LMFDB - Embedded newform 4033.2.a.c.1.12

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			1.12
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)

$f(q)$	$=$	$q-2.25323 q^{2} -3.09773 q^{3} +3.07703 q^{4} +4.21432 q^{5} +6.97988 q^{6} -2.71387 q^{7} -2.42679 q^{8} +6.59591 q^{9} +O(q^{10})$	\(q-2.25323 q^{2} -3.09773 q^{3} +3.07703 q^{4} +4.21432 q^{5} +6.97988 q^{6} -2.71387 q^{7} -2.42679 q^{8} +6.59591 q^{9} -9.49583 q^{10} -5.27116 q^{11} -9.53179 q^{12} +6.49332 q^{13} +6.11496 q^{14} -13.0548 q^{15} -0.685952 q^{16} -6.74728 q^{17} -14.8621 q^{18} +3.73708 q^{19} +12.9676 q^{20} +8.40683 q^{21} +11.8771 q^{22} +2.37719 q^{23} +7.51753 q^{24} +12.7605 q^{25} -14.6309 q^{26} -11.1391 q^{27} -8.35066 q^{28} -3.48753 q^{29} +29.4155 q^{30} +6.22056 q^{31} +6.39918 q^{32} +16.3286 q^{33} +15.2032 q^{34} -11.4371 q^{35} +20.2958 q^{36} +1.00000 q^{37} -8.42049 q^{38} -20.1145 q^{39} -10.2273 q^{40} -7.24759 q^{41} -18.9425 q^{42} -2.56694 q^{43} -16.2195 q^{44} +27.7973 q^{45} -5.35635 q^{46} -7.19003 q^{47} +2.12489 q^{48} +0.365094 q^{49} -28.7524 q^{50} +20.9012 q^{51} +19.9801 q^{52} -2.10804 q^{53} +25.0990 q^{54} -22.2144 q^{55} +6.58599 q^{56} -11.5765 q^{57} +7.85819 q^{58} +11.8319 q^{59} -40.1701 q^{60} +3.62469 q^{61} -14.0163 q^{62} -17.9004 q^{63} -13.0469 q^{64} +27.3649 q^{65} -36.7920 q^{66} -14.1243 q^{67} -20.7616 q^{68} -7.36389 q^{69} +25.7704 q^{70} -8.75155 q^{71} -16.0069 q^{72} -3.39991 q^{73} -2.25323 q^{74} -39.5286 q^{75} +11.4991 q^{76} +14.3052 q^{77} +45.3226 q^{78} +9.60315 q^{79} -2.89083 q^{80} +14.7183 q^{81} +16.3305 q^{82} -8.49065 q^{83} +25.8681 q^{84} -28.4352 q^{85} +5.78391 q^{86} +10.8034 q^{87} +12.7920 q^{88} +7.44998 q^{89} -62.6336 q^{90} -17.6220 q^{91} +7.31469 q^{92} -19.2696 q^{93} +16.2008 q^{94} +15.7493 q^{95} -19.8229 q^{96} +0.510399 q^{97} -0.822639 q^{98} -34.7681 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.25323	−1.59327	−0.796636	−	0.604460i	$-0.793389\pi$
$2$	−2.25323	−1.59327	−0.796636	+	0.604460i	$0.793389\pi$
$3$	−3.09773	−1.78847	−0.894237	−	0.447595i	$-0.852281\pi$
$3$	−3.09773	−1.78847	−0.894237	+	0.447595i	$0.852281\pi$
$4$	3.07703	1.53851
$5$	4.21432	1.88470	0.942352	−	0.334624i	$-0.108609\pi$
$5$	4.21432	1.88470	0.942352	+	0.334624i	$0.108609\pi$
$6$	6.97988	2.84952
$7$	−2.71387	−1.02575	−0.512873	−	0.858464i	$-0.671419\pi$
$7$	−2.71387	−1.02575	−0.512873	+	0.858464i	$0.671419\pi$
$8$	−2.42679	−0.857999
$9$	6.59591	2.19864
$10$	−9.49583	−3.00284
$11$	−5.27116	−1.58931	−0.794657	−	0.607059i	$-0.792349\pi$
$11$	−5.27116	−1.58931	−0.794657	+	0.607059i	$0.792349\pi$
$12$	−9.53179	−2.75159
$13$	6.49332	1.80092	0.900461	−	0.434937i	$-0.143229\pi$
$13$	6.49332	1.80092	0.900461	+	0.434937i	$0.143229\pi$
$14$	6.11496	1.63429
$15$	−13.0548	−3.37074
$16$	−0.685952	−0.171488
$17$	−6.74728	−1.63646	−0.818228	−	0.574894i	$-0.805043\pi$
$17$	−6.74728	−1.63646	−0.818228	+	0.574894i	$0.805043\pi$
$18$	−14.8621	−3.50302
$19$	3.73708	0.857345	0.428673	−	0.903460i	$-0.358981\pi$
$19$	3.73708	0.857345	0.428673	+	0.903460i	$0.358981\pi$
$20$	12.9676	2.89964
$21$	8.40683	1.83452
$22$	11.8771	2.53221
$23$	2.37719	0.495679	0.247840	−	0.968801i	$-0.420279\pi$
$23$	2.37719	0.495679	0.247840	+	0.968801i	$0.420279\pi$
$24$	7.51753	1.53451
$25$	12.7605	2.55211
$26$	−14.6309	−2.86936
$27$	−11.1391	−2.14373
$28$	−8.35066	−1.57813
$29$	−3.48753	−0.647617	−0.323809	−	0.946123i	$-0.604963\pi$
$29$	−3.48753	−0.647617	−0.323809	+	0.946123i	$0.604963\pi$
$30$	29.4155	5.37051
$31$	6.22056	1.11725	0.558623	−	0.829422i	$-0.311330\pi$
$31$	6.22056	1.11725	0.558623	+	0.829422i	$0.311330\pi$
$32$	6.39918	1.13123
$33$	16.3286	2.84244
$34$	15.2032	2.60732
$35$	−11.4371	−1.93323
$36$	20.2958	3.38263
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	−8.42049	−1.36598
$39$	−20.1145	−3.22090
$40$	−10.2273	−1.61707
$41$	−7.24759	−1.13188	−0.565942	−	0.824445i	$-0.691487\pi$
$41$	−7.24759	−1.13188	−0.565942	+	0.824445i	$0.691487\pi$
$42$	−18.9425	−2.92289
$43$	−2.56694	−0.391455	−0.195728	−	0.980658i	$-0.562707\pi$
$43$	−2.56694	−0.391455	−0.195728	+	0.980658i	$0.562707\pi$
$44$	−16.2195	−2.44518
$45$	27.7973	4.14378
$46$	−5.35635	−0.789751
$47$	−7.19003	−1.04877	−0.524387	−	0.851480i	$-0.675705\pi$
$47$	−7.19003	−1.04877	−0.524387	+	0.851480i	$0.675705\pi$
$48$	2.12489	0.306702
$49$	0.365094	0.0521562
$50$	−28.7524	−4.06620
$51$	20.9012	2.92676
$52$	19.9801	2.77074
$53$	−2.10804	−0.289561	−0.144781	−	0.989464i	$-0.546248\pi$
$53$	−2.10804	−0.289561	−0.144781	+	0.989464i	$0.546248\pi$
$54$	25.0990	3.41554
$55$	−22.2144	−2.99538
$56$	6.58599	0.880090
$57$	−11.5765	−1.53334
$58$	7.85819	1.03183
$59$	11.8319	1.54039	0.770193	−	0.637811i	$-0.220160\pi$
$59$	11.8319	1.54039	0.770193	+	0.637811i	$0.220160\pi$
$60$	−40.1701	−5.18593
$61$	3.62469	0.464094	0.232047	−	0.972705i	$-0.425458\pi$
$61$	3.62469	0.464094	0.232047	+	0.972705i	$0.425458\pi$
$62$	−14.0163	−1.78008
$63$	−17.9004	−2.25524
$64$	−13.0469	−1.63086
$65$	27.3649	3.39420
$66$	−36.7920	−4.52879
$67$	−14.1243	−1.72556	−0.862782	−	0.505577i	$-0.831280\pi$
$67$	−14.1243	−1.72556	−0.862782	+	0.505577i	$0.831280\pi$
$68$	−20.7616	−2.51771
$69$	−7.36389	−0.886509
$70$	25.7704	3.08016
$71$	−8.75155	−1.03862	−0.519309	−	0.854586i	$-0.673811\pi$
$71$	−8.75155	−1.03862	−0.519309	+	0.854586i	$0.673811\pi$
$72$	−16.0069	−1.88643
$73$	−3.39991	−0.397930	−0.198965	−	0.980007i	$-0.563758\pi$
$73$	−3.39991	−0.397930	−0.198965	+	0.980007i	$0.563758\pi$
