LMFDB - Embedded newform 4015.2.a.b.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4015,2,Mod(1,4015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, 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("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.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:	$32.0599364115$
Analytic rank:	$1$
Dimension:	$23$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.152616 q^{2} -0.242697 q^{3} -1.97671 q^{4} +1.00000 q^{5} -0.0370393 q^{6} +2.57515 q^{7} -0.606909 q^{8} -2.94110 q^{9} +O(q^{10})$	\(q+0.152616 q^{2} -0.242697 q^{3} -1.97671 q^{4} +1.00000 q^{5} -0.0370393 q^{6} +2.57515 q^{7} -0.606909 q^{8} -2.94110 q^{9} +0.152616 q^{10} +1.00000 q^{11} +0.479741 q^{12} -5.70753 q^{13} +0.393008 q^{14} -0.242697 q^{15} +3.86079 q^{16} +2.87905 q^{17} -0.448858 q^{18} +2.41491 q^{19} -1.97671 q^{20} -0.624979 q^{21} +0.152616 q^{22} -1.51249 q^{23} +0.147295 q^{24} +1.00000 q^{25} -0.871060 q^{26} +1.44188 q^{27} -5.09031 q^{28} +3.21051 q^{29} -0.0370393 q^{30} -8.11234 q^{31} +1.80304 q^{32} -0.242697 q^{33} +0.439388 q^{34} +2.57515 q^{35} +5.81369 q^{36} +5.40627 q^{37} +0.368553 q^{38} +1.38520 q^{39} -0.606909 q^{40} -6.04633 q^{41} -0.0953817 q^{42} +5.90093 q^{43} -1.97671 q^{44} -2.94110 q^{45} -0.230830 q^{46} -1.56113 q^{47} -0.937002 q^{48} -0.368623 q^{49} +0.152616 q^{50} -0.698735 q^{51} +11.2821 q^{52} -13.2479 q^{53} +0.220054 q^{54} +1.00000 q^{55} -1.56288 q^{56} -0.586090 q^{57} +0.489974 q^{58} -5.06506 q^{59} +0.479741 q^{60} +5.31613 q^{61} -1.23807 q^{62} -7.57376 q^{63} -7.44641 q^{64} -5.70753 q^{65} -0.0370393 q^{66} -5.36965 q^{67} -5.69104 q^{68} +0.367077 q^{69} +0.393008 q^{70} +9.38616 q^{71} +1.78498 q^{72} -1.00000 q^{73} +0.825082 q^{74} -0.242697 q^{75} -4.77357 q^{76} +2.57515 q^{77} +0.211403 q^{78} -6.12238 q^{79} +3.86079 q^{80} +8.47335 q^{81} -0.922765 q^{82} +10.3551 q^{83} +1.23540 q^{84} +2.87905 q^{85} +0.900576 q^{86} -0.779179 q^{87} -0.606909 q^{88} +3.09220 q^{89} -0.448858 q^{90} -14.6977 q^{91} +2.98976 q^{92} +1.96884 q^{93} -0.238254 q^{94} +2.41491 q^{95} -0.437591 q^{96} -7.97109 q^{97} -0.0562576 q^{98} -2.94110 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q - 5 q^{2} - 3 q^{3} + 15 q^{4} + 23 q^{5} - 15 q^{6} - 10 q^{7} - 12 q^{8} + 8 q^{9}+O(q^{10}) $ 23 * q - 5 * q^2 - 3 * q^3 + 15 * q^4 + 23 * q^5 - 15 * q^6 - 10 * q^7 - 12 * q^8 + 8 * q^9	\( 23 q - 5 q^{2} - 3 q^{3} + 15 q^{4} + 23 q^{5} - 15 q^{6} - 10 q^{7} - 12 q^{8} + 8 q^{9} - 5 q^{10} + 23 q^{11} + 4 q^{12} - 19 q^{13} - 5 q^{14} - 3 q^{15} - q^{16} - 26 q^{17} + 5 q^{18} - 34 q^{19} + 15 q^{20} - 26 q^{21} - 5 q^{22} - 4 q^{23} - 23 q^{24} + 23 q^{25} - 13 q^{26} - 3 q^{27} - 28 q^{28} - 36 q^{29} - 15 q^{30} - 24 q^{31} - 19 q^{32} - 3 q^{33} - 4 q^{34} - 10 q^{35} - 14 q^{36} + 4 q^{37} - 15 q^{38} - 34 q^{39} - 12 q^{40} - 74 q^{41} + 7 q^{42} - 15 q^{43} + 15 q^{44} + 8 q^{45} + 3 q^{46} + q^{47} + 29 q^{48} + q^{49} - 5 q^{50} - 47 q^{51} - 23 q^{52} - 6 q^{53} - 11 q^{54} + 23 q^{55} - 20 q^{56} - 19 q^{57} + 22 q^{58} - 17 q^{59} + 4 q^{60} - 59 q^{61} + 38 q^{62} - 21 q^{63} - 18 q^{64} - 19 q^{65} - 15 q^{66} + 12 q^{67} + 5 q^{68} - 8 q^{69} - 5 q^{70} - 34 q^{71} + 21 q^{72} - 23 q^{73} - 