LMFDB - Embedded newform 8033.2.a.b.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8033,2,Mod(1,8033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8033, 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("8033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8033 = 29 \cdot 277 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8033.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:	$64.1438279437$
Analytic rank:	$1$
Dimension:	$153$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	8033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.25207 q^{2} +0.273415 q^{3} +3.07181 q^{4} -3.19262 q^{5} -0.615750 q^{6} -2.20872 q^{7} -2.41378 q^{8} -2.92524 q^{9} +O(q^{10})$	\(q-2.25207 q^{2} +0.273415 q^{3} +3.07181 q^{4} -3.19262 q^{5} -0.615750 q^{6} -2.20872 q^{7} -2.41378 q^{8} -2.92524 q^{9} +7.19000 q^{10} -4.44004 q^{11} +0.839879 q^{12} +2.32945 q^{13} +4.97418 q^{14} -0.872912 q^{15} -0.707612 q^{16} +5.91815 q^{17} +6.58785 q^{18} -5.24442 q^{19} -9.80712 q^{20} -0.603898 q^{21} +9.99927 q^{22} -5.44287 q^{23} -0.659965 q^{24} +5.19284 q^{25} -5.24607 q^{26} -1.62005 q^{27} -6.78476 q^{28} -1.00000 q^{29} +1.96586 q^{30} -3.42001 q^{31} +6.42116 q^{32} -1.21397 q^{33} -13.3281 q^{34} +7.05161 q^{35} -8.98579 q^{36} -0.627581 q^{37} +11.8108 q^{38} +0.636907 q^{39} +7.70630 q^{40} +9.27167 q^{41} +1.36002 q^{42} +9.00149 q^{43} -13.6389 q^{44} +9.33920 q^{45} +12.2577 q^{46} +10.5322 q^{47} -0.193472 q^{48} -2.12156 q^{49} -11.6946 q^{50} +1.61811 q^{51} +7.15562 q^{52} -3.59009 q^{53} +3.64847 q^{54} +14.1754 q^{55} +5.33137 q^{56} -1.43390 q^{57} +2.25207 q^{58} -4.89827 q^{59} -2.68142 q^{60} -11.9296 q^{61} +7.70210 q^{62} +6.46104 q^{63} -13.0457 q^{64} -7.43705 q^{65} +2.73395 q^{66} +6.98670 q^{67} +18.1794 q^{68} -1.48816 q^{69} -15.8807 q^{70} +5.59182 q^{71} +7.06091 q^{72} -5.67648 q^{73} +1.41336 q^{74} +1.41980 q^{75} -16.1098 q^{76} +9.80680 q^{77} -1.43436 q^{78} -17.1316 q^{79} +2.25914 q^{80} +8.33278 q^{81} -20.8804 q^{82} +9.68969 q^{83} -1.85506 q^{84} -18.8944 q^{85} -20.2720 q^{86} -0.273415 q^{87} +10.7173 q^{88} +1.42383 q^{89} -21.0325 q^{90} -5.14510 q^{91} -16.7195 q^{92} -0.935084 q^{93} -23.7192 q^{94} +16.7434 q^{95} +1.75564 q^{96} +6.56900 q^{97} +4.77790 q^{98} +12.9882 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 153 q - 3 q^{2} - 12 q^{3} + 135 q^{4} - 11 q^{5} - 17 q^{6} - 76 q^{7} - 12 q^{8} + 133 q^{9}+O(q^{10}) $ 153 * q - 3 * q^2 - 12 * q^3 + 135 * q^4 - 11 * q^5 - 17 * q^6 - 76 * q^7 - 12 * q^8 + 133 * q^9	\( 153 q - 3 q^{2} - 12 q^{3} + 135 q^{4} - 11 q^{5} - 17 q^{6} - 76 q^{7} - 12 q^{8} + 133 q^{9} - 30 q^{10} + 4 q^{11} - 39 q^{12} - 65 q^{13} + q^{14} - 26 q^{15} + 107 q^{16} - 20 q^{17} - 21 q^{18} - 65 q^{19} - 23 q^{20} - 24 q^{21} - 59 q^{22} - 62 q^{23} - 59 q^{24} + 102 q^{25} - 18 q^{26} - 57 q^{27} - 155 q^{28} - 153 q^{29} - 82 q^{30} - 49 q^{31} - 17 q^{32} - 59 q^{33} - 68 q^{34} - 36 q^{35} + 74 q^{36} - 30 q^{37} - 67 q^{38} - 47 q^{39} - 108 q^{40} - 9 q^{41} - 62 q^{42} - 90 q^{43} - 14 q^{44} - 56 q^{45} - 52 q^{46} - 54 q^{47} - 76 q^{48} + 101 q^{49} - 36 q^{50} - 60 q^{51} - 191 q^{52} - 38 q^{53} - 82 q^{54} - 215 q^{55} + 24 q^{56} - 52 q^{57} + 3 q^{58} - 55 q^{59} - 60 q^{60} - 90 q^{61} - 66 q^{62} - 229 q^{63} + 52 q^{64} - 67 q^{65} - 29 q^{66} - 114 q^{67} - 78 q^{68} - 68 q^{69} - 61 q^{70} - 52 q^{71} - 47 q^{72} - 83 q^{73} - 21 q^{74} - 47 q^{75} - 100 q^{76} - 32 q^{77} - 17 q^{78} - 151 q^{79} - 24 q^{80} + 81 q^{81} - 151 q^{82} - 94 q^{83} - 84 q^{84} - 77 q^{85} - 43 q^{86} + 12 q^{87} - 121 q^{88} + 11 q^{89} - 14 q^{90} - 66 q^{91} - 156 q^{92} - 66 q^{93} - 22 q^{94} - 67 q^{95} - 131 q^{96} - 78 q^{97} - 67 q^{98} - 41 q^{99}+O(q^{100}) \) 153 * q - 3 * q^2 - 12 * q^3 + 135 * q^4 - 11 * q^5 - 17 * q^6 - 76 * q^7 - 12 * q^8 + 133 * q^9 - 30 * q^10 + 4 * q^11 - 39 * q^12 - 65 * q^13 + q^14 - 26 * q^15 + 107 * q^16 - 20 * q^17 - 21 * q^18 - 65 * q^19 - 23 * q^20 - 24 * q^21 - 59 * q^22 - 62 * q^23 - 59 * q^24 + 102 * q^25 - 18 * q^26 - 57 * q^27 - 155 * q^28 - 153 * q^29 - 82 * q^30 - 49 * q^31 - 17 * q^32 - 59 * q^33 - 68 * q^34 - 36 * q^35 + 74 * q^36 - 30 * q^37 - 67 * q^38 - 47 * q^39 - 108 * q^40 - 9 * q^41 - 62 * q^42 - 90 * q^43 - 14 * q^44 - 56 * q^45 - 52 * q^46 - 54 * q^47 - 76 * q^48 + 101 * q^49 - 36 * q^50 - 60 * q^51 - 191 * q^52 - 38 * q^53 - 82 * q^54 - 215 * q^55 + 24 * q^56 - 52 * q^57 + 3 * q^58 - 55 * q^59 - 60 * q^60 - 90 * q^61 - 66 * q^62 - 229 * q^63 + 52 * q^64 - 67 * q^65 - 29 * q^66 - 114 * q^67 - 78 * q^68 - 68 * q^69 - 61 * q^70 - 52 * q^71 - 47 * q^72 - 83 * q^73 - 21 * q^74 - 47 * q^75 - 100 * q^76 - 32 * q^77 - 17 * q^78 - 151 * q^79 - 24 * q^80 + 81 * q^81 - 151 * q^82 - 94 * q^83 - 84 * q^84 - 77 * q^85 - 43 * q^86 + 12 * q^87 - 121 * q^88 + 11 * q^89 - 14 * q^90 - 66 * q^91 - 156 * q^92 - 66 * q^93 - 22 * q^94 - 67 * q^95 - 131 * q^96 - 78 * q^97 - 67 * q^98 - 41 * 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 $

$2$	−2.25207	−1.59245	−0.796226	−	0.604999i	$-0.793173\pi$
$2$	−2.25207	−1.59245	−0.796226	+	0.604999i	$0.793173\pi$
$3$	0.273415	0.157856	0.0789282	−	0.996880i	$-0.474850\pi$
$3$	0.273415	0.157856	0.0789282	+	0.996880i	$0.474850\pi$
$4$	3.07181	1.53590
$5$	−3.19262	−1.42778	−0.713892	−	0.700256i	$-0.753069\pi$
$5$	−3.19262	−1.42778	−0.713892	+	0.700256i	$0.753069\pi$
$6$	−0.615750	−0.251379
$7$	−2.20872	−0.834817	−0.417409	−	0.908719i	$-0.637062\pi$
$7$	−2.20872	−0.834817	−0.417409	+	0.908719i	$0.637062\pi$
$8$	−2.41378	−0.853401
$9$	−2.92524	−0.975081
$10$	7.19000	2.27368
$11$	−4.44004	−1.33872	−0.669361	−	0.742937i	$-0.733432\pi$
$11$	−4.44004	−1.33872	−0.669361	+	0.742937i	$0.733432\pi$
$12$	0.839879	0.242452
$13$	2.32945	0.646073	0.323036	−	0.946387i	$-0.395296\pi$
$13$	2.32945	0.646073	0.323036	+	0.946387i	$0.395296\pi$
$14$	4.97418	1.32941
$15$	−0.872912	−0.225385
$16$	−0.707612	−0.176903
$17$	5.91815	1.43536	0.717682	−	0.696371i	$-0.245203\pi$
$17$	5.91815	1.43536	0.717682	+	0.696371i	$0.245203\pi$
$18$	6.58785	1.55277
$19$	−5.24442	−1.20315	−0.601576	−	0.798816i	$-0.705460\pi$
$19$	−5.24442	−1.20315	−0.601576	+	0.798816i	$0.705460\pi$
$20$	−9.80712	−2.19294
