LMFDB - Embedded newform 8049.2.a.a.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8049,2,Mod(1,8049)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8049, 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("8049.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8049 = 3 \cdot 2683 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8049.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:	$64.2715885869$
Analytic rank:	$1$
Dimension:	$95$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	8049.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.50719 q^{2} +1.00000 q^{3} +4.28600 q^{4} -3.32561 q^{5} -2.50719 q^{6} -4.48246 q^{7} -5.73145 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.50719 q^{2} +1.00000 q^{3} +4.28600 q^{4} -3.32561 q^{5} -2.50719 q^{6} -4.48246 q^{7} -5.73145 q^{8} +1.00000 q^{9} +8.33794 q^{10} -5.03676 q^{11} +4.28600 q^{12} -5.28870 q^{13} +11.2384 q^{14} -3.32561 q^{15} +5.79782 q^{16} +1.22231 q^{17} -2.50719 q^{18} -3.35429 q^{19} -14.2536 q^{20} -4.48246 q^{21} +12.6281 q^{22} +3.08422 q^{23} -5.73145 q^{24} +6.05970 q^{25} +13.2598 q^{26} +1.00000 q^{27} -19.2118 q^{28} +4.49131 q^{29} +8.33794 q^{30} -3.42705 q^{31} -3.07334 q^{32} -5.03676 q^{33} -3.06455 q^{34} +14.9069 q^{35} +4.28600 q^{36} -5.10511 q^{37} +8.40985 q^{38} -5.28870 q^{39} +19.0606 q^{40} +5.90734 q^{41} +11.2384 q^{42} +3.13061 q^{43} -21.5876 q^{44} -3.32561 q^{45} -7.73272 q^{46} +9.42102 q^{47} +5.79782 q^{48} +13.0924 q^{49} -15.1928 q^{50} +1.22231 q^{51} -22.6674 q^{52} +7.88706 q^{53} -2.50719 q^{54} +16.7503 q^{55} +25.6910 q^{56} -3.35429 q^{57} -11.2606 q^{58} -0.0840582 q^{59} -14.2536 q^{60} +4.25142 q^{61} +8.59227 q^{62} -4.48246 q^{63} -3.89018 q^{64} +17.5882 q^{65} +12.6281 q^{66} +3.18113 q^{67} +5.23881 q^{68} +3.08422 q^{69} -37.3745 q^{70} -16.8171 q^{71} -5.73145 q^{72} +2.32298 q^{73} +12.7995 q^{74} +6.05970 q^{75} -14.3765 q^{76} +22.5770 q^{77} +13.2598 q^{78} -3.00405 q^{79} -19.2813 q^{80} +1.00000 q^{81} -14.8108 q^{82} +17.5584 q^{83} -19.2118 q^{84} -4.06492 q^{85} -7.84903 q^{86} +4.49131 q^{87} +28.8679 q^{88} +0.778879 q^{89} +8.33794 q^{90} +23.7064 q^{91} +13.2190 q^{92} -3.42705 q^{93} -23.6203 q^{94} +11.1551 q^{95} -3.07334 q^{96} -5.10710 q^{97} -32.8252 q^{98} -5.03676 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 95 q - 9 q^{2} + 95 q^{3} + 65 q^{4} - 15 q^{5} - 9 q^{6} - 36 q^{7} - 27 q^{8} + 95 q^{9}+O(q^{10}) $ 95 * q - 9 * q^2 + 95 * q^3 + 65 * q^4 - 15 * q^5 - 9 * q^6 - 36 * q^7 - 27 * q^8 + 95 * q^9	\( 95 q - 9 q^{2} + 95 q^{3} + 65 q^{4} - 15 q^{5} - 9 q^{6} - 36 q^{7} - 27 q^{8} + 95 q^{9} - 36 q^{10} - 48 q^{11} + 65 q^{12} - 73 q^{13} - 17 q^{14} - 15 q^{15} + 13 q^{16} - 9 q^{17} - 9 q^{18} - 66 q^{19} - 35 q^{20} - 36 q^{21} - 37 q^{22} - 58 q^{23} - 27 q^{24} + 24 q^{25} - 25 q^{26} + 95 q^{27} - 75 q^{28} - 31 q^{29} - 36 q^{30} - 129 q^{31} - 53 q^{32} - 48 q^{33} - 61 q^{34} - 38 q^{35} + 65 q^{36} - 127 q^{37} + q^{38} - 73 q^{39} - 74 q^{40} - 31 q^{41} - 17 q^{42} - 62 q^{43} - 76 q^{44} - 15 q^{45} - 60 q^{46} - 75 q^{47} + 13 q^{48} + 5 q^{49} - 30 q^{50} - 9 q^{51} - 137 q^{52} - 28 q^{53} - 9 q^{54} - 117 q^{55} - 23 q^{56} - 66 q^{57} - 90 q^{58} - 60 q^{59} - 35 q^{60} - 96 q^{61} + 10 q^{62} - 36 q^{63} - 75 q^{64} - 28 q^{65} - 37 q^{66} - 116 q^{67} + 3 q^{68} - 58 q^{69} - 73 q^{70} - 144 q^{71} - 27 q^{72} - 121 q^{73} - 16 q^{74} + 24 q^{75} - 118 q^{76} - 3 q^{77} - 25 q^{78} - 135 q^{79} - 36 q^{80} + 95 q^{81} - 102 q^{82} - 21 q^{83} - 75 q^{84} - 129 q^{85} - 46 q^{86} - 31 q^{87} - 77 q^{88} - 63 q^{89} - 36 q^{90} - 123 q^{91} - 42 q^{92} - 129 q^{93} - 44 q^{94} - 80 q^{95} - 53 q^{96} - 144 q^{97} + 10 q^{98} - 48 q^{99}+O(q^{100}) \) 95 * q - 9 * q^2 + 95 * q^3 + 65 * q^4 - 15 * q^5 - 9 * q^6 - 36 * q^7 - 27 * q^8 + 95 * q^9 - 36 * q^10 - 48 * q^11 + 65 * q^12 - 73 * q^13 - 17 * q^14 - 15 * q^15 + 13 * q^16 - 9 * q^17 - 9 * q^18 - 66 * q^19 - 35 * q^20 - 36 * q^21 - 37 * q^22 - 58 * q^23 - 27 * q^24 + 24 * q^25 - 25 * q^26 + 95 * q^27 - 75 * q^28 - 31 * q^29 - 36 * q^30 - 129 * q^31 - 53 * q^32 - 48 * q^33 - 61 * q^34 - 38 * q^35 + 65 * q^36 - 127 * q^37 + q^38 - 73 * q^39 - 74 * q^40 - 31 * q^41 - 17 * q^42 - 62 * q^43 - 76 * q^44 - 15 * q^45 - 60 * q^46 - 75 * q^47 + 13 * q^48 + 5 * q^49 - 30 * q^50 - 9 * q^51 - 137 * q^52 - 28 * q^53 - 9 * q^54 - 117 * q^55 - 23 * q^56 - 66 * q^57 - 90 * q^58 - 60 * q^59 - 35 * q^60 - 96 * q^61 + 10 * q^62 - 36 * q^63 - 75 * q^64 - 28 * q^65 - 37 * q^66 - 116 * q^67 + 3 * q^68 - 58 * q^69 - 73 * q^70 - 144 * q^71 - 27 * q^72 - 121 * q^73 - 16 * q^74 + 24 * q^75 - 118 * q^76 - 3 * q^77 - 25 * q^78 - 135 * q^79 - 36 * q^80 + 95 * q^81 - 102 * q^82 - 21 * q^83 - 75 * q^84 - 129 * q^85 - 46 * q^86 - 31 * q^87 - 77 * q^88 - 63 * q^89 - 36 * q^90 - 123 * q^91 - 42 * q^92 - 129 * q^93 - 44 * q^94 - 80 * q^95 - 53 * q^96 - 144 * q^97 + 10 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.50719	−1.77285	−0.886426	−	0.462871i	$-0.846819\pi$
$2$	−2.50719	−1.77285	−0.886426	+	0.462871i	$0.846819\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.28600	2.14300
$5$	−3.32561	−1.48726	−0.743630	−	0.668592i	$-0.766897\pi$
$5$	−3.32561	−1.48726	−0.743630	+	0.668592i	$0.766897\pi$
$6$	−2.50719	−1.02356
$7$	−4.48246	−1.69421	−0.847105	−	0.531426i	$-0.821656\pi$
$7$	−4.48246	−1.69421	−0.847105	+	0.531426i	$0.821656\pi$
$8$	−5.73145	−2.02637
$9$	1.00000	0.333333
$10$	8.33794	2.63669
$11$	−5.03676	−1.51864	−0.759320	−	0.650717i	$-0.774468\pi$
$11$	−5.03676	−1.51864	−0.759320	+	0.650717i	$0.774468\pi$
$12$	4.28600	1.23726
$13$	−5.28870	−1.46682	−0.733411	−	0.679785i	$-0.762073\pi$
$13$	−5.28870	−1.46682	−0.733411	+	0.679785i	$0.762073\pi$
$14$	11.2384	3.00358
$15$	−3.32561	−0.858669
$16$	5.79782	1.44945
$17$	1.22231	0.296453	0.148226	−	0.988953i	$-0.452644\pi$
$17$	1.22231	0.296453	0.148226	+	0.988953i	$0.452644\pi$
$18$	−2.50719	−0.590950
$19$	−3.35429	−0.769528	−0.384764	−	0.923015i	$-0.625717\pi$
$19$	−3.35429	−0.769528	−0.384764	+	0.923015i	$0.625717\pi$
$20$	−14.2536	−3.18720
$21$	−4.48246	−0.978152
$22$	12.6281	2.69232
$23$	3.08422	0.643103	0.321552	−	0.946892i	$-0.395796\pi$
