LMFDB - Embedded newform 547.2.a.c.1.12

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			1.12
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)

$f(q)$	$=$	$q+0.0847555 q^{2} -1.52830 q^{3} -1.99282 q^{4} +2.94110 q^{5} -0.129532 q^{6} -4.64869 q^{7} -0.338413 q^{8} -0.664306 q^{9} +O(q^{10})$	\(q+0.0847555 q^{2} -1.52830 q^{3} -1.99282 q^{4} +2.94110 q^{5} -0.129532 q^{6} -4.64869 q^{7} -0.338413 q^{8} -0.664306 q^{9} +0.249274 q^{10} +2.78082 q^{11} +3.04562 q^{12} +5.35656 q^{13} -0.394002 q^{14} -4.49487 q^{15} +3.95695 q^{16} +1.40669 q^{17} -0.0563036 q^{18} -2.15975 q^{19} -5.86106 q^{20} +7.10458 q^{21} +0.235690 q^{22} +2.38974 q^{23} +0.517196 q^{24} +3.65005 q^{25} +0.453998 q^{26} +5.60015 q^{27} +9.26399 q^{28} -3.67642 q^{29} -0.380965 q^{30} +10.1058 q^{31} +1.01220 q^{32} -4.24992 q^{33} +0.119224 q^{34} -13.6722 q^{35} +1.32384 q^{36} +7.29220 q^{37} -0.183050 q^{38} -8.18642 q^{39} -0.995306 q^{40} +2.27928 q^{41} +0.602153 q^{42} +2.86694 q^{43} -5.54166 q^{44} -1.95379 q^{45} +0.202543 q^{46} -9.60447 q^{47} -6.04740 q^{48} +14.6103 q^{49} +0.309361 q^{50} -2.14984 q^{51} -10.6746 q^{52} +11.9835 q^{53} +0.474644 q^{54} +8.17865 q^{55} +1.57318 q^{56} +3.30073 q^{57} -0.311597 q^{58} +1.64320 q^{59} +8.95745 q^{60} -6.27880 q^{61} +0.856523 q^{62} +3.08815 q^{63} -7.82811 q^{64} +15.7542 q^{65} -0.360204 q^{66} +2.21952 q^{67} -2.80327 q^{68} -3.65223 q^{69} -1.15880 q^{70} +8.64425 q^{71} +0.224810 q^{72} +2.32372 q^{73} +0.618054 q^{74} -5.57836 q^{75} +4.30398 q^{76} -12.9272 q^{77} -0.693844 q^{78} -16.2986 q^{79} +11.6378 q^{80} -6.56578 q^{81} +0.193181 q^{82} -12.8465 q^{83} -14.1581 q^{84} +4.13720 q^{85} +0.242989 q^{86} +5.61867 q^{87} -0.941065 q^{88} +14.4369 q^{89} -0.165594 q^{90} -24.9010 q^{91} -4.76231 q^{92} -15.4447 q^{93} -0.814031 q^{94} -6.35202 q^{95} -1.54694 q^{96} +11.2887 q^{97} +1.23831 q^{98} -1.84731 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.0847555	0.0599312	0.0299656	−	0.999551i	$-0.490460\pi$
$2$	0.0847555	0.0599312	0.0299656	+	0.999551i	$0.490460\pi$
$3$	−1.52830	−0.882363	−0.441182	−	0.897418i	$-0.645441\pi$
$3$	−1.52830	−0.882363	−0.441182	+	0.897418i	$0.645441\pi$
$4$	−1.99282	−0.996408
$5$	2.94110	1.31530	0.657649	−	0.753324i	$-0.271551\pi$
$5$	2.94110	1.31530	0.657649	+	0.753324i	$0.271551\pi$
$6$	−0.129532	−0.0528811
$7$	−4.64869	−1.75704	−0.878520	−	0.477706i	$-0.841469\pi$
$7$	−4.64869	−1.75704	−0.878520	+	0.477706i	$0.841469\pi$
$8$	−0.338413	−0.119647
$9$	−0.664306	−0.221435
$10$	0.249274	0.0788274
$11$	2.78082	0.838448	0.419224	−	0.907883i	$-0.362302\pi$
$11$	2.78082	0.838448	0.419224	+	0.907883i	$0.362302\pi$
$12$	3.04562	0.879194
$13$	5.35656	1.48564	0.742822	−	0.669489i	$-0.233487\pi$
$13$	5.35656	1.48564	0.742822	+	0.669489i	$0.233487\pi$
$14$	−0.394002	−0.105301
$15$	−4.49487	−1.16057
$16$	3.95695	0.989238
$17$	1.40669	0.341172	0.170586	−	0.985343i	$-0.445434\pi$
$17$	1.40669	0.341172	0.170586	+	0.985343i	$0.445434\pi$
$18$	−0.0563036	−0.0132709
$19$	−2.15975	−0.495480	−0.247740	−	0.968827i	$-0.579688\pi$
$19$	−2.15975	−0.495480	−0.247740	+	0.968827i	$0.579688\pi$
$20$	−5.86106	−1.31057
$21$	7.10458	1.55035
$22$	0.235690	0.0502492
$23$	2.38974	0.498295	0.249147	−	0.968466i	$-0.419850\pi$
$23$	2.38974	0.498295	0.249147	+	0.968466i	$0.419850\pi$
$24$	0.517196	0.105572
$25$	3.65005	0.730009
$26$	0.453998	0.0890364
$27$	5.60015	1.07775
$28$	9.26399	1.75073
$29$	−3.67642	−0.682694	−0.341347	−	0.939937i	$-0.610883\pi$
$29$	−3.67642	−0.682694	−0.341347	+	0.939937i	$0.610883\pi$
$30$	−0.380965	−0.0695544
$31$	10.1058	1.81506	0.907529	−	0.419989i	$-0.137966\pi$
$31$	10.1058	1.81506	0.907529	+	0.419989i	$0.137966\pi$
$32$	1.01220	0.178933
$33$	−4.24992	−0.739816
$34$	0.119224	0.0204468
$35$	−13.6722	−2.31103
$36$	1.32384	0.220640
$37$	7.29220	1.19883	0.599416	−	0.800438i	$-0.295400\pi$
$37$	7.29220	1.19883	0.599416	+	0.800438i	$0.295400\pi$
$38$	−0.183050	−0.0296947
$39$	−8.18642	−1.31088
$40$	−0.995306	−0.157372
$41$	2.27928	0.355964	0.177982	−	0.984034i	$-0.443043\pi$
$41$	2.27928	0.355964	0.177982	+	0.984034i	$0.443043\pi$
$42$	0.602153	0.0929142
$43$	2.86694	0.437204	0.218602	−	0.975814i	$-0.429850\pi$
$43$	2.86694	0.437204	0.218602	+	0.975814i	$0.429850\pi$
$44$	−5.54166	−0.835436
$45$	−1.95379	−0.291254
$46$	0.202543	0.0298634
$47$	−9.60447	−1.40096	−0.700478	−	0.713674i	$-0.747030\pi$
$47$	−9.60447	−1.40096	−0.700478	+	0.713674i	$0.747030\pi$
$48$	−6.04740	−0.872867
$49$	14.6103	2.08719
$50$	0.309361	0.0437503
$51$	−2.14984	−0.301037
$52$	−10.6746	−1.48031
$53$	11.9835	1.64606	0.823028	−	0.568000i	$-0.192283\pi$
$53$	11.9835	1.64606	0.823028	+	0.568000i	$0.192283\pi$
$54$	0.474644	0.0645908
$55$	8.17865	1.10281
$56$	1.57318	0.210225
$57$	3.30073	0.437193
$58$	−0.311597	−0.0409147
$59$	1.64320	0.213926	0.106963	−	0.994263i	$-0.465887\pi$
$59$	1.64320	0.213926	0.106963	+	0.994263i	$0.465887\pi$
$60$	8.95745	1.15640
$61$	−6.27880	−0.803918	−0.401959	−	0.915658i	$-0.631671\pi$
$61$	−6.27880	−0.803918	−0.401959	+	0.915658i	$0.631671\pi$
$62$	0.856523	0.108779
$63$	3.08815	0.389071
$64$	−7.82811	−0.978514
$65$	15.7542	1.95406
$66$	−0.360204	−0.0443380
$67$	2.21952	0.271158	0.135579	−	0.990767i	$-0.456711\pi$
$67$	2.21952	0.271158	0.135579	+	0.990767i	$0.456711\pi$
$68$	−2.80327	−0.339946
$69$	−3.65223	−0.439677
$70$	−1.15880	−0.138503
$71$	8.64425	1.02588	0.512942	−	0.858423i	$-0.328556\pi$
$71$	8.64425	1.02588	0.512942	+	0.858423i	$0.328556\pi$
$72$	0.224810	0.0264941
$73$	2.32372	0.271971	0.135986	−	0.990711i	$-0.456580\pi$
$73$	2.32372	0.271971	0.135986	+	0.990711i	$0.456580\pi$
