LMFDB - Embedded newform 547.2.a.c.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,2,Mod(1,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("547.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	547.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:	$4.36781699056$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	547.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.12450 q^{2} +1.64314 q^{3} -0.735491 q^{4} +3.20489 q^{5} -1.84772 q^{6} -0.477395 q^{7} +3.07607 q^{8} -0.300096 q^{9} +O(q^{10})$	\(q-1.12450 q^{2} +1.64314 q^{3} -0.735491 q^{4} +3.20489 q^{5} -1.84772 q^{6} -0.477395 q^{7} +3.07607 q^{8} -0.300096 q^{9} -3.60392 q^{10} -2.01359 q^{11} -1.20851 q^{12} +4.76641 q^{13} +0.536832 q^{14} +5.26609 q^{15} -1.98807 q^{16} +5.32895 q^{17} +0.337460 q^{18} +3.11718 q^{19} -2.35717 q^{20} -0.784425 q^{21} +2.26429 q^{22} -8.35957 q^{23} +5.05441 q^{24} +5.27135 q^{25} -5.35985 q^{26} -5.42251 q^{27} +0.351119 q^{28} +3.14221 q^{29} -5.92173 q^{30} -0.615476 q^{31} -3.91655 q^{32} -3.30860 q^{33} -5.99242 q^{34} -1.53000 q^{35} +0.220718 q^{36} +8.45170 q^{37} -3.50528 q^{38} +7.83187 q^{39} +9.85848 q^{40} +9.49181 q^{41} +0.882089 q^{42} -6.62047 q^{43} +1.48097 q^{44} -0.961778 q^{45} +9.40037 q^{46} +9.76891 q^{47} -3.26668 q^{48} -6.77209 q^{49} -5.92766 q^{50} +8.75619 q^{51} -3.50565 q^{52} -12.1412 q^{53} +6.09764 q^{54} -6.45333 q^{55} -1.46850 q^{56} +5.12195 q^{57} -3.53343 q^{58} +7.86749 q^{59} -3.87316 q^{60} +11.3443 q^{61} +0.692106 q^{62} +0.143264 q^{63} +8.38031 q^{64} +15.2758 q^{65} +3.72053 q^{66} +10.5603 q^{67} -3.91939 q^{68} -13.7359 q^{69} +1.72049 q^{70} -6.65628 q^{71} -0.923118 q^{72} -13.0215 q^{73} -9.50397 q^{74} +8.66156 q^{75} -2.29266 q^{76} +0.961275 q^{77} -8.80697 q^{78} -9.15953 q^{79} -6.37156 q^{80} -8.00965 q^{81} -10.6736 q^{82} -8.75178 q^{83} +0.576938 q^{84} +17.0787 q^{85} +7.44474 q^{86} +5.16308 q^{87} -6.19393 q^{88} +17.8609 q^{89} +1.08152 q^{90} -2.27546 q^{91} +6.14839 q^{92} -1.01131 q^{93} -10.9852 q^{94} +9.99023 q^{95} -6.43543 q^{96} -11.2075 q^{97} +7.61525 q^{98} +0.604270 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 4 q^{2} + 8 q^{3} + 26 q^{4} + 29 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 29 q^{9}+O(q^{10}) $ 25 * q + 4 * q^2 + 8 * q^3 + 26 * q^4 + 29 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 29 * q^9	\( 25 q + 4 q^{2} + 8 q^{3} + 26 q^{4} + 29 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 29 q^{9} - q^{10} + 10 q^{11} + 14 q^{12} + 19 q^{13} + 9 q^{14} + 5 q^{15} + 16 q^{16} + 40 q^{17} - 8 q^{18} + 33 q^{20} - 8 q^{21} - 10 q^{22} + 26 q^{23} - 16 q^{24} + 36 q^{25} - 8 q^{26} + 11 q^{27} - 8 q^{28} + 30 q^{29} - 20 q^{30} - 5 q^{31} + 6 q^{32} + 10 q^{33} - 7 q^{34} + 11 q^{35} + 13 q^{36} + 26 q^{37} + 25 q^{38} - 17 q^{39} - 25 q^{40} + 9 q^{41} - 16 q^{42} - 10 q^{43} + 64 q^{45} - 34 q^{46} + 28 q^{47} + 23 q^{48} + 20 q^{49} - 9 q^{50} - 9 q^{51} - 2 q^{52} + 80 q^{53} - 13 q^{54} - q^{55} + 7 q^{56} - 8 q^{57} - 24 q^{58} - 2 q^{59} - 14 q^{60} + 22 q^{61} + 36 q^{62} - 9 q^{63} - 28 q^{64} + 30 q^{65} - 42 q^{66} - 16 q^{67} + 59 q^{68} + 22 q^{69} - 61 q^{70} - q^{71} - 44 q^{72} + 2 q^{73} - 8 q^{74} - 31 q^{75} - 46 q^{76} + 67 q^{77} - q^{78} - 34 q^{79} + 30 q^{80} - 11 q^{81} - 4 q^{82} + 15 q^{83} - 87 q^{84} + 15 q^{85} - 44 q^{86} - 29 q^{87} - 55 q^{88} + 38 q^{89} - 90 q^{90} - 41 q^{91} + 40 q^{92} - 4 q^{93} - 46 q^{94} - 46 q^{95} - 87 q^{96} - 2 q^{97} - 14 q^{98} - 41 q^{99}+O(q^{100}) \) 25 * q + 4 * q^2 + 8 * q^3 + 26 * q^4 + 29 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 29 * q^9 - q^10 + 10 * q^11 + 14 * q^12 + 19 * q^13 + 9 * q^14 + 5 * q^15 + 16 * q^16 + 40 * q^17 - 8 * q^18 + 33 * q^20 - 8 * q^21 - 10 * q^22 + 26 * q^23 - 16 * q^24 + 36 * q^25 - 8 * q^26 + 11 * q^27 - 8 * q^28 + 30 * q^29 - 20 * q^30 - 5 * q^31 + 6 * q^32 + 10 * q^33 - 7 * q^34 + 11 * q^35 + 13 * q^36 + 26 * q^37 + 25 * q^38 - 17 * q^39 - 25 * q^40 + 9 * q^41 - 16 * q^42 - 10 * q^43 + 64 * q^45 - 34 * q^46 + 28 * q^47 + 23 * q^48 + 20 * q^49 - 9 * q^50 - 9 * q^51 - 2 * q^52 + 80 * q^53 - 13 * q^54 - q^55 + 7 * q^56 - 8 * q^57 - 24 * q^58 - 2 * q^59 - 14 * q^60 + 22 * q^61 + 36 * q^62 - 9 * q^63 - 28 * q^64 + 30 * q^65 - 42 * q^66 - 16 * q^67 + 59 * q^68 + 22 * q^69 - 61 * q^70 - q^71 - 44 * q^72 + 2 * q^73 - 8 * q^74 - 31 * q^75 - 46 * q^76 + 67 * q^77 - q^78 - 34 * q^79 + 30 * q^80 - 11 * q^81 - 4 * q^82 + 15 * q^83 - 87 * q^84 + 15 * q^85 - 44 * q^86 - 29 * q^87 - 55 * q^88 + 38 * q^89 - 90 * q^90 - 41 * q^91 + 40 * q^92 - 4 * q^93 - 46 * q^94 - 46 * q^95 - 87 * q^96 - 2 * q^97 - 14 * q^98 - 41 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.12450	−0.795144	−0.397572	−	0.917571i	$-0.630147\pi$
$2$	−1.12450	−0.795144	−0.397572	+	0.917571i	$0.630147\pi$
$3$	1.64314	0.948666	0.474333	−	0.880345i	$-0.342689\pi$
$3$	1.64314	0.948666	0.474333	+	0.880345i	$0.342689\pi$
$4$	−0.735491	−0.367745
$5$	3.20489	1.43327	0.716636	−	0.697447i	$-0.245681\pi$
$5$	3.20489	1.43327	0.716636	+	0.697447i	$0.245681\pi$
$6$	−1.84772	−0.754327
$7$	−0.477395	−0.180438	−0.0902191	−	0.995922i	$-0.528757\pi$
$7$	−0.477395	−0.180438	−0.0902191	+	0.995922i	$0.528757\pi$
$8$	3.07607	1.08756
$9$	−0.300096	−0.100032
$10$	−3.60392	−1.13966
$11$	−2.01359	−0.607119	−0.303559	−	0.952812i	$-0.598175\pi$
$11$	−2.01359	−0.607119	−0.303559	+	0.952812i	$0.598175\pi$
$12$	−1.20851	−0.348868
$13$	4.76641	1.32196	0.660982	−	0.750401i	$-0.270140\pi$
$13$	4.76641	1.32196	0.660982	+	0.750401i	$0.270140\pi$
$14$	0.536832	0.143474
$15$	5.26609	1.35970
$16$	−1.98807	−0.497018
$17$	5.32895	1.29246	0.646230	−	0.763143i	$-0.276345\pi$
$17$	5.32895	1.29246	0.646230	+	0.763143i	$0.276345\pi$
$18$	0.337460	0.0795400
$19$	3.11718	0.715130	0.357565	−	0.933888i	$-0.383607\pi$
$19$	3.11718	0.715130	0.357565	+	0.933888i	$0.383607\pi$
$20$	−2.35717	−0.527080
$21$	−0.784425	−0.171176
$22$	2.26429	0.482747
$23$	−8.35957	−1.74309	−0.871546	−	0.490314i	$-0.836882\pi$
$23$	−8.35957	−1.74309	−0.871546	+	0.490314i	$0.836882\pi$
$24$	5.05441	1.03173
$25$	5.27135	1.05427
$26$	−5.35985	−1.05115
$27$	−5.42251	−1.04356
$28$	0.351119	0.0663553
