LMFDB - Embedded newform 6017.2.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6017,2,Mod(1,6017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6017, 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("6017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6017 = 11 \cdot 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6017.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:	$48.0459868962$
Analytic rank:	$1$
Dimension:	$106$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.76753 q^{2} -2.67959 q^{3} +5.65924 q^{4} +2.34491 q^{5} +7.41585 q^{6} -2.59530 q^{7} -10.1271 q^{8} +4.18020 q^{9} +O(q^{10})$	\(q-2.76753 q^{2} -2.67959 q^{3} +5.65924 q^{4} +2.34491 q^{5} +7.41585 q^{6} -2.59530 q^{7} -10.1271 q^{8} +4.18020 q^{9} -6.48960 q^{10} +1.00000 q^{11} -15.1644 q^{12} +4.83498 q^{13} +7.18257 q^{14} -6.28338 q^{15} +16.7085 q^{16} -1.57013 q^{17} -11.5688 q^{18} -3.15115 q^{19} +13.2704 q^{20} +6.95433 q^{21} -2.76753 q^{22} +1.05830 q^{23} +27.1364 q^{24} +0.498582 q^{25} -13.3810 q^{26} -3.16246 q^{27} -14.6874 q^{28} -2.77317 q^{29} +17.3895 q^{30} +3.26591 q^{31} -25.9872 q^{32} -2.67959 q^{33} +4.34540 q^{34} -6.08573 q^{35} +23.6568 q^{36} -4.96234 q^{37} +8.72090 q^{38} -12.9558 q^{39} -23.7470 q^{40} +7.87936 q^{41} -19.2463 q^{42} -1.52434 q^{43} +5.65924 q^{44} +9.80218 q^{45} -2.92888 q^{46} +2.09019 q^{47} -44.7720 q^{48} -0.264435 q^{49} -1.37984 q^{50} +4.20731 q^{51} +27.3623 q^{52} +0.760993 q^{53} +8.75220 q^{54} +2.34491 q^{55} +26.2827 q^{56} +8.44378 q^{57} +7.67484 q^{58} +8.30600 q^{59} -35.5592 q^{60} +3.19891 q^{61} -9.03852 q^{62} -10.8489 q^{63} +38.5035 q^{64} +11.3376 q^{65} +7.41585 q^{66} -7.44214 q^{67} -8.88576 q^{68} -2.83581 q^{69} +16.8424 q^{70} +0.478170 q^{71} -42.3332 q^{72} -4.36898 q^{73} +13.7334 q^{74} -1.33599 q^{75} -17.8331 q^{76} -2.59530 q^{77} +35.8555 q^{78} -13.5573 q^{79} +39.1799 q^{80} -4.06652 q^{81} -21.8064 q^{82} -3.93301 q^{83} +39.3562 q^{84} -3.68181 q^{85} +4.21867 q^{86} +7.43096 q^{87} -10.1271 q^{88} +14.5055 q^{89} -27.1279 q^{90} -12.5482 q^{91} +5.98918 q^{92} -8.75130 q^{93} -5.78467 q^{94} -7.38914 q^{95} +69.6351 q^{96} -0.483083 q^{97} +0.731833 q^{98} +4.18020 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9}+O(q^{10}) $ 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9} - 30 q^{10} + 106 q^{11} - 26 q^{12} - 72 q^{13} + 3 q^{14} - 46 q^{15} + 75 q^{16} - 65 q^{17} - 37 q^{18} - 63 q^{19} - 25 q^{20} - 27 q^{21} - 13 q^{22} - 23 q^{23} - 56 q^{24} + 74 q^{25} + 2 q^{26} - 54 q^{27} - 115 q^{28} - 45 q^{29} - 14 q^{30} - 89 q^{31} - 96 q^{32} - 15 q^{33} - 26 q^{34} - 52 q^{35} + 91 q^{36} - 35 q^{37} + 7 q^{38} - 34 q^{39} - 74 q^{40} - 32 q^{41} - 94 q^{43} + 93 q^{44} - 46 q^{45} - 20 q^{46} - 105 q^{47} - 57 q^{48} + 80 q^{49} - 60 q^{50} - 36 q^{51} - 137 q^{52} - 61 q^{54} - 12 q^{55} + 32 q^{56} - 71 q^{57} - 28 q^{58} - 15 q^{59} - 21 q^{60} - 80 q^{61} - 84 q^{62} - 182 q^{63} + 55 q^{64} - 73 q^{65} - 22 q^{66} - 58 q^{67} - 145 q^{68} - 8 q^{69} - 39 q^{70} - 11 q^{71} - 100 q^{72} - 155 q^{73} - 15 q^{74} - 15 q^{75} - 132 q^{76} - 66 q^{77} - 45 q^{78} - 50 q^{79} - 28 q^{80} + 114 q^{81} - 57 q^{82} - 96 q^{83} - 27 q^{84} - 74 q^{85} + 54 q^{86} - 182 q^{87} - 39 q^{88} + 9 q^{89} - 53 q^{90} + 6 q^{91} - 18 q^{92} - 26 q^{93} - 33 q^{94} - 49 q^{95} - 56 q^{96} - 102 q^{97} - 76 q^{98} + 97 q^{99}+O(q^{100}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9 - 30 * q^10 + 106 * q^11 - 26 * q^12 - 72 * q^13 + 3 * q^14 - 46 * q^15 + 75 * q^16 - 65 * q^17 - 37 * q^18 - 63 * q^19 - 25 * q^20 - 27 * q^21 - 13 * q^22 - 23 * q^23 - 56 * q^24 + 74 * q^25 + 2 * q^26 - 54 * q^27 - 115 * q^28 - 45 * q^29 - 14 * q^30 - 89 * q^31 - 96 * q^32 - 15 * q^33 - 26 * q^34 - 52 * q^35 + 91 * q^36 - 35 * q^37 + 7 * q^38 - 34 * q^39 - 74 * q^40 - 32 * q^41 - 94 * q^43 + 93 * q^44 - 46 * q^45 - 20 * q^46 - 105 * q^47 - 57 * q^48 + 80 * q^49 - 60 * q^50 - 36 * q^51 - 137 * q^52 - 61 * q^54 - 12 * q^55 + 32 * q^56 - 71 * q^57 - 28 * q^58 - 15 * q^59 - 21 * q^60 - 80 * q^61 - 84 * q^62 - 182 * q^63 + 55 * q^64 - 73 * q^65 - 22 * q^66 - 58 * q^67 - 145 * q^68 - 8 * q^69 - 39 * q^70 - 11 * q^71 - 100 * q^72 - 155 * q^73 - 15 * q^74 - 15 * q^75 - 132 * q^76 - 66 * q^77 - 45 * q^78 - 50 * q^79 - 28 * q^80 + 114 * q^81 - 57 * q^82 - 96 * q^83 - 27 * q^84 - 74 * q^85 + 54 * q^86 - 182 * q^87 - 39 * q^88 + 9 * q^89 - 53 * q^90 + 6 * q^91 - 18 * q^92 - 26 * q^93 - 33 * q^94 - 49 * q^95 - 56 * q^96 - 102 * q^97 - 76 * q^98 + 97 * 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 $

$2$	−2.76753	−1.95694	−0.978471	−	0.206386i	$-0.933830\pi$
$2$	−2.76753	−1.95694	−0.978471	+	0.206386i	$0.933830\pi$
$3$	−2.67959	−1.54706	−0.773531	−	0.633759i	$-0.781511\pi$
$3$	−2.67959	−1.54706	−0.773531	+	0.633759i	$0.781511\pi$
$4$	5.65924	2.82962
$5$	2.34491	1.04867	0.524337	−	0.851511i	$-0.324313\pi$
$5$	2.34491	1.04867	0.524337	+	0.851511i	$0.324313\pi$
$6$	7.41585	3.02751
$7$	−2.59530	−0.980930	−0.490465	−	0.871461i	$-0.663173\pi$
$7$	−2.59530	−0.980930	−0.490465	+	0.871461i	$0.663173\pi$
$8$	−10.1271	−3.58046
$9$	4.18020	1.39340
$10$	−6.48960	−2.05219
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−15.1644	−4.37760
$13$	4.83498	1.34098	0.670491	−	0.741918i	$-0.266084\pi$
$13$	4.83498	1.34098	0.670491	+	0.741918i	$0.266084\pi$
$14$	7.18257	1.91962
$15$	−6.28338	−1.62236
$16$	16.7085	4.17713
$17$	−1.57013	−0.380813	−0.190407	−	0.981705i	$-0.560981\pi$
$17$	−1.57013	−0.380813	−0.190407	+	0.981705i	$0.560981\pi$
$18$	−11.5688	−2.72680
$19$	−3.15115	−0.722923	−0.361461	−	0.932387i	$-0.617722\pi$
$19$	−3.15115	−0.722923	−0.361461	+	0.932387i	$0.617722\pi$
$20$	13.2704	2.96735
$21$	6.95433	1.51756
$22$	−2.76753	−0.590040
$23$	1.05830	0.220671	0.110335	−	0.993894i	$-0.464807\pi$
$23$	1.05830	0.220671	0.110335	+	0.993894i	$0.464807\pi$
$24$	27.1364	5.53919
$25$	0.498582	0.0997164
$26$	−13.3810	−2.62422
$27$	−3.16246	−0.608615
$28$	−14.6874	−2.77566
$29$	−2.77317	−0.514965	−0.257482	−	0.966283i	$-0.582893\pi$
$29$	−2.77317	−0.514965	−0.257482	+	0.966283i	$0.582893\pi$
