LMFDB - Embedded newform 1205.2.a.d.1.25

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			1.25
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)

$f(q)$	$=$	$q+2.63003 q^{2} -1.40060 q^{3} +4.91705 q^{4} -1.00000 q^{5} -3.68362 q^{6} +1.05429 q^{7} +7.67192 q^{8} -1.03832 q^{9} +O(q^{10})$	\(q+2.63003 q^{2} -1.40060 q^{3} +4.91705 q^{4} -1.00000 q^{5} -3.68362 q^{6} +1.05429 q^{7} +7.67192 q^{8} -1.03832 q^{9} -2.63003 q^{10} +0.340120 q^{11} -6.88683 q^{12} +6.67580 q^{13} +2.77280 q^{14} +1.40060 q^{15} +10.3433 q^{16} +1.88405 q^{17} -2.73080 q^{18} -0.838634 q^{19} -4.91705 q^{20} -1.47663 q^{21} +0.894526 q^{22} +0.613843 q^{23} -10.7453 q^{24} +1.00000 q^{25} +17.5576 q^{26} +5.65607 q^{27} +5.18398 q^{28} +1.63368 q^{29} +3.68362 q^{30} +6.39503 q^{31} +11.8593 q^{32} -0.476373 q^{33} +4.95511 q^{34} -1.05429 q^{35} -5.10545 q^{36} -2.44693 q^{37} -2.20563 q^{38} -9.35014 q^{39} -7.67192 q^{40} -3.67966 q^{41} -3.88359 q^{42} -4.17929 q^{43} +1.67239 q^{44} +1.03832 q^{45} +1.61443 q^{46} +0.850277 q^{47} -14.4868 q^{48} -5.88848 q^{49} +2.63003 q^{50} -2.63881 q^{51} +32.8253 q^{52} -7.75319 q^{53} +14.8756 q^{54} -0.340120 q^{55} +8.08840 q^{56} +1.17459 q^{57} +4.29664 q^{58} +2.57044 q^{59} +6.88683 q^{60} -1.92112 q^{61} +16.8191 q^{62} -1.09468 q^{63} +10.5037 q^{64} -6.67580 q^{65} -1.25287 q^{66} +8.14434 q^{67} +9.26398 q^{68} -0.859749 q^{69} -2.77280 q^{70} -7.56392 q^{71} -7.96589 q^{72} -6.53710 q^{73} -6.43550 q^{74} -1.40060 q^{75} -4.12360 q^{76} +0.358584 q^{77} -24.5911 q^{78} -0.258974 q^{79} -10.3433 q^{80} -4.80695 q^{81} -9.67761 q^{82} -5.90935 q^{83} -7.26069 q^{84} -1.88405 q^{85} -10.9916 q^{86} -2.28814 q^{87} +2.60938 q^{88} +3.73938 q^{89} +2.73080 q^{90} +7.03821 q^{91} +3.01830 q^{92} -8.95688 q^{93} +2.23625 q^{94} +0.838634 q^{95} -16.6101 q^{96} +17.9225 q^{97} -15.4869 q^{98} -0.353153 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.63003	1.85971	0.929855	−	0.367925i	$-0.119932\pi$
$2$	2.63003	1.85971	0.929855	+	0.367925i	$0.119932\pi$
$3$	−1.40060	−0.808637	−0.404319	−	0.914618i	$-0.632491\pi$
$3$	−1.40060	−0.808637	−0.404319	+	0.914618i	$0.632491\pi$
$4$	4.91705	2.45852
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−3.68362	−1.50383
$7$	1.05429	0.398483	0.199241	−	0.979950i	$-0.436152\pi$
$7$	1.05429	0.398483	0.199241	+	0.979950i	$0.436152\pi$
$8$	7.67192	2.71243
$9$	−1.03832	−0.346106
$10$	−2.63003	−0.831688
$11$	0.340120	0.102550	0.0512751	−	0.998685i	$-0.483671\pi$
$11$	0.340120	0.102550	0.0512751	+	0.998685i	$0.483671\pi$
$12$	−6.88683	−1.98806
$13$	6.67580	1.85153	0.925767	−	0.378094i	$-0.123420\pi$
$13$	6.67580	1.85153	0.925767	+	0.378094i	$0.123420\pi$
$14$	2.77280	0.741063
$15$	1.40060	0.361634
$16$	10.3433	2.58582
$17$	1.88405	0.456950	0.228475	−	0.973550i	$-0.426626\pi$
$17$	1.88405	0.456950	0.228475	+	0.973550i	$0.426626\pi$
$18$	−2.73080	−0.643656
$19$	−0.838634	−0.192396	−0.0961979	−	0.995362i	$-0.530668\pi$
$19$	−0.838634	−0.192396	−0.0961979	+	0.995362i	$0.530668\pi$
$20$	−4.91705	−1.09949
$21$	−1.47663	−0.322228
$22$	0.894526	0.190714
$23$	0.613843	0.127995	0.0639976	−	0.997950i	$-0.479615\pi$
$23$	0.613843	0.127995	0.0639976	+	0.997950i	$0.479615\pi$
$24$	−10.7453	−2.19338
$25$	1.00000	0.200000
$26$	17.5576	3.44332
$27$	5.65607	1.08851
$28$	5.18398	0.979680
$29$	1.63368	0.303368	0.151684	−	0.988429i	$-0.451530\pi$
$29$	1.63368	0.303368	0.151684	+	0.988429i	$0.451530\pi$
$30$	3.68362	0.672534
$31$	6.39503	1.14858	0.574290	−	0.818652i	$-0.305278\pi$
$31$	6.39503	1.14858	0.574290	+	0.818652i	$0.305278\pi$
$32$	11.8593	2.09644
$33$	−0.476373	−0.0829259
$34$	4.95511	0.849795
$35$	−1.05429	−0.178207
$36$	−5.10545	−0.850909
$37$	−2.44693	−0.402273	−0.201137	−	0.979563i	$-0.564464\pi$
$37$	−2.44693	−0.402273	−0.201137	+	0.979563i	$0.564464\pi$
$38$	−2.20563	−0.357800
$39$	−9.35014	−1.49722
$40$	−7.67192	−1.21304
$41$	−3.67966	−0.574666	−0.287333	−	0.957831i	$-0.592769\pi$
$41$	−3.67966	−0.574666	−0.287333	+	0.957831i	$0.592769\pi$
$42$	−3.88359	−0.599251
$43$	−4.17929	−0.637335	−0.318668	−	0.947866i	$-0.603235\pi$
$43$	−4.17929	−0.637335	−0.318668	+	0.947866i	$0.603235\pi$
$44$	1.67239	0.252122
$45$	1.03832	0.154783
$46$	1.61443	0.238034
$47$	0.850277	0.124026	0.0620128	−	0.998075i	$-0.480248\pi$
$47$	0.850277	0.124026	0.0620128	+	0.998075i	$0.480248\pi$
$48$	−14.4868	−2.09099
$49$	−5.88848	−0.841211
$50$	2.63003	0.371942
$51$	−2.63881	−0.369507
$52$	32.8253	4.55204
$53$	−7.75319	−1.06498	−0.532491	−	0.846435i	$-0.678744\pi$
$53$	−7.75319	−1.06498	−0.532491	+	0.846435i	$0.678744\pi$
$54$	14.8756	2.02432
$55$	−0.340120	−0.0458618
$56$	8.08840	1.08086
$57$	1.17459	0.155578
$58$	4.29664	0.564176
$59$	2.57044	0.334642	0.167321	−	0.985902i	$-0.446488\pi$
$59$	2.57044	0.334642	0.167321	+	0.985902i	$0.446488\pi$
$60$	6.88683	0.889085
$61$	−1.92112	−0.245975	−0.122987	−	0.992408i	$-0.539247\pi$
$61$	−1.92112	−0.245975	−0.122987	+	0.992408i	$0.539247\pi$
$62$	16.8191	2.13603
$63$	−1.09468	−0.137917
$64$	10.5037	1.31296
$65$	−6.67580	−0.828031
$66$	−1.25287	−0.154218
$67$	8.14434	0.994989	0.497495	−	0.867467i	$-0.334253\pi$
$67$	8.14434	0.994989	0.497495	+	0.867467i	$0.334253\pi$
$68$	9.26398	1.12342
$69$	−0.859749	−0.103502
$70$	−2.77280	−0.331413
$71$	−7.56392	−0.897672	−0.448836	−	0.893614i	$-0.648161\pi$
$71$	−7.56392	−0.897672	−0.448836	+	0.893614i	$0.648161\pi$
$72$	−7.96589	−0.938789
$73$	−6.53710	−0.765109	−0.382555	−	0.923933i	$-0.624956\pi$
$73$	−6.53710	−0.765109	−0.382555	+	0.923933i	$0.624956\pi$
