LMFDB - Embedded newform 1205.2.a.e.1.7

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			1.7
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)

$f(q)$	$=$	$q-1.25748 q^{2} -2.42991 q^{3} -0.418732 q^{4} +1.00000 q^{5} +3.05557 q^{6} +3.44014 q^{7} +3.04152 q^{8} +2.90444 q^{9} +O(q^{10})$	\(q-1.25748 q^{2} -2.42991 q^{3} -0.418732 q^{4} +1.00000 q^{5} +3.05557 q^{6} +3.44014 q^{7} +3.04152 q^{8} +2.90444 q^{9} -1.25748 q^{10} +6.10481 q^{11} +1.01748 q^{12} +2.91218 q^{13} -4.32592 q^{14} -2.42991 q^{15} -2.98720 q^{16} +2.89053 q^{17} -3.65229 q^{18} +0.435190 q^{19} -0.418732 q^{20} -8.35922 q^{21} -7.67670 q^{22} -0.0375202 q^{23} -7.39060 q^{24} +1.00000 q^{25} -3.66202 q^{26} +0.232203 q^{27} -1.44050 q^{28} -1.49920 q^{29} +3.05557 q^{30} -3.02438 q^{31} -2.32668 q^{32} -14.8341 q^{33} -3.63480 q^{34} +3.44014 q^{35} -1.21618 q^{36} +6.11186 q^{37} -0.547245 q^{38} -7.07632 q^{39} +3.04152 q^{40} -0.436153 q^{41} +10.5116 q^{42} -3.05957 q^{43} -2.55628 q^{44} +2.90444 q^{45} +0.0471811 q^{46} +8.14790 q^{47} +7.25861 q^{48} +4.83457 q^{49} -1.25748 q^{50} -7.02371 q^{51} -1.21942 q^{52} -0.115328 q^{53} -0.291992 q^{54} +6.10481 q^{55} +10.4633 q^{56} -1.05747 q^{57} +1.88522 q^{58} -10.3018 q^{59} +1.01748 q^{60} -1.01774 q^{61} +3.80311 q^{62} +9.99168 q^{63} +8.90016 q^{64} +2.91218 q^{65} +18.6537 q^{66} -0.262383 q^{67} -1.21036 q^{68} +0.0911705 q^{69} -4.32592 q^{70} +2.18460 q^{71} +8.83391 q^{72} +7.24400 q^{73} -7.68557 q^{74} -2.42991 q^{75} -0.182228 q^{76} +21.0014 q^{77} +8.89837 q^{78} -3.71002 q^{79} -2.98720 q^{80} -9.27755 q^{81} +0.548456 q^{82} +3.99801 q^{83} +3.50027 q^{84} +2.89053 q^{85} +3.84737 q^{86} +3.64291 q^{87} +18.5679 q^{88} -8.60342 q^{89} -3.65229 q^{90} +10.0183 q^{91} +0.0157109 q^{92} +7.34895 q^{93} -10.2459 q^{94} +0.435190 q^{95} +5.65361 q^{96} +0.615933 q^{97} -6.07940 q^{98} +17.7310 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 6 q^{2} + 15 q^{3} + 32 q^{4} + 25 q^{5} - q^{6} + 19 q^{7} + 15 q^{8} + 32 q^{9}+O(q^{10}) $ 25 * q + 6 * q^2 + 15 * q^3 + 32 * q^4 + 25 * q^5 - q^6 + 19 * q^7 + 15 * q^8 + 32 * q^9	\( 25 q + 6 q^{2} + 15 q^{3} + 32 q^{4} + 25 q^{5} - q^{6} + 19 q^{7} + 15 q^{8} + 32 q^{9} + 6 q^{10} + 2 q^{11} + 20 q^{12} + 14 q^{13} - 5 q^{14} + 15 q^{15} + 38 q^{16} + 7 q^{17} + 9 q^{18} + 30 q^{19} + 32 q^{20} + q^{21} + q^{22} + 43 q^{23} - 6 q^{24} + 25 q^{25} - 22 q^{26} + 42 q^{27} + 32 q^{28} - 4 q^{29} - q^{30} + 14 q^{31} + 26 q^{32} + 4 q^{33} + 7 q^{34} + 19 q^{35} + 15 q^{36} + 16 q^{37} + 14 q^{38} - 21 q^{39} + 15 q^{40} - q^{41} - 25 q^{42} + 35 q^{43} - 52 q^{44} + 32 q^{45} - 27 q^{46} + 50 q^{47} + 26 q^{48} + 46 q^{49} + 6 q^{50} - 7 q^{51} + 3 q^{52} + 4 q^{53} - 31 q^{54} + 2 q^{55} - 51 q^{56} + 2 q^{58} + 6 q^{59} + 20 q^{60} + 19 q^{61} + 28 q^{63} + 49 q^{64} + 14 q^{65} - 27 q^{66} + 65 q^{67} - 25 q^{68} + 2 q^{69} - 5 q^{70} - 34 q^{71} - 10 q^{72} + 8 q^{73} - 42 q^{74} + 15 q^{75} + 71 q^{76} + q^{77} - 59 q^{78} - 12 q^{79} + 38 q^{80} + 29 q^{81} + 11 q^{82} + 41 q^{83} - 10 q^{84} + 7 q^{85} - 13 q^{86} + 40 q^{87} - 52 q^{88} - 24 q^{89} + 9 q^{90} + 46 q^{91} + 85 q^{92} - 30 q^{93} + 14 q^{94} + 30 q^{95} - 30 q^{96} + 9 q^{97} - 64 q^{98} + 2 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 + 15 * q^3 + 32 * q^4 + 25 * q^5 - q^6 + 19 * q^7 + 15 * q^8 + 32 * q^9 + 6 * q^10 + 2 * q^11 + 20 * q^12 + 14 * q^13 - 5 * q^14 + 15 * q^15 + 38 * q^16 + 7 * q^17 + 9 * q^18 + 30 * q^19 + 32 * q^20 + q^21 + q^22 + 43 * q^23 - 6 * q^24 + 25 * q^25 - 22 * q^26 + 42 * q^27 + 32 * q^28 - 4 * q^29 - q^30 + 14 * q^31 + 26 * q^32 + 4 * q^33 + 7 * q^34 + 19 * q^35 + 15 * q^36 + 16 * q^37 + 14 * q^38 - 21 * q^39 + 15 * q^40 - q^41 - 25 * q^42 + 35 * q^43 - 52 * q^44 + 32 * q^45 - 27 * q^46 + 50 * q^47 + 26 * q^48 + 46 * q^49 + 6 * q^50 - 7 * q^51 + 3 * q^52 + 4 * q^53 - 31 * q^54 + 2 * q^55 - 51 * q^56 + 2 * q^58 + 6 * q^59 + 20 * q^60 + 19 * q^61 + 28 * q^63 + 49 * q^64 + 14 * q^65 - 27 * q^66 + 65 * q^67 - 25 * q^68 + 2 * q^69 - 5 * q^70 - 34 * q^71 - 10 * q^72 + 8 * q^73 - 42 * q^74 + 15 * q^75 + 71 * q^76 + q^77 - 59 * q^78 - 12 * q^79 + 38 * q^80 + 29 * q^81 + 11 * q^82 + 41 * q^83 - 10 * q^84 + 7 * q^85 - 13 * q^86 + 40 * q^87 - 52 * q^88 - 24 * q^89 + 9 * q^90 + 46 * q^91 + 85 * q^92 - 30 * q^93 + 14 * q^94 + 30 * q^95 - 30 * q^96 + 9 * q^97 - 64 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.25748	−0.889176	−0.444588	−	0.895735i	$-0.646650\pi$
$2$	−1.25748	−0.889176	−0.444588	+	0.895735i	$0.646650\pi$
$3$	−2.42991	−1.40291	−0.701453	−	0.712716i	$-0.747465\pi$
$3$	−2.42991	−1.40291	−0.701453	+	0.712716i	$0.747465\pi$
$4$	−0.418732	−0.209366
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	3.05557	1.24743
$7$	3.44014	1.30025	0.650126	−	0.759827i	$-0.274716\pi$
$7$	3.44014	1.30025	0.650126	+	0.759827i	$0.274716\pi$
$8$	3.04152	1.07534
$9$	2.90444	0.968146
$10$	−1.25748	−0.397652
$11$	6.10481	1.84067	0.920334	−	0.391133i	$-0.127917\pi$
$11$	6.10481	1.84067	0.920334	+	0.391133i	$0.127917\pi$
$12$	1.01748	0.293721
$13$	2.91218	0.807693	0.403847	−	0.914827i	$-0.367673\pi$
$13$	2.91218	0.807693	0.403847	+	0.914827i	$0.367673\pi$
$14$	−4.32592	−1.15615
$15$	−2.42991	−0.627399
$16$	−2.98720	−0.746800
$17$	2.89053	0.701057	0.350528	−	0.936552i	$-0.386002\pi$
$17$	2.89053	0.701057	0.350528	+	0.936552i	$0.386002\pi$
$18$	−3.65229	−0.860853
$19$	0.435190	0.0998395	0.0499197	−	0.998753i	$-0.484103\pi$
$19$	0.435190	0.0998395	0.0499197	+	0.998753i	$0.484103\pi$
$20$	−0.418732	−0.0936313
$21$	−8.35922	−1.82413
$22$	−7.67670	−1.63668
$23$	−0.0375202	−0.00782350	−0.00391175	−	0.999992i	$-0.501245\pi$
$23$	−0.0375202	−0.00782350	−0.00391175	+	0.999992i	$0.501245\pi$
$24$	−7.39060	−1.50860
$25$	1.00000	0.200000
$26$	−3.66202	−0.718182
$27$	0.232203	0.0446876
$28$	−1.44050	−0.272228
$29$	−1.49920	−0.278394	−0.139197	−	0.990265i	$-0.544452\pi$
$29$	−1.49920	−0.278394	−0.139197	+	0.990265i	$0.544452\pi$
$30$	3.05557	0.557868
$31$	−3.02438	−0.543194	−0.271597	−	0.962411i	$-0.587552\pi$
$31$	−3.02438	−0.543194	−0.271597	+	0.962411i	$0.587552\pi$
$32$	−2.32668	−0.411303
$33$	−14.8341	−2.58229
$34$	−3.63480	−0.623363