$29$	3.14221	0.583493	0.291747	−	0.956496i	$-0.405764\pi$
$29$	3.14221	0.583493	0.291747	+	0.956496i	$0.405764\pi$
$30$	−5.92173	−1.08116
$31$	−0.615476	−0.110543	−0.0552714	−	0.998471i	$-0.517602\pi$
$31$	−0.615476	−0.110543	−0.0552714	+	0.998471i	$0.517602\pi$
$32$	−3.91655	−0.692354
$33$	−3.30860	−0.575953
$34$	−5.99242	−1.02769
$35$	−1.53000	−0.258617
$36$	0.220718	0.0367864
$37$	8.45170	1.38945	0.694726	−	0.719275i	$-0.255526\pi$
$37$	8.45170	1.38945	0.694726	+	0.719275i	$0.255526\pi$
$38$	−3.50528	−0.568631
$39$	7.83187	1.25410
$40$	9.85848	1.55876
$41$	9.49181	1.48237	0.741185	−	0.671300i	$-0.234264\pi$
$41$	9.49181	1.48237	0.741185	+	0.671300i	$0.234264\pi$
$42$	0.882089	0.136109
$43$	−6.62047	−1.00961	−0.504806	−	0.863233i	$-0.668436\pi$
$43$	−6.62047	−1.00961	−0.504806	+	0.863233i	$0.668436\pi$
$44$	1.48097	0.223265
$45$	−0.961778	−0.143373
$46$	9.40037	1.38601
$47$	9.76891	1.42494	0.712471	−	0.701701i	$-0.247576\pi$
$47$	9.76891	1.42494	0.712471	+	0.701701i	$0.247576\pi$
$48$	−3.26668	−0.471504
$49$	−6.77209	−0.967442
$50$	−5.92766	−0.838297
$51$	8.75619	1.22611
$52$	−3.50565	−0.486147
$53$	−12.1412	−1.66772	−0.833861	−	0.551975i	$-0.813874\pi$
$53$	−12.1412	−1.66772	−0.833861	+	0.551975i	$0.813874\pi$
$54$	6.09764	0.829784
$55$	−6.45333	−0.870167
$56$	−1.46850	−0.196236
$57$	5.12195	0.678419
$58$	−3.53343	−0.463962
$59$	7.86749	1.02426	0.512130	−	0.858908i	$-0.328857\pi$
$59$	7.86749	1.02426	0.512130	+	0.858908i	$0.328857\pi$
$60$	−3.87316	−0.500023
$61$	11.3443	1.45249	0.726243	−	0.687438i	$-0.241265\pi$
$61$	11.3443	1.45249	0.726243	+	0.687438i	$0.241265\pi$
$62$	0.692106	0.0878975
$63$	0.143264	0.0180496
$64$	8.38031	1.04754
$65$	15.2758	1.89474
$66$	3.72053	0.457966
$67$	10.5603	1.29015	0.645074	−	0.764120i	$-0.276826\pi$
$67$	10.5603	1.29015	0.645074	+	0.764120i	$0.276826\pi$
$68$	−3.91939	−0.475296
$69$	−13.7359	−1.65361
$70$	1.72049	0.205638
$71$	−6.65628	−0.789955	−0.394978	−	0.918691i	$-0.629248\pi$
$71$	−6.65628	−0.789955	−0.394978	+	0.918691i	$0.629248\pi$
$72$	−0.923118	−0.108790
$73$	−13.0215	−1.52405	−0.762026	−	0.647546i	$-0.775795\pi$
$73$	−13.0215	−1.52405	−0.762026	+	0.647546i	$0.775795\pi$
$74$	−9.50397	−1.10481
$75$	8.66156	1.00015
$76$	−2.29266	−0.262986
$77$	0.961275	0.109547
$78$	−8.80697	−0.997193
$79$	−9.15953	−1.03053	−0.515264	−	0.857031i	$-0.672306\pi$
$79$	−9.15953	−1.03053	−0.515264	+	0.857031i	$0.672306\pi$
$80$	−6.37156	−0.712362
$81$	−8.00965	−0.889961
$82$	−10.6736	−1.17870
$83$	−8.75178	−0.960633	−0.480316	−	0.877095i	$-0.659478\pi$
$83$	−8.75178	−0.960633	−0.480316	+	0.877095i	$0.659478\pi$
$84$	0.576938	0.0629491
$85$	17.0787	1.85245
$86$	7.44474	0.802787
$87$	5.16308	0.553541
$88$	−6.19393	−0.660275
$89$	17.8609	1.89325	0.946626	−	0.322335i	$-0.104468\pi$
$89$	17.8609	1.89325	0.946626	+	0.322335i	$0.104468\pi$
$90$	1.08152	0.114002
$91$	−2.27546	−0.238533
$92$	6.14839	0.641014
$93$	−1.01131	−0.104868
$94$	−10.9852	−1.13303
$95$	9.99023	1.02498
$96$	−6.43543	−0.656813
$97$	−11.2075	−1.13795	−0.568975	−	0.822355i	$-0.692660\pi$
$97$	−11.2075	−1.13795	−0.568975	+	0.822355i	$0.692660\pi$
$98$	7.61525	0.769256
$99$	0.604270	0.0607314
$100$	−3.87703	−0.387703
$101$	−5.79188	−0.576314	−0.288157	−	0.957583i	$-0.593042\pi$
$101$	−5.79188	−0.576314	−0.288157	+	0.957583i	$0.593042\pi$
$102$	−9.84637	−0.974936
$103$	−4.93441	−0.486201	−0.243101	−	0.970001i	$-0.578165\pi$
$103$	−4.93441	−0.486201	−0.243101	+	0.970001i	$0.578165\pi$
$104$	14.6618	1.43771
$105$	−2.51400	−0.245341
$106$	13.6528	1.32608
$107$	8.66134	0.837324	0.418662	−	0.908142i	$-0.362499\pi$
$107$	8.66134	0.837324	0.418662	+	0.908142i	$0.362499\pi$
$108$	3.98821	0.383766
$109$	−15.3515	−1.47041	−0.735205	−	0.677845i	$-0.762914\pi$
$109$	−15.3515	−1.47041	−0.735205	+	0.677845i	$0.762914\pi$
$110$	7.25680	0.691908
$111$	13.8873	1.31813
$112$	0.949094	0.0896810
$113$	7.81950	0.735597	0.367798	−	0.929906i	$-0.380112\pi$
$113$	7.81950	0.735597	0.367798	+	0.929906i	$0.380112\pi$
$114$	−5.75966	−0.539441
$115$	−26.7916	−2.49833
$116$	−2.31107	−0.214577
$117$	−1.43038	−0.132239
$118$	−8.84702	−0.814434
$119$	−2.54401	−0.233209
$120$	16.1988	1.47875
$121$	−6.94547	−0.631407
$122$	−12.7567	−1.15494
$123$	15.5963	1.40628
$124$	0.452677	0.0406516
$125$	0.869654	0.0777842
$126$	−0.161101	−0.0143520
$127$	−11.0110	−0.977070	−0.488535	−	0.872544i	$-0.662469\pi$
$127$	−11.0110	−0.977070	−0.488535	+	0.872544i	$0.662469\pi$
$128$	−1.59060	−0.140591
$129$	−10.8783	−0.957785
$130$	−17.1778	−1.50659
$131$	−5.99170	−0.523498	−0.261749	−	0.965136i	$-0.584299\pi$
$131$	−5.99170	−0.523498	−0.261749	+	0.965136i	$0.584299\pi$
$132$	2.43345	0.211804
$133$	−1.48812	−0.129037
$134$	−11.8751	−1.02585
$135$	−17.3786	−1.49571
$136$	16.3922	1.40562
$137$	−15.1752	−1.29650	−0.648250	−	0.761427i	$-0.724499\pi$
$137$	−15.1752	−1.29650	−0.648250	+	0.761427i	$0.724499\pi$
$138$	15.4461	1.31486
$139$	−17.9144	−1.51948	−0.759742	−	0.650225i	$-0.774675\pi$
$139$	−17.9144	−1.51948	−0.759742	+	0.650225i	$0.774675\pi$
$140$	1.12530	0.0951053
$141$	16.0517	1.35179
$142$	7.48501	0.628128
$143$	−9.59758	−0.802590
$144$	0.596613	0.0497178
$145$	10.0704	0.836305
$146$	14.6427	1.21184
$147$	−11.1275	−0.917780
$148$	−6.21615	−0.510965
$149$	−13.6327	−1.11683	−0.558417	−	0.829561i	$-0.688591\pi$
$149$	−13.6327	−1.11683	−0.558417	+	0.829561i	$0.688591\pi$
$150$	−9.73996	−0.795264
$151$	−11.7611	−0.957102	−0.478551	−	0.878060i	$-0.658838\pi$
$151$	−11.7611	−0.957102	−0.478551	+	0.878060i	$0.658838\pi$
$152$	9.58866	0.777743
$153$	−1.59920	−0.129287
$154$	−1.08096	−0.0871060
$155$	−1.97254	−0.158438
$156$	−5.76027	−0.461191
$157$	3.59096	0.286590	0.143295	−	0.989680i	$-0.454230\pi$
$157$	3.59096	0.286590	0.143295	+	0.989680i	$0.454230\pi$
$158$	10.2999	0.819419
$159$	−19.9497	−1.58211
$160$	−12.5521	−0.992332
$161$	3.99081	0.314520
$162$	9.00689	0.707648
$163$	−2.78765	−0.218345	−0.109173	−	0.994023i	$-0.534820\pi$
$163$	−2.78765	−0.218345	−0.109173	+	0.994023i	$0.534820\pi$
$164$	−6.98114	−0.545135
$165$	−10.6037	−0.825498
$166$	9.84141	0.763842
$167$	23.9926	1.85661	0.928303	−	0.371825i	$-0.121268\pi$
$167$	23.9926	1.85661	0.928303	+	0.371825i	$0.121268\pi$
$168$	−2.41295	−0.186163