$21$	−0.603898	−0.131781
$22$	9.99927	2.13185
$23$	−5.44287	−1.13492	−0.567458	−	0.823402i	$-0.692073\pi$
$23$	−5.44287	−1.13492	−0.567458	+	0.823402i	$0.692073\pi$
$24$	−0.659965	−0.134715
$25$	5.19284	1.03857
$26$	−5.24607	−1.02884
$27$	−1.62005	−0.311779
$28$	−6.78476	−1.28220
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	1.96586	0.358915
$31$	−3.42001	−0.614252	−0.307126	−	0.951669i	$-0.599367\pi$
$31$	−3.42001	−0.614252	−0.307126	+	0.951669i	$0.599367\pi$
$32$	6.42116	1.13511
$33$	−1.21397	−0.211326
$34$	−13.3281	−2.28575
$35$	7.05161	1.19194
$36$	−8.98579	−1.49763
$37$	−0.627581	−0.103174	−0.0515869	−	0.998669i	$-0.516428\pi$
$37$	−0.627581	−0.103174	−0.0515869	+	0.998669i	$0.516428\pi$
$38$	11.8108	1.91596
$39$	0.636907	0.101987
$40$	7.70630	1.21847
$41$	9.27167	1.44799	0.723996	−	0.689804i	$-0.242303\pi$
$41$	9.27167	1.44799	0.723996	+	0.689804i	$0.242303\pi$
$42$	1.36002	0.209855
$43$	9.00149	1.37271	0.686357	−	0.727264i	$-0.259209\pi$
$43$	9.00149	1.37271	0.686357	+	0.727264i	$0.259209\pi$
$44$	−13.6389	−2.05615
$45$	9.33920	1.39221
$46$	12.2577	1.80730
$47$	10.5322	1.53628	0.768139	−	0.640283i	$-0.221183\pi$
$47$	10.5322	1.53628	0.768139	+	0.640283i	$0.221183\pi$
$48$	−0.193472	−0.0279253
$49$	−2.12156	−0.303080
$50$	−11.6946	−1.65387
$51$	1.61811	0.226581
$52$	7.15562	0.992306
$53$	−3.59009	−0.493137	−0.246569	−	0.969125i	$-0.579303\pi$
$53$	−3.59009	−0.493137	−0.246569	+	0.969125i	$0.579303\pi$
$54$	3.64847	0.496494
$55$	14.1754	1.91141
$56$	5.33137	0.712434
$57$	−1.43390	−0.189925
$58$	2.25207	0.295711
$59$	−4.89827	−0.637701	−0.318850	−	0.947805i	$-0.603297\pi$
$59$	−4.89827	−0.637701	−0.318850	+	0.947805i	$0.603297\pi$
$60$	−2.68142	−0.346170
$61$	−11.9296	−1.52743	−0.763716	−	0.645552i	$-0.776627\pi$
$61$	−11.9296	−1.52743	−0.763716	+	0.645552i	$0.776627\pi$
$62$	7.70210	0.978167
$63$	6.46104	0.814015
$64$	−13.0457	−1.63071
$65$	−7.43705	−0.922452
$66$	2.73395	0.336526
$67$	6.98670	0.853561	0.426781	−	0.904355i	$-0.359648\pi$
$67$	6.98670	0.853561	0.426781	+	0.904355i	$0.359648\pi$
$68$	18.1794	2.20458
$69$	−1.48816	−0.179154
$70$	−15.8807	−1.89811
$71$	5.59182	0.663627	0.331813	−	0.943345i	$-0.392340\pi$
$71$	5.59182	0.663627	0.331813	+	0.943345i	$0.392340\pi$
$72$	7.06091	0.832136
$73$	−5.67648	−0.664381	−0.332191	−	0.943212i	$-0.607788\pi$
$73$	−5.67648	−0.664381	−0.332191	+	0.943212i	$0.607788\pi$
$74$	1.41336	0.164299
$75$	1.41980	0.163945
$76$	−16.1098	−1.84793
$77$	9.80680	1.11759
$78$	−1.43436	−0.162409
$79$	−17.1316	−1.92746	−0.963729	−	0.266883i	$-0.914006\pi$
$79$	−17.1316	−1.92746	−0.963729	+	0.266883i	$0.914006\pi$
$80$	2.25914	0.252579
$81$	8.33278	0.925865
$82$	−20.8804	−2.30586
$83$	9.68969	1.06358	0.531791	−	0.846876i	$-0.321519\pi$
$83$	9.68969	1.06358	0.531791	+	0.846876i	$0.321519\pi$
$84$	−1.85506	−0.202403
$85$	−18.8944	−2.04939
$86$	−20.2720	−2.18598
$87$	−0.273415	−0.0293132
$88$	10.7173	1.14247
$89$	1.42383	0.150925	0.0754626	−	0.997149i	$-0.475957\pi$
$89$	1.42383	0.150925	0.0754626	+	0.997149i	$0.475957\pi$
$90$	−21.0325	−2.21702
$91$	−5.14510	−0.539353
$92$	−16.7195	−1.74312
$93$	−0.935084	−0.0969637
$94$	−23.7192	−2.44645
$95$	16.7434	1.71784
$96$	1.75564	0.179185
$97$	6.56900	0.666981	0.333490	−	0.942753i	$-0.391774\pi$
$97$	6.56900	0.666981	0.333490	+	0.942753i	$0.391774\pi$
$98$	4.77790	0.482641
$99$	12.9882	1.30536
$100$	15.9514	1.59514
$101$	2.36591	0.235417	0.117708	−	0.993048i	$-0.462445\pi$
$101$	2.36591	0.235417	0.117708	+	0.993048i	$0.462445\pi$
$102$	−3.64410	−0.360820
$103$	8.82154	0.869212	0.434606	−	0.900621i	$-0.356888\pi$
$103$	8.82154	0.869212	0.434606	+	0.900621i	$0.356888\pi$
$104$	−5.62278	−0.551359
$105$	1.92802	0.188155
$106$	8.08514	0.785298
$107$	12.1159	1.17129	0.585644	−	0.810569i	$-0.300842\pi$
$107$	12.1159	1.17129	0.585644	+	0.810569i	$0.300842\pi$
$108$	−4.97649	−0.478863
$109$	17.4438	1.67082	0.835408	−	0.549630i	$-0.185231\pi$
$109$	17.4438	1.67082	0.835408	+	0.549630i	$0.185231\pi$
$110$	−31.9239	−3.04382
$111$	−0.171590	−0.0162866
$112$	1.56292	0.147682
$113$	4.78814	0.450430	0.225215	−	0.974309i	$-0.427691\pi$
$113$	4.78814	0.450430	0.225215	+	0.974309i	$0.427691\pi$
$114$	3.22925	0.302447
$115$	17.3770	1.62042
$116$	−3.07181	−0.285210
$117$	−6.81420	−0.629973
$118$	11.0312	1.01551
$119$	−13.0715	−1.19827
$120$	2.10702	0.192344
$121$	8.71395	0.792177
$122$	26.8663	2.43236
$123$	2.53502	0.228575
$124$	−10.5056	−0.943433
$125$	−0.615660	−0.0550663
$126$	−14.5507	−1.29628
$127$	−1.84286	−0.163528	−0.0817638	−	0.996652i	$-0.526055\pi$
$127$	−1.84286	−0.163528	−0.0817638	+	0.996652i	$0.526055\pi$
$128$	16.5374	1.46171
$129$	2.46115	0.216692
$130$	16.7487	1.46896
$131$	9.84255	0.859948	0.429974	−	0.902841i	$-0.358523\pi$
$131$	9.84255	0.859948	0.429974	+	0.902841i	$0.358523\pi$
$132$	−3.72910	−0.324576
$133$	11.5834	1.00441
$134$	−15.7345	−1.35926
$135$	5.17222	0.445154
$136$	−14.2851	−1.22494
$137$	−7.44649	−0.636196	−0.318098	−	0.948058i	$-0.603044\pi$
$137$	−7.44649	−0.636196	−0.318098	+	0.948058i	$0.603044\pi$
$138$	3.35145	0.285294
$139$	14.9436	1.26750	0.633748	−	0.773540i	$-0.281516\pi$
$139$	14.9436	1.26750	0.633748	+	0.773540i	$0.281516\pi$
$140$	21.6612	1.83070
$141$	2.87966	0.242511
$142$	−12.5932	−1.05679
$143$	−10.3428	−0.864912
$144$	2.06994	0.172495
$145$	3.19262	0.265133
$146$	12.7838	1.05800
$147$	−0.580067	−0.0478432
$148$	−1.92781	−0.158465
$149$	−11.2344	−0.920361	−0.460180	−	0.887825i	$-0.652215\pi$
$149$	−11.2344	−0.920361	−0.460180	+	0.887825i	$0.652215\pi$
$150$	−3.19749	−0.261074
$151$	−10.7540	−0.875146	−0.437573	−	0.899183i	$-0.644162\pi$
$151$	−10.7540	−0.875146	−0.437573	+	0.899183i	$0.644162\pi$
$152$	12.6589	1.02677
$153$	−17.3120	−1.39960
$154$	−22.0856	−1.77971
$155$	10.9188	0.877020
$156$	1.95646	0.156642
$157$	7.59433	0.606094	0.303047	−	0.952976i	$-0.401996\pi$
$157$	7.59433	0.606094	0.303047	+	0.952976i	$0.401996\pi$
$158$	38.5816	3.06938
$159$	−0.981587	−0.0778449
$160$	−20.5003	−1.62069
$161$	12.0218	0.947448
$162$	−18.7660	−1.47440
$163$	7.84349	0.614350	0.307175	−	0.951653i	$-0.400616\pi$
$163$	7.84349	0.614350	0.307175	+	0.951653i	$0.400616\pi$
$164$	28.4808	2.22398
$165$	3.87576	0.301728
$166$	−21.8218	−1.69370
