LMFDB - Embedded newform 161.2.a.d.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [161,2,Mod(1,161)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(161, 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("161.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 161 = 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	161.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:	$1.28559147254$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.2147108.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 9x^{3} + 17x^{2} + 16x - 27 $ x^5 - 2x^4 - 9x^3 + 17x^2 + 16x - 27
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.23828$ of defining polynomial
Character	$\chi$	$=$	161.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.23828 q^{2} +2.68857 q^{3} -0.466664 q^{4} -1.86253 q^{5} +3.32920 q^{6} +1.00000 q^{7} -3.05442 q^{8} +4.22838 q^{9} +O(q^{10})$	\(q+1.23828 q^{2} +2.68857 q^{3} -0.466664 q^{4} -1.86253 q^{5} +3.32920 q^{6} +1.00000 q^{7} -3.05442 q^{8} +4.22838 q^{9} -2.30633 q^{10} -0.846153 q^{11} -1.25466 q^{12} +2.55110 q^{13} +1.23828 q^{14} -5.00754 q^{15} -2.84890 q^{16} -7.07080 q^{17} +5.23592 q^{18} -0.476559 q^{19} +0.869177 q^{20} +2.68857 q^{21} -1.04777 q^{22} -1.00000 q^{23} -8.21201 q^{24} -1.53098 q^{25} +3.15897 q^{26} +3.30259 q^{27} -0.466664 q^{28} +8.63827 q^{29} -6.20073 q^{30} +3.31143 q^{31} +2.58111 q^{32} -2.27494 q^{33} -8.75562 q^{34} -1.86253 q^{35} -1.97324 q^{36} +7.85369 q^{37} -0.590113 q^{38} +6.85879 q^{39} +5.68895 q^{40} +2.82603 q^{41} +3.32920 q^{42} -0.274938 q^{43} +0.394869 q^{44} -7.87550 q^{45} -1.23828 q^{46} -13.4756 q^{47} -7.65944 q^{48} +1.00000 q^{49} -1.89578 q^{50} -19.0103 q^{51} -1.19051 q^{52} +8.93333 q^{53} +4.08953 q^{54} +1.57599 q^{55} -3.05442 q^{56} -1.28126 q^{57} +10.6966 q^{58} +1.66091 q^{59} +2.33684 q^{60} -11.7162 q^{61} +4.10048 q^{62} +4.22838 q^{63} +8.89393 q^{64} -4.75150 q^{65} -2.81701 q^{66} -2.82636 q^{67} +3.29969 q^{68} -2.68857 q^{69} -2.30633 q^{70} +9.92823 q^{71} -12.9153 q^{72} +7.31556 q^{73} +9.72506 q^{74} -4.11614 q^{75} +0.222393 q^{76} -0.846153 q^{77} +8.49310 q^{78} +11.7795 q^{79} +5.30616 q^{80} -3.80592 q^{81} +3.49942 q^{82} +3.72506 q^{83} -1.25466 q^{84} +13.1696 q^{85} -0.340450 q^{86} +23.2246 q^{87} +2.58451 q^{88} -8.76310 q^{89} -9.75207 q^{90} +2.55110 q^{91} +0.466664 q^{92} +8.90301 q^{93} -16.6865 q^{94} +0.887605 q^{95} +6.93948 q^{96} +1.82229 q^{97} +1.23828 q^{98} -3.57786 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 2 q^{2} + 12 q^{4} - 4 q^{5} - 3 q^{6} + 5 q^{7} + 3 q^{8} + 11 q^{9}+O(q^{10}) $ 5 * q + 2 * q^2 + 12 * q^4 - 4 * q^5 - 3 * q^6 + 5 * q^7 + 3 * q^8 + 11 * q^9	\( 5 q + 2 q^{2} + 12 q^{4} - 4 q^{5} - 3 q^{6} + 5 q^{7} + 3 q^{8} + 11 q^{9} - 8 q^{10} - 4 q^{11} + 3 q^{12} - 6 q^{13} + 2 q^{14} + 10 q^{15} + 10 q^{16} - 12 q^{17} - 19 q^{18} + 6 q^{19} + 14 q^{22} - 5 q^{23} - 36 q^{24} + 19 q^{25} + q^{26} + 12 q^{28} - 4 q^{29} - 48 q^{30} + 30 q^{31} + 8 q^{32} - 22 q^{33} + 6 q^{34} - 4 q^{35} - q^{36} + 4 q^{37} - 40 q^{38} + 16 q^{39} - 50 q^{40} + 6 q^{41} - 3 q^{42} - 12 q^{43} - 26 q^{44} - 12 q^{45} - 2 q^{46} + 10 q^{47} + 25 q^{48} + 5 q^{49} - 2 q^{50} - 4 q^{51} - 21 q^{52} + 16 q^{53} + 33 q^{54} + 18 q^{55} + 3 q^{56} + 6 q^{57} + 13 q^{58} + 22 q^{59} + 30 q^{60} - 18 q^{61} + 15 q^{62} + 11 q^{63} + 25 q^{64} - 26 q^{65} + 4 q^{66} - 2 q^{67} + 12 q^{68} - 8 q^{70} + 4 q^{71} - 41 q^{72} - 2 q^{73} + 38 q^{74} - 30 q^{75} + 10 q^{76} - 4 q^{77} + 41 q^{78} + 30 q^{79} - 10 q^{80} - 3 q^{81} - 7 q^{82} + 8 q^{83} + 3 q^{84} - 12 q^{85} + 8 q^{86} - 12 q^{87} + 4 q^{88} - 20 q^{89} + 34 q^{90} - 6 q^{91} - 12 q^{92} - 26 q^{93} - 25 q^{94} + 8 q^{95} - q^{96} - 12 q^{97} + 2 q^{98} - 8 q^{99}+O(q^{100}) \) 5 * q + 2 * q^2 + 12 * q^4 - 4 * q^5 - 3 * q^6 + 5 * q^7 + 3 * q^8 + 11 * q^9 - 8 * q^10 - 4 * q^11 + 3 * q^12 - 6 * q^13 + 2 * q^14 + 10 * q^15 + 10 * q^16 - 12 * q^17 - 19 * q^18 + 6 * q^19 + 14 * q^22 - 5 * q^23 - 36 * q^24 + 19 * q^25 + q^26 + 12 * q^28 - 4 * q^29 - 48 * q^30 + 30 * q^31 + 8 * q^32 - 22 * q^33 + 6 * q^34 - 4 * q^35 - q^36 + 4 * q^37 - 40 * q^38 + 16 * q^39 - 50 * q^40 + 6 * q^41 - 3 * q^42 - 12 * q^43 - 26 * q^44 - 12 * q^45 - 2 * q^46 + 10 * q^47 + 25 * q^48 + 5 * q^49 - 2 * q^50 - 4 * q^51 - 21 * q^52 + 16 * q^53 + 33 * q^54 + 18 * q^55 + 3 * q^56 + 6 * q^57 + 13 * q^58 + 22 * q^59 + 30 * q^60 - 18 * q^61 + 15 * q^62 + 11 * q^63 + 25 * q^64 - 26 * q^65 + 4 * q^66 - 2 * q^67 + 12 * q^68 - 8 * q^70 + 4 * q^71 - 41 * q^72 - 2 * q^73 + 38 * q^74 - 30 * q^75 + 10 * q^76 - 4 * q^77 + 41 * q^78 + 30 * q^79 - 10 * q^80 - 3 * q^81 - 7 * q^82 + 8 * q^83 + 3 * q^84 - 12 * q^85 + 8 * q^86 - 12 * q^87 + 4 * q^88 - 20 * q^89 + 34 * q^90 - 6 * q^91 - 12 * q^92 - 26 * q^93 - 25 * q^94 + 8 * q^95 - q^96 - 12 * q^97 + 2 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.23828	0.875596	0.437798	−	0.899073i	$-0.355759\pi$
$2$	1.23828	0.875596	0.437798	+	0.899073i	$0.355759\pi$
$3$	2.68857	1.55224	0.776122	−	0.630583i	$-0.217184\pi$
$3$	2.68857	1.55224	0.776122	+	0.630583i	$0.217184\pi$
$4$	−0.466664	−0.233332
$5$	−1.86253	−0.832949	−0.416475	−	0.909147i	$-0.636735\pi$
$5$	−1.86253	−0.832949	−0.416475	+	0.909147i	$0.636735\pi$
$6$	3.32920	1.35914
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−3.05442	−1.07990
$9$	4.22838	1.40946
$10$	−2.30633	−0.729327
$11$	−0.846153	−0.255125	−0.127562	−	0.991831i	$-0.540715\pi$
$11$	−0.846153	−0.255125	−0.127562	+	0.991831i	$0.540715\pi$
$12$	−1.25466	−0.362188
$13$	2.55110	0.707547	0.353773	−	0.935331i	$-0.384898\pi$
$13$	2.55110	0.707547	0.353773	+	0.935331i	$0.384898\pi$
$14$	1.23828	0.330944
$15$	−5.00754	−1.29294
$16$	−2.84890	−0.712224
$17$	−7.07080	−1.71492	−0.857460	−	0.514550i	$-0.827959\pi$
$17$	−7.07080	−1.71492	−0.857460	+	0.514550i	$0.827959\pi$
$18$	5.23592	1.23412
$19$	−0.476559	−0.109330	−0.0546650	−	0.998505i	$-0.517409\pi$
$19$	−0.476559	−0.109330	−0.0546650	+	0.998505i	$0.517409\pi$
$20$	0.869177	0.194354
$21$	2.68857	0.586693
$22$	−1.04777	−0.223386
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−8.21201	−1.67627
$25$	−1.53098	−0.306196
$26$	3.15897	0.619525
$27$	3.30259	0.635584
$28$	−0.466664	−0.0881912
