LMFDB - Embedded newform 83.2.a.b.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [83,2,Mod(1,83)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(83, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("83.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 83 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	83.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:	$0.662758336777$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.9059636.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 8x^{4} + 11x^{3} + 4x^{2} - 4x - 1 $ x^6 - x^5 - 8x^4 + 11x^3 + 4x^2 - 4x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.537266$ of defining polynomial
Character	$\chi$	$=$	83.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.62359 q^{2} -1.49589 q^{3} +4.88322 q^{4} -3.47366 q^{5} -3.92460 q^{6} -1.39854 q^{7} +7.56440 q^{8} -0.762314 q^{9} +O(q^{10})$	\(q+2.62359 q^{2} -1.49589 q^{3} +4.88322 q^{4} -3.47366 q^{5} -3.92460 q^{6} -1.39854 q^{7} +7.56440 q^{8} -0.762314 q^{9} -9.11346 q^{10} +1.06333 q^{11} -7.30477 q^{12} +6.94081 q^{13} -3.66920 q^{14} +5.19621 q^{15} +10.0794 q^{16} -1.62502 q^{17} -2.00000 q^{18} -2.37554 q^{19} -16.9627 q^{20} +2.09206 q^{21} +2.78973 q^{22} -5.23023 q^{23} -11.3155 q^{24} +7.06631 q^{25} +18.2098 q^{26} +5.62801 q^{27} -6.82939 q^{28} +1.37575 q^{29} +13.6327 q^{30} -2.98057 q^{31} +11.3155 q^{32} -1.59062 q^{33} -4.26339 q^{34} +4.85806 q^{35} -3.72255 q^{36} +5.84507 q^{37} -6.23245 q^{38} -10.3827 q^{39} -26.2762 q^{40} +2.13212 q^{41} +5.48872 q^{42} -6.24182 q^{43} +5.19246 q^{44} +2.64802 q^{45} -13.7220 q^{46} +1.67158 q^{47} -15.0777 q^{48} -5.04408 q^{49} +18.5391 q^{50} +2.43085 q^{51} +33.8935 q^{52} +3.44474 q^{53} +14.7656 q^{54} -3.69363 q^{55} -10.5791 q^{56} +3.55355 q^{57} +3.60940 q^{58} -14.2631 q^{59} +25.3743 q^{60} +6.40582 q^{61} -7.81980 q^{62} +1.06613 q^{63} +9.52838 q^{64} -24.1100 q^{65} -4.17313 q^{66} +6.41293 q^{67} -7.93534 q^{68} +7.82385 q^{69} +12.7456 q^{70} +2.29930 q^{71} -5.76645 q^{72} +11.6934 q^{73} +15.3351 q^{74} -10.5704 q^{75} -11.6003 q^{76} -1.48710 q^{77} -27.2399 q^{78} -10.7208 q^{79} -35.0125 q^{80} -6.13193 q^{81} +5.59380 q^{82} +1.00000 q^{83} +10.2160 q^{84} +5.64477 q^{85} -16.3760 q^{86} -2.05797 q^{87} +8.04342 q^{88} -13.6752 q^{89} +6.94732 q^{90} -9.70701 q^{91} -25.5404 q^{92} +4.45861 q^{93} +4.38555 q^{94} +8.25183 q^{95} -16.9268 q^{96} -3.25565 q^{97} -13.2336 q^{98} -0.810588 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} + q^{3} + 7 q^{4} + 2 q^{5} - 7 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 6 * q + q^2 + q^3 + 7 * q^4 + 2 * q^5 - 7 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9	\( 6 q + q^{2} + q^{3} + 7 q^{4} + 2 q^{5} - 7 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9} - 6 q^{10} - 3 q^{11} - 9 q^{12} + 14 q^{13} - 15 q^{14} - 6 q^{15} + q^{16} - 5 q^{17} - 12 q^{18} - 4 q^{19} - 20 q^{20} - 2 q^{21} - q^{22} - 5 q^{23} - 17 q^{24} + 14 q^{25} - 2 q^{26} + 10 q^{27} + 9 q^{28} - q^{29} + 18 q^{30} + 3 q^{31} + 17 q^{32} + 2 q^{33} + 15 q^{34} - 10 q^{35} - 8 q^{36} + 39 q^{37} - 6 q^{38} - 8 q^{39} - 18 q^{40} - q^{41} + 17 q^{42} - 8 q^{43} + 27 q^{44} + 10 q^{45} - 12 q^{46} - 12 q^{47} + 7 q^{48} + 11 q^{49} + 35 q^{50} - 24 q^{51} + 36 q^{52} + 14 q^{53} + 19 q^{54} - 24 q^{55} - 23 q^{56} - 10 q^{57} + 25 q^{58} - 17 q^{59} - 5 q^{61} + 5 q^{62} - 11 q^{63} + 9 q^{64} - 8 q^{65} - 39 q^{66} + 16 q^{67} - 15 q^{68} + 8 q^{69} - 10 q^{70} - 26 q^{71} + 10 q^{72} - 6 q^{73} + 23 q^{74} - 45 q^{75} - 28 q^{76} + 6 q^{77} - 18 q^{78} - 12 q^{79} - 60 q^{80} - 34 q^{81} + 10 q^{82} + 6 q^{83} + 41 q^{84} + 18 q^{85} + 16 q^{86} - 3 q^{87} - 17 q^{88} - 22 q^{89} - 4 q^{90} - 2 q^{91} + 2 q^{92} + 34 q^{93} - 8 q^{94} - 4 q^{95} - 19 q^{96} + 6 q^{97} - 30 q^{98} - 18 q^{99}+O(q^{100}) \) 6 * q + q^2 + q^3 + 7 * q^4 + 2 * q^5 - 7 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9 - 6 * q^10 - 3 * q^11 - 9 * q^12 + 14 * q^13 - 15 * q^14 - 6 * q^15 + q^16 - 5 * q^17 - 12 * q^18 - 4 * q^19 - 20 * q^20 - 2 * q^21 - q^22 - 5 * q^23 - 17 * q^24 + 14 * q^25 - 2 * q^26 + 10 * q^27 + 9 * q^28 - q^29 + 18 * q^30 + 3 * q^31 + 17 * q^32 + 2 * q^33 + 15 * q^34 - 10 * q^35 - 8 * q^36 + 39 * q^37 - 6 * q^38 - 8 * q^39 - 18 * q^40 - q^41 + 17 * q^42 - 8 * q^43 + 27 * q^44 + 10 * q^45 - 12 * q^46 - 12 * q^47 + 7 * q^48 + 11 * q^49 + 35 * q^50 - 24 * q^51 + 36 * q^52 + 14 * q^53 + 19 * q^54 - 24 * q^55 - 23 * q^56 - 10 * q^57 + 25 * q^58 - 17 * q^59 - 5 * q^61 + 5 * q^62 - 11 * q^63 + 9 * q^64 - 8 * q^65 - 39 * q^66 + 16 * q^67 - 15 * q^68 + 8 * q^69 - 10 * q^70 - 26 * q^71 + 10 * q^72 - 6 * q^73 + 23 * q^74 - 45 * q^75 - 28 * q^76 + 6 * q^77 - 18 * q^78 - 12 * q^79 - 60 * q^80 - 34 * q^81 + 10 * q^82 + 6 * q^83 + 41 * q^84 + 18 * q^85 + 16 * q^86 - 3 * q^87 - 17 * q^88 - 22 * q^89 - 4 * q^90 - 2 * q^91 + 2 * q^92 + 34 * q^93 - 8 * q^94 - 4 * q^95 - 19 * q^96 + 6 * q^97 - 30 * q^98 - 18 * 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 $

$2$	2.62359	1.85516	0.927579	−	0.373627i	$-0.121886\pi$
$2$	2.62359	1.85516	0.927579	+	0.373627i	$0.121886\pi$
$3$	−1.49589	−0.863652	−0.431826	−	0.901957i	$-0.642131\pi$
$3$	−1.49589	−0.863652	−0.431826	+	0.901957i	$0.642131\pi$
$4$	4.88322	2.44161
$5$	−3.47366	−1.55347	−0.776734	−	0.629829i	$-0.783125\pi$
$5$	−3.47366	−1.55347	−0.776734	+	0.629829i	$0.783125\pi$
$6$	−3.92460	−1.60221
$7$	−1.39854	−0.528599	−0.264300	−	0.964441i	$-0.585141\pi$
$7$	−1.39854	−0.528599	−0.264300	+	0.964441i	$0.585141\pi$
$8$	7.56440	2.67442
$9$	−0.762314	−0.254105
$10$	−9.11346	−2.88193
$11$	1.06333	0.320605	0.160302	−	0.987068i	$-0.448753\pi$
$11$	1.06333	0.320605	0.160302	+	0.987068i	$0.448753\pi$
$12$	−7.30477	−2.10870
$13$	6.94081	1.92503	0.962517	−	0.271221i	$-0.0874273\pi$
$13$	6.94081	1.92503	0.962517	+	0.271221i	$0.0874273\pi$
$14$	−3.66920	−0.980635
$15$	5.19621	1.34166
$16$	10.0794	2.51986
$17$	−1.62502	−0.394126	−0.197063	−	0.980391i	$-0.563140\pi$
$17$	−1.62502	−0.394126	−0.197063	+	0.980391i	$0.563140\pi$
$18$	−2.00000	−0.471405
$19$	−2.37554	−0.544987	−0.272493	−	0.962158i	$-0.587848\pi$
$19$	−2.37554	−0.544987	−0.272493	+	0.962158i	$0.587848\pi$
$20$	−16.9627	−3.79297
