LMFDB - Embedded newform 6005.2.a.e.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6005,2,Mod(1,6005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6005, 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("6005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6005 = 5 \cdot 1201 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6005.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:	$47.9501664138$
Analytic rank:	$1$
Dimension:	$88$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	6005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.21323 q^{2} -3.30657 q^{3} +2.89841 q^{4} +1.00000 q^{5} +7.31821 q^{6} -1.75850 q^{7} -1.98838 q^{8} +7.93340 q^{9} +O(q^{10})$	\(q-2.21323 q^{2} -3.30657 q^{3} +2.89841 q^{4} +1.00000 q^{5} +7.31821 q^{6} -1.75850 q^{7} -1.98838 q^{8} +7.93340 q^{9} -2.21323 q^{10} -1.41426 q^{11} -9.58378 q^{12} +6.37747 q^{13} +3.89197 q^{14} -3.30657 q^{15} -1.39606 q^{16} +5.66946 q^{17} -17.5585 q^{18} +3.56162 q^{19} +2.89841 q^{20} +5.81460 q^{21} +3.13008 q^{22} -4.98391 q^{23} +6.57472 q^{24} +1.00000 q^{25} -14.1148 q^{26} -16.3126 q^{27} -5.09684 q^{28} +4.39018 q^{29} +7.31821 q^{30} +8.18670 q^{31} +7.06656 q^{32} +4.67634 q^{33} -12.5478 q^{34} -1.75850 q^{35} +22.9942 q^{36} -5.92369 q^{37} -7.88270 q^{38} -21.0875 q^{39} -1.98838 q^{40} +4.90053 q^{41} -12.8691 q^{42} -9.26427 q^{43} -4.09909 q^{44} +7.93340 q^{45} +11.0306 q^{46} -0.752947 q^{47} +4.61616 q^{48} -3.90768 q^{49} -2.21323 q^{50} -18.7465 q^{51} +18.4845 q^{52} -5.63464 q^{53} +36.1037 q^{54} -1.41426 q^{55} +3.49657 q^{56} -11.7768 q^{57} -9.71649 q^{58} +3.28232 q^{59} -9.58378 q^{60} -11.0519 q^{61} -18.1191 q^{62} -13.9509 q^{63} -12.8478 q^{64} +6.37747 q^{65} -10.3498 q^{66} -4.25209 q^{67} +16.4324 q^{68} +16.4796 q^{69} +3.89197 q^{70} +7.64807 q^{71} -15.7746 q^{72} +3.27383 q^{73} +13.1105 q^{74} -3.30657 q^{75} +10.3230 q^{76} +2.48697 q^{77} +46.6716 q^{78} +15.0568 q^{79} -1.39606 q^{80} +30.1386 q^{81} -10.8460 q^{82} -17.3867 q^{83} +16.8531 q^{84} +5.66946 q^{85} +20.5040 q^{86} -14.5164 q^{87} +2.81208 q^{88} -8.34891 q^{89} -17.5585 q^{90} -11.2148 q^{91} -14.4454 q^{92} -27.0699 q^{93} +1.66645 q^{94} +3.56162 q^{95} -23.3661 q^{96} -19.2057 q^{97} +8.64861 q^{98} -11.2199 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 14 q^{2} - 34 q^{3} + 66 q^{4} + 88 q^{5} - q^{6} - 35 q^{7} - 39 q^{8} + 72 q^{9}+O(q^{10}) $ 88 * q - 14 * q^2 - 34 * q^3 + 66 * q^4 + 88 * q^5 - q^6 - 35 * q^7 - 39 * q^8 + 72 * q^9	\( 88 q - 14 q^{2} - 34 q^{3} + 66 q^{4} + 88 q^{5} - q^{6} - 35 q^{7} - 39 q^{8} + 72 q^{9} - 14 q^{10} - 26 q^{11} - 64 q^{12} - 31 q^{13} - 17 q^{14} - 34 q^{15} + 34 q^{16} - 31 q^{17} - 42 q^{18} - 56 q^{19} + 66 q^{20} - q^{21} - 49 q^{22} - 74 q^{23} - 3 q^{24} + 88 q^{25} - q^{26} - 130 q^{27} - 57 q^{28} - 6 q^{29} - q^{30} - 37 q^{31} - 87 q^{32} - 43 q^{33} - 35 q^{34} - 35 q^{35} + 53 q^{36} - 67 q^{37} - 40 q^{38} - 21 q^{39} - 39 q^{40} + 2 q^{41} - 15 q^{42} - 136 q^{43} - 15 q^{44} + 72 q^{45} - 16 q^{46} - 139 q^{47} - 71 q^{48} + 41 q^{49} - 14 q^{50} - 71 q^{51} - 71 q^{52} - 75 q^{53} + 26 q^{54} - 26 q^{55} - 22 q^{56} - 34 q^{57} - 65 q^{58} - 41 q^{59} - 64 q^{60} - 11 q^{61} - 30 q^{62} - 114 q^{63} - 33 q^{64} - 31 q^{65} + 24 q^{66} - 209 q^{67} - 42 q^{68} - 22 q^{69} - 17 q^{70} - 43 q^{71} - 80 q^{72} - 50 q^{73} + 9 q^{74} - 34 q^{75} - 62 q^{76} - 49 q^{77} - 19 q^{78} - 77 q^{79} + 34 q^{80} + 72 q^{81} - 107 q^{82} - 113 q^{83} + 19 q^{84} - 31 q^{85} + 14 q^{86} - 87 q^{87} - 107 q^{88} - 5 q^{89} - 42 q^{90} - 159 q^{91} - 100 q^{92} - 82 q^{93} - 31 q^{94} - 56 q^{95} + 58 q^{96} - 105 q^{97} - 29 q^{98} - 68 q^{99}+O(q^{100}) \) 88 * q - 14 * q^2 - 34 * q^3 + 66 * q^4 + 88 * q^5 - q^6 - 35 * q^7 - 39 * q^8 + 72 * q^9 - 14 * q^10 - 26 * q^11 - 64 * q^12 - 31 * q^13 - 17 * q^14 - 34 * q^15 + 34 * q^16 - 31 * q^17 - 42 * q^18 - 56 * q^19 + 66 * q^20 - q^21 - 49 * q^22 - 74 * q^23 - 3 * q^24 + 88 * q^25 - q^26 - 130 * q^27 - 57 * q^28 - 6 * q^29 - q^30 - 37 * q^31 - 87 * q^32 - 43 * q^33 - 35 * q^34 - 35 * q^35 + 53 * q^36 - 67 * q^37 - 40 * q^38 - 21 * q^39 - 39 * q^40 + 2 * q^41 - 15 * q^42 - 136 * q^43 - 15 * q^44 + 72 * q^45 - 16 * q^46 - 139 * q^47 - 71 * q^48 + 41 * q^49 - 14 * q^50 - 71 * q^51 - 71 * q^52 - 75 * q^53 + 26 * q^54 - 26 * q^55 - 22 * q^56 - 34 * q^57 - 65 * q^58 - 41 * q^59 - 64 * q^60 - 11 * q^61 - 30 * q^62 - 114 * q^63 - 33 * q^64 - 31 * q^65 + 24 * q^66 - 209 * q^67 - 42 * q^68 - 22 * q^69 - 17 * q^70 - 43 * q^71 - 80 * q^72 - 50 * q^73 + 9 * q^74 - 34 * q^75 - 62 * q^76 - 49 * q^77 - 19 * q^78 - 77 * q^79 + 34 * q^80 + 72 * q^81 - 107 * q^82 - 113 * q^83 + 19 * q^84 - 31 * q^85 + 14 * q^86 - 87 * q^87 - 107 * q^88 - 5 * q^89 - 42 * q^90 - 159 * q^91 - 100 * q^92 - 82 * q^93 - 31 * q^94 - 56 * q^95 + 58 * q^96 - 105 * q^97 - 29 * q^98 - 68 * 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 $

$2$	−2.21323	−1.56499	−0.782496	−	0.622655i	$-0.786054\pi$
$2$	−2.21323	−1.56499	−0.782496	+	0.622655i	$0.786054\pi$
$3$	−3.30657	−1.90905	−0.954524	−	0.298133i	$-0.903636\pi$
$3$	−3.30657	−1.90905	−0.954524	+	0.298133i	$0.903636\pi$
$4$	2.89841	1.44920
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	7.31821	2.98765
$7$	−1.75850	−0.664650	−0.332325	−	0.943165i	$-0.607833\pi$
$7$	−1.75850	−0.664650	−0.332325	+	0.943165i	$0.607833\pi$
$8$	−1.98838	−0.702999
$9$	7.93340	2.64447
$10$	−2.21323	−0.699886
$11$	−1.41426	−0.426415	−0.213207	−	0.977007i	$-0.568391\pi$
$11$	−1.41426	−0.426415	−0.213207	+	0.977007i	$0.568391\pi$
$12$	−9.58378	−2.76660
$13$	6.37747	1.76879	0.884395	−	0.466739i	$-0.154571\pi$
$13$	6.37747	1.76879	0.884395	+	0.466739i	$0.154571\pi$
$14$	3.89197	1.04017
$15$	−3.30657	−0.853753
$16$	−1.39606	−0.349014
$17$	5.66946	1.37505	0.687523	−	0.726163i	$-0.258698\pi$
$17$	5.66946	1.37505	0.687523	+	0.726163i	$0.258698\pi$
$18$	−17.5585	−4.13857
$19$	3.56162	0.817092	0.408546	−	0.912738i	$-0.366036\pi$
$19$	3.56162	0.817092	0.408546	+	0.912738i	$0.366036\pi$
$20$	2.89841	0.648103
$21$	5.81460	1.26885
$22$	3.13008	0.667336
$23$	−4.98391	−1.03922	−0.519608	−	0.854405i	$-0.673922\pi$
