LMFDB - Embedded newform 1205.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1205,2,Mod(1,1205)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1205, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1205.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1205 = 5 \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1205.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:	$9.62197344356$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1205.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.82262 q^{2} -2.39134 q^{3} +5.96719 q^{4} -1.00000 q^{5} +6.74985 q^{6} +0.875274 q^{7} -11.1979 q^{8} +2.71851 q^{9} +O(q^{10})$	\(q-2.82262 q^{2} -2.39134 q^{3} +5.96719 q^{4} -1.00000 q^{5} +6.74985 q^{6} +0.875274 q^{7} -11.1979 q^{8} +2.71851 q^{9} +2.82262 q^{10} -3.86157 q^{11} -14.2696 q^{12} -0.582652 q^{13} -2.47057 q^{14} +2.39134 q^{15} +19.6730 q^{16} -2.93934 q^{17} -7.67332 q^{18} +2.08453 q^{19} -5.96719 q^{20} -2.09308 q^{21} +10.8998 q^{22} +0.349389 q^{23} +26.7779 q^{24} +1.00000 q^{25} +1.64460 q^{26} +0.673145 q^{27} +5.22293 q^{28} +3.11646 q^{29} -6.74985 q^{30} -4.04618 q^{31} -33.1336 q^{32} +9.23433 q^{33} +8.29663 q^{34} -0.875274 q^{35} +16.2218 q^{36} -5.70743 q^{37} -5.88384 q^{38} +1.39332 q^{39} +11.1979 q^{40} -11.6663 q^{41} +5.90797 q^{42} -7.84129 q^{43} -23.0427 q^{44} -2.71851 q^{45} -0.986192 q^{46} +5.82783 q^{47} -47.0448 q^{48} -6.23389 q^{49} -2.82262 q^{50} +7.02895 q^{51} -3.47679 q^{52} +10.7860 q^{53} -1.90003 q^{54} +3.86157 q^{55} -9.80121 q^{56} -4.98482 q^{57} -8.79657 q^{58} +1.51778 q^{59} +14.2696 q^{60} -4.55591 q^{61} +11.4208 q^{62} +2.37944 q^{63} +54.1777 q^{64} +0.582652 q^{65} -26.0650 q^{66} -3.14491 q^{67} -17.5396 q^{68} -0.835508 q^{69} +2.47057 q^{70} +5.72049 q^{71} -30.4415 q^{72} -11.4155 q^{73} +16.1099 q^{74} -2.39134 q^{75} +12.4388 q^{76} -3.37994 q^{77} -3.93281 q^{78} -10.7741 q^{79} -19.6730 q^{80} -9.76524 q^{81} +32.9295 q^{82} +11.0219 q^{83} -12.4898 q^{84} +2.93934 q^{85} +22.1330 q^{86} -7.45250 q^{87} +43.2414 q^{88} -7.49366 q^{89} +7.67332 q^{90} -0.509980 q^{91} +2.08487 q^{92} +9.67580 q^{93} -16.4498 q^{94} -2.08453 q^{95} +79.2337 q^{96} +3.87107 q^{97} +17.5959 q^{98} -10.4977 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 4 q^{2} + 9 q^{3} + 36 q^{4} - 25 q^{5} + 7 q^{6} + 7 q^{7} - 15 q^{8} + 36 q^{9}+O(q^{10}) $ 25 * q - 4 * q^2 + 9 * q^3 + 36 * q^4 - 25 * q^5 + 7 * q^6 + 7 * q^7 - 15 * q^8 + 36 * q^9	\( 25 q - 4 q^{2} + 9 q^{3} + 36 q^{4} - 25 q^{5} + 7 q^{6} + 7 q^{7} - 15 q^{8} + 36 q^{9} + 4 q^{10} + 10 q^{11} + 22 q^{12} + 10 q^{13} + 13 q^{14} - 9 q^{15} + 54 q^{16} + q^{17} - 13 q^{18} + 50 q^{19} - 36 q^{20} + 9 q^{21} + 11 q^{22} - 31 q^{23} + 22 q^{24} + 25 q^{25} + 8 q^{26} + 42 q^{27} + 14 q^{28} + 4 q^{29} - 7 q^{30} + 34 q^{31} - 44 q^{32} + 28 q^{33} + 33 q^{34} - 7 q^{35} + 83 q^{36} + 14 q^{37} - 10 q^{38} + 23 q^{39} + 15 q^{40} + 11 q^{41} + 23 q^{42} + 49 q^{43} + 20 q^{44} - 36 q^{45} + 27 q^{46} - 28 q^{47} + 30 q^{48} + 66 q^{49} - 4 q^{50} + 49 q^{51} + 39 q^{52} - 16 q^{53} + 5 q^{54} - 10 q^{55} + 51 q^{56} + 10 q^{57} - 8 q^{58} + 30 q^{59} - 22 q^{60} + 35 q^{61} - 18 q^{62} + 73 q^{64} - 10 q^{65} - 13 q^{66} + 37 q^{67} + 11 q^{68} - 4 q^{69} - 13 q^{70} + 12 q^{71} - 90 q^{72} + 36 q^{73} - 12 q^{74} + 9 q^{75} + 57 q^{76} - 31 q^{77} - 9 q^{78} + 16 q^{79} - 54 q^{80} + 65 q^{81} - 11 q^{82} + 43 q^{83} - 62 q^{84} - q^{85} - 9 q^{86} - 22 q^{87} + 20 q^{88} + 38 q^{89} + 13 q^{90} + 86 q^{91} - 119 q^{92} + 10 q^{93} - 18 q^{94} - 50 q^{95} - 34 q^{96} + 17 q^{97} - 32 q^{98} + 26 q^{99}+O(q^{100}) \) 25 * q - 4 * q^2 + 9 * q^3 + 36 * q^4 - 25 * q^5 + 7 * q^6 + 7 * q^7 - 15 * q^8 + 36 * q^9 + 4 * q^10 + 10 * q^11 + 22 * q^12 + 10 * q^13 + 13 * q^14 - 9 * q^15 + 54 * q^16 + q^17 - 13 * q^18 + 50 * q^19 - 36 * q^20 + 9 * q^21 + 11 * q^22 - 31 * q^23 + 22 * q^24 + 25 * q^25 + 8 * q^26 + 42 * q^27 + 14 * q^28 + 4 * q^29 - 7 * q^30 + 34 * q^31 - 44 * q^32 + 28 * q^33 + 33 * q^34 - 7 * q^35 + 83 * q^36 + 14 * q^37 - 10 * q^38 + 23 * q^39 + 15 * q^40 + 11 * q^41 + 23 * q^42 + 49 * q^43 + 20 * q^44 - 36 * q^45 + 27 * q^46 - 28 * q^47 + 30 * q^48 + 66 * q^49 - 4 * q^50 + 49 * q^51 + 39 * q^52 - 16 * q^53 + 5 * q^54 - 10 * q^55 + 51 * q^56 + 10 * q^57 - 8 * q^58 + 30 * q^59 - 22 * q^60 + 35 * q^61 - 18 * q^62 + 73 * q^64 - 10 * q^65 - 13 * q^66 + 37 * q^67 + 11 * q^68 - 4 * q^69 - 13 * q^70 + 12 * q^71 - 90 * q^72 + 36 * q^73 - 12 * q^74 + 9 * q^75 + 57 * q^76 - 31 * q^77 - 9 * q^78 + 16 * q^79 - 54 * q^80 + 65 * q^81 - 11 * q^82 + 43 * q^83 - 62 * q^84 - q^85 - 9 * q^86 - 22 * q^87 + 20 * q^88 + 38 * q^89 + 13 * q^90 + 86 * q^91 - 119 * q^92 + 10 * q^93 - 18 * q^94 - 50 * q^95 - 34 * q^96 + 17 * q^97 - 32 * q^98 + 26 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.82262	−1.99589	−0.997947	−	0.0640413i	$-0.979601\pi$
$2$	−2.82262	−1.99589	−0.997947	+	0.0640413i	$0.979601\pi$
$3$	−2.39134	−1.38064	−0.690320	−	0.723504i	$-0.742530\pi$
$3$	−2.39134	−1.38064	−0.690320	+	0.723504i	$0.742530\pi$
$4$	5.96719	2.98359
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	6.74985	2.75561
$7$	0.875274	0.330823	0.165411	−	0.986225i	$-0.447105\pi$
$7$	0.875274	0.330823	0.165411	+	0.986225i	$0.447105\pi$
$8$	−11.1979	−3.95905
$9$	2.71851	0.906169
$10$	2.82262	0.892591
$11$	−3.86157	−1.16431	−0.582154	−	0.813079i	$-0.697790\pi$
$11$	−3.86157	−1.16431	−0.582154	+	0.813079i	$0.697790\pi$
$12$	−14.2696	−4.11927
$13$	−0.582652	−0.161598	−0.0807992	−	0.996730i	$-0.525747\pi$
$13$	−0.582652	−0.161598	−0.0807992	+	0.996730i	$0.525747\pi$
$14$	−2.47057	−0.660287
$15$	2.39134	0.617441
$16$	19.6730	4.91824
$17$	−2.93934	−0.712894	−0.356447	−	0.934316i	$-0.616012\pi$
$17$	−2.93934	−0.712894	−0.356447	+	0.934316i	$0.616012\pi$
$18$	−7.67332	−1.80862
$19$	2.08453	0.478224	0.239112	−	0.970992i	$-0.423144\pi$
$19$	2.08453	0.478224	0.239112	+	0.970992i	$0.423144\pi$
$20$	−5.96719	−1.33430
$21$	−2.09308	−0.456747
$22$	10.8998	2.32384
$23$	0.349389	0.0728526	0.0364263	−	0.999336i	$-0.488403\pi$
$23$	0.349389	0.0728526	0.0364263	+	0.999336i	$0.488403\pi$
$24$	26.7779	5.46602
$25$	1.00000	0.200000
