LMFDB - Embedded newform 6031.2.a.e.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6031,2,Mod(1,6031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6031, 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("6031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6031 = 37 \cdot 163 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6031.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:	$48.1577774590$
Analytic rank:	$0$
Dimension:	$134$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	6031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.53107 q^{2} -0.695993 q^{3} +4.40632 q^{4} +1.03970 q^{5} +1.76161 q^{6} +0.140699 q^{7} -6.09057 q^{8} -2.51559 q^{9} +O(q^{10})$	\(q-2.53107 q^{2} -0.695993 q^{3} +4.40632 q^{4} +1.03970 q^{5} +1.76161 q^{6} +0.140699 q^{7} -6.09057 q^{8} -2.51559 q^{9} -2.63157 q^{10} -0.963359 q^{11} -3.06677 q^{12} -5.17518 q^{13} -0.356118 q^{14} -0.723627 q^{15} +6.60303 q^{16} +0.161912 q^{17} +6.36715 q^{18} +5.31840 q^{19} +4.58127 q^{20} -0.0979252 q^{21} +2.43833 q^{22} +6.26958 q^{23} +4.23900 q^{24} -3.91901 q^{25} +13.0988 q^{26} +3.83881 q^{27} +0.619963 q^{28} +5.46675 q^{29} +1.83155 q^{30} +7.93228 q^{31} -4.53159 q^{32} +0.670491 q^{33} -0.409812 q^{34} +0.146285 q^{35} -11.0845 q^{36} +1.00000 q^{37} -13.4612 q^{38} +3.60189 q^{39} -6.33240 q^{40} -11.3662 q^{41} +0.247856 q^{42} +6.93593 q^{43} -4.24487 q^{44} -2.61547 q^{45} -15.8687 q^{46} -5.41143 q^{47} -4.59566 q^{48} -6.98020 q^{49} +9.91930 q^{50} -0.112690 q^{51} -22.8035 q^{52} +6.59853 q^{53} -9.71631 q^{54} -1.00161 q^{55} -0.856935 q^{56} -3.70157 q^{57} -13.8367 q^{58} +0.613933 q^{59} -3.18853 q^{60} -3.98555 q^{61} -20.0772 q^{62} -0.353940 q^{63} -1.73628 q^{64} -5.38066 q^{65} -1.69706 q^{66} +6.85939 q^{67} +0.713438 q^{68} -4.36358 q^{69} -0.370258 q^{70} -6.28955 q^{71} +15.3214 q^{72} -13.3107 q^{73} -2.53107 q^{74} +2.72761 q^{75} +23.4346 q^{76} -0.135543 q^{77} -9.11664 q^{78} +0.851597 q^{79} +6.86520 q^{80} +4.87499 q^{81} +28.7686 q^{82} -14.4566 q^{83} -0.431490 q^{84} +0.168341 q^{85} -17.5553 q^{86} -3.80482 q^{87} +5.86740 q^{88} +2.79736 q^{89} +6.61995 q^{90} -0.728141 q^{91} +27.6258 q^{92} -5.52081 q^{93} +13.6967 q^{94} +5.52956 q^{95} +3.15396 q^{96} -17.3208 q^{97} +17.6674 q^{98} +2.42342 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9}+O(q^{10}) $ 134 * q + 9 * q^2 + 7 * q^3 + 149 * q^4 + 22 * q^5 + 20 * q^6 + 11 * q^7 + 27 * q^8 + 181 * q^9	\( 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9} + 15 q^{10} + 20 q^{11} + 28 q^{12} + 11 q^{13} + 17 q^{14} - 13 q^{15} + 143 q^{16} + 76 q^{17} + 23 q^{18} + 15 q^{19} + 67 q^{20} + 63 q^{21} + 2 q^{22} + 22 q^{23} + 33 q^{24} + 160 q^{25} + 65 q^{26} + 31 q^{27} + 10 q^{28} + 73 q^{29} + 20 q^{30} + 10 q^{31} + 53 q^{32} + 72 q^{33} - 7 q^{34} + 52 q^{35} + 201 q^{36} + 134 q^{37} + 70 q^{38} + 6 q^{39} + 11 q^{40} + 182 q^{41} - 15 q^{42} + 12 q^{43} + 33 q^{44} + 29 q^{45} + 24 q^{46} + 80 q^{47} + 21 q^{48} + 229 q^{49} + 37 q^{50} + 57 q^{51} - 15 q^{52} + 75 q^{53} + 95 q^{54} - 9 q^{55} + 39 q^{56} + 19 q^{57} - 21 q^{58} + 91 q^{59} + 62 q^{60} + 58 q^{61} + 108 q^{62} + 9 q^{63} + 167 q^{64} + 76 q^{65} + 105 q^{66} - 17 q^{67} + 109 q^{68} + 48 q^{69} - 55 q^{70} + 56 q^{71} + 48 q^{72} + 54 q^{73} + 9 q^{74} + 28 q^{75} + 82 q^{76} + 156 q^{77} + 16 q^{78} - 2 q^{79} + 98 q^{80} + 270 q^{81} - 42 q^{82} + 130 q^{83} + 229 q^{84} + 22 q^{85} + 72 q^{86} + 22 q^{87} + 61 q^{88} + 157 q^{89} + 176 q^{90} + 31 q^{91} - 18 q^{92} + 36 q^{93} + 83 q^{94} + 98 q^{95} + 111 q^{96} + 35 q^{97} + 53 q^{98} + 55 q^{99}+O(q^{100}) \) 134 * q + 9 * q^2 + 7 * q^3 + 149 * q^4 + 22 * q^5 + 20 * q^6 + 11 * q^7 + 27 * q^8 + 181 * q^9 + 15 * q^10 + 20 * q^11 + 28 * q^12 + 11 * q^13 + 17 * q^14 - 13 * q^15 + 143 * q^16 + 76 * q^17 + 23 * q^18 + 15 * q^19 + 67 * q^20 + 63 * q^21 + 2 * q^22 + 22 * q^23 + 33 * q^24 + 160 * q^25 + 65 * q^26 + 31 * q^27 + 10 * q^28 + 73 * q^29 + 20 * q^30 + 10 * q^31 + 53 * q^32 + 72 * q^33 - 7 * q^34 + 52 * q^35 + 201 * q^36 + 134 * q^37 + 70 * q^38 + 6 * q^39 + 11 * q^40 + 182 * q^41 - 15 * q^42 + 12 * q^43 + 33 * q^44 + 29 * q^45 + 24 * q^46 + 80 * q^47 + 21 * q^48 + 229 * q^49 + 37 * q^50 + 57 * q^51 - 15 * q^52 + 75 * q^53 + 95 * q^54 - 9 * q^55 + 39 * q^56 + 19 * q^57 - 21 * q^58 + 91 * q^59 + 62 * q^60 + 58 * q^61 + 108 * q^62 + 9 * q^63 + 167 * q^64 + 76 * q^65 + 105 * q^66 - 17 * q^67 + 109 * q^68 + 48 * q^69 - 55 * q^70 + 56 * q^71 + 48 * q^72 + 54 * q^73 + 9 * q^74 + 28 * q^75 + 82 * q^76 + 156 * q^77 + 16 * q^78 - 2 * q^79 + 98 * q^80 + 270 * q^81 - 42 * q^82 + 130 * q^83 + 229 * q^84 + 22 * q^85 + 72 * q^86 + 22 * q^87 + 61 * q^88 + 157 * q^89 + 176 * q^90 + 31 * q^91 - 18 * q^92 + 36 * q^93 + 83 * q^94 + 98 * q^95 + 111 * q^96 + 35 * q^97 + 53 * q^98 + 55 * 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 $

$2$	−2.53107	−1.78974	−0.894869	−	0.446329i	$-0.852731\pi$
$2$	−2.53107	−1.78974	−0.894869	+	0.446329i	$0.852731\pi$
$3$	−0.695993	−0.401832	−0.200916	−	0.979608i	$-0.564392\pi$
$3$	−0.695993	−0.401832	−0.200916	+	0.979608i	$0.564392\pi$
$4$	4.40632	2.20316
$5$	1.03970	0.464970	0.232485	−	0.972600i	$-0.425314\pi$
$5$	1.03970	0.464970	0.232485	+	0.972600i	$0.425314\pi$
$6$	1.76161	0.719173
$7$	0.140699	0.0531791	0.0265895	−	0.999646i	$-0.491535\pi$
$7$	0.140699	0.0531791	0.0265895	+	0.999646i	$0.491535\pi$
$8$	−6.09057	−2.15334
$9$	−2.51559	−0.838531
$10$	−2.63157	−0.832174
$11$	−0.963359	−0.290464	−0.145232	−	0.989398i	$-0.546393\pi$
$11$	−0.963359	−0.290464	−0.145232	+	0.989398i	$0.546393\pi$
$12$	−3.06677	−0.885300
$13$	−5.17518	−1.43534	−0.717669	−	0.696385i	$-0.754791\pi$
$13$	−5.17518	−1.43534	−0.717669	+	0.696385i	$0.754791\pi$
$14$	−0.356118	−0.0951766
$15$	−0.723627	−0.186840
$16$	6.60303	1.65076
$17$	0.161912	0.0392695	0.0196348	−	0.999807i	$-0.493750\pi$
$17$	0.161912	0.0392695	0.0196348	+	0.999807i	$0.493750\pi$
$18$	6.36715	1.50075
$19$	5.31840	1.22012	0.610062	−	0.792353i	$-0.291144\pi$
$19$	5.31840	1.22012	0.610062	+	0.792353i	$0.291144\pi$
$20$	4.58127	1.02440
$21$	−0.0979252	−0.0213690
$22$	2.43833	0.519853
$23$	6.26958	1.30730	0.653648	−	0.756798i	$-0.273238\pi$