$23$	−4.98391	−1.03922	−0.519608	+	0.854405i	$0.673922\pi$
$24$	6.57472	1.34206
$25$	1.00000	0.200000
$26$	−14.1148	−2.76814
$27$	−16.3126	−3.13937
$28$	−5.09684	−0.963213
$29$	4.39018	0.815236	0.407618	−	0.913153i	$-0.366360\pi$
$29$	4.39018	0.815236	0.407618	+	0.913153i	$0.366360\pi$
$30$	7.31821	1.33612
$31$	8.18670	1.47038	0.735188	−	0.677864i	$-0.237094\pi$
$31$	8.18670	1.47038	0.735188	+	0.677864i	$0.237094\pi$
$32$	7.06656	1.24920
$33$	4.67634	0.814047
$34$	−12.5478	−2.15194
$35$	−1.75850	−0.297241
$36$	22.9942	3.83237
$37$	−5.92369	−0.973848	−0.486924	−	0.873444i	$-0.661881\pi$
$37$	−5.92369	−0.973848	−0.486924	+	0.873444i	$0.661881\pi$
$38$	−7.88270	−1.27874
$39$	−21.0875	−3.37671
$40$	−1.98838	−0.314391
$41$	4.90053	0.765335	0.382667	−	0.923886i	$-0.375006\pi$
$41$	4.90053	0.765335	0.382667	+	0.923886i	$0.375006\pi$
$42$	−12.8691	−1.98574
$43$	−9.26427	−1.41279	−0.706394	−	0.707819i	$-0.749679\pi$
$43$	−9.26427	−1.41279	−0.706394	+	0.707819i	$0.749679\pi$
$44$	−4.09909	−0.617962
$45$	7.93340	1.18264
$46$	11.0306	1.62637
$47$	−0.752947	−0.109829	−0.0549143	−	0.998491i	$-0.517489\pi$
$47$	−0.752947	−0.109829	−0.0549143	+	0.998491i	$0.517489\pi$
$48$	4.61616	0.666285
$49$	−3.90768	−0.558240
$50$	−2.21323	−0.312999
$51$	−18.7465	−2.62503
$52$	18.4845	2.56334
$53$	−5.63464	−0.773977	−0.386988	−	0.922085i	$-0.626485\pi$
$53$	−5.63464	−0.773977	−0.386988	+	0.922085i	$0.626485\pi$
$54$	36.1037	4.91309
$55$	−1.41426	−0.190698
$56$	3.49657	0.467249
$57$	−11.7768	−1.55987
$58$	−9.71649	−1.27584
$59$	3.28232	0.427322	0.213661	−	0.976908i	$-0.431461\pi$
$59$	3.28232	0.427322	0.213661	+	0.976908i	$0.431461\pi$
$60$	−9.58378	−1.23726
$61$	−11.0519	−1.41505	−0.707527	−	0.706686i	$-0.750189\pi$
$61$	−11.0519	−1.41505	−0.707527	+	0.706686i	$0.750189\pi$
$62$	−18.1191	−2.30113
$63$	−13.9509	−1.75765
$64$	−12.8478	−1.60598
$65$	6.37747	0.791027
$66$	−10.3498	−1.27398
$67$	−4.25209	−0.519475	−0.259738	−	0.965679i	$-0.583636\pi$
$67$	−4.25209	−0.519475	−0.259738	+	0.965679i	$0.583636\pi$
$68$	16.4324	1.99272
$69$	16.4796	1.98391
$70$	3.89197	0.465180
$71$	7.64807	0.907659	0.453829	−	0.891089i	$-0.350058\pi$
$71$	7.64807	0.907659	0.453829	+	0.891089i	$0.350058\pi$
$72$	−15.7746	−1.85906
$73$	3.27383	0.383173	0.191587	−	0.981476i	$-0.438637\pi$
$73$	3.27383	0.383173	0.191587	+	0.981476i	$0.438637\pi$
$74$	13.1105	1.52407
$75$	−3.30657	−0.381810
$76$	10.3230	1.18413
$77$	2.48697	0.283417
$78$	46.6716	5.28452
$79$	15.0568	1.69403	0.847014	−	0.531571i	$-0.178398\pi$
$79$	15.0568	1.69403	0.847014	+	0.531571i	$0.178398\pi$
$80$	−1.39606	−0.156084
$81$	30.1386	3.34874
$82$	−10.8460	−1.19774
$83$	−17.3867	−1.90844	−0.954222	−	0.299100i	$-0.903314\pi$
$83$	−17.3867	−1.90844	−0.954222	+	0.299100i	$0.903314\pi$
$84$	16.8531	1.83882
$85$	5.66946	0.614939
$86$	20.5040	2.21100
$87$	−14.5164	−1.55632
$88$	2.81208	0.299769
$89$	−8.34891	−0.884982	−0.442491	−	0.896773i	$-0.645905\pi$
$89$	−8.34891	−0.884982	−0.442491	+	0.896773i	$0.645905\pi$
$90$	−17.5585	−1.85083
$91$	−11.2148	−1.17563
$92$	−14.4454	−1.50604
$93$	−27.0699	−2.80702
$94$	1.66645	0.171881
$95$	3.56162	0.365415
$96$	−23.3661	−2.38479
$97$	−19.2057	−1.95005	−0.975024	−	0.222100i	$-0.928709\pi$
$97$	−19.2057	−1.95005	−0.975024	+	0.222100i	$0.928709\pi$
$98$	8.64861	0.873642
$99$	−11.2199	−1.12764
$100$	2.89841	0.289841
$101$	−12.4981	−1.24361	−0.621804	−	0.783173i	$-0.713600\pi$
$101$	−12.4981	−1.24361	−0.621804	+	0.783173i	$0.713600\pi$
$102$	41.4903	4.10815
$103$	−14.6960	−1.44804	−0.724020	−	0.689779i	$-0.757707\pi$
$103$	−14.6960	−1.44804	−0.724020	+	0.689779i	$0.757707\pi$
$104$	−12.6808	−1.24346
$105$	5.81460	0.567447
$106$	12.4708	1.21127
$107$	2.99789	0.289817	0.144909	−	0.989445i	$-0.453711\pi$
$107$	2.99789	0.289817	0.144909	+	0.989445i	$0.453711\pi$
$108$	−47.2806	−4.54958
$109$	−18.0284	−1.72681	−0.863403	−	0.504514i	$-0.831672\pi$
$109$	−18.0284	−1.72681	−0.863403	+	0.504514i	$0.831672\pi$
$110$	3.13008	0.298442
$111$	19.5871	1.85912
$112$	2.45496	0.231972
$113$	−8.87769	−0.835142	−0.417571	−	0.908644i	$-0.637119\pi$
$113$	−8.87769	−0.835142	−0.417571	+	0.908644i	$0.637119\pi$
$114$	26.0647	2.44118
$115$	−4.98391	−0.464752
$116$	12.7245	1.18144
$117$	50.5950	4.67751
$118$	−7.26455	−0.668756
$119$	−9.96974	−0.913925
$120$	6.57472	0.600187
$121$	−8.99987	−0.818170
$122$	24.4605	2.21455
$123$	−16.2040	−1.46106
$124$	23.7284	2.13087
$125$	1.00000	0.0894427
$126$	30.8766	2.75070
$127$	6.59658	0.585352	0.292676	−	0.956212i	$-0.405454\pi$
$127$	6.59658	0.585352	0.292676	+	0.956212i	$0.405454\pi$
$128$	14.3022	1.26414
$129$	30.6329	2.69708
$130$	−14.1148	−1.23795
$131$	−5.76425	−0.503625	−0.251813	−	0.967776i	$-0.581027\pi$
$131$	−5.76425	−0.503625	−0.251813	+	0.967776i	$0.581027\pi$
$132$	13.5539	1.17972
$133$	−6.26311	−0.543081
$134$	9.41086	0.812975
$135$	−16.3126	−1.40397
$136$	−11.2731	−0.966656
$137$	15.9338	1.36131	0.680657	−	0.732602i	$-0.261694\pi$
$137$	15.9338	1.36131	0.680657	+	0.732602i	$0.261694\pi$
$138$	−36.4733	−3.10481
$139$	−7.86966	−0.667496	−0.333748	−	0.942662i	$-0.608313\pi$
$139$	−7.86966	−0.667496	−0.333748	+	0.942662i	$0.608313\pi$
$140$	−5.09684	−0.430762
$141$	2.48967	0.209668
$142$	−16.9270	−1.42048
$143$	−9.01938	−0.754239
$144$	−11.0755	−0.922956
$145$	4.39018	0.364584
$146$	−7.24576	−0.599663
$147$	12.9210	1.06571
$148$	−17.1693	−1.41130
$149$	−0.985931	−0.0807706	−0.0403853	−	0.999184i	$-0.512859\pi$
$149$	−0.985931	−0.0807706	−0.0403853	+	0.999184i	$0.512859\pi$
$150$	7.31821	0.597530
$151$	−1.66557	−0.135542	−0.0677712	−	0.997701i	$-0.521589\pi$
$151$	−1.66557	−0.135542	−0.0677712	+	0.997701i	$0.521589\pi$
$152$	−7.08186	−0.574415
$153$	44.9781	3.63626
$154$	−5.50425	−0.443545
$155$	8.18670	0.657572
$156$	−61.1202	−4.89353
$157$	4.38148	0.349681	0.174840	−	0.984597i	$-0.444059\pi$
$157$	4.38148	0.349681	0.174840	+	0.984597i	$0.444059\pi$
$158$	−33.3243	−2.65114
$159$	18.6313	1.47756
$160$	7.06656	0.558661
$161$	8.76420	0.690716
$162$	−66.7039	−5.24075
$163$	15.2070	1.19111	0.595553	−	0.803316i	$-0.296933\pi$
$163$	15.2070	1.19111	0.595553	+	0.803316i	$0.296933\pi$
$164$	14.2037	1.10913
$165$	4.67634	0.364053
$166$	38.4809	2.98670