$23$	3.08422	0.643103	0.321552	+	0.946892i	$0.395796\pi$
$24$	−5.73145	−1.16993
$25$	6.05970	1.21194
$26$	13.2598	2.60046
$27$	1.00000	0.192450
$28$	−19.2118	−3.63069
$29$	4.49131	0.834016	0.417008	−	0.908903i	$-0.363079\pi$
$29$	4.49131	0.834016	0.417008	+	0.908903i	$0.363079\pi$
$30$	8.33794	1.52229
$31$	−3.42705	−0.615516	−0.307758	−	0.951465i	$-0.599579\pi$
$31$	−3.42705	−0.615516	−0.307758	+	0.951465i	$0.599579\pi$
$32$	−3.07334	−0.543296
$33$	−5.03676	−0.876787
$34$	−3.06455	−0.525567
$35$	14.9069	2.51973
$36$	4.28600	0.714334
$37$	−5.10511	−0.839276	−0.419638	−	0.907692i	$-0.637843\pi$
$37$	−5.10511	−0.839276	−0.419638	+	0.907692i	$0.637843\pi$
$38$	8.40985	1.36426
$39$	−5.28870	−0.846870
$40$	19.0606	3.01374
$41$	5.90734	0.922571	0.461285	−	0.887252i	$-0.347388\pi$
$41$	5.90734	0.922571	0.461285	+	0.887252i	$0.347388\pi$
$42$	11.2384	1.73412
$43$	3.13061	0.477413	0.238707	−	0.971092i	$-0.423277\pi$
$43$	3.13061	0.477413	0.238707	+	0.971092i	$0.423277\pi$
$44$	−21.5876	−3.25445
$45$	−3.32561	−0.495753
$46$	−7.73272	−1.14013
$47$	9.42102	1.37420	0.687099	−	0.726564i	$-0.258884\pi$
$47$	9.42102	1.37420	0.687099	+	0.726564i	$0.258884\pi$
$48$	5.79782	0.836843
$49$	13.0924	1.87034
$50$	−15.1928	−2.14859
$51$	1.22231	0.171157
$52$	−22.6674	−3.14340
$53$	7.88706	1.08337	0.541685	−	0.840581i	$-0.317786\pi$
$53$	7.88706	1.08337	0.541685	+	0.840581i	$0.317786\pi$
$54$	−2.50719	−0.341185
$55$	16.7503	2.25861
$56$	25.6910	3.43310
$57$	−3.35429	−0.444287
$58$	−11.2606	−1.47859
$59$	−0.0840582	−0.0109434	−0.00547172	−	0.999985i	$-0.501742\pi$
$59$	−0.0840582	−0.0109434	−0.00547172	+	0.999985i	$0.501742\pi$
$60$	−14.2536	−1.84013
$61$	4.25142	0.544339	0.272169	−	0.962249i	$-0.412259\pi$
$61$	4.25142	0.544339	0.272169	+	0.962249i	$0.412259\pi$
$62$	8.59227	1.09122
$63$	−4.48246	−0.564736
$64$	−3.89018	−0.486272
$65$	17.5882	2.18154
$66$	12.6281	1.55441
$67$	3.18113	0.388637	0.194318	−	0.980938i	$-0.437750\pi$
$67$	3.18113	0.388637	0.194318	+	0.980938i	$0.437750\pi$
$68$	5.23881	0.635299
$69$	3.08422	0.371296
$70$	−37.3745	−4.46710
$71$	−16.8171	−1.99583	−0.997914	−	0.0645583i	$-0.979436\pi$
$71$	−16.8171	−1.99583	−0.997914	+	0.0645583i	$0.979436\pi$
$72$	−5.73145	−0.675457
$73$	2.32298	0.271884	0.135942	−	0.990717i	$-0.456594\pi$
$73$	2.32298	0.271884	0.135942	+	0.990717i	$0.456594\pi$
$74$	12.7995	1.48791
$75$	6.05970	0.699714
$76$	−14.3765	−1.64910
$77$	22.5770	2.57289
$78$	13.2598	1.50137
$79$	−3.00405	−0.337982	−0.168991	−	0.985618i	$-0.554051\pi$
$79$	−3.00405	−0.337982	−0.168991	+	0.985618i	$0.554051\pi$
$80$	−19.2813	−2.15571
$81$	1.00000	0.111111
$82$	−14.8108	−1.63558
$83$	17.5584	1.92728	0.963641	−	0.267199i	$-0.0860981\pi$
$83$	17.5584	1.92728	0.963641	+	0.267199i	$0.0860981\pi$
$84$	−19.2118	−2.09618
$85$	−4.06492	−0.440902
$86$	−7.84903	−0.846383
$87$	4.49131	0.481519
$88$	28.8679	3.07733
$89$	0.778879	0.0825610	0.0412805	−	0.999148i	$-0.486856\pi$
$89$	0.778879	0.0825610	0.0412805	+	0.999148i	$0.486856\pi$
$90$	8.33794	0.878896
$91$	23.7064	2.48510
$92$	13.2190	1.37817
$93$	−3.42705	−0.355369
$94$	−23.6203	−2.43625
$95$	11.1551	1.14449
$96$	−3.07334	−0.313672
$97$	−5.10710	−0.518548	−0.259274	−	0.965804i	$-0.583483\pi$
$97$	−5.10710	−0.518548	−0.259274	+	0.965804i	$0.583483\pi$
$98$	−32.8252	−3.31584
$99$	−5.03676	−0.506213
$100$	25.9719	2.59719
$101$	−10.0721	−1.00221	−0.501105	−	0.865387i	$-0.667073\pi$
$101$	−10.0721	−1.00221	−0.501105	+	0.865387i	$0.667073\pi$
$102$	−3.06455	−0.303436
$103$	−11.2486	−1.10836	−0.554179	−	0.832397i	$-0.686968\pi$
$103$	−11.2486	−1.10836	−0.554179	+	0.832397i	$0.686968\pi$
$104$	30.3119	2.97233
$105$	14.9069	1.45477
$106$	−19.7743	−1.92065
$107$	−4.29982	−0.415679	−0.207840	−	0.978163i	$-0.566643\pi$
$107$	−4.29982	−0.415679	−0.207840	+	0.978163i	$0.566643\pi$
$108$	4.28600	0.412421
$109$	20.2759	1.94208	0.971041	−	0.238912i	$-0.0767909\pi$
$109$	20.2759	1.94208	0.971041	+	0.238912i	$0.0767909\pi$
$110$	−41.9962	−4.00418
$111$	−5.10511	−0.484556
$112$	−25.9885	−2.45568
$113$	8.32078	0.782753	0.391377	−	0.920231i	$-0.371999\pi$
$113$	8.32078	0.782753	0.391377	+	0.920231i	$0.371999\pi$
$114$	8.40985	0.787655
$115$	−10.2569	−0.956461
$116$	19.2498	1.78730
$117$	−5.28870	−0.488941
$118$	0.210750	0.0194011
$119$	−5.47893	−0.502253
$120$	19.0606	1.73998
$121$	14.3689	1.30627
$122$	−10.6591	−0.965032
$123$	5.90734	0.532647
$124$	−14.6884	−1.31905
$125$	−3.52415	−0.315209
$126$	11.2384	1.00119
$127$	−11.0961	−0.984619	−0.492309	−	0.870420i	$-0.663847\pi$
$127$	−11.0961	−0.984619	−0.492309	+	0.870420i	$0.663847\pi$
$128$	15.9001	1.40538
$129$	3.13061	0.275635
$130$	−44.0969	−3.86755
$131$	4.17459	0.364735	0.182368	−	0.983230i	$-0.441624\pi$
$131$	4.17459	0.364735	0.182368	+	0.983230i	$0.441624\pi$
$132$	−21.5876	−1.87896
$133$	15.0355	1.30374
$134$	−7.97570	−0.688995
$135$	−3.32561	−0.286223
$136$	−7.00558	−0.600724
$137$	−15.0202	−1.28326	−0.641629	−	0.767015i	$-0.721741\pi$
$137$	−15.0202	−1.28326	−0.641629	+	0.767015i	$0.721741\pi$
$138$	−7.73272	−0.658252
$139$	1.53536	0.130228	0.0651138	−	0.997878i	$-0.479259\pi$
$139$	1.53536	0.130228	0.0651138	+	0.997878i	$0.479259\pi$
$140$	63.8911	5.39978
$141$	9.42102	0.793393
$142$	42.1638	3.53831
$143$	26.6379	2.22757
$144$	5.79782	0.483152
$145$	−14.9364	−1.24040
$146$	−5.82414	−0.482009
$147$	13.0924	1.07984
$148$	−21.8805	−1.79857
$149$	18.2116	1.49195	0.745975	−	0.665974i	$-0.231984\pi$
$149$	18.2116	1.49195	0.745975	+	0.665974i	$0.231984\pi$
$150$	−15.1928	−1.24049
$151$	−12.6710	−1.03115	−0.515577	−	0.856843i	$-0.672422\pi$
$151$	−12.6710	−1.03115	−0.515577	+	0.856843i	$0.672422\pi$
$152$	19.2250	1.55935
$153$	1.22231	0.0988176
$154$	−56.6050	−4.56136
$155$	11.3970	0.915432
$156$	−22.6674	−1.81484
$157$	−12.0697	−0.963268	−0.481634	−	0.876372i	$-0.659957\pi$
$157$	−12.0697	−0.963268	−0.481634	+	0.876372i	$0.659957\pi$
$158$	7.53173	0.599192
$159$	7.88706	0.625484
$160$	10.2208	0.808021
$161$	−13.8249	−1.08955
$162$	−2.50719	−0.196983
$163$	11.2116	0.878160	0.439080	−	0.898448i	$-0.355304\pi$
$163$	11.2116	0.878160	0.439080	+	0.898448i	$0.355304\pi$
$164$	25.3189	1.97707
$165$	16.7503	1.30401
$166$	−44.0222	−3.41679
$167$	4.81992	0.372977	0.186488	−	0.982457i	$-0.440289\pi$