$169$	9.71868	0.747591
$170$	−19.2051	−1.47296
$171$	−0.935454	−0.0715360
$172$	4.86930	0.371280
$173$	−6.40799	−0.487190	−0.243595	−	0.969877i	$-0.578327\pi$
$173$	−6.40799	−0.487190	−0.243595	+	0.969877i	$0.578327\pi$
$174$	−5.80591	−0.440145
$175$	−2.51651	−0.190231
$176$	4.00315	0.301749
$177$	12.9274	0.971681
$178$	−20.0846	−1.50541
$179$	6.95679	0.519975	0.259987	−	0.965612i	$-0.416282\pi$
$179$	6.95679	0.519975	0.259987	+	0.965612i	$0.416282\pi$
$180$	0.707379	0.0527249
$181$	−16.9630	−1.26085	−0.630424	−	0.776251i	$-0.717119\pi$
$181$	−16.9630	−1.26085	−0.630424	+	0.776251i	$0.717119\pi$
$182$	2.55876	0.189668
$183$	18.6402	1.37793
$184$	−25.7146	−1.89571
$185$	27.0868	1.99146
$186$	1.13723	0.0833854
$187$	−10.7303	−0.784676
$188$	−7.18495	−0.524016
$189$	2.58868	0.188299
$190$	−11.2341	−0.815004
$191$	−5.80268	−0.419867	−0.209934	−	0.977716i	$-0.567325\pi$
$191$	−5.80268	−0.419867	−0.209934	+	0.977716i	$0.567325\pi$
$192$	13.7700	0.993765
$193$	18.6628	1.34338	0.671689	−	0.740833i	$-0.265569\pi$
$193$	18.6628	1.34338	0.671689	+	0.740833i	$0.265569\pi$
$194$	12.6029	0.904834
$195$	25.1003	1.79747
$196$	4.98081	0.355772
$197$	−16.0723	−1.14511	−0.572553	−	0.819868i	$-0.694047\pi$
$197$	−16.0723	−1.14511	−0.572553	+	0.819868i	$0.694047\pi$
$198$	−0.679504	−0.0482902
$199$	12.6031	0.893409	0.446704	−	0.894682i	$-0.352598\pi$
$199$	12.6031	0.893409	0.446704	+	0.894682i	$0.352598\pi$
$200$	16.2150	1.14658
$201$	17.3521	1.22392
$202$	6.51299	0.458253
$203$	−1.50007	−0.105284
$204$	−6.44010	−0.450897
$205$	30.4202	2.12464
$206$	5.54876	0.386600
$207$	2.50868	0.174365
$208$	−9.47597	−0.657040
$209$	−6.27671	−0.434169
$210$	2.82700	0.195082
$211$	−10.1908	−0.701564	−0.350782	−	0.936457i	$-0.614084\pi$
$211$	−10.1908	−0.701564	−0.350782	+	0.936457i	$0.614084\pi$
$212$	8.92974	0.613297
$213$	−10.9372	−0.749404
$214$	−9.73972	−0.665793
$215$	−21.2179	−1.44705
$216$	−16.6800	−1.13493
$217$	0.293825	0.0199461
$218$	17.2629	1.16919
$219$	−21.3961	−1.44582
$220$	4.74637	0.320000
$221$	25.3999	1.70859
$222$	−15.6163	−1.04810
$223$	6.27947	0.420504	0.210252	−	0.977647i	$-0.432571\pi$
$223$	6.27947	0.420504	0.210252	+	0.977647i	$0.432571\pi$
$224$	1.86974	0.124927
$225$	−1.58191	−0.105461
$226$	−8.79306	−0.584905
$227$	−0.588713	−0.0390742	−0.0195371	−	0.999809i	$-0.506219\pi$
$227$	−0.588713	−0.0390742	−0.0195371	+	0.999809i	$0.506219\pi$
$228$	−3.76715	−0.249486
$229$	−2.99765	−0.198090	−0.0990450	−	0.995083i	$-0.531579\pi$
$229$	−2.99765	−0.198090	−0.0990450	+	0.995083i	$0.531579\pi$
$230$	30.1272	1.98653
$231$	1.57951	0.103924
$232$	9.66565	0.634581
$233$	0.790948	0.0518167	0.0259084	−	0.999664i	$-0.491752\pi$
$233$	0.790948	0.0518167	0.0259084	+	0.999664i	$0.491752\pi$
$234$	1.60847	0.105149
$235$	31.3083	2.04233
$236$	−5.78647	−0.376667
$237$	−15.0504	−0.977627
$238$	2.86075	0.185435
$239$	26.2494	1.69793	0.848966	−	0.528447i	$-0.177226\pi$
$239$	26.2494	1.69793	0.848966	+	0.528447i	$0.177226\pi$
$240$	−10.4694	−0.675794
$241$	−14.7073	−0.947380	−0.473690	−	0.880692i	$-0.657078\pi$
$241$	−14.7073	−0.947380	−0.473690	+	0.880692i	$0.657078\pi$
$242$	7.81021	0.502059
$243$	3.10658	0.199287
$244$	−8.34362	−0.534145
$245$	−21.7039	−1.38661
$246$	−17.5382	−1.11819
$247$	14.8578	0.945376
$248$	−1.89325	−0.120221
$249$	−14.3804	−0.911320
$250$	−0.977930	−0.0618497
$251$	−0.995852	−0.0628576	−0.0314288	−	0.999506i	$-0.510006\pi$
$251$	−0.995852	−0.0628576	−0.0314288	+	0.999506i	$0.510006\pi$
$252$	−0.105370	−0.00663766
$253$	16.8327	1.05826
$254$	12.3819	0.776912
$255$	28.0627	1.75735
$256$	−14.9720	−0.935749
$257$	−8.92443	−0.556691	−0.278345	−	0.960481i	$-0.589786\pi$
$257$	−8.92443	−0.556691	−0.278345	+	0.960481i	$0.589786\pi$
$258$	12.2327	0.761577
$259$	−4.03480	−0.250710
$260$	−11.2352	−0.696781
$261$	−0.942965	−0.0583681
$262$	6.73770	0.416256
$263$	−3.06500	−0.188996	−0.0944981	−	0.995525i	$-0.530125\pi$
$263$	−3.06500	−0.188996	−0.0944981	+	0.995525i	$0.530125\pi$
$264$	−10.1775	−0.626381
$265$	−38.9113	−2.39030
$266$	1.67340	0.102603
$267$	29.3479	1.79606
$268$	−7.76702	−0.474446
$269$	24.7874	1.51131	0.755656	−	0.654968i	$-0.227318\pi$
$269$	24.7874	1.51131	0.755656	+	0.654968i	$0.227318\pi$
$270$	19.5423	1.18931
$271$	6.55308	0.398071	0.199036	−	0.979992i	$-0.436219\pi$
$271$	6.55308	0.398071	0.199036	+	0.979992i	$0.436219\pi$
$272$	−10.5943	−0.642375
$273$	−3.73889	−0.226288
$274$	17.0645	1.03091
$275$	−10.6143	−0.640068
$276$	10.1027	0.608108
$277$	−13.3895	−0.804498	−0.402249	−	0.915530i	$-0.631771\pi$
$277$	−13.3895	−0.804498	−0.402249	+	0.915530i	$0.631771\pi$
$278$	20.1449	1.20821
$279$	0.184702	0.0110578
$280$	−4.70639	−0.281260
$281$	4.31099	0.257172	0.128586	−	0.991698i	$-0.458956\pi$
$281$	4.31099	0.257172	0.128586	+	0.991698i	$0.458956\pi$
$282$	−18.0502	−1.07487
$283$	−31.4141	−1.86738	−0.933688	−	0.358087i	$-0.883429\pi$
$283$	−31.4141	−1.86738	−0.933688	+	0.358087i	$0.883429\pi$
$284$	4.89563	0.290502
$285$	16.4153	0.972360
$286$	10.7925	0.638175
$287$	−4.53134	−0.267476
$288$	1.17534	0.0692577
$289$	11.3977	0.670451
$290$	−11.3243	−0.664983
$291$	−18.4155	−1.07953
$292$	9.57720	0.560463
$293$	13.1853	0.770295	0.385147	−	0.922855i	$-0.374151\pi$
$293$	13.1853	0.770295	0.385147	+	0.922855i	$0.374151\pi$
$294$	12.5129	0.729767
$295$	25.2145	1.46804
$296$	25.9980	1.51111
$297$	10.9187	0.633567
$298$	15.3300	0.888044
$299$	−39.8452	−2.30431
$300$	−6.37050	−0.367801
$301$	3.16058	0.182173
$302$	13.2254	0.761034
$303$	−9.51686	−0.546729
$304$	−6.19717	−0.355432
$305$	36.3572	2.08181
$306$	1.79830	0.102802
$307$	15.2326	0.869369	0.434685	−	0.900583i	$-0.356860\pi$
$307$	15.2326	0.869369	0.434685	+	0.900583i	$0.356860\pi$
$308$	−0.707009	−0.0402856
$309$	−8.10791	−0.461243
$310$	2.21813	0.125981
$311$	6.61471	0.375086	0.187543	−	0.982256i	$-0.439948\pi$
$311$	6.61471	0.375086	0.187543	+	0.982256i	$0.439948\pi$
$312$	24.0914	1.36391
$313$	4.84654	0.273943	0.136971	−	0.990575i	$-0.456263\pi$
$313$	4.84654	0.273943	0.136971	+	0.990575i	$0.456263\pi$
$314$	−4.03805	−0.227880
$315$	0.459147	0.0258700
$316$	6.73676	0.378972
$317$	0.628994	0.0353278	0.0176639	−	0.999844i	$-0.494377\pi$
