LMFDB - Embedded newform 6033.2.a.d.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6033,2,Mod(1,6033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6033, 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("6033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6033 = 3 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6033.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:	$48.1737475394$
Analytic rank:	$1$
Dimension:	$84$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.41532 q^{2} -1.00000 q^{3} +3.83378 q^{4} -1.96861 q^{5} +2.41532 q^{6} -4.53404 q^{7} -4.42916 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.41532 q^{2} -1.00000 q^{3} +3.83378 q^{4} -1.96861 q^{5} +2.41532 q^{6} -4.53404 q^{7} -4.42916 q^{8} +1.00000 q^{9} +4.75483 q^{10} -5.37589 q^{11} -3.83378 q^{12} -1.70137 q^{13} +10.9512 q^{14} +1.96861 q^{15} +3.03029 q^{16} +2.69389 q^{17} -2.41532 q^{18} +5.61419 q^{19} -7.54721 q^{20} +4.53404 q^{21} +12.9845 q^{22} -3.38072 q^{23} +4.42916 q^{24} -1.12457 q^{25} +4.10934 q^{26} -1.00000 q^{27} -17.3825 q^{28} -6.32616 q^{29} -4.75483 q^{30} -1.20242 q^{31} +1.53919 q^{32} +5.37589 q^{33} -6.50661 q^{34} +8.92576 q^{35} +3.83378 q^{36} -3.96747 q^{37} -13.5601 q^{38} +1.70137 q^{39} +8.71929 q^{40} +10.7936 q^{41} -10.9512 q^{42} -2.02837 q^{43} -20.6100 q^{44} -1.96861 q^{45} +8.16552 q^{46} -12.1279 q^{47} -3.03029 q^{48} +13.5575 q^{49} +2.71620 q^{50} -2.69389 q^{51} -6.52266 q^{52} -4.43992 q^{53} +2.41532 q^{54} +10.5830 q^{55} +20.0820 q^{56} -5.61419 q^{57} +15.2797 q^{58} -7.47854 q^{59} +7.54721 q^{60} +13.5016 q^{61} +2.90423 q^{62} -4.53404 q^{63} -9.77823 q^{64} +3.34933 q^{65} -12.9845 q^{66} +10.7299 q^{67} +10.3278 q^{68} +3.38072 q^{69} -21.5586 q^{70} +6.42020 q^{71} -4.42916 q^{72} +11.6782 q^{73} +9.58271 q^{74} +1.12457 q^{75} +21.5236 q^{76} +24.3745 q^{77} -4.10934 q^{78} -2.97918 q^{79} -5.96546 q^{80} +1.00000 q^{81} -26.0700 q^{82} -0.547679 q^{83} +17.3825 q^{84} -5.30322 q^{85} +4.89916 q^{86} +6.32616 q^{87} +23.8107 q^{88} +7.42009 q^{89} +4.75483 q^{90} +7.71406 q^{91} -12.9609 q^{92} +1.20242 q^{93} +29.2929 q^{94} -11.0522 q^{95} -1.53919 q^{96} +0.665806 q^{97} -32.7458 q^{98} -5.37589 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 13 q^{2} - 84 q^{3} + 81 q^{4} - 10 q^{5} + 13 q^{6} - 32 q^{7} - 39 q^{8} + 84 q^{9}+O(q^{10}) $ 84 * q - 13 * q^2 - 84 * q^3 + 81 * q^4 - 10 * q^5 + 13 * q^6 - 32 * q^7 - 39 * q^8 + 84 * q^9	\( 84 q - 13 q^{2} - 84 q^{3} + 81 q^{4} - 10 q^{5} + 13 q^{6} - 32 q^{7} - 39 q^{8} + 84 q^{9} + 13 q^{10} - 20 q^{11} - 81 q^{12} + 7 q^{13} - 9 q^{14} + 10 q^{15} + 83 q^{16} - 39 q^{17} - 13 q^{18} + 13 q^{19} - 26 q^{20} + 32 q^{21} - 21 q^{22} - 93 q^{23} + 39 q^{24} + 66 q^{25} - 34 q^{26} - 84 q^{27} - 59 q^{28} - 39 q^{29} - 13 q^{30} + 8 q^{31} - 96 q^{32} + 20 q^{33} - 69 q^{35} + 81 q^{36} + 6 q^{37} - 59 q^{38} - 7 q^{39} + 28 q^{40} - 23 q^{41} + 9 q^{42} - 74 q^{43} - 43 q^{44} - 10 q^{45} - 6 q^{46} - 77 q^{47} - 83 q^{48} + 100 q^{49} - 74 q^{50} + 39 q^{51} - 44 q^{52} - 66 q^{53} + 13 q^{54} - 60 q^{55} - 31 q^{56} - 13 q^{57} - 39 q^{58} - 36 q^{59} + 26 q^{60} + 104 q^{61} - 53 q^{62} - 32 q^{63} + 85 q^{64} - 47 q^{65} + 21 q^{66} - 65 q^{67} - 118 q^{68} + 93 q^{69} - 3 q^{70} - 68 q^{71} - 39 q^{72} + 8 q^{73} - 30 q^{74} - 66 q^{75} + 71 q^{76} - 83 q^{77} + 34 q^{78} - 24 q^{79} - 67 q^{80} + 84 q^{81} - 9 q^{82} - 95 q^{83} + 59 q^{84} + 24 q^{85} - 32 q^{86} + 39 q^{87} - 65 q^{88} - 44 q^{89} + 13 q^{90} + 8 q^{91} - 184 q^{92} - 8 q^{93} + 61 q^{94} - 153 q^{95} + 96 q^{96} + 19 q^{97} - 67 q^{98} - 20 q^{99}+O(q^{100}) \) 84 * q - 13 * q^2 - 84 * q^3 + 81 * q^4 - 10 * q^5 + 13 * q^6 - 32 * q^7 - 39 * q^8 + 84 * q^9 + 13 * q^10 - 20 * q^11 - 81 * q^12 + 7 * q^13 - 9 * q^14 + 10 * q^15 + 83 * q^16 - 39 * q^17 - 13 * q^18 + 13 * q^19 - 26 * q^20 + 32 * q^21 - 21 * q^22 - 93 * q^23 + 39 * q^24 + 66 * q^25 - 34 * q^26 - 84 * q^27 - 59 * q^28 - 39 * q^29 - 13 * q^30 + 8 * q^31 - 96 * q^32 + 20 * q^33 - 69 * q^35 + 81 * q^36 + 6 * q^37 - 59 * q^38 - 7 * q^39 + 28 * q^40 - 23 * q^41 + 9 * q^42 - 74 * q^43 - 43 * q^44 - 10 * q^45 - 6 * q^46 - 77 * q^47 - 83 * q^48 + 100 * q^49 - 74 * q^50 + 39 * q^51 - 44 * q^52 - 66 * q^53 + 13 * q^54 - 60 * q^55 - 31 * q^56 - 13 * q^57 - 39 * q^58 - 36 * q^59 + 26 * q^60 + 104 * q^61 - 53 * q^62 - 32 * q^63 + 85 * q^64 - 47 * q^65 + 21 * q^66 - 65 * q^67 - 118 * q^68 + 93 * q^69 - 3 * q^70 - 68 * q^71 - 39 * q^72 + 8 * q^73 - 30 * q^74 - 66 * q^75 + 71 * q^76 - 83 * q^77 + 34 * q^78 - 24 * q^79 - 67 * q^80 + 84 * q^81 - 9 * q^82 - 95 * q^83 + 59 * q^84 + 24 * q^85 - 32 * q^86 + 39 * q^87 - 65 * q^88 - 44 * q^89 + 13 * q^90 + 8 * q^91 - 184 * q^92 - 8 * q^93 + 61 * q^94 - 153 * q^95 + 96 * q^96 + 19 * q^97 - 67 * q^98 - 20 * 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 $

$2$	−2.41532	−1.70789	−0.853945	−	0.520363i	$-0.825797\pi$
$2$	−2.41532	−1.70789	−0.853945	+	0.520363i	$0.825797\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.83378	1.91689
$5$	−1.96861	−0.880389	−0.440195	−	0.897902i	$-0.645091\pi$
$5$	−1.96861	−0.880389	−0.440195	+	0.897902i	$0.645091\pi$
$6$	2.41532	0.986051
$7$	−4.53404	−1.71371	−0.856853	−	0.515561i	$-0.827584\pi$
$7$	−4.53404	−1.71371	−0.856853	+	0.515561i	$0.827584\pi$
$8$	−4.42916	−1.56594
$9$	1.00000	0.333333
$10$	4.75483	1.50361
$11$	−5.37589	−1.62089	−0.810446	−	0.585814i	$-0.800775\pi$
$11$	−5.37589	−1.62089	−0.810446	+	0.585814i	$0.800775\pi$
$12$	−3.83378	−1.10672
$13$	−1.70137	−0.471874	−0.235937	−	0.971768i	$-0.575816\pi$
$13$	−1.70137	−0.471874	−0.235937	+	0.971768i	$0.575816\pi$
$14$	10.9512	2.92682
$15$	1.96861	0.508293
$16$	3.03029	0.757573
$17$	2.69389	0.653364	0.326682	−	0.945134i	$-0.394069\pi$
$17$	2.69389	0.653364	0.326682	+	0.945134i	$0.394069\pi$
$18$	−2.41532	−0.569297
$19$	5.61419	1.28798	0.643992	−	0.765032i	$-0.277277\pi$
$19$	5.61419	1.28798	0.643992	+	0.765032i	$0.277277\pi$
$20$	−7.54721	−1.68761
$21$	4.53404	0.989409
$22$	12.9845	2.76830
$23$	−3.38072	−0.704929	−0.352464	−	0.935825i	$-0.614656\pi$
$23$	−3.38072	−0.704929	−0.352464	+	0.935825i	$0.614656\pi$
$24$	4.42916	0.904098
