LMFDB - Embedded newform 4031.2.a.c.1.53

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			1.53
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)

$f(q)$	$=$	$q+2.03681 q^{2} -0.170234 q^{3} +2.14858 q^{4} +1.50583 q^{5} -0.346735 q^{6} -1.01284 q^{7} +0.302638 q^{8} -2.97102 q^{9} +O(q^{10})$	\(q+2.03681 q^{2} -0.170234 q^{3} +2.14858 q^{4} +1.50583 q^{5} -0.346735 q^{6} -1.01284 q^{7} +0.302638 q^{8} -2.97102 q^{9} +3.06709 q^{10} +2.43446 q^{11} -0.365763 q^{12} +0.0345133 q^{13} -2.06297 q^{14} -0.256345 q^{15} -3.68075 q^{16} -4.92118 q^{17} -6.05140 q^{18} -3.12788 q^{19} +3.23541 q^{20} +0.172421 q^{21} +4.95852 q^{22} -8.28451 q^{23} -0.0515195 q^{24} -2.73247 q^{25} +0.0702969 q^{26} +1.01647 q^{27} -2.17618 q^{28} -1.00000 q^{29} -0.522124 q^{30} +9.68585 q^{31} -8.10226 q^{32} -0.414428 q^{33} -10.0235 q^{34} -1.52517 q^{35} -6.38349 q^{36} +1.73158 q^{37} -6.37089 q^{38} -0.00587535 q^{39} +0.455723 q^{40} -7.33312 q^{41} +0.351188 q^{42} -1.00862 q^{43} +5.23064 q^{44} -4.47386 q^{45} -16.8740 q^{46} -10.4452 q^{47} +0.626591 q^{48} -5.97415 q^{49} -5.56551 q^{50} +0.837753 q^{51} +0.0741547 q^{52} +10.4561 q^{53} +2.07036 q^{54} +3.66588 q^{55} -0.306526 q^{56} +0.532472 q^{57} -2.03681 q^{58} +1.45628 q^{59} -0.550778 q^{60} +6.62243 q^{61} +19.7282 q^{62} +3.00918 q^{63} -9.14124 q^{64} +0.0519712 q^{65} -0.844110 q^{66} -1.04793 q^{67} -10.5736 q^{68} +1.41031 q^{69} -3.10648 q^{70} +6.89273 q^{71} -0.899145 q^{72} +1.40174 q^{73} +3.52690 q^{74} +0.465160 q^{75} -6.72051 q^{76} -2.46572 q^{77} -0.0119670 q^{78} -11.9222 q^{79} -5.54260 q^{80} +8.74002 q^{81} -14.9361 q^{82} +1.87341 q^{83} +0.370461 q^{84} -7.41047 q^{85} -2.05437 q^{86} +0.170234 q^{87} +0.736760 q^{88} +10.2737 q^{89} -9.11239 q^{90} -0.0349566 q^{91} -17.8000 q^{92} -1.64886 q^{93} -21.2748 q^{94} -4.71006 q^{95} +1.37928 q^{96} -12.4558 q^{97} -12.1682 q^{98} -7.23282 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.03681	1.44024	0.720120	−	0.693849i	$-0.244087\pi$
$2$	2.03681	1.44024	0.720120	+	0.693849i	$0.244087\pi$
$3$	−0.170234	−0.0982849	−0.0491424	−	0.998792i	$-0.515649\pi$
$3$	−0.170234	−0.0982849	−0.0491424	+	0.998792i	$0.515649\pi$
$4$	2.14858	1.07429
$5$	1.50583	0.673429	0.336714	−	0.941607i	$-0.390684\pi$
$5$	1.50583	0.673429	0.336714	+	0.941607i	$0.390684\pi$
$6$	−0.346735	−0.141554
$7$	−1.01284	−0.382819	−0.191409	−	0.981510i	$-0.561306\pi$
$7$	−1.01284	−0.382819	−0.191409	+	0.981510i	$0.561306\pi$
$8$	0.302638	0.106999
$9$	−2.97102	−0.990340
$10$	3.06709	0.969900
$11$	2.43446	0.734016	0.367008	−	0.930218i	$-0.380382\pi$
$11$	2.43446	0.734016	0.367008	+	0.930218i	$0.380382\pi$
$12$	−0.365763	−0.105587
$13$	0.0345133	0.00957226	0.00478613	−	0.999989i	$-0.498477\pi$
$13$	0.0345133	0.00957226	0.00478613	+	0.999989i	$0.498477\pi$
$14$	−2.06297	−0.551351
$15$	−0.256345	−0.0661879
$16$	−3.68075	−0.920188
$17$	−4.92118	−1.19356	−0.596780	−	0.802405i	$-0.703554\pi$
$17$	−4.92118	−1.19356	−0.596780	+	0.802405i	$0.703554\pi$
$18$	−6.05140	−1.42633
$19$	−3.12788	−0.717584	−0.358792	−	0.933417i	$-0.616811\pi$
$19$	−3.12788	−0.717584	−0.358792	+	0.933417i	$0.616811\pi$
$20$	3.23541	0.723460
$21$	0.172421	0.0376253
$22$	4.95852	1.05716
$23$	−8.28451	−1.72744	−0.863720	−	0.503972i	$-0.831872\pi$
$23$	−8.28451	−1.72744	−0.863720	+	0.503972i	$0.831872\pi$
$24$	−0.0515195	−0.0105164
$25$	−2.73247	−0.546494
$26$	0.0702969	0.0137864
$27$	1.01647	0.195620
$28$	−2.17618	−0.411260
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−0.522124	−0.0953264
$31$	9.68585	1.73963	0.869815	−	0.493379i	$-0.164238\pi$
$31$	9.68585	1.73963	0.869815	+	0.493379i	$0.164238\pi$
$32$	−8.10226	−1.43229
$33$	−0.414428	−0.0721427
$34$	−10.0235	−1.71901
$35$	−1.52517	−0.257801
$36$	−6.38349	−1.06391
$37$	1.73158	0.284670	0.142335	−	0.989819i	$-0.454539\pi$
$37$	1.73158	0.284670	0.142335	+	0.989819i	$0.454539\pi$
$38$	−6.37089	−1.03349
$39$	−0.00587535	−0.000940809 0
$40$	0.455723	0.0720561
$41$	−7.33312	−1.14524	−0.572620	−	0.819821i	$-0.694073\pi$
$41$	−7.33312	−1.14524	−0.572620	+	0.819821i	$0.694073\pi$
$42$	0.351188	0.0541895
$43$	−1.00862	−0.153813	−0.0769067	−	0.997038i	$-0.524504\pi$
$43$	−1.00862	−0.153813	−0.0769067	+	0.997038i	$0.524504\pi$
$44$	5.23064	0.788548
$45$	−4.47386	−0.666924
$46$	−16.8740	−2.48793
$47$	−10.4452	−1.52358	−0.761791	−	0.647822i	$-0.775680\pi$
$47$	−10.4452	−1.52358	−0.761791	+	0.647822i	$0.775680\pi$
$48$	0.626591	0.0904406
$49$	−5.97415	−0.853450
$50$	−5.56551	−0.787082
$51$	0.837753	0.117309
$52$	0.0741547	0.0102834
$53$	10.4561	1.43626	0.718130	−	0.695909i	$-0.244998\pi$
$53$	10.4561	1.43626	0.718130	+	0.695909i	$0.244998\pi$
$54$	2.07036	0.281740
$55$	3.66588	0.494308
$56$	−0.306526	−0.0409612
$57$	0.532472	0.0705277
$58$	−2.03681	−0.267446
$59$	1.45628	0.189592	0.0947959	−	0.995497i	$-0.469780\pi$
$59$	1.45628	0.189592	0.0947959	+	0.995497i	$0.469780\pi$
$60$	−0.550778	−0.0711051
$61$	6.62243	0.847916	0.423958	−	0.905682i	$-0.360640\pi$
$61$	6.62243	0.847916	0.423958	+	0.905682i	$0.360640\pi$
$62$	19.7282	2.50548
$63$	3.00918	0.379121
$64$	−9.14124	−1.14266
$65$	0.0519712	0.00644624
$66$	−0.844110	−0.103903
$67$	−1.04793	−0.128026	−0.0640128	−	0.997949i	$-0.520390\pi$
$67$	−1.04793	−0.128026	−0.0640128	+	0.997949i	$0.520390\pi$
$68$	−10.5736	−1.28223
$69$	1.41031	0.169781
$70$	−3.10648	−0.371296
$71$	6.89273	0.818016	0.409008	−	0.912531i	$-0.365875\pi$
$71$	6.89273	0.818016	0.409008	+	0.912531i	$0.365875\pi$
$72$	−0.899145	−0.105965
$73$	1.40174	0.164062	0.0820308	−	0.996630i	$-0.473859\pi$