$23$	6.26958	1.30730	0.653648	+	0.756798i	$0.273238\pi$
$24$	4.23900	0.865281
$25$	−3.91901	−0.783803
$26$	13.0988	2.56888
$27$	3.83881	0.738780
$28$	0.619963	0.117162
$29$	5.46675	1.01515	0.507575	−	0.861607i	$-0.330542\pi$
$29$	5.46675	1.01515	0.507575	+	0.861607i	$0.330542\pi$
$30$	1.83155	0.334394
$31$	7.93228	1.42468	0.712340	−	0.701835i	$-0.247635\pi$
$31$	7.93228	1.42468	0.712340	+	0.701835i	$0.247635\pi$
$32$	−4.53159	−0.801080
$33$	0.670491	0.116717
$34$	−0.409812	−0.0702822
$35$	0.146285	0.0247267
$36$	−11.0845	−1.84742
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	−13.4612	−2.18370
$39$	3.60189	0.576764
$40$	−6.33240	−1.00124
$41$	−11.3662	−1.77510	−0.887550	−	0.460711i	$-0.847595\pi$
$41$	−11.3662	−1.77510	−0.887550	+	0.460711i	$0.847595\pi$
$42$	0.247856	0.0382450
$43$	6.93593	1.05772	0.528860	−	0.848709i	$-0.322620\pi$
$43$	6.93593	1.05772	0.528860	+	0.848709i	$0.322620\pi$
$44$	−4.24487	−0.639938
$45$	−2.61547	−0.389892
$46$	−15.8687	−2.33972
$47$	−5.41143	−0.789338	−0.394669	−	0.918823i	$-0.629141\pi$
$47$	−5.41143	−0.789338	−0.394669	+	0.918823i	$0.629141\pi$
$48$	−4.59566	−0.663327
$49$	−6.98020	−0.997172
$50$	9.91930	1.40280
$51$	−0.112690	−0.0157797
$52$	−22.8035	−3.16228
$53$	6.59853	0.906378	0.453189	−	0.891414i	$-0.350286\pi$
$53$	6.59853	0.906378	0.453189	+	0.891414i	$0.350286\pi$
$54$	−9.71631	−1.32222
$55$	−1.00161	−0.135057
$56$	−0.856935	−0.114513
$57$	−3.70157	−0.490285
$58$	−13.8367	−1.81685
$59$	0.613933	0.0799273	0.0399636	−	0.999201i	$-0.487276\pi$
$59$	0.613933	0.0799273	0.0399636	+	0.999201i	$0.487276\pi$
$60$	−3.18853	−0.411638
$61$	−3.98555	−0.510297	−0.255148	−	0.966902i	$-0.582124\pi$
$61$	−3.98555	−0.510297	−0.255148	+	0.966902i	$0.582124\pi$
$62$	−20.0772	−2.54980
$63$	−0.353940	−0.0445923
$64$	−1.73628	−0.217035
$65$	−5.38066	−0.667389
$66$	−1.69706	−0.208894
$67$	6.85939	0.838008	0.419004	−	0.907984i	$-0.362379\pi$
$67$	6.85939	0.838008	0.419004	+	0.907984i	$0.362379\pi$
$68$	0.713438	0.0865171
$69$	−4.36358	−0.525313
$70$	−0.370258	−0.0442543
$71$	−6.28955	−0.746432	−0.373216	−	0.927744i	$-0.621745\pi$
$71$	−6.28955	−0.746432	−0.373216	+	0.927744i	$0.621745\pi$
$72$	15.3214	1.80564
$73$	−13.3107	−1.55790	−0.778950	−	0.627087i	$-0.784247\pi$
$73$	−13.3107	−1.55790	−0.778950	+	0.627087i	$0.784247\pi$
$74$	−2.53107	−0.294231
$75$	2.72761	0.314957
$76$	23.4346	2.68813
$77$	−0.135543	−0.0154466
$78$	−9.11664	−1.03226
$79$	0.851597	0.0958121	0.0479061	−	0.998852i	$-0.484745\pi$
$79$	0.851597	0.0958121	0.0479061	+	0.998852i	$0.484745\pi$
$80$	6.86520	0.767552
$81$	4.87499	0.541666
$82$	28.7686	3.17696
$83$	−14.4566	−1.58681	−0.793407	−	0.608691i	$-0.791695\pi$
$83$	−14.4566	−1.58681	−0.793407	+	0.608691i	$0.791695\pi$
$84$	−0.431490	−0.0470794
$85$	0.168341	0.0182592
$86$	−17.5553	−1.89304
$87$	−3.80482	−0.407920
$88$	5.86740	0.625467
$89$	2.79736	0.296519	0.148260	−	0.988948i	$-0.452633\pi$
$89$	2.79736	0.296519	0.148260	+	0.988948i	$0.452633\pi$
$90$	6.61995	0.697804
$91$	−0.728141	−0.0763299
$92$	27.6258	2.88019
$93$	−5.52081	−0.572482
$94$	13.6967	1.41271
$95$	5.52956	0.567321
$96$	3.15396	0.321899
$97$	−17.3208	−1.75866	−0.879332	−	0.476210i	$-0.842010\pi$
$97$	−17.3208	−1.75866	−0.879332	+	0.476210i	$0.842010\pi$
$98$	17.6674	1.78468
$99$	2.42342	0.243563
$100$	−17.2684	−1.72684
$101$	18.3705	1.82793	0.913966	−	0.405791i	$-0.133004\pi$
$101$	18.3705	1.82793	0.913966	+	0.405791i	$0.133004\pi$
$102$	0.285226	0.0282416
$103$	0.0343415	0.00338377	0.00169188	−	0.999999i	$-0.499461\pi$
$103$	0.0343415	0.00338377	0.00169188	+	0.999999i	$0.499461\pi$
$104$	31.5198	3.09077
$105$	−0.101813	−0.00993596
$106$	−16.7014	−1.62218
$107$	5.34800	0.517011	0.258506	−	0.966010i	$-0.416770\pi$
$107$	5.34800	0.517011	0.258506	+	0.966010i	$0.416770\pi$
$108$	16.9151	1.62765
$109$	4.10569	0.393254	0.196627	−	0.980478i	$-0.437001\pi$
$109$	4.10569	0.393254	0.196627	+	0.980478i	$0.437001\pi$
$110$	2.53514	0.241716
$111$	−0.695993	−0.0660607
$112$	0.929037	0.0877857
$113$	−6.43585	−0.605434	−0.302717	−	0.953080i	$-0.597894\pi$
$113$	−6.43585	−0.605434	−0.302717	+	0.953080i	$0.597894\pi$
$114$	9.36893	0.877481
$115$	6.51851	0.607854
$116$	24.0883	2.23654
$117$	13.0187	1.20358
$118$	−1.55391	−0.143049
$119$	0.0227809	0.00208832
$120$	4.40730	0.402330
$121$	−10.0719	−0.915631
$122$	10.0877	0.913297
$123$	7.91079	0.713292
$124$	34.9522	3.13880
$125$	−9.27314	−0.829415
$126$	0.895849	0.0798085
$127$	−8.12238	−0.720745	−0.360372	−	0.932809i	$-0.617350\pi$
$127$	−8.12238	−0.720745	−0.360372	+	0.932809i	$0.617350\pi$
$128$	13.4578	1.18951
$129$	−4.82736	−0.425025
$130$	13.6188	1.19445
$131$	15.8466	1.38453	0.692263	−	0.721645i	$-0.256614\pi$
$131$	15.8466	1.38453	0.692263	+	0.721645i	$0.256614\pi$
$132$	2.95440	0.257147
$133$	0.748291	0.0648851
$134$	−17.3616	−1.49981
$135$	3.99123	0.343511
$136$	−0.986139	−0.0845608
$137$	−11.2359	−0.959946	−0.479973	−	0.877283i	$-0.659354\pi$
$137$	−11.2359	−0.959946	−0.479973	+	0.877283i	$0.659354\pi$
$138$	11.0445	0.940173
$139$	−1.30544	−0.110726	−0.0553632	−	0.998466i	$-0.517632\pi$
$139$	−1.30544	−0.110726	−0.0553632	+	0.998466i	$0.517632\pi$
$140$	0.644579	0.0544768
$141$	3.76632	0.317181
$142$	15.9193	1.33592
$143$	4.98556	0.416913
$144$	−16.6105	−1.38421
$145$	5.68381	0.472015
$146$	33.6903	2.78823
$147$	4.85817	0.400695
$148$	4.40632	0.362197
$149$	9.40724	0.770671	0.385336	−	0.922776i	$-0.374086\pi$
$149$	9.40724	0.770671	0.385336	+	0.922776i	$0.374086\pi$
$150$	−6.90377	−0.563690
$151$	−11.6112	−0.944910	−0.472455	−	0.881355i	$-0.656632\pi$
$151$	−11.6112	−0.944910	−0.472455	+	0.881355i	$0.656632\pi$
$152$	−32.3921	−2.62735
$153$	−0.407306	−0.0329287
$154$	0.343069	0.0276453
$155$	8.24723	0.662433
$156$	15.8711	1.27070
$157$	9.92459	0.792068	0.396034	−	0.918236i	$-0.370386\pi$
$157$	9.92459	0.792068	0.396034	+	0.918236i	$0.370386\pi$
$158$	−2.15545	−0.171479
$159$	−4.59253	−0.364212
$160$	−4.71151	−0.372478
$161$	0.882120	0.0695208
$162$	−12.3390	−0.969440
$163$	−1.00000	−0.0783260
$163$	−1.00000	−0.0783260
$164$	−50.0831	−3.91083
$165$	0.697112	0.0542701
$166$	36.5906	2.83998
$167$	5.07767	0.392922	0.196461	−	0.980512i	$-0.437055\pi$
$167$	5.07767	0.392922	0.196461	+	0.980512i	$0.437055\pi$
