LMFDB - Embedded newform 1205.2.a.d.1.15

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			1.15
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)

$f(q)$	$=$	$q+0.355815 q^{2} +0.886461 q^{3} -1.87340 q^{4} -1.00000 q^{5} +0.315416 q^{6} -4.33523 q^{7} -1.37821 q^{8} -2.21419 q^{9} +O(q^{10})$	\(q+0.355815 q^{2} +0.886461 q^{3} -1.87340 q^{4} -1.00000 q^{5} +0.315416 q^{6} -4.33523 q^{7} -1.37821 q^{8} -2.21419 q^{9} -0.355815 q^{10} +4.19994 q^{11} -1.66069 q^{12} +1.37659 q^{13} -1.54254 q^{14} -0.886461 q^{15} +3.25640 q^{16} -2.36547 q^{17} -0.787841 q^{18} +8.50414 q^{19} +1.87340 q^{20} -3.84302 q^{21} +1.49440 q^{22} +3.14415 q^{23} -1.22173 q^{24} +1.00000 q^{25} +0.489810 q^{26} -4.62217 q^{27} +8.12161 q^{28} +10.6346 q^{29} -0.315416 q^{30} +1.37682 q^{31} +3.91510 q^{32} +3.72308 q^{33} -0.841671 q^{34} +4.33523 q^{35} +4.14805 q^{36} -2.82307 q^{37} +3.02590 q^{38} +1.22029 q^{39} +1.37821 q^{40} -2.36682 q^{41} -1.36740 q^{42} -2.46126 q^{43} -7.86814 q^{44} +2.21419 q^{45} +1.11873 q^{46} -4.36826 q^{47} +2.88667 q^{48} +11.7943 q^{49} +0.355815 q^{50} -2.09690 q^{51} -2.57889 q^{52} +8.75198 q^{53} -1.64464 q^{54} -4.19994 q^{55} +5.97487 q^{56} +7.53859 q^{57} +3.78396 q^{58} +8.02028 q^{59} +1.66069 q^{60} +3.25499 q^{61} +0.489892 q^{62} +9.59902 q^{63} -5.11976 q^{64} -1.37659 q^{65} +1.32473 q^{66} -5.05257 q^{67} +4.43147 q^{68} +2.78716 q^{69} +1.54254 q^{70} -7.73338 q^{71} +3.05162 q^{72} +1.97219 q^{73} -1.00449 q^{74} +0.886461 q^{75} -15.9316 q^{76} -18.2077 q^{77} +0.434198 q^{78} -13.8552 q^{79} -3.25640 q^{80} +2.54518 q^{81} -0.842151 q^{82} -13.2407 q^{83} +7.19949 q^{84} +2.36547 q^{85} -0.875754 q^{86} +9.42717 q^{87} -5.78840 q^{88} +11.9290 q^{89} +0.787841 q^{90} -5.96783 q^{91} -5.89023 q^{92} +1.22049 q^{93} -1.55429 q^{94} -8.50414 q^{95} +3.47058 q^{96} +10.7410 q^{97} +4.19657 q^{98} -9.29945 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.355815	0.251599	0.125800	−	0.992056i	$-0.459850\pi$
$2$	0.355815	0.251599	0.125800	+	0.992056i	$0.459850\pi$
$3$	0.886461	0.511798	0.255899	−	0.966703i	$-0.417628\pi$
$3$	0.886461	0.511798	0.255899	+	0.966703i	$0.417628\pi$
$4$	−1.87340	−0.936698
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.315416	0.128768
$7$	−4.33523	−1.63856	−0.819282	−	0.573390i	$-0.805628\pi$
$7$	−4.33523	−1.63856	−0.819282	+	0.573390i	$0.805628\pi$
$8$	−1.37821	−0.487272
$9$	−2.21419	−0.738062
$10$	−0.355815	−0.112519
$11$	4.19994	1.26633	0.633164	−	0.774017i	$-0.281756\pi$
$11$	4.19994	1.26633	0.633164	+	0.774017i	$0.281756\pi$
$12$	−1.66069	−0.479401
$13$	1.37659	0.381797	0.190898	−	0.981610i	$-0.438860\pi$
$13$	1.37659	0.381797	0.190898	+	0.981610i	$0.438860\pi$
$14$	−1.54254	−0.412261
$15$	−0.886461	−0.228883
$16$	3.25640	0.814101
$17$	−2.36547	−0.573712	−0.286856	−	0.957974i	$-0.592610\pi$
$17$	−2.36547	−0.573712	−0.286856	+	0.957974i	$0.592610\pi$
$18$	−0.787841	−0.185696
$19$	8.50414	1.95098	0.975492	−	0.220034i	$-0.0706169\pi$
$19$	8.50414	1.95098	0.975492	+	0.220034i	$0.0706169\pi$
$20$	1.87340	0.418904
$21$	−3.84302	−0.838615
$22$	1.49440	0.318607
$23$	3.14415	0.655600	0.327800	−	0.944747i	$-0.393693\pi$
$23$	3.14415	0.655600	0.327800	+	0.944747i	$0.393693\pi$
$24$	−1.22173	−0.249385
$25$	1.00000	0.200000
$26$	0.489810	0.0960597
$27$	−4.62217	−0.889538
$28$	8.12161	1.53484
$29$	10.6346	1.97480	0.987400	−	0.158247i	$-0.0505843\pi$
$29$	10.6346	1.97480	0.987400	+	0.158247i	$0.0505843\pi$
$30$	−0.315416	−0.0575868
$31$	1.37682	0.247284	0.123642	−	0.992327i	$-0.460543\pi$
$31$	1.37682	0.247284	0.123642	+	0.992327i	$0.460543\pi$
$32$	3.91510	0.692099
$33$	3.72308	0.648105
$34$	−0.841671	−0.144345
$35$	4.33523	0.732788
$36$	4.14805	0.691341
$37$	−2.82307	−0.464110	−0.232055	−	0.972703i	$-0.574545\pi$
$37$	−2.82307	−0.464110	−0.232055	+	0.972703i	$0.574545\pi$
$38$	3.02590	0.490866
$39$	1.22029	0.195403
$40$	1.37821	0.217914
$41$	−2.36682	−0.369636	−0.184818	−	0.982773i	$-0.559170\pi$
$41$	−2.36682	−0.369636	−0.184818	+	0.982773i	$0.559170\pi$
$42$	−1.36740	−0.210995
$43$	−2.46126	−0.375339	−0.187670	−	0.982232i	$-0.560093\pi$
$43$	−2.46126	−0.375339	−0.187670	+	0.982232i	$0.560093\pi$
$44$	−7.86814	−1.18617
$45$	2.21419	0.330071
$46$	1.11873	0.164948
$47$	−4.36826	−0.637176	−0.318588	−	0.947893i	$-0.603209\pi$
$47$	−4.36826	−0.637176	−0.318588	+	0.947893i	$0.603209\pi$
$48$	2.88667	0.416656
$49$	11.7943	1.68489
$50$	0.355815	0.0503198
$51$	−2.09690	−0.293625
$52$	−2.57889	−0.357628
$53$	8.75198	1.20218	0.601089	−	0.799182i	$-0.294734\pi$
$53$	8.75198	1.20218	0.601089	+	0.799182i	$0.294734\pi$
$54$	−1.64464	−0.223807
$55$	−4.19994	−0.566319
$56$	5.97487	0.798426
$57$	7.53859	0.998511
$58$	3.78396	0.496858
$59$	8.02028	1.04415	0.522076	−	0.852899i	$-0.325158\pi$
$59$	8.02028	1.04415	0.522076	+	0.852899i	$0.325158\pi$
$60$	1.66069	0.214394
$61$	3.25499	0.416759	0.208379	−	0.978048i	$-0.433181\pi$
$61$	3.25499	0.416759	0.208379	+	0.978048i	$0.433181\pi$
$62$	0.489892	0.0622164
$63$	9.59902	1.20936
$64$	−5.11976	−0.639969
$65$	−1.37659	−0.170745
$66$	1.32473	0.163063
$67$	−5.05257	−0.617270	−0.308635	−	0.951181i	$-0.599872\pi$
$67$	−5.05257	−0.617270	−0.308635	+	0.951181i	$0.599872\pi$
$68$	4.43147	0.537395
$69$	2.78716	0.335535
$70$	1.54254	0.184369
$71$	−7.73338	−0.917783	−0.458892	−	0.888492i	$-0.651753\pi$
$71$	−7.73338	−0.917783	−0.458892	+	0.888492i	$0.651753\pi$
$72$	3.05162	0.359637
$73$	1.97219	0.230827	0.115413	−	0.993318i	$-0.463181\pi$
$73$	1.97219	0.230827	0.115413	+	0.993318i	$0.463181\pi$