$167$	4.81992	0.372977	0.186488	+	0.982457i	$0.440289\pi$
$168$	25.6910	1.98210
$169$	14.9704	1.15157
$170$	10.1915	0.781654
$171$	−3.35429	−0.256509
$172$	13.4178	1.02310
$173$	0.610334	0.0464029	0.0232014	−	0.999731i	$-0.492614\pi$
$173$	0.610334	0.0464029	0.0232014	+	0.999731i	$0.492614\pi$
$174$	−11.2606	−0.853662
$175$	−27.1623	−2.05328
$176$	−29.2022	−2.20120
$177$	−0.0840582	−0.00631820
$178$	−1.95280	−0.146368
$179$	2.94305	0.219974	0.109987	−	0.993933i	$-0.464919\pi$
$179$	2.94305	0.219974	0.109987	+	0.993933i	$0.464919\pi$
$180$	−14.2536	−1.06240
$181$	−25.7388	−1.91315	−0.956576	−	0.291484i	$-0.905851\pi$
$181$	−25.7388	−1.91315	−0.956576	+	0.291484i	$0.905851\pi$
$182$	−59.4364	−4.40572
$183$	4.25142	0.314274
$184$	−17.6770	−1.30317
$185$	16.9776	1.24822
$186$	8.59227	0.630016
$187$	−6.15646	−0.450205
$188$	40.3785	2.94491
$189$	−4.48246	−0.326051
$190$	−27.9679	−2.02901
$191$	−6.12980	−0.443537	−0.221768	−	0.975099i	$-0.571183\pi$
$191$	−6.12980	−0.443537	−0.221768	+	0.975099i	$0.571183\pi$
$192$	−3.89018	−0.280749
$193$	11.0014	0.791897	0.395949	−	0.918273i	$-0.370416\pi$
$193$	11.0014	0.791897	0.395949	+	0.918273i	$0.370416\pi$
$194$	12.8045	0.919308
$195$	17.5882	1.25952
$196$	56.1141	4.00815
$197$	5.67015	0.403982	0.201991	−	0.979387i	$-0.435259\pi$
$197$	5.67015	0.403982	0.201991	+	0.979387i	$0.435259\pi$
$198$	12.6281	0.897441
$199$	24.5552	1.74067	0.870337	−	0.492456i	$-0.163901\pi$
$199$	24.5552	1.74067	0.870337	+	0.492456i	$0.163901\pi$
$200$	−34.7308	−2.45584
$201$	3.18113	0.224380
$202$	25.2526	1.77677
$203$	−20.1321	−1.41300
$204$	5.23881	0.366790
$205$	−19.6455	−1.37210
$206$	28.2024	1.96495
$207$	3.08422	0.214368
$208$	−30.6629	−2.12609
$209$	16.8948	1.16864
$210$	−37.3745	−2.57908
$211$	13.7775	0.948482	0.474241	−	0.880395i	$-0.342722\pi$
$211$	13.7775	0.948482	0.474241	+	0.880395i	$0.342722\pi$
$212$	33.8039	2.32166
$213$	−16.8171	−1.15229
$214$	10.7805	0.736937
$215$	−10.4112	−0.710037
$216$	−5.73145	−0.389976
$217$	15.3616	1.04281
$218$	−50.8356	−3.44302
$219$	2.32298	0.156972
$220$	71.7919	4.84021
$221$	−6.46441	−0.434844
$222$	12.7995	0.859046
$223$	−12.2575	−0.820822	−0.410411	−	0.911901i	$-0.634615\pi$
$223$	−12.2575	−0.820822	−0.410411	+	0.911901i	$0.634615\pi$
$224$	13.7761	0.920456
$225$	6.05970	0.403980
$226$	−20.8618	−1.38771
$227$	−7.58659	−0.503539	−0.251770	−	0.967787i	$-0.581013\pi$
$227$	−7.58659	−0.503539	−0.251770	+	0.967787i	$0.581013\pi$
$228$	−14.3765	−0.952108
$229$	−2.18641	−0.144482	−0.0722411	−	0.997387i	$-0.523015\pi$
$229$	−2.18641	−0.144482	−0.0722411	+	0.997387i	$0.523015\pi$
$230$	25.7160	1.69566
$231$	22.5770	1.48546
$232$	−25.7417	−1.69003
$233$	−19.0523	−1.24816	−0.624080	−	0.781360i	$-0.714526\pi$
$233$	−19.0523	−1.24816	−0.624080	+	0.781360i	$0.714526\pi$
$234$	13.2598	0.866819
$235$	−31.3307	−2.04379
$236$	−0.360274	−0.0234518
$237$	−3.00405	−0.195134
$238$	13.7367	0.890420
$239$	−22.7840	−1.47377	−0.736887	−	0.676016i	$-0.763705\pi$
$239$	−22.7840	−1.47377	−0.736887	+	0.676016i	$0.763705\pi$
$240$	−19.2813	−1.24460
$241$	−15.1210	−0.974027	−0.487014	−	0.873394i	$-0.661914\pi$
$241$	−15.1210	−0.974027	−0.487014	+	0.873394i	$0.661914\pi$
$242$	−36.0257	−2.31582
$243$	1.00000	0.0641500
$244$	18.2216	1.16652
$245$	−43.5403	−2.78169
$246$	−14.8108	−0.944303
$247$	17.7399	1.12876
$248$	19.6420	1.24727
$249$	17.5584	1.11272
$250$	8.83570	0.558819
$251$	−25.3825	−1.60213	−0.801066	−	0.598577i	$-0.795733\pi$
$251$	−25.3825	−1.60213	−0.801066	+	0.598577i	$0.795733\pi$
$252$	−19.2118	−1.21023
$253$	−15.5345	−0.976643
$254$	27.8200	1.74558
$255$	−4.06492	−0.254555
$256$	−32.0842	−2.00526
$257$	14.7568	0.920507	0.460253	−	0.887788i	$-0.347759\pi$
$257$	14.7568	0.920507	0.460253	+	0.887788i	$0.347759\pi$
$258$	−7.84903	−0.488659
$259$	22.8834	1.42191
$260$	75.3830	4.67505
$261$	4.49131	0.278005
$262$	−10.4665	−0.646622
$263$	9.53601	0.588015	0.294008	−	0.955803i	$-0.405011\pi$
$263$	9.53601	0.588015	0.294008	+	0.955803i	$0.405011\pi$
$264$	28.8679	1.77670
$265$	−26.2293	−1.61125
$266$	−37.6968	−2.31134
$267$	0.778879	0.0476666
$268$	13.6343	0.832850
$269$	−21.6559	−1.32038	−0.660191	−	0.751097i	$-0.729525\pi$
$269$	−21.6559	−1.32038	−0.660191	+	0.751097i	$0.729525\pi$
$270$	8.33794	0.507431
$271$	−1.95022	−0.118467	−0.0592336	−	0.998244i	$-0.518866\pi$
$271$	−1.95022	−0.118467	−0.0592336	+	0.998244i	$0.518866\pi$
$272$	7.08671	0.429695
$273$	23.7064	1.43478
$274$	37.6584	2.27503
$275$	−30.5212	−1.84050
$276$	13.2190	0.795688
$277$	−0.719711	−0.0432432	−0.0216216	−	0.999766i	$-0.506883\pi$
$277$	−0.719711	−0.0432432	−0.0216216	+	0.999766i	$0.506883\pi$
$278$	−3.84944	−0.230874
$279$	−3.42705	−0.205172
$280$	−85.4382	−5.10591
$281$	−3.20822	−0.191387	−0.0956933	−	0.995411i	$-0.530507\pi$
$281$	−3.20822	−0.191387	−0.0956933	+	0.995411i	$0.530507\pi$
$282$	−23.6203	−1.40657
$283$	13.7295	0.816133	0.408066	−	0.912952i	$-0.366203\pi$
$283$	13.7295	0.816133	0.408066	+	0.912952i	$0.366203\pi$
$284$	−72.0783	−4.27706
$285$	11.1551	0.660770
$286$	−66.7863	−3.94916
$287$	−26.4794	−1.56303
$288$	−3.07334	−0.181099
$289$	−15.5060	−0.912116
$290$	37.4483	2.19904
$291$	−5.10710	−0.299384
$292$	9.95628	0.582647
$293$	8.81548	0.515006	0.257503	−	0.966278i	$-0.417100\pi$
$293$	8.81548	0.515006	0.257503	+	0.966278i	$0.417100\pi$
$294$	−32.8252	−1.91440
$295$	0.279545	0.0162757
$296$	29.2597	1.70068
$297$	−5.03676	−0.292262
$298$	−45.6599	−2.64501
$299$	−16.3115	−0.943318
$300$	25.9719	1.49949
$301$	−14.0328	−0.808838
$302$	31.7687	1.82808
$303$	−10.0721	−0.578626
$304$	−19.4476	−1.11540
$305$	−14.1386	−0.809573
$306$	−3.06455	−0.175189
$307$	4.45929	0.254505	0.127252	−	0.991870i	$-0.459384\pi$
$307$	4.45929	0.254505	0.127252	+	0.991870i	$0.459384\pi$
$308$	96.7653	5.51372
$309$	−11.2486	−0.639911
$310$	−28.5746	−1.62293
$311$	7.86697	0.446095	0.223047	−	0.974808i	$-0.428400\pi$
$311$	7.86697	0.446095	0.223047	+	0.974808i	$0.428400\pi$
$312$	30.3119	1.71607
$313$	14.8203	0.837694	0.418847	−	0.908057i	$-0.362434\pi$
$313$	14.8203	0.837694	0.418847	+	0.908057i	$0.362434\pi$
$314$	30.2611	1.70773
$315$	14.9069	0.839909
$316$	−12.8754	−0.724296
