LMFDB - Embedded newform 4033.2.a.d.1.33

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4033,2,Mod(1,4033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4033, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4033 = 37 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4033.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:	$32.2036671352$
Analytic rank:	$1$
Dimension:	$79$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.33
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.809519 q^{2} -1.08931 q^{3} -1.34468 q^{4} -2.50127 q^{5} +0.881820 q^{6} -3.62619 q^{7} +2.70758 q^{8} -1.81340 q^{9} +O(q^{10})$	\(q-0.809519 q^{2} -1.08931 q^{3} -1.34468 q^{4} -2.50127 q^{5} +0.881820 q^{6} -3.62619 q^{7} +2.70758 q^{8} -1.81340 q^{9} +2.02483 q^{10} -2.58329 q^{11} +1.46478 q^{12} -2.30053 q^{13} +2.93547 q^{14} +2.72467 q^{15} +0.497519 q^{16} +4.94167 q^{17} +1.46798 q^{18} -6.46982 q^{19} +3.36341 q^{20} +3.95006 q^{21} +2.09122 q^{22} +1.34753 q^{23} -2.94941 q^{24} +1.25636 q^{25} +1.86233 q^{26} +5.24330 q^{27} +4.87607 q^{28} +7.59046 q^{29} -2.20567 q^{30} +0.604483 q^{31} -5.81791 q^{32} +2.81402 q^{33} -4.00037 q^{34} +9.07010 q^{35} +2.43844 q^{36} -1.00000 q^{37} +5.23744 q^{38} +2.50600 q^{39} -6.77240 q^{40} +2.15126 q^{41} -3.19765 q^{42} -5.03150 q^{43} +3.47370 q^{44} +4.53580 q^{45} -1.09085 q^{46} +6.54836 q^{47} -0.541954 q^{48} +6.14929 q^{49} -1.01705 q^{50} -5.38303 q^{51} +3.09348 q^{52} +1.09055 q^{53} -4.24455 q^{54} +6.46152 q^{55} -9.81822 q^{56} +7.04766 q^{57} -6.14462 q^{58} +12.4547 q^{59} -3.66381 q^{60} +1.19567 q^{61} -0.489340 q^{62} +6.57573 q^{63} +3.71467 q^{64} +5.75426 q^{65} -2.27800 q^{66} +1.30652 q^{67} -6.64496 q^{68} -1.46788 q^{69} -7.34242 q^{70} -5.85115 q^{71} -4.90992 q^{72} +6.54153 q^{73} +0.809519 q^{74} -1.36857 q^{75} +8.69983 q^{76} +9.36752 q^{77} -2.02866 q^{78} -11.4472 q^{79} -1.24443 q^{80} -0.271408 q^{81} -1.74149 q^{82} -1.28918 q^{83} -5.31157 q^{84} -12.3605 q^{85} +4.07310 q^{86} -8.26839 q^{87} -6.99448 q^{88} +0.371036 q^{89} -3.67181 q^{90} +8.34218 q^{91} -1.81199 q^{92} -0.658471 q^{93} -5.30102 q^{94} +16.1828 q^{95} +6.33753 q^{96} -3.57431 q^{97} -4.97796 q^{98} +4.68453 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) $ 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + 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 $

$2$	−0.809519	−0.572416	−0.286208	−	0.958167i	$-0.592395\pi$
$2$	−0.809519	−0.572416	−0.286208	+	0.958167i	$0.592395\pi$
$3$	−1.08931	−0.628916	−0.314458	−	0.949271i	$-0.601823\pi$
$3$	−1.08931	−0.628916	−0.314458	+	0.949271i	$0.601823\pi$
$4$	−1.34468	−0.672339
$5$	−2.50127	−1.11860	−0.559301	−	0.828964i	$-0.688931\pi$
$5$	−2.50127	−1.11860	−0.559301	+	0.828964i	$0.688931\pi$
$6$	0.881820	0.360002
$7$	−3.62619	−1.37057	−0.685286	−	0.728274i	$-0.740323\pi$
$7$	−3.62619	−1.37057	−0.685286	+	0.728274i	$0.740323\pi$
$8$	2.70758	0.957275
$9$	−1.81340	−0.604465
$10$	2.02483	0.640307
$11$	−2.58329	−0.778892	−0.389446	−	0.921049i	$-0.627334\pi$
$11$	−2.58329	−0.778892	−0.389446	+	0.921049i	$0.627334\pi$
$12$	1.46478	0.422845
$13$	−2.30053	−0.638053	−0.319027	−	0.947746i	$-0.603356\pi$
$13$	−2.30053	−0.638053	−0.319027	+	0.947746i	$0.603356\pi$
$14$	2.93547	0.784538
$15$	2.72467	0.703507
$16$	0.497519	0.124380
$17$	4.94167	1.19853	0.599265	−	0.800551i	$-0.295460\pi$
$17$	4.94167	1.19853	0.599265	+	0.800551i	$0.295460\pi$
$18$	1.46798	0.346006
$19$	−6.46982	−1.48428	−0.742139	−	0.670246i	$-0.766189\pi$
$19$	−6.46982	−1.48428	−0.742139	+	0.670246i	$0.766189\pi$
$20$	3.36341	0.752081
$21$	3.95006	0.861974
$22$	2.09122	0.445851
$23$	1.34753	0.280979	0.140490	−	0.990082i	$-0.455132\pi$
$23$	1.34753	0.280979	0.140490	+	0.990082i	$0.455132\pi$
$24$	−2.94941	−0.602045
$25$	1.25636	0.251273
$26$	1.86233	0.365232
$27$	5.24330	1.00907
$28$	4.87607	0.921490
$29$	7.59046	1.40951	0.704757	−	0.709449i	$-0.251056\pi$
$29$	7.59046	1.40951	0.704757	+	0.709449i	$0.251056\pi$
$30$	−2.20567	−0.402699
$31$	0.604483	0.108568	0.0542841	−	0.998526i	$-0.482712\pi$
$31$	0.604483	0.108568	0.0542841	+	0.998526i	$0.482712\pi$
$32$	−5.81791	−1.02847
$33$	2.81402	0.489857
$34$	−4.00037	−0.686058
$35$	9.07010	1.53313
$36$	2.43844	0.406406
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	5.23744	0.849625
$39$	2.50600	0.401282
$40$	−6.77240	−1.07081
$41$	2.15126	0.335971	0.167985	−	0.985789i	$-0.446274\pi$
$41$	2.15126	0.335971	0.167985	+	0.985789i	$0.446274\pi$
$42$	−3.19765	−0.493408
$43$	−5.03150	−0.767297	−0.383648	−	0.923479i	$-0.625333\pi$
$43$	−5.03150	−0.767297	−0.383648	+	0.923479i	$0.625333\pi$
$44$	3.47370	0.523680
$45$	4.53580	0.676157
$46$	−1.09085	−0.160837
$47$	6.54836	0.955176	0.477588	−	0.878584i	$-0.341511\pi$
$47$	6.54836	0.955176	0.477588	+	0.878584i	$0.341511\pi$
$48$	−0.541954	−0.0782244
$49$	6.14929	0.878469
$50$	−1.01705	−0.143833
$51$	−5.38303	−0.753774
$52$	3.09348	0.428988
$53$	1.09055	0.149798	0.0748991	−	0.997191i	$-0.476137\pi$
$53$	1.09055	0.149798	0.0748991	+	0.997191i	$0.476137\pi$
$54$	−4.24455	−0.577610
$55$	6.46152	0.871271
$56$	−9.81822	−1.31201
$57$	7.04766	0.933485
$58$	−6.14462	−0.806829
$59$	12.4547	1.62146	0.810731	−	0.585419i	$-0.199070\pi$
$59$	12.4547	1.62146	0.810731	+	0.585419i	$0.199070\pi$
$60$	−3.66381	−0.472995
$61$	1.19567	0.153089	0.0765446	−	0.997066i	$-0.475611\pi$
$61$	1.19567	0.153089	0.0765446	+	0.997066i	$0.475611\pi$
$62$	−0.489340	−0.0621463
$63$	6.57573	0.828464
$64$	3.71467	0.464334
$65$	5.75426	0.713728
$66$	−2.27800	−0.280402
$67$	1.30652	0.159617	0.0798083	−	0.996810i	$-0.474569\pi$
