LMFDB - Embedded newform 6033.2.a.c.1.8

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:	$0$
Dimension:	$82$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
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)

$f(q)$	$=$	$q-2.34798 q^{2} -1.00000 q^{3} +3.51301 q^{4} +0.242883 q^{5} +2.34798 q^{6} -0.571157 q^{7} -3.55251 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.34798 q^{2} -1.00000 q^{3} +3.51301 q^{4} +0.242883 q^{5} +2.34798 q^{6} -0.571157 q^{7} -3.55251 q^{8} +1.00000 q^{9} -0.570284 q^{10} -0.420562 q^{11} -3.51301 q^{12} +2.88848 q^{13} +1.34106 q^{14} -0.242883 q^{15} +1.31521 q^{16} +1.47020 q^{17} -2.34798 q^{18} +1.36494 q^{19} +0.853250 q^{20} +0.571157 q^{21} +0.987472 q^{22} +5.83343 q^{23} +3.55251 q^{24} -4.94101 q^{25} -6.78210 q^{26} -1.00000 q^{27} -2.00648 q^{28} +3.46112 q^{29} +0.570284 q^{30} +4.76523 q^{31} +4.01693 q^{32} +0.420562 q^{33} -3.45199 q^{34} -0.138724 q^{35} +3.51301 q^{36} +2.97447 q^{37} -3.20484 q^{38} -2.88848 q^{39} -0.862845 q^{40} +9.02310 q^{41} -1.34106 q^{42} -7.29688 q^{43} -1.47744 q^{44} +0.242883 q^{45} -13.6968 q^{46} +7.37779 q^{47} -1.31521 q^{48} -6.67378 q^{49} +11.6014 q^{50} -1.47020 q^{51} +10.1473 q^{52} -8.36187 q^{53} +2.34798 q^{54} -0.102147 q^{55} +2.02904 q^{56} -1.36494 q^{57} -8.12665 q^{58} +0.215905 q^{59} -0.853250 q^{60} +2.51070 q^{61} -11.1887 q^{62} -0.571157 q^{63} -12.0621 q^{64} +0.701563 q^{65} -0.987472 q^{66} +0.957142 q^{67} +5.16481 q^{68} -5.83343 q^{69} +0.325722 q^{70} -4.70798 q^{71} -3.55251 q^{72} -0.504793 q^{73} -6.98400 q^{74} +4.94101 q^{75} +4.79503 q^{76} +0.240207 q^{77} +6.78210 q^{78} +11.9252 q^{79} +0.319443 q^{80} +1.00000 q^{81} -21.1861 q^{82} +16.3840 q^{83} +2.00648 q^{84} +0.357086 q^{85} +17.1329 q^{86} -3.46112 q^{87} +1.49405 q^{88} +16.2594 q^{89} -0.570284 q^{90} -1.64978 q^{91} +20.4929 q^{92} -4.76523 q^{93} -17.3229 q^{94} +0.331520 q^{95} -4.01693 q^{96} +9.69021 q^{97} +15.6699 q^{98} -0.420562 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 82 q + 13 q^{2} - 82 q^{3} + 87 q^{4} + 7 q^{5} - 13 q^{6} + 30 q^{7} + 39 q^{8} + 82 q^{9}+O(q^{10}) $ 82 * q + 13 * q^2 - 82 * q^3 + 87 * q^4 + 7 * q^5 - 13 * q^6 + 30 * q^7 + 39 * q^8 + 82 * q^9	\( 82 q + 13 q^{2} - 82 q^{3} + 87 q^{4} + 7 q^{5} - 13 q^{6} + 30 q^{7} + 39 q^{8} + 82 q^{9} - 9 q^{10} + 28 q^{11} - 87 q^{12} - 14 q^{13} + 21 q^{14} - 7 q^{15} + 93 q^{16} + 25 q^{17} + 13 q^{18} - 7 q^{19} + 40 q^{20} - 30 q^{21} + 31 q^{22} + 97 q^{23} - 39 q^{24} + 83 q^{25} + 22 q^{26} - 82 q^{27} + 53 q^{28} + 45 q^{29} + 9 q^{30} - 11 q^{31} + 86 q^{32} - 28 q^{33} - 30 q^{34} + 69 q^{35} + 87 q^{36} + 8 q^{37} + 33 q^{38} + 14 q^{39} - 38 q^{40} + 12 q^{41} - 21 q^{42} + 68 q^{43} + 77 q^{44} + 7 q^{45} - 14 q^{46} + 85 q^{47} - 93 q^{48} + 68 q^{49} + 56 q^{50} - 25 q^{51} - 18 q^{52} + 58 q^{53} - 13 q^{54} + 68 q^{55} + 59 q^{56} + 7 q^{57} + 27 q^{58} + 40 q^{59} - 40 q^{60} - 116 q^{61} + 79 q^{62} + 30 q^{63} + 127 q^{64} + 66 q^{65} - 31 q^{66} + 51 q^{67} + 94 q^{68} - 97 q^{69} + q^{70} + 101 q^{71} + 39 q^{72} + 12 q^{73} + 72 q^{74} - 83 q^{75} - 3 q^{76} + 101 q^{77} - 22 q^{78} + 26 q^{79} + 61 q^{80} + 82 q^{81} + 31 q^{82} + 94 q^{83} - 53 q^{84} - 8 q^{85} + 68 q^{86} - 45 q^{87} + 91 q^{88} + 40 q^{89} - 9 q^{90} - 6 q^{91} + 180 q^{92} + 11 q^{93} - 31 q^{94} + 153 q^{95} - 86 q^{96} - 39 q^{97} + 115 q^{98} + 28 q^{99}+O(q^{100}) \) 82 * q + 13 * q^2 - 82 * q^3 + 87 * q^4 + 7 * q^5 - 13 * q^6 + 30 * q^7 + 39 * q^8 + 82 * q^9 - 9 * q^10 + 28 * q^11 - 87 * q^12 - 14 * q^13 + 21 * q^14 - 7 * q^15 + 93 * q^16 + 25 * q^17 + 13 * q^18 - 7 * q^19 + 40 * q^20 - 30 * q^21 + 31 * q^22 + 97 * q^23 - 39 * q^24 + 83 * q^25 + 22 * q^26 - 82 * q^27 + 53 * q^28 + 45 * q^29 + 9 * q^30 - 11 * q^31 + 86 * q^32 - 28 * q^33 - 30 * q^34 + 69 * q^35 + 87 * q^36 + 8 * q^37 + 33 * q^38 + 14 * q^39 - 38 * q^40 + 12 * q^41 - 21 * q^42 + 68 * q^43 + 77 * q^44 + 7 * q^45 - 14 * q^46 + 85 * q^47 - 93 * q^48 + 68 * q^49 + 56 * q^50 - 25 * q^51 - 18 * q^52 + 58 * q^53 - 13 * q^54 + 68 * q^55 + 59 * q^56 + 7 * q^57 + 27 * q^58 + 40 * q^59 - 40 * q^60 - 116 * q^61 + 79 * q^62 + 30 * q^63 + 127 * q^64 + 66 * q^65 - 31 * q^66 + 51 * q^67 + 94 * q^68 - 97 * q^69 + q^70 + 101 * q^71 + 39 * q^72 + 12 * q^73 + 72 * q^74 - 83 * q^75 - 3 * q^76 + 101 * q^77 - 22 * q^78 + 26 * q^79 + 61 * q^80 + 82 * q^81 + 31 * q^82 + 94 * q^83 - 53 * q^84 - 8 * q^85 + 68 * q^86 - 45 * q^87 + 91 * q^88 + 40 * q^89 - 9 * q^90 - 6 * q^91 + 180 * q^92 + 11 * q^93 - 31 * q^94 + 153 * q^95 - 86 * q^96 - 39 * q^97 + 115 * q^98 + 28 * 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 $

$2$	−2.34798	−1.66027	−0.830136	−	0.557561i	$-0.811737\pi$
$2$	−2.34798	−1.66027	−0.830136	+	0.557561i	$0.811737\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.51301	1.75650
$5$	0.242883	0.108621	0.0543103	−	0.998524i	$-0.482704\pi$
$5$	0.242883	0.108621	0.0543103	+	0.998524i	$0.482704\pi$
$6$	2.34798	0.958559
$7$	−0.571157	−0.215877	−0.107938	−	0.994158i	$-0.534425\pi$
$7$	−0.571157	−0.215877	−0.107938	+	0.994158i	$0.534425\pi$
$8$	−3.55251	−1.25600
$9$	1.00000	0.333333
$10$	−0.570284	−0.180340
$11$	−0.420562	−0.126804	−0.0634021	−	0.997988i	$-0.520195\pi$
$11$	−0.420562	−0.126804	−0.0634021	+	0.997988i	$0.520195\pi$
$12$	−3.51301	−1.01412
$13$	2.88848	0.801121	0.400560	−	0.916270i	$-0.368815\pi$
$13$	2.88848	0.801121	0.400560	+	0.916270i	$0.368815\pi$
$14$	1.34106	0.358415
$15$	−0.242883	−0.0627121
$16$	1.31521	0.328803
$17$	1.47020	0.356575	0.178287	−	0.983978i	$-0.442944\pi$
$17$	1.47020	0.356575	0.178287	+	0.983978i	$0.442944\pi$
$18$	−2.34798	−0.553424
$19$	1.36494	0.313138	0.156569	−	0.987667i	$-0.449957\pi$
$19$	1.36494	0.313138	0.156569	+	0.987667i	$0.449957\pi$
$20$	0.853250	0.190793
$21$	0.571157	0.124637
$22$	0.987472	0.210530
$23$	5.83343	1.21635	0.608177	−	0.793801i	$-0.291901\pi$
$23$	5.83343	1.21635	0.608177	+	0.793801i	$0.291901\pi$
$24$	3.55251	0.725154
$25$	−4.94101	−0.988202
$26$	−6.78210	−1.33008
$27$	−1.00000	−0.192450
$28$	−2.00648	−0.379189
$29$	3.46112	0.642715	0.321357	−	0.946958i	$-0.395861\pi$
$29$	3.46112	0.642715	0.321357	+	0.946958i	$0.395861\pi$
$30$	0.570284	0.104119
