LMFDB - Embedded newform 3703.2.a.j.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3703,2,Mod(1,3703)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3703, 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("3703.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3703 = 7 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3703.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:	$29.5686038685$
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:	no (minimal twist has level 161)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.23828$ of defining polynomial
Character	$\chi$	$=$	3703.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.23828 q^{2} +2.68857 q^{3} -0.466664 q^{4} +1.86253 q^{5} +3.32920 q^{6} -1.00000 q^{7} -3.05442 q^{8} +4.22838 q^{9} +O(q^{10})$	\(q+1.23828 q^{2} +2.68857 q^{3} -0.466664 q^{4} +1.86253 q^{5} +3.32920 q^{6} -1.00000 q^{7} -3.05442 q^{8} +4.22838 q^{9} +2.30633 q^{10} +0.846153 q^{11} -1.25466 q^{12} +2.55110 q^{13} -1.23828 q^{14} +5.00754 q^{15} -2.84890 q^{16} +7.07080 q^{17} +5.23592 q^{18} +0.476559 q^{19} -0.869177 q^{20} -2.68857 q^{21} +1.04777 q^{22} -8.21201 q^{24} -1.53098 q^{25} +3.15897 q^{26} +3.30259 q^{27} +0.466664 q^{28} +8.63827 q^{29} +6.20073 q^{30} +3.31143 q^{31} +2.58111 q^{32} +2.27494 q^{33} +8.75562 q^{34} -1.86253 q^{35} -1.97324 q^{36} -7.85369 q^{37} +0.590113 q^{38} +6.85879 q^{39} -5.68895 q^{40} +2.82603 q^{41} -3.32920 q^{42} +0.274938 q^{43} -0.394869 q^{44} +7.87550 q^{45} -13.4756 q^{47} -7.65944 q^{48} +1.00000 q^{49} -1.89578 q^{50} +19.0103 q^{51} -1.19051 q^{52} -8.93333 q^{53} +4.08953 q^{54} +1.57599 q^{55} +3.05442 q^{56} +1.28126 q^{57} +10.6966 q^{58} +1.66091 q^{59} -2.33684 q^{60} +11.7162 q^{61} +4.10048 q^{62} -4.22838 q^{63} +8.89393 q^{64} +4.75150 q^{65} +2.81701 q^{66} +2.82636 q^{67} -3.29969 q^{68} -2.30633 q^{70} +9.92823 q^{71} -12.9153 q^{72} +7.31556 q^{73} -9.72506 q^{74} -4.11614 q^{75} -0.222393 q^{76} -0.846153 q^{77} +8.49310 q^{78} -11.7795 q^{79} -5.30616 q^{80} -3.80592 q^{81} +3.49942 q^{82} -3.72506 q^{83} +1.25466 q^{84} +13.1696 q^{85} +0.340450 q^{86} +23.2246 q^{87} -2.58451 q^{88} +8.76310 q^{89} +9.75207 q^{90} -2.55110 q^{91} +8.90301 q^{93} -16.6865 q^{94} +0.887605 q^{95} +6.93948 q^{96} -1.82229 q^{97} +1.23828 q^{98} +3.57786 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	\( 5 q + 2 q^{2} + 12 q^{4} + 4 q^{5} - 3 q^{6} - 5 q^{7} + 3 q^{8} + 11 q^{9} + 8 q^{10} + 4 q^{11} + 3 q^{12} - 6 q^{13} - 2 q^{14} - 10 q^{15} + 10 q^{16} + 12 q^{17} - 19 q^{18} - 6 q^{19} - 14 q^{22} - 36 q^{24} + 19 q^{25} + q^{26} - 12 q^{28} - 4 q^{29} + 48 q^{30} + 30 q^{31} + 8 q^{32} + 22 q^{33} - 6 q^{34} - 4 q^{35} - q^{36} - 4 q^{37} + 40 q^{38} + 16 q^{39} + 50 q^{40} + 6 q^{41} + 3 q^{42} + 12 q^{43} + 26 q^{44} + 12 q^{45} + 10 q^{47} + 25 q^{48} + 5 q^{49} - 2 q^{50} + 4 q^{51} - 21 q^{52} - 16 q^{53} + 33 q^{54} + 18 q^{55} - 3 q^{56} - 6 q^{57} + 13 q^{58} + 22 q^{59} - 30 q^{60} + 18 q^{61} + 15 q^{62} - 11 q^{63} + 25 q^{64} + 26 q^{65} - 4 q^{66} + 2 q^{67} - 12 q^{68} - 8 q^{70} + 4 q^{71} - 41 q^{72} - 2 q^{73} - 38 q^{74} - 30 q^{75} - 10 q^{76} - 4 q^{77} + 41 q^{78} - 