$74$	−1.00449	−0.116770
$75$	0.886461	0.102360
$76$	−15.9316	−1.82748
$77$	−18.2077	−2.07496
$78$	0.434198	0.0491632
$79$	−13.8552	−1.55883	−0.779415	−	0.626508i	$-0.784484\pi$
$79$	−13.8552	−1.55883	−0.779415	+	0.626508i	$0.784484\pi$
$80$	−3.25640	−0.364077
$81$	2.54518	0.282798
$82$	−0.842151	−0.0930000
$83$	−13.2407	−1.45336	−0.726680	−	0.686976i	$-0.758938\pi$
$83$	−13.2407	−1.45336	−0.726680	+	0.686976i	$0.758938\pi$
$84$	7.19949	0.785529
$85$	2.36547	0.256572
$86$	−0.875754	−0.0944350
$87$	9.42717	1.01070
$88$	−5.78840	−0.617046
$89$	11.9290	1.26447	0.632236	−	0.774776i	$-0.282137\pi$
$89$	11.9290	1.26447	0.632236	+	0.774776i	$0.282137\pi$
$90$	0.787841	0.0830457
$91$	−5.96783	−0.625598
$92$	−5.89023	−0.614099
$93$	1.22049	0.126559
$94$	−1.55429	−0.160313
$95$	−8.50414	−0.872507
$96$	3.47058	0.354215
$97$	10.7410	1.09058	0.545292	−	0.838246i	$-0.316419\pi$
$97$	10.7410	1.09058	0.545292	+	0.838246i	$0.316419\pi$
$98$	4.19657	0.423918
$99$	−9.29945	−0.934629
$100$	−1.87340	−0.187340
$101$	10.0755	1.00255	0.501275	−	0.865288i	$-0.332865\pi$
$101$	10.0755	1.00255	0.501275	+	0.865288i	$0.332865\pi$
$102$	−0.746109	−0.0738758
$103$	2.72151	0.268158	0.134079	−	0.990971i	$-0.457192\pi$
$103$	2.72151	0.268158	0.134079	+	0.990971i	$0.457192\pi$
$104$	−1.89723	−0.186039
$105$	3.84302	0.375040
$106$	3.11409	0.302467
$107$	14.2123	1.37396	0.686979	−	0.726677i	$-0.258936\pi$
$107$	14.2123	1.37396	0.686979	+	0.726677i	$0.258936\pi$
$108$	8.65916	0.833228
$109$	−20.3541	−1.94957	−0.974785	−	0.223145i	$-0.928368\pi$
$109$	−20.3541	−1.94957	−0.974785	+	0.223145i	$0.928368\pi$
$110$	−1.49440	−0.142485
$111$	−2.50254	−0.237531
$112$	−14.1173	−1.33396
$113$	5.53974	0.521135	0.260567	−	0.965456i	$-0.416090\pi$
$113$	5.53974	0.521135	0.260567	+	0.965456i	$0.416090\pi$
$114$	2.68234	0.251224
$115$	−3.14415	−0.293193
$116$	−19.9228	−1.84979
$117$	−3.04802	−0.281790
$118$	2.85374	0.262708
$119$	10.2549	0.940064
$120$	1.22173	0.111528
$121$	6.63947	0.603588
$122$	1.15817	0.104856
$123$	−2.09810	−0.189179
$124$	−2.57932	−0.231630
$125$	−1.00000	−0.0894427
$126$	3.41547	0.304275
$127$	19.1164	1.69631	0.848153	−	0.529751i	$-0.177715\pi$
$127$	19.1164	1.69631	0.848153	+	0.529751i	$0.177715\pi$
$128$	−9.65189	−0.853114
$129$	−2.18181	−0.192098
$130$	−0.489810	−0.0429592
$131$	1.88381	0.164589	0.0822945	−	0.996608i	$-0.473775\pi$
$131$	1.88381	0.164589	0.0822945	+	0.996608i	$0.473775\pi$
$132$	−6.97480	−0.607079
$133$	−36.8675	−3.19681
$134$	−1.79778	−0.155305
$135$	4.62217	0.397813
$136$	3.26013	0.279553
$137$	13.3429	1.13996	0.569981	−	0.821658i	$-0.306950\pi$
$137$	13.3429	1.13996	0.569981	+	0.821658i	$0.306950\pi$
$138$	0.991715	0.0844204
$139$	12.3412	1.04677	0.523384	−	0.852097i	$-0.324669\pi$
$139$	12.3412	1.04677	0.523384	+	0.852097i	$0.324669\pi$
$140$	−8.12161	−0.686401
$141$	−3.87229	−0.326106
$142$	−2.75165	−0.230913
$143$	5.78158	0.483480
$144$	−7.21029	−0.600857
$145$	−10.6346	−0.883157
$146$	0.701733	0.0580759
$147$	10.4551	0.862326
$148$	5.28873	0.434731
$149$	3.06504	0.251098	0.125549	−	0.992087i	$-0.459931\pi$
$149$	3.06504	0.251098	0.125549	+	0.992087i	$0.459931\pi$
$150$	0.315416	0.0257536
$151$	14.4168	1.17322	0.586610	−	0.809870i	$-0.300462\pi$
$151$	14.4168	1.17322	0.586610	+	0.809870i	$0.300462\pi$
$152$	−11.7205	−0.950659
$153$	5.23760	0.423435
$154$	−6.47857	−0.522058
$155$	−1.37682	−0.110589
$156$	−2.28609	−0.183034
$157$	−16.2098	−1.29368	−0.646841	−	0.762625i	$-0.723910\pi$
$157$	−16.2098	−1.29368	−0.646841	+	0.762625i	$0.723910\pi$
$158$	−4.92988	−0.392200
$159$	7.75829	0.615273
$160$	−3.91510	−0.309516
$161$	−13.6306	−1.07424
$162$	0.905615	0.0711518
$163$	18.6379	1.45983	0.729915	−	0.683538i	$-0.239560\pi$
$163$	18.6379	1.45983	0.729915	+	0.683538i	$0.239560\pi$
$164$	4.43400	0.346237
$165$	−3.72308	−0.289841
$166$	−4.71125	−0.365664
$167$	14.4286	1.11652	0.558259	−	0.829667i	$-0.311470\pi$
$167$	14.4286	1.11652	0.558259	+	0.829667i	$0.311470\pi$
$168$	5.29649	0.408633
$169$	−11.1050	−0.854231
$170$	0.841671	0.0645532
$171$	−18.8298	−1.43995
$172$	4.61092	0.351579
$173$	0.530858	0.0403604	0.0201802	−	0.999796i	$-0.493576\pi$
$173$	0.530858	0.0403604	0.0201802	+	0.999796i	$0.493576\pi$
$174$	3.35433	0.254291
$175$	−4.33523	−0.327713
$176$	13.6767	1.03092
$177$	7.10967	0.534395
$178$	4.24452	0.318140
$179$	−2.89929	−0.216703	−0.108352	−	0.994113i	$-0.534557\pi$
$179$	−2.89929	−0.216703	−0.108352	+	0.994113i	$0.534557\pi$
$180$	−4.14805	−0.309177
$181$	20.1290	1.49618	0.748089	−	0.663599i	$-0.230972\pi$
$181$	20.1290	1.49618	0.748089	+	0.663599i	$0.230972\pi$
$182$	−2.12344	−0.157400
$183$	2.88542	0.213297
$184$	−4.33330	−0.319455
$185$	2.82307	0.207556
$186$	0.434270	0.0318422
$187$	−9.93484	−0.726508
$188$	8.18347	0.596841
$189$	20.0382	1.45756
$190$	−3.02590	−0.219522
$191$	4.82710	0.349277	0.174638	−	0.984633i	$-0.444124\pi$
$191$	4.82710	0.349277	0.174638	+	0.984633i	$0.444124\pi$
$192$	−4.53846	−0.327535
$193$	7.53440	0.542338	0.271169	−	0.962532i	$-0.412590\pi$
$193$	7.53440	0.542338	0.271169	+	0.962532i	$0.412590\pi$
$194$	3.82181	0.274390
$195$	−1.22029	−0.0873868
$196$	−22.0953	−1.57824
$197$	−3.20929	−0.228652	−0.114326	−	0.993443i	$-0.536471\pi$
$197$	−3.20929	−0.228652	−0.114326	+	0.993443i	$0.536471\pi$
$198$	−3.30888	−0.235152
$199$	3.70296	0.262496	0.131248	−	0.991350i	$-0.458102\pi$
$199$	3.70296	0.262496	0.131248	+	0.991350i	$0.458102\pi$
$200$	−1.37821	−0.0974543
$201$	−4.47891	−0.315918
$202$	3.58501	0.252241
$203$	−46.1036	−3.23584
$204$	3.92833	0.275038
$205$	2.36682	0.165306
