LMFDB - Embedded newform 1205.2.a.d.1.16

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			1.16
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)

$f(q)$	$=$	$q+0.747372 q^{2} -2.67711 q^{3} -1.44143 q^{4} -1.00000 q^{5} -2.00080 q^{6} -3.83700 q^{7} -2.57203 q^{8} +4.16691 q^{9} +O(q^{10})$	\(q+0.747372 q^{2} -2.67711 q^{3} -1.44143 q^{4} -1.00000 q^{5} -2.00080 q^{6} -3.83700 q^{7} -2.57203 q^{8} +4.16691 q^{9} -0.747372 q^{10} -2.47614 q^{11} +3.85888 q^{12} -5.59417 q^{13} -2.86767 q^{14} +2.67711 q^{15} +0.960603 q^{16} -5.49636 q^{17} +3.11423 q^{18} +2.62194 q^{19} +1.44143 q^{20} +10.2721 q^{21} -1.85060 q^{22} -7.47263 q^{23} +6.88561 q^{24} +1.00000 q^{25} -4.18092 q^{26} -3.12393 q^{27} +5.53079 q^{28} -0.734243 q^{29} +2.00080 q^{30} +3.92979 q^{31} +5.86199 q^{32} +6.62890 q^{33} -4.10783 q^{34} +3.83700 q^{35} -6.00632 q^{36} -4.79602 q^{37} +1.95956 q^{38} +14.9762 q^{39} +2.57203 q^{40} -7.98571 q^{41} +7.67706 q^{42} +2.88103 q^{43} +3.56920 q^{44} -4.16691 q^{45} -5.58484 q^{46} +6.57769 q^{47} -2.57164 q^{48} +7.72257 q^{49} +0.747372 q^{50} +14.7144 q^{51} +8.06363 q^{52} -10.5638 q^{53} -2.33474 q^{54} +2.47614 q^{55} +9.86889 q^{56} -7.01921 q^{57} -0.548753 q^{58} +8.06673 q^{59} -3.85888 q^{60} -14.6321 q^{61} +2.93702 q^{62} -15.9884 q^{63} +2.45989 q^{64} +5.59417 q^{65} +4.95425 q^{66} +13.4374 q^{67} +7.92265 q^{68} +20.0050 q^{69} +2.86767 q^{70} -2.58407 q^{71} -10.7174 q^{72} +7.39305 q^{73} -3.58442 q^{74} -2.67711 q^{75} -3.77935 q^{76} +9.50095 q^{77} +11.1928 q^{78} -15.3518 q^{79} -0.960603 q^{80} -4.13761 q^{81} -5.96829 q^{82} +9.72367 q^{83} -14.8065 q^{84} +5.49636 q^{85} +2.15320 q^{86} +1.96565 q^{87} +6.36872 q^{88} +10.3559 q^{89} -3.11423 q^{90} +21.4648 q^{91} +10.7713 q^{92} -10.5205 q^{93} +4.91598 q^{94} -2.62194 q^{95} -15.6932 q^{96} -8.19650 q^{97} +5.77164 q^{98} -10.3178 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.747372	0.528472	0.264236	−	0.964458i	$-0.414880\pi$
$2$	0.747372	0.528472	0.264236	+	0.964458i	$0.414880\pi$
$3$	−2.67711	−1.54563	−0.772814	−	0.634632i	$-0.781152\pi$
$3$	−2.67711	−1.54563	−0.772814	+	0.634632i	$0.781152\pi$
$4$	−1.44143	−0.720717
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.00080	−0.816822
$7$	−3.83700	−1.45025	−0.725125	−	0.688617i	$-0.758218\pi$
$7$	−3.83700	−1.45025	−0.725125	+	0.688617i	$0.758218\pi$
$8$	−2.57203	−0.909351
$9$	4.16691	1.38897
$10$	−0.747372	−0.236340
$11$	−2.47614	−0.746585	−0.373292	−	0.927714i	$-0.621771\pi$
$11$	−2.47614	−0.746585	−0.373292	+	0.927714i	$0.621771\pi$
$12$	3.85888	1.11396
$13$	−5.59417	−1.55154	−0.775771	−	0.631014i	$-0.782639\pi$
$13$	−5.59417	−1.55154	−0.775771	+	0.631014i	$0.782639\pi$
$14$	−2.86767	−0.766417
$15$	2.67711	0.691226
$16$	0.960603	0.240151
$17$	−5.49636	−1.33306	−0.666532	−	0.745476i	$-0.732222\pi$
$17$	−5.49636	−1.33306	−0.666532	+	0.745476i	$0.732222\pi$
$18$	3.11423	0.734031
$19$	2.62194	0.601514	0.300757	−	0.953701i	$-0.402761\pi$
$19$	2.62194	0.601514	0.300757	+	0.953701i	$0.402761\pi$
$20$	1.44143	0.322315
$21$	10.2721	2.24155
$22$	−1.85060	−0.394549
$23$	−7.47263	−1.55815	−0.779076	−	0.626930i	$-0.784311\pi$
$23$	−7.47263	−1.55815	−0.779076	+	0.626930i	$0.784311\pi$
$24$	6.88561	1.40552
$25$	1.00000	0.200000
$26$	−4.18092	−0.819947
$27$	−3.12393	−0.601201
$28$	5.53079	1.04522
$29$	−0.734243	−0.136346	−0.0681728	−	0.997674i	$-0.521717\pi$
$29$	−0.734243	−0.136346	−0.0681728	+	0.997674i	$0.521717\pi$
$30$	2.00080	0.365294
$31$	3.92979	0.705811	0.352905	−	0.935659i	$-0.385194\pi$
$31$	3.92979	0.705811	0.352905	+	0.935659i	$0.385194\pi$
$32$	5.86199	1.03626
$33$	6.62890	1.15394
$34$	−4.10783	−0.704487
$35$	3.83700	0.648571
$36$	−6.00632	−1.00105
$37$	−4.79602	−0.788461	−0.394231	−	0.919012i	$-0.628989\pi$
$37$	−4.79602	−0.788461	−0.394231	+	0.919012i	$0.628989\pi$
$38$	1.95956	0.317883
$39$	14.9762	2.39811
$40$	2.57203	0.406674
$41$	−7.98571	−1.24716	−0.623579	−	0.781760i	$-0.714322\pi$
$41$	−7.98571	−1.24716	−0.623579	+	0.781760i	$0.714322\pi$
$42$	7.67706	1.18460
$43$	2.88103	0.439353	0.219676	−	0.975573i	$-0.429500\pi$
$43$	2.88103	0.439353	0.219676	+	0.975573i	$0.429500\pi$
$44$	3.56920	0.538076
$45$	−4.16691	−0.621166
$46$	−5.58484	−0.823439
$47$	6.57769	0.959455	0.479727	−	0.877418i	$-0.340736\pi$
$47$	6.57769	0.959455	0.479727	+	0.877418i	$0.340736\pi$
$48$	−2.57164	−0.371184
$49$	7.72257	1.10322
$50$	0.747372	0.105694
$51$	14.7144	2.06042
$52$	8.06363	1.11822
$53$	−10.5638	−1.45105	−0.725525	−	0.688195i	$-0.758403\pi$
$53$	−10.5638	−1.45105	−0.725525	+	0.688195i	$0.758403\pi$
$54$	−2.33474	−0.317718
$55$	2.47614	0.333883
$56$	9.86889	1.31879
$57$	−7.01921	−0.929717
$58$	−0.548753	−0.0720548
$59$	8.06673	1.05020	0.525099	−	0.851041i	$-0.324028\pi$
$59$	8.06673	1.05020	0.525099	+	0.851041i	$0.324028\pi$
$60$	−3.85888	−0.498179
$61$	−14.6321	−1.87345	−0.936723	−	0.350073i	$-0.886157\pi$
$61$	−14.6321	−1.87345	−0.936723	+	0.350073i	$0.886157\pi$
$62$	2.93702	0.373001
$63$	−15.9884	−2.01435
$64$	2.45989	0.307486
$65$	5.59417	0.693871
$66$	4.95425	0.609826
$67$	13.4374	1.64164	0.820822	−	0.571184i	$-0.193516\pi$
$67$	13.4374	1.64164	0.820822	+	0.571184i	$0.193516\pi$
$68$	7.92265	0.960762
$69$	20.0050	2.40832
$70$	2.86767	0.342752
$71$	−2.58407	−0.306673	−0.153336	−	0.988174i	$-0.549002\pi$
$71$	−2.58407	−0.306673	−0.153336	+	0.988174i	$0.549002\pi$
$72$	−10.7174	−1.26306
$73$	7.39305	0.865291	0.432645	−	0.901564i	$-0.357580\pi$
$73$	7.39305	0.865291	0.432645	+	0.901564i	$0.357580\pi$