$25$	−1.12457	−0.224915
$26$	4.10934	0.805909
$27$	−1.00000	−0.192450
$28$	−17.3825	−3.28498
$29$	−6.32616	−1.17474	−0.587369	−	0.809319i	$-0.699836\pi$
$29$	−6.32616	−1.17474	−0.587369	+	0.809319i	$0.699836\pi$
$30$	−4.75483	−0.868109
$31$	−1.20242	−0.215961	−0.107981	−	0.994153i	$-0.534438\pi$
$31$	−1.20242	−0.215961	−0.107981	+	0.994153i	$0.534438\pi$
$32$	1.53919	0.272094
$33$	5.37589	0.935822
$34$	−6.50661	−1.11587
$35$	8.92576	1.50873
$36$	3.83378	0.638963
$37$	−3.96747	−0.652248	−0.326124	−	0.945327i	$-0.605743\pi$
$37$	−3.96747	−0.652248	−0.326124	+	0.945327i	$0.605743\pi$
$38$	−13.5601	−2.19973
$39$	1.70137	0.272437
$40$	8.71929	1.37864
$41$	10.7936	1.68568	0.842838	−	0.538168i	$-0.180883\pi$
$41$	10.7936	1.68568	0.842838	+	0.538168i	$0.180883\pi$
$42$	−10.9512	−1.68980
$43$	−2.02837	−0.309323	−0.154662	−	0.987968i	$-0.549429\pi$
$43$	−2.02837	−0.309323	−0.154662	+	0.987968i	$0.549429\pi$
$44$	−20.6100	−3.10707
$45$	−1.96861	−0.293463
$46$	8.16552	1.20394
$47$	−12.1279	−1.76904	−0.884521	−	0.466501i	$-0.845514\pi$
$47$	−12.1279	−1.76904	−0.884521	+	0.466501i	$0.845514\pi$
$48$	−3.03029	−0.437385
$49$	13.5575	1.93679
$50$	2.71620	0.384129
$51$	−2.69389	−0.377220
$52$	−6.52266	−0.904530
$53$	−4.43992	−0.609870	−0.304935	−	0.952373i	$-0.598635\pi$
$53$	−4.43992	−0.609870	−0.304935	+	0.952373i	$0.598635\pi$
$54$	2.41532	0.328684
$55$	10.5830	1.42702
$56$	20.0820	2.68357
$57$	−5.61419	−0.743618
$58$	15.2797	2.00632
$59$	−7.47854	−0.973622	−0.486811	−	0.873507i	$-0.661840\pi$
$59$	−7.47854	−0.973622	−0.486811	+	0.873507i	$0.661840\pi$
$60$	7.54721	0.974341
$61$	13.5016	1.72871	0.864354	−	0.502884i	$-0.167728\pi$
$61$	13.5016	1.72871	0.864354	+	0.502884i	$0.167728\pi$
$62$	2.90423	0.368838
$63$	−4.53404	−0.571235
$64$	−9.77823	−1.22228
$65$	3.34933	0.415433
$66$	−12.9845	−1.59828
$67$	10.7299	1.31087	0.655433	−	0.755254i	$-0.272486\pi$
$67$	10.7299	1.31087	0.655433	+	0.755254i	$0.272486\pi$
$68$	10.3278	1.25243
$69$	3.38072	0.406991
$70$	−21.5586	−2.57674
$71$	6.42020	0.761938	0.380969	−	0.924588i	$-0.375590\pi$
$71$	6.42020	0.761938	0.380969	+	0.924588i	$0.375590\pi$
$72$	−4.42916	−0.521982
$73$	11.6782	1.36683	0.683413	−	0.730032i	$-0.260495\pi$
$73$	11.6782	1.36683	0.683413	+	0.730032i	$0.260495\pi$
$74$	9.58271	1.11397
$75$	1.12457	0.129854
$76$	21.5236	2.46892
$77$	24.3745	2.77773
$78$	−4.10934	−0.465292
$79$	−2.97918	−0.335183	−0.167592	−	0.985856i	$-0.553599\pi$
$79$	−2.97918	−0.335183	−0.167592	+	0.985856i	$0.553599\pi$
$80$	−5.96546	−0.666959
$81$	1.00000	0.111111
$82$	−26.0700	−2.87895
$83$	−0.547679	−0.0601155	−0.0300578	−	0.999548i	$-0.509569\pi$
$83$	−0.547679	−0.0601155	−0.0300578	+	0.999548i	$0.509569\pi$
$84$	17.3825	1.89659
$85$	−5.30322	−0.575215
$86$	4.89916	0.528290
$87$	6.32616	0.678236
$88$	23.8107	2.53823
$89$	7.42009	0.786528	0.393264	−	0.919426i	$-0.371346\pi$
$89$	7.42009	0.786528	0.393264	+	0.919426i	$0.371346\pi$
$90$	4.75483	0.501203
$91$	7.71406	0.808653
$92$	−12.9609	−1.35127
$93$	1.20242	0.124685
$94$	29.2929	3.02133
$95$	−11.0522	−1.13393
$96$	−1.53919	−0.157093
$97$	0.665806	0.0676024	0.0338012	−	0.999429i	$-0.489239\pi$
$97$	0.665806	0.0676024	0.0338012	+	0.999429i	$0.489239\pi$
$98$	−32.7458	−3.30782
$99$	−5.37589	−0.540297
$100$	−4.31136	−0.431136
$101$	−6.56660	−0.653401	−0.326701	−	0.945128i	$-0.605937\pi$
$101$	−6.56660	−0.653401	−0.326701	+	0.945128i	$0.605937\pi$
$102$	6.50661	0.644250
$103$	−0.490325	−0.0483132	−0.0241566	−	0.999708i	$-0.507690\pi$
$103$	−0.490325	−0.0483132	−0.0241566	+	0.999708i	$0.507690\pi$
$104$	7.53562	0.738928
$105$	−8.92576	−0.871065
$106$	10.7238	1.04159
$107$	0.457065	0.0441861	0.0220931	−	0.999756i	$-0.492967\pi$
$107$	0.457065	0.0441861	0.0220931	+	0.999756i	$0.492967\pi$
$108$	−3.83378	−0.368905
$109$	17.7294	1.69817	0.849083	−	0.528259i	$-0.177155\pi$
$109$	17.7294	1.69817	0.849083	+	0.528259i	$0.177155\pi$
$110$	−25.5614	−2.43719
$111$	3.96747	0.376575
$112$	−13.7395	−1.29826
$113$	8.78236	0.826175	0.413087	−	0.910691i	$-0.364450\pi$
$113$	8.78236	0.826175	0.413087	+	0.910691i	$0.364450\pi$
$114$	13.5601	1.27002
$115$	6.65532	0.620612
$116$	−24.2531	−2.25184
$117$	−1.70137	−0.157291
$118$	18.0631	1.66284
$119$	−12.2142	−1.11967
$120$	−8.71929	−0.795959
$121$	17.9002	1.62729
$122$	−32.6108	−2.95244
$123$	−10.7936	−0.973225
$124$	−4.60981	−0.413973
$125$	12.0569	1.07840
$126$	10.9512	0.975607
$127$	1.43117	0.126996	0.0634979	−	0.997982i	$-0.479774\pi$
$127$	1.43117	0.126996	0.0634979	+	0.997982i	$0.479774\pi$
$128$	20.5392	1.81542
$129$	2.02837	0.178588
$130$	−8.08970	−0.709513
$131$	−18.8506	−1.64699	−0.823494	−	0.567325i	$-0.807978\pi$
$131$	−18.8506	−1.64699	−0.823494	+	0.567325i	$0.807978\pi$
$132$	20.6100	1.79387
$133$	−25.4550	−2.20723
$134$	−25.9161	−2.23881
$135$	1.96861	0.169431
$136$	−11.9317	−1.02313
$137$	−10.4669	−0.894248	−0.447124	−	0.894472i	$-0.647552\pi$
$137$	−10.4669	−0.894248	−0.447124	+	0.894472i	$0.647552\pi$
$138$	−8.16552	−0.695095
$139$	8.65629	0.734217	0.367108	−	0.930178i	$-0.380348\pi$
$139$	8.65629	0.734217	0.367108	+	0.930178i	$0.380348\pi$
$140$	34.2194	2.89206
$141$	12.1279	1.02136
$142$	−15.5069	−1.30131
$143$	9.14635	0.764856
$144$	3.03029	0.252524
$145$	12.4537	1.03423
$146$	−28.2065	−2.33439
$147$	−13.5575	−1.11821
$148$	−15.2104	−1.25029
$149$	8.67715	0.710860	0.355430	−	0.934703i	$-0.384334\pi$
$149$	8.67715	0.710860	0.355430	+	0.934703i	$0.384334\pi$
$150$	−2.71620	−0.221777
$151$	5.78122	0.470469	0.235234	−	0.971939i	$-0.424414\pi$
$151$	5.78122	0.470469	0.235234	+	0.971939i	$0.424414\pi$
$152$	−24.8662	−2.01691
$153$	2.69389	0.217788
$154$	−58.8723	−4.74406
$155$	2.36710	0.190130
$156$	6.52266	0.522230
$157$	−0.822662	−0.0656556	−0.0328278	−	0.999461i	$-0.510451\pi$
$157$	−0.822662	−0.0656556	−0.0328278	+	0.999461i	$0.510451\pi$
$158$	7.19567	0.572456
$159$	4.43992	0.352109
$160$	−3.03007	−0.239548
$161$	15.3283	1.20804
$162$	−2.41532	−0.189766
$163$	19.2511	1.50786	0.753930	−	0.656955i	$-0.228156\pi$
$163$	19.2511	1.50786	0.753930	+	0.656955i	$0.228156\pi$
$164$	41.3802	3.23125
$165$	−10.5830	−0.823888
$166$	1.32282	0.102671
$167$	−6.52250	−0.504726	−0.252363	−	0.967633i	$-0.581208\pi$