$74$	−2.25323	−0.261932
$75$	−39.5286	−4.56437
$76$	11.4991	1.31904
$77$	14.3052	1.63023
$78$	45.3226	5.13177
$79$	9.60315	1.08044	0.540219	−	0.841524i	$-0.318341\pi$
$79$	9.60315	1.08044	0.540219	+	0.841524i	$0.318341\pi$
$80$	−2.89083	−0.323204
$81$	14.7183	1.63536
$82$	16.3305	1.80340
$83$	−8.49065	−0.931970	−0.465985	−	0.884793i	$-0.654300\pi$
$83$	−8.49065	−0.931970	−0.465985	+	0.884793i	$0.654300\pi$
$84$	25.8681	2.82244
$85$	−28.4352	−3.08423
$86$	5.78391	0.623695
$87$	10.8034	1.15825
$88$	12.7920	1.36363
$89$	7.44998	0.789697	0.394848	−	0.918746i	$-0.370797\pi$
$89$	7.44998	0.789697	0.394848	+	0.918746i	$0.370797\pi$
$90$	−62.6336	−6.60216
$91$	−17.6220	−1.84729
$92$	7.31469	0.762609
$93$	−19.2696	−1.99816
$94$	16.2008	1.67098
$95$	15.7493	1.61584
$96$	−19.8229	−2.02317
$97$	0.510399	0.0518232	0.0259116	−	0.999664i	$-0.491751\pi$
$97$	0.510399	0.0518232	0.0259116	+	0.999664i	$0.491751\pi$
$98$	−0.822639	−0.0830991
$99$	−34.7681	−3.49432
$100$	39.2645	3.92645
$101$	−0.265131	−0.0263816	−0.0131908	−	0.999913i	$-0.504199\pi$
$101$	−0.265131	−0.0263816	−0.0131908	+	0.999913i	$0.504199\pi$
$102$	−47.0952	−4.66312
$103$	−19.5995	−1.93119	−0.965597	−	0.260045i	$-0.916263\pi$
$103$	−19.5995	−1.93119	−0.965597	+	0.260045i	$0.916263\pi$
$104$	−15.7579	−1.54519
$105$	35.4291	3.45753
$106$	4.74988	0.461349
$107$	−1.88409	−0.182142	−0.0910710	−	0.995844i	$-0.529029\pi$
$107$	−1.88409	−0.182142	−0.0910710	+	0.995844i	$0.529029\pi$
$108$	−34.2754	−3.29816
$109$	1.00000	0.0957826
$109$	1.00000	0.0957826
$110$	50.0540	4.77246
$111$	−3.09773	−0.294023
$112$	1.86159	0.175903
$113$	−3.81141	−0.358547	−0.179274	−	0.983799i	$-0.557375\pi$
$113$	−3.81141	−0.358547	−0.179274	+	0.983799i	$0.557375\pi$
$114$	26.0844	2.44302
$115$	10.0183	0.934208
$116$	−10.7312	−0.996369
$117$	42.8293	3.95957
$118$	−26.6600	−2.45425
$119$	18.3113	1.67859
$120$	31.6813	2.89209
$121$	16.7851	1.52592
$122$	−8.16724	−0.739427
$123$	22.4511	2.02434
$124$	19.1408	1.71890
$125$	32.7054	2.92526
$126$	40.3337	3.59322
$127$	10.2357	0.908275	0.454138	−	0.890932i	$-0.349947\pi$
$127$	10.2357	0.908275	0.454138	+	0.890932i	$0.349947\pi$
$128$	16.5993	1.46718
$129$	7.95169	0.700107
$130$	−61.6594	−5.40789
$131$	12.1690	1.06321	0.531604	−	0.846993i	$-0.321590\pi$
$131$	12.1690	1.06321	0.531604	+	0.846993i	$0.321590\pi$
$132$	50.2436	4.37314
$133$	−10.1420	−0.879419
$134$	31.8253	2.74929
$135$	−46.9439	−4.04029
$136$	16.3742	1.40408
$137$	−8.36979	−0.715080	−0.357540	−	0.933898i	$-0.616384\pi$
$137$	−8.36979	−0.715080	−0.357540	+	0.933898i	$0.616384\pi$
$138$	16.5925	1.41245
$139$	8.79403	0.745900	0.372950	−	0.927851i	$-0.378346\pi$
$139$	8.79403	0.745900	0.372950	+	0.927851i	$0.378346\pi$
$140$	−35.1924	−2.97430
$141$	22.2727	1.87570
$142$	19.7192	1.65480
$143$	−34.2273	−2.86223
$144$	−4.52448	−0.377040
$145$	−14.6976	−1.22057
$146$	7.66078	0.634010
$147$	−1.13096	−0.0932800
$148$	3.07703	0.252930
$149$	0.363686	0.0297943	0.0148972	−	0.999889i	$-0.495258\pi$
$149$	0.363686	0.0297943	0.0148972	+	0.999889i	$0.495258\pi$
$150$	89.0670	7.27229
$151$	19.4246	1.58075	0.790376	−	0.612622i	$-0.209885\pi$
$151$	19.4246	1.58075	0.790376	+	0.612622i	$0.209885\pi$
$152$	−9.06911	−0.735602
$153$	−44.5045	−3.59797
$154$	−32.2329	−2.59740
$155$	26.2155	2.10568
$156$	−61.8929	−4.95540
$157$	−8.41449	−0.671550	−0.335775	−	0.941942i	$-0.608998\pi$
$157$	−8.41449	−0.671550	−0.335775	+	0.941942i	$0.608998\pi$
$158$	−21.6381	−1.72143
$159$	6.53012	0.517872
$160$	26.9682	2.13203
$161$	−6.45139	−0.508441
$162$	−33.1636	−2.60558
$163$	−0.955548	−0.0748443	−0.0374222	−	0.999300i	$-0.511915\pi$
$163$	−0.955548	−0.0748443	−0.0374222	+	0.999300i	$0.511915\pi$
$164$	−22.3011	−1.74142
$165$	68.8140	5.35716
$166$	19.1314	1.48488
$167$	18.8719	1.46035	0.730175	−	0.683260i	$-0.239438\pi$
$167$	18.8719	1.46035	0.730175	+	0.683260i	$0.239438\pi$
$168$	−20.4016	−1.57402
$169$	29.1632	2.24332
$170$	64.0710	4.91402
$171$	24.6494	1.88499
$172$	−7.89856	−0.602260
$173$	−1.16604	−0.0886525	−0.0443262	−	0.999017i	$-0.514114\pi$
$173$	−1.16604	−0.0886525	−0.0443262	+	0.999017i	$0.514114\pi$
$174$	−24.3425	−1.84540
$175$	−34.6304	−2.61781
$176$	3.61576	0.272548
$177$	−36.6521	−2.75494
$178$	−16.7865	−1.25820
$179$	−11.8652	−0.886847	−0.443423	−	0.896312i	$-0.646236\pi$
$179$	−11.8652	−0.886847	−0.443423	+	0.896312i	$0.646236\pi$
$180$	85.5331	6.37526
$181$	−10.0031	−0.743528	−0.371764	−	0.928327i	$-0.621247\pi$
$181$	−10.0031	−0.743528	−0.371764	+	0.928327i	$0.621247\pi$
$182$	39.7064	2.94323
$183$	−11.2283	−0.830019
$184$	−5.76895	−0.425292
$185$	4.21432	0.309843
$186$	43.4188	3.18362
$187$	35.5660	2.60084
$188$	−22.1239	−1.61355
$189$	30.2302	2.19892
$190$	−35.4867	−2.57447
$191$	−14.5262	−1.05108	−0.525538	−	0.850770i	$-0.676136\pi$
$191$	−14.5262	−1.05108	−0.525538	+	0.850770i	$0.676136\pi$
$192$	40.4157	2.91675
$193$	8.88339	0.639441	0.319720	−	0.947512i	$-0.396411\pi$
$193$	8.88339	0.639441	0.319720	+	0.947512i	$0.396411\pi$
$194$	−1.15005	−0.0825684
$195$	−84.7691	−6.07044
$196$	1.12340	0.0802431
$197$	−18.4866	−1.31712	−0.658559	−	0.752529i	$-0.728834\pi$
$197$	−18.4866	−1.31712	−0.658559	+	0.752529i	$0.728834\pi$
$198$	78.3403	5.56740
$199$	9.97633	0.707203	0.353602	−	0.935396i	$-0.384957\pi$
$199$	9.97633	0.707203	0.353602	+	0.935396i	$0.384957\pi$
$200$	−30.9671	−2.18971
$201$	43.7534	3.08612
$202$	0.597401	0.0420330
$203$	9.46470	0.664291
$204$	64.3137	4.50286
$205$	−30.5437	−2.13327