$74$	−3.58442	−0.416680
$75$	−2.67711	−0.309126
$76$	−3.77935	−0.433521
$77$	9.50095	1.08273
$78$	11.1928	1.26733
$79$	−15.3518	−1.72721	−0.863606	−	0.504166i	$-0.831800\pi$
$79$	−15.3518	−1.72721	−0.863606	+	0.504166i	$0.831800\pi$
$80$	−0.960603	−0.107399
$81$	−4.13761	−0.459735
$82$	−5.96829	−0.659088
$83$	9.72367	1.06731	0.533656	−	0.845702i	$-0.320818\pi$
$83$	9.72367	1.06731	0.533656	+	0.845702i	$0.320818\pi$
$84$	−14.8065	−1.61552
$85$	5.49636	0.596164
$86$	2.15320	0.232186
$87$	1.96565	0.210740
$88$	6.36872	0.678907
$89$	10.3559	1.09772	0.548862	−	0.835913i	$-0.315061\pi$
$89$	10.3559	1.09772	0.548862	+	0.835913i	$0.315061\pi$
$90$	−3.11423	−0.328269
$91$	21.4648	2.25012
$92$	10.7713	1.12299
$93$	−10.5205	−1.09092
$94$	4.91598	0.507045
$95$	−2.62194	−0.269005
$96$	−15.6932	−1.60168
$97$	−8.19650	−0.832229	−0.416114	−	0.909312i	$-0.636608\pi$
$97$	−8.19650	−0.832229	−0.416114	+	0.909312i	$0.636608\pi$
$98$	5.77164	0.583023
$99$	−10.3178	−1.03698
$100$	−1.44143	−0.144143
$101$	−9.06717	−0.902217	−0.451109	−	0.892469i	$-0.648971\pi$
$101$	−9.06717	−0.902217	−0.451109	+	0.892469i	$0.648971\pi$
$102$	10.9971	1.08888
$103$	−1.86556	−0.183819	−0.0919095	−	0.995767i	$-0.529297\pi$
$103$	−1.86556	−0.183819	−0.0919095	+	0.995767i	$0.529297\pi$
$104$	14.3884	1.41090
$105$	−10.2721	−1.00245
$106$	−7.89510	−0.766840
$107$	−9.73392	−0.941013	−0.470507	−	0.882396i	$-0.655929\pi$
$107$	−9.73392	−0.941013	−0.470507	+	0.882396i	$0.655929\pi$
$108$	4.50295	0.433296
$109$	−7.74347	−0.741689	−0.370845	−	0.928695i	$-0.620932\pi$
$109$	−7.74347	−0.741689	−0.370845	+	0.928695i	$0.620932\pi$
$110$	1.85060	0.176448
$111$	12.8395	1.21867
$112$	−3.68584	−0.348279
$113$	−7.03099	−0.661420	−0.330710	−	0.943732i	$-0.607288\pi$
$113$	−7.03099	−0.661420	−0.330710	+	0.943732i	$0.607288\pi$
$114$	−5.24596	−0.491330
$115$	7.47263	0.696827
$116$	1.05836	0.0982666
$117$	−23.3104	−2.15504
$118$	6.02885	0.555001
$119$	21.0896	1.93328
$120$	−6.88561	−0.628567
$121$	−4.86873	−0.442612
$122$	−10.9356	−0.990063
$123$	21.3786	1.92764
$124$	−5.66453	−0.508690
$125$	−1.00000	−0.0894427
$126$	−11.9493	−1.06453
$127$	0.388169	0.0344444	0.0172222	−	0.999852i	$-0.494518\pi$
$127$	0.388169	0.0344444	0.0172222	+	0.999852i	$0.494518\pi$
$128$	−9.88554	−0.873766
$129$	−7.71282	−0.679076
$130$	4.18092	0.366691
$131$	−0.851631	−0.0744074	−0.0372037	−	0.999308i	$-0.511845\pi$
$131$	−0.851631	−0.0744074	−0.0372037	+	0.999308i	$0.511845\pi$
$132$	−9.55512	−0.831666
$133$	−10.0604	−0.872345
$134$	10.0428	0.867563
$135$	3.12393	0.268865
$136$	14.1368	1.21222
$137$	−10.5196	−0.898747	−0.449373	−	0.893344i	$-0.648353\pi$
$137$	−10.5196	−0.898747	−0.449373	+	0.893344i	$0.648353\pi$
$138$	14.9512	1.27273
$139$	−11.5711	−0.981445	−0.490722	−	0.871316i	$-0.663267\pi$
$139$	−11.5711	−0.981445	−0.490722	+	0.871316i	$0.663267\pi$
$140$	−5.53079	−0.467437
$141$	−17.6092	−1.48296
$142$	−1.93126	−0.162068
$143$	13.8519	1.15836
$144$	4.00274	0.333562
$145$	0.734243	0.0609756
$146$	5.52536	0.457282
$147$	−20.6742	−1.70518
$148$	6.91315	0.568258
$149$	−2.82127	−0.231128	−0.115564	−	0.993300i	$-0.536867\pi$
$149$	−2.82127	−0.231128	−0.115564	+	0.993300i	$0.536867\pi$
$150$	−2.00080	−0.163364
$151$	−15.2230	−1.23883	−0.619415	−	0.785063i	$-0.712630\pi$
$151$	−15.2230	−1.23883	−0.619415	+	0.785063i	$0.712630\pi$
$152$	−6.74371	−0.546987
$153$	−22.9028	−1.85158
$154$	7.10075	0.572195
$155$	−3.92979	−0.315648
$156$	−21.5872	−1.72836
$157$	9.41621	0.751495	0.375748	−	0.926722i	$-0.377386\pi$
$157$	9.41621	0.751495	0.375748	+	0.926722i	$0.377386\pi$
$158$	−11.4735	−0.912784
$159$	28.2805	2.24279
$160$	−5.86199	−0.463431
$161$	28.6725	2.25971
$162$	−3.09234	−0.242957
$163$	−17.4413	−1.36611	−0.683053	−	0.730369i	$-0.739348\pi$
$163$	−17.4413	−1.36611	−0.683053	+	0.730369i	$0.739348\pi$
$164$	11.5109	0.898848
$165$	−6.62890	−0.516059
$166$	7.26720	0.564044
$167$	−10.3380	−0.799981	−0.399991	−	0.916519i	$-0.630987\pi$
$167$	−10.3380	−0.799981	−0.399991	+	0.916519i	$0.630987\pi$
$168$	−26.4201	−2.03835
$169$	18.2947	1.40728
$170$	4.10783	0.315056
$171$	10.9254	0.835484
$172$	−4.15281	−0.316649
$173$	1.02173	0.0776805	0.0388403	−	0.999245i	$-0.487634\pi$
$173$	1.02173	0.0776805	0.0388403	+	0.999245i	$0.487634\pi$
$174$	1.46907	0.111370
$175$	−3.83700	−0.290050
$176$	−2.37859	−0.179293
$177$	−21.5955	−1.62322
$178$	7.73971	0.580116
$179$	15.7956	1.18062	0.590310	−	0.807177i	$-0.299005\pi$
$179$	15.7956	1.18062	0.590310	+	0.807177i	$0.299005\pi$
$180$	6.00632	0.447685
$181$	1.54985	0.115200	0.0575999	−	0.998340i	$-0.481655\pi$
$181$	1.54985	0.115200	0.0575999	+	0.998340i	$0.481655\pi$
$182$	16.0422	1.18913
$183$	39.1716	2.89565
$184$	19.2199	1.41691
$185$	4.79602	0.352611
$186$	−7.86271	−0.576522
$187$	13.6098	0.995245
$188$	−9.48131	−0.691496
$189$	11.9865	0.871892
$190$	−1.95956	−0.142162
$191$	−20.8574	−1.50919	−0.754594	−	0.656192i	$-0.772166\pi$
$191$	−20.8574	−1.50919	−0.754594	+	0.656192i	$0.772166\pi$
$192$	−6.58538	−0.475259
$193$	26.2580	1.89009	0.945046	−	0.326937i	$-0.106016\pi$
$193$	26.2580	1.89009	0.945046	+	0.326937i	$0.106016\pi$
$194$	−6.12584	−0.439809
$195$	−14.9762	−1.07247
$196$	−11.1316	−0.795113
$197$	14.0682	1.00232	0.501158	−	0.865356i	$-0.332907\pi$
$197$	14.0682	1.00232	0.501158	+	0.865356i	$0.332907\pi$
$198$	−7.71127	−0.548016
$199$	22.6111	1.60286	0.801430	−	0.598089i	$-0.204073\pi$
$199$	22.6111	1.60286	0.801430	+	0.598089i	$0.204073\pi$
$200$	−2.57203	−0.181870
$201$	−35.9735	−2.53737
$202$	−6.77655	−0.476797
