LMFDB - Embedded newform 1205.2.a.e.1.2

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			1.2
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)

$f(q)$	$=$	$q-2.51976 q^{2} -0.981670 q^{3} +4.34921 q^{4} +1.00000 q^{5} +2.47358 q^{6} +3.43036 q^{7} -5.91946 q^{8} -2.03632 q^{9} +O(q^{10})$	\(q-2.51976 q^{2} -0.981670 q^{3} +4.34921 q^{4} +1.00000 q^{5} +2.47358 q^{6} +3.43036 q^{7} -5.91946 q^{8} -2.03632 q^{9} -2.51976 q^{10} -1.87152 q^{11} -4.26949 q^{12} +1.10988 q^{13} -8.64370 q^{14} -0.981670 q^{15} +6.21722 q^{16} +7.45383 q^{17} +5.13106 q^{18} +0.382278 q^{19} +4.34921 q^{20} -3.36748 q^{21} +4.71578 q^{22} -0.968812 q^{23} +5.81095 q^{24} +1.00000 q^{25} -2.79664 q^{26} +4.94401 q^{27} +14.9194 q^{28} -1.15751 q^{29} +2.47358 q^{30} +7.77088 q^{31} -3.82700 q^{32} +1.83721 q^{33} -18.7819 q^{34} +3.43036 q^{35} -8.85640 q^{36} -1.40405 q^{37} -0.963249 q^{38} -1.08954 q^{39} -5.91946 q^{40} -9.48464 q^{41} +8.48526 q^{42} +0.798882 q^{43} -8.13962 q^{44} -2.03632 q^{45} +2.44118 q^{46} -3.17648 q^{47} -6.10325 q^{48} +4.76738 q^{49} -2.51976 q^{50} -7.31721 q^{51} +4.82711 q^{52} +1.59200 q^{53} -12.4577 q^{54} -1.87152 q^{55} -20.3059 q^{56} -0.375270 q^{57} +2.91664 q^{58} -3.55443 q^{59} -4.26949 q^{60} +5.43481 q^{61} -19.5808 q^{62} -6.98533 q^{63} -2.79129 q^{64} +1.10988 q^{65} -4.62934 q^{66} +6.40408 q^{67} +32.4183 q^{68} +0.951053 q^{69} -8.64370 q^{70} -11.6986 q^{71} +12.0539 q^{72} +1.90914 q^{73} +3.53788 q^{74} -0.981670 q^{75} +1.66261 q^{76} -6.41998 q^{77} +2.74538 q^{78} +14.9335 q^{79} +6.21722 q^{80} +1.25559 q^{81} +23.8991 q^{82} +6.79774 q^{83} -14.6459 q^{84} +7.45383 q^{85} -2.01299 q^{86} +1.13629 q^{87} +11.0784 q^{88} -8.09378 q^{89} +5.13106 q^{90} +3.80730 q^{91} -4.21357 q^{92} -7.62844 q^{93} +8.00397 q^{94} +0.382278 q^{95} +3.75685 q^{96} +4.75513 q^{97} -12.0127 q^{98} +3.81102 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 6 q^{2} + 15 q^{3} + 32 q^{4} + 25 q^{5} - q^{6} + 19 q^{7} + 15 q^{8} + 32 q^{9}+O(q^{10}) $ 25 * q + 6 * q^2 + 15 * q^3 + 32 * q^4 + 25 * q^5 - q^6 + 19 * q^7 + 15 * q^8 + 32 * q^9	\( 25 q + 6 q^{2} + 15 q^{3} + 32 q^{4} + 25 q^{5} - q^{6} + 19 q^{7} + 15 q^{8} + 32 q^{9} + 6 q^{10} + 2 q^{11} + 20 q^{12} + 14 q^{13} - 5 q^{14} + 15 q^{15} + 38 q^{16} + 7 q^{17} + 9 q^{18} + 30 q^{19} + 32 q^{20} + q^{21} + q^{22} + 43 q^{23} - 6 q^{24} + 25 q^{25} - 22 q^{26} + 42 q^{27} + 32 q^{28} - 4 q^{29} - q^{30} + 14 q^{31} + 26 q^{32} + 4 q^{33} + 7 q^{34} + 19 q^{35} + 15 q^{36} + 16 q^{37} + 14 q^{38} - 21 q^{39} + 15 q^{40} - q^{41} - 25 q^{42} + 35 q^{43} - 52 q^{44} + 32 q^{45} - 27 q^{46} + 50 q^{47} + 26 q^{48} + 46 q^{49} + 6 q^{50} - 7 q^{51} + 3 q^{52} + 4 q^{53} - 31 q^{54} + 2 q^{55} - 51 q^{56} + 2 q^{58} + 6 q^{59} + 20 q^{60} + 19 q^{61} + 28 q^{63} + 49 q^{64} + 14 q^{65} - 27 q^{66} + 65 q^{67} - 25 q^{68} + 2 q^{69} - 5 q^{70} - 34 q^{71} - 10 q^{72} + 8 q^{73} - 42 q^{74} + 15 q^{75} + 71 q^{76} + q^{77} - 59 q^{78} - 12 q^{79} + 38 q^{80} + 29 q^{81} + 11 q^{82} + 41 q^{83} - 10 q^{84} + 7 q^{85} - 13 q^{86} + 40 q^{87} - 52 q^{88} - 24 q^{89} + 9 q^{90} + 46 q^{91} + 85 q^{92} - 30 q^{93} + 14 q^{94} + 30 q^{95} - 30 q^{96} + 9 q^{97} - 64 q^{98} + 2 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 + 15 * q^3 + 32 * q^4 + 25 * q^5 - q^6 + 19 * q^7 + 15 * q^8 + 32 * q^9 + 6 * q^10 + 2 * q^11 + 20 * q^12 + 14 * q^13 - 5 * q^14 + 15 * q^15 + 38 * q^16 + 7 * q^17 + 9 * q^18 + 30 * q^19 + 32 * q^20 + q^21 + q^22 + 43 * q^23 - 6 * q^24 + 25 * q^25 - 22 * q^26 + 42 * q^27 + 32 * q^28 - 4 * q^29 - q^30 + 14 * q^31 + 26 * q^32 + 4 * q^33 + 7 * q^34 + 19 * q^35 + 15 * q^36 + 16 * q^37 + 14 * q^38 - 21 * q^39 + 15 * q^40 - q^41 - 25 * q^42 + 35 * q^43 - 52 * q^44 + 32 * q^45 - 27 * q^46 + 50 * q^47 + 26 * q^48 + 46 * q^49 + 6 * q^50 - 7 * q^51 + 3 * q^52 + 4 * q^53 - 31 * q^54 + 2 * q^55 - 51 * q^56 + 2 * q^58 + 6 * q^59 + 20 * q^60 + 19 * q^61 + 28 * q^63 + 49 * q^64 + 14 * q^65 - 27 * q^66 + 65 * q^67 - 25 * q^68 + 2 * q^69 - 5 * q^70 - 34 * q^71 - 10 * q^72 + 8 * q^73 - 42 * q^74 + 15 * q^75 + 71 * q^76 + q^77 - 59 * q^78 - 12 * q^79 + 38 * q^80 + 29 * q^81 + 11 * q^82 + 41 * q^83 - 10 * q^84 + 7 * q^85 - 13 * q^86 + 40 * q^87 - 52 * q^88 - 24 * q^89 + 9 * q^90 + 46 * q^91 + 85 * q^92 - 30 * q^93 + 14 * q^94 + 30 * q^95 - 30 * q^96 + 9 * q^97 - 64 * q^98 + 2 * 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 $

$2$	−2.51976	−1.78174	−0.890871	−	0.454256i	$-0.849905\pi$
$2$	−2.51976	−1.78174	−0.890871	+	0.454256i	$0.849905\pi$
$3$	−0.981670	−0.566767	−0.283384	−	0.959007i	$-0.591457\pi$
$3$	−0.981670	−0.566767	−0.283384	+	0.959007i	$0.591457\pi$
$4$	4.34921	2.17461
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.47358	1.00983
$7$	3.43036	1.29655	0.648277	−	0.761404i	$-0.275490\pi$
$7$	3.43036	1.29655	0.648277	+	0.761404i	$0.275490\pi$
$8$	−5.91946	−2.09284
$9$	−2.03632	−0.678775
$10$	−2.51976	−0.796819
$11$	−1.87152	−0.564284	−0.282142	−	0.959373i	$-0.591045\pi$
$11$	−1.87152	−0.564284	−0.282142	+	0.959373i	$0.591045\pi$
$12$	−4.26949	−1.23250
$13$	1.10988	0.307826	0.153913	−	0.988084i	$-0.450812\pi$
$13$	1.10988	0.307826	0.153913	+	0.988084i	$0.450812\pi$
$14$	−8.64370	−2.31013
$15$	−0.981670	−0.253466
$16$	6.21722	1.55430
$17$	7.45383	1.80782	0.903910	−	0.427722i	$-0.140684\pi$
$17$	7.45383	1.80782	0.903910	+	0.427722i	$0.140684\pi$
$18$	5.13106	1.20940
$19$	0.382278	0.0877005	0.0438502	−	0.999038i	$-0.486038\pi$
$19$	0.382278	0.0877005	0.0438502	+	0.999038i	$0.486038\pi$
$20$	4.34921	0.972513
$21$	−3.36748	−0.734845
$22$	4.71578	1.00541
$23$	−0.968812	−0.202011	−0.101006	−	0.994886i	$-0.532206\pi$
$23$	−0.968812	−0.202011	−0.101006	+	0.994886i	$0.532206\pi$
$24$	5.81095	1.18616
$25$	1.00000	0.200000
$26$	−2.79664	−0.548466
$27$	4.94401	0.951475
$28$	14.9194	2.81950
$29$	−1.15751	−0.214943	−0.107472	−	0.994208i	$-0.534275\pi$
$29$	−1.15751	−0.214943	−0.107472	+	0.994208i	$0.534275\pi$
$30$	2.47358	0.451611
$31$	7.77088	1.39569	0.697846	−	0.716248i	$-0.254142\pi$
$31$	7.77088	1.39569	0.697846	+	0.716248i	$0.254142\pi$
$32$	−3.82700	−0.676525