9 q^{74} - 3 q^{75} - 53 q^{76} - 10 q^{77} + 23 q^{78} - 62 q^{79} - q^{80} + 7 q^{81} + 24 q^{82} - 8 q^{83} + 46 q^{84} - 26 q^{85} - 11 q^{86} + q^{87} - 12 q^{88} - 77 q^{89} + 5 q^{90} - 6 q^{91} + 47 q^{92} - 32 q^{94} - 34 q^{95} - 53 q^{96} - 21 q^{97} - 3 q^{98} + 8 q^{99}+O(q^{100}) \) 23 * q - 5 * q^2 - 3 * q^3 + 15 * q^4 + 23 * q^5 - 15 * q^6 - 10 * q^7 - 12 * q^8 + 8 * q^9 - 5 * q^10 + 23 * q^11 + 4 * q^12 - 19 * q^13 - 5 * q^14 - 3 * q^15 - q^16 - 26 * q^17 + 5 * q^18 - 34 * q^19 + 15 * q^20 - 26 * q^21 - 5 * q^22 - 4 * q^23 - 23 * q^24 + 23 * q^25 - 13 * q^26 - 3 * q^27 - 28 * q^28 - 36 * q^29 - 15 * q^30 - 24 * q^31 - 19 * q^32 - 3 * q^33 - 4 * q^34 - 10 * q^35 - 14 * q^36 + 4 * q^37 - 15 * q^38 - 34 * q^39 - 12 * q^40 - 74 * q^41 + 7 * q^42 - 15 * q^43 + 15 * q^44 + 8 * q^45 + 3 * q^46 + q^47 + 29 * q^48 + q^49 - 5 * q^50 - 47 * q^51 - 23 * q^52 - 6 * q^53 - 11 * q^54 + 23 * q^55 - 20 * q^56 - 19 * q^57 + 22 * q^58 - 17 * q^59 + 4 * q^60 - 59 * q^61 + 38 * q^62 - 21 * q^63 - 18 * q^64 - 19 * q^65 - 15 * q^66 + 12 * q^67 + 5 * q^68 - 8 * q^69 - 5 * q^70 - 34 * q^71 + 21 * q^72 - 23 * q^73 - 9 * q^74 - 3 * q^75 - 53 * q^76 - 10 * q^77 + 23 * q^78 - 62 * q^79 - q^80 + 7 * q^81 + 24 * q^82 - 8 * q^83 + 46 * q^84 - 26 * q^85 - 11 * q^86 + q^87 - 12 * q^88 - 77 * q^89 + 5 * q^90 - 6 * q^91 + 47 * q^92 - 32 * q^94 - 34 * q^95 - 53 * q^96 - 21 * q^97 - 3 * q^98 + 8 * 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 $

$2$	0.152616	0.107916	0.0539578	−	0.998543i	$-0.482816\pi$
$2$	0.152616	0.107916	0.0539578	+	0.998543i	$0.482816\pi$
$3$	−0.242697	−0.140121	−0.0700605	−	0.997543i	$-0.522319\pi$
$3$	−0.242697	−0.140121	−0.0700605	+	0.997543i	$0.522319\pi$
$4$	−1.97671	−0.988354
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.0370393	−0.0151212
$7$	2.57515	0.973314	0.486657	−	0.873593i	$-0.338216\pi$
$7$	2.57515	0.973314	0.486657	+	0.873593i	$0.338216\pi$
$8$	−0.606909	−0.214575
$9$	−2.94110	−0.980366
$10$	0.152616	0.0482614
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.479741	0.138489
$13$	−5.70753	−1.58298	−0.791492	−	0.611179i	$-0.790696\pi$
$13$	−5.70753	−1.58298	−0.791492	+	0.611179i	$0.790696\pi$
$14$	0.393008	0.105036
$15$	−0.242697	−0.0626640
$16$	3.86079	0.965198
$17$	2.87905	0.698272	0.349136	−	0.937072i	$-0.386475\pi$
$17$	2.87905	0.698272	0.349136	+	0.937072i	$0.386475\pi$
$18$	−0.448858	−0.105797
$19$	2.41491	0.554018	0.277009	−	0.960867i	$-0.410657\pi$
$19$	2.41491	0.554018	0.277009	+	0.960867i	$0.410657\pi$
$20$	−1.97671	−0.442005
$21$	−0.624979	−0.136382
$22$	0.152616	0.0325378
$23$	−1.51249	−0.315377	−0.157688	−	0.987489i	$-0.550404\pi$
$23$	−1.51249	−0.315377	−0.157688	+	0.987489i	$0.550404\pi$
$24$	0.147295	0.0300664
$25$	1.00000	0.200000
$26$	−0.871060	−0.170829
$27$	1.44188	0.277491
$28$	−5.09031	−0.961979
$29$	3.21051	0.596176	0.298088	−	0.954538i	$-0.403651\pi$
$29$	3.21051	0.596176	0.298088	+	0.954538i	$0.403651\pi$
$30$	−0.0370393	−0.00676243
$31$	−8.11234	−1.45702	−0.728509	−	0.685036i	$-0.759787\pi$
$31$	−8.11234	−1.45702	−0.728509	+	0.685036i	$0.759787\pi$
$32$	1.80304	0.318735
$33$	−0.242697	−0.0422481
$34$	0.439388	0.0753544
$35$	2.57515	0.435279
$36$	5.81369	0.968949
$37$	5.40627	0.888785	0.444392	−	0.895832i	$-0.353420\pi$