$21$	2.09206	0.456526
$22$	2.78973	0.594772
$23$	−5.23023	−1.09058	−0.545290	−	0.838248i	$-0.683580\pi$
$23$	−5.23023	−1.09058	−0.545290	+	0.838248i	$0.683580\pi$
$24$	−11.3155	−2.30977
$25$	7.06631	1.41326
$26$	18.2098	3.57124
$27$	5.62801	1.08311
$28$	−6.82939	−1.29063
$29$	1.37575	0.255470	0.127735	−	0.991808i	$-0.459229\pi$
$29$	1.37575	0.255470	0.127735	+	0.991808i	$0.459229\pi$
$30$	13.6327	2.48898
$31$	−2.98057	−0.535327	−0.267663	−	0.963512i	$-0.586251\pi$
$31$	−2.98057	−0.535327	−0.267663	+	0.963512i	$0.586251\pi$
$32$	11.3155	2.00032
$33$	−1.59062	−0.276891
$34$	−4.26339	−0.731165
$35$	4.85806	0.821162
$36$	−3.72255	−0.620425
$37$	5.84507	0.960923	0.480462	−	0.877016i	$-0.340469\pi$
$37$	5.84507	0.960923	0.480462	+	0.877016i	$0.340469\pi$
$38$	−6.23245	−1.01104
$39$	−10.3827	−1.66256
$40$	−26.2762	−4.15462
$41$	2.13212	0.332981	0.166490	−	0.986043i	$-0.446757\pi$
$41$	2.13212	0.332981	0.166490	+	0.986043i	$0.446757\pi$
$42$	5.48872	0.846928
$43$	−6.24182	−0.951869	−0.475934	−	0.879481i	$-0.657890\pi$
$43$	−6.24182	−0.951869	−0.475934	+	0.879481i	$0.657890\pi$
$44$	5.19246	0.782792
$45$	2.64802	0.394744
$46$	−13.7220	−2.02320
$47$	1.67158	0.243825	0.121913	−	0.992541i	$-0.461097\pi$
$47$	1.67158	0.243825	0.121913	+	0.992541i	$0.461097\pi$
$48$	−15.0777	−2.17628
$49$	−5.04408	−0.720583
$50$	18.5391	2.62183
$51$	2.43085	0.340387
$52$	33.8935	4.70019
$53$	3.44474	0.473171	0.236586	−	0.971611i	$-0.423972\pi$
$53$	3.44474	0.473171	0.236586	+	0.971611i	$0.423972\pi$
$54$	14.7656	2.00934
$55$	−3.69363	−0.498049
$56$	−10.5791	−1.41370
$57$	3.55355	0.470679
$58$	3.60940	0.473937
$59$	−14.2631	−1.85690	−0.928449	−	0.371459i	$-0.878858\pi$
$59$	−14.2631	−1.85690	−0.928449	+	0.371459i	$0.878858\pi$
$60$	25.3743	3.27580
$61$	6.40582	0.820181	0.410091	−	0.912045i	$-0.365497\pi$
$61$	6.40582	0.820181	0.410091	+	0.912045i	$0.365497\pi$
$62$	−7.81980	−0.993116
$63$	1.06613	0.134320
$64$	9.52838	1.19105
$65$	−24.1100	−2.99048
$66$	−4.17313	−0.513677
$67$	6.41293	0.783464	0.391732	−	0.920079i	$-0.371876\pi$
$67$	6.41293	0.783464	0.391732	+	0.920079i	$0.371876\pi$
$68$	−7.93534	−0.962302
$69$	7.82385	0.941881
$70$	12.7456	1.52338
$71$	2.29930	0.272877	0.136438	−	0.990649i	$-0.456434\pi$
$71$	2.29930	0.272877	0.136438	+	0.990649i	$0.456434\pi$
$72$	−5.76645	−0.679583
$73$	11.6934	1.36861	0.684306	−	0.729195i	$-0.260105\pi$
$73$	11.6934	1.36861	0.684306	+	0.729195i	$0.260105\pi$
$74$	15.3351	1.78266
$75$	−10.5704	−1.22057
$76$	−11.6003	−1.33065
$77$	−1.48710	−0.169471
$78$	−27.2399	−3.08431
$79$	−10.7208	−1.20619	−0.603094	−	0.797670i	$-0.706066\pi$
$79$	−10.7208	−1.20619	−0.603094	+	0.797670i	$0.706066\pi$
$80$	−35.0125	−3.91452
$81$	−6.13193	−0.681326
$82$	5.59380	0.617732
$83$	1.00000	0.109764
$83$	1.00000	0.109764
$84$	10.2160	1.11466
$85$	5.64477	0.612261
$86$	−16.3760	−1.76587
$87$	−2.05797	−0.220637
$88$	8.04342	0.857431
$89$	−13.6752	−1.44957	−0.724786	−	0.688974i	$-0.758061\pi$
$89$	−13.6752	−1.44957	−0.724786	+	0.688974i	$0.758061\pi$
$90$	6.94732	0.732312
$91$	−9.70701	−1.01757
$92$	−25.5404	−2.66277
$93$	4.45861	0.462336
$94$	4.38555	0.452335
$95$	8.25183	0.846620
$96$	−16.9268	−1.72758
$97$	−3.25565	−0.330561	−0.165280	−	0.986247i	$-0.552853\pi$
$97$	−3.25565	−0.330561	−0.165280	+	0.986247i	$0.552853\pi$
$98$	−13.2336	−1.33680
$99$	−0.810588	−0.0814672
$100$	34.5064	3.45064
$101$	10.2254	1.01746	0.508732	−	0.860925i	$-0.330115\pi$
$101$	10.2254	1.01746	0.508732	+	0.860925i	$0.330115\pi$
$102$	6.37756	0.631473
$103$	6.57410	0.647765	0.323883	−	0.946097i	$-0.395012\pi$
$103$	6.57410	0.647765	0.323883	+	0.946097i	$0.395012\pi$
$104$	52.5031	5.14835
$105$	−7.26712	−0.709198
$106$	9.03758	0.877807
$107$	−2.25826	−0.218315	−0.109157	−	0.994024i	$-0.534815\pi$
$107$	−2.25826	−0.218315	−0.109157	+	0.994024i	$0.534815\pi$
$108$	27.4828	2.64454
$109$	1.72696	0.165413	0.0827063	−	0.996574i	$-0.473644\pi$
$109$	1.72696	0.165413	0.0827063	+	0.996574i	$0.473644\pi$
$110$	−9.69057	−0.923960
$111$	−8.74357	−0.829903
$112$	−14.0965	−1.33200
$113$	−7.25737	−0.682716	−0.341358	−	0.939933i	$-0.610887\pi$
$113$	−7.25737	−0.682716	−0.341358	+	0.939933i	$0.610887\pi$
$114$	9.32306	0.873184
$115$	18.1681	1.69418
$116$	6.71809	0.623759
$117$	−5.29108	−0.489160
$118$	−37.4206	−3.44484
$119$	2.27266	0.208334
$120$	39.3062	3.58815
$121$	−9.86934	−0.897213
$122$	16.8062	1.52157
$123$	−3.18941	−0.287580
$124$	−14.5548	−1.30706
$125$	−7.17766	−0.641990
$126$	2.79708	0.249184
$127$	14.3520	1.27353	0.636767	−	0.771057i	$-0.280272\pi$
$127$	14.3520	1.27353	0.636767	+	0.771057i	$0.280272\pi$
$128$	2.36755	0.209264
$129$	9.33708	0.822084
$130$	−63.2548	−5.54781
$131$	16.1776	1.41344	0.706720	−	0.707494i	$-0.250174\pi$
$131$	16.1776	1.41344	0.706720	+	0.707494i	$0.250174\pi$
$132$	−7.76734	−0.676060
$133$	3.32230	0.288080
$134$	16.8249	1.45345
$135$	−19.5498	−1.68258
$136$	−12.2923	−1.05406
$137$	−3.97641	−0.339728	−0.169864	−	0.985468i	$-0.554333\pi$
$137$	−3.97641	−0.339728	−0.169864	+	0.985468i	$0.554333\pi$
$138$	20.5266	1.74734
$139$	10.3614	0.878843	0.439421	−	0.898281i	$-0.355184\pi$
$139$	10.3614	0.878843	0.439421	+	0.898281i	$0.355184\pi$
$140$	23.7230	2.00496
$141$	−2.50050	−0.210580
$142$	6.03242	0.506229
$143$	7.38034	0.617175
$144$	−7.68370	−0.640308
$145$	−4.77888	−0.396864
$146$	30.6788	2.53899
$147$	7.54539	0.622333
$148$	28.5428	2.34620
$149$	5.41100	0.443286	0.221643	−	0.975128i	$-0.428858\pi$
$149$	5.41100	0.443286	0.221643	+	0.975128i	$0.428858\pi$
$150$	−27.7325	−2.26435
$151$	2.62790	0.213855	0.106928	−	0.994267i	$-0.465899\pi$
$151$	2.62790	0.213855	0.106928	+	0.994267i	$0.465899\pi$
$152$	−17.9696	−1.45752
$153$	1.23878	0.100149
$154$	−3.90155	−0.314396
$155$	10.3535	0.831613
$156$	−50.7010	−4.05933
$157$	1.05919	0.0845325	0.0422663	−	0.999106i	$-0.486542\pi$
$157$	1.05919	0.0845325	0.0422663	+	0.999106i	$0.486542\pi$
$158$	−28.1271	−2.23767
$159$	−5.15295	−0.408655
$160$	−39.3062	−3.10743
$161$	7.31470	0.576479
$162$	−16.0877	−1.26397
$163$	14.9052	1.16746	0.583732	−	0.811946i	$-0.301592\pi$
$163$	14.9052	1.16746	0.583732	+	0.811946i	$0.301592\pi$
$164$	10.4116	0.813010
$165$	5.52526	0.430141
$166$	2.62359	0.203630
$167$	−4.16459	−0.322266	−0.161133	−	0.986933i	$-0.551515\pi$
