LMFDB - Embedded newform 4031.2.a.c.1.59

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:	$1$
Dimension:	$61$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.59
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)

$f(q)$	$=$	$q+2.53772 q^{2} +0.285178 q^{3} +4.44002 q^{4} +0.796665 q^{5} +0.723701 q^{6} -4.79173 q^{7} +6.19208 q^{8} -2.91867 q^{9} +O(q^{10})$	\(q+2.53772 q^{2} +0.285178 q^{3} +4.44002 q^{4} +0.796665 q^{5} +0.723701 q^{6} -4.79173 q^{7} +6.19208 q^{8} -2.91867 q^{9} +2.02171 q^{10} +1.54971 q^{11} +1.26619 q^{12} -5.02316 q^{13} -12.1601 q^{14} +0.227191 q^{15} +6.83373 q^{16} -1.17589 q^{17} -7.40677 q^{18} -8.12663 q^{19} +3.53721 q^{20} -1.36649 q^{21} +3.93273 q^{22} +3.47312 q^{23} +1.76584 q^{24} -4.36532 q^{25} -12.7474 q^{26} -1.68787 q^{27} -21.2754 q^{28} -1.00000 q^{29} +0.576547 q^{30} +2.69512 q^{31} +4.95792 q^{32} +0.441942 q^{33} -2.98407 q^{34} -3.81740 q^{35} -12.9590 q^{36} -0.742083 q^{37} -20.6231 q^{38} -1.43249 q^{39} +4.93302 q^{40} +4.24308 q^{41} -3.46778 q^{42} -3.87094 q^{43} +6.88074 q^{44} -2.32521 q^{45} +8.81380 q^{46} +7.59056 q^{47} +1.94883 q^{48} +15.9606 q^{49} -11.0780 q^{50} -0.335337 q^{51} -22.3029 q^{52} +1.60143 q^{53} -4.28335 q^{54} +1.23460 q^{55} -29.6708 q^{56} -2.31753 q^{57} -2.53772 q^{58} -7.23792 q^{59} +1.00873 q^{60} -12.2953 q^{61} +6.83946 q^{62} +13.9855 q^{63} -1.08564 q^{64} -4.00178 q^{65} +1.12153 q^{66} +6.44378 q^{67} -5.22096 q^{68} +0.990455 q^{69} -9.68750 q^{70} -4.42671 q^{71} -18.0727 q^{72} +15.0871 q^{73} -1.88320 q^{74} -1.24489 q^{75} -36.0824 q^{76} -7.42578 q^{77} -3.63526 q^{78} -2.60803 q^{79} +5.44420 q^{80} +8.27468 q^{81} +10.7677 q^{82} +10.4739 q^{83} -6.06725 q^{84} -0.936788 q^{85} -9.82336 q^{86} -0.285178 q^{87} +9.59593 q^{88} +3.80181 q^{89} -5.90072 q^{90} +24.0696 q^{91} +15.4207 q^{92} +0.768588 q^{93} +19.2627 q^{94} -6.47420 q^{95} +1.41389 q^{96} +2.33492 q^{97} +40.5036 q^{98} -4.52309 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9}+O(q^{10}) $ 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9	\( 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9} - 16 q^{10} - 3 q^{11} - 18 q^{12} - 28 q^{13} - 14 q^{14} - 12 q^{15} + 11 q^{16} - 21 q^{17} - 17 q^{18} - 36 q^{19} - 16 q^{20} - 12 q^{21} - 42 q^{22} - 15 q^{23} - 28 q^{24} - 16 q^{25} - 13 q^{26} - 10 q^{27} - 25 q^{28} - 61 q^{29} - 12 q^{30} - 18 q^{31} - 3 q^{32} - 42 q^{33} - 22 q^{34} - 29 q^{35} - 38 q^{36} - 30 q^{37} - 27 q^{38} - 31 q^{39} - 22 q^{40} - 28 q^{41} - 9 q^{42} - 58 q^{43} - 2 q^{44} - 31 q^{45} - 40 q^{46} - 6 q^{47} - 37 q^{48} - 37 q^{49} - 15 q^{50} - 44 q^{51} - 43 q^{52} - 27 q^{53} - 18 q^{54} - 38 q^{55} - 22 q^{56} - 50 q^{57} + q^{58} - 24 q^{59} + 6 q^{60} - 76 q^{61} - 17 q^{62} - 6 q^{63} - 60 q^{64} - 65 q^{65} - 7 q^{66} - 45 q^{67} - 31 q^{68} - 16 q^{69} - 48 q^{70} - 28 q^{71} - 40 q^{72} - 50 q^{73} - 17 q^{74} - 35 q^{75} - 100 q^{76} + q^{77} - 6 q^{78} - 66 q^{79} - 10 q^{80} - 63 q^{81} - 5 q^{82} - 9 q^{83} - 24 q^{84} - 77 q^{85} + 29 q^{86} + 4 q^{87} - 62 q^{88} - 30 q^{89} + 50 q^{90} - 52 q^{91} - 53 q^{92} - 42 q^{93} - 92 q^{94} - 20 q^{95} - 47 q^{96} - 34 q^{97} + 36 q^{98} - 29 q^{99}+O(q^{100}) \) 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9 - 16 * q^10 - 3 * q^11 - 18 * q^12 - 28 * q^13 - 14 * q^14 - 12 * q^15 + 11 * q^16 - 21 * q^17 - 17 * q^18 - 36 * q^19 - 16 * q^20 - 12 * q^21 - 42 * q^22 - 15 * q^23 - 28 * q^24 - 16 * q^25 - 13 * q^26 - 10 * q^27 - 25 * q^28 - 61 * q^29 - 12 * q^30 - 18 * q^31 - 3 * q^32 - 42 * q^33 - 22 * q^34 - 29 * q^35 - 38 * q^36 - 30 * q^37 - 27 * q^38 - 31 * q^39 - 22 * q^40 - 28 * q^41 - 9 * q^42 - 58 * q^43 - 2 * q^44 - 31 * q^45 - 40 * q^46 - 6 * q^47 - 37 * q^48 - 37 * q^49 - 15 * q^50 - 44 * q^51 - 43 * q^52 - 27 * q^53 - 18 * q^54 - 38 * q^55 - 22 * q^56 - 50 * q^57 + q^58 - 24 * q^59 + 6 * q^60 - 76 * q^61 - 17 * q^62 - 6 * q^63 - 60 * q^64 - 65 * q^65 - 7 * q^66 - 45 * q^67 - 31 * q^68 - 16 * q^69 - 48 * q^70 - 28 * q^71 - 40 * q^72 - 50 * q^73 - 17 * q^74 - 35 * q^75 - 100 * q^76 + q^77 - 6 * q^78 - 66 * q^79 - 10 * q^80 - 63 * q^81 - 5 * q^82 - 9 * q^83 - 24 * q^84 - 77 * q^85 + 29 * q^86 + 4 * q^87 - 62 * q^88 - 30 * q^89 + 50 * q^90 - 52 * q^91 - 53 * q^92 - 42 * q^93 - 92 * q^94 - 20 * q^95 - 47 * q^96 - 34 * q^97 + 36 * q^98 - 29 * 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 $

$2$	2.53772	1.79444	0.897219	−	0.441585i	$-0.145584\pi$
$2$	2.53772	1.79444	0.897219	+	0.441585i	$0.145584\pi$
$3$	0.285178	0.164647	0.0823237	−	0.996606i	$-0.473766\pi$
$3$	0.285178	0.164647	0.0823237	+	0.996606i	$0.473766\pi$
$4$	4.44002	2.22001
$5$	0.796665	0.356280	0.178140	−	0.984005i	$-0.442992\pi$
$5$	0.796665	0.356280	0.178140	+	0.984005i	$0.442992\pi$
$6$	0.723701	0.295450
$7$	−4.79173	−1.81110	−0.905551	−	0.424237i	$-0.860542\pi$
$7$	−4.79173	−1.81110	−0.905551	+	0.424237i	$0.860542\pi$
$8$	6.19208	2.18923
$9$	−2.91867	−0.972891
$10$	2.02171	0.639322
$11$	1.54971	0.467255	0.233627	−	0.972326i	$-0.424940\pi$
$11$	1.54971	0.467255	0.233627	+	0.972326i	$0.424940\pi$
$12$	1.26619	0.365519
$13$	−5.02316	−1.39317	−0.696587	−	0.717472i	$-0.745299\pi$
$13$	−5.02316	−1.39317	−0.696587	+	0.717472i	$0.745299\pi$
$14$	−12.1601	−3.24991
$15$	0.227191	0.0586605
$16$	6.83373	1.70843
$17$	−1.17589	−0.285194	−0.142597	−	0.989781i	$-0.545545\pi$
$17$	−1.17589	−0.285194	−0.142597	+	0.989781i	$0.545545\pi$
$18$	−7.40677	−1.74579
$19$	−8.12663	−1.86438	−0.932188	−	0.361975i	$-0.882103\pi$
$19$	−8.12663	−1.86438	−0.932188	+	0.361975i	$0.882103\pi$
$20$	3.53721	0.790944
$21$	−1.36649	−0.298193
$22$	3.93273	0.838460
$23$	3.47312	0.724195	0.362098	−	0.932140i	$-0.382061\pi$
$23$	3.47312	0.724195	0.362098	+	0.932140i	$0.382061\pi$
$24$	1.76584	0.360451
$25$	−4.36532	−0.873065
$26$	−12.7474	−2.49997
$27$	−1.68787	−0.324831
$28$	−21.2754	−4.02066
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	0.576547	0.105263
$31$	2.69512	0.484058	0.242029	−	0.970269i	$-0.422187\pi$
$31$	2.69512	0.484058	0.242029	+	0.970269i	$0.422187\pi$
$32$	4.95792	0.876445
$33$	0.441942	0.0769323