$73$	1.40174	0.164062	0.0820308	+	0.996630i	$0.473859\pi$
$74$	3.52690	0.409994
$75$	0.465160	0.0537120
$76$	−6.72051	−0.770896
$77$	−2.46572	−0.280995
$78$	−0.0119670	−0.00135499
$79$	−11.9222	−1.34136	−0.670679	−	0.741748i	$-0.733997\pi$
$79$	−11.9222	−1.34136	−0.670679	+	0.741748i	$0.733997\pi$
$80$	−5.54260	−0.619681
$81$	8.74002	0.971114
$82$	−14.9361	−1.64942
$83$	1.87341	0.205634	0.102817	−	0.994700i	$-0.467214\pi$
$83$	1.87341	0.205634	0.102817	+	0.994700i	$0.467214\pi$
$84$	0.370461	0.0404206
$85$	−7.41047	−0.803778
$86$	−2.05437	−0.221528
$87$	0.170234	0.0182510
$88$	0.736760	0.0785389
$89$	10.2737	1.08901	0.544505	−	0.838757i	$-0.316717\pi$
$89$	10.2737	1.08901	0.544505	+	0.838757i	$0.316717\pi$
$90$	−9.11239	−0.960530
$91$	−0.0349566	−0.00366444
$92$	−17.8000	−1.85578
$93$	−1.64886	−0.170979
$94$	−21.2748	−2.19433
$95$	−4.71006	−0.483242
$96$	1.37928	0.140773
$97$	−12.4558	−1.26470	−0.632349	−	0.774683i	$-0.717909\pi$
$97$	−12.4558	−1.26470	−0.632349	+	0.774683i	$0.717909\pi$
$98$	−12.1682	−1.22917
$99$	−7.23282	−0.726926
$100$	−5.87094	−0.587094
$101$	−7.53128	−0.749391	−0.374695	−	0.927148i	$-0.622253\pi$
$101$	−7.53128	−0.749391	−0.374695	+	0.927148i	$0.622253\pi$
$102$	1.70634	0.168953
$103$	−0.367942	−0.0362544	−0.0181272	−	0.999836i	$-0.505770\pi$
$103$	−0.367942	−0.0362544	−0.0181272	+	0.999836i	$0.505770\pi$
$104$	0.0104450	0.00102422
$105$	0.259637	0.0253380
$106$	21.2971	2.06856
$107$	4.97793	0.481235	0.240617	−	0.970620i	$-0.422650\pi$
$107$	4.97793	0.481235	0.240617	+	0.970620i	$0.422650\pi$
$108$	2.18398	0.210153
$109$	2.76330	0.264676	0.132338	−	0.991205i	$-0.457752\pi$
$109$	2.76330	0.264676	0.132338	+	0.991205i	$0.457752\pi$
$110$	7.46670	0.711922
$111$	−0.294775	−0.0279788
$112$	3.72803	0.352266
$113$	13.8124	1.29936	0.649679	−	0.760209i	$-0.274903\pi$
$113$	13.8124	1.29936	0.649679	+	0.760209i	$0.274903\pi$
$114$	1.08454	0.101577
$115$	−12.4751	−1.16331
$116$	−2.14858	−0.199491
$117$	−0.102540	−0.00947980
$118$	2.96617	0.273058
$119$	4.98438	0.456918
$120$	−0.0775797	−0.00708203
$121$	−5.07342	−0.461220
$122$	13.4886	1.22120
$123$	1.24835	0.112560
$124$	20.8109	1.86887
$125$	−11.6438	−1.04145
$126$	6.12912	0.546025
$127$	−11.4209	−1.01344	−0.506719	−	0.862111i	$-0.669142\pi$
$127$	−11.4209	−1.01344	−0.506719	+	0.862111i	$0.669142\pi$
$128$	−2.41443	−0.213407
$129$	0.171702	0.0151175
$130$	0.105855	0.00928413
$131$	−11.2474	−0.982686	−0.491343	−	0.870966i	$-0.663494\pi$
$131$	−11.2474	−0.982686	−0.491343	+	0.870966i	$0.663494\pi$
$132$	−0.890434	−0.0775023
$133$	3.16805	0.274705
$134$	−2.13444	−0.184388
$135$	1.53064	0.131736
$136$	−1.48934	−0.127710
$137$	8.48412	0.724847	0.362424	−	0.932013i	$-0.381949\pi$
$137$	8.48412	0.724847	0.362424	+	0.932013i	$0.381949\pi$
$138$	2.87253	0.244526
$139$	−1.00000	−0.0848189
$139$	−1.00000	−0.0848189
$140$	−3.27696	−0.276954
$141$	1.77812	0.149745
$142$	14.0392	1.17814
$143$	0.0840211	0.00702620
$144$	10.9356	0.911299
$145$	−1.50583	−0.125053
$146$	2.85508	0.236288
$147$	1.01701	0.0838812
$148$	3.72045	0.305819
$149$	15.4003	1.26164	0.630821	−	0.775928i	$-0.282718\pi$
$149$	15.4003	1.26164	0.630821	+	0.775928i	$0.282718\pi$
$150$	0.947441	0.0773582
$151$	−9.56215	−0.778157	−0.389078	−	0.921205i	$-0.627206\pi$
$151$	−9.56215	−0.778157	−0.389078	+	0.921205i	$0.627206\pi$
$152$	−0.946616	−0.0767807
$153$	14.6209	1.18203
$154$	−5.02220	−0.404701
$155$	14.5853	1.17152
$156$	−0.0126237	−0.00101070
$157$	7.35152	0.586715	0.293358	−	0.956003i	$-0.405227\pi$
$157$	7.35152	0.586715	0.293358	+	0.956003i	$0.405227\pi$
$158$	−24.2833	−1.93188
$159$	−1.77999	−0.141163
$160$	−12.2007	−0.964546
$161$	8.39092	0.661297
$162$	17.8017	1.39864
$163$	−6.77419	−0.530595	−0.265298	−	0.964167i	$-0.585470\pi$
$163$	−6.77419	−0.530595	−0.265298	+	0.964167i	$0.585470\pi$
$164$	−15.7558	−1.23032
$165$	−0.624059	−0.0485830
$166$	3.81578	0.296162
$167$	13.5614	1.04941	0.524706	−	0.851283i	$-0.324175\pi$
$167$	13.5614	1.04941	0.524706	+	0.851283i	$0.324175\pi$
$168$	0.0521812	0.00402587
$169$	−12.9988	−0.999908
$170$	−15.0937	−1.15763
$171$	9.29299	0.710653
$172$	−2.16711	−0.165241
$173$	−2.07601	−0.157836	−0.0789181	−	0.996881i	$-0.525147\pi$
$173$	−2.07601	−0.157836	−0.0789181	+	0.996881i	$0.525147\pi$
$174$	0.346735	0.0262859
$175$	2.76756	0.209208
$176$	−8.96063	−0.675433
$177$	−0.247909	−0.0186340
$178$	20.9256	1.56844
$179$	−21.1937	−1.58409	−0.792045	−	0.610463i	$-0.790983\pi$
$179$	−21.1937	−1.58409	−0.792045	+	0.610463i	$0.790983\pi$
$180$	−9.61247	−0.716471
$181$	−18.4484	−1.37126	−0.685628	−	0.727952i	$-0.740472\pi$
$181$	−18.4484	−1.37126	−0.685628	+	0.727952i	$0.740472\pi$
$182$	−0.0711998	−0.00527768
$183$	−1.12737	−0.0833373
$184$	−2.50721	−0.184834
$185$	2.60747	0.191705
$186$	−3.35842	−0.246251
$187$	−11.9804	−0.876093
$188$	−22.4423	−1.63677
$189$	−1.02953	−0.0748872
$190$	−9.59349	−0.695985
$191$	4.42005	0.319824	0.159912	−	0.987131i	$-0.448879\pi$
$191$	4.42005	0.319824	0.159912	+	0.987131i	$0.448879\pi$
$192$	1.55615	0.112306
$193$	24.2726	1.74718	0.873588	−	0.486666i	$-0.161787\pi$
$193$	24.2726	1.74718	0.873588	+	0.486666i	$0.161787\pi$
$194$	−25.3701	−1.82147
$195$	−0.00884729	−0.000633568 0
$196$	−12.8360	−0.916854
$197$	−23.5688	−1.67921	−0.839604	−	0.543199i	$-0.817213\pi$
$197$	−23.5688	−1.67921	−0.839604	+	0.543199i	$0.817213\pi$
$198$	−14.7319	−1.04695
$199$	−6.19702	−0.439295	−0.219647	−	0.975579i	$-0.570491\pi$
$199$	−6.19702	−0.439295	−0.219647	+	0.975579i	$0.570491\pi$
$200$	−0.826950	−0.0584742
$201$	0.178395	0.0125830
$202$	−15.3398	−1.07930
$203$	1.01284	0.0710877
$204$	1.79998	0.126024