$206$	44.1620	3.07692
$207$	15.6797	1.08982
$208$	−4.45411	−0.308837
$209$	−19.6987	−1.36259
$210$	−79.8298	−5.50878
$211$	−20.6958	−1.42476	−0.712380	−	0.701794i	$-0.752383\pi$
$211$	−20.6958	−1.42476	−0.712380	+	0.701794i	$0.752383\pi$
$212$	−6.48649	−0.445494
$213$	27.1099	1.85754
$214$	4.24528	0.290202
$215$	−10.8179	−0.737777
$216$	27.0323	1.83932
$217$	−16.8818	−1.14601
$218$	−2.25323	−0.152608
$219$	10.5320	0.711687
$220$	−68.3542	−4.60844
$221$	−43.8122	−2.94713
$222$	6.97988	0.468459
$223$	1.98096	0.132655	0.0663274	−	0.997798i	$-0.478872\pi$
$223$	1.98096	0.132655	0.0663274	+	0.997798i	$0.478872\pi$
$224$	−17.3666	−1.16035
$225$	84.1673	5.61115
$226$	8.58797	0.571263
$227$	23.4725	1.55792	0.778962	−	0.627071i	$-0.215746\pi$
$227$	23.4725	1.55792	0.778962	+	0.627071i	$0.215746\pi$
$228$	−35.6211	−2.35906
$229$	−9.25664	−0.611696	−0.305848	−	0.952080i	$-0.598940\pi$
$229$	−9.25664	−0.611696	−0.305848	+	0.952080i	$0.598940\pi$
$230$	−22.5734	−1.48845
$231$	−44.3137	−2.91563
$232$	8.46349	0.555655
$233$	9.61814	0.630105	0.315053	−	0.949074i	$-0.397978\pi$
$233$	9.61814	0.630105	0.315053	+	0.949074i	$0.397978\pi$
$234$	−96.5041	−6.30867
$235$	−30.3011	−1.97663
$236$	36.4072	2.36991
$237$	−29.7479	−1.93234
$238$	−41.2594	−2.67445
$239$	11.8012	0.763356	0.381678	−	0.924295i	$-0.375346\pi$
$239$	11.8012	0.763356	0.381678	+	0.924295i	$0.375346\pi$
$240$	8.95499	0.578042
$241$	−9.99901	−0.644093	−0.322046	−	0.946724i	$-0.604371\pi$
$241$	−9.99901	−0.644093	−0.322046	+	0.946724i	$0.604371\pi$
$242$	−37.8206	−2.43120
$243$	−12.1758	−0.781077
$244$	11.1533	0.714015
$245$	1.53862	0.0982990
$246$	−50.5873	−3.22533
$247$	24.2660	1.54401
$248$	−15.0960	−0.958596
$249$	26.3017	1.66680
$250$	−73.6927	−4.66073
$251$	−4.48969	−0.283387	−0.141693	−	0.989911i	$-0.545255\pi$
$251$	−4.48969	−0.283387	−0.141693	+	0.989911i	$0.545255\pi$
$252$	−55.0802	−3.46972
$253$	−12.5306	−0.787789
$254$	−23.0634	−1.44713
$255$	88.0846	5.51607
$256$	−11.3081	−0.706755
$257$	−1.16187	−0.0724754	−0.0362377	−	0.999343i	$-0.511537\pi$
$257$	−1.16187	−0.0724754	−0.0362377	+	0.999343i	$0.511537\pi$
$258$	−17.9170	−1.11546
$259$	−2.71387	−0.168632
$260$	84.2027	5.22203
$261$	−23.0034	−1.42388
$262$	−27.4194	−1.69398
$263$	−17.4847	−1.07815	−0.539076	−	0.842257i	$-0.681227\pi$
$263$	−17.4847	−1.07815	−0.539076	+	0.842257i	$0.681227\pi$
$264$	−39.6261	−2.43882
$265$	−8.88395	−0.545737
$266$	22.8521	1.40115
$267$	−23.0780	−1.41235
$268$	−43.4610	−2.65480
$269$	10.0133	0.610520	0.305260	−	0.952269i	$-0.401257\pi$
$269$	10.0133	0.610520	0.305260	+	0.952269i	$0.401257\pi$
$270$	105.775	6.43728
$271$	−2.36241	−0.143506	−0.0717530	−	0.997422i	$-0.522859\pi$
$271$	−2.36241	−0.143506	−0.0717530	+	0.997422i	$0.522859\pi$
$272$	4.62831	0.280633
$273$	54.5882	3.30383
$274$	18.8590	1.13932
$275$	−67.2627	−4.05610
$276$	−22.6589	−1.36391
$277$	−10.9540	−0.658164	−0.329082	−	0.944301i	$-0.606739\pi$
$277$	−10.9540	−0.658164	−0.329082	+	0.944301i	$0.606739\pi$
$278$	−19.8149	−1.18842
$279$	41.0302	2.45642
$280$	27.7555	1.65871
$281$	−3.93808	−0.234926	−0.117463	−	0.993077i	$-0.537476\pi$
$281$	−3.93808	−0.234926	−0.117463	+	0.993077i	$0.537476\pi$
$282$	−50.1855	−2.98850
$283$	11.2392	0.668101	0.334050	−	0.942555i	$-0.391584\pi$
$283$	11.2392	0.668101	0.334050	+	0.942555i	$0.391584\pi$
$284$	−26.9288	−1.59793
$285$	−48.7869	−2.88989
$286$	77.1218	4.56031
$287$	19.6690	1.16103
$288$	42.2084	2.48716
$289$	28.5258	1.67799
$290$	33.1169	1.94469
$291$	−1.58108	−0.0926844
$292$	−10.4616	−0.612221
$293$	−17.5614	−1.02595	−0.512974	−	0.858404i	$-0.671456\pi$
$293$	−17.5614	−1.02595	−0.512974	+	0.858404i	$0.671456\pi$
$294$	2.54831	0.148620
$295$	49.8636	2.90317
$296$	−2.42679	−0.141054
$297$	58.7161	3.40706
$298$	−0.819467	−0.0474705
$299$	15.4359	0.892679
$300$	−121.631	−7.02235
$301$	6.96635	0.401534
$302$	−43.7680	−2.51857
$303$	0.821304	0.0471827
$304$	−2.56346	−0.147024
$305$	15.2756	0.874679
$306$	100.279	5.73255
$307$	−28.0412	−1.60040	−0.800199	−	0.599735i	$-0.795273\pi$
$307$	−28.0412	−1.60040	−0.800199	+	0.599735i	$0.795273\pi$
$308$	44.0176	2.50814
$309$	60.7138	3.45389
$310$	−59.0694	−3.35491
$311$	−16.2213	−0.919826	−0.459913	−	0.887964i	$-0.652119\pi$
$311$	−16.2213	−0.919826	−0.459913	+	0.887964i	$0.652119\pi$
$312$	48.8137	2.76353
$313$	8.63958	0.488338	0.244169	−	0.969733i	$-0.421485\pi$
$313$	8.63958	0.488338	0.244169	+	0.969733i	$0.421485\pi$
$314$	18.9598	1.06996
$315$	−75.4383	−4.25046
$316$	29.5492	1.66227
$317$	−11.1788	−0.627862	−0.313931	−	0.949446i	$-0.601646\pi$
$317$	−11.1788	−0.627862	−0.313931	+	0.949446i	$0.601646\pi$
$318$	−14.7138	−0.825111
$319$	18.3833	1.02927
$320$	−54.9839	−3.07369
$321$	5.83640	0.325756
$322$	14.5365	0.810085
$323$	−25.2151	−1.40301
$324$	45.2886	2.51603
$325$	82.8582	4.59614
$326$	2.15307	0.119247
$327$	−3.09773	−0.171305
$328$	17.5884	0.971156
$329$	19.5128	1.07578
$330$	−155.054	−8.53542
$331$	−17.2809	−0.949841	−0.474921	−	0.880029i	$-0.657523\pi$
$331$	−17.2809	−0.949841	−0.474921	+	0.880029i	$0.657523\pi$
$332$	−26.1260	−1.43385
$333$	6.59591	0.361454
$334$	−42.5226	−2.32673
$335$	−59.5246	−3.25217
$336$	−5.76668	−0.314598
$337$	−2.83699	−0.154541	−0.0772703	−	0.997010i	$-0.524620\pi$
$337$	−2.83699	−0.154541	−0.0772703	+	0.997010i	$0.524620\pi$
$338$	−65.7112	−3.57422
$339$	11.8067	0.641252
$340$	−87.4960	−4.74514
$341$	−32.7895	−1.77565
$342$	−55.5408	−3.00330
$343$	18.0063	0.972248
$344$	6.22943	0.335868
$345$	−31.0338	−1.67081