$33$	1.83721	0.319818
$34$	−18.7819	−3.22107
$35$	3.43036	0.579837
$36$	−8.85640	−1.47607
$37$	−1.40405	−0.230825	−0.115412	−	0.993318i	$-0.536819\pi$
$37$	−1.40405	−0.230825	−0.115412	+	0.993318i	$0.536819\pi$
$38$	−0.963249	−0.156260
$39$	−1.08954	−0.174466
$40$	−5.91946	−0.935949
$41$	−9.48464	−1.48125	−0.740626	−	0.671917i	$-0.765471\pi$
$41$	−9.48464	−1.48125	−0.740626	+	0.671917i	$0.765471\pi$
$42$	8.48526	1.30930
$43$	0.798882	0.121828	0.0609142	−	0.998143i	$-0.480598\pi$
$43$	0.798882	0.121828	0.0609142	+	0.998143i	$0.480598\pi$
$44$	−8.13962	−1.22709
$45$	−2.03632	−0.303557
$46$	2.44118	0.359932
$47$	−3.17648	−0.463337	−0.231668	−	0.972795i	$-0.574418\pi$
$47$	−3.17648	−0.463337	−0.231668	+	0.972795i	$0.574418\pi$
$48$	−6.10325	−0.880929
$49$	4.76738	0.681055
$50$	−2.51976	−0.356348
$51$	−7.31721	−1.02461
$52$	4.82711	0.669400
$53$	1.59200	0.218677	0.109339	−	0.994005i	$-0.465127\pi$
$53$	1.59200	0.218677	0.109339	+	0.994005i	$0.465127\pi$
$54$	−12.4577	−1.69528
$55$	−1.87152	−0.252355
$56$	−20.3059	−2.71349
$57$	−0.375270	−0.0497058
$58$	2.91664	0.382974
$59$	−3.55443	−0.462747	−0.231374	−	0.972865i	$-0.574322\pi$
$59$	−3.55443	−0.462747	−0.231374	+	0.972865i	$0.574322\pi$
$60$	−4.26949	−0.551189
$61$	5.43481	0.695856	0.347928	−	0.937521i	$-0.386885\pi$
$61$	5.43481	0.695856	0.347928	+	0.937521i	$0.386885\pi$
$62$	−19.5808	−2.48676
$63$	−6.98533	−0.880069
$64$	−2.79129	−0.348911
$65$	1.10988	0.137664
$66$	−4.62934	−0.569832
$67$	6.40408	0.782383	0.391191	−	0.920309i	$-0.372063\pi$
$67$	6.40408	0.782383	0.391191	+	0.920309i	$0.372063\pi$
$68$	32.4183	3.93130
$69$	0.951053	0.114493
$70$	−8.64370	−1.03312
$71$	−11.6986	−1.38837	−0.694187	−	0.719795i	$-0.744236\pi$
$71$	−11.6986	−1.38837	−0.694187	+	0.719795i	$0.744236\pi$
$72$	12.0539	1.42057
$73$	1.90914	0.223448	0.111724	−	0.993739i	$-0.464363\pi$
$73$	1.90914	0.223448	0.111724	+	0.993739i	$0.464363\pi$
$74$	3.53788	0.411270
$75$	−0.981670	−0.113353
$76$	1.66261	0.190714
$77$	−6.41998	−0.731625
$78$	2.74538	0.310853
$79$	14.9335	1.68015	0.840075	−	0.542470i	$-0.182511\pi$
$79$	14.9335	1.68015	0.840075	+	0.542470i	$0.182511\pi$
$80$	6.21722	0.695106
$81$	1.25559	0.139510
$82$	23.8991	2.63921
$83$	6.79774	0.746149	0.373075	−	0.927801i	$-0.378304\pi$
$83$	6.79774	0.746149	0.373075	+	0.927801i	$0.378304\pi$
$84$	−14.6459	−1.59800
$85$	7.45383	0.808482
$86$	−2.01299	−0.217067
$87$	1.13629	0.121823
$88$	11.0784	1.18096
$89$	−8.09378	−0.857939	−0.428969	−	0.903319i	$-0.641123\pi$
$89$	−8.09378	−0.857939	−0.428969	+	0.903319i	$0.641123\pi$
$90$	5.13106	0.540861
$91$	3.80730	0.399113
$92$	−4.21357	−0.439295
$93$	−7.62844	−0.791032
$94$	8.00397	0.825546
$95$	0.382278	0.0392209
$96$	3.75685	0.383432
$97$	4.75513	0.482810	0.241405	−	0.970424i	$-0.422392\pi$
$97$	4.75513	0.482810	0.241405	+	0.970424i	$0.422392\pi$
$98$	−12.0127	−1.21346
$99$	3.81102	0.383021
$100$	4.34921	0.434921
$101$	−0.0502281	−0.00499788	−0.00249894	−	0.999997i	$-0.500795\pi$
$101$	−0.0502281	−0.00499788	−0.00249894	+	0.999997i	$0.500795\pi$
$102$	18.4376	1.82560
$103$	−6.69861	−0.660034	−0.330017	−	0.943975i	$-0.607054\pi$
$103$	−6.69861	−0.660034	−0.330017	+	0.943975i	$0.607054\pi$
$104$	−6.56990	−0.644232
$105$	−3.36748	−0.328633
$106$	−4.01145	−0.389627
$107$	11.2943	1.09186	0.545930	−	0.837831i	$-0.316177\pi$
$107$	11.2943	1.09186	0.545930	+	0.837831i	$0.316177\pi$
$108$	21.5025	2.06908
$109$	13.1303	1.25766	0.628828	−	0.777544i	$-0.283535\pi$
$109$	13.1303	1.25766	0.628828	+	0.777544i	$0.283535\pi$
$110$	4.71578	0.449632
$111$	1.37831	0.130824
$112$	21.3273	2.01524
$113$	10.6851	1.00517	0.502583	−	0.864529i	$-0.332383\pi$
$113$	10.6851	1.00517	0.502583	+	0.864529i	$0.332383\pi$
$114$	0.945593	0.0885629
$115$	−0.968812	−0.0903422
$116$	−5.03423	−0.467417
$117$	−2.26008	−0.208944
$118$	8.95632	0.824496
$119$	25.5693	2.34394
$120$	5.81095	0.530465
$121$	−7.49742	−0.681584
$122$	−13.6944	−1.23984
$123$	9.31079	0.839525
$124$	33.7972	3.03508
$125$	1.00000	0.0894427
$126$	17.6014	1.56806
$127$	−13.8395	−1.22806	−0.614028	−	0.789284i	$-0.710452\pi$
$127$	−13.8395	−1.22806	−0.614028	+	0.789284i	$0.710452\pi$
$128$	14.6874	1.29819
$129$	−0.784239	−0.0690484
$130$	−2.79664	−0.245282
$131$	4.00488	0.349908	0.174954	−	0.984577i	$-0.444022\pi$
$131$	4.00488	0.349908	0.174954	+	0.984577i	$0.444022\pi$
$132$	7.99042	0.695477
$133$	1.31135	0.113709
$134$	−16.1368	−1.39400
$135$	4.94401	0.425512
$136$	−44.1227	−3.78349
$137$	5.67674	0.484997	0.242498	−	0.970152i	$-0.422033\pi$
$137$	5.67674	0.484997	0.242498	+	0.970152i	$0.422033\pi$
$138$	−2.39643	−0.203998
$139$	18.3263	1.55441	0.777207	−	0.629245i	$-0.216636\pi$
$139$	18.3263	1.55441	0.777207	+	0.629245i	$0.216636\pi$
$140$	14.9194	1.26092
$141$	3.11825	0.262604
$142$	29.4778	2.47372
$143$	−2.07716	−0.173701
$144$	−12.6603	−1.05502
$145$	−1.15751	−0.0961256
$146$	−4.81058	−0.398126
$147$	−4.67999	−0.385999
$148$	−6.10652	−0.501953
$149$	15.5188	1.27135	0.635675	−	0.771957i	$-0.280722\pi$
$149$	15.5188	1.27135	0.635675	+	0.771957i	$0.280722\pi$
$150$	2.47358	0.201967
$151$	−17.9688	−1.46228	−0.731140	−	0.682228i	$-0.761011\pi$
$151$	−17.9688	−1.46228	−0.731140	+	0.682228i	$0.761011\pi$
$152$	−2.26288	−0.183544
$153$	−15.1784	−1.22710
$154$	16.1768	1.30357
$155$	7.77088	0.624172
$156$	−4.73863	−0.379394
$157$	−7.48723	−0.597546	−0.298773	−	0.954324i	$-0.596577\pi$
$157$	−7.48723	−0.597546	−0.298773	+	0.954324i	$0.596577\pi$
$158$	−37.6289	−2.99359
$159$	−1.56281	−0.123939
$160$	−3.82700	−0.302551
$161$	−3.32338	−0.261919
$162$	−3.16379	−0.248571
$163$	17.0246	1.33347	0.666733	−	0.745296i	$-0.267692\pi$
$163$	17.0246	1.33347	0.666733	+	0.745296i	$0.267692\pi$
$164$	−41.2507	−3.22114
$165$	1.83721	0.143027
$166$	−17.1287	−1.32945
$167$	16.3123	1.26229	0.631143	−	0.775667i	$-0.282586\pi$
$167$	16.3123	1.26229	0.631143	+	0.775667i	$0.282586\pi$
$168$	19.9337	1.53792
$169$	−11.7682	−0.905243
$170$	−18.7819	−1.44051
$171$	−0.778441	−0.0595289
$172$	3.47451	0.264929
$173$	−10.7287	−0.815691	−0.407846	−	0.913051i	$-0.633720\pi$
$173$	−10.7287	−0.815691	−0.407846	+	0.913051i	$0.633720\pi$
$174$	−2.86318	−0.217057