$317$	0.628994	0.0353278	0.0176639	+	0.999844i	$0.494377\pi$
$318$	22.4335	1.25801
$319$	−6.32711	−0.354250
$320$	26.8580	1.50141
$321$	14.2318	0.794341
$322$	−4.48769	−0.250089
$323$	16.6113	0.924276
$324$	5.89103	0.327279
$325$	25.1254	1.39371
$326$	3.13472	0.173616
$327$	−25.2247	−1.39493
$328$	29.1975	1.61216
$329$	−4.66362	−0.257114
$330$	11.9239	0.656390
$331$	2.04344	0.112318	0.0561589	−	0.998422i	$-0.482115\pi$
$331$	2.04344	0.112318	0.0561589	+	0.998422i	$0.482115\pi$
$332$	6.43686	0.353268
$333$	−2.53633	−0.138990
$334$	−26.9798	−1.47627
$335$	33.8447	1.84913
$336$	1.55949	0.0850773
$337$	10.7179	0.583843	0.291921	−	0.956442i	$-0.405705\pi$
$337$	10.7179	0.583843	0.291921	+	0.956442i	$0.405705\pi$
$338$	−10.9287	−0.594442
$339$	12.8485	0.697836
$340$	−12.5612	−0.681229
$341$	1.23931	0.0671127
$342$	1.05192	0.0568814
$343$	6.57472	0.355002
$344$	−20.3650	−1.09801
$345$	−44.0222	−2.37008
$346$	7.20581	0.387387
$347$	1.99078	0.106871	0.0534353	−	0.998571i	$-0.482983\pi$
$347$	1.99078	0.106871	0.0534353	+	0.998571i	$0.482983\pi$
$348$	−3.79740	−0.203562
$349$	0.669835	0.0358555	0.0179277	−	0.999839i	$-0.494293\pi$
$349$	0.669835	0.0358555	0.0179277	+	0.999839i	$0.494293\pi$
$350$	2.82983	0.151261
$351$	−25.8459	−1.37955
$352$	7.88630	0.420341
$353$	−14.5611	−0.775010	−0.387505	−	0.921868i	$-0.626663\pi$
$353$	−14.5611	−0.775010	−0.387505	+	0.921868i	$0.626663\pi$
$354$	−14.5369	−0.772626
$355$	−21.3327	−1.13222
$356$	−13.1365	−0.696235
$357$	−4.18016	−0.221237
$358$	−7.82293	−0.413455
$359$	12.5743	0.663647	0.331824	−	0.943341i	$-0.392336\pi$
$359$	12.5743	0.663647	0.331824	+	0.943341i	$0.392336\pi$
$360$	−2.95850	−0.155926
$361$	−9.28320	−0.488590
$362$	19.0749	1.00256
$363$	−11.4124	−0.598994
$364$	1.67358	0.0877194
$365$	−41.7326	−2.18438
$366$	−20.9610	−1.09565
$367$	−1.04392	−0.0544924	−0.0272462	−	0.999629i	$-0.508674\pi$
$367$	−1.04392	−0.0544924	−0.0272462	+	0.999629i	$0.508674\pi$
$368$	16.6194	0.866347
$369$	−2.84846	−0.148285
$370$	−30.4592	−1.58350
$371$	5.79614	0.300921
$372$	0.743812	0.0385648
$373$	24.8109	1.28466	0.642329	−	0.766429i	$-0.277968\pi$
$373$	24.8109	1.28466	0.642329	+	0.766429i	$0.277968\pi$
$374$	12.0663	0.623931
$375$	1.42896	0.0737913
$376$	30.0499	1.54970
$377$	14.9771	0.771358
$378$	−2.91098	−0.149725
$379$	34.3072	1.76224	0.881122	−	0.472888i	$-0.156789\pi$
$379$	34.3072	1.76224	0.881122	+	0.472888i	$0.156789\pi$
$380$	−7.34772	−0.376930
$381$	−18.0926	−0.926913
$382$	6.52514	0.333855
$383$	23.0399	1.17728	0.588642	−	0.808394i	$-0.299663\pi$
$383$	23.0399	1.17728	0.588642	+	0.808394i	$0.299663\pi$
$384$	−2.61358	−0.133374
$385$	3.08078	0.157011
$386$	−20.9864	−1.06818
$387$	1.98678	0.100994
$388$	8.24302	0.418476
$389$	−26.0973	−1.32318	−0.661592	−	0.749864i	$-0.730119\pi$
$389$	−26.0973	−1.32318	−0.661592	+	0.749864i	$0.730119\pi$
$390$	−28.2254	−1.42925
$391$	−44.5477	−2.25287
$392$	−20.8314	−1.05215
$393$	−9.84520	−0.496625
$394$	18.0734	0.910525
$395$	−29.3553	−1.47703
$396$	−0.444435	−0.0223337
$397$	5.67515	0.284828	0.142414	−	0.989807i	$-0.454514\pi$
$397$	5.67515	0.284828	0.142414	+	0.989807i	$0.454514\pi$
$398$	−14.1722	−0.710389
$399$	−2.44519	−0.122413
$400$	−10.4798	−0.523991
$401$	35.5293	1.77425	0.887124	−	0.461532i	$-0.152700\pi$
$401$	35.5293	1.77425	0.887124	+	0.461532i	$0.152700\pi$
$402$	−19.5125	−0.973194
$403$	−2.93361	−0.146134
$404$	4.25988	0.211937
$405$	−25.6701	−1.27556
$406$	1.68684	0.0837164
$407$	−17.0182	−0.843562
$408$	26.9347	1.33346
$409$	12.4360	0.614922	0.307461	−	0.951561i	$-0.400521\pi$
$409$	12.4360	0.614922	0.307461	+	0.951561i	$0.400521\pi$
$410$	−34.2077	−1.68940
$411$	−24.9349	−1.22995
$412$	3.62921	0.178798
$413$	−3.75590	−0.184816
$414$	−2.82102	−0.138645
$415$	−28.0485	−1.37685
$416$	−18.6679	−0.915268
$417$	−29.4359	−1.44148
$418$	7.05818	0.345227
$419$	−18.1724	−0.887782	−0.443891	−	0.896081i	$-0.646402\pi$
$419$	−18.1724	−0.887782	−0.443891	+	0.896081i	$0.646402\pi$
$420$	1.84902	0.0902232
$421$	17.2430	0.840372	0.420186	−	0.907438i	$-0.361965\pi$
$421$	17.2430	0.840372	0.420186	+	0.907438i	$0.361965\pi$
$422$	11.4596	0.557845
$423$	−2.93162	−0.142540
$424$	−37.3472	−1.81374
$425$	28.0907	1.36260
$426$	12.2989	0.595884
$427$	−5.41570	−0.262084
$428$	−6.37034	−0.307922
$429$	−15.7701	−0.761390
$430$	23.8596	1.15061
$431$	1.07106	0.0515913	0.0257957	−	0.999667i	$-0.491788\pi$
$431$	1.07106	0.0515913	0.0257957	+	0.999667i	$0.491788\pi$
$432$	10.7803	0.518670
$433$	−4.68472	−0.225133	−0.112567	−	0.993644i	$-0.535907\pi$
$433$	−4.68472	−0.225133	−0.112567	+	0.993644i	$0.535907\pi$
$434$	−0.330407	−0.0158601
$435$	16.5471	0.793375
$436$	11.2909	0.540737
$437$	−26.0583	−1.24654
$438$	24.0600	1.14963
$439$	−23.9843	−1.14471	−0.572354	−	0.820007i	$-0.693970\pi$
$439$	−23.9843	−1.14471	−0.572354	+	0.820007i	$0.693970\pi$
$440$	−19.8509	−0.946355
$441$	2.03228	0.0967753
$442$	−28.5623	−1.35857
$443$	−12.1643	−0.577942	−0.288971	−	0.957338i	$-0.593313\pi$
$443$	−12.1643	−0.577942	−0.288971	+	0.957338i	$0.593313\pi$
$444$	−10.2140	−0.484735
$445$	57.2423	2.71355
$446$	−7.06129	−0.334362
$447$	−22.4004	−1.05950
$448$	−4.00072	−0.189016
$449$	−9.04190	−0.426713	−0.213357	−	0.976974i	$-0.568440\pi$
$449$	−9.04190	−0.426713	−0.213357	+	0.976974i	$0.568440\pi$
$450$	1.77887	0.0838567
$451$	−19.1126	−0.899975
$452$	−5.75117	−0.270512
$453$	−19.3251	−0.907971
$454$	0.662010	0.0310697
$455$	−7.29261	−0.341883
$456$	15.7555	0.737819
$457$	−9.46519	−0.442763	−0.221382	−	0.975187i	$-0.571057\pi$
$457$	−9.46519	−0.442763	−0.221382	+	0.975187i	$0.571057\pi$
$458$	3.37086	0.157510
$459$	−28.8963	−1.34876
$460$	19.7049	0.918748
$461$	−16.0945	−0.749595	−0.374797	−	0.927107i	$-0.622288\pi$
$461$	−16.0945	−0.749595	−0.374797	+	0.927107i	$0.622288\pi$
$462$	−1.77616	−0.0826345
$463$	−3.39705	−0.157874	−0.0789372	−	0.996880i	$-0.525153\pi$
$463$	−3.39705	−0.157874	−0.0789372	+	0.996880i	$0.525153\pi$
$464$	−6.24693	−0.290007
$465$	−3.24115	−0.150305
$466$	−0.889424	−0.0412018
$467$	19.9447	0.922933	0.461466	−	0.887158i	$-0.347324\pi$
$467$	19.9447	0.922933	0.461466	+	0.887158i	$0.347324\pi$
$468$	1.05203	0.0486303
$469$	−5.04144	−0.232792
$470$	−35.2063	−1.62395
$471$	5.90044	0.271878
