LMFDB - Embedded newform 6035.2.a.h.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6035,2,Mod(1,6035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6035, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6035 = 5 \cdot 17 \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6035.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1897176198$
Analytic rank:	$0$
Dimension:	$59$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	6035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.46188 q^{2} +1.88140 q^{3} +4.06087 q^{4} +1.00000 q^{5} -4.63179 q^{6} -1.20679 q^{7} -5.07361 q^{8} +0.539668 q^{9} +O(q^{10})$	\(q-2.46188 q^{2} +1.88140 q^{3} +4.06087 q^{4} +1.00000 q^{5} -4.63179 q^{6} -1.20679 q^{7} -5.07361 q^{8} +0.539668 q^{9} -2.46188 q^{10} +2.83098 q^{11} +7.64012 q^{12} -1.86554 q^{13} +2.97097 q^{14} +1.88140 q^{15} +4.36890 q^{16} -1.00000 q^{17} -1.32860 q^{18} +6.36164 q^{19} +4.06087 q^{20} -2.27045 q^{21} -6.96953 q^{22} +4.52532 q^{23} -9.54550 q^{24} +1.00000 q^{25} +4.59274 q^{26} -4.62887 q^{27} -4.90060 q^{28} -3.61475 q^{29} -4.63179 q^{30} +9.88942 q^{31} -0.608505 q^{32} +5.32620 q^{33} +2.46188 q^{34} -1.20679 q^{35} +2.19152 q^{36} +8.10689 q^{37} -15.6616 q^{38} -3.50983 q^{39} -5.07361 q^{40} +6.48718 q^{41} +5.58958 q^{42} -3.53327 q^{43} +11.4962 q^{44} +0.539668 q^{45} -11.1408 q^{46} +1.82596 q^{47} +8.21966 q^{48} -5.54367 q^{49} -2.46188 q^{50} -1.88140 q^{51} -7.57571 q^{52} -8.01539 q^{53} +11.3957 q^{54} +2.83098 q^{55} +6.12277 q^{56} +11.9688 q^{57} +8.89908 q^{58} +11.1754 q^{59} +7.64012 q^{60} -0.268954 q^{61} -24.3466 q^{62} -0.651264 q^{63} -7.23974 q^{64} -1.86554 q^{65} -13.1125 q^{66} +2.01532 q^{67} -4.06087 q^{68} +8.51393 q^{69} +2.97097 q^{70} -1.00000 q^{71} -2.73807 q^{72} -4.35399 q^{73} -19.9582 q^{74} +1.88140 q^{75} +25.8338 q^{76} -3.41638 q^{77} +8.64078 q^{78} -1.53862 q^{79} +4.36890 q^{80} -10.3278 q^{81} -15.9707 q^{82} -4.83390 q^{83} -9.21999 q^{84} -1.00000 q^{85} +8.69850 q^{86} -6.80079 q^{87} -14.3633 q^{88} +5.31722 q^{89} -1.32860 q^{90} +2.25131 q^{91} +18.3767 q^{92} +18.6060 q^{93} -4.49531 q^{94} +6.36164 q^{95} -1.14484 q^{96} +7.25798 q^{97} +13.6479 q^{98} +1.52779 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 59 q + 2 q^{2} + 6 q^{3} + 76 q^{4} + 59 q^{5} + 14 q^{6} + 9 q^{7} + 6 q^{8} + 97 q^{9}+O(q^{10}) $ 59 * q + 2 * q^2 + 6 * q^3 + 76 * q^4 + 59 * q^5 + 14 * q^6 + 9 * q^7 + 6 * q^8 + 97 * q^9	\( 59 q + 2 q^{2} + 6 q^{3} + 76 q^{4} + 59 q^{5} + 14 q^{6} + 9 q^{7} + 6 q^{8} + 97 q^{9} + 2 q^{10} + 6 q^{11} + 16 q^{12} + 25 q^{13} + 8 q^{14} + 6 q^{15} + 114 q^{16} - 59 q^{17} + 3 q^{18} + 35 q^{19} + 76 q^{20} + 41 q^{21} + 13 q^{22} - 2 q^{23} + 35 q^{24} + 59 q^{25} + 10 q^{26} + 27 q^{27} + 28 q^{28} + 10 q^{29} + 14 q^{30} + 15 q^{31} + 19 q^{32} - 3 q^{33} - 2 q^{34} + 9 q^{35} + 160 q^{36} + 56 q^{37} + 17 q^{38} + 25 q^{39} + 6 q^{40} + 47 q^{41} + 46 q^{42} + 27 q^{43} + 39 q^{44} + 97 q^{45} + 4 q^{46} - 8 q^{47} + 58 q^{48} + 174 q^{49} + 2 q^{50} - 6 q^{51} + 13 q^{52} + 17 q^{53} + 48 q^{54} + 6 q^{55} + 33 q^{56} + 6 q^{57} + 32 q^{58} + 30 q^{59} + 16 q^{60} + 85 q^{61} - 3 q^{62} + 14 q^{63} + 168 q^{64} + 25 q^{65} + 87 q^{66} + 21 q^{67} - 76 q^{68} + 111 q^{69} + 8 q^{70} - 59 q^{71} - 52 q^{72} + 41 q^{73} + 11 q^{74} + 6 q^{75} + 118 q^{76} + 55 q^{77} - 54 q^{78} + 43 q^{79} + 114 q^{80} + 207 q^{81} + 45 q^{82} + 10 q^{83} + 62 q^{84} - 59 q^{85} + 19 q^{86} + 8 q^{87} + 35 q^{88} + 86 q^{89} + 3 q^{90} + 47 q^{91} - 98 q^{92} + 41 q^{93} + 30 q^{94} + 35 q^{95} + 69 q^{96} + 72 q^{97} + 14 q^{98} + 25 q^{99}+O(q^{100}) \) 59 * q + 2 * q^2 + 6 * q^3 + 76 * q^4 + 59 * q^5 + 14 * q^6 + 9 * q^7 + 6 * q^8 + 97 * q^9 + 2 * q^10 + 6 * q^11 + 16 * q^12 + 25 * q^13 + 8 * q^14 + 6 * q^15 + 114 * q^16 - 59 * q^17 + 3 * q^18 + 35 * q^19 + 76 * q^20 + 41 * q^21 + 13 * q^22 - 2 * q^23 + 35 * q^24 + 59 * q^25 + 10 * q^26 + 27 * q^27 + 28 * q^28 + 10 * q^29 + 14 * q^30 + 15 * q^31 + 19 * q^32 - 3 * q^33 - 2 * q^34 + 9 * q^35 + 160 * q^36 + 56 * q^37 + 17 * q^38 + 25 * q^39 + 6 * q^40 + 47 * q^41 + 46 * q^42 + 27 * q^43 + 39 * q^44 + 97 * q^45 + 4 * q^46 - 8 * q^47 + 58 * q^48 + 174 * q^49 + 2 * q^50 - 6 * q^51 + 13 * q^52 + 17 * q^53 + 48 * q^54 + 6 * q^55 + 33 * q^56 + 6 * q^57 + 32 * q^58 + 30 * q^59 + 16 * q^60 + 85 * q^61 - 3 * q^62 + 14 * q^63 + 168 * q^64 + 25 * q^65 + 87 * q^66 + 21 * q^67 - 76 * q^68 + 111 * q^69 + 8 * q^70 - 59 * q^71 - 52 * q^72 + 41 * q^73 + 11 * q^74 + 6 * q^75 + 118 * q^76 + 55 * q^77 - 54 * q^78 + 43 * q^79 + 114 * q^80 + 207 * q^81 + 45 * q^82 + 10 * q^83 + 62 * q^84 - 59 * q^85 + 19 * q^86 + 8 * q^87 + 35 * q^88 + 86 * q^89 + 3 * q^90 + 47 * q^91 - 98 * q^92 + 41 * q^93 + 30 * q^94 + 35 * q^95 + 69 * q^96 + 72 * q^97 + 14 * q^98 + 25 * 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 $

$2$	−2.46188	−1.74081	−0.870407	−	0.492333i	$-0.836144\pi$
$2$	−2.46188	−1.74081	−0.870407	+	0.492333i	$0.836144\pi$
$3$	1.88140	1.08623	0.543114	−	0.839659i	$-0.317245\pi$
$3$	1.88140	1.08623	0.543114	+	0.839659i	$0.317245\pi$
$4$	4.06087	2.03043
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−4.63179	−1.89092
$7$	−1.20679	−0.456123	−0.228061	−	0.973647i	$-0.573239\pi$
$7$	−1.20679	−0.456123	−0.228061	+	0.973647i	$0.573239\pi$
$8$	−5.07361	−1.79379
$9$	0.539668	0.179889
$10$	−2.46188	−0.778516
$11$	2.83098	0.853571	0.426786	−	0.904353i	$-0.359646\pi$
$11$	2.83098	0.853571	0.426786	+	0.904353i	$0.359646\pi$
$12$	7.64012	2.20551
$13$	−1.86554	−0.517408	−0.258704	−	0.965957i	$-0.583295\pi$
$13$	−1.86554	−0.517408	−0.258704	+	0.965957i	$0.583295\pi$
$14$	2.97097	0.794024
$15$	1.88140	0.485776
$16$	4.36890	1.09223
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.32860	−0.313154
$19$	6.36164	1.45946	0.729730	−	0.683735i	$-0.239646\pi$
$19$	6.36164	1.45946	0.729730	+	0.683735i	$0.239646\pi$
$20$	4.06087	0.908037
$21$	−2.27045	−0.495453
$22$	−6.96953	−1.48591
$23$	4.52532	0.943594	0.471797	−	0.881707i	$-0.343606\pi$
$23$	4.52532	0.943594	0.471797	+	0.881707i	$0.343606\pi$
$24$	−9.54550	−1.94847
$25$	1.00000	0.200000
$26$	4.59274	0.900710
$27$	−4.62887	−0.890826