$175$	3.43036	0.259311
$176$	−11.6356	−0.877068
$177$	3.48928	0.262270
$178$	20.3944	1.52863
$179$	5.20903	0.389341	0.194671	−	0.980869i	$-0.437636\pi$
$179$	5.20903	0.389341	0.194671	+	0.980869i	$0.437636\pi$
$180$	−8.85640	−0.660117
$181$	10.7430	0.798523	0.399262	−	0.916837i	$-0.369266\pi$
$181$	10.7430	0.798523	0.399262	+	0.916837i	$0.369266\pi$
$182$	−9.59349	−0.711117
$183$	−5.33519	−0.394389
$184$	5.73484	0.422778
$185$	−1.40405	−0.103228
$186$	19.2219	1.40942
$187$	−13.9500	−1.02012
$188$	−13.8152	−1.00757
$189$	16.9597	1.23364
$190$	−0.963249	−0.0698815
$191$	13.8569	1.00265	0.501324	−	0.865260i	$-0.332847\pi$
$191$	13.8569	1.00265	0.501324	+	0.865260i	$0.332847\pi$
$192$	2.74012	0.197751
$193$	−14.1907	−1.02147	−0.510733	−	0.859739i	$-0.670626\pi$
$193$	−14.1907	−1.02147	−0.510733	+	0.859739i	$0.670626\pi$
$194$	−11.9818	−0.860243
$195$	−1.08954	−0.0780234
$196$	20.7344	1.48103
$197$	17.4404	1.24257	0.621287	−	0.783583i	$-0.286610\pi$
$197$	17.4404	1.24257	0.621287	+	0.783583i	$0.286610\pi$
$198$	−9.60286	−0.682446
$199$	25.6545	1.81860	0.909299	−	0.416144i	$-0.136619\pi$
$199$	25.6545	1.81860	0.909299	+	0.416144i	$0.136619\pi$
$200$	−5.91946	−0.418569
$201$	−6.28669	−0.443429
$202$	0.126563	0.00890493
$203$	−3.97066	−0.278686
$204$	−31.8241	−2.22813
$205$	−9.48464	−0.662436
$206$	16.8789	1.17601
$207$	1.97282	0.137120
$208$	6.90038	0.478455
$209$	−0.715439	−0.0494880
$210$	8.48526	0.585539
$211$	12.9800	0.893581	0.446791	−	0.894639i	$-0.352567\pi$
$211$	12.9800	0.893581	0.446791	+	0.894639i	$0.352567\pi$
$212$	6.92393	0.475537
$213$	11.4842	0.786885
$214$	−28.4589	−1.94541
$215$	0.798882	0.0544833
$216$	−29.2658	−1.99129
$217$	26.6569	1.80959
$218$	−33.0853	−2.24082
$219$	−1.87414	−0.126643
$220$	−8.13962	−0.548773
$221$	8.27288	0.556494
$222$	−3.47303	−0.233094
$223$	−6.16318	−0.412717	−0.206359	−	0.978476i	$-0.566161\pi$
$223$	−6.16318	−0.412717	−0.206359	+	0.978476i	$0.566161\pi$
$224$	−13.1280	−0.877152
$225$	−2.03632	−0.135755
$226$	−26.9238	−1.79095
$227$	20.2073	1.34121	0.670604	−	0.741816i	$-0.266035\pi$
$227$	20.2073	1.34121	0.670604	+	0.741816i	$0.266035\pi$
$228$	−1.63213	−0.108090
$229$	4.37991	0.289432	0.144716	−	0.989473i	$-0.453773\pi$
$229$	4.37991	0.289432	0.144716	+	0.989473i	$0.453773\pi$
$230$	2.44118	0.160966
$231$	6.30230	0.414661
$232$	6.85180	0.449843
$233$	8.11576	0.531681	0.265841	−	0.964017i	$-0.414351\pi$
$233$	8.11576	0.531681	0.265841	+	0.964017i	$0.414351\pi$
$234$	5.69487	0.372285
$235$	−3.17648	−0.207210
$236$	−15.4590	−1.00629
$237$	−14.6598	−0.952254
$238$	−64.4287	−4.17629
$239$	20.0529	1.29712	0.648558	−	0.761165i	$-0.275372\pi$
$239$	20.0529	1.29712	0.648558	+	0.761165i	$0.275372\pi$
$240$	−6.10325	−0.393963
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	18.8917	1.21441
$243$	−16.0646	−1.03054
$244$	23.6371	1.51321
$245$	4.76738	0.304577
$246$	−23.4610	−1.49582
$247$	0.424283	0.0269965
$248$	−45.9994	−2.92097
$249$	−6.67314	−0.422893
$250$	−2.51976	−0.159364
$251$	−12.2010	−0.770123	−0.385062	−	0.922891i	$-0.625820\pi$
$251$	−12.2010	−0.770123	−0.385062	+	0.922891i	$0.625820\pi$
$252$	−30.3807	−1.91380
$253$	1.81315	0.113992
$254$	34.8723	2.18808
$255$	−7.31721	−0.458221
$256$	−31.4262	−1.96414
$257$	−14.2764	−0.890538	−0.445269	−	0.895397i	$-0.646892\pi$
$257$	−14.2764	−0.890538	−0.445269	+	0.895397i	$0.646892\pi$
$258$	1.97610	0.123026
$259$	−4.81640	−0.299277
$260$	4.82711	0.299365
$261$	2.35706	0.145898
$262$	−10.0913	−0.623445
$263$	−24.0223	−1.48128	−0.740639	−	0.671903i	$-0.765477\pi$
$263$	−24.0223	−1.48128	−0.740639	+	0.671903i	$0.765477\pi$
$264$	−10.8753	−0.669328
$265$	1.59200	0.0977955
$266$	−3.30429	−0.202599
$267$	7.94542	0.486252
$268$	27.8527	1.70137
$269$	−25.9526	−1.58236	−0.791179	−	0.611584i	$-0.790532\pi$
$269$	−25.9526	−1.58236	−0.791179	+	0.611584i	$0.790532\pi$
$270$	−12.4577	−0.758154
$271$	7.11206	0.432027	0.216013	−	0.976390i	$-0.430695\pi$
$271$	7.11206	0.432027	0.216013	+	0.976390i	$0.430695\pi$
$272$	46.3421	2.80990
$273$	−3.73751	−0.226204
$274$	−14.3041	−0.864139
$275$	−1.87152	−0.112857
$276$	4.13633	0.248978
$277$	17.3210	1.04072	0.520358	−	0.853948i	$-0.325799\pi$
$277$	17.3210	1.04072	0.520358	+	0.853948i	$0.325799\pi$
$278$	−46.1779	−2.76957
$279$	−15.8240	−0.947360
$280$	−20.3059	−1.21351
$281$	−15.2364	−0.908928	−0.454464	−	0.890765i	$-0.650169\pi$
$281$	−15.2364	−0.908928	−0.454464	+	0.890765i	$0.650169\pi$
$282$	−7.85726	−0.467893
$283$	−5.75349	−0.342010	−0.171005	−	0.985270i	$-0.554701\pi$
$283$	−5.75349	−0.342010	−0.171005	+	0.985270i	$0.554701\pi$
$284$	−50.8799	−3.01916
$285$	−0.375270	−0.0222291
$286$	5.23396	0.309491
$287$	−32.5357	−1.92052
$288$	7.79302	0.459208
$289$	38.5597	2.26821
$290$	2.91664	0.171271
$291$	−4.66797	−0.273641
$292$	8.30325	0.485911
$293$	−4.41376	−0.257855	−0.128927	−	0.991654i	$-0.541153\pi$
$293$	−4.41376	−0.257855	−0.128927	+	0.991654i	$0.541153\pi$
$294$	11.7925	0.687752
$295$	−3.55443	−0.206947
$296$	8.31122	0.483080
$297$	−9.25279	−0.536902
$298$	−39.1037	−2.26522
$299$	−1.07527	−0.0621843
$300$	−4.26949	−0.246499
$301$	2.74046	0.157957
$302$	45.2771	2.60541
$303$	0.0493074	0.00283263
$304$	2.37670	0.136313
$305$	5.43481	0.311196
$306$	38.2460	2.18638
$307$	−14.9232	−0.851713	−0.425856	−	0.904791i	$-0.640027\pi$
$307$	−14.9232	−0.851713	−0.425856	+	0.904791i	$0.640027\pi$
$308$	−27.9219	−1.59100
$309$	6.57582	0.374086
$310$	−19.5808	−1.11211
$311$	4.63145	0.262625	0.131313	−	0.991341i	$-0.458081\pi$
$311$	4.63145	0.262625	0.131313	+	0.991341i	$0.458081\pi$
$312$	6.44947	0.365129
$313$	4.18264	0.236417	0.118208	−	0.992989i	$-0.462285\pi$
$313$	4.18264	0.236417	0.118208	+	0.992989i	$0.462285\pi$
$314$	18.8661	1.06467
$315$	−6.98533	−0.393579
$316$	64.9489	3.65366
$317$	9.77381	0.548952	0.274476	−	0.961594i	$-0.411496\pi$
$317$	9.77381	0.548952	0.274476	+	0.961594i	$0.411496\pi$
$318$	3.93792	0.220828
$319$	2.16629	0.121289
$320$	−2.79129	−0.156038
$321$	−11.0873	−0.618830
$322$	8.37412	0.466672
$323$	2.84943	0.158547
$324$	5.46082	0.303379
$325$	1.10988	0.0615652
$326$	−42.8979	−2.37589
$327$	−12.8896	−0.712799
$328$	56.1439	3.10003