$472$	24.2009	1.11394
$473$	13.3309	0.612955
$474$	16.9242	0.777355
$475$	16.4317	0.753940
$476$	1.87110	0.0857615
$477$	3.64353	0.166826
$478$	−29.5175	−1.35010
$479$	−22.1824	−1.01354	−0.506770	−	0.862081i	$-0.669161\pi$
$479$	−22.1824	−1.01354	−0.506770	+	0.862081i	$0.669161\pi$
$480$	−20.6249	−0.941392
$481$	40.2843	1.83681
$482$	16.5384	0.753304
$483$	6.55746	0.298375
$484$	5.10833	0.232197
$485$	−35.9189	−1.63099
$486$	−3.49336	−0.158462
$487$	2.14685	0.0972829	0.0486414	−	0.998816i	$-0.484511\pi$
$487$	2.14685	0.0972829	0.0486414	+	0.998816i	$0.484511\pi$
$488$	34.8958	1.57966
$489$	−4.58049	−0.207137
$490$	24.4061	1.10255
$491$	0.473589	0.0213728	0.0106864	−	0.999943i	$-0.496598\pi$
$491$	0.473589	0.0213728	0.0106864	+	0.999943i	$0.496598\pi$
$492$	−11.4710	−0.517151
$493$	16.7447	0.754141
$494$	−16.7076	−0.751711
$495$	1.93662	0.0870447
$496$	1.22361	0.0549418
$497$	3.17767	0.142538
$498$	16.1708	0.724631
$499$	−14.5629	−0.651923	−0.325962	−	0.945383i	$-0.605688\pi$
$499$	−14.5629	−0.651923	−0.325962	+	0.945383i	$0.605688\pi$
$500$	−0.639623	−0.0286048
$501$	39.4232	1.76130
$502$	1.11984	0.0499809
$503$	16.9679	0.756561	0.378280	−	0.925691i	$-0.376515\pi$
$503$	16.9679	0.756561	0.378280	+	0.925691i	$0.376515\pi$
$504$	0.440691	0.0196300
$505$	−18.5624	−0.826015
$506$	−18.9285	−0.841473
$507$	15.9691	0.709214
$508$	8.09851	0.359313
$509$	17.7487	0.786698	0.393349	−	0.919389i	$-0.371316\pi$
$509$	17.7487	0.786698	0.393349	+	0.919389i	$0.371316\pi$
$510$	−31.5566	−1.39735
$511$	6.21640	0.274997
$512$	20.0173	0.884647
$513$	−16.9029	−0.746283
$514$	10.0356	0.442650
$515$	−15.8143	−0.696859
$516$	8.00093	0.352221
$517$	−19.6705	−0.865109
$518$	4.53715	0.199351
$519$	−10.5292	−0.462181
$520$	46.9896	2.06063
$521$	−24.6985	−1.08206	−0.541030	−	0.841003i	$-0.681965\pi$
$521$	−24.6985	−1.08206	−0.541030	+	0.841003i	$0.681965\pi$
$522$	1.06037	0.0464111
$523$	−10.7941	−0.471993	−0.235996	−	0.971754i	$-0.575835\pi$
$523$	−10.7941	−0.471993	−0.235996	+	0.971754i	$0.575835\pi$
$524$	4.40684	0.192514
$525$	−4.13498	−0.180465
$526$	3.44661	0.150279
$527$	−3.27984	−0.142872
$528$	6.57773	0.286259
$529$	46.8825	2.03837
$530$	43.7559	1.90063
$531$	−2.36101	−0.102459
$532$	1.09450	0.0474527
$533$	45.2418	1.95964
$534$	−33.0019	−1.42813
$535$	27.7587	1.20011
$536$	32.4843	1.40311
$537$	11.4310	0.493282
$538$	−27.8735	−1.20171
$539$	13.6362	0.587352
$540$	12.7818	0.550041
$541$	5.34235	0.229686	0.114843	−	0.993384i	$-0.463364\pi$
$541$	5.34235	0.229686	0.114843	+	0.993384i	$0.463364\pi$
$542$	−7.36896	−0.316524
$543$	−27.8725	−1.19612
$544$	−20.8711	−0.894839
$545$	−49.2001	−2.10750
$546$	4.20440	0.179932
$547$	1.00000	0.0427569
$547$	1.00000	0.0427569
$548$	11.1612	0.476782
$549$	−3.40438	−0.145295
$550$	11.9358	0.508946
$551$	9.79482	0.417273
$552$	−42.2527	−1.79839
$553$	4.37271	0.185947
$554$	15.0566	0.639692
$555$	44.5074	1.88923
$556$	13.1759	0.558783
$557$	27.6956	1.17350	0.586750	−	0.809768i	$-0.300407\pi$
$557$	27.6956	1.17350	0.586750	+	0.809768i	$0.300407\pi$
$558$	−0.207698	−0.00879258
$559$	−31.5559	−1.33467
$560$	3.04175	0.128537
$561$	−17.6313	−0.744396
$562$	−4.84773	−0.204489
$563$	−32.1975	−1.35696	−0.678481	−	0.734618i	$-0.737361\pi$
$563$	−32.1975	−1.35696	−0.678481	+	0.734618i	$0.737361\pi$
$564$	−11.8059	−0.497116
$565$	25.0607	1.05431
$566$	35.3253	1.48483
$567$	3.82376	0.160583
$568$	−20.4752	−0.859120
$569$	38.3179	1.60637	0.803185	−	0.595729i	$-0.203137\pi$
$569$	38.3179	1.60637	0.803185	+	0.595729i	$0.203137\pi$
$570$	−18.4591	−0.773167
$571$	14.8663	0.622133	0.311067	−	0.950388i	$-0.399314\pi$
$571$	14.8663	0.622133	0.311067	+	0.950388i	$0.399314\pi$
$572$	7.05893	0.295149
$573$	−9.53461	−0.398314
$574$	5.09550	0.212682
$575$	−44.0662	−1.83769
$576$	−2.51490	−0.104788
$577$	0.757265	0.0315254	0.0157627	−	0.999876i	$-0.494982\pi$
$577$	0.757265	0.0315254	0.0157627	+	0.999876i	$0.494982\pi$
$578$	−12.8167	−0.533105
$579$	30.6656	1.27442
$580$	−7.40672	−0.307547
$581$	4.17805	0.173335
$582$	20.7083	0.858386
$583$	24.4473	1.01251
$584$	−40.0551	−1.65749
$585$	−4.58423	−0.189534
$586$	−14.8269	−0.612496
$587$	−10.3351	−0.426574	−0.213287	−	0.976990i	$-0.568417\pi$
$587$	−10.3351	−0.426574	−0.213287	+	0.976990i	$0.568417\pi$
$588$	8.18417	0.337509
$589$	−1.91855	−0.0790525
$590$	−28.3538	−1.16731
$591$	−26.4091	−1.08632
$592$	−16.8026	−0.690582
$593$	−13.4845	−0.553742	−0.276871	−	0.960907i	$-0.589298\pi$
$593$	−13.4845	−0.553742	−0.276871	+	0.960907i	$0.589298\pi$
$594$	−12.2781	−0.503777
$595$	−8.15328	−0.334252
$596$	10.0267	0.410710
$597$	20.7086	0.847547
$598$	44.8060	1.83226
$599$	20.5973	0.841582	0.420791	−	0.907158i	$-0.361753\pi$
$599$	20.5973	0.841582	0.420791	+	0.907158i	$0.361753\pi$
$600$	26.6436	1.08772
$601$	5.33901	0.217783	0.108891	−	0.994054i	$-0.465270\pi$
$601$	5.33901	0.217783	0.108891	+	0.994054i	$0.465270\pi$
$602$	−3.55408	−0.144853
$603$	−3.16912	−0.129056
$604$	8.65016	0.351970
$605$	−22.2595	−0.904978
$606$	10.7017	0.434729
$607$	22.8721	0.928350	0.464175	−	0.885743i	$-0.346351\pi$
$607$	22.8721	0.928350	0.464175	+	0.885743i	$0.346351\pi$
$608$	−12.2086	−0.495123
$609$	−2.46483	−0.0998798
$610$	−40.8839	−1.65534
$611$	46.5627	1.88372
$612$	1.17620	0.0475449
$613$	−9.93746	−0.401370	−0.200685	−	0.979656i	$-0.564317\pi$
$613$	−9.93746	−0.401370	−0.200685	+	0.979656i	$0.564317\pi$
$614$	−17.1291	−0.691274
$615$	49.9847	2.01558
$616$	2.95695	0.119139
$617$	36.3368	1.46287	0.731433	−	0.681913i	$-0.238852\pi$
$617$	36.3368	1.46287	0.731433	+	0.681913i	$0.238852\pi$
$618$	9.11738	0.366755
$619$	−8.07356	−0.324504	−0.162252	−	0.986749i	$-0.551876\pi$
$619$	−8.07356	−0.324504	−0.162252	+	0.986749i	$0.551876\pi$
$620$	1.45078	0.0582649
$621$	45.3299	1.81903
$622$	−7.43827	−0.298247
$623$	−8.52669	−0.341615
$624$	−15.5703	−0.623312
$625$	−23.5696	−0.942784
$626$	−5.44996	−0.217824
$627$	−10.3135	−0.411881
$628$	−2.64112	−0.105392
$629$	45.0387	1.79581
$630$	−0.516313	−0.0205704
$631$	−7.11575	−0.283274	−0.141637	−	0.989919i	$-0.545237\pi$
$631$	−7.11575	−0.283274	−0.141637	+	0.989919i	$0.545237\pi$
$632$	−28.1754	−1.12076
$633$	−16.7449	−0.665550
$634$	−0.707307	−0.0280907
$635$	−35.2892	−1.40041
