LMFDB - Embedded newform 4033.2.a.c.1.18

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:	$77$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
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)

$f(q)$	$=$	$q-1.78823 q^{2} +2.78240 q^{3} +1.19778 q^{4} -2.10202 q^{5} -4.97558 q^{6} -2.70114 q^{7} +1.43455 q^{8} +4.74173 q^{9} +O(q^{10})$	\(q-1.78823 q^{2} +2.78240 q^{3} +1.19778 q^{4} -2.10202 q^{5} -4.97558 q^{6} -2.70114 q^{7} +1.43455 q^{8} +4.74173 q^{9} +3.75890 q^{10} +3.93666 q^{11} +3.33270 q^{12} -6.77398 q^{13} +4.83028 q^{14} -5.84864 q^{15} -4.96088 q^{16} +6.00146 q^{17} -8.47932 q^{18} -3.18902 q^{19} -2.51776 q^{20} -7.51565 q^{21} -7.03967 q^{22} -0.759006 q^{23} +3.99149 q^{24} -0.581526 q^{25} +12.1135 q^{26} +4.84617 q^{27} -3.23538 q^{28} +4.13153 q^{29} +10.4587 q^{30} +7.00483 q^{31} +6.00211 q^{32} +10.9533 q^{33} -10.7320 q^{34} +5.67785 q^{35} +5.67956 q^{36} +1.00000 q^{37} +5.70272 q^{38} -18.8479 q^{39} -3.01545 q^{40} +9.83180 q^{41} +13.4397 q^{42} -6.90597 q^{43} +4.71526 q^{44} -9.96719 q^{45} +1.35728 q^{46} -4.59077 q^{47} -13.8031 q^{48} +0.296181 q^{49} +1.03991 q^{50} +16.6984 q^{51} -8.11376 q^{52} -9.99885 q^{53} -8.66609 q^{54} -8.27492 q^{55} -3.87494 q^{56} -8.87313 q^{57} -7.38814 q^{58} +9.15037 q^{59} -7.00540 q^{60} -0.435289 q^{61} -12.5263 q^{62} -12.8081 q^{63} -0.811423 q^{64} +14.2390 q^{65} -19.5871 q^{66} -10.5871 q^{67} +7.18844 q^{68} -2.11185 q^{69} -10.1533 q^{70} -16.1503 q^{71} +6.80226 q^{72} -0.259503 q^{73} -1.78823 q^{74} -1.61804 q^{75} -3.81976 q^{76} -10.6335 q^{77} +33.7045 q^{78} +3.43324 q^{79} +10.4279 q^{80} -0.741213 q^{81} -17.5816 q^{82} -5.22693 q^{83} -9.00212 q^{84} -12.6152 q^{85} +12.3495 q^{86} +11.4955 q^{87} +5.64735 q^{88} +7.31595 q^{89} +17.8237 q^{90} +18.2975 q^{91} -0.909124 q^{92} +19.4902 q^{93} +8.20938 q^{94} +6.70338 q^{95} +16.7003 q^{96} +0.841504 q^{97} -0.529640 q^{98} +18.6666 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 77 q - 9 q^{2} - 27 q^{3} + 73 q^{4} - 16 q^{5} - 2 q^{6} - 23 q^{7} - 24 q^{8} + 66 q^{9}+O(q^{10}) $ 77 * q - 9 * q^2 - 27 * q^3 + 73 * q^4 - 16 * q^5 - 2 * q^6 - 23 * q^7 - 24 * q^8 + 66 * q^9	\( 77 q - 9 q^{2} - 27 q^{3} + 73 q^{4} - 16 q^{5} - 2 q^{6} - 23 q^{7} - 24 q^{8} + 66 q^{9} - 11 q^{10} - 33 q^{11} - 52 q^{12} - 10 q^{13} - 18 q^{14} - 33 q^{15} + 53 q^{16} - 44 q^{17} - 27 q^{18} - 9 q^{19} - 45 q^{20} - 7 q^{21} - 3 q^{22} - 74 q^{23} + 21 q^{24} + 59 q^{25} - 47 q^{26} - 99 q^{27} - 49 q^{28} - 9 q^{29} - 39 q^{30} - 27 q^{31} - 47 q^{32} - 28 q^{33} - 23 q^{34} - 48 q^{35} + 77 q^{36} + 77 q^{37} - 66 q^{38} - 11 q^{39} - 2 q^{40} - 37 q^{41} - 24 q^{42} - 44 q^{43} - 54 q^{44} - 36 q^{45} - 41 q^{46} - 150 q^{47} - 135 q^{48} + 64 q^{49} + 4 q^{50} + 3 q^{51} - 57 q^{52} - 72 q^{53} + 21 q^{54} - 65 q^{55} - 92 q^{56} - 13 q^{57} - 12 q^{58} - 70 q^{59} - 22 q^{60} + 15 q^{61} - 86 q^{62} - 108 q^{63} + 10 q^{64} - 53 q^{65} - 55 q^{66} - 48 q^{67} - 70 q^{68} - 2 q^{69} + 11 q^{70} - 127 q^{71} - 12 q^{72} - 33 q^{73} - 9 q^{74} - 115 q^{75} - 24 q^{76} - 40 q^{77} + 81 q^{78} - 7 q^{79} - 62 q^{80} + 53 q^{81} - 68 q^{82} - 164 q^{83} + 7 q^{84} - 9 q^{85} - 50 q^{86} - 75 q^{87} - 82 q^{88} - 26 q^{89} + 23 q^{90} + 16 q^{91} - 117 q^{92} + 19 q^{93} + 23 q^{94} - 92 q^{95} - 35 q^{96} - 19 q^{97} - 10 q^{98} - 19 q^{99}+O(q^{100}) \) 77 * q - 9 * q^2 - 27 * q^3 + 73 * q^4 - 16 * q^5 - 2 * q^6 - 23 * q^7 - 24 * q^8 + 66 * q^9 - 11 * q^10 - 33 * q^11 - 52 * q^12 - 10 * q^13 - 18 * q^14 - 33 * q^15 + 53 * q^16 - 44 * q^17 - 27 * q^18 - 9 * q^19 - 45 * q^20 - 7 * q^21 - 3 * q^22 - 74 * q^23 + 21 * q^24 + 59 * q^25 - 47 * q^26 - 99 * q^27 - 49 * q^28 - 9 * q^29 - 39 * q^30 - 27 * q^31 - 47 * q^32 - 28 * q^33 - 23 * q^34 - 48 * q^35 + 77 * q^36 + 77 * q^37 - 66 * q^38 - 11 * q^39 - 2 * q^40 - 37 * q^41 - 24 * q^42 - 44 * q^43 - 54 * q^44 - 36 * q^45 - 41 * q^46 - 150 * q^47 - 135 * q^48 + 64 * q^49 + 4 * q^50 + 3 * q^51 - 57 * q^52 - 72 * q^53 + 21 * q^54 - 65 * q^55 - 92 * q^56 - 13 * q^57 - 12 * q^58 - 70 * q^59 - 22 * q^60 + 15 * q^61 - 86 * q^62 - 108 * q^63 + 10 * q^64 - 53 * q^65 - 55 * q^66 - 48 * q^67 - 70 * q^68 - 2 * q^69 + 11 * q^70 - 127 * q^71 - 12 * q^72 - 33 * q^73 - 9 * q^74 - 115 * q^75 - 24 * q^76 - 40 * q^77 + 81 * q^78 - 7 * q^79 - 62 * q^80 + 53 * q^81 - 68 * q^82 - 164 * q^83 + 7 * q^84 - 9 * q^85 - 50 * q^86 - 75 * q^87 - 82 * q^88 - 26 * q^89 + 23 * q^90 + 16 * q^91 - 117 * q^92 + 19 * q^93 + 23 * q^94 - 92 * q^95 - 35 * q^96 - 19 * q^97 - 10 * q^98 - 19 * 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 $

$2$	−1.78823	−1.26447	−0.632236	−	0.774776i	$-0.717863\pi$
$2$	−1.78823	−1.26447	−0.632236	+	0.774776i	$0.717863\pi$
$3$	2.78240	1.60642	0.803208	−	0.595698i	$-0.203125\pi$
$3$	2.78240	1.60642	0.803208	+	0.595698i	$0.203125\pi$
$4$	1.19778	0.598891
$5$	−2.10202	−0.940050	−0.470025	−	0.882653i	$-0.655755\pi$
$5$	−2.10202	−0.940050	−0.470025	+	0.882653i	$0.655755\pi$
$6$	−4.97558	−2.03127
$7$	−2.70114	−1.02094	−0.510468	−	0.859897i	$-0.670528\pi$
$7$	−2.70114	−1.02094	−0.510468	+	0.859897i	$0.670528\pi$
$8$	1.43455	0.507191
$9$	4.74173	1.58058
$10$	3.75890	1.18867
$11$	3.93666	1.18695	0.593474	−	0.804853i	$-0.297756\pi$
$11$	3.93666	1.18695	0.593474	+	0.804853i	$0.297756\pi$
$12$	3.33270	0.962069
$13$	−6.77398	−1.87877	−0.939383	−	0.342871i	$-0.888601\pi$
$13$	−6.77398	−1.87877	−0.939383	+	0.342871i	$0.888601\pi$
$14$	4.83028	1.29095
$15$	−5.84864	−1.51011
$16$	−4.96088	−1.24022
$17$	6.00146	1.45557	0.727784	−	0.685807i	$-0.240551\pi$
$17$	6.00146	1.45557	0.727784	+	0.685807i	$0.240551\pi$
$18$	−8.47932	−1.99859
$19$	−3.18902	−0.731612	−0.365806	−	0.930691i	$-0.619207\pi$
$19$	−3.18902	−0.731612	−0.365806	+	0.930691i	$0.619207\pi$
$20$	−2.51776	−0.562988
$21$	−7.51565	−1.64005
$22$	−7.03967	−1.50086
$23$	−0.759006	−0.158264	−0.0791318	−	0.996864i	$-0.525215\pi$
$23$	−0.759006	−0.158264	−0.0791318	+	0.996864i	$0.525215\pi$
$24$	3.99149	0.814760
$25$	−0.581526	−0.116305
$26$	12.1135	2.37565
$27$	4.84617	0.932646
$28$	−3.23538	−0.611430
$29$	4.13153	0.767205	0.383602	−	0.923498i	$-0.374683\pi$
