LMFDB - Embedded newform 4031.2.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4031,2,Mod(1,4031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4031, 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("4031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4031 = 29 \cdot 139 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4031.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.1876970548$
Analytic rank:	$0$
Dimension:	$98$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	4031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.76750 q^{2} +0.603367 q^{3} +5.65907 q^{4} +3.54828 q^{5} -1.66982 q^{6} +1.63115 q^{7} -10.1265 q^{8} -2.63595 q^{9} +O(q^{10})$	\(q-2.76750 q^{2} +0.603367 q^{3} +5.65907 q^{4} +3.54828 q^{5} -1.66982 q^{6} +1.63115 q^{7} -10.1265 q^{8} -2.63595 q^{9} -9.81988 q^{10} +2.00713 q^{11} +3.41449 q^{12} -1.95461 q^{13} -4.51422 q^{14} +2.14092 q^{15} +16.7069 q^{16} +7.86913 q^{17} +7.29499 q^{18} +3.64239 q^{19} +20.0800 q^{20} +0.984183 q^{21} -5.55474 q^{22} +9.31928 q^{23} -6.10998 q^{24} +7.59031 q^{25} +5.40940 q^{26} -3.40054 q^{27} +9.23080 q^{28} +1.00000 q^{29} -5.92499 q^{30} +5.29310 q^{31} -25.9834 q^{32} +1.21104 q^{33} -21.7778 q^{34} +5.78779 q^{35} -14.9170 q^{36} +8.99437 q^{37} -10.0803 q^{38} -1.17935 q^{39} -35.9316 q^{40} +2.72014 q^{41} -2.72373 q^{42} +3.02984 q^{43} +11.3585 q^{44} -9.35309 q^{45} -25.7911 q^{46} -3.91236 q^{47} +10.0804 q^{48} -4.33934 q^{49} -21.0062 q^{50} +4.74797 q^{51} -11.0613 q^{52} -9.09533 q^{53} +9.41101 q^{54} +7.12188 q^{55} -16.5178 q^{56} +2.19770 q^{57} -2.76750 q^{58} -11.9989 q^{59} +12.1156 q^{60} +12.0778 q^{61} -14.6487 q^{62} -4.29963 q^{63} +38.4954 q^{64} -6.93552 q^{65} -3.35155 q^{66} -5.75198 q^{67} +44.5319 q^{68} +5.62294 q^{69} -16.0177 q^{70} -4.11448 q^{71} +26.6929 q^{72} -15.7838 q^{73} -24.8919 q^{74} +4.57974 q^{75} +20.6125 q^{76} +3.27394 q^{77} +3.26385 q^{78} -7.70768 q^{79} +59.2808 q^{80} +5.85607 q^{81} -7.52798 q^{82} +0.936447 q^{83} +5.56956 q^{84} +27.9219 q^{85} -8.38508 q^{86} +0.603367 q^{87} -20.3252 q^{88} -14.2946 q^{89} +25.8847 q^{90} -3.18827 q^{91} +52.7384 q^{92} +3.19368 q^{93} +10.8275 q^{94} +12.9242 q^{95} -15.6775 q^{96} -3.66196 q^{97} +12.0091 q^{98} -5.29070 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 98 q + 6 q^{2} + 6 q^{3} + 116 q^{4} + q^{5} + 7 q^{6} + 12 q^{7} + 15 q^{8} + 136 q^{9}+O(q^{10}) $ 98 * q + 6 * q^2 + 6 * q^3 + 116 * q^4 + q^5 + 7 * q^6 + 12 * q^7 + 15 * q^8 + 136 * q^9	\( 98 q + 6 q^{2} + 6 q^{3} + 116 q^{4} + q^{5} + 7 q^{6} + 12 q^{7} + 15 q^{8} + 136 q^{9} + 16 q^{10} + 25 q^{11} + 8 q^{12} + 18 q^{13} + 34 q^{14} + 14 q^{15} + 136 q^{16} + 35 q^{17} + 20 q^{18} + 48 q^{19} - 20 q^{20} + 62 q^{21} + 32 q^{22} + q^{23} + 8 q^{24} + 173 q^{25} + 15 q^{26} + 18 q^{27} + 37 q^{28} + 98 q^{29} - 6 q^{30} + 20 q^{31} + 16 q^{32} + 24 q^{33} - 6 q^{34} + 11 q^{35} + 155 q^{36} + 62 q^{37} - 5 q^{38} + 45 q^{39} + 38 q^{40} + 50 q^{41} + 7 q^{42} + 72 q^{43} + 92 q^{44} - 13 q^{45} + 32 q^{46} - 16 q^{47} - 13 q^{48} + 194 q^{49} + 50 q^{50} + 2 q^{51} + 83 q^{52} - 11 q^{53} + 58 q^{54} + 32 q^{55} + 106 q^{56} + 84 q^{57} + 6 q^{58} + 20 q^{59} + 62 q^{60} + 142 q^{61} - 27 q^{62} + 26 q^{63} + 213 q^{64} + 13 q^{65} - 35 q^{66} + 5 q^{67} + 69 q^{68} + 68 q^{69} - 2 q^{70} - 10 q^{71} - 9 q^{72} + 74 q^{73} + 21 q^{74} + 19 q^{75} + 116 q^{76} + 41 q^{77} - 162 q^{78} + 104 q^{79} - 86 q^{80} + 230 q^{81} + 53 q^{82} - 19 q^{83} + 76 q^{84} + 125 q^{85} + 9 q^{86} + 6 q^{87} + 68 q^{88} + 120 q^{89} + 122 q^{90} + 30 q^{91} + 3 q^{92} - 56 q^{93} + 22 q^{94} + 32 q^{95} - 55 q^{96} + 98 q^{97} - 15 q^{98} + 69 q^{99}+O(q^{100}) \) 98 * q + 6 * q^2 + 6 * q^3 + 116 * q^4 + q^5 + 7 * q^6 + 12 * q^7 + 15 * q^8 + 136 * q^9 + 16 * q^10 + 25 * q^11 + 8 * q^12 + 18 * q^13 + 34 * q^14 + 14 * q^15 + 136 * q^16 + 35 * q^17 + 20 * q^18 + 48 * q^19 - 20 * q^20 + 62 * q^21 + 32 * q^22 + q^23 + 8 * q^24 + 173 * q^25 + 15 * q^26 + 18 * q^27 + 37 * q^28 + 98 * q^29 - 6 * q^30 + 20 * q^31 + 16 * q^32 + 24 * q^33 - 6 * q^34 + 11 * q^35 + 155 * q^36 + 62 * q^37 - 5 * q^38 + 45 * q^39 + 38 * q^40 + 50 * q^41 + 7 * q^42 + 72 * q^43 + 92 * q^44 - 13 * q^45 + 32 * q^46 - 16 * q^47 - 13 * q^48 + 194 * q^49 + 50 * q^50 + 2 * q^51 + 83 * q^52 - 11 * q^53 + 58 * q^54 + 32 * q^55 + 106 * q^56 + 84 * q^57 + 6 * q^58 + 20 * q^59 + 62 * q^60 + 142 * q^61 - 27 * q^62 + 26 * q^63 + 213 * q^64 + 13 * q^65 - 35 * q^66 + 5 * q^67 + 69 * q^68 + 68 * q^69 - 2 * q^70 - 10 * q^71 - 9 * q^72 + 74 * q^73 + 21 * q^74 + 19 * q^75 + 116 * q^76 + 41 * q^77 - 162 * q^78 + 104 * q^79 - 86 * q^80 + 230 * q^81 + 53 * q^82 - 19 * q^83 + 76 * q^84 + 125 * q^85 + 9 * q^86 + 6 * q^87 + 68 * q^88 + 120 * q^89 + 122 * q^90 + 30 * q^91 + 3 * q^92 - 56 * q^93 + 22 * q^94 + 32 * q^95 - 55 * q^96 + 98 * q^97 - 15 * q^98 + 69 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.76750	−1.95692	−0.978460	−	0.206438i	$-0.933813\pi$
$2$	−2.76750	−1.95692	−0.978460	+	0.206438i	$0.933813\pi$
$3$	0.603367	0.348354	0.174177	−	0.984714i	$-0.444274\pi$
$3$	0.603367	0.348354	0.174177	+	0.984714i	$0.444274\pi$
$4$	5.65907	2.82953
$5$	3.54828	1.58684	0.793420	−	0.608674i	$-0.208298\pi$
$5$	3.54828	1.58684	0.793420	+	0.608674i	$0.208298\pi$
$6$	−1.66982	−0.681701
$7$	1.63115	0.616518	0.308259	−	0.951303i	$-0.400254\pi$
$7$	1.63115	0.616518	0.308259	+	0.951303i	$0.400254\pi$
$8$	−10.1265	−3.58025
$9$	−2.63595	−0.878649
$10$	−9.81988	−3.10532
$11$	2.00713	0.605173	0.302587	−	0.953122i	$-0.402150\pi$
$11$	2.00713	0.605173	0.302587	+	0.953122i	$0.402150\pi$
$12$	3.41449	0.985679
$13$	−1.95461	−0.542112	−0.271056	−	0.962564i	$-0.587373\pi$
$13$	−1.95461	−0.542112	−0.271056	+	0.962564i	$0.587373\pi$
$14$	−4.51422	−1.20648
$15$	2.14092	0.552782
$16$	16.7069	4.17673
$17$	7.86913	1.90854	0.954272	−	0.298940i	$-0.0966332\pi$
$17$	7.86913	1.90854	0.954272	+	0.298940i	$0.0966332\pi$
$18$	7.29499	1.71945
$19$	3.64239	0.835622	0.417811	−	0.908534i	$-0.362797\pi$
$19$	3.64239	0.835622	0.417811	+	0.908534i	$0.362797\pi$
$20$	20.0800	4.49002
$21$	0.984183	0.214766
$22$	−5.55474	−1.18428
