LMFDB - Embedded newform 4029.2.a.l.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.16757 q^{2} -1.00000 q^{3} +2.69838 q^{4} +2.47527 q^{5} +2.16757 q^{6} +5.12027 q^{7} -1.51379 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.16757 q^{2} -1.00000 q^{3} +2.69838 q^{4} +2.47527 q^{5} +2.16757 q^{6} +5.12027 q^{7} -1.51379 q^{8} +1.00000 q^{9} -5.36532 q^{10} +2.42824 q^{11} -2.69838 q^{12} +7.04772 q^{13} -11.0986 q^{14} -2.47527 q^{15} -2.11551 q^{16} -1.00000 q^{17} -2.16757 q^{18} +2.52534 q^{19} +6.67921 q^{20} -5.12027 q^{21} -5.26339 q^{22} -3.87880 q^{23} +1.51379 q^{24} +1.12694 q^{25} -15.2765 q^{26} -1.00000 q^{27} +13.8164 q^{28} -0.167280 q^{29} +5.36532 q^{30} +5.21971 q^{31} +7.61310 q^{32} -2.42824 q^{33} +2.16757 q^{34} +12.6740 q^{35} +2.69838 q^{36} +2.43133 q^{37} -5.47385 q^{38} -7.04772 q^{39} -3.74703 q^{40} -1.78589 q^{41} +11.0986 q^{42} -0.311392 q^{43} +6.55231 q^{44} +2.47527 q^{45} +8.40759 q^{46} +3.61845 q^{47} +2.11551 q^{48} +19.2172 q^{49} -2.44273 q^{50} +1.00000 q^{51} +19.0174 q^{52} +5.51254 q^{53} +2.16757 q^{54} +6.01054 q^{55} -7.75101 q^{56} -2.52534 q^{57} +0.362592 q^{58} +3.98504 q^{59} -6.67921 q^{60} -4.00554 q^{61} -11.3141 q^{62} +5.12027 q^{63} -12.2709 q^{64} +17.4450 q^{65} +5.26339 q^{66} -14.4965 q^{67} -2.69838 q^{68} +3.87880 q^{69} -27.4719 q^{70} -6.09993 q^{71} -1.51379 q^{72} +7.55480 q^{73} -5.27009 q^{74} -1.12694 q^{75} +6.81431 q^{76} +12.4333 q^{77} +15.2765 q^{78} +1.00000 q^{79} -5.23645 q^{80} +1.00000 q^{81} +3.87105 q^{82} +2.53409 q^{83} -13.8164 q^{84} -2.47527 q^{85} +0.674966 q^{86} +0.167280 q^{87} -3.67584 q^{88} -14.5588 q^{89} -5.36532 q^{90} +36.0863 q^{91} -10.4665 q^{92} -5.21971 q^{93} -7.84325 q^{94} +6.25088 q^{95} -7.61310 q^{96} +7.77175 q^{97} -41.6547 q^{98} +2.42824 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9} + 17 q^{10} + 8 q^{11} - 41 q^{12} + 17 q^{13} + q^{14} + q^{15} + 55 q^{16} - 32 q^{17} - q^{18} + 48 q^{19} - 7 q^{20} - 4 q^{21} - 4 q^{22} - 19 q^{23} + 3 q^{24} + 63 q^{25} + 27 q^{26} - 32 q^{27} + 17 q^{28} - 15 q^{29} - 17 q^{30} + 20 q^{31} + 13 q^{32} - 8 q^{33} + q^{34} + 22 q^{35} + 41 q^{36} + 6 q^{37} + 11 q^{38} - 17 q^{39} + 47 q^{40} + q^{41} - q^{42} + 40 q^{43} + 22 q^{44} - q^{45} + 5 q^{46} - 5 q^{47} - 55 q^{48} + 88 q^{49} + 17 q^{50} + 32 q^{51} + 23 q^{52} - 34 q^{53} + q^{54} + 48 q^{55} - 48 q^{57} - 9 q^{58} + 41 q^{59} + 7 q^{60} + 20 q^{61} + 15 q^{62} + 4 q^{63} + 93 q^{64} - 58 q^{65} + 4 q^{66} + 52 q^{67} - 41 q^{68} + 19 q^{69} + 25 q^{70} + q^{71} - 3 q^{72} + 19 q^{73} + 12 q^{74} - 63 q^{75} + 128 q^{76} - 20 q^{77} - 27 q^{78} + 32 q^{79} - 16 q^{80} + 32 q^{81} - 5 q^{82} + 31 q^{83} - 17 q^{84} + q^{85} - 62 q^{86} + 15 q^{87} + 35 q^{88} + 18 q^{89} + 17 q^{90} + 48 q^{91} - 75 q^{92} - 20 q^{93} + 29 q^{94} + 5 q^{95} - 13 q^{96} + 17 q^{97} + 30 q^{98} + 8 q^{99}+O(q^{100}) \) 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9 + 17 * q^10 + 8 * q^11 - 41 * q^12 + 17 * q^13 + q^14 + q^15 + 55 * q^16 - 32 * q^17 - q^18 + 48 * q^19 - 7 * q^20 - 4 * q^21 - 4 * q^22 - 19 * q^23 + 3 * q^24 + 63 * q^25 + 27 * q^26 - 32 * q^27 + 17 * q^28 - 15 * q^29 - 17 * q^30 + 20 * q^31 + 13 * q^32 - 8 * q^33 + q^34 + 22 * q^35 + 41 * q^36 + 6 * q^37 + 11 * q^38 - 17 * q^39 + 47 * q^40 + q^41 - q^42 + 40 * q^43 + 22 * q^44 - q^45 + 5 * q^46 - 5 * q^47 - 55 * q^48 + 88 * q^49 + 17 * q^50 + 32 * q^51 + 23 * q^52 - 34 * q^53 + q^54 + 48 * q^55 - 48 * q^57 - 9 * q^58 + 41 * q^59 + 7 * q^60 + 20 * q^61 + 15 * q^62 + 4 * q^63 + 93 * q^64 - 58 * q^65 + 4 * q^66 + 52 * q^67 - 41 * q^68 + 19 * q^69 + 25 * q^70 + q^71 - 3 * q^72 + 19 * q^73 + 12 * q^74 - 63 * q^75 + 128 * q^76 - 20 * q^77 - 27 * q^78 + 32 * q^79 - 16 * q^80 + 32 * q^81 - 5 * q^82 + 31 * q^83 - 17 * q^84 + q^85 - 62 * q^86 + 15 * q^87 + 35 * q^88 + 18 * q^89 + 17 * q^90 + 48 * q^91 - 75 * q^92 - 20 * q^93 + 29 * q^94 + 5 * q^95 - 13 * q^96 + 17 * q^97 + 30 * q^98 + 8 * 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 $

$2$	−2.16757	−1.53271	−0.766353	−	0.642419i	$-0.777931\pi$
$2$	−2.16757	−1.53271	−0.766353	+	0.642419i	$0.777931\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.69838	1.34919
$5$	2.47527	1.10697	0.553486	−	0.832858i	$-0.313297\pi$
$5$	2.47527	1.10697	0.553486	+	0.832858i	$0.313297\pi$
$6$	2.16757	0.884909
$7$	5.12027	1.93528	0.967641	−	0.252332i	$-0.0811974\pi$
$7$	5.12027	1.93528	0.967641	+	0.252332i	$0.0811974\pi$
$8$	−1.51379	−0.535205
$9$	1.00000	0.333333
$10$	−5.36532	−1.69666
$11$	2.42824	0.732142	0.366071	−	0.930587i	$-0.380703\pi$
$11$	2.42824	0.732142	0.366071	+	0.930587i	$0.380703\pi$
$12$	−2.69838	−0.778955
$13$	7.04772	1.95469	0.977343	−	0.211661i	$-0.0678873\pi$
$13$	7.04772	1.95469	0.977343	+	0.211661i	$0.0678873\pi$
$14$	−11.0986	−2.96622
$15$	−2.47527	−0.639111
$16$	−2.11551	−0.528877
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.16757	−0.510902
$19$	2.52534	0.579352	0.289676	−	0.957125i	$-0.406453\pi$
$19$	2.52534	0.579352	0.289676	+	0.957125i	$0.406453\pi$
$20$	6.67921	1.49352
$21$	−5.12027	−1.11734
$22$	−5.26339	−1.12216
$23$	−3.87880	−0.808786	−0.404393	−	0.914585i	$-0.632517\pi$
$23$	−3.87880	−0.808786	−0.404393	+	0.914585i	$0.632517\pi$
$24$	1.51379	0.309001
$25$	1.12694	0.225388
$26$	−15.2765	−2.99596
$27$	−1.00000	−0.192450
$28$	13.8164	2.61106
$29$	−0.167280	−0.0310631	−0.0155316	−	0.999879i	$-0.504944\pi$
$29$	−0.167280	−0.0310631	−0.0155316	+	0.999879i	$0.504944\pi$
$30$	5.36532	0.979570
$31$	5.21971	0.937487	0.468743	−	0.883334i	$-0.344707\pi$
$31$	5.21971	0.937487	0.468743	+	0.883334i	$0.344707\pi$
$32$	7.61310	1.34582
$33$	−2.42824	−0.422702
$34$	2.16757	0.371736
$35$	12.6740	2.14230
$36$	2.69838	0.449730
$37$	2.43133	0.399708	0.199854	−	0.979826i	$-0.435953\pi$
$37$	2.43133	0.399708	0.199854	+	0.979826i	$0.435953\pi$
$38$	−5.47385	−0.887976
$39$	−7.04772	−1.12854
$40$	−3.74703	−0.592457
$41$	−1.78589	−0.278909	−0.139455	−	0.990228i	$-0.544535\pi$
$41$	−1.78589	−0.278909	−0.139455	+	0.990228i	$0.544535\pi$