$26$	1.64460	0.322534
$27$	0.673145	0.129547
$28$	5.22293	0.987041
$29$	3.11646	0.578711	0.289356	−	0.957222i	$-0.406559\pi$
$29$	3.11646	0.578711	0.289356	+	0.957222i	$0.406559\pi$
$30$	−6.74985	−1.23235
$31$	−4.04618	−0.726716	−0.363358	−	0.931650i	$-0.618370\pi$
$31$	−4.04618	−0.726716	−0.363358	+	0.931650i	$0.618370\pi$
$32$	−33.1336	−5.85725
$33$	9.23433	1.60749
$34$	8.29663	1.42286
$35$	−0.875274	−0.147948
$36$	16.2218	2.70364
$37$	−5.70743	−0.938296	−0.469148	−	0.883120i	$-0.655439\pi$
$37$	−5.70743	−0.938296	−0.469148	+	0.883120i	$0.655439\pi$
$38$	−5.88384	−0.954485
$39$	1.39332	0.223109
$40$	11.1979	1.77054
$41$	−11.6663	−1.82197	−0.910984	−	0.412441i	$-0.864676\pi$
$41$	−11.6663	−1.82197	−0.910984	+	0.412441i	$0.864676\pi$
$42$	5.90797	0.911619
$43$	−7.84129	−1.19579	−0.597893	−	0.801576i	$-0.703995\pi$
$43$	−7.84129	−1.19579	−0.597893	+	0.801576i	$0.703995\pi$
$44$	−23.0427	−3.47382
$45$	−2.71851	−0.405251
$46$	−0.986192	−0.145406
$47$	5.82783	0.850076	0.425038	−	0.905175i	$-0.360261\pi$
$47$	5.82783	0.850076	0.425038	+	0.905175i	$0.360261\pi$
$48$	−47.0448	−6.79033
$49$	−6.23389	−0.890556
$50$	−2.82262	−0.399179
$51$	7.02895	0.984250
$52$	−3.47679	−0.482144
$53$	10.7860	1.48157	0.740784	−	0.671743i	$-0.234454\pi$
$53$	10.7860	1.48157	0.740784	+	0.671743i	$0.234454\pi$
$54$	−1.90003	−0.258562
$55$	3.86157	0.520694
$56$	−9.80121	−1.30974
$57$	−4.98482	−0.660256
$58$	−8.79657	−1.15505
$59$	1.51778	0.197599	0.0987993	−	0.995107i	$-0.468500\pi$
$59$	1.51778	0.197599	0.0987993	+	0.995107i	$0.468500\pi$
$60$	14.2696	1.84219
$61$	−4.55591	−0.583325	−0.291662	−	0.956521i	$-0.594208\pi$
$61$	−4.55591	−0.583325	−0.291662	+	0.956521i	$0.594208\pi$
$62$	11.4208	1.45045
$63$	2.37944	0.299781
$64$	54.1777	6.77221
$65$	0.582652	0.0722690
$66$	−26.0650	−3.20838
$67$	−3.14491	−0.384212	−0.192106	−	0.981374i	$-0.561532\pi$
$67$	−3.14491	−0.384212	−0.192106	+	0.981374i	$0.561532\pi$
$68$	−17.5396	−2.12699
$69$	−0.835508	−0.100583
$70$	2.47057	0.295289
$71$	5.72049	0.678897	0.339449	−	0.940625i	$-0.389760\pi$
$71$	5.72049	0.678897	0.339449	+	0.940625i	$0.389760\pi$
$72$	−30.4415	−3.58756
$73$	−11.4155	−1.33608	−0.668039	−	0.744126i	$-0.732866\pi$
$73$	−11.4155	−1.33608	−0.668039	+	0.744126i	$0.732866\pi$
$74$	16.1099	1.87274
$75$	−2.39134	−0.276128
$76$	12.4388	1.42683
$77$	−3.37994	−0.385179
$78$	−3.93281	−0.445303
$79$	−10.7741	−1.21218	−0.606091	−	0.795396i	$-0.707263\pi$
$79$	−10.7741	−1.21218	−0.606091	+	0.795396i	$0.707263\pi$
$80$	−19.6730	−2.19951
$81$	−9.76524	−1.08503
$82$	32.9295	3.63646
$83$	11.0219	1.20981	0.604906	−	0.796297i	$-0.293211\pi$
$83$	11.0219	1.20981	0.604906	+	0.796297i	$0.293211\pi$
$84$	−12.4898	−1.36275
$85$	2.93934	0.318816
$86$	22.1330	2.38666
$87$	−7.45250	−0.798992
$88$	43.2414	4.60955
$89$	−7.49366	−0.794326	−0.397163	−	0.917748i	$-0.630005\pi$
$89$	−7.49366	−0.794326	−0.397163	+	0.917748i	$0.630005\pi$
$90$	7.67332	0.808838
$91$	−0.509980	−0.0534604
$92$	2.08487	0.217363
$93$	9.67580	1.00333
$94$	−16.4498	−1.69666
$95$	−2.08453	−0.213868
$96$	79.2337	8.08676
$97$	3.87107	0.393047	0.196524	−	0.980499i	$-0.437035\pi$
$97$	3.87107	0.393047	0.196524	+	0.980499i	$0.437035\pi$
$98$	17.5959	1.77746
$99$	−10.4977	−1.05506
$100$	5.96719	0.596719
$101$	14.9796	1.49053	0.745263	−	0.666771i	$-0.232324\pi$
$101$	14.9796	1.49053	0.745263	+	0.666771i	$0.232324\pi$
$102$	−19.8401	−1.96446
$103$	19.8287	1.95378	0.976891	−	0.213738i	$-0.0685640\pi$
$103$	19.8287	1.95378	0.976891	+	0.213738i	$0.0685640\pi$
$104$	6.52446	0.639776
$105$	2.09308	0.204264
$106$	−30.4447	−2.95706
$107$	−2.47924	−0.239678	−0.119839	−	0.992793i	$-0.538238\pi$
$107$	−2.47924	−0.239678	−0.119839	+	0.992793i	$0.538238\pi$
$108$	4.01679	0.386515
$109$	2.46586	0.236187	0.118093	−	0.993003i	$-0.462322\pi$
$109$	2.46586	0.236187	0.118093	+	0.993003i	$0.462322\pi$
$110$	−10.8998	−1.03925
$111$	13.6484	1.29545
$112$	17.2193	1.62707
$113$	−17.5877	−1.65451	−0.827255	−	0.561827i	$-0.810099\pi$
$113$	−17.5877	−1.65451	−0.827255	+	0.561827i	$0.810099\pi$
$114$	14.0703	1.31780
$115$	−0.349389	−0.0325807
$116$	18.5965	1.72664
$117$	−1.58394	−0.146436
$118$	−4.28413	−0.394386
$119$	−2.57272	−0.235841
$120$	−26.7779	−2.44448
$121$	3.91174	0.355613
$122$	12.8596	1.16425
$123$	27.8981	2.51548
$124$	−24.1443	−2.16823
$125$	−1.00000	−0.0894427
$126$	−6.71626	−0.598332
$127$	5.83290	0.517586	0.258793	−	0.965933i	$-0.416675\pi$
$127$	5.83290	0.517586	0.258793	+	0.965933i	$0.416675\pi$
$128$	−86.6558	−7.65936
$129$	18.7512	1.65095
$130$	−1.64460	−0.144241
$131$	17.7946	1.55472	0.777361	−	0.629054i	$-0.216558\pi$
$131$	17.7946	1.55472	0.777361	+	0.629054i	$0.216558\pi$
$132$	55.1030	4.79610
$133$	1.82454	0.158207
$134$	8.87690	0.766847
$135$	−0.673145	−0.0579351
$136$	32.9143	2.82238
$137$	18.5668	1.58627	0.793135	−	0.609046i	$-0.208447\pi$
$137$	18.5668	1.58627	0.793135	+	0.609046i	$0.208447\pi$
$138$	2.35832	0.200754
$139$	6.46549	0.548396	0.274198	−	0.961673i	$-0.411588\pi$
$139$	6.46549	0.548396	0.274198	+	0.961673i	$0.411588\pi$
$140$	−5.22293	−0.441418
$141$	−13.9363	−1.17365
$142$	−16.1468	−1.35501
$143$	2.24995	0.188150
$144$	53.4811	4.45676
$145$	−3.11646	−0.258808
$146$	32.2215	2.66667
$147$	14.9074	1.22954
$148$	−34.0573	−2.79949
$149$	20.0818	1.64517	0.822584	−	0.568643i	$-0.192531\pi$
$149$	20.0818	1.64517	0.822584	+	0.568643i	$0.192531\pi$
$150$	6.74985	0.551123
$151$	3.95379	0.321755	0.160877	−	0.986974i	$-0.448568\pi$
$151$	3.95379	0.321755	0.160877	+	0.986974i	$0.448568\pi$
$152$	−23.3423	−1.89331
$153$	−7.99060	−0.646002
$154$	9.54028	0.768777
$155$	4.04618	0.324997
$156$	8.31419	0.665668
$157$	20.0077	1.59679	0.798395	−	0.602135i	$-0.205683\pi$
$157$	20.0077	1.59679	0.798395	+	0.602135i	$0.205683\pi$
$158$	30.4112	2.41939
$159$	−25.7930	−2.04551
$160$	33.1336	2.61944
$161$	0.305811	0.0241013
$162$	27.5636	2.16560
$163$	10.4933	0.821895	0.410947	−	0.911659i	$-0.365198\pi$
$163$	10.4933	0.821895	0.410947	+	0.911659i	$0.365198\pi$
$164$	−69.6150	−5.43602
$165$	−9.23433	−0.718892
$166$	−31.1107	−2.41466
$167$	−18.8619	−1.45958	−0.729789	−	0.683672i	$-0.760382\pi$
$167$	−18.8619	−1.45958	−0.729789	+	0.683672i	$0.760382\pi$
