LMFDB - Embedded newform 4033.2.a.c.1.13

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			1.13
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)

$f(q)$	$=$	$q-2.16010 q^{2} -1.27573 q^{3} +2.66602 q^{4} -3.85876 q^{5} +2.75571 q^{6} +4.13321 q^{7} -1.43868 q^{8} -1.37250 q^{9} +O(q^{10})$	\(q-2.16010 q^{2} -1.27573 q^{3} +2.66602 q^{4} -3.85876 q^{5} +2.75571 q^{6} +4.13321 q^{7} -1.43868 q^{8} -1.37250 q^{9} +8.33530 q^{10} -1.69034 q^{11} -3.40114 q^{12} +0.739372 q^{13} -8.92814 q^{14} +4.92275 q^{15} -2.22436 q^{16} -3.74928 q^{17} +2.96474 q^{18} +1.53553 q^{19} -10.2876 q^{20} -5.27287 q^{21} +3.65129 q^{22} +1.06976 q^{23} +1.83537 q^{24} +9.89004 q^{25} -1.59712 q^{26} +5.57815 q^{27} +11.0192 q^{28} +2.28894 q^{29} -10.6336 q^{30} -6.79638 q^{31} +7.68220 q^{32} +2.15642 q^{33} +8.09881 q^{34} -15.9491 q^{35} -3.65913 q^{36} +1.00000 q^{37} -3.31690 q^{38} -0.943241 q^{39} +5.55152 q^{40} -2.69734 q^{41} +11.3899 q^{42} +8.08618 q^{43} -4.50648 q^{44} +5.29617 q^{45} -2.31079 q^{46} -7.30426 q^{47} +2.83769 q^{48} +10.0834 q^{49} -21.3635 q^{50} +4.78308 q^{51} +1.97118 q^{52} -10.9530 q^{53} -12.0494 q^{54} +6.52260 q^{55} -5.94636 q^{56} -1.95893 q^{57} -4.94433 q^{58} +14.6621 q^{59} +13.1242 q^{60} -11.7906 q^{61} +14.6808 q^{62} -5.67285 q^{63} -12.1456 q^{64} -2.85306 q^{65} -4.65807 q^{66} -10.0426 q^{67} -9.99567 q^{68} -1.36473 q^{69} +34.4516 q^{70} -11.4280 q^{71} +1.97459 q^{72} +8.90501 q^{73} -2.16010 q^{74} -12.6171 q^{75} +4.09377 q^{76} -6.98651 q^{77} +2.03749 q^{78} -1.53896 q^{79} +8.58328 q^{80} -2.99872 q^{81} +5.82652 q^{82} +13.5616 q^{83} -14.0576 q^{84} +14.4676 q^{85} -17.4669 q^{86} -2.92007 q^{87} +2.43185 q^{88} +6.14450 q^{89} -11.4402 q^{90} +3.05598 q^{91} +2.85201 q^{92} +8.67037 q^{93} +15.7779 q^{94} -5.92525 q^{95} -9.80044 q^{96} +10.5330 q^{97} -21.7812 q^{98} +2.31999 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.16010	−1.52742	−0.763710	−	0.645559i	$-0.776624\pi$
$2$	−2.16010	−1.52742	−0.763710	+	0.645559i	$0.776624\pi$
$3$	−1.27573	−0.736545	−0.368272	−	0.929718i	$-0.620051\pi$
$3$	−1.27573	−0.736545	−0.368272	+	0.929718i	$0.620051\pi$
$4$	2.66602	1.33301
$5$	−3.85876	−1.72569	−0.862845	−	0.505468i	$-0.831320\pi$
$5$	−3.85876	−1.72569	−0.862845	+	0.505468i	$0.831320\pi$
$6$	2.75571	1.12501
$7$	4.13321	1.56221	0.781103	−	0.624402i	$-0.214657\pi$
$7$	4.13321	1.56221	0.781103	+	0.624402i	$0.214657\pi$
$8$	−1.43868	−0.508650
$9$	−1.37250	−0.457502
$10$	8.33530	2.63585
$11$	−1.69034	−0.509655	−0.254828	−	0.966986i	$-0.582019\pi$
$11$	−1.69034	−0.509655	−0.254828	+	0.966986i	$0.582019\pi$
$12$	−3.40114	−0.981823
$13$	0.739372	0.205065	0.102532	−	0.994730i	$-0.467305\pi$
$13$	0.739372	0.205065	0.102532	+	0.994730i	$0.467305\pi$
$14$	−8.92814	−2.38614
$15$	4.92275	1.27105
$16$	−2.22436	−0.556090
$17$	−3.74928	−0.909334	−0.454667	−	0.890662i	$-0.650242\pi$
$17$	−3.74928	−0.909334	−0.454667	+	0.890662i	$0.650242\pi$
$18$	2.96474	0.698797
$19$	1.53553	0.352275	0.176138	−	0.984366i	$-0.443640\pi$
$19$	1.53553	0.352275	0.176138	+	0.984366i	$0.443640\pi$
$20$	−10.2876	−2.30037
$21$	−5.27287	−1.15063
$22$	3.65129	0.778458
$23$	1.06976	0.223061	0.111530	−	0.993761i	$-0.464425\pi$
$23$	1.06976	0.223061	0.111530	+	0.993761i	$0.464425\pi$
$24$	1.83537	0.374643
$25$	9.89004	1.97801
$26$	−1.59712	−0.313220
$27$	5.57815	1.07352
$28$	11.0192	2.08244
$29$	2.28894	0.425045	0.212523	−	0.977156i	$-0.431832\pi$
$29$	2.28894	0.425045	0.212523	+	0.977156i	$0.431832\pi$
$30$	−10.6336	−1.94143
$31$	−6.79638	−1.22067	−0.610333	−	0.792145i	$-0.708964\pi$
$31$	−6.79638	−1.22067	−0.610333	+	0.792145i	$0.708964\pi$
$32$	7.68220	1.35803
$33$	2.15642	0.375384
$34$	8.09881	1.38893
$35$	−15.9491	−2.69588
$36$	−3.65913	−0.609855
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	−3.31690	−0.538072
$39$	−0.943241	−0.151039
$40$	5.55152	0.877772
$41$	−2.69734	−0.421254	−0.210627	−	0.977566i	$-0.567551\pi$
$41$	−2.69734	−0.421254	−0.210627	+	0.977566i	$0.567551\pi$
$42$	11.3899	1.75750
$43$	8.08618	1.23313	0.616565	−	0.787304i	$-0.288524\pi$
$43$	8.08618	1.23313	0.616565	+	0.787304i	$0.288524\pi$
$44$	−4.50648	−0.679377
$45$	5.29617	0.789506
$46$	−2.31079	−0.340708
$47$	−7.30426	−1.06544	−0.532718	−	0.846293i	$-0.678829\pi$
$47$	−7.30426	−1.06544	−0.532718	+	0.846293i	$0.678829\pi$
$48$	2.83769	0.409586
$49$	10.0834	1.44049
$50$	−21.3635	−3.02125
$51$	4.78308	0.669765
$52$	1.97118	0.273354
$53$	−10.9530	−1.50451	−0.752256	−	0.658870i	$-0.771035\pi$
$53$	−10.9530	−1.50451	−0.752256	+	0.658870i	$0.771035\pi$
$54$	−12.0494	−1.63971
$55$	6.52260	0.879508
$56$	−5.94636	−0.794616
$57$	−1.95893	−0.259466
$58$	−4.94433	−0.649222
$59$	14.6621	1.90884	0.954418	−	0.298472i	$-0.0964771\pi$
$59$	14.6621	1.90884	0.954418	+	0.298472i	$0.0964771\pi$
$60$	13.1242	1.69432
$61$	−11.7906	−1.50963	−0.754817	−	0.655935i	$-0.772274\pi$
$61$	−11.7906	−1.50963	−0.754817	+	0.655935i	$0.772274\pi$
$62$	14.6808	1.86447
$63$	−5.67285	−0.714712
$64$	−12.1456	−1.51820
$65$	−2.85306	−0.353879
$66$	−4.65807	−0.573369
$67$	−10.0426	−1.22690	−0.613448	−	0.789735i	$-0.710218\pi$
$67$	−10.0426	−1.22690	−0.613448	+	0.789735i	$0.710218\pi$
$68$	−9.99567	−1.21215
$69$	−1.36473	−0.164294
$70$	34.4516	4.11775
$71$	−11.4280	−1.35626	−0.678128	−	0.734944i	$-0.737208\pi$
$71$	−11.4280	−1.35626	−0.678128	+	0.734944i	$0.737208\pi$
$72$	1.97459	0.232708
$73$	8.90501	1.04225	0.521126	−	0.853479i	$-0.325512\pi$
$73$	8.90501	1.04225	0.521126	+	0.853479i	$0.325512\pi$