$74$	−6.43550	−0.748112
$75$	−1.40060	−0.161727
$76$	−4.12360	−0.473010
$77$	0.358584	0.0408645
$78$	−24.5911	−2.78440
$79$	−0.258974	−0.0291368	−0.0145684	−	0.999894i	$-0.504637\pi$
$79$	−0.258974	−0.0291368	−0.0145684	+	0.999894i	$0.504637\pi$
$80$	−10.3433	−1.15641
$81$	−4.80695	−0.534105
$82$	−9.67761	−1.06871
$83$	−5.90935	−0.648635	−0.324317	−	0.945948i	$-0.605135\pi$
$83$	−5.90935	−0.648635	−0.324317	+	0.945948i	$0.605135\pi$
$84$	−7.26069	−0.792206
$85$	−1.88405	−0.204354
$86$	−10.9916	−1.18526
$87$	−2.28814	−0.245314
$88$	2.60938	0.278161
$89$	3.73938	0.396373	0.198187	−	0.980164i	$-0.436495\pi$
$89$	3.73938	0.396373	0.198187	+	0.980164i	$0.436495\pi$
$90$	2.73080	0.287852
$91$	7.03821	0.737805
$92$	3.01830	0.314679
$93$	−8.95688	−0.928785
$94$	2.23625	0.230652
$95$	0.838634	0.0860420
$96$	−16.6101	−1.69526
$97$	17.9225	1.81975	0.909877	−	0.414879i	$-0.136176\pi$
$97$	17.9225	1.81975	0.909877	+	0.414879i	$0.136176\pi$
$98$	−15.4869	−1.56441
$99$	−0.353153	−0.0354932
$100$	4.91705	0.491705
$101$	−0.845554	−0.0841358	−0.0420679	−	0.999115i	$-0.513395\pi$
$101$	−0.845554	−0.0841358	−0.0420679	+	0.999115i	$0.513395\pi$
$102$	−6.94014	−0.687176
$103$	0.956502	0.0942469	0.0471235	−	0.998889i	$-0.484995\pi$
$103$	0.956502	0.0942469	0.0471235	+	0.998889i	$0.484995\pi$
$104$	51.2163	5.02217
$105$	1.47663	0.144105
$106$	−20.3911	−1.98056
$107$	−6.25907	−0.605087	−0.302544	−	0.953136i	$-0.597836\pi$
$107$	−6.25907	−0.605087	−0.302544	+	0.953136i	$0.597836\pi$
$108$	27.8112	2.67613
$109$	−12.6376	−1.21047	−0.605233	−	0.796048i	$-0.706920\pi$
$109$	−12.6376	−1.21047	−0.605233	+	0.796048i	$0.706920\pi$
$110$	−0.894526	−0.0852897
$111$	3.42718	0.325293
$112$	10.9048	1.03040
$113$	−8.31845	−0.782534	−0.391267	−	0.920277i	$-0.627963\pi$
$113$	−8.31845	−0.782534	−0.391267	+	0.920277i	$0.627963\pi$
$114$	3.08921	0.289331
$115$	−0.613843	−0.0572412
$116$	8.03291	0.745837
$117$	−6.93160	−0.640826
$118$	6.76032	0.622338
$119$	1.98633	0.182087
$120$	10.7453	0.980908
$121$	−10.8843	−0.989483
$122$	−5.05261	−0.457442
$123$	5.15373	0.464697
$124$	31.4447	2.82381
$125$	−1.00000	−0.0894427
$126$	−2.87905	−0.256486
$127$	4.71260	0.418176	0.209088	−	0.977897i	$-0.432951\pi$
$127$	4.71260	0.418176	0.209088	+	0.977897i	$0.432951\pi$
$128$	3.90639	0.345279
$129$	5.85352	0.515373
$130$	−17.5576	−1.53990
$131$	−13.5244	−1.18163	−0.590814	−	0.806808i	$-0.701193\pi$
$131$	−13.5244	−1.18163	−0.590814	+	0.806808i	$0.701193\pi$
$132$	−2.34235	−0.203875
$133$	−0.884160	−0.0766664
$134$	21.4198	1.85039
$135$	−5.65607	−0.486797
$136$	14.4543	1.23945
$137$	−12.2503	−1.04661	−0.523306	−	0.852145i	$-0.675302\pi$
$137$	−12.2503	−1.04661	−0.523306	+	0.852145i	$0.675302\pi$
$138$	−2.26117	−0.192483
$139$	−11.7399	−0.995762	−0.497881	−	0.867245i	$-0.665888\pi$
$139$	−11.7399	−0.995762	−0.497881	+	0.867245i	$0.665888\pi$
$140$	−5.18398	−0.438126
$141$	−1.19090	−0.100292
$142$	−19.8933	−1.66941
$143$	2.27058	0.189875
$144$	−10.7396	−0.894967
$145$	−1.63368	−0.135670
$146$	−17.1928	−1.42288
$147$	8.24741	0.680235
$148$	−12.0317	−0.988999
$149$	16.7360	1.37107	0.685533	−	0.728042i	$-0.259569\pi$
$149$	16.7360	1.37107	0.685533	+	0.728042i	$0.259569\pi$
$150$	−3.68362	−0.300766
$151$	5.05216	0.411139	0.205570	−	0.978642i	$-0.434095\pi$
$151$	5.05216	0.411139	0.205570	+	0.978642i	$0.434095\pi$
$152$	−6.43393	−0.521861
$153$	−1.95624	−0.158153
$154$	0.943087	0.0759961
$155$	−6.39503	−0.513661
$156$	−45.9751	−3.68095
$157$	2.40755	0.192144	0.0960718	−	0.995374i	$-0.469372\pi$
$157$	2.40755	0.192144	0.0960718	+	0.995374i	$0.469372\pi$
$158$	−0.681109	−0.0541861
$159$	10.8591	0.861185
$160$	−11.8593	−0.937558
$161$	0.647166	0.0510039
$162$	−12.6424	−0.993282
$163$	−22.4228	−1.75629	−0.878145	−	0.478395i	$-0.841219\pi$
$163$	−22.4228	−1.75629	−0.878145	+	0.478395i	$0.841219\pi$
$164$	−18.0931	−1.41283
$165$	0.476373	0.0370856
$166$	−15.5417	−1.20627
$167$	2.55035	0.197352	0.0986760	−	0.995120i	$-0.468539\pi$
$167$	2.55035	0.197352	0.0986760	+	0.995120i	$0.468539\pi$
$168$	−11.3286	−0.874023
$169$	31.5663	2.42818
$170$	−4.95511	−0.380040
$171$	0.870767	0.0665892
$172$	−20.5498	−1.56691
$173$	−14.3207	−1.08878	−0.544391	−	0.838832i	$-0.683239\pi$
$173$	−14.3207	−1.08878	−0.544391	+	0.838832i	$0.683239\pi$
$174$	−6.01787	−0.456214
$175$	1.05429	0.0796966
$176$	3.51796	0.265176
$177$	−3.60016	−0.270604
$178$	9.83467	0.737139
$179$	4.89603	0.365946	0.182973	−	0.983118i	$-0.441428\pi$
$179$	4.89603	0.365946	0.182973	+	0.983118i	$0.441428\pi$
$180$	5.10545	0.380538
$181$	11.3118	0.840797	0.420398	−	0.907340i	$-0.361890\pi$
$181$	11.3118	0.840797	0.420398	+	0.907340i	$0.361890\pi$
$182$	18.5107	1.37210
$183$	2.69073	0.198904
$184$	4.70936	0.347179
$185$	2.44693	0.179902
$186$	−23.5569	−1.72727
$187$	0.640805	0.0468603
$188$	4.18086	0.304920
$189$	5.96312	0.433753
$190$	2.20563	0.160013
$191$	22.7536	1.64640	0.823198	−	0.567755i	$-0.192188\pi$
$191$	22.7536	1.64640	0.823198	+	0.567755i	$0.192188\pi$
$192$	−14.7114	−1.06171
$193$	−26.7507	−1.92556	−0.962780	−	0.270287i	$-0.912881\pi$
$193$	−26.7507	−1.92556	−0.962780	+	0.270287i	$0.912881\pi$
$194$	47.1367	3.38421
$195$	9.35014	0.669577
$196$	−28.9540	−2.06814
$197$	−10.3126	−0.734746	−0.367373	−	0.930074i	$-0.619743\pi$
$197$	−10.3126	−0.734746	−0.367373	+	0.930074i	$0.619743\pi$
$198$	−0.928801	−0.0660070
$199$	7.83878	0.555676	0.277838	−	0.960628i	$-0.410382\pi$
$199$	7.83878	0.555676	0.277838	+	0.960628i	$0.410382\pi$
$200$	7.67192	0.542487
$201$	−11.4070	−0.804585
$202$	−2.22383	−0.156468