$167$	−6.52250	−0.504726	−0.252363	+	0.967633i	$0.581208\pi$
$168$	−20.0820	−1.54936
$169$	−10.1054	−0.777335
$170$	12.8090	0.982404
$171$	5.61419	0.429328
$172$	−7.77631	−0.592938
$173$	6.45087	0.490450	0.245225	−	0.969466i	$-0.421138\pi$
$173$	6.45087	0.490450	0.245225	+	0.969466i	$0.421138\pi$
$174$	−15.2797	−1.15835
$175$	5.09886	0.385437
$176$	−16.2905	−1.22794
$177$	7.47854	0.562121
$178$	−17.9219	−1.34330
$179$	−12.6077	−0.942347	−0.471174	−	0.882040i	$-0.656170\pi$
$179$	−12.6077	−0.942347	−0.471174	+	0.882040i	$0.656170\pi$
$180$	−7.54721	−0.562536
$181$	−16.6180	−1.23521	−0.617603	−	0.786490i	$-0.711896\pi$
$181$	−16.6180	−1.23521	−0.617603	+	0.786490i	$0.711896\pi$
$182$	−18.6319	−1.38109
$183$	−13.5016	−0.998070
$184$	14.9737	1.10388
$185$	7.81040	0.574232
$186$	−2.90423	−0.212949
$187$	−14.4821	−1.05903
$188$	−46.4958	−3.39105
$189$	4.53404	0.329803
$190$	26.6945	1.93662
$191$	15.8699	1.14831	0.574153	−	0.818748i	$-0.305332\pi$
$191$	15.8699	1.14831	0.574153	+	0.818748i	$0.305332\pi$
$192$	9.77823	0.705683
$193$	−11.7646	−0.846838	−0.423419	−	0.905934i	$-0.639170\pi$
$193$	−11.7646	−0.846838	−0.423419	+	0.905934i	$0.639170\pi$
$194$	−1.60814	−0.115457
$195$	−3.34933	−0.239850
$196$	51.9765	3.71261
$197$	−5.09166	−0.362765	−0.181383	−	0.983413i	$-0.558057\pi$
$197$	−5.09166	−0.362765	−0.181383	+	0.983413i	$0.558057\pi$
$198$	12.9845	0.922768
$199$	0.340417	0.0241315	0.0120658	−	0.999927i	$-0.496159\pi$
$199$	0.340417	0.0241315	0.0120658	+	0.999927i	$0.496159\pi$
$200$	4.98091	0.352204
$201$	−10.7299	−0.756828
$202$	15.8605	1.11594
$203$	28.6831	2.01316
$204$	−10.3278	−0.723089
$205$	−21.2484	−1.48405
$206$	1.18429	0.0825136
$207$	−3.38072	−0.234976
$208$	−5.15563	−0.357479
$209$	−30.1813	−2.08768
$210$	21.5586	1.48768
$211$	22.8548	1.57339	0.786696	−	0.617341i	$-0.211790\pi$
$211$	22.8548	1.57339	0.786696	+	0.617341i	$0.211790\pi$
$212$	−17.0217	−1.16905
$213$	−6.42020	−0.439905
$214$	−1.10396	−0.0754650
$215$	3.99307	0.272325
$216$	4.42916	0.301366
$217$	5.45182	0.370094
$218$	−42.8221	−2.90028
$219$	−11.6782	−0.789138
$220$	40.5730	2.73543
$221$	−4.58329	−0.308306
$222$	−9.58271	−0.643150
$223$	−5.19337	−0.347774	−0.173887	−	0.984766i	$-0.555633\pi$
$223$	−5.19337	−0.347774	−0.173887	+	0.984766i	$0.555633\pi$
$224$	−6.97877	−0.466289
$225$	−1.12457	−0.0749715
$226$	−21.2122	−1.41102
$227$	13.8616	0.920024	0.460012	−	0.887913i	$-0.347845\pi$
$227$	13.8616	0.920024	0.460012	+	0.887913i	$0.347845\pi$
$228$	−21.5236	−1.42543
$229$	16.9886	1.12264	0.561321	−	0.827598i	$-0.310293\pi$
$229$	16.9886	1.12264	0.561321	+	0.827598i	$0.310293\pi$
$230$	−16.0747	−1.05994
$231$	−24.3745	−1.60372
$232$	28.0196	1.83958
$233$	−3.88888	−0.254769	−0.127385	−	0.991853i	$-0.540658\pi$
$233$	−3.88888	−0.254769	−0.127385	+	0.991853i	$0.540658\pi$
$234$	4.10934	0.268636
$235$	23.8752	1.55745
$236$	−28.6710	−1.86633
$237$	2.97918	0.193518
$238$	29.5012	1.91228
$239$	10.3059	0.666632	0.333316	−	0.942815i	$-0.391832\pi$
$239$	10.3059	0.666632	0.333316	+	0.942815i	$0.391832\pi$
$240$	5.96546	0.385069
$241$	−7.47916	−0.481775	−0.240887	−	0.970553i	$-0.577438\pi$
$241$	−7.47916	−0.481775	−0.240887	+	0.970553i	$0.577438\pi$
$242$	−43.2347	−2.77923
$243$	−1.00000	−0.0641500
$244$	51.7623	3.31374
$245$	−26.6895	−1.70513
$246$	26.0700	1.66216
$247$	−9.55179	−0.607766
$248$	5.32571	0.338183
$249$	0.547679	0.0347077
$250$	−29.1213	−1.84179
$251$	12.4707	0.787141	0.393570	−	0.919294i	$-0.371240\pi$
$251$	12.4707	0.787141	0.393570	+	0.919294i	$0.371240\pi$
$252$	−17.3825	−1.09499
$253$	18.1744	1.14261
$254$	−3.45673	−0.216895
$255$	5.30322	0.332100
$256$	−30.0523	−1.87827
$257$	−23.8600	−1.48834	−0.744172	−	0.667988i	$-0.767156\pi$
$257$	−23.8600	−1.48834	−0.744172	+	0.667988i	$0.767156\pi$
$258$	−4.89916	−0.305008
$259$	17.9887	1.11776
$260$	12.8406	0.796338
$261$	−6.32616	−0.391579
$262$	45.5303	2.81287
$263$	10.1958	0.628702	0.314351	−	0.949307i	$-0.398213\pi$
$263$	10.1958	0.628702	0.314351	+	0.949307i	$0.398213\pi$
$264$	−23.8107	−1.46545
$265$	8.74048	0.536923
$266$	61.4819	3.76970
$267$	−7.42009	−0.454102
$268$	41.1360	2.51278
$269$	26.9130	1.64091	0.820456	−	0.571710i	$-0.193720\pi$
$269$	26.9130	1.64091	0.820456	+	0.571710i	$0.193720\pi$
$270$	−4.75483	−0.289370
$271$	−25.9269	−1.57495	−0.787473	−	0.616349i	$-0.788611\pi$
$271$	−25.9269	−1.57495	−0.787473	+	0.616349i	$0.788611\pi$
$272$	8.16327	0.494971
$273$	−7.71406	−0.466876
$274$	25.2809	1.52728
$275$	6.04558	0.364562
$276$	12.9609	0.780156
$277$	22.0209	1.32311	0.661553	−	0.749898i	$-0.269898\pi$
$277$	22.0209	1.32311	0.661553	+	0.749898i	$0.269898\pi$
$278$	−20.9077	−1.25396
$279$	−1.20242	−0.0719870
$280$	−39.5336	−2.36259
$281$	23.0441	1.37469	0.687347	−	0.726329i	$-0.258775\pi$
$281$	23.0441	1.37469	0.687347	+	0.726329i	$0.258775\pi$
$282$	−29.2929	−1.74436
$283$	−3.72911	−0.221673	−0.110836	−	0.993839i	$-0.535353\pi$
$283$	−3.72911	−0.221673	−0.110836	+	0.993839i	$0.535353\pi$
$284$	24.6136	1.46055
$285$	11.0522	0.654673
$286$	−22.0914	−1.30629
$287$	−48.9386	−2.88875
$288$	1.53919	0.0906979
$289$	−9.74296	−0.573115
$290$	−30.0798	−1.76635
$291$	−0.665806	−0.0390302
$292$	44.7715	2.62005
$293$	−23.2085	−1.35585	−0.677927	−	0.735129i	$-0.737122\pi$
$293$	−23.2085	−1.35585	−0.677927	+	0.735129i	$0.737122\pi$
$294$	32.7458	1.90977
$295$	14.7223	0.857167
$296$	17.5726	1.02138
$297$	5.37589	0.311941
$298$	−20.9581	−1.21407
$299$	5.75184	0.332637
$300$	4.31136	0.248916
$301$	9.19670	0.530089
$302$	−13.9635	−0.803509
$303$	6.56660	0.377241
$304$	17.0126	0.975741
$305$	−26.5795	−1.52194
$306$	−6.50661	−0.371958
$307$	−11.2415	−0.641584	−0.320792	−	0.947150i	$-0.603949\pi$
$307$	−11.2415	−0.641584	−0.320792	+	0.947150i	$0.603949\pi$
$308$	93.4464	5.32460
$309$	0.490325	0.0278936
$310$	−5.71730	−0.324721
$311$	−17.7383	−1.00585	−0.502923	−	0.864331i	$-0.667742\pi$
$311$	−17.7383	−1.00585	−0.502923	+	0.864331i	$0.667742\pi$
$312$	−7.53562	−0.426620
$313$	−27.9720	−1.58107	−0.790535	−	0.612417i	$-0.790197\pi$
$313$	−27.9720	−1.58107	−0.790535	+	0.612417i	$0.790197\pi$
$314$	1.98699	0.112132
$315$	8.92576	0.502910
$316$	−11.4215	−0.642509
$317$	11.6894	0.656543	0.328272	−	0.944583i	$-0.393534\pi$