$167$	21.7652	1.68424	0.842120	−	0.539290i	$-0.181307\pi$
$167$	21.7652	1.68424	0.842120	+	0.539290i	$0.181307\pi$
$168$	1.45768	0.112462
$169$	−7.57367	−0.582590
$170$	42.5515	3.26355
$171$	15.3412	1.17317
$172$	27.6509	2.10836
$173$	−3.67659	−0.279526	−0.139763	−	0.990185i	$-0.544634\pi$
$173$	−3.67659	−0.279526	−0.139763	+	0.990185i	$0.544634\pi$
$174$	0.615750	0.0466799
$175$	−11.4695	−0.867014
$176$	3.14183	0.236824
$177$	−1.33926	−0.100665
$178$	−3.20655	−0.240341
$179$	−11.6404	−0.870045	−0.435022	−	0.900420i	$-0.643260\pi$
$179$	−11.6404	−0.870045	−0.435022	+	0.900420i	$0.643260\pi$
$180$	28.6882	2.13829
$181$	−5.58569	−0.415181	−0.207590	−	0.978216i	$-0.566562\pi$
$181$	−5.58569	−0.415181	−0.207590	+	0.978216i	$0.566562\pi$
$182$	11.5871	0.858893
$183$	−3.26174	−0.241115
$184$	13.1379	0.968540
$185$	2.00363	0.147310
$186$	2.10587	0.154410
$187$	−26.2768	−1.92155
$188$	32.3529	2.35958
$189$	3.57824	0.260279
$190$	−37.7074	−2.73558
$191$	6.29284	0.455334	0.227667	−	0.973739i	$-0.426890\pi$
$191$	6.29284	0.455334	0.227667	+	0.973739i	$0.426890\pi$
$192$	−3.56688	−0.257418
$193$	1.18913	0.0855953	0.0427976	−	0.999084i	$-0.486373\pi$
$193$	1.18913	0.0855953	0.0427976	+	0.999084i	$0.486373\pi$
$194$	−14.7938	−1.06214
$195$	−2.03340	−0.145615
$196$	−6.51703	−0.465502
$197$	8.74622	0.623142	0.311571	−	0.950223i	$-0.399145\pi$
$197$	8.74622	0.623142	0.311571	+	0.950223i	$0.399145\pi$
$198$	−29.2503	−2.07873
$199$	−27.0394	−1.91677	−0.958387	−	0.285471i	$-0.907850\pi$
$199$	−27.0394	−1.91677	−0.958387	+	0.285471i	$0.907850\pi$
$200$	−12.5344	−0.886315
$201$	1.91027	0.134740
$202$	−5.32819	−0.374890
$203$	2.20872	0.155022
$204$	4.97054	0.348007
$205$	−29.6010	−2.06742
$206$	−19.8667	−1.38418
$207$	15.9217	1.10664
$208$	−1.64835	−0.114292
$209$	23.2854	1.61069
$210$	−4.34202	−0.299628
$211$	−17.4653	−1.20236	−0.601181	−	0.799113i	$-0.705303\pi$
$211$	−17.4653	−1.20236	−0.601181	+	0.799113i	$0.705303\pi$
$212$	−11.0281	−0.757412
$213$	1.52889	0.104758
$214$	−27.2858	−1.86522
$215$	−28.7384	−1.95994
$216$	3.91046	0.266073
$217$	7.55384	0.512788
$218$	−39.2847	−2.66069
$219$	−1.55204	−0.104877
$220$	43.5440	2.93574
$221$	13.7860	0.927349
$222$	0.386433	0.0259357
$223$	−13.5058	−0.904413	−0.452206	−	0.891913i	$-0.649363\pi$
$223$	−13.5058	−0.904413	−0.452206	+	0.891913i	$0.649363\pi$
$224$	−14.1825	−0.947610
$225$	−15.1903	−1.01269
$226$	−10.7832	−0.717289
$227$	1.55992	0.103536	0.0517678	−	0.998659i	$-0.483514\pi$
$227$	1.55992	0.103536	0.0517678	+	0.998659i	$0.483514\pi$
$228$	−4.40468	−0.291707
$229$	16.0607	1.06132	0.530660	−	0.847585i	$-0.321944\pi$
$229$	16.0607	1.06132	0.530660	+	0.847585i	$0.321944\pi$
$230$	−39.1342	−2.58044
$231$	2.68133	0.176418
$232$	2.41378	0.158473
$233$	22.9504	1.50353	0.751765	−	0.659431i	$-0.229203\pi$
$233$	22.9504	1.50353	0.751765	+	0.659431i	$0.229203\pi$
$234$	15.3460	1.00320
$235$	−33.6253	−2.19347
$236$	−15.0466	−0.979447
$237$	−4.68405	−0.304262
$238$	29.4380	1.90818
$239$	−1.29213	−0.0835810	−0.0417905	−	0.999126i	$-0.513306\pi$
$239$	−1.29213	−0.0835810	−0.0417905	+	0.999126i	$0.513306\pi$
$240$	0.617683	0.0398713
$241$	16.5588	1.06665	0.533323	−	0.845911i	$-0.320943\pi$
$241$	16.5588	1.06665	0.533323	+	0.845911i	$0.320943\pi$
$242$	−19.6244	−1.26150
$243$	7.13847	0.457933
$244$	−36.6455	−2.34599
$245$	6.77334	0.432733
$246$	−5.70903	−0.363995
$247$	−12.2166	−0.777324
$248$	8.25517	0.524204
$249$	2.64931	0.167893
$250$	1.38651	0.0876904
$251$	−26.6258	−1.68060	−0.840301	−	0.542119i	$-0.817622\pi$
$251$	−26.6258	−1.68060	−0.840301	+	0.542119i	$0.817622\pi$
$252$	19.8471	1.25025
$253$	24.1666	1.51934
$254$	4.15025	0.260410
$255$	−5.16603	−0.323509
$256$	−11.1520	−0.696999
$257$	4.13759	0.258096	0.129048	−	0.991638i	$-0.458808\pi$
$257$	4.13759	0.258096	0.129048	+	0.991638i	$0.458808\pi$
$258$	−5.54267	−0.345071
$259$	1.38615	0.0861312
$260$	−22.8452	−1.41680
$261$	2.92524	0.181068
$262$	−22.1661	−1.36943
$263$	−14.6688	−0.904514	−0.452257	−	0.891888i	$-0.649381\pi$
$263$	−14.6688	−0.904514	−0.452257	+	0.891888i	$0.649381\pi$
$264$	2.93027	0.180346
$265$	11.4618	0.704094
$266$	−26.0867	−1.59948
$267$	0.389296	0.0238245
$268$	21.4618	1.31099
$269$	4.89313	0.298340	0.149170	−	0.988812i	$-0.452340\pi$
$269$	4.89313	0.298340	0.149170	+	0.988812i	$0.452340\pi$
$270$	−11.6482	−0.708886
$271$	−28.5059	−1.73161	−0.865805	−	0.500381i	$-0.833193\pi$
$271$	−28.5059	−1.73161	−0.865805	+	0.500381i	$0.833193\pi$
$272$	−4.18776	−0.253920
$273$	−1.40675	−0.0851403
$274$	16.7700	1.01311
$275$	−23.0564	−1.39035
$276$	−4.57135	−0.275163
$277$	−1.00000	−0.0600842
$277$	−1.00000	−0.0600842
$278$	−33.6539	−2.01843
$279$	10.0044	0.598946
$280$	−17.0210	−1.01720
$281$	28.1541	1.67953	0.839766	−	0.542948i	$-0.182692\pi$
$281$	28.1541	1.67953	0.839766	+	0.542948i	$0.182692\pi$
$282$	−6.48520	−0.386188
$283$	13.5315	0.804365	0.402183	−	0.915560i	$-0.368252\pi$
$283$	13.5315	0.804365	0.402183	+	0.915560i	$0.368252\pi$
$284$	17.1770	1.01927
$285$	4.57792	0.271172
$286$	23.2928	1.37733
$287$	−20.4785	−1.20881
$288$	−18.7835	−1.10683
$289$	18.0245	1.06027
$290$	−7.19000	−0.422211
$291$	1.79607	0.105287
$292$	−17.4370	−1.02043
$293$	16.9691	0.991345	0.495672	−	0.868510i	$-0.334922\pi$
$293$	16.9691	0.991345	0.495672	+	0.868510i	$0.334922\pi$
$294$	1.30635	0.0761879
$295$	15.6383	0.910499
$296$	1.51485	0.0880486
$297$	7.19310	0.417386
$298$	25.3007	1.46563
$299$	−12.6789	−0.733239
$300$	4.36136	0.251803
$301$	−19.8818	−1.14597
$302$	24.2187	1.39363
$303$	0.646876	0.0371621
$304$	3.71102	0.212841
$305$	38.0868	2.18084
$306$	38.9879	2.22879
$307$	5.29009	0.301922	0.150961	−	0.988540i	$-0.451763\pi$
$307$	5.29009	0.301922	0.150961	+	0.988540i	$0.451763\pi$
$308$	30.1246	1.71651
$309$	2.41194	0.137211
$310$	−24.5899	−1.39661
$311$	−7.32441	−0.415329	−0.207664	−	0.978200i	$-0.566586\pi$
$311$	−7.32441	−0.415329	−0.207664	+	0.978200i	$0.566586\pi$
$312$	−1.53736	−0.0870356
$313$	−23.6521	−1.33690	−0.668449	−	0.743758i	$-0.733042\pi$
$313$	−23.6521	−1.33690	−0.668449	+	0.743758i	$0.733042\pi$
$314$	−17.1030	−0.965175
$315$	−20.6277	−1.16224
$316$	−52.6251	−2.96039
$317$	−10.6878	−0.600285	−0.300142	−	0.953894i	$-0.597034\pi$
$317$	−10.6878	−0.600285	−0.300142	+	0.953894i	$0.597034\pi$