$34$	−2.98407	−0.511764
$35$	−3.81740	−0.645259
$36$	−12.9590	−2.15983
$37$	−0.742083	−0.121998	−0.0609989	−	0.998138i	$-0.519429\pi$
$37$	−0.742083	−0.121998	−0.0609989	+	0.998138i	$0.519429\pi$
$38$	−20.6231	−3.34551
$39$	−1.43249	−0.229382
$40$	4.93302	0.779979
$41$	4.24308	0.662658	0.331329	−	0.943515i	$-0.392503\pi$
$41$	4.24308	0.662658	0.331329	+	0.943515i	$0.392503\pi$
$42$	−3.46778	−0.535089
$43$	−3.87094	−0.590313	−0.295156	−	0.955449i	$-0.595372\pi$
$43$	−3.87094	−0.590313	−0.295156	+	0.955449i	$0.595372\pi$
$44$	6.88074	1.03731
$45$	−2.32521	−0.346621
$46$	8.81380	1.29952
$47$	7.59056	1.10720	0.553598	−	0.832784i	$-0.313254\pi$
$47$	7.59056	1.10720	0.553598	+	0.832784i	$0.313254\pi$
$48$	1.94883	0.281289
$49$	15.9606	2.28009
$50$	−11.0780	−1.56666
$51$	−0.335337	−0.0469565
$52$	−22.3029	−3.09286
$53$	1.60143	0.219973	0.109986	−	0.993933i	$-0.464919\pi$
$53$	1.60143	0.219973	0.109986	+	0.993933i	$0.464919\pi$
$54$	−4.28335	−0.582890
$55$	1.23460	0.166473
$56$	−29.6708	−3.96492
$57$	−2.31753	−0.306965
$58$	−2.53772	−0.333219
$59$	−7.23792	−0.942296	−0.471148	−	0.882054i	$-0.656160\pi$
$59$	−7.23792	−0.942296	−0.471148	+	0.882054i	$0.656160\pi$
$60$	1.00873	0.130227
$61$	−12.2953	−1.57426	−0.787128	−	0.616789i	$-0.788433\pi$
$61$	−12.2953	−1.57426	−0.787128	+	0.616789i	$0.788433\pi$
$62$	6.83946	0.868612
$63$	13.9855	1.76201
$64$	−1.08564	−0.135705
$65$	−4.00178	−0.496359
$66$	1.12153	0.138050
$67$	6.44378	0.787233	0.393617	−	0.919275i	$-0.371224\pi$
$67$	6.44378	0.787233	0.393617	+	0.919275i	$0.371224\pi$
$68$	−5.22096	−0.633134
$69$	0.990455	0.119237
$70$	−9.68750	−1.15788
$71$	−4.42671	−0.525354	−0.262677	−	0.964884i	$-0.584605\pi$
$71$	−4.42671	−0.525354	−0.262677	+	0.964884i	$0.584605\pi$
$72$	−18.0727	−2.12988
$73$	15.0871	1.76581	0.882904	−	0.469554i	$-0.155585\pi$
$73$	15.0871	1.76581	0.882904	+	0.469554i	$0.155585\pi$
$74$	−1.88320	−0.218917
$75$	−1.24489	−0.143748
$76$	−36.0824	−4.13893
$77$	−7.42578	−0.846246
$78$	−3.63526	−0.411613
$79$	−2.60803	−0.293426	−0.146713	−	0.989179i	$-0.546869\pi$
$79$	−2.60803	−0.293426	−0.146713	+	0.989179i	$0.546869\pi$
$80$	5.44420	0.608680
$81$	8.27468	0.919409
$82$	10.7677	1.18910
$83$	10.4739	1.14966	0.574831	−	0.818272i	$-0.305068\pi$
$83$	10.4739	1.14966	0.574831	+	0.818272i	$0.305068\pi$
$84$	−6.06725	−0.661992
$85$	−0.936788	−0.101609
$86$	−9.82336	−1.05928
$87$	−0.285178	−0.0305742
$88$	9.59593	1.02293
$89$	3.80181	0.402991	0.201495	−	0.979489i	$-0.435420\pi$
$89$	3.80181	0.402991	0.201495	+	0.979489i	$0.435420\pi$
$90$	−5.90072	−0.621991
$91$	24.0696	2.52318
$92$	15.4207	1.60772
$93$	0.768588	0.0796989
$94$	19.2627	1.98680
$95$	−6.47420	−0.664239
$96$	1.41389	0.144304
$97$	2.33492	0.237075	0.118538	−	0.992950i	$-0.462179\pi$
$97$	2.33492	0.237075	0.118538	+	0.992950i	$0.462179\pi$
$98$	40.5036	4.09148
$99$	−4.52309	−0.454588
$100$	−19.3821	−1.93821
$101$	17.6804	1.75927	0.879635	−	0.475650i	$-0.157787\pi$
$101$	17.6804	1.75927	0.879635	+	0.475650i	$0.157787\pi$
$102$	−0.850990	−0.0842606
$103$	−3.17646	−0.312986	−0.156493	−	0.987679i	$-0.550019\pi$
$103$	−3.17646	−0.312986	−0.156493	+	0.987679i	$0.550019\pi$
$104$	−31.1038	−3.04998
$105$	−1.08864	−0.106240
$106$	4.06397	0.394728
$107$	−10.2925	−0.995018	−0.497509	−	0.867459i	$-0.665752\pi$
$107$	−10.2925	−0.995018	−0.497509	+	0.867459i	$0.665752\pi$
$108$	−7.49419	−0.721129
$109$	−11.3574	−1.08784	−0.543921	−	0.839136i	$-0.683061\pi$
$109$	−11.3574	−1.08784	−0.543921	+	0.839136i	$0.683061\pi$
$110$	3.13307	0.298726
$111$	−0.211626	−0.0200866
$112$	−32.7454	−3.09415
$113$	−11.9089	−1.12030	−0.560148	−	0.828393i	$-0.689256\pi$
$113$	−11.9089	−1.12030	−0.560148	+	0.828393i	$0.689256\pi$
$114$	−5.88124	−0.550829
$115$	2.76691	0.258016
$116$	−4.44002	−0.412245
$117$	14.6610	1.35541
$118$	−18.3678	−1.69089
$119$	5.63453	0.516516
$120$	1.40679	0.128421
$121$	−8.59840	−0.781673
$122$	−31.2021	−2.82491
$123$	1.21003	0.109105
$124$	11.9664	1.07461
$125$	−7.46103	−0.667335
$126$	35.4912	3.16181
$127$	−9.67962	−0.858928	−0.429464	−	0.903084i	$-0.641297\pi$
$127$	−9.67962	−0.858928	−0.429464	+	0.903084i	$0.641297\pi$
$128$	−12.6709	−1.11996
$129$	−1.10390	−0.0971934
$130$	−10.1554	−0.890687
$131$	7.30840	0.638538	0.319269	−	0.947664i	$-0.396563\pi$
$131$	7.30840	0.638538	0.319269	+	0.947664i	$0.396563\pi$
$132$	1.96223	0.170790
$133$	38.9406	3.37658
$134$	16.3525	1.41264
$135$	−1.34467	−0.115731
$136$	−7.28119	−0.624357
$137$	−15.6435	−1.33651	−0.668257	−	0.743930i	$-0.732959\pi$
$137$	−15.6435	−1.33651	−0.668257	+	0.743930i	$0.732959\pi$
$138$	2.51350	0.213963
$139$	−1.00000	−0.0848189
$139$	−1.00000	−0.0848189
$140$	−16.9493	−1.43248
$141$	2.16466	0.182297
$142$	−11.2337	−0.942715
$143$	−7.78444	−0.650967
$144$	−19.9454	−1.66212
$145$	−0.796665	−0.0661595
$146$	38.2867	3.16863
$147$	4.55162	0.375411
$148$	−3.29486	−0.270836
$149$	10.4692	0.857667	0.428834	−	0.903384i	$-0.358925\pi$
$149$	10.4692	0.857667	0.428834	+	0.903384i	$0.358925\pi$
$150$	−3.15919	−0.257947
$151$	−3.19515	−0.260018	−0.130009	−	0.991513i	$-0.541501\pi$
$151$	−3.19515	−0.260018	−0.130009	+	0.991513i	$0.541501\pi$
$152$	−50.3207	−4.08155
$153$	3.43203	0.277463
$154$	−18.8445	−1.51854
$155$	2.14711	0.172460
$156$	−6.36030	−0.509231
$157$	15.4995	1.23700	0.618499	−	0.785786i	$-0.287741\pi$
$157$	15.4995	1.23700	0.618499	+	0.785786i	$0.287741\pi$
$158$	−6.61844	−0.526535
$159$	0.456691	0.0362179
$160$	3.94981	0.312260
$161$	−16.6422	−1.31159
$162$	20.9988	1.64982
$163$	2.82163	0.221007	0.110504	−	0.993876i	$-0.464754\pi$
$163$	2.82163	0.221007	0.110504	+	0.993876i	$0.464754\pi$
$164$	18.8394	1.47111
$165$	0.352080	0.0274094
$166$	26.5798	2.06300
$167$	−12.9137	−0.999296	−0.499648	−	0.866229i	$-0.666537\pi$
$167$	−12.9137	−0.999296	−0.499648	+	0.866229i	$0.666537\pi$
$168$	−8.46144	−0.652814
$169$	12.2321	0.940934
$170$	−2.37731	−0.182331
$171$	23.7190	1.81383
$172$	−17.1870	−1.31050
$173$	−21.2376	−1.61466	−0.807332	−	0.590098i	$-0.799089\pi$
$173$	−21.2376	−1.61466	−0.807332	+	0.590098i	$0.799089\pi$
$174$	−0.723701	−0.0548636
$175$	20.9174	1.58121