$35$	3.44014	0.581490
$36$	−1.21618	−0.202697
$37$	6.11186	1.00478	0.502392	−	0.864640i	$-0.332454\pi$
$37$	6.11186	1.00478	0.502392	+	0.864640i	$0.332454\pi$
$38$	−0.547245	−0.0887749
$39$	−7.07632	−1.13312
$40$	3.04152	0.480906
$41$	−0.436153	−0.0681156	−0.0340578	−	0.999420i	$-0.510843\pi$
$41$	−0.436153	−0.0681156	−0.0340578	+	0.999420i	$0.510843\pi$
$42$	10.5116	1.62197
$43$	−3.05957	−0.466581	−0.233290	−	0.972407i	$-0.574949\pi$
$43$	−3.05957	−0.466581	−0.233290	+	0.972407i	$0.574949\pi$
$44$	−2.55628	−0.385374
$45$	2.90444	0.432968
$46$	0.0471811	0.00695647
$47$	8.14790	1.18849	0.594247	−	0.804283i	$-0.297450\pi$
$47$	8.14790	1.18849	0.594247	+	0.804283i	$0.297450\pi$
$48$	7.25861	1.04769
$49$	4.83457	0.690653
$50$	−1.25748	−0.177835
$51$	−7.02371	−0.983517
$52$	−1.21942	−0.169104
$53$	−0.115328	−0.0158415	−0.00792073	−	0.999969i	$-0.502521\pi$
$53$	−0.115328	−0.0158415	−0.00792073	+	0.999969i	$0.502521\pi$
$54$	−0.291992	−0.0397351
$55$	6.10481	0.823172
$56$	10.4633	1.39821
$57$	−1.05747	−0.140065
$58$	1.88522	0.247541
$59$	−10.3018	−1.34118	−0.670589	−	0.741829i	$-0.733958\pi$
$59$	−10.3018	−1.34118	−0.670589	+	0.741829i	$0.733958\pi$
$60$	1.01748	0.131356
$61$	−1.01774	−0.130308	−0.0651542	−	0.997875i	$-0.520754\pi$
$61$	−1.01774	−0.130308	−0.0651542	+	0.997875i	$0.520754\pi$
$62$	3.80311	0.482995
$63$	9.99168	1.25883
$64$	8.90016	1.11252
$65$	2.91218	0.361212
$66$	18.6537	2.29611
$67$	−0.262383	−0.0320552	−0.0160276	−	0.999872i	$-0.505102\pi$
$67$	−0.262383	−0.0320552	−0.0160276	+	0.999872i	$0.505102\pi$
$68$	−1.21036	−0.146777
$69$	0.0911705	0.0109756
$70$	−4.32592	−0.517047
$71$	2.18460	0.259264	0.129632	−	0.991562i	$-0.458620\pi$
$71$	2.18460	0.259264	0.129632	+	0.991562i	$0.458620\pi$
$72$	8.83391	1.04109
$73$	7.24400	0.847846	0.423923	−	0.905698i	$-0.360653\pi$
$73$	7.24400	0.847846	0.423923	+	0.905698i	$0.360653\pi$
$74$	−7.68557	−0.893429
$75$	−2.42991	−0.280581
$76$	−0.182228	−0.0209030
$77$	21.0014	2.39333
$78$	8.89837	1.00754
$79$	−3.71002	−0.417410	−0.208705	−	0.977979i	$-0.566925\pi$
$79$	−3.71002	−0.417410	−0.208705	+	0.977979i	$0.566925\pi$
$80$	−2.98720	−0.333979
$81$	−9.27755	−1.03084
$82$	0.548456	0.0605668
$83$	3.99801	0.438838	0.219419	−	0.975631i	$-0.429584\pi$
$83$	3.99801	0.438838	0.219419	+	0.975631i	$0.429584\pi$
$84$	3.50027	0.381911
$85$	2.89053	0.313522
$86$	3.84737	0.414872
$87$	3.64291	0.390561
$88$	18.5679	1.97934
$89$	−8.60342	−0.911960	−0.455980	−	0.889990i	$-0.650711\pi$
$89$	−8.60342	−0.911960	−0.455980	+	0.889990i	$0.650711\pi$
$90$	−3.65229	−0.384985
$91$	10.0183	1.05020
$92$	0.0157109	0.00163798
$93$	7.34895	0.762051
$94$	−10.2459	−1.05678
$95$	0.435190	0.0446496
$96$	5.65361	0.577019
$97$	0.615933	0.0625386	0.0312693	−	0.999511i	$-0.490045\pi$
$97$	0.615933	0.0625386	0.0312693	+	0.999511i	$0.490045\pi$
$98$	−6.07940	−0.614112
$99$	17.7310	1.78204
$100$	−0.418732	−0.0418732
$101$	5.45701	0.542993	0.271497	−	0.962439i	$-0.412481\pi$
$101$	5.45701	0.542993	0.271497	+	0.962439i	$0.412481\pi$
$102$	8.83221	0.874520
$103$	6.11470	0.602499	0.301250	−	0.953545i	$-0.402596\pi$
$103$	6.11470	0.602499	0.301250	+	0.953545i	$0.402596\pi$
$104$	8.85745	0.868545
$105$	−8.35922	−0.815776
$106$	0.145023	0.0140859
$107$	−0.399986	−0.0386681	−0.0193341	−	0.999813i	$-0.506155\pi$
$107$	−0.399986	−0.0386681	−0.0193341	+	0.999813i	$0.506155\pi$
$108$	−0.0972310	−0.00935606
$109$	−17.9680	−1.72102	−0.860512	−	0.509430i	$-0.829856\pi$
$109$	−17.9680	−1.72102	−0.860512	+	0.509430i	$0.829856\pi$
$110$	−7.67670	−0.731945
$111$	−14.8512	−1.40962
$112$	−10.2764	−0.971027
$113$	−16.1077	−1.51528	−0.757642	−	0.652671i	$-0.773648\pi$
$113$	−16.1077	−1.51528	−0.757642	+	0.652671i	$0.773648\pi$
$114$	1.32975	0.124543
$115$	−0.0375202	−0.00349878
$116$	0.627763	0.0582863
$117$	8.45825	0.781966
$118$	12.9543	1.19254
$119$	9.94383	0.911550
$120$	−7.39060	−0.674667
$121$	26.2687	2.38806
$122$	1.27979	0.115867
$123$	1.05981	0.0955599
$124$	1.26640	0.113726
$125$	1.00000	0.0894427
$126$	−12.5644	−1.11932
$127$	19.9234	1.76791	0.883956	−	0.467570i	$-0.154870\pi$
$127$	19.9234	1.76791	0.883956	+	0.467570i	$0.154870\pi$
$128$	−6.53846	−0.577924
$129$	7.43447	0.654569
$130$	−3.66202	−0.321181
$131$	−15.4494	−1.34982	−0.674910	−	0.737900i	$-0.735817\pi$
$131$	−15.4494	−1.34982	−0.674910	+	0.737900i	$0.735817\pi$
$132$	6.21152	0.540643
$133$	1.49712	0.129816
$134$	0.329943	0.0285027
$135$	0.232203	0.0199849
$136$	8.79160	0.753874
$137$	5.30038	0.452842	0.226421	−	0.974030i	$-0.427297\pi$
$137$	5.30038	0.452842	0.226421	+	0.974030i	$0.427297\pi$
$138$	−0.114646	−0.00975927
$139$	22.6764	1.92339	0.961693	−	0.274129i	$-0.0883895\pi$
$139$	22.6764	1.92339	0.961693	+	0.274129i	$0.0883895\pi$
$140$	−1.44050	−0.121744
$141$	−19.7986	−1.66735
$142$	−2.74710	−0.230531
$143$	17.7783	1.48670
$144$	−8.67614	−0.723012
$145$	−1.49920	−0.124502
$146$	−9.10921	−0.753884
$147$	−11.7475	−0.968921
$148$	−2.55923	−0.210368
$149$	−12.3612	−1.01267	−0.506335	−	0.862337i	$-0.669000\pi$
$149$	−12.3612	−1.01267	−0.506335	+	0.862337i	$0.669000\pi$
$150$	3.05557	0.249486
$151$	−9.45769	−0.769656	−0.384828	−	0.922988i	$-0.625739\pi$
$151$	−9.45769	−0.769656	−0.384828	+	0.922988i	$0.625739\pi$
$152$	1.32364	0.107361
$153$	8.39537	0.678725
$154$	−26.4089	−2.12809
$155$	−3.02438	−0.242924
$156$	2.96308	0.237237
$157$	−9.24840	−0.738103	−0.369051	−	0.929409i	$-0.620317\pi$
$157$	−9.24840	−0.738103	−0.369051	+	0.929409i	$0.620317\pi$
$158$	4.66529	0.371151
$159$	0.280235	0.0222241
$160$	−2.32668	−0.183940
$161$	−0.129075	−0.0101725
$162$	11.6664	0.916597
$163$	13.3085	1.04241	0.521203	−	0.853433i	$-0.325484\pi$
$163$	13.3085	1.04241	0.521203	+	0.853433i	$0.325484\pi$
$164$	0.182631	0.0142611
$165$	−14.8341	−1.15483
$166$	−5.02743	−0.390204
$167$	−12.5141	−0.968367	−0.484183	−	0.874967i	$-0.660883\pi$
$167$	−12.5141	−0.968367	−0.484183	+	0.874967i	$0.660883\pi$
$168$	−25.4247	−1.96156
$169$	−4.51921	−0.347631
$170$	−3.63480	−0.278776
$171$	1.26398	0.0966592
$172$	1.28114	0.0976861
$173$	−16.9914	−1.29183	−0.645916	−	0.763409i	$-0.723524\pi$
$173$	−16.9914	−1.29183	−0.645916	+	0.763409i	$0.723524\pi$
$174$	−4.58090	−0.347277
