LMFDB - Embedded newform 8041.2.a.h.1.6

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:	$74$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
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)

$f(q)$	$=$	$q-2.60873 q^{2} -2.96905 q^{3} +4.80548 q^{4} -3.25113 q^{5} +7.74546 q^{6} +1.59414 q^{7} -7.31874 q^{8} +5.81527 q^{9} +O(q^{10})$	\(q-2.60873 q^{2} -2.96905 q^{3} +4.80548 q^{4} -3.25113 q^{5} +7.74546 q^{6} +1.59414 q^{7} -7.31874 q^{8} +5.81527 q^{9} +8.48133 q^{10} -1.00000 q^{11} -14.2677 q^{12} +1.81074 q^{13} -4.15867 q^{14} +9.65278 q^{15} +9.48166 q^{16} -1.00000 q^{17} -15.1705 q^{18} +4.69747 q^{19} -15.6232 q^{20} -4.73307 q^{21} +2.60873 q^{22} +4.13085 q^{23} +21.7297 q^{24} +5.56986 q^{25} -4.72374 q^{26} -8.35869 q^{27} +7.66058 q^{28} -5.75040 q^{29} -25.1815 q^{30} +6.91195 q^{31} -10.0976 q^{32} +2.96905 q^{33} +2.60873 q^{34} -5.18274 q^{35} +27.9452 q^{36} +5.37571 q^{37} -12.2544 q^{38} -5.37618 q^{39} +23.7942 q^{40} -9.53969 q^{41} +12.3473 q^{42} -1.00000 q^{43} -4.80548 q^{44} -18.9062 q^{45} -10.7763 q^{46} -0.376346 q^{47} -28.1515 q^{48} -4.45873 q^{49} -14.5303 q^{50} +2.96905 q^{51} +8.70148 q^{52} +12.9147 q^{53} +21.8056 q^{54} +3.25113 q^{55} -11.6671 q^{56} -13.9470 q^{57} +15.0012 q^{58} +7.29818 q^{59} +46.3862 q^{60} -13.6935 q^{61} -18.0314 q^{62} +9.27033 q^{63} +7.37867 q^{64} -5.88696 q^{65} -7.74546 q^{66} +4.29525 q^{67} -4.80548 q^{68} -12.2647 q^{69} +13.5204 q^{70} -5.06254 q^{71} -42.5604 q^{72} +4.54831 q^{73} -14.0238 q^{74} -16.5372 q^{75} +22.5736 q^{76} -1.59414 q^{77} +14.0250 q^{78} -16.1876 q^{79} -30.8261 q^{80} +7.37156 q^{81} +24.8865 q^{82} +15.2986 q^{83} -22.7447 q^{84} +3.25113 q^{85} +2.60873 q^{86} +17.0732 q^{87} +7.31874 q^{88} -9.48628 q^{89} +49.3212 q^{90} +2.88657 q^{91} +19.8507 q^{92} -20.5219 q^{93} +0.981784 q^{94} -15.2721 q^{95} +29.9804 q^{96} -14.5698 q^{97} +11.6316 q^{98} -5.81527 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9}+O(q^{10}) $ 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9} - 9 q^{10} - 74 q^{11} - 3 q^{12} + 4 q^{13} - 5 q^{14} - 17 q^{15} + 85 q^{16} - 74 q^{17} - 23 q^{18} - 21 q^{20} - 22 q^{21} + 7 q^{22} - 23 q^{23} - 51 q^{24} + 90 q^{25} - 46 q^{26} - 27 q^{27} - 61 q^{28} - 63 q^{29} - 22 q^{30} - 31 q^{31} - 69 q^{32} + 3 q^{33} + 7 q^{34} - 20 q^{35} + 51 q^{36} + 8 q^{37} - 2 q^{38} - 77 q^{39} - 37 q^{40} - 64 q^{41} + 13 q^{42} - 74 q^{43} - 79 q^{44} - 12 q^{45} - 53 q^{46} - 32 q^{47} + 2 q^{48} + 78 q^{49} - 104 q^{50} + 3 q^{51} + 13 q^{52} + 25 q^{53} - 110 q^{54} + 6 q^{55} - 29 q^{56} - 29 q^{57} - 14 q^{58} - 61 q^{59} - 82 q^{60} - 36 q^{61} - 63 q^{62} - 104 q^{63} + 107 q^{64} - 65 q^{65} + 12 q^{66} + 33 q^{67} - 79 q^{68} - 34 q^{69} - 3 q^{70} - 168 q^{71} - 67 q^{72} - 47 q^{73} - 54 q^{74} - 53 q^{75} - 4 q^{76} + 16 q^{77} - 3 q^{78} - 79 q^{79} - 59 q^{80} + 70 q^{81} - 18 q^{82} - 36 q^{83} - 118 q^{84} + 6 q^{85} + 7 q^{86} - 24 q^{87} + 21 q^{88} - 24 q^{89} + 25 q^{90} - 14 q^{91} - 18 q^{92} - 13 q^{93} + 9 q^{94} - 155 q^{95} - 50 q^{96} + q^{97} - 60 q^{98} - 75 q^{99}+O(q^{100}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9 - 9 * q^10 - 74 * q^11 - 3 * q^12 + 4 * q^13 - 5 * q^14 - 17 * q^15 + 85 * q^16 - 74 * q^17 - 23 * q^18 - 21 * q^20 - 22 * q^21 + 7 * q^22 - 23 * q^23 - 51 * q^24 + 90 * q^25 - 46 * q^26 - 27 * q^27 - 61 * q^28 - 63 * q^29 - 22 * q^30 - 31 * q^31 - 69 * q^32 + 3 * q^33 + 7 * q^34 - 20 * q^35 + 51 * q^36 + 8 * q^37 - 2 * q^38 - 77 * q^39 - 37 * q^40 - 64 * q^41 + 13 * q^42 - 74 * q^43 - 79 * q^44 - 12 * q^45 - 53 * q^46 - 32 * q^47 + 2 * q^48 + 78 * q^49 - 104 * q^50 + 3 * q^51 + 13 * q^52 + 25 * q^53 - 110 * q^54 + 6 * q^55 - 29 * q^56 - 29 * q^57 - 14 * q^58 - 61 * q^59 - 82 * q^60 - 36 * q^61 - 63 * q^62 - 104 * q^63 + 107 * q^64 - 65 * q^65 + 12 * q^66 + 33 * q^67 - 79 * q^68 - 34 * q^69 - 3 * q^70 - 168 * q^71 - 67 * q^72 - 47 * q^73 - 54 * q^74 - 53 * q^75 - 4 * q^76 + 16 * q^77 - 3 * q^78 - 79 * q^79 - 59 * q^80 + 70 * q^81 - 18 * q^82 - 36 * q^83 - 118 * q^84 + 6 * q^85 + 7 * q^86 - 24 * q^87 + 21 * q^88 - 24 * q^89 + 25 * q^90 - 14 * q^91 - 18 * q^92 - 13 * q^93 + 9 * q^94 - 155 * q^95 - 50 * q^96 + q^97 - 60 * q^98 - 75 * 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 $

$2$	−2.60873	−1.84465	−0.922326	−	0.386413i	$-0.873714\pi$
$2$	−2.60873	−1.84465	−0.922326	+	0.386413i	$0.873714\pi$
$3$	−2.96905	−1.71418	−0.857092	−	0.515164i	$-0.827731\pi$
$3$	−2.96905	−1.71418	−0.857092	+	0.515164i	$0.827731\pi$
$4$	4.80548	2.40274
$5$	−3.25113	−1.45395	−0.726975	−	0.686664i	$-0.759074\pi$
$5$	−3.25113	−1.45395	−0.726975	+	0.686664i	$0.759074\pi$
$6$	7.74546	3.16207
$7$	1.59414	0.602527	0.301263	−	0.953541i	$-0.402592\pi$
$7$	1.59414	0.602527	0.301263	+	0.953541i	$0.402592\pi$
$8$	−7.31874	−2.58756
$9$	5.81527	1.93842
$10$	8.48133	2.68203
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−14.2677	−4.11873
$13$	1.81074	0.502209	0.251105	−	0.967960i	$-0.419206\pi$
$13$	1.81074	0.502209	0.251105	+	0.967960i	$0.419206\pi$
$14$	−4.15867	−1.11145
$15$	9.65278	2.49234
$16$	9.48166	2.37041
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−15.1705	−3.57572
$19$	4.69747	1.07767	0.538837	−	0.842410i	$-0.318864\pi$
$19$	4.69747	1.07767	0.538837	+	0.842410i	$0.318864\pi$
$20$	−15.6232	−3.49346
$21$	−4.73307	−1.03284
$22$	2.60873	0.556183
$23$	4.13085	0.861342	0.430671	−	0.902509i	$-0.358277\pi$
$23$	4.13085	0.861342	0.430671	+	0.902509i	$0.358277\pi$
$24$	21.7297	4.43556
$25$	5.56986	1.11397
$26$	−4.72374	−0.926401
$27$	−8.35869	−1.60863
$28$	7.66058	1.44771
$29$	−5.75040	−1.06782	−0.533911	−	0.845541i	$-0.679278\pi$
$29$	−5.75040	−1.06782	−0.533911	+	0.845541i	$0.679278\pi$
$30$	−25.1815	−4.59749
$31$	6.91195	1.24142	0.620711	−	0.784039i	$-0.286844\pi$
$31$	6.91195	1.24142	0.620711	+	0.784039i	$0.286844\pi$
$32$	−10.0976	−1.78502
$33$	2.96905	0.516846
$34$	2.60873	0.447394
$35$	−5.18274	−0.876044
$36$	27.9452	4.65753
$37$	5.37571	0.883762	0.441881	−	0.897074i	$-0.354311\pi$
