LMFDB - Embedded newform 6023.2.a.c.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6023,2,Mod(1,6023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6023, 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("6023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6023 = 19 \cdot 317 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6023.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:	$48.0938971374$
Analytic rank:	$0$
Dimension:	$138$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	6023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.67164 q^{2} -1.61720 q^{3} +5.13764 q^{4} -4.16220 q^{5} +4.32056 q^{6} -1.04033 q^{7} -8.38264 q^{8} -0.384677 q^{9} +O(q^{10})$	\(q-2.67164 q^{2} -1.61720 q^{3} +5.13764 q^{4} -4.16220 q^{5} +4.32056 q^{6} -1.04033 q^{7} -8.38264 q^{8} -0.384677 q^{9} +11.1199 q^{10} -3.04836 q^{11} -8.30858 q^{12} +2.33644 q^{13} +2.77939 q^{14} +6.73109 q^{15} +12.1201 q^{16} -5.80233 q^{17} +1.02772 q^{18} +1.00000 q^{19} -21.3839 q^{20} +1.68242 q^{21} +8.14412 q^{22} +5.03372 q^{23} +13.5564 q^{24} +12.3239 q^{25} -6.24212 q^{26} +5.47369 q^{27} -5.34485 q^{28} -1.75907 q^{29} -17.9830 q^{30} -0.324203 q^{31} -15.6152 q^{32} +4.92980 q^{33} +15.5017 q^{34} +4.33007 q^{35} -1.97633 q^{36} -8.14505 q^{37} -2.67164 q^{38} -3.77848 q^{39} +34.8902 q^{40} -6.21363 q^{41} -4.49482 q^{42} +7.87426 q^{43} -15.6614 q^{44} +1.60110 q^{45} -13.4483 q^{46} +12.3725 q^{47} -19.6006 q^{48} -5.91771 q^{49} -32.9250 q^{50} +9.38350 q^{51} +12.0038 q^{52} -10.1980 q^{53} -14.6237 q^{54} +12.6879 q^{55} +8.72073 q^{56} -1.61720 q^{57} +4.69959 q^{58} -3.35693 q^{59} +34.5819 q^{60} -10.5434 q^{61} +0.866152 q^{62} +0.400191 q^{63} +17.4779 q^{64} -9.72473 q^{65} -13.1706 q^{66} -1.61236 q^{67} -29.8103 q^{68} -8.14051 q^{69} -11.5684 q^{70} -0.936919 q^{71} +3.22461 q^{72} -9.07312 q^{73} +21.7606 q^{74} -19.9302 q^{75} +5.13764 q^{76} +3.17131 q^{77} +10.0947 q^{78} +11.4970 q^{79} -50.4462 q^{80} -7.69799 q^{81} +16.6006 q^{82} -9.64145 q^{83} +8.64368 q^{84} +24.1504 q^{85} -21.0371 q^{86} +2.84476 q^{87} +25.5533 q^{88} -13.5771 q^{89} -4.27756 q^{90} -2.43067 q^{91} +25.8614 q^{92} +0.524299 q^{93} -33.0548 q^{94} -4.16220 q^{95} +25.2528 q^{96} -10.0919 q^{97} +15.8100 q^{98} +1.17263 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9}+O(q^{10}) $ 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9} + 40 q^{10} + 4 q^{11} + 69 q^{12} + 72 q^{13} + 3 q^{14} + 30 q^{15} + 191 q^{16} + 31 q^{17} + 31 q^{18} + 138 q^{19} + 16 q^{20} + 16 q^{21} + 95 q^{22} + 34 q^{23} + 3 q^{24} + 244 q^{25} - 13 q^{26} + 107 q^{27} + 43 q^{28} + 30 q^{29} - 14 q^{30} + 60 q^{31} + 62 q^{32} + 77 q^{33} + 36 q^{34} + 2 q^{35} + 205 q^{36} + 142 q^{37} + 11 q^{38} + 20 q^{39} + 76 q^{40} + 46 q^{41} - 21 q^{42} + 69 q^{43} - 7 q^{44} + 30 q^{45} + 39 q^{46} + 8 q^{47} + 116 q^{48} + 236 q^{49} + 34 q^{51} + 165 q^{52} + 49 q^{53} + 6 q^{55} - 33 q^{56} + 29 q^{57} + 75 q^{58} + 8 q^{59} - 24 q^{60} + 38 q^{61} - 10 q^{62} + 2 q^{63} + 251 q^{64} + 72 q^{65} - 15 q^{66} + 158 q^{67} - 19 q^{68} + 33 q^{69} + 48 q^{70} + 23 q^{71} + 88 q^{72} + 134 q^{73} + 4 q^{74} + 118 q^{75} + 157 q^{76} + 13 q^{77} + 12 q^{78} + 78 q^{79} - 48 q^{80} + 254 q^{81} + 89 q^{82} - 27 q^{83} - 15 q^{84} + 37 q^{85} + 66 q^{86} + 43 q^{87} + 224 q^{88} + 26 q^{89} + 38 q^{90} + 108 q^{91} + 113 q^{92} + 83 q^{93} + 48 q^{94} + 12 q^{95} + 40 q^{96} + 254 q^{97} + 47 q^{98} + 11 q^{99}+O(q^{100}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9 + 40 * q^10 + 4 * q^11 + 69 * q^12 + 72 * q^13 + 3 * q^14 + 30 * q^15 + 191 * q^16 + 31 * q^17 + 31 * q^18 + 138 * q^19 + 16 * q^20 + 16 * q^21 + 95 * q^22 + 34 * q^23 + 3 * q^24 + 244 * q^25 - 13 * q^26 + 107 * q^27 + 43 * q^28 + 30 * q^29 - 14 * q^30 + 60 * q^31 + 62 * q^32 + 77 * q^33 + 36 * q^34 + 2 * q^35 + 205 * q^36 + 142 * q^37 + 11 * q^38 + 20 * q^39 + 76 * q^40 + 46 * q^41 - 21 * q^42 + 69 * q^43 - 7 * q^44 + 30 * q^45 + 39 * q^46 + 8 * q^47 + 116 * q^48 + 236 * q^49 + 34 * q^51 + 165 * q^52 + 49 * q^53 + 6 * q^55 - 33 * q^56 + 29 * q^57 + 75 * q^58 + 8 * q^59 - 24 * q^60 + 38 * q^61 - 10 * q^62 + 2 * q^63 + 251 * q^64 + 72 * q^65 - 15 * q^66 + 158 * q^67 - 19 * q^68 + 33 * q^69 + 48 * q^70 + 23 * q^71 + 88 * q^72 + 134 * q^73 + 4 * q^74 + 118 * q^75 + 157 * q^76 + 13 * q^77 + 12 * q^78 + 78 * q^79 - 48 * q^80 + 254 * q^81 + 89 * q^82 - 27 * q^83 - 15 * q^84 + 37 * q^85 + 66 * q^86 + 43 * q^87 + 224 * q^88 + 26 * q^89 + 38 * q^90 + 108 * q^91 + 113 * q^92 + 83 * q^93 + 48 * q^94 + 12 * q^95 + 40 * q^96 + 254 * q^97 + 47 * q^98 + 11 * 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 $

$2$	−2.67164	−1.88913	−0.944566	−	0.328321i	$-0.893517\pi$
$2$	−2.67164	−1.88913	−0.944566	+	0.328321i	$0.893517\pi$
$3$	−1.61720	−0.933689	−0.466844	−	0.884340i	$-0.654609\pi$
$3$	−1.61720	−0.933689	−0.466844	+	0.884340i	$0.654609\pi$
$4$	5.13764	2.56882
$5$	−4.16220	−1.86139	−0.930696	−	0.365794i	$-0.880798\pi$
$5$	−4.16220	−1.86139	−0.930696	+	0.365794i	$0.880798\pi$
$6$	4.32056	1.76386
$7$	−1.04033	−0.393209	−0.196604	−	0.980483i	$-0.562991\pi$
$7$	−1.04033	−0.393209	−0.196604	+	0.980483i	$0.562991\pi$
$8$	−8.38264	−2.96371
$9$	−0.384677	−0.128226
$10$	11.1199	3.51642
$11$	−3.04836	−0.919116	−0.459558	−	0.888148i	$-0.651992\pi$
$11$	−3.04836	−0.919116	−0.459558	+	0.888148i	$0.651992\pi$
$12$	−8.30858	−2.39848
$13$	2.33644	0.648012	0.324006	−	0.946055i	$-0.394970\pi$
$13$	2.33644	0.648012	0.324006	+	0.946055i	$0.394970\pi$
$14$	2.77939	0.742823
$15$	6.73109	1.73796
$16$	12.1201	3.03002
$17$	−5.80233	−1.40727	−0.703635	−	0.710561i	$-0.748441\pi$
$17$	−5.80233	−1.40727	−0.703635	+	0.710561i	$0.748441\pi$
$18$	1.02772	0.242235
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−21.3839	−4.78158
$21$	1.68242	0.367134
$22$	8.14412	1.73633
$23$	5.03372	1.04960	0.524801	−	0.851225i	$-0.324140\pi$
$23$	5.03372	1.04960	0.524801	+	0.851225i	$0.324140\pi$
$24$	13.5564	2.76718
$25$	12.3239	2.46478
$26$	−6.24212	−1.22418
$27$	5.47369	1.05341
$28$	−5.34485	−1.01008