$168$	0.596421	0.0460149
$169$	13.7825	1.06019
$170$	−0.426083	−0.0326791
$171$	−13.3789	−1.02311
$172$	30.5619	2.33033
$173$	−1.62668	−0.123675	−0.0618373	−	0.998086i	$-0.519696\pi$
$173$	−1.62668	−0.123675	−0.0618373	+	0.998086i	$0.519696\pi$
$174$	9.63028	0.730070
$175$	−0.551400	−0.0416819
$176$	−6.36108	−0.479485
$177$	−0.427293	−0.0321173
$178$	−7.08031	−0.530692
$179$	20.0536	1.49888	0.749438	−	0.662075i	$-0.230324\pi$
$179$	20.0536	1.49888	0.749438	+	0.662075i	$0.230324\pi$
$180$	−11.5246	−0.858995
$181$	−2.98214	−0.221661	−0.110830	−	0.993839i	$-0.535351\pi$
$181$	−2.98214	−0.221661	−0.110830	+	0.993839i	$0.535351\pi$
$182$	1.84298	0.136610
$183$	2.77391	0.205053
$184$	−38.1853	−2.81506
$185$	1.03970	0.0764406
$186$	13.9736	1.02459
$187$	−0.155980	−0.0114064
$188$	−23.8445	−1.73904
$189$	0.540116	0.0392876
$190$	−13.9957	−1.01536
$191$	−11.1054	−0.803558	−0.401779	−	0.915737i	$-0.631608\pi$
$191$	−11.1054	−0.803558	−0.401779	+	0.915737i	$0.631608\pi$
$192$	1.20844	0.0872115
$193$	−18.7570	−1.35016	−0.675079	−	0.737746i	$-0.735890\pi$
$193$	−18.7570	−1.35016	−0.675079	+	0.737746i	$0.735890\pi$
$194$	43.8402	3.14755
$195$	3.74490	0.268178
$196$	−30.7570	−2.19693
$197$	−8.00215	−0.570130	−0.285065	−	0.958508i	$-0.592015\pi$
$197$	−8.00215	−0.570130	−0.285065	+	0.958508i	$0.592015\pi$
$198$	−6.13385	−0.435913
$199$	9.16238	0.649504	0.324752	−	0.945799i	$-0.394719\pi$
$199$	9.16238	0.649504	0.324752	+	0.945799i	$0.394719\pi$
$200$	23.8690	1.68780
$201$	−4.77409	−0.336738
$202$	−46.4970	−3.27152
$203$	0.769165	0.0539848
$204$	−0.496548	−0.0347653
$205$	−11.8175	−0.825369
$206$	−0.0869208	−0.00605606
$207$	−15.7717	−1.09621
$208$	−34.1719	−2.36939
$209$	−5.12353	−0.354402
$210$	0.257697	0.0177828
$211$	24.8476	1.71058	0.855290	−	0.518149i	$-0.173379\pi$
$211$	24.8476	1.71058	0.855290	+	0.518149i	$0.173379\pi$
$212$	29.0753	1.99690
$213$	4.37748	0.299940
$214$	−13.5362	−0.925314
$215$	7.21132	0.491808
$216$	−23.3806	−1.59085
$217$	1.11606	0.0757632
$218$	−10.3918	−0.703822
$219$	9.26415	0.626013
$220$	−4.41341	−0.297552
$221$	−0.837926	−0.0563650
$222$	1.76161	0.118231
$223$	16.4909	1.10432	0.552158	−	0.833740i	$-0.313805\pi$
$223$	16.4909	1.10432	0.552158	+	0.833740i	$0.313805\pi$
$224$	−0.637588	−0.0426007
$225$	9.85865	0.657243
$226$	16.2896	1.08357
$227$	24.7725	1.64421	0.822103	−	0.569339i	$-0.192801\pi$
$227$	24.7725	1.64421	0.822103	+	0.569339i	$0.192801\pi$
$228$	−16.3103	−1.08018
$229$	−10.8625	−0.717811	−0.358906	−	0.933374i	$-0.616850\pi$
$229$	−10.8625	−0.717811	−0.358906	+	0.933374i	$0.616850\pi$
$230$	−16.4988	−1.08790
$231$	0.0943371	0.00620693
$232$	−33.2957	−2.18597
$233$	−14.9021	−0.976272	−0.488136	−	0.872768i	$-0.662323\pi$
$233$	−14.9021	−0.976272	−0.488136	+	0.872768i	$0.662323\pi$
$234$	−32.9511	−2.15408
$235$	−5.62629	−0.367019
$236$	2.70519	0.176093
$237$	−0.592706	−0.0385004
$238$	−0.0576600	−0.00373754
$239$	16.8412	1.08937	0.544683	−	0.838642i	$-0.316650\pi$
$239$	16.8412	1.08937	0.544683	+	0.838642i	$0.316650\pi$
$240$	−4.77813	−0.308427
$241$	17.2530	1.11136	0.555681	−	0.831396i	$-0.312458\pi$
$241$	17.2530	1.11136	0.555681	+	0.831396i	$0.312458\pi$
$242$	25.4928	1.63874
$243$	−14.9094	−0.956439
$244$	−17.5616	−1.12427
$245$	−7.25735	−0.463655
$246$	−20.0228	−1.27661
$247$	−27.5237	−1.75129
$248$	−48.3121	−3.06782
$249$	10.0617	0.637633
$250$	23.4710	1.48443
$251$	6.27204	0.395888	0.197944	−	0.980213i	$-0.436574\pi$
$251$	6.27204	0.395888	0.197944	+	0.980213i	$0.436574\pi$
$252$	−1.55958	−0.0982440
$253$	−6.03985	−0.379722
$254$	20.5583	1.28994
$255$	−0.117164	−0.00733711
$256$	−30.5902	−1.91188
$257$	−23.6735	−1.47671	−0.738356	−	0.674411i	$-0.764398\pi$
$257$	−23.6735	−1.47671	−0.738356	+	0.674411i	$0.764398\pi$
$258$	12.2184	0.760683
$259$	0.140699	0.00874258
$260$	−23.7089	−1.47036
$261$	−13.7521	−0.851236
$262$	−40.1089	−2.47794
$263$	24.9349	1.53755	0.768777	−	0.639517i	$-0.220866\pi$
$263$	24.9349	1.53755	0.768777	+	0.639517i	$0.220866\pi$
$264$	−4.08367	−0.251333
$265$	6.86052	0.421439
$266$	−1.89398	−0.116127
$267$	−1.94694	−0.119151
$268$	30.2247	1.84627
$269$	23.9270	1.45886	0.729428	−	0.684058i	$-0.239787\pi$
$269$	23.9270	1.45886	0.729428	+	0.684058i	$0.239787\pi$
$270$	−10.1021	−0.614794
$271$	19.6171	1.19165	0.595827	−	0.803113i	$-0.296824\pi$
$271$	19.6171	1.19165	0.595827	+	0.803113i	$0.296824\pi$
$272$	1.06911	0.0648245
$273$	0.506781	0.0306718
$274$	28.4388	1.71805
$275$	3.77542	0.227666
$276$	−19.2273	−1.15735
$277$	−14.4511	−0.868282	−0.434141	−	0.900845i	$-0.642948\pi$
$277$	−14.4511	−0.868282	−0.434141	+	0.900845i	$0.642948\pi$
$278$	3.30417	0.198171
$279$	−19.9544	−1.19464
$280$	−0.890959	−0.0532450
$281$	18.8407	1.12394	0.561970	−	0.827158i	$-0.310044\pi$
$281$	18.8407	1.12394	0.561970	+	0.827158i	$0.310044\pi$
$282$	−9.53282	−0.567671
$283$	1.72669	0.102641	0.0513205	−	0.998682i	$-0.483657\pi$
$283$	1.72669	0.102641	0.0513205	+	0.998682i	$0.483657\pi$
$284$	−27.7138	−1.64451
$285$	−3.84854	−0.227968
$286$	−12.6188	−0.746165
$287$	−1.59921	−0.0943982
$288$	11.3996	0.671730
$289$	−16.9738	−0.998458
$290$	−14.3861	−0.844783
$291$	12.0552	0.706687
$292$	−58.6512	−3.43230
$293$	24.9847	1.45962	0.729811	−	0.683649i	$-0.239608\pi$
$293$	24.9847	1.45962	0.729811	+	0.683649i	$0.239608\pi$
$294$	−12.2964	−0.717140
$295$	0.638309	0.0371638
$296$	−6.09057	−0.354007
$297$	−3.69815	−0.214589
$298$	−23.8104	−1.37930
$299$	−32.4462	−1.87641
$300$	12.0187	0.693901
$301$	0.975875	0.0562485
$302$	29.3889	1.69114
$303$	−12.7857	−0.734521
$304$	35.1175	2.01413
$305$	−4.14379	−0.237273
$306$	1.03092	0.0589338
$307$	−22.1240	−1.26268	−0.631341	−	0.775505i	$-0.717495\pi$
$307$	−22.1240	−1.26268	−0.631341	+	0.775505i	$0.717495\pi$
$308$	−0.597247	−0.0340313
$309$	−0.0239014	−0.00135971
$310$	−20.8743	−1.18558
$311$	19.1456	1.08565	0.542825	−	0.839846i	$-0.317355\pi$
$311$	19.1456	1.08565	0.542825	+	0.839846i	$0.317355\pi$
$312$	−21.9376	−1.24197
$313$	−21.3523	−1.20690	−0.603450	−	0.797401i	$-0.706208\pi$
$313$	−21.3523	−1.20690	−0.603450	+	0.797401i	$0.706208\pi$
$314$	−25.1198	−1.41759
$315$	−0.367994	−0.0207341
$316$	3.75241	0.211090
$317$	12.2500	0.688027	0.344014	−	0.938965i	$-0.388213\pi$