$67$	1.30652	0.159617	0.0798083	+	0.996810i	$0.474569\pi$
$68$	−6.64496	−0.805819
$69$	−1.46788	−0.176712
$70$	−7.34242	−0.877587
$71$	−5.85115	−0.694404	−0.347202	−	0.937790i	$-0.612868\pi$
$71$	−5.85115	−0.694404	−0.347202	+	0.937790i	$0.612868\pi$
$72$	−4.90992	−0.578639
$73$	6.54153	0.765629	0.382814	−	0.923825i	$-0.374955\pi$
$73$	6.54153	0.765629	0.382814	+	0.923825i	$0.374955\pi$
$74$	0.809519	0.0941047
$75$	−1.36857	−0.158029
$76$	8.69983	0.997939
$77$	9.36752	1.06753
$78$	−2.02866	−0.229700
$79$	−11.4472	−1.28791	−0.643954	−	0.765064i	$-0.722707\pi$
$79$	−11.4472	−1.28791	−0.643954	+	0.765064i	$0.722707\pi$
$80$	−1.24443	−0.139132
$81$	−0.271408	−0.0301565
$82$	−1.74149	−0.192315
$83$	−1.28918	−0.141506	−0.0707530	−	0.997494i	$-0.522540\pi$
$83$	−1.28918	−0.141506	−0.0707530	+	0.997494i	$0.522540\pi$
$84$	−5.31157	−0.579539
$85$	−12.3605	−1.34068
$86$	4.07310	0.439213
$87$	−8.26839	−0.886465
$88$	−6.99448	−0.745614
$89$	0.371036	0.0393297	0.0196649	−	0.999807i	$-0.493740\pi$
$89$	0.371036	0.0393297	0.0196649	+	0.999807i	$0.493740\pi$
$90$	−3.67181	−0.387043
$91$	8.34218	0.874498
$92$	−1.81199	−0.188913
$93$	−0.658471	−0.0682803
$94$	−5.30102	−0.546759
$95$	16.1828	1.66032
$96$	6.33753	0.646822
$97$	−3.57431	−0.362916	−0.181458	−	0.983399i	$-0.558082\pi$
$97$	−3.57431	−0.362916	−0.181458	+	0.983399i	$0.558082\pi$
$98$	−4.97796	−0.502850
$99$	4.68453	0.470813
$100$	−1.68940	−0.168940
$101$	5.07887	0.505366	0.252683	−	0.967549i	$-0.418687\pi$
$101$	5.07887	0.505366	0.252683	+	0.967549i	$0.418687\pi$
$102$	4.35766	0.431473
$103$	10.7900	1.06317	0.531583	−	0.847006i	$-0.321597\pi$
$103$	10.7900	1.06317	0.531583	+	0.847006i	$0.321597\pi$
$104$	−6.22888	−0.610792
$105$	−9.88018	−0.964207
$106$	−0.882819	−0.0857469
$107$	0.0974368	0.00941957	0.00470979	−	0.999989i	$-0.498501\pi$
$107$	0.0974368	0.00941957	0.00470979	+	0.999989i	$0.498501\pi$
$108$	−7.05055	−0.678440
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	−5.23072	−0.498730
$111$	1.08931	0.103393
$112$	−1.80410	−0.170471
$113$	1.47054	0.138336	0.0691682	−	0.997605i	$-0.477965\pi$
$113$	1.47054	0.138336	0.0691682	+	0.997605i	$0.477965\pi$
$114$	−5.70522	−0.534342
$115$	−3.37054	−0.314304
$116$	−10.2067	−0.947672
$117$	4.17178	0.385681
$118$	−10.0823	−0.928151
$119$	−17.9194	−1.64267
$120$	7.37727	0.673449
$121$	−4.32660	−0.393327
$122$	−0.967914	−0.0876308
$123$	−2.34340	−0.211297
$124$	−0.812835	−0.0729947
$125$	9.36386	0.837529
$126$	−5.32318	−0.474226
$127$	−18.0964	−1.60580	−0.802898	−	0.596116i	$-0.796710\pi$
$127$	−18.0964	−1.60580	−0.802898	+	0.596116i	$0.796710\pi$
$128$	8.62873	0.762679
$129$	5.48088	0.482565
$130$	−4.65818	−0.408550
$131$	−5.46762	−0.477708	−0.238854	−	0.971055i	$-0.576772\pi$
$131$	−5.46762	−0.477708	−0.238854	+	0.971055i	$0.576772\pi$
$132$	−3.78395	−0.329350
$133$	23.4608	2.03431
$134$	−1.05765	−0.0913672
$135$	−13.1149	−1.12875
$136$	13.3800	1.14732
$137$	8.31693	0.710563	0.355282	−	0.934759i	$-0.384385\pi$
$137$	8.31693	0.710563	0.355282	+	0.934759i	$0.384385\pi$
$138$	1.18828	0.101153
$139$	2.43570	0.206593	0.103297	−	0.994651i	$-0.467061\pi$
$139$	2.43570	0.206593	0.103297	+	0.994651i	$0.467061\pi$
$140$	−12.1964	−1.03078
$141$	−7.13322	−0.600725
$142$	4.73662	0.397488
$143$	5.94295	0.496975
$144$	−0.902199	−0.0751832
$145$	−18.9858	−1.57669
$146$	−5.29550	−0.438258
$147$	−6.69850	−0.552483
$148$	1.34468	0.110532
$149$	8.16289	0.668730	0.334365	−	0.942444i	$-0.391478\pi$
$149$	8.16289	0.668730	0.334365	+	0.942444i	$0.391478\pi$
$150$	1.10789	0.0904585
$151$	5.10342	0.415311	0.207655	−	0.978202i	$-0.433417\pi$
$151$	5.10342	0.415311	0.207655	+	0.978202i	$0.433417\pi$
$152$	−17.5176	−1.42086
$153$	−8.96120	−0.724470
$154$	−7.58319	−0.611071
$155$	−1.51198	−0.121445
$156$	−3.36977	−0.269797
$157$	12.8593	1.02628	0.513142	−	0.858304i	$-0.328481\pi$
$157$	12.8593	1.02628	0.513142	+	0.858304i	$0.328481\pi$
$158$	9.26670	0.737219
$159$	−1.18795	−0.0942104
$160$	14.5522	1.15045
$161$	−4.88640	−0.385103
$162$	0.219710	0.0172621
$163$	8.28767	0.649141	0.324570	−	0.945862i	$-0.394780\pi$
$163$	8.28767	0.649141	0.324570	+	0.945862i	$0.394780\pi$
$164$	−2.89276	−0.225887
$165$	−7.03862	−0.547956
$166$	1.04362	0.0810004
$167$	4.22554	0.326982	0.163491	−	0.986545i	$-0.447724\pi$
$167$	4.22554	0.326982	0.163491	+	0.986545i	$0.447724\pi$
$168$	10.6951	0.825146
$169$	−7.70754	−0.592888
$170$	10.0060	0.767427
$171$	11.7323	0.897194
$172$	6.76575	0.515884
$173$	−17.4185	−1.32431	−0.662154	−	0.749368i	$-0.730357\pi$
$173$	−17.4185	−1.32431	−0.662154	+	0.749368i	$0.730357\pi$
$174$	6.69342	0.507427
$175$	−4.55582	−0.344387
$176$	−1.28524	−0.0968784
$177$	−13.5671	−1.01976
$178$	−0.300361	−0.0225130
$179$	−10.5448	−0.788152	−0.394076	−	0.919078i	$-0.628935\pi$
$179$	−10.5448	−0.788152	−0.394076	+	0.919078i	$0.628935\pi$
$180$	−6.09919	−0.454607
$181$	5.58335	0.415007	0.207504	−	0.978234i	$-0.433466\pi$
$181$	5.58335	0.415007	0.207504	+	0.978234i	$0.433466\pi$
$182$	−6.75316	−0.500577
$183$	−1.30245	−0.0962802
$184$	3.64855	0.268974
$185$	2.50127	0.183897
$186$	0.533045	0.0390847
$187$	−12.7658	−0.933526
$188$	−8.80544	−0.642203
$189$	−19.0132	−1.38301
$190$	−13.1003	−0.950393
$191$	−11.5285	−0.834175	−0.417088	−	0.908866i	$-0.636949\pi$
$191$	−11.5285	−0.834175	−0.417088	+	0.908866i	$0.636949\pi$
$192$	−4.04645	−0.292027
$193$	2.07174	0.149127	0.0745637	−	0.997216i	$-0.476244\pi$
$193$	2.07174	0.149127	0.0745637	+	0.997216i	$0.476244\pi$
$194$	2.89347	0.207739
$195$	−6.26820	−0.448875
$196$	−8.26881	−0.590630
$197$	9.84761	0.701613	0.350807	−	0.936448i	$-0.385907\pi$