$37$	5.37571	0.883762	0.441881	+	0.897074i	$0.354311\pi$
$38$	−12.2544	−1.98793
$39$	−5.37618	−0.860879
$40$	23.7942	3.76219
$41$	−9.53969	−1.48985	−0.744925	−	0.667148i	$-0.767515\pi$
$41$	−9.53969	−1.48985	−0.744925	+	0.667148i	$0.767515\pi$
$42$	12.3473	1.90523
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−4.80548	−0.724453
$45$	−18.9062	−2.81837
$46$	−10.7763	−1.58888
$47$	−0.376346	−0.0548956	−0.0274478	−	0.999623i	$-0.508738\pi$
$47$	−0.376346	−0.0548956	−0.0274478	+	0.999623i	$0.508738\pi$
$48$	−28.1515	−4.06332
$49$	−4.45873	−0.636962
$50$	−14.5303	−2.05489
$51$	2.96905	0.415750
$52$	8.70148	1.20668
$53$	12.9147	1.77397	0.886983	−	0.461803i	$-0.152797\pi$
$53$	12.9147	1.77397	0.886983	+	0.461803i	$0.152797\pi$
$54$	21.8056	2.96736
$55$	3.25113	0.438383
$56$	−11.6671	−1.55908
$57$	−13.9470	−1.84733
$58$	15.0012	1.96976
$59$	7.29818	0.950142	0.475071	−	0.879947i	$-0.342422\pi$
$59$	7.29818	0.950142	0.475071	+	0.879947i	$0.342422\pi$
$60$	46.3862	5.98843
$61$	−13.6935	−1.75327	−0.876635	−	0.481155i	$-0.840217\pi$
$61$	−13.6935	−1.75327	−0.876635	+	0.481155i	$0.840217\pi$
$62$	−18.0314	−2.28999
$63$	9.27033	1.16795
$64$	7.37867	0.922334
$65$	−5.88696	−0.730187
$66$	−7.74546	−0.953400
$67$	4.29525	0.524748	0.262374	−	0.964966i	$-0.415495\pi$
$67$	4.29525	0.524748	0.262374	+	0.964966i	$0.415495\pi$
$68$	−4.80548	−0.582750
$69$	−12.2647	−1.47650
$70$	13.5204	1.61600
$71$	−5.06254	−0.600813	−0.300407	−	0.953811i	$-0.597122\pi$
$71$	−5.06254	−0.600813	−0.300407	+	0.953811i	$0.597122\pi$
$72$	−42.5604	−5.01580
$73$	4.54831	0.532339	0.266170	−	0.963926i	$-0.414242\pi$
$73$	4.54831	0.532339	0.266170	+	0.963926i	$0.414242\pi$
$74$	−14.0238	−1.63023
$75$	−16.5372	−1.90955
$76$	22.5736	2.58937
$77$	−1.59414	−0.181669
$78$	14.0250	1.58802
$79$	−16.1876	−1.82125	−0.910626	−	0.413231i	$-0.864400\pi$
$79$	−16.1876	−1.82125	−0.910626	+	0.413231i	$0.864400\pi$
$80$	−30.8261	−3.44647
$81$	7.37156	0.819063
$82$	24.8865	2.74825
$83$	15.2986	1.67924	0.839621	−	0.543172i	$-0.182777\pi$
$83$	15.2986	1.67924	0.839621	+	0.543172i	$0.182777\pi$
$84$	−22.7447	−2.48165
$85$	3.25113	0.352635
$86$	2.60873	0.281307
$87$	17.0732	1.83044
$88$	7.31874	0.780180
$89$	−9.48628	−1.00554	−0.502772	−	0.864419i	$-0.667686\pi$
$89$	−9.48628	−1.00554	−0.502772	+	0.864419i	$0.667686\pi$
$90$	49.3212	5.19891
$91$	2.88657	0.302594
$92$	19.8507	2.06958
$93$	−20.5219	−2.12803
$94$	0.981784	0.101263
$95$	−15.2721	−1.56688
$96$	29.9804	3.05986
$97$	−14.5698	−1.47934	−0.739668	−	0.672972i	$-0.765017\pi$
$97$	−14.5698	−1.47934	−0.739668	+	0.672972i	$0.765017\pi$
$98$	11.6316	1.17497
$99$	−5.81527	−0.584457
$100$	26.7658	2.67658
$101$	−13.8225	−1.37539	−0.687695	−	0.726000i	$-0.741377\pi$
$101$	−13.8225	−1.37539	−0.687695	+	0.726000i	$0.741377\pi$
$102$	−7.74546	−0.766915
$103$	8.32313	0.820102	0.410051	−	0.912063i	$-0.365511\pi$
$103$	8.32313	0.820102	0.410051	+	0.912063i	$0.365511\pi$
$104$	−13.2523	−1.29950
$105$	15.3878	1.50170
$106$	−33.6909	−3.27235
$107$	−6.33685	−0.612606	−0.306303	−	0.951934i	$-0.599092\pi$
$107$	−6.33685	−0.612606	−0.306303	+	0.951934i	$0.599092\pi$
$108$	−40.1675	−3.86512
$109$	6.98356	0.668904	0.334452	−	0.942413i	$-0.391449\pi$
$109$	6.98356	0.668904	0.334452	+	0.942413i	$0.391449\pi$
$110$	−8.48133	−0.808663
$111$	−15.9608	−1.51493
$112$	15.1150	1.42824
$113$	0.875000	0.0823130	0.0411565	−	0.999153i	$-0.486896\pi$
$113$	0.875000	0.0823130	0.0411565	+	0.999153i	$0.486896\pi$
$114$	36.3841	3.40768
$115$	−13.4299	−1.25235
$116$	−27.6334	−2.56570
$117$	10.5300	0.973494
$118$	−19.0390	−1.75268
$119$	−1.59414	−0.146134
$120$	−70.6461	−6.44908
$121$	1.00000	0.0909091
$122$	35.7226	3.23417
$123$	28.3238	2.55388
$124$	33.2152	2.98281
$125$	−1.85268	−0.165709
$126$	−24.1838	−2.15446
$127$	−8.50275	−0.754497	−0.377249	−	0.926112i	$-0.623130\pi$
$127$	−8.50275	−0.754497	−0.377249	+	0.926112i	$0.623130\pi$
$128$	0.946285	0.0836405
$129$	2.96905	0.261410
$130$	15.3575	1.34694
$131$	−18.5961	−1.62475	−0.812376	−	0.583134i	$-0.801826\pi$
$131$	−18.5961	−1.62475	−0.812376	+	0.583134i	$0.801826\pi$
$132$	14.2677	1.24185
$133$	7.48841	0.649327
$134$	−11.2051	−0.967977
$135$	27.1752	2.33887
$136$	7.31874	0.627576
$137$	−17.1202	−1.46268	−0.731339	−	0.682014i	$-0.761104\pi$
$137$	−17.1202	−1.46268	−0.731339	+	0.682014i	$0.761104\pi$
$138$	31.9953	2.72362
$139$	13.1505	1.11541	0.557707	−	0.830038i	$-0.311681\pi$
$139$	13.1505	1.11541	0.557707	+	0.830038i	$0.311681\pi$
$140$	−24.9056	−2.10490
$141$	1.11739	0.0941012
$142$	13.2068	1.10829
$143$	−1.81074	−0.151422
$144$	55.1384	4.59487
$145$	18.6953	1.55256
$146$	−11.8653	−0.981980
$147$	13.2382	1.09187
$148$	25.8329	2.12345
$149$	21.4174	1.75458	0.877289	−	0.479962i	$-0.159350\pi$
$149$	21.4174	1.75458	0.877289	+	0.479962i	$0.159350\pi$
$150$	43.1411	3.52246
$151$	−19.1695	−1.55999	−0.779994	−	0.625787i	$-0.784778\pi$
$151$	−19.1695	−1.55999	−0.779994	+	0.625787i	$0.784778\pi$
$152$	−34.3796	−2.78855
$153$	−5.81527	−0.470137
$154$	4.15867	0.335115
$155$	−22.4717	−1.80497
$156$	−25.8351	−2.06847
$157$	−4.77162	−0.380816	−0.190408	−	0.981705i	$-0.560981\pi$
$157$	−4.77162	−0.380816	−0.190408	+	0.981705i	$0.560981\pi$
$158$	42.2292	3.35958
$159$	−38.3443	−3.04090
$160$	32.8287	2.59534
$161$	6.58513	0.518981
$162$	−19.2304	−1.51089
$163$	−8.88173	−0.695671	−0.347835	−	0.937556i	$-0.613083\pi$
$163$	−8.88173	−0.695671	−0.347835	+	0.937556i	$0.613083\pi$
$164$	−45.8428	−3.57972
$165$	−9.65278	−0.751468
$166$	−39.9100	−3.09762
$167$	19.9773	1.54589	0.772945	−	0.634473i	$-0.218783\pi$
$167$	19.9773	1.54589	0.772945	+	0.634473i	$0.218783\pi$
$168$	34.6401	2.67254
$169$	−9.72122	−0.747786
$170$	−8.48133	−0.650488
$171$	27.3171	2.08899
$172$	−4.80548	−0.366414
$173$	−7.58300	−0.576525	−0.288262	−	0.957551i	$-0.593078\pi$
$173$	−7.58300	−0.576525	−0.288262	+	0.957551i	$0.593078\pi$
$174$	−44.5395	−3.37653
$175$	8.87911	0.671197
$176$	−9.48166	−0.714707
$177$	−21.6687	−1.62872
$178$	24.7472	1.85488
$179$	−5.31093	−0.396958	−0.198479	−	0.980105i	$-0.563600\pi$