$167$	−12.1629	−0.941192	−0.470596	−	0.882349i	$-0.655961\pi$
$167$	−12.1629	−0.941192	−0.470596	+	0.882349i	$0.655961\pi$
$168$	−11.5616	−0.892000
$169$	27.6721	2.12862
$170$	−12.5478	−0.962376
$171$	28.2558	2.16077
$172$	−26.8516	−2.04742
$173$	13.3700	1.01651	0.508253	−	0.861208i	$-0.330292\pi$
$173$	13.3700	1.01651	0.508253	+	0.861208i	$0.330292\pi$
$174$	32.1283	2.43564
$175$	−1.75850	−0.132930
$176$	1.97438	0.148825
$177$	−10.8532	−0.815778
$178$	18.4781	1.38499
$179$	−14.3501	−1.07258	−0.536290	−	0.844034i	$-0.680175\pi$
$179$	−14.3501	−1.07258	−0.536290	+	0.844034i	$0.680175\pi$
$180$	22.9942	1.71389
$181$	6.35877	0.472644	0.236322	−	0.971675i	$-0.424058\pi$
$181$	6.35877	0.472644	0.236322	+	0.971675i	$0.424058\pi$
$182$	24.8209	1.83985
$183$	36.5440	2.70141
$184$	9.90991	0.730568
$185$	−5.92369	−0.435518
$186$	59.9120	4.39296
$187$	−8.01808	−0.586340
$188$	−2.18235	−0.159164
$189$	28.6858	2.08658
$190$	−7.88270	−0.571871
$191$	13.1222	0.949488	0.474744	−	0.880124i	$-0.342541\pi$
$191$	13.1222	0.949488	0.474744	+	0.880124i	$0.342541\pi$
$192$	42.4823	3.06590
$193$	17.6345	1.26936	0.634678	−	0.772777i	$-0.281133\pi$
$193$	17.6345	1.26936	0.634678	+	0.772777i	$0.281133\pi$
$194$	42.5068	3.05181
$195$	−21.0875	−1.51011
$196$	−11.3260	−0.809003
$197$	7.05391	0.502570	0.251285	−	0.967913i	$-0.419147\pi$
$197$	7.05391	0.502570	0.251285	+	0.967913i	$0.419147\pi$
$198$	24.8322	1.76475
$199$	−2.85062	−0.202075	−0.101037	−	0.994883i	$-0.532216\pi$
$199$	−2.85062	−0.202075	−0.101037	+	0.994883i	$0.532216\pi$
$200$	−1.98838	−0.140600
$201$	14.0598	0.991703
$202$	27.6612	1.94624
$203$	−7.72013	−0.541847
$204$	−54.3349	−3.80420
$205$	4.90053	0.342268
$206$	32.5257	2.26617
$207$	−39.5393	−2.74817
$208$	−8.90330	−0.617333
$209$	−5.03705	−0.348420
$210$	−12.8691	−0.888050
$211$	−11.0620	−0.761537	−0.380769	−	0.924670i	$-0.624341\pi$
$211$	−11.0620	−0.761537	−0.380769	+	0.924670i	$0.624341\pi$
$212$	−16.3315	−1.12165
$213$	−25.2889	−1.73276
$214$	−6.63504	−0.453562
$215$	−9.26427	−0.631818
$216$	32.4357	2.20697
$217$	−14.3963	−0.977286
$218$	39.9011	2.70244
$219$	−10.8252	−0.731496
$220$	−4.09909	−0.276361
$221$	36.1568	2.43217
$222$	−43.3508	−2.90952
$223$	−7.19544	−0.481842	−0.240921	−	0.970545i	$-0.577450\pi$
$223$	−7.19544	−0.481842	−0.240921	+	0.970545i	$0.577450\pi$
$224$	−12.4265	−0.830284
$225$	7.93340	0.528893
$226$	19.6484	1.30699
$227$	2.11977	0.140694	0.0703471	−	0.997523i	$-0.477589\pi$
$227$	2.11977	0.140694	0.0703471	+	0.997523i	$0.477589\pi$
$228$	−34.1338	−2.26057
$229$	3.58754	0.237071	0.118536	−	0.992950i	$-0.462180\pi$
$229$	3.58754	0.237071	0.118536	+	0.992950i	$0.462180\pi$
$230$	11.0306	0.727333
$231$	−8.22334	−0.541056
$232$	−8.72935	−0.573110
$233$	−14.2110	−0.930996	−0.465498	−	0.885049i	$-0.654125\pi$
$233$	−14.2110	−0.930996	−0.465498	+	0.885049i	$0.654125\pi$
$234$	−111.979	−7.32027
$235$	−0.752947	−0.0491169
$236$	9.51350	0.619276
$237$	−49.7865	−3.23398
$238$	22.0654	1.43029
$239$	−9.65240	−0.624362	−0.312181	−	0.950023i	$-0.601060\pi$
$239$	−9.65240	−0.624362	−0.312181	+	0.950023i	$0.601060\pi$
$240$	4.61616	0.297972
$241$	−17.1502	−1.10474	−0.552369	−	0.833600i	$-0.686276\pi$
$241$	−17.1502	−1.10474	−0.552369	+	0.833600i	$0.686276\pi$
$242$	19.9188	1.28043
$243$	−50.7176	−3.25354
$244$	−32.0330	−2.05070
$245$	−3.90768	−0.249652
$246$	35.8631	2.28655
$247$	22.7141	1.44526
$248$	−16.2783	−1.03367
$249$	57.4905	3.64331
$250$	−2.21323	−0.139977
$251$	3.37939	0.213305	0.106653	−	0.994296i	$-0.465987\pi$
$251$	3.37939	0.213305	0.106653	+	0.994296i	$0.465987\pi$
$252$	−40.4353	−2.54719
$253$	7.04853	0.443137
$254$	−14.5998	−0.916071
$255$	−18.7465	−1.17395
$256$	−5.95835	−0.372397
$257$	19.4592	1.21383	0.606916	−	0.794766i	$-0.292406\pi$
$257$	19.4592	1.21383	0.606916	+	0.794766i	$0.292406\pi$
$258$	−67.7979	−4.22091
$259$	10.4168	0.647269
$260$	18.4845	1.14636
$261$	34.8290	2.15586
$262$	12.7576	0.788170
$263$	−11.8290	−0.729407	−0.364704	−	0.931124i	$-0.618830\pi$
$263$	−11.8290	−0.729407	−0.364704	+	0.931124i	$0.618830\pi$
$264$	−9.29835	−0.572274
$265$	−5.63464	−0.346133
$266$	13.8617	0.849917
$267$	27.6062	1.68947
$268$	−12.3243	−0.752825
$269$	3.58178	0.218385	0.109193	−	0.994021i	$-0.465173\pi$
$269$	3.58178	0.218385	0.109193	+	0.994021i	$0.465173\pi$
$270$	36.1037	2.19720
$271$	−30.8656	−1.87495	−0.937475	−	0.348053i	$-0.886843\pi$
$271$	−30.8656	−1.87495	−0.937475	+	0.348053i	$0.886843\pi$
$272$	−7.91489	−0.479911
$273$	37.0824	2.24433
$274$	−35.2652	−2.13045
$275$	−1.41426	−0.0852830
$276$	47.7647	2.87510
$277$	10.4875	0.630132	0.315066	−	0.949070i	$-0.397973\pi$
$277$	10.4875	0.630132	0.315066	+	0.949070i	$0.397973\pi$
$278$	17.4174	1.04463
$279$	64.9484	3.88836
$280$	3.49657	0.208960
$281$	28.6662	1.71008	0.855042	−	0.518559i	$-0.173531\pi$
$281$	28.6662	1.71008	0.855042	+	0.518559i	$0.173531\pi$
$282$	−5.51023	−0.328129
$283$	−7.62727	−0.453394	−0.226697	−	0.973965i	$-0.572793\pi$
$283$	−7.62727	−0.453394	−0.226697	+	0.973965i	$0.572793\pi$
$284$	22.1672	1.31538
$285$	−11.7768	−0.697594
$286$	19.9620	1.18038
$287$	−8.61759	−0.508680
$288$	56.0619	3.30348
$289$	15.1428	0.890752
$290$	−9.71649	−0.570572
$291$	63.5051	3.72274
$292$	9.48890	0.555296
$293$	18.3935	1.07456	0.537279	−	0.843405i	$-0.319452\pi$
$293$	18.3935	1.07456	0.537279	+	0.843405i	$0.319452\pi$
$294$	−28.5972	−1.66782
$295$	3.28232	0.191104
$296$	11.7786	0.684615
$297$	23.0703	1.33867
$298$	2.18210	0.126405
$299$	−31.7847	−1.83816
$300$	−9.58378	−0.553320
$301$	16.2912	0.939010
$302$	3.68630	0.212123
$303$	41.3259	2.37411
$304$	−4.97223	−0.285177
$305$	−11.0519	−0.632832
$306$	−99.5471	−5.69073
$307$	−28.3885	−1.62022	−0.810108	−	0.586281i	$-0.800591\pi$
$307$	−28.3885	−1.62022	−0.810108	+	0.586281i	$0.800591\pi$
$308$	7.20825	0.410728
$309$	48.5933	2.76438
$310$	−18.1191	−1.02910
$311$	−23.5820	−1.33721	−0.668606	−	0.743616i	$-0.733109\pi$
$311$	−23.5820	−1.33721	−0.668606	+	0.743616i	$0.733109\pi$
$312$	41.9301	2.37382
$313$	15.1001	0.853508	0.426754	−	0.904368i	$-0.359657\pi$
$313$	15.1001	0.853508	0.426754	+	0.904368i	$0.359657\pi$
$314$	−9.69725	−0.547248
$315$	−13.9509	−0.786043
$316$	43.6408	2.45499