$176$	10.5903	0.798273
$177$	−2.06409	−0.155147
$178$	9.64792	0.723142
$179$	−13.2653	−0.991498	−0.495749	−	0.868466i	$-0.665106\pi$
$179$	−13.2653	−0.991498	−0.495749	+	0.868466i	$0.665106\pi$
$180$	−10.3240	−0.769503
$181$	18.9995	1.41222	0.706110	−	0.708102i	$-0.250448\pi$
$181$	18.9995	1.41222	0.706110	+	0.708102i	$0.250448\pi$
$182$	61.0819	4.52769
$183$	−3.50636	−0.259197
$184$	21.5058	1.58543
$185$	−0.591192	−0.0434653
$186$	1.95046	0.143015
$187$	−1.82228	−0.133259
$188$	33.7022	2.45799
$189$	8.08783	0.588303
$190$	−16.4297	−1.19194
$191$	1.90555	0.137881	0.0689405	−	0.997621i	$-0.478038\pi$
$191$	1.90555	0.137881	0.0689405	+	0.997621i	$0.478038\pi$
$192$	−0.309601	−0.0223435
$193$	−14.8013	−1.06542	−0.532709	−	0.846299i	$-0.678826\pi$
$193$	−14.8013	−1.06542	−0.532709	+	0.846299i	$0.678826\pi$
$194$	5.92537	0.425417
$195$	−1.14122	−0.0817243
$196$	70.8655	5.06182
$197$	−2.78404	−0.198355	−0.0991773	−	0.995070i	$-0.531621\pi$
$197$	−2.78404	−0.198355	−0.0991773	+	0.995070i	$0.531621\pi$
$198$	−11.4783	−0.815730
$199$	−6.37861	−0.452167	−0.226084	−	0.974108i	$-0.572592\pi$
$199$	−6.37861	−0.452167	−0.226084	+	0.974108i	$0.572592\pi$
$200$	−27.0305	−1.91134
$201$	1.83762	0.129616
$202$	44.8680	3.15690
$203$	4.79173	0.336313
$204$	−1.48890	−0.104244
$205$	3.38031	0.236091
$206$	−8.06097	−0.561634
$207$	−10.1369	−0.704563
$208$	−34.3269	−2.38014
$209$	−12.5939	−0.871139
$210$	−2.76266	−0.190641
$211$	−4.96941	−0.342108	−0.171054	−	0.985262i	$-0.554717\pi$
$211$	−4.96941	−0.342108	−0.171054	+	0.985262i	$0.554717\pi$
$212$	7.11036	0.488342
$213$	−1.26240	−0.0864981
$214$	−26.1196	−1.78550
$215$	−3.08384	−0.210316
$216$	−10.4515	−0.711131
$217$	−12.9143	−0.876679
$218$	−28.8219	−1.95207
$219$	4.30249	0.290735
$220$	5.48164	0.369572
$221$	5.90667	0.397326
$222$	−0.537046	−0.0360442
$223$	18.4599	1.23617	0.618083	−	0.786113i	$-0.287910\pi$
$223$	18.4599	1.23617	0.618083	+	0.786113i	$0.287910\pi$
$224$	−23.7570	−1.58733
$225$	12.7410	0.849397
$226$	−30.2215	−2.01030
$227$	−14.7954	−0.982004	−0.491002	−	0.871158i	$-0.663369\pi$
$227$	−14.7954	−0.982004	−0.491002	+	0.871158i	$0.663369\pi$
$228$	−10.2899	−0.681464
$229$	−20.1165	−1.32934	−0.664669	−	0.747138i	$-0.731427\pi$
$229$	−20.1165	−1.32934	−0.664669	+	0.747138i	$0.731427\pi$
$230$	7.02165	0.462994
$231$	−2.11767	−0.139332
$232$	−6.19208	−0.406530
$233$	13.6728	0.895736	0.447868	−	0.894100i	$-0.352184\pi$
$233$	13.6728	0.895736	0.447868	+	0.894100i	$0.352184\pi$
$234$	37.2054	2.43219
$235$	6.04713	0.394471
$236$	−32.1365	−2.09191
$237$	−0.743751	−0.0483118
$238$	14.2989	0.926857
$239$	−3.37243	−0.218144	−0.109072	−	0.994034i	$-0.534788\pi$
$239$	−3.37243	−0.218144	−0.109072	+	0.994034i	$0.534788\pi$
$240$	1.55256	0.100218
$241$	−16.2913	−1.04941	−0.524706	−	0.851283i	$-0.675825\pi$
$241$	−16.2913	−1.04941	−0.524706	+	0.851283i	$0.675825\pi$
$242$	−21.8203	−1.40266
$243$	7.42337	0.476210
$244$	−54.5915	−3.49487
$245$	12.7153	0.812350
$246$	3.07072	0.195782
$247$	40.8213	2.59740
$248$	16.6884	1.05972
$249$	2.98693	0.189289
$250$	−18.9340	−1.19749
$251$	23.3630	1.47466	0.737330	−	0.675533i	$-0.236086\pi$
$251$	23.3630	1.47466	0.737330	+	0.675533i	$0.236086\pi$
$252$	62.0958	3.91167
$253$	5.38232	0.338384
$254$	−24.5642	−1.54129
$255$	−0.267151	−0.0167296
$256$	−29.9839	−1.87399
$257$	18.4379	1.15013	0.575063	−	0.818109i	$-0.304977\pi$
$257$	18.4379	1.15013	0.575063	+	0.818109i	$0.304977\pi$
$258$	−2.80140	−0.174408
$259$	3.55586	0.220950
$260$	−17.7680	−1.10192
$261$	2.91867	0.180661
$262$	18.5467	1.14582
$263$	−18.7904	−1.15867	−0.579334	−	0.815090i	$-0.696687\pi$
$263$	−18.7904	−1.15867	−0.579334	+	0.815090i	$0.696687\pi$
$264$	2.73654	0.168423
$265$	1.27580	0.0783718
$266$	98.8202	6.05906
$267$	1.08419	0.0663513
$268$	28.6105	1.74767
$269$	−4.77448	−0.291105	−0.145553	−	0.989351i	$-0.546496\pi$
$269$	−4.77448	−0.291105	−0.145553	+	0.989351i	$0.546496\pi$
$270$	−3.41240	−0.207672
$271$	19.7178	1.19777	0.598886	−	0.800834i	$-0.295610\pi$
$271$	19.7178	1.19777	0.598886	+	0.800834i	$0.295610\pi$
$272$	−8.03570	−0.487236
$273$	6.86411	0.415435
$274$	−39.6988	−2.39829
$275$	−6.76498	−0.407944
$276$	4.39764	0.264707
$277$	−19.8208	−1.19092	−0.595459	−	0.803386i	$-0.703030\pi$
$277$	−19.8208	−1.19092	−0.595459	+	0.803386i	$0.703030\pi$
$278$	−2.53772	−0.152202
$279$	−7.86618	−0.470936
$280$	−23.6377	−1.41262
$281$	−4.91402	−0.293146	−0.146573	−	0.989200i	$-0.546824\pi$
$281$	−4.91402	−0.293146	−0.146573	+	0.989200i	$0.546824\pi$
$282$	5.49329	0.327121
$283$	24.2398	1.44091	0.720453	−	0.693504i	$-0.243934\pi$
$283$	24.2398	1.44091	0.720453	+	0.693504i	$0.243934\pi$
$284$	−19.6547	−1.16629
$285$	−1.84630	−0.109365
$286$	−19.7547	−1.16812
$287$	−20.3317	−1.20014
$288$	−14.4706	−0.852686
$289$	−15.6173	−0.918664
$290$	−2.02171	−0.118719
$291$	0.665867	0.0390338
$292$	66.9868	3.92011
$293$	−18.0032	−1.05176	−0.525878	−	0.850560i	$-0.676263\pi$
$293$	−18.0032	−1.05176	−0.525878	+	0.850560i	$0.676263\pi$
$294$	11.5507	0.673652
$295$	−5.76620	−0.335721
$296$	−4.59504	−0.267081
$297$	−2.61571	−0.151779
$298$	26.5678	1.53903
$299$	−17.4460	−1.00893
$300$	−5.52735	−0.319122
$301$	18.5485	1.06912
$302$	−8.10839	−0.466585
$303$	5.04206	0.289659
$304$	−55.5352	−3.18516
$305$	−9.79527	−0.560876
$306$	8.70953	0.497891
$307$	−13.3837	−0.763851	−0.381925	−	0.924193i	$-0.624739\pi$
$307$	−13.3837	−0.763851	−0.381925	+	0.924193i	$0.624739\pi$
$308$	−32.9706	−1.87867
$309$	−0.905856	−0.0515323
$310$	5.44876	0.309469
$311$	−14.3619	−0.814391	−0.407195	−	0.913341i	$-0.633493\pi$
$311$	−14.3619	−0.814391	−0.407195	+	0.913341i	$0.633493\pi$
$312$	−8.87011	−0.502171
$313$	−25.1419	−1.42111	−0.710553	−	0.703644i	$-0.751555\pi$
$313$	−25.1419	−1.42111	−0.710553	+	0.703644i	$0.751555\pi$
$314$	39.3335	2.21972
$315$	11.1418	0.627767
$316$	−11.5797	−0.651409
$317$	−4.54696	−0.255382	−0.127691	−	0.991814i	$-0.540757\pi$
$317$	−4.54696	−0.255382	−0.127691	+	0.991814i	$0.540757\pi$
$318$	1.15895	0.0649909
$319$	−1.54971	−0.0867670
$320$	−0.864894	−0.0483491
$321$	−2.93520	−0.163827
$322$	−42.2333	−2.35357
$323$	9.55599	0.531710