$179$	−5.31093	−0.396958	−0.198479	+	0.980105i	$0.563600\pi$
$180$	−90.8534	−6.77181
$181$	12.8739	0.956911	0.478456	−	0.878112i	$-0.341197\pi$
$181$	12.8739	0.956911	0.478456	+	0.878112i	$0.341197\pi$
$182$	−7.53028	−0.558181
$183$	40.6567	3.00543
$184$	−30.2326	−2.22878
$185$	−17.4771	−1.28495
$186$	53.5362	3.92546
$187$	1.00000	0.0731272
$188$	−1.80852	−0.131900
$189$	−13.3249	−0.969242
$190$	39.8408	2.89036
$191$	8.48748	0.614133	0.307066	−	0.951688i	$-0.400653\pi$
$191$	8.48748	0.614133	0.307066	+	0.951688i	$0.400653\pi$
$192$	−21.9077	−1.58105
$193$	−12.2060	−0.878605	−0.439302	−	0.898339i	$-0.644774\pi$
$193$	−12.2060	−0.878605	−0.439302	+	0.898339i	$0.644774\pi$
$194$	38.0086	2.72886
$195$	17.4787	1.25167
$196$	−21.4263	−1.53045
$197$	17.1909	1.22480	0.612401	−	0.790548i	$-0.290204\pi$
$197$	17.1909	1.22480	0.612401	+	0.790548i	$0.290204\pi$
$198$	15.1705	1.07812
$199$	11.5722	0.820332	0.410166	−	0.912011i	$-0.365471\pi$
$199$	11.5722	0.820332	0.410166	+	0.912011i	$0.365471\pi$
$200$	−40.7643	−2.88247
$201$	−12.7528	−0.899514
$202$	36.0592	2.53711
$203$	−9.16691	−0.643391
$204$	14.2677	0.998940
$205$	31.0148	2.16617
$206$	−21.7128	−1.51280
$207$	24.0220	1.66965
$208$	17.1688	1.19044
$209$	−4.69747	−0.324931
$210$	−40.1427	−2.77011
$211$	1.58698	0.109252	0.0546260	−	0.998507i	$-0.482603\pi$
$211$	1.58698	0.109252	0.0546260	+	0.998507i	$0.482603\pi$
$212$	62.0611	4.26237
$213$	15.0310	1.02990
$214$	16.5311	1.13004
$215$	3.25113	0.221725
$216$	61.1750	4.16243
$217$	11.0186	0.747990
$218$	−18.2182	−1.23389
$219$	−13.5042	−0.912527
$220$	15.6232	1.05332
$221$	−1.81074	−0.121804
$222$	41.6374	2.79452
$223$	−7.23984	−0.484815	−0.242408	−	0.970174i	$-0.577937\pi$
$223$	−7.23984	−0.484815	−0.242408	+	0.970174i	$0.577937\pi$
$224$	−16.0970	−1.07552
$225$	32.3902	2.15935
$226$	−2.28264	−0.151839
$227$	−12.7854	−0.848595	−0.424297	−	0.905523i	$-0.639479\pi$
$227$	−12.7854	−0.848595	−0.424297	+	0.905523i	$0.639479\pi$
$228$	−67.0222	−4.43865
$229$	0.882512	0.0583180	0.0291590	−	0.999575i	$-0.490717\pi$
$229$	0.882512	0.0583180	0.0291590	+	0.999575i	$0.490717\pi$
$230$	35.0351	2.31015
$231$	4.73307	0.311413
$232$	42.0856	2.76306
$233$	−5.36742	−0.351632	−0.175816	−	0.984423i	$-0.556256\pi$
$233$	−5.36742	−0.351632	−0.175816	+	0.984423i	$0.556256\pi$
$234$	−27.4698	−1.79576
$235$	1.22355	0.0798155
$236$	35.0713	2.28294
$237$	48.0620	3.12196
$238$	4.15867	0.269567
$239$	−15.8882	−1.02772	−0.513862	−	0.857873i	$-0.671786\pi$
$239$	−15.8882	−1.02772	−0.513862	+	0.857873i	$0.671786\pi$
$240$	91.5244	5.90787
$241$	12.2815	0.791118	0.395559	−	0.918441i	$-0.370551\pi$
$241$	12.2815	0.791118	0.395559	+	0.918441i	$0.370551\pi$
$242$	−2.60873	−0.167696
$243$	3.18950	0.204607
$244$	−65.8037	−4.21265
$245$	14.4959	0.926111
$246$	−73.8893	−4.71101
$247$	8.50591	0.541218
$248$	−50.5867	−3.21226
$249$	−45.4224	−2.87853
$250$	4.83315	0.305675
$251$	7.85545	0.495831	0.247916	−	0.968782i	$-0.420254\pi$
$251$	7.85545	0.495831	0.247916	+	0.968782i	$0.420254\pi$
$252$	44.5484	2.80628
$253$	−4.13085	−0.259704
$254$	22.1814	1.39178
$255$	−9.65278	−0.604481
$256$	−17.2259	−1.07662
$257$	24.2294	1.51139	0.755695	−	0.654924i	$-0.227299\pi$
$257$	24.2294	1.51139	0.755695	+	0.654924i	$0.227299\pi$
$258$	−7.74546	−0.482211
$259$	8.56961	0.532490
$260$	−28.2896	−1.75445
$261$	−33.4401	−2.06989
$262$	48.5123	2.99710
$263$	15.4347	0.951744	0.475872	−	0.879515i	$-0.342133\pi$
$263$	15.4347	0.951744	0.475872	+	0.879515i	$0.342133\pi$
$264$	−21.7297	−1.33737
$265$	−41.9873	−2.57926
$266$	−19.5352	−1.19778
$267$	28.1653	1.72369
$268$	20.6407	1.26083
$269$	11.9601	0.729219	0.364609	−	0.931161i	$-0.381203\pi$
$269$	11.9601	0.729219	0.364609	+	0.931161i	$0.381203\pi$
$270$	−70.8928	−4.31440
$271$	4.22191	0.256463	0.128231	−	0.991744i	$-0.459070\pi$
$271$	4.22191	0.256463	0.128231	+	0.991744i	$0.459070\pi$
$272$	−9.48166	−0.574910
$273$	−8.57037	−0.518702
$274$	44.6620	2.69813
$275$	−5.56986	−0.335875
$276$	−58.9378	−3.54764
$277$	−2.91244	−0.174991	−0.0874957	−	0.996165i	$-0.527886\pi$
$277$	−2.91244	−0.174991	−0.0874957	+	0.996165i	$0.527886\pi$
$278$	−34.3062	−2.05755
$279$	40.1948	2.40640
$280$	37.9311	2.26682
$281$	−12.8974	−0.769393	−0.384697	−	0.923043i	$-0.625694\pi$
$281$	−12.8974	−0.769393	−0.384697	+	0.923043i	$0.625694\pi$
$282$	−2.91497	−0.173584
$283$	30.5390	1.81536	0.907679	−	0.419665i	$-0.137853\pi$
$283$	30.5390	1.81536	0.907679	+	0.419665i	$0.137853\pi$
$284$	−24.3279	−1.44360
$285$	45.3437	2.68593
$286$	4.72374	0.279320
$287$	−15.2076	−0.897674
$288$	−58.7204	−3.46013
$289$	1.00000	0.0588235
$290$	−48.7710	−2.86393
$291$	43.2584	2.53585
$292$	21.8568	1.27907
$293$	20.5839	1.20252	0.601261	−	0.799053i	$-0.294665\pi$
$293$	20.5839	1.20252	0.601261	+	0.799053i	$0.294665\pi$
$294$	−34.5349	−2.01412
$295$	−23.7274	−1.38146
$296$	−39.3434	−2.28679
$297$	8.35869	0.485020
$298$	−55.8721	−3.23659
$299$	7.47990	0.432574
$300$	−79.4691	−4.58815
$301$	−1.59414	−0.0918844
$302$	50.0080	2.87763
$303$	41.0397	2.35767
$304$	44.5398	2.55453
$305$	44.5193	2.54917
$306$	15.1705	0.867238
$307$	−0.239582	−0.0136736	−0.00683682	−	0.999977i	$-0.502176\pi$
$307$	−0.239582	−0.0136736	−0.00683682	+	0.999977i	$0.502176\pi$
$308$	−7.66058	−0.436502
$309$	−24.7118	−1.40581
$310$	58.6225	3.32953
$311$	−3.04378	−0.172597	−0.0862986	−	0.996269i	$-0.527504\pi$
$311$	−3.04378	−0.172597	−0.0862986	+	0.996269i	$0.527504\pi$
$312$	39.3469	2.22758
$313$	11.4824	0.649021	0.324511	−	0.945882i	$-0.394800\pi$
$313$	11.4824	0.649021	0.324511	+	0.945882i	$0.394800\pi$
$314$	12.4479	0.702474
$315$	−30.1391	−1.69814
$316$	−77.7894	−4.37599
$317$	4.51377	0.253519	0.126759	−	0.991933i	$-0.459542\pi$
$317$	4.51377	0.253519	0.126759	+	0.991933i	$0.459542\pi$
$318$	100.030	5.60940
$319$	5.75040	0.321960
$320$	−23.9890	−1.34103
$321$	18.8144	1.05012
$322$	−17.1788	−0.957339
$323$	−4.69747	−0.261374
$324$	35.4239	1.96799
$325$	10.0856	0.559447
$326$	23.1700	1.28327
$327$	−20.7346	−1.14662
$328$	69.8185	3.85508
$329$	−0.599946	−0.0330761