$346$	2.62735	0.141247
$347$	20.7927	1.11621	0.558106	−	0.829769i	$-0.311528\pi$
$347$	20.7927	1.11621	0.558106	+	0.829769i	$0.311528\pi$
$348$	33.2424	1.78198
$349$	−26.7752	−1.43325	−0.716623	−	0.697461i	$-0.754313\pi$
$349$	−26.7752	−1.43325	−0.716623	+	0.697461i	$0.754313\pi$
$350$	78.0302	4.17089
$351$	−72.3300	−3.86069
$352$	−33.7311	−1.79787
$353$	10.0894	0.537007	0.268504	−	0.963279i	$-0.413471\pi$
$353$	10.0894	0.537007	0.268504	+	0.963279i	$0.413471\pi$
$354$	82.5854	4.38936
$355$	−36.8819	−1.95749
$356$	22.9238	1.21496
$357$	−56.7232	−3.00211
$358$	26.7350	1.41299
$359$	8.14282	0.429762	0.214881	−	0.976640i	$-0.431064\pi$
$359$	8.14282	0.429762	0.214881	+	0.976640i	$0.431064\pi$
$360$	−67.4582	−3.55536
$361$	−5.03423	−0.264959
$362$	22.5393	1.18464
$363$	−51.9956	−2.72906
$364$	−54.2235	−2.84208
$365$	−14.3283	−0.749980
$366$	25.2999	1.32245
$367$	−1.58332	−0.0826489	−0.0413244	−	0.999146i	$-0.513158\pi$
$367$	−1.58332	−0.0826489	−0.0413244	+	0.999146i	$0.513158\pi$
$368$	−1.63064	−0.0850031
$369$	−47.8045	−2.48860
$370$	−9.49583	−0.493665
$371$	5.72094	0.297016
$372$	−59.2931	−3.07420
$373$	5.55671	0.287715	0.143858	−	0.989598i	$-0.454049\pi$
$373$	5.55671	0.287715	0.143858	+	0.989598i	$0.454049\pi$
$374$	−80.1382	−4.14385
$375$	−101.312	−5.23175
$376$	17.4487	0.899847
$377$	−22.6456	−1.16631
$378$	−68.1154	−3.50348
$379$	20.5129	1.05367	0.526837	−	0.849966i	$-0.323378\pi$
$379$	20.5129	1.05367	0.526837	+	0.849966i	$0.323378\pi$
$380$	48.4610	2.48599
$381$	−31.7075	−1.62443
$382$	32.7307	1.67465
$383$	−34.9937	−1.78810	−0.894048	−	0.447971i	$-0.852147\pi$
$383$	−34.9937	−1.78810	−0.894048	+	0.447971i	$0.852147\pi$
$384$	−51.4200	−2.62401
$385$	60.2869	3.07250
$386$	−20.0163	−1.01880
$387$	−16.9313	−0.860668
$388$	1.57051	0.0797307
$389$	3.15579	0.160005	0.0800025	−	0.996795i	$-0.474507\pi$
$389$	3.15579	0.160005	0.0800025	+	0.996795i	$0.474507\pi$
$390$	191.004	9.67186
$391$	−16.0396	−0.811157
$392$	−0.886005	−0.0447500
$393$	−37.6961	−1.90152
$394$	41.6546	2.09853
$395$	40.4708	2.03631
$396$	−106.982	−5.37606
$397$	17.7287	0.889776	0.444888	−	0.895586i	$-0.353243\pi$
$397$	17.7287	0.889776	0.444888	+	0.895586i	$0.353243\pi$
$398$	−22.4789	−1.12677
$399$	31.4170	1.57282
$400$	−8.75312	−0.437656
$401$	−20.8703	−1.04221	−0.521106	−	0.853492i	$-0.674481\pi$
$401$	−20.8703	−1.04221	−0.521106	+	0.853492i	$0.674481\pi$
$402$	−98.5862	−4.91703
$403$	40.3921	2.01207
$404$	−0.815817	−0.0405884
$405$	62.0276	3.08218
$406$	−21.3261	−1.05840
$407$	−5.27116	−0.261281
$408$	−50.7229	−2.51116
$409$	15.2990	0.756485	0.378242	−	0.925707i	$-0.376529\pi$
$409$	15.2990	0.756485	0.378242	+	0.925707i	$0.376529\pi$
$410$	68.8219	3.39887
$411$	25.9273	1.27890
$412$	−60.3081	−2.97117
$413$	−32.1103	−1.58005
$414$	−35.3300	−1.73638
$415$	−35.7824	−1.75649
$416$	41.5519	2.03725
$417$	−27.2415	−1.33402
$418$	44.3857	2.17098
$419$	6.42955	0.314104	0.157052	−	0.987590i	$-0.449801\pi$
$419$	6.42955	0.314104	0.157052	+	0.987590i	$0.449801\pi$
$420$	109.016	5.31945
$421$	−24.2121	−1.18002	−0.590012	−	0.807395i	$-0.700877\pi$
$421$	−24.2121	−1.18002	−0.590012	+	0.807395i	$0.700877\pi$
$422$	46.6324	2.27003
$423$	−47.4247	−2.30587
$424$	5.11576	0.248443
$425$	−86.0989	−4.17641
$426$	−61.0848	−2.95957
$427$	−9.83693	−0.476043
$428$	−5.79740	−0.280228
$429$	106.027	5.11902
$430$	24.3753	1.17548
$431$	25.1440	1.21114	0.605572	−	0.795790i	$-0.292944\pi$
$431$	25.1440	1.21114	0.605572	+	0.795790i	$0.292944\pi$
$432$	7.64092	0.367624
$433$	10.3898	0.499300	0.249650	−	0.968336i	$-0.419684\pi$
$433$	10.3898	0.499300	0.249650	+	0.968336i	$0.419684\pi$
$434$	38.0385	1.82591
$435$	45.5290	2.18295
$436$	3.07703	0.147363
$437$	8.88376	0.424968
$438$	−23.7310	−1.13391
$439$	30.0645	1.43490	0.717450	−	0.696610i	$-0.245309\pi$
$439$	30.0645	1.43490	0.717450	+	0.696610i	$0.245309\pi$
$440$	53.9096	2.57004
$441$	2.40812	0.114673
$442$	98.7189	4.69558
$443$	−7.47006	−0.354913	−0.177457	−	0.984129i	$-0.556787\pi$
$443$	−7.47006	−0.354913	−0.177457	+	0.984129i	$0.556787\pi$
$444$	−9.53179	−0.452359
$445$	31.3966	1.48834
$446$	−4.46355	−0.211355
$447$	−1.12660	−0.0532864
$448$	35.4076	1.67285
$449$	−19.4443	−0.917633	−0.458817	−	0.888531i	$-0.651726\pi$
$449$	−19.4443	−0.917633	−0.458817	+	0.888531i	$0.651726\pi$
$450$	−189.648	−8.94009
$451$	38.2032	1.79892
$452$	−11.7278	−0.551630
$453$	−60.1721	−2.82713
$454$	−52.8889	−2.48220
$455$	−74.2649	−3.48159
$456$	28.0936	1.31560
$457$	−18.4159	−0.861461	−0.430731	−	0.902481i	$-0.641744\pi$
$457$	−18.4159	−0.861461	−0.430731	+	0.902481i	$0.641744\pi$
$458$	20.8573	0.974598
$459$	75.1589	3.50812
$460$	30.8265	1.43729
$461$	33.5363	1.56194	0.780971	−	0.624568i	$-0.214725\pi$
$461$	33.5363	1.56194	0.780971	+	0.624568i	$0.214725\pi$
$462$	99.8488	4.64539
$463$	−22.1475	−1.02928	−0.514641	−	0.857406i	$-0.672075\pi$
$463$	−22.1475	−1.02928	−0.514641	+	0.857406i	$0.672075\pi$
$464$	2.39228	0.111059
$465$	−81.2083	−3.76595
$466$	−21.6718	−1.00393
$467$	−23.6788	−1.09572	−0.547862	−	0.836569i	$-0.684558\pi$
$467$	−23.6788	−1.09572	−0.547862	+	0.836569i	$0.684558\pi$
$468$	131.787	6.09186
$469$	38.3316	1.76999
$470$	68.2752	3.14930
$471$	26.0658	1.20105
$472$	−28.7136	−1.32165
$473$	13.5308	0.622145
$474$	67.0288	3.07873
$475$	47.6871	2.18804
$476$	56.3442	2.58253
$477$	−13.9044	−0.636639
$478$	−26.5908	−1.21623
$479$	−7.06734	−0.322915	−0.161457	−	0.986880i	$-0.551619\pi$
$479$	−7.06734	−0.322915	−0.161457	+	0.986880i	$0.551619\pi$