$324$	36.7397	2.04110
$325$	21.9277	1.21633
$326$	7.16051	0.396584
$327$	−3.23888	−0.179110
$328$	26.2735	1.45071
$329$	−36.3719	−2.00525
$330$	0.893480	0.0491845
$331$	1.69402	0.0931119	0.0465559	−	0.998916i	$-0.485175\pi$
$331$	1.69402	0.0931119	0.0465559	+	0.998916i	$0.485175\pi$
$332$	46.5044	2.55226
$333$	2.16590	0.118691
$334$	−32.7715	−1.79317
$335$	5.13354	0.280475
$336$	−9.33824	−0.509443
$337$	−18.9476	−1.03214	−0.516070	−	0.856547i	$-0.672605\pi$
$337$	−18.9476	−1.03214	−0.516070	+	0.856547i	$0.672605\pi$
$338$	31.0417	1.68845
$339$	−3.39615	−0.184454
$340$	−4.15936	−0.225573
$341$	4.17665	0.226178
$342$	60.1921	3.25482
$343$	−42.9369	−2.31838
$344$	−23.9692	−1.29233
$345$	0.789061	0.0424816
$346$	−53.8950	−2.89741
$347$	15.2909	0.820860	0.410430	−	0.911892i	$-0.365379\pi$
$347$	15.2909	0.820860	0.410430	+	0.911892i	$0.365379\pi$
$348$	−1.26619	−0.0678751
$349$	21.9159	1.17313	0.586566	−	0.809901i	$-0.300479\pi$
$349$	21.9159	1.17313	0.586566	+	0.809901i	$0.300479\pi$
$350$	53.0826	2.83738
$351$	8.47846	0.452547
$352$	7.68334	0.409523
$353$	−3.17192	−0.168824	−0.0844121	−	0.996431i	$-0.526901\pi$
$353$	−3.17192	−0.168824	−0.0844121	+	0.996431i	$0.526901\pi$
$354$	−5.23809	−0.278401
$355$	−3.52661	−0.187173
$356$	16.8801	0.894643
$357$	1.60684	0.0850431
$358$	−33.6637	−1.77918
$359$	−27.4520	−1.44886	−0.724431	−	0.689347i	$-0.757898\pi$
$359$	−27.4520	−1.44886	−0.724431	+	0.689347i	$0.757898\pi$
$360$	−14.3979	−0.758834
$361$	47.0420	2.47590
$362$	48.2154	2.53414
$363$	−2.45207	−0.128700
$364$	106.870	5.60149
$365$	12.0193	0.629121
$366$	−8.89815	−0.465114
$367$	28.3318	1.47891	0.739454	−	0.673207i	$-0.235084\pi$
$367$	28.3318	1.47891	0.739454	+	0.673207i	$0.235084\pi$
$368$	23.7343	1.23724
$369$	−12.3842	−0.644694
$370$	−1.50028	−0.0779958
$371$	−7.67360	−0.398393
$372$	3.41255	0.176932
$373$	25.6096	1.32602	0.663009	−	0.748612i	$-0.269279\pi$
$373$	25.6096	1.32602	0.663009	+	0.748612i	$0.269279\pi$
$374$	−4.62444	−0.239124
$375$	−2.12772	−0.109875
$376$	47.0014	2.42391
$377$	5.02316	0.258706
$378$	20.5246	1.05567
$379$	2.89663	0.148790	0.0743949	−	0.997229i	$-0.476297\pi$
$379$	2.89663	0.148790	0.0743949	+	0.997229i	$0.476297\pi$
$380$	−28.7456	−1.47462
$381$	−2.76041	−0.141420
$382$	4.83576	0.247419
$383$	−5.79718	−0.296222	−0.148111	−	0.988971i	$-0.547319\pi$
$383$	−5.79718	−0.296222	−0.148111	+	0.988971i	$0.547319\pi$
$384$	−3.61346	−0.184399
$385$	−5.91586	−0.301500
$386$	−37.5614	−1.91183
$387$	11.2980	0.574310
$388$	10.3671	0.526309
$389$	25.0477	1.26997	0.634983	−	0.772526i	$-0.281007\pi$
$389$	25.0477	1.26997	0.634983	+	0.772526i	$0.281007\pi$
$390$	−2.89609	−0.146649
$391$	−4.08399	−0.206536
$392$	98.8296	4.99165
$393$	2.08419	0.105134
$394$	−7.06511	−0.355935
$395$	−2.07773	−0.104542
$396$	−20.0826	−1.00919
$397$	14.5316	0.729323	0.364661	−	0.931140i	$-0.381185\pi$
$397$	14.5316	0.729323	0.364661	+	0.931140i	$0.381185\pi$
$398$	−16.1871	−0.811387
$399$	11.1050	0.555944
$400$	−29.8315	−1.49157
$401$	−20.6903	−1.03323	−0.516613	−	0.856219i	$-0.672807\pi$
$401$	−20.6903	−1.03323	−0.516613	+	0.856219i	$0.672807\pi$
$402$	4.66337	0.232588
$403$	−13.5380	−0.674377
$404$	78.5015	3.90559
$405$	6.59215	0.327567
$406$	12.1601	0.603493
$407$	−1.15001	−0.0570040
$408$	−2.07643	−0.102799
$409$	11.8991	0.588372	0.294186	−	0.955748i	$-0.404951\pi$
$409$	11.8991	0.588372	0.294186	+	0.955748i	$0.404951\pi$
$410$	8.57829	0.423651
$411$	−4.46118	−0.220054
$412$	−14.1036	−0.694832
$413$	34.6821	1.70660
$414$	−25.7246	−1.26429
$415$	8.34420	0.409601
$416$	−24.9044	−1.22104
$417$	−0.285178	−0.0139652
$418$	−31.9598	−1.56320
$419$	−8.87022	−0.433339	−0.216669	−	0.976245i	$-0.569519\pi$
$419$	−8.87022	−0.433339	−0.216669	+	0.976245i	$0.569519\pi$
$420$	−4.83357	−0.235854
$421$	−23.6182	−1.15108	−0.575540	−	0.817774i	$-0.695208\pi$
$421$	−23.6182	−1.15108	−0.575540	+	0.817774i	$0.695208\pi$
$422$	−12.6110	−0.613892
$423$	−22.1544	−1.07718
$424$	9.91616	0.481571
$425$	5.13313	0.248993
$426$	−3.20361	−0.155216
$427$	58.9159	2.85114
$428$	−45.6991	−2.20895
$429$	−2.21995	−0.107180
$430$	−7.82593	−0.377400
$431$	17.0125	0.819463	0.409731	−	0.912206i	$-0.365622\pi$
$431$	17.0125	0.819463	0.409731	+	0.912206i	$0.365622\pi$
$432$	−11.5345	−0.554952
$433$	19.1772	0.921596	0.460798	−	0.887505i	$-0.347563\pi$
$433$	19.1772	0.921596	0.460798	+	0.887505i	$0.347563\pi$
$434$	−32.7728	−1.57315
$435$	−0.227191	−0.0108930
$436$	−50.4271	−2.41502
$437$	−28.2247	−1.35017
$438$	10.9185	0.521707
$439$	−19.2404	−0.918294	−0.459147	−	0.888360i	$-0.651845\pi$
$439$	−19.2404	−0.918294	−0.459147	+	0.888360i	$0.651845\pi$
$440$	7.64474	0.364449
$441$	−46.5839	−2.21828
$442$	14.9895	0.712976
$443$	−22.5443	−1.07111	−0.535557	−	0.844499i	$-0.679898\pi$
$443$	−22.5443	−1.07111	−0.535557	+	0.844499i	$0.679898\pi$
$444$	−0.939621	−0.0445925
$445$	3.02877	0.143577
$446$	46.8460	2.21822
$447$	2.98557	0.141213
$448$	5.20211	0.245776
$449$	21.6798	1.02313	0.511566	−	0.859244i	$-0.329066\pi$
$449$	21.6798	1.02313	0.511566	+	0.859244i	$0.329066\pi$
$450$	32.3330	1.52419
$451$	6.57554	0.309630
$452$	−52.8758	−2.48707
$453$	−0.911185	−0.0428112
$454$	−37.5465	−1.76215
$455$	19.1754	0.898958
$456$	−14.3503	−0.672017
$457$	−23.7798	−1.11237	−0.556187	−	0.831057i	$-0.687736\pi$
$457$	−23.7798	−1.11237	−0.556187	+	0.831057i	$0.687736\pi$
$458$	−51.0501	−2.38541
$459$	1.98475	0.0926401
$460$	12.2851	0.572798
$461$	−18.2163	−0.848420	−0.424210	−	0.905564i	$-0.639448\pi$
$461$	−18.2163	−0.848420	−0.424210	+	0.905564i	$0.639448\pi$
$462$	−5.37404	−0.250023
$463$	3.50654	0.162963	0.0814813	−	0.996675i	$-0.474035\pi$
$463$	3.50654	0.162963	0.0814813	+	0.996675i	$0.474035\pi$
$464$	−6.83373	−0.317248
$465$	0.612308	0.0283951
$466$	34.6978	1.60734
$467$	−5.00400	−0.231557	−0.115779	−	0.993275i	$-0.536936\pi$
$467$	−5.00400	−0.231557	−0.115779	+	0.993275i	$0.536936\pi$
$468$	65.0950	3.00902
$469$	−30.8768	−1.42576
$470$	15.3459	0.707855
$471$	4.42012	0.203668
$472$	−44.8178	−2.06291
$473$	−5.99883	−0.275826
$474$	−1.88743	−0.0866926
$475$	35.4754	1.62772
$476$	25.0174	1.14667