$37$	5.40627	0.888785	0.444392	+	0.895832i	$0.353420\pi$
$38$	0.368553	0.0597872
$39$	1.38520	0.221809
$40$	−0.606909	−0.0959607
$41$	−6.04633	−0.944278	−0.472139	−	0.881524i	$-0.656518\pi$
$41$	−6.04633	−0.944278	−0.472139	+	0.881524i	$0.656518\pi$
$42$	−0.0953817	−0.0147177
$43$	5.90093	0.899884	0.449942	−	0.893058i	$-0.351445\pi$
$43$	5.90093	0.899884	0.449942	+	0.893058i	$0.351445\pi$
$44$	−1.97671	−0.298000
$45$	−2.94110	−0.438433
$46$	−0.230830	−0.0340341
$47$	−1.56113	−0.227715	−0.113857	−	0.993497i	$-0.536321\pi$
$47$	−1.56113	−0.227715	−0.113857	+	0.993497i	$0.536321\pi$
$48$	−0.937002	−0.135245
$49$	−0.368623	−0.0526604
$50$	0.152616	0.0215831
$51$	−0.698735	−0.0978425
$52$	11.2821	1.56455
$53$	−13.2479	−1.81973	−0.909867	−	0.414900i	$-0.863816\pi$
$53$	−13.2479	−1.81973	−0.909867	+	0.414900i	$0.863816\pi$
$54$	0.220054	0.0299456
$55$	1.00000	0.134840
$56$	−1.56288	−0.208848
$57$	−0.586090	−0.0776295
$58$	0.489974	0.0643368
$59$	−5.06506	−0.659415	−0.329707	−	0.944083i	$-0.606950\pi$
$59$	−5.06506	−0.659415	−0.329707	+	0.944083i	$0.606950\pi$
$60$	0.479741	0.0619342
$61$	5.31613	0.680661	0.340330	−	0.940306i	$-0.389461\pi$
$61$	5.31613	0.680661	0.340330	+	0.940306i	$0.389461\pi$
$62$	−1.23807	−0.157235
$63$	−7.57376	−0.954204
$64$	−7.44641	−0.930802
$65$	−5.70753	−0.707932
$66$	−0.0370393	−0.00455923
$67$	−5.36965	−0.656007	−0.328004	−	0.944676i	$-0.606376\pi$
$67$	−5.36965	−0.656007	−0.328004	+	0.944676i	$0.606376\pi$
$68$	−5.69104	−0.690140
$69$	0.367077	0.0441909
$70$	0.393008	0.0469734
$71$	9.38616	1.11393	0.556966	−	0.830535i	$-0.311965\pi$
$71$	9.38616	1.11393	0.556966	+	0.830535i	$0.311965\pi$
$72$	1.78498	0.210362
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	0.825082	0.0959138
$75$	−0.242697	−0.0280242
$76$	−4.77357	−0.547566
$77$	2.57515	0.293465
$78$	0.211403	0.0239367
$79$	−6.12238	−0.688822	−0.344411	−	0.938819i	$-0.611921\pi$
$79$	−6.12238	−0.688822	−0.344411	+	0.938819i	$0.611921\pi$
$80$	3.86079	0.431650
$81$	8.47335	0.941484
$82$	−0.922765	−0.101902
$83$	10.3551	1.13663	0.568313	−	0.822813i	$-0.307596\pi$
$83$	10.3551	1.13663	0.568313	+	0.822813i	$0.307596\pi$
$84$	1.23540	0.134793
$85$	2.87905	0.312277
$86$	0.900576	0.0971116
$87$	−0.779179	−0.0835368
$88$	−0.606909	−0.0646967
$89$	3.09220	0.327773	0.163886	−	0.986479i	$-0.447597\pi$
$89$	3.09220	0.327773	0.163886	+	0.986479i	$0.447597\pi$
$90$	−0.448858	−0.0473138
$91$	−14.6977	−1.54074
$92$	2.98976	0.311704
$93$	1.96884	0.204159
$94$	−0.238254	−0.0245740
$95$	2.41491	0.247764
$96$	−0.437591	−0.0446614
$97$	−7.97109	−0.809342	−0.404671	−	0.914462i	$-0.632614\pi$
$97$	−7.97109	−0.809342	−0.404671	+	0.914462i	$0.632614\pi$
$98$	−0.0562576	−0.00568288
$99$	−2.94110	−0.295592
$100$	−1.97671	−0.197671
$101$	−10.5141	−1.04619	−0.523095	−	0.852274i	$-0.675223\pi$
$101$	−10.5141	−1.04619	−0.523095	+	0.852274i	$0.675223\pi$
$102$	−0.106638	−0.0105587
$103$	−16.1691	−1.59319	−0.796593	−	0.604516i	$-0.793367\pi$
$103$	−16.1691	−1.59319	−0.796593	+	0.604516i	$0.793367\pi$
$104$	3.46395	0.339668
$105$	−0.624979	−0.0609917
$106$	−2.02183	−0.196378
$107$	−1.11430	−0.107724	−0.0538619	−	0.998548i	$-0.517153\pi$
$107$	−1.11430	−0.107724	−0.0538619	+	0.998548i	$0.517153\pi$
$108$	−2.85019	−0.274259
