553	0.220874
$652$	−2.06967	−0.0810545
$653$	28.7612	1.12551	0.562757	−	0.826622i	$-0.309741\pi$
$653$	28.7612	1.12551	0.562757	+	0.826622i	$0.309741\pi$
$654$	57.2229	2.23759
$655$	−20.0669	−0.784078
$656$	8.81058	0.343995
$657$	104.573	4.07980
$658$	−3.43276	−0.133823
$659$	−50.5041	−1.96736	−0.983679	−	0.179930i	$-0.942413\pi$
$659$	−50.5041	−1.96736	−0.983679	+	0.179930i	$0.942413\pi$
$660$	−26.6622	−1.03783
$661$	18.3062	0.712029	0.356015	−	0.934480i	$-0.384135\pi$
$661$	18.3062	0.712029	0.356015	+	0.934480i	$0.384135\pi$
$662$	8.65592	0.336422
$663$	77.3214	3.00291
$664$	−15.6390	−0.606910
$665$	0.190869	0.00740158
$666$	−26.0339	−1.00879
$667$	17.5668	0.680190
$668$	−5.84623	−0.226197
$669$	24.4777	0.946363
$670$	−25.7728	−0.995689
$671$	−0.209906	−0.00810333
$672$	1.07400	0.0414303
$673$	1.04139	0.0401426	0.0200713	−	0.999799i	$-0.493611\pi$
$673$	1.04139	0.0401426	0.0200713	+	0.999799i	$0.493611\pi$
$674$	17.7777	0.684771
$675$	−80.8404	−3.11155
$676$	4.68358	0.180138
$677$	−2.70988	−0.104149	−0.0520746	−	0.998643i	$-0.516583\pi$
$677$	−2.70988	−0.104149	−0.0520746	+	0.998643i	$0.516583\pi$
$678$	0.718773	0.0276043
$679$	−4.99108	−0.191540
$680$	17.4933	0.670838
$681$	62.9338	2.41163
$682$	−13.4155	−0.513708
$683$	−19.7718	−0.756548	−0.378274	−	0.925694i	$-0.623482\pi$
$683$	−19.7718	−0.756548	−0.378274	+	0.925694i	$0.623482\pi$
$684$	1.48717	0.0568634
$685$	−45.6310	−1.74347
$686$	4.50736	0.172092
$687$	82.2500	3.13803
$688$	9.34626	0.356323
$689$	13.6749	0.520974
$690$	−47.3931	−1.80422
$691$	−17.4003	−0.661939	−0.330969	−	0.943641i	$-0.607376\pi$
$691$	−17.4003	−0.661939	−0.330969	+	0.943641i	$0.607376\pi$
$692$	−12.8602	−0.488873
$693$	6.60287	0.250822
$694$	−7.21325	−0.273811
$695$	44.4986	1.68793
$696$	12.7977	0.485094
$697$	−48.9313	−1.85341
$698$	16.9363	0.641048
$699$	10.7790	0.407698
$700$	−1.59650	−0.0603422
$701$	25.4248	0.960282	0.480141	−	0.877191i	$-0.340586\pi$
$701$	25.4248	0.960282	0.480141	+	0.877191i	$0.340586\pi$
$702$	−69.0740	−2.60703
$703$	−0.610842	−0.0230383
$704$	−2.55668	−0.0963584
$705$	110.355	4.15622
$706$	2.37733	0.0894718
$707$	−3.42014	−0.128628
$708$	−24.4511	−0.918927
$709$	5.79169	0.217511	0.108756	−	0.994069i	$-0.465313\pi$
$709$	5.79169	0.217511	0.108756	+	0.994069i	$0.465313\pi$
$710$	34.3503	1.28914
$711$	−44.8343	−1.68142
$712$	8.20418	0.307464
$713$	−23.8466	−0.893063
$714$	−5.96466	−0.223222
$715$	33.8649	1.26648
$716$	−14.2717	−0.533360
$717$	41.8137	1.56156
$718$	18.0119	0.672197
$719$	−7.25159	−0.270439	−0.135219	−	0.990816i	$-0.543174\pi$
