LMFDB - Embedded newform 4033.2.a.d.1.9

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			1.9
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)

$f(q)$	$=$	$q-2.50108 q^{2} -2.74712 q^{3} +4.25541 q^{4} +3.75941 q^{5} +6.87078 q^{6} -1.77571 q^{7} -5.64098 q^{8} +4.54668 q^{9} +O(q^{10})$	\(q-2.50108 q^{2} -2.74712 q^{3} +4.25541 q^{4} +3.75941 q^{5} +6.87078 q^{6} -1.77571 q^{7} -5.64098 q^{8} +4.54668 q^{9} -9.40258 q^{10} +4.50342 q^{11} -11.6901 q^{12} -2.22949 q^{13} +4.44119 q^{14} -10.3275 q^{15} +5.59772 q^{16} +2.78903 q^{17} -11.3716 q^{18} -6.60953 q^{19} +15.9978 q^{20} +4.87809 q^{21} -11.2634 q^{22} +5.39913 q^{23} +15.4965 q^{24} +9.13313 q^{25} +5.57615 q^{26} -4.24891 q^{27} -7.55638 q^{28} +1.55088 q^{29} +25.8300 q^{30} -4.02437 q^{31} -2.71842 q^{32} -12.3714 q^{33} -6.97558 q^{34} -6.67561 q^{35} +19.3480 q^{36} -1.00000 q^{37} +16.5310 q^{38} +6.12469 q^{39} -21.2067 q^{40} +11.6153 q^{41} -12.2005 q^{42} -10.9960 q^{43} +19.1639 q^{44} +17.0928 q^{45} -13.5037 q^{46} -9.73430 q^{47} -15.3776 q^{48} -3.84686 q^{49} -22.8427 q^{50} -7.66179 q^{51} -9.48742 q^{52} -10.7722 q^{53} +10.6269 q^{54} +16.9302 q^{55} +10.0167 q^{56} +18.1572 q^{57} -3.87888 q^{58} -2.95304 q^{59} -43.9480 q^{60} +6.72393 q^{61} +10.0653 q^{62} -8.07357 q^{63} -4.39647 q^{64} -8.38157 q^{65} +30.9420 q^{66} -3.18113 q^{67} +11.8685 q^{68} -14.8321 q^{69} +16.6962 q^{70} +10.1420 q^{71} -25.6477 q^{72} -6.37886 q^{73} +2.50108 q^{74} -25.0898 q^{75} -28.1263 q^{76} -7.99676 q^{77} -15.3184 q^{78} -10.5416 q^{79} +21.0441 q^{80} -1.96776 q^{81} -29.0508 q^{82} -6.27102 q^{83} +20.7583 q^{84} +10.4851 q^{85} +27.5019 q^{86} -4.26046 q^{87} -25.4037 q^{88} -16.4692 q^{89} -42.7505 q^{90} +3.95893 q^{91} +22.9755 q^{92} +11.0554 q^{93} +24.3463 q^{94} -24.8479 q^{95} +7.46782 q^{96} -12.3723 q^{97} +9.62132 q^{98} +20.4756 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.50108	−1.76853	−0.884266	−	0.466983i	$-0.845341\pi$
$2$	−2.50108	−1.76853	−0.884266	+	0.466983i	$0.845341\pi$
$3$	−2.74712	−1.58605	−0.793026	−	0.609188i	$-0.791495\pi$
$3$	−2.74712	−1.58605	−0.793026	+	0.609188i	$0.791495\pi$
$4$	4.25541	2.12771
$5$	3.75941	1.68126	0.840629	−	0.541612i	$-0.182186\pi$
$5$	3.75941	1.68126	0.840629	+	0.541612i	$0.182186\pi$
$6$	6.87078	2.80498
$7$	−1.77571	−0.671155	−0.335577	−	0.942013i	$-0.608931\pi$
$7$	−1.77571	−0.671155	−0.335577	+	0.942013i	$0.608931\pi$
$8$	−5.64098	−1.99439
$9$	4.54668	1.51556
$10$	−9.40258	−2.97336
$11$	4.50342	1.35783	0.678916	−	0.734216i	$-0.262450\pi$
$11$	4.50342	1.35783	0.678916	+	0.734216i	$0.262450\pi$
$12$	−11.6901	−3.37465
$13$	−2.22949	−0.618350	−0.309175	−	0.951005i	$-0.600053\pi$
$13$	−2.22949	−0.618350	−0.309175	+	0.951005i	$0.600053\pi$
$14$	4.44119	1.18696
$15$	−10.3275	−2.66656
$16$	5.59772	1.39943
$17$	2.78903	0.676438	0.338219	−	0.941067i	$-0.390176\pi$
$17$	2.78903	0.676438	0.338219	+	0.941067i	$0.390176\pi$
$18$	−11.3716	−2.68032
$19$	−6.60953	−1.51633	−0.758165	−	0.652063i	$-0.773904\pi$
$19$	−6.60953	−1.51633	−0.758165	+	0.652063i	$0.773904\pi$
$20$	15.9978	3.57722
$21$	4.87809	1.06449
$22$	−11.2634	−2.40137
$23$	5.39913	1.12580	0.562898	−	0.826526i	$-0.309686\pi$
$23$	5.39913	1.12580	0.562898	+	0.826526i	$0.309686\pi$
$24$	15.4965	3.16320
$25$	9.13313	1.82663
$26$	5.57615	1.09357
$27$	−4.24891	−0.817703
$28$	−7.55638	−1.42802
$29$	1.55088	0.287991	0.143996	−	0.989578i	$-0.454005\pi$
$29$	1.55088	0.287991	0.143996	+	0.989578i	$0.454005\pi$
$30$	25.8300	4.71590
$31$	−4.02437	−0.722797	−0.361399	−	0.932411i	$-0.617701\pi$
$31$	−4.02437	−0.722797	−0.361399	+	0.932411i	$0.617701\pi$
$32$	−2.71842	−0.480552
$33$	−12.3714	−2.15359
$34$	−6.97558	−1.19630
$35$	−6.67561	−1.12838
$36$	19.3480	3.22467
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	16.5310	2.68168
$39$	6.12469	0.980736
$40$	−21.2067	−3.35308
$41$	11.6153	1.81400	0.907001	−	0.421128i	$-0.138366\pi$
$41$	11.6153	1.81400	0.907001	+	0.421128i	$0.138366\pi$
$42$	−12.2005	−1.88258
$43$	−10.9960	−1.67688	−0.838438	−	0.544997i	$-0.816531\pi$
$43$	−10.9960	−1.67688	−0.838438	+	0.544997i	$0.816531\pi$
$44$	19.1639	2.88907
$45$	17.0928	2.54804
$46$	−13.5037	−1.99101
$47$	−9.73430	−1.41989	−0.709947	−	0.704255i	$-0.751281\pi$
$47$	−9.73430	−1.41989	−0.709947	+	0.704255i	$0.751281\pi$
$48$	−15.3776	−2.21957
$49$	−3.84686	−0.549551
$50$	−22.8427	−3.23045
$51$	−7.66179	−1.07287
$52$	−9.48742	−1.31567
$53$	−10.7722	−1.47968	−0.739841	−	0.672782i	$-0.765099\pi$
$53$	−10.7722	−1.47968	−0.739841	+	0.672782i	$0.765099\pi$
$54$	10.6269	1.44613
$55$	16.9302	2.28286
$56$	10.0167	1.33854
$57$	18.1572	2.40498
$58$	−3.87888	−0.509322
$59$	−2.95304	−0.384453	−0.192227	−	0.981351i	$-0.561571\pi$
$59$	−2.95304	−0.384453	−0.192227	+	0.981351i	$0.561571\pi$
$60$	−43.9480	−5.67366
$61$	6.72393	0.860911	0.430456	−	0.902612i	$-0.358353\pi$
$61$	6.72393	0.860911	0.430456	+	0.902612i	$0.358353\pi$
$62$	10.0653	1.27829
$63$	−8.07357	−1.01717
$64$	−4.39647	−0.549559
$65$	−8.38157	−1.03961
$66$	30.9420	3.80870
$67$	−3.18113	−0.388636	−0.194318	−	0.980939i	$-0.562249\pi$
$67$	−3.18113	−0.388636	−0.194318	+	0.980939i	$0.562249\pi$
$68$	11.8685	1.43926
$69$	−14.8321	−1.78557
$70$	16.6962	1.99558
$71$	10.1420	1.20364	0.601818	−	0.798633i	$-0.294443\pi$
$71$	10.1420	1.20364	0.601818	+	0.798633i	$0.294443\pi$
$72$	−25.6477	−3.02261
$73$	−6.37886	−0.746589	−0.373294	−	0.927713i	$-0.621772\pi$
$73$	−6.37886	−0.746589	−0.373294	+	0.927713i	$0.621772\pi$