$109$	10.1587	0.973022	0.486511	−	0.873674i	$-0.338269\pi$
$109$	10.1587	0.973022	0.486511	+	0.873674i	$0.338269\pi$
$110$	0.152616	0.0145513
$111$	−1.31208	−0.124537
$112$	9.94211	0.939441
$113$	−1.27109	−0.119574	−0.0597870	−	0.998211i	$-0.519042\pi$
$113$	−1.27109	−0.119574	−0.0597870	+	0.998211i	$0.519042\pi$
$114$	−0.0894466	−0.00837744
$115$	−1.51249	−0.141041
$116$	−6.34624	−0.589233
$117$	16.7864	1.55190
$118$	−0.773009	−0.0711612
$119$	7.41397	0.679637
$120$	0.147295	0.0134461
$121$	1.00000	0.0909091
$122$	0.811326	0.0734540
$123$	1.46742	0.132313
$124$	16.0357	1.44005
$125$	1.00000	0.0894427
$126$	−1.15588	−0.102974
$127$	−21.1996	−1.88116	−0.940578	−	0.339578i	$-0.889716\pi$
$127$	−21.1996	−1.88116	−0.940578	+	0.339578i	$0.889716\pi$
$128$	−4.74251	−0.419183
$129$	−1.43214	−0.126093
$130$	−0.871060	−0.0763970
$131$	−20.8276	−1.81971	−0.909857	−	0.414923i	$-0.863809\pi$
$131$	−20.8276	−1.81971	−0.909857	+	0.414923i	$0.863809\pi$
$132$	0.479741	0.0417561
$133$	6.21874	0.539233
$134$	−0.819494	−0.0707935
$135$	1.44188	0.124098
$136$	−1.74732	−0.149831
$137$	3.60984	0.308410	0.154205	−	0.988039i	$-0.450718\pi$
$137$	3.60984	0.308410	0.154205	+	0.988039i	$0.450718\pi$
$138$	0.0560218	0.00476889
$139$	−0.976892	−0.0828589	−0.0414295	−	0.999141i	$-0.513191\pi$
$139$	−0.976892	−0.0828589	−0.0414295	+	0.999141i	$0.513191\pi$
$140$	−5.09031	−0.430210
$141$	0.378882	0.0319076
$142$	1.43248	0.120211
$143$	−5.70753	−0.477288
$144$	−11.3550	−0.946248
$145$	3.21051	0.266618
$146$	−0.152616	−0.0126306
$147$	0.0894634	0.00737882
$148$	−10.6866	−0.878434
$149$	4.65733	0.381543	0.190772	−	0.981634i	$-0.438901\pi$
$149$	4.65733	0.381543	0.190772	+	0.981634i	$0.438901\pi$
$150$	−0.0370393	−0.00302425
$151$	−17.9060	−1.45717	−0.728585	−	0.684956i	$-0.759822\pi$
$151$	−17.9060	−1.45717	−0.728585	+	0.684956i	$0.759822\pi$
$152$	−1.46563	−0.118878
$153$	−8.46756	−0.684562
$154$	0.393008	0.0316695
$155$	−8.11234	−0.651599
$156$	−2.73813	−0.219226
$157$	4.25839	0.339857	0.169928	−	0.985456i	$-0.445646\pi$
$157$	4.25839	0.339857	0.169928	+	0.985456i	$0.445646\pi$
$158$	−0.934372	−0.0743347
$159$	3.21521	0.254983
$160$	1.80304	0.142542
$161$	−3.89489	−0.306960
$162$	1.29317	0.101601
$163$	−21.1121	−1.65363	−0.826813	−	0.562477i	$-0.809849\pi$
$163$	−21.1121	−1.65363	−0.826813	+	0.562477i	$0.809849\pi$
$164$	11.9518	0.933281
$165$	−0.242697	−0.0188939
$166$	1.58036	0.122660
$167$	10.8070	0.836268	0.418134	−	0.908385i	$-0.362684\pi$
$167$	10.8070	0.836268	0.418134	+	0.908385i	$0.362684\pi$
$168$	0.379305	0.0292640
$169$	19.5759	1.50584
$170$	0.439388	0.0336995
$171$	−7.10248	−0.543140
$172$	−11.6644	−0.889404
$173$	−15.4506	−1.17469	−0.587344	−	0.809337i	$-0.699826\pi$
$173$	−15.4506	−1.17469	−0.587344	+	0.809337i	$0.699826\pi$
$174$	−0.118915	−0.00901493
$175$	2.57515	0.194663
$176$	3.86079	0.291018
$177$	1.22927	0.0923979
$178$	0.471919	0.0353718
$179$	−10.8479	−0.810809	−0.405405	−	0.914137i	$-0.632869\pi$
$179$	−10.8479	−0.810809	−0.405405	+	0.914137i	$0.632869\pi$
$180$	5.81369	0.433327
$181$	−26.1243	−1.94180	−0.970900	−	0.239484i	$-0.923022\pi$
$181$	−26.1243	−1.94180	−0.970900	+	0.239484i	$0.923022\pi$
$182$	−2.24311	−0.166270
$183$	−1.29021	−0.0953749
$184$	0.917945	0.0676718
$185$	5.40627	0.397477
$186$	0.300476	0.0220319
