LMFDB - Embedded newform 6029.2.a.a.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6029,2,Mod(1,6029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6029, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6029 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6029.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:	$48.1418073786$
Analytic rank:	$1$
Dimension:	$234$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	6029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.64551 q^{2} -0.0881828 q^{3} +4.99870 q^{4} -0.825561 q^{5} +0.233288 q^{6} -0.584332 q^{7} -7.93309 q^{8} -2.99222 q^{9} +O(q^{10})$	\(q-2.64551 q^{2} -0.0881828 q^{3} +4.99870 q^{4} -0.825561 q^{5} +0.233288 q^{6} -0.584332 q^{7} -7.93309 q^{8} -2.99222 q^{9} +2.18403 q^{10} +0.245313 q^{11} -0.440800 q^{12} +0.646922 q^{13} +1.54585 q^{14} +0.0728003 q^{15} +10.9896 q^{16} +3.59560 q^{17} +7.91595 q^{18} +6.11874 q^{19} -4.12673 q^{20} +0.0515280 q^{21} -0.648976 q^{22} +6.59755 q^{23} +0.699562 q^{24} -4.31845 q^{25} -1.71144 q^{26} +0.528411 q^{27} -2.92090 q^{28} -1.97662 q^{29} -0.192594 q^{30} -7.61107 q^{31} -13.2070 q^{32} -0.0216324 q^{33} -9.51219 q^{34} +0.482401 q^{35} -14.9572 q^{36} -10.6394 q^{37} -16.1872 q^{38} -0.0570475 q^{39} +6.54925 q^{40} +0.901037 q^{41} -0.136318 q^{42} +2.74622 q^{43} +1.22625 q^{44} +2.47026 q^{45} -17.4539 q^{46} -0.279745 q^{47} -0.969097 q^{48} -6.65856 q^{49} +11.4245 q^{50} -0.317070 q^{51} +3.23377 q^{52} -4.58132 q^{53} -1.39792 q^{54} -0.202521 q^{55} +4.63555 q^{56} -0.539568 q^{57} +5.22915 q^{58} +14.0454 q^{59} +0.363907 q^{60} -11.8442 q^{61} +20.1351 q^{62} +1.74845 q^{63} +12.9598 q^{64} -0.534074 q^{65} +0.0572286 q^{66} +9.97298 q^{67} +17.9733 q^{68} -0.581791 q^{69} -1.27620 q^{70} -10.5984 q^{71} +23.7376 q^{72} -4.56429 q^{73} +28.1465 q^{74} +0.380813 q^{75} +30.5858 q^{76} -0.143344 q^{77} +0.150919 q^{78} +13.5795 q^{79} -9.07261 q^{80} +8.93007 q^{81} -2.38370 q^{82} +1.59659 q^{83} +0.257573 q^{84} -2.96839 q^{85} -7.26514 q^{86} +0.174304 q^{87} -1.94609 q^{88} +7.82421 q^{89} -6.53510 q^{90} -0.378017 q^{91} +32.9792 q^{92} +0.671166 q^{93} +0.740067 q^{94} -5.05139 q^{95} +1.16463 q^{96} -5.14192 q^{97} +17.6153 q^{98} -0.734030 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9}+O(q^{10}) $ 234 * q - 10 * q^2 - 43 * q^3 + 202 * q^4 - 24 * q^5 - 40 * q^6 - 61 * q^7 - 27 * q^8 + 203 * q^9	\( 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9} - 89 q^{10} - 55 q^{11} - 75 q^{12} - 49 q^{13} - 42 q^{14} - 43 q^{15} + 142 q^{16} - 40 q^{17} - 30 q^{18} - 235 q^{19} - 62 q^{20} - 62 q^{21} - 63 q^{22} - 30 q^{23} - 108 q^{24} + 170 q^{25} - 44 q^{26} - 160 q^{27} - 147 q^{28} - 76 q^{29} - 15 q^{30} - 175 q^{31} - 49 q^{32} - 43 q^{33} - 104 q^{34} - 87 q^{35} + 124 q^{36} - 77 q^{37} - 18 q^{38} - 104 q^{39} - 247 q^{40} - 60 q^{41} - 6 q^{42} - 201 q^{43} - 89 q^{44} - 102 q^{45} - 128 q^{46} - 27 q^{47} - 130 q^{48} + 123 q^{49} - 33 q^{50} - 220 q^{51} - 125 q^{52} - 34 q^{53} - 126 q^{54} - 176 q^{55} - 125 q^{56} - 17 q^{57} - 46 q^{58} - 172 q^{59} - 61 q^{60} - 243 q^{61} - 37 q^{62} - 137 q^{63} + 39 q^{64} - 31 q^{65} - 142 q^{66} - 132 q^{67} - 106 q^{68} - 115 q^{69} - 60 q^{70} - 68 q^{71} - 66 q^{72} - 109 q^{73} - 74 q^{74} - 256 q^{75} - 412 q^{76} - 32 q^{77} - 38 q^{78} - 297 q^{79} - 111 q^{80} + 142 q^{81} - 94 q^{82} - 100 q^{83} - 134 q^{84} - 90 q^{85} + q^{86} - 103 q^{87} - 143 q^{88} - 77 q^{89} - 181 q^{90} - 418 q^{91} - 19 q^{92} + 5 q^{93} - 231 q^{94} - 92 q^{95} - 189 q^{96} - 141 q^{97} - 25 q^{98} - 244 q^{99}+O(q^{100}) \) 234 * q - 10 * q^2 - 43 * q^3 + 202 * q^4 - 24 * q^5 - 40 * q^6 - 61 * q^7 - 27 * q^8 + 203 * q^9 - 89 * q^10 - 55 * q^11 - 75 * q^12 - 49 * q^13 - 42 * q^14 - 43 * q^15 + 142 * q^16 - 40 * q^17 - 30 * q^18 - 235 * q^19 - 62 * q^20 - 62 * q^21 - 63 * q^22 - 30 * q^23 - 108 * q^24 + 170 * q^25 - 44 * q^26 - 160 * q^27 - 147 * q^28 - 76 * q^29 - 15 * q^30 - 175 * q^31 - 49 * q^32 - 43 * q^33 - 104 * q^34 - 87 * q^35 + 124 * q^36 - 77 * q^37 - 18 * q^38 - 104 * q^39 - 247 * q^40 - 60 * q^41 - 6 * q^42 - 201 * q^43 - 89 * q^44 - 102 * q^45 - 128 * q^46 - 27 * q^47 - 130 * q^48 + 123 * q^49 - 33 * q^50 - 220 * q^51 - 125 * q^52 - 34 * q^53 - 126 * q^54 - 176 * q^55 - 125 * q^56 - 17 * q^57 - 46 * q^58 - 172 * q^59 - 61 * q^60 - 243 * q^61 - 37 * q^62 - 137 * q^63 + 39 * q^64 - 31 * q^65 - 142 * q^66 - 132 * q^67 - 106 * q^68 - 115 * q^69 - 60 * q^70 - 68 * q^71 - 66 * q^72 - 109 * q^73 - 74 * q^74 - 256 * q^75 - 412 * q^76 - 32 * q^77 - 38 * q^78 - 297 * q^79 - 111 * q^80 + 142 * q^81 - 94 * q^82 - 100 * q^83 - 134 * q^84 - 90 * q^85 + q^86 - 103 * q^87 - 143 * q^88 - 77 * q^89 - 181 * q^90 - 418 * q^91 - 19 * q^92 + 5 * q^93 - 231 * q^94 - 92 * q^95 - 189 * q^96 - 141 * q^97 - 25 * q^98 - 244 * 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 $

$2$	−2.64551	−1.87066	−0.935328	−	0.353783i	$-0.884895\pi$
$2$	−2.64551	−1.87066	−0.935328	+	0.353783i	$0.884895\pi$
$3$	−0.0881828	−0.0509124	−0.0254562	−	0.999676i	$-0.508104\pi$
$3$	−0.0881828	−0.0509124	−0.0254562	+	0.999676i	$0.508104\pi$
$4$	4.99870	2.49935
$5$	−0.825561	−0.369202	−0.184601	−	0.982814i	$-0.559099\pi$
$5$	−0.825561	−0.369202	−0.184601	+	0.982814i	$0.559099\pi$
$6$	0.233288	0.0952395
$7$	−0.584332	−0.220857	−0.110428	−	0.993884i	$-0.535222\pi$
$7$	−0.584332	−0.220857	−0.110428	+	0.993884i	$0.535222\pi$
$8$	−7.93309	−2.80477
$9$	−2.99222	−0.997408
$10$	2.18403	0.690650
$11$	0.245313	0.0739645	0.0369823	−	0.999316i	$-0.488225\pi$
$11$	0.245313	0.0739645	0.0369823	+	0.999316i	$0.488225\pi$
$12$	−0.440800	−0.127248
$13$	0.646922	0.179424	0.0897120	−	0.995968i	$-0.471405\pi$
$13$	0.646922	0.179424	0.0897120	+	0.995968i	$0.471405\pi$
$14$	1.54585	0.413147
$15$	0.0728003	0.0187970
$16$	10.9896	2.74741
$17$	3.59560	0.872062	0.436031	−	0.899932i	$-0.356384\pi$
$17$	3.59560	0.872062	0.436031	+	0.899932i	$0.356384\pi$
$18$	7.91595	1.86581
$19$	6.11874	1.40374	0.701868	−	0.712307i	$-0.252350\pi$
$19$	6.11874	1.40374	0.701868	+	0.712307i	$0.252350\pi$
$20$	−4.12673	−0.922766
$21$	0.0515280	0.0112443
$22$	−0.648976	−0.138362
$23$	6.59755	1.37568	0.687842	−	0.725860i	$-0.258558\pi$
$23$	6.59755	1.37568	0.687842	+	0.725860i	$0.258558\pi$