$203$	2.81729	0.197735
$204$	−21.2098	−1.48498
$205$	7.98571	0.557746
$206$	−1.39427	−0.0971432
$207$	−31.1378	−2.16422
$208$	−5.37377	−0.372604
$209$	−6.49229	−0.449081
$210$	−7.67706	−0.529767
$211$	−8.87403	−0.610914	−0.305457	−	0.952206i	$-0.598809\pi$
$211$	−8.87403	−0.610914	−0.305457	+	0.952206i	$0.598809\pi$
$212$	15.2270	1.04580
$213$	6.91784	0.474002
$214$	−7.27486	−0.497299
$215$	−2.88103	−0.196485
$216$	8.03486	0.546703
$217$	−15.0786	−1.02360
$218$	−5.78725	−0.391962
$219$	−19.7920	−1.33742
$220$	−3.56920	−0.240635
$221$	30.7476	2.06831
$222$	9.59587	0.644032
$223$	−8.69020	−0.581939	−0.290969	−	0.956732i	$-0.593978\pi$
$223$	−8.69020	−0.581939	−0.290969	+	0.956732i	$0.593978\pi$
$224$	−22.4925	−1.50284
$225$	4.16691	0.277794
$226$	−5.25477	−0.349542
$227$	−8.10671	−0.538061	−0.269031	−	0.963132i	$-0.586703\pi$
$227$	−8.10671	−0.538061	−0.269031	+	0.963132i	$0.586703\pi$
$228$	10.1177	0.670063
$229$	−16.7496	−1.10685	−0.553424	−	0.832900i	$-0.686679\pi$
$229$	−16.7496	−1.10685	−0.553424	+	0.832900i	$0.686679\pi$
$230$	5.58484	0.368253
$231$	−25.4351	−1.67351
$232$	1.88850	0.123986
$233$	−13.2872	−0.870477	−0.435238	−	0.900315i	$-0.643336\pi$
$233$	−13.2872	−0.870477	−0.435238	+	0.900315i	$0.643336\pi$
$234$	−17.4215	−1.13888
$235$	−6.57769	−0.429081
$236$	−11.6277	−0.756896
$237$	41.0984	2.66963
$238$	15.7617	1.02168
$239$	−12.5786	−0.813645	−0.406822	−	0.913507i	$-0.633363\pi$
$239$	−12.5786	−0.813645	−0.406822	+	0.913507i	$0.633363\pi$
$240$	2.57164	0.165999
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	−3.63875	−0.233908
$243$	20.4486	1.31178
$244$	21.0912	1.35022
$245$	−7.72257	−0.493377
$246$	15.9778	1.01871
$247$	−14.6676	−0.933274
$248$	−10.1075	−0.641830
$249$	−26.0313	−1.64967
$250$	−0.747372	−0.0472680
$251$	1.80443	0.113894	0.0569472	−	0.998377i	$-0.481863\pi$
$251$	1.80443	0.113894	0.0569472	+	0.998377i	$0.481863\pi$
$252$	23.0463	1.45178
$253$	18.5033	1.16329
$254$	0.290107	0.0182029
$255$	−14.7144	−0.921449
$256$	−12.3079	−0.769247
$257$	−11.2731	−0.703196	−0.351598	−	0.936151i	$-0.614362\pi$
$257$	−11.2731	−0.703196	−0.351598	+	0.936151i	$0.614362\pi$
$258$	−5.76435	−0.358873
$259$	18.4023	1.14347
$260$	−8.06363	−0.500085
$261$	−3.05952	−0.189380
$262$	−0.636486	−0.0393222
$263$	−15.4290	−0.951393	−0.475696	−	0.879610i	$-0.657804\pi$
$263$	−15.4290	−0.951393	−0.475696	+	0.879610i	$0.657804\pi$
$264$	−17.0497	−1.04934
$265$	10.5638	0.648930
$266$	−7.51885	−0.461010
$267$	−27.7239	−1.69667
$268$	−19.3692	−1.18316
$269$	1.94026	0.118300	0.0591499	−	0.998249i	$-0.481161\pi$
$269$	1.94026	0.118300	0.0591499	+	0.998249i	$0.481161\pi$
$270$	2.33474	0.142088
$271$	5.19543	0.315600	0.157800	−	0.987471i	$-0.449560\pi$
$271$	5.19543	0.315600	0.157800	+	0.987471i	$0.449560\pi$
$272$	−5.27983	−0.320136
$273$	−57.4636	−3.47786
$274$	−7.86203	−0.474963
$275$	−2.47614	−0.149317
$276$	−28.8360	−1.73572
$277$	20.0343	1.20374	0.601872	−	0.798592i	$-0.294422\pi$
$277$	20.0343	1.20374	0.601872	+	0.798592i	$0.294422\pi$
$278$	−8.64789	−0.518666
$279$	16.3751	0.980349
$280$	−9.86889	−0.589779
$281$	6.81935	0.406808	0.203404	−	0.979095i	$-0.434799\pi$
$281$	6.81935	0.406808	0.203404	+	0.979095i	$0.434799\pi$
$282$	−13.1606	−0.783703
$283$	23.2743	1.38351	0.691756	−	0.722131i	$-0.256837\pi$
$283$	23.2743	1.38351	0.691756	+	0.722131i	$0.256837\pi$
$284$	3.72477	0.221024
$285$	7.01921	0.415782
$286$	10.3526	0.612160
$287$	30.6412	1.80869
$288$	24.4264	1.43934
$289$	13.2100	0.777060
$290$	0.548753	0.0322239
$291$	21.9429	1.28632
$292$	−10.6566	−0.623630
$293$	−17.7771	−1.03855	−0.519275	−	0.854607i	$-0.673798\pi$
$293$	−17.7771	−1.03855	−0.519275	+	0.854607i	$0.673798\pi$
$294$	−15.4513	−0.901138
$295$	−8.06673	−0.469663
$296$	12.3355	0.716988
$297$	7.73530	0.448848
$298$	−2.10854	−0.122144
$299$	41.8031	2.41754
$300$	3.85888	0.222792
$301$	−11.0545	−0.637171
$302$	−11.3773	−0.654687
$303$	24.2738	1.39449
$304$	2.51864	0.144454
$305$	14.6321	0.837830
$306$	−17.1169	−0.978510
$307$	17.9360	1.02366	0.511832	−	0.859086i	$-0.328967\pi$
$307$	17.9360	1.02366	0.511832	+	0.859086i	$0.328967\pi$
$308$	−13.6950	−0.780345
$309$	4.99430	0.284116
$310$	−2.93702	−0.166811
$311$	−22.7225	−1.28847	−0.644237	−	0.764826i	$-0.722825\pi$
$311$	−22.7225	−1.28847	−0.644237	+	0.764826i	$0.722825\pi$
$312$	−38.5192	−2.18072
$313$	−2.79846	−0.158178	−0.0790891	−	0.996868i	$-0.525201\pi$
$313$	−2.79846	−0.158178	−0.0790891	+	0.996868i	$0.525201\pi$
$314$	7.03741	0.397144
$315$	15.9884	0.900845
$316$	22.1286	1.24483
$317$	23.5836	1.32459	0.662293	−	0.749245i	$-0.269584\pi$
$317$	23.5836	1.32459	0.662293	+	0.749245i	$0.269584\pi$
$318$	21.1360	1.18525
$319$	1.81809	0.101793
$320$	−2.45989	−0.137512
$321$	26.0587	1.45446
$322$	21.4290	1.19419
$323$	−14.4111	−0.801857
$324$	5.96410	0.331339
$325$	−5.59417	−0.310309
$326$	−13.0351	−0.721949
$327$	20.7301	1.14638
$328$	20.5395	1.13410
$329$	−25.2386	−1.39145
$330$	−4.95425	−0.272723
$331$	14.4819	0.795996	0.397998	−	0.917386i	$-0.369705\pi$
$331$	14.4819	0.795996	0.397998	+	0.917386i	$0.369705\pi$
$332$	−14.0160	−0.769230
$333$	−19.9846	−1.09515
$334$	−7.72636	−0.422768
$335$	−13.4374	−0.734166
$336$	9.86738	0.538310
$337$	−0.479030	−0.0260944	−0.0130472	−	0.999915i	$-0.504153\pi$
$337$	−0.479030	−0.0260944	−0.0130472	+	0.999915i	$0.504153\pi$
$338$	13.6729	0.743710
$339$	18.8227	1.02231
$340$	−7.92265	−0.429666
$341$	−9.73071	−0.526947
$342$	8.16532	0.441530
$343$	−2.77252	−0.149702
$344$	−7.41010	−0.399526
$345$	−20.0050	−1.07704
$346$	0.763611	0.0410520
