LMFDB - Embedded newform 6005.2.a.e.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6005,2,Mod(1,6005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6005, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6005 = 5 \cdot 1201 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6005.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:	$47.9501664138$
Analytic rank:	$1$
Dimension:	$88$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	6005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.69844 q^{2} +0.716329 q^{3} +5.28159 q^{4} +1.00000 q^{5} -1.93297 q^{6} +1.67359 q^{7} -8.85517 q^{8} -2.48687 q^{9} +O(q^{10})$	\(q-2.69844 q^{2} +0.716329 q^{3} +5.28159 q^{4} +1.00000 q^{5} -1.93297 q^{6} +1.67359 q^{7} -8.85517 q^{8} -2.48687 q^{9} -2.69844 q^{10} +4.26204 q^{11} +3.78336 q^{12} -4.25737 q^{13} -4.51608 q^{14} +0.716329 q^{15} +13.3320 q^{16} +5.06321 q^{17} +6.71068 q^{18} -2.93009 q^{19} +5.28159 q^{20} +1.19884 q^{21} -11.5009 q^{22} -2.77707 q^{23} -6.34322 q^{24} +1.00000 q^{25} +11.4883 q^{26} -3.93041 q^{27} +8.83921 q^{28} -8.13916 q^{29} -1.93297 q^{30} +10.1163 q^{31} -18.2652 q^{32} +3.05302 q^{33} -13.6628 q^{34} +1.67359 q^{35} -13.1346 q^{36} -8.13563 q^{37} +7.90668 q^{38} -3.04968 q^{39} -8.85517 q^{40} -2.20652 q^{41} -3.23500 q^{42} +0.947068 q^{43} +22.5103 q^{44} -2.48687 q^{45} +7.49377 q^{46} -5.27148 q^{47} +9.55009 q^{48} -4.19910 q^{49} -2.69844 q^{50} +3.62693 q^{51} -22.4857 q^{52} +0.317441 q^{53} +10.6060 q^{54} +4.26204 q^{55} -14.8199 q^{56} -2.09891 q^{57} +21.9630 q^{58} -1.61471 q^{59} +3.78336 q^{60} +3.59317 q^{61} -27.2983 q^{62} -4.16200 q^{63} +22.6237 q^{64} -4.25737 q^{65} -8.23840 q^{66} -3.19344 q^{67} +26.7418 q^{68} -1.98930 q^{69} -4.51608 q^{70} +4.31989 q^{71} +22.0217 q^{72} -5.47601 q^{73} +21.9535 q^{74} +0.716329 q^{75} -15.4755 q^{76} +7.13290 q^{77} +8.22939 q^{78} -2.90936 q^{79} +13.3320 q^{80} +4.64515 q^{81} +5.95417 q^{82} +5.72177 q^{83} +6.33178 q^{84} +5.06321 q^{85} -2.55561 q^{86} -5.83032 q^{87} -37.7411 q^{88} -10.4591 q^{89} +6.71068 q^{90} -7.12509 q^{91} -14.6674 q^{92} +7.24662 q^{93} +14.2248 q^{94} -2.93009 q^{95} -13.0839 q^{96} -12.7701 q^{97} +11.3310 q^{98} -10.5991 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 14 q^{2} - 34 q^{3} + 66 q^{4} + 88 q^{5} - q^{6} - 35 q^{7} - 39 q^{8} + 72 q^{9}+O(q^{10}) $ 88 * q - 14 * q^2 - 34 * q^3 + 66 * q^4 + 88 * q^5 - q^6 - 35 * q^7 - 39 * q^8 + 72 * q^9	\( 88 q - 14 q^{2} - 34 q^{3} + 66 q^{4} + 88 q^{5} - q^{6} - 35 q^{7} - 39 q^{8} + 72 q^{9} - 14 q^{10} - 26 q^{11} - 64 q^{12} - 31 q^{13} - 17 q^{14} - 34 q^{15} + 34 q^{16} - 31 q^{17} - 42 q^{18} - 56 q^{19} + 66 q^{20} - q^{21} - 49 q^{22} - 74 q^{23} - 3 q^{24} + 88 q^{25} - q^{26} - 130 q^{27} - 57 q^{28} - 6 q^{29} - q^{30} - 37 q^{31} - 87 q^{32} - 43 q^{33} - 35 q^{34} - 35 q^{35} + 53 q^{36} - 67 q^{37} - 40 q^{38} - 21 q^{39} - 39 q^{40} + 2 q^{41} - 15 q^{42} - 136 q^{43} - 15 q^{44} + 72 q^{45} - 16 q^{46} - 139 q^{47} - 71 q^{48} + 41 q^{49} - 14 q^{50} - 71 q^{51} - 71 q^{52} - 75 q^{53} + 26 q^{54} - 26 q^{55} - 22 q^{56} - 34 q^{57} - 65 q^{58} - 41 q^{59} - 64 q^{60} - 11 q^{61} - 30 q^{62} - 114 q^{63} - 33 q^{64} - 31 q^{65} + 24 q^{66} - 209 q^{67} - 42 q^{68} - 22 q^{69} - 17 q^{70} - 43 q^{71} - 80 q^{72} - 50 q^{73} + 9 q^{74} - 34 q^{75} - 62 q^{76} - 49 q^{77} - 19 q^{78} - 77 q^{79} + 34 q^{80} + 72 q^{81} - 107 q^{82} - 113 q^{83} + 19 q^{84} - 31 q^{85} + 14 q^{86} - 87 q^{87} - 107 q^{88} - 5 q^{89} - 42 q^{90} - 159 q^{91} - 100 q^{92} - 82 q^{93} - 31 q^{94} - 56 q^{95} + 58 q^{96} - 105 q^{97} - 29 q^{98} - 68 q^{99}+O(q^{100}) \) 88 * q - 14 * q^2 - 34 * q^3 + 66 * q^4 + 88 * q^5 - q^6 - 35 * q^7 - 39 * q^8 + 72 * q^9 - 14 * q^10 - 26 * q^11 - 64 * q^12 - 31 * q^13 - 17 * q^14 - 34 * q^15 + 34 * q^16 - 31 * q^17 - 42 * q^18 - 56 * q^19 + 66 * q^20 - q^21 - 49 * q^22 - 74 * q^23 - 3 * q^24 + 88 * q^25 - q^26 - 130 * q^27 - 57 * q^28 - 6 * q^29 - q^30 - 37 * q^31 - 87 * q^32 - 43 * q^33 - 35 * q^34 - 35 * q^35 + 53 * q^36 - 67 * q^37 - 40 * q^38 - 21 * q^39 - 39 * q^40 + 2 * q^41 - 15 * q^42 - 136 * q^43 - 15 * q^44 + 72 * q^45 - 16 * q^46 - 139 * q^47 - 71 * q^48 + 41 * q^49 - 14 * q^50 - 71 * q^51 - 71 * q^52 - 75 * q^53 + 26 * q^54 - 26 * q^55 - 22 * q^56 - 34 * q^57 - 65 * q^58 - 41 * q^59 - 64 * q^60 - 11 * q^61 - 30 * q^62 - 114 * q^63 - 33 * q^64 - 31 * q^65 + 24 * q^66 - 209 * q^67 - 42 * q^68 - 22 * q^69 - 17 * q^70 - 43 * q^71 - 80 * q^72 - 50 * q^73 + 9 * q^74 - 34 * q^75 - 62 * q^76 - 49 * q^77 - 19 * q^78 - 77 * q^79 + 34 * q^80 + 72 * q^81 - 107 * q^82 - 113 * q^83 + 19 * q^84 - 31 * q^85 + 14 * q^86 - 87 * q^87 - 107 * q^88 - 5 * q^89 - 42 * q^90 - 159 * q^91 - 100 * q^92 - 82 * q^93 - 31 * q^94 - 56 * q^95 + 58 * q^96 - 105 * q^97 - 29 * q^98 - 68 * 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 $

$2$	−2.69844	−1.90809	−0.954043	−	0.299669i	$-0.903124\pi$
$2$	−2.69844	−1.90809	−0.954043	+	0.299669i	$0.903124\pi$
$3$	0.716329	0.413573	0.206786	−	0.978386i	$-0.433699\pi$
$3$	0.716329	0.413573	0.206786	+	0.978386i	$0.433699\pi$
$4$	5.28159	2.64079
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.93297	−0.789133
$7$	1.67359	0.632557	0.316279	−	0.948666i	$-0.397567\pi$
$7$	1.67359	0.632557	0.316279	+	0.948666i	$0.397567\pi$
$8$	−8.85517	−3.13077
$9$	−2.48687	−0.828957
$10$	−2.69844	−0.853322
$11$	4.26204	1.28505	0.642526	−	0.766264i	$-0.277886\pi$
$11$	4.26204	1.28505	0.642526	+	0.766264i	$0.277886\pi$
$12$	3.78336	1.09216
$13$	−4.25737	−1.18078	−0.590391	−	0.807117i	$-0.701027\pi$
$13$	−4.25737	−1.18078	−0.590391	+	0.807117i	$0.701027\pi$
$14$	−4.51608	−1.20697
$15$	0.716329	0.184955
$16$	13.3320	3.33299
$17$	5.06321	1.22801	0.614005	−	0.789302i	$-0.289558\pi$
$17$	5.06321	1.22801	0.614005	+	0.789302i	$0.289558\pi$
$18$	6.71068	1.58172
$19$	−2.93009	−0.672209	−0.336105	−	0.941825i	$-0.609110\pi$
$19$	−2.93009	−0.672209	−0.336105	+	0.941825i	$0.609110\pi$
$20$	5.28159	1.18100
$21$	1.19884	0.261609
$22$	−11.5009	−2.45199
$23$	−2.77707	−0.579060	−0.289530	−	0.957169i	$-0.593499\pi$
$23$	−2.77707	−0.579060	−0.289530	+	0.957169i	$0.593499\pi$
$24$	−6.34322	−1.29480