$317$	12.2500	0.688027	0.344014	+	0.938965i	$0.388213\pi$
$318$	11.6240	0.651843
$319$	−5.26644	−0.294864
$320$	−1.80522	−0.100915
$321$	−3.72217	−0.207751
$322$	−2.23271	−0.124424
$323$	0.861115	0.0479137
$324$	21.4808	1.19338
$325$	20.2816	1.12502
$326$	2.53107	0.140183
$327$	−2.85753	−0.158022
$328$	69.2266	3.82240
$329$	−0.761381	−0.0419763
$330$	−1.76444	−0.0971293
$331$	3.97780	0.218639	0.109320	−	0.994007i	$-0.465133\pi$
$331$	3.97780	0.218639	0.109320	+	0.994007i	$0.465133\pi$
$332$	−63.7003	−3.49601
$333$	−2.51559	−0.137854
$334$	−12.8520	−0.703228
$335$	7.13174	0.389649
$336$	−0.646603	−0.0352751
$337$	9.82596	0.535254	0.267627	−	0.963523i	$-0.413760\pi$
$337$	9.82596	0.535254	0.267627	+	0.963523i	$0.413760\pi$
$338$	−34.8845	−1.89747
$339$	4.47931	0.243283
$340$	0.741765	0.0402279
$341$	−7.64163	−0.413818
$342$	33.8630	1.83110
$343$	−1.96699	−0.106208
$344$	−42.2438	−2.27763
$345$	−4.53683	−0.244255
$346$	4.11726	0.221345
$347$	11.6303	0.624349	0.312174	−	0.950025i	$-0.398943\pi$
$347$	11.6303	0.624349	0.312174	+	0.950025i	$0.398943\pi$
$348$	−16.7653	−0.898713
$349$	30.7547	1.64626	0.823129	−	0.567854i	$-0.192226\pi$
$349$	30.7547	1.64626	0.823129	+	0.567854i	$0.192226\pi$
$350$	1.39563	0.0745997
$351$	−19.8666	−1.06040
$352$	4.36555	0.232684
$353$	−3.99349	−0.212552	−0.106276	−	0.994337i	$-0.533893\pi$
$353$	−3.99349	−0.212552	−0.106276	+	0.994337i	$0.533893\pi$
$354$	1.08151	0.0574816
$355$	−6.53927	−0.347069
$356$	12.3261	0.653279
$357$	−0.0158553	−0.000839152 0
$358$	−50.7571	−2.68259
$359$	35.9958	1.89979	0.949893	−	0.312575i	$-0.101192\pi$
$359$	35.9958	1.89979	0.949893	+	0.312575i	$0.101192\pi$
$360$	15.9297	0.839571
$361$	9.28537	0.488704
$362$	7.54800	0.396714
$363$	7.01000	0.367930
$364$	−3.20842	−0.168167
$365$	−13.8392	−0.724376
$366$	−7.02097	−0.366992
$367$	7.34501	0.383407	0.191703	−	0.981453i	$-0.438599\pi$
$367$	7.34501	0.383407	0.191703	+	0.981453i	$0.438599\pi$
$368$	41.3982	2.15803
$369$	28.5927	1.48848
$370$	−2.63157	−0.136809
$371$	0.928404	0.0482003
$372$	−24.3265	−1.26127
$373$	35.6716	1.84701	0.923503	−	0.383591i	$-0.125313\pi$
$373$	35.6716	1.84701	0.923503	+	0.383591i	$0.125313\pi$
$374$	0.394796	0.0204144
$375$	6.45404	0.333285
$376$	32.9587	1.69972
$377$	−28.2915	−1.45708
$378$	−1.36707	−0.0703146
$379$	−26.5893	−1.36580	−0.682901	−	0.730511i	$-0.739282\pi$
$379$	−26.5893	−1.36580	−0.682901	+	0.730511i	$0.739282\pi$
$380$	24.3650	1.24990
$381$	5.65312	0.289618
$382$	28.1085	1.43816
$383$	−14.0327	−0.717038	−0.358519	−	0.933522i	$-0.616718\pi$
$383$	−14.0327	−0.717038	−0.358519	+	0.933522i	$0.616718\pi$
$384$	−9.36655	−0.477985
$385$	−0.140925	−0.00718220
$386$	47.4753	2.41643
$387$	−17.4480	−0.886931
$388$	−76.3211	−3.87462
$389$	8.35937	0.423837	0.211918	−	0.977287i	$-0.432029\pi$
$389$	8.35937	0.423837	0.211918	+	0.977287i	$0.432029\pi$
$390$	−9.47861	−0.479968
$391$	1.01512	0.0513369
$392$	42.5134	2.14725
$393$	−11.0291	−0.556346
$394$	20.2540	1.02038
$395$	0.885409	0.0445498
$396$	10.6784	0.536608
$397$	35.0520	1.75921	0.879605	−	0.475705i	$-0.157807\pi$
$397$	35.0520	1.75921	0.879605	+	0.475705i	$0.157807\pi$
$398$	−23.1906	−1.16244
$399$	−0.520805	−0.0260729
$400$	−25.8774	−1.29387
$401$	−7.20176	−0.359639	−0.179819	−	0.983700i	$-0.557551\pi$
$401$	−7.20176	−0.359639	−0.179819	+	0.983700i	$0.557551\pi$
$402$	12.0836	0.602673
$403$	−41.0510	−2.04490
$404$	80.9463	4.02723
$405$	5.06855	0.251858
$406$	−1.94681	−0.0966186
$407$	−0.963359	−0.0477519
$408$	0.686346	0.0339792
$409$	−2.69732	−0.133374	−0.0666868	−	0.997774i	$-0.521243\pi$
$409$	−2.69732	−0.133374	−0.0666868	+	0.997774i	$0.521243\pi$
$410$	29.9109	1.47719
$411$	7.82009	0.385737
$412$	0.151320	0.00745499
$413$	0.0863795	0.00425046
$414$	39.9193	1.96193
$415$	−15.0306	−0.737821
$416$	23.4518	1.14982
$417$	0.908580	0.0444934
$418$	12.9680	0.634286
$419$	7.03609	0.343736	0.171868	−	0.985120i	$-0.445020\pi$
$419$	7.03609	0.343736	0.171868	+	0.985120i	$0.445020\pi$
$420$	−0.448622	−0.0218905
$421$	−16.9455	−0.825871	−0.412935	−	0.910760i	$-0.635496\pi$
$421$	−16.9455	−0.825871	−0.412935	+	0.910760i	$0.635496\pi$
$422$	−62.8911	−3.06149
$423$	13.6130	0.661885
$424$	−40.1888	−1.95174
$425$	−0.634537	−0.0307796
$426$	−11.0797	−0.536814
$427$	−0.560761	−0.0271371
$428$	23.5650	1.13906
$429$	−3.46991	−0.167529
$430$	−18.2524	−0.880207
$431$	−8.23442	−0.396638	−0.198319	−	0.980138i	$-0.563548\pi$
$431$	−8.23442	−0.396638	−0.198319	+	0.980138i	$0.563548\pi$
$432$	25.3478	1.21955
$433$	−16.5458	−0.795140	−0.397570	−	0.917572i	$-0.630146\pi$
$433$	−16.5458	−0.795140	−0.397570	+	0.917572i	$0.630146\pi$
$434$	−2.82483	−0.135596
$435$	−3.95589	−0.189671
$436$	18.0910	0.866402
$437$	33.3441	1.59506
$438$	−23.4482	−1.12040
$439$	−18.7711	−0.895894	−0.447947	−	0.894060i	$-0.647845\pi$
$439$	−18.7711	−0.895894	−0.447947	+	0.894060i	$0.647845\pi$
$440$	6.10037	0.290824
$441$	17.5594	0.836160
$442$	2.12085	0.100879
$443$	16.2233	0.770791	0.385396	−	0.922751i	$-0.374065\pi$
$443$	16.2233	0.770791	0.385396	+	0.922751i	$0.374065\pi$
$444$	−3.06677	−0.145542
$445$	2.90842	0.137873
$446$	−41.7397	−1.97643
$447$	−6.54738	−0.309680
$448$	−0.244292	−0.0115417
$449$	7.52690	0.355216	0.177608	−	0.984101i	$-0.443164\pi$
$449$	7.52690	0.355216	0.177608	+	0.984101i	$0.443164\pi$
$450$	−24.9529	−1.17629
$451$	10.9497	0.515602
$452$	−28.3584	−1.33387
$453$	8.08134	0.379695
$454$	−62.7009	−2.94270
$455$	−0.757051	−0.0354911
$456$	22.5447	1.05575
$457$	−11.4473	−0.535482	−0.267741	−	0.963491i	$-0.586277\pi$
$457$	−11.4473	−0.535482	−0.267741	+	0.963491i	$0.586277\pi$
$458$	27.4937	1.28469
$459$	0.621552	0.0290116
$460$	28.7226	1.33920
$461$	−7.73090	−0.360064	−0.180032	−	0.983661i	$-0.557620\pi$
$461$	−7.73090	−0.360064	−0.180032	+	0.983661i	$0.557620\pi$
$462$	−0.238774	−0.0111088
$463$	36.4200	1.69258	0.846290	−	0.532723i	$-0.178831\pi$
$463$	36.4200	1.69258	0.846290	+	0.532723i	$0.178831\pi$
$464$	36.0971	1.67577
$465$	−5.74001	−0.266187
$466$	37.7184	1.74727
$467$	31.7076	1.46725	0.733627	−	0.679552i	$-0.237826\pi$
$467$	31.7076	1.46725	0.733627	+	0.679552i	$0.237826\pi$
$468$	57.3644	2.65167
$469$	0.965107	0.0445645
$470$	14.2405	0.656867
$471$	−6.90745	−0.318278