$28$	−4.90060	−0.926126
$29$	−3.61475	−0.671242	−0.335621	−	0.941997i	$-0.608946\pi$
$29$	−3.61475	−0.671242	−0.335621	+	0.941997i	$0.608946\pi$
$30$	−4.63179	−0.845645
$31$	9.88942	1.77619	0.888096	−	0.459658i	$-0.152028\pi$
$31$	9.88942	1.77619	0.888096	+	0.459658i	$0.152028\pi$
$32$	−0.608505	−0.107569
$33$	5.32620	0.927172
$34$	2.46188	0.422209
$35$	−1.20679	−0.203984
$36$	2.19152	0.365253
$37$	8.10689	1.33276	0.666382	−	0.745610i	$-0.267842\pi$
$37$	8.10689	1.33276	0.666382	+	0.745610i	$0.267842\pi$
$38$	−15.6616	−2.54065
$39$	−3.50983	−0.562022
$40$	−5.07361	−0.802208
$41$	6.48718	1.01313	0.506564	−	0.862203i	$-0.330915\pi$
$41$	6.48718	1.01313	0.506564	+	0.862203i	$0.330915\pi$
$42$	5.58958	0.862491
$43$	−3.53327	−0.538819	−0.269410	−	0.963026i	$-0.586829\pi$
$43$	−3.53327	−0.538819	−0.269410	+	0.963026i	$0.586829\pi$
$44$	11.4962	1.73312
$45$	0.539668	0.0804490
$46$	−11.1408	−1.64262
$47$	1.82596	0.266344	0.133172	−	0.991093i	$-0.457484\pi$
$47$	1.82596	0.266344	0.133172	+	0.991093i	$0.457484\pi$
$48$	8.21966	1.18641
$49$	−5.54367	−0.791952
$50$	−2.46188	−0.348163
$51$	−1.88140	−0.263449
$52$	−7.57571	−1.05056
$53$	−8.01539	−1.10100	−0.550499	−	0.834836i	$-0.685563\pi$
$53$	−8.01539	−1.10100	−0.550499	+	0.834836i	$0.685563\pi$
$54$	11.3957	1.55076
$55$	2.83098	0.381729
$56$	6.12277	0.818189
$57$	11.9688	1.58531
$58$	8.89908	1.16851
$59$	11.1754	1.45492	0.727458	−	0.686152i	$-0.240702\pi$
$59$	11.1754	1.45492	0.727458	+	0.686152i	$0.240702\pi$
$60$	7.64012	0.986335
$61$	−0.268954	−0.0344360	−0.0172180	−	0.999852i	$-0.505481\pi$
$61$	−0.268954	−0.0344360	−0.0172180	+	0.999852i	$0.505481\pi$
$62$	−24.3466	−3.09202
$63$	−0.651264	−0.0820516
$64$	−7.23974	−0.904967
$65$	−1.86554	−0.231392
$66$	−13.1125	−1.61403
$67$	2.01532	0.246211	0.123105	−	0.992394i	$-0.460715\pi$
$67$	2.01532	0.246211	0.123105	+	0.992394i	$0.460715\pi$
$68$	−4.06087	−0.492452
$69$	8.51393	1.02496
$70$	2.97097	0.355099
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	−2.73807	−0.322684
$73$	−4.35399	−0.509596	−0.254798	−	0.966994i	$-0.582009\pi$
$73$	−4.35399	−0.509596	−0.254798	+	0.966994i	$0.582009\pi$
$74$	−19.9582	−2.32010
$75$	1.88140	0.217245
$76$	25.8338	2.96334
$77$	−3.41638	−0.389333
$78$	8.64078	0.978376
$79$	−1.53862	−0.173108	−0.0865539	−	0.996247i	$-0.527585\pi$
$79$	−1.53862	−0.173108	−0.0865539	+	0.996247i	$0.527585\pi$
$80$	4.36890	0.488458
$81$	−10.3278	−1.14753
$82$	−15.9707	−1.76367
$83$	−4.83390	−0.530590	−0.265295	−	0.964167i	$-0.585469\pi$
$83$	−4.83390	−0.530590	−0.265295	+	0.964167i	$0.585469\pi$
$84$	−9.21999	−1.00598
$85$	−1.00000	−0.108465
$86$	8.69850	0.937984
$87$	−6.80079	−0.729121
$88$	−14.3633	−1.53113
$89$	5.31722	0.563624	0.281812	−	0.959470i	$-0.409065\pi$
$89$	5.31722	0.563624	0.281812	+	0.959470i	$0.409065\pi$
$90$	−1.32860	−0.140047
$91$	2.25131	0.236001
$92$	18.3767	1.91590
$93$	18.6060	1.92935
$94$	−4.49531	−0.463656
$95$	6.36164	0.652691
$96$	−1.14484	−0.116845
$97$	7.25798	0.736936	0.368468	−	0.929640i	$-0.379882\pi$
$97$	7.25798	0.736936	0.368468	+	0.929640i	$0.379882\pi$
$98$	13.6479	1.37864
$99$	1.52779	0.153548
$100$	4.06087	0.406087
$101$	−5.19263	−0.516686	−0.258343	−	0.966053i	$-0.583176\pi$
$101$	−5.19263	−0.516686	−0.258343	+	0.966053i	$0.583176\pi$
$102$	4.63179	0.458615
$103$	−15.8628	−1.56301	−0.781505	−	0.623900i	$-0.785547\pi$
$103$	−15.8628	−1.56301	−0.781505	+	0.623900i	$0.785547\pi$
$104$	9.46502	0.928122
$105$	−2.27045	−0.221573
$106$	19.7330	1.91663
$107$	−14.8018	−1.43095	−0.715473	−	0.698641i	$-0.753789\pi$
$107$	−14.8018	−1.43095	−0.715473	+	0.698641i	$0.753789\pi$
$108$	−18.7972	−1.80876
$109$	−11.6696	−1.11775	−0.558873	−	0.829253i	$-0.688766\pi$
$109$	−11.6696	−1.11775	−0.558873	+	0.829253i	$0.688766\pi$
$110$	−6.96953	−0.664518
$111$	15.2523	1.44769
$112$	−5.27233	−0.498189
$113$	7.47612	0.703294	0.351647	−	0.936133i	$-0.385622\pi$
$113$	7.47612	0.703294	0.351647	+	0.936133i	$0.385622\pi$
$114$	−29.4658	−2.75972
$115$	4.52532	0.421988
$116$	−14.6790	−1.36291
$117$	−1.00677	−0.0930761
$118$	−27.5126	−2.53274
$119$	1.20679	0.110626
$120$	−9.54550	−0.871381
$121$	−2.98558	−0.271416
$122$	0.662133	0.0599467
$123$	12.2050	1.10049
$124$	40.1596	3.60644
$125$	1.00000	0.0894427
$126$	1.60334	0.142837
$127$	10.3989	0.922752	0.461376	−	0.887205i	$-0.347356\pi$
$127$	10.3989	0.922752	0.461376	+	0.887205i	$0.347356\pi$
$128$	19.0404	1.68295
$129$	−6.64750	−0.585280
$130$	4.59274	0.402810
$131$	−6.55120	−0.572381	−0.286190	−	0.958173i	$-0.592389\pi$
$131$	−6.55120	−0.572381	−0.286190	+	0.958173i	$0.592389\pi$
$132$	21.6290	1.88256
$133$	−7.67715	−0.665693
$134$	−4.96149	−0.428607
$135$	−4.62887	−0.398390
$136$	5.07361	0.435059
$137$	−14.5766	−1.24536	−0.622681	−	0.782476i	$-0.713956\pi$
$137$	−14.5766	−1.24536	−0.622681	+	0.782476i	$0.713956\pi$
$138$	−20.9603	−1.78426
$139$	10.8608	0.921198	0.460599	−	0.887608i	$-0.347635\pi$
$139$	10.8608	0.921198	0.460599	+	0.887608i	$0.347635\pi$
$140$	−4.90060	−0.414176
$141$	3.43537	0.289310
$142$	2.46188	0.206597
$143$	−5.28130	−0.441644
$144$	2.35776	0.196480
$145$	−3.61475	−0.300188
$146$	10.7190	0.887112
$147$	−10.4299	−0.860240
$148$	32.9210	2.70609
$149$	−16.0184	−1.31227	−0.656137	−	0.754641i	$-0.727811\pi$
$149$	−16.0184	−1.31227	−0.656137	+	0.754641i	$0.727811\pi$
$150$	−4.63179	−0.378184
$151$	18.8468	1.53373	0.766867	−	0.641806i	$-0.221814\pi$
$151$	18.8468	1.53373	0.766867	+	0.641806i	$0.221814\pi$
$152$	−32.2765	−2.61797
$153$	−0.539668	−0.0436296
$154$	8.41074	0.677756
$155$	9.88942	0.794337
$156$	−14.2529	−1.14115
$157$	8.23805	0.657468	0.328734	−	0.944423i	$-0.393378\pi$
$157$	8.23805	0.657468	0.328734	+	0.944423i	$0.393378\pi$
$158$	3.78789	0.301348
$159$	−15.0802	−1.19593
$160$	−0.608505	−0.0481065
$161$	−5.46109	−0.430394
$162$	25.4257	1.99763
$163$	3.51700	0.275472	0.137736	−	0.990469i	$-0.456017\pi$
$163$	3.51700	0.275472	0.137736	+	0.990469i	$0.456017\pi$
$164$	26.3436	2.05709
$165$	5.32620	0.414644
$166$	11.9005	0.923658
$167$	2.26426	0.175213	0.0876067	−	0.996155i	$-0.472078\pi$
$167$	2.26426	0.175213	0.0876067	+	0.996155i	$0.472078\pi$
$168$	11.5194	0.888739
$169$	−9.51976	−0.732289
$170$	2.46188	0.188818