$167$	−4.16459	−0.322266	−0.161133	+	0.986933i	$0.551515\pi$
$168$	15.8252	1.22094
$169$	35.1748	2.70576
$170$	14.8096	1.13584
$171$	1.81091	0.138484
$172$	−30.4802	−2.32409
$173$	11.9585	0.909188	0.454594	−	0.890699i	$-0.349784\pi$
$173$	11.9585	0.909188	0.454594	+	0.890699i	$0.349784\pi$
$174$	−5.39926	−0.409317
$175$	−9.88253	−0.747049
$176$	10.7177	0.807879
$177$	21.3360	1.60371
$178$	−35.8782	−2.68918
$179$	−19.0882	−1.42672	−0.713359	−	0.700799i	$-0.752827\pi$
$179$	−19.0882	−1.42672	−0.713359	+	0.700799i	$0.752827\pi$
$180$	12.9309	0.963811
$181$	−7.80594	−0.580211	−0.290105	−	0.956995i	$-0.593690\pi$
$181$	−7.80594	−0.580211	−0.290105	+	0.956995i	$0.593690\pi$
$182$	−25.4672	−1.88776
$183$	−9.58240	−0.708351
$184$	−39.5636	−2.91667
$185$	−20.3038	−1.49276
$186$	11.6976	0.857707
$187$	−1.72793	−0.126358
$188$	8.16272	0.595327
$189$	−7.87100	−0.572531
$190$	21.6494	1.57061
$191$	7.28051	0.526799	0.263400	−	0.964687i	$-0.415156\pi$
$191$	7.28051	0.526799	0.263400	+	0.964687i	$0.415156\pi$
$192$	−14.2534	−1.02865
$193$	−10.1628	−0.731534	−0.365767	−	0.930706i	$-0.619193\pi$
$193$	−10.1628	−0.731534	−0.365767	+	0.930706i	$0.619193\pi$
$194$	−8.54149	−0.613243
$195$	36.0659	2.58273
$196$	−24.6314	−1.75938
$197$	−9.62889	−0.686030	−0.343015	−	0.939330i	$-0.611448\pi$
$197$	−9.62889	−0.686030	−0.343015	+	0.939330i	$0.611448\pi$
$198$	−2.12665	−0.151134
$199$	−5.84297	−0.414197	−0.207099	−	0.978320i	$-0.566402\pi$
$199$	−5.84297	−0.414197	−0.207099	+	0.978320i	$0.566402\pi$
$200$	53.4524	3.77966
$201$	−9.59304	−0.676641
$202$	26.8272	1.88756
$203$	−1.92404	−0.135041
$204$	11.8704	0.831094
$205$	−7.40625	−0.517275
$206$	17.2477	1.20171
$207$	3.98708	0.277121
$208$	69.9595	4.85082
$209$	−2.52597	−0.174725
$210$	−19.0659	−1.31567
$211$	−22.7130	−1.56363	−0.781815	−	0.623511i	$-0.785706\pi$
$211$	−22.7130	−1.56363	−0.781815	+	0.623511i	$0.785706\pi$
$212$	16.8214	1.15530
$213$	−3.43950	−0.235671
$214$	−5.92476	−0.405008
$215$	21.6820	1.47870
$216$	42.5725	2.89669
$217$	4.16846	0.282973
$218$	4.53083	0.306867
$219$	−17.4921	−1.18201
$220$	−18.0368	−1.21604
$221$	−11.2790	−0.758705
$222$	−22.9396	−1.53960
$223$	8.75473	0.586260	0.293130	−	0.956073i	$-0.405303\pi$
$223$	8.75473	0.586260	0.293130	+	0.956073i	$0.405303\pi$
$224$	−15.8252	−1.05737
$225$	−5.38675	−0.359117
$226$	−19.0404	−1.26655
$227$	14.1575	0.939668	0.469834	−	0.882755i	$-0.344314\pi$
$227$	14.1575	0.939668	0.469834	+	0.882755i	$0.344314\pi$
$228$	17.3528	1.14922
$229$	−23.8613	−1.57680	−0.788398	−	0.615166i	$-0.789089\pi$
$229$	−23.8613	−1.57680	−0.788398	+	0.615166i	$0.789089\pi$
$230$	47.6655	3.14297
$231$	2.22454	0.146364
$232$	10.4067	0.683234
$233$	12.4505	0.815662	0.407831	−	0.913058i	$-0.366285\pi$
$233$	12.4505	0.815662	0.407831	+	0.913058i	$0.366285\pi$
$234$	−13.8816	−0.907470
$235$	−5.80651	−0.378775
$236$	−69.6500	−4.53383
$237$	16.0372	1.04173
$238$	5.96253	0.386493
$239$	−10.8793	−0.703722	−0.351861	−	0.936052i	$-0.614451\pi$
$239$	−10.8793	−0.703722	−0.351861	+	0.936052i	$0.614451\pi$
$240$	52.3749	3.38078
$241$	21.1992	1.36556	0.682782	−	0.730622i	$-0.260770\pi$
$241$	21.1992	1.36556	0.682782	+	0.730622i	$0.260770\pi$
$242$	−25.8931	−1.66447
$243$	−7.71132	−0.494682
$244$	31.2811	2.00256
$245$	17.5214	1.11940
$246$	−8.36771	−0.533506
$247$	−16.4882	−1.04912
$248$	−22.5462	−1.43169
$249$	−1.49589	−0.0947982
$250$	−18.8312	−1.19099
$251$	−11.1453	−0.703482	−0.351741	−	0.936097i	$-0.614410\pi$
$251$	−11.1453	−0.703482	−0.351741	+	0.936097i	$0.614410\pi$
$252$	5.20614	0.327956
$253$	−5.56144	−0.349645
$254$	37.6537	2.36261
$255$	−8.44395	−0.528781
$256$	−12.8453	−0.802830
$257$	−15.2740	−0.952766	−0.476383	−	0.879238i	$-0.658052\pi$
$257$	−15.2740	−0.952766	−0.476383	+	0.879238i	$0.658052\pi$
$258$	24.4967	1.52510
$259$	−8.17457	−0.507943
$260$	−117.735	−7.30159
$261$	−1.04875	−0.0649161
$262$	42.4433	2.62215
$263$	24.8019	1.52935	0.764674	−	0.644417i	$-0.222900\pi$
$263$	24.8019	1.52935	0.764674	+	0.644417i	$0.222900\pi$
$264$	−12.0321	−0.740523
$265$	−11.9658	−0.735056
$266$	8.71634	0.534433
$267$	20.4566	1.25193
$268$	31.3158	1.91292
$269$	−11.1294	−0.678569	−0.339285	−	0.940684i	$-0.610185\pi$
$269$	−11.1294	−0.678569	−0.339285	+	0.940684i	$0.610185\pi$
$270$	−51.2906	−3.12145
$271$	−4.56087	−0.277053	−0.138526	−	0.990359i	$-0.544237\pi$
$271$	−4.56087	−0.277053	−0.138526	+	0.990359i	$0.544237\pi$
$272$	−16.3793	−0.993141
$273$	14.5206	0.878828
$274$	−10.4325	−0.630249
$275$	7.51379	0.453098
$276$	38.2056	2.29971
$277$	−6.00358	−0.360720	−0.180360	−	0.983601i	$-0.557726\pi$
$277$	−6.00358	−0.360720	−0.180360	+	0.983601i	$0.557726\pi$
$278$	27.1841	1.63039
$279$	2.27213	0.136029
$280$	36.7483	2.19613
$281$	18.7076	1.11600	0.558002	−	0.829840i	$-0.311568\pi$
$281$	18.7076	1.11600	0.558002	+	0.829840i	$0.311568\pi$
$282$	−6.56030	−0.390660
$283$	−27.5628	−1.63844	−0.819219	−	0.573481i	$-0.805593\pi$
$283$	−27.5628	−1.63844	−0.819219	+	0.573481i	$0.805593\pi$
$284$	11.2280	0.666259
$285$	−12.3438	−0.731185
$286$	19.3630	1.14496
$287$	−2.98185	−0.176013
$288$	−8.62597	−0.508290
$289$	−14.3593	−0.844665
$290$	−12.5378	−0.736246
$291$	4.87009	0.285490
$292$	57.1017	3.34162
$293$	10.8097	0.631509	0.315755	−	0.948841i	$-0.397742\pi$
$293$	10.8097	0.631509	0.315755	+	0.948841i	$0.397742\pi$
$294$	19.7960	1.15453
$295$	49.5452	2.88463
$296$	44.2144	2.56991
$297$	5.98440	0.347250
$298$	14.1962	0.822366
$299$	−36.3021	−2.09940
$300$	−51.6177	−2.98015
$301$	8.72945	0.503157
$302$	6.89453	0.396736
$303$	−15.2960	−0.878735
$304$	−23.9441	−1.37329
$305$	−22.2516	−1.27412
$306$	3.25004	0.185793
$307$	−14.0286	−0.800653	−0.400327	−	0.916373i	$-0.631103\pi$
$307$	−14.0286	−0.800653	−0.400327	+	0.916373i	$0.631103\pi$
$308$	−7.26187	−0.413783
$309$	−9.83413	−0.559444
$310$	27.1633	1.54277
$311$	−16.9088	−0.958812	−0.479406	−	0.877593i	$-0.659148\pi$
$311$	−16.9088	−0.958812	−0.479406	+	0.877593i	$0.659148\pi$
$312$	−78.5388	−4.44638
$313$	−33.3174	−1.88321	−0.941604	−	0.336722i	$-0.890682\pi$
$313$	−33.3174	−1.88321	−0.941604	+	0.336722i	$0.890682\pi$
$314$	2.77888	0.156821
$315$	−3.70337	−0.208661
$316$	−52.3523	−2.94505
$317$	32.9568	1.85104	0.925519	−	0.378702i	$-0.123629\pi$
$317$	32.9568	1.85104	0.925519	+	0.378702i	$0.123629\pi$