$74$	0.618054	0.0718474
$75$	−5.57836	−0.644133
$76$	4.30398	0.493700
$77$	−12.9272	−1.47319
$78$	−0.693844	−0.0785624
$79$	−16.2986	−1.83373	−0.916866	−	0.399195i	$-0.869290\pi$
$79$	−16.2986	−1.83373	−0.916866	+	0.399195i	$0.869290\pi$
$80$	11.6378	1.30114
$81$	−6.56578	−0.729531
$82$	0.193181	0.0213333
$83$	−12.8465	−1.41008	−0.705042	−	0.709165i	$-0.749072\pi$
$83$	−12.8465	−1.41008	−0.705042	+	0.709165i	$0.749072\pi$
$84$	−14.1581	−1.54478
$85$	4.13720	0.448743
$86$	0.242989	0.0262022
$87$	5.61867	0.602384
$88$	−0.941065	−0.100318
$89$	14.4369	1.53031	0.765153	−	0.643848i	$-0.222663\pi$
$89$	14.4369	1.53031	0.765153	+	0.643848i	$0.222663\pi$
$90$	−0.165594	−0.0174552
$91$	−24.9010	−2.61033
$92$	−4.76231	−0.496505
$93$	−15.4447	−1.60154
$94$	−0.814031	−0.0839609
$95$	−6.35202	−0.651703
$96$	−1.54694	−0.157884
$97$	11.2887	1.14619	0.573096	−	0.819488i	$-0.305742\pi$
$97$	11.2887	1.14619	0.573096	+	0.819488i	$0.305742\pi$
$98$	1.23831	0.125088
$99$	−1.84731	−0.185662
$100$	−7.27387	−0.727387
$101$	−17.9891	−1.78998	−0.894991	−	0.446084i	$-0.852818\pi$
$101$	−17.9891	−1.78998	−0.894991	+	0.446084i	$0.852818\pi$
$102$	−0.182211	−0.0180415
$103$	1.53975	0.151716	0.0758582	−	0.997119i	$-0.475830\pi$
$103$	1.53975	0.151716	0.0758582	+	0.997119i	$0.475830\pi$
$104$	−1.81273	−0.177753
$105$	20.8953	2.03917
$106$	1.01567	0.0986501
$107$	−3.36667	−0.325468	−0.162734	−	0.986670i	$-0.552031\pi$
$107$	−3.36667	−0.325468	−0.162734	+	0.986670i	$0.552031\pi$
$108$	−11.1601	−1.07388
$109$	−7.88786	−0.755520	−0.377760	−	0.925904i	$-0.623306\pi$
$109$	−7.88786	−0.755520	−0.377760	+	0.925904i	$0.623306\pi$
$110$	0.693186	0.0660927
$111$	−11.1447	−1.05780
$112$	−18.3946	−1.73813
$113$	3.51040	0.330231	0.165115	−	0.986274i	$-0.447200\pi$
$113$	3.51040	0.330231	0.165115	+	0.986274i	$0.447200\pi$
$114$	0.279755	0.0262015
$115$	7.02845	0.655406
$116$	7.32643	0.680242
$117$	−3.55840	−0.328974
$118$	0.139270	0.0128208
$119$	−6.53925	−0.599453
$120$	1.52112	0.138859
$121$	−3.26705	−0.297005
$122$	−0.532163	−0.0481798
$123$	−3.48342	−0.314089
$124$	−20.1390	−1.80854
$125$	−3.97034	−0.355118
$126$	0.261738	0.0233175
$127$	18.2622	1.62051	0.810254	−	0.586078i	$-0.199329\pi$
$127$	18.2622	1.62051	0.810254	+	0.586078i	$0.199329\pi$
$128$	−2.68787	−0.237577
$129$	−4.38154	−0.385773
$130$	1.33525	0.117109
$131$	−11.6505	−1.01791	−0.508957	−	0.860792i	$-0.669969\pi$
$131$	−11.6505	−1.01791	−0.508957	+	0.860792i	$0.669969\pi$
$132$	8.46930	0.737158
$133$	10.0400	0.870578
$134$	0.188117	0.0162508
$135$	16.4706	1.41756
$136$	−0.476042	−0.0408202
$137$	8.38758	0.716599	0.358300	−	0.933607i	$-0.383357\pi$
$137$	8.38758	0.716599	0.358300	+	0.933607i	$0.383357\pi$
$138$	−0.309547	−0.0263503
$139$	−0.904433	−0.0767130	−0.0383565	−	0.999264i	$-0.512212\pi$
$139$	−0.904433	−0.0767130	−0.0383565	+	0.999264i	$0.512212\pi$
$140$	27.2463	2.30273
$141$	14.6785	1.23615
$142$	0.732648	0.0614824
$143$	14.8956	1.24563
$144$	−2.62863	−0.219052
$145$	−10.8127	−0.897947
$146$	0.196948	0.0162996
$147$	−22.3289	−1.84166
$148$	−14.5320	−1.19453
$149$	9.10673	0.746052	0.373026	−	0.927821i	$-0.378320\pi$
$149$	9.10673	0.746052	0.373026	+	0.927821i	$0.378320\pi$
$150$	−0.472796	−0.0386037
$151$	8.75404	0.712394	0.356197	−	0.934411i	$-0.384073\pi$
$151$	8.75404	0.712394	0.356197	+	0.934411i	$0.384073\pi$
$152$	0.730886	0.0592827
$153$	−0.934471	−0.0755475
$154$	−1.09565	−0.0882898
$155$	29.7222	2.38734
$156$	16.3140	1.30617
$157$	11.4003	0.909844	0.454922	−	0.890531i	$-0.349667\pi$
$157$	11.4003	0.909844	0.454922	+	0.890531i	$0.349667\pi$
$158$	−1.38139	−0.109898
$159$	−18.3143	−1.45242
$160$	2.97698	0.235351
$161$	−11.1091	−0.875524
$162$	−0.556486	−0.0437217
$163$	−2.76918	−0.216899	−0.108449	−	0.994102i	$-0.534589\pi$
$163$	−2.76918	−0.216899	−0.108449	+	0.994102i	$0.534589\pi$
$164$	−4.54219	−0.354685
$165$	−12.4994	−0.973078
$166$	−1.08881	−0.0845081
$167$	−1.37128	−0.106113	−0.0530564	−	0.998592i	$-0.516896\pi$
$167$	−1.37128	−0.106113	−0.0530564	+	0.998592i	$0.516896\pi$
$168$	−2.40428	−0.185495
$169$	15.6928	1.20714
$170$	0.350651	0.0268937
$171$	1.43473	0.109717
$172$	−5.71328	−0.435634
$173$	22.4815	1.70924	0.854618	−	0.519257i	$-0.173791\pi$
$173$	22.4815	1.70924	0.854618	+	0.519257i	$0.173791\pi$
$174$	0.476213	0.0361016
$175$	−16.9679	−1.28266
$176$	11.0036	0.829424
$177$	−2.51129	−0.188760
$178$	1.22361	0.0917131
$179$	21.3902	1.59878	0.799390	−	0.600812i	$-0.205156\pi$
$179$	21.3902	1.59878	0.799390	+	0.600812i	$0.205156\pi$
$180$	3.89354	0.290207
$181$	−14.9655	−1.11238	−0.556188	−	0.831057i	$-0.687737\pi$
$181$	−14.9655	−1.11238	−0.556188	+	0.831057i	$0.687737\pi$
$182$	−2.11050	−0.156440
$183$	9.59588	0.709348
$184$	−0.808718	−0.0596195
$185$	21.4471	1.57682
$186$	−1.30902	−0.0959822
$187$	3.91174	0.286055
$188$	19.1399	1.39592
$189$	−26.0334	−1.89365
$190$	−0.538369	−0.0390574
$191$	−19.8852	−1.43884	−0.719421	−	0.694574i	$-0.755593\pi$
$191$	−19.8852	−1.43884	−0.719421	+	0.694574i	$0.755593\pi$
$192$	11.9637	0.863405
$193$	−25.0217	−1.80110	−0.900551	−	0.434750i	$-0.856837\pi$
$193$	−25.0217	−1.80110	−0.900551	+	0.434750i	$0.856837\pi$
$194$	0.956778	0.0686927
$195$	−24.0771	−1.72419
$196$	−29.1157	−2.07969
$197$	13.6464	0.972264	0.486132	−	0.873885i	$-0.338407\pi$
$197$	13.6464	0.972264	0.486132	+	0.873885i	$0.338407\pi$
$198$	−0.156570	−0.0111269
$199$	16.7797	1.18948	0.594742	−	0.803916i	$-0.297254\pi$
$199$	16.7797	1.18948	0.594742	+	0.803916i	$0.297254\pi$
$200$	−1.23522	−0.0873435
$201$	−3.39209	−0.239259
$202$	−1.52468	−0.107276
$203$	17.0905	1.19952
$204$	4.28423	0.299956