$329$	−10.8965	−0.600741
$330$	−4.62934	−0.254837
$331$	−1.93296	−0.106245	−0.0531225	−	0.998588i	$-0.516917\pi$
$331$	−1.93296	−0.106245	−0.0531225	+	0.998588i	$0.516917\pi$
$332$	29.5648	1.62258
$333$	2.85910	0.156678
$334$	−41.1032	−2.24907
$335$	6.40408	0.349892
$336$	−20.9364	−1.14217
$337$	−8.51417	−0.463797	−0.231898	−	0.972740i	$-0.574494\pi$
$337$	−8.51417	−0.463797	−0.231898	+	0.972740i	$0.574494\pi$
$338$	29.6530	1.61291
$339$	−10.4892	−0.569695
$340$	32.4183	1.75813
$341$	−14.5433	−0.787566
$342$	1.96149	0.106065
$343$	−7.65869	−0.413530
$344$	−4.72895	−0.254968
$345$	0.951053	0.0512030
$346$	27.0339	1.45335
$347$	25.0125	1.34274	0.671372	−	0.741121i	$-0.265706\pi$
$347$	25.0125	1.34274	0.671372	+	0.741121i	$0.265706\pi$
$348$	4.94196	0.264917
$349$	−12.8968	−0.690351	−0.345175	−	0.938538i	$-0.612181\pi$
$349$	−12.8968	−0.690351	−0.345175	+	0.938538i	$0.612181\pi$
$350$	−8.64370	−0.462025
$351$	5.48726	0.292889
$352$	7.16230	0.381752
$353$	−3.56038	−0.189500	−0.0947500	−	0.995501i	$-0.530205\pi$
$353$	−3.56038	−0.189500	−0.0947500	+	0.995501i	$0.530205\pi$
$354$	−8.79215	−0.467298
$355$	−11.6986	−0.620899
$356$	−35.2016	−1.86568
$357$	−25.1007	−1.32847
$358$	−13.1255	−0.693706
$359$	−15.8493	−0.836496	−0.418248	−	0.908333i	$-0.637356\pi$
$359$	−15.8493	−0.836496	−0.418248	+	0.908333i	$0.637356\pi$
$360$	12.0539	0.635298
$361$	−18.8539	−0.992309
$362$	−27.0699	−1.42276
$363$	7.36000	0.386300
$364$	16.5587	0.867914
$365$	1.90914	0.0999289
$366$	13.4434	0.702699
$367$	7.46514	0.389677	0.194839	−	0.980835i	$-0.437582\pi$
$367$	7.46514	0.389677	0.194839	+	0.980835i	$0.437582\pi$
$368$	−6.02331	−0.313987
$369$	19.3138	1.00544
$370$	3.53788	0.183926
$371$	5.46112	0.283527
$372$	−33.1777	−1.72018
$373$	14.9933	0.776325	0.388162	−	0.921591i	$-0.373110\pi$
$373$	14.9933	0.776325	0.388162	+	0.921591i	$0.373110\pi$
$374$	35.1507	1.81760
$375$	−0.981670	−0.0506932
$376$	18.8030	0.969692
$377$	−1.28469	−0.0661651
$378$	−42.7345	−2.19803
$379$	−28.1082	−1.44382	−0.721911	−	0.691986i	$-0.756736\pi$
$379$	−28.1082	−1.44382	−0.721911	+	0.691986i	$0.756736\pi$
$380$	1.66261	0.0852899
$381$	13.5858	0.696022
$382$	−34.9160	−1.78646
$383$	32.4702	1.65915	0.829576	−	0.558394i	$-0.188582\pi$
$383$	32.4702	1.65915	0.829576	+	0.558394i	$0.188582\pi$
$384$	−14.4182	−0.735774
$385$	−6.41998	−0.327192
$386$	35.7571	1.81999
$387$	−1.62678	−0.0826940
$388$	20.6811	1.04992
$389$	17.1898	0.871556	0.435778	−	0.900054i	$-0.356473\pi$
$389$	17.1898	0.871556	0.435778	+	0.900054i	$0.356473\pi$
$390$	2.74538	0.139018
$391$	−7.22136	−0.365200
$392$	−28.2203	−1.42534
$393$	−3.93147	−0.198316
$394$	−43.9456	−2.21395
$395$	14.9335	0.751386
$396$	16.5749	0.832921
$397$	−10.4435	−0.524143	−0.262072	−	0.965048i	$-0.584406\pi$
$397$	−10.4435	−0.524143	−0.262072	+	0.965048i	$0.584406\pi$
$398$	−64.6432	−3.24027
$399$	−1.28731	−0.0644463
$400$	6.21722	0.310861
$401$	31.7825	1.58714	0.793572	−	0.608476i	$-0.208219\pi$
$401$	31.7825	1.58714	0.793572	+	0.608476i	$0.208219\pi$
$402$	15.8410	0.790076
$403$	8.62476	0.429630
$404$	−0.218452	−0.0108684
$405$	1.25559	0.0623907
$406$	10.0051	0.496546
$407$	2.62771	0.130251
$408$	43.3139	2.14436
$409$	−17.4800	−0.864329	−0.432165	−	0.901795i	$-0.642250\pi$
$409$	−17.4800	−0.864329	−0.432165	+	0.901795i	$0.642250\pi$
$410$	23.8991	1.18029
$411$	−5.57269	−0.274880
$412$	−29.1337	−1.43531
$413$	−12.1930	−0.599977
$414$	−4.97103	−0.244313
$415$	6.79774	0.333688
$416$	−4.24752	−0.208252
$417$	−17.9903	−0.880991
$418$	1.80274	0.0881748
$419$	15.4246	0.753539	0.376769	−	0.926307i	$-0.377035\pi$
$419$	15.4246	0.753539	0.376769	+	0.926307i	$0.377035\pi$
$420$	−14.6459	−0.714646
$421$	14.9823	0.730193	0.365096	−	0.930970i	$-0.381036\pi$
$421$	14.9823	0.730193	0.365096	+	0.930970i	$0.381036\pi$
$422$	−32.7066	−1.59213
$423$	6.46834	0.314501
$424$	−9.42375	−0.457658
$425$	7.45383	0.361564
$426$	−28.9375	−1.40203
$427$	18.6434	0.902216
$428$	49.1212	2.37436
$429$	2.03909	0.0984481
$430$	−2.01299	−0.0970752
$431$	−10.6039	−0.510774	−0.255387	−	0.966839i	$-0.582203\pi$
$431$	−10.6039	−0.510774	−0.255387	+	0.966839i	$0.582203\pi$
$432$	30.7380	1.47888
$433$	22.9054	1.10076	0.550382	−	0.834913i	$-0.314482\pi$
$433$	22.9054	1.10076	0.550382	+	0.834913i	$0.314482\pi$
$434$	−67.1692	−3.22422
$435$	1.13629	0.0544808
$436$	57.1065	2.73491
$437$	−0.370355	−0.0177165
$438$	4.72240	0.225645
$439$	−9.82711	−0.469022	−0.234511	−	0.972113i	$-0.575349\pi$
$439$	−9.82711	−0.469022	−0.234511	+	0.972113i	$0.575349\pi$
$440$	11.0784	0.528140
$441$	−9.70793	−0.462283
$442$	−20.8457	−0.991529
$443$	21.5634	1.02451	0.512255	−	0.858833i	$-0.328810\pi$
$443$	21.5634	1.02451	0.512255	+	0.858833i	$0.328810\pi$
$444$	5.99458	0.284490
$445$	−8.09378	−0.383682
$446$	15.5298	0.735356
$447$	−15.2344	−0.720560
$448$	−9.57513	−0.452382
$449$	−35.3104	−1.66640	−0.833200	−	0.552971i	$-0.813494\pi$
$449$	−35.3104	−1.66640	−0.833200	+	0.552971i	$0.813494\pi$
$450$	5.13106	0.241880
$451$	17.7507	0.835846
$452$	46.4715	2.18584
$453$	17.6394	0.828772
$454$	−50.9177	−2.38969
$455$	3.80730	0.178489
$456$	2.22140	0.104026
$457$	−31.8842	−1.49148	−0.745741	−	0.666236i	$-0.767904\pi$
$457$	−31.8842	−1.49148	−0.745741	+	0.666236i	$0.767904\pi$
$458$	−11.0363	−0.515694
$459$	36.8518	1.72010
$460$	−4.21357	−0.196459
$461$	−38.9255	−1.81294	−0.906470	−	0.422269i	$-0.861234\pi$
$461$	−38.9255	−1.81294	−0.906470	+	0.422269i	$0.861234\pi$
$462$	−15.8803	−0.738819
$463$	6.39964	0.297417	0.148708	−	0.988881i	$-0.452488\pi$
$463$	6.39964	0.297417	0.148708	+	0.988881i	$0.452488\pi$
$464$	−7.19646	−0.334087
$465$	−7.62844	−0.353760
$466$	−20.4498	−0.947319
$467$	−13.9677	−0.646349	−0.323174	−	0.946339i	$-0.604750\pi$
$467$	−13.9677	−0.646349	−0.323174	+	0.946339i	$0.604750\pi$
$468$	−9.82956	−0.454372
$469$	21.9683	1.01440
$470$	8.00397	0.369196
$471$	7.34999	0.338670
$472$	21.0403	0.968458
$473$	−1.49512	−0.0687458
$474$	36.9391	1.69667
$475$	0.382278	0.0175401
$476$	111.207	5.09714
$477$	−3.24182	−0.148433
$478$	−50.5287	−2.31113
$479$	24.3699	1.11349	0.556744	−	0.830684i	$-0.312050\pi$