$317$	0.972499	0.0546210	0.0273105	−	0.999627i	$-0.491306\pi$
$317$	0.972499	0.0546210	0.0273105	+	0.999627i	$0.491306\pi$
$318$	−19.7743	−1.10889
$319$	−22.6217	−1.26657
$320$	12.9372	0.723213
$321$	−4.29982	−0.239992
$322$	34.6616	1.93161
$323$	−4.09997	−0.228129
$324$	4.28600	0.238111
$325$	−32.0479	−1.77770
$326$	−28.1096	−1.55685
$327$	20.2759	1.12126
$328$	−33.8576	−1.86947
$329$	−42.2293	−2.32818
$330$	−41.9962	−2.31182
$331$	−23.7301	−1.30432	−0.652162	−	0.758080i	$-0.726138\pi$
$331$	−23.7301	−1.30432	−0.652162	+	0.758080i	$0.726138\pi$
$332$	75.2553	4.13017
$333$	−5.10511	−0.279759
$334$	−12.0845	−0.661232
$335$	−10.5792	−0.578004
$336$	−25.9885	−1.41779
$337$	27.2464	1.48421	0.742103	−	0.670286i	$-0.233829\pi$
$337$	27.2464	1.48421	0.742103	+	0.670286i	$0.233829\pi$
$338$	−37.5336	−2.04156
$339$	8.32078	0.451923
$340$	−17.4222	−0.944854
$341$	17.2612	0.934748
$342$	8.40985	0.454753
$343$	−27.3090	−1.47454
$344$	−17.9429	−0.967417
$345$	−10.2569	−0.552213
$346$	−1.53022	−0.0822654
$347$	−23.4864	−1.26082	−0.630408	−	0.776264i	$-0.717113\pi$
$347$	−23.4864	−1.26082	−0.630408	+	0.776264i	$0.717113\pi$
$348$	19.2498	1.03190
$349$	0.986594	0.0528112	0.0264056	−	0.999651i	$-0.491594\pi$
$349$	0.986594	0.0528112	0.0264056	+	0.999651i	$0.491594\pi$
$350$	68.1011	3.64016
$351$	−5.28870	−0.282290
$352$	15.4797	0.825071
$353$	5.76007	0.306578	0.153289	−	0.988181i	$-0.451013\pi$
$353$	5.76007	0.306578	0.153289	+	0.988181i	$0.451013\pi$
$354$	0.210750	0.0112012
$355$	55.9273	2.96831
$356$	3.33828	0.176928
$357$	−5.47893	−0.289976
$358$	−7.37879	−0.389981
$359$	15.6605	0.826530	0.413265	−	0.910611i	$-0.364388\pi$
$359$	15.6605	0.826530	0.413265	+	0.910611i	$0.364388\pi$
$360$	19.0606	1.00458
$361$	−7.74871	−0.407827
$362$	64.5321	3.39173
$363$	14.3689	0.754174
$364$	101.606	5.32558
$365$	−7.72531	−0.404361
$366$	−10.6591	−0.557161
$367$	−2.99434	−0.156303	−0.0781516	−	0.996941i	$-0.524902\pi$
$367$	−2.99434	−0.156303	−0.0781516	+	0.996941i	$0.524902\pi$
$368$	17.8817	0.932149
$369$	5.90734	0.307524
$370$	−42.5662	−2.21291
$371$	−35.3534	−1.83546
$372$	−14.6884	−0.761556
$373$	8.72474	0.451750	0.225875	−	0.974156i	$-0.427476\pi$
$373$	8.72474	0.451750	0.225875	+	0.974156i	$0.427476\pi$
$374$	15.4354	0.798147
$375$	−3.52415	−0.181986
$376$	−53.9961	−2.78464
$377$	−23.7532	−1.22335
$378$	11.2384	0.578039
$379$	−38.0185	−1.95288	−0.976439	−	0.215791i	$-0.930767\pi$
$379$	−38.0185	−1.95288	−0.976439	+	0.215791i	$0.930767\pi$
$380$	47.8107	2.45264
$381$	−11.0961	−0.568470
$382$	15.3686	0.786325
$383$	31.9113	1.63059	0.815295	−	0.579045i	$-0.196575\pi$
$383$	31.9113	1.63059	0.815295	+	0.579045i	$0.196575\pi$
$384$	15.9001	0.811399
$385$	−75.0825	−3.82656
$386$	−27.5826	−1.40392
$387$	3.13061	0.159138
$388$	−21.8891	−1.11125
$389$	−5.76415	−0.292254	−0.146127	−	0.989266i	$-0.546681\pi$
$389$	−5.76415	−0.292254	−0.146127	+	0.989266i	$0.546681\pi$
$390$	−44.0969	−2.23293
$391$	3.76986	0.190650
$392$	−75.0384	−3.79001
$393$	4.17459	0.210580
$394$	−14.2161	−0.716199
$395$	9.99031	0.502667
$396$	−21.5876	−1.08482
$397$	5.63488	0.282806	0.141403	−	0.989952i	$-0.454839\pi$
$397$	5.63488	0.282806	0.141403	+	0.989952i	$0.454839\pi$
$398$	−61.5647	−3.08596
$399$	15.0355	0.752715
$400$	35.1330	1.75665
$401$	−11.5499	−0.576775	−0.288388	−	0.957514i	$-0.593119\pi$
$401$	−11.5499	−0.576775	−0.288388	+	0.957514i	$0.593119\pi$
$402$	−7.97570	−0.397792
$403$	18.1247	0.902853
$404$	−43.1690	−2.14774
$405$	−3.32561	−0.165251
$406$	50.4750	2.50503
$407$	25.7132	1.27456
$408$	−7.00558	−0.346828
$409$	30.2002	1.49330	0.746651	−	0.665216i	$-0.231661\pi$
$409$	30.2002	1.49330	0.746651	+	0.665216i	$0.231661\pi$
$410$	49.2550	2.43253
$411$	−15.0202	−0.740890
$412$	−48.2116	−2.37521
$413$	0.376787	0.0185405
$414$	−7.73272	−0.380042
$415$	−58.3924	−2.86637
$416$	16.2540	0.796918
$417$	1.53536	0.0751870
$418$	−42.3584	−2.07182
$419$	32.4646	1.58600	0.793000	−	0.609221i	$-0.208518\pi$
$419$	32.4646	1.58600	0.793000	+	0.609221i	$0.208518\pi$
$420$	63.8911	3.11757
$421$	26.9933	1.31557	0.657786	−	0.753205i	$-0.271493\pi$
$421$	26.9933	1.31557	0.657786	+	0.753205i	$0.271493\pi$
$422$	−34.5428	−1.68152
$423$	9.42102	0.458066
$424$	−45.2042	−2.19531
$425$	7.40681	0.359283
$426$	42.1638	2.04284
$427$	−19.0568	−0.922224
$428$	−18.4290	−0.890801
$429$	26.6379	1.28609
$430$	26.1028	1.25879
$431$	−17.0235	−0.819993	−0.409997	−	0.912087i	$-0.634470\pi$
$431$	−17.0235	−0.819993	−0.409997	+	0.912087i	$0.634470\pi$
$432$	5.79782	0.278948
$433$	26.4954	1.27329	0.636644	−	0.771157i	$-0.280322\pi$
$433$	26.4954	1.27329	0.636644	+	0.771157i	$0.280322\pi$
$434$	−38.5145	−1.84875
$435$	−14.9364	−0.716144
$436$	86.9027	4.16189
$437$	−10.3454	−0.494886
$438$	−5.82414	−0.278288
$439$	−3.20928	−0.153170	−0.0765852	−	0.997063i	$-0.524402\pi$
$439$	−3.20928	−0.153170	−0.0765852	+	0.997063i	$0.524402\pi$
$440$	−96.0035	−4.57679
$441$	13.0924	0.623448
$442$	16.2075	0.770913
$443$	1.60384	0.0762009	0.0381005	−	0.999274i	$-0.487869\pi$
$443$	1.60384	0.0762009	0.0381005	+	0.999274i	$0.487869\pi$
$444$	−21.8805	−1.03840
$445$	−2.59025	−0.122790
$446$	30.7319	1.45520
$447$	18.2116	0.861378
$448$	17.4376	0.823847
$449$	29.1893	1.37753	0.688765	−	0.724985i	$-0.258153\pi$
$449$	29.1893	1.37753	0.688765	+	0.724985i	$0.258153\pi$
$450$	−15.1928	−0.716196
$451$	−29.7538	−1.40105
$452$	35.6629	1.67744
$453$	−12.6710	−0.595337
$454$	19.0210	0.892701
$455$	−78.8382	−3.69599
$456$	19.2250	0.900291
$457$	19.6835	0.920757	0.460379	−	0.887723i	$-0.347714\pi$
$457$	19.6835	0.920757	0.460379	+	0.887723i	$0.347714\pi$
$458$	5.48175	0.256145
$459$	1.22231	0.0570524
$460$	−43.9611	−2.04970
$461$	−18.2784	−0.851309	−0.425655	−	0.904886i	$-0.639956\pi$
$461$	−18.2784	−0.851309	−0.425655	+	0.904886i	$0.639956\pi$
$462$	−56.6050	−2.63350
$463$	−27.6399	−1.28453	−0.642267	−	0.766481i	$-0.722006\pi$
$463$	−27.6399	−1.28453	−0.642267	+	0.766481i	$0.722006\pi$
$464$	26.0398	1.20887
$465$	11.3970	0.528525
$466$	47.7678	2.21280
$467$	−24.1373	−1.11694	−0.558471	−	0.829524i	$-0.688612\pi$
$467$	−24.1373	−1.11694	−0.558471	+	0.829524i	$0.688612\pi$
$468$	−22.6674	−1.04780
$469$	−14.2593	−0.658432
$470$	78.5520	3.62333
$471$	−12.0697	−0.556143
$472$	0.481775	0.0221755