$317$	−13.1733	−0.739887	−0.369944	−	0.929054i	$-0.620623\pi$
$317$	−13.1733	−0.739887	−0.369944	+	0.929054i	$0.620623\pi$
$318$	−41.2355	−2.31237
$319$	−6.20884	−0.347629
$320$	−12.8478	−0.718216
$321$	−9.91274	−0.553275
$322$	−19.3972	−1.08097
$323$	20.1925	1.12354
$324$	87.3540	4.85300
$325$	6.37747	0.353758
$326$	−33.6567	−1.86407
$327$	59.6121	3.29656
$328$	−9.74413	−0.538030
$329$	1.32406	0.0729977
$330$	−10.3498	−0.569740
$331$	17.8972	0.983719	0.491859	−	0.870675i	$-0.336317\pi$
$331$	17.8972	0.983719	0.491859	+	0.870675i	$0.336317\pi$
$332$	−50.3939	−2.76572
$333$	−46.9950	−2.57531
$334$	26.9193	1.47296
$335$	−4.25209	−0.232316
$336$	−8.11751	−0.442847
$337$	−24.8081	−1.35138	−0.675691	−	0.737185i	$-0.736154\pi$
$337$	−24.8081	−1.35138	−0.675691	+	0.737185i	$0.736154\pi$
$338$	−61.2448	−3.33128
$339$	29.3547	1.59433
$340$	16.4324	0.891172
$341$	−11.5781	−0.626990
$342$	−62.5366	−3.38159
$343$	19.1811	1.03568
$344$	18.4209	0.993188
$345$	16.4796	0.887234
$346$	−29.5910	−1.59082
$347$	19.6964	1.05736	0.528679	−	0.848822i	$-0.322688\pi$
$347$	19.6964	1.05736	0.528679	+	0.848822i	$0.322688\pi$
$348$	−42.0745	−2.25543
$349$	−12.4834	−0.668222	−0.334111	−	0.942534i	$-0.608436\pi$
$349$	−12.4834	−0.668222	−0.334111	+	0.942534i	$0.608436\pi$
$350$	3.89197	0.208035
$351$	−104.033	−5.55288
$352$	−9.99394	−0.532679
$353$	22.4562	1.19522	0.597612	−	0.801786i	$-0.296116\pi$
$353$	22.4562	1.19522	0.597612	+	0.801786i	$0.296116\pi$
$354$	24.0207	1.27669
$355$	7.64807	0.405917
$356$	−24.1985	−1.28252
$357$	32.9656	1.74473
$358$	31.7602	1.67858
$359$	−30.1873	−1.59323	−0.796614	−	0.604489i	$-0.793377\pi$
$359$	−30.1873	−1.59323	−0.796614	+	0.604489i	$0.793377\pi$
$360$	−15.7746	−0.831396
$361$	−6.31485	−0.332360
$362$	−14.0734	−0.739684
$363$	29.7587	1.56193
$364$	−32.5050	−1.70372
$365$	3.27383	0.171360
$366$	−80.8804	−4.22768
$367$	−6.67536	−0.348451	−0.174226	−	0.984706i	$-0.555742\pi$
$367$	−6.67536	−0.348451	−0.174226	+	0.984706i	$0.555742\pi$
$368$	6.95782	0.362701
$369$	38.8779	2.02390
$370$	13.1105	0.681583
$371$	9.90850	0.514424
$372$	−78.4596	−4.06794
$373$	13.7500	0.711948	0.355974	−	0.934496i	$-0.384149\pi$
$373$	13.7500	0.711948	0.355974	+	0.934496i	$0.384149\pi$
$374$	17.7459	0.917618
$375$	−3.30657	−0.170751
$376$	1.49715	0.0772095
$377$	27.9982	1.44198
$378$	−63.4883	−3.26549
$379$	−25.9804	−1.33452	−0.667262	−	0.744824i	$-0.732534\pi$
$379$	−25.9804	−1.33452	−0.667262	+	0.744824i	$0.732534\pi$
$380$	10.3230	0.529560
$381$	−21.8120	−1.11746
$382$	−29.0425	−1.48594
$383$	−16.7450	−0.855631	−0.427815	−	0.903866i	$-0.640717\pi$
$383$	−16.7450	−0.855631	−0.427815	+	0.903866i	$0.640717\pi$
$384$	−47.2911	−2.41331
$385$	2.48697	0.126748
$386$	−39.0292	−1.98653
$387$	−73.4971	−3.73607
$388$	−55.6660	−2.82601
$389$	9.99885	0.506962	0.253481	−	0.967340i	$-0.418425\pi$
$389$	9.99885	0.506962	0.253481	+	0.967340i	$0.418425\pi$
$390$	46.6716	2.36331
$391$	−28.2561	−1.42897
$392$	7.76996	0.392442
$393$	19.0599	0.961445
$394$	−15.6119	−0.786518
$395$	15.0568	0.757592
$396$	−32.5197	−1.63418
$397$	−27.5823	−1.38432	−0.692159	−	0.721746i	$-0.743340\pi$
$397$	−27.5823	−1.38432	−0.692159	+	0.721746i	$0.743340\pi$
$398$	6.30908	0.316246
$399$	20.7094	1.03677
$400$	−1.39606	−0.0698028
$401$	−17.0172	−0.849798	−0.424899	−	0.905241i	$-0.639690\pi$
$401$	−17.0172	−0.849798	−0.424899	+	0.905241i	$0.639690\pi$
$402$	−31.1177	−1.55201
$403$	52.2104	2.60079
$404$	−36.2246	−1.80224
$405$	30.1386	1.49760
$406$	17.0864	0.847986
$407$	8.37762	0.415263
$408$	37.2751	1.84539
$409$	0.672432	0.0332496	0.0166248	−	0.999862i	$-0.494708\pi$
$409$	0.672432	0.0332496	0.0166248	+	0.999862i	$0.494708\pi$
$410$	−10.8460	−0.535647
$411$	−52.6862	−2.59882
$412$	−42.5949	−2.09850
$413$	−5.77196	−0.284020
$414$	87.5098	4.30087
$415$	−17.3867	−0.853482
$416$	45.0668	2.20958
$417$	26.0216	1.27428
$418$	11.1482	0.545275
$419$	13.5291	0.660941	0.330470	−	0.943816i	$-0.392793\pi$
$419$	13.5291	0.660941	0.330470	+	0.943816i	$0.392793\pi$
$420$	16.8531	0.822346
$421$	−37.4882	−1.82706	−0.913532	−	0.406766i	$-0.866656\pi$
$421$	−37.4882	−1.82706	−0.913532	+	0.406766i	$0.866656\pi$
$422$	24.4827	1.19180
$423$	−5.97343	−0.290438
$424$	11.2038	0.544105
$425$	5.66946	0.275009
$426$	55.9702	2.71176
$427$	19.4348	0.940516
$428$	8.68911	0.420004
$429$	29.8232	1.43988
$430$	20.5040	0.988790
$431$	−14.4354	−0.695330	−0.347665	−	0.937619i	$-0.613025\pi$
$431$	−14.4354	−0.695330	−0.347665	+	0.937619i	$0.613025\pi$
$432$	22.7734	1.09568
$433$	−16.0558	−0.771593	−0.385796	−	0.922584i	$-0.626073\pi$
$433$	−16.0558	−0.771593	−0.385796	+	0.922584i	$0.626073\pi$
$434$	31.8624	1.52944
$435$	−14.5164	−0.696009
$436$	−52.2536	−2.50249
$437$	−17.7508	−0.849136
$438$	23.9586	1.14479
$439$	32.1758	1.53567	0.767833	−	0.640650i	$-0.221335\pi$
$439$	32.1758	1.53567	0.767833	+	0.640650i	$0.221335\pi$
$440$	2.81208	0.134061
$441$	−31.0012	−1.47625
$442$	−80.0234	−3.80633
$443$	−1.60687	−0.0763446	−0.0381723	−	0.999271i	$-0.512154\pi$
$443$	−1.60687	−0.0763446	−0.0381723	+	0.999271i	$0.512154\pi$
$444$	56.7713	2.69425
$445$	−8.34891	−0.395776
$446$	15.9252	0.754080
$447$	3.26005	0.154195
$448$	22.5929	1.06742
$449$	−6.64889	−0.313781	−0.156890	−	0.987616i	$-0.550147\pi$
$449$	−6.64889	−0.313781	−0.156890	+	0.987616i	$0.550147\pi$
$450$	−17.5585	−0.827714
$451$	−6.93062	−0.326350
$452$	−25.7311	−1.21029
$453$	5.50733	0.258757
$454$	−4.69155	−0.220185
$455$	−11.2148	−0.525757
$456$	23.4167	1.09659
$457$	−13.5646	−0.634524	−0.317262	−	0.948338i	$-0.602763\pi$
$457$	−13.5646	−0.634524	−0.317262	+	0.948338i	$0.602763\pi$
$458$	−7.94007	−0.371015
$459$	−92.4838	−4.31677
$460$	−14.4454	−0.673520
$461$	5.14324	0.239544	0.119772	−	0.992801i	$-0.461784\pi$
$461$	5.14324	0.239544	0.119772	+	0.992801i	$0.461784\pi$
$462$	18.2002	0.846749
$463$	−7.06479	−0.328329	−0.164164	−	0.986433i	$-0.552493\pi$
$463$	−7.06479	−0.328329	−0.164164	+	0.986433i	$0.552493\pi$
$464$	−6.12894	−0.284529
$465$	−27.0699	−1.25534
$466$	31.4523	1.45700
$467$	−20.3291	−0.940716	−0.470358	−	0.882476i	$-0.655875\pi$
$467$	−20.3291	−0.940716	−0.470358	+	0.882476i	$0.655875\pi$
$468$	146.645	6.77866
$469$	7.47729	0.345269
$470$	1.66645	0.0768676