$206$	0.968354	0.0674684
$207$	−6.96173	−0.483874
$208$	4.48272	0.310821
$209$	35.7169	2.47059
$210$	1.36740	0.0943597
$211$	−8.24645	−0.567709	−0.283855	−	0.958867i	$-0.591613\pi$
$211$	−8.24645	−0.567709	−0.283855	+	0.958867i	$0.591613\pi$
$212$	−16.3959	−1.12608
$213$	−6.85534	−0.469720
$214$	5.05696	0.345687
$215$	2.46126	0.167857
$216$	6.37033	0.433446
$217$	−5.96882	−0.405190
$218$	−7.24230	−0.490510
$219$	1.74827	0.118137
$220$	7.86814	0.530470
$221$	−3.25628	−0.219041
$222$	−0.890442	−0.0597625
$223$	−3.69589	−0.247495	−0.123747	−	0.992314i	$-0.539491\pi$
$223$	−3.69589	−0.247495	−0.123747	+	0.992314i	$0.539491\pi$
$224$	−16.9729	−1.13405
$225$	−2.21419	−0.147612
$226$	1.97112	0.131117
$227$	−3.00437	−0.199407	−0.0997034	−	0.995017i	$-0.531789\pi$
$227$	−3.00437	−0.199407	−0.0997034	+	0.995017i	$0.531789\pi$
$228$	−14.1228	−0.935303
$229$	20.5949	1.36095	0.680474	−	0.732772i	$-0.261774\pi$
$229$	20.5949	1.36095	0.680474	+	0.732772i	$0.261774\pi$
$230$	−1.11873	−0.0737672
$231$	−16.1404	−1.06196
$232$	−14.6568	−0.962263
$233$	−5.75706	−0.377157	−0.188579	−	0.982058i	$-0.560388\pi$
$233$	−5.75706	−0.377157	−0.188579	+	0.982058i	$0.560388\pi$
$234$	−1.08453	−0.0708980
$235$	4.36826	0.284954
$236$	−15.0252	−0.978055
$237$	−12.2821	−0.797807
$238$	3.64884	0.236519
$239$	−7.64491	−0.494508	−0.247254	−	0.968951i	$-0.579528\pi$
$239$	−7.64491	−0.494508	−0.247254	+	0.968951i	$0.579528\pi$
$240$	−2.88667	−0.186334
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	2.36242	0.151862
$243$	16.1227	1.03427
$244$	−6.09789	−0.390377
$245$	−11.7943	−0.753507
$246$	−0.746534	−0.0475973
$247$	11.7067	0.744879
$248$	−1.89755	−0.120494
$249$	−11.7374	−0.743827
$250$	−0.355815	−0.0225037
$251$	14.8787	0.939134	0.469567	−	0.882897i	$-0.344410\pi$
$251$	14.8787	0.939134	0.469567	+	0.882897i	$0.344410\pi$
$252$	−17.9828	−1.13281
$253$	13.2052	0.830205
$254$	6.80190	0.426789
$255$	2.09690	0.131313
$256$	6.80523	0.425327
$257$	−14.4148	−0.899169	−0.449585	−	0.893238i	$-0.648428\pi$
$257$	−14.4148	−0.899169	−0.449585	+	0.893238i	$0.648428\pi$
$258$	−0.776322	−0.0483317
$259$	12.2387	0.760474
$260$	2.57889	0.159936
$261$	−23.5470	−1.45752
$262$	0.670287	0.0414105
$263$	31.8372	1.96316	0.981582	−	0.191039i	$-0.0611857\pi$
$263$	31.8372	1.96316	0.981582	+	0.191039i	$0.0611857\pi$
$264$	−5.13119	−0.315803
$265$	−8.75198	−0.537630
$266$	−13.1180	−0.804316
$267$	10.5746	0.647154
$268$	9.46546	0.578195
$269$	−28.4598	−1.73522	−0.867612	−	0.497241i	$-0.834346\pi$
$269$	−28.4598	−1.73522	−0.867612	+	0.497241i	$0.834346\pi$
$270$	1.64464	0.100089
$271$	8.03969	0.488377	0.244188	−	0.969728i	$-0.421479\pi$
$271$	8.03969	0.488377	0.244188	+	0.969728i	$0.421479\pi$
$272$	−7.70294	−0.467059
$273$	−5.29025	−0.320180
$274$	4.74761	0.286814
$275$	4.19994	0.253266
$276$	−5.22146	−0.314295
$277$	−28.7989	−1.73036	−0.865178	−	0.501465i	$-0.832795\pi$
$277$	−28.7989	−1.73036	−0.865178	+	0.501465i	$0.832795\pi$
$278$	4.39119	0.263366
$279$	−3.04853	−0.182511
$280$	−5.97487	−0.357067
$281$	19.8137	1.18198	0.590992	−	0.806678i	$-0.298737\pi$
$281$	19.8137	1.18198	0.590992	+	0.806678i	$0.298737\pi$
$282$	−1.37782	−0.0820479
$283$	19.1005	1.13541	0.567704	−	0.823233i	$-0.307832\pi$
$283$	19.1005	1.13541	0.567704	+	0.823233i	$0.307832\pi$
$284$	14.4877	0.859686
$285$	−7.53859	−0.446548
$286$	2.05717	0.121643
$287$	10.2607	0.605672
$288$	−8.66876	−0.510812
$289$	−11.4045	−0.670855
$290$	−3.78396	−0.222202
$291$	9.52148	0.558159
$292$	−3.69469	−0.216215
$293$	−20.7855	−1.21430	−0.607151	−	0.794586i	$-0.707688\pi$
$293$	−20.7855	−1.21430	−0.607151	+	0.794586i	$0.707688\pi$
$294$	3.72010	0.216960
$295$	−8.02028	−0.466959
$296$	3.89079	0.226147
$297$	−19.4128	−1.12645
$298$	1.09059	0.0631761
$299$	4.32819	0.250306
$300$	−1.66069	−0.0958801
$301$	10.6701	0.615017
$302$	5.12970	0.295181
$303$	8.93154	0.513104
$304$	27.6929	1.58830
$305$	−3.25499	−0.186380
$306$	1.86362	0.106536
$307$	33.2376	1.89697	0.948486	−	0.316818i	$-0.102614\pi$
$307$	33.2376	1.89697	0.948486	+	0.316818i	$0.102614\pi$
$308$	34.1102	1.94361
$309$	2.41251	0.137243
$310$	−0.489892	−0.0278240
$311$	−33.3072	−1.88868	−0.944339	−	0.328975i	$-0.893297\pi$
$311$	−33.3072	−1.88868	−0.944339	+	0.328975i	$0.893297\pi$
$312$	−1.68182	−0.0952143
$313$	−2.15855	−0.122008	−0.0610042	−	0.998138i	$-0.519430\pi$
$313$	−2.15855	−0.122008	−0.0610042	+	0.998138i	$0.519430\pi$
$314$	−5.76769	−0.325489
$315$	−9.59902	−0.540843
$316$	25.9563	1.46015
$317$	−23.2922	−1.30822	−0.654110	−	0.756399i	$-0.726957\pi$
$317$	−23.2922	−1.30822	−0.654110	+	0.756399i	$0.726957\pi$
$318$	2.76052	0.154802
$319$	44.6647	2.50074
$320$	5.11976	0.286203
$321$	12.5987	0.703189
$322$	−4.84998	−0.270279
$323$	−20.1163	−1.11930
$324$	−4.76814	−0.264897
$325$	1.37659	0.0763593
$326$	6.63163	0.367292
$327$	−18.0431	−0.997787
$328$	3.26198	0.180113
$329$	18.9374	1.04405
$330$	−1.32473	−0.0729238
$331$	8.99081	0.494180	0.247090	−	0.968993i	$-0.420526\pi$
$331$	8.99081	0.494180	0.247090	+	0.968993i	$0.420526\pi$
$332$	24.8051	1.36136
$333$	6.25080	0.342542
$334$	5.13391	0.280915
$335$	5.05257	0.276051
$336$	−12.5144	−0.682717
$337$	7.74491	0.421892	0.210946	−	0.977498i	$-0.432346\pi$
$337$	7.74491	0.421892	0.210946	+	0.977498i	$0.432346\pi$
$338$	−3.95133	−0.214924
$339$	4.91076	0.266716
$340$	−4.43147	−0.240330
$341$	5.78255	0.313142
$342$	−6.69991	−0.362290
$343$	−20.7842	−1.12224
$344$	3.39214	0.182892
$345$	−2.78716	−0.150056
$346$	0.188887	0.0101546
$347$	−31.4997	−1.69099	−0.845495	−	0.533983i	$-0.820695\pi$