$25$	1.00000	0.200000
$26$	11.4883	2.25304
$27$	−3.93041	−0.756407
$28$	8.83921	1.67045
$29$	−8.13916	−1.51140	−0.755702	−	0.654916i	$-0.772704\pi$
$29$	−8.13916	−1.51140	−0.755702	+	0.654916i	$0.772704\pi$
$30$	−1.93297	−0.352911
$31$	10.1163	1.81694	0.908472	−	0.417945i	$-0.137249\pi$
$31$	10.1163	1.81694	0.908472	+	0.417945i	$0.137249\pi$
$32$	−18.2652	−3.22887
$33$	3.05302	0.531463
$34$	−13.6628	−2.34315
$35$	1.67359	0.282888
$36$	−13.1346	−2.18910
$37$	−8.13563	−1.33749	−0.668745	−	0.743492i	$-0.733168\pi$
$37$	−8.13563	−1.33749	−0.668745	+	0.743492i	$0.733168\pi$
$38$	7.90668	1.28263
$39$	−3.04968	−0.488340
$40$	−8.85517	−1.40012
$41$	−2.20652	−0.344601	−0.172300	−	0.985044i	$-0.555120\pi$
$41$	−2.20652	−0.344601	−0.172300	+	0.985044i	$0.555120\pi$
$42$	−3.23500	−0.499172
$43$	0.947068	0.144427	0.0722133	−	0.997389i	$-0.476994\pi$
$43$	0.947068	0.144427	0.0722133	+	0.997389i	$0.476994\pi$
$44$	22.5103	3.39356
$45$	−2.48687	−0.370721
$46$	7.49377	1.10490
$47$	−5.27148	−0.768925	−0.384462	−	0.923141i	$-0.625613\pi$
$47$	−5.27148	−0.768925	−0.384462	+	0.923141i	$0.625613\pi$
$48$	9.55009	1.37844
$49$	−4.19910	−0.599871
$50$	−2.69844	−0.381617
$51$	3.62693	0.507872
$52$	−22.4857	−3.11820
$53$	0.317441	0.0436038	0.0218019	−	0.999762i	$-0.493060\pi$
$53$	0.317441	0.0436038	0.0218019	+	0.999762i	$0.493060\pi$
$54$	10.6060	1.44329
$55$	4.26204	0.574693
$56$	−14.8199	−1.98039
$57$	−2.09891	−0.278008
$58$	21.9630	2.88389
$59$	−1.61471	−0.210218	−0.105109	−	0.994461i	$-0.533519\pi$
$59$	−1.61471	−0.210218	−0.105109	+	0.994461i	$0.533519\pi$
$60$	3.78336	0.488429
$61$	3.59317	0.460058	0.230029	−	0.973184i	$-0.426118\pi$
$61$	3.59317	0.460058	0.230029	+	0.973184i	$0.426118\pi$
$62$	−27.2983	−3.46689
$63$	−4.16200	−0.524363
$64$	22.6237	2.82796
$65$	−4.25737	−0.528062
$66$	−8.23840	−1.01408
$67$	−3.19344	−0.390141	−0.195071	−	0.980789i	$-0.562494\pi$
$67$	−3.19344	−0.390141	−0.195071	+	0.980789i	$0.562494\pi$
$68$	26.7418	3.24292
$69$	−1.98930	−0.239484
$70$	−4.51608	−0.539775
$71$	4.31989	0.512677	0.256339	−	0.966587i	$-0.417484\pi$
$71$	4.31989	0.512677	0.256339	+	0.966587i	$0.417484\pi$
$72$	22.0217	2.59528
$73$	−5.47601	−0.640918	−0.320459	−	0.947262i	$-0.603837\pi$
$73$	−5.47601	−0.640918	−0.320459	+	0.947262i	$0.603837\pi$
$74$	21.9535	2.55205
$75$	0.716329	0.0827146
$76$	−15.4755	−1.77517
$77$	7.13290	0.812869
$78$	8.22939	0.931794
$79$	−2.90936	−0.327329	−0.163664	−	0.986516i	$-0.552331\pi$
$79$	−2.90936	−0.327329	−0.163664	+	0.986516i	$0.552331\pi$
$80$	13.3320	1.49056
$81$	4.64515	0.516128
$82$	5.95417	0.657528
$83$	5.72177	0.628046	0.314023	−	0.949415i	$-0.398323\pi$
$83$	5.72177	0.628046	0.314023	+	0.949415i	$0.398323\pi$
$84$	6.33178	0.690854
$85$	5.06321	0.549183
$86$	−2.55561	−0.275578
$87$	−5.83032	−0.625076
$88$	−37.7411	−4.02321
$89$	−10.4591	−1.10867	−0.554333	−	0.832295i	$-0.687027\pi$
$89$	−10.4591	−1.10867	−0.554333	+	0.832295i	$0.687027\pi$
$90$	6.71068	0.707368
$91$	−7.12509	−0.746913
$92$	−14.6674	−1.52918
$93$	7.24662	0.751439
$94$	14.2248	1.46717
$95$	−2.93009	−0.300621
$96$	−13.0839	−1.33537
$97$	−12.7701	−1.29661	−0.648305	−	0.761381i	$-0.724522\pi$
$97$	−12.7701	−1.29661	−0.648305	+	0.761381i	$0.724522\pi$
$98$	11.3310	1.14461
$99$	−10.5991	−1.06525
$100$	5.28159	0.528159
$101$	15.8447	1.57660	0.788302	−	0.615289i	$-0.210961\pi$
$101$	15.8447	1.57660	0.788302	+	0.615289i	$0.210961\pi$
$102$	−9.78706	−0.969063
$103$	−5.35856	−0.527994	−0.263997	−	0.964523i	$-0.585041\pi$
$103$	−5.35856	−0.527994	−0.263997	+	0.964523i	$0.585041\pi$
$104$	37.6997	3.69676
$105$	1.19884	0.116995
$106$	−0.856595	−0.0831999
$107$	14.2017	1.37293	0.686463	−	0.727165i	$-0.259162\pi$
$107$	14.2017	1.37293	0.686463	+	0.727165i	$0.259162\pi$
$108$	−20.7588	−1.99752
$109$	2.71247	0.259808	0.129904	−	0.991527i	$-0.458533\pi$
$109$	2.71247	0.259808	0.129904	+	0.991527i	$0.458533\pi$
$110$	−11.5009	−1.09656
$111$	−5.82779	−0.553149
$112$	22.3123	2.10831
$113$	−9.39506	−0.883813	−0.441906	−	0.897061i	$-0.645698\pi$
$113$	−9.39506	−0.883813	−0.441906	+	0.897061i	$0.645698\pi$
$114$	5.66379	0.530462
$115$	−2.77707	−0.258964
$116$	−42.9877	−3.99130
$117$	10.5875	0.978819
$118$	4.35721	0.401114
$119$	8.47374	0.776787
$120$	−6.34322	−0.579054
$121$	7.16496	0.651360
$122$	−9.69596	−0.877831
$123$	−1.58060	−0.142518
$124$	53.4302	4.79818
$125$	1.00000	0.0894427
$126$	11.2309	1.00053
$127$	−17.2177	−1.52782	−0.763910	−	0.645323i	$-0.776723\pi$
$127$	−17.2177	−1.52782	−0.763910	+	0.645323i	$0.776723\pi$
$128$	−24.5183	−2.16713
$129$	0.678413	0.0597309
$130$	11.4883	1.00759
$131$	−3.30644	−0.288885	−0.144443	−	0.989513i	$-0.546139\pi$
$131$	−3.30644	−0.288885	−0.144443	+	0.989513i	$0.546139\pi$
$132$	16.1248	1.40348
$133$	−4.90377	−0.425211
$134$	8.61732	0.744423
$135$	−3.93041	−0.338276
$136$	−44.8356	−3.84462
$137$	2.14239	0.183037	0.0915185	−	0.995803i	$-0.470828\pi$
$137$	2.14239	0.183037	0.0915185	+	0.995803i	$0.470828\pi$
$138$	5.36801	0.456955
$139$	−3.05936	−0.259492	−0.129746	−	0.991547i	$-0.541416\pi$
$139$	−3.05936	−0.259492	−0.129746	+	0.991547i	$0.541416\pi$
$140$	8.83921	0.747049
$141$	−3.77612	−0.318006
$142$	−11.6570	−0.978232
$143$	−18.1451	−1.51737
$144$	−33.1549	−2.76291
$145$	−8.13916	−0.675920
$146$	14.7767	1.22293
$147$	−3.00794	−0.248091
$148$	−42.9690	−3.53203
$149$	−6.53949	−0.535736	−0.267868	−	0.963456i	$-0.586319\pi$
$149$	−6.53949	−0.535736	−0.267868	+	0.963456i	$0.586319\pi$
$150$	−1.93297	−0.157827
$151$	−9.00395	−0.732731	−0.366366	−	0.930471i	$-0.619398\pi$
$151$	−9.00395	−0.732731	−0.366366	+	0.930471i	$0.619398\pi$
$152$	25.9465	2.10454
$153$	−12.5916	−1.01797
$154$	−19.2477	−1.55102
$155$	10.1163	0.812562
$156$	−16.1072	−1.28960
$157$	−24.4174	−1.94872	−0.974360	−	0.224994i	$-0.927764\pi$
$157$	−24.4174	−1.94872	−0.974360	+	0.224994i	$0.927764\pi$
$158$	7.85074	0.624571
$159$	0.227392	0.0180334
$160$	−18.2652	−1.44399
$161$	−4.64768	−0.366289
$162$	−12.5347	−0.984816
$163$	−8.17529	−0.640338	−0.320169	−	0.947360i	$-0.603740\pi$
$163$	−8.17529	−0.640338	−0.320169	+	0.947360i	$0.603740\pi$
$164$	−11.6539	−0.910019
$165$	3.05302	0.237677
$166$	−15.4399	−1.19837
$167$	−0.124966	−0.00967017	−0.00483509	−	0.999988i	$-0.501539\pi$