$29$	4.13153	0.767205	0.383602	+	0.923498i	$0.374683\pi$
$30$	10.4587	1.90950
$31$	7.00483	1.25810	0.629052	−	0.777363i	$-0.283443\pi$
$31$	7.00483	1.25810	0.629052	+	0.777363i	$0.283443\pi$
$32$	6.00211	1.06103
$33$	10.9533	1.90673
$34$	−10.7320	−1.84052
$35$	5.67785	0.959732
$36$	5.67956	0.946593
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	5.70272	0.925104
$39$	−18.8479	−3.01808
$40$	−3.01545	−0.476785
$41$	9.83180	1.53547	0.767735	−	0.640768i	$-0.221384\pi$
$41$	9.83180	1.53547	0.767735	+	0.640768i	$0.221384\pi$
$42$	13.4397	2.07380
$43$	−6.90597	−1.05315	−0.526575	−	0.850129i	$-0.676524\pi$
$43$	−6.90597	−1.05315	−0.526575	+	0.850129i	$0.676524\pi$
$44$	4.71526	0.710852
$45$	−9.96719	−1.48582
$46$	1.35728	0.200120
$47$	−4.59077	−0.669633	−0.334817	−	0.942283i	$-0.608674\pi$
$47$	−4.59077	−0.669633	−0.334817	+	0.942283i	$0.608674\pi$
$48$	−13.8031	−1.99231
$49$	0.296181	0.0423115
$50$	1.03991	0.147065
$51$	16.6984	2.33825
$52$	−8.11376	−1.12518
$53$	−9.99885	−1.37345	−0.686724	−	0.726918i	$-0.740952\pi$
$53$	−9.99885	−1.37345	−0.686724	+	0.726918i	$0.740952\pi$
$54$	−8.66609	−1.17931
$55$	−8.27492	−1.11579
$56$	−3.87494	−0.517810
$57$	−8.87313	−1.17527
$58$	−7.38814	−0.970110
$59$	9.15037	1.19128	0.595638	−	0.803253i	$-0.296899\pi$
$59$	9.15037	1.19128	0.595638	+	0.803253i	$0.296899\pi$
$60$	−7.00540	−0.904393
$61$	−0.435289	−0.0557330	−0.0278665	−	0.999612i	$-0.508871\pi$
$61$	−0.435289	−0.0557330	−0.0278665	+	0.999612i	$0.508871\pi$
$62$	−12.5263	−1.59084
$63$	−12.8081	−1.61367
$64$	−0.811423	−0.101428
$65$	14.2390	1.76613
$66$	−19.5871	−2.41101
$67$	−10.5871	−1.29343	−0.646713	−	0.762734i	$-0.723857\pi$
$67$	−10.5871	−1.29343	−0.646713	+	0.762734i	$0.723857\pi$
$68$	7.18844	0.871726
$69$	−2.11185	−0.254237
$70$	−10.1533	−1.21355
$71$	−16.1503	−1.91669	−0.958345	−	0.285615i	$-0.907802\pi$
$71$	−16.1503	−1.91669	−0.958345	+	0.285615i	$0.907802\pi$
$72$	6.80226	0.801654
$73$	−0.259503	−0.0303725	−0.0151862	−	0.999885i	$-0.504834\pi$
$73$	−0.259503	−0.0303725	−0.0151862	+	0.999885i	$0.504834\pi$
$74$	−1.78823	−0.207878
$75$	−1.61804	−0.186835
$76$	−3.81976	−0.438156
$77$	−10.6335	−1.21180
$78$	33.7045	3.81628
$79$	3.43324	0.386269	0.193135	−	0.981172i	$-0.438135\pi$
$79$	3.43324	0.386269	0.193135	+	0.981172i	$0.438135\pi$
$80$	10.4279	1.16587
$81$	−0.741213	−0.0823570
$82$	−17.5816	−1.94156
$83$	−5.22693	−0.573731	−0.286865	−	0.957971i	$-0.592613\pi$
$83$	−5.22693	−0.573731	−0.286865	+	0.957971i	$0.592613\pi$
$84$	−9.00212	−0.982211
$85$	−12.6152	−1.36831
$86$	12.3495	1.33168
$87$	11.4955	1.23245
$88$	5.64735	0.602009
$89$	7.31595	0.775490	0.387745	−	0.921767i	$-0.373254\pi$
$89$	7.31595	0.775490	0.387745	+	0.921767i	$0.373254\pi$
$90$	17.8237	1.87878
$91$	18.2975	1.91810
$92$	−0.909124	−0.0947827
$93$	19.4902	2.02104
$94$	8.20938	0.846733
$95$	6.70338	0.687753
$96$	16.7003	1.70446
$97$	0.841504	0.0854418	0.0427209	−	0.999087i	$-0.486397\pi$
$97$	0.841504	0.0854418	0.0427209	+	0.999087i	$0.486397\pi$
$98$	−0.529640	−0.0535017
$99$	18.6666	1.87606
$100$	−0.696542	−0.0696542
$101$	−1.18872	−0.118282	−0.0591408	−	0.998250i	$-0.518836\pi$
$101$	−1.18872	−0.118282	−0.0591408	+	0.998250i	$0.518836\pi$
$102$	−29.8607	−2.95665
$103$	−6.76122	−0.666203	−0.333101	−	0.942891i	$-0.608095\pi$
$103$	−6.76122	−0.666203	−0.333101	+	0.942891i	$0.608095\pi$
$104$	−9.71764	−0.952893
$105$	15.7980	1.54173
$106$	17.8803	1.73669
$107$	−7.45845	−0.721035	−0.360518	−	0.932752i	$-0.617400\pi$
$107$	−7.45845	−0.721035	−0.360518	+	0.932752i	$0.617400\pi$
$108$	5.80466	0.558553
$109$	1.00000	0.0957826
$109$	1.00000	0.0957826
$110$	14.7975	1.41089
$111$	2.78240	0.264093
$112$	13.4001	1.26619
$113$	2.80653	0.264016	0.132008	−	0.991249i	$-0.457858\pi$
$113$	2.80653	0.264016	0.132008	+	0.991249i	$0.457858\pi$
$114$	15.8672	1.48610
$115$	1.59544	0.148776
$116$	4.94867	0.459472
$117$	−32.1204	−2.96953
$118$	−16.3630	−1.50634
$119$	−16.2108	−1.48604
$120$	−8.39019	−0.765916
$121$	4.49729	0.408844
$122$	0.778398	0.0704729
$123$	27.3560	2.46660
$124$	8.39026	0.753468
$125$	11.7325	1.04938
$126$	22.9039	2.04044
$127$	−14.1158	−1.25257	−0.626286	−	0.779593i	$-0.715426\pi$
$127$	−14.1158	−1.25257	−0.626286	+	0.779593i	$0.715426\pi$
$128$	−10.5532	−0.932781
$129$	−19.2151	−1.69180
$130$	−25.4627	−2.23323
$131$	3.59864	0.314414	0.157207	−	0.987566i	$-0.449751\pi$
$131$	3.59864	0.314414	0.157207	+	0.987566i	$0.449751\pi$
$132$	13.1197	1.14193
$133$	8.61402	0.746930
$134$	18.9323	1.63550
$135$	−10.1867	−0.876734
$136$	8.60941	0.738251
$137$	−9.05309	−0.773457	−0.386729	−	0.922194i	$-0.626395\pi$
$137$	−9.05309	−0.773457	−0.386729	+	0.922194i	$0.626395\pi$
$138$	3.77649	0.321476
$139$	−13.3809	−1.13495	−0.567475	−	0.823391i	$-0.692080\pi$
$139$	−13.3809	−1.13495	−0.567475	+	0.823391i	$0.692080\pi$
$140$	6.80083	0.574775
$141$	−12.7734	−1.07571
$142$	28.8805	2.42360
$143$	−26.6669	−2.23000
$144$	−23.5231	−1.96026
$145$	−8.68453	−0.721211
$146$	0.464052	0.0384052
$147$	0.824091	0.0679699
$148$	1.19778	0.0984571
$149$	−7.79199	−0.638345	−0.319172	−	0.947697i	$-0.603405\pi$
$149$	−7.79199	−0.638345	−0.319172	+	0.947697i	$0.603405\pi$
$150$	2.89343	0.236247
$151$	−23.6795	−1.92701	−0.963504	−	0.267693i	$-0.913739\pi$
$151$	−23.6795	−1.92701	−0.963504	+	0.267693i	$0.913739\pi$
$152$	−4.57483	−0.371067
$153$	28.4573	2.30063
$154$	19.0152	1.53229
$155$	−14.7243	−1.18268
$156$	−22.5757	−1.80750
$157$	4.77220	0.380863	0.190432	−	0.981700i	$-0.439011\pi$
$157$	4.77220	0.380863	0.190432	+	0.981700i	$0.439011\pi$
$158$	−6.13943	−0.488427
$159$	−27.8208	−2.20633
$160$	−12.6165	−0.997425
$161$	2.05018	0.161577
$162$	1.32546	0.104138
$163$	−4.12655	−0.323216	−0.161608	−	0.986855i	$-0.551668\pi$
$163$	−4.12655	−0.323216	−0.161608	+	0.986855i	$0.551668\pi$
$164$	11.7764	0.919579
$165$	−23.0241	−1.79242
$166$	9.34698	0.725467
$167$	16.5259	1.27881	0.639406	−	0.768869i	$-0.279180\pi$
$167$	16.5259	1.27881	0.639406	+	0.768869i	$0.279180\pi$
$168$	−10.7816	−0.831819
$169$	32.8869	2.52976
$170$	22.5589	1.73019
$171$	−15.1215	−1.15637
$172$	−8.27185	−0.630722
$173$	−19.3852	−1.47383	−0.736917	−	0.675984i	$-0.763719\pi$