$318$	−13.5192	−0.758120
$319$	1.46287	0.0819048
$320$	−33.0984	−1.85025
$321$	3.37811	0.188548
$322$	19.1908	1.06946
$323$	3.86031	0.214793
$324$	−29.9436	−1.66353
$325$	49.0459	2.72058
$326$	39.1051	2.16583
$327$	−2.58334	−0.142859
$328$	16.1282	0.890530
$329$	−2.33778	−0.128886
$330$	14.4960	0.797980
$331$	−9.40625	−0.517014	−0.258507	−	0.966009i	$-0.583231\pi$
$331$	−9.40625	−0.517014	−0.258507	+	0.966009i	$0.583231\pi$
$332$	4.88322	0.268002
$333$	−4.45578	−0.244175
$334$	−10.9262	−0.597854
$335$	−22.2763	−1.21709
$336$	21.0868	1.15038
$337$	−12.3969	−0.675302	−0.337651	−	0.941271i	$-0.609632\pi$
$337$	−12.3969	−0.675302	−0.337651	+	0.941271i	$0.609632\pi$
$338$	92.2844	5.01961
$339$	10.8562	0.589629
$340$	27.5647	1.49490
$341$	−3.16932	−0.171628
$342$	4.75109	0.256909
$343$	16.8442	0.909499
$344$	−47.2156	−2.54570
$345$	−27.1774	−1.46318
$346$	31.3742	1.68669
$347$	−3.64455	−0.195649	−0.0978247	−	0.995204i	$-0.531188\pi$
$347$	−3.64455	−0.195649	−0.0978247	+	0.995204i	$0.531188\pi$
$348$	−10.0495	−0.538711
$349$	0.975754	0.0522309	0.0261155	−	0.999659i	$-0.491686\pi$
$349$	0.975754	0.0522309	0.0261155	+	0.999659i	$0.491686\pi$
$350$	−25.9277	−1.38589
$351$	39.0629	2.08502
$352$	12.0321	0.641311
$353$	−14.7188	−0.783404	−0.391702	−	0.920092i	$-0.628114\pi$
$353$	−14.7188	−0.783404	−0.391702	+	0.920092i	$0.628114\pi$
$354$	55.9770	2.97514
$355$	−7.98698	−0.423905
$356$	−66.7792	−3.53929
$357$	−3.39965	−0.179928
$358$	−50.0796	−2.64679
$359$	29.2877	1.54575	0.772874	−	0.634559i	$-0.218818\pi$
$359$	29.2877	1.54575	0.772874	+	0.634559i	$0.218818\pi$
$360$	20.0307	1.05571
$361$	−13.3568	−0.702989
$362$	−20.4796	−1.07638
$363$	14.7634	0.774880
$364$	−47.4015	−2.48452
$365$	−40.6190	−2.12610
$366$	−25.1403	−1.31410
$367$	26.0568	1.36015	0.680077	−	0.733140i	$-0.261946\pi$
$367$	26.0568	1.36015	0.680077	+	0.733140i	$0.261946\pi$
$368$	−52.7178	−2.74811
$369$	−1.62534	−0.0846120
$370$	−53.2688	−2.76931
$371$	−4.81761	−0.250118
$372$	21.7724	1.12885
$373$	8.19379	0.424258	0.212129	−	0.977242i	$-0.431960\pi$
$373$	8.19379	0.424258	0.212129	+	0.977242i	$0.431960\pi$
$374$	−4.53337	−0.234415
$375$	10.7370	0.554456
$376$	12.6445	0.652091
$377$	9.54880	0.491788
$378$	−20.6503	−1.06214
$379$	18.8813	0.969868	0.484934	−	0.874551i	$-0.338844\pi$
$379$	18.8813	0.969868	0.484934	+	0.874551i	$0.338844\pi$
$380$	40.2955	2.06712
$381$	−21.4690	−1.09989
$382$	19.1011	0.977296
$383$	−0.170622	−0.00871836	−0.00435918	−	0.999990i	$-0.501388\pi$
$383$	−0.170622	−0.00871836	−0.00435918	+	0.999990i	$0.501388\pi$
$384$	−3.54160	−0.180732
$385$	5.16570	0.263268
$386$	−26.6630	−1.35711
$387$	4.75823	0.241874
$388$	−15.8981	−0.807102
$389$	20.1447	1.02138	0.510689	−	0.859765i	$-0.329390\pi$
$389$	20.1447	1.02138	0.510689	+	0.859765i	$0.329390\pi$
$390$	94.6222	4.79138
$391$	8.49924	0.429825
$392$	−38.1554	−1.92714
$393$	−24.1998	−1.22072
$394$	−25.2623	−1.27269
$395$	37.2405	1.87378
$396$	−3.95828	−0.198911
$397$	−29.2882	−1.46993	−0.734966	−	0.678104i	$-0.762802\pi$
$397$	−29.2882	−1.46993	−0.734966	+	0.678104i	$0.762802\pi$
$398$	−15.3296	−0.768402
$399$	−4.96979	−0.248801
$400$	71.2244	3.56122
$401$	−10.5183	−0.525259	−0.262629	−	0.964897i	$-0.584590\pi$
$401$	−10.5183	−0.525259	−0.262629	+	0.964897i	$0.584590\pi$
$402$	−25.1682	−1.25528
$403$	−20.6876	−1.03052
$404$	49.9328	2.48425
$405$	21.3003	1.05842
$406$	−5.04789	−0.250523
$407$	6.21521	0.308076
$408$	18.3879	0.910339
$409$	31.6167	1.56334	0.781671	−	0.623690i	$-0.214367\pi$
$409$	31.6167	1.56334	0.781671	+	0.623690i	$0.214367\pi$
$410$	−19.4310	−0.959627
$411$	5.94828	0.293407
$412$	32.1028	1.58159
$413$	19.9476	0.981555
$414$	10.4605	0.514104
$415$	−3.47366	−0.170515
$416$	78.5388	3.85068
$417$	−15.4995	−0.759014
$418$	−6.62712	−0.324143
$419$	27.4502	1.34103	0.670515	−	0.741896i	$-0.266073\pi$
$419$	27.4502	1.34103	0.670515	+	0.741896i	$0.266073\pi$
$420$	−35.4870	−1.73159
$421$	−25.6565	−1.25042	−0.625210	−	0.780456i	$-0.714987\pi$
$421$	−25.6565	−1.25042	−0.625210	+	0.780456i	$0.714987\pi$
$422$	−59.5897	−2.90078
$423$	−1.27427	−0.0619572
$424$	26.0574	1.26546
$425$	−11.4829	−0.557003
$426$	−9.02383	−0.437206
$427$	−8.95881	−0.433547
$428$	−11.0276	−0.533039
$429$	−11.0402	−0.533025
$430$	56.8846	2.74322
$431$	11.7860	0.567714	0.283857	−	0.958867i	$-0.408386\pi$
$431$	11.7860	0.567714	0.283857	+	0.958867i	$0.408386\pi$
$432$	56.7271	2.72929
$433$	−32.5285	−1.56322	−0.781610	−	0.623767i	$-0.785601\pi$
$433$	−32.5285	−1.56322	−0.781610	+	0.623767i	$0.785601\pi$
$434$	10.9363	0.524960
$435$	7.14868	0.342753
$436$	8.43313	0.403874
$437$	12.4246	0.594351
$438$	−45.8921	−2.19281
$439$	3.15031	0.150356	0.0751781	−	0.997170i	$-0.476047\pi$
$439$	3.15031	0.150356	0.0751781	+	0.997170i	$0.476047\pi$
$440$	−27.9401	−1.33199
$441$	3.84517	0.183104
$442$	−29.5914	−1.40752
$443$	38.2965	1.81952	0.909761	−	0.415133i	$-0.136265\pi$
$443$	38.2965	1.81952	0.909761	+	0.415133i	$0.136265\pi$
$444$	−42.6968	−2.02630
$445$	47.5031	2.25186
$446$	22.9688	1.08761
$447$	−8.09425	−0.382845
$448$	−13.3258	−0.629587
$449$	8.41795	0.397268	0.198634	−	0.980074i	$-0.436350\pi$
$449$	8.41795	0.397268	0.198634	+	0.980074i	$0.436350\pi$
$450$	−14.1326	−0.666218
$451$	2.26713	0.106755
$452$	−35.4394	−1.66693
$453$	−3.93105	−0.184697
$454$	37.1436	1.74323
$455$	33.7189	1.58076
$456$	26.8805	1.25879
$457$	27.4888	1.28587	0.642937	−	0.765919i	$-0.277716\pi$
$457$	27.4888	1.28587	0.642937	+	0.765919i	$0.277716\pi$
$458$	−62.6021	−2.92521
$459$	−9.14563	−0.426881
$460$	88.7187	4.13653
$461$	−26.0110	−1.21145	−0.605727	−	0.795672i	$-0.707118\pi$
$461$	−26.0110	−1.21145	−0.605727	+	0.795672i	$0.707118\pi$
$462$	5.83629	0.271529
$463$	0.163132	0.00758139	0.00379069	−	0.999993i	$-0.498793\pi$
$463$	0.163132	0.00758139	0.00379069	+	0.999993i	$0.498793\pi$
$464$	13.8668	0.643748
$465$	−15.4877	−0.718224
$466$	32.6651	1.51318
$467$	−20.8826	−0.966329	−0.483165	−	0.875529i	$-0.660513\pi$
$467$	−20.8826	−0.966329	−0.483165	+	0.875529i	$0.660513\pi$
$468$	−25.8375	−1.19434
$469$	−8.96875	−0.414139
$470$	−15.2339	−0.702688
$471$	−1.58443	−0.0730067
$472$	−107.892	−4.96613
$473$	−6.63709	−0.305174
$474$	42.0750	1.93257
$475$	−16.7863	−0.770209
$476$	11.0979	0.508672