$42$	11.0986	1.71255
$43$	−0.311392	−0.0474869	−0.0237434	−	0.999718i	$-0.507558\pi$
$43$	−0.311392	−0.0474869	−0.0237434	+	0.999718i	$0.507558\pi$
$44$	6.55231	0.987798
$45$	2.47527	0.368991
$46$	8.40759	1.23963
$47$	3.61845	0.527805	0.263902	−	0.964549i	$-0.414990\pi$
$47$	3.61845	0.527805	0.263902	+	0.964549i	$0.414990\pi$
$48$	2.11551	0.305347
$49$	19.2172	2.74531
$50$	−2.44273	−0.345454
$51$	1.00000	0.140028
$52$	19.0174	2.63724
$53$	5.51254	0.757206	0.378603	−	0.925559i	$-0.376405\pi$
$53$	5.51254	0.757206	0.378603	+	0.925559i	$0.376405\pi$
$54$	2.16757	0.294970
$55$	6.01054	0.810461
$56$	−7.75101	−1.03577
$57$	−2.52534	−0.334489
$58$	0.362592	0.0476106
$59$	3.98504	0.518808	0.259404	−	0.965769i	$-0.416474\pi$
$59$	3.98504	0.518808	0.259404	+	0.965769i	$0.416474\pi$
$60$	−6.67921	−0.862282
$61$	−4.00554	−0.512857	−0.256428	−	0.966563i	$-0.582546\pi$
$61$	−4.00554	−0.512857	−0.256428	+	0.966563i	$0.582546\pi$
$62$	−11.3141	−1.43689
$63$	5.12027	0.645094
$64$	−12.2709	−1.53387
$65$	17.4450	2.16378
$66$	5.26339	0.647879
$67$	−14.4965	−1.77103	−0.885514	−	0.464613i	$-0.846194\pi$
$67$	−14.4965	−1.77103	−0.885514	+	0.464613i	$0.846194\pi$
$68$	−2.69838	−0.327227
$69$	3.87880	0.466953
$70$	−27.4719	−3.28352
$71$	−6.09993	−0.723929	−0.361964	−	0.932192i	$-0.617894\pi$
$71$	−6.09993	−0.723929	−0.361964	+	0.932192i	$0.617894\pi$
$72$	−1.51379	−0.178402
$73$	7.55480	0.884223	0.442111	−	0.896960i	$-0.354230\pi$
$73$	7.55480	0.884223	0.442111	+	0.896960i	$0.354230\pi$
$74$	−5.27009	−0.612635
$75$	−1.12694	−0.130128
$76$	6.81431	0.781655
$77$	12.4333	1.41690
$78$	15.2765	1.72972
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	−5.23645	−0.585452
$81$	1.00000	0.111111
$82$	3.87105	0.427486
$83$	2.53409	0.278153	0.139076	−	0.990282i	$-0.455587\pi$
$83$	2.53409	0.278153	0.139076	+	0.990282i	$0.455587\pi$
$84$	−13.8164	−1.50750
$85$	−2.47527	−0.268480
$86$	0.674966	0.0727835
$87$	0.167280	0.0179343
$88$	−3.67584	−0.391846
$89$	−14.5588	−1.54323	−0.771613	−	0.636093i	$-0.780550\pi$
$89$	−14.5588	−1.54323	−0.771613	+	0.636093i	$0.780550\pi$
$90$	−5.36532	−0.565555
$91$	36.0863	3.78287
$92$	−10.4665	−1.09121
$93$	−5.21971	−0.541258
$94$	−7.84325	−0.808969
$95$	6.25088	0.641326
$96$	−7.61310	−0.777009
$97$	7.77175	0.789101	0.394551	−	0.918874i	$-0.370900\pi$
$97$	7.77175	0.789101	0.394551	+	0.918874i	$0.370900\pi$
$98$	−41.6547	−4.20776
$99$	2.42824	0.244047
$100$	3.04091	0.304091
$101$	−0.229038	−0.0227901	−0.0113951	−	0.999935i	$-0.503627\pi$
$101$	−0.229038	−0.0227901	−0.0113951	+	0.999935i	$0.503627\pi$
$102$	−2.16757	−0.214622
$103$	10.1599	1.00108	0.500541	−	0.865713i	$-0.333135\pi$
$103$	10.1599	1.00108	0.500541	+	0.865713i	$0.333135\pi$
$104$	−10.6688	−1.04616
$105$	−12.6740	−1.23686
$106$	−11.9489	−1.16058
$107$	11.6953	1.13062	0.565311	−	0.824878i	$-0.308756\pi$
$107$	11.6953	1.13062	0.565311	+	0.824878i	$0.308756\pi$
$108$	−2.69838	−0.259652
$109$	−16.3823	−1.56914	−0.784569	−	0.620042i	$-0.787116\pi$
$109$	−16.3823	−1.56914	−0.784569	+	0.620042i	$0.787116\pi$
$110$	−13.0283	−1.24220
$111$	−2.43133	−0.230772
$112$	−10.8320	−1.02353
$113$	−7.09186	−0.667146	−0.333573	−	0.942724i	$-0.608254\pi$
$113$	−7.09186	−0.667146	−0.333573	+	0.942724i	$0.608254\pi$
$114$	5.47385	0.512673
$115$	−9.60106	−0.895304
$116$	−0.451385	−0.0419100
$117$	7.04772	0.651562
$118$	−8.63788	−0.795181
$119$	−5.12027	−0.469375
$120$	3.74703	0.342055
$121$	−5.10365	−0.463968
$122$	8.68231	0.786059
$123$	1.78589	0.161028
$124$	14.0847	1.26485
$125$	−9.58685	−0.857474
$126$	−11.0986	−0.988740
$127$	16.8219	1.49271	0.746353	−	0.665551i	$-0.231803\pi$
$127$	16.8219	1.49271	0.746353	+	0.665551i	$0.231803\pi$
$128$	11.3720	1.00515
$129$	0.311392	0.0274166
$130$	−37.8133	−3.31645
$131$	7.84035	0.685015	0.342507	−	0.939515i	$-0.388724\pi$
$131$	7.84035	0.685015	0.342507	+	0.939515i	$0.388724\pi$
$132$	−6.55231	−0.570305
$133$	12.9304	1.12121
$134$	31.4222	2.71447
$135$	−2.47527	−0.213037
$136$	1.51379	0.129806
$137$	−10.3154	−0.881307	−0.440654	−	0.897677i	$-0.645253\pi$
$137$	−10.3154	−0.881307	−0.440654	+	0.897677i	$0.645253\pi$
$138$	−8.40759	−0.715701
$139$	−15.8844	−1.34729	−0.673647	−	0.739053i	$-0.735273\pi$
$139$	−15.8844	−1.34729	−0.673647	+	0.739053i	$0.735273\pi$
$140$	34.1994	2.89037
$141$	−3.61845	−0.304728
$142$	13.2221	1.10957
$143$	17.1136	1.43111
$144$	−2.11551	−0.176292
$145$	−0.414062	−0.0343860
$146$	−16.3756	−1.35525
$147$	−19.2172	−1.58501
$148$	6.56065	0.539282
$149$	−6.51186	−0.533473	−0.266736	−	0.963770i	$-0.585945\pi$
$149$	−6.51186	−0.533473	−0.266736	+	0.963770i	$0.585945\pi$
$150$	2.44273	0.199448
$151$	4.73906	0.385660	0.192830	−	0.981232i	$-0.438233\pi$
$151$	4.73906	0.385660	0.192830	+	0.981232i	$0.438233\pi$
$152$	−3.82282	−0.310072
$153$	−1.00000	−0.0808452
$154$	−26.9500	−2.17169
$155$	12.9202	1.03777
$156$	−19.0174	−1.52261
$157$	−2.23083	−0.178039	−0.0890196	−	0.996030i	$-0.528373\pi$
$157$	−2.23083	−0.178039	−0.0890196	+	0.996030i	$0.528373\pi$
$158$	−2.16757	−0.172443
$159$	−5.51254	−0.437173
$160$	18.8444	1.48978
$161$	−19.8605	−1.56523
$162$	−2.16757	−0.170301
$163$	2.89238	0.226548	0.113274	−	0.993564i	$-0.463866\pi$
$163$	2.89238	0.226548	0.113274	+	0.993564i	$0.463866\pi$
$164$	−4.81901	−0.376301
$165$	−6.01054	−0.467920
$166$	−5.49283	−0.426327
$167$	−21.7528	−1.68328	−0.841640	−	0.540039i	$-0.818409\pi$
$167$	−21.7528	−1.68328	−0.841640	+	0.540039i	$0.818409\pi$
$168$	7.75101	0.598004
$169$	36.6704	2.82080
$170$	5.36532	0.411501
$171$	2.52534	0.193117
$172$	−0.840255	−0.0640688
$173$	−18.8395	−1.43234	−0.716170	−	0.697926i	$-0.754107\pi$
$173$	−18.8395	−1.43234	−0.716170	+	0.697926i	$0.754107\pi$
$174$	−0.362592	−0.0274880
$175$	5.77025	0.436190
$176$	−5.13696	−0.387213
$177$	−3.98504	−0.299534
$178$	31.5572	2.36531
$179$	4.98517	0.372609	0.186305	−	0.982492i	$-0.440349\pi$
$179$	4.98517	0.372609	0.186305	+	0.982492i	$0.440349\pi$
$180$	6.67921	0.497839
$181$	−9.78562	−0.727359	−0.363680	−	0.931524i	$-0.618480\pi$