$173$	−19.3852	−1.47383	−0.736917	+	0.675984i	$0.763719\pi$
$174$	−20.5567	−1.55840
$175$	1.57079	0.118740
$176$	−19.5293	−1.47208
$177$	25.4599	1.91369
$178$	−13.0826	−0.980586
$179$	8.10242	0.605604	0.302802	−	0.953054i	$-0.402078\pi$
$179$	8.10242	0.605604	0.302802	+	0.953054i	$0.402078\pi$
$180$	−11.9385	−0.889845
$181$	−11.9563	−0.888706	−0.444353	−	0.895852i	$-0.646566\pi$
$181$	−11.9563	−0.888706	−0.444353	+	0.895852i	$0.646566\pi$
$182$	−32.7202	−2.42539
$183$	−1.21115	−0.0895305
$184$	−1.08883	−0.0802699
$185$	−2.10202	−0.154543
$186$	−34.8531	−2.55555
$187$	23.6257	1.72768
$188$	−5.49875	−0.401037
$189$	−13.0902	−0.952172
$190$	−11.9872	−0.869644
$191$	7.48022	0.541250	0.270625	−	0.962685i	$-0.412770\pi$
$191$	7.48022	0.541250	0.270625	+	0.962685i	$0.412770\pi$
$192$	−2.25770	−0.162935
$193$	0.175460	0.0126299	0.00631494	−	0.999980i	$-0.497990\pi$
$193$	0.175460	0.0126299	0.00631494	+	0.999980i	$0.497990\pi$
$194$	−1.50481	−0.108039
$195$	39.6186	2.83715
$196$	0.354760	0.0253400
$197$	−6.85264	−0.488230	−0.244115	−	0.969746i	$-0.578498\pi$
$197$	−6.85264	−0.488230	−0.244115	+	0.969746i	$0.578498\pi$
$198$	−33.3802	−2.37223
$199$	−13.0809	−0.927280	−0.463640	−	0.886024i	$-0.653457\pi$
$199$	−13.0809	−0.927280	−0.463640	+	0.886024i	$0.653457\pi$
$200$	−0.834230	−0.0589890
$201$	−29.4576	−2.07778
$202$	2.12570	0.149564
$203$	−11.1598	−0.783268
$204$	20.0011	1.40036
$205$	−20.6666	−1.44342
$206$	12.0906	0.842395
$207$	−3.59900	−0.250148
$208$	33.6049	2.33008
$209$	−12.5541	−0.868386
$210$	−28.2506	−1.94947
$211$	11.4402	0.787577	0.393789	−	0.919201i	$-0.371164\pi$
$211$	11.4402	0.787577	0.393789	+	0.919201i	$0.371164\pi$
$212$	−11.9765	−0.822546
$213$	−44.9366	−3.07900
$214$	13.3375	0.911730
$215$	14.5165	0.990014
$216$	6.95209	0.473030
$217$	−18.9211	−1.28444
$218$	−1.78823	−0.121115
$219$	−0.722039	−0.0487909
$220$	−9.91156	−0.668237
$221$	−40.6538	−2.73467
$222$	−4.97558	−0.333939
$223$	−5.31659	−0.356025	−0.178013	−	0.984028i	$-0.556967\pi$
$223$	−5.31659	−0.356025	−0.178013	+	0.984028i	$0.556967\pi$
$224$	−16.2126	−1.08325
$225$	−2.75744	−0.183829
$226$	−5.01873	−0.333841
$227$	−16.6263	−1.10352	−0.551762	−	0.834001i	$-0.686044\pi$
$227$	−16.6263	−1.10352	−0.551762	+	0.834001i	$0.686044\pi$
$228$	−10.6281	−0.703862
$229$	10.9037	0.720535	0.360267	−	0.932849i	$-0.382685\pi$
$229$	10.9037	0.720535	0.360267	+	0.932849i	$0.382685\pi$
$230$	−2.85302	−0.188123
$231$	−29.5866	−1.94665
$232$	5.92689	0.389120
$233$	20.1429	1.31961	0.659804	−	0.751438i	$-0.270639\pi$
$233$	20.1429	1.31961	0.659804	+	0.751438i	$0.270639\pi$
$234$	57.4388	3.75489
$235$	9.64988	0.629489
$236$	10.9602	0.713445
$237$	9.55262	0.620509
$238$	28.9887	1.87906
$239$	−0.657911	−0.0425567	−0.0212784	−	0.999774i	$-0.506774\pi$
$239$	−0.657911	−0.0425567	−0.0212784	+	0.999774i	$0.506774\pi$
$240$	29.0144	1.87287
$241$	−14.2570	−0.918375	−0.459188	−	0.888339i	$-0.651859\pi$
$241$	−14.2570	−0.918375	−0.459188	+	0.888339i	$0.651859\pi$
$242$	−8.04221	−0.516973
$243$	−16.6009	−1.06495
$244$	−0.521381	−0.0333780
$245$	−0.622576	−0.0397749
$246$	−48.9189	−3.11895
$247$	21.6024	1.37453
$248$	10.0488	0.638099
$249$	−14.5434	−0.921650
$250$	−20.9804	−1.32692
$251$	−12.1221	−0.765139	−0.382569	−	0.923927i	$-0.624961\pi$
$251$	−12.1221	−0.765139	−0.382569	+	0.923927i	$0.624961\pi$
$252$	−15.3413	−0.966411
$253$	−2.98795	−0.187851
$254$	25.2423	1.58384
$255$	−35.1004	−2.19807
$256$	20.4945	1.28090
$257$	−31.4020	−1.95880	−0.979402	−	0.201920i	$-0.935282\pi$
$257$	−31.4020	−1.95880	−0.979402	+	0.201920i	$0.935282\pi$
$258$	34.3612	2.13923
$259$	−2.70114	−0.167841
$260$	17.0553	1.05772
$261$	19.5906	1.21263
$262$	−6.43521	−0.397569
$263$	−2.41584	−0.148967	−0.0744836	−	0.997222i	$-0.523731\pi$
$263$	−2.41584	−0.148967	−0.0744836	+	0.997222i	$0.523731\pi$
$264$	15.7132	0.967078
$265$	21.0178	1.29111
$266$	−15.4039	−0.944473
$267$	20.3559	1.24576
$268$	−12.6811	−0.774621
$269$	22.9177	1.39732	0.698658	−	0.715456i	$-0.253781\pi$
$269$	22.9177	1.39732	0.698658	+	0.715456i	$0.253781\pi$
$270$	18.2163	1.10861
$271$	−7.54401	−0.458266	−0.229133	−	0.973395i	$-0.573589\pi$
$271$	−7.54401	−0.458266	−0.229133	+	0.973395i	$0.573589\pi$
$272$	−29.7725	−1.80522
$273$	50.9109	3.08127
$274$	16.1890	0.978016
$275$	−2.28927	−0.138048
$276$	−2.52954	−0.152260
$277$	−23.6157	−1.41893	−0.709466	−	0.704740i	$-0.751064\pi$
$277$	−23.6157	−1.41893	−0.709466	+	0.704740i	$0.751064\pi$
$278$	23.9281	1.43511
$279$	33.2150	1.98853
$280$	8.14518	0.486767
$281$	−4.78297	−0.285328	−0.142664	−	0.989771i	$-0.545567\pi$
$281$	−4.78297	−0.285328	−0.142664	+	0.989771i	$0.545567\pi$
$282$	22.8417	1.36021
$283$	−2.65441	−0.157788	−0.0788941	−	0.996883i	$-0.525139\pi$
$283$	−2.65441	−0.157788	−0.0788941	+	0.996883i	$0.525139\pi$
$284$	−19.3446	−1.14789
$285$	18.6515	1.10482
$286$	47.6866	2.81977
$287$	−26.5571	−1.56762
$288$	28.4604	1.67704
$289$	19.0175	1.11868
$290$	15.5300	0.911952
$291$	2.34140	0.137255
$292$	−0.310828	−0.0181898
$293$	3.88314	0.226855	0.113428	−	0.993546i	$-0.463817\pi$
$293$	3.88314	0.226855	0.113428	+	0.993546i	$0.463817\pi$
$294$	−1.47367	−0.0859461
$295$	−19.2342	−1.11986
$296$	1.43455	0.0833817
$297$	19.0777	1.10700
$298$	13.9339	0.807169
$299$	5.14149	0.297340
$300$	−1.93806	−0.111894
$301$	18.6540	1.07520
$302$	42.3445	2.43665
$303$	−3.30748	−0.190010
$304$	15.8204	0.907361
$305$	0.914984	0.0523918
$306$	−50.8883	−2.90909
$307$	−16.3745	−0.934544	−0.467272	−	0.884114i	$-0.654763\pi$
$307$	−16.3745	−0.934544	−0.467272	+	0.884114i	$0.654763\pi$
$308$	−12.7366	−0.725735
$309$	−18.8124	−1.07020
$310$	26.3304	1.49547
$311$	−32.0913	−1.81973	−0.909865	−	0.414904i	$-0.863815\pi$
$311$	−32.0913	−1.81973	−0.909865	+	0.414904i	$0.863815\pi$
$312$	−27.0383	−1.53074
$313$	26.2680	1.48475	0.742376	−	0.669983i	$-0.233699\pi$
$313$	26.2680	1.48475	0.742376	+	0.669983i	$0.233699\pi$
$314$	−8.53381	−0.481591
$315$	26.9228	1.51693
$316$	4.11227	0.231333
$317$	21.0135	1.18023	0.590117	−	0.807317i	$-0.299081\pi$
$317$	21.0135	1.18023	0.590117	+	0.807317i	$0.299081\pi$
$318$	49.7501	2.78984
$319$	16.2644	0.910632
$320$	1.70562	0.0953473