$168$	23.4380	1.80828
$169$	−12.6605	−0.973886
$170$	−8.29663	−0.636322
$171$	5.66681	0.433352
$172$	−46.7905	−3.56774
$173$	−0.345627	−0.0262775	−0.0131388	−	0.999914i	$-0.504182\pi$
$173$	−0.345627	−0.0262775	−0.0131388	+	0.999914i	$0.504182\pi$
$174$	21.0356	1.59470
$175$	0.875274	0.0661645
$176$	−75.9686	−5.72635
$177$	−3.62954	−0.272813
$178$	21.1518	1.58539
$179$	−7.98056	−0.596495	−0.298248	−	0.954489i	$-0.596402\pi$
$179$	−7.98056	−0.596495	−0.298248	+	0.954489i	$0.596402\pi$
$180$	−16.2218	−1.20911
$181$	6.75810	0.502325	0.251163	−	0.967945i	$-0.419187\pi$
$181$	6.75810	0.502325	0.251163	+	0.967945i	$0.419187\pi$
$182$	1.43948	0.106701
$183$	10.8947	0.805362
$184$	−3.91241	−0.288427
$185$	5.70743	0.419619
$186$	−27.3111	−2.00255
$187$	11.3505	0.830027
$188$	34.7758	2.53628
$189$	0.589187	0.0428570
$190$	5.88384	0.426859
$191$	12.9405	0.936345	0.468172	−	0.883637i	$-0.344913\pi$
$191$	12.9405	0.936345	0.468172	+	0.883637i	$0.344913\pi$
$192$	−129.557	−9.34999
$193$	8.90975	0.641338	0.320669	−	0.947191i	$-0.396092\pi$
$193$	8.90975	0.641338	0.320669	+	0.947191i	$0.396092\pi$
$194$	−10.9265	−0.784481
$195$	−1.39332	−0.0997776
$196$	−37.1988	−2.65706
$197$	−16.0917	−1.14649	−0.573245	−	0.819384i	$-0.694316\pi$
$197$	−16.0917	−1.14649	−0.573245	+	0.819384i	$0.694316\pi$
$198$	29.6311	2.10579
$199$	−12.9171	−0.915668	−0.457834	−	0.889038i	$-0.651375\pi$
$199$	−12.9171	−0.915668	−0.457834	+	0.889038i	$0.651375\pi$
$200$	−11.1979	−0.791809
$201$	7.52056	0.530459
$202$	−42.2817	−2.97493
$203$	2.72775	0.191451
$204$	41.9431	2.93660
$205$	11.6663	0.814809
$206$	−55.9690	−3.89954
$207$	0.949816	0.0660168
$208$	−11.4625	−0.794781
$209$	−8.04956	−0.556800
$210$	−5.90797	−0.407689
$211$	16.8567	1.16046	0.580231	−	0.814452i	$-0.302962\pi$
$211$	16.8567	1.16046	0.580231	+	0.814452i	$0.302962\pi$
$212$	64.3620	4.42040
$213$	−13.6796	−0.937313
$214$	6.99797	0.478371
$215$	7.84129	0.534772
$216$	−7.53780	−0.512882
$217$	−3.54152	−0.240414
$218$	−6.96019	−0.471404
$219$	27.2982	1.84464
$220$	23.0427	1.55354
$221$	1.71261	0.115203
$222$	−38.5243	−2.58558
$223$	19.1445	1.28201	0.641005	−	0.767537i	$-0.278518\pi$
$223$	19.1445	1.28201	0.641005	+	0.767537i	$0.278518\pi$
$224$	−29.0010	−1.93771
$225$	2.71851	0.181234
$226$	49.6434	3.30223
$227$	−22.0068	−1.46064	−0.730321	−	0.683104i	$-0.760629\pi$
$227$	−22.0068	−1.46064	−0.730321	+	0.683104i	$0.760629\pi$
$228$	−29.7454	−1.96994
$229$	14.2044	0.938653	0.469326	−	0.883025i	$-0.344497\pi$
$229$	14.2044	0.938653	0.469326	+	0.883025i	$0.344497\pi$
$230$	0.986192	0.0650276
$231$	8.08257	0.531794
$232$	−34.8977	−2.29114
$233$	23.0830	1.51222	0.756108	−	0.654447i	$-0.227098\pi$
$233$	23.0830	1.51222	0.756108	+	0.654447i	$0.227098\pi$
$234$	4.47087	0.292270
$235$	−5.82783	−0.380166
$236$	9.05690	0.589554
$237$	25.7645	1.67359
$238$	7.26183	0.470714
$239$	2.58179	0.167002	0.0835011	−	0.996508i	$-0.473390\pi$
$239$	2.58179	0.167002	0.0835011	+	0.996508i	$0.473390\pi$
$240$	47.0448	3.03673
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	−11.0414	−0.709766
$243$	21.3326	1.36849
$244$	−27.1860	−1.74041
$245$	6.23389	0.398269
$246$	−78.7457	−5.02064
$247$	−1.21455	−0.0772803
$248$	45.3086	2.87710
$249$	−26.3571	−1.67031
$250$	2.82262	0.178518
$251$	10.6808	0.674165	0.337083	−	0.941475i	$-0.390560\pi$
$251$	10.6808	0.674165	0.337083	+	0.941475i	$0.390560\pi$
$252$	14.1986	0.894426
$253$	−1.34919	−0.0848229
$254$	−16.4641	−1.03305
$255$	−7.02895	−0.440170
$256$	136.241	8.51507
$257$	4.68459	0.292217	0.146108	−	0.989269i	$-0.453325\pi$
$257$	4.68459	0.292217	0.146108	+	0.989269i	$0.453325\pi$
$258$	−52.9275	−3.29512
$259$	−4.99557	−0.310409
$260$	3.47679	0.215622
$261$	8.47211	0.524410
$262$	−50.2275	−3.10306
$263$	13.5038	0.832682	0.416341	−	0.909208i	$-0.363312\pi$
$263$	13.5038	0.832682	0.416341	+	0.909208i	$0.363312\pi$
$264$	−103.405	−6.36413
$265$	−10.7860	−0.662578
$266$	−5.14997	−0.315765
$267$	17.9199	1.09668
$268$	−18.7663	−1.14633
$269$	−11.5617	−0.704931	−0.352466	−	0.935825i	$-0.614657\pi$
$269$	−11.5617	−0.704931	−0.352466	+	0.935825i	$0.614657\pi$
$270$	1.90003	0.115632
$271$	−0.360776	−0.0219156	−0.0109578	−	0.999940i	$-0.503488\pi$
$271$	−0.360776	−0.0219156	−0.0109578	+	0.999940i	$0.503488\pi$
$272$	−57.8255	−3.50618
$273$	1.21954	0.0738097
$274$	−52.4071	−3.16603
$275$	−3.86157	−0.232862
$276$	−4.98563	−0.300100
$277$	−14.0418	−0.843688	−0.421844	−	0.906669i	$-0.638617\pi$
$277$	−14.0418	−0.843688	−0.421844	+	0.906669i	$0.638617\pi$
$278$	−18.2496	−1.09454
$279$	−10.9996	−0.658527
$280$	9.80121	0.585734
$281$	−29.4531	−1.75702	−0.878511	−	0.477722i	$-0.841463\pi$
$281$	−29.4531	−1.75702	−0.878511	+	0.477722i	$0.841463\pi$
$282$	39.3370	2.34248
$283$	18.0379	1.07224	0.536122	−	0.844141i	$-0.319889\pi$
$283$	18.0379	1.07224	0.536122	+	0.844141i	$0.319889\pi$
$284$	34.1353	2.02555
$285$	4.98482	0.295275
$286$	−6.35076	−0.375528
$287$	−10.2112	−0.602749
$288$	−90.0739	−5.30766
$289$	−8.36031	−0.491783
$290$	8.79657	0.516553
$291$	−9.25703	−0.542657
$292$	−68.1182	−3.98632
$293$	13.5687	0.792692	0.396346	−	0.918101i	$-0.370278\pi$
$293$	13.5687	0.792692	0.396346	+	0.918101i	$0.370278\pi$
$294$	−42.0778	−2.45403
$295$	−1.51778	−0.0883688
$296$	63.9111	3.71476
$297$	−2.59940	−0.150832
$298$	−56.6834	−3.28358
$299$	−0.203572	−0.0117729
$300$	−14.2696	−0.823855
$301$	−6.86328	−0.395593
$302$	−11.1601	−0.642189
$303$	−35.8213	−2.05788
$304$	41.0089	2.35202
$305$	4.55591	0.260871
$306$	22.5544	1.28935
$307$	7.21586	0.411831	0.205916	−	0.978570i	$-0.433983\pi$
$307$	7.21586	0.411831	0.205916	+	0.978570i	$0.433983\pi$
$308$	−20.1687	−1.14922
$309$	−47.4172	−2.69747
$310$	−11.4208	−0.648660
$311$	27.9272	1.58361	0.791803	−	0.610777i	$-0.209143\pi$
$311$	27.9272	1.58361	0.791803	+	0.610777i	$0.209143\pi$
$312$	−15.6022	−0.883301
$313$	1.75711	0.0993176	0.0496588	−	0.998766i	$-0.484187\pi$
$313$	1.75711	0.0993176	0.0496588	+	0.998766i	$0.484187\pi$
$314$	−56.4742	−3.18702
$315$	−2.37944	−0.134066
$316$	−64.2911	−3.61666
$317$	−21.5589	−1.21087	−0.605433	−	0.795896i	$-0.707000\pi$
$317$	−21.5589	−1.21087	−0.605433	+	0.795896i	$0.707000\pi$
$318$	72.8037	4.08263
$319$	−12.0344	−0.673798