$30$	17.3895	3.17487
$31$	3.26591	0.586575	0.293288	−	0.956024i	$-0.405251\pi$
$31$	3.26591	0.586575	0.293288	+	0.956024i	$0.405251\pi$
$32$	−25.9872	−4.59394
$33$	−2.67959	−0.466457
$34$	4.34540	0.745229
$35$	−6.08573	−1.02868
$36$	23.6568	3.94279
$37$	−4.96234	−0.815804	−0.407902	−	0.913026i	$-0.633739\pi$
$37$	−4.96234	−0.815804	−0.407902	+	0.913026i	$0.633739\pi$
$38$	8.72090	1.41472
$39$	−12.9558	−2.07458
$40$	−23.7470	−3.75473
$41$	7.87936	1.23055	0.615275	−	0.788313i	$-0.289045\pi$
$41$	7.87936	1.23055	0.615275	+	0.788313i	$0.289045\pi$
$42$	−19.2463	−2.96977
$43$	−1.52434	−0.232460	−0.116230	−	0.993222i	$-0.537081\pi$
$43$	−1.52434	−0.232460	−0.116230	+	0.993222i	$0.537081\pi$
$44$	5.65924	0.853162
$45$	9.80218	1.46122
$46$	−2.92888	−0.431840
$47$	2.09019	0.304885	0.152443	−	0.988312i	$-0.451286\pi$
$47$	2.09019	0.304885	0.152443	+	0.988312i	$0.451286\pi$
$48$	−44.7720	−6.46228
$49$	−0.264435	−0.0377765
$50$	−1.37984	−0.195139
$51$	4.20731	0.589142
$52$	27.3623	3.79447
$53$	0.760993	0.104530	0.0522652	−	0.998633i	$-0.483356\pi$
$53$	0.760993	0.104530	0.0522652	+	0.998633i	$0.483356\pi$
$54$	8.75220	1.19102
$55$	2.34491	0.316187
$56$	26.2827	3.51218
$57$	8.44378	1.11841
$58$	7.67484	1.00776
$59$	8.30600	1.08135	0.540675	−	0.841232i	$-0.318169\pi$
$59$	8.30600	1.08135	0.540675	+	0.841232i	$0.318169\pi$
$60$	−35.5592	−4.59067
$61$	3.19891	0.409579	0.204789	−	0.978806i	$-0.434349\pi$
$61$	3.19891	0.409579	0.204789	+	0.978806i	$0.434349\pi$
$62$	−9.03852	−1.14789
$63$	−10.8489	−1.36683
$64$	38.5035	4.81294
$65$	11.3376	1.40625
$66$	7.41585	0.912828
$67$	−7.44214	−0.909202	−0.454601	−	0.890695i	$-0.650218\pi$
$67$	−7.44214	−0.909202	−0.454601	+	0.890695i	$0.650218\pi$
$68$	−8.88576	−1.07756
$69$	−2.83581	−0.341392
$70$	16.8424	2.01306
$71$	0.478170	0.0567483	0.0283741	−	0.999597i	$-0.490967\pi$
$71$	0.478170	0.0567483	0.0283741	+	0.999597i	$0.490967\pi$
$72$	−42.3332	−4.98901
$73$	−4.36898	−0.511351	−0.255675	−	0.966763i	$-0.582298\pi$
$73$	−4.36898	−0.511351	−0.255675	+	0.966763i	$0.582298\pi$
$74$	13.7334	1.59648
$75$	−1.33599	−0.154267
$76$	−17.8331	−2.04560
$77$	−2.59530	−0.295762
$78$	35.8555	4.05984
$79$	−13.5573	−1.52531	−0.762656	−	0.646804i	$-0.776105\pi$
$79$	−13.5573	−1.52531	−0.762656	+	0.646804i	$0.776105\pi$
$80$	39.1799	4.38044
$81$	−4.06652	−0.451835
$82$	−21.8064	−2.40811
$83$	−3.93301	−0.431704	−0.215852	−	0.976426i	$-0.569253\pi$
$83$	−3.93301	−0.431704	−0.215852	+	0.976426i	$0.569253\pi$
$84$	39.3562	4.29412
$85$	−3.68181	−0.399349
$86$	4.21867	0.454911
$87$	7.43096	0.796683
$88$	−10.1271	−1.07955
$89$	14.5055	1.53758	0.768791	−	0.639501i	$-0.220859\pi$
$89$	14.5055	1.53758	0.768791	+	0.639501i	$0.220859\pi$
$90$	−27.1279	−2.85953
$91$	−12.5482	−1.31541
$92$	5.98918	0.624415
$93$	−8.75130	−0.907468
$94$	−5.78467	−0.596643
$95$	−7.38914	−0.758110
$96$	69.6351	7.10710
$97$	−0.483083	−0.0490496	−0.0245248	−	0.999699i	$-0.507807\pi$
$97$	−0.483083	−0.0490496	−0.0245248	+	0.999699i	$0.507807\pi$
$98$	0.731833	0.0739263
$99$	4.18020	0.420126
$100$	2.82159	0.282159
$101$	7.61480	0.757701	0.378851	−	0.925458i	$-0.376319\pi$
$101$	7.61480	0.757701	0.378851	+	0.925458i	$0.376319\pi$
$102$	−11.6439	−1.15292
$103$	5.27641	0.519900	0.259950	−	0.965622i	$-0.416294\pi$
$103$	5.27641	0.519900	0.259950	+	0.965622i	$0.416294\pi$
$104$	−48.9642	−4.80133
$105$	16.3072	1.59142
$106$	−2.10607	−0.204560
$107$	−13.3985	−1.29528	−0.647642	−	0.761945i	$-0.724245\pi$
$107$	−13.3985	−1.29528	−0.647642	+	0.761945i	$0.724245\pi$
$108$	−17.8971	−1.72215
$109$	7.00535	0.670991	0.335495	−	0.942042i	$-0.391096\pi$
$109$	7.00535	0.670991	0.335495	+	0.942042i	$0.391096\pi$
$110$	−6.48960	−0.618759
$111$	13.2970	1.26210
$112$	−43.3635	−4.09747
$113$	−18.2537	−1.71716	−0.858581	−	0.512678i	$-0.828654\pi$
$113$	−18.2537	−1.71716	−0.858581	+	0.512678i	$0.828654\pi$
$114$	−23.3684	−2.18866
$115$	2.48162	0.231412
$116$	−15.6940	−1.45715
$117$	20.2112	1.86852
$118$	−22.9871	−2.11614
$119$	4.07496	0.373551
$120$	63.6323	5.80880
$121$	1.00000	0.0909091
$122$	−8.85310	−0.801522
$123$	−21.1135	−1.90374
$124$	18.4826	1.65978
$125$	−10.5554	−0.944104
$126$	30.0246	2.67480
$127$	−10.4582	−0.928015	−0.464008	−	0.885831i	$-0.653589\pi$
$127$	−10.4582	−0.928015	−0.464008	+	0.885831i	$0.653589\pi$
$128$	−54.5852	−4.82470
$129$	4.08461	0.359630
$130$	−31.3771	−2.75195
$131$	−10.1453	−0.886403	−0.443202	−	0.896422i	$-0.646157\pi$
$131$	−10.1453	−0.886403	−0.443202	+	0.896422i	$0.646157\pi$
$132$	−15.1644	−1.31990
$133$	8.17816	0.709136
$134$	20.5964	1.77925
$135$	−7.41566	−0.638239
$136$	15.9008	1.36349
$137$	−10.9591	−0.936298	−0.468149	−	0.883650i	$-0.655079\pi$
$137$	−10.9591	−0.936298	−0.468149	+	0.883650i	$0.655079\pi$
$138$	7.84820	0.668083
$139$	−18.8862	−1.60191	−0.800955	−	0.598724i	$-0.795675\pi$
$139$	−18.8862	−1.60191	−0.800955	+	0.598724i	$0.795675\pi$
$140$	−34.4406	−2.91076
$141$	−5.60085	−0.471677
$142$	−1.32335	−0.111053
$143$	4.83498	0.404321
$144$	69.8449	5.82041
$145$	−6.50282	−0.540030
$146$	12.0913	1.00068
$147$	0.708578	0.0584425
$148$	−28.0831	−2.30842
$149$	−4.87364	−0.399264	−0.199632	−	0.979871i	$-0.563975\pi$
$149$	−4.87364	−0.399264	−0.199632	+	0.979871i	$0.563975\pi$
$150$	3.69741	0.301892
$151$	−19.8255	−1.61337	−0.806687	−	0.590979i	$-0.798741\pi$
$151$	−19.8255	−1.61337	−0.806687	+	0.590979i	$0.798741\pi$
$152$	31.9119	2.58839
$153$	−6.56347	−0.530625
$154$	7.18257	0.578788
$155$	7.65826	0.615126
$156$	−73.3198	−5.87028
$157$	−0.374807	−0.0299128	−0.0149564	−	0.999888i	$-0.504761\pi$
$157$	−0.374807	−0.0299128	−0.0149564	+	0.999888i	$0.504761\pi$
$158$	37.5202	2.98495
$159$	−2.03915	−0.161715
$160$	−60.9376	−4.81754
$161$	−2.74660	−0.216463
$162$	11.2542	0.884215
$163$	20.5773	1.61174	0.805871	−	0.592091i	$-0.201697\pi$
$163$	20.5773	1.61174	0.805871	+	0.592091i	$0.201697\pi$
$164$	44.5912	3.48199
$165$	−6.28338	−0.489161
$166$	10.8847	0.844819
$167$	4.54815	0.351946	0.175973	−	0.984395i	$-0.443693\pi$
$167$	4.54815	0.351946	0.175973	+	0.984395i	$0.443693\pi$
$168$	−70.4270	−5.43356
$169$	10.3770	0.798232