$24$	0.699562	0.142798
$25$	−4.31845	−0.863690
$26$	−1.71144	−0.335641
$27$	0.528411	0.101693
$28$	−2.92090	−0.551998
$29$	−1.97662	−0.367048	−0.183524	−	0.983015i	$-0.558751\pi$
$29$	−1.97662	−0.367048	−0.183524	+	0.983015i	$0.558751\pi$
$30$	−0.192594	−0.0351626
$31$	−7.61107	−1.36699	−0.683495	−	0.729956i	$-0.739541\pi$
$31$	−7.61107	−1.36699	−0.683495	+	0.729956i	$0.739541\pi$
$32$	−13.2070	−2.33468
$33$	−0.0216324	−0.00376571
$34$	−9.51219	−1.63133
$35$	0.482401	0.0815407
$36$	−14.9572	−2.49287
$37$	−10.6394	−1.74910	−0.874550	−	0.484936i	$-0.838843\pi$
$37$	−10.6394	−1.74910	−0.874550	+	0.484936i	$0.838843\pi$
$38$	−16.1872	−2.62590
$39$	−0.0570475	−0.00913491
$40$	6.54925	1.03553
$41$	0.901037	0.140718	0.0703592	−	0.997522i	$-0.477585\pi$
$41$	0.901037	0.140718	0.0703592	+	0.997522i	$0.477585\pi$
$42$	−0.136318	−0.0210343
$43$	2.74622	0.418794	0.209397	−	0.977831i	$-0.432850\pi$
$43$	2.74622	0.418794	0.209397	+	0.977831i	$0.432850\pi$
$44$	1.22625	0.184863
$45$	2.47026	0.368245
$46$	−17.4539	−2.57343
$47$	−0.279745	−0.0408050	−0.0204025	−	0.999792i	$-0.506495\pi$
$47$	−0.279745	−0.0408050	−0.0204025	+	0.999792i	$0.506495\pi$
$48$	−0.969097	−0.139877
$49$	−6.65856	−0.951222
$50$	11.4245	1.61567
$51$	−0.317070	−0.0443987
$52$	3.23377	0.448444
$53$	−4.58132	−0.629292	−0.314646	−	0.949209i	$-0.601886\pi$
$53$	−4.58132	−0.629292	−0.314646	+	0.949209i	$0.601886\pi$
$54$	−1.39792	−0.190232
$55$	−0.202521	−0.0273079
$56$	4.63555	0.619452
$57$	−0.539568	−0.0714675
$58$	5.22915	0.686621
$59$	14.0454	1.82856	0.914278	−	0.405088i	$-0.132759\pi$
$59$	14.0454	1.82856	0.914278	+	0.405088i	$0.132759\pi$
$60$	0.363907	0.0469802
$61$	−11.8442	−1.51650	−0.758249	−	0.651965i	$-0.773945\pi$
$61$	−11.8442	−1.51650	−0.758249	+	0.651965i	$0.773945\pi$
$62$	20.1351	2.55717
$63$	1.74845	0.220284
$64$	12.9598	1.61998
$65$	−0.534074	−0.0662437
$66$	0.0572286	0.00704435
$67$	9.97298	1.21839	0.609197	−	0.793019i	$-0.291492\pi$
$67$	9.97298	1.21839	0.609197	+	0.793019i	$0.291492\pi$
$68$	17.9733	2.17959
$69$	−0.581791	−0.0700394
$70$	−1.27620	−0.152535
$71$	−10.5984	−1.25780	−0.628899	−	0.777487i	$-0.716494\pi$
$71$	−10.5984	−1.25780	−0.628899	+	0.777487i	$0.716494\pi$
$72$	23.7376	2.79750
$73$	−4.56429	−0.534210	−0.267105	−	0.963667i	$-0.586067\pi$
$73$	−4.56429	−0.534210	−0.267105	+	0.963667i	$0.586067\pi$
$74$	28.1465	3.27196
$75$	0.380813	0.0439725
$76$	30.5858	3.50843
$77$	−0.143344	−0.0163356
$78$	0.150919	0.0170883
$79$	13.5795	1.52781	0.763906	−	0.645328i	$-0.223279\pi$
$79$	13.5795	1.52781	0.763906	+	0.645328i	$0.223279\pi$
$80$	−9.07261	−1.01435
$81$	8.93007	0.992231
$82$	−2.38370	−0.263236
$83$	1.59659	0.175248	0.0876241	−	0.996154i	$-0.472073\pi$
$83$	1.59659	0.175248	0.0876241	+	0.996154i	$0.472073\pi$
$84$	0.257573	0.0281036
$85$	−2.96839	−0.321967
$86$	−7.26514	−0.783420
$87$	0.174304	0.0186873
$88$	−1.94609	−0.207454
$89$	7.82421	0.829365	0.414682	−	0.909966i	$-0.363893\pi$
$89$	7.82421	0.829365	0.414682	+	0.909966i	$0.363893\pi$
$90$	−6.53510	−0.688860
$91$	−0.378017	−0.0396270
$92$	32.9792	3.43832
$93$	0.671166	0.0695967
$94$	0.740067	0.0763321
$95$	−5.05139	−0.518262
$96$	1.16463	0.118864
$97$	−5.14192	−0.522083	−0.261042	−	0.965328i	$-0.584066\pi$
$97$	−5.14192	−0.522083	−0.261042	+	0.965328i	$0.584066\pi$
$98$	17.6153	1.77941
$99$	−0.734030	−0.0737728
$100$	−21.5866	−2.15866
$101$	19.7400	1.96420	0.982101	−	0.188355i	$-0.0603156\pi$
$101$	19.7400	1.96420	0.982101	+	0.188355i	$0.0603156\pi$
$102$	0.838812	0.0830547
$103$	−7.55360	−0.744278	−0.372139	−	0.928177i	$-0.621376\pi$
$103$	−7.55360	−0.744278	−0.372139	+	0.928177i	$0.621376\pi$
$104$	−5.13209	−0.503243
$105$	−0.0425395	−0.00415143
$106$	12.1199	1.17719
$107$	−5.57107	−0.538575	−0.269288	−	0.963060i	$-0.586788\pi$
$107$	−5.57107	−0.538575	−0.269288	+	0.963060i	$0.586788\pi$
$108$	2.64137	0.254166
$109$	4.89740	0.469086	0.234543	−	0.972106i	$-0.424641\pi$
$109$	4.89740	0.469086	0.234543	+	0.972106i	$0.424641\pi$
$110$	0.535769	0.0510836
$111$	0.938209	0.0890508
$112$	−6.42159	−0.606783
$113$	−8.45647	−0.795518	−0.397759	−	0.917490i	$-0.630212\pi$
$113$	−8.45647	−0.795518	−0.397759	+	0.917490i	$0.630212\pi$
$114$	1.42743	0.133691
$115$	−5.44668	−0.507906
$116$	−9.88052	−0.917383
$117$	−1.93574	−0.178959
$118$	−37.1572	−3.42060
$119$	−2.10102	−0.192601
$120$	−0.577531	−0.0527212
$121$	−10.9398	−0.994529
$122$	31.3340	2.83685
$123$	−0.0794560	−0.00716431
$124$	−38.0455	−3.41659
$125$	7.69295	0.688078
$126$	−4.62554	−0.412076
$127$	15.1224	1.34189	0.670946	−	0.741506i	$-0.265888\pi$
$127$	15.1224	1.34189	0.670946	+	0.741506i	$0.265888\pi$
$128$	−7.87139	−0.695739
$129$	−0.242169	−0.0213218
$130$	1.41290	0.123919
$131$	7.43059	0.649213	0.324607	−	0.945849i	$-0.394768\pi$
$131$	7.43059	0.649213	0.324607	+	0.945849i	$0.394768\pi$
$132$	−0.108134	−0.00941184
$133$	−3.57537	−0.310024
$134$	−26.3836	−2.27920
$135$	−0.436236	−0.0375452
$136$	−28.5242	−2.44593
$137$	−1.52132	−0.129975	−0.0649874	−	0.997886i	$-0.520701\pi$
$137$	−1.52132	−0.129975	−0.0649874	+	0.997886i	$0.520701\pi$
$138$	1.53913	0.131020
$139$	−7.26170	−0.615930	−0.307965	−	0.951398i	$-0.599648\pi$
$139$	−7.26170	−0.615930	−0.307965	+	0.951398i	$0.599648\pi$
$140$	2.41138	0.203799
$141$	0.0246687	0.00207748
$142$	28.0381	2.35291
$143$	0.158698	0.0132710
$144$	−32.8834	−2.74029
$145$	1.63182	0.135515
$146$	12.0749	0.999323
$147$	0.587170	0.0484290
$148$	−53.1830	−4.37162
$149$	−5.63727	−0.461823	−0.230911	−	0.972975i	$-0.574171\pi$
$149$	−5.63727	−0.461823	−0.230911	+	0.972975i	$0.574171\pi$
$150$	−1.00744	−0.0822574
$151$	11.0862	0.902183	0.451092	−	0.892478i	$-0.351035\pi$
$151$	11.0862	0.902183	0.451092	+	0.892478i	$0.351035\pi$
$152$	−48.5405	−3.93715
$153$	−10.7588	−0.869801
$154$	0.379217	0.0305582
$155$	6.28341	0.504695
$156$	−0.285163	−0.0228313
$157$	−5.98795	−0.477891	−0.238945	−	0.971033i	$-0.576802\pi$
$157$	−5.98795	−0.477891	−0.238945	+	0.971033i	$0.576802\pi$
$158$	−35.9246	−2.85801
$159$	0.403994	0.0320388
$160$	10.9031	0.861969
$161$	−3.85516	−0.303829
$162$	−23.6246	−1.85612
$163$	11.6502	0.912512	0.456256	−	0.889848i	$-0.349190\pi$
$163$	11.6502	0.912512	0.456256	+	0.889848i	$0.349190\pi$
$164$	4.50402	0.351705
$165$	0.0178588	0.00139031
$166$	−4.22378	−0.327829