$29$	8.63827	1.60409	0.802043	−	0.597266i	$-0.203746\pi$
$29$	8.63827	1.60409	0.802043	+	0.597266i	$0.203746\pi$
$30$	−6.20073	−1.13209
$31$	3.31143	0.594751	0.297376	−	0.954761i	$-0.403889\pi$
$31$	3.31143	0.594751	0.297376	+	0.954761i	$0.403889\pi$
$32$	2.58111	0.456280
$33$	−2.27494	−0.396016
$34$	−8.75562	−1.50158
$35$	−1.86253	−0.314825
$36$	−1.97324	−0.328873
$37$	7.85369	1.29114	0.645569	−	0.763702i	$-0.276620\pi$
$37$	7.85369	1.29114	0.645569	+	0.763702i	$0.276620\pi$
$38$	−0.590113	−0.0957289
$39$	6.85879	1.09829
$40$	5.68895	0.899502
$41$	2.82603	0.441352	0.220676	−	0.975347i	$-0.429174\pi$
$41$	2.82603	0.441352	0.220676	+	0.975347i	$0.429174\pi$
$42$	3.32920	0.513706
$43$	−0.274938	−0.0419276	−0.0209638	−	0.999780i	$-0.506673\pi$
$43$	−0.274938	−0.0419276	−0.0209638	+	0.999780i	$0.506673\pi$
$44$	0.394869	0.0595288
$45$	−7.87550	−1.17401
$46$	−1.23828	−0.182574
$47$	−13.4756	−1.96562	−0.982808	−	0.184631i	$-0.940891\pi$
$47$	−13.4756	−1.96562	−0.982808	+	0.184631i	$0.940891\pi$
$48$	−7.65944	−1.10555
$49$	1.00000	0.142857
$50$	−1.89578	−0.268104
$51$	−19.0103	−2.66197
$52$	−1.19051	−0.165093
$53$	8.93333	1.22709	0.613544	−	0.789661i	$-0.289744\pi$
$53$	8.93333	1.22709	0.613544	+	0.789661i	$0.289744\pi$
$54$	4.08953	0.556515
$55$	1.57599	0.212506
$56$	−3.05442	−0.408164
$57$	−1.28126	−0.169707
$58$	10.6966	1.40453
$59$	1.66091	0.216232	0.108116	−	0.994138i	$-0.465518\pi$
$59$	1.66091	0.216232	0.108116	+	0.994138i	$0.465518\pi$
$60$	2.33684	0.301685
$61$	−11.7162	−1.50011	−0.750054	−	0.661376i	$-0.769973\pi$
$61$	−11.7162	−1.50011	−0.750054	+	0.661376i	$0.769973\pi$
$62$	4.10048	0.520762
$63$	4.22838	0.532726
$64$	8.89393	1.11174
$65$	−4.75150	−0.589351
$66$	−2.81701	−0.346750
$67$	−2.82636	−0.345295	−0.172648	−	0.984984i	$-0.555232\pi$
$67$	−2.82636	−0.345295	−0.172648	+	0.984984i	$0.555232\pi$
$68$	3.29969	0.400146
$69$	−2.68857	−0.323665
$70$	−2.30633	−0.275660
$71$	9.92823	1.17826	0.589132	−	0.808037i	$-0.299470\pi$
$71$	9.92823	1.17826	0.589132	+	0.808037i	$0.299470\pi$
$72$	−12.9153	−1.52208
$73$	7.31556	0.856222	0.428111	−	0.903726i	$-0.359179\pi$
$73$	7.31556	0.856222	0.428111	+	0.903726i	$0.359179\pi$
$74$	9.72506	1.13052
$75$	−4.11614	−0.475290
$76$	0.222393	0.0255102
$77$	−0.846153	−0.0964281
$78$	8.49310	0.961654
$79$	11.7795	1.32530	0.662648	−	0.748931i	$-0.269433\pi$
$79$	11.7795	1.32530	0.662648	+	0.748931i	$0.269433\pi$
$80$	5.30616	0.593246
$81$	−3.80592	−0.422880
$82$	3.49942	0.386446
$83$	3.72506	0.408879	0.204439	−	0.978879i	$-0.434463\pi$
$83$	3.72506	0.408879	0.204439	+	0.978879i	$0.434463\pi$
$84$	−1.25466	−0.136894
$85$	13.1696	1.42844
$86$	−0.340450	−0.0367117
$87$	23.2246	2.48993
$88$	2.58451	0.275509
$89$	−8.76310	−0.928887	−0.464444	−	0.885603i	$-0.653746\pi$
$89$	−8.76310	−0.928887	−0.464444	+	0.885603i	$0.653746\pi$
$90$	−9.75207	−1.02796
$91$	2.55110	0.267428
$92$	0.466664	0.0486531
$93$	8.90301	0.923199
$94$	−16.6865	−1.72108
$95$	0.887605	0.0910664
$96$	6.93948	0.708258
$97$	1.82229	0.185026	0.0925130	−	0.995711i	$-0.470510\pi$
$97$	1.82229	0.185026	0.0925130	+	0.995711i	$0.470510\pi$
$98$	1.23828	0.125085
$99$	−3.57786	−0.359589
$100$	0.714453	0.0714453
$101$	−14.7870	−1.47136	−0.735682	−	0.677327i	$-0.763138\pi$
$101$	−14.7870	−1.47136	−0.735682	+	0.677327i	$0.763138\pi$
$102$	−23.5401	−2.33081
$103$	10.9333	1.07729	0.538646	−	0.842532i	$-0.318936\pi$
$103$	10.9333	1.07729	0.538646	+	0.842532i	$0.318936\pi$
$104$	−7.79212	−0.764080
$105$	−5.00754	−0.488686
$106$	11.0620	1.07443
$107$	−17.2636	−1.66893	−0.834466	−	0.551059i	$-0.814224\pi$
$107$	−17.2636	−1.66893	−0.834466	+	0.551059i	$0.814224\pi$
$108$	−1.54120	−0.148302
$109$	−13.2438	−1.26852	−0.634262	−	0.773118i	$-0.718696\pi$
$109$	−13.2438	−1.26852	−0.634262	+	0.773118i	$0.718696\pi$
$110$	1.95151	0.186069
$111$	21.1152	2.00416
$112$	−2.84890	−0.269195
$113$	−7.10219	−0.668118	−0.334059	−	0.942552i	$-0.608419\pi$
$113$	−7.10219	−0.668118	−0.334059	+	0.942552i	$0.608419\pi$
$114$	−1.58656	−0.148595
$115$	1.86253	0.173682
$116$	−4.03117	−0.374285
$117$	10.7870	0.997260
$118$	2.05667	0.189332
$119$	−7.07080	−0.648179
$120$	15.2951	1.39625
$121$	−10.2840	−0.934911
$122$	−14.5080	−1.31349
$123$	7.59798	0.685087
$124$	−1.54533	−0.138775
$125$	12.1641	1.08799
$126$	5.23592	0.466453
$127$	16.1101	1.42954	0.714768	−	0.699361i	$-0.246532\pi$
$127$	16.1101	1.42954	0.714768	+	0.699361i	$0.246532\pi$
$128$	5.85095	0.517156
$129$	−0.739189	−0.0650819
$130$	−5.88368	−0.516033
$131$	−0.854665	−0.0746724	−0.0373362	−	0.999303i	$-0.511887\pi$
$131$	−0.854665	−0.0746724	−0.0373362	+	0.999303i	$0.511887\pi$
$132$	1.06163	0.0924032
$133$	−0.476559	−0.0413229
$134$	−3.49983	−0.302339
$135$	−6.15118	−0.529409
$136$	21.5972	1.85194
$137$	7.11516	0.607889	0.303945	−	0.952690i	$-0.401696\pi$
$137$	7.11516	0.607889	0.303945	+	0.952690i	$0.401696\pi$
$138$	−3.32920	−0.283400
$139$	10.7111	0.908505	0.454253	−	0.890873i	$-0.349906\pi$
$139$	10.7111	0.908505	0.454253	+	0.890873i	$0.349906\pi$
$140$	0.869177	0.0734588
$141$	−36.2300	−3.05112
$142$	12.2939	1.03168
$143$	−2.15862	−0.180513
$144$	−12.0462	−1.00385
$145$	−16.0890	−1.33612
$146$	9.05871	0.749704
$147$	2.68857	0.221749
$148$	−3.66504	−0.301264
$149$	−6.43632	−0.527284	−0.263642	−	0.964621i	$-0.584924\pi$
$149$	−6.43632	−0.527284	−0.263642	+	0.964621i	$0.584924\pi$
$150$	−5.09693	−0.416162
$151$	0.803480	0.0653863	0.0326931	−	0.999465i	$-0.489592\pi$
$151$	0.803480	0.0653863	0.0326931	+	0.999465i	$0.489592\pi$
$152$	1.45561	0.118066
$153$	−29.8981	−2.41711
$154$	−1.04777	−0.0844320
$155$	−6.16765	−0.495398
$156$	−3.20075	−0.256265
$157$	−14.7959	−1.18084	−0.590419	−	0.807097i	$-0.701038\pi$
$157$	−14.7959	−1.18084	−0.590419	+	0.807097i	$0.701038\pi$
$158$	14.5863	1.16042
$159$	24.0178	1.90474
$160$	−4.80740	−0.380058
$161$	−1.00000	−0.0788110
$162$	−4.71279	−0.370272
$163$	3.13373	0.245453	0.122726	−	0.992441i	$-0.460836\pi$
$163$	3.13373	0.245453	0.122726	+	0.992441i	$0.460836\pi$
$164$	−1.31881	−0.102982
$165$	4.23714	0.329861
$166$	4.61267	0.358012
$167$	−23.4168	−1.81204	−0.906022	−	0.423230i	$-0.860896\pi$
$167$	−23.4168	−1.81204	−0.906022	+	0.423230i	$0.860896\pi$
$168$	−8.21201	−0.633570
$169$	−6.49191	−0.499377