$170$	10.1895	0.781502
$171$	−13.1724	−1.00732
$172$	−8.62662	−0.657774
$173$	23.3608	1.77609	0.888045	−	0.459756i	$-0.152063\pi$
$173$	23.3608	1.77609	0.888045	+	0.459756i	$0.152063\pi$
$174$	−20.5654	−1.55906
$175$	−1.29397	−0.0978148
$176$	16.7085	1.25945
$177$	−22.2567	−1.67291
$178$	−40.1445	−3.00896
$179$	10.7005	0.799789	0.399895	−	0.916561i	$-0.369047\pi$
$179$	10.7005	0.799789	0.399895	+	0.916561i	$0.369047\pi$
$180$	55.4729	4.13470
$181$	19.7792	1.47018	0.735089	−	0.677971i	$-0.237141\pi$
$181$	19.7792	1.47018	0.735089	+	0.677971i	$0.237141\pi$
$182$	34.7276	2.57418
$183$	−8.57177	−0.633644
$184$	−10.7175	−0.790103
$185$	−11.6362	−0.855512
$186$	24.2195	1.77586
$187$	−1.57013	−0.114820
$188$	11.8289	0.862710
$189$	8.20751	0.597009
$190$	20.4497	1.48358
$191$	−5.76313	−0.417006	−0.208503	−	0.978022i	$-0.566859\pi$
$191$	−5.76313	−0.417006	−0.208503	+	0.978022i	$0.566859\pi$
$192$	−103.174	−7.44591
$193$	12.5873	0.906057	0.453029	−	0.891496i	$-0.350344\pi$
$193$	12.5873	0.906057	0.453029	+	0.891496i	$0.350344\pi$
$194$	1.33695	0.0959873
$195$	−30.3800	−2.17556
$196$	−1.49650	−0.106893
$197$	8.12958	0.579209	0.289604	−	0.957146i	$-0.406476\pi$
$197$	8.12958	0.579209	0.289604	+	0.957146i	$0.406476\pi$
$198$	−11.5688	−0.822162
$199$	−9.40327	−0.666580	−0.333290	−	0.942824i	$-0.608159\pi$
$199$	−9.40327	−0.666580	−0.333290	+	0.942824i	$0.608159\pi$
$200$	−5.04917	−0.357030
$201$	19.9419	1.40659
$202$	−21.0742	−1.48278
$203$	7.19720	0.505144
$204$	23.8102	1.66705
$205$	18.4764	1.29044
$206$	−14.6026	−1.01741
$207$	4.42391	0.307483
$208$	80.7853	5.60145
$209$	−3.15115	−0.217969
$210$	−45.1308	−3.11432
$211$	−15.1946	−1.04604	−0.523019	−	0.852321i	$-0.675194\pi$
$211$	−15.1946	−1.04604	−0.523019	+	0.852321i	$0.675194\pi$
$212$	4.30664	0.295781
$213$	−1.28130	−0.0877931
$214$	37.0809	2.53480
$215$	−3.57444	−0.243775
$216$	32.0264	2.17912
$217$	−8.47601	−0.575389
$218$	−19.3875	−1.31309
$219$	11.7071	0.791091
$220$	13.2704	0.894689
$221$	−7.59156	−0.510664
$222$	−36.8000	−2.46985
$223$	2.83111	0.189585	0.0947926	−	0.995497i	$-0.469781\pi$
$223$	2.83111	0.189585	0.0947926	+	0.995497i	$0.469781\pi$
$224$	67.4446	4.50633
$225$	2.08417	0.138945
$226$	50.5177	3.36039
$227$	16.4286	1.09040	0.545202	−	0.838305i	$-0.316453\pi$
$227$	16.4286	1.09040	0.545202	+	0.838305i	$0.316453\pi$
$228$	47.7854	3.16466
$229$	8.15162	0.538674	0.269337	−	0.963046i	$-0.413195\pi$
$229$	8.15162	0.538674	0.269337	+	0.963046i	$0.413195\pi$
$230$	−6.86795	−0.452859
$231$	6.95433	0.457561
$232$	28.0841	1.84381
$233$	−20.2574	−1.32711	−0.663554	−	0.748128i	$-0.730953\pi$
$233$	−20.2574	−1.32711	−0.663554	+	0.748128i	$0.730953\pi$
$234$	−55.9351	−3.65659
$235$	4.90130	0.319725
$236$	47.0057	3.05981
$237$	36.3279	2.35975
$238$	−11.2776	−0.731018
$239$	14.5530	0.941357	0.470679	−	0.882305i	$-0.344009\pi$
$239$	14.5530	0.941357	0.470679	+	0.882305i	$0.344009\pi$
$240$	−104.986	−6.77682
$241$	28.4585	1.83317	0.916586	−	0.399838i	$-0.130933\pi$
$241$	28.4585	1.83317	0.916586	+	0.399838i	$0.130933\pi$
$242$	−2.76753	−0.177904
$243$	20.3840	1.30763
$244$	18.1034	1.15895
$245$	−0.620076	−0.0396152
$246$	58.4322	3.72550
$247$	−15.2357	−0.969426
$248$	−33.0741	−2.10021
$249$	10.5389	0.667873
$250$	29.2124	1.84756
$251$	−0.352474	−0.0222480	−0.0111240	−	0.999938i	$-0.503541\pi$
$251$	−0.352474	−0.0222480	−0.0111240	+	0.999938i	$0.503541\pi$
$252$	−61.3963	−3.86760
$253$	1.05830	0.0665348
$254$	28.9434	1.81607
$255$	9.86575	0.617817
$256$	74.0594	4.62871
$257$	12.0977	0.754637	0.377318	−	0.926084i	$-0.376846\pi$
$257$	12.0977	0.754637	0.377318	+	0.926084i	$0.376846\pi$
$258$	−11.3043	−0.703775
$259$	12.8787	0.800247
$260$	64.1620	3.97916
$261$	−11.5924	−0.717552
$262$	28.0776	1.73464
$263$	7.88835	0.486417	0.243208	−	0.969974i	$-0.421800\pi$
$263$	7.88835	0.486417	0.243208	+	0.969974i	$0.421800\pi$
$264$	27.1364	1.67013
$265$	1.78446	0.109618
$266$	−22.6333	−1.38774
$267$	−38.8688	−2.37873
$268$	−42.1168	−2.57270
$269$	13.9394	0.849901	0.424951	−	0.905217i	$-0.360291\pi$
$269$	13.9394	0.849901	0.424951	+	0.905217i	$0.360291\pi$
$270$	20.5231	1.24900
$271$	−13.6281	−0.827849	−0.413925	−	0.910311i	$-0.635842\pi$
$271$	−13.6281	−0.827849	−0.413925	+	0.910311i	$0.635842\pi$
$272$	−26.2346	−1.59071
$273$	33.6240	2.03502
$274$	30.3296	1.83228
$275$	0.498582	0.0300656
$276$	−16.0485	−0.966008
$277$	−1.10973	−0.0666775	−0.0333387	−	0.999444i	$-0.510614\pi$
$277$	−1.10973	−0.0666775	−0.0333387	+	0.999444i	$0.510614\pi$
$278$	52.2683	3.13485
$279$	13.6522	0.817334
$280$	61.6305	3.68313
$281$	4.75075	0.283406	0.141703	−	0.989909i	$-0.454742\pi$
$281$	4.75075	0.283406	0.141703	+	0.989909i	$0.454742\pi$
$282$	15.5005	0.923043
$283$	−17.0013	−1.01063	−0.505313	−	0.862936i	$-0.668623\pi$
$283$	−17.0013	−1.01063	−0.505313	+	0.862936i	$0.668623\pi$
$284$	2.70608	0.160576
$285$	19.7999	1.17284
$286$	−13.3810	−0.791233
$287$	−20.4493	−1.20708
$288$	−108.632	−6.40119
$289$	−14.5347	−0.854981
$290$	17.9968	1.05681
$291$	1.29446	0.0758828
$292$	−24.7251	−1.44693
$293$	−27.3560	−1.59815	−0.799077	−	0.601228i	$-0.794678\pi$
$293$	−27.3560	−1.59815	−0.799077	+	0.601228i	$0.794678\pi$
$294$	−1.96101	−0.114369
$295$	19.4768	1.13398
$296$	50.2540	2.92095
$297$	−3.16246	−0.183504
$298$	13.4880	0.781337
$299$	5.11686	0.295916
$300$	−7.56071	−0.436518
$301$	3.95612	0.228027
$302$	54.8676	3.15728
$303$	−20.4046	−1.17221
$304$	−52.6510	−3.01974
$305$	7.50115	0.429514
$306$	18.1646	1.03840
$307$	−11.0899	−0.632934	−0.316467	−	0.948604i	$-0.602497\pi$
$307$	−11.0899	−0.632934	−0.316467	+	0.948604i	$0.602497\pi$
$308$	−14.6874	−0.836893
$309$	−14.1386	−0.804317
$310$	−21.1945	−1.20377
$311$	12.7481	0.722878	0.361439	−	0.932396i	$-0.382286\pi$
$311$	12.7481	0.722878	0.361439	+	0.932396i	$0.382286\pi$
$312$	131.204	7.42795
$313$	23.1882	1.31068	0.655338	−	0.755335i	$-0.272526\pi$
$313$	23.1882	1.31068	0.655338	+	0.755335i	$0.272526\pi$
$314$	1.03729	0.0585377
$315$	−25.4396	−1.43336
$316$	−76.7238	−4.31605
$317$	−20.0562	−1.12647	−0.563234	−	0.826298i	$-0.690443\pi$