$330$	25.1815	1.38620
$331$	12.3813	0.680538	0.340269	−	0.940328i	$-0.389482\pi$
$331$	12.3813	0.680538	0.340269	+	0.940328i	$0.389482\pi$
$332$	73.5172	4.03478
$333$	31.2612	1.71310
$334$	−52.1154	−2.85163
$335$	−13.9644	−0.762957
$336$	−44.8774	−2.44826
$337$	−31.8580	−1.73541	−0.867707	−	0.497076i	$-0.834407\pi$
$337$	−31.8580	−1.73541	−0.867707	+	0.497076i	$0.834407\pi$
$338$	25.3600	1.37940
$339$	−2.59792	−0.141100
$340$	15.6232	0.847289
$341$	−6.91195	−0.374303
$342$	−71.2629	−3.85346
$343$	−18.2668	−0.986313
$344$	7.31874	0.394600
$345$	39.8742	2.14675
$346$	19.7820	1.06349
$347$	−12.4880	−0.670392	−0.335196	−	0.942148i	$-0.608803\pi$
$347$	−12.4880	−0.670392	−0.335196	+	0.942148i	$0.608803\pi$
$348$	82.0450	4.39808
$349$	16.9986	0.909917	0.454958	−	0.890513i	$-0.349654\pi$
$349$	16.9986	0.909917	0.454958	+	0.890513i	$0.349654\pi$
$350$	−23.1632	−1.23813
$351$	−15.1354	−0.807869
$352$	10.0976	0.538205
$353$	−2.00274	−0.106595	−0.0532974	−	0.998579i	$-0.516973\pi$
$353$	−2.00274	−0.106595	−0.0532974	+	0.998579i	$0.516973\pi$
$354$	56.5278	3.00442
$355$	16.4590	0.873553
$356$	−45.5861	−2.41606
$357$	4.73307	0.250501
$358$	13.8548	0.732248
$359$	33.8528	1.78668	0.893342	−	0.449377i	$-0.148354\pi$
$359$	33.8528	1.78668	0.893342	+	0.449377i	$0.148354\pi$
$360$	138.370	7.29272
$361$	3.06624	0.161381
$362$	−33.5846	−1.76517
$363$	−2.96905	−0.155835
$364$	13.8713	0.727055
$365$	−14.7871	−0.773995
$366$	−106.062	−5.54396
$367$	−14.8207	−0.773634	−0.386817	−	0.922157i	$-0.626425\pi$
$367$	−14.8207	−0.773634	−0.386817	+	0.922157i	$0.626425\pi$
$368$	39.1673	2.04174
$369$	−55.4759	−2.88796
$370$	45.5932	2.37028
$371$	20.5877	1.06886
$372$	−98.6177	−5.11309
$373$	−12.0042	−0.621554	−0.310777	−	0.950483i	$-0.600589\pi$
$373$	−12.0042	−0.621554	−0.310777	+	0.950483i	$0.600589\pi$
$374$	−2.60873	−0.134894
$375$	5.50071	0.284055
$376$	2.75437	0.142046
$377$	−10.4125	−0.536270
$378$	34.7610	1.78791
$379$	3.62001	0.185947	0.0929736	−	0.995669i	$-0.470363\pi$
$379$	3.62001	0.185947	0.0929736	+	0.995669i	$0.470363\pi$
$380$	−73.3897	−3.76481
$381$	25.2451	1.29335
$382$	−22.1416	−1.13286
$383$	−5.96235	−0.304662	−0.152331	−	0.988330i	$-0.548678\pi$
$383$	−5.96235	−0.304662	−0.152331	+	0.988330i	$0.548678\pi$
$384$	−2.80957	−0.143375
$385$	5.18274	0.264137
$386$	31.8421	1.62072
$387$	−5.81527	−0.295607
$388$	−70.0147	−3.55446
$389$	−9.77144	−0.495432	−0.247716	−	0.968833i	$-0.579680\pi$
$389$	−9.77144	−0.495432	−0.247716	+	0.968833i	$0.579680\pi$
$390$	−45.5972	−2.30890
$391$	−4.13085	−0.208906
$392$	32.6323	1.64818
$393$	55.2129	2.78512
$394$	−44.8464	−2.25933
$395$	52.6282	2.64801
$396$	−27.9452	−1.40430
$397$	−26.0150	−1.30566	−0.652828	−	0.757506i	$-0.726418\pi$
$397$	−26.0150	−1.30566	−0.652828	+	0.757506i	$0.726418\pi$
$398$	−30.1888	−1.51323
$399$	−22.2335	−1.11307
$400$	52.8115	2.64057
$401$	−1.16894	−0.0583739	−0.0291869	−	0.999574i	$-0.509292\pi$
$401$	−1.16894	−0.0583739	−0.0291869	+	0.999574i	$0.509292\pi$
$402$	33.2687	1.65929
$403$	12.5157	0.623454
$404$	−66.4237	−3.30470
$405$	−23.9659	−1.19088
$406$	23.9140	1.18683
$407$	−5.37571	−0.266464
$408$	−21.7297	−1.07578
$409$	27.1121	1.34061	0.670303	−	0.742088i	$-0.266164\pi$
$409$	27.1121	1.34061	0.670303	+	0.742088i	$0.266164\pi$
$410$	−80.9093	−3.99582
$411$	50.8308	2.50730
$412$	39.9966	1.97049
$413$	11.6343	0.572486
$414$	−62.6670	−3.07991
$415$	−49.7378	−2.44153
$416$	−18.2842	−0.896456
$417$	−39.0447	−1.91203
$418$	12.2544	0.599384
$419$	−5.96316	−0.291320	−0.145660	−	0.989335i	$-0.546530\pi$
$419$	−5.96316	−0.291320	−0.145660	+	0.989335i	$0.546530\pi$
$420$	73.9459	3.60819
$421$	−1.10182	−0.0536993	−0.0268497	−	0.999639i	$-0.508548\pi$
$421$	−1.10182	−0.0536993	−0.0268497	+	0.999639i	$0.508548\pi$
$422$	−4.14000	−0.201532
$423$	−2.18855	−0.106411
$424$	−94.5190	−4.59025
$425$	−5.56986	−0.270178
$426$	−39.2117	−1.89981
$427$	−21.8293	−1.05639
$428$	−30.4516	−1.47193
$429$	5.37618	0.259565
$430$	−8.48133	−0.409006
$431$	−24.6680	−1.18821	−0.594107	−	0.804386i	$-0.702494\pi$
$431$	−24.6680	−1.18821	−0.594107	+	0.804386i	$0.702494\pi$
$432$	−79.2542	−3.81312
$433$	0.227496	0.0109328	0.00546638	−	0.999985i	$-0.498260\pi$
$433$	0.227496	0.0109328	0.00546638	+	0.999985i	$0.498260\pi$
$434$	−28.7445	−1.37978
$435$	−55.5073	−2.66137
$436$	33.5594	1.60720
$437$	19.4046	0.928246
$438$	35.2287	1.68329
$439$	37.5252	1.79098	0.895489	−	0.445084i	$-0.146826\pi$
$439$	37.5252	1.79098	0.895489	+	0.445084i	$0.146826\pi$
$440$	−23.7942	−1.13434
$441$	−25.9287	−1.23470
$442$	4.72374	0.224685
$443$	40.3721	1.91814	0.959068	−	0.283175i	$-0.0913878\pi$
$443$	40.3721	1.91814	0.959068	+	0.283175i	$0.0913878\pi$
$444$	−76.6991	−3.63998
$445$	30.8412	1.46201
$446$	18.8868	0.894316
$447$	−63.5893	−3.00767
$448$	11.7626	0.555731
$449$	12.0272	0.567597	0.283799	−	0.958884i	$-0.408405\pi$
$449$	12.0272	0.567597	0.283799	+	0.958884i	$0.408405\pi$
$450$	−84.4974	−3.98325
$451$	9.53969	0.449207
$452$	4.20479	0.197777
$453$	56.9151	2.67411
$454$	33.3536	1.56536
$455$	−9.38461	−0.439957
$456$	102.075	4.78009
$457$	−1.49360	−0.0698677	−0.0349339	−	0.999390i	$-0.511122\pi$
$457$	−1.49360	−0.0698677	−0.0349339	+	0.999390i	$0.511122\pi$
$458$	−2.30224	−0.107576
$459$	8.35869	0.390150
$460$	−64.5373	−3.00907
$461$	−16.6832	−0.777014	−0.388507	−	0.921446i	$-0.627009\pi$
$461$	−16.6832	−0.777014	−0.388507	+	0.921446i	$0.627009\pi$
$462$	−12.3473	−0.574449
$463$	−27.8073	−1.29231	−0.646157	−	0.763205i	$-0.723625\pi$
$463$	−27.8073	−1.29231	−0.646157	+	0.763205i	$0.723625\pi$
$464$	−54.5233	−2.53118
$465$	66.7195	3.09404
$466$	14.0022	0.648638
$467$	−7.32219	−0.338831	−0.169415	−	0.985545i	$-0.554188\pi$
$467$	−7.32219	−0.338831	−0.169415	+	0.985545i	$0.554188\pi$
$468$	50.6014	2.33905
$469$	6.84720	0.316175
$470$	−3.19191	−0.147232
$471$	14.1672	0.652789
$472$	−53.4135	−2.45855
$473$	1.00000	0.0459800
$474$	−125.381	−5.75893
$475$	26.1643	1.20050
$476$	−7.66058	−0.351122
$477$	75.1023	3.43870
$478$	41.4481	1.89579
$479$	−13.7632	−0.628857	−0.314428	−	0.949281i	$-0.601813\pi$