$347$	−18.5939	−0.998174	−0.499087	−	0.866552i	$-0.666331\pi$
$347$	−18.5939	−0.998174	−0.499087	+	0.866552i	$0.666331\pi$
$348$	−2.83335	−0.151884
$349$	30.5711	1.63643	0.818217	−	0.574910i	$-0.194963\pi$
$349$	30.5711	1.63643	0.818217	+	0.574910i	$0.194963\pi$
$350$	−2.86767	−0.153283
$351$	17.4758	0.932789
$352$	−14.5151	−0.773659
$353$	8.65794	0.460816	0.230408	−	0.973094i	$-0.425994\pi$
$353$	8.65794	0.460816	0.230408	+	0.973094i	$0.425994\pi$
$354$	−16.1399	−0.857825
$355$	2.58407	0.137148
$356$	−14.9274	−0.791148
$357$	−56.4590	−2.98813
$358$	11.8052	0.623925
$359$	32.8189	1.73211	0.866057	−	0.499946i	$-0.166647\pi$
$359$	32.8189	1.73211	0.866057	+	0.499946i	$0.166647\pi$
$360$	10.7174	0.564858
$361$	−12.1254	−0.638181
$362$	1.15832	0.0608799
$363$	13.0341	0.684113
$364$	−30.9401	−1.62170
$365$	−7.39305	−0.386970
$366$	29.2758	1.53027
$367$	−1.51766	−0.0792214	−0.0396107	−	0.999215i	$-0.512612\pi$
$367$	−1.51766	−0.0792214	−0.0396107	+	0.999215i	$0.512612\pi$
$368$	−7.17823	−0.374191
$369$	−33.2757	−1.73226
$370$	3.58442	0.186345
$371$	40.5333	2.10439
$372$	15.1646	0.786246
$373$	−18.6485	−0.965582	−0.482791	−	0.875736i	$-0.660377\pi$
$373$	−18.6485	−0.965582	−0.482791	+	0.875736i	$0.660377\pi$
$374$	10.1716	0.525959
$375$	2.67711	0.138245
$376$	−16.9180	−0.872481
$377$	4.10748	0.211546
$378$	8.95840	0.460771
$379$	24.9716	1.28270	0.641352	−	0.767247i	$-0.278374\pi$
$379$	24.9716	1.28270	0.641352	+	0.767247i	$0.278374\pi$
$380$	3.77935	0.193877
$381$	−1.03917	−0.0532383
$382$	−15.5882	−0.797563
$383$	3.95979	0.202336	0.101168	−	0.994869i	$-0.467742\pi$
$383$	3.95979	0.202336	0.101168	+	0.994869i	$0.467742\pi$
$384$	26.4647	1.35052
$385$	−9.50095	−0.484213
$386$	19.6245	0.998861
$387$	12.0050	0.610247
$388$	11.8147	0.599802
$389$	11.1909	0.567402	0.283701	−	0.958913i	$-0.408438\pi$
$389$	11.1909	0.567402	0.283701	+	0.958913i	$0.408438\pi$
$390$	−11.1928	−0.566769
$391$	41.0723	2.07712
$392$	−19.8627	−1.00322
$393$	2.27991	0.115006
$394$	10.5142	0.529696
$395$	15.3518	0.772433
$396$	14.8725	0.747371
$397$	29.7187	1.49154	0.745770	−	0.666204i	$-0.232082\pi$
$397$	29.7187	1.49154	0.745770	+	0.666204i	$0.232082\pi$
$398$	16.8989	0.847066
$399$	26.9327	1.34832
$400$	0.960603	0.0480302
$401$	27.5489	1.37573	0.687863	−	0.725841i	$-0.258549\pi$
$401$	27.5489	1.37573	0.687863	+	0.725841i	$0.258549\pi$
$402$	−26.8856	−1.34093
$403$	−21.9839	−1.09510
$404$	13.0697	0.650244
$405$	4.13761	0.205600
$406$	2.10557	0.104497
$407$	11.8756	0.588653
$408$	−37.8458	−1.87365
$409$	−34.5436	−1.70807	−0.854036	−	0.520213i	$-0.825852\pi$
$409$	−34.5436	−1.70807	−0.854036	+	0.520213i	$0.825852\pi$
$410$	5.96829	0.294753
$411$	28.1620	1.38913
$412$	2.68908	0.132481
$413$	−30.9520	−1.52305
$414$	−23.2715	−1.14373
$415$	−9.72367	−0.477316
$416$	−32.7930	−1.60781
$417$	30.9770	1.51695
$418$	−4.85216	−0.237327
$419$	−17.9479	−0.876814	−0.438407	−	0.898776i	$-0.644457\pi$
$419$	−17.9479	−0.876814	−0.438407	+	0.898776i	$0.644457\pi$
$420$	14.8065	0.722484
$421$	14.7869	0.720671	0.360336	−	0.932823i	$-0.382662\pi$
$421$	14.7869	0.720671	0.360336	+	0.932823i	$0.382662\pi$
$422$	−6.63221	−0.322851
$423$	27.4086	1.33265
$424$	27.1705	1.31951
$425$	−5.49636	−0.266613
$426$	5.17020	0.250497
$427$	56.1433	2.71696
$428$	14.0308	0.678205
$429$	−37.0831	−1.79039
$430$	−2.15320	−0.103837
$431$	37.7847	1.82002	0.910012	−	0.414583i	$-0.136072\pi$
$431$	37.7847	1.82002	0.910012	+	0.414583i	$0.136072\pi$
$432$	−3.00086	−0.144379
$433$	6.44876	0.309907	0.154954	−	0.987922i	$-0.450477\pi$
$433$	6.44876	0.309907	0.154954	+	0.987922i	$0.450477\pi$
$434$	−11.2693	−0.540945
$435$	−1.96565	−0.0942456
$436$	11.1617	0.534548
$437$	−19.5928	−0.937250
$438$	−14.7920	−0.706788
$439$	−31.4719	−1.50207	−0.751035	−	0.660262i	$-0.770445\pi$
$439$	−31.4719	−1.50207	−0.751035	+	0.660262i	$0.770445\pi$
$440$	−6.36872	−0.303617
$441$	32.1792	1.53234
$442$	22.9799	1.09304
$443$	−15.5605	−0.739304	−0.369652	−	0.929170i	$-0.620523\pi$
$443$	−15.5605	−0.739304	−0.369652	+	0.929170i	$0.620523\pi$
$444$	−18.5073	−0.878316
$445$	−10.3559	−0.490917
$446$	−6.49482	−0.307538
$447$	7.55285	0.357238
$448$	−9.43858	−0.445931
$449$	−19.7867	−0.933790	−0.466895	−	0.884313i	$-0.654627\pi$
$449$	−19.7867	−0.933790	−0.466895	+	0.884313i	$0.654627\pi$
$450$	3.11423	0.146806
$451$	19.7737	0.931109
$452$	10.1347	0.476697
$453$	40.7536	1.91477
$454$	−6.05873	−0.284350
$455$	−21.4648	−1.00629
$456$	18.0536	0.845439
$457$	−15.5395	−0.726905	−0.363453	−	0.931613i	$-0.618402\pi$
$457$	−15.5395	−0.726905	−0.363453	+	0.931613i	$0.618402\pi$
$458$	−12.5182	−0.584938
$459$	17.1703	0.801440
$460$	−10.7713	−0.502215
$461$	−4.48495	−0.208885	−0.104443	−	0.994531i	$-0.533306\pi$
$461$	−4.48495	−0.208885	−0.104443	+	0.994531i	$0.533306\pi$
$462$	−19.0095	−0.884401
$463$	−14.2913	−0.664172	−0.332086	−	0.943249i	$-0.607752\pi$
$463$	−14.2913	−0.664172	−0.332086	+	0.943249i	$0.607752\pi$
$464$	−0.705317	−0.0327435
$465$	10.5205	0.487875
$466$	−9.93052	−0.460022
$467$	5.23677	0.242329	0.121164	−	0.992632i	$-0.461337\pi$
$467$	5.23677	0.242329	0.121164	+	0.992632i	$0.461337\pi$
$468$	33.6004	1.55318
$469$	−51.5595	−2.38080
$470$	−4.91598	−0.226757
$471$	−25.2082	−1.16153
$472$	−20.7479	−0.954999
$473$	−7.13383	−0.328014
$474$	30.7158	1.41082
$475$	2.62194	0.120303
$476$	−30.3992	−1.39335
$477$	−44.0184	−2.01546
$478$	−9.40093	−0.429988
$479$	−14.3139	−0.654018	−0.327009	−	0.945021i	$-0.606041\pi$
$479$	−14.3139	−0.654018	−0.327009	+	0.945021i	$0.606041\pi$