$318$	2.21060	0.123964
$319$	4.44004	0.248594
$320$	41.6499	2.32830
$321$	3.31267	0.184895
$322$	−27.0738	−1.50877
$323$	−31.0373	−1.72696
$324$	25.5967	1.42204
$325$	12.0964	0.670990
$326$	−17.6641	−0.978322
$327$	4.76941	0.263749
$328$	−22.3798	−1.23572
$329$	−23.2627	−1.28251
$330$	−8.72848	−0.480487
$331$	19.1363	1.05182	0.525912	−	0.850539i	$-0.323724\pi$
$331$	19.1363	1.05182	0.525912	+	0.850539i	$0.323724\pi$
$332$	29.7649	1.63356
$333$	1.83583	0.100603
$334$	−49.0166	−2.68207
$335$	−22.3059	−1.21870
$336$	0.427325	0.0233125
$337$	18.0480	0.983140	0.491570	−	0.870838i	$-0.336423\pi$
$337$	18.0480	0.983140	0.491570	+	0.870838i	$0.336423\pi$
$338$	17.0564	0.927747
$339$	1.30915	0.0711033
$340$	−58.0401	−3.14766
$341$	15.1850	0.822313
$342$	−34.5494	−1.86822
$343$	20.1470	1.08783
$344$	−21.7277	−1.17148
$345$	4.75115	0.255793
$346$	8.27994	0.445132
$347$	−28.0767	−1.50724	−0.753619	−	0.657311i	$-0.771694\pi$
$347$	−28.0767	−1.50724	−0.753619	+	0.657311i	$0.771694\pi$
$348$	−0.839879	−0.0450223
$349$	−23.6868	−1.26792	−0.633962	−	0.773364i	$-0.718573\pi$
$349$	−23.6868	−1.26792	−0.633962	+	0.773364i	$0.718573\pi$
$350$	25.8301	1.38068
$351$	−3.77383	−0.201432
$352$	−28.5102	−1.51960
$353$	−4.85334	−0.258317	−0.129159	−	0.991624i	$-0.541228\pi$
$353$	−4.85334	−0.258317	−0.129159	+	0.991624i	$0.541228\pi$
$354$	3.01611	0.160304
$355$	−17.8526	−0.947516
$356$	4.37372	0.231807
$357$	−3.57396	−0.189154
$358$	26.2150	1.38551
$359$	19.1488	1.01064	0.505318	−	0.862933i	$-0.331375\pi$
$359$	19.1488	1.01064	0.505318	+	0.862933i	$0.331375\pi$
$360$	−22.5428	−1.18811
$361$	8.50393	0.447575
$362$	12.5793	0.661156
$363$	2.38253	0.125050
$364$	−15.8047	−0.828394
$365$	18.1228	0.948593
$366$	7.34567	0.383964
$367$	2.12707	0.111032	0.0555159	−	0.998458i	$-0.482320\pi$
$367$	2.12707	0.111032	0.0555159	+	0.998458i	$0.482320\pi$
$368$	3.85144	0.200770
$369$	−27.1219	−1.41191
$370$	−4.51231	−0.234584
$371$	7.92951	0.411680
$372$	−2.87240	−0.148927
$373$	−28.7560	−1.48893	−0.744466	−	0.667661i	$-0.767296\pi$
$373$	−28.7560	−1.48893	−0.744466	+	0.667661i	$0.767296\pi$
$374$	59.1772	3.05998
$375$	−0.168331	−0.00869257
$376$	−25.4224	−1.31106
$377$	−2.32945	−0.119973
$378$	−8.05844	−0.414481
$379$	−6.72845	−0.345617	−0.172809	−	0.984955i	$-0.555284\pi$
$379$	−6.72845	−0.345617	−0.172809	+	0.984955i	$0.555284\pi$
$380$	51.4327	2.63844
$381$	−0.503867	−0.0258139
$382$	−14.1719	−0.725098
$383$	−18.5869	−0.949749	−0.474874	−	0.880054i	$-0.657506\pi$
$383$	−18.5869	−0.949749	−0.474874	+	0.880054i	$0.657506\pi$
$384$	4.52157	0.230741
$385$	−31.3094	−1.59567
$386$	−2.67800	−0.136306
$387$	−26.3316	−1.33851
$388$	20.1787	1.02442
$389$	4.67897	0.237233	0.118617	−	0.992940i	$-0.462154\pi$
$389$	4.67897	0.237233	0.118617	+	0.992940i	$0.462154\pi$
$390$	4.57936	0.231885
$391$	−32.2117	−1.62902
$392$	5.12099	0.258649
$393$	2.69111	0.135748
$394$	−19.6971	−0.992324
$395$	54.6948	2.75199
$396$	39.8972	2.00491
$397$	20.2748	1.01756	0.508781	−	0.860896i	$-0.330096\pi$
$397$	20.2748	1.01756	0.508781	+	0.860896i	$0.330096\pi$
$398$	60.8946	3.05237
$399$	3.16709	0.158553
$400$	−3.67452	−0.183726
$401$	−22.4958	−1.12339	−0.561693	−	0.827346i	$-0.689850\pi$
$401$	−22.4958	−1.12339	−0.561693	+	0.827346i	$0.689850\pi$
$402$	−4.30206	−0.214567
$403$	−7.96674	−0.396852
$404$	7.26762	0.361578
$405$	−26.6034	−1.32194
$406$	−4.97418	−0.246865
$407$	2.78649	0.138121
$408$	−3.90578	−0.193365
$409$	31.6922	1.56708	0.783539	−	0.621342i	$-0.213412\pi$
$409$	31.6922	1.56708	0.783539	+	0.621342i	$0.213412\pi$
$410$	66.6633	3.29227
$411$	−2.03598	−0.100428
$412$	27.0981	1.33503
$413$	10.8189	0.532364
$414$	−35.8568	−1.76227
$415$	−30.9355	−1.51857
$416$	14.9578	0.733364
$417$	4.08580	0.200082
$418$	−52.4403	−2.56494
$419$	23.2260	1.13466	0.567332	−	0.823489i	$-0.307976\pi$
$419$	23.2260	1.13466	0.567332	+	0.823489i	$0.307976\pi$
$420$	5.92250	0.288988
$421$	−37.6743	−1.83613	−0.918067	−	0.396425i	$-0.870251\pi$
$421$	−37.6743	−1.83613	−0.918067	+	0.396425i	$0.870251\pi$
$422$	39.3330	1.91470
$423$	−30.8092	−1.49800
$424$	8.66571	0.420844
$425$	30.7320	1.49072
$426$	−3.44316	−0.166822
$427$	26.3492	1.27513
$428$	37.2177	1.79898
$429$	−2.82789	−0.136532
$430$	64.7207	3.12111
$431$	31.1553	1.50070	0.750348	−	0.661042i	$-0.229886\pi$
$431$	31.1553	1.50070	0.750348	+	0.661042i	$0.229886\pi$
$432$	1.14637	0.0551547
$433$	9.91411	0.476442	0.238221	−	0.971211i	$-0.423436\pi$
$433$	9.91411	0.476442	0.238221	+	0.971211i	$0.423436\pi$
$434$	−17.0118	−0.816591
$435$	0.872912	0.0418529
$436$	53.5841	2.56621
$437$	28.5447	1.36548
$438$	3.49529	0.167011
$439$	12.4836	0.595811	0.297906	−	0.954595i	$-0.403712\pi$
$439$	12.4836	0.595811	0.297906	+	0.954595i	$0.403712\pi$
$440$	−34.2163	−1.63120
$441$	6.20608	0.295528
$442$	−31.0471	−1.47676
$443$	−25.1886	−1.19675	−0.598374	−	0.801217i	$-0.704186\pi$
$443$	−25.1886	−1.19675	−0.598374	+	0.801217i	$0.704186\pi$
$444$	−0.527093	−0.0250147
$445$	−4.54574	−0.215489
$446$	30.4159	1.44023
$447$	−3.07167	−0.145285
$448$	28.8142	1.36134
$449$	−20.2805	−0.957098	−0.478549	−	0.878061i	$-0.658837\pi$
$449$	−20.2805	−0.957098	−0.478549	+	0.878061i	$0.658837\pi$
$450$	34.2096	1.61266
$451$	−41.1666	−1.93846
$452$	14.7082	0.691818
$453$	−2.94030	−0.138147
$454$	−3.51305	−0.164875
$455$	16.4263	0.770079
$456$	3.46114	0.162083
$457$	5.66568	0.265029	0.132515	−	0.991181i	$-0.457695\pi$
$457$	5.66568	0.265029	0.132515	+	0.991181i	$0.457695\pi$
$458$	−36.1697	−1.69010
$459$	−9.58772	−0.447517
$460$	53.3789	2.48880
$461$	0.221701	0.0103257	0.00516283	−	0.999987i	$-0.498357\pi$
$461$	0.221701	0.0103257	0.00516283	+	0.999987i	$0.498357\pi$
$462$	−6.03853	−0.280938
$463$	−5.44889	−0.253231	−0.126616	−	0.991952i	$-0.540411\pi$
$463$	−5.44889	−0.253231	−0.126616	+	0.991952i	$0.540411\pi$
$464$	0.707612	0.0328501
$465$	2.98537	0.138443
$466$	−51.6858	−2.39430
$467$	−33.3121	−1.54150	−0.770749	−	0.637139i	$-0.780118\pi$
$467$	−33.3121	−1.54150	−0.770749	+	0.637139i	$0.780118\pi$
$468$	−20.9319	−0.967579
$469$	−15.4317	−0.712568
$470$	75.7265	3.49300
$471$	2.07641	0.0956758
$472$	11.8234	0.544215
$473$	−39.9670	−1.83768
$474$	10.5488	0.484522
$475$	−27.2334	−1.24955