$203$	1.72237	0.120887
$204$	−12.9751	−0.908442
$205$	3.67966	0.256999
$206$	2.51563	0.175272
$207$	−0.637364	−0.0442998
$208$	69.0497	4.78773
$209$	−0.285236	−0.0197302
$210$	3.88359	0.267993
$211$	22.0494	1.51795	0.758973	−	0.651122i	$-0.225702\pi$
$211$	22.0494	1.51795	0.758973	+	0.651122i	$0.225702\pi$
$212$	−38.1228	−2.61829
$213$	10.5940	0.725891
$214$	−16.4615	−1.12529
$215$	4.17929	0.285025
$216$	43.3929	2.95252
$217$	6.74219	0.457690
$218$	−33.2374	−2.25112
$219$	9.15587	0.618696
$220$	−1.67239	−0.112752
$221$	12.5776	0.846058
$222$	9.01357	0.604951
$223$	13.3306	0.892680	0.446340	−	0.894863i	$-0.352727\pi$
$223$	13.3306	0.892680	0.446340	+	0.894863i	$0.352727\pi$
$224$	12.5031	0.835396
$225$	−1.03832	−0.0692211
$226$	−21.8778	−1.45529
$227$	−0.973112	−0.0645877	−0.0322939	−	0.999478i	$-0.510281\pi$
$227$	−0.973112	−0.0645877	−0.0322939	+	0.999478i	$0.510281\pi$
$228$	5.77552	0.382493
$229$	23.3499	1.54301	0.771504	−	0.636225i	$-0.219505\pi$
$229$	23.3499	1.54301	0.771504	+	0.636225i	$0.219505\pi$
$230$	−1.61443	−0.106452
$231$	−0.502233	−0.0330445
$232$	12.5335	0.822865
$233$	−8.88083	−0.581802	−0.290901	−	0.956753i	$-0.593955\pi$
$233$	−8.88083	−0.581802	−0.290901	+	0.956753i	$0.593955\pi$
$234$	−18.2303	−1.19175
$235$	−0.850277	−0.0554660
$236$	12.6390	0.822727
$237$	0.362719	0.0235611
$238$	5.22411	0.338629
$239$	−26.7991	−1.73349	−0.866746	−	0.498750i	$-0.833792\pi$
$239$	−26.7991	−1.73349	−0.866746	+	0.498750i	$0.833792\pi$
$240$	14.4868	0.935119
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	−28.6261	−1.84015
$243$	−10.2356	−0.656614
$244$	−9.44626	−0.604735
$245$	5.88848	0.376201
$246$	13.5545	0.864201
$247$	−5.59855	−0.356227
$248$	49.0622	3.11545
$249$	8.27664	0.524510
$250$	−2.63003	−0.166338
$251$	27.0375	1.70659	0.853296	−	0.521427i	$-0.174600\pi$
$251$	27.0375	1.70659	0.853296	+	0.521427i	$0.174600\pi$
$252$	−5.38261	−0.339073
$253$	0.208781	0.0131259
$254$	12.3943	0.777686
$255$	2.63881	0.165248
$256$	−10.7334	−0.670838
$257$	−14.2022	−0.885909	−0.442954	−	0.896544i	$-0.646070\pi$
$257$	−14.2022	−0.885909	−0.442954	+	0.896544i	$0.646070\pi$
$258$	15.3949	0.958445
$259$	−2.57977	−0.160299
$260$	−32.8253	−2.03574
$261$	−1.69628	−0.104997
$262$	−35.5694	−2.19749
$263$	−6.25591	−0.385756	−0.192878	−	0.981223i	$-0.561782\pi$
$263$	−6.25591	−0.385756	−0.192878	+	0.981223i	$0.561782\pi$
$264$	−3.65470	−0.224931
$265$	7.75319	0.476275
$266$	−2.32537	−0.142577
$267$	−5.23737	−0.320522
$268$	40.0461	2.44621
$269$	−18.2012	−1.10975	−0.554873	−	0.831935i	$-0.687233\pi$
$269$	−18.2012	−1.10975	−0.554873	+	0.831935i	$0.687233\pi$
$270$	−14.8756	−0.905302
$271$	2.18669	0.132832	0.0664160	−	0.997792i	$-0.478844\pi$
$271$	2.18669	0.132832	0.0664160	+	0.997792i	$0.478844\pi$
$272$	19.4873	1.18159
$273$	−9.85772	−0.596616
$274$	−32.2186	−1.94640
$275$	0.340120	0.0205100
$276$	−4.22743	−0.254461
$277$	30.7385	1.84690	0.923449	−	0.383720i	$-0.125357\pi$
$277$	30.7385	1.84690	0.923449	+	0.383720i	$0.125357\pi$
$278$	−30.8762	−1.85183
$279$	−6.64006	−0.397530
$280$	−8.08840	−0.483375
$281$	−11.4664	−0.684029	−0.342014	−	0.939695i	$-0.611109\pi$
$281$	−11.4664	−0.684029	−0.342014	+	0.939695i	$0.611109\pi$
$282$	−3.13210	−0.186514
$283$	−7.18393	−0.427040	−0.213520	−	0.976939i	$-0.568493\pi$
$283$	−7.18393	−0.427040	−0.213520	+	0.976939i	$0.568493\pi$
$284$	−37.1922	−2.20695
$285$	−1.17459	−0.0695768
$286$	5.97168	0.353113
$287$	−3.87941	−0.228995
$288$	−12.3137	−0.725590
$289$	−13.4503	−0.791197
$290$	−4.29664	−0.252307
$291$	−25.1023	−1.47152
$292$	−32.1432	−1.88104
$293$	14.3751	0.839805	0.419903	−	0.907569i	$-0.362064\pi$
$293$	14.3751	0.839805	0.419903	+	0.907569i	$0.362064\pi$
$294$	21.6909	1.26504
$295$	−2.57044	−0.149657
$296$	−18.7727	−1.09114
$297$	1.92374	0.111627
$298$	44.0161	2.54979
$299$	4.09790	0.236987
$300$	−6.88683	−0.397611
$301$	−4.40617	−0.253967
$302$	13.2873	0.764600
$303$	1.18428	0.0680354
$304$	−8.67422	−0.497501
$305$	1.92112	0.110003
$306$	−5.14498	−0.294119
$307$	27.1770	1.55107	0.775537	−	0.631302i	$-0.217479\pi$
$307$	27.1770	1.55107	0.775537	+	0.631302i	$0.217479\pi$
$308$	1.76318	0.100466
$309$	−1.33968	−0.0762116
$310$	−16.8191	−0.955261
$311$	2.64295	0.149868	0.0749341	−	0.997188i	$-0.476125\pi$
$311$	2.64295	0.149868	0.0749341	+	0.997188i	$0.476125\pi$
$312$	−71.7335	−4.06111
$313$	1.22280	0.0691167	0.0345584	−	0.999403i	$-0.488998\pi$
$313$	1.22280	0.0691167	0.0345584	+	0.999403i	$0.488998\pi$
$314$	6.33193	0.357332
$315$	1.09468	0.0616784
$316$	−1.27339	−0.0716337
$317$	−7.27855	−0.408804	−0.204402	−	0.978887i	$-0.565525\pi$
$317$	−7.27855	−0.408804	−0.204402	+	0.978887i	$0.565525\pi$
$318$	28.5598	1.60155
$319$	0.555649	0.0311104
$320$	−10.5037	−0.587173
$321$	8.76646	0.489296
$322$	1.70207	0.0948524
$323$	−1.58003	−0.0879152
$324$	−23.6360	−1.31311
$325$	6.67580	0.370307
$326$	−58.9726	−3.26619
$327$	17.7003	0.978828
$328$	−28.2301	−1.55874
$329$	0.896436	0.0494221
$330$	1.25287	0.0689685
$331$	21.7820	1.19725	0.598624	−	0.801030i	$-0.295714\pi$
$331$	21.7820	1.19725	0.598624	+	0.801030i	$0.295714\pi$
$332$	−29.0565	−1.59469
$333$	2.54069	0.139229
$334$	6.70749	0.367018
$335$	−8.14434	−0.444973
$336$	−15.2732	−0.833224
$337$	−10.3985	−0.566444	−0.283222	−	0.959054i	$-0.591403\pi$
$337$	−10.3985	−0.566444	−0.283222	+	0.959054i	$0.591403\pi$
$338$	83.0204	4.51571
$339$	11.6508	0.632786
$340$	−9.26398	−0.502410
$341$	2.17508	0.117787
$342$	2.29014	0.123837
$343$	−13.5881	−0.733691
$344$	−32.0632	−1.72873
$345$	0.859749	0.0462874