$317$	11.6894	0.656543	0.328272	+	0.944583i	$0.393534\pi$
$318$	−10.7238	−0.601363
$319$	34.0087	1.90412
$320$	19.2495	1.07608
$321$	−0.457065	−0.0255109
$322$	−37.0228	−2.06320
$323$	15.1240	0.841523
$324$	3.83378	0.212988
$325$	1.91331	0.106131
$326$	−46.4975	−2.57526
$327$	−17.7294	−0.980437
$328$	−47.8065	−2.63967
$329$	54.9886	3.03162
$330$	25.5614	1.40711
$331$	24.2000	1.33015	0.665076	−	0.746775i	$-0.268399\pi$
$331$	24.2000	1.33015	0.665076	+	0.746775i	$0.268399\pi$
$332$	−2.09968	−0.115235
$333$	−3.96747	−0.217416
$334$	15.7539	0.862016
$335$	−21.1230	−1.15407
$336$	13.7395	0.749549
$337$	−16.1084	−0.877483	−0.438742	−	0.898613i	$-0.644576\pi$
$337$	−16.1084	−0.877483	−0.438742	+	0.898613i	$0.644576\pi$
$338$	24.4077	1.32760
$339$	−8.78236	−0.476992
$340$	−20.3314	−1.10262
$341$	6.46408	0.350050
$342$	−13.5601	−0.733245
$343$	−29.7321	−1.60538
$344$	8.98396	0.484383
$345$	−6.65532	−0.358310
$346$	−15.5809	−0.837635
$347$	31.0649	1.66765	0.833824	−	0.552030i	$-0.186147\pi$
$347$	31.0649	1.66765	0.833824	+	0.552030i	$0.186147\pi$
$348$	24.2531	1.30010
$349$	17.0698	0.913723	0.456862	−	0.889538i	$-0.348973\pi$
$349$	17.0698	0.913723	0.456862	+	0.889538i	$0.348973\pi$
$350$	−12.3154	−0.658285
$351$	1.70137	0.0908122
$352$	−8.27454	−0.441034
$353$	27.3817	1.45738	0.728691	−	0.684842i	$-0.240129\pi$
$353$	27.3817	1.45738	0.728691	+	0.684842i	$0.240129\pi$
$354$	−18.0631	−0.960041
$355$	−12.6389	−0.670802
$356$	28.4470	1.50769
$357$	12.2142	0.646444
$358$	30.4518	1.60943
$359$	−30.6894	−1.61973	−0.809863	−	0.586618i	$-0.800459\pi$
$359$	−30.6894	−1.61973	−0.809863	+	0.586618i	$0.800459\pi$
$360$	8.71929	0.459547
$361$	12.5192	0.658903
$362$	40.1378	2.10960
$363$	−17.9002	−0.939516
$364$	29.5740	1.55010
$365$	−22.9898	−1.20334
$366$	32.6108	1.70459
$367$	−35.0459	−1.82938	−0.914691	−	0.404154i	$-0.867566\pi$
$367$	−35.0459	−1.82938	−0.914691	+	0.404154i	$0.867566\pi$
$368$	−10.2446	−0.534035
$369$	10.7936	0.561892
$370$	−18.8646	−0.980725
$371$	20.1308	1.04514
$372$	4.60981	0.239008
$373$	−18.8491	−0.975969	−0.487984	−	0.872852i	$-0.662268\pi$
$373$	−18.8491	−0.975969	−0.487984	+	0.872852i	$0.662268\pi$
$374$	34.9788	1.80871
$375$	−12.0569	−0.622616
$376$	53.7166	2.77022
$377$	10.7631	0.554328
$378$	−10.9512	−0.563267
$379$	37.5411	1.92836	0.964179	−	0.265251i	$-0.0854548\pi$
$379$	37.5411	1.92836	0.964179	+	0.265251i	$0.0854548\pi$
$380$	−42.3715	−2.17361
$381$	−1.43117	−0.0733210
$382$	−38.3309	−1.96118
$383$	−10.3227	−0.527464	−0.263732	−	0.964596i	$-0.584953\pi$
$383$	−10.3227	−0.527464	−0.263732	+	0.964596i	$0.584953\pi$
$384$	−20.5392	−1.04814
$385$	−47.9839	−2.44549
$386$	28.4154	1.44631
$387$	−2.02837	−0.103108
$388$	2.55255	0.129586
$389$	−7.76922	−0.393915	−0.196958	−	0.980412i	$-0.563106\pi$
$389$	−7.76922	−0.393915	−0.196958	+	0.980412i	$0.563106\pi$
$390$	8.08970	0.409638
$391$	−9.10728	−0.460575
$392$	−60.0484	−3.03290
$393$	18.8506	0.950889
$394$	12.2980	0.619564
$395$	5.86484	0.295092
$396$	−20.6100	−1.03569
$397$	35.4859	1.78099	0.890493	−	0.454996i	$-0.150359\pi$
$397$	35.4859	1.78099	0.890493	+	0.454996i	$0.150359\pi$
$398$	−0.822217	−0.0412140
$399$	25.4550	1.27434
$400$	−3.40778	−0.170389
$401$	−33.8473	−1.69025	−0.845127	−	0.534565i	$-0.820475\pi$
$401$	−33.8473	−1.69025	−0.845127	+	0.534565i	$0.820475\pi$
$402$	25.9161	1.29258
$403$	2.04576	0.101906
$404$	−25.1749	−1.25250
$405$	−1.96861	−0.0978210
$406$	−69.2788	−3.43825
$407$	21.3287	1.05722
$408$	11.9317	0.590706
$409$	1.78039	0.0880344	0.0440172	−	0.999031i	$-0.485984\pi$
$409$	1.78039	0.0880344	0.0440172	+	0.999031i	$0.485984\pi$
$410$	51.3216	2.53460
$411$	10.4669	0.516294
$412$	−1.87980	−0.0926110
$413$	33.9080	1.66850
$414$	8.16552	0.401314
$415$	1.07817	0.0529251
$416$	−2.61873	−0.128394
$417$	−8.65629	−0.423900
$418$	72.8975	3.56553
$419$	−17.2406	−0.842260	−0.421130	−	0.907000i	$-0.638366\pi$
$419$	−17.2406	−0.842260	−0.421130	+	0.907000i	$0.638366\pi$
$420$	−34.2194	−1.66973
$421$	−0.959567	−0.0467664	−0.0233832	−	0.999727i	$-0.507444\pi$
$421$	−0.959567	−0.0467664	−0.0233832	+	0.999727i	$0.507444\pi$
$422$	−55.2018	−2.68718
$423$	−12.1279	−0.589680
$424$	19.6651	0.955023
$425$	−3.02947	−0.146951
$426$	15.5069	0.751310
$427$	−61.2170	−2.96250
$428$	1.75228	0.0846998
$429$	−9.14635	−0.441590
$430$	−9.64454	−0.465101
$431$	−8.29484	−0.399548	−0.199774	−	0.979842i	$-0.564021\pi$
$431$	−8.29484	−0.399548	−0.199774	+	0.979842i	$0.564021\pi$
$432$	−3.03029	−0.145795
$433$	19.6062	0.942216	0.471108	−	0.882076i	$-0.343854\pi$
$433$	19.6062	0.942216	0.471108	+	0.882076i	$0.343854\pi$
$434$	−13.1679	−0.632080
$435$	−12.4537	−0.597111
$436$	67.9705	3.25519
$437$	−18.9800	−0.907937
$438$	28.2065	1.34776
$439$	22.0424	1.05203	0.526014	−	0.850476i	$-0.323686\pi$
$439$	22.0424	1.05203	0.526014	+	0.850476i	$0.323686\pi$
$440$	−46.8739	−2.23463
$441$	13.5575	0.645596
$442$	11.0701	0.526552
$443$	29.8108	1.41635	0.708176	−	0.706036i	$-0.249518\pi$
$443$	29.8108	1.41635	0.708176	+	0.706036i	$0.249518\pi$
$444$	15.2104	0.721853
$445$	−14.6073	−0.692450
$446$	12.5437	0.593959
$447$	−8.67715	−0.410415
$448$	44.3349	2.09463
$449$	7.94191	0.374802	0.187401	−	0.982284i	$-0.439994\pi$
$449$	7.94191	0.374802	0.187401	+	0.982284i	$0.439994\pi$
$450$	2.71620	0.128043
$451$	−58.0251	−2.73230
$452$	33.6696	1.58368
$453$	−5.78122	−0.271625
$454$	−33.4801	−1.57130
$455$	−15.1860	−0.711930
$456$	24.8662	1.16446
$457$	−0.285135	−0.0133380	−0.00666902	−	0.999978i	$-0.502123\pi$
$457$	−0.285135	−0.0133380	−0.00666902	+	0.999978i	$0.502123\pi$
$458$	−41.0330	−1.91735
$459$	−2.69389	−0.125740
$460$	25.5150	1.18964
$461$	−16.5096	−0.768930	−0.384465	−	0.923140i	$-0.625614\pi$
$461$	−16.5096	−0.768930	−0.384465	+	0.923140i	$0.625614\pi$
$462$	58.8723	2.73898
$463$	8.18264	0.380280	0.190140	−	0.981757i	$-0.439106\pi$
$463$	8.18264	0.380280	0.190140	+	0.981757i	$0.439106\pi$
$464$	−19.1701	−0.889950
$465$	−2.36710	−0.109772
$466$	9.39290	0.435118
$467$	−23.0873	−1.06835	−0.534177	−	0.845373i	$-0.679378\pi$
$467$	−23.0873	−1.06835	−0.534177	+	0.845373i	$0.679378\pi$
$468$	−6.52266	−0.301510
$469$	−48.6498	−2.24644
$470$	−57.6662	−2.65995
$471$	0.822662	0.0379063
$472$	33.1236	1.52464