$636$	14.6728	0.581814
$637$	−32.2786	−1.27892
$638$	7.11486	0.281680
$639$	1.99753	0.0790209
$640$	−5.09772	−0.201505
$641$	9.80203	0.387157	0.193578	−	0.981085i	$-0.437991\pi$
$641$	9.80203	0.387157	0.193578	+	0.981085i	$0.437991\pi$
$642$	−16.0037	−0.631616
$643$	−37.9339	−1.49597	−0.747984	−	0.663716i	$-0.768978\pi$
$643$	−37.9339	−1.49597	−0.747984	+	0.663716i	$0.768978\pi$
$644$	−2.93521	−0.115663
$645$	−34.8640	−1.37277
$646$	−18.6794	−0.734933
$647$	46.4530	1.82626	0.913128	−	0.407672i	$-0.133659\pi$
$647$	46.4530	1.82626	0.913128	+	0.407672i	$0.133659\pi$
$648$	−24.6383	−0.967882
$649$	−15.8419	−0.621847
$650$	−28.2536	−1.10820
$651$	0.482795	0.0189222
$652$	2.05029	0.0802955
$653$	43.2629	1.69301	0.846504	−	0.532382i	$-0.178703\pi$
$653$	43.2629	1.69301	0.846504	+	0.532382i	$0.178703\pi$
$654$	28.3653	1.10917
$655$	−19.2028	−0.750315
$656$	−18.8704	−0.736765
$657$	3.90771	0.152454
$658$	5.24426	0.204443
$659$	−14.0190	−0.546104	−0.273052	−	0.961999i	$-0.588033\pi$
$659$	−14.0190	−0.546104	−0.273052	+	0.961999i	$0.588033\pi$
$660$	7.79894	0.303573
$661$	−35.7415	−1.39018	−0.695092	−	0.718920i	$-0.744637\pi$
$661$	−35.7415	−1.39018	−0.695092	+	0.718920i	$0.744637\pi$
$662$	−2.29786	−0.0893089
$663$	41.7356	1.62088
$664$	−26.9211	−1.04474
$665$	−4.76928	−0.184945
$666$	2.85211	0.110517
$667$	−26.2675	−1.01708
$668$	−17.6464	−0.682758
$669$	10.3180	0.398918
$670$	−38.0585	−1.47033
$671$	−22.8427	−0.881832
$672$	3.07224	0.118514
$673$	19.2256	0.741092	0.370546	−	0.928814i	$-0.379171\pi$
$673$	19.2256	0.741092	0.370546	+	0.928814i	$0.379171\pi$
$674$	−12.0523	−0.464239
$675$	−28.5840	−1.10020
$676$	−7.14800	−0.274923
$677$	43.8724	1.68615	0.843077	−	0.537792i	$-0.180741\pi$
$677$	43.8724	1.68615	0.843077	+	0.537792i	$0.180741\pi$
$678$	−14.4482	−0.554880
$679$	5.35040	0.205330
$680$	52.5353	2.01464
$681$	−0.967337	−0.0370684
$682$	−1.39361	−0.0533642
$683$	−8.32337	−0.318485	−0.159243	−	0.987239i	$-0.550905\pi$
$683$	−8.32337	−0.318485	−0.159243	+	0.987239i	$0.550905\pi$
$684$	0.688018	0.0263070
$685$	−48.6348	−1.85824
$686$	−7.39330	−0.282278
$687$	−4.92555	−0.187921
$688$	13.1620	0.501795
$689$	−57.8699	−2.20467
$690$	49.5032	1.88455
$691$	8.80984	0.335142	0.167571	−	0.985860i	$-0.446408\pi$
$691$	8.80984	0.335142	0.167571	+	0.985860i	$0.446408\pi$
$692$	4.71302	0.179162
$693$	−0.288475	−0.0109583
$694$	−2.23864	−0.0849775
$695$	−57.4139	−2.17783
$696$	15.8820	0.602006
$697$	50.5813	1.91590
$698$	−0.753233	−0.0285103
$699$	1.29964	0.0491568
$700$	1.85087	0.0699564
$701$	−40.3765	−1.52500	−0.762500	−	0.646989i	$-0.776028\pi$
$701$	−40.3765	−1.52500	−0.762500	+	0.646989i	$0.776028\pi$
$702$	29.0639	1.09694
$703$	26.3455	0.993638
$704$	−16.8745	−0.635981
$705$	51.4439	1.93749
$706$	16.3740	0.616245
$707$	2.76501	0.103989
$708$	−9.50796	−0.357331
$709$	−18.0480	−0.677808	−0.338904	−	0.940821i	$-0.610056\pi$
$709$	−18.0480	−0.677808	−0.338904	+	0.940821i	$0.610056\pi$
$710$	23.9887	0.900279
$711$	2.74874	0.103086
$712$	54.9414	2.05902
$713$	5.14512	0.192686
$714$	4.70061	0.175916
$715$	−30.7592	−1.15033
$716$	−5.11665	−0.191218
$717$	43.1314	1.61077
$718$	−14.1399	−0.527695
$719$	−19.9041	−0.742296	−0.371148	−	0.928574i	$-0.621036\pi$
$719$	−19.9041	−0.742296	−0.371148	+	0.928574i	$0.621036\pi$
$720$	1.91208	0.0712591
$721$	2.35566	0.0877293
$722$	10.4390	0.388499
$723$	−24.1661	−0.898747
$724$	12.4761	0.463671
$725$	16.5637	0.615160
$726$	12.8333	0.476287
$727$	14.1523	0.524879	0.262439	−	0.964949i	$-0.415473\pi$
$727$	14.1523	0.524879	0.262439	+	0.964949i	$0.415473\pi$
$728$	−6.99947	−0.259418
$729$	29.1335	1.07902
$730$	46.9284	1.73690
$731$	−35.2801	−1.30488
$732$	−13.7097	−0.506726
$733$	−1.46363	−0.0540604	−0.0270302	−	0.999635i	$-0.508605\pi$
$733$	−1.46363	−0.0540604	−0.0270302	+	0.999635i	$0.508605\pi$
$734$	1.17390	0.0433293
$735$	−35.6624	−1.31543
$736$	32.7407	1.20684
$737$	−21.2641	−0.783274
$738$	3.20310	0.117908
$739$	−29.5621	−1.08746	−0.543729	−	0.839261i	$-0.682988\pi$
$739$	−29.5621	−1.08746	−0.543729	+	0.839261i	$0.682988\pi$
$740$	−19.9221	−0.732351
$741$	24.4133	0.896847
$742$	−6.51778	−0.239275
$743$	43.2429	1.58643	0.793214	−	0.608943i	$-0.208406\pi$
$743$	43.2429	1.58643	0.793214	+	0.608943i	$0.208406\pi$
$744$	−3.11087	−0.114050
$745$	−43.6913	−1.60073
$746$	−27.8999	−1.02149
$747$	2.62638	0.0960942
$748$	7.89203	0.288561
$749$	−4.13488	−0.151085
$750$	−1.60687	−0.0586747
$751$	45.3350	1.65430	0.827148	−	0.561984i	$-0.189962\pi$
$751$	45.3350	1.65430	0.827148	+	0.561984i	$0.189962\pi$
$752$	−19.4213	−0.708222
$753$	−1.63632	−0.0596309
$754$	−16.8418	−0.613341
$755$	−37.6930	−1.37179
$756$	−1.90395	−0.0692460
$757$	−11.8137	−0.429377	−0.214689	−	0.976683i	$-0.568874\pi$
$757$	−11.8137	−0.429377	−0.214689	+	0.976683i	$0.568874\pi$
$758$	−38.5786	−1.40124
$759$	27.6585	1.00394
$760$	30.7306	1.11472
$761$	−2.16601	−0.0785178	−0.0392589	−	0.999229i	$-0.512500\pi$
$761$	−2.16601	−0.0785178	−0.0392589	+	0.999229i	$0.512500\pi$
$762$	20.3452	0.737030
$763$	7.32874	0.265318
$764$	4.26782	0.154404
$765$	−5.12526	−0.185304
$766$	−25.9085	−0.936111
$767$	37.4997	1.35404
$768$	−24.6011	−0.887714
$769$	4.14420	0.149444	0.0747218	−	0.997204i	$-0.476193\pi$
$769$	4.14420	0.149444	0.0747218	+	0.997204i	$0.476193\pi$
$770$	−3.46435	−0.124847
$771$	−14.6641	−0.528114
$772$	−13.7263	−0.494021
$773$	−14.3304	−0.515430	−0.257715	−	0.966221i	$-0.582970\pi$
$773$	−14.3304	−0.515430	−0.257715	+	0.966221i	$0.582970\pi$
$774$	−2.23414	−0.0803045
$775$	−3.24439	−0.116542
$776$	−34.4751	−1.23758
$777$	−6.62973	−0.237840
$778$	29.3465	1.05212
$779$	29.5876	1.06009
$780$	−18.4611	−0.661012
$781$	13.4030	0.479597
$782$	50.0941	1.79136
$783$	−17.0387	−0.608912
$784$	13.4634	0.480836
$785$	11.5086	0.410761
$786$	11.0710	0.394888
$787$	−13.2339	−0.471739	−0.235869	−	0.971785i	$-0.575794\pi$
$787$	−13.2339	−0.471739	−0.235869	+	0.971785i	$0.575794\pi$
$788$	11.8211	0.421108
$789$	−5.03623	−0.179294
$790$	33.0102	1.17445
$791$	−3.73299	−0.132730
$792$	1.85878	0.0660488
$793$	54.0715	1.92014
$794$	−6.38173	−0.226479
$795$	−63.9366	−2.26760
$796$	−9.26945	−0.328547
$797$	17.8863	0.633564	0.316782	−	0.948498i	$-0.397398\pi$