$479$	24.3699	1.11349	0.556744	+	0.830684i	$0.312050\pi$
$480$	3.75685	0.171476
$481$	−1.55833	−0.0710538
$482$	2.51976	0.114772
$483$	3.26246	0.148447
$484$	−32.6079	−1.48218
$485$	4.75513	0.215919
$486$	40.4790	1.83616
$487$	37.0364	1.67828	0.839139	−	0.543917i	$-0.183059\pi$
$487$	37.0364	1.67828	0.839139	+	0.543917i	$0.183059\pi$
$488$	−32.1711	−1.45632
$489$	−16.7125	−0.755765
$490$	−12.0127	−0.542677
$491$	14.1478	0.638483	0.319242	−	0.947673i	$-0.396572\pi$
$491$	14.1478	0.638483	0.319242	+	0.947673i	$0.396572\pi$
$492$	40.4946	1.82564
$493$	−8.62785	−0.388579
$494$	−1.06909	−0.0481008
$495$	3.81102	0.171292
$496$	48.3132	2.16933
$497$	−40.1306	−1.80010
$498$	16.8147	0.753487
$499$	29.5685	1.32367	0.661834	−	0.749650i	$-0.269778\pi$
$499$	29.5685	1.32367	0.661834	+	0.749650i	$0.269778\pi$
$500$	4.34921	0.194503
$501$	−16.0133	−0.715422
$502$	30.7438	1.37216
$503$	−1.97852	−0.0882178	−0.0441089	−	0.999027i	$-0.514045\pi$
$503$	−1.97852	−0.0882178	−0.0441089	+	0.999027i	$0.514045\pi$
$504$	41.3494	1.84185
$505$	−0.0502281	−0.00223512
$506$	−4.56871	−0.203104
$507$	11.5525	0.513062
$508$	−60.1909	−2.67054
$509$	−5.91307	−0.262092	−0.131046	−	0.991376i	$-0.541834\pi$
$509$	−5.91307	−0.262092	−0.131046	+	0.991376i	$0.541834\pi$
$510$	18.4376	0.816432
$511$	6.54904	0.289712
$512$	49.8118	2.20139
$513$	1.88998	0.0834448
$514$	35.9732	1.58671
$515$	−6.69861	−0.295176
$516$	−3.41082	−0.150153
$517$	5.94483	0.261453
$518$	12.1362	0.533234
$519$	10.5321	0.462307
$520$	−6.56990	−0.288109
$521$	−35.7821	−1.56764	−0.783820	−	0.620988i	$-0.786732\pi$
$521$	−35.7821	−1.56764	−0.783820	+	0.620988i	$0.786732\pi$
$522$	−5.93923	−0.259953
$523$	−31.3530	−1.37097	−0.685487	−	0.728085i	$-0.740410\pi$
$523$	−31.3530	−1.37097	−0.685487	+	0.728085i	$0.740410\pi$
$524$	17.4180	0.760911
$525$	−3.36748	−0.146969
$526$	60.5305	2.63926
$527$	57.9229	2.52316
$528$	11.4223	0.497094
$529$	−22.0614	−0.959191
$530$	−4.01145	−0.174246
$531$	7.23797	0.314101
$532$	5.70334	0.247271
$533$	−10.5268	−0.455968
$534$	−20.0206	−0.866375
$535$	11.2943	0.488294
$536$	−37.9087	−1.63741
$537$	−5.11355	−0.220666
$538$	65.3944	2.81935
$539$	−8.92224	−0.384308
$540$	21.5025	0.925322
$541$	−20.7980	−0.894174	−0.447087	−	0.894491i	$-0.647539\pi$
$541$	−20.7980	−0.894174	−0.447087	+	0.894491i	$0.647539\pi$
$542$	−17.9207	−0.769760
$543$	−10.5461	−0.452577
$544$	−28.5258	−1.22304
$545$	13.1303	0.562441
$546$	9.41764	0.403038
$547$	−38.2235	−1.63432	−0.817159	−	0.576412i	$-0.804452\pi$
$547$	−38.2235	−1.63432	−0.817159	+	0.576412i	$0.804452\pi$
$548$	24.6894	1.05468
$549$	−11.0670	−0.472330
$550$	4.71578	0.201082
$551$	−0.442488	−0.0188506
$552$	−5.62972	−0.239617
$553$	51.2273	2.17841
$554$	−43.6447	−1.85429
$555$	1.37831	0.0585062
$556$	79.7048	3.38024
$557$	39.8662	1.68918	0.844592	−	0.535411i	$-0.179843\pi$
$557$	39.8662	1.68918	0.844592	+	0.535411i	$0.179843\pi$
$558$	39.8728	1.68795
$559$	0.886665	0.0375019
$560$	21.3273	0.901243
$561$	13.6943	0.578173
$562$	38.3922	1.61948
$563$	−17.3653	−0.731860	−0.365930	−	0.930642i	$-0.619249\pi$
$563$	−17.3653	−0.731860	−0.365930	+	0.930642i	$0.619249\pi$
$564$	13.5619	0.571060
$565$	10.6851	0.449523
$566$	14.4974	0.609373
$567$	4.30713	0.180882
$568$	69.2496	2.90565
$569$	1.01358	0.0424917	0.0212458	−	0.999774i	$-0.493237\pi$
$569$	1.01358	0.0424917	0.0212458	+	0.999774i	$0.493237\pi$
$570$	0.945593	0.0396065
$571$	−1.37234	−0.0574308	−0.0287154	−	0.999588i	$-0.509142\pi$
$571$	−1.37234	−0.0574308	−0.0287154	+	0.999588i	$0.509142\pi$
$572$	−9.03402	−0.377731
$573$	−13.6029	−0.568268
$574$	81.9824	3.42188
$575$	−0.968812	−0.0404022
$576$	5.68397	0.236832
$577$	−25.7644	−1.07259	−0.536293	−	0.844032i	$-0.680176\pi$
$577$	−25.7644	−1.07259	−0.536293	+	0.844032i	$0.680176\pi$
$578$	−97.1612	−4.04137
$579$	13.9305	0.578934
$580$	−5.03423	−0.209035
$581$	23.3187	0.967424
$582$	11.7622	0.487558
$583$	−2.97945	−0.123396
$584$	−11.3011	−0.467642
$585$	−2.26008	−0.0934428
$586$	11.1216	0.459431
$587$	38.4469	1.58687	0.793437	−	0.608652i	$-0.208289\pi$
$587$	38.4469	1.58687	0.793437	+	0.608652i	$0.208289\pi$
$588$	−20.3543	−0.839397
$589$	2.97063	0.122403
$590$	8.95632	0.368726
$591$	−17.1207	−0.704251
$592$	−8.72929	−0.358772
$593$	−36.6838	−1.50642	−0.753212	−	0.657778i	$-0.771496\pi$
$593$	−36.6838	−1.50642	−0.753212	+	0.657778i	$0.771496\pi$
$594$	23.3149	0.956620
$595$	25.5693	1.04824
$596$	67.4946	2.76469
$597$	−25.1842	−1.03072
$598$	2.70942	0.110796
$599$	5.21173	0.212945	0.106473	−	0.994316i	$-0.466044\pi$
$599$	5.21173	0.212945	0.106473	+	0.994316i	$0.466044\pi$
$600$	5.81095	0.237231
$601$	−39.7890	−1.62303	−0.811514	−	0.584333i	$-0.801356\pi$
$601$	−39.7890	−1.62303	−0.811514	+	0.584333i	$0.801356\pi$
$602$	−6.90530	−0.281439
$603$	−13.0408	−0.531062
$604$	−78.1501	−3.17988
$605$	−7.49742	−0.304814
$606$	−0.124243	−0.00504702
$607$	11.1454	0.452379	0.226190	−	0.974083i	$-0.427373\pi$
$607$	11.1454	0.452379	0.226190	+	0.974083i	$0.427373\pi$
$608$	−1.46298	−0.0593316
$609$	3.89788	0.157950
$610$	−13.6944	−0.554472
$611$	−3.52551	−0.142627
$612$	−66.0142	−2.66846
$613$	−10.8362	−0.437670	−0.218835	−	0.975762i	$-0.570226\pi$
$613$	−10.8362	−0.437670	−0.218835	+	0.975762i	$0.570226\pi$
$614$	37.6030	1.51753
$615$	9.31079	0.375447
$616$	38.0028	1.53118
$617$	−22.5157	−0.906448	−0.453224	−	0.891397i	$-0.649726\pi$
$617$	−22.5157	−0.906448	−0.453224	+	0.891397i	$0.649726\pi$
$618$	−16.5695	−0.666524
$619$	−2.09011	−0.0840087	−0.0420043	−	0.999117i	$-0.513374\pi$
$619$	−2.09011	−0.0840087	−0.0420043	+	0.999117i	$0.513374\pi$
$620$	33.7972	1.35733
$621$	−4.78981	−0.192209
$622$	−11.6702	−0.467931
$623$	−27.7646	−1.11236
$624$	−6.77389	−0.271173
$625$	1.00000	0.0400000
$626$	−10.5393	−0.421233
$627$	0.702325	0.0280482
$628$	−32.5636	−1.29943
$629$	−10.4656	−0.417289
$630$	17.6014	0.701256
$631$	−28.0315	−1.11592	−0.557958	−	0.829869i	$-0.688415\pi$
$631$	−28.0315	−1.11592	−0.557958	+	0.829869i	$0.688415\pi$
$632$	−88.3982	−3.51629
$633$	−12.7421	−0.506453
$634$	−24.6277	−0.978090
$635$	−13.8395	−0.549204
$636$	−6.79701	−0.269519
$637$	5.29123	0.209646
$638$	−5.45854	−0.216106
$639$	23.8222	0.942393