$175$	3.44014	0.260050
$176$	−18.2363	−1.37461
$177$	25.0324	1.88155
$178$	10.8187	0.810893
$179$	13.0149	0.972782	0.486391	−	0.873741i	$-0.338313\pi$
$179$	13.0149	0.972782	0.486391	+	0.873741i	$0.338313\pi$
$180$	−1.21618	−0.0906488
$181$	−5.50027	−0.408832	−0.204416	−	0.978884i	$-0.565530\pi$
$181$	−5.50027	−0.408832	−0.204416	+	0.978884i	$0.565530\pi$
$182$	−12.5979	−0.933816
$183$	2.47302	0.182811
$184$	−0.114118	−0.00841292
$185$	6.11186	0.449353
$186$	−9.24120	−0.677597
$187$	17.6461	1.29041
$188$	−3.41179	−0.248830
$189$	0.798813	0.0581051
$190$	−0.547245	−0.0397013
$191$	4.98997	0.361062	0.180531	−	0.983569i	$-0.442218\pi$
$191$	4.98997	0.361062	0.180531	+	0.983569i	$0.442218\pi$
$192$	−21.6266	−1.56076
$193$	−20.5174	−1.47688	−0.738438	−	0.674321i	$-0.764436\pi$
$193$	−20.5174	−1.47688	−0.738438	+	0.674321i	$0.764436\pi$
$194$	−0.774527	−0.0556078
$195$	−7.07632	−0.506746
$196$	−2.02439	−0.144599
$197$	−1.57731	−0.112378	−0.0561892	−	0.998420i	$-0.517895\pi$
$197$	−1.57731	−0.112378	−0.0561892	+	0.998420i	$0.517895\pi$
$198$	−22.2965	−1.58454
$199$	18.3247	1.29901	0.649503	−	0.760359i	$-0.274977\pi$
$199$	18.3247	1.29901	0.649503	+	0.760359i	$0.274977\pi$
$200$	3.04152	0.215068
$201$	0.637567	0.0449705
$202$	−6.86211	−0.482816
$203$	−5.15745	−0.361982
$204$	2.94105	0.205915
$205$	−0.436153	−0.0304622
$206$	−7.68914	−0.535728
$207$	−0.108975	−0.00757429
$208$	−8.69926	−0.603185
$209$	2.65675	0.183771
$210$	10.5116	0.725368
$211$	25.8400	1.77890	0.889448	−	0.457036i	$-0.151089\pi$
$211$	25.8400	1.77890	0.889448	+	0.457036i	$0.151089\pi$
$212$	0.0482914	0.00331667
$213$	−5.30836	−0.363723
$214$	0.502976	0.0343828
$215$	−3.05957	−0.208661
$216$	0.706251	0.0480543
$217$	−10.4043	−0.706289
$218$	22.5945	1.53029
$219$	−17.6022	−1.18945
$220$	−2.55628	−0.172344
$221$	8.41775	0.566239
$222$	18.6752	1.25340
$223$	6.13852	0.411066	0.205533	−	0.978650i	$-0.434107\pi$
$223$	6.13852	0.411066	0.205533	+	0.978650i	$0.434107\pi$
$224$	−8.00411	−0.534797
$225$	2.90444	0.193629
$226$	20.2552	1.34735
$227$	−16.2377	−1.07774	−0.538868	−	0.842390i	$-0.681148\pi$
$227$	−16.2377	−1.07774	−0.538868	+	0.842390i	$0.681148\pi$
$228$	0.442797	0.0293249
$229$	−25.1507	−1.66200	−0.831002	−	0.556269i	$-0.812232\pi$
$229$	−25.1507	−1.66200	−0.831002	+	0.556269i	$0.812232\pi$
$230$	0.0471811	0.00311103
$231$	−51.0314	−3.35762
$232$	−4.55984	−0.299368
$233$	−14.1976	−0.930117	−0.465059	−	0.885280i	$-0.653967\pi$
$233$	−14.1976	−0.930117	−0.465059	+	0.885280i	$0.653967\pi$
$234$	−10.6361	−0.695305
$235$	8.14790	0.531510
$236$	4.31369	0.280797
$237$	9.01500	0.585587
$238$	−12.5042	−0.810528
$239$	−10.1054	−0.653666	−0.326833	−	0.945082i	$-0.605981\pi$
$239$	−10.1054	−0.653666	−0.326833	+	0.945082i	$0.605981\pi$
$240$	7.25861	0.468541
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	−33.0325	−2.12341
$243$	21.8470	1.40148
$244$	0.426161	0.0272822
$245$	4.83457	0.308869
$246$	−1.33270	−0.0849695
$247$	1.26735	0.0806397
$248$	−9.19870	−0.584118
$249$	−9.71478	−0.615649
$250$	−1.25748	−0.0795303
$251$	26.8384	1.69402	0.847012	−	0.531574i	$-0.178399\pi$
$251$	26.8384	1.69402	0.847012	+	0.531574i	$0.178399\pi$
$252$	−4.18384	−0.263557
$253$	−0.229054	−0.0144005
$254$	−25.0533	−1.57199
$255$	−7.02371	−0.439842
$256$	−9.57831	−0.598645
$257$	6.47501	0.403900	0.201950	−	0.979396i	$-0.435272\pi$
$257$	6.47501	0.403900	0.201950	+	0.979396i	$0.435272\pi$
$258$	−9.34874	−0.582027
$259$	21.0257	1.30647
$260$	−1.21942	−0.0756254
$261$	−4.35433	−0.269526
$262$	19.4274	1.20023
$263$	−7.24781	−0.446919	−0.223460	−	0.974713i	$-0.571735\pi$
$263$	−7.24781	−0.446919	−0.223460	+	0.974713i	$0.571735\pi$
$264$	−45.1182	−2.77683
$265$	−0.115328	−0.00708452
$266$	−1.88260	−0.115430
$267$	20.9055	1.27940
$268$	0.109868	0.00671128
$269$	32.2305	1.96513	0.982565	−	0.185917i	$-0.0595255\pi$
$269$	32.2305	1.96513	0.982565	+	0.185917i	$0.0595255\pi$
$270$	−0.291992	−0.0177701
$271$	−2.03102	−0.123376	−0.0616879	−	0.998095i	$-0.519648\pi$
$271$	−2.03102	−0.123376	−0.0616879	+	0.998095i	$0.519648\pi$
$272$	−8.63459	−0.523549
$273$	−24.3435	−1.47334
$274$	−6.66515	−0.402656
$275$	6.10481	0.368134
$276$	−0.0381760	−0.00229793
$277$	25.3320	1.52205	0.761025	−	0.648723i	$-0.224696\pi$
$277$	25.3320	1.52205	0.761025	+	0.648723i	$0.224696\pi$
$278$	−28.5152	−1.71023
$279$	−8.78412	−0.525892
$280$	10.4633	0.625299
$281$	−25.0267	−1.49297	−0.746483	−	0.665404i	$-0.768259\pi$
$281$	−25.0267	−1.49297	−0.746483	+	0.665404i	$0.768259\pi$
$282$	24.8965	1.48256
$283$	8.12232	0.482822	0.241411	−	0.970423i	$-0.422390\pi$
$283$	8.12232	0.482822	0.241411	+	0.970423i	$0.422390\pi$
$284$	−0.914760	−0.0542810
$285$	−1.05747	−0.0626392
$286$	−22.3559	−1.32193
$287$	−1.50043	−0.0885674
$288$	−6.75770	−0.398201
$289$	−8.64483	−0.508520
$290$	1.88522	0.110704
$291$	−1.49666	−0.0877358
$292$	−3.03329	−0.177510
$293$	1.24229	0.0725753	0.0362877	−	0.999341i	$-0.488447\pi$
$293$	1.24229	0.0725753	0.0362877	+	0.999341i	$0.488447\pi$
$294$	14.7724	0.861542
$295$	−10.3018	−0.599793
$296$	18.5893	1.08048
$297$	1.41756	0.0822550
$298$	15.5440	0.900442
$299$	−0.109266	−0.00631899
$300$	1.01748	0.0587442
$301$	−10.5254	−0.606672
$302$	11.8929	0.684359
$303$	−13.2600	−0.761769
$304$	−1.30000	−0.0745601
$305$	−1.01774	−0.0582757
$306$	−10.5570	−0.603506
$307$	28.3495	1.61799	0.808997	−	0.587813i	$-0.200011\pi$
$307$	28.3495	1.61799	0.808997	+	0.587813i	$0.200011\pi$
$308$	−8.79396	−0.501082
$309$	−14.8581	−0.845250
$310$	3.80311	0.216002
$311$	−17.7992	−1.00930	−0.504651	−	0.863323i	$-0.668379\pi$
$311$	−17.7992	−1.00930	−0.504651	+	0.863323i	$0.668379\pi$
$312$	−21.5228	−1.21849
$313$	31.5016	1.78057	0.890287	−	0.455401i	$-0.150504\pi$
$313$	31.5016	1.78057	0.890287	+	0.455401i	$0.150504\pi$
$314$	11.6297	0.656303
$315$	9.99168	0.562967
$316$	1.55350	0.0873915
$317$	11.4499	0.643091	0.321546	−	0.946894i	$-0.395798\pi$
$317$	11.4499	0.643091	0.321546	+	0.946894i	$0.395798\pi$
$318$	−0.352391	−0.0197611
$319$	−9.15232	−0.512431
$320$	8.90016	0.497534
$321$	0.971928	0.0542477
$322$	0.162310	0.00904516
$323$	1.25793	0.0699931
$324$	3.88481	0.215823
$325$	2.91218	0.161539
$326$	−16.7353	−0.926882