$197$	9.84761	0.701613	0.350807	+	0.936448i	$0.385907\pi$
$198$	−3.79222	−0.269501
$199$	−10.4385	−0.739964	−0.369982	−	0.929039i	$-0.620636\pi$
$199$	−10.4385	−0.739964	−0.369982	+	0.929039i	$0.620636\pi$
$200$	3.40170	0.240537
$201$	−1.42321	−0.100385
$202$	−4.11144	−0.289280
$203$	−27.5245	−1.93184
$204$	7.23844	0.506792
$205$	−5.38090	−0.375818
$206$	−8.73467	−0.608574
$207$	−2.44360	−0.169842
$208$	−1.14456	−0.0793609
$209$	16.7134	1.15609
$210$	7.99820	0.551928
$211$	6.42625	0.442402	0.221201	−	0.975228i	$-0.429002\pi$
$211$	6.42625	0.442402	0.221201	+	0.975228i	$0.429002\pi$
$212$	−1.46644	−0.100715
$213$	6.37374	0.436722
$214$	−0.0788769	−0.00539192
$215$	12.5852	0.858300
$216$	14.1967	0.965960
$217$	−2.19197	−0.148801
$218$	0.809519	0.0548275
$219$	−7.12578	−0.481516
$220$	−8.68867	−0.585790
$221$	−11.3685	−0.764726
$222$	−0.881820	−0.0591839
$223$	−21.8023	−1.45999	−0.729996	−	0.683451i	$-0.760478\pi$
$223$	−21.8023	−1.45999	−0.729996	+	0.683451i	$0.760478\pi$
$224$	21.0969	1.40960
$225$	−2.27828	−0.151886
$226$	−1.19043	−0.0791861
$227$	−4.92795	−0.327080	−0.163540	−	0.986537i	$-0.552291\pi$
$227$	−4.92795	−0.327080	−0.163540	+	0.986537i	$0.552291\pi$
$228$	−9.47684	−0.627619
$229$	−1.65671	−0.109479	−0.0547393	−	0.998501i	$-0.517433\pi$
$229$	−1.65671	−0.109479	−0.0547393	+	0.998501i	$0.517433\pi$
$230$	2.72851	0.179913
$231$	−10.2042	−0.671385
$232$	20.5518	1.34929
$233$	10.3970	0.681127	0.340564	−	0.940221i	$-0.389382\pi$
$233$	10.3970	0.681127	0.340564	+	0.940221i	$0.389382\pi$
$234$	−3.37713	−0.220770
$235$	−16.3792	−1.06846
$236$	−16.7476	−1.09017
$237$	12.4696	0.809985
$238$	14.5061	0.940293
$239$	−3.88735	−0.251452	−0.125726	−	0.992065i	$-0.540126\pi$
$239$	−3.88735	−0.251452	−0.125726	+	0.992065i	$0.540126\pi$
$240$	1.35558	0.0875020
$241$	7.59287	0.489100	0.244550	−	0.969637i	$-0.421360\pi$
$241$	7.59287	0.489100	0.244550	+	0.969637i	$0.421360\pi$
$242$	3.50246	0.225147
$243$	−15.4342	−0.990107
$244$	−1.60779	−0.102928
$245$	−15.3810	−0.982658
$246$	1.89703	0.120950
$247$	14.8840	0.947048
$248$	1.63669	0.103930
$249$	1.40432	0.0889953
$250$	−7.58022	−0.479415
$251$	−0.389633	−0.0245934	−0.0122967	−	0.999924i	$-0.503914\pi$
$251$	−0.389633	−0.0245934	−0.0122967	+	0.999924i	$0.503914\pi$
$252$	−8.84224	−0.557009
$253$	−3.48106	−0.218853
$254$	14.6494	0.919184
$255$	13.4644	0.843174
$256$	−14.4145	−0.900904
$257$	1.34390	0.0838300	0.0419150	−	0.999121i	$-0.486654\pi$
$257$	1.34390	0.0838300	0.0419150	+	0.999121i	$0.486654\pi$
$258$	−4.43688	−0.276228
$259$	3.62619	0.225321
$260$	−7.73763	−0.479868
$261$	−13.7645	−0.852002
$262$	4.42614	0.273448
$263$	3.42104	0.210950	0.105475	−	0.994422i	$-0.466364\pi$
$263$	3.42104	0.210950	0.105475	+	0.994422i	$0.466364\pi$
$264$	7.61918	0.468928
$265$	−2.72775	−0.167565
$266$	−18.9920	−1.16447
$267$	−0.404174	−0.0247351
$268$	−1.75685	−0.107317
$269$	−8.38303	−0.511122	−0.255561	−	0.966793i	$-0.582260\pi$
$269$	−8.38303	−0.511122	−0.255561	+	0.966793i	$0.582260\pi$
$270$	10.6168	0.646116
$271$	2.09678	0.127370	0.0636852	−	0.997970i	$-0.479715\pi$
$271$	2.09678	0.127370	0.0636852	+	0.997970i	$0.479715\pi$
$272$	2.45857	0.149073
$273$	−9.08725	−0.549986
$274$	−6.73271	−0.406738
$275$	−3.24555	−0.195714
$276$	1.97383	0.118811
$277$	−2.81547	−0.169165	−0.0845825	−	0.996416i	$-0.526956\pi$
$277$	−2.81547	−0.169165	−0.0845825	+	0.996416i	$0.526956\pi$
$278$	−1.97175	−0.118257
$279$	−1.09617	−0.0656257
$280$	24.5580	1.46762
$281$	7.23191	0.431420	0.215710	−	0.976458i	$-0.430793\pi$
$281$	7.23191	0.431420	0.215710	+	0.976458i	$0.430793\pi$
$282$	5.77447	0.343865
$283$	28.2493	1.67925	0.839624	−	0.543168i	$-0.182775\pi$
$283$	28.2493	1.67925	0.839624	+	0.543168i	$0.182775\pi$
$284$	7.86792	0.466875
$285$	−17.6281	−1.04420
$286$	−4.81093	−0.284476
$287$	−7.80090	−0.460473
$288$	10.5502	0.621675
$289$	7.42007	0.436475
$290$	15.3694	0.902521
$291$	3.89354	0.228244
$292$	−8.79626	−0.514762
$293$	7.68965	0.449234	0.224617	−	0.974447i	$-0.427887\pi$
$293$	7.68965	0.449234	0.224617	+	0.974447i	$0.427887\pi$
$294$	5.42256	0.316250
$295$	−31.1526	−1.81377
$296$	−2.70758	−0.157375
$297$	−13.5450	−0.785959
$298$	−6.60801	−0.382792
$299$	−3.10004	−0.179280
$300$	1.84029	0.106249
$301$	18.2452	1.05164
$302$	−4.13132	−0.237731
$303$	−5.53248	−0.317833
$304$	−3.21886	−0.184614
$305$	−2.99068	−0.171246
$306$	7.25426	0.414698
$307$	14.9118	0.851062	0.425531	−	0.904944i	$-0.360087\pi$
$307$	14.9118	0.851062	0.425531	+	0.904944i	$0.360087\pi$
$308$	−12.5963	−0.717741
$309$	−11.7536	−0.668641
$310$	1.22397	0.0695170
$311$	12.6371	0.716586	0.358293	−	0.933609i	$-0.383359\pi$
$311$	12.6371	0.716586	0.358293	+	0.933609i	$0.383359\pi$
$312$	6.78521	0.384137
$313$	−3.75216	−0.212085	−0.106042	−	0.994362i	$-0.533818\pi$
$313$	−3.75216	−0.212085	−0.106042	+	0.994362i	$0.533818\pi$
$314$	−10.4099	−0.587462
$315$	−16.4477	−0.926722
$316$	15.3928	0.865911
$317$	−22.8450	−1.28310	−0.641550	−	0.767081i	$-0.721708\pi$
$317$	−22.8450	−1.28310	−0.641550	+	0.767081i	$0.721708\pi$
$318$	0.961666	0.0539276
$319$	−19.6084	−1.09786
$320$	−9.29141	−0.519406
$321$	−0.106139	−0.00592411
$322$	3.95564	0.220439
$323$	−31.9717	−1.77895
$324$	0.364957	0.0202754
$325$	−2.89031	−0.160325
$326$	−6.70903	−0.371579
$327$	1.08931	0.0602392
$328$	5.82472	0.321616
$329$	−23.7456	−1.30914
$330$	5.69790	0.313659
$331$	12.4419	0.683870	0.341935	−	0.939724i	$-0.388918\pi$
$331$	12.4419	0.683870	0.341935	+	0.939724i	$0.388918\pi$
$332$	1.73354	0.0951401
$333$	1.81340	0.0993735
$334$	−3.42066	−0.187170
$335$	−3.26796	−0.178548