$74$	2.50108	0.290745
$75$	−25.0898	−2.89712
$76$	−28.1263	−3.22631
$77$	−7.99676	−0.911315
$78$	−15.3184	−1.73446
$79$	−10.5416	−1.18602	−0.593009	−	0.805196i	$-0.702060\pi$
$79$	−10.5416	−1.18602	−0.593009	+	0.805196i	$0.702060\pi$
$80$	21.0441	2.35280
$81$	−1.96776	−0.218640
$82$	−29.0508	−3.20812
$83$	−6.27102	−0.688334	−0.344167	−	0.938908i	$-0.611839\pi$
$83$	−6.27102	−0.688334	−0.344167	+	0.938908i	$0.611839\pi$
$84$	20.7583	2.26491
$85$	10.4851	1.13727
$86$	27.5019	2.96561
$87$	−4.26046	−0.456769
$88$	−25.4037	−2.70804
$89$	−16.4692	−1.74573	−0.872864	−	0.487964i	$-0.837740\pi$
$89$	−16.4692	−1.74573	−0.872864	+	0.487964i	$0.837740\pi$
$90$	−42.7505	−4.50630
$91$	3.95893	0.415009
$92$	22.9755	2.39536
$93$	11.0554	1.14639
$94$	24.3463	2.51113
$95$	−24.8479	−2.54934
$96$	7.46782	0.762181
$97$	−12.3723	−1.25622	−0.628111	−	0.778124i	$-0.716171\pi$
$97$	−12.3723	−1.25622	−0.628111	+	0.778124i	$0.716171\pi$
$98$	9.62132	0.971900
$99$	20.4756	2.05787
$100$	38.8652	3.88652
$101$	3.73452	0.371598	0.185799	−	0.982588i	$-0.440513\pi$
$101$	3.73452	0.371598	0.185799	+	0.982588i	$0.440513\pi$
$102$	19.1628	1.89740
$103$	1.87238	0.184491	0.0922456	−	0.995736i	$-0.470596\pi$
$103$	1.87238	0.184491	0.0922456	+	0.995736i	$0.470596\pi$
$104$	12.5765	1.23323
$105$	18.3387	1.78967
$106$	26.9423	2.61687
$107$	−5.66160	−0.547328	−0.273664	−	0.961825i	$-0.588236\pi$
$107$	−5.66160	−0.547328	−0.273664	+	0.961825i	$0.588236\pi$
$108$	−18.0809	−1.73983
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	−42.3438	−4.03732
$111$	2.74712	0.260745
$112$	−9.93993	−0.939235
$113$	−7.62153	−0.716974	−0.358487	−	0.933535i	$-0.616707\pi$
$113$	−7.62153	−0.716974	−0.358487	+	0.933535i	$0.616707\pi$
$114$	−45.4126	−4.25328
$115$	20.2975	1.89275
$116$	6.59964	0.612761
$117$	−10.1368	−0.937146
$118$	7.38580	0.679918
$119$	−4.95250	−0.453995
$120$	58.2574	5.31815
$121$	9.28078	0.843707
$122$	−16.8171	−1.52255
$123$	−31.9086	−2.87710
$124$	−17.1253	−1.53790
$125$	15.5381	1.38977
$126$	20.1927	1.79891
$127$	−5.33994	−0.473843	−0.236921	−	0.971529i	$-0.576138\pi$
$127$	−5.33994	−0.473843	−0.236921	+	0.971529i	$0.576138\pi$
$128$	16.4328	1.45246
$129$	30.2074	2.65961
$130$	20.9630	1.83858
$131$	2.03375	0.177689	0.0888447	−	0.996045i	$-0.471683\pi$
$131$	2.03375	0.177689	0.0888447	+	0.996045i	$0.471683\pi$
$132$	−52.6456	−4.58221
$133$	11.7366	1.01769
$134$	7.95626	0.687316
$135$	−15.9734	−1.37477
$136$	−15.7328	−1.34908
$137$	−3.64660	−0.311550	−0.155775	−	0.987793i	$-0.549788\pi$
$137$	−3.64660	−0.311550	−0.155775	+	0.987793i	$0.549788\pi$
$138$	37.0962	3.15784
$139$	20.6974	1.75553	0.877766	−	0.479090i	$-0.159033\pi$
$139$	20.6974	1.75553	0.877766	+	0.479090i	$0.159033\pi$
$140$	−28.4075	−2.40087
$141$	26.7413	2.25202
$142$	−25.3660	−2.12867
$143$	−10.0403	−0.839616
$144$	25.4510	2.12092
$145$	5.83039	0.484187
$146$	15.9540	1.32037
$147$	10.5678	0.871617
$148$	−4.25541	−0.349793
$149$	13.8189	1.13209	0.566044	−	0.824375i	$-0.308473\pi$
$149$	13.8189	1.13209	0.566044	+	0.824375i	$0.308473\pi$
$150$	62.7517	5.12365
$151$	4.94410	0.402345	0.201172	−	0.979556i	$-0.435525\pi$
$151$	4.94410	0.402345	0.201172	+	0.979556i	$0.435525\pi$
$152$	37.2842	3.02415
$153$	12.6808	1.02518
$154$	20.0006	1.61169
$155$	−15.1292	−1.21521
$156$	26.0631	2.08672
$157$	22.3443	1.78327	0.891634	−	0.452756i	$-0.149559\pi$
$157$	22.3443	1.78327	0.891634	+	0.452756i	$0.149559\pi$
$158$	26.3653	2.09751
$159$	29.5927	2.34685
$160$	−10.2196	−0.807932
$161$	−9.58728	−0.755583
$162$	4.92154	0.386673
$163$	−9.37314	−0.734161	−0.367081	−	0.930189i	$-0.619643\pi$
$163$	−9.37314	−0.734161	−0.367081	+	0.930189i	$0.619643\pi$
$164$	49.4278	3.85967
$165$	−46.5092	−3.62074
$166$	15.6843	1.21734
$167$	14.8931	1.15246	0.576231	−	0.817287i	$-0.304523\pi$
$167$	14.8931	1.15246	0.576231	+	0.817287i	$0.304523\pi$
$168$	−27.5172	−2.12300
$169$	−8.02936	−0.617643
$170$	−26.2240	−2.01129
$171$	−30.0514	−2.29809
$172$	−46.7926	−3.56790
$173$	20.4389	1.55394	0.776971	−	0.629536i	$-0.216755\pi$
$173$	20.4389	1.55394	0.776971	+	0.629536i	$0.216755\pi$
$174$	10.6558	0.807810
$175$	−16.2178	−1.22595
$176$	25.2089	1.90019
$177$	8.11237	0.609763
$178$	41.1907	3.08738
$179$	−15.7357	−1.17614	−0.588070	−	0.808810i	$-0.700112\pi$
$179$	−15.7357	−1.17614	−0.588070	+	0.808810i	$0.700112\pi$
$180$	72.7369	5.42149
$181$	−5.37184	−0.399286	−0.199643	−	0.979869i	$-0.563978\pi$
$181$	−5.37184	−0.399286	−0.199643	+	0.979869i	$0.563978\pi$
$182$	−9.90161	−0.733957
$183$	−18.4715	−1.36545
$184$	−30.4564	−2.24527
$185$	−3.75941	−0.276397
$186$	−27.6505	−2.02743
$187$	12.5602	0.918489
$188$	−41.4235	−3.02112
$189$	7.54482	0.548805
$190$	62.1466	4.50859
$191$	5.53808	0.400722	0.200361	−	0.979722i	$-0.435789\pi$
$191$	5.53808	0.400722	0.200361	+	0.979722i	$0.435789\pi$
$192$	12.0776	0.871628
$193$	−10.0808	−0.725628	−0.362814	−	0.931862i	$-0.618184\pi$
$193$	−10.0808	−0.725628	−0.362814	+	0.931862i	$0.618184\pi$
$194$	30.9443	2.22167
$195$	23.0252	1.64887
$196$	−16.3700	−1.16928
$197$	−0.686420	−0.0489054	−0.0244527	−	0.999701i	$-0.507784\pi$
$197$	−0.686420	−0.0489054	−0.0244527	+	0.999701i	$0.507784\pi$
$198$	−51.2111	−3.63942
$199$	−17.1729	−1.21735	−0.608676	−	0.793419i	$-0.708299\pi$
$199$	−17.1729	−1.21735	−0.608676	+	0.793419i	$0.708299\pi$
$200$	−51.5198	−3.64300
$201$	8.73894	0.616397
$202$	−9.34033	−0.657184
$203$	−2.75391	−0.193287
$204$	−32.6041	−2.28274
$205$	43.6666	3.04980