$479$	−13.7632	−0.628857	−0.314428	+	0.949281i	$0.601813\pi$
$480$	−97.4702	−4.44888
$481$	9.73402	0.443833
$482$	−32.0390	−1.45934
$483$	−19.5516	−0.889629
$484$	4.80548	0.218431
$485$	47.3682	2.15088
$486$	−8.32055	−0.377428
$487$	−39.5802	−1.79355	−0.896774	−	0.442488i	$-0.854096\pi$
$487$	−39.5802	−1.79355	−0.896774	+	0.442488i	$0.854096\pi$
$488$	100.219	4.53670
$489$	26.3703	1.19251
$490$	−37.8160	−1.70835
$491$	37.1026	1.67442	0.837208	−	0.546885i	$-0.184187\pi$
$491$	37.1026	1.67442	0.837208	+	0.546885i	$0.184187\pi$
$492$	136.110	6.13629
$493$	5.75040	0.258985
$494$	−22.1896	−0.998358
$495$	18.9062	0.849771
$496$	65.5367	2.94269
$497$	−8.07038	−0.362006
$498$	118.495	5.30988
$499$	22.9519	1.02747	0.513734	−	0.857950i	$-0.328262\pi$
$499$	22.9519	1.02747	0.513734	+	0.857950i	$0.328262\pi$
$500$	−8.90302	−0.398155
$501$	−59.3137	−2.64994
$502$	−20.4927	−0.914636
$503$	20.4303	0.910941	0.455470	−	0.890251i	$-0.349471\pi$
$503$	20.4303	0.910941	0.455470	+	0.890251i	$0.349471\pi$
$504$	−67.8471	−3.02215
$505$	44.9388	1.99975
$506$	10.7763	0.479064
$507$	28.8628	1.28184
$508$	−40.8598	−1.81286
$509$	19.9939	0.886212	0.443106	−	0.896469i	$-0.353876\pi$
$509$	19.9939	0.886212	0.443106	+	0.896469i	$0.353876\pi$
$510$	25.1815	1.11506
$511$	7.25062	0.320748
$512$	43.0453	1.90235
$513$	−39.2647	−1.73358
$514$	−63.2081	−2.78799
$515$	−27.0596	−1.19239
$516$	14.2677	0.628101
$517$	0.376346	0.0165517
$518$	−22.3558	−0.982258
$519$	22.5143	0.988269
$520$	43.0851	1.88941
$521$	39.7576	1.74181	0.870905	−	0.491451i	$-0.163533\pi$
$521$	39.7576	1.74181	0.870905	+	0.491451i	$0.163533\pi$
$522$	87.2363	3.81823
$523$	−38.9045	−1.70117	−0.850587	−	0.525834i	$-0.823753\pi$
$523$	−38.9045	−1.70117	−0.850587	+	0.525834i	$0.823753\pi$
$524$	−89.3633	−3.90385
$525$	−26.3625	−1.15056
$526$	−40.2650	−1.75564
$527$	−6.91195	−0.301089
$528$	28.1515	1.22514
$529$	−5.93608	−0.258090
$530$	109.533	4.75783
$531$	42.4409	1.84178
$532$	35.9854	1.56016
$533$	−17.2739	−0.748216
$534$	−73.4756	−3.17960
$535$	20.6019	0.890699
$536$	−31.4358	−1.35782
$537$	15.7684	0.680458
$538$	−31.2006	−1.34515
$539$	4.45873	0.192051
$540$	130.590	5.61969
$541$	9.45081	0.406322	0.203161	−	0.979145i	$-0.434879\pi$
$541$	9.45081	0.406322	0.203161	+	0.979145i	$0.434879\pi$
$542$	−11.0138	−0.473085
$543$	−38.2234	−1.64032
$544$	10.0976	0.432932
$545$	−22.7045	−0.972553
$546$	22.3578	0.956825
$547$	−17.6118	−0.753025	−0.376513	−	0.926411i	$-0.622877\pi$
$547$	−17.6118	−0.753025	−0.376513	+	0.926411i	$0.622877\pi$
$548$	−82.2708	−3.51443
$549$	−79.6313	−3.39858
$550$	14.5303	0.619572
$551$	−27.0123	−1.15076
$552$	89.7622	3.82053
$553$	−25.8053	−1.09735
$554$	7.59776	0.322798
$555$	51.8906	2.20263
$556$	63.1947	2.68005
$557$	30.6758	1.29977	0.649887	−	0.760031i	$-0.274816\pi$
$557$	30.6758	1.29977	0.649887	+	0.760031i	$0.274816\pi$
$558$	−104.858	−4.43897
$559$	−1.81074	−0.0765862
$560$	−49.1410	−2.07659
$561$	−2.96905	−0.125353
$562$	33.6458	1.41926
$563$	−20.8870	−0.880281	−0.440140	−	0.897929i	$-0.645071\pi$
$563$	−20.8870	−0.880281	−0.440140	+	0.897929i	$0.645071\pi$
$564$	5.36959	0.226101
$565$	−2.84474	−0.119679
$566$	−79.6682	−3.34870
$567$	11.7513	0.493507
$568$	37.0514	1.55464
$569$	20.9626	0.878798	0.439399	−	0.898292i	$-0.355191\pi$
$569$	20.9626	0.878798	0.439399	+	0.898292i	$0.355191\pi$
$570$	−118.289	−4.95460
$571$	−25.7086	−1.07587	−0.537937	−	0.842985i	$-0.680796\pi$
$571$	−25.7086	−1.07587	−0.537937	+	0.842985i	$0.680796\pi$
$572$	−8.70148	−0.363827
$573$	−25.1998	−1.05274
$574$	39.6724	1.65590
$575$	23.0082	0.959510
$576$	42.9090	1.78787
$577$	1.00680	0.0419135	0.0209568	−	0.999780i	$-0.493329\pi$
$577$	1.00680	0.0419135	0.0209568	+	0.999780i	$0.493329\pi$
$578$	−2.60873	−0.108509
$579$	36.2402	1.50609
$580$	89.8399	3.73040
$581$	24.3881	1.01179
$582$	−112.849	−4.67776
$583$	−12.9147	−0.534871
$584$	−33.2879	−1.37746
$585$	−34.2343	−1.41541
$586$	−53.6978	−2.21823
$587$	−14.7231	−0.607689	−0.303845	−	0.952722i	$-0.598270\pi$
$587$	−14.7231	−0.607689	−0.303845	+	0.952722i	$0.598270\pi$
$588$	63.6159	2.62348
$589$	32.4687	1.33785
$590$	61.8983	2.54831
$591$	−51.0407	−2.09953
$592$	50.9707	2.09488
$593$	−40.6048	−1.66744	−0.833720	−	0.552188i	$-0.813793\pi$
$593$	−40.6048	−1.66744	−0.833720	+	0.552188i	$0.813793\pi$
$594$	−21.8056	−0.894693
$595$	5.18274	0.212472
$596$	102.921	4.21579
$597$	−34.3585	−1.40620
$598$	−19.5130	−0.797948
$599$	−30.3352	−1.23946	−0.619732	−	0.784813i	$-0.712759\pi$
$599$	−30.3352	−1.23946	−0.619732	+	0.784813i	$0.712759\pi$
$600$	121.031	4.94109
$601$	−3.86014	−0.157458	−0.0787292	−	0.996896i	$-0.525086\pi$
$601$	−3.86014	−0.157458	−0.0787292	+	0.996896i	$0.525086\pi$
$602$	4.15867	0.169495
$603$	24.9780	1.01718
$604$	−92.1184	−3.74824
$605$	−3.25113	−0.132177
$606$	−107.062	−4.34908
$607$	2.29625	0.0932021	0.0466010	−	0.998914i	$-0.485161\pi$
$607$	2.29625	0.0932021	0.0466010	+	0.998914i	$0.485161\pi$
$608$	−47.4333	−1.92367
$609$	27.2170	1.10289
$610$	−116.139	−4.70233
$611$	−0.681464	−0.0275691
$612$	−27.9452	−1.12962
$613$	2.88865	0.116671	0.0583357	−	0.998297i	$-0.481421\pi$
$613$	2.88865	0.116671	0.0583357	+	0.998297i	$0.481421\pi$
$614$	0.625004	0.0252231
$615$	−92.0846	−3.71321
$616$	11.6671	0.470079
$617$	41.9705	1.68967	0.844835	−	0.535027i	$-0.179699\pi$
$617$	41.9705	1.68967	0.844835	+	0.535027i	$0.179699\pi$
$618$	64.4664	2.59322
$619$	−35.7356	−1.43633	−0.718167	−	0.695871i	$-0.755019\pi$
$619$	−35.7356	−1.43633	−0.718167	+	0.695871i	$0.755019\pi$
$620$	−107.987	−4.33686
$621$	−34.5285	−1.38558
$622$	7.94042	0.318382
$623$	−15.1224	−0.605867
$624$	−50.9752	−2.04064
$625$	−21.8260	−0.873039
$626$	−29.9544	−1.19722
$627$	13.9470	0.556991
$628$	−22.9299	−0.915003
$629$	−5.37571	−0.214344
$630$	78.6247	3.13248
$631$	48.3511	1.92483	0.962413	−	0.271591i	$-0.0875499\pi$
$631$	48.3511	1.92483	0.962413	+	0.271591i	$0.0875499\pi$
$632$	118.473	4.71261
$633$	−4.71182	−0.187278
$634$	−11.7752	−0.467654
$635$	27.6436	1.09700
$636$	−184.263	−7.30649