$31$	4.76523	0.855860	0.427930	−	0.903812i	$-0.359243\pi$
$31$	4.76523	0.855860	0.427930	+	0.903812i	$0.359243\pi$
$32$	4.01693	0.710100
$33$	0.420562	0.0732105
$34$	−3.45199	−0.592011
$35$	−0.138724	−0.0234487
$36$	3.51301	0.585501
$37$	2.97447	0.489000	0.244500	−	0.969649i	$-0.421376\pi$
$37$	2.97447	0.489000	0.244500	+	0.969649i	$0.421376\pi$
$38$	−3.20484	−0.519894
$39$	−2.88848	−0.462527
$40$	−0.862845	−0.136428
$41$	9.02310	1.40917	0.704586	−	0.709619i	$-0.251133\pi$
$41$	9.02310	1.40917	0.704586	+	0.709619i	$0.251133\pi$
$42$	−1.34106	−0.206931
$43$	−7.29688	−1.11276	−0.556382	−	0.830927i	$-0.687811\pi$
$43$	−7.29688	−1.11276	−0.556382	+	0.830927i	$0.687811\pi$
$44$	−1.47744	−0.222732
$45$	0.242883	0.0362069
$46$	−13.6968	−2.01948
$47$	7.37779	1.07616	0.538080	−	0.842893i	$-0.319150\pi$
$47$	7.37779	1.07616	0.538080	+	0.842893i	$0.319150\pi$
$48$	−1.31521	−0.189835
$49$	−6.67378	−0.953397
$50$	11.6014	1.64068
$51$	−1.47020	−0.205869
$52$	10.1473	1.40717
$53$	−8.36187	−1.14859	−0.574296	−	0.818648i	$-0.694724\pi$
$53$	−8.36187	−1.14859	−0.574296	+	0.818648i	$0.694724\pi$
$54$	2.34798	0.319520
$55$	−0.102147	−0.0137736
$56$	2.02904	0.271142
$57$	−1.36494	−0.180790
$58$	−8.12665	−1.06708
$59$	0.215905	0.0281084	0.0140542	−	0.999901i	$-0.495526\pi$
$59$	0.215905	0.0281084	0.0140542	+	0.999901i	$0.495526\pi$
$60$	−0.853250	−0.110154
$61$	2.51070	0.321462	0.160731	−	0.986998i	$-0.448615\pi$
$61$	2.51070	0.321462	0.160731	+	0.986998i	$0.448615\pi$
$62$	−11.1887	−1.42096
$63$	−0.571157	−0.0719590
$64$	−12.0621	−1.50776
$65$	0.701563	0.0870182
$66$	−0.987472	−0.121549
$67$	0.957142	0.116933	0.0584667	−	0.998289i	$-0.481379\pi$
$67$	0.957142	0.116933	0.0584667	+	0.998289i	$0.481379\pi$
$68$	5.16481	0.626325
$69$	−5.83343	−0.702263
$70$	0.325722	0.0389312
$71$	−4.70798	−0.558734	−0.279367	−	0.960184i	$-0.590125\pi$
$71$	−4.70798	−0.558734	−0.279367	+	0.960184i	$0.590125\pi$
$72$	−3.55251	−0.418668
$73$	−0.504793	−0.0590815	−0.0295408	−	0.999564i	$-0.509404\pi$
$73$	−0.504793	−0.0590815	−0.0295408	+	0.999564i	$0.509404\pi$
$74$	−6.98400	−0.811874
$75$	4.94101	0.570538
$76$	4.79503	0.550028
$77$	0.240207	0.0273741
$78$	6.78210	0.767921
$79$	11.9252	1.34169	0.670844	−	0.741598i	$-0.265932\pi$
$79$	11.9252	1.34169	0.670844	+	0.741598i	$0.265932\pi$
$80$	0.319443	0.0357148
$81$	1.00000	0.111111
$82$	−21.1861	−2.33961
$83$	16.3840	1.79838	0.899189	−	0.437560i	$-0.144157\pi$
$83$	16.3840	1.79838	0.899189	+	0.437560i	$0.144157\pi$
$84$	2.00648	0.218925
$85$	0.357086	0.0387314
$86$	17.1329	1.84749
$87$	−3.46112	−0.371072
$88$	1.49405	0.159267
$89$	16.2594	1.72350	0.861748	−	0.507336i	$-0.169370\pi$
$89$	16.2594	1.72350	0.861748	+	0.507336i	$0.169370\pi$
$90$	−0.570284	−0.0601133
$91$	−1.64978	−0.172943
$92$	20.4929	2.13653
$93$	−4.76523	−0.494131
$94$	−17.3229	−1.78672
$95$	0.331520	0.0340132
$96$	−4.01693	−0.409977
$97$	9.69021	0.983891	0.491946	−	0.870626i	$-0.336286\pi$
$97$	9.69021	0.983891	0.491946	+	0.870626i	$0.336286\pi$
$98$	15.6699	1.58290
$99$	−0.420562	−0.0422681
$100$	−17.3578	−1.73578
$101$	−5.12175	−0.509633	−0.254816	−	0.966989i	$-0.582015\pi$
$101$	−5.12175	−0.509633	−0.254816	+	0.966989i	$0.582015\pi$
$102$	3.45199	0.341798
$103$	−6.14681	−0.605663	−0.302832	−	0.953044i	$-0.597932\pi$
$103$	−6.14681	−0.605663	−0.302832	+	0.953044i	$0.597932\pi$
$104$	−10.2614	−1.00621
$105$	0.138724	0.0135381
$106$	19.6335	1.90697
$107$	2.11389	0.204358	0.102179	−	0.994766i	$-0.467419\pi$
$107$	2.11389	0.204358	0.102179	+	0.994766i	$0.467419\pi$
$108$	−3.51301	−0.338039
$109$	−14.1952	−1.35965	−0.679825	−	0.733374i	$-0.737944\pi$
$109$	−14.1952	−1.35965	−0.679825	+	0.733374i	$0.737944\pi$
$110$	0.239840	0.0228679
$111$	−2.97447	−0.282324
$112$	−0.751193	−0.0709810
$113$	−3.02675	−0.284733	−0.142366	−	0.989814i	$-0.545471\pi$
$113$	−3.02675	−0.284733	−0.142366	+	0.989814i	$0.545471\pi$
$114$	3.20484	0.300161
$115$	1.41684	0.132121
$116$	12.1590	1.12893
$117$	2.88848	0.267040
$118$	−0.506941	−0.0466677
$119$	−0.839712	−0.0769763
$120$	0.862845	0.0787667
$121$	−10.8231	−0.983921
$122$	−5.89507	−0.533715
$123$	−9.02310	−0.813586
$124$	16.7403	1.50332
$125$	−2.41450	−0.215960
$126$	1.34106	0.119472
$127$	−1.88632	−0.167384	−0.0836919	−	0.996492i	$-0.526671\pi$
$127$	−1.88632	−0.167384	−0.0836919	+	0.996492i	$0.526671\pi$
$128$	20.2877	1.79320
$129$	7.29688	0.642455
$130$	−1.64726	−0.144474
$131$	−20.0670	−1.75326	−0.876631	−	0.481163i	$-0.840215\pi$
$131$	−20.0670	−1.75326	−0.876631	+	0.481163i	$0.840215\pi$
$132$	1.47744	0.128595
$133$	−0.779593	−0.0675993
$134$	−2.24735	−0.194141
$135$	−0.242883	−0.0209040
$136$	−5.22289	−0.447859
$137$	8.08966	0.691146	0.345573	−	0.938392i	$-0.387684\pi$
$137$	8.08966	0.691146	0.345573	+	0.938392i	$0.387684\pi$
$138$	13.6968	1.16595
$139$	9.04638	0.767304	0.383652	−	0.923478i	$-0.374666\pi$
$139$	9.04638	0.767304	0.383652	+	0.923478i	$0.374666\pi$
$140$	−0.487340	−0.0411877
$141$	−7.37779	−0.621322
$142$	11.0542	0.927651
$143$	−1.21479	−0.101586
$144$	1.31521	0.109601
$145$	0.840649	0.0698121
$146$	1.18524	0.0980914
$147$	6.67378	0.550444
$148$	10.4493	0.858931
$149$	−8.51571	−0.697634	−0.348817	−	0.937191i	$-0.613417\pi$
$149$	−8.51571	−0.697634	−0.348817	+	0.937191i	$0.613417\pi$
$150$	−11.6014	−0.947249
$151$	−13.2754	−1.08034	−0.540170	−	0.841556i	$-0.681640\pi$
$151$	−13.2754	−1.08034	−0.540170	+	0.841556i	$0.681640\pi$
$152$	−4.84896	−0.393302
$153$	1.47020	0.118858
$154$	−0.564001	−0.0454485
$155$	1.15739	0.0929641
$156$	−10.1473	−0.812431
$157$	13.3219	1.06320	0.531600	−	0.846995i	$-0.321591\pi$
$157$	13.3219	1.06320	0.531600	+	0.846995i	$0.321591\pi$
$158$	−28.0001	−2.22757
$159$	8.36187	0.663140
$160$	0.975645	0.0771315
$161$	−3.33180	−0.262583
$162$	−2.34798	−0.184475
$163$	−1.55334	−0.121667	−0.0608335	−	0.998148i	$-0.519376\pi$
$163$	−1.55334	−0.121667	−0.0608335	+	0.998148i	$0.519376\pi$
$164$	31.6982	2.47522
$165$	0.102147	0.00795217
$166$	−38.4693	−2.98580
$167$	−10.0948	−0.781157	−0.390578	−	0.920570i	$-0.627725\pi$
$167$	−10.0948	−0.781157	−0.390578	+	0.920570i	$0.627725\pi$
$168$	−2.02904	−0.156544
$169$	−4.65667	−0.358206
$170$	−0.838430	−0.0643046
$171$	1.36494	0.104379
$172$	−25.6340	−1.95458