$477$	−4.67404	−0.214010
$478$	−8.55829	−0.391447
$479$	−5.29017	−0.241714	−0.120857	−	0.992670i	$-0.538564\pi$
$479$	−5.29017	−0.241714	−0.120857	+	0.992670i	$0.538564\pi$
$480$	1.12640	0.0514127
$481$	3.72760	0.169964
$482$	−41.3426	−1.88311
$483$	−4.74599	−0.215950
$484$	−38.1771	−1.73532
$485$	1.86015	0.0844651
$486$	18.8384	0.854529
$487$	39.4915	1.78953	0.894766	−	0.446536i	$-0.147342\pi$
$487$	39.4915	1.78953	0.894766	+	0.446536i	$0.147342\pi$
$488$	−76.1338	−3.44641
$489$	0.804666	0.0363883
$490$	32.2678	1.45771
$491$	5.22939	0.235999	0.118000	−	0.993014i	$-0.462352\pi$
$491$	5.22939	0.235999	0.118000	+	0.993014i	$0.462352\pi$
$492$	5.37256	0.242214
$493$	1.17589	0.0529593
$494$	103.593	4.66087
$495$	−3.60339	−0.161960
$496$	18.4177	0.826981
$497$	21.2116	0.951470
$498$	7.57998	0.339667
$499$	9.84913	0.440908	0.220454	−	0.975397i	$-0.429246\pi$
$499$	9.84913	0.440908	0.220454	+	0.975397i	$0.429246\pi$
$500$	−33.1271	−1.48149
$501$	−3.68271	−0.164531
$502$	59.2887	2.64619
$503$	−36.0985	−1.60955	−0.804776	−	0.593578i	$-0.797715\pi$
$503$	−36.0985	−1.60955	−0.804776	+	0.593578i	$0.797715\pi$
$504$	86.5993	3.85744
$505$	14.0854	0.626792
$506$	13.6588	0.607209
$507$	3.48833	0.154922
$508$	−42.9777	−1.90683
$509$	−30.9886	−1.37355	−0.686773	−	0.726872i	$-0.740973\pi$
$509$	−30.9886	−1.37355	−0.686773	+	0.726872i	$0.740973\pi$
$510$	−0.677954	−0.0300203
$511$	−72.2931	−3.19806
$512$	−50.7489	−2.24281
$513$	13.7167	0.605608
$514$	46.7903	2.06383
$515$	−2.53058	−0.111511
$516$	−4.90136	−0.215770
$517$	11.7632	0.517343
$518$	9.02377	0.396482
$519$	−6.05648	−0.265850
$520$	−24.7793	−1.08665
$521$	25.5141	1.11779	0.558897	−	0.829237i	$-0.311225\pi$
$521$	25.5141	1.11779	0.558897	+	0.829237i	$0.311225\pi$
$522$	7.40677	0.324186
$523$	−30.9044	−1.35135	−0.675676	−	0.737198i	$-0.736148\pi$
$523$	−30.9044	−1.35135	−0.675676	+	0.737198i	$0.736148\pi$
$524$	32.4494	1.41756
$525$	5.96518	0.260342
$526$	−47.6849	−2.07916
$527$	−3.16916	−0.138051
$528$	3.02011	0.131434
$529$	−10.9375	−0.475542
$530$	3.23762	0.140633
$531$	21.1251	0.916752
$532$	172.897	7.49603
$533$	−21.3137	−0.923197
$534$	2.75137	0.119063
$535$	−8.19971	−0.354504
$536$	39.9004	1.72344
$537$	−3.78298	−0.163248
$538$	−12.1163	−0.522370
$539$	24.7343	1.06538
$540$	−5.97036	−0.256923
$541$	33.5001	1.44028	0.720140	−	0.693829i	$-0.244078\pi$
$541$	33.5001	1.44028	0.720140	+	0.693829i	$0.244078\pi$
$542$	50.0383	2.14933
$543$	5.41823	0.232518
$544$	−5.82996	−0.249957
$545$	−9.04806	−0.387576
$546$	17.4192	0.745473
$547$	−14.9992	−0.641321	−0.320661	−	0.947194i	$-0.603905\pi$
$547$	−14.9992	−0.641321	−0.320661	+	0.947194i	$0.603905\pi$
$548$	−69.4574	−2.96707
$549$	35.8861	1.53158
$550$	−17.1676	−0.732030
$551$	8.12663	0.346206
$552$	6.13298	0.261037
$553$	12.4970	0.531425
$554$	−50.2997	−2.13703
$555$	−0.168595	−0.00715645
$556$	−4.44002	−0.188299
$557$	−15.2914	−0.647918	−0.323959	−	0.946071i	$-0.605014\pi$
$557$	−15.2914	−0.647918	−0.323959	+	0.946071i	$0.605014\pi$
$558$	−19.9622	−0.845065
$559$	19.4443	0.822408
$560$	−26.0871	−1.10238
$561$	−0.519674	−0.0219407
$562$	−12.4704	−0.526033
$563$	10.8072	0.455470	0.227735	−	0.973723i	$-0.426868\pi$
$563$	10.8072	0.455470	0.227735	+	0.973723i	$0.426868\pi$
$564$	9.61112	0.404701
$565$	−9.48741	−0.399138
$566$	61.5138	2.58562
$567$	−39.6500	−1.66514
$568$	−27.4106	−1.15012
$569$	−21.3874	−0.896608	−0.448304	−	0.893881i	$-0.647972\pi$
$569$	−21.3874	−0.896608	−0.448304	+	0.893881i	$0.647972\pi$
$570$	−4.68538	−0.196249
$571$	17.3643	0.726674	0.363337	−	0.931658i	$-0.381637\pi$
$571$	17.3643	0.726674	0.363337	+	0.931658i	$0.381637\pi$
$572$	−34.5630	−1.44515
$573$	0.543421	0.0227018
$574$	−51.5961	−2.15358
$575$	−15.1613	−0.632269
$576$	3.16864	0.132027
$577$	−32.1823	−1.33977	−0.669884	−	0.742465i	$-0.733656\pi$
$577$	−32.1823	−1.33977	−0.669884	+	0.742465i	$0.733656\pi$
$578$	−39.6323	−1.64849
$579$	−4.22099	−0.175418
$580$	−3.53721	−0.146875
$581$	−50.1881	−2.08215
$582$	1.68978	0.0700438
$583$	2.48174	0.102783
$584$	93.4203	3.86576
$585$	11.6799	0.482904
$586$	−45.6870	−1.88731
$587$	16.7695	0.692153	0.346077	−	0.938206i	$-0.387514\pi$
$587$	16.7695	0.692153	0.346077	+	0.938206i	$0.387514\pi$
$588$	20.2093	0.833416
$589$	−21.9022	−0.902466
$590$	−14.6330	−0.602431
$591$	−0.793946	−0.0326586
$592$	−5.07120	−0.208425
$593$	−19.3815	−0.795903	−0.397952	−	0.917406i	$-0.630279\pi$
$593$	−19.3815	−0.795903	−0.397952	+	0.917406i	$0.630279\pi$
$594$	−6.63794	−0.272358
$595$	4.48883	0.184024
$596$	46.4833	1.90403
$597$	−1.81904	−0.0744482
$598$	−44.2731	−1.81046
$599$	23.7607	0.970838	0.485419	−	0.874282i	$-0.338667\pi$
$599$	23.7607	0.970838	0.485419	+	0.874282i	$0.338667\pi$
$600$	−7.70848	−0.314697
$601$	−36.3121	−1.48120	−0.740600	−	0.671946i	$-0.765459\pi$
$601$	−36.3121	−1.48120	−0.740600	+	0.671946i	$0.765459\pi$
$602$	47.0708	1.91846
$603$	−18.8073	−0.765892
$604$	−14.1865	−0.577241
$605$	−6.85005	−0.278494
$606$	12.7953	0.519775
$607$	30.8715	1.25303	0.626517	−	0.779408i	$-0.284480\pi$
$607$	30.8715	1.25303	0.626517	+	0.779408i	$0.284480\pi$
$608$	−40.2912	−1.63402
$609$	1.36649	0.0553731
$610$	−24.8576	−1.00646
$611$	−38.1286	−1.54252
$612$	15.2383	0.615971
$613$	35.0427	1.41536	0.707681	−	0.706532i	$-0.249742\pi$
$613$	35.0427	1.41536	0.707681	+	0.706532i	$0.249742\pi$
$614$	−33.9642	−1.37068
$615$	0.963990	0.0388718
$616$	−45.9811	−1.85263
$617$	−31.6013	−1.27222	−0.636111	−	0.771598i	$-0.719458\pi$
$617$	−31.6013	−1.27222	−0.636111	+	0.771598i	$0.719458\pi$
$618$	−2.29881	−0.0924716
$619$	35.7655	1.43754	0.718769	−	0.695249i	$-0.244706\pi$
$619$	35.7655	1.43754	0.718769	+	0.695249i	$0.244706\pi$
$620$	9.53321	0.382863
$621$	−5.86218	−0.235241
$622$	−36.4466	−1.46137
$623$	−18.2172	−0.729857
$624$	−9.78927	−0.391884
$625$	15.8827	0.635307
$626$	−63.8031	−2.55009
$627$	−3.59150	−0.143431
$628$	68.8182	2.74615
$629$	0.872606	0.0347931
$630$	28.2746	1.12649
$631$	12.6991	0.505542	0.252771	−	0.967526i	$-0.418658\pi$
$631$	12.6991	0.505542	0.252771	+	0.967526i	$0.418658\pi$
$632$	−16.1491	−0.642378
$633$	−1.41716	−0.0563272
