LMFDB - Embedded newform 8041.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$1$
Dimension:	$62$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.76025 q^{2} +2.03734 q^{3} +5.61901 q^{4} -1.74676 q^{5} -5.62359 q^{6} +0.752232 q^{7} -9.98938 q^{8} +1.15077 q^{9} +O(q^{10})$	\(q-2.76025 q^{2} +2.03734 q^{3} +5.61901 q^{4} -1.74676 q^{5} -5.62359 q^{6} +0.752232 q^{7} -9.98938 q^{8} +1.15077 q^{9} +4.82150 q^{10} +1.00000 q^{11} +11.4478 q^{12} +4.52896 q^{13} -2.07635 q^{14} -3.55875 q^{15} +16.3352 q^{16} -1.00000 q^{17} -3.17641 q^{18} +1.06391 q^{19} -9.81506 q^{20} +1.53256 q^{21} -2.76025 q^{22} +3.11782 q^{23} -20.3518 q^{24} -1.94883 q^{25} -12.5011 q^{26} -3.76752 q^{27} +4.22680 q^{28} -4.87542 q^{29} +9.82306 q^{30} +1.70626 q^{31} -25.1106 q^{32} +2.03734 q^{33} +2.76025 q^{34} -1.31397 q^{35} +6.46617 q^{36} +4.18155 q^{37} -2.93666 q^{38} +9.22705 q^{39} +17.4490 q^{40} +4.86129 q^{41} -4.23024 q^{42} +1.00000 q^{43} +5.61901 q^{44} -2.01012 q^{45} -8.60597 q^{46} -4.89953 q^{47} +33.2805 q^{48} -6.43415 q^{49} +5.37927 q^{50} -2.03734 q^{51} +25.4483 q^{52} -13.7224 q^{53} +10.3993 q^{54} -1.74676 q^{55} -7.51433 q^{56} +2.16754 q^{57} +13.4574 q^{58} -11.9804 q^{59} -19.9966 q^{60} -5.21846 q^{61} -4.70972 q^{62} +0.865645 q^{63} +36.6412 q^{64} -7.91101 q^{65} -5.62359 q^{66} -15.8971 q^{67} -5.61901 q^{68} +6.35207 q^{69} +3.62689 q^{70} +1.37961 q^{71} -11.4955 q^{72} -0.0721326 q^{73} -11.5421 q^{74} -3.97044 q^{75} +5.97810 q^{76} +0.752232 q^{77} -25.4690 q^{78} -1.47368 q^{79} -28.5337 q^{80} -11.1280 q^{81} -13.4184 q^{82} +0.0601585 q^{83} +8.61144 q^{84} +1.74676 q^{85} -2.76025 q^{86} -9.93290 q^{87} -9.98938 q^{88} -7.97441 q^{89} +5.54843 q^{90} +3.40683 q^{91} +17.5190 q^{92} +3.47624 q^{93} +13.5239 q^{94} -1.85839 q^{95} -51.1589 q^{96} -13.5288 q^{97} +17.7599 q^{98} +1.15077 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9}+O(q^{10}) $ 62 * q - 7 * q^2 - 8 * q^3 + 49 * q^4 - 13 * q^5 - 2 * q^6 - 11 * q^7 - 9 * q^8 + 40 * q^9	\( 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9} - 7 q^{10} + 62 q^{11} - 17 q^{12} - 31 q^{14} - 20 q^{15} + 27 q^{16} - 62 q^{17} + 3 q^{18} - 29 q^{20} - 18 q^{21} - 7 q^{22} - 50 q^{23} - 31 q^{24} + 35 q^{25} - 32 q^{26} - 14 q^{27} - 13 q^{28} - 26 q^{29} - 10 q^{30} - 58 q^{31} - 5 q^{32} - 8 q^{33} + 7 q^{34} - 32 q^{35} - 29 q^{36} - 41 q^{37} - 10 q^{38} - 53 q^{39} - 31 q^{40} - 55 q^{41} - 7 q^{42} + 62 q^{43} + 49 q^{44} - 34 q^{45} - 39 q^{46} - 31 q^{47} - 30 q^{48} + 35 q^{49} - 40 q^{50} + 8 q^{51} + 13 q^{52} - 74 q^{53} + 48 q^{54} - 13 q^{55} - 75 q^{56} - 43 q^{57} - 46 q^{58} - 65 q^{59} - 8 q^{60} - 14 q^{61} - 29 q^{62} - 23 q^{63} - 15 q^{64} - 9 q^{65} - 2 q^{66} - q^{67} - 49 q^{68} - 59 q^{69} - 31 q^{70} - 141 q^{71} + 9 q^{72} - 4 q^{73} - 94 q^{74} - 43 q^{75} + 34 q^{76} - 11 q^{77} - 11 q^{78} - 63 q^{79} - 41 q^{80} - 30 q^{81} + 38 q^{82} - 44 q^{83} - 16 q^{84} + 13 q^{85} - 7 q^{86} - 8 q^{87} - 9 q^{88} - 58 q^{89} - 55 q^{90} - 78 q^{91} - 104 q^{92} - 5 q^{94} - 99 q^{95} - 148 q^{96} - 26 q^{97} + 16 q^{98} + 40 q^{99}+O(q^{100}) \) 62 * q - 7 * q^2 - 8 * q^3 + 49 * q^4 - 13 * q^5 - 2 * q^6 - 11 * q^7 - 9 * q^8 + 40 * q^9 - 7 * q^10 + 62 * q^11 - 17 * q^12 - 31 * q^14 - 20 * q^15 + 27 * q^16 - 62 * q^17 + 3 * q^18 - 29 * q^20 - 18 * q^21 - 7 * q^22 - 50 * q^23 - 31 * q^24 + 35 * q^25 - 32 * q^26 - 14 * q^27 - 13 * q^28 - 26 * q^29 - 10 * q^30 - 58 * q^31 - 5 * q^32 - 8 * q^33 + 7 * q^34 - 32 * q^35 - 29 * q^36 - 41 * q^37 - 10 * q^38 - 53 * q^39 - 31 * q^40 - 55 * q^41 - 7 * q^42 + 62 * q^43 + 49 * q^44 - 34 * q^45 - 39 * q^46 - 31 * q^47 - 30 * q^48 + 35 * q^49 - 40 * q^50 + 8 * q^51 + 13 * q^52 - 74 * q^53 + 48 * q^54 - 13 * q^55 - 75 * q^56 - 43 * q^57 - 46 * q^58 - 65 * q^59 - 8 * q^60 - 14 * q^61 - 29 * q^62 - 23 * q^63 - 15 * q^64 - 9 * q^65 - 2 * q^66 - q^67 - 49 * q^68 - 59 * q^69 - 31 * q^70 - 141 * q^71 + 9 * q^72 - 4 * q^73 - 94 * q^74 - 43 * q^75 + 34 * q^76 - 11 * q^77 - 11 * q^78 - 63 * q^79 - 41 * q^80 - 30 * q^81 + 38 * q^82 - 44 * q^83 - 16 * q^84 + 13 * q^85 - 7 * q^86 - 8 * q^87 - 9 * q^88 - 58 * q^89 - 55 * q^90 - 78 * q^91 - 104 * q^92 - 5 * q^94 - 99 * q^95 - 148 * q^96 - 26 * q^97 + 16 * q^98 + 40 * 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 $

$2$	−2.76025	−1.95179	−0.975897	−	0.218230i	$-0.929972\pi$
$2$	−2.76025	−1.95179	−0.975897	+	0.218230i	$0.929972\pi$
$3$	2.03734	1.17626	0.588130	−	0.808766i	$-0.299864\pi$
$3$	2.03734	1.17626	0.588130	+	0.808766i	$0.299864\pi$
$4$	5.61901	2.80950
$5$	−1.74676	−0.781175	−0.390587	−	0.920566i	$-0.627728\pi$
$5$	−1.74676	−0.781175	−0.390587	+	0.920566i	$0.627728\pi$
$6$	−5.62359	−2.29582
$7$	0.752232	0.284317	0.142159	−	0.989844i	$-0.454596\pi$
$7$	0.752232	0.284317	0.142159	+	0.989844i	$0.454596\pi$
$8$	−9.98938	−3.53178
$9$	1.15077	0.383589
$10$	4.82150	1.52469
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	11.4478	3.30471
$13$	4.52896	1.25611	0.628054	−	0.778170i	$-0.283852\pi$
$13$	4.52896	1.25611	0.628054	+	0.778170i	$0.283852\pi$
$14$	−2.07635	−0.554929
$15$	−3.55875	−0.918865
$16$	16.3352	4.08381
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−3.17641	−0.748688
$19$	1.06391	0.244077	0.122039	−	0.992525i	$-0.461057\pi$
$19$	1.06391	0.244077	0.122039	+	0.992525i	$0.461057\pi$
$20$	−9.81506	−2.19471
$21$	1.53256	0.334431
$22$	−2.76025	−0.588488
$23$	3.11782	0.650110	0.325055	−	0.945695i	$-0.394617\pi$
$23$	3.11782	0.650110	0.325055	+	0.945695i	$0.394617\pi$
$24$	−20.3518	−4.15429
$25$	−1.94883	−0.389766
$26$	−12.5011	−2.45167
$27$	−3.76752	−0.725060
$28$	4.22680	0.798790
$29$	−4.87542	−0.905342	−0.452671	−	0.891678i	$-0.649529\pi$
$29$	−4.87542	−0.905342	−0.452671	+	0.891678i	$0.649529\pi$
$30$	9.82306	1.79344
$31$	1.70626	0.306454	0.153227	−	0.988191i	$-0.451033\pi$
$31$	1.70626	0.306454	0.153227	+	0.988191i	$0.451033\pi$
$32$	−25.1106	−4.43897
$33$	2.03734	0.354656
$34$	2.76025	0.473380
$35$	−1.31397	−0.222101
$36$	6.46617	1.07770
$37$	4.18155	0.687442	0.343721	−	0.939072i	$-0.388313\pi$