$346$	−37.6638	−2.02482
$347$	−33.3363	−1.78959	−0.894795	−	0.446478i	$-0.852678\pi$
$347$	−33.3363	−1.78959	−0.894795	+	0.446478i	$0.852678\pi$
$348$	−11.2509	−0.603111
$349$	−1.05667	−0.0565625	−0.0282813	−	0.999600i	$-0.509003\pi$
$349$	−1.05667	−0.0565625	−0.0282813	+	0.999600i	$0.509003\pi$
$350$	2.77280	0.148213
$351$	37.7588	2.01542
$352$	4.03358	0.214990
$353$	−20.8908	−1.11190	−0.555952	−	0.831214i	$-0.687646\pi$
$353$	−20.8908	−1.11190	−0.555952	+	0.831214i	$0.687646\pi$
$354$	−9.46852	−0.503246
$355$	7.56392	0.401451
$356$	18.3867	0.974493
$357$	−2.78206	−0.147242
$358$	12.8767	0.680554
$359$	−4.92712	−0.260043	−0.130022	−	0.991511i	$-0.541505\pi$
$359$	−4.92712	−0.260043	−0.130022	+	0.991511i	$0.541505\pi$
$360$	7.96589	0.419839
$361$	−18.2967	−0.962984
$362$	29.7503	1.56364
$363$	15.2446	0.800133
$364$	34.6072	1.81391
$365$	6.53710	0.342167
$366$	7.07669	0.369904
$367$	17.5814	0.917741	0.458870	−	0.888503i	$-0.348254\pi$
$367$	17.5814	0.917741	0.458870	+	0.888503i	$0.348254\pi$
$368$	6.34915	0.330972
$369$	3.82065	0.198895
$370$	6.43550	0.334566
$371$	−8.17408	−0.424377
$372$	−44.0414	−2.28344
$373$	−5.62638	−0.291323	−0.145661	−	0.989334i	$-0.546531\pi$
$373$	−5.62638	−0.291323	−0.145661	+	0.989334i	$0.546531\pi$
$374$	1.68533	0.0871466
$375$	1.40060	0.0723267
$376$	6.52326	0.336412
$377$	10.9062	0.561695
$378$	15.6832	0.806655
$379$	33.1203	1.70128	0.850639	−	0.525751i	$-0.176215\pi$
$379$	33.1203	1.70128	0.850639	+	0.525751i	$0.176215\pi$
$380$	4.12360	0.211536
$381$	−6.60047	−0.338152
$382$	59.8427	3.06182
$383$	12.0598	0.616229	0.308115	−	0.951349i	$-0.400302\pi$
$383$	12.0598	0.616229	0.308115	+	0.951349i	$0.400302\pi$
$384$	−5.47129	−0.279206
$385$	−0.358584	−0.0182751
$386$	−70.3552	−3.58098
$387$	4.33942	0.220585
$388$	88.1258	4.47391
$389$	31.1477	1.57925	0.789625	−	0.613590i	$-0.210275\pi$
$389$	31.1477	1.57925	0.789625	+	0.613590i	$0.210275\pi$
$390$	24.5911	1.24522
$391$	1.15651	0.0584874
$392$	−45.1760	−2.28173
$393$	18.9422	0.955509
$394$	−27.1226	−1.36641
$395$	0.258974	0.0130304
$396$	−1.73647	−0.0872608
$397$	−16.5885	−0.832553	−0.416277	−	0.909238i	$-0.636665\pi$
$397$	−16.5885	−0.832553	−0.416277	+	0.909238i	$0.636665\pi$
$398$	20.6162	1.03340
$399$	1.23836	0.0619953
$400$	10.3433	0.517164
$401$	32.2622	1.61110	0.805549	−	0.592529i	$-0.201870\pi$
$401$	32.2622	1.61110	0.805549	+	0.592529i	$0.201870\pi$
$402$	−30.0006	−1.49630
$403$	42.6919	2.12664
$404$	−4.15763	−0.206850
$405$	4.80695	0.238859
$406$	4.52988	0.224814
$407$	−0.832252	−0.0412532
$408$	−20.2447	−1.00226
$409$	−20.5807	−1.01765	−0.508825	−	0.860870i	$-0.669920\pi$
$409$	−20.5807	−1.01765	−0.508825	+	0.860870i	$0.669920\pi$
$410$	9.67761	0.477943
$411$	17.1578	0.846330
$412$	4.70317	0.231708
$413$	2.70998	0.133349
$414$	−1.67628	−0.0823849
$415$	5.90935	0.290078
$416$	79.1702	3.88164
$417$	16.4429	0.805210
$418$	−0.750180	−0.0366925
$419$	−25.8936	−1.26499	−0.632493	−	0.774566i	$-0.717968\pi$
$419$	−25.8936	−1.26499	−0.632493	+	0.774566i	$0.717968\pi$
$420$	7.26069	0.354285
$421$	25.0218	1.21949	0.609743	−	0.792599i	$-0.291273\pi$
$421$	25.0218	1.21949	0.609743	+	0.792599i	$0.291273\pi$
$422$	57.9906	2.82294
$423$	−0.882857	−0.0429260
$424$	−59.4819	−2.88870
$425$	1.88405	0.0913900
$426$	27.8626	1.34995
$427$	−2.02541	−0.0980166
$428$	−30.7762	−1.48762
$429$	−3.18017	−0.153540
$430$	10.9916	0.530064
$431$	−6.85922	−0.330397	−0.165199	−	0.986260i	$-0.552826\pi$
$431$	−6.85922	−0.330397	−0.165199	+	0.986260i	$0.552826\pi$
$432$	58.5023	2.81469
$433$	−24.6281	−1.18355	−0.591776	−	0.806103i	$-0.701573\pi$
$433$	−24.6281	−1.18355	−0.591776	+	0.806103i	$0.701573\pi$
$434$	17.7321	0.851170
$435$	2.28814	0.109708
$436$	−62.1399	−2.97596
$437$	−0.514790	−0.0246257
$438$	24.0802	1.15060
$439$	−33.4693	−1.59740	−0.798701	−	0.601729i	$-0.794479\pi$
$439$	−33.4693	−1.59740	−0.798701	+	0.601729i	$0.794479\pi$
$440$	−2.60938	−0.124397
$441$	6.11411	0.291148
$442$	33.0794	1.57342
$443$	21.0492	1.00008	0.500039	−	0.866003i	$-0.333319\pi$
$443$	21.0492	1.00008	0.500039	+	0.866003i	$0.333319\pi$
$444$	16.8516	0.799742
$445$	−3.73938	−0.177263
$446$	35.0598	1.66013
$447$	−23.4405	−1.10870
$448$	11.0739	0.523191
$449$	20.9547	0.988913	0.494456	−	0.869202i	$-0.335367\pi$
$449$	20.9547	0.988913	0.494456	+	0.869202i	$0.335367\pi$
$450$	−2.73080	−0.128731
$451$	−1.25153	−0.0589321
$452$	−40.9022	−1.92388
$453$	−7.07607	−0.332463
$454$	−2.55931	−0.120114
$455$	−7.03821	−0.329956
$456$	9.01137	0.421996
$457$	7.68098	0.359301	0.179650	−	0.983731i	$-0.442503\pi$
$457$	7.68098	0.359301	0.179650	+	0.983731i	$0.442503\pi$
$458$	61.4110	2.86955
$459$	10.6563	0.497395
$460$	−3.01830	−0.140729
$461$	11.9447	0.556319	0.278160	−	0.960535i	$-0.410276\pi$
$461$	11.9447	0.556319	0.278160	+	0.960535i	$0.410276\pi$
$462$	−1.32089	−0.0614533
$463$	27.7857	1.29131	0.645655	−	0.763630i	$-0.276585\pi$
$463$	27.7857	1.29131	0.645655	+	0.763630i	$0.276585\pi$
$464$	16.8977	0.784454
$465$	8.95688	0.415365
$466$	−23.3568	−1.08198
$467$	−0.688082	−0.0318407	−0.0159203	−	0.999873i	$-0.505068\pi$
$467$	−0.688082	−0.0318407	−0.0159203	+	0.999873i	$0.505068\pi$
$468$	−34.0830	−1.57549
$469$	8.58646	0.396486
$470$	−2.23625	−0.103151
$471$	−3.37202	−0.155375
$472$	19.7202	0.907696
$473$	−1.42146	−0.0653588
$474$	0.953962	0.0438169
$475$	−0.838634	−0.0384791
$476$	9.76689	0.447665
$477$	8.05027	0.368596
$478$	−70.4825	−3.22379
$479$	31.3059	1.43040	0.715202	−	0.698918i	$-0.246335\pi$
$479$	31.3059	1.43040	0.715202	+	0.698918i	$0.246335\pi$