$637$	−8.07361	−0.319888
$638$	−15.0012	−0.593905
$639$	−29.4401	−1.16463
$640$	−3.07650	−0.121609
$641$	−4.21843	−0.166618	−0.0833091	−	0.996524i	$-0.526549\pi$
$641$	−4.21843	−0.166618	−0.0833091	+	0.996524i	$0.526549\pi$
$642$	−49.0818	−1.93710
$643$	−3.73961	−0.147476	−0.0737380	−	0.997278i	$-0.523493\pi$
$643$	−3.73961	−0.147476	−0.0737380	+	0.997278i	$0.523493\pi$
$644$	31.6447	1.24698
$645$	−9.65278	−0.380078
$646$	12.2544	0.482145
$647$	−15.4099	−0.605825	−0.302912	−	0.953018i	$-0.597959\pi$
$647$	−15.4099	−0.605825	−0.302912	+	0.953018i	$0.597959\pi$
$648$	−53.9505	−2.11938
$649$	−7.29818	−0.286479
$650$	−26.3105	−1.03198
$651$	−32.7147	−1.28219
$652$	−42.6810	−1.67152
$653$	−4.82253	−0.188720	−0.0943600	−	0.995538i	$-0.530080\pi$
$653$	−4.82253	−0.188720	−0.0943600	+	0.995538i	$0.530080\pi$
$654$	54.0909	2.11512
$655$	60.4585	2.36231
$656$	−90.4521	−3.53156
$657$	26.4496	1.03190
$658$	1.56510	0.0610138
$659$	−49.4168	−1.92501	−0.962503	−	0.271271i	$-0.912556\pi$
$659$	−49.4168	−1.92501	−0.962503	+	0.271271i	$0.912556\pi$
$660$	−46.3862	−1.80558
$661$	−0.847788	−0.0329751	−0.0164876	−	0.999864i	$-0.505248\pi$
$661$	−0.847788	−0.0329751	−0.0164876	+	0.999864i	$0.505248\pi$
$662$	−32.2995	−1.25536
$663$	5.37618	0.208794
$664$	−111.967	−4.34515
$665$	−24.3458	−0.944089
$666$	−81.5521	−3.16008
$667$	−23.7540	−0.919760
$668$	96.0005	3.71437
$669$	21.4955	0.831062
$670$	36.4294	1.40739
$671$	13.6935	0.528631
$672$	47.7928	1.84365
$673$	7.17717	0.276659	0.138330	−	0.990386i	$-0.455827\pi$
$673$	7.17717	0.276659	0.138330	+	0.990386i	$0.455827\pi$
$674$	83.1089	3.20123
$675$	−46.5567	−1.79197
$676$	−46.7151	−1.79673
$677$	−30.7832	−1.18309	−0.591547	−	0.806271i	$-0.701482\pi$
$677$	−30.7832	−1.18309	−0.591547	+	0.806271i	$0.701482\pi$
$678$	6.77727	0.260280
$679$	−23.2262	−0.891339
$680$	−23.7942	−0.912465
$681$	37.9604	1.45465
$682$	18.0314	0.690458
$683$	−20.6073	−0.788516	−0.394258	−	0.919000i	$-0.628998\pi$
$683$	−20.6073	−0.788516	−0.394258	+	0.919000i	$0.628998\pi$
$684$	131.272	5.01929
$685$	55.6601	2.12666
$686$	47.6531	1.81940
$687$	−2.62022	−0.0999678
$688$	−9.48166	−0.361485
$689$	23.3851	0.890902
$690$	−104.021	−3.96001
$691$	18.7235	0.712275	0.356137	−	0.934434i	$-0.384094\pi$
$691$	18.7235	0.712275	0.356137	+	0.934434i	$0.384094\pi$
$692$	−36.4399	−1.38524
$693$	−9.27033	−0.352151
$694$	32.5779	1.23664
$695$	−42.7542	−1.62176
$696$	−124.954	−4.73639
$697$	9.53969	0.361342
$698$	−44.3449	−1.67848
$699$	15.9362	0.602761
$700$	42.6683	1.61271
$701$	−37.3124	−1.40927	−0.704635	−	0.709570i	$-0.748889\pi$
$701$	−37.3124	−1.40927	−0.704635	+	0.709570i	$0.748889\pi$
$702$	39.4842	1.49024
$703$	25.2523	0.952407
$704$	−7.37867	−0.278094
$705$	−3.63278	−0.136818
$706$	5.22460	0.196630
$707$	−22.0349	−0.828709
$708$	−104.128	−3.91338
$709$	26.7686	1.00532	0.502659	−	0.864485i	$-0.332355\pi$
$709$	26.7686	1.00532	0.502659	+	0.864485i	$0.332355\pi$
$710$	−42.9371	−1.61140
$711$	−94.1356	−3.53036
$712$	69.4276	2.60191
$713$	28.5522	1.06929
$714$	−12.3473	−0.462086
$715$	5.88696	0.220160
$716$	−25.5216	−0.953786
$717$	47.1730	1.76171
$718$	−88.3129	−3.29581
$719$	11.0080	0.410528	0.205264	−	0.978707i	$-0.434195\pi$
$719$	11.0080	0.410528	0.205264	+	0.978707i	$0.434195\pi$
$720$	−179.262	−6.68071
$721$	13.2682	0.494133
$722$	−7.99900	−0.297692
$723$	−36.4643	−1.35612
$724$	61.8653	2.29921
$725$	−32.0289	−1.18952
$726$	7.74546	0.287461
$727$	−5.89956	−0.218802	−0.109401	−	0.993998i	$-0.534893\pi$
$727$	−5.89956	−0.218802	−0.109401	+	0.993998i	$0.534893\pi$
$728$	−21.1260	−0.782982
$729$	−31.5845	−1.16980
$730$	38.5757	1.42775
$731$	1.00000	0.0369863
$732$	195.375	7.22126
$733$	23.8522	0.881000	0.440500	−	0.897752i	$-0.354801\pi$
$733$	23.8522	0.881000	0.440500	+	0.897752i	$0.354801\pi$
$734$	38.6632	1.42708
$735$	−43.0392	−1.58752
$736$	−41.7118	−1.53752
$737$	−4.29525	−0.158217
$738$	144.722	5.32728
$739$	−36.1696	−1.33052	−0.665260	−	0.746612i	$-0.731679\pi$
$739$	−36.1696	−1.33052	−0.665260	+	0.746612i	$0.731679\pi$
$740$	−83.9860	−3.08739
$741$	−25.2545	−0.927746
$742$	−53.7078	−1.97168
$743$	−29.0942	−1.06736	−0.533681	−	0.845686i	$-0.679192\pi$
$743$	−29.0942	−1.06736	−0.533681	+	0.845686i	$0.679192\pi$
$744$	150.195	5.50640
$745$	−69.6307	−2.55107
$746$	31.3157	1.14655
$747$	88.9657	3.25508
$748$	4.80548	0.175706
$749$	−10.1018	−0.369111
$750$	−14.3499	−0.523983
$751$	−2.72045	−0.0992705	−0.0496352	−	0.998767i	$-0.515806\pi$
$751$	−2.72045	−0.0992705	−0.0496352	+	0.998767i	$0.515806\pi$
$752$	−3.56838	−0.130125
$753$	−23.3232	−0.849946
$754$	27.1634	0.989231
$755$	62.3224	2.26815
$756$	−64.0324	−2.32884
$757$	23.9358	0.869960	0.434980	−	0.900440i	$-0.356755\pi$
$757$	23.9358	0.869960	0.434980	+	0.900440i	$0.356755\pi$
$758$	−9.44363	−0.343008
$759$	12.2647	0.445181
$760$	111.772	4.05441
$761$	6.37894	0.231236	0.115618	−	0.993294i	$-0.463115\pi$
$761$	6.37894	0.231236	0.115618	+	0.993294i	$0.463115\pi$
$762$	−65.8577	−2.38577
$763$	11.1327	0.403032
$764$	40.7864	1.47560
$765$	18.9062	0.683556
$766$	15.5542	0.561995
$767$	13.2151	0.477170
$768$	51.1447	1.84553
$769$	−49.7356	−1.79351	−0.896756	−	0.442525i	$-0.854083\pi$
$769$	−49.7356	−1.79351	−0.896756	+	0.442525i	$0.854083\pi$
$770$	−13.5204	−0.487241
$771$	−71.9384	−2.59080
$772$	−58.6555	−2.11106
$773$	23.1714	0.833419	0.416709	−	0.909040i	$-0.363183\pi$
$773$	23.1714	0.833419	0.416709	+	0.909040i	$0.363183\pi$
$774$	15.1705	0.545292
$775$	38.4986	1.38291
$776$	106.632	3.82787
$777$	−25.4436	−0.912785
$778$	25.4911	0.913898
$779$	−44.8124	−1.60557
$780$	83.9934	3.00745
$781$	5.06254	0.181152
$782$	10.7763	0.385359
$783$	48.0658	1.71773
$784$	−42.2762	−1.50986
$785$	15.5132	0.553688
$786$	−144.036	−5.13758
$787$	12.7998	0.456263	0.228131	−	0.973630i	$-0.426738\pi$
$787$	12.7998	0.456263	0.228131	+	0.973630i	$0.426738\pi$
$788$	82.6105	2.94288
$789$	−45.8264	−1.63146
$790$	−137.293	−4.88466
$791$	1.39487	0.0495958
$792$	42.5604	1.51232
$793$	−24.7953	−0.880509
$794$	67.8662	2.40848
$795$	124.662	4.42132