$29$	−1.75907	−0.326651	−0.163325	−	0.986572i	$-0.552222\pi$
$29$	−1.75907	−0.326651	−0.163325	+	0.986572i	$0.552222\pi$
$30$	−17.9830	−3.28324
$31$	−0.324203	−0.0582285	−0.0291143	−	0.999576i	$-0.509269\pi$
$31$	−0.324203	−0.0582285	−0.0291143	+	0.999576i	$0.509269\pi$
$32$	−15.6152	−2.76040
$33$	4.92980	0.858168
$34$	15.5017	2.65852
$35$	4.33007	0.731915
$36$	−1.97633	−0.329388
$37$	−8.14505	−1.33904	−0.669519	−	0.742795i	$-0.733500\pi$
$37$	−8.14505	−1.33904	−0.669519	+	0.742795i	$0.733500\pi$
$38$	−2.67164	−0.433397
$39$	−3.77848	−0.605041
$40$	34.8902	5.51663
$41$	−6.21363	−0.970405	−0.485203	−	0.874402i	$-0.661254\pi$
$41$	−6.21363	−0.970405	−0.485203	+	0.874402i	$0.661254\pi$
$42$	−4.49482	−0.693565
$43$	7.87426	1.20081	0.600406	−	0.799695i	$-0.295006\pi$
$43$	7.87426	1.20081	0.600406	+	0.799695i	$0.295006\pi$
$44$	−15.6614	−2.36104
$45$	1.60110	0.238678
$46$	−13.4483	−1.98284
$47$	12.3725	1.80472	0.902358	−	0.430988i	$-0.141835\pi$
$47$	12.3725	1.80472	0.902358	+	0.430988i	$0.141835\pi$
$48$	−19.6006	−2.82910
$49$	−5.91771	−0.845387
$50$	−32.9250	−4.65629
$51$	9.38350	1.31395
$52$	12.0038	1.66463
$53$	−10.1980	−1.40080	−0.700401	−	0.713749i	$-0.746996\pi$
$53$	−10.1980	−1.40080	−0.700401	+	0.713749i	$0.746996\pi$
$54$	−14.6237	−1.99003
$55$	12.6879	1.71083
$56$	8.72073	1.16536
$57$	−1.61720	−0.214203
$58$	4.69959	0.617086
$59$	−3.35693	−0.437035	−0.218518	−	0.975833i	$-0.570122\pi$
$59$	−3.35693	−0.437035	−0.218518	+	0.975833i	$0.570122\pi$
$60$	34.5819	4.46451
$61$	−10.5434	−1.34994	−0.674970	−	0.737845i	$-0.735843\pi$
$61$	−10.5434	−1.34994	−0.674970	+	0.737845i	$0.735843\pi$
$62$	0.866152	0.110001
$63$	0.400191	0.0504194
$64$	17.4779	2.18474
$65$	−9.72473	−1.20620
$66$	−13.1706	−1.62119
$67$	−1.61236	−0.196981	−0.0984905	−	0.995138i	$-0.531401\pi$
$67$	−1.61236	−0.196981	−0.0984905	+	0.995138i	$0.531401\pi$
$68$	−29.8103	−3.61503
$69$	−8.14051	−0.980002
$70$	−11.5684	−1.38268
$71$	−0.936919	−0.111192	−0.0555959	−	0.998453i	$-0.517706\pi$
$71$	−0.936919	−0.111192	−0.0555959	+	0.998453i	$0.517706\pi$
$72$	3.22461	0.380023
$73$	−9.07312	−1.06193	−0.530964	−	0.847394i	$-0.678170\pi$
$73$	−9.07312	−1.06193	−0.530964	+	0.847394i	$0.678170\pi$
$74$	21.7606	2.52962
$75$	−19.9302	−2.30134
$76$	5.13764	0.589328
$77$	3.17131	0.361404
$78$	10.0947	1.14300
$79$	11.4970	1.29352	0.646758	−	0.762695i	$-0.276124\pi$
$79$	11.4970	1.29352	0.646758	+	0.762695i	$0.276124\pi$
$80$	−50.4462	−5.64006
$81$	−7.69799	−0.855333
$82$	16.6006	1.83322
$83$	−9.64145	−1.05829	−0.529143	−	0.848533i	$-0.677487\pi$
$83$	−9.64145	−1.05829	−0.529143	+	0.848533i	$0.677487\pi$
$84$	8.64368	0.943102
$85$	24.1504	2.61948
$86$	−21.0371	−2.26849
$87$	2.84476	0.304990
$88$	25.5533	2.72399
$89$	−13.5771	−1.43917	−0.719583	−	0.694407i	$-0.755667\pi$
$89$	−13.5771	−1.43917	−0.719583	+	0.694407i	$0.755667\pi$
$90$	−4.27756	−0.450894
$91$	−2.43067	−0.254804
$92$	25.8614	2.69624
$93$	0.524299	0.0543673
$94$	−33.0548	−3.40935
$95$	−4.16220	−0.427033
$96$	25.2528	2.57735
$97$	−10.0919	−1.02468	−0.512338	−	0.858784i	$-0.671221\pi$
$97$	−10.0919	−1.02468	−0.512338	+	0.858784i	$0.671221\pi$
$98$	15.8100	1.59705
$99$	1.17263	0.117854
$100$	63.3158	6.33158
$101$	−1.23730	−0.123116	−0.0615579	−	0.998104i	$-0.519607\pi$
$101$	−1.23730	−0.123116	−0.0615579	+	0.998104i	$0.519607\pi$
$102$	−25.0693	−2.48223
$103$	−3.93371	−0.387600	−0.193800	−	0.981041i	$-0.562081\pi$
$103$	−3.93371	−0.387600	−0.193800	+	0.981041i	$0.562081\pi$
$104$	−19.5855	−1.92052
$105$	−7.00257	−0.683381
$106$	27.2453	2.64630
$107$	17.0428	1.64759	0.823796	−	0.566886i	$-0.191852\pi$
$107$	17.0428	1.64759	0.823796	+	0.566886i	$0.191852\pi$
$108$	28.1218	2.70603
$109$	−7.55827	−0.723951	−0.361976	−	0.932188i	$-0.617898\pi$
$109$	−7.55827	−0.723951	−0.361976	+	0.932188i	$0.617898\pi$
$110$	−33.8974	−3.23199
$111$	13.1721	1.25024
$112$	−12.6089	−1.19143
$113$	−4.06677	−0.382570	−0.191285	−	0.981535i	$-0.561265\pi$
$113$	−4.06677	−0.382570	−0.191285	+	0.981535i	$0.561265\pi$
$114$	4.32056	0.404658
$115$	−20.9513	−1.95372
$116$	−9.03746	−0.839107
$117$	−0.898774	−0.0830917
$118$	8.96850	0.825617
$119$	6.03635	0.553351
$120$	−56.4243	−5.15081
$121$	−1.70749	−0.155226
$122$	28.1680	2.55021
$123$	10.0487	0.906057
$124$	−1.66564	−0.149579
$125$	−30.4835	−2.72653
$126$	−1.06917	−0.0952489
$127$	−17.1072	−1.51802	−0.759008	−	0.651081i	$-0.774316\pi$
$127$	−17.1072	−1.51802	−0.759008	+	0.651081i	$0.774316\pi$
$128$	−15.4643	−1.36686
$129$	−12.7342	−1.12119
$130$	25.9809	2.27868
$131$	−5.75511	−0.502826	−0.251413	−	0.967880i	$-0.580895\pi$
$131$	−5.75511	−0.502826	−0.251413	+	0.967880i	$0.580895\pi$
$132$	25.3275	2.20448
$133$	−1.04033	−0.0902082
$134$	4.30764	0.372123
$135$	−22.7826	−1.96081
$136$	48.6388	4.17074
$137$	13.5884	1.16093	0.580466	−	0.814284i	$-0.302870\pi$
$137$	13.5884	1.16093	0.580466	+	0.814284i	$0.302870\pi$
$138$	21.7485	1.85135
$139$	−9.84927	−0.835404	−0.417702	−	0.908584i	$-0.637164\pi$
$139$	−9.84927	−0.835404	−0.417702	+	0.908584i	$0.637164\pi$
$140$	22.2463	1.88016
$141$	−20.0088	−1.68504
$142$	2.50311	0.210056
$143$	−7.12232	−0.595598
$144$	−4.66231	−0.388526
$145$	7.32159	0.608025
$146$	24.2401	2.00612
$147$	9.57010	0.789328
$148$	−41.8464	−3.43975
$149$	−13.6820	−1.12087	−0.560437	−	0.828197i	$-0.689367\pi$
$149$	−13.6820	−1.12087	−0.560437	+	0.828197i	$0.689367\pi$
$150$	53.2461	4.34753
$151$	−22.0734	−1.79631	−0.898155	−	0.439680i	$-0.855092\pi$
$151$	−22.0734	−1.79631	−0.898155	+	0.439680i	$0.855092\pi$
$152$	−8.38264	−0.679922
$153$	2.23202	0.180448
$154$	−8.47258	−0.682740
$155$	1.34940	0.108386
$156$	−19.4125	−1.55424
$157$	−15.6345	−1.24777	−0.623883	−	0.781518i	$-0.714446\pi$
$157$	−15.6345	−1.24777	−0.623883	+	0.781518i	$0.714446\pi$
$158$	−30.7159	−2.44362
$159$	16.4922	1.30791
$160$	64.9935	5.13818
$161$	−5.23674	−0.412713
$162$	20.5662	1.61584
$163$	−3.65432	−0.286228	−0.143114	−	0.989706i	$-0.545712\pi$
$163$	−3.65432	−0.286228	−0.143114	+	0.989706i	$0.545712\pi$
$164$	−31.9234	−2.49280
$165$	−20.5188	−1.59739
$166$	25.7584	1.99924
$167$	18.3461	1.41966	0.709832	−	0.704371i	$-0.248771\pi$