$480$	16.6101	0.758144
$481$	−16.3352	−0.744823
$482$	2.63003	0.119795
$483$	−0.906422	−0.0412436
$484$	−53.5187	−2.43267
$485$	−17.9225	−0.813818
$486$	−26.9199	−1.22111
$487$	19.6517	0.890505	0.445253	−	0.895405i	$-0.353114\pi$
$487$	19.6517	0.890505	0.445253	+	0.895405i	$0.353114\pi$
$488$	−14.7387	−0.667190
$489$	31.4054	1.42020
$490$	15.4869	0.699626
$491$	−1.74379	−0.0786963	−0.0393481	−	0.999226i	$-0.512528\pi$
$491$	−1.74379	−0.0786963	−0.0393481	+	0.999226i	$0.512528\pi$
$492$	25.3412	1.14247
$493$	3.07795	0.138624
$494$	−14.7244	−0.662480
$495$	0.353153	0.0158730
$496$	66.1455	2.97002
$497$	−7.97453	−0.357707
$498$	21.7678	0.975438
$499$	12.1886	0.545637	0.272818	−	0.962066i	$-0.412044\pi$
$499$	12.1886	0.545637	0.272818	+	0.962066i	$0.412044\pi$
$500$	−4.91705	−0.219897
$501$	−3.57202	−0.159586
$502$	71.1094	3.17377
$503$	3.81849	0.170258	0.0851289	−	0.996370i	$-0.472870\pi$
$503$	3.81849	0.170258	0.0851289	+	0.996370i	$0.472870\pi$
$504$	−8.39832	−0.374091
$505$	0.845554	0.0376267
$506$	0.549099	0.0244104
$507$	−44.2119	−1.96352
$508$	23.1721	1.02809
$509$	27.0780	1.20021	0.600106	−	0.799921i	$-0.295125\pi$
$509$	27.0780	1.20021	0.600106	+	0.799921i	$0.295125\pi$
$510$	6.94014	0.307314
$511$	−6.89197	−0.304883
$512$	−36.0420	−1.59284
$513$	−4.74337	−0.209425
$514$	−37.3522	−1.64753
$515$	−0.956502	−0.0421485
$516$	28.7820	1.26706
$517$	0.289197	0.0127188
$518$	−6.78486	−0.298110
$519$	20.0576	0.880430
$520$	−51.2163	−2.24598
$521$	42.2190	1.84965	0.924823	−	0.380397i	$-0.124213\pi$
$521$	42.2190	1.84965	0.924823	+	0.380397i	$0.124213\pi$
$522$	−4.46127	−0.195264
$523$	11.7103	0.512057	0.256028	−	0.966669i	$-0.417586\pi$
$523$	11.7103	0.512057	0.256028	+	0.966669i	$0.417586\pi$
$524$	−66.4999	−2.90506
$525$	−1.47663	−0.0644456
$526$	−16.4532	−0.717394
$527$	12.0486	0.524844
$528$	−4.92726	−0.214431
$529$	−22.6232	−0.983617
$530$	20.3911	0.885733
$531$	−2.66893	−0.115822
$532$	−4.34746	−0.188486
$533$	−24.5647	−1.06401
$534$	−13.7744	−0.596078
$535$	6.25907	0.270603
$536$	62.4827	2.69884
$537$	−6.85738	−0.295918
$538$	−47.8696	−2.06380
$539$	−2.00279	−0.0862664
$540$	−27.8112	−1.19680
$541$	−45.8157	−1.96977	−0.984886	−	0.173204i	$-0.944588\pi$
$541$	−45.8157	−1.96977	−0.984886	+	0.173204i	$0.944588\pi$
$542$	5.75106	0.247029
$543$	−15.8433	−0.679900
$544$	22.3435	0.957969
$545$	12.6376	0.541337
$546$	−25.9261	−1.10953
$547$	9.27779	0.396690	0.198345	−	0.980132i	$-0.436443\pi$
$547$	9.27779	0.396690	0.198345	+	0.980132i	$0.436443\pi$
$548$	−60.2353	−2.57312
$549$	1.99473	0.0851332
$550$	0.894526	0.0381427
$551$	−1.37006	−0.0583666
$552$	−6.59593	−0.280742
$553$	−0.273033	−0.0116105
$554$	80.8432	3.43470
$555$	−3.42718	−0.145476
$556$	−57.7255	−2.44811
$557$	−22.4092	−0.949507	−0.474753	−	0.880119i	$-0.657463\pi$
$557$	−22.4092	−0.949507	−0.474753	+	0.880119i	$0.657463\pi$
$558$	−17.4636	−0.739291
$559$	−27.9001	−1.18005
$560$	−10.9048	−0.460811
$561$	−0.897512	−0.0378930
$562$	−30.1570	−1.27210
$563$	29.0486	1.22425	0.612126	−	0.790760i	$-0.290314\pi$
$563$	29.0486	1.22425	0.612126	+	0.790760i	$0.290314\pi$
$564$	−5.85571	−0.246570
$565$	8.31845	0.349960
$566$	−18.8939	−0.794171
$567$	−5.06790	−0.212832
$568$	−58.0298	−2.43488
$569$	−27.4610	−1.15123	−0.575613	−	0.817722i	$-0.695237\pi$
$569$	−27.4610	−1.15123	−0.575613	+	0.817722i	$0.695237\pi$
$570$	−3.08921	−0.129393
$571$	−43.0161	−1.80017	−0.900083	−	0.435718i	$-0.856495\pi$
$571$	−43.0161	−1.80017	−0.900083	+	0.435718i	$0.856495\pi$
$572$	11.1645	0.466813
$573$	−31.8688	−1.33134
$574$	−10.2030	−0.425864
$575$	0.613843	0.0255990
$576$	−10.9061	−0.454422
$577$	−3.73661	−0.155557	−0.0777785	−	0.996971i	$-0.524783\pi$
$577$	−3.73661	−0.155557	−0.0777785	+	0.996971i	$0.524783\pi$
$578$	−35.3748	−1.47140
$579$	37.4671	1.55708
$580$	−8.03291	−0.333548
$581$	−6.23014	−0.258470
$582$	−66.0197	−2.73660
$583$	−2.63702	−0.109214
$584$	−50.1521	−2.07531
$585$	6.93160	0.286586
$586$	37.8070	1.56179
$587$	29.2099	1.20562	0.602812	−	0.797884i	$-0.294047\pi$
$587$	29.2099	1.20562	0.602812	+	0.797884i	$0.294047\pi$
$588$	40.5529	1.67237
$589$	−5.36308	−0.220982
$590$	−6.76032	−0.278318
$591$	14.4439	0.594143
$592$	−25.3093	−1.04021
$593$	−34.1877	−1.40392	−0.701961	−	0.712215i	$-0.747692\pi$
$593$	−34.1877	−1.40392	−0.701961	+	0.712215i	$0.747692\pi$
$594$	5.05950	0.207594
$595$	−1.98633	−0.0814316
$596$	82.2917	3.37080
$597$	−10.9790	−0.449341
$598$	10.7776	0.440728
$599$	21.0328	0.859378	0.429689	−	0.902977i	$-0.358623\pi$
$599$	21.0328	0.859378	0.429689	+	0.902977i	$0.358623\pi$
$600$	−10.7453	−0.438675
$601$	−27.0695	−1.10419	−0.552093	−	0.833783i	$-0.686171\pi$
$601$	−27.0695	−1.10419	−0.552093	+	0.833783i	$0.686171\pi$
$602$	−11.5883	−0.472306
$603$	−8.45640	−0.344371
$604$	24.8417	1.01080
$605$	10.8843	0.442510
$606$	3.11470	0.126526
$607$	37.6086	1.52649	0.763244	−	0.646111i	$-0.223606\pi$
$607$	37.6086	1.52649	0.763244	+	0.646111i	$0.223606\pi$
$608$	−9.94558	−0.403347
$609$	−2.41235	−0.0977535
$610$	5.05261	0.204574
$611$	5.67628	0.229638
$612$	−9.61895	−0.388823
$613$	−1.33214	−0.0538046	−0.0269023	−	0.999638i	$-0.508564\pi$
$613$	−1.33214	−0.0538046	−0.0269023	+	0.999638i	$0.508564\pi$
$614$	71.4763	2.88455
$615$	−5.15373	−0.207819
$616$	2.75103	0.110842
$617$	−18.6238	−0.749767	−0.374884	−	0.927072i	$-0.622317\pi$
$617$	−18.6238	−0.749767	−0.374884	+	0.927072i	$0.622317\pi$
$618$	−3.52339	−0.141732
$619$	27.4064	1.10156	0.550778	−	0.834651i	$-0.314331\pi$
$619$	27.4064	1.10156	0.550778	+	0.834651i	$0.314331\pi$