30 q^{79} + 10 q^{80} - 3 q^{81} - 7 q^{82} - 8 q^{83} - 3 q^{84} - 12 q^{85} - 8 q^{86} - 12 q^{87} - 4 q^{88} + 20 q^{89} - 34 q^{90} + 6 q^{91} - 26 q^{93} - 25 q^{94} + 8 q^{95} - q^{96} + 12 q^{97} + 2 q^{98} + 8 q^{99}+O(q^{100}) \) 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 - 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 + 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 - 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	$-0.363265\pi$
$5$	1.86253	0.832949	0.416475	+	0.909147i	$0.363265\pi$
$6$	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	$-0.459285\pi$
$11$	0.846153	0.255125	0.127562	+	0.991831i	$0.459285\pi$
$12$	−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	$-0.172041\pi$
$17$	7.07080	1.71492	0.857460	+	0.514550i	$0.172041\pi$
$18$	5.23592	1.23412
$19$	0.476559	0.109330	0.0546650	−	0.998505i	$-0.482591\pi$
$19$	0.476559	0.109330	0.0546650	+	0.998505i	$0.482591\pi$
$20$	−0.869177	−0.194354
$21$	−2.68857	−0.586693
$22$	1.04777	0.223386
$23$	0	0
$23$	0	0
$24$	−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	$-0.723380\pi$
$37$	−7.85369	−1.29114	−0.645569	+	0.763702i	$0.723380\pi$
$38$	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	$-0.493327\pi$
$43$	0.274938	0.0419276	0.0209638	+	0.999780i	$0.493327\pi$
$44$	−0.394869	−0.0595288
$45$	7.87550	1.17401
$46$	0	0
$47$	−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	$-0.710256\pi$
$53$	−8.93333	−1.22709	−0.613544	+	0.789661i	$0.710256\pi$
$54$	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	$-0.230027\pi$
$61$	11.7162	1.50011	0.750054	+	0.661376i	$0.230027\pi$
$62$	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	$-0.444768\pi$
$67$	2.82636	0.345295	0.172648	+	0.984984i	$0.444768\pi$
$68$	−3.29969	−0.400146
$69$	0	0
$70$	−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	$-0.730567\pi$
$79$	−11.7795	−1.32530	−0.662648	+	0.748931i	$0.730567\pi$
$80$	−5.30616	−0.593246
$81$	−3.80592	−0.422880
$82$	3.49942	0.386446
$83$	−3.72506	−0.408879	−0.204439	−	0.978879i	$-0.565537\pi$
$83$	−3.72506	−0.408879	−0.204439	+	0.978879i	$0.565537\pi$
$84$	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	$-0.346254\pi$
$89$	8.76310	0.928887	0.464444	+	0.885603i	$0.346254\pi$
$90$	9.75207	1.02796
$91$	−2.55110	−0.267428
$92$	0	0
$93$	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	$-0.529490\pi$
$97$	−1.82229	−0.185026	−0.0925130	+	0.995711i	$0.529490\pi$
$98$	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	$-0.681064\pi$
$103$	−10.9333	−1.07729	−0.538646	+	0.842532i	$0.681064\pi$
$104$	−7.79212	−0.764080
$105$	−5.00754	−0.488686
$106$	−11.0620	−1.07443
$107$	17.2636	1.66893	0.834466	−	0.551059i	$-0.185776\pi$
$107$	17.2636	1.66893	0.834466	+	0.551059i	$0.185776\pi$
$108$	−1.54120	−0.148302
$109$	13.2438	1.26852	0.634262	−	0.773118i	$-0.281304\pi$
$109$	13.2438	1.26852	0.634262	+	0.773118i	$0.281304\pi$
$110$	1.95151	0.186069
$111$	−21.1152	−2.00416
$112$	2.84890	0.269195
$113$	7.10219	0.668118	0.334059	−	0.942552i	$-0.391581\pi$
$113$	7.10219	0.668118	0.334059	+	0.942552i	$0.391581\pi$
$114$	1.58656	0.148595
$115$	0	0
$116$	−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	$-0.598304\pi$