$167$	18.3461	1.41966	0.709832	+	0.704371i	$0.248771\pi$
$168$	−14.1031	−1.08808
$169$	−7.54105	−0.580081
$170$	−64.5212	−4.94855
$171$	−0.384677	−0.0294170
$172$	40.4551	3.08467
$173$	18.4931	1.40600	0.703002	−	0.711188i	$-0.251843\pi$
$173$	18.4931	1.40600	0.703002	+	0.711188i	$0.251843\pi$
$174$	−7.60016	−0.576166
$175$	−12.8209	−0.969172
$176$	−36.9464	−2.78494
$177$	5.42882	0.408055
$178$	36.2730	2.71877
$179$	−11.0859	−0.828596	−0.414298	−	0.910141i	$-0.635973\pi$
$179$	−11.0859	−0.828596	−0.414298	+	0.910141i	$0.635973\pi$
$180$	8.22588	0.613121
$181$	14.1946	1.05508	0.527540	−	0.849530i	$-0.323115\pi$
$181$	14.1946	1.05508	0.527540	+	0.849530i	$0.323115\pi$
$182$	6.49388	0.481358
$183$	17.0507	1.26042
$184$	−42.1958	−3.11072
$185$	33.9013	2.49247
$186$	−1.40074	−0.102707
$187$	17.6876	1.29344
$188$	63.5655	4.63599
$189$	−5.69445	−0.414210
$190$	11.1199	0.806721
$191$	19.6898	1.42470	0.712350	−	0.701824i	$-0.247631\pi$
$191$	19.6898	1.42470	0.712350	+	0.701824i	$0.247631\pi$
$192$	−28.2652	−2.03987
$193$	27.1420	1.95372	0.976861	−	0.213876i	$-0.0686089\pi$
$193$	27.1420	1.95372	0.976861	+	0.213876i	$0.0686089\pi$
$194$	26.9619	1.93575
$195$	15.7268	1.12622
$196$	−30.4031	−2.17165
$197$	−2.87161	−0.204594	−0.102297	−	0.994754i	$-0.532619\pi$
$197$	−2.87161	−0.204594	−0.102297	+	0.994754i	$0.532619\pi$
$198$	−3.13285	−0.222642
$199$	−8.40868	−0.596075	−0.298038	−	0.954554i	$-0.596332\pi$
$199$	−8.40868	−0.596075	−0.298038	+	0.954554i	$0.596332\pi$
$200$	−103.307	−7.30489
$201$	2.60750	0.183919
$202$	3.30561	0.232582
$203$	1.83001	0.128442
$204$	48.2091	3.37531
$205$	25.8623	1.80630
$206$	10.5094	0.732228
$207$	−1.93635	−0.134586
$208$	28.3178	1.96349
$209$	−3.04836	−0.210860
$210$	18.7083	1.29100
$211$	−3.55450	−0.244702	−0.122351	−	0.992487i	$-0.539043\pi$
$211$	−3.55450	−0.244702	−0.122351	+	0.992487i	$0.539043\pi$
$212$	−52.3937	−3.59841
$213$	1.51518	0.103819
$214$	−45.5322	−3.11252
$215$	−32.7742	−2.23518
$216$	−45.8839	−3.12201
$217$	0.337278	0.0228960
$218$	20.1930	1.36764
$219$	14.6730	0.991510
$220$	65.1858	4.39483
$221$	−13.5568	−0.911928
$222$	−35.1912	−2.36188
$223$	−7.31254	−0.489684	−0.244842	−	0.969563i	$-0.578736\pi$
$223$	−7.31254	−0.489684	−0.244842	+	0.969563i	$0.578736\pi$
$224$	16.2450	1.08541
$225$	−4.74071	−0.316048
$226$	10.8649	0.722725
$227$	3.35384	0.222602	0.111301	−	0.993787i	$-0.464498\pi$
$227$	3.35384	0.222602	0.111301	+	0.993787i	$0.464498\pi$
$228$	−8.30858	−0.550249
$229$	−14.1190	−0.933008	−0.466504	−	0.884519i	$-0.654487\pi$
$229$	−14.1190	−0.933008	−0.466504	+	0.884519i	$0.654487\pi$
$230$	55.9743	3.69084
$231$	−5.12863	−0.337439
$232$	14.7456	0.968098
$233$	−24.1498	−1.58210	−0.791051	−	0.611750i	$-0.790466\pi$
$233$	−24.1498	−1.58210	−0.791051	+	0.611750i	$0.790466\pi$
$234$	2.40120	0.156971
$235$	−51.4968	−3.35928
$236$	−17.2467	−1.12267
$237$	−18.5930	−1.20774
$238$	−16.1269	−1.04535
$239$	−8.32764	−0.538670	−0.269335	−	0.963047i	$-0.586804\pi$
$239$	−8.32764	−0.538670	−0.269335	+	0.963047i	$0.586804\pi$
$240$	81.5814	5.26606
$241$	−3.48591	−0.224548	−0.112274	−	0.993677i	$-0.535813\pi$
$241$	−3.48591	−0.224548	−0.112274	+	0.993677i	$0.535813\pi$
$242$	4.56179	0.293243
$243$	−3.97189	−0.254797
$244$	−54.1680	−3.46775
$245$	24.6307	1.57360
$246$	−26.8464	−1.71166
$247$	2.33644	0.148664
$248$	2.71767	0.172573
$249$	15.5921	0.988110
$250$	81.4409	5.15077
$251$	−26.9291	−1.69975	−0.849876	−	0.526983i	$-0.823323\pi$
$251$	−26.9291	−1.69975	−0.849876	+	0.526983i	$0.823323\pi$
$252$	2.05604	0.129518
$253$	−15.3446	−0.964706
$254$	45.7042	2.86773
$255$	−39.0560	−2.44578
$256$	6.35910	0.397444
$257$	−22.0219	−1.37369	−0.686844	−	0.726805i	$-0.741005\pi$
$257$	−22.0219	−1.37369	−0.686844	+	0.726805i	$0.741005\pi$
$258$	34.0212	2.11807
$259$	8.47356	0.526521
$260$	−49.9622	−3.09852
$261$	0.676672	0.0418849
$262$	15.3756	0.949905
$263$	−14.3123	−0.882532	−0.441266	−	0.897376i	$-0.645470\pi$
$263$	−14.3123	−0.882532	−0.441266	+	0.897376i	$0.645470\pi$
$264$	−41.3247	−2.54336
$265$	42.4461	2.60744
$266$	2.77939	0.170415
$267$	21.9568	1.34373
$268$	−8.28372	−0.506009
$269$	3.83296	0.233699	0.116850	−	0.993150i	$-0.462720\pi$
$269$	3.83296	0.233699	0.116850	+	0.993150i	$0.462720\pi$
$270$	60.8667	3.70423
$271$	16.7472	1.01732	0.508659	−	0.860968i	$-0.330141\pi$
$271$	16.7472	1.01732	0.508659	+	0.860968i	$0.330141\pi$
$272$	−70.3247	−4.26406
$273$	3.93088	0.237907
$274$	−36.3032	−2.19316
$275$	−37.5677	−2.26542
$276$	−41.8230	−2.51745
$277$	−25.5135	−1.53296	−0.766479	−	0.642269i	$-0.777993\pi$
$277$	−25.5135	−1.53296	−0.766479	+	0.642269i	$0.777993\pi$
$278$	26.3137	1.57819
$279$	0.124713	0.00746638
$280$	−36.2974	−2.16918
$281$	−3.81583	−0.227633	−0.113817	−	0.993502i	$-0.536308\pi$
$281$	−3.81583	−0.227633	−0.113817	+	0.993502i	$0.536308\pi$
$282$	53.4562	3.18327
$283$	−7.00144	−0.416193	−0.208096	−	0.978108i	$-0.566727\pi$
$283$	−7.00144	−0.416193	−0.208096	+	0.978108i	$0.566727\pi$
$284$	−4.81356	−0.285632
$285$	6.73109	0.398715
$286$	19.0282	1.12516
$287$	6.46423	0.381572
$288$	6.00679	0.353954
$289$	16.6670	0.980411
$290$	−19.5606	−1.14864
$291$	16.3206	0.956729
$292$	−46.6144	−2.72790
$293$	−5.26343	−0.307493	−0.153746	−	0.988110i	$-0.549134\pi$
$293$	−5.26343	−0.307493	−0.153746	+	0.988110i	$0.549134\pi$
$294$	−25.5678	−1.49115
$295$	13.9722	0.813494
$296$	68.2770	3.96852
$297$	−16.6858	−0.968207
$298$	36.5534	2.11748
$299$	11.7610	0.680155
$300$	−102.394	−5.91172
$301$	−8.19184	−0.472170
$302$	58.9722	3.39347
$303$	2.00095	0.114952
$304$	12.1201	0.695134
$305$	43.8836	2.51277
$306$	−5.96314	−0.340890
$307$	−21.5139	−1.22786	−0.613931	−	0.789359i	$-0.710413\pi$
$307$	−21.5139	−1.22786	−0.613931	+	0.789359i	$0.710413\pi$
$308$	16.2930	0.928383
$309$	6.36158	0.361898
$310$	−3.60510	−0.204756
$311$	14.3762	0.815199	0.407600	−	0.913161i	$-0.366366\pi$
$311$	14.3762	0.815199	0.407600	+	0.913161i	$0.366366\pi$
$312$	31.6737	1.79317
$313$	23.1971	1.31118	0.655590	−	0.755117i	$-0.272420\pi$
$313$	23.1971	1.31118	0.655590	+	0.755117i	$0.272420\pi$
$314$	41.7696	2.35719
$315$	−1.66568	−0.0938502
$316$	59.0676	3.32281