$476$	−40.1533	−1.84042
$477$	10.5019	0.480849
$478$	2.90996	0.133099
$479$	35.4717	1.62074	0.810372	−	0.585915i	$-0.199265\pi$
$479$	35.4717	1.62074	0.810372	+	0.585915i	$0.199265\pi$
$480$	−5.60511	−0.255837
$481$	−1.46192	−0.0666577
$482$	−37.2916	−1.69858
$483$	3.28694	0.149561
$484$	26.7676	1.21671
$485$	−20.9723	−0.952305
$486$	−16.0763	−0.729236
$487$	−12.1322	−0.549762	−0.274881	−	0.961478i	$-0.588639\pi$
$487$	−12.1322	−0.549762	−0.274881	+	0.961478i	$0.588639\pi$
$488$	28.7955	1.30351
$489$	2.14453	0.0969790
$490$	−15.2540	−0.689107
$491$	6.85393	0.309314	0.154657	−	0.987968i	$-0.450573\pi$
$491$	6.85393	0.309314	0.154657	+	0.987968i	$0.450573\pi$
$492$	7.78709	0.351069
$493$	−5.91815	−0.266540
$494$	27.5126	1.23785
$495$	−41.4664	−1.86378
$496$	2.42004	0.108663
$497$	−12.3508	−0.554007
$498$	−5.96643	−0.267362
$499$	18.1739	0.813573	0.406787	−	0.913523i	$-0.366649\pi$
$499$	18.1739	0.813573	0.406787	+	0.913523i	$0.366649\pi$
$500$	−1.89119	−0.0845765
$501$	5.95093	0.265868
$502$	59.9630	2.67628
$503$	16.3262	0.727951	0.363975	−	0.931409i	$-0.381419\pi$
$503$	16.3262	0.727951	0.363975	+	0.931409i	$0.381419\pi$
$504$	−15.5956	−0.694681
$505$	−7.55346	−0.336125
$506$	−54.4247	−2.41947
$507$	−2.07076	−0.0919656
$508$	−5.66092	−0.251163
$509$	3.55257	0.157465	0.0787325	−	0.996896i	$-0.474913\pi$
$509$	3.55257	0.157465	0.0787325	+	0.996896i	$0.474913\pi$
$510$	11.6342	0.515173
$511$	12.5377	0.554637
$512$	−7.95974	−0.351774
$513$	8.49623	0.375118
$514$	−9.31812	−0.411005
$515$	−28.1639	−1.24105
$516$	7.56017	0.332818
$517$	−46.7634	−2.05665
$518$	−3.12170	−0.137160
$519$	−1.00524	−0.0441250
$520$	17.9514	0.787222
$521$	−11.1638	−0.489097	−0.244549	−	0.969637i	$-0.578640\pi$
$521$	−11.1638	−0.489097	−0.244549	+	0.969637i	$0.578640\pi$
$522$	−6.58785	−0.288342
$523$	20.5939	0.900508	0.450254	−	0.892901i	$-0.351333\pi$
$523$	20.5939	0.900508	0.450254	+	0.892901i	$0.351333\pi$
$524$	30.2344	1.32080
$525$	−3.13594	−0.136864
$526$	33.0350	1.44040
$527$	−20.2402	−0.881675
$528$	0.859024	0.0373842
$529$	6.62484	0.288036
$530$	−25.8128	−1.12124
$531$	14.3286	0.621810
$532$	35.5821	1.54268
$533$	21.5979	0.935508
$534$	−0.876720	−0.0379394
$535$	−38.6815	−1.67235
$536$	−16.8644	−0.728430
$537$	−3.18267	−0.137342
$538$	−11.0197	−0.475092
$539$	9.41982	0.405740
$540$	15.8881	0.683713
$541$	−36.2744	−1.55956	−0.779780	−	0.626054i	$-0.784669\pi$
$541$	−36.2744	−1.55956	−0.779780	+	0.626054i	$0.784669\pi$
$542$	64.1972	2.75751
$543$	−1.52721	−0.0655390
$544$	38.0014	1.62930
$545$	−55.6916	−2.38556
$546$	3.16809	0.135582
$547$	34.8178	1.48870	0.744351	−	0.667788i	$-0.232759\pi$
$547$	34.8178	1.48870	0.744351	+	0.667788i	$0.232759\pi$
$548$	−22.8742	−0.977136
$549$	34.8971	1.48937
$550$	51.9246	2.21407
$551$	5.24442	0.223420
$552$	3.59211	0.152890
$553$	37.8389	1.60908
$554$	2.25207	0.0956812
$555$	0.547823	0.0232538
$556$	45.9037	1.94675
$557$	13.8356	0.586234	0.293117	−	0.956077i	$-0.405308\pi$
$557$	13.8356	0.586234	0.293117	+	0.956077i	$0.405308\pi$
$558$	−22.5305	−0.953793
$559$	20.9685	0.886874
$560$	−4.98980	−0.210858
$561$	−7.18449	−0.303329
$562$	−63.4049	−2.67457
$563$	−0.694972	−0.0292896	−0.0146448	−	0.999893i	$-0.504662\pi$
$563$	−0.694972	−0.0292896	−0.0146448	+	0.999893i	$0.504662\pi$
$564$	8.84577	0.372474
$565$	−15.2867	−0.643117
$566$	−30.4739	−1.28091
$567$	−18.4048	−0.772928
$568$	−13.4974	−0.566340
$569$	28.1896	1.18177	0.590884	−	0.806756i	$-0.298779\pi$
$569$	28.1896	1.18177	0.590884	+	0.806756i	$0.298779\pi$
$570$	−10.3098	−0.431829
$571$	−21.1622	−0.885612	−0.442806	−	0.896617i	$-0.646017\pi$
$571$	−21.1622	−0.885612	−0.442806	+	0.896617i	$0.646017\pi$
$572$	−31.7712	−1.32842
$573$	1.72056	0.0718774
$574$	46.1190	1.92497
$575$	−28.2639	−1.17869
$576$	38.1617	1.59007
$577$	−22.2523	−0.926377	−0.463188	−	0.886260i	$-0.653295\pi$
$577$	−22.2523	−0.926377	−0.463188	+	0.886260i	$0.653295\pi$
$578$	−40.5925	−1.68843
$579$	0.325126	0.0135118
$580$	9.80712	0.407219
$581$	−21.4018	−0.887897
$582$	−4.04486	−0.167665
$583$	15.9402	0.660174
$584$	13.7018	0.566984
$585$	21.7552	0.899466
$586$	−38.2155	−1.57867
$587$	−29.9228	−1.23505	−0.617523	−	0.786553i	$-0.711864\pi$
$587$	−29.9228	−1.23505	−0.617523	+	0.786553i	$0.711864\pi$
$588$	−1.78186	−0.0734825
$589$	17.9360	0.739039
$590$	−35.2186	−1.44993
$591$	2.39135	0.0983670
$592$	0.444084	0.0182518
$593$	−8.81685	−0.362065	−0.181032	−	0.983477i	$-0.557944\pi$
$593$	−8.81685	−0.362065	−0.181032	+	0.983477i	$0.557944\pi$
$594$	−16.1993	−0.664667
$595$	41.7325	1.71087
$596$	−34.5100	−1.41359
$597$	−7.39300	−0.302575
$598$	28.5537	1.16765
$599$	−3.65333	−0.149271	−0.0746354	−	0.997211i	$-0.523779\pi$
$599$	−3.65333	−0.149271	−0.0746354	+	0.997211i	$0.523779\pi$
$600$	−3.42709	−0.139911
$601$	10.7684	0.439252	0.219626	−	0.975584i	$-0.429516\pi$
$601$	10.7684	0.439252	0.219626	+	0.975584i	$0.429516\pi$
$602$	44.7751	1.82490
$603$	−20.4378	−0.832292
$604$	−33.0341	−1.34414
$605$	−27.8203	−1.13106
$606$	−1.45681	−0.0591788
$607$	−1.07871	−0.0437833	−0.0218917	−	0.999760i	$-0.506969\pi$
$607$	−1.07871	−0.0437833	−0.0218917	+	0.999760i	$0.506969\pi$
$608$	−33.6752	−1.36571
$609$	0.603898	0.0244712
$610$	−85.7740	−3.47289
$611$	24.5342	0.992548
$612$	−53.1793	−2.14964
$613$	36.0575	1.45635	0.728175	−	0.685391i	$-0.240369\pi$
$613$	36.0575	1.45635	0.728175	+	0.685391i	$0.240369\pi$
$614$	−11.9136	−0.480796
$615$	−8.09336	−0.326356
$616$	−23.6715	−0.953751
$617$	−0.704048	−0.0283439	−0.0141720	−	0.999900i	$-0.504511\pi$
$617$	−0.704048	−0.0283439	−0.0141720	+	0.999900i	$0.504511\pi$
$618$	−5.43186	−0.218502
$619$	−9.61979	−0.386652	−0.193326	−	0.981135i	$-0.561928\pi$
$619$	−9.61979	−0.386652	−0.193326	+	0.981135i	$0.561928\pi$
$620$	33.5405	1.34702
$621$	8.81774	0.353844
$622$	16.4951	0.661391
$623$	−3.14483	−0.125995
$624$	−0.450683	−0.0180418
$625$	−23.9986	−0.959945
$626$	53.2662	2.12895
$627$	6.36659	0.254257
$628$	23.3283	0.930902
$629$	−3.71412	−0.148092
$630$	46.4549	1.85081
$631$	−45.7175	−1.81998	−0.909992	−	0.414627i	$-0.863912\pi$
$631$	−45.7175	−1.81998	−0.909992	+	0.414627i	$0.863912\pi$
$632$	41.3520	1.64490
$633$	−4.77528	−0.189800
$634$	24.0696	0.955925
$635$	5.88357	0.233482
$636$	−3.01525	−0.119562
