LMFDB - Embedded newform 1205.2.a.e.1.5

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			1.5
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)

$f(q)$	$=$	$q-1.83164 q^{2} +0.379920 q^{3} +1.35491 q^{4} +1.00000 q^{5} -0.695877 q^{6} -4.92875 q^{7} +1.18157 q^{8} -2.85566 q^{9} +O(q^{10})$	\(q-1.83164 q^{2} +0.379920 q^{3} +1.35491 q^{4} +1.00000 q^{5} -0.695877 q^{6} -4.92875 q^{7} +1.18157 q^{8} -2.85566 q^{9} -1.83164 q^{10} -5.22455 q^{11} +0.514759 q^{12} -4.04771 q^{13} +9.02771 q^{14} +0.379920 q^{15} -4.87404 q^{16} +0.556876 q^{17} +5.23055 q^{18} -2.38523 q^{19} +1.35491 q^{20} -1.87253 q^{21} +9.56951 q^{22} +9.05967 q^{23} +0.448901 q^{24} +1.00000 q^{25} +7.41395 q^{26} -2.22468 q^{27} -6.67803 q^{28} +6.65787 q^{29} -0.695877 q^{30} +6.74406 q^{31} +6.56436 q^{32} -1.98491 q^{33} -1.02000 q^{34} -4.92875 q^{35} -3.86917 q^{36} +1.11993 q^{37} +4.36888 q^{38} -1.53780 q^{39} +1.18157 q^{40} -8.11343 q^{41} +3.42981 q^{42} +8.45122 q^{43} -7.07881 q^{44} -2.85566 q^{45} -16.5941 q^{46} +11.3134 q^{47} -1.85174 q^{48} +17.2926 q^{49} -1.83164 q^{50} +0.211568 q^{51} -5.48429 q^{52} -4.22222 q^{53} +4.07482 q^{54} -5.22455 q^{55} -5.82365 q^{56} -0.906195 q^{57} -12.1948 q^{58} +0.217559 q^{59} +0.514759 q^{60} -7.17902 q^{61} -12.3527 q^{62} +14.0748 q^{63} -2.27548 q^{64} -4.04771 q^{65} +3.63565 q^{66} +3.80405 q^{67} +0.754518 q^{68} +3.44195 q^{69} +9.02771 q^{70} -8.97571 q^{71} -3.37416 q^{72} -0.421188 q^{73} -2.05132 q^{74} +0.379920 q^{75} -3.23177 q^{76} +25.7505 q^{77} +2.81671 q^{78} -12.2433 q^{79} -4.87404 q^{80} +7.72178 q^{81} +14.8609 q^{82} +4.00734 q^{83} -2.53712 q^{84} +0.556876 q^{85} -15.4796 q^{86} +2.52946 q^{87} -6.17316 q^{88} -3.16765 q^{89} +5.23055 q^{90} +19.9501 q^{91} +12.2751 q^{92} +2.56220 q^{93} -20.7220 q^{94} -2.38523 q^{95} +2.49393 q^{96} -12.6870 q^{97} -31.6738 q^{98} +14.9195 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.83164	−1.29517	−0.647583	−	0.761995i	$-0.724220\pi$
$2$	−1.83164	−1.29517	−0.647583	+	0.761995i	$0.724220\pi$
$3$	0.379920	0.219347	0.109673	−	0.993968i	$-0.465019\pi$
$3$	0.379920	0.219347	0.109673	+	0.993968i	$0.465019\pi$
$4$	1.35491	0.677457
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.695877	−0.284091
$7$	−4.92875	−1.86289	−0.931446	−	0.363879i	$-0.881452\pi$
$7$	−4.92875	−1.86289	−0.931446	+	0.363879i	$0.881452\pi$
$8$	1.18157	0.417747
$9$	−2.85566	−0.951887
$10$	−1.83164	−0.579216
$11$	−5.22455	−1.57526	−0.787631	−	0.616148i	$-0.788692\pi$
$11$	−5.22455	−1.57526	−0.787631	+	0.616148i	$0.788692\pi$
$12$	0.514759	0.148598
$13$	−4.04771	−1.12263	−0.561316	−	0.827602i	$-0.689705\pi$
$13$	−4.04771	−1.12263	−0.561316	+	0.827602i	$0.689705\pi$
$14$	9.02771	2.41276
$15$	0.379920	0.0980949
$16$	−4.87404	−1.21851
$17$	0.556876	0.135062	0.0675311	−	0.997717i	$-0.478488\pi$
$17$	0.556876	0.135062	0.0675311	+	0.997717i	$0.478488\pi$
$18$	5.23055	1.23285
$19$	−2.38523	−0.547208	−0.273604	−	0.961842i	$-0.588216\pi$
$19$	−2.38523	−0.547208	−0.273604	+	0.961842i	$0.588216\pi$
$20$	1.35491	0.302968
$21$	−1.87253	−0.408620
$22$	9.56951	2.04023
$23$	9.05967	1.88907	0.944536	−	0.328407i	$-0.106512\pi$
$23$	9.05967	1.88907	0.944536	+	0.328407i	$0.106512\pi$
$24$	0.448901	0.0916316
$25$	1.00000	0.200000
$26$	7.41395	1.45399
$27$	−2.22468	−0.428140
$28$	−6.67803	−1.26203
$29$	6.65787	1.23634	0.618168	−	0.786046i	$-0.287875\pi$
$29$	6.65787	1.23634	0.618168	+	0.786046i	$0.287875\pi$
$30$	−0.695877	−0.127049
$31$	6.74406	1.21127	0.605634	−	0.795743i	$-0.292919\pi$
$31$	6.74406	1.21127	0.605634	+	0.795743i	$0.292919\pi$
$32$	6.56436	1.16042
$33$	−1.98491	−0.345529
$34$	−1.02000	−0.174928
$35$	−4.92875	−0.833111
$36$	−3.86917	−0.644862
$37$	1.11993	0.184116	0.0920580	−	0.995754i	$-0.470655\pi$
$37$	1.11993	0.184116	0.0920580	+	0.995754i	$0.470655\pi$
$38$	4.36888	0.708726
$39$	−1.53780	−0.246246
$40$	1.18157	0.186822
$41$	−8.11343	−1.26710	−0.633552	−	0.773700i	$-0.718404\pi$
$41$	−8.11343	−1.26710	−0.633552	+	0.773700i	$0.718404\pi$
$42$	3.42981	0.529231
$43$	8.45122	1.28880	0.644400	−	0.764689i	$-0.277107\pi$
$43$	8.45122	1.28880	0.644400	+	0.764689i	$0.277107\pi$
$44$	−7.07881	−1.06717
$45$	−2.85566	−0.425697
$46$	−16.5941	−2.44666
$47$	11.3134	1.65022	0.825112	−	0.564969i	$-0.191112\pi$
$47$	11.3134	1.65022	0.825112	+	0.564969i	$0.191112\pi$
$48$	−1.85174	−0.267276
$49$	17.2926	2.47037
$50$	−1.83164	−0.259033
$51$	0.211568	0.0296255
$52$	−5.48429	−0.760534
$53$	−4.22222	−0.579967	−0.289983	−	0.957032i	$-0.593650\pi$
$53$	−4.22222	−0.579967	−0.289983	+	0.957032i	$0.593650\pi$
$54$	4.07482	0.554513
$55$	−5.22455	−0.704478
$56$	−5.82365	−0.778218
$57$	−0.906195	−0.120028
$58$	−12.1948	−1.60126
$59$	0.217559	0.0283238	0.0141619	−	0.999900i	$-0.495492\pi$
$59$	0.217559	0.0283238	0.0141619	+	0.999900i	$0.495492\pi$
$60$	0.514759	0.0664551
$61$	−7.17902	−0.919180	−0.459590	−	0.888131i	$-0.652004\pi$
$61$	−7.17902	−0.919180	−0.459590	+	0.888131i	$0.652004\pi$
$62$	−12.3527	−1.56880
$63$	14.0748	1.77326
$64$	−2.27548	−0.284435
$65$	−4.04771	−0.502056
$66$	3.63565	0.447517
$67$	3.80405	0.464739	0.232369	−	0.972628i	$-0.425352\pi$
$67$	3.80405	0.464739	0.232369	+	0.972628i	$0.425352\pi$
$68$	0.754518	0.0914988
$69$	3.44195	0.414362
$70$	9.02771	1.07902
$71$	−8.97571	−1.06522	−0.532610	−	0.846361i	$-0.678789\pi$
$71$	−8.97571	−1.06522	−0.532610	+	0.846361i	$0.678789\pi$
$72$	−3.37416	−0.397648
$73$	−0.421188	−0.0492963	−0.0246482	−	0.999696i	$-0.507847\pi$
$73$	−0.421188	−0.0492963	−0.0246482	+	0.999696i	$0.507847\pi$