$797$	17.8863	0.633564	0.316782	+	0.948498i	$0.397398\pi$
$798$	2.74963	0.0973358
$799$	52.0580	1.84168
$800$	−20.6455	−0.729929
$801$	−5.35999	−0.189386
$802$	−39.9528	−1.41078
$803$	26.2199	0.925281
$804$	−12.7623	−0.450091
$805$	12.7901	0.450793
$806$	3.29886	0.116197
$807$	40.7291	1.43373
$808$	−17.8162	−0.626773
$809$	13.1398	0.461972	0.230986	−	0.972957i	$-0.425805\pi$
$809$	13.1398	0.461972	0.230986	+	0.972957i	$0.425805\pi$
$810$	28.8661	1.01425
$811$	7.20666	0.253060	0.126530	−	0.991963i	$-0.459616\pi$
$811$	7.20666	0.253060	0.126530	+	0.991963i	$0.459616\pi$
$812$	1.10329	0.0387179
$813$	10.7676	0.377637
$814$	19.1371	0.670754
$815$	−8.93412	−0.312949
$816$	−17.4079	−0.609400
$817$	−20.6372	−0.722004
$818$	−13.9844	−0.488952
$819$	0.682857	0.0238610
$820$	−22.3738	−0.781327
$821$	41.8240	1.45967	0.729833	−	0.683626i	$-0.239598\pi$
$821$	41.8240	1.45967	0.729833	+	0.683626i	$0.239598\pi$
$822$	28.0394	0.977985
$823$	46.2562	1.61239	0.806195	−	0.591650i	$-0.201523\pi$
$823$	46.2562	1.61239	0.806195	+	0.591650i	$0.201523\pi$
$824$	−15.1786	−0.528771
$825$	−17.4408	−0.607211
$826$	4.22352	0.146955
$827$	−20.3709	−0.708364	−0.354182	−	0.935176i	$-0.615241\pi$
$827$	−20.3709	−0.708364	−0.354182	+	0.935176i	$0.615241\pi$
$828$	−1.84511	−0.0641220
$829$	−17.5728	−0.610330	−0.305165	−	0.952299i	$-0.598712\pi$
$829$	−17.5728	−0.610330	−0.305165	+	0.952299i	$0.598712\pi$
$830$	31.5407	1.09479
$831$	−22.0008	−0.763200
$832$	39.9440	1.38481
$833$	−36.0881	−1.25038
$834$	33.1008	1.14619
$835$	76.8939	2.66102
$836$	4.61646	0.159664
$837$	3.33743	0.115358
$838$	20.4350	0.705915
$839$	−39.3285	−1.35777	−0.678885	−	0.734245i	$-0.737537\pi$
$839$	−39.3285	−1.35777	−0.678885	+	0.734245i	$0.737537\pi$
$840$	−7.73324	−0.266822
$841$	−19.1265	−0.659535
$842$	−19.3898	−0.668217
$843$	7.08356	0.243971
$844$	7.49525	0.257997
$845$	31.1473	1.07150
$846$	3.29661	0.113340
$847$	3.31573	0.113930
$848$	24.1376	0.828887
$849$	−51.6178	−1.77152
$850$	−31.5882	−1.08346
$851$	−70.6526	−2.42194
$852$	8.04420	0.275590
$853$	38.9384	1.33323	0.666613	−	0.745404i	$-0.267743\pi$
$853$	38.9384	1.33323	0.666613	+	0.745404i	$0.267743\pi$
$854$	6.08997	0.208395
$855$	−2.99803	−0.102531
$856$	26.6429	0.910636
$857$	−50.6493	−1.73015	−0.865074	−	0.501645i	$-0.832728\pi$
$857$	−50.6493	−1.73015	−0.865074	+	0.501645i	$0.832728\pi$
$858$	17.7336	0.605415
$859$	−30.7691	−1.04983	−0.524914	−	0.851155i	$-0.675903\pi$
$859$	−30.7691	−1.04983	−0.524914	+	0.851155i	$0.675903\pi$
$860$	15.6056	0.532146
$861$	−7.44561	−0.253746
$862$	−1.20442	−0.0410226
$863$	43.2797	1.47326	0.736628	−	0.676298i	$-0.236417\pi$
$863$	43.2797	1.47326	0.736628	+	0.676298i	$0.236417\pi$
$864$	21.2375	0.722516
$865$	−20.5369	−0.698277
$866$	5.26798	0.179013
$867$	18.7279	0.636034
$868$	−0.216106	−0.00733511
$869$	18.4435	0.625653
$870$	−18.6073	−0.630847
$871$	50.3348	1.70553
$872$	−47.2224	−1.59915
$873$	3.36333	0.113832
$874$	29.3026	0.991176
$875$	−0.415168	−0.0140352
$876$	15.7367	0.531693
$877$	9.79385	0.330715	0.165357	−	0.986234i	$-0.447122\pi$
$877$	9.79385	0.330715	0.165357	+	0.986234i	$0.447122\pi$
$878$	26.9704	0.910208
$879$	21.6653	0.730753
$880$	12.8297	0.432488
$881$	4.47932	0.150912	0.0754560	−	0.997149i	$-0.475959\pi$
$881$	4.47932	0.150912	0.0754560	+	0.997149i	$0.475959\pi$
$882$	−2.28531	−0.0769503
$883$	−27.1048	−0.912148	−0.456074	−	0.889942i	$-0.650745\pi$
$883$	−27.1048	−0.912148	−0.456074	+	0.889942i	$0.650745\pi$
$884$	−18.6814	−0.628325
$885$	41.4309	1.39268
$886$	13.6788	0.459547
$887$	3.52657	0.118410	0.0592052	−	0.998246i	$-0.481143\pi$
$887$	3.52657	0.118410	0.0592052	+	0.998246i	$0.481143\pi$
$888$	42.7184	1.43353
$889$	5.25660	0.176301
$890$	−64.3692	−2.15766
$891$	16.1281	0.540312
$892$	−4.61849	−0.154639
$893$	30.4514	1.01902
$894$	25.1893	0.842457
$895$	22.2958	0.745265
$896$	0.759345	0.0253679
$897$	−65.4711	−2.18602
$898$	10.1676	0.339299
$899$	−1.93396	−0.0645010
$900$	1.16348	0.0387828
$901$	−64.6998	−2.15546
$902$	21.4922	0.715610
$903$	5.19326	0.172821
$904$	24.0533	0.800002
$905$	−54.3646	−1.80714
$906$	21.7311	0.721968
$907$	−10.9143	−0.362404	−0.181202	−	0.983446i	$-0.557999\pi$
$907$	−10.9143	−0.362404	−0.181202	+	0.983446i	$0.557999\pi$
$908$	0.432993	0.0143694
$909$	1.73812	0.0576499
$910$	8.20056	0.271846
$911$	12.9074	0.427641	0.213821	−	0.976873i	$-0.431409\pi$
$911$	12.9074	0.427641	0.213821	+	0.976873i	$0.431409\pi$
$912$	−10.1828	−0.337187
$913$	17.6225	0.583218
$914$	10.6436	0.352061
$915$	59.7400	1.97494
$916$	2.20474	0.0728467
$917$	2.86041	0.0944590
$918$	32.4940	1.07246
$919$	−32.0108	−1.05594	−0.527970	−	0.849263i	$-0.677047\pi$
$919$	−32.0108	−1.05594	−0.527970	+	0.849263i	$0.677047\pi$
$920$	−82.4127	−2.71707
$921$	25.0292	0.824741
$922$	18.0983	0.596036
$923$	−31.7266	−1.04429
$924$	−1.16171	−0.0382176
$925$	44.5519	1.46486
$926$	3.82000	0.125533
$927$	1.48080	0.0486358
$928$	−12.3066	−0.403984
$929$	−23.8619	−0.782885	−0.391442	−	0.920203i	$-0.628024\pi$
$929$	−23.8619	−0.782885	−0.391442	+	0.920203i	$0.628024\pi$
$930$	3.64469	0.119514
$931$	−21.1098	−0.691847
$932$	−0.581735	−0.0190554
$933$	10.8689	0.355831
$934$	−22.4279	−0.733865
$935$	−34.3894	−1.12466
$936$	−4.39996	−0.143817
$937$	−24.1398	−0.788613	−0.394307	−	0.918979i	$-0.629015\pi$
$937$	−24.1398	−0.788613	−0.394307	+	0.918979i	$0.629015\pi$
$938$	5.66912	0.185103
$939$	7.96354	0.259880
$940$	−23.0270	−0.751058
$941$	22.8955	0.746371	0.373185	−	0.927757i	$-0.378266\pi$
$941$	22.8955	0.746371	0.373185	+	0.927757i	$0.378266\pi$
$942$	−6.63507	−0.216182
$943$	−79.3474	−2.58391
$944$	−15.6411	−0.509075
$945$	8.29644	0.269883
$946$	−14.9906	−0.487387
$947$	61.4951	1.99832	0.999161	−	0.0409453i	$-0.0130369\pi$
$947$	61.4951	1.99832	0.999161	+	0.0409453i	$0.0130369\pi$
$948$	11.0694	0.359518
$949$	−62.0659	−2.01474
$950$	−18.4776	−0.599491
$951$	1.03352	0.0335143
$952$	−7.82555	−0.253628
$953$	3.92165	0.127035	0.0635173	−	0.997981i	$-0.479768\pi$
$953$	3.92165	0.127035	0.0635173	+	0.997981i	$0.479768\pi$
$954$	−4.09716	−0.132651
$955$	−18.5970	−0.601784
$956$	−19.3062	−0.624407
$957$	−10.3963	−0.336065
$958$	24.9442	0.805911
$959$	7.24453	0.233938
$960$	44.1315	1.42434