$205$	6.70358	0.468198
$206$	0.130503	0.00909255
$207$	−1.58752	−0.110340
$208$	21.1957	1.46965
$209$	−6.00586	−0.415434
$210$	1.77099	0.122210
$211$	25.4327	1.75086	0.875430	−	0.483344i	$-0.160578\pi$
$211$	25.4327	1.75086	0.875430	+	0.483344i	$0.160578\pi$
$212$	−23.8809	−1.64014
$213$	−13.2110	−0.905202
$214$	−0.285344	−0.0195057
$215$	8.43194	0.575054
$216$	−1.89516	−0.128950
$217$	−46.9788	−3.18913
$218$	−0.668539	−0.0452792
$219$	−3.55134	−0.239977
$220$	−16.2986	−1.09885
$221$	7.53501	0.506860
$222$	−0.944571	−0.0633955
$223$	−0.184506	−0.0123555	−0.00617773	−	0.999981i	$-0.501966\pi$
$223$	−0.184506	−0.0123555	−0.00617773	+	0.999981i	$0.501966\pi$
$224$	−4.70540	−0.314393
$225$	−2.42475	−0.161650
$226$	0.297526	0.0197911
$227$	−2.11097	−0.140110	−0.0700551	−	0.997543i	$-0.522318\pi$
$227$	−2.11097	−0.140110	−0.0700551	+	0.997543i	$0.522318\pi$
$228$	−6.57776	−0.435623
$229$	2.02619	0.133895	0.0669473	−	0.997757i	$-0.478674\pi$
$229$	2.02619	0.133895	0.0669473	+	0.997757i	$0.478674\pi$
$230$	0.595699	0.0392793
$231$	19.7565	1.29989
$232$	1.24415	0.0816824
$233$	15.5109	1.01615	0.508076	−	0.861312i	$-0.330357\pi$
$233$	15.5109	1.01615	0.508076	+	0.861312i	$0.330357\pi$
$234$	−0.301594	−0.0197158
$235$	−28.2477	−1.84267
$236$	−3.27459	−0.213157
$237$	24.9091	1.61802
$238$	−0.554238	−0.0359259
$239$	4.08398	0.264171	0.132085	−	0.991238i	$-0.457833\pi$
$239$	4.08398	0.264171	0.132085	+	0.991238i	$0.457833\pi$
$240$	−17.7860	−1.14808
$241$	−2.12764	−0.137054	−0.0685268	−	0.997649i	$-0.521830\pi$
$241$	−2.12764	−0.137054	−0.0685268	+	0.997649i	$0.521830\pi$
$242$	−0.276901	−0.0177999
$243$	−6.76599	−0.434038
$244$	12.5125	0.801031
$245$	42.9704	2.74528
$246$	−0.295239	−0.0188237
$247$	−11.5688	−0.736106
$248$	−3.41994	−0.217166
$249$	19.6332	1.24421
$250$	−0.336509	−0.0212827
$251$	−10.4127	−0.657246	−0.328623	−	0.944461i	$-0.606585\pi$
$251$	−10.4127	−0.657246	−0.328623	+	0.944461i	$0.606585\pi$
$252$	−6.15413	−0.387673
$253$	6.64542	0.417794
$254$	1.54782	0.0971190
$255$	−6.32288	−0.395954
$256$	15.4284	0.964276
$257$	−0.327510	−0.0204295	−0.0102148	−	0.999948i	$-0.503252\pi$
$257$	−0.327510	−0.0204295	−0.0102148	+	0.999948i	$0.503252\pi$
$258$	−0.371359	−0.0231198
$259$	−33.8992	−2.10639
$260$	−31.3952	−1.94705
$261$	2.44227	0.151173
$262$	−0.987448	−0.0610048
$263$	9.50790	0.586282	0.293141	−	0.956069i	$-0.405299\pi$
$263$	9.50790	0.586282	0.293141	+	0.956069i	$0.405299\pi$
$264$	1.43823	0.0885168
$265$	35.2445	2.16506
$266$	0.850944	0.0521748
$267$	−22.0639	−1.35029
$268$	−4.42310	−0.270184
$269$	−21.9510	−1.33838	−0.669189	−	0.743093i	$-0.733358\pi$
$269$	−21.9510	−1.33838	−0.669189	+	0.743093i	$0.733358\pi$
$270$	1.39597	0.0849562
$271$	5.51281	0.334880	0.167440	−	0.985882i	$-0.446450\pi$
$271$	5.51281	0.334880	0.167440	+	0.985882i	$0.446450\pi$
$272$	5.56619	0.337500
$273$	38.0562	2.30326
$274$	0.710893	0.0429466
$275$	10.1501	0.612075
$276$	7.27822	0.438098
$277$	−13.7102	−0.823764	−0.411882	−	0.911237i	$-0.635128\pi$
$277$	−13.7102	−0.823764	−0.411882	+	0.911237i	$0.635128\pi$
$278$	−0.0766557	−0.00459750
$279$	−6.71336	−0.401918
$280$	4.62687	0.276508
$281$	10.0263	0.598118	0.299059	−	0.954235i	$-0.403327\pi$
$281$	10.0263	0.598118	0.299059	+	0.954235i	$0.403327\pi$
$282$	1.24408	0.0740840
$283$	5.19316	0.308701	0.154351	−	0.988016i	$-0.450671\pi$
$283$	5.19316	0.308701	0.154351	+	0.988016i	$0.450671\pi$
$284$	−17.2264	−1.02220
$285$	9.70778	0.575039
$286$	1.26249	0.0746524
$287$	−10.5957	−0.625442
$288$	−0.672411	−0.0396222
$289$	−15.0212	−0.883602
$290$	−0.916437	−0.0538150
$291$	−17.2525	−1.01136
$292$	−4.63075	−0.270994
$293$	28.9718	1.69255	0.846276	−	0.532745i	$-0.178839\pi$
$293$	28.9718	1.69255	0.846276	+	0.532745i	$0.178839\pi$
$294$	−1.89250	−0.110373
$295$	4.83280	0.281376
$296$	−2.46778	−0.143437
$297$	15.5730	0.903637
$298$	0.771846	0.0447118
$299$	12.8008	0.740288
$300$	11.1166	0.641820
$301$	−13.3275	−0.768185
$302$	0.741953	0.0426946
$303$	27.4927	1.57941
$304$	−8.54601	−0.490147
$305$	−18.4666	−1.05739
$306$	−0.0792016	−0.00452765
$307$	19.8358	1.13209	0.566045	−	0.824374i	$-0.308473\pi$
$307$	19.8358	1.13209	0.566045	+	0.824374i	$0.308473\pi$
$308$	25.7615	1.46790
$309$	−2.35320	−0.133869
$310$	2.51912	0.143076
$311$	10.4506	0.592602	0.296301	−	0.955095i	$-0.404247\pi$
$311$	10.4506	0.592602	0.296301	+	0.955095i	$0.404247\pi$
$312$	2.77039	0.156843
$313$	−1.36047	−0.0768980	−0.0384490	−	0.999261i	$-0.512242\pi$
$313$	−1.36047	−0.0768980	−0.0384490	+	0.999261i	$0.512242\pi$
$314$	0.966240	0.0545281
$315$	9.08256	0.511744
$316$	32.4801	1.82715
$317$	−19.0275	−1.06869	−0.534346	−	0.845266i	$-0.679442\pi$
$317$	−19.0275	−1.06869	−0.534346	+	0.845266i	$0.679442\pi$
$318$	−1.55224	−0.0870452
$319$	−10.2235	−0.572404
$320$	−23.0232	−1.28704
$321$	5.14528	0.287181
$322$	−0.941561	−0.0524712
$323$	−3.03809	−0.169044
$324$	13.0844	0.726911
$325$	19.5517	1.08453
$326$	−0.234703	−0.0129990
$327$	12.0550	0.666643
$328$	−0.771338	−0.0425900
$329$	44.6482	2.46153
$330$	−1.05939	−0.0583177
$331$	18.5257	1.01826	0.509131	−	0.860689i	$-0.329967\pi$
$331$	18.5257	1.01826	0.509131	+	0.860689i	$0.329967\pi$
$332$	25.6007	1.40502
$333$	−4.84426	−0.265464
$334$	−0.116223	−0.00635946
$335$	6.52782	0.356653
$336$	28.1125	1.53366
$337$	7.08764	0.386088	0.193044	−	0.981190i	$-0.438164\pi$
$337$	7.08764	0.386088	0.193044	+	0.981190i	$0.438164\pi$
$338$	1.33005	0.0723451
$339$	−5.36494	−0.291383
$340$	−8.24469	−0.447131
$341$	28.1024	1.52183
$342$	0.121601	0.00657546
$343$	−35.3781	−1.91024
$344$	−0.970210	−0.0523102
$345$	−10.7416	−0.578306