$137$	−7.11516	−0.607889	−0.303945	+	0.952690i	$0.598304\pi$
$138$	0	0
$139$	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	$-0.415076\pi$
$149$	6.43632	0.527284	0.263642	+	0.964621i	$0.415076\pi$
$150$	−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	$-0.298962\pi$
$157$	14.7959	1.18084	0.590419	+	0.807097i	$0.298962\pi$
$158$	−14.5863	−1.16042
$159$	−24.0178	−1.90474
$160$	4.80740	0.380058
$161$	0	0
$162$	−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	$-0.445145\pi$
$181$	4.61403	0.342958	0.171479	+	0.985188i	$0.445145\pi$
$182$	−3.15897	−0.234158
$183$	31.4998	2.32853
$184$	0	0
$185$	−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	$-0.574896\pi$
$191$	−6.44380	−0.466257	−0.233129	+	0.972446i	$0.574896\pi$
$192$	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	$-0.729208\pi$
$199$	−18.6052	−1.31889	−0.659443	+	0.751754i	$0.729208\pi$
$200$	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
$207$	0	0
$208$	−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	$-0.640976\pi$
$227$	−12.9135	−0.857102	−0.428551	+	0.903518i	$0.640976\pi$
$228$	−0.597918	−0.0395981
$229$	−28.4835	−1.88224	−0.941120	−	0.338074i	$-0.890225\pi$
$229$	−28.4835	−1.88224	−0.941120	+	0.338074i	$0.890225\pi$
$230$	0	0
$231$	−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	$-0.520841\pi$
$241$	−2.03140	−0.130854	−0.0654269	+	0.997857i	$0.520841\pi$
$242$	−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	$-0.833425\pi$
$251$	−27.4454	−1.73234	−0.866169	+	0.499750i	$0.833425\pi$
$252$	1.97324	0.124302
$253$	0	0
$254$	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	$-0.608691\pi$
$263$	−10.8612	−0.669732	−0.334866	+	0.942266i	$0.608691\pi$
$264$	−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
$276$	0	0
$277$	−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	$-0.774628\pi$
$281$	−25.4680	−1.51929	−0.759646	+	0.650337i	$0.774628\pi$
$282$	−44.8629	−2.67154
$283$	8.06860	0.479629	0.239814	−	0.970819i	$-0.422913\pi$
$283$	8.06860	0.479629	0.239814	+	0.970819i	$0.422913\pi$
$284$	−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	$-0.380260\pi$
$293$	12.5766	0.734730	0.367365	+	0.930077i	$0.380260\pi$
$294$	3.32920	0.194163
$295$	3.09350	0.180110
$296$	23.9885	1.39430
$297$	2.79450	0.162153
$298$	7.96996	0.461688
$299$	0	0
$300$	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	$-0.427140\pi$
$313$	8.02863	0.453805	0.226903	+	0.973917i	$0.427140\pi$
$314$	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
$322$	0	0
$323$	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	$-0.490816\pi$
$337$	1.05919	0.0576978	0.0288489	+	0.999584i	$0.490816\pi$
$338$	−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
$345$	0	0
$346$	−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	$-0.573079\pi$
$359$	−8.62376	−0.455145	−0.227572	+	0.973761i	$0.573079\pi$
$360$	−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	$-0.511654\pi$
$367$	−1.40241	−0.0732050	−0.0366025	+	0.999330i	$0.511654\pi$
$368$	0	0
$369$	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	$-0.544518\pi$
$373$	−5.38461	−0.278805	−0.139402	+	0.990236i	$0.544518\pi$