$327$	43.6606	2.41444
$328$	−1.32657	−0.0732474
$329$	28.0299	1.54534
$330$	18.6537	1.02685
$331$	−18.2040	−1.00058	−0.500292	−	0.865857i	$-0.666774\pi$
$331$	−18.2040	−1.00058	−0.500292	+	0.865857i	$0.666774\pi$
$332$	−1.67409	−0.0918778
$333$	17.7515	0.972777
$334$	15.7362	0.861048
$335$	−0.262383	−0.0143355
$336$	24.9706	1.36226
$337$	−2.20700	−0.120223	−0.0601115	−	0.998192i	$-0.519146\pi$
$337$	−2.20700	−0.120223	−0.0601115	+	0.998192i	$0.519146\pi$
$338$	5.68283	0.309105
$339$	39.1401	2.12580
$340$	−1.21036	−0.0656409
$341$	−18.4632	−0.999841
$342$	−1.58944	−0.0859471
$343$	−7.44938	−0.402229
$344$	−9.30575	−0.501732
$345$	0.0911705	0.00490845
$346$	21.3664	1.14867
$347$	−16.6349	−0.893008	−0.446504	−	0.894782i	$-0.647331\pi$
$347$	−16.6349	−0.893008	−0.446504	+	0.894782i	$0.647331\pi$
$348$	−1.52540	−0.0817702
$349$	13.9627	0.747405	0.373702	−	0.927549i	$-0.378088\pi$
$349$	13.9627	0.747405	0.373702	+	0.927549i	$0.378088\pi$
$350$	−4.32592	−0.231230
$351$	0.676218	0.0360939
$352$	−14.2039	−0.757072
$353$	−6.49106	−0.345484	−0.172742	−	0.984967i	$-0.555263\pi$
$353$	−6.49106	−0.345484	−0.172742	+	0.984967i	$0.555263\pi$
$354$	−31.4778	−1.67303
$355$	2.18460	0.115946
$356$	3.60253	0.190934
$357$	−24.1626	−1.27882
$358$	−16.3661	−0.864974
$359$	30.0584	1.58642	0.793211	−	0.608948i	$-0.208408\pi$
$359$	30.0584	1.58642	0.793211	+	0.608948i	$0.208408\pi$
$360$	8.83391	0.465588
$361$	−18.8106	−0.990032
$362$	6.91651	0.363524
$363$	−63.8304	−3.35023
$364$	−4.19499	−0.219877
$365$	7.24400	0.379168
$366$	−3.10978	−0.162551
$367$	−26.8651	−1.40235	−0.701173	−	0.712992i	$-0.747340\pi$
$367$	−26.8651	−1.40235	−0.701173	+	0.712992i	$0.747340\pi$
$368$	0.112080	0.00584259
$369$	−1.26678	−0.0659459
$370$	−7.68557	−0.399554
$371$	−0.396743	−0.0205979
$372$	−3.07724	−0.159548
$373$	16.6377	0.861469	0.430734	−	0.902479i	$-0.358255\pi$
$373$	16.6377	0.861469	0.430734	+	0.902479i	$0.358255\pi$
$374$	−22.1897	−1.14740
$375$	−2.42991	−0.125480
$376$	24.7820	1.27803
$377$	−4.36594	−0.224857
$378$	−1.00449	−0.0516656
$379$	32.1591	1.65190	0.825952	−	0.563741i	$-0.190638\pi$
$379$	32.1591	1.65190	0.825952	+	0.563741i	$0.190638\pi$
$380$	−0.182228	−0.00934810
$381$	−48.4119	−2.48022
$382$	−6.27481	−0.321047
$383$	−4.63427	−0.236800	−0.118400	−	0.992966i	$-0.537777\pi$
$383$	−4.63427	−0.236800	−0.118400	+	0.992966i	$0.537777\pi$
$384$	15.8878	0.810773
$385$	21.0014	1.07033
$386$	25.8003	1.31320
$387$	−8.88634	−0.451718
$388$	−0.257911	−0.0130935
$389$	−37.5478	−1.90375	−0.951874	−	0.306489i	$-0.900846\pi$
$389$	−37.5478	−1.90375	−0.951874	+	0.306489i	$0.900846\pi$
$390$	8.89837	0.450586
$391$	−0.108453	−0.00548472
$392$	14.7044	0.742686
$393$	37.5406	1.89367
$394$	1.98344	0.0999243
$395$	−3.71002	−0.186671
$396$	−7.42456	−0.373098
$397$	−4.56801	−0.229262	−0.114631	−	0.993408i	$-0.536569\pi$
$397$	−4.56801	−0.229262	−0.114631	+	0.993408i	$0.536569\pi$
$398$	−23.0431	−1.15504
$399$	−3.63785	−0.182120
$400$	−2.98720	−0.149360
$401$	−4.51361	−0.225399	−0.112699	−	0.993629i	$-0.535950\pi$
$401$	−4.51361	−0.225399	−0.112699	+	0.993629i	$0.535950\pi$
$402$	−0.801730	−0.0399867
$403$	−8.80754	−0.438735
$404$	−2.28503	−0.113684
$405$	−9.27755	−0.461005
$406$	6.48542	0.321866
$407$	37.3117	1.84947
$408$	−21.3628	−1.05761
$409$	−8.25303	−0.408086	−0.204043	−	0.978962i	$-0.565408\pi$
$409$	−8.25303	−0.408086	−0.204043	+	0.978962i	$0.565408\pi$
$410$	0.548456	0.0270863
$411$	−12.8794	−0.635295
$412$	−2.56042	−0.126143
$413$	−35.4396	−1.74387
$414$	0.137035	0.00673488
$415$	3.99801	0.196254
$416$	−6.77571	−0.332207
$417$	−55.1015	−2.69833
$418$	−3.34083	−0.163405
$419$	24.3109	1.18767	0.593833	−	0.804588i	$-0.297614\pi$
$419$	24.3109	1.18767	0.593833	+	0.804588i	$0.297614\pi$
$420$	3.50027	0.170796
$421$	28.2937	1.37895	0.689475	−	0.724310i	$-0.257841\pi$
$421$	28.2937	1.37895	0.689475	+	0.724310i	$0.257841\pi$
$422$	−32.4934	−1.58175
$423$	23.6651	1.15064
$424$	−0.350771	−0.0170350
$425$	2.89053	0.140211
$426$	6.67518	0.323414
$427$	−3.50117	−0.169434
$428$	0.167487	0.00809579
$429$	−43.1996	−2.08570
$430$	3.84737	0.185536
$431$	−18.6546	−0.898561	−0.449280	−	0.893391i	$-0.648320\pi$
$431$	−18.6546	−0.898561	−0.449280	+	0.893391i	$0.648320\pi$
$432$	−0.693638	−0.0333727
$433$	−16.7317	−0.804072	−0.402036	−	0.915624i	$-0.631697\pi$
$433$	−16.7317	−0.804072	−0.402036	+	0.915624i	$0.631697\pi$
$434$	13.0832	0.628015
$435$	3.64291	0.174664
$436$	7.52379	0.360324
$437$	−0.0163284	−0.000781094 0
$438$	22.1345	1.05763
$439$	36.5936	1.74652	0.873260	−	0.487255i	$-0.162002\pi$
$439$	36.5936	1.74652	0.873260	+	0.487255i	$0.162002\pi$
$440$	18.5679	0.885189
$441$	14.0417	0.668653
$442$	−10.5852	−0.503486
$443$	−22.6142	−1.07443	−0.537216	−	0.843445i	$-0.680524\pi$
$443$	−22.6142	−1.07443	−0.537216	+	0.843445i	$0.680524\pi$
$444$	6.21869	0.295126
$445$	−8.60342	−0.407841
$446$	−7.71910	−0.365510
$447$	30.0366	1.42068
$448$	30.6178	1.44656
$449$	−4.96373	−0.234253	−0.117126	−	0.993117i	$-0.537368\pi$
$449$	−4.96373	−0.234253	−0.117126	+	0.993117i	$0.537368\pi$
$450$	−3.65229	−0.172171
$451$	−2.66263	−0.125378
$452$	6.74480	0.317249
$453$	22.9813	1.07975
$454$	20.4187	0.958297
$455$	10.0183	0.469666
$456$	−3.21632	−0.150618
$457$	23.3650	1.09297	0.546485	−	0.837469i	$-0.315965\pi$
$457$	23.3650	1.09297	0.546485	+	0.837469i	$0.315965\pi$
$458$	31.6266	1.47781
$459$	0.671191	0.0313285
$460$	0.0157109	0.000732525 0
$461$	6.46899	0.301291	0.150645	−	0.988588i	$-0.451865\pi$
$461$	6.46899	0.301291	0.150645	+	0.988588i	$0.451865\pi$
$462$	64.1712	2.98552
$463$	1.70184	0.0790913	0.0395456	−	0.999218i	$-0.487409\pi$
$463$	1.70184	0.0790913	0.0395456	+	0.999218i	$0.487409\pi$
$464$	4.47840	0.207905
$465$	7.34895	0.340800
$466$	17.8533	0.827038
$467$	−26.8597	−1.24292	−0.621460	−	0.783446i	$-0.713460\pi$
$467$	−26.8597	−1.24292	−0.621460	+	0.783446i	$0.713460\pi$
$468$	−3.54174	−0.163717
$469$	−0.902636	−0.0416798
$470$	−10.2459	−0.472606
$471$	22.4727	1.03549
$472$	−31.3331	−1.44222
$473$	−18.6781	−0.858820
$474$	−11.3362	−0.520690
$475$	0.435190	0.0199679
$476$	−4.16380	−0.190848
$477$	−0.334962	−0.0153369
$478$	12.7074	0.581224
$479$	−0.239763	−0.0109551	−0.00547754	−	0.999985i	$-0.501744\pi$