$167$	−0.124966	−0.00967017	−0.00483509	+	0.999988i	$0.501539\pi$
$168$	−10.6159	−0.819038
$169$	5.12522	0.394248
$170$	−13.6628	−1.04789
$171$	7.28677	0.557233
$172$	5.00202	0.381401
$173$	−12.4615	−0.947430	−0.473715	−	0.880678i	$-0.657087\pi$
$173$	−12.4615	−0.947430	−0.473715	+	0.880678i	$0.657087\pi$
$174$	15.7328	1.19270
$175$	1.67359	0.126511
$176$	56.8214	4.28307
$177$	−1.15667	−0.0869405
$178$	28.2234	2.11543
$179$	11.6552	0.871149	0.435574	−	0.900153i	$-0.356545\pi$
$179$	11.6552	0.871149	0.435574	+	0.900153i	$0.356545\pi$
$180$	−13.1346	−0.978997
$181$	−19.4415	−1.44507	−0.722536	−	0.691333i	$-0.757024\pi$
$181$	−19.4415	−1.44507	−0.722536	+	0.691333i	$0.757024\pi$
$182$	19.2266	1.42517
$183$	2.57389	0.190268
$184$	24.5915	1.81291
$185$	−8.13563	−0.598143
$186$	−19.5546	−1.43381
$187$	21.5796	1.57806
$188$	−27.8418	−2.03057
$189$	−6.57789	−0.478471
$190$	7.90668	0.573611
$191$	5.26482	0.380949	0.190474	−	0.981692i	$-0.438997\pi$
$191$	5.26482	0.380949	0.190474	+	0.981692i	$0.438997\pi$
$192$	16.2060	1.16957
$193$	−12.1365	−0.873601	−0.436801	−	0.899558i	$-0.643888\pi$
$193$	−12.1365	−0.873601	−0.436801	+	0.899558i	$0.643888\pi$
$194$	34.4594	2.47404
$195$	−3.04968	−0.218392
$196$	−22.1779	−1.58414
$197$	−8.82580	−0.628812	−0.314406	−	0.949289i	$-0.601805\pi$
$197$	−8.82580	−0.628812	−0.314406	+	0.949289i	$0.601805\pi$
$198$	28.6012	2.03260
$199$	20.3199	1.44044	0.720219	−	0.693747i	$-0.244041\pi$
$199$	20.3199	1.44044	0.720219	+	0.693747i	$0.244041\pi$
$200$	−8.85517	−0.626155
$201$	−2.28756	−0.161352
$202$	−42.7559	−3.00830
$203$	−13.6216	−0.956049
$204$	19.1559	1.34118
$205$	−2.20652	−0.154110
$206$	14.4597	1.00746
$207$	6.90623	0.480016
$208$	−56.7592	−3.93554
$209$	−12.4882	−0.863824
$210$	−3.23500	−0.223236
$211$	−8.95758	−0.616665	−0.308333	−	0.951279i	$-0.599771\pi$
$211$	−8.95758	−0.616665	−0.308333	+	0.951279i	$0.599771\pi$
$212$	1.67659	0.115149
$213$	3.09447	0.212029
$214$	−38.3223	−2.61966
$215$	0.947068	0.0645895
$216$	34.8044	2.36814
$217$	16.9306	1.14932
$218$	−7.31945	−0.495735
$219$	−3.92262	−0.265066
$220$	22.5103	1.51765
$221$	−21.5560	−1.45001
$222$	15.7260	1.05546
$223$	18.5606	1.24291	0.621454	−	0.783451i	$-0.286542\pi$
$223$	18.5606	1.24291	0.621454	+	0.783451i	$0.286542\pi$
$224$	−30.5685	−2.04244
$225$	−2.48687	−0.165791
$226$	25.3520	1.68639
$227$	9.73177	0.645920	0.322960	−	0.946413i	$-0.395322\pi$
$227$	9.73177	0.645920	0.322960	+	0.946413i	$0.395322\pi$
$228$	−11.0856	−0.734161
$229$	9.65446	0.637985	0.318992	−	0.947757i	$-0.396656\pi$
$229$	9.65446	0.637985	0.318992	+	0.947757i	$0.396656\pi$
$230$	7.49377	0.494125
$231$	5.10951	0.336181
$232$	72.0736	4.73186
$233$	−0.166011	−0.0108757	−0.00543786	−	0.999985i	$-0.501731\pi$
$233$	−0.166011	−0.0108757	−0.00543786	+	0.999985i	$0.501731\pi$
$234$	−28.5699	−1.86767
$235$	−5.27148	−0.343874
$236$	−8.52826	−0.555142
$237$	−2.08406	−0.135374
$238$	−22.8659	−1.48218
$239$	−11.1255	−0.719646	−0.359823	−	0.933021i	$-0.617163\pi$
$239$	−11.1255	−0.719646	−0.359823	+	0.933021i	$0.617163\pi$
$240$	9.55009	0.616456
$241$	−22.7160	−1.46326	−0.731632	−	0.681699i	$-0.761241\pi$
$241$	−22.7160	−1.46326	−0.731632	+	0.681699i	$0.761241\pi$
$242$	−19.3342	−1.24285
$243$	15.1187	0.969864
$244$	18.9776	1.21492
$245$	−4.19910	−0.268271
$246$	4.26515	0.271936
$247$	12.4745	0.793733
$248$	−89.5817	−5.68844
$249$	4.09867	0.259743
$250$	−2.69844	−0.170664
$251$	24.9474	1.57467	0.787334	−	0.616526i	$-0.211461\pi$
$251$	24.9474	1.57467	0.787334	+	0.616526i	$0.211461\pi$
$252$	−21.9820	−1.38473
$253$	−11.8360	−0.744123
$254$	46.4608	2.91521
$255$	3.62693	0.227127
$256$	20.9137	1.30711
$257$	−25.2008	−1.57198	−0.785992	−	0.618237i	$-0.787847\pi$
$257$	−25.2008	−1.57198	−0.785992	+	0.618237i	$0.787847\pi$
$258$	−1.83066	−0.113972
$259$	−13.6157	−0.846039
$260$	−22.4857	−1.39450
$261$	20.2410	1.25289
$262$	8.92225	0.551218
$263$	9.15026	0.564229	0.282115	−	0.959381i	$-0.408964\pi$
$263$	9.15026	0.564229	0.282115	+	0.959381i	$0.408964\pi$
$264$	−27.0350	−1.66389
$265$	0.317441	0.0195002
$266$	13.2325	0.811339
$267$	−7.49219	−0.458514
$268$	−16.8664	−1.03028
$269$	−21.7152	−1.32400	−0.661999	−	0.749505i	$-0.730292\pi$
$269$	−21.7152	−1.32400	−0.661999	+	0.749505i	$0.730292\pi$
$270$	10.6060	0.645459
$271$	15.8213	0.961075	0.480538	−	0.876974i	$-0.340442\pi$
$271$	15.8213	0.961075	0.480538	+	0.876974i	$0.340442\pi$
$272$	67.5027	4.09295
$273$	−5.10391	−0.308903
$274$	−5.78112	−0.349250
$275$	4.26204	0.257010
$276$	−10.5067	−0.632427
$277$	5.52261	0.331822	0.165911	−	0.986141i	$-0.446944\pi$
$277$	5.52261	0.331822	0.165911	+	0.986141i	$0.446944\pi$
$278$	8.25551	0.495132
$279$	−25.1580	−1.50617
$280$	−14.8199	−0.885659
$281$	25.9899	1.55043	0.775215	−	0.631697i	$-0.217641\pi$
$281$	25.9899	1.55043	0.775215	+	0.631697i	$0.217641\pi$
$282$	10.1896	0.606784
$283$	27.8283	1.65422	0.827110	−	0.562039i	$-0.189983\pi$
$283$	27.8283	1.65422	0.827110	+	0.562039i	$0.189983\pi$
$284$	22.8159	1.35387
$285$	−2.09891	−0.124329
$286$	48.9634	2.89527
$287$	−3.69281	−0.217980
$288$	45.4233	2.67659
$289$	8.63613	0.508008
$290$	21.9630	1.28971
$291$	−9.14762	−0.536243
$292$	−28.9220	−1.69253
$293$	−8.16816	−0.477189	−0.238594	−	0.971119i	$-0.576687\pi$
$293$	−8.16816	−0.477189	−0.238594	+	0.971119i	$0.576687\pi$
$294$	8.11674	0.473378
$295$	−1.61471	−0.0940123
$296$	72.0424	4.18738
$297$	−16.7515	−0.972023
$298$	17.6464	1.02223
$299$	11.8230	0.683744
$300$	3.78336	0.218432
$301$	1.58500	0.0913581
$302$	24.2966	1.39811
$303$	11.3500	0.652041
$304$	−39.0639	−2.24047
$305$	3.59317	0.205744
$306$	33.9776	1.94237
$307$	1.89490	0.108148	0.0540739	−	0.998537i	$-0.482779\pi$
$307$	1.89490	0.108148	0.0540739	+	0.998537i	$0.482779\pi$
$308$	37.6730	2.14662
$309$	−3.83849	−0.218364
$310$	−27.2983	−1.55044
$311$	6.46585	0.366645	0.183322	−	0.983053i	$-0.441315\pi$
$311$	6.46585	0.366645	0.183322	+	0.983053i	$0.441315\pi$
$312$	27.0054	1.52888
$313$	−12.6420	−0.714567	−0.357284	−	0.933996i	$-0.616297\pi$
$313$	−12.6420	−0.714567	−0.357284	+	0.933996i	$0.616297\pi$
$314$	65.8889	3.71833
$315$	−4.16200	−0.234502
$316$	−15.3660	−0.864407
$317$	11.7830	0.661799	0.330899	−	0.943666i	$-0.392648\pi$