$317$	−20.0562	−1.12647	−0.563234	+	0.826298i	$0.690443\pi$
$318$	5.64341	0.316467
$319$	−2.77317	−0.155268
$320$	90.2870	5.04720
$321$	35.9026	2.00389
$322$	7.60132	0.423605
$323$	4.94772	0.275299
$324$	−23.0134	−1.27852
$325$	2.41063	0.133718
$326$	−56.9485	−3.15409
$327$	−18.7715	−1.03806
$328$	−79.7948	−4.40593
$329$	−5.42466	−0.299071
$330$	17.3895	0.957259
$331$	−34.8398	−1.91497	−0.957484	−	0.288486i	$-0.906848\pi$
$331$	−34.8398	−1.91497	−0.957484	+	0.288486i	$0.906848\pi$
$332$	−22.2578	−1.22156
$333$	−20.7436	−1.13674
$334$	−12.5872	−0.688739
$335$	−17.4511	−0.953456
$336$	116.197	6.33904
$337$	−12.7390	−0.693937	−0.346969	−	0.937877i	$-0.612789\pi$
$337$	−12.7390	−0.693937	−0.346969	+	0.937877i	$0.612789\pi$
$338$	−28.7188	−1.56209
$339$	48.9124	2.65656
$340$	−20.8363	−1.13001
$341$	3.26591	0.176859
$342$	36.4551	1.97127
$343$	18.8534	1.01799
$344$	15.4371	0.832314
$345$	−6.64971	−0.358008
$346$	−64.6519	−3.47571
$347$	−26.3773	−1.41601	−0.708004	−	0.706209i	$-0.750404\pi$
$347$	−26.3773	−1.41601	−0.708004	+	0.706209i	$0.750404\pi$
$348$	42.0536	2.25431
$349$	−12.0583	−0.645466	−0.322733	−	0.946490i	$-0.604602\pi$
$349$	−12.0583	−0.645466	−0.322733	+	0.946490i	$0.604602\pi$
$350$	3.58110	0.191418
$351$	−15.2904	−0.816142
$352$	−25.9872	−1.38512
$353$	28.9669	1.54175	0.770877	−	0.636984i	$-0.219818\pi$
$353$	28.9669	1.54175	0.770877	+	0.636984i	$0.219818\pi$
$354$	61.5961	3.27380
$355$	1.12126	0.0595104
$356$	82.0902	4.35077
$357$	−10.9192	−0.577907
$358$	−29.6139	−1.56514
$359$	30.9236	1.63209	0.816043	−	0.577992i	$-0.196163\pi$
$359$	30.9236	1.63209	0.816043	+	0.577992i	$0.196163\pi$
$360$	−99.2673	−5.23185
$361$	−9.07028	−0.477383
$362$	−54.7396	−2.87705
$363$	−2.67959	−0.140642
$364$	−71.0133	−3.72211
$365$	−10.2448	−0.536240
$366$	23.7227	1.24000
$367$	0.117527	0.00613488	0.00306744	−	0.999995i	$-0.499024\pi$
$367$	0.117527	0.00613488	0.00306744	+	0.999995i	$0.499024\pi$
$368$	17.6826	0.921771
$369$	32.9373	1.71465
$370$	32.2036	1.67419
$371$	−1.97500	−0.102537
$372$	−49.5257	−2.56779
$373$	26.2717	1.36030	0.680148	−	0.733075i	$-0.261915\pi$
$373$	26.2717	1.36030	0.680148	+	0.733075i	$0.261915\pi$
$374$	4.34540	0.224695
$375$	28.2841	1.46059
$376$	−21.1675	−1.09163
$377$	−13.4082	−0.690559
$378$	−22.7146	−1.16831
$379$	−10.9948	−0.564764	−0.282382	−	0.959302i	$-0.591125\pi$
$379$	−10.9948	−0.564764	−0.282382	+	0.959302i	$0.591125\pi$
$380$	−41.8169	−2.14516
$381$	28.0237	1.43570
$382$	15.9497	0.816056
$383$	6.21619	0.317632	0.158816	−	0.987308i	$-0.449232\pi$
$383$	6.21619	0.317632	0.158816	+	0.987308i	$0.449232\pi$
$384$	146.266	7.46411
$385$	−6.08573	−0.310157
$386$	−34.8359	−1.77310
$387$	−6.37206	−0.323910
$388$	−2.73388	−0.138792
$389$	−0.423588	−0.0214768	−0.0107384	−	0.999942i	$-0.503418\pi$
$389$	−0.423588	−0.0214768	−0.0107384	+	0.999942i	$0.503418\pi$
$390$	84.0778	4.25744
$391$	−1.66167	−0.0840344
$392$	2.67795	0.135257
$393$	27.1854	1.37132
$394$	−22.4989	−1.13348
$395$	−31.7905	−1.59955
$396$	23.6568	1.18880
$397$	−12.9970	−0.652301	−0.326150	−	0.945318i	$-0.605752\pi$
$397$	−12.9970	−0.652301	−0.326150	+	0.945318i	$0.605752\pi$
$398$	26.0239	1.30446
$399$	−21.9141	−1.09708
$400$	8.33056	0.416528
$401$	20.8329	1.04034	0.520172	−	0.854061i	$-0.325868\pi$
$401$	20.8329	1.04034	0.520172	+	0.854061i	$0.325868\pi$
$402$	−55.1898	−2.75262
$403$	15.7906	0.786587
$404$	43.0940	2.14401
$405$	−9.53560	−0.473828
$406$	−19.9185	−0.988538
$407$	−4.96234	−0.245974
$408$	−42.6077	−2.10940
$409$	−0.965610	−0.0477464	−0.0238732	−	0.999715i	$-0.507600\pi$
$409$	−0.965610	−0.0477464	−0.0238732	+	0.999715i	$0.507600\pi$
$410$	−51.1339	−2.52533
$411$	29.3658	1.44851
$412$	29.8605	1.47112
$413$	−21.5565	−1.06073
$414$	−12.2433	−0.601726
$415$	−9.22254	−0.452717
$416$	−125.648	−6.16039
$417$	50.6074	2.47826
$418$	8.72090	0.426553
$419$	12.4059	0.606066	0.303033	−	0.952980i	$-0.402001\pi$
$419$	12.4059	0.606066	0.303033	+	0.952980i	$0.402001\pi$
$420$	92.2866	4.50313
$421$	−12.6096	−0.614555	−0.307278	−	0.951620i	$-0.599418\pi$
$421$	−12.6096	−0.614555	−0.307278	+	0.951620i	$0.599418\pi$
$422$	42.0515	2.04704
$423$	8.73741	0.424827
$424$	−7.70662	−0.374267
$425$	−0.782840	−0.0379733
$426$	3.54604	0.171806
$427$	−8.30213	−0.401768
$428$	−75.8255	−3.66516
$429$	−12.9558	−0.625510
$430$	9.89238	0.477053
$431$	31.8829	1.53575	0.767874	−	0.640601i	$-0.221315\pi$
$431$	31.8829	1.53575	0.767874	+	0.640601i	$0.221315\pi$
$432$	−52.8399	−2.54226
$433$	26.2392	1.26098	0.630488	−	0.776199i	$-0.282855\pi$
$433$	26.2392	1.26098	0.630488	+	0.776199i	$0.282855\pi$
$434$	23.4576	1.12600
$435$	17.4249	0.835460
$436$	39.6449	1.89865
$437$	−3.33486	−0.159528
$438$	−32.3997	−1.54812
$439$	−7.62837	−0.364082	−0.182041	−	0.983291i	$-0.558270\pi$
$439$	−7.62837	−0.364082	−0.182041	+	0.983291i	$0.558270\pi$
$440$	−23.7470	−1.13209
$441$	−1.10539	−0.0526377
$442$	21.0099	0.999339
$443$	31.2874	1.48651	0.743256	−	0.669007i	$-0.233281\pi$
$443$	31.2874	1.48651	0.743256	+	0.669007i	$0.233281\pi$
$444$	75.2511	3.57126
$445$	34.0141	1.61242
$446$	−7.83519	−0.371007
$447$	13.0594	0.617687
$448$	−99.9280	−4.72115
$449$	7.79128	0.367693	0.183847	−	0.982955i	$-0.441145\pi$
$449$	7.79128	0.367693	0.183847	+	0.982955i	$0.441145\pi$
$450$	−5.76802	−0.271907
$451$	7.87936	0.371025
$452$	−103.302	−4.85892
$453$	53.1241	2.49599
$454$	−45.4666	−2.13386
$455$	−29.4244	−1.37944
$456$	−85.5107	−4.00441
$457$	2.59913	0.121582	0.0607910	−	0.998151i	$-0.480638\pi$
$457$	2.59913	0.121582	0.0607910	+	0.998151i	$0.480638\pi$
$458$	−22.5599	−1.05415
$459$	4.96548	0.231769
$460$	14.0441	0.654807
$461$	12.3598	0.575652	0.287826	−	0.957683i	$-0.407068\pi$
$461$	12.3598	0.575652	0.287826	+	0.957683i	$0.407068\pi$
$462$	−19.2463	−0.895421
$463$	−35.0196	−1.62750	−0.813750	−	0.581215i	$-0.802578\pi$
$463$	−35.0196	−1.62750	−0.813750	+	0.581215i	$0.802578\pi$
$464$	−46.3356	−2.15107
$465$	−20.5210	−0.951638
$466$	56.0631	2.59707
$467$	1.75566	0.0812423	0.0406211	−	0.999175i	$-0.487066\pi$
$467$	1.75566	0.0812423	0.0406211	+	0.999175i	$0.487066\pi$
$468$	114.380	5.28721
$469$	19.3146	0.891863