$796$	55.6100	1.97104
$797$	24.8969	0.881892	0.440946	−	0.897534i	$-0.354643\pi$
$797$	24.8969	0.881892	0.440946	+	0.897534i	$0.354643\pi$
$798$	58.0011	2.05322
$799$	0.376346	0.0133141
$800$	−56.2423	−1.98847
$801$	−55.1653	−1.94917
$802$	3.04944	0.107679
$803$	−4.54831	−0.160506
$804$	−61.2833	−2.16130
$805$	−21.4091	−0.754573
$806$	−32.6502	−1.15005
$807$	−35.5101	−1.25001
$808$	101.163	3.55891
$809$	−23.9454	−0.841875	−0.420938	−	0.907090i	$-0.638299\pi$
$809$	−23.9454	−0.841875	−0.420938	+	0.907090i	$0.638299\pi$
$810$	62.5207	2.19675
$811$	−0.699274	−0.0245548	−0.0122774	−	0.999925i	$-0.503908\pi$
$811$	−0.699274	−0.0245548	−0.0122774	+	0.999925i	$0.503908\pi$
$812$	−44.0514	−1.54590
$813$	−12.5351	−0.439624
$814$	14.0238	0.491534
$815$	28.8757	1.01147
$816$	28.1515	0.985501
$817$	−4.69747	−0.164344
$818$	−70.7281	−2.47295
$819$	16.7862	0.586556
$820$	149.041	5.20473
$821$	−34.4903	−1.20372	−0.601861	−	0.798601i	$-0.705574\pi$
$821$	−34.4903	−1.20372	−0.601861	+	0.798601i	$0.705574\pi$
$822$	−132.604	−4.62509
$823$	18.3424	0.639377	0.319689	−	0.947523i	$-0.396422\pi$
$823$	18.3424	0.639377	0.319689	+	0.947523i	$0.396422\pi$
$824$	−60.9148	−2.12207
$825$	16.5372	0.575751
$826$	−30.3507	−1.05604
$827$	−49.4339	−1.71899	−0.859493	−	0.511148i	$-0.829220\pi$
$827$	−49.4339	−1.71899	−0.859493	+	0.511148i	$0.829220\pi$
$828$	115.437	4.01172
$829$	−6.03377	−0.209561	−0.104781	−	0.994495i	$-0.533414\pi$
$829$	−6.03377	−0.209561	−0.104781	+	0.994495i	$0.533414\pi$
$830$	129.753	4.50378
$831$	8.64718	0.299967
$832$	13.3609	0.463205
$833$	4.45873	0.154486
$834$	101.857	3.52702
$835$	−64.9489	−2.24765
$836$	−22.5736	−0.780724
$837$	−57.7748	−1.99699
$838$	15.5563	0.537383
$839$	−13.0219	−0.449566	−0.224783	−	0.974409i	$-0.572167\pi$
$839$	−13.0219	−0.449566	−0.224783	+	0.974409i	$0.572167\pi$
$840$	−112.620	−3.88574
$841$	4.06708	0.140244
$842$	2.87435	0.0990566
$843$	38.2930	1.31888
$844$	7.62619	0.262504
$845$	31.6050	1.08724
$846$	5.70934	0.196291
$847$	1.59414	0.0547751
$848$	122.452	4.20503
$849$	−90.6720	−3.11186
$850$	14.5303	0.498384
$851$	22.2063	0.761221
$852$	72.2309	2.47459
$853$	45.5974	1.56123	0.780613	−	0.625015i	$-0.214907\pi$
$853$	45.5974	1.56123	0.780613	+	0.625015i	$0.214907\pi$
$854$	56.9467	1.94868
$855$	−88.8114	−3.03729
$856$	46.3777	1.58516
$857$	35.5379	1.21395	0.606976	−	0.794720i	$-0.292383\pi$
$857$	35.5379	1.21395	0.606976	+	0.794720i	$0.292383\pi$
$858$	−14.0250	−0.478806
$859$	39.1597	1.33611	0.668057	−	0.744111i	$-0.267126\pi$
$859$	39.1597	1.33611	0.668057	+	0.744111i	$0.267126\pi$
$860$	15.6232	0.532748
$861$	45.1520	1.53878
$862$	64.3521	2.19184
$863$	−29.8935	−1.01759	−0.508794	−	0.860888i	$-0.669909\pi$
$863$	−29.8935	−1.01759	−0.508794	+	0.860888i	$0.669909\pi$
$864$	84.4029	2.87144
$865$	24.6533	0.838239
$866$	−0.593476	−0.0201671
$867$	−2.96905	−0.100834
$868$	52.9495	1.79722
$869$	16.1876	0.549128
$870$	144.804	4.90930
$871$	7.77758	0.263533
$872$	−51.1109	−1.73083
$873$	−84.7271	−2.86758
$874$	−50.6213	−1.71229
$875$	−2.95343	−0.0998440
$876$	−64.8939	−2.19256
$877$	−53.7496	−1.81500	−0.907498	−	0.420057i	$-0.862010\pi$
$877$	−53.7496	−1.81500	−0.907498	+	0.420057i	$0.862010\pi$
$878$	−97.8930	−3.30373
$879$	−61.1146	−2.06134
$880$	30.8261	1.03915
$881$	−44.2598	−1.49115	−0.745575	−	0.666421i	$-0.767825\pi$
$881$	−44.2598	−1.49115	−0.745575	+	0.666421i	$0.767825\pi$
$882$	67.6411	2.27759
$883$	−16.5230	−0.556043	−0.278022	−	0.960575i	$-0.589679\pi$
$883$	−16.5230	−0.556043	−0.278022	+	0.960575i	$0.589679\pi$
$884$	−8.70148	−0.292662
$885$	70.4478	2.36808
$886$	−105.320	−3.53829
$887$	−13.9824	−0.469483	−0.234742	−	0.972058i	$-0.575424\pi$
$887$	−13.9824	−0.469483	−0.234742	+	0.972058i	$0.575424\pi$
$888$	116.813	3.91998
$889$	−13.5545	−0.454605
$890$	−80.4563	−2.69690
$891$	−7.37156	−0.246957
$892$	−34.7909	−1.16488
$893$	−1.76787	−0.0591596
$894$	165.887	5.54810
$895$	17.2665	0.577157
$896$	1.50851	0.0503956
$897$	−22.2082	−0.741511
$898$	−31.3757	−1.04702
$899$	−39.7465	−1.32562
$900$	155.651	5.18835
$901$	−12.9147	−0.430250
$902$	−24.8865	−0.828630
$903$	4.73307	0.157507
$904$	−6.40389	−0.212990
$905$	−41.8548	−1.39130
$906$	−148.476	−4.93279
$907$	28.6175	0.950230	0.475115	−	0.879924i	$-0.342406\pi$
$907$	28.6175	0.950230	0.475115	+	0.879924i	$0.342406\pi$
$908$	−61.4398	−2.03895
$909$	−80.3816	−2.66609
$910$	24.4819	0.811568
$911$	−11.0349	−0.365601	−0.182801	−	0.983150i	$-0.558516\pi$
$911$	−11.0349	−0.365601	−0.182801	+	0.983150i	$0.558516\pi$
$912$	−132.241	−4.37894
$913$	−15.2986	−0.506311
$914$	3.89641	0.128882
$915$	−132.180	−4.36974
$916$	4.24089	0.140123
$917$	−29.6447	−0.978956
$918$	−21.8056	−0.719691
$919$	3.35703	0.110738	0.0553691	−	0.998466i	$-0.482366\pi$
$919$	3.35703	0.110738	0.0553691	+	0.998466i	$0.482366\pi$
$920$	98.2902	3.24053
$921$	0.711330	0.0234391
$922$	43.5220	1.43332
$923$	−9.16695	−0.301734
$924$	22.7447	0.748245
$925$	29.9420	0.984485
$926$	72.5417	2.38387
$927$	48.4012	1.58971
$928$	58.0654	1.90609
$929$	10.9834	0.360353	0.180177	−	0.983634i	$-0.442333\pi$
$929$	10.9834	0.360353	0.180177	+	0.983634i	$0.442333\pi$
$930$	−174.053	−5.70743
$931$	−20.9448	−0.686437
$932$	−25.7930	−0.844879
$933$	9.03716	0.295863
$934$	19.1016	0.625024
$935$	−3.25113	−0.106323
$936$	−77.0659	−2.51898
$937$	−13.3610	−0.436483	−0.218242	−	0.975895i	$-0.570032\pi$
$937$	−13.3610	−0.436483	−0.218242	+	0.975895i	$0.570032\pi$
$938$	−17.8625	−0.583232
$939$	−34.0917	−1.11254
$940$	5.87974	0.191776
$941$	22.2933	0.726742	0.363371	−	0.931645i	$-0.381626\pi$
$941$	22.2933	0.726742	0.363371	+	0.931645i	$0.381626\pi$
$942$	−36.9584	−1.20417
$943$	−39.4070	−1.28327
$944$	69.1989	2.25223
$945$	43.3209	1.40923
$946$	−2.60873	−0.0848172
$947$	24.5177	0.796720	0.398360	−	0.917229i	$-0.369580\pi$
$947$	24.5177	0.796720	0.398360	+	0.917229i	$0.369580\pi$
$948$	230.961	7.50125
$949$	8.23581	0.267346
$950$	−68.2555	−2.21450
$951$	−13.4016	−0.434578
$952$	11.6671	0.378131
$953$	−20.9074	−0.677257	−0.338628	−	0.940920i	$-0.609963\pi$