$480$	15.6932	0.716293
$481$	26.8298	1.22333
$482$	0.747372	0.0340419
$483$	−76.7594	−3.49267
$484$	7.01795	0.318998
$485$	8.19650	0.372184
$486$	15.2827	0.693239
$487$	−31.0784	−1.40830	−0.704148	−	0.710053i	$-0.748671\pi$
$487$	−31.0784	−1.40830	−0.704148	+	0.710053i	$0.748671\pi$
$488$	37.6342	1.70362
$489$	46.6922	2.11149
$490$	−5.77164	−0.260736
$491$	−6.23064	−0.281185	−0.140592	−	0.990068i	$-0.544901\pi$
$491$	−6.23064	−0.281185	−0.140592	+	0.990068i	$0.544901\pi$
$492$	−30.8158	−1.38929
$493$	4.03567	0.181757
$494$	−10.9621	−0.493209
$495$	10.3178	0.463753
$496$	3.77497	0.169501
$497$	9.91508	0.444752
$498$	−19.4551	−0.871803
$499$	−26.4181	−1.18264	−0.591318	−	0.806438i	$-0.701392\pi$
$499$	−26.4181	−1.18264	−0.591318	+	0.806438i	$0.701392\pi$
$500$	1.44143	0.0644629
$501$	27.6760	1.23647
$502$	1.34858	0.0601900
$503$	23.4011	1.04340	0.521702	−	0.853128i	$-0.325297\pi$
$503$	23.4011	1.04340	0.521702	+	0.853128i	$0.325297\pi$
$504$	41.1227	1.83175
$505$	9.06717	0.403484
$506$	13.8288	0.614767
$507$	−48.9769	−2.17514
$508$	−0.559521	−0.0248247
$509$	−28.8577	−1.27909	−0.639546	−	0.768752i	$-0.720878\pi$
$509$	−28.8577	−1.27909	−0.639546	+	0.768752i	$0.720878\pi$
$510$	−10.9971	−0.486960
$511$	−28.3671	−1.25489
$512$	10.5725	0.467241
$513$	−8.19076	−0.361631
$514$	−8.42519	−0.371619
$515$	1.86556	0.0822063
$516$	11.1175	0.489422
$517$	−16.2873	−0.716314
$518$	13.7534	0.604290
$519$	−2.73528	−0.120065
$520$	−14.3884	−0.630972
$521$	36.4659	1.59760	0.798801	−	0.601596i	$-0.205468\pi$
$521$	36.4659	1.59760	0.798801	+	0.601596i	$0.205468\pi$
$522$	−2.28660	−0.100082
$523$	22.8308	0.998322	0.499161	−	0.866509i	$-0.333642\pi$
$523$	22.8308	0.998322	0.499161	+	0.866509i	$0.333642\pi$
$524$	1.22757	0.0536267
$525$	10.2721	0.448310
$526$	−11.5312	−0.502784
$527$	−21.5995	−0.940891
$528$	6.36774	0.277120
$529$	32.8402	1.42784
$530$	7.89510	0.342941
$531$	33.6133	1.45869
$532$	14.5014	0.628714
$533$	44.6734	1.93502
$534$	−20.7200	−0.896644
$535$	9.73392	0.420834
$536$	−34.5615	−1.49283
$537$	−42.2866	−1.82480
$538$	1.45010	0.0625182
$539$	−19.1222	−0.823651
$540$	−4.50295	−0.193776
$541$	−12.2704	−0.527546	−0.263773	−	0.964585i	$-0.584967\pi$
$541$	−12.2704	−0.527546	−0.263773	+	0.964585i	$0.584967\pi$
$542$	3.88292	0.166786
$543$	−4.14913	−0.178056
$544$	−32.2197	−1.38141
$545$	7.74347	0.331694
$546$	−42.9467	−1.83795
$547$	−16.7192	−0.714863	−0.357432	−	0.933939i	$-0.616347\pi$
$547$	−16.7192	−0.714863	−0.357432	+	0.933939i	$0.616347\pi$
$548$	15.1633	0.647742
$549$	−60.9705	−2.60216
$550$	−1.85060	−0.0789098
$551$	−1.92514	−0.0820138
$552$	−51.4536	−2.19001
$553$	58.9049	2.50489
$554$	14.9731	0.636145
$555$	−12.8395	−0.545005
$556$	16.6789	0.707344
$557$	40.4505	1.71394	0.856972	−	0.515363i	$-0.172343\pi$
$557$	40.4505	1.71394	0.856972	+	0.515363i	$0.172343\pi$
$558$	12.2383	0.518087
$559$	−16.1170	−0.681674
$560$	3.68584	0.155755
$561$	−36.4348	−1.53828
$562$	5.09659	0.214987
$563$	−33.2026	−1.39932	−0.699660	−	0.714476i	$-0.746665\pi$
$563$	−33.2026	−1.39932	−0.699660	+	0.714476i	$0.746665\pi$
$564$	25.3825	1.06880
$565$	7.03099	0.295796
$566$	17.3946	0.731148
$567$	15.8760	0.666730
$568$	6.64632	0.278873
$569$	−38.7764	−1.62559	−0.812795	−	0.582549i	$-0.802055\pi$
$569$	−38.7764	−1.62559	−0.812795	+	0.582549i	$0.802055\pi$
$570$	5.24596	0.219729
$571$	45.4826	1.90339	0.951693	−	0.307051i	$-0.0993421\pi$
$571$	45.4826	1.90339	0.951693	+	0.307051i	$0.0993421\pi$
$572$	−19.9667	−0.834848
$573$	55.8375	2.33264
$574$	22.9004	0.955842
$575$	−7.47263	−0.311630
$576$	10.2501	0.427088
$577$	37.5355	1.56262	0.781312	−	0.624141i	$-0.214551\pi$
$577$	37.5355	1.56262	0.781312	+	0.624141i	$0.214551\pi$
$578$	9.87280	0.410654
$579$	−70.2955	−2.92138
$580$	−1.05836	−0.0439462
$581$	−37.3097	−1.54787
$582$	16.3995	0.679782
$583$	26.1575	1.08333
$584$	−19.0152	−0.786853
$585$	23.3104	0.963765
$586$	−13.2861	−0.548844
$587$	−2.76395	−0.114080	−0.0570401	−	0.998372i	$-0.518166\pi$
$587$	−2.76395	−0.114080	−0.0570401	+	0.998372i	$0.518166\pi$
$588$	29.8005	1.22895
$589$	10.3037	0.424555
$590$	−6.02885	−0.248204
$591$	−37.6620	−1.54921
$592$	−4.60708	−0.189350
$593$	−24.6338	−1.01159	−0.505794	−	0.862654i	$-0.668800\pi$
$593$	−24.6338	−1.01159	−0.505794	+	0.862654i	$0.668800\pi$
$594$	5.78115	0.237203
$595$	−21.0896	−0.864587
$596$	4.06668	0.166578
$597$	−60.5324	−2.47743
$598$	31.2425	1.27760
$599$	−9.11518	−0.372436	−0.186218	−	0.982508i	$-0.559623\pi$
$599$	−9.11518	−0.372436	−0.186218	+	0.982508i	$0.559623\pi$
$600$	6.88561	0.281104
$601$	1.13523	0.0463072	0.0231536	−	0.999732i	$-0.492629\pi$
$601$	1.13523	0.0463072	0.0231536	+	0.999732i	$0.492629\pi$
$602$	−8.26183	−0.336727
$603$	55.9926	2.28019
$604$	21.9430	0.892847
$605$	4.86873	0.197942
$606$	18.1416	0.736951
$607$	7.16702	0.290900	0.145450	−	0.989366i	$-0.453537\pi$
$607$	7.16702	0.290900	0.145450	+	0.989366i	$0.453537\pi$
$608$	15.3698	0.623327
$609$	−7.54220	−0.305625
$610$	10.9356	0.442770
$611$	−36.7967	−1.48864
$612$	33.0129	1.33447
$613$	−21.3988	−0.864290	−0.432145	−	0.901804i	$-0.642243\pi$
$613$	−21.3988	−0.864290	−0.432145	+	0.901804i	$0.642243\pi$
$614$	13.4049	0.540977
$615$	−21.3786	−0.862068
$616$	−24.4368	−0.984585
$617$	−9.46792	−0.381164	−0.190582	−	0.981671i	$-0.561038\pi$
$617$	−9.46792	−0.381164	−0.190582	+	0.981671i	$0.561038\pi$
$618$	3.73260	0.150147
$619$	26.4727	1.06403	0.532013	−	0.846736i	$-0.321436\pi$
$619$	26.4727	1.06403	0.532013	+	0.846736i	$0.321436\pi$
$620$	5.66453	0.227493