$320$	−54.1777	−3.02862
$321$	5.92872	0.330909
$322$	−0.863189	−0.0481036
$323$	−6.12713	−0.340923
$324$	−58.2710	−3.23728
$325$	−0.582652	−0.0323197
$326$	−29.6185	−1.64042
$327$	−5.89671	−0.326089
$328$	130.638	7.21326
$329$	5.10095	0.281224
$330$	26.0650	1.43483
$331$	31.6052	1.73718	0.868589	−	0.495533i	$-0.165027\pi$
$331$	31.6052	1.73718	0.868589	+	0.495533i	$0.165027\pi$
$332$	65.7698	3.60959
$333$	−15.5157	−0.850254
$334$	53.2400	2.91316
$335$	3.14491	0.171825
$336$	−41.1771	−2.24639
$337$	−4.42993	−0.241314	−0.120657	−	0.992694i	$-0.538500\pi$
$337$	−4.42993	−0.241314	−0.120657	+	0.992694i	$0.538500\pi$
$338$	35.7358	1.94377
$339$	42.0581	2.28428
$340$	17.5396	0.951217
$341$	15.6246	0.846121
$342$	−15.9953	−0.864924
$343$	−11.5833	−0.625439
$344$	87.8058	4.73417
$345$	0.835508	0.0449822
$346$	0.975574	0.0524472
$347$	32.8108	1.76138	0.880689	−	0.473695i	$-0.157080\pi$
$347$	32.8108	1.76138	0.880689	+	0.473695i	$0.157080\pi$
$348$	−44.4705	−2.38387
$349$	−26.7722	−1.43308	−0.716542	−	0.697544i	$-0.754276\pi$
$349$	−26.7722	−1.43308	−0.716542	+	0.697544i	$0.754276\pi$
$350$	−2.47057	−0.132057
$351$	−0.392209	−0.0209346
$352$	127.948	6.81964
$353$	11.7696	0.626434	0.313217	−	0.949682i	$-0.398593\pi$
$353$	11.7696	0.626434	0.313217	+	0.949682i	$0.398593\pi$
$354$	10.2448	0.544505
$355$	−5.72049	−0.303612
$356$	−44.7161	−2.36995
$357$	6.15226	0.325612
$358$	22.5261	1.19054
$359$	27.2430	1.43783	0.718916	−	0.695097i	$-0.244639\pi$
$359$	27.2430	1.43783	0.718916	+	0.695097i	$0.244639\pi$
$360$	30.4415	1.60441
$361$	−14.6547	−0.771302
$362$	−19.0755	−1.00259
$363$	−9.35430	−0.490973
$364$	−3.04315	−0.159504
$365$	11.4155	0.597512
$366$	−30.7517	−1.60742
$367$	7.35808	0.384089	0.192044	−	0.981386i	$-0.438488\pi$
$367$	7.35808	0.384089	0.192044	+	0.981386i	$0.438488\pi$
$368$	6.87352	0.358307
$369$	−31.7149	−1.65101
$370$	−16.1099	−0.837514
$371$	9.44070	0.490137
$372$	57.7373	2.99354
$373$	16.8192	0.870865	0.435433	−	0.900221i	$-0.356595\pi$
$373$	16.8192	0.870865	0.435433	+	0.900221i	$0.356595\pi$
$374$	−32.0380	−1.65665
$375$	2.39134	0.123488
$376$	−65.2593	−3.36549
$377$	−1.81581	−0.0935189
$378$	−1.66305	−0.0855381
$379$	−17.7702	−0.912792	−0.456396	−	0.889777i	$-0.650860\pi$
$379$	−17.7702	−0.912792	−0.456396	+	0.889777i	$0.650860\pi$
$380$	−12.4388	−0.638096
$381$	−13.9484	−0.714600
$382$	−36.5262	−1.86885
$383$	−5.54121	−0.283142	−0.141571	−	0.989928i	$-0.545215\pi$
$383$	−5.54121	−0.283142	−0.141571	+	0.989928i	$0.545215\pi$
$384$	207.223	10.5748
$385$	3.37994	0.172257
$386$	−25.1489	−1.28004
$387$	−21.3166	−1.08358
$388$	23.0994	1.17269
$389$	0.784106	0.0397557	0.0198779	−	0.999802i	$-0.493672\pi$
$389$	0.784106	0.0397557	0.0198779	+	0.999802i	$0.493672\pi$
$390$	3.93281	0.199146
$391$	−1.02697	−0.0519362
$392$	69.8064	3.52575
$393$	−42.5530	−2.14651
$394$	45.4209	2.28827
$395$	10.7741	0.542104
$396$	−62.6418	−3.14787
$397$	30.0330	1.50732	0.753658	−	0.657267i	$-0.228288\pi$
$397$	30.0330	1.50732	0.753658	+	0.657267i	$0.228288\pi$
$398$	36.4600	1.82758
$399$	−4.36309	−0.218427
$400$	19.6730	0.983649
$401$	−5.90379	−0.294821	−0.147410	−	0.989075i	$-0.547094\pi$
$401$	−5.90379	−0.294821	−0.147410	+	0.989075i	$0.547094\pi$
$402$	−21.2277	−1.05874
$403$	2.35751	0.117436
$404$	89.3861	4.44713
$405$	9.76524	0.485239
$406$	−7.69941	−0.382116
$407$	22.0397	1.09246
$408$	−78.7093	−3.89669
$409$	8.25561	0.408214	0.204107	−	0.978949i	$-0.434571\pi$
$409$	8.25561	0.408214	0.204107	+	0.978949i	$0.434571\pi$
$410$	−32.9295	−1.62627
$411$	−44.3996	−2.19007
$412$	118.322	5.82929
$413$	1.32848	0.0653701
$414$	−2.68097	−0.131763
$415$	−11.0219	−0.541044
$416$	19.3053	0.946523
$417$	−15.4612	−0.757138
$418$	22.7209	1.11131
$419$	−10.2035	−0.498472	−0.249236	−	0.968443i	$-0.580179\pi$
$419$	−10.2035	−0.498472	−0.249236	+	0.968443i	$0.580179\pi$
$420$	12.4898	0.609440
$421$	19.0614	0.928994	0.464497	−	0.885575i	$-0.346235\pi$
$421$	19.0614	0.928994	0.464497	+	0.885575i	$0.346235\pi$
$422$	−47.5800	−2.31616
$423$	15.8430	0.770313
$424$	−120.780	−5.86560
$425$	−2.93934	−0.142579
$426$	38.6124	1.87078
$427$	−3.98767	−0.192977
$428$	−14.7941	−0.715101
$429$	−5.38040	−0.259768
$430$	−22.1330	−1.06735
$431$	4.82231	0.232283	0.116141	−	0.993233i	$-0.462947\pi$
$431$	4.82231	0.232283	0.116141	+	0.993233i	$0.462947\pi$
$432$	13.2428	0.637143
$433$	−0.0847613	−0.00407337	−0.00203669	−	0.999998i	$-0.500648\pi$
$433$	−0.0847613	−0.00407337	−0.00203669	+	0.999998i	$0.500648\pi$
$434$	9.99637	0.479841
$435$	7.45250	0.357320
$436$	14.7143	0.704685
$437$	0.728312	0.0348399
$438$	−77.0526	−3.68172
$439$	20.8527	0.995247	0.497624	−	0.867393i	$-0.334206\pi$
$439$	20.8527	0.995247	0.497624	+	0.867393i	$0.334206\pi$
$440$	−43.2414	−2.06145
$441$	−16.9469	−0.806995
$442$	−4.83404	−0.229932
$443$	−37.6155	−1.78717	−0.893583	−	0.448897i	$-0.851817\pi$
$443$	−37.6155	−1.78717	−0.893583	+	0.448897i	$0.851817\pi$
$444$	81.4426	3.86510
$445$	7.49366	0.355233
$446$	−54.0377	−2.55876
$447$	−48.0225	−2.27139
$448$	47.4203	2.24040
$449$	−2.90799	−0.137237	−0.0686183	−	0.997643i	$-0.521859\pi$
$449$	−2.90799	−0.137237	−0.0686183	+	0.997643i	$0.521859\pi$
$450$	−7.67332	−0.361724
$451$	45.0502	2.12133
$452$	−104.949	−4.93639
$453$	−9.45486	−0.444228
$454$	62.1168	2.91529
$455$	0.509980	0.0239082
$456$	55.8194	2.61398
$457$	20.1272	0.941510	0.470755	−	0.882264i	$-0.343982\pi$
$457$	20.1272	0.941510	0.470755	+	0.882264i	$0.343982\pi$
$458$	−40.0936	−1.87345
$459$	−1.97860	−0.0923531
$460$	−2.08487	−0.0972076
$461$	−24.1119	−1.12300	−0.561502	−	0.827476i	$-0.689776\pi$
$461$	−24.1119	−1.12300	−0.561502	+	0.827476i	$0.689776\pi$
$462$	−22.8140	−1.06141
$463$	−6.04174	−0.280784	−0.140392	−	0.990096i	$-0.544836\pi$
$463$	−6.04174	−0.280784	−0.140392	+	0.990096i	$0.544836\pi$
$464$	61.3099	2.84624
$465$	−9.67580	−0.448704
$466$	−65.1545	−3.01822
$467$	−3.37791	−0.156311	−0.0781555	−	0.996941i	$-0.524903\pi$
$467$	−3.37791	−0.156311	−0.0781555	+	0.996941i	$0.524903\pi$
$468$	−9.45169	−0.436904
$469$	−2.75266	−0.127106
$470$	16.4498	0.758771
$471$	−47.8452	−2.20459
$472$	−16.9959	−0.782302
$473$	30.2797	1.39226
$474$	−72.7235	−3.34030
$475$	2.08453	0.0956448