$346$	1.90543	0.102437
$347$	−20.2070	−1.08477	−0.542385	−	0.840130i	$-0.682479\pi$
$347$	−20.2070	−1.08477	−0.542385	+	0.840130i	$0.682479\pi$
$348$	−11.1970	−0.600221
$349$	3.51996	0.188419	0.0942097	−	0.995552i	$-0.469968\pi$
$349$	3.51996	0.188419	0.0942097	+	0.995552i	$0.469968\pi$
$350$	−1.43813	−0.0768711
$351$	29.9976	1.60115
$352$	2.81474	0.150026
$353$	−20.9979	−1.11761	−0.558803	−	0.829300i	$-0.688739\pi$
$353$	−20.9979	−1.11761	−0.558803	+	0.829300i	$0.688739\pi$
$354$	−0.212846	−0.0113126
$355$	25.4236	1.34934
$356$	−28.7701	−1.52481
$357$	9.99393	0.528935
$358$	1.81294	0.0958168
$359$	−33.7901	−1.78337	−0.891685	−	0.452656i	$-0.850477\pi$
$359$	−33.7901	−1.78337	−0.891685	+	0.452656i	$0.850477\pi$
$360$	0.661188	0.0348477
$361$	−14.3355	−0.754500
$362$	−1.26841	−0.0666660
$363$	4.99303	0.262066
$364$	49.6231	2.60096
$365$	6.83429	0.357723
$366$	0.813304	0.0425121
$367$	3.76165	0.196357	0.0981783	−	0.995169i	$-0.468698\pi$
$367$	3.76165	0.196357	0.0981783	+	0.995169i	$0.468698\pi$
$368$	9.45607	0.492932
$369$	−1.51414	−0.0788230
$370$	1.81776	0.0945007
$371$	−55.7075	−2.89219
$372$	30.7784	1.59579
$373$	−26.2062	−1.35691	−0.678453	−	0.734644i	$-0.737349\pi$
$373$	−26.2062	−1.35691	−0.678453	+	0.734644i	$0.737349\pi$
$374$	0.331542	0.0171436
$375$	6.06787	0.313343
$376$	3.25028	0.167620
$377$	−19.6930	−1.01424
$378$	−2.20647	−0.113489
$379$	7.52773	0.386674	0.193337	−	0.981132i	$-0.438069\pi$
$379$	7.52773	0.386674	0.193337	+	0.981132i	$0.438069\pi$
$380$	12.6584	0.649363
$381$	−27.9101	−1.42988
$382$	−1.68538	−0.0862315
$383$	1.59445	0.0814724	0.0407362	−	0.999170i	$-0.487030\pi$
$383$	1.59445	0.0814724	0.0407362	+	0.999170i	$0.487030\pi$
$384$	4.10787	0.209629
$385$	−38.0200	−1.93768
$386$	−2.12073	−0.107942
$387$	−1.90453	−0.0968125
$388$	−22.4963	−1.14208
$389$	−22.1850	−1.12482	−0.562412	−	0.826857i	$-0.690126\pi$
$389$	−22.1850	−1.12482	−0.562412	+	0.826857i	$0.690126\pi$
$390$	−2.04066	−0.103333
$391$	3.36161	0.170004
$392$	−4.94433	−0.249726
$393$	17.8055	0.898169
$394$	1.15661	0.0582690
$395$	−47.9357	−2.41190
$396$	3.68136	0.184995
$397$	−30.4321	−1.52734	−0.763672	−	0.645604i	$-0.776606\pi$
$397$	−30.4321	−1.52734	−0.763672	+	0.645604i	$0.776606\pi$
$398$	1.42218	0.0712872
$399$	−15.3441	−0.768166
$400$	14.4431	0.722153
$401$	−32.5921	−1.62757	−0.813785	−	0.581166i	$-0.802597\pi$
$401$	−32.5921	−1.62757	−0.813785	+	0.581166i	$0.802597\pi$
$402$	−0.287498	−0.0143391
$403$	54.1324	2.69653
$404$	35.8490	1.78355
$405$	−19.3106	−0.959551
$406$	1.44852	0.0718887
$407$	20.2783	1.00516
$408$	0.727533	0.0360183
$409$	−26.4812	−1.30941	−0.654706	−	0.755884i	$-0.727208\pi$
$409$	−26.4812	−1.30941	−0.654706	+	0.755884i	$0.727208\pi$
$410$	0.568165	0.0280597
$411$	−12.8187	−0.632301
$412$	−3.06845	−0.151171
$413$	−7.63871	−0.375876
$414$	−0.134551	−0.00661281
$415$	−37.7827	−1.85468
$416$	5.42191	0.265831
$417$	1.38224	0.0676887
$418$	−0.509030	−0.0248975
$419$	−2.19584	−0.107274	−0.0536369	−	0.998561i	$-0.517081\pi$
$419$	−2.19584	−0.107274	−0.0536369	+	0.998561i	$0.517081\pi$
$420$	−41.6404	−2.03184
$421$	−27.9354	−1.36149	−0.680745	−	0.732521i	$-0.738344\pi$
$421$	−27.9354	−1.36149	−0.680745	+	0.732521i	$0.738344\pi$
$422$	2.15556	0.104931
$423$	6.38031	0.310221
$424$	−4.05537	−0.196946
$425$	5.13447	0.249059
$426$	−1.11970	−0.0542498
$427$	29.1882	1.41252
$428$	6.70916	0.324299
$429$	−22.7649	−1.09910
$430$	0.714654	0.0344637
$431$	16.1210	0.776522	0.388261	−	0.921549i	$-0.373076\pi$
$431$	16.1210	0.776522	0.388261	+	0.921549i	$0.373076\pi$
$432$	22.1595	1.06615
$433$	−23.2765	−1.11860	−0.559299	−	0.828966i	$-0.688930\pi$
$433$	−23.2765	−1.11860	−0.559299	+	0.828966i	$0.688930\pi$
$434$	−3.98171	−0.191128
$435$	16.5250	0.792315
$436$	15.7191	0.752806
$437$	−5.16122	−0.246895
$438$	−0.300996	−0.0143821
$439$	−20.6030	−0.983327	−0.491664	−	0.870785i	$-0.663611\pi$
$439$	−20.6030	−0.983327	−0.491664	+	0.870785i	$0.663611\pi$
$440$	−2.76776	−0.131948
$441$	−9.70573	−0.462178
$442$	0.638634	0.0303767
$443$	26.9601	1.28091	0.640456	−	0.767995i	$-0.278745\pi$
$443$	26.9601	1.28091	0.640456	+	0.767995i	$0.278745\pi$
$444$	22.2093	1.05400
$445$	42.4603	2.01281
$446$	−0.0156379	−0.000740477 0
$447$	−13.9178	−0.658289
$448$	36.3905	1.71929
$449$	33.6414	1.58763	0.793817	−	0.608156i	$-0.208091\pi$
$449$	33.6414	1.58763	0.793817	+	0.608156i	$0.208091\pi$
$450$	−0.205511	−0.00968787
$451$	6.33826	0.298457
$452$	−6.99558	−0.329045
$453$	−13.3788	−0.628590
$454$	−0.178917	−0.00839697
$455$	−73.2363	−3.43337
$456$	−1.11701	−0.0523089
$457$	−0.297488	−0.0139159	−0.00695795	−	0.999976i	$-0.502215\pi$
$457$	−0.297488	−0.0139159	−0.00695795	+	0.999976i	$0.502215\pi$
$458$	0.171731	0.00802446
$459$	7.87766	0.367698
$460$	−14.0064	−0.653052
$461$	−1.01271	−0.0471668	−0.0235834	−	0.999722i	$-0.507508\pi$
$461$	−1.01271	−0.0471668	−0.0235834	+	0.999722i	$0.507508\pi$
$462$	1.67448	0.0779037
$463$	33.1333	1.53984	0.769919	−	0.638142i	$-0.220297\pi$
$463$	33.1333	1.53984	0.769919	+	0.638142i	$0.220297\pi$
$464$	−14.5474	−0.675347
$465$	−45.4243	−2.10650
$466$	1.31463	0.0608992
$467$	34.3481	1.58944	0.794721	−	0.606975i	$-0.207617\pi$
$467$	34.3481	1.58944	0.794721	+	0.606975i	$0.207617\pi$
$468$	7.09124	0.327792
$469$	−10.3179	−0.476435
$470$	−2.39414	−0.110434
$471$	−17.4231	−0.802813
$472$	−0.556079	−0.0255956
$473$	7.97243	0.366573
$474$	2.11118	0.0969697
$475$	−7.88317	−0.361705
$476$	13.0315	0.597299
$477$	−7.96070	−0.364495
$478$	0.346140	0.0158321
$479$	9.11785	0.416605	0.208303	−	0.978064i	$-0.433206\pi$
$479$	9.11785	0.416605	0.208303	+	0.978064i	$0.433206\pi$