$206$	−4.68298	−0.326279
$207$	24.5481	1.70621
$208$	−12.4801	−0.865339
$209$	−29.7655	−2.05892
$210$	−45.8666	−3.16510
$211$	−4.67839	−0.322073	−0.161037	−	0.986948i	$-0.551484\pi$
$211$	−4.67839	−0.322073	−0.161037	+	0.986948i	$0.551484\pi$
$212$	−45.8404	−3.14833
$213$	−27.8614	−1.90903
$214$	14.1601	0.967967
$215$	−41.3385	−2.81926
$216$	23.9680	1.63082
$217$	7.14610	0.485109
$218$	2.50108	0.169395
$219$	17.5235	1.18413
$220$	72.0449	4.85727
$221$	−6.21812	−0.418276
$222$	−6.87078	−0.461136
$223$	−4.38034	−0.293329	−0.146665	−	0.989186i	$-0.546854\pi$
$223$	−4.38034	−0.293329	−0.146665	+	0.989186i	$0.546854\pi$
$224$	4.82711	0.322525
$225$	41.5254	2.76836
$226$	19.0621	1.26799
$227$	−4.94781	−0.328398	−0.164199	−	0.986427i	$-0.552504\pi$
$227$	−4.94781	−0.328398	−0.164199	+	0.986427i	$0.552504\pi$
$228$	77.2663	5.11709
$229$	−2.70576	−0.178802	−0.0894008	−	0.995996i	$-0.528495\pi$
$229$	−2.70576	−0.178802	−0.0894008	+	0.995996i	$0.528495\pi$
$230$	−50.7657	−3.34739
$231$	21.9681	1.44539
$232$	−8.74848	−0.574366
$233$	28.9503	1.89660	0.948299	−	0.317379i	$-0.102803\pi$
$233$	28.9503	1.89660	0.948299	+	0.317379i	$0.102803\pi$
$234$	25.3529	1.65737
$235$	−36.5952	−2.38721
$236$	−12.5664	−0.818004
$237$	28.9590	1.88109
$238$	12.3866	0.802904
$239$	−0.0952732	−0.00616271	−0.00308136	−	0.999995i	$-0.500981\pi$
$239$	−0.0952732	−0.00616271	−0.00308136	+	0.999995i	$0.500981\pi$
$240$	−57.8107	−3.73167
$241$	4.45281	0.286831	0.143415	−	0.989663i	$-0.454191\pi$
$241$	4.45281	0.286831	0.143415	+	0.989663i	$0.454191\pi$
$242$	−23.2120	−1.49212
$243$	18.1524	1.16448
$244$	28.6131	1.83177
$245$	−14.4619	−0.923937
$246$	79.8060	5.08825
$247$	14.7359	0.937623
$248$	22.7014	1.44154
$249$	17.2273	1.09173
$250$	−38.8621	−2.45785
$251$	−11.9965	−0.757215	−0.378607	−	0.925557i	$-0.623597\pi$
$251$	−11.9965	−0.757215	−0.378607	+	0.925557i	$0.623597\pi$
$252$	−34.3564	−2.16425
$253$	24.3145	1.52864
$254$	13.3556	0.838006
$255$	−28.8038	−1.80376
$256$	−32.3068	−2.01917
$257$	−5.09848	−0.318035	−0.159017	−	0.987276i	$-0.550833\pi$
$257$	−5.09848	−0.318035	−0.159017	+	0.987276i	$0.550833\pi$
$258$	−75.5512	−4.70361
$259$	1.77571	0.110337
$260$	−35.6671	−2.21198
$261$	7.05135	0.436468
$262$	−5.08657	−0.314249
$263$	−19.2074	−1.18438	−0.592188	−	0.805800i	$-0.701736\pi$
$263$	−19.2074	−1.18438	−0.592188	+	0.805800i	$0.701736\pi$
$264$	69.7870	4.29509
$265$	−40.4972	−2.48773
$266$	−29.3542	−1.79982
$267$	45.2428	2.76881
$268$	−13.5370	−0.826904
$269$	−10.2788	−0.626711	−0.313356	−	0.949636i	$-0.601453\pi$
$269$	−10.2788	−0.626711	−0.313356	+	0.949636i	$0.601453\pi$
$270$	39.9507	2.43132
$271$	5.71771	0.347326	0.173663	−	0.984805i	$-0.444440\pi$
$271$	5.71771	0.347326	0.173663	+	0.984805i	$0.444440\pi$
$272$	15.6122	0.946629
$273$	−10.8757	−0.658225
$274$	9.12045	0.550987
$275$	41.1303	2.48025
$276$	−63.1166	−3.79917
$277$	22.7137	1.36474	0.682368	−	0.731009i	$-0.260950\pi$
$277$	22.7137	1.36474	0.682368	+	0.731009i	$0.260950\pi$
$278$	−51.7660	−3.10472
$279$	−18.2975	−1.09544
$280$	37.6570	2.25043
$281$	−22.4531	−1.33944	−0.669721	−	0.742613i	$-0.733586\pi$
$281$	−22.4531	−1.33944	−0.669721	+	0.742613i	$0.733586\pi$
$282$	−66.8822	−3.98278
$283$	−15.9034	−0.945360	−0.472680	−	0.881234i	$-0.656713\pi$
$283$	−15.9034	−0.945360	−0.472680	+	0.881234i	$0.656713\pi$
$284$	43.1585	2.56098
$285$	68.2602	4.04338
$286$	25.1117	1.48489
$287$	−20.6254	−1.21748
$288$	−12.3598	−0.728305
$289$	−9.22133	−0.542431
$290$	−14.5823	−0.856301
$291$	33.9883	1.99243
$292$	−27.1447	−1.58852
$293$	28.0829	1.64062	0.820311	−	0.571918i	$-0.193800\pi$
$293$	28.0829	1.64062	0.820311	+	0.571918i	$0.193800\pi$
$294$	−26.4309	−1.54148
$295$	−11.1017	−0.646365
$296$	5.64098	0.327875
$297$	−19.1346	−1.11030
$298$	−34.5622	−2.00214
$299$	−12.0373	−0.696136
$300$	−106.768	−6.16423
$301$	19.5257	1.12544
$302$	−12.3656	−0.711560
$303$	−10.2592	−0.589374
$304$	−36.9983	−2.12200
$305$	25.2780	1.44741
$306$	−31.7157	−1.81307
$307$	−12.7842	−0.729633	−0.364816	−	0.931079i	$-0.618868\pi$
$307$	−12.7842	−0.729633	−0.364816	+	0.931079i	$0.618868\pi$
$308$	−34.0295	−1.93901
$309$	−5.14366	−0.292613
$310$	37.8394	2.14914
$311$	14.7539	0.836619	0.418309	−	0.908305i	$-0.362623\pi$
$311$	14.7539	0.836619	0.418309	+	0.908305i	$0.362623\pi$
$312$	−34.5493	−1.95597
$313$	−5.22249	−0.295192	−0.147596	−	0.989048i	$-0.547154\pi$
$313$	−5.22249	−0.295192	−0.147596	+	0.989048i	$0.547154\pi$
$314$	−55.8849	−3.15377
$315$	−30.3518	−1.71013
$316$	−44.8587	−2.52350
$317$	−2.84700	−0.159904	−0.0799518	−	0.996799i	$-0.525477\pi$
$317$	−2.84700	−0.159904	−0.0799518	+	0.996799i	$0.525477\pi$
$318$	−74.0137	−4.15048
$319$	6.98426	0.391044
$320$	−16.5281	−0.923949
$321$	15.5531	0.868090
$322$	23.9786	1.33627
$323$	−18.4341	−1.02570
$324$	−8.37365	−0.465203
$325$	−20.3623	−1.12949
$326$	23.4430	1.29839
$327$	2.74712	0.151916
$328$	−65.5216	−3.61782
$329$	17.2853	0.952968
$330$	116.323	6.40340
$331$	−17.4093	−0.956902	−0.478451	−	0.878114i	$-0.658802\pi$
$331$	−17.4093	−0.956902	−0.478451	+	0.878114i	$0.658802\pi$
$332$	−26.6858	−1.46457
$333$	−4.54668	−0.249156
$334$	−37.2488	−2.03817
$335$	−11.9591	−0.653398
$336$	27.3062	1.48967
$337$	−12.7783	−0.696078	−0.348039	−	0.937480i	$-0.613152\pi$
$337$	−12.7783	−0.696078	−0.348039	+	0.937480i	$0.613152\pi$
$338$	20.0821	1.09232
$339$	20.9373	1.13716
$340$	44.6184	2.41977
$341$	−18.1234	−0.981437
$342$	75.1610	4.06424
$343$	19.2609	1.03999