$74$	−2.05132	−0.238461
$75$	0.379920	0.0438694
$76$	−3.23177	−0.370710
$77$	25.7505	2.93454
$78$	2.81671	0.318929
$79$	−12.2433	−1.37748	−0.688739	−	0.725009i	$-0.741836\pi$
$79$	−12.2433	−1.37748	−0.688739	+	0.725009i	$0.741836\pi$
$80$	−4.87404	−0.544934
$81$	7.72178	0.857976
$82$	14.8609	1.64111
$83$	4.00734	0.439863	0.219931	−	0.975515i	$-0.429417\pi$
$83$	4.00734	0.439863	0.219931	+	0.975515i	$0.429417\pi$
$84$	−2.53712	−0.276822
$85$	0.556876	0.0604017
$86$	−15.4796	−1.66921
$87$	2.52946	0.271186
$88$	−6.17316	−0.658061
$89$	−3.16765	−0.335770	−0.167885	−	0.985807i	$-0.553694\pi$
$89$	−3.16765	−0.335770	−0.167885	+	0.985807i	$0.553694\pi$
$90$	5.23055	0.551348
$91$	19.9501	2.09134
$92$	12.2751	1.27976
$93$	2.56220	0.265688
$94$	−20.7220	−2.13732
$95$	−2.38523	−0.244719
$96$	2.49393	0.254536
$97$	−12.6870	−1.28816	−0.644082	−	0.764956i	$-0.722761\pi$
$97$	−12.6870	−1.28816	−0.644082	+	0.764956i	$0.722761\pi$
$98$	−31.6738	−3.19954
$99$	14.9195	1.49947
$100$	1.35491	0.135491
$101$	−5.48433	−0.545712	−0.272856	−	0.962055i	$-0.587968\pi$
$101$	−5.48433	−0.545712	−0.272856	+	0.962055i	$0.587968\pi$
$102$	−0.387517	−0.0383699
$103$	14.1709	1.39631	0.698153	−	0.715949i	$-0.254006\pi$
$103$	14.1709	1.39631	0.698153	+	0.715949i	$0.254006\pi$
$104$	−4.78264	−0.468976
$105$	−1.87253	−0.182740
$106$	7.73360	0.751154
$107$	9.19260	0.888683	0.444341	−	0.895858i	$-0.353438\pi$
$107$	9.19260	0.888683	0.444341	+	0.895858i	$0.353438\pi$
$108$	−3.01425	−0.290047
$109$	−4.98204	−0.477193	−0.238596	−	0.971119i	$-0.576687\pi$
$109$	−4.98204	−0.477193	−0.238596	+	0.971119i	$0.576687\pi$
$110$	9.56951	0.912417
$111$	0.425485	0.0403853
$112$	24.0229	2.26995
$113$	−11.3082	−1.06379	−0.531895	−	0.846810i	$-0.678520\pi$
$113$	−11.3082	−1.06379	−0.531895	+	0.846810i	$0.678520\pi$
$114$	1.65983	0.155457
$115$	9.05967	0.844819
$116$	9.02084	0.837564
$117$	11.5589	1.06862
$118$	−0.398490	−0.0366840
$119$	−2.74470	−0.251606
$120$	0.448901	0.0409789
$121$	16.2959	1.48145
$122$	13.1494	1.19049
$123$	−3.08245	−0.277935
$124$	9.13762	0.820582
$125$	1.00000	0.0894427
$126$	−25.7801	−2.29667
$127$	1.73294	0.153774	0.0768868	−	0.997040i	$-0.475502\pi$
$127$	1.73294	0.153774	0.0768868	+	0.997040i	$0.475502\pi$
$128$	−8.96085	−0.792035
$129$	3.21079	0.282694
$130$	7.41395	0.650246
$131$	−5.90986	−0.516347	−0.258173	−	0.966099i	$-0.583121\pi$
$131$	−5.90986	−0.516347	−0.258173	+	0.966099i	$0.583121\pi$
$132$	−2.68938	−0.234081
$133$	11.7562	1.01939
$134$	−6.96766	−0.601914
$135$	−2.22468	−0.191470
$136$	0.657987	0.0564219
$137$	−14.5777	−1.24546	−0.622730	−	0.782437i	$-0.713976\pi$
$137$	−14.5777	−1.24546	−0.622730	+	0.782437i	$0.713976\pi$
$138$	−6.30442	−0.536668
$139$	21.3548	1.81129	0.905645	−	0.424037i	$-0.139387\pi$
$139$	21.3548	1.81129	0.905645	+	0.424037i	$0.139387\pi$
$140$	−6.67803	−0.564396
$141$	4.29817	0.361972
$142$	16.4403	1.37964
$143$	21.1474	1.76844
$144$	13.9186	1.15988
$145$	6.65787	0.552906
$146$	0.771466	0.0638470
$147$	6.56979	0.541868
$148$	1.51741	0.124731
$149$	6.97429	0.571356	0.285678	−	0.958326i	$-0.407781\pi$
$149$	6.97429	0.571356	0.285678	+	0.958326i	$0.407781\pi$
$150$	−0.695877	−0.0568182
$151$	10.2159	0.831361	0.415681	−	0.909511i	$-0.363543\pi$
$151$	10.2159	0.831361	0.415681	+	0.909511i	$0.363543\pi$
$152$	−2.81831	−0.228595
$153$	−1.59025	−0.128564
$154$	−47.1657	−3.80072
$155$	6.74406	0.541696
$156$	−2.08359	−0.166821
$157$	18.4697	1.47404	0.737020	−	0.675871i	$-0.236232\pi$
$157$	18.4697	1.47404	0.737020	+	0.675871i	$0.236232\pi$
$158$	22.4253	1.78406
$159$	−1.60411	−0.127214
$160$	6.56436	0.518958
$161$	−44.6529	−3.51914
$162$	−14.1435	−1.11122
$163$	13.0987	1.02597	0.512983	−	0.858399i	$-0.328540\pi$
$163$	13.0987	1.02597	0.512983	+	0.858399i	$0.328540\pi$
$164$	−10.9930	−0.858408
$165$	−1.98491	−0.154525
$166$	−7.34001	−0.569695
$167$	3.14405	0.243294	0.121647	−	0.992573i	$-0.461182\pi$
$167$	3.14405	0.243294	0.121647	+	0.992573i	$0.461182\pi$
$168$	−2.21252	−0.170700
$169$	3.38392	0.260301
$170$	−1.02000	−0.0782302
$171$	6.81140	0.520881
$172$	11.4507	0.873106
$173$	−5.66775	−0.430911	−0.215456	−	0.976514i	$-0.569124\pi$
$173$	−5.66775	−0.430911	−0.215456	+	0.976514i	$0.569124\pi$
$174$	−4.63306	−0.351232
$175$	−4.92875	−0.372578
$176$	25.4647	1.91947
$177$	0.0826550	0.00621273
$178$	5.80200	0.434878
$179$	3.54362	0.264862	0.132431	−	0.991192i	$-0.457722\pi$
$179$	3.54362	0.264862	0.132431	+	0.991192i	$0.457722\pi$
$180$	−3.86917	−0.288391
$181$	5.45665	0.405590	0.202795	−	0.979221i	$-0.434998\pi$
$181$	5.45665	0.405590	0.202795	+	0.979221i	$0.434998\pi$
$182$	−36.5415	−2.70864
$183$	−2.72745	−0.201619
$184$	10.7046	0.789155
$185$	1.11993	0.0823392
$186$	−4.69304	−0.344110
$187$	−2.90943	−0.212758
$188$	15.3286	1.11796
$189$	10.9649	0.797579
$190$	4.36888	0.316952
$191$	2.03395	0.147171	0.0735857	−	0.997289i	$-0.476556\pi$
$191$	2.03395	0.147171	0.0735857	+	0.997289i	$0.476556\pi$
$192$	−0.864499	−0.0623898
$193$	−26.4905	−1.90683	−0.953414	−	0.301666i	$-0.902457\pi$
$193$	−26.4905	−1.90683	−0.953414	+	0.301666i	$0.902457\pi$
$194$	23.2380	1.66839
$195$	−1.53780	−0.110124
$196$	23.4299	1.67357
$197$	2.39811	0.170858	0.0854292	−	0.996344i	$-0.472774\pi$
$197$	2.39811	0.170858	0.0854292	+	0.996344i	$0.472774\pi$
$198$	−27.3273	−1.94206
$199$	−10.1186	−0.717287	−0.358644	−	0.933475i	$-0.616761\pi$
$199$	−10.1186	−0.717287	−0.358644	+	0.933475i	$0.616761\pi$
$200$	1.18157	0.0835495
$201$	1.44524	0.101939
$202$	10.0453	0.706788
$203$	−32.8150	−2.30316
$204$	0.286657	0.0200700