$634$	−11.5389	−0.458268
$635$	−7.71142	−0.306018
$636$	2.02772	0.0804042
$637$	−80.1729	−3.17656
$638$	−3.93273	−0.155698
$639$	12.9201	0.511112
$640$	−10.0945	−0.399019
$641$	8.81038	0.347989	0.173995	−	0.984747i	$-0.444332\pi$
$641$	8.81038	0.347989	0.173995	+	0.984747i	$0.444332\pi$
$642$	−7.44872	−0.293977
$643$	−42.1082	−1.66059	−0.830293	−	0.557328i	$-0.811827\pi$
$643$	−42.1082	−1.66059	−0.830293	+	0.557328i	$0.811827\pi$
$644$	−73.8918	−2.91175
$645$	−0.879443	−0.0346280
$646$	24.2504	0.954120
$647$	−19.1129	−0.751406	−0.375703	−	0.926740i	$-0.622599\pi$
$647$	−19.1129	−0.751406	−0.375703	+	0.926740i	$0.622599\pi$
$648$	51.2375	2.01280
$649$	−11.2167	−0.440293
$650$	55.6464	2.18263
$651$	−3.68286	−0.144343
$652$	12.5281	0.490638
$653$	−25.3308	−0.991271	−0.495635	−	0.868531i	$-0.665065\pi$
$653$	−25.3308	−0.991271	−0.495635	+	0.868531i	$0.665065\pi$
$654$	−8.21937	−0.321403
$655$	5.82235	0.227498
$656$	28.9961	1.13211
$657$	−44.0342	−1.71794
$658$	−92.3016	−3.59829
$659$	42.0640	1.63858	0.819291	−	0.573378i	$-0.194367\pi$
$659$	42.0640	1.63858	0.819291	+	0.573378i	$0.194367\pi$
$660$	1.56324	0.0608491
$661$	−38.9926	−1.51664	−0.758318	−	0.651885i	$-0.773979\pi$
$661$	−38.9926	−1.51664	−0.758318	+	0.651885i	$0.773979\pi$
$662$	4.29895	0.167084
$663$	1.68445	0.0654186
$664$	64.8553	2.51688
$665$	31.0226	1.20300
$666$	5.49644	0.212983
$667$	−3.47312	−0.134480
$668$	−57.3373	−2.21845
$669$	5.26435	0.203532
$670$	13.0275	0.503295
$671$	−19.0542	−0.735579
$672$	−6.77497	−0.261350
$673$	−19.4113	−0.748252	−0.374126	−	0.927378i	$-0.622057\pi$
$673$	−19.4113	−0.748252	−0.374126	+	0.927378i	$0.622057\pi$
$674$	−48.0836	−1.85211
$675$	7.36811	0.283599
$676$	54.3109	2.08888
$677$	30.4024	1.16846	0.584230	−	0.811588i	$-0.301396\pi$
$677$	30.4024	1.16846	0.584230	+	0.811588i	$0.301396\pi$
$678$	−8.61848	−0.330991
$679$	−11.1883	−0.429367
$680$	−5.80067	−0.222446
$681$	−4.21931	−0.161684
$682$	10.5992	0.405863
$683$	24.8688	0.951577	0.475788	−	0.879560i	$-0.342163\pi$
$683$	24.8688	0.951577	0.475788	+	0.879560i	$0.342163\pi$
$684$	105.313	4.02673
$685$	−12.4626	−0.476173
$686$	−108.962	−4.16018
$687$	−5.73678	−0.218872
$688$	−26.4530	−1.00851
$689$	−8.04422	−0.306460
$690$	2.00242	0.0762307
$691$	−11.2010	−0.426107	−0.213054	−	0.977040i	$-0.568341\pi$
$691$	−11.2010	−0.426107	−0.213054	+	0.977040i	$0.568341\pi$
$692$	−94.2952	−3.58457
$693$	21.6734	0.823306
$694$	38.8041	1.47298
$695$	−0.796665	−0.0302192
$696$	−1.76584	−0.0669341
$697$	−4.98938	−0.188986
$698$	55.6165	2.10511
$699$	3.89918	0.147480
$700$	92.8738	3.51030
$701$	13.0843	0.494185	0.247093	−	0.968992i	$-0.420525\pi$
$701$	13.0843	0.494185	0.247093	+	0.968992i	$0.420525\pi$
$702$	21.5159	0.812067
$703$	6.03063	0.227450
$704$	−1.68243	−0.0634090
$705$	1.72451	0.0649487
$706$	−8.04943	−0.302944
$707$	−84.7198	−3.18622
$708$	−9.16461	−0.344427
$709$	−19.3395	−0.726310	−0.363155	−	0.931729i	$-0.618300\pi$
$709$	−19.3395	−0.726310	−0.363155	+	0.931729i	$0.618300\pi$
$710$	−8.94954	−0.335870
$711$	7.61198	0.285472
$712$	23.5411	0.882240
$713$	9.36047	0.350552
$714$	4.07771	0.152605
$715$	−6.20159	−0.231926
$716$	−58.8984	−2.20114
$717$	−0.961742	−0.0359169
$718$	−69.6656	−2.59990
$719$	25.3379	0.944944	0.472472	−	0.881346i	$-0.343362\pi$
$719$	25.3379	0.944944	0.472472	+	0.881346i	$0.343362\pi$
$720$	−15.8898	−0.592179
$721$	15.2207	0.566850
$722$	119.379	4.44284
$723$	−4.64590	−0.172783
$724$	84.3581	3.13514
$725$	4.36532	0.162124
$726$	−6.22267	−0.230945
$727$	−16.9623	−0.629096	−0.314548	−	0.949242i	$-0.601853\pi$
$727$	−16.9623	−0.629096	−0.314548	+	0.949242i	$0.601853\pi$
$728$	149.041	5.52383
$729$	−22.7071	−0.841002
$730$	30.5017	1.12892
$731$	4.55179	0.168354
$732$	−15.5683	−0.575420
$733$	27.4412	1.01356	0.506782	−	0.862074i	$-0.330835\pi$
$733$	27.4412	1.01356	0.506782	+	0.862074i	$0.330835\pi$
$734$	71.8981	2.65381
$735$	3.62612	0.133751
$736$	17.2195	0.634717
$737$	9.98599	0.367839
$738$	−31.4275	−1.15686
$739$	27.5380	1.01300	0.506502	−	0.862239i	$-0.330938\pi$
$739$	27.5380	1.01300	0.506502	+	0.862239i	$0.330938\pi$
$740$	−2.62490	−0.0964934
$741$	11.6413	0.427655
$742$	−19.4734	−0.714892
$743$	−22.0284	−0.808143	−0.404071	−	0.914727i	$-0.632405\pi$
$743$	−22.0284	−0.808143	−0.404071	+	0.914727i	$0.632405\pi$
$744$	4.75916	0.174479
$745$	8.34042	0.305569
$746$	64.9901	2.37946
$747$	−30.5699	−1.11850
$748$	−8.09097	−0.295835
$749$	49.3190	1.80208
$750$	−5.39955	−0.197164
$751$	29.3811	1.07213	0.536066	−	0.844176i	$-0.319910\pi$
$751$	29.3811	1.07213	0.536066	+	0.844176i	$0.319910\pi$
$752$	51.8718	1.89157
$753$	6.66260	0.242799
$754$	12.7474	0.464232
$755$	−2.54546	−0.0926389
$756$	35.9101	1.30604
$757$	−27.3024	−0.992321	−0.496160	−	0.868231i	$-0.665257\pi$
$757$	−27.3024	−0.992321	−0.496160	+	0.868231i	$0.665257\pi$
$758$	7.35083	0.266994
$759$	1.53492	0.0557140
$760$	−40.0888	−1.45417
$761$	27.5381	0.998257	0.499128	−	0.866528i	$-0.333654\pi$
$761$	27.5381	0.998257	0.499128	+	0.866528i	$0.333654\pi$
$762$	−7.00515	−0.253770
$763$	54.4216	1.97019
$764$	8.46070	0.306097
$765$	2.73418	0.0988545
$766$	−14.7116	−0.531552
$767$	36.3572	1.31278
$768$	−8.55074	−0.308548
$769$	−12.9940	−0.468576	−0.234288	−	0.972167i	$-0.575276\pi$
$769$	−12.9940	−0.468576	−0.234288	+	0.972167i	$0.575276\pi$
$770$	−15.0128	−0.541024
$771$	5.25808	0.189365
$772$	−65.7178	−2.36524
$773$	11.7387	0.422211	0.211105	−	0.977463i	$-0.432294\pi$
$773$	11.7387	0.422211	0.211105	+	0.977463i	$0.432294\pi$
$774$	28.6712	1.03056
$775$	−11.7651	−0.422614
$776$	14.4580	0.519013
$777$	1.01405	0.0363789
$778$	63.5639	2.27888
$779$	−34.4819	−1.23544
$780$	−5.06703	−0.181429
$781$	−6.86011	−0.245474
$782$	−10.3640	−0.370617
$783$	1.68787	0.0603197
$784$	109.071	3.89538
$785$	12.3479	0.440717
$786$	5.28909	0.188656
$787$	53.6141	1.91114	0.955568	−	0.294772i	$-0.0952436\pi$
$787$	53.6141	1.91114	0.955568	+	0.294772i	$0.0952436\pi$
$788$	−12.3612	−0.440349
$789$	−5.35861	−0.190772
$790$	−5.27268	−0.187594
$791$	57.0642	2.02897
$792$	−28.0074	−0.995199
$793$	61.7615	2.19321
$794$	36.8772	1.30872
$795$	0.363830	0.0129037