$336$	1.96523	0.107212
$337$	−13.7563	−0.749351	−0.374675	−	0.927156i	$-0.622246\pi$
$337$	−13.7563	−0.749351	−0.374675	+	0.927156i	$0.622246\pi$
$338$	6.23940	0.339379
$339$	−1.60188	−0.0870020
$340$	16.6208	0.901392
$341$	−1.56156	−0.0845630
$342$	−9.49755	−0.513569
$343$	3.08485	0.166566
$344$	−13.6232	−0.734514
$345$	3.67157	0.197671
$346$	14.1006	0.758055
$347$	12.3554	0.663272	0.331636	−	0.943407i	$-0.392399\pi$
$347$	12.3554	0.663272	0.331636	+	0.943407i	$0.392399\pi$
$348$	11.1183	0.596005
$349$	4.77722	0.255719	0.127859	−	0.991792i	$-0.459189\pi$
$349$	4.77722	0.255719	0.127859	+	0.991792i	$0.459189\pi$
$350$	3.68802	0.197133
$351$	−12.0624	−0.643842
$352$	15.0294	0.801068
$353$	9.90577	0.527231	0.263615	−	0.964628i	$-0.415085\pi$
$353$	9.90577	0.527231	0.263615	+	0.964628i	$0.415085\pi$
$354$	10.9828	0.583729
$355$	14.6353	0.776763
$356$	−0.498924	−0.0264429
$357$	19.5199	1.03310
$358$	8.53618	0.451151
$359$	−13.2299	−0.698246	−0.349123	−	0.937077i	$-0.613520\pi$
$359$	−13.2299	−0.698246	−0.349123	+	0.937077i	$0.613520\pi$
$360$	12.2810	0.647268
$361$	22.8585	1.20308
$362$	−4.51983	−0.237557
$363$	4.71302	0.247370
$364$	−11.2176	−0.587960
$365$	−16.3622	−0.856435
$366$	1.05436	0.0551124
$367$	−26.6457	−1.39089	−0.695447	−	0.718577i	$-0.744794\pi$
$367$	−26.6457	−1.39089	−0.695447	+	0.718577i	$0.744794\pi$
$368$	0.670421	0.0349481
$369$	−3.90109	−0.203083
$370$	−2.02483	−0.105266
$371$	−3.95454	−0.205309
$372$	0.885432	0.0459075
$373$	15.4686	0.800932	0.400466	−	0.916312i	$-0.368848\pi$
$373$	15.4686	0.800932	0.400466	+	0.916312i	$0.368848\pi$
$374$	10.3341	0.534365
$375$	−10.2002	−0.526735
$376$	17.7302	0.914366
$377$	−17.4621	−0.899345
$378$	15.3916	0.791657
$379$	−24.7222	−1.26989	−0.634947	−	0.772556i	$-0.718978\pi$
$379$	−24.7222	−1.26989	−0.634947	+	0.772556i	$0.718978\pi$
$380$	−21.7606	−1.11630
$381$	19.7127	1.00991
$382$	9.33256	0.477496
$383$	0.721590	0.0368715	0.0184358	−	0.999830i	$-0.494131\pi$
$383$	0.721590	0.0368715	0.0184358	+	0.999830i	$0.494131\pi$
$384$	−9.39939	−0.479661
$385$	−23.4307	−1.19414
$386$	−1.67712	−0.0853629
$387$	9.12410	0.463804
$388$	4.80630	0.244003
$389$	−3.61437	−0.183256	−0.0916279	−	0.995793i	$-0.529207\pi$
$389$	−3.61437	−0.183256	−0.0916279	+	0.995793i	$0.529207\pi$
$390$	5.07422	0.256943
$391$	6.65904	0.336762
$392$	16.6497	0.840936
$393$	5.95595	0.300438
$394$	−7.97183	−0.401615
$395$	28.6325	1.44066
$396$	−6.29919	−0.316546
$397$	12.8784	0.646346	0.323173	−	0.946340i	$-0.395250\pi$
$397$	12.8784	0.646346	0.323173	+	0.946340i	$0.395250\pi$
$398$	8.45015	0.423568
$399$	−25.5562	−1.27941
$400$	0.625064	0.0312532
$401$	10.1542	0.507079	0.253539	−	0.967325i	$-0.418405\pi$
$401$	10.1542	0.507079	0.253539	+	0.967325i	$0.418405\pi$
$402$	1.15211	0.0574622
$403$	−1.39063	−0.0692723
$404$	−6.82945	−0.339778
$405$	0.678866	0.0337331
$406$	22.2816	1.10582
$407$	2.58329	0.128049
$408$	−14.5750	−0.721569
$409$	−21.2363	−1.05007	−0.525033	−	0.851082i	$-0.675947\pi$
$409$	−21.2363	−1.05007	−0.525033	+	0.851082i	$0.675947\pi$
$410$	4.35594	0.215124
$411$	−9.05975	−0.446884
$412$	−14.5090	−0.714808
$413$	−45.1631	−2.22233
$414$	1.97814	0.0972205
$415$	3.22459	0.158289
$416$	13.3843	0.656220
$417$	−2.65324	−0.129930
$418$	−13.5298	−0.661766
$419$	−34.7608	−1.69818	−0.849088	−	0.528252i	$-0.822848\pi$
$419$	−34.7608	−1.69818	−0.849088	+	0.528252i	$0.822848\pi$
$420$	13.2857	0.648274
$421$	22.5222	1.09767	0.548833	−	0.835932i	$-0.315072\pi$
$421$	22.5222	1.09767	0.548833	+	0.835932i	$0.315072\pi$
$422$	−5.20218	−0.253238
$423$	−11.8748	−0.577371
$424$	2.95274	0.143398
$425$	6.20853	0.301158
$426$	−5.15967	−0.249987
$427$	−4.33571	−0.209820
$428$	−0.131021	−0.00633315
$429$	−6.47374	−0.312555
$430$	−10.1879	−0.491305
$431$	5.18327	0.249669	0.124835	−	0.992178i	$-0.460160\pi$
$431$	5.18327	0.249669	0.124835	+	0.992178i	$0.460160\pi$
$432$	2.60864	0.125508
$433$	−15.1321	−0.727201	−0.363601	−	0.931555i	$-0.618453\pi$
$433$	−15.1321	−0.727201	−0.363601	+	0.931555i	$0.618453\pi$
$434$	1.77444	0.0851760
$435$	20.6815	0.991602
$436$	1.34468	0.0643984
$437$	−8.71827	−0.417051
$438$	5.76846	0.275628
$439$	−41.1635	−1.96463	−0.982313	−	0.187246i	$-0.940044\pi$
$439$	−41.1635	−1.96463	−0.982313	+	0.187246i	$0.940044\pi$
$440$	17.4951	0.834046
$441$	−11.1511	−0.531004
$442$	9.20300	0.437742
$443$	7.68919	0.365324	0.182662	−	0.983176i	$-0.441529\pi$
$443$	7.68919	0.365324	0.182662	+	0.983176i	$0.441529\pi$
$444$	−1.46478	−0.0695152
$445$	−0.928062	−0.0439943
$446$	17.6494	0.835724
$447$	−8.89194	−0.420575
$448$	−13.4701	−0.636404
$449$	−34.6294	−1.63426	−0.817132	−	0.576450i	$-0.804437\pi$
$449$	−34.6294	−1.63426	−0.817132	+	0.576450i	$0.804437\pi$
$450$	1.84431	0.0869418
$451$	−5.55734	−0.261685
$452$	−1.97740	−0.0930091
$453$	−5.55923	−0.261195
$454$	3.98927	0.187226
$455$	−20.8661	−0.978217
$456$	19.0821	0.893602
$457$	−12.3183	−0.576224	−0.288112	−	0.957597i	$-0.593028\pi$
$457$	−12.3183	−0.576224	−0.288112	+	0.957597i	$0.593028\pi$
$458$	1.34114	0.0626673
$459$	25.9106	1.20940
$460$	4.53229	0.211319
$461$	−0.843244	−0.0392738	−0.0196369	−	0.999807i	$-0.506251\pi$
$461$	−0.843244	−0.0392738	−0.0196369	+	0.999807i	$0.506251\pi$
$462$	8.26047	0.384312
$463$	38.0472	1.76820	0.884102	−	0.467293i	$-0.154771\pi$
$463$	38.0472	1.76820	0.884102	+	0.467293i	$0.154771\pi$
$464$	3.77640	0.175315
$465$	1.64702	0.0763785
$466$	−8.41653	−0.389888
$467$	−5.02518	−0.232538	−0.116269	−	0.993218i	$-0.537093\pi$
$467$	−5.02518	−0.232538	−0.116269	+	0.993218i	$0.537093\pi$
$468$	−5.60970	−0.259309
$469$	−4.73769	−0.218766