$479$	−0.239763	−0.0109551	−0.00547754	+	0.999985i	$0.501744\pi$
$480$	5.65361	0.258051
$481$	17.7988	0.811557
$482$	1.25748	0.0572769
$483$	0.313639	0.0142711
$484$	−10.9995	−0.499979
$485$	0.615933	0.0279681
$486$	−27.4722	−1.24617
$487$	−20.0006	−0.906316	−0.453158	−	0.891430i	$-0.649703\pi$
$487$	−20.0006	−0.906316	−0.453158	+	0.891430i	$0.649703\pi$
$488$	−3.09548	−0.140126
$489$	−32.3385	−1.46240
$490$	−6.07940	−0.274639
$491$	27.0575	1.22109	0.610544	−	0.791982i	$-0.290951\pi$
$491$	27.0575	1.22109	0.610544	+	0.791982i	$0.290951\pi$
$492$	−0.443777	−0.0200070
$493$	−4.33348	−0.195170
$494$	−1.59368	−0.0717029
$495$	17.7310	0.796951
$496$	9.03442	0.405657
$497$	7.51532	0.337108
$498$	12.2162	0.547420
$499$	−40.8570	−1.82901	−0.914506	−	0.404572i	$-0.867420\pi$
$499$	−40.8570	−1.82901	−0.914506	+	0.404572i	$0.867420\pi$
$500$	−0.418732	−0.0187263
$501$	30.4080	1.35853
$502$	−33.7489	−1.50629
$503$	−11.8362	−0.527752	−0.263876	−	0.964557i	$-0.585001\pi$
$503$	−11.8362	−0.527752	−0.263876	+	0.964557i	$0.585001\pi$
$504$	30.3899	1.35367
$505$	5.45701	0.242834
$506$	0.288031	0.0128046
$507$	10.9812	0.487694
$508$	−8.34255	−0.370141
$509$	33.7105	1.49419	0.747095	−	0.664717i	$-0.231448\pi$
$509$	33.7105	1.49419	0.747095	+	0.664717i	$0.231448\pi$
$510$	8.83221	0.391097
$511$	24.9204	1.10241
$512$	25.1215	1.11022
$513$	0.101053	0.00446158
$514$	−8.14223	−0.359138
$515$	6.11470	0.269446
$516$	−3.11305	−0.137044
$517$	49.7414	2.18762
$518$	−26.4394	−1.16168
$519$	41.2875	1.81232
$520$	8.85745	0.388425
$521$	10.1651	0.445342	0.222671	−	0.974894i	$-0.428522\pi$
$521$	10.1651	0.445342	0.222671	+	0.974894i	$0.428522\pi$
$522$	5.47550	0.239656
$523$	18.5411	0.810745	0.405373	−	0.914152i	$-0.367142\pi$
$523$	18.5411	0.810745	0.405373	+	0.914152i	$0.367142\pi$
$524$	6.46916	0.282606
$525$	−8.35922	−0.364826
$526$	9.11401	0.397390
$527$	−8.74206	−0.380810
$528$	44.3124	1.92845
$529$	−22.9986	−0.999939
$530$	0.145023	0.00629938
$531$	−29.9209	−1.29846
$532$	−0.626890	−0.0271791
$533$	−1.27016	−0.0550166
$534$	−26.2883	−1.13761
$535$	−0.399986	−0.0172929
$536$	−0.798044	−0.0344702
$537$	−31.6251	−1.36472
$538$	−40.5294	−1.74735
$539$	29.5141	1.27126
$540$	−0.0972310	−0.00418416
$541$	16.2722	0.699599	0.349799	−	0.936825i	$-0.386250\pi$
$541$	16.2722	0.699599	0.349799	+	0.936825i	$0.386250\pi$
$542$	2.55398	0.109703
$543$	13.3651	0.573553
$544$	−6.72534	−0.288347
$545$	−17.9680	−0.769666
$546$	30.6116	1.31006
$547$	34.0181	1.45451	0.727254	−	0.686369i	$-0.240796\pi$
$547$	34.0181	1.45451	0.727254	+	0.686369i	$0.240796\pi$
$548$	−2.21944	−0.0948098
$549$	−2.95597	−0.126158
$550$	−7.67670	−0.327336
$551$	−0.652436	−0.0277947
$552$	0.277297	0.0118025
$553$	−12.7630	−0.542738
$554$	−31.8545	−1.35337
$555$	−14.8512	−0.630400
$556$	−9.49533	−0.402692
$557$	6.49624	0.275255	0.137627	−	0.990484i	$-0.456052\pi$
$557$	6.49624	0.275255	0.137627	+	0.990484i	$0.456052\pi$
$558$	11.0459	0.467610
$559$	−8.91003	−0.376854
$560$	−10.2764	−0.434257
$561$	−42.8784	−1.81033
$562$	31.4707	1.32751
$563$	−4.51807	−0.190414	−0.0952070	−	0.995457i	$-0.530351\pi$
$563$	−4.51807	−0.190414	−0.0952070	+	0.995457i	$0.530351\pi$
$564$	8.29032	0.349085
$565$	−16.1077	−0.677655
$566$	−10.2137	−0.429314
$567$	−31.9161	−1.34035
$568$	6.64449	0.278797
$569$	19.3782	0.812374	0.406187	−	0.913790i	$-0.366858\pi$
$569$	19.3782	0.812374	0.406187	+	0.913790i	$0.366858\pi$
$570$	1.32975	0.0556972
$571$	27.9986	1.17171	0.585853	−	0.810417i	$-0.300760\pi$
$571$	27.9986	1.17171	0.585853	+	0.810417i	$0.300760\pi$
$572$	−7.44434	−0.311264
$573$	−12.1252	−0.506536
$574$	1.88676	0.0787520
$575$	−0.0375202	−0.00156470
$576$	25.8500	1.07708
$577$	−36.6737	−1.52674	−0.763372	−	0.645959i	$-0.776458\pi$
$577$	−36.6737	−1.52674	−0.763372	+	0.645959i	$0.776458\pi$
$578$	10.8707	0.452163
$579$	49.8554	2.07192
$580$	0.627763	0.0260664
$581$	13.7537	0.570600
$582$	1.88203	0.0780125
$583$	−0.704053	−0.0291589
$584$	22.0327	0.911722
$585$	8.45825	0.349706
$586$	−1.56216	−0.0645322
$587$	−37.3165	−1.54022	−0.770109	−	0.637912i	$-0.779798\pi$
$587$	−37.3165	−1.54022	−0.770109	+	0.637912i	$0.779798\pi$
$588$	4.91907	0.202859
$589$	−1.31618	−0.0542322
$590$	12.9543	0.533321
$591$	3.83271	0.157657
$592$	−18.2573	−0.750372
$593$	2.82141	0.115861	0.0579307	−	0.998321i	$-0.481550\pi$
$593$	2.82141	0.115861	0.0579307	+	0.998321i	$0.481550\pi$
$594$	−1.78256	−0.0731392
$595$	9.94383	0.407657
$596$	5.17604	0.212019
$597$	−44.5274	−1.82238
$598$	0.137400	0.00561869
$599$	−41.0397	−1.67684	−0.838419	−	0.545026i	$-0.816520\pi$
$599$	−41.0397	−1.67684	−0.838419	+	0.545026i	$0.816520\pi$
$600$	−7.39060	−0.301720
$601$	22.5878	0.921375	0.460687	−	0.887562i	$-0.347603\pi$
$601$	22.5878	0.921375	0.460687	+	0.887562i	$0.347603\pi$
$602$	13.2355	0.539438
$603$	−0.762076	−0.0310342
$604$	3.96024	0.161140
$605$	26.2687	1.06797
$606$	16.6743	0.677346
$607$	7.99865	0.324655	0.162328	−	0.986737i	$-0.448100\pi$
$607$	7.99865	0.324655	0.162328	+	0.986737i	$0.448100\pi$
$608$	−1.01255	−0.0410643
$609$	12.5321	0.507827
$610$	1.27979	0.0518174
$611$	23.7282	0.959939
$612$	−3.51541	−0.142102
$613$	36.9494	1.49237	0.746187	−	0.665737i	$-0.231883\pi$
$613$	36.9494	1.49237	0.746187	+	0.665737i	$0.231883\pi$
$614$	−35.6491	−1.43868
$615$	1.05981	0.0427357
$616$	63.8761	2.57364
$617$	−14.3909	−0.579354	−0.289677	−	0.957124i	$-0.593548\pi$
$617$	−14.3909	−0.579354	−0.289677	+	0.957124i	$0.593548\pi$
$618$	18.6839	0.751576
$619$	−8.64732	−0.347565	−0.173782	−	0.984784i	$-0.555599\pi$
$619$	−8.64732	−0.347565	−0.173782	+	0.984784i	$0.555599\pi$
$620$	1.26640	0.0508600
$621$	−0.00871232	−0.000349613 0
$622$	22.3823	0.897448
$623$	−29.5970	−1.18578
$624$	21.1384	0.846213
$625$	1.00000	0.0400000
$626$	−39.6127	−1.58324
$627$	−6.45566	−0.257814
$628$	3.87260	0.154534
$629$	17.6665	0.704410
$630$	−12.5644	−0.500577
$631$	−29.5033	−1.17451	−0.587254	−	0.809403i	$-0.699791\pi$
$631$	−29.5033	−1.17451	−0.587254	+	0.809403i	$0.699791\pi$
$632$	−11.2841	−0.448857
$633$	−62.7887	−2.49563
$634$	−14.3981	−0.571821
$635$	19.9234	0.790634
$636$	−0.117343	−0.00465297
$637$	14.0791	0.557836
$638$	11.5089	0.455642