$473$	10.9043	0.501379
$474$	−7.19567	−0.330508
$475$	−6.31357	−0.289686
$476$	−46.8265	−2.14629
$477$	−4.43992	−0.203290
$478$	−24.8920	−1.13853
$479$	−14.0990	−0.644201	−0.322101	−	0.946705i	$-0.604389\pi$
$479$	−14.0990	−0.644201	−0.322101	+	0.946705i	$0.604389\pi$
$480$	3.03007	0.138303
$481$	6.75011	0.307779
$482$	18.0646	0.822819
$483$	−15.3283	−0.697463
$484$	68.6253	3.11933
$485$	−1.31071	−0.0595164
$486$	2.41532	0.109561
$487$	−12.7234	−0.576552	−0.288276	−	0.957547i	$-0.593082\pi$
$487$	−12.7234	−0.576552	−0.288276	+	0.957547i	$0.593082\pi$
$488$	−59.8009	−2.70706
$489$	−19.2511	−0.870563
$490$	64.4637	2.91217
$491$	−33.6131	−1.51694	−0.758469	−	0.651709i	$-0.774052\pi$
$491$	−33.6131	−1.51694	−0.758469	+	0.651709i	$0.774052\pi$
$492$	−41.3802	−1.86556
$493$	−17.0420	−0.767532
$494$	23.0706	1.03800
$495$	10.5830	0.475672
$496$	−3.64368	−0.163606
$497$	−29.1095	−1.30574
$498$	−1.32282	−0.0592770
$499$	2.38317	0.106685	0.0533426	−	0.998576i	$-0.483012\pi$
$499$	2.38317	0.106685	0.0533426	+	0.998576i	$0.483012\pi$
$500$	46.2235	2.06718
$501$	6.52250	0.291404
$502$	−30.1206	−1.34435
$503$	−15.6188	−0.696407	−0.348203	−	0.937419i	$-0.613208\pi$
$503$	−15.6188	−0.696407	−0.348203	+	0.937419i	$0.613208\pi$
$504$	20.0820	0.894523
$505$	12.9271	0.575248
$506$	−43.8969	−1.95146
$507$	10.1054	0.448795
$508$	5.48678	0.243437
$509$	−3.29404	−0.146006	−0.0730028	−	0.997332i	$-0.523258\pi$
$509$	−3.29404	−0.146006	−0.0730028	+	0.997332i	$0.523258\pi$
$510$	−12.8090	−0.567191
$511$	−52.9493	−2.34234
$512$	31.5075	1.39245
$513$	−5.61419	−0.247873
$514$	57.6295	2.54193
$515$	0.965260	0.0425344
$516$	7.77631	0.342333
$517$	65.1984	2.86742
$518$	−43.4484	−1.90901
$519$	−6.45087	−0.283162
$520$	−14.8347	−0.650545
$521$	−20.0188	−0.877041	−0.438520	−	0.898721i	$-0.644497\pi$
$521$	−20.0188	−0.877041	−0.438520	+	0.898721i	$0.644497\pi$
$522$	15.2797	0.668775
$523$	−26.7902	−1.17145	−0.585727	−	0.810509i	$-0.699191\pi$
$523$	−26.7902	−1.17145	−0.585727	+	0.810509i	$0.699191\pi$
$524$	−72.2691	−3.15709
$525$	−5.09886	−0.222532
$526$	−24.6262	−1.07375
$527$	−3.23919	−0.141101
$528$	16.2905	0.708953
$529$	−11.5707	−0.503076
$530$	−21.1111	−0.917006
$531$	−7.47854	−0.324541
$532$	−97.5887	−4.23101
$533$	−18.3638	−0.795426
$534$	17.9219	0.775556
$535$	−0.899782	−0.0389010
$536$	−47.5244	−2.05274
$537$	12.6077	0.544065
$538$	−65.0034	−2.80250
$539$	−72.8838	−3.13933
$540$	7.54721	0.324780
$541$	23.9002	1.02755	0.513776	−	0.857925i	$-0.328246\pi$
$541$	23.9002	1.02755	0.513776	+	0.857925i	$0.328246\pi$
$542$	62.6217	2.68983
$543$	16.6180	0.713146
$544$	4.14642	0.177776
$545$	−34.9022	−1.49505
$546$	18.6319	0.797373
$547$	−29.3877	−1.25653	−0.628265	−	0.778000i	$-0.716235\pi$
$547$	−29.3877	−1.25653	−0.628265	+	0.778000i	$0.716235\pi$
$548$	−40.1278	−1.71417
$549$	13.5016	0.576236
$550$	−14.6020	−0.622632
$551$	−35.5163	−1.51304
$552$	−14.9737	−0.637325
$553$	13.5077	0.574406
$554$	−53.1875	−2.25972
$555$	−7.81040	−0.331533
$556$	33.1863	1.40741
$557$	19.1255	0.810373	0.405186	−	0.914234i	$-0.367207\pi$
$557$	19.1255	0.810373	0.405186	+	0.914234i	$0.367207\pi$
$558$	2.90423	0.122946
$559$	3.45099	0.145962
$560$	27.0476	1.14297
$561$	14.4821	0.611433
$562$	−55.6588	−2.34783
$563$	17.6953	0.745767	0.372884	−	0.927878i	$-0.378369\pi$
$563$	17.6953	0.745767	0.372884	+	0.927878i	$0.378369\pi$
$564$	46.4958	1.95783
$565$	−17.2890	−0.727356
$566$	9.00701	0.378593
$567$	−4.53404	−0.190412
$568$	−28.4361	−1.19315
$569$	18.9007	0.792358	0.396179	−	0.918173i	$-0.370336\pi$
$569$	18.9007	0.792358	0.396179	+	0.918173i	$0.370336\pi$
$570$	−26.6945	−1.11811
$571$	−17.0671	−0.714237	−0.357118	−	0.934059i	$-0.616241\pi$
$571$	−17.0671	−0.714237	−0.357118	+	0.934059i	$0.616241\pi$
$572$	35.0651	1.46614
$573$	−15.8699	−0.662974
$574$	118.202	4.93367
$575$	3.80186	0.158549
$576$	−9.77823	−0.407426
$577$	33.1348	1.37942	0.689710	−	0.724085i	$-0.257738\pi$
$577$	33.1348	1.37942	0.689710	+	0.724085i	$0.257738\pi$
$578$	23.5324	0.978818
$579$	11.7646	0.488922
$580$	47.7449	1.98250
$581$	2.48320	0.103020
$582$	1.60814	0.0666594
$583$	23.8685	0.988534
$584$	−51.7245	−2.14037
$585$	3.34933	0.138478
$586$	56.0560	2.31565
$587$	−2.48868	−0.102719	−0.0513595	−	0.998680i	$-0.516355\pi$
$587$	−2.48868	−0.102719	−0.0513595	+	0.998680i	$0.516355\pi$
$588$	−51.9765	−2.14348
$589$	−6.75062	−0.278154
$590$	−35.5591	−1.46395
$591$	5.09166	0.209443
$592$	−12.0226	−0.494125
$593$	17.1755	0.705311	0.352656	−	0.935753i	$-0.385279\pi$
$593$	17.1755	0.705311	0.352656	+	0.935753i	$0.385279\pi$
$594$	−12.9845	−0.532760
$595$	24.0450	0.985749
$596$	33.2663	1.36264
$597$	−0.340417	−0.0139324
$598$	−13.8925	−0.568108
$599$	20.2677	0.828115	0.414058	−	0.910251i	$-0.364111\pi$
$599$	20.2677	0.828115	0.414058	+	0.910251i	$0.364111\pi$
$600$	−4.98091	−0.203345
$601$	20.9288	0.853705	0.426853	−	0.904321i	$-0.359622\pi$
$601$	20.9288	0.853705	0.426853	+	0.904321i	$0.359622\pi$
$602$	−22.2130	−0.905334
$603$	10.7299	0.436955
$604$	22.1639	0.901836
$605$	−35.2385	−1.43265
$606$	−15.8605	−0.644287
$607$	−48.0309	−1.94951	−0.974757	−	0.223269i	$-0.928327\pi$
$607$	−48.0309	−1.94951	−0.974757	+	0.223269i	$0.928327\pi$
$608$	8.64133	0.350452
$609$	−28.6831	−1.16230
$610$	64.1980	2.59930
$611$	20.6341	0.834764
$612$	10.3278	0.417475
$613$	−25.7481	−1.03995	−0.519977	−	0.854180i	$-0.674060\pi$
$613$	−25.7481	−1.03995	−0.519977	+	0.854180i	$0.674060\pi$
$614$	27.1518	1.09576
$615$	21.2484	0.856817
$616$	−107.959	−4.34977
$617$	13.4103	0.539878	0.269939	−	0.962877i	$-0.412996\pi$
$617$	13.4103	0.539878	0.269939	+	0.962877i	$0.412996\pi$
$618$	−1.18429	−0.0476393
$619$	9.33090	0.375040	0.187520	−	0.982261i	$-0.439955\pi$
$619$	9.33090	0.375040	0.187520	+	0.982261i	$0.439955\pi$
$620$	9.07493	0.364458
$621$	3.38072	0.135664
$622$	42.8437	1.71787
$623$	−33.6430	−1.34788
$624$	5.15563	0.206390
$625$	−18.1125	−0.724499
$626$	67.5613	2.70029
$627$	30.1813	1.20532
$628$	−3.15390	−0.125854
$629$	−10.6879	−0.426155
$630$	−21.5586	−0.858914
$631$	39.1498	1.55853	0.779264	−	0.626696i	$-0.215593\pi$
$631$	39.1498	1.55853	0.779264	+	0.626696i	$0.215593\pi$
$632$	13.1952	0.524879
$633$	−22.8548	−0.908398