$477$	−2.62597	−0.120235
$478$	−28.5428	−1.30552
$479$	−10.2731	−0.469388	−0.234694	−	0.972069i	$-0.575409\pi$
$479$	−10.2731	−0.469388	−0.234694	+	0.972069i	$0.575409\pi$
$480$	58.7978	2.68374
$481$	40.5695	1.84981
$482$	55.6181	2.53334
$483$	−10.9420	−0.497878
$484$	−48.1942	−2.19065
$485$	11.3090	0.513516
$486$	−20.2314	−0.917713
$487$	−36.9711	−1.67532	−0.837660	−	0.546192i	$-0.816077\pi$
$487$	−36.9711	−1.67532	−0.837660	+	0.546192i	$0.816077\pi$
$488$	48.4562	2.19351
$489$	−22.2965	−1.00828
$490$	45.9690	2.07667
$491$	22.1271	0.998582	0.499291	−	0.866434i	$-0.333594\pi$
$491$	22.1271	0.998582	0.499291	+	0.866434i	$0.333594\pi$
$492$	−15.5746	−0.702158
$493$	−2.23562	−0.100687
$494$	−43.2583	−1.94628
$495$	2.81571	0.126557
$496$	−30.0425	−1.34895
$497$	−3.21567	−0.144242
$498$	−3.92460	−0.175866
$499$	−21.6116	−0.967469	−0.483735	−	0.875215i	$-0.660720\pi$
$499$	−21.6116	−0.967469	−0.483735	+	0.875215i	$0.660720\pi$
$500$	−35.0501	−1.56749
$501$	6.22976	0.278325
$502$	−29.2406	−1.30507
$503$	−33.6599	−1.50082	−0.750411	−	0.660972i	$-0.770144\pi$
$503$	−33.6599	−1.50082	−0.750411	+	0.660972i	$0.770144\pi$
$504$	8.06462	0.359227
$505$	−35.5195	−1.58060
$506$	−14.5909	−0.648646
$507$	−52.6177	−2.33683
$508$	70.0840	3.10947
$509$	23.9050	1.05957	0.529785	−	0.848132i	$-0.322273\pi$
$509$	23.9050	1.05957	0.529785	+	0.848132i	$0.322273\pi$
$510$	−22.1535	−0.980972
$511$	−16.3538	−0.723448
$512$	−38.4358	−1.69864
$513$	−13.3696	−0.590281
$514$	−40.0727	−1.76753
$515$	−22.8362	−1.00628
$516$	45.5950	2.00721
$517$	1.77744	0.0781716
$518$	−21.4467	−0.942315
$519$	−17.8886	−0.785222
$520$	−182.378	−7.99780
$521$	3.73649	0.163698	0.0818492	−	0.996645i	$-0.473917\pi$
$521$	3.73649	0.163698	0.0818492	+	0.996645i	$0.473917\pi$
$522$	−2.75150	−0.120430
$523$	1.82341	0.0797320	0.0398660	−	0.999205i	$-0.487307\pi$
$523$	1.82341	0.0797320	0.0398660	+	0.999205i	$0.487307\pi$
$524$	78.9986	3.45107
$525$	14.7832	0.645191
$526$	65.0699	2.83718
$527$	4.84349	0.210986
$528$	−16.0325	−0.697726
$529$	4.35535	0.189363
$530$	−31.3935	−1.36365
$531$	10.8730	0.471847
$532$	16.2235	0.703379
$533$	14.7986	0.640999
$534$	53.6698	2.32252
$535$	7.84444	0.339145
$536$	48.5100	2.09531
$537$	28.5538	1.23219
$538$	−29.1989	−1.25885
$539$	−5.36350	−0.231022
$540$	−95.4660	−4.10820
$541$	−0.394719	−0.0169703	−0.00848514	−	0.999964i	$-0.502701\pi$
$541$	−0.394719	−0.0169703	−0.00848514	+	0.999964i	$0.502701\pi$
$542$	−11.9658	−0.513977
$543$	11.6768	0.501100
$544$	−18.3879	−0.788376
$545$	−5.99887	−0.256963
$546$	38.0962	1.63036
$547$	31.0024	1.32557	0.662783	−	0.748811i	$-0.269375\pi$
$547$	31.0024	1.32557	0.662783	+	0.748811i	$0.269375\pi$
$548$	−19.4177	−0.829484
$549$	−4.88325	−0.208412
$550$	19.7131	0.840569
$551$	−3.26815	−0.139228
$552$	59.1828	2.51899
$553$	14.9935	0.637590
$554$	−15.7509	−0.669193
$555$	30.3722	1.28923
$556$	50.5971	2.14579
$557$	37.7865	1.60107	0.800533	−	0.599288i	$-0.204550\pi$
$557$	37.7865	1.60107	0.800533	+	0.599288i	$0.204550\pi$
$558$	5.96115	0.252355
$559$	−43.3233	−1.83238
$560$	48.9665	2.06921
$561$	2.58479	0.109130
$562$	49.0811	2.07036
$563$	−12.3885	−0.522112	−0.261056	−	0.965324i	$-0.584071\pi$
$563$	−12.3885	−0.522112	−0.261056	+	0.965324i	$0.584071\pi$
$564$	−12.2105	−0.514156
$565$	25.2096	1.06058
$566$	−72.3135	−3.03956
$567$	8.57577	0.360148
$568$	17.3928	0.729787
$569$	−7.63212	−0.319955	−0.159978	−	0.987121i	$-0.551142\pi$
$569$	−7.63212	−0.319955	−0.159978	+	0.987121i	$0.551142\pi$
$570$	−32.3851	−1.35646
$571$	−22.4292	−0.938635	−0.469317	−	0.883030i	$-0.655500\pi$
$571$	−22.4292	−0.938635	−0.469317	+	0.883030i	$0.655500\pi$
$572$	36.0399	1.50690
$573$	−10.8908	−0.454971
$574$	−7.82317	−0.326533
$575$	−36.9585	−1.54127
$576$	−7.26362	−0.302651
$577$	14.6835	0.611280	0.305640	−	0.952147i	$-0.401130\pi$
$577$	14.6835	0.611280	0.305640	+	0.952147i	$0.401130\pi$
$578$	−37.6729	−1.56699
$579$	15.2024	0.631791
$580$	−23.3363	−0.968989
$581$	−1.39854	−0.0580213
$582$	12.7771	0.529629
$583$	3.66288	0.151701
$584$	88.4538	3.66025
$585$	18.3794	0.759895
$586$	28.3602	1.17155
$587$	5.98987	0.247228	0.123614	−	0.992330i	$-0.460551\pi$
$587$	5.98987	0.247228	0.123614	+	0.992330i	$0.460551\pi$
$588$	36.8458	1.51950
$589$	7.08048	0.291746
$590$	129.986	5.35145
$591$	14.4038	0.592492
$592$	58.9150	2.42139
$593$	36.7653	1.50977	0.754885	−	0.655857i	$-0.227692\pi$
$593$	36.7653	1.50977	0.754885	+	0.655857i	$0.227692\pi$
$594$	15.7006	0.644204
$595$	−7.89445	−0.323641
$596$	26.4231	1.08233
$597$	8.74044	0.357723
$598$	−95.2417	−3.89472
$599$	−0.569066	−0.0232514	−0.0116257	−	0.999932i	$-0.503701\pi$
$599$	−0.569066	−0.0232514	−0.0116257	+	0.999932i	$0.503701\pi$
$600$	−79.9589	−3.26431
$601$	30.8003	1.25637	0.628185	−	0.778064i	$-0.283798\pi$
$601$	30.8003	1.25637	0.628185	+	0.778064i	$0.283798\pi$
$602$	22.9025	0.933436
$603$	−4.88867	−0.199082
$604$	12.8326	0.522152
$605$	34.2827	1.39379
$606$	−40.1305	−1.63019
$607$	−23.6371	−0.959399	−0.479700	−	0.877433i	$-0.659254\pi$
$607$	−23.6371	−0.959399	−0.479700	+	0.877433i	$0.659254\pi$
$608$	−26.8805	−1.09015
$609$	2.87815	0.116629
$610$	−58.3792	−2.36370
$611$	11.6021	0.469372
$612$	6.04923	0.244525
$613$	45.1045	1.82175	0.910877	−	0.412677i	$-0.135406\pi$
$613$	45.1045	1.82175	0.910877	+	0.412677i	$0.135406\pi$
$614$	−36.8052	−1.48534
$615$	11.0789	0.446746
$616$	−11.2491	−0.453237
$617$	9.06163	0.364807	0.182404	−	0.983224i	$-0.441612\pi$
$617$	9.06163	0.364807	0.182404	+	0.983224i	$0.441612\pi$
$618$	−25.8007	−1.03786
$619$	7.74466	0.311284	0.155642	−	0.987814i	$-0.450255\pi$
$619$	7.74466	0.311284	0.155642	+	0.987814i	$0.450255\pi$
$620$	50.5584	2.03048
$621$	−29.4358	−1.18122
$622$	−44.3618	−1.77875
$623$	19.1254	0.766242
$624$	−104.652	−4.18942
$625$	−10.3988	−0.415952
$626$	−87.4111	−3.49365
$627$	3.77858	0.150902
$628$	5.17226	0.206396
$629$	−9.49836	−0.378724
$630$	−9.71612	−0.387099
$631$	28.8513	1.14855	0.574276	−	0.818662i	$-0.305284\pi$
$631$	28.8513	1.14855	0.574276	+	0.818662i	$0.305284\pi$
$632$	−81.0967	−3.22585
$633$	33.9762	1.35043
$634$	86.4651	3.43397
$635$	−49.8539	−1.97839
$636$	−25.1630	−0.997778
$637$	−35.0100	−1.38715
$638$	3.83796	0.151946
$639$	−1.75279	−0.0693392
$640$	−8.22408	−0.325085