$796$	−28.3211	−1.00382
$797$	−22.5292	−0.798025	−0.399012	−	0.916946i	$-0.630647\pi$
$797$	−22.5292	−0.798025	−0.399012	+	0.916946i	$0.630647\pi$
$798$	28.1813	0.997608
$799$	−8.92564	−0.315766
$800$	−21.6429	−0.765194
$801$	−11.0962	−0.392066
$802$	−52.5062	−1.85406
$803$	23.3806	0.825082
$804$	8.15908	0.287749
$805$	−13.2583	−0.467293
$806$	−34.3557	−1.21013
$807$	−1.36157	−0.0479297
$808$	109.479	3.85145
$809$	−37.3781	−1.31414	−0.657072	−	0.753828i	$-0.728205\pi$
$809$	−37.3781	−1.31414	−0.657072	+	0.753828i	$0.728205\pi$
$810$	16.7290	0.587798
$811$	15.4022	0.540844	0.270422	−	0.962742i	$-0.412837\pi$
$811$	15.4022	0.540844	0.270422	+	0.962742i	$0.412837\pi$
$812$	21.2754	0.746619
$813$	5.62308	0.197210
$814$	−2.91841	−0.102290
$815$	2.24790	0.0787404
$816$	−2.29160	−0.0802221
$817$	31.4577	1.10056
$818$	30.1966	1.05580
$819$	−70.2513	−2.45478
$820$	15.0087	0.524125
$821$	−21.4154	−0.747401	−0.373701	−	0.927549i	$-0.621911\pi$
$821$	−21.4154	−0.747401	−0.373701	+	0.927549i	$0.621911\pi$
$822$	−11.3212	−0.394873
$823$	4.06262	0.141614	0.0708071	−	0.997490i	$-0.477443\pi$
$823$	4.06262	0.141614	0.0708071	+	0.997490i	$0.477443\pi$
$824$	−19.6689	−0.685199
$825$	−1.92922	−0.0671669
$826$	88.0135	3.06238
$827$	2.78910	0.0969864	0.0484932	−	0.998824i	$-0.484558\pi$
$827$	2.78910	0.0969864	0.0484932	+	0.998824i	$0.484558\pi$
$828$	−45.0080	−1.56414
$829$	−48.2172	−1.67465	−0.837327	−	0.546702i	$-0.815883\pi$
$829$	−48.2172	−1.67465	−0.837327	+	0.546702i	$0.815883\pi$
$830$	21.1752	0.735003
$831$	−5.65246	−0.196082
$832$	5.45336	0.189061
$833$	−18.7679	−0.650270
$834$	−0.723701	−0.0250597
$835$	−10.2879	−0.356029
$836$	−55.9172	−1.93394
$837$	−4.54902	−0.157237
$838$	−22.5101	−0.777600
$839$	17.7255	0.611952	0.305976	−	0.952039i	$-0.401017\pi$
$839$	17.7255	0.611952	0.305976	+	0.952039i	$0.401017\pi$
$840$	−6.74093	−0.232584
$841$	1.00000	0.0344828
$842$	−59.9363	−2.06554
$843$	−1.40137	−0.0482657
$844$	−22.0643	−0.759484
$845$	9.74492	0.335236
$846$	−56.2215	−1.93294
$847$	41.2012	1.41569
$848$	10.9437	0.375809
$849$	6.91265	0.237241
$850$	13.0264	0.446803
$851$	−2.57734	−0.0883502
$852$	−5.60507	−0.192027
$853$	−14.3916	−0.492760	−0.246380	−	0.969173i	$-0.579241\pi$
$853$	−14.3916	−0.492760	−0.246380	+	0.969173i	$0.579241\pi$
$854$	149.512	5.11620
$855$	18.8961	0.646232
$856$	−63.7323	−2.17832
$857$	−13.0574	−0.446031	−0.223016	−	0.974815i	$-0.571590\pi$
$857$	−13.0574	−0.446031	−0.223016	+	0.974815i	$0.571590\pi$
$858$	−5.63360	−0.192328
$859$	40.9730	1.39798	0.698990	−	0.715132i	$-0.253633\pi$
$859$	40.9730	1.39798	0.698990	+	0.715132i	$0.253633\pi$
$860$	−13.6923	−0.466904
$861$	−5.79814	−0.197600
$862$	43.1729	1.47048
$863$	24.0975	0.820289	0.410145	−	0.912020i	$-0.365478\pi$
$863$	24.0975	0.820289	0.410145	+	0.912020i	$0.365478\pi$
$864$	−8.36835	−0.284697
$865$	−16.9192	−0.575271
$866$	48.6663	1.65375
$867$	−4.45370	−0.151256
$868$	−57.3397	−1.94624
$869$	−4.04168	−0.137105
$870$	−0.576547	−0.0195468
$871$	−32.3682	−1.09675
$872$	−70.3260	−2.38154
$873$	−6.81487	−0.230648
$874$	−71.6264	−2.42280
$875$	35.7512	1.20861
$876$	19.1031	0.645436
$877$	5.67715	0.191704	0.0958518	−	0.995396i	$-0.469443\pi$
$877$	5.67715	0.191704	0.0958518	+	0.995396i	$0.469443\pi$
$878$	−48.8267	−1.64782
$879$	−5.13410	−0.173169
$880$	8.43692	0.284409
$881$	−3.40518	−0.114723	−0.0573617	−	0.998353i	$-0.518269\pi$
$881$	−3.40518	−0.114723	−0.0573617	+	0.998353i	$0.518269\pi$
$882$	−118.217	−3.98057
$883$	52.0600	1.75196	0.875979	−	0.482349i	$-0.160216\pi$
$883$	52.0600	1.75196	0.875979	+	0.482349i	$0.160216\pi$
$884$	26.2257	0.882067
$885$	−1.64439	−0.0552756
$886$	−57.2112	−1.92205
$887$	26.9795	0.905885	0.452942	−	0.891540i	$-0.350374\pi$
$887$	26.9795	0.905885	0.452942	+	0.891540i	$0.350374\pi$
$888$	−1.31040	−0.0439742
$889$	46.3821	1.55561
$890$	7.68616	0.257641
$891$	12.8233	0.429598
$892$	81.9623	2.74430
$893$	−61.6856	−2.06423
$894$	7.57654	0.253397
$895$	−10.5680	−0.353251
$896$	60.7155	2.02836
$897$	−4.97522	−0.166118
$898$	55.0172	1.83595
$899$	−2.69512	−0.0898873
$900$	56.5701	1.88567
$901$	−1.88310	−0.0627350
$902$	16.6869	0.555612
$903$	5.28961	0.176027
$904$	−73.7409	−2.45259
$905$	15.1362	0.503145
$906$	−2.31233	−0.0768221
$907$	40.4906	1.34447	0.672235	−	0.740338i	$-0.265335\pi$
$907$	40.4906	1.34447	0.672235	+	0.740338i	$0.265335\pi$
$908$	−65.6918	−2.18006
$909$	−51.6034	−1.71158
$910$	48.6618	1.61312
$911$	10.0305	0.332325	0.166162	−	0.986098i	$-0.446862\pi$
$911$	10.0305	0.332325	0.166162	+	0.986098i	$0.446862\pi$
$912$	−15.8374	−0.524428
$913$	16.2315	0.537185
$914$	−60.3466	−1.99609
$915$	−2.79339	−0.0923467
$916$	−89.3177	−2.95114
$917$	−35.0199	−1.15646
$918$	5.03673	0.166237
$919$	−50.0023	−1.64942	−0.824712	−	0.565553i	$-0.808663\pi$
$919$	−50.0023	−1.64942	−0.824712	+	0.565553i	$0.808663\pi$
$920$	17.1330	0.564857
$921$	−3.81674	−0.125766
$922$	−46.2280	−1.52244
$923$	22.2361	0.731909
$924$	−9.40248	−0.309319
$925$	3.23943	0.106512
$926$	8.89861	0.292426
$927$	9.27106	0.304501
$928$	−4.95792	−0.162752
$929$	−40.1577	−1.31753	−0.658765	−	0.752349i	$-0.728921\pi$
$929$	−40.1577	−1.31753	−0.658765	+	0.752349i	$0.728921\pi$
$930$	1.55386	0.0509532
$931$	−129.706	−4.25095
$932$	60.7075	1.98854
$933$	−4.09570	−0.134087
$934$	−12.6987	−0.415516
$935$	−1.45175	−0.0474773
$936$	90.7819	2.96730
$937$	−15.2280	−0.497476	−0.248738	−	0.968571i	$-0.580016\pi$
$937$	−15.2280	−0.497476	−0.248738	+	0.968571i	$0.580016\pi$
$938$	−78.3568	−2.55844
$939$	−7.16991	−0.233981
$940$	26.8494	0.875730
$941$	−40.3162	−1.31427	−0.657135	−	0.753773i	$-0.728232\pi$
$941$	−40.3162	−1.31427	−0.657135	+	0.753773i	$0.728232\pi$
$942$	11.2170	0.365470
$943$	14.7367	0.479893
$944$	−49.4620	−1.60985
$945$	6.44329	0.209600
$946$	−15.2233	−0.494954
$947$	−35.7960	−1.16321	−0.581607	−	0.813470i	$-0.697576\pi$
$947$	−35.7960	−1.16321	−0.581607	+	0.813470i	$0.697576\pi$
$948$	−3.30227	−0.107253
$949$	−75.7847	−2.46008
$950$	90.0265	2.92085
$951$	−1.29669	−0.0420480
$952$	34.8895	1.13077
$953$	28.1088	0.910534	0.455267	−	0.890355i	$-0.349544\pi$