$321$	−20.7524	−1.15828
$322$	−3.66621	−0.204310
$323$	−19.1388	−1.06491
$324$	−0.887812	−0.0493229
$325$	3.93925	0.218510
$326$	7.37924	0.408698
$327$	2.78240	0.153867
$328$	14.1042	0.778776
$329$	12.4003	0.683653
$330$	41.1725	2.26647
$331$	−21.4714	−1.18017	−0.590086	−	0.807340i	$-0.700906\pi$
$331$	−21.4714	−1.18017	−0.590086	+	0.807340i	$0.700906\pi$
$332$	−6.26073	−0.343602
$333$	4.74173	0.259845
$334$	−29.5522	−1.61702
$335$	22.2544	1.21589
$336$	37.2843	2.03402
$337$	−14.6881	−0.800113	−0.400056	−	0.916491i	$-0.631009\pi$
$337$	−14.6881	−0.800113	−0.400056	+	0.916491i	$0.631009\pi$
$338$	−58.8094	−3.19881
$339$	7.80887	0.424119
$340$	−15.1102	−0.819467
$341$	27.5756	1.49330
$342$	27.0408	1.46220
$343$	18.1080	0.977739
$344$	−9.90698	−0.534148
$345$	4.43915	0.238996
$346$	34.6654	1.86362
$347$	36.8520	1.97832	0.989158	−	0.146854i	$-0.0469147\pi$
$347$	36.8520	1.97832	0.989158	+	0.146854i	$0.0469147\pi$
$348$	13.7692	0.738104
$349$	26.8690	1.43826	0.719132	−	0.694873i	$-0.244540\pi$
$349$	26.8690	1.43826	0.719132	+	0.694873i	$0.244540\pi$
$350$	−2.80893	−0.150144
$351$	−32.8279	−1.75222
$352$	23.6283	1.25939
$353$	−36.0355	−1.91797	−0.958987	−	0.283449i	$-0.908521\pi$
$353$	−36.0355	−1.91797	−0.958987	+	0.283449i	$0.908521\pi$
$354$	−45.5284	−2.41980
$355$	33.9482	1.80178
$356$	8.76292	0.464434
$357$	−45.1049	−2.38720
$358$	−14.4890	−0.765769
$359$	18.5854	0.980898	0.490449	−	0.871470i	$-0.336833\pi$
$359$	18.5854	0.980898	0.490449	+	0.871470i	$0.336833\pi$
$360$	−14.2985	−0.753595
$361$	−8.83012	−0.464743
$362$	21.3807	1.12375
$363$	12.5132	0.656775
$364$	21.9164	1.14873
$365$	0.545479	0.0285517
$366$	2.16581	0.113209
$367$	−14.0103	−0.731330	−0.365665	−	0.930746i	$-0.619158\pi$
$367$	−14.0103	−0.731330	−0.365665	+	0.930746i	$0.619158\pi$
$368$	3.76534	0.196282
$369$	46.6197	2.42692
$370$	3.75890	0.195416
$371$	27.0083	1.40220
$372$	23.3450	1.21038
$373$	7.74637	0.401092	0.200546	−	0.979684i	$-0.435728\pi$
$373$	7.74637	0.401092	0.200546	+	0.979684i	$0.435728\pi$
$374$	−42.2483	−2.18461
$375$	32.6443	1.68575
$376$	−6.58571	−0.339632
$377$	−27.9869	−1.44140
$378$	23.4084	1.20400
$379$	32.9230	1.69114	0.845569	−	0.533866i	$-0.179261\pi$
$379$	32.9230	1.69114	0.845569	+	0.533866i	$0.179261\pi$
$380$	8.02919	0.411889
$381$	−39.2757	−2.01215
$382$	−13.3764	−0.684396
$383$	0.823920	0.0421003	0.0210502	−	0.999778i	$-0.493299\pi$
$383$	0.823920	0.0421003	0.0210502	+	0.999778i	$0.493299\pi$
$384$	−29.3632	−1.49844
$385$	22.3518	1.13915
$386$	−0.313763	−0.0159701
$387$	−32.7462	−1.66458
$388$	1.00794	0.0511703
$389$	−14.1751	−0.718704	−0.359352	−	0.933202i	$-0.617002\pi$
$389$	−14.1751	−0.718704	−0.359352	+	0.933202i	$0.617002\pi$
$390$	−70.8474	−3.58750
$391$	−4.55514	−0.230363
$392$	0.424887	0.0214600
$393$	10.0128	0.505081
$394$	12.2541	0.617354
$395$	−7.21672	−0.363113
$396$	22.3585	1.12356
$397$	21.1231	1.06014	0.530068	−	0.847955i	$-0.322166\pi$
$397$	21.1231	1.06014	0.530068	+	0.847955i	$0.322166\pi$
$398$	23.3917	1.17252
$399$	23.9676	1.19988
$400$	2.88488	0.144244
$401$	−15.0252	−0.750322	−0.375161	−	0.926960i	$-0.622413\pi$
$401$	−15.0252	−0.750322	−0.375161	+	0.926960i	$0.622413\pi$
$402$	52.6771	2.62730
$403$	−47.4506	−2.36368
$404$	−1.42382	−0.0708378
$405$	1.55804	0.0774198
$406$	19.9564	0.990421
$407$	3.93666	0.195133
$408$	23.9548	1.18594
$409$	−12.1723	−0.601882	−0.300941	−	0.953643i	$-0.597301\pi$
$409$	−12.1723	−0.601882	−0.300941	+	0.953643i	$0.597301\pi$
$410$	36.9567	1.82516
$411$	−25.1893	−1.24250
$412$	−8.09847	−0.398983
$413$	−24.7165	−1.21622
$414$	6.43585	0.316305
$415$	10.9871	0.539336
$416$	−40.6582	−1.99343
$417$	−37.2308	−1.82320
$418$	22.4497	1.09805
$419$	3.62103	0.176899	0.0884495	−	0.996081i	$-0.471809\pi$
$419$	3.62103	0.176899	0.0884495	+	0.996081i	$0.471809\pi$
$420$	18.9226	0.923328
$421$	3.23248	0.157542	0.0787708	−	0.996893i	$-0.474900\pi$
$421$	3.23248	0.157542	0.0787708	+	0.996893i	$0.474900\pi$
$422$	−20.4578	−0.995870
$423$	−21.7682	−1.05841
$424$	−14.3439	−0.696601
$425$	−3.49000	−0.169290
$426$	80.3571	3.89331
$427$	1.17578	0.0568999
$428$	−8.93360	−0.431822
$429$	−74.1978	−3.58230
$430$	−25.9588	−1.25185
$431$	2.25650	0.108692	0.0543458	−	0.998522i	$-0.482693\pi$
$431$	2.25650	0.108692	0.0543458	+	0.998522i	$0.482693\pi$
$432$	−24.0413	−1.15669
$433$	−31.5848	−1.51787	−0.758934	−	0.651168i	$-0.774279\pi$
$433$	−31.5848	−1.51787	−0.758934	+	0.651168i	$0.774279\pi$
$434$	33.8353	1.62415
$435$	−24.1638	−1.15857
$436$	1.19778	0.0573634
$437$	2.42049	0.115788
$438$	1.29118	0.0616947
$439$	13.0297	0.621875	0.310938	−	0.950430i	$-0.399357\pi$
$439$	13.0297	0.621875	0.310938	+	0.950430i	$0.399357\pi$
$440$	−11.8708	−0.565919
$441$	1.40441	0.0668765
$442$	72.6985	3.45791
$443$	−33.0720	−1.57130	−0.785649	−	0.618672i	$-0.787671\pi$
$443$	−33.0720	−1.57130	−0.785649	+	0.618672i	$0.787671\pi$
$444$	3.33270	0.158163
$445$	−15.3783	−0.728999
$446$	9.50731	0.450184
$447$	−21.6804	−1.02545
$448$	2.19177	0.103551
$449$	9.55322	0.450844	0.225422	−	0.974261i	$-0.427624\pi$
$449$	9.55322	0.450844	0.225422	+	0.974261i	$0.427624\pi$
$450$	4.93095	0.232447
$451$	38.7045	1.82252
$452$	3.36161	0.158117
$453$	−65.8857	−3.09558
$454$	29.7317	1.39538
$455$	−38.4617	−1.80311
$456$	−12.7290	−0.596089
$457$	−16.8717	−0.789227	−0.394614	−	0.918847i	$-0.629122\pi$
$457$	−16.8717	−0.789227	−0.394614	+	0.918847i	$0.629122\pi$
$458$	−19.4983	−0.911096
$459$	29.0841	1.35753
$460$	1.91099	0.0891005
$461$	12.4727	0.580913	0.290456	−	0.956888i	$-0.406193\pi$
$461$	12.4727	0.580913	0.290456	+	0.956888i	$0.406193\pi$
$462$	52.9077	2.46149
$463$	−7.20181	−0.334696	−0.167348	−	0.985898i	$-0.553520\pi$
$463$	−7.20181	−0.334696	−0.167348	+	0.985898i	$0.553520\pi$
$464$	−20.4960	−0.951503
$465$	−40.9687	−1.89988
$466$	−36.0203	−1.66861
$467$	31.6042	1.46247	0.731234	−	0.682126i	$-0.238945\pi$
$467$	31.6042	1.46247	0.731234	+	0.682126i	$0.238945\pi$
$468$	−38.4732	−1.77843
$469$	28.5974	1.32051
$470$	−17.2563	−0.795972
$471$	13.2782	0.611825
$472$	13.1267	0.604205
$473$	−27.1864	−1.25003
$474$	−17.0823	−0.784617
$475$	1.85450	0.0850904
$476$	−19.4170	−0.889977