$23$	9.31928	1.94320	0.971602	−	0.236621i	$-0.0760399\pi$
$23$	9.31928	1.94320	0.971602	+	0.236621i	$0.0760399\pi$
$24$	−6.10998	−1.24719
$25$	7.59031	1.51806
$26$	5.40940	1.06087
$27$	−3.40054	−0.654435
$28$	9.23080	1.74446
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−5.92499	−1.08175
$31$	5.29310	0.950669	0.475335	−	0.879805i	$-0.342327\pi$
$31$	5.29310	0.950669	0.475335	+	0.879805i	$0.342327\pi$
$32$	−25.9834	−4.59327
$33$	1.21104	0.210815
$34$	−21.7778	−3.73487
$35$	5.78779	0.978315
$36$	−14.9170	−2.48617
$37$	8.99437	1.47866	0.739332	−	0.673341i	$-0.235141\pi$
$37$	8.99437	1.47866	0.739332	+	0.673341i	$0.235141\pi$
$38$	−10.0803	−1.63525
$39$	−1.17935	−0.188847
$40$	−35.9316	−5.68128
$41$	2.72014	0.424814	0.212407	−	0.977181i	$-0.431870\pi$
$41$	2.72014	0.424814	0.212407	+	0.977181i	$0.431870\pi$
$42$	−2.72373	−0.420281
$43$	3.02984	0.462046	0.231023	−	0.972948i	$-0.425793\pi$
$43$	3.02984	0.462046	0.231023	+	0.972948i	$0.425793\pi$
$44$	11.3585	1.71236
$45$	−9.35309	−1.39428
$46$	−25.7911	−3.80269
$47$	−3.91236	−0.570676	−0.285338	−	0.958427i	$-0.592106\pi$
$47$	−3.91236	−0.570676	−0.285338	+	0.958427i	$0.592106\pi$
$48$	10.0804	1.45498
$49$	−4.33934	−0.619906
$50$	−21.0062	−2.97073
$51$	4.74797	0.664849
$52$	−11.0613	−1.53392
$53$	−9.09533	−1.24934	−0.624670	−	0.780889i	$-0.714766\pi$
$53$	−9.09533	−1.24934	−0.624670	+	0.780889i	$0.714766\pi$
$54$	9.41101	1.28068
$55$	7.12188	0.960313
$56$	−16.5178	−2.20729
$57$	2.19770	0.291092
$58$	−2.76750	−0.363391
$59$	−11.9989	−1.56212	−0.781060	−	0.624456i	$-0.785321\pi$
$59$	−11.9989	−1.56212	−0.781060	+	0.624456i	$0.785321\pi$
$60$	12.1156	1.56412
$61$	12.0778	1.54641	0.773203	−	0.634158i	$-0.218653\pi$
$61$	12.0778	1.54641	0.773203	+	0.634158i	$0.218653\pi$
$62$	−14.6487	−1.86038
$63$	−4.29963	−0.541703
$64$	38.4954	4.81192
$65$	−6.93552	−0.860246
$66$	−3.35155	−0.412547
$67$	−5.75198	−0.702716	−0.351358	−	0.936241i	$-0.614280\pi$
$67$	−5.75198	−0.702716	−0.351358	+	0.936241i	$0.614280\pi$
$68$	44.5319	5.40029
$69$	5.62294	0.676923
$70$	−16.0177	−1.91448
$71$	−4.11448	−0.488299	−0.244149	−	0.969738i	$-0.578509\pi$
$71$	−4.11448	−0.488299	−0.244149	+	0.969738i	$0.578509\pi$
$72$	26.6929	3.14578
$73$	−15.7838	−1.84736	−0.923678	−	0.383170i	$-0.874832\pi$
$73$	−15.7838	−1.84736	−0.923678	+	0.383170i	$0.874832\pi$
$74$	−24.8919	−2.89363
$75$	4.57974	0.528823
$76$	20.6125	2.36442
$77$	3.27394	0.373100
$78$	3.26385	0.369558
$79$	−7.70768	−0.867181	−0.433591	−	0.901110i	$-0.642754\pi$
$79$	−7.70768	−0.867181	−0.433591	+	0.901110i	$0.642754\pi$
$80$	59.2808	6.62780
$81$	5.85607	0.650674
$82$	−7.52798	−0.831327
$83$	0.936447	0.102788	0.0513942	−	0.998678i	$-0.483634\pi$
$83$	0.936447	0.102788	0.0513942	+	0.998678i	$0.483634\pi$
$84$	5.56956	0.607689
$85$	27.9219	3.02855
$86$	−8.38508	−0.904187
$87$	0.603367	0.0646877
$88$	−20.3252	−2.16667
$89$	−14.2946	−1.51522	−0.757610	−	0.652708i	$-0.773633\pi$
$89$	−14.2946	−1.51522	−0.757610	+	0.652708i	$0.773633\pi$
$90$	25.8847	2.72849
$91$	−3.18827	−0.334222
$92$	52.7384	5.49836
$93$	3.19368	0.331170
$94$	10.8275	1.11677
$95$	12.9242	1.32600
$96$	−15.6775	−1.60008
$97$	−3.66196	−0.371815	−0.185908	−	0.982567i	$-0.559523\pi$
$97$	−3.66196	−0.371815	−0.185908	+	0.982567i	$0.559523\pi$
$98$	12.0091	1.21311
$99$	−5.29070	−0.531735
$100$	42.9541	4.29541
$101$	19.3492	1.92532	0.962661	−	0.270709i	$-0.0872583\pi$
$101$	19.3492	1.92532	0.962661	+	0.270709i	$0.0872583\pi$
$102$	−13.1400	−1.30106
$103$	−1.94773	−0.191916	−0.0959579	−	0.995385i	$-0.530591\pi$
$103$	−1.94773	−0.191916	−0.0959579	+	0.995385i	$0.530591\pi$
$104$	19.7933	1.94090
$105$	3.49216	0.340800
$106$	25.1713	2.44486
$107$	−11.3091	−1.09329	−0.546646	−	0.837364i	$-0.684095\pi$
$107$	−11.3091	−1.09329	−0.546646	+	0.837364i	$0.684095\pi$
$108$	−19.2439	−1.85175
$109$	−0.887913	−0.0850466	−0.0425233	−	0.999095i	$-0.513540\pi$
$109$	−0.887913	−0.0850466	−0.0425233	+	0.999095i	$0.513540\pi$
$110$	−19.7098	−1.87926
$111$	5.42690	0.515099
$112$	27.2515	2.57502
$113$	−6.97509	−0.656162	−0.328081	−	0.944650i	$-0.606402\pi$
$113$	−6.97509	−0.656162	−0.328081	+	0.944650i	$0.606402\pi$
$114$	−6.08214	−0.569644
$115$	33.0674	3.08355
$116$	5.65907	0.525431
$117$	5.15226	0.476327
$118$	33.2069	3.05694
$119$	12.8357	1.17665
$120$	−21.6799	−1.97910
$121$	−6.97142	−0.633765
$122$	−33.4254	−3.02619
$123$	1.64124	0.147986
$124$	29.9540	2.68995
$125$	9.19116	0.822083
$126$	11.8992	1.06007
$127$	11.2577	0.998960	0.499480	−	0.866325i	$-0.333524\pi$
$127$	11.2577	0.998960	0.499480	+	0.866325i	$0.333524\pi$
$128$	−54.5692	−4.82328
$129$	1.82810	0.160956
$130$	19.1941	1.68343
$131$	−4.16326	−0.363746	−0.181873	−	0.983322i	$-0.558216\pi$
$131$	−4.16326	−0.363746	−0.181873	+	0.983322i	$0.558216\pi$
$132$	6.85334	0.596507
$133$	5.94130	0.515176
$134$	15.9186	1.37516
$135$	−12.0661	−1.03848
$136$	−79.6865	−6.83306
$137$	−11.2955	−0.965043	−0.482522	−	0.875884i	$-0.660279\pi$
$137$	−11.2955	−0.965043	−0.482522	+	0.875884i	$0.660279\pi$
$138$	−15.5615	−1.32468
$139$	−1.00000	−0.0848189
$139$	−1.00000	−0.0848189
$140$	32.7535	2.76818
$141$	−2.36059	−0.198797
$142$	11.3868	0.955561
$143$	−3.92317	−0.328072
$144$	−44.0385	−3.66988
$145$	3.54828	0.294669
$146$	43.6817	3.61513
$147$	−2.61822	−0.215947
$148$	50.8997	4.18393
$149$	−14.4655	−1.18506	−0.592530	−	0.805548i	$-0.701871\pi$
$149$	−14.4655	−1.18506	−0.592530	+	0.805548i	$0.701871\pi$
$150$	−12.6744	−1.03486
$151$	24.4204	1.98730	0.993652	−	0.112501i	$-0.0358862\pi$
$151$	24.4204	1.98730	0.993652	+	0.112501i	$0.0358862\pi$
$152$	−36.8846	−2.99174
$153$	−20.7426	−1.67694
$154$	−9.06063	−0.730127
$155$	18.7814	1.50856
$156$	−6.67401	−0.534349
$157$	−17.0057	−1.35720	−0.678599	−	0.734509i	$-0.737413\pi$
$157$	−17.0057	−1.35720	−0.678599	+	0.734509i	$0.737413\pi$
$158$	21.3310	1.69700
$159$	−5.48782	−0.435213
$160$	−92.1966	−7.28878
$161$	15.2012	1.19802
$162$	−16.2067	−1.27332
$163$	1.59669	0.125063	0.0625313	−	0.998043i	$-0.480083\pi$
$163$	1.59669	0.125063	0.0625313	+	0.998043i	$0.480083\pi$
$164$	15.3934	1.20203
$165$	4.29710	0.334529
$166$	−2.59162	−0.201149
$167$	−16.3813	−1.26763	−0.633813	−	0.773486i	$-0.718511\pi$
$167$	−16.3813	−1.26763	−0.633813	+	0.773486i	$0.718511\pi$