$317$	11.7830	0.661799	0.330899	+	0.943666i	$0.392648\pi$
$318$	−0.613604	−0.0344092
$319$	−34.6894	−1.94223
$320$	22.6237	1.26470
$321$	10.1731	0.567805
$322$	12.5415	0.698910
$323$	−14.8357	−0.825480
$324$	24.5338	1.36299
$325$	−4.25737	−0.236157
$326$	22.0605	1.22182
$327$	1.94302	0.107449
$328$	19.5391	1.07887
$329$	−8.82230	−0.486389
$330$	−8.23840	−0.453509
$331$	−17.7888	−0.977762	−0.488881	−	0.872351i	$-0.662595\pi$
$331$	−17.7888	−0.977762	−0.488881	+	0.872351i	$0.662595\pi$
$332$	30.2200	1.65854
$333$	20.2323	1.10872
$334$	0.337214	0.0184515
$335$	−3.19344	−0.174476
$336$	15.9829	0.871940
$337$	−18.4671	−1.00597	−0.502985	−	0.864295i	$-0.667765\pi$
$337$	−18.4671	−1.00597	−0.502985	+	0.864295i	$0.667765\pi$
$338$	−13.8301	−0.752259
$339$	−6.72996	−0.365521
$340$	26.7418	1.45028
$341$	43.1161	2.33487
$342$	−19.6629	−1.06325
$343$	−18.7427	−1.01201
$344$	−8.38645	−0.452167
$345$	−1.98930	−0.107100
$346$	33.6266	1.80778
$347$	−0.196464	−0.0105467	−0.00527336	−	0.999986i	$-0.501679\pi$
$347$	−0.196464	−0.0105467	−0.00527336	+	0.999986i	$0.501679\pi$
$348$	−30.7933	−1.65070
$349$	−6.69778	−0.358524	−0.179262	−	0.983801i	$-0.557371\pi$
$349$	−6.69778	−0.358524	−0.179262	+	0.983801i	$0.557371\pi$
$350$	−4.51608	−0.241395
$351$	16.7332	0.893153
$352$	−77.8471	−4.14926
$353$	−10.3055	−0.548505	−0.274253	−	0.961658i	$-0.588430\pi$
$353$	−10.3055	−0.548505	−0.274253	+	0.961658i	$0.588430\pi$
$354$	3.12120	0.165890
$355$	4.31989	0.229276
$356$	−55.2408	−2.92776
$357$	6.06999	0.321258
$358$	−31.4508	−1.66223
$359$	35.3491	1.86565	0.932826	−	0.360327i	$-0.117335\pi$
$359$	35.3491	1.86565	0.932826	+	0.360327i	$0.117335\pi$
$360$	22.0217	1.16064
$361$	−10.4146	−0.548135
$362$	52.4616	2.75732
$363$	5.13247	0.269385
$364$	−37.6318	−1.97244
$365$	−5.47601	−0.286627
$366$	−6.94550	−0.363047
$367$	1.78742	0.0933028	0.0466514	−	0.998911i	$-0.485145\pi$
$367$	1.78742	0.0933028	0.0466514	+	0.998911i	$0.485145\pi$
$368$	−37.0239	−1.93000
$369$	5.48734	0.285659
$370$	21.9535	1.14131
$371$	0.531265	0.0275819
$372$	38.2736	1.98440
$373$	30.6175	1.58531	0.792656	−	0.609669i	$-0.208697\pi$
$373$	30.6175	1.58531	0.792656	+	0.609669i	$0.208697\pi$
$374$	−58.2313	−3.01107
$375$	0.716329	0.0369911
$376$	46.6799	2.40733
$377$	34.6514	1.78464
$378$	17.7500	0.912964
$379$	−21.9954	−1.12983	−0.564913	−	0.825151i	$-0.691090\pi$
$379$	−21.9954	−1.12983	−0.564913	+	0.825151i	$0.691090\pi$
$380$	−15.4755	−0.793878
$381$	−12.3335	−0.631865
$382$	−14.2068	−0.726884
$383$	−20.2837	−1.03645	−0.518223	−	0.855245i	$-0.673406\pi$
$383$	−20.2837	−1.03645	−0.518223	+	0.855245i	$0.673406\pi$
$384$	−17.5631	−0.896265
$385$	7.13290	0.363526
$386$	32.7495	1.66691
$387$	−2.35524	−0.119723
$388$	−67.4465	−3.42408
$389$	15.9067	0.806500	0.403250	−	0.915090i	$-0.367881\pi$
$389$	15.9067	0.806500	0.403250	+	0.915090i	$0.367881\pi$
$390$	8.22939	0.416711
$391$	−14.0609	−0.711091
$392$	37.1837	1.87806
$393$	−2.36850	−0.119475
$394$	23.8159	1.19983
$395$	−2.90936	−0.146386
$396$	−55.9803	−2.81311
$397$	−27.1377	−1.36200	−0.681001	−	0.732283i	$-0.738455\pi$
$397$	−27.1377	−1.36200	−0.681001	+	0.732283i	$0.738455\pi$
$398$	−54.8320	−2.74848
$399$	−3.51272	−0.175856
$400$	13.3320	0.666599
$401$	16.0670	0.802350	0.401175	−	0.916001i	$-0.368602\pi$
$401$	16.0670	0.802350	0.401175	+	0.916001i	$0.368602\pi$
$402$	6.17284	0.307873
$403$	−43.0689	−2.14542
$404$	83.6850	4.16348
$405$	4.64515	0.230819
$406$	36.7571	1.82422
$407$	−34.6744	−1.71874
$408$	−32.1171	−1.59003
$409$	13.1334	0.649403	0.324702	−	0.945817i	$-0.394736\pi$
$409$	13.1334	0.649403	0.324702	+	0.945817i	$0.394736\pi$
$410$	5.95417	0.294056
$411$	1.53466	0.0756991
$412$	−28.3017	−1.39432
$413$	−2.70237	−0.132975
$414$	−18.6361	−0.915912
$415$	5.72177	0.280871
$416$	77.7619	3.81259
$417$	−2.19151	−0.107319
$418$	33.6986	1.64825
$419$	33.3643	1.62995	0.814977	−	0.579494i	$-0.196750\pi$
$419$	33.3643	1.62995	0.814977	+	0.579494i	$0.196750\pi$
$420$	6.33178	0.308959
$421$	17.6772	0.861535	0.430767	−	0.902463i	$-0.358243\pi$
$421$	17.6772	0.861535	0.430767	+	0.902463i	$0.358243\pi$
$422$	24.1715	1.17665
$423$	13.1095	0.637406
$424$	−2.81099	−0.136514
$425$	5.06321	0.245602
$426$	−8.35024	−0.404570
$427$	6.01349	0.291013
$428$	75.0073	3.62561
$429$	−12.9979	−0.627542
$430$	−2.55561	−0.123242
$431$	16.5674	0.798024	0.399012	−	0.916946i	$-0.369353\pi$
$431$	16.5674	0.798024	0.399012	+	0.916946i	$0.369353\pi$
$432$	−52.4001	−2.52110
$433$	−0.809926	−0.0389225	−0.0194613	−	0.999811i	$-0.506195\pi$
$433$	−0.809926	−0.0389225	−0.0194613	+	0.999811i	$0.506195\pi$
$434$	−45.6861	−2.19301
$435$	−5.83032	−0.279542
$436$	14.3262	0.686098
$437$	8.13709	0.389250
$438$	10.5850	0.505770
$439$	−2.81093	−0.134158	−0.0670792	−	0.997748i	$-0.521368\pi$
$439$	−2.81093	−0.134158	−0.0670792	+	0.997748i	$0.521368\pi$
$440$	−37.7411	−1.79923
$441$	10.4426	0.497268
$442$	58.1676	2.76675
$443$	−16.4487	−0.781502	−0.390751	−	0.920496i	$-0.627785\pi$
$443$	−16.4487	−0.781502	−0.390751	+	0.920496i	$0.627785\pi$
$444$	−30.7800	−1.46075
$445$	−10.4591	−0.495811
$446$	−50.0846	−2.37158
$447$	−4.68443	−0.221566
$448$	37.8628	1.78885
$449$	25.5298	1.20482	0.602412	−	0.798185i	$-0.294206\pi$
$449$	25.5298	1.20482	0.602412	+	0.798185i	$0.294206\pi$
$450$	6.71068	0.316344
$451$	−9.40428	−0.442830
$452$	−49.6208	−2.33397
$453$	−6.44980	−0.303038
$454$	−26.2606	−1.23247
$455$	−7.12509	−0.334030
$456$	18.5862	0.870379
$457$	−16.4819	−0.770991	−0.385495	−	0.922710i	$-0.625969\pi$
$457$	−16.4819	−0.770991	−0.385495	+	0.922710i	$0.625969\pi$
$458$	−26.0520	−1.21733
$459$	−19.9005	−0.928876
$460$	−14.6674	−0.683869
$461$	−3.91327	−0.182259	−0.0911296	−	0.995839i	$-0.529048\pi$
$461$	−3.91327	−0.182259	−0.0911296	+	0.995839i	$0.529048\pi$
$462$	−13.7877	−0.641462
$463$	7.77511	0.361340	0.180670	−	0.983544i	$-0.442173\pi$
$463$	7.77511	0.361340	0.180670	+	0.983544i	$0.442173\pi$
$464$	−108.511	−5.03750
$465$	7.24662	0.336054
$466$	0.447970	0.0207518
$467$	−26.0959	−1.20758	−0.603788	−	0.797145i	$-0.706343\pi$
$467$	−26.0959	−1.20758	−0.603788	+	0.797145i	$0.706343\pi$
$468$	55.9190	2.58486
$469$	−5.34451	−0.246787
$470$	14.2248	0.656140
$471$	−17.4909	−0.805938