$477$	−47.4118	−2.17084
$478$	1.17650	0.0538118
$479$	−30.7261	−1.40391	−0.701956	−	0.712220i	$-0.747690\pi$
$479$	−30.7261	−1.40391	−0.701956	+	0.712220i	$0.747690\pi$
$480$	−35.1042	−1.60228
$481$	−6.77398	−0.308867
$482$	25.4949	1.16126
$483$	5.70442	0.259560
$484$	5.38677	0.244853
$485$	−1.76886	−0.0803196
$486$	29.6862	1.34659
$487$	−20.5462	−0.931039	−0.465520	−	0.885038i	$-0.654133\pi$
$487$	−20.5462	−0.931039	−0.465520	+	0.885038i	$0.654133\pi$
$488$	−0.624445	−0.0282673
$489$	−11.4817	−0.519220
$490$	1.11331	0.0502943
$491$	−25.3948	−1.14605	−0.573025	−	0.819538i	$-0.694230\pi$
$491$	−25.3948	−1.14605	−0.573025	+	0.819538i	$0.694230\pi$
$492$	32.7665	1.47723
$493$	24.7952	1.11672
$494$	−38.6302	−1.73805
$495$	−39.2374	−1.76359
$496$	−34.7501	−1.56033
$497$	43.6243	1.95682
$498$	26.0070	1.16540
$499$	−11.5170	−0.515570	−0.257785	−	0.966202i	$-0.582993\pi$
$499$	−11.5170	−0.515570	−0.257785	+	0.966202i	$0.582993\pi$
$500$	14.0529	0.628466
$501$	45.9816	2.05431
$502$	21.6771	0.967497
$503$	43.6694	1.94712	0.973562	−	0.228423i	$-0.0733569\pi$
$503$	43.6694	1.94712	0.973562	+	0.228423i	$0.0733569\pi$
$504$	−18.3739	−0.818438
$505$	2.49870	0.111191
$506$	5.34315	0.237532
$507$	91.5043	4.06385
$508$	−16.9076	−0.750155
$509$	24.5143	1.08658	0.543288	−	0.839546i	$-0.317179\pi$
$509$	24.5143	1.08658	0.543288	+	0.839546i	$0.317179\pi$
$510$	62.7677	2.77940
$511$	0.700954	0.0310084
$512$	−15.5425	−0.686887
$513$	−15.4546	−0.682335
$514$	56.1542	2.47685
$515$	14.2122	0.626264
$516$	−23.0155	−1.01320
$517$	−18.0723	−0.794820
$518$	4.83028	0.212230
$519$	−53.9374	−2.36759
$520$	20.4266	0.895767
$521$	−37.2286	−1.63102	−0.815508	−	0.578746i	$-0.803542\pi$
$521$	−37.2286	−1.63102	−0.815508	+	0.578746i	$0.803542\pi$
$522$	−35.0325	−1.53333
$523$	−1.64243	−0.0718184	−0.0359092	−	0.999355i	$-0.511433\pi$
$523$	−1.64243	−0.0718184	−0.0359092	+	0.999355i	$0.511433\pi$
$524$	4.31039	0.188300
$525$	4.37055	0.190746
$526$	4.32009	0.188365
$527$	42.0392	1.83126
$528$	−54.3383	−2.36477
$529$	−22.4239	−0.974953
$530$	−37.5847	−1.63257
$531$	43.3885	1.88290
$532$	10.3177	0.447330
$533$	−66.6005	−2.88479
$534$	−36.4011	−1.57523
$535$	15.6778	0.677810
$536$	−15.1878	−0.656014
$537$	22.5441	0.972852
$538$	−40.9822	−1.76687
$539$	1.16596	0.0502215
$540$	−12.2015	−0.525068
$541$	33.9018	1.45755	0.728776	−	0.684752i	$-0.240089\pi$
$541$	33.9018	1.45755	0.728776	+	0.684752i	$0.240089\pi$
$542$	13.4905	0.579465
$543$	−33.2672	−1.42763
$544$	36.0214	1.54441
$545$	−2.10202	−0.0900405
$546$	−91.0406	−3.89618
$547$	5.57659	0.238438	0.119219	−	0.992868i	$-0.461961\pi$
$547$	5.57659	0.238438	0.119219	+	0.992868i	$0.461961\pi$
$548$	−10.8436	−0.463217
$549$	−2.06402	−0.0880902
$550$	4.09375	0.174558
$551$	−13.1755	−0.561297
$552$	−3.02957	−0.128947
$553$	−9.27367	−0.394356
$554$	42.2305	1.79420
$555$	−5.84864	−0.248261
$556$	−16.0274	−0.679711
$557$	−15.9952	−0.677739	−0.338869	−	0.940833i	$-0.610044\pi$
$557$	−15.9952	−0.677739	−0.338869	+	0.940833i	$0.610044\pi$
$558$	−59.3962	−2.51444
$559$	46.7809	1.97862
$560$	−28.1671	−1.19028
$561$	65.7360	2.77538
$562$	8.55307	0.360790
$563$	−26.7907	−1.12909	−0.564546	−	0.825402i	$-0.690949\pi$
$563$	−26.7907	−1.12909	−0.564546	+	0.825402i	$0.690949\pi$
$564$	−15.2997	−0.644233
$565$	−5.89937	−0.248188
$566$	4.74670	0.199519
$567$	2.00212	0.0840813
$568$	−23.1685	−0.972128
$569$	12.7764	0.535613	0.267807	−	0.963473i	$-0.413701\pi$
$569$	12.7764	0.535613	0.267807	+	0.963473i	$0.413701\pi$
$570$	−33.3532	−1.39701
$571$	28.4365	1.19003	0.595015	−	0.803715i	$-0.297146\pi$
$571$	28.4365	1.19003	0.595015	+	0.803715i	$0.297146\pi$
$572$	−31.9411	−1.33552
$573$	20.8129	0.869473
$574$	47.4903	1.98221
$575$	0.441382	0.0184069
$576$	−3.84754	−0.160314
$577$	11.2263	0.467358	0.233679	−	0.972314i	$-0.424924\pi$
$577$	11.2263	0.467358	0.233679	+	0.972314i	$0.424924\pi$
$578$	−34.0077	−1.41453
$579$	0.488199	0.0202888
$580$	−10.4022	−0.431927
$581$	14.1187	0.585742
$582$	−4.18697	−0.173555
$583$	−39.3621	−1.63021
$584$	−0.372270	−0.0154047
$585$	67.5176	2.79151
$586$	−6.94396	−0.286852
$587$	−19.0259	−0.785282	−0.392641	−	0.919692i	$-0.628438\pi$
$587$	−19.0259	−0.785282	−0.392641	+	0.919692i	$0.628438\pi$
$588$	0.987082	0.0407066
$589$	−22.3386	−0.920445
$590$	34.3953	1.41603
$591$	−19.0668	−0.784302
$592$	−4.96088	−0.203891
$593$	11.6814	0.479700	0.239850	−	0.970810i	$-0.422902\pi$
$593$	11.6814	0.479700	0.239850	+	0.970810i	$0.422902\pi$
$594$	−34.1154	−1.39977
$595$	34.0754	1.39695
$596$	−9.33311	−0.382299
$597$	−36.3962	−1.48960
$598$	−9.19419	−0.375978
$599$	4.17039	0.170397	0.0851987	−	0.996364i	$-0.472847\pi$
$599$	4.17039	0.170397	0.0851987	+	0.996364i	$0.472847\pi$
$600$	−2.32116	−0.0947609
$601$	−3.93243	−0.160407	−0.0802036	−	0.996779i	$-0.525557\pi$
$601$	−3.93243	−0.160407	−0.0802036	+	0.996779i	$0.525557\pi$
$602$	−33.3577	−1.35956
$603$	−50.2013	−2.04436
$604$	−28.3629	−1.15407
$605$	−9.45338	−0.384334
$606$	5.91454	0.240262
$607$	10.4646	0.424747	0.212373	−	0.977189i	$-0.431881\pi$
$607$	10.4646	0.424747	0.212373	+	0.977189i	$0.431881\pi$
$608$	−19.1409	−0.776266
$609$	−31.0511	−1.25825
$610$	−1.63621	−0.0662481
$611$	31.0978	1.25808
$612$	34.0856	1.37783
$613$	25.1831	1.01714	0.508568	−	0.861022i	$-0.330175\pi$
$613$	25.1831	1.01714	0.508568	+	0.861022i	$0.330175\pi$
$614$	29.2815	1.18171
$615$	−57.5027	−2.31873
$616$	−15.2543	−0.614613
$617$	26.3726	1.06172	0.530860	−	0.847459i	$-0.321869\pi$
$617$	26.3726	1.06172	0.530860	+	0.847459i	$0.321869\pi$
$618$	33.6410	1.35324
$619$	−7.11938	−0.286152	−0.143076	−	0.989712i	$-0.545699\pi$
$619$	−7.11938	−0.286152	−0.143076	+	0.989712i	$0.545699\pi$
$620$	−17.6365	−0.708298
$621$	−3.67827	−0.147604
$622$	57.3868	2.30100
$623$	−19.7614	−0.791726
$624$	93.5022	3.74308
$625$	−21.7542	−0.870168
$626$	−46.9733	−1.87743
$627$	−34.9305	−1.39499
$628$	5.71606	0.228096
$629$	6.00146	0.239294
$630$	−48.1443	−1.91811
$631$	−29.3342	−1.16777	−0.583887	−	0.811835i	$-0.698469\pi$
$631$	−29.3342	−1.16777	−0.583887	+	0.811835i	$0.698469\pi$
$632$	4.92516	0.195912
$633$	31.8312	1.26518
$634$	−37.5770	−1.49237
$635$	29.6716	1.17748