$205$	−11.0424	−0.771238
$206$	−0.749426	−0.0522150
$207$	24.6135	1.71075
$208$	−0.127035	−0.00880828
$209$	−7.61468	−0.526719
$210$	0.528831	0.0364928
$211$	18.9077	1.30166	0.650829	−	0.759224i	$-0.274421\pi$
$211$	18.9077	1.30166	0.650829	+	0.759224i	$0.274421\pi$
$212$	22.4659	1.54296
$213$	−1.17338	−0.0803986
$214$	10.1391	0.693094
$215$	−1.51882	−0.103582
$216$	0.307624	0.0209311
$217$	−9.81025	−0.665963
$218$	5.62830	0.381197
$219$	−0.238625	−0.0161248
$220$	7.87646	0.531031
$221$	−0.169846	−0.0114251
$222$	−0.600400	−0.0402962
$223$	−13.3271	−0.892446	−0.446223	−	0.894922i	$-0.647231\pi$
$223$	−13.3271	−0.892446	−0.446223	+	0.894922i	$0.647231\pi$
$224$	8.20633	0.548308
$225$	8.11822	0.541214
$226$	28.1331	1.87139
$227$	9.44944	0.627182	0.313591	−	0.949558i	$-0.398468\pi$
$227$	9.44944	0.627182	0.313591	+	0.949558i	$0.398468\pi$
$228$	1.14406	0.0757674
$229$	−6.05909	−0.400396	−0.200198	−	0.979755i	$-0.564159\pi$
$229$	−6.05909	−0.400396	−0.200198	+	0.979755i	$0.564159\pi$
$230$	−25.4094	−1.67544
$231$	0.419751	0.0276176
$232$	−0.302638	−0.0198692
$233$	2.23532	0.146441	0.0732205	−	0.997316i	$-0.476672\pi$
$233$	2.23532	0.146441	0.0732205	+	0.997316i	$0.476672\pi$
$234$	−0.208854	−0.0136532
$235$	−15.7287	−1.02602
$236$	3.12895	0.203677
$237$	2.02958	0.131835
$238$	10.1522	0.658071
$239$	0.480428	0.0310763	0.0155382	−	0.999879i	$-0.495054\pi$
$239$	0.480428	0.0310763	0.0155382	+	0.999879i	$0.495054\pi$
$240$	0.943541	0.0609053
$241$	23.0219	1.48297	0.741484	−	0.670970i	$-0.234122\pi$
$241$	23.0219	1.48297	0.741484	+	0.670970i	$0.234122\pi$
$242$	−10.3336	−0.664268
$243$	−4.53727	−0.291066
$244$	14.2289	0.910909
$245$	−8.99607	−0.574738
$246$	2.54265	0.162113
$247$	−0.107953	−0.00686891
$248$	2.93131	0.186138
$249$	−0.318919	−0.0202107
$250$	−23.7162	−1.49994
$251$	−2.82288	−0.178179	−0.0890894	−	0.996024i	$-0.528396\pi$
$251$	−2.82288	−0.178179	−0.0890894	+	0.996024i	$0.528396\pi$
$252$	6.46548	0.407287
$253$	−20.1683	−1.26797
$254$	−23.2621	−1.45959
$255$	1.26152	0.0789992
$256$	13.3648	0.835298
$257$	−15.3228	−0.955810	−0.477905	−	0.878411i	$-0.658604\pi$
$257$	−15.3228	−0.955810	−0.477905	+	0.878411i	$0.658604\pi$
$258$	0.349724	0.0217729
$259$	−1.75382	−0.108977
$260$	0.111665	0.00692514
$261$	2.97102	0.183902
$262$	−22.9087	−1.41530
$263$	19.6933	1.21434	0.607170	−	0.794572i	$-0.292305\pi$
$263$	19.6933	1.21434	0.607170	+	0.794572i	$0.292305\pi$
$264$	−0.125422	−0.00771918
$265$	15.7452	0.967219
$266$	6.45271	0.395641
$267$	−1.74894	−0.107033
$268$	−2.25158	−0.137537
$269$	−21.1614	−1.29024	−0.645118	−	0.764083i	$-0.723192\pi$
$269$	−21.1614	−1.29024	−0.645118	+	0.764083i	$0.723192\pi$
$270$	3.11762	0.189732
$271$	14.9384	0.907445	0.453722	−	0.891143i	$-0.350096\pi$
$271$	14.9384	0.907445	0.453722	+	0.891143i	$0.350096\pi$
$272$	18.1136	1.09830
$273$	0.00595081	0.000360159 0
$274$	17.2805	1.04395
$275$	−6.65207	−0.401135
$276$	3.03017	0.182395
$277$	12.8538	0.772310	0.386155	−	0.922434i	$-0.373803\pi$
$277$	12.8538	0.772310	0.386155	+	0.922434i	$0.373803\pi$
$278$	−2.03681	−0.122160
$279$	−28.7768	−1.72282
$280$	−0.461576	−0.0275845
$281$	−7.39979	−0.441434	−0.220717	−	0.975338i	$-0.570840\pi$
$281$	−7.39979	−0.441434	−0.220717	+	0.975338i	$0.570840\pi$
$282$	3.62170	0.215669
$283$	5.33826	0.317327	0.158663	−	0.987333i	$-0.449282\pi$
$283$	5.33826	0.317327	0.158663	+	0.987333i	$0.449282\pi$
$284$	14.8096	0.878789
$285$	0.801814	0.0474954
$286$	0.171135	0.0101194
$287$	7.42730	0.438420
$288$	24.0720	1.41846
$289$	7.21797	0.424586
$290$	−3.06709	−0.180106
$291$	2.12041	0.124301
$292$	3.01177	0.176250
$293$	−15.6429	−0.913868	−0.456934	−	0.889501i	$-0.651052\pi$
$293$	−15.6429	−0.913868	−0.456934	+	0.889501i	$0.651052\pi$
$294$	2.07144	0.120809
$295$	2.19292	0.127677
$296$	0.524044	0.0304594
$297$	2.47456	0.143588
$298$	31.3675	1.81707
$299$	−0.285926	−0.0165355
$300$	0.999435	0.0577024
$301$	1.02158	0.0588827
$302$	−19.4763	−1.12073
$303$	1.28208	0.0736538
$304$	11.5129	0.660313
$305$	9.97228	0.571011
$306$	29.7800	1.70241
$307$	6.12509	0.349577	0.174789	−	0.984606i	$-0.444076\pi$
$307$	6.12509	0.349577	0.174789	+	0.984606i	$0.444076\pi$
$308$	−5.29782	−0.301871
$309$	0.0626363	0.00356326
$310$	29.7074	1.68727
$311$	−13.1011	−0.742893	−0.371446	−	0.928454i	$-0.621138\pi$
$311$	−13.1011	−0.742893	−0.371446	+	0.928454i	$0.621138\pi$
$312$	−0.00177811	−0.000100665 0
$313$	−14.8626	−0.840086	−0.420043	−	0.907504i	$-0.637985\pi$
$313$	−14.8626	−0.840086	−0.420043	+	0.907504i	$0.637985\pi$
$314$	14.9736	0.845011
$315$	4.53132	0.255311
$316$	−25.6160	−1.44101
$317$	−2.33451	−0.131119	−0.0655594	−	0.997849i	$-0.520883\pi$
$317$	−2.33451	−0.131119	−0.0655594	+	0.997849i	$0.520883\pi$
$318$	−3.62550	−0.203308
$319$	−2.43446	−0.136303
$320$	−13.7652	−0.769497
$321$	−0.847415	−0.0472981
$322$	17.0907	0.952426
$323$	15.3928	0.856480
$324$	18.7787	1.04326
$325$	−0.0943064	−0.00523118
$326$	−13.7977	−0.764185
$327$	−0.470408	−0.0260136
$328$	−2.21928	−0.122539
$329$	10.5793	0.583256
$330$	−1.27109	−0.0699711
$331$	15.5730	0.855972	0.427986	−	0.903785i	$-0.359223\pi$
$331$	15.5730	0.855972	0.427986	+	0.903785i	$0.359223\pi$
$332$	4.02519	0.220911
$333$	−5.14457	−0.281921
$334$	27.6220	1.51141
$335$	−1.57801	−0.0862161
$336$	−0.634639	−0.0346224
$337$	−8.40819	−0.458024	−0.229012	−	0.973424i	$-0.573549\pi$
$337$	−8.40819	−0.458024	−0.229012	+	0.973424i	$0.573549\pi$
$338$	−26.4761	−1.44011
$339$	−2.35134	−0.127707
$340$	−15.9220	−0.863493
$341$	23.5798	1.27692
$342$	18.9280	1.02351
$343$	13.1408	0.709536
$344$	−0.305248	−0.0164579