$476$	−15.3519	−0.703655
$477$	29.3218	1.34255
$478$	−7.28741	−0.333319
$479$	−1.50496	−0.0687634	−0.0343817	−	0.999409i	$-0.510946\pi$
$479$	−1.50496	−0.0687634	−0.0343817	+	0.999409i	$0.510946\pi$
$480$	−79.2337	−3.61651
$481$	3.32544	0.151627
$482$	−2.82262	−0.128567
$483$	−0.731298	−0.0332752
$484$	23.3421	1.06100
$485$	−3.87107	−0.175776
$486$	−60.2138	−2.73135
$487$	−5.05466	−0.229049	−0.114524	−	0.993420i	$-0.536534\pi$
$487$	−5.05466	−0.229049	−0.114524	+	0.993420i	$0.536534\pi$
$488$	51.0165	2.30941
$489$	−25.0929	−1.13474
$490$	−17.5959	−0.794903
$491$	−2.67521	−0.120731	−0.0603653	−	0.998176i	$-0.519227\pi$
$491$	−2.67521	−0.120731	−0.0603653	+	0.998176i	$0.519227\pi$
$492$	166.473	7.50519
$493$	−9.16031	−0.412559
$494$	3.42823	0.154243
$495$	10.4977	0.471837
$496$	−79.6004	−3.57417
$497$	5.00700	0.224595
$498$	74.3962	3.33377
$499$	−0.844066	−0.0377856	−0.0188928	−	0.999822i	$-0.506014\pi$
$499$	−0.844066	−0.0377856	−0.0188928	+	0.999822i	$0.506014\pi$
$500$	−5.96719	−0.266861
$501$	45.1052	2.01515
$502$	−30.1478	−1.34556
$503$	31.8346	1.41944	0.709718	−	0.704486i	$-0.248822\pi$
$503$	31.8346	1.41944	0.709718	+	0.704486i	$0.248822\pi$
$504$	−26.6447	−1.18685
$505$	−14.9796	−0.666583
$506$	3.80825	0.169298
$507$	30.2756	1.34459
$508$	34.8060	1.54427
$509$	39.1345	1.73461	0.867304	−	0.497779i	$-0.165851\pi$
$509$	39.1345	1.73461	0.867304	+	0.497779i	$0.165851\pi$
$510$	19.8401	0.878533
$511$	−9.99166	−0.442005
$512$	−211.246	−9.33582
$513$	1.40319	0.0619524
$514$	−13.2228	−0.583233
$515$	−19.8287	−0.873758
$516$	111.892	4.92577
$517$	−22.5046	−0.989750
$518$	14.1006	0.619544
$519$	0.826512	0.0362798
$520$	−6.52446	−0.286116
$521$	−8.26390	−0.362048	−0.181024	−	0.983479i	$-0.557941\pi$
$521$	−8.26390	−0.362048	−0.181024	+	0.983479i	$0.557941\pi$
$522$	−23.9135	−1.04667
$523$	−24.9962	−1.09301	−0.546503	−	0.837457i	$-0.684041\pi$
$523$	−24.9962	−1.09301	−0.546503	+	0.837457i	$0.684041\pi$
$524$	106.184	4.63866
$525$	−2.09308	−0.0913494
$526$	−38.1162	−1.66195
$527$	11.8931	0.518071
$528$	181.667	7.90603
$529$	−22.8779	−0.994692
$530$	30.4447	1.32244
$531$	4.12611	0.179058
$532$	10.8874	0.472027
$533$	6.79738	0.294427
$534$	−50.5810	−2.18886
$535$	2.47924	0.107187
$536$	35.2163	1.52111
$537$	19.0842	0.823545
$538$	32.6344	1.40697
$539$	24.0726	1.03688
$540$	−4.01679	−0.172855
$541$	37.4455	1.60991	0.804955	−	0.593336i	$-0.202190\pi$
$541$	37.4455	1.60991	0.804955	+	0.593336i	$0.202190\pi$
$542$	1.01834	0.0437412
$543$	−16.1609	−0.693531
$544$	97.3908	4.17559
$545$	−2.46586	−0.105626
$546$	−3.44229	−0.147316
$547$	−40.9984	−1.75297	−0.876483	−	0.481433i	$-0.840116\pi$
$547$	−40.9984	−1.75297	−0.876483	+	0.481433i	$0.840116\pi$
$548$	110.792	4.73279
$549$	−12.3853	−0.528591
$550$	10.8998	0.464767
$551$	6.49635	0.276754
$552$	9.35591	0.398214
$553$	−9.43029	−0.401017
$554$	39.6346	1.68391
$555$	−13.6484	−0.579342
$556$	38.5808	1.63619
$557$	−34.6422	−1.46784	−0.733918	−	0.679238i	$-0.762310\pi$
$557$	−34.6422	−1.46784	−0.733918	+	0.679238i	$0.762310\pi$
$558$	31.0476	1.31435
$559$	4.56874	0.193237
$560$	−17.2193	−0.727646
$561$	−27.1428	−1.14597
$562$	83.1348	3.50683
$563$	−14.9416	−0.629712	−0.314856	−	0.949139i	$-0.601956\pi$
$563$	−14.9416	−0.629712	−0.314856	+	0.949139i	$0.601956\pi$
$564$	−83.1607	−3.50170
$565$	17.5877	0.739919
$566$	−50.9142	−2.14008
$567$	−8.54727	−0.358951
$568$	−64.0573	−2.68779
$569$	−33.8353	−1.41845	−0.709224	−	0.704983i	$-0.750954\pi$
$569$	−33.8353	−1.41845	−0.709224	+	0.704983i	$0.750954\pi$
$570$	−14.0703	−0.589338
$571$	12.5673	0.525925	0.262962	−	0.964806i	$-0.415300\pi$
$571$	12.5673	0.525925	0.262962	+	0.964806i	$0.415300\pi$
$572$	13.4259	0.561364
$573$	−30.9452	−1.29276
$574$	28.8224	1.20302
$575$	0.349389	0.0145705
$576$	147.282	6.13676
$577$	−21.5147	−0.895668	−0.447834	−	0.894117i	$-0.647804\pi$
$577$	−21.5147	−0.895668	−0.447834	+	0.894117i	$0.647804\pi$
$578$	23.5980	0.981547
$579$	−21.3062	−0.885457
$580$	−18.5965	−0.772177
$581$	9.64719	0.400233
$582$	26.1291	1.08309
$583$	−41.6509	−1.72500
$584$	127.829	5.28960
$585$	1.58394	0.0654880
$586$	−38.2993	−1.58213
$587$	−24.6605	−1.01785	−0.508924	−	0.860812i	$-0.669956\pi$
$587$	−24.6605	−1.01785	−0.508924	+	0.860812i	$0.669956\pi$
$588$	88.9551	3.66844
$589$	−8.43439	−0.347533
$590$	4.28413	0.176375
$591$	38.4808	1.58289
$592$	−112.282	−4.61477
$593$	−25.4243	−1.04405	−0.522026	−	0.852930i	$-0.674823\pi$
$593$	−25.4243	−1.04405	−0.522026	+	0.852930i	$0.674823\pi$
$594$	7.33712	0.301046
$595$	2.57272	0.105471
$596$	119.832	4.90852
$597$	30.8891	1.26421
$598$	0.574607	0.0234974
$599$	13.4986	0.551537	0.275768	−	0.961224i	$-0.411068\pi$
$599$	13.4986	0.551537	0.275768	+	0.961224i	$0.411068\pi$
$600$	26.7779	1.09320
$601$	−16.8884	−0.688893	−0.344447	−	0.938806i	$-0.611933\pi$
$601$	−16.8884	−0.688893	−0.344447	+	0.938806i	$0.611933\pi$
$602$	19.3724	0.789562
$603$	−8.54947	−0.348161
$604$	23.5930	0.959986
$605$	−3.91174	−0.159035
$606$	101.110	4.10731
$607$	26.6758	1.08274	0.541369	−	0.840785i	$-0.317906\pi$
$607$	26.6758	1.08274	0.541369	+	0.840785i	$0.317906\pi$
$608$	−69.0680	−2.80108
$609$	−6.52299	−0.264325
$610$	−12.8596	−0.520671
$611$	−3.39559	−0.137371
$612$	−47.6814	−1.92741
$613$	−6.89142	−0.278342	−0.139171	−	0.990268i	$-0.544444\pi$
$613$	−6.89142	−0.278342	−0.139171	+	0.990268i	$0.544444\pi$
$614$	−20.3676	−0.821971
$615$	−27.8981	−1.12496
$616$	37.8481	1.52494
$617$	4.43494	0.178544	0.0892719	−	0.996007i	$-0.471546\pi$
$617$	4.43494	0.178544	0.0892719	+	0.996007i	$0.471546\pi$
$618$	133.841	5.38387
$619$	7.38111	0.296672	0.148336	−	0.988937i	$-0.452608\pi$
$619$	7.38111	0.296672	0.148336	+	0.988937i	$0.452608\pi$
$620$	24.1443	0.969660
$621$	0.235190	0.00943783
$622$	−78.8279	−3.16071
$623$	−6.55901	−0.262781
$624$	27.4107	1.09731
$625$	1.00000	0.0400000
$626$	−4.95965	−0.198227
$627$	19.2492	0.768741
$628$	119.390	4.76417
$629$	16.7760	0.668905
$630$	6.71626	0.267582
$631$	−39.4029	−1.56860	−0.784301	−	0.620380i	$-0.786978\pi$
$631$	−39.4029	−1.56860	−0.784301	+	0.620380i	$0.786978\pi$
$632$	120.647	4.79908
$633$	−40.3101	−1.60218
$634$	60.8525	2.41676
$635$	−5.83290	−0.231471
$636$	−153.911	−6.10299