$74$	−2.16010	−0.251106
$75$	−12.6171	−1.45689
$76$	4.09377	0.469587
$77$	−6.98651	−0.796187
$78$	2.03749	0.230701
$79$	−1.53896	−0.173147	−0.0865735	−	0.996245i	$-0.527592\pi$
$79$	−1.53896	−0.173147	−0.0865735	+	0.996245i	$0.527592\pi$
$80$	8.58328	0.959640
$81$	−2.99872	−0.333191
$82$	5.82652	0.643432
$83$	13.5616	1.48857	0.744287	−	0.667860i	$-0.232790\pi$
$83$	13.5616	1.48857	0.744287	+	0.667860i	$0.232790\pi$
$84$	−14.0576	−1.53381
$85$	14.4676	1.56923
$86$	−17.4669	−1.88351
$87$	−2.92007	−0.313065
$88$	2.43185	0.259236
$89$	6.14450	0.651316	0.325658	−	0.945488i	$-0.394414\pi$
$89$	6.14450	0.651316	0.325658	+	0.945488i	$0.394414\pi$
$90$	−11.4402	−1.20591
$91$	3.05598	0.320354
$92$	2.85201	0.297343
$93$	8.67037	0.899075
$94$	15.7779	1.62737
$95$	−5.92525	−0.607918
$96$	−9.80044	−1.00025
$97$	10.5330	1.06946	0.534731	−	0.845022i	$-0.320413\pi$
$97$	10.5330	1.06946	0.534731	+	0.845022i	$0.320413\pi$
$98$	−21.7812	−2.20023
$99$	2.31999	0.233168
$100$	26.3671	2.63671
$101$	−10.0857	−1.00357	−0.501785	−	0.864993i	$-0.667323\pi$
$101$	−10.0857	−1.00357	−0.501785	+	0.864993i	$0.667323\pi$
$102$	−10.3319	−1.02301
$103$	16.8159	1.65692	0.828460	−	0.560048i	$-0.189217\pi$
$103$	16.8159	1.65692	0.828460	+	0.560048i	$0.189217\pi$
$104$	−1.06372	−0.104306
$105$	20.3468	1.98564
$106$	23.6596	2.29802
$107$	15.3751	1.48636	0.743182	−	0.669089i	$-0.233315\pi$
$107$	15.3751	1.48636	0.743182	+	0.669089i	$0.233315\pi$
$108$	14.8715	1.43101
$109$	1.00000	0.0957826
$109$	1.00000	0.0957826
$110$	−14.0895	−1.34338
$111$	−1.27573	−0.121087
$112$	−9.19375	−0.868728
$113$	14.1555	1.33164	0.665820	−	0.746113i	$-0.268082\pi$
$113$	14.1555	1.33164	0.665820	+	0.746113i	$0.268082\pi$
$114$	4.23148	0.396314
$115$	−4.12796	−0.384934
$116$	6.10236	0.566590
$117$	−1.01479	−0.0938175
$118$	−31.6715	−2.91560
$119$	−15.4965	−1.42057
$120$	−7.08226	−0.646519
$121$	−8.14277	−0.740251
$122$	25.4689	2.30585
$123$	3.44109	0.310273
$124$	−18.1193	−1.62716
$125$	−18.8695	−1.68774
$126$	12.2539	1.09166
$127$	15.0244	1.33320	0.666598	−	0.745418i	$-0.267750\pi$
$127$	15.0244	1.33320	0.666598	+	0.745418i	$0.267750\pi$
$128$	10.8712	0.960892
$129$	−10.3158	−0.908256
$130$	6.16289	0.540521
$131$	15.1280	1.32174	0.660870	−	0.750501i	$-0.270188\pi$
$131$	15.1280	1.32174	0.660870	+	0.750501i	$0.270188\pi$
$132$	5.74906	0.500392
$133$	6.34667	0.550326
$134$	21.6930	1.87399
$135$	−21.5248	−1.85256
$136$	5.39401	0.462532
$137$	5.29173	0.452103	0.226051	−	0.974115i	$-0.427418\pi$
$137$	5.29173	0.452103	0.226051	+	0.974115i	$0.427418\pi$
$138$	2.94795	0.250946
$139$	17.7903	1.50895	0.754475	−	0.656329i	$-0.227892\pi$
$139$	17.7903	1.50895	0.754475	+	0.656329i	$0.227892\pi$
$140$	−42.5206	−3.59365
$141$	9.31829	0.784741
$142$	24.6856	2.07157
$143$	−1.24979	−0.104512
$144$	3.05295	0.254412
$145$	−8.83247	−0.733496
$146$	−19.2357	−1.59196
$147$	−12.8637	−1.06098
$148$	2.66602	0.219146
$149$	11.8688	0.972327	0.486163	−	0.873868i	$-0.338396\pi$
$149$	11.8688	0.972327	0.486163	+	0.873868i	$0.338396\pi$
$150$	27.2541	2.22529
$151$	12.0014	0.976664	0.488332	−	0.872658i	$-0.337605\pi$
$151$	12.0014	0.976664	0.488332	+	0.872658i	$0.337605\pi$
$152$	−2.20914	−0.179185
$153$	5.14590	0.416022
$154$	15.0915	1.21611
$155$	26.2256	2.10649
$156$	−2.51470	−0.201337
$157$	−18.8177	−1.50181	−0.750907	−	0.660407i	$-0.770384\pi$
$157$	−18.8177	−1.50181	−0.750907	+	0.660407i	$0.770384\pi$
$158$	3.32432	0.264468
$159$	13.9731	1.10814
$160$	−29.6438	−2.34355
$161$	4.42155	0.348467
$162$	6.47752	0.508922
$163$	4.98458	0.390422	0.195211	−	0.980761i	$-0.437461\pi$
$163$	4.98458	0.390422	0.195211	+	0.980761i	$0.437461\pi$
$164$	−7.19118	−0.561537
$165$	−8.32110	−0.647797
$166$	−29.2943	−2.27368
$167$	−16.9640	−1.31271	−0.656355	−	0.754452i	$-0.727903\pi$
$167$	−16.9640	−1.31271	−0.656355	+	0.754452i	$0.727903\pi$
$168$	7.58597	0.585270
$169$	−12.4533	−0.957948
$170$	−31.2514	−2.39687
$171$	−2.10752	−0.161166
$172$	21.5580	1.64378
$173$	0.0278455	0.00211705	0.00105853	−	0.999999i	$-0.499663\pi$
$173$	0.0278455	0.00211705	0.00105853	+	0.999999i	$0.499663\pi$
$174$	6.30765	0.478181
$175$	40.8776	3.09006
$176$	3.75992	0.283414
$177$	−18.7049	−1.40594
$178$	−13.2727	−0.994833
$179$	2.55883	0.191256	0.0956278	−	0.995417i	$-0.469514\pi$
$179$	2.55883	0.191256	0.0956278	+	0.995417i	$0.469514\pi$
$180$	14.1197	1.05242
$181$	−7.03971	−0.523257	−0.261629	−	0.965169i	$-0.584260\pi$
$181$	−7.03971	−0.523257	−0.261629	+	0.965169i	$0.584260\pi$
$182$	−6.60121	−0.489314
$183$	15.0417	1.11191
$184$	−1.53904	−0.113460
$185$	−3.85876	−0.283702
$186$	−18.7288	−1.37327
$187$	6.33754	0.463447
$188$	−19.4733	−1.42024
$189$	23.0557	1.67705
$190$	12.7991	0.928546
$191$	−9.29713	−0.672717	−0.336358	−	0.941734i	$-0.609195\pi$
$191$	−9.29713	−0.672717	−0.336358	+	0.941734i	$0.609195\pi$
$192$	15.4945	1.11822
$193$	−21.6921	−1.56143	−0.780716	−	0.624886i	$-0.785145\pi$
$193$	−21.6921	−1.56143	−0.780716	+	0.624886i	$0.785145\pi$
$194$	−22.7523	−1.63352
$195$	3.63974	0.260647
$196$	26.8826	1.92019
$197$	−2.75122	−0.196016	−0.0980082	−	0.995186i	$-0.531247\pi$
$197$	−2.75122	−0.196016	−0.0980082	+	0.995186i	$0.531247\pi$
$198$	−5.01141	−0.356146
$199$	−14.4928	−1.02737	−0.513683	−	0.857980i	$-0.671719\pi$
$199$	−14.4928	−1.02737	−0.513683	+	0.857980i	$0.671719\pi$
$200$	−14.2286	−1.00611
$201$	12.8117	0.903665
$202$	21.7862	1.53287
$203$	9.46066	0.664008
$204$	12.7518	0.892805
$205$	10.4084	0.726954
$206$	−36.3240	−2.53081
$207$	−1.46825	−0.102051