$173$	17.2207	1.30927	0.654634	−	0.755946i	$-0.272823\pi$
$173$	17.2207	1.30927	0.654634	+	0.755946i	$0.272823\pi$
$174$	8.12665	0.616080
$175$	2.82209	0.213330
$176$	−0.553129	−0.0416937
$177$	−0.215905	−0.0162284
$178$	−38.1768	−2.86147
$179$	11.8324	0.884396	0.442198	−	0.896918i	$-0.354199\pi$
$179$	11.8324	0.884396	0.442198	+	0.896918i	$0.354199\pi$
$180$	0.853250	0.0635975
$181$	4.70237	0.349525	0.174762	−	0.984611i	$-0.444084\pi$
$181$	4.70237	0.349525	0.174762	+	0.984611i	$0.444084\pi$
$182$	3.87364	0.287133
$183$	−2.51070	−0.185596
$184$	−20.7233	−1.52775
$185$	0.722449	0.0531155
$186$	11.1887	0.820392
$187$	−0.618309	−0.0452152
$188$	25.9182	1.89028
$189$	0.571157	0.0415455
$190$	−0.778402	−0.0564712
$191$	18.1643	1.31432	0.657160	−	0.753752i	$-0.271758\pi$
$191$	18.1643	1.31432	0.657160	+	0.753752i	$0.271758\pi$
$192$	12.0621	0.870508
$193$	10.4894	0.755041	0.377520	−	0.926001i	$-0.376777\pi$
$193$	10.4894	0.755041	0.377520	+	0.926001i	$0.376777\pi$
$194$	−22.7524	−1.63353
$195$	−0.701563	−0.0502400
$196$	−23.4450	−1.67465
$197$	20.1704	1.43708	0.718540	−	0.695485i	$-0.244811\pi$
$197$	20.1704	1.43708	0.718540	+	0.695485i	$0.244811\pi$
$198$	0.987472	0.0701765
$199$	5.42185	0.384345	0.192172	−	0.981361i	$-0.438447\pi$
$199$	5.42185	0.384345	0.192172	+	0.981361i	$0.438447\pi$
$200$	17.5530	1.24118
$201$	−0.957142	−0.0675116
$202$	12.0258	0.846129
$203$	−1.97684	−0.138747
$204$	−5.16481	−0.361609
$205$	2.19156	0.153065
$206$	14.4326	1.00557
$207$	5.83343	0.405452
$208$	3.79897	0.263411
$209$	−0.574041	−0.0397072
$210$	−0.325722	−0.0224769
$211$	−20.5328	−1.41353	−0.706767	−	0.707446i	$-0.749847\pi$
$211$	−20.5328	−1.41353	−0.706767	+	0.707446i	$0.749847\pi$
$212$	−29.3753	−2.01751
$213$	4.70798	0.322585
$214$	−4.96338	−0.339290
$215$	−1.77229	−0.120869
$216$	3.55251	0.241718
$217$	−2.72169	−0.184761
$218$	33.3300	2.25739
$219$	0.504793	0.0341107
$220$	−0.358845	−0.0241933
$221$	4.24663	0.285659
$222$	6.98400	0.468735
$223$	2.89841	0.194092	0.0970459	−	0.995280i	$-0.469061\pi$
$223$	2.89841	0.194092	0.0970459	+	0.995280i	$0.469061\pi$
$224$	−2.29430	−0.153294
$225$	−4.94101	−0.329401
$226$	7.10675	0.472734
$227$	21.4076	1.42087	0.710437	−	0.703761i	$-0.248498\pi$
$227$	21.4076	1.42087	0.710437	+	0.703761i	$0.248498\pi$
$228$	−4.79503	−0.317559
$229$	0.833593	0.0550854	0.0275427	−	0.999621i	$-0.491232\pi$
$229$	0.833593	0.0550854	0.0275427	+	0.999621i	$0.491232\pi$
$230$	−3.32672	−0.219357
$231$	−0.240207	−0.0158045
$232$	−12.2957	−0.807252
$233$	−26.1263	−1.71159	−0.855794	−	0.517316i	$-0.826931\pi$
$233$	−26.1263	−1.71159	−0.855794	+	0.517316i	$0.826931\pi$
$234$	−6.78210	−0.443360
$235$	1.79194	0.116893
$236$	0.758476	0.0493726
$237$	−11.9252	−0.774624
$238$	1.97163	0.127802
$239$	−4.71233	−0.304815	−0.152408	−	0.988318i	$-0.548703\pi$
$239$	−4.71233	−0.304815	−0.152408	+	0.988318i	$0.548703\pi$
$240$	−0.319443	−0.0206200
$241$	0.841105	0.0541803	0.0270902	−	0.999633i	$-0.491376\pi$
$241$	0.841105	0.0541803	0.0270902	+	0.999633i	$0.491376\pi$
$242$	25.4125	1.63358
$243$	−1.00000	−0.0641500
$244$	8.82011	0.564650
$245$	−1.62095	−0.103559
$246$	21.1861	1.35077
$247$	3.94259	0.250861
$248$	−16.9285	−1.07496
$249$	−16.3840	−1.03829
$250$	5.66920	0.358552
$251$	3.16561	0.199811	0.0999056	−	0.994997i	$-0.468146\pi$
$251$	3.16561	0.199811	0.0999056	+	0.994997i	$0.468146\pi$
$252$	−2.00648	−0.126396
$253$	−2.45332	−0.154239
$254$	4.42904	0.277903
$255$	−0.357086	−0.0223616
$256$	−23.5109	−1.46943
$257$	−26.0869	−1.62726	−0.813629	−	0.581384i	$-0.802512\pi$
$257$	−26.0869	−1.62726	−0.813629	+	0.581384i	$0.802512\pi$
$258$	−17.1329	−1.06665
$259$	−1.69889	−0.105564
$260$	2.46460	0.152848
$261$	3.46112	0.214238
$262$	47.1169	2.91089
$263$	1.35825	0.0837532	0.0418766	−	0.999123i	$-0.486666\pi$
$263$	1.35825	0.0837532	0.0418766	+	0.999123i	$0.486666\pi$
$264$	−1.49405	−0.0919526
$265$	−2.03096	−0.124761
$266$	1.83047	0.112233
$267$	−16.2594	−0.995061
$268$	3.36245	0.205394
$269$	−23.4519	−1.42989	−0.714944	−	0.699181i	$-0.753548\pi$
$269$	−23.4519	−1.42989	−0.714944	+	0.699181i	$0.753548\pi$
$270$	0.570284	0.0347064
$271$	10.1012	0.613602	0.306801	−	0.951774i	$-0.400741\pi$
$271$	10.1012	0.613602	0.306801	+	0.951774i	$0.400741\pi$
$272$	1.93362	0.117243
$273$	1.64978	0.0998490
$274$	−18.9944	−1.14749
$275$	2.07800	0.125308
$276$	−20.4929	−1.23353
$277$	−26.4062	−1.58660	−0.793299	−	0.608832i	$-0.791638\pi$
$277$	−26.4062	−1.58660	−0.793299	+	0.608832i	$0.791638\pi$
$278$	−21.2407	−1.27393
$279$	4.76523	0.285287
$280$	0.492820	0.0294516
$281$	−15.8352	−0.944649	−0.472325	−	0.881425i	$-0.656585\pi$
$281$	−15.8352	−0.944649	−0.472325	+	0.881425i	$0.656585\pi$
$282$	17.3229	1.03156
$283$	−12.2934	−0.730765	−0.365382	−	0.930857i	$-0.619062\pi$
$283$	−12.2934	−0.730765	−0.365382	+	0.930857i	$0.619062\pi$
$284$	−16.5392	−0.981419
$285$	−0.331520	−0.0196375
$286$	2.85229	0.168660
$287$	−5.15361	−0.304208
$288$	4.01693	0.236700
$289$	−14.8385	−0.872854
$290$	−1.97383	−0.115907
$291$	−9.69021	−0.568050
$292$	−1.77334	−0.103777
$293$	−19.3666	−1.13141	−0.565703	−	0.824609i	$-0.691395\pi$
$293$	−19.3666	−1.13141	−0.565703	+	0.824609i	$0.691395\pi$
$294$	−15.6699	−0.913887
$295$	0.0524397	0.00305316
$296$	−10.5669	−0.614186
$297$	0.420562	0.0244035
$298$	19.9947	1.15826
$299$	16.8498	0.974447
$300$	17.3578	1.00215
$301$	4.16766	0.240220
$302$	31.1705	1.79366
$303$	5.12175	0.294237
$304$	1.79518	0.102961
$305$	0.609806	0.0349174
$306$	−3.45199	−0.197337
$307$	−19.2231	−1.09712	−0.548560	−	0.836112i	$-0.684824\pi$
$307$	−19.2231	−1.09712	−0.548560	+	0.836112i	$0.684824\pi$
$308$	0.843849	0.0480828
$309$	6.14681	0.349680
$310$	−2.71754	−0.154346
$311$	−3.51765	−0.199468	−0.0997338	−	0.995014i	$-0.531799\pi$
$311$	−3.51765	−0.199468	−0.0997338	+	0.995014i	$0.531799\pi$
$312$	10.2614	0.580936
$313$	7.89578	0.446296	0.223148	−	0.974785i	$-0.428367\pi$
$313$	7.89578	0.446296	0.223148	+	0.974785i	$0.428367\pi$
$314$	−31.2795	−1.76520
$315$	−0.138724	−0.00781623
$316$	41.8933	2.35668
$317$	6.85000	0.384734	0.192367	−	0.981323i	$-0.438384\pi$
$317$	6.85000	0.384734	0.192367	+	0.981323i	$0.438384\pi$
$318$	−19.6335	−1.10099
$319$	−1.45562	−0.0814990