$205$	−8.11343	−0.566666
$206$	−25.9561	−1.80845
$207$	−25.8714	−1.79818
$208$	19.7287	1.36794
$209$	12.4617	0.861996
$210$	3.42981	0.236679
$211$	−25.8670	−1.78076	−0.890380	−	0.455217i	$-0.849562\pi$
$211$	−25.8670	−1.78076	−0.890380	+	0.455217i	$0.849562\pi$
$212$	−5.72075	−0.392902
$213$	−3.41005	−0.233653
$214$	−16.8376	−1.15099
$215$	8.45122	0.576369
$216$	−2.62861	−0.178855
$217$	−33.2398	−2.25646
$218$	9.12531	0.618044
$219$	−0.160018	−0.0108130
$220$	−7.07881	−0.477253
$221$	−2.25407	−0.151625
$222$	−0.779337	−0.0523057
$223$	22.5978	1.51326	0.756631	−	0.653842i	$-0.226844\pi$
$223$	22.5978	1.51326	0.756631	+	0.653842i	$0.226844\pi$
$224$	−32.3541	−2.16175
$225$	−2.85566	−0.190377
$226$	20.7127	1.37779
$227$	−2.05614	−0.136471	−0.0682355	−	0.997669i	$-0.521737\pi$
$227$	−2.05614	−0.136471	−0.0682355	+	0.997669i	$0.521737\pi$
$228$	−1.22782	−0.0813141
$229$	14.0922	0.931236	0.465618	−	0.884986i	$-0.345832\pi$
$229$	14.0922	0.931236	0.465618	+	0.884986i	$0.345832\pi$
$230$	−16.5941	−1.09418
$231$	9.78313	0.643683
$232$	7.86673	0.516476
$233$	14.7638	0.967210	0.483605	−	0.875286i	$-0.339327\pi$
$233$	14.7638	0.967210	0.483605	+	0.875286i	$0.339327\pi$
$234$	−21.1717	−1.38404
$235$	11.3134	0.738003
$236$	0.294773	0.0191881
$237$	−4.65147	−0.302146
$238$	5.02731	0.325872
$239$	−5.73887	−0.371216	−0.185608	−	0.982624i	$-0.559426\pi$
$239$	−5.73887	−0.371216	−0.185608	+	0.982624i	$0.559426\pi$
$240$	−1.85174	−0.119530
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	−29.8483	−1.91872
$243$	9.60771	0.616335
$244$	−9.72695	−0.622704
$245$	17.2926	1.10478
$246$	5.64595	0.359973
$247$	9.65469	0.614313
$248$	7.96857	0.506004
$249$	1.52247	0.0964825
$250$	−1.83164	−0.115843
$251$	−7.26230	−0.458392	−0.229196	−	0.973380i	$-0.573610\pi$
$251$	−7.26230	−0.458392	−0.229196	+	0.973380i	$0.573610\pi$
$252$	19.0702	1.20131
$253$	−47.3327	−2.97578
$254$	−3.17413	−0.199162
$255$	0.211568	0.0132489
$256$	20.9640	1.31025
$257$	11.0709	0.690583	0.345291	−	0.938496i	$-0.387780\pi$
$257$	11.0709	0.690583	0.345291	+	0.938496i	$0.387780\pi$
$258$	−5.88102	−0.366136
$259$	−5.51987	−0.342988
$260$	−5.48429	−0.340121
$261$	−19.0126	−1.17685
$262$	10.8247	0.668755
$263$	−0.774498	−0.0477576	−0.0238788	−	0.999715i	$-0.507602\pi$
$263$	−0.774498	−0.0477576	−0.0238788	+	0.999715i	$0.507602\pi$
$264$	−2.34531	−0.144344
$265$	−4.22222	−0.259369
$266$	−21.5331	−1.32028
$267$	−1.20345	−0.0736501
$268$	5.15416	0.314840
$269$	1.53178	0.0933940	0.0466970	−	0.998909i	$-0.485130\pi$
$269$	1.53178	0.0933940	0.0466970	+	0.998909i	$0.485130\pi$
$270$	4.07482	0.247986
$271$	14.6431	0.889504	0.444752	−	0.895654i	$-0.353292\pi$
$271$	14.6431	0.889504	0.444752	+	0.895654i	$0.353292\pi$
$272$	−2.71423	−0.164575
$273$	7.57945	0.458729
$274$	26.7012	1.61308
$275$	−5.22455	−0.315052
$276$	4.66354	0.280712
$277$	24.0252	1.44354	0.721768	−	0.692135i	$-0.243330\pi$
$277$	24.0252	1.44354	0.721768	+	0.692135i	$0.243330\pi$
$278$	−39.1143	−2.34592
$279$	−19.2587	−1.15299
$280$	−5.82365	−0.348030
$281$	11.8211	0.705187	0.352594	−	0.935777i	$-0.385300\pi$
$281$	11.8211	0.705187	0.352594	+	0.935777i	$0.385300\pi$
$282$	−7.87272	−0.468814
$283$	−4.14754	−0.246546	−0.123273	−	0.992373i	$-0.539339\pi$
$283$	−4.14754	−0.246546	−0.123273	+	0.992373i	$0.539339\pi$
$284$	−12.1613	−0.721641
$285$	−0.906195	−0.0536784
$286$	−38.7345	−2.29042
$287$	39.9891	2.36048
$288$	−18.7456	−1.10459
$289$	−16.6899	−0.981758
$290$	−12.1948	−0.716106
$291$	−4.82003	−0.282555
$292$	−0.570673	−0.0333961
$293$	20.1192	1.17538	0.587689	−	0.809087i	$-0.300038\pi$
$293$	20.1192	1.17538	0.587689	+	0.809087i	$0.300038\pi$
$294$	−12.0335	−0.701809
$295$	0.217559	0.0126668
$296$	1.32328	0.0769140
$297$	11.6230	0.674433
$298$	−12.7744	−0.740001
$299$	−36.6709	−2.12073
$300$	0.514759	0.0297196
$301$	−41.6540	−2.40090
$302$	−18.7119	−1.07675
$303$	−2.08361	−0.119700
$304$	11.6257	0.666778
$305$	−7.17902	−0.411070
$306$	2.91277	0.166512
$307$	−21.7565	−1.24171	−0.620854	−	0.783927i	$-0.713214\pi$
$307$	−21.7565	−1.24171	−0.620854	+	0.783927i	$0.713214\pi$
$308$	34.8897	1.98803
$309$	5.38383	0.306275
$310$	−12.3527	−0.701586
$311$	−5.98062	−0.339130	−0.169565	−	0.985519i	$-0.554236\pi$
$311$	−5.98062	−0.339130	−0.169565	+	0.985519i	$0.554236\pi$
$312$	−1.81702	−0.102869
$313$	31.4466	1.77747	0.888734	−	0.458424i	$-0.151586\pi$
$313$	31.4466	1.77747	0.888734	+	0.458424i	$0.151586\pi$
$314$	−33.8298	−1.90913
$315$	14.0748	0.793027
$316$	−16.5886	−0.933182
$317$	−25.4338	−1.42850	−0.714252	−	0.699889i	$-0.753233\pi$
$317$	−25.4338	−1.42850	−0.714252	+	0.699889i	$0.753233\pi$
$318$	2.93815	0.164763
$319$	−34.7844	−1.94755
$320$	−2.27548	−0.127203
$321$	3.49245	0.194930
$322$	81.7881	4.55787
$323$	−1.32827	−0.0739072
$324$	10.4623	0.581241
$325$	−4.04771	−0.224526
$326$	−23.9921	−1.32880
$327$	−1.89278	−0.104671
$328$	−9.58657	−0.529330
$329$	−55.7608	−3.07419
$330$	3.63565	0.200136
$331$	25.9342	1.42547	0.712736	−	0.701433i	$-0.247456\pi$
$331$	25.9342	1.42547	0.712736	+	0.701433i	$0.247456\pi$
$332$	5.42960	0.297988
$333$	−3.19815	−0.175258
$334$	−5.75878	−0.315107
$335$	3.80405	0.207838
$336$	9.12678	0.497907
$337$	19.3154	1.05218	0.526089	−	0.850430i	$-0.323658\pi$
$337$	19.3154	1.05218	0.526089	+	0.850430i	$0.323658\pi$
$338$	−6.19813	−0.337134
$339$	−4.29623	−0.233339
$340$	0.754518	0.0409195
$341$	−35.2347	−1.90806
$342$	−12.4760	−0.674627
$343$	−50.7295	−2.73914
$344$	9.98570	0.538393
$345$	3.44195	0.185308
$346$	10.3813	0.558102
$347$	21.0092	1.12783	0.563916	−	0.825832i	$-0.309294\pi$