$637$	−4.94207	−0.195812
$638$	−9.99927	−0.395875
$639$	−16.3574	−0.647090
$640$	−52.7976	−2.08701
$641$	−43.2512	−1.70832	−0.854161	−	0.520009i	$-0.825928\pi$
$641$	−43.2512	−1.70832	−0.854161	+	0.520009i	$0.825928\pi$
$642$	−7.46036	−0.294437
$643$	0.555801	0.0219187	0.0109593	−	0.999940i	$-0.496511\pi$
$643$	0.555801	0.0219187	0.0109593	+	0.999940i	$0.496511\pi$
$644$	36.9286	1.45519
$645$	−7.85751	−0.309389
$646$	69.8980	2.75010
$647$	−5.13439	−0.201854	−0.100927	−	0.994894i	$-0.532181\pi$
$647$	−5.13439	−0.201854	−0.100927	+	0.994894i	$0.532181\pi$
$648$	−20.1135	−0.790134
$649$	21.7485	0.853704
$650$	−27.2420	−1.06852
$651$	2.06534	0.0809469
$652$	24.0937	0.943582
$653$	−3.02618	−0.118423	−0.0592117	−	0.998245i	$-0.518859\pi$
$653$	−3.02618	−0.118423	−0.0592117	+	0.998245i	$0.518859\pi$
$654$	−10.7410	−0.420008
$655$	−31.4236	−1.22782
$656$	−6.56075	−0.256154
$657$	16.6051	0.647826
$658$	52.3891	2.04234
$659$	−27.8021	−1.08302	−0.541508	−	0.840695i	$-0.682147\pi$
$659$	−27.8021	−1.08302	−0.541508	+	0.840695i	$0.682147\pi$
$660$	11.9056	0.463425
$661$	41.0337	1.59603	0.798013	−	0.602640i	$-0.205885\pi$
$661$	41.0337	1.59603	0.798013	+	0.602640i	$0.205885\pi$
$662$	−43.0962	−1.67498
$663$	3.76931	0.146388
$664$	−23.3888	−0.907662
$665$	−36.9816	−1.43408
$666$	−4.13441	−0.160205
$667$	5.44287	0.210749
$668$	66.8584	2.58683
$669$	−3.69268	−0.142767
$670$	50.2344	1.94072
$671$	52.9680	2.04481
$672$	−3.87772	−0.149586
$673$	−0.377076	−0.0145352	−0.00726761	−	0.999974i	$-0.502313\pi$
$673$	−0.377076	−0.0145352	−0.00726761	+	0.999974i	$0.502313\pi$
$674$	−40.6454	−1.56560
$675$	−8.41267	−0.323804
$676$	−23.2649	−0.894802
$677$	50.9952	1.95991	0.979953	−	0.199231i	$-0.0638443\pi$
$677$	50.9952	1.95991	0.979953	+	0.199231i	$0.0638443\pi$
$678$	−2.94830	−0.113229
$679$	−14.5091	−0.556807
$680$	45.6071	1.74895
$681$	0.426506	0.0163437
$682$	−34.1976	−1.30949
$683$	−9.75605	−0.373305	−0.186652	−	0.982426i	$-0.559764\pi$
$683$	−9.75605	−0.373305	−0.186652	+	0.982426i	$0.559764\pi$
$684$	47.1252	1.80188
$685$	23.7738	0.908351
$686$	−45.3723	−1.73232
$687$	4.39124	0.167536
$688$	−6.36957	−0.242837
$689$	−8.36294	−0.318603
$690$	−10.6999	−0.407338
$691$	−12.1987	−0.464062	−0.232031	−	0.972708i	$-0.574537\pi$
$691$	−12.1987	−0.464062	−0.232031	+	0.972708i	$0.574537\pi$
$692$	−11.2938	−0.429325
$693$	−28.6873	−1.08974
$694$	63.2307	2.40021
$695$	−47.7091	−1.80971
$696$	0.659965	0.0250159
$697$	54.8712	2.07839
$698$	53.3442	2.01911
$699$	6.27499	0.237342
$700$	−35.2322	−1.33165
$701$	33.1007	1.25020	0.625099	−	0.780545i	$-0.285059\pi$
$701$	33.1007	1.25020	0.625099	+	0.780545i	$0.285059\pi$
$702$	8.49892	0.320771
$703$	3.29130	0.124134
$704$	57.9232	2.18306
$705$	−9.19368	−0.346254
$706$	10.9300	0.411358
$707$	−5.22563	−0.196530
$708$	−4.11396	−0.154612
$709$	35.2441	1.32362	0.661810	−	0.749672i	$-0.269789\pi$
$709$	35.2441	1.32362	0.661810	+	0.749672i	$0.269789\pi$
$710$	40.2052	1.50887
$711$	50.1142	1.87943
$712$	−3.43681	−0.128800
$713$	18.6147	0.697125
$714$	8.04880	0.301219
$715$	33.0208	1.23491
$716$	−35.7571	−1.33631
$717$	−0.353288	−0.0131938
$718$	−43.1244	−1.60939
$719$	−0.986714	−0.0367982	−0.0183991	−	0.999831i	$-0.505857\pi$
$719$	−0.986714	−0.0367982	−0.0183991	+	0.999831i	$0.505857\pi$
$720$	−6.60853	−0.246286
$721$	−19.4843	−0.725633
$722$	−19.1514	−0.712742
$723$	4.52743	0.168377
$724$	−17.1582	−0.637678
$725$	−5.19284	−0.192857
$726$	−5.36561	−0.199136
$727$	−50.5488	−1.87475	−0.937375	−	0.348323i	$-0.886751\pi$
$727$	−50.5488	−1.87475	−0.937375	+	0.348323i	$0.886751\pi$
$728$	12.4191	0.460284
$729$	−23.0466	−0.853577
$730$	−40.8139	−1.51059
$731$	53.2722	1.97034
$732$	−10.0194	−0.370329
$733$	14.6374	0.540643	0.270322	−	0.962770i	$-0.412870\pi$
$733$	14.6374	0.540643	0.270322	+	0.962770i	$0.412870\pi$
$734$	−4.79029	−0.176813
$735$	1.85194	0.0683097
$736$	−34.9495	−1.28826
$737$	−31.0212	−1.14268
$738$	61.0804	2.24840
$739$	8.25419	0.303635	0.151818	−	0.988409i	$-0.451487\pi$
$739$	8.25419	0.303635	0.151818	+	0.988409i	$0.451487\pi$
$740$	6.15477	0.226254
$741$	−3.34021	−0.122706
$742$	−17.8578	−0.655580
$743$	−18.3830	−0.674408	−0.337204	−	0.941432i	$-0.609481\pi$
$743$	−18.3830	−0.674408	−0.337204	+	0.941432i	$0.609481\pi$
$744$	2.25709	0.0827489
$745$	35.8673	1.31408
$746$	64.7606	2.37105
$747$	−28.3447	−1.03708
$748$	−80.7174	−2.95132
$749$	−26.7606	−0.977811
$750$	0.379092	0.0138425
$751$	−51.4914	−1.87895	−0.939473	−	0.342623i	$-0.888685\pi$
$751$	−51.4914	−1.87895	−0.939473	+	0.342623i	$0.888685\pi$
$752$	−7.45271	−0.271772
$753$	−7.27989	−0.265294
$754$	5.24607	0.191051
$755$	34.3334	1.24952
$756$	10.9917	0.399763
$757$	45.7418	1.66251	0.831257	−	0.555889i	$-0.187622\pi$
$757$	45.7418	1.66251	0.831257	+	0.555889i	$0.187622\pi$
$758$	15.1529	0.550379
$759$	6.60751	0.239837
$760$	−40.4151	−1.46601
$761$	−17.8125	−0.645704	−0.322852	−	0.946449i	$-0.604642\pi$
$761$	−17.8125	−0.645704	−0.322852	+	0.946449i	$0.604642\pi$
$762$	1.13474	0.0411074
$763$	−38.5285	−1.39483
$764$	19.3304	0.699349
$765$	55.2708	1.99832
$766$	41.8591	1.51243
$767$	−11.4103	−0.412001
$768$	−3.04912	−0.110026
$769$	−43.8750	−1.58217	−0.791087	−	0.611703i	$-0.790485\pi$
$769$	−43.8750	−1.58217	−0.791087	+	0.611703i	$0.790485\pi$
$770$	70.5109	2.54104
$771$	1.13128	0.0407420
$772$	3.65277	0.131466
$773$	5.87130	0.211176	0.105588	−	0.994410i	$-0.466328\pi$
$773$	5.87130	0.211176	0.105588	+	0.994410i	$0.466328\pi$
$774$	59.3005	2.13151
$775$	−17.7596	−0.637943
$776$	−15.8561	−0.569202
$777$	0.378995	0.0135964
$778$	−10.5373	−0.377782
$779$	−48.6245	−1.74215
$780$	−6.24622	−0.223651
$781$	−24.8279	−0.888412
$782$	72.5430	2.59413
$783$	1.62005	0.0578960
$784$	1.50124	0.0536158
$785$	−24.2458	−0.865371
$786$	−6.06055	−0.216173
$787$	43.4240	1.54790	0.773950	−	0.633247i	$-0.218278\pi$
$787$	43.4240	1.54790	0.773950	+	0.633247i	$0.218278\pi$
$788$	26.8667	0.957087
$789$	−4.01066	−0.142783
$790$	−123.176	−4.38242
$791$	−10.5757	−0.376027
$792$	−31.3507	−1.11400
$793$	−27.7894	−0.986832
$794$	−45.6602	−1.62042
$795$	3.13384	0.111146
$796$	−83.0600	−2.94398
$797$	−3.29243	−0.116624	−0.0583119	−	0.998298i	$-0.518572\pi$
$797$	−3.29243	−0.116624	−0.0583119	+	0.998298i	$0.518572\pi$