$168$	−9.96631	−0.768917
$169$	−9.17949	−0.706114
$170$	−77.2739	−5.92664
$171$	−9.60116	−0.734219
$172$	17.1461	1.30737
$173$	1.03206	0.0784662	0.0392331	−	0.999230i	$-0.487509\pi$
$173$	1.03206	0.0784662	0.0392331	+	0.999230i	$0.487509\pi$
$174$	−1.66982	−0.126589
$175$	12.3810	0.935912
$176$	33.5330	2.52764
$177$	−7.23972	−0.544171
$178$	39.5602	2.96516
$179$	−22.6790	−1.69511	−0.847555	−	0.530708i	$-0.821926\pi$
$179$	−22.6790	−1.69511	−0.847555	+	0.530708i	$0.821926\pi$
$180$	−52.9298	−3.94515
$181$	14.2202	1.05698	0.528491	−	0.848939i	$-0.322758\pi$
$181$	14.2202	1.05698	0.528491	+	0.848939i	$0.322758\pi$
$182$	8.82355	0.654045
$183$	7.28736	0.538697
$184$	−94.3714	−6.95715
$185$	31.9146	2.34640
$186$	−8.83852	−0.648072
$187$	15.7944	1.15500
$188$	−22.1403	−1.61475
$189$	−5.54681	−0.403471
$190$	−35.7679	−2.59487
$191$	−16.3763	−1.18494	−0.592472	−	0.805591i	$-0.701848\pi$
$191$	−16.3763	−1.18494	−0.592472	+	0.805591i	$0.701848\pi$
$192$	23.2268	1.67625
$193$	18.6561	1.34290	0.671448	−	0.741052i	$-0.265673\pi$
$193$	18.6561	1.34290	0.671448	+	0.741052i	$0.265673\pi$
$194$	10.1345	0.727613
$195$	−4.18466	−0.299670
$196$	−24.5566	−1.75404
$197$	0.0410840	0.00292711	0.00146356	−	0.999999i	$-0.499534\pi$
$197$	0.0410840	0.00292711	0.00146356	+	0.999999i	$0.499534\pi$
$198$	14.6420	1.04056
$199$	19.0557	1.35082	0.675411	−	0.737441i	$-0.263966\pi$
$199$	19.0557	1.35082	0.675411	+	0.737441i	$0.263966\pi$
$200$	−76.8631	−5.43504
$201$	−3.47055	−0.244794
$202$	−53.5491	−3.76770
$203$	1.63115	0.114484
$204$	26.8691	1.88121
$205$	9.65181	0.674112
$206$	5.39035	0.375564
$207$	−24.5651	−1.70740
$208$	−32.6555	−2.26425
$209$	7.31077	0.505696
$210$	−9.66456	−0.666918
$211$	23.8598	1.64258	0.821288	−	0.570513i	$-0.193256\pi$
$211$	23.8598	1.64258	0.821288	+	0.570513i	$0.193256\pi$
$212$	−51.4711	−3.53505
$213$	−2.48254	−0.170101
$214$	31.2979	2.13948
$215$	10.7507	0.733193
$216$	34.4355	2.34304
$217$	8.63386	0.586104
$218$	2.45730	0.166429
$219$	−9.52343	−0.643534
$220$	40.3032	2.71724
$221$	−15.3811	−1.03464
$222$	−15.0190	−1.00801
$223$	−0.540056	−0.0361648	−0.0180824	−	0.999836i	$-0.505756\pi$
$223$	−0.540056	−0.0361648	−0.0180824	+	0.999836i	$0.505756\pi$
$224$	−42.3829	−2.83183
$225$	−20.0077	−1.33384
$226$	19.3036	1.28406
$227$	16.1089	1.06919	0.534594	−	0.845109i	$-0.320465\pi$
$227$	16.1089	1.06919	0.534594	+	0.845109i	$0.320465\pi$
$228$	12.4369	0.823656
$229$	11.0840	0.732448	0.366224	−	0.930527i	$-0.380650\pi$
$229$	11.0840	0.732448	0.366224	+	0.930527i	$0.380650\pi$
$230$	−91.5142	−6.03427
$231$	1.97539	0.129971
$232$	−10.1265	−0.664836
$233$	4.69091	0.307312	0.153656	−	0.988124i	$-0.450895\pi$
$233$	4.69091	0.307312	0.153656	+	0.988124i	$0.450895\pi$
$234$	−14.2589	−0.932133
$235$	−13.8821	−0.905571
$236$	−67.9024	−4.42007
$237$	−4.65056	−0.302086
$238$	−35.5229	−2.30261
$239$	12.2738	0.793927	0.396963	−	0.917834i	$-0.370064\pi$
$239$	12.2738	0.793927	0.396963	+	0.917834i	$0.370064\pi$
$240$	35.7681	2.30882
$241$	−23.5813	−1.51900	−0.759501	−	0.650506i	$-0.774557\pi$
$241$	−23.5813	−1.51900	−0.759501	+	0.650506i	$0.774557\pi$
$242$	19.2934	1.24023
$243$	13.7350	0.881100
$244$	68.3492	4.37561
$245$	−15.3972	−0.983692
$246$	−4.54214	−0.289596
$247$	−7.11947	−0.453001
$248$	−53.6005	−3.40363
$249$	0.565021	0.0358068
$250$	−25.4366	−1.60875
$251$	−1.77874	−0.112273	−0.0561366	−	0.998423i	$-0.517878\pi$
$251$	−1.77874	−0.112273	−0.0561366	+	0.998423i	$0.517878\pi$
$252$	−24.3319	−1.53277
$253$	18.7050	1.17598
$254$	−31.1557	−1.95488
$255$	16.8471	1.05501
$256$	74.0296	4.62685
$257$	−8.81949	−0.550145	−0.275072	−	0.961424i	$-0.588702\pi$
$257$	−8.81949	−0.550145	−0.275072	+	0.961424i	$0.588702\pi$
$258$	−5.05928	−0.314977
$259$	14.6712	0.911623
$260$	−39.2486	−2.43409
$261$	−2.63595	−0.163161
$262$	11.5218	0.711821
$263$	21.9541	1.35375	0.676873	−	0.736099i	$-0.263334\pi$
$263$	21.9541	1.35375	0.676873	+	0.736099i	$0.263334\pi$
$264$	−12.2635	−0.754769
$265$	−32.2728	−1.98250
$266$	−16.4426	−1.00816
$267$	−8.62486	−0.527833
$268$	−32.5508	−1.98836
$269$	17.9609	1.09509	0.547547	−	0.836775i	$-0.315562\pi$
$269$	17.9609	1.09509	0.547547	+	0.836775i	$0.315562\pi$
$270$	33.3929	2.03223
$271$	15.7224	0.955067	0.477533	−	0.878614i	$-0.341531\pi$
$271$	15.7224	0.955067	0.477533	+	0.878614i	$0.341531\pi$
$272$	131.469	7.97146
$273$	−1.92370	−0.116427
$274$	31.2604	1.88851
$275$	15.2348	0.918691
$276$	31.8206	1.91538
$277$	−4.97851	−0.299130	−0.149565	−	0.988752i	$-0.547787\pi$
$277$	−4.97851	−0.299130	−0.149565	+	0.988752i	$0.547787\pi$
$278$	2.76750	0.165984
$279$	−13.9523	−0.835305
$280$	−58.6099	−3.50261
$281$	17.2427	1.02862	0.514308	−	0.857606i	$-0.328049\pi$
$281$	17.2427	1.02862	0.514308	+	0.857606i	$0.328049\pi$
$282$	6.53293	0.389030
$283$	−7.85386	−0.466863	−0.233432	−	0.972373i	$-0.574996\pi$
$283$	−7.85386	−0.466863	−0.233432	+	0.972373i	$0.574996\pi$
$284$	−23.2841	−1.38166
$285$	7.79806	0.461917
$286$	10.8574	0.642010
$287$	4.43696	0.261905
$288$	68.4910	4.03587
$289$	44.9232	2.64254
$290$	−9.81988	−0.576643
$291$	−2.20950	−0.129523
$292$	−89.3217	−5.22715
$293$	−8.90737	−0.520374	−0.260187	−	0.965558i	$-0.583784\pi$
$293$	−8.90737	−0.520374	−0.260187	+	0.965558i	$0.583784\pi$
$294$	7.24592	0.422590
$295$	−42.5754	−2.47883
$296$	−91.0812	−5.29399
$297$	−6.82534	−0.396047
$298$	40.0333	2.31907
$299$	−18.2156	−1.05343
$300$	25.9171	1.49632
$301$	4.94213	0.284859
$302$	−67.5835	−3.88899
$303$	11.6747	0.670694
$304$	60.8531	3.49017
$305$	42.8555	2.45390
$306$	57.4052	3.28164
$307$	−11.2388	−0.641431	−0.320716	−	0.947176i	$-0.603923\pi$
$307$	−11.2388	−0.641431	−0.320716	+	0.947176i	$0.603923\pi$
$308$	18.5274	1.05570
$309$	−1.17520	−0.0668546
$310$	−51.9776	−2.95213
$311$	2.46817	0.139957	0.0699786	−	0.997548i	$-0.477707\pi$
$311$	2.46817	0.139957	0.0699786	+	0.997548i	$0.477707\pi$
$312$	11.9426	0.676119
$313$	−1.40490	−0.0794098	−0.0397049	−	0.999211i	$-0.512642\pi$
$313$	−1.40490	−0.0794098	−0.0397049	+	0.999211i	$0.512642\pi$
$314$	47.0632	2.65593
$315$	−15.2563	−0.859596
$316$	−43.6183	−2.45372
$317$	−7.83327	−0.439960	−0.219980	−	0.975504i	$-0.570599\pi$