$471$	−14.4877	−0.667557
$472$	−6.52651	−0.300407
$473$	13.1021	0.602433
$474$	110.189	5.06116
$475$	3.56162	0.163418
$476$	−28.8964	−1.32446
$477$	−44.7018	−2.04676
$478$	21.3630	0.977122
$479$	25.0546	1.14477	0.572387	−	0.819984i	$-0.306018\pi$
$479$	25.0546	1.14477	0.572387	+	0.819984i	$0.306018\pi$
$480$	−23.3661	−1.06651
$481$	−37.7781	−1.72253
$482$	37.9573	1.72891
$483$	−28.9794	−1.31861
$484$	−26.0853	−1.18569
$485$	−19.2057	−0.872088
$486$	112.250	5.09176
$487$	11.8732	0.538024	0.269012	−	0.963137i	$-0.413303\pi$
$487$	11.8732	0.538024	0.269012	+	0.963137i	$0.413303\pi$
$488$	21.9755	0.994782
$489$	−50.2831	−2.27388
$490$	8.64861	0.390704
$491$	−0.788457	−0.0355826	−0.0177913	−	0.999842i	$-0.505663\pi$
$491$	−0.788457	−0.0355826	−0.0177913	+	0.999842i	$0.505663\pi$
$492$	−46.9656	−2.11737
$493$	24.8899	1.12099
$494$	−50.2717	−2.26183
$495$	−11.2199	−0.504296
$496$	−11.4291	−0.513182
$497$	−13.4491	−0.603276
$498$	−127.240	−5.70176
$499$	30.7816	1.37797	0.688986	−	0.724775i	$-0.258056\pi$
$499$	30.7816	1.37797	0.688986	+	0.724775i	$0.258056\pi$
$500$	2.89841	0.129621
$501$	40.2174	1.79678
$502$	−7.47939	−0.333821
$503$	12.6963	0.566098	0.283049	−	0.959105i	$-0.408654\pi$
$503$	12.6963	0.566098	0.283049	+	0.959105i	$0.408654\pi$
$504$	27.7397	1.23562
$505$	−12.4981	−0.556158
$506$	−15.6000	−0.693507
$507$	−91.4996	−4.06364
$508$	19.1196	0.848293
$509$	−27.6214	−1.22430	−0.612148	−	0.790743i	$-0.709694\pi$
$509$	−27.6214	−1.22430	−0.612148	+	0.790743i	$0.709694\pi$
$510$	41.4903	1.83722
$511$	−5.75703	−0.254676
$512$	−15.4171	−0.681346
$513$	−58.0994	−2.56515
$514$	−43.0678	−1.89964
$515$	−14.6960	−0.647583
$516$	88.7867	3.90862
$517$	1.06486	0.0468326
$518$	−23.0548	−1.01297
$519$	−44.2090	−1.94056
$520$	−12.6808	−0.556091
$521$	30.1040	1.31888	0.659441	−	0.751756i	$-0.270793\pi$
$521$	30.1040	1.31888	0.659441	+	0.751756i	$0.270793\pi$
$522$	−77.0848	−3.37391
$523$	1.20578	0.0527250	0.0263625	−	0.999652i	$-0.491608\pi$
$523$	1.20578	0.0527250	0.0263625	+	0.999652i	$0.491608\pi$
$524$	−16.7071	−0.729855
$525$	5.81460	0.253770
$526$	26.1803	1.14152
$527$	46.4142	2.02183
$528$	−6.52844	−0.284114
$529$	1.83933	0.0799710
$530$	12.4708	0.541696
$531$	26.0400	1.13004
$532$	−18.1530	−0.787034
$533$	31.2530	1.35372
$534$	−61.0991	−2.64402
$535$	2.99789	0.129610
$536$	8.45477	0.365190
$537$	47.4497	2.04761
$538$	−7.92732	−0.341771
$539$	5.52647	0.238042
$540$	−47.2806	−2.03463
$541$	−31.1045	−1.33728	−0.668642	−	0.743584i	$-0.733124\pi$
$541$	−31.1045	−1.33728	−0.668642	+	0.743584i	$0.733124\pi$
$542$	68.3127	2.93428
$543$	−21.0257	−0.902300
$544$	40.0636	1.71771
$545$	−18.0284	−0.772251
$546$	−82.0721	−3.51236
$547$	−16.8140	−0.718915	−0.359458	−	0.933161i	$-0.617038\pi$
$547$	−16.8140	−0.718915	−0.359458	+	0.933161i	$0.617038\pi$
$548$	46.1826	1.97282
$549$	−87.6794	−3.74206
$550$	3.13008	0.133467
$551$	15.6362	0.666123
$552$	−32.7678	−1.39469
$553$	−26.4774	−1.12594
$554$	−23.2113	−0.986152
$555$	19.5871	0.831426
$556$	−22.8095	−0.967337
$557$	6.61948	0.280476	0.140238	−	0.990118i	$-0.455213\pi$
$557$	6.61948	0.280476	0.140238	+	0.990118i	$0.455213\pi$
$558$	−143.746	−6.08525
$559$	−59.0825	−2.49893
$560$	2.45496	0.103741
$561$	26.5123	1.11935
$562$	−63.4451	−2.67627
$563$	24.4468	1.03031	0.515155	−	0.857097i	$-0.327734\pi$
$563$	24.4468	1.03031	0.515155	+	0.857097i	$0.327734\pi$
$564$	7.21608	0.303852
$565$	−8.87769	−0.373487
$566$	16.8809	0.709559
$567$	−52.9988	−2.22574
$568$	−15.2073	−0.638083
$569$	−21.7949	−0.913691	−0.456846	−	0.889546i	$-0.651021\pi$
$569$	−21.7949	−0.913691	−0.456846	+	0.889546i	$0.651021\pi$
$570$	26.0647	1.09173
$571$	25.6516	1.07349	0.536743	−	0.843746i	$-0.319655\pi$
$571$	25.6516	1.07349	0.536743	+	0.843746i	$0.319655\pi$
$572$	−26.1418	−1.09304
$573$	−43.3894	−1.81262
$574$	19.0727	0.796081
$575$	−4.98391	−0.207843
$576$	−101.927	−4.24696
$577$	−41.8920	−1.74399	−0.871994	−	0.489517i	$-0.837173\pi$
$577$	−41.8920	−1.74399	−0.871994	+	0.489517i	$0.837173\pi$
$578$	−33.5145	−1.39402
$579$	−58.3096	−2.42326
$580$	12.7245	0.528357
$581$	30.5746	1.26845
$582$	−140.552	−5.82605
$583$	7.96883	0.330035
$584$	−6.50963	−0.269370
$585$	50.5950	2.09185
$586$	−40.7091	−1.68168
$587$	18.8402	0.777619	0.388810	−	0.921318i	$-0.372886\pi$
$587$	18.8402	0.777619	0.388810	+	0.921318i	$0.372886\pi$
$588$	37.4503	1.54443
$589$	29.1579	1.20143
$590$	−7.26455	−0.299077
$591$	−23.3242	−0.959431
$592$	8.26980	0.339887
$593$	−14.0499	−0.576961	−0.288480	−	0.957486i	$-0.593150\pi$
$593$	−14.0499	−0.576961	−0.288480	+	0.957486i	$0.593150\pi$
$594$	−51.0599	−2.09501
$595$	−9.96974	−0.408720
$596$	−2.85763	−0.117053
$597$	9.42576	0.385771
$598$	70.3470	2.87670
$599$	38.7788	1.58446	0.792229	−	0.610224i	$-0.208921\pi$
$599$	38.7788	1.58446	0.792229	+	0.610224i	$0.208921\pi$
$600$	6.57472	0.268412
$601$	12.9244	0.527198	0.263599	−	0.964632i	$-0.415090\pi$
$601$	12.9244	0.527198	0.263599	+	0.964632i	$0.415090\pi$
$602$	−36.0563	−1.46954
$603$	−33.7335	−1.37373
$604$	−4.82751	−0.196428
$605$	−8.99987	−0.365897
$606$	−91.4638	−3.71546
$607$	−27.1158	−1.10060	−0.550298	−	0.834969i	$-0.685486\pi$
$607$	−27.1158	−1.10060	−0.550298	+	0.834969i	$0.685486\pi$
$608$	25.1684	1.02071
$609$	25.5271	1.03441
$610$	24.4605	0.990377
$611$	−4.80190	−0.194264
$612$	130.365	5.26968
$613$	−14.4932	−0.585376	−0.292688	−	0.956208i	$-0.594550\pi$
$613$	−14.4932	−0.585376	−0.292688	+	0.956208i	$0.594550\pi$
$614$	62.8303	2.53563
$615$	−16.2040	−0.653406
$616$	−4.94505	−0.199242
$617$	−48.9862	−1.97211	−0.986056	−	0.166413i	$-0.946781\pi$
$617$	−48.9862	−1.97211	−0.986056	+	0.166413i	$0.946781\pi$
$618$	−107.548	−4.32623
$619$	−17.0116	−0.683755	−0.341877	−	0.939745i	$-0.611063\pi$
$619$	−17.0116	−0.683755	−0.341877	+	0.939745i	$0.611063\pi$
$620$	23.7284	0.952955
$621$	81.3006	3.26248
$622$	52.1925	2.09273
$623$	14.6815	0.588204
$624$	29.4394	1.17852
$625$	1.00000	0.0400000
$626$	−33.4200	−1.33573
$627$	16.6554	0.665151
$628$	12.6993	0.506758
$629$	−33.5841	−1.33909
$630$	30.8766	1.23015
$631$	−17.3368	−0.690167	−0.345084	−	0.938572i	$-0.612149\pi$
$631$	−17.3368	−0.690167	−0.345084	+	0.938572i	$0.612149\pi$