$347$	−31.4997	−1.69099	−0.845495	+	0.533983i	$0.820695\pi$
$348$	−17.6608	−0.946720
$349$	−17.6257	−0.943483	−0.471741	−	0.881737i	$-0.656374\pi$
$349$	−17.6257	−0.943483	−0.471741	+	0.881737i	$0.656374\pi$
$350$	−1.54254	−0.0824523
$351$	−6.36282	−0.339622
$352$	16.4432	0.876424
$353$	−30.0545	−1.59964	−0.799819	−	0.600241i	$-0.795071\pi$
$353$	−30.0545	−1.59964	−0.799819	+	0.600241i	$0.795071\pi$
$354$	2.52973	0.134453
$355$	7.73338	0.410445
$356$	−22.3477	−1.18443
$357$	9.09056	0.481123
$358$	−1.03161	−0.0545224
$359$	−29.8983	−1.57797	−0.788986	−	0.614411i	$-0.789394\pi$
$359$	−29.8983	−1.57797	−0.788986	+	0.614411i	$0.789394\pi$
$360$	−3.05162	−0.160834
$361$	53.3205	2.80634
$362$	7.16220	0.376437
$363$	5.88563	0.308916
$364$	11.1801	0.585997
$365$	−1.97219	−0.103229
$366$	1.02668	0.0536652
$367$	−14.8032	−0.772723	−0.386362	−	0.922347i	$-0.626268\pi$
$367$	−14.8032	−0.772723	−0.386362	+	0.922347i	$0.626268\pi$
$368$	10.2386	0.533725
$369$	5.24059	0.272814
$370$	1.00449	0.0522210
$371$	−37.9419	−1.96985
$372$	−2.28647	−0.118548
$373$	−1.84791	−0.0956809	−0.0478405	−	0.998855i	$-0.515234\pi$
$373$	−1.84791	−0.0956809	−0.0478405	+	0.998855i	$0.515234\pi$
$374$	−3.53497	−0.182789
$375$	−0.886461	−0.0457766
$376$	6.02038	0.310478
$377$	14.6395	0.753972
$378$	7.12989	0.366722
$379$	21.3577	1.09707	0.548535	−	0.836128i	$-0.315186\pi$
$379$	21.3577	1.09707	0.548535	+	0.836128i	$0.315186\pi$
$380$	15.9316	0.817275
$381$	16.9459	0.868167
$382$	1.71756	0.0878778
$383$	−22.9982	−1.17515	−0.587577	−	0.809168i	$-0.699918\pi$
$383$	−22.9982	−1.17515	−0.587577	+	0.809168i	$0.699918\pi$
$384$	−8.55602	−0.436623
$385$	18.2077	0.927951
$386$	2.68085	0.136452
$387$	5.44970	0.277024
$388$	−20.1222	−1.02155
$389$	−2.52836	−0.128193	−0.0640964	−	0.997944i	$-0.520417\pi$
$389$	−2.52836	−0.128193	−0.0640964	+	0.997944i	$0.520417\pi$
$390$	−0.434198	−0.0219865
$391$	−7.43740	−0.376126
$392$	−16.2550	−0.821001
$393$	1.66992	0.0842364
$394$	−1.14191	−0.0575287
$395$	13.8552	0.697130
$396$	17.4215	0.875465
$397$	−34.2967	−1.72130	−0.860650	−	0.509197i	$-0.829943\pi$
$397$	−34.2967	−1.72130	−0.860650	+	0.509197i	$0.829943\pi$
$398$	1.31757	0.0660437
$399$	−32.6816	−1.63612
$400$	3.25640	0.162820
$401$	−9.43790	−0.471306	−0.235653	−	0.971837i	$-0.575723\pi$
$401$	−9.43790	−0.471306	−0.235653	+	0.971837i	$0.575723\pi$
$402$	−1.59366	−0.0794846
$403$	1.89531	0.0944121
$404$	−18.8754	−0.939086
$405$	−2.54518	−0.126471
$406$	−16.4043	−0.814133
$407$	−11.8567	−0.587716
$408$	2.88997	0.143075
$409$	−28.1486	−1.39186	−0.695930	−	0.718110i	$-0.745008\pi$
$409$	−28.1486	−1.39186	−0.695930	+	0.718110i	$0.745008\pi$
$410$	0.842151	0.0415909
$411$	11.8280	0.583431
$412$	−5.09847	−0.251183
$413$	−34.7698	−1.71091
$414$	−2.47709	−0.121742
$415$	13.2407	0.649962
$416$	5.38948	0.264241
$417$	10.9400	0.535734
$418$	12.7086	0.621598
$419$	−4.04373	−0.197549	−0.0987745	−	0.995110i	$-0.531492\pi$
$419$	−4.04373	−0.197549	−0.0987745	+	0.995110i	$0.531492\pi$
$420$	−7.19949	−0.351299
$421$	−10.9544	−0.533886	−0.266943	−	0.963712i	$-0.586014\pi$
$421$	−10.9544	−0.533886	−0.266943	+	0.963712i	$0.586014\pi$
$422$	−2.93421	−0.142835
$423$	9.67214	0.470275
$424$	−12.0621	−0.585787
$425$	−2.36547	−0.114742
$426$	−2.43923	−0.118181
$427$	−14.1111	−0.682886
$428$	−26.6253	−1.28698
$429$	5.12514	0.247444
$430$	0.875754	0.0422326
$431$	22.4072	1.07932	0.539659	−	0.841883i	$-0.318553\pi$
$431$	22.4072	1.07932	0.539659	+	0.841883i	$0.318553\pi$
$432$	−15.0517	−0.724173
$433$	1.26933	0.0610002	0.0305001	−	0.999535i	$-0.490290\pi$
$433$	1.26933	0.0610002	0.0305001	+	0.999535i	$0.490290\pi$
$434$	−2.12380	−0.101946
$435$	−9.42717	−0.451998
$436$	38.1313	1.82616
$437$	26.7383	1.27907
$438$	0.622059	0.0297231
$439$	17.6018	0.840090	0.420045	−	0.907503i	$-0.362014\pi$
$439$	17.6018	0.840090	0.420045	+	0.907503i	$0.362014\pi$
$440$	5.78840	0.275951
$441$	−26.1147	−1.24356
$442$	−1.15863	−0.0551106
$443$	19.1562	0.910137	0.455069	−	0.890456i	$-0.349615\pi$
$443$	19.1562	0.910137	0.455069	+	0.890456i	$0.349615\pi$
$444$	4.68825	0.222495
$445$	−11.9290	−0.565489
$446$	−1.31505	−0.0622695
$447$	2.71704	0.128512
$448$	22.1953	1.04863
$449$	26.3724	1.24459	0.622295	−	0.782782i	$-0.286200\pi$
$449$	26.3724	1.24459	0.622295	+	0.782782i	$0.286200\pi$
$450$	−0.787841	−0.0371392
$451$	−9.94051	−0.468080
$452$	−10.3781	−0.488146
$453$	12.7799	0.600452
$454$	−1.06900	−0.0501706
$455$	5.96783	0.279776
$456$	−10.3898	−0.486546
$457$	35.5012	1.66068	0.830338	−	0.557260i	$-0.188147\pi$
$457$	35.5012	1.66068	0.830338	+	0.557260i	$0.188147\pi$
$458$	7.32797	0.342413
$459$	10.9336	0.510338
$460$	5.89023	0.274634
$461$	−10.9470	−0.509853	−0.254926	−	0.966960i	$-0.582051\pi$
$461$	−10.9470	−0.509853	−0.254926	+	0.966960i	$0.582051\pi$
$462$	−5.74300	−0.267189
$463$	−31.8605	−1.48068	−0.740342	−	0.672230i	$-0.765336\pi$
$463$	−31.8605	−1.48068	−0.740342	+	0.672230i	$0.765336\pi$
$464$	34.6306	1.60769
$465$	−1.22049	−0.0565991
$466$	−2.04845	−0.0948925
$467$	−21.0300	−0.973150	−0.486575	−	0.873639i	$-0.661754\pi$
$467$	−21.0300	−0.973150	−0.486575	+	0.873639i	$0.661754\pi$
$468$	5.71015	0.263952
$469$	21.9041	1.01144
$470$	1.55429	0.0716941
$471$	−14.3694	−0.662105
$472$	−11.0536	−0.508785
$473$	−10.3371	−0.475303
$474$	−4.37015	−0.200728
$475$	8.50414	0.390197
$476$	−19.2115	−0.880556
$477$	−19.3785	−0.887282
$478$	−2.72017	−0.124418
$479$	8.65838	0.395612	0.197806	−	0.980241i	$-0.436618\pi$
$479$	8.65838	0.395612	0.197806	+	0.980241i	$0.436618\pi$
$480$	−3.47058	−0.158410