$317$	−7.83327	−0.439960	−0.219980	+	0.975504i	$0.570599\pi$
$318$	15.1876	0.851676
$319$	2.00713	0.112378
$320$	136.593	7.63576
$321$	−6.82353	−0.380852
$322$	−42.0693	−2.34443
$323$	28.6625	1.59482
$324$	33.1399	1.84110
$325$	−14.8361	−0.822960
$326$	−4.41885	−0.244738
$327$	−0.535737	−0.0296263
$328$	−27.5454	−1.52094
$329$	−6.38165	−0.351832
$330$	−11.8922	−0.654646
$331$	0.616015	0.0338592	0.0169296	−	0.999857i	$-0.494611\pi$
$331$	0.616015	0.0338592	0.0169296	+	0.999857i	$0.494611\pi$
$332$	5.29942	0.290843
$333$	−23.7087	−1.29923
$334$	45.3354	2.48064
$335$	−20.4096	−1.11510
$336$	16.4427	0.897020
$337$	5.75679	0.313592	0.156796	−	0.987631i	$-0.449883\pi$
$337$	5.75679	0.313592	0.156796	+	0.987631i	$0.449883\pi$
$338$	25.4042	1.38181
$339$	−4.20854	−0.228577
$340$	158.012	8.56939
$341$	10.6240	0.575320
$342$	26.5712	1.43681
$343$	−18.4962	−0.998701
$344$	−30.6816	−1.65424
$345$	19.9518	1.07417
$346$	−2.85623	−0.153552
$347$	3.61984	0.194323	0.0971616	−	0.995269i	$-0.469024\pi$
$347$	3.61984	0.194323	0.0971616	+	0.995269i	$0.469024\pi$
$348$	3.41449	0.183036
$349$	31.6291	1.69307	0.846533	−	0.532337i	$-0.178686\pi$
$349$	31.6291	1.69307	0.846533	+	0.532337i	$0.178686\pi$
$350$	−34.2643	−1.83150
$351$	6.64675	0.354777
$352$	−52.1522	−2.77972
$353$	−17.6698	−0.940467	−0.470233	−	0.882542i	$-0.655830\pi$
$353$	−17.6698	−0.940467	−0.470233	+	0.882542i	$0.655830\pi$
$354$	20.0359	1.06490
$355$	−14.5993	−0.774852
$356$	−80.8938	−4.28736
$357$	7.74466	0.409891
$358$	62.7642	3.31719
$359$	−3.83913	−0.202622	−0.101311	−	0.994855i	$-0.532304\pi$
$359$	−3.83913	−0.202622	−0.101311	+	0.994855i	$0.532304\pi$
$360$	94.7138	4.99186
$361$	−5.73297	−0.301735
$362$	−39.3546	−2.06843
$363$	−4.20632	−0.220775
$364$	−18.0426	−0.945692
$365$	−56.0054	−2.93146
$366$	−20.1678	−1.05419
$367$	5.94711	0.310436	0.155218	−	0.987880i	$-0.450392\pi$
$367$	5.94711	0.310436	0.155218	+	0.987880i	$0.450392\pi$
$368$	155.696	8.11623
$369$	−7.17014	−0.373263
$370$	−88.3236	−4.59173
$371$	−14.8359	−0.770240
$372$	18.0733	0.937055
$373$	−5.17954	−0.268186	−0.134093	−	0.990969i	$-0.542812\pi$
$373$	−5.17954	−0.268186	−0.134093	+	0.990969i	$0.542812\pi$
$374$	−43.7110	−2.26024
$375$	5.54564	0.286376
$376$	39.6184	2.04316
$377$	−1.95461	−0.100668
$378$	15.3508	0.789560
$379$	9.41612	0.483673	0.241837	−	0.970317i	$-0.422250\pi$
$379$	9.41612	0.483673	0.241837	+	0.970317i	$0.422250\pi$
$380$	73.1392	3.75196
$381$	6.79253	0.347992
$382$	45.3213	2.31884
$383$	3.40253	0.173861	0.0869305	−	0.996214i	$-0.472294\pi$
$383$	3.40253	0.173861	0.0869305	+	0.996214i	$0.472294\pi$
$384$	−32.9253	−1.68021
$385$	11.6169	0.592050
$386$	−51.6308	−2.62794
$387$	−7.98650	−0.405976
$388$	−20.7233	−1.05206
$389$	−18.0428	−0.914808	−0.457404	−	0.889259i	$-0.651221\pi$
$389$	−18.0428	−0.914808	−0.457404	+	0.889259i	$0.651221\pi$
$390$	11.5811	0.586430
$391$	73.3346	3.70869
$392$	43.9422	2.21942
$393$	−2.51197	−0.126712
$394$	−0.113700	−0.00572813
$395$	−27.3490	−1.37608
$396$	−29.9404	−1.50456
$397$	9.06306	0.454862	0.227431	−	0.973794i	$-0.426967\pi$
$397$	9.06306	0.454862	0.227431	+	0.973794i	$0.426967\pi$
$398$	−52.7367	−2.64345
$399$	3.58478	0.179464
$400$	126.811	6.34053
$401$	8.73285	0.436098	0.218049	−	0.975938i	$-0.430031\pi$
$401$	8.73285	0.436098	0.218049	+	0.975938i	$0.430031\pi$
$402$	9.60476	0.479042
$403$	−10.3460	−0.515370
$404$	109.499	5.44776
$405$	20.7790	1.03252
$406$	−4.51422	−0.224037
$407$	18.0529	0.894848
$408$	−48.0802	−2.38032
$409$	10.7119	0.529668	0.264834	−	0.964294i	$-0.414683\pi$
$409$	10.7119	0.529668	0.264834	+	0.964294i	$0.414683\pi$
$410$	−26.7114	−1.31918
$411$	−6.81535	−0.336177
$412$	−11.0223	−0.543032
$413$	−19.5720	−0.963074
$414$	67.9841	3.34123
$415$	3.32278	0.163109
$416$	50.7876	2.49007
$417$	−0.603367	−0.0295470
$418$	−20.2326	−0.989607
$419$	−12.8993	−0.630171	−0.315085	−	0.949063i	$-0.602033\pi$
$419$	−12.8993	−0.630171	−0.315085	+	0.949063i	$0.602033\pi$
$420$	19.7624	0.964305
$421$	38.1031	1.85703	0.928515	−	0.371295i	$-0.121086\pi$
$421$	38.1031	1.85703	0.928515	+	0.371295i	$0.121086\pi$
$422$	−66.0321	−3.21439
$423$	10.3128	0.501424
$424$	92.1036	4.47295
$425$	59.7291	2.89729
$426$	6.87043	0.332874
$427$	19.7008	0.953387
$428$	−63.9989	−3.09350
$429$	−2.36711	−0.114285
$430$	−29.7526	−1.43480
$431$	13.9410	0.671516	0.335758	−	0.941948i	$-0.391008\pi$
$431$	13.9410	0.671516	0.335758	+	0.941948i	$0.391008\pi$
$432$	−56.8126	−2.73340
$433$	−12.7801	−0.614170	−0.307085	−	0.951682i	$-0.599354\pi$
$433$	−12.7801	−0.614170	−0.307085	+	0.951682i	$0.599354\pi$
$434$	−23.8942	−1.14696
$435$	2.14092	0.102649
$436$	−5.02476	−0.240642
$437$	33.9445	1.62379
$438$	26.3561	1.25934
$439$	−6.27910	−0.299685	−0.149842	−	0.988710i	$-0.547877\pi$
$439$	−6.27910	−0.299685	−0.149842	+	0.988710i	$0.547877\pi$
$440$	−72.1195	−3.43816
$441$	11.4383	0.544680
$442$	42.5672	2.02472
$443$	−24.9396	−1.18491	−0.592457	−	0.805602i	$-0.701842\pi$
$443$	−24.9396	−1.18491	−0.592457	+	0.805602i	$0.701842\pi$
$444$	30.7112	1.45749
$445$	−50.7211	−2.40441
$446$	1.49461	0.0707716
$447$	−8.72800	−0.412820
$448$	62.7919	2.96664
$449$	14.2677	0.673336	0.336668	−	0.941623i	$-0.390700\pi$
$449$	14.2677	0.673336	0.336668	+	0.941623i	$0.390700\pi$
$450$	55.3713	2.61023
$451$	5.45968	0.257086
$452$	−39.4725	−1.85663
$453$	14.7345	0.692285
$454$	−44.5815	−2.09231
$455$	−11.3129	−0.530357
$456$	−22.2549	−1.04218
$457$	−4.66582	−0.218258	−0.109129	−	0.994028i	$-0.534806\pi$
$457$	−4.66582	−0.218258	−0.109129	+	0.994028i	$0.534806\pi$
$458$	−30.6749	−1.43334
$459$	−26.7593	−1.24902
$460$	187.131	8.72502
$461$	−23.1527	−1.07833	−0.539164	−	0.842201i	$-0.681260\pi$
$461$	−23.1527	−1.07833	−0.539164	+	0.842201i	$0.681260\pi$
$462$	−5.46689	−0.254343
$463$	−25.9408	−1.20557	−0.602785	−	0.797903i	$-0.705943\pi$
$463$	−25.9408	−1.20557	−0.602785	+	0.797903i	$0.705943\pi$
$464$	16.7069	0.775598
$465$	11.3321	0.525513
$466$	−12.9821	−0.601384
$467$	42.3646	1.96040	0.980201	−	0.198006i	$-0.0634465\pi$
$467$	42.3646	1.96040	0.980201	+	0.198006i	$0.0634465\pi$
$468$	29.1570	1.34778
$469$	−9.38235	−0.433237
$470$	38.4189	1.77213
$471$	−10.2606	−0.472786
$472$	121.506	5.59278