$632$	−29.9387	−1.19090
$633$	36.5772	1.45381
$634$	29.1556	1.15792
$635$	6.59658	0.261777
$636$	54.0011	2.14128
$637$	−24.9211	−0.987410
$638$	13.7416	0.544036
$639$	60.6752	2.40027
$640$	14.3022	0.565343
$641$	−27.1103	−1.07079	−0.535396	−	0.844601i	$-0.679837\pi$
$641$	−27.1103	−1.07079	−0.535396	+	0.844601i	$0.679837\pi$
$642$	21.9392	0.865872
$643$	11.6770	0.460498	0.230249	−	0.973132i	$-0.426046\pi$
$643$	11.6770	0.460498	0.230249	+	0.973132i	$0.426046\pi$
$644$	25.4022	1.00099
$645$	30.6329	1.20617
$646$	−44.6907	−1.75833
$647$	11.4300	0.449360	0.224680	−	0.974433i	$-0.427866\pi$
$647$	11.4300	0.449360	0.224680	+	0.974433i	$0.427866\pi$
$648$	−59.9271	−2.35416
$649$	−4.64205	−0.182216
$650$	−14.1148	−0.553629
$651$	47.6024	1.86569
$652$	44.0762	1.72616
$653$	25.9529	1.01562	0.507808	−	0.861470i	$-0.330456\pi$
$653$	25.9529	1.01562	0.507808	+	0.861470i	$0.330456\pi$
$654$	−131.936	−5.15909
$655$	−5.76425	−0.225228
$656$	−6.84142	−0.267113
$657$	25.9726	1.01329
$658$	−2.93045	−0.114241
$659$	−34.3043	−1.33630	−0.668152	−	0.744024i	$-0.732915\pi$
$659$	−34.3043	−1.33630	−0.668152	+	0.744024i	$0.732915\pi$
$660$	13.5539	0.527586
$661$	−8.07834	−0.314211	−0.157105	−	0.987582i	$-0.550216\pi$
$661$	−8.07834	−0.314211	−0.157105	+	0.987582i	$0.550216\pi$
$662$	−39.6107	−1.53951
$663$	−119.555	−4.64313
$664$	34.5715	1.34163
$665$	−6.26311	−0.242873
$666$	104.011	4.03034
$667$	−21.8802	−0.847206
$668$	−35.2530	−1.36398
$669$	23.7922	0.919861
$670$	9.41086	0.363573
$671$	15.6303	0.603400
$672$	41.0892	1.58505
$673$	22.8377	0.880327	0.440163	−	0.897918i	$-0.354920\pi$
$673$	22.8377	0.880327	0.440163	+	0.897918i	$0.354920\pi$
$674$	54.9060	2.11490
$675$	−16.3126	−0.627873
$676$	80.2049	3.08480
$677$	−4.77156	−0.183386	−0.0916931	−	0.995787i	$-0.529228\pi$
$677$	−4.77156	−0.183386	−0.0916931	+	0.995787i	$0.529228\pi$
$678$	−64.9688	−2.49511
$679$	33.7733	1.29610
$680$	−11.2731	−0.432302
$681$	−7.00917	−0.268592
$682$	25.6251	0.981235
$683$	13.4433	0.514393	0.257197	−	0.966359i	$-0.417201\pi$
$683$	13.4433	0.514393	0.257197	+	0.966359i	$0.417201\pi$
$684$	81.8967	3.13140
$685$	15.9338	0.608799
$686$	−42.4524	−1.62084
$687$	−11.8625	−0.452581
$688$	12.9334	0.493083
$689$	−35.9347	−1.36900
$690$	−36.4733	−1.38851
$691$	44.1211	1.67845	0.839224	−	0.543786i	$-0.183010\pi$
$691$	44.1211	1.67845	0.839224	+	0.543786i	$0.183010\pi$
$692$	38.7518	1.47312
$693$	19.7301	0.749486
$694$	−43.5927	−1.65476
$695$	−7.86966	−0.298513
$696$	28.8642	1.09409
$697$	27.7834	1.05237
$698$	27.6287	1.04576
$699$	46.9898	1.77732
$700$	−5.09684	−0.192643
$701$	−8.77431	−0.331401	−0.165701	−	0.986176i	$-0.552989\pi$
$701$	−8.77431	−0.331401	−0.165701	+	0.986176i	$0.552989\pi$
$702$	230.250	8.69022
$703$	−21.0979	−0.795724
$704$	18.1702	0.684814
$705$	2.48967	0.0937665
$706$	−49.7008	−1.87052
$707$	21.9779	0.826565
$708$	−31.4570	−1.18223
$709$	−46.4474	−1.74437	−0.872184	−	0.489179i	$-0.837297\pi$
$709$	−46.4474	−1.74437	−0.872184	+	0.489179i	$0.837297\pi$
$710$	−16.9270	−0.635258
$711$	119.452	4.47980
$712$	16.6008	0.622142
$713$	−40.8018	−1.52804
$714$	−72.9607	−2.73049
$715$	−9.01938	−0.337306
$716$	−41.5925	−1.55439
$717$	31.9163	1.19194
$718$	66.8117	2.49339
$719$	−17.0092	−0.634334	−0.317167	−	0.948370i	$-0.602732\pi$
$719$	−17.0092	−0.634334	−0.317167	+	0.948370i	$0.602732\pi$
$720$	−11.0755	−0.412759
$721$	25.8429	0.962440
$722$	13.9762	0.520142
$723$	56.7082	2.10900
$724$	18.4303	0.684956
$725$	4.39018	0.163047
$726$	−65.8630	−2.44440
$727$	−2.35940	−0.0875054	−0.0437527	−	0.999042i	$-0.513931\pi$
$727$	−2.35940	−0.0875054	−0.0437527	+	0.999042i	$0.513931\pi$
$728$	22.2992	0.826465
$729$	77.2854	2.86242
$730$	−7.24576	−0.268178
$731$	−52.5234	−1.94265
$732$	105.919	3.91489
$733$	−2.67642	−0.0988560	−0.0494280	−	0.998778i	$-0.515740\pi$
$733$	−2.67642	−0.0988560	−0.0494280	+	0.998778i	$0.515740\pi$
$734$	14.7741	0.545323
$735$	12.9210	0.476599
$736$	−35.2191	−1.29819
$737$	6.01355	0.221512
$738$	−86.0459	−3.16739
$739$	−39.0062	−1.43487	−0.717433	−	0.696627i	$-0.754683\pi$
$739$	−39.0062	−1.43487	−0.717433	+	0.696627i	$0.754683\pi$
$740$	−17.1693	−0.631154
$741$	−75.1058	−2.75908
$742$	−21.9298	−0.805070
$743$	−7.91776	−0.290474	−0.145237	−	0.989397i	$-0.546395\pi$
$743$	−7.91776	−0.290474	−0.145237	+	0.989397i	$0.546395\pi$
$744$	53.8253	1.97333
$745$	−0.985931	−0.0361217
$746$	−30.4320	−1.11419
$747$	−137.936	−5.04682
$748$	−23.2396	−0.849726
$749$	−5.27179	−0.192627
$750$	7.31821	0.267223
$751$	−24.6760	−0.900441	−0.450220	−	0.892918i	$-0.648655\pi$
$751$	−24.6760	−0.900441	−0.450220	+	0.892918i	$0.648655\pi$
$752$	1.05116	0.0383318
$753$	−11.1742	−0.407210
$754$	−61.9666	−2.25669
$755$	−1.66557	−0.0606164
$756$	83.1429	3.02388
$757$	−31.7681	−1.15463	−0.577315	−	0.816521i	$-0.695900\pi$
$757$	−31.7681	−1.15463	−0.577315	+	0.816521i	$0.695900\pi$
$758$	57.5007	2.08852
$759$	−23.3065	−0.845971
$760$	−7.08186	−0.256886
$761$	−19.6610	−0.712711	−0.356356	−	0.934350i	$-0.615981\pi$
$761$	−19.6610	−0.712711	−0.356356	+	0.934350i	$0.615981\pi$
$762$	48.2752	1.74882
$763$	31.7029	1.14772
$764$	38.0334	1.37600
$765$	44.9781	1.62619
$766$	37.0607	1.33906
$767$	20.9329	0.755843
$768$	19.7017	0.710924
$769$	−16.6797	−0.601484	−0.300742	−	0.953706i	$-0.597234\pi$
$769$	−16.6797	−0.601484	−0.300742	+	0.953706i	$0.597234\pi$
$770$	−5.50425	−0.198359
$771$	−64.3432	−2.31726
$772$	51.1118	1.83955
$773$	37.5716	1.35135	0.675677	−	0.737197i	$-0.263851\pi$
$773$	37.5716	1.35135	0.675677	+	0.737197i	$0.263851\pi$
$774$	162.666	5.84692
$775$	8.18670	0.294075
$776$	38.1883	1.37088
$777$	−34.4439	−1.23567
$778$	−22.1298	−0.793391
$779$	17.4538	0.625349
$780$	−61.1202	−2.18845
$781$	−10.8163	−0.387039
$782$	62.5373	2.23633
$783$	−71.6153	−2.55932
$784$	5.45534	0.194834
$785$	4.38148	0.156382
$786$	−42.1840	−1.50465
$787$	26.2070	0.934179	0.467090	−	0.884210i	$-0.345303\pi$
$787$	26.2070	0.934179	0.467090	+	0.884210i	$0.345303\pi$
$788$	20.4451	0.728326
$789$	39.1134	1.39247
$790$	−33.3243	−1.18563
$791$	15.6114	0.555078
$792$	22.3094	0.792730
$793$	−70.4833	−2.50294
$794$	61.0461	2.16645
$795$	18.6313	0.660785
$796$	−8.26224	−0.292847