$481$	−3.88620	−0.177196
$482$	0.355815	0.0162069
$483$	−12.0830	−0.549796
$484$	−12.4384	−0.565380
$485$	−10.7410	−0.487724
$486$	5.73671	0.260222
$487$	−24.5204	−1.11113	−0.555564	−	0.831474i	$-0.687497\pi$
$487$	−24.5204	−1.11113	−0.555564	+	0.831474i	$0.687497\pi$
$488$	−4.48607	−0.203075
$489$	16.5217	0.747139
$490$	−4.19657	−0.189582
$491$	11.5987	0.523443	0.261721	−	0.965143i	$-0.415710\pi$
$491$	11.5987	0.523443	0.261721	+	0.965143i	$0.415710\pi$
$492$	3.93056	0.177204
$493$	−25.1559	−1.13297
$494$	4.16542	0.187411
$495$	9.29945	0.417979
$496$	4.48347	0.201314
$497$	33.5260	1.50385
$498$	−4.17634	−0.187146
$499$	8.26526	0.370004	0.185002	−	0.982738i	$-0.440771\pi$
$499$	8.26526	0.370004	0.185002	+	0.982738i	$0.440771\pi$
$500$	1.87340	0.0837808
$501$	12.7904	0.571432
$502$	5.29405	0.236285
$503$	−10.4795	−0.467256	−0.233628	−	0.972326i	$-0.575060\pi$
$503$	−10.4795	−0.467256	−0.233628	+	0.972326i	$0.575060\pi$
$504$	−13.2295	−0.589288
$505$	−10.0755	−0.448354
$506$	4.69862	0.208879
$507$	−9.84416	−0.437194
$508$	−35.8126	−1.58893
$509$	−5.77886	−0.256144	−0.128072	−	0.991765i	$-0.540879\pi$
$509$	−5.77886	−0.256144	−0.128072	+	0.991765i	$0.540879\pi$
$510$	0.746109	0.0330382
$511$	−8.54989	−0.378225
$512$	21.7252	0.960126
$513$	−39.3076	−1.73547
$514$	−5.12899	−0.226230
$515$	−2.72151	−0.119924
$516$	4.08740	0.179938
$517$	−18.3464	−0.806874
$518$	4.35470	0.191335
$519$	0.470585	0.0206564
$520$	1.89723	0.0831990
$521$	25.7131	1.12651	0.563256	−	0.826283i	$-0.309549\pi$
$521$	25.7131	1.12651	0.563256	+	0.826283i	$0.309549\pi$
$522$	−8.37839	−0.366712
$523$	36.8450	1.61112	0.805560	−	0.592514i	$-0.201865\pi$
$523$	36.8450	1.61112	0.805560	+	0.592514i	$0.201865\pi$
$524$	−3.52912	−0.154170
$525$	−3.84302	−0.167723
$526$	11.3281	0.493931
$527$	−3.25683	−0.141870
$528$	12.1239	0.527623
$529$	−13.1143	−0.570188
$530$	−3.11409	−0.135267
$531$	−17.7584	−0.770649
$532$	69.0673	2.99445
$533$	−3.25814	−0.141126
$534$	3.76260	0.162824
$535$	−14.2123	−0.614453
$536$	6.96351	0.300778
$537$	−2.57011	−0.110908
$538$	−10.1264	−0.436581
$539$	49.5351	2.13363
$540$	−8.65916	−0.372631
$541$	32.0998	1.38008	0.690039	−	0.723772i	$-0.257593\pi$
$541$	32.0998	1.38008	0.690039	+	0.723772i	$0.257593\pi$
$542$	2.86064	0.122875
$543$	17.8436	0.765741
$544$	−9.26107	−0.397065
$545$	20.3541	0.871874
$546$	−1.88235	−0.0805571
$547$	−8.15963	−0.348881	−0.174440	−	0.984668i	$-0.555812\pi$
$547$	−8.15963	−0.348881	−0.174440	+	0.984668i	$0.555812\pi$
$548$	−24.9966	−1.06780
$549$	−7.20716	−0.307594
$550$	1.49440	0.0637214
$551$	90.4383	3.85280
$552$	−3.84130	−0.163497
$553$	60.0655	2.55424
$554$	−10.2471	−0.435356
$555$	2.50254	0.106227
$556$	−23.1200	−0.980505
$557$	−13.7738	−0.583616	−0.291808	−	0.956477i	$-0.594257\pi$
$557$	−13.7738	−0.583616	−0.291808	+	0.956477i	$0.594257\pi$
$558$	−1.08471	−0.0459195
$559$	−3.38814	−0.143303
$560$	14.1173	0.596564
$561$	−8.80685	−0.371826
$562$	7.04999	0.297386
$563$	−10.2103	−0.430312	−0.215156	−	0.976580i	$-0.569026\pi$
$563$	−10.2103	−0.430312	−0.215156	+	0.976580i	$0.569026\pi$
$564$	7.25433	0.305462
$565$	−5.53974	−0.233059
$566$	6.79625	0.285668
$567$	−11.0340	−0.463383
$568$	10.6582	0.447210
$569$	10.8730	0.455819	0.227909	−	0.973682i	$-0.426811\pi$
$569$	10.8730	0.455819	0.227909	+	0.973682i	$0.426811\pi$
$570$	−2.68234	−0.112351
$571$	−31.5845	−1.32177	−0.660886	−	0.750487i	$-0.729819\pi$
$571$	−31.5845	−1.32177	−0.660886	+	0.750487i	$0.729819\pi$
$572$	−10.8312	−0.452875
$573$	4.27904	0.178759
$574$	3.65092	0.152387
$575$	3.14415	0.131120
$576$	11.3361	0.472337
$577$	4.15068	0.172795	0.0863976	−	0.996261i	$-0.472464\pi$
$577$	4.15068	0.172795	0.0863976	+	0.996261i	$0.472464\pi$
$578$	−4.05790	−0.168786
$579$	6.67896	0.277568
$580$	19.9228	0.827251
$581$	57.4017	2.38142
$582$	3.38789	0.140432
$583$	36.7578	1.52235
$584$	−2.71809	−0.112475
$585$	3.04802	0.126020
$586$	−7.39580	−0.305518
$587$	5.91155	0.243996	0.121998	−	0.992530i	$-0.461070\pi$
$587$	5.91155	0.243996	0.121998	+	0.992530i	$0.461070\pi$
$588$	−19.5866	−0.807739
$589$	11.7087	0.482447
$590$	−2.85374	−0.117486
$591$	−2.84491	−0.117024
$592$	−9.19305	−0.377832
$593$	31.3425	1.28708	0.643541	−	0.765412i	$-0.277465\pi$
$593$	31.3425	1.28708	0.643541	+	0.765412i	$0.277465\pi$
$594$	−6.90738	−0.283413
$595$	−10.2549	−0.420409
$596$	−5.74204	−0.235203
$597$	3.28253	0.134345
$598$	1.54004	0.0629768
$599$	6.40219	0.261586	0.130793	−	0.991410i	$-0.458248\pi$
$599$	6.40219	0.261586	0.130793	+	0.991410i	$0.458248\pi$
$600$	−1.22173	−0.0498770
$601$	−14.3131	−0.583842	−0.291921	−	0.956442i	$-0.594294\pi$
$601$	−14.3131	−0.583842	−0.291921	+	0.956442i	$0.594294\pi$
$602$	3.79660	0.154738
$603$	11.1873	0.455583
$604$	−27.0083	−1.09895
$605$	−6.63947	−0.269933
$606$	3.17797	0.129096
$607$	12.8918	0.523263	0.261632	−	0.965168i	$-0.415739\pi$
$607$	12.8918	0.523263	0.261632	+	0.965168i	$0.415739\pi$
$608$	33.2946	1.35027
$609$	−40.8690	−1.65610
$610$	−1.15817	−0.0468931
$611$	−6.01329	−0.243272
$612$	−9.81210	−0.396631
$613$	−3.07774	−0.124309	−0.0621543	−	0.998067i	$-0.519797\pi$
$613$	−3.07774	−0.124309	−0.0621543	+	0.998067i	$0.519797\pi$
$614$	11.8265	0.477277
$615$	2.09810	0.0846034
$616$	25.0941	1.01107
$617$	−30.9284	−1.24513	−0.622566	−	0.782567i	$-0.713910\pi$
$617$	−30.9284	−1.24513	−0.622566	+	0.782567i	$0.713910\pi$
$618$	0.858408	0.0345302
$619$	12.9999	0.522510	0.261255	−	0.965270i	$-0.415864\pi$
$619$	12.9999	0.522510	0.261255	+	0.965270i	$0.415864\pi$
$620$	2.57932	0.103588
$621$	−14.5328	−0.583181
$622$	−11.8512	−0.475190