$641$	−32.9442	−1.30122	−0.650609	−	0.759413i	$-0.725486\pi$
$641$	−32.9442	−1.30122	−0.650609	+	0.759413i	$0.725486\pi$
$642$	8.86278	0.349786
$643$	−27.0589	−1.06710	−0.533549	−	0.845769i	$-0.679142\pi$
$643$	−27.0589	−1.06710	−0.533549	+	0.845769i	$0.679142\pi$
$644$	35.7193	1.40754
$645$	−32.4338	−1.27708
$646$	10.1279	0.398475
$647$	−13.8665	−0.545148	−0.272574	−	0.962135i	$-0.587875\pi$
$647$	−13.8665	−0.545148	−0.272574	+	0.962135i	$0.587875\pi$
$648$	−46.3844	−1.82215
$649$	−15.1663	−0.595330
$650$	128.676	5.04710
$651$	−6.23555	−0.244390
$652$	72.7854	2.85049
$653$	−1.98969	−0.0778627	−0.0389313	−	0.999242i	$-0.512395\pi$
$653$	−1.98969	−0.0778627	−0.0389313	+	0.999242i	$0.512395\pi$
$654$	−6.77762	−0.265026
$655$	−56.1953	−2.19573
$656$	21.4905	0.839065
$657$	−8.91407	−0.347771
$658$	−6.13337	−0.239104
$659$	1.08449	0.0422457	0.0211228	−	0.999777i	$-0.493276\pi$
$659$	1.08449	0.0422457	0.0211228	+	0.999777i	$0.493276\pi$
$660$	26.9811	1.05024
$661$	6.73926	0.262127	0.131063	−	0.991374i	$-0.458161\pi$
$661$	6.73926	0.262127	0.131063	+	0.991374i	$0.458161\pi$
$662$	−24.6781	−0.959143
$663$	16.8721	0.655257
$664$	7.56440	0.293556
$665$	−11.5405	−0.447522
$666$	−11.6901	−0.452983
$667$	−7.19548	−0.278610
$668$	−20.3366	−0.786848
$669$	−13.0961	−0.506325
$670$	−58.4440	−2.25789
$671$	6.81147	0.262954
$672$	23.6728	0.913197
$673$	−14.2533	−0.549426	−0.274713	−	0.961526i	$-0.588583\pi$
$673$	−14.2533	−0.549426	−0.274713	+	0.961526i	$0.588583\pi$
$674$	−32.5244	−1.25279
$675$	39.7692	1.53072
$676$	171.767	6.60641
$677$	−17.0568	−0.655544	−0.327772	−	0.944757i	$-0.606298\pi$
$677$	−17.0568	−0.655544	−0.327772	+	0.944757i	$0.606298\pi$
$678$	28.4823	1.09386
$679$	4.55316	0.174734
$680$	42.6993	1.63744
$681$	−21.1781	−0.811547
$682$	−8.31499	−0.318398
$683$	−6.35895	−0.243319	−0.121659	−	0.992572i	$-0.538822\pi$
$683$	−6.35895	−0.243319	−0.121659	+	0.992572i	$0.538822\pi$
$684$	8.84308	0.338124
$685$	13.8127	0.527757
$686$	44.1921	1.68726
$687$	35.6938	1.36180
$688$	−62.9140	−2.39858
$689$	23.9093	0.910871
$690$	−71.3024	−2.71443
$691$	46.9219	1.78500	0.892498	−	0.451052i	$-0.148951\pi$
$691$	46.9219	1.78500	0.892498	+	0.451052i	$0.148951\pi$
$692$	58.3961	2.21989
$693$	1.13364	0.0430635
$694$	−9.56179	−0.362961
$695$	−35.9920	−1.36525
$696$	−15.5673	−0.590076
$697$	−3.46474	−0.131236
$698$	2.55998	0.0968966
$699$	−18.6246	−0.704448
$700$	−48.2586	−1.82400
$701$	48.7061	1.83960	0.919802	−	0.392382i	$-0.128349\pi$
$701$	48.7061	1.83960	0.919802	+	0.392382i	$0.128349\pi$
$702$	102.485	3.86805
$703$	−13.8852	−0.523690
$704$	10.1318	0.381855
$705$	8.68590	0.327130
$706$	−38.6162	−1.45334
$707$	−14.3006	−0.537830
$708$	104.189	3.91565
$709$	−24.3894	−0.915963	−0.457981	−	0.888962i	$-0.651427\pi$
$709$	−24.3894	−0.915963	−0.457981	+	0.888962i	$0.651427\pi$
$710$	−20.9546	−0.786411
$711$	8.17265	0.306498
$712$	−103.445	−3.87676
$713$	15.5891	0.583816
$714$	−8.91928	−0.333796
$715$	−25.6368	−0.958761
$716$	−93.2119	−3.48349
$717$	16.2742	0.607771
$718$	76.8390	2.86761
$719$	32.9091	1.22730	0.613650	−	0.789578i	$-0.289700\pi$
$719$	32.9091	1.22730	0.613650	+	0.789578i	$0.289700\pi$
$720$	26.6905	0.994698
$721$	−9.19415	−0.342408
$722$	−35.0428	−1.30416
$723$	−31.7117	−1.17937
$724$	−38.1182	−1.41665
$725$	9.72146	0.361046
$726$	38.7332	1.43752
$727$	17.9811	0.666881	0.333440	−	0.942771i	$-0.391790\pi$
$727$	17.9811	0.666881	0.333440	+	0.942771i	$0.391790\pi$
$728$	−73.4277	−2.72141
$729$	29.9311	1.10856
$730$	−106.568	−3.94424
$731$	10.1431	0.375156
$732$	−46.7930	−1.72952
$733$	3.99502	0.147559	0.0737797	−	0.997275i	$-0.476494\pi$
$733$	3.99502	0.147559	0.0737797	+	0.997275i	$0.476494\pi$
$734$	68.3624	2.52330
$735$	−26.2101	−0.966775
$736$	−59.1828	−2.18151
$737$	6.81903	0.251182
$738$	−4.26423	−0.156969
$739$	−46.9876	−1.72847	−0.864233	−	0.503091i	$-0.832196\pi$
$739$	−46.9876	−1.72847	−0.864233	+	0.503091i	$0.832196\pi$
$740$	−99.1479	−3.64475
$741$	24.6645	0.906074
$742$	−12.6394	−0.464008
$743$	44.7182	1.64055	0.820276	−	0.571968i	$-0.193820\pi$
$743$	44.7182	1.64055	0.820276	+	0.571968i	$0.193820\pi$
$744$	33.7267	1.23648
$745$	−18.7960	−0.688631
$746$	21.4971	0.787066
$747$	−0.762314	−0.0278916
$748$	−8.43785	−0.308518
$749$	3.15828	0.115401
$750$	28.1695	1.02860
$751$	−22.5522	−0.822942	−0.411471	−	0.911423i	$-0.634985\pi$
$751$	−22.5522	−0.822942	−0.411471	+	0.911423i	$0.634985\pi$
$752$	16.8486	0.614406
$753$	16.6721	0.607564
$754$	25.0521	0.912345
$755$	−9.12843	−0.332217
$756$	−38.4359	−1.39790
$757$	6.44573	0.234274	0.117137	−	0.993116i	$-0.462628\pi$
$757$	6.44573	0.234274	0.117137	+	0.993116i	$0.462628\pi$
$758$	49.5368	1.79926
$759$	8.31930	0.301971
$760$	62.4201	2.26422
$761$	−0.271511	−0.00984225	−0.00492113	−	0.999988i	$-0.501566\pi$
$761$	−0.271511	−0.00984225	−0.00492113	+	0.999988i	$0.501566\pi$
$762$	−56.3258	−2.04047
$763$	−2.41522	−0.0874370
$764$	35.5524	1.28624
$765$	−4.30309	−0.155578
$766$	−0.447641	−0.0161739
$767$	−98.9975	−3.57459
$768$	19.2151	0.693366
$769$	−11.3883	−0.410673	−0.205337	−	0.978691i	$-0.565829\pi$
$769$	−11.3883	−0.410673	−0.205337	+	0.978691i	$0.565829\pi$
$770$	13.5527	0.488404
$771$	22.8482	0.822859
$772$	−49.6272	−1.78612
$773$	−11.8597	−0.426565	−0.213283	−	0.976991i	$-0.568416\pi$
$773$	−11.8597	−0.426565	−0.213283	+	0.976991i	$0.568416\pi$
$774$	12.4836	0.448715
$775$	−21.0617	−0.756557
$776$	−24.6270	−0.884059
$777$	12.2283	0.438686
$778$	52.8515	1.89482
$779$	−5.06494	−0.181470
$780$	176.118	6.30604
$781$	2.44490	0.0874855
$782$	22.2985	0.797394
$783$	7.74272	0.276702
$784$	−50.8415	−1.81577
$785$	−3.67926	−0.131319
$786$	−63.4904	−2.26463
$787$	41.7805	1.48932	0.744658	−	0.667447i	$-0.232613\pi$
$787$	41.7805	1.48932	0.744658	+	0.667447i	$0.232613\pi$
$788$	−47.0201	−1.67502
$789$	−37.1008	−1.32082
$790$	97.7039	3.47615
$791$	10.1497	0.360883
$792$	−6.13161	−0.217877
$793$	44.4616	1.57888
$794$	−76.8402	−2.72696
$795$	17.8996	0.634833
$796$	−28.5326	−1.01131
$797$	−42.0843	−1.49070	−0.745352	−	0.666671i	$-0.767719\pi$
$797$	−42.0843	−1.49070	−0.745352	+	0.666671i	$0.767719\pi$
$798$	−13.0387	−0.461564
$799$	−2.71636	−0.0960978
$800$	79.9589	2.82697
$801$	10.4248	0.368343
$802$	−27.5957	−0.974438
$803$	12.4339	0.438784