$345$	2.12369	0.114336
$346$	−4.22843	−0.227322
$347$	−5.05081	−0.271142	−0.135571	−	0.990768i	$-0.543287\pi$
$347$	−5.05081	−0.271142	−0.135571	+	0.990768i	$0.543287\pi$
$348$	0.365763	0.0196070
$349$	−22.2685	−1.19201	−0.596003	−	0.802982i	$-0.703245\pi$
$349$	−22.2685	−1.19201	−0.596003	+	0.802982i	$0.703245\pi$
$350$	5.63699	0.301310
$351$	0.0350818	0.00187253
$352$	−19.7246	−1.05132
$353$	36.4120	1.93801	0.969006	−	0.247036i	$-0.0794564\pi$
$353$	36.4120	1.93801	0.969006	+	0.247036i	$0.0794564\pi$
$354$	−0.504944	−0.0268375
$355$	10.3793	0.550876
$356$	22.0739	1.16992
$357$	−0.848513	−0.0449081
$358$	−43.1674	−2.28147
$359$	−19.8935	−1.04994	−0.524968	−	0.851122i	$-0.675923\pi$
$359$	−19.8935	−1.04994	−0.524968	+	0.851122i	$0.675923\pi$
$360$	−1.35396	−0.0713601
$361$	−9.21638	−0.485073
$362$	−37.5758	−1.97494
$363$	0.863671	0.0453310
$364$	−0.0751071	−0.00393668
$365$	2.11079	0.110484
$366$	−2.29623	−0.120026
$367$	6.54056	0.341415	0.170707	−	0.985322i	$-0.445395\pi$
$367$	6.54056	0.341415	0.170707	+	0.985322i	$0.445395\pi$
$368$	30.4932	1.58957
$369$	21.7868	1.13418
$370$	5.31092	0.276102
$371$	−10.5904	−0.549828
$372$	−3.54272	−0.183682
$373$	17.5626	0.909356	0.454678	−	0.890656i	$-0.349754\pi$
$373$	17.5626	0.909356	0.454678	+	0.890656i	$0.349754\pi$
$374$	−24.4017	−1.26178
$375$	1.98218	0.102359
$376$	−3.16111	−0.163022
$377$	−0.0345133	−0.00177752
$378$	−2.09695	−0.107856
$379$	23.1885	1.19111	0.595557	−	0.803313i	$-0.296931\pi$
$379$	23.1885	1.19111	0.595557	+	0.803313i	$0.296931\pi$
$380$	−10.1200	−0.519143
$381$	1.94422	0.0996056
$382$	9.00279	0.460623
$383$	29.6244	1.51374	0.756869	−	0.653566i	$-0.226728\pi$
$383$	29.6244	1.51374	0.756869	+	0.653566i	$0.226728\pi$
$384$	0.411018	0.0209747
$385$	−3.71297	−0.189230
$386$	49.4385	2.51635
$387$	2.99664	0.152328
$388$	−26.7624	−1.35866
$389$	−12.7698	−0.647457	−0.323729	−	0.946150i	$-0.604936\pi$
$389$	−12.7698	−0.647457	−0.323729	+	0.946150i	$0.604936\pi$
$390$	−0.0180202	−0.000912490 0
$391$	40.7695	2.06180
$392$	−1.80801	−0.0913181
$393$	1.91469	0.0965831
$394$	−48.0051	−2.41846
$395$	−17.9529	−0.903309
$396$	−15.5403	−0.780931
$397$	−7.74311	−0.388615	−0.194308	−	0.980941i	$-0.562246\pi$
$397$	−7.74311	−0.388615	−0.194308	+	0.980941i	$0.562246\pi$
$398$	−12.6221	−0.632690
$399$	−0.539311	−0.0269993
$400$	10.0575	0.502877
$401$	−10.4761	−0.523151	−0.261575	−	0.965183i	$-0.584242\pi$
$401$	−10.4761	−0.523151	−0.261575	+	0.965183i	$0.584242\pi$
$402$	0.363355	0.0181225
$403$	0.334290	0.0166522
$404$	−16.1816	−0.805065
$405$	13.1610	0.653976
$406$	2.06297	0.102383
$407$	4.21546	0.208953
$408$	0.253536	0.0125519
$409$	−4.05589	−0.200551	−0.100275	−	0.994960i	$-0.531972\pi$
$409$	−4.05589	−0.200551	−0.100275	+	0.994960i	$0.531972\pi$
$410$	−22.4913	−1.11077
$411$	−1.44429	−0.0712415
$412$	−0.790554	−0.0389478
$413$	−1.47499	−0.0725794
$414$	50.1329	2.46390
$415$	2.82105	0.138480
$416$	−0.279636	−0.0137103
$417$	0.170234	0.00833641
$418$	−15.5096	−0.758601
$419$	24.1838	1.18146	0.590728	−	0.806871i	$-0.298841\pi$
$419$	24.1838	1.18146	0.590728	+	0.806871i	$0.298841\pi$
$420$	0.557852	0.0272204
$421$	−13.8360	−0.674324	−0.337162	−	0.941447i	$-0.609467\pi$
$421$	−13.8360	−0.674324	−0.337162	+	0.941447i	$0.609467\pi$
$422$	38.5113	1.87470
$423$	31.0328	1.50887
$424$	3.16443	0.153678
$425$	13.4470	0.652273
$426$	−2.38995	−0.115793
$427$	−6.70749	−0.324598
$428$	10.6955	0.516987
$429$	−0.0143033	−0.000690569 0
$430$	−3.09354	−0.149184
$431$	22.6231	1.08972	0.544859	−	0.838528i	$-0.316583\pi$
$431$	22.6231	1.08972	0.544859	+	0.838528i	$0.316583\pi$
$432$	−3.74139	−0.180008
$433$	29.0798	1.39749	0.698744	−	0.715372i	$-0.253743\pi$
$433$	29.0798	1.39749	0.698744	+	0.715372i	$0.253743\pi$
$434$	−19.9816	−0.959147
$435$	0.256345	0.0122908
$436$	5.93718	0.284339
$437$	25.9129	1.23958
$438$	−0.486033	−0.0232236
$439$	−17.1170	−0.816952	−0.408476	−	0.912769i	$-0.633940\pi$
$439$	−17.1170	−0.816952	−0.408476	+	0.912769i	$0.633940\pi$
$440$	1.10944	0.0528904
$441$	17.7493	0.845205
$442$	−0.345943	−0.0164549
$443$	−28.8863	−1.37243	−0.686214	−	0.727400i	$-0.740729\pi$
$443$	−28.8863	−1.37243	−0.686214	+	0.727400i	$0.740729\pi$
$444$	−0.633349	−0.0300574
$445$	15.4705	0.733371
$446$	−27.1447	−1.28534
$447$	−2.62166	−0.124000
$448$	9.25865	0.437430
$449$	−17.0999	−0.806993	−0.403496	−	0.914981i	$-0.632205\pi$
$449$	−17.0999	−0.806993	−0.403496	+	0.914981i	$0.632205\pi$
$450$	16.5352	0.779479
$451$	−17.8522	−0.840625
$452$	29.6770	1.39589
$453$	1.62781	0.0764810
$454$	19.2467	0.903292
$455$	−0.0526387	−0.00246774
$456$	0.161147	0.00754638
$457$	12.6451	0.591513	0.295756	−	0.955263i	$-0.404428\pi$
$457$	12.6451	0.591513	0.295756	+	0.955263i	$0.404428\pi$
$458$	−12.3412	−0.576666
$459$	−5.00224	−0.233485
$460$	−26.8038	−1.24973
$461$	−40.1256	−1.86883	−0.934417	−	0.356181i	$-0.884079\pi$
$461$	−40.1256	−1.86883	−0.934417	+	0.356181i	$0.884079\pi$
$462$	0.854952	0.0397760
$463$	29.0763	1.35129	0.675645	−	0.737227i	$-0.263865\pi$
$463$	29.0763	1.35129	0.675645	+	0.737227i	$0.263865\pi$
$464$	3.68075	0.170875
$465$	−2.48291	−0.115142
$466$	4.55293	0.210910
$467$	36.4398	1.68623	0.843117	−	0.537730i	$-0.180718\pi$
$467$	36.4398	1.68623	0.843117	+	0.537730i	$0.180718\pi$
$468$	−0.220315	−0.0101841
$469$	1.06139	0.0490106
$470$	−32.0363	−1.47772
$471$	−1.25148	−0.0576653
$472$	0.440727	0.0202861
$473$	−2.45545	−0.112902
$474$	4.13386	0.189874
$475$	8.54683	0.392155
$476$	10.7094	0.490863
$477$	−31.0654	−1.42239
$478$	0.978540	0.0447574
$479$	−21.8916	−1.00025	−0.500127	−	0.865952i	$-0.666713\pi$