$344$	62.0283	3.34434
$345$	−55.7597	−3.00200
$346$	−51.1194	−2.74820
$347$	16.9491	0.909875	0.454938	−	0.890523i	$-0.349662\pi$
$347$	16.9491	0.909875	0.454938	+	0.890523i	$0.349662\pi$
$348$	−18.1300	−0.971870
$349$	−6.61386	−0.354032	−0.177016	−	0.984208i	$-0.556644\pi$
$349$	−6.61386	−0.354032	−0.177016	+	0.984208i	$0.556644\pi$
$350$	40.5620	2.16813
$351$	9.47292	0.505627
$352$	−12.2422	−0.652509
$353$	−17.1758	−0.914178	−0.457089	−	0.889421i	$-0.651108\pi$
$353$	−17.1758	−0.914178	−0.457089	+	0.889421i	$0.651108\pi$
$354$	−20.2897	−1.07839
$355$	38.1279	2.02362
$356$	−70.0831	−3.71440
$357$	13.6051	0.720059
$358$	39.3562	2.08004
$359$	5.68775	0.300188	0.150094	−	0.988672i	$-0.452042\pi$
$359$	5.68775	0.300188	0.150094	+	0.988672i	$0.452042\pi$
$360$	−96.4201	−5.08179
$361$	24.6859	1.29926
$362$	13.4354	0.706150
$363$	−25.4954	−1.33816
$364$	16.8469	0.883017
$365$	−23.9807	−1.25521
$366$	46.1986	2.41484
$367$	10.7412	0.560686	0.280343	−	0.959900i	$-0.409552\pi$
$367$	10.7412	0.560686	0.280343	+	0.959900i	$0.409552\pi$
$368$	30.2228	1.57547
$369$	52.8109	2.74923
$370$	9.40258	0.488817
$371$	19.1284	0.993095
$372$	47.0454	2.43919
$373$	−29.8133	−1.54367	−0.771836	−	0.635821i	$-0.780662\pi$
$373$	−29.8133	−1.54367	−0.771836	+	0.635821i	$0.780662\pi$
$374$	−31.4140	−1.62438
$375$	−42.6851	−2.20425
$376$	54.9110	2.83182
$377$	−3.45768	−0.178079
$378$	−18.8702	−0.970579
$379$	−30.0416	−1.54313	−0.771567	−	0.636149i	$-0.780527\pi$
$379$	−30.0416	−1.54313	−0.771567	+	0.636149i	$0.780527\pi$
$380$	−105.738	−5.42425
$381$	14.6695	0.751539
$382$	−13.8512	−0.708689
$383$	18.5881	0.949810	0.474905	−	0.880037i	$-0.342482\pi$
$383$	18.5881	0.949810	0.474905	+	0.880037i	$0.342482\pi$
$384$	−45.1428	−2.30368
$385$	−30.0631	−1.53216
$386$	25.2128	1.28330
$387$	−49.9953	−2.54140
$388$	−52.6495	−2.67287
$389$	34.1304	1.73048	0.865241	−	0.501356i	$-0.167165\pi$
$389$	34.1304	1.73048	0.865241	+	0.501356i	$0.167165\pi$
$390$	−57.5879	−2.91608
$391$	15.0583	0.761531
$392$	21.7001	1.09602
$393$	−5.58695	−0.281824
$394$	1.71679	0.0864908
$395$	−39.6300	−1.99400
$396$	87.1321	4.37855
$397$	−26.9599	−1.35308	−0.676540	−	0.736405i	$-0.736522\pi$
$397$	−26.9599	−1.35308	−0.676540	+	0.736405i	$0.736522\pi$
$398$	42.9507	2.15293
$399$	−32.2418	−1.61411
$400$	51.1247	2.55624
$401$	−13.5162	−0.674968	−0.337484	−	0.941331i	$-0.609576\pi$
$401$	−13.5162	−0.674968	−0.337484	+	0.941331i	$0.609576\pi$
$402$	−21.8568	−1.09012
$403$	8.97230	0.446942
$404$	15.8919	0.790652
$405$	−7.39762	−0.367591
$406$	6.88776	0.341834
$407$	−4.50342	−0.223226
$408$	43.2200	2.13971
$409$	13.2780	0.656556	0.328278	−	0.944581i	$-0.393532\pi$
$409$	13.2780	0.656556	0.328278	+	0.944581i	$0.393532\pi$
$410$	−109.214	−5.39368
$411$	10.0177	0.494135
$412$	7.96776	0.392543
$413$	5.24374	0.258028
$414$	−61.3968	−3.01749
$415$	−23.5753	−1.15727
$416$	6.06069	0.297150
$417$	−56.8583	−2.78436
$418$	74.4459	3.64127
$419$	−29.3218	−1.43247	−0.716233	−	0.697861i	$-0.754135\pi$
$419$	−29.3218	−1.43247	−0.716233	+	0.697861i	$0.754135\pi$
$420$	78.0388	3.80790
$421$	28.5734	1.39258	0.696291	−	0.717760i	$-0.254832\pi$
$421$	28.5734	1.39258	0.696291	+	0.717760i	$0.254832\pi$
$422$	11.7010	0.569597
$423$	−44.2587	−2.15193
$424$	60.7660	2.95106
$425$	25.4725	1.23560
$426$	69.6835	3.37618
$427$	−11.9397	−0.577804
$428$	−24.0925	−1.16455
$429$	27.5820	1.33167
$430$	103.391	4.98595
$431$	29.3912	1.41573	0.707863	−	0.706350i	$-0.249659\pi$
$431$	29.3912	1.41573	0.707863	+	0.706350i	$0.249659\pi$
$432$	−23.7842	−1.14432
$433$	−30.0483	−1.44403	−0.722014	−	0.691879i	$-0.756783\pi$
$433$	−30.0483	−1.44403	−0.722014	+	0.691879i	$0.756783\pi$
$434$	−17.8730	−0.857931
$435$	−16.0168	−0.767946
$436$	−4.25541	−0.203797
$437$	−35.6857	−1.70708
$438$	−43.8277	−2.09417
$439$	−1.81365	−0.0865608	−0.0432804	−	0.999063i	$-0.513781\pi$
$439$	−1.81365	−0.0865608	−0.0432804	+	0.999063i	$0.513781\pi$
$440$	−95.5028	−4.55292
$441$	−17.4904	−0.832878
$442$	15.5520	0.739734
$443$	9.68617	0.460204	0.230102	−	0.973167i	$-0.426094\pi$
$443$	9.68617	0.460204	0.230102	+	0.973167i	$0.426094\pi$
$444$	11.6901	0.554790
$445$	−61.9143	−2.93502
$446$	10.9556	0.518762
$447$	−37.9622	−1.79555
$448$	7.80685	0.368839
$449$	9.52376	0.449454	0.224727	−	0.974422i	$-0.427851\pi$
$449$	9.52376	0.449454	0.224727	+	0.974422i	$0.427851\pi$
$450$	−103.858	−4.89593
$451$	52.3085	2.46311
$452$	−32.4328	−1.52551
$453$	−13.5820	−0.638140
$454$	12.3749	0.580782
$455$	14.8832	0.697736
$456$	−102.424	−4.79645
$457$	25.1797	1.17786	0.588929	−	0.808185i	$-0.299550\pi$
$457$	25.1797	1.17786	0.588929	+	0.808185i	$0.299550\pi$
$458$	6.76733	0.316217
$459$	−11.8503	−0.553125
$460$	86.3743	4.02722
$461$	22.1288	1.03064	0.515319	−	0.856998i	$-0.327673\pi$
$461$	22.1288	1.03064	0.515319	+	0.856998i	$0.327673\pi$
$462$	−54.9439	−2.55622
$463$	21.1050	0.980834	0.490417	−	0.871488i	$-0.336845\pi$
$463$	21.1050	0.980834	0.490417	+	0.871488i	$0.336845\pi$
$464$	8.68140	0.403024
$465$	41.5618	1.92738
$466$	−72.4071	−3.35420
$467$	−36.7561	−1.70087	−0.850435	−	0.526080i	$-0.823661\pi$
$467$	−36.7561	−1.70087	−0.850435	+	0.526080i	$0.823661\pi$
$468$	−43.1362	−1.99397
$469$	5.64875	0.260835
$470$	91.5276	4.22185
$471$	−61.3825	−2.82836
$472$	16.6581	0.766749
$473$	−49.5197	−2.27692
$474$	−72.4288	−3.32676
$475$	−60.3657	−2.76977
$476$	−21.0749	−0.965968
$477$	−48.9779	−2.24254
$478$	0.238286	0.0108990
$479$	−30.3823	−1.38820	−0.694102	−	0.719876i	$-0.744199\pi$