$470$	13.2593	0.611606
$471$	−14.0078	−0.645446
$472$	33.7221	1.55218
$473$	12.9978	0.597641
$474$	−10.0943	−0.463649
$475$	−8.12844	−0.372958
$476$	24.0959	1.10443
$477$	−1.97759	−0.0905478
$478$	3.14688	0.143935
$479$	42.1857	1.92751	0.963757	−	0.266781i	$-0.0859600\pi$
$479$	42.1857	1.92751	0.963757	+	0.266781i	$0.0859600\pi$
$480$	−15.8519	−0.723537
$481$	2.30053	0.104895
$482$	−6.14657	−0.279969
$483$	5.32283	0.242197
$484$	5.81789	0.264449
$485$	8.94032	0.405959
$486$	12.4943	0.566754
$487$	14.9015	0.675253	0.337626	−	0.941280i	$-0.390376\pi$
$487$	14.9015	0.675253	0.337626	+	0.941280i	$0.390376\pi$
$488$	3.23736	0.146548
$489$	−9.02788	−0.408255
$490$	12.4512	0.562490
$491$	35.8856	1.61950	0.809748	−	0.586777i	$-0.199604\pi$
$491$	35.8856	1.61950	0.809748	+	0.586777i	$0.199604\pi$
$492$	3.15112	0.142064
$493$	37.5095	1.68934
$494$	−12.0489	−0.542106
$495$	−11.7173	−0.526653
$496$	0.300742	0.0135037
$497$	21.2174	0.951731
$498$	−1.13683	−0.0509424
$499$	38.8857	1.74076	0.870381	−	0.492378i	$-0.163872\pi$
$499$	38.8857	1.74076	0.870381	+	0.492378i	$0.163872\pi$
$500$	−12.5914	−0.563104
$501$	−4.60294	−0.205644
$502$	0.315415	0.0140777
$503$	−24.8958	−1.11005	−0.555025	−	0.831834i	$-0.687291\pi$
$503$	−24.8958	−1.11005	−0.555025	+	0.831834i	$0.687291\pi$
$504$	17.8043	0.793067
$505$	−12.7036	−0.565304
$506$	2.81799	0.125275
$507$	8.39593	0.372876
$508$	24.3338	1.07964
$509$	12.6466	0.560549	0.280274	−	0.959920i	$-0.409575\pi$
$509$	12.6466	0.560549	0.280274	+	0.959920i	$0.409575\pi$
$510$	−10.8997	−0.482647
$511$	−23.7209	−1.04935
$512$	−5.58867	−0.246987
$513$	−33.9232	−1.49774
$514$	−1.08791	−0.0479857
$515$	−26.9886	−1.18926
$516$	−7.37003	−0.324447
$517$	−16.9163	−0.743979
$518$	−2.93547	−0.128977
$519$	18.9743	0.832877
$520$	15.5801	0.683234
$521$	34.9764	1.53234	0.766171	−	0.642637i	$-0.222159\pi$
$521$	34.9764	1.53234	0.766171	+	0.642637i	$0.222159\pi$
$522$	11.1426	0.487700
$523$	−17.8640	−0.781138	−0.390569	−	0.920574i	$-0.627722\pi$
$523$	−17.8640	−0.781138	−0.390569	+	0.920574i	$0.627722\pi$
$524$	7.35220	0.321182
$525$	4.96271	0.216590
$526$	−2.76940	−0.120752
$527$	2.98715	0.130122
$528$	1.40003	0.0609283
$529$	−21.1842	−0.921051
$530$	2.20817	0.0959168
$531$	−22.5853	−0.980117
$532$	−31.5473	−1.36775
$533$	−4.94906	−0.214367
$534$	0.327187	0.0141588
$535$	−0.243716	−0.0105368
$536$	3.53750	0.152797
$537$	11.4865	0.495681
$538$	6.78622	0.292575
$539$	−15.8854	−0.684233
$540$	17.6353	0.758905
$541$	31.1643	1.33986	0.669929	−	0.742425i	$-0.266324\pi$
$541$	31.1643	1.33986	0.669929	+	0.742425i	$0.266324\pi$
$542$	−1.69739	−0.0729089
$543$	−6.08202	−0.261004
$544$	−28.7502	−1.23265
$545$	2.50127	0.107143
$546$	7.35631	0.314821
$547$	−7.60954	−0.325360	−0.162680	−	0.986679i	$-0.552014\pi$
$547$	−7.60954	−0.325360	−0.162680	+	0.986679i	$0.552014\pi$
$548$	−11.1836	−0.477740
$549$	−2.16821	−0.0925371
$550$	2.62734	0.112030
$551$	−49.1089	−2.09211
$552$	−3.97441	−0.169162
$553$	41.5097	1.76517
$554$	2.27917	0.0968328
$555$	−2.72467	−0.115656
$556$	−3.27524	−0.138901
$557$	18.9819	0.804290	0.402145	−	0.915576i	$-0.368265\pi$
$557$	18.9819	0.804290	0.402145	+	0.915576i	$0.368265\pi$
$558$	0.887367	0.0375653
$559$	11.5751	0.489576
$560$	4.51255	0.190690
$561$	13.9059	0.587109
$562$	−5.85437	−0.246952
$563$	5.84164	0.246196	0.123098	−	0.992395i	$-0.460717\pi$
$563$	5.84164	0.246196	0.123098	+	0.992395i	$0.460717\pi$
$564$	9.59188	0.403891
$565$	−3.67821	−0.154744
$566$	−22.8684	−0.961229
$567$	0.984179	0.0413316
$568$	−15.8425	−0.664736
$569$	−6.24895	−0.261969	−0.130985	−	0.991384i	$-0.541814\pi$
$569$	−6.24895	−0.261969	−0.130985	+	0.991384i	$0.541814\pi$
$570$	14.2703	0.597717
$571$	29.7271	1.24404	0.622020	−	0.783001i	$-0.286312\pi$
$571$	29.7271	1.24404	0.622020	+	0.783001i	$0.286312\pi$
$572$	−7.99136	−0.334136
$573$	12.5582	0.524626
$574$	6.31498	0.263582
$575$	1.69299	0.0706024
$576$	−6.73617	−0.280674
$577$	18.3357	0.763327	0.381664	−	0.924301i	$-0.375351\pi$
$577$	18.3357	0.763327	0.381664	+	0.924301i	$0.375351\pi$
$578$	−6.00669	−0.249845
$579$	−2.25678	−0.0937885
$580$	25.5298	1.06007
$581$	4.67482	0.193944
$582$	−3.15190	−0.130650
$583$	−2.81720	−0.116677
$584$	17.7117	0.732917
$585$	−10.4348	−0.431424
$586$	−6.22492	−0.257149
$587$	11.2863	0.465837	0.232918	−	0.972496i	$-0.425172\pi$
$587$	11.2863	0.465837	0.232918	+	0.972496i	$0.425172\pi$
$588$	9.00733	0.371456
$589$	−3.91089	−0.161145
$590$	25.2186	1.03823
$591$	−10.7271	−0.441255
$592$	−0.497519	−0.0204479
$593$	−22.9909	−0.944122	−0.472061	−	0.881566i	$-0.656490\pi$
$593$	−22.9909	−0.944122	−0.472061	+	0.881566i	$0.656490\pi$
$594$	10.9649	0.449896
$595$	44.8214	1.83750
$596$	−10.9765	−0.449613
$597$	11.3708	0.465375
$598$	2.50954	0.102623
$599$	39.6799	1.62128	0.810639	−	0.585547i	$-0.199120\pi$
$599$	39.6799	1.62128	0.810639	+	0.585547i	$0.199120\pi$
$600$	−3.70552	−0.151277
$601$	−12.1974	−0.497543	−0.248772	−	0.968562i	$-0.580027\pi$
$601$	−12.1974	−0.497543	−0.248772	+	0.968562i	$0.580027\pi$
$602$	−14.7698	−0.601974
$603$	−2.36923	−0.0964827
$604$	−6.86247	−0.279230
$605$	10.8220	0.439977
$606$	4.47865	0.181933
$607$	−35.5554	−1.44315	−0.721575	−	0.692336i	$-0.756582\pi$
$607$	−35.5554	−1.44315	−0.721575	+	0.692336i	$0.756582\pi$
$608$	37.6408	1.52654
$609$	29.9828	1.21496
$610$	2.42102	0.0980241
$611$	−15.0647	−0.609453
$612$	12.0499	0.487090
$613$	−20.5750	−0.831015	−0.415508	−	0.909590i	$-0.636396\pi$
$613$	−20.5750	−0.831015	−0.415508	+	0.909590i	$0.636396\pi$
$614$	−12.0714	−0.487162
$615$	5.86148	0.236358
$616$	25.3633	1.02192