$480$	−4.54971	−0.207665
$481$	39.0612	1.78104
$482$	−0.180330	−0.00821379
$483$	16.9781	0.772530
$484$	6.51064	0.295938
$485$	33.2011	1.50758
$486$	−0.573455	−0.0260124
$487$	−3.33368	−0.151064	−0.0755318	−	0.997143i	$-0.524065\pi$
$487$	−3.33368	−0.151064	−0.0755318	+	0.997143i	$0.524065\pi$
$488$	2.12483	0.0961865
$489$	4.23212	0.191383
$490$	3.64198	0.164528
$491$	−21.7334	−0.980815	−0.490408	−	0.871493i	$-0.663152\pi$
$491$	−21.7334	−0.980815	−0.490408	+	0.871493i	$0.663152\pi$
$492$	6.94181	0.312961
$493$	−5.17158	−0.232916
$494$	−0.980521	−0.0441157
$495$	−5.43313	−0.244201
$496$	39.9882	1.79552
$497$	−40.1844	−1.80252
$498$	1.66403	0.0745668
$499$	−21.4881	−0.961939	−0.480970	−	0.876737i	$-0.659715\pi$
$499$	−21.4881	−0.961939	−0.480970	+	0.876737i	$0.659715\pi$
$500$	7.91217	0.353843
$501$	2.09572	0.0936299
$502$	−0.882537	−0.0393896
$503$	5.33645	0.237941	0.118970	−	0.992898i	$-0.462041\pi$
$503$	5.33645	0.237941	0.118970	+	0.992898i	$0.462041\pi$
$504$	−1.04507	−0.0465512
$505$	−52.9077	−2.35436
$506$	0.563236	0.0250389
$507$	−23.9832	−1.06513
$508$	−36.3932	−1.61469
$509$	−0.276967	−0.0122764	−0.00613818	−	0.999981i	$-0.501954\pi$
$509$	−0.276967	−0.0122764	−0.00613818	+	0.999981i	$0.501954\pi$
$510$	−0.535899	−0.0237300
$511$	−10.8023	−0.477864
$512$	6.68339	0.295367
$513$	−12.0949	−0.534003
$514$	−0.0277583	−0.00122437
$515$	4.52856	0.199552
$516$	8.73160	0.384387
$517$	−26.7083	−1.17463
$518$	−2.87314	−0.126239
$519$	−34.3584	−1.50817
$520$	−5.33142	−0.233798
$521$	31.3340	1.37277	0.686384	−	0.727240i	$-0.259197\pi$
$521$	31.3340	1.37277	0.686384	+	0.727240i	$0.259197\pi$
$522$	0.206996	0.00905996
$523$	−12.8336	−0.561175	−0.280587	−	0.959828i	$-0.590529\pi$
$523$	−12.8336	−0.561175	−0.280587	+	0.959828i	$0.590529\pi$
$524$	23.2174	1.01426
$525$	25.9321	1.13177
$526$	0.805847	0.0351366
$527$	14.2157	0.619247
$528$	−16.8167	−0.731853
$529$	−17.2892	−0.751703
$530$	2.98717	0.129754
$531$	−1.09159	−0.0473708
$532$	−20.0079	−0.867451
$533$	12.2091	0.528835
$534$	−1.87003	−0.0809242
$535$	−9.90170	−0.428088
$536$	−0.751115	−0.0324432
$537$	−32.6906	−1.41070
$538$	−1.86047	−0.0802105
$539$	40.6287	1.75000
$540$	−32.8228	−1.41247
$541$	2.66821	0.114715	0.0573576	−	0.998354i	$-0.481732\pi$
$541$	2.66821	0.114715	0.0573576	+	0.998354i	$0.481732\pi$
$542$	0.467241	0.0200697
$543$	22.8717	0.981519
$544$	1.42385	0.0610470
$545$	−23.1990	−0.993734
$546$	3.22547	0.138037
$547$	1.00000	0.0427569
$547$	1.00000	0.0427569
$548$	−16.7149	−0.714025
$549$	4.17105	0.178016
$550$	0.860278	0.0366824
$551$	7.94014	0.338261
$552$	1.23596	0.0526061
$553$	75.7670	3.22194
$554$	−1.16201	−0.0493691
$555$	−32.7775	−1.39133
$556$	1.80237	0.0764375
$557$	0.915238	0.0387799	0.0193899	−	0.999812i	$-0.493828\pi$
$557$	0.915238	0.0387799	0.0193899	+	0.999812i	$0.493828\pi$
$558$	−0.568994	−0.0240874
$559$	15.3569	0.649529
$560$	−54.1004	−2.28616
$561$	−5.97830	−0.252404
$562$	0.849782	0.0358459
$563$	−12.4608	−0.525160	−0.262580	−	0.964910i	$-0.584573\pi$
$563$	−12.4608	−0.525160	−0.262580	+	0.964910i	$0.584573\pi$
$564$	−29.2515	−1.23171
$565$	10.3244	0.434352
$566$	0.440149	0.0185008
$567$	30.5223	1.28182
$568$	−2.92533	−0.122744
$569$	−20.7408	−0.869501	−0.434750	−	0.900551i	$-0.643163\pi$
$569$	−20.7408	−0.869501	−0.434750	+	0.900551i	$0.643163\pi$
$570$	0.822788	0.0344628
$571$	26.5763	1.11218	0.556092	−	0.831121i	$-0.312300\pi$
$571$	26.5763	1.11218	0.556092	+	0.831121i	$0.312300\pi$
$572$	−29.6842	−1.24116
$573$	30.3905	1.26958
$574$	−0.898041	−0.0374835
$575$	8.72265	0.363760
$576$	5.20026	0.216678
$577$	14.7103	0.612396	0.306198	−	0.951968i	$-0.400943\pi$
$577$	14.7103	0.612396	0.306198	+	0.951968i	$0.400943\pi$
$578$	−1.27313	−0.0529553
$579$	38.2406	1.58923
$580$	21.5477	0.894721
$581$	59.7193	2.47758
$582$	−1.46224	−0.0606119
$583$	33.3239	1.38013
$584$	−0.786378	−0.0325406
$585$	−10.4656	−0.432699
$586$	2.45552	0.101437
$587$	−35.5599	−1.46771	−0.733857	−	0.679304i	$-0.762282\pi$
$587$	−35.5599	−1.46771	−0.733857	+	0.679304i	$0.762282\pi$
$588$	44.4975	1.83504
$589$	−21.8260	−0.899324
$590$	0.409606	0.0168632
$591$	−20.8557	−0.857890
$592$	28.8549	1.18593
$593$	6.76762	0.277913	0.138956	−	0.990298i	$-0.455625\pi$
$593$	6.76762	0.277913	0.138956	+	0.990298i	$0.455625\pi$
$594$	1.31990	0.0541560
$595$	−19.2326	−0.788459
$596$	−18.1480	−0.743373
$597$	−25.6444	−1.04956
$598$	1.08494	0.0443663
$599$	−9.54078	−0.389826	−0.194913	−	0.980821i	$-0.562442\pi$
$599$	−9.54078	−0.389826	−0.194913	+	0.980821i	$0.562442\pi$
$600$	1.88779	0.0770687
$601$	21.2895	0.868419	0.434209	−	0.900812i	$-0.357028\pi$
$601$	21.2895	0.868419	0.434209	+	0.900812i	$0.357028\pi$
$602$	−1.12958	−0.0460382
$603$	−1.47444	−0.0600439
$604$	−17.4452	−0.709835
$605$	−9.60872	−0.390650
$606$	2.33016	0.0946562
$607$	−13.0669	−0.530371	−0.265186	−	0.964197i	$-0.585433\pi$
$607$	−13.0669	−0.530371	−0.265186	+	0.964197i	$0.585433\pi$
$608$	−2.18609	−0.0886578
$609$	−26.1194	−1.05841
$610$	−1.56514	−0.0633708
$611$	−51.4469	−2.08132
$612$	1.86223	0.0752762
$613$	−1.13988	−0.0460392	−0.0230196	−	0.999735i	$-0.507328\pi$
$613$	−1.13988	−0.0460392	−0.0230196	+	0.999735i	$0.507328\pi$
$614$	1.68119	0.0678475
$615$	−10.2451	−0.413121
$616$	4.37472	0.176263
$617$	−18.5454	−0.746611	−0.373305	−	0.927709i	$-0.621776\pi$
$617$	−18.5454	−0.746611	−0.373305	+	0.927709i	$0.621776\pi$
$618$	−0.199447	−0.00802293
$619$	4.04717	0.162670	0.0813348	−	0.996687i	$-0.474082\pi$
$619$	4.04717	0.162670	0.0813348	+	0.996687i	$0.474082\pi$
$620$	−59.2308	−2.37877
$621$	13.3829	0.537037
$622$	0.885750	0.0355153