$187$	2.87905	0.210537
$188$	3.08591	0.225063
$189$	3.71306	0.270086
$190$	0.368553	0.0267376
$191$	26.4559	1.91428	0.957140	−	0.289625i	$-0.0935306\pi$
$191$	26.4559	1.91428	0.957140	+	0.289625i	$0.0935306\pi$
$192$	1.80722	0.130425
$193$	20.7189	1.49138	0.745689	−	0.666294i	$-0.232120\pi$
$193$	20.7189	1.49138	0.745689	+	0.666294i	$0.232120\pi$
$194$	−1.21651	−0.0873407
$195$	1.38520	0.0991962
$196$	0.728659	0.0520471
$197$	12.7996	0.911931	0.455966	−	0.889997i	$-0.349294\pi$
$197$	12.7996	0.911931	0.455966	+	0.889997i	$0.349294\pi$
$198$	−0.448858	−0.0318990
$199$	11.9526	0.847297	0.423648	−	0.905827i	$-0.360749\pi$
$199$	11.9526	0.847297	0.423648	+	0.905827i	$0.360749\pi$
$200$	−0.606909	−0.0429149
$201$	1.30320	0.0919204
$202$	−1.60462	−0.112900
$203$	8.26753	0.580267
$204$	1.38120	0.0967030
$205$	−6.04633	−0.422294
$206$	−2.46766	−0.171930
$207$	4.44839	0.309185
$208$	−22.0356	−1.52789
$209$	2.41491	0.167043
$210$	−0.0953817	−0.00658196
$211$	12.7322	0.876519	0.438260	−	0.898848i	$-0.355595\pi$
$211$	12.7322	0.876519	0.438260	+	0.898848i	$0.355595\pi$
$212$	26.1872	1.79854
$213$	−2.27799	−0.156085
$214$	−0.170060	−0.0116251
$215$	5.90093	0.402440
$216$	−0.875092	−0.0595425
$217$	−20.8905	−1.41814
$218$	1.55037	0.105004
$219$	0.242697	0.0163999
$220$	−1.97671	−0.133270
$221$	−16.4323	−1.10535
$222$	−0.200245	−0.0134395
$223$	−3.20310	−0.214495	−0.107248	−	0.994232i	$-0.534204\pi$
$223$	−3.20310	−0.214495	−0.107248	+	0.994232i	$0.534204\pi$
$224$	4.64308	0.310229
$225$	−2.94110	−0.196073
$226$	−0.193988	−0.0129039
$227$	−26.8982	−1.78529	−0.892647	−	0.450757i	$-0.851154\pi$
$227$	−26.8982	−1.78529	−0.892647	+	0.450757i	$0.851154\pi$
$228$	1.15853	0.0767254
$229$	−28.4028	−1.87691	−0.938454	−	0.345405i	$-0.887742\pi$
$229$	−28.4028	−1.87691	−0.938454	+	0.345405i	$0.887742\pi$
$230$	−0.230830	−0.0152205
$231$	−0.624979	−0.0411206
$232$	−1.94848	−0.127924
$233$	−8.14206	−0.533404	−0.266702	−	0.963779i	$-0.585934\pi$
$233$	−8.14206	−0.533404	−0.266702	+	0.963779i	$0.585934\pi$
$234$	2.56187	0.167475
$235$	−1.56113	−0.101837
$236$	10.0122	0.651736
$237$	1.48588	0.0965184
$238$	1.13149	0.0733435
$239$	24.7096	1.59833	0.799165	−	0.601111i	$-0.205275\pi$
$239$	24.7096	1.59833	0.799165	+	0.601111i	$0.205275\pi$
$240$	−0.937002	−0.0604832
$241$	24.2948	1.56496	0.782482	−	0.622673i	$-0.213953\pi$
$241$	24.2948	1.56496	0.782482	+	0.622673i	$0.213953\pi$
$242$	0.152616	0.00981052
$243$	−6.38211	−0.409412
$244$	−10.5084	−0.672734
$245$	−0.368623	−0.0235504
$246$	0.223952	0.0142787
$247$	−13.7832	−0.877001
$248$	4.92345	0.312639
$249$	−2.51316	−0.159265
$250$	0.152616	0.00965227
$251$	−24.4244	−1.54166	−0.770829	−	0.637043i	$-0.780158\pi$
$251$	−24.4244	−1.54166	−0.770829	+	0.637043i	$0.780158\pi$
$252$	14.9711	0.943091
$253$	−1.51249	−0.0950896
$254$	−3.23539	−0.203006
$255$	−0.698735	−0.0437565
$256$	14.1690	0.885565
$257$	−30.3911	−1.89574	−0.947871	−	0.318653i	$-0.896769\pi$
$257$	−30.3911	−1.89574	−0.947871	+	0.318653i	$0.896769\pi$
$258$	−0.218567	−0.0136074
$259$	13.9219	0.865066
$260$	11.2821	0.699688
$261$	−9.44242	−0.584471
$262$	−3.17862	−0.196376
$263$	−16.1564	−0.996246	−0.498123	−	0.867106i	$-0.665977\pi$
$263$	−16.1564	−0.996246	−0.498123	+	0.867106i	$0.665977\pi$