$719$	−7.25159	−0.270439	−0.135219	+	0.990816i	$0.543174\pi$
$720$	−25.0769	−0.934562
$721$	−1.05862	−0.0394250
$722$	−18.9651	−0.705808
$723$	45.8582	1.70548
$724$	15.7941	0.586983
$725$	−19.0238	−0.706527
$726$	14.7774	0.548439
$727$	2.32087	0.0860762	0.0430381	−	0.999073i	$-0.486296\pi$
$727$	2.32087	0.0860762	0.0430381	+	0.999073i	$0.486296\pi$
$728$	−1.36413	−0.0505581
$729$	79.6623	2.95046
$730$	−41.3738	−1.53131
$731$	−51.9064	−1.91983
$732$	−0.271819	−0.0100467
$733$	−37.8696	−1.39875	−0.699374	−	0.714756i	$-0.746538\pi$
$733$	−37.8696	−1.39875	−0.699374	+	0.714756i	$0.746538\pi$
$734$	−1.86969	−0.0690116
$735$	−71.9019	−2.65214
$736$	−4.54459	−0.167516
$737$	−20.9193	−0.770574
$738$	70.1439	2.58203
$739$	−15.1668	−0.557919	−0.278960	−	0.960303i	$-0.589990\pi$
$739$	−15.1668	−0.557919	−0.278960	+	0.960303i	$0.589990\pi$
$740$	10.3001	0.378640
$741$	−2.60071	−0.0955395
$742$	−1.05490	−0.0387266
$743$	7.39989	0.271475	0.135738	−	0.990745i	$-0.456660\pi$
$743$	7.39989	0.271475	0.135738	+	0.990745i	$0.456660\pi$
$744$	−17.3726	−0.636909
$745$	40.5069	1.48406
$746$	−25.5755	−0.936386
$747$	−124.507	−4.55547
$748$	14.1990	0.519168
$749$	1.84001	0.0672325
$750$	−0.818465	−0.0298861
$751$	−29.8139	−1.08792	−0.543961	−	0.839110i	$-0.683076\pi$
$751$	−29.8139	−1.08792	−0.543961	+	0.839110i	$0.683076\pi$
$752$	10.5821	0.385890
$753$	75.4866	2.75089
$754$	−16.2549	−0.591968
$755$	59.9016	2.18004
$756$	5.32845	0.193794
$757$	42.7292	1.55302	0.776510	−	0.630104i	$-0.216988\pi$
$757$	42.7292	1.55302	0.776510	+	0.630104i	$0.216988\pi$
$758$	3.11206	0.113035
$759$	−38.4682	−1.39631
$760$	−0.588389	−0.0213431
$761$	−45.0772	−1.63405	−0.817024	−	0.576603i	$-0.804378\pi$
$761$	−45.0772	−1.63405	−0.817024	+	0.576603i	$0.804378\pi$
$762$	57.4669	2.08181
$763$	5.60672	0.202977
$764$	6.22779	0.225314
$765$	139.270	5.03531
$766$	−31.2186	−1.12797
$767$	31.0564	1.12138
$768$	−3.31079	−0.119468
$769$	−14.4997	−0.522874	−0.261437	−	0.965221i	$-0.584196\pi$
$769$	−14.4997	−0.522874	−0.261437	+	0.965221i	$0.584196\pi$
$770$	−2.61238	−0.0941436
$771$	74.3588	2.67797
$772$	25.4199	0.914882
$773$	5.01860	0.180507	0.0902533	−	0.995919i	$-0.471232\pi$
$773$	5.01860	0.180507	0.0902533	+	0.995919i	$0.471232\pi$
$774$	74.4086	2.67456
$775$	25.8245	0.927642
$776$	15.3859	0.552322
$777$	−3.51201	−0.125993
$778$	32.6819	1.17170
$779$	1.64581	0.0589673
$780$	43.8536	1.57021
$781$	27.8816	0.997683
$782$	25.2393	0.902556
$783$	63.4934	2.26907
$784$	−6.89477	−0.246242
$785$	−55.6223	−1.98525
$786$	−21.0922	−0.752335