$167$	20.4237	1.58044	0.790218	−	0.612826i	$-0.209967\pi$
$167$	20.4237	1.58044	0.790218	+	0.612826i	$0.209967\pi$
$168$	−0.408776	−0.0315378
$169$	−12.5815	−0.967807
$170$	7.85289	0.602289
$171$	−18.3086	−1.40010
$172$	13.7275	1.04671
$173$	7.25272	0.551414	0.275707	−	0.961242i	$-0.411088\pi$
$173$	7.25272	0.551414	0.275707	+	0.961242i	$0.411088\pi$
$174$	−0.461121	−0.0349575
$175$	2.52341	0.190752
$176$	2.69590	0.203211
$177$	−1.23856	−0.0930961
$178$	−20.6990	−1.55146
$179$	2.52505	0.188731	0.0943654	−	0.995538i	$-0.469918\pi$
$179$	2.52505	0.188731	0.0943654	+	0.995538i	$0.469918\pi$
$180$	12.3481	0.920374
$181$	3.99957	0.297285	0.148643	−	0.988891i	$-0.452510\pi$
$181$	3.99957	0.297285	0.148643	+	0.988891i	$0.452510\pi$
$182$	1.00005	0.0741284
$183$	1.04446	0.0772086
$184$	−52.3390	−3.85848
$185$	8.78344	0.645771
$186$	−1.77557	−0.130191
$187$	0.882047	0.0645016
$188$	−1.39836	−0.101986
$189$	−0.308767	−0.0224595
$190$	13.3635	0.969489
$191$	−21.6976	−1.56999	−0.784993	−	0.619504i	$-0.787334\pi$
$191$	−21.6976	−1.56999	−0.784993	+	0.619504i	$0.787334\pi$
$192$	−1.14283	−0.0824769
$193$	−19.3967	−1.39620	−0.698101	−	0.715999i	$-0.745971\pi$
$193$	−19.3967	−1.39620	−0.698101	+	0.715999i	$0.745971\pi$
$194$	13.6030	0.976638
$195$	0.0470962	0.00337263
$196$	−33.2841	−2.37744
$197$	12.9667	0.923841	0.461920	−	0.886921i	$-0.347161\pi$
$197$	12.9667	0.923841	0.461920	+	0.886921i	$0.347161\pi$
$198$	1.94188	0.138004
$199$	25.1686	1.78415	0.892076	−	0.451885i	$-0.149248\pi$
$199$	25.1686	1.78415	0.892076	+	0.451885i	$0.149248\pi$
$200$	34.2586	2.42245
$201$	−0.879446	−0.0620313
$202$	−52.2223	−3.67435
$203$	1.15500	0.0810651
$204$	−1.58494	−0.110968
$205$	−0.743861	−0.0519535
$206$	19.9831	1.39229
$207$	−19.7414	−1.37212
$208$	7.10944	0.492951
$209$	1.50100	0.103827
$210$	0.112539	0.00776590
$211$	−19.9750	−1.37514	−0.687570	−	0.726119i	$-0.741322\pi$
$211$	−19.9750	−1.37514	−0.687570	+	0.726119i	$0.741322\pi$
$212$	−22.9006	−1.57282
$213$	0.934597	0.0640375
$214$	14.7383	1.00749
$215$	−2.26717	−0.154620
$216$	−4.19193	−0.285225
$217$	4.44739	0.301909
$218$	−12.9561	−0.877499
$219$	0.402492	0.0271979
$220$	−1.01234	−0.0682520
$221$	2.32608	0.156469
$222$	−2.48204	−0.166583
$223$	16.0220	1.07291	0.536455	−	0.843929i	$-0.319763\pi$
$223$	16.0220	1.07291	0.536455	+	0.843929i	$0.319763\pi$
$224$	7.71724	0.515630
$225$	12.9218	0.861451
$226$	22.3716	1.48814
$227$	13.2632	0.880309	0.440155	−	0.897922i	$-0.354924\pi$
$227$	13.2632	0.880309	0.440155	+	0.897922i	$0.354924\pi$
$228$	−2.69714	−0.178622
$229$	−9.65949	−0.638317	−0.319159	−	0.947701i	$-0.603400\pi$
$229$	−9.65949	−0.638317	−0.319159	+	0.947701i	$0.603400\pi$
$230$	14.4092	0.950116
$231$	0.0126405	0.000831682 0
$232$	15.6807	1.02949
$233$	−6.66716	−0.436780	−0.218390	−	0.975862i	$-0.570080\pi$
$233$	−6.66716	−0.436780	−0.218390	+	0.975862i	$0.570080\pi$
$234$	5.12100	0.334771
$235$	0.230946	0.0150653
$236$	70.2088	4.57020
$237$	−1.19748	−0.0777845
$238$	5.55827	0.360289
$239$	−9.38065	−0.606784	−0.303392	−	0.952866i	$-0.598119\pi$
$239$	−9.38065	−0.606784	−0.303392	+	0.952866i	$0.598119\pi$
$240$	0.800048	0.0516429
$241$	−15.6581	−1.00863	−0.504313	−	0.863521i	$-0.668254\pi$
$241$	−15.6581	−1.00863	−0.504313	+	0.863521i	$0.668254\pi$
$242$	28.9414	1.86042
$243$	−2.37271	−0.152210
$244$	−59.2058	−3.79026
$245$	5.49704	0.351193
$246$	0.210201	0.0134020
$247$	3.95835	0.251864
$248$	60.3793	3.83409
$249$	−0.140792	−0.00892231
$250$	−20.3517	−1.28716
$251$	−2.72082	−0.171737	−0.0858685	−	0.996306i	$-0.527366\pi$
$251$	−2.72082	−0.171737	−0.0858685	+	0.996306i	$0.527366\pi$
$252$	8.73999	0.550568
$253$	1.61846	0.101752
$254$	−40.0063	−2.51022
$255$	0.261761	0.0163921
$256$	−5.09585	−0.318491
$257$	−24.7856	−1.54609	−0.773043	−	0.634354i	$-0.781266\pi$
$257$	−24.7856	−1.54609	−0.773043	+	0.634354i	$0.781266\pi$
$258$	0.640661	0.0398858
$259$	6.21691	0.386300
$260$	−2.66968	−0.165566
$261$	5.91448	0.366097
$262$	−19.6577	−1.21445
$263$	16.5676	1.02160	0.510801	−	0.859699i	$-0.329349\pi$
$263$	16.5676	1.02160	0.510801	+	0.859699i	$0.329349\pi$
$264$	0.171611	0.0105620
$265$	3.78216	0.232336
$266$	9.45867	0.579948
$267$	−0.689961	−0.0422249
$268$	49.8520	3.04519
$269$	−18.0640	−1.10138	−0.550692	−	0.834709i	$-0.685636\pi$
$269$	−18.0640	−1.10138	−0.550692	+	0.834709i	$0.685636\pi$
$270$	1.15406	0.0702341
$271$	−23.6803	−1.43848	−0.719238	−	0.694764i	$-0.755509\pi$
$271$	−23.6803	−1.43848	−0.719238	+	0.694764i	$0.755509\pi$
$272$	39.5143	2.39591
$273$	0.0333346	0.00201750
$274$	4.02465	0.243138
$275$	−1.05937	−0.0638824
$276$	−2.90820	−0.175053
$277$	−17.9001	−1.07551	−0.537757	−	0.843100i	$-0.680728\pi$
$277$	−17.9001	−1.07551	−0.537757	+	0.843100i	$0.680728\pi$
$278$	19.2109	1.15219
$279$	22.7740	1.36345
$280$	−3.82693	−0.228703
$281$	6.11676	0.364896	0.182448	−	0.983216i	$-0.441598\pi$
$281$	6.11676	0.364896	0.182448	+	0.983216i	$0.441598\pi$
$282$	−0.0652612	−0.00388625
$283$	17.3661	1.03231	0.516154	−	0.856496i	$-0.327363\pi$
$283$	17.3661	1.03231	0.516154	+	0.856496i	$0.327363\pi$
$284$	−52.9783	−3.14368
$285$	0.445446	0.0263860
$286$	−0.419837	−0.0248255
$287$	−0.526505	−0.0310786
$288$	39.5182	2.32863
$289$	−4.07165	−0.239509
$290$	−4.31698	−0.253502
$291$	0.453429	0.0265805
$292$	−22.8155	−1.33518
$293$	11.2075	0.654749	0.327375	−	0.944895i	$-0.393836\pi$
$293$	11.2075	0.654749	0.327375	+	0.944895i	$0.393836\pi$
$294$	−1.55336	−0.0905940
$295$	−11.5953	−0.675106
$296$	84.4030	4.90582
$297$	0.129626	0.00752166
$298$	14.9134	0.863912
$299$	4.26810	0.246831
$300$	1.90357	0.109903
$301$	−1.60470	−0.0924935
$302$	−29.3286	−1.68767
$303$	−1.74073	−0.100002
$304$	67.2427	3.85663
$305$	9.77814	0.559894
$306$	28.4626	1.62710
$307$	−24.6434	−1.40647	−0.703237	−	0.710956i	$-0.748263\pi$
$307$	−24.6434	−1.40647	−0.703237	+	0.710956i	$0.748263\pi$
$308$	−0.716534	−0.0408283
$309$	0.666098	0.0378930
$310$	−16.6228	−0.944111
$311$	−5.55584	−0.315043	−0.157521	−	0.987516i	$-0.550350\pi$
$311$	−5.55584	−0.315043	−0.157521	+	0.987516i	$0.550350\pi$
$312$	0.452563	0.0256213
$313$	27.9965	1.58246	0.791229	−	0.611520i	$-0.209442\pi$
$313$	27.9965	1.58246	0.791229	+	0.611520i	$0.209442\pi$
$314$	15.8412	0.893969
$315$	−1.44345	−0.0813294
$316$	67.8798	3.81854
$317$	21.9811	1.23458	0.617291	−	0.786735i	$-0.288230\pi$