$37$	4.18155	0.687442	0.343721	+	0.939072i	$0.388313\pi$
$38$	−2.93666	−0.476388
$39$	9.22705	1.47751
$40$	17.4490	2.75894
$41$	4.86129	0.759206	0.379603	−	0.925149i	$-0.376061\pi$
$41$	4.86129	0.759206	0.379603	+	0.925149i	$0.376061\pi$
$42$	−4.23024	−0.652741
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	5.61901	0.847097
$45$	−2.01012	−0.299650
$46$	−8.60597	−1.26888
$47$	−4.89953	−0.714669	−0.357335	−	0.933976i	$-0.616314\pi$
$47$	−4.89953	−0.714669	−0.357335	+	0.933976i	$0.616314\pi$
$48$	33.2805	4.80362
$49$	−6.43415	−0.919164
$50$	5.37927	0.760743
$51$	−2.03734	−0.285285
$52$	25.4483	3.52904
$53$	−13.7224	−1.88491	−0.942456	−	0.334331i	$-0.891490\pi$
$53$	−13.7224	−1.88491	−0.942456	+	0.334331i	$0.891490\pi$
$54$	10.3993	1.41517
$55$	−1.74676	−0.235533
$56$	−7.51433	−1.00415
$57$	2.16754	0.287098
$58$	13.4574	1.76704
$59$	−11.9804	−1.55972	−0.779860	−	0.625954i	$-0.784710\pi$
$59$	−11.9804	−1.55972	−0.779860	+	0.625954i	$0.784710\pi$
$60$	−19.9966	−2.58155
$61$	−5.21846	−0.668156	−0.334078	−	0.942546i	$-0.608425\pi$
$61$	−5.21846	−0.668156	−0.334078	+	0.942546i	$0.608425\pi$
$62$	−4.70972	−0.598135
$63$	0.865645	0.109061
$64$	36.6412	4.58016
$65$	−7.91101	−0.981240
$66$	−5.62359	−0.692216
$67$	−15.8971	−1.94213	−0.971067	−	0.238807i	$-0.923244\pi$
$67$	−15.8971	−1.94213	−0.971067	+	0.238807i	$0.923244\pi$
$68$	−5.61901	−0.681405
$69$	6.35207	0.764699
$70$	3.62689	0.433496
$71$	1.37961	0.163729	0.0818645	−	0.996643i	$-0.473913\pi$
$71$	1.37961	0.163729	0.0818645	+	0.996643i	$0.473913\pi$
$72$	−11.4955	−1.35475
$73$	−0.0721326	−0.00844248	−0.00422124	−	0.999991i	$-0.501344\pi$
$73$	−0.0721326	−0.00844248	−0.00422124	+	0.999991i	$0.501344\pi$
$74$	−11.5421	−1.34175
$75$	−3.97044	−0.458466
$76$	5.97810	0.685735
$77$	0.752232	0.0857248
$78$	−25.4690	−2.88380
$79$	−1.47368	−0.165802	−0.0829008	−	0.996558i	$-0.526418\pi$
$79$	−1.47368	−0.165802	−0.0829008	+	0.996558i	$0.526418\pi$
$80$	−28.5337	−3.19017
$81$	−11.1280	−1.23645
$82$	−13.4184	−1.48181
$83$	0.0601585	0.00660326	0.00330163	−	0.999995i	$-0.498949\pi$
$83$	0.0601585	0.00660326	0.00330163	+	0.999995i	$0.498949\pi$
$84$	8.61144	0.939585
$85$	1.74676	0.189463
$86$	−2.76025	−0.297646
$87$	−9.93290	−1.06492
$88$	−9.98938	−1.06487
$89$	−7.97441	−0.845286	−0.422643	−	0.906296i	$-0.638898\pi$
$89$	−7.97441	−0.845286	−0.422643	+	0.906296i	$0.638898\pi$
$90$	5.54843	0.584856
$91$	3.40683	0.357133
$92$	17.5190	1.82649
$93$	3.47624	0.360470
$94$	13.5239	1.39489
$95$	−1.85839	−0.190667
$96$	−51.1589	−5.22139
$97$	−13.5288	−1.37364	−0.686819	−	0.726828i	$-0.740994\pi$
$97$	−13.5288	−1.37364	−0.686819	+	0.726828i	$0.740994\pi$
$98$	17.7599	1.79402
$99$	1.15077	0.115657
$100$	−10.9505	−1.09505
$101$	−6.51298	−0.648066	−0.324033	−	0.946046i	$-0.605039\pi$
$101$	−6.51298	−0.648066	−0.324033	+	0.946046i	$0.605039\pi$
$102$	5.62359	0.556818
$103$	17.2562	1.70031	0.850153	−	0.526536i	$-0.176509\pi$
$103$	17.2562	1.70031	0.850153	+	0.526536i	$0.176509\pi$
$104$	−45.2415	−4.43630
$105$	−2.67701	−0.261249
$106$	37.8772	3.67896
$107$	15.1868	1.46816	0.734082	−	0.679061i	$-0.237613\pi$
$107$	15.1868	1.46816	0.734082	+	0.679061i	$0.237613\pi$
$108$	−21.1697	−2.03706
$109$	−1.09984	−0.105345	−0.0526727	−	0.998612i	$-0.516774\pi$
$109$	−1.09984	−0.105345	−0.0526727	+	0.998612i	$0.516774\pi$
$110$	4.82150	0.459712
$111$	8.51925	0.808611
$112$	12.2879	1.16110
$113$	2.80583	0.263950	0.131975	−	0.991253i	$-0.457868\pi$
$113$	2.80583	0.263950	0.131975	+	0.991253i	$0.457868\pi$
$114$	−5.98298	−0.560357
$115$	−5.44608	−0.507850
$116$	−27.3950	−2.54356
$117$	5.21179	0.481830
$118$	33.0690	3.04425
$119$	−0.752232	−0.0689570
$120$	35.5497	3.24523
$121$	1.00000	0.0909091
$122$	14.4043	1.30410
$123$	9.90412	0.893024
$124$	9.58750	0.860983
$125$	12.1379	1.08565
$126$	−2.38940	−0.212865
$127$	−5.78281	−0.513142	−0.256571	−	0.966525i	$-0.582593\pi$
$127$	−5.78281	−0.513142	−0.256571	+	0.966525i	$0.582593\pi$
$128$	−50.9180	−4.50055
$129$	2.03734	0.179378
$130$	21.8364	1.91518
$131$	10.3824	0.907118	0.453559	−	0.891226i	$-0.350154\pi$
$131$	10.3824	0.907118	0.453559	+	0.891226i	$0.350154\pi$
$132$	11.4478	0.996407
$133$	0.800306	0.0693953
$134$	43.8799	3.79065
$135$	6.58095	0.566398
$136$	9.98938	0.856582
$137$	3.75798	0.321066	0.160533	−	0.987030i	$-0.448679\pi$
$137$	3.75798	0.321066	0.160533	+	0.987030i	$0.448679\pi$
$138$	−17.5333	−1.49254
$139$	1.10036	0.0933317	0.0466659	−	0.998911i	$-0.485140\pi$
$139$	1.10036	0.0933317	0.0466659	+	0.998911i	$0.485140\pi$
$140$	−7.38320	−0.623994
$141$	−9.98202	−0.840638
$142$	−3.80806	−0.319566
$143$	4.52896	0.378731
$144$	18.7981	1.56650
$145$	8.51618	0.707230
$146$	0.199104	0.0164780
$147$	−13.1086	−1.08118
$148$	23.4961	1.93137
$149$	4.02170	0.329470	0.164735	−	0.986338i	$-0.447323\pi$
$149$	4.02170	0.329470	0.164735	+	0.986338i	$0.447323\pi$
$150$	10.9594	0.894832
$151$	16.7655	1.36436	0.682178	−	0.731186i	$-0.261033\pi$
$151$	16.7655	1.36436	0.682178	+	0.731186i	$0.261033\pi$
$152$	−10.6278	−0.862026
$153$	−1.15077	−0.0930341
$154$	−2.07635	−0.167317
$155$	−2.98043	−0.239394
$156$	51.8469	4.15107
$157$	18.6101	1.48525	0.742625	−	0.669707i	$-0.233580\pi$
$157$	18.6101	1.48525	0.742625	+	0.669707i	$0.233580\pi$
$158$	4.06772	0.323611
$159$	−27.9572	−2.21715
$160$	43.8622	3.46761
$161$	2.34532	0.184837
$162$	30.7162	2.41329
$163$	−12.7666	−0.999959	−0.499979	−	0.866037i	$-0.666659\pi$
$163$	−12.7666	−0.999959	−0.499979	+	0.866037i	$0.666659\pi$
$164$	27.3156	2.13299
$165$	−3.55875	−0.277048
$166$	−0.166053	−0.0128882
$167$	−23.8112	−1.84256	−0.921282	−	0.388894i	$-0.872857\pi$
$167$	−23.8112	−1.84256	−0.921282	+	0.388894i	$0.872857\pi$
$168$	−15.3093	−1.18114
$169$	7.51151	0.577808
$170$	−4.82150	−0.369792
$171$	1.22431	0.0936254
$172$	5.61901	0.428445
$173$	−9.00012	−0.684266	−0.342133	−	0.939651i	$-0.611149\pi$
$173$	−9.00012	−0.684266	−0.342133	+	0.939651i	$0.611149\pi$
$174$	27.4173	2.07850
$175$	−1.46597	−0.110817
$176$	16.3352	1.23131
$177$	−24.4083	−1.83464
$178$	22.0114	1.64983
$179$	−3.43498	−0.256742	−0.128371	−	0.991726i	$-0.540975\pi$