$620$	−31.4447	−1.26285
$621$	3.47194	0.139324
$622$	6.95105	0.278712
$623$	3.94237	0.157948
$624$	−96.7111	−3.87154
$625$	1.00000	0.0400000
$626$	3.21600	0.128537
$627$	0.399502	0.0159546
$628$	11.8381	0.472390
$629$	−4.61015	−0.183819
$630$	2.87905	0.114704
$631$	27.0454	1.07666	0.538330	−	0.842734i	$-0.319056\pi$
$631$	27.0454	1.07666	0.538330	+	0.842734i	$0.319056\pi$
$632$	−1.98683	−0.0790318
$633$	−30.8825	−1.22747
$634$	−19.1428	−0.760257
$635$	−4.71260	−0.187014
$636$	53.3949	2.11724
$637$	−39.3103	−1.55753
$638$	1.46137	0.0578563
$639$	7.85374	0.310689
$640$	−3.90639	−0.154414
$641$	−25.3918	−1.00292	−0.501458	−	0.865182i	$-0.667203\pi$
$641$	−25.3918	−1.00292	−0.501458	+	0.865182i	$0.667203\pi$
$642$	23.0560	0.909950
$643$	−36.4163	−1.43612	−0.718059	−	0.695982i	$-0.754969\pi$
$643$	−36.4163	−1.43612	−0.718059	+	0.695982i	$0.754969\pi$
$644$	3.18215	0.125394
$645$	−5.85352	−0.230482
$646$	−4.15552	−0.163497
$647$	−30.1565	−1.18557	−0.592786	−	0.805360i	$-0.701972\pi$
$647$	−30.1565	−1.18557	−0.592786	+	0.805360i	$0.701972\pi$
$648$	−36.8785	−1.44873
$649$	0.874258	0.0343176
$650$	17.5576	0.688664
$651$	−9.44312	−0.370105
$652$	−110.254	−4.31788
$653$	−13.0434	−0.510428	−0.255214	−	0.966885i	$-0.582146\pi$
$653$	−13.0434	−0.510428	−0.255214	+	0.966885i	$0.582146\pi$
$654$	46.5523	1.82034
$655$	13.5244	0.528440
$656$	−38.0597	−1.48598
$657$	6.78758	0.264809
$658$	2.35765	0.0919108
$659$	23.8553	0.929270	0.464635	−	0.885502i	$-0.346186\pi$
$659$	23.8553	0.929270	0.464635	+	0.885502i	$0.346186\pi$
$660$	2.34235	0.0911758
$661$	21.4176	0.833047	0.416524	−	0.909125i	$-0.363248\pi$
$661$	21.4176	0.833047	0.416524	+	0.909125i	$0.363248\pi$
$662$	57.2873	2.22654
$663$	−17.6161	−0.684155
$664$	−45.3361	−1.75938
$665$	0.884160	0.0342862
$666$	6.68209	0.258926
$667$	1.00283	0.0388296
$668$	12.5402	0.485195
$669$	−18.6708	−0.721855
$670$	−21.4198	−0.827520
$671$	−0.653413	−0.0252247
$672$	−17.5118	−0.675533
$673$	−33.7918	−1.30258	−0.651289	−	0.758830i	$-0.725771\pi$
$673$	−33.7918	−1.30258	−0.651289	+	0.758830i	$0.725771\pi$
$674$	−27.3484	−1.05342
$675$	5.65607	0.217702
$676$	155.213	5.96974
$677$	−33.1742	−1.27499	−0.637495	−	0.770455i	$-0.720029\pi$
$677$	−33.1742	−1.27499	−0.637495	+	0.770455i	$0.720029\pi$
$678$	30.6420	1.17680
$679$	18.8954	0.725140
$680$	−14.4543	−0.554297
$681$	1.36294	0.0522280
$682$	5.72052	0.219050
$683$	38.5145	1.47372	0.736858	−	0.676047i	$-0.236309\pi$
$683$	38.5145	1.47372	0.736858	+	0.676047i	$0.236309\pi$
$684$	4.28161	0.163711
$685$	12.2503	0.468059
$686$	−35.7372	−1.36445
$687$	−32.7040	−1.24773
$688$	−43.2275	−1.64803
$689$	−51.7588	−1.97185
$690$	2.26117	0.0860811
$691$	13.4298	0.510894	0.255447	−	0.966823i	$-0.417777\pi$
$691$	13.4298	0.510894	0.255447	+	0.966823i	$0.417777\pi$
$692$	−70.4155	−2.67680
$693$	−0.372324	−0.0141434
$694$	−87.6755	−3.32812
$695$	11.7399	0.445318
$696$	−17.5544	−0.665399
$697$	−6.93267	−0.262594
$698$	−2.77908	−0.105190
$699$	12.4385	0.470467
$700$	5.18398	0.195936
$701$	40.6852	1.53666	0.768330	−	0.640054i	$-0.221088\pi$
$701$	40.6852	1.53666	0.768330	+	0.640054i	$0.221088\pi$
$702$	99.3067	3.74809
$703$	2.05208	0.0773957
$704$	3.57251	0.134644
$705$	1.19090	0.0448519
$706$	−54.9434	−2.06782
$707$	−0.891456	−0.0335267
$708$	−17.7022	−0.665288
$709$	−4.38707	−0.164760	−0.0823800	−	0.996601i	$-0.526252\pi$
$709$	−4.38707	−0.164760	−0.0823800	+	0.996601i	$0.526252\pi$
$710$	19.8933	0.746583
$711$	0.268897	0.0100844
$712$	28.6882	1.07514
$713$	3.92554	0.147013
$714$	−7.31689	−0.273828
$715$	−2.27058	−0.0849147
$716$	24.0740	0.899688
$717$	37.5349	1.40177
$718$	−12.9585	−0.483605
$719$	−11.4502	−0.427021	−0.213511	−	0.976941i	$-0.568490\pi$
$719$	−11.4502	−0.427021	−0.213511	+	0.976941i	$0.568490\pi$
$720$	10.7396	0.400241
$721$	1.00843	0.0375558
$722$	−48.1208	−1.79087
$723$	−1.40060	−0.0520889
$724$	55.6205	2.06712
$725$	1.63368	0.0606735
$726$	40.0937	1.48802
$727$	−36.1917	−1.34228	−0.671138	−	0.741333i	$-0.734194\pi$
$727$	−36.1917	−1.34228	−0.671138	+	0.741333i	$0.734194\pi$
$728$	53.9966	2.00125
$729$	28.7568	1.06507
$730$	17.1928	0.636332
$731$	−7.87400	−0.291230
$732$	13.2304	0.489011
$733$	−27.6382	−1.02084	−0.510420	−	0.859925i	$-0.670510\pi$
$733$	−27.6382	−1.02084	−0.510420	+	0.859925i	$0.670510\pi$
$734$	46.2395	1.70673
$735$	−8.24741	−0.304210
$736$	7.27973	0.268335
$737$	2.77005	0.102036
$738$	10.0484	0.369888
$739$	−15.7570	−0.579630	−0.289815	−	0.957083i	$-0.593594\pi$
$739$	−15.7570	−0.579630	−0.289815	+	0.957083i	$0.593594\pi$
$740$	12.0317	0.442294
$741$	7.84134	0.288059
$742$	−21.4981	−0.789219
$743$	−15.0656	−0.552702	−0.276351	−	0.961057i	$-0.589125\pi$
$743$	−15.0656	−0.552702	−0.276351	+	0.961057i	$0.589125\pi$
$744$	−68.7165	−2.51927
$745$	−16.7360	−0.613159
$746$	−14.7975	−0.541776
$747$	6.13577	0.224496
$748$	3.15087	0.115207
$749$	−6.59885	−0.241117
$750$	3.68362	0.134507
$751$	52.9339	1.93158	0.965792	−	0.259317i	$-0.0834975\pi$
$751$	52.9339	1.93158	0.965792	+	0.259317i	$0.0834975\pi$
$752$	8.79465	0.320708
$753$	−37.8688	−1.38001
$754$	28.6835	1.04459
$755$	−5.05216	−0.183867
$756$	29.3209	1.06639
$757$	23.7838	0.864436	0.432218	−	0.901769i	$-0.357731\pi$
$757$	23.7838	0.864436	0.432218	+	0.901769i	$0.357731\pi$
$758$	87.1074	3.16388
$759$	−0.292418	−0.0106141
$760$	6.43393	0.233383
$761$	−13.4064	−0.485981	−0.242990	−	0.970029i	$-0.578128\pi$
$761$	−13.4064	−0.485981	−0.242990	+	0.970029i	$0.578128\pi$
$762$	−17.3594	−0.628866
$763$	−13.3237	−0.482350
$764$	111.881	4.04770