$636$	−33.3232	−1.32135
$637$	−2.00632	−0.0794934
$638$	−29.0846	−1.15147
$639$	−76.5803	−3.02947
$640$	22.1830	0.876861
$641$	−14.2890	−0.564381	−0.282190	−	0.959358i	$-0.591061\pi$
$641$	−14.2890	−0.564381	−0.282190	+	0.959358i	$0.591061\pi$
$642$	37.1101	1.46462
$643$	−10.6239	−0.418966	−0.209483	−	0.977812i	$-0.567178\pi$
$643$	−10.6239	−0.418966	−0.209483	+	0.977812i	$0.567178\pi$
$644$	2.45567	0.0967671
$645$	40.3905	1.59038
$646$	34.2247	1.34655
$647$	36.9129	1.45120	0.725598	−	0.688119i	$-0.241563\pi$
$647$	36.9129	1.45120	0.725598	+	0.688119i	$0.241563\pi$
$648$	−1.06331	−0.0417708
$649$	36.0219	1.41398
$650$	−7.04430	−0.276300
$651$	−52.6459	−2.06335
$652$	−4.94271	−0.193571
$653$	−32.4831	−1.27116	−0.635580	−	0.772035i	$-0.719239\pi$
$653$	−32.4831	−1.27116	−0.635580	+	0.772035i	$0.719239\pi$
$654$	−4.97558	−0.194560
$655$	−7.56440	−0.295565
$656$	−48.7744	−1.90432
$657$	−1.23049	−0.0480060
$658$	−22.1747	−0.864461
$659$	7.88394	0.307115	0.153557	−	0.988140i	$-0.450927\pi$
$659$	7.88394	0.307115	0.153557	+	0.988140i	$0.450927\pi$
$660$	−27.5779	−1.07347
$661$	5.11501	0.198951	0.0994754	−	0.995040i	$-0.468284\pi$
$661$	5.11501	0.198951	0.0994754	+	0.995040i	$0.468284\pi$
$662$	38.3958	1.49230
$663$	−113.115	−4.39302
$664$	−7.49831	−0.290991
$665$	−18.1068	−0.702152
$666$	−8.47932	−0.328567
$667$	−3.13585	−0.121421
$668$	19.7944	0.765870
$669$	−14.7929	−0.571925
$670$	−39.7960	−1.53745
$671$	−1.71358	−0.0661522
$672$	−45.1098	−1.74015
$673$	−7.50326	−0.289229	−0.144615	−	0.989488i	$-0.546194\pi$
$673$	−7.50326	−0.289229	−0.144615	+	0.989488i	$0.546194\pi$
$674$	26.2658	1.01172
$675$	−2.81818	−0.108472
$676$	39.3913	1.51505
$677$	−15.5864	−0.599033	−0.299516	−	0.954091i	$-0.596825\pi$
$677$	−15.5864	−0.599033	−0.299516	+	0.954091i	$0.596825\pi$
$678$	−13.9641	−0.536287
$679$	−2.27302	−0.0872307
$680$	−18.0971	−0.693993
$681$	−46.2609	−1.77272
$682$	−49.3117	−1.88824
$683$	6.82105	0.261000	0.130500	−	0.991448i	$-0.458342\pi$
$683$	6.82105	0.261000	0.130500	+	0.991448i	$0.458342\pi$
$684$	−18.1122	−0.692539
$685$	19.0297	0.727089
$686$	−32.3813	−1.23632
$687$	30.3383	1.15748
$688$	34.2597	1.30614
$689$	67.7321	2.58039
$690$	−7.93824	−0.302204
$691$	−21.8120	−0.829768	−0.414884	−	0.909874i	$-0.636178\pi$
$691$	−21.8120	−0.829768	−0.414884	+	0.909874i	$0.636178\pi$
$692$	−23.2193	−0.882666
$693$	−50.4211	−1.91534
$694$	−65.8999	−2.50153
$695$	28.1268	1.06691
$696$	16.4910	0.625088
$697$	59.0051	2.23498
$698$	−48.0481	−1.81865
$699$	56.0456	2.11984
$700$	1.88146	0.0711125
$701$	19.3683	0.731530	0.365765	−	0.930707i	$-0.380807\pi$
$701$	19.3683	0.731530	0.365765	+	0.930707i	$0.380807\pi$
$702$	58.7039	2.21564
$703$	−3.18902	−0.120276
$704$	−3.19429	−0.120390
$705$	26.8498	1.01122
$706$	64.4399	2.42523
$707$	3.21089	0.120758
$708$	30.4955	1.14609
$709$	−7.76462	−0.291607	−0.145803	−	0.989314i	$-0.546577\pi$
$709$	−7.76462	−0.291607	−0.145803	+	0.989314i	$0.546577\pi$
$710$	−60.7074	−2.27831
$711$	16.2795	0.610528
$712$	10.4951	0.393321
$713$	−5.31670	−0.199112
$714$	80.6581	3.01855
$715$	56.0542	2.09631
$716$	9.70494	0.362691
$717$	−1.83057	−0.0683639
$718$	−33.2350	−1.24032
$719$	−25.8127	−0.962650	−0.481325	−	0.876542i	$-0.659844\pi$
$719$	−25.8127	−0.962650	−0.481325	+	0.876542i	$0.659844\pi$
$720$	49.4460	1.84275
$721$	18.2630	0.680151
$722$	15.7903	0.587655
$723$	−39.6687	−1.47529
$724$	−14.3211	−0.532238
$725$	−2.40259	−0.0892300
$726$	−22.3766	−0.830474
$727$	−12.4894	−0.463204	−0.231602	−	0.972811i	$-0.574397\pi$
$727$	−12.4894	−0.463204	−0.231602	+	0.972811i	$0.574397\pi$
$728$	26.2487	0.972843
$729$	−43.9665	−1.62839
$730$	−0.975444	−0.0361028
$731$	−41.4459	−1.53293
$732$	−1.45069	−0.0536190
$733$	35.6254	1.31585	0.657927	−	0.753081i	$-0.271433\pi$
$733$	35.6254	1.31585	0.657927	+	0.753081i	$0.271433\pi$
$734$	25.0536	0.924747
$735$	−1.73225	−0.0638951
$736$	−4.55564	−0.167923
$737$	−41.6780	−1.53523
$738$	−83.3670	−3.06878
$739$	28.5841	1.05148	0.525741	−	0.850644i	$-0.323788\pi$
$739$	28.5841	1.05148	0.525741	+	0.850644i	$0.323788\pi$
$740$	−2.51776	−0.0925546
$741$	60.1064	2.20807
$742$	−48.2973	−1.77305
$743$	8.02060	0.294247	0.147124	−	0.989118i	$-0.452999\pi$
$743$	8.02060	0.294247	0.147124	+	0.989118i	$0.452999\pi$
$744$	27.9597	1.02505
$745$	16.3789	0.600076
$746$	−13.8523	−0.507170
$747$	−24.7847	−0.906824
$748$	28.2984	1.03469
$749$	20.1463	0.736131
$750$	−58.3757	−2.13158
$751$	−30.1413	−1.09987	−0.549936	−	0.835207i	$-0.685348\pi$
$751$	−30.1413	−1.09987	−0.549936	+	0.835207i	$0.685348\pi$
$752$	22.7743	0.830493
$753$	−33.7284	−1.22913
$754$	50.0471	1.82261
$755$	49.7747	1.81149
$756$	−15.6792	−0.570248
$757$	−47.4022	−1.72286	−0.861431	−	0.507875i	$-0.830431\pi$
$757$	−47.4022	−1.72286	−0.861431	+	0.507875i	$0.830431\pi$
$758$	−58.8740	−2.13840
$759$	−8.31365	−0.301766
$760$	9.61636	0.348822
$761$	41.3674	1.49957	0.749784	−	0.661683i	$-0.230157\pi$
$761$	41.3674	1.49957	0.749784	+	0.661683i	$0.230157\pi$
$762$	70.2341	2.54431
$763$	−2.70114	−0.0977880
$764$	8.95968	0.324150
$765$	−59.8176	−2.16271
$766$	−1.47336	−0.0532347
$767$	−61.9844	−2.23813
$768$	57.0237	2.05767
$769$	−50.6174	−1.82531	−0.912656	−	0.408729i	$-0.865972\pi$
$769$	−50.6174	−1.82531	−0.912656	+	0.408729i	$0.865972\pi$
$770$	−39.9702	−1.44043
$771$	−87.3728	−3.14666
$772$	0.210163	0.00756392
$773$	47.8950	1.72266	0.861332	−	0.508042i	$-0.169631\pi$
$773$	47.8950	1.72266	0.861332	+	0.508042i	$0.169631\pi$
$774$	58.5579	2.10482
$775$	−4.07349	−0.146324
$776$	1.20718	0.0433353
$777$	−7.51565	−0.269623
$778$	25.3483	0.908782
$779$	−31.3539	−1.12337
$780$	47.4545	1.69914
$781$	−63.5783	−2.27501
$782$	8.14566	0.291288
$783$	20.0221	0.715531
$784$	−1.46932	−0.0524756
$785$	−10.0312	−0.358030
$786$	−17.9053	−0.638661
$787$	22.3680	0.797333	0.398667	−	0.917096i	$-0.369473\pi$
$787$	22.3680	0.797333	0.398667	+	0.917096i	$0.369473\pi$
$788$	−8.20797	−0.292397
$789$	−6.72183	−0.239304
$790$	12.9052	0.459146
$791$	−7.58083	−0.269543
$792$	26.7782	0.951521
$793$	2.94864	0.104709
$794$	−37.7730	−1.34051
$795$	58.4797	2.07406
$796$	−15.6681	−0.555340
$797$	35.1360	1.24458	0.622290	−	0.782787i	$-0.286202\pi$