$472$	−3.73920	−0.172111
$473$	−6.68179	−0.307229
$474$	1.50018	0.0689055
$475$	−20.8429	−0.956337
$476$	0.100380	0.00460090
$477$	−16.5992	−0.760026
$478$	−42.6263	−1.94968
$479$	18.9739	0.866941	0.433470	−	0.901168i	$-0.357289\pi$
$479$	18.9739	0.866941	0.433470	+	0.901168i	$0.357289\pi$
$480$	3.27918	0.149673
$481$	−5.17518	−0.235968
$482$	−43.6685	−1.98905
$483$	−0.613950	−0.0279357
$484$	−44.3802	−2.01728
$485$	−18.0085	−0.817726
$486$	37.7368	1.71177
$487$	−16.0949	−0.729331	−0.364665	−	0.931139i	$-0.618817\pi$
$487$	−16.0949	−0.729331	−0.364665	+	0.931139i	$0.618817\pi$
$488$	24.2743	1.09884
$489$	0.695993	0.0314739
$490$	18.3689	0.829821
$491$	9.97666	0.450240	0.225120	−	0.974331i	$-0.427723\pi$
$491$	9.97666	0.450240	0.225120	+	0.974331i	$0.427723\pi$
$492$	34.8575	1.57150
$493$	0.885136	0.0398645
$494$	69.6644	3.13435
$495$	2.51964	0.113249
$496$	52.3771	2.35180
$497$	−0.884931	−0.0396946
$498$	−25.4668	−1.14119
$499$	−25.5850	−1.14534	−0.572672	−	0.819785i	$-0.694093\pi$
$499$	−25.5850	−1.14534	−0.572672	+	0.819785i	$0.694093\pi$
$500$	−40.8604	−1.82733
$501$	−3.53403	−0.157889
$502$	−15.8750	−0.708535
$503$	20.2071	0.900990	0.450495	−	0.892779i	$-0.351247\pi$
$503$	20.2071	0.900990	0.450495	+	0.892779i	$0.351247\pi$
$504$	2.15570	0.0960225
$505$	19.0999	0.849934
$506$	15.2873	0.679603
$507$	−9.59253	−0.426019
$508$	−35.7898	−1.58792
$509$	−16.3761	−0.725858	−0.362929	−	0.931817i	$-0.618223\pi$
$509$	−16.3761	−0.725858	−0.362929	+	0.931817i	$0.618223\pi$
$510$	0.296551	0.0131315
$511$	−1.87280	−0.0828476
$512$	50.5102	2.23226
$513$	20.4163	0.901404
$514$	59.9193	2.64293
$515$	0.0357050	0.00157335
$516$	−21.2709	−0.936399
$517$	5.21315	0.229274
$518$	−0.356118	−0.0156469
$519$	1.13216	0.0496964
$520$	32.7713	1.43712
$521$	42.7150	1.87138	0.935690	−	0.352823i	$-0.114778\pi$
$521$	42.7150	1.87138	0.935690	+	0.352823i	$0.114778\pi$
$522$	34.8076	1.52349
$523$	−4.38372	−0.191687	−0.0958433	−	0.995396i	$-0.530555\pi$
$523$	−4.38372	−0.191687	−0.0958433	+	0.995396i	$0.530555\pi$
$524$	69.8253	3.05033
$525$	0.383770	0.0167491
$526$	−63.1121	−2.75182
$527$	1.28434	0.0559465
$528$	4.42727	0.192672
$529$	16.3076	0.709025
$530$	−17.3645	−0.754265
$531$	−1.54441	−0.0670215
$532$	3.29721	0.142952
$533$	58.8221	2.54787
$534$	4.92785	0.213249
$535$	5.56034	0.240395
$536$	−41.7776	−1.80452
$537$	−13.9572	−0.602296
$538$	−60.5609	−2.61097
$539$	6.72444	0.289642
$540$	17.5867	0.756809
$541$	18.2790	0.785877	0.392938	−	0.919565i	$-0.371459\pi$
$541$	18.2790	0.785877	0.392938	+	0.919565i	$0.371459\pi$
$542$	−49.6523	−2.13275
$543$	2.07555	0.0890702
$544$	−0.733721	−0.0314580
$545$	4.26871	0.182851
$546$	−1.28270	−0.0548944
$547$	−32.6994	−1.39813	−0.699063	−	0.715060i	$-0.746399\pi$
$547$	−32.6994	−1.39813	−0.699063	+	0.715060i	$0.746399\pi$
$548$	−49.5089	−2.11492
$549$	10.0260	0.427900
$550$	−9.55585	−0.407463
$551$	29.0744	1.23861
$552$	26.5767	1.13118
$553$	0.119818	0.00509520
$554$	36.5768	1.55400
$555$	−0.723627	−0.0307163
$556$	−5.75221	−0.243948
$557$	−11.0176	−0.466832	−0.233416	−	0.972377i	$-0.574990\pi$
$557$	−11.0176	−0.466832	−0.233416	+	0.972377i	$0.574990\pi$
$558$	50.5060	2.13809
$559$	−35.8947	−1.51818
$560$	0.965924	0.0408177
$561$	0.108561	0.00458344
$562$	−47.6871	−2.01156
$563$	29.8763	1.25914	0.629568	−	0.776946i	$-0.283232\pi$
$563$	29.8763	1.25914	0.629568	+	0.776946i	$0.283232\pi$
$564$	16.5956	0.698801
$565$	−6.69139	−0.281509
$566$	−4.37037	−0.183700
$567$	0.685905	0.0288053
$568$	38.3070	1.60732
$569$	12.6018	0.528294	0.264147	−	0.964482i	$-0.414910\pi$
$569$	12.6018	0.528294	0.264147	+	0.964482i	$0.414910\pi$
$570$	9.74092	0.408002
$571$	−37.9567	−1.58844	−0.794220	−	0.607630i	$-0.792120\pi$
$571$	−37.9567	−1.58844	−0.794220	+	0.607630i	$0.792120\pi$
$572$	21.9680	0.918527
$573$	7.72928	0.322895
$574$	4.04771	0.168948
$575$	−24.5706	−1.02466
$576$	4.36777	0.181990
$577$	32.5174	1.35372	0.676858	−	0.736114i	$-0.263341\pi$
$577$	32.5174	1.35372	0.676858	+	0.736114i	$0.263341\pi$
$578$	42.9619	1.78698
$579$	13.0547	0.542536
$580$	25.0447	1.03992
$581$	−2.03402	−0.0843853
$582$	−30.5125	−1.26478
$583$	−6.35675	−0.263270
$584$	81.0698	3.35469
$585$	13.5356	0.559626
$586$	−63.2381	−2.61234
$587$	−10.9994	−0.453993	−0.226996	−	0.973896i	$-0.572891\pi$
$587$	−10.9994	−0.453993	−0.226996	+	0.973896i	$0.572891\pi$
$588$	21.4067	0.882796
$589$	42.1870	1.73829
$590$	−1.61561	−0.0665134
$591$	5.56944	0.229096
$592$	6.60303	0.271383
$593$	11.1741	0.458867	0.229433	−	0.973324i	$-0.426313\pi$
$593$	11.1741	0.458867	0.229433	+	0.973324i	$0.426313\pi$
$594$	9.36029	0.384057
$595$	0.0236854	0.000971005 0
$596$	41.4513	1.69791
$597$	−6.37695	−0.260991
$598$	82.1236	3.35829
$599$	35.9788	1.47005	0.735026	−	0.678038i	$-0.237170\pi$
$599$	35.9788	1.47005	0.735026	+	0.678038i	$0.237170\pi$
$600$	−16.6127	−0.678210
$601$	13.8140	0.563483	0.281742	−	0.959490i	$-0.409088\pi$
$601$	13.8140	0.563483	0.281742	+	0.959490i	$0.409088\pi$
$602$	−2.47001	−0.100670
$603$	−17.2554	−0.702696
$604$	−51.1629	−2.08179
$605$	−10.4718	−0.425741
$606$	32.3616	1.31460
$607$	25.5875	1.03856	0.519281	−	0.854603i	$-0.326200\pi$
$607$	25.5875	1.03856	0.519281	+	0.854603i	$0.326200\pi$
$608$	−24.1008	−0.977417
$609$	−0.535333	−0.0216928
$610$	10.4882	0.424656
$611$	28.0051	1.13297
$612$	−1.79472	−0.0725473
$613$	−12.5517	−0.506958	−0.253479	−	0.967341i	$-0.581575\pi$
$613$	−12.5517	−0.506958	−0.253479	+	0.967341i	$0.581575\pi$
$614$	55.9974	2.25987
$615$	8.22488	0.331659
$616$	0.825535	0.0332618
$617$	2.52537	0.101667	0.0508337	−	0.998707i	$-0.483812\pi$
$617$	2.52537	0.101667	0.0508337	+	0.998707i	$0.483812\pi$
$618$	0.0604963	0.00243352
$619$	29.8454	1.19959	0.599794	−	0.800155i	$-0.295249\pi$
$619$	29.8454	1.19959	0.599794	+	0.800155i	$0.295249\pi$
$620$	36.3399	1.45945
$621$	24.0677	0.965805
$622$	−48.4590	−1.94303
$623$	0.393584	0.0157686
$624$	23.7834	0.952097
$625$	9.95375	0.398150
$626$	54.0441	2.16004
$627$	3.56594	0.142410
$628$	43.7309	1.74505
$629$	0.161912	0.00645587
$630$	0.931418	0.0371086
$631$	−11.2275	−0.446958	−0.223479	−	0.974709i	$-0.571741\pi$
$631$	−11.2275	−0.446958	−0.223479	+	0.974709i	$0.571741\pi$
$632$	−5.18671	−0.206316
$633$	−17.2938	−0.687366