$317$	21.9811	1.23458	0.617291	+	0.786735i	$0.288230\pi$
$318$	−1.06877	−0.0599335
$319$	−0.484889	−0.0271486
$320$	−10.6991	−0.598099
$321$	0.491273	0.0274202
$322$	10.1988	0.568359
$323$	22.0006	1.22414
$324$	44.6388	2.47993
$325$	−2.79370	−0.154967
$326$	−30.8206	−1.70700
$327$	−0.431867	−0.0238823
$328$	−7.14801	−0.394683
$329$	0.163464	0.00901205
$330$	−0.0472457	−0.00260079
$331$	−15.6318	−0.859202	−0.429601	−	0.903019i	$-0.641346\pi$
$331$	−15.6318	−0.859202	−0.429601	+	0.903019i	$0.641346\pi$
$332$	7.98087	0.438007
$333$	31.8353	1.74457
$334$	−54.0311	−2.95645
$335$	−8.23331	−0.449834
$336$	0.566274	0.0308928
$337$	−4.52574	−0.246533	−0.123267	−	0.992374i	$-0.539337\pi$
$337$	−4.52574	−0.246533	−0.123267	+	0.992374i	$0.539337\pi$
$338$	33.2844	1.81043
$339$	0.745715	0.0405017
$340$	−14.8381	−0.804709
$341$	−1.86709	−0.101109
$342$	48.4356	2.61910
$343$	7.98113	0.430940
$344$	−21.7860	−1.17462
$345$	0.480304	0.0258587
$346$	−19.1871	−1.03151
$347$	−17.4793	−0.938337	−0.469169	−	0.883109i	$-0.655446\pi$
$347$	−17.4793	−0.938337	−0.469169	+	0.883109i	$0.655446\pi$
$348$	0.871292	0.0467062
$349$	−17.7831	−0.951909	−0.475955	−	0.879470i	$-0.657897\pi$
$349$	−17.7831	−0.951909	−0.475955	+	0.879470i	$0.657897\pi$
$350$	−6.67569	−0.356831
$351$	0.341841	0.0182461
$352$	−3.23983	−0.172684
$353$	−33.9672	−1.80789	−0.903946	−	0.427646i	$-0.859343\pi$
$353$	−33.9672	−1.80789	−0.903946	+	0.427646i	$0.859343\pi$
$354$	3.27663	0.174151
$355$	8.74962	0.464382
$356$	39.1109	2.07287
$357$	0.185274	0.00980575
$358$	−6.68002	−0.353050
$359$	−29.1620	−1.53911	−0.769556	−	0.638580i	$-0.779522\pi$
$359$	−29.1620	−1.53911	−0.769556	+	0.638580i	$0.779522\pi$
$360$	−19.5968	−1.03284
$361$	18.4390	0.970472
$362$	−10.5809	−0.556119
$363$	0.964705	0.0506339
$364$	−1.88960	−0.0990418
$365$	3.76810	0.197231
$366$	−2.76312	−0.144431
$367$	31.7844	1.65913	0.829565	−	0.558410i	$-0.188588\pi$
$367$	31.7844	1.65913	0.829565	+	0.558410i	$0.188588\pi$
$368$	72.5046	3.77957
$369$	−2.69611	−0.140354
$370$	−23.2366	−1.20802
$371$	2.67701	0.138983
$372$	3.35496	0.173947
$373$	−15.6887	−0.812332	−0.406166	−	0.913799i	$-0.633135\pi$
$373$	−15.6887	−0.812332	−0.406166	+	0.913799i	$0.633135\pi$
$374$	−2.33346	−0.120660
$375$	−0.678386	−0.0350317
$376$	2.21924	0.114449
$377$	−1.27872	−0.0658573
$378$	0.816846	0.0420140
$379$	−17.0362	−0.875093	−0.437546	−	0.899196i	$-0.644152\pi$
$379$	−17.0362	−0.875093	−0.437546	+	0.899196i	$0.644152\pi$
$380$	−25.2504	−1.29532
$381$	−1.33353	−0.0683190
$382$	57.4013	2.93690
$383$	−23.4994	−1.20076	−0.600381	−	0.799714i	$-0.704984\pi$
$383$	−23.4994	−1.20076	−0.600381	+	0.799714i	$0.704984\pi$
$384$	0.694121	0.0354217
$385$	0.118339	0.00603112
$386$	51.3140	2.61181
$387$	−8.21730	−0.417709
$388$	−25.7030	−1.30487
$389$	4.48048	0.227169	0.113585	−	0.993528i	$-0.463767\pi$
$389$	4.48048	0.227169	0.113585	+	0.993528i	$0.463767\pi$
$390$	−0.124593	−0.00630902
$391$	23.7222	1.19968
$392$	52.8229	2.66796
$393$	−0.655250	−0.0330530
$394$	−34.3035	−1.72819
$395$	−11.2107	−0.564071
$396$	−3.66920	−0.184384
$397$	12.3191	0.618276	0.309138	−	0.951017i	$-0.399960\pi$
$397$	12.3191	0.618276	0.309138	+	0.951017i	$0.399960\pi$
$398$	−66.5836	−3.33753
$399$	0.315287	0.0157841
$400$	−47.4582	−2.37291
$401$	−29.4493	−1.47063	−0.735314	−	0.677727i	$-0.762965\pi$
$401$	−29.4493	−1.47063	−0.735314	+	0.677727i	$0.762965\pi$
$402$	2.32658	0.116039
$403$	−4.92377	−0.245271
$404$	98.6743	4.90923
$405$	−7.37232	−0.366334
$406$	−3.05556	−0.151645
$407$	−2.60997	−0.129371
$408$	2.51535	0.124528
$409$	15.0612	0.744728	0.372364	−	0.928087i	$-0.378547\pi$
$409$	15.0612	0.744728	0.372364	+	0.928087i	$0.378547\pi$
$410$	1.96789	0.0971872
$411$	0.134154	0.00661733
$412$	−37.7582	−1.86021
$413$	−8.20717	−0.403848
$414$	52.2259	2.56676
$415$	−1.31808	−0.0647020
$416$	−8.54388	−0.418898
$417$	0.640358	0.0313584
$418$	−3.97092	−0.194224
$419$	−31.9844	−1.56254	−0.781269	−	0.624194i	$-0.785427\pi$
$419$	−31.9844	−1.56254	−0.781269	+	0.624194i	$0.785427\pi$
$420$	−0.212642	−0.0103759
$421$	−11.1102	−0.541479	−0.270739	−	0.962653i	$-0.587268\pi$
$421$	−11.1102	−0.541479	−0.270739	+	0.962653i	$0.587268\pi$
$422$	52.8441	2.57241
$423$	0.837059	0.0406992
$424$	36.3440	1.76502
$425$	−15.5274	−0.753191
$426$	−2.47248	−0.119792
$427$	6.92096	0.334929
$428$	−27.8481	−1.34609
$429$	−0.0139945	−0.000675659 0
$430$	5.99782	0.289240
$431$	−12.2652	−0.590796	−0.295398	−	0.955374i	$-0.595452\pi$
$431$	−12.2652	−0.590796	−0.295398	+	0.955374i	$0.595452\pi$
$432$	5.80704	0.279392
$433$	−27.9192	−1.34171	−0.670855	−	0.741589i	$-0.734073\pi$
$433$	−27.9192	−1.34171	−0.670855	+	0.741589i	$0.734073\pi$
$434$	−11.7656	−0.564767
$435$	−0.143898	−0.00689939
$436$	24.4807	1.17241
$437$	40.3687	1.93110
$438$	−1.06480	−0.0508779
$439$	−29.1692	−1.39217	−0.696086	−	0.717959i	$-0.745077\pi$
$439$	−29.1692	−1.39217	−0.696086	+	0.717959i	$0.745077\pi$
$440$	1.60661	0.0765923
$441$	19.9239	0.948757
$442$	−6.15365	−0.292699
$443$	17.1878	0.816616	0.408308	−	0.912844i	$-0.366119\pi$
$443$	17.1878	0.816616	0.408308	+	0.912844i	$0.366119\pi$
$444$	4.68983	0.222569
$445$	−6.45936	−0.306203
$446$	−42.3862	−2.00704
$447$	0.497110	0.0235125
$448$	−7.57284	−0.357783
$449$	−17.1226	−0.808064	−0.404032	−	0.914745i	$-0.632392\pi$
$449$	−17.1226	−0.808064	−0.404032	+	0.914745i	$0.632392\pi$
$450$	−34.1846	−1.61148
$451$	0.221036	0.0104082
$452$	−42.2714	−1.98828
$453$	−0.977614	−0.0459323
$454$	−35.0879	−1.64676
$455$	0.312076	0.0146304
$456$	4.28044	0.200450
$457$	−0.0856985	−0.00400881	−0.00200440	−	0.999998i	$-0.500638\pi$
$457$	−0.0856985	−0.00400881	−0.00200440	+	0.999998i	$0.500638\pi$
$458$	25.5542	1.19407
$459$	1.89996	0.0886824
$460$	−27.2263	−1.26943
$461$	37.2261	1.73379	0.866896	−	0.498489i	$-0.166111\pi$
$461$	37.2261	1.73379	0.866896	+	0.498489i	$0.166111\pi$
$462$	−0.0334405	−0.00155579
$463$	0.182278	0.00847117	0.00423559	−	0.999991i	$-0.498652\pi$
$463$	0.182278	0.00847117	0.00423559	+	0.999991i	$0.498652\pi$
$464$	−21.7223	−1.00843
$465$	−0.554089	−0.0256952
$466$	17.6380	0.817065
$467$	−26.9417	−1.24671	−0.623357	−	0.781937i	$-0.714232\pi$
$467$	−26.9417	−1.24671	−0.623357	+	0.781937i	$0.714232\pi$
$468$	−9.67617	−0.447281
$469$	−5.82753	−0.269090
$470$	−0.610970	−0.0281820