$171$	3.43317	0.262541
$172$	−14.3482	−1.09404
$173$	16.4099	1.24762	0.623810	−	0.781576i	$-0.285584\pi$
$173$	16.4099	1.24762	0.623810	+	0.781576i	$0.285584\pi$
$174$	16.7427	1.26926
$175$	−1.20679	−0.0912245
$176$	12.3683	0.932292
$177$	21.0254	1.58037
$178$	−13.0904	−0.981164
$179$	25.4935	1.90548	0.952738	−	0.303792i	$-0.0982529\pi$
$179$	25.4935	1.90548	0.952738	+	0.303792i	$0.0982529\pi$
$180$	2.19152	0.163346
$181$	22.8637	1.69945	0.849724	−	0.527228i	$-0.176769\pi$
$181$	22.8637	1.69945	0.849724	+	0.527228i	$0.176769\pi$
$182$	−5.54246	−0.410834
$183$	−0.506010	−0.0374054
$184$	−22.9597	−1.69261
$185$	8.10689	0.596030
$186$	−45.8057	−3.35864
$187$	−2.83098	−0.207021
$188$	7.41500	0.540794
$189$	5.58606	0.406326
$190$	−15.6616	−1.13621
$191$	26.5622	1.92198	0.960988	−	0.276590i	$-0.0892044\pi$
$191$	26.5622	1.92198	0.960988	+	0.276590i	$0.0892044\pi$
$192$	−13.6209	−0.983000
$193$	16.7206	1.20357	0.601787	−	0.798657i	$-0.294456\pi$
$193$	16.7206	1.20357	0.601787	+	0.798657i	$0.294456\pi$
$194$	−17.8683	−1.28287
$195$	−3.50983	−0.251344
$196$	−22.5121	−1.60801
$197$	20.2166	1.44037	0.720185	−	0.693782i	$-0.244057\pi$
$197$	20.2166	1.44037	0.720185	+	0.693782i	$0.244057\pi$
$198$	−3.76123	−0.267299
$199$	19.2284	1.36306	0.681531	−	0.731789i	$-0.261314\pi$
$199$	19.2284	1.36306	0.681531	+	0.731789i	$0.261314\pi$
$200$	−5.07361	−0.358759
$201$	3.79163	0.267441
$202$	12.7836	0.899454
$203$	4.36223	0.306169
$204$	−7.64012	−0.534915
$205$	6.48718	0.453084
$206$	39.0524	2.72091
$207$	2.44217	0.169742
$208$	−8.15036	−0.565126
$209$	18.0096	1.24575
$210$	5.58958	0.385718
$211$	14.7226	1.01354	0.506772	−	0.862080i	$-0.330838\pi$
$211$	14.7226	1.01354	0.506772	+	0.862080i	$0.330838\pi$
$212$	−32.5494	−2.23550
$213$	−1.88140	−0.128911
$214$	36.4403	2.49101
$215$	−3.53327	−0.240967
$216$	23.4851	1.59796
$217$	−11.9344	−0.810161
$218$	28.7292	1.94579
$219$	−8.19160	−0.553537
$220$	11.4962	0.775074
$221$	1.86554	0.125490
$222$	−37.5494	−2.52015
$223$	27.9295	1.87030	0.935148	−	0.354258i	$-0.115266\pi$
$223$	27.9295	1.87030	0.935148	+	0.354258i	$0.115266\pi$
$224$	0.734335	0.0490648
$225$	0.539668	0.0359779
$226$	−18.4053	−1.22430
$227$	8.71159	0.578209	0.289104	−	0.957298i	$-0.406643\pi$
$227$	8.71159	0.578209	0.289104	+	0.957298i	$0.406643\pi$
$228$	48.6037	3.21886
$229$	−26.0850	−1.72374	−0.861872	−	0.507125i	$-0.830708\pi$
$229$	−26.0850	−1.72374	−0.861872	+	0.507125i	$0.830708\pi$
$230$	−11.1408	−0.734603
$231$	−6.42759	−0.422904
$232$	18.3398	1.20407
$233$	−27.0492	−1.77205	−0.886025	−	0.463638i	$-0.846544\pi$
$233$	−27.0492	−1.77205	−0.886025	+	0.463638i	$0.846544\pi$
$234$	2.47855	0.162028
$235$	1.82596	0.119113
$236$	45.3819	2.95411
$237$	−2.89475	−0.188034
$238$	−2.97097	−0.192579
$239$	−21.6207	−1.39853	−0.699263	−	0.714864i	$-0.746488\pi$
$239$	−21.6207	−1.39853	−0.699263	+	0.714864i	$0.746488\pi$
$240$	8.21966	0.530577
$241$	15.6694	1.00935	0.504677	−	0.863308i	$-0.331612\pi$
$241$	15.6694	1.00935	0.504677	+	0.863308i	$0.331612\pi$
$242$	7.35015	0.472485
$243$	−5.54405	−0.355651
$244$	−1.09219	−0.0699201
$245$	−5.54367	−0.354172
$246$	−30.0472	−1.91574
$247$	−11.8679	−0.755136
$248$	−50.1751	−3.18612
$249$	−9.09450	−0.576341
$250$	−2.46188	−0.155703
$251$	−4.51023	−0.284683	−0.142342	−	0.989818i	$-0.545463\pi$
$251$	−4.51023	−0.284683	−0.142342	+	0.989818i	$0.545463\pi$
$252$	−2.64470	−0.166600
$253$	12.8111	0.805424
$254$	−25.6008	−1.60634
$255$	−1.88140	−0.117818
$256$	−32.3957	−2.02473
$257$	−26.1056	−1.62842	−0.814212	−	0.580567i	$-0.802831\pi$
$257$	−26.1056	−1.62842	−0.814212	+	0.580567i	$0.802831\pi$
$258$	16.3654	1.01886
$259$	−9.78329	−0.607904
$260$	−7.57571	−0.469825
$261$	−1.95076	−0.120749
$262$	16.1283	0.996408
$263$	7.07642	0.436351	0.218175	−	0.975910i	$-0.429990\pi$
$263$	7.07642	0.436351	0.218175	+	0.975910i	$0.429990\pi$
$264$	−27.0231	−1.66315
$265$	−8.01539	−0.492382
$266$	18.9002	1.15885
$267$	10.0038	0.612223
$268$	8.18395	0.499915
$269$	−6.10431	−0.372187	−0.186093	−	0.982532i	$-0.559583\pi$
$269$	−6.10431	−0.372187	−0.186093	+	0.982532i	$0.559583\pi$
$270$	11.3957	0.693522
$271$	21.4650	1.30391	0.651953	−	0.758259i	$-0.273950\pi$
$271$	21.4650	1.30391	0.651953	+	0.758259i	$0.273950\pi$
$272$	−4.36890	−0.264904
$273$	4.23561	0.256351
$274$	35.8858	2.16794
$275$	2.83098	0.170714
$276$	34.5739	2.08111
$277$	−22.3247	−1.34136	−0.670680	−	0.741747i	$-0.733997\pi$
$277$	−22.3247	−1.34136	−0.670680	+	0.741747i	$0.733997\pi$
$278$	−26.7379	−1.60363
$279$	5.33700	0.319518
$280$	6.12277	0.365905
$281$	17.3377	1.03428	0.517141	−	0.855900i	$-0.326996\pi$
$281$	17.3377	1.03428	0.517141	+	0.855900i	$0.326996\pi$
$282$	−8.45748	−0.503636
$283$	13.6204	0.809649	0.404825	−	0.914394i	$-0.367333\pi$
$283$	13.6204	0.809649	0.404825	+	0.914394i	$0.367333\pi$
$284$	−4.06087	−0.240968
$285$	11.9688	0.708970
$286$	13.0019	0.768820
$287$	−7.82864	−0.462110
$288$	−0.328390	−0.0193506
$289$	1.00000	0.0588235
$290$	8.89908	0.522572
$291$	13.6552	0.800480
$292$	−17.6810	−1.03470
$293$	−2.66013	−0.155406	−0.0777032	−	0.996977i	$-0.524759\pi$
$293$	−2.66013	−0.155406	−0.0777032	+	0.996977i	$0.524759\pi$
$294$	25.6771	1.49752
$295$	11.1754	0.650658
$296$	−41.1312	−2.39070
$297$	−13.1042	−0.760384
$298$	39.4353	2.28443
$299$	−8.44216	−0.488223
$300$	7.64012	0.441102
$301$	4.26391	0.245768
$302$	−46.3987	−2.66995
$303$	−9.76942	−0.561238
$304$	27.7934	1.59406
$305$	−0.268954	−0.0154003
$306$	1.32860	0.0759510
$307$	0.157254	0.00897497	0.00448749	−	0.999990i	$-0.498572\pi$
$307$	0.157254	0.00897497	0.00448749	+	0.999990i	$0.498572\pi$
$308$	−13.8735	−0.790515
$309$	−29.8443	−1.69778
$310$	−24.3466	−1.38279
$311$	1.69650	0.0961994	0.0480997	−	0.998843i	$-0.484683\pi$
$311$	1.69650	0.0961994	0.0480997	+	0.998843i	$0.484683\pi$
$312$	17.8075	1.00815
$313$	26.8693	1.51874	0.759371	−	0.650658i	$-0.225507\pi$
$313$	26.8693	1.51874	0.759371	+	0.650658i	$0.225507\pi$
$314$	−20.2811	−1.14453
$315$	−0.651264	−0.0366946
$316$	−6.24811	−0.351484
$317$	27.3841	1.53804	0.769022	−	0.639222i	$-0.220744\pi$
$317$	27.3841	1.53804	0.769022	+	0.639222i	$0.220744\pi$
$318$	37.1256	2.08190
$319$	−10.2333	−0.572953