$470$	−13.5645	−0.625684
$471$	1.00433	0.0462770
$472$	−84.1155	−3.87173
$473$	−1.52434	−0.0700894
$474$	−100.539	−4.61790
$475$	−1.57110	−0.0720872
$476$	23.0612	1.05701
$477$	3.18110	0.145653
$478$	−40.2760	−1.84218
$479$	−34.9581	−1.59728	−0.798639	−	0.601810i	$-0.794446\pi$
$479$	−34.9581	−1.59728	−0.798639	+	0.601810i	$0.794446\pi$
$480$	163.288	7.45303
$481$	−23.9928	−1.09398
$482$	−78.7598	−3.58741
$483$	7.35977	0.334881
$484$	5.65924	0.257238
$485$	−1.13278	−0.0514371
$486$	−56.4133	−2.55896
$487$	14.7032	0.666264	0.333132	−	0.942880i	$-0.391894\pi$
$487$	14.7032	0.666264	0.333132	+	0.942880i	$0.391894\pi$
$488$	−32.3956	−1.46648
$489$	−55.1389	−2.49347
$490$	1.71608	0.0775246
$491$	−35.6718	−1.60984	−0.804922	−	0.593380i	$-0.797793\pi$
$491$	−35.6718	−1.60984	−0.804922	+	0.593380i	$0.797793\pi$
$492$	−119.486	−5.38685
$493$	4.35425	0.196105
$494$	42.1654	1.89711
$495$	9.80218	0.440575
$496$	54.5685	2.45020
$497$	−1.24099	−0.0556661
$498$	−29.1666	−1.30699
$499$	−30.7157	−1.37502	−0.687512	−	0.726173i	$-0.741297\pi$
$499$	−30.7157	−1.37502	−0.687512	+	0.726173i	$0.741297\pi$
$500$	−59.7355	−2.67145
$501$	−12.1872	−0.544483
$502$	0.975484	0.0435380
$503$	−21.4954	−0.958431	−0.479215	−	0.877697i	$-0.659079\pi$
$503$	−21.4954	−0.958431	−0.479215	+	0.877697i	$0.659079\pi$
$504$	109.867	4.89387
$505$	17.8560	0.794581
$506$	−2.92888	−0.130205
$507$	−27.8062	−1.23492
$508$	−59.1855	−2.62593
$509$	7.38957	0.327537	0.163768	−	0.986499i	$-0.447635\pi$
$509$	7.38957	0.327537	0.163768	+	0.986499i	$0.447635\pi$
$510$	−27.3038	−1.20903
$511$	11.3388	0.501599
$512$	−95.7915	−4.23343
$513$	9.96536	0.439982
$514$	−33.4809	−1.47678
$515$	12.3727	0.545205
$516$	23.1158	1.01762
$517$	2.09019	0.0919264
$518$	−35.6424	−1.56604
$519$	−62.5974	−2.74772
$520$	−114.816	−5.03503
$521$	32.2438	1.41263	0.706314	−	0.707899i	$-0.250357\pi$
$521$	32.2438	1.41263	0.706314	+	0.707899i	$0.250357\pi$
$522$	32.0824	1.40421
$523$	35.1882	1.53867	0.769336	−	0.638845i	$-0.220587\pi$
$523$	35.1882	1.53867	0.769336	+	0.638845i	$0.220587\pi$
$524$	−57.4150	−2.50818
$525$	3.46730	0.151326
$526$	−21.8313	−0.951889
$527$	−5.12792	−0.223376
$528$	−44.7720	−1.94845
$529$	−21.8800	−0.951304
$530$	−4.93854	−0.214516
$531$	34.7208	1.50675
$532$	46.2822	2.00659
$533$	38.0965	1.65014
$534$	107.571	4.65504
$535$	−31.4183	−1.35833
$536$	75.3670	3.25536
$537$	−28.6728	−1.23732
$538$	−38.5778	−1.66321
$539$	−0.264435	−0.0113900
$540$	−41.9670	−1.80597
$541$	−1.59121	−0.0684113	−0.0342056	−	0.999415i	$-0.510890\pi$
$541$	−1.59121	−0.0684113	−0.0342056	+	0.999415i	$0.510890\pi$
$542$	37.7163	1.62005
$543$	−53.0002	−2.27446
$544$	40.8034	1.74943
$545$	16.4269	0.703650
$546$	−93.0556	−3.98241
$547$	1.00000	0.0427569
$547$	1.00000	0.0427569
$548$	−62.0201	−2.64937
$549$	13.3721	0.570707
$550$	−1.37984	−0.0588367
$551$	8.73867	0.372280
$552$	28.7185	1.22234
$553$	35.1851	1.49622
$554$	3.07123	0.130484
$555$	31.1803	1.32353
$556$	−106.882	−4.53280
$557$	−14.7719	−0.625907	−0.312954	−	0.949768i	$-0.601318\pi$
$557$	−14.7719	−0.625907	−0.312954	+	0.949768i	$0.601318\pi$
$558$	−37.7828	−1.59947
$559$	−7.37017	−0.311725
$560$	−101.683	−4.29691
$561$	4.20731	0.177633
$562$	−13.1478	−0.554608
$563$	−17.0871	−0.720135	−0.360067	−	0.932926i	$-0.617246\pi$
$563$	−17.0871	−0.720135	−0.360067	+	0.932926i	$0.617246\pi$
$564$	−31.6965	−1.33467
$565$	−42.8032	−1.80074
$566$	47.0518	1.97773
$567$	10.5538	0.443219
$568$	−4.84245	−0.203185
$569$	−30.6916	−1.28666	−0.643329	−	0.765590i	$-0.722447\pi$
$569$	−30.6916	−1.28666	−0.643329	+	0.765590i	$0.722447\pi$
$570$	−54.7968	−2.29518
$571$	10.5882	0.443104	0.221552	−	0.975149i	$-0.428888\pi$
$571$	10.5882	0.443104	0.221552	+	0.975149i	$0.428888\pi$
$572$	27.3623	1.14408
$573$	15.4428	0.645134
$574$	56.5941	2.36219
$575$	0.527650	0.0220045
$576$	160.952	6.70635
$577$	−23.0617	−0.960070	−0.480035	−	0.877249i	$-0.659376\pi$
$577$	−23.0617	−0.960070	−0.480035	+	0.877249i	$0.659376\pi$
$578$	40.2252	1.67315
$579$	−33.7289	−1.40173
$580$	−36.8010	−1.52808
$581$	10.2073	0.423471
$582$	−3.58247	−0.148498
$583$	0.760993	0.0315171
$584$	44.2450	1.83087
$585$	47.3933	1.95947
$586$	75.7086	3.12749
$587$	−3.57697	−0.147637	−0.0738186	−	0.997272i	$-0.523519\pi$
$587$	−3.57697	−0.147637	−0.0738186	+	0.997272i	$0.523519\pi$
$588$	4.01001	0.165370
$589$	−10.2914	−0.424048
$590$	−53.9027	−2.21914
$591$	−21.7840	−0.896072
$592$	−82.9133	−3.40772
$593$	3.19176	0.131070	0.0655349	−	0.997850i	$-0.479125\pi$
$593$	3.19176	0.131070	0.0655349	+	0.997850i	$0.479125\pi$
$594$	8.75220	0.359107
$595$	9.55540	0.391733
$596$	−27.5811	−1.12977
$597$	25.1969	1.03124
$598$	−14.1611	−0.579090
$599$	−42.1356	−1.72161	−0.860807	−	0.508932i	$-0.830041\pi$
$599$	−42.1356	−1.72161	−0.860807	+	0.508932i	$0.830041\pi$
$600$	13.5297	0.552348
$601$	−29.4312	−1.20052	−0.600261	−	0.799804i	$-0.704937\pi$
$601$	−29.4312	−1.20052	−0.600261	+	0.799804i	$0.704937\pi$
$602$	−10.9487	−0.446236
$603$	−31.1096	−1.26688
$604$	−112.197	−4.56523
$605$	2.34491	0.0953340
$606$	56.4703	2.29395
$607$	13.4651	0.546533	0.273267	−	0.961938i	$-0.411896\pi$
$607$	13.4651	0.546533	0.273267	+	0.961938i	$0.411896\pi$
$608$	81.8896	3.32106
$609$	−19.2855	−0.781490
$610$	−20.7597	−0.840535
$611$	10.1060	0.408846
$612$	−37.1443	−1.50147
$613$	−39.9387	−1.61311	−0.806555	−	0.591159i	$-0.798670\pi$
$613$	−39.9387	−1.61311	−0.806555	+	0.591159i	$0.798670\pi$
$614$	30.6917	1.23861
$615$	−49.5091	−1.99640
$616$	26.2827	1.05896
$617$	31.5094	1.26852	0.634261	−	0.773119i	$-0.281305\pi$
$617$	31.5094	1.26852	0.634261	+	0.773119i	$0.281305\pi$
$618$	39.1291	1.57400
$619$	−41.3778	−1.66311	−0.831557	−	0.555440i	$-0.812550\pi$
$619$	−41.3778	−1.66311	−0.831557	+	0.555440i	$0.812550\pi$
$620$	43.3399	1.74057
$621$	−3.34683	−0.134304
$622$	−35.2808	−1.41463
$623$	−37.6461	−1.50826
$624$	−216.471	−8.66579
$625$	−27.2443	−1.08977
$626$	−64.1742	−2.56492
$627$	8.44378	0.337212
$628$	−2.12112	−0.0846419
$629$	7.79154	0.310669
$630$	70.4048	2.80500
$631$	12.3307	0.490879	0.245439	−	0.969412i	$-0.421068\pi$
$631$	12.3307	0.490879	0.245439	+	0.969412i	$0.421068\pi$