$374$	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	$-0.736518\pi$
$379$	−26.3413	−1.35306	−0.676532	+	0.736413i	$0.736518\pi$
$380$	−0.414214	−0.0212487
$381$	43.3130	2.21899
$382$	−7.97923	−0.408253
$383$	−23.4277	−1.19710	−0.598550	−	0.801085i	$-0.704256\pi$
$383$	−23.4277	−1.19710	−0.598550	+	0.801085i	$0.704256\pi$
$384$	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	$-0.388162\pi$
$389$	13.5760	0.688330	0.344165	+	0.938909i	$0.388162\pi$
$390$	15.8187	0.801009
$391$	0	0
$392$	−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	$-0.772882\pi$
$401$	−30.2805	−1.51213	−0.756067	+	0.654494i	$0.772882\pi$
$402$	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
$414$	0	0
$415$	−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	$-0.542620\pi$
$419$	−5.46520	−0.266992	−0.133496	+	0.991049i	$0.542620\pi$
$420$	2.33684	0.114026
$421$	6.55232	0.319340	0.159670	−	0.987170i	$-0.448957\pi$
$421$	6.55232	0.319340	0.159670	+	0.987170i	$0.448957\pi$
$422$	−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	$-0.439171\pi$
$431$	7.88645	0.379877	0.189938	+	0.981796i	$0.439171\pi$
$432$	−9.40874	−0.452678
$433$	33.7313	1.62102	0.810511	−	0.585723i	$-0.199189\pi$
$433$	33.7313	1.62102	0.810511	+	0.585723i	$0.199189\pi$
$434$	−4.10048	−0.196829
$435$	43.2565	2.07399
$436$	−6.18040	−0.295988
$437$	0	0
$438$	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	$-0.520919\pi$
$457$	−2.80779	−0.131343	−0.0656714	+	0.997841i	$0.520919\pi$
$458$	−35.2705	−1.64808
$459$	23.3520	1.08998
$460$	0	0
$461$	−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	$-0.547538\pi$
$467$	−6.43084	−0.297584	−0.148792	+	0.988869i	$0.547538\pi$
$468$	−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	$-0.695105\pi$
$479$	−25.1810	−1.15055	−0.575276	+	0.817960i	$0.695105\pi$
$480$	12.9250	0.589943
$481$	−20.0355	−0.913541
$482$	−2.51544	−0.114575
$483$	0	0
$484$	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	$-0.590206\pi$
$503$	−12.5421	−0.559223	−0.279612	+	0.960113i	$0.590206\pi$
$504$	12.9153	0.575291
$505$	−27.5413	−1.22557
$506$	0	0
$507$	−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	$-0.631933\pi$
$521$	−18.3842	−0.805426	−0.402713	+	0.915326i	$0.631933\pi$
$522$	45.2293	1.97963
$523$	−21.0572	−0.920769	−0.460384	−	0.887720i	$-0.652288\pi$
$523$	−21.0572	−0.920769	−0.460384	+	0.887720i	$0.652288\pi$
$524$	0.398841	0.0174235
$525$	4.11614	0.179643
$526$	−13.4492	−0.586414
$527$	23.4145	1.01995
$528$	−6.48106	−0.282052
$529$	0	0
$530$	−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
$552$	0	0
$553$	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	$-0.340839\pi$
$557$	22.6305	0.958885	0.479443	+	0.877573i	$0.340839\pi$
$558$	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	$-0.353585\pi$
$563$	21.0667	0.887854	0.443927	+	0.896063i	$0.353585\pi$
$564$	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	$-0.180227\pi$
$569$	40.2625	1.68789	0.843945	+	0.536430i	$0.180227\pi$
$570$	2.95501	0.123772
$571$	−7.61151	−0.318532	−0.159266	−	0.987236i	$-0.550913\pi$
$571$	−7.61151	−0.318532	−0.159266	+	0.987236i	$0.550913\pi$
$572$	−1.00735	−0.0421194
$573$	−17.3246	−0.723745
$574$	−3.49942	−0.146063