$480$	−83.5402	−3.81307
$481$	6.49332	0.296070
$482$	22.5300	1.02621
$483$	19.9847	0.909333
$484$	51.6482	2.34764
$485$	2.15099	0.0976713
$486$	27.4348	1.24447
$487$	0.633314	0.0286982	0.0143491	−	0.999897i	$-0.495432\pi$
$487$	0.633314	0.0286982	0.0143491	+	0.999897i	$0.495432\pi$
$488$	−8.79635	−0.398192
$489$	2.96003	0.133857
$490$	−3.46687	−0.156617
$491$	28.2116	1.27317	0.636586	−	0.771206i	$-0.280346\pi$
$491$	28.2116	1.27317	0.636586	+	0.771206i	$0.280346\pi$
$492$	69.0826	3.11448
$493$	23.5313	1.05980
$494$	−54.6769	−2.46003
$495$	−146.524	−6.58576
$496$	−4.26701	−0.191594
$497$	23.7506	1.06536
$498$	−59.2637	−2.65567
$499$	−40.4238	−1.80962	−0.904809	−	0.425818i	$-0.859987\pi$
$499$	−40.4238	−1.80962	−0.904809	+	0.425818i	$0.859987\pi$
$500$	100.635	4.50055
$501$	−58.4599	−2.61180
$502$	10.1163	0.451512
$503$	−37.3979	−1.66749	−0.833746	−	0.552149i	$-0.813808\pi$
$503$	−37.3979	−1.66749	−0.833746	+	0.552149i	$0.813808\pi$
$504$	43.4406	1.93500
$505$	−1.11735	−0.0497214
$506$	28.2342	1.25516
$507$	−90.3395	−4.01212
$508$	31.4957	1.39739
$509$	−5.92704	−0.262711	−0.131356	−	0.991335i	$-0.541933\pi$
$509$	−5.92704	−0.262711	−0.131356	+	0.991335i	$0.541933\pi$
$510$	−198.474	−8.78860
$511$	9.22693	0.408175
$512$	−7.71886	−0.341129
$513$	−41.6279	−1.83791
$514$	2.61795	0.115473
$515$	−82.5985	−3.63973
$516$	24.4676	1.07713
$517$	37.8997	1.66683
$518$	6.11496	0.268676
$519$	3.61208	0.158553
$520$	−66.4089	−2.91222
$521$	1.99652	0.0874692	0.0437346	−	0.999043i	$-0.486074\pi$
$521$	1.99652	0.0874692	0.0437346	+	0.999043i	$0.486074\pi$
$522$	51.8319	2.26862
$523$	−7.00425	−0.306274	−0.153137	−	0.988205i	$-0.548938\pi$
$523$	−7.00425	−0.306274	−0.153137	+	0.988205i	$0.548938\pi$
$524$	37.4443	1.63576
$525$	107.276	4.68189
$526$	39.3970	1.71779
$527$	−41.9719	−1.82832
$528$	−11.2006	−0.487445
$529$	−17.3490	−0.754302
$530$	20.0176	0.869507
$531$	78.0423	3.38675
$532$	−31.2071	−1.35300
$533$	−47.0609	−2.03843
$534$	52.0000	2.25026
$535$	−7.94017	−0.343283
$536$	34.2768	1.48053
$537$	36.7551	1.58610
$538$	−22.5622	−0.972724
$539$	−1.92447	−0.0828926
$540$	−144.448	−6.21605
$541$	−25.3987	−1.09197	−0.545987	−	0.837794i	$-0.683845\pi$
$541$	−25.3987	−1.09197	−0.545987	+	0.837794i	$0.683845\pi$
$542$	5.32303	0.228644
$543$	30.9870	1.32978
$544$	−43.1771	−1.85120
$545$	4.21432	0.180522
$546$	−123.000	−5.26390
$547$	9.13682	0.390662	0.195331	−	0.980737i	$-0.437422\pi$
$547$	9.13682	0.390662	0.195331	+	0.980737i	$0.437422\pi$
$548$	−25.7541	−1.10016
$549$	23.9081	1.02037
$550$	151.558	6.46246
$551$	−13.0332	−0.555232
$552$	17.8706	0.760624
$553$	−26.0617	−1.10826
$554$	24.6819	1.04863
$555$	−13.0548	−0.554146
$556$	27.0595	1.14758
$557$	−32.5340	−1.37851	−0.689255	−	0.724519i	$-0.742062\pi$
$557$	−32.5340	−1.37851	−0.689255	+	0.724519i	$0.742062\pi$
$558$	−92.4504	−3.91374
$559$	−16.6680	−0.704980
$560$	7.84533	0.331526
$561$	−110.174	−4.65154
$562$	8.87337	0.374301
$563$	−17.3775	−0.732376	−0.366188	−	0.930541i	$-0.619337\pi$
$563$	−17.3775	−0.732376	−0.366188	+	0.930541i	$0.619337\pi$
$564$	68.5338	2.88579
$565$	−16.0625	−0.675755
$566$	−25.3245	−1.06447
$567$	−39.9435	−1.67747
$568$	21.2382	0.891134
$569$	−21.3143	−0.893540	−0.446770	−	0.894649i	$-0.647426\pi$
$569$	−21.3143	−0.893540	−0.446770	+	0.894649i	$0.647426\pi$
$570$	109.928	4.60438
$571$	−29.8805	−1.25046	−0.625230	−	0.780440i	$-0.714995\pi$
$571$	−29.8805	−1.25046	−0.625230	+	0.780440i	$0.714995\pi$
$572$	−105.318	−4.40358
$573$	44.9981	1.87982
$574$	−44.3188	−1.84983
$575$	30.3342	1.26503
$576$	−86.0562	−3.58567
$577$	5.90022	0.245629	0.122815	−	0.992430i	$-0.460808\pi$
$577$	5.90022	0.245629	0.122815	+	0.992430i	$0.460808\pi$
$578$	−64.2751	−2.67349
$579$	−27.5183	−1.14362
$580$	−45.2248	−1.87786
$581$	23.0425	0.955965
$582$	3.56252	0.147671
$583$	11.1118	0.460203
$584$	8.25087	0.341424
$585$	180.497	7.46262
$586$	39.5698	1.63461
$587$	−34.6413	−1.42980	−0.714900	−	0.699226i	$-0.753528\pi$
$587$	−34.6413	−1.42980	−0.714900	+	0.699226i	$0.753528\pi$
$588$	−3.48000	−0.143513
$589$	23.2467	0.957865
$590$	−112.354	−4.62554
$591$	57.2666	2.35563
$592$	−0.685952	−0.0281925
$593$	4.64599	0.190788	0.0953940	−	0.995440i	$-0.469589\pi$
$593$	4.64599	0.190788	0.0953940	+	0.995440i	$0.469589\pi$
$594$	−132.301	−5.42837
$595$	77.1696	3.16364
$596$	1.11907	0.0458390
$597$	−30.9039	−1.26481
$598$	−34.7805	−1.42228
$599$	−24.8981	−1.01731	−0.508654	−	0.860971i	$-0.669857\pi$
$599$	−24.8981	−1.01731	−0.508654	+	0.860971i	$0.669857\pi$
$600$	95.9276	3.91623
$601$	22.7459	0.927823	0.463912	−	0.885882i	$-0.346446\pi$
$601$	22.7459	0.927823	0.463912	+	0.885882i	$0.346446\pi$
$602$	−15.6968	−0.639753
$603$	−93.1629	−3.79389
$604$	59.7701	2.43201
$605$	70.7378	2.87590
$606$	−1.85058	−0.0751749
$607$	4.79525	0.194633	0.0973165	−	0.995253i	$-0.468974\pi$
$607$	4.79525	0.194633	0.0973165	+	0.995253i	$0.468974\pi$
$608$	23.9143	0.969851
$609$	−29.3190	−1.18807
$610$	−34.4194	−1.39360
$611$	−46.6871	−1.88876
$612$	−136.941	−5.53553
$613$	−4.22608	−0.170690	−0.0853449	−	0.996351i	$-0.527199\pi$
$613$	−4.22608	−0.170690	−0.0853449	+	0.996351i	$0.527199\pi$
$614$	63.1832	2.54987
$615$	94.6161	3.81529
$616$	−34.7158	−1.39874
$617$	−0.657747	−0.0264799	−0.0132399	−	0.999912i	$-0.504215\pi$
$617$	−0.657747	−0.0264799	−0.0132399	+	0.999912i	$0.504215\pi$
$618$	−136.802	−5.50298
$619$	47.2382	1.89866	0.949331	−	0.314278i	$-0.101762\pi$
$619$	47.2382	1.89866	0.949331	+	0.314278i	$0.101762\pi$