$179$	−3.43498	−0.256742	−0.128371	+	0.991726i	$0.540975\pi$
$180$	−11.2949	−0.841869
$181$	−8.47922	−0.630256	−0.315128	−	0.949049i	$-0.602047\pi$
$181$	−8.47922	−0.630256	−0.315128	+	0.949049i	$0.602047\pi$
$182$	−9.40373	−0.697051
$183$	−10.6318	−0.785925
$184$	−31.1451	−2.29605
$185$	−7.30416	−0.537012
$186$	−9.59532	−0.703563
$187$	−1.00000	−0.0731272
$188$	−27.5305	−2.00787
$189$	−2.83405	−0.206147
$190$	5.12963	0.372143
$191$	−12.9953	−0.940310	−0.470155	−	0.882584i	$-0.655802\pi$
$191$	−12.9953	−0.940310	−0.470155	+	0.882584i	$0.655802\pi$
$192$	74.6508	5.38746
$193$	−5.32205	−0.383090	−0.191545	−	0.981484i	$-0.561350\pi$
$193$	−5.32205	−0.383090	−0.191545	+	0.981484i	$0.561350\pi$
$194$	37.3428	2.68106
$195$	−16.1174	−1.15419
$196$	−36.1535	−2.58239
$197$	25.4009	1.80974	0.904871	−	0.425686i	$-0.139967\pi$
$197$	25.4009	1.80974	0.904871	+	0.425686i	$0.139967\pi$
$198$	−3.17641	−0.225738
$199$	25.4994	1.80760	0.903802	−	0.427951i	$-0.140764\pi$
$199$	25.4994	1.80760	0.903802	+	0.427951i	$0.140764\pi$
$200$	19.4676	1.37657
$201$	−32.3878	−2.28446
$202$	17.9775	1.26489
$203$	−3.66745	−0.257404
$204$	−11.4478	−0.801510
$205$	−8.49151	−0.593073
$206$	−47.6316	−3.31865
$207$	3.58789	0.249375
$208$	73.9816	5.12970
$209$	1.06391	0.0735920
$210$	7.38922	0.509905
$211$	6.32269	0.435272	0.217636	−	0.976030i	$-0.430165\pi$
$211$	6.32269	0.435272	0.217636	+	0.976030i	$0.430165\pi$
$212$	−77.1060	−5.29566
$213$	2.81073	0.192588
$214$	−41.9195	−2.86556
$215$	−1.74676	−0.119128
$216$	37.6352	2.56075
$217$	1.28351	0.0871301
$218$	3.03584	0.205613
$219$	−0.146959	−0.00993056
$220$	−9.81506	−0.661731
$221$	−4.52896	−0.304651
$222$	−23.5153	−1.57824
$223$	−4.34054	−0.290664	−0.145332	−	0.989383i	$-0.546425\pi$
$223$	−4.34054	−0.290664	−0.145332	+	0.989383i	$0.546425\pi$
$224$	−18.8890	−1.26208
$225$	−2.24265	−0.149510
$226$	−7.74481	−0.515177
$227$	−0.0336354	−0.00223246	−0.00111623	−	0.999999i	$-0.500355\pi$
$227$	−0.0336354	−0.00223246	−0.00111623	+	0.999999i	$0.500355\pi$
$228$	12.1794	0.806604
$229$	−21.7939	−1.44018	−0.720092	−	0.693878i	$-0.755901\pi$
$229$	−21.7939	−1.44018	−0.720092	+	0.693878i	$0.755901\pi$
$230$	15.0326	0.991218
$231$	1.53256	0.100835
$232$	48.7024	3.19747
$233$	−0.168777	−0.0110570	−0.00552849	−	0.999985i	$-0.501760\pi$
$233$	−0.168777	−0.0110570	−0.00552849	+	0.999985i	$0.501760\pi$
$234$	−14.3859	−0.940433
$235$	8.55830	0.558282
$236$	−67.3181	−4.38204
$237$	−3.00239	−0.195026
$238$	2.07635	0.134590
$239$	−8.13645	−0.526303	−0.263152	−	0.964754i	$-0.584762\pi$
$239$	−8.13645	−0.526303	−0.263152	+	0.964754i	$0.584762\pi$
$240$	−58.1330	−3.75247
$241$	6.88614	0.443575	0.221787	−	0.975095i	$-0.428811\pi$
$241$	6.88614	0.443575	0.221787	+	0.975095i	$0.428811\pi$
$242$	−2.76025	−0.177436
$243$	−11.3691	−0.729326
$244$	−29.3226	−1.87719
$245$	11.2389	0.718028
$246$	−27.3379	−1.74300
$247$	4.81840	0.306587
$248$	−17.0445	−1.08233
$249$	0.122564	0.00776715
$250$	−33.5038	−2.11897
$251$	3.12754	0.197409	0.0987044	−	0.995117i	$-0.468530\pi$
$251$	3.12754	0.197409	0.0987044	+	0.995117i	$0.468530\pi$
$252$	4.86407	0.306407
$253$	3.11782	0.196016
$254$	15.9620	1.00155
$255$	3.55875	0.222858
$256$	67.2640	4.20400
$257$	−6.23451	−0.388898	−0.194449	−	0.980913i	$-0.562292\pi$
$257$	−6.23451	−0.388898	−0.194449	+	0.980913i	$0.562292\pi$
$258$	−5.62359	−0.350109
$259$	3.14550	0.195452
$260$	−44.4520	−2.75680
$261$	−5.61047	−0.347280
$262$	−28.6582	−1.77051
$263$	21.8798	1.34916	0.674582	−	0.738200i	$-0.264324\pi$
$263$	21.8798	1.34916	0.674582	+	0.738200i	$0.264324\pi$
$264$	−20.3518	−1.25257
$265$	23.9697	1.47245
$266$	−2.20905	−0.135445
$267$	−16.2466	−0.994277
$268$	−89.3256	−5.45643
$269$	11.1045	0.677053	0.338526	−	0.940957i	$-0.390072\pi$
$269$	11.1045	0.677053	0.338526	+	0.940957i	$0.390072\pi$
$270$	−18.1651	−1.10549
$271$	2.88526	0.175267	0.0876334	−	0.996153i	$-0.472070\pi$
$271$	2.88526	0.175267	0.0876334	+	0.996153i	$0.472070\pi$
$272$	−16.3352	−0.990468
$273$	6.94089	0.420082
$274$	−10.3730	−0.626655
$275$	−1.94883	−0.117519
$276$	35.6923	2.14842
$277$	4.85952	0.291980	0.145990	−	0.989286i	$-0.453363\pi$
$277$	4.85952	0.291980	0.145990	+	0.989286i	$0.453363\pi$
$278$	−3.03729	−0.182164
$279$	1.96351	0.117552
$280$	13.1257	0.784413
$281$	−29.8297	−1.77949	−0.889744	−	0.456460i	$-0.849117\pi$
$281$	−29.8297	−1.77949	−0.889744	+	0.456460i	$0.849117\pi$
$282$	27.5529	1.64075
$283$	−5.65587	−0.336207	−0.168103	−	0.985769i	$-0.553764\pi$
$283$	−5.65587	−0.336207	−0.168103	+	0.985769i	$0.553764\pi$
$284$	7.75201	0.459997
$285$	−3.78618	−0.224274
$286$	−12.5011	−0.739205
$287$	3.65682	0.215855
$288$	−28.8965	−1.70274
$289$	1.00000	0.0588235
$290$	−23.5068	−1.38037
$291$	−27.5627	−1.61576
$292$	−0.405314	−0.0237192
$293$	−11.1946	−0.653997	−0.326999	−	0.945025i	$-0.606037\pi$
$293$	−11.1946	−0.653997	−0.326999	+	0.945025i	$0.606037\pi$
$294$	36.1830	2.11023
$295$	20.9269	1.21841
$296$	−41.7711	−2.42789
$297$	−3.76752	−0.218614
$298$	−11.1009	−0.643059
$299$	14.1205	0.816609
$300$	−22.3099	−1.28806
$301$	0.752232	0.0433580
$302$	−46.2770	−2.66294
$303$	−13.2692	−0.762295
$304$	17.3792	0.996763
$305$	9.11540	0.521946
$306$	3.17641	0.181583
$307$	−23.1513	−1.32131	−0.660656	−	0.750689i	$-0.729722\pi$
$307$	−23.1513	−1.32131	−0.660656	+	0.750689i	$0.729722\pi$
$308$	4.22680	0.240844
$309$	35.1568	2.00000
$310$	8.22675	0.467248
$311$	−6.58204	−0.373233	−0.186617	−	0.982433i	$-0.559752\pi$
$311$	−6.58204	−0.373233	−0.186617	+	0.982433i	$0.559752\pi$
$312$	−92.1725	−5.21824
$313$	1.83403	0.103666	0.0518329	−	0.998656i	$-0.483494\pi$
$313$	1.83403	0.103666	0.0518329	+	0.998656i	$0.483494\pi$
$314$	−51.3687	−2.89890
$315$	−1.51207	−0.0851957
$316$	−8.28060	−0.465820
$317$	27.3112	1.53395	0.766975	−	0.641677i	$-0.221761\pi$
$317$	27.3112	1.53395	0.766975	+	0.641677i	$0.221761\pi$
$318$	77.1689	4.32742
$319$	−4.87542	−0.272971
$320$	−64.0035	−3.57790
$321$	30.9408	1.72694
$322$	−6.47369	−0.360765
$323$	−1.06391	−0.0591974
$324$	−62.5285	−3.47381
$325$	−8.82618	−0.489588
$326$	35.2391	1.95171
$327$	−2.24075	−0.123914