$471$	0.528035	0.0243306
$472$	−111.423	−5.12868
$473$	0.673682	0.0309759
$474$	3.16793	0.145508
$475$	−26.4235	−1.21239
$476$	−10.5024	−0.481377
$477$	13.7083	0.627661
$478$	24.8166	1.13508
$479$	1.64945	0.0753655	0.0376827	−	0.999290i	$-0.488002\pi$
$479$	1.64945	0.0753655	0.0376827	+	0.999290i	$0.488002\pi$
$480$	−0.961470	−0.0438849
$481$	−6.88284	−0.313831
$482$	41.4236	1.88679
$483$	0.339959	0.0154687
$484$	−54.6849	−2.48568
$485$	4.24497	0.192754
$486$	6.27703	0.284732
$487$	31.0654	1.40771	0.703854	−	0.710345i	$-0.251461\pi$
$487$	31.0654	1.40771	0.703854	+	0.710345i	$0.251461\pi$
$488$	93.9613	4.25343
$489$	−1.02735	−0.0464582
$490$	−14.5425	−0.656962
$491$	−2.58451	−0.116638	−0.0583188	−	0.998298i	$-0.518574\pi$
$491$	−2.58451	−0.116638	−0.0583188	+	0.998298i	$0.518574\pi$
$492$	−0.397177	−0.0179061
$493$	−7.10712	−0.320089
$494$	−10.4718	−0.471150
$495$	0.605987	0.0272371
$496$	−83.6429	−3.75568
$497$	6.19298	0.277793
$498$	0.372465	0.0166906
$499$	−27.5234	−1.23212	−0.616058	−	0.787701i	$-0.711271\pi$
$499$	−27.5234	−1.23212	−0.616058	+	0.787701i	$0.711271\pi$
$500$	38.4548	1.71975
$501$	−1.80102	−0.0804638
$502$	7.19796	0.321261
$503$	18.1509	0.809309	0.404655	−	0.914470i	$-0.367392\pi$
$503$	18.1509	0.809309	0.404655	+	0.914470i	$0.367392\pi$
$504$	−13.8706	−0.617846
$505$	−16.2966	−0.725187
$506$	−4.28165	−0.190343
$507$	1.10947	0.0492734
$508$	75.5922	3.35386
$509$	3.82860	0.169700	0.0848499	−	0.996394i	$-0.472959\pi$
$509$	3.82860	0.169700	0.0848499	+	0.996394i	$0.472959\pi$
$510$	−0.692490	−0.0306640
$511$	2.66706	0.117984
$512$	29.2239	1.29152
$513$	3.23321	0.142750
$514$	65.5705	2.89219
$515$	6.23596	0.274789
$516$	−1.21053	−0.0532907
$517$	−0.0686249	−0.00301812
$518$	−16.4469	−0.722635
$519$	−0.639565	−0.0280738
$520$	4.23686	0.185798
$521$	−32.4566	−1.42195	−0.710976	−	0.703216i	$-0.751746\pi$
$521$	−32.4566	−1.42195	−0.710976	+	0.703216i	$0.751746\pi$
$522$	−15.6468	−0.684841
$523$	4.45848	0.194956	0.0974779	−	0.995238i	$-0.468922\pi$
$523$	4.45848	0.194956	0.0974779	+	0.995238i	$0.468922\pi$
$524$	37.1433	1.62261
$525$	−0.222521	−0.00971162
$526$	−43.8297	−1.91107
$527$	−27.3664	−1.19210
$528$	−0.237732	−0.0103459
$529$	20.5277	0.892508
$530$	−10.0057	−0.434621
$531$	−42.0270	−1.82382
$532$	−17.8722	−0.774859
$533$	0.582901	0.0252483
$534$	1.82530	0.0789883
$535$	4.59926	0.198843
$536$	−79.1166	−3.41732
$537$	−0.222666	−0.00960873
$538$	47.7885	2.06031
$539$	−1.63343	−0.0703567
$540$	−2.18061	−0.0938386
$541$	7.31875	0.314658	0.157329	−	0.987546i	$-0.449712\pi$
$541$	7.31875	0.314658	0.157329	+	0.987546i	$0.449712\pi$
$542$	62.6464	2.69089
$543$	−0.352693	−0.0151355
$544$	−47.4870	−2.03599
$545$	−4.04311	−0.173188
$546$	−0.0881870	−0.00377406
$547$	5.44344	0.232745	0.116372	−	0.993206i	$-0.462873\pi$
$547$	5.44344	0.232745	0.116372	+	0.993206i	$0.462873\pi$
$548$	−7.60461	−0.324853
$549$	35.4406	1.51257
$550$	2.80257	0.119502
$551$	−12.0944	−0.515239
$552$	4.61540	0.196444
$553$	−7.93492	−0.337427
$554$	47.3549	2.01192
$555$	−0.774549	−0.0328778
$556$	−36.2991	−1.53942
$557$	13.0010	0.550871	0.275435	−	0.961320i	$-0.411178\pi$
$557$	13.0010	0.550871	0.275435	+	0.961320i	$0.411178\pi$
$558$	−60.2489	−2.55054
$559$	1.77659	0.0751418
$560$	5.30141	0.224026
$561$	−0.0777814	−0.00328393
$562$	−16.1819	−0.682594
$563$	17.4861	0.736950	0.368475	−	0.929638i	$-0.379880\pi$
$563$	17.4861	0.736950	0.368475	+	0.929638i	$0.379880\pi$
$564$	0.123311	0.00519235
$565$	6.98133	0.293707
$566$	−45.9421	−1.93109
$567$	−5.21813	−0.219141
$568$	84.0780	3.52784
$569$	20.8338	0.873399	0.436700	−	0.899607i	$-0.356147\pi$
$569$	20.8338	0.873399	0.436700	+	0.899607i	$0.356147\pi$
$570$	−1.17843	−0.0493590
$571$	−19.6525	−0.822431	−0.411215	−	0.911538i	$-0.634896\pi$
$571$	−19.6525	−0.822431	−0.411215	+	0.911538i	$0.634896\pi$
$572$	0.793286	0.0331689
$573$	1.91336	0.0799318
$574$	1.39287	0.0581373
$575$	−28.4912	−1.18816
$576$	−38.7787	−1.61578
$577$	30.6035	1.27404	0.637020	−	0.770847i	$-0.280167\pi$
$577$	30.6035	1.27404	0.637020	+	0.770847i	$0.280167\pi$
$578$	10.7716	0.448038
$579$	1.71045	0.0710840
$580$	8.15697	0.338700
$581$	−0.932937	−0.0387047
$582$	−1.19955	−0.0497230
$583$	−1.12386	−0.0465453
$584$	36.2089	1.49834
$585$	1.59807	0.0660720
$586$	−29.6495	−1.22481
$587$	−18.5135	−0.764135	−0.382067	−	0.924134i	$-0.624788\pi$
$587$	−18.5135	−0.764135	−0.382067	+	0.924134i	$0.624788\pi$
$588$	2.93509	0.121041
$589$	−46.5702	−1.91889
$590$	30.6755	1.26289
$591$	−1.14344	−0.0470349
$592$	−116.923	−4.80549
$593$	22.7769	0.935335	0.467667	−	0.883904i	$-0.345094\pi$
$593$	22.7769	0.935335	0.467667	+	0.883904i	$0.345094\pi$
$594$	−0.342926	−0.0140704
$595$	1.73452	0.0711085
$596$	−28.1790	−1.15426
$597$	−2.21944	−0.0908354
$598$	−11.2913	−0.461735
$599$	−33.8975	−1.38502	−0.692508	−	0.721411i	$-0.743494\pi$
$599$	−33.8975	−1.38502	−0.692508	+	0.721411i	$0.743494\pi$
$600$	−3.02102	−0.123333
$601$	−26.6717	−1.08796	−0.543982	−	0.839097i	$-0.683084\pi$
$601$	−26.6717	−1.08796	−0.543982	+	0.839097i	$0.683084\pi$
$602$	4.24525	0.173024
$603$	−29.8414	−1.21524
$604$	55.4167	2.25487
$605$	9.03149	0.367182
$606$	4.60511	0.187070
$607$	30.4833	1.23728	0.618640	−	0.785675i	$-0.287684\pi$
$607$	30.4833	1.23728	0.618640	+	0.785675i	$0.287684\pi$
$608$	−80.8099	−3.27727
$609$	−0.101851	−0.00412722
$610$	−25.8681	−1.04737
$611$	−0.180973	−0.00732139
$612$	−53.7803	−2.17394
$613$	−33.8127	−1.36568	−0.682842	−	0.730566i	$-0.739256\pi$
$613$	−33.8127	−1.36568	−0.682842	+	0.730566i	$0.739256\pi$
$614$	65.1943	2.63103
$615$	0.0655958	0.00264508
$616$	1.13716	0.0458175
$617$	−27.5354	−1.10853	−0.554267	−	0.832339i	$-0.687001\pi$
$617$	−27.5354	−1.10853	−0.554267	+	0.832339i	$0.687001\pi$
$618$	−1.76217	−0.0708847
$619$	−15.8108	−0.635490	−0.317745	−	0.948176i	$-0.602926\pi$
$619$	−15.8108	−0.635490	−0.317745	+	0.948176i	$0.602926\pi$
$620$	31.4089	1.26141
$621$	3.48622	0.139897
$622$	14.6980	0.589337
$623$	−4.57194	−0.183171
$624$	−0.626930	−0.0250973
$625$	15.2412	0.609650
$626$	−74.0650	−2.96023
$627$	−0.132363	−0.00528606
$628$	−29.9320	−1.19442
$629$	−38.2549	−1.52532
$630$	3.81866	0.152139
$631$	19.2353	0.765744	0.382872	−	0.923801i	$-0.374935\pi$
$631$	19.2353	0.765744	0.382872	+	0.923801i	$0.374935\pi$