$473$	6.08129	0.279618
$474$	12.8704	0.591158
$475$	27.6469	1.26853
$476$	72.6383	3.32937
$477$	23.9748	1.09773
$478$	−33.9678	−1.55365
$479$	4.27797	0.195465	0.0977326	−	0.995213i	$-0.468841\pi$
$479$	4.27797	0.195465	0.0977326	+	0.995213i	$0.468841\pi$
$480$	−55.6284	−2.53908
$481$	−17.5805	−0.801602
$482$	65.2612	2.97256
$483$	9.17188	0.417335
$484$	−39.4517	−1.79326
$485$	−12.9937	−0.590012
$486$	−38.0116	−1.72424
$487$	−12.7240	−0.576579	−0.288289	−	0.957543i	$-0.593086\pi$
$487$	−12.7240	−0.576579	−0.288289	+	0.957543i	$0.593086\pi$
$488$	−122.306	−5.53652
$489$	0.963392	0.0435661
$490$	42.6118	1.92501
$491$	−27.4302	−1.23791	−0.618953	−	0.785428i	$-0.712443\pi$
$491$	−27.4302	−1.23791	−0.618953	+	0.785428i	$0.712443\pi$
$492$	9.28789	0.418730
$493$	7.86913	0.354408
$494$	19.7032	0.886487
$495$	−18.7729	−0.843779
$496$	88.4314	3.97069
$497$	−6.71134	−0.301045
$498$	−1.56370	−0.0700710
$499$	−11.3455	−0.507892	−0.253946	−	0.967218i	$-0.581729\pi$
$499$	−11.3455	−0.507892	−0.253946	+	0.967218i	$0.581729\pi$
$500$	52.0134	2.32611
$501$	−9.88396	−0.441583
$502$	4.92267	0.219710
$503$	−29.4217	−1.31185	−0.655924	−	0.754827i	$-0.727721\pi$
$503$	−29.4217	−1.31185	−0.655924	+	0.754827i	$0.727721\pi$
$504$	43.5401	1.93943
$505$	68.6566	3.05518
$506$	−51.7662	−2.30129
$507$	−5.53860	−0.245978
$508$	63.7081	2.82659
$509$	25.0866	1.11194	0.555972	−	0.831201i	$-0.312346\pi$
$509$	25.0866	1.11194	0.555972	+	0.831201i	$0.312346\pi$
$510$	−46.6245	−2.06457
$511$	−25.7458	−1.13893
$512$	−95.7387	−4.23109
$513$	−12.3861	−0.546861
$514$	24.4080	1.07659
$515$	−6.91110	−0.304540
$516$	10.3454	0.455429
$517$	−7.85262	−0.345358
$518$	−40.6025	−1.78397
$519$	0.622712	0.0273340
$520$	70.2324	3.07989
$521$	−17.3165	−0.758651	−0.379326	−	0.925263i	$-0.623844\pi$
$521$	−17.3165	−0.758651	−0.379326	+	0.925263i	$0.623844\pi$
$522$	7.29499	0.319293
$523$	5.82895	0.254882	0.127441	−	0.991846i	$-0.459324\pi$
$523$	5.82895	0.254882	0.127441	+	0.991846i	$0.459324\pi$
$524$	−23.5602	−1.02923
$525$	7.47026	0.326029
$526$	−60.7580	−2.64917
$527$	41.6521	1.81439
$528$	20.2327	0.880514
$529$	63.8490	2.77604
$530$	89.3151	3.87960
$531$	31.6284	1.37256
$532$	33.6222	1.45771
$533$	−5.31682	−0.230297
$534$	23.8693	1.03293
$535$	−40.1279	−1.73488
$536$	58.2472	2.51590
$537$	−13.6838	−0.590498
$538$	−49.7068	−2.14301
$539$	−8.70964	−0.375151
$540$	−68.2828	−2.93843
$541$	−4.66792	−0.200689	−0.100345	−	0.994953i	$-0.531995\pi$
$541$	−4.66792	−0.200689	−0.100345	+	0.994953i	$0.531995\pi$
$542$	−43.5117	−1.86899
$543$	8.58003	0.368204
$544$	−204.467	−8.76645
$545$	−3.15057	−0.134955
$546$	5.32384	0.227839
$547$	−21.4804	−0.918434	−0.459217	−	0.888324i	$-0.651870\pi$
$547$	−21.4804	−0.918434	−0.459217	+	0.888324i	$0.651870\pi$
$548$	−63.9222	−2.73062
$549$	−31.8365	−1.35875
$550$	−42.1622	−1.79780
$551$	3.64239	0.155171
$552$	−56.9406	−2.42355
$553$	−12.5724	−0.534633
$554$	13.7780	0.585372
$555$	19.2562	0.817380
$556$	−5.65907	−0.239998
$557$	−23.0638	−0.977244	−0.488622	−	0.872495i	$-0.662500\pi$
$557$	−23.0638	−0.977244	−0.488622	+	0.872495i	$0.662500\pi$
$558$	38.6131	1.63462
$559$	−5.92216	−0.250481
$560$	96.6960	4.08615
$561$	9.52981	0.402349
$562$	−47.7193	−2.01292
$563$	−20.6906	−0.872003	−0.436002	−	0.899946i	$-0.643606\pi$
$563$	−20.6906	−0.872003	−0.436002	+	0.899946i	$0.643606\pi$
$564$	−13.3587	−0.562503
$565$	−24.7496	−1.04122
$566$	21.7356	0.913614
$567$	9.55214	0.401152
$568$	41.6652	1.74823
$569$	31.4275	1.31751	0.658755	−	0.752358i	$-0.271083\pi$
$569$	31.4275	1.31751	0.658755	+	0.752358i	$0.271083\pi$
$570$	−21.5811	−0.903935
$571$	16.6016	0.694754	0.347377	−	0.937726i	$-0.387072\pi$
$571$	16.6016	0.694754	0.347377	+	0.937726i	$0.387072\pi$
$572$	−22.2015	−0.928290
$573$	−9.88089	−0.412780
$574$	−12.2793	−0.512528
$575$	70.7363	2.94991
$576$	−101.472	−4.22799
$577$	−45.6547	−1.90063	−0.950314	−	0.311293i	$-0.899238\pi$
$577$	−45.6547	−1.90063	−0.950314	+	0.311293i	$0.899238\pi$
$578$	−124.325	−5.17123
$579$	11.2565	0.467803
$580$	20.0800	0.833775
$581$	1.52749	0.0633709
$582$	6.11481	0.253467
$583$	−18.2555	−0.756067
$584$	159.834	6.61399
$585$	18.2817	0.755854
$586$	24.6512	1.01833
$587$	−31.7886	−1.31206	−0.656029	−	0.754736i	$-0.727765\pi$
$587$	−31.7886	−1.31206	−0.656029	+	0.754736i	$0.727765\pi$
$588$	−14.8167	−0.611029
$589$	19.2796	0.794401
$590$	117.827	4.85088
$591$	0.0247887	0.00101967
$592$	150.268	6.17598
$593$	26.3983	1.08405	0.542023	−	0.840364i	$-0.317658\pi$
$593$	26.3983	1.08405	0.542023	+	0.840364i	$0.317658\pi$
$594$	18.8892	0.775031
$595$	45.5449	1.86716
$596$	−81.8612	−3.35317
$597$	11.4976	0.470564
$598$	50.4117	2.06149
$599$	12.5882	0.514341	0.257170	−	0.966366i	$-0.417210\pi$
$599$	12.5882	0.514341	0.257170	+	0.966366i	$0.417210\pi$
$600$	−46.3766	−1.89332
$601$	−34.6531	−1.41353	−0.706766	−	0.707448i	$-0.749846\pi$
$601$	−34.6531	−1.41353	−0.706766	+	0.707448i	$0.749846\pi$
$602$	−13.6773	−0.557447
$603$	15.1619	0.617441
$604$	138.197	5.62314
$605$	−24.7366	−1.00568
$606$	−32.3097	−1.31249
$607$	−46.8924	−1.90330	−0.951651	−	0.307181i	$-0.900614\pi$
$607$	−46.8924	−1.90330	−0.951651	+	0.307181i	$0.900614\pi$
$608$	−94.6419	−3.83824
$609$	0.984183	0.0398811
$610$	−118.603	−4.80208
$611$	7.64714	0.309370
$612$	−117.384	−4.74496
$613$	−22.5128	−0.909284	−0.454642	−	0.890674i	$-0.650233\pi$
$613$	−22.5128	−0.909284	−0.454642	+	0.890674i	$0.650233\pi$
$614$	31.1034	1.25523
$615$	5.82358	0.234830
$616$	−33.1535	−1.33579
$617$	23.4913	0.945723	0.472861	−	0.881137i	$-0.343221\pi$
$617$	23.4913	0.945723	0.472861	+	0.881137i	$0.343221\pi$
$618$	3.25236	0.130829
$619$	−23.9489	−0.962589	−0.481295	−	0.876559i	$-0.659833\pi$
$619$	−23.9489	−0.962589	−0.481295	+	0.876559i	$0.659833\pi$
$620$	106.285	4.26852
$621$	−31.6906	−1.27170
$622$	−6.83067	−0.273885
$623$	−23.3166	−0.934160
$624$	−19.7033	−0.788762
$625$	−5.33871	−0.213549
$626$	3.88807	0.155398
$627$	4.41108	0.176161
$628$	−96.2361	−3.84024
$629$	70.7778	2.82210
$630$	42.2219	1.68216
$631$	26.1384	1.04055	0.520276	−	0.853998i	$-0.325829\pi$
$631$	26.1384	1.04055	0.520276	+	0.853998i	$0.325829\pi$
$632$	78.0516	3.10473
$633$	14.3962	0.572198
$634$	21.6786	0.860967