$632$	137.295	5.46132
$633$	40.7153	1.61829
$634$	55.5062	2.20443
$635$	−24.5235	−0.973185
$636$	−11.5400	−0.457592
$637$	−1.27854	−0.0506576
$638$	7.67484	0.303850
$639$	1.99885	0.0790731
$640$	−127.997	−5.05953
$641$	−44.2626	−1.74827	−0.874133	−	0.485687i	$-0.838570\pi$
$641$	−44.2626	−1.74827	−0.874133	+	0.485687i	$0.838570\pi$
$642$	−99.3615	−3.92149
$643$	−29.3680	−1.15816	−0.579081	−	0.815270i	$-0.696588\pi$
$643$	−29.3680	−1.15816	−0.579081	+	0.815270i	$0.696588\pi$
$644$	−15.5437	−0.612507
$645$	9.57803	0.377135
$646$	−13.6930	−0.538743
$647$	28.2325	1.10994	0.554968	−	0.831872i	$-0.312731\pi$
$647$	28.2325	1.10994	0.554968	+	0.831872i	$0.312731\pi$
$648$	41.1819	1.61778
$649$	8.30600	0.326039
$650$	−6.67151	−0.261678
$651$	22.7122	0.890163
$652$	116.452	4.56062
$653$	32.5393	1.27336	0.636680	−	0.771128i	$-0.280307\pi$
$653$	32.5393	1.27336	0.636680	+	0.771128i	$0.280307\pi$
$654$	51.9506	2.03143
$655$	−23.7899	−0.929548
$656$	131.652	5.14016
$657$	−18.2632	−0.712516
$658$	15.0129	0.585265
$659$	30.2874	1.17983	0.589915	−	0.807466i	$-0.299161\pi$
$659$	30.2874	1.17983	0.589915	+	0.807466i	$0.299161\pi$
$660$	−35.5592	−1.38414
$661$	−40.5808	−1.57841	−0.789206	−	0.614129i	$-0.789507\pi$
$661$	−40.5808	−1.57841	−0.789206	+	0.614129i	$0.789507\pi$
$662$	96.4203	3.74748
$663$	20.3423	0.790028
$664$	39.8299	1.54570
$665$	19.1770	0.743653
$666$	57.4086	2.22454
$667$	−2.93485	−0.113638
$668$	25.7391	0.995875
$669$	−7.58622	−0.293300
$670$	48.2965	1.86586
$671$	3.19891	0.123493
$672$	−180.724	−6.97157
$673$	−3.02994	−0.116796	−0.0583978	−	0.998293i	$-0.518599\pi$
$673$	−3.02994	−0.116796	−0.0583978	+	0.998293i	$0.518599\pi$
$674$	35.2556	1.35799
$675$	−1.57674	−0.0606889
$676$	58.7261	2.25869
$677$	−27.6777	−1.06374	−0.531869	−	0.846826i	$-0.678510\pi$
$677$	−27.6777	−1.06374	−0.531869	+	0.846826i	$0.678510\pi$
$678$	−135.367	−5.19873
$679$	1.25374	0.0481143
$680$	37.2860	1.42985
$681$	−44.0219	−1.68692
$682$	−9.03852	−0.346103
$683$	10.4081	0.398256	0.199128	−	0.979974i	$-0.436189\pi$
$683$	10.4081	0.398256	0.199128	+	0.979974i	$0.436189\pi$
$684$	−74.5459	−2.85033
$685$	−25.6980	−0.981871
$686$	−52.1773	−1.99214
$687$	−21.8430	−0.833363
$688$	−25.4695	−0.971016
$689$	3.67938	0.140173
$690$	18.4033	0.700601
$691$	−34.1734	−1.30002	−0.650009	−	0.759927i	$-0.725235\pi$
$691$	−34.1734	−1.30002	−0.650009	+	0.759927i	$0.725235\pi$
$692$	132.205	5.02566
$693$	−10.8489	−0.412114
$694$	73.0001	2.77104
$695$	−44.2865	−1.67988
$696$	−75.2538	−2.85249
$697$	−12.3717	−0.468610
$698$	33.3717	1.26314
$699$	54.2816	2.05312
$700$	−7.32287	−0.276779
$701$	38.5653	1.45659	0.728296	−	0.685263i	$-0.240313\pi$
$701$	38.5653	1.45659	0.728296	+	0.685263i	$0.240313\pi$
$702$	42.3167	1.59714
$703$	15.6371	0.589763
$704$	38.5035	1.45115
$705$	−13.1335	−0.494635
$706$	−80.1670	−3.01712
$707$	−19.7627	−0.743252
$708$	−125.956	−4.73371
$709$	9.70096	0.364327	0.182164	−	0.983268i	$-0.441690\pi$
$709$	9.70096	0.364327	0.182164	+	0.983268i	$0.441690\pi$
$710$	−3.10313	−0.116458
$711$	−56.6721	−2.12537
$712$	−146.898	−5.50525
$713$	3.45632	0.129440
$714$	30.2193	1.13093
$715$	11.3376	0.424001
$716$	60.5564	2.26310
$717$	−38.9961	−1.45634
$718$	−85.5821	−3.19389
$719$	−19.3648	−0.722186	−0.361093	−	0.932530i	$-0.617596\pi$
$719$	−19.3648	−0.722186	−0.361093	+	0.932530i	$0.617596\pi$
$720$	163.780	6.10371
$721$	−13.6938	−0.509985
$722$	25.1023	0.934210
$723$	−76.2571	−2.83603
$724$	111.935	4.16004
$725$	−1.38265	−0.0513504
$726$	7.41585	0.275228
$727$	−5.55638	−0.206075	−0.103037	−	0.994677i	$-0.532856\pi$
$727$	−5.55638	−0.206075	−0.103037	+	0.994677i	$0.532856\pi$
$728$	127.077	4.70977
$729$	−42.4211	−1.57115
$730$	28.3530	1.04939
$731$	2.39342	0.0885239
$732$	−48.5097	−1.79297
$733$	−29.5290	−1.09068	−0.545339	−	0.838216i	$-0.683599\pi$
$733$	−29.5290	−1.09068	−0.545339	+	0.838216i	$0.683599\pi$
$734$	−0.325261	−0.0120056
$735$	1.66155	0.0612871
$736$	−27.5023	−1.01375
$737$	−7.44214	−0.274135
$738$	−91.1551	−3.35547
$739$	−34.6556	−1.27483	−0.637414	−	0.770522i	$-0.719996\pi$
$739$	−34.6556	−1.27483	−0.637414	+	0.770522i	$0.719996\pi$
$740$	−65.8522	−2.42077
$741$	40.8255	1.49976
$742$	5.46588	0.200659
$743$	−45.6529	−1.67484	−0.837421	−	0.546559i	$-0.815938\pi$
$743$	−45.6529	−1.67484	−0.837421	+	0.546559i	$0.815938\pi$
$744$	88.6250	3.24915
$745$	−11.4282	−0.418698
$746$	−72.7077	−2.66202
$747$	−16.4408	−0.601537
$748$	−8.88576	−0.324896
$749$	34.7732	1.27058
$750$	−78.2773	−2.85828
$751$	−7.15516	−0.261095	−0.130548	−	0.991442i	$-0.541674\pi$
$751$	−7.15516	−0.261095	−0.130548	+	0.991442i	$0.541674\pi$
$752$	34.9239	1.27355
$753$	0.944487	0.0344190
$754$	37.1077	1.35138
$755$	−46.4888	−1.69190
$756$	46.4483	1.68931
$757$	20.4453	0.743098	0.371549	−	0.928413i	$-0.378827\pi$
$757$	20.4453	0.743098	0.371549	+	0.928413i	$0.378827\pi$
$758$	30.4284	1.10521
$759$	−2.83581	−0.102933
$760$	74.8303	2.71438
$761$	12.8012	0.464043	0.232021	−	0.972711i	$-0.425466\pi$
$761$	12.8012	0.464043	0.232021	+	0.972711i	$0.425466\pi$
$762$	−77.5565	−2.80958
$763$	−18.1810	−0.658195
$764$	−32.6150	−1.17997
$765$	−15.3907	−0.556453
$766$	−17.2035	−0.621588
$767$	40.1594	1.45007
$768$	−198.449	−7.16091
$769$	12.6425	0.455902	0.227951	−	0.973673i	$-0.426797\pi$
$769$	12.6425	0.455902	0.227951	+	0.973673i	$0.426797\pi$
$770$	16.8424	0.606960
$771$	−32.4170	−1.16747
$772$	71.2348	2.56380
$773$	−16.0415	−0.576974	−0.288487	−	0.957484i	$-0.593152\pi$
$773$	−16.0415	−0.576974	−0.288487	+	0.957484i	$0.593152\pi$
$774$	17.6349	0.633873
$775$	1.62832	0.0584911
$776$	4.89221	0.175620
$777$	−34.5098	−1.23803
$778$	1.17229	0.0420288
$779$	−24.8290	−0.889592
$780$	−171.928	−6.15601
$781$	0.478170	0.0171103
$782$	4.59874	0.164450
$783$	8.77003	0.313415
$784$	−4.41832	−0.157797
$785$	−0.878886	−0.0313688
$786$	−75.2364	−2.68359
$787$	−22.8750	−0.815405	−0.407703	−	0.913115i	$-0.633670\pi$
$787$	−22.8750	−0.815405	−0.407703	+	0.913115i	$0.633670\pi$
$788$	46.0073	1.63894
$789$	−21.1375	−0.752517
$790$	87.9813	3.13023
$791$	47.3737	1.68442
$792$	−42.3332	−1.50424