$953$	28.1088	0.910534	0.455267	+	0.890355i	$0.349544\pi$
$954$	−11.8614	−0.384027
$955$	1.51809	0.0491242
$956$	−14.9737	−0.484283
$957$	−0.441942	−0.0142860
$958$	−13.4250	−0.433741
$959$	74.9594	2.42056
$960$	−0.246649	−0.00796055
$961$	−23.7363	−0.765688
$962$	9.45961	0.304990
$963$	30.0406	0.968044
$964$	−72.3335	−2.32971
$965$	−11.7916	−0.379586
$966$	−12.0440	−0.387509
$967$	7.92826	0.254956	0.127478	−	0.991841i	$-0.459312\pi$
$967$	7.92826	0.254956	0.127478	+	0.991841i	$0.459312\pi$
$968$	−53.2420	−1.71126
$969$	2.72516	0.0875446
$970$	4.72054	0.151567
$971$	−26.3203	−0.844659	−0.422329	−	0.906442i	$-0.638787\pi$
$971$	−26.3203	−0.844659	−0.422329	+	0.906442i	$0.638787\pi$
$972$	32.9599	1.05719
$973$	4.79173	0.153616
$974$	100.218	3.21120
$975$	6.25330	0.200266
$976$	−84.0230	−2.68951
$977$	48.9090	1.56474	0.782369	−	0.622816i	$-0.214011\pi$
$977$	48.9090	1.56474	0.782369	+	0.622816i	$0.214011\pi$
$978$	2.04202	0.0652965
$979$	5.89169	0.188299
$980$	56.4561	1.80342
$981$	33.1486	1.05835
$982$	13.2707	0.423486
$983$	51.0295	1.62759	0.813793	−	0.581154i	$-0.197399\pi$
$983$	51.0295	1.62759	0.813793	+	0.581154i	$0.197399\pi$
$984$	7.49261	0.238856
$985$	−2.21795	−0.0706697
$986$	2.98407	0.0950322
$987$	−10.3724	−0.330158
$988$	181.248	5.76625
$989$	−13.4442	−0.427501
$990$	−9.14440	−0.290628
$991$	−0.670377	−0.0212952	−0.0106476	−	0.999943i	$-0.503389\pi$
$991$	−0.670377	−0.0212952	−0.0106476	+	0.999943i	$0.503389\pi$
$992$	13.3622	0.424250
$993$	0.483097	0.0153306
$994$	53.8291	1.70735
$995$	−5.08161	−0.161098
$996$	13.2620	0.420223
$997$	6.41044	0.203021	0.101510	−	0.994834i	$-0.467632\pi$
$997$	6.41044	0.203021	0.101510	+	0.994834i	$0.467632\pi$
$998$	24.9943	0.791182
$999$	1.25254	0.0396287

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.c.1.59	✓	61

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.c.1.59	✓	61	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)

\(f(q)\)	\(=\)	\(q+2.53772 q^{2} +0.285178 q^{3} +4.44002 q^{4} +0.796665 q^{5} +0.723701 q^{6} -4.79173 q^{7} +6.19208 q^{8} -2.91867 q^{9} +O(q^{10})\)	\(q+2.53772 q^{2} +0.285178 q^{3} +4.44002 q^{4} +0.796665 q^{5} +0.723701 q^{6} -4.79173 q^{7} +6.19208 q^{8} -2.91867 q^{9} +2.02171 q^{10} +1.54971 q^{11} +1.26619 q^{12} -5.02316 q^{13} -12.1601 q^{14} +0.227191 q^{15} +6.83373 q^{16} -1.17589 q^{17} -7.40677 q^{18} -8.12663 q^{19} +3.53721 q^{20} -1.36649 q^{21} +3.93273 q^{22} +3.47312 q^{23} +1.76584 q^{24} -4.36532 q^{25} -12.7474 q^{26} -1.68787 q^{27} -21.2754 q^{28} -1.00000 q^{29} +0.576547 q^{30} +2.69512 q^{31} +4.95792 q^{32} +0.441942 q^{33} -2.98407 q^{34} -3.81740 q^{35} -12.9590 q^{36} -0.742083 q^{37} -20.6231 q^{38} -1.43249 q^{39} +4.93302 q^{40} +4.24308 q^{41} -3.46778 q^{42} -3.87094 q^{43} +6.88074 q^{44} -2.32521 q^{45} +8.81380 q^{46} +7.59056 q^{47} +1.94883 q^{48} +15.9606 q^{49} -11.0780 q^{50} -0.335337 q^{51} -22.3029 q^{52} +1.60143 q^{53} -4.28335 q^{54} +1.23460 q^{55} -29.6708 q^{56} -2.31753 q^{57} -2.53772 q^{58} -7.23792 q^{59} +1.00873 q^{60} -12.2953 q^{61} +6.83946 q^{62} +13.9855 q^{63} -1.08564 q^{64} -4.00178 q^{65} +1.12153 q^{66} +6.44378 q^{67} -5.22096 q^{68} +0.990455 q^{69} -9.68750 q^{70} -4.42671 q^{71} -18.0727 q^{72} +15.0871 q^{73} -1.88320 q^{74} -1.24489 q^{75} -36.0824 q^{76} -7.42578 q^{77} -3.63526 q^{78} -2.60803 q^{79} +5.44420 q^{80} +8.27468 q^{81} +10.7677 q^{82} +10.4739 q^{83} -6.06725 q^{84} -0.936788 q^{85} -9.82336 q^{86} -0.285178 q^{87} +9.59593 q^{88} +3.80181 q^{89} -5.90072 q^{90} +24.0696 q^{91} +15.4207 q^{92} +0.768588 q^{93} +19.2627 q^{94} -6.47420 q^{95} +1.41389 q^{96} +2.33492 q^{97} +40.5036 q^{98} -4.52309 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9}+O(q^{10}) \) 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9	\( 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9} - 16 q^{10} - 3 q^{11} - 18 q^{12} - 28 q^{13} - 14 q^{14} - 12 q^{15} + 11 q^{16} - 21 q^{17} - 17 q^{18} - 36 q^{19} - 16 q^{20} - 12 q^{21} - 42 q^{22} - 15 q^{23} - 28 q^{24} - 16 q^{25} - 13 q^{26} - 10 q^{27} - 25 q^{28} - 61 q^{29} - 12 q^{30} - 18 q^{31} - 3 q^{32} - 42 q^{33} - 22 q^{34} - 29 q^{35} - 38 q^{36} - 30 q^{37} - 27 q^{38} - 31 q^{39} - 22 q^{40} - 28 q^{41} - 9 q^{42} - 58 q^{43} - 2 q^{44} - 31 q^{45} - 40 q^{46} - 6 q^{47} - 37 q^{48} - 37 q^{49} - 15 q^{50} - 44 q^{51} - 43 q^{52} - 27 q^{53} - 18 q^{54} - 38 q^{55} - 22 q^{56} - 50 q^{57} + q^{58} - 24 q^{59} + 6 q^{60} - 76 q^{61} - 17 q^{62} - 6 q^{63} - 60 q^{64} - 65 q^{65} - 7 q^{66} - 45 q^{67} - 31 q^{68} - 16 q^{69} - 48 q^{70} - 28 q^{71} - 40 q^{72} - 50 q^{73} - 17 q^{74} - 35 q^{75} - 100 q^{76} + q^{77} - 6 q^{78} - 66 q^{79} - 10 q^{80} - 63 q^{81} - 5 q^{82} - 9 q^{83} - 24 q^{84} - 77 q^{85} + 29 q^{86} + 4 q^{87} - 62 q^{88} - 30 q^{89} + 50 q^{90} - 52 q^{91} - 53 q^{92} - 42 q^{93} - 92 q^{94} - 20 q^{95} - 47 q^{96} - 34 q^{97} + 36 q^{98} - 29 q^{99}+O(q^{100}) \) 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9 - 16 * q^10 - 3 * q^11 - 18 * q^12 - 28 * q^13 - 14 * q^14 - 12 * q^15 + 11 * q^16 - 21 * q^17 - 17 * q^18 - 36 * q^19 - 16 * q^20 - 12 * q^21 - 42 * q^22 - 15 * q^23 - 28 * q^24 - 16 * q^25 - 13 * q^26 - 10 * q^27 - 25 * q^28 - 61 * q^29 - 12 * q^30 - 18 * q^31 - 3 * q^32 - 42 * q^33 - 22 * q^34 - 29 * q^35 - 38 * q^36 - 30 * q^37 - 27 * q^38 - 31 * q^39 - 22 * q^40 - 28 * q^41 - 9 * q^42 - 58 * q^43 - 2 * q^44 - 31 * q^45 - 40 * q^46 - 6 * q^47 - 37 * q^48 - 37 * q^49 - 15 * q^50 - 44 * q^51 - 43 * q^52 - 27 * q^53 - 18 * q^54 - 38 * q^55 - 22 * q^56 - 50 * q^57 + q^58 - 24 * q^59 + 6 * q^60 - 76 * q^61 - 17 * q^62 - 6 * q^63 - 60 * q^64 - 65 * q^65 - 7 * q^66 - 45 * q^67 - 31 * q^68 - 16 * q^69 - 48 * q^70 - 28 * q^71 - 40 * q^72 - 50 * q^73 - 17 * q^74 - 35 * q^75 - 100 * q^76 + q^77 - 6 * q^78 - 66 * q^79 - 10 * q^80 - 63 * q^81 - 5 * q^82 - 9 * q^83 - 24 * q^84 - 77 * q^85 + 29 * q^86 + 4 * q^87 - 62 * q^88 - 30 * q^89 + 50 * q^90 - 52 * q^91 - 53 * q^92 - 42 * q^93 - 92 * q^94 - 20 * q^95 - 47 * q^96 - 34 * q^97 + 36 * q^98 - 29 * q^99

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