$632$	−107.727	−4.28516
$633$	1.76146	0.0700116
$634$	−58.1511	−2.30948
$635$	−12.4844	−0.495429
$636$	2.01944	0.0800762
$637$	−4.30757	−0.170672
$638$	1.28278	0.0507856
$639$	31.7128	1.25454
$640$	6.49831	0.256868
$641$	−49.9988	−1.97483	−0.987417	−	0.158140i	$-0.949450\pi$
$641$	−49.9988	−1.97483	−0.987417	+	0.158140i	$0.949450\pi$
$642$	−1.29966	−0.0512937
$643$	34.8865	1.37579	0.687895	−	0.725811i	$-0.258535\pi$
$643$	34.8865	1.37579	0.687895	+	0.725811i	$0.258535\pi$
$644$	−19.2708	−0.759376
$645$	0.199926	0.00787206
$646$	−58.2026	−2.28995
$647$	−3.50870	−0.137941	−0.0689706	−	0.997619i	$-0.521971\pi$
$647$	−3.50870	−0.137941	−0.0689706	+	0.997619i	$0.521971\pi$
$648$	−70.8431	−2.78298
$649$	3.44551	0.135248
$650$	7.39076	0.289889
$651$	−0.392184	−0.0153709
$652$	58.2358	2.28069
$653$	−7.00621	−0.274174	−0.137087	−	0.990559i	$-0.543774\pi$
$653$	−7.00621	−0.274174	−0.137087	+	0.990559i	$0.543774\pi$
$654$	1.14251	0.0446756
$655$	−6.13440	−0.239691
$656$	9.90207	0.386611
$657$	13.6574	0.532825
$658$	−0.432444	−0.0168584
$659$	−38.9681	−1.51798	−0.758991	−	0.651101i	$-0.774307\pi$
$659$	−38.9681	−1.51798	−0.758991	+	0.651101i	$0.774307\pi$
$660$	0.0892710	0.00347487
$661$	41.2984	1.60632	0.803161	−	0.595762i	$-0.203150\pi$
$661$	41.2984	1.60632	0.803161	+	0.595762i	$0.203150\pi$
$662$	41.3541	1.60727
$663$	−0.205120	−0.00796620
$664$	−12.6659	−0.491531
$665$	2.95169	0.114462
$666$	−84.2206	−3.26348
$667$	−13.0408	−0.504943
$668$	102.092	3.95007
$669$	−1.41286	−0.0546244
$670$	21.7813	0.841484
$671$	−2.90554	−0.112167
$672$	−0.680528	−0.0262519
$673$	−39.5989	−1.52643	−0.763213	−	0.646147i	$-0.776379\pi$
$673$	−39.5989	−1.52643	−0.763213	+	0.646147i	$0.776379\pi$
$674$	11.9729	0.461178
$675$	−2.28192	−0.0878310
$676$	−62.8911	−2.41889
$677$	11.4119	0.438595	0.219298	−	0.975658i	$-0.429623\pi$
$677$	11.4119	0.438595	0.219298	+	0.975658i	$0.429623\pi$
$678$	−1.97279	−0.0757647
$679$	3.00459	0.115306
$680$	23.5485	0.903043
$681$	−1.16959	−0.0448186
$682$	4.93941	0.189140
$683$	41.2142	1.57702	0.788509	−	0.615023i	$-0.210853\pi$
$683$	41.2142	1.57702	0.788509	+	0.615023i	$0.210853\pi$
$684$	−91.5195	−3.49933
$685$	1.25594	0.0479870
$686$	−21.1141	−0.806141
$687$	0.851801	0.0324983
$688$	30.1799	1.15060
$689$	−2.96376	−0.112910
$690$	−1.27065	−0.0483727
$691$	−48.9412	−1.86181	−0.930905	−	0.365262i	$-0.880979\pi$
$691$	−48.9412	−1.86181	−0.930905	+	0.365262i	$0.880979\pi$
$692$	36.2542	1.37818
$693$	0.428917	0.0162932
$694$	46.2416	1.75531
$695$	5.99498	0.227402
$696$	−1.38277	−0.0524136
$697$	3.23977	0.122715
$698$	47.0454	1.78069
$699$	0.587929	0.0222375
$700$	12.6138	0.476755
$701$	−21.1160	−0.797539	−0.398769	−	0.917051i	$-0.630563\pi$
$701$	−21.1160	−0.797539	−0.398769	+	0.917051i	$0.630563\pi$
$702$	−0.904343	−0.0341322
$703$	−65.0995	−2.45527
$704$	3.17921	0.119821
$705$	−0.0203655	−0.000767009 0
$706$	89.8605	3.38194
$707$	−11.5347	−0.433807
$708$	−6.19121	−0.232680
$709$	−25.9757	−0.975537	−0.487768	−	0.872973i	$-0.662189\pi$
$709$	−25.9757	−0.975537	−0.487768	+	0.872973i	$0.662189\pi$
$710$	−23.1472	−0.868698
$711$	−40.6329	−1.52385
$712$	−62.0702	−2.32618
$713$	−50.2145	−1.88055
$714$	−0.490144	−0.0183432
$715$	−0.131015	−0.00489969
$716$	12.6220	0.471705
$717$	0.827213	0.0308928
$718$	77.1482	2.87915
$719$	13.0396	0.486295	0.243148	−	0.969989i	$-0.421820\pi$
$719$	13.0396	0.486295	0.243148	+	0.969989i	$0.421820\pi$
$720$	27.1473	1.01172
$721$	4.41381	0.164379
$722$	−48.7804	−1.81542
$723$	1.38078	0.0513516
$724$	19.9926	0.743021
$725$	8.53591	0.317016
$726$	−2.55213	−0.0947185
$727$	−14.6807	−0.544478	−0.272239	−	0.962230i	$-0.587764\pi$
$727$	−14.6807	−0.544478	−0.272239	+	0.962230i	$0.587764\pi$
$728$	2.99884	0.111145
$729$	−26.5810	−0.984481
$730$	−9.96853	−0.368952
$731$	9.87431	0.365215
$732$	5.22094	0.192971
$733$	−41.4745	−1.53190	−0.765948	−	0.642902i	$-0.777730\pi$
$733$	−41.4745	−1.53190	−0.765948	+	0.642902i	$0.777730\pi$
$734$	−84.0858	−3.10366
$735$	−0.484745	−0.0178801
$736$	−87.1336	−3.21179
$737$	2.44650	0.0901180
$738$	7.13256	0.262553
$739$	29.9998	1.10356	0.551779	−	0.833990i	$-0.313949\pi$
$739$	29.9998	1.10356	0.551779	+	0.833990i	$0.313949\pi$
$740$	43.9058	1.61401
$741$	−0.349059	−0.0128230
$742$	−7.08204	−0.259990
$743$	−22.3875	−0.821318	−0.410659	−	0.911789i	$-0.634701\pi$
$743$	−22.3875	−0.821318	−0.410659	+	0.911789i	$0.634701\pi$
$744$	−5.32442	−0.195203
$745$	4.65391	0.170506
$746$	41.5047	1.51959
$747$	−4.77735	−0.174794
$748$	4.40909	0.161212
$749$	3.25535	0.118948
$750$	1.79467	0.0655322
$751$	4.66035	0.170059	0.0850293	−	0.996378i	$-0.472902\pi$
$751$	4.66035	0.170059	0.0850293	+	0.996378i	$0.472902\pi$
$752$	−3.07429	−0.112108
$753$	0.239930	0.00874354
$754$	3.38285	0.123196
$755$	−9.15235	−0.333088
$756$	−1.54344	−0.0561343
$757$	43.0500	1.56468	0.782340	−	0.622852i	$-0.214026\pi$
$757$	43.0500	1.56468	0.782340	+	0.622852i	$0.214026\pi$
$758$	45.0695	1.63700
$759$	−0.142721	−0.00518043
$760$	40.0731	1.45361
$761$	−28.6529	−1.03867	−0.519334	−	0.854572i	$-0.673820\pi$
$761$	−28.6529	−1.03867	−0.519334	+	0.854572i	$0.673820\pi$
$762$	3.52787	0.127801
$763$	−2.86171	−0.103601
$764$	−108.460	−3.92395
$765$	8.88208	0.321132
$766$	62.1677	2.24621
$767$	9.08628	0.328087
$768$	0.449366	0.0162151
$769$	35.1258	1.26667	0.633335	−	0.773878i	$-0.281686\pi$
$769$	35.1258	1.26667	0.633335	+	0.773878i	$0.281686\pi$
$770$	−0.313067	−0.0112822
$771$	2.18567	0.0787149
$772$	−96.9581	−3.48960
$773$	−7.68513	−0.276415	−0.138207	−	0.990403i	$-0.544134\pi$
$773$	−7.68513	−0.276415	−0.138207	+	0.990403i	$0.544134\pi$
$774$	21.7389	0.781390
$775$	32.8680	1.18065
$776$	40.7913	1.46432
$777$	−0.548225	−0.0196675
$778$	−11.8531	−0.424955
$779$	5.51321	0.197531
$780$	0.235420	0.00842938
$781$	−2.59992	−0.0930325
$782$	−62.7571	−2.24419
$783$	−1.04447	−0.0373262
$784$	−73.1751	−2.61340
$785$	4.94342	0.176438
$786$	1.73347	0.0618308
$787$	−11.2417	−0.400722	−0.200361	−	0.979722i	$-0.564212\pi$
$787$	−11.2417	−0.400722	−0.200361	+	0.979722i	$0.564212\pi$
$788$	64.8168	2.30900
$789$	−1.46098	−0.0520122
$790$	29.6580	1.05518
$791$	4.94138	0.175695
$792$	5.82313	0.206916
$793$	−7.66230	−0.272096
$794$	−32.5901	−1.15658
$795$	−0.333521	−0.0118288
$796$	125.810	4.45922
$797$	−33.4469	−1.18475	−0.592374	−	0.805663i	$-0.701809\pi$