$473$	−15.7681	−0.725019
$474$	7.53173	0.345944
$475$	−20.3260	−0.932621
$476$	−23.4827	−1.07633
$477$	7.88706	0.361123
$478$	57.1238	2.61278
$479$	38.0326	1.73775	0.868877	−	0.495028i	$-0.164842\pi$
$479$	38.0326	1.73775	0.868877	+	0.495028i	$0.164842\pi$
$480$	10.2208	0.466511
$481$	26.9994	1.23107
$482$	37.9111	1.72681
$483$	−13.8249	−0.629053
$484$	61.5853	2.79933
$485$	16.9842	0.771215
$486$	−2.50719	−0.113728
$487$	−14.2620	−0.646273	−0.323137	−	0.946352i	$-0.604737\pi$
$487$	−14.2620	−0.646273	−0.323137	+	0.946352i	$0.604737\pi$
$488$	−24.3668	−1.10303
$489$	11.2116	0.507006
$490$	109.164	4.93152
$491$	7.16955	0.323557	0.161779	−	0.986827i	$-0.448277\pi$
$491$	7.16955	0.323557	0.161779	+	0.986827i	$0.448277\pi$
$492$	25.3189	1.14146
$493$	5.48976	0.247246
$494$	−44.4772	−2.00112
$495$	16.7503	0.752870
$496$	−19.8694	−0.892163
$497$	75.3821	3.38135
$498$	−44.0222	−1.97268
$499$	37.4745	1.67759	0.838794	−	0.544449i	$-0.183261\pi$
$499$	37.4745	1.67759	0.838794	+	0.544449i	$0.183261\pi$
$500$	−15.1045	−0.675494
$501$	4.81992	0.215338
$502$	63.6388	2.84034
$503$	−22.5859	−1.00706	−0.503528	−	0.863979i	$-0.667965\pi$
$503$	−22.5859	−1.00706	−0.503528	+	0.863979i	$0.667965\pi$
$504$	25.6910	1.14437
$505$	33.4958	1.49055
$506$	38.9478	1.73144
$507$	14.9704	0.664858
$508$	−47.5579	−2.11004
$509$	36.7978	1.63103	0.815517	−	0.578732i	$-0.196452\pi$
$509$	36.7978	1.63103	0.815517	+	0.578732i	$0.196452\pi$
$510$	10.1915	0.451288
$511$	−10.4126	−0.460628
$512$	48.6411	2.14965
$513$	−3.35429	−0.148096
$514$	−36.9982	−1.63192
$515$	37.4085	1.64842
$516$	13.4178	0.590686
$517$	−47.4514	−2.08691
$518$	−57.3732	−2.52083
$519$	0.610334	0.0267907
$520$	−100.806	−4.42062
$521$	4.74956	0.208082	0.104041	−	0.994573i	$-0.466823\pi$
$521$	4.74956	0.208082	0.104041	+	0.994573i	$0.466823\pi$
$522$	−11.2606	−0.492862
$523$	42.2386	1.84696	0.923482	−	0.383642i	$-0.125330\pi$
$523$	42.2386	1.84696	0.923482	+	0.383642i	$0.125330\pi$
$524$	17.8923	0.781629
$525$	−27.1623	−1.18546
$526$	−23.9086	−1.04246
$527$	−4.18891	−0.182472
$528$	−29.2022	−1.27086
$529$	−13.4876	−0.586418
$530$	65.7618	2.85651
$531$	−0.0840582	−0.00364782
$532$	64.4421	2.79392
$533$	−31.2421	−1.35325
$534$	−1.95280	−0.0845058
$535$	14.2995	0.618222
$536$	−18.2325	−0.787523
$537$	2.94305	0.127002
$538$	54.2954	2.34084
$539$	−65.9433	−2.84038
$540$	−14.2536	−0.613377
$541$	−0.675418	−0.0290385	−0.0145192	−	0.999895i	$-0.504622\pi$
$541$	−0.675418	−0.0290385	−0.0145192	+	0.999895i	$0.504622\pi$
$542$	4.88956	0.210025
$543$	−25.7388	−1.10456
$544$	−3.75657	−0.161062
$545$	−67.4299	−2.88838
$546$	−59.4364	−2.54364
$547$	23.6747	1.01226	0.506128	−	0.862458i	$-0.331076\pi$
$547$	23.6747	1.01226	0.506128	+	0.862458i	$0.331076\pi$
$548$	−64.3764	−2.75003
$549$	4.25142	0.181446
$550$	76.5226	3.26293
$551$	−15.0652	−0.641798
$552$	−17.6770	−0.752384
$553$	13.4655	0.572612
$554$	1.80445	0.0766638
$555$	16.9776	0.720660
$556$	6.58056	0.279078
$557$	22.3438	0.946738	0.473369	−	0.880864i	$-0.343038\pi$
$557$	22.3438	0.946738	0.473369	+	0.880864i	$0.343038\pi$
$558$	8.59227	0.363740
$559$	−16.5569	−0.700281
$560$	86.4276	3.65223
$561$	−6.15646	−0.259926
$562$	8.04363	0.339300
$563$	−29.7708	−1.25469	−0.627345	−	0.778742i	$-0.715858\pi$
$563$	−29.7708	−1.25469	−0.627345	+	0.778742i	$0.715858\pi$
$564$	40.3785	1.70024
$565$	−27.6717	−1.16416
$566$	−34.4224	−1.44688
$567$	−4.48246	−0.188245
$568$	96.3866	4.04429
$569$	14.6483	0.614090	0.307045	−	0.951695i	$-0.400660\pi$
$569$	14.6483	0.614090	0.307045	+	0.951695i	$0.400660\pi$
$570$	−27.9679	−1.17145
$571$	−7.71803	−0.322989	−0.161495	−	0.986874i	$-0.551631\pi$
$571$	−7.71803	−0.322989	−0.161495	+	0.986874i	$0.551631\pi$
$572$	114.170	4.77370
$573$	−6.12980	−0.256076
$574$	66.3888	2.77102
$575$	18.6894	0.779403
$576$	−3.89018	−0.162091
$577$	−34.1319	−1.42093	−0.710464	−	0.703733i	$-0.751515\pi$
$577$	−34.1319	−1.42093	−0.710464	+	0.703733i	$0.751515\pi$
$578$	38.8764	1.61705
$579$	11.0014	0.457202
$580$	−64.0173	−2.65817
$581$	−78.7047	−3.26522
$582$	12.8045	0.530763
$583$	−39.7252	−1.64525
$584$	−13.3140	−0.550938
$585$	17.5882	0.727182
$586$	−22.1021	−0.913029
$587$	16.5688	0.683867	0.341933	−	0.939724i	$-0.388918\pi$
$587$	16.5688	0.683867	0.341933	+	0.939724i	$0.388918\pi$
$588$	56.1141	2.31411
$589$	11.4953	0.473657
$590$	−0.700873	−0.0288545
$591$	5.67015	0.233239
$592$	−29.5985	−1.21649
$593$	32.6461	1.34062	0.670308	−	0.742083i	$-0.266162\pi$
$593$	32.6461	1.34062	0.670308	+	0.742083i	$0.266162\pi$
$594$	12.6281	0.518138
$595$	18.2208	0.746980
$596$	78.0549	3.19725
$597$	24.5552	1.00498
$598$	40.8960	1.67236
$599$	−10.0312	−0.409864	−0.204932	−	0.978776i	$-0.565697\pi$
$599$	−10.0312	−0.409864	−0.204932	+	0.978776i	$0.565697\pi$
$600$	−34.7308	−1.41788
$601$	16.0844	0.656098	0.328049	−	0.944661i	$-0.393609\pi$
$601$	16.0844	0.656098	0.328049	+	0.944661i	$0.393609\pi$
$602$	35.1829	1.43395
$603$	3.18113	0.129546
$604$	−54.3081	−2.20976
$605$	−47.7855	−1.94276
$606$	25.2526	1.02582
$607$	36.5096	1.48188	0.740939	−	0.671573i	$-0.234381\pi$
$607$	36.5096	1.48188	0.740939	+	0.671573i	$0.234381\pi$
$608$	10.3089	0.418081
$609$	−20.1321	−0.815794
$610$	35.4481	1.43525
$611$	−49.8250	−2.01570
$612$	5.23881	0.211766
$613$	−14.0427	−0.567177	−0.283589	−	0.958946i	$-0.591525\pi$
$613$	−14.0427	−0.567177	−0.283589	+	0.958946i	$0.591525\pi$
$614$	−11.1803	−0.451199
$615$	−19.6455	−0.792183
$616$	−129.399	−5.21364
$617$	21.1688	0.852224	0.426112	−	0.904670i	$-0.359883\pi$
$617$	21.1688	0.852224	0.426112	+	0.904670i	$0.359883\pi$
$618$	28.2024	1.13447
$619$	18.7351	0.753026	0.376513	−	0.926411i	$-0.377123\pi$
$619$	18.7351	0.753026	0.376513	+	0.926411i	$0.377123\pi$
$620$	48.8478	1.96177
$621$	3.08422	0.123765
$622$	−19.7240	−0.790860
$623$	−3.49129	−0.139876
$624$	−30.6629	−1.22750
$625$	−18.5785	−0.743142
$626$	−37.1574	−1.48511
$627$	16.8948	0.674712
$628$	−51.7309	−2.06429
$629$	−6.24001	−0.248806
$630$	−37.3745	−1.48903
$631$	15.2905	0.608704	0.304352	−	0.952560i	$-0.401560\pi$
$631$	15.2905	0.608704	0.304352	+	0.952560i	$0.401560\pi$
$632$	17.2176	0.684878
$633$	13.7775	0.547606
$634$	−2.43824	−0.0968348
$635$	36.9013	1.46438