$623$	−51.7150	−2.07192
$624$	3.97376	0.159078
$625$	1.00000	0.0400000
$626$	−0.768044	−0.0306972
$627$	31.6616	1.26444
$628$	30.3674	1.21179
$629$	6.67790	0.266265
$630$	−3.41547	−0.136076
$631$	14.5975	0.581116	0.290558	−	0.956857i	$-0.406159\pi$
$631$	14.5975	0.581116	0.290558	+	0.956857i	$0.406159\pi$
$632$	19.0954	0.759574
$633$	−7.31016	−0.290553
$634$	−8.28771	−0.329147
$635$	−19.1164	−0.758611
$636$	−14.5344	−0.576325
$637$	16.2358	0.643287
$638$	15.8924	0.629185
$639$	17.1231	0.677381
$640$	9.65189	0.381524
$641$	−10.3567	−0.409066	−0.204533	−	0.978860i	$-0.565567\pi$
$641$	−10.3567	−0.409066	−0.204533	+	0.978860i	$0.565567\pi$
$642$	4.48280	0.176922
$643$	36.4499	1.43744	0.718722	−	0.695298i	$-0.244727\pi$
$643$	36.4499	1.43744	0.718722	+	0.695298i	$0.244727\pi$
$644$	25.5355	1.00624
$645$	2.18181	0.0859088
$646$	−7.15769	−0.281616
$647$	21.8176	0.857740	0.428870	−	0.903366i	$-0.358912\pi$
$647$	21.8176	0.857740	0.428870	+	0.903366i	$0.358912\pi$
$648$	−3.50780	−0.137800
$649$	33.6847	1.32224
$650$	0.489810	0.0192119
$651$	−5.29113	−0.207376
$652$	−34.9161	−1.36742
$653$	−25.7730	−1.00858	−0.504288	−	0.863536i	$-0.668245\pi$
$653$	−25.7730	−1.00858	−0.504288	+	0.863536i	$0.668245\pi$
$654$	−6.42001	−0.251042
$655$	−1.88381	−0.0736064
$656$	−7.70733	−0.300921
$657$	−4.36679	−0.170365
$658$	6.73822	0.262683
$659$	−49.0803	−1.91190	−0.955949	−	0.293532i	$-0.905169\pi$
$659$	−49.0803	−1.91190	−0.955949	+	0.293532i	$0.905169\pi$
$660$	6.97480	0.271494
$661$	20.0184	0.778626	0.389313	−	0.921106i	$-0.372713\pi$
$661$	20.0184	0.778626	0.389313	+	0.921106i	$0.372713\pi$
$662$	3.19906	0.124335
$663$	−2.88657	−0.112105
$664$	18.2485	0.708181
$665$	36.8675	1.42966
$666$	2.22413	0.0861833
$667$	33.4368	1.29468
$668$	−27.0305	−1.04584
$669$	−3.27626	−0.126668
$670$	1.79778	0.0694543
$671$	13.6708	0.527754
$672$	−15.0458	−0.580404
$673$	49.6142	1.91249	0.956244	−	0.292572i	$-0.0945110\pi$
$673$	49.6142	1.91249	0.956244	+	0.292572i	$0.0945110\pi$
$674$	2.75575	0.106148
$675$	−4.62217	−0.177908
$676$	20.8041	0.800157
$677$	12.9122	0.496256	0.248128	−	0.968727i	$-0.420185\pi$
$677$	12.9122	0.496256	0.248128	+	0.968727i	$0.420185\pi$
$678$	1.74732	0.0671055
$679$	−46.5648	−1.78699
$680$	−3.26013	−0.125020
$681$	−2.66325	−0.102056
$682$	2.05752	0.0787863
$683$	34.7992	1.33156	0.665778	−	0.746150i	$-0.268100\pi$
$683$	34.7992	1.33156	0.665778	+	0.746150i	$0.268100\pi$
$684$	35.2756	1.34880
$685$	−13.3429	−0.509807
$686$	−7.39534	−0.282355
$687$	18.2566	0.696531
$688$	−8.01486	−0.305564
$689$	12.0479	0.458987
$690$	−0.991715	−0.0377539
$691$	16.5349	0.629017	0.314509	−	0.949255i	$-0.398160\pi$
$691$	16.5349	0.629017	0.314509	+	0.949255i	$0.398160\pi$
$692$	−0.994508	−0.0378055
$693$	40.3153	1.53145
$694$	−11.2081	−0.425452
$695$	−12.3412	−0.468129
$696$	−12.9926	−0.492485
$697$	5.59866	0.212064
$698$	−6.27149	−0.237379
$699$	−5.10341	−0.193029
$700$	8.12161	0.306968
$701$	−39.1534	−1.47880	−0.739402	−	0.673264i	$-0.764892\pi$
$701$	−39.1534	−1.47880	−0.739402	+	0.673264i	$0.764892\pi$
$702$	−2.26399	−0.0854487
$703$	−24.0078	−0.905471
$704$	−21.5026	−0.810412
$705$	3.87229	0.145839
$706$	−10.6938	−0.402468
$707$	−43.6797	−1.64274
$708$	−13.3192	−0.500567
$709$	−3.68348	−0.138336	−0.0691679	−	0.997605i	$-0.522034\pi$
$709$	−3.68348	−0.138336	−0.0691679	+	0.997605i	$0.522034\pi$
$710$	2.75165	0.103268
$711$	30.6780	1.15051
$712$	−16.4407	−0.616141
$713$	4.32892	0.162119
$714$	3.23456	0.121050
$715$	−5.78158	−0.216219
$716$	5.43152	0.202985
$717$	−6.77692	−0.253089
$718$	−10.6383	−0.397016
$719$	40.9505	1.52720	0.763598	−	0.645692i	$-0.223431\pi$
$719$	40.9505	1.52720	0.763598	+	0.645692i	$0.223431\pi$
$720$	7.21029	0.268711
$721$	−11.7984	−0.439395
$722$	18.9722	0.706073
$723$	0.886461	0.0329678
$724$	−37.7096	−1.40147
$725$	10.6346	0.394960
$726$	2.09420	0.0777229
$727$	19.0775	0.707545	0.353772	−	0.935332i	$-0.384899\pi$
$727$	19.0775	0.707545	0.353772	+	0.935332i	$0.384899\pi$
$728$	8.22493	0.304836
$729$	6.65661	0.246541
$730$	−0.701733	−0.0259723
$731$	5.82205	0.215336
$732$	−5.40554	−0.199794
$733$	28.1421	1.03945	0.519726	−	0.854333i	$-0.326034\pi$
$733$	28.1421	1.03945	0.519726	+	0.854333i	$0.326034\pi$
$734$	−5.26722	−0.194417
$735$	−10.4551	−0.385644
$736$	12.3097	0.453740
$737$	−21.2205	−0.781666
$738$	1.86468	0.0686398
$739$	10.3260	0.379847	0.189923	−	0.981799i	$-0.439176\pi$
$739$	10.3260	0.379847	0.189923	+	0.981799i	$0.439176\pi$
$740$	−5.28873	−0.194417
$741$	10.3775	0.381228
$742$	−13.5003	−0.495611
$743$	20.9971	0.770309	0.385154	−	0.922852i	$-0.374148\pi$
$743$	20.9971	0.770309	0.385154	+	0.922852i	$0.374148\pi$
$744$	−1.68210	−0.0616688
$745$	−3.06504	−0.112294
$746$	−0.657512	−0.0240732
$747$	29.3175	1.07267
$748$	18.6119	0.680518
$749$	−61.6138	−2.25132
$750$	−0.315416	−0.0115174
$751$	−31.2453	−1.14016	−0.570079	−	0.821590i	$-0.693087\pi$
$751$	−31.2453	−1.14016	−0.570079	+	0.821590i	$0.693087\pi$
$752$	−14.2248	−0.518725
$753$	13.1894	0.480647
$754$	5.20895	0.189699
$755$	−14.4168	−0.524679
$756$	−37.5395	−1.36530
$757$	14.8139	0.538422	0.269211	−	0.963081i	$-0.413237\pi$
$757$	14.8139	0.538422	0.269211	+	0.963081i	$0.413237\pi$
$758$	7.59938	0.276022
$759$	11.7059	0.424898
$760$	11.7205	0.425148
$761$	−12.4610	−0.451709	−0.225855	−	0.974161i	$-0.572517\pi$
$761$	−12.4610	−0.451709	−0.225855	+	0.974161i	$0.572517\pi$
$762$	6.02962	0.218430
$763$	88.2398	3.19450
$764$	−9.04307	−0.327167
$765$	−5.23760	−0.189366
$766$	−8.18311	−0.295668
$767$	11.0406	0.398654
$768$	6.03257	0.217681