$617$	7.27827	0.293012	0.146506	−	0.989210i	$-0.453197\pi$
$617$	7.27827	0.293012	0.146506	+	0.989210i	$0.453197\pi$
$618$	9.51480	0.382741
$619$	11.3456	0.456020	0.228010	−	0.973659i	$-0.426778\pi$
$619$	11.3456	0.456020	0.228010	+	0.973659i	$0.426778\pi$
$620$	2.03312	0.0816521
$621$	7.06550	0.283529
$622$	−10.2300	−0.410186
$623$	−1.34545	−0.0539042
$624$	1.24678	0.0499113
$625$	−29.7034	−1.18813
$626$	3.03745	0.121401
$627$	−18.2062	−0.727084
$628$	−17.2916	−0.690012
$629$	−4.94167	−0.197037
$630$	13.3147	0.530471
$631$	−15.2314	−0.606350	−0.303175	−	0.952935i	$-0.598047\pi$
$631$	−15.2314	−0.606350	−0.303175	+	0.952935i	$0.598047\pi$
$632$	−30.9942	−1.23288
$633$	−7.00021	−0.278233
$634$	18.4934	0.734468
$635$	45.2640	1.79625
$636$	1.59741	0.0633414
$637$	−14.1466	−0.560510
$638$	15.8734	0.628433
$639$	10.6105	0.419743
$640$	−21.5828	−0.853135
$641$	−3.67562	−0.145178	−0.0725892	−	0.997362i	$-0.523126\pi$
$641$	−3.67562	−0.145178	−0.0725892	+	0.997362i	$0.523126\pi$
$642$	0.0859217	0.00339106
$643$	23.5259	0.927771	0.463885	−	0.885895i	$-0.346455\pi$
$643$	23.5259	0.927771	0.463885	+	0.885895i	$0.346455\pi$
$644$	6.57064	0.258920
$645$	−13.7092	−0.539798
$646$	25.8817	1.01830
$647$	11.8553	0.466081	0.233040	−	0.972467i	$-0.425133\pi$
$647$	11.8553	0.466081	0.233040	+	0.972467i	$0.425133\pi$
$648$	−0.734860	−0.0288680
$649$	−32.1741	−1.26294
$650$	2.33976	0.0917728
$651$	2.38774	0.0935831
$652$	−11.1443	−0.436443
$653$	26.4331	1.03441	0.517204	−	0.855862i	$-0.326973\pi$
$653$	26.4331	1.03441	0.517204	+	0.855862i	$0.326973\pi$
$654$	−0.881820	−0.0344819
$655$	13.6760	0.534366
$656$	1.07029	0.0417880
$657$	−11.8624	−0.462796
$658$	19.2225	0.749372
$659$	−9.86078	−0.384122	−0.192061	−	0.981383i	$-0.561517\pi$
$659$	−9.86078	−0.384122	−0.192061	+	0.981383i	$0.561517\pi$
$660$	9.46468	0.368412
$661$	35.9700	1.39907	0.699536	−	0.714597i	$-0.253390\pi$
$661$	35.9700	1.39907	0.699536	+	0.714597i	$0.253390\pi$
$662$	−10.0720	−0.391459
$663$	12.3838	0.480948
$664$	−3.49056	−0.135460
$665$	−58.6819	−2.27559
$666$	−1.46798	−0.0568830
$667$	10.2284	0.396044
$668$	−5.68200	−0.219843
$669$	23.7496	0.918212
$670$	2.64547	0.102204
$671$	−3.08875	−0.119240
$672$	−22.9811	−0.886516
$673$	4.91348	0.189401	0.0947004	−	0.995506i	$-0.469811\pi$
$673$	4.91348	0.189401	0.0947004	+	0.995506i	$0.469811\pi$
$674$	11.1360	0.428941
$675$	6.58748	0.253552
$676$	10.3642	0.398622
$677$	−6.09396	−0.234210	−0.117105	−	0.993120i	$-0.537361\pi$
$677$	−6.09396	−0.234210	−0.117105	+	0.993120i	$0.537361\pi$
$678$	1.29675	0.0498013
$679$	12.9611	0.497403
$680$	−33.4669	−1.28340
$681$	5.36809	0.205705
$682$	1.26411	0.0484052
$683$	−44.6851	−1.70983	−0.854913	−	0.518771i	$-0.826390\pi$
$683$	−44.6851	−1.70983	−0.854913	+	0.518771i	$0.826390\pi$
$684$	−15.7762	−0.603219
$685$	−20.8029	−0.794838
$686$	−2.49725	−0.0953454
$687$	1.80468	0.0688527
$688$	−2.50327	−0.0954362
$689$	−2.50884	−0.0955792
$690$	−2.97221	−0.113150
$691$	14.9908	0.570276	0.285138	−	0.958486i	$-0.407961\pi$
$691$	14.9908	0.570276	0.285138	+	0.958486i	$0.407961\pi$
$692$	23.4223	0.890384
$693$	−16.9870	−0.645284
$694$	−10.0019	−0.379668
$695$	−6.09235	−0.231096
$696$	−22.3874	−0.848590
$697$	10.6308	0.402671
$698$	−3.86725	−0.146378
$699$	−11.3255	−0.428372
$700$	6.12611	0.231545
$701$	15.6101	0.589586	0.294793	−	0.955561i	$-0.404749\pi$
$701$	15.6101	0.589586	0.294793	+	0.955561i	$0.404749\pi$
$702$	9.76473	0.368546
$703$	6.46982	0.244014
$704$	−9.59609	−0.361666
$705$	17.8421	0.671973
$706$	−8.01891	−0.301796
$707$	−18.4170	−0.692641
$708$	18.2433	0.685627
$709$	48.7435	1.83060	0.915300	−	0.402772i	$-0.131953\pi$
$709$	48.7435	1.83060	0.915300	+	0.402772i	$0.131953\pi$
$710$	−11.8476	−0.444632
$711$	20.7583	0.778495
$712$	1.00461	0.0376493
$713$	0.814558	0.0305054
$714$	−15.8017	−0.591365
$715$	−14.8649	−0.555917
$716$	14.1793	0.529906
$717$	4.23454	0.158142
$718$	10.7098	0.399688
$719$	−41.3577	−1.54238	−0.771190	−	0.636605i	$-0.780338\pi$
$719$	−41.3577	−1.54238	−0.771190	+	0.636605i	$0.780338\pi$
$720$	2.25664	0.0841002
$721$	−39.1265	−1.45715
$722$	−18.5044	−0.688663
$723$	−8.27102	−0.307602
$724$	−7.50781	−0.279026
$725$	9.53637	0.354172
$726$	−3.81528	−0.141598
$727$	16.4458	0.609939	0.304970	−	0.952362i	$-0.401354\pi$
$727$	16.4458	0.609939	0.304970	+	0.952362i	$0.401354\pi$
$728$	22.5871	0.837135
$729$	17.6270	0.652850
$730$	13.2455	0.490237
$731$	−24.8640	−0.919628
$732$	1.75138	0.0647330
$733$	−50.1225	−1.85132	−0.925659	−	0.378359i	$-0.876488\pi$
$733$	−50.1225	−1.85132	−0.925659	+	0.378359i	$0.876488\pi$
$734$	21.5702	0.796171
$735$	16.7548	0.618009
$736$	−7.83981	−0.288979
$737$	−3.37512	−0.124324
$738$	3.15801	0.116248
$739$	33.8087	1.24367	0.621836	−	0.783147i	$-0.286387\pi$
$739$	33.8087	1.24367	0.621836	+	0.783147i	$0.286387\pi$
$740$	−3.36341	−0.123641
$741$	−16.2134	−0.595613
$742$	3.20127	0.117522
$743$	−35.7808	−1.31267	−0.656336	−	0.754469i	$-0.727894\pi$
$743$	−35.7808	−1.31267	−0.656336	+	0.754469i	$0.727894\pi$
$744$	−1.78286	−0.0653630
$745$	−20.4176	−0.748043
$746$	−12.5221	−0.458467
$747$	2.33780	0.0855355
$748$	17.1659	0.627646
$749$	−0.353325	−0.0129102
$750$	8.25724	0.301512
$751$	−20.2917	−0.740454	−0.370227	−	0.928941i	$-0.620720\pi$
$751$	−20.2917	−0.740454	−0.370227	+	0.928941i	$0.620720\pi$
$752$	3.25793	0.118805
$753$	0.424432	0.0154672
$754$	14.1359	0.514800
$755$	−12.7651	−0.464568
$756$	25.5667	0.929851
$757$	2.92991	0.106489	0.0532447	−	0.998581i	$-0.483044\pi$
$757$	2.92991	0.106489	0.0532447	+	0.998581i	$0.483044\pi$
$758$	20.0131	0.726908
$759$	3.79197	0.137640