$635$	39.9455	1.58519
$636$	−31.0559	−1.23145
$637$	8.48174	0.336059
$638$	−5.55474	−0.219914
$639$	10.8456	0.429043
$640$	−193.627	−7.65378
$641$	45.2762	1.78830	0.894152	−	0.447763i	$-0.147779\pi$
$641$	45.2762	1.78830	0.894152	+	0.447763i	$0.147779\pi$
$642$	18.8841	0.745297
$643$	14.7293	0.580867	0.290434	−	0.956895i	$-0.406200\pi$
$643$	14.7293	0.580867	0.290434	+	0.956895i	$0.406200\pi$
$644$	86.0244	3.38984
$645$	6.48663	0.255411
$646$	−79.3234	−3.12094
$647$	−15.5605	−0.611746	−0.305873	−	0.952072i	$-0.598948\pi$
$647$	−15.5605	−0.611746	−0.305873	+	0.952072i	$0.598948\pi$
$648$	−59.3013	−2.32958
$649$	−24.0833	−0.945353
$650$	41.0590	1.61047
$651$	5.20938	0.204172
$652$	9.03579	0.353869
$653$	18.3764	0.719124	0.359562	−	0.933121i	$-0.382926\pi$
$653$	18.3764	0.719124	0.359562	+	0.933121i	$0.382926\pi$
$654$	1.48265	0.0579763
$655$	−14.7724	−0.577207
$656$	45.4451	1.77433
$657$	41.6053	1.62318
$658$	17.6612	0.688506
$659$	0.770804	0.0300263	0.0150131	−	0.999887i	$-0.495221\pi$
$659$	0.770804	0.0300263	0.0150131	+	0.999887i	$0.495221\pi$
$660$	24.3176	0.946561
$661$	33.5754	1.30593	0.652965	−	0.757388i	$-0.273525\pi$
$661$	33.5754	1.30593	0.652965	+	0.757388i	$0.273525\pi$
$662$	−1.70482	−0.0662598
$663$	−9.28045	−0.360423
$664$	−9.48291	−0.368008
$665$	21.0814	0.817502
$666$	65.6138	2.54248
$667$	9.31928	0.360844
$668$	−92.7031	−3.58679
$669$	−0.325852	−0.0125982
$670$	56.4837	2.18216
$671$	24.2418	0.935844
$672$	−25.5725	−0.986479
$673$	45.6078	1.75805	0.879027	−	0.476773i	$-0.158194\pi$
$673$	45.6078	1.75805	0.879027	+	0.476773i	$0.158194\pi$
$674$	−15.9319	−0.613675
$675$	−25.8112	−0.993473
$676$	−51.9473	−1.99797
$677$	−15.7225	−0.604263	−0.302132	−	0.953266i	$-0.597698\pi$
$677$	−15.7225	−0.604263	−0.302132	+	0.953266i	$0.597698\pi$
$678$	11.6471	0.447306
$679$	−5.97321	−0.229231
$680$	−282.750	−10.8430
$681$	9.71960	0.372456
$682$	−29.4018	−1.12585
$683$	21.5630	0.825086	0.412543	−	0.910938i	$-0.364641\pi$
$683$	21.5630	0.825086	0.412543	+	0.910938i	$0.364641\pi$
$684$	−54.3336	−2.07750
$685$	−40.0798	−1.53137
$686$	51.1883	1.95438
$687$	6.68769	0.255151
$688$	50.6192	1.92984
$689$	17.7779	0.677282
$690$	−55.2166	−2.10206
$691$	−39.8663	−1.51659	−0.758293	−	0.651913i	$-0.773967\pi$
$691$	−39.8663	−1.51659	−0.758293	+	0.651913i	$0.773967\pi$
$692$	5.84051	0.222023
$693$	−8.62993	−0.327824
$694$	−10.0179	−0.380275
$695$	−3.54828	−0.134594
$696$	−6.10998	−0.231598
$697$	21.4051	0.810776
$698$	−87.5335	−3.31319
$699$	2.83034	0.107053
$700$	70.0647	2.64820
$701$	−4.33218	−0.163624	−0.0818120	−	0.996648i	$-0.526071\pi$
$701$	−4.33218	−0.163624	−0.0818120	+	0.996648i	$0.526071\pi$
$702$	−18.3949	−0.694271
$703$	32.7610	1.23561
$704$	77.2654	2.91205
$705$	−8.37603	−0.315459
$706$	48.9011	1.84042
$707$	31.5616	1.18700
$708$	−40.9700	−1.53975
$709$	−3.28421	−0.123341	−0.0616705	−	0.998097i	$-0.519643\pi$
$709$	−3.28421	−0.123341	−0.0616705	+	0.998097i	$0.519643\pi$
$710$	40.4037	1.51632
$711$	20.3170	0.761948
$712$	144.753	5.42486
$713$	49.3279	1.84734
$714$	−21.4334	−0.802124
$715$	−13.9205	−0.520598
$716$	−128.342	−4.79637
$717$	7.40561	0.276568
$718$	10.6248	0.396514
$719$	−37.4447	−1.39645	−0.698225	−	0.715878i	$-0.746027\pi$
$719$	−37.4447	−1.39645	−0.698225	+	0.715878i	$0.746027\pi$
$720$	−156.261	−5.82351
$721$	−3.17705	−0.118319
$722$	15.8660	0.590471
$723$	−14.2281	−0.529150
$724$	80.4733	2.99077
$725$	7.59031	0.281897
$726$	11.6410	0.432038
$727$	38.6672	1.43409	0.717043	−	0.697029i	$-0.245495\pi$
$727$	38.6672	1.43409	0.717043	+	0.697029i	$0.245495\pi$
$728$	32.2860	1.19660
$729$	−9.28097	−0.343740
$730$	154.995	5.73663
$731$	23.8422	0.881835
$732$	41.2396	1.52426
$733$	−8.60188	−0.317718	−0.158859	−	0.987301i	$-0.550781\pi$
$733$	−8.60188	−0.317718	−0.158859	+	0.987301i	$0.550781\pi$
$734$	−16.4586	−0.607499
$735$	−9.29017	−0.342673
$736$	−242.147	−8.92565
$737$	−11.5450	−0.425265
$738$	19.8434	0.730445
$739$	−0.855576	−0.0314729	−0.0157364	−	0.999876i	$-0.505009\pi$
$739$	−0.855576	−0.0314729	−0.0157364	+	0.999876i	$0.505009\pi$
$740$	180.607	6.63923
$741$	−4.29565	−0.157805
$742$	41.0583	1.50730
$743$	2.89880	0.106347	0.0531733	−	0.998585i	$-0.483066\pi$
$743$	2.89880	0.106347	0.0531733	+	0.998585i	$0.483066\pi$
$744$	−32.3407	−1.18567
$745$	−51.3277	−1.88050
$746$	14.3344	0.524819
$747$	−2.46843	−0.0903150
$748$	89.3815	3.26811
$749$	−18.4468	−0.674033
$750$	−15.3476	−0.560414
$751$	12.1810	0.444491	0.222245	−	0.974991i	$-0.428661\pi$
$751$	12.1810	0.444491	0.222245	+	0.974991i	$0.428661\pi$
$752$	−65.3633	−2.38356
$753$	−1.07323	−0.0391108
$754$	5.40940	0.196999
$755$	86.6505	3.15353
$756$	−31.3897	−1.14163
$757$	−11.8034	−0.429001	−0.214501	−	0.976724i	$-0.568812\pi$
$757$	−11.8034	−0.429001	−0.214501	+	0.976724i	$0.568812\pi$
$758$	−26.0591	−0.946510
$759$	11.2860	0.409656
$760$	−130.877	−4.74741
$761$	−8.98774	−0.325805	−0.162903	−	0.986642i	$-0.552086\pi$
$761$	−8.98774	−0.325805	−0.162903	+	0.986642i	$0.552086\pi$
$762$	−18.7983	−0.680992
$763$	−1.44832	−0.0524327
$764$	−92.6744	−3.35284
$765$	−73.6007	−2.66104
$766$	−9.41650	−0.340232
$767$	23.4531	0.846844
$768$	44.6670	1.61178
$769$	−22.5382	−0.812748	−0.406374	−	0.913707i	$-0.633207\pi$
$769$	−22.5382	−0.812748	−0.406374	+	0.913707i	$0.633207\pi$
$770$	−32.1497	−1.15859
$771$	−5.32139	−0.191645
$772$	105.576	3.79977
$773$	−8.91885	−0.320789	−0.160394	−	0.987053i	$-0.551277\pi$
$773$	−8.91885	−0.320789	−0.160394	+	0.987053i	$0.551277\pi$
$774$	22.1026	0.794463
$775$	40.1763	1.44318
$776$	37.0827	1.33119
$777$	8.85210	0.317567
$778$	49.9336	1.79021
$779$	9.90781	0.354984
$780$	−23.6813	−0.847926
$781$	−8.25830	−0.295505
$782$	−202.954	−7.25761
$783$	−3.40054	−0.121526
$784$	−72.4970	−2.58918
$785$	−60.3409	−2.15366
$786$	6.95189	0.247966
$787$	−18.0584	−0.643712	−0.321856	−	0.946789i	$-0.604307\pi$
$787$	−18.0584	−0.643712	−0.321856	+	0.946789i	$0.604307\pi$
$788$	0.232497	0.00828237
$789$	13.2464	0.471583
$790$	75.6885	2.69287
$791$	−11.3774	−0.404535
$792$	53.5761	1.90374
$793$	−23.6075	−0.838326
$794$	−25.0820	−0.890128
$795$	−19.4723	−0.690613
$796$	107.837	3.82220
$797$	5.28890	0.187343	0.0936713	−	0.995603i	$-0.470140\pi$