$264$	0.147295	0.00906536
$265$	−13.2479	−0.813810
$266$	0.949078	0.0581917
$267$	−0.750467	−0.0459279
$268$	10.6142	0.648367
$269$	−20.1953	−1.23133	−0.615664	−	0.788009i	$-0.711112\pi$
$269$	−20.1953	−1.23133	−0.615664	+	0.788009i	$0.711112\pi$
$270$	0.220054	0.0133921
$271$	−4.61812	−0.280531	−0.140265	−	0.990114i	$-0.544796\pi$
$271$	−4.61812	−0.280531	−0.140265	+	0.990114i	$0.544796\pi$
$272$	11.1154	0.673970
$273$	3.56709	0.215890
$274$	0.550919	0.0332822
$275$	1.00000	0.0603023
$276$	−0.725604	−0.0436762
$277$	−21.3978	−1.28567	−0.642835	−	0.766005i	$-0.722242\pi$
$277$	−21.3978	−1.28567	−0.642835	+	0.766005i	$0.722242\pi$
$278$	−0.149089	−0.00894178
$279$	23.8592	1.42841
$280$	−1.56288	−0.0933998
$281$	−19.0661	−1.13739	−0.568693	−	0.822550i	$-0.692551\pi$
$281$	−19.0661	−1.13739	−0.568693	+	0.822550i	$0.692551\pi$
$282$	0.0578234	0.00344333
$283$	8.82218	0.524424	0.262212	−	0.965010i	$-0.415548\pi$
$283$	8.82218	0.524424	0.262212	+	0.965010i	$0.415548\pi$
$284$	−18.5537	−1.10096
$285$	−0.586090	−0.0347170
$286$	−0.871060	−0.0515068
$287$	−15.5702	−0.919079
$288$	−5.30290	−0.312477
$289$	−8.71109	−0.512417
$290$	0.489974	0.0287723
$291$	1.93456	0.113406
$292$	1.97671	0.115678
$293$	1.11414	0.0650886	0.0325443	−	0.999470i	$-0.489639\pi$
$293$	1.11414	0.0650886	0.0325443	+	0.999470i	$0.489639\pi$
$294$	0.0136535	0.000796290 0
$295$	−5.06506	−0.294899
$296$	−3.28111	−0.190711
$297$	1.44188	0.0836666
$298$	0.710782	0.0411745
$299$	8.63260	0.499236
$300$	0.479741	0.0276978
$301$	15.1958	0.875869
$302$	−2.73274	−0.157251
$303$	2.55173	0.146593
$304$	9.32346	0.534737
$305$	5.31613	0.304401
$306$	−1.29228	−0.0738749
$307$	−21.9358	−1.25194	−0.625972	−	0.779846i	$-0.715297\pi$
$307$	−21.9358	−1.25194	−0.625972	+	0.779846i	$0.715297\pi$
$308$	−5.09031	−0.290048
$309$	3.92418	0.223239
$310$	−1.23807	−0.0703177
$311$	32.4235	1.83857	0.919283	−	0.393598i	$-0.128770\pi$
$311$	32.4235	1.83857	0.919283	+	0.393598i	$0.128770\pi$
$312$	−0.840689	−0.0475947
$313$	−1.40179	−0.0792341	−0.0396170	−	0.999215i	$-0.512614\pi$
$313$	−1.40179	−0.0792341	−0.0396170	+	0.999215i	$0.512614\pi$
$314$	0.649898	0.0366758
$315$	−7.57376	−0.426733
$316$	12.1022	0.680800
$317$	21.2224	1.19197	0.595984	−	0.802996i	$-0.296762\pi$
$317$	21.2224	1.19197	0.595984	+	0.802996i	$0.296762\pi$
$318$	0.490692	0.0275166
$319$	3.21051	0.179754
$320$	−7.44641	−0.416267
$321$	0.270438	0.0150944
$322$	−0.594422	−0.0331258
$323$	6.95263	0.386855
$324$	−16.7494	−0.930519
$325$	−5.70753	−0.316597
$326$	−3.22204	−0.178452
$327$	−2.46547	−0.136341
$328$	3.66957	0.202618
$329$	−4.02015	−0.221638
$330$	−0.0370393	−0.00203895
$331$	−17.9993	−0.989332	−0.494666	−	0.869083i	$-0.664710\pi$
$331$	−17.9993	−0.989332	−0.494666	+	0.869083i	$0.664710\pi$
$332$	−20.4691	−1.12339
$333$	−15.9004	−0.871334
$334$	1.64931	0.0902464
$335$	−5.36965	−0.293375
$336$	−2.41292	−0.131635
$337$	24.3839	1.32827	0.664137	−	0.747611i	$-0.268799\pi$
$337$	24.3839	1.32827	0.664137	+	0.747611i	$0.268799\pi$
$338$	2.98760	0.162504
$339$	0.308489	0.0167548
$340$	−5.69104	−0.308640
$341$	−8.11234	−0.439308
$342$	−1.08395	−0.0586133
$343$	−18.9753	−1.02457
$344$	−3.58133	−0.193092
$345$	0.367077	0.0197628
$346$	−2.35801	−0.126767
$347$	−8.54846	−0.458905	−0.229453	−	0.973320i	$-0.573694\pi$