$479$	−30.3823	−1.38820	−0.694102	+	0.719876i	$0.744199\pi$
$480$	28.0745	1.28142
$481$	2.22949	0.101656
$482$	−11.1369	−0.507270
$483$	26.3374	1.19839
$484$	39.4936	1.79516
$485$	−46.5127	−2.11203
$486$	−45.4007	−2.05942
$487$	33.0725	1.49866	0.749330	−	0.662197i	$-0.230376\pi$
$487$	33.0725	1.49866	0.749330	+	0.662197i	$0.230376\pi$
$488$	−37.9295	−1.71699
$489$	25.7492	1.16442
$490$	36.1704	1.63401
$491$	8.48729	0.383026	0.191513	−	0.981490i	$-0.438661\pi$
$491$	8.48729	0.383026	0.191513	+	0.981490i	$0.438661\pi$
$492$	−135.784	−6.12163
$493$	4.32544	0.194808
$494$	−36.8557	−1.65822
$495$	76.9760	3.45982
$496$	−22.5273	−1.01151
$497$	−18.0093	−0.807826
$498$	−43.0868	−1.93077
$499$	2.15049	0.0962692	0.0481346	−	0.998841i	$-0.484672\pi$
$499$	2.15049	0.0962692	0.0481346	+	0.998841i	$0.484672\pi$
$500$	66.1211	2.95702
$501$	−40.9131	−1.82786
$502$	30.0043	1.33916
$503$	−2.94521	−0.131320	−0.0656601	−	0.997842i	$-0.520915\pi$
$503$	−2.94521	−0.131320	−0.0656601	+	0.997842i	$0.520915\pi$
$504$	45.5428	2.02864
$505$	14.0396	0.624752
$506$	−60.8127	−2.70345
$507$	22.0576	0.979613
$508$	−22.7236	−1.00820
$509$	27.1085	1.20156	0.600782	−	0.799413i	$-0.294856\pi$
$509$	27.1085	1.20156	0.600782	+	0.799413i	$0.294856\pi$
$510$	72.0406	3.19001
$511$	11.3270	0.501076
$512$	47.9364	2.11851
$513$	28.0833	1.23991
$514$	12.7517	0.562454
$515$	7.03904	0.310177
$516$	128.545	5.65888
$517$	−43.8376	−1.92798
$518$	−4.44119	−0.195135
$519$	−56.1482	−2.46463
$520$	47.2803	2.07338
$521$	−28.5679	−1.25158	−0.625790	−	0.779991i	$-0.715223\pi$
$521$	−28.5679	−1.25158	−0.625790	+	0.779991i	$0.715223\pi$
$522$	−17.6360	−0.771907
$523$	8.28521	0.362287	0.181143	−	0.983457i	$-0.442020\pi$
$523$	8.28521	0.362287	0.181143	+	0.983457i	$0.442020\pi$
$524$	8.65444	0.378071
$525$	44.5522	1.94442
$526$	48.0392	2.09461
$527$	−11.2241	−0.488928
$528$	−69.2519	−3.01380
$529$	6.15058	0.267416
$530$	101.287	4.39962
$531$	−13.4265	−0.582662
$532$	49.9441	2.16535
$533$	−25.8962	−1.12169
$534$	−113.156	−4.89674
$535$	−21.2842	−0.920198
$536$	17.9447	0.775091
$537$	43.2278	1.86542
$538$	25.7082	1.10836
$539$	−17.3240	−0.746198
$540$	−67.9733	−2.92510
$541$	9.46904	0.407106	0.203553	−	0.979064i	$-0.434751\pi$
$541$	9.46904	0.407106	0.203553	+	0.979064i	$0.434751\pi$
$542$	−14.3005	−0.614258
$543$	14.7571	0.633288
$544$	−7.58173	−0.325064
$545$	−3.75941	−0.161035
$546$	27.2009	1.16409
$547$	−39.1040	−1.67197	−0.835983	−	0.548755i	$-0.815102\pi$
$547$	−39.1040	−1.67197	−0.835983	+	0.548755i	$0.815102\pi$
$548$	−15.5178	−0.662888
$549$	30.5715	1.30476
$550$	−102.870	−4.38640
$551$	−10.2506	−0.436690
$552$	83.6673	3.56112
$553$	18.7187	0.796002
$554$	−56.8089	−2.41358
$555$	10.3275	0.438380
$556$	88.0761	3.73526
$557$	−8.96933	−0.380043	−0.190021	−	0.981780i	$-0.560856\pi$
$557$	−8.96933	−0.380043	−0.190021	+	0.981780i	$0.560856\pi$
$558$	45.7635	1.93732
$559$	24.5156	1.03690
$560$	−37.3682	−1.57910
$561$	−34.5043	−1.45677
$562$	56.1571	2.36885
$563$	−36.8971	−1.55503	−0.777513	−	0.628867i	$-0.783519\pi$
$563$	−36.8971	−1.55503	−0.777513	+	0.628867i	$0.783519\pi$
$564$	113.795	4.79165
$565$	−28.6524	−1.20542
$566$	39.7758	1.67190
$567$	3.49417	0.146742
$568$	−57.2109	−2.40052
$569$	−6.15740	−0.258131	−0.129066	−	0.991636i	$-0.541198\pi$
$569$	−6.15740	−0.258131	−0.129066	+	0.991636i	$0.541198\pi$
$570$	−170.724	−7.15086
$571$	−14.5119	−0.607303	−0.303652	−	0.952783i	$-0.598206\pi$
$571$	−14.5119	−0.607303	−0.303652	+	0.952783i	$0.598206\pi$
$572$	−42.7258	−1.78646
$573$	−15.2138	−0.635565
$574$	51.5857	2.15315
$575$	49.3109	2.05641
$576$	−19.9893	−0.832888
$577$	−42.7898	−1.78136	−0.890681	−	0.454629i	$-0.849772\pi$
$577$	−42.7898	−1.78136	−0.890681	+	0.454629i	$0.849772\pi$
$578$	23.0633	0.959308
$579$	27.6930	1.15088
$580$	24.8107	1.03021
$581$	11.1355	0.461978
$582$	−85.0076	−3.52368
$583$	−48.5119	−2.00916
$584$	35.9830	1.48899
$585$	−38.1083	−1.57558
$586$	−70.2377	−2.90149
$587$	−29.9670	−1.23687	−0.618436	−	0.785835i	$-0.712233\pi$
$587$	−29.9670	−1.23687	−0.618436	+	0.785835i	$0.712233\pi$
$588$	44.9703	1.85455
$589$	26.5992	1.09600
$590$	27.7662	1.14312
$591$	1.88568	0.0775665
$592$	−5.59772	−0.230065
$593$	−16.3470	−0.671292	−0.335646	−	0.941988i	$-0.608955\pi$
$593$	−16.3470	−0.671292	−0.335646	+	0.941988i	$0.608955\pi$
$594$	47.8572	1.96361
$595$	−18.6184	−0.763282
$596$	58.8052	2.40875
$597$	47.1759	1.93078
$598$	30.1063	1.23114
$599$	−21.9570	−0.897138	−0.448569	−	0.893748i	$-0.648066\pi$
$599$	−21.9570	−0.897138	−0.448569	+	0.893748i	$0.648066\pi$
$600$	141.531	5.77798
$601$	−17.1625	−0.700073	−0.350036	−	0.936736i	$-0.613831\pi$
$601$	−17.1625	−0.700073	−0.350036	+	0.936736i	$0.613831\pi$
$602$	−48.8354	−1.99038
$603$	−14.4635	−0.589001
$604$	21.0392	0.856072
$605$	34.8902	1.41849
$606$	25.6590	1.04233
$607$	−40.3817	−1.63904	−0.819521	−	0.573049i	$-0.805760\pi$
$607$	−40.3817	−1.63904	−0.819521	+	0.573049i	$0.805760\pi$
$608$	17.9674	0.728676
$609$	7.56533	0.306562
$610$	−63.2223	−2.55980
$611$	21.7026	0.877992
$612$	53.9621	2.18129
$613$	−38.1289	−1.54001	−0.770007	−	0.638036i	$-0.779747\pi$
$613$	−38.1289	−1.54001	−0.770007	+	0.638036i	$0.779747\pi$
$614$	31.9743	1.29038
$615$	−119.957	−4.83715
$616$	45.1095	1.81752
$617$	39.2989	1.58211	0.791057	−	0.611743i	$-0.209531\pi$
$617$	39.2989	1.58211	0.791057	+	0.611743i	$0.209531\pi$
$618$	12.8647	0.517495
$619$	47.8885	1.92480	0.962400	−	0.271637i	$-0.0875651\pi$