$797$	35.1360	1.24458	0.622290	+	0.782787i	$0.286202\pi$
$798$	−42.8597	−1.51722
$799$	−27.5513	−0.974696
$800$	−3.49039	−0.123404
$801$	34.6903	1.22572
$802$	26.8686	0.948762
$803$	−1.02157	−0.0360506
$804$	−35.2838	−1.24436
$805$	−4.30952	−0.151891
$806$	84.8528	2.98881
$807$	63.7661	2.24467
$808$	−1.70528	−0.0599914
$809$	7.04084	0.247543	0.123771	−	0.992311i	$-0.460501\pi$
$809$	7.04084	0.247543	0.123771	+	0.992311i	$0.460501\pi$
$810$	−2.78615	−0.0978952
$811$	26.9729	0.947146	0.473573	−	0.880755i	$-0.342964\pi$
$811$	26.9729	0.947146	0.473573	+	0.880755i	$0.342964\pi$
$812$	−13.3671	−0.469092
$813$	−20.9904	−0.736166
$814$	−7.03967	−0.246740
$815$	8.67408	0.303840
$816$	−82.8389	−2.89994
$817$	22.0233	0.770498
$818$	21.7670	0.761064
$819$	86.7618	3.03170
$820$	−24.7541	−0.864451
$821$	46.4733	1.62193	0.810964	−	0.585096i	$-0.198943\pi$
$821$	46.4733	1.62193	0.810964	+	0.585096i	$0.198943\pi$
$822$	45.0443	1.57110
$823$	7.03604	0.245261	0.122630	−	0.992452i	$-0.460867\pi$
$823$	7.03604	0.245261	0.122630	+	0.992452i	$0.460867\pi$
$824$	−9.69933	−0.337892
$825$	−6.36966	−0.221763
$826$	44.1988	1.53787
$827$	50.5036	1.75618	0.878091	−	0.478494i	$-0.158817\pi$
$827$	50.5036	1.75618	0.878091	+	0.478494i	$0.158817\pi$
$828$	−4.31081	−0.149811
$829$	−13.4652	−0.467665	−0.233832	−	0.972277i	$-0.575127\pi$
$829$	−13.4652	−0.467665	−0.233832	+	0.972277i	$0.575127\pi$
$830$	−19.6475	−0.681975
$831$	−65.7083	−2.27940
$832$	5.49656	0.190559
$833$	1.77751	0.0615872
$834$	66.5775	2.30539
$835$	−34.7377	−1.20215
$836$	−15.0371	−0.520069
$837$	33.9466	1.17337
$838$	−6.47525	−0.223684
$839$	−12.3017	−0.424703	−0.212351	−	0.977193i	$-0.568112\pi$
$839$	−12.3017	−0.424703	−0.212351	+	0.977193i	$0.568112\pi$
$840$	22.6631	0.781952
$841$	−11.9305	−0.411396
$842$	−5.78044	−0.199207
$843$	−13.3081	−0.458356
$844$	13.7029	0.471673
$845$	−69.1287	−2.37810
$846$	38.9266	1.33833
$847$	−12.1478	−0.417404
$848$	49.6031	1.70338
$849$	−7.38561	−0.253474
$850$	6.24095	0.214063
$851$	−0.759006	−0.0260184
$852$	−53.8242	−1.84399
$853$	35.2408	1.20662	0.603311	−	0.797506i	$-0.293848\pi$
$853$	35.2408	1.20662	0.603311	+	0.797506i	$0.293848\pi$
$854$	−2.10257	−0.0719483
$855$	31.7856	1.08704
$856$	−10.6995	−0.365703
$857$	7.60745	0.259866	0.129933	−	0.991523i	$-0.458524\pi$
$857$	7.60745	0.259866	0.129933	+	0.991523i	$0.458524\pi$
$858$	132.683	4.52972
$859$	56.1782	1.91678	0.958388	−	0.285470i	$-0.0921497\pi$
$859$	56.1782	1.91678	0.958388	+	0.285470i	$0.0921497\pi$
$860$	17.3876	0.592911
$861$	−73.8924	−2.51825
$862$	−4.03514	−0.137438
$863$	42.7233	1.45432	0.727159	−	0.686469i	$-0.240840\pi$
$863$	42.7233	1.45432	0.727159	+	0.686469i	$0.240840\pi$
$864$	29.0873	0.989569
$865$	40.7481	1.38548
$866$	56.4810	1.91930
$867$	52.9142	1.79706
$868$	−22.6633	−0.769243
$869$	13.5155	0.458481
$870$	43.2106	1.46498
$871$	71.7171	2.43004
$872$	1.43455	0.0485801
$873$	3.99018	0.135047
$874$	−4.32840	−0.146410
$875$	−31.6911	−1.07135
$876$	−0.864846	−0.0292204
$877$	57.9878	1.95811	0.979054	−	0.203601i	$-0.0652645\pi$
$877$	57.9878	1.95811	0.979054	+	0.203601i	$0.0652645\pi$
$878$	−23.3002	−0.786344
$879$	10.8044	0.364424
$880$	41.0509	1.38383
$881$	−49.4646	−1.66650	−0.833252	−	0.552893i	$-0.813524\pi$
$881$	−49.4646	−1.66650	−0.833252	+	0.552893i	$0.813524\pi$
$882$	−2.51141	−0.0845635
$883$	−2.51710	−0.0847070	−0.0423535	−	0.999103i	$-0.513486\pi$
$883$	−2.51710	−0.0847070	−0.0423535	+	0.999103i	$0.513486\pi$
$884$	−48.6944	−1.63777
$885$	−53.5172	−1.79896
$886$	59.1405	1.98686
$887$	−19.6261	−0.658981	−0.329490	−	0.944159i	$-0.606877\pi$
$887$	−19.6261	−0.658981	−0.329490	+	0.944159i	$0.606877\pi$
$888$	3.99149	0.133946
$889$	38.1287	1.27880
$890$	27.4999	0.921800
$891$	−2.91790	−0.0977535
$892$	−6.36812	−0.213220
$893$	14.6401	0.489912
$894$	38.7696	1.29665
$895$	−17.0314	−0.569298
$896$	28.5058	0.952310
$897$	14.3057	0.477652
$898$	−17.0834	−0.570080
$899$	28.9406	0.965224
$900$	−3.30281	−0.110094
$901$	−60.0077	−1.99915
$902$	−69.2126	−2.30453
$903$	51.9028	1.72722
$904$	4.02611	0.133906
$905$	25.1324	0.835429
$906$	117.819	3.91428
$907$	24.4150	0.810687	0.405344	−	0.914164i	$-0.367152\pi$
$907$	24.4150	0.810687	0.405344	+	0.914164i	$0.367152\pi$
$908$	−19.9147	−0.660891
$909$	−5.63656	−0.186953
$910$	68.7785	2.27998
$911$	−46.4723	−1.53970	−0.769848	−	0.638228i	$-0.779668\pi$
$911$	−46.4723	−1.53970	−0.769848	+	0.638228i	$0.779668\pi$
$912$	44.0185	1.45760
$913$	−20.5767	−0.680988
$914$	30.1706	0.997956
$915$	2.54585	0.0841631
$916$	13.0602	0.431522
$917$	−9.72044	−0.320997
$918$	−52.0092	−1.71656
$919$	12.8499	0.423880	0.211940	−	0.977283i	$-0.432022\pi$
$919$	12.8499	0.423880	0.211940	+	0.977283i	$0.432022\pi$
$920$	2.28875	0.0754577
$921$	−45.5604	−1.50127
$922$	−22.3042	−0.734549
$923$	109.402	3.60101
$924$	−35.4383	−1.16583
$925$	−0.581526	−0.0191205
$926$	12.8785	0.423214
$927$	−32.0598	−1.05298
$928$	24.7979	0.814030
$929$	−32.3342	−1.06085	−0.530426	−	0.847732i	$-0.677968\pi$
$929$	−32.3342	−1.06085	−0.530426	+	0.847732i	$0.677968\pi$
$930$	73.2617	2.40235
$931$	−0.944527	−0.0309556
$932$	24.1268	0.790301
$933$	−89.2907	−2.92325
$934$	−56.5158	−1.84925
$935$	−49.6616	−1.62411
$936$	−46.0784	−1.50612
$937$	1.44495	0.0472044	0.0236022	−	0.999721i	$-0.492486\pi$
$937$	1.44495	0.0472044	0.0236022	+	0.999721i	$0.492486\pi$
$938$	−51.1389	−1.66974
$939$	73.0878	2.38513
$940$	11.5585	0.376995
$941$	30.5512	0.995941	0.497971	−	0.867194i	$-0.334079\pi$
$941$	30.5512	0.995941	0.497971	+	0.867194i	$0.334079\pi$
$942$	−23.7444	−0.773636
$943$	−7.46239	−0.243009
$944$	−45.3939	−1.47745
$945$	27.5158	0.895090
$946$	48.6157	1.58063
$947$	26.2437	0.852806	0.426403	−	0.904533i	$-0.359781\pi$
$947$	26.2437	0.852806	0.426403	+	0.904533i	$0.359781\pi$
$948$	11.4420	0.371618
$949$	1.75787	0.0570628
$950$	−3.31628	−0.107594
$951$	58.4678	1.89595
$952$	−23.2553	−0.753707
$953$	−18.7506	−0.607392	−0.303696	−	0.952769i	$-0.598221\pi$
$953$	−18.7506	−0.607392	−0.303696	+	0.952769i	$0.598221\pi$
$954$	84.7835	2.74497
$955$	−15.7235	−0.508802
$956$	−0.788034	−0.0254869
$957$	45.2540	1.46285
$958$	54.9455	1.77521