$797$	−13.5027	−0.478290	−0.239145	−	0.970984i	$-0.576867\pi$
$797$	−13.5027	−0.478290	−0.239145	+	0.970984i	$0.576867\pi$
$798$	−45.8348	−1.62253
$799$	−4.26881	−0.151019
$800$	7.06656	0.249841
$801$	−66.2352	−2.34031
$802$	37.6630	1.32993
$803$	−4.63004	−0.163391
$804$	40.7511	1.43718
$805$	8.76420	0.308897
$806$	−115.554	−4.07021
$807$	−11.8434	−0.416908
$808$	24.8510	0.874255
$809$	51.5901	1.81381	0.906905	−	0.421334i	$-0.138438\pi$
$809$	51.5901	1.81381	0.906905	+	0.421334i	$0.138438\pi$
$810$	−66.7039	−2.34374
$811$	0.458462	0.0160988	0.00804939	−	0.999968i	$-0.497438\pi$
$811$	0.458462	0.0160988	0.00804939	+	0.999968i	$0.497438\pi$
$812$	−22.3761	−0.785246
$813$	102.059	3.57937
$814$	−18.5416	−0.649884
$815$	15.2070	0.532679
$816$	26.1711	0.916173
$817$	−32.9958	−1.15438
$818$	−1.48825	−0.0520354
$819$	−88.9713	−3.10891
$820$	14.2037	0.496016
$821$	5.44952	0.190189	0.0950947	−	0.995468i	$-0.469685\pi$
$821$	5.44952	0.190189	0.0950947	+	0.995468i	$0.469685\pi$
$822$	116.607	4.06713
$823$	45.6465	1.59114	0.795568	−	0.605865i	$-0.207173\pi$
$823$	45.6465	1.59114	0.795568	+	0.605865i	$0.207173\pi$
$824$	29.2212	1.01797
$825$	4.67634	0.162809
$826$	12.7747	0.444489
$827$	−40.1101	−1.39477	−0.697383	−	0.716698i	$-0.745652\pi$
$827$	−40.1101	−1.39477	−0.697383	+	0.716698i	$0.745652\pi$
$828$	−114.601	−3.98266
$829$	−21.4879	−0.746307	−0.373153	−	0.927770i	$-0.621724\pi$
$829$	−21.4879	−0.746307	−0.373153	+	0.927770i	$0.621724\pi$
$830$	38.4809	1.33569
$831$	−34.6776	−1.20295
$832$	−81.9367	−2.84064
$833$	−22.1544	−0.767606
$834$	−57.5919	−1.99424
$835$	−12.1629	−0.420914
$836$	−14.5994	−0.504931
$837$	−133.547	−4.61605
$838$	−29.9431	−1.03437
$839$	51.9675	1.79412	0.897059	−	0.441912i	$-0.145700\pi$
$839$	51.9675	1.79412	0.897059	+	0.441912i	$0.145700\pi$
$840$	−11.5616	−0.398915
$841$	−9.72634	−0.335391
$842$	82.9702	2.85934
$843$	−94.7868	−3.26463
$844$	−32.0621	−1.10362
$845$	27.6721	0.951948
$846$	13.2206	0.454534
$847$	15.8263	0.543797
$848$	7.86627	0.270129
$849$	25.2201	0.865552
$850$	−12.5478	−0.430387
$851$	29.5231	1.01204
$852$	−73.2974	−2.51113
$853$	−25.4040	−0.869816	−0.434908	−	0.900475i	$-0.643219\pi$
$853$	−25.4040	−0.869816	−0.434908	+	0.900475i	$0.643219\pi$
$854$	−43.0138	−1.47190
$855$	28.2558	0.966327
$856$	−5.96096	−0.203741
$857$	17.2590	0.589557	0.294778	−	0.955566i	$-0.404754\pi$
$857$	17.2590	0.589557	0.294778	+	0.955566i	$0.404754\pi$
$858$	−66.0057	−2.25340
$859$	−14.4909	−0.494424	−0.247212	−	0.968961i	$-0.579514\pi$
$859$	−14.4909	−0.494424	−0.247212	+	0.968961i	$0.579514\pi$
$860$	−26.8516	−0.915632
$861$	28.4946	0.971095
$862$	31.9490	1.08819
$863$	47.1849	1.60619	0.803097	−	0.595848i	$-0.203184\pi$
$863$	47.1849	1.60619	0.803097	+	0.595848i	$0.203184\pi$
$864$	−115.274	−3.92171
$865$	13.3700	0.454595
$866$	35.5353	1.20754
$867$	−50.0707	−1.70049
$868$	−41.7264	−1.41628
$869$	−21.2943	−0.722358
$870$	32.1283	1.08925
$871$	−27.1175	−0.918843
$872$	35.8473	1.21394
$873$	−152.367	−5.15684
$874$	39.2867	1.32889
$875$	−1.75850	−0.0594481
$876$	−31.3757	−1.06009
$877$	−7.23788	−0.244406	−0.122203	−	0.992505i	$-0.538996\pi$
$877$	−7.23788	−0.244406	−0.122203	+	0.992505i	$0.538996\pi$
$878$	−71.2126	−2.40331
$879$	−60.8193	−2.05138
$880$	1.97438	0.0665565
$881$	22.3412	0.752694	0.376347	−	0.926479i	$-0.377180\pi$
$881$	22.3412	0.752694	0.376347	+	0.926479i	$0.377180\pi$
$882$	68.6129	2.31032
$883$	50.8611	1.71161	0.855807	−	0.517296i	$-0.173061\pi$
$883$	50.8611	1.71161	0.855807	+	0.517296i	$0.173061\pi$
$884$	104.797	3.52471
$885$	−10.8532	−0.364827
$886$	3.55638	0.119479
$887$	−2.96240	−0.0994678	−0.0497339	−	0.998763i	$-0.515837\pi$
$887$	−2.96240	−0.0994678	−0.0497339	+	0.998763i	$0.515837\pi$
$888$	−38.9466	−1.30696
$889$	−11.6001	−0.389054
$890$	18.4781	0.619387
$891$	−42.6238	−1.42795
$892$	−20.8553	−0.698287
$893$	−2.68171	−0.0897401
$894$	−7.21525	−0.241314
$895$	−14.3501	−0.479672
$896$	−25.1504	−0.840214
$897$	105.098	3.50913
$898$	14.7156	0.491065
$899$	35.9411	1.19870
$900$	22.9942	0.766474
$901$	−31.9453	−1.06425
$902$	15.3391	0.510736
$903$	−53.8680	−1.79262
$904$	17.6522	0.587104
$905$	6.35877	0.211373
$906$	−12.1890	−0.404953
$907$	10.5716	0.351023	0.175512	−	0.984477i	$-0.443842\pi$
$907$	10.5716	0.351023	0.175512	+	0.984477i	$0.443842\pi$
$908$	6.14396	0.203894
$909$	−99.1525	−3.28868
$910$	24.8209	0.822805
$911$	24.0762	0.797679	0.398840	−	0.917021i	$-0.369413\pi$
$911$	24.0762	0.797679	0.398840	+	0.917021i	$0.369413\pi$
$912$	16.4410	0.544416
$913$	24.5893	0.813789
$914$	30.0216	0.993025
$915$	36.5440	1.20811
$916$	10.3982	0.343565
$917$	10.1364	0.334735
$918$	204.688	6.75572
$919$	−41.6721	−1.37463	−0.687317	−	0.726357i	$-0.741212\pi$
$919$	−41.6721	−1.37463	−0.687317	+	0.726357i	$0.741212\pi$
$920$	9.90991	0.326720
$921$	93.8684	3.09307
$922$	−11.3832	−0.374885
$923$	48.7753	1.60546
$924$	−23.8346	−0.784100
$925$	−5.92369	−0.194770
$926$	15.6360	0.513832
$927$	−116.589	−3.82929
$928$	31.0235	1.01840
$929$	19.7462	0.647851	0.323926	−	0.946083i	$-0.394997\pi$
$929$	19.7462	0.647851	0.323926	+	0.946083i	$0.394997\pi$
$930$	59.9120	1.96459
$931$	−13.9177	−0.456133
$932$	−41.1893	−1.34920
$933$	77.9755	2.55280
$934$	44.9930	1.47221
$935$	−8.01808	−0.262219
$936$	−100.602	−3.28828
$937$	50.8359	1.66074	0.830368	−	0.557216i	$-0.188130\pi$
$937$	50.8359	1.66074	0.830368	+	0.557216i	$0.188130\pi$
$938$	−16.5490	−0.540344
$939$	−49.9295	−1.62939
$940$	−2.18235	−0.0711803
$941$	9.53341	0.310780	0.155390	−	0.987853i	$-0.450337\pi$
$941$	9.53341	0.310780	0.155390	+	0.987853i	$0.450337\pi$
$942$	32.0646	1.04472
$943$	−24.4238	−0.795348
$944$	−4.58231	−0.149141
$945$	28.6858	0.933148
$946$	−28.9979	−0.942804
$947$	51.4667	1.67244	0.836222	−	0.548391i	$-0.184759\pi$
$947$	51.4667	1.67244	0.836222	+	0.548391i	$0.184759\pi$
$948$	−144.301	−4.68669
$949$	20.8788	0.677753
$950$	−7.88270	−0.255749
$951$	43.5585	1.41248
$952$	19.8237	0.642488
$953$	17.8156	0.577105	0.288553	−	0.957464i	$-0.406826\pi$
$953$	17.8156	0.577105	0.288553	+	0.957464i	$0.406826\pi$
$954$	98.9356	3.20316
$955$	13.1222	0.424624
$956$	−27.9766	−0.904827
$957$	20.5300	0.663640
$958$	−55.4517	−1.79156
$959$	−28.0195	−0.904798