$620$	80.6657	3.23961
$621$	−26.4799	−1.06260
$622$	36.5503	1.46553
$623$	−20.2183	−0.810029
$624$	13.7976	0.552346
$625$	74.0285	2.96114
$626$	−19.4669	−0.778055
$627$	61.0213	2.43696
$628$	−25.8916	−1.03319
$629$	−6.74728	−0.269032
$630$	169.979	6.77214
$631$	−13.7415	−0.547042	−0.273521	−	0.961866i	$-0.588188\pi$
$631$	−13.7415	−0.547042	−0.273521	+	0.961866i	$0.588188\pi$
$632$	−23.3048	−0.927016
$633$	64.1100	2.54814
$634$	25.1883	1.00036
$635$	43.1367	1.71183
$636$	20.0934	0.796754
$637$	2.37067	0.0939293
$638$	−41.4217	−1.63990
$639$	−57.7244	−2.28354
$640$	69.9547	2.76520
$641$	−35.4842	−1.40154	−0.700771	−	0.713387i	$-0.747160\pi$
$641$	−35.4842	−1.40154	−0.700771	+	0.713387i	$0.747160\pi$
$642$	−13.1507	−0.519018
$643$	30.0138	1.18363	0.591814	−	0.806075i	$-0.298412\pi$
$643$	30.0138	1.18363	0.591814	+	0.806075i	$0.298412\pi$
$644$	−19.8511	−0.782244
$645$	33.5110	1.31949
$646$	56.8154	2.23537
$647$	−28.1806	−1.10789	−0.553947	−	0.832552i	$-0.686879\pi$
$647$	−28.1806	−1.10789	−0.553947	+	0.832552i	$0.686879\pi$
$648$	−35.7182	−1.40314
$649$	−62.3679	−2.44816
$650$	−186.698	−7.32291
$651$	52.2952	2.04961
$652$	−2.94025	−0.115149
$653$	40.9791	1.60364	0.801818	−	0.597568i	$-0.203866\pi$
$653$	40.9791	1.60364	0.801818	+	0.597568i	$0.203866\pi$
$654$	6.97988	0.272935
$655$	51.2840	2.00383
$656$	4.97151	0.194105
$657$	−22.4255	−0.874903
$658$	−43.9668	−1.71400
$659$	−24.5298	−0.955547	−0.477773	−	0.878483i	$-0.658556\pi$
$659$	−24.5298	−0.955547	−0.477773	+	0.878483i	$0.658556\pi$
$660$	211.743	8.24207
$661$	−23.2170	−0.903038	−0.451519	−	0.892262i	$-0.649118\pi$
$661$	−23.2170	−0.903038	−0.451519	+	0.892262i	$0.649118\pi$
$662$	38.9377	1.51336
$663$	135.718	5.27086
$664$	20.6050	0.799630
$665$	−42.7415	−1.65744
$666$	−14.8621	−0.575894
$667$	−8.29052	−0.321010
$668$	58.0693	2.24677
$669$	−6.13647	−0.237250
$670$	134.122	5.18160
$671$	−19.1063	−0.737590
$672$	53.7968	2.07526
$673$	−37.4165	−1.44230	−0.721149	−	0.692780i	$-0.756386\pi$
$673$	−37.4165	−1.44230	−0.721149	+	0.692780i	$0.756386\pi$
$674$	6.39238	0.246225
$675$	−142.141	−5.47102
$676$	89.7359	3.45138
$677$	26.6868	1.02566	0.512828	−	0.858491i	$-0.328598\pi$
$677$	26.6868	1.02566	0.512828	+	0.858491i	$0.328598\pi$
$678$	−26.6032	−1.02169
$679$	−1.38516	−0.0531575
$680$	69.0063	2.64627
$681$	−72.7114	−2.78631
$682$	73.8823	2.82910
$683$	−18.4639	−0.706502	−0.353251	−	0.935529i	$-0.614924\pi$
$683$	−18.4639	−0.706502	−0.353251	+	0.935529i	$0.614924\pi$
$684$	75.8470	2.90008
$685$	−35.2730	−1.34771
$686$	−40.5722	−1.54905
$687$	28.6745	1.09400
$688$	1.76080	0.0671299
$689$	−13.6881	−0.521477
$690$	69.9263	2.66205
$691$	3.10743	0.118212	0.0591061	−	0.998252i	$-0.481175\pi$
$691$	3.10743	0.118212	0.0591061	+	0.998252i	$0.481175\pi$
$692$	−3.58794	−0.136393
$693$	94.3560	3.58429
$694$	−46.8507	−1.77843
$695$	37.0609	1.40580
$696$	−26.2176	−0.993775
$697$	48.9016	1.85228
$698$	60.3307	2.28355
$699$	−29.7944	−1.12693
$700$	−106.559	−4.02754
$701$	12.4002	0.468350	0.234175	−	0.972195i	$-0.424761\pi$
$701$	12.4002	0.468350	0.234175	+	0.972195i	$0.424761\pi$
$702$	162.976	6.15112
$703$	3.73708	0.140947
$704$	68.7723	2.59195
$705$	93.8645	3.53514
$706$	−22.7338	−0.855598
$707$	0.719532	0.0270608
$708$	−112.779	−4.23851
$709$	−16.3903	−0.615550	−0.307775	−	0.951459i	$-0.599584\pi$
$709$	−16.3903	−0.615550	−0.307775	+	0.951459i	$0.599584\pi$
$710$	83.1032	3.11881
$711$	63.3415	2.37549
$712$	−18.0795	−0.677559
$713$	14.7875	0.553795
$714$	127.810	4.78318
$715$	−144.245	−5.39445
$716$	−36.5096	−1.36443
$717$	−36.5569	−1.36524
$718$	−18.3476	−0.684727
$719$	−1.85548	−0.0691978	−0.0345989	−	0.999401i	$-0.511015\pi$
$719$	−1.85548	−0.0691978	−0.0345989	+	0.999401i	$0.511015\pi$
$720$	−19.0676	−0.710608
$721$	53.1904	1.98091
$722$	11.3433	0.422152
$723$	30.9742	1.15194
$724$	−30.7799	−1.14393
$725$	−44.5027	−1.65279
$726$	117.158	4.34813
$727$	10.0650	0.373291	0.186646	−	0.982427i	$-0.440238\pi$
$727$	10.0650	0.373291	0.186646	+	0.982427i	$0.440238\pi$
$728$	42.7649	1.58497
$729$	−6.43759	−0.238429
$730$	32.2850	1.19492
$731$	17.3199	0.640599
$732$	−34.5498	−1.27700
$733$	34.7477	1.28344	0.641718	−	0.766941i	$-0.278222\pi$
$733$	34.7477	1.28344	0.641718	+	0.766941i	$0.278222\pi$
$734$	3.56759	0.131682
$735$	−4.76623	−0.175805
$736$	15.2121	0.560725
$737$	74.4516	2.74246
$738$	107.714	3.96502
$739$	5.89184	0.216735	0.108367	−	0.994111i	$-0.465438\pi$
$739$	5.89184	0.216735	0.108367	+	0.994111i	$0.465438\pi$
$740$	12.9676	0.476698
$741$	−75.1696	−2.76142
$742$	−12.8906	−0.473228
$743$	−34.1682	−1.25351	−0.626755	−	0.779217i	$-0.715617\pi$
$743$	−34.1682	−1.25351	−0.626755	+	0.779217i	$0.715617\pi$
$744$	46.7632	1.71442
$745$	1.53269	0.0561535
$746$	−12.5205	−0.458409
$747$	−56.0036	−2.04906
$748$	109.438	4.00143
$749$	5.11318	0.186831
$750$	228.280	8.33560
$751$	−31.1495	−1.13666	−0.568331	−	0.822800i	$-0.692411\pi$
$751$	−31.1495	−1.13666	−0.568331	+	0.822800i	$0.692411\pi$
$752$	4.93202	0.179852
$753$	13.9078	0.506830
$754$	51.0257	1.85825
$755$	81.8616	2.97925
$756$	93.0191	3.38307
$757$	−18.9369	−0.688275	−0.344138	−	0.938919i	$-0.611829\pi$
$757$	−18.9369	−0.688275	−0.344138	+	0.938919i	$0.611829\pi$
$758$	−46.2201	−1.67879
$759$	38.8162	1.40894
$760$	−38.2202	−1.38639
$761$	14.4161	0.522583	0.261292	−	0.965260i	$-0.415852\pi$
$761$	14.4161	0.522583	0.261292	+	0.965260i	$0.415852\pi$
$762$	71.4442	2.58815
$763$	−2.71387	−0.0982487
$764$	−44.6974	−1.61710