$619$	47.8885	1.92480	0.962400	+	0.271637i	$0.0875651\pi$
$620$	−64.3811	−2.58561
$621$	−22.9404	−0.920566
$622$	−36.9008	−1.47959
$623$	29.2444	1.17165
$624$	34.2843	1.37247
$625$	12.7484	0.509936
$626$	13.0619	0.522057
$627$	81.7694	3.26555
$628$	95.0842	3.79427
$629$	−2.78903	−0.111206
$630$	75.9124	3.02442
$631$	−3.39586	−0.135187	−0.0675935	−	0.997713i	$-0.521532\pi$
$631$	−3.39586	−0.135187	−0.0675935	+	0.997713i	$0.521532\pi$
$632$	59.4647	2.36538
$633$	12.8521	0.510825
$634$	7.12059	0.282795
$635$	−20.0750	−0.796651
$636$	125.929	4.99341
$637$	8.57655	0.339815
$638$	−17.4682	−0.691573
$639$	46.1125	1.82418
$640$	61.7774	2.44197
$641$	−4.24075	−0.167499	−0.0837497	−	0.996487i	$-0.526690\pi$
$641$	−4.24075	−0.167499	−0.0837497	+	0.996487i	$0.526690\pi$
$642$	−38.8996	−1.53524
$643$	36.9933	1.45888	0.729438	−	0.684047i	$-0.239782\pi$
$643$	36.9933	1.45888	0.729438	+	0.684047i	$0.239782\pi$
$644$	−40.7978	−1.60766
$645$	113.562	4.47149
$646$	46.1053	1.81399
$647$	1.07387	0.0422183	0.0211092	−	0.999777i	$-0.493280\pi$
$647$	1.07387	0.0422183	0.0211092	+	0.999777i	$0.493280\pi$
$648$	11.1001	0.436054
$649$	−13.2988	−0.522023
$650$	50.9277	1.99755
$651$	−19.6312	−0.769407
$652$	−39.8866	−1.56208
$653$	−5.36182	−0.209824	−0.104912	−	0.994481i	$-0.533456\pi$
$653$	−5.36182	−0.209824	−0.104912	+	0.994481i	$0.533456\pi$
$654$	−6.87078	−0.268669
$655$	7.64568	0.298742
$656$	65.0192	2.53857
$657$	−29.0026	−1.13150
$658$	−43.2319	−1.68536
$659$	45.0898	1.75645	0.878224	−	0.478250i	$-0.158729\pi$
$659$	45.0898	1.75645	0.878224	+	0.478250i	$0.158729\pi$
$660$	−197.916	−7.70388
$661$	−21.3253	−0.829457	−0.414729	−	0.909945i	$-0.636123\pi$
$661$	−21.3253	−0.829457	−0.414729	+	0.909945i	$0.636123\pi$
$662$	43.5421	1.69231
$663$	17.0819	0.663407
$664$	35.3747	1.37280
$665$	44.1226	1.71100
$666$	11.3716	0.440641
$667$	8.37340	0.324219
$668$	63.3762	2.45210
$669$	12.0333	0.465235
$670$	29.9108	1.15555
$671$	30.2807	1.16897
$672$	−13.2607	−0.511541
$673$	41.9257	1.61612	0.808058	−	0.589103i	$-0.200519\pi$
$673$	41.9257	1.61612	0.808058	+	0.589103i	$0.200519\pi$
$674$	31.9596	1.23104
$675$	−38.8058	−1.49364
$676$	−34.1682	−1.31416
$677$	15.6844	0.602799	0.301399	−	0.953498i	$-0.402546\pi$
$677$	15.6844	0.602799	0.301399	+	0.953498i	$0.402546\pi$
$678$	−52.3659	−2.01110
$679$	21.9697	0.843119
$680$	−59.1461	−2.26815
$681$	13.5922	0.520856
$682$	45.3281	1.73570
$683$	47.2032	1.80618	0.903090	−	0.429451i	$-0.141293\pi$
$683$	47.2032	1.80618	0.903090	+	0.429451i	$0.141293\pi$
$684$	−127.881	−4.88966
$685$	−13.7091	−0.523796
$686$	−48.1730	−1.83925
$687$	7.43305	0.283589
$688$	−61.5527	−2.34667
$689$	24.0167	0.914962
$690$	139.460	5.30914
$691$	−35.3951	−1.34649	−0.673246	−	0.739419i	$-0.735101\pi$
$691$	−35.3951	−1.34649	−0.673246	+	0.739419i	$0.735101\pi$
$692$	86.9761	3.30633
$693$	−36.3587	−1.38115
$694$	−42.3911	−1.60914
$695$	77.8100	2.95150
$696$	24.0331	0.910974
$697$	32.3953	1.22706
$698$	16.5418	0.626117
$699$	−79.5300	−3.00810
$700$	−69.0133	−2.60846
$701$	38.7447	1.46337	0.731683	−	0.681645i	$-0.238735\pi$
$701$	38.7447	1.46337	0.731683	+	0.681645i	$0.238735\pi$
$702$	−23.6925	−0.894217
$703$	6.60953	0.249283
$704$	−19.7991	−0.746208
$705$	100.531	3.78623
$706$	42.9582	1.61675
$707$	−6.63141	−0.249400
$708$	34.5215	1.29740
$709$	−37.8365	−1.42098	−0.710490	−	0.703707i	$-0.751527\pi$
$709$	−37.8365	−1.42098	−0.710490	+	0.703707i	$0.751527\pi$
$710$	−95.3612	−3.57884
$711$	−47.9291	−1.79748
$712$	92.9022	3.48166
$713$	−21.7281	−0.813722
$714$	−34.0275	−1.27345
$715$	−37.7457	−1.41161
$716$	−66.9618	−2.50248
$717$	0.261727	0.00977438
$718$	−14.2255	−0.530892
$719$	−26.3921	−0.984259	−0.492129	−	0.870522i	$-0.663781\pi$
$719$	−26.3921	−0.984259	−0.492129	+	0.870522i	$0.663781\pi$
$720$	95.6808	3.56581
$721$	−3.32480	−0.123822
$722$	−61.7414	−2.29778
$723$	−12.2324	−0.454929
$724$	−22.8594	−0.849563
$725$	14.1644	0.526052
$726$	63.7662	2.36658
$727$	4.00161	0.148411	0.0742057	−	0.997243i	$-0.476358\pi$
$727$	4.00161	0.148411	0.0742057	+	0.997243i	$0.476358\pi$
$728$	−22.3322	−0.827688
$729$	−43.9636	−1.62828
$730$	59.9777	2.21988
$731$	−30.6682	−1.13430
$732$	−78.6037	−2.90528
$733$	−24.6358	−0.909944	−0.454972	−	0.890506i	$-0.650351\pi$
$733$	−24.6358	−0.909944	−0.454972	+	0.890506i	$0.650351\pi$
$734$	−26.8646	−0.991591
$735$	39.7286	1.46541
$736$	−14.6771	−0.541004
$737$	−14.3259	−0.527703
$738$	−132.085	−4.86210
$739$	−8.83046	−0.324834	−0.162417	−	0.986722i	$-0.551929\pi$
$739$	−8.83046	−0.324834	−0.162417	+	0.986722i	$0.551929\pi$
$740$	−15.9978	−0.588092
$741$	−40.4813	−1.48712
$742$	−47.8416	−1.75632
$743$	−23.7277	−0.870485	−0.435242	−	0.900313i	$-0.643337\pi$
$743$	−23.7277	−0.870485	−0.435242	+	0.900313i	$0.643337\pi$
$744$	−62.3634	−2.28635
$745$	51.9509	1.90333
$746$	74.5655	2.73004
$747$	−28.5123	−1.04321
$748$	53.4487	1.95428
$749$	10.0533	0.367341
$750$	106.759	3.89828
$751$	−18.5947	−0.678530	−0.339265	−	0.940691i	$-0.610178\pi$
$751$	−18.5947	−0.678530	−0.339265	+	0.940691i	$0.610178\pi$
$752$	−54.4899	−1.98704
$753$	32.9559	1.20098
$754$	8.64794	0.314939
$755$	18.5869	0.676445
$756$	32.1063	1.16770
$757$	25.8715	0.940315	0.470157	−	0.882583i	$-0.344197\pi$
$757$	25.8715	0.940315	0.470157	+	0.882583i	$0.344197\pi$
$758$	75.1365	2.72908
$759$	−66.7950	−2.42450
$760$	140.166	5.08437
$761$	21.1880	0.768065	0.384032	−	0.923320i	$-0.374535\pi$
$761$	21.1880	0.768065	0.384032	+	0.923320i	$0.374535\pi$