$960$	42.4823	1.37111
$961$	36.0221	1.16200
$962$	83.6118	2.69575
$963$	23.7835	0.766412
$964$	−49.7081	−1.60099
$965$	17.6345	0.567673
$966$	64.1383	2.06361
$967$	7.35619	0.236559	0.118280	−	0.992980i	$-0.462262\pi$
$967$	7.35619	0.236559	0.118280	+	0.992980i	$0.462262\pi$
$968$	17.8952	0.575173
$969$	−66.7678	−2.14489
$970$	42.5068	1.36481
$971$	15.7621	0.505829	0.252915	−	0.967489i	$-0.418611\pi$
$971$	15.7621	0.505829	0.252915	+	0.967489i	$0.418611\pi$
$972$	−147.000	−4.71503
$973$	13.8388	0.443651
$974$	−26.2781	−0.842004
$975$	−21.0875	−0.675341
$976$	15.4291	0.493874
$977$	−1.55023	−0.0495964	−0.0247982	−	0.999692i	$-0.507894\pi$
$977$	−1.55023	−0.0495964	−0.0247982	+	0.999692i	$0.507894\pi$
$978$	111.288	3.55861
$979$	11.8075	0.377370
$980$	−11.3260	−0.361797
$981$	−143.026	−4.56648
$982$	1.74504	0.0556865
$983$	−26.6716	−0.850693	−0.425346	−	0.905031i	$-0.639848\pi$
$983$	−26.6716	−0.850693	−0.425346	+	0.905031i	$0.639848\pi$
$984$	32.2196	1.02712
$985$	7.05391	0.224756
$986$	−55.0873	−1.75434
$987$	−4.37809	−0.139356
$988$	65.8347	2.09448
$989$	46.1722	1.46819
$990$	24.8322	0.789219
$991$	29.8067	0.946842	0.473421	−	0.880836i	$-0.343019\pi$
$991$	29.8067	0.946842	0.473421	+	0.880836i	$0.343019\pi$
$992$	57.8519	1.83680
$993$	−59.1783	−1.87797
$994$	29.7661	0.944122
$995$	−2.85062	−0.0903706
$996$	166.631	5.27990
$997$	−36.1045	−1.14344	−0.571720	−	0.820449i	$-0.693724\pi$
$997$	−36.1045	−1.14344	−0.571720	+	0.820449i	$0.693724\pi$
$998$	−68.1268	−2.15652
$999$	96.6310	3.05727

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6005.2.a.e.1.13	✓	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6005.2.a.e.1.13	✓	88	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:	\( N \)	\(=\)	\( 6005 = 5 \cdot 1201 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.21323 q^{2} -3.30657 q^{3} +2.89841 q^{4} +1.00000 q^{5} +7.31821 q^{6} -1.75850 q^{7} -1.98838 q^{8} +7.93340 q^{9} +O(q^{10})\)	\(q-2.21323 q^{2} -3.30657 q^{3} +2.89841 q^{4} +1.00000 q^{5} +7.31821 q^{6} -1.75850 q^{7} -1.98838 q^{8} +7.93340 q^{9} -2.21323 q^{10} -1.41426 q^{11} -9.58378 q^{12} +6.37747 q^{13} +3.89197 q^{14} -3.30657 q^{15} -1.39606 q^{16} +5.66946 q^{17} -17.5585 q^{18} +3.56162 q^{19} +2.89841 q^{20} +5.81460 q^{21} +3.13008 q^{22} -4.98391 q^{23} +6.57472 q^{24} +1.00000 q^{25} -14.1148 q^{26} -16.3126 q^{27} -5.09684 q^{28} +4.39018 q^{29} +7.31821 q^{30} +8.18670 q^{31} +7.06656 q^{32} +4.67634 q^{33} -12.5478 q^{34} -1.75850 q^{35} +22.9942 q^{36} -5.92369 q^{37} -7.88270 q^{38} -21.0875 q^{39} -1.98838 q^{40} +4.90053 q^{41} -12.8691 q^{42} -9.26427 q^{43} -4.09909 q^{44} +7.93340 q^{45} +11.0306 q^{46} -0.752947 q^{47} +4.61616 q^{48} -3.90768 q^{49} -2.21323 q^{50} -18.7465 q^{51} +18.4845 q^{52} -5.63464 q^{53} +36.1037 q^{54} -1.41426 q^{55} +3.49657 q^{56} -11.7768 q^{57} -9.71649 q^{58} +3.28232 q^{59} -9.58378 q^{60} -11.0519 q^{61} -18.1191 q^{62} -13.9509 q^{63} -12.8478 q^{64} +6.37747 q^{65} -10.3498 q^{66} -4.25209 q^{67} +16.4324 q^{68} +16.4796 q^{69} +3.89197 q^{70} +7.64807 q^{71} -15.7746 q^{72} +3.27383 q^{73} +13.1105 q^{74} -3.30657 q^{75} +10.3230 q^{76} +2.48697 q^{77} +46.6716 q^{78} +15.0568 q^{79} -1.39606 q^{80} +30.1386 q^{81} -10.8460 q^{82} -17.3867 q^{83} +16.8531 q^{84} +5.66946 q^{85} +20.5040 q^{86} -14.5164 q^{87} +2.81208 q^{88} -8.34891 q^{89} -17.5585 q^{90} -11.2148 q^{91} -14.4454 q^{92} -27.0699 q^{93} +1.66645 q^{94} +3.56162 q^{95} -23.3661 q^{96} -19.2057 q^{97} +8.64861 q^{98} -11.2199 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 14 q^{2} - 34 q^{3} + 66 q^{4} + 88 q^{5} - q^{6} - 35 q^{7} - 39 q^{8} + 72 q^{9}+O(q^{10}) \) 88 * q - 14 * q^2 - 34 * q^3 + 66 * q^4 + 88 * q^5 - q^6 - 35 * q^7 - 39 * q^8 + 72 * q^9	\( 88 q - 14 q^{2} - 34 q^{3} + 66 q^{4} + 88 q^{5} - q^{6} - 35 q^{7} - 39 q^{8} + 72 q^{9} - 14 q^{10} - 26 q^{11} - 64 q^{12} - 31 q^{13} - 17 q^{14} - 34 q^{15} + 34 q^{16} - 31 q^{17} - 42 q^{18} - 56 q^{19} + 66 q^{20} - q^{21} - 49 q^{22} - 74 q^{23} - 3 q^{24} + 88 q^{25} - q^{26} - 130 q^{27} - 57 q^{28} - 6 q^{29} - q^{30} - 37 q^{31} - 87 q^{32} - 43 q^{33} - 35 q^{34} - 35 q^{35} + 53 q^{36} - 67 q^{37} - 40 q^{38} - 21 q^{39} - 39 q^{40} + 2 q^{41} - 15 q^{42} - 136 q^{43} - 15 q^{44} + 72 q^{45} - 16 q^{46} - 139 q^{47} - 71 q^{48} + 41 q^{49} - 14 q^{50} - 71 q^{51} - 71 q^{52} - 75 q^{53} + 26 q^{54} - 26 q^{55} - 22 q^{56} - 34 q^{57} - 65 q^{58} - 41 q^{59} - 64 q^{60} - 11 q^{61} - 30 q^{62} - 114 q^{63} - 33 q^{64} - 31 q^{65} + 24 q^{66} - 209 q^{67} - 42 q^{68} - 22 q^{69} - 17 q^{70} - 43 q^{71} - 80 q^{72} - 50 q^{73} + 9 q^{74} - 34 q^{75} - 62 q^{76} - 49 q^{77} - 19 q^{78} - 77 q^{79} + 34 q^{80} + 72 q^{81} - 107 q^{82} - 113 q^{83} + 19 q^{84} - 31 q^{85} + 14 q^{86} - 87 q^{87} - 107 q^{88} - 5 q^{89} - 42 q^{90} - 159 q^{91} - 100 q^{92} - 82 q^{93} - 31 q^{94} - 56 q^{95} + 58 q^{96} - 105 q^{97} - 29 q^{98} - 68 q^{99}+O(q^{100}) \) 88 * q - 14 * q^2 - 34 * q^3 + 66 * q^4 + 88 * q^5 - q^6 - 35 * q^7 - 39 * q^8 + 72 * q^9 - 14 * q^10 - 26 * q^11 - 64 * q^12 - 31 * q^13 - 17 * q^14 - 34 * q^15 + 34 * q^16 - 31 * q^17 - 42 * q^18 - 56 * q^19 + 66 * q^20 - q^21 - 49 * q^22 - 74 * q^23 - 3 * q^24 + 88 * q^25 - q^26 - 130 * q^27 - 57 * q^28 - 6 * q^29 - q^30 - 37 * q^31 - 87 * q^32 - 43 * q^33 - 35 * q^34 - 35 * q^35 + 53 * q^36 - 67 * q^37 - 40 * q^38 - 21 * q^39 - 39 * q^40 + 2 * q^41 - 15 * q^42 - 136 * q^43 - 15 * q^44 + 72 * q^45 - 16 * q^46 - 139 * q^47 - 71 * q^48 + 41 * q^49 - 14 * q^50 - 71 * q^51 - 71 * q^52 - 75 * q^53 + 26 * q^54 - 26 * q^55 - 22 * q^56 - 34 * q^57 - 65 * q^58 - 41 * q^59 - 64 * q^60 - 11 * q^61 - 30 * q^62 - 114 * q^63 - 33 * q^64 - 31 * q^65 + 24 * q^66 - 209 * q^67 - 42 * q^68 - 22 * q^69 - 17 * q^70 - 43 * q^71 - 80 * q^72 - 50 * q^73 + 9 * q^74 - 34 * q^75 - 62 * q^76 - 49 * q^77 - 19 * q^78 - 77 * q^79 + 34 * q^80 + 72 * q^81 - 107 * q^82 - 113 * q^83 + 19 * q^84 - 31 * q^85 + 14 * q^86 - 87 * q^87 - 107 * q^88 - 5 * q^89 - 42 * q^90 - 159 * q^91 - 100 * q^92 - 82 * q^93 - 31 * q^94 - 56 * q^95 + 58 * q^96 - 105 * q^97 - 29 * q^98 - 68 * q^99

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