$623$	−67.1126	−2.68881
$624$	−32.3933	−1.29677
$625$	−29.9274	−1.19710
$626$	−0.115307	−0.00460859
$627$	9.17874	0.366564
$628$	−22.7187	−0.906576
$629$	10.2579	0.409007
$630$	0.769797	0.0306694
$631$	−47.6195	−1.89570	−0.947851	−	0.318714i	$-0.896749\pi$
$631$	−47.6195	−1.89570	−0.947851	+	0.318714i	$0.896749\pi$
$632$	5.51565	0.219401
$633$	−38.8688	−1.54490
$634$	−1.61269	−0.0640480
$635$	53.7109	2.13145
$636$	36.4971	1.44720
$637$	78.2611	3.10082
$638$	−0.866494	−0.0343048
$639$	−5.74243	−0.227167
$640$	−7.90530	−0.312484
$641$	−28.8575	−1.13980	−0.569901	−	0.821713i	$-0.693019\pi$
$641$	−28.8575	−1.13980	−0.569901	+	0.821713i	$0.693019\pi$
$642$	0.436090	0.0172111
$643$	−14.7371	−0.581174	−0.290587	−	0.956849i	$-0.593851\pi$
$643$	−14.7371	−0.581174	−0.290587	+	0.956849i	$0.593851\pi$
$644$	22.1385	0.872379
$645$	−12.8865	−0.507406
$646$	−0.257495	−0.0101310
$647$	−13.3480	−0.524762	−0.262381	−	0.964964i	$-0.584508\pi$
$647$	−13.3480	−0.524762	−0.262381	+	0.964964i	$0.584508\pi$
$648$	2.22195	0.0872863
$649$	4.56943	0.179366
$650$	1.65711	0.0649974
$651$	71.7976	2.81397
$652$	5.51846	0.216120
$653$	12.7054	0.497201	0.248600	−	0.968606i	$-0.420029\pi$
$653$	12.7054	0.497201	0.248600	+	0.968606i	$0.420029\pi$
$654$	1.02173	0.0399527
$655$	−34.2654	−1.33886
$656$	9.01900	0.352133
$657$	−1.54366	−0.0602241
$658$	3.78418	0.147523
$659$	8.02697	0.312686	0.156343	−	0.987703i	$-0.450029\pi$
$659$	8.02697	0.312686	0.156343	+	0.987703i	$0.450029\pi$
$660$	24.9090	0.969583
$661$	30.7078	1.19439	0.597197	−	0.802094i	$-0.296281\pi$
$661$	30.7078	1.19439	0.597197	+	0.802094i	$0.296281\pi$
$662$	1.57015	0.0610257
$663$	−11.5157	−0.447234
$664$	4.34742	0.168713
$665$	29.5286	1.14507
$666$	−0.410577	−0.0159096
$667$	−8.78568	−0.340183
$668$	2.73271	0.105732
$669$	0.281980	0.0109020
$670$	0.553269	0.0213746
$671$	−17.4602	−0.674044
$672$	7.19126	0.277409
$673$	4.98589	0.192192	0.0960959	−	0.995372i	$-0.469364\pi$
$673$	4.98589	0.192192	0.0960959	+	0.995372i	$0.469364\pi$
$674$	0.600716	0.0231387
$675$	20.4408	0.786767
$676$	−31.2728	−1.20280
$677$	−2.23582	−0.0859295	−0.0429648	−	0.999077i	$-0.513680\pi$
$677$	−2.23582	−0.0859295	−0.0429648	+	0.999077i	$0.513680\pi$
$678$	−0.454708	−0.0174629
$679$	−52.4776	−2.01391
$680$	−1.40008	−0.0536908
$681$	3.22619	0.123628
$682$	2.38184	0.0912052
$683$	10.0295	0.383768	0.191884	−	0.981418i	$-0.438540\pi$
$683$	10.0295	0.383768	0.191884	+	0.981418i	$0.438540\pi$
$684$	−2.85916	−0.109323
$685$	24.6687	0.942541
$686$	−2.99849	−0.114483
$687$	−3.09663	−0.118144
$688$	11.3443	0.432499
$689$	64.1902	2.44545
$690$	−0.910406	−0.0346586
$691$	−31.5478	−1.20014	−0.600068	−	0.799949i	$-0.704860\pi$
$691$	−31.5478	−1.20014	−0.600068	+	0.799949i	$0.704860\pi$
$692$	−44.8015	−1.70310
$693$	8.58759	0.326216
$694$	−1.71266	−0.0650116
$695$	−2.66002	−0.100900
$696$	−1.90143	−0.0720735
$697$	3.20623	0.121445
$698$	0.298336	0.0112922
$699$	−23.7053	−0.896615
$700$	33.8140	1.27805
$701$	−25.0997	−0.948003	−0.474002	−	0.880524i	$-0.657191\pi$
$701$	−25.0997	−0.948003	−0.474002	+	0.880524i	$0.657191\pi$
$702$	2.54246	0.0959589
$703$	−15.7493	−0.593996
$704$	−21.7685	−0.820433
$705$	43.1708	1.62591
$706$	−1.77969	−0.0669795
$707$	83.6258	3.14507
$708$	5.00454	0.188082
$709$	−14.7989	−0.555783	−0.277892	−	0.960612i	$-0.589636\pi$
$709$	−14.7989	−0.555783	−0.277892	+	0.960612i	$0.589636\pi$
$710$	2.15479	0.0808677
$711$	10.8272	0.406053
$712$	−4.88563	−0.183097
$713$	24.1502	0.904434
$714$	0.847040	0.0316997
$715$	43.8095	1.63838
$716$	−42.6268	−1.59304
$717$	−6.24154	−0.233095
$718$	−2.86389	−0.106880
$719$	38.3784	1.43127	0.715637	−	0.698473i	$-0.246137\pi$
$719$	38.3784	1.43127	0.715637	+	0.698473i	$0.246137\pi$
$720$	−7.73104	−0.288119
$721$	−7.15784	−0.266572
$722$	−1.21501	−0.0452181
$723$	3.25167	0.120931
$724$	29.8235	1.10838
$725$	−13.4191	−0.498373
$726$	0.423187	0.0157059
$727$	39.5118	1.46541	0.732706	−	0.680545i	$-0.238257\pi$
$727$	39.5118	1.46541	0.732706	+	0.680545i	$0.238257\pi$
$728$	8.42683	0.312319
$729$	30.0378	1.11251
$730$	0.579244	0.0214388
$731$	4.03289	0.149162
$732$	−19.1228	−0.706800
$733$	−20.0492	−0.740533	−0.370267	−	0.928926i	$-0.620734\pi$
$733$	−20.0492	−0.740533	−0.370267	+	0.928926i	$0.620734\pi$
$734$	0.318821	0.0117679
$735$	−65.6715	−2.42233
$736$	2.41889	0.0891615
$737$	6.17208	0.227352
$738$	−0.128332	−0.00472395
$739$	−17.7203	−0.651851	−0.325926	−	0.945395i	$-0.605676\pi$
$739$	−17.7203	−0.651851	−0.325926	+	0.945395i	$0.605676\pi$
$740$	−42.7401	−1.57116
$741$	17.6806	0.649513
$742$	−4.72151	−0.173332
$743$	−31.1197	−1.14167	−0.570836	−	0.821064i	$-0.693381\pi$
$743$	−31.1197	−1.14167	−0.570836	+	0.821064i	$0.693381\pi$
$744$	5.22669	0.191620
$745$	26.7838	0.981281
$746$	−2.22112	−0.0813210
$747$	8.53400	0.312243
$748$	−7.79538	−0.285027
$749$	15.6506	0.571861
$750$	0.514285	0.0187790
$751$	0.262341	0.00957295	0.00478648	−	0.999989i	$-0.498476\pi$
$751$	0.262341	0.00957295	0.00478648	+	0.999989i	$0.498476\pi$
$752$	−38.0044	−1.38588
$753$	15.9138	0.579930
$754$	−1.66909	−0.0607846
$755$	25.7465	0.937010
$756$	51.8797	1.88685
$757$	0.515028	0.0187190	0.00935951	−	0.999956i	$-0.497021\pi$
$757$	0.515028	0.0187190	0.00935951	+	0.999956i	$0.497021\pi$
$758$	0.638017	0.0231738
$759$	−10.1562	−0.368646
$760$	2.14961	0.0779744
$761$	−10.0389	−0.363911	−0.181956	−	0.983307i	$-0.558243\pi$
$761$	−10.0389	−0.363911	−0.181956	+	0.983307i	$0.558243\pi$
$762$	−2.36553	−0.0856942
$763$	36.6682	1.32748
$764$	39.6275	1.43367
$765$	−2.74837	−0.0993675
$766$	0.135138	0.00488274
$767$	8.80188	0.317817
$768$	−23.5792	−0.850841