$639$	6.34503	0.251005
$640$	−6.53846	−0.258455
$641$	−40.8613	−1.61392	−0.806961	−	0.590604i	$-0.798889\pi$
$641$	−40.8613	−1.61392	−0.806961	+	0.590604i	$0.798889\pi$
$642$	−1.22218	−0.0482358
$643$	38.6132	1.52275	0.761377	−	0.648309i	$-0.224523\pi$
$643$	38.6132	1.52275	0.761377	+	0.648309i	$0.224523\pi$
$644$	0.0540477	0.00212978
$645$	7.43447	0.292732
$646$	−1.58183	−0.0622362
$647$	0.729963	0.0286978	0.0143489	−	0.999897i	$-0.495432\pi$
$647$	0.729963	0.0286978	0.0143489	+	0.999897i	$0.495432\pi$
$648$	−28.2178	−1.10850
$649$	−62.8904	−2.46866
$650$	−3.66202	−0.143636
$651$	25.2814	0.990858
$652$	−5.57271	−0.218244
$653$	14.7794	0.578362	0.289181	−	0.957274i	$-0.406617\pi$
$653$	14.7794	0.578362	0.289181	+	0.957274i	$0.406617\pi$
$654$	−54.9025	−2.14686
$655$	−15.4494	−0.603658
$656$	1.30288	0.0508687
$657$	21.0397	0.820839
$658$	−35.2472	−1.37408
$659$	−4.67319	−0.182042	−0.0910208	−	0.995849i	$-0.529013\pi$
$659$	−4.67319	−0.182042	−0.0910208	+	0.995849i	$0.529013\pi$
$660$	6.21152	0.241783
$661$	0.560779	0.0218118	0.0109059	−	0.999941i	$-0.496528\pi$
$661$	0.560779	0.0218118	0.0109059	+	0.999941i	$0.496528\pi$
$662$	22.8913	0.889696
$663$	−20.4543	−0.794380
$664$	12.1600	0.471900
$665$	1.49712	0.0580556
$666$	−22.3223	−0.864970
$667$	0.0562502	0.00217802
$668$	5.24004	0.202743
$669$	−14.9160	−0.576687
$670$	0.329943	0.0127468
$671$	−6.21312	−0.239855
$672$	19.4492	0.750270
$673$	−16.5422	−0.637655	−0.318827	−	0.947813i	$-0.603289\pi$
$673$	−16.5422	−0.637655	−0.318827	+	0.947813i	$0.603289\pi$
$674$	2.77527	0.106899
$675$	0.232203	0.00893752
$676$	1.89234	0.0727822
$677$	−27.2288	−1.04649	−0.523243	−	0.852183i	$-0.675278\pi$
$677$	−27.2288	−1.04649	−0.523243	+	0.852183i	$0.675278\pi$
$678$	−49.2181	−1.89021
$679$	2.11890	0.0813158
$680$	8.79160	0.337143
$681$	39.4561	1.51196
$682$	23.2173	0.889035
$683$	−10.6627	−0.407996	−0.203998	−	0.978971i	$-0.565394\pi$
$683$	−10.6627	−0.407996	−0.203998	+	0.978971i	$0.565394\pi$
$684$	−0.529270	−0.0202372
$685$	5.30038	0.202517
$686$	9.36749	0.357652
$687$	61.1138	2.33164
$688$	9.13955	0.348442
$689$	−0.335855	−0.0127951
$690$	−0.114646	−0.00436448
$691$	17.2235	0.655212	0.327606	−	0.944814i	$-0.393758\pi$
$691$	17.2235	0.655212	0.327606	+	0.944814i	$0.393758\pi$
$692$	7.11484	0.270466
$693$	60.9973	2.31710
$694$	20.9181	0.794041
$695$	22.6764	0.860164
$696$	11.0800	0.419986
$697$	−1.26071	−0.0477529
$698$	−17.5578	−0.664574
$699$	34.4989	1.30487
$700$	−1.44050	−0.0544457
$701$	−24.1883	−0.913580	−0.456790	−	0.889575i	$-0.651001\pi$
$701$	−24.1883	−0.913580	−0.456790	+	0.889575i	$0.651001\pi$
$702$	−0.850334	−0.0320938
$703$	2.65982	0.100317
$704$	54.3338	2.04778
$705$	−19.7986	−0.745659
$706$	8.16241	0.307196
$707$	18.7729	0.706027
$708$	−10.4818	−0.393932
$709$	−20.1645	−0.757293	−0.378647	−	0.925541i	$-0.623610\pi$
$709$	−20.1645	−0.757293	−0.378647	+	0.925541i	$0.623610\pi$
$710$	−2.74710	−0.103097
$711$	−10.7755	−0.404114
$712$	−26.1675	−0.980667
$713$	0.113475	0.00424968
$714$	30.3841	1.13709
$715$	17.7783	0.664871
$716$	−5.44977	−0.203668
$717$	24.5552	0.917032
$718$	−37.7980	−1.41061
$719$	51.1719	1.90839	0.954196	−	0.299183i	$-0.0967142\pi$
$719$	51.1719	1.90839	0.954196	+	0.299183i	$0.0967142\pi$
$720$	−8.67614	−0.323341
$721$	21.0354	0.783400
$722$	23.6541	0.880313
$723$	2.42991	0.0903691
$724$	2.30314	0.0855956
$725$	−1.49920	−0.0556788
$726$	80.2657	2.97894
$727$	1.28264	0.0475705	0.0237852	−	0.999717i	$-0.492428\pi$
$727$	1.28264	0.0475705	0.0237852	+	0.999717i	$0.492428\pi$
$728$	30.4709	1.12933
$729$	−25.2534	−0.935311
$730$	−9.10921	−0.337147
$731$	−8.84379	−0.327099
$732$	−1.03553	−0.0382743
$733$	−34.6260	−1.27894	−0.639470	−	0.768816i	$-0.720846\pi$
$733$	−34.6260	−1.27894	−0.639470	+	0.768816i	$0.720846\pi$
$734$	33.7824	1.24693
$735$	−11.7475	−0.433315
$736$	0.0872975	0.00321783
$737$	−1.60180	−0.0590030
$738$	1.59296	0.0586375
$739$	−16.5790	−0.609868	−0.304934	−	0.952373i	$-0.598634\pi$
$739$	−16.5790	−0.609868	−0.304934	+	0.952373i	$0.598634\pi$
$740$	−2.55923	−0.0940792
$741$	−3.07955	−0.113130
$742$	0.498899	0.0183151
$743$	46.9842	1.72368	0.861842	−	0.507177i	$-0.169311\pi$
$743$	46.9842	1.72368	0.861842	+	0.507177i	$0.169311\pi$
$744$	22.3520	0.819463
$745$	−12.3612	−0.452880
$746$	−20.9217	−0.765997
$747$	11.6120	0.424860
$748$	−7.38900	−0.270169
$749$	−1.37601	−0.0502782
$750$	3.05557	0.111574
$751$	0.574306	0.0209567	0.0104784	−	0.999945i	$-0.496665\pi$
$751$	0.574306	0.0209567	0.0104784	+	0.999945i	$0.496665\pi$
$752$	−24.3394	−0.887567
$753$	−65.2147	−2.37656
$754$	5.49010	0.199938
$755$	−9.45769	−0.344200
$756$	−0.334489	−0.0121652
$757$	30.4564	1.10696	0.553479	−	0.832863i	$-0.313300\pi$
$757$	30.4564	1.10696	0.553479	+	0.832863i	$0.313300\pi$
$758$	−40.4396	−1.46883
$759$	0.556578	0.0202025
$760$	1.32364	0.0480134
$761$	42.4908	1.54029	0.770144	−	0.637870i	$-0.220184\pi$
$761$	42.4908	1.54029	0.770144	+	0.637870i	$0.220184\pi$
$762$	60.8772	2.20535
$763$	−61.8125	−2.23776
$764$	−2.08946	−0.0755940
$765$	8.39537	0.303535
$766$	5.82752	0.210557
$767$	−30.0006	−1.08326
$768$	23.2744	0.839842
$769$	−53.7911	−1.93976	−0.969878	−	0.243593i	$-0.921674\pi$
$769$	−53.7911	−1.93976	−0.969878	+	0.243593i	$0.921674\pi$
$770$	−26.4089	−0.951712
$771$	−15.7337	−0.566634
$772$	8.59130	0.309208
$773$	54.0892	1.94545	0.972726	−	0.231956i	$-0.0745124\pi$
$773$	54.0892	1.94545	0.972726	+	0.231956i	$0.0745124\pi$
$774$	11.1744	0.401657
$775$	−3.02438	−0.108639
$776$	1.87337	0.0672502
$777$	−51.0903	−1.83286
$778$	47.2158	1.69277
$779$	−0.189809	−0.00680063
$780$	2.96308	0.106095
$781$	13.3365	0.477219
$782$	0.136378	0.00487688
$783$	−0.348119	−0.0124408
$784$	−14.4418	−0.515779
$785$	−9.24840	−0.330090
$786$	−47.2067	−1.68381
$787$	−25.8938	−0.923015	−0.461507	−	0.887136i	$-0.652691\pi$
$787$	−25.8938	−0.923015	−0.461507	+	0.887136i	$0.652691\pi$
$788$	0.660469	0.0235282
$789$	17.6115	0.626986
$790$	4.66529	0.165984
$791$	−55.4127	−1.97025
$792$	53.9293	1.91629
$793$	−2.96385	−0.105249
$794$	5.74421	0.203854
$795$	0.280235	0.00993892
$796$	−7.67315	−0.271968
$797$	−28.5753	−1.01219	−0.506095	−	0.862478i	$-0.668911\pi$