$787$	13.1761	0.469676	0.234838	−	0.972035i	$-0.424544\pi$
$787$	13.1761	0.469676	0.234838	+	0.972035i	$0.424544\pi$
$788$	−22.8101	−0.812576
$789$	−71.0493	−2.52942
$790$	17.7384	0.631103
$791$	0.0704257	0.00250405
$792$	−20.3546	−0.723268
$793$	0.345250	0.0122602
$794$	−19.8313	−0.703787
$795$	33.9126	1.20276
$796$	15.3368	0.543598
$797$	−37.0878	−1.31372	−0.656859	−	0.754013i	$-0.728116\pi$
$797$	−37.0878	−1.31372	−0.656859	+	0.754013i	$0.728116\pi$
$798$	0.200622	0.00710193
$799$	−58.7700	−2.07913
$800$	4.92152	0.174002
$801$	65.3161	2.30783
$802$	25.8535	0.912919
$803$	−33.5824	−1.18510
$804$	−27.0897	−0.955379
$805$	−4.64360	−0.163665
$806$	22.0657	0.777230
$807$	67.2484	2.36726
$808$	10.5432	0.370909
$809$	−28.2504	−0.993232	−0.496616	−	0.867970i	$-0.665424\pi$
$809$	−28.2504	−0.993232	−0.496616	+	0.867970i	$0.665424\pi$
$810$	−96.0663	−3.37543
$811$	−29.5670	−1.03824	−0.519119	−	0.854702i	$-0.673740\pi$
$811$	−29.5670	−1.03824	−0.519119	+	0.854702i	$0.673740\pi$
$812$	1.25392	0.0440040
$813$	84.7012	2.97060
$814$	8.36045	0.293034
$815$	6.51914	0.228355
$816$	18.3871	0.643679
$817$	1.74587	0.0610804
$818$	13.6379	0.476839
$819$	−10.8603	−0.379489
$820$	−27.7519	−0.969140
$821$	−13.3623	−0.466349	−0.233174	−	0.972435i	$-0.574911\pi$
$821$	−13.3623	−0.466349	−0.233174	+	0.972435i	$0.574911\pi$
$822$	−47.9626	−1.67289
$823$	−55.5256	−1.93550	−0.967751	−	0.251910i	$-0.918941\pi$
$823$	−55.5256	−1.93550	−0.967751	+	0.251910i	$0.918941\pi$
$824$	3.26338	0.113685
$825$	41.6588	1.45037
$826$	−2.39573	−0.0833580
$827$	−46.2641	−1.60876	−0.804380	−	0.594115i	$-0.797502\pi$
$827$	−46.2641	−1.60876	−0.804380	+	0.594115i	$0.797502\pi$
$828$	−36.1810	−1.25738
$829$	54.6455	1.89792	0.948958	−	0.315404i	$-0.102140\pi$
$829$	54.6455	1.89792	0.948958	+	0.315404i	$0.102140\pi$
$830$	49.2603	1.70985
$831$	−83.9401	−2.91185
$832$	4.20519	0.145789
$833$	38.2915	1.32672
$834$	46.7724	1.61959
$835$	18.4147	0.637268
$836$	−0.477586	−0.0165177
$837$	−86.1909	−2.97919
$838$	−14.6236	−0.505166
$839$	24.0574	0.830554	0.415277	−	0.909695i	$-0.363685\pi$
$839$	24.0574	0.830554	0.415277	+	0.909695i	$0.363685\pi$
$840$	−3.38292	−0.116722
$841$	−14.0584	−0.484772
$842$	−20.0651	−0.691488
$843$	−85.1407	−2.93240
$844$	−14.6365	−0.503811
$845$	−14.7526	−0.507503
$846$	84.2477	2.89650
$847$	1.44789	0.0497502
$848$	3.25192	0.111672
$849$	−77.0819	−2.64544
$850$	−27.3326	−0.937502
$851$	14.8610	0.509429
$852$	36.1055	1.23695
$853$	−17.6782	−0.605291	−0.302646	−	0.953103i	$-0.597870\pi$