$320$	−2.92968	−0.163774
$321$	−2.11389	−0.117986
$322$	7.82301	0.435959
$323$	2.00672	0.111657
$324$	3.51301	0.195167
$325$	−14.2720	−0.791669
$326$	3.64721	0.202000
$327$	14.1952	0.784994
$328$	−32.0547	−1.76992
$329$	−4.21387	−0.232318
$330$	−0.239840	−0.0132028
$331$	−2.96821	−0.163147	−0.0815737	−	0.996667i	$-0.525995\pi$
$331$	−2.96821	−0.163147	−0.0815737	+	0.996667i	$0.525995\pi$
$332$	57.5572	3.15886
$333$	2.97447	0.163000
$334$	23.7023	1.29693
$335$	0.232473	0.0127014
$336$	0.751193	0.0409809
$337$	4.12763	0.224846	0.112423	−	0.993660i	$-0.464139\pi$
$337$	4.12763	0.224846	0.112423	+	0.993660i	$0.464139\pi$
$338$	10.9338	0.594719
$339$	3.02675	0.164391
$340$	1.25444	0.0680318
$341$	−2.00408	−0.108527
$342$	−3.20484	−0.173298
$343$	7.80987	0.421693
$344$	25.9223	1.39764
$345$	−1.41684	−0.0762802
$346$	−40.4339	−2.17374
$347$	−11.5145	−0.618132	−0.309066	−	0.951041i	$-0.600016\pi$
$347$	−11.5145	−0.618132	−0.309066	+	0.951041i	$0.600016\pi$
$348$	−12.1590	−0.651789
$349$	5.50371	0.294607	0.147303	−	0.989091i	$-0.452941\pi$
$349$	5.50371	0.294607	0.147303	+	0.989091i	$0.452941\pi$
$350$	−6.62621	−0.354186
$351$	−2.88848	−0.154176
$352$	−1.68937	−0.0900438
$353$	33.9358	1.80622	0.903111	−	0.429407i	$-0.141277\pi$
$353$	33.9358	1.80622	0.903111	+	0.429407i	$0.141277\pi$
$354$	0.506941	0.0269436
$355$	−1.14349	−0.0606901
$356$	57.1195	3.02733
$357$	0.839712	0.0444423
$358$	−27.7823	−1.46834
$359$	−25.7415	−1.35859	−0.679293	−	0.733867i	$-0.737713\pi$
$359$	−25.7415	−1.35859	−0.679293	+	0.733867i	$0.737713\pi$
$360$	−0.862845	−0.0454759
$361$	−17.1369	−0.901945
$362$	−11.0411	−0.580306
$363$	10.8231	0.568067
$364$	−5.79568	−0.303776
$365$	−0.122606	−0.00641747
$366$	5.89507	0.308140
$367$	13.7226	0.716312	0.358156	−	0.933662i	$-0.383406\pi$
$367$	13.7226	0.716312	0.358156	+	0.933662i	$0.383406\pi$
$368$	7.67221	0.399941
$369$	9.02310	0.469724
$370$	−1.69630	−0.0881862
$371$	4.77594	0.247954
$372$	−16.7403	−0.867944
$373$	6.61625	0.342576	0.171288	−	0.985221i	$-0.445207\pi$
$373$	6.61625	0.342576	0.171288	+	0.985221i	$0.445207\pi$
$374$	1.45178	0.0750696
$375$	2.41450	0.124684
$376$	−26.2097	−1.35166
$377$	9.99740	0.514892
$378$	−1.34106	−0.0689769
$379$	12.1057	0.621830	0.310915	−	0.950438i	$-0.399365\pi$
$379$	12.1057	0.621830	0.310915	+	0.950438i	$0.399365\pi$
$380$	1.16463	0.0597444
$381$	1.88632	0.0966391
$382$	−42.6493	−2.18213
$383$	27.8995	1.42560	0.712798	−	0.701369i	$-0.247427\pi$
$383$	27.8995	1.42560	0.712798	+	0.701369i	$0.247427\pi$
$384$	−20.2877	−1.03530
$385$	0.0583422	0.00297339
$386$	−24.6288	−1.25357
$387$	−7.29688	−0.370921
$388$	34.0418	1.72821
$389$	−18.8000	−0.953196	−0.476598	−	0.879121i	$-0.658130\pi$
$389$	−18.8000	−0.953196	−0.476598	+	0.879121i	$0.658130\pi$
$390$	1.64726	0.0834121
$391$	8.57628	0.433721
$392$	23.7087	1.19747
$393$	20.0670	1.01225
$394$	−47.3597	−2.38595
$395$	2.89643	0.145735
$396$	−1.47744	−0.0742441
$397$	−24.8418	−1.24677	−0.623386	−	0.781914i	$-0.714244\pi$
$397$	−24.8418	−1.24677	−0.623386	+	0.781914i	$0.714244\pi$
$398$	−12.7304	−0.638117
$399$	0.779593	0.0390284
$400$	−6.49848	−0.324924
$401$	34.4751	1.72161	0.860803	−	0.508939i	$-0.169962\pi$
$401$	34.4751	1.72161	0.860803	+	0.508939i	$0.169962\pi$
$402$	2.24735	0.112088
$403$	13.7643	0.685647
$404$	−17.9927	−0.895172
$405$	0.242883	0.0120690
$406$	4.64159	0.230358
$407$	−1.25095	−0.0620073
$408$	5.22289	0.258572
$409$	−20.5367	−1.01548	−0.507738	−	0.861512i	$-0.669518\pi$
$409$	−20.5367	−1.01548	−0.507738	+	0.861512i	$0.669518\pi$
$410$	−5.14573	−0.254130
$411$	−8.08966	−0.399034
$412$	−21.5938	−1.06385
$413$	−0.123316	−0.00606797
$414$	−13.6968	−0.673160
$415$	3.97940	0.195341
$416$	11.6028	0.568876
$417$	−9.04638	−0.443003
$418$	1.34784	0.0659248
$419$	25.9726	1.26884	0.634421	−	0.772988i	$-0.281239\pi$
$419$	25.9726	1.26884	0.634421	+	0.772988i	$0.281239\pi$
$420$	0.487340	0.0237797
$421$	−16.9382	−0.825516	−0.412758	−	0.910841i	$-0.635435\pi$
$421$	−16.9382	−0.825516	−0.412758	+	0.910841i	$0.635435\pi$
$422$	48.2105	2.34685
$423$	7.37779	0.358720
$424$	29.7057	1.44263
$425$	−7.26425	−0.352368
$426$	−11.0542	−0.535580
$427$	−1.43400	−0.0693963
$428$	7.42613	0.358955
$429$	1.21479	0.0586504
$430$	4.16130	0.200676
$431$	37.6494	1.81351	0.906755	−	0.421658i	$-0.138552\pi$
$431$	37.6494	1.81351	0.906755	+	0.421658i	$0.138552\pi$
$432$	−1.31521	−0.0632782
$433$	17.6170	0.846619	0.423309	−	0.905985i	$-0.360868\pi$
$433$	17.6170	0.846619	0.423309	+	0.905985i	$0.360868\pi$
$434$	6.39048	0.306753
$435$	−0.840649	−0.0403060
$436$	−49.8677	−2.38823
$437$	7.96226	0.380887
$438$	−1.18524	−0.0566331
$439$	10.0292	0.478668	0.239334	−	0.970937i	$-0.423071\pi$
$439$	10.0292	0.478668	0.239334	+	0.970937i	$0.423071\pi$
$440$	0.362880	0.0172996
$441$	−6.67378	−0.317799
$442$	−9.97101	−0.474273
$443$	−1.08124	−0.0513711	−0.0256856	−	0.999670i	$-0.508177\pi$
$443$	−1.08124	−0.0513711	−0.0256856	+	0.999670i	$0.508177\pi$
$444$	−10.4493	−0.495904
$445$	3.94914	0.187207
$446$	−6.80541	−0.322245
$447$	8.51571	0.402779
$448$	6.88935	0.325491
$449$	−6.71342	−0.316826	−0.158413	−	0.987373i	$-0.550638\pi$
$449$	−6.71342	−0.316826	−0.158413	+	0.987373i	$0.550638\pi$
$450$	11.6014	0.546895
$451$	−3.79478	−0.178689
$452$	−10.6330	−0.500134
$453$	13.2754	0.623735
$454$	−50.2646	−2.35904
$455$	−0.400703	−0.0187852
$456$	4.84896	0.227073
$457$	9.93143	0.464573	0.232286	−	0.972647i	$-0.425379\pi$
$457$	9.93143	0.464573	0.232286	+	0.972647i	$0.425379\pi$
$458$	−1.95726	−0.0914568
$459$	−1.47020	−0.0686229
$460$	4.97738	0.232071
$461$	−12.6060	−0.587118	−0.293559	−	0.955941i	$-0.594840\pi$
$461$	−12.6060	−0.587118	−0.293559	+	0.955941i	$0.594840\pi$
$462$	0.564001	0.0262397
$463$	16.9520	0.787825	0.393913	−	0.919148i	$-0.371121\pi$
$463$	16.9520	0.787825	0.393913	+	0.919148i	$0.371121\pi$
$464$	4.55212	0.211327
$465$	−1.15739	−0.0536728
$466$	61.3439	2.84170
$467$	7.91921	0.366457	0.183229	−	0.983070i	$-0.441345\pi$
$467$	7.91921	0.366457	0.183229	+	0.983070i	$0.441345\pi$
$468$	10.1473	0.469057
$469$	−0.546678	−0.0252432
$470$	−4.20744	−0.194075
$471$	−13.3219	−0.613839
$472$	−0.767006	−0.0353043
$473$	3.06879	0.141103
$474$	28.0001	1.28609
$475$	−6.74416	−0.309443