$328$	−48.5613	−2.68135
$329$	−3.68558	−0.203193
$330$	9.82306	0.540741
$331$	−8.88706	−0.488477	−0.244239	−	0.969715i	$-0.578538\pi$
$331$	−8.88706	−0.488477	−0.244239	+	0.969715i	$0.578538\pi$
$332$	0.338031	0.0185519
$333$	4.81199	0.263696
$334$	65.7249	3.59631
$335$	27.7683	1.51715
$336$	25.0346	1.36575
$337$	−2.07709	−0.113146	−0.0565732	−	0.998398i	$-0.518017\pi$
$337$	−2.07709	−0.113146	−0.0565732	+	0.998398i	$0.518017\pi$
$338$	−20.7337	−1.12776
$339$	5.71644	0.310475
$340$	9.81506	0.532296
$341$	1.70626	0.0923993
$342$	−3.37941	−0.182738
$343$	−10.1056	−0.545651
$344$	−9.98938	−0.538591
$345$	−11.0955	−0.597364
$346$	24.8426	1.33555
$347$	2.57890	0.138442	0.0692212	−	0.997601i	$-0.477949\pi$
$347$	2.57890	0.138442	0.0692212	+	0.997601i	$0.477949\pi$
$348$	−55.8130	−2.99189
$349$	−23.6810	−1.26761	−0.633806	−	0.773492i	$-0.718508\pi$
$349$	−23.6810	−1.26761	−0.633806	+	0.773492i	$0.718508\pi$
$350$	4.04646	0.216292
$351$	−17.0630	−0.910753
$352$	−25.1106	−1.33840
$353$	3.31387	0.176380	0.0881898	−	0.996104i	$-0.471892\pi$
$353$	3.31387	0.176380	0.0881898	+	0.996104i	$0.471892\pi$
$354$	67.3730	3.58083
$355$	−2.40984	−0.127901
$356$	−44.8083	−2.37483
$357$	−1.53256	−0.0811114
$358$	9.48142	0.501108
$359$	−19.3351	−1.02047	−0.510233	−	0.860036i	$-0.670441\pi$
$359$	−19.3351	−1.02047	−0.510233	+	0.860036i	$0.670441\pi$
$360$	20.0798	1.05830
$361$	−17.8681	−0.940426
$362$	23.4048	1.23013
$363$	2.03734	0.106933
$364$	19.1430	1.00337
$365$	0.125998	0.00659506
$366$	29.3465	1.53396
$367$	−31.8875	−1.66451	−0.832256	−	0.554392i	$-0.812951\pi$
$367$	−31.8875	−1.66451	−0.832256	+	0.554392i	$0.812951\pi$
$368$	50.9303	2.65492
$369$	5.59422	0.291223
$370$	20.1613	1.04814
$371$	−10.3224	−0.535912
$372$	19.5330	1.01274
$373$	−34.6803	−1.79568	−0.897839	−	0.440323i	$-0.854864\pi$
$373$	−34.6803	−1.79568	−0.897839	+	0.440323i	$0.854864\pi$
$374$	2.76025	0.142729
$375$	24.7291	1.27701
$376$	48.9432	2.52405
$377$	−22.0806	−1.13721
$378$	7.82270	0.402356
$379$	−14.4100	−0.740191	−0.370095	−	0.928994i	$-0.620675\pi$
$379$	−14.4100	−0.740191	−0.370095	+	0.928994i	$0.620675\pi$
$380$	−10.4423	−0.535679
$381$	−11.7816	−0.603588
$382$	35.8705	1.83529
$383$	−1.35638	−0.0693077	−0.0346539	−	0.999399i	$-0.511033\pi$
$383$	−1.35638	−0.0693077	−0.0346539	+	0.999399i	$0.511033\pi$
$384$	−103.737	−5.29382
$385$	−1.31397	−0.0669661
$386$	14.6902	0.747713
$387$	1.15077	0.0584968
$388$	−76.0182	−3.85924
$389$	−23.2682	−1.17974	−0.589872	−	0.807497i	$-0.700822\pi$
$389$	−23.2682	−1.17974	−0.589872	+	0.807497i	$0.700822\pi$
$390$	44.4883	2.25275
$391$	−3.11782	−0.157675
$392$	64.2731	3.24628
$393$	21.1526	1.06701
$394$	−70.1131	−3.53225
$395$	2.57416	0.129520
$396$	6.46617	0.324938
$397$	21.3132	1.06968	0.534840	−	0.844953i	$-0.320372\pi$
$397$	21.3132	1.06968	0.534840	+	0.844953i	$0.320372\pi$
$398$	−70.3848	−3.52807
$399$	1.63050	0.0816270
$400$	−31.8346	−1.59173
$401$	−26.7568	−1.33617	−0.668085	−	0.744085i	$-0.732886\pi$
$401$	−26.7568	−1.33617	−0.668085	+	0.744085i	$0.732886\pi$
$402$	89.3985	4.45879
$403$	7.72760	0.384939
$404$	−36.5965	−1.82074
$405$	19.4380	0.965882
$406$	10.1231	0.502400
$407$	4.18155	0.207272
$408$	20.3518	1.00756
$409$	22.0546	1.09053	0.545266	−	0.838263i	$-0.316429\pi$
$409$	22.0546	1.09053	0.545266	+	0.838263i	$0.316429\pi$
$410$	23.4387	1.15756
$411$	7.65630	0.377658
$412$	96.9628	4.77701
$413$	−9.01207	−0.443455
$414$	−9.90348	−0.486730
$415$	−0.105083	−0.00515830
$416$	−113.725	−5.57583
$417$	2.24182	0.109782
$418$	−2.93666	−0.143637
$419$	24.3404	1.18910	0.594552	−	0.804057i	$-0.297329\pi$
$419$	24.3404	1.18910	0.594552	+	0.804057i	$0.297329\pi$
$420$	−15.0421	−0.733980
$421$	−19.9657	−0.973069	−0.486534	−	0.873661i	$-0.661739\pi$
$421$	−19.9657	−0.973069	−0.486534	+	0.873661i	$0.661739\pi$
$422$	−17.4522	−0.849561
$423$	−5.63822	−0.274140
$424$	137.078	6.65709
$425$	1.94883	0.0945321
$426$	−7.75833	−0.375892
$427$	−3.92550	−0.189968
$428$	85.3348	4.12481
$429$	9.22705	0.445486
$430$	4.82150	0.232513
$431$	−30.5489	−1.47149	−0.735745	−	0.677259i	$-0.763168\pi$
$431$	−30.5489	−1.47149	−0.735745	+	0.677259i	$0.763168\pi$
$432$	−61.5433	−2.96100
$433$	−28.7210	−1.38024	−0.690121	−	0.723694i	$-0.742443\pi$
$433$	−28.7210	−1.38024	−0.690121	+	0.723694i	$0.742443\pi$
$434$	−3.54280	−0.170060
$435$	17.3504	0.831887
$436$	−6.18000	−0.295969
$437$	3.31707	0.158677
$438$	0.405644	0.0193824
$439$	30.7482	1.46753	0.733765	−	0.679403i	$-0.237761\pi$
$439$	30.7482	1.46753	0.733765	+	0.679403i	$0.237761\pi$
$440$	17.4490	0.831851
$441$	−7.40421	−0.352582
$442$	12.5011	0.594616
$443$	7.82086	0.371580	0.185790	−	0.982589i	$-0.440516\pi$
$443$	7.82086	0.371580	0.185790	+	0.982589i	$0.440516\pi$
$444$	47.8697	2.27180
$445$	13.9294	0.660316
$446$	11.9810	0.567317
$447$	8.19358	0.387543
$448$	27.5627	1.30222
$449$	5.90323	0.278591	0.139295	−	0.990251i	$-0.455516\pi$
$449$	5.90323	0.278591	0.139295	+	0.990251i	$0.455516\pi$
$450$	6.19029	0.291813
$451$	4.86129	0.228909
$452$	15.7660	0.741570
$453$	34.1571	1.60484
$454$	0.0928421	0.00435730
$455$	−5.95092	−0.278983
$456$	−21.6524	−1.01397
$457$	8.55998	0.400419	0.200209	−	0.979753i	$-0.435838\pi$
$457$	8.55998	0.400419	0.200209	+	0.979753i	$0.435838\pi$
$458$	60.1569	2.81095
$459$	3.76752	0.175853
$460$	−30.6016	−1.42681
$461$	9.42761	0.439087	0.219544	−	0.975603i	$-0.429543\pi$
$461$	9.42761	0.439087	0.219544	+	0.975603i	$0.429543\pi$
$462$	−4.23024	−0.196809
$463$	−16.0651	−0.746608	−0.373304	−	0.927709i	$-0.621775\pi$
$463$	−16.0651	−0.746608	−0.373304	+	0.927709i	$0.621775\pi$
$464$	−79.6410	−3.69724
$465$	−6.07216	−0.281590
$466$	0.465869	0.0215809
$467$	13.0579	0.604245	0.302123	−	0.953269i	$-0.402305\pi$
$467$	13.0579	0.604245	0.302123	+	0.953269i	$0.402305\pi$
$468$	29.2851	1.35370
$469$	−11.9583	−0.552182
$470$	−23.6231	−1.08965
$471$	37.9152	1.74704
$472$	119.677	5.50858
$473$	1.00000	0.0459800
$474$	8.28735	0.380651
$475$	−2.07337	−0.0951330
$476$	−4.22680	−0.193735
$477$	−15.7913	−0.723032
$478$	22.4587	1.02724
$479$	−28.1410	−1.28580	−0.642898	−	0.765952i	$-0.722268\pi$