$181$	−9.78562	−0.727359	−0.363680	+	0.931524i	$0.618480\pi$
$182$	−78.2197	−5.79803
$183$	4.00554	0.296098
$184$	5.87168	0.432866
$185$	6.01819	0.442466
$186$	11.3141	0.829590
$187$	−2.42824	−0.177570
$188$	9.76394	0.712108
$189$	−5.12027	−0.372445
$190$	−13.5492	−0.982965
$191$	−25.8552	−1.87081	−0.935407	−	0.353573i	$-0.884967\pi$
$191$	−25.8552	−1.87081	−0.935407	+	0.353573i	$0.884967\pi$
$192$	12.2709	0.885579
$193$	−16.6091	−1.19555	−0.597775	−	0.801664i	$-0.703948\pi$
$193$	−16.6091	−1.19555	−0.597775	+	0.801664i	$0.703948\pi$
$194$	−16.8458	−1.20946
$195$	−17.4450	−1.24926
$196$	51.8553	3.70395
$197$	−11.8671	−0.845496	−0.422748	−	0.906247i	$-0.638934\pi$
$197$	−11.8671	−0.845496	−0.422748	+	0.906247i	$0.638934\pi$
$198$	−5.26339	−0.374053
$199$	−14.9683	−1.06108	−0.530539	−	0.847661i	$-0.678010\pi$
$199$	−14.9683	−1.06108	−0.530539	+	0.847661i	$0.678010\pi$
$200$	−1.70595	−0.120629
$201$	14.4965	1.02250
$202$	0.496456	0.0349306
$203$	−0.856519	−0.0601159
$204$	2.69838	0.188924
$205$	−4.42055	−0.308745
$206$	−22.0223	−1.53436
$207$	−3.87880	−0.269595
$208$	−14.9095	−1.03379
$209$	6.13212	0.424168
$210$	27.4719	1.89574
$211$	−0.457690	−0.0315087	−0.0157543	−	0.999876i	$-0.505015\pi$
$211$	−0.457690	−0.0315087	−0.0157543	+	0.999876i	$0.505015\pi$
$212$	14.8749	1.02161
$213$	6.09993	0.417960
$214$	−25.3503	−1.73291
$215$	−0.770779	−0.0525667
$216$	1.51379	0.103000
$217$	26.7263	1.81430
$218$	35.5098	2.40503
$219$	−7.55480	−0.510506
$220$	16.2187	1.09347
$221$	−7.04772	−0.474081
$222$	5.27009	0.353705
$223$	−5.26003	−0.352238	−0.176119	−	0.984369i	$-0.556354\pi$
$223$	−5.26003	−0.352238	−0.176119	+	0.984369i	$0.556354\pi$
$224$	38.9812	2.60454
$225$	1.12694	0.0751294
$226$	15.3721	1.02254
$227$	−18.9322	−1.25658	−0.628289	−	0.777980i	$-0.716244\pi$
$227$	−18.9322	−1.25658	−0.628289	+	0.777980i	$0.716244\pi$
$228$	−6.81431	−0.451289
$229$	20.5447	1.35763	0.678817	−	0.734308i	$-0.262493\pi$
$229$	20.5447	1.35763	0.678817	+	0.734308i	$0.262493\pi$
$230$	20.8110	1.37224
$231$	−12.4333	−0.818048
$232$	0.253227	0.0166251
$233$	−8.43882	−0.552845	−0.276423	−	0.961036i	$-0.589149\pi$
$233$	−8.43882	−0.552845	−0.276423	+	0.961036i	$0.589149\pi$
$234$	−15.2765	−0.998653
$235$	8.95661	0.584265
$236$	10.7532	0.699971
$237$	−1.00000	−0.0649570
$238$	11.0986	0.719414
$239$	17.9252	1.15948	0.579742	−	0.814800i	$-0.303153\pi$
$239$	17.9252	1.15948	0.579742	+	0.814800i	$0.303153\pi$
$240$	5.23645	0.338011
$241$	11.7543	0.757161	0.378580	−	0.925568i	$-0.376412\pi$
$241$	11.7543	0.757161	0.378580	+	0.925568i	$0.376412\pi$
$242$	11.0625	0.711128
$243$	−1.00000	−0.0641500
$244$	−10.8085	−0.691941
$245$	47.5677	3.03899
$246$	−3.87105	−0.246809
$247$	17.7979	1.13245
$248$	−7.90153	−0.501748
$249$	−2.53409	−0.160592
$250$	20.7802	1.31426
$251$	−9.50606	−0.600017	−0.300009	−	0.953936i	$-0.596990\pi$
$251$	−9.50606	−0.600017	−0.300009	+	0.953936i	$0.596990\pi$
$252$	13.8164	0.870354
$253$	−9.41866	−0.592146
$254$	−36.4628	−2.28788
$255$	2.47527	0.155007
$256$	−0.107735	−0.00673344
$257$	−12.9516	−0.807900	−0.403950	−	0.914781i	$-0.632363\pi$
$257$	−12.9516	−0.807900	−0.403950	+	0.914781i	$0.632363\pi$
$258$	−0.674966	−0.0420216
$259$	12.4491	0.773548
$260$	47.0732	2.91935
$261$	−0.167280	−0.0103544
$262$	−16.9945	−1.04993
$263$	3.46583	0.213712	0.106856	−	0.994275i	$-0.465922\pi$
$263$	3.46583	0.213712	0.106856	+	0.994275i	$0.465922\pi$
$264$	3.67584	0.226232
$265$	13.6450	0.838207
$266$	−28.0276	−1.71848
$267$	14.5588	0.890982
$268$	−39.1170	−2.38945
$269$	17.0451	1.03926	0.519631	−	0.854391i	$-0.326070\pi$
$269$	17.0451	1.03926	0.519631	+	0.854391i	$0.326070\pi$
$270$	5.36532	0.326523
$271$	−12.5484	−0.762260	−0.381130	−	0.924522i	$-0.624465\pi$
$271$	−12.5484	−0.762260	−0.381130	+	0.924522i	$0.624465\pi$
$272$	2.11551	0.128272
$273$	−36.0863	−2.18404
$274$	22.3595	1.35079
$275$	2.73648	0.165016
$276$	10.4665	0.630008
$277$	−26.0702	−1.56641	−0.783203	−	0.621766i	$-0.786415\pi$
$277$	−26.0702	−1.56641	−0.783203	+	0.621766i	$0.786415\pi$
$278$	34.4305	2.06501
$279$	5.21971	0.312496
$280$	−19.1858	−1.14657
$281$	26.3755	1.57343	0.786715	−	0.617316i	$-0.211780\pi$
$281$	26.3755	1.57343	0.786715	+	0.617316i	$0.211780\pi$
$282$	7.84325	0.467059
$283$	−26.2567	−1.56080	−0.780400	−	0.625280i	$-0.784985\pi$
$283$	−26.2567	−1.56080	−0.780400	+	0.625280i	$0.784985\pi$
$284$	−16.4599	−0.976717
$285$	−6.25088	−0.370270
$286$	−37.0949	−2.19347
$287$	−9.14425	−0.539768
$288$	7.61310	0.448606
$289$	1.00000	0.0588235
$290$	0.897511	0.0527037
$291$	−7.77175	−0.455588
$292$	20.3857	1.19298
$293$	−21.0956	−1.23242	−0.616210	−	0.787582i	$-0.711333\pi$
$293$	−21.0956	−1.23242	−0.616210	+	0.787582i	$0.711333\pi$
$294$	41.6547	2.42935
$295$	9.86404	0.574307
$296$	−3.68052	−0.213926
$297$	−2.42824	−0.140901
$298$	14.1149	0.817657
$299$	−27.3367	−1.58092
$300$	−3.04091	−0.175567
$301$	−1.59441	−0.0919005
$302$	−10.2723	−0.591103
$303$	0.229038	0.0131579
$304$	−5.34237	−0.306406
$305$	−9.91478	−0.567718
$306$	2.16757	0.123912
$307$	8.16138	0.465795	0.232897	−	0.972501i	$-0.425179\pi$
$307$	8.16138	0.465795	0.232897	+	0.972501i	$0.425179\pi$
$308$	33.5496	1.91167
$309$	−10.1599	−0.577975
$310$	−28.0054	−1.59060
$311$	−6.22138	−0.352782	−0.176391	−	0.984320i	$-0.556442\pi$
$311$	−6.22138	−0.352782	−0.176391	+	0.984320i	$0.556442\pi$
$312$	10.6688	0.604000
$313$	−1.24037	−0.0701097	−0.0350549	−	0.999385i	$-0.511161\pi$
$313$	−1.24037	−0.0701097	−0.0350549	+	0.999385i	$0.511161\pi$
$314$	4.83548	0.272882
$315$	12.6740	0.714101
$316$	2.69838	0.151796
$317$	35.2664	1.98076	0.990380	−	0.138372i	$-0.0441869\pi$
$317$	35.2664	1.98076	0.990380	+	0.138372i	$0.0441869\pi$
$318$	11.9489	0.670058
$319$	−0.406196	−0.0227426
$320$	−30.3738	−1.69795
$321$	−11.6953	−0.652765
$322$	43.0492	2.39904
$323$	−2.52534	−0.140513
$324$	2.69838	0.149910
$325$	7.94237	0.440563
$326$	−6.26944	−0.347232
$327$	16.3823	0.905942
$328$	2.70346	0.149274
$329$	18.5274	1.02145
$330$	13.0283	0.717184