$208$	−1.64463	−0.114035
$209$	−2.59556	−0.179539
$210$	−43.9510	−3.03291
$211$	11.8050	0.812690	0.406345	−	0.913720i	$-0.366803\pi$
$211$	11.8050	0.812690	0.406345	+	0.913720i	$0.366803\pi$
$212$	−29.2010	−2.00553
$213$	14.5791	0.998943
$214$	−33.2117	−2.27030
$215$	−31.2026	−2.12800
$216$	−8.02517	−0.546043
$217$	−28.0909	−1.90693
$218$	−2.16010	−0.146300
$219$	−11.3604	−0.767666
$220$	17.3894	1.17239
$221$	−2.77211	−0.186472
$222$	2.75571	0.184951
$223$	−4.09278	−0.274073	−0.137036	−	0.990566i	$-0.543758\pi$
$223$	−4.09278	−0.274073	−0.137036	+	0.990566i	$0.543758\pi$
$224$	31.7521	2.12153
$225$	−13.5741	−0.904942
$226$	−30.5773	−2.03397
$227$	−7.34611	−0.487579	−0.243789	−	0.969828i	$-0.578391\pi$
$227$	−7.34611	−0.487579	−0.243789	+	0.969828i	$0.578391\pi$
$228$	−5.22255	−0.345872
$229$	−19.9860	−1.32071	−0.660357	−	0.750952i	$-0.729595\pi$
$229$	−19.9860	−1.32071	−0.660357	+	0.750952i	$0.729595\pi$
$230$	8.91679	0.587956
$231$	8.91292	0.586427
$232$	−3.29305	−0.216199
$233$	−25.9258	−1.69845	−0.849227	−	0.528028i	$-0.822932\pi$
$233$	−25.9258	−1.69845	−0.849227	+	0.528028i	$0.822932\pi$
$234$	2.19205	0.143299
$235$	28.1854	1.83861
$236$	39.0894	2.54450
$237$	1.96331	0.127531
$238$	33.4741	2.16980
$239$	13.2619	0.857842	0.428921	−	0.903342i	$-0.358894\pi$
$239$	13.2619	0.857842	0.428921	+	0.903342i	$0.358894\pi$
$240$	−10.9500	−0.706818
$241$	6.77857	0.436646	0.218323	−	0.975877i	$-0.429941\pi$
$241$	6.77857	0.436646	0.218323	+	0.975877i	$0.429941\pi$
$242$	17.5892	1.13067
$243$	−12.9089	−0.828105
$244$	−31.4341	−2.01236
$245$	−38.9095	−2.48584
$246$	−7.43309	−0.473917
$247$	1.13533	0.0722393
$248$	9.77781	0.620891
$249$	−17.3009	−1.09640
$250$	40.7600	2.57789
$251$	24.4358	1.54237	0.771187	−	0.636609i	$-0.219664\pi$
$251$	24.4358	1.54237	0.771187	+	0.636609i	$0.219664\pi$
$252$	−15.1240	−0.952719
$253$	−1.80826	−0.113684
$254$	−32.4541	−2.03635
$255$	−18.4568	−1.15581
$256$	0.808192	0.0505120
$257$	−22.2109	−1.38548	−0.692739	−	0.721188i	$-0.743596\pi$
$257$	−22.2109	−1.38548	−0.692739	+	0.721188i	$0.743596\pi$
$258$	22.2832	1.38729
$259$	4.13321	0.256825
$260$	−7.60633	−0.471724
$261$	−3.14158	−0.194459
$262$	−32.6780	−2.01885
$263$	−24.2247	−1.49376	−0.746880	−	0.664959i	$-0.768449\pi$
$263$	−24.2247	−1.49376	−0.746880	+	0.664959i	$0.768449\pi$
$264$	−3.10239	−0.190939
$265$	42.2651	2.59632
$266$	−13.7094	−0.840580
$267$	−7.83875	−0.479723
$268$	−26.7738	−1.63547
$269$	−18.8783	−1.15103	−0.575514	−	0.817792i	$-0.695198\pi$
$269$	−18.8783	−1.15103	−0.575514	+	0.817792i	$0.695198\pi$
$270$	46.4956	2.82963
$271$	−3.83575	−0.233005	−0.116503	−	0.993190i	$-0.537168\pi$
$271$	−3.83575	−0.233005	−0.116503	+	0.993190i	$0.537168\pi$
$272$	8.33975	0.505672
$273$	−3.89861	−0.235955
$274$	−11.4307	−0.690551
$275$	−16.7175	−1.00810
$276$	−3.63841	−0.219006
$277$	6.48170	0.389448	0.194724	−	0.980858i	$-0.437619\pi$
$277$	6.48170	0.389448	0.194724	+	0.980858i	$0.437619\pi$
$278$	−38.4287	−2.30480
$279$	9.32806	0.558456
$280$	22.9456	1.37126
$281$	4.30618	0.256885	0.128442	−	0.991717i	$-0.459002\pi$
$281$	4.30618	0.256885	0.128442	+	0.991717i	$0.459002\pi$
$282$	−20.1284	−1.19863
$283$	9.24536	0.549580	0.274790	−	0.961504i	$-0.411392\pi$
$283$	9.24536	0.549580	0.274790	+	0.961504i	$0.411392\pi$
$284$	−30.4674	−1.80791
$285$	7.55904	0.447759
$286$	2.69966	0.159634
$287$	−11.1487	−0.658086
$288$	−10.5439	−0.621302
$289$	−2.94291	−0.173112
$290$	19.0790	1.12036
$291$	−13.4373	−0.787707
$292$	23.7410	1.38934
$293$	−11.4274	−0.667594	−0.333797	−	0.942645i	$-0.608330\pi$
$293$	−11.4274	−0.667594	−0.333797	+	0.942645i	$0.608330\pi$
$294$	27.7870	1.62057
$295$	−56.5774	−3.29406
$296$	−1.43868	−0.0836215
$297$	−9.42895	−0.547123
$298$	−25.6377	−1.48515
$299$	0.790952	0.0457419
$300$	−33.6374	−1.94206
$301$	33.4219	1.92640
$302$	−25.9243	−1.49178
$303$	12.8667	0.739174
$304$	−3.41558	−0.195897
$305$	45.4972	2.60516
$306$	−11.1157	−0.635440
$307$	0.841020	0.0479996	0.0239998	−	0.999712i	$-0.492360\pi$
$307$	0.841020	0.0479996	0.0239998	+	0.999712i	$0.492360\pi$
$308$	−18.6262	−1.06133
$309$	−21.4526	−1.22040
$310$	−56.6499	−3.21750
$311$	2.34822	0.133155	0.0665776	−	0.997781i	$-0.478792\pi$
$311$	2.34822	0.133155	0.0665776	+	0.997781i	$0.478792\pi$
$312$	1.35702	0.0768262
$313$	1.88671	0.106643	0.0533216	−	0.998577i	$-0.483019\pi$
$313$	1.88671	0.106643	0.0533216	+	0.998577i	$0.483019\pi$
$314$	40.6481	2.29390
$315$	21.8902	1.23337
$316$	−4.10292	−0.230807
$317$	−2.92597	−0.164339	−0.0821694	−	0.996618i	$-0.526185\pi$
$317$	−2.92597	−0.164339	−0.0821694	+	0.996618i	$0.526185\pi$
$318$	−30.1833	−1.69260
$319$	−3.86907	−0.216627
$320$	46.8669	2.61994
$321$	−19.6145	−1.09477
$322$	−9.55098	−0.532255
$323$	−5.75714	−0.320336
$324$	−7.99465	−0.444147
$325$	7.31242	0.405620
$326$	−10.7672	−0.596339
$327$	−1.27573	−0.0705482
$328$	3.88061	0.214271
$329$	−30.1900	−1.66443
$330$	17.9744	0.989458
$331$	13.6515	0.750354	0.375177	−	0.926953i	$-0.377582\pi$
$331$	13.6515	0.750354	0.375177	+	0.926953i	$0.377582\pi$
$332$	36.1554	1.98429
$333$	−1.37250	−0.0752128
$334$	36.6438	2.00506
$335$	38.7519	2.11724
$336$	11.7288	0.639857
$337$	18.4159	1.00318	0.501588	−	0.865107i	$-0.332749\pi$
$337$	18.4159	1.00318	0.501588	+	0.865107i	$0.332749\pi$
$338$	26.9004	1.46319
$339$	−18.0587	−0.980812
$340$	38.5709	2.09180
$341$	11.4882	0.622119
$342$	4.55246	0.246169
$343$	12.7444	0.688132
$344$	−11.6334	−0.627232
$345$	5.26617	0.283521
$346$	−0.0601490	−0.00323363