$798$	−7.13250	−0.252488
$799$	62.3312	2.20512
$800$	33.3440	1.17889
$801$	−4.16504	−0.147164
$802$	50.6621	1.78894
$803$	25.2038	0.889422
$804$	5.86798	0.206948
$805$	−38.3810	−1.35275
$806$	17.9416	0.631967
$807$	1.33786	0.0470948
$808$	−5.71080	−0.200905
$809$	−41.7746	−1.46872	−0.734359	−	0.678761i	$-0.762517\pi$
$809$	−41.7746	−1.46872	−0.734359	+	0.678761i	$0.762517\pi$
$810$	59.9127	2.10512
$811$	36.3579	1.27670	0.638350	−	0.769746i	$-0.279617\pi$
$811$	36.3579	1.27670	0.638350	+	0.769746i	$0.279617\pi$
$812$	6.78476	0.238098
$813$	−7.79395	−0.273346
$814$	−6.27535	−0.219951
$815$	−25.0413	−0.877159
$816$	−1.14500	−0.0400829
$817$	−47.2076	−1.65158
$818$	−71.3730	−2.49550
$819$	15.0507	0.525913
$820$	−90.9284	−3.17536
$821$	−11.2928	−0.394122	−0.197061	−	0.980391i	$-0.563140\pi$
$821$	−11.2928	−0.394122	−0.197061	+	0.980391i	$0.563140\pi$
$822$	4.58517	0.159926
$823$	−36.1932	−1.26162	−0.630808	−	0.775939i	$-0.717276\pi$
$823$	−36.1932	−1.26162	−0.630808	+	0.775939i	$0.717276\pi$
$824$	−21.2933	−0.741787
$825$	−6.30397	−0.219476
$826$	−24.3649	−0.847764
$827$	21.6346	0.752310	0.376155	−	0.926557i	$-0.377246\pi$
$827$	21.6346	0.752310	0.376155	+	0.926557i	$0.377246\pi$
$828$	48.9085	1.69969
$829$	−6.84417	−0.237708	−0.118854	−	0.992912i	$-0.537922\pi$
$829$	−6.84417	−0.237708	−0.118854	+	0.992912i	$0.537922\pi$
$830$	69.6689	2.41824
$831$	−0.273415	−0.00948467
$832$	−30.3892	−1.05356
$833$	−12.5557	−0.435030
$834$	−9.20149	−0.318622
$835$	−69.4880	−2.40473
$836$	71.5283	2.47386
$837$	5.54060	0.191511
$838$	−52.3065	−1.80690
$839$	6.68708	0.230863	0.115432	−	0.993315i	$-0.463175\pi$
$839$	6.68708	0.230863	0.115432	+	0.993315i	$0.463175\pi$
$840$	−4.65382	−0.160572
$841$	1.00000	0.0344828
$842$	84.8451	2.92396
$843$	7.69776	0.265125
$844$	−53.6501	−1.84671
$845$	24.1799	0.831813
$846$	69.3845	2.38549
$847$	−19.2467	−0.661323
$848$	2.54040	0.0872375
$849$	3.69972	0.126974
$850$	−69.2106	−2.37390
$851$	3.41584	0.117094
$852$	4.69645	0.160898
$853$	18.0397	0.617667	0.308834	−	0.951116i	$-0.400061\pi$
$853$	18.0397	0.617667	0.308834	+	0.951116i	$0.400061\pi$
$854$	−59.3402	−2.03058
$855$	−48.9787	−1.67504
$856$	−29.2451	−0.999578
$857$	34.4745	1.17763	0.588813	−	0.808269i	$-0.299595\pi$
$857$	34.4745	1.17763	0.588813	+	0.808269i	$0.299595\pi$
$858$	6.36860	0.217421
$859$	−17.4891	−0.596719	−0.298359	−	0.954454i	$-0.596439\pi$
$859$	−17.4891	−0.596719	−0.298359	+	0.954454i	$0.596439\pi$
$860$	−88.2787	−3.01028
$861$	−5.59914	−0.190818
$862$	−70.1638	−2.38979
$863$	−24.1929	−0.823537	−0.411769	−	0.911288i	$-0.635089\pi$
$863$	−24.1929	−0.823537	−0.411769	+	0.911288i	$0.635089\pi$
$864$	−10.4026	−0.353904
$865$	11.7380	0.399103
$866$	−22.3272	−0.758710
$867$	4.92819	0.167370
$868$	23.2040	0.787594
$869$	76.0651	2.58033
$870$	−1.96586	−0.0666488
$871$	16.2752	0.551463
$872$	−42.1056	−1.42588
$873$	−19.2159	−0.650361
$874$	−64.2846	−2.17446
$875$	1.35982	0.0459703
$876$	−4.76756	−0.161081
$877$	−3.75455	−0.126782	−0.0633911	−	0.997989i	$-0.520192\pi$
$877$	−3.75455	−0.126782	−0.0633911	+	0.997989i	$0.520192\pi$
$878$	−28.1140	−0.948801
$879$	4.63961	0.156490
$880$	−10.0307	−0.338134
$881$	−24.2711	−0.817713	−0.408857	−	0.912599i	$-0.634072\pi$
$881$	−24.2711	−0.817713	−0.408857	+	0.912599i	$0.634072\pi$
$882$	−13.9765	−0.470614
$883$	−27.1397	−0.913323	−0.456661	−	0.889641i	$-0.650955\pi$
$883$	−27.1397	−0.913323	−0.456661	+	0.889641i	$0.650955\pi$
$884$	42.3480	1.42432
$885$	4.27576	0.143728
$886$	56.7265	1.90576
$887$	−0.799445	−0.0268427	−0.0134214	−	0.999910i	$-0.504272\pi$
$887$	−0.799445	−0.0268427	−0.0134214	+	0.999910i	$0.504272\pi$
$888$	0.414182	0.0138990
$889$	4.07037	0.136516
$890$	10.2373	0.343155
$891$	−36.9979	−1.23948
$892$	−41.4871	−1.38909
$893$	−55.2352	−1.84838
$894$	6.91760	0.231359
$895$	37.1634	1.24224
$896$	−36.5264	−1.22026
$897$	−3.46660	−0.115746
$898$	45.6732	1.52413
$899$	3.42001	0.114064
$900$	−46.6617	−1.55539
$901$	−21.2467	−0.707831
$902$	92.7099	3.08690
$903$	−5.43598	−0.180898
$904$	−11.5575	−0.384398
$905$	17.8330	0.592789
$906$	6.62175	0.219993
$907$	9.31371	0.309257	0.154628	−	0.987973i	$-0.450582\pi$
$907$	9.31371	0.309257	0.154628	+	0.987973i	$0.450582\pi$
$908$	4.79177	0.159021
$909$	−6.92087	−0.229551
$910$	−36.9932	−1.22631
$911$	−39.1149	−1.29593	−0.647967	−	0.761669i	$-0.724380\pi$
$911$	−39.1149	−1.29593	−0.647967	+	0.761669i	$0.724380\pi$
$912$	1.01465	0.0335984
$913$	−43.0226	−1.42384
$914$	−12.7595	−0.422046
$915$	10.4135	0.344260
$916$	49.3353	1.63008
$917$	−21.7394	−0.717899
$918$	21.5922	0.712649
$919$	30.0485	0.991209	0.495604	−	0.868548i	$-0.334947\pi$
$919$	30.0485	0.991209	0.495604	+	0.868548i	$0.334947\pi$
$920$	−41.9444	−1.38287
$921$	1.44639	0.0476603
$922$	−0.499286	−0.0164431
$923$	13.0259	0.428751
$924$	8.23653	0.270962
$925$	−3.25893	−0.107153
$926$	12.2713	0.403259
$927$	−25.8052	−0.847553
$928$	−6.42116	−0.210785
$929$	32.8023	1.07621	0.538104	−	0.842878i	$-0.319141\pi$
$929$	32.8023	1.07621	0.538104	+	0.842878i	$0.319141\pi$
$930$	−6.72325	−0.220464
$931$	11.1264	0.364652
$932$	70.4992	2.30928
$933$	−2.00260	−0.0655623
$934$	75.0210	2.45476
$935$	83.8920	2.74356
$936$	16.4480	0.537620
$937$	19.3705	0.632806	0.316403	−	0.948625i	$-0.397525\pi$
$937$	19.3705	0.632806	0.316403	+	0.948625i	$0.397525\pi$
$938$	34.7531	1.13473
$939$	−6.46686	−0.211038
$940$	−103.291	−3.36897
$941$	15.8162	0.515595	0.257797	−	0.966199i	$-0.417003\pi$
$941$	15.8162	0.515595	0.257797	+	0.966199i	$0.417003\pi$
$942$	−4.67621	−0.152359
$943$	−50.4645	−1.64335
$944$	3.46608	0.112811
$945$	−11.4240	−0.371622
$946$	90.0083	2.92642
$947$	−0.347164	−0.0112813	−0.00564066	−	0.999984i	$-0.501795\pi$
$947$	−0.347164	−0.0112813	−0.00564066	+	0.999984i	$0.501795\pi$
$948$	−14.3885	−0.467317
$949$	−13.2231	−0.429239
$950$	61.3315	1.98986
$951$	−2.92220	−0.0947588
$952$	31.5519	1.02260
$953$	−13.4946	−0.437132	−0.218566	−	0.975822i	$-0.570138\pi$
$953$	−13.4946	−0.437132	−0.218566	+	0.975822i	$0.570138\pi$
$954$	−23.6510	−0.765729
$955$	−20.0907	−0.650119
$956$	−3.96918	−0.128372
$957$	1.21397	0.0392422
$958$	−79.8847	−2.58096
$959$	16.4472	0.531108
$960$	11.3877	0.367537
$961$	−19.3035	−0.622694
$962$	3.29234	0.106149