$636$	33.8039	1.34041
$637$	−69.2419	−2.74346
$638$	56.7168	2.24544
$639$	−16.8171	−0.665276
$640$	−52.8776	−2.09017
$641$	−9.50842	−0.375560	−0.187780	−	0.982211i	$-0.560129\pi$
$641$	−9.50842	−0.375560	−0.187780	+	0.982211i	$0.560129\pi$
$642$	10.7805	0.425471
$643$	30.6089	1.20710	0.603549	−	0.797326i	$-0.293753\pi$
$643$	30.6089	1.20710	0.603549	+	0.797326i	$0.293753\pi$
$644$	−59.2534	−2.33491
$645$	−10.4112	−0.409940
$646$	10.2794	0.404438
$647$	−15.5438	−0.611091	−0.305545	−	0.952178i	$-0.598839\pi$
$647$	−15.5438	−0.611091	−0.305545	+	0.952178i	$0.598839\pi$
$648$	−5.73145	−0.225152
$649$	0.423381	0.0166192
$650$	80.3503	3.15160
$651$	15.3616	0.602069
$652$	48.0530	1.88190
$653$	33.2640	1.30172	0.650860	−	0.759198i	$-0.274408\pi$
$653$	33.2640	1.30172	0.650860	+	0.759198i	$0.274408\pi$
$654$	−50.8356	−1.98783
$655$	−13.8831	−0.542456
$656$	34.2497	1.33722
$657$	2.32298	0.0906279
$658$	105.877	4.12751
$659$	−2.25431	−0.0878156	−0.0439078	−	0.999036i	$-0.513981\pi$
$659$	−2.25431	−0.0878156	−0.0439078	+	0.999036i	$0.513981\pi$
$660$	71.7919	2.79450
$661$	−32.0009	−1.24469	−0.622346	−	0.782743i	$-0.713820\pi$
$661$	−32.0009	−1.24469	−0.622346	+	0.782743i	$0.713820\pi$
$662$	59.4958	2.31237
$663$	−6.46441	−0.251057
$664$	−100.635	−3.90539
$665$	−50.0022	−1.93900
$666$	12.7995	0.495970
$667$	13.8522	0.536358
$668$	20.6582	0.799290
$669$	−12.2575	−0.473902
$670$	26.5241	1.02471
$671$	−21.4134	−0.826655
$672$	13.7761	0.531426
$673$	13.8088	0.532289	0.266145	−	0.963933i	$-0.414250\pi$
$673$	13.8088	0.532289	0.266145	+	0.963933i	$0.414250\pi$
$674$	−68.3119	−2.63128
$675$	6.05970	0.233238
$676$	64.1631	2.46781
$677$	47.4252	1.82270	0.911349	−	0.411634i	$-0.135042\pi$
$677$	47.4252	1.82270	0.911349	+	0.411634i	$0.135042\pi$
$678$	−20.8618	−0.801192
$679$	22.8924	0.878528
$680$	23.2979	0.893432
$681$	−7.58659	−0.290719
$682$	−43.2772	−1.65717
$683$	43.5600	1.66678	0.833389	−	0.552687i	$-0.186397\pi$
$683$	43.5600	1.66678	0.833389	+	0.552687i	$0.186397\pi$
$684$	−14.3765	−0.549700
$685$	49.9512	1.90854
$686$	68.4687	2.61415
$687$	−2.18641	−0.0834168
$688$	18.1507	0.691989
$689$	−41.7123	−1.58911
$690$	25.7160	0.978992
$691$	−27.7254	−1.05473	−0.527363	−	0.849640i	$-0.676819\pi$
$691$	−27.7254	−1.05473	−0.527363	+	0.849640i	$0.676819\pi$
$692$	2.61590	0.0994414
$693$	22.5770	0.857631
$694$	58.8849	2.23524
$695$	−5.10602	−0.193682
$696$	−25.7417	−0.975737
$697$	7.22057	0.273499
$698$	−2.47358	−0.0936264
$699$	−19.0523	−0.720626
$700$	−116.418	−4.40018
$701$	−10.0631	−0.380078	−0.190039	−	0.981777i	$-0.560861\pi$
$701$	−10.0631	−0.380078	−0.190039	+	0.981777i	$0.560861\pi$
$702$	13.2598	0.500458
$703$	17.1241	0.645846
$704$	19.5939	0.738473
$705$	−31.3307	−1.17998
$706$	−14.4416	−0.543517
$707$	45.1477	1.69795
$708$	−0.360274	−0.0135399
$709$	5.67994	0.213315	0.106657	−	0.994296i	$-0.465985\pi$
$709$	5.67994	0.213315	0.106657	+	0.994296i	$0.465985\pi$
$710$	−140.220	−5.26238
$711$	−3.00405	−0.112661
$712$	−4.46410	−0.167299
$713$	−10.5698	−0.395841
$714$	13.7367	0.514084
$715$	−88.5874	−3.31298
$716$	12.6139	0.471405
$717$	−22.7840	−0.850883
$718$	−39.2639	−1.46531
$719$	−10.8660	−0.405232	−0.202616	−	0.979258i	$-0.564944\pi$
$719$	−10.8660	−0.405232	−0.202616	+	0.979258i	$0.564944\pi$
$720$	−19.2813	−0.718572
$721$	50.4214	1.87779
$722$	19.4275	0.723017
$723$	−15.1210	−0.562355
$724$	−110.317	−4.09989
$725$	27.2160	1.01078
$726$	−36.0257	−1.33704
$727$	−29.9243	−1.10983	−0.554916	−	0.831906i	$-0.687250\pi$
$727$	−29.9243	−1.10983	−0.554916	+	0.831906i	$0.687250\pi$
$728$	−135.872	−5.03574
$729$	1.00000	0.0370370
$730$	19.3688	0.716873
$731$	3.82656	0.141531
$732$	18.2216	0.673490
$733$	15.3480	0.566891	0.283446	−	0.958988i	$-0.408522\pi$
$733$	15.3480	0.566891	0.283446	+	0.958988i	$0.408522\pi$
$734$	7.50738	0.277102
$735$	−43.5403	−1.60601
$736$	−9.47886	−0.349395
$737$	−16.0226	−0.590200
$738$	−14.8108	−0.545194
$739$	−25.4412	−0.935868	−0.467934	−	0.883763i	$-0.655001\pi$
$739$	−25.4412	−0.935868	−0.467934	+	0.883763i	$0.655001\pi$
$740$	72.7662	2.67494
$741$	17.7399	0.651690
$742$	88.6376	3.25399
$743$	−3.03495	−0.111342	−0.0556708	−	0.998449i	$-0.517730\pi$
$743$	−3.03495	−0.111342	−0.0556708	+	0.998449i	$0.517730\pi$
$744$	19.6420	0.720109
$745$	−60.5646	−2.21892
$746$	−21.8746	−0.800885
$747$	17.5584	0.642428
$748$	−26.3866	−0.964790
$749$	19.2737	0.704247
$750$	8.83570	0.322634
$751$	41.3998	1.51070	0.755349	−	0.655322i	$-0.227467\pi$
$751$	41.3998	1.51070	0.755349	+	0.655322i	$0.227467\pi$
$752$	54.6214	1.99184
$753$	−25.3825	−0.924991
$754$	59.5538	2.16882
$755$	42.1389	1.53359
$756$	−19.2118	−0.698727
$757$	23.9321	0.869825	0.434913	−	0.900473i	$-0.356779\pi$
$757$	23.9321	0.869825	0.434913	+	0.900473i	$0.356779\pi$
$758$	95.3196	3.46216
$759$	−15.5345	−0.563865
$760$	−63.9347	−2.31916
$761$	53.5956	1.94284	0.971420	−	0.237367i	$-0.0762844\pi$
$761$	53.5956	1.94284	0.971420	+	0.237367i	$0.0762844\pi$
$762$	27.8200	1.00781
$763$	−90.8860	−3.29029
$764$	−26.2724	−0.950501
$765$	−4.06492	−0.146967
$766$	−80.0077	−2.89079
$767$	0.444559	0.0160521
$768$	−32.0842	−1.15774
$769$	−30.0047	−1.08200	−0.540998	−	0.841024i	$-0.681953\pi$
$769$	−30.0047	−1.08200	−0.540998	+	0.841024i	$0.681953\pi$
$770$	188.246	6.78392
$771$	14.7568	0.531455
$772$	47.1520	1.69704
$773$	53.0381	1.90765	0.953824	−	0.300366i	$-0.0971087\pi$
$773$	53.0381	1.90765	0.953824	+	0.300366i	$0.0971087\pi$
$774$	−7.84903	−0.282128
$775$	−20.7669	−0.745969
$776$	29.2711	1.05077
$777$	22.8834	0.820939
$778$	14.4518	0.518123
$779$	−19.8149	−0.709944
$780$	75.3830	2.69914
$781$	84.7039	3.03094
$782$	−9.45175	−0.337994
$783$	4.49131	0.160506
$784$	75.9074	2.71098
$785$	40.1392	1.43263
$786$	−10.4665	−0.373327
$787$	40.7143	1.45131	0.725653	−	0.688061i	$-0.241538\pi$
$787$	40.7143	1.45131	0.725653	+	0.688061i	$0.241538\pi$
$788$	24.3023	0.865733
$789$	9.53601	0.339491
$790$	−25.0476	−0.891154
$791$	−37.2975	−1.32615
$792$	28.8679	1.02578
$793$	−22.4845	−0.798448
$794$	−14.1277	−0.501374
$795$	−26.2293	−0.930257
$796$	105.244	3.73027
$797$	12.9773	0.459679	0.229839	−	0.973229i	$-0.426180\pi$
$797$	12.9773	0.459679	0.229839	+	0.973229i	$0.426180\pi$
$798$	−37.6968	−1.33445