$347$	−8.54846	−0.458905	−0.229453	+	0.973320i	$0.573694\pi$
$348$	1.54021	0.0825640
$349$	−33.9923	−1.81957	−0.909783	−	0.415084i	$-0.863752\pi$
$349$	−33.9923	−1.81957	−0.909783	+	0.415084i	$0.863752\pi$
$350$	0.393008	0.0210072
$351$	−8.22960	−0.439264
$352$	1.80304	0.0961021
$353$	−19.2427	−1.02419	−0.512094	−	0.858929i	$-0.671130\pi$
$353$	−19.2427	−1.02419	−0.512094	+	0.858929i	$0.671130\pi$
$354$	0.187607	0.00997118
$355$	9.38616	0.498166
$356$	−6.11238	−0.323956
$357$	−1.79935	−0.0952314
$358$	−1.65556	−0.0874990
$359$	−17.7830	−0.938551	−0.469275	−	0.883052i	$-0.655485\pi$
$359$	−17.7830	−0.938551	−0.469275	+	0.883052i	$0.655485\pi$
$360$	1.78498	0.0940766
$361$	−13.1682	−0.693064
$362$	−3.98697	−0.209551
$363$	−0.242697	−0.0127383
$364$	29.0531	1.52280
$365$	−1.00000	−0.0523424
$366$	−0.196906	−0.0102924
$367$	−36.3295	−1.89638	−0.948192	−	0.317699i	$-0.897090\pi$
$367$	−36.3295	−1.89638	−0.948192	+	0.317699i	$0.897090\pi$
$368$	−5.83942	−0.304401
$369$	17.7828	0.925738
$370$	0.825082	0.0428940
$371$	−34.1152	−1.77117
$372$	−3.89182	−0.201781
$373$	30.3421	1.57105	0.785526	−	0.618829i	$-0.212392\pi$
$373$	30.3421	1.57105	0.785526	+	0.618829i	$0.212392\pi$
$374$	0.439388	0.0227202
$375$	−0.242697	−0.0125328
$376$	0.947465	0.0488618
$377$	−18.3241	−0.943738
$378$	0.566672	0.0291465
$379$	−27.0372	−1.38881	−0.694404	−	0.719585i	$-0.744332\pi$
$379$	−27.0372	−1.38881	−0.694404	+	0.719585i	$0.744332\pi$
$380$	−4.77357	−0.244879
$381$	5.14506	0.263589
$382$	4.03759	0.206581
$383$	6.38544	0.326281	0.163140	−	0.986603i	$-0.447838\pi$
$383$	6.38544	0.326281	0.163140	+	0.986603i	$0.447838\pi$
$384$	1.15099	0.0587363
$385$	2.57515	0.131242
$386$	3.16203	0.160943
$387$	−17.3552	−0.882216
$388$	15.7565	0.799917
$389$	2.68308	0.136037	0.0680187	−	0.997684i	$-0.478332\pi$
$389$	2.68308	0.136037	0.0680187	+	0.997684i	$0.478332\pi$
$390$	0.211403	0.0107048
$391$	−4.35454	−0.220219
$392$	0.223720	0.0112996
$393$	5.05478	0.254980
$394$	1.95342	0.0984117
$395$	−6.12238	−0.308051
$396$	5.81369	0.292149
$397$	25.1285	1.26116	0.630581	−	0.776124i	$-0.282817\pi$
$397$	25.1285	1.26116	0.630581	+	0.776124i	$0.282817\pi$
$398$	1.82415	0.0914366
$399$	−1.50927	−0.0755579
$400$	3.86079	0.193040
$401$	−18.4012	−0.918911	−0.459455	−	0.888201i	$-0.651955\pi$
$401$	−18.4012	−0.918911	−0.459455	+	0.888201i	$0.651955\pi$
$402$	0.198888	0.00991965
$403$	46.3014	2.30644
$404$	20.7833	1.03401
$405$	8.47335	0.421044
$406$	1.26176	0.0626199
$407$	5.40627	0.267979
$408$	0.424068	0.0209945
$409$	32.4274	1.60343	0.801715	−	0.597706i	$-0.203921\pi$
$409$	32.4274	1.60343	0.801715	+	0.597706i	$0.203921\pi$
$410$	−0.922765	−0.0455721
$411$	−0.876097	−0.0432147
$412$	31.9616	1.57463
$413$	−13.0433	−0.641818
$414$	0.678895	0.0333659
$415$	10.3551	0.508314
$416$	−10.2909	−0.504552
$417$	0.237089	0.0116103
$418$	0.368553	0.0180265
$419$	−36.7834	−1.79699	−0.898493	−	0.438987i	$-0.855337\pi$
$419$	−36.7834	−1.79699	−0.898493	+	0.438987i	$0.855337\pi$
$420$	1.23540	0.0602814
$421$	28.9213	1.40954	0.704770	−	0.709436i	$-0.251050\pi$
$421$	28.9213	1.40954	0.704770	+	0.709436i	$0.251050\pi$
$422$	1.94313	0.0945902
$423$	4.59145	0.223244
$424$	8.04024	0.390469
$425$	2.87905	0.139654
$426$	−0.347657	−0.0168441