$575$	0	0
$576$	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
$598$	0	0
$599$	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	$-0.375061\pi$
$613$	18.9408	0.765012	0.382506	+	0.923953i	$0.375061\pi$
$614$	0.729040	0.0294217
$615$	14.1515	0.570642
$616$	2.58451	0.104133
$617$	2.22511	0.0895797	0.0447898	−	0.998996i	$-0.485738\pi$
$617$	2.22511	0.0895797	0.0447898	+	0.998996i	$0.485738\pi$
$618$	−36.3992	−1.46419
$619$	15.2083	0.611272	0.305636	−	0.952148i	$-0.401131\pi$
$619$	15.2083	0.611272	0.305636	+	0.952148i	$0.401131\pi$
$620$	−2.87822	−0.115592
$621$	0	0
$622$	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	$-0.539130\pi$
$631$	−6.16049	−0.245245	−0.122623	+	0.992453i	$0.539130\pi$
$632$	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	$-0.604713\pi$
$641$	−16.3586	−0.646126	−0.323063	+	0.946377i	$0.604713\pi$
$642$	57.4738	2.26831
$643$	30.8553	1.21681	0.608407	−	0.793625i	$-0.291809\pi$
$643$	30.8553	1.21681	0.608407	+	0.793625i	$0.291809\pi$
$644$	0	0
$645$	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	$-0.180258\pi$
$659$	43.3271	1.68779	0.843893	+	0.536512i	$0.180258\pi$
$660$	−1.97732	−0.0769672
$661$	−18.2262	−0.708917	−0.354458	−	0.935072i	$-0.615335\pi$
$661$	−18.2262	−0.708917	−0.354458	+	0.935072i	$0.615335\pi$
$662$	28.1776	1.09516
$663$	48.4971	1.88347
$664$	11.3779	0.441548
$665$	−0.887605	−0.0344199
$666$	−41.1213	−1.59342
$667$	0	0
$668$	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	$-0.449673\pi$
$677$	8.19344	0.314899	0.157450	+	0.987527i	$0.449673\pi$
$678$	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
$690$	0	0
$691$	−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	$-0.778283\pi$
$701$	−40.6182	−1.53413	−0.767063	+	0.641571i	$0.778283\pi$
$702$	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	$-0.240595\pi$
$709$	38.7523	1.45537	0.727687	+	0.685910i	$0.240595\pi$
$710$	22.8978	0.859339
$711$	−49.8082	−1.86795
$712$	−26.7662	−1.00311
$713$	0	0
$714$	−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	$-0.449498\pi$
$727$	8.51989	0.315985	0.157993	+	0.987440i	$0.449498\pi$
$728$	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	$-0.274941\pi$
$733$	35.1739	1.29918	0.649590	+	0.760285i	$0.274941\pi$
$734$	−1.73657	−0.0640980
$735$	5.00754	0.184706
$736$	0	0
$737$	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	$-0.379072\pi$
$743$	20.2165	0.741670	0.370835	+	0.928699i	$0.379072\pi$
$744$	−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	$-0.692074\pi$
$751$	−31.1017	−1.13492	−0.567459	+	0.823401i	$0.692074\pi$
$752$	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	$-0.430184\pi$
$757$	11.9728	0.435158	0.217579	+	0.976043i	$0.430184\pi$
$758$	−32.6179	−1.18474
$759$	0	0
$760$	−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	$-0.167698\pi$
$769$	47.9412	1.72880	0.864401	+	0.502802i	$0.167698\pi$
$770$	−1.95151	−0.0703276
$771$	−67.6565	−2.43659
$772$	−4.73200	−0.170308
$773$	−22.7079	−0.816748	−0.408374	−	0.912815i	$-0.633904\pi$
$773$	−22.7079	−0.816748	−0.408374	+	0.912815i	$0.633904\pi$
$774$	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
$782$	0	0