$853$	−17.6782	−0.605291	−0.302646	+	0.953103i	$0.597870\pi$
$854$	−0.0266330	−0.000911362 0
$855$	−4.68436	−0.160202
$856$	−5.67217	−0.193871
$857$	−17.0575	−0.582673	−0.291337	−	0.956621i	$-0.594100\pi$
$857$	−17.0575	−0.582673	−0.291337	+	0.956621i	$0.594100\pi$
$858$	35.5953	1.21520
$859$	4.73893	0.161690	0.0808451	−	0.996727i	$-0.474238\pi$
$859$	4.73893	0.161690	0.0808451	+	0.996727i	$0.474238\pi$
$860$	−29.4393	−1.00387
$861$	9.46252	0.322482
$862$	28.2115	0.960887
$863$	49.5561	1.68691	0.843455	−	0.537200i	$-0.180518\pi$
$863$	49.5561	1.68691	0.843455	+	0.537200i	$0.180518\pi$
$864$	−16.4259	−0.558821
$865$	40.5077	1.37730
$866$	12.4218	0.422110
$867$	−45.8334	−1.55658
$868$	−1.70217	−0.0577755
$869$	14.3980	0.488417
$870$	−40.3106	−1.36666
$871$	34.4078	1.16586
$872$	−17.2838	−0.585302
$873$	122.492	4.14574
$874$	−0.848926	−0.0287154
$875$	−0.0801936	−0.00271104
$876$	−43.4878	−1.46932
$877$	10.0351	0.338860	0.169430	−	0.985542i	$-0.445807\pi$
$877$	10.0351	0.338860	0.169430	+	0.985542i	$0.445807\pi$
$878$	23.5543	0.794918
$879$	72.4120	2.44240
$880$	8.05314	0.271471
$881$	−27.4317	−0.924196	−0.462098	−	0.886829i	$-0.652903\pi$
$881$	−27.4317	−0.924196	−0.462098	+	0.886829i	$0.652903\pi$
$882$	−54.8915	−1.84829
$883$	43.5842	1.46672	0.733362	−	0.679838i	$-0.237950\pi$
$883$	43.5842	1.46672	0.733362	+	0.679838i	$0.237950\pi$
$884$	−23.3544	−0.785492
$885$	77.0170	2.58890
$886$	−2.92417	−0.0982395
$887$	−5.42561	−0.182174	−0.0910871	−	0.995843i	$-0.529034\pi$
$887$	−5.42561	−0.182174	−0.0910871	+	0.995843i	$0.529034\pi$
$888$	10.8264	0.363311
$889$	5.63064	0.188845
$890$	−25.8419	−0.866221
$891$	−77.9755	−2.61228
$892$	−7.39331	−0.247546
$893$	1.97673	0.0661488
$894$	42.5767	1.42398
$895$	44.9538	1.50264
$896$	−0.324393	−0.0108372
$897$	63.2720	2.11259
$898$	−17.8403	−0.595339
$899$	−20.2829	−0.676474
$900$	39.1818	1.30606
$901$	−18.0602	−0.601673
$902$	−22.5258	−0.750027
$903$	10.0378	0.334039
$904$	−0.217100	−0.00722065
$905$	−49.7489	−1.65371
$906$	62.9624	2.09179
$907$	33.5216	1.11307	0.556533	−	0.830825i	$-0.312131\pi$
$907$	33.5216	1.11307	0.556533	+	0.830825i	$0.312131\pi$
$908$	−19.0087	−0.630826
$909$	83.9379	2.78404
$910$	4.29680	0.142438
$911$	6.80006	0.225296	0.112648	−	0.993635i	$-0.464067\pi$
$911$	6.80006	0.225296	0.112648	+	0.993635i	$0.464067\pi$
$912$	−0.618453	−0.0204790
$913$	39.9838	1.32327
$914$	−19.4613	−0.643723
$915$	0.856188	0.0283047
$916$	−24.8430	−0.820836
$917$	−2.06663	−0.0682460
$918$	91.2247	3.01086
$919$	−31.4201	−1.03645	−0.518227	−	0.855243i	$-0.673408\pi$