$634$	−28.2337	−1.12130
$635$	−2.81742	−0.111806
$636$	17.0217	0.674953
$637$	−23.0663	−0.913920
$638$	−82.1420	−3.25203
$639$	6.42020	0.253979
$640$	−40.4336	−1.59828
$641$	−1.71777	−0.0678480	−0.0339240	−	0.999424i	$-0.510800\pi$
$641$	−1.71777	−0.0678480	−0.0339240	+	0.999424i	$0.510800\pi$
$642$	1.10396	0.0435698
$643$	0.0733525	0.00289274	0.00144637	−	0.999999i	$-0.499540\pi$
$643$	0.0733525	0.00289274	0.00144637	+	0.999999i	$0.499540\pi$
$644$	58.7654	2.31568
$645$	−3.99307	−0.157227
$646$	−36.5294	−1.43723
$647$	−8.65748	−0.340361	−0.170180	−	0.985413i	$-0.554435\pi$
$647$	−8.65748	−0.340361	−0.170180	+	0.985413i	$0.554435\pi$
$648$	−4.42916	−0.173994
$649$	40.2038	1.57814
$650$	−4.62126	−0.181261
$651$	−5.45182	−0.213674
$652$	73.8043	2.89040
$653$	−30.2410	−1.18342	−0.591711	−	0.806150i	$-0.701547\pi$
$653$	−30.2410	−1.18342	−0.591711	+	0.806150i	$0.701547\pi$
$654$	42.8221	1.67448
$655$	37.1096	1.44999
$656$	32.7077	1.27702
$657$	11.6782	0.455609
$658$	−132.815	−5.17767
$659$	21.6307	0.842611	0.421306	−	0.906919i	$-0.361572\pi$
$659$	21.6307	0.842611	0.421306	+	0.906919i	$0.361572\pi$
$660$	−40.5730	−1.57930
$661$	−43.2492	−1.68220	−0.841099	−	0.540881i	$-0.818091\pi$
$661$	−43.2492	−1.68220	−0.841099	+	0.540881i	$0.818091\pi$
$662$	−58.4508	−2.27175
$663$	4.58329	0.178000
$664$	2.42576	0.0941376
$665$	50.1109	1.94322
$666$	9.58271	0.371323
$667$	21.3870	0.828107
$668$	−25.0058	−0.967503
$669$	5.19337	0.200787
$670$	51.0188	1.97103
$671$	−72.5833	−2.80205
$672$	6.97877	0.269212
$673$	31.9610	1.23201	0.616003	−	0.787744i	$-0.288751\pi$
$673$	31.9610	1.23201	0.616003	+	0.787744i	$0.288751\pi$
$674$	38.9071	1.49864
$675$	1.12457	0.0432848
$676$	−38.7417	−1.49006
$677$	−21.6088	−0.830492	−0.415246	−	0.909709i	$-0.636305\pi$
$677$	−21.6088	−0.830492	−0.415246	+	0.909709i	$0.636305\pi$
$678$	21.2122	0.814650
$679$	−3.01879	−0.115851
$680$	23.4888	0.900755
$681$	−13.8616	−0.531176
$682$	−15.6128	−0.597846
$683$	−8.82263	−0.337589	−0.168794	−	0.985651i	$-0.553987\pi$
$683$	−8.82263	−0.337589	−0.168794	+	0.985651i	$0.553987\pi$
$684$	21.5236	0.822974
$685$	20.6053	0.787286
$686$	71.8125	2.74181
$687$	−16.9886	−0.648157
$688$	−6.14654	−0.234335
$689$	7.55393	0.287782
$690$	16.0747	0.611955
$691$	−17.8298	−0.678276	−0.339138	−	0.940737i	$-0.610135\pi$
$691$	−17.8298	−0.678276	−0.339138	+	0.940737i	$0.610135\pi$
$692$	24.7312	0.940138
$693$	24.3745	0.925911
$694$	−75.0316	−2.84816
$695$	−17.0409	−0.646397
$696$	−28.0196	−1.06208
$697$	29.0767	1.10136
$698$	−41.2290	−1.56054
$699$	3.88888	0.147091
$700$	19.5479	0.738840
$701$	−29.3757	−1.10950	−0.554752	−	0.832016i	$-0.687187\pi$
$701$	−29.3757	−1.10950	−0.554752	+	0.832016i	$0.687187\pi$
$702$	−4.10934	−0.155097
$703$	−22.2741	−0.840085
$704$	52.5667	1.98118
$705$	−23.8752	−0.899191
$706$	−66.1357	−2.48905
$707$	29.7732	1.11974
$708$	28.6710	1.07752
$709$	30.6316	1.15039	0.575197	−	0.818015i	$-0.304925\pi$
$709$	30.6316	1.15039	0.575197	+	0.818015i	$0.304925\pi$
$710$	30.5270	1.14566
$711$	−2.97918	−0.111728
$712$	−32.8647	−1.23166
$713$	4.06505	0.152237
$714$	−29.5012	−1.10406
$715$	−18.0056	−0.673372
$716$	−48.3353	−1.80637
$717$	−10.3059	−0.384880
$718$	74.1249	2.76632
$719$	26.0086	0.969956	0.484978	−	0.874526i	$-0.338828\pi$
$719$	26.0086	0.969956	0.484978	+	0.874526i	$0.338828\pi$
$720$	−5.96546	−0.222320
$721$	2.22315	0.0827946
$722$	−30.2378	−1.12533
$723$	7.47916	0.278153
$724$	−63.7097	−2.36775
$725$	7.11423	0.264216
$726$	43.2347	1.60459
$727$	5.81159	0.215540	0.107770	−	0.994176i	$-0.465629\pi$
$727$	5.81159	0.215540	0.107770	+	0.994176i	$0.465629\pi$
$728$	−34.1668	−1.26631
$729$	1.00000	0.0370370
$730$	55.5277	2.05517
$731$	−5.46420	−0.202101
$732$	−51.7623	−1.91319
$733$	−26.2839	−0.970818	−0.485409	−	0.874287i	$-0.661329\pi$
$733$	−26.2839	−0.970818	−0.485409	+	0.874287i	$0.661329\pi$
$734$	84.6471	3.12438
$735$	26.6895	0.984456
$736$	−5.20358	−0.191807
$737$	−57.6827	−2.12477
$738$	−26.0700	−0.959649
$739$	−13.8809	−0.510618	−0.255309	−	0.966860i	$-0.582177\pi$
$739$	−13.8809	−0.510618	−0.255309	+	0.966860i	$0.582177\pi$
$740$	29.9433	1.10074
$741$	9.55179	0.350894
$742$	−48.6223	−1.78498
$743$	11.7980	0.432828	0.216414	−	0.976302i	$-0.430564\pi$
$743$	11.7980	0.432828	0.216414	+	0.976302i	$0.430564\pi$
$744$	−5.32571	−0.195250
$745$	−17.0819	−0.625834
$746$	45.5266	1.66685
$747$	−0.547679	−0.0200385
$748$	−55.5210	−2.03005
$749$	−2.07235	−0.0757220
$750$	29.1213	1.06336
$751$	−50.9617	−1.85962	−0.929810	−	0.368041i	$-0.880029\pi$
$751$	−50.9617	−1.85962	−0.929810	+	0.368041i	$0.880029\pi$
$752$	−36.7512	−1.34018
$753$	−12.4707	−0.454456
$754$	−25.9964	−0.946732
$755$	−11.3810	−0.414196
$756$	17.3825	0.632195
$757$	−28.4250	−1.03312	−0.516562	−	0.856250i	$-0.672789\pi$
$757$	−28.4250	−1.03312	−0.516562	+	0.856250i	$0.672789\pi$
$758$	−90.6739	−3.29342
$759$	−18.1744	−0.659688
$760$	48.9518	1.77567
$761$	8.77039	0.317926	0.158963	−	0.987285i	$-0.449185\pi$
$761$	8.77039	0.317926	0.158963	+	0.987285i	$0.449185\pi$
$762$	3.45673	0.125224
$763$	−80.3857	−2.91016
$764$	60.8416	2.20117
$765$	−5.30322	−0.191738
$766$	24.9326	0.900850
$767$	12.7237	0.459427
$768$	30.0523	1.08442
$769$	2.55780	0.0922366	0.0461183	−	0.998936i	$-0.485315\pi$
$769$	2.55780	0.0922366	0.0461183	+	0.998936i	$0.485315\pi$
$770$	115.897	4.17662
$771$	23.8600	0.859296
$772$	−45.1030	−1.62329
$773$	−53.6914	−1.93115	−0.965573	−	0.260132i	$-0.916234\pi$
$773$	−53.6914	−1.93115	−0.965573	+	0.260132i	$0.916234\pi$
$774$	4.89916	0.176097
$775$	1.35221	0.0485728
$776$	−2.94896	−0.105862
$777$	−17.9887	−0.645340
$778$	18.7652	0.672764
$779$	60.5973	2.17112
$780$	−12.8406	−0.459766
$781$	−34.5143	−1.23502
$782$	21.9970	0.786612
$783$	6.32616	0.226079
$784$	41.0832	1.46726
$785$	1.61950	0.0578025
$786$	−45.5303	−1.62401
$787$	13.4435	0.479211	0.239605	−	0.970870i	$-0.422982\pi$
$787$	13.4435	0.479211	0.239605	+	0.970870i	$0.422982\pi$
$788$	−19.5203	−0.695381
$789$	−10.1958	−0.362981
$790$	−14.1655	−0.503985
$791$	−39.8196	−1.41582
$792$	23.8107	0.846075
$793$	−22.9712	−0.815732
$794$	−85.7099	−3.04173
$795$	−8.74048	−0.309993
$796$	1.30508	0.0462575
$797$	−27.8803	−0.987570	−0.493785	−	0.869584i	$-0.664387\pi$