$331$	14.7850	0.812659	0.406330	−	0.913727i	$-0.366808\pi$
$331$	14.7850	0.812659	0.406330	+	0.913727i	$0.366808\pi$
$332$	6.83794	0.375281
$333$	2.43133	0.133236
$334$	47.1507	2.57997
$335$	−35.8827	−1.96048
$336$	10.8320	0.590933
$337$	2.79095	0.152033	0.0760163	−	0.997107i	$-0.475780\pi$
$337$	2.79095	0.152033	0.0760163	+	0.997107i	$0.475780\pi$
$338$	−79.4858	−4.32346
$339$	7.09186	0.385177
$340$	−6.67921	−0.362231
$341$	12.6747	0.686373
$342$	−5.47385	−0.295992
$343$	62.5554	3.37768
$344$	0.471382	0.0254152
$345$	9.60106	0.516904
$346$	40.8360	2.19536
$347$	−13.7185	−0.736448	−0.368224	−	0.929737i	$-0.620034\pi$
$347$	−13.7185	−0.736448	−0.368224	+	0.929737i	$0.620034\pi$
$348$	0.451385	0.0241968
$349$	21.4013	1.14559	0.572794	−	0.819700i	$-0.305860\pi$
$349$	21.4013	1.14559	0.572794	+	0.819700i	$0.305860\pi$
$350$	−12.5074	−0.668551
$351$	−7.04772	−0.376180
$352$	18.4864	0.985330
$353$	18.8139	1.00137	0.500683	−	0.865631i	$-0.333082\pi$
$353$	18.8139	1.00137	0.500683	+	0.865631i	$0.333082\pi$
$354$	8.63788	0.459098
$355$	−15.0989	−0.801369
$356$	−39.2850	−2.08210
$357$	5.12027	0.270994
$358$	−10.8057	−0.571101
$359$	9.97827	0.526633	0.263316	−	0.964710i	$-0.415184\pi$
$359$	9.97827	0.526633	0.263316	+	0.964710i	$0.415184\pi$
$360$	−3.74703	−0.197486
$361$	−12.6227	−0.664352
$362$	21.2111	1.11483
$363$	5.10365	0.267872
$364$	97.3744	5.10381
$365$	18.7001	0.978810
$366$	−8.68231	−0.453831
$367$	−17.1927	−0.897451	−0.448726	−	0.893670i	$-0.648122\pi$
$367$	−17.1927	−0.897451	−0.448726	+	0.893670i	$0.648122\pi$
$368$	8.20563	0.427748
$369$	−1.78589	−0.0929697
$370$	−13.0449	−0.678171
$371$	28.2257	1.46541
$372$	−14.0847	−0.730260
$373$	−9.83404	−0.509187	−0.254594	−	0.967048i	$-0.581942\pi$
$373$	−9.83404	−0.509187	−0.254594	+	0.967048i	$0.581942\pi$
$374$	5.26339	0.272163
$375$	9.58685	0.495063
$376$	−5.47756	−0.282484
$377$	−1.17894	−0.0607186
$378$	11.0986	0.570849
$379$	−8.75990	−0.449966	−0.224983	−	0.974363i	$-0.572233\pi$
$379$	−8.75990	−0.449966	−0.224983	+	0.974363i	$0.572233\pi$
$380$	16.8672	0.865271
$381$	−16.8219	−0.861814
$382$	56.0430	2.86741
$383$	−30.0557	−1.53577	−0.767886	−	0.640586i	$-0.778691\pi$
$383$	−30.0557	−1.53577	−0.767886	+	0.640586i	$0.778691\pi$
$384$	−11.3720	−0.580324
$385$	30.7756	1.56847
$386$	36.0015	1.83243
$387$	−0.311392	−0.0158290
$388$	20.9711	1.06465
$389$	−22.0219	−1.11655	−0.558277	−	0.829655i	$-0.688537\pi$
$389$	−22.0219	−1.11655	−0.558277	+	0.829655i	$0.688537\pi$
$390$	37.8133	1.91475
$391$	3.87880	0.196159
$392$	−29.0908	−1.46931
$393$	−7.84035	−0.395493
$394$	25.7228	1.29590
$395$	2.47527	0.124544
$396$	6.55231	0.329266
$397$	32.9750	1.65497	0.827483	−	0.561491i	$-0.189772\pi$
$397$	32.9750	1.65497	0.827483	+	0.561491i	$0.189772\pi$
$398$	32.4450	1.62632
$399$	−12.9304	−0.647330
$400$	−2.38405	−0.119203
$401$	−11.5924	−0.578895	−0.289448	−	0.957194i	$-0.593472\pi$
$401$	−11.5924	−0.578895	−0.289448	+	0.957194i	$0.593472\pi$
$402$	−31.4222	−1.56720
$403$	36.7870	1.83249
$404$	−0.618031	−0.0307482
$405$	2.47527	0.122997
$406$	1.85657	0.0921400
$407$	5.90385	0.292643
$408$	−1.51379	−0.0749437
$409$	−9.12106	−0.451007	−0.225504	−	0.974242i	$-0.572403\pi$
$409$	−9.12106	−0.451007	−0.225504	+	0.974242i	$0.572403\pi$
$410$	9.58188	0.473215
$411$	10.3154	0.508823
$412$	27.4152	1.35065
$413$	20.4045	1.00404
$414$	8.40759	0.413210
$415$	6.27255	0.307907
$416$	53.6550	2.63065
$417$	15.8844	0.777861
$418$	−13.2918	−0.650124
$419$	37.1938	1.81704	0.908519	−	0.417843i	$-0.137214\pi$
$419$	37.1938	1.81704	0.908519	+	0.417843i	$0.137214\pi$
$420$	−34.1994	−1.66876
$421$	17.5319	0.854453	0.427226	−	0.904145i	$-0.359491\pi$
$421$	17.5319	0.854453	0.427226	+	0.904145i	$0.359491\pi$
$422$	0.992078	0.0482936
$423$	3.61845	0.175935
$424$	−8.34483	−0.405261
$425$	−1.12694	−0.0546647
$426$	−13.2221	−0.640611
$427$	−20.5095	−0.992522
$428$	31.5582	1.52542
$429$	−17.1136	−0.826250
$430$	1.67072	0.0805693
$431$	7.03499	0.338864	0.169432	−	0.985542i	$-0.445807\pi$
$431$	7.03499	0.338864	0.169432	+	0.985542i	$0.445807\pi$
$432$	2.11551	0.101782
$433$	14.4485	0.694351	0.347176	−	0.937800i	$-0.387141\pi$
$433$	14.4485	0.694351	0.347176	+	0.937800i	$0.387141\pi$
$434$	−57.9313	−2.78079
$435$	0.414062	0.0198528
$436$	−44.2056	−2.11706
$437$	−9.79527	−0.468571
$438$	16.3756	0.782456
$439$	−9.18460	−0.438357	−0.219179	−	0.975685i	$-0.570338\pi$
$439$	−9.18460	−0.438357	−0.219179	+	0.975685i	$0.570338\pi$
$440$	−9.09868	−0.433763
$441$	19.2172	0.915105
$442$	15.2765	0.726627
$443$	15.7669	0.749106	0.374553	−	0.927205i	$-0.377796\pi$
$443$	15.7669	0.749106	0.374553	+	0.927205i	$0.377796\pi$
$444$	−6.56065	−0.311355
$445$	−36.0368	−1.70831
$446$	11.4015	0.539877
$447$	6.51186	0.308001
$448$	−62.8306	−2.96847
$449$	13.9609	0.658854	0.329427	−	0.944181i	$-0.393144\pi$
$449$	13.9609	0.658854	0.329427	+	0.944181i	$0.393144\pi$
$450$	−2.44273	−0.115151
$451$	−4.33657	−0.204201
$452$	−19.1365	−0.900106
$453$	−4.73906	−0.222661
$454$	41.0371	1.92596
$455$	89.3231	4.18753
$456$	3.82282	0.179020
$457$	−18.3974	−0.860592	−0.430296	−	0.902688i	$-0.641591\pi$
$457$	−18.3974	−0.860592	−0.430296	+	0.902688i	$0.641591\pi$
$458$	−44.5322	−2.08085
$459$	1.00000	0.0466760
$460$	−25.9073	−1.20793
$461$	−20.5938	−0.959151	−0.479575	−	0.877501i	$-0.659209\pi$
$461$	−20.5938	−0.959151	−0.479575	+	0.877501i	$0.659209\pi$
$462$	26.9500	1.25383
$463$	−9.84685	−0.457622	−0.228811	−	0.973471i	$-0.573484\pi$
$463$	−9.84685	−0.457622	−0.228811	+	0.973471i	$0.573484\pi$
$464$	0.353882	0.0164286
$465$	−12.9202	−0.599158
$466$	18.2918	0.847350
$467$	−28.1626	−1.30321	−0.651604	−	0.758559i	$-0.725904\pi$
$467$	−28.1626	−1.30321	−0.651604	+	0.758559i	$0.725904\pi$
$468$	19.0174	0.879081
$469$	−74.2260	−3.42744
$470$	−19.4141	−0.895507
$471$	2.23083	0.102791
$472$	−6.03251	−0.277669
$473$	−0.756135	−0.0347671
$474$	2.16757	0.0995600
$475$	2.84590	0.130579
$476$	−13.8164	−0.633275
$477$	5.51254	0.252402
$478$	−38.8542	−1.77715
$479$	−3.28478	−0.150085	−0.0750427	−	0.997180i	$-0.523909\pi$