$804$	−46.8450	−1.65209
$805$	−25.4088	−0.895542
$806$	−54.2758	−1.91178
$807$	16.6483	0.586048
$808$	77.3489	2.72112
$809$	26.3288	0.925673	0.462836	−	0.886444i	$-0.346832\pi$
$809$	26.3288	0.925673	0.462836	+	0.886444i	$0.346832\pi$
$810$	55.8831	1.96353
$811$	3.94749	0.138615	0.0693075	−	0.997595i	$-0.477921\pi$
$811$	3.94749	0.138615	0.0693075	+	0.997595i	$0.477921\pi$
$812$	−9.39552	−0.329718
$813$	6.82255	0.239277
$814$	16.3062	0.571530
$815$	−51.7755	−1.81362
$816$	24.5016	0.857728
$817$	14.8277	0.518756
$818$	82.9491	2.90025
$819$	7.39979	0.258570
$820$	−36.1664	−1.26298
$821$	−49.4287	−1.72507	−0.862537	−	0.505995i	$-0.831126\pi$
$821$	−49.4287	−1.72507	−0.862537	+	0.505995i	$0.831126\pi$
$822$	15.6058	0.544316
$823$	−37.1462	−1.29484	−0.647418	−	0.762135i	$-0.724151\pi$
$823$	−37.1462	−1.29484	−0.647418	+	0.762135i	$0.724151\pi$
$824$	49.7291	1.73240
$825$	−11.2398	−0.391319
$826$	52.3342	1.82094
$827$	−34.6553	−1.20508	−0.602542	−	0.798087i	$-0.705845\pi$
$827$	−34.6553	−1.20508	−0.602542	+	0.798087i	$0.705845\pi$
$828$	19.4698	0.676623
$829$	40.3493	1.40139	0.700695	−	0.713461i	$-0.252873\pi$
$829$	40.3493	1.40139	0.700695	+	0.713461i	$0.252873\pi$
$830$	−9.11346	−0.316333
$831$	8.98069	0.311537
$832$	66.1347	2.29281
$833$	8.19674	0.284000
$834$	−40.6644	−1.40809
$835$	14.4664	0.500629
$836$	−12.3349	−0.426612
$837$	−16.7747	−0.579818
$838$	72.0181	2.48782
$839$	20.5533	0.709577	0.354789	−	0.934947i	$-0.384553\pi$
$839$	20.5533	0.709577	0.354789	+	0.934947i	$0.384553\pi$
$840$	−54.9714	−1.89669
$841$	−27.1073	−0.934735
$842$	−67.3121	−2.31973
$843$	−27.9845	−0.963839
$844$	−110.913	−3.81778
$845$	−122.185	−4.20331
$846$	−3.34317	−0.114940
$847$	13.8027	0.474266
$848$	34.7210	1.19232
$849$	41.2309	1.41504
$850$	−30.1264	−1.03333
$851$	−30.5711	−1.04796
$852$	−16.7958	−0.575416
$853$	23.3773	0.800424	0.400212	−	0.916423i	$-0.368936\pi$
$853$	23.3773	0.800424	0.400212	+	0.916423i	$0.368936\pi$
$854$	−23.5042	−0.804298
$855$	−6.29049	−0.215130
$856$	−17.0824	−0.583865
$857$	−47.1685	−1.61124	−0.805622	−	0.592430i	$-0.798169\pi$
$857$	−47.1685	−1.61124	−0.805622	+	0.592430i	$0.798169\pi$
$858$	−28.9649	−0.988845
$859$	30.1869	1.02996	0.514982	−	0.857201i	$-0.327799\pi$
$859$	30.1869	1.02996	0.514982	+	0.857201i	$0.327799\pi$
$860$	105.878	3.61041
$861$	4.46053	0.152014
$862$	30.9217	1.05320
$863$	−12.0608	−0.410553	−0.205276	−	0.978704i	$-0.565809\pi$
$863$	−12.0608	−0.410553	−0.205276	+	0.978704i	$0.565809\pi$
$864$	63.6838	2.16657
$865$	−41.5398	−1.41239
$866$	−85.3415	−2.90002
$867$	21.4799	0.729497
$868$	20.3555	0.690911
$869$	−11.3997	−0.386710
$870$	18.7552	0.635861
$871$	44.5109	1.50820
$872$	13.0634	0.442383
$873$	2.48183	0.0839971
$874$	32.5972	1.10262
$875$	10.0383	0.339355
$876$	−85.4178	−2.88600
$877$	13.5589	0.457851	0.228926	−	0.973444i	$-0.426479\pi$
$877$	13.5589	0.457851	0.228926	+	0.973444i	$0.426479\pi$
$878$	8.26512	0.278934
$879$	−16.1701	−0.545404
$880$	−37.2297	−1.25501
$881$	−9.39923	−0.316668	−0.158334	−	0.987386i	$-0.550612\pi$
$881$	−9.39923	−0.316668	−0.158334	+	0.987386i	$0.550612\pi$
$882$	10.0882	0.339686
$883$	15.7525	0.530112	0.265056	−	0.964233i	$-0.414610\pi$
$883$	15.7525	0.530112	0.265056	+	0.964233i	$0.414610\pi$
$884$	−55.0777	−1.85246
$885$	−74.1141	−2.49132
$886$	100.474	3.37550
$887$	−12.3057	−0.413185	−0.206592	−	0.978427i	$-0.566237\pi$
$887$	−12.3057	−0.413185	−0.206592	+	0.978427i	$0.566237\pi$
$888$	−66.1399	−2.21951
$889$	−20.0719	−0.673188
$890$	124.629	4.17756
$891$	−6.52024	−0.218436
$892$	42.7513	1.43142
$893$	−3.97092	−0.132882
$894$	−21.2360	−0.710238
$895$	66.3059	2.21636
$896$	−3.31112	−0.110617
$897$	54.3039	1.81315
$898$	22.0852	0.736994
$899$	−4.10052	−0.136760
$900$	−26.3047	−0.876824
$901$	−5.59777	−0.186489
$902$	5.94803	0.198048
$903$	−13.0583	−0.434553
$904$	−54.8976	−1.82587
$905$	27.1152	0.901339
$906$	−10.3135	−0.342642
$907$	15.7557	0.523159	0.261579	−	0.965182i	$-0.415757\pi$
$907$	15.7557	0.523159	0.261579	+	0.965182i	$0.415757\pi$
$908$	69.1344	2.29431
$909$	−7.79495	−0.258542
$910$	88.4645	2.93257
$911$	4.14545	0.137345	0.0686724	−	0.997639i	$-0.478124\pi$
$911$	4.14545	0.137345	0.0686724	+	0.997639i	$0.478124\pi$
$912$	35.8178	1.18605
$913$	1.06333	0.0351909
$914$	72.1195	2.38550
$915$	33.2860	1.10040
$916$	−116.520	−3.84992
$917$	−22.6250	−0.747143
$918$	−23.9944	−0.791933
$919$	−10.1036	−0.333288	−0.166644	−	0.986017i	$-0.553293\pi$
$919$	−10.1036	−0.333288	−0.166644	+	0.986017i	$0.553293\pi$
$920$	137.430	4.53095
$921$	20.9852	0.691486
$922$	−68.2423	−2.24744
$923$	15.9590	0.525297
$924$	10.8630	0.357365
$925$	41.3031	1.35804
$926$	0.427991	0.0140647
$927$	−5.01153	−0.164600
$928$	15.5673	0.511021
$929$	3.85509	0.126481	0.0632407	−	0.997998i	$-0.479856\pi$
$929$	3.85509	0.126481	0.0632407	+	0.997998i	$0.479856\pi$
$930$	−40.6333	−1.33242
$931$	11.9824	0.392708
$932$	60.7988	1.99153
$933$	25.2937	0.828080
$934$	−54.7873	−1.79269
$935$	6.00223	0.196294
$936$	−40.0238	−1.30822
$937$	−26.5350	−0.866860	−0.433430	−	0.901187i	$-0.642697\pi$
$937$	−26.5350	−0.866860	−0.433430	+	0.901187i	$0.642697\pi$
$938$	−23.5303	−0.768293
$939$	49.8391	1.62644
$940$	−28.3545	−0.924822
$941$	−38.4637	−1.25388	−0.626940	−	0.779068i	$-0.715693\pi$
$941$	−38.4637	−1.25388	−0.626940	+	0.779068i	$0.715693\pi$
$942$	−4.15690	−0.135439
$943$	−11.1515	−0.363142
$944$	−143.764	−4.67912
$945$	27.3412	0.889409
$946$	−17.4130	−0.566145
$947$	44.2032	1.43641	0.718206	−	0.695831i	$-0.244964\pi$
$947$	44.2032	1.43641	0.718206	+	0.695831i	$0.244964\pi$
$948$	78.3132	2.54350
$949$	81.1619	2.63463
$950$	−44.0404	−1.42886
$951$	−49.2997	−1.59865
$952$	17.1913	0.557174
$953$	−14.3324	−0.464272	−0.232136	−	0.972683i	$-0.574571\pi$
$953$	−14.3324	−0.464272	−0.232136	+	0.972683i	$0.574571\pi$
$954$	−6.88948	−0.223055
$955$	−25.2900	−0.818365
$956$	−53.1259	−1.71822
$957$	−2.18829	−0.0707373
$958$	−26.9523	−0.870788
$959$	5.56118	0.179580
$960$	49.5115	1.59798
$961$	−22.1162	−0.713425
$962$	106.438	3.43169
$963$	1.72151	0.0554748
$964$	103.521	3.33418
$965$	35.3021	1.13642
$966$	−28.7073	−0.923642
$967$	−50.6852	−1.62993	−0.814964	−	0.579512i	$-0.803243\pi$
$967$	−50.6852	−1.62993	−0.814964	+	0.579512i	$0.803243\pi$