$797$	−27.8803	−0.987570	−0.493785	+	0.869584i	$0.664387\pi$
$798$	−61.4819	−2.17644
$799$	−32.6713	−1.15583
$800$	−1.73094	−0.0611978
$801$	7.42009	0.262176
$802$	81.7521	2.88677
$803$	−62.7806	−2.21548
$804$	−41.1360	−1.45076
$805$	−30.1755	−1.06355
$806$	−4.94116	−0.174045
$807$	−26.9130	−0.947381
$808$	29.0845	1.02319
$809$	31.1699	1.09587	0.547937	−	0.836519i	$-0.315413\pi$
$809$	31.1699	1.09587	0.547937	+	0.836519i	$0.315413\pi$
$810$	4.75483	0.167068
$811$	28.5355	1.00202	0.501009	−	0.865442i	$-0.332962\pi$
$811$	28.5355	1.00202	0.501009	+	0.865442i	$0.332962\pi$
$812$	109.964	3.85900
$813$	25.9269	0.909295
$814$	−51.5156	−1.80562
$815$	−37.8978	−1.32750
$816$	−8.16327	−0.285772
$817$	−11.3876	−0.398403
$818$	−4.30021	−0.150353
$819$	7.71406	0.269551
$820$	−81.4615	−2.84476
$821$	−46.3478	−1.61755	−0.808775	−	0.588118i	$-0.799869\pi$
$821$	−46.3478	−1.61755	−0.808775	+	0.588118i	$0.799869\pi$
$822$	−25.2809	−0.881774
$823$	−46.4595	−1.61948	−0.809739	−	0.586790i	$-0.800391\pi$
$823$	−46.4595	−1.61948	−0.809739	+	0.586790i	$0.800391\pi$
$824$	2.17173	0.0756558
$825$	−6.04558	−0.210480
$826$	−81.8987	−2.84962
$827$	6.96859	0.242322	0.121161	−	0.992633i	$-0.461338\pi$
$827$	6.96859	0.242322	0.121161	+	0.992633i	$0.461338\pi$
$828$	−12.9609	−0.450423
$829$	−50.4754	−1.75308	−0.876542	−	0.481325i	$-0.840156\pi$
$829$	−50.4754	−1.75308	−0.876542	+	0.481325i	$0.840156\pi$
$830$	−2.60412	−0.0903902
$831$	−22.0209	−0.763896
$832$	16.6363	0.576761
$833$	36.5225	1.26543
$834$	20.9077	0.723975
$835$	12.8403	0.444355
$836$	−115.708	−4.00185
$837$	1.20242	0.0415617
$838$	41.6417	1.43849
$839$	−21.6674	−0.748043	−0.374021	−	0.927420i	$-0.622021\pi$
$839$	−21.6674	−0.748043	−0.374021	+	0.927420i	$0.622021\pi$
$840$	39.5336	1.36404
$841$	11.0203	0.380010
$842$	2.31766	0.0798719
$843$	−23.0441	−0.793680
$844$	87.6203	3.01602
$845$	19.8935	0.684358
$846$	29.2929	1.00711
$847$	−81.1602	−2.78870
$848$	−13.4543	−0.462021
$849$	3.72911	0.127983
$850$	7.31715	0.250976
$851$	13.4129	0.459788
$852$	−24.6136	−0.843249
$853$	46.8309	1.60346	0.801730	−	0.597687i	$-0.203913\pi$
$853$	46.8309	1.60346	0.801730	+	0.597687i	$0.203913\pi$
$854$	147.859	5.05962
$855$	−11.0522	−0.377976
$856$	−2.02441	−0.0691930
$857$	32.2150	1.10044	0.550221	−	0.835019i	$-0.314543\pi$
$857$	32.2150	1.10044	0.550221	+	0.835019i	$0.314543\pi$
$858$	22.0914	0.754187
$859$	−23.5695	−0.804181	−0.402091	−	0.915600i	$-0.631716\pi$
$859$	−23.5695	−0.804181	−0.402091	+	0.915600i	$0.631716\pi$
$860$	15.3085	0.522016
$861$	48.9386	1.66782
$862$	20.0347	0.682384
$863$	2.54873	0.0867597	0.0433798	−	0.999059i	$-0.486187\pi$
$863$	2.54873	0.0867597	0.0433798	+	0.999059i	$0.486187\pi$
$864$	−1.53919	−0.0523645
$865$	−12.6992	−0.431787
$866$	−47.3554	−1.60920
$867$	9.74296	0.330888
$868$	20.9011	0.709429
$869$	16.0157	0.543296
$870$	30.0798	1.01980
$871$	−18.2555	−0.618563
$872$	−78.5262	−2.65923
$873$	0.665806	0.0225341
$874$	45.8428	1.55066
$875$	−54.6665	−1.84806
$876$	−44.7715	−1.51269
$877$	−15.2919	−0.516372	−0.258186	−	0.966095i	$-0.583125\pi$
$877$	−15.2919	−0.516372	−0.258186	+	0.966095i	$0.583125\pi$
$878$	−53.2396	−1.79675
$879$	23.2085	0.782803
$880$	32.0697	1.08107
$881$	45.8826	1.54582	0.772911	−	0.634514i	$-0.218800\pi$
$881$	45.8826	1.54582	0.772911	+	0.634514i	$0.218800\pi$
$882$	−32.7458	−1.10261
$883$	−39.6299	−1.33365	−0.666826	−	0.745213i	$-0.732348\pi$
$883$	−39.6299	−1.33365	−0.666826	+	0.745213i	$0.732348\pi$
$884$	−17.5713	−0.590987
$885$	−14.7223	−0.494885
$886$	−72.0026	−2.41897
$887$	8.11234	0.272386	0.136193	−	0.990682i	$-0.456513\pi$
$887$	8.11234	0.272386	0.136193	+	0.990682i	$0.456513\pi$
$888$	−17.5726	−0.589696
$889$	−6.48898	−0.217633
$890$	35.2812	1.18263
$891$	−5.37589	−0.180099
$892$	−19.9102	−0.666643
$893$	−68.0886	−2.27850
$894$	20.9581	0.700944
$895$	24.8197	0.829633
$896$	−93.1255	−3.11110
$897$	−5.75184	−0.192048
$898$	−19.1823	−0.640120
$899$	7.60671	0.253698
$900$	−4.31136	−0.143712
$901$	−11.9607	−0.398467
$902$	140.149	4.66646
$903$	−9.19670	−0.306047
$904$	−38.8985	−1.29374
$905$	32.7144	1.08746
$906$	13.9635	0.463906
$907$	−23.8761	−0.792794	−0.396397	−	0.918079i	$-0.629740\pi$
$907$	−23.8761	−0.792794	−0.396397	+	0.918079i	$0.629740\pi$
$908$	53.1421	1.76358
$909$	−6.56660	−0.217800
$910$	36.6790	1.21590
$911$	43.3480	1.43618	0.718092	−	0.695948i	$-0.245016\pi$
$911$	43.3480	1.43618	0.718092	+	0.695948i	$0.245016\pi$
$912$	−17.0126	−0.563345
$913$	2.94426	0.0974408
$914$	0.688691	0.0227799
$915$	26.5795	0.878690
$916$	65.1307	2.15198
$917$	85.4695	2.82245
$918$	6.50661	0.214750
$919$	4.11656	0.135793	0.0678964	−	0.997692i	$-0.478371\pi$
$919$	4.11656	0.135793	0.0678964	+	0.997692i	$0.478371\pi$
$920$	−29.4775	−0.971844
$921$	11.2415	0.370419
$922$	39.8760	1.31325
$923$	−10.9231	−0.359539
$924$	−93.4464	−3.07416
$925$	4.46171	0.146700
$926$	−19.7637	−0.649476
$927$	−0.490325	−0.0161044
$928$	−9.73719	−0.319639
$929$	49.2607	1.61619	0.808095	−	0.589052i	$-0.200499\pi$
$929$	49.2607	1.61619	0.808095	+	0.589052i	$0.200499\pi$
$930$	5.71730	0.187478
$931$	76.1145	2.49455
$932$	−14.9091	−0.488364
$933$	17.7383	0.580725
$934$	55.7633	1.82463
$935$	28.5095	0.932361
$936$	7.53562	0.246309
$937$	−2.36250	−0.0771794	−0.0385897	−	0.999255i	$-0.512287\pi$
$937$	−2.36250	−0.0771794	−0.0385897	+	0.999255i	$0.512287\pi$
$938$	117.505	3.83667
$939$	27.9720	0.912831
$940$	91.5321	2.98545
$941$	−3.88961	−0.126798	−0.0633989	−	0.997988i	$-0.520194\pi$
$941$	−3.88961	−0.126798	−0.0633989	+	0.997988i	$0.520194\pi$
$942$	−1.98699	−0.0647397
$943$	−36.4901	−1.18828
$944$	−22.6621	−0.737590
$945$	−8.92576	−0.290355
$946$	−26.3373	−0.856301
$947$	36.3471	1.18112	0.590561	−	0.806993i	$-0.298906\pi$
$947$	36.3471	1.18112	0.590561	+	0.806993i	$0.298906\pi$
$948$	11.4215	0.370953
$949$	−19.8688	−0.644970
$950$	15.2493	0.494752
$951$	−11.6894	−0.379055
$952$	54.0987	1.75335
$953$	29.3620	0.951127	0.475564	−	0.879681i	$-0.342244\pi$
$953$	29.3620	0.951127	0.475564	+	0.879681i	$0.342244\pi$
$954$	10.7238	0.347197
$955$	−31.2416	−1.01096
$956$	39.5104	1.27786
$957$	−34.0087	−1.09935
$958$	34.0537	1.10022
$959$	47.4574	1.53248
$960$	−19.2495	−0.621276