$919$	−31.4201	−1.03645	−0.518227	+	0.855243i	$0.673408\pi$
$920$	14.3147	0.471943
$921$	26.5806	0.875861
$922$	−29.5434	−0.972960
$923$	−45.8592	−1.50948
$924$	−2.74586	−0.0903322
$925$	−16.0936	−0.529153
$926$	−12.8755	−0.423115
$927$	25.9808	0.853323
$928$	−3.86544	−0.126889
$929$	−14.2053	−0.466060	−0.233030	−	0.972470i	$-0.574864\pi$
$929$	−14.2053	−0.466060	−0.233030	+	0.972470i	$0.574864\pi$
$930$	54.7208	1.79437
$931$	−1.28794	−0.0422105
$932$	−3.25571	−0.106644
$933$	74.7305	2.44657
$934$	18.2795	0.598124
$935$	−44.7248	−1.46266
$936$	33.4789	1.09429
$937$	−2.22718	−0.0727589	−0.0363795	−	0.999338i	$-0.511582\pi$
$937$	−2.22718	−0.0727589	−0.0363795	+	0.999338i	$0.511582\pi$
$938$	−2.65426	−0.0866646
$939$	−96.9170	−3.16277
$940$	−33.3320	−1.08717
$941$	4.38623	0.142987	0.0714936	−	0.997441i	$-0.477223\pi$
$941$	4.38623	0.142987	0.0714936	+	0.997441i	$0.477223\pi$
$942$	−58.4644	−1.90487
$943$	−40.0404	−1.30390
$944$	7.38527	0.240370
$945$	−16.7838	−0.545976
$946$	−23.8954	−0.776906
$947$	−49.6544	−1.61355	−0.806776	−	0.590857i	$-0.798790\pi$
$947$	−49.6544	−1.61355	−0.806776	+	0.590857i	$0.798790\pi$
$948$	18.6447	0.605553
$949$	55.2358	1.79303
$950$	0.919336	0.0298272
$951$	−17.0752	−0.553700
$952$	1.80158	0.0583896
$953$	20.2390	0.655604	0.327802	−	0.944746i	$-0.393692\pi$
$953$	20.2390	0.655604	0.327802	+	0.944746i	$0.393692\pi$
$954$	25.8896	0.838208
$955$	−19.6166	−0.634777
$956$	−12.6295	−0.408468
$957$	−32.7195	−1.05767
$958$	21.1560	0.683521
$959$	−4.69940	−0.151751
$960$	10.4285	0.336577
$961$	−3.46632	−0.111817
$962$	−13.7511	−0.443354
$963$	−45.1580	−1.45520
$964$	−13.8511	−0.446115
$965$	−80.0687	−2.57750
$966$	−4.88087	−0.157039
$967$	−15.7064	−0.505085	−0.252543	−	0.967586i	$-0.581267\pi$
$967$	−15.7064	−0.505085	−0.252543	+	0.967586i	$0.581267\pi$
$968$	−4.46340	−0.143459
$969$	3.43471	0.110339
$970$	−48.4632	−1.55606
$971$	−46.2868	−1.48542	−0.742708	−	0.669616i	$-0.766459\pi$
$971$	−46.2868	−1.48542	−0.742708	+	0.669616i	$0.766459\pi$
$972$	−51.6972	−1.65819
$973$	4.58278	0.146917
$974$	−23.6842	−0.758891
$975$	−68.5197	−2.19439
$976$	0.0821010	0.00262799
$977$	36.5671	1.16988	0.584942	−	0.811075i	$-0.301117\pi$
$977$	36.5671	1.16988	0.584942	+	0.811075i	$0.301117\pi$
$978$	6.85224	0.219111
$979$	−20.9754	−0.670378
$980$	21.7174	0.693738
$981$	−137.602	−4.39328
$982$	−22.9577	−0.732610
$983$	−40.6917	−1.29786	−0.648932	−	0.760846i	$-0.724784\pi$
$983$	−40.6917	−1.29786	−0.648932	+	0.760846i	$0.724784\pi$
$984$	−29.1700	−0.929905
$985$	71.8482	2.28927
$986$	21.4675	0.683665