$797$	−33.4469	−1.18475	−0.592374	+	0.805663i	$0.701809\pi$
$798$	−0.834093	−0.0295266
$799$	−1.00585	−0.0355845
$800$	57.0336	2.01644
$801$	−23.4118	−0.827215
$802$	77.9083	2.75104
$803$	−1.11968	−0.0395126
$804$	−4.39609	−0.155038
$805$	3.18267	0.112174
$806$	13.0259	0.458817
$807$	1.59294	0.0560741
$808$	−156.599	−5.50914
$809$	−38.1856	−1.34253	−0.671266	−	0.741216i	$-0.734249\pi$
$809$	−38.1856	−1.34253	−0.671266	+	0.741216i	$0.734249\pi$
$810$	19.5035	0.685284
$811$	−28.2631	−0.992451	−0.496225	−	0.868194i	$-0.665281\pi$
$811$	−28.2631	−0.992451	−0.496225	+	0.868194i	$0.665281\pi$
$812$	5.77350	0.202610
$813$	2.08820	0.0732362
$814$	6.90469	0.242009
$815$	−9.61793	−0.336901
$816$	−3.48449	−0.121981
$817$	16.8034	0.587877
$818$	−39.8445	−1.39313
$819$	1.13111	0.0395243
$820$	−3.71834	−0.129850
$821$	16.9929	0.593055	0.296527	−	0.955024i	$-0.404171\pi$
$821$	16.9929	0.593055	0.296527	+	0.955024i	$0.404171\pi$
$822$	−0.354905	−0.0123787
$823$	−27.3130	−0.952073	−0.476037	−	0.879426i	$-0.657927\pi$
$823$	−27.3130	−0.952073	−0.476037	+	0.879426i	$0.657927\pi$
$824$	59.9234	2.08753
$825$	0.0934183	0.00325241
$826$	21.7121	0.755461
$827$	12.4694	0.433604	0.216802	−	0.976216i	$-0.430437\pi$
$827$	12.4694	0.433604	0.216802	+	0.976216i	$0.430437\pi$
$828$	−98.6812	−3.42941
$829$	−47.3570	−1.64478	−0.822388	−	0.568927i	$-0.807359\pi$
$829$	−47.3570	−1.64478	−0.822388	+	0.568927i	$0.807359\pi$
$830$	3.48699	0.121035
$831$	1.57848	0.0547570
$832$	8.38400	0.290663
$833$	−23.9415	−0.829524
$834$	−1.69407	−0.0586609
$835$	−16.8610	−0.583500
$836$	7.50308	0.259499
$837$	−4.02178	−0.139013
$838$	84.6148	2.92297
$839$	−1.18118	−0.0407790	−0.0203895	−	0.999792i	$-0.506491\pi$
$839$	−1.18118	−0.0407790	−0.0203895	+	0.999792i	$0.506491\pi$
$840$	0.337470	0.0116438
$841$	−25.0930	−0.865276
$842$	29.3922	1.01292
$843$	−0.539394	−0.0185777
$844$	−99.8493	−3.43696
$845$	10.3868	0.357316
$846$	−2.21445	−0.0761342
$847$	6.39248	0.219648
$848$	−50.3470	−1.72892
$849$	−1.53139	−0.0525572
$850$	41.0779	1.40896
$851$	−70.1937	−2.40621
$852$	4.67177	0.160052
$853$	28.5724	0.978301	0.489151	−	0.872199i	$-0.337307\pi$
$853$	28.5724	0.978301	0.489151	+	0.872199i	$0.337307\pi$
$854$	−18.3094	−0.626536
$855$	15.1149	0.516919
$856$	44.1958	1.51058
$857$	12.8243	0.438069	0.219034	−	0.975717i	$-0.429709\pi$
$857$	12.8243	0.438069	0.219034	+	0.975717i	$0.429709\pi$
$858$	0.0370224	0.00126393
$859$	1.35874	0.0463595	0.0231797	−	0.999731i	$-0.492621\pi$
$859$	1.35874	0.0463595	0.0231797	+	0.999731i	$0.492621\pi$
$860$	−11.3329	−0.386449
$861$	0.0464287	0.00158229
$862$	32.4478	1.10517
$863$	−20.0149	−0.681315	−0.340658	−	0.940187i	$-0.610650\pi$
$863$	−20.0149	−0.681315	−0.340658	+	0.940187i	$0.610650\pi$
$864$	−6.97870	−0.237420
$865$	−5.98756	−0.203583
$866$	73.8603	2.50988
$867$	0.359049	0.0121940
$868$	22.2312	0.754576
$869$	3.33122	0.113004
$870$	0.380684	0.0129064
$871$	6.45175	0.218609
$872$	−38.8515	−1.31568
$873$	15.3858	0.520730
$874$	−106.796	−3.61242
$875$	−4.49523	−0.151967
$876$	2.01194	0.0679771
$877$	7.05251	0.238146	0.119073	−	0.992885i	$-0.462008\pi$
$877$	7.05251	0.238146	0.119073	+	0.992885i	$0.462008\pi$
$878$	77.1674	2.60427
$879$	−0.988310	−0.0333349
$880$	−2.22563	−0.0750258
$881$	24.6912	0.831867	0.415934	−	0.909395i	$-0.363455\pi$
$881$	24.6912	0.831867	0.415934	+	0.909395i	$0.363455\pi$
$882$	−52.7088	−1.77480
$883$	45.2556	1.52297	0.761486	−	0.648182i	$-0.224470\pi$
$883$	45.2556	1.52297	0.761486	+	0.648182i	$0.224470\pi$
$884$	11.6274	0.391071
$885$	1.02251	0.0343713
$886$	−45.4704	−1.52761
$887$	−3.23693	−0.108686	−0.0543428	−	0.998522i	$-0.517306\pi$
$887$	−3.23693	−0.108686	−0.0543428	+	0.998522i	$0.517306\pi$
$888$	−7.44289	−0.249767
$889$	−8.83647	−0.296366
$890$	17.0883	0.572801
$891$	2.19066	0.0733899
$892$	80.0890	2.68158
$893$	−1.71169	−0.0572794
$894$	−1.31511	−0.0439838
$895$	−2.08458	−0.0696798
$896$	4.59950	0.153659
$897$	−0.376374	−0.0125667
$898$	45.2978	1.51161
$899$	15.0442	0.501751
$900$	64.5921	2.15307
$901$	−16.4726	−0.548782
$902$	−0.584752	−0.0194701
$903$	0.141507	0.00470907
$904$	67.0859	2.23124
$905$	−3.30189	−0.109758
$906$	2.58628	0.0859235
$907$	−44.2568	−1.46952	−0.734762	−	0.678325i	$-0.762706\pi$
$907$	−44.2568	−1.46952	−0.734762	+	0.678325i	$0.762706\pi$
$908$	66.2988	2.20020
$909$	−59.0665	−1.95911
$910$	−0.825600	−0.0273684
$911$	49.7672	1.64886	0.824431	−	0.565963i	$-0.191495\pi$
$911$	49.7672	1.64886	0.824431	+	0.565963i	$0.191495\pi$
$912$	−5.92965	−0.196350
$913$	0.391663	0.0129622
$914$	0.226716	0.00749910
$915$	−0.862264	−0.0285056
$916$	−48.2849	−1.59538
$917$	−4.34193	−0.143383
$918$	−5.02635	−0.165894
$919$	26.9712	0.889699	0.444850	−	0.895605i	$-0.353257\pi$
$919$	26.9712	0.889699	0.444850	+	0.895605i	$0.353257\pi$
$920$	43.2090	1.42456
$921$	2.17313	0.0716069
$922$	−98.4819	−3.24333
$923$	−6.85634	−0.225679
$924$	0.0631860	0.00207867
$925$	45.9455	1.51068
$926$	−0.482217	−0.0158466
$927$	22.6021	0.742349
$928$	26.1051	0.856941
$929$	36.0006	1.18114	0.590571	−	0.806986i	$-0.298903\pi$
$929$	36.0006	1.18114	0.590571	+	0.806986i	$0.298903\pi$
$930$	1.46584	0.0480669
$931$	−40.7420	−1.33526
$932$	−33.3271	−1.09167
$933$	0.489930	0.0160396
$934$	71.2745	2.33217
$935$	−0.728183	−0.0238141
$936$	15.3564	0.501939
$937$	−49.1006	−1.60405	−0.802024	−	0.597292i	$-0.796243\pi$
$937$	−49.1006	−1.60405	−0.802024	+	0.597292i	$0.796243\pi$
$938$	15.4168	0.503375
$939$	−2.46881	−0.0805667
$940$	1.15443	0.0376534
$941$	−38.8271	−1.26573	−0.632864	−	0.774263i	$-0.718121\pi$
$941$	−38.8271	−1.26573	−0.632864	+	0.774263i	$0.718121\pi$
$942$	−1.39692	−0.0455141
$943$	5.94464	0.193584
$944$	154.354	5.02379
$945$	0.254906	0.00829210
$946$	−1.78223	−0.0579453
$947$	9.51219	0.309104	0.154552	−	0.987985i	$-0.450607\pi$
$947$	9.51219	0.309104	0.154552	+	0.987985i	$0.450607\pi$
$948$	−5.98584	−0.194411
$949$	−2.95274	−0.0958501
$950$	69.9034	2.26797
$951$	−1.93836	−0.0628555
$952$	16.6676	0.540200
$953$	−33.6459	−1.08990	−0.544949	−	0.838469i	$-0.683451\pi$
$953$	−33.6459	−1.08990	−0.544949	+	0.838469i	$0.683451\pi$
$954$	−36.2655	−1.17414
$955$	17.9127	0.579642
$956$	−46.8911	−1.51657
$957$	0.0427589	0.00138220
$958$	−4.36364	−0.140983
$959$	0.888953	0.0287058
$960$	0.943479	0.0304507