$472$	14.2986	0.658145
$473$	4.03644	0.185596
$474$	5.62371	0.258306
$475$	−2.93009	−0.134442
$476$	44.7548	2.05133
$477$	−0.789434	−0.0361457
$478$	30.0214	1.37315
$479$	18.1113	0.827525	0.413762	−	0.910385i	$-0.364214\pi$
$479$	18.1113	0.827525	0.413762	+	0.910385i	$0.364214\pi$
$480$	−13.0839	−0.597197
$481$	34.6364	1.57928
$482$	61.2977	2.79204
$483$	−3.32927	−0.151487
$484$	37.8423	1.72011
$485$	−12.7701	−0.579862
$486$	−40.7969	−1.85058
$487$	−22.1470	−1.00358	−0.501788	−	0.864991i	$-0.667324\pi$
$487$	−22.1470	−1.00358	−0.501788	+	0.864991i	$0.667324\pi$
$488$	−31.8181	−1.44034
$489$	−5.85620	−0.264826
$490$	11.3310	0.511883
$491$	−18.7322	−0.845372	−0.422686	−	0.906276i	$-0.638913\pi$
$491$	−18.7322	−0.845372	−0.422686	+	0.906276i	$0.638913\pi$
$492$	−8.34806	−0.376359
$493$	−41.2103	−1.85602
$494$	−33.6617	−1.51451
$495$	−10.5991	−0.476396
$496$	134.871	6.05587
$497$	7.22973	0.324298
$498$	−11.0600	−0.495611
$499$	−9.11426	−0.408010	−0.204005	−	0.978970i	$-0.565396\pi$
$499$	−9.11426	−0.408010	−0.204005	+	0.978970i	$0.565396\pi$
$500$	5.28159	0.236200
$501$	−0.0895169	−0.00399932
$502$	−67.3192	−3.00460
$503$	40.2324	1.79387	0.896937	−	0.442159i	$-0.145787\pi$
$503$	40.2324	1.79387	0.896937	+	0.442159i	$0.145787\pi$
$504$	36.8552	1.64166
$505$	15.8447	0.705079
$506$	31.9387	1.41985
$507$	3.67135	0.163050
$508$	−90.9365	−4.03466
$509$	−23.9419	−1.06121	−0.530603	−	0.847621i	$-0.678034\pi$
$509$	−23.9419	−1.06121	−0.530603	+	0.847621i	$0.678034\pi$
$510$	−9.78706	−0.433378
$511$	−9.16459	−0.405417
$512$	−7.39784	−0.326941
$513$	11.5165	0.508464
$514$	68.0029	2.99948
$515$	−5.35856	−0.236126
$516$	3.58309	0.157737
$517$	−22.4672	−0.988108
$518$	36.7412	1.61431
$519$	−8.92654	−0.391832
$520$	37.6997	1.65324
$521$	20.3772	0.892742	0.446371	−	0.894848i	$-0.352716\pi$
$521$	20.3772	0.892742	0.446371	+	0.894848i	$0.352716\pi$
$522$	−54.6193	−2.39062
$523$	43.9526	1.92191	0.960956	−	0.276703i	$-0.0892417\pi$
$523$	43.9526	1.92191	0.960956	+	0.276703i	$0.0892417\pi$
$524$	−17.4633	−0.762886
$525$	1.19884	0.0523217
$526$	−24.6914	−1.07660
$527$	51.2211	2.23123
$528$	40.7028	1.77136
$529$	−15.2879	−0.664689
$530$	−0.856595	−0.0372081
$531$	4.01559	0.174262
$532$	−25.8997	−1.12289
$533$	9.39399	0.406899
$534$	20.2172	0.874885
$535$	14.2017	0.613991
$536$	28.2785	1.22144
$537$	8.34895	0.360284
$538$	58.5971	2.52630
$539$	−17.8967	−0.770866
$540$	−20.7588	−0.893316
$541$	−17.0117	−0.731388	−0.365694	−	0.930735i	$-0.619168\pi$
$541$	−17.0117	−0.731388	−0.365694	+	0.930735i	$0.619168\pi$
$542$	−42.6928	−1.83381
$543$	−13.9265	−0.597643
$544$	−92.4808	−3.96508
$545$	2.71247	0.116190
$546$	13.7726	0.589413
$547$	−3.84779	−0.164520	−0.0822598	−	0.996611i	$-0.526214\pi$
$547$	−3.84779	−0.164520	−0.0822598	+	0.996611i	$0.526214\pi$
$548$	11.3152	0.483363
$549$	−8.93575	−0.381369
$550$	−11.5009	−0.490398
$551$	23.8485	1.01598
$552$	17.6156	0.749769
$553$	−4.86907	−0.207054
$554$	−14.9024	−0.633144
$555$	−5.82779	−0.247376
$556$	−16.1583	−0.685264
$557$	32.3526	1.37083	0.685413	−	0.728155i	$-0.259622\pi$
$557$	32.3526	1.37083	0.685413	+	0.728155i	$0.259622\pi$
$558$	67.8874	2.87390
$559$	−4.03202	−0.170536
$560$	22.3123	0.942865
$561$	15.4581	0.652642
$562$	−70.1324	−2.95835
$563$	−36.8970	−1.55502	−0.777512	−	0.628868i	$-0.783519\pi$
$563$	−36.8970	−1.55502	−0.777512	+	0.628868i	$0.783519\pi$
$564$	−19.9439	−0.839789
$565$	−9.39506	−0.395253
$566$	−75.0930	−3.15640
$567$	7.77407	0.326480
$568$	−38.2534	−1.60508
$569$	6.52908	0.273713	0.136857	−	0.990591i	$-0.456300\pi$
$569$	6.52908	0.273713	0.136857	+	0.990591i	$0.456300\pi$
$570$	5.66379	0.237230
$571$	−43.5925	−1.82429	−0.912145	−	0.409869i	$-0.865575\pi$
$571$	−43.5925	−1.82429	−0.912145	+	0.409869i	$0.865575\pi$
$572$	−95.8348	−4.00705
$573$	3.77135	0.157550
$574$	9.96484	0.415924
$575$	−2.77707	−0.115812
$576$	−56.2622	−2.34426
$577$	−6.26137	−0.260664	−0.130332	−	0.991470i	$-0.541604\pi$
$577$	−6.26137	−0.260664	−0.130332	+	0.991470i	$0.541604\pi$
$578$	−23.3041	−0.969323
$579$	−8.69370	−0.361298
$580$	−42.9877	−1.78497
$581$	9.57589	0.397275
$582$	24.6843	1.02320
$583$	1.35294	0.0560332
$584$	48.4910	2.00657
$585$	10.5875	0.437741
$586$	22.0413	0.910517
$587$	−8.79001	−0.362803	−0.181401	−	0.983409i	$-0.558063\pi$
$587$	−8.79001	−0.362803	−0.181401	+	0.983409i	$0.558063\pi$
$588$	−15.8867	−0.655156
$589$	−29.6418	−1.22137
$590$	4.35721	0.179384
$591$	−6.32218	−0.260060
$592$	−108.464	−4.45785
$593$	−38.7576	−1.59158	−0.795791	−	0.605571i	$-0.792945\pi$
$593$	−38.7576	−1.59158	−0.795791	+	0.605571i	$0.792945\pi$
$594$	45.2031	1.85470
$595$	8.47374	0.347390
$596$	−34.5389	−1.41477
$597$	14.5557	0.595726
$598$	−31.9038	−1.30464
$599$	−15.6549	−0.639644	−0.319822	−	0.947478i	$-0.603623\pi$
$599$	−15.6549	−0.639644	−0.319822	+	0.947478i	$0.603623\pi$
$600$	−6.34322	−0.258961
$601$	−27.6599	−1.12827	−0.564135	−	0.825682i	$-0.690790\pi$
$601$	−27.6599	−1.12827	−0.564135	+	0.825682i	$0.690790\pi$
$602$	−4.27704	−0.174319
$603$	7.94169	0.323410
$604$	−47.5551	−1.93499
$605$	7.16496	0.291297
$606$	−30.6273	−1.24415
$607$	34.4550	1.39849	0.699243	−	0.714884i	$-0.253521\pi$
$607$	34.4550	1.39849	0.699243	+	0.714884i	$0.253521\pi$
$608$	53.5188	2.17047
$609$	−9.75756	−0.395396
$610$	−9.69596	−0.392578
$611$	22.4427	0.907933
$612$	−66.5034	−2.68824
$613$	−3.52665	−0.142440	−0.0712199	−	0.997461i	$-0.522689\pi$
$613$	−3.52665	−0.142440	−0.0712199	+	0.997461i	$0.522689\pi$
$614$	−5.11328	−0.206355
$615$	−1.58060	−0.0637358
$616$	−63.1630	−2.54491
$617$	−38.7198	−1.55880	−0.779401	−	0.626526i	$-0.784476\pi$
$617$	−38.7198	−1.55880	−0.779401	+	0.626526i	$0.784476\pi$
$618$	10.3579	0.416658
$619$	−15.1432	−0.608656	−0.304328	−	0.952567i	$-0.598432\pi$
$619$	−15.1432	−0.608656	−0.304328	+	0.952567i	$0.598432\pi$
$620$	53.4302	2.14581
$621$	10.9150	0.438005
$622$	−17.4477	−0.699590
$623$	−17.5043	−0.701295
$624$	−40.6583	−1.62763
$625$	1.00000	0.0400000
$626$	34.1137	1.36346
$627$	−8.94564	−0.357254
$628$	−128.963	−5.14617
$629$	−41.1924	−1.64245
$630$	11.2309	0.447451
$631$	−22.1255	−0.880803	−0.440401	−	0.897801i	$-0.645164\pi$
$631$	−22.1255	−0.880803	−0.440401	+	0.897801i	$0.645164\pi$
$632$	25.7629	1.02479