$347$	21.0092	1.12783	0.563916	+	0.825832i	$0.309294\pi$
$348$	3.42720	0.183717
$349$	−18.7354	−1.00288	−0.501442	−	0.865191i	$-0.667197\pi$
$349$	−18.7354	−1.00288	−0.501442	+	0.865191i	$0.667197\pi$
$350$	9.02771	0.482551
$351$	9.00486	0.480644
$352$	−34.2958	−1.82797
$353$	−6.18488	−0.329188	−0.164594	−	0.986361i	$-0.552631\pi$
$353$	−6.18488	−0.329188	−0.164594	+	0.986361i	$0.552631\pi$
$354$	−0.151394	−0.00804652
$355$	−8.97571	−0.476381
$356$	−4.29189	−0.227470
$357$	−1.04277	−0.0551891
$358$	−6.49064	−0.343041
$359$	9.14025	0.482404	0.241202	−	0.970475i	$-0.422458\pi$
$359$	9.14025	0.482404	0.241202	+	0.970475i	$0.422458\pi$
$360$	−3.37416	−0.177834
$361$	−13.3107	−0.700563
$362$	−9.99463	−0.525306
$363$	6.19115	0.324951
$364$	27.0307	1.41679
$365$	−0.421188	−0.0220460
$366$	4.99572	0.261131
$367$	29.8036	1.55573	0.777867	−	0.628429i	$-0.216302\pi$
$367$	29.8036	1.55573	0.777867	+	0.628429i	$0.216302\pi$
$368$	−44.1572	−2.30185
$369$	23.1692	1.20614
$370$	−2.05132	−0.106643
$371$	20.8103	1.08042
$372$	3.47156	0.179992
$373$	13.3204	0.689702	0.344851	−	0.938657i	$-0.387929\pi$
$373$	13.3204	0.689702	0.344851	+	0.938657i	$0.387929\pi$
$374$	5.32903	0.275557
$375$	0.379920	0.0196190
$376$	13.3675	0.689377
$377$	−26.9491	−1.38795
$378$	−20.0838	−1.03300
$379$	25.8846	1.32960	0.664801	−	0.747021i	$-0.268516\pi$
$379$	25.8846	1.32960	0.664801	+	0.747021i	$0.268516\pi$
$380$	−3.23177	−0.165787
$381$	0.658379	0.0337298
$382$	−3.72547	−0.190611
$383$	−3.81566	−0.194971	−0.0974857	−	0.995237i	$-0.531080\pi$
$383$	−3.81566	−0.194971	−0.0974857	+	0.995237i	$0.531080\pi$
$384$	−3.40441	−0.173730
$385$	25.7505	1.31237
$386$	48.5211	2.46966
$387$	−24.1338	−1.22679
$388$	−17.1897	−0.872676
$389$	−3.18024	−0.161244	−0.0806222	−	0.996745i	$-0.525691\pi$
$389$	−3.18024	−0.161244	−0.0806222	+	0.996745i	$0.525691\pi$
$390$	2.81671	0.142630
$391$	5.04511	0.255142
$392$	20.4324	1.03199
$393$	−2.24527	−0.113259
$394$	−4.39248	−0.221290
$395$	−12.2433	−0.616027
$396$	20.2147	1.01583
$397$	−36.4160	−1.82767	−0.913833	−	0.406091i	$-0.866892\pi$
$397$	−36.4160	−1.82767	−0.913833	+	0.406091i	$0.866892\pi$
$398$	18.5336	0.929007
$399$	4.46641	0.223600
$400$	−4.87404	−0.243702
$401$	28.8255	1.43948	0.719739	−	0.694245i	$-0.244261\pi$
$401$	28.8255	1.43948	0.719739	+	0.694245i	$0.244261\pi$
$402$	−2.64715	−0.132028
$403$	−27.2980	−1.35981
$404$	−7.43080	−0.369696
$405$	7.72178	0.383698
$406$	60.1053	2.98298
$407$	−5.85115	−0.290031
$408$	0.249982	0.0123760
$409$	24.6560	1.21916	0.609581	−	0.792724i	$-0.291338\pi$
$409$	24.6560	1.21916	0.609581	+	0.792724i	$0.291338\pi$
$410$	14.8609	0.733927
$411$	−5.53837	−0.273188
$412$	19.2004	0.945936
$413$	−1.07229	−0.0527641
$414$	47.3871	2.32895
$415$	4.00734	0.196713
$416$	−26.5706	−1.30273
$417$	8.11311	0.397301
$418$	−22.8254	−1.11643
$419$	−4.40891	−0.215389	−0.107695	−	0.994184i	$-0.534347\pi$
$419$	−4.40891	−0.215389	−0.107695	+	0.994184i	$0.534347\pi$
$420$	−2.53712	−0.123799
$421$	32.9792	1.60731	0.803653	−	0.595098i	$-0.202887\pi$
$421$	32.9792	1.60731	0.803653	+	0.595098i	$0.202887\pi$
$422$	47.3792	2.30638
$423$	−32.3071	−1.57083
$424$	−4.98884	−0.242280
$425$	0.556876	0.0270124
$426$	6.24599	0.302619
$427$	35.3836	1.71233
$428$	12.4552	0.602044
$429$	8.03434	0.387901
$430$	−15.4796	−0.746494
$431$	−2.99726	−0.144373	−0.0721865	−	0.997391i	$-0.522998\pi$
$431$	−2.99726	−0.144373	−0.0721865	+	0.997391i	$0.522998\pi$
$432$	10.8432	0.521693
$433$	16.3586	0.786143	0.393071	−	0.919508i	$-0.371413\pi$
$433$	16.3586	0.786143	0.393071	+	0.919508i	$0.371413\pi$
$434$	60.8834	2.92250
$435$	2.52946	0.121278
$436$	−6.75023	−0.323277
$437$	−21.6094	−1.03372
$438$	0.293095	0.0140046
$439$	29.6061	1.41302	0.706511	−	0.707702i	$-0.250268\pi$
$439$	29.6061	1.41302	0.706511	+	0.707702i	$0.250268\pi$
$440$	−6.17316	−0.294294
$441$	−49.3817	−2.35151
$442$	4.12865	0.196380
$443$	−11.1974	−0.532003	−0.266001	−	0.963973i	$-0.585703\pi$
$443$	−11.1974	−0.532003	−0.266001	+	0.963973i	$0.585703\pi$
$444$	0.576496	0.0273593
$445$	−3.16765	−0.150161
$446$	−41.3911	−1.95993
$447$	2.64967	0.125325
$448$	11.2153	0.529871
$449$	4.13664	0.195220	0.0976101	−	0.995225i	$-0.468880\pi$
$449$	4.13664	0.195220	0.0976101	+	0.995225i	$0.468880\pi$
$450$	5.23055	0.246570
$451$	42.3890	1.99602
$452$	−15.3217	−0.720672
$453$	3.88124	0.182356
$454$	3.76612	0.176753
$455$	19.9501	0.935276
$456$	−1.07073	−0.0501416
$457$	15.9535	0.746272	0.373136	−	0.927777i	$-0.378283\pi$
$457$	15.9535	0.746272	0.373136	+	0.927777i	$0.378283\pi$
$458$	−25.8118	−1.20611
$459$	−1.23887	−0.0578256
$460$	12.2751	0.572328
$461$	−21.1920	−0.987011	−0.493506	−	0.869743i	$-0.664285\pi$
$461$	−21.1920	−0.987011	−0.493506	+	0.869743i	$0.664285\pi$
$462$	−17.9192	−0.833676
$463$	−21.5739	−1.00262	−0.501312	−	0.865267i	$-0.667149\pi$
$463$	−21.5739	−1.00262	−0.501312	+	0.865267i	$0.667149\pi$
$464$	−32.4507	−1.50649
$465$	2.56220	0.118819
$466$	−27.0420	−1.25270
$467$	35.5787	1.64639	0.823194	−	0.567760i	$-0.192190\pi$
$467$	35.5787	1.64639	0.823194	+	0.567760i	$0.192190\pi$
$468$	15.6613	0.723942
$469$	−18.7492	−0.865759
$470$	−20.7220	−0.955837
$471$	7.01700	0.323326
$472$	0.257061	0.0118322
$473$	−44.1539	−2.03020
$474$	8.51984	0.391329
$475$	−2.38523	−0.109442
$476$	−3.71883	−0.170452
$477$	12.0572	0.552063
$478$	10.5115	0.480787
$479$	15.7663	0.720381	0.360191	−	0.932879i	$-0.382712\pi$
$479$	15.7663	0.720381	0.360191	+	0.932879i	$0.382712\pi$
$480$	2.49393	0.113832
$481$	−4.53316	−0.206694
$482$	1.83164	0.0834290