$621$	23.3440	0.936763
$622$	−16.9822	−0.680923
$623$	−39.7356	−1.59197
$624$	14.3862	0.575908
$625$	1.00000	0.0400000
$626$	−2.09149	−0.0835928
$627$	17.3806	0.694113
$628$	−13.5729	−0.541616
$629$	26.3607	1.05107
$630$	11.9493	0.476072
$631$	−2.75087	−0.109511	−0.0547553	−	0.998500i	$-0.517438\pi$
$631$	−2.75087	−0.109511	−0.0547553	+	0.998500i	$0.517438\pi$
$632$	39.4853	1.57064
$633$	23.7567	0.944246
$634$	17.6257	0.700006
$635$	−0.388169	−0.0154040
$636$	−40.7644	−1.61641
$637$	−43.2014	−1.71170
$638$	1.35879	0.0537950
$639$	−10.7676	−0.425959
$640$	9.88554	0.390760
$641$	−26.0437	−1.02866	−0.514331	−	0.857592i	$-0.671960\pi$
$641$	−26.0437	−1.02866	−0.514331	+	0.857592i	$0.671960\pi$
$642$	19.4756	0.768640
$643$	27.7207	1.09320	0.546598	−	0.837395i	$-0.315922\pi$
$643$	27.7207	1.09320	0.546598	+	0.837395i	$0.315922\pi$
$644$	−41.3295	−1.62861
$645$	7.71282	0.303692
$646$	−10.7705	−0.423759
$647$	−7.98473	−0.313912	−0.156956	−	0.987606i	$-0.550168\pi$
$647$	−7.98473	−0.313912	−0.156956	+	0.987606i	$0.550168\pi$
$648$	10.6421	0.418060
$649$	−19.9744	−0.784062
$650$	−4.18092	−0.163989
$651$	40.3670	1.58211
$652$	25.1405	0.984576
$653$	−24.1564	−0.945313	−0.472656	−	0.881247i	$-0.656705\pi$
$653$	−24.1564	−0.945313	−0.472656	+	0.881247i	$0.656705\pi$
$654$	15.4931	0.605828
$655$	0.851631	0.0332760
$656$	−7.67109	−0.299506
$657$	30.8061	1.20186
$658$	−18.8626	−0.735342
$659$	10.6027	0.413022	0.206511	−	0.978444i	$-0.433789\pi$
$659$	10.6027	0.413022	0.206511	+	0.978444i	$0.433789\pi$
$660$	9.55512	0.371933
$661$	29.9915	1.16653	0.583267	−	0.812281i	$-0.301774\pi$
$661$	29.9915	1.16653	0.583267	+	0.812281i	$0.301774\pi$
$662$	10.8234	0.420662
$663$	−82.3146	−3.19683
$664$	−25.0096	−0.970561
$665$	10.0604	0.390125
$666$	−14.9359	−0.578755
$667$	5.48673	0.212447
$668$	14.9016	0.576560
$669$	23.2646	0.899462
$670$	−10.0428	−0.387986
$671$	36.2311	1.39869
$672$	60.2148	2.32284
$673$	−41.0199	−1.58120	−0.790601	−	0.612332i	$-0.790232\pi$
$673$	−41.0199	−1.58120	−0.790601	+	0.612332i	$0.790232\pi$
$674$	−0.358014	−0.0137902
$675$	−3.12393	−0.120240
$676$	−26.3706	−1.01425
$677$	36.3496	1.39703	0.698514	−	0.715597i	$-0.253845\pi$
$677$	36.3496	1.39703	0.698514	+	0.715597i	$0.253845\pi$
$678$	14.0676	0.540262
$679$	31.4500	1.20694
$680$	−14.1368	−0.542123
$681$	21.7025	0.831643
$682$	−7.27246	−0.278477
$683$	−31.5009	−1.20535	−0.602674	−	0.797987i	$-0.705898\pi$
$683$	−31.5009	−1.20535	−0.602674	+	0.797987i	$0.705898\pi$
$684$	−15.7482	−0.602148
$685$	10.5196	0.401932
$686$	−2.07210	−0.0791133
$687$	44.8406	1.71078
$688$	2.76753	0.105511
$689$	59.0957	2.25137
$690$	−14.9512	−0.569183
$691$	49.6794	1.88989	0.944947	−	0.327222i	$-0.106113\pi$
$691$	49.6794	1.88989	0.944947	+	0.327222i	$0.106113\pi$
$692$	−1.47275	−0.0559857
$693$	39.5896	1.50388
$694$	−13.8966	−0.527507
$695$	11.5711	0.438916
$696$	−5.05571	−0.191636
$697$	43.8923	1.66254
$698$	22.8480	0.864809
$699$	35.5714	1.34543
$700$	5.53079	0.209044
$701$	−51.0141	−1.92678	−0.963389	−	0.268108i	$-0.913602\pi$
$701$	−51.0141	−1.92678	−0.963389	+	0.268108i	$0.913602\pi$
$702$	13.0609	0.492953
$703$	−12.5749	−0.474270
$704$	−6.09102	−0.229564
$705$	17.6092	0.663200
$706$	6.47071	0.243528
$707$	34.7908	1.30844
$708$	31.1285	1.16988
$709$	45.7409	1.71784	0.858918	−	0.512114i	$-0.171137\pi$
$709$	45.7409	1.71784	0.858918	+	0.512114i	$0.171137\pi$
$710$	1.93126	0.0724790
$711$	−63.9695	−2.39904
$712$	−26.6357	−0.998216
$713$	−29.3659	−1.09976
$714$	−42.1959	−1.57914
$715$	−13.8519	−0.518033
$716$	−22.7684	−0.850893
$717$	33.6744	1.25759
$718$	24.5279	0.915373
$719$	−23.0370	−0.859137	−0.429568	−	0.903034i	$-0.641334\pi$
$719$	−23.0370	−0.859137	−0.429568	+	0.903034i	$0.641334\pi$
$720$	−4.00274	−0.149173
$721$	7.15815	0.266583
$722$	−9.06222	−0.337261
$723$	−2.67711	−0.0995627
$724$	−2.23401	−0.0830265
$725$	−0.734243	−0.0272691
$726$	9.74133	0.361535
$727$	−11.9029	−0.441455	−0.220727	−	0.975336i	$-0.570843\pi$
$727$	−11.9029	−0.441455	−0.220727	+	0.975336i	$0.570843\pi$
$728$	−55.2082	−2.04615
$729$	−42.3304	−1.56779
$730$	−5.52536	−0.204503
$731$	−15.8352	−0.585685
$732$	−56.4634	−2.08695
$733$	16.2064	0.598596	0.299298	−	0.954160i	$-0.403247\pi$
$733$	16.2064	0.598596	0.299298	+	0.954160i	$0.403247\pi$
$734$	−1.13426	−0.0418663
$735$	20.6742	0.762578
$736$	−43.8045	−1.61466
$737$	−33.2730	−1.22563
$738$	−24.8693	−0.915452
$739$	−36.7319	−1.35120	−0.675602	−	0.737267i	$-0.736116\pi$
$739$	−36.7319	−1.35120	−0.675602	+	0.737267i	$0.736116\pi$
$740$	−6.91315	−0.254133
$741$	39.2666	1.44250
$742$	30.2935	1.11211
$743$	−44.7600	−1.64208	−0.821042	−	0.570868i	$-0.806607\pi$
$743$	−44.7600	−1.64208	−0.821042	+	0.570868i	$0.806607\pi$
$744$	27.0590	0.992031
$745$	2.82127	0.103363
$746$	−13.9374	−0.510283
$747$	40.5176	1.48246
$748$	−19.6176	−0.717290
$749$	37.3490	1.36470
$750$	2.00080	0.0730587
$751$	−3.22667	−0.117743	−0.0588714	−	0.998266i	$-0.518750\pi$
$751$	−3.22667	−0.117743	−0.0588714	+	0.998266i	$0.518750\pi$
$752$	6.31855	0.230414
$753$	−4.83064	−0.176038
$754$	3.06982	0.111796
$755$	15.2230	0.554022
$756$	−17.2778	−0.628388
$757$	−26.8732	−0.976721	−0.488361	−	0.872642i	$-0.662405\pi$
$757$	−26.8732	−0.976721	−0.488361	+	0.872642i	$0.662405\pi$
$758$	18.6631	0.677873
$759$	−49.5353	−1.79802
$760$	6.74371	0.244620
$761$	−25.0853	−0.909342	−0.454671	−	0.890660i	$-0.650243\pi$
$761$	−25.0853	−0.909342	−0.454671	+	0.890660i	$0.650243\pi$
$762$	−0.776647	−0.0281350
$763$	29.7117	1.07564
$764$	30.0646	1.08770
$765$	22.9028	0.828054