$479$	−3.28478	−0.150085	−0.0750427	+	0.997180i	$0.523909\pi$
$480$	−18.8444	−0.860127
$481$	17.1353	0.781304
$482$	−25.4783	−1.16051
$483$	19.8605	0.903685
$484$	−13.7716	−0.625981
$485$	19.2371	0.873514
$486$	2.16757	0.0983232
$487$	23.1347	1.04833	0.524167	−	0.851615i	$-0.324377\pi$
$487$	23.1347	1.04833	0.524167	+	0.851615i	$0.324377\pi$
$488$	6.06354	0.274484
$489$	−2.89238	−0.130798
$490$	−103.107	−4.65788
$491$	34.0061	1.53467	0.767336	−	0.641245i	$-0.221582\pi$
$491$	34.0061	1.53467	0.767336	+	0.641245i	$0.221582\pi$
$492$	4.81901	0.217258
$493$	0.167280	0.00753391
$494$	−38.5782	−1.73571
$495$	6.01054	0.270154
$496$	−11.0423	−0.495815
$497$	−31.2333	−1.40101
$498$	5.49283	0.246140
$499$	−11.3575	−0.508431	−0.254216	−	0.967148i	$-0.581817\pi$
$499$	−11.3575	−0.508431	−0.254216	+	0.967148i	$0.581817\pi$
$500$	−25.8690	−1.15689
$501$	21.7528	0.971842
$502$	20.6051	0.919650
$503$	27.9115	1.24451	0.622256	−	0.782814i	$-0.286216\pi$
$503$	27.9115	1.24451	0.622256	+	0.782814i	$0.286216\pi$
$504$	−7.75101	−0.345258
$505$	−0.566929	−0.0252280
$506$	20.4156	0.907586
$507$	−36.6704	−1.62859
$508$	45.3920	2.01394
$509$	−41.2250	−1.82727	−0.913634	−	0.406538i	$-0.866736\pi$
$509$	−41.2250	−1.82727	−0.913634	+	0.406538i	$0.866736\pi$
$510$	−5.36532	−0.237581
$511$	38.6827	1.71122
$512$	−22.5104	−0.994830
$513$	−2.52534	−0.111496
$514$	28.0736	1.23827
$515$	25.1484	1.10817
$516$	0.840255	0.0369902
$517$	8.78645	0.386428
$518$	−26.9843	−1.18562
$519$	18.8395	0.826962
$520$	−26.4080	−1.15807
$521$	5.89619	0.258317	0.129158	−	0.991624i	$-0.458772\pi$
$521$	5.89619	0.258317	0.129158	+	0.991624i	$0.458772\pi$
$522$	0.362592	0.0158702
$523$	−21.6793	−0.947971	−0.473986	−	0.880533i	$-0.657185\pi$
$523$	−21.6793	−0.947971	−0.473986	+	0.880533i	$0.657185\pi$
$524$	21.1562	0.924215
$525$	−5.77025	−0.251834
$526$	−7.51244	−0.327558
$527$	−5.21971	−0.227374
$528$	5.13696	0.223558
$529$	−7.95491	−0.345866
$530$	−29.5766	−1.28472
$531$	3.98504	0.172936
$532$	34.8911	1.51272
$533$	−12.5865	−0.545180
$534$	−31.5572	−1.36561
$535$	28.9489	1.25157
$536$	21.9446	0.947863
$537$	−4.98517	−0.215126
$538$	−36.9466	−1.59288
$539$	46.6640	2.00996
$540$	−6.67921	−0.287427
$541$	−19.7845	−0.850603	−0.425301	−	0.905052i	$-0.639832\pi$
$541$	−19.7845	−0.850603	−0.425301	+	0.905052i	$0.639832\pi$
$542$	27.1995	1.16832
$543$	9.78562	0.419941
$544$	−7.61310	−0.326409
$545$	−40.5505	−1.73699
$546$	78.2197	3.34749
$547$	32.5031	1.38973	0.694865	−	0.719140i	$-0.255464\pi$
$547$	32.5031	1.38973	0.694865	+	0.719140i	$0.255464\pi$
$548$	−27.8350	−1.18905
$549$	−4.00554	−0.170952
$550$	−5.93153	−0.252921
$551$	−0.422438	−0.0179965
$552$	−5.87168	−0.249915
$553$	5.12027	0.217736
$554$	56.5091	2.40084
$555$	−6.01819	−0.255458
$556$	−42.8620	−1.81775
$557$	−14.9361	−0.632863	−0.316432	−	0.948615i	$-0.602485\pi$
$557$	−14.9361	−0.632863	−0.316432	+	0.948615i	$0.602485\pi$
$558$	−11.3141	−0.478964
$559$	−2.19461	−0.0928220
$560$	−26.8120	−1.13302
$561$	2.42824	0.102520
$562$	−57.1708	−2.41161
$563$	−15.6638	−0.660151	−0.330075	−	0.943955i	$-0.607074\pi$
$563$	−15.6638	−0.660151	−0.330075	+	0.943955i	$0.607074\pi$
$564$	−9.76394	−0.411136
$565$	−17.5542	−0.738512
$566$	56.9134	2.39225
$567$	5.12027	0.215031
$568$	9.23401	0.387450
$569$	−35.5884	−1.49194	−0.745972	−	0.665977i	$-0.768015\pi$
$569$	−35.5884	−1.49194	−0.745972	+	0.665977i	$0.768015\pi$
$570$	13.5492	0.567515
$571$	−31.1674	−1.30431	−0.652157	−	0.758084i	$-0.726136\pi$
$571$	−31.1674	−1.30431	−0.652157	+	0.758084i	$0.726136\pi$
$572$	46.1789	1.93084
$573$	25.8552	1.08011
$574$	19.8208	0.827306
$575$	−4.37118	−0.182291
$576$	−12.2709	−0.511289
$577$	13.7522	0.572513	0.286256	−	0.958153i	$-0.407589\pi$
$577$	13.7522	0.572513	0.286256	+	0.958153i	$0.407589\pi$
$578$	−2.16757	−0.0901592
$579$	16.6091	0.690251
$580$	−1.11730	−0.0463932
$581$	12.9752	0.538304
$582$	16.8458	0.698283
$583$	13.3858	0.554382
$584$	−11.4364	−0.473241
$585$	17.4450	0.721261
$586$	45.7263	1.88894
$587$	7.23914	0.298791	0.149396	−	0.988778i	$-0.452267\pi$
$587$	7.23914	0.298791	0.149396	+	0.988778i	$0.452267\pi$
$588$	−51.8553	−2.13848
$589$	13.1815	0.543135
$590$	−21.3810	−0.880244
$591$	11.8671	0.488147
$592$	−5.14350	−0.211397
$593$	−32.2811	−1.32563	−0.662813	−	0.748785i	$-0.730638\pi$
$593$	−32.2811	−1.32563	−0.662813	+	0.748785i	$0.730638\pi$
$594$	5.26339	0.215960
$595$	−12.6740	−0.519585
$596$	−17.5715	−0.719756
$597$	14.9683	0.612613
$598$	59.2543	2.42309
$599$	14.3937	0.588112	0.294056	−	0.955788i	$-0.404995\pi$
$599$	14.3937	0.588112	0.294056	+	0.955788i	$0.404995\pi$
$600$	1.70595	0.0696451
$601$	−4.39997	−0.179479	−0.0897393	−	0.995965i	$-0.528603\pi$
$601$	−4.39997	−0.179479	−0.0897393	+	0.995965i	$0.528603\pi$
$602$	3.45601	0.140857
$603$	−14.4965	−0.590343
$604$	12.7878	0.520328
$605$	−12.6329	−0.513600
$606$	−0.496456	−0.0201672
$607$	−46.3385	−1.88082	−0.940411	−	0.340040i	$-0.889559\pi$
$607$	−46.3385	−1.88082	−0.940411	+	0.340040i	$0.889559\pi$
$608$	19.2256	0.779702
$609$	0.856519	0.0347079
$610$	21.4910	0.870146
$611$	25.5018	1.03169
$612$	−2.69838	−0.109076
$613$	−20.9925	−0.847880	−0.423940	−	0.905690i	$-0.639353\pi$
$613$	−20.9925	−0.847880	−0.423940	+	0.905690i	$0.639353\pi$
$614$	−17.6904	−0.713927
$615$	4.42055	0.178254
$616$	−18.8213	−0.758332
$617$	21.3941	0.861296	0.430648	−	0.902520i	$-0.358285\pi$
$617$	21.3941	0.861296	0.430648	+	0.902520i	$0.358285\pi$
$618$	22.0223	0.885865
$619$	10.8163	0.434743	0.217371	−	0.976089i	$-0.430252\pi$
$619$	10.8163	0.434743	0.217371	+	0.976089i	$0.430252\pi$
$620$	34.8635	1.40015
$621$	3.87880	0.155651
$622$	13.4853	0.540712
$623$	−74.5448	−2.98658
$624$	14.9095	0.596858
$625$	−29.3647	−1.17459
$626$	2.68859	0.107458
$627$	−6.13212	−0.244893
$628$	−6.01961	−0.240209
$629$	−2.43133	−0.0969435
$630$	−27.4719	−1.09451
$631$	30.5181	1.21491	0.607453	−	0.794356i	$-0.292191\pi$
$631$	30.5181	1.21491	0.607453	+	0.794356i	$0.292191\pi$
$632$	−1.51379	−0.0602153
$633$	0.457690	0.0181916
$634$	−76.4426	−3.03592