$762$	−36.6895	−1.32912
$763$	1.77571	0.0642850
$764$	23.5668	0.852618
$765$	47.6723	1.72359
$766$	−46.4905	−1.67977
$767$	6.58379	0.237727
$768$	88.7506	3.20251
$769$	18.3133	0.660394	0.330197	−	0.943912i	$-0.392885\pi$
$769$	18.3133	0.660394	0.330197	+	0.943912i	$0.392885\pi$
$770$	75.1902	2.70967
$771$	14.0061	0.504419
$772$	−42.8978	−1.54392
$773$	24.6088	0.885118	0.442559	−	0.896740i	$-0.354071\pi$
$773$	24.6088	0.885118	0.442559	+	0.896740i	$0.354071\pi$
$774$	125.042	4.49456
$775$	−36.7550	−1.32028
$776$	69.7921	2.50539
$777$	−4.87809	−0.175000
$778$	−85.3630	−3.06041
$779$	−76.7715	−2.75063
$780$	97.9818	3.50831
$781$	45.6737	1.63434
$782$	−37.6621	−1.34679
$783$	−6.58955	−0.235491
$784$	−21.5337	−0.769059
$785$	84.0013	2.99813
$786$	13.9734	0.498416
$787$	24.0390	0.856897	0.428449	−	0.903566i	$-0.359060\pi$
$787$	24.0390	0.856897	0.428449	+	0.903566i	$0.359060\pi$
$788$	−2.92100	−0.104056
$789$	52.7649	1.87848
$790$	99.1180	3.52646
$791$	13.5336	0.481200
$792$	−115.502	−4.10420
$793$	−14.9910	−0.532345
$794$	67.4291	2.39297
$795$	111.251	3.94566
$796$	−73.0776	−2.59017
$797$	−51.9727	−1.84097	−0.920484	−	0.390779i	$-0.872206\pi$
$797$	−51.9727	−1.84097	−0.920484	+	0.390779i	$0.872206\pi$
$798$	80.6395	2.85461
$799$	−27.1492	−0.960470
$800$	−24.8276	−0.877789
$801$	−74.8800	−2.64575
$802$	33.8052	1.19370
$803$	−28.7267	−1.01374
$804$	37.1878	1.31151
$805$	−36.0425	−1.27033
$806$	−22.4405	−0.790432
$807$	28.2372	0.993996
$808$	−21.0663	−0.741111
$809$	−51.6974	−1.81759	−0.908793	−	0.417248i	$-0.862995\pi$
$809$	−51.6974	−1.81759	−0.908793	+	0.417248i	$0.862995\pi$
$810$	18.5021	0.650096
$811$	−36.2942	−1.27446	−0.637230	−	0.770674i	$-0.719920\pi$
$811$	−36.2942	−1.27446	−0.637230	+	0.770674i	$0.719920\pi$
$812$	−11.7190	−0.411257
$813$	−15.7073	−0.550877
$814$	11.2634	0.394783
$815$	−35.2374	−1.23431
$816$	−42.8886	−1.50140
$817$	72.6785	2.54270
$818$	−33.2094	−1.16114
$819$	18.0000	0.628970
$820$	185.819	6.48909
$821$	6.98642	0.243828	0.121914	−	0.992541i	$-0.461097\pi$
$821$	6.98642	0.243828	0.121914	+	0.992541i	$0.461097\pi$
$822$	−25.0550	−0.873893
$823$	37.5741	1.30975	0.654875	−	0.755737i	$-0.272721\pi$
$823$	37.5741	1.30975	0.654875	+	0.755737i	$0.272721\pi$
$824$	−10.5621	−0.367947
$825$	−112.990	−3.93380
$826$	−13.1150	−0.456330
$827$	32.0081	1.11303	0.556516	−	0.830837i	$-0.312138\pi$
$827$	32.0081	1.11303	0.556516	+	0.830837i	$0.312138\pi$
$828$	104.462	3.63032
$829$	5.74489	0.199528	0.0997642	−	0.995011i	$-0.468191\pi$
$829$	5.74489	0.199528	0.0997642	+	0.995011i	$0.468191\pi$
$830$	58.9638	2.04666
$831$	−62.3974	−2.16454
$832$	9.80190	0.339820
$833$	−10.7290	−0.371738
$834$	142.207	4.92424
$835$	55.9891	1.93758
$836$	−126.664	−4.38078
$837$	17.0992	0.591033
$838$	73.3364	2.53336
$839$	−1.50858	−0.0520820	−0.0260410	−	0.999661i	$-0.508290\pi$
$839$	−1.50858	−0.0520820	−0.0260410	+	0.999661i	$0.508290\pi$
$840$	−103.448	−3.56930
$841$	−26.5948	−0.917061
$842$	−71.4644	−2.46283
$843$	61.6815	2.12442
$844$	−19.9085	−0.685278
$845$	−30.1856	−1.03842
$846$	110.695	3.80576
$847$	−16.4800	−0.566258
$848$	−60.3001	−2.07071
$849$	43.6886	1.49939
$850$	−63.7089	−2.18520
$851$	−5.39913	−0.185080
$852$	−118.562	−4.06185
$853$	−42.4939	−1.45496	−0.727482	−	0.686127i	$-0.759309\pi$
$853$	−42.4939	−1.45496	−0.727482	+	0.686127i	$0.759309\pi$
$854$	29.8623	1.02187
$855$	−112.975	−3.86367
$856$	31.9370	1.09158
$857$	14.0921	0.481376	0.240688	−	0.970603i	$-0.422627\pi$
$857$	14.0921	0.481376	0.240688	+	0.970603i	$0.422627\pi$
$858$	−68.9850	−2.35511
$859$	22.2933	0.760636	0.380318	−	0.924856i	$-0.375815\pi$
$859$	22.2933	0.760636	0.380318	+	0.924856i	$0.375815\pi$
$860$	−175.912	−5.99856
$861$	56.6604	1.93098
$862$	−73.5099	−2.50376
$863$	50.3130	1.71267	0.856337	−	0.516417i	$-0.172734\pi$
$863$	50.3130	1.71267	0.856337	+	0.516417i	$0.172734\pi$
$864$	11.5503	0.392949
$865$	76.8382	2.61258
$866$	75.1532	2.55381
$867$	25.3321	0.860324
$868$	30.4096	1.03217
$869$	−47.4731	−1.61041
$870$	40.0593	1.35814
$871$	7.09230	0.240313
$872$	5.64098	0.191028
$873$	−56.2530	−1.90388
$874$	89.2529	3.01902
$875$	−27.5911	−0.932751
$876$	74.5697	2.51948
$877$	−10.1060	−0.341256	−0.170628	−	0.985336i	$-0.554580\pi$
$877$	−10.1060	−0.341256	−0.170628	+	0.985336i	$0.554580\pi$
$878$	4.53609	0.153086
$879$	−77.1472	−2.60211
$880$	94.7705	3.19471
$881$	−47.2631	−1.59233	−0.796167	−	0.605077i	$-0.793142\pi$
$881$	−47.2631	−1.59233	−0.796167	+	0.605077i	$0.793142\pi$
$882$	43.7450	1.47297
$883$	49.0860	1.65187	0.825937	−	0.563762i	$-0.190647\pi$
$883$	49.0860	1.65187	0.825937	+	0.563762i	$0.190647\pi$
$884$	−26.4607	−0.889969
$885$	30.4977	1.02517
$886$	−24.2259	−0.813886
$887$	−8.79015	−0.295144	−0.147572	−	0.989051i	$-0.547146\pi$
$887$	−8.79015	−0.295144	−0.147572	+	0.989051i	$0.547146\pi$
$888$	−15.4965	−0.520027
$889$	9.48217	0.318022
$890$	154.853	5.19067
$891$	−8.86166	−0.296877
$892$	−18.6402	−0.624118
$893$	64.3391	2.15303
$894$	94.9466	3.17549
$895$	−59.1568	−1.97739
$896$	−29.1798	−0.974828
$897$	33.0680	1.10411
$898$	−23.8197	−0.794874
$899$	−6.24131	−0.208159
$900$	176.708	5.89026
$901$	−30.0441	−1.00091
$902$	−130.828	−4.35609
$903$	−53.6395	−1.78501
$904$	42.9929	1.42992
$905$	−20.1949	−0.671302
$906$	33.9698	1.12857
$907$	36.5862	1.21483	0.607413	−	0.794386i	$-0.292207\pi$
$907$	36.5862	1.21483	0.607413	+	0.794386i	$0.292207\pi$
$908$	−21.0550	−0.698735
$909$	16.9796	0.563179
$910$	−37.2242	−1.23397