$968$	−74.6556	−2.39952
$969$	−5.77459	−0.185507
$970$	29.6702	0.952653
$971$	46.3370	1.48703	0.743513	−	0.668722i	$-0.233158\pi$
$971$	46.3370	1.48703	0.743513	+	0.668722i	$0.233158\pi$
$972$	−37.6561	−1.20782
$973$	−14.4909	−0.464555
$974$	−96.9970	−3.10798
$975$	−73.3673	−2.34963
$976$	64.5670	2.06674
$977$	44.5055	1.42386	0.711929	−	0.702251i	$-0.247822\pi$
$977$	44.5055	1.42386	0.711929	+	0.702251i	$0.247822\pi$
$978$	−58.4969	−1.87052
$979$	−14.5412	−0.464739
$980$	85.5610	2.73315
$981$	−1.31649	−0.0420321
$982$	58.0524	1.85253
$983$	60.5615	1.93161	0.965806	−	0.259266i	$-0.0834807\pi$
$983$	60.5615	1.93161	0.965806	+	0.259266i	$0.0834807\pi$
$984$	−24.1260	−0.769108
$985$	33.4475	1.06573
$986$	−5.86535	−0.186791
$987$	3.49706	0.111313
$988$	−80.5156	−2.56154
$989$	32.6462	1.03809
$990$	7.38726	0.234783
$991$	6.75003	0.214422	0.107211	−	0.994236i	$-0.465808\pi$
$991$	6.75003	0.214422	0.107211	+	0.994236i	$0.465808\pi$
$992$	−33.7267	−1.07082
$993$	14.0707	0.446521
$994$	−8.43659	−0.267592
$995$	20.2965	0.643442
$996$	−7.30477	−0.231460
$997$	18.1266	0.574076	0.287038	−	0.957919i	$-0.407329\pi$
$997$	18.1266	0.574076	0.287038	+	0.957919i	$0.407329\pi$
$998$	−56.7000	−1.79481
$999$	32.8961	1.04079

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	83.2.a.b.1.6	✓	6
3.2	odd	2		747.2.a.j.1.1		6
4.3	odd	2		1328.2.a.l.1.5		6
5.4	even	2		2075.2.a.g.1.1		6
7.6	odd	2		4067.2.a.d.1.6		6
8.3	odd	2		5312.2.a.bo.1.2		6
8.5	even	2		5312.2.a.bn.1.5		6
83.82	odd	2		6889.2.a.e.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
83.2.a.b.1.6	✓	6	1.1	even	1	trivial
747.2.a.j.1.1		6	3.2	odd	2
1328.2.a.l.1.5		6	4.3	odd	2
2075.2.a.g.1.1		6	5.4	even	2
4067.2.a.d.1.6		6	7.6	odd	2
5312.2.a.bn.1.5		6	8.5	even	2
5312.2.a.bo.1.2		6	8.3	odd	2
6889.2.a.e.1.1		6	83.82	odd	2

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:	\( N \)	\(=\)	\( 83 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	83.a (trivial)

\(f(q)\)	\(=\)	\(q+2.62359 q^{2} -1.49589 q^{3} +4.88322 q^{4} -3.47366 q^{5} -3.92460 q^{6} -1.39854 q^{7} +7.56440 q^{8} -0.762314 q^{9} +O(q^{10})\)	\(q+2.62359 q^{2} -1.49589 q^{3} +4.88322 q^{4} -3.47366 q^{5} -3.92460 q^{6} -1.39854 q^{7} +7.56440 q^{8} -0.762314 q^{9} -9.11346 q^{10} +1.06333 q^{11} -7.30477 q^{12} +6.94081 q^{13} -3.66920 q^{14} +5.19621 q^{15} +10.0794 q^{16} -1.62502 q^{17} -2.00000 q^{18} -2.37554 q^{19} -16.9627 q^{20} +2.09206 q^{21} +2.78973 q^{22} -5.23023 q^{23} -11.3155 q^{24} +7.06631 q^{25} +18.2098 q^{26} +5.62801 q^{27} -6.82939 q^{28} +1.37575 q^{29} +13.6327 q^{30} -2.98057 q^{31} +11.3155 q^{32} -1.59062 q^{33} -4.26339 q^{34} +4.85806 q^{35} -3.72255 q^{36} +5.84507 q^{37} -6.23245 q^{38} -10.3827 q^{39} -26.2762 q^{40} +2.13212 q^{41} +5.48872 q^{42} -6.24182 q^{43} +5.19246 q^{44} +2.64802 q^{45} -13.7220 q^{46} +1.67158 q^{47} -15.0777 q^{48} -5.04408 q^{49} +18.5391 q^{50} +2.43085 q^{51} +33.8935 q^{52} +3.44474 q^{53} +14.7656 q^{54} -3.69363 q^{55} -10.5791 q^{56} +3.55355 q^{57} +3.60940 q^{58} -14.2631 q^{59} +25.3743 q^{60} +6.40582 q^{61} -7.81980 q^{62} +1.06613 q^{63} +9.52838 q^{64} -24.1100 q^{65} -4.17313 q^{66} +6.41293 q^{67} -7.93534 q^{68} +7.82385 q^{69} +12.7456 q^{70} +2.29930 q^{71} -5.76645 q^{72} +11.6934 q^{73} +15.3351 q^{74} -10.5704 q^{75} -11.6003 q^{76} -1.48710 q^{77} -27.2399 q^{78} -10.7208 q^{79} -35.0125 q^{80} -6.13193 q^{81} +5.59380 q^{82} +1.00000 q^{83} +10.2160 q^{84} +5.64477 q^{85} -16.3760 q^{86} -2.05797 q^{87} +8.04342 q^{88} -13.6752 q^{89} +6.94732 q^{90} -9.70701 q^{91} -25.5404 q^{92} +4.45861 q^{93} +4.38555 q^{94} +8.25183 q^{95} -16.9268 q^{96} -3.25565 q^{97} -13.2336 q^{98} -0.810588 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} + q^{3} + 7 q^{4} + 2 q^{5} - 7 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 6 * q + q^2 + q^3 + 7 * q^4 + 2 * q^5 - 7 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9	\( 6 q + q^{2} + q^{3} + 7 q^{4} + 2 q^{5} - 7 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9} - 6 q^{10} - 3 q^{11} - 9 q^{12} + 14 q^{13} - 15 q^{14} - 6 q^{15} + q^{16} - 5 q^{17} - 12 q^{18} - 4 q^{19} - 20 q^{20} - 2 q^{21} - q^{22} - 5 q^{23} - 17 q^{24} + 14 q^{25} - 2 q^{26} + 10 q^{27} + 9 q^{28} - q^{29} + 18 q^{30} + 3 q^{31} + 17 q^{32} + 2 q^{33} + 15 q^{34} - 10 q^{35} - 8 q^{36} + 39 q^{37} - 6 q^{38} - 8 q^{39} - 18 q^{40} - q^{41} + 17 q^{42} - 8 q^{43} + 27 q^{44} + 10 q^{45} - 12 q^{46} - 12 q^{47} + 7 q^{48} + 11 q^{49} + 35 q^{50} - 24 q^{51} + 36 q^{52} + 14 q^{53} + 19 q^{54} - 24 q^{55} - 23 q^{56} - 10 q^{57} + 25 q^{58} - 17 q^{59} - 5 q^{61} + 5 q^{62} - 11 q^{63} + 9 q^{64} - 8 q^{65} - 39 q^{66} + 16 q^{67} - 15 q^{68} + 8 q^{69} - 10 q^{70} - 26 q^{71} + 10 q^{72} - 6 q^{73} + 23 q^{74} - 45 q^{75} - 28 q^{76} + 6 q^{77} - 18 q^{78} - 12 q^{79} - 60 q^{80} - 34 q^{81} + 10 q^{82} + 6 q^{83} + 41 q^{84} + 18 q^{85} + 16 q^{86} - 3 q^{87} - 17 q^{88} - 22 q^{89} - 4 q^{90} - 2 q^{91} + 2 q^{92} + 34 q^{93} - 8 q^{94} - 4 q^{95} - 19 q^{96} + 6 q^{97} - 30 q^{98} - 18 q^{99}+O(q^{100}) \) 6 * q + q^2 + q^3 + 7 * q^4 + 2 * q^5 - 7 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9 - 6 * q^10 - 3 * q^11 - 9 * q^12 + 14 * q^13 - 15 * q^14 - 6 * q^15 + q^16 - 5 * q^17 - 12 * q^18 - 4 * q^19 - 20 * q^20 - 2 * q^21 - q^22 - 5 * q^23 - 17 * q^24 + 14 * q^25 - 2 * q^26 + 10 * q^27 + 9 * q^28 - q^29 + 18 * q^30 + 3 * q^31 + 17 * q^32 + 2 * q^33 + 15 * q^34 - 10 * q^35 - 8 * q^36 + 39 * q^37 - 6 * q^38 - 8 * q^39 - 18 * q^40 - q^41 + 17 * q^42 - 8 * q^43 + 27 * q^44 + 10 * q^45 - 12 * q^46 - 12 * q^47 + 7 * q^48 + 11 * q^49 + 35 * q^50 - 24 * q^51 + 36 * q^52 + 14 * q^53 + 19 * q^54 - 24 * q^55 - 23 * q^56 - 10 * q^57 + 25 * q^58 - 17 * q^59 - 5 * q^61 + 5 * q^62 - 11 * q^63 + 9 * q^64 - 8 * q^65 - 39 * q^66 + 16 * q^67 - 15 * q^68 + 8 * q^69 - 10 * q^70 - 26 * q^71 + 10 * q^72 - 6 * q^73 + 23 * q^74 - 45 * q^75 - 28 * q^76 + 6 * q^77 - 18 * q^78 - 12 * q^79 - 60 * q^80 - 34 * q^81 + 10 * q^82 + 6 * q^83 + 41 * q^84 + 18 * q^85 + 16 * q^86 - 3 * q^87 - 17 * q^88 - 22 * q^89 - 4 * q^90 - 2 * q^91 + 2 * q^92 + 34 * q^93 - 8 * q^94 - 4 * q^95 - 19 * q^96 + 6 * q^97 - 30 * q^98 - 18 * q^99

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