$987$	11.3652	0.361757
$988$	0.785526	0.0249909
$989$	−42.4749	−1.35062
$990$	64.1137	2.03767
$991$	−0.660095	−0.0209686	−0.0104843	−	0.999945i	$-0.503337\pi$
$991$	−0.660095	−0.0209686	−0.0104843	+	0.999945i	$0.503337\pi$
$992$	5.24725	0.166601
$993$	−28.6579	−0.909432
$994$	3.53763	0.112207
$995$	−48.3085	−1.53148
$996$	51.7773	1.64063
$997$	25.2024	0.798169	0.399084	−	0.916914i	$-0.369328\pi$
$997$	25.2024	0.798169	0.399084	+	0.916914i	$0.369328\pi$
$998$	−14.8318	−0.469493
$999$	53.7134	1.69942

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6046.2.a.e.1.2	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6046.2.a.e.1.2	✓	56	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.31079 q^{3} +1.00000 q^{4} -3.14984 q^{5} -3.31079 q^{6} -0.324393 q^{7} +1.00000 q^{8} +7.96133 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.31079 q^{3} +1.00000 q^{4} -3.14984 q^{5} -3.31079 q^{6} -0.324393 q^{7} +1.00000 q^{8} +7.96133 q^{9} -3.14984 q^{10} -2.55668 q^{11} -3.31079 q^{12} +4.20519 q^{13} -0.324393 q^{14} +10.4285 q^{15} +1.00000 q^{16} -5.55370 q^{17} +7.96133 q^{18} +0.186799 q^{19} -3.14984 q^{20} +1.07400 q^{21} -2.55668 q^{22} -4.54459 q^{23} -3.31079 q^{24} +4.92152 q^{25} +4.20519 q^{26} -16.4259 q^{27} -0.324393 q^{28} -3.86544 q^{29} +10.4285 q^{30} +5.24725 q^{31} +1.00000 q^{32} +8.46462 q^{33} -5.55370 q^{34} +1.02179 q^{35} +7.96133 q^{36} -3.27004 q^{37} +0.186799 q^{38} -13.9225 q^{39} -3.14984 q^{40} +8.81058 q^{41} +1.07400 q^{42} +9.34626 q^{43} -2.55668 q^{44} -25.0769 q^{45} -4.54459 q^{46} +10.5821 q^{47} -3.31079 q^{48} -6.89477 q^{49} +4.92152 q^{50} +18.3871 q^{51} +4.20519 q^{52} +3.25192 q^{53} -16.4259 q^{54} +8.05314 q^{55} -0.324393 q^{56} -0.618453 q^{57} -3.86544 q^{58} +7.38527 q^{59} +10.4285 q^{60} +0.0821010 q^{61} +5.24725 q^{62} -2.58260 q^{63} +1.00000 q^{64} -13.2457 q^{65} +8.46462 q^{66} +8.18224 q^{67} -5.55370 q^{68} +15.0462 q^{69} +1.02179 q^{70} -10.9054 q^{71} +7.96133 q^{72} +13.1352 q^{73} -3.27004 q^{74} -16.2941 q^{75} +0.186799 q^{76} +0.829368 q^{77} -13.9225 q^{78} -5.63151 q^{79} -3.14984 q^{80} +30.4988 q^{81} +8.81058 q^{82} -15.6390 q^{83} +1.07400 q^{84} +17.4933 q^{85} +9.34626 q^{86} +12.7977 q^{87} -2.55668 q^{88} +8.20418 q^{89} -25.0769 q^{90} -1.36413 q^{91} -4.54459 q^{92} -17.3726 q^{93} +10.5821 q^{94} -0.588389 q^{95} -3.31079 q^{96} +15.3859 q^{97} -6.89477 q^{98} -20.3546 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 56 q^{2} - 18 q^{3} + 56 q^{4} - 17 q^{5} - 18 q^{6} - 35 q^{7} + 56 q^{8} + 