$799$	11.5154	0.407385
$800$	−18.6235	−0.658442
$801$	0.778879	0.0275203
$802$	28.9578	1.02254
$803$	−11.7003	−0.412893
$804$	13.6343	0.480846
$805$	45.9761	1.62045
$806$	−45.4420	−1.60062
$807$	−21.6559	−0.762323
$808$	57.7276	2.03085
$809$	−30.3334	−1.06647	−0.533234	−	0.845968i	$-0.679023\pi$
$809$	−30.3334	−1.06647	−0.533234	+	0.845968i	$0.679023\pi$
$810$	8.33794	0.292965
$811$	−29.0472	−1.01999	−0.509993	−	0.860179i	$-0.670352\pi$
$811$	−29.0472	−1.01999	−0.509993	+	0.860179i	$0.670352\pi$
$812$	−86.2863	−3.02806
$813$	−1.95022	−0.0683971
$814$	−64.4680	−2.25960
$815$	−37.2854	−1.30605
$816$	7.08671	0.248084
$817$	−10.5010	−0.367383
$818$	−75.7175	−2.64740
$819$	23.7064	0.828368
$820$	−84.2007	−2.94042
$821$	11.6256	0.405736	0.202868	−	0.979206i	$-0.434974\pi$
$821$	11.6256	0.405736	0.202868	+	0.979206i	$0.434974\pi$
$822$	37.6584	1.31349
$823$	−38.2117	−1.33197	−0.665987	−	0.745963i	$-0.731990\pi$
$823$	−38.2117	−1.33197	−0.665987	+	0.745963i	$0.731990\pi$
$824$	64.4708	2.24595
$825$	−30.5212	−1.06261
$826$	−0.944677	−0.0328695
$827$	−3.13193	−0.108908	−0.0544540	−	0.998516i	$-0.517342\pi$
$827$	−3.13193	−0.108908	−0.0544540	+	0.998516i	$0.517342\pi$
$828$	13.2190	0.459391
$829$	18.5219	0.643291	0.321646	−	0.946860i	$-0.395764\pi$
$829$	18.5219	0.643291	0.321646	+	0.946860i	$0.395764\pi$
$830$	146.401	5.08165
$831$	−0.719711	−0.0249665
$832$	20.5740	0.713275
$833$	16.0029	0.554469
$834$	−3.84944	−0.133295
$835$	−16.0292	−0.554713
$836$	72.4110	2.50439
$837$	−3.42705	−0.118456
$838$	−81.3950	−2.81174
$839$	−32.6258	−1.12637	−0.563184	−	0.826332i	$-0.690424\pi$
$839$	−32.6258	−1.12637	−0.563184	+	0.826332i	$0.690424\pi$
$840$	−85.4382	−2.94790
$841$	−8.82811	−0.304418
$842$	−67.6773	−2.33231
$843$	−3.20822	−0.110497
$844$	59.0504	2.03260
$845$	−49.7857	−1.71268
$846$	−23.6203	−0.812083
$847$	−64.4081	−2.21309
$848$	45.7277	1.57030
$849$	13.7295	0.471194
$850$	−18.5703	−0.636955
$851$	−15.7453	−0.539741
$852$	−72.0783	−2.46936
$853$	−20.4311	−0.699548	−0.349774	−	0.936834i	$-0.613742\pi$
$853$	−20.4311	−0.699548	−0.349774	+	0.936834i	$0.613742\pi$
$854$	47.7790	1.63497
$855$	11.1551	0.381496
$856$	24.6442	0.842321
$857$	−45.0725	−1.53965	−0.769823	−	0.638258i	$-0.779655\pi$
$857$	−45.0725	−1.53965	−0.769823	+	0.638258i	$0.779655\pi$
$858$	−66.7863	−2.28005
$859$	−40.8181	−1.39270	−0.696348	−	0.717704i	$-0.745193\pi$
$859$	−40.8181	−1.39270	−0.696348	+	0.717704i	$0.745193\pi$
$860$	−44.6224	−1.52161
$861$	−26.4794	−0.902415
$862$	42.6811	1.45373
$863$	−2.33972	−0.0796451	−0.0398225	−	0.999207i	$-0.512679\pi$
$863$	−2.33972	−0.0796451	−0.0398225	+	0.999207i	$0.512679\pi$
$864$	−3.07334	−0.104557
$865$	−2.02974	−0.0690131
$866$	−66.4291	−2.25735
$867$	−15.5060	−0.526610
$868$	65.8399	2.23475
$869$	15.1307	0.513273
$870$	37.4483	1.26962
$871$	−16.8241	−0.570061
$872$	−116.210	−3.93538
$873$	−5.10710	−0.172849
$874$	25.9378	0.877359
$875$	15.7968	0.534030
$876$	9.95628	0.336392
$877$	−37.0476	−1.25101	−0.625505	−	0.780220i	$-0.715107\pi$
$877$	−37.0476	−1.25101	−0.625505	+	0.780220i	$0.715107\pi$
$878$	8.04627	0.271548
$879$	8.81548	0.297339
$880$	97.1153	3.27375
$881$	−29.7737	−1.00310	−0.501551	−	0.865128i	$-0.667237\pi$
$881$	−29.7737	−1.00310	−0.501551	+	0.865128i	$0.667237\pi$
$882$	−32.8252	−1.10528
$883$	−51.0653	−1.71849	−0.859243	−	0.511568i	$-0.829065\pi$
$883$	−51.0653	−1.71849	−0.859243	+	0.511568i	$0.829065\pi$
$884$	−27.7065	−0.931871
$885$	0.279545	0.00939680
$886$	−4.02114	−0.135093
$887$	−53.5828	−1.79914	−0.899568	−	0.436782i	$-0.856118\pi$
$887$	−53.5828	−1.79914	−0.899568	+	0.436782i	$0.856118\pi$
$888$	29.2597	0.981891
$889$	49.7377	1.66815
$890$	6.49424	0.217688
$891$	−5.03676	−0.168738
$892$	−52.5357	−1.75902
$893$	−31.6009	−1.05748
$894$	−45.6599	−1.52709
$895$	−9.78745	−0.327158
$896$	−71.2715	−2.38101
$897$	−16.3115	−0.544625
$898$	−73.1832	−2.44216
$899$	−15.3920	−0.513350
$900$	25.9719	0.865730
$901$	9.64040	0.321168
$902$	74.5985	2.48386
$903$	−14.0328	−0.466983
$904$	−47.6901	−1.58615
$905$	85.5973	2.84535
$906$	31.7687	1.05544
$907$	−1.72151	−0.0571617	−0.0285808	−	0.999591i	$-0.509099\pi$
$907$	−1.72151	−0.0571617	−0.0285808	+	0.999591i	$0.509099\pi$
$908$	−32.5161	−1.07909
$909$	−10.0721	−0.334070
$910$	197.662	6.55245
$911$	−35.9088	−1.18971	−0.594856	−	0.803832i	$-0.702791\pi$
$911$	−35.9088	−1.18971	−0.594856	+	0.803832i	$0.702791\pi$
$912$	−19.4476	−0.643974
$913$	−88.4373	−2.92685
$914$	−49.3504	−1.63237
$915$	−14.1386	−0.467407
$916$	−9.37097	−0.309625
$917$	−18.7124	−0.617938
$918$	−3.06455	−0.101145
$919$	−33.0629	−1.09064	−0.545322	−	0.838227i	$-0.683593\pi$
$919$	−33.0629	−1.09064	−0.545322	+	0.838227i	$0.683593\pi$
$920$	58.7869	1.93815
$921$	4.45929	0.146938
$922$	45.8274	1.50924
$923$	88.9409	2.92752
$924$	96.7653	3.18335
$925$	−30.9355	−1.01715
$926$	69.2985	2.27729
$927$	−11.2486	−0.369453
$928$	−13.8034	−0.453117
$929$	−29.8533	−0.979456	−0.489728	−	0.871875i	$-0.662904\pi$
$929$	−29.8533	−0.979456	−0.489728	+	0.871875i	$0.662904\pi$
$930$	−28.5746	−0.936997
$931$	−43.9158	−1.43928
$932$	−81.6584	−2.67481
$933$	7.86697	0.257553
$934$	60.5168	1.98017
$935$	20.4740	0.669572
$936$	30.3119	0.990776
$937$	−38.9771	−1.27333	−0.636663	−	0.771142i	$-0.719686\pi$
$937$	−38.9771	−1.27333	−0.636663	+	0.771142i	$0.719686\pi$
$938$	35.7507	1.16730
$939$	14.8203	0.483643
$940$	−134.283	−4.37984
$941$	54.2751	1.76932	0.884658	−	0.466240i	$-0.154392\pi$
$941$	54.2751	1.76932	0.884658	+	0.466240i	$0.154392\pi$
$942$	30.2611	0.985959
$943$	18.2195	0.593309
$944$	−0.487354	−0.0158620
$945$	14.9069	0.484922
$946$	39.5337	1.28535
$947$	40.5551	1.31786	0.658932	−	0.752203i	$-0.271009\pi$
$947$	40.5551	1.31786	0.658932	+	0.752203i	$0.271009\pi$
$948$	−12.8754	−0.418173
$949$	−12.2855	−0.398805
$950$	50.9612	1.65340
$951$	0.972499	0.0315354
$952$	31.4022	1.01775
$953$	−4.84595	−0.156976	−0.0784879	−	0.996915i	$-0.525009\pi$
$953$	−4.84595	−0.156976	−0.0784879	+	0.996915i	$0.525009\pi$
$954$	−19.7743	−0.640218
$955$	20.3853	0.659654
$956$	−97.6522	−3.15830
$957$	−22.6217	−0.731254
$958$	−95.3550	−3.08078
$959$	67.3272	2.17411
$960$	12.9372	0.417547
$961$	−19.2553	−0.621139
$962$	−67.6927	−2.18250
$963$	−4.29982	−0.138560