$797$	5.28890	0.187343	0.0936713	+	0.995603i	$0.470140\pi$
$798$	−9.92089	−0.351196
$799$	−30.7868	−1.08916
$800$	−197.222	−6.97286
$801$	37.6797	1.33135
$802$	−24.1682	−0.853408
$803$	−31.6802	−1.11797
$804$	−19.6401	−0.692652
$805$	53.9380	1.90107
$806$	28.6325	1.00854
$807$	10.8370	0.381480
$808$	−195.940	−6.89313
$809$	−34.0460	−1.19699	−0.598496	−	0.801126i	$-0.704235\pi$
$809$	−34.0460	−1.19699	−0.598496	+	0.801126i	$0.704235\pi$
$810$	−57.5059	−2.02055
$811$	−49.8297	−1.74976	−0.874878	−	0.484343i	$-0.839059\pi$
$811$	−49.8297	−1.74976	−0.874878	+	0.484343i	$0.839059\pi$
$812$	9.23080	0.323938
$813$	9.48636	0.332701
$814$	−49.9614	−1.75115
$815$	5.66552	0.198454
$816$	79.3239	2.77689
$817$	11.0359	0.386096
$818$	−29.6451	−1.03652
$819$	8.40412	0.293664
$820$	54.6203	1.90742
$821$	−38.7193	−1.35131	−0.675656	−	0.737217i	$-0.736140\pi$
$821$	−38.7193	−1.35131	−0.675656	+	0.737217i	$0.736140\pi$
$822$	18.8615	0.657871
$823$	12.5201	0.436424	0.218212	−	0.975901i	$-0.429978\pi$
$823$	12.5201	0.436424	0.218212	+	0.975901i	$0.429978\pi$
$824$	19.7237	0.687106
$825$	9.19215	0.320030
$826$	54.1655	1.88466
$827$	−52.8718	−1.83853	−0.919266	−	0.393637i	$-0.871217\pi$
$827$	−52.8718	−1.83853	−0.919266	+	0.393637i	$0.871217\pi$
$828$	−139.016	−4.83113
$829$	−1.46001	−0.0507083	−0.0253541	−	0.999679i	$-0.508071\pi$
$829$	−1.46001	−0.0507083	−0.0253541	+	0.999679i	$0.508071\pi$
$830$	−9.19580	−0.319191
$831$	−3.00387	−0.104203
$832$	−75.2436	−2.60860
$833$	−34.1468	−1.18312
$834$	1.66982	0.0578211
$835$	−58.1257	−2.01152
$836$	41.3721	1.43088
$837$	−17.9994	−0.622151
$838$	35.6988	1.23319
$839$	14.5157	0.501137	0.250568	−	0.968099i	$-0.419382\pi$
$839$	14.5157	0.501137	0.250568	+	0.968099i	$0.419382\pi$
$840$	−35.3633	−1.22015
$841$	1.00000	0.0344828
$842$	−105.450	−3.63406
$843$	10.4037	0.358322
$844$	135.024	4.64773
$845$	−32.5714	−1.12049
$846$	−28.5406	−0.981246
$847$	−11.3714	−0.390727
$848$	−151.955	−5.21815
$849$	−4.73876	−0.162634
$850$	−165.300	−5.66976
$851$	83.8210	2.87335
$852$	−14.0489	−0.481306
$853$	30.3802	1.04020	0.520100	−	0.854106i	$-0.325895\pi$
$853$	30.3802	1.04020	0.520100	+	0.854106i	$0.325895\pi$
$854$	−54.5219	−1.86570
$855$	−34.0676	−1.16509
$856$	114.521	3.91425
$857$	−1.79152	−0.0611973	−0.0305987	−	0.999532i	$-0.509741\pi$
$857$	−1.79152	−0.0611973	−0.0305987	+	0.999532i	$0.509741\pi$
$858$	6.55098	0.223647
$859$	22.9177	0.781943	0.390972	−	0.920403i	$-0.372139\pi$
$859$	22.9177	0.781943	0.390972	+	0.920403i	$0.372139\pi$
$860$	60.8391	2.07459
$861$	2.67711	0.0912358
$862$	−38.5818	−1.31410
$863$	−23.5522	−0.801726	−0.400863	−	0.916138i	$-0.631290\pi$
$863$	−23.5522	−0.801726	−0.400863	+	0.916138i	$0.631290\pi$
$864$	88.3578	3.00599
$865$	3.66205	0.124513
$866$	35.3688	1.20188
$867$	27.1051	0.920539
$868$	48.8596	1.65840
$869$	−15.4703	−0.524795
$870$	−5.92499	−0.200876
$871$	11.2429	0.380951
$872$	8.99143	0.304488
$873$	9.65273	0.326695
$874$	−93.9414	−3.17762
$875$	14.9922	0.506828
$876$	−53.8937	−1.82090
$877$	12.7394	0.430178	0.215089	−	0.976594i	$-0.430996\pi$
$877$	12.7394	0.430178	0.215089	+	0.976594i	$0.430996\pi$
$878$	17.3774	0.586459
$879$	−5.37441	−0.181274
$880$	118.984	4.01097
$881$	4.58539	0.154486	0.0772429	−	0.997012i	$-0.475388\pi$
$881$	4.58539	0.154486	0.0772429	+	0.997012i	$0.475388\pi$
$882$	−31.6555	−1.06590
$883$	−3.63470	−0.122317	−0.0611587	−	0.998128i	$-0.519480\pi$
$883$	−3.63470	−0.122317	−0.0611587	+	0.998128i	$0.519480\pi$
$884$	−87.0427	−2.92756
$885$	−25.6886	−0.863512
$886$	69.0203	2.31878
$887$	7.69792	0.258471	0.129235	−	0.991614i	$-0.458748\pi$
$887$	7.69792	0.258471	0.129235	+	0.991614i	$0.458748\pi$
$888$	−54.9554	−1.84418
$889$	18.3630	0.615877
$890$	140.371	4.70524
$891$	11.7539	0.393771
$892$	−3.05621	−0.102330
$893$	−14.2503	−0.476869
$894$	24.1548	0.807856
$895$	−80.4716	−2.68987
$896$	−89.0107	−2.97364
$897$	−10.9907	−0.366968
$898$	−39.4860	−1.31767
$899$	5.29310	0.176535
$900$	−113.225	−3.77416
$901$	−71.5723	−2.38442
$902$	−15.1097	−0.503097
$903$	2.98192	0.0992319
$904$	70.6331	2.34922
$905$	50.4575	1.67726
$906$	−40.7776	−1.35475
$907$	19.4563	0.646036	0.323018	−	0.946393i	$-0.395303\pi$
$907$	19.4563	0.646036	0.323018	+	0.946393i	$0.395303\pi$
$908$	91.1616	3.02530
$909$	−51.0036	−1.69168
$910$	31.3085	1.03787
$911$	−6.61264	−0.219086	−0.109543	−	0.993982i	$-0.534939\pi$
$911$	−6.61264	−0.219086	−0.109543	+	0.993982i	$0.534939\pi$
$912$	36.7168	1.21581
$913$	1.87957	0.0622048
$914$	12.9127	0.427113
$915$	25.8576	0.854826
$916$	62.7248	2.07249
$917$	−6.79091	−0.224256
$918$	74.0565	2.44423
$919$	12.7824	0.421651	0.210826	−	0.977524i	$-0.432385\pi$
$919$	12.7824	0.421651	0.210826	+	0.977524i	$0.432385\pi$
$920$	−334.857	−11.0399
$921$	−6.78111	−0.223445
$922$	64.0751	2.11020
$923$	8.04221	0.264713
$924$	11.1788	0.367757
$925$	68.2701	2.24471
$926$	71.7912	2.35920
$927$	5.13412	0.168627
$928$	−25.9834	−0.852948
$929$	−0.917464	−0.0301010	−0.0150505	−	0.999887i	$-0.504791\pi$
$929$	−0.917464	−0.0301010	−0.0150505	+	0.999887i	$0.504791\pi$
$930$	−31.3616	−1.02839
$931$	−15.8056	−0.518007
$932$	26.5462	0.869549
$933$	1.48921	0.0487546
$934$	−117.244	−3.83635
$935$	56.0429	1.83280
$936$	−52.1742	−1.70537
$937$	27.0613	0.884053	0.442027	−	0.897002i	$-0.354260\pi$
$937$	27.0613	0.884053	0.442027	+	0.897002i	$0.354260\pi$
$938$	25.9657	0.847809
$939$	−0.847671	−0.0276627
$940$	−78.5600	−2.56234
$941$	35.5029	1.15736	0.578681	−	0.815554i	$-0.303568\pi$
$941$	35.5029	1.15736	0.578681	+	0.815554i	$0.303568\pi$
$942$	28.3964	0.925203
$943$	25.3497	0.825500
$944$	−200.464	−6.52454
$945$	−19.6816	−0.640244
$946$	−16.8300	−0.547190
$947$	−60.6850	−1.97200	−0.985999	−	0.166750i	$-0.946673\pi$
$947$	−60.6850	−1.97200	−0.985999	+	0.166750i	$0.946673\pi$
$948$	−26.3178	−0.854763
$949$	30.8513	1.00147
$950$	−76.5129	−2.48241
$951$	−4.72634	−0.153262
$952$	−129.981	−4.21270
$953$	7.88149	0.255307	0.127653	−	0.991819i	$-0.459256\pi$
$953$	7.88149	0.255307	0.127653	+	0.991819i	$0.459256\pi$
$954$	−66.3504	−2.14817
$955$	−58.1076	−1.88032
$956$	69.4583	2.24644
$957$	1.21104	0.0391473
$958$	−11.8393	−0.382510
$959$	−18.4247	−0.594966
$960$	82.4154	2.65995