$170$	16.3076	1.25074
$171$	−2.01507	−0.154097
$172$	0.128304	0.00978306
$173$	−0.645424	−0.0490706	−0.0245353	−	0.999699i	$-0.507811\pi$
$173$	−0.645424	−0.0490706	−0.0245353	+	0.999699i	$0.507811\pi$
$174$	28.7585	2.18018
$175$	−1.53098	−0.115731
$176$	2.41060	0.181706
$177$	4.46547	0.335645
$178$	−10.8512	−0.813330
$179$	−16.9141	−1.26422	−0.632110	−	0.774879i	$-0.717811\pi$
$179$	−16.9141	−1.26422	−0.632110	+	0.774879i	$0.717811\pi$
$180$	3.67521	0.273934
$181$	−4.61403	−0.342958	−0.171479	−	0.985188i	$-0.554855\pi$
$181$	−4.61403	−0.342958	−0.171479	+	0.985188i	$0.554855\pi$
$182$	3.15897	0.234158
$183$	−31.4998	−2.32853
$184$	3.05442	0.225175
$185$	−14.6277	−1.07545
$186$	11.0244	0.808349
$187$	5.98298	0.437519
$188$	6.28857	0.458641
$189$	3.30259	0.240228
$190$	1.09910	0.0797373
$191$	6.44380	0.466257	0.233129	−	0.972446i	$-0.425104\pi$
$191$	6.44380	0.466257	0.233129	+	0.972446i	$0.425104\pi$
$192$	23.9119	1.72569
$193$	10.1400	0.729897	0.364948	−	0.931028i	$-0.381087\pi$
$193$	10.1400	0.729897	0.364948	+	0.931028i	$0.381087\pi$
$194$	2.25651	0.162008
$195$	−12.7747	−0.914816
$196$	−0.466664	−0.0333332
$197$	−2.37475	−0.169194	−0.0845970	−	0.996415i	$-0.526960\pi$
$197$	−2.37475	−0.169194	−0.0845970	+	0.996415i	$0.526960\pi$
$198$	−4.43039	−0.314854
$199$	18.6052	1.31889	0.659443	−	0.751754i	$-0.270792\pi$
$199$	18.6052	1.31889	0.659443	+	0.751754i	$0.270792\pi$
$200$	4.67625	0.330661
$201$	−7.59887	−0.535983
$202$	−18.3105	−1.28832
$203$	8.63827	0.606288
$204$	8.87143	0.621124
$205$	−5.26358	−0.367624
$206$	13.5385	0.943273
$207$	−4.22838	−0.293893
$208$	−7.26781	−0.503932
$209$	0.403242	0.0278928
$210$	−6.20073	−0.427891
$211$	−21.1247	−1.45429	−0.727144	−	0.686485i	$-0.759153\pi$
$211$	−21.1247	−1.45429	−0.727144	+	0.686485i	$0.759153\pi$
$212$	−4.16886	−0.286319
$213$	26.6927	1.82895
$214$	−21.3771	−1.46131
$215$	0.512080	0.0349236
$216$	−10.0875	−0.686368
$217$	3.31143	0.224795
$218$	−16.3995	−1.11071
$219$	19.6684	1.32906
$220$	−0.735456	−0.0495845
$221$	−18.0383	−1.21339
$222$	26.1465	1.75484
$223$	−21.5426	−1.44260	−0.721301	−	0.692622i	$-0.756456\pi$
$223$	−21.5426	−1.44260	−0.721301	+	0.692622i	$0.756456\pi$
$224$	2.58111	0.172458
$225$	−6.47356	−0.431571
$226$	−8.79450	−0.585001
$227$	12.9135	0.857102	0.428551	−	0.903518i	$-0.359024\pi$
$227$	12.9135	0.857102	0.428551	+	0.903518i	$0.359024\pi$
$228$	0.597918	0.0395981
$229$	28.4835	1.88224	0.941120	−	0.338074i	$-0.109775\pi$
$229$	28.4835	1.88224	0.941120	+	0.338074i	$0.109775\pi$
$230$	2.30633	0.152075
$231$	−2.27494	−0.149680
$232$	−26.3849	−1.73225
$233$	2.58296	0.169215	0.0846077	−	0.996414i	$-0.473036\pi$
$233$	2.58296	0.169215	0.0846077	+	0.996414i	$0.473036\pi$
$234$	13.3573	0.873197
$235$	25.0987	1.63726
$236$	−0.775087	−0.0504539
$237$	31.6699	2.05718
$238$	−8.75562	−0.567543
$239$	11.9610	0.773692	0.386846	−	0.922144i	$-0.373565\pi$
$239$	11.9610	0.773692	0.386846	+	0.922144i	$0.373565\pi$
$240$	14.2660	0.920863
$241$	2.03140	0.130854	0.0654269	−	0.997857i	$-0.479159\pi$
$241$	2.03140	0.130854	0.0654269	+	0.997857i	$0.479159\pi$
$242$	−12.7345	−0.818604
$243$	−20.1402	−1.29200
$244$	5.46754	0.350023
$245$	−1.86253	−0.118993
$246$	9.40842	0.599859
$247$	−1.21575	−0.0773562
$248$	−10.1145	−0.642272
$249$	10.0151	0.634680
$250$	15.0626	0.952643
$251$	27.4454	1.73234	0.866169	−	0.499750i	$-0.166575\pi$
$251$	27.4454	1.73234	0.866169	+	0.499750i	$0.166575\pi$
$252$	−1.97324	−0.124302
$253$	0.846153	0.0531972
$254$	19.9488	1.25170
$255$	35.4073	2.21729
$256$	−10.5427	−0.658922
$257$	−25.1645	−1.56972	−0.784860	−	0.619673i	$-0.787265\pi$
$257$	−25.1645	−1.56972	−0.784860	+	0.619673i	$0.787265\pi$
$258$	−0.915322	−0.0569855
$259$	7.85369	0.488005
$260$	2.21735	0.137514
$261$	36.5259	2.26090
$262$	−1.05831	−0.0653828
$263$	10.8612	0.669732	0.334866	−	0.942266i	$-0.391309\pi$
$263$	10.8612	0.669732	0.334866	+	0.942266i	$0.391309\pi$
$264$	6.94861	0.427658
$265$	−16.6386	−1.02210
$266$	−0.590113	−0.0361821
$267$	−23.5602	−1.44186
$268$	1.31896	0.0805685
$269$	−2.02133	−0.123243	−0.0616215	−	0.998100i	$-0.519627\pi$
$269$	−2.02133	−0.123243	−0.0616215	+	0.998100i	$0.519627\pi$
$270$	−7.61688	−0.463549
$271$	−4.05733	−0.246465	−0.123233	−	0.992378i	$-0.539326\pi$
$271$	−4.05733	−0.246465	−0.123233	+	0.992378i	$0.539326\pi$
$272$	20.1440	1.22141
$273$	6.85879	0.415113
$274$	8.81056	0.532265
$275$	1.29544	0.0781181
$276$	1.25466	0.0755215
$277$	−31.6071	−1.89909	−0.949544	−	0.313634i	$-0.898454\pi$
$277$	−31.6071	−1.89909	−0.949544	+	0.313634i	$0.898454\pi$
$278$	13.2634	0.795483
$279$	14.0020	0.838279
$280$	5.68895	0.339980
$281$	25.4680	1.51929	0.759646	−	0.650337i	$-0.225372\pi$
$281$	25.4680	1.51929	0.759646	+	0.650337i	$0.225372\pi$
$282$	−44.8629	−2.67154
$283$	−8.06860	−0.479629	−0.239814	−	0.970819i	$-0.577087\pi$
$283$	−8.06860	−0.479629	−0.239814	+	0.970819i	$0.577087\pi$
$284$	−4.63315	−0.274927
$285$	2.38639	0.141357
$286$	−2.67297	−0.158056
$287$	2.82603	0.166816
$288$	10.9139	0.643109
$289$	32.9962	1.94095
$290$	−19.9227	−1.16990
$291$	4.89936	0.287205
$292$	−3.41391	−0.199784
$293$	−12.5766	−0.734730	−0.367365	−	0.930077i	$-0.619740\pi$
$293$	−12.5766	−0.734730	−0.367365	+	0.930077i	$0.619740\pi$
$294$	3.32920	0.194163
$295$	−3.09350	−0.180110
$296$	−23.9885	−1.39430
$297$	−2.79450	−0.162153
$298$	−7.96996	−0.461688
$299$	−2.55110	−0.147534
$300$	1.92085	0.110900
$301$	−0.274938	−0.0158472
$302$	0.994933	0.0572519
$303$	−39.7559	−2.28391
$304$	1.35767	0.0778675
$305$	21.8218	1.24951
$306$	−37.0221	−2.11641
$307$	0.588753	0.0336019	0.0168009	−	0.999859i	$-0.494652\pi$
$307$	0.588753	0.0336019	0.0168009	+	0.999859i	$0.494652\pi$
$308$	0.394869	0.0224998
$309$	29.3950	1.67222
$310$	−7.63727	−0.433768
$311$	2.32490	0.131833	0.0659165	−	0.997825i	$-0.479003\pi$
$311$	2.32490	0.131833	0.0659165	+	0.997825i	$0.479003\pi$
$312$	−20.9496	−1.18604
$313$	−8.02863	−0.453805	−0.226903	−	0.973917i	$-0.572860\pi$
$313$	−8.02863	−0.453805	−0.226903	+	0.973917i	$0.572860\pi$
$314$	−18.3214	−1.03394
$315$	−7.87550	−0.443734
$316$	−5.49706	−0.309234
$317$	27.0431	1.51889	0.759445	−	0.650572i	$-0.225471\pi$
$317$	27.0431	1.51889	0.759445	+	0.650572i	$0.225471\pi$
$318$	29.7408	1.66778