$633$	−6.41658	−0.255036
$634$	−31.7957	−1.26277
$635$	−17.2177	−0.683262
$636$	1.20099	0.0476224
$637$	17.8771	0.708318
$638$	93.6073	3.70595
$639$	−10.7430	−0.424988
$640$	−24.5183	−0.969169
$641$	−32.3965	−1.27958	−0.639792	−	0.768548i	$-0.720979\pi$
$641$	−32.3965	−1.27958	−0.639792	+	0.768548i	$0.720979\pi$
$642$	−27.4514	−1.08342
$643$	−19.0650	−0.751850	−0.375925	−	0.926650i	$-0.622675\pi$
$643$	−19.0650	−0.751850	−0.375925	+	0.926650i	$0.622675\pi$
$644$	−24.5471	−0.967293
$645$	0.678413	0.0267125
$646$	40.0332	1.57509
$647$	8.41629	0.330879	0.165439	−	0.986220i	$-0.447096\pi$
$647$	8.41629	0.330879	0.165439	+	0.986220i	$0.447096\pi$
$648$	−41.1336	−1.61588
$649$	−6.88197	−0.270141
$650$	11.4883	0.450607
$651$	12.1279	0.475328
$652$	−43.1785	−1.69100
$653$	32.5049	1.27202	0.636008	−	0.771682i	$-0.280584\pi$
$653$	32.5049	1.27202	0.636008	+	0.771682i	$0.280584\pi$
$654$	−5.24313	−0.205023
$655$	−3.30644	−0.129193
$656$	−29.4173	−1.14855
$657$	13.6181	0.531294
$658$	23.8064	0.928072
$659$	−11.8453	−0.461427	−0.230714	−	0.973022i	$-0.574106\pi$
$659$	−11.8453	−0.461427	−0.230714	+	0.973022i	$0.574106\pi$
$660$	16.1248	0.627657
$661$	−11.3152	−0.440110	−0.220055	−	0.975487i	$-0.570624\pi$
$661$	−11.3152	−0.440110	−0.220055	+	0.975487i	$0.570624\pi$
$662$	48.0021	1.86565
$663$	−15.4412	−0.599686
$664$	−50.6672	−1.96627
$665$	−4.90377	−0.190160
$666$	−54.5956	−2.11554
$667$	22.6030	0.875193
$668$	−0.660019	−0.0255369
$669$	13.2955	0.514033
$670$	8.61732	0.332916
$671$	15.3142	0.591199
$672$	−21.8971	−0.844699
$673$	9.22150	0.355463	0.177731	−	0.984079i	$-0.443124\pi$
$673$	9.22150	0.355463	0.177731	+	0.984079i	$0.443124\pi$
$674$	49.8325	1.91948
$675$	−3.93041	−0.151281
$676$	27.0693	1.04113
$677$	−15.6036	−0.599696	−0.299848	−	0.953987i	$-0.596936\pi$
$677$	−15.6036	−0.599696	−0.299848	+	0.953987i	$0.596936\pi$
$678$	18.1604	0.697446
$679$	−21.3720	−0.820180
$680$	−44.8356	−1.71937
$681$	6.97115	0.267135
$682$	−116.346	−4.45513
$683$	7.58284	0.290149	0.145075	−	0.989421i	$-0.453658\pi$
$683$	7.58284	0.290149	0.145075	+	0.989421i	$0.453658\pi$
$684$	38.4857	1.47154
$685$	2.14239	0.0818566
$686$	50.5761	1.93100
$687$	6.91577	0.263853
$688$	12.6263	0.481373
$689$	−1.35146	−0.0514866
$690$	5.36801	0.204357
$691$	5.96510	0.226923	0.113462	−	0.993542i	$-0.463806\pi$
$691$	5.96510	0.226923	0.113462	+	0.993542i	$0.463806\pi$
$692$	−65.8165	−2.50197
$693$	−17.7386	−0.673834
$694$	0.530145	0.0201240
$695$	−3.05936	−0.116048
$696$	51.6284	1.95697
$697$	−11.1721	−0.423173
$698$	18.0736	0.684094
$699$	−0.118918	−0.00449790
$700$	8.83921	0.334091
$701$	−18.4069	−0.695221	−0.347610	−	0.937639i	$-0.613007\pi$
$701$	−18.4069	−0.695221	−0.347610	+	0.937639i	$0.613007\pi$
$702$	−45.1536	−1.70421
$703$	23.8382	0.899073
$704$	96.4230	3.63408
$705$	−3.77612	−0.142217
$706$	27.8087	1.04660
$707$	26.5175	0.997292
$708$	−6.10904	−0.229592
$709$	−52.1671	−1.95917	−0.979587	−	0.201019i	$-0.935575\pi$
$709$	−52.1671	−1.95917	−0.979587	+	0.201019i	$0.935575\pi$
$710$	−11.6570	−0.437479
$711$	7.23521	0.271341
$712$	92.6174	3.47098
$713$	−28.0938	−1.05212
$714$	−16.3795	−0.612988
$715$	−18.1451	−0.678587
$716$	61.5578	2.30052
$717$	−7.96949	−0.297626
$718$	−95.3874	−3.55983
$719$	−52.7778	−1.96828	−0.984140	−	0.177393i	$-0.943234\pi$
$719$	−52.7778	−1.96828	−0.984140	+	0.177393i	$0.943234\pi$
$720$	−33.1549	−1.23561
$721$	−8.96802	−0.333987
$722$	28.1031	1.04589
$723$	−16.2721	−0.605167
$724$	−102.682	−3.81614
$725$	−8.13916	−0.302281
$726$	−13.8497	−0.514009
$727$	37.3116	1.38381	0.691905	−	0.721989i	$-0.256772\pi$
$727$	37.3116	1.38381	0.691905	+	0.721989i	$0.256772\pi$
$728$	63.0939	2.33842
$729$	−3.10549	−0.115018
$730$	14.7767	0.546910
$731$	4.79521	0.177357
$732$	13.5942	0.502457
$733$	−21.1948	−0.782849	−0.391425	−	0.920210i	$-0.628018\pi$
$733$	−21.1948	−0.782849	−0.391425	+	0.920210i	$0.628018\pi$
$734$	−4.82326	−0.178030
$735$	−3.00794	−0.110949
$736$	50.7239	1.86971
$737$	−13.6106	−0.501352
$738$	−14.8073	−0.545063
$739$	9.40984	0.346147	0.173073	−	0.984909i	$-0.444630\pi$
$739$	9.40984	0.346147	0.173073	+	0.984909i	$0.444630\pi$
$740$	−42.9690	−1.57957
$741$	8.93585	0.328267
$742$	−1.43359	−0.0526287
$743$	15.6618	0.574576	0.287288	−	0.957844i	$-0.407246\pi$
$743$	15.6618	0.574576	0.287288	+	0.957844i	$0.407246\pi$
$744$	−64.1700	−2.35259
$745$	−6.53949	−0.239588
$746$	−82.6195	−3.02491
$747$	−14.2293	−0.520623
$748$	113.975	4.16732
$749$	23.7677	0.868454
$750$	−1.93297	−0.0705822
$751$	7.92430	0.289162	0.144581	−	0.989493i	$-0.453817\pi$
$751$	7.92430	0.289162	0.144581	+	0.989493i	$0.453817\pi$
$752$	−70.2793	−2.56282
$753$	17.8706	0.651240
$754$	−93.5048	−3.40525
$755$	−9.00395	−0.327687
$756$	−34.7417	−1.26354
$757$	−5.15296	−0.187288	−0.0936438	−	0.995606i	$-0.529851\pi$
$757$	−5.15296	−0.187288	−0.0936438	+	0.995606i	$0.529851\pi$
$758$	59.3532	2.15580
$759$	−8.47847	−0.307749
$760$	25.9465	0.941177
$761$	37.0585	1.34337	0.671684	−	0.740838i	$-0.265571\pi$
$761$	37.0585	1.34337	0.671684	+	0.740838i	$0.265571\pi$
$762$	33.2813	1.20565
$763$	4.53956	0.164343
$764$	27.8066	1.00601
$765$	−12.5916	−0.455249
$766$	54.7342	1.97763
$767$	6.87444	0.248222
$768$	14.9811	0.540583
$769$	−14.4992	−0.522854	−0.261427	−	0.965223i	$-0.584193\pi$
$769$	−14.4992	−0.522854	−0.261427	+	0.965223i	$0.584193\pi$
$770$	−19.2477	−0.693639
$771$	−18.0521	−0.650130
$772$	−64.0997	−2.30700
$773$	−14.7600	−0.530880	−0.265440	−	0.964127i	$-0.585517\pi$
$773$	−14.7600	−0.530880	−0.265440	+	0.964127i	$0.585517\pi$
$774$	6.35547	0.228443
$775$	10.1163	0.363389
$776$	113.082	4.05939
$777$	−9.75333	−0.349899
$778$	−42.9232	−1.53887
$779$	6.46531	0.231644
$780$	−16.1072	−0.576729
$781$	18.4115	0.658817
$782$	37.9426	1.35682
$783$	31.9902	1.14324
$784$	−55.9823	−1.99937
$785$	−24.4174	−0.871494
$786$	6.39127	0.227969
$787$	33.4981	1.19408	0.597040	−	0.802211i	$-0.296343\pi$
$787$	33.4981	1.19408	0.597040	+	0.802211i	$0.296343\pi$
$788$	−46.6142	−1.66056
$789$	6.55460	0.233350
$790$	7.85074	0.279317
$791$	−15.7235	−0.559062
$792$	93.8572	3.33507
$793$	−15.2975	−0.543229
$794$	73.2295	2.59882
$795$	0.227392	0.00806477
$796$	107.321	3.80390