$347$	21.1476	1.13526	0.567631	−	0.823283i	$-0.307860\pi$
$347$	21.1476	1.13526	0.567631	+	0.823283i	$0.307860\pi$
$348$	−7.78499	−0.417319
$349$	23.6844	1.26780	0.633898	−	0.773416i	$-0.281454\pi$
$349$	23.6844	1.26780	0.633898	+	0.773416i	$0.281454\pi$
$350$	−88.2996	−4.71981
$351$	4.12433	0.220140
$352$	−12.9855	−0.692129
$353$	4.37166	0.232680	0.116340	−	0.993209i	$-0.462884\pi$
$353$	4.37166	0.232680	0.116340	+	0.993209i	$0.462884\pi$
$354$	40.4044	2.14747
$355$	44.0980	2.34048
$356$	16.3814	0.868212
$357$	19.7695	1.04631
$358$	−5.52732	−0.292128
$359$	11.1474	0.588338	0.294169	−	0.955753i	$-0.404957\pi$
$359$	11.1474	0.588338	0.294169	+	0.955753i	$0.404957\pi$
$360$	−7.61948	−0.401582
$361$	−16.6421	−0.875902
$362$	15.2065	0.799234
$363$	10.3880	0.545228
$364$	8.14731	0.427035
$365$	−34.3623	−1.79861
$366$	−32.4915	−1.69836
$367$	−24.8248	−1.29584	−0.647921	−	0.761707i	$-0.724361\pi$
$367$	−24.8248	−1.29584	−0.647921	+	0.761707i	$0.724361\pi$
$368$	−2.37954	−0.124042
$369$	3.70211	0.192724
$370$	8.33530	0.433332
$371$	−45.2711	−2.35036
$372$	23.1154	1.19848
$373$	−19.5886	−1.01426	−0.507128	−	0.861871i	$-0.669293\pi$
$373$	−19.5886	−1.01426	−0.507128	+	0.861871i	$0.669293\pi$
$374$	−13.6897	−0.707878
$375$	24.0725	1.24310
$376$	10.5085	0.541934
$377$	1.69238	0.0871618
$378$	−49.8025	−2.56156
$379$	−16.1773	−0.830971	−0.415485	−	0.909600i	$-0.636388\pi$
$379$	−16.1773	−0.830971	−0.415485	+	0.909600i	$0.636388\pi$
$380$	−15.7969	−0.810362
$381$	−19.1671	−0.981958
$382$	20.0827	1.02752
$383$	−2.17697	−0.111238	−0.0556190	−	0.998452i	$-0.517713\pi$
$383$	−2.17697	−0.111238	−0.0556190	+	0.998452i	$0.517713\pi$
$384$	−13.8688	−0.707740
$385$	26.9593	1.37397
$386$	46.8571	2.38496
$387$	−11.0983	−0.564159
$388$	28.0812	1.42561
$389$	−2.80124	−0.142029	−0.0710143	−	0.997475i	$-0.522624\pi$
$389$	−2.80124	−0.142029	−0.0710143	+	0.997475i	$0.522624\pi$
$390$	−7.86220	−0.398118
$391$	−4.01084	−0.202837
$392$	−14.5068	−0.732704
$393$	−19.2993	−0.973520
$394$	5.94291	0.299399
$395$	5.93850	0.298798
$396$	6.18516	0.310816
$397$	−15.5250	−0.779179	−0.389590	−	0.920989i	$-0.627383\pi$
$397$	−15.5250	−0.779179	−0.389590	+	0.920989i	$0.627383\pi$
$398$	31.3058	1.56922
$399$	−8.09666	−0.405340
$400$	−21.9990	−1.09995
$401$	6.13030	0.306133	0.153066	−	0.988216i	$-0.451085\pi$
$401$	6.13030	0.306133	0.153066	+	0.988216i	$0.451085\pi$
$402$	−27.6744	−1.38028
$403$	−5.02505	−0.250316
$404$	−26.8888	−1.33777
$405$	11.5713	0.574984
$406$	−20.4359	−1.01422
$407$	−1.69034	−0.0837868
$408$	−6.88131	−0.340676
$409$	−17.9298	−0.886570	−0.443285	−	0.896381i	$-0.646187\pi$
$409$	−17.9298	−0.886570	−0.443285	+	0.896381i	$0.646187\pi$
$410$	−22.4832	−1.11036
$411$	−6.75084	−0.332994
$412$	44.8316	2.20870
$413$	60.6013	2.98200
$414$	3.17157	0.155874
$415$	−52.3308	−2.56882
$416$	5.68000	0.278485
$417$	−22.6956	−1.11141
$418$	5.60667	0.274231
$419$	−26.1860	−1.27927	−0.639634	−	0.768680i	$-0.720914\pi$
$419$	−26.1860	−1.27927	−0.639634	+	0.768680i	$0.720914\pi$
$420$	54.2450	2.64688
$421$	9.14790	0.445841	0.222921	−	0.974837i	$-0.428441\pi$
$421$	9.14790	0.445841	0.222921	+	0.974837i	$0.428441\pi$
$422$	−25.5000	−1.24132
$423$	10.0251	0.487438
$424$	15.7579	0.765270
$425$	−37.0805	−1.79867
$426$	−31.4923	−1.52581
$427$	−48.7331	−2.35836
$428$	40.9903	1.98134
$429$	1.59439	0.0769781
$430$	67.4008	3.25035
$431$	19.4589	0.937303	0.468652	−	0.883383i	$-0.344740\pi$
$431$	19.4589	0.937303	0.468652	+	0.883383i	$0.344740\pi$
$432$	−12.4078	−0.596972
$433$	−31.3484	−1.50651	−0.753255	−	0.657729i	$-0.771517\pi$
$433$	−31.3484	−1.50651	−0.753255	+	0.657729i	$0.771517\pi$
$434$	60.6790	2.91269
$435$	11.2679	0.540253
$436$	2.66602	0.127679
$437$	1.64265	0.0785788
$438$	24.5396	1.17255
$439$	−8.79631	−0.419825	−0.209913	−	0.977720i	$-0.567318\pi$
$439$	−8.79631	−0.419825	−0.209913	+	0.977720i	$0.567318\pi$
$440$	−9.38393	−0.447361
$441$	−13.8395	−0.659025
$442$	5.98803	0.284822
$443$	20.2473	0.961976	0.480988	−	0.876727i	$-0.340278\pi$
$443$	20.2473	0.961976	0.480988	+	0.876727i	$0.340278\pi$
$444$	−3.40114	−0.161411
$445$	−23.7102	−1.12397
$446$	8.84080	0.418624
$447$	−15.1414	−0.716162
$448$	−50.2002	−2.37174
$449$	−25.5690	−1.20667	−0.603337	−	0.797486i	$-0.706163\pi$
$449$	−25.5690	−1.20667	−0.603337	+	0.797486i	$0.706163\pi$
$450$	29.3215	1.38223
$451$	4.55941	0.214694
$452$	37.7390	1.77509
$453$	−15.3106	−0.719357
$454$	15.8683	0.744737
$455$	−11.7923	−0.552831
$456$	2.81827	0.131978
$457$	−25.9854	−1.21555	−0.607774	−	0.794110i	$-0.707937\pi$
$457$	−25.9854	−1.21555	−0.607774	+	0.794110i	$0.707937\pi$
$458$	43.1718	2.01728
$459$	−20.9140	−0.976184
$460$	−11.0052	−0.513122
$461$	−36.8509	−1.71632	−0.858159	−	0.513384i	$-0.828392\pi$
$461$	−36.8509	−1.71632	−0.858159	+	0.513384i	$0.828392\pi$
$462$	−19.2528	−0.895721
$463$	−37.7023	−1.75217	−0.876087	−	0.482153i	$-0.839855\pi$
$463$	−37.7023	−1.75217	−0.876087	+	0.482153i	$0.839855\pi$
$464$	−5.09143	−0.236364
$465$	−33.4569	−1.55153
$466$	56.0022	2.59425
$467$	37.5672	1.73840	0.869201	−	0.494459i	$-0.164634\pi$
$467$	37.5672	1.73840	0.869201	+	0.494459i	$0.164634\pi$
$468$	−2.70546	−0.125060
$469$	−41.5081	−1.91667
$470$	−60.8832	−2.80833
$471$	24.0064	1.10615
$472$	−21.0940	−0.970929
$473$	−13.6684	−0.628472
$474$	−4.24094	−0.194793
$475$	15.1865	0.696803
$476$	−41.3142	−1.89363
$477$	15.0331	0.688317
$478$	−28.6470	−1.31029
$479$	−27.9664	−1.27782	−0.638908	−	0.769283i	$-0.720613\pi$
$479$	−27.9664	−1.27782	−0.638908	+	0.769283i	$0.720613\pi$