$640$	14.6874	0.580570
$641$	−40.0600	−1.58228	−0.791138	−	0.611637i	$-0.790511\pi$
$641$	−40.0600	−1.58228	−0.791138	+	0.611637i	$0.790511\pi$
$642$	27.9373	1.10260
$643$	11.4947	0.453308	0.226654	−	0.973975i	$-0.427221\pi$
$643$	11.4947	0.453308	0.226654	+	0.973975i	$0.427221\pi$
$644$	−14.4541	−0.569570
$645$	−0.784239	−0.0308794
$646$	−7.17990	−0.282489
$647$	45.1132	1.77358	0.886792	−	0.462169i	$-0.152929\pi$
$647$	45.1132	1.77358	0.886792	+	0.462169i	$0.152929\pi$
$648$	−7.43241	−0.291973
$649$	6.65217	0.261121
$650$	−2.79664	−0.109693
$651$	−26.1683	−1.02562
$652$	74.0434	2.89976
$653$	−26.0449	−1.01921	−0.509607	−	0.860407i	$-0.670209\pi$
$653$	−26.0449	−1.01921	−0.509607	+	0.860407i	$0.670209\pi$
$654$	32.4789	1.27002
$655$	4.00488	0.156483
$656$	−58.9681	−2.30232
$657$	−3.88763	−0.151671
$658$	27.4565	1.07037
$659$	−0.171196	−0.00666885	−0.00333442	−	0.999994i	$-0.501061\pi$
$659$	−0.171196	−0.00666885	−0.00333442	+	0.999994i	$0.501061\pi$
$660$	7.99042	0.311027
$661$	21.3608	0.830839	0.415419	−	0.909630i	$-0.363635\pi$
$661$	21.3608	0.830839	0.415419	+	0.909630i	$0.363635\pi$
$662$	4.87060	0.189301
$663$	−8.12123	−0.315403
$664$	−40.2390	−1.56157
$665$	1.31135	0.0508520
$666$	−7.20427	−0.279160
$667$	1.12140	0.0434210
$668$	70.9457	2.74497
$669$	6.05021	0.233915
$670$	−16.1368	−0.623418
$671$	−10.1713	−0.392660
$672$	12.8874	0.497141
$673$	23.1925	0.894007	0.447003	−	0.894532i	$-0.352491\pi$
$673$	23.1925	0.894007	0.447003	+	0.894532i	$0.352491\pi$
$674$	21.4537	0.826366
$675$	4.94401	0.190295
$676$	−51.1822	−1.96855
$677$	−35.1589	−1.35127	−0.675634	−	0.737238i	$-0.736130\pi$
$677$	−35.1589	−1.35127	−0.675634	+	0.737238i	$0.736130\pi$
$678$	26.4303	1.01505
$679$	16.3118	0.625990
$680$	−44.1227	−1.69203
$681$	−19.8369	−0.760153
$682$	36.6458	1.40324
$683$	−28.0812	−1.07450	−0.537249	−	0.843424i	$-0.680537\pi$
$683$	−28.0812	−1.07450	−0.537249	+	0.843424i	$0.680537\pi$
$684$	−3.38561	−0.129452
$685$	5.67674	0.216897
$686$	19.2981	0.736804
$687$	−4.29962	−0.164041
$688$	4.96682	0.189358
$689$	1.76693	0.0673146
$690$	−2.39643	−0.0912305
$691$	−26.5877	−1.01144	−0.505721	−	0.862697i	$-0.668774\pi$
$691$	−26.5877	−1.01144	−0.505721	+	0.862697i	$0.668774\pi$
$692$	−46.6616	−1.77381
$693$	13.0732	0.496608
$694$	−63.0257	−2.39242
$695$	18.3263	0.695155
$696$	−6.72621	−0.254956
$697$	−70.6969	−2.67784
$698$	32.4969	1.23003
$699$	−7.96700	−0.301340
$700$	14.9194	0.563899
$701$	−9.57677	−0.361709	−0.180855	−	0.983510i	$-0.557886\pi$
$701$	−9.57677	−0.361709	−0.180855	+	0.983510i	$0.557886\pi$
$702$	−13.8266	−0.521852
$703$	−0.536737	−0.0202434
$704$	5.22395	0.196885
$705$	3.11825	0.117440
$706$	8.97132	0.337640
$707$	−0.172300	−0.00648002
$708$	15.1756	0.570334
$709$	11.5773	0.434794	0.217397	−	0.976083i	$-0.430243\pi$
$709$	11.5773	0.434794	0.217397	+	0.976083i	$0.430243\pi$
$710$	29.4778	1.10628
$711$	−30.4094	−1.14044
$712$	47.9108	1.79553
$713$	−7.52852	−0.281945
$714$	63.2477	2.36699
$715$	−2.07716	−0.0776815
$716$	22.6552	0.846664
$717$	−19.6854	−0.735163
$718$	39.9366	1.49042
$719$	−26.2990	−0.980788	−0.490394	−	0.871501i	$-0.663147\pi$
$719$	−26.2990	−0.980788	−0.490394	+	0.871501i	$0.663147\pi$
$720$	−12.6603	−0.471820
$721$	−22.9787	−0.855770
$722$	47.5073	1.76804
$723$	0.981670	0.0365087
$724$	46.7237	1.73647
$725$	−1.15751	−0.0429887
$726$	−18.5455	−0.688286
$727$	17.1972	0.637810	0.318905	−	0.947787i	$-0.396685\pi$
$727$	17.1972	0.637810	0.318905	+	0.947787i	$0.396685\pi$
$728$	−22.5371	−0.835282
$729$	12.0034	0.444569
$730$	−4.81058	−0.178048
$731$	5.95474	0.220244
$732$	−23.2039	−0.857640
$733$	21.5546	0.796138	0.398069	−	0.917355i	$-0.369680\pi$
$733$	21.5546	0.796138	0.398069	+	0.917355i	$0.369680\pi$
$734$	−18.8104	−0.694304
$735$	−4.67999	−0.172624
$736$	3.70765	0.136666
$737$	−11.9853	−0.441486
$738$	−48.6662	−1.79143
$739$	−31.9324	−1.17465	−0.587326	−	0.809351i	$-0.699819\pi$
$739$	−31.9324	−1.17465	−0.587326	+	0.809351i	$0.699819\pi$
$740$	−6.10652	−0.224480
$741$	−0.416506	−0.0153007
$742$	−13.7607	−0.505173
$743$	26.0253	0.954776	0.477388	−	0.878693i	$-0.341584\pi$
$743$	26.0253	0.954776	0.477388	+	0.878693i	$0.341584\pi$
$744$	45.1562	1.65551
$745$	15.5188	0.568565
$746$	−37.7796	−1.38321
$747$	−13.8424	−0.506467
$748$	−60.6714	−2.21837
$749$	38.7435	1.41566
$750$	2.47358	0.0903222
$751$	−16.6205	−0.606492	−0.303246	−	0.952912i	$-0.598070\pi$
$751$	−16.6205	−0.606492	−0.303246	+	0.952912i	$0.598070\pi$
$752$	−19.7488	−0.720166
$753$	11.9774	0.436481
$754$	3.23713	0.117889
$755$	−17.9688	−0.653951
$756$	73.7615	2.68268
$757$	−51.5997	−1.87542	−0.937711	−	0.347416i	$-0.887059\pi$
$757$	−51.5997	−1.87542	−0.937711	+	0.347416i	$0.887059\pi$
$758$	70.8261	2.57252
$759$	−1.77991	−0.0646067
$760$	−2.26288	−0.0820832
$761$	44.4538	1.61145	0.805724	−	0.592291i	$-0.201776\pi$
$761$	44.4538	1.61145	0.805724	+	0.592291i	$0.201776\pi$
$762$	−34.2331	−1.24013
$763$	45.0417	1.63062
$764$	60.2664	2.18036
$765$	−15.1784	−0.548777
$766$	−81.8173	−2.95618
$767$	−3.94500	−0.142446
$768$	30.8501	1.11321
$769$	−41.2174	−1.48634	−0.743169	−	0.669104i	$-0.766678\pi$
$769$	−41.2174	−1.48634	−0.743169	+	0.669104i	$0.766678\pi$
$770$	16.1768	0.582973
$771$	14.0147	0.504728
$772$	−61.7182	−2.22129
$773$	−12.1501	−0.437008	−0.218504	−	0.975836i	$-0.570118\pi$
$773$	−12.1501	−0.437008	−0.218504	+	0.975836i	$0.570118\pi$
$774$	4.09911	0.147339
$775$	7.77088	0.279138
$776$	−28.1478	−1.01045
$777$	4.72812	0.169620
$778$	−43.3142	−1.55289
$779$	−3.62577	−0.129907
$780$	−4.73863	−0.169670
$781$	21.8942	0.783436
$782$	18.1961	0.650692
$783$	−5.72271	−0.204513
$784$	29.6398	1.05857
$785$	−7.48723	−0.267231
$786$	9.90637	0.353348
$787$	0.746889	0.0266237	0.0133119	−	0.999911i	$-0.495763\pi$
$787$	0.746889	0.0266237	0.0133119	+	0.999911i	$0.495763\pi$
$788$	75.8518	2.70211
$789$	23.5820	0.839540
$790$	−37.6289	−1.33878
$791$	36.6536	1.30325
$792$	−22.5591	−0.801604
$793$	6.03200	0.214203
$794$	26.3151	0.933888
$795$	−1.56281	−0.0554273
$796$	111.577	3.95473
$797$	−25.7328	−0.911501	−0.455751	−	0.890108i	$-0.650629\pi$
$797$	−25.7328	−0.911501	−0.455751	+	0.890108i	$0.650629\pi$