$317$	−1.00000	−0.0561656
$317$	−1.00000	−0.0561656
$318$	−44.0611	−2.47082
$319$	5.36227	0.300230
$320$	−72.7465	−4.06666
$321$	−27.5616	−1.53834
$322$	13.9907	0.779669
$323$	−5.80233	−0.322850
$324$	−39.5495	−2.19720
$325$	28.7940	1.59721
$326$	9.76301	0.540723
$327$	12.2232	0.675945
$328$	52.0866	2.87600
$329$	−12.8715	−0.709629
$330$	54.8188	3.01768
$331$	−6.02118	−0.330954	−0.165477	−	0.986214i	$-0.552916\pi$
$331$	−6.02118	−0.330954	−0.165477	+	0.986214i	$0.552916\pi$
$332$	−49.5343	−2.71855
$333$	3.13321	0.171699
$334$	−49.0141	−2.68193
$335$	6.71096	0.366659
$336$	20.3911	1.11242
$337$	−20.7264	−1.12904	−0.564519	−	0.825420i	$-0.690938\pi$
$337$	−20.7264	−1.12904	−0.564519	+	0.825420i	$0.690938\pi$
$338$	20.1469	1.09585
$339$	6.57677	0.357201
$340$	124.076	6.72898
$341$	0.988287	0.0535188
$342$	1.02772	0.0555725
$343$	13.4387	0.725622
$344$	−66.0070	−3.55886
$345$	33.8824	1.82417
$346$	−49.4068	−2.65613
$347$	−13.2861	−0.713233	−0.356616	−	0.934251i	$-0.616070\pi$
$347$	−13.2861	−0.713233	−0.356616	+	0.934251i	$0.616070\pi$
$348$	14.6153	0.783465
$349$	−32.4262	−1.73573	−0.867867	−	0.496797i	$-0.834509\pi$
$349$	−32.4262	−1.73573	−0.867867	+	0.496797i	$0.834509\pi$
$350$	34.2529	1.83089
$351$	12.7889	0.682623
$352$	47.6007	2.53713
$353$	−25.2519	−1.34402	−0.672011	−	0.740541i	$-0.734569\pi$
$353$	−25.2519	−1.34402	−0.672011	+	0.740541i	$0.734569\pi$
$354$	−14.5038	−0.770869
$355$	3.89964	0.206972
$356$	−69.7541	−3.69696
$357$	−9.76195	−0.516657
$358$	29.6174	1.56533
$359$	−19.6082	−1.03488	−0.517439	−	0.855720i	$-0.673115\pi$
$359$	−19.6082	−1.03488	−0.517439	+	0.855720i	$0.673115\pi$
$360$	−13.4214	−0.707372
$361$	1.00000	0.0526316
$362$	−37.9229	−1.99318
$363$	2.76134	0.144933
$364$	−12.4879	−0.654545
$365$	37.7641	1.97666
$366$	−45.5532	−2.38111
$367$	−4.80609	−0.250876	−0.125438	−	0.992101i	$-0.540034\pi$
$367$	−4.80609	−0.250876	−0.125438	+	0.992101i	$0.540034\pi$
$368$	61.0091	3.18032
$369$	2.39024	0.124431
$370$	−90.5720	−4.70861
$371$	10.6093	0.550808
$372$	2.69366	0.139660
$373$	23.6491	1.22450	0.612252	−	0.790663i	$-0.290264\pi$
$373$	23.6491	1.22450	0.612252	+	0.790663i	$0.290264\pi$
$374$	−47.2548	−2.44349
$375$	49.2978	2.54573
$376$	−103.714	−5.34865
$377$	−4.10996	−0.211673
$378$	15.2135	0.782498
$379$	−13.7173	−0.704611	−0.352306	−	0.935885i	$-0.614602\pi$
$379$	−13.7173	−0.704611	−0.352306	+	0.935885i	$0.614602\pi$
$380$	−21.3839	−1.09697
$381$	27.6657	1.41735
$382$	−52.6039	−2.69145
$383$	19.1847	0.980295	0.490147	−	0.871640i	$-0.336943\pi$
$383$	19.1847	0.980295	0.490147	+	0.871640i	$0.336943\pi$
$384$	25.0088	1.27622
$385$	−13.1996	−0.672715
$386$	−72.5135	−3.69084
$387$	−3.02904	−0.153975
$388$	−51.8485	−2.63221
$389$	−18.3500	−0.930382	−0.465191	−	0.885210i	$-0.654014\pi$
$389$	−18.3500	−0.930382	−0.465191	+	0.885210i	$0.654014\pi$
$390$	−42.0163	−2.12758
$391$	−29.2073	−1.47708
$392$	49.6060	2.50548
$393$	9.30714	0.469483
$394$	7.67190	0.386505
$395$	−47.8529	−2.40774
$396$	6.02457	0.302746
$397$	20.9568	1.05179	0.525895	−	0.850550i	$-0.323731\pi$
$397$	20.9568	1.05179	0.525895	+	0.850550i	$0.323731\pi$
$398$	22.4649	1.12607
$399$	1.68242	0.0842264
$400$	149.367	7.46833
$401$	−11.4033	−0.569456	−0.284728	−	0.958608i	$-0.591903\pi$
$401$	−11.4033	−0.569456	−0.284728	+	0.958608i	$0.591903\pi$
$402$	−6.96629	−0.347447
$403$	−0.757480	−0.0377328
$404$	−6.35680	−0.316262
$405$	32.0406	1.59211
$406$	−4.88913	−0.242644
$407$	24.8291	1.23073
$408$	−78.6585	−3.89418
$409$	−31.2879	−1.54709	−0.773544	−	0.633743i	$-0.781518\pi$
$409$	−31.2879	−1.54709	−0.773544	+	0.633743i	$0.781518\pi$
$410$	−69.0948	−3.41235
$411$	−21.9751	−1.08395
$412$	−20.2100	−0.995675
$413$	3.49232	0.171846
$414$	5.17323	0.254251
$415$	40.1296	1.96989
$416$	−36.4839	−1.78877
$417$	15.9282	0.780007
$418$	8.14412	0.398342
$419$	17.4061	0.850342	0.425171	−	0.905113i	$-0.360214\pi$
$419$	17.4061	0.850342	0.425171	+	0.905113i	$0.360214\pi$
$420$	−35.9767	−1.75548
$421$	20.1433	0.981724	0.490862	−	0.871237i	$-0.336682\pi$
$421$	20.1433	0.981724	0.490862	+	0.871237i	$0.336682\pi$
$422$	9.49634	0.462274
$423$	−4.75941	−0.231411
$424$	85.4861	4.15157
$425$	−71.5073	−3.46861
$426$	−4.04802	−0.196127
$427$	10.9686	0.530808
$428$	87.5599	4.23237
$429$	11.5182	0.556103
$430$	87.5608	4.22256
$431$	−10.8931	−0.524701	−0.262351	−	0.964973i	$-0.584498\pi$
$431$	−10.8931	−0.524701	−0.262351	+	0.964973i	$0.584498\pi$
$432$	66.3415	3.19186
$433$	21.9064	1.05276	0.526378	−	0.850251i	$-0.323550\pi$
$433$	21.9064	1.05276	0.526378	+	0.850251i	$0.323550\pi$
$434$	−0.901086	−0.0432535
$435$	−11.8404	−0.567706
$436$	−38.8317	−1.85970
$437$	5.03372	0.240795
$438$	−39.2010	−1.87309
$439$	3.55903	0.169863	0.0849317	−	0.996387i	$-0.472933\pi$
$439$	3.55903	0.169863	0.0849317	+	0.996387i	$0.472933\pi$
$440$	−106.358	−5.07042
$441$	2.27640	0.108400
$442$	36.2188	1.72275
$443$	37.2309	1.76889	0.884446	−	0.466642i	$-0.154536\pi$
$443$	37.2309	1.76889	0.884446	+	0.466642i	$0.154536\pi$
$444$	67.6738	3.21166
$445$	56.5104	2.67885
$446$	19.5365	0.925078
$447$	22.1265	1.04655
$448$	−18.1828	−0.859058
$449$	13.3387	0.629492	0.314746	−	0.949176i	$-0.398081\pi$
$449$	13.3387	0.629492	0.314746	+	0.949176i	$0.398081\pi$
$450$	12.6655	0.597056
$451$	18.9414	0.891915
$452$	−20.8936	−0.982753
$453$	35.6971	1.67719
$454$	−8.96023	−0.420525
$455$	10.1169	0.474290
$456$	13.5564	0.634835
$457$	−22.4537	−1.05034	−0.525171	−	0.850997i	$-0.675999\pi$
$457$	−22.4537	−1.05034	−0.525171	+	0.850997i	$0.675999\pi$
$458$	37.7207	1.76257
$459$	−31.7601	−1.48244
$460$	−107.640	−5.01876
$461$	−14.4923	−0.674973	−0.337486	−	0.941330i	$-0.609577\pi$
$461$	−14.4923	−0.674973	−0.337486	+	0.941330i	$0.609577\pi$
$462$	13.7018	0.637467
$463$	5.11286	0.237615	0.118807	−	0.992917i	$-0.462093\pi$
$463$	5.11286	0.237615	0.118807	+	0.992917i	$0.462093\pi$
$464$	−21.3200	−0.989758
$465$	−2.18224	−0.101199
$466$	64.5194	2.98880
$467$	−8.55194	−0.395737	−0.197868	−	0.980229i	$-0.563402\pi$
$467$	−8.55194	−0.395737	−0.197868	+	0.980229i	$0.563402\pi$
$468$	−4.61758	−0.213448
$469$	1.67739	0.0774546
$470$	137.581	6.34613