$480$	37.8175	1.72613
$481$	0.739372	0.0337125
$482$	−14.6424	−0.666942
$483$	−5.64072	−0.256662
$484$	−21.7088	−0.986764
$485$	−40.6442	−1.84556
$486$	27.8845	1.26486
$487$	−0.717920	−0.0325321	−0.0162660	−	0.999868i	$-0.505178\pi$
$487$	−0.717920	−0.0325321	−0.0162660	+	0.999868i	$0.505178\pi$
$488$	16.9629	0.767875
$489$	−6.35899	−0.287564
$490$	84.0483	3.79692
$491$	23.3940	1.05575	0.527877	−	0.849321i	$-0.322988\pi$
$491$	23.3940	1.05575	0.527877	+	0.849321i	$0.322988\pi$
$492$	9.17403	0.413597
$493$	−8.58186	−0.386508
$494$	−2.45242	−0.110340
$495$	−8.95230	−0.402376
$496$	15.1176	0.678801
$497$	−47.2344	−2.11875
$498$	37.3717	1.67467
$499$	27.0887	1.21266	0.606328	−	0.795215i	$-0.292642\pi$
$499$	27.0887	1.21266	0.606328	+	0.795215i	$0.292642\pi$
$500$	−50.3066	−2.24978
$501$	21.6415	0.966871
$502$	−52.7837	−2.35585
$503$	−36.2766	−1.61749	−0.808746	−	0.588158i	$-0.799853\pi$
$503$	−36.2766	−1.61749	−0.808746	+	0.588158i	$0.799853\pi$
$504$	8.16141	0.363538
$505$	38.9185	1.73185
$506$	3.90601	0.173643
$507$	15.8871	0.705572
$508$	40.0553	1.77717
$509$	35.1187	1.55661	0.778305	−	0.627887i	$-0.216080\pi$
$509$	35.1187	1.55661	0.778305	+	0.627887i	$0.216080\pi$
$510$	39.8684	1.76540
$511$	36.8063	1.62821
$512$	−23.4883	−1.03804
$513$	8.56543	0.378173
$514$	47.9778	2.11621
$515$	−64.8886	−2.85933
$516$	−27.5022	−1.21072
$517$	12.3466	0.543005
$518$	−8.92814	−0.392280
$519$	−0.0355234	−0.00155930
$520$	4.10464	0.180000
$521$	7.92683	0.347281	0.173640	−	0.984809i	$-0.444447\pi$
$521$	7.92683	0.347281	0.173640	+	0.984809i	$0.444447\pi$
$522$	6.78612	0.297020
$523$	−36.3440	−1.58921	−0.794606	−	0.607125i	$-0.792323\pi$
$523$	−36.3440	−1.58921	−0.794606	+	0.607125i	$0.792323\pi$
$524$	40.3316	1.76189
$525$	−52.1489	−2.27597
$526$	52.3278	2.28160
$527$	25.4815	1.10999
$528$	−4.79665	−0.208748
$529$	−21.8556	−0.950244
$530$	−91.2967	−3.96568
$531$	−20.1237	−0.873296
$532$	16.9204	0.733592
$533$	−1.99434	−0.0863844
$534$	16.9325	0.732739
$535$	−59.3288	−2.56501
$536$	14.4481	0.624061
$537$	−3.26438	−0.140868
$538$	40.7789	1.75810
$539$	−17.0444	−0.734152
$540$	−57.3855	−2.46948
$541$	7.39152	0.317786	0.158893	−	0.987296i	$-0.449207\pi$
$541$	7.39152	0.317786	0.158893	+	0.987296i	$0.449207\pi$
$542$	8.28559	0.355897
$543$	8.98079	0.385403
$544$	−28.8027	−1.23491
$545$	−3.85876	−0.165291
$546$	8.42139	0.360402
$547$	27.5657	1.17862	0.589312	−	0.807906i	$-0.299399\pi$
$547$	27.5657	1.17862	0.589312	+	0.807906i	$0.299399\pi$
$548$	14.1079	0.602659
$549$	16.1827	0.690660
$550$	36.1114	1.53980
$551$	3.51474	0.149733
$552$	1.96341	0.0835682
$553$	−6.36086	−0.270491
$554$	−14.0011	−0.594850
$555$	4.92275	0.208959
$556$	47.4293	2.01145
$557$	−12.9337	−0.548018	−0.274009	−	0.961727i	$-0.588350\pi$
$557$	−12.9337	−0.548018	−0.274009	+	0.961727i	$0.588350\pi$
$558$	−20.1495	−0.852998
$559$	5.97869	0.252872
$560$	35.4765	1.49916
$561$	−8.08501	−0.341349
$562$	−9.30177	−0.392371
$563$	−28.6548	−1.20766	−0.603829	−	0.797114i	$-0.706359\pi$
$563$	−28.6548	−1.20766	−0.603829	+	0.797114i	$0.706359\pi$
$564$	24.8428	1.04607
$565$	−54.6228	−2.29800
$566$	−19.9709	−0.839439
$567$	−12.3943	−0.520513
$568$	16.4412	0.689859
$569$	−33.5333	−1.40579	−0.702894	−	0.711295i	$-0.748109\pi$
$569$	−33.5333	−1.40579	−0.702894	+	0.711295i	$0.748109\pi$
$570$	−16.3283	−0.683916
$571$	5.52429	0.231184	0.115592	−	0.993297i	$-0.463123\pi$
$571$	5.52429	0.231184	0.115592	+	0.993297i	$0.463123\pi$
$572$	−3.33196	−0.139316
$573$	11.8607	0.495486
$574$	24.0822	1.00517
$575$	10.5800	0.441216
$576$	16.6699	0.694578
$577$	4.58618	0.190925	0.0954626	−	0.995433i	$-0.469567\pi$
$577$	4.58618	0.190925	0.0954626	+	0.995433i	$0.469567\pi$
$578$	6.35698	0.264415
$579$	27.6733	1.15006
$580$	−23.5476	−0.977760
$581$	56.0527	2.32546
$582$	29.0258	1.20316
$583$	18.5143	0.766783
$584$	−12.8115	−0.530142
$585$	3.91584	0.161900
$586$	24.6842	1.01970
$587$	−27.5393	−1.13667	−0.568335	−	0.822797i	$-0.692412\pi$
$587$	−27.5393	−1.13667	−0.568335	+	0.822797i	$0.692412\pi$
$588$	−34.2951	−1.41430
$589$	−10.4361	−0.430010
$590$	122.213	5.03142
$591$	3.50982	0.144375
$592$	−2.22436	−0.0914207
$593$	0.931100	0.0382357	0.0191178	−	0.999817i	$-0.493914\pi$
$593$	0.931100	0.0382357	0.0191178	+	0.999817i	$0.493914\pi$
$594$	20.3674	0.835687
$595$	59.7975	2.45146
$596$	31.6424	1.29612
$597$	18.4889	0.756701
$598$	−1.70853	−0.0698671
$599$	25.7223	1.05099	0.525493	−	0.850798i	$-0.323881\pi$
$599$	25.7223	1.05099	0.525493	+	0.850798i	$0.323881\pi$
$600$	18.1519	0.741048
$601$	20.4693	0.834961	0.417481	−	0.908686i	$-0.362913\pi$
$601$	20.4693	0.834961	0.417481	+	0.908686i	$0.362913\pi$
$602$	−72.1945	−2.94243
$603$	13.7835	0.561307
$604$	31.9962	1.30191
$605$	31.4210	1.27744
$606$	−27.7934	−1.12903
$607$	38.7864	1.57429	0.787146	−	0.616767i	$-0.211558\pi$
$607$	38.7864	1.57429	0.787146	+	0.616767i	$0.211558\pi$
$608$	11.7963	0.478401
$609$	−12.0693	−0.489072
$610$	−98.2784	−3.97918
$611$	−5.40056	−0.218483
$612$	13.7191	0.554562
$613$	−30.7883	−1.24353	−0.621764	−	0.783205i	$-0.713584\pi$
$613$	−30.7883	−1.24353	−0.621764	+	0.783205i	$0.713584\pi$
$614$	−1.81669	−0.0733155
$615$	−13.2783	−0.535434
$616$	10.0513	0.404980
$617$	3.20829	0.129161	0.0645804	−	0.997913i	$-0.479429\pi$
$617$	3.20829	0.129161	0.0645804	+	0.997913i	$0.479429\pi$
$618$	46.3397	1.86406
$619$	−3.58932	−0.144267	−0.0721335	−	0.997395i	$-0.522981\pi$
$619$	−3.58932	−0.144267	−0.0721335	+	0.997395i	$0.522981\pi$
$620$	69.9181	2.80798