$783$	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	$-0.382451\pi$
$787$	20.2521	0.721910	0.360955	+	0.932583i	$0.382451\pi$
$788$	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	$-0.371927\pi$
$797$	22.1099	0.783172	0.391586	+	0.920142i	$0.371927\pi$
$798$	−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
$805$	0	0
$806$	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	$-0.416820\pi$
$827$	14.8594	0.516710	0.258355	+	0.966050i	$0.416820\pi$
$828$	0	0
$829$	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	$-0.382332\pi$
$839$	20.9307	0.722609	0.361304	+	0.932448i	$0.382332\pi$
$840$	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
$851$	0	0
$852$	−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	0
$875$	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	$-0.532450\pi$
$881$	−6.04127	−0.203536	−0.101768	+	0.994808i	$0.532450\pi$
$882$	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
$897$	0	0
$898$	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	$-0.543585\pi$
$907$	−8.22173	−0.272998	−0.136499	+	0.990640i	$0.543585\pi$
$908$	6.02629	0.199989
$909$	−62.5252	−2.07383
$910$	−5.88368	−0.195042
$911$	21.5853	0.715154	0.357577	−	0.933884i	$-0.383603\pi$
$911$	21.5853	0.715154	0.357577	+	0.933884i	$0.383603\pi$
$912$	−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	$-0.283754\pi$
$919$	38.0934	1.25658	0.628292	+	0.777978i	$0.283754\pi$
$920$	0	0
$921$	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	$-0.400475\pi$
$937$	18.8314	0.615194	0.307597	+	0.951517i	$0.400475\pi$
$938$	−3.49983	−0.114273
$939$	21.5855	0.704416
$940$	11.7127	0.382025
$941$	−25.4216	−0.828721	−0.414360	−	0.910113i	$-0.635995\pi$
$941$	−25.4216	−0.828721	−0.414360	+	0.910113i	$0.635995\pi$
$942$	49.2583	1.60492
$943$	0	0
$944$	−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	$-0.664536\pi$
$953$	−30.5121	−0.988383	−0.494192	+	0.869353i	$0.664536\pi$
$954$	−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
$966$	0	0
$967$	−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	$-0.535602\pi$
$971$	−6.95588	−0.223225	−0.111612	+	0.993752i	$0.535602\pi$
$972$	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	$-0.379196\pi$
$977$	23.1596	0.740942	0.370471	+	0.928844i	$0.379196\pi$
$978$	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	$-0.559941\pi$
$983$	−11.7384	−0.374397	−0.187198	+	0.982322i	$0.559941\pi$
$984$	−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	0
$990$	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	3703.2.a.j.1.3		5
23.22	odd	2		161.2.a.d.1.3	✓	5
69.68	even	2		1449.2.a.r.1.3		5
92.91	even	2		2576.2.a.bd.1.1		5
115.114	odd	2		4025.2.a.p.1.3		5
161.160	even	2		1127.2.a.h.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.2.a.d.1.3	✓	5	23.22	odd	2
1127.2.a.h.1.3		5	161.160	even	2
1449.2.a.r.1.3		5	69.68	even	2
2576.2.a.bd.1.1		5	92.91	even	2
3703.2.a.j.1.3		5	1.1	even	1	trivial
4025.2.a.p.1.3		5	115.114	odd	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:	\( N \)	\(=\)	\( 3703 = 7 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3703.a (trivial)

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

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