$319$	−7.30930	−0.409242
$320$	−16.5652	−0.926024
$321$	−46.4143	−2.59059
$322$	−1.23828	−0.0690066
$323$	3.36965	0.187492
$324$	1.77608	0.0986714
$325$	−3.90567	−0.216648
$326$	3.88043	0.214917
$327$	−35.6068	−1.96906
$328$	−8.63189	−0.476617
$329$	−13.4756	−0.742933
$330$	5.24677	0.288825
$331$	22.7555	1.25075	0.625377	−	0.780323i	$-0.284945\pi$
$331$	22.7555	1.25075	0.625377	+	0.780323i	$0.284945\pi$
$332$	−1.73835	−0.0954045
$333$	33.2084	1.81981
$334$	−28.9965	−1.58662
$335$	5.26419	0.287613
$336$	−7.65944	−0.417857
$337$	−1.05919	−0.0576978	−0.0288489	−	0.999584i	$-0.509184\pi$
$337$	−1.05919	−0.0576978	−0.0288489	+	0.999584i	$0.509184\pi$
$338$	−8.03879	−0.437253
$339$	−19.0947	−1.03708
$340$	−6.14577	−0.333301
$341$	−2.80198	−0.151736
$342$	−2.49522	−0.134926
$343$	1.00000	0.0539949
$344$	0.839776	0.0452777
$345$	5.00754	0.269597
$346$	−0.799215	−0.0429660
$347$	14.2245	0.763611	0.381806	−	0.924243i	$-0.375302\pi$
$347$	14.2245	0.763611	0.381806	+	0.924243i	$0.375302\pi$
$348$	−10.8381	−0.580982
$349$	−23.4865	−1.25721	−0.628603	−	0.777727i	$-0.716373\pi$
$349$	−23.4865	−1.25721	−0.628603	+	0.777727i	$0.716373\pi$
$350$	−1.89578	−0.101334
$351$	8.42523	0.449706
$352$	−2.18401	−0.116408
$353$	−1.19652	−0.0636843	−0.0318422	−	0.999493i	$-0.510137\pi$
$353$	−1.19652	−0.0636843	−0.0318422	+	0.999493i	$0.510137\pi$
$354$	5.52949	0.293889
$355$	−18.4916	−0.981434
$356$	4.08943	0.216739
$357$	−19.0103	−1.00613
$358$	−20.9444	−1.10695
$359$	8.62376	0.455145	0.227572	−	0.973761i	$-0.426921\pi$
$359$	8.62376	0.455145	0.227572	+	0.973761i	$0.426921\pi$
$360$	24.0551	1.26781
$361$	−18.7729	−0.988047
$362$	−5.71346	−0.300293
$363$	−27.6493	−1.45121
$364$	−1.19051	−0.0623994
$365$	−13.6255	−0.713189
$366$	−39.0056	−2.03885
$367$	1.40241	0.0732050	0.0366025	−	0.999330i	$-0.488346\pi$
$367$	1.40241	0.0732050	0.0366025	+	0.999330i	$0.488346\pi$
$368$	2.84890	0.148509
$369$	11.9496	0.622069
$370$	−18.1132	−0.941662
$371$	8.93333	0.463795
$372$	−4.15472	−0.215412
$373$	5.38461	0.278805	0.139402	−	0.990236i	$-0.455482\pi$
$373$	5.38461	0.278805	0.139402	+	0.990236i	$0.455482\pi$
$374$	7.40860	0.383089
$375$	32.7041	1.68883
$376$	41.1601	2.12267
$377$	22.0371	1.13497
$378$	4.08953	0.210343
$379$	26.3413	1.35306	0.676532	−	0.736413i	$-0.263482\pi$
$379$	26.3413	1.35306	0.676532	+	0.736413i	$0.263482\pi$
$380$	−0.414214	−0.0212487
$381$	43.3130	2.21899
$382$	7.97923	0.408253
$383$	23.4277	1.19710	0.598550	−	0.801085i	$-0.295744\pi$
$383$	23.4277	1.19710	0.598550	+	0.801085i	$0.295744\pi$
$384$	15.7307	0.802752
$385$	1.57599	0.0803197
$386$	12.5562	0.639094
$387$	−1.16254	−0.0590954
$388$	−0.850399	−0.0431725
$389$	−13.5760	−0.688330	−0.344165	−	0.938909i	$-0.611838\pi$
$389$	−13.5760	−0.688330	−0.344165	+	0.938909i	$0.611838\pi$
$390$	−15.8187	−0.801009
$391$	7.07080	0.357586
$392$	−3.05442	−0.154271
$393$	−2.29782	−0.115910
$394$	−2.94060	−0.148146
$395$	−21.9396	−1.10390
$396$	1.66966	0.0839036
$397$	3.24696	0.162960	0.0814801	−	0.996675i	$-0.474035\pi$
$397$	3.24696	0.162960	0.0814801	+	0.996675i	$0.474035\pi$
$398$	23.0384	1.15481
$399$	−1.28126	−0.0641432
$400$	4.36160	0.218080
$401$	30.2805	1.51213	0.756067	−	0.654494i	$-0.227118\pi$
$401$	30.2805	1.51213	0.756067	+	0.654494i	$0.227118\pi$
$402$	−9.40952	−0.469304
$403$	8.44779	0.420814
$404$	6.90057	0.343316
$405$	7.08864	0.352237
$406$	10.6966	0.530863
$407$	−6.64542	−0.329401
$408$	58.0654	2.87467
$409$	12.3775	0.612029	0.306014	−	0.952027i	$-0.401004\pi$
$409$	12.3775	0.612029	0.306014	+	0.952027i	$0.401004\pi$
$410$	−6.51778	−0.321890
$411$	19.1296	0.943592
$412$	−5.10219	−0.251367
$413$	1.66091	0.0817280
$414$	−5.23592	−0.257332
$415$	−6.93804	−0.340575
$416$	6.58466	0.322840
$417$	28.7975	1.41022
$418$	0.499326	0.0244228
$419$	5.46520	0.266992	0.133496	−	0.991049i	$-0.457380\pi$
$419$	5.46520	0.266992	0.133496	+	0.991049i	$0.457380\pi$
$420$	2.33684	0.114026
$421$	−6.55232	−0.319340	−0.159670	−	0.987170i	$-0.551043\pi$
$421$	−6.55232	−0.319340	−0.159670	+	0.987170i	$0.551043\pi$
$422$	−26.1583	−1.27337
$423$	−56.9800	−2.77046
$424$	−27.2861	−1.32513
$425$	10.8252	0.525101
$426$	33.0530	1.60142
$427$	−11.7162	−0.566988
$428$	8.05629	0.389416
$429$	−5.80359	−0.280200
$430$	0.634099	0.0305789
$431$	−7.88645	−0.379877	−0.189938	−	0.981796i	$-0.560829\pi$
$431$	−7.88645	−0.379877	−0.189938	+	0.981796i	$0.560829\pi$
$432$	−9.40874	−0.452678
$433$	−33.7313	−1.62102	−0.810511	−	0.585723i	$-0.800811\pi$
$433$	−33.7313	−1.62102	−0.810511	+	0.585723i	$0.800811\pi$
$434$	4.10048	0.196829
$435$	−43.2565	−2.07399
$436$	6.18040	0.295988
$437$	0.476559	0.0227969
$438$	24.3549	1.16372
$439$	−13.6800	−0.652909	−0.326455	−	0.945213i	$-0.605854\pi$
$439$	−13.6800	−0.652909	−0.326455	+	0.945213i	$0.605854\pi$
$440$	−4.81372	−0.229485
$441$	4.22838	0.201352
$442$	−22.3364	−1.06244
$443$	−17.2726	−0.820646	−0.410323	−	0.911940i	$-0.634584\pi$
$443$	−17.2726	−0.820646	−0.410323	+	0.911940i	$0.634584\pi$
$444$	−9.85369	−0.467635
$445$	16.3216	0.773716
$446$	−26.6758	−1.26314
$447$	−17.3045	−0.818473
$448$	8.89393	0.420199
$449$	8.26286	0.389949	0.194974	−	0.980808i	$-0.437538\pi$
$449$	8.26286	0.389949	0.194974	+	0.980808i	$0.437538\pi$
$450$	−8.01608	−0.377882
$451$	−2.39126	−0.112600
$452$	3.31434	0.155893
$453$	2.16021	0.101495
$454$	15.9906	0.750475
$455$	−4.75150	−0.222754
$456$	3.91350	0.183267
$457$	2.80779	0.131343	0.0656714	−	0.997841i	$-0.479081\pi$
$457$	2.80779	0.131343	0.0656714	+	0.997841i	$0.479081\pi$
$458$	35.2705	1.64808
$459$	−23.3520	−1.08998
$460$	−0.869177	−0.0405256
$461$	−0.220189	−0.0102552	−0.00512761	−	0.999987i	$-0.501632\pi$
$461$	−0.220189	−0.0102552	−0.00512761	+	0.999987i	$0.501632\pi$
$462$	−2.81701	−0.131059
$463$	25.5262	1.18630	0.593152	−	0.805091i	$-0.297883\pi$
$463$	25.5262	1.18630	0.593152	+	0.805091i	$0.297883\pi$
$464$	−24.6095	−1.14247
$465$	−16.5821	−0.768978
$466$	3.19843	0.148164
$467$	6.43084	0.297584	0.148792	−	0.988869i	$-0.452462\pi$
$467$	6.43084	0.297584	0.148792	+	0.988869i	$0.452462\pi$
$468$	−5.03392	−0.232693
$469$	−2.82636	−0.130509
$470$	31.0792	1.43358
$471$	−39.7796	−1.83295
$472$	−5.07312	−0.233509
$473$	0.232640	0.0106968
$474$	39.2162	1.80126