$621$	5.96729	0.239459
$622$	−5.07238	−0.203384
$623$	25.3965	1.01749
$624$	2.09811	0.0839916
$625$	23.3627	0.934509
$626$	−4.07548	−0.162889
$627$	3.31125	0.132238
$628$	−50.1684	−2.00194
$629$	−3.74928	−0.149494
$630$	−47.2849	−1.88388
$631$	−8.74448	−0.348112	−0.174056	−	0.984736i	$-0.555687\pi$
$631$	−8.74448	−0.348112	−0.174056	+	0.984736i	$0.555687\pi$
$632$	2.21408	0.0880712
$633$	−15.0600	−0.598583
$634$	6.32038	0.251015
$635$	−57.9754	−2.30068
$636$	37.2527	1.47717
$637$	7.45539	0.295393
$638$	8.35758	0.330880
$639$	15.6850	0.620489
$640$	−41.9496	−1.65820
$641$	−0.279950	−0.0110573	−0.00552867	−	0.999985i	$-0.501760\pi$
$641$	−0.279950	−0.0110573	−0.00552867	+	0.999985i	$0.501760\pi$
$642$	42.3692	1.67218
$643$	23.7284	0.935757	0.467878	−	0.883793i	$-0.345019\pi$
$643$	23.7284	0.935757	0.467878	+	0.883793i	$0.345019\pi$
$644$	11.7880	0.464511
$645$	39.8062	1.56737
$646$	12.4360	0.489287
$647$	24.4014	0.959318	0.479659	−	0.877455i	$-0.340760\pi$
$647$	24.4014	0.959318	0.479659	+	0.877455i	$0.340760\pi$
$648$	4.31419	0.169477
$649$	−24.7838	−0.972849
$650$	−15.7955	−0.619552
$651$	35.8364	1.40454
$652$	13.2890	0.520438
$653$	25.5180	0.998598	0.499299	−	0.866430i	$-0.333591\pi$
$653$	25.5180	0.998598	0.499299	+	0.866430i	$0.333591\pi$
$654$	2.75571	0.107757
$655$	−58.3753	−2.28091
$656$	5.99986	0.234255
$657$	−12.2222	−0.476832
$658$	65.2134	2.54228
$659$	−47.5517	−1.85235	−0.926175	−	0.377095i	$-0.876923\pi$
$659$	−47.5517	−1.85235	−0.926175	+	0.377095i	$0.876923\pi$
$660$	−22.1843	−0.863521
$661$	−14.0929	−0.548150	−0.274075	−	0.961708i	$-0.588372\pi$
$661$	−14.0929	−0.548150	−0.274075	+	0.961708i	$0.588372\pi$
$662$	−29.4886	−1.14611
$663$	3.53647	0.137345
$664$	−19.5107	−0.757163
$665$	−24.4903	−0.949693
$666$	2.96474	0.114882
$667$	2.44862	0.0948109
$668$	−45.2263	−1.74986
$669$	5.22129	0.201867
$670$	−83.7080	−3.23392
$671$	19.9301	0.769393
$672$	−40.5072	−1.56260
$673$	24.8021	0.956052	0.478026	−	0.878346i	$-0.341352\pi$
$673$	24.8021	0.956052	0.478026	+	0.878346i	$0.341352\pi$
$674$	−39.7801	−1.53227
$675$	55.1681	2.12342
$676$	−33.2009	−1.27696
$677$	−23.0304	−0.885131	−0.442565	−	0.896736i	$-0.645932\pi$
$677$	−23.0304	−0.885131	−0.442565	+	0.896736i	$0.645932\pi$
$678$	39.0085	1.49811
$679$	43.5350	1.67072
$680$	−20.8142	−0.798188
$681$	9.37168	0.359124
$682$	−24.8156	−0.950237
$683$	16.5723	0.634123	0.317061	−	0.948405i	$-0.397304\pi$
$683$	16.5723	0.634123	0.317061	+	0.948405i	$0.397304\pi$
$684$	−5.61871	−0.214837
$685$	−20.4195	−0.780190
$686$	−27.5291	−1.05107
$687$	25.4968	0.972765
$688$	−17.9866	−0.685732
$689$	−8.09835	−0.308523
$690$	−11.3754	−0.433056
$691$	0.117661	0.00447602	0.00223801	−	0.999997i	$-0.499288\pi$
$691$	0.117661	0.00447602	0.00223801	+	0.999997i	$0.499288\pi$
$692$	0.0742367	0.00282206
$693$	9.58902	0.364257
$694$	−45.6809	−1.73402
$695$	−68.6484	−2.60398
$696$	4.20105	0.159240
$697$	10.1131	0.383060
$698$	−51.1606	−1.93646
$699$	33.0744	1.25099
$700$	108.981	4.11908
$701$	41.1451	1.55403	0.777015	−	0.629482i	$-0.216733\pi$
$701$	41.1451	1.55403	0.777015	+	0.629482i	$0.216733\pi$
$702$	−8.90895	−0.336247
$703$	1.53553	0.0579137
$704$	20.5301	0.773757
$705$	−35.9570	−1.35422
$706$	−9.44321	−0.355400
$707$	−41.6865	−1.56778
$708$	−49.8676	−1.87414
$709$	−18.2020	−0.683589	−0.341795	−	0.939775i	$-0.611035\pi$
$709$	−18.2020	−0.683589	−0.341795	+	0.939775i	$0.611035\pi$
$710$	−95.2560	−3.57489
$711$	2.11224	0.0792150
$712$	−8.83996	−0.331292
$713$	−7.27051	−0.272283
$714$	−42.7040	−1.59816
$715$	4.82263	0.180356
$716$	6.82190	0.254946
$717$	−16.9187	−0.631839
$718$	−24.0795	−0.898640
$719$	−36.6339	−1.36621	−0.683107	−	0.730318i	$-0.739372\pi$
$719$	−36.6339	−1.36621	−0.683107	+	0.730318i	$0.739372\pi$
$720$	−11.7806	−0.439037
$721$	69.5036	2.58845
$722$	35.9487	1.33787
$723$	−8.64765	−0.321610
$724$	−18.7680	−0.697509
$725$	22.6377	0.840743
$726$	−22.4391	−0.832793
$727$	−26.2747	−0.974476	−0.487238	−	0.873269i	$-0.661996\pi$
$727$	−26.2747	−0.974476	−0.487238	+	0.873269i	$0.661996\pi$
$728$	−4.39657	−0.162948
$729$	25.4644	0.943128
$730$	74.2260	2.74723
$731$	−30.3173	−1.12133
$732$	40.1015	1.48219
$733$	−34.5161	−1.27488	−0.637441	−	0.770499i	$-0.720007\pi$
$733$	−34.5161	−1.27488	−0.637441	+	0.770499i	$0.720007\pi$
$734$	53.6239	1.97930
$735$	49.6381	1.83093
$736$	8.21812	0.302924
$737$	16.9753	0.625295
$738$	−7.99693	−0.294371
$739$	−8.74957	−0.321858	−0.160929	−	0.986966i	$-0.551449\pi$
$739$	−8.74957	−0.321858	−0.160929	+	0.986966i	$0.551449\pi$
$740$	−10.2876	−0.378178
$741$	−1.44838	−0.0532075
$742$	97.7900	3.58999
$743$	−40.1774	−1.47396	−0.736982	−	0.675912i	$-0.763750\pi$
$743$	−40.1774	−1.47396	−0.736982	+	0.675912i	$0.763750\pi$
$744$	−12.4739	−0.457314
$745$	−45.7987	−1.67794
$746$	42.3132	1.54920
$747$	−18.6133	−0.681025
$748$	16.8960	0.617780
$749$	63.5484	2.32201
$750$	−51.9989	−1.89873
$751$	21.0837	0.769356	0.384678	−	0.923051i	$-0.374312\pi$
$751$	21.0837	0.769356	0.384678	+	0.923051i	$0.374312\pi$
$752$	16.2473	0.592479
$753$	−31.1735	−1.13603
$754$	−3.65570	−0.133133
$755$	−46.3107	−1.68542
$756$	61.4669	2.23553
$757$	−24.1424	−0.877470	−0.438735	−	0.898616i	$-0.644573\pi$
$757$	−24.1424	−0.877470	−0.438735	+	0.898616i	$0.644573\pi$
$758$	34.9445	1.26924
$759$	2.30685	0.0837335
$760$	8.52453	0.309217
$761$	−31.2762	−1.13376	−0.566880	−	0.823800i	$-0.691850\pi$
$761$	−31.2762	−1.13376	−0.566880	+	0.823800i	$0.691850\pi$
$762$	41.4027	1.49986
$763$	4.13321	0.149632
$764$	−24.7864	−0.896740