$471$	25.2840	1.16502
$472$	28.1399	1.29525
$473$	−24.0036	−1.10369
$474$	49.6736	2.28158
$475$	12.3239	0.565459
$476$	31.0126	1.42146
$477$	3.92293	0.179619
$478$	22.2484	1.01762
$479$	−32.5435	−1.48695	−0.743475	−	0.668764i	$-0.766824\pi$
$479$	−32.5435	−1.48695	−0.743475	+	0.668764i	$0.766824\pi$
$480$	−105.107	−4.79746
$481$	−19.0304	−0.867713
$482$	9.31310	0.424200
$483$	8.46883	0.385345
$484$	−8.77246	−0.398748
$485$	42.0045	1.90732
$486$	10.6115	0.481345
$487$	−30.4936	−1.38180	−0.690900	−	0.722951i	$-0.742785\pi$
$487$	−30.4936	−1.38180	−0.690900	+	0.722951i	$0.742785\pi$
$488$	88.3812	4.00083
$489$	5.90975	0.267248
$490$	−65.8042	−2.97273
$491$	34.3169	1.54870	0.774351	−	0.632756i	$-0.218076\pi$
$491$	34.3169	1.54870	0.774351	+	0.632756i	$0.218076\pi$
$492$	51.6264	2.32750
$493$	10.2067	0.459686
$494$	−6.24212	−0.280846
$495$	−4.88073	−0.219373
$496$	−3.92936	−0.176434
$497$	0.974707	0.0437216
$498$	−41.6565	−1.86667
$499$	−32.4459	−1.45248	−0.726238	−	0.687443i	$-0.758733\pi$
$499$	−32.4459	−1.45248	−0.726238	+	0.687443i	$0.758733\pi$
$500$	−156.613	−7.00396
$501$	−29.6693	−1.32552
$502$	71.9449	3.21106
$503$	−22.3514	−0.996602	−0.498301	−	0.867004i	$-0.666042\pi$
$503$	−22.3514	−0.996602	−0.498301	+	0.867004i	$0.666042\pi$
$504$	−3.35466	−0.149428
$505$	5.14988	0.229167
$506$	40.9952	1.82246
$507$	12.1954	0.541615
$508$	−87.8905	−3.89951
$509$	17.9706	0.796533	0.398266	−	0.917270i	$-0.369612\pi$
$509$	17.9706	0.796533	0.398266	+	0.917270i	$0.369612\pi$
$510$	104.343	4.62040
$511$	9.43905	0.417559
$512$	13.9393	0.616038
$513$	5.47369	0.241669
$514$	58.8345	2.59508
$515$	16.3729	0.721475
$516$	−65.4238	−2.88012
$517$	−37.7159	−1.65874
$518$	−22.6383	−0.994668
$519$	−29.9070	−1.31277
$520$	81.5189	3.57484
$521$	8.10528	0.355099	0.177549	−	0.984112i	$-0.443183\pi$
$521$	8.10528	0.355099	0.177549	+	0.984112i	$0.443183\pi$
$522$	−1.80782	−0.0791262
$523$	−24.7587	−1.08262	−0.541312	−	0.840822i	$-0.682072\pi$
$523$	−24.7587	−1.08262	−0.541312	+	0.840822i	$0.682072\pi$
$524$	−29.5677	−1.29167
$525$	20.7340	0.904905
$526$	38.2372	1.66722
$527$	1.88113	0.0819433
$528$	59.7496	2.60027
$529$	2.33831	0.101666
$530$	−113.401	−4.92580
$531$	1.29133	0.0560391
$532$	−5.34485	−0.231729
$533$	−14.5178	−0.628834
$534$	−58.6605	−2.53849
$535$	−70.9356	−3.06681
$536$	13.5158	0.583795
$537$	17.9280	0.773651
$538$	−10.2403	−0.441489
$539$	18.0393	0.777009
$540$	−117.049	−5.03697
$541$	16.0266	0.689039	0.344520	−	0.938779i	$-0.388042\pi$
$541$	16.0266	0.689039	0.344520	+	0.938779i	$0.388042\pi$
$542$	−44.7424	−1.92185
$543$	−22.9555	−0.985116
$544$	90.6043	3.88463
$545$	31.4590	1.34756
$546$	−10.5019	−0.449439
$547$	22.7385	0.972229	0.486114	−	0.873895i	$-0.338414\pi$
$547$	22.7385	0.972229	0.486114	+	0.873895i	$0.338414\pi$
$548$	69.8122	2.98223
$549$	4.05579	0.173097
$550$	100.367	4.27967
$551$	−1.75907	−0.0749388
$552$	68.2390	2.90444
$553$	−11.9607	−0.508622
$554$	68.1628	2.89596
$555$	−54.8251	−2.32720
$556$	−50.6020	−2.14600
$557$	−9.91004	−0.419902	−0.209951	−	0.977712i	$-0.567330\pi$
$557$	−9.91004	−0.419902	−0.209951	+	0.977712i	$0.567330\pi$
$558$	−0.333188	−0.0141050
$559$	18.3977	0.778141
$560$	52.4808	2.21772
$561$	−28.6043	−1.20767
$562$	10.1945	0.430030
$563$	−15.3760	−0.648022	−0.324011	−	0.946053i	$-0.605032\pi$
$563$	−15.3760	−0.648022	−0.324011	+	0.946053i	$0.605032\pi$
$564$	−102.798	−4.32857
$565$	16.9267	0.712112
$566$	18.7053	0.786243
$567$	8.00847	0.336324
$568$	7.85386	0.329540
$569$	23.9237	1.00293	0.501466	−	0.865177i	$-0.332794\pi$
$569$	23.9237	1.00293	0.501466	+	0.865177i	$0.332794\pi$
$570$	−17.9830	−0.753226
$571$	29.5454	1.23644	0.618219	−	0.786006i	$-0.287854\pi$
$571$	29.5454	1.23644	0.618219	+	0.786006i	$0.287854\pi$
$572$	−36.5919	−1.52998
$573$	−31.8422	−1.33023
$574$	−17.2701	−0.720839
$575$	62.0350	2.58704
$576$	−6.72334	−0.280139
$577$	27.7926	1.15702	0.578510	−	0.815676i	$-0.303635\pi$
$577$	27.7926	1.15702	0.578510	+	0.815676i	$0.303635\pi$
$578$	−44.5281	−1.85213
$579$	−43.8939	−1.82417
$580$	37.6157	1.56191
$581$	10.0303	0.416127
$582$	−43.6026	−1.80739
$583$	31.0872	1.28750
$584$	76.0567	3.14725
$585$	3.74088	0.154666
$586$	14.0620	0.580894
$587$	−37.4986	−1.54773	−0.773866	−	0.633350i	$-0.781679\pi$
$587$	−37.4986	−1.54773	−0.773866	+	0.633350i	$0.781679\pi$
$588$	49.1677	2.02764
$589$	−0.324203	−0.0133585
$590$	−37.3287	−1.53680
$591$	4.64396	0.191027
$592$	−98.7187	−4.05731
$593$	2.89002	0.118679	0.0593395	−	0.998238i	$-0.481101\pi$
$593$	2.89002	0.118679	0.0593395	+	0.998238i	$0.481101\pi$
$594$	44.5783	1.82907
$595$	−25.1245	−1.03000
$596$	−70.2933	−2.87933
$597$	13.5985	0.556549
$598$	−31.4211	−1.28490
$599$	29.1027	1.18910	0.594552	−	0.804057i	$-0.297330\pi$
$599$	29.1027	1.18910	0.594552	+	0.804057i	$0.297330\pi$
$600$	167.067	6.82050
$601$	32.1642	1.31200	0.656002	−	0.754759i	$-0.272246\pi$
$601$	32.1642	1.31200	0.656002	+	0.754759i	$0.272246\pi$
$602$	21.8856	0.891991
$603$	0.620237	0.0252580
$604$	−113.405	−4.61440
$605$	7.10690	0.288937
$606$	−5.34582	−0.217159
$607$	20.6652	0.838776	0.419388	−	0.907807i	$-0.362245\pi$
$607$	20.6652	0.838776	0.419388	+	0.907807i	$0.362245\pi$
$608$	−15.6152	−0.633279
$609$	−2.95949	−0.119925
$610$	−117.241	−4.74695
$611$	28.9076	1.16948
$612$	11.4673	0.463539
$613$	21.7251	0.877467	0.438734	−	0.898617i	$-0.355427\pi$
$613$	21.7251	0.877467	0.438734	+	0.898617i	$0.355427\pi$
$614$	57.4773	2.31960
$615$	−41.8245	−1.68653
$616$	−26.5839	−1.07110
$617$	4.81993	0.194043	0.0970215	−	0.995282i	$-0.469068\pi$
$617$	4.81993	0.194043	0.0970215	+	0.995282i	$0.469068\pi$
$618$	−16.9958	−0.683673
$619$	−40.7592	−1.63825	−0.819125	−	0.573615i	$-0.805540\pi$
$619$	−40.7592	−1.63825	−0.819125	+	0.573615i	$0.805540\pi$
$620$	6.93271	0.278425
$621$	27.5530	1.10566
$622$	−38.4080	−1.54002
$623$	14.1247	0.565892
$624$	−45.7955	−1.83329
$625$	65.2590	2.61036
$626$	−61.9743	−2.47699
$627$	4.92980	0.196877
$628$	−80.3242	−3.20529
$629$	47.2602	1.88439
$630$	4.45008	0.177295
$631$	33.3879	1.32915	0.664576	−	0.747221i	$-0.268612\pi$
$631$	33.3879	1.32915	0.664576	+	0.747221i	$0.268612\pi$