$765$	1.95624	0.0707281
$766$	31.7177	1.14601
$767$	17.1597	0.619602
$768$	15.0332	0.542465
$769$	5.63293	0.203129	0.101564	−	0.994829i	$-0.467615\pi$
$769$	5.63293	0.203129	0.101564	+	0.994829i	$0.467615\pi$
$770$	−0.943087	−0.0339865
$771$	19.8916	0.716379
$772$	−131.535	−4.73404
$773$	25.2946	0.909782	0.454891	−	0.890547i	$-0.349678\pi$
$773$	25.2946	0.909782	0.454891	+	0.890547i	$0.349678\pi$
$774$	11.4128	0.410225
$775$	6.39503	0.229716
$776$	137.500	4.93596
$777$	3.61323	0.129624
$778$	81.9193	2.93695
$779$	3.08589	0.110563
$780$	45.9751	1.64617
$781$	−2.57264	−0.0920564
$782$	3.04166	0.108770
$783$	9.24023	0.330219
$784$	−60.9062	−2.17522
$785$	−2.40755	−0.0859292
$786$	49.8186	1.77697
$787$	0.967855	0.0345003	0.0172501	−	0.999851i	$-0.494509\pi$
$787$	0.967855	0.0345003	0.0172501	+	0.999851i	$0.494509\pi$
$788$	−50.7078	−1.80639
$789$	8.76203	0.311937
$790$	0.681109	0.0242328
$791$	−8.77003	−0.311826
$792$	−2.70936	−0.0962729
$793$	−12.8250	−0.455430
$794$	−43.6282	−1.54831
$795$	−10.8591	−0.385134
$796$	38.5437	1.36614
$797$	−14.8849	−0.527252	−0.263626	−	0.964625i	$-0.584918\pi$
$797$	−14.8849	−0.527252	−0.263626	+	0.964625i	$0.584918\pi$
$798$	3.25691	0.115293
$799$	1.60197	0.0566735
$800$	11.8593	0.419289
$801$	−3.88266	−0.137187
$802$	84.8506	2.99618
$803$	−2.22340	−0.0784621
$804$	−56.0886	−1.97809
$805$	−0.647166	−0.0228096
$806$	112.281	3.95493
$807$	25.4926	0.897381
$808$	−6.48703	−0.228213
$809$	0.815220	0.0286616	0.0143308	−	0.999897i	$-0.495438\pi$
$809$	0.815220	0.0286616	0.0143308	+	0.999897i	$0.495438\pi$
$810$	12.6424	0.444209
$811$	1.64228	0.0576682	0.0288341	−	0.999584i	$-0.490821\pi$
$811$	1.64228	0.0576682	0.0288341	+	0.999584i	$0.490821\pi$
$812$	8.46898	0.297203
$813$	−3.06268	−0.107413
$814$	−2.18885	−0.0767190
$815$	22.4228	0.785437
$816$	−27.2939	−0.955478
$817$	3.50489	0.122621
$818$	−54.1278	−1.89253
$819$	−7.30789	−0.255358
$820$	18.0931	0.631837
$821$	−22.1336	−0.772467	−0.386234	−	0.922401i	$-0.626224\pi$
$821$	−22.1336	−0.772467	−0.386234	+	0.922401i	$0.626224\pi$
$822$	45.1254	1.57393
$823$	−4.14878	−0.144617	−0.0723087	−	0.997382i	$-0.523037\pi$
$823$	−4.14878	−0.144617	−0.0723087	+	0.997382i	$0.523037\pi$
$824$	7.33821	0.255639
$825$	−0.476373	−0.0165852
$826$	7.12732	0.247991
$827$	25.2438	0.877813	0.438907	−	0.898533i	$-0.355366\pi$
$827$	25.2438	0.877813	0.438907	+	0.898533i	$0.355366\pi$
$828$	−3.13395	−0.108912
$829$	4.46911	0.155219	0.0776093	−	0.996984i	$-0.475271\pi$
$829$	4.46911	0.155219	0.0776093	+	0.996984i	$0.475271\pi$
$830$	15.5417	0.539462
$831$	−43.0524	−1.49347
$832$	70.1204	2.43099
$833$	−11.0942	−0.384391
$834$	43.2452	1.49746
$835$	−2.55035	−0.0882585
$836$	−1.40252	−0.0485072
$837$	36.1707	1.25024
$838$	−68.1009	−2.35251
$839$	22.4342	0.774515	0.387258	−	0.921972i	$-0.373422\pi$
$839$	22.4342	0.774515	0.387258	+	0.921972i	$0.373422\pi$
$840$	11.3286	0.390875
$841$	−26.3311	−0.907968
$842$	65.8080	2.26789
$843$	16.0599	0.553131
$844$	108.418	3.73191
$845$	−31.5663	−1.08592
$846$	−2.32194	−0.0798299
$847$	−11.4752	−0.394292
$848$	−80.1934	−2.75385
$849$	10.0618	0.345321
$850$	4.95511	0.169959
$851$	−1.50203	−0.0514890
$852$	52.0914	1.78462
$853$	−29.4281	−1.00760	−0.503800	−	0.863821i	$-0.668065\pi$
$853$	−29.4281	−1.00760	−0.503800	+	0.863821i	$0.668065\pi$
$854$	−5.32690	−0.182283
$855$	−0.870767	−0.0297796
$856$	−48.0191	−1.64126
$857$	46.8759	1.60125	0.800625	−	0.599166i	$-0.204501\pi$
$857$	46.8759	1.60125	0.800625	+	0.599166i	$0.204501\pi$
$858$	−8.36394	−0.285540
$859$	−6.14715	−0.209738	−0.104869	−	0.994486i	$-0.533442\pi$
$859$	−6.14715	−0.209738	−0.104869	+	0.994486i	$0.533442\pi$
$860$	20.5498	0.700741
$861$	5.43351	0.185174
$862$	−18.0399	−0.614443
$863$	−23.1181	−0.786950	−0.393475	−	0.919335i	$-0.628727\pi$
$863$	−23.1181	−0.786950	−0.393475	+	0.919335i	$0.628727\pi$
$864$	67.0769	2.28200
$865$	14.3207	0.486918
$866$	−64.7726	−2.20106
$867$	18.8386	0.639791
$868$	33.1517	1.12524
$869$	−0.0880823	−0.00298799
$870$	6.01787	0.204025
$871$	54.3700	1.84226
$872$	−96.9550	−3.28331
$873$	−18.6092	−0.629827
$874$	−1.35391	−0.0457967
$875$	−1.05429	−0.0356414
$876$	45.0198	1.52108
$877$	15.5761	0.525969	0.262984	−	0.964800i	$-0.415293\pi$
$877$	15.5761	0.525969	0.262984	+	0.964800i	$0.415293\pi$
$878$	−88.0251	−2.97070
$879$	−20.1338	−0.679098
$880$	−3.51796	−0.118590
$881$	−39.6132	−1.33460	−0.667302	−	0.744787i	$-0.732551\pi$
$881$	−39.6132	−1.33460	−0.667302	+	0.744787i	$0.732551\pi$
$882$	16.0803	0.541451
$883$	42.6806	1.43632	0.718158	−	0.695880i	$-0.244985\pi$
$883$	42.6806	1.43632	0.718158	+	0.695880i	$0.244985\pi$
$884$	61.8445	2.08006
$885$	3.60016	0.121018
$886$	55.3600	1.85986
$887$	−25.9509	−0.871345	−0.435672	−	0.900105i	$-0.643489\pi$
$887$	−25.9509	−0.871345	−0.435672	+	0.900105i	$0.643489\pi$
$888$	26.2930	0.882337
$889$	4.96843	0.166636
$890$	−9.83467	−0.329659
$891$	−1.63494	−0.0547726
$892$	65.5470	2.19468
$893$	−0.713071	−0.0238620
$894$	−61.6491	−2.06185
$895$	−4.89603	−0.163656
$896$	4.11845	0.137588
$897$	−5.73952	−0.191637
$898$	55.1114	1.83909
$899$	10.4475	0.348442
$900$	−5.10545	−0.170182
$901$	−14.6074	−0.486644
$902$	−3.29155	−0.109597
$903$	6.17128	0.205367
$904$	−63.8185	−2.12257
$905$	−11.3118	−0.376016
$906$	−18.6103	−0.618284
$907$	5.90063	0.195927	0.0979636	−	0.995190i	$-0.468767\pi$
$907$	5.90063	0.195927	0.0979636	+	0.995190i	$0.468767\pi$
$908$	−4.78484	−0.158790
$909$	0.877953	0.0291199
$910$	−18.5107	−0.613623
$911$	−50.2483	−1.66480	−0.832399	−	0.554176i	$-0.813033\pi$