$479$	−21.8916	−1.00025	−0.500127	+	0.865952i	$0.666713\pi$
$480$	2.07697	0.0948003
$481$	0.0597626	0.00272494
$482$	46.8911	2.13583
$483$	−1.42842	−0.0649955
$484$	−10.9007	−0.495485
$485$	−18.7564	−0.851685
$486$	−9.24155	−0.419205
$487$	−39.0693	−1.77040	−0.885199	−	0.465212i	$-0.845978\pi$
$487$	−39.0693	−1.77040	−0.885199	+	0.465212i	$0.845978\pi$
$488$	2.00420	0.0907260
$489$	1.15320	0.0521495
$490$	−18.3233	−0.827760
$491$	−16.3402	−0.737423	−0.368712	−	0.929544i	$-0.620201\pi$
$491$	−16.3402	−0.737423	−0.368712	+	0.929544i	$0.620201\pi$
$492$	2.68218	0.120922
$493$	4.92118	0.221639
$494$	−0.219880	−0.00989288
$495$	−10.8914	−0.489533
$496$	−35.6512	−1.60079
$497$	−6.98126	−0.313152
$498$	−0.649577	−0.0291082
$499$	−29.7823	−1.33324	−0.666618	−	0.745399i	$-0.732259\pi$
$499$	−29.7823	−1.33324	−0.666618	+	0.745399i	$0.732259\pi$
$500$	−25.0177	−1.11883
$501$	−2.30862	−0.103141
$502$	−5.74967	−0.256620
$503$	−12.6595	−0.564457	−0.282229	−	0.959347i	$-0.591074\pi$
$503$	−12.6595	−0.564457	−0.282229	+	0.959347i	$0.591074\pi$
$504$	0.910694	0.0405655
$505$	−11.3409	−0.504661
$506$	−41.0789	−1.82618
$507$	2.21284	0.0982759
$508$	−24.5387	−1.08873
$509$	38.5431	1.70839	0.854197	−	0.519949i	$-0.174049\pi$
$509$	38.5431	1.70839	0.854197	+	0.519949i	$0.174049\pi$
$510$	2.56947	0.113778
$511$	−1.41975	−0.0628059
$512$	32.0503	1.41644
$513$	−3.17940	−0.140374
$514$	−31.2096	−1.37660
$515$	−0.554059	−0.0244147
$516$	0.368917	0.0162407
$517$	−25.4283	−1.11833
$518$	−3.57220	−0.156953
$519$	0.353408	0.0155129
$520$	0.0157285	0.000689740 0
$521$	−26.1705	−1.14655	−0.573276	−	0.819363i	$-0.694328\pi$
$521$	−26.1705	−1.14655	−0.573276	+	0.819363i	$0.694328\pi$
$522$	6.05140	0.264862
$523$	14.8280	0.648384	0.324192	−	0.945991i	$-0.394908\pi$
$523$	14.8280	0.648384	0.324192	+	0.945991i	$0.394908\pi$
$524$	−24.1659	−1.05569
$525$	−0.471134	−0.0205620
$526$	40.1114	1.74894
$527$	−47.6657	−2.07635
$528$	1.52541	0.0663848
$529$	45.6331	1.98405
$530$	32.0699	1.39303
$531$	−4.32665	−0.187760
$532$	6.80683	0.295113
$533$	−0.253090	−0.0109625
$534$	−3.56225	−0.154154
$535$	7.49593	0.324077
$536$	−0.317145	−0.0136986
$537$	3.60789	0.155692
$538$	−43.1018	−1.85825
$539$	−14.5438	−0.626446
$540$	3.28871	0.141523
$541$	−36.6923	−1.57753	−0.788764	−	0.614697i	$-0.789278\pi$
$541$	−36.6923	−1.57753	−0.788764	+	0.614697i	$0.789278\pi$
$542$	30.4267	1.30694
$543$	3.14055	0.134774
$544$	39.8727	1.70953
$545$	4.16106	0.178240
$546$	0.0121207	0.000518716 0
$547$	−13.9839	−0.597908	−0.298954	−	0.954267i	$-0.596638\pi$
$547$	−13.9839	−0.597908	−0.298954	+	0.954267i	$0.596638\pi$
$548$	18.2289	0.778698
$549$	−19.6754	−0.839725
$550$	−13.5490	−0.577731
$551$	3.12788	0.133252
$552$	0.426814	0.0181664
$553$	12.0754	0.513497
$554$	26.1807	1.11231
$555$	−0.443882	−0.0188417
$556$	−2.14858	−0.0911203
$557$	14.0581	0.595662	0.297831	−	0.954619i	$-0.403737\pi$
$557$	14.0581	0.595662	0.297831	+	0.954619i	$0.403737\pi$
$558$	−58.6129	−2.48128
$559$	−0.0348109	−0.00147234
$560$	5.61379	0.237226
$561$	2.03947	0.0861066
$562$	−15.0719	−0.635772
$563$	14.7281	0.620716	0.310358	−	0.950620i	$-0.399551\pi$
$563$	14.7281	0.620716	0.310358	+	0.950620i	$0.399551\pi$
$564$	3.82045	0.160870
$565$	20.7991	0.875025
$566$	10.8730	0.457027
$567$	−8.85228	−0.371761
$568$	2.08601	0.0875268
$569$	−29.7648	−1.24781	−0.623903	−	0.781502i	$-0.714454\pi$
$569$	−29.7648	−1.24781	−0.623903	+	0.781502i	$0.714454\pi$
$570$	1.63314	0.0684048
$571$	21.6863	0.907544	0.453772	−	0.891118i	$-0.350078\pi$
$571$	21.6863	0.907544	0.453772	+	0.891118i	$0.350078\pi$
$572$	0.180526	0.00754819
$573$	−0.752445	−0.0314338
$574$	15.1280	0.631430
$575$	22.6372	0.944035
$576$	27.1588	1.13162
$577$	16.1305	0.671520	0.335760	−	0.941948i	$-0.391007\pi$
$577$	16.1305	0.671520	0.335760	+	0.941948i	$0.391007\pi$
$578$	14.7016	0.611506
$579$	−4.13202	−0.171721
$580$	−3.23541	−0.134343
$581$	−1.89747	−0.0787205
$582$	4.31887	0.179023
$583$	25.4550	1.05424
$584$	0.424222	0.0175544
$585$	−0.154408	−0.00638397
$586$	−31.8616	−1.31619
$587$	17.0245	0.702675	0.351338	−	0.936249i	$-0.385727\pi$
$587$	17.0245	0.702675	0.351338	+	0.936249i	$0.385727\pi$
$588$	2.18512	0.0901129
$589$	−30.2961	−1.24833
$590$	4.46655	0.183885
$591$	4.01222	0.165041
$592$	−6.37353	−0.261950
$593$	−2.42773	−0.0996950	−0.0498475	−	0.998757i	$-0.515874\pi$
$593$	−2.42773	−0.0996950	−0.0498475	+	0.998757i	$0.515874\pi$
$594$	5.04020	0.206802
$595$	7.50565	0.307701
$596$	33.0889	1.35537
$597$	1.05495	0.0431760
$598$	−0.582376	−0.0238151
$599$	25.7757	1.05317	0.526584	−	0.850123i	$-0.323472\pi$
$599$	25.7757	1.05317	0.526584	+	0.850123i	$0.323472\pi$
$600$	0.140775	0.00574713
$601$	−2.48737	−0.101462	−0.0507311	−	0.998712i	$-0.516155\pi$
$601$	−2.48737	−0.101462	−0.0507311	+	0.998712i	$0.516155\pi$
$602$	2.08076	0.0848053
$603$	3.11344	0.126789
$604$	−20.5451	−0.835968
$605$	−7.63973	−0.310599
$606$	2.61136	0.106079
$607$	16.9633	0.688519	0.344259	−	0.938875i	$-0.388130\pi$
$607$	16.9633	0.688519	0.344259	+	0.938875i	$0.388130\pi$
$608$	25.3429	1.02779
$609$	−0.172421	−0.00698685
$610$	20.3116	0.822393
$611$	−0.360497	−0.0145841
$612$	31.4143	1.26985
$613$	−23.7890	−0.960829	−0.480415	−	0.877041i	$-0.659514\pi$
$613$	−23.7890	−0.960829	−0.480415	+	0.877041i	$0.659514\pi$
$614$	12.4756	0.503475
$615$	1.87980	0.0758010
$616$	−0.746223	−0.0300662
$617$	−11.6370	−0.468488	−0.234244	−	0.972178i	$-0.575262\pi$
$617$	−11.6370	−0.468488	−0.234244	+	0.972178i	$0.575262\pi$
$618$	0.127578	0.00513195
$619$	−2.10486	−0.0846015	−0.0423007	−	0.999105i	$-0.513469\pi$