$637$	3.63219	0.143913
$638$	33.9686	1.34483
$639$	15.5512	0.615196
$640$	86.6558	3.42537
$641$	33.5054	1.32339	0.661693	−	0.749775i	$-0.269838\pi$
$641$	33.5054	1.32339	0.661693	+	0.749775i	$0.269838\pi$
$642$	−16.7345	−0.660459
$643$	−10.6479	−0.419914	−0.209957	−	0.977711i	$-0.567332\pi$
$643$	−10.6479	−0.419914	−0.209957	+	0.977711i	$0.567332\pi$
$644$	1.82483	0.0719085
$645$	−18.7512	−0.738328
$646$	17.2946	0.680446
$647$	−11.2025	−0.440417	−0.220209	−	0.975453i	$-0.570674\pi$
$647$	−11.2025	−0.440417	−0.220209	+	0.975453i	$0.570674\pi$
$648$	109.350	4.29567
$649$	−5.86103	−0.230066
$650$	1.64460	0.0645067
$651$	8.46898	0.331925
$652$	62.6152	2.45220
$653$	−6.39411	−0.250221	−0.125110	−	0.992143i	$-0.539929\pi$
$653$	−6.39411	−0.250221	−0.125110	+	0.992143i	$0.539929\pi$
$654$	16.6442	0.650839
$655$	−17.7946	−0.695293
$656$	−229.511	−8.96089
$657$	−31.0330	−1.21071
$658$	−14.3980	−0.561294
$659$	4.95824	0.193145	0.0965727	−	0.995326i	$-0.469212\pi$
$659$	4.95824	0.193145	0.0965727	+	0.995326i	$0.469212\pi$
$660$	−55.1030	−2.14488
$661$	−17.7462	−0.690246	−0.345123	−	0.938557i	$-0.612163\pi$
$661$	−17.7462	−0.690246	−0.345123	+	0.938557i	$0.612163\pi$
$662$	−89.2095	−3.46722
$663$	−4.09543	−0.159053
$664$	−123.422	−4.78970
$665$	−1.82454	−0.0707525
$666$	43.7949	1.69702
$667$	1.08885	0.0421606
$668$	−112.553	−4.35479
$669$	−45.7810	−1.77000
$670$	−8.87690	−0.342944
$671$	17.5930	0.679170
$672$	69.3512	2.67528
$673$	−30.4347	−1.17317	−0.586586	−	0.809887i	$-0.699528\pi$
$673$	−30.4347	−1.17317	−0.586586	+	0.809887i	$0.699528\pi$
$674$	12.5040	0.481637
$675$	0.673145	0.0259094
$676$	−75.5477	−2.90568
$677$	8.31341	0.319510	0.159755	−	0.987157i	$-0.448930\pi$
$677$	8.31341	0.319510	0.159755	+	0.987157i	$0.448930\pi$
$678$	−118.714	−4.55919
$679$	3.38824	0.130029
$680$	−32.9143	−1.26221
$681$	52.6257	2.01662
$682$	−44.1024	−1.68877
$683$	19.7934	0.757373	0.378687	−	0.925525i	$-0.376376\pi$
$683$	19.7934	0.757373	0.378687	+	0.925525i	$0.376376\pi$
$684$	33.8149	1.29295
$685$	−18.5668	−0.709402
$686$	32.6952	1.24831
$687$	−33.9675	−1.29594
$688$	−154.262	−5.88117
$689$	−6.28447	−0.239419
$690$	−2.35832	−0.0897798
$691$	50.0679	1.90467	0.952337	−	0.305048i	$-0.0986725\pi$
$691$	50.0679	1.90467	0.952337	+	0.305048i	$0.0986725\pi$
$692$	−2.06242	−0.0784015
$693$	−9.18838	−0.349038
$694$	−92.6125	−3.51552
$695$	−6.46549	−0.245250
$696$	83.4522	3.16325
$697$	34.2911	1.29887
$698$	75.5679	2.86029
$699$	−55.1993	−2.08783
$700$	5.22293	0.197408
$701$	−2.90213	−0.109612	−0.0548059	−	0.998497i	$-0.517454\pi$
$701$	−2.90213	−0.109612	−0.0548059	+	0.998497i	$0.517454\pi$
$702$	1.10706	0.0417832
$703$	−11.8973	−0.448716
$704$	−209.211	−7.88493
$705$	13.9363	0.524872
$706$	−33.2212	−1.25030
$707$	13.1113	0.493100
$708$	−21.6581	−0.813962
$709$	8.06909	0.303041	0.151520	−	0.988454i	$-0.451583\pi$
$709$	8.06909	0.303041	0.151520	+	0.988454i	$0.451583\pi$
$710$	16.1468	0.605978
$711$	−29.2895	−1.09844
$712$	83.9130	3.14477
$713$	−1.41369	−0.0529431
$714$	−17.3655	−0.649887
$715$	−2.24995	−0.0841434
$716$	−47.6215	−1.77970
$717$	−6.17394	−0.230570
$718$	−76.8967	−2.86976
$719$	10.4158	0.388443	0.194221	−	0.980958i	$-0.437782\pi$
$719$	10.4158	0.388443	0.194221	+	0.980958i	$0.437782\pi$
$720$	−53.4811	−1.99312
$721$	17.3556	0.646355
$722$	41.3648	1.53944
$723$	−2.39134	−0.0889349
$724$	40.3269	1.49874
$725$	3.11646	0.115742
$726$	26.4036	0.979931
$727$	21.2166	0.786879	0.393439	−	0.919351i	$-0.371285\pi$
$727$	21.2166	0.786879	0.393439	+	0.919351i	$0.371285\pi$
$728$	5.71069	0.211652
$729$	−21.7177	−0.804360
$730$	−32.2215	−1.19257
$731$	23.0482	0.852468
$732$	65.0110	2.40287
$733$	16.0821	0.594007	0.297003	−	0.954876i	$-0.404013\pi$
$733$	16.0821	0.594007	0.297003	+	0.954876i	$0.404013\pi$
$734$	−20.7691	−0.766600
$735$	−14.9074	−0.549866
$736$	−11.5765	−0.426716
$737$	12.1443	0.447341
$738$	89.5191	3.29525
$739$	−12.6559	−0.465555	−0.232777	−	0.972530i	$-0.574781\pi$
$739$	−12.6559	−0.465555	−0.232777	+	0.972530i	$0.574781\pi$
$740$	34.0573	1.25197
$741$	2.90441	0.106696
$742$	−26.6475	−0.978261
$743$	0.448745	0.0164629	0.00823143	−	0.999966i	$-0.497380\pi$
$743$	0.448745	0.0164629	0.00823143	+	0.999966i	$0.497380\pi$
$744$	−108.348	−3.97224
$745$	−20.0818	−0.735742
$746$	−47.4742	−1.73815
$747$	29.9631	1.09629
$748$	67.7303	2.47647
$749$	−2.17002	−0.0792908
$750$	−6.74985	−0.246470
$751$	9.51089	0.347057	0.173529	−	0.984829i	$-0.444483\pi$
$751$	9.51089	0.347057	0.173529	+	0.984829i	$0.444483\pi$
$752$	114.651	4.18088
$753$	−25.5414	−0.930780
$754$	5.12534	0.186654
$755$	−3.95379	−0.143893
$756$	3.51579	0.127868
$757$	28.1606	1.02351	0.511757	−	0.859130i	$-0.328995\pi$
$757$	28.1606	1.02351	0.511757	+	0.859130i	$0.328995\pi$
$758$	50.1584	1.82184
$759$	3.22637	0.117110
$760$	23.3423	0.846714
$761$	8.38239	0.303861	0.151931	−	0.988391i	$-0.451451\pi$
$761$	8.38239	0.303861	0.151931	+	0.988391i	$0.451451\pi$
$762$	39.3711	1.42627
$763$	2.15830	0.0781359
$764$	77.2187	2.79367
$765$	7.99060	0.288901
$766$	15.6407	0.565123
$767$	−0.884339	−0.0319316
$768$	−325.799	−11.7563
$769$	53.2813	1.92137	0.960686	−	0.277637i	$-0.0895512\pi$
$769$	53.2813	1.92137	0.960686	+	0.277637i	$0.0895512\pi$
$770$	−9.54028	−0.343808
$771$	−11.2024	−0.403446
$772$	53.1662	1.91349
$773$	22.0092	0.791618	0.395809	−	0.918333i	$-0.370464\pi$
$773$	22.0092	0.791618	0.395809	+	0.918333i	$0.370464\pi$
$774$	60.1687	2.16272
$775$	−4.04618	−0.145343
$776$	−43.3477	−1.55609
$777$	11.9461	0.428564
$778$	−2.21323	−0.0793483
$779$	−24.3187	−0.871309
$780$	−8.31419	−0.297696
$781$	−22.0901	−0.790445
$782$	2.89875	0.103659
$783$	2.09783	0.0749702
$784$	−122.639	−4.37997
$785$	−20.0077	−0.714106
$786$	120.111	4.28422
$787$	−42.1989	−1.50423	−0.752115	−	0.659032i	$-0.770966\pi$
$787$	−42.1989	−1.50423	−0.752115	+	0.659032i	$0.770966\pi$
$788$	−96.0225	−3.42066
$789$	−32.2923	−1.14964
$790$	−30.4112	−1.08198
$791$	−15.3940	−0.547349
$792$	117.552	4.17703
$793$	2.65451	0.0942644
$794$	−84.7719	−3.00844
$795$	25.7930	0.914782
$796$	−77.0787	−2.73198
$797$	−40.1568	−1.42243	−0.711214	−	0.702976i	$-0.751854\pi$
$797$	−40.1568	−1.42243	−0.711214	+	0.702976i	$0.751854\pi$