$769$	8.69289	0.313474	0.156737	−	0.987640i	$-0.449903\pi$
$769$	8.69289	0.313474	0.156737	+	0.987640i	$0.449903\pi$
$770$	6.47857	0.233472
$771$	−12.7781	−0.460194
$772$	−14.1149	−0.508007
$773$	−23.1946	−0.834253	−0.417127	−	0.908848i	$-0.636963\pi$
$773$	−23.1946	−0.834253	−0.417127	+	0.908848i	$0.636963\pi$
$774$	1.93908	0.0696989
$775$	1.37682	0.0494567
$776$	−14.8034	−0.531410
$777$	10.8491	0.389209
$778$	−0.899627	−0.0322532
$779$	−20.1278	−0.721153
$780$	2.28609	0.0818551
$781$	−32.4797	−1.16222
$782$	−2.64634	−0.0946329
$783$	−49.1550	−1.75666
$784$	38.4069	1.37167
$785$	16.2098	0.578552
$786$	0.594183	0.0211938
$787$	−23.1198	−0.824132	−0.412066	−	0.911154i	$-0.635193\pi$
$787$	−23.1198	−0.824132	−0.412066	+	0.911154i	$0.635193\pi$
$788$	6.01227	0.214178
$789$	28.2224	1.00474
$790$	4.92988	0.175397
$791$	−24.0161	−0.853913
$792$	12.8166	0.455418
$793$	4.48078	0.159117
$794$	−12.2033	−0.433078
$795$	−7.75829	−0.275158
$796$	−6.93710	−0.245879
$797$	13.3633	0.473353	0.236676	−	0.971589i	$-0.423942\pi$
$797$	13.3633	0.473353	0.236676	+	0.971589i	$0.423942\pi$
$798$	−11.6286	−0.411647
$799$	10.3330	0.365555
$800$	3.91510	0.138420
$801$	−26.4130	−0.933259
$802$	−3.35815	−0.118580
$803$	8.28306	0.292303
$804$	8.39076	0.295919
$805$	13.6306	0.480416
$806$	0.674379	0.0237540
$807$	−25.2285	−0.888085
$808$	−13.8862	−0.488514
$809$	−34.6054	−1.21666	−0.608331	−	0.793683i	$-0.708161\pi$
$809$	−34.6054	−1.21666	−0.608331	+	0.793683i	$0.708161\pi$
$810$	−0.905615	−0.0318201
$811$	−34.9682	−1.22790	−0.613950	−	0.789345i	$-0.710420\pi$
$811$	−34.9682	−1.22790	−0.613950	+	0.789345i	$0.710420\pi$
$812$	86.3702	3.03100
$813$	7.12687	0.249950
$814$	−4.21880	−0.147869
$815$	−18.6379	−0.652856
$816$	−6.82835	−0.239040
$817$	−20.9309	−0.732281
$818$	−10.0157	−0.350191
$819$	13.2139	0.461731
$820$	−4.43400	−0.154842
$821$	39.2399	1.36948	0.684741	−	0.728787i	$-0.259916\pi$
$821$	39.2399	1.36948	0.684741	+	0.728787i	$0.259916\pi$
$822$	4.20857	0.146791
$823$	2.78038	0.0969181	0.0484591	−	0.998825i	$-0.484569\pi$
$823$	2.78038	0.0969181	0.0484591	+	0.998825i	$0.484569\pi$
$824$	−3.75082	−0.130666
$825$	3.72308	0.129621
$826$	−12.3716	−0.430463
$827$	−0.909625	−0.0316307	−0.0158154	−	0.999875i	$-0.505034\pi$
$827$	−0.909625	−0.0316307	−0.0158154	+	0.999875i	$0.505034\pi$
$828$	13.0421	0.453244
$829$	−23.2589	−0.807816	−0.403908	−	0.914800i	$-0.632348\pi$
$829$	−23.2589	−0.807816	−0.403908	+	0.914800i	$0.632348\pi$
$830$	4.71125	0.163530
$831$	−25.5291	−0.885594
$832$	−7.04779	−0.244338
$833$	−27.8990	−0.966643
$834$	3.89261	0.134790
$835$	−14.4286	−0.499322
$836$	−66.9118	−2.31419
$837$	−6.36389	−0.219968
$838$	−1.43882	−0.0497031
$839$	−10.5975	−0.365867	−0.182933	−	0.983125i	$-0.558559\pi$
$839$	−10.5975	−0.365867	−0.182933	+	0.983125i	$0.558559\pi$
$840$	−5.29649	−0.182746
$841$	84.0951	2.89983
$842$	−3.89775	−0.134325
$843$	17.5640	0.604937
$844$	15.4489	0.531772
$845$	11.1050	0.382024
$846$	3.44149	0.118321
$847$	−28.7837	−0.989018
$848$	28.5000	0.978694
$849$	16.9319	0.581100
$850$	−0.841671	−0.0288691
$851$	−8.87615	−0.304271
$852$	12.8428	0.439986
$853$	12.6679	0.433740	0.216870	−	0.976200i	$-0.430415\pi$
$853$	12.6679	0.433740	0.216870	+	0.976200i	$0.430415\pi$
$854$	−5.02096	−0.171814
$855$	18.8298	0.643964
$856$	−19.5876	−0.669490
$857$	46.5974	1.59174	0.795868	−	0.605470i	$-0.207015\pi$
$857$	46.5974	1.59174	0.795868	+	0.605470i	$0.207015\pi$
$858$	1.82360	0.0622568
$859$	3.29957	0.112580	0.0562899	−	0.998414i	$-0.482073\pi$
$859$	3.29957	0.112580	0.0562899	+	0.998414i	$0.482073\pi$
$860$	−4.61092	−0.157231
$861$	9.09574	0.309982
$862$	7.97283	0.271556
$863$	−39.5629	−1.34674	−0.673369	−	0.739306i	$-0.735154\pi$
$863$	−39.5629	−1.34674	−0.673369	+	0.739306i	$0.735154\pi$
$864$	−18.0963	−0.615648
$865$	−0.530858	−0.0180497
$866$	0.451647	0.0153476
$867$	−10.1097	−0.343342
$868$	11.1820	0.379541
$869$	−58.1909	−1.97399
$870$	−3.35433	−0.113722
$871$	−6.95530	−0.235671
$872$	28.0523	0.949970
$873$	−23.7826	−0.804919
$874$	9.51388	0.321812
$875$	4.33523	0.146558
$876$	−3.27519	−0.110659
$877$	−20.5522	−0.694000	−0.347000	−	0.937865i	$-0.612800\pi$
$877$	−20.5522	−0.694000	−0.347000	+	0.937865i	$0.612800\pi$
$878$	6.26300	0.211366
$879$	−18.4256	−0.621478
$880$	−13.6767	−0.461041
$881$	−2.99641	−0.100952	−0.0504759	−	0.998725i	$-0.516074\pi$
$881$	−2.99641	−0.100952	−0.0504759	+	0.998725i	$0.516074\pi$
$882$	−9.29200	−0.312878
$883$	−3.33266	−0.112153	−0.0560765	−	0.998426i	$-0.517859\pi$
$883$	−3.33266	−0.112153	−0.0560765	+	0.998426i	$0.517859\pi$
$884$	6.10030	0.205175
$885$	−7.10967	−0.238989
$886$	6.81605	0.228990
$887$	17.5420	0.589001	0.294501	−	0.955651i	$-0.404847\pi$
$887$	17.5420	0.589001	0.294501	+	0.955651i	$0.404847\pi$
$888$	3.44903	0.115742
$889$	−82.8741	−2.77951
$890$	−4.24452	−0.142276
$891$	10.6896	0.358116
$892$	6.92386	0.231828
$893$	−37.1483	−1.24312
$894$	0.966763	0.0323334
$895$	2.89929	0.0969126
$896$	41.8432	1.39788
$897$	3.83678	0.128106
$898$	9.38370	0.313138
$899$	14.6419	0.488336
$900$	4.14805	0.138268
$901$	−20.7026	−0.689703
$902$	−3.53698	−0.117769
$903$	9.45867	0.314765
$904$	−7.63493	−0.253934
$905$	−20.1290	−0.669111
$906$	4.54728	0.151073
$907$	14.4933	0.481243	0.240621	−	0.970619i	$-0.422649\pi$
$907$	14.4933	0.481243	0.240621	+	0.970619i	$0.422649\pi$
$908$	5.62837	0.186784
$909$	−22.3090	−0.739944
$910$	2.12344	0.0703914
$911$	−17.0735	−0.565669	−0.282834	−	0.959169i	$-0.591275\pi$
$911$	−17.0735	−0.565669	−0.282834	+	0.959169i	$0.591275\pi$