$320$	−7.23974	−0.404714
$321$	−27.8481	−1.55433
$322$	13.4446	0.749237
$323$	−6.36164	−0.353971
$324$	−41.9397	−2.32998
$325$	−1.86554	−0.103482
$326$	−8.65843	−0.479546
$327$	−21.9552	−1.21413
$328$	−32.9134	−1.81734
$329$	−2.20355	−0.121486
$330$	−13.1125	−0.721818
$331$	33.8073	1.85822	0.929108	−	0.369808i	$-0.120576\pi$
$331$	33.8073	1.85822	0.929108	+	0.369808i	$0.120576\pi$
$332$	−19.6298	−1.07733
$333$	4.37503	0.239750
$334$	−5.57433	−0.305014
$335$	2.01532	0.110109
$336$	−9.91937	−0.541146
$337$	−5.12255	−0.279043	−0.139521	−	0.990219i	$-0.544556\pi$
$337$	−5.12255	−0.279043	−0.139521	+	0.990219i	$0.544556\pi$
$338$	23.4365	1.27478
$339$	14.0656	0.763937
$340$	−4.06087	−0.220231
$341$	27.9967	1.51611
$342$	−8.45207	−0.457036
$343$	15.1375	0.817350
$344$	17.9265	0.966530
$345$	8.51393	0.458375
$346$	−40.3992	−2.17187
$347$	1.90409	0.102217	0.0511084	−	0.998693i	$-0.483725\pi$
$347$	1.90409	0.102217	0.0511084	+	0.998693i	$0.483725\pi$
$348$	−27.6171	−1.48043
$349$	−5.78920	−0.309889	−0.154944	−	0.987923i	$-0.549520\pi$
$349$	−5.78920	−0.309889	−0.154944	+	0.987923i	$0.549520\pi$
$350$	2.97097	0.158805
$351$	8.63534	0.460920
$352$	−1.72266	−0.0918182
$353$	−24.9296	−1.32687	−0.663435	−	0.748234i	$-0.730902\pi$
$353$	−24.9296	−1.32687	−0.663435	+	0.748234i	$0.730902\pi$
$354$	−51.7622	−2.75113
$355$	−1.00000	−0.0530745
$356$	21.5925	1.14440
$357$	2.27045	0.120165
$358$	−62.7621	−3.31708
$359$	−13.9801	−0.737842	−0.368921	−	0.929461i	$-0.620273\pi$
$359$	−13.9801	−0.737842	−0.368921	+	0.929461i	$0.620273\pi$
$360$	−2.73807	−0.144309
$361$	21.4705	1.13003
$362$	−56.2878	−2.95842
$363$	−5.61707	−0.294820
$364$	9.14226	0.479185
$365$	−4.35399	−0.227898
$366$	1.24574	0.0651158
$367$	−3.87350	−0.202195	−0.101098	−	0.994877i	$-0.532235\pi$
$367$	−3.87350	−0.202195	−0.101098	+	0.994877i	$0.532235\pi$
$368$	19.7707	1.03062
$369$	3.50092	0.182251
$370$	−19.9582	−1.03758
$371$	9.67287	0.502190
$372$	75.5563	3.91741
$373$	−0.920308	−0.0476518	−0.0238259	−	0.999716i	$-0.507585\pi$
$373$	−0.920308	−0.0476518	−0.0238259	+	0.999716i	$0.507585\pi$
$374$	6.96953	0.360386
$375$	1.88140	0.0971551
$376$	−9.26424	−0.477766
$377$	6.74346	0.347306
$378$	−13.7522	−0.707338
$379$	12.5805	0.646217	0.323108	−	0.946362i	$-0.395272\pi$
$379$	12.5805	0.646217	0.323108	+	0.946362i	$0.395272\pi$
$380$	25.8338	1.32524
$381$	19.5645	1.00232
$382$	−65.3931	−3.34580
$383$	22.5878	1.15418	0.577092	−	0.816679i	$-0.304187\pi$
$383$	22.5878	1.15418	0.577092	+	0.816679i	$0.304187\pi$
$384$	35.8226	1.82807
$385$	−3.41638	−0.174115
$386$	−41.1641	−2.09520
$387$	−1.90679	−0.0969278
$388$	29.4737	1.49630
$389$	−19.3484	−0.981000	−0.490500	−	0.871441i	$-0.663186\pi$
$389$	−19.3484	−0.981000	−0.490500	+	0.871441i	$0.663186\pi$
$390$	8.64078	0.437543
$391$	−4.52532	−0.228855
$392$	28.1264	1.42060
$393$	−12.3254	−0.621735
$394$	−49.7708	−2.50742
$395$	−1.53862	−0.0774162
$396$	6.20414	0.311770
$397$	−22.2694	−1.11767	−0.558834	−	0.829280i	$-0.688751\pi$
$397$	−22.2694	−1.11767	−0.558834	+	0.829280i	$0.688751\pi$
$398$	−47.3380	−2.37284
$399$	−14.4438	−0.723094
$400$	4.36890	0.218445
$401$	−16.7396	−0.835935	−0.417968	−	0.908462i	$-0.637257\pi$
$401$	−16.7396	−0.835935	−0.417968	+	0.908462i	$0.637257\pi$
$402$	−9.33454	−0.465565
$403$	−18.4491	−0.919015
$404$	−21.0866	−1.04910
$405$	−10.3278	−0.513191
$406$	−10.7393	−0.532982
$407$	22.9504	1.13761
$408$	9.54550	0.472572
$409$	−14.2508	−0.704656	−0.352328	−	0.935877i	$-0.614610\pi$
$409$	−14.2508	−0.704656	−0.352328	+	0.935877i	$0.614610\pi$
$410$	−15.9707	−0.788736
$411$	−27.4244	−1.35274
$412$	−64.4168	−3.17359
$413$	−13.4864	−0.663620
$414$	−6.01233	−0.295490
$415$	−4.83390	−0.237287
$416$	1.13519	0.0556572
$417$	20.4334	1.00063
$418$	−44.3376	−2.16863
$419$	22.4667	1.09757	0.548785	−	0.835964i	$-0.315091\pi$
$419$	22.4667	1.09757	0.548785	+	0.835964i	$0.315091\pi$
$420$	−9.21999	−0.449890
$421$	27.0285	1.31729	0.658645	−	0.752454i	$-0.271130\pi$
$421$	27.0285	1.31729	0.658645	+	0.752454i	$0.271130\pi$
$422$	−36.2453	−1.76439
$423$	0.985415	0.0479125
$424$	40.6670	1.97496
$425$	−1.00000	−0.0485071
$426$	4.63179	0.224411
$427$	0.324570	0.0157071
$428$	−60.1082	−2.90544
$429$	−9.93623	−0.479726
$430$	8.69850	0.419479
$431$	−15.7527	−0.758780	−0.379390	−	0.925237i	$-0.623866\pi$
$431$	−15.7527	−0.758780	−0.379390	+	0.925237i	$0.623866\pi$
$432$	−20.2231	−0.972984
$433$	−10.1170	−0.486190	−0.243095	−	0.970003i	$-0.578163\pi$
$433$	−10.1170	−0.486190	−0.243095	+	0.970003i	$0.578163\pi$
$434$	29.3811	1.41034
$435$	−6.80079	−0.326073
$436$	−47.3887	−2.26951
$437$	28.7884	1.37714
$438$	20.1668	0.963605
$439$	0.923441	0.0440735	0.0220367	−	0.999757i	$-0.492985\pi$
$439$	0.923441	0.0440735	0.0220367	+	0.999757i	$0.492985\pi$
$440$	−14.3633	−0.684742
$441$	−2.99174	−0.142464
$442$	−4.59274	−0.218454
$443$	−26.0513	−1.23774	−0.618868	−	0.785495i	$-0.712408\pi$
$443$	−26.0513	−1.23774	−0.618868	+	0.785495i	$0.712408\pi$
$444$	61.9376	2.93943
$445$	5.31722	0.252060
$446$	−68.7591	−3.25584
$447$	−30.1369	−1.42543
$448$	8.73682	0.412776
$449$	−12.7835	−0.603290	−0.301645	−	0.953420i	$-0.597536\pi$
$449$	−12.7835	−0.603290	−0.301645	+	0.953420i	$0.597536\pi$
$450$	−1.32860	−0.0626308
$451$	18.3650	0.864776
$452$	30.3595	1.42799
$453$	35.4585	1.66598
$454$	−21.4469	−1.00655
$455$	2.25131	0.105543
$456$	−60.7250	−2.84371
$457$	7.60106	0.355562	0.177781	−	0.984070i	$-0.443108\pi$
$457$	7.60106	0.355562	0.177781	+	0.984070i	$0.443108\pi$
$458$	64.2182	3.00072
$459$	4.62887	0.216057
$460$	18.3767	0.856818
$461$	−25.3038	−1.17851	−0.589257	−	0.807945i	$-0.700580\pi$
$461$	−25.3038	−1.17851	−0.589257	+	0.807945i	$0.700580\pi$
$462$	15.8240	0.736197
$463$	15.5358	0.722010	0.361005	−	0.932564i	$-0.382434\pi$
$463$	15.5358	0.722010	0.361005	+	0.932564i	$0.382434\pi$
$464$	−15.7925	−0.733148
$465$	18.6060	0.862830
$466$	66.5918	3.08481
$467$	−4.42158	−0.204606	−0.102303	−	0.994753i	$-0.532621\pi$
$467$	−4.42158	−0.204606	−0.102303	+	0.994753i	$0.532621\pi$
$468$	−4.08837	−0.188985
$469$	−2.43206	−0.112302
$470$	−4.49531	−0.207353
$471$	15.4991	0.714159
$472$	−56.6998	−2.60982
$473$	−10.0026	−0.459920
$474$	7.12654	0.327333