$798$	12.3153	0.435958
$799$	−17.1299	−0.606014
$800$	−33.1336	−1.17145
$801$	−20.3716	−0.719794
$802$	16.6641	0.588432
$803$	44.0816	1.55561
$804$	44.8766	1.58267
$805$	−0.305811	−0.0107784
$806$	−6.65437	−0.234390
$807$	27.6480	0.973257
$808$	−167.740	−5.90106
$809$	35.1051	1.23423	0.617114	−	0.786874i	$-0.288302\pi$
$809$	35.1051	1.23423	0.617114	+	0.786874i	$0.288302\pi$
$810$	−27.5636	−0.968485
$811$	28.9245	1.01568	0.507838	−	0.861453i	$-0.330445\pi$
$811$	28.9245	1.01568	0.507838	+	0.861453i	$0.330445\pi$
$812$	16.2770	0.571212
$813$	0.862739	0.0302576
$814$	−62.2096	−2.18044
$815$	−10.4933	−0.367563
$816$	138.280	4.84078
$817$	−16.3454	−0.571854
$818$	−23.3025	−0.814752
$819$	−1.38638	−0.0484442
$820$	69.6150	2.43106
$821$	−3.08954	−0.107826	−0.0539129	−	0.998546i	$-0.517169\pi$
$821$	−3.08954	−0.107826	−0.0539129	+	0.998546i	$0.517169\pi$
$822$	125.323	4.37115
$823$	−30.6217	−1.06741	−0.533703	−	0.845672i	$-0.679200\pi$
$823$	−30.6217	−1.06741	−0.533703	+	0.845672i	$0.679200\pi$
$824$	−222.040	−7.73511
$825$	9.23433	0.321498
$826$	−3.74979	−0.130472
$827$	−20.3196	−0.706581	−0.353290	−	0.935514i	$-0.614937\pi$
$827$	−20.3196	−0.706581	−0.353290	+	0.935514i	$0.614937\pi$
$828$	5.66773	0.196967
$829$	20.4430	0.710015	0.355007	−	0.934864i	$-0.384478\pi$
$829$	20.4430	0.710015	0.355007	+	0.934864i	$0.384478\pi$
$830$	31.1107	1.07987
$831$	33.5786	1.16483
$832$	−31.5667	−1.09438
$833$	18.3235	0.634872
$834$	43.6411	1.51117
$835$	18.8619	0.652743
$836$	−48.0333	−1.66127
$837$	−2.72367	−0.0941438
$838$	28.8005	0.994897
$839$	−20.6751	−0.713784	−0.356892	−	0.934146i	$-0.616164\pi$
$839$	−20.6751	−0.713784	−0.356892	+	0.934146i	$0.616164\pi$
$840$	−23.4380	−0.808689
$841$	−19.2877	−0.665093
$842$	−53.8030	−1.85417
$843$	70.4323	2.42582
$844$	100.587	3.46235
$845$	12.6605	0.435535
$846$	−44.7188	−1.53746
$847$	3.42385	0.117645
$848$	212.192	7.28672
$849$	−43.1348	−1.48038
$850$	8.29663	0.284572
$851$	−1.99411	−0.0683573
$852$	−81.6290	−2.79656
$853$	−44.7345	−1.53168	−0.765839	−	0.643032i	$-0.777676\pi$
$853$	−44.7345	−1.53168	−0.765839	+	0.643032i	$0.777676\pi$
$854$	11.2557	0.385162
$855$	−5.66681	−0.193801
$856$	27.7623	0.948895
$857$	−25.2320	−0.861908	−0.430954	−	0.902374i	$-0.641823\pi$
$857$	−25.2320	−0.861908	−0.430954	+	0.902374i	$0.641823\pi$
$858$	15.1868	0.518470
$859$	29.3453	1.00125	0.500624	−	0.865665i	$-0.333104\pi$
$859$	29.3453	1.00125	0.500624	+	0.865665i	$0.333104\pi$
$860$	46.7905	1.59554
$861$	24.4185	0.832179
$862$	−13.6116	−0.463611
$863$	53.4748	1.82030	0.910152	−	0.414273i	$-0.135964\pi$
$863$	53.4748	1.82030	0.910152	+	0.414273i	$0.135964\pi$
$864$	−22.3037	−0.758788
$865$	0.345627	0.0117517
$866$	0.239249	0.00813002
$867$	19.9923	0.678975
$868$	−21.1329	−0.717298
$869$	41.6050	1.41135
$870$	−21.0356	−0.713173
$871$	1.83239	0.0620881
$872$	−27.6124	−0.935074
$873$	10.5235	0.356167
$874$	−2.05575	−0.0695367
$875$	−0.875274	−0.0295897
$876$	162.894	5.50367
$877$	−55.8081	−1.88451	−0.942253	−	0.334901i	$-0.891297\pi$
$877$	−55.8081	−1.88451	−0.942253	+	0.334901i	$0.891297\pi$
$878$	−58.8594	−1.98641
$879$	−32.4474	−1.09442
$880$	75.9686	2.56090
$881$	−51.5903	−1.73812	−0.869061	−	0.494705i	$-0.835276\pi$
$881$	−51.5903	−1.73812	−0.869061	+	0.494705i	$0.835276\pi$
$882$	47.8346	1.61068
$883$	15.8447	0.533216	0.266608	−	0.963805i	$-0.414097\pi$
$883$	15.8447	0.533216	0.266608	+	0.963805i	$0.414097\pi$
$884$	10.2195	0.343718
$885$	3.62954	0.122006
$886$	106.174	3.56700
$887$	−12.1704	−0.408641	−0.204321	−	0.978904i	$-0.565499\pi$
$887$	−12.1704	−0.408641	−0.204321	+	0.978904i	$0.565499\pi$
$888$	−152.833	−5.12874
$889$	5.10538	0.171229
$890$	−21.1518	−0.709009
$891$	37.7092	1.26331
$892$	114.239	3.82500
$893$	12.1483	0.406527
$894$	135.549	4.53345
$895$	7.98056	0.266761
$896$	−75.8476	−2.53389
$897$	0.486810	0.0162541
$898$	8.20815	0.273910
$899$	−12.6097	−0.420559
$900$	16.2218	0.540728
$901$	−31.7036	−1.05620
$902$	−127.160	−4.23396
$903$	16.4124	0.546172
$904$	196.945	6.55028
$905$	−6.75810	−0.224647
$906$	26.6875	0.886632
$907$	2.07612	0.0689366	0.0344683	−	0.999406i	$-0.489026\pi$
$907$	2.07612	0.0689366	0.0344683	+	0.999406i	$0.489026\pi$
$908$	−131.319	−4.35796
$909$	40.7221	1.35067
$910$	−1.43948	−0.0477183
$911$	36.6227	1.21336	0.606681	−	0.794945i	$-0.292500\pi$
$911$	36.6227	1.21336	0.606681	+	0.794945i	$0.292500\pi$
$912$	−98.0662	−3.24730
$913$	−42.5619	−1.40859
$914$	−56.8114	−1.87916
$915$	−10.8947	−0.360169
$916$	84.7603	2.80056
$917$	15.5752	0.514338
$918$	5.58484	0.184327
$919$	−3.00350	−0.0990763	−0.0495382	−	0.998772i	$-0.515775\pi$
$919$	−3.00350	−0.0990763	−0.0495382	+	0.998772i	$0.515775\pi$
$920$	3.91241	0.128988
$921$	−17.2556	−0.568591
$922$	68.0588	2.24140
$923$	−3.33305	−0.109709
$924$	48.2303	1.58666
$925$	−5.70743	−0.187659
$926$	17.0536	0.560414
$927$	53.9045	1.77046
$928$	−103.259	−3.38966
$929$	−16.4969	−0.541245	−0.270623	−	0.962686i	$-0.587230\pi$
$929$	−16.4969	−0.541245	−0.270623	+	0.962686i	$0.587230\pi$
$930$	27.3111	0.895567
$931$	−12.9947	−0.425885
$932$	137.741	4.51184
$933$	−66.7834	−2.18639
$934$	9.53456	0.311980
$935$	−11.3505	−0.371200
$936$	17.7368	0.579745
$937$	42.2935	1.38167	0.690835	−	0.723013i	$-0.257243\pi$
$937$	42.2935	1.38167	0.690835	+	0.723013i	$0.257243\pi$
$938$	7.76972	0.253690
$939$	−4.20184	−0.137122
$940$	−34.7758	−1.13426
$941$	17.0813	0.556834	0.278417	−	0.960460i	$-0.410190\pi$
$941$	17.0813	0.556834	0.278417	+	0.960460i	$0.410190\pi$
$942$	135.049	4.40013
$943$	−4.07607	−0.132735
$944$	29.8593	0.971838
$945$	−0.589187	−0.0191663
$946$	−85.4682	−2.77881
$947$	14.3511	0.466347	0.233174	−	0.972435i	$-0.425089\pi$
$947$	14.3511	0.466347	0.233174	+	0.972435i	$0.425089\pi$
$948$	153.742	4.99330
$949$	6.65124	0.215908
$950$	−5.88384	−0.190897
$951$	51.5545	1.67177
$952$	28.8090	0.933707
$953$	−15.9982	−0.518233	−0.259117	−	0.965846i	$-0.583431\pi$
$953$	−15.9982	−0.518233	−0.259117	+	0.965846i	$0.583431\pi$
$954$	−82.7643	−2.67959
$955$	−12.9405	−0.418746
$956$	15.4060	0.498267
$957$	28.7784	0.930273
$958$	4.24793	0.137244
$959$	16.2511	0.524774
$960$	129.557	4.18144
$961$	−14.6284	−0.471884
$962$	−9.38646	−0.302632