$479$	−28.1410	−1.28580	−0.642898	+	0.765952i	$0.722268\pi$
$480$	89.3624	4.07882
$481$	18.9381	0.863502
$482$	−19.0075	−0.865767
$483$	4.77823	0.217417
$484$	5.61901	0.255409
$485$	23.6315	1.07305
$486$	31.3815	1.42350
$487$	−4.39108	−0.198979	−0.0994895	−	0.995039i	$-0.531721\pi$
$487$	−4.39108	−0.198979	−0.0994895	+	0.995039i	$0.531721\pi$
$488$	52.1292	2.35978
$489$	−26.0100	−1.17621
$490$	−31.0223	−1.40144
$491$	6.67929	0.301432	0.150716	−	0.988577i	$-0.451842\pi$
$491$	6.67929	0.301432	0.150716	+	0.988577i	$0.451842\pi$
$492$	55.6513	2.50895
$493$	4.87542	0.219578
$494$	−13.3000	−0.598396
$495$	−2.01012	−0.0903480
$496$	27.8722	1.25150
$497$	1.03778	0.0465510
$498$	−0.338307	−0.0151599
$499$	−9.65421	−0.432182	−0.216091	−	0.976373i	$-0.569331\pi$
$499$	−9.65421	−0.432182	−0.216091	+	0.976373i	$0.569331\pi$
$500$	68.2031	3.05014
$501$	−48.5116	−2.16734
$502$	−8.63281	−0.385301
$503$	23.2334	1.03593	0.517964	−	0.855403i	$-0.326690\pi$
$503$	23.2334	1.03593	0.517964	+	0.855403i	$0.326690\pi$
$504$	−8.64726	−0.385180
$505$	11.3766	0.506253
$506$	−8.60597	−0.382582
$507$	15.3035	0.679653
$508$	−32.4937	−1.44167
$509$	−43.5344	−1.92963	−0.964814	−	0.262932i	$-0.915310\pi$
$509$	−43.5344	−1.92963	−0.964814	+	0.262932i	$0.915310\pi$
$510$	−9.82306	−0.434972
$511$	−0.0542605	−0.00240034
$512$	−83.8300	−3.70480
$513$	−4.00829	−0.176970
$514$	17.2088	0.759049
$515$	−30.1425	−1.32824
$516$	11.4478	0.503963
$517$	−4.89953	−0.215481
$518$	−8.68237	−0.381481
$519$	−18.3363	−0.804876
$520$	79.0261	3.46552
$521$	26.2463	1.14987	0.574936	−	0.818198i	$-0.305027\pi$
$521$	26.2463	1.14987	0.574936	+	0.818198i	$0.305027\pi$
$522$	15.4863	0.677819
$523$	−15.5937	−0.681863	−0.340931	−	0.940088i	$-0.610742\pi$
$523$	−15.5937	−0.681863	−0.340931	+	0.940088i	$0.610742\pi$
$524$	58.3390	2.54855
$525$	−2.98669	−0.130350
$526$	−60.3937	−2.63329
$527$	−1.70626	−0.0743260
$528$	33.2805	1.44835
$529$	−13.2792	−0.577357
$530$	−66.1624	−2.87391
$531$	−13.7867	−0.598292
$532$	4.49692	0.194966
$533$	22.0166	0.953645
$534$	44.8448	1.94062
$535$	−26.5277	−1.14689
$536$	158.802	6.85919
$537$	−6.99823	−0.301996
$538$	−30.6512	−1.32147
$539$	−6.43415	−0.277138
$540$	36.9784	1.59130
$541$	11.5030	0.494553	0.247277	−	0.968945i	$-0.420464\pi$
$541$	11.5030	0.494553	0.247277	+	0.968945i	$0.420464\pi$
$542$	−7.96404	−0.342085
$543$	−17.2751	−0.741345
$544$	25.1106	1.07661
$545$	1.92116	0.0822932
$546$	−19.1586	−0.819913
$547$	23.0208	0.984299	0.492149	−	0.870511i	$-0.336211\pi$
$547$	23.0208	0.984299	0.492149	+	0.870511i	$0.336211\pi$
$548$	21.1161	0.902037
$549$	−6.00524	−0.256297
$550$	5.37927	0.229373
$551$	−5.18699	−0.220973
$552$	−63.4532	−2.70075
$553$	−1.10855	−0.0471402
$554$	−13.4135	−0.569885
$555$	−14.8811	−0.631667
$556$	6.18296	0.262216
$557$	9.60076	0.406797	0.203399	−	0.979096i	$-0.434801\pi$
$557$	9.60076	0.406797	0.203399	+	0.979096i	$0.434801\pi$
$558$	−5.41980	−0.229438
$559$	4.52896	0.191555
$560$	−21.4640	−0.907019
$561$	−2.03734	−0.0860167
$562$	82.3375	3.47320
$563$	42.9373	1.80959	0.904796	−	0.425844i	$-0.140023\pi$
$563$	42.9373	1.80959	0.904796	+	0.425844i	$0.140023\pi$
$564$	−56.0890	−2.36177
$565$	−4.90111	−0.206191
$566$	15.6116	0.656207
$567$	−8.37087	−0.351543
$568$	−13.7814	−0.578255
$569$	−15.6869	−0.657629	−0.328815	−	0.944394i	$-0.606649\pi$
$569$	−15.6869	−0.657629	−0.328815	+	0.944394i	$0.606649\pi$
$570$	10.4508	0.437737
$571$	41.6261	1.74200	0.870998	−	0.491286i	$-0.163473\pi$
$571$	41.6261	1.74200	0.870998	+	0.491286i	$0.163473\pi$
$572$	25.4483	1.06405
$573$	−26.4760	−1.10605
$574$	−10.0938	−0.421305
$575$	−6.07610	−0.253391
$576$	42.1656	1.75690
$577$	−6.73691	−0.280461	−0.140231	−	0.990119i	$-0.544784\pi$
$577$	−6.73691	−0.280461	−0.140231	+	0.990119i	$0.544784\pi$
$578$	−2.76025	−0.114811
$579$	−10.8428	−0.450613
$580$	47.8525	1.98697
$581$	0.0452532	0.00187742
$582$	76.0802	3.15363
$583$	−13.7224	−0.568322
$584$	0.720560	0.0298170
$585$	−9.10374	−0.376393
$586$	30.9000	1.27647
$587$	−37.9312	−1.56559	−0.782793	−	0.622282i	$-0.786206\pi$
$587$	−37.9312	−1.56559	−0.782793	+	0.622282i	$0.786206\pi$
$588$	−73.6571	−3.03757
$589$	1.81531	0.0747984
$590$	−57.7637	−2.37809
$591$	51.7504	2.12873
$592$	68.3065	2.80738
$593$	27.4560	1.12748	0.563740	−	0.825952i	$-0.309362\pi$
$593$	27.4560	1.12748	0.563740	+	0.825952i	$0.309362\pi$
$594$	10.3993	0.426689
$595$	1.31397	0.0538675
$596$	22.5980	0.925648
$597$	51.9510	2.12621
$598$	−38.9761	−1.59385
$599$	−14.1104	−0.576537	−0.288268	−	0.957550i	$-0.593080\pi$
$599$	−14.1104	−0.576537	−0.288268	+	0.957550i	$0.593080\pi$
$600$	39.6622	1.61920
$601$	22.7126	0.926467	0.463234	−	0.886236i	$-0.346689\pi$
$601$	22.7126	0.926467	0.463234	+	0.886236i	$0.346689\pi$
$602$	−2.07635	−0.0846258
$603$	−18.2938	−0.744982
$604$	94.2054	3.83316
$605$	−1.74676	−0.0710159
$606$	36.6263	1.48784
$607$	−47.4333	−1.92526	−0.962630	−	0.270821i	$-0.912705\pi$
$607$	−47.4333	−1.92526	−0.962630	+	0.270821i	$0.912705\pi$
$608$	−26.7154	−1.08345
$609$	−7.47185	−0.302775
$610$	−25.1608	−1.01873
$611$	−22.1898	−0.897702
$612$	−6.46617	−0.261380
$613$	5.77304	0.233171	0.116586	−	0.993181i	$-0.462805\pi$
$613$	5.77304	0.233171	0.116586	+	0.993181i	$0.462805\pi$
$614$	63.9034	2.57893
$615$	−17.3001	−0.697608
$616$	−7.51433	−0.302761
$617$	−28.9389	−1.16504	−0.582518	−	0.812818i	$-0.697932\pi$
$617$	−28.9389	−1.16504	−0.582518	+	0.812818i	$0.697932\pi$
$618$	−97.0418	−3.90360
$619$	−13.0552	−0.524731	−0.262366	−	0.964969i	$-0.584503\pi$
$619$	−13.0552	−0.524731	−0.262366	+	0.964969i	$0.584503\pi$
$620$	−16.7471	−0.672578
$621$	−11.7464	−0.471369
$622$	18.1681	0.728475
$623$	−5.99861	−0.240329
$624$	150.726	6.03387
$625$	−11.4579	−0.458316
$626$	−5.06240	−0.202334
$627$	2.16754	0.0865634
$628$	104.570	4.17282
$629$	−4.18155	−0.166729
$630$	4.17371	0.166285
$631$	47.4805	1.89017	0.945084	−	0.326826i	$-0.105979\pi$
$631$	47.4805	1.89017	0.945084	+	0.326826i	$0.105979\pi$
$632$	14.7211	0.585575
$633$	12.8815	0.511993
$634$	−75.3859	−2.99396
$635$	10.1012	0.400853
$636$	−157.091	−6.22908