$793$	15.4667	0.549238
$794$	35.9696	1.27651
$795$	−4.78161	−0.169586
$796$	−53.2154	−1.88617
$797$	−5.01257	−0.177554	−0.0887771	−	0.996052i	$-0.528296\pi$
$797$	−5.01257	−0.177554	−0.0887771	+	0.996052i	$0.528296\pi$
$798$	60.6480	2.14692
$799$	−3.28188	−0.116104
$800$	−12.9568	−0.458091
$801$	60.6360	2.14247
$802$	−57.6557	−2.03589
$803$	−4.36898	−0.154178
$804$	112.856	3.98012
$805$	−6.44053	−0.226999
$806$	−43.7011	−1.53930
$807$	−37.3519	−1.31485
$808$	−77.1156	−2.71292
$809$	−12.6219	−0.443764	−0.221882	−	0.975074i	$-0.571220\pi$
$809$	−12.6219	−0.443764	−0.221882	+	0.975074i	$0.571220\pi$
$810$	26.3901	0.927253
$811$	30.9353	1.08629	0.543143	−	0.839641i	$-0.317234\pi$
$811$	30.9353	1.08629	0.543143	+	0.839641i	$0.317234\pi$
$812$	40.7307	1.42937
$813$	36.5178	1.28073
$814$	13.7334	0.481357
$815$	48.2519	1.69019
$816$	70.2980	2.46092
$817$	4.80343	0.168051
$818$	2.67236	0.0934368
$819$	−52.4540	−1.83289
$820$	104.562	3.65147
$821$	−41.0581	−1.43294	−0.716468	−	0.697620i	$-0.754242\pi$
$821$	−41.0581	−1.43294	−0.716468	+	0.697620i	$0.754242\pi$
$822$	−81.2710	−2.83465
$823$	36.9226	1.28704	0.643520	−	0.765429i	$-0.277473\pi$
$823$	36.9226	1.28704	0.643520	+	0.765429i	$0.277473\pi$
$824$	−53.4345	−1.86148
$825$	−1.33599	−0.0465134
$826$	59.6584	2.07578
$827$	50.3993	1.75256	0.876278	−	0.481805i	$-0.160019\pi$
$827$	50.3993	1.75256	0.876278	+	0.481805i	$0.160019\pi$
$828$	25.0360	0.870060
$829$	−35.6741	−1.23901	−0.619507	−	0.784991i	$-0.712667\pi$
$829$	−35.6741	−1.23901	−0.619507	+	0.784991i	$0.712667\pi$
$830$	25.5237	0.885940
$831$	2.97363	0.103154
$832$	186.164	6.45406
$833$	0.415199	0.0143858
$834$	−140.058	−4.84980
$835$	10.6650	0.369077
$836$	−17.8331	−0.616770
$837$	−10.3283	−0.356998
$838$	−34.3336	−1.18604
$839$	12.1663	0.420028	0.210014	−	0.977698i	$-0.432649\pi$
$839$	12.1663	0.420028	0.210014	+	0.977698i	$0.432649\pi$
$840$	−165.145	−5.69803
$841$	−21.3095	−0.734811
$842$	34.8975	1.20265
$843$	−12.7301	−0.438446
$844$	−85.9898	−2.95989
$845$	24.3331	0.837085
$846$	−24.1811	−0.831362
$847$	−2.59530	−0.0891754
$848$	12.7151	0.436637
$849$	45.5566	1.56350
$850$	2.16654	0.0743116
$851$	−5.25165	−0.180024
$852$	−7.25117	−0.248421
$853$	−10.6006	−0.362958	−0.181479	−	0.983395i	$-0.558088\pi$
$853$	−10.6006	−0.362958	−0.181479	+	0.983395i	$0.558088\pi$
$854$	22.9764	0.786237
$855$	−30.8881	−1.05635
$856$	135.688	4.63771
$857$	6.47711	0.221254	0.110627	−	0.993862i	$-0.464714\pi$
$857$	6.47711	0.221254	0.110627	+	0.993862i	$0.464714\pi$
$858$	35.8555	1.22409
$859$	38.5183	1.31423	0.657113	−	0.753792i	$-0.271777\pi$
$859$	38.5183	1.31423	0.657113	+	0.753792i	$0.271777\pi$
$860$	−20.2286	−0.689790
$861$	54.7957	1.86743
$862$	−88.2371	−3.00537
$863$	−42.1746	−1.43564	−0.717820	−	0.696229i	$-0.754860\pi$
$863$	−42.1746	−1.43564	−0.717820	+	0.696229i	$0.754860\pi$
$864$	82.1835	2.79594
$865$	54.7789	1.86254
$866$	−72.6179	−2.46766
$867$	38.9470	1.32271
$868$	−47.9678	−1.62813
$869$	−13.5573	−0.459899
$870$	−48.2240	−1.63495
$871$	−35.9826	−1.21922
$872$	−70.9436	−2.40245
$873$	−2.01938	−0.0683458
$874$	9.22934	0.312187
$875$	27.3944	0.926100
$876$	66.2532	2.23849
$877$	−1.90536	−0.0643393	−0.0321697	−	0.999482i	$-0.510242\pi$
$877$	−1.90536	−0.0643393	−0.0321697	+	0.999482i	$0.510242\pi$
$878$	21.1118	0.712488
$879$	73.3029	2.47244
$880$	39.1799	1.32075
$881$	−43.1569	−1.45399	−0.726996	−	0.686641i	$-0.759084\pi$
$881$	−43.1569	−1.45399	−0.726996	+	0.686641i	$0.759084\pi$
$882$	3.05921	0.103009
$883$	−15.1326	−0.509252	−0.254626	−	0.967040i	$-0.581952\pi$
$883$	−15.1326	−0.509252	−0.254626	+	0.967040i	$0.581952\pi$
$884$	−42.9625	−1.44498
$885$	−52.1898	−1.75434
$886$	−86.5890	−2.90902
$887$	−18.5314	−0.622222	−0.311111	−	0.950374i	$-0.600701\pi$
$887$	−18.5314	−0.622222	−0.311111	+	0.950374i	$0.600701\pi$
$888$	−134.660	−4.51889
$889$	27.1421	0.910318
$890$	−94.1350	−3.15541
$891$	−4.06652	−0.136234
$892$	16.0219	0.536454
$893$	−6.58649	−0.220409
$894$	−36.1422	−1.20878
$895$	25.0915	0.838718
$896$	141.665	4.73269
$897$	−13.7111	−0.457800
$898$	−21.5626	−0.719554
$899$	−9.05693	−0.302066
$900$	11.7948	0.393161
$901$	−1.19486	−0.0398066
$902$	−21.8064	−0.726074
$903$	−10.6008	−0.352772
$904$	184.856	6.14823
$905$	46.3804	1.54174
$906$	−147.023	−4.88450
$907$	−53.2697	−1.76879	−0.884396	−	0.466738i	$-0.845429\pi$
$907$	−53.2697	−1.76879	−0.884396	+	0.466738i	$0.845429\pi$
$908$	92.9733	3.08543
$909$	31.8314	1.05578
$910$	81.4329	2.69947
$911$	7.76012	0.257104	0.128552	−	0.991703i	$-0.458967\pi$
$911$	7.76012	0.257104	0.128552	+	0.991703i	$0.458967\pi$
$912$	141.083	4.67172
$913$	−3.93301	−0.130164
$914$	−7.19317	−0.237929
$915$	−20.1000	−0.664485
$916$	46.1320	1.52424
$917$	26.3302	0.869499
$918$	−13.7421	−0.453558
$919$	49.7322	1.64051	0.820256	−	0.571996i	$-0.193831\pi$
$919$	49.7322	1.64051	0.820256	+	0.571996i	$0.193831\pi$
$920$	−25.1315	−0.828560
$921$	29.7164	0.979188
$922$	−34.2061	−1.12652
$923$	2.31194	0.0760984
$924$	39.3562	1.29472
$925$	−2.47413	−0.0813490
$926$	96.9180	3.18492
$927$	22.0564	0.724429
$928$	72.0670	2.36572
$929$	9.54202	0.313063	0.156532	−	0.987673i	$-0.449969\pi$
$929$	9.54202	0.313063	0.156532	+	0.987673i	$0.449969\pi$
$930$	56.7925	1.86230
$931$	0.833274	0.0273095
$932$	−114.642	−3.75521
$933$	−34.1596	−1.11834
$934$	−4.85885	−0.158986
$935$	−3.68181	−0.120408
$936$	−204.680	−6.69018
$937$	−59.6580	−1.94894	−0.974470	−	0.224516i	$-0.927920\pi$
$937$	−59.6580	−1.94894	−0.974470	+	0.224516i	$0.927920\pi$
$938$	−53.4537	−1.74532
$939$	−62.1350	−2.02770
$940$	27.7376	0.904701
$941$	46.4903	1.51554	0.757771	−	0.652521i	$-0.226289\pi$
$941$	46.4903	1.51554	0.757771	+	0.652521i	$0.226289\pi$
$942$	−2.77951	−0.0905614
$943$	8.33873	0.271547
$944$	138.781	4.51694
$945$	19.2458	0.626067
$946$	4.21867	0.137161
$947$	−54.2903	−1.76420	−0.882100	−	0.471063i	$-0.843870\pi$
$947$	−54.2903	−1.76420	−0.882100	+	0.471063i	$0.843870\pi$
$948$	205.588	6.67720
$949$	−21.1239	−0.685712
$950$	4.34808	0.141070
$951$	53.7424	1.74272
$952$	−41.2674	−1.33748
$953$	26.3785	0.854482	0.427241	−	0.904138i	$-0.359486\pi$