$619$	−2.10486	−0.0846015	−0.0423007	+	0.999105i	$0.513469\pi$
$620$	31.3377	1.25855
$621$	−8.42098	−0.337922
$622$	−26.6843	−1.06994
$623$	−10.4057	−0.416894
$624$	0.0216257	0.000865721 0
$625$	−3.87128	−0.154851
$626$	−30.2723	−1.20993
$627$	1.29628	0.0517685
$628$	15.7954	0.630304
$629$	−8.52142	−0.339771
$630$	9.22943	0.367709
$631$	0.198793	0.00791384	0.00395692	−	0.999992i	$-0.498740\pi$
$631$	0.198793	0.00791384	0.00395692	+	0.999992i	$0.498740\pi$
$632$	−3.60813	−0.143524
$633$	−3.21874	−0.127933
$634$	−4.75494	−0.188843
$635$	−17.1979	−0.682478
$636$	−3.82447	−0.151650
$637$	−0.206187	−0.00816944
$638$	−4.95852	−0.196310
$639$	−20.4784	−0.810114
$640$	−3.63572	−0.143715
$641$	−27.5640	−1.08871	−0.544357	−	0.838853i	$-0.683226\pi$
$641$	−27.5640	−1.08871	−0.544357	+	0.838853i	$0.683226\pi$
$642$	−1.72602	−0.0681206
$643$	1.47674	0.0582369	0.0291185	−	0.999576i	$-0.490730\pi$
$643$	1.47674	0.0582369	0.0291185	+	0.999576i	$0.490730\pi$
$644$	18.0286	0.710426
$645$	0.258555	0.0101806
$646$	31.3522	1.23354
$647$	29.6733	1.16658	0.583289	−	0.812265i	$-0.301766\pi$
$647$	29.6733	1.16658	0.583289	+	0.812265i	$0.301766\pi$
$648$	2.64507	0.103908
$649$	3.54526	0.139164
$650$	−0.192084	−0.00753416
$651$	1.67004	0.0654541
$652$	−14.5549	−0.570014
$653$	−32.5454	−1.27360	−0.636800	−	0.771029i	$-0.719742\pi$
$653$	−32.5454	−1.27360	−0.636800	+	0.771029i	$0.719742\pi$
$654$	−0.958130	−0.0374659
$655$	−16.9366	−0.661769
$656$	26.9914	1.05384
$657$	−4.16461	−0.162477
$658$	21.5480	0.840029
$659$	−7.59993	−0.296051	−0.148026	−	0.988984i	$-0.547292\pi$
$659$	−7.59993	−0.296051	−0.148026	+	0.988984i	$0.547292\pi$
$660$	−1.34084	−0.0521923
$661$	−17.2837	−0.672259	−0.336129	−	0.941816i	$-0.609118\pi$
$661$	−17.2837	−0.672259	−0.336129	+	0.941816i	$0.609118\pi$
$662$	31.7193	1.23280
$663$	0.0289136	0.00112291
$664$	0.566967	0.0220026
$665$	4.77056	0.184994
$666$	−10.4785	−0.406033
$667$	8.28451	0.320778
$668$	29.1378	1.12738
$669$	2.26872	0.0877139
$670$	−3.21411	−0.124172
$671$	16.1220	0.622384
$672$	−1.39700	−0.0538904
$673$	2.08023	0.0801868	0.0400934	−	0.999196i	$-0.487234\pi$
$673$	2.08023	0.0801868	0.0400934	+	0.999196i	$0.487234\pi$
$674$	−17.1259	−0.659664
$675$	−2.77748	−0.106905
$676$	−27.9290	−1.07419
$677$	9.98093	0.383598	0.191799	−	0.981434i	$-0.438568\pi$
$677$	9.98093	0.383598	0.191799	+	0.981434i	$0.438568\pi$
$678$	−4.78922	−0.183929
$679$	12.6158	0.484151
$680$	−2.24269	−0.0860033
$681$	−1.60862	−0.0616425
$682$	48.0274	1.83907
$683$	11.7465	0.449468	0.224734	−	0.974420i	$-0.427849\pi$
$683$	11.7465	0.449468	0.224734	+	0.974420i	$0.427849\pi$
$684$	19.9668	0.763449
$685$	12.7757	0.488133
$686$	26.7652	1.02190
$687$	1.03147	0.0393529
$688$	3.71249	0.141537
$689$	0.360875	0.0137483
$690$	4.32555	0.164671
$691$	11.1562	0.424402	0.212201	−	0.977226i	$-0.431937\pi$
$691$	11.1562	0.424402	0.212201	+	0.977226i	$0.431937\pi$
$692$	−4.46048	−0.169562
$693$	7.32572	0.278281
$694$	−10.2875	−0.390510
$695$	−1.50583	−0.0571195
$696$	0.0515195	0.00195284
$697$	36.0876	1.36691
$698$	−45.3566	−1.71677
$699$	−0.380529	−0.0143929
$700$	5.94634	0.224751
$701$	3.01139	0.113739	0.0568693	−	0.998382i	$-0.481888\pi$
$701$	3.01139	0.113739	0.0568693	+	0.998382i	$0.481888\pi$
$702$	0.0714549	0.00269689
$703$	−5.41618	−0.204275
$704$	−22.2540	−0.838727
$705$	2.67756	0.100843
$706$	74.1641	2.79120
$707$	7.62801	0.286881
$708$	−0.532654	−0.0200184
$709$	47.3904	1.77978	0.889892	−	0.456170i	$-0.150779\pi$
$709$	47.3904	1.77978	0.889892	+	0.456170i	$0.150779\pi$
$710$	21.1406	0.793394
$711$	35.4212	1.32840
$712$	3.10922	0.116523
$713$	−80.2425	−3.00511
$714$	−1.72826	−0.0646784
$715$	0.126522	0.00473164
$716$	−45.5364	−1.70178
$717$	−0.0817854	−0.00305433
$718$	−40.5191	−1.51216
$719$	14.6678	0.547015	0.273508	−	0.961870i	$-0.411816\pi$
$719$	14.6678	0.547015	0.273508	+	0.961870i	$0.411816\pi$
$720$	16.4672	0.613695
$721$	0.372668	0.0138789
$722$	−18.7720	−0.698621
$723$	−3.91911	−0.145753
$724$	−39.6379	−1.47313
$725$	2.73247	0.101481
$726$	1.75913	0.0652875
$727$	−52.7706	−1.95715	−0.978576	−	0.205885i	$-0.933993\pi$
$727$	−52.7706	−1.95715	−0.978576	+	0.205885i	$0.933993\pi$
$728$	−0.0105792	−0.000392091 0
$729$	−25.4477	−0.942506
$730$	4.29928	0.159123
$731$	4.96361	0.183586
$732$	−2.42224	−0.0895286
$733$	0.253759	0.00937280	0.00468640	−	0.999989i	$-0.498508\pi$
$733$	0.253759	0.00937280	0.00468640	+	0.999989i	$0.498508\pi$
$734$	13.3219	0.491719
$735$	1.53144	0.0564880
$736$	67.1233	2.47420
$737$	−2.55115	−0.0939728
$738$	44.3756	1.63349
$739$	5.82211	0.214170	0.107085	−	0.994250i	$-0.465848\pi$
$739$	5.82211	0.214170	0.107085	+	0.994250i	$0.465848\pi$
$740$	5.60238	0.205948
$741$	0.0183774	0.000675110 0
$742$	−21.5707	−0.791884
$743$	24.0314	0.881628	0.440814	−	0.897598i	$-0.354690\pi$
$743$	24.0314	0.881628	0.440814	+	0.897598i	$0.354690\pi$
$744$	−0.499010	−0.0182946
$745$	23.1903	0.849626
$746$	35.7716	1.30969
$747$	−5.56595	−0.203647
$748$	−25.7409	−0.941180
$749$	−5.04187	−0.184226
$750$	4.03731	0.147422
$751$	−38.8198	−1.41655	−0.708277	−	0.705935i	$-0.750527\pi$
$751$	−38.8198	−1.41655	−0.708277	+	0.705935i	$0.750527\pi$
$752$	38.4460	1.40198
$753$	0.480552	0.0175123
$754$	−0.0702969	−0.00256006
$755$	−14.3990	−0.524033
$756$	−2.21203	−0.0804507
$757$	−22.5666	−0.820199	−0.410099	−	0.912041i	$-0.634506\pi$
$757$	−22.5666	−0.820199	−0.410099	+	0.912041i	$0.634506\pi$
$758$	47.2306	1.71549
$759$	3.43333	0.124622
$760$	−1.42545	−0.0517064
$761$	−19.5364	−0.708194	−0.354097	−	0.935209i	$-0.615212\pi$
$761$	−19.5364	−0.708194	−0.354097	+	0.935209i	$0.615212\pi$
$762$	3.96001	0.143456