$635$	41.6388	1.65238
$636$	−14.8749	−0.589830
$637$	135.438	5.36623
$638$	0.880460	0.0348577
$639$	−6.09993	−0.241310
$640$	28.1487	1.11267
$641$	8.01768	0.316679	0.158340	−	0.987385i	$-0.449386\pi$
$641$	8.01768	0.316679	0.158340	+	0.987385i	$0.449386\pi$
$642$	25.3503	1.00050
$643$	5.53766	0.218384	0.109192	−	0.994021i	$-0.465174\pi$
$643$	5.53766	0.218384	0.109192	+	0.994021i	$0.465174\pi$
$644$	−53.5912	−2.11179
$645$	0.770779	0.0303494
$646$	5.47385	0.215366
$647$	37.5761	1.47727	0.738634	−	0.674107i	$-0.235471\pi$
$647$	37.5761	1.47727	0.738634	+	0.674107i	$0.235471\pi$
$648$	−1.51379	−0.0594672
$649$	9.67664	0.379841
$650$	−17.2157	−0.675254
$651$	−26.7263	−1.04749
$652$	7.80473	0.305657
$653$	−47.8755	−1.87351	−0.936757	−	0.349979i	$-0.886189\pi$
$653$	−47.8755	−1.87351	−0.936757	+	0.349979i	$0.886189\pi$
$654$	−35.5098	−1.38854
$655$	19.4070	0.758293
$656$	3.77807	0.147509
$657$	7.55480	0.294741
$658$	−40.1596	−1.56558
$659$	14.5584	0.567114	0.283557	−	0.958955i	$-0.408486\pi$
$659$	14.5584	0.567114	0.283557	+	0.958955i	$0.408486\pi$
$660$	−16.2187	−0.631312
$661$	46.5140	1.80919	0.904593	−	0.426276i	$-0.140175\pi$
$661$	46.5140	1.80919	0.904593	+	0.426276i	$0.140175\pi$
$662$	−32.0477	−1.24557
$663$	7.04772	0.273711
$664$	−3.83608	−0.148869
$665$	32.0062	1.24115
$666$	−5.27009	−0.204212
$667$	0.648846	0.0251234
$668$	−58.6972	−2.27106
$669$	5.26003	0.203364
$670$	77.7784	3.00484
$671$	−9.72641	−0.375484
$672$	−38.9812	−1.50373
$673$	−46.0261	−1.77418	−0.887088	−	0.461601i	$-0.847275\pi$
$673$	−46.0261	−1.77418	−0.887088	+	0.461601i	$0.847275\pi$
$674$	−6.04959	−0.233022
$675$	−1.12694	−0.0433760
$676$	98.9506	3.80579
$677$	10.7557	0.413374	0.206687	−	0.978407i	$-0.433732\pi$
$677$	10.7557	0.413374	0.206687	+	0.978407i	$0.433732\pi$
$678$	−15.3721	−0.590363
$679$	39.7935	1.52713
$680$	3.74703	0.143692
$681$	18.9322	0.725485
$682$	−27.4733	−1.05201
$683$	18.2625	0.698793	0.349397	−	0.936975i	$-0.386387\pi$
$683$	18.2625	0.698793	0.349397	+	0.936975i	$0.386387\pi$
$684$	6.81431	0.260552
$685$	−25.5335	−0.975583
$686$	−135.594	−5.17699
$687$	−20.5447	−0.783830
$688$	0.658753	0.0251147
$689$	38.8509	1.48010
$690$	−20.8110	−0.792262
$691$	−41.2896	−1.57073	−0.785365	−	0.619034i	$-0.787524\pi$
$691$	−41.2896	−1.57073	−0.785365	+	0.619034i	$0.787524\pi$
$692$	−50.8361	−1.93250
$693$	12.4333	0.472300
$694$	29.7359	1.12876
$695$	−39.3180	−1.49142
$696$	−0.253227	−0.00959853
$697$	1.78589	0.0676454
$698$	−46.3890	−1.75585
$699$	8.43882	0.319185
$700$	15.5703	0.588503
$701$	−14.1273	−0.533580	−0.266790	−	0.963755i	$-0.585963\pi$
$701$	−14.1273	−0.533580	−0.266790	+	0.963755i	$0.585963\pi$
$702$	15.2765	0.576573
$703$	6.13992	0.231572
$704$	−29.7968	−1.12301
$705$	−8.95661	−0.337326
$706$	−40.7806	−1.53480
$707$	−1.17274	−0.0441053
$708$	−10.7532	−0.404128
$709$	−15.2007	−0.570874	−0.285437	−	0.958398i	$-0.592139\pi$
$709$	−15.2007	−0.570874	−0.285437	+	0.958398i	$0.592139\pi$
$710$	32.7281	1.22826
$711$	1.00000	0.0375029
$712$	22.0389	0.825942
$713$	−20.2462	−0.758226
$714$	−11.0986	−0.415354
$715$	42.3606	1.58420
$716$	13.4519	0.502720
$717$	−17.9252	−0.669429
$718$	−21.6286	−0.807174
$719$	12.4689	0.465012	0.232506	−	0.972595i	$-0.425307\pi$
$719$	12.4689	0.465012	0.232506	+	0.972595i	$0.425307\pi$
$720$	−5.23645	−0.195151
$721$	52.0213	1.93737
$722$	27.3606	1.01826
$723$	−11.7543	−0.437147
$724$	−26.4053	−0.981346
$725$	−0.188515	−0.00700126
$726$	−11.0625	−0.410570
$727$	−27.4760	−1.01903	−0.509515	−	0.860462i	$-0.670175\pi$
$727$	−27.4760	−1.01903	−0.509515	+	0.860462i	$0.670175\pi$
$728$	−54.6270	−2.02461
$729$	1.00000	0.0370370
$730$	−40.5340	−1.50023
$731$	0.311392	0.0115173
$732$	10.8085	0.399492
$733$	−29.6131	−1.09378	−0.546892	−	0.837203i	$-0.684189\pi$
$733$	−29.6131	−1.09378	−0.546892	+	0.837203i	$0.684189\pi$
$734$	37.2664	1.37553
$735$	−47.5677	−1.75456
$736$	−29.5297	−1.08848
$737$	−35.2009	−1.29664
$738$	3.87105	0.142495
$739$	7.13099	0.262318	0.131159	−	0.991361i	$-0.458130\pi$
$739$	7.13099	0.262318	0.131159	+	0.991361i	$0.458130\pi$
$740$	16.2394	0.596971
$741$	−17.7979	−0.653821
$742$	−61.1814	−2.24604
$743$	14.1961	0.520805	0.260402	−	0.965500i	$-0.416145\pi$
$743$	14.1961	0.520805	0.260402	+	0.965500i	$0.416145\pi$
$744$	7.90153	0.289684
$745$	−16.1186	−0.590539
$746$	21.3160	0.780435
$747$	2.53409	0.0927176
$748$	−6.55231	−0.239576
$749$	59.8829	2.18807
$750$	−20.7802	−0.758786
$751$	48.4564	1.76820	0.884100	−	0.467298i	$-0.154772\pi$
$751$	48.4564	1.76820	0.884100	+	0.467298i	$0.154772\pi$
$752$	−7.65485	−0.279144
$753$	9.50606	0.346420
$754$	2.55545	0.0930639
$755$	11.7304	0.426915
$756$	−13.8164	−0.502499
$757$	−32.3755	−1.17671	−0.588354	−	0.808603i	$-0.700224\pi$
$757$	−32.3755	−1.17671	−0.588354	+	0.808603i	$0.700224\pi$
$758$	18.9877	0.689665
$759$	9.41866	0.341876
$760$	−9.46251	−0.343241
$761$	41.4460	1.50242	0.751209	−	0.660064i	$-0.229471\pi$
$761$	41.4460	1.50242	0.751209	+	0.660064i	$0.229471\pi$
$762$	36.4628	1.32091
$763$	−83.8817	−3.03672
$764$	−69.7670	−2.52408
$765$	−2.47527	−0.0894934
$766$	65.1479	2.35389
$767$	28.0855	1.01411
$768$	0.107735	0.00388755
$769$	−42.1921	−1.52149	−0.760743	−	0.649054i	$-0.775165\pi$
$769$	−42.1921	−1.52149	−0.760743	+	0.649054i	$0.775165\pi$
$770$	−66.7084	−2.40400
$771$	12.9516	0.466441
$772$	−44.8177	−1.61302
$773$	−40.0966	−1.44218	−0.721088	−	0.692844i	$-0.756358\pi$
$773$	−40.0966	−1.44218	−0.721088	+	0.692844i	$0.756358\pi$
$774$	0.674966	0.0242612
$775$	5.88230	0.211299
$776$	−11.7648	−0.422331
$777$	−12.4491	−0.446608
$778$	47.7341	1.71135
$779$	−4.50997	−0.161586
$780$	−47.0732	−1.68549
$781$	−14.8121	−0.530018
$782$	−8.40759	−0.300655
$783$	0.167280	0.00597810
$784$	−40.6542	−1.45193
$785$	−5.52189	−0.197085
$786$	16.9945	0.606175
$787$	19.5618	0.697303	0.348652	−	0.937252i	$-0.386640\pi$
$787$	19.5618	0.697303	0.348652	+	0.937252i	$0.386640\pi$
$788$	−32.0219	−1.14073
$789$	−3.46583	−0.123387
$790$	−5.36532	−0.190890
$791$	−36.3123	−1.29112
$792$	−3.67584	−0.130615