$637$	−29.1400	−1.15457
$638$	13.4574	0.532783
$639$	1.58761	0.0628047
$640$	88.9414	3.51572
$641$	−3.24618	−0.128216	−0.0641081	−	0.997943i	$-0.520420\pi$
$641$	−3.24618	−0.128216	−0.0641081	+	0.997943i	$0.520420\pi$
$642$	−85.4044	−3.37064
$643$	33.0591	1.30372	0.651861	−	0.758338i	$-0.273988\pi$
$643$	33.0591	1.30372	0.651861	+	0.758338i	$0.273988\pi$
$644$	13.1784	0.519301
$645$	−3.55875	−0.140126
$646$	2.93666	0.115541
$647$	13.4072	0.527090	0.263545	−	0.964647i	$-0.415108\pi$
$647$	13.4072	0.527090	0.263545	+	0.964647i	$0.415108\pi$
$648$	111.162	4.36686
$649$	−11.9804	−0.470273
$650$	24.3625	0.955576
$651$	2.61494	0.102488
$652$	−71.7357	−2.80939
$653$	7.87336	0.308108	0.154054	−	0.988062i	$-0.450767\pi$
$653$	7.87336	0.308108	0.154054	+	0.988062i	$0.450767\pi$
$654$	6.18504	0.241854
$655$	−18.1356	−0.708618
$656$	79.4103	3.10045
$657$	−0.0830079	−0.00323845
$658$	10.1731	0.396591
$659$	−6.32816	−0.246510	−0.123255	−	0.992375i	$-0.539333\pi$
$659$	−6.32816	−0.246510	−0.123255	+	0.992375i	$0.539333\pi$
$660$	−19.9966	−0.778368
$661$	30.5093	1.18667	0.593337	−	0.804954i	$-0.297810\pi$
$661$	30.5093	1.18667	0.593337	+	0.804954i	$0.297810\pi$
$662$	24.5306	0.953407
$663$	−9.22705	−0.358349
$664$	−0.600946	−0.0233212
$665$	−1.39794	−0.0542099
$666$	−13.2823	−0.514680
$667$	−15.2007	−0.588572
$668$	−133.795	−5.17669
$669$	−8.84318	−0.341897
$670$	−76.6477	−2.96116
$671$	−5.21846	−0.201456
$672$	−38.4834	−1.48453
$673$	25.9788	1.00141	0.500705	−	0.865618i	$-0.333074\pi$
$673$	25.9788	1.00141	0.500705	+	0.865618i	$0.333074\pi$
$674$	5.73330	0.220839
$675$	7.34226	0.282604
$676$	42.2072	1.62335
$677$	−31.6859	−1.21779	−0.608894	−	0.793252i	$-0.708386\pi$
$677$	−31.6859	−1.21779	−0.608894	+	0.793252i	$0.708386\pi$
$678$	−15.7788	−0.605983
$679$	−10.1768	−0.390549
$680$	−17.4490	−0.669140
$681$	−0.0685268	−0.00262595
$682$	−4.70972	−0.180345
$683$	15.9808	0.611487	0.305744	−	0.952114i	$-0.401095\pi$
$683$	15.9808	0.611487	0.305744	+	0.952114i	$0.401095\pi$
$684$	6.87941	0.263041
$685$	−6.56430	−0.250809
$686$	27.8940	1.06500
$687$	−44.4018	−1.69403
$688$	16.3352	0.622774
$689$	−62.1481	−2.36765
$690$	30.6265	1.16593
$691$	−7.36622	−0.280224	−0.140112	−	0.990136i	$-0.544746\pi$
$691$	−7.36622	−0.280224	−0.140112	+	0.990136i	$0.544746\pi$
$692$	−50.5717	−1.92245
$693$	0.865645	0.0328831
$694$	−7.11841	−0.270211
$695$	−1.92207	−0.0729084
$696$	99.2235	3.76106
$697$	−4.86129	−0.184134
$698$	65.3655	2.47412
$699$	−0.343857	−0.0130059
$700$	−8.23731	−0.311341
$701$	−12.5171	−0.472763	−0.236381	−	0.971660i	$-0.575961\pi$
$701$	−12.5171	−0.472763	−0.236381	+	0.971660i	$0.575961\pi$
$702$	47.0981	1.77760
$703$	4.44878	0.167789
$704$	36.6412	1.38097
$705$	17.4362	0.656685
$706$	−9.14713	−0.344257
$707$	−4.89928	−0.184256
$708$	−137.150	−5.15442
$709$	−38.8496	−1.45903	−0.729514	−	0.683966i	$-0.760254\pi$
$709$	−38.8496	−1.45903	−0.729514	+	0.683966i	$0.760254\pi$
$710$	6.65177	0.249637
$711$	−1.69586	−0.0635998
$712$	79.6594	2.98536
$713$	5.31982	0.199229
$714$	4.23024	0.158313
$715$	−7.91101	−0.295855
$716$	−19.3012	−0.721318
$717$	−16.5767	−0.619070
$718$	53.3698	1.99174
$719$	−33.0514	−1.23261	−0.616305	−	0.787508i	$-0.711371\pi$
$719$	−33.0514	−1.23261	−0.616305	+	0.787508i	$0.711371\pi$
$720$	−32.8357	−1.22371
$721$	12.9807	0.483426
$722$	49.3205	1.83552
$723$	14.0294	0.521760
$724$	−47.6448	−1.77071
$725$	9.50136	0.352872
$726$	−5.62359	−0.208711
$727$	−9.48724	−0.351862	−0.175931	−	0.984402i	$-0.556294\pi$
$727$	−9.48724	−0.351862	−0.175931	+	0.984402i	$0.556294\pi$
$728$	−34.0321	−1.26132
$729$	10.2214	0.378571
$730$	−0.347788	−0.0128722
$731$	−1.00000	−0.0369863
$732$	−59.7401	−2.20806
$733$	−31.0911	−1.14838	−0.574188	−	0.818723i	$-0.694682\pi$
$733$	−31.0911	−1.14838	−0.574188	+	0.818723i	$0.694682\pi$
$734$	88.0175	3.24879
$735$	22.8975	0.844588
$736$	−78.2903	−2.88582
$737$	−15.8971	−0.585575
$738$	−15.4415	−0.568408
$739$	−9.97953	−0.367103	−0.183551	−	0.983010i	$-0.558759\pi$
$739$	−9.97953	−0.367103	−0.183551	+	0.983010i	$0.558759\pi$
$740$	−41.0421	−1.50874
$741$	9.81673	0.360627
$742$	28.4925	1.04599
$743$	15.2501	0.559473	0.279736	−	0.960077i	$-0.409753\pi$
$743$	15.2501	0.559473	0.279736	+	0.960077i	$0.409753\pi$
$744$	−34.7255	−1.27310
$745$	−7.02494	−0.257374
$746$	95.7265	3.50480
$747$	0.0692285	0.00253294
$748$	−5.61901	−0.205451
$749$	11.4240	0.417424
$750$	−68.2587	−2.49246
$751$	20.7522	0.757258	0.378629	−	0.925548i	$-0.376396\pi$
$751$	20.7522	0.757258	0.378629	+	0.925548i	$0.376396\pi$
$752$	−80.0348	−2.91857
$753$	6.37188	0.232204
$754$	60.9480	2.21960
$755$	−29.2853	−1.06580
$756$	−15.9245	−0.579170
$757$	−33.8602	−1.23067	−0.615335	−	0.788266i	$-0.710979\pi$
$757$	−33.8602	−1.23067	−0.615335	+	0.788266i	$0.710979\pi$
$758$	39.7752	1.44470
$759$	6.35207	0.230565
$760$	18.5642	0.673393
$761$	−33.7217	−1.22241	−0.611205	−	0.791472i	$-0.709315\pi$
$761$	−33.7217	−1.22241	−0.611205	+	0.791472i	$0.709315\pi$
$762$	32.5202	1.17808
$763$	−0.827335	−0.0299515
$764$	−73.0209	−2.64180
$765$	2.01012	0.0726759
$766$	3.74395	0.135274
$767$	−54.2589	−1.95918
$768$	137.040	4.94500
$769$	−31.8077	−1.14701	−0.573507	−	0.819200i	$-0.694418\pi$
$769$	−31.8077	−1.14701	−0.573507	+	0.819200i	$0.694418\pi$
$770$	3.62689	0.130704
$771$	−12.7018	−0.457446
$772$	−29.9046	−1.07629
$773$	−35.2462	−1.26772	−0.633860	−	0.773448i	$-0.718530\pi$
$773$	−35.2462	−1.26772	−0.633860	+	0.773448i	$0.718530\pi$
$774$	−3.17641	−0.114174
$775$	−3.32522	−0.119445
$776$	135.144	4.85139
$777$	6.40845	0.229902
$778$	64.2261	2.30262
$779$	5.17196	0.185305
$780$	−90.5640	−3.24271
$781$	1.37961	0.0493662
$782$	8.60597	0.307749
$783$	18.3682	0.656427
$784$	−105.103	−3.75369
$785$	−32.5074	−1.16024
$786$	−58.3866	−2.08258
$787$	−5.63740	−0.200952	−0.100476	−	0.994940i	$-0.532036\pi$
$787$	−5.63740	−0.200952	−0.100476	+	0.994940i	$0.532036\pi$
$788$	142.728	5.08448
$789$	44.5766	1.58697
$790$	−7.10534	−0.252797
$791$	2.11064	0.0750456
$792$	−11.4955	−0.408473
$793$	−23.6342	−0.839276
$794$	−58.8299	−2.08780
$795$	48.8344	1.73198
$796$	143.281	5.07847