$763$	−2.79879	−0.101323
$764$	9.49685	0.343584
$765$	22.0166	0.796014
$766$	60.3393	2.18015
$767$	0.0502611	0.00181482
$768$	−2.27514	−0.0820971
$769$	5.36285	0.193389	0.0966947	−	0.995314i	$-0.469173\pi$
$769$	5.36285	0.193389	0.0966947	+	0.995314i	$0.469173\pi$
$770$	−7.56260	−0.272537
$771$	2.60847	0.0939417
$772$	52.1516	1.87698
$773$	7.72880	0.277986	0.138993	−	0.990293i	$-0.455614\pi$
$773$	7.72880	0.277986	0.138993	+	0.990293i	$0.455614\pi$
$774$	6.10357	0.219388
$775$	−26.4663	−0.950696
$776$	−3.76962	−0.135321
$777$	0.298561	0.0107108
$778$	−26.0097	−0.932494
$779$	22.9371	0.821807
$780$	−0.0190092	−0.000680637 0
$781$	16.7800	0.600437
$782$	83.0397	2.96949
$783$	−1.01647	−0.0363258
$784$	21.9894	0.785334
$785$	11.0702	0.395111
$786$	3.89985	0.139103
$787$	−15.1172	−0.538870	−0.269435	−	0.963019i	$-0.586837\pi$
$787$	−15.1172	−0.538870	−0.269435	+	0.963019i	$0.586837\pi$
$788$	−50.6396	−1.80396
$789$	−3.35248	−0.119351
$790$	−36.5666	−1.30098
$791$	−13.9898	−0.497419
$792$	−2.18893	−0.0777802
$793$	0.228562	0.00811647
$794$	−15.7712	−0.559699
$795$	−2.68037	−0.0950630
$796$	−13.3148	−0.471931
$797$	−11.8446	−0.419558	−0.209779	−	0.977749i	$-0.567274\pi$
$797$	−11.8446	−0.419558	−0.209779	+	0.977749i	$0.567274\pi$
$798$	−1.09847	−0.0388855
$799$	51.4025	1.81849
$800$	22.1392	0.782738
$801$	−30.5234	−1.07849
$802$	−21.3378	−0.753463
$803$	3.41248	0.120424
$804$	0.383296	0.0135178
$805$	12.6353	0.445336
$806$	0.680885	0.0239832
$807$	3.60240	0.126811
$808$	−2.27926	−0.0801839
$809$	3.32161	0.116782	0.0583908	−	0.998294i	$-0.481403\pi$
$809$	3.32161	0.116782	0.0583908	+	0.998294i	$0.481403\pi$
$810$	26.8064	0.941883
$811$	−29.5808	−1.03872	−0.519361	−	0.854555i	$-0.673830\pi$
$811$	−29.5808	−1.03872	−0.519361	+	0.854555i	$0.673830\pi$
$812$	2.17618	0.0763690
$813$	−2.54303	−0.0891881
$814$	8.58608	0.300942
$815$	−10.2008	−0.357318
$816$	−3.08356	−0.107946
$817$	3.15485	0.110374
$818$	−8.26107	−0.288842
$819$	0.103857	0.00362905
$820$	−23.7256	−0.828535
$821$	−33.2328	−1.15983	−0.579916	−	0.814676i	$-0.696915\pi$
$821$	−33.2328	−1.15983	−0.579916	+	0.814676i	$0.696915\pi$
$822$	−2.94174	−0.102605
$823$	14.3814	0.501303	0.250651	−	0.968077i	$-0.419355\pi$
$823$	14.3814	0.501303	0.250651	+	0.968077i	$0.419355\pi$
$824$	−0.111353	−0.00387918
$825$	1.13241	0.0394255
$826$	−3.00427	−0.104532
$827$	33.5615	1.16705	0.583524	−	0.812096i	$-0.301673\pi$
$827$	33.5615	1.16705	0.583524	+	0.812096i	$0.301673\pi$
$828$	52.8841	1.83785
$829$	36.7732	1.27718	0.638592	−	0.769545i	$-0.279517\pi$
$829$	36.7732	1.27718	0.638592	+	0.769545i	$0.279517\pi$
$830$	5.74593	0.199444
$831$	−2.18816	−0.0759064
$832$	−0.315494	−0.0109378
$833$	29.3998	1.01864
$834$	0.346735	0.0120064
$835$	20.4212	0.706705
$836$	−16.3608	−0.565850
$837$	9.84540	0.340307
$838$	49.2577	1.70158
$839$	−6.99386	−0.241455	−0.120727	−	0.992686i	$-0.538523\pi$
$839$	−6.99386	−0.241455	−0.120727	+	0.992686i	$0.538523\pi$
$840$	0.0785761	0.00271113
$841$	1.00000	0.0344828
$842$	−28.1812	−0.971189
$843$	1.25970	0.0433863
$844$	40.6248	1.39836
$845$	−19.5740	−0.673367
$846$	63.2078	2.17313
$847$	5.13859	0.176564
$848$	−38.4864	−1.32163
$849$	−0.908755	−0.0311884
$850$	27.3889	0.939430
$851$	−14.3453	−0.491751
$852$	−2.52111	−0.0863716
$853$	−1.95728	−0.0670159	−0.0335080	−	0.999438i	$-0.510668\pi$
$853$	−1.95728	−0.0670159	−0.0335080	+	0.999438i	$0.510668\pi$
$854$	−13.6619	−0.467499
$855$	13.9937	0.478574
$856$	1.50651	0.0514916
$857$	−35.6903	−1.21916	−0.609578	−	0.792726i	$-0.708661\pi$
$857$	−35.6903	−1.21916	−0.609578	+	0.792726i	$0.708661\pi$
$858$	−0.0291330	−0.000994585 0
$859$	−51.5426	−1.75861	−0.879305	−	0.476258i	$-0.841993\pi$
$859$	−51.5426	−1.75861	−0.879305	+	0.476258i	$0.841993\pi$
$860$	−3.26331	−0.111278
$861$	−1.26438	−0.0430900
$862$	46.0790	1.56946
$863$	2.24414	0.0763915	0.0381958	−	0.999270i	$-0.487839\pi$
$863$	2.24414	0.0763915	0.0381958	+	0.999270i	$0.487839\pi$
$864$	−8.23573	−0.280185
$865$	−3.12612	−0.106291
$866$	59.2300	2.01272
$867$	−1.22875	−0.0417304
$868$	−21.0782	−0.715439
$869$	−29.0242	−0.984578
$870$	0.522124	0.0177017
$871$	−0.0361677	−0.00122549
$872$	0.836280	0.0283200
$873$	37.0066	1.25248
$874$	52.7797	1.78530
$875$	11.7934	0.398688
$876$	−0.512706	−0.0173227
$877$	−26.4797	−0.894156	−0.447078	−	0.894495i	$-0.647535\pi$
$877$	−26.4797	−0.894156	−0.447078	+	0.894495i	$0.647535\pi$
$878$	−34.8641	−1.17661
$879$	2.66296	0.0898194
$880$	−13.4932	−0.454856
$881$	29.6955	1.00047	0.500234	−	0.865890i	$-0.333247\pi$
$881$	29.6955	1.00047	0.500234	+	0.865890i	$0.333247\pi$
$882$	36.1519	1.21730
$883$	18.1198	0.609779	0.304889	−	0.952388i	$-0.401380\pi$
$883$	18.1198	0.609779	0.304889	+	0.952388i	$0.401380\pi$
$884$	−0.364928	−0.0122739
$885$	−0.373310	−0.0125487
$886$	−58.8357	−1.97663
$887$	−30.1034	−1.01077	−0.505387	−	0.862893i	$-0.668650\pi$
$887$	−30.1034	−1.01077	−0.505387	+	0.862893i	$0.668650\pi$
$888$	−0.0892102	−0.00299370
$889$	11.5676	0.387963
$890$	31.5104	1.05623
$891$	21.2772	0.712813
$892$	−28.6343	−0.958748
$893$	32.6712	1.09330
$894$	−5.33982	−0.178590
$895$	−31.9141	−1.06677
$896$	2.44544	0.0816963
$897$	0.0486744	0.00162519
$898$	−34.8292	−1.16226
$899$	−9.68585	−0.323041
$900$	17.4427	0.581423
$901$	−51.4565	−1.71426
$902$	−36.3614	−1.21070
$903$	−0.173908	−0.00578728
$904$	4.18015	0.139030
$905$	−27.7802	−0.923443
$906$	3.31553	0.110151
$907$	9.07658	0.301383	0.150691	−	0.988581i	$-0.451850\pi$
$907$	9.07658	0.301383	0.150691	+	0.988581i	$0.451850\pi$
$908$	20.3029	0.673776
$909$	22.3756	0.742152
$910$	−0.107215	−0.00355414