$797$	−28.5753	−1.01219	−0.506095	+	0.862478i	$0.668911\pi$
$798$	4.57454	0.161937
$799$	23.5518	0.833201
$800$	−2.32668	−0.0822606
$801$	−24.9881	−0.882911
$802$	5.67580	0.200419
$803$	44.2232	1.56060
$804$	−0.266970	−0.00941529
$805$	−0.129075	−0.00454929
$806$	11.0753	0.390112
$807$	−78.3172	−2.75689
$808$	16.5976	0.583902
$809$	−50.2451	−1.76653	−0.883263	−	0.468879i	$-0.844658\pi$
$809$	−50.2451	−1.76653	−0.883263	+	0.468879i	$0.844658\pi$
$810$	11.6664	0.409915
$811$	38.8564	1.36443	0.682217	−	0.731150i	$-0.261016\pi$
$811$	38.8564	1.36443	0.682217	+	0.731150i	$0.261016\pi$
$812$	2.15959	0.0757868
$813$	4.93519	0.173085
$814$	−46.9189	−1.64451
$815$	13.3085	0.466178
$816$	20.9812	0.734490
$817$	−1.33150	−0.0465832
$818$	10.3781	0.362860
$819$	29.0976	1.01675
$820$	0.182631	0.00637776
$821$	33.0877	1.15477	0.577385	−	0.816472i	$-0.304073\pi$
$821$	33.0877	1.15477	0.577385	+	0.816472i	$0.304073\pi$
$822$	16.1957	0.564889
$823$	0.254874	0.00888435	0.00444218	−	0.999990i	$-0.498586\pi$
$823$	0.254874	0.00888435	0.00444218	+	0.999990i	$0.498586\pi$
$824$	18.5980	0.647891
$825$	−14.8341	−0.516457
$826$	44.5647	1.55061
$827$	−48.2635	−1.67829	−0.839143	−	0.543910i	$-0.816943\pi$
$827$	−48.2635	−1.67829	−0.839143	+	0.543910i	$0.816943\pi$
$828$	0.0456314	0.00158580
$829$	−40.0346	−1.39046	−0.695230	−	0.718787i	$-0.744698\pi$
$829$	−40.0346	−1.39046	−0.695230	+	0.718787i	$0.744698\pi$
$830$	−5.02743	−0.174505
$831$	−61.5543	−2.13529
$832$	25.9189	0.898575
$833$	13.9745	0.484187
$834$	69.2893	2.39929
$835$	−12.5141	−0.433067
$836$	−1.11247	−0.0384755
$837$	−0.702271	−0.0242740
$838$	−30.5706	−1.05604
$839$	−17.5710	−0.606619	−0.303309	−	0.952892i	$-0.598092\pi$
$839$	−17.5710	−0.606619	−0.303309	+	0.952892i	$0.598092\pi$
$840$	−25.4247	−0.877236
$841$	−26.7524	−0.922497
$842$	−35.5789	−1.22613
$843$	60.8125	2.09449
$844$	−10.8200	−0.372441
$845$	−4.51921	−0.155465
$846$	−29.7585	−1.02312
$847$	90.3679	3.10508
$848$	0.344507	0.0118304
$849$	−19.7365	−0.677354
$850$	−3.63480	−0.124673
$851$	−0.229318	−0.00786092
$852$	2.22278	0.0761512
$853$	19.5879	0.670676	0.335338	−	0.942098i	$-0.391149\pi$
$853$	19.5879	0.670676	0.335338	+	0.942098i	$0.391149\pi$
$854$	4.40267	0.150656
$855$	1.26398	0.0432273
$856$	−1.21656	−0.0415813
$857$	9.38946	0.320738	0.160369	−	0.987057i	$-0.448732\pi$
$857$	9.38946	0.320738	0.160369	+	0.987057i	$0.448732\pi$
$858$	54.3228	1.85455
$859$	−40.9326	−1.39660	−0.698301	−	0.715804i	$-0.746060\pi$
$859$	−40.9326	−1.39660	−0.698301	+	0.715804i	$0.746060\pi$
$860$	1.28114	0.0436866
$861$	3.64590	0.124252
$862$	23.4579	0.798979
$863$	10.2287	0.348190	0.174095	−	0.984729i	$-0.444300\pi$
$863$	10.2287	0.348190	0.174095	+	0.984729i	$0.444300\pi$
$864$	−0.540263	−0.0183801
$865$	−16.9914	−0.577725
$866$	21.0398	0.714962
$867$	21.0061	0.713405
$868$	4.35661	0.147873
$869$	−22.6490	−0.768313
$870$	−4.58090	−0.155307
$871$	−0.764108	−0.0258908
$872$	−54.6501	−1.85069
$873$	1.78894	0.0605465
$874$	0.0205327	0.000694530 0
$875$	3.44014	0.116298
$876$	7.37062	0.249030
$877$	−12.6843	−0.428319	−0.214160	−	0.976799i	$-0.568701\pi$
$877$	−12.6843	−0.428319	−0.214160	+	0.976799i	$0.568701\pi$
$878$	−46.0160	−1.55296
$879$	−3.01864	−0.101816
$880$	−18.2363	−0.614745
$881$	30.5518	1.02931	0.514657	−	0.857396i	$-0.327919\pi$
$881$	30.5518	1.02931	0.514657	+	0.857396i	$0.327919\pi$
$882$	−17.6572	−0.594550
$883$	11.1859	0.376435	0.188217	−	0.982127i	$-0.439729\pi$
$883$	11.1859	0.376435	0.188217	+	0.982127i	$0.439729\pi$
$884$	−3.52478	−0.118551
$885$	25.0324	0.841453
$886$	28.4370	0.955359
$887$	−17.5867	−0.590504	−0.295252	−	0.955419i	$-0.595404\pi$
$887$	−17.5867	−0.590504	−0.295252	+	0.955419i	$0.595404\pi$
$888$	−45.1703	−1.51582
$889$	68.5392	2.29873
$890$	10.8187	0.362643
$891$	−56.6377	−1.89743
$892$	−2.57040	−0.0860633
$893$	3.54589	0.118659
$894$	−37.7706	−1.26324
$895$	13.0149	0.435041
$896$	−22.4932	−0.751446
$897$	0.265505	0.00886495
$898$	6.24181	0.208292
$899$	4.53414	0.151222
$900$	−1.21618	−0.0405394
$901$	−0.333358	−0.0111058
$902$	3.34822	0.111483
$903$	25.5756	0.851104
$904$	−48.9918	−1.62944
$905$	−5.50027	−0.182835
$906$	−28.8986	−0.960092
$907$	−1.47883	−0.0491036	−0.0245518	−	0.999699i	$-0.507816\pi$
$907$	−1.47883	−0.0491036	−0.0245518	+	0.999699i	$0.507816\pi$
$908$	6.79926	0.225641
$909$	15.8496	0.525697
$910$	−12.5979	−0.417615
$911$	−39.8388	−1.31992	−0.659960	−	0.751301i	$-0.729427\pi$
$911$	−39.8388	−1.31992	−0.659960	+	0.751301i	$0.729427\pi$
$912$	3.15888	0.104601
$913$	24.4071	0.807756
$914$	−29.3812	−0.971843
$915$	2.47302	0.0817554
$916$	10.5314	0.347967
$917$	−53.1481	−1.75510
$918$	−0.844013	−0.0278566
$919$	−10.1754	−0.335655	−0.167828	−	0.985816i	$-0.553675\pi$
$919$	−10.1754	−0.335655	−0.167828	+	0.985816i	$0.553675\pi$
$920$	−0.114118	−0.00376237
$921$	−68.8867	−2.26989
$922$	−8.13465	−0.267900
$923$	6.36194	0.209406
$924$	21.3685	0.702972
$925$	6.11186	0.200957
$926$	−2.14004	−0.0703261
$927$	17.7598	0.583307
$928$	3.48816	0.114504
$929$	15.1566	0.497273	0.248636	−	0.968597i	$-0.420018\pi$
$929$	15.1566	0.497273	0.248636	+	0.968597i	$0.420018\pi$
$930$	−9.24120	−0.303031
$931$	2.10396	0.0689544
$932$	5.94500	0.194735
$933$	43.2505	1.41596
$934$	33.7757	1.10517
$935$	17.6461	0.577090
$936$	25.7259	0.840878
$937$	21.5489	0.703973	0.351987	−	0.936005i	$-0.385506\pi$
$937$	21.5489	0.703973	0.351987	+	0.936005i	$0.385506\pi$
$938$	1.13505	0.0370607
$939$	−76.5458	−2.49798
$940$	−3.41179	−0.111280
$941$	4.96936	0.161996	0.0809982	−	0.996714i	$-0.474189\pi$
$941$	4.96936	0.161996	0.0809982	+	0.996714i	$0.474189\pi$
$942$	−28.2591	−0.920732
$943$	0.0163645	0.000532903 0
$944$	30.7735	1.00159
$945$	0.798813	0.0259854
$946$	23.4874	0.763642
$947$	43.1691	1.40281	0.701403	−	0.712765i	$-0.252557\pi$
$947$	43.1691	1.40281	0.701403	+	0.712765i	$0.252557\pi$
$948$	−3.77487	−0.122602
$949$	21.0958	0.684799
$950$	−0.547245	−0.0177550
$951$	−27.8222	−0.902197
$952$	30.2444	0.980225
$953$	−29.6499	−0.960455	−0.480228	−	0.877144i	$-0.659446\pi$
$953$	−29.6499	−0.960455	−0.480228	+	0.877144i	$0.659446\pi$
$954$	0.421210	0.0136372
$955$	4.98997	0.161472
$956$	4.23147	0.136855
$957$	22.2393	0.718893