$961$	−2.98305	−0.0962276
$962$	48.6541	1.56867
$963$	29.8102	0.960620
$964$	−133.448	−4.29807
$965$	66.1972	2.13096
$966$	−25.3832	−0.816691
$967$	−9.83490	−0.316269	−0.158134	−	0.987418i	$-0.550548\pi$
$967$	−9.83490	−0.316269	−0.158134	+	0.987418i	$0.550548\pi$
$968$	70.5959	2.26904
$969$	17.2940	0.555563
$970$	35.9600	1.15461
$971$	−38.5945	−1.23856	−0.619279	−	0.785171i	$-0.712575\pi$
$971$	−38.5945	−1.23856	−0.619279	+	0.785171i	$0.712575\pi$
$972$	77.7272	2.49310
$973$	−1.63115	−0.0522923
$974$	35.2136	1.12832
$975$	−8.95163	−0.286682
$976$	201.783	6.45891
$977$	3.68879	0.118015	0.0590075	−	0.998258i	$-0.481206\pi$
$977$	3.68879	0.118015	0.0590075	+	0.998258i	$0.481206\pi$
$978$	−2.66619	−0.0852553
$979$	−28.6911	−0.916971
$980$	−87.1339	−2.78339
$981$	2.34049	0.0747262
$982$	75.9130	2.42248
$983$	−15.5289	−0.495296	−0.247648	−	0.968850i	$-0.579658\pi$
$983$	−15.5289	−0.495296	−0.247648	+	0.968850i	$0.579658\pi$
$984$	−16.6200	−0.529825
$985$	0.145778	0.00464486
$986$	−21.7778	−0.693547
$987$	−3.85047	−0.122562
$988$	−40.2896	−1.28178
$989$	28.2359	0.897850
$990$	51.9540	1.65121
$991$	−46.5909	−1.48001	−0.740004	−	0.672602i	$-0.765177\pi$
$991$	−46.5909	−1.48001	−0.740004	+	0.672602i	$0.765177\pi$
$992$	−137.533	−4.36668
$993$	0.371683	0.0117950
$994$	18.5736	0.589120
$995$	67.6150	2.14354
$996$	3.19749	0.101316
$997$	−16.7210	−0.529559	−0.264779	−	0.964309i	$-0.585299\pi$
$997$	−16.7210	−0.529559	−0.264779	+	0.964309i	$0.585299\pi$
$998$	31.3986	0.993904
$999$	−30.5857	−0.967690

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.d.1.2	✓	98

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.d.1.2	✓	98	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4031 = 29 \cdot 139 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.76750 q^{2} +0.603367 q^{3} +5.65907 q^{4} +3.54828 q^{5} -1.66982 q^{6} +1.63115 q^{7} -10.1265 q^{8} -2.63595 q^{9} +O(q^{10})\)	\(q-2.76750 q^{2} +0.603367 q^{3} +5.65907 q^{4} +3.54828 q^{5} -1.66982 q^{6} +1.63115 q^{7} -10.1265 q^{8} -2.63595 q^{9} -9.81988 q^{10} +2.00713 q^{11} +3.41449 q^{12} -1.95461 q^{13} -4.51422 q^{14} +2.14092 q^{15} +16.7069 q^{16} +7.86913 q^{17} +7.29499 q^{18} +3.64239 q^{19} +20.0800 q^{20} +0.984183 q^{21} -5.55474 q^{22} +9.31928 q^{23} -6.10998 q^{24} +7.59031 q^{25} +5.40940 q^{26} -3.40054 q^{27} +9.23080 q^{28} +1.00000 q^{29} -5.92499 q^{30} +5.29310 q^{31} -25.9834 q^{32} +1.21104 q^{33} -21.7778 q^{34} +5.78779 q^{35} -14.9170 q^{36} +8.99437 q^{37} -10.0803 q^{38} -1.17935 q^{39} -35.9316 q^{40} +2.72014 q^{41} -2.72373 q^{42} +3.02984 q^{43} +11.3585 q^{44} -9.35309 q^{45} -25.7911 q^{46} -3.91236 q^{47} +10.0804 q^{48} -4.33934 q^{49} -21.0062 q^{50} +4.74797 q^{51} -11.0613 q^{52} -9.09533 q^{53} +9.41101 q^{54} +7.12188 q^{55} -16.5178 q^{56} +2.19770 q^{57} -2.76750 q^{58} -11.9989 q^{59} +12.1156 q^{60} +12.0778 q^{61} -14.6487 q^{62} -4.29963 q^{63} +38.4954 q^{64} -6.93552 q^{65} -3.35155 q^{66} -5.75198 q^{67} +44.5319 q^{68} +5.62294 q^{69} -16.0177 q^{70} -4.11448 q^{71} +26.6929 q^{72} -15.7838 q^{73} -24.8919 q^{74} +4.57974 q^{75} +20.6125 q^{76} +3.27394 q^{77} +3.26385 q^{78} -7.70768 q^{79} +59.2808 q^{80} +5.85607 q^{81} -7.52798 q^{82} +0.936447 q^{83} +5.56956 q^{84} +27.9219 q^{85} -8.38508 q^{86} +0.603367 q^{87} -20.3252 q^{88} -14.2946 q^{89} +25.8847 q^{90} -3.18827 q^{91} +52.7384 q^{92} +3.19368 q^{93} +10.8275 q^{94} +12.9242 q^{95} -15.6775 q^{96} -3.66196 q^{97} +12.0091 q^{98} -5.29070 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 98 q + 6 q^{2} + 6 q^{3} + 116 q^{4} + q^{5} + 7 q^{6} + 12 q^{7} + 15 q^{8} + 136 q^{9}+O(q^{10}) \) 98 * q + 6 * q^2 + 6 * q^3 + 116 * q^4 + q^5 + 7 * q^6 + 12 * q^7 + 15 * q^8 + 136 * q^9	\( 98 q + 6 q^{2} + 6 q^{3} + 116 q^{4} + q^{5} + 7 q^{6} + 12 q^{7} + 15 q^{8} + 136 q^{9} + 16 q^{10} + 25 q^{11} + 8 q^{12} + 18 q^{13} + 34 q^{14} + 14 q^{15} + 136 q^{16} + 35 q^{17} + 20 q^{18} + 48 q^{19} - 20 q^{20} + 62 q^{21} + 32 q^{22} + q^{23} + 8 q^{24} + 173 q^{25} + 15 q^{26} + 18 q^{27} + 37 q^{28} + 98 q^{29} - 6 q^{30} + 20 q^{31} + 16 q^{32} + 24 q^{33} - 6 q^{34} + 11 q^{35} + 155 q^{36} + 62 q^{37} - 5 q^{38} + 45 q^{39} + 38 q^{40} + 50 q^{41} + 7 q^{42} + 72 q^{43} + 92 q^{44} - 13 q^{45} + 32 q^{46} - 16 q^{47} - 13 q^{48} + 194 q^{49} + 50 q^{50} + 2 q^{51} + 83 q^{52} - 11 q^{53} + 58 q^{54} + 32 q^{55} + 106 q^{56} + 84 q^{57} + 6 q^{58} + 20 q^{59} + 62 q^{60} + 142 q^{61} - 27 q^{62} + 26 q^{63} + 213 q^{64} + 13 q^{65} - 35 q^{66} + 5 q^{67} + 69 q^{68} + 68 q^{69} - 2 q^{70} - 10 q^{71} - 9 q^{72} + 74 q^{73} + 21 q^{74} + 19 q^{75} + 116 q^{76} + 41 q^{77} - 162 q^{78} + 104 q^{79} - 86 q^{80} + 230 q^{81} + 53 q^{82} - 19 q^{83} + 76 q^{84} + 125 q^{85} + 9 q^{86} + 6 q^{87} + 68 q^{88} + 120 q^{89} + 122 q^{90} + 30 q^{91} + 3 q^{92} - 56 q^{93} + 22 q^{94} + 32 q^{95} - 55 q^{96} + 98 q^{97} - 15 q^{98} + 69 q^{99}+O(q^{100}) \) 98 * q + 6 * q^2 + 6 * q^3 + 116 * q^4 + q^5 + 7 * q^6 + 12 * q^7 + 15 * q^8 + 136 * q^9 + 16 * q^10 + 25 * q^11 + 8 * q^12 + 18 * q^13 + 34 * q^14 + 14 * q^15 + 136 * q^16 + 35 * q^17 + 20 * q^18 + 48 * q^19 - 20 * q^20 + 62 * q^21 + 32 * q^22 + q^23 + 8 * q^24 + 173 * q^25 + 15 * q^26 + 18 * q^27 + 37 * q^28 + 98 * q^29 - 6 * q^30 + 20 * q^31 + 16 * q^32 + 24 * q^33 - 6 * q^34 + 11 * q^35 + 155 * q^36 + 62 * q^37 - 5 * q^38 + 45 * q^39 + 38 * q^40 + 50 * q^41 + 7 * q^42 + 72 * q^43 + 92 * q^44 - 13 * q^45 + 32 * q^46 - 16 * q^47 - 13 * q^48 + 194 * q^49 + 50 * q^50 + 2 * q^51 + 83 * q^52 - 11 * q^53 + 58 * q^54 + 32 * q^55 + 106 * q^56 + 84 * q^57 + 6 * q^58 + 20 * q^59 + 62 * q^60 + 142 * q^61 - 27 * q^62 + 26 * q^63 + 213 * q^64 + 13 * q^65 - 35 * q^66 + 5 * q^67 + 69 * q^68 + 68 * q^69 - 2 * q^70 - 10 * q^71 - 9 * q^72 + 74 * q^73 + 21 * q^74 + 19 * q^75 + 116 * q^76 + 41 * q^77 - 162 * q^78 + 104 * q^79 - 86 * q^80 + 230 * q^81 + 53 * q^82 - 19 * q^83 + 76 * q^84 + 125 * q^85 + 9 * q^86 + 6 * q^87 + 68 * q^88 + 120 * q^89 + 122 * q^90 + 30 * q^91 + 3 * q^92 - 56 * q^93 + 22 * q^94 + 32 * q^95 - 55 * q^96 + 98 * q^97 - 15 * q^98 + 69 * q^99

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