$475$	0.729601	0.0334764
$476$	3.29969	0.151241
$477$	37.7736	1.72953
$478$	14.8110	0.677441
$479$	25.1810	1.15055	0.575276	−	0.817960i	$-0.304895\pi$
$479$	25.1810	1.15055	0.575276	+	0.817960i	$0.304895\pi$
$480$	−12.9250	−0.589943
$481$	20.0355	0.913541
$482$	2.51544	0.114575
$483$	−2.68857	−0.122334
$484$	4.79919	0.218145
$485$	−3.39408	−0.154117
$486$	−24.9392	−1.13127
$487$	37.4074	1.69509	0.847545	−	0.530724i	$-0.178080\pi$
$487$	37.4074	1.69509	0.847545	+	0.530724i	$0.178080\pi$
$488$	35.7863	1.61997
$489$	8.42523	0.381002
$490$	−2.30633	−0.104190
$491$	−8.61145	−0.388629	−0.194315	−	0.980939i	$-0.562248\pi$
$491$	−8.61145	−0.388629	−0.194315	+	0.980939i	$0.562248\pi$
$492$	−3.54571	−0.159853
$493$	−61.0795	−2.75088
$494$	−1.50543	−0.0677327
$495$	6.66388	0.299519
$496$	−9.43393	−0.423596
$497$	9.92823	0.445342
$498$	12.4015	0.555723
$499$	−31.2249	−1.39782	−0.698909	−	0.715211i	$-0.746331\pi$
$499$	−31.2249	−1.39782	−0.698909	+	0.715211i	$0.746331\pi$
$500$	−5.67657	−0.253864
$501$	−62.9575	−2.81274
$502$	33.9851	1.51683
$503$	12.5421	0.559223	0.279612	−	0.960113i	$-0.409794\pi$
$503$	12.5421	0.559223	0.279612	+	0.960113i	$0.409794\pi$
$504$	−12.9153	−0.575291
$505$	27.5413	1.22557
$506$	1.04777	0.0465792
$507$	−17.4539	−0.775156
$508$	−7.51799	−0.333557
$509$	12.5436	0.555986	0.277993	−	0.960583i	$-0.410331\pi$
$509$	12.5436	0.555986	0.277993	+	0.960583i	$0.410331\pi$
$510$	43.8441	1.94145
$511$	7.31556	0.323621
$512$	−24.7568	−1.09410
$513$	−1.57388	−0.0694885
$514$	−31.1607	−1.37444
$515$	−20.3637	−0.897330
$516$	0.344953	0.0151857
$517$	11.4024	0.501477
$518$	9.72506	0.427295
$519$	−1.73526	−0.0761696
$520$	14.5131	0.636440
$521$	18.3842	0.805426	0.402713	−	0.915326i	$-0.368067\pi$
$521$	18.3842	0.805426	0.402713	+	0.915326i	$0.368067\pi$
$522$	45.2293	1.97963
$523$	21.0572	0.920769	0.460384	−	0.887720i	$-0.347712\pi$
$523$	21.0572	0.920769	0.460384	+	0.887720i	$0.347712\pi$
$524$	0.398841	0.0174235
$525$	−4.11614	−0.179643
$526$	13.4492	0.586414
$527$	−23.4145	−1.01995
$528$	6.48106	0.282052
$529$	1.00000	0.0434783
$530$	−20.6032	−0.894947
$531$	7.02297	0.304771
$532$	0.222393	0.00964196
$533$	7.20949	0.312278
$534$	−29.1741	−1.26249
$535$	32.1539	1.39014
$536$	8.63290	0.372885
$537$	−45.4747	−1.96238
$538$	−2.50298	−0.107911
$539$	−0.846153	−0.0364464
$540$	2.87054	0.123528
$541$	30.0230	1.29079	0.645395	−	0.763849i	$-0.276693\pi$
$541$	30.0230	1.29079	0.645395	+	0.763849i	$0.276693\pi$
$542$	−5.02411	−0.215804
$543$	−12.4051	−0.532354
$544$	−18.2505	−0.782484
$545$	24.6670	1.05662
$546$	8.49310	0.363471
$547$	−9.39847	−0.401849	−0.200925	−	0.979607i	$-0.564395\pi$
$547$	−9.39847	−0.401849	−0.200925	+	0.979607i	$0.564395\pi$
$548$	−3.32039	−0.141840
$549$	−49.5407	−2.11435
$550$	1.60412	0.0683999
$551$	−4.11664	−0.175375
$552$	8.21201	0.349526
$553$	11.7795	0.500915
$554$	−39.1384	−1.66283
$555$	−39.3276	−1.66937
$556$	−4.99850	−0.211983
$557$	−22.6305	−0.958885	−0.479443	−	0.877573i	$-0.659161\pi$
$557$	−22.6305	−0.958885	−0.479443	+	0.877573i	$0.659161\pi$
$558$	17.3384	0.733993
$559$	−0.701393	−0.0296658
$560$	5.30616	0.224226
$561$	16.0856	0.679136
$562$	31.5365	1.33029
$563$	−21.0667	−0.887854	−0.443927	−	0.896063i	$-0.646415\pi$
$563$	−21.0667	−0.887854	−0.443927	+	0.896063i	$0.646415\pi$
$564$	16.9072	0.711923
$565$	13.2281	0.556508
$566$	−9.99118	−0.419961
$567$	−3.80592	−0.159833
$568$	−30.3250	−1.27241
$569$	−40.2625	−1.68789	−0.843945	−	0.536430i	$-0.819773\pi$
$569$	−40.2625	−1.68789	−0.843945	+	0.536430i	$0.819773\pi$
$570$	2.95501	0.123772
$571$	7.61151	0.318532	0.159266	−	0.987236i	$-0.449087\pi$
$571$	7.61151	0.318532	0.159266	+	0.987236i	$0.449087\pi$
$572$	1.00735	0.0421194
$573$	17.3246	0.723745
$574$	3.49942	0.146063
$575$	1.53098	0.0638462
$576$	37.6069	1.56696
$577$	18.6364	0.775845	0.387923	−	0.921692i	$-0.373193\pi$
$577$	18.6364	0.775845	0.387923	+	0.921692i	$0.373193\pi$
$578$	40.8585	1.69949
$579$	27.2622	1.13298
$580$	7.50818	0.311760
$581$	3.72506	0.154542
$582$	6.06677	0.251476
$583$	−7.55896	−0.313060
$584$	−22.3448	−0.924634
$585$	−20.0912	−0.830667
$586$	−15.5733	−0.643327
$587$	40.9445	1.68996	0.844981	−	0.534797i	$-0.179612\pi$
$587$	40.9445	1.68996	0.844981	+	0.534797i	$0.179612\pi$
$588$	−1.25466	−0.0517412
$589$	−1.57809	−0.0650242
$590$	−3.83061	−0.157704
$591$	−6.38467	−0.262630
$592$	−22.3743	−0.919580
$593$	20.5649	0.844501	0.422251	−	0.906479i	$-0.361240\pi$
$593$	20.5649	0.844501	0.422251	+	0.906479i	$0.361240\pi$
$594$	−3.46037	−0.141981
$595$	13.1696	0.539900
$596$	3.00360	0.123032
$597$	50.0213	2.04723
$598$	−3.15897	−0.129180
$599$	2.94630	0.120382	0.0601912	−	0.998187i	$-0.480829\pi$
$599$	2.94630	0.120382	0.0601912	+	0.998187i	$0.480829\pi$
$600$	12.5724	0.513266
$601$	37.8860	1.54540	0.772702	−	0.634769i	$-0.218905\pi$
$601$	37.8860	1.54540	0.772702	+	0.634769i	$0.218905\pi$
$602$	−0.340450	−0.0138757
$603$	−11.9510	−0.486681
$604$	−0.374955	−0.0152567
$605$	19.1543	0.778734
$606$	−49.2289	−1.99979
$607$	−7.00707	−0.284408	−0.142204	−	0.989837i	$-0.545419\pi$
$607$	−7.00707	−0.284408	−0.142204	+	0.989837i	$0.545419\pi$
$608$	−1.23005	−0.0498851
$609$	23.2246	0.941107
$610$	27.0215	1.09407
$611$	−34.3775	−1.39077
$612$	13.9524	0.563990
$613$	−18.9408	−0.765012	−0.382506	−	0.923953i	$-0.624939\pi$
$613$	−18.9408	−0.765012	−0.382506	+	0.923953i	$0.624939\pi$
$614$	0.729040	0.0294217
$615$	−14.1515	−0.570642
$616$	2.58451	0.104133
$617$	−2.22511	−0.0895797	−0.0447898	−	0.998996i	$-0.514262\pi$
$617$	−2.22511	−0.0895797	−0.0447898	+	0.998996i	$0.514262\pi$
$618$	36.3992	1.46419
$619$	−15.2083	−0.611272	−0.305636	−	0.952148i	$-0.598869\pi$
$619$	−15.2083	−0.611272	−0.305636	+	0.952148i	$0.598869\pi$
$620$	2.87822	0.115592
$621$	−3.30259	−0.132529
$622$	2.87888	0.115432
$623$	−8.76310	−0.351086
$624$	−19.5400	−0.782225
$625$	−15.0012	−0.600049
$626$	−9.94169	−0.397350
$627$	1.08414	0.0432964
$628$	6.90470	0.275527
$629$	−55.5319	−2.21420
$630$	−9.75207	−0.388532
$631$	6.16049	0.245245	0.122623	−	0.992453i	$-0.460870\pi$
$631$	6.16049	0.245245	0.122623	+	0.992453i	$0.460870\pi$
$632$	−35.9795	−1.43119
$633$	−56.7953	−2.25741
$634$	33.4869	1.32993
$635$	−30.0055	−1.19073
$636$	−11.2083	−0.444437