$911$	−50.2483	−1.66480	−0.832399	+	0.554176i	$0.813033\pi$
$912$	12.1491	0.402298
$913$	−2.00989	−0.0665176
$914$	20.2012	0.668196
$915$	−2.69073	−0.0889527
$916$	114.813	3.79352
$917$	−14.2585	−0.470859
$918$	28.0265	0.925011
$919$	−14.8216	−0.488921	−0.244460	−	0.969659i	$-0.578611\pi$
$919$	−14.8216	−0.488921	−0.244460	+	0.969659i	$0.578611\pi$
$920$	−4.70936	−0.155263
$921$	−38.0641	−1.25426
$922$	31.4148	1.03459
$923$	−50.4952	−1.66207
$924$	−2.46951	−0.0812408
$925$	−2.44693	−0.0804547
$926$	73.0771	2.40146
$927$	−0.993152	−0.0326194
$928$	19.3743	0.635993
$929$	−14.1382	−0.463858	−0.231929	−	0.972733i	$-0.574504\pi$
$929$	−14.1382	−0.463858	−0.231929	+	0.972733i	$0.574504\pi$
$930$	23.5569	0.772460
$931$	4.93828	0.161845
$932$	−43.6675	−1.43038
$933$	−3.70173	−0.121189
$934$	−1.80968	−0.0592144
$935$	−0.640805	−0.0209566
$936$	−53.1787	−1.73820
$937$	55.6047	1.81653	0.908263	−	0.418399i	$-0.137409\pi$
$937$	55.6047	1.81653	0.908263	+	0.418399i	$0.137409\pi$
$938$	22.5826	0.737349
$939$	−1.71265	−0.0558904
$940$	−4.18086	−0.136364
$941$	−49.0980	−1.60055	−0.800274	−	0.599635i	$-0.795313\pi$
$941$	−49.0980	−1.60055	−0.800274	+	0.599635i	$0.795313\pi$
$942$	−8.86851	−0.288952
$943$	−2.25873	−0.0735545
$944$	26.5868	0.865325
$945$	−5.96312	−0.193980
$946$	−3.73848	−0.121549
$947$	−50.8425	−1.65216	−0.826079	−	0.563554i	$-0.809434\pi$
$947$	−50.8425	−1.65216	−0.826079	+	0.563554i	$0.809434\pi$
$948$	1.78351	0.0579257
$949$	−43.6404	−1.41663
$950$	−2.20563	−0.0715601
$951$	10.1943	0.330574
$952$	15.2390	0.493898
$953$	−22.7876	−0.738161	−0.369081	−	0.929397i	$-0.620327\pi$
$953$	−22.7876	−0.738161	−0.369081	+	0.929397i	$0.620327\pi$
$954$	21.1724	0.685483
$955$	−22.7536	−0.736291
$956$	−131.773	−4.26183
$957$	−0.778243	−0.0251570
$958$	82.3354	2.66014
$959$	−12.9153	−0.417057
$960$	14.7114	0.474810
$961$	9.89637	0.319238
$962$	−42.9621	−1.38516
$963$	6.49890	0.209424
$964$	4.91705	0.158368
$965$	26.7507	0.861136
$966$	−2.38392	−0.0767012
$967$	−25.3877	−0.816413	−0.408207	−	0.912890i	$-0.633846\pi$
$967$	−25.3877	−0.816413	−0.408207	+	0.912890i	$0.633846\pi$
$968$	−83.5037	−2.68391
$969$	2.21299	0.0710915
$970$	−47.1367	−1.51347
$971$	−33.7404	−1.08278	−0.541391	−	0.840771i	$-0.682102\pi$
$971$	−33.7404	−1.08278	−0.541391	+	0.840771i	$0.682102\pi$
$972$	−50.3289	−1.61430
$973$	−12.3772	−0.396794
$974$	51.6846	1.65608
$975$	−9.35014	−0.299444
$976$	−19.8707	−0.636046
$977$	5.59644	0.179046	0.0895230	−	0.995985i	$-0.471466\pi$
$977$	5.59644	0.179046	0.0895230	+	0.995985i	$0.471466\pi$
$978$	82.5971	2.64116
$979$	1.27184	0.0406481
$980$	28.9540	0.924900
$981$	13.1219	0.418949
$982$	−4.58623	−0.146352
$983$	−44.6820	−1.42513	−0.712567	−	0.701604i	$-0.752468\pi$
$983$	−44.6820	−1.42513	−0.712567	+	0.701604i	$0.752468\pi$
$984$	39.5391	1.26046
$985$	10.3126	0.328588
$986$	8.09509	0.257800
$987$	−1.25555	−0.0399646
$988$	−27.5284	−0.875794
$989$	−2.56543	−0.0815759
$990$	0.928801	0.0295192
$991$	39.6401	1.25921	0.629605	−	0.776915i	$-0.283217\pi$
$991$	39.6401	1.25921	0.629605	+	0.776915i	$0.283217\pi$
$992$	75.8404	2.40793
$993$	−30.5079	−0.968140
$994$	−20.9732	−0.665231
$995$	−7.83878	−0.248506
$996$	40.6966	1.28952
$997$	−15.8185	−0.500976	−0.250488	−	0.968120i	$-0.580591\pi$
$997$	−15.8185	−0.500976	−0.250488	+	0.968120i	$0.580591\pi$
$998$	32.0564	1.01473
$999$	−13.8400	−0.437879

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.d.1.25	✓	25	1.1	even	1	trivial
6025.2.a.k.1.1		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)

\(f(q)\)	\(=\)	\(q+2.63003 q^{2} -1.40060 q^{3} +4.91705 q^{4} -1.00000 q^{5} -3.68362 q^{6} +1.05429 q^{7} +7.67192 q^{8} -1.03832 q^{9} +O(q^{10})\)	\(q+2.63003 q^{2} -1.40060 q^{3} +4.91705 q^{4} -1.00000 q^{5} -3.68362 q^{6} +1.05429 q^{7} +7.67192 q^{8} -1.03832 q^{9} -2.63003 q^{10} +0.340120 q^{11} -6.88683 q^{12} +6.67580 q^{13} +2.77280 q^{14} +1.40060 q^{15} +10.3433 q^{16} +1.88405 q^{17} -2.73080 q^{18} -0.838634 q^{19} -4.91705 q^{20} -1.47663 q^{21} +0.894526 q^{22} +0.613843 q^{23} -10.7453 q^{24} +1.00000 q^{25} +17.5576 q^{26} +5.65607 q^{27} +5.18398 q^{28} +1.63368 q^{29} +3.68362 q^{30} +6.39503 q^{31} +11.8593 q^{32} -0.476373 q^{33} +4.95511 q^{34} -1.05429 q^{35} -5.10545 q^{36} -2.44693 q^{37} -2.20563 q^{38} -9.35014 q^{39} -7.67192 q^{40} -3.67966 q^{41} -3.88359 q^{42} -4.17929 q^{43} +1.67239 q^{44} +1.03832 q^{45} +1.61443 q^{46} +0.850277 q^{47} -14.4868 q^{48} -5.88848 q^{49} +2.63003 q^{50} -2.63881 q^{51} +32.8253 q^{52} -7.75319 q^{53} +14.8756 q^{54} -0.340120 q^{55} +8.08840 q^{56} +1.17459 q^{57} +4.29664 q^{58} +2.57044 q^{59} +6.88683 q^{60} -1.92112 q^{61} +16.8191 q^{62} -1.09468 q^{63} +10.5037 q^{64} -6.67580 q^{65} -1.25287 q^{66} +8.14434 q^{67} +9.26398 q^{68} -0.859749 q^{69} -2.77280 q^{70} -7.56392 q^{71} -7.96589 q^{72} -6.53710 q^{73} -6.43550 q^{74} -1.40060 q^{75} -4.12360 q^{76} +0.358584 q^{77} -24.5911 q^{78} -0.258974 q^{79} -10.3433 q^{80} -4.80695 q^{81} -9.67761 q^{82} -5.90935 q^{83} -7.26069 q^{84} -1.88405 q^{85} -10.9916 q^{86} -2.28814 q^{87} +2.60938 q^{88} +3.73938 q^{89} +2.73080 q^{90} +7.03821 q^{91} +3.01830 q^{92} -8.95688 q^{93} +2.23625 q^{94} +0.838634 q^{95} -16.6101 q^{96} +17.9225 q^{97} -15.4869 q^{98} -0.353153 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 4 q^{2} + 9 q^{3} + 36 q^{4} - 25 q^{5} + 7 q^{6} + 7 q^{7} - 15 q^{8} + 36 q^{9}+O(q^{10}) \) 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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