$959$	24.4537	0.789651
$960$	4.74572	0.153167
$961$	18.0676	0.582827
$962$	12.1135	0.390554
$963$	−35.3659	−1.13965
$964$	−17.0768	−0.550007
$965$	−0.368820	−0.0118727
$966$	−10.2008	−0.328207
$967$	43.9447	1.41317	0.706584	−	0.707630i	$-0.250235\pi$
$967$	43.9447	1.41317	0.706584	+	0.707630i	$0.250235\pi$
$968$	6.45160	0.207362
$969$	−53.2517	−1.71069
$970$	3.16313	0.101562
$971$	−11.6688	−0.374471	−0.187236	−	0.982315i	$-0.559953\pi$
$971$	−11.6688	−0.374471	−0.187236	+	0.982315i	$0.559953\pi$
$972$	−19.8842	−0.637787
$973$	36.1436	1.15871
$974$	36.7415	1.17727
$975$	10.9606	0.351019
$976$	2.15942	0.0691212
$977$	−19.8935	−0.636448	−0.318224	−	0.948016i	$-0.603086\pi$
$977$	−19.8935	−0.636448	−0.318224	+	0.948016i	$0.603086\pi$
$978$	20.5320	0.656540
$979$	28.8004	0.920466
$980$	−0.745711	−0.0238209
$981$	4.74173	0.151392
$982$	45.4118	1.44915
$983$	31.8038	1.01438	0.507192	−	0.861833i	$-0.330683\pi$
$983$	31.8038	1.01438	0.507192	+	0.861833i	$0.330683\pi$
$984$	39.2436	1.25104
$985$	14.4044	0.458961
$986$	−44.3396	−1.41206
$987$	34.5027	1.09823
$988$	25.8750	0.823193
$989$	5.24167	0.166675
$990$	70.1657	2.23001
$991$	−41.5154	−1.31878	−0.659390	−	0.751801i	$-0.729185\pi$
$991$	−41.5154	−1.31878	−0.659390	+	0.751801i	$0.729185\pi$
$992$	42.0438	1.33489
$993$	−59.7418	−1.89585
$994$	−78.0105	−2.47434
$995$	27.4963	0.871690
$996$	−17.4198	−0.551968
$997$	−41.5377	−1.31551	−0.657756	−	0.753231i	$-0.728494\pi$
$997$	−41.5377	−1.31551	−0.657756	+	0.753231i	$0.728494\pi$
$998$	20.5950	0.651924
$999$	4.84617	0.153326

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.c.1.18	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.c.1.18	✓	77	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)

\(f(q)\)	\(=\)	\(q-1.78823 q^{2} +2.78240 q^{3} +1.19778 q^{4} -2.10202 q^{5} -4.97558 q^{6} -2.70114 q^{7} +1.43455 q^{8} +4.74173 q^{9} +O(q^{10})\)	\(q-1.78823 q^{2} +2.78240 q^{3} +1.19778 q^{4} -2.10202 q^{5} -4.97558 q^{6} -2.70114 q^{7} +1.43455 q^{8} +4.74173 q^{9} +3.75890 q^{10} +3.93666 q^{11} +3.33270 q^{12} -6.77398 q^{13} +4.83028 q^{14} -5.84864 q^{15} -4.96088 q^{16} +6.00146 q^{17} -8.47932 q^{18} -3.18902 q^{19} -2.51776 q^{20} -7.51565 q^{21} -7.03967 q^{22} -0.759006 q^{23} +3.99149 q^{24} -0.581526 q^{25} +12.1135 q^{26} +4.84617 q^{27} -3.23538 q^{28} +4.13153 q^{29} +10.4587 q^{30} +7.00483 q^{31} +6.00211 q^{32} +10.9533 q^{33} -10.7320 q^{34} +5.67785 q^{35} +5.67956 q^{36} +1.00000 q^{37} +5.70272 q^{38} -18.8479 q^{39} -3.01545 q^{40} +9.83180 q^{41} +13.4397 q^{42} -6.90597 q^{43} +4.71526 q^{44} -9.96719 q^{45} +1.35728 q^{46} -4.59077 q^{47} -13.8031 q^{48} +0.296181 q^{49} +1.03991 q^{50} +16.6984 q^{51} -8.11376 q^{52} -9.99885 q^{53} -8.66609 q^{54} -8.27492 q^{55} -3.87494 q^{56} -8.87313 q^{57} -7.38814 q^{58} +9.15037 q^{59} -7.00540 q^{60} -0.435289 q^{61} -12.5263 q^{62} -12.8081 q^{63} -0.811423 q^{64} +14.2390 q^{65} -19.5871 q^{66} -10.5871 q^{67} +7.18844 q^{68} -2.11185 q^{69} -10.1533 q^{70} -16.1503 q^{71} +6.80226 q^{72} -0.259503 q^{73} -1.78823 q^{74} -1.61804 q^{75} -3.81976 q^{76} -10.6335 q^{77} +33.7045 q^{78} +3.43324 q^{79} +10.4279 q^{80} -0.741213 q^{81} -17.5816 q^{82} -5.22693 q^{83} -9.00212 q^{84} -12.6152 q^{85} +12.3495 q^{86} +11.4955 q^{87} +5.64735 q^{88} +7.31595 q^{89} +17.8237 q^{90} +18.2975 q^{91} -0.909124 q^{92} +19.4902 q^{93} +8.20938 q^{94} +6.70338 q^{95} +16.7003 q^{96} +0.841504 q^{97} -0.529640 q^{98} +18.6666 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 9 q^{2} - 27 q^{3} + 73 q^{4} - 16 q^{5} - 2 q^{6} - 23 q^{7} - 24 q^{8} + 66 q^{9}+O(q^{10}) \) 77 * q - 9 * q^2 - 27 * q^3 + 73 * q^4 - 16 * q^5 - 2 * q^6 - 23 * q^7 - 24 * q^8 + 66 * q^9	\( 77 q - 9 q^{2} - 27 q^{3} + 73 q^{4} - 16 q^{5} - 2 q^{6} - 23 q^{7} - 24 q^{8} + 66 q^{9} - 11 q^{10} - 33 q^{11} - 52 q^{12} - 10 q^{13} - 18 q^{14} - 33 q^{15} + 53 q^{16} - 44 q^{17} - 27 q^{18} - 9 q^{19} - 45 q^{20} - 7 q^{21} - 3 q^{22} - 74 q^{23} + 21 q^{24} + 59 q^{25} - 47 q^{26} - 99 q^{27} - 49 q^{28} - 9 q^{29} - 39 q^{30} - 27 q^{31} - 47 q^{32} - 28 q^{33} - 23 q^{34} - 48 q^{35} + 77 q^{36} + 77 q^{37} - 66 q^{38} - 11 q^{39} - 2 q^{40} - 37 q^{41} - 24 q^{42} - 44 q^{43} - 54 q^{44} - 36 q^{45} - 41 q^{46} - 150 q^{47} - 135 q^{48} + 64 q^{49} + 4 q^{50} + 3 q^{51} - 57 q^{52} - 72 q^{53} + 21 q^{54} - 65 q^{55} - 92 q^{56} - 13 q^{57} - 12 q^{58} - 70 q^{59} - 22 q^{60} + 15 q^{61} - 86 q^{62} - 108 q^{63} + 10 q^{64} - 53 q^{65} - 55 q^{66} - 48 q^{67} - 70 q^{68} - 2 q^{69} + 11 q^{70} - 127 q^{71} - 12 q^{72} - 33 q^{73} - 9 q^{74} - 115 q^{75} - 24 q^{76} - 40 q^{77} + 81 q^{78} - 7 q^{79} - 62 q^{80} + 53 q^{81} - 68 q^{82} - 164 q^{83} + 7 q^{84} - 9 q^{85} - 50 q^{86} - 75 q^{87} - 82 q^{88} - 26 q^{89} + 23 q^{90} + 16 q^{91} - 117 q^{92} + 19 q^{93} + 23 q^{94} - 92 q^{95} - 35 q^{96} - 19 q^{97} - 10 q^{98} - 19 q^{99}+O(q^{100}) \) 77 * q - 9 * q^2 - 27 * q^3 + 73 * q^4 - 16 * q^5 - 2 * q^6 - 23 * q^7 - 24 * q^8 + 66 * q^9 - 11 * q^10 - 33 * q^11 - 52 * q^12 - 10 * q^13 - 18 * q^14 - 33 * q^15 + 53 * q^16 - 44 * q^17 - 27 * q^18 - 9 * q^19 - 45 * q^20 - 7 * q^21 - 3 * q^22 - 74 * q^23 + 21 * q^24 + 59 * q^25 - 47 * q^26 - 99 * q^27 - 49 * q^28 - 9 * q^29 - 39 * q^30 - 27 * q^31 - 47 * q^32 - 28 * q^33 - 23 * q^34 - 48 * q^35 + 77 * q^36 + 77 * q^37 - 66 * q^38 - 11 * q^39 - 2 * q^40 - 37 * q^41 - 24 * q^42 - 44 * q^43 - 54 * q^44 - 36 * q^45 - 41 * q^46 - 150 * q^47 - 135 * q^48 + 64 * q^49 + 4 * q^50 + 3 * q^51 - 57 * q^52 - 72 * q^53 + 21 * q^54 - 65 * q^55 - 92 * q^56 - 13 * q^57 - 12 * q^58 - 70 * q^59 - 22 * q^60 + 15 * q^61 - 86 * q^62 - 108 * q^63 + 10 * q^64 - 53 * q^65 - 55 * q^66 - 48 * q^67 - 70 * q^68 - 2 * q^69 + 11 * q^70 - 127 * q^71 - 12 * q^72 - 33 * q^73 - 9 * q^74 - 115 * q^75 - 24 * q^76 - 40 * q^77 + 81 * q^78 - 7 * q^79 - 62 * q^80 + 53 * q^81 - 68 * q^82 - 164 * q^83 + 7 * q^84 - 9 * q^85 - 50 * q^86 - 75 * q^87 - 82 * q^88 - 26 * q^89 + 23 * q^90 + 16 * q^91 - 117 * q^92 + 19 * q^93 + 23 * q^94 - 92 * q^95 - 35 * q^96 - 19 * q^97 - 10 * q^98 - 19 * q^99

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