$765$	−19.8568	−0.717924
$766$	4.70247	0.169907
$767$	10.8407	0.391435
$768$	−1.03104	−0.0372044
$769$	−23.0058	−0.829611	−0.414806	−	0.909910i	$-0.636150\pi$
$769$	−23.0058	−0.829611	−0.414806	+	0.909910i	$0.636150\pi$
$770$	−58.2347	−2.09863
$771$	28.3352	1.02047
$772$	−57.8317	−2.08141
$773$	49.8200	1.79190	0.895951	−	0.444152i	$-0.146495\pi$
$773$	49.8200	1.79190	0.895951	+	0.444152i	$0.146495\pi$
$774$	23.9735	0.861708
$775$	−67.2165	−2.41449
$776$	−15.1536	−0.543981
$777$	−5.27287	−0.189163
$778$	6.05095	0.216937
$779$	−4.14185	−0.148397
$780$	9.70365	0.347446
$781$	19.3172	0.691223
$782$	8.66380	0.309817
$783$	12.7680	0.456292
$784$	−22.4292	−0.801041
$785$	72.6130	2.59167
$786$	41.6884	1.48697
$787$	−29.5002	−1.05157	−0.525784	−	0.850618i	$-0.676228\pi$
$787$	−29.5002	−1.05157	−0.525784	+	0.850618i	$0.676228\pi$
$788$	−7.33482	−0.261292
$789$	30.9043	1.10022
$790$	−12.8277	−0.456390
$791$	58.5077	2.08030
$792$	−3.33773	−0.118601
$793$	−8.71765	−0.309573
$794$	33.5356	1.19013
$795$	−53.9190	−1.91231
$796$	−38.6381	−1.36949
$797$	7.62277	0.270012	0.135006	−	0.990845i	$-0.456895\pi$
$797$	7.62277	0.270012	0.135006	+	0.990845i	$0.456895\pi$
$798$	17.4896	0.619125
$799$	27.3857	0.968836
$800$	75.9773	2.68620
$801$	−8.43336	−0.297978
$802$	−13.2420	−0.467593
$803$	−15.0525	−0.531190
$804$	34.1562	1.20460
$805$	−17.0617	−0.601346
$806$	10.8546	0.382337
$807$	24.0836	0.847784
$808$	14.5101	0.510465
$809$	34.3850	1.20891	0.604457	−	0.796638i	$-0.293390\pi$
$809$	34.3850	1.20891	0.604457	+	0.796638i	$0.293390\pi$
$810$	−24.9952	−0.878243
$811$	−25.3179	−0.889030	−0.444515	−	0.895771i	$-0.646624\pi$
$811$	−25.3179	−0.889030	−0.444515	+	0.895771i	$0.646624\pi$
$812$	25.2223	0.885131
$813$	4.89339	0.171619
$814$	3.65129	0.127978
$815$	−19.2343	−0.673748
$816$	−10.6393	−0.372450
$817$	12.4166	0.434401
$818$	38.7301	1.35417
$819$	−4.19434	−0.146562
$820$	27.7491	0.969039
$821$	−31.1026	−1.08549	−0.542744	−	0.839898i	$-0.682615\pi$
$821$	−31.1026	−1.08549	−0.542744	+	0.839898i	$0.682615\pi$
$822$	14.5825	0.508622
$823$	28.6739	0.999508	0.499754	−	0.866167i	$-0.333424\pi$
$823$	28.6739	0.999508	0.499754	+	0.866167i	$0.333424\pi$
$824$	−24.1927	−0.842792
$825$	21.3271	0.742513
$826$	−130.905	−4.55476
$827$	24.8485	0.864068	0.432034	−	0.901857i	$-0.357796\pi$
$827$	24.8485	0.864068	0.432034	+	0.901857i	$0.357796\pi$
$828$	−3.91440	−0.136035
$829$	−30.2082	−1.04917	−0.524586	−	0.851357i	$-0.675780\pi$
$829$	−30.2082	−1.04917	−0.524586	+	0.851357i	$0.675780\pi$
$830$	113.040	3.92366
$831$	−8.26892	−0.286846
$832$	−8.98010	−0.311329
$833$	−37.8055	−1.30988
$834$	49.0248	1.69759
$835$	65.4599	2.26533
$836$	−6.91984	−0.239328
$837$	−37.9112	−1.31040
$838$	56.5643	1.95398
$839$	26.4789	0.914154	0.457077	−	0.889427i	$-0.348896\pi$
$839$	26.4789	0.914154	0.457077	+	0.889427i	$0.348896\pi$
$840$	−29.2724	−1.01000
$841$	−23.7608	−0.819337
$842$	−19.7604	−0.680987
$843$	−5.49353	−0.189207
$844$	31.4724	1.08333
$845$	48.0544	1.65312
$846$	−21.6553	−0.744523
$847$	−33.6557	−1.15643
$848$	24.3635	0.836645
$849$	−11.7946	−0.404790
$850$	80.0976	2.74732
$851$	1.06976	0.0366710
$852$	38.8682	1.33160
$853$	−36.1028	−1.23614	−0.618069	−	0.786124i	$-0.712085\pi$
$853$	−36.1028	−1.23614	−0.618069	+	0.786124i	$0.712085\pi$
$854$	105.268	3.60221
$855$	8.13243	0.278123
$856$	−22.1198	−0.756039
$857$	−30.2922	−1.03476	−0.517381	−	0.855755i	$-0.673093\pi$
$857$	−30.2922	−1.03476	−0.517381	+	0.855755i	$0.673093\pi$
$858$	−3.44405	−0.117578
$859$	13.0750	0.446113	0.223056	−	0.974806i	$-0.428397\pi$
$859$	13.0750	0.446113	0.223056	+	0.974806i	$0.428397\pi$
$860$	−83.1870	−2.83665
$861$	14.2227	0.484710
$862$	−42.0332	−1.43166
$863$	6.06077	0.206311	0.103155	−	0.994665i	$-0.467106\pi$
$863$	6.06077	0.206311	0.103155	+	0.994665i	$0.467106\pi$
$864$	42.8524	1.45787
$865$	−0.107449	−0.00365338
$866$	67.7157	2.30107
$867$	3.75437	0.127505
$868$	−74.8909	−2.54196
$869$	2.60137	0.0882453
$870$	−24.3397	−0.825193
$871$	−7.42520	−0.251593
$872$	−1.43868	−0.0487198
$873$	−14.4566	−0.489280
$874$	−3.54829	−0.120023
$875$	−77.9916	−2.63660
$876$	−30.2872	−1.02331
$877$	−6.06047	−0.204648	−0.102324	−	0.994751i	$-0.532628\pi$
$877$	−6.06047	−0.204648	−0.102324	+	0.994751i	$0.532628\pi$
$878$	19.0009	0.641249
$879$	14.5783	0.491713
$880$	−14.5086	−0.489086
$881$	−7.47372	−0.251796	−0.125898	−	0.992043i	$-0.540181\pi$
$881$	−7.47372	−0.251796	−0.125898	+	0.992043i	$0.540181\pi$
$882$	29.8947	1.00661
$883$	−22.2790	−0.749748	−0.374874	−	0.927076i	$-0.622314\pi$
$883$	−22.2790	−0.749748	−0.374874	+	0.927076i	$0.622314\pi$
$884$	−7.39052	−0.248570
$885$	72.1776	2.42622
$886$	−43.7361	−1.46934
$887$	−12.3369	−0.414232	−0.207116	−	0.978316i	$-0.566408\pi$
$887$	−12.3369	−0.414232	−0.207116	+	0.978316i	$0.566408\pi$
$888$	1.83537	0.0615910
$889$	62.0988	2.08273
$890$	51.2163	1.71677
$891$	5.06884	0.169812
$892$	−10.9114	−0.365342
$893$	−11.2159	−0.375326
$894$	32.7069	1.09388
$895$	−9.87390	−0.330048
$896$	44.9331	1.50111
$897$	−1.00904	−0.0336910
$898$	55.2315	1.84310
$899$	−15.5565	−0.518838
$900$	−36.1890	−1.20630
$901$	41.0659	1.36810
$902$	−9.84878	−0.327929
$903$	−42.6374	−1.41888
$904$	−20.3652	−0.677338
$905$	27.1646	0.902980
$906$	33.0725	1.09876
$907$	−35.5287	−1.17971	−0.589856	−	0.807509i	$-0.700815\pi$
$907$	−35.5287	−1.17971	−0.589856	+	0.807509i	$0.700815\pi$
$908$	−19.5849	−0.649948
$909$	13.8427	0.459134
$910$	25.4725	0.844405
$911$	−12.0532	−0.399341	−0.199671	−	0.979863i	$-0.563987\pi$