$637$	2.55110	0.101078
$638$	−9.05096	−0.358331
$639$	41.9804	1.66072
$640$	−10.8976	−0.430764
$641$	16.3586	0.646126	0.323063	−	0.946377i	$-0.395287\pi$
$641$	16.3586	0.646126	0.323063	+	0.946377i	$0.395287\pi$
$642$	−57.4738	−2.26831
$643$	−30.8553	−1.21681	−0.608407	−	0.793625i	$-0.708191\pi$
$643$	−30.8553	−1.21681	−0.608407	+	0.793625i	$0.708191\pi$
$644$	0.466664	0.0183891
$645$	1.37676	0.0542099
$646$	4.17257	0.164168
$647$	10.3205	0.405742	0.202871	−	0.979206i	$-0.434973\pi$
$647$	10.3205	0.405742	0.202871	+	0.979206i	$0.434973\pi$
$648$	11.6249	0.456668
$649$	−1.40538	−0.0551662
$650$	−4.83631	−0.189696
$651$	8.90301	0.348936
$652$	−1.46240	−0.0572720
$653$	1.58679	0.0620961	0.0310480	−	0.999518i	$-0.490116\pi$
$653$	1.58679	0.0620961	0.0310480	+	0.999518i	$0.490116\pi$
$654$	−44.0912	−1.72410
$655$	1.59184	0.0621983
$656$	−8.05108	−0.314342
$657$	30.9330	1.20681
$658$	−16.6865	−0.650509
$659$	−43.3271	−1.68779	−0.843893	−	0.536512i	$-0.819742\pi$
$659$	−43.3271	−1.68779	−0.843893	+	0.536512i	$0.819742\pi$
$660$	−1.97732	−0.0769672
$661$	18.2262	0.708917	0.354458	−	0.935072i	$-0.384665\pi$
$661$	18.2262	0.708917	0.354458	+	0.935072i	$0.384665\pi$
$662$	28.1776	1.09516
$663$	−48.4971	−1.88347
$664$	−11.3779	−0.441548
$665$	0.887605	0.0344199
$666$	41.1213	1.59342
$667$	−8.63827	−0.334475
$668$	10.9278	0.422808
$669$	−57.9188	−2.23927
$670$	6.51854	0.251833
$671$	9.91372	0.382715
$672$	6.93948	0.267696
$673$	6.47655	0.249653	0.124826	−	0.992179i	$-0.460163\pi$
$673$	6.47655	0.249653	0.124826	+	0.992179i	$0.460163\pi$
$674$	−1.31157	−0.0505199
$675$	−5.05620	−0.194613
$676$	3.02954	0.116521
$677$	−8.19344	−0.314899	−0.157450	−	0.987527i	$-0.550327\pi$
$677$	−8.19344	−0.314899	−0.157450	+	0.987527i	$0.550327\pi$
$678$	−23.6446	−0.908065
$679$	1.82229	0.0699332
$680$	−40.2254	−1.54257
$681$	34.7189	1.33043
$682$	−3.46963	−0.132859
$683$	−7.95826	−0.304514	−0.152257	−	0.988341i	$-0.548654\pi$
$683$	−7.95826	−0.304514	−0.152257	+	0.988341i	$0.548654\pi$
$684$	0.940363	0.0359557
$685$	−13.2522	−0.506341
$686$	1.23828	0.0472777
$687$	76.5796	2.92169
$688$	0.783270	0.0298619
$689$	22.7898	0.868222
$690$	6.20073	0.236058
$691$	−3.66850	−0.139556	−0.0697782	−	0.997563i	$-0.522229\pi$
$691$	−3.66850	−0.139556	−0.0697782	+	0.997563i	$0.522229\pi$
$692$	0.301196	0.0114498
$693$	−3.57786	−0.135912
$694$	17.6139	0.668615
$695$	−19.9498	−0.756739
$696$	−70.9375	−2.68888
$697$	−19.9823	−0.756884
$698$	−29.0829	−1.10080
$699$	6.94446	0.262664
$700$	0.714453	0.0270038
$701$	40.6182	1.53413	0.767063	−	0.641571i	$-0.221717\pi$
$701$	40.6182	1.53413	0.767063	+	0.641571i	$0.221717\pi$
$702$	10.4328	0.393760
$703$	−3.74274	−0.141160
$704$	−7.52562	−0.283633
$705$	67.4795	2.54142
$706$	−1.48163	−0.0557617
$707$	−14.7870	−0.556123
$708$	−2.08387	−0.0783168
$709$	−38.7523	−1.45537	−0.727687	−	0.685910i	$-0.759405\pi$
$709$	−38.7523	−1.45537	−0.727687	+	0.685910i	$0.759405\pi$
$710$	−22.8978	−0.859339
$711$	49.8082	1.86795
$712$	26.7662	1.00311
$713$	−3.31143	−0.124014
$714$	−23.5401	−0.880965
$715$	4.02049	0.150358
$716$	7.89321	0.294983
$717$	32.1579	1.20096
$718$	10.6786	0.398523
$719$	34.5902	1.29000	0.644998	−	0.764184i	$-0.276858\pi$
$719$	34.5902	1.29000	0.644998	+	0.764184i	$0.276858\pi$
$720$	22.4365	0.836158
$721$	10.9333	0.407178
$722$	−23.2461	−0.865130
$723$	5.46154	0.203117
$724$	2.15320	0.0800231
$725$	−13.2250	−0.491164
$726$	−34.2375	−1.27067
$727$	−8.51989	−0.315985	−0.157993	−	0.987440i	$-0.550502\pi$
$727$	−8.51989	−0.315985	−0.157993	+	0.987440i	$0.550502\pi$
$728$	−7.79212	−0.288795
$729$	−42.7306	−1.58261
$730$	−16.8721	−0.624465
$731$	1.94403	0.0719026
$732$	14.6998	0.543322
$733$	−35.1739	−1.29918	−0.649590	−	0.760285i	$-0.725059\pi$
$733$	−35.1739	−1.29918	−0.649590	+	0.760285i	$0.725059\pi$
$734$	1.73657	0.0640980
$735$	−5.00754	−0.184706
$736$	−2.58111	−0.0951410
$737$	2.39154	0.0880934
$738$	14.7969	0.544681
$739$	15.1355	0.556769	0.278384	−	0.960470i	$-0.410201\pi$
$739$	15.1355	0.556769	0.278384	+	0.960470i	$0.410201\pi$
$740$	6.82624	0.250938
$741$	−3.26862	−0.120076
$742$	11.0620	0.406097
$743$	−20.2165	−0.741670	−0.370835	−	0.928699i	$-0.620928\pi$
$743$	−20.2165	−0.741670	−0.370835	+	0.928699i	$0.620928\pi$
$744$	−27.1935	−0.996963
$745$	11.9878	0.439201
$746$	6.66765	0.244120
$747$	15.7510	0.576299
$748$	−2.79204	−0.102087
$749$	−17.2636	−0.630797
$750$	40.4968	1.47874
$751$	31.1017	1.13492	0.567459	−	0.823401i	$-0.307926\pi$
$751$	31.1017	1.13492	0.567459	+	0.823401i	$0.307926\pi$
$752$	38.3905	1.39996
$753$	73.7888	2.68901
$754$	27.2880	0.993772
$755$	−1.49651	−0.0544634
$756$	−1.54120	−0.0560530
$757$	−11.9728	−0.435158	−0.217579	−	0.976043i	$-0.569816\pi$
$757$	−11.9728	−0.435158	−0.217579	+	0.976043i	$0.569816\pi$
$758$	32.6179	1.18474
$759$	2.27494	0.0825750
$760$	−2.71112	−0.0983426
$761$	17.8372	0.646597	0.323299	−	0.946297i	$-0.395208\pi$
$761$	17.8372	0.646597	0.323299	+	0.946297i	$0.395208\pi$
$762$	53.6335	1.94294
$763$	−13.2438	−0.479457
$764$	−3.00709	−0.108793
$765$	55.6861	2.01333
$766$	29.0101	1.04818
$767$	4.23714	0.152994
$768$	−28.3449	−1.02281
$769$	−47.9412	−1.72880	−0.864401	−	0.502802i	$-0.832302\pi$
$769$	−47.9412	−1.72880	−0.864401	+	0.502802i	$0.832302\pi$
$770$	1.95151	0.0703276
$771$	−67.6565	−2.43659
$772$	−4.73200	−0.170308
$773$	22.7079	0.816748	0.408374	−	0.912815i	$-0.366096\pi$
$773$	22.7079	0.816748	0.408374	+	0.912815i	$0.366096\pi$
$774$	−1.43955	−0.0517437
$775$	−5.06973	−0.182110
$776$	−5.56605	−0.199810
$777$	21.1152	0.757502
$778$	−16.8109	−0.602699
$779$	−1.34677	−0.0482531
$780$	5.96150	0.213456
$781$	−8.40080	−0.300604
$782$	8.75562	0.313100
$783$	28.5287	1.01953
$784$	−2.84890	−0.101746
$785$	27.5577	0.983578
$786$	−2.84535	−0.101490
$787$	−20.2521	−0.721910	−0.360955	−	0.932583i	$-0.617549\pi$
$787$	−20.2521	−0.721910	−0.360955	+	0.932583i	$0.617549\pi$
$788$	1.10821	0.0394784
$789$	29.2011	1.03959
$790$	−27.1674	−0.966573
$791$	−7.10219	−0.252525
$792$	10.9283	0.388320
$793$	−29.8892	−1.06140
$794$	4.02064	0.142687
$795$	−44.7340	−1.58655
$796$	−8.68237	−0.307739
$797$	−22.1099	−0.783172	−0.391586	−	0.920142i	$-0.628073\pi$
$797$	−22.1099	−0.783172	−0.391586	+	0.920142i	$0.628073\pi$