$483$	−16.9645	−0.771912
$484$	22.0796	1.00362
$485$	−12.6870	−0.576085
$486$	−17.5979	−0.798256
$487$	−17.6572	−0.800124	−0.400062	−	0.916488i	$-0.631011\pi$
$487$	−17.6572	−0.800124	−0.400062	+	0.916488i	$0.631011\pi$
$488$	−8.48251	−0.383985
$489$	4.97644	0.225043
$490$	−31.6738	−1.43088
$491$	20.7092	0.934591	0.467296	−	0.884101i	$-0.345228\pi$
$491$	20.7092	0.934591	0.467296	+	0.884101i	$0.345228\pi$
$492$	−4.17646	−0.188289
$493$	3.70761	0.166982
$494$	−17.6839	−0.795638
$495$	14.9195	0.670584
$496$	−32.8708	−1.47594
$497$	44.2390	1.98439
$498$	−2.78862	−0.124961
$499$	4.10904	0.183946	0.0919730	−	0.995762i	$-0.470683\pi$
$499$	4.10904	0.183946	0.0919730	+	0.995762i	$0.470683\pi$
$500$	1.35491	0.0605936
$501$	1.19449	0.0533658
$502$	13.3019	0.593694
$503$	1.24611	0.0555613	0.0277806	−	0.999614i	$-0.491156\pi$
$503$	1.24611	0.0555613	0.0277806	+	0.999614i	$0.491156\pi$
$504$	16.6304	0.740776
$505$	−5.48433	−0.244050
$506$	86.6966	3.85413
$507$	1.28562	0.0570963
$508$	2.34798	0.104175
$509$	6.68184	0.296167	0.148084	−	0.988975i	$-0.452689\pi$
$509$	6.68184	0.296167	0.148084	+	0.988975i	$0.452689\pi$
$510$	−0.387517	−0.0171596
$511$	2.07593	0.0918337
$512$	−20.4769	−0.904959
$513$	5.30637	0.234282
$514$	−20.2779	−0.894420
$515$	14.1709	0.624447
$516$	4.35034	0.191513
$517$	−59.1073	−2.59953
$518$	10.1104	0.444227
$519$	−2.15329	−0.0945190
$520$	−4.78264	−0.209733
$521$	2.82269	0.123664	0.0618321	−	0.998087i	$-0.480306\pi$
$521$	2.82269	0.123664	0.0618321	+	0.998087i	$0.480306\pi$
$522$	34.8243	1.52422
$523$	26.2760	1.14897	0.574484	−	0.818516i	$-0.305203\pi$
$523$	26.2760	1.14897	0.574484	+	0.818516i	$0.305203\pi$
$524$	−8.00735	−0.349803
$525$	−1.87253	−0.0817239
$526$	1.41860	0.0618540
$527$	3.75560	0.163597
$528$	9.67453	0.421030
$529$	59.0777	2.56859
$530$	7.73360	0.335926
$531$	−0.621274	−0.0269610
$532$	15.9286	0.690593
$533$	32.8408	1.42249
$534$	2.20430	0.0953892
$535$	9.19260	0.397431
$536$	4.49475	0.194143
$537$	1.34629	0.0580967
$538$	−2.80567	−0.120961
$539$	−90.3459	−3.89147
$540$	−3.01425	−0.129713
$541$	21.9175	0.942309	0.471154	−	0.882051i	$-0.343837\pi$
$541$	21.9175	0.942309	0.471154	+	0.882051i	$0.343837\pi$
$542$	−26.8209	−1.15206
$543$	2.07309	0.0889648
$544$	3.65553	0.156730
$545$	−4.98204	−0.213407
$546$	−13.8828	−0.594131
$547$	−27.8971	−1.19279	−0.596397	−	0.802690i	$-0.703402\pi$
$547$	−27.8971	−1.19279	−0.596397	+	0.802690i	$0.703402\pi$
$548$	−19.7516	−0.843745
$549$	20.5009	0.874955
$550$	9.56951	0.408045
$551$	−15.8805	−0.676533
$552$	4.06690	0.173099
$553$	60.3442	2.56610
$554$	−44.0056	−1.86962
$555$	0.425485	0.0180608
$556$	28.9339	1.22707
$557$	40.9290	1.73422	0.867108	−	0.498120i	$-0.165976\pi$
$557$	40.9290	1.73422	0.867108	+	0.498120i	$0.165976\pi$
$558$	35.2751	1.49332
$559$	−34.2081	−1.44685
$560$	24.0229	1.01515
$561$	−1.10535	−0.0466679
$562$	−21.6520	−0.913335
$563$	−25.1932	−1.06177	−0.530883	−	0.847445i	$-0.678140\pi$
$563$	−25.1932	−1.06177	−0.530883	+	0.847445i	$0.678140\pi$
$564$	5.82365	0.245220
$565$	−11.3082	−0.475742
$566$	7.59681	0.319318
$567$	−38.0587	−1.59832
$568$	−10.6054	−0.444993
$569$	30.8647	1.29392	0.646959	−	0.762525i	$-0.276041\pi$
$569$	30.8647	1.29392	0.646959	+	0.762525i	$0.276041\pi$
$570$	1.65983	0.0695224
$571$	15.9778	0.668651	0.334325	−	0.942458i	$-0.391492\pi$
$571$	15.9778	0.668651	0.334325	+	0.942458i	$0.391492\pi$
$572$	28.6529	1.19804
$573$	0.772738	0.0322816
$574$	−73.2456	−3.05721
$575$	9.05967	0.377814
$576$	6.49799	0.270750
$577$	−2.08113	−0.0866384	−0.0433192	−	0.999061i	$-0.513793\pi$
$577$	−2.08113	−0.0866384	−0.0433192	+	0.999061i	$0.513793\pi$
$578$	30.5699	1.27154
$579$	−10.0643	−0.418257
$580$	9.02084	0.374570
$581$	−19.7512	−0.819417
$582$	8.82856	0.365956
$583$	22.0592	0.913599
$584$	−0.497662	−0.0205934
$585$	11.5589	0.477901
$586$	−36.8512	−1.52231
$587$	9.51608	0.392771	0.196385	−	0.980527i	$-0.437080\pi$
$587$	9.51608	0.392771	0.196385	+	0.980527i	$0.437080\pi$
$588$	8.90150	0.367092
$589$	−16.0861	−0.662816
$590$	−0.398490	−0.0164056
$591$	0.911090	0.0374772
$592$	−5.45860	−0.224347
$593$	39.7431	1.63205	0.816026	−	0.578015i	$-0.196173\pi$
$593$	39.7431	1.63205	0.816026	+	0.578015i	$0.196173\pi$
$594$	−21.2891	−0.873503
$595$	−2.74470	−0.112522
$596$	9.44956	0.387069
$597$	−3.84425	−0.157335
$598$	67.1679	2.74670
$599$	−36.9508	−1.50977	−0.754884	−	0.655859i	$-0.772307\pi$
$599$	−36.9508	−1.50977	−0.754884	+	0.655859i	$0.772307\pi$
$600$	0.448901	0.0183263
$601$	−4.83311	−0.197147	−0.0985733	−	0.995130i	$-0.531428\pi$
$601$	−4.83311	−0.197147	−0.0985733	+	0.995130i	$0.531428\pi$
$602$	76.2952	3.10956
$603$	−10.8631	−0.442379
$604$	13.8417	0.563211
$605$	16.2959	0.662524
$606$	3.81642	0.155032
$607$	−46.4410	−1.88498	−0.942491	−	0.334233i	$-0.891523\pi$
$607$	−46.4410	−1.88498	−0.942491	+	0.334233i	$0.891523\pi$
$608$	−15.6575	−0.634994
$609$	−12.4671	−0.505191
$610$	13.1494	0.532404
$611$	−45.7932	−1.85259
$612$	−2.15465	−0.0870965
$613$	−10.7941	−0.435971	−0.217985	−	0.975952i	$-0.569949\pi$
$613$	−10.7941	−0.435971	−0.217985	+	0.975952i	$0.569949\pi$
$614$	39.8501	1.60822
$615$	−3.08245	−0.124297
$616$	30.4260	1.22590
$617$	−31.7648	−1.27880	−0.639401	−	0.768874i	$-0.720818\pi$
$617$	−31.7648	−1.27880	−0.639401	+	0.768874i	$0.720818\pi$
$618$	−9.86124	−0.396677
$619$	3.51748	0.141380	0.0706898	−	0.997498i	$-0.477480\pi$
$619$	3.51748	0.141380	0.0706898	+	0.997498i	$0.477480\pi$
$620$	9.13762	0.366975
$621$	−20.1549	−0.808788
$622$	10.9544	0.439230
$623$	15.6126	0.625504