$953$	−20.9074	−0.677257	−0.338628	+	0.940920i	$0.609963\pi$
$954$	−195.922	−6.34320
$955$	−27.5939	−0.892918
$956$	−76.3506	−2.46935
$957$	−17.0732	−0.551899
$958$	35.9045	1.16002
$959$	−27.2919	−0.881302
$960$	71.2247	2.29877
$961$	16.7750	0.541130
$962$	−25.3934	−0.818718
$963$	−36.8505	−1.18749
$964$	59.0183	1.90085
$965$	39.6832	1.27745
$966$	51.0049	1.64106
$967$	9.57907	0.308042	0.154021	−	0.988068i	$-0.450778\pi$
$967$	9.57907	0.308042	0.154021	+	0.988068i	$0.450778\pi$
$968$	−7.31874	−0.235233
$969$	13.9470	0.448043
$970$	−123.571	−3.96762
$971$	−34.7502	−1.11519	−0.557594	−	0.830114i	$-0.688275\pi$
$971$	−34.7502	−1.11519	−0.557594	+	0.830114i	$0.688275\pi$
$972$	15.3271	0.491616
$973$	20.9638	0.672067
$974$	103.254	3.30847
$975$	−29.9446	−0.958994
$976$	−129.837	−4.15598
$977$	4.11433	0.131629	0.0658146	−	0.997832i	$-0.479035\pi$
$977$	4.11433	0.131629	0.0658146	+	0.997832i	$0.479035\pi$
$978$	−68.7931	−2.19976
$979$	9.48628	0.303183
$980$	69.6598	2.22520
$981$	40.6113	1.29662
$982$	−96.7906	−3.08871
$983$	−28.6602	−0.914119	−0.457060	−	0.889436i	$-0.651097\pi$
$983$	−28.6602	−0.914119	−0.457060	+	0.889436i	$0.651097\pi$
$984$	−207.295	−6.60832
$985$	−55.8899	−1.78080
$986$	−15.0012	−0.477737
$987$	1.78127	0.0566985
$988$	40.8749	1.30041
$989$	−4.13085	−0.131353
$990$	−49.3212	−1.56753
$991$	−48.5431	−1.54202	−0.771011	−	0.636822i	$-0.780248\pi$
$991$	−48.5431	−1.54202	−0.771011	+	0.636822i	$0.780248\pi$
$992$	−69.7943	−2.21597
$993$	−36.7607	−1.16657
$994$	21.0534	0.667775
$995$	−37.6228	−1.19272
$996$	−218.276	−6.91635
$997$	−1.69951	−0.0538240	−0.0269120	−	0.999638i	$-0.508567\pi$
$997$	−1.69951	−0.0538240	−0.0269120	+	0.999638i	$0.508567\pi$
$998$	−59.8753	−1.89532
$999$	−44.9339	−1.42165

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.h.1.6	✓	74

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.h.1.6	✓	74	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)

\(f(q)\)	\(=\)	\(q-2.60873 q^{2} -2.96905 q^{3} +4.80548 q^{4} -3.25113 q^{5} +7.74546 q^{6} +1.59414 q^{7} -7.31874 q^{8} +5.81527 q^{9} +O(q^{10})\)	\(q-2.60873 q^{2} -2.96905 q^{3} +4.80548 q^{4} -3.25113 q^{5} +7.74546 q^{6} +1.59414 q^{7} -7.31874 q^{8} +5.81527 q^{9} +8.48133 q^{10} -1.00000 q^{11} -14.2677 q^{12} +1.81074 q^{13} -4.15867 q^{14} +9.65278 q^{15} +9.48166 q^{16} -1.00000 q^{17} -15.1705 q^{18} +4.69747 q^{19} -15.6232 q^{20} -4.73307 q^{21} +2.60873 q^{22} +4.13085 q^{23} +21.7297 q^{24} +5.56986 q^{25} -4.72374 q^{26} -8.35869 q^{27} +7.66058 q^{28} -5.75040 q^{29} -25.1815 q^{30} +6.91195 q^{31} -10.0976 q^{32} +2.96905 q^{33} +2.60873 q^{34} -5.18274 q^{35} +27.9452 q^{36} +5.37571 q^{37} -12.2544 q^{38} -5.37618 q^{39} +23.7942 q^{40} -9.53969 q^{41} +12.3473 q^{42} -1.00000 q^{43} -4.80548 q^{44} -18.9062 q^{45} -10.7763 q^{46} -0.376346 q^{47} -28.1515 q^{48} -4.45873 q^{49} -14.5303 q^{50} +2.96905 q^{51} +8.70148 q^{52} +12.9147 q^{53} +21.8056 q^{54} +3.25113 q^{55} -11.6671 q^{56} -13.9470 q^{57} +15.0012 q^{58} +7.29818 q^{59} +46.3862 q^{60} -13.6935 q^{61} -18.0314 q^{62} +9.27033 q^{63} +7.37867 q^{64} -5.88696 q^{65} -7.74546 q^{66} +4.29525 q^{67} -4.80548 q^{68} -12.2647 q^{69} +13.5204 q^{70} -5.06254 q^{71} -42.5604 q^{72} +4.54831 q^{73} -14.0238 q^{74} -16.5372 q^{75} +22.5736 q^{76} -1.59414 q^{77} +14.0250 q^{78} -16.1876 q^{79} -30.8261 q^{80} +7.37156 q^{81} +24.8865 q^{82} +15.2986 q^{83} -22.7447 q^{84} +3.25113 q^{85} +2.60873 q^{86} +17.0732 q^{87} +7.31874 q^{88} -9.48628 q^{89} +49.3212 q^{90} +2.88657 q^{91} +19.8507 q^{92} -20.5219 q^{93} +0.981784 q^{94} -15.2721 q^{95} +29.9804 q^{96} -14.5698 q^{97} +11.6316 q^{98} -5.81527 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9}+O(q^{10}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9} - 9 q^{10} - 74 q^{11} - 3 q^{12} + 4 q^{13} - 5 q^{14} - 17 q^{15} + 85 q^{16} - 74 q^{17} - 23 q^{18} - 21 q^{20} - 22 q^{21} + 7 q^{22} - 23 q^{23} - 51 q^{24} + 90 q^{25} - 46 q^{26} - 27 q^{27} - 61 q^{28} - 63 q^{29} - 22 q^{30} - 31 q^{31} - 69 q^{32} + 3 q^{33} + 7 q^{34} - 20 q^{35} + 51 q^{36} + 8 q^{37} - 2 q^{38} - 77 q^{39} - 37 q^{40} - 64 q^{41} + 13 q^{42} - 74 q^{43} - 79 q^{44} - 12 q^{45} - 53 q^{46} - 32 q^{47} + 2 q^{48} + 78 q^{49} - 104 q^{50} + 3 q^{51} + 13 q^{52} + 25 q^{53} - 110 q^{54} + 6 q^{55} - 29 q^{56} - 29 q^{57} - 14 q^{58} - 61 q^{59} - 82 q^{60} - 36 q^{61} - 63 q^{62} - 104 q^{63} + 107 q^{64} - 65 q^{65} + 12 q^{66} + 33 q^{67} - 79 q^{68} - 34 q^{69} - 3 q^{70} - 168 q^{71} - 67 q^{72} - 47 q^{73} - 54 q^{74} - 53 q^{75} - 4 q^{76} + 16 q^{77} - 3 q^{78} - 79 q^{79} - 59 q^{80} + 70 q^{81} - 18 q^{82} - 36 q^{83} - 118 q^{84} + 6 q^{85} + 7 q^{86} - 24 q^{87} + 21 q^{88} - 24 q^{89} + 25 q^{90} - 14 q^{91} - 18 q^{92} - 13 q^{93} + 9 q^{94} - 155 q^{95} - 50 q^{96} + q^{97} - 60 q^{98} - 75 q^{99}+O(q^{100}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9 - 9 * q^10 - 74 * q^11 - 3 * q^12 + 4 * q^13 - 5 * q^14 - 17 * q^15 + 85 * q^16 - 74 * q^17 - 23 * q^18 - 21 * q^20 - 22 * q^21 + 7 * q^22 - 23 * q^23 - 51 * q^24 + 90 * q^25 - 46 * q^26 - 27 * q^27 - 61 * q^28 - 63 * q^29 - 22 * q^30 - 31 * q^31 - 69 * q^32 + 3 * q^33 + 7 * q^34 - 20 * q^35 + 51 * q^36 + 8 * q^37 - 2 * q^38 - 77 * q^39 - 37 * q^40 - 64 * q^41 + 13 * q^42 - 74 * q^43 - 79 * q^44 - 12 * q^45 - 53 * q^46 - 32 * q^47 + 2 * q^48 + 78 * q^49 - 104 * q^50 + 3 * q^51 + 13 * q^52 + 25 * q^53 - 110 * q^54 + 6 * q^55 - 29 * q^56 - 29 * q^57 - 14 * q^58 - 61 * q^59 - 82 * q^60 - 36 * q^61 - 63 * q^62 - 104 * q^63 + 107 * q^64 - 65 * q^65 + 12 * q^66 + 33 * q^67 - 79 * q^68 - 34 * q^69 - 3 * q^70 - 168 * q^71 - 67 * q^72 - 47 * q^73 - 54 * q^74 - 53 * q^75 - 4 * q^76 + 16 * q^77 - 3 * q^78 - 79 * q^79 - 59 * q^80 + 70 * q^81 - 18 * q^82 - 36 * q^83 - 118 * q^84 + 6 * q^85 + 7 * q^86 - 24 * q^87 + 21 * q^88 - 24 * q^89 + 25 * q^90 - 14 * q^91 - 18 * q^92 - 13 * q^93 + 9 * q^94 - 155 * q^95 - 50 * q^96 + q^97 - 60 * q^98 - 75 * q^99

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