$798$	−1.58656	−0.0561635
$799$	95.2831	3.37087
$800$	−3.95162	−0.139711
$801$	−37.0538	−1.30923
$802$	37.4957	1.32402
$803$	−6.19008	−0.218443
$804$	3.54612	0.125062
$805$	1.86253	0.0656456
$806$	10.4607	0.368463
$807$	−5.43449	−0.191303
$808$	45.1658	1.58893
$809$	−35.3424	−1.24257	−0.621287	−	0.783583i	$-0.713390\pi$
$809$	−35.3424	−1.24257	−0.621287	+	0.783583i	$0.713390\pi$
$810$	8.77771	0.308417
$811$	−15.3968	−0.540654	−0.270327	−	0.962769i	$-0.587132\pi$
$811$	−15.3968	−0.540654	−0.270327	+	0.962769i	$0.587132\pi$
$812$	−4.03117	−0.141466
$813$	−10.9084	−0.382574
$814$	−8.22889	−0.288422
$815$	−5.83667	−0.204450
$816$	54.1584	1.89592
$817$	0.131024	0.00458395
$818$	15.3268	0.535890
$819$	10.7870	0.376929
$820$	2.45632	0.0857785
$821$	−47.6244	−1.66210	−0.831052	−	0.556195i	$-0.812261\pi$
$821$	−47.6244	−1.66210	−0.831052	+	0.556195i	$0.812261\pi$
$822$	23.6878	0.826205
$823$	24.1554	0.842006	0.421003	−	0.907059i	$-0.361678\pi$
$823$	24.1554	0.842006	0.421003	+	0.907059i	$0.361678\pi$
$824$	−33.3950	−1.16337
$825$	3.48288	0.121258
$826$	2.05667	0.0715607
$827$	−14.8594	−0.516710	−0.258355	−	0.966050i	$-0.583180\pi$
$827$	−14.8594	−0.516710	−0.258355	+	0.966050i	$0.583180\pi$
$828$	1.97324	0.0685747
$829$	20.2699	0.704003	0.352001	−	0.935999i	$-0.385501\pi$
$829$	20.2699	0.704003	0.352001	+	0.935999i	$0.385501\pi$
$830$	−8.59124	−0.298206
$831$	−84.9778	−2.94785
$832$	22.6893	0.786609
$833$	−7.07080	−0.244989
$834$	35.6594	1.23478
$835$	43.6145	1.50934
$836$	−0.188178	−0.00650829
$837$	10.9363	0.378015
$838$	6.76744	0.233777
$839$	−20.9307	−0.722609	−0.361304	−	0.932448i	$-0.617668\pi$
$839$	−20.9307	−0.722609	−0.361304	+	0.932448i	$0.617668\pi$
$840$	15.2951	0.527732
$841$	45.6197	1.57309
$842$	−8.11360	−0.279613
$843$	68.4723	2.35831
$844$	9.85816	0.339332
$845$	12.0914	0.415956
$846$	−70.5571	−2.42580
$847$	−10.2840	−0.353363
$848$	−25.4501	−0.873961
$849$	−21.6930	−0.744501
$850$	13.4047	0.459776
$851$	−7.85369	−0.269221
$852$	−12.4565	−0.426753
$853$	−28.3729	−0.971470	−0.485735	−	0.874106i	$-0.661448\pi$
$853$	−28.3729	−0.971470	−0.485735	+	0.874106i	$0.661448\pi$
$854$	−14.5080	−0.496452
$855$	3.75314	0.128355
$856$	52.7302	1.80228
$857$	−32.4441	−1.10827	−0.554134	−	0.832428i	$-0.686950\pi$
$857$	−32.4441	−1.10827	−0.554134	+	0.832428i	$0.686950\pi$
$858$	−7.18646	−0.245342
$859$	32.7552	1.11759	0.558797	−	0.829305i	$-0.311263\pi$
$859$	32.7552	1.11759	0.558797	+	0.829305i	$0.311263\pi$
$860$	−0.238970	−0.00814880
$861$	7.59798	0.258938
$862$	−9.76562	−0.332618
$863$	5.88556	0.200347	0.100173	−	0.994970i	$-0.468060\pi$
$863$	5.88556	0.200347	0.100173	+	0.994970i	$0.468060\pi$
$864$	8.52436	0.290004
$865$	1.20212	0.0408734
$866$	−41.7688	−1.41936
$867$	88.7124	3.01283
$868$	−1.54533	−0.0524518
$869$	−9.96724	−0.338116
$870$	−53.5636	−1.81598
$871$	−7.21033	−0.244313
$872$	40.4521	1.36988
$873$	7.70536	0.260787
$874$	0.590113	0.0199609
$875$	12.1641	0.411223
$876$	−9.17852	−0.310114
$877$	−53.7879	−1.81629	−0.908144	−	0.418658i	$-0.862501\pi$
$877$	−53.7879	−1.81629	−0.908144	+	0.418658i	$0.862501\pi$
$878$	−16.9396	−0.571685
$879$	−33.8129	−1.14048
$880$	−4.48982	−0.151352
$881$	6.04127	0.203536	0.101768	−	0.994808i	$-0.467550\pi$
$881$	6.04127	0.203536	0.101768	+	0.994808i	$0.467550\pi$
$882$	5.23592	0.176303
$883$	44.1976	1.48737	0.743683	−	0.668532i	$-0.233077\pi$
$883$	44.1976	1.48737	0.743683	+	0.668532i	$0.233077\pi$
$884$	8.41782	0.283122
$885$	−8.31707	−0.279575
$886$	−21.3883	−0.718554
$887$	−36.4986	−1.22550	−0.612752	−	0.790275i	$-0.709937\pi$
$887$	−36.4986	−1.22550	−0.612752	+	0.790275i	$0.709937\pi$
$888$	−64.4946	−2.16430
$889$	16.1101	0.540314
$890$	20.2106	0.677462
$891$	3.22039	0.107887
$892$	10.0532	0.336605
$893$	6.42191	0.214901
$894$	−21.4278	−0.716652
$895$	31.5030	1.05303
$896$	5.85095	0.195466
$897$	−6.85879	−0.229008
$898$	10.2317	0.341437
$899$	28.6051	0.954033
$900$	3.02098	0.100699
$901$	−63.1658	−2.10436
$902$	−2.96105	−0.0985920
$903$	−0.739189	−0.0245987
$904$	21.6931	0.721501
$905$	8.59377	0.285667
$906$	2.67494	0.0888690
$907$	8.22173	0.272998	0.136499	−	0.990640i	$-0.456415\pi$
$907$	8.22173	0.272998	0.136499	+	0.990640i	$0.456415\pi$
$908$	−6.02629	−0.199989
$909$	−62.5252	−2.07383
$910$	−5.88368	−0.195042
$911$	−21.5853	−0.715154	−0.357577	−	0.933884i	$-0.616397\pi$
$911$	−21.5853	−0.715154	−0.357577	+	0.933884i	$0.616397\pi$
$912$	3.65017	0.120869
$913$	−3.15197	−0.104315
$914$	3.47683	0.115003
$915$	58.6694	1.93955
$916$	−13.2922	−0.439187
$917$	−0.854665	−0.0282235
$918$	−28.9163	−0.954379
$919$	−38.0934	−1.25658	−0.628292	−	0.777978i	$-0.716246\pi$
$919$	−38.0934	−1.25658	−0.628292	+	0.777978i	$0.716246\pi$
$920$	−5.68895	−0.187559
$921$	1.58290	0.0521583
$922$	−0.272656	−0.00897943
$923$	25.3279	0.833677
$924$	1.06163	0.0349251
$925$	−12.0238	−0.395341
$926$	31.6086	1.03872
$927$	46.2303	1.51840
$928$	22.2963	0.731913
$929$	−9.15900	−0.300497	−0.150249	−	0.988648i	$-0.548007\pi$
$929$	−9.15900	−0.300497	−0.150249	+	0.988648i	$0.548007\pi$
$930$	−20.5333	−0.673314
$931$	−0.476559	−0.0156186
$932$	−1.20538	−0.0394834
$933$	6.25065	0.204637
$934$	7.96317	0.260563
$935$	−11.1435	−0.364431
$936$	−32.9481	−1.07694
$937$	−18.8314	−0.615194	−0.307597	−	0.951517i	$-0.599525\pi$
$937$	−18.8314	−0.615194	−0.307597	+	0.951517i	$0.599525\pi$
$938$	−3.49983	−0.114273
$939$	−21.5855	−0.704416
$940$	−11.7127	−0.382025
$941$	25.4216	0.828721	0.414360	−	0.910113i	$-0.364005\pi$
$941$	25.4216	0.828721	0.414360	+	0.910113i	$0.364005\pi$
$942$	−49.2583	−1.60492
$943$	−2.82603	−0.0920283
$944$	−4.73176	−0.154006
$945$	−6.15118	−0.200098
$946$	0.288073	0.00936605
$947$	33.3211	1.08279	0.541395	−	0.840768i	$-0.317896\pi$
$947$	33.3211	1.08279	0.541395	+	0.840768i	$0.317896\pi$
$948$	−14.7792	−0.480007
$949$	18.6627	0.605817
$950$	0.903450	0.0293118
$951$	72.7070	2.35769
$952$	21.5972	0.699969
$953$	30.5121	0.988383	0.494192	−	0.869353i	$-0.335464\pi$
$953$	30.5121	0.988383	0.494192	+	0.869353i	$0.335464\pi$
$954$	46.7742	1.51437
$955$	−12.0018	−0.388369
$956$	−5.58176	−0.180527
$957$	−19.6515	−0.635244
$958$	31.1812	1.00742
$959$	7.11516	0.229761
$960$	−44.5367	−1.43741
$961$	−20.0344	−0.646271
$962$	24.8096	0.799893