$624$	7.49531	0.300053
$625$	1.00000	0.0400000
$626$	−57.5989	−2.30212
$627$	4.73446	0.189076
$628$	25.0248	0.998598
$629$	0.623664	0.0248671
$630$	−25.7801	−1.02710
$631$	−13.5654	−0.540030	−0.270015	−	0.962856i	$-0.587029\pi$
$631$	−13.5654	−0.540030	−0.270015	+	0.962856i	$0.587029\pi$
$632$	−14.4663	−0.575438
$633$	−9.82741	−0.390604
$634$	46.5856	1.85015
$635$	1.73294	0.0687696
$636$	−2.17343	−0.0861819
$637$	−69.9952	−2.77331
$638$	63.7126	2.52240
$639$	25.6316	1.01397
$640$	−8.96085	−0.354209
$641$	21.7899	0.860648	0.430324	−	0.902674i	$-0.358399\pi$
$641$	21.7899	0.860648	0.430324	+	0.902674i	$0.358399\pi$
$642$	−6.39693	−0.252467
$643$	−0.860307	−0.0339272	−0.0169636	−	0.999856i	$-0.505400\pi$
$643$	−0.860307	−0.0339272	−0.0169636	+	0.999856i	$0.505400\pi$
$644$	−60.5008	−2.38406
$645$	3.21079	0.126425
$646$	2.43292	0.0957221
$647$	−5.40617	−0.212539	−0.106269	−	0.994337i	$-0.533891\pi$
$647$	−5.40617	−0.212539	−0.106269	+	0.994337i	$0.533891\pi$
$648$	9.12381	0.358417
$649$	−1.13665	−0.0446173
$650$	7.41395	0.290799
$651$	−12.6285	−0.494948
$652$	17.7476	0.695048
$653$	47.5956	1.86256	0.931280	−	0.364304i	$-0.118693\pi$
$653$	47.5956	1.86256	0.931280	+	0.364304i	$0.118693\pi$
$654$	3.46689	0.135566
$655$	−5.90986	−0.230917
$656$	39.5451	1.54398
$657$	1.20277	0.0469245
$658$	102.134	3.98159
$659$	−5.06785	−0.197415	−0.0987077	−	0.995116i	$-0.531471\pi$
$659$	−5.06785	−0.197415	−0.0987077	+	0.995116i	$0.531471\pi$
$660$	−2.68938	−0.104684
$661$	−6.99024	−0.271889	−0.135944	−	0.990716i	$-0.543407\pi$
$661$	−6.99024	−0.271889	−0.135944	+	0.990716i	$0.543407\pi$
$662$	−47.5021	−1.84622
$663$	−0.856366	−0.0332585
$664$	4.73494	0.183751
$665$	11.7562	0.455885
$666$	5.85787	0.226988
$667$	60.3181	2.33553
$668$	4.25992	0.164821
$669$	8.58536	0.331929
$670$	−6.96766	−0.269184
$671$	37.5072	1.44795
$672$	−12.2920	−0.474172
$673$	−4.09280	−0.157766	−0.0788829	−	0.996884i	$-0.525135\pi$
$673$	−4.09280	−0.157766	−0.0788829	+	0.996884i	$0.525135\pi$
$674$	−35.3789	−1.36275
$675$	−2.22468	−0.0856281
$676$	4.58492	0.176343
$677$	−10.3383	−0.397332	−0.198666	−	0.980067i	$-0.563661\pi$
$677$	−10.3383	−0.397332	−0.198666	+	0.980067i	$0.563661\pi$
$678$	7.86915	0.302213
$679$	62.5308	2.39971
$680$	0.657987	0.0252326
$681$	−0.781170	−0.0299345
$682$	64.5373	2.47126
$683$	14.6166	0.559290	0.279645	−	0.960104i	$-0.409783\pi$
$683$	14.6166	0.559290	0.279645	+	0.960104i	$0.409783\pi$
$684$	9.22885	0.352874
$685$	−14.5777	−0.556986
$686$	92.9183	3.54764
$687$	5.35389	0.204264
$688$	−41.1916	−1.57041
$689$	17.0903	0.651089
$690$	−6.30442	−0.240005
$691$	10.6918	0.406736	0.203368	−	0.979102i	$-0.434811\pi$
$691$	10.6918	0.406736	0.203368	+	0.979102i	$0.434811\pi$
$692$	−7.67931	−0.291924
$693$	−73.5347	−2.79335
$694$	−38.4813	−1.46073
$695$	21.3548	0.810033
$696$	2.98873	0.113287
$697$	−4.51817	−0.171138
$698$	34.3166	1.29890
$699$	5.60907	0.212155
$700$	−6.67803	−0.252406
$701$	13.0633	0.493395	0.246697	−	0.969093i	$-0.420655\pi$
$701$	13.0633	0.493395	0.246697	+	0.969093i	$0.420655\pi$
$702$	−16.4937	−0.622514
$703$	−2.67130	−0.100750
$704$	11.8883	0.448059
$705$	4.29817	0.161879
$706$	11.3285	0.426353
$707$	27.0309	1.01660
$708$	0.111990	0.00420885
$709$	37.9921	1.42682	0.713412	−	0.700745i	$-0.247149\pi$
$709$	37.9921	1.42682	0.713412	+	0.700745i	$0.247149\pi$
$710$	16.4403	0.616993
$711$	34.9627	1.31120
$712$	−3.74279	−0.140267
$713$	61.0990	2.28817
$714$	1.90998	0.0714791
$715$	21.1474	0.790869
$716$	4.80129	0.179433
$717$	−2.18031	−0.0814252
$718$	−16.7417	−0.624793
$719$	−18.8710	−0.703770	−0.351885	−	0.936043i	$-0.614459\pi$
$719$	−18.8710	−0.703770	−0.351885	+	0.936043i	$0.614459\pi$
$720$	13.9186	0.518715
$721$	−69.8451	−2.60117
$722$	24.3804	0.907346
$723$	−0.379920	−0.0141294
$724$	7.39329	0.274769
$725$	6.65787	0.247267
$726$	−11.3400	−0.420866
$727$	−35.5318	−1.31780	−0.658900	−	0.752230i	$-0.728978\pi$
$727$	−35.5318	−1.31780	−0.658900	+	0.752230i	$0.728978\pi$
$728$	23.5724	0.873653
$729$	−19.5152	−0.722785
$730$	0.771466	0.0285532
$731$	4.70628	0.174068
$732$	−3.69546	−0.136588
$733$	−29.5982	−1.09323	−0.546616	−	0.837383i	$-0.684084\pi$
$733$	−29.5982	−1.09323	−0.546616	+	0.837383i	$0.684084\pi$
$734$	−54.5895	−2.01493
$735$	6.56979	0.242331
$736$	59.4709	2.19213
$737$	−19.8745	−0.732085
$738$	−42.4377	−1.56215
$739$	17.8029	0.654892	0.327446	−	0.944870i	$-0.393812\pi$
$739$	17.8029	0.654892	0.327446	+	0.944870i	$0.393812\pi$
$740$	1.51741	0.0557812
$741$	3.66801	0.134748
$742$	−38.1170	−1.39932
$743$	−29.3667	−1.07736	−0.538680	−	0.842510i	$-0.681077\pi$
$743$	−29.3667	−1.07736	−0.538680	+	0.842510i	$0.681077\pi$
$744$	3.02742	0.110991
$745$	6.97429	0.255518
$746$	−24.3981	−0.893279
$747$	−11.4436	−0.418700
$748$	−3.94202	−0.144135
$749$	−45.3080	−1.65552
$750$	−0.695877	−0.0254099
$751$	−22.1126	−0.806901	−0.403451	−	0.915001i	$-0.632189\pi$
$751$	−22.1126	−0.806901	−0.403451	+	0.915001i	$0.632189\pi$
$752$	−55.1418	−2.01081
$753$	−2.75909	−0.100547
$754$	49.3611	1.79763
$755$	10.2159	0.371796
$756$	14.8565	0.540325
$757$	−3.31457	−0.120470	−0.0602350	−	0.998184i	$-0.519185\pi$
$757$	−3.31457	−0.120470	−0.0602350	+	0.998184i	$0.519185\pi$
$758$	−47.4113	−1.72206
$759$	−17.9826	−0.652729
$760$	−2.81831	−0.102231
$761$	−42.8678	−1.55396	−0.776978	−	0.629528i	$-0.783248\pi$
$761$	−42.8678	−1.55396	−0.776978	+	0.629528i	$0.783248\pi$
$762$	−1.20591	−0.0436857
$763$	24.5552	0.888959
$764$	2.75582	0.0997022
$765$	−1.59025	−0.0574956
$766$	6.98893	0.252520
$767$	−0.880614	−0.0317971
$768$	7.96465	0.287400