$765$	−187.556	−6.78111
$766$	78.8488	2.84892
$767$	76.8284	2.77411
$768$	35.0293	1.26401
$769$	−26.4863	−0.955121	−0.477561	−	0.878599i	$-0.658479\pi$
$769$	−26.4863	−0.955121	−0.477561	+	0.878599i	$0.658479\pi$
$770$	−135.840	−4.89533
$771$	3.59915	0.129620
$772$	27.3345	0.983788
$773$	−46.3856	−1.66838	−0.834188	−	0.551481i	$-0.814063\pi$
$773$	−46.3856	−1.66838	−0.834188	+	0.551481i	$0.814063\pi$
$774$	38.1501	1.37128
$775$	79.3777	2.85133
$776$	−1.23863	−0.0444643
$777$	8.40683	0.301593
$778$	−7.11071	−0.254931
$779$	−27.0848	−0.970415
$780$	−260.837	−9.33946
$781$	46.1308	1.65069
$782$	36.1408	1.29239
$783$	38.8480	1.38832
$784$	−0.250437	−0.00894418
$785$	−35.4614	−1.26567
$786$	84.9379	3.02964
$787$	11.2850	0.402265	0.201133	−	0.979564i	$-0.435538\pi$
$787$	11.2850	0.402265	0.201133	+	0.979564i	$0.435538\pi$
$788$	−56.8839	−2.02641
$789$	54.1628	1.92825
$790$	−91.1898	−3.24439
$791$	10.3437	0.367779
$792$	84.3747	2.99813
$793$	23.5362	0.835797
$794$	−39.9467	−1.41765
$795$	27.5200	0.976035
$796$	30.6975	1.08804
$797$	11.5861	0.410399	0.205200	−	0.978720i	$-0.434216\pi$
$797$	11.5861	0.410399	0.205200	+	0.978720i	$0.434216\pi$
$798$	−70.7896	−2.50592
$799$	48.5131	1.71627
$800$	81.6570	2.88701
$801$	49.1394	1.73626
$802$	47.0255	1.66053
$803$	17.9215	0.632435
$804$	134.630	4.74805
$805$	−27.1883	−0.958261
$806$	−91.0125	−3.20578
$807$	−31.0184	−1.09190
$808$	0.643418	0.0226354
$809$	23.5414	0.827673	0.413837	−	0.910351i	$-0.364189\pi$
$809$	23.5414	0.827673	0.413837	+	0.910351i	$0.364189\pi$
$810$	−139.762	−4.91074
$811$	−23.9526	−0.841089	−0.420544	−	0.907272i	$-0.638161\pi$
$811$	−23.9526	−0.841089	−0.420544	+	0.907272i	$0.638161\pi$
$812$	29.1231	1.02202
$813$	7.31809	0.256656
$814$	11.8771	0.416292
$815$	−4.02699	−0.141059
$816$	−14.3373	−0.501904
$817$	−9.59288	−0.335612
$818$	−34.4720	−1.20529
$819$	−116.233	−4.06152
$820$	−93.9839	−3.28206
$821$	44.1792	1.54186	0.770932	−	0.636918i	$-0.219791\pi$
$821$	44.1792	1.54186	0.770932	+	0.636918i	$0.219791\pi$
$822$	−58.4201	−2.03764
$823$	−2.86645	−0.0999183	−0.0499591	−	0.998751i	$-0.515909\pi$
$823$	−2.86645	−0.0999183	−0.0499591	+	0.998751i	$0.515909\pi$
$824$	47.5638	1.65696
$825$	208.362	7.25422
$826$	72.3518	2.51744
$827$	44.0422	1.53150	0.765749	−	0.643139i	$-0.222368\pi$
$827$	44.0422	1.53150	0.765749	+	0.643139i	$0.222368\pi$
$828$	48.2470	1.67670
$829$	6.76420	0.234930	0.117465	−	0.993077i	$-0.462523\pi$
$829$	6.76420	0.234930	0.117465	+	0.993077i	$0.462523\pi$
$830$	80.6258	2.79856
$831$	33.9326	1.17711
$832$	−84.7177	−2.93706
$833$	−2.46339	−0.0853514
$834$	61.3813	2.12546
$835$	79.5323	2.75233
$836$	−60.6136	−2.09636
$837$	−69.2917	−2.39507
$838$	−14.4872	−0.500453
$839$	−45.9721	−1.58713	−0.793566	−	0.608484i	$-0.791778\pi$
$839$	−45.9721	−1.58713	−0.793566	+	0.608484i	$0.791778\pi$
$840$	−85.9790	−2.96656
$841$	−16.8372	−0.580592
$842$	54.5552	1.88010
$843$	12.1991	0.420159
$844$	−63.6817	−2.19201
$845$	122.903	4.22799
$846$	106.859	3.67388
$847$	−45.5525	−1.56520
$848$	1.44601	0.0496563
$849$	−34.8160	−1.19488
$850$	194.000	6.65416
$851$	2.37719	0.0814891
$852$	83.4180	2.85785
$853$	−29.1768	−0.998996	−0.499498	−	0.866315i	$-0.666482\pi$
$853$	−29.1768	−0.998996	−0.499498	+	0.866315i	$0.666482\pi$
$854$	22.1648	0.758465
$855$	103.881	3.55265
$856$	4.57229	0.156278
$857$	−3.44148	−0.117559	−0.0587793	−	0.998271i	$-0.518721\pi$
$857$	−3.44148	−0.117559	−0.0587793	+	0.998271i	$0.518721\pi$
$858$	−238.902	−8.15599
$859$	14.6352	0.499346	0.249673	−	0.968330i	$-0.419677\pi$
$859$	14.6352	0.499346	0.249673	+	0.968330i	$0.419677\pi$
$860$	−33.2871	−1.13508
$861$	−60.9293	−2.07646
$862$	−56.6551	−1.92968
$863$	10.0899	0.343463	0.171732	−	0.985144i	$-0.445064\pi$
$863$	10.0899	0.343463	0.171732	+	0.985144i	$0.445064\pi$
$864$	−71.2814	−2.42504
$865$	−4.91407	−0.167084
$866$	−23.4105	−0.795521
$867$	−88.3652	−3.00104
$868$	−51.9458	−1.76315
$869$	−50.6197	−1.71716
$870$	−102.587	−3.47803
$871$	−91.7138	−3.10760
$872$	−2.42679	−0.0821814
$873$	3.36655	0.113940
$874$	−20.0171	−0.677089
$875$	−88.7582	−3.00058
$876$	32.4073	1.09494
$877$	−15.5836	−0.526221	−0.263111	−	0.964766i	$-0.584748\pi$
$877$	−15.5836	−0.526221	−0.263111	+	0.964766i	$0.584748\pi$
$878$	−67.7421	−2.28618
$879$	54.4004	1.83488
$880$	15.2380	0.513673
$881$	−10.1020	−0.340345	−0.170172	−	0.985414i	$-0.554432\pi$
$881$	−10.1020	−0.340345	−0.170172	+	0.985414i	$0.554432\pi$
$882$	−5.42605	−0.182705
$883$	33.2059	1.11747	0.558733	−	0.829347i	$-0.311287\pi$
$883$	33.2059	1.11747	0.558733	+	0.829347i	$0.311287\pi$
$884$	−134.812	−4.53420
$885$	−154.464	−5.19224
$886$	16.8317	0.565473
$887$	−27.2739	−0.915767	−0.457884	−	0.889012i	$-0.651392\pi$
$887$	−27.2739	−0.915767	−0.457884	+	0.889012i	$0.651392\pi$
$888$	7.51753	0.252272
$889$	−27.7785	−0.931660
$890$	−70.7437	−2.37134
$891$	−77.5823	−2.59911
$892$	6.09547	0.204091
$893$	−26.8697	−0.899160
$894$	2.53848	0.0848996
$895$	−50.0038	−1.67144
$896$	−45.0482	−1.50496
$897$	−47.8161	−1.59653
$898$	43.8124	1.46204
$899$	−21.6944	−0.723548
$900$	258.985	8.63284
$901$	14.2235	0.473854
$902$	−86.0805	−2.86617
$903$	−21.5799	−0.718133
$904$	9.24949	0.307633
$905$	−42.1565	−1.40133
$906$	135.581	4.50439
$907$	−48.4024	−1.60717	−0.803587	−	0.595187i	$-0.797078\pi$
$907$	−48.4024	−1.60717	−0.803587	+	0.595187i	$0.797078\pi$
$908$	72.2256	2.39689
$909$	−1.74878	−0.0580034
$910$	167.336	5.54712
$911$	−47.0014	−1.55722	−0.778612	−	0.627505i	$-0.784076\pi$