$798$	3.24373	0.114827
$799$	−23.6769	−0.837629
$800$	−3.82700	−0.135305
$801$	16.4816	0.582347
$802$	−80.0845	−2.82788
$803$	−3.57299	−0.126088
$804$	−27.3421	−0.964283
$805$	−3.32338	−0.117134
$806$	−21.7324	−0.765490
$807$	25.4769	0.896829
$808$	0.297323	0.0104598
$809$	30.8559	1.08483	0.542417	−	0.840109i	$-0.317509\pi$
$809$	30.8559	1.08483	0.542417	+	0.840109i	$0.317509\pi$
$810$	−3.16379	−0.111164
$811$	−39.8195	−1.39825	−0.699127	−	0.714998i	$-0.746428\pi$
$811$	−39.8195	−1.39825	−0.699127	+	0.714998i	$0.746428\pi$
$812$	−17.2692	−0.606032
$813$	−6.98169	−0.244859
$814$	−6.62120	−0.232073
$815$	17.0246	0.596344
$816$	−45.4926	−1.59256
$817$	0.305395	0.0106844
$818$	44.0454	1.54001
$819$	−7.75289	−0.270908
$820$	−41.2507	−1.44054
$821$	−4.41164	−0.153967	−0.0769836	−	0.997032i	$-0.524529\pi$
$821$	−4.41164	−0.153967	−0.0769836	+	0.997032i	$0.524529\pi$
$822$	14.0419	0.489766
$823$	−8.70674	−0.303498	−0.151749	−	0.988419i	$-0.548491\pi$
$823$	−8.70674	−0.303498	−0.151749	+	0.988419i	$0.548491\pi$
$824$	39.6521	1.38135
$825$	1.83721	0.0639635
$826$	30.7234	1.06900
$827$	−17.4816	−0.607896	−0.303948	−	0.952689i	$-0.598305\pi$
$827$	−17.4816	−0.607896	−0.303948	+	0.952689i	$0.598305\pi$
$828$	8.58019	0.298182
$829$	−37.7568	−1.31135	−0.655673	−	0.755045i	$-0.727615\pi$
$829$	−37.7568	−1.31135	−0.655673	+	0.755045i	$0.727615\pi$
$830$	−17.1287	−0.594546
$831$	−17.0035	−0.589844
$832$	−3.09800	−0.107404
$833$	35.5353	1.23122
$834$	45.3314	1.56970
$835$	16.3123	0.564511
$836$	−3.11160	−0.107617
$837$	38.4193	1.32797
$838$	−38.8662	−1.34261
$839$	−43.5820	−1.50462	−0.752309	−	0.658810i	$-0.771060\pi$
$839$	−43.5820	−1.50462	−0.752309	+	0.658810i	$0.771060\pi$
$840$	19.9337	0.687777
$841$	−27.6602	−0.953799
$842$	−37.7519	−1.30102
$843$	14.9571	0.515151
$844$	56.4528	1.94319
$845$	−11.7682	−0.404837
$846$	−16.2987	−0.560360
$847$	−25.7189	−0.883711
$848$	9.89778	0.339891
$849$	5.64803	0.193840
$850$	−18.7819	−0.644214
$851$	1.36026	0.0466292
$852$	49.9472	1.71116
$853$	−32.4389	−1.11069	−0.555344	−	0.831621i	$-0.687413\pi$
$853$	−32.4389	−1.11069	−0.555344	+	0.831621i	$0.687413\pi$
$854$	−46.9769	−1.60752
$855$	−0.778441	−0.0266221
$856$	−66.8560	−2.28509
$857$	−12.7795	−0.436540	−0.218270	−	0.975888i	$-0.570041\pi$
$857$	−12.7795	−0.436540	−0.218270	+	0.975888i	$0.570041\pi$
$858$	−5.13802	−0.175409
$859$	−51.2097	−1.74725	−0.873626	−	0.486599i	$-0.838237\pi$
$859$	−51.2097	−1.74725	−0.873626	+	0.486599i	$0.838237\pi$
$860$	3.47451	0.118480
$861$	31.9394	1.08849
$862$	26.7194	0.910068
$863$	13.7189	0.466996	0.233498	−	0.972357i	$-0.424983\pi$
$863$	13.7189	0.466996	0.233498	+	0.972357i	$0.424983\pi$
$864$	−18.9207	−0.643696
$865$	−10.7287	−0.364788
$866$	−57.7162	−1.96128
$867$	−37.8528	−1.28555
$868$	115.937	3.93515
$869$	−27.9483	−0.948081
$870$	−2.86318	−0.0970708
$871$	7.10777	0.240838
$872$	−77.7244	−2.63208
$873$	−9.68298	−0.327719
$874$	0.933207	0.0315662
$875$	3.43036	0.115967
$876$	−8.15105	−0.275398
$877$	23.9251	0.807894	0.403947	−	0.914782i	$-0.367638\pi$
$877$	23.9251	0.807894	0.403947	+	0.914782i	$0.367638\pi$
$878$	24.7620	0.835677
$879$	4.33286	0.146144
$880$	−11.6356	−0.392237
$881$	−4.05478	−0.136609	−0.0683045	−	0.997665i	$-0.521759\pi$
$881$	−4.05478	−0.136609	−0.0683045	+	0.997665i	$0.521759\pi$
$882$	24.4617	0.823668
$883$	51.7657	1.74206	0.871028	−	0.491234i	$-0.163454\pi$
$883$	51.7657	1.74206	0.871028	+	0.491234i	$0.163454\pi$
$884$	35.9805	1.21015
$885$	3.48928	0.117291
$886$	−54.3348	−1.82541
$887$	10.5310	0.353598	0.176799	−	0.984247i	$-0.443426\pi$
$887$	10.5310	0.353598	0.176799	+	0.984247i	$0.443426\pi$
$888$	−8.15888	−0.273794
$889$	−47.4745	−1.59224
$890$	20.3944	0.683622
$891$	−2.34986	−0.0787232
$892$	−26.8050	−0.897498
$893$	−1.21430	−0.0406349
$894$	38.3870	1.28385
$895$	5.20903	0.174119
$896$	50.3831	1.68318
$897$	1.05556	0.0352440
$898$	88.9739	2.96910
$899$	−8.99483	−0.299995
$900$	−8.85640	−0.295213
$901$	11.8665	0.395330
$902$	−44.7275	−1.48926
$903$	−2.69022	−0.0895250
$904$	−63.2497	−2.10365
$905$	10.7430	0.357111
$906$	−44.4472	−1.47666
$907$	43.1179	1.43171	0.715853	−	0.698251i	$-0.246038\pi$
$907$	43.1179	1.43171	0.715853	+	0.698251i	$0.246038\pi$
$908$	87.8859	2.91660
$909$	0.102281	0.00339243
$910$	−9.59349	−0.318021
$911$	9.63945	0.319369	0.159685	−	0.987168i	$-0.448952\pi$
$911$	9.63945	0.319369	0.159685	+	0.987168i	$0.448952\pi$
$912$	−2.33314	−0.0772579
$913$	−12.7221	−0.421040
$914$	80.3408	2.65744
$915$	−5.33519	−0.176376
$916$	19.0491	0.629401
$917$	13.7382	0.453674
$918$	−92.8579	−3.06477
$919$	48.8895	1.61272	0.806359	−	0.591427i	$-0.201435\pi$
$919$	48.8895	1.61272	0.806359	+	0.591427i	$0.201435\pi$
$920$	5.73484	0.189072
$921$	14.6497	0.482723
$922$	98.0831	3.23019
$923$	−12.9841	−0.427377
$924$	27.4100	0.901724
$925$	−1.40405	−0.0461649
$926$	−16.1256	−0.529920
$927$	13.6405	0.448014
$928$	4.42978	0.145415
$929$	49.9653	1.63931	0.819653	−	0.572860i	$-0.194166\pi$
$929$	49.9653	1.63931	0.819653	+	0.572860i	$0.194166\pi$
$930$	19.2219	0.630310
$931$	1.82246	0.0597288
$932$	35.2972	1.15620
$933$	−4.54655	−0.148847
$934$	35.1954	1.15163
$935$	−13.9500	−0.456213
$936$	13.3784	0.437288
$937$	−9.40745	−0.307328	−0.153664	−	0.988123i	$-0.549107\pi$
$937$	−9.40745	−0.307328	−0.153664	+	0.988123i	$0.549107\pi$
$938$	−55.3550	−1.80740
$939$	−4.10597	−0.133993
$940$	−13.8152	−0.450601
$941$	−55.9829	−1.82499	−0.912495	−	0.409087i	$-0.865847\pi$
$941$	−55.9829	−1.82499	−0.912495	+	0.409087i	$0.865847\pi$
$942$	−18.5202	−0.603422
$943$	9.18883	0.299230
$944$	−22.0987	−0.719250
$945$	16.9597	0.551700
$946$	3.76735	0.122487
$947$	39.6437	1.28825	0.644124	−	0.764921i	$-0.277222\pi$
$947$	39.6437	1.28825	0.644124	+	0.764921i	$0.277222\pi$
$948$	−63.7584	−2.07078
$949$	2.11892	0.0687830
$950$	−0.963249	−0.0312519
$951$	−9.59465	−0.311128
$952$	−151.357	−4.90550
$953$	−0.806129	−0.0261131	−0.0130565	−	0.999915i	$-0.504156\pi$
$953$	−0.806129	−0.0261131	−0.0130565	+	0.999915i	$0.504156\pi$
$954$	8.16862	0.264469
$955$	13.8569	0.448398
$956$	87.2144	2.82072
$957$	−2.12658	−0.0687426
$958$	−61.4064	−1.98395