$958$	0.301499	0.00974099
$959$	18.2341	0.588808
$960$	−21.6266	−0.697994
$961$	−21.8531	−0.704940
$962$	−22.3818	−0.721617
$963$	−1.16174	−0.0374364
$964$	0.418732	0.0134865
$965$	−20.5174	−0.660479
$966$	−0.394397	−0.0126895
$967$	−46.8305	−1.50597	−0.752984	−	0.658038i	$-0.771386\pi$
$967$	−46.8305	−1.50597	−0.752984	+	0.658038i	$0.771386\pi$
$968$	79.8967	2.56798
$969$	−3.05665	−0.0981938
$970$	−0.774527	−0.0248686
$971$	−30.5519	−0.980456	−0.490228	−	0.871594i	$-0.663087\pi$
$971$	−30.5519	−0.980456	−0.490228	+	0.871594i	$0.663087\pi$
$972$	−9.14802	−0.293423
$973$	78.0100	2.50088
$974$	25.1505	0.805874
$975$	−7.07632	−0.226624
$976$	3.04020	0.0973143
$977$	−12.3905	−0.396406	−0.198203	−	0.980161i	$-0.563511\pi$
$977$	−12.3905	−0.396406	−0.198203	+	0.980161i	$0.563511\pi$
$978$	40.6652	1.30033
$979$	−52.5222	−1.67862
$980$	−2.02439	−0.0646668
$981$	−52.1870	−1.66620
$982$	−34.0244	−1.08576
$983$	25.7281	0.820599	0.410299	−	0.911951i	$-0.365424\pi$
$983$	25.7281	0.820599	0.410299	+	0.911951i	$0.365424\pi$
$984$	3.22343	0.102759
$985$	−1.57731	−0.0502572
$986$	5.44928	0.173541
$987$	−68.1101	−2.16797
$988$	−0.530681	−0.0168832
$989$	0.114796	0.00365029
$990$	−22.2965	−0.708630
$991$	−50.3530	−1.59951	−0.799757	−	0.600323i	$-0.795039\pi$
$991$	−50.3530	−1.59951	−0.799757	+	0.600323i	$0.795039\pi$
$992$	7.03676	0.223417
$993$	44.2341	1.40373
$994$	−9.45040	−0.299748
$995$	18.3247	0.580933
$996$	4.06789	0.128896
$997$	−40.3647	−1.27836	−0.639181	−	0.769057i	$-0.720726\pi$
$997$	−40.3647	−1.27836	−0.639181	+	0.769057i	$0.720726\pi$
$998$	51.3771	1.62631
$999$	1.41919	0.0449013

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1205.2.a.e.1.7	✓	25
5.4	even	2		6025.2.a.j.1.19		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.e.1.7	✓	25	1.1	even	1	trivial
6025.2.a.j.1.19		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)

\(f(q)\)	\(=\)	\(q-1.25748 q^{2} -2.42991 q^{3} -0.418732 q^{4} +1.00000 q^{5} +3.05557 q^{6} +3.44014 q^{7} +3.04152 q^{8} +2.90444 q^{9} +O(q^{10})\)	\(q-1.25748 q^{2} -2.42991 q^{3} -0.418732 q^{4} +1.00000 q^{5} +3.05557 q^{6} +3.44014 q^{7} +3.04152 q^{8} +2.90444 q^{9} -1.25748 q^{10} +6.10481 q^{11} +1.01748 q^{12} +2.91218 q^{13} -4.32592 q^{14} -2.42991 q^{15} -2.98720 q^{16} +2.89053 q^{17} -3.65229 q^{18} +0.435190 q^{19} -0.418732 q^{20} -8.35922 q^{21} -7.67670 q^{22} -0.0375202 q^{23} -7.39060 q^{24} +1.00000 q^{25} -3.66202 q^{26} +0.232203 q^{27} -1.44050 q^{28} -1.49920 q^{29} +3.05557 q^{30} -3.02438 q^{31} -2.32668 q^{32} -14.8341 q^{33} -3.63480 q^{34} +3.44014 q^{35} -1.21618 q^{36} +6.11186 q^{37} -0.547245 q^{38} -7.07632 q^{39} +3.04152 q^{40} -0.436153 q^{41} +10.5116 q^{42} -3.05957 q^{43} -2.55628 q^{44} +2.90444 q^{45} +0.0471811 q^{46} +8.14790 q^{47} +7.25861 q^{48} +4.83457 q^{49} -1.25748 q^{50} -7.02371 q^{51} -1.21942 q^{52} -0.115328 q^{53} -0.291992 q^{54} +6.10481 q^{55} +10.4633 q^{56} -1.05747 q^{57} +1.88522 q^{58} -10.3018 q^{59} +1.01748 q^{60} -1.01774 q^{61} +3.80311 q^{62} +9.99168 q^{63} +8.90016 q^{64} +2.91218 q^{65} +18.6537 q^{66} -0.262383 q^{67} -1.21036 q^{68} +0.0911705 q^{69} -4.32592 q^{70} +2.18460 q^{71} +8.83391 q^{72} +7.24400 q^{73} -7.68557 q^{74} -2.42991 q^{75} -0.182228 q^{76} +21.0014 q^{77} +8.89837 q^{78} -3.71002 q^{79} -2.98720 q^{80} -9.27755 q^{81} +0.548456 q^{82} +3.99801 q^{83} +3.50027 q^{84} +2.89053 q^{85} +3.84737 q^{86} +3.64291 q^{87} +18.5679 q^{88} -8.60342 q^{89} -3.65229 q^{90} +10.0183 q^{91} +0.0157109 q^{92} +7.34895 q^{93} -10.2459 q^{94} +0.435190 q^{95} +5.65361 q^{96} +0.615933 q^{97} -6.07940 q^{98} +17.7310 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 6 q^{2} + 15 q^{3} + 32 q^{4} + 25 q^{5} - q^{6} + 19 q^{7} + 15 q^{8} + 32 q^{9}+O(q^{10}) \) 25 * q + 6 * q^2 + 15 * q^3 + 32 * q^4 + 25 * q^5 - q^6 + 19 * q^7 + 15 * q^8 + 32 * q^9	\( 25 q + 6 q^{2} + 15 q^{3} + 32 q^{4} + 25 q^{5} - q^{6} + 19 q^{7} + 15 q^{8} + 32 q^{9} + 6 q^{10} + 2 q^{11} + 20 q^{12} + 14 q^{13} - 5 q^{14} + 15 q^{15} + 38 q^{16} + 7 q^{17} + 9 q^{18} + 30 q^{19} + 32 q^{20} + q^{21} + q^{22} + 43 q^{23} - 6 q^{24} + 25 q^{25} - 22 q^{26} + 42 q^{27} + 32 q^{28} - 4 q^{29} - q^{30} + 14 q^{31} + 26 q^{32} + 4 q^{33} + 7 q^{34} + 19 q^{35} + 15 q^{36} + 16 q^{37} + 14 q^{38} - 21 q^{39} + 15 q^{40} - q^{41} - 25 q^{42} + 35 q^{43} - 52 q^{44} + 32 q^{45} - 27 q^{46} + 50 q^{47} + 26 q^{48} + 46 q^{49} + 6 q^{50} - 7 q^{51} + 3 q^{52} + 4 q^{53} - 31 q^{54} + 2 q^{55} - 51 q^{56} + 2 q^{58} + 6 q^{59} + 20 q^{60} + 19 q^{61} + 28 q^{63} + 49 q^{64} + 14 q^{65} - 27 q^{66} + 65 q^{67} - 25 q^{68} + 2 q^{69} - 5 q^{70} - 34 q^{71} - 10 q^{72} + 8 q^{73} - 42 q^{74} + 15 q^{75} + 71 q^{76} + q^{77} - 59 q^{78} - 12 q^{79} + 38 q^{80} + 29 q^{81} + 11 q^{82} + 41 q^{83} - 10 q^{84} + 7 q^{85} - 13 q^{86} + 40 q^{87} - 52 q^{88} - 24 q^{89} + 9 q^{90} + 46 q^{91} + 85 q^{92} - 30 q^{93} + 14 q^{94} + 30 q^{95} - 30 q^{96} + 9 q^{97} - 64 q^{98} + 2 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 + 15 * q^3 + 32 * q^4 + 25 * q^5 - q^6 + 19 * q^7 + 15 * q^8 + 32 * q^9 + 6 * q^10 + 2 * q^11 + 20 * q^12 + 14 * q^13 - 5 * q^14 + 15 * q^15 + 38 * q^16 + 7 * q^17 + 9 * q^18 + 30 * q^19 + 32 * q^20 + q^21 + q^22 + 43 * q^23 - 6 * q^24 + 25 * q^25 - 22 * q^26 + 42 * q^27 + 32 * q^28 - 4 * q^29 - q^30 + 14 * q^31 + 26 * q^32 + 4 * q^33 + 7 * q^34 + 19 * q^35 + 15 * q^36 + 16 * q^37 + 14 * q^38 - 21 * q^39 + 15 * q^40 - q^41 - 25 * q^42 + 35 * q^43 - 52 * q^44 + 32 * q^45 - 27 * q^46 + 50 * q^47 + 26 * q^48 + 46 * q^49 + 6 * q^50 - 7 * q^51 + 3 * q^52 + 4 * q^53 - 31 * q^54 + 2 * q^55 - 51 * q^56 + 2 * q^58 + 6 * q^59 + 20 * q^60 + 19 * q^61 + 28 * q^63 + 49 * q^64 + 14 * q^65 - 27 * q^66 + 65 * q^67 - 25 * q^68 + 2 * q^69 - 5 * q^70 - 34 * q^71 - 10 * q^72 + 8 * q^73 - 42 * q^74 + 15 * q^75 + 71 * q^76 + q^77 - 59 * q^78 - 12 * q^79 + 38 * q^80 + 29 * q^81 + 11 * q^82 + 41 * q^83 - 10 * q^84 + 7 * q^85 - 13 * q^86 + 40 * q^87 - 52 * q^88 - 24 * q^89 + 9 * q^90 + 46 * q^91 + 85 * q^92 - 30 * q^93 + 14 * q^94 + 30 * q^95 - 30 * q^96 + 9 * q^97 - 64 * q^98 + 2 * q^99

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