$475$	6.36164	0.291892
$476$	4.90060	0.224619
$477$	−4.32565	−0.198058
$478$	53.2276	2.43457
$479$	23.4474	1.07134	0.535669	−	0.844428i	$-0.320060\pi$
$479$	23.4474	1.07134	0.535669	+	0.844428i	$0.320060\pi$
$480$	−1.14484	−0.0522546
$481$	−15.1237	−0.689583
$482$	−38.5762	−1.75710
$483$	−10.2745	−0.467506
$484$	−12.1240	−0.551093
$485$	7.25798	0.329568
$486$	13.6488	0.619122
$487$	2.70419	0.122538	0.0612692	−	0.998121i	$-0.480485\pi$
$487$	2.70419	0.122538	0.0612692	+	0.998121i	$0.480485\pi$
$488$	1.36457	0.0617711
$489$	6.61688	0.299226
$490$	13.6479	0.616547
$491$	23.1016	1.04256	0.521280	−	0.853386i	$-0.325455\pi$
$491$	23.1016	1.04256	0.521280	+	0.853386i	$0.325455\pi$
$492$	49.5628	2.23446
$493$	3.61475	0.162800
$494$	29.2174	1.31455
$495$	1.52779	0.0686689
$496$	43.2059	1.94000
$497$	1.20679	0.0541318
$498$	22.3896	1.00330
$499$	39.4544	1.76622	0.883110	−	0.469166i	$-0.155446\pi$
$499$	39.4544	1.76622	0.883110	+	0.469166i	$0.155446\pi$
$500$	4.06087	0.181607
$501$	4.25997	0.190322
$502$	11.1037	0.495581
$503$	9.44865	0.421294	0.210647	−	0.977562i	$-0.432443\pi$
$503$	9.44865	0.421294	0.210647	+	0.977562i	$0.432443\pi$
$504$	3.30426	0.147184
$505$	−5.19263	−0.231069
$506$	−31.5393	−1.40209
$507$	−17.9105	−0.795433
$508$	42.2285	1.87359
$509$	−29.8827	−1.32453	−0.662265	−	0.749270i	$-0.730405\pi$
$509$	−29.8827	−1.32453	−0.662265	+	0.749270i	$0.730405\pi$
$510$	4.63179	0.205099
$511$	5.25434	0.232438
$512$	41.6737	1.84174
$513$	−29.4472	−1.30013
$514$	64.2690	2.83478
$515$	−15.8628	−0.698999
$516$	−26.9946	−1.18837
$517$	5.16926	0.227344
$518$	24.0853	1.05825
$519$	30.8736	1.35520
$520$	9.46502	0.415069
$521$	−14.4123	−0.631416	−0.315708	−	0.948856i	$-0.602242\pi$
$521$	−14.4123	−0.631416	−0.315708	+	0.948856i	$0.602242\pi$
$522$	4.80255	0.210202
$523$	−23.9445	−1.04702	−0.523511	−	0.852019i	$-0.675378\pi$
$523$	−23.9445	−1.04702	−0.523511	+	0.852019i	$0.675378\pi$
$524$	−26.6035	−1.16218
$525$	−2.27045	−0.0990905
$526$	−17.4213	−0.759606
$527$	−9.88942	−0.430790
$528$	23.2696	1.01268
$529$	−2.52151	−0.109631
$530$	19.7330	0.857145
$531$	6.03102	0.261724
$532$	−31.1759	−1.35165
$533$	−12.1021	−0.524200
$534$	−24.6282	−1.06577
$535$	−14.8018	−0.639938
$536$	−10.2250	−0.441651
$537$	47.9636	2.06978
$538$	15.0281	0.647908
$539$	−15.6940	−0.675988
$540$	−18.7972	−0.808904
$541$	−3.16395	−0.136029	−0.0680144	−	0.997684i	$-0.521666\pi$
$541$	−3.16395	−0.136029	−0.0680144	+	0.997684i	$0.521666\pi$
$542$	−52.8443	−2.26986
$543$	43.0158	1.84599
$544$	0.608505	0.0260894
$545$	−11.6696	−0.499871
$546$	−10.4276	−0.446259
$547$	16.4507	0.703381	0.351691	−	0.936116i	$-0.385607\pi$
$547$	16.4507	0.703381	0.351691	+	0.936116i	$0.385607\pi$
$548$	−59.1935	−2.52862
$549$	−0.145146	−0.00619468
$550$	−6.96953	−0.297182
$551$	−22.9957	−0.979651
$552$	−43.1964	−1.83856
$553$	1.85678	0.0789584
$554$	54.9607	2.33506
$555$	15.2523	0.647424
$556$	44.1041	1.87043
$557$	−5.88667	−0.249426	−0.124713	−	0.992193i	$-0.539801\pi$
$557$	−5.88667	−0.249426	−0.124713	+	0.992193i	$0.539801\pi$
$558$	−13.1391	−0.556221
$559$	6.59146	0.278789
$560$	−5.27233	−0.222797
$561$	−5.32620	−0.224872
$562$	−42.6835	−1.80049
$563$	7.71241	0.325039	0.162520	−	0.986705i	$-0.448038\pi$
$563$	7.71241	0.325039	0.162520	+	0.986705i	$0.448038\pi$
$564$	13.9506	0.587426
$565$	7.47612	0.314523
$566$	−33.5318	−1.40945
$567$	12.4634	0.523414
$568$	5.07361	0.212884
$569$	22.3793	0.938190	0.469095	−	0.883148i	$-0.344580\pi$
$569$	22.3793	0.938190	0.469095	+	0.883148i	$0.344580\pi$
$570$	−29.4658	−1.23419
$571$	1.60668	0.0672376	0.0336188	−	0.999435i	$-0.489297\pi$
$571$	1.60668	0.0672376	0.0336188	+	0.999435i	$0.489297\pi$
$572$	−21.4466	−0.896729
$573$	49.9742	2.08770
$574$	19.2732	0.804448
$575$	4.52532	0.188719
$576$	−3.90706	−0.162794
$577$	−21.9272	−0.912841	−0.456421	−	0.889764i	$-0.650869\pi$
$577$	−21.9272	−0.912841	−0.456421	+	0.889764i	$0.650869\pi$
$578$	−2.46188	−0.102401
$579$	31.4581	1.30736
$580$	−14.6790	−0.609513
$581$	5.83349	0.242014
$582$	−33.6174	−1.39349
$583$	−22.6914	−0.939781
$584$	22.0905	0.914109
$585$	−1.00677	−0.0416249
$586$	6.54892	0.270534
$587$	−24.6403	−1.01701	−0.508506	−	0.861058i	$-0.669802\pi$
$587$	−24.6403	−1.01701	−0.508506	+	0.861058i	$0.669802\pi$
$588$	−42.3542	−1.74666
$589$	62.9129	2.59228
$590$	−27.5126	−1.13268
$591$	38.0354	1.56457
$592$	35.4182	1.45568
$593$	−38.7344	−1.59063	−0.795316	−	0.606195i	$-0.792695\pi$
$593$	−38.7344	−1.59063	−0.795316	+	0.606195i	$0.792695\pi$
$594$	32.2610	1.32369
$595$	1.20679	0.0494734
$596$	−65.0484	−2.66449
$597$	36.1763	1.48060
$598$	20.7836	0.849905
$599$	5.20929	0.212846	0.106423	−	0.994321i	$-0.466060\pi$
$599$	5.20929	0.212846	0.106423	+	0.994321i	$0.466060\pi$
$600$	−9.54550	−0.389693
$601$	35.5396	1.44969	0.724846	−	0.688911i	$-0.241911\pi$
$601$	35.5396	1.44969	0.724846	+	0.688911i	$0.241911\pi$
$602$	−10.4972	−0.427836
$603$	1.08761	0.0442907
$604$	76.5345	3.11415
$605$	−2.98558	−0.121381
$606$	24.0512	0.977012
$607$	−37.5520	−1.52419	−0.762095	−	0.647465i	$-0.775829\pi$
$607$	−37.5520	−1.52419	−0.762095	+	0.647465i	$0.775829\pi$
$608$	−3.87109	−0.156993
$609$	8.20710	0.332569
$610$	0.662133	0.0268090
$611$	−3.40641	−0.137809
$612$	−2.19152	−0.0885869
$613$	31.2766	1.26325	0.631626	−	0.775273i	$-0.282388\pi$
$613$	31.2766	1.26325	0.631626	+	0.775273i	$0.282388\pi$
$614$	−0.387141	−0.0156238
$615$	12.2050	0.492153
$616$	17.3334	0.698383
$617$	32.2725	1.29924	0.649621	−	0.760259i	$-0.274928\pi$
$617$	32.2725	1.29924	0.649621	+	0.760259i	$0.274928\pi$
$618$	73.4732	2.95552
$619$	36.3699	1.46183	0.730915	−	0.682469i	$-0.239094\pi$
$619$	36.3699	1.46183	0.730915	+	0.682469i	$0.239094\pi$
$620$	40.1596	1.61285
$621$	−20.9471	−0.840578
$622$	−4.17657	−0.167465
$623$	−6.41675	−0.257081
$624$	−15.3341	−0.613855
$625$	1.00000	0.0400000
$626$	−66.1490	−2.64385
$627$	33.8834	1.35317
$628$	33.4536	1.33494
$629$	−8.10689	−0.323243
$630$	1.60334	0.0638784
$631$	22.3696	0.890520	0.445260	−	0.895401i	$-0.353111\pi$
$631$	22.3696	0.890520	0.445260	+	0.895401i	$0.353111\pi$
$632$	7.80634	0.310519
$633$	27.6991	1.10094
$634$	−67.4164	−2.67745
$635$	10.3989	0.412667