$959$	19.4733	0.628825
$960$	2.74012	0.0884371
$961$	29.3866	0.947954
$962$	3.92663	0.126600
$963$	−22.9988	−0.741126
$964$	−4.34921	−0.140079
$965$	−14.1907	−0.456814
$966$	−8.22062	−0.264494
$967$	29.8213	0.958990	0.479495	−	0.877545i	$-0.340820\pi$
$967$	29.8213	0.958990	0.479495	+	0.877545i	$0.340820\pi$
$968$	44.3807	1.42645
$969$	−2.79720	−0.0898591
$970$	−11.9818	−0.384712
$971$	43.1288	1.38407	0.692034	−	0.721865i	$-0.256715\pi$
$971$	43.1288	1.38407	0.692034	+	0.721865i	$0.256715\pi$
$972$	−69.8683	−2.24103
$973$	62.8657	2.01538
$974$	−93.3229	−2.99026
$975$	−1.08954	−0.0348931
$976$	33.7894	1.08157
$977$	−9.28056	−0.296912	−0.148456	−	0.988919i	$-0.547430\pi$
$977$	−9.28056	−0.296912	−0.148456	+	0.988919i	$0.547430\pi$
$978$	42.1116	1.34658
$979$	15.1476	0.484121
$980$	20.7344	0.662335
$981$	−26.7376	−0.853665
$982$	−35.6492	−1.13761
$983$	−17.9567	−0.572731	−0.286366	−	0.958120i	$-0.592447\pi$
$983$	−17.9567	−0.572731	−0.286366	+	0.958120i	$0.592447\pi$
$984$	−55.1148	−1.75700
$985$	17.4404	0.555696
$986$	21.7402	0.692348
$987$	10.6967	0.340481
$988$	1.84530	0.0587067
$989$	−0.773967	−0.0246107
$990$	−9.60286	−0.305199
$991$	−41.8518	−1.32947	−0.664734	−	0.747081i	$-0.731455\pi$
$991$	−41.8518	−1.32947	−0.664734	+	0.747081i	$0.731455\pi$
$992$	−29.7392	−0.944220
$993$	1.89753	0.0602162
$994$	101.120	3.20732
$995$	25.6545	0.813302
$996$	−29.0229	−0.919626
$997$	37.9785	1.20279	0.601396	−	0.798951i	$-0.294611\pi$
$997$	37.9785	1.20279	0.601396	+	0.798951i	$0.294611\pi$
$998$	−74.5057	−2.35844
$999$	−6.94164	−0.219624

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1205.2.a.e.1.2	✓	25
5.4	even	2		6025.2.a.j.1.24		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.e.1.2	✓	25	1.1	even	1	trivial
6025.2.a.j.1.24		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)

\(f(q)\)	\(=\)	\(q-2.51976 q^{2} -0.981670 q^{3} +4.34921 q^{4} +1.00000 q^{5} +2.47358 q^{6} +3.43036 q^{7} -5.91946 q^{8} -2.03632 q^{9} +O(q^{10})\)	\(q-2.51976 q^{2} -0.981670 q^{3} +4.34921 q^{4} +1.00000 q^{5} +2.47358 q^{6} +3.43036 q^{7} -5.91946 q^{8} -2.03632 q^{9} -2.51976 q^{10} -1.87152 q^{11} -4.26949 q^{12} +1.10988 q^{13} -8.64370 q^{14} -0.981670 q^{15} +6.21722 q^{16} +7.45383 q^{17} +5.13106 q^{18} +0.382278 q^{19} +4.34921 q^{20} -3.36748 q^{21} +4.71578 q^{22} -0.968812 q^{23} +5.81095 q^{24} +1.00000 q^{25} -2.79664 q^{26} +4.94401 q^{27} +14.9194 q^{28} -1.15751 q^{29} +2.47358 q^{30} +7.77088 q^{31} -3.82700 q^{32} +1.83721 q^{33} -18.7819 q^{34} +3.43036 q^{35} -8.85640 q^{36} -1.40405 q^{37} -0.963249 q^{38} -1.08954 q^{39} -5.91946 q^{40} -9.48464 q^{41} +8.48526 q^{42} +0.798882 q^{43} -8.13962 q^{44} -2.03632 q^{45} +2.44118 q^{46} -3.17648 q^{47} -6.10325 q^{48} +4.76738 q^{49} -2.51976 q^{50} -7.31721 q^{51} +4.82711 q^{52} +1.59200 q^{53} -12.4577 q^{54} -1.87152 q^{55} -20.3059 q^{56} -0.375270 q^{57} +2.91664 q^{58} -3.55443 q^{59} -4.26949 q^{60} +5.43481 q^{61} -19.5808 q^{62} -6.98533 q^{63} -2.79129 q^{64} +1.10988 q^{65} -4.62934 q^{66} +6.40408 q^{67} +32.4183 q^{68} +0.951053 q^{69} -8.64370 q^{70} -11.6986 q^{71} +12.0539 q^{72} +1.90914 q^{73} +3.53788 q^{74} -0.981670 q^{75} +1.66261 q^{76} -6.41998 q^{77} +2.74538 q^{78} +14.9335 q^{79} +6.21722 q^{80} +1.25559 q^{81} +23.8991 q^{82} +6.79774 q^{83} -14.6459 q^{84} +7.45383 q^{85} -2.01299 q^{86} +1.13629 q^{87} +11.0784 q^{88} -8.09378 q^{89} +5.13106 q^{90} +3.80730 q^{91} -4.21357 q^{92} -7.62844 q^{93} +8.00397 q^{94} +0.382278 q^{95} +3.75685 q^{96} +4.75513 q^{97} -12.0127 q^{98} +3.81102 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 6 q^{2} + 15 q^{3} + 32 q^{4} + 25 q^{5} - q^{6} + 19 q^{7} + 15 q^{8} + 32 q^{9}+O(q^{10}) \) 25 * q + 6 * q^2 + 15 * q^3 + 32 * q^4 + 25 * q^5 - q^6 + 19 * q^7 + 15 * q^8 + 32 * q^9	\( 25 q + 6 q^{2} + 15 q^{3} + 32 q^{4} + 25 q^{5} - q^{6} + 19 q^{7} + 15 q^{8} + 32 q^{9} + 6 q^{10} + 2 q^{11} + 20 q^{12} + 14 q^{13} - 5 q^{14} + 15 q^{15} + 38 q^{16} + 7 q^{17} + 9 q^{18} + 30 q^{19} + 32 q^{20} + q^{21} + q^{22} + 43 q^{23} - 6 q^{24} + 25 q^{25} - 22 q^{26} + 42 q^{27} + 32 q^{28} - 4 q^{29} - q^{30} + 14 q^{31} + 26 q^{32} + 4 q^{33} + 7 q^{34} + 19 q^{35} + 15 q^{36} + 16 q^{37} + 14 q^{38} - 21 q^{39} + 15 q^{40} - q^{41} - 25 q^{42} + 35 q^{43} - 52 q^{44} + 32 q^{45} - 27 q^{46} + 50 q^{47} + 26 q^{48} + 46 q^{49} + 6 q^{50} - 7 q^{51} + 3 q^{52} + 4 q^{53} - 31 q^{54} + 2 q^{55} - 51 q^{56} + 2 q^{58} + 6 q^{59} + 20 q^{60} + 19 q^{61} + 28 q^{63} + 49 q^{64} + 14 q^{65} - 27 q^{66} + 65 q^{67} - 25 q^{68} + 2 q^{69} - 5 q^{70} - 34 q^{71} - 10 q^{72} + 8 q^{73} - 42 q^{74} + 15 q^{75} + 71 q^{76} + q^{77} - 59 q^{78} - 12 q^{79} + 38 q^{80} + 29 q^{81} + 11 q^{82} + 41 q^{83} - 10 q^{84} + 7 q^{85} - 13 q^{86} + 40 q^{87} - 52 q^{88} - 24 q^{89} + 9 q^{90} + 46 q^{91} + 85 q^{92} - 30 q^{93} + 14 q^{94} + 30 q^{95} - 30 q^{96} + 9 q^{97} - 64 q^{98} + 2 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 + 15 * q^3 + 32 * q^4 + 25 * q^5 - q^6 + 19 * q^7 + 15 * q^8 + 32 * q^9 + 6 * q^10 + 2 * q^11 + 20 * q^12 + 14 * q^13 - 5 * q^14 + 15 * q^15 + 38 * q^16 + 7 * q^17 + 9 * q^18 + 30 * q^19 + 32 * q^20 + q^21 + q^22 + 43 * q^23 - 6 * q^24 + 25 * q^25 - 22 * q^26 + 42 * q^27 + 32 * q^28 - 4 * q^29 - q^30 + 14 * q^31 + 26 * q^32 + 4 * q^33 + 7 * q^34 + 19 * q^35 + 15 * q^36 + 16 * q^37 + 14 * q^38 - 21 * q^39 + 15 * q^40 - q^41 - 25 * q^42 + 35 * q^43 - 52 * q^44 + 32 * q^45 - 27 * q^46 + 50 * q^47 + 26 * q^48 + 46 * q^49 + 6 * q^50 - 7 * q^51 + 3 * q^52 + 4 * q^53 - 31 * q^54 + 2 * q^55 - 51 * q^56 + 2 * q^58 + 6 * q^59 + 20 * q^60 + 19 * q^61 + 28 * q^63 + 49 * q^64 + 14 * q^65 - 27 * q^66 + 65 * q^67 - 25 * q^68 + 2 * q^69 - 5 * q^70 - 34 * q^71 - 10 * q^72 + 8 * q^73 - 42 * q^74 + 15 * q^75 + 71 * q^76 + q^77 - 59 * q^78 - 12 * q^79 + 38 * q^80 + 29 * q^81 + 11 * q^82 + 41 * q^83 - 10 * q^84 + 7 * q^85 - 13 * q^86 + 40 * q^87 - 52 * q^88 - 24 * q^89 + 9 * q^90 + 46 * q^91 + 85 * q^92 - 30 * q^93 + 14 * q^94 + 30 * q^95 - 30 * q^96 + 9 * q^97 - 64 * q^98 + 2 * q^99

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