$769$	38.9180	1.40342	0.701710	−	0.712463i	$-0.252420\pi$
$769$	38.9180	1.40342	0.701710	+	0.712463i	$0.252420\pi$
$770$	−3.22241	−0.116127
$771$	0.500533	0.0180263
$772$	49.8637	1.79463
$773$	18.5245	0.666280	0.333140	−	0.942877i	$-0.391892\pi$
$773$	18.5245	0.666280	0.333140	+	0.942877i	$0.391892\pi$
$774$	−0.161419	−0.00580209
$775$	36.8867	1.32501
$776$	−3.82024	−0.137139
$777$	51.8081	1.85860
$778$	−1.88030	−0.0674120
$779$	−4.92266	−0.176373
$780$	47.9812	1.71800
$781$	24.0381	0.860150
$782$	0.284915	0.0101885
$783$	−20.5885	−0.735773
$784$	57.8123	2.06473
$785$	33.5294	1.19672
$786$	1.50911	0.0538283
$787$	21.1876	0.755256	0.377628	−	0.925957i	$-0.376740\pi$
$787$	21.1876	0.755256	0.377628	+	0.925957i	$0.376740\pi$
$788$	−27.1947	−0.968772
$789$	−14.5309	−0.517314
$790$	−4.06281	−0.144548
$791$	−16.3188	−0.580228
$792$	0.625156	0.0222139
$793$	−33.6328	−1.19434
$794$	−2.57929	−0.0915356
$795$	−53.8642	−1.91036
$796$	−33.4390	−1.18521
$797$	39.4183	1.39627	0.698135	−	0.715966i	$-0.254014\pi$
$797$	39.4183	1.39627	0.698135	+	0.715966i	$0.254014\pi$
$798$	−1.30050	−0.0460371
$799$	−13.5105	−0.477967
$800$	3.69458	0.130623
$801$	−9.59051	−0.338864
$802$	−2.76236	−0.0975422
$803$	6.46185	0.228034
$804$	6.75981	0.238400
$805$	−32.6731	−1.15157
$806$	4.58802	0.161606
$807$	33.5477	1.18093
$808$	6.08775	0.214166
$809$	−41.9914	−1.47634	−0.738169	−	0.674615i	$-0.764310\pi$
$809$	−41.9914	−1.47634	−0.738169	+	0.674615i	$0.764310\pi$
$810$	−1.63668	−0.0575070
$811$	−16.3648	−0.574645	−0.287323	−	0.957834i	$-0.592765\pi$
$811$	−16.3648	−0.574645	−0.287323	+	0.957834i	$0.592765\pi$
$812$	−34.0583	−1.19521
$813$	−8.42522	−0.295485
$814$	1.71870	0.0602403
$815$	−8.14441	−0.285286
$816$	−8.50680	−0.297798
$817$	−6.19186	−0.216626
$818$	−2.24443	−0.0784746
$819$	16.5419	0.578021
$820$	−13.3590	−0.466517
$821$	−0.148690	−0.00518932	−0.00259466	−	0.999997i	$-0.500826\pi$
$821$	−0.148690	−0.00518932	−0.00259466	+	0.999997i	$0.500826\pi$
$822$	−1.08646	−0.0378945
$823$	−45.4805	−1.58535	−0.792675	−	0.609645i	$-0.791312\pi$
$823$	−45.4805	−1.58535	−0.792675	+	0.609645i	$0.791312\pi$
$824$	−0.521073	−0.0181524
$825$	−15.5124	−0.540072
$826$	−0.647423	−0.0225267
$827$	10.3297	0.359199	0.179599	−	0.983740i	$-0.442520\pi$
$827$	10.3297	0.359199	0.179599	+	0.983740i	$0.442520\pi$
$828$	3.16363	0.109944
$829$	−20.9572	−0.727873	−0.363936	−	0.931424i	$-0.618567\pi$
$829$	−20.9572	−0.727873	−0.363936	+	0.931424i	$0.618567\pi$
$830$	−3.20230	−0.111153
$831$	20.9532	0.726859
$832$	−41.9318	−1.45372
$833$	20.5522	0.712090
$834$	0.117153	0.00405667
$835$	−4.03306	−0.139570
$836$	11.9686	0.413942
$837$	56.5941	1.95618
$838$	−0.186109	−0.00642904
$839$	14.6027	0.504140	0.252070	−	0.967709i	$-0.418889\pi$
$839$	14.6027	0.504140	0.252070	+	0.967709i	$0.418889\pi$
$840$	−7.07123	−0.243981
$841$	−15.4839	−0.533928
$842$	−2.36768	−0.0815957
$843$	−15.3231	−0.527757
$844$	−50.6828	−1.74457
$845$	46.1539	1.58774
$846$	0.540766	0.0185919
$847$	15.1875	0.521850
$848$	47.4180	1.62834
$849$	−7.93669	−0.272387
$850$	0.435175	0.0149264
$851$	17.4265	0.597371
$852$	26.3271	0.901951
$853$	−8.03808	−0.275219	−0.137609	−	0.990487i	$-0.543942\pi$
$853$	−8.03808	−0.275219	−0.137609	+	0.990487i	$0.543942\pi$
$854$	2.47386	0.0846538
$855$	4.21969	0.144310
$856$	1.13933	0.0389414
$857$	1.95137	0.0666575	0.0333288	−	0.999444i	$-0.489389\pi$
$857$	1.95137	0.0666575	0.0333288	+	0.999444i	$0.489389\pi$
$858$	−1.92945	−0.0658705
$859$	−25.0516	−0.854748	−0.427374	−	0.904075i	$-0.640561\pi$
$859$	−25.0516	−0.854748	−0.427374	+	0.904075i	$0.640561\pi$
$860$	−16.8033	−0.572988
$861$	16.1933	0.551867
$862$	1.36635	0.0465379
$863$	−37.4577	−1.27508	−0.637538	−	0.770419i	$-0.720047\pi$
$863$	−37.4577	−1.27508	−0.637538	+	0.770419i	$0.720047\pi$
$864$	5.66847	0.192845
$865$	66.1202	2.24816
$866$	−1.97281	−0.0670389
$867$	22.9569	0.779658
$868$	93.6202	3.17768
$869$	−45.3233	−1.53749
$870$	1.40059	0.0474844
$871$	11.8890	0.402843
$872$	2.66936	0.0903958
$873$	−7.49914	−0.253808
$874$	−0.437442	−0.0147967
$875$	18.4569	0.623957
$876$	7.07717	0.239115
$877$	38.2689	1.29225	0.646124	−	0.763233i	$-0.276389\pi$
$877$	38.2689	1.29225	0.646124	+	0.763233i	$0.276389\pi$
$878$	−1.74622	−0.0589320
$879$	−44.2776	−1.49345
$880$	32.3625	1.09094
$881$	−11.5315	−0.388506	−0.194253	−	0.980951i	$-0.562228\pi$
$881$	−11.5315	−0.388506	−0.194253	+	0.980951i	$0.562228\pi$
$882$	−0.822614	−0.0276989
$883$	−17.0395	−0.573424	−0.286712	−	0.958017i	$-0.592562\pi$
$883$	−17.0395	−0.573424	−0.286712	+	0.958017i	$0.592562\pi$
$884$	−15.0159	−0.505039
$885$	−7.38595	−0.248276
$886$	2.28502	0.0767666
$887$	2.94617	0.0989227	0.0494613	−	0.998776i	$-0.484250\pi$
$887$	2.94617	0.0989227	0.0494613	+	0.998776i	$0.484250\pi$
$888$	3.77150	0.126563
$889$	−84.8954	−2.84730
$890$	3.59874	0.120630
$891$	−18.2582	−0.611674
$892$	0.367687	0.0123111
$893$	20.7432	0.694145
$894$	−1.17961	−0.0394521
$895$	62.9107	2.10287
$896$	12.4951	0.417432
$897$	−19.5634	−0.653203
$898$	2.85129	0.0951488
$899$	−37.1532	−1.23913
$900$	4.83208	0.161069
$901$	16.8570	0.561588
$902$	0.537202	0.0178869
$903$	20.3684	0.677818
$904$	−1.18797	−0.0395111
$905$	−44.0149	−1.46311
$906$	−1.13393	−0.0376722
$907$	33.3216	1.10642	0.553212	−	0.833040i	$-0.313402\pi$
$907$	33.3216	1.10642	0.553212	+	0.833040i	$0.313402\pi$
$908$	4.20678	0.139607
$909$	11.9503	0.396365
$910$	−6.20718	−0.205766
$911$	49.1040	1.62689	0.813445	−	0.581642i	$-0.197590\pi$
$911$	49.1040	1.62689	0.813445	+	0.581642i	$0.197590\pi$
$912$	13.0608	0.432488
$913$	−35.7237	−1.18228
$914$	−0.0252137	−0.000833996 0