$636$	−61.2385	−2.42827
$637$	10.3419	0.409762
$638$	25.1931	0.997404
$639$	−0.539668	−0.0213489
$640$	19.0404	0.752638
$641$	−42.0802	−1.66207	−0.831035	−	0.556220i	$-0.812251\pi$
$641$	−42.0802	−1.66207	−0.831035	+	0.556220i	$0.812251\pi$
$642$	68.5589	2.70580
$643$	46.6091	1.83808	0.919042	−	0.394159i	$-0.128964\pi$
$643$	46.6091	1.83808	0.919042	+	0.394159i	$0.128964\pi$
$644$	−22.1768	−0.873887
$645$	−6.64750	−0.261745
$646$	15.6616	0.616198
$647$	25.1388	0.988310	0.494155	−	0.869374i	$-0.335478\pi$
$647$	25.1388	0.988310	0.494155	+	0.869374i	$0.335478\pi$
$648$	52.3991	2.05843
$649$	31.6373	1.24187
$650$	4.59274	0.180142
$651$	−22.4534	−0.880019
$652$	14.2820	0.559328
$653$	23.4946	0.919416	0.459708	−	0.888070i	$-0.347954\pi$
$653$	23.4946	0.919416	0.459708	+	0.888070i	$0.347954\pi$
$654$	54.0512	2.11357
$655$	−6.55120	−0.255976
$656$	28.3419	1.10656
$657$	−2.34971	−0.0916709
$658$	5.42488	0.211484
$659$	18.1521	0.707104	0.353552	−	0.935415i	$-0.384974\pi$
$659$	18.1521	0.707104	0.353552	+	0.935415i	$0.384974\pi$
$660$	21.6290	0.841907
$661$	1.22327	0.0475799	0.0237899	−	0.999717i	$-0.492427\pi$
$661$	1.22327	0.0475799	0.0237899	+	0.999717i	$0.492427\pi$
$662$	−83.2296	−3.23481
$663$	3.50983	0.136310
$664$	24.5253	0.951768
$665$	−7.67715	−0.297707
$666$	−10.7708	−0.417360
$667$	−16.3579	−0.633380
$668$	9.19484	0.355759
$669$	52.5465	2.03157
$670$	−4.96149	−0.191679
$671$	−0.761402	−0.0293936
$672$	1.38158	0.0532956
$673$	−16.9599	−0.653756	−0.326878	−	0.945067i	$-0.605997\pi$
$673$	−16.9599	−0.653756	−0.326878	+	0.945067i	$0.605997\pi$
$674$	12.6111	0.485762
$675$	−4.62887	−0.178165
$676$	−38.6585	−1.48686
$677$	−41.3189	−1.58801	−0.794007	−	0.607909i	$-0.792009\pi$
$677$	−41.3189	−1.58801	−0.794007	+	0.607909i	$0.792009\pi$
$678$	−34.6278	−1.32987
$679$	−8.75884	−0.336133
$680$	5.07361	0.194564
$681$	16.3900	0.628066
$682$	−68.9246	−2.63926
$683$	−31.9522	−1.22262	−0.611308	−	0.791393i	$-0.709356\pi$
$683$	−31.9522	−1.22262	−0.611308	+	0.791393i	$0.709356\pi$
$684$	13.9417	0.533073
$685$	−14.5766	−0.556942
$686$	−37.2668	−1.42285
$687$	−49.0763	−1.87238
$688$	−15.4365	−0.588512
$689$	14.9530	0.569665
$690$	−20.9603	−0.797945
$691$	−9.71502	−0.369577	−0.184788	−	0.982778i	$-0.559160\pi$
$691$	−9.71502	−0.369577	−0.184788	+	0.982778i	$0.559160\pi$
$692$	66.6383	2.53321
$693$	−1.84371	−0.0700369
$694$	−4.68764	−0.177940
$695$	10.8608	0.411972
$696$	34.5046	1.30789
$697$	−6.48718	−0.245719
$698$	14.2523	0.539458
$699$	−50.8903	−1.92485
$700$	−4.90060	−0.185225
$701$	29.8439	1.12719	0.563595	−	0.826051i	$-0.309418\pi$
$701$	29.8439	1.12719	0.563595	+	0.826051i	$0.309418\pi$
$702$	−21.2592	−0.802377
$703$	51.5731	1.94512
$704$	−20.4955	−0.772454
$705$	3.43537	0.129384
$706$	61.3738	2.30983
$707$	6.26640	0.235672
$708$	85.3815	3.20883
$709$	40.9154	1.53661	0.768306	−	0.640083i	$-0.221100\pi$
$709$	40.9154	1.53661	0.768306	+	0.640083i	$0.221100\pi$
$710$	2.46188	0.0923928
$711$	−0.830342	−0.0311402
$712$	−26.9775	−1.01102
$713$	44.7527	1.67600
$714$	−5.58958	−0.209185
$715$	−5.28130	−0.197509
$716$	103.526	3.86894
$717$	−40.6772	−1.51912
$718$	34.4174	1.28444
$719$	−7.66500	−0.285856	−0.142928	−	0.989733i	$-0.545652\pi$
$719$	−7.66500	−0.285856	−0.142928	+	0.989733i	$0.545652\pi$
$720$	2.35776	0.0878684
$721$	19.1430	0.712924
$722$	−52.8578	−1.96716
$723$	29.4804	1.09639
$724$	92.8466	3.45062
$725$	−3.61475	−0.134248
$726$	13.8286	0.513226
$727$	−23.8197	−0.883423	−0.441711	−	0.897157i	$-0.645628\pi$
$727$	−23.8197	−0.883423	−0.441711	+	0.897157i	$0.645628\pi$
$728$	−11.4223	−0.423337
$729$	20.5527	0.761212
$730$	10.7190	0.396728
$731$	3.53327	0.130683
$732$	−2.05484	−0.0759491
$733$	−49.0333	−1.81109	−0.905544	−	0.424253i	$-0.860537\pi$
$733$	−49.0333	−1.81109	−0.905544	+	0.424253i	$0.860537\pi$
$734$	9.53611	0.351984
$735$	−10.4299	−0.384711
$736$	−2.75368	−0.101502
$737$	5.70533	0.210158
$738$	−8.61886	−0.317265
$739$	−46.8618	−1.72384	−0.861920	−	0.507044i	$-0.830738\pi$
$739$	−46.8618	−1.72384	−0.861920	+	0.507044i	$0.830738\pi$
$740$	32.9210	1.21020
$741$	−22.3283	−0.820249
$742$	−23.8135	−0.874220
$743$	−37.3156	−1.36898	−0.684489	−	0.729023i	$-0.739975\pi$
$743$	−37.3156	−1.36898	−0.684489	+	0.729023i	$0.739975\pi$
$744$	−94.3994	−3.46085
$745$	−16.0184	−0.586867
$746$	2.26569	0.0829529
$747$	−2.60870	−0.0954474
$748$	−11.4962	−0.420343
$749$	17.8626	0.652686
$750$	−4.63179	−0.169129
$751$	−17.0063	−0.620569	−0.310284	−	0.950644i	$-0.600424\pi$
$751$	−17.0063	−0.620569	−0.310284	+	0.950644i	$0.600424\pi$
$752$	7.97746	0.290908
$753$	−8.48555	−0.309231
$754$	−16.6016	−0.604594
$755$	18.8468	0.685907
$756$	22.6842	0.825018
$757$	8.89564	0.323318	0.161659	−	0.986847i	$-0.448316\pi$
$757$	8.89564	0.323318	0.161659	+	0.986847i	$0.448316\pi$
$758$	−30.9717	−1.12494
$759$	24.1027	0.874874
$760$	−32.2765	−1.17079
$761$	25.1574	0.911956	0.455978	−	0.889991i	$-0.349290\pi$
$761$	25.1574	0.911956	0.455978	+	0.889991i	$0.349290\pi$
$762$	−48.1654	−1.74485
$763$	14.0827	0.509829
$764$	107.866	3.90244
$765$	−0.539668	−0.0195117
$766$	−55.6086	−2.00922
$767$	−20.8482	−0.752785
$768$	−60.9494	−2.19932
$769$	−15.2091	−0.548453	−0.274227	−	0.961665i	$-0.588422\pi$
$769$	−15.2091	−0.548453	−0.274227	+	0.961665i	$0.588422\pi$
$770$	8.41074	0.303102
$771$	−49.1152	−1.76884
$772$	67.9001	2.44378
$773$	−47.4725	−1.70747	−0.853734	−	0.520710i	$-0.825667\pi$
$773$	−47.4725	−1.70747	−0.853734	+	0.520710i	$0.825667\pi$
$774$	4.69430	0.168733
$775$	9.88942	0.355238
$776$	−36.8242	−1.32191
$777$	−18.4063	−0.660322
$778$	47.6334	1.70774
$779$	41.2691	1.47862
$780$	−14.2529	−0.510337
$781$	−2.83098	−0.101300
$782$	11.1408	0.398394
$783$	16.7322	0.597960
$784$	−24.2197	−0.864991
$785$	8.23805	0.294029
$786$	30.3437	1.08233
$787$	16.7760	0.597999	0.299000	−	0.954253i	$-0.403347\pi$
$787$	16.7760	0.597999	0.299000	+	0.954253i	$0.403347\pi$
$788$	82.0967	2.92457
$789$	13.3136	0.473976
$790$	3.78789	0.134767
$791$	−9.02208	−0.320788
$792$	−7.75140	−0.275434
$793$	0.501745	0.0178175
$794$	54.8246	1.94565
$795$	−15.0802	−0.534838
$796$	78.0838	2.76761
$797$	8.26503	0.292763	0.146381	−	0.989228i	$-0.453237\pi$