$797$	24.3030	0.860857	0.430428	−	0.902625i	$-0.358363\pi$
$797$	24.3030	0.860857	0.430428	+	0.902625i	$0.358363\pi$
$798$	−4.50059	−0.159319
$799$	4.89953	0.173333
$800$	48.9363	1.73016
$801$	−9.17670	−0.324243
$802$	73.8556	2.60793
$803$	−0.0721326	−0.00254550
$804$	−181.987	−6.41819
$805$	−4.09672	−0.144390
$806$	−21.3302	−0.751323
$807$	22.6237	0.796391
$808$	65.0607	2.28883
$809$	9.42900	0.331506	0.165753	−	0.986167i	$-0.446995\pi$
$809$	9.42900	0.331506	0.165753	+	0.986167i	$0.446995\pi$
$810$	−53.6539	−1.88520
$811$	18.5862	0.652651	0.326326	−	0.945257i	$-0.394189\pi$
$811$	18.5862	0.652651	0.326326	+	0.945257i	$0.394189\pi$
$812$	−20.6074	−0.723178
$813$	5.87826	0.206160
$814$	−11.5421	−0.404552
$815$	22.3002	0.781142
$816$	−33.2805	−1.16505
$817$	1.06391	0.0372214
$818$	−60.8764	−2.12849
$819$	3.92047	0.136992
$820$	−47.7138	−1.66624
$821$	18.6331	0.650301	0.325151	−	0.945662i	$-0.394585\pi$
$821$	18.6331	0.650301	0.325151	+	0.945662i	$0.394585\pi$
$822$	−21.1333	−0.737110
$823$	22.1216	0.771111	0.385556	−	0.922685i	$-0.374010\pi$
$823$	22.1216	0.771111	0.385556	+	0.922685i	$0.374010\pi$
$824$	−172.379	−6.00510
$825$	−3.97044	−0.138233
$826$	24.8756	0.865533
$827$	−11.3211	−0.393672	−0.196836	−	0.980436i	$-0.563067\pi$
$827$	−11.3211	−0.393672	−0.196836	+	0.980436i	$0.563067\pi$
$828$	20.1604	0.700621
$829$	52.2354	1.81421	0.907104	−	0.420906i	$-0.138288\pi$
$829$	52.2354	1.81421	0.907104	+	0.420906i	$0.138288\pi$
$830$	0.290054	0.0100679
$831$	9.90050	0.343445
$832$	165.947	5.75317
$833$	6.43415	0.222930
$834$	−6.18800	−0.214273
$835$	41.5924	1.43937
$836$	5.97810	0.206757
$837$	−6.42838	−0.222197
$838$	−67.1856	−2.32089
$839$	−25.8141	−0.891200	−0.445600	−	0.895232i	$-0.647010\pi$
$839$	−25.8141	−0.891200	−0.445600	+	0.895232i	$0.647010\pi$
$840$	26.7416	0.922674
$841$	−5.23031	−0.180356
$842$	55.1104	1.89923
$843$	−60.7733	−2.09314
$844$	35.5272	1.22290
$845$	−13.1208	−0.451369
$846$	15.5629	0.535064
$847$	0.752232	0.0258470
$848$	−224.158	−7.69761
$849$	−11.5230	−0.395467
$850$	−5.37927	−0.184507
$851$	13.0373	0.446913
$852$	15.7935	0.541077
$853$	−1.54453	−0.0528836	−0.0264418	−	0.999650i	$-0.508418\pi$
$853$	−1.54453	−0.0528836	−0.0264418	+	0.999650i	$0.508418\pi$
$854$	10.8354	0.370779
$855$	−2.13858	−0.0731378
$856$	−151.707	−5.18523
$857$	−16.6306	−0.568089	−0.284044	−	0.958811i	$-0.591676\pi$
$857$	−16.6306	−0.568089	−0.284044	+	0.958811i	$0.591676\pi$
$858$	−25.4690	−0.869498
$859$	−18.2379	−0.622270	−0.311135	−	0.950366i	$-0.600709\pi$
$859$	−18.2379	−0.622270	−0.311135	+	0.950366i	$0.600709\pi$
$860$	−9.81506	−0.334691
$861$	7.45020	0.253902
$862$	84.3228	2.87205
$863$	35.5396	1.20978	0.604891	−	0.796308i	$-0.293217\pi$
$863$	35.5396	1.20978	0.604891	+	0.796308i	$0.293217\pi$
$864$	94.6047	3.21852
$865$	15.7210	0.534532
$866$	79.2772	2.69395
$867$	2.03734	0.0691918
$868$	7.21203	0.244792
$869$	−1.47368	−0.0499911
$870$	−47.8915	−1.62367
$871$	−71.9972	−2.43953
$872$	10.9867	0.372057
$873$	−15.5685	−0.526913
$874$	−9.15596	−0.309705
$875$	9.13055	0.308669
$876$	−0.825763	−0.0278999
$877$	−55.9436	−1.88908	−0.944541	−	0.328394i	$-0.893493\pi$
$877$	−55.9436	−1.88908	−0.944541	+	0.328394i	$0.893493\pi$
$878$	−84.8728	−2.86432
$879$	−22.8073	−0.769272
$880$	−28.5337	−0.961871
$881$	−54.2748	−1.82856	−0.914282	−	0.405077i	$-0.867245\pi$
$881$	−54.2748	−1.82856	−0.914282	+	0.405077i	$0.867245\pi$
$882$	20.4375	0.688167
$883$	29.6637	0.998263	0.499131	−	0.866526i	$-0.333653\pi$
$883$	29.6637	0.998263	0.499131	+	0.866526i	$0.333653\pi$
$884$	−25.4483	−0.855918
$885$	42.6354	1.43317
$886$	−21.5876	−0.725248
$887$	−19.7301	−0.662471	−0.331236	−	0.943548i	$-0.607465\pi$
$887$	−19.7301	−0.662471	−0.331236	+	0.943548i	$0.607465\pi$
$888$	−85.1020	−2.85584
$889$	−4.35002	−0.145895
$890$	−38.4486	−1.28880
$891$	−11.1280	−0.372803
$892$	−24.3895	−0.816622
$893$	−5.21264	−0.174434
$894$	−22.6164	−0.756405
$895$	6.00008	0.200561
$896$	−38.3021	−1.27958
$897$	28.7683	0.960545
$898$	−16.2944	−0.543752
$899$	−8.31874	−0.277446
$900$	−12.6015	−0.420049
$901$	13.7224	0.457158
$902$	−13.4184	−0.446784
$903$	1.53256	0.0510003
$904$	−28.0285	−0.932215
$905$	14.8112	0.492340
$906$	−94.2822	−3.13232
$907$	−43.0618	−1.42985	−0.714923	−	0.699204i	$-0.753538\pi$
$907$	−43.0618	−1.42985	−0.714923	+	0.699204i	$0.753538\pi$
$908$	−0.188997	−0.00627209
$909$	−7.49493	−0.248591
$910$	16.4261	0.544518
$911$	−12.9855	−0.430228	−0.215114	−	0.976589i	$-0.569012\pi$
$911$	−12.9855	−0.430228	−0.215114	+	0.976589i	$0.569012\pi$
$912$	35.4073	1.17245
$913$	0.0601585	0.00199096
$914$	−23.6277	−0.781535
$915$	18.5712	0.613945
$916$	−122.460	−4.04620
$917$	7.81001	0.257909
$918$	−10.3993	−0.343229
$919$	34.7814	1.14733	0.573666	−	0.819090i	$-0.305521\pi$
$919$	34.7814	1.14733	0.573666	+	0.819090i	$0.305521\pi$
$920$	54.4030	1.79361
$921$	−47.1671	−1.55421
$922$	−26.0226	−0.857008
$923$	6.24818	0.205661
$924$	8.61144	0.283296
$925$	−8.14913	−0.267942
$926$	44.3438	1.45723
$927$	19.8579	0.652219
$928$	122.425	4.01879
$929$	−39.1762	−1.28533	−0.642665	−	0.766147i	$-0.722171\pi$
$929$	−39.1762	−1.28533	−0.642665	+	0.766147i	$0.722171\pi$
$930$	16.7607	0.549606
$931$	−6.84534	−0.224347
$932$	−0.948361	−0.0310646
$933$	−13.4099	−0.439020
$934$	−36.0430	−1.17936
$935$	1.74676	0.0571252
$936$	−52.0625	−1.70172
$937$	28.9256	0.944959	0.472480	−	0.881342i	$-0.343359\pi$
$937$	28.9256	0.944959	0.472480	+	0.881342i	$0.343359\pi$
$938$	33.0079	1.07775
$939$	3.73656	0.121938
$940$	48.0891	1.56849
$941$	20.5068	0.668503	0.334251	−	0.942484i	$-0.391517\pi$
$941$	20.5068	0.668503	0.334251	+	0.942484i	$0.391517\pi$
$942$	−104.656	−3.40987
$943$	15.1566	0.493567
$944$	−195.703	−6.36959
$945$	4.95041	0.161037
$946$	−2.76025	−0.0897436
$947$	45.8891	1.49120	0.745598	−	0.666396i	$-0.232164\pi$
$947$	45.8891	1.49120	0.745598	+	0.666396i	$0.232164\pi$
$948$	−16.8704	−0.547926
$949$	−0.326686	−0.0106047
$950$	5.72304	0.185680
$951$	55.6423	1.80433
$952$	7.51433	0.243541
$953$	32.0317	1.03761	0.518804	−	0.854893i	$-0.326377\pi$
$953$	32.0317	1.03761	0.518804	+	0.854893i	$0.326377\pi$