$476$	−2.94992	−0.135209
$477$	−8.36187	−0.382864
$478$	11.0645	0.506076
$479$	5.12525	0.234179	0.117089	−	0.993121i	$-0.462644\pi$
$479$	5.12525	0.234179	0.117089	+	0.993121i	$0.462644\pi$
$480$	−0.975645	−0.0445319
$481$	8.59171	0.391748
$482$	−1.97490	−0.0899541
$483$	3.33180	0.151602
$484$	−38.0217	−1.72826
$485$	2.35359	0.106871
$486$	2.34798	0.106507
$487$	17.4201	0.789381	0.394691	−	0.918814i	$-0.370852\pi$
$487$	17.4201	0.789381	0.394691	+	0.918814i	$0.370852\pi$
$488$	−8.91930	−0.403758
$489$	1.55334	0.0702444
$490$	3.80595	0.171935
$491$	−2.51520	−0.113509	−0.0567546	−	0.998388i	$-0.518075\pi$
$491$	−2.51520	−0.113509	−0.0567546	+	0.998388i	$0.518075\pi$
$492$	−31.6982	−1.42907
$493$	5.08853	0.229176
$494$	−9.25713	−0.416498
$495$	−0.102147	−0.00459119
$496$	6.26729	0.281410
$497$	2.68899	0.120618
$498$	38.4693	1.72385
$499$	14.6518	0.655903	0.327951	−	0.944695i	$-0.393642\pi$
$499$	14.6518	0.655903	0.327951	+	0.944695i	$0.393642\pi$
$500$	−8.48217	−0.379334
$501$	10.0948	0.451001
$502$	−7.43278	−0.331741
$503$	35.6179	1.58812	0.794062	−	0.607836i	$-0.207962\pi$
$503$	35.6179	1.58812	0.794062	+	0.607836i	$0.207962\pi$
$504$	2.02904	0.0903807
$505$	−1.24399	−0.0553566
$506$	5.76035	0.256079
$507$	4.65667	0.206810
$508$	−6.62666	−0.294010
$509$	4.89398	0.216922	0.108461	−	0.994101i	$-0.465408\pi$
$509$	4.89398	0.216922	0.108461	+	0.994101i	$0.465408\pi$
$510$	0.838430	0.0371263
$511$	0.288316	0.0127543
$512$	14.6278	0.646461
$513$	−1.36494	−0.0602634
$514$	61.2516	2.70169
$515$	−1.49296	−0.0657875
$516$	25.6340	1.12847
$517$	−3.10282	−0.136462
$518$	3.98896	0.175265
$519$	−17.2207	−0.755906
$520$	−2.49231	−0.109295
$521$	39.7084	1.73966	0.869829	−	0.493353i	$-0.164229\pi$
$521$	39.7084	1.73966	0.869829	+	0.493353i	$0.164229\pi$
$522$	−8.12665	−0.355694
$523$	2.27910	0.0996582	0.0498291	−	0.998758i	$-0.484132\pi$
$523$	2.27910	0.0996582	0.0498291	+	0.998758i	$0.484132\pi$
$524$	−70.4956	−3.07961
$525$	−2.82209	−0.123166
$526$	−3.18914	−0.139053
$527$	7.00582	0.305178
$528$	0.553129	0.0240718
$529$	11.0289	0.479518
$530$	4.76865	0.207137
$531$	0.215905	0.00936948
$532$	−2.73872	−0.118738
$533$	26.0631	1.12892
$534$	38.1768	1.65207
$535$	0.513429	0.0221975
$536$	−3.40026	−0.146869
$537$	−11.8324	−0.510606
$538$	55.0646	2.37400
$539$	2.80674	0.120895
$540$	−0.853250	−0.0367180
$541$	21.4978	0.924263	0.462132	−	0.886811i	$-0.347085\pi$
$541$	21.4978	0.924263	0.462132	+	0.886811i	$0.347085\pi$
$542$	−23.7173	−1.01875
$543$	−4.70237	−0.201798
$544$	5.90568	0.253204
$545$	−3.44776	−0.147686
$546$	−3.87364	−0.165776
$547$	23.4522	1.00275	0.501373	−	0.865231i	$-0.332829\pi$
$547$	23.4522	1.00275	0.501373	+	0.865231i	$0.332829\pi$
$548$	28.4191	1.21400
$549$	2.51070	0.107154
$550$	−4.87910	−0.208046
$551$	4.72422	0.201258
$552$	20.7233	0.882044
$553$	−6.81115	−0.289640
$554$	62.0013	2.63418
$555$	−0.722449	−0.0306662
$556$	31.7800	1.34777
$557$	−38.4501	−1.62918	−0.814592	−	0.580034i	$-0.803039\pi$
$557$	−38.4501	−1.62918	−0.814592	+	0.580034i	$0.803039\pi$
$558$	−11.1887	−0.473654
$559$	−21.0769	−0.891459
$560$	−0.182452	−0.00771000
$561$	0.618309	0.0261050
$562$	37.1807	1.56837
$563$	36.0730	1.52030	0.760148	−	0.649750i	$-0.225126\pi$
$563$	36.0730	1.52030	0.760148	+	0.649750i	$0.225126\pi$
$564$	−25.9182	−1.09135
$565$	−0.735147	−0.0309279
$566$	28.8646	1.21327
$567$	−0.571157	−0.0239863
$568$	16.7252	0.701772
$569$	40.0926	1.68077	0.840384	−	0.541991i	$-0.182329\pi$
$569$	40.0926	1.68077	0.840384	+	0.541991i	$0.182329\pi$
$570$	0.778402	0.0326037
$571$	3.53507	0.147938	0.0739691	−	0.997261i	$-0.476433\pi$
$571$	3.53507	0.147938	0.0739691	+	0.997261i	$0.476433\pi$
$572$	−4.26756	−0.178435
$573$	−18.1643	−0.758822
$574$	12.1006	0.505068
$575$	−28.8230	−1.20200
$576$	−12.0621	−0.502588
$577$	13.7405	0.572027	0.286013	−	0.958226i	$-0.407670\pi$
$577$	13.7405	0.572027	0.286013	+	0.958226i	$0.407670\pi$
$578$	34.8406	1.44918
$579$	−10.4894	−0.435923
$580$	2.95321	0.122625
$581$	−9.35783	−0.388228
$582$	22.7524	0.943118
$583$	3.51669	0.145646
$584$	1.79328	0.0742066
$585$	0.701563	0.0290061
$586$	45.4723	1.87844
$587$	−36.3630	−1.50086	−0.750430	−	0.660950i	$-0.770153\pi$
$587$	−36.3630	−1.50086	−0.750430	+	0.660950i	$0.770153\pi$
$588$	23.4450	0.966857
$589$	6.50423	0.268002
$590$	−0.123127	−0.00506907
$591$	−20.1704	−0.829699
$592$	3.91206	0.160785
$593$	32.0091	1.31446	0.657229	−	0.753691i	$-0.271728\pi$
$593$	32.0091	1.31446	0.657229	+	0.753691i	$0.271728\pi$
$594$	−0.987472	−0.0405164
$595$	−0.203952	−0.00836121
$596$	−29.9158	−1.22540
$597$	−5.42185	−0.221901
$598$	−39.5629	−1.61785
$599$	−17.4381	−0.712503	−0.356252	−	0.934390i	$-0.615945\pi$
$599$	−17.4381	−0.712503	−0.356252	+	0.934390i	$0.615945\pi$
$600$	−17.5530	−0.716598
$601$	15.4028	0.628292	0.314146	−	0.949375i	$-0.398282\pi$
$601$	15.4028	0.628292	0.314146	+	0.949375i	$0.398282\pi$
$602$	−9.78559	−0.398831
$603$	0.957142	0.0389778
$604$	−46.6367	−1.89762
$605$	−2.62875	−0.106874
$606$	−12.0258	−0.488513
$607$	36.8374	1.49518	0.747592	−	0.664158i	$-0.231210\pi$
$607$	36.8374	1.49518	0.747592	+	0.664158i	$0.231210\pi$
$608$	5.48286	0.222359
$609$	1.97684	0.0801058
$610$	−1.43181	−0.0579724
$611$	21.3106	0.862135
$612$	5.16481	0.208775
$613$	0.0760720	0.00307252	0.00153626	−	0.999999i	$-0.499511\pi$
$613$	0.0760720	0.00307252	0.00153626	+	0.999999i	$0.499511\pi$
$614$	45.1354	1.82152
$615$	−2.19156	−0.0883722
$616$	−0.853338	−0.0343820
$617$	−1.78171	−0.0717291	−0.0358645	−	0.999357i	$-0.511418\pi$
$617$	−1.78171	−0.0717291	−0.0358645	+	0.999357i	$0.511418\pi$
$618$	−14.4326	−0.580564
$619$	−22.0114	−0.884712	−0.442356	−	0.896839i	$-0.645857\pi$
$619$	−22.0114	−0.884712	−0.442356	+	0.896839i	$0.645857\pi$
$620$	4.06593	0.163292
$621$	−5.83343	−0.234088
$622$	8.25937	0.331171
$623$	−9.28668	−0.372063
$624$	−3.79897	−0.152080
$625$	24.1186	0.964744
$626$	−18.5391	−0.740973
$627$	0.574041	0.0229250
$628$	46.7998	1.86752
$629$	4.37306	0.174365
$630$	0.325722	0.0129771
$631$	−22.9548	−0.913818	−0.456909	−	0.889514i	$-0.651043\pi$
$631$	−22.9548	−0.913818	−0.456909	+	0.889514i	$0.651043\pi$
$632$	−42.3644	−1.68517
$633$	20.5328	0.816105
$634$	−16.0837	−0.638764
$635$	−0.458155	−0.0181813