$963$	−6.73984	−0.217188
$964$	5.96719	0.192190
$965$	−8.90975	−0.286815
$966$	2.06418	0.0664138
$967$	9.15411	0.294376	0.147188	−	0.989109i	$-0.452978\pi$
$967$	9.15411	0.294376	0.147188	+	0.989109i	$0.452978\pi$
$968$	−43.8032	−1.40789
$969$	14.6521	0.470692
$970$	10.9265	0.350830
$971$	46.2181	1.48321	0.741605	−	0.670837i	$-0.234065\pi$
$971$	46.2181	1.48321	0.741605	+	0.670837i	$0.234065\pi$
$972$	127.296	4.08301
$973$	5.65908	0.181422
$974$	14.2674	0.457157
$975$	1.39332	0.0446219
$976$	−89.6284	−2.86893
$977$	−10.6150	−0.339604	−0.169802	−	0.985478i	$-0.554313\pi$
$977$	−10.6150	−0.339604	−0.169802	+	0.985478i	$0.554313\pi$
$978$	70.8278	2.26482
$979$	28.9373	0.924840
$980$	37.1988	1.18827
$981$	6.70346	0.214025
$982$	7.55111	0.240966
$983$	7.16851	0.228640	0.114320	−	0.993444i	$-0.463531\pi$
$983$	7.16851	0.228640	0.114320	+	0.993444i	$0.463531\pi$
$984$	−312.399	−9.95892
$985$	16.0917	0.512726
$986$	25.8561	0.823425
$987$	−12.1981	−0.388270
$988$	−7.24748	−0.230573
$989$	−2.73966	−0.0871161
$990$	−29.6311	−0.941737
$991$	−53.7983	−1.70896	−0.854480	−	0.519484i	$-0.826124\pi$
$991$	−53.7983	−1.70896	−0.854480	+	0.519484i	$0.826124\pi$
$992$	134.065	4.25656
$993$	−75.5788	−2.39842
$994$	−14.1329	−0.448267
$995$	12.9171	0.409499
$996$	−157.278	−4.98354
$997$	4.14619	0.131311	0.0656556	−	0.997842i	$-0.479086\pi$
$997$	4.14619	0.131311	0.0656556	+	0.997842i	$0.479086\pi$
$998$	2.38248	0.0754160
$999$	−3.84193	−0.121553

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1205.2.a.d.1.1	✓	25
5.4	even	2		6025.2.a.k.1.25		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.d.1.1	✓	25	1.1	even	1	trivial
6025.2.a.k.1.25		25	5.4	even	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:	\( N \)	\(=\)	\( 1205 = 5 \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1205.a (trivial)

\(f(q)\)	\(=\)	\(q-2.82262 q^{2} -2.39134 q^{3} +5.96719 q^{4} -1.00000 q^{5} +6.74985 q^{6} +0.875274 q^{7} -11.1979 q^{8} +2.71851 q^{9} +O(q^{10})\)	\(q-2.82262 q^{2} -2.39134 q^{3} +5.96719 q^{4} -1.00000 q^{5} +6.74985 q^{6} +0.875274 q^{7} -11.1979 q^{8} +2.71851 q^{9} +2.82262 q^{10} -3.86157 q^{11} -14.2696 q^{12} -0.582652 q^{13} -2.47057 q^{14} +2.39134 q^{15} +19.6730 q^{16} -2.93934 q^{17} -7.67332 q^{18} +2.08453 q^{19} -5.96719 q^{20} -2.09308 q^{21} +10.8998 q^{22} +0.349389 q^{23} +26.7779 q^{24} +1.00000 q^{25} +1.64460 q^{26} +0.673145 q^{27} +5.22293 q^{28} +3.11646 q^{29} -6.74985 q^{30} -4.04618 q^{31} -33.1336 q^{32} +9.23433 q^{33} +8.29663 q^{34} -0.875274 q^{35} +16.2218 q^{36} -5.70743 q^{37} -5.88384 q^{38} +1.39332 q^{39} +11.1979 q^{40} -11.6663 q^{41} +5.90797 q^{42} -7.84129 q^{43} -23.0427 q^{44} -2.71851 q^{45} -0.986192 q^{46} +5.82783 q^{47} -47.0448 q^{48} -6.23389 q^{49} -2.82262 q^{50} +7.02895 q^{51} -3.47679 q^{52} +10.7860 q^{53} -1.90003 q^{54} +3.86157 q^{55} -9.80121 q^{56} -4.98482 q^{57} -8.79657 q^{58} +1.51778 q^{59} +14.2696 q^{60} -4.55591 q^{61} +11.4208 q^{62} +2.37944 q^{63} +54.1777 q^{64} +0.582652 q^{65} -26.0650 q^{66} -3.14491 q^{67} -17.5396 q^{68} -0.835508 q^{69} +2.47057 q^{70} +5.72049 q^{71} -30.4415 q^{72} -11.4155 q^{73} +16.1099 q^{74} -2.39134 q^{75} +12.4388 q^{76} -3.37994 q^{77} -3.93281 q^{78} -10.7741 q^{79} -19.6730 q^{80} -9.76524 q^{81} +32.9295 q^{82} +11.0219 q^{83} -12.4898 q^{84} +2.93934 q^{85} +22.1330 q^{86} -7.45250 q^{87} +43.2414 q^{88} -7.49366 q^{89} +7.67332 q^{90} -0.509980 q^{91} +2.08487 q^{92} +9.67580 q^{93} -16.4498 q^{94} -2.08453 q^{95} +79.2337 q^{96} +3.87107 q^{97} +17.5959 q^{98} -10.4977 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 4 q^{2} + 9 q^{3} + 36 q^{4} - 25 q^{5} + 7 q^{6} + 7 q^{7} - 15 q^{8} + 36 q^{9}+O(q^{10}) \) 25 * q - 4 * q^2 + 9 * q^3 + 36 * q^4 - 25 * q^5 + 7 * q^6 + 7 * q^7 - 15 * q^8 + 36 * q^9	\( 25 q - 4 q^{2} + 9 q^{3} + 36 q^{4} - 25 q^{5} + 7 q^{6} + 7 q^{7} - 15 q^{8} + 36 q^{9} + 4 q^{10} + 10 q^{11} + 22 q^{12} + 10 q^{13} + 13 q^{14} - 9 q^{15} + 54 q^{16} + q^{17} - 13 q^{18} + 50 q^{19} - 36 q^{20} + 9 q^{21} + 11 q^{22} - 31 q^{23} + 22 q^{24} + 25 q^{25} + 8 q^{26} + 42 q^{27} + 14 q^{28} + 4 q^{29} - 7 q^{30} + 34 q^{31} - 44 q^{32} + 28 q^{33} + 33 q^{34} - 7 q^{35} + 83 q^{36} + 14 q^{37} - 10 q^{38} + 23 q^{39} + 15 q^{40} + 11 q^{41} + 23 q^{42} + 49 q^{43} + 20 q^{44} - 36 q^{45} + 27 q^{46} - 28 q^{47} + 30 q^{48} + 66 q^{49} - 4 q^{50} + 49 q^{51} + 39 q^{52} - 16 q^{53} + 5 q^{54} - 10 q^{55} + 51 q^{56} + 10 q^{57} - 8 q^{58} + 30 q^{59} - 22 q^{60} + 35 q^{61} - 18 q^{62} + 73 q^{64} - 10 q^{65} - 13 q^{66} + 37 q^{67} + 11 q^{68} - 4 q^{69} - 13 q^{70} + 12 q^{71} - 90 q^{72} + 36 q^{73} - 12 q^{74} + 9 q^{75} + 57 q^{76} - 31 q^{77} - 9 q^{78} + 16 q^{79} - 54 q^{80} + 65 q^{81} - 11 q^{82} + 43 q^{83} - 62 q^{84} - q^{85} - 9 q^{86} - 22 q^{87} + 20 q^{88} + 38 q^{89} + 13 q^{90} + 86 q^{91} - 119 q^{92} + 10 q^{93} - 18 q^{94} - 50 q^{95} - 34 q^{96} + 17 q^{97} - 32 q^{98} + 26 q^{99}+O(q^{100}) \) 25 * q - 4 * q^2 + 9 * q^3 + 36 * q^4 - 25 * q^5 + 7 * q^6 + 7 * q^7 - 15 * q^8 + 36 * q^9 + 4 * q^10 + 10 * q^11 + 22 * q^12 + 10 * q^13 + 13 * q^14 - 9 * q^15 + 54 * q^16 + q^17 - 13 * q^18 + 50 * q^19 - 36 * q^20 + 9 * q^21 + 11 * q^22 - 31 * q^23 + 22 * q^24 + 25 * q^25 + 8 * q^26 + 42 * q^27 + 14 * q^28 + 4 * q^29 - 7 * q^30 + 34 * q^31 - 44 * q^32 + 28 * q^33 + 33 * q^34 - 7 * q^35 + 83 * q^36 + 14 * q^37 - 10 * q^38 + 23 * q^39 + 15 * q^40 + 11 * q^41 + 23 * q^42 + 49 * q^43 + 20 * q^44 - 36 * q^45 + 27 * q^46 - 28 * q^47 + 30 * q^48 + 66 * q^49 - 4 * q^50 + 49 * q^51 + 39 * q^52 - 16 * q^53 + 5 * q^54 - 10 * q^55 + 51 * q^56 + 10 * q^57 - 8 * q^58 + 30 * q^59 - 22 * q^60 + 35 * q^61 - 18 * q^62 + 73 * q^64 - 10 * q^65 - 13 * q^66 + 37 * q^67 + 11 * q^68 - 4 * q^69 - 13 * q^70 + 12 * q^71 - 90 * q^72 + 36 * q^73 - 12 * q^74 + 9 * q^75 + 57 * q^76 - 31 * q^77 - 9 * q^78 + 16 * q^79 - 54 * q^80 + 65 * q^81 - 11 * q^82 + 43 * q^83 - 62 * q^84 - q^85 - 9 * q^86 - 22 * q^87 + 20 * q^88 + 38 * q^89 + 13 * q^90 + 86 * q^91 - 119 * q^92 + 10 * q^93 - 18 * q^94 - 50 * q^95 - 34 * q^96 + 17 * q^97 - 32 * q^98 + 26 * q^99

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