$911$	−12.0532	−0.399341	−0.199671	+	0.979863i	$0.563987\pi$
$912$	4.35737	0.144287
$913$	−22.9236	−0.758660
$914$	56.1311	1.85665
$915$	−58.0423	−1.91882
$916$	−53.2832	−1.76053
$917$	62.5272	2.06483
$918$	45.1764	1.49104
$919$	45.5640	1.50302	0.751509	−	0.659722i	$-0.229326\pi$
$919$	45.5640	1.50302	0.751509	+	0.659722i	$0.229326\pi$
$920$	5.93880	0.195797
$921$	−1.07292	−0.0353538
$922$	79.6016	2.62154
$923$	−8.44955	−0.278120
$924$	23.7621	0.781715
$925$	9.89004	0.325183
$926$	81.4406	2.67631
$927$	−23.0799	−0.758044
$928$	17.5841	0.577225
$929$	28.6496	0.939963	0.469981	−	0.882676i	$-0.344261\pi$
$929$	28.6496	0.939963	0.469981	+	0.882676i	$0.344261\pi$
$930$	72.2701	2.36983
$931$	15.4834	0.507448
$932$	−69.1188	−2.26406
$933$	−2.99570	−0.0980748
$934$	−81.1488	−2.65527
$935$	−24.4551	−0.799766
$936$	1.45996	0.0477202
$937$	45.0034	1.47020	0.735098	−	0.677961i	$-0.237136\pi$
$937$	45.0034	1.47020	0.735098	+	0.677961i	$0.237136\pi$
$938$	89.6616	2.92755
$939$	−2.40694	−0.0785475
$940$	75.1430	2.45089
$941$	50.9431	1.66070	0.830348	−	0.557245i	$-0.188141\pi$
$941$	50.9431	1.66070	0.830348	+	0.557245i	$0.188141\pi$
$942$	−51.8561	−1.68956
$943$	−2.88551	−0.0939653
$944$	−32.6137	−1.06149
$945$	−88.9663	−2.89407
$946$	29.5250	0.959940
$947$	−32.9776	−1.07163	−0.535814	−	0.844336i	$-0.679995\pi$
$947$	−32.9776	−1.07163	−0.535814	+	0.844336i	$0.679995\pi$
$948$	5.23423	0.170000
$949$	6.58412	0.213729
$950$	−32.8043	−1.06431
$951$	3.73276	0.121043
$952$	22.2946	0.722571
$953$	−17.0492	−0.552278	−0.276139	−	0.961118i	$-0.589055\pi$
$953$	−17.0492	−0.552278	−0.276139	+	0.961118i	$0.589055\pi$
$954$	−32.4729	−1.05135
$955$	35.8754	1.16090
$956$	35.3566	1.14351
$957$	4.93591	0.159555
$958$	60.4101	1.95176
$959$	21.8718	0.706278
$960$	−59.7897	−1.92970
$961$	15.1908	0.490025
$962$	−1.59712	−0.0514931
$963$	−21.1024	−0.680014
$964$	18.0718	0.582055
$965$	83.7047	2.69455
$966$	12.1845	0.392030
$967$	20.1201	0.647020	0.323510	−	0.946225i	$-0.395137\pi$
$967$	20.1201	0.647020	0.323510	+	0.946225i	$0.395137\pi$
$968$	11.7148	0.376529
$969$	7.34457	0.235942
$970$	87.7956	2.81895
$971$	32.1204	1.03079	0.515397	−	0.856952i	$-0.327645\pi$
$971$	32.1204	1.03079	0.515397	+	0.856952i	$0.327645\pi$
$972$	−34.4154	−1.10387
$973$	73.5308	2.35729
$974$	1.55078	0.0496902
$975$	−9.32870	−0.298757
$976$	26.2266	0.839493
$977$	−11.2025	−0.358399	−0.179200	−	0.983813i	$-0.557351\pi$
$977$	−11.2025	−0.358399	−0.179200	+	0.983813i	$0.557351\pi$
$978$	13.7360	0.439230
$979$	−10.3863	−0.331947
$980$	−103.734	−3.31365
$981$	−1.37250	−0.0438207
$982$	−50.5333	−1.61258
$983$	−38.1760	−1.21763	−0.608813	−	0.793314i	$-0.708354\pi$
$983$	−38.1760	−1.21763	−0.608813	+	0.793314i	$0.708354\pi$
$984$	−4.95062	−0.157820
$985$	10.6163	0.338264
$986$	18.5377	0.590360
$987$	38.5144	1.22593
$988$	3.02681	0.0962958
$989$	8.65028	0.275063
$990$	19.3379	0.614597
$991$	−9.42279	−0.299325	−0.149662	−	0.988737i	$-0.547819\pi$
$991$	−9.42279	−0.299325	−0.149662	+	0.988737i	$0.547819\pi$
$992$	−52.2111	−1.65770
$993$	−17.4157	−0.552669
$994$	102.031	3.23622
$995$	55.9241	1.77291
$996$	−46.1247	−1.46152
$997$	−53.3359	−1.68917	−0.844583	−	0.535425i	$-0.820151\pi$
$997$	−53.3359	−1.68917	−0.844583	+	0.535425i	$0.820151\pi$
$998$	−58.5142	−1.85223
$999$	5.57815	0.176485

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.c.1.13	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.c.1.13	✓	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)

\(f(q)\)	\(=\)	\(q-2.16010 q^{2} -1.27573 q^{3} +2.66602 q^{4} -3.85876 q^{5} +2.75571 q^{6} +4.13321 q^{7} -1.43868 q^{8} -1.37250 q^{9} +O(q^{10})\)	\(q-2.16010 q^{2} -1.27573 q^{3} +2.66602 q^{4} -3.85876 q^{5} +2.75571 q^{6} +4.13321 q^{7} -1.43868 q^{8} -1.37250 q^{9} +8.33530 q^{10} -1.69034 q^{11} -3.40114 q^{12} +0.739372 q^{13} -8.92814 q^{14} +4.92275 q^{15} -2.22436 q^{16} -3.74928 q^{17} +2.96474 q^{18} +1.53553 q^{19} -10.2876 q^{20} -5.27287 q^{21} +3.65129 q^{22} +1.06976 q^{23} +1.83537 q^{24} +9.89004 q^{25} -1.59712 q^{26} +5.57815 q^{27} +11.0192 q^{28} +2.28894 q^{29} -10.6336 q^{30} -6.79638 q^{31} +7.68220 q^{32} +2.15642 q^{33} +8.09881 q^{34} -15.9491 q^{35} -3.65913 q^{36} +1.00000 q^{37} -3.31690 q^{38} -0.943241 q^{39} +5.55152 q^{40} -2.69734 q^{41} +11.3899 q^{42} +8.08618 q^{43} -4.50648 q^{44} +5.29617 q^{45} -2.31079 q^{46} -7.30426 q^{47} +2.83769 q^{48} +10.0834 q^{49} -21.3635 q^{50} +4.78308 q^{51} +1.97118 q^{52} -10.9530 q^{53} -12.0494 q^{54} +6.52260 q^{55} -5.94636 q^{56} -1.95893 q^{57} -4.94433 q^{58} +14.6621 q^{59} +13.1242 q^{60} -11.7906 q^{61} +14.6808 q^{62} -5.67285 q^{63} -12.1456 q^{64} -2.85306 q^{65} -4.65807 q^{66} -10.0426 q^{67} -9.99567 q^{68} -1.36473 q^{69} +34.4516 q^{70} -11.4280 q^{71} +1.97459 q^{72} +8.90501 q^{73} -2.16010 q^{74} -12.6171 q^{75} +4.09377 q^{76} -6.98651 q^{77} +2.03749 q^{78} -1.53896 q^{79} +8.58328 q^{80} -2.99872 q^{81} +5.82652 q^{82} +13.5616 q^{83} -14.0576 q^{84} +14.4676 q^{85} -17.4669 q^{86} -2.92007 q^{87} +2.43185 q^{88} +6.14450 q^{89} -11.4402 q^{90} +3.05598 q^{91} +2.85201 q^{92} +8.67037 q^{93} +15.7779 q^{94} -5.92525 q^{95} -9.80044 q^{96} +10.5330 q^{97} -21.7812 q^{98} +2.31999 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 9 q^{2} - 27 q^{3} + 73 q^{4} - 16 q^{5} - 2 q^{6} - 23 q^{7} - 24 q^{8} + 66 q^{9}+O(q^{10}) \) 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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