$636$	29.3753	1.16481
$637$	−19.2771	−0.763786
$638$	3.41776	0.135310
$639$	−4.70798	−0.186245
$640$	4.92754	0.194778
$641$	47.0213	1.85723	0.928616	−	0.371043i	$-0.121000\pi$
$641$	47.0213	1.85723	0.928616	+	0.371043i	$0.121000\pi$
$642$	4.96338	0.195889
$643$	34.5170	1.36122	0.680609	−	0.732647i	$-0.261715\pi$
$643$	34.5170	1.36122	0.680609	+	0.732647i	$0.261715\pi$
$644$	−11.7047	−0.461228
$645$	1.77229	0.0697838
$646$	−4.71175	−0.185381
$647$	23.3820	0.919243	0.459621	−	0.888115i	$-0.347985\pi$
$647$	23.3820	0.919243	0.459621	+	0.888115i	$0.347985\pi$
$648$	−3.55251	−0.139556
$649$	−0.0908015	−0.00356427
$650$	33.5104	1.31439
$651$	2.72169	0.106672
$652$	−5.45689	−0.213708
$653$	16.5330	0.646987	0.323493	−	0.946230i	$-0.395143\pi$
$653$	16.5330	0.646987	0.323493	+	0.946230i	$0.395143\pi$
$654$	−33.3300	−1.30330
$655$	−4.87394	−0.190440
$656$	11.8673	0.463340
$657$	−0.504793	−0.0196938
$658$	9.89409	0.385712
$659$	26.8096	1.04435	0.522176	−	0.852838i	$-0.325120\pi$
$659$	26.8096	1.04435	0.522176	+	0.852838i	$0.325120\pi$
$660$	0.358845	0.0139680
$661$	12.3809	0.481563	0.240781	−	0.970579i	$-0.422596\pi$
$661$	12.3809	0.481563	0.240781	+	0.970579i	$0.422596\pi$
$662$	6.96929	0.270869
$663$	−4.24663	−0.164926
$664$	−58.2044	−2.25877
$665$	−0.189350	−0.00734267
$666$	−6.98400	−0.270625
$667$	20.1902	0.781769
$668$	−35.4630	−1.37211
$669$	−2.89841	−0.112059
$670$	−0.545843	−0.0210878
$671$	−1.05591	−0.0407628
$672$	2.29430	0.0885045
$673$	−38.8502	−1.49756	−0.748782	−	0.662816i	$-0.769361\pi$
$673$	−38.8502	−1.49756	−0.748782	+	0.662816i	$0.769361\pi$
$674$	−9.69159	−0.373306
$675$	4.94101	0.190179
$676$	−16.3589	−0.629190
$677$	30.8470	1.18555	0.592773	−	0.805370i	$-0.298033\pi$
$677$	30.8470	1.18555	0.592773	+	0.805370i	$0.298033\pi$
$678$	−7.10675	−0.272933
$679$	−5.53463	−0.212399
$680$	−1.26855	−0.0486467
$681$	−21.4076	−0.820342
$682$	4.70553	0.180184
$683$	−48.5825	−1.85896	−0.929478	−	0.368877i	$-0.879742\pi$
$683$	−48.5825	−1.85896	−0.929478	+	0.368877i	$0.879742\pi$
$684$	4.79503	0.183343
$685$	1.96484	0.0750727
$686$	−18.3374	−0.700126
$687$	−0.833593	−0.0318036
$688$	−9.59696	−0.365881
$689$	−24.1531	−0.920160
$690$	3.32672	0.126646
$691$	44.1216	1.67846	0.839232	−	0.543773i	$-0.183005\pi$
$691$	44.1216	1.67846	0.839232	+	0.543773i	$0.183005\pi$
$692$	60.4966	2.29973
$693$	0.240207	0.00912471
$694$	27.0359	1.02627
$695$	2.19721	0.0833450
$696$	12.2957	0.466067
$697$	13.2657	0.502475
$698$	−12.9226	−0.489128
$699$	26.1263	0.988186
$700$	9.91403	0.374715
$701$	−29.7318	−1.12296	−0.561478	−	0.827492i	$-0.689767\pi$
$701$	−29.7318	−1.12296	−0.561478	+	0.827492i	$0.689767\pi$
$702$	6.78210	0.255974
$703$	4.05997	0.153124
$704$	5.07287	0.191191
$705$	−1.79194	−0.0674883
$706$	−79.6806	−2.99882
$707$	2.92532	0.110018
$708$	−0.758476	−0.0285053
$709$	−14.6473	−0.550091	−0.275045	−	0.961431i	$-0.588693\pi$
$709$	−14.6473	−0.550091	−0.275045	+	0.961431i	$0.588693\pi$
$710$	2.68489	0.100762
$711$	11.9252	0.447229
$712$	−57.7619	−2.16472
$713$	27.7976	1.04103
$714$	−1.97163	−0.0737863
$715$	−0.295051	−0.0110343
$716$	41.5674	1.55344
$717$	4.71233	0.175985
$718$	60.4406	2.25562
$719$	−4.36655	−0.162845	−0.0814225	−	0.996680i	$-0.525946\pi$
$719$	−4.36655	−0.162845	−0.0814225	+	0.996680i	$0.525946\pi$
$720$	0.319443	0.0119049
$721$	3.51079	0.130749
$722$	40.2372	1.49747
$723$	−0.841105	−0.0312810
$724$	16.5195	0.613942
$725$	−17.1014	−0.635132
$726$	−25.4125	−0.943146
$727$	6.10062	0.226259	0.113130	−	0.993580i	$-0.463912\pi$
$727$	6.10062	0.226259	0.113130	+	0.993580i	$0.463912\pi$
$728$	5.86085	0.217218
$729$	1.00000	0.0370370
$730$	0.287875	0.0106547
$731$	−10.7278	−0.396784
$732$	−8.82011	−0.326001
$733$	44.6070	1.64760	0.823799	−	0.566882i	$-0.191851\pi$
$733$	44.6070	1.64760	0.823799	+	0.566882i	$0.191851\pi$
$734$	−32.2203	−1.18927
$735$	1.62095	0.0597896
$736$	23.4325	0.863734
$737$	−0.402538	−0.0148277
$738$	−21.1861	−0.779870
$739$	33.2116	1.22171	0.610853	−	0.791744i	$-0.290826\pi$
$739$	33.2116	1.22171	0.610853	+	0.791744i	$0.290826\pi$
$740$	2.53797	0.0932976
$741$	−3.94259	−0.144835
$742$	−11.2138	−0.411672
$743$	16.8702	0.618907	0.309453	−	0.950915i	$-0.399854\pi$
$743$	16.8702	0.618907	0.309453	+	0.950915i	$0.399854\pi$
$744$	16.9285	0.620630
$745$	−2.06832	−0.0757775
$746$	−15.5348	−0.568770
$747$	16.3840	0.599459
$748$	−2.17212	−0.0794207
$749$	−1.20736	−0.0441161
$750$	−5.66920	−0.207010
$751$	−23.1859	−0.846067	−0.423034	−	0.906114i	$-0.639035\pi$
$751$	−23.1859	−0.846067	−0.423034	+	0.906114i	$0.639035\pi$
$752$	9.70336	0.353845
$753$	−3.16561	−0.115361
$754$	−23.4737	−0.854861
$755$	−3.22438	−0.117347
$756$	2.00648	0.0729749
$757$	1.46129	0.0531114	0.0265557	−	0.999647i	$-0.491546\pi$
$757$	1.46129	0.0531114	0.0265557	+	0.999647i	$0.491546\pi$
$758$	−28.4240	−1.03241
$759$	2.45332	0.0890499
$760$	−1.17773	−0.0427207
$761$	34.3238	1.24424	0.622118	−	0.782924i	$-0.286273\pi$
$761$	34.3238	1.24424	0.622118	+	0.782924i	$0.286273\pi$
$762$	−4.42904	−0.160447
$763$	8.10766	0.293517
$764$	63.8112	2.30861
$765$	0.357086	0.0129105
$766$	−65.5074	−2.36688
$767$	0.623638	0.0225183
$768$	23.5109	0.848377
$769$	−36.9790	−1.33350	−0.666749	−	0.745282i	$-0.732315\pi$
$769$	−36.9790	−1.33350	−0.666749	+	0.745282i	$0.732315\pi$
$770$	−0.136986	−0.00493664
$771$	26.0869	0.939498
$772$	36.8492	1.32623
$773$	−1.06077	−0.0381532	−0.0190766	−	0.999818i	$-0.506073\pi$
$773$	−1.06077	−0.0381532	−0.0190766	+	0.999818i	$0.506073\pi$
$774$	17.1329	0.615831
$775$	−23.5450	−0.845762
$776$	−34.4246	−1.23577
$777$	1.69889	0.0609473
$778$	44.1419	1.58257
$779$	12.3160	0.441265
$780$	−2.46460	−0.0882468
$781$	1.98000	0.0708499
$782$	−20.1369	−0.720096
$783$	−3.46112	−0.123691
$784$	−8.77744	−0.313480
$785$	3.23565	0.115485
$786$	−47.1169	−1.68061
$787$	24.3150	0.866735	0.433368	−	0.901217i	$-0.357325\pi$
$787$	24.3150	0.866735	0.433368	+	0.901217i	$0.357325\pi$
$788$	70.8588	2.52424
$789$	−1.35825	−0.0483550
$790$	−6.80075	−0.241960
$791$	1.72875	0.0614673
$792$	1.49405	0.0530889
$793$	7.25211	0.257530
$794$	58.3280	2.06998
$795$	2.03096	0.0720306
$796$	19.0470	0.675103
$797$	−16.5812	−0.587336	−0.293668	−	0.955907i	$-0.594876\pi$