$961$	−29.5542	−0.953361
$962$	−16.3037	−0.525652
$963$	0.457065	0.0147287
$964$	−28.6734	−0.923509
$965$	23.1600	0.745547
$966$	37.0228	1.19119
$967$	8.47798	0.272634	0.136317	−	0.990665i	$-0.456474\pi$
$967$	8.47798	0.272634	0.136317	+	0.990665i	$0.456474\pi$
$968$	−79.2828	−2.54825
$969$	−15.1240	−0.485853
$970$	3.16579	0.101647
$971$	−7.00570	−0.224823	−0.112412	−	0.993662i	$-0.535858\pi$
$971$	−7.00570	−0.224823	−0.112412	+	0.993662i	$0.535858\pi$
$972$	−3.83378	−0.122968
$973$	−39.2480	−1.25823
$974$	30.7311	0.984687
$975$	−1.91331	−0.0612749
$976$	40.9139	1.30962
$977$	8.10579	0.259327	0.129664	−	0.991558i	$-0.458610\pi$
$977$	8.10579	0.259327	0.129664	+	0.991558i	$0.458610\pi$
$978$	46.4975	1.48683
$979$	−39.8896	−1.27488
$980$	−102.322	−3.26854
$981$	17.7294	0.566055
$982$	81.1864	2.59076
$983$	−34.1150	−1.08810	−0.544050	−	0.839053i	$-0.683110\pi$
$983$	−34.1150	−1.08810	−0.544050	+	0.839053i	$0.683110\pi$
$984$	47.8065	1.52402
$985$	10.0235	0.319375
$986$	41.1618	1.31086
$987$	−54.9886	−1.75030
$988$	−36.6194	−1.16502
$989$	6.85734	0.218051
$990$	−25.5614	−0.812395
$991$	−52.6395	−1.67215	−0.836074	−	0.548616i	$-0.815155\pi$
$991$	−52.6395	−1.67215	−0.836074	+	0.548616i	$0.815155\pi$
$992$	−1.85076	−0.0587617
$993$	−24.2000	−0.767964
$994$	70.3087	2.23006
$995$	−0.670149	−0.0212452
$996$	2.09968	0.0665308
$997$	2.95998	0.0937436	0.0468718	−	0.998901i	$-0.485075\pi$
$997$	2.95998	0.0937436	0.0468718	+	0.998901i	$0.485075\pi$
$998$	−5.75612	−0.182207
$999$	3.96747	0.125525

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6033.2.a.d.1.11	✓	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6033.2.a.d.1.11	✓	84	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:	\( N \)	\(=\)	\( 6033 = 3 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.41532 q^{2} -1.00000 q^{3} +3.83378 q^{4} -1.96861 q^{5} +2.41532 q^{6} -4.53404 q^{7} -4.42916 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.41532 q^{2} -1.00000 q^{3} +3.83378 q^{4} -1.96861 q^{5} +2.41532 q^{6} -4.53404 q^{7} -4.42916 q^{8} +1.00000 q^{9} +4.75483 q^{10} -5.37589 q^{11} -3.83378 q^{12} -1.70137 q^{13} +10.9512 q^{14} +1.96861 q^{15} +3.03029 q^{16} +2.69389 q^{17} -2.41532 q^{18} +5.61419 q^{19} -7.54721 q^{20} +4.53404 q^{21} +12.9845 q^{22} -3.38072 q^{23} +4.42916 q^{24} -1.12457 q^{25} +4.10934 q^{26} -1.00000 q^{27} -17.3825 q^{28} -6.32616 q^{29} -4.75483 q^{30} -1.20242 q^{31} +1.53919 q^{32} +5.37589 q^{33} -6.50661 q^{34} +8.92576 q^{35} +3.83378 q^{36} -3.96747 q^{37} -13.5601 q^{38} +1.70137 q^{39} +8.71929 q^{40} +10.7936 q^{41} -10.9512 q^{42} -2.02837 q^{43} -20.6100 q^{44} -1.96861 q^{45} +8.16552 q^{46} -12.1279 q^{47} -3.03029 q^{48} +13.5575 q^{49} +2.71620 q^{50} -2.69389 q^{51} -6.52266 q^{52} -4.43992 q^{53} +2.41532 q^{54} +10.5830 q^{55} +20.0820 q^{56} -5.61419 q^{57} +15.2797 q^{58} -7.47854 q^{59} +7.54721 q^{60} +13.5016 q^{61} +2.90423 q^{62} -4.53404 q^{63} -9.77823 q^{64} +3.34933 q^{65} -12.9845 q^{66} +10.7299 q^{67} +10.3278 q^{68} +3.38072 q^{69} -21.5586 q^{70} +6.42020 q^{71} -4.42916 q^{72} +11.6782 q^{73} +9.58271 q^{74} +1.12457 q^{75} +21.5236 q^{76} +24.3745 q^{77} -4.10934 q^{78} -2.97918 q^{79} -5.96546 q^{80} +1.00000 q^{81} -26.0700 q^{82} -0.547679 q^{83} +17.3825 q^{84} -5.30322 q^{85} +4.89916 q^{86} +6.32616 q^{87} +23.8107 q^{88} +7.42009 q^{89} +4.75483 q^{90} +7.71406 q^{91} -12.9609 q^{92} +1.20242 q^{93} +29.2929 q^{94} -11.0522 q^{95} -1.53919 q^{96} +0.665806 q^{97} -32.7458 q^{98} -5.37589 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 13 q^{2} - 84 q^{3} + 81 q^{4} - 10 q^{5} + 13 q^{6} - 32 q^{7} - 39 q^{8} + 84 q^{9}+O(q^{10}) \) 84 * q - 13 * q^2 - 84 * q^3 + 81 * q^4 - 10 * q^5 + 13 * q^6 - 32 * q^7 - 39 * q^8 + 84 * q^9	\( 84 q - 13 q^{2} - 84 q^{3} + 81 q^{4} - 10 q^{5} + 13 q^{6} - 32 q^{7} - 39 q^{8} + 84 q^{9} + 13 q^{10} - 20 q^{11} - 81 q^{12} + 7 q^{13} - 9 q^{14} + 10 q^{15} + 83 q^{16} - 39 q^{17} - 13 q^{18} + 13 q^{19} - 26 q^{20} + 32 q^{21} - 21 q^{22} - 93 q^{23} + 39 q^{24} + 66 q^{25} - 34 q^{26} - 84 q^{27} - 59 q^{28} - 39 q^{29} - 13 q^{30} + 8 q^{31} - 96 q^{32} + 20 q^{33} - 69 q^{35} + 81 q^{36} + 6 q^{37} - 59 q^{38} - 7 q^{39} + 28 q^{40} - 23 q^{41} + 9 q^{42} - 74 q^{43} - 43 q^{44} - 10 q^{45} - 6 q^{46} - 77 q^{47} - 83 q^{48} + 100 q^{49} - 74 q^{50} + 39 q^{51} - 44 q^{52} - 66 q^{53} + 13 q^{54} - 60 q^{55} - 31 q^{56} - 13 q^{57} - 39 q^{58} - 36 q^{59} + 26 q^{60} + 104 q^{61} - 53 q^{62} - 32 q^{63} + 85 q^{64} - 47 q^{65} + 21 q^{66} - 65 q^{67} - 118 q^{68} + 93 q^{69} - 3 q^{70} - 68 q^{71} - 39 q^{72} + 8 q^{73} - 30 q^{74} - 66 q^{75} + 71 q^{76} - 83 q^{77} + 34 q^{78} - 24 q^{79} - 67 q^{80} + 84 q^{81} - 9 q^{82} - 95 q^{83} + 59 q^{84} + 24 q^{85} - 32 q^{86} + 39 q^{87} - 65 q^{88} - 44 q^{89} + 13 q^{90} + 8 q^{91} - 184 q^{92} - 8 q^{93} + 61 q^{94} - 153 q^{95} + 96 q^{96} + 19 q^{97} - 67 q^{98} - 20 q^{99}+O(q^{100}) \) 84 * q - 13 * q^2 - 84 * q^3 + 81 * q^4 - 10 * q^5 + 13 * q^6 - 32 * q^7 - 39 * q^8 + 84 * q^9 + 13 * q^10 - 20 * q^11 - 81 * q^12 + 7 * q^13 - 9 * q^14 + 10 * q^15 + 83 * q^16 - 39 * q^17 - 13 * q^18 + 13 * q^19 - 26 * q^20 + 32 * q^21 - 21 * q^22 - 93 * q^23 + 39 * q^24 + 66 * q^25 - 34 * q^26 - 84 * q^27 - 59 * q^28 - 39 * q^29 - 13 * q^30 + 8 * q^31 - 96 * q^32 + 20 * q^33 - 69 * q^35 + 81 * q^36 + 6 * q^37 - 59 * q^38 - 7 * q^39 + 28 * q^40 - 23 * q^41 + 9 * q^42 - 74 * q^43 - 43 * q^44 - 10 * q^45 - 6 * q^46 - 77 * q^47 - 83 * q^48 + 100 * q^49 - 74 * q^50 + 39 * q^51 - 44 * q^52 - 66 * q^53 + 13 * q^54 - 60 * q^55 - 31 * q^56 - 13 * q^57 - 39 * q^58 - 36 * q^59 + 26 * q^60 + 104 * q^61 - 53 * q^62 - 32 * q^63 + 85 * q^64 - 47 * q^65 + 21 * q^66 - 65 * q^67 - 118 * q^68 + 93 * q^69 - 3 * q^70 - 68 * q^71 - 39 * q^72 + 8 * q^73 - 30 * q^74 - 66 * q^75 + 71 * q^76 - 83 * q^77 + 34 * q^78 - 24 * q^79 - 67 * q^80 + 84 * q^81 - 9 * q^82 - 95 * q^83 + 59 * q^84 + 24 * q^85 - 32 * q^86 + 39 * q^87 - 65 * q^88 - 44 * q^89 + 13 * q^90 + 8 * q^91 - 184 * q^92 - 8 * q^93 + 61 * q^94 - 153 * q^95 + 96 * q^96 + 19 * q^97 - 67 * q^98 - 20 * q^99

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