$963$	−35.4419	−1.14210
$964$	50.8655	1.63827
$965$	−3.79644	−0.122212
$966$	−7.40240	−0.238168
$967$	−15.2617	−0.490783	−0.245391	−	0.969424i	$-0.578916\pi$
$967$	−15.2617	−0.490783	−0.245391	+	0.969424i	$0.578916\pi$
$968$	−21.0336	−0.676045
$969$	−8.48607	−0.272612
$970$	47.2311	1.51650
$971$	17.4516	0.560048	0.280024	−	0.959993i	$-0.409658\pi$
$971$	17.4516	0.560048	0.280024	+	0.959993i	$0.409658\pi$
$972$	21.9280	0.703341
$973$	−33.0061	−1.05813
$974$	27.3225	0.875470
$975$	3.30735	0.105920
$976$	8.44155	0.270207
$977$	−56.9356	−1.82153	−0.910766	−	0.412923i	$-0.864508\pi$
$977$	−56.9356	−1.82153	−0.910766	+	0.412923i	$0.864508\pi$
$978$	−4.82963	−0.154434
$979$	−6.32184	−0.202047
$980$	20.8064	0.664636
$981$	−51.0275	−1.62918
$982$	−15.4355	−0.492567
$983$	−15.0546	−0.480168	−0.240084	−	0.970752i	$-0.577175\pi$
$983$	−15.0546	−0.480168	−0.240084	+	0.970752i	$0.577175\pi$
$984$	−6.11898	−0.195066
$985$	−27.9234	−0.889713
$986$	13.3281	0.424453
$987$	−6.36037	−0.202453
$988$	−37.5271	−1.19389
$989$	−48.9940	−1.55792
$990$	93.3852	2.96798
$991$	−47.3897	−1.50538	−0.752692	−	0.658373i	$-0.771245\pi$
$991$	−47.3897	−1.50538	−0.752692	+	0.658373i	$0.771245\pi$
$992$	−21.9604	−0.697245
$993$	5.23215	0.166037
$994$	27.8147	0.882230
$995$	86.3267	2.73674
$996$	8.13817	0.257868
$997$	30.0347	0.951208	0.475604	−	0.879660i	$-0.342230\pi$
$997$	30.0347	0.951208	0.475604	+	0.879660i	$0.342230\pi$
$998$	−40.9287	−1.29558
$999$	1.01671	0.0321674

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8033.2.a.b.1.18	✓	153

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8033.2.a.b.1.18	✓	153	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:	\( N \)	\(=\)	\( 8033 = 29 \cdot 277 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.25207 q^{2} +0.273415 q^{3} +3.07181 q^{4} -3.19262 q^{5} -0.615750 q^{6} -2.20872 q^{7} -2.41378 q^{8} -2.92524 q^{9} +O(q^{10})\)	\(q-2.25207 q^{2} +0.273415 q^{3} +3.07181 q^{4} -3.19262 q^{5} -0.615750 q^{6} -2.20872 q^{7} -2.41378 q^{8} -2.92524 q^{9} +7.19000 q^{10} -4.44004 q^{11} +0.839879 q^{12} +2.32945 q^{13} +4.97418 q^{14} -0.872912 q^{15} -0.707612 q^{16} +5.91815 q^{17} +6.58785 q^{18} -5.24442 q^{19} -9.80712 q^{20} -0.603898 q^{21} +9.99927 q^{22} -5.44287 q^{23} -0.659965 q^{24} +5.19284 q^{25} -5.24607 q^{26} -1.62005 q^{27} -6.78476 q^{28} -1.00000 q^{29} +1.96586 q^{30} -3.42001 q^{31} +6.42116 q^{32} -1.21397 q^{33} -13.3281 q^{34} +7.05161 q^{35} -8.98579 q^{36} -0.627581 q^{37} +11.8108 q^{38} +0.636907 q^{39} +7.70630 q^{40} +9.27167 q^{41} +1.36002 q^{42} +9.00149 q^{43} -13.6389 q^{44} +9.33920 q^{45} +12.2577 q^{46} +10.5322 q^{47} -0.193472 q^{48} -2.12156 q^{49} -11.6946 q^{50} +1.61811 q^{51} +7.15562 q^{52} -3.59009 q^{53} +3.64847 q^{54} +14.1754 q^{55} +5.33137 q^{56} -1.43390 q^{57} +2.25207 q^{58} -4.89827 q^{59} -2.68142 q^{60} -11.9296 q^{61} +7.70210 q^{62} +6.46104 q^{63} -13.0457 q^{64} -7.43705 q^{65} +2.73395 q^{66} +6.98670 q^{67} +18.1794 q^{68} -1.48816 q^{69} -15.8807 q^{70} +5.59182 q^{71} +7.06091 q^{72} -5.67648 q^{73} +1.41336 q^{74} +1.41980 q^{75} -16.1098 q^{76} +9.80680 q^{77} -1.43436 q^{78} -17.1316 q^{79} +2.25914 q^{80} +8.33278 q^{81} -20.8804 q^{82} +9.68969 q^{83} -1.85506 q^{84} -18.8944 q^{85} -20.2720 q^{86} -0.273415 q^{87} +10.7173 q^{88} +1.42383 q^{89} -21.0325 q^{90} -5.14510 q^{91} -16.7195 q^{92} -0.935084 q^{93} -23.7192 q^{94} +16.7434 q^{95} +1.75564 q^{96} +6.56900 q^{97} +4.77790 q^{98} +12.9882 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 153 q - 3 q^{2} - 12 q^{3} + 135 q^{4} - 11 q^{5} - 17 q^{6} - 76 q^{7} - 12 q^{8} + 133 q^{9}+O(q^{10}) \) 153 * q - 3 * q^2 - 12 * q^3 + 135 * q^4 - 11 * q^5 - 17 * q^6 - 76 * q^7 - 12 * q^8 + 133 * q^9	\( 153 q - 3 q^{2} - 12 q^{3} + 135 q^{4} - 11 q^{5} - 17 q^{6} - 76 q^{7} - 12 q^{8} + 133 q^{9} - 30 q^{10} + 4 q^{11} - 39 q^{12} - 65 q^{13} + q^{14} - 26 q^{15} + 107 q^{16} - 20 q^{17} - 21 q^{18} - 65 q^{19} - 23 q^{20} - 24 q^{21} - 59 q^{22} - 62 q^{23} - 59 q^{24} + 102 q^{25} - 18 q^{26} - 57 q^{27} - 155 q^{28} - 153 q^{29} - 82 q^{30} - 49 q^{31} - 17 q^{32} - 59 q^{33} - 68 q^{34} - 36 q^{35} + 74 q^{36} - 30 q^{37} - 67 q^{38} - 47 q^{39} - 108 q^{40} - 9 q^{41} - 62 q^{42} - 90 q^{43} - 14 q^{44} - 56 q^{45} - 52 q^{46} - 54 q^{47} - 76 q^{48} + 101 q^{49} - 36 q^{50} - 60 q^{51} - 191 q^{52} - 38 q^{53} - 82 q^{54} - 215 q^{55} + 24 q^{56} - 52 q^{57} + 3 q^{58} - 55 q^{59} - 60 q^{60} - 90 q^{61} - 66 q^{62} - 229 q^{63} + 52 q^{64} - 67 q^{65} - 29 q^{66} - 114 q^{67} - 78 q^{68} - 68 q^{69} - 61 q^{70} - 52 q^{71} - 47 q^{72} - 83 q^{73} - 21 q^{74} - 47 q^{75} - 100 q^{76} - 32 q^{77} - 17 q^{78} - 151 q^{79} - 24 q^{80} + 81 q^{81} - 151 q^{82} - 94 q^{83} - 84 q^{84} - 77 q^{85} - 43 q^{86} + 12 q^{87} - 121 q^{88} + 11 q^{89} - 14 q^{90} - 66 q^{91} - 156 q^{92} - 66 q^{93} - 22 q^{94} - 67 q^{95} - 131 q^{96} - 78 q^{97} - 67 q^{98} - 41 q^{99}+O(q^{100}) \) 153 * q - 3 * q^2 - 12 * q^3 + 135 * q^4 - 11 * q^5 - 17 * q^6 - 76 * q^7 - 12 * q^8 + 133 * q^9 - 30 * q^10 + 4 * q^11 - 39 * q^12 - 65 * q^13 + q^14 - 26 * q^15 + 107 * q^16 - 20 * q^17 - 21 * q^18 - 65 * q^19 - 23 * q^20 - 24 * q^21 - 59 * q^22 - 62 * q^23 - 59 * q^24 + 102 * q^25 - 18 * q^26 - 57 * q^27 - 155 * q^28 - 153 * q^29 - 82 * q^30 - 49 * q^31 - 17 * q^32 - 59 * q^33 - 68 * q^34 - 36 * q^35 + 74 * q^36 - 30 * q^37 - 67 * q^38 - 47 * q^39 - 108 * q^40 - 9 * q^41 - 62 * q^42 - 90 * q^43 - 14 * q^44 - 56 * q^45 - 52 * q^46 - 54 * q^47 - 76 * q^48 + 101 * q^49 - 36 * q^50 - 60 * q^51 - 191 * q^52 - 38 * q^53 - 82 * q^54 - 215 * q^55 + 24 * q^56 - 52 * q^57 + 3 * q^58 - 55 * q^59 - 60 * q^60 - 90 * q^61 - 66 * q^62 - 229 * q^63 + 52 * q^64 - 67 * q^65 - 29 * q^66 - 114 * q^67 - 78 * q^68 - 68 * q^69 - 61 * q^70 - 52 * q^71 - 47 * q^72 - 83 * q^73 - 21 * q^74 - 47 * q^75 - 100 * q^76 - 32 * q^77 - 17 * q^78 - 151 * q^79 - 24 * q^80 + 81 * q^81 - 151 * q^82 - 94 * q^83 - 84 * q^84 - 77 * q^85 - 43 * q^86 + 12 * q^87 - 121 * q^88 + 11 * q^89 - 14 * q^90 - 66 * q^91 - 156 * q^92 - 66 * q^93 - 22 * q^94 - 67 * q^95 - 131 * q^96 - 78 * q^97 - 67 * q^98 - 41 * q^99

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