$911$	42.6023	1.41148	0.705738	−	0.708473i	$-0.250616\pi$
$911$	42.6023	1.41148	0.705738	+	0.708473i	$0.250616\pi$
$912$	−1.95990	−0.0648988
$913$	4.56074	0.150939
$914$	25.7556	0.851920
$915$	−1.69762	−0.0561217
$916$	−13.0185	−0.430142
$917$	11.3918	0.376191
$918$	−10.1886	−0.336274
$919$	−20.7830	−0.685567	−0.342784	−	0.939414i	$-0.611370\pi$
$919$	−20.7830	−0.685567	−0.342784	+	0.939414i	$0.611370\pi$
$920$	−3.77544	−0.124473
$921$	−1.04270	−0.0343582
$922$	−81.7280	−2.69157
$923$	0.237891	0.00783027
$924$	0.901871	0.0296694
$925$	−4.73149	−0.155571
$926$	59.2229	1.94618
$927$	1.09316	0.0359042
$928$	8.10226	0.265970
$929$	37.6325	1.23468	0.617341	−	0.786696i	$-0.288210\pi$
$929$	37.6325	1.23468	0.617341	+	0.786696i	$0.288210\pi$
$930$	−5.05722	−0.165833
$931$	18.6864	0.612422
$932$	4.80278	0.157320
$933$	2.23025	0.0730151
$934$	74.2209	2.42858
$935$	−18.0405	−0.589986
$936$	−0.0310324	−0.00101433
$937$	−31.6169	−1.03288	−0.516439	−	0.856324i	$-0.672743\pi$
$937$	−31.6169	−1.03288	−0.516439	+	0.856324i	$0.672743\pi$
$938$	2.16186	0.0705871
$939$	2.53013	0.0825678
$940$	−33.7944	−1.10225
$941$	5.32439	0.173570	0.0867850	−	0.996227i	$-0.472341\pi$
$941$	5.32439	0.173570	0.0867850	+	0.996227i	$0.472341\pi$
$942$	−2.54903	−0.0830518
$943$	60.7513	1.97833
$944$	−5.36022	−0.174460
$945$	−1.55030	−0.0504312
$946$	−5.00127	−0.162605
$947$	7.73925	0.251492	0.125746	−	0.992062i	$-0.459868\pi$
$947$	7.73925	0.251492	0.125746	+	0.992062i	$0.459868\pi$
$948$	4.36072	0.141629
$949$	0.0483788	0.00157044
$950$	17.4082	0.564798
$951$	0.397413	0.0128870
$952$	1.50847	0.0488897
$953$	21.0642	0.682335	0.341168	−	0.940003i	$-0.389178\pi$
$953$	21.0642	0.682335	0.341168	+	0.940003i	$0.389178\pi$
$954$	−63.2742	−2.04858
$955$	6.65586	0.215378
$956$	1.03224	0.0333851
$957$	0.414428	0.0133966
$958$	−44.5890	−1.44060
$959$	−8.59309	−0.277485
$960$	2.34331	0.0756299
$961$	62.8156	2.02631
$962$	0.121725	0.00392457
$963$	−14.7895	−0.476586
$964$	49.4644	1.59314
$965$	36.5504	1.17660
$966$	−2.90942	−0.0936091
$967$	19.7767	0.635975	0.317987	−	0.948095i	$-0.396993\pi$
$967$	19.7767	0.635975	0.317987	+	0.948095i	$0.396993\pi$
$968$	−1.53541	−0.0493501
$969$	−2.62039	−0.0841791
$970$	−38.2032	−1.22663
$971$	−7.74733	−0.248624	−0.124312	−	0.992243i	$-0.539672\pi$
$971$	−7.74733	−0.248624	−0.124312	+	0.992243i	$0.539672\pi$
$972$	−9.74871	−0.312690
$973$	1.01284	0.0324703
$974$	−79.5766	−2.54980
$975$	0.0160542	0.000514146 0
$976$	−24.3755	−0.780242
$977$	−30.4289	−0.973507	−0.486753	−	0.873539i	$-0.661819\pi$
$977$	−30.4289	−0.973507	−0.486753	+	0.873539i	$0.661819\pi$
$978$	2.34885	0.0751078
$979$	25.0109	0.799352
$980$	−19.3288	−0.617436
$981$	−8.20981	−0.262119
$982$	−33.2819	−1.06207
$983$	28.9982	0.924899	0.462449	−	0.886646i	$-0.346971\pi$
$983$	28.9982	0.924899	0.462449	+	0.886646i	$0.346971\pi$
$984$	0.377798	0.0120438
$985$	−35.4907	−1.13083
$986$	10.0235	0.319213
$987$	−1.80096	−0.0573253
$988$	−0.231947	−0.00737921
$989$	8.35594	0.265704
$990$	−22.1837	−0.705045
$991$	−1.35063	−0.0429042	−0.0214521	−	0.999770i	$-0.506829\pi$
$991$	−1.35063	−0.0429042	−0.0214521	+	0.999770i	$0.506829\pi$
$992$	−78.4773	−2.49166
$993$	−2.65107	−0.0841291
$994$	−14.2195	−0.451014
$995$	−9.33167	−0.295834
$996$	−0.685225	−0.0217122
$997$	−18.6600	−0.590968	−0.295484	−	0.955348i	$-0.595481\pi$
$997$	−18.6600	−0.590968	−0.295484	+	0.955348i	$0.595481\pi$
$998$	−60.6607	−1.92018
$999$	1.76011	0.0556873

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.c.1.53	✓	61

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.c.1.53	✓	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)

\(f(q)\)	\(=\)	\(q+2.03681 q^{2} -0.170234 q^{3} +2.14858 q^{4} +1.50583 q^{5} -0.346735 q^{6} -1.01284 q^{7} +0.302638 q^{8} -2.97102 q^{9} +O(q^{10})\)	\(q+2.03681 q^{2} -0.170234 q^{3} +2.14858 q^{4} +1.50583 q^{5} -0.346735 q^{6} -1.01284 q^{7} +0.302638 q^{8} -2.97102 q^{9} +3.06709 q^{10} +2.43446 q^{11} -0.365763 q^{12} +0.0345133 q^{13} -2.06297 q^{14} -0.256345 q^{15} -3.68075 q^{16} -4.92118 q^{17} -6.05140 q^{18} -3.12788 q^{19} +3.23541 q^{20} +0.172421 q^{21} +4.95852 q^{22} -8.28451 q^{23} -0.0515195 q^{24} -2.73247 q^{25} +0.0702969 q^{26} +1.01647 q^{27} -2.17618 q^{28} -1.00000 q^{29} -0.522124 q^{30} +9.68585 q^{31} -8.10226 q^{32} -0.414428 q^{33} -10.0235 q^{34} -1.52517 q^{35} -6.38349 q^{36} +1.73158 q^{37} -6.37089 q^{38} -0.00587535 q^{39} +0.455723 q^{40} -7.33312 q^{41} +0.351188 q^{42} -1.00862 q^{43} +5.23064 q^{44} -4.47386 q^{45} -16.8740 q^{46} -10.4452 q^{47} +0.626591 q^{48} -5.97415 q^{49} -5.56551 q^{50} +0.837753 q^{51} +0.0741547 q^{52} +10.4561 q^{53} +2.07036 q^{54} +3.66588 q^{55} -0.306526 q^{56} +0.532472 q^{57} -2.03681 q^{58} +1.45628 q^{59} -0.550778 q^{60} +6.62243 q^{61} +19.7282 q^{62} +3.00918 q^{63} -9.14124 q^{64} +0.0519712 q^{65} -0.844110 q^{66} -1.04793 q^{67} -10.5736 q^{68} +1.41031 q^{69} -3.10648 q^{70} +6.89273 q^{71} -0.899145 q^{72} +1.40174 q^{73} +3.52690 q^{74} +0.465160 q^{75} -6.72051 q^{76} -2.46572 q^{77} -0.0119670 q^{78} -11.9222 q^{79} -5.54260 q^{80} +8.74002 q^{81} -14.9361 q^{82} +1.87341 q^{83} +0.370461 q^{84} -7.41047 q^{85} -2.05437 q^{86} +0.170234 q^{87} +0.736760 q^{88} +10.2737 q^{89} -9.11239 q^{90} -0.0349566 q^{91} -17.8000 q^{92} -1.64886 q^{93} -21.2748 q^{94} -4.71006 q^{95} +1.37928 q^{96} -12.4558 q^{97} -12.1682 q^{98} -7.23282 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9}+O(q^{10}) \) 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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