$797$	8.26503	0.292763	0.146381	+	0.989228i	$0.453237\pi$
$798$	35.5589	1.25877
$799$	−1.82596	−0.0645980
$800$	−0.608505	−0.0215139
$801$	2.86953	0.101390
$802$	41.2109	1.45521
$803$	−12.3260	−0.434976
$804$	15.3973	0.543021
$805$	−5.46109	−0.192478
$806$	45.4195	1.59983
$807$	−11.4847	−0.404279
$808$	26.3454	0.926828
$809$	−38.9034	−1.36777	−0.683886	−	0.729589i	$-0.739711\pi$
$809$	−38.9034	−1.36777	−0.683886	+	0.729589i	$0.739711\pi$
$810$	25.4257	0.893369
$811$	−52.1986	−1.83294	−0.916470	−	0.400103i	$-0.868974\pi$
$811$	−52.1986	−1.83294	−0.916470	+	0.400103i	$0.868974\pi$
$812$	17.7144	0.621655
$813$	40.3843	1.41634
$814$	−56.5012	−1.98037
$815$	3.51700	0.123195
$816$	−8.21966	−0.287746
$817$	−22.4774	−0.786385
$818$	35.0838	1.22668
$819$	1.21496	0.0424541
$820$	26.3436	0.919958
$821$	39.1231	1.36540	0.682702	−	0.730697i	$-0.260805\pi$
$821$	39.1231	1.36540	0.682702	+	0.730697i	$0.260805\pi$
$822$	67.5156	2.35488
$823$	52.9936	1.84724	0.923621	−	0.383307i	$-0.125215\pi$
$823$	52.9936	1.84724	0.923621	+	0.383307i	$0.125215\pi$
$824$	80.4817	2.80371
$825$	5.32620	0.185434
$826$	33.2018	1.15524
$827$	−14.1087	−0.490609	−0.245304	−	0.969446i	$-0.578888\pi$
$827$	−14.1087	−0.490609	−0.245304	+	0.969446i	$0.578888\pi$
$828$	9.91732	0.344651
$829$	46.8569	1.62741	0.813704	−	0.581280i	$-0.197448\pi$
$829$	46.8569	1.62741	0.813704	+	0.581280i	$0.197448\pi$
$830$	11.9005	0.413072
$831$	−42.0016	−1.45702
$832$	13.5060	0.468237
$833$	5.54367	0.192077
$834$	−50.3047	−1.74191
$835$	2.26426	0.0783578
$836$	73.1348	2.52942
$837$	−45.7768	−1.58228
$838$	−55.3103	−1.91066
$839$	5.62560	0.194217	0.0971086	−	0.995274i	$-0.469041\pi$
$839$	5.62560	0.194217	0.0971086	+	0.995274i	$0.469041\pi$
$840$	11.5194	0.397456
$841$	−15.9336	−0.549434
$842$	−66.5411	−2.29316
$843$	32.6192	1.12347
$844$	59.7865	2.05793
$845$	−9.51976	−0.327490
$846$	−2.42598	−0.0834068
$847$	3.60296	0.123799
$848$	−35.0185	−1.20254
$849$	25.6254	0.879463
$850$	2.46188	0.0844419
$851$	36.6862	1.25759
$852$	−7.64012	−0.261746
$853$	43.0734	1.47480	0.737402	−	0.675454i	$-0.236052\pi$
$853$	43.0734	1.47480	0.737402	+	0.675454i	$0.236052\pi$
$854$	−0.799054	−0.0273431
$855$	3.43317	0.117412
$856$	75.0987	2.56682
$857$	20.8025	0.710600	0.355300	−	0.934752i	$-0.384379\pi$
$857$	20.8025	0.710600	0.355300	+	0.934752i	$0.384379\pi$
$858$	24.4618	0.835114
$859$	20.8906	0.712777	0.356388	−	0.934338i	$-0.384008\pi$
$859$	20.8906	0.712777	0.356388	+	0.934338i	$0.384008\pi$
$860$	−14.3482	−0.489268
$861$	−14.7288	−0.501957
$862$	38.7812	1.32089
$863$	−23.7248	−0.807602	−0.403801	−	0.914847i	$-0.632311\pi$
$863$	−23.7248	−0.807602	−0.403801	+	0.914847i	$0.632311\pi$
$864$	2.81669	0.0958257
$865$	16.4099	0.557953
$866$	24.9067	0.846366
$867$	1.88140	0.0638957
$868$	−48.4641	−1.64498
$869$	−4.35578	−0.147760
$870$	16.7427	0.567632
$871$	−3.75966	−0.127391
$872$	59.2071	2.00501
$873$	3.91690	0.132567
$874$	−70.8738	−2.39734
$875$	−1.20679	−0.0407968
$876$	−33.2650	−1.12392
$877$	52.4460	1.77098	0.885488	−	0.464663i	$-0.153824\pi$
$877$	52.4460	1.77098	0.885488	+	0.464663i	$0.153824\pi$
$878$	−2.27340	−0.0767237
$879$	−5.00477	−0.168807
$880$	12.3683	0.416934
$881$	−30.5681	−1.02986	−0.514932	−	0.857231i	$-0.672183\pi$
$881$	−30.5681	−1.02986	−0.514932	+	0.857231i	$0.672183\pi$
$882$	7.36531	0.248003
$883$	−17.6465	−0.593851	−0.296925	−	0.954901i	$-0.595961\pi$
$883$	−17.6465	−0.593851	−0.296925	+	0.954901i	$0.595961\pi$
$884$	7.57571	0.254799
$885$	21.0254	0.706763
$886$	64.1353	2.15467
$887$	−36.3575	−1.22077	−0.610383	−	0.792106i	$-0.708985\pi$
$887$	−36.3575	−1.22077	−0.610383	+	0.792106i	$0.708985\pi$
$888$	−77.3843	−2.59685
$889$	−12.5492	−0.420888
$890$	−13.0904	−0.438790
$891$	−29.2376	−0.979498
$892$	113.418	3.79751
$893$	11.6161	0.388719
$894$	74.1936	2.48141
$895$	25.4935	0.852155
$896$	−22.9777	−0.767631
$897$	−15.8831	−0.530321
$898$	31.4715	1.05022
$899$	−35.7477	−1.19225
$900$	2.19152	0.0730507
$901$	8.01539	0.267031
$902$	−45.2126	−1.50541
$903$	8.02212	0.266959
$904$	−37.9309	−1.26156
$905$	22.8637	0.760016
$906$	−87.2946	−2.90017
$907$	−35.4988	−1.17872	−0.589359	−	0.807871i	$-0.700620\pi$
$907$	−35.4988	−1.17872	−0.589359	+	0.807871i	$0.700620\pi$
$908$	35.3766	1.17401
$909$	−2.80230	−0.0929463
$910$	−5.54246	−0.183731
$911$	51.1553	1.69485	0.847425	−	0.530915i	$-0.178151\pi$
$911$	51.1553	1.69485	0.847425	+	0.530915i	$0.178151\pi$
$912$	52.2905	1.73151
$913$	−13.6847	−0.452896
$914$	−18.7129	−0.618968
$915$	−0.506010	−0.0167282
$916$	−105.928	−3.49995
$917$	7.90590	0.261076
$918$	−11.3957	−0.376115
$919$	−3.59727	−0.118663	−0.0593315	−	0.998238i	$-0.518897\pi$
$919$	−3.59727	−0.118663	−0.0593315	+	0.998238i	$0.518897\pi$
$920$	−22.9597	−0.756959
$921$	0.295858	0.00974886
$922$	62.2950	2.05158
$923$	1.86554	0.0614050
$924$	−26.1016	−0.858679
$925$	8.10689	0.266553
$926$	−38.2473	−1.25688
$927$	−8.56065	−0.281169
$928$	2.19959	0.0722051
$929$	−37.8018	−1.24024	−0.620119	−	0.784508i	$-0.712916\pi$
$929$	−37.8018	−1.24024	−0.620119	+	0.784508i	$0.712916\pi$
$930$	−45.8057	−1.50203
$931$	−35.2668	−1.15582
$932$	−109.843	−3.59803
$933$	3.19179	0.104494
$934$	10.8854	0.356181
$935$	−2.83098	−0.0925828
$936$	5.10797	0.166959
$937$	−35.4072	−1.15670	−0.578352	−	0.815788i	$-0.696304\pi$
$937$	−35.4072	−1.15670	−0.578352	+	0.815788i	$0.696304\pi$
$938$	5.98746	0.195497
$939$	50.5519	1.64970
$940$	7.41500	0.241851
$941$	49.0777	1.59989	0.799944	−	0.600074i	$-0.204862\pi$
$941$	49.0777	1.59989	0.799944	+	0.600074i	$0.204862\pi$
$942$	−38.1569	−1.24322
$943$	29.3565	0.955981
$944$	48.8243	1.58910
$945$	5.58606	0.181715
$946$	24.6252	0.800636
$947$	23.7790	0.772713	0.386357	−	0.922350i	$-0.373733\pi$
$947$	23.7790	0.772713	0.386357	+	0.922350i	$0.373733\pi$
$948$	−11.7552	−0.381791
$949$	8.12254	0.263669
$950$	−15.6616	−0.508130
$951$	51.5205	1.67067
$952$	−6.12277	−0.198440
$953$	−1.45359	−0.0470865	−0.0235433	−	0.999723i	$-0.507495\pi$
$953$	−1.45359	−0.0470865	−0.0235433	+	0.999723i	$0.507495\pi$
$954$	10.6492	0.344782
$955$	26.5622	0.859534
$956$	−87.7987	−2.83961
$957$	−19.2529	−0.622357
$958$	−57.7247	−1.86500
$959$	17.5908	0.568037
$960$	−13.6209	−0.439611
$961$	66.8006	2.15486