$964$	−64.8085	−2.08734
$965$	−36.5864	−1.17776
$966$	34.6616	1.11522
$967$	54.5887	1.75545	0.877727	−	0.479161i	$-0.159059\pi$
$967$	54.5887	1.75545	0.877727	+	0.479161i	$0.159059\pi$
$968$	−82.3548	−2.64698
$969$	−4.09997	−0.131710
$970$	−42.5827	−1.36725
$971$	−4.75861	−0.152711	−0.0763555	−	0.997081i	$-0.524328\pi$
$971$	−4.75861	−0.152711	−0.0763555	+	0.997081i	$0.524328\pi$
$972$	4.28600	0.137474
$973$	−6.88219	−0.220633
$974$	35.7576	1.14575
$975$	−32.0479	−1.02636
$976$	24.6490	0.788994
$977$	−29.3725	−0.939709	−0.469854	−	0.882744i	$-0.655694\pi$
$977$	−29.3725	−0.939709	−0.469854	+	0.882744i	$0.655694\pi$
$978$	−28.1096	−0.898846
$979$	−3.92302	−0.125380
$980$	−186.614	−5.96116
$981$	20.2759	0.647361
$982$	−17.9754	−0.573619
$983$	60.3984	1.92641	0.963205	−	0.268766i	$-0.0866158\pi$
$983$	60.3984	1.92641	0.963205	+	0.268766i	$0.0866158\pi$
$984$	−33.8576	−1.07934
$985$	−18.8567	−0.600825
$986$	−13.7639	−0.438331
$987$	−42.2293	−1.34417
$988$	76.0331	2.41894
$989$	9.65547	0.307026
$990$	−41.9962	−1.33473
$991$	−7.13915	−0.226783	−0.113391	−	0.993550i	$-0.536171\pi$
$991$	−7.13915	−0.226783	−0.113391	+	0.993550i	$0.536171\pi$
$992$	10.5325	0.334407
$993$	−23.7301	−0.753051
$994$	−188.997	−5.99463
$995$	−81.6612	−2.58883
$996$	75.2553	2.38456
$997$	−32.9630	−1.04395	−0.521974	−	0.852961i	$-0.674804\pi$
$997$	−32.9630	−1.04395	−0.521974	+	0.852961i	$0.674804\pi$
$998$	−93.9557	−2.97411
$999$	−5.10511	−0.161519

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8049.2.a.a.1.5	✓	95

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8049.2.a.a.1.5	✓	95	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 8049 = 3 \cdot 2683 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8049.a (trivial)

\(f(q)\)	\(=\)	\(q-2.50719 q^{2} +1.00000 q^{3} +4.28600 q^{4} -3.32561 q^{5} -2.50719 q^{6} -4.48246 q^{7} -5.73145 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.50719 q^{2} +1.00000 q^{3} +4.28600 q^{4} -3.32561 q^{5} -2.50719 q^{6} -4.48246 q^{7} -5.73145 q^{8} +1.00000 q^{9} +8.33794 q^{10} -5.03676 q^{11} +4.28600 q^{12} -5.28870 q^{13} +11.2384 q^{14} -3.32561 q^{15} +5.79782 q^{16} +1.22231 q^{17} -2.50719 q^{18} -3.35429 q^{19} -14.2536 q^{20} -4.48246 q^{21} +12.6281 q^{22} +3.08422 q^{23} -5.73145 q^{24} +6.05970 q^{25} +13.2598 q^{26} +1.00000 q^{27} -19.2118 q^{28} +4.49131 q^{29} +8.33794 q^{30} -3.42705 q^{31} -3.07334 q^{32} -5.03676 q^{33} -3.06455 q^{34} +14.9069 q^{35} +4.28600 q^{36} -5.10511 q^{37} +8.40985 q^{38} -5.28870 q^{39} +19.0606 q^{40} +5.90734 q^{41} +11.2384 q^{42} +3.13061 q^{43} -21.5876 q^{44} -3.32561 q^{45} -7.73272 q^{46} +9.42102 q^{47} +5.79782 q^{48} +13.0924 q^{49} -15.1928 q^{50} +1.22231 q^{51} -22.6674 q^{52} +7.88706 q^{53} -2.50719 q^{54} +16.7503 q^{55} +25.6910 q^{56} -3.35429 q^{57} -11.2606 q^{58} -0.0840582 q^{59} -14.2536 q^{60} +4.25142 q^{61} +8.59227 q^{62} -4.48246 q^{63} -3.89018 q^{64} +17.5882 q^{65} +12.6281 q^{66} +3.18113 q^{67} +5.23881 q^{68} +3.08422 q^{69} -37.3745 q^{70} -16.8171 q^{71} -5.73145 q^{72} +2.32298 q^{73} +12.7995 q^{74} +6.05970 q^{75} -14.3765 q^{76} +22.5770 q^{77} +13.2598 q^{78} -3.00405 q^{79} -19.2813 q^{80} +1.00000 q^{81} -14.8108 q^{82} +17.5584 q^{83} -19.2118 q^{84} -4.06492 q^{85} -7.84903 q^{86} +4.49131 q^{87} +28.8679 q^{88} +0.778879 q^{89} +8.33794 q^{90} +23.7064 q^{91} +13.2190 q^{92} -3.42705 q^{93} -23.6203 q^{94} +11.1551 q^{95} -3.07334 q^{96} -5.10710 q^{97} -32.8252 q^{98} -5.03676 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 95 q - 9 q^{2} + 95 q^{3} + 65 q^{4} - 15 q^{5} - 9 q^{6} - 36 q^{7} - 27 q^{8} + 95 q^{9}+O(q^{10}) \) 95 * q - 9 * q^2 + 95 * q^3 + 65 * q^4 - 15 * q^5 - 9 * q^6 - 36 * q^7 - 27 * q^8 + 95 * q^9	\( 95 q - 9 q^{2} + 95 q^{3} + 65 q^{4} - 15 q^{5} - 9 q^{6} - 36 q^{7} - 27 q^{8} + 95 q^{9} - 36 q^{10} - 48 q^{11} + 65 q^{12} - 73 q^{13} - 17 q^{14} - 15 q^{15} + 13 q^{16} - 9 q^{17} - 9 q^{18} - 66 q^{19} - 35 q^{20} - 36 q^{21} - 37 q^{22} - 58 q^{23} - 27 q^{24} + 24 q^{25} - 25 q^{26} + 95 q^{27} - 75 q^{28} - 31 q^{29} - 36 q^{30} - 129 q^{31} - 53 q^{32} - 48 q^{33} - 61 q^{34} - 38 q^{35} + 65 q^{36} - 127 q^{37} + q^{38} - 73 q^{39} - 74 q^{40} - 31 q^{41} - 17 q^{42} - 62 q^{43} - 76 q^{44} - 15 q^{45} - 60 q^{46} - 75 q^{47} + 13 q^{48} + 5 q^{49} - 30 q^{50} - 9 q^{51} - 137 q^{52} - 28 q^{53} - 9 q^{54} - 117 q^{55} - 23 q^{56} - 66 q^{57} - 90 q^{58} - 60 q^{59} - 35 q^{60} - 96 q^{61} + 10 q^{62} - 36 q^{63} - 75 q^{64} - 28 q^{65} - 37 q^{66} - 116 q^{67} + 3 q^{68} - 58 q^{69} - 73 q^{70} - 144 q^{71} - 27 q^{72} - 121 q^{73} - 16 q^{74} + 24 q^{75} - 118 q^{76} - 3 q^{77} - 25 q^{78} - 135 q^{79} - 36 q^{80} + 95 q^{81} - 102 q^{82} - 21 q^{83} - 75 q^{84} - 129 q^{85} - 46 q^{86} - 31 q^{87} - 77 q^{88} - 63 q^{89} - 36 q^{90} - 123 q^{91} - 42 q^{92} - 129 q^{93} - 44 q^{94} - 80 q^{95} - 53 q^{96} - 144 q^{97} + 10 q^{98} - 48 q^{99}+O(q^{100}) \) 95 * q - 9 * q^2 + 95 * q^3 + 65 * q^4 - 15 * q^5 - 9 * q^6 - 36 * q^7 - 27 * q^8 + 95 * q^9 - 36 * q^10 - 48 * q^11 + 65 * q^12 - 73 * q^13 - 17 * q^14 - 15 * q^15 + 13 * q^16 - 9 * q^17 - 9 * q^18 - 66 * q^19 - 35 * q^20 - 36 * q^21 - 37 * q^22 - 58 * q^23 - 27 * q^24 + 24 * q^25 - 25 * q^26 + 95 * q^27 - 75 * q^28 - 31 * q^29 - 36 * q^30 - 129 * q^31 - 53 * q^32 - 48 * q^33 - 61 * q^34 - 38 * q^35 + 65 * q^36 - 127 * q^37 + q^38 - 73 * q^39 - 74 * q^40 - 31 * q^41 - 17 * q^42 - 62 * q^43 - 76 * q^44 - 15 * q^45 - 60 * q^46 - 75 * q^47 + 13 * q^48 + 5 * q^49 - 30 * q^50 - 9 * q^51 - 137 * q^52 - 28 * q^53 - 9 * q^54 - 117 * q^55 - 23 * q^56 - 66 * q^57 - 90 * q^58 - 60 * q^59 - 35 * q^60 - 96 * q^61 + 10 * q^62 - 36 * q^63 - 75 * q^64 - 28 * q^65 - 37 * q^66 - 116 * q^67 + 3 * q^68 - 58 * q^69 - 73 * q^70 - 144 * q^71 - 27 * q^72 - 121 * q^73 - 16 * q^74 + 24 * q^75 - 118 * q^76 - 3 * q^77 - 25 * q^78 - 135 * q^79 - 36 * q^80 + 95 * q^81 - 102 * q^82 - 21 * q^83 - 75 * q^84 - 129 * q^85 - 46 * q^86 - 31 * q^87 - 77 * q^88 - 63 * q^89 - 36 * q^90 - 123 * q^91 - 42 * q^92 - 129 * q^93 - 44 * q^94 - 80 * q^95 - 53 * q^96 - 144 * q^97 + 10 * q^98 - 48 * q^99

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