$797$	−16.5812	−0.587336	−0.293668	+	0.955907i	$0.594876\pi$
$798$	−1.83047	−0.0647979
$799$	10.8468	0.383732
$800$	−19.8477	−0.701722
$801$	16.2594	0.574499
$802$	−80.9469	−2.85833
$803$	0.212297	0.00749179
$804$	−3.36245	−0.118584
$805$	−0.809239	−0.0285219
$806$	−32.3182	−1.13836
$807$	23.4519	0.825547
$808$	18.1951	0.640100
$809$	−32.4871	−1.14218	−0.571092	−	0.820886i	$-0.693480\pi$
$809$	−32.4871	−1.14218	−0.571092	+	0.820886i	$0.693480\pi$
$810$	−0.570284	−0.0200378
$811$	31.9035	1.12028	0.560142	−	0.828397i	$-0.310747\pi$
$811$	31.9035	1.12028	0.560142	+	0.828397i	$0.310747\pi$
$812$	−6.94467	−0.243710
$813$	−10.1012	−0.354263
$814$	2.93721	0.102949
$815$	−0.377280	−0.0132155
$816$	−1.93362	−0.0676903
$817$	−9.95978	−0.348449
$818$	48.2198	1.68597
$819$	−1.64978	−0.0576478
$820$	7.69896	0.268859
$821$	−39.7609	−1.38766	−0.693832	−	0.720137i	$-0.744079\pi$
$821$	−39.7609	−1.38766	−0.693832	+	0.720137i	$0.744079\pi$
$822$	18.9944	0.662504
$823$	−34.6368	−1.20736	−0.603681	−	0.797226i	$-0.706300\pi$
$823$	−34.6368	−1.20736	−0.603681	+	0.797226i	$0.706300\pi$
$824$	21.8366	0.760715
$825$	−2.07800	−0.0723467
$826$	0.289543	0.0100745
$827$	50.7365	1.76428	0.882141	−	0.470985i	$-0.156101\pi$
$827$	50.7365	1.76428	0.882141	+	0.470985i	$0.156101\pi$
$828$	20.4929	0.712177
$829$	16.7304	0.581072	0.290536	−	0.956864i	$-0.406166\pi$
$829$	16.7304	0.581072	0.290536	+	0.956864i	$0.406166\pi$
$830$	−9.34354	−0.324319
$831$	26.4062	0.916023
$832$	−34.8412	−1.20790
$833$	−9.81176	−0.339957
$834$	21.2407	0.735505
$835$	−2.45185	−0.0848497
$836$	−2.01661	−0.0697459
$837$	−4.76523	−0.164710
$838$	−60.9830	−2.10662
$839$	−4.46605	−0.154185	−0.0770927	−	0.997024i	$-0.524564\pi$
$839$	−4.46605	−0.154185	−0.0770927	+	0.997024i	$0.524564\pi$
$840$	−0.492820	−0.0170039
$841$	−17.0206	−0.586918
$842$	39.7705	1.37058
$843$	15.8352	0.545393
$844$	−72.1318	−2.48288
$845$	−1.13103	−0.0389085
$846$	−17.3229	−0.595573
$847$	6.18170	0.212406
$848$	−10.9976	−0.377661
$849$	12.2934	0.421907
$850$	17.0563	0.585026
$851$	17.3514	0.594798
$852$	16.5392	0.566623
$853$	36.2916	1.24260	0.621301	−	0.783572i	$-0.286605\pi$
$853$	36.2916	1.24260	0.621301	+	0.783572i	$0.286605\pi$
$854$	3.36701	0.115217
$855$	0.331520	0.0113377
$856$	−7.50964	−0.256674
$857$	27.0531	0.924117	0.462058	−	0.886850i	$-0.347111\pi$
$857$	27.0531	0.924117	0.462058	+	0.886850i	$0.347111\pi$
$858$	−2.85229	−0.0973757
$859$	49.7342	1.69691	0.848454	−	0.529268i	$-0.177534\pi$
$859$	49.7342	1.69691	0.848454	+	0.529268i	$0.177534\pi$
$860$	−6.22607	−0.212307
$861$	5.15361	0.175634
$862$	−88.4001	−3.01092
$863$	11.5896	0.394513	0.197257	−	0.980352i	$-0.436797\pi$
$863$	11.5896	0.394513	0.197257	+	0.980352i	$0.436797\pi$
$864$	−4.01693	−0.136659
$865$	4.18262	0.142213
$866$	−41.3644	−1.40562
$867$	14.8385	0.503943
$868$	−9.56133	−0.324533
$869$	−5.01528	−0.170132
$870$	1.97383	0.0669190
$871$	2.76469	0.0936778
$872$	50.4285	1.70773
$873$	9.69021	0.327964
$874$	−18.6952	−0.632376
$875$	1.37906	0.0466207
$876$	1.77334	0.0599157
$877$	22.3115	0.753404	0.376702	−	0.926334i	$-0.377058\pi$
$877$	22.3115	0.753404	0.376702	+	0.926334i	$0.377058\pi$
$878$	−23.5484	−0.794719
$879$	19.3666	0.653218
$880$	−0.134346	−0.00452879
$881$	−4.47136	−0.150644	−0.0753220	−	0.997159i	$-0.523998\pi$
$881$	−4.47136	−0.150644	−0.0753220	+	0.997159i	$0.523998\pi$
$882$	15.6699	0.527633
$883$	−41.8469	−1.40826	−0.704130	−	0.710071i	$-0.748663\pi$
$883$	−41.8469	−1.40826	−0.704130	+	0.710071i	$0.748663\pi$
$884$	14.9185	0.501762
$885$	−0.0524397	−0.00176274
$886$	2.53872	0.0852900
$887$	33.3732	1.12056	0.560281	−	0.828303i	$-0.310693\pi$
$887$	33.3732	1.12056	0.560281	+	0.828303i	$0.310693\pi$
$888$	10.5669	0.354600
$889$	1.07738	0.0361343
$890$	−9.27250	−0.310815
$891$	−0.420562	−0.0140894
$892$	10.1821	0.340923
$893$	10.0702	0.336987
$894$	−19.9947	−0.668723
$895$	2.87389	0.0960636
$896$	−11.5875	−0.387110
$897$	−16.8498	−0.562597
$898$	15.7630	0.526017
$899$	16.4930	0.550074
$900$	−17.3578	−0.578593
$901$	−12.2936	−0.409559
$902$	8.91006	0.296672
$903$	−4.16766	−0.138691
$904$	10.7526	0.357625
$905$	1.14213	0.0379656
$906$	−31.1705	−1.03557
$907$	55.8614	1.85485	0.927424	−	0.374012i	$-0.122018\pi$
$907$	55.8614	1.85485	0.927424	+	0.374012i	$0.122018\pi$
$908$	75.2051	2.49577
$909$	−5.12175	−0.169878
$910$	0.940842	0.0311886
$911$	−3.79744	−0.125815	−0.0629074	−	0.998019i	$-0.520037\pi$
$911$	−3.79744	−0.125815	−0.0629074	+	0.998019i	$0.520037\pi$
$912$	−1.79518	−0.0594444
$913$	−6.89049	−0.228042
$914$	−23.3188	−0.771318
$915$	−0.609806	−0.0201596
$916$	2.92842	0.0967577
$917$	11.4614	0.378489
$918$	3.45199	0.113933
$919$	−18.2102	−0.600700	−0.300350	−	0.953829i	$-0.597103\pi$
$919$	−18.2102	−0.600700	−0.300350	+	0.953829i	$0.597103\pi$
$920$	−5.03335	−0.165945
$921$	19.2231	0.633422
$922$	29.5985	0.974776
$923$	−13.5989	−0.447614
$924$	−0.843849	−0.0277606
$925$	−14.6969	−0.483231
$926$	−39.8029	−1.30800
$927$	−6.14681	−0.201888
$928$	13.9031	0.456392
$929$	27.2118	0.892791	0.446395	−	0.894836i	$-0.352707\pi$
$929$	27.2118	0.892791	0.446395	+	0.894836i	$0.352707\pi$
$930$	2.71754	0.0891115
$931$	−9.10929	−0.298545
$932$	−91.7818	−3.00641
$933$	3.51765	0.115163
$934$	−18.5941	−0.608419
$935$	−0.150177	−0.00491130
$936$	−10.2614	−0.335403
$937$	−34.1452	−1.11548	−0.557738	−	0.830017i	$-0.688331\pi$
$937$	−34.1452	−1.11548	−0.557738	+	0.830017i	$0.688331\pi$
$938$	1.28359	0.0419107
$939$	−7.89578	−0.257669
$940$	6.29510	0.205323
$941$	−43.4405	−1.41612	−0.708060	−	0.706153i	$-0.750429\pi$
$941$	−43.4405	−1.41612	−0.708060	+	0.706153i	$0.750429\pi$
$942$	31.2795	1.01914
$943$	52.6356	1.71405
$944$	0.283961	0.00924215
$945$	0.138724	0.00451270
$946$	−7.20546	−0.234270
$947$	−23.5708	−0.765948	−0.382974	−	0.923759i	$-0.625100\pi$
$947$	−23.5708	−0.765948	−0.382974	+	0.923759i	$0.625100\pi$
$948$	−41.8933	−1.36063
$949$	−1.45808	−0.0473314
$950$	15.8352	0.513760
$951$	−6.85000	−0.222126
$952$	2.98309	0.0966825
$953$	42.5899	1.37962	0.689812	−	0.723989i	$-0.257693\pi$
$953$	42.5899	1.37962	0.689812	+	0.723989i	$0.257693\pi$
$954$	19.6335	0.635658
$955$	4.41179	0.142762
$956$	−16.5545	−0.535409
$957$	1.45562	0.0470535
$958$	−12.0340	−0.388801