$961$	26.9284	0.868660
$962$	18.2086	0.587069
$963$	16.6699	0.537179
$964$	−78.2702	−2.52091
$965$	16.0131	0.515481
$966$	−0.899363	−0.0289365
$967$	−48.6411	−1.56419	−0.782097	−	0.623157i	$-0.785850\pi$
$967$	−48.6411	−1.56419	−0.782097	+	0.623157i	$0.785850\pi$
$968$	86.7866	2.78943
$969$	−1.94007	−0.0623241
$970$	−11.2301	−0.360577
$971$	−23.8517	−0.765437	−0.382718	−	0.923865i	$-0.625012\pi$
$971$	−23.8517	−0.765437	−0.382718	+	0.923865i	$0.625012\pi$
$972$	−11.8605	−0.380425
$973$	4.24324	0.136032
$974$	−82.1837	−2.63334
$975$	0.246357	0.00788972
$976$	−130.164	−4.16644
$977$	−12.6436	−0.404503	−0.202252	−	0.979334i	$-0.564826\pi$
$977$	−12.6436	−0.404503	−0.202252	+	0.979334i	$0.564826\pi$
$978$	2.71785	0.0869073
$979$	1.91938	0.0613436
$980$	27.4781	0.877755
$981$	−14.6541	−0.467870
$982$	6.83735	0.218189
$983$	2.26115	0.0721194	0.0360597	−	0.999350i	$-0.488519\pi$
$983$	2.26115	0.0721194	0.0360597	+	0.999350i	$0.488519\pi$
$984$	0.630332	0.0200942
$985$	−10.7048	−0.341084
$986$	18.8019	0.598776
$987$	−0.0144147	−0.000458825 0
$988$	19.7866	0.629496
$989$	18.1183	0.576129
$990$	−1.60314	−0.0509512
$991$	−5.26432	−0.167227	−0.0836133	−	0.996498i	$-0.526646\pi$
$991$	−5.26432	−0.167227	−0.0836133	+	0.996498i	$0.526646\pi$
$992$	100.519	3.19148
$993$	1.37846	0.0437440
$994$	−16.3836	−0.519655
$995$	−20.7782	−0.658713
$996$	−0.703776	−0.0223000
$997$	−30.2912	−0.959331	−0.479665	−	0.877452i	$-0.659242\pi$
$997$	−30.2912	−0.959331	−0.479665	+	0.877452i	$0.659242\pi$
$998$	72.8132	2.30486
$999$	−5.62196	−0.177871

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6029.2.a.a.1.8	✓	234

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6029.2.a.a.1.8	✓	234	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:	\( N \)	\(=\)	\( 6029 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6029.a (trivial)

\(f(q)\)	\(=\)	\(q-2.64551 q^{2} -0.0881828 q^{3} +4.99870 q^{4} -0.825561 q^{5} +0.233288 q^{6} -0.584332 q^{7} -7.93309 q^{8} -2.99222 q^{9} +O(q^{10})\)	\(q-2.64551 q^{2} -0.0881828 q^{3} +4.99870 q^{4} -0.825561 q^{5} +0.233288 q^{6} -0.584332 q^{7} -7.93309 q^{8} -2.99222 q^{9} +2.18403 q^{10} +0.245313 q^{11} -0.440800 q^{12} +0.646922 q^{13} +1.54585 q^{14} +0.0728003 q^{15} +10.9896 q^{16} +3.59560 q^{17} +7.91595 q^{18} +6.11874 q^{19} -4.12673 q^{20} +0.0515280 q^{21} -0.648976 q^{22} +6.59755 q^{23} +0.699562 q^{24} -4.31845 q^{25} -1.71144 q^{26} +0.528411 q^{27} -2.92090 q^{28} -1.97662 q^{29} -0.192594 q^{30} -7.61107 q^{31} -13.2070 q^{32} -0.0216324 q^{33} -9.51219 q^{34} +0.482401 q^{35} -14.9572 q^{36} -10.6394 q^{37} -16.1872 q^{38} -0.0570475 q^{39} +6.54925 q^{40} +0.901037 q^{41} -0.136318 q^{42} +2.74622 q^{43} +1.22625 q^{44} +2.47026 q^{45} -17.4539 q^{46} -0.279745 q^{47} -0.969097 q^{48} -6.65856 q^{49} +11.4245 q^{50} -0.317070 q^{51} +3.23377 q^{52} -4.58132 q^{53} -1.39792 q^{54} -0.202521 q^{55} +4.63555 q^{56} -0.539568 q^{57} +5.22915 q^{58} +14.0454 q^{59} +0.363907 q^{60} -11.8442 q^{61} +20.1351 q^{62} +1.74845 q^{63} +12.9598 q^{64} -0.534074 q^{65} +0.0572286 q^{66} +9.97298 q^{67} +17.9733 q^{68} -0.581791 q^{69} -1.27620 q^{70} -10.5984 q^{71} +23.7376 q^{72} -4.56429 q^{73} +28.1465 q^{74} +0.380813 q^{75} +30.5858 q^{76} -0.143344 q^{77} +0.150919 q^{78} +13.5795 q^{79} -9.07261 q^{80} +8.93007 q^{81} -2.38370 q^{82} +1.59659 q^{83} +0.257573 q^{84} -2.96839 q^{85} -7.26514 q^{86} +0.174304 q^{87} -1.94609 q^{88} +7.82421 q^{89} -6.53510 q^{90} -0.378017 q^{91} +32.9792 q^{92} +0.671166 q^{93} +0.740067 q^{94} -5.05139 q^{95} +1.16463 q^{96} -5.14192 q^{97} +17.6153 q^{98} -0.734030 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9}+O(q^{10}) \) 234 * q - 10 * q^2 - 43 * q^3 + 202 * q^4 - 24 * q^5 - 40 * q^6 - 61 * q^7 - 27 * q^8 + 203 * q^9	\( 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9} - 89 q^{10} - 55 q^{11} - 75 q^{12} - 49 q^{13} - 42 q^{14} - 43 q^{15} + 142 q^{16} - 40 q^{17} - 30 q^{18} - 235 q^{19} - 62 q^{20} - 62 q^{21} - 63 q^{22} - 30 q^{23} - 108 q^{24} + 170 q^{25} - 44 q^{26} - 160 q^{27} - 147 q^{28} - 76 q^{29} - 15 q^{30} - 175 q^{31} - 49 q^{32} - 43 q^{33} - 104 q^{34} - 87 q^{35} + 124 q^{36} - 77 q^{37} - 18 q^{38} - 104 q^{39} - 247 q^{40} - 60 q^{41} - 6 q^{42} - 201 q^{43} - 89 q^{44} - 102 q^{45} - 128 q^{46} - 27 q^{47} - 130 q^{48} + 123 q^{49} - 33 q^{50} - 220 q^{51} - 125 q^{52} - 34 q^{53} - 126 q^{54} - 176 q^{55} - 125 q^{56} - 17 q^{57} - 46 q^{58} - 172 q^{59} - 61 q^{60} - 243 q^{61} - 37 q^{62} - 137 q^{63} + 39 q^{64} - 31 q^{65} - 142 q^{66} - 132 q^{67} - 106 q^{68} - 115 q^{69} - 60 q^{70} - 68 q^{71} - 66 q^{72} - 109 q^{73} - 74 q^{74} - 256 q^{75} - 412 q^{76} - 32 q^{77} - 38 q^{78} - 297 q^{79} - 111 q^{80} + 142 q^{81} - 94 q^{82} - 100 q^{83} - 134 q^{84} - 90 q^{85} + q^{86} - 103 q^{87} - 143 q^{88} - 77 q^{89} - 181 q^{90} - 418 q^{91} - 19 q^{92} + 5 q^{93} - 231 q^{94} - 92 q^{95} - 189 q^{96} - 141 q^{97} - 25 q^{98} - 244 q^{99}+O(q^{100}) \) 234 * q - 10 * q^2 - 43 * q^3 + 202 * q^4 - 24 * q^5 - 40 * q^6 - 61 * q^7 - 27 * q^8 + 203 * q^9 - 89 * q^10 - 55 * q^11 - 75 * q^12 - 49 * q^13 - 42 * q^14 - 43 * q^15 + 142 * q^16 - 40 * q^17 - 30 * q^18 - 235 * q^19 - 62 * q^20 - 62 * q^21 - 63 * q^22 - 30 * q^23 - 108 * q^24 + 170 * q^25 - 44 * q^26 - 160 * q^27 - 147 * q^28 - 76 * q^29 - 15 * q^30 - 175 * q^31 - 49 * q^32 - 43 * q^33 - 104 * q^34 - 87 * q^35 + 124 * q^36 - 77 * q^37 - 18 * q^38 - 104 * q^39 - 247 * q^40 - 60 * q^41 - 6 * q^42 - 201 * q^43 - 89 * q^44 - 102 * q^45 - 128 * q^46 - 27 * q^47 - 130 * q^48 + 123 * q^49 - 33 * q^50 - 220 * q^51 - 125 * q^52 - 34 * q^53 - 126 * q^54 - 176 * q^55 - 125 * q^56 - 17 * q^57 - 46 * q^58 - 172 * q^59 - 61 * q^60 - 243 * q^61 - 37 * q^62 - 137 * q^63 + 39 * q^64 - 31 * q^65 - 142 * q^66 - 132 * q^67 - 106 * q^68 - 115 * q^69 - 60 * q^70 - 68 * q^71 - 66 * q^72 - 109 * q^73 - 74 * q^74 - 256 * q^75 - 412 * q^76 - 32 * q^77 - 38 * q^78 - 297 * q^79 - 111 * q^80 + 142 * q^81 - 94 * q^82 - 100 * q^83 - 134 * q^84 - 90 * q^85 + q^86 - 103 * q^87 - 143 * q^88 - 77 * q^89 - 181 * q^90 - 418 * q^91 - 19 * q^92 + 5 * q^93 - 231 * q^94 - 92 * q^95 - 189 * q^96 - 141 * q^97 - 25 * q^98 - 244 * q^99

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