$632$	−96.3755	−3.83361
$633$	5.74833	0.228475
$634$	2.67164	0.106104
$635$	71.2035	2.82562
$636$	84.7308	3.35980
$637$	−13.8264	−0.547821
$638$	−14.3260	−0.567174
$639$	0.360411	0.0142576
$640$	64.3654	2.54427
$641$	−0.560600	−0.0221424	−0.0110712	−	0.999939i	$-0.503524\pi$
$641$	−0.560600	−0.0221424	−0.0110712	+	0.999939i	$0.503524\pi$
$642$	73.6346	2.90612
$643$	−7.28781	−0.287403	−0.143702	−	0.989621i	$-0.545901\pi$
$643$	−7.28781	−0.287403	−0.143702	+	0.989621i	$0.545901\pi$
$644$	−26.9045	−1.06019
$645$	53.0023	2.08696
$646$	15.5017	0.609907
$647$	29.2219	1.14883	0.574415	−	0.818564i	$-0.305229\pi$
$647$	29.2219	1.14883	0.574415	+	0.818564i	$0.305229\pi$
$648$	64.5295	2.53496
$649$	10.2331	0.401686
$650$	−76.9272	−3.01733
$651$	−0.545445	−0.0213777
$652$	−18.7746	−0.735269
$653$	10.9902	0.430079	0.215039	−	0.976605i	$-0.431012\pi$
$653$	10.9902	0.430079	0.215039	+	0.976605i	$0.431012\pi$
$654$	−32.6560	−1.27695
$655$	23.9539	0.935956
$656$	−75.3097	−2.94035
$657$	3.49022	0.136166
$658$	34.3880	1.34058
$659$	−30.9209	−1.20451	−0.602254	−	0.798305i	$-0.705731\pi$
$659$	−30.9209	−1.20451	−0.602254	+	0.798305i	$0.705731\pi$
$660$	−105.418	−4.10340
$661$	−25.5818	−0.995018	−0.497509	−	0.867459i	$-0.665752\pi$
$661$	−25.5818	−0.995018	−0.497509	+	0.867459i	$0.665752\pi$
$662$	16.0864	0.625216
$663$	21.9240	0.851457
$664$	80.8208	3.13645
$665$	4.33007	0.167913
$666$	−8.37080	−0.324362
$667$	−8.85465	−0.342853
$668$	94.2558	3.64686
$669$	11.8258	0.457212
$670$	−17.9292	−0.692667
$671$	32.1400	1.24075
$672$	−26.2713	−1.01344
$673$	−0.440965	−0.0169979	−0.00849897	−	0.999964i	$-0.502705\pi$
$673$	−0.440965	−0.0169979	−0.00849897	+	0.999964i	$0.502705\pi$
$674$	55.3734	2.13290
$675$	67.4571	2.59643
$676$	−38.7432	−1.49012
$677$	28.2985	1.08760	0.543800	−	0.839215i	$-0.316985\pi$
$677$	28.2985	1.08760	0.543800	+	0.839215i	$0.316985\pi$
$678$	−17.5707	−0.674800
$679$	10.4989	0.402912
$680$	−202.444	−7.76339
$681$	−5.42381	−0.207841
$682$	−2.64034	−0.101104
$683$	−4.73469	−0.181168	−0.0905839	−	0.995889i	$-0.528873\pi$
$683$	−4.73469	−0.181168	−0.0905839	+	0.995889i	$0.528873\pi$
$684$	−1.97633	−0.0755669
$685$	−56.5575	−2.16095
$686$	−35.9033	−1.37080
$687$	22.8331	0.871138
$688$	95.4366	3.63849
$689$	−23.8270	−0.907737
$690$	−90.5215	−3.44609
$691$	17.3363	0.659503	0.329751	−	0.944068i	$-0.393035\pi$
$691$	17.3363	0.659503	0.329751	+	0.944068i	$0.393035\pi$
$692$	95.0109	3.61177
$693$	−1.21993	−0.0463412
$694$	35.4955	1.34739
$695$	40.9946	1.55501
$696$	−23.8466	−0.903902
$697$	36.0535	1.36562
$698$	86.6309	3.27903
$699$	39.0549	1.47719
$700$	−65.8694	−2.48963
$701$	−34.0398	−1.28566	−0.642832	−	0.766007i	$-0.722241\pi$
$701$	−34.0398	−1.28566	−0.642832	+	0.766007i	$0.722241\pi$
$702$	−34.1674	−1.28957
$703$	−8.14505	−0.307196
$704$	−53.2790	−2.00803
$705$	83.2805	3.13652
$706$	67.4639	2.53904
$707$	1.28720	0.0484102
$708$	27.8913	1.04822
$709$	11.3899	0.427758	0.213879	−	0.976860i	$-0.431390\pi$
$709$	11.3899	0.427758	0.213879	+	0.976860i	$0.431390\pi$
$710$	−10.4184	−0.390997
$711$	−4.42264	−0.165862
$712$	113.812	4.26527
$713$	−1.63195	−0.0611168
$714$	26.0804	0.976034
$715$	29.6445	1.10864
$716$	−56.9552	−2.12851
$717$	13.4674	0.502950
$718$	52.3859	1.95502
$719$	42.8861	1.59938	0.799691	−	0.600412i	$-0.204997\pi$
$719$	42.8861	1.59938	0.799691	+	0.600412i	$0.204997\pi$
$720$	19.4055	0.723199
$721$	4.09236	0.152408
$722$	−2.67164	−0.0994280
$723$	5.63741	0.209657
$724$	72.9270	2.71031
$725$	−21.6786	−0.805122
$726$	−7.37730	−0.273797
$727$	−4.91649	−0.182342	−0.0911712	−	0.995835i	$-0.529061\pi$
$727$	−4.91649	−0.182342	−0.0911712	+	0.995835i	$0.529061\pi$
$728$	20.3755	0.755165
$729$	29.5173	1.09323
$730$	−100.892	−3.73418
$731$	−45.6890	−1.68987
$732$	87.6003	3.23780
$733$	−46.8354	−1.72990	−0.864952	−	0.501855i	$-0.832651\pi$
$733$	−46.8354	−1.72990	−0.864952	+	0.501855i	$0.832651\pi$
$734$	12.8401	0.473938
$735$	−39.8326	−1.46925
$736$	−78.6024	−2.89732
$737$	4.91505	0.181048
$738$	−6.38584	−0.235066
$739$	19.6653	0.723398	0.361699	−	0.932295i	$-0.382197\pi$
$739$	19.6653	0.723398	0.361699	+	0.932295i	$0.382197\pi$
$740$	174.173	6.40272
$741$	−3.77848	−0.138806
$742$	−28.3442	−1.04055
$743$	−18.5505	−0.680551	−0.340276	−	0.940326i	$-0.610520\pi$
$743$	−18.5505	−0.680551	−0.340276	+	0.940326i	$0.610520\pi$
$744$	−4.39501	−0.161129
$745$	56.9473	2.08639
$746$	−63.1818	−2.31325
$747$	3.70884	0.135699
$748$	90.8725	3.32263
$749$	−17.7302	−0.647847
$750$	−131.706	−4.80922
$751$	−5.48817	−0.200266	−0.100133	−	0.994974i	$-0.531927\pi$
$751$	−5.48817	−0.200266	−0.100133	+	0.994974i	$0.531927\pi$
$752$	149.956	5.46832
$753$	43.5497	1.58704
$754$	10.9803	0.399879
$755$	91.8740	3.34364
$756$	−29.2560	−1.06403
$757$	−33.3205	−1.21105	−0.605527	−	0.795825i	$-0.707037\pi$
$757$	−33.3205	−1.21105	−0.605527	+	0.795825i	$0.707037\pi$
$758$	36.6477	1.33110
$759$	24.8152	0.900735
$760$	34.8902	1.26560
$761$	27.9208	1.01213	0.506064	−	0.862496i	$-0.331100\pi$
$761$	27.9208	1.01213	0.506064	+	0.862496i	$0.331100\pi$
$762$	−73.9126	−2.67757
$763$	7.86311	0.284664
$764$	101.159	3.65980
$765$	−9.29011	−0.335885
$766$	−51.2547	−1.85191
$767$	−7.84327	−0.283204
$768$	−10.2839	−0.371089
$769$	12.7452	0.459605	0.229803	−	0.973237i	$-0.426192\pi$
$769$	12.7452	0.459605	0.229803	+	0.973237i	$0.426192\pi$
$770$	35.2646	1.27085
$771$	35.6137	1.28260
$772$	139.446	5.01876
$773$	−5.05353	−0.181763	−0.0908815	−	0.995862i	$-0.528968\pi$
$773$	−5.05353	−0.181763	−0.0908815	+	0.995862i	$0.528968\pi$
$774$	8.09250	0.290879
$775$	−3.99544	−0.143520
$776$	84.5967	3.03684
$777$	−13.7034	−0.491607
$778$	49.0245	1.75761
$779$	−6.21363	−0.222626
$780$	80.7986	2.89306
$781$	2.85607	0.102198
$782$	78.0312	2.79039
$783$	−9.62858	−0.344097
$784$	−71.7231	−2.56154
$785$	65.0737	2.32258
$786$	−24.8653	−0.886915
$787$	35.7628	1.27481	0.637404	−	0.770530i	$-0.280008\pi$
$787$	35.7628	1.27481	0.637404	+	0.770530i	$0.280008\pi$
$788$	−14.7533	−0.525565
$789$	23.1457	0.824010
$790$	127.846	4.54854
$791$	4.23079	0.150430
$792$	−9.82976	−0.349285
$793$	−24.6339	−0.874777