$911$	−47.0014	−1.55722	−0.778612	+	0.627505i	$0.784076\pi$
$912$	7.94089	0.262949
$913$	44.7556	1.48119
$914$	41.4953	1.37254
$915$	−47.3197	−1.56434
$916$	−28.4830	−0.941103
$917$	−33.0250	−1.09058
$918$	−169.350	−5.58938
$919$	−16.8310	−0.555204	−0.277602	−	0.960696i	$-0.589540\pi$
$919$	−16.8310	−0.555204	−0.277602	+	0.960696i	$0.589540\pi$
$920$	−24.3122	−0.801550
$921$	86.8640	2.86227
$922$	−75.5649	−2.48860
$923$	−56.8266	−1.87047
$924$	−136.355	−4.48573
$925$	12.7605	0.419564
$926$	49.9033	1.63992
$927$	−129.276	−4.24599
$928$	−22.3173	−0.732602
$929$	17.0596	0.559706	0.279853	−	0.960043i	$-0.409714\pi$
$929$	17.0596	0.559706	0.279853	+	0.960043i	$0.409714\pi$
$930$	182.981	6.00017
$931$	1.36438	0.0447159
$932$	29.5953	0.969426
$933$	50.2491	1.64508
$934$	53.3537	1.74579
$935$	149.887	4.90181
$936$	−103.938	−3.39731
$937$	35.6184	1.16360	0.581801	−	0.813331i	$-0.302348\pi$
$937$	35.6184	1.16360	0.581801	+	0.813331i	$0.302348\pi$
$938$	−86.3699	−2.82008
$939$	−26.7630	−0.873379
$940$	−93.2374	−3.04107
$941$	−26.5251	−0.864693	−0.432346	−	0.901708i	$-0.642314\pi$
$941$	−26.5251	−0.864693	−0.432346	+	0.901708i	$0.642314\pi$
$942$	−58.7321	−1.91360
$943$	−17.2289	−0.561051
$944$	−8.11614	−0.264158
$945$	127.400	4.14432
$946$	−30.4879	−0.991246
$947$	−5.47403	−0.177882	−0.0889411	−	0.996037i	$-0.528348\pi$
$947$	−5.47403	−0.177882	−0.0889411	+	0.996037i	$0.528348\pi$
$948$	−91.5352	−2.97293
$949$	−22.0767	−0.716641
$950$	−107.450	−3.48613
$951$	34.6288	1.12291
$952$	−44.4375	−1.44023
$953$	12.9858	0.420651	0.210326	−	0.977631i	$-0.432548\pi$
$953$	12.9858	0.420651	0.210326	+	0.977631i	$0.432548\pi$
$954$	31.3298	1.01434
$955$	−61.2180	−1.98097
$956$	36.3126	1.17443
$957$	−56.9464	−1.84082
$958$	15.9243	0.514491
$959$	22.7145	0.733491
$960$	170.325	5.49722
$961$	7.69537	0.248238
$962$	−14.6309	−0.471719
$963$	−12.4273	−0.400464
$964$	−30.7672	−0.990946
$965$	37.4375	1.20516
$966$	−45.0300	−1.44881
$967$	55.7432	1.79258	0.896290	−	0.443469i	$-0.146253\pi$
$967$	55.7432	1.79258	0.896290	+	0.443469i	$0.146253\pi$
$968$	−40.7339	−1.30924
$969$	78.1096	2.50924
$970$	−4.84666	−0.155617
$971$	−47.4591	−1.52303	−0.761517	−	0.648145i	$-0.775545\pi$
$971$	−47.4591	−1.52303	−0.761517	+	0.648145i	$0.775545\pi$
$972$	−37.4652	−1.20170
$973$	−23.8659	−0.765105
$974$	−1.42700	−0.0457240
$975$	−256.672	−8.22008
$976$	−2.48636	−0.0795866
$977$	10.3715	0.331814	0.165907	−	0.986141i	$-0.446945\pi$
$977$	10.3715	0.331814	0.165907	+	0.986141i	$0.446945\pi$
$978$	−6.66961	−0.213271
$979$	−39.2700	−1.25508
$980$	4.73439	0.151234
$981$	6.59591	0.210591
$982$	−63.5671	−2.02851
$983$	17.6788	0.563866	0.281933	−	0.959434i	$-0.409024\pi$
$983$	17.6788	0.563866	0.281933	+	0.959434i	$0.409024\pi$
$984$	−54.4840	−1.73689
$985$	−77.9087	−2.48238
$986$	−53.0214	−1.68855
$987$	−60.4453	−1.92400
$988$	74.6673	2.37548
$989$	−6.10212	−0.194036
$990$	330.151	10.4929
$991$	6.14140	0.195088	0.0975439	−	0.995231i	$-0.468901\pi$
$991$	6.14140	0.195088	0.0975439	+	0.995231i	$0.468901\pi$
$992$	39.8065	1.26386
$993$	53.5313	1.69877
$994$	−53.5154	−1.69741
$995$	42.0435	1.33287
$996$	80.9311	2.56440
$997$	−26.2703	−0.831988	−0.415994	−	0.909367i	$-0.636566\pi$
$997$	−26.2703	−0.831988	−0.415994	+	0.909367i	$0.636566\pi$
$998$	91.0840	2.88321
$999$	−11.1391	−0.352427

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.c.1.12	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.c.1.12	✓	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)

\(f(q)\)	\(=\)	\(q-2.25323 q^{2} -3.09773 q^{3} +3.07703 q^{4} +4.21432 q^{5} +6.97988 q^{6} -2.71387 q^{7} -2.42679 q^{8} +6.59591 q^{9} +O(q^{10})\)	\(q-2.25323 q^{2} -3.09773 q^{3} +3.07703 q^{4} +4.21432 q^{5} +6.97988 q^{6} -2.71387 q^{7} -2.42679 q^{8} +6.59591 q^{9} -9.49583 q^{10} -5.27116 q^{11} -9.53179 q^{12} +6.49332 q^{13} +6.11496 q^{14} -13.0548 q^{15} -0.685952 q^{16} -6.74728 q^{17} -14.8621 q^{18} +3.73708 q^{19} +12.9676 q^{20} +8.40683 q^{21} +11.8771 q^{22} +2.37719 q^{23} +7.51753 q^{24} +12.7605 q^{25} -14.6309 q^{26} -11.1391 q^{27} -8.35066 q^{28} -3.48753 q^{29} +29.4155 q^{30} +6.22056 q^{31} +6.39918 q^{32} +16.3286 q^{33} +15.2032 q^{34} -11.4371 q^{35} +20.2958 q^{36} +1.00000 q^{37} -8.42049 q^{38} -20.1145 q^{39} -10.2273 q^{40} -7.24759 q^{41} -18.9425 q^{42} -2.56694 q^{43} -16.2195 q^{44} +27.7973 q^{45} -5.35635 q^{46} -7.19003 q^{47} +2.12489 q^{48} +0.365094 q^{49} -28.7524 q^{50} +20.9012 q^{51} +19.9801 q^{52} -2.10804 q^{53} +25.0990 q^{54} -22.2144 q^{55} +6.58599 q^{56} -11.5765 q^{57} +7.85819 q^{58} +11.8319 q^{59} -40.1701 q^{60} +3.62469 q^{61} -14.0163 q^{62} -17.9004 q^{63} -13.0469 q^{64} +27.3649 q^{65} -36.7920 q^{66} -14.1243 q^{67} -20.7616 q^{68} -7.36389 q^{69} +25.7704 q^{70} -8.75155 q^{71} -16.0069 q^{72} -3.39991 q^{73} -2.25323 q^{74} -39.5286 q^{75} +11.4991 q^{76} +14.3052 q^{77} +45.3226 q^{78} +9.60315 q^{79} -2.89083 q^{80} +14.7183 q^{81} +16.3305 q^{82} -8.49065 q^{83} +25.8681 q^{84} -28.4352 q^{85} +5.78391 q^{86} +10.8034 q^{87} +12.7920 q^{88} +7.44998 q^{89} -62.6336 q^{90} -17.6220 q^{91} +7.31469 q^{92} -19.2696 q^{93} +16.2008 q^{94} +15.7493 q^{95} -19.8229 q^{96} +0.510399 q^{97} -0.822639 q^{98} -34.7681 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 9 q^{2} - 27 q^{3} + 73 q^{4} - 16 q^{5} - 2 q^{6} - 23 q^{7} - 24 q^{8} + 66 q^{9}+O(q^{10}) \) 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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