$760$	43.8162	1.58938
$761$	41.9715	1.52147	0.760733	−	0.649065i	$-0.224840\pi$
$761$	41.9715	1.52147	0.760733	+	0.649065i	$0.224840\pi$
$762$	−15.9578	−0.578089
$763$	3.62619	0.131277
$764$	15.5022	0.560849
$765$	22.4144	0.810394
$766$	−0.584141	−0.0211059
$767$	−28.6524	−1.03458
$768$	15.7019	0.566593
$769$	−45.7057	−1.64819	−0.824096	−	0.566451i	$-0.808316\pi$
$769$	−45.7057	−1.64819	−0.824096	+	0.566451i	$0.808316\pi$
$770$	18.9676	0.683545
$771$	−1.46393	−0.0527220
$772$	−2.78583	−0.100264
$773$	−41.9145	−1.50756	−0.753779	−	0.657128i	$-0.771771\pi$
$773$	−41.9145	−1.50756	−0.753779	+	0.657128i	$0.771771\pi$
$774$	−7.38614	−0.265489
$775$	0.759449	0.0272802
$776$	−9.67773	−0.347410
$777$	−3.95006	−0.141708
$778$	2.92590	0.104899
$779$	−13.9183	−0.498674
$780$	8.42871	0.301796
$781$	15.1152	0.540866
$782$	−5.39062	−0.192768
$783$	39.7991	1.42230
$784$	3.05939	0.109264
$785$	−32.1646	−1.14801
$786$	−4.82146	−0.171976
$787$	−37.0924	−1.32220	−0.661101	−	0.750297i	$-0.729911\pi$
$787$	−37.0924	−1.32220	−0.661101	+	0.750297i	$0.729911\pi$
$788$	−13.2419	−0.471722
$789$	−3.72659	−0.132670
$790$	−23.1786	−0.824656
$791$	−5.33245	−0.189600
$792$	12.6838	0.450698
$793$	−2.75067	−0.0976791
$794$	−10.4253	−0.369979
$795$	2.97138	0.105384
$796$	14.0364	0.497507
$797$	−30.8480	−1.09269	−0.546345	−	0.837560i	$-0.683981\pi$
$797$	−30.8480	−1.09269	−0.546345	+	0.837560i	$0.683981\pi$
$798$	20.6882	0.732355
$799$	32.3598	1.14481
$800$	−7.30941	−0.258427
$801$	−0.672835	−0.0237735
$802$	−8.22006	−0.290260
$803$	−16.8987	−0.596342
$804$	1.91376	0.0674930
$805$	12.2222	0.430777
$806$	1.12574	0.0396526
$807$	9.13175	0.321453
$808$	13.7515	0.483774
$809$	17.4175	0.612366	0.306183	−	0.951973i	$-0.400948\pi$
$809$	17.4175	0.612366	0.306183	+	0.951973i	$0.400948\pi$
$810$	−0.549555	−0.0193094
$811$	17.4656	0.613301	0.306651	−	0.951822i	$-0.400792\pi$
$811$	17.4656	0.613301	0.306651	+	0.951822i	$0.400792\pi$
$812$	37.0116	1.29885
$813$	−2.28405	−0.0801053
$814$	−2.09122	−0.0732974
$815$	−20.7297	−0.726131
$816$	−2.67816	−0.0937543
$817$	32.5529	1.13888
$818$	17.1912	0.601075
$819$	−15.1277	−0.528604
$820$	7.23558	0.252677
$821$	31.7867	1.10936	0.554682	−	0.832062i	$-0.312840\pi$
$821$	31.7867	1.10936	0.554682	+	0.832062i	$0.312840\pi$
$822$	7.33404	0.255804
$823$	−27.2991	−0.951588	−0.475794	−	0.879557i	$-0.657839\pi$
$823$	−27.2991	−0.951588	−0.475794	+	0.879557i	$0.657839\pi$
$824$	29.2147	1.01774
$825$	3.53542	0.123088
$826$	36.5604	1.27210
$827$	24.2097	0.841853	0.420926	−	0.907095i	$-0.361705\pi$
$827$	24.2097	0.841853	0.420926	+	0.907095i	$0.361705\pi$
$828$	3.28586	0.114192
$829$	−7.90920	−0.274698	−0.137349	−	0.990523i	$-0.543858\pi$
$829$	−7.90920	−0.274698	−0.137349	+	0.990523i	$0.543858\pi$
$830$	−2.61037	−0.0906073
$831$	3.06692	0.106390
$832$	−8.54573	−0.296270
$833$	30.3877	1.05287
$834$	2.14785	0.0743740
$835$	−10.5692	−0.365763
$836$	−22.4742	−0.777286
$837$	3.16948	0.109553
$838$	28.1395	0.972064
$839$	28.2392	0.974926	0.487463	−	0.873144i	$-0.337922\pi$
$839$	28.2392	0.974926	0.487463	+	0.873144i	$0.337922\pi$
$840$	−26.7514	−0.923011
$841$	28.6151	0.986728
$842$	−18.2322	−0.628322
$843$	−7.87782	−0.271326
$844$	−8.64125	−0.297444
$845$	19.2787	0.663206
$846$	9.61285	0.330497
$847$	15.6891	0.539083
$848$	0.542568	0.0186319
$849$	−30.7724	−1.05611
$850$	−5.02592	−0.172388
$851$	−1.34753	−0.0461927
$852$	−8.57064	−0.293625
$853$	−47.5967	−1.62968	−0.814840	−	0.579686i	$-0.803175\pi$
$853$	−47.5967	−1.62968	−0.814840	+	0.579686i	$0.803175\pi$
$854$	3.50984	0.120104
$855$	−29.3458	−1.00360
$856$	0.263818	0.00901712
$857$	−25.9225	−0.885497	−0.442749	−	0.896646i	$-0.645997\pi$
$857$	−25.9225	−0.885497	−0.442749	+	0.896646i	$0.645997\pi$
$858$	5.24062	0.178912
$859$	−24.6501	−0.841051	−0.420525	−	0.907281i	$-0.638154\pi$
$859$	−24.6501	−0.841051	−0.420525	+	0.907281i	$0.638154\pi$
$860$	−16.9230	−0.577069
$861$	8.49763	0.289598
$862$	−4.19596	−0.142915
$863$	−50.7866	−1.72880	−0.864398	−	0.502808i	$-0.832300\pi$
$863$	−50.7866	−1.72880	−0.864398	+	0.502808i	$0.832300\pi$
$864$	−30.5051	−1.03780
$865$	43.5685	1.48137
$866$	12.2497	0.416262
$867$	−8.08279	−0.274506
$868$	2.94750	0.100045
$869$	29.5714	1.00314
$870$	−16.7421	−0.567609
$871$	−3.00569	−0.101844
$872$	−2.70758	−0.0916903
$873$	6.48164	0.219370
$874$	7.05760	0.238727
$875$	−33.9552	−1.14789
$876$	9.58189	0.323742
$877$	−10.7490	−0.362967	−0.181483	−	0.983394i	$-0.558090\pi$
$877$	−10.7490	−0.362967	−0.181483	+	0.983394i	$0.558090\pi$
$878$	33.3226	1.12458
$879$	−8.37644	−0.282530
$880$	3.21473	0.108368
$881$	10.3008	0.347044	0.173522	−	0.984830i	$-0.444485\pi$
$881$	10.3008	0.347044	0.173522	+	0.984830i	$0.444485\pi$
$882$	9.02702	0.303956
$883$	−19.0438	−0.640874	−0.320437	−	0.947270i	$-0.603830\pi$
$883$	−19.0438	−0.640874	−0.320437	+	0.947270i	$0.603830\pi$
$884$	15.2869	0.514156
$885$	33.9349	1.14071
$886$	−6.22454	−0.209118
$887$	−0.213239	−0.00715987	−0.00357993	−	0.999994i	$-0.501140\pi$
$887$	−0.213239	−0.00715987	−0.00357993	+	0.999994i	$0.501140\pi$
$888$	2.94941	0.0989756
$889$	65.6211	2.20086
$890$	0.751284	0.0251831
$891$	0.701127	0.0234886
$892$	29.3171	0.981610
$893$	−42.3667	−1.41775
$894$	7.19820	0.240744
$895$	26.3753	0.881629
$896$	−31.2894	−1.04531
$897$	3.37691	0.112752
$898$	28.0332	0.935480
$899$	4.58830	0.153028
$900$	3.06356	0.102119
$901$	5.38912	0.179538
$902$	4.49878	0.149793
$903$	−19.8747	−0.661390
$904$	3.98160	0.132426
$905$	−13.9655	−0.464228
$906$	4.50030	0.149513
$907$	2.92703	0.0971904	0.0485952	−	0.998819i	$-0.484526\pi$