$794$	−55.9888	−1.98697
$795$	−68.6437	−2.43454
$796$	−43.2008	−1.53121
$797$	−43.6847	−1.54739	−0.773695	−	0.633558i	$-0.781594\pi$
$797$	−43.6847	−1.54739	−0.773695	+	0.633558i	$0.781594\pi$
$798$	−4.49482	−0.159115
$799$	−71.7893	−2.53972
$800$	−192.440	−6.80378
$801$	5.22278	0.184538
$802$	30.4656	1.07578
$803$	27.6582	0.976035
$804$	13.3964	0.472455
$805$	21.7963	0.768220
$806$	2.02371	0.0712822
$807$	−6.19864	−0.218202
$808$	10.3718	0.364880
$809$	29.8130	1.04817	0.524085	−	0.851666i	$-0.324408\pi$
$809$	29.8130	1.04817	0.524085	+	0.851666i	$0.324408\pi$
$810$	−85.6008	−3.00771
$811$	13.3128	0.467475	0.233738	−	0.972300i	$-0.424904\pi$
$811$	13.3128	0.467475	0.233738	+	0.972300i	$0.424904\pi$
$812$	9.40196	0.329944
$813$	−27.0835	−0.949859
$814$	−66.3342	−2.32501
$815$	15.2100	0.532783
$816$	113.729	3.98130
$817$	7.87426	0.275485
$818$	83.5899	2.92265
$819$	0.935023	0.0326724
$820$	132.871	4.64007
$821$	−13.8494	−0.483347	−0.241673	−	0.970358i	$-0.577696\pi$
$821$	−13.8494	−0.483347	−0.241673	+	0.970358i	$0.577696\pi$
$822$	58.7094	2.04772
$823$	20.2774	0.706825	0.353412	−	0.935468i	$-0.385021\pi$
$823$	20.2774	0.706825	0.353412	+	0.935468i	$0.385021\pi$
$824$	32.9749	1.14873
$825$	60.7543	2.11519
$826$	−9.33022	−0.324640
$827$	13.9473	0.484996	0.242498	−	0.970152i	$-0.422033\pi$
$827$	13.9473	0.484996	0.242498	+	0.970152i	$0.422033\pi$
$828$	−9.94829	−0.345727
$829$	−35.2211	−1.22328	−0.611639	−	0.791137i	$-0.709490\pi$
$829$	−35.2211	−1.22328	−0.611639	+	0.791137i	$0.709490\pi$
$830$	−107.212	−3.72137
$831$	41.2603	1.43131
$832$	40.8361	1.41574
$833$	34.3365	1.18969
$834$	−42.5544	−1.47354
$835$	−76.3602	−2.64255
$836$	−15.6614	−0.541661
$837$	−1.77458	−0.0613386
$838$	−46.5027	−1.60641
$839$	−2.74244	−0.0946794	−0.0473397	−	0.998879i	$-0.515074\pi$
$839$	−2.74244	−0.0946794	−0.0473397	+	0.998879i	$0.515074\pi$
$840$	58.7000	2.02534
$841$	−25.9057	−0.893299
$842$	−53.8155	−1.85461
$843$	6.17095	0.212539
$844$	−18.2618	−0.628596
$845$	31.3873	1.07976
$846$	12.7154	0.437165
$847$	1.77635	0.0610362
$848$	−123.601	−4.24446
$849$	11.3227	0.388594
$850$	191.041	6.55267
$851$	−40.9999	−1.40546
$852$	7.78446	0.266691
$853$	−25.7472	−0.881569	−0.440784	−	0.897613i	$-0.645300\pi$
$853$	−25.7472	−0.881569	−0.440784	+	0.897613i	$0.645300\pi$
$854$	−29.3041	−1.00277
$855$	1.60110	0.0547565
$856$	−142.864	−4.88299
$857$	−21.3922	−0.730745	−0.365372	−	0.930861i	$-0.619058\pi$
$857$	−21.3922	−0.730745	−0.365372	+	0.930861i	$0.619058\pi$
$858$	−30.7724	−1.05055
$859$	−8.44449	−0.288122	−0.144061	−	0.989569i	$-0.546016\pi$
$859$	−8.44449	−0.288122	−0.144061	+	0.989569i	$0.546016\pi$
$860$	−168.382	−5.74178
$861$	−10.4539	−0.356269
$862$	29.1024	0.991230
$863$	43.7973	1.49088	0.745439	−	0.666574i	$-0.232240\pi$
$863$	43.7973	1.49088	0.745439	+	0.666574i	$0.232240\pi$
$864$	−85.4726	−2.90784
$865$	−76.9719	−2.61712
$866$	−58.5260	−1.98880
$867$	−26.9538	−0.915399
$868$	1.73282	0.0588156
$869$	−35.0471	−1.18889
$870$	31.6334	1.07247
$871$	−3.76718	−0.127646
$872$	63.3583	2.14558
$873$	3.88212	0.131390
$874$	−13.4483	−0.454894
$875$	31.7130	1.07209
$876$	75.3847	2.54701
$877$	54.3117	1.83398	0.916988	−	0.398914i	$-0.130613\pi$
$877$	54.3117	1.83398	0.916988	+	0.398914i	$0.130613\pi$
$878$	−9.50844	−0.320894
$879$	8.51199	0.287102
$880$	153.778	5.18386
$881$	−46.6570	−1.57191	−0.785957	−	0.618282i	$-0.787829\pi$
$881$	−46.6570	−1.57191	−0.785957	+	0.618282i	$0.787829\pi$
$882$	−6.08173	−0.204782
$883$	49.4825	1.66522	0.832609	−	0.553862i	$-0.186846\pi$
$883$	49.4825	1.66522	0.832609	+	0.553862i	$0.186846\pi$
$884$	−69.6499	−2.34258
$885$	−22.5958	−0.759550
$886$	−99.4674	−3.34167
$887$	−1.87316	−0.0628946	−0.0314473	−	0.999505i	$-0.510012\pi$
$887$	−1.87316	−0.0628946	−0.0314473	+	0.999505i	$0.510012\pi$
$888$	−110.417	−3.70536
$889$	17.7971	0.596897
$890$	−150.975	−5.06070
$891$	23.4663	0.786150
$892$	−37.5692	−1.25791
$893$	12.3725	0.414030
$894$	−59.1140	−1.97707
$895$	46.1415	1.54234
$896$	16.0880	0.537462
$897$	−19.0198	−0.635053
$898$	−35.6361	−1.18919
$899$	0.570294	0.0190204
$900$	−24.3561	−0.811870
$901$	59.1721	1.97131
$902$	−50.6045	−1.68495
$903$	13.2478	0.440860
$904$	34.0903	1.13383
$905$	−59.0809	−1.96392
$906$	−95.3695	−3.16844
$907$	38.1366	1.26630	0.633152	−	0.774028i	$-0.281761\pi$
$907$	38.1366	1.26630	0.633152	+	0.774028i	$0.281761\pi$
$908$	17.2308	0.571825
$909$	0.475960	0.0157866
$910$	−27.0288	−0.895996
$911$	21.7889	0.721898	0.360949	−	0.932586i	$-0.382453\pi$
$911$	21.7889	0.721898	0.360949	+	0.932586i	$0.382453\pi$
$912$	−19.6006	−0.649039
$913$	29.3906	0.972688
$914$	59.9882	1.98423
$915$	−70.9684	−2.34614
$916$	−72.5382	−2.39673
$917$	5.98722	0.197715
$918$	84.8515	2.80052
$919$	−31.3810	−1.03516	−0.517582	−	0.855634i	$-0.673168\pi$
$919$	−31.3810	−1.03516	−0.517582	+	0.855634i	$0.673168\pi$
$920$	175.627	5.79027
$921$	34.7922	1.14644
$922$	38.7181	1.27511
$923$	−2.18906	−0.0720536
$924$	−26.3491	−0.866820
$925$	−100.379	−3.30043
$926$	−13.6597	−0.448885
$927$	1.51321	0.0497002
$928$	27.4681	0.901686
$929$	2.80077	0.0918904	0.0459452	−	0.998944i	$-0.485370\pi$
$929$	2.80077	0.0918904	0.0459452	+	0.998944i	$0.485370\pi$
$930$	5.83015	0.191178
$931$	−5.91771	−0.193945
$932$	−124.073	−4.06414
$933$	−23.2491	−0.761142
$934$	22.8477	0.747599
$935$	−73.6193	−2.40761
$936$	7.53410	0.246260
$937$	39.4852	1.28992	0.644962	−	0.764214i	$-0.276873\pi$
$937$	39.4852	1.28992	0.644962	+	0.764214i	$0.276873\pi$
$938$	−4.48137	−0.146322
$939$	−37.5143	−1.22423
$940$	−264.572	−8.62940
$941$	−46.4198	−1.51324	−0.756621	−	0.653854i	$-0.773151\pi$
$941$	−46.4198	−1.51324	−0.756621	+	0.653854i	$0.773151\pi$
$942$	−67.5496	−2.20088
$943$	−31.2776	−1.01854
$944$	−40.6863	−1.32423
$945$	23.7014	0.771008
$946$	64.1289	2.08501
$947$	−30.1384	−0.979365	−0.489683	−	0.871901i	$-0.662887\pi$
$947$	−30.1384	−0.979365	−0.489683	+	0.871901i	$0.662887\pi$
$948$	−95.5239	−3.10247
$949$	−21.1988	−0.688142
$950$	−32.9250	−1.06823
$951$	1.61720	0.0524412
$952$	−50.6005	−1.63997
$953$	24.4220	0.791106	0.395553	−	0.918443i	$-0.370553\pi$