$959$	−4.62046	−0.149203
$960$	2.92968	0.0945551
$961$	−8.29260	−0.267503
$962$	−20.1732	−0.650409
$963$	2.11389	0.0681193
$964$	2.95481	0.0951680
$965$	2.54769	0.0820130
$966$	−7.82301	−0.251701
$967$	−49.8924	−1.60443	−0.802215	−	0.597035i	$-0.796345\pi$
$967$	−49.8924	−1.60443	−0.802215	+	0.597035i	$0.796345\pi$
$968$	38.4493	1.23581
$969$	−2.00672	−0.0644652
$970$	−5.52617	−0.177435
$971$	18.8772	0.605800	0.302900	−	0.953022i	$-0.402045\pi$
$971$	18.8772	0.605800	0.302900	+	0.953022i	$0.402045\pi$
$972$	−3.51301	−0.112680
$973$	−5.16690	−0.165643
$974$	−40.9021	−1.31059
$975$	14.2720	0.457070
$976$	3.30211	0.105698
$977$	−9.70661	−0.310542	−0.155271	−	0.987872i	$-0.549625\pi$
$977$	−9.70661	−0.310542	−0.155271	+	0.987872i	$0.549625\pi$
$978$	−3.64721	−0.116625
$979$	−6.83810	−0.218547
$980$	−5.69440	−0.181901
$981$	−14.1952	−0.453217
$982$	5.90563	0.188456
$983$	−33.4815	−1.06790	−0.533948	−	0.845517i	$-0.679292\pi$
$983$	−33.4815	−1.06790	−0.533948	+	0.845517i	$0.679292\pi$
$984$	32.0547	1.02187
$985$	4.89905	0.156097
$986$	−11.9478	−0.380494
$987$	4.21387	0.134129
$988$	13.8504	0.440639
$989$	−42.5659	−1.35352
$990$	0.239840	0.00762262
$991$	49.4531	1.57093	0.785464	−	0.618907i	$-0.212424\pi$
$991$	49.4531	1.57093	0.785464	+	0.618907i	$0.212424\pi$
$992$	19.1416	0.607747
$993$	2.96821	0.0941932
$994$	−6.31370	−0.200259
$995$	1.31688	0.0417477
$996$	−57.5572	−1.82377
$997$	49.2921	1.56110	0.780548	−	0.625096i	$-0.214940\pi$
$997$	49.2921	1.56110	0.780548	+	0.625096i	$0.214940\pi$
$998$	−34.4020	−1.08898
$999$	−2.97447	−0.0941081

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6033.2.a.c.1.8	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6033.2.a.c.1.8	✓	82	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)

\(f(q)\)	\(=\)	\(q-2.34798 q^{2} -1.00000 q^{3} +3.51301 q^{4} +0.242883 q^{5} +2.34798 q^{6} -0.571157 q^{7} -3.55251 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.34798 q^{2} -1.00000 q^{3} +3.51301 q^{4} +0.242883 q^{5} +2.34798 q^{6} -0.571157 q^{7} -3.55251 q^{8} +1.00000 q^{9} -0.570284 q^{10} -0.420562 q^{11} -3.51301 q^{12} +2.88848 q^{13} +1.34106 q^{14} -0.242883 q^{15} +1.31521 q^{16} +1.47020 q^{17} -2.34798 q^{18} +1.36494 q^{19} +0.853250 q^{20} +0.571157 q^{21} +0.987472 q^{22} +5.83343 q^{23} +3.55251 q^{24} -4.94101 q^{25} -6.78210 q^{26} -1.00000 q^{27} -2.00648 q^{28} +3.46112 q^{29} +0.570284 q^{30} +4.76523 q^{31} +4.01693 q^{32} +0.420562 q^{33} -3.45199 q^{34} -0.138724 q^{35} +3.51301 q^{36} +2.97447 q^{37} -3.20484 q^{38} -2.88848 q^{39} -0.862845 q^{40} +9.02310 q^{41} -1.34106 q^{42} -7.29688 q^{43} -1.47744 q^{44} +0.242883 q^{45} -13.6968 q^{46} +7.37779 q^{47} -1.31521 q^{48} -6.67378 q^{49} +11.6014 q^{50} -1.47020 q^{51} +10.1473 q^{52} -8.36187 q^{53} +2.34798 q^{54} -0.102147 q^{55} +2.02904 q^{56} -1.36494 q^{57} -8.12665 q^{58} +0.215905 q^{59} -0.853250 q^{60} +2.51070 q^{61} -11.1887 q^{62} -0.571157 q^{63} -12.0621 q^{64} +0.701563 q^{65} -0.987472 q^{66} +0.957142 q^{67} +5.16481 q^{68} -5.83343 q^{69} +0.325722 q^{70} -4.70798 q^{71} -3.55251 q^{72} -0.504793 q^{73} -6.98400 q^{74} +4.94101 q^{75} +4.79503 q^{76} +0.240207 q^{77} +6.78210 q^{78} +11.9252 q^{79} +0.319443 q^{80} +1.00000 q^{81} -21.1861 q^{82} +16.3840 q^{83} +2.00648 q^{84} +0.357086 q^{85} +17.1329 q^{86} -3.46112 q^{87} +1.49405 q^{88} +16.2594 q^{89} -0.570284 q^{90} -1.64978 q^{91} +20.4929 q^{92} -4.76523 q^{93} -17.3229 q^{94} +0.331520 q^{95} -4.01693 q^{96} +9.69021 q^{97} +15.6699 q^{98} -0.420562 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 13 q^{2} - 82 q^{3} + 87 q^{4} + 7 q^{5} - 13 q^{6} + 30 q^{7} + 39 q^{8} + 82 q^{9}+O(q^{10}) \) 82 * q + 13 * q^2 - 82 * q^3 + 87 * q^4 + 7 * q^5 - 13 * q^6 + 30 * q^7 + 39 * q^8 + 82 * q^9	\( 82 q + 13 q^{2} - 82 q^{3} + 87 q^{4} + 7 q^{5} - 13 q^{6} + 30 q^{7} + 39 q^{8} + 82 q^{9} - 9 q^{10} + 28 q^{11} - 87 q^{12} - 14 q^{13} + 21 q^{14} - 7 q^{15} + 93 q^{16} + 25 q^{17} + 13 q^{18} - 7 q^{19} + 40 q^{20} - 30 q^{21} + 31 q^{22} + 97 q^{23} - 39 q^{24} + 83 q^{25} + 22 q^{26} - 82 q^{27} + 53 q^{28} + 45 q^{29} + 9 q^{30} - 11 q^{31} + 86 q^{32} - 28 q^{33} - 30 q^{34} + 69 q^{35} + 87 q^{36} + 8 q^{37} + 33 q^{38} + 14 q^{39} - 38 q^{40} + 12 q^{41} - 21 q^{42} + 68 q^{43} + 77 q^{44} + 7 q^{45} - 14 q^{46} + 85 q^{47} - 93 q^{48} + 68 q^{49} + 56 q^{50} - 25 q^{51} - 18 q^{52} + 58 q^{53} - 13 q^{54} + 68 q^{55} + 59 q^{56} + 7 q^{57} + 27 q^{58} + 40 q^{59} - 40 q^{60} - 116 q^{61} + 79 q^{62} + 30 q^{63} + 127 q^{64} + 66 q^{65} - 31 q^{66} + 51 q^{67} + 94 q^{68} - 97 q^{69} + q^{70} + 101 q^{71} + 39 q^{72} + 12 q^{73} + 72 q^{74} - 83 q^{75} - 3 q^{76} + 101 q^{77} - 22 q^{78} + 26 q^{79} + 61 q^{80} + 82 q^{81} + 31 q^{82} + 94 q^{83} - 53 q^{84} - 8 q^{85} + 68 q^{86} - 45 q^{87} + 91 q^{88} + 40 q^{89} - 9 q^{90} - 6 q^{91} + 180 q^{92} + 11 q^{93} - 31 q^{94} + 153 q^{95} - 86 q^{96} - 39 q^{97} + 115 q^{98} + 28 q^{99}+O(q^{100}) \) 82 * q + 13 * q^2 - 82 * q^3 + 87 * q^4 + 7 * q^5 - 13 * q^6 + 30 * q^7 + 39 * q^8 + 82 * q^9 - 9 * q^10 + 28 * q^11 - 87 * q^12 - 14 * q^13 + 21 * q^14 - 7 * q^15 + 93 * q^16 + 25 * q^17 + 13 * q^18 - 7 * q^19 + 40 * q^20 - 30 * q^21 + 31 * q^22 + 97 * q^23 - 39 * q^24 + 83 * q^25 + 22 * q^26 - 82 * q^27 + 53 * q^28 + 45 * q^29 + 9 * q^30 - 11 * q^31 + 86 * q^32 - 28 * q^33 - 30 * q^34 + 69 * q^35 + 87 * q^36 + 8 * q^37 + 33 * q^38 + 14 * q^39 - 38 * q^40 + 12 * q^41 - 21 * q^42 + 68 * q^43 + 77 * q^44 + 7 * q^45 - 14 * q^46 + 85 * q^47 - 93 * q^48 + 68 * q^49 + 56 * q^50 - 25 * q^51 - 18 * q^52 + 58 * q^53 - 13 * q^54 + 68 * q^55 + 59 * q^56 + 7 * q^57 + 27 * q^58 + 40 * q^59 - 40 * q^60 - 116 * q^61 + 79 * q^62 + 30 * q^63 + 127 * q^64 + 66 * q^65 - 31 * q^66 + 51 * q^67 + 94 * q^68 - 97 * q^69 + q^70 + 101 * q^71 + 39 * q^72 + 12 * q^73 + 72 * q^74 - 83 * q^75 - 3 * q^76 + 101 * q^77 - 22 * q^78 + 26 * q^79 + 61 * q^80 + 82 * q^81 + 31 * q^82 + 94 * q^83 - 53 * q^84 - 8 * q^85 + 68 * q^86 - 45 * q^87 + 91 * q^88 + 40 * q^89 - 9 * q^90 - 6 * q^91 + 180 * q^92 + 11 * q^93 - 31 * q^94 + 153 * q^95 - 86 * q^96 - 39 * q^97 + 115 * q^98 + 28 * q^99

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