$907$	2.92703	0.0971904	0.0485952	+	0.998819i	$0.484526\pi$
$908$	6.62651	0.219909
$909$	−9.21000	−0.305476
$910$	16.8915	0.559947
$911$	15.2662	0.505793	0.252896	−	0.967493i	$-0.418617\pi$
$911$	15.2662	0.505793	0.252896	+	0.967493i	$0.418617\pi$
$912$	3.50634	0.116107
$913$	3.33033	0.110218
$914$	9.97188	0.329840
$915$	3.25779	0.107699
$916$	2.22774	0.0736067
$917$	19.8267	0.654734
$918$	−20.9751	−0.692283
$919$	21.3691	0.704902	0.352451	−	0.935830i	$-0.385348\pi$
$919$	21.3691	0.704902	0.352451	+	0.935830i	$0.385348\pi$
$920$	−9.12601	−0.300875
$921$	−16.2436	−0.535246
$922$	0.682622	0.0224810
$923$	13.4608	0.443067
$924$	13.7213	0.451399
$925$	−1.25636	−0.0413090
$926$	−30.8000	−1.01215
$927$	−19.5665	−0.642647
$928$	−44.1607	−1.44964
$929$	−32.9023	−1.07949	−0.539745	−	0.841828i	$-0.681479\pi$
$929$	−32.9023	−1.07949	−0.539745	+	0.841828i	$0.681479\pi$
$930$	−1.33329	−0.0437203
$931$	−39.7848	−1.30389
$932$	−13.9806	−0.457949
$933$	−13.7658	−0.450672
$934$	4.06798	0.133108
$935$	31.9307	1.04424
$936$	11.2954	0.369203
$937$	56.0046	1.82959	0.914796	−	0.403917i	$-0.132351\pi$
$937$	56.0046	1.82959	0.914796	+	0.403917i	$0.132351\pi$
$938$	3.83525	0.125225
$939$	4.08728	0.133383
$940$	22.0248	0.718370
$941$	31.4493	1.02522	0.512608	−	0.858623i	$-0.328679\pi$
$941$	31.4493	1.02522	0.512608	+	0.858623i	$0.328679\pi$
$942$	11.3396	0.369464
$943$	2.89889	0.0944009
$944$	6.19644	0.201677
$945$	47.5572	1.54704
$946$	−10.5220	−0.342100
$947$	13.8843	0.451179	0.225590	−	0.974222i	$-0.427569\pi$
$947$	13.8843	0.451179	0.225590	+	0.974222i	$0.427569\pi$
$948$	−16.7676	−0.544585
$949$	−15.0490	−0.488512
$950$	6.58012	0.213487
$951$	24.8853	0.806962
$952$	−48.5184	−1.57249
$953$	32.9112	1.06610	0.533050	−	0.846084i	$-0.321046\pi$
$953$	32.9112	1.06610	0.533050	+	0.846084i	$0.321046\pi$
$954$	1.60090	0.0518310
$955$	28.8360	0.933111
$956$	5.22724	0.169061
$957$	21.3597	0.690461
$958$	−34.1501	−1.10334
$959$	−30.1588	−0.973879
$960$	10.1213	0.326662
$961$	−30.6346	−0.988213
$962$	−1.86233	−0.0600438
$963$	−0.176691	−0.00569380
$964$	−10.2100	−0.328841
$965$	−5.18199	−0.166814
$966$	−4.30893	−0.138638
$967$	57.6052	1.85246	0.926228	−	0.376963i	$-0.123032\pi$
$967$	57.6052	1.85246	0.926228	+	0.376963i	$0.123032\pi$
$968$	−11.7146	−0.376522
$969$	34.8272	1.11881
$970$	−7.23736	−0.232378
$971$	−6.97385	−0.223802	−0.111901	−	0.993719i	$-0.535694\pi$
$971$	−6.97385	−0.223802	−0.111901	+	0.993719i	$0.535694\pi$
$972$	20.7541	0.665688
$973$	−8.83233	−0.283151
$974$	−12.0631	−0.386526
$975$	3.14845	0.100831
$976$	0.594866	0.0190412
$977$	−13.2383	−0.423532	−0.211766	−	0.977320i	$-0.567921\pi$
$977$	−13.2383	−0.423532	−0.211766	+	0.977320i	$0.567921\pi$
$978$	7.30824	0.233692
$979$	−0.958494	−0.0306336
$980$	20.6826	0.660680
$981$	1.81340	0.0578973
$982$	−29.0501	−0.927026
$983$	−56.0197	−1.78675	−0.893375	−	0.449312i	$-0.851669\pi$
$983$	−56.0197	−1.78675	−0.893375	+	0.449312i	$0.851669\pi$
$984$	−6.34495	−0.202270
$985$	−24.6316	−0.784827
$986$	−30.3647	−0.967009
$987$	25.8664	0.823337
$988$	−20.0142	−0.636738
$989$	−6.78010	−0.215594
$990$	9.48537	0.301465
$991$	30.4278	0.966572	0.483286	−	0.875463i	$-0.339443\pi$
$991$	30.4278	0.966572	0.483286	+	0.875463i	$0.339443\pi$
$992$	−3.51683	−0.111659
$993$	−13.5532	−0.430097
$994$	−17.1759	−0.544787
$995$	26.1095	0.827726
$996$	−1.88836	−0.0598351
$997$	8.14942	0.258095	0.129047	−	0.991638i	$-0.458808\pi$
$997$	8.14942	0.258095	0.129047	+	0.991638i	$0.458808\pi$
$998$	−31.4787	−0.996441
$999$	−5.24330	−0.165891

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.d.1.33	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.d.1.33	✓	79	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:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q-0.809519 q^{2} -1.08931 q^{3} -1.34468 q^{4} -2.50127 q^{5} +0.881820 q^{6} -3.62619 q^{7} +2.70758 q^{8} -1.81340 q^{9} +O(q^{10})\)	\(q-0.809519 q^{2} -1.08931 q^{3} -1.34468 q^{4} -2.50127 q^{5} +0.881820 q^{6} -3.62619 q^{7} +2.70758 q^{8} -1.81340 q^{9} +2.02483 q^{10} -2.58329 q^{11} +1.46478 q^{12} -2.30053 q^{13} +2.93547 q^{14} +2.72467 q^{15} +0.497519 q^{16} +4.94167 q^{17} +1.46798 q^{18} -6.46982 q^{19} +3.36341 q^{20} +3.95006 q^{21} +2.09122 q^{22} +1.34753 q^{23} -2.94941 q^{24} +1.25636 q^{25} +1.86233 q^{26} +5.24330 q^{27} +4.87607 q^{28} +7.59046 q^{29} -2.20567 q^{30} +0.604483 q^{31} -5.81791 q^{32} +2.81402 q^{33} -4.00037 q^{34} +9.07010 q^{35} +2.43844 q^{36} -1.00000 q^{37} +5.23744 q^{38} +2.50600 q^{39} -6.77240 q^{40} +2.15126 q^{41} -3.19765 q^{42} -5.03150 q^{43} +3.47370 q^{44} +4.53580 q^{45} -1.09085 q^{46} +6.54836 q^{47} -0.541954 q^{48} +6.14929 q^{49} -1.01705 q^{50} -5.38303 q^{51} +3.09348 q^{52} +1.09055 q^{53} -4.24455 q^{54} +6.46152 q^{55} -9.81822 q^{56} +7.04766 q^{57} -6.14462 q^{58} +12.4547 q^{59} -3.66381 q^{60} +1.19567 q^{61} -0.489340 q^{62} +6.57573 q^{63} +3.71467 q^{64} +5.75426 q^{65} -2.27800 q^{66} +1.30652 q^{67} -6.64496 q^{68} -1.46788 q^{69} -7.34242 q^{70} -5.85115 q^{71} -4.90992 q^{72} +6.54153 q^{73} +0.809519 q^{74} -1.36857 q^{75} +8.69983 q^{76} +9.36752 q^{77} -2.02866 q^{78} -11.4472 q^{79} -1.24443 q^{80} -0.271408 q^{81} -1.74149 q^{82} -1.28918 q^{83} -5.31157 q^{84} -12.3605 q^{85} +4.07310 q^{86} -8.26839 q^{87} -6.99448 q^{88} +0.371036 q^{89} -3.67181 q^{90} +8.34218 q^{91} -1.81199 q^{92} -0.658471 q^{93} -5.30102 q^{94} +16.1828 q^{95} +6.33753 q^{96} -3.57431 q^{97} -4.97796 q^{98} +4.68453 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + q^99

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