$953$	24.4220	0.791106	0.395553	+	0.918443i	$0.370553\pi$
$954$	−10.4806	−0.339323
$955$	−81.9527	−2.65193
$956$	−42.7844	−1.38375
$957$	−8.67185	−0.280321
$958$	86.9444	2.80905
$959$	−14.1364	−0.456489
$960$	117.645	3.79699
$961$	−30.8949	−0.996609
$962$	50.8424	1.63922
$963$	−6.55598	−0.211263
$964$	−17.9094	−0.576822
$965$	−112.970	−3.63664
$966$	−22.6256	−0.727968
$967$	47.3160	1.52158	0.760790	−	0.648998i	$-0.224812\pi$
$967$	47.3160	1.52158	0.760790	+	0.648998i	$0.224812\pi$
$968$	14.3133	0.460045
$969$	9.38350	0.301441
$970$	−112.221	−3.60319
$971$	23.5563	0.755957	0.377979	−	0.925814i	$-0.376619\pi$
$971$	23.5563	0.755957	0.377979	+	0.925814i	$0.376619\pi$
$972$	−20.4062	−0.654528
$973$	10.2465	0.328488
$974$	81.4679	2.61040
$975$	−46.5656	−1.49129
$976$	−127.786	−4.09034
$977$	−26.5625	−0.849811	−0.424905	−	0.905238i	$-0.639693\pi$
$977$	−26.5625	−0.849811	−0.424905	+	0.905238i	$0.639693\pi$
$978$	−15.7887	−0.504867
$979$	41.3878	1.32276
$980$	126.544	4.04229
$981$	2.90749	0.0928290
$982$	−91.6824	−2.92570
$983$	−22.3512	−0.712891	−0.356446	−	0.934316i	$-0.616011\pi$
$983$	−22.3512	−0.712891	−0.356446	+	0.934316i	$0.616011\pi$
$984$	−84.2342	−2.68529
$985$	11.9522	0.380829
$986$	−27.2685	−0.868407
$987$	20.8158	0.662573
$988$	12.0038	0.381892
$989$	39.6368	1.26038
$990$	13.0395	0.414424
$991$	24.7351	0.785738	0.392869	−	0.919595i	$-0.371483\pi$
$991$	24.7351	0.785738	0.392869	+	0.919595i	$0.371483\pi$
$992$	5.06248	0.160734
$993$	9.73743	0.309008
$994$	−2.60406	−0.0825959
$995$	34.9986	1.10953
$996$	80.1067	2.53828
$997$	−46.3282	−1.46723	−0.733614	−	0.679567i	$-0.762168\pi$
$997$	−46.3282	−1.46723	−0.733614	+	0.679567i	$0.762168\pi$
$998$	86.6836	2.74392
$999$	−44.5835	−1.41056

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.c.1.6	✓	138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.c.1.6	✓	138	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:	\( N \)	\(=\)	\( 6023 = 19 \cdot 317 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.67164 q^{2} -1.61720 q^{3} +5.13764 q^{4} -4.16220 q^{5} +4.32056 q^{6} -1.04033 q^{7} -8.38264 q^{8} -0.384677 q^{9} +O(q^{10})\)	\(q-2.67164 q^{2} -1.61720 q^{3} +5.13764 q^{4} -4.16220 q^{5} +4.32056 q^{6} -1.04033 q^{7} -8.38264 q^{8} -0.384677 q^{9} +11.1199 q^{10} -3.04836 q^{11} -8.30858 q^{12} +2.33644 q^{13} +2.77939 q^{14} +6.73109 q^{15} +12.1201 q^{16} -5.80233 q^{17} +1.02772 q^{18} +1.00000 q^{19} -21.3839 q^{20} +1.68242 q^{21} +8.14412 q^{22} +5.03372 q^{23} +13.5564 q^{24} +12.3239 q^{25} -6.24212 q^{26} +5.47369 q^{27} -5.34485 q^{28} -1.75907 q^{29} -17.9830 q^{30} -0.324203 q^{31} -15.6152 q^{32} +4.92980 q^{33} +15.5017 q^{34} +4.33007 q^{35} -1.97633 q^{36} -8.14505 q^{37} -2.67164 q^{38} -3.77848 q^{39} +34.8902 q^{40} -6.21363 q^{41} -4.49482 q^{42} +7.87426 q^{43} -15.6614 q^{44} +1.60110 q^{45} -13.4483 q^{46} +12.3725 q^{47} -19.6006 q^{48} -5.91771 q^{49} -32.9250 q^{50} +9.38350 q^{51} +12.0038 q^{52} -10.1980 q^{53} -14.6237 q^{54} +12.6879 q^{55} +8.72073 q^{56} -1.61720 q^{57} +4.69959 q^{58} -3.35693 q^{59} +34.5819 q^{60} -10.5434 q^{61} +0.866152 q^{62} +0.400191 q^{63} +17.4779 q^{64} -9.72473 q^{65} -13.1706 q^{66} -1.61236 q^{67} -29.8103 q^{68} -8.14051 q^{69} -11.5684 q^{70} -0.936919 q^{71} +3.22461 q^{72} -9.07312 q^{73} +21.7606 q^{74} -19.9302 q^{75} +5.13764 q^{76} +3.17131 q^{77} +10.0947 q^{78} +11.4970 q^{79} -50.4462 q^{80} -7.69799 q^{81} +16.6006 q^{82} -9.64145 q^{83} +8.64368 q^{84} +24.1504 q^{85} -21.0371 q^{86} +2.84476 q^{87} +25.5533 q^{88} -13.5771 q^{89} -4.27756 q^{90} -2.43067 q^{91} +25.8614 q^{92} +0.524299 q^{93} -33.0548 q^{94} -4.16220 q^{95} +25.2528 q^{96} -10.0919 q^{97} +15.8100 q^{98} +1.17263 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9}+O(q^{10}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9} + 40 q^{10} + 4 q^{11} + 69 q^{12} + 72 q^{13} + 3 q^{14} + 30 q^{15} + 191 q^{16} + 31 q^{17} + 31 q^{18} + 138 q^{19} + 16 q^{20} + 16 q^{21} + 95 q^{22} + 34 q^{23} + 3 q^{24} + 244 q^{25} - 13 q^{26} + 107 q^{27} + 43 q^{28} + 30 q^{29} - 14 q^{30} + 60 q^{31} + 62 q^{32} + 77 q^{33} + 36 q^{34} + 2 q^{35} + 205 q^{36} + 142 q^{37} + 11 q^{38} + 20 q^{39} + 76 q^{40} + 46 q^{41} - 21 q^{42} + 69 q^{43} - 7 q^{44} + 30 q^{45} + 39 q^{46} + 8 q^{47} + 116 q^{48} + 236 q^{49} + 34 q^{51} + 165 q^{52} + 49 q^{53} + 6 q^{55} - 33 q^{56} + 29 q^{57} + 75 q^{58} + 8 q^{59} - 24 q^{60} + 38 q^{61} - 10 q^{62} + 2 q^{63} + 251 q^{64} + 72 q^{65} - 15 q^{66} + 158 q^{67} - 19 q^{68} + 33 q^{69} + 48 q^{70} + 23 q^{71} + 88 q^{72} + 134 q^{73} + 4 q^{74} + 118 q^{75} + 157 q^{76} + 13 q^{77} + 12 q^{78} + 78 q^{79} - 48 q^{80} + 254 q^{81} + 89 q^{82} - 27 q^{83} - 15 q^{84} + 37 q^{85} + 66 q^{86} + 43 q^{87} + 224 q^{88} + 26 q^{89} + 38 q^{90} + 108 q^{91} + 113 q^{92} + 83 q^{93} + 48 q^{94} + 12 q^{95} + 40 q^{96} + 254 q^{97} + 47 q^{98} + 11 q^{99}+O(q^{100}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9 + 40 * q^10 + 4 * q^11 + 69 * q^12 + 72 * q^13 + 3 * q^14 + 30 * q^15 + 191 * q^16 + 31 * q^17 + 31 * q^18 + 138 * q^19 + 16 * q^20 + 16 * q^21 + 95 * q^22 + 34 * q^23 + 3 * q^24 + 244 * q^25 - 13 * q^26 + 107 * q^27 + 43 * q^28 + 30 * q^29 - 14 * q^30 + 60 * q^31 + 62 * q^32 + 77 * q^33 + 36 * q^34 + 2 * q^35 + 205 * q^36 + 142 * q^37 + 11 * q^38 + 20 * q^39 + 76 * q^40 + 46 * q^41 - 21 * q^42 + 69 * q^43 - 7 * q^44 + 30 * q^45 + 39 * q^46 + 8 * q^47 + 116 * q^48 + 236 * q^49 + 34 * q^51 + 165 * q^52 + 49 * q^53 + 6 * q^55 - 33 * q^56 + 29 * q^57 + 75 * q^58 + 8 * q^59 - 24 * q^60 + 38 * q^61 - 10 * q^62 + 2 * q^63 + 251 * q^64 + 72 * q^65 - 15 * q^66 + 158 * q^67 - 19 * q^68 + 33 * q^69 + 48 * q^70 + 23 * q^71 + 88 * q^72 + 134 * q^73 + 4 * q^74 + 118 * q^75 + 157 * q^76 + 13 * q^77 + 12 * q^78 + 78 * q^79 - 48 * q^80 + 254 * q^81 + 89 * q^82 - 27 * q^83 - 15 * q^84 + 37 * q^85 + 66 * q^86 + 43 * q^87 + 224 * q^88 + 26 * q^89 + 38 * q^90 + 108 * q^91 + 113 * q^92 + 83 * q^93 + 48 * q^94 + 12 * q^95 + 40 * q^96 + 254 * q^97 + 47 * q^98 + 11 * q^99

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