$912$	24.5487	0.812888
$913$	−55.6103	−1.84043
$914$	12.6319	0.417825
$915$	−2.88542	−0.0953891
$916$	−38.5824	−1.27480
$917$	−8.16675	−0.269690
$918$	3.89035	0.128401
$919$	37.8494	1.24854	0.624268	−	0.781210i	$-0.285397\pi$
$919$	37.8494	1.24854	0.624268	+	0.781210i	$0.285397\pi$
$920$	4.33330	0.142865
$921$	29.4639	0.970868
$922$	−3.89511	−0.128278
$923$	−10.6457	−0.350406
$924$	30.2374	0.994738
$925$	−2.82307	−0.0928220
$926$	−11.3364	−0.372539
$927$	−6.02593	−0.197918
$928$	41.6356	1.36676
$929$	6.67476	0.218992	0.109496	−	0.993987i	$-0.465076\pi$
$929$	6.67476	0.218992	0.109496	+	0.993987i	$0.465076\pi$
$930$	−0.434270	−0.0142403
$931$	100.300	3.28720
$932$	10.7853	0.353283
$933$	−29.5255	−0.966622
$934$	−7.48277	−0.244844
$935$	9.93484	0.324904
$936$	4.20082	0.137308
$937$	18.5999	0.607631	0.303816	−	0.952731i	$-0.401739\pi$
$937$	18.5999	0.607631	0.303816	+	0.952731i	$0.401739\pi$
$938$	7.79380	0.254476
$939$	−1.91347	−0.0624437
$940$	−8.18347	−0.266915
$941$	−43.8972	−1.43101	−0.715504	−	0.698609i	$-0.753803\pi$
$941$	−43.8972	−1.43101	−0.715504	+	0.698609i	$0.753803\pi$
$942$	−5.11283	−0.166585
$943$	−7.44164	−0.242333
$944$	26.1173	0.850045
$945$	−20.0382	−0.651843
$946$	−3.67811	−0.119586
$947$	−20.8599	−0.677856	−0.338928	−	0.940812i	$-0.610064\pi$
$947$	−20.8599	−0.677856	−0.338928	+	0.940812i	$0.610064\pi$
$948$	23.0092	0.747304
$949$	2.71489	0.0881289
$950$	3.02590	0.0981732
$951$	−20.6476	−0.669545
$952$	−14.1334	−0.458066
$953$	−42.8038	−1.38655	−0.693276	−	0.720672i	$-0.743833\pi$
$953$	−42.8038	−1.38655	−0.693276	+	0.720672i	$0.743833\pi$
$954$	−6.89517	−0.223239
$955$	−4.82710	−0.156201
$956$	14.3219	0.463205
$957$	39.5935	1.27988
$958$	3.08078	0.0995355
$959$	−57.8447	−1.86790
$960$	4.53846	0.146478
$961$	−29.1044	−0.938851
$962$	−1.38277	−0.0445822
$963$	−31.4688	−1.01407
$964$	−1.87340	−0.0603380
$965$	−7.53440	−0.242541
$966$	−4.29932	−0.138328
$967$	31.2225	1.00405	0.502024	−	0.864854i	$-0.332589\pi$
$967$	31.2225	1.00405	0.502024	+	0.864854i	$0.332589\pi$
$968$	−9.15060	−0.294111
$969$	−17.8323	−0.572857
$970$	−3.82181	−0.122711
$971$	−16.0467	−0.514964	−0.257482	−	0.966283i	$-0.582893\pi$
$971$	−16.0467	−0.514964	−0.257482	+	0.966283i	$0.582893\pi$
$972$	−30.2042	−0.968802
$973$	−53.5020	−1.71520
$974$	−8.72474	−0.279559
$975$	1.22029	0.0390806
$976$	10.5996	0.339284
$977$	33.4068	1.06878	0.534390	−	0.845238i	$-0.320542\pi$
$977$	33.4068	1.06878	0.534390	+	0.845238i	$0.320542\pi$
$978$	5.87868	0.187979
$979$	50.1010	1.60124
$980$	22.0953	0.705809
$981$	45.0678	1.43890
$982$	4.12700	0.131698
$983$	−43.0585	−1.37335	−0.686677	−	0.726963i	$-0.740931\pi$
$983$	−43.0585	−1.37335	−0.686677	+	0.726963i	$0.740931\pi$
$984$	2.89162	0.0921815
$985$	3.20929	0.102256
$986$	−8.95085	−0.285053
$987$	16.7873	0.534345
$988$	−21.9313	−0.697727
$989$	−7.73857	−0.246072
$990$	3.30888	0.105163
$991$	−24.9994	−0.794132	−0.397066	−	0.917790i	$-0.629972\pi$
$991$	−24.9994	−0.794132	−0.397066	+	0.917790i	$0.629972\pi$
$992$	5.39038	0.171145
$993$	7.97000	0.252920
$994$	11.9291	0.378367
$995$	−3.70296	−0.117392
$996$	21.9888	0.696742
$997$	−40.9195	−1.29593	−0.647967	−	0.761668i	$-0.724381\pi$
$997$	−40.9195	−1.29593	−0.647967	+	0.761668i	$0.724381\pi$
$998$	2.94090	0.0930927
$999$	13.0487	0.412843

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1205.2.a.d.1.15	✓	25
5.4	even	2		6025.2.a.k.1.11		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.d.1.15	✓	25	1.1	even	1	trivial
6025.2.a.k.1.11		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)

\(f(q)\)	\(=\)	\(q+0.355815 q^{2} +0.886461 q^{3} -1.87340 q^{4} -1.00000 q^{5} +0.315416 q^{6} -4.33523 q^{7} -1.37821 q^{8} -2.21419 q^{9} +O(q^{10})\)	\(q+0.355815 q^{2} +0.886461 q^{3} -1.87340 q^{4} -1.00000 q^{5} +0.315416 q^{6} -4.33523 q^{7} -1.37821 q^{8} -2.21419 q^{9} -0.355815 q^{10} +4.19994 q^{11} -1.66069 q^{12} +1.37659 q^{13} -1.54254 q^{14} -0.886461 q^{15} +3.25640 q^{16} -2.36547 q^{17} -0.787841 q^{18} +8.50414 q^{19} +1.87340 q^{20} -3.84302 q^{21} +1.49440 q^{22} +3.14415 q^{23} -1.22173 q^{24} +1.00000 q^{25} +0.489810 q^{26} -4.62217 q^{27} +8.12161 q^{28} +10.6346 q^{29} -0.315416 q^{30} +1.37682 q^{31} +3.91510 q^{32} +3.72308 q^{33} -0.841671 q^{34} +4.33523 q^{35} +4.14805 q^{36} -2.82307 q^{37} +3.02590 q^{38} +1.22029 q^{39} +1.37821 q^{40} -2.36682 q^{41} -1.36740 q^{42} -2.46126 q^{43} -7.86814 q^{44} +2.21419 q^{45} +1.11873 q^{46} -4.36826 q^{47} +2.88667 q^{48} +11.7943 q^{49} +0.355815 q^{50} -2.09690 q^{51} -2.57889 q^{52} +8.75198 q^{53} -1.64464 q^{54} -4.19994 q^{55} +5.97487 q^{56} +7.53859 q^{57} +3.78396 q^{58} +8.02028 q^{59} +1.66069 q^{60} +3.25499 q^{61} +0.489892 q^{62} +9.59902 q^{63} -5.11976 q^{64} -1.37659 q^{65} +1.32473 q^{66} -5.05257 q^{67} +4.43147 q^{68} +2.78716 q^{69} +1.54254 q^{70} -7.73338 q^{71} +3.05162 q^{72} +1.97219 q^{73} -1.00449 q^{74} +0.886461 q^{75} -15.9316 q^{76} -18.2077 q^{77} +0.434198 q^{78} -13.8552 q^{79} -3.25640 q^{80} +2.54518 q^{81} -0.842151 q^{82} -13.2407 q^{83} +7.19949 q^{84} +2.36547 q^{85} -0.875754 q^{86} +9.42717 q^{87} -5.78840 q^{88} +11.9290 q^{89} +0.787841 q^{90} -5.96783 q^{91} -5.89023 q^{92} +1.22049 q^{93} -1.55429 q^{94} -8.50414 q^{95} +3.47058 q^{96} +10.7410 q^{97} +4.19657 q^{98} -9.29945 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 4 q^{2} + 9 q^{3} + 36 q^{4} - 25 q^{5} + 7 q^{6} + 7 q^{7} - 15 q^{8} + 36 q^{9}+O(q^{10}) \) 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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