$766$	2.95944	0.106929
$767$	−45.1266	−1.62943
$768$	32.9497	1.18897
$769$	−6.13295	−0.221160	−0.110580	−	0.993867i	$-0.535271\pi$
$769$	−6.13295	−0.221160	−0.110580	+	0.993867i	$0.535271\pi$
$770$	−7.10075	−0.255893
$771$	30.1793	1.08688
$772$	−37.8492	−1.36222
$773$	−51.3409	−1.84660	−0.923301	−	0.384076i	$-0.874520\pi$
$773$	−51.3409	−1.84660	−0.923301	+	0.384076i	$0.874520\pi$
$774$	8.97219	0.322499
$775$	3.92979	0.141162
$776$	21.0817	0.756788
$777$	−49.2651	−1.76737
$778$	8.36378	0.299856
$779$	−20.9380	−0.750183
$780$	21.5872	0.772946
$781$	6.39852	0.228957
$782$	30.6963	1.09770
$783$	2.29373	0.0819711
$784$	7.41833	0.264940
$785$	−9.41621	−0.336079
$786$	1.70394	0.0607776
$787$	−3.22878	−0.115094	−0.0575468	−	0.998343i	$-0.518328\pi$
$787$	−3.22878	−0.115094	−0.0575468	+	0.998343i	$0.518328\pi$
$788$	−20.2784	−0.722387
$789$	41.3051	1.47050
$790$	11.4735	0.408209
$791$	26.9779	0.959225
$792$	26.5378	0.942981
$793$	81.8543	2.90673
$794$	22.2109	0.788237
$795$	−28.2805	−1.00300
$796$	−32.5924	−1.15521
$797$	51.7901	1.83450	0.917249	−	0.398313i	$-0.130404\pi$
$797$	51.7901	1.83450	0.917249	+	0.398313i	$0.130404\pi$
$798$	20.1288	0.712551
$799$	−36.1534	−1.27901
$800$	5.86199	0.207253
$801$	43.1521	1.52470
$802$	20.5893	0.727033
$803$	−18.3062	−0.646013
$804$	51.8534	1.82873
$805$	−28.6725	−1.01057
$806$	−16.4302	−0.578727
$807$	−5.19429	−0.182848
$808$	23.3211	0.820432
$809$	16.2602	0.571677	0.285839	−	0.958278i	$-0.407728\pi$
$809$	16.2602	0.571677	0.285839	+	0.958278i	$0.407728\pi$
$810$	3.09234	0.108654
$811$	22.0626	0.774723	0.387361	−	0.921928i	$-0.373387\pi$
$811$	22.0626	0.774723	0.387361	+	0.921928i	$0.373387\pi$
$812$	−4.06094	−0.142511
$813$	−13.9087	−0.487800
$814$	8.87552	0.311087
$815$	17.4413	0.610941
$816$	14.1347	0.494812
$817$	7.55388	0.264277
$818$	−25.8170	−0.902669
$819$	89.4419	3.12535
$820$	−11.5109	−0.401977
$821$	−35.9057	−1.25312	−0.626558	−	0.779375i	$-0.715537\pi$
$821$	−35.9057	−1.25312	−0.626558	+	0.779375i	$0.715537\pi$
$822$	21.0475	0.734116
$823$	15.9802	0.557035	0.278517	−	0.960431i	$-0.410157\pi$
$823$	15.9802	0.557035	0.278517	+	0.960431i	$0.410157\pi$
$824$	4.79828	0.167156
$825$	6.62890	0.230789
$826$	−23.1327	−0.804890
$827$	20.8031	0.723393	0.361697	−	0.932296i	$-0.382198\pi$
$827$	20.8031	0.723393	0.361697	+	0.932296i	$0.382198\pi$
$828$	44.8830	1.55979
$829$	3.13960	0.109043	0.0545215	−	0.998513i	$-0.482637\pi$
$829$	3.13960	0.109043	0.0545215	+	0.998513i	$0.482637\pi$
$830$	−7.26720	−0.252248
$831$	−53.6340	−1.86054
$832$	−13.7610	−0.477077
$833$	−42.4461	−1.47067
$834$	23.1513	0.801665
$835$	10.3380	0.357762
$836$	9.35821	0.323660
$837$	−12.2764	−0.424334
$838$	−13.4138	−0.463372
$839$	5.69071	0.196465	0.0982325	−	0.995163i	$-0.468681\pi$
$839$	5.69071	0.196465	0.0982325	+	0.995163i	$0.468681\pi$
$840$	26.4201	0.911580
$841$	−28.4609	−0.981410
$842$	11.0513	0.380855
$843$	−18.2561	−0.628775
$844$	12.7913	0.440296
$845$	−18.2947	−0.629357
$846$	20.4844	0.704270
$847$	18.6813	0.641897
$848$	−10.1476	−0.348471
$849$	−62.3078	−2.13840
$850$	−4.10783	−0.140897
$851$	35.8389	1.22854
$852$	−9.97161	−0.341622
$853$	8.00296	0.274016	0.137008	−	0.990570i	$-0.456251\pi$
$853$	8.00296	0.274016	0.137008	+	0.990570i	$0.456251\pi$
$854$	41.9599	1.43584
$855$	−10.9254	−0.373640
$856$	25.0360	0.855711
$857$	32.7358	1.11824	0.559118	−	0.829088i	$-0.311140\pi$
$857$	32.7358	1.11824	0.559118	+	0.829088i	$0.311140\pi$
$858$	−27.7149	−0.946172
$859$	−35.8509	−1.22322	−0.611609	−	0.791160i	$-0.709478\pi$
$859$	−35.8509	−1.22322	−0.611609	+	0.791160i	$0.709478\pi$
$860$	4.15281	0.141610
$861$	−82.0297	−2.79556
$862$	28.2392	0.961831
$863$	−9.47058	−0.322382	−0.161191	−	0.986923i	$-0.551534\pi$
$863$	−9.47058	−0.322382	−0.161191	+	0.986923i	$0.551534\pi$
$864$	−18.3125	−0.623003
$865$	−1.02173	−0.0347398
$866$	4.81962	0.163777
$867$	−35.3646	−1.20105
$868$	21.7348	0.737728
$869$	38.0132	1.28951
$870$	−1.46907	−0.0498062
$871$	−75.1713	−2.54708
$872$	19.9164	0.674456
$873$	−34.1540	−1.15594
$874$	−14.6431	−0.495310
$875$	3.83700	0.129714
$876$	28.5289	0.963901
$877$	−33.8801	−1.14405	−0.572024	−	0.820237i	$-0.693842\pi$
$877$	−33.8801	−1.14405	−0.572024	+	0.820237i	$0.693842\pi$
$878$	−23.5212	−0.793802
$879$	47.5912	1.60521
$880$	2.37859	0.0801822
$881$	−19.1538	−0.645308	−0.322654	−	0.946517i	$-0.604575\pi$
$881$	−19.1538	−0.645308	−0.322654	+	0.946517i	$0.604575\pi$
$882$	24.0499	0.809801
$883$	20.3371	0.684398	0.342199	−	0.939627i	$-0.388828\pi$
$883$	20.3371	0.684398	0.342199	+	0.939627i	$0.388828\pi$
$884$	−44.3206	−1.49066
$885$	21.5955	0.725925
$886$	−11.6295	−0.390701
$887$	−7.73801	−0.259817	−0.129908	−	0.991526i	$-0.541468\pi$
$887$	−7.73801	−0.259817	−0.129908	+	0.991526i	$0.541468\pi$
$888$	−33.0235	−1.10820
$889$	−1.48941	−0.0499531
$890$	−7.73971	−0.259436
$891$	10.2453	0.343231
$892$	12.5264	0.419414
$893$	17.2463	0.577125
$894$	5.64479	0.188790
$895$	−15.7956	−0.527989
$896$	37.9308	1.26718
$897$	−111.912	−3.73662
$898$	−14.7880	−0.493482
$899$	−2.88542	−0.0962342
$900$	−6.00632	−0.200211
$901$	58.0625	1.93434
$902$	14.7783	0.492065
$903$	29.5941	0.984830
$904$	18.0839	0.601463
$905$	−1.54985	−0.0515189
$906$	30.4581	1.01190
$907$	5.03755	0.167269	0.0836346	−	0.996496i	$-0.473347\pi$
$907$	5.03755	0.167269	0.0836346	+	0.996496i	$0.473347\pi$
$908$	11.6853	0.387790
$909$	−37.7821	−1.25315
$910$	−16.0422	−0.531794
$911$	2.94211	0.0974766	0.0487383	−	0.998812i	$-0.484480\pi$
$911$	2.94211	0.0974766	0.0487383	+	0.998812i	$0.484480\pi$