$634$	−31.0056	−1.23139
$635$	−8.44487	−0.335125
$636$	−20.2362	−0.802417
$637$	36.1238	1.43128
$638$	13.3297	0.527730
$639$	15.8220	0.625907
$640$	13.9922	0.553089
$641$	−3.64645	−0.144026	−0.0720130	−	0.997404i	$-0.522942\pi$
$641$	−3.64645	−0.144026	−0.0720130	+	0.997404i	$0.522942\pi$
$642$	9.42109	0.371821
$643$	18.5704	0.732346	0.366173	−	0.930547i	$-0.380668\pi$
$643$	18.5704	0.732346	0.366173	+	0.930547i	$0.380668\pi$
$644$	3.88691	0.153166
$645$	−5.01903	−0.197624
$646$	−2.17954	−0.0857530
$647$	21.1368	0.830975	0.415488	−	0.909599i	$-0.363611\pi$
$647$	21.1368	0.830975	0.415488	+	0.909599i	$0.363611\pi$
$648$	−29.6915	−1.16639
$649$	−0.591438	−0.0232160
$650$	−51.3342	−2.01349
$651$	−0.776771	−0.0304440
$652$	−4.40632	−0.172565
$653$	−42.0771	−1.64661	−0.823303	−	0.567603i	$-0.807871\pi$
$653$	−42.0771	−1.64661	−0.823303	+	0.567603i	$0.807871\pi$
$654$	7.23262	0.282818
$655$	16.4758	0.643763
$656$	−75.0513	−2.93026
$657$	33.4843	1.30635
$658$	1.92711	0.0751265
$659$	7.49926	0.292130	0.146065	−	0.989275i	$-0.453339\pi$
$659$	7.49926	0.292130	0.146065	+	0.989275i	$0.453339\pi$
$660$	3.07170	0.119566
$661$	−2.31422	−0.0900127	−0.0450064	−	0.998987i	$-0.514331\pi$
$661$	−2.31422	−0.0900127	−0.0450064	+	0.998987i	$0.514331\pi$
$662$	−10.0681	−0.391307
$663$	0.583191	0.0226493
$664$	88.0488	3.41696
$665$	0.778002	0.0301696
$666$	6.36715	0.246722
$667$	34.2742	1.32710
$668$	22.3739	0.865671
$669$	−11.4776	−0.443749
$670$	−18.0509	−0.697369
$671$	3.83951	0.148223
$672$	0.443757	0.0171183
$673$	−30.7796	−1.18647	−0.593234	−	0.805030i	$-0.702149\pi$
$673$	−30.7796	−1.18647	−0.593234	+	0.805030i	$0.702149\pi$
$674$	−24.8702	−0.957964
$675$	−15.0444	−0.579058
$676$	60.7302	2.33578
$677$	−13.1796	−0.506534	−0.253267	−	0.967396i	$-0.581505\pi$
$677$	−13.1796	−0.506534	−0.253267	+	0.967396i	$0.581505\pi$
$678$	−11.3374	−0.435412
$679$	−2.43702	−0.0935241
$680$	−1.02529	−0.0393182
$681$	−17.2415	−0.660694
$682$	19.3415	0.740625
$683$	−40.2761	−1.54112	−0.770562	−	0.637365i	$-0.780024\pi$
$683$	−40.2761	−1.54112	−0.770562	+	0.637365i	$0.780024\pi$
$684$	−58.9519	−2.25408
$685$	−11.6820	−0.446346
$686$	4.97860	0.190084
$687$	7.56019	0.288439
$688$	45.7981	1.74604
$689$	−34.1486	−1.30096
$690$	11.4831	0.437152
$691$	2.79819	0.106448	0.0532240	−	0.998583i	$-0.483050\pi$
$691$	2.79819	0.106448	0.0532240	+	0.998583i	$0.483050\pi$
$692$	−7.16770	−0.272475
$693$	0.340972	0.0129524
$694$	−29.4372	−1.11742
$695$	−1.35728	−0.0514844
$696$	23.1735	0.878391
$697$	−1.84033	−0.0697074
$698$	−77.8422	−2.94637
$699$	10.3718	0.392297
$700$	−2.42964	−0.0918319
$701$	12.8826	0.486567	0.243284	−	0.969955i	$-0.421775\pi$
$701$	12.8826	0.486567	0.243284	+	0.969955i	$0.421775\pi$
$702$	50.2837	1.89784
$703$	5.31840	0.200587
$704$	1.67266	0.0630407
$705$	3.91586	0.147480
$706$	10.1078	0.380412
$707$	2.58470	0.0972077
$708$	−1.88279	−0.0707596
$709$	50.4099	1.89318	0.946592	−	0.322434i	$-0.104501\pi$
$709$	50.4099	1.89318	0.946592	+	0.322434i	$0.104501\pi$
$710$	16.5514	0.621162
$711$	−2.14227	−0.0803415
$712$	−17.0375	−0.638507
$713$	49.7320	1.86248
$714$	0.0401309	0.00150186
$715$	5.18350	0.193852
$716$	88.3626	3.30226
$717$	−11.7214	−0.437742
$718$	−91.1080	−3.40012
$719$	9.23035	0.344234	0.172117	−	0.985077i	$-0.444939\pi$
$719$	9.23035	0.344234	0.172117	+	0.985077i	$0.444939\pi$
$720$	−17.2700	−0.643617
$721$	0.00483180	0.000179946 0
$722$	−23.5019	−0.874651
$723$	−12.0079	−0.446580
$724$	−13.1403	−0.488354
$725$	−21.4243	−0.795678
$726$	−17.7428	−0.658497
$727$	40.9591	1.51909	0.759545	−	0.650455i	$-0.225422\pi$
$727$	40.9591	1.51909	0.759545	+	0.650455i	$0.225422\pi$
$728$	4.43479	0.164364
$729$	−4.24814	−0.157338
$730$	35.0280	1.29644
$731$	1.12301	0.0415361
$732$	12.2227	0.451766
$733$	52.0903	1.92400	0.962000	−	0.273050i	$-0.0880325\pi$
$733$	52.0903	1.92400	0.962000	+	0.273050i	$0.0880325\pi$
$734$	−18.5908	−0.686197
$735$	5.05106	0.186311
$736$	−28.4111	−1.04725
$737$	−6.60805	−0.243411
$738$	−72.3702	−2.66398
$739$	11.0708	0.407246	0.203623	−	0.979049i	$-0.434728\pi$
$739$	11.0708	0.407246	0.203623	+	0.979049i	$0.434728\pi$
$740$	4.58127	0.168411
$741$	19.1563	0.703724
$742$	−2.34986	−0.0862660
$743$	1.47698	0.0541852	0.0270926	−	0.999633i	$-0.491375\pi$
$743$	1.47698	0.0541852	0.0270926	+	0.999633i	$0.491375\pi$
$744$	33.6249	1.23275
$745$	9.78075	0.358339
$746$	−90.2874	−3.30566
$747$	36.3669	1.33059
$748$	−0.687297	−0.0251301
$749$	0.752457	0.0274942
$750$	−16.3356	−0.596493
$751$	1.87041	0.0682521	0.0341260	−	0.999418i	$-0.489135\pi$
$751$	1.87041	0.0682521	0.0341260	+	0.999418i	$0.489135\pi$
$752$	−35.7318	−1.30301
$753$	−4.36530	−0.159080
$754$	71.6077	2.60780
$755$	−12.0723	−0.439355
$756$	2.37992	0.0865570
$757$	−12.0929	−0.439525	−0.219763	−	0.975553i	$-0.570528\pi$
$757$	−12.0929	−0.439525	−0.219763	+	0.975553i	$0.570528\pi$
$758$	67.2994	2.44443
$759$	4.20369	0.152584
$760$	−33.6782	−1.22164
$761$	17.8325	0.646426	0.323213	−	0.946326i	$-0.395237\pi$
$761$	17.8325	0.646426	0.323213	+	0.946326i	$0.395237\pi$
$762$	−14.3084	−0.518340
$763$	0.577665	0.0209129
$764$	−48.9339	−1.77037
$765$	−0.423478	−0.0153109
$766$	35.5178	1.28331
$767$	−3.17722	−0.114723
$768$	21.2905	0.768256
$769$	14.4799	0.522159	0.261080	−	0.965317i	$-0.415922\pi$
$769$	14.4799	0.522159	0.261080	+	0.965317i	$0.415922\pi$
$770$	0.356691	0.0128542
$771$	16.4766	0.593390
$772$	−82.6493	−2.97461
$773$	24.8630	0.894259	0.447129	−	0.894469i	$-0.352446\pi$
$773$	24.8630	0.894259	0.447129	+	0.894469i	$0.352446\pi$
$774$	44.1621	1.58737
$775$	−31.0867	−1.11667
$776$	105.494	3.78700
$777$	−0.0979252	−0.00351305
$778$	−21.1582	−0.758557
$779$	−60.4499	−2.16584
$780$	16.5012	0.590839
$781$	6.05909	0.216811
$782$	−2.56935	−0.0918797
$783$	20.9859	0.749973
$784$	−46.0905	−1.64609
$785$	10.3186	0.368288
$786$	27.9155	0.995714
$787$	−27.3344	−0.974366	−0.487183	−	0.873300i	$-0.661976\pi$
$787$	−27.3344	−0.974366	−0.487183	+	0.873300i	$0.661976\pi$
$788$	−35.2601	−1.25609
$789$	−17.3545	−0.617838
$790$	−2.24103	−0.0797324
$791$	−0.905515	−0.0321964
$792$	−14.7600	−0.524474
$793$	20.6259	0.732448
$794$	−88.7191	−3.14852
$795$	−4.77488	−0.169347
$796$	40.3724	1.43096
$797$	15.4414	0.546963	0.273482	−	0.961877i	$-0.411825\pi$