$954$	43.5879	1.41121
$955$	22.6997	0.734547
$956$	−45.7188	−1.47865
$957$	−9.93290	−0.321085
$958$	77.6764	2.50961
$959$	2.82688	0.0912846
$960$	−130.397	−4.20855
$961$	−28.0887	−0.906086
$962$	−52.2739	−1.68538
$963$	17.4765	0.563172
$964$	38.6932	1.24623
$965$	9.29635	0.299260
$966$	−13.1891	−0.424353
$967$	−0.945979	−0.0304206	−0.0152103	−	0.999884i	$-0.504842\pi$
$967$	−0.945979	−0.0304206	−0.0152103	+	0.999884i	$0.504842\pi$
$968$	−9.98938	−0.321071
$969$	−2.16754	−0.0696316
$970$	−65.2290	−2.09438
$971$	15.2115	0.488162	0.244081	−	0.969755i	$-0.421514\pi$
$971$	15.2115	0.488162	0.244081	+	0.969755i	$0.421514\pi$
$972$	−63.8829	−2.04904
$973$	0.827730	0.0265358
$974$	12.1205	0.388366
$975$	−17.9820	−0.575884
$976$	−85.2447	−2.72862
$977$	28.6973	0.918107	0.459053	−	0.888409i	$-0.348189\pi$
$977$	28.6973	0.918107	0.459053	+	0.888409i	$0.348189\pi$
$978$	71.7942	2.29572
$979$	−7.97441	−0.254863
$980$	63.1515	2.01730
$981$	−1.26566	−0.0404094
$982$	−18.4365	−0.588333
$983$	1.58561	0.0505730	0.0252865	−	0.999680i	$-0.491950\pi$
$983$	1.58561	0.0505730	0.0252865	+	0.999680i	$0.491950\pi$
$984$	−98.9360	−3.15396
$985$	−44.3693	−1.41372
$986$	−13.4574	−0.428571
$987$	−7.50880	−0.239008
$988$	27.0746	0.861358
$989$	3.11782	0.0991409
$990$	5.54843	0.176341
$991$	−13.1632	−0.418144	−0.209072	−	0.977900i	$-0.567044\pi$
$991$	−13.1632	−0.418144	−0.209072	+	0.977900i	$0.567044\pi$
$992$	−42.8453	−1.36034
$993$	−18.1060	−0.574576
$994$	−2.86455	−0.0908579
$995$	−44.5413	−1.41205
$996$	0.688686	0.0218218
$997$	2.63113	0.0833287	0.0416643	−	0.999132i	$-0.486734\pi$
$997$	2.63113	0.0833287	0.0416643	+	0.999132i	$0.486734\pi$
$998$	26.6481	0.843530
$999$	−15.7541	−0.498437

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.d.1.1	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.d.1.1	✓	62	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.76025 q^{2} +2.03734 q^{3} +5.61901 q^{4} -1.74676 q^{5} -5.62359 q^{6} +0.752232 q^{7} -9.98938 q^{8} +1.15077 q^{9} +O(q^{10})\)	\(q-2.76025 q^{2} +2.03734 q^{3} +5.61901 q^{4} -1.74676 q^{5} -5.62359 q^{6} +0.752232 q^{7} -9.98938 q^{8} +1.15077 q^{9} +4.82150 q^{10} +1.00000 q^{11} +11.4478 q^{12} +4.52896 q^{13} -2.07635 q^{14} -3.55875 q^{15} +16.3352 q^{16} -1.00000 q^{17} -3.17641 q^{18} +1.06391 q^{19} -9.81506 q^{20} +1.53256 q^{21} -2.76025 q^{22} +3.11782 q^{23} -20.3518 q^{24} -1.94883 q^{25} -12.5011 q^{26} -3.76752 q^{27} +4.22680 q^{28} -4.87542 q^{29} +9.82306 q^{30} +1.70626 q^{31} -25.1106 q^{32} +2.03734 q^{33} +2.76025 q^{34} -1.31397 q^{35} +6.46617 q^{36} +4.18155 q^{37} -2.93666 q^{38} +9.22705 q^{39} +17.4490 q^{40} +4.86129 q^{41} -4.23024 q^{42} +1.00000 q^{43} +5.61901 q^{44} -2.01012 q^{45} -8.60597 q^{46} -4.89953 q^{47} +33.2805 q^{48} -6.43415 q^{49} +5.37927 q^{50} -2.03734 q^{51} +25.4483 q^{52} -13.7224 q^{53} +10.3993 q^{54} -1.74676 q^{55} -7.51433 q^{56} +2.16754 q^{57} +13.4574 q^{58} -11.9804 q^{59} -19.9966 q^{60} -5.21846 q^{61} -4.70972 q^{62} +0.865645 q^{63} +36.6412 q^{64} -7.91101 q^{65} -5.62359 q^{66} -15.8971 q^{67} -5.61901 q^{68} +6.35207 q^{69} +3.62689 q^{70} +1.37961 q^{71} -11.4955 q^{72} -0.0721326 q^{73} -11.5421 q^{74} -3.97044 q^{75} +5.97810 q^{76} +0.752232 q^{77} -25.4690 q^{78} -1.47368 q^{79} -28.5337 q^{80} -11.1280 q^{81} -13.4184 q^{82} +0.0601585 q^{83} +8.61144 q^{84} +1.74676 q^{85} -2.76025 q^{86} -9.93290 q^{87} -9.98938 q^{88} -7.97441 q^{89} +5.54843 q^{90} +3.40683 q^{91} +17.5190 q^{92} +3.47624 q^{93} +13.5239 q^{94} -1.85839 q^{95} -51.1589 q^{96} -13.5288 q^{97} +17.7599 q^{98} +1.15077 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9}+O(q^{10}) \) 62 * q - 7 * q^2 - 8 * q^3 + 49 * q^4 - 13 * q^5 - 2 * q^6 - 11 * q^7 - 9 * q^8 + 40 * q^9	\( 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9} - 7 q^{10} + 62 q^{11} - 17 q^{12} - 31 q^{14} - 20 q^{15} + 27 q^{16} - 62 q^{17} + 3 q^{18} - 29 q^{20} - 18 q^{21} - 7 q^{22} - 50 q^{23} - 31 q^{24} + 35 q^{25} - 32 q^{26} - 14 q^{27} - 13 q^{28} - 26 q^{29} - 10 q^{30} - 58 q^{31} - 5 q^{32} - 8 q^{33} + 7 q^{34} - 32 q^{35} - 29 q^{36} - 41 q^{37} - 10 q^{38} - 53 q^{39} - 31 q^{40} - 55 q^{41} - 7 q^{42} + 62 q^{43} + 49 q^{44} - 34 q^{45} - 39 q^{46} - 31 q^{47} - 30 q^{48} + 35 q^{49} - 40 q^{50} + 8 q^{51} + 13 q^{52} - 74 q^{53} + 48 q^{54} - 13 q^{55} - 75 q^{56} - 43 q^{57} - 46 q^{58} - 65 q^{59} - 8 q^{60} - 14 q^{61} - 29 q^{62} - 23 q^{63} - 15 q^{64} - 9 q^{65} - 2 q^{66} - q^{67} - 49 q^{68} - 59 q^{69} - 31 q^{70} - 141 q^{71} + 9 q^{72} - 4 q^{73} - 94 q^{74} - 43 q^{75} + 34 q^{76} - 11 q^{77} - 11 q^{78} - 63 q^{79} - 41 q^{80} - 30 q^{81} + 38 q^{82} - 44 q^{83} - 16 q^{84} + 13 q^{85} - 7 q^{86} - 8 q^{87} - 9 q^{88} - 58 q^{89} - 55 q^{90} - 78 q^{91} - 104 q^{92} - 5 q^{94} - 99 q^{95} - 148 q^{96} - 26 q^{97} + 16 q^{98} + 40 q^{99}+O(q^{100}) \) 62 * q - 7 * q^2 - 8 * q^3 + 49 * q^4 - 13 * q^5 - 2 * q^6 - 11 * q^7 - 9 * q^8 + 40 * q^9 - 7 * q^10 + 62 * q^11 - 17 * q^12 - 31 * q^14 - 20 * q^15 + 27 * q^16 - 62 * q^17 + 3 * q^18 - 29 * q^20 - 18 * q^21 - 7 * q^22 - 50 * q^23 - 31 * q^24 + 35 * q^25 - 32 * q^26 - 14 * q^27 - 13 * q^28 - 26 * q^29 - 10 * q^30 - 58 * q^31 - 5 * q^32 - 8 * q^33 + 7 * q^34 - 32 * q^35 - 29 * q^36 - 41 * q^37 - 10 * q^38 - 53 * q^39 - 31 * q^40 - 55 * q^41 - 7 * q^42 + 62 * q^43 + 49 * q^44 - 34 * q^45 - 39 * q^46 - 31 * q^47 - 30 * q^48 + 35 * q^49 - 40 * q^50 + 8 * q^51 + 13 * q^52 - 74 * q^53 + 48 * q^54 - 13 * q^55 - 75 * q^56 - 43 * q^57 - 46 * q^58 - 65 * q^59 - 8 * q^60 - 14 * q^61 - 29 * q^62 - 23 * q^63 - 15 * q^64 - 9 * q^65 - 2 * q^66 - q^67 - 49 * q^68 - 59 * q^69 - 31 * q^70 - 141 * q^71 + 9 * q^72 - 4 * q^73 - 94 * q^74 - 43 * q^75 + 34 * q^76 - 11 * q^77 - 11 * q^78 - 63 * q^79 - 41 * q^80 - 30 * q^81 + 38 * q^82 - 44 * q^83 - 16 * q^84 + 13 * q^85 - 7 * q^86 - 8 * q^87 - 9 * q^88 - 58 * q^89 - 55 * q^90 - 78 * q^91 - 104 * q^92 - 5 * q^94 - 99 * q^95 - 148 * q^96 - 26 * q^97 + 16 * q^98 + 40 * q^99

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