$915$	28.2224	0.933004
$916$	−4.03783	−0.133414
$917$	54.1598	1.78851
$918$	0.667675	0.0220366
$919$	−26.0558	−0.859501	−0.429750	−	0.902948i	$-0.641398\pi$
$919$	−26.0558	−0.859501	−0.429750	+	0.902948i	$0.641398\pi$
$920$	−2.37852	−0.0784174
$921$	−30.3150	−0.998914
$922$	−0.0858331	−0.00282676
$923$	46.3035	1.52410
$924$	−39.3712	−1.29522
$925$	26.6169	0.875158
$926$	2.80823	0.0922843
$927$	−1.02287	−0.0335954
$928$	−3.72127	−0.122157
$929$	−35.4283	−1.16236	−0.581182	−	0.813774i	$-0.697409\pi$
$929$	−35.4283	−1.16236	−0.581182	+	0.813774i	$0.697409\pi$
$930$	−3.84996	−0.126245
$931$	−31.5546	−1.03416
$932$	−30.9104	−1.01250
$933$	−15.9717	−0.522890
$934$	2.91119	0.0952571
$935$	11.5048	0.376247
$936$	1.20421	0.0393608
$937$	−4.19429	−0.137021	−0.0685107	−	0.997650i	$-0.521825\pi$
$937$	−4.19429	−0.137021	−0.0685107	+	0.997650i	$0.521825\pi$
$938$	−0.874496	−0.0285533
$939$	2.07920	0.0678520
$940$	56.2924	1.83606
$941$	25.9751	0.846764	0.423382	−	0.905951i	$-0.360843\pi$
$941$	25.9751	0.846764	0.423382	+	0.905951i	$0.360843\pi$
$942$	−1.47670	−0.0481135
$943$	5.44688	0.177375
$944$	6.50204	0.211623
$945$	−76.5666	−2.49071
$946$	0.675708	0.0219692
$947$	32.0372	1.04107	0.520534	−	0.853841i	$-0.325733\pi$
$947$	32.0372	1.04107	0.520534	+	0.853841i	$0.325733\pi$
$948$	−49.6392	−1.61221
$949$	12.4472	0.404052
$950$	−0.668142	−0.0216774
$951$	29.0797	0.942975
$952$	2.21297	0.0717228
$953$	−21.1530	−0.685213	−0.342607	−	0.939479i	$-0.611310\pi$
$953$	−21.1530	−0.685213	−0.342607	+	0.939479i	$0.611310\pi$
$954$	−0.674713	−0.0218446
$955$	−58.4843	−1.89251
$956$	−8.13863	−0.263222
$957$	15.6245	0.505068
$958$	0.772788	0.0249676
$959$	−38.9913	−1.25909
$960$	35.1863	1.13563
$961$	71.1275	2.29444
$962$	3.31065	0.106740
$963$	2.23650	0.0720702
$964$	4.24001	0.136561
$965$	−73.5913	−2.36899
$966$	1.43899	0.0462986
$967$	−4.43778	−0.142709	−0.0713547	−	0.997451i	$-0.522732\pi$
$967$	−4.43778	−0.142709	−0.0713547	+	0.997451i	$0.522732\pi$
$968$	1.10561	0.0355358
$969$	4.64310	0.149158
$970$	2.81398	0.0903513
$971$	−55.4001	−1.77787	−0.888936	−	0.458031i	$-0.848555\pi$
$971$	−55.4001	−1.77787	−0.888936	+	0.458031i	$0.848555\pi$
$972$	13.4834	0.432479
$973$	4.20443	0.134788
$974$	−0.282548	−0.00905342
$975$	−29.8808	−0.956952
$976$	−24.8449	−0.795266
$977$	15.6172	0.499638	0.249819	−	0.968293i	$-0.419629\pi$
$977$	15.6172	0.499638	0.249819	+	0.968293i	$0.419629\pi$
$978$	0.358696	0.0114698
$979$	40.1463	1.28308
$980$	−85.6321	−2.73542
$981$	5.23995	0.167299
$982$	−1.84203	−0.0587814
$983$	40.5818	1.29436	0.647180	−	0.762338i	$-0.275948\pi$
$983$	40.5818	1.29436	0.647180	+	0.762338i	$0.275948\pi$
$984$	1.17883	0.0375799
$985$	40.1353	1.27882
$986$	−0.438319	−0.0139589
$987$	−68.2357	−2.17197
$988$	23.0545	0.733462
$989$	6.85123	0.217856
$990$	−0.460488	−0.0146353
$991$	−50.8000	−1.61372	−0.806858	−	0.590746i	$-0.798834\pi$
$991$	−50.8000	−1.61372	−0.806858	+	0.590746i	$0.798834\pi$
$992$	10.2291	0.324774
$993$	−28.3127	−0.898477
$994$	−3.40585	−0.108027
$995$	49.3508	1.56453
$996$	−39.1255	−1.23974
$997$	3.62691	0.114865	0.0574327	−	0.998349i	$-0.481709\pi$
$997$	3.62691	0.114865	0.0574327	+	0.998349i	$0.481709\pi$
$998$	−1.82123	−0.0576502
$999$	40.8374	1.29204

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.a.c.1.12	✓	25
3.2	odd	2		4923.2.a.n.1.14		25
4.3	odd	2		8752.2.a.v.1.19		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.a.c.1.12	✓	25	1.1	even	1	trivial
4923.2.a.n.1.14		25	3.2	odd	2
8752.2.a.v.1.19		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)

\(f(q)\)	\(=\)	\(q+0.0847555 q^{2} -1.52830 q^{3} -1.99282 q^{4} +2.94110 q^{5} -0.129532 q^{6} -4.64869 q^{7} -0.338413 q^{8} -0.664306 q^{9} +O(q^{10})\)	\(q+0.0847555 q^{2} -1.52830 q^{3} -1.99282 q^{4} +2.94110 q^{5} -0.129532 q^{6} -4.64869 q^{7} -0.338413 q^{8} -0.664306 q^{9} +0.249274 q^{10} +2.78082 q^{11} +3.04562 q^{12} +5.35656 q^{13} -0.394002 q^{14} -4.49487 q^{15} +3.95695 q^{16} +1.40669 q^{17} -0.0563036 q^{18} -2.15975 q^{19} -5.86106 q^{20} +7.10458 q^{21} +0.235690 q^{22} +2.38974 q^{23} +0.517196 q^{24} +3.65005 q^{25} +0.453998 q^{26} +5.60015 q^{27} +9.26399 q^{28} -3.67642 q^{29} -0.380965 q^{30} +10.1058 q^{31} +1.01220 q^{32} -4.24992 q^{33} +0.119224 q^{34} -13.6722 q^{35} +1.32384 q^{36} +7.29220 q^{37} -0.183050 q^{38} -8.18642 q^{39} -0.995306 q^{40} +2.27928 q^{41} +0.602153 q^{42} +2.86694 q^{43} -5.54166 q^{44} -1.95379 q^{45} +0.202543 q^{46} -9.60447 q^{47} -6.04740 q^{48} +14.6103 q^{49} +0.309361 q^{50} -2.14984 q^{51} -10.6746 q^{52} +11.9835 q^{53} +0.474644 q^{54} +8.17865 q^{55} +1.57318 q^{56} +3.30073 q^{57} -0.311597 q^{58} +1.64320 q^{59} +8.95745 q^{60} -6.27880 q^{61} +0.856523 q^{62} +3.08815 q^{63} -7.82811 q^{64} +15.7542 q^{65} -0.360204 q^{66} +2.21952 q^{67} -2.80327 q^{68} -3.65223 q^{69} -1.15880 q^{70} +8.64425 q^{71} +0.224810 q^{72} +2.32372 q^{73} +0.618054 q^{74} -5.57836 q^{75} +4.30398 q^{76} -12.9272 q^{77} -0.693844 q^{78} -16.2986 q^{79} +11.6378 q^{80} -6.56578 q^{81} +0.193181 q^{82} -12.8465 q^{83} -14.1581 q^{84} +4.13720 q^{85} +0.242989 q^{86} +5.61867 q^{87} -0.941065 q^{88} +14.4369 q^{89} -0.165594 q^{90} -24.9010 q^{91} -4.76231 q^{92} -15.4447 q^{93} -0.814031 q^{94} -6.35202 q^{95} -1.54694 q^{96} +11.2887 q^{97} +1.23831 q^{98} -1.84731 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 4 q^{2} + 8 q^{3} + 26 q^{4} + 29 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 29 q^{9}+O(q^{10}) \) 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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