$769$	28.5499	1.02954	0.514768	−	0.857329i	$-0.327878\pi$
$769$	28.5499	1.02954	0.514768	+	0.857329i	$0.327878\pi$
$770$	−47.1657	−1.69973
$771$	4.20605	0.151477
$772$	−35.8923	−1.29179
$773$	−18.7081	−0.672884	−0.336442	−	0.941704i	$-0.609224\pi$
$773$	−18.7081	−0.672884	−0.336442	+	0.941704i	$0.609224\pi$
$774$	44.2045	1.58890
$775$	6.74406	0.242254
$776$	−14.9905	−0.538128
$777$	−2.09711	−0.0752334
$778$	5.82506	0.208838
$779$	19.3524	0.693370
$780$	−2.08359	−0.0746045
$781$	46.8940	1.67800
$782$	−9.24084	−0.330452
$783$	−14.8117	−0.529325
$784$	−84.2846	−3.01017
$785$	18.4697	0.659211
$786$	4.11254	0.146689
$787$	27.9867	0.997617	0.498809	−	0.866712i	$-0.333771\pi$
$787$	27.9867	0.997617	0.498809	+	0.866712i	$0.333771\pi$
$788$	3.24923	0.115749
$789$	−0.294247	−0.0104755
$790$	22.4253	0.797858
$791$	55.7355	1.98173
$792$	17.6285	0.626400
$793$	29.0586	1.03190
$794$	66.7010	2.36713
$795$	−1.60411	−0.0568918
$796$	−13.7098	−0.485931
$797$	−23.6404	−0.837386	−0.418693	−	0.908128i	$-0.637512\pi$
$797$	−23.6404	−0.837386	−0.418693	+	0.908128i	$0.637512\pi$
$798$	−8.18086	−0.289599
$799$	6.30014	0.222883
$800$	6.56436	0.232085
$801$	9.04573	0.319615
$802$	−52.7981	−1.86436
$803$	2.20052	0.0776546
$804$	1.95817	0.0690593
$805$	−44.6529	−1.57381
$806$	50.0001	1.76118
$807$	0.581952	0.0204857
$808$	−6.48011	−0.227970
$809$	−34.5712	−1.21546	−0.607730	−	0.794144i	$-0.707920\pi$
$809$	−34.5712	−1.21546	−0.607730	+	0.794144i	$0.707920\pi$
$810$	−14.1435	−0.496953
$811$	−29.9435	−1.05146	−0.525729	−	0.850652i	$-0.676207\pi$
$811$	−29.9435	−1.05146	−0.525729	+	0.850652i	$0.676207\pi$
$812$	−44.4615	−1.56029
$813$	5.56320	0.195110
$814$	10.7172	0.375638
$815$	13.0987	0.458826
$816$	−1.03119	−0.0360989
$817$	−20.1581	−0.705242
$818$	−45.1610	−1.57902
$819$	−56.9708	−1.99072
$820$	−10.9930	−0.383892
$821$	−42.5819	−1.48612	−0.743059	−	0.669226i	$-0.766626\pi$
$821$	−42.5819	−1.48612	−0.743059	+	0.669226i	$0.766626\pi$
$822$	10.1443	0.353824
$823$	32.0728	1.11799	0.558993	−	0.829172i	$-0.311188\pi$
$823$	32.0728	1.11799	0.558993	+	0.829172i	$0.311188\pi$
$824$	16.7439	0.583303
$825$	−1.98491	−0.0691057
$826$	1.96406	0.0683383
$827$	−2.00554	−0.0697396	−0.0348698	−	0.999392i	$-0.511102\pi$
$827$	−2.00554	−0.0697396	−0.0348698	+	0.999392i	$0.511102\pi$
$828$	−35.0534	−1.21819
$829$	−2.34233	−0.0813525	−0.0406763	−	0.999172i	$-0.512951\pi$
$829$	−2.34233	−0.0813525	−0.0406763	+	0.999172i	$0.512951\pi$
$830$	−7.34001	−0.254776
$831$	9.12766	0.316635
$832$	9.21046	0.319315
$833$	9.62982	0.333653
$834$	−14.8603	−0.514571
$835$	3.14405	0.108804
$836$	16.8846	0.583965
$837$	−15.0034	−0.518593
$838$	8.07555	0.278965
$839$	20.1394	0.695289	0.347644	−	0.937626i	$-0.386982\pi$
$839$	20.1394	0.695289	0.347644	+	0.937626i	$0.386982\pi$
$840$	−2.21252	−0.0763393
$841$	15.3273	0.528527
$842$	−60.4060	−2.08173
$843$	4.49107	0.154681
$844$	−35.0476	−1.20639
$845$	3.38392	0.116410
$846$	59.1751	2.03448
$847$	−80.3186	−2.75978
$848$	20.5793	0.706695
$849$	−1.57573	−0.0540790
$850$	−1.02000	−0.0349856
$851$	10.1462	0.347808
$852$	−4.62032	−0.158290
$853$	−15.3073	−0.524111	−0.262055	−	0.965053i	$-0.584400\pi$
$853$	−15.3073	−0.524111	−0.262055	+	0.965053i	$0.584400\pi$
$854$	−64.8101	−2.21776
$855$	6.81140	0.232945
$856$	10.8617	0.371245
$857$	−23.0179	−0.786275	−0.393138	−	0.919480i	$-0.628610\pi$
$857$	−23.0179	−0.786275	−0.393138	+	0.919480i	$0.628610\pi$
$858$	−14.7160	−0.502397
$859$	12.3970	0.422980	0.211490	−	0.977380i	$-0.432168\pi$
$859$	12.3970	0.422980	0.211490	+	0.977380i	$0.432168\pi$
$860$	11.4507	0.390465
$861$	15.1926	0.517764
$862$	5.48991	0.186987
$863$	2.62714	0.0894290	0.0447145	−	0.999000i	$-0.485762\pi$
$863$	2.62714	0.0894290	0.0447145	+	0.999000i	$0.485762\pi$
$864$	−14.6036	−0.496825
$865$	−5.66775	−0.192709
$866$	−29.9630	−1.01819
$867$	−6.34082	−0.215346
$868$	−45.0370	−1.52866
$869$	63.9657	2.16989
$870$	−4.63306	−0.157076
$871$	−15.3977	−0.521731
$872$	−5.88662	−0.199346
$873$	36.2296	1.22619
$874$	39.5806	1.33883
$875$	−4.92875	−0.166622
$876$	−0.216810	−0.00732534
$877$	34.3063	1.15844	0.579221	−	0.815171i	$-0.303357\pi$
$877$	34.3063	1.15844	0.579221	+	0.815171i	$0.303357\pi$
$878$	−54.2277	−1.83010
$879$	7.64370	0.257816
$880$	25.4647	0.858413
$881$	−15.5213	−0.522926	−0.261463	−	0.965213i	$-0.584205\pi$
$881$	−15.5213	−0.522926	−0.261463	+	0.965213i	$0.584205\pi$
$882$	90.4497	3.04560
$883$	0.854482	0.0287556	0.0143778	−	0.999897i	$-0.495423\pi$
$883$	0.854482	0.0287556	0.0143778	+	0.999897i	$0.495423\pi$
$884$	−3.05407	−0.102719
$885$	0.0826550	0.00277842
$886$	20.5096	0.689032
$887$	1.98559	0.0666697	0.0333348	−	0.999444i	$-0.489387\pi$
$887$	1.98559	0.0666697	0.0333348	+	0.999444i	$0.489387\pi$
$888$	0.502740	0.0168708
$889$	−8.54123	−0.286464
$890$	5.80200	0.194483
$891$	−40.3428	−1.35154
$892$	30.6181	1.02517
$893$	−26.9849	−0.903017
$894$	−4.85325	−0.162317
$895$	3.54362	0.118450
$896$	44.1658	1.47548
$897$	−13.9320	−0.465176
$898$	−7.57685	−0.252843
$899$	44.9011	1.49754
$900$	−3.86917	−0.128972
$901$	−2.35125	−0.0783316
$902$	−77.6415	−2.58518
$903$	−15.8252	−0.526629
$904$	−13.3615	−0.444396
$905$	5.45665	0.181385
$906$	−7.10904	−0.236182
$907$	−10.3684	−0.344277	−0.172139	−	0.985073i	$-0.555068\pi$
$907$	−10.3684	−0.344277	−0.172139	+	0.985073i	$0.555068\pi$
$908$	−2.78590	−0.0924532
$909$	15.6614	0.519456
$910$	−36.5415	−1.21134
$911$	−39.9365	−1.32315	−0.661577	−	0.749877i	$-0.730113\pi$
$911$	−39.9365	−1.32315	−0.661577	+	0.749877i	$0.730113\pi$
$912$	4.41683	0.146256