$963$	−72.9970	−2.35230
$964$	−0.947980	−0.0305324
$965$	−18.8862	−0.607967
$966$	−3.32920	−0.107115
$967$	−23.0298	−0.740587	−0.370294	−	0.928915i	$-0.620743\pi$
$967$	−23.0298	−0.740587	−0.370294	+	0.928915i	$0.620743\pi$
$968$	31.4117	1.00961
$969$	9.05953	0.291034
$970$	−4.20282	−0.134944
$971$	6.95588	0.223225	0.111612	−	0.993752i	$-0.464398\pi$
$971$	6.95588	0.223225	0.111612	+	0.993752i	$0.464398\pi$
$972$	9.39873	0.301464
$973$	10.7111	0.343383
$974$	46.3208	1.48421
$975$	−10.5007	−0.336290
$976$	33.3783	1.06841
$977$	−23.1596	−0.740942	−0.370471	−	0.928844i	$-0.620804\pi$
$977$	−23.1596	−0.740942	−0.370471	+	0.928844i	$0.620804\pi$
$978$	10.4328	0.333604
$979$	7.41493	0.236982
$980$	0.869177	0.0277648
$981$	−55.9998	−1.78794
$982$	−10.6634	−0.340282
$983$	11.7384	0.374397	0.187198	−	0.982322i	$-0.440059\pi$
$983$	11.7384	0.374397	0.187198	+	0.982322i	$0.440059\pi$
$984$	−23.2074	−0.739825
$985$	4.42305	0.140930
$986$	−75.6334	−2.40866
$987$	−36.2300	−1.15321
$988$	0.567346	0.0180497
$989$	0.274938	0.00874252
$990$	8.25174	0.262258
$991$	−14.8198	−0.470766	−0.235383	−	0.971903i	$-0.575634\pi$
$991$	−14.8198	−0.470766	−0.235383	+	0.971903i	$0.575634\pi$
$992$	8.54718	0.271373
$993$	61.1796	1.94148
$994$	12.2939	0.389939
$995$	−34.6527	−1.09857
$996$	−4.67368	−0.148091
$997$	−8.94358	−0.283246	−0.141623	−	0.989921i	$-0.545232\pi$
$997$	−8.94358	−0.283246	−0.141623	+	0.989921i	$0.545232\pi$
$998$	−38.6651	−1.22392
$999$	25.9375	0.820628

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	161.2.a.d.1.3	✓	5
3.2	odd	2		1449.2.a.r.1.3		5
4.3	odd	2		2576.2.a.bd.1.1		5
5.4	even	2		4025.2.a.p.1.3		5
7.6	odd	2		1127.2.a.h.1.3		5
23.22	odd	2		3703.2.a.j.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.2.a.d.1.3	✓	5	1.1	even	1	trivial
1127.2.a.h.1.3		5	7.6	odd	2
1449.2.a.r.1.3		5	3.2	odd	2
2576.2.a.bd.1.1		5	4.3	odd	2
3703.2.a.j.1.3		5	23.22	odd	2
4025.2.a.p.1.3		5	5.4	even	2

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:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	161.a (trivial)

\(f(q)\)	\(=\)	\(q+1.23828 q^{2} +2.68857 q^{3} -0.466664 q^{4} -1.86253 q^{5} +3.32920 q^{6} +1.00000 q^{7} -3.05442 q^{8} +4.22838 q^{9} +O(q^{10})\)	\(q+1.23828 q^{2} +2.68857 q^{3} -0.466664 q^{4} -1.86253 q^{5} +3.32920 q^{6} +1.00000 q^{7} -3.05442 q^{8} +4.22838 q^{9} -2.30633 q^{10} -0.846153 q^{11} -1.25466 q^{12} +2.55110 q^{13} +1.23828 q^{14} -5.00754 q^{15} -2.84890 q^{16} -7.07080 q^{17} +5.23592 q^{18} -0.476559 q^{19} +0.869177 q^{20} +2.68857 q^{21} -1.04777 q^{22} -1.00000 q^{23} -8.21201 q^{24} -1.53098 q^{25} +3.15897 q^{26} +3.30259 q^{27} -0.466664 q^{28} +8.63827 q^{29} -6.20073 q^{30} +3.31143 q^{31} +2.58111 q^{32} -2.27494 q^{33} -8.75562 q^{34} -1.86253 q^{35} -1.97324 q^{36} +7.85369 q^{37} -0.590113 q^{38} +6.85879 q^{39} +5.68895 q^{40} +2.82603 q^{41} +3.32920 q^{42} -0.274938 q^{43} +0.394869 q^{44} -7.87550 q^{45} -1.23828 q^{46} -13.4756 q^{47} -7.65944 q^{48} +1.00000 q^{49} -1.89578 q^{50} -19.0103 q^{51} -1.19051 q^{52} +8.93333 q^{53} +4.08953 q^{54} +1.57599 q^{55} -3.05442 q^{56} -1.28126 q^{57} +10.6966 q^{58} +1.66091 q^{59} +2.33684 q^{60} -11.7162 q^{61} +4.10048 q^{62} +4.22838 q^{63} +8.89393 q^{64} -4.75150 q^{65} -2.81701 q^{66} -2.82636 q^{67} +3.29969 q^{68} -2.68857 q^{69} -2.30633 q^{70} +9.92823 q^{71} -12.9153 q^{72} +7.31556 q^{73} +9.72506 q^{74} -4.11614 q^{75} +0.222393 q^{76} -0.846153 q^{77} +8.49310 q^{78} +11.7795 q^{79} +5.30616 q^{80} -3.80592 q^{81} +3.49942 q^{82} +3.72506 q^{83} -1.25466 q^{84} +13.1696 q^{85} -0.340450 q^{86} +23.2246 q^{87} +2.58451 q^{88} -8.76310 q^{89} -9.75207 q^{90} +2.55110 q^{91} +0.466664 q^{92} +8.90301 q^{93} -16.6865 q^{94} +0.887605 q^{95} +6.93948 q^{96} +1.82229 q^{97} +1.23828 q^{98} -3.57786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 2 q^{2} + 12 q^{4} - 4 q^{5} - 3 q^{6} + 5 q^{7} + 3 q^{8} + 11 q^{9}+O(q^{10}) \) 5 * q + 2 * q^2 + 12 * q^4 - 4 * q^5 - 3 * q^6 + 5 * q^7 + 3 * q^8 + 11 * q^9	\( 5 q + 2 q^{2} + 12 q^{4} - 4 q^{5} - 3 q^{6} + 5 q^{7} + 3 q^{8} + 11 q^{9} - 8 q^{10} - 4 q^{11} + 3 q^{12} - 6 q^{13} + 2 q^{14} + 10 q^{15} + 10 q^{16} - 12 q^{17} - 19 q^{18} + 6 q^{19} + 14 q^{22} - 5 q^{23} - 36 q^{24} + 19 q^{25} + q^{26} + 12 q^{28} - 4 q^{29} - 48 q^{30} + 30 q^{31} + 8 q^{32} - 22 q^{33} + 6 q^{34} - 4 q^{35} - q^{36} + 4 q^{37} - 40 q^{38} + 16 q^{39} - 50 q^{40} + 6 q^{41} - 3 q^{42} - 12 q^{43} - 26 q^{44} - 12 q^{45} - 2 q^{46} + 10 q^{47} + 25 q^{48} + 5 q^{49} - 2 q^{50} - 4 q^{51} - 21 q^{52} + 16 q^{53} + 33 q^{54} + 18 q^{55} + 3 q^{56} + 6 q^{57} + 13 q^{58} + 22 q^{59} + 30 q^{60} - 18 q^{61} + 15 q^{62} + 11 q^{63} + 25 q^{64} - 26 q^{65} + 4 q^{66} - 2 q^{67} + 12 q^{68} - 8 q^{70} + 4 q^{71} - 41 q^{72} - 2 q^{73} + 38 q^{74} - 30 q^{75} + 10 q^{76} - 4 q^{77} + 41 q^{78} + 30 q^{79} - 10 q^{80} - 3 q^{81} - 7 q^{82} + 8 q^{83} + 3 q^{84} - 12 q^{85} + 8 q^{86} - 12 q^{87} + 4 q^{88} - 20 q^{89} + 34 q^{90} - 6 q^{91} - 12 q^{92} - 26 q^{93} - 25 q^{94} + 8 q^{95} - q^{96} - 12 q^{97} + 2 q^{98} - 8 q^{99}+O(q^{100}) \) 5 * q + 2 * q^2 + 12 * q^4 - 4 * q^5 - 3 * q^6 + 5 * q^7 + 3 * q^8 + 11 * q^9 - 8 * q^10 - 4 * q^11 + 3 * q^12 - 6 * q^13 + 2 * q^14 + 10 * q^15 + 10 * q^16 - 12 * q^17 - 19 * q^18 + 6 * q^19 + 14 * q^22 - 5 * q^23 - 36 * q^24 + 19 * q^25 + q^26 + 12 * q^28 - 4 * q^29 - 48 * q^30 + 30 * q^31 + 8 * q^32 - 22 * q^33 + 6 * q^34 - 4 * q^35 - q^36 + 4 * q^37 - 40 * q^38 + 16 * q^39 - 50 * q^40 + 6 * q^41 - 3 * q^42 - 12 * q^43 - 26 * q^44 - 12 * q^45 - 2 * q^46 + 10 * q^47 + 25 * q^48 + 5 * q^49 - 2 * q^50 - 4 * q^51 - 21 * q^52 + 16 * q^53 + 33 * q^54 + 18 * q^55 + 3 * q^56 + 6 * q^57 + 13 * q^58 + 22 * q^59 + 30 * q^60 - 18 * q^61 + 15 * q^62 + 11 * q^63 + 25 * q^64 - 26 * q^65 + 4 * q^66 - 2 * q^67 + 12 * q^68 - 8 * q^70 + 4 * q^71 - 41 * q^72 - 2 * q^73 + 38 * q^74 - 30 * q^75 + 10 * q^76 - 4 * q^77 + 41 * q^78 + 30 * q^79 - 10 * q^80 - 3 * q^81 - 7 * q^82 + 8 * q^83 + 3 * q^84 - 12 * q^85 + 8 * q^86 - 12 * q^87 + 4 * q^88 - 20 * q^89 + 34 * q^90 - 6 * q^91 - 12 * q^92 - 26 * q^93 - 25 * q^94 + 8 * q^95 - q^96 - 12 * q^97 + 2 * q^98 - 8 * q^99

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