$793$	−28.2299	−1.00247
$794$	−71.4757	−2.53658
$795$	−13.6450	−0.483939
$796$	−40.3903	−1.43159
$797$	8.01909	0.284051	0.142025	−	0.989863i	$-0.454639\pi$
$797$	8.01909	0.284051	0.142025	+	0.989863i	$0.454639\pi$
$798$	28.0276	0.992167
$799$	−3.61845	−0.128011
$800$	8.57952	0.303332
$801$	−14.5588	−0.514408
$802$	25.1273	0.887277
$803$	18.3449	0.647376
$804$	39.1170	1.37955
$805$	−49.1601	−1.73266
$806$	−79.7386	−2.80867
$807$	−17.0451	−0.600018
$808$	0.346715	0.0121974
$809$	52.4358	1.84354	0.921772	−	0.387732i	$-0.126742\pi$
$809$	52.4358	1.84354	0.921772	+	0.387732i	$0.126742\pi$
$810$	−5.36532	−0.188518
$811$	38.9257	1.36687	0.683433	−	0.730013i	$-0.260486\pi$
$811$	38.9257	1.36687	0.683433	+	0.730013i	$0.260486\pi$
$812$	−2.31121	−0.0811077
$813$	12.5484	0.440091
$814$	−12.7970	−0.448536
$815$	7.15940	0.250783
$816$	−2.11551	−0.0740576
$817$	−0.786370	−0.0275116
$818$	19.7706	0.691262
$819$	36.0863	1.26096
$820$	−11.9283	−0.416555
$821$	29.4619	1.02823	0.514113	−	0.857722i	$-0.328121\pi$
$821$	29.4619	1.02823	0.514113	+	0.857722i	$0.328121\pi$
$822$	−22.3595	−0.779876
$823$	−16.6954	−0.581965	−0.290983	−	0.956728i	$-0.593982\pi$
$823$	−16.6954	−0.581965	−0.290983	+	0.956728i	$0.593982\pi$
$824$	−15.3799	−0.535784
$825$	−2.73648	−0.0952721
$826$	−44.2283	−1.53890
$827$	41.0647	1.42796	0.713980	−	0.700167i	$-0.246891\pi$
$827$	41.0647	1.42796	0.713980	+	0.700167i	$0.246891\pi$
$828$	−10.4665	−0.363735
$829$	18.6798	0.648776	0.324388	−	0.945924i	$-0.394842\pi$
$829$	18.6798	0.648776	0.324388	+	0.945924i	$0.394842\pi$
$830$	−13.5962	−0.471932
$831$	26.0702	0.904365
$832$	−86.4822	−2.99823
$833$	−19.2172	−0.665837
$834$	−34.4305	−1.19223
$835$	−53.8439	−1.86334
$836$	16.5468	0.572282
$837$	−5.21971	−0.180419
$838$	−80.6204	−2.78499
$839$	11.2582	0.388675	0.194338	−	0.980935i	$-0.437744\pi$
$839$	11.2582	0.388675	0.194338	+	0.980935i	$0.437744\pi$
$840$	19.1858	0.661974
$841$	−28.9720	−0.999035
$842$	−38.0017	−1.30963
$843$	−26.3755	−0.908420
$844$	−1.23502	−0.0425112
$845$	90.7689	3.12255
$846$	−7.84325	−0.269656
$847$	−26.1321	−0.897910
$848$	−11.6618	−0.400469
$849$	26.2567	0.901129
$850$	2.44273	0.0837849
$851$	−9.43064	−0.323278
$852$	16.4599	0.563908
$853$	−2.47791	−0.0848421	−0.0424211	−	0.999100i	$-0.513507\pi$
$853$	−2.47791	−0.0848421	−0.0424211	+	0.999100i	$0.513507\pi$
$854$	44.4558	1.52125
$855$	6.25088	0.213775
$856$	−17.7041	−0.605115
$857$	10.1054	0.345195	0.172598	−	0.984992i	$-0.444784\pi$
$857$	10.1054	0.345195	0.172598	+	0.984992i	$0.444784\pi$
$858$	37.0949	1.26640
$859$	43.5451	1.48574	0.742871	−	0.669435i	$-0.233464\pi$
$859$	43.5451	1.48574	0.742871	+	0.669435i	$0.233464\pi$
$860$	−2.07985	−0.0709224
$861$	9.14425	0.311635
$862$	−15.2489	−0.519379
$863$	44.8796	1.52772	0.763859	−	0.645383i	$-0.223302\pi$
$863$	44.8796	1.52772	0.763859	+	0.645383i	$0.223302\pi$
$864$	−7.61310	−0.259003
$865$	−46.6328	−1.58556
$866$	−31.3182	−1.06424
$867$	−1.00000	−0.0339618
$868$	72.1178	2.44784
$869$	2.42824	0.0823724
$870$	−0.897511	−0.0304285
$871$	−102.167	−3.46180
$872$	24.7993	0.839810
$873$	7.77175	0.263034
$874$	21.2320	0.718182
$875$	−49.0873	−1.65945
$876$	−20.3857	−0.688770
$877$	26.1083	0.881614	0.440807	−	0.897602i	$-0.354692\pi$
$877$	26.1083	0.881614	0.440807	+	0.897602i	$0.354692\pi$
$878$	19.9083	0.671873
$879$	21.0956	0.711538
$880$	−12.7153	−0.428634
$881$	−16.8874	−0.568950	−0.284475	−	0.958683i	$-0.591819\pi$
$881$	−16.8874	−0.568950	−0.284475	+	0.958683i	$0.591819\pi$
$882$	−41.6547	−1.40259
$883$	−0.726610	−0.0244524	−0.0122262	−	0.999925i	$-0.503892\pi$
$883$	−0.726610	−0.0244524	−0.0122262	+	0.999925i	$0.503892\pi$
$884$	−19.0174	−0.639625
$885$	−9.86404	−0.331576
$886$	−34.1759	−1.14816
$887$	−11.5875	−0.389072	−0.194536	−	0.980895i	$-0.562320\pi$
$887$	−11.5875	−0.389072	−0.194536	+	0.980895i	$0.562320\pi$
$888$	3.68052	0.123510
$889$	86.1329	2.88881
$890$	78.1124	2.61834
$891$	2.42824	0.0813491
$892$	−14.1936	−0.475235
$893$	9.13779	0.305784
$894$	−14.1149	−0.472074
$895$	12.3396	0.412468
$896$	58.2277	1.94525
$897$	27.3367	0.912746
$898$	−30.2612	−1.00983
$899$	−0.873152	−0.0291213
$900$	3.04091	0.101364
$901$	−5.51254	−0.183649
$902$	9.39984	0.312980
$903$	1.59441	0.0530588
$904$	10.7356	0.357060
$905$	−24.2220	−0.805167
$906$	10.2723	0.341273
$907$	−18.7024	−0.621003	−0.310502	−	0.950573i	$-0.600497\pi$
$907$	−18.7024	−0.621003	−0.310502	+	0.950573i	$0.600497\pi$
$908$	−51.0864	−1.69536
$909$	−0.229038	−0.00759670
$910$	−193.614	−6.41826
$911$	18.4736	0.612057	0.306028	−	0.952022i	$-0.401000\pi$
$911$	18.4736	0.612057	0.306028	+	0.952022i	$0.401000\pi$
$912$	5.34237	0.176904
$913$	6.15338	0.203647
$914$	39.8777	1.31904
$915$	9.91478	0.327772
$916$	55.4375	1.83171
$917$	40.1448	1.32570
$918$	−2.16757	−0.0715406
$919$	41.5190	1.36959	0.684793	−	0.728738i	$-0.259893\pi$
$919$	41.5190	1.36959	0.684793	+	0.728738i	$0.259893\pi$
$920$	14.5340	0.479171
$921$	−8.16138	−0.268927
$922$	44.6387	1.47010
$923$	−42.9906	−1.41505
$924$	−33.5496	−1.10370
$925$	2.73997	0.0900895
$926$	21.3438	0.701400
$927$	10.1599	0.333694
$928$	−1.27352	−0.0418053
$929$	14.8350	0.486721	0.243361	−	0.969936i	$-0.421750\pi$
$929$	14.8350	0.486721	0.243361	+	0.969936i	$0.421750\pi$
$930$	28.0054	0.918334
$931$	48.5299	1.59050
$932$	−22.7711	−0.745893
$933$	6.22138	0.203679
$934$	61.0444	1.99744
$935$	−6.01054	−0.196566
$936$	−10.6688	−0.348719
$937$	−29.3327	−0.958258	−0.479129	−	0.877744i	$-0.659047\pi$
$937$	−29.3327	−0.958258	−0.479129	+	0.877744i	$0.659047\pi$
$938$	160.890	5.25326
$939$	1.24037	0.0404779
$940$	24.1683	0.788284
$941$	52.4865	1.71101	0.855505	−	0.517794i	$-0.173247\pi$
$941$	52.4865	1.71101	0.855505	+	0.517794i	$0.173247\pi$
$942$	−4.83548	−0.157548
$943$	6.92711	0.225578
$944$	−8.43039	−0.274386
$945$	−12.6740	−0.412287
$946$	1.63898	0.0532878
$947$	−12.9005	−0.419208	−0.209604	−	0.977786i	$-0.567218\pi$
$947$	−12.9005	−0.419208	−0.209604	+	0.977786i	$0.567218\pi$
$948$	−2.69838	−0.0876393
$949$	53.2442	1.72838