$961$	−30.6212	−0.987780
$962$	−45.2999	−1.46053
$963$	−2.59924	−0.0837593
$964$	10.8171	0.348395
$965$	59.8123	1.92543
$966$	−7.37389	−0.237251
$967$	−38.7433	−1.24590	−0.622950	−	0.782261i	$-0.714066\pi$
$967$	−38.7433	−1.24590	−0.622950	+	0.782261i	$0.714066\pi$
$968$	−21.3648	−0.686689
$969$	27.2946	0.876829
$970$	40.3909	1.29687
$971$	23.1661	0.743437	0.371719	−	0.928345i	$-0.378769\pi$
$971$	23.1661	0.743437	0.371719	+	0.928345i	$0.378769\pi$
$972$	−2.28486	−0.0732869
$973$	8.55226	0.274173
$974$	−2.41414	−0.0773539
$975$	41.2846	1.32216
$976$	−22.5532	−0.721912
$977$	−41.0197	−1.31234	−0.656168	−	0.754614i	$-0.727824\pi$
$977$	−41.0197	−1.31234	−0.656168	+	0.754614i	$0.727824\pi$
$978$	5.15078	0.164704
$979$	−35.9644	−1.14943
$980$	15.9630	0.509919
$981$	4.60694	0.147088
$982$	−0.532553	−0.0169944
$983$	39.0113	1.24427	0.622134	−	0.782911i	$-0.286266\pi$
$983$	39.0113	1.24427	0.622134	+	0.782911i	$0.286266\pi$
$984$	47.9755	1.52940
$985$	−51.5101	−1.64125
$986$	−18.8294	−0.599651
$987$	−7.66298	−0.243915
$988$	−10.9277	−0.347658
$989$	55.3443	1.75985
$990$	−2.17774	−0.0692131
$991$	2.29321	0.0728461	0.0364231	−	0.999336i	$-0.488404\pi$
$991$	2.29321	0.0728461	0.0364231	+	0.999336i	$0.488404\pi$
$992$	2.41054	0.0765348
$993$	3.35766	0.106552
$994$	−3.57330	−0.113338
$995$	40.3915	1.28050
$996$	10.5766	0.335134
$997$	39.2163	1.24199	0.620997	−	0.783813i	$-0.286728\pi$
$997$	39.2163	1.24199	0.620997	+	0.783813i	$0.286728\pi$
$998$	16.3760	0.518373
$999$	−45.8295	−1.44998

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.a.c.1.8	✓	25
3.2	odd	2		4923.2.a.n.1.18		25
4.3	odd	2		8752.2.a.v.1.9		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.a.c.1.8	✓	25	1.1	even	1	trivial
4923.2.a.n.1.18		25	3.2	odd	2
8752.2.a.v.1.9		25	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	547.a (trivial)

\(f(q)\)	\(=\)	\(q-1.12450 q^{2} +1.64314 q^{3} -0.735491 q^{4} +3.20489 q^{5} -1.84772 q^{6} -0.477395 q^{7} +3.07607 q^{8} -0.300096 q^{9} +O(q^{10})\)	\(q-1.12450 q^{2} +1.64314 q^{3} -0.735491 q^{4} +3.20489 q^{5} -1.84772 q^{6} -0.477395 q^{7} +3.07607 q^{8} -0.300096 q^{9} -3.60392 q^{10} -2.01359 q^{11} -1.20851 q^{12} +4.76641 q^{13} +0.536832 q^{14} +5.26609 q^{15} -1.98807 q^{16} +5.32895 q^{17} +0.337460 q^{18} +3.11718 q^{19} -2.35717 q^{20} -0.784425 q^{21} +2.26429 q^{22} -8.35957 q^{23} +5.05441 q^{24} +5.27135 q^{25} -5.35985 q^{26} -5.42251 q^{27} +0.351119 q^{28} +3.14221 q^{29} -5.92173 q^{30} -0.615476 q^{31} -3.91655 q^{32} -3.30860 q^{33} -5.99242 q^{34} -1.53000 q^{35} +0.220718 q^{36} +8.45170 q^{37} -3.50528 q^{38} +7.83187 q^{39} +9.85848 q^{40} +9.49181 q^{41} +0.882089 q^{42} -6.62047 q^{43} +1.48097 q^{44} -0.961778 q^{45} +9.40037 q^{46} +9.76891 q^{47} -3.26668 q^{48} -6.77209 q^{49} -5.92766 q^{50} +8.75619 q^{51} -3.50565 q^{52} -12.1412 q^{53} +6.09764 q^{54} -6.45333 q^{55} -1.46850 q^{56} +5.12195 q^{57} -3.53343 q^{58} +7.86749 q^{59} -3.87316 q^{60} +11.3443 q^{61} +0.692106 q^{62} +0.143264 q^{63} +8.38031 q^{64} +15.2758 q^{65} +3.72053 q^{66} +10.5603 q^{67} -3.91939 q^{68} -13.7359 q^{69} +1.72049 q^{70} -6.65628 q^{71} -0.923118 q^{72} -13.0215 q^{73} -9.50397 q^{74} +8.66156 q^{75} -2.29266 q^{76} +0.961275 q^{77} -8.80697 q^{78} -9.15953 q^{79} -6.37156 q^{80} -8.00965 q^{81} -10.6736 q^{82} -8.75178 q^{83} +0.576938 q^{84} +17.0787 q^{85} +7.44474 q^{86} +5.16308 q^{87} -6.19393 q^{88} +17.8609 q^{89} +1.08152 q^{90} -2.27546 q^{91} +6.14839 q^{92} -1.01131 q^{93} -10.9852 q^{94} +9.99023 q^{95} -6.43543 q^{96} -11.2075 q^{97} +7.61525 q^{98} +0.604270 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 4 q^{2} + 8 q^{3} + 26 q^{4} + 29 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 29 q^{9}+O(q^{10}) \) 25 * q + 4 * q^2 + 8 * q^3 + 26 * q^4 + 29 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 29 * q^9	\( 25 q + 4 q^{2} + 8 q^{3} + 26 q^{4} + 29 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 29 q^{9} - q^{10} + 10 q^{11} + 14 q^{12} + 19 q^{13} + 9 q^{14} + 5 q^{15} + 16 q^{16} + 40 q^{17} - 8 q^{18} + 33 q^{20} - 8 q^{21} - 10 q^{22} + 26 q^{23} - 16 q^{24} + 36 q^{25} - 8 q^{26} + 11 q^{27} - 8 q^{28} + 30 q^{29} - 20 q^{30} - 5 q^{31} + 6 q^{32} + 10 q^{33} - 7 q^{34} + 11 q^{35} + 13 q^{36} + 26 q^{37} + 25 q^{38} - 17 q^{39} - 25 q^{40} + 9 q^{41} - 16 q^{42} - 10 q^{43} + 64 q^{45} - 34 q^{46} + 28 q^{47} + 23 q^{48} + 20 q^{49} - 9 q^{50} - 9 q^{51} - 2 q^{52} + 80 q^{53} - 13 q^{54} - q^{55} + 7 q^{56} - 8 q^{57} - 24 q^{58} - 2 q^{59} - 14 q^{60} + 22 q^{61} + 36 q^{62} - 9 q^{63} - 28 q^{64} + 30 q^{65} - 42 q^{66} - 16 q^{67} + 59 q^{68} + 22 q^{69} - 61 q^{70} - q^{71} - 44 q^{72} + 2 q^{73} - 8 q^{74} - 31 q^{75} - 46 q^{76} + 67 q^{77} - q^{78} - 34 q^{79} + 30 q^{80} - 11 q^{81} - 4 q^{82} + 15 q^{83} - 87 q^{84} + 15 q^{85} - 44 q^{86} - 29 q^{87} - 55 q^{88} + 38 q^{89} - 90 q^{90} - 41 q^{91} + 40 q^{92} - 4 q^{93} - 46 q^{94} - 46 q^{95} - 87 q^{96} - 2 q^{97} - 14 q^{98} - 41 q^{99}+O(q^{100}) \) 25 * q + 4 * q^2 + 8 * q^3 + 26 * q^4 + 29 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 29 * q^9 - q^10 + 10 * q^11 + 14 * q^12 + 19 * q^13 + 9 * q^14 + 5 * q^15 + 16 * q^16 + 40 * q^17 - 8 * q^18 + 33 * q^20 - 8 * q^21 - 10 * q^22 + 26 * q^23 - 16 * q^24 + 36 * q^25 - 8 * q^26 + 11 * q^27 - 8 * q^28 + 30 * q^29 - 20 * q^30 - 5 * q^31 + 6 * q^32 + 10 * q^33 - 7 * q^34 + 11 * q^35 + 13 * q^36 + 26 * q^37 + 25 * q^38 - 17 * q^39 - 25 * q^40 + 9 * q^41 - 16 * q^42 - 10 * q^43 + 64 * q^45 - 34 * q^46 + 28 * q^47 + 23 * q^48 + 20 * q^49 - 9 * q^50 - 9 * q^51 - 2 * q^52 + 80 * q^53 - 13 * q^54 - q^55 + 7 * q^56 - 8 * q^57 - 24 * q^58 - 2 * q^59 - 14 * q^60 + 22 * q^61 + 36 * q^62 - 9 * q^63 - 28 * q^64 + 30 * q^65 - 42 * q^66 - 16 * q^67 + 59 * q^68 + 22 * q^69 - 61 * q^70 - q^71 - 44 * q^72 + 2 * q^73 - 8 * q^74 - 31 * q^75 - 46 * q^76 + 67 * q^77 - q^78 - 34 * q^79 + 30 * q^80 - 11 * q^81 - 4 * q^82 + 15 * q^83 - 87 * q^84 + 15 * q^85 - 44 * q^86 - 29 * q^87 - 55 * q^88 + 38 * q^89 - 90 * q^90 - 41 * q^91 + 40 * q^92 - 4 * q^93 - 46 * q^94 - 46 * q^95 - 87 * q^96 - 2 * q^97 - 14 * q^98 - 41 * q^99

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