$797$	24.1362	0.854947	0.427473	−	0.904028i	$-0.359404\pi$
$797$	24.1362	0.854947	0.427473	+	0.904028i	$0.359404\pi$
$798$	9.47886	0.335548
$799$	−26.6906	−0.944247
$800$	−18.2652	−0.645773
$801$	26.0105	0.919037
$802$	−43.3560	−1.53095
$803$	−23.3389	−0.823613
$804$	−12.0819	−0.426097
$805$	−4.64768	−0.163809
$806$	116.219	4.09364
$807$	−15.5552	−0.547570
$808$	−140.307	−4.93599
$809$	20.2042	0.710341	0.355170	−	0.934802i	$-0.384423\pi$
$809$	20.2042	0.710341	0.355170	+	0.934802i	$0.384423\pi$
$810$	−12.5347	−0.440423
$811$	20.8584	0.732439	0.366220	−	0.930528i	$-0.380652\pi$
$811$	20.8584	0.732439	0.366220	+	0.930528i	$0.380652\pi$
$812$	−71.9437	−2.52473
$813$	11.3333	0.397475
$814$	93.5667	3.27951
$815$	−8.17529	−0.286368
$816$	48.3541	1.69273
$817$	−2.77500	−0.0970848
$818$	−35.4396	−1.23912
$819$	17.7192	0.619159
$820$	−11.6539	−0.406973
$821$	−18.6210	−0.649878	−0.324939	−	0.945735i	$-0.605344\pi$
$821$	−18.6210	−0.649878	−0.324939	+	0.945735i	$0.605344\pi$
$822$	−4.14119	−0.144441
$823$	5.97187	0.208166	0.104083	−	0.994569i	$-0.466809\pi$
$823$	5.97187	0.208166	0.104083	+	0.994569i	$0.466809\pi$
$824$	47.4509	1.65303
$825$	3.05302	0.106293
$826$	7.29219	0.253728
$827$	−42.2029	−1.46754	−0.733769	−	0.679399i	$-0.762241\pi$
$827$	−42.2029	−1.46754	−0.733769	+	0.679399i	$0.762241\pi$
$828$	36.4758	1.26762
$829$	53.7949	1.86837	0.934187	−	0.356784i	$-0.116127\pi$
$829$	53.7949	1.86837	0.934187	+	0.356784i	$0.116127\pi$
$830$	−15.4399	−0.535925
$831$	3.95601	0.137232
$832$	−96.3175	−3.33921
$833$	−21.2609	−0.736648
$834$	5.91366	0.204773
$835$	−0.124966	−0.00432463
$836$	−65.9573	−2.28118
$837$	−39.7613	−1.37435
$838$	−90.0316	−3.11009
$839$	53.8247	1.85823	0.929117	−	0.369787i	$-0.120569\pi$
$839$	53.8247	1.85823	0.929117	+	0.369787i	$0.120569\pi$
$840$	−10.6159	−0.366285
$841$	37.2459	1.28434
$842$	−47.7009	−1.64388
$843$	18.6174	0.641216
$844$	−47.3102	−1.62849
$845$	5.12522	0.176313
$846$	−35.3752	−1.21623
$847$	11.9912	0.412022
$848$	4.23211	0.145331
$849$	19.9342	0.684141
$850$	−13.6628	−0.468630
$851$	22.5933	0.774487
$852$	16.3437	0.559926
$853$	15.1118	0.517417	0.258708	−	0.965956i	$-0.416703\pi$
$853$	15.1118	0.517417	0.258708	+	0.965956i	$0.416703\pi$
$854$	−16.2271	−0.555278
$855$	7.28677	0.249202
$856$	−125.758	−4.29832
$857$	−22.1192	−0.755579	−0.377789	−	0.925892i	$-0.623316\pi$
$857$	−22.1192	−0.755579	−0.377789	+	0.925892i	$0.623316\pi$
$858$	35.0739	1.19740
$859$	42.4226	1.44744	0.723721	−	0.690093i	$-0.242430\pi$
$859$	42.4226	1.44744	0.723721	+	0.690093i	$0.242430\pi$
$860$	5.00202	0.170568
$861$	−2.64527	−0.0901505
$862$	−44.7062	−1.52270
$863$	12.8185	0.436348	0.218174	−	0.975910i	$-0.429990\pi$
$863$	12.8185	0.436348	0.218174	+	0.975910i	$0.429990\pi$
$864$	71.7898	2.44234
$865$	−12.4615	−0.423704
$866$	2.18554	0.0742676
$867$	6.18632	0.210098
$868$	89.4202	3.03512
$869$	−12.3998	−0.420634
$870$	15.7328	0.533391
$871$	13.5957	0.460672
$872$	−24.0194	−0.813399
$873$	31.7577	1.07483
$874$	−21.9574	−0.742722
$875$	1.67359	0.0565776
$876$	−20.7177	−0.699986
$877$	52.1473	1.76089	0.880445	−	0.474148i	$-0.157244\pi$
$877$	52.1473	1.76089	0.880445	+	0.474148i	$0.157244\pi$
$878$	7.58514	0.255986
$879$	−5.85109	−0.197352
$880$	56.8214	1.91545
$881$	−26.0449	−0.877476	−0.438738	−	0.898615i	$-0.644574\pi$
$881$	−26.0449	−0.877476	−0.438738	+	0.898615i	$0.644574\pi$
$882$	−28.1788	−0.948830
$883$	−49.8067	−1.67613	−0.838064	−	0.545572i	$-0.816313\pi$
$883$	−49.8067	−1.67613	−0.838064	+	0.545572i	$0.816313\pi$
$884$	−113.850	−3.82918
$885$	−1.15667	−0.0388810
$886$	44.3859	1.49117
$887$	−26.9690	−0.905531	−0.452766	−	0.891630i	$-0.649563\pi$
$887$	−26.9690	−0.905531	−0.452766	+	0.891630i	$0.649563\pi$
$888$	51.6061	1.73179
$889$	−28.8153	−0.966434
$890$	28.2234	0.946050
$891$	19.7978	0.663251
$892$	98.0293	3.28226
$893$	15.4459	0.516878
$894$	12.6407	0.422767
$895$	11.6552	0.389590
$896$	−41.0335	−1.37083
$897$	8.46919	0.282778
$898$	−68.8906	−2.29891
$899$	−82.3383	−2.74614
$900$	−13.1346	−0.437821
$901$	1.60727	0.0535459
$902$	25.3769	0.844958
$903$	1.13538	0.0377832
$904$	83.1948	2.76702
$905$	−19.4415	−0.646256
$906$	17.4044	0.578222
$907$	52.1943	1.73308	0.866541	−	0.499105i	$-0.166338\pi$
$907$	52.1943	1.73308	0.866541	+	0.499105i	$0.166338\pi$
$908$	51.3992	1.70574
$909$	−39.4037	−1.30694
$910$	19.2266	0.637357
$911$	−6.77842	−0.224579	−0.112289	−	0.993676i	$-0.535818\pi$
$911$	−6.77842	−0.224579	−0.112289	+	0.993676i	$0.535818\pi$
$912$	−27.9826	−0.926598
$913$	24.3864	0.807072
$914$	44.4754	1.47112
$915$	2.57389	0.0850903
$916$	50.9909	1.68479
$917$	−5.53363	−0.182737
$918$	53.7003	1.77237
$919$	−10.1385	−0.334439	−0.167220	−	0.985920i	$-0.553479\pi$
$919$	−10.1385	−0.334439	−0.167220	+	0.985920i	$0.553479\pi$
$920$	24.5915	0.810756
$921$	1.35737	0.0447270
$922$	10.5597	0.347766
$923$	−18.3914	−0.605360
$924$	26.9863	0.887784
$925$	−8.13563	−0.267498
$926$	−20.9807	−0.689467
$927$	13.3260	0.437685
$928$	148.664	4.88012
$929$	−30.1562	−0.989393	−0.494696	−	0.869066i	$-0.664721\pi$
$929$	−30.1562	−0.989393	−0.494696	+	0.869066i	$0.664721\pi$
$930$	−19.5546	−0.641220
$931$	12.3037	0.403239
$932$	−0.876800	−0.0287205
$933$	4.63168	0.151634
$934$	70.4183	2.30416
$935$	21.5796	0.705729
$936$	−93.7545	−3.06446
$937$	−50.7129	−1.65672	−0.828359	−	0.560198i	$-0.810725\pi$
$937$	−50.7129	−1.65672	−0.828359	+	0.560198i	$0.810725\pi$
$938$	14.4219	0.470890
$939$	−9.05583	−0.295526
$940$	−27.8418	−0.908099
$941$	−31.2941	−1.02016	−0.510080	−	0.860127i	$-0.670384\pi$
$941$	−31.2941	−1.02016	−0.510080	+	0.860127i	$0.670384\pi$
$942$	47.1982	1.53780
$943$	6.12768	0.199545
$944$	−21.5273	−0.700655
$945$	−6.57789	−0.213979
$946$	−10.8921	−0.354133
$947$	−37.0450	−1.20380	−0.601900	−	0.798571i	$-0.705590\pi$
$947$	−37.0450	−1.20380	−0.601900	+	0.798571i	$0.705590\pi$
$948$	−11.0071	−0.357495
$949$	23.3134	0.756785
$950$	7.90668	0.256527
$951$	8.44051	0.273702
$952$	−75.0364	−2.43194
$953$	24.5055	0.793810	0.396905	−	0.917860i	$-0.370084\pi$
$953$	24.5055	0.793810	0.396905	+	0.917860i	$0.370084\pi$
$954$	2.13024	0.0689691
$955$	5.26482	0.170366
$956$	−58.7600	−1.90044
$957$	−24.8490	−0.803255
$958$	−48.8722	−1.57899
$959$	3.58549	0.115781