$912$	−6.74268	−0.223272
$913$	−24.0772	−0.796838
$914$	−11.6138	−0.384149
$915$	−39.1716	−1.29497
$916$	24.1435	0.797724
$917$	3.26771	0.107909
$918$	12.8326	0.423538
$919$	11.9266	0.393421	0.196710	−	0.980462i	$-0.436974\pi$
$919$	11.9266	0.393421	0.196710	+	0.980462i	$0.436974\pi$
$920$	−19.2199	−0.633660
$921$	−48.0167	−1.58220
$922$	−3.35193	−0.110390
$923$	14.4557	0.475816
$924$	36.6630	1.20612
$925$	−4.79602	−0.157692
$926$	−10.6809	−0.350997
$927$	−7.77361	−0.255319
$928$	−4.30413	−0.141290
$929$	50.2817	1.64969	0.824845	−	0.565359i	$-0.191262\pi$
$929$	50.2817	1.64969	0.824845	+	0.565359i	$0.191262\pi$
$930$	7.86271	0.257828
$931$	20.2481	0.663605
$932$	19.1527	0.627368
$933$	60.8306	1.99150
$934$	3.91382	0.128064
$935$	−13.6098	−0.445087
$936$	59.9550	1.95969
$937$	−1.26913	−0.0414607	−0.0207304	−	0.999785i	$-0.506599\pi$
$937$	−1.26913	−0.0414607	−0.0207304	+	0.999785i	$0.506599\pi$
$938$	−38.5341	−1.25818
$939$	7.49178	0.244485
$940$	9.48131	0.309246
$941$	38.1542	1.24379	0.621896	−	0.783100i	$-0.286363\pi$
$941$	38.1542	1.24379	0.621896	+	0.783100i	$0.286363\pi$
$942$	−18.8399	−0.613838
$943$	59.6742	1.94326
$944$	7.74893	0.252206
$945$	−11.9865	−0.389922
$946$	−5.33163	−0.173346
$947$	16.0318	0.520963	0.260482	−	0.965479i	$-0.416119\pi$
$947$	16.0318	0.520963	0.260482	+	0.965479i	$0.416119\pi$
$948$	−59.2407	−1.92405
$949$	−41.3579	−1.34254
$950$	1.95956	0.0635766
$951$	−63.1358	−2.04732
$952$	−54.2430	−1.75803
$953$	9.05600	0.293353	0.146676	−	0.989185i	$-0.453142\pi$
$953$	9.05600	0.293353	0.146676	+	0.989185i	$0.453142\pi$
$954$	−32.8981	−1.06512
$955$	20.8574	0.674929
$956$	18.1313	0.586408
$957$	−4.86722	−0.157335
$958$	−10.6978	−0.345630
$959$	40.3636	1.30341
$960$	6.58538	0.212542
$961$	−15.5568	−0.501831
$962$	20.0518	0.646496
$963$	−40.5603	−1.30704
$964$	−1.44143	−0.0464255
$965$	−26.2580	−0.845275
$966$	−57.3678	−1.84578
$967$	−34.0984	−1.09653	−0.548265	−	0.836305i	$-0.684711\pi$
$967$	−34.0984	−1.09653	−0.548265	+	0.836305i	$0.684711\pi$
$968$	12.5225	0.402489
$969$	38.5801	1.23937
$970$	6.12584	0.196689
$971$	−8.14305	−0.261323	−0.130661	−	0.991427i	$-0.541710\pi$
$971$	−8.14305	−0.261323	−0.130661	+	0.991427i	$0.541710\pi$
$972$	−29.4754	−0.945423
$973$	44.3982	1.42334
$974$	−23.2271	−0.744245
$975$	14.9762	0.479622
$976$	−14.0556	−0.449909
$977$	11.0047	0.352072	0.176036	−	0.984384i	$-0.443672\pi$
$977$	11.0047	0.352072	0.176036	+	0.984384i	$0.443672\pi$
$978$	34.8964	1.11586
$979$	−25.6427	−0.819543
$980$	11.1316	0.355585
$981$	−32.2663	−1.03018
$982$	−4.65661	−0.148598
$983$	11.9288	0.380469	0.190235	−	0.981739i	$-0.439075\pi$
$983$	11.9288	0.380469	0.190235	+	0.981739i	$0.439075\pi$
$984$	−54.9864	−1.75290
$985$	−14.0682	−0.448250
$986$	3.01615	0.0960537
$987$	67.5665	2.15066
$988$	21.1423	0.672627
$989$	−21.5289	−0.684578
$990$	7.71127	0.245080
$991$	7.47954	0.237596	0.118798	−	0.992918i	$-0.462096\pi$
$991$	7.47954	0.237596	0.118798	+	0.992918i	$0.462096\pi$
$992$	23.0364	0.731406
$993$	−38.7696	−1.23031
$994$	7.41026	0.235039
$995$	−22.6111	−0.716821
$996$	37.5224	1.18894
$997$	27.7974	0.880353	0.440176	−	0.897911i	$-0.354916\pi$
$997$	27.7974	0.880353	0.440176	+	0.897911i	$0.354916\pi$
$998$	−19.7442	−0.624990
$999$	14.9825	0.474024

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1205.2.a.d.1.16	✓	25
5.4	even	2		6025.2.a.k.1.10		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.d.1.16	✓	25	1.1	even	1	trivial
6025.2.a.k.1.10		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)

\(f(q)\)	\(=\)	\(q+0.747372 q^{2} -2.67711 q^{3} -1.44143 q^{4} -1.00000 q^{5} -2.00080 q^{6} -3.83700 q^{7} -2.57203 q^{8} +4.16691 q^{9} +O(q^{10})\)	\(q+0.747372 q^{2} -2.67711 q^{3} -1.44143 q^{4} -1.00000 q^{5} -2.00080 q^{6} -3.83700 q^{7} -2.57203 q^{8} +4.16691 q^{9} -0.747372 q^{10} -2.47614 q^{11} +3.85888 q^{12} -5.59417 q^{13} -2.86767 q^{14} +2.67711 q^{15} +0.960603 q^{16} -5.49636 q^{17} +3.11423 q^{18} +2.62194 q^{19} +1.44143 q^{20} +10.2721 q^{21} -1.85060 q^{22} -7.47263 q^{23} +6.88561 q^{24} +1.00000 q^{25} -4.18092 q^{26} -3.12393 q^{27} +5.53079 q^{28} -0.734243 q^{29} +2.00080 q^{30} +3.92979 q^{31} +5.86199 q^{32} +6.62890 q^{33} -4.10783 q^{34} +3.83700 q^{35} -6.00632 q^{36} -4.79602 q^{37} +1.95956 q^{38} +14.9762 q^{39} +2.57203 q^{40} -7.98571 q^{41} +7.67706 q^{42} +2.88103 q^{43} +3.56920 q^{44} -4.16691 q^{45} -5.58484 q^{46} +6.57769 q^{47} -2.57164 q^{48} +7.72257 q^{49} +0.747372 q^{50} +14.7144 q^{51} +8.06363 q^{52} -10.5638 q^{53} -2.33474 q^{54} +2.47614 q^{55} +9.86889 q^{56} -7.01921 q^{57} -0.548753 q^{58} +8.06673 q^{59} -3.85888 q^{60} -14.6321 q^{61} +2.93702 q^{62} -15.9884 q^{63} +2.45989 q^{64} +5.59417 q^{65} +4.95425 q^{66} +13.4374 q^{67} +7.92265 q^{68} +20.0050 q^{69} +2.86767 q^{70} -2.58407 q^{71} -10.7174 q^{72} +7.39305 q^{73} -3.58442 q^{74} -2.67711 q^{75} -3.77935 q^{76} +9.50095 q^{77} +11.1928 q^{78} -15.3518 q^{79} -0.960603 q^{80} -4.13761 q^{81} -5.96829 q^{82} +9.72367 q^{83} -14.8065 q^{84} +5.49636 q^{85} +2.15320 q^{86} +1.96565 q^{87} +6.36872 q^{88} +10.3559 q^{89} -3.11423 q^{90} +21.4648 q^{91} +10.7713 q^{92} -10.5205 q^{93} +4.91598 q^{94} -2.62194 q^{95} -15.6932 q^{96} -8.19650 q^{97} +5.77164 q^{98} -10.3178 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 4 q^{2} + 9 q^{3} + 36 q^{4} - 25 q^{5} + 7 q^{6} + 7 q^{7} - 15 q^{8} + 36 q^{9}+O(q^{10}) \) 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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