$950$	−6.16871	−0.200139
$951$	−35.2664	−1.14359
$952$	7.75101	0.251212
$953$	−35.3562	−1.14530	−0.572649	−	0.819801i	$-0.694084\pi$
$953$	−35.3562	−1.14530	−0.572649	+	0.819801i	$0.694084\pi$
$954$	−11.9489	−0.386858
$955$	−63.9984	−2.07094
$956$	48.3690	1.56436
$957$	0.406196	0.0131304
$958$	7.12000	0.230037
$959$	−52.8179	−1.70558
$960$	30.3738	0.980312
$961$	−3.75467	−0.121118
$962$	−37.1421	−1.19751
$963$	11.6953	0.376874
$964$	31.7175	1.02155
$965$	−41.1119	−1.32344
$966$	−43.0492	−1.38508
$967$	36.8112	1.18377	0.591884	−	0.806023i	$-0.298384\pi$
$967$	36.8112	1.18377	0.591884	+	0.806023i	$0.298384\pi$
$968$	7.72585	0.248318
$969$	2.52534	0.0811255
$970$	−41.6979	−1.33884
$971$	21.6642	0.695239	0.347619	−	0.937636i	$-0.386990\pi$
$971$	21.6642	0.695239	0.347619	+	0.937636i	$0.386990\pi$
$972$	−2.69838	−0.0865505
$973$	−81.3323	−2.60739
$974$	−50.1463	−1.60679
$975$	−7.94237	−0.254359
$976$	8.47375	0.271238
$977$	11.2438	0.359722	0.179861	−	0.983692i	$-0.442435\pi$
$977$	11.2438	0.359722	0.179861	+	0.983692i	$0.442435\pi$
$978$	6.26944	0.200475
$979$	−35.3522	−1.12986
$980$	128.356	4.10017
$981$	−16.3823	−0.523046
$982$	−73.7107	−2.35220
$983$	−17.6194	−0.561970	−0.280985	−	0.959712i	$-0.590661\pi$
$983$	−17.6194	−0.561970	−0.280985	+	0.959712i	$0.590661\pi$
$984$	−2.70346	−0.0861832
$985$	−29.3742	−0.935941
$986$	−0.362592	−0.0115473
$987$	−18.5274	−0.589735
$988$	48.0254	1.52789
$989$	1.20783	0.0384067
$990$	−13.0283	−0.414066
$991$	62.4034	1.98231	0.991154	−	0.132718i	$-0.0423704\pi$
$991$	62.4034	1.98231	0.991154	+	0.132718i	$0.0423704\pi$
$992$	39.7381	1.26169
$993$	−14.7850	−0.469189
$994$	67.7005	2.14733
$995$	−37.0506	−1.17458
$996$	−6.83794	−0.216668
$997$	−49.3450	−1.56277	−0.781386	−	0.624048i	$-0.785487\pi$
$997$	−49.3450	−1.56277	−0.781386	+	0.624048i	$0.785487\pi$
$998$	24.6182	0.779276
$999$	−2.43133	−0.0769239

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.l.1.6	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.l.1.6	✓	32	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q-2.16757 q^{2} -1.00000 q^{3} +2.69838 q^{4} +2.47527 q^{5} +2.16757 q^{6} +5.12027 q^{7} -1.51379 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.16757 q^{2} -1.00000 q^{3} +2.69838 q^{4} +2.47527 q^{5} +2.16757 q^{6} +5.12027 q^{7} -1.51379 q^{8} +1.00000 q^{9} -5.36532 q^{10} +2.42824 q^{11} -2.69838 q^{12} +7.04772 q^{13} -11.0986 q^{14} -2.47527 q^{15} -2.11551 q^{16} -1.00000 q^{17} -2.16757 q^{18} +2.52534 q^{19} +6.67921 q^{20} -5.12027 q^{21} -5.26339 q^{22} -3.87880 q^{23} +1.51379 q^{24} +1.12694 q^{25} -15.2765 q^{26} -1.00000 q^{27} +13.8164 q^{28} -0.167280 q^{29} +5.36532 q^{30} +5.21971 q^{31} +7.61310 q^{32} -2.42824 q^{33} +2.16757 q^{34} +12.6740 q^{35} +2.69838 q^{36} +2.43133 q^{37} -5.47385 q^{38} -7.04772 q^{39} -3.74703 q^{40} -1.78589 q^{41} +11.0986 q^{42} -0.311392 q^{43} +6.55231 q^{44} +2.47527 q^{45} +8.40759 q^{46} +3.61845 q^{47} +2.11551 q^{48} +19.2172 q^{49} -2.44273 q^{50} +1.00000 q^{51} +19.0174 q^{52} +5.51254 q^{53} +2.16757 q^{54} +6.01054 q^{55} -7.75101 q^{56} -2.52534 q^{57} +0.362592 q^{58} +3.98504 q^{59} -6.67921 q^{60} -4.00554 q^{61} -11.3141 q^{62} +5.12027 q^{63} -12.2709 q^{64} +17.4450 q^{65} +5.26339 q^{66} -14.4965 q^{67} -2.69838 q^{68} +3.87880 q^{69} -27.4719 q^{70} -6.09993 q^{71} -1.51379 q^{72} +7.55480 q^{73} -5.27009 q^{74} -1.12694 q^{75} +6.81431 q^{76} +12.4333 q^{77} +15.2765 q^{78} +1.00000 q^{79} -5.23645 q^{80} +1.00000 q^{81} +3.87105 q^{82} +2.53409 q^{83} -13.8164 q^{84} -2.47527 q^{85} +0.674966 q^{86} +0.167280 q^{87} -3.67584 q^{88} -14.5588 q^{89} -5.36532 q^{90} +36.0863 q^{91} -10.4665 q^{92} -5.21971 q^{93} -7.84325 q^{94} +6.25088 q^{95} -7.61310 q^{96} +7.77175 q^{97} -41.6547 q^{98} +2.42824 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9} + 17 q^{10} + 8 q^{11} - 41 q^{12} + 17 q^{13} + q^{14} + q^{15} + 55 q^{16} - 32 q^{17} - q^{18} + 48 q^{19} - 7 q^{20} - 4 q^{21} - 4 q^{22} - 19 q^{23} + 3 q^{24} + 63 q^{25} + 27 q^{26} - 32 q^{27} + 17 q^{28} - 15 q^{29} - 17 q^{30} + 20 q^{31} + 13 q^{32} - 8 q^{33} + q^{34} + 22 q^{35} + 41 q^{36} + 6 q^{37} + 11 q^{38} - 17 q^{39} + 47 q^{40} + q^{41} - q^{42} + 40 q^{43} + 22 q^{44} - q^{45} + 5 q^{46} - 5 q^{47} - 55 q^{48} + 88 q^{49} + 17 q^{50} + 32 q^{51} + 23 q^{52} - 34 q^{53} + q^{54} + 48 q^{55} - 48 q^{57} - 9 q^{58} + 41 q^{59} + 7 q^{60} + 20 q^{61} + 15 q^{62} + 4 q^{63} + 93 q^{64} - 58 q^{65} + 4 q^{66} + 52 q^{67} - 41 q^{68} + 19 q^{69} + 25 q^{70} + q^{71} - 3 q^{72} + 19 q^{73} + 12 q^{74} - 63 q^{75} + 128 q^{76} - 20 q^{77} - 27 q^{78} + 32 q^{79} - 16 q^{80} + 32 q^{81} - 5 q^{82} + 31 q^{83} - 17 q^{84} + q^{85} - 62 q^{86} + 15 q^{87} + 35 q^{88} + 18 q^{89} + 17 q^{90} + 48 q^{91} - 75 q^{92} - 20 q^{93} + 29 q^{94} + 5 q^{95} - 13 q^{96} + 17 q^{97} + 30 q^{98} + 8 q^{99}+O(q^{100}) \) 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9 + 17 * q^10 + 8 * q^11 - 41 * q^12 + 17 * q^13 + q^14 + q^15 + 55 * q^16 - 32 * q^17 - q^18 + 48 * q^19 - 7 * q^20 - 4 * q^21 - 4 * q^22 - 19 * q^23 + 3 * q^24 + 63 * q^25 + 27 * q^26 - 32 * q^27 + 17 * q^28 - 15 * q^29 - 17 * q^30 + 20 * q^31 + 13 * q^32 - 8 * q^33 + q^34 + 22 * q^35 + 41 * q^36 + 6 * q^37 + 11 * q^38 - 17 * q^39 + 47 * q^40 + q^41 - q^42 + 40 * q^43 + 22 * q^44 - q^45 + 5 * q^46 - 5 * q^47 - 55 * q^48 + 88 * q^49 + 17 * q^50 + 32 * q^51 + 23 * q^52 - 34 * q^53 + q^54 + 48 * q^55 - 48 * q^57 - 9 * q^58 + 41 * q^59 + 7 * q^60 + 20 * q^61 + 15 * q^62 + 4 * q^63 + 93 * q^64 - 58 * q^65 + 4 * q^66 + 52 * q^67 - 41 * q^68 + 19 * q^69 + 25 * q^70 + q^71 - 3 * q^72 + 19 * q^73 + 12 * q^74 - 63 * q^75 + 128 * q^76 - 20 * q^77 - 27 * q^78 + 32 * q^79 - 16 * q^80 + 32 * q^81 - 5 * q^82 + 31 * q^83 - 17 * q^84 + q^85 - 62 * q^86 + 15 * q^87 + 35 * q^88 + 18 * q^89 + 17 * q^90 + 48 * q^91 - 75 * q^92 - 20 * q^93 + 29 * q^94 + 5 * q^95 - 13 * q^96 + 17 * q^97 + 30 * q^98 + 8 * q^99

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