$960$	16.2060	0.523047
$961$	71.3399	2.30129
$962$	−93.4643	−3.01341
$963$	−35.3177	−1.13810
$964$	−119.976	−3.86418
$965$	−12.1365	−0.390686
$966$	8.98384	0.289050
$967$	45.6586	1.46828	0.734141	−	0.678997i	$-0.237585\pi$
$967$	45.6586	1.46828	0.734141	+	0.678997i	$0.237585\pi$
$968$	−63.4469	−2.03926
$969$	−10.6272	−0.341396
$970$	34.4594	1.10643
$971$	−46.7481	−1.50022	−0.750109	−	0.661314i	$-0.769999\pi$
$971$	−46.7481	−1.50022	−0.750109	+	0.661314i	$0.769999\pi$
$972$	79.8506	2.56121
$973$	−5.12011	−0.164143
$974$	59.7624	1.91491
$975$	−3.04968	−0.0976680
$976$	47.9041	1.53337
$977$	−55.2715	−1.76829	−0.884145	−	0.467212i	$-0.845259\pi$
$977$	−55.2715	−1.76829	−0.884145	+	0.467212i	$0.845259\pi$
$978$	15.8026	0.505312
$979$	−44.5772	−1.42469
$980$	−22.1779	−0.708447
$981$	−6.74557	−0.215370
$982$	50.5478	1.61304
$983$	0.302454	0.00964678	0.00482339	−	0.999988i	$-0.498465\pi$
$983$	0.302454	0.00964678	0.00482339	+	0.999988i	$0.498465\pi$
$984$	13.9964	0.446190
$985$	−8.82580	−0.281213
$986$	111.204	3.54144
$987$	−6.31967	−0.201157
$988$	65.8851	2.09608
$989$	−2.63008	−0.0836316
$990$	28.6012	0.909005
$991$	33.7549	1.07226	0.536129	−	0.844136i	$-0.319886\pi$
$991$	33.7549	1.07226	0.536129	+	0.844136i	$0.319886\pi$
$992$	−184.777	−5.86667
$993$	−12.7427	−0.404376
$994$	−19.5090	−0.618788
$995$	20.3199	0.644184
$996$	21.6475	0.685927
$997$	−51.6440	−1.63558	−0.817791	−	0.575516i	$-0.804801\pi$
$997$	−51.6440	−1.63558	−0.817791	+	0.575516i	$0.804801\pi$
$998$	24.5943	0.778519
$999$	31.9763	1.01169

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6005.2.a.e.1.3	✓	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6005.2.a.e.1.3	✓	88	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:	\( N \)	\(=\)	\( 6005 = 5 \cdot 1201 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.69844 q^{2} +0.716329 q^{3} +5.28159 q^{4} +1.00000 q^{5} -1.93297 q^{6} +1.67359 q^{7} -8.85517 q^{8} -2.48687 q^{9} +O(q^{10})\)	\(q-2.69844 q^{2} +0.716329 q^{3} +5.28159 q^{4} +1.00000 q^{5} -1.93297 q^{6} +1.67359 q^{7} -8.85517 q^{8} -2.48687 q^{9} -2.69844 q^{10} +4.26204 q^{11} +3.78336 q^{12} -4.25737 q^{13} -4.51608 q^{14} +0.716329 q^{15} +13.3320 q^{16} +5.06321 q^{17} +6.71068 q^{18} -2.93009 q^{19} +5.28159 q^{20} +1.19884 q^{21} -11.5009 q^{22} -2.77707 q^{23} -6.34322 q^{24} +1.00000 q^{25} +11.4883 q^{26} -3.93041 q^{27} +8.83921 q^{28} -8.13916 q^{29} -1.93297 q^{30} +10.1163 q^{31} -18.2652 q^{32} +3.05302 q^{33} -13.6628 q^{34} +1.67359 q^{35} -13.1346 q^{36} -8.13563 q^{37} +7.90668 q^{38} -3.04968 q^{39} -8.85517 q^{40} -2.20652 q^{41} -3.23500 q^{42} +0.947068 q^{43} +22.5103 q^{44} -2.48687 q^{45} +7.49377 q^{46} -5.27148 q^{47} +9.55009 q^{48} -4.19910 q^{49} -2.69844 q^{50} +3.62693 q^{51} -22.4857 q^{52} +0.317441 q^{53} +10.6060 q^{54} +4.26204 q^{55} -14.8199 q^{56} -2.09891 q^{57} +21.9630 q^{58} -1.61471 q^{59} +3.78336 q^{60} +3.59317 q^{61} -27.2983 q^{62} -4.16200 q^{63} +22.6237 q^{64} -4.25737 q^{65} -8.23840 q^{66} -3.19344 q^{67} +26.7418 q^{68} -1.98930 q^{69} -4.51608 q^{70} +4.31989 q^{71} +22.0217 q^{72} -5.47601 q^{73} +21.9535 q^{74} +0.716329 q^{75} -15.4755 q^{76} +7.13290 q^{77} +8.22939 q^{78} -2.90936 q^{79} +13.3320 q^{80} +4.64515 q^{81} +5.95417 q^{82} +5.72177 q^{83} +6.33178 q^{84} +5.06321 q^{85} -2.55561 q^{86} -5.83032 q^{87} -37.7411 q^{88} -10.4591 q^{89} +6.71068 q^{90} -7.12509 q^{91} -14.6674 q^{92} +7.24662 q^{93} +14.2248 q^{94} -2.93009 q^{95} -13.0839 q^{96} -12.7701 q^{97} +11.3310 q^{98} -10.5991 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 14 q^{2} - 34 q^{3} + 66 q^{4} + 88 q^{5} - q^{6} - 35 q^{7} - 39 q^{8} + 72 q^{9}+O(q^{10}) \) 88 * q - 14 * q^2 - 34 * q^3 + 66 * q^4 + 88 * q^5 - q^6 - 35 * q^7 - 39 * q^8 + 72 * q^9	\( 88 q - 14 q^{2} - 34 q^{3} + 66 q^{4} + 88 q^{5} - q^{6} - 35 q^{7} - 39 q^{8} + 72 q^{9} - 14 q^{10} - 26 q^{11} - 64 q^{12} - 31 q^{13} - 17 q^{14} - 34 q^{15} + 34 q^{16} - 31 q^{17} - 42 q^{18} - 56 q^{19} + 66 q^{20} - q^{21} - 49 q^{22} - 74 q^{23} - 3 q^{24} + 88 q^{25} - q^{26} - 130 q^{27} - 57 q^{28} - 6 q^{29} - q^{30} - 37 q^{31} - 87 q^{32} - 43 q^{33} - 35 q^{34} - 35 q^{35} + 53 q^{36} - 67 q^{37} - 40 q^{38} - 21 q^{39} - 39 q^{40} + 2 q^{41} - 15 q^{42} - 136 q^{43} - 15 q^{44} + 72 q^{45} - 16 q^{46} - 139 q^{47} - 71 q^{48} + 41 q^{49} - 14 q^{50} - 71 q^{51} - 71 q^{52} - 75 q^{53} + 26 q^{54} - 26 q^{55} - 22 q^{56} - 34 q^{57} - 65 q^{58} - 41 q^{59} - 64 q^{60} - 11 q^{61} - 30 q^{62} - 114 q^{63} - 33 q^{64} - 31 q^{65} + 24 q^{66} - 209 q^{67} - 42 q^{68} - 22 q^{69} - 17 q^{70} - 43 q^{71} - 80 q^{72} - 50 q^{73} + 9 q^{74} - 34 q^{75} - 62 q^{76} - 49 q^{77} - 19 q^{78} - 77 q^{79} + 34 q^{80} + 72 q^{81} - 107 q^{82} - 113 q^{83} + 19 q^{84} - 31 q^{85} + 14 q^{86} - 87 q^{87} - 107 q^{88} - 5 q^{89} - 42 q^{90} - 159 q^{91} - 100 q^{92} - 82 q^{93} - 31 q^{94} - 56 q^{95} + 58 q^{96} - 105 q^{97} - 29 q^{98} - 68 q^{99}+O(q^{100}) \) 88 * q - 14 * q^2 - 34 * q^3 + 66 * q^4 + 88 * q^5 - q^6 - 35 * q^7 - 39 * q^8 + 72 * q^9 - 14 * q^10 - 26 * q^11 - 64 * q^12 - 31 * q^13 - 17 * q^14 - 34 * q^15 + 34 * q^16 - 31 * q^17 - 42 * q^18 - 56 * q^19 + 66 * q^20 - q^21 - 49 * q^22 - 74 * q^23 - 3 * q^24 + 88 * q^25 - q^26 - 130 * q^27 - 57 * q^28 - 6 * q^29 - q^30 - 37 * q^31 - 87 * q^32 - 43 * q^33 - 35 * q^34 - 35 * q^35 + 53 * q^36 - 67 * q^37 - 40 * q^38 - 21 * q^39 - 39 * q^40 + 2 * q^41 - 15 * q^42 - 136 * q^43 - 15 * q^44 + 72 * q^45 - 16 * q^46 - 139 * q^47 - 71 * q^48 + 41 * q^49 - 14 * q^50 - 71 * q^51 - 71 * q^52 - 75 * q^53 + 26 * q^54 - 26 * q^55 - 22 * q^56 - 34 * q^57 - 65 * q^58 - 41 * q^59 - 64 * q^60 - 11 * q^61 - 30 * q^62 - 114 * q^63 - 33 * q^64 - 31 * q^65 + 24 * q^66 - 209 * q^67 - 42 * q^68 - 22 * q^69 - 17 * q^70 - 43 * q^71 - 80 * q^72 - 50 * q^73 + 9 * q^74 - 34 * q^75 - 62 * q^76 - 49 * q^77 - 19 * q^78 - 77 * q^79 + 34 * q^80 + 72 * q^81 - 107 * q^82 - 113 * q^83 + 19 * q^84 - 31 * q^85 + 14 * q^86 - 87 * q^87 - 107 * q^88 - 5 * q^89 - 42 * q^90 - 159 * q^91 - 100 * q^92 - 82 * q^93 - 31 * q^94 - 56 * q^95 + 58 * q^96 - 105 * q^97 - 29 * q^98 - 68 * q^99

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