$797$	15.4414	0.546963	0.273482	+	0.961877i	$0.411825\pi$
$798$	1.31820	0.0466636
$799$	−0.876178	−0.0309970
$800$	17.7594	0.627888
$801$	−7.03701	−0.248641
$802$	18.2282	0.643659
$803$	12.8230	0.452513
$804$	−21.0362	−0.741888
$805$	0.917145	0.0323251
$806$	103.903	3.65983
$807$	−16.6530	−0.586214
$808$	−111.887	−3.93616
$809$	−1.36320	−0.0479275	−0.0239638	−	0.999713i	$-0.507629\pi$
$809$	−1.36320	−0.0479275	−0.0239638	+	0.999713i	$0.507629\pi$
$810$	−12.8289	−0.450760
$811$	−27.9722	−0.982237	−0.491118	−	0.871093i	$-0.663412\pi$
$811$	−27.9722	−0.982237	−0.491118	+	0.871093i	$0.663412\pi$
$812$	3.38919	0.118937
$813$	−13.6534	−0.478844
$814$	2.43833	0.0854634
$815$	−1.03970	−0.0364193
$816$	−0.744095	−0.0260485
$817$	36.8880	1.29055
$818$	6.82710	0.238704
$819$	1.83171	0.0640050
$820$	−52.0716	−1.81842
$821$	−13.2763	−0.463345	−0.231673	−	0.972794i	$-0.574420\pi$
$821$	−13.2763	−0.463345	−0.231673	+	0.972794i	$0.574420\pi$
$822$	−19.7932	−0.690368
$823$	−48.5501	−1.69235	−0.846175	−	0.532905i	$-0.821100\pi$
$823$	−48.5501	−1.69235	−0.846175	+	0.532905i	$0.821100\pi$
$824$	−0.209159	−0.00728641
$825$	−2.62766	−0.0914835
$826$	−0.218633	−0.00760721
$827$	−42.1085	−1.46425	−0.732127	−	0.681168i	$-0.761472\pi$
$827$	−42.1085	−1.46425	−0.732127	+	0.681168i	$0.761472\pi$
$828$	−69.4952	−2.41513
$829$	14.5465	0.505221	0.252611	−	0.967568i	$-0.418711\pi$
$829$	14.5465	0.505221	0.252611	+	0.967568i	$0.418711\pi$
$830$	38.0434	1.32051
$831$	10.0579	0.348903
$832$	8.98555	0.311518
$833$	−1.13018	−0.0391585
$834$	−2.29968	−0.0796315
$835$	5.27928	0.182697
$836$	−22.5759	−0.780804
$837$	30.4506	1.05253
$838$	−17.8089	−0.615197
$839$	−25.2250	−0.870865	−0.435432	−	0.900221i	$-0.643404\pi$
$839$	−25.2250	−0.870865	−0.435432	+	0.900221i	$0.643404\pi$
$840$	0.620101	0.0213955
$841$	0.885409	0.0305313
$842$	42.8901	1.47809
$843$	−13.1130	−0.451635
$844$	109.487	3.76868
$845$	14.3297	0.492958
$846$	−34.4554	−1.18460
$847$	−1.41711	−0.0486924
$848$	43.5703	1.49621
$849$	−1.20176	−0.0412444
$850$	1.60606	0.0550874
$851$	6.26958	0.214918
$852$	19.2886	0.660817
$853$	−8.41417	−0.288096	−0.144048	−	0.989571i	$-0.546012\pi$
$853$	−8.41417	−0.288096	−0.144048	+	0.989571i	$0.546012\pi$
$854$	1.41933	0.0485683
$855$	−13.9101	−0.475717
$856$	−32.5724	−1.11330
$857$	−1.08653	−0.0371151	−0.0185575	−	0.999828i	$-0.505907\pi$
$857$	−1.08653	−0.0371151	−0.0185575	+	0.999828i	$0.505907\pi$
$858$	8.78259	0.299833
$859$	−28.5911	−0.975515	−0.487758	−	0.872979i	$-0.662185\pi$
$859$	−28.5911	−0.975515	−0.487758	+	0.872979i	$0.662185\pi$
$860$	31.7754	1.08353
$861$	1.11304	0.0379322
$862$	20.8419	0.709878
$863$	−40.0675	−1.36391	−0.681957	−	0.731392i	$-0.738871\pi$
$863$	−40.0675	−1.36391	−0.681957	+	0.731392i	$0.738871\pi$
$864$	−17.3959	−0.591822
$865$	−1.69127	−0.0575050
$866$	41.8786	1.42309
$867$	11.8136	0.401212
$868$	4.91772	0.166918
$869$	−0.820393	−0.0278299
$870$	10.0126	0.339460
$871$	−35.4986	−1.20282
$872$	−25.0060	−0.846811
$873$	43.5722	1.47469
$874$	−84.3963	−2.85475
$875$	−1.30472	−0.0441075
$876$	40.8208	1.37921
$877$	37.5557	1.26816	0.634082	−	0.773266i	$-0.281378\pi$
$877$	37.5557	1.26816	0.634082	+	0.773266i	$0.281378\pi$
$878$	47.5109	1.60341
$879$	−17.3892	−0.586522
$880$	−6.61365	−0.222946
$881$	30.0107	1.01108	0.505542	−	0.862802i	$-0.331292\pi$
$881$	30.0107	1.01108	0.505542	+	0.862802i	$0.331292\pi$
$882$	−44.4440	−1.49651
$883$	37.2935	1.25503	0.627513	−	0.778606i	$-0.284073\pi$
$883$	37.2935	1.25503	0.627513	+	0.778606i	$0.284073\pi$
$884$	−3.69217	−0.124181
$885$	−0.444259	−0.0149336
$886$	−41.0623	−1.37951
$887$	4.78558	0.160684	0.0803421	−	0.996767i	$-0.474399\pi$
$887$	4.78558	0.160684	0.0803421	+	0.996767i	$0.474399\pi$
$888$	4.23900	0.142251
$889$	−1.14281	−0.0383285
$890$	−7.36143	−0.246756
$891$	−4.69637	−0.157334
$892$	72.6644	2.43298
$893$	−28.7802	−0.963091
$894$	16.5719	0.554246
$895$	20.8498	0.696932
$896$	1.89350	0.0632573
$897$	22.5823	0.754002
$898$	−19.0511	−0.635744
$899$	43.3638	1.44627
$900$	43.4404	1.44801
$901$	1.06838	0.0355931
$902$	−27.7145	−0.922792
$903$	−0.679202	−0.0226024
$904$	39.1980	1.30371
$905$	−3.10054	−0.103065
$906$	−20.4545	−0.679554
$907$	−20.5301	−0.681692	−0.340846	−	0.940119i	$-0.610714\pi$
$907$	−20.5301	−0.681692	−0.340846	+	0.940119i	$0.610714\pi$
$908$	109.155	3.62245
$909$	−46.2127	−1.53278
$910$	1.91615	0.0635198
$911$	−24.6637	−0.817146	−0.408573	−	0.912726i	$-0.633974\pi$
$911$	−24.6637	−0.817146	−0.408573	+	0.912726i	$0.633974\pi$
$912$	−24.4416	−0.809341
$913$	13.9269	0.460912
$914$	28.9739	0.958373
$915$	2.88405	0.0953437
$916$	−47.8635	−1.58145
$917$	2.22960	0.0736278
$918$	−1.57319	−0.0519231
$919$	44.1109	1.45508	0.727541	−	0.686064i	$-0.240663\pi$
$919$	44.1109	1.45508	0.727541	+	0.686064i	$0.240663\pi$
$920$	−39.7014	−1.30892
$921$	15.3981	0.507386
$922$	19.5675	0.644420
$923$	32.5496	1.07138
$924$	0.415680	0.0136749
$925$	−3.91901	−0.128856
$926$	−92.1815	−3.02927
$927$	−0.0863893	−0.00283740
$928$	−24.7731	−0.813217
$929$	42.1392	1.38254	0.691272	−	0.722595i	$-0.257051\pi$
$929$	42.1392	1.38254	0.691272	+	0.722595i	$0.257051\pi$
$930$	14.5284	0.476405
$931$	−37.1235	−1.21667
$932$	−65.6636	−2.15088
$933$	−13.3252	−0.436248
$934$	−80.2543	−2.62600
$935$	−0.162173	−0.00530362
$936$	−79.2911	−2.59171
$937$	−24.5641	−0.802473	−0.401237	−	0.915974i	$-0.631420\pi$
$937$	−24.5641	−0.802473	−0.401237	+	0.915974i	$0.631420\pi$
$938$	−2.44275	−0.0797587
$939$	14.8610	0.484971
$940$	−24.7912	−0.808601
$941$	−44.6160	−1.45444	−0.727220	−	0.686404i	$-0.759188\pi$
$941$	−44.6160	−1.45444	−0.727220	+	0.686404i	$0.759188\pi$
$942$	17.4832	0.569635
$943$	−71.2612	−2.32058
$944$	4.05382	0.131941
$945$	0.561561	0.0182676
$946$	16.9121	0.549859
$947$	−23.9047	−0.776798	−0.388399	−	0.921491i	$-0.626972\pi$
$947$	−23.9047	−0.776798	−0.388399	+	0.921491i	$0.626972\pi$
$948$	−2.61165	−0.0848225
$949$	68.8853	2.23611
$950$	52.7548	1.71159
$951$	−8.52590	−0.276471
$952$	−0.138748	−0.00449686
$953$	−34.6843	−1.12353	−0.561767	−	0.827295i	$-0.689878\pi$
$953$	−34.6843	−1.12353	−0.561767	+	0.827295i	$0.689878\pi$
$954$	42.0138	1.36025
$955$	−11.5463	−0.373630
$956$	74.2077	2.40005