$953$	26.3785	0.854482	0.427241	+	0.904138i	$0.359486\pi$
$954$	−8.80381	−0.285034
$955$	−13.5140	−0.437303
$956$	82.3591	2.66368
$957$	7.43096	0.240209
$958$	96.7478	3.12578
$959$	28.4421	0.918442
$960$	−241.932	−7.80833
$961$	−20.3338	−0.655930
$962$	66.4009	2.14085
$963$	−56.0085	−1.80485
$964$	161.053	5.18718
$965$	29.5161	0.950158
$966$	−20.3684	−0.655343
$967$	−22.8620	−0.735192	−0.367596	−	0.929986i	$-0.619819\pi$
$967$	−22.8620	−0.735192	−0.367596	+	0.929986i	$0.619819\pi$
$968$	−10.1271	−0.325496
$969$	−13.2579	−0.425904
$970$	3.13502	0.100659
$971$	26.3239	0.844773	0.422387	−	0.906416i	$-0.361192\pi$
$971$	26.3239	0.844773	0.422387	+	0.906416i	$0.361192\pi$
$972$	115.358	3.70010
$973$	49.0154	1.57136
$974$	−40.6915	−1.30384
$975$	−6.45951	−0.206870
$976$	53.4491	1.71086
$977$	−5.94244	−0.190116	−0.0950578	−	0.995472i	$-0.530304\pi$
$977$	−5.94244	−0.190116	−0.0950578	+	0.995472i	$0.530304\pi$
$978$	152.599	4.87957
$979$	14.5055	0.463598
$980$	−3.50916	−0.112096
$981$	29.2838	0.934959
$982$	98.7228	3.15037
$983$	7.00473	0.223416	0.111708	−	0.993741i	$-0.464368\pi$
$983$	7.00473	0.223416	0.111708	+	0.993741i	$0.464368\pi$
$984$	213.817	6.81625
$985$	19.0631	0.607401
$986$	−12.0505	−0.383767
$987$	14.5359	0.462682
$988$	−86.2226	−2.74311
$989$	−1.61321	−0.0512972
$990$	−27.1279	−0.862180
$991$	42.8626	1.36158	0.680788	−	0.732480i	$-0.261637\pi$
$991$	42.8626	1.36158	0.680788	+	0.732480i	$0.261637\pi$
$992$	−84.8720	−2.69469
$993$	93.3563	2.96257
$994$	3.43449	0.108935
$995$	−22.0498	−0.699025
$996$	59.6419	1.88983
$997$	7.31448	0.231652	0.115826	−	0.993270i	$-0.463049\pi$
$997$	7.31448	0.231652	0.115826	+	0.993270i	$0.463049\pi$
$998$	85.0068	2.69084
$999$	15.6932	0.496511

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.c.1.2	✓	106

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.c.1.2	✓	106	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:	\( N \)	\(=\)	\( 6017 = 11 \cdot 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.76753 q^{2} -2.67959 q^{3} +5.65924 q^{4} +2.34491 q^{5} +7.41585 q^{6} -2.59530 q^{7} -10.1271 q^{8} +4.18020 q^{9} +O(q^{10})\)	\(q-2.76753 q^{2} -2.67959 q^{3} +5.65924 q^{4} +2.34491 q^{5} +7.41585 q^{6} -2.59530 q^{7} -10.1271 q^{8} +4.18020 q^{9} -6.48960 q^{10} +1.00000 q^{11} -15.1644 q^{12} +4.83498 q^{13} +7.18257 q^{14} -6.28338 q^{15} +16.7085 q^{16} -1.57013 q^{17} -11.5688 q^{18} -3.15115 q^{19} +13.2704 q^{20} +6.95433 q^{21} -2.76753 q^{22} +1.05830 q^{23} +27.1364 q^{24} +0.498582 q^{25} -13.3810 q^{26} -3.16246 q^{27} -14.6874 q^{28} -2.77317 q^{29} +17.3895 q^{30} +3.26591 q^{31} -25.9872 q^{32} -2.67959 q^{33} +4.34540 q^{34} -6.08573 q^{35} +23.6568 q^{36} -4.96234 q^{37} +8.72090 q^{38} -12.9558 q^{39} -23.7470 q^{40} +7.87936 q^{41} -19.2463 q^{42} -1.52434 q^{43} +5.65924 q^{44} +9.80218 q^{45} -2.92888 q^{46} +2.09019 q^{47} -44.7720 q^{48} -0.264435 q^{49} -1.37984 q^{50} +4.20731 q^{51} +27.3623 q^{52} +0.760993 q^{53} +8.75220 q^{54} +2.34491 q^{55} +26.2827 q^{56} +8.44378 q^{57} +7.67484 q^{58} +8.30600 q^{59} -35.5592 q^{60} +3.19891 q^{61} -9.03852 q^{62} -10.8489 q^{63} +38.5035 q^{64} +11.3376 q^{65} +7.41585 q^{66} -7.44214 q^{67} -8.88576 q^{68} -2.83581 q^{69} +16.8424 q^{70} +0.478170 q^{71} -42.3332 q^{72} -4.36898 q^{73} +13.7334 q^{74} -1.33599 q^{75} -17.8331 q^{76} -2.59530 q^{77} +35.8555 q^{78} -13.5573 q^{79} +39.1799 q^{80} -4.06652 q^{81} -21.8064 q^{82} -3.93301 q^{83} +39.3562 q^{84} -3.68181 q^{85} +4.21867 q^{86} +7.43096 q^{87} -10.1271 q^{88} +14.5055 q^{89} -27.1279 q^{90} -12.5482 q^{91} +5.98918 q^{92} -8.75130 q^{93} -5.78467 q^{94} -7.38914 q^{95} +69.6351 q^{96} -0.483083 q^{97} +0.731833 q^{98} +4.18020 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9}+O(q^{10}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9} - 30 q^{10} + 106 q^{11} - 26 q^{12} - 72 q^{13} + 3 q^{14} - 46 q^{15} + 75 q^{16} - 65 q^{17} - 37 q^{18} - 63 q^{19} - 25 q^{20} - 27 q^{21} - 13 q^{22} - 23 q^{23} - 56 q^{24} + 74 q^{25} + 2 q^{26} - 54 q^{27} - 115 q^{28} - 45 q^{29} - 14 q^{30} - 89 q^{31} - 96 q^{32} - 15 q^{33} - 26 q^{34} - 52 q^{35} + 91 q^{36} - 35 q^{37} + 7 q^{38} - 34 q^{39} - 74 q^{40} - 32 q^{41} - 94 q^{43} + 93 q^{44} - 46 q^{45} - 20 q^{46} - 105 q^{47} - 57 q^{48} + 80 q^{49} - 60 q^{50} - 36 q^{51} - 137 q^{52} - 61 q^{54} - 12 q^{55} + 32 q^{56} - 71 q^{57} - 28 q^{58} - 15 q^{59} - 21 q^{60} - 80 q^{61} - 84 q^{62} - 182 q^{63} + 55 q^{64} - 73 q^{65} - 22 q^{66} - 58 q^{67} - 145 q^{68} - 8 q^{69} - 39 q^{70} - 11 q^{71} - 100 q^{72} - 155 q^{73} - 15 q^{74} - 15 q^{75} - 132 q^{76} - 66 q^{77} - 45 q^{78} - 50 q^{79} - 28 q^{80} + 114 q^{81} - 57 q^{82} - 96 q^{83} - 27 q^{84} - 74 q^{85} + 54 q^{86} - 182 q^{87} - 39 q^{88} + 9 q^{89} - 53 q^{90} + 6 q^{91} - 18 q^{92} - 26 q^{93} - 33 q^{94} - 49 q^{95} - 56 q^{96} - 102 q^{97} - 76 q^{98} + 97 q^{99}+O(q^{100}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9 - 30 * q^10 + 106 * q^11 - 26 * q^12 - 72 * q^13 + 3 * q^14 - 46 * q^15 + 75 * q^16 - 65 * q^17 - 37 * q^18 - 63 * q^19 - 25 * q^20 - 27 * q^21 - 13 * q^22 - 23 * q^23 - 56 * q^24 + 74 * q^25 + 2 * q^26 - 54 * q^27 - 115 * q^28 - 45 * q^29 - 14 * q^30 - 89 * q^31 - 96 * q^32 - 15 * q^33 - 26 * q^34 - 52 * q^35 + 91 * q^36 - 35 * q^37 + 7 * q^38 - 34 * q^39 - 74 * q^40 - 32 * q^41 - 94 * q^43 + 93 * q^44 - 46 * q^45 - 20 * q^46 - 105 * q^47 - 57 * q^48 + 80 * q^49 - 60 * q^50 - 36 * q^51 - 137 * q^52 - 61 * q^54 - 12 * q^55 + 32 * q^56 - 71 * q^57 - 28 * q^58 - 15 * q^59 - 21 * q^60 - 80 * q^61 - 84 * q^62 - 182 * q^63 + 55 * q^64 - 73 * q^65 - 22 * q^66 - 58 * q^67 - 145 * q^68 - 8 * q^69 - 39 * q^70 - 11 * q^71 - 100 * q^72 - 155 * q^73 - 15 * q^74 - 15 * q^75 - 132 * q^76 - 66 * q^77 - 45 * q^78 - 50 * q^79 - 28 * q^80 + 114 * q^81 - 57 * q^82 - 96 * q^83 - 27 * q^84 - 74 * q^85 + 54 * q^86 - 182 * q^87 - 39 * q^88 + 9 * q^89 - 53 * q^90 + 6 * q^91 - 18 * q^92 - 26 * q^93 - 33 * q^94 - 49 * q^95 - 56 * q^96 - 102 * q^97 - 76 * q^98 + 97 * q^99

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