$911$	−52.0158	−1.72336	−0.861679	−	0.507453i	$-0.830587\pi$
$911$	−52.0158	−1.72336	−0.861679	+	0.507453i	$0.830587\pi$
$912$	101.639	3.36560
$913$	−28.2410	−0.934642
$914$	−62.9765	−2.08308
$915$	−69.4417	−2.29567
$916$	−11.5141	−0.380438
$917$	−3.61134	−0.119257
$918$	29.6386	0.978220
$919$	−30.5085	−1.00638	−0.503191	−	0.864175i	$-0.667841\pi$
$919$	−30.5085	−1.00638	−0.503191	+	0.864175i	$0.667841\pi$
$920$	−114.498	−3.77488
$921$	35.1197	1.15724
$922$	−55.3459	−1.82272
$923$	−22.6116	−0.744269
$924$	93.4832	3.07537
$925$	−9.13313	−0.300295
$926$	−52.7854	−1.73464
$927$	8.51311	0.279607
$928$	−4.21593	−0.138395
$929$	−17.6283	−0.578367	−0.289183	−	0.957274i	$-0.593384\pi$
$929$	−17.6283	−0.578367	−0.289183	+	0.957274i	$0.593384\pi$
$930$	−103.950	−3.40864
$931$	25.4259	0.833301
$932$	123.196	4.03541
$933$	−40.5308	−1.32692
$934$	91.9301	3.00804
$935$	47.2187	1.54422
$936$	57.1814	1.86903
$937$	−13.6281	−0.445211	−0.222606	−	0.974909i	$-0.571456\pi$
$937$	−13.6281	−0.445211	−0.222606	+	0.974909i	$0.571456\pi$
$938$	−14.1280	−0.461295
$939$	14.3468	0.468190
$940$	−155.728	−5.07928
$941$	−16.9766	−0.553421	−0.276711	−	0.960953i	$-0.589244\pi$
$941$	−16.9766	−0.553421	−0.276711	+	0.960953i	$0.589244\pi$
$942$	153.523	5.00204
$943$	62.7124	2.04220
$944$	−16.5303	−0.538016
$945$	28.3640	0.922682
$946$	123.853	4.02680
$947$	−52.7863	−1.71532	−0.857662	−	0.514214i	$-0.828084\pi$
$947$	−52.7863	−1.71532	−0.857662	+	0.514214i	$0.828084\pi$
$948$	123.232	4.00240
$949$	14.2216	0.461653
$950$	150.980	4.89842
$951$	7.82106	0.253615
$952$	27.9369	0.905441
$953$	−29.5778	−0.958120	−0.479060	−	0.877782i	$-0.659022\pi$
$953$	−29.5778	−0.958120	−0.479060	+	0.877782i	$0.659022\pi$
$954$	122.498	3.96601
$955$	20.8199	0.673716
$956$	−0.405427	−0.0131124
$957$	−19.1866	−0.620215
$958$	75.9888	2.45509
$959$	6.47530	0.209098
$960$	45.4047	1.46543
$961$	−14.8045	−0.477564
$962$	−5.57615	−0.179782
$963$	−25.7415	−0.829507
$964$	18.9486	0.610292
$965$	−37.8976	−1.21997
$966$	−65.8720	−2.11940
$967$	−20.1261	−0.647210	−0.323605	−	0.946192i	$-0.604895\pi$
$967$	−20.1261	−0.647210	−0.323605	+	0.946192i	$0.604895\pi$
$968$	−52.3527	−1.68268
$969$	50.6408	1.62682
$970$	116.332	3.73520
$971$	−11.7292	−0.376407	−0.188203	−	0.982130i	$-0.560266\pi$
$971$	−11.7292	−0.376407	−0.188203	+	0.982130i	$0.560266\pi$
$972$	77.2460	2.47767
$973$	−36.7526	−1.17823
$974$	−82.7171	−2.65043
$975$	55.9376	1.79144
$976$	37.6387	1.20479
$977$	31.0277	0.992665	0.496333	−	0.868132i	$-0.334680\pi$
$977$	31.0277	0.992665	0.496333	+	0.868132i	$0.334680\pi$
$978$	−64.4008	−2.05931
$979$	−74.1675	−2.37040
$980$	−61.5414	−1.96587
$981$	−4.54668	−0.145164
$982$	−21.2274	−0.677394
$983$	−25.3519	−0.808599	−0.404299	−	0.914627i	$-0.632485\pi$
$983$	−25.3519	−0.808599	−0.404299	+	0.914627i	$0.632485\pi$
$984$	179.996	5.73805
$985$	−2.58053	−0.0822226
$986$	−10.8183	−0.344525
$987$	−47.4848	−1.51146
$988$	62.7074	1.99499
$989$	−59.3689	−1.88782
$990$	−192.523	−6.11880
$991$	−46.7573	−1.48529	−0.742647	−	0.669683i	$-0.766430\pi$
$991$	−46.7573	−1.48529	−0.742647	+	0.669683i	$0.766430\pi$
$992$	10.9399	0.347342
$993$	47.8255	1.51770
$994$	45.0427	1.42867
$995$	−64.5597	−2.04668
$996$	73.3091	2.32289
$997$	−5.36141	−0.169798	−0.0848989	−	0.996390i	$-0.527057\pi$
$997$	−5.36141	−0.169798	−0.0848989	+	0.996390i	$0.527057\pi$
$998$	−5.37856	−0.170255
$999$	4.24891	0.134429

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.d.1.9	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.d.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-2.50108 q^{2} -2.74712 q^{3} +4.25541 q^{4} +3.75941 q^{5} +6.87078 q^{6} -1.77571 q^{7} -5.64098 q^{8} +4.54668 q^{9} +O(q^{10})\)	\(q-2.50108 q^{2} -2.74712 q^{3} +4.25541 q^{4} +3.75941 q^{5} +6.87078 q^{6} -1.77571 q^{7} -5.64098 q^{8} +4.54668 q^{9} -9.40258 q^{10} +4.50342 q^{11} -11.6901 q^{12} -2.22949 q^{13} +4.44119 q^{14} -10.3275 q^{15} +5.59772 q^{16} +2.78903 q^{17} -11.3716 q^{18} -6.60953 q^{19} +15.9978 q^{20} +4.87809 q^{21} -11.2634 q^{22} +5.39913 q^{23} +15.4965 q^{24} +9.13313 q^{25} +5.57615 q^{26} -4.24891 q^{27} -7.55638 q^{28} +1.55088 q^{29} +25.8300 q^{30} -4.02437 q^{31} -2.71842 q^{32} -12.3714 q^{33} -6.97558 q^{34} -6.67561 q^{35} +19.3480 q^{36} -1.00000 q^{37} +16.5310 q^{38} +6.12469 q^{39} -21.2067 q^{40} +11.6153 q^{41} -12.2005 q^{42} -10.9960 q^{43} +19.1639 q^{44} +17.0928 q^{45} -13.5037 q^{46} -9.73430 q^{47} -15.3776 q^{48} -3.84686 q^{49} -22.8427 q^{50} -7.66179 q^{51} -9.48742 q^{52} -10.7722 q^{53} +10.6269 q^{54} +16.9302 q^{55} +10.0167 q^{56} +18.1572 q^{57} -3.87888 q^{58} -2.95304 q^{59} -43.9480 q^{60} +6.72393 q^{61} +10.0653 q^{62} -8.07357 q^{63} -4.39647 q^{64} -8.38157 q^{65} +30.9420 q^{66} -3.18113 q^{67} +11.8685 q^{68} -14.8321 q^{69} +16.6962 q^{70} +10.1420 q^{71} -25.6477 q^{72} -6.37886 q^{73} +2.50108 q^{74} -25.0898 q^{75} -28.1263 q^{76} -7.99676 q^{77} -15.3184 q^{78} -10.5416 q^{79} +21.0441 q^{80} -1.96776 q^{81} -29.0508 q^{82} -6.27102 q^{83} +20.7583 q^{84} +10.4851 q^{85} +27.5019 q^{86} -4.26046 q^{87} -25.4037 q^{88} -16.4692 q^{89} -42.7505 q^{90} +3.95893 q^{91} +22.9755 q^{92} +11.0554 q^{93} +24.3463 q^{94} -24.8479 q^{95} +7.46782 q^{96} -12.3723 q^{97} +9.62132 q^{98} +20.4756 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) \) 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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