$962$	37.2328	1.20044
$963$	−7.98807	−0.257412
$964$	63.6313	2.04943
$965$	16.7206	0.538255
$966$	25.2946	0.813841
$967$	16.3433	0.525565	0.262783	−	0.964855i	$-0.415360\pi$
$967$	16.3433	0.525565	0.262783	+	0.964855i	$0.415360\pi$
$968$	15.1477	0.486865
$969$	−11.9688	−0.384493
$970$	−17.8683	−0.573716
$971$	7.15577	0.229640	0.114820	−	0.993386i	$-0.463371\pi$
$971$	7.15577	0.229640	0.114820	+	0.993386i	$0.463371\pi$
$972$	−22.5136	−0.722125
$973$	−13.1066	−0.420179
$974$	−6.65739	−0.213316
$975$	−3.50983	−0.112404
$976$	−1.17503	−0.0376119
$977$	−10.7789	−0.344848	−0.172424	−	0.985023i	$-0.555160\pi$
$977$	−10.7789	−0.344848	−0.172424	+	0.985023i	$0.555160\pi$
$978$	−16.2900	−0.520896
$979$	15.0529	0.481093
$980$	−22.5121	−0.719122
$981$	−6.29772	−0.201071
$982$	−56.8734	−1.81490
$983$	48.8472	1.55798	0.778992	−	0.627034i	$-0.215731\pi$
$983$	48.8472	1.55798	0.778992	+	0.627034i	$0.215731\pi$
$984$	−61.9234	−1.97404
$985$	20.2166	0.644153
$986$	−8.89908	−0.283405
$987$	−4.14576	−0.131961
$988$	−48.1939	−1.53325
$989$	−15.9892	−0.508426
$990$	−3.76123	−0.119540
$991$	10.0913	0.320560	0.160280	−	0.987072i	$-0.448760\pi$
$991$	10.0913	0.320560	0.160280	+	0.987072i	$0.448760\pi$
$992$	−6.01776	−0.191064
$993$	63.6051	2.01845
$994$	−2.97097	−0.0942334
$995$	19.2284	0.609580
$996$	−36.9316	−1.17022
$997$	−2.99248	−0.0947729	−0.0473864	−	0.998877i	$-0.515089\pi$
$997$	−2.99248	−0.0947729	−0.0473864	+	0.998877i	$0.515089\pi$
$998$	−97.1320	−3.07466
$999$	−37.5257	−1.18726

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6035.2.a.h.1.6	✓	59

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6035.2.a.h.1.6	✓	59	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:	\( N \)	\(=\)	\( 6035 = 5 \cdot 17 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.46188 q^{2} +1.88140 q^{3} +4.06087 q^{4} +1.00000 q^{5} -4.63179 q^{6} -1.20679 q^{7} -5.07361 q^{8} +0.539668 q^{9} +O(q^{10})\)	\(q-2.46188 q^{2} +1.88140 q^{3} +4.06087 q^{4} +1.00000 q^{5} -4.63179 q^{6} -1.20679 q^{7} -5.07361 q^{8} +0.539668 q^{9} -2.46188 q^{10} +2.83098 q^{11} +7.64012 q^{12} -1.86554 q^{13} +2.97097 q^{14} +1.88140 q^{15} +4.36890 q^{16} -1.00000 q^{17} -1.32860 q^{18} +6.36164 q^{19} +4.06087 q^{20} -2.27045 q^{21} -6.96953 q^{22} +4.52532 q^{23} -9.54550 q^{24} +1.00000 q^{25} +4.59274 q^{26} -4.62887 q^{27} -4.90060 q^{28} -3.61475 q^{29} -4.63179 q^{30} +9.88942 q^{31} -0.608505 q^{32} +5.32620 q^{33} +2.46188 q^{34} -1.20679 q^{35} +2.19152 q^{36} +8.10689 q^{37} -15.6616 q^{38} -3.50983 q^{39} -5.07361 q^{40} +6.48718 q^{41} +5.58958 q^{42} -3.53327 q^{43} +11.4962 q^{44} +0.539668 q^{45} -11.1408 q^{46} +1.82596 q^{47} +8.21966 q^{48} -5.54367 q^{49} -2.46188 q^{50} -1.88140 q^{51} -7.57571 q^{52} -8.01539 q^{53} +11.3957 q^{54} +2.83098 q^{55} +6.12277 q^{56} +11.9688 q^{57} +8.89908 q^{58} +11.1754 q^{59} +7.64012 q^{60} -0.268954 q^{61} -24.3466 q^{62} -0.651264 q^{63} -7.23974 q^{64} -1.86554 q^{65} -13.1125 q^{66} +2.01532 q^{67} -4.06087 q^{68} +8.51393 q^{69} +2.97097 q^{70} -1.00000 q^{71} -2.73807 q^{72} -4.35399 q^{73} -19.9582 q^{74} +1.88140 q^{75} +25.8338 q^{76} -3.41638 q^{77} +8.64078 q^{78} -1.53862 q^{79} +4.36890 q^{80} -10.3278 q^{81} -15.9707 q^{82} -4.83390 q^{83} -9.21999 q^{84} -1.00000 q^{85} +8.69850 q^{86} -6.80079 q^{87} -14.3633 q^{88} +5.31722 q^{89} -1.32860 q^{90} +2.25131 q^{91} +18.3767 q^{92} +18.6060 q^{93} -4.49531 q^{94} +6.36164 q^{95} -1.14484 q^{96} +7.25798 q^{97} +13.6479 q^{98} +1.52779 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 59 q + 2 q^{2} + 6 q^{3} + 76 q^{4} + 59 q^{5} + 14 q^{6} + 9 q^{7} + 6 q^{8} + 97 q^{9}+O(q^{10}) \) 59 * q + 2 * q^2 + 6 * q^3 + 76 * q^4 + 59 * q^5 + 14 * q^6 + 9 * q^7 + 6 * q^8 + 97 * q^9	\( 59 q + 2 q^{2} + 6 q^{3} + 76 q^{4} + 59 q^{5} + 14 q^{6} + 9 q^{7} + 6 q^{8} + 97 q^{9} + 2 q^{10} + 6 q^{11} + 16 q^{12} + 25 q^{13} + 8 q^{14} + 6 q^{15} + 114 q^{16} - 59 q^{17} + 3 q^{18} + 35 q^{19} + 76 q^{20} + 41 q^{21} + 13 q^{22} - 2 q^{23} + 35 q^{24} + 59 q^{25} + 10 q^{26} + 27 q^{27} + 28 q^{28} + 10 q^{29} + 14 q^{30} + 15 q^{31} + 19 q^{32} - 3 q^{33} - 2 q^{34} + 9 q^{35} + 160 q^{36} + 56 q^{37} + 17 q^{38} + 25 q^{39} + 6 q^{40} + 47 q^{41} + 46 q^{42} + 27 q^{43} + 39 q^{44} + 97 q^{45} + 4 q^{46} - 8 q^{47} + 58 q^{48} + 174 q^{49} + 2 q^{50} - 6 q^{51} + 13 q^{52} + 17 q^{53} + 48 q^{54} + 6 q^{55} + 33 q^{56} + 6 q^{57} + 32 q^{58} + 30 q^{59} + 16 q^{60} + 85 q^{61} - 3 q^{62} + 14 q^{63} + 168 q^{64} + 25 q^{65} + 87 q^{66} + 21 q^{67} - 76 q^{68} + 111 q^{69} + 8 q^{70} - 59 q^{71} - 52 q^{72} + 41 q^{73} + 11 q^{74} + 6 q^{75} + 118 q^{76} + 55 q^{77} - 54 q^{78} + 43 q^{79} + 114 q^{80} + 207 q^{81} + 45 q^{82} + 10 q^{83} + 62 q^{84} - 59 q^{85} + 19 q^{86} + 8 q^{87} + 35 q^{88} + 86 q^{89} + 3 q^{90} + 47 q^{91} - 98 q^{92} + 41 q^{93} + 30 q^{94} + 35 q^{95} + 69 q^{96} + 72 q^{97} + 14 q^{98} + 25 q^{99}+O(q^{100}) \) 59 * q + 2 * q^2 + 6 * q^3 + 76 * q^4 + 59 * q^5 + 14 * q^6 + 9 * q^7 + 6 * q^8 + 97 * q^9 + 2 * q^10 + 6 * q^11 + 16 * q^12 + 25 * q^13 + 8 * q^14 + 6 * q^15 + 114 * q^16 - 59 * q^17 + 3 * q^18 + 35 * q^19 + 76 * q^20 + 41 * q^21 + 13 * q^22 - 2 * q^23 + 35 * q^24 + 59 * q^25 + 10 * q^26 + 27 * q^27 + 28 * q^28 + 10 * q^29 + 14 * q^30 + 15 * q^31 + 19 * q^32 - 3 * q^33 - 2 * q^34 + 9 * q^35 + 160 * q^36 + 56 * q^37 + 17 * q^38 + 25 * q^39 + 6 * q^40 + 47 * q^41 + 46 * q^42 + 27 * q^43 + 39 * q^44 + 97 * q^45 + 4 * q^46 - 8 * q^47 + 58 * q^48 + 174 * q^49 + 2 * q^50 - 6 * q^51 + 13 * q^52 + 17 * q^53 + 48 * q^54 + 6 * q^55 + 33 * q^56 + 6 * q^57 + 32 * q^58 + 30 * q^59 + 16 * q^60 + 85 * q^61 - 3 * q^62 + 14 * q^63 + 168 * q^64 + 25 * q^65 + 87 * q^66 + 21 * q^67 - 76 * q^68 + 111 * q^69 + 8 * q^70 - 59 * q^71 - 52 * q^72 + 41 * q^73 + 11 * q^74 + 6 * q^75 + 118 * q^76 + 55 * q^77 - 54 * q^78 + 43 * q^79 + 114 * q^80 + 207 * q^81 + 45 * q^82 + 10 * q^83 + 62 * q^84 - 59 * q^85 + 19 * q^86 + 8 * q^87 + 35 * q^88 + 86 * q^89 + 3 * q^90 + 47 * q^91 - 98 * q^92 + 41 * q^93 + 30 * q^94 + 35 * q^95 + 69 * q^96 + 72 * q^97 + 14 * q^98 + 25 * q^99

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