34 q^{9}+O(q^{10}) \) 56 * q + 56 * q^2 - 18 * q^3 + 56 * q^4 - 17 * q^5 - 18 * q^6 - 35 * q^7 + 56 * q^8 + 34 * q^9	\( 56 q + 56 q^{2} - 18 q^{3} + 56 q^{4} - 17 q^{5} - 18 q^{6} - 35 q^{7} + 56 q^{8} + 34 q^{9} - 17 q^{10} - 53 q^{11} - 18 q^{12} - 21 q^{13} - 35 q^{14} - 36 q^{15} + 56 q^{16} - 22 q^{17} + 34 q^{18} - 31 q^{19} - 17 q^{20} - 23 q^{21} - 53 q^{22} - 59 q^{23} - 18 q^{24} + 41 q^{25} - 21 q^{26} - 63 q^{27} - 35 q^{28} - 88 q^{29} - 36 q^{30} - 44 q^{31} + 56 q^{32} + 4 q^{33} - 22 q^{34} - 51 q^{35} + 34 q^{36} - 60 q^{37} - 31 q^{38} - 62 q^{39} - 17 q^{40} - 39 q^{41} - 23 q^{42} - 66 q^{43} - 53 q^{44} - 34 q^{45} - 59 q^{46} - 51 q^{47} - 18 q^{48} + 41 q^{49} + 41 q^{50} - 48 q^{51} - 21 q^{52} - 75 q^{53} - 63 q^{54} - 41 q^{55} - 35 q^{56} - 12 q^{57} - 88 q^{58} - 77 q^{59} - 36 q^{60} - 43 q^{61} - 44 q^{62} - 88 q^{63} + 56 q^{64} - 54 q^{65} + 4 q^{66} - 62 q^{67} - 22 q^{68} - 48 q^{69} - 51 q^{70} - 122 q^{71} + 34 q^{72} - 7 q^{73} - 60 q^{74} - 63 q^{75} - 31 q^{76} - 39 q^{77} - 62 q^{78} - 91 q^{79} - 17 q^{80} + 8 q^{81} - 39 q^{82} - 51 q^{83} - 23 q^{84} - 72 q^{85} - 66 q^{86} - 19 q^{87} - 53 q^{88} - 62 q^{89} - 34 q^{90} - 48 q^{91} - 59 q^{92} - 41 q^{93} - 51 q^{94} - 120 q^{95} - 18 q^{96} + 6 q^{97} + 41 q^{98} - 128 q^{99}+O(q^{100}) \) 56 * q + 56 * q^2 - 18 * q^3 + 56 * q^4 - 17 * q^5 - 18 * q^6 - 35 * q^7 + 56 * q^8 + 34 * q^9 - 17 * q^10 - 53 * q^11 - 18 * q^12 - 21 * q^13 - 35 * q^14 - 36 * q^15 + 56 * q^16 - 22 * q^17 + 34 * q^18 - 31 * q^19 - 17 * q^20 - 23 * q^21 - 53 * q^22 - 59 * q^23 - 18 * q^24 + 41 * q^25 - 21 * q^26 - 63 * q^27 - 35 * q^28 - 88 * q^29 - 36 * q^30 - 44 * q^31 + 56 * q^32 + 4 * q^33 - 22 * q^34 - 51 * q^35 + 34 * q^36 - 60 * q^37 - 31 * q^38 - 62 * q^39 - 17 * q^40 - 39 * q^41 - 23 * q^42 - 66 * q^43 - 53 * q^44 - 34 * q^45 - 59 * q^46 - 51 * q^47 - 18 * q^48 + 41 * q^49 + 41 * q^50 - 48 * q^51 - 21 * q^52 - 75 * q^53 - 63 * q^54 - 41 * q^55 - 35 * q^56 - 12 * q^57 - 88 * q^58 - 77 * q^59 - 36 * q^60 - 43 * q^61 - 44 * q^62 - 88 * q^63 + 56 * q^64 - 54 * q^65 + 4 * q^66 - 62 * q^67 - 22 * q^68 - 48 * q^69 - 51 * q^70 - 122 * q^71 + 34 * q^72 - 7 * q^73 - 60 * q^74 - 63 * q^75 - 31 * q^76 - 39 * q^77 - 62 * q^78 - 91 * q^79 - 17 * q^80 + 8 * q^81 - 39 * q^82 - 51 * q^83 - 23 * q^84 - 72 * q^85 - 66 * q^86 - 19 * q^87 - 53 * q^88 - 62 * q^89 - 34 * q^90 - 48 * q^91 - 59 * q^92 - 41 * q^93 - 51 * q^94 - 120 * q^95 - 18 * q^96 + 6 * q^97 + 41 * q^98 - 128 * q^99

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