$913$	−20.9365	−0.692899
$914$	−29.2210	−0.966546
$915$	−2.72745	−0.0901669
$916$	19.0937	0.630872
$917$	29.1282	0.961899
$918$	2.26917	0.0748938
$919$	−27.9228	−0.921087	−0.460544	−	0.887637i	$-0.652345\pi$
$919$	−27.9228	−0.921087	−0.460544	+	0.887637i	$0.652345\pi$
$920$	10.7046	0.352921
$921$	−8.26572	−0.272365
$922$	38.8162	1.27834
$923$	36.3310	1.19585
$924$	13.2553	0.436067
$925$	1.11993	0.0368232
$926$	39.5156	1.29856
$927$	−40.4674	−1.32912
$928$	43.7046	1.43468
$929$	−17.5331	−0.575241	−0.287620	−	0.957744i	$-0.592864\pi$
$929$	−17.5331	−0.575241	−0.287620	+	0.957744i	$0.592864\pi$
$930$	−4.69304	−0.153891
$931$	−41.2467	−1.35181
$932$	20.0037	0.655243
$933$	−2.27216	−0.0743871
$934$	−65.1675	−2.13235
$935$	−2.90943	−0.0951484
$936$	13.6576	0.446412
$937$	−9.46361	−0.309163	−0.154581	−	0.987980i	$-0.549403\pi$
$937$	−9.46361	−0.309163	−0.154581	+	0.987980i	$0.549403\pi$
$938$	34.3419	1.12130
$939$	11.9472	0.389882
$940$	15.3286	0.499965
$941$	−12.0417	−0.392549	−0.196275	−	0.980549i	$-0.562884\pi$
$941$	−12.0417	−0.392549	−0.196275	+	0.980549i	$0.562884\pi$
$942$	−12.8526	−0.418761
$943$	−73.5050	−2.39365
$944$	−1.06039	−0.0345128
$945$	10.9649	0.356688
$946$	80.8741	2.62944
$947$	−56.4293	−1.83370	−0.916852	−	0.399227i	$-0.869279\pi$
$947$	−56.4293	−1.83370	−0.916852	+	0.399227i	$0.869279\pi$
$948$	−6.30234	−0.204691
$949$	1.70484	0.0553416
$950$	4.36888	0.141745
$951$	−9.66280	−0.313338
$952$	−3.24305	−0.105108
$953$	6.18561	0.200371	0.100186	−	0.994969i	$-0.468056\pi$
$953$	6.18561	0.200371	0.100186	+	0.994969i	$0.468056\pi$
$954$	−22.0845	−0.715014
$955$	2.03395	0.0658170
$956$	−7.77566	−0.251483
$957$	−13.2153	−0.427190
$958$	−28.8782	−0.933013
$959$	71.8500	2.32016
$960$	−0.864499	−0.0279016
$961$	14.4823	0.467172
$962$	8.30313	0.267704
$963$	−26.2510	−0.845925
$964$	−1.35491	−0.0436388
$965$	−26.4905	−0.852759
$966$	31.0729	0.999755
$967$	−46.5948	−1.49839	−0.749194	−	0.662351i	$-0.769559\pi$
$967$	−46.5948	−1.49839	−0.749194	+	0.662351i	$0.769559\pi$
$968$	19.2547	0.618871
$969$	−0.504638	−0.0162113
$970$	23.2380	0.746126
$971$	16.1047	0.516824	0.258412	−	0.966035i	$-0.416801\pi$
$971$	16.1047	0.516824	0.258412	+	0.966035i	$0.416801\pi$
$972$	13.0176	0.417540
$973$	−105.252	−3.37424
$974$	32.3417	1.03629
$975$	−1.53780	−0.0492491
$976$	34.9908	1.12003
$977$	18.7044	0.598405	0.299203	−	0.954190i	$-0.403279\pi$
$977$	18.7044	0.598405	0.299203	+	0.954190i	$0.403279\pi$
$978$	−9.11507	−0.291468
$979$	16.5495	0.528926
$980$	23.4299	0.748442
$981$	14.2270	0.454234
$982$	−37.9318	−1.21045
$983$	33.5568	1.07030	0.535148	−	0.844758i	$-0.320256\pi$
$983$	33.5568	1.07030	0.535148	+	0.844758i	$0.320256\pi$
$984$	−3.64213	−0.116107
$985$	2.39811	0.0764102
$986$	−6.79101	−0.216270
$987$	−21.1846	−0.674314
$988$	13.0813	0.416171
$989$	76.5653	2.43464
$990$	−27.3273	−0.868518
$991$	−62.1083	−1.97293	−0.986467	−	0.163961i	$-0.947573\pi$
$991$	−62.1083	−1.97293	−0.986467	+	0.163961i	$0.947573\pi$
$992$	44.2704	1.40559
$993$	9.85292	0.312673
$994$	−81.0301	−2.57012
$995$	−10.1186	−0.320781
$996$	2.06281	0.0653627
$997$	−21.4030	−0.677840	−0.338920	−	0.940815i	$-0.610062\pi$
$997$	−21.4030	−0.677840	−0.338920	+	0.940815i	$0.610062\pi$
$998$	−7.52629	−0.238241
$999$	−2.49150	−0.0788275

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1205.2.a.e.1.5	✓	25
5.4	even	2		6025.2.a.j.1.21		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.e.1.5	✓	25	1.1	even	1	trivial
6025.2.a.j.1.21		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)

\(f(q)\)	\(=\)	\(q-1.83164 q^{2} +0.379920 q^{3} +1.35491 q^{4} +1.00000 q^{5} -0.695877 q^{6} -4.92875 q^{7} +1.18157 q^{8} -2.85566 q^{9} +O(q^{10})\)	\(q-1.83164 q^{2} +0.379920 q^{3} +1.35491 q^{4} +1.00000 q^{5} -0.695877 q^{6} -4.92875 q^{7} +1.18157 q^{8} -2.85566 q^{9} -1.83164 q^{10} -5.22455 q^{11} +0.514759 q^{12} -4.04771 q^{13} +9.02771 q^{14} +0.379920 q^{15} -4.87404 q^{16} +0.556876 q^{17} +5.23055 q^{18} -2.38523 q^{19} +1.35491 q^{20} -1.87253 q^{21} +9.56951 q^{22} +9.05967 q^{23} +0.448901 q^{24} +1.00000 q^{25} +7.41395 q^{26} -2.22468 q^{27} -6.67803 q^{28} +6.65787 q^{29} -0.695877 q^{30} +6.74406 q^{31} +6.56436 q^{32} -1.98491 q^{33} -1.02000 q^{34} -4.92875 q^{35} -3.86917 q^{36} +1.11993 q^{37} +4.36888 q^{38} -1.53780 q^{39} +1.18157 q^{40} -8.11343 q^{41} +3.42981 q^{42} +8.45122 q^{43} -7.07881 q^{44} -2.85566 q^{45} -16.5941 q^{46} +11.3134 q^{47} -1.85174 q^{48} +17.2926 q^{49} -1.83164 q^{50} +0.211568 q^{51} -5.48429 q^{52} -4.22222 q^{53} +4.07482 q^{54} -5.22455 q^{55} -5.82365 q^{56} -0.906195 q^{57} -12.1948 q^{58} +0.217559 q^{59} +0.514759 q^{60} -7.17902 q^{61} -12.3527 q^{62} +14.0748 q^{63} -2.27548 q^{64} -4.04771 q^{65} +3.63565 q^{66} +3.80405 q^{67} +0.754518 q^{68} +3.44195 q^{69} +9.02771 q^{70} -8.97571 q^{71} -3.37416 q^{72} -0.421188 q^{73} -2.05132 q^{74} +0.379920 q^{75} -3.23177 q^{76} +25.7505 q^{77} +2.81671 q^{78} -12.2433 q^{79} -4.87404 q^{80} +7.72178 q^{81} +14.8609 q^{82} +4.00734 q^{83} -2.53712 q^{84} +0.556876 q^{85} -15.4796 q^{86} +2.52946 q^{87} -6.17316 q^{88} -3.16765 q^{89} +5.23055 q^{90} +19.9501 q^{91} +12.2751 q^{92} +2.56220 q^{93} -20.7220 q^{94} -2.38523 q^{95} +2.49393 q^{96} -12.6870 q^{97} -31.6738 q^{98} +14.9195 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 6 q^{2} + 15 q^{3} + 32 q^{4} + 25 q^{5} - q^{6} + 19 q^{7} + 15 q^{8} + 32 q^{9}+O(q^{10}) \) 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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