$957$	3.66541	0.118486
$958$	−48.0243	−1.55160
$959$	−1.58087	−0.0510490
$960$	1.25642	0.0405507
$961$	31.9211	1.02971
$962$	13.0988	0.422321
$963$	−13.4534	−0.433530
$964$	76.0221	2.44851
$965$	−19.5017	−0.627783
$966$	1.55395	0.0499975
$967$	38.2000	1.22843	0.614215	−	0.789139i	$-0.289473\pi$
$967$	38.2000	1.22843	0.614215	+	0.789139i	$0.289473\pi$
$968$	61.3439	1.97167
$969$	−0.599330	−0.0192533
$970$	45.5809	1.46351
$971$	29.1481	0.935407	0.467704	−	0.883885i	$-0.345081\pi$
$971$	29.1481	0.935407	0.467704	+	0.883885i	$0.345081\pi$
$972$	−65.6956	−2.10719
$973$	−0.183674	−0.00588832
$974$	40.7374	1.30531
$975$	−14.1159	−0.452069
$976$	−26.3167	−0.842376
$977$	4.50175	0.144024	0.0720119	−	0.997404i	$-0.477058\pi$
$977$	4.50175	0.144024	0.0720119	+	0.997404i	$0.477058\pi$
$978$	−1.76161	−0.0563300
$979$	−2.69486	−0.0861280
$980$	−31.9782	−1.02151
$981$	−10.3283	−0.329756
$982$	−25.2516	−0.805812
$983$	−4.72159	−0.150595	−0.0752977	−	0.997161i	$-0.523991\pi$
$983$	−4.72159	−0.150595	−0.0752977	+	0.997161i	$0.523991\pi$
$984$	−48.1812	−1.53596
$985$	−8.31987	−0.265093
$986$	−2.24034	−0.0713470
$987$	0.529916	0.0168674
$988$	−121.278	−3.85837
$989$	43.4853	1.38275
$990$	−6.37739	−0.202687
$991$	51.9267	1.64951	0.824753	−	0.565493i	$-0.191314\pi$
$991$	51.9267	1.64951	0.824753	+	0.565493i	$0.191314\pi$
$992$	−35.9459	−1.14128
$993$	−2.76852	−0.0878563
$994$	2.23982	0.0710429
$995$	9.52616	0.302000
$996$	44.3350	1.40481
$997$	−51.5288	−1.63193	−0.815967	−	0.578098i	$-0.803795\pi$
$997$	−51.5288	−1.63193	−0.815967	+	0.578098i	$0.803795\pi$
$998$	64.7575	2.04986
$999$	3.83881	0.121455

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.e.1.8	✓	134

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.e.1.8	✓	134	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:	\( N \)	\(=\)	\( 6031 = 37 \cdot 163 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.53107 q^{2} -0.695993 q^{3} +4.40632 q^{4} +1.03970 q^{5} +1.76161 q^{6} +0.140699 q^{7} -6.09057 q^{8} -2.51559 q^{9} +O(q^{10})\)	\(q-2.53107 q^{2} -0.695993 q^{3} +4.40632 q^{4} +1.03970 q^{5} +1.76161 q^{6} +0.140699 q^{7} -6.09057 q^{8} -2.51559 q^{9} -2.63157 q^{10} -0.963359 q^{11} -3.06677 q^{12} -5.17518 q^{13} -0.356118 q^{14} -0.723627 q^{15} +6.60303 q^{16} +0.161912 q^{17} +6.36715 q^{18} +5.31840 q^{19} +4.58127 q^{20} -0.0979252 q^{21} +2.43833 q^{22} +6.26958 q^{23} +4.23900 q^{24} -3.91901 q^{25} +13.0988 q^{26} +3.83881 q^{27} +0.619963 q^{28} +5.46675 q^{29} +1.83155 q^{30} +7.93228 q^{31} -4.53159 q^{32} +0.670491 q^{33} -0.409812 q^{34} +0.146285 q^{35} -11.0845 q^{36} +1.00000 q^{37} -13.4612 q^{38} +3.60189 q^{39} -6.33240 q^{40} -11.3662 q^{41} +0.247856 q^{42} +6.93593 q^{43} -4.24487 q^{44} -2.61547 q^{45} -15.8687 q^{46} -5.41143 q^{47} -4.59566 q^{48} -6.98020 q^{49} +9.91930 q^{50} -0.112690 q^{51} -22.8035 q^{52} +6.59853 q^{53} -9.71631 q^{54} -1.00161 q^{55} -0.856935 q^{56} -3.70157 q^{57} -13.8367 q^{58} +0.613933 q^{59} -3.18853 q^{60} -3.98555 q^{61} -20.0772 q^{62} -0.353940 q^{63} -1.73628 q^{64} -5.38066 q^{65} -1.69706 q^{66} +6.85939 q^{67} +0.713438 q^{68} -4.36358 q^{69} -0.370258 q^{70} -6.28955 q^{71} +15.3214 q^{72} -13.3107 q^{73} -2.53107 q^{74} +2.72761 q^{75} +23.4346 q^{76} -0.135543 q^{77} -9.11664 q^{78} +0.851597 q^{79} +6.86520 q^{80} +4.87499 q^{81} +28.7686 q^{82} -14.4566 q^{83} -0.431490 q^{84} +0.168341 q^{85} -17.5553 q^{86} -3.80482 q^{87} +5.86740 q^{88} +2.79736 q^{89} +6.61995 q^{90} -0.728141 q^{91} +27.6258 q^{92} -5.52081 q^{93} +13.6967 q^{94} +5.52956 q^{95} +3.15396 q^{96} -17.3208 q^{97} +17.6674 q^{98} +2.42342 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9}+O(q^{10}) \) 134 * q + 9 * q^2 + 7 * q^3 + 149 * q^4 + 22 * q^5 + 20 * q^6 + 11 * q^7 + 27 * q^8 + 181 * q^9	\( 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9} + 15 q^{10} + 20 q^{11} + 28 q^{12} + 11 q^{13} + 17 q^{14} - 13 q^{15} + 143 q^{16} + 76 q^{17} + 23 q^{18} + 15 q^{19} + 67 q^{20} + 63 q^{21} + 2 q^{22} + 22 q^{23} + 33 q^{24} + 160 q^{25} + 65 q^{26} + 31 q^{27} + 10 q^{28} + 73 q^{29} + 20 q^{30} + 10 q^{31} + 53 q^{32} + 72 q^{33} - 7 q^{34} + 52 q^{35} + 201 q^{36} + 134 q^{37} + 70 q^{38} + 6 q^{39} + 11 q^{40} + 182 q^{41} - 15 q^{42} + 12 q^{43} + 33 q^{44} + 29 q^{45} + 24 q^{46} + 80 q^{47} + 21 q^{48} + 229 q^{49} + 37 q^{50} + 57 q^{51} - 15 q^{52} + 75 q^{53} + 95 q^{54} - 9 q^{55} + 39 q^{56} + 19 q^{57} - 21 q^{58} + 91 q^{59} + 62 q^{60} + 58 q^{61} + 108 q^{62} + 9 q^{63} + 167 q^{64} + 76 q^{65} + 105 q^{66} - 17 q^{67} + 109 q^{68} + 48 q^{69} - 55 q^{70} + 56 q^{71} + 48 q^{72} + 54 q^{73} + 9 q^{74} + 28 q^{75} + 82 q^{76} + 156 q^{77} + 16 q^{78} - 2 q^{79} + 98 q^{80} + 270 q^{81} - 42 q^{82} + 130 q^{83} + 229 q^{84} + 22 q^{85} + 72 q^{86} + 22 q^{87} + 61 q^{88} + 157 q^{89} + 176 q^{90} + 31 q^{91} - 18 q^{92} + 36 q^{93} + 83 q^{94} + 98 q^{95} + 111 q^{96} + 35 q^{97} + 53 q^{98} + 55 q^{99}+O(q^{100}) \) 134 * q + 9 * q^2 + 7 * q^3 + 149 * q^4 + 22 * q^5 + 20 * q^6 + 11 * q^7 + 27 * q^8 + 181 * q^9 + 15 * q^10 + 20 * q^11 + 28 * q^12 + 11 * q^13 + 17 * q^14 - 13 * q^15 + 143 * q^16 + 76 * q^17 + 23 * q^18 + 15 * q^19 + 67 * q^20 + 63 * q^21 + 2 * q^22 + 22 * q^23 + 33 * q^24 + 160 * q^25 + 65 * q^26 + 31 * q^27 + 10 * q^28 + 73 * q^29 + 20 * q^30 + 10 * q^31 + 53 * q^32 + 72 * q^33 - 7 * q^34 + 52 * q^35 + 201 * q^36 + 134 * q^37 + 70 * q^38 + 6 * q^39 + 11 * q^40 + 182 * q^41 - 15 * q^42 + 12 * q^43 + 33 * q^44 + 29 * q^45 + 24 * q^46 + 80 * q^47 + 21 * q^48 + 229 * q^49 + 37 * q^50 + 57 * q^51 - 15 * q^52 + 75 * q^53 + 95 * q^54 - 9 * q^55 + 39 * q^56 + 19 * q^57 - 21 * q^58 + 91 * q^59 + 62 * q^60 + 58 * q^61 + 108 * q^62 + 9 * q^63 + 167 * q^64 + 76 * q^65 + 105 * q^66 - 17 * q^67 + 109 * q^68 + 48 * q^69 - 55 * q^70 + 56 * q^71 + 48 * q^72 + 54 * q^73 + 9 * q^74 + 28 * q^75 + 82 * q^76 + 156 * q^77 + 16 * q^78 - 2 * q^79 + 98 * q^80 + 270 * q^81 - 42 * q^82 + 130 * q^83 + 229 * q^84 + 22 * q^85 + 72 * q^86 + 22 * q^87 + 61 * q^88 + 157 * q^89 + 176 * q^90 + 31 * q^91 - 18 * q^92 + 36 * q^93 + 83 * q^94 + 98 * q^95 + 111 * q^96 + 35 * q^97 + 53 * q^98 + 55 * q^99

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