$427$	13.6898	0.662497
$428$	2.20265	0.106469
$429$	1.38520	0.0668780
$430$	0.900576	0.0434296
$431$	12.0964	0.582665	0.291332	−	0.956622i	$-0.405901\pi$
$431$	12.0964	0.582665	0.291332	+	0.956622i	$0.405901\pi$
$432$	5.56682	0.267834
$433$	6.55373	0.314952	0.157476	−	0.987523i	$-0.449664\pi$
$433$	6.55373	0.314952	0.157476	+	0.987523i	$0.449664\pi$
$434$	−3.18821	−0.153039
$435$	−0.779179	−0.0373588
$436$	−20.0807	−0.961691
$437$	−3.65253	−0.174724
$438$	0.0370393	0.00176981
$439$	9.99982	0.477265	0.238633	−	0.971110i	$-0.423301\pi$
$439$	9.99982	0.477265	0.238633	+	0.971110i	$0.423301\pi$
$440$	−0.606909	−0.0289332
$441$	1.08416	0.0516264
$442$	−2.50782	−0.119285
$443$	−12.1819	−0.578781	−0.289390	−	0.957211i	$-0.593453\pi$
$443$	−12.1819	−0.578781	−0.289390	+	0.957211i	$0.593453\pi$
$444$	2.59360	0.123087
$445$	3.09220	0.146584
$446$	−0.488843	−0.0231474
$447$	−1.13032	−0.0534622
$448$	−19.1756	−0.905962
$449$	6.97850	0.329336	0.164668	−	0.986349i	$-0.447345\pi$
$449$	6.97850	0.329336	0.164668	+	0.986349i	$0.447345\pi$
$450$	−0.448858	−0.0211594
$451$	−6.04633	−0.284711
$452$	2.51257	0.118181
$453$	4.34573	0.204180
$454$	−4.10508	−0.192661
$455$	−14.6977	−0.689040
$456$	0.355703	0.0166573
$457$	25.6666	1.20063	0.600316	−	0.799763i	$-0.295042\pi$
$457$	25.6666	1.20063	0.600316	+	0.799763i	$0.295042\pi$
$458$	−4.33471	−0.202548
$459$	4.15125	0.193764
$460$	2.98976	0.139398
$461$	16.7102	0.778272	0.389136	−	0.921180i	$-0.372774\pi$
$461$	16.7102	0.778272	0.389136	+	0.921180i	$0.372774\pi$
$462$	−0.0953817	−0.00443756
$463$	33.1014	1.53835	0.769176	−	0.639037i	$-0.220667\pi$
$463$	33.1014	1.53835	0.769176	+	0.639037i	$0.220667\pi$
$464$	12.3951	0.575428
$465$	1.96884	0.0913026
$466$	−1.24261	−0.0575627
$467$	29.5501	1.36741	0.683707	−	0.729757i	$-0.260367\pi$
$467$	29.5501	1.36741	0.683707	+	0.729757i	$0.260367\pi$
$468$	−33.1818	−1.53383
$469$	−13.8276	−0.638501
$470$	−0.238254	−0.0109898
$471$	−1.03350	−0.0476210
$472$	3.07403	0.141494
$473$	5.90093	0.271325
$474$	0.226769	0.0104158
$475$	2.41491	0.110804
$476$	−14.6553	−0.671722
$477$	38.9633	1.78401
$478$	3.77107	0.172485
$479$	17.2171	0.786670	0.393335	−	0.919395i	$-0.371321\pi$
$479$	17.2171	0.786670	0.393335	+	0.919395i	$0.371321\pi$
$480$	−0.437591	−0.0199732
$481$	−30.8564	−1.40693
$482$	3.70777	0.168884
$483$	0.945277	0.0430116
$484$	−1.97671	−0.0898504
$485$	−7.97109	−0.361949
$486$	−0.974011	−0.0441820
$487$	16.8275	0.762527	0.381263	−	0.924466i	$-0.375489\pi$
$487$	16.8275	0.762527	0.381263	+	0.924466i	$0.375489\pi$
$488$	−3.22641	−0.146053
$489$	5.12383	0.231708
$490$	−0.0562576	−0.00254146
$491$	27.7071	1.25040	0.625202	−	0.780463i	$-0.285016\pi$
$491$	27.7071	1.25040	0.625202	+	0.780463i	$0.285016\pi$
$492$	−2.90067	−0.130772
$493$	9.24320	0.416293
$494$	−2.10353	−0.0946422
$495$	−2.94110	−0.132193
$496$	−31.3201	−1.40631
$497$	24.1707	1.08421
$498$	−0.383548	−0.0171872
$499$	−13.1864	−0.590305	−0.295153	−	0.955450i	$-0.595370\pi$
$499$	−13.1864	−0.590305	−0.295153	+	0.955450i	$0.595370\pi$
$500$	−1.97671	−0.0884011
$501$	−2.62281	−0.117179
$502$	−3.72756	−0.166369
$503$	9.79276	0.436638	0.218319	−	0.975878i	$-0.429943\pi$
$503$	9.79276	0.436638	0.218319	+	0.975878i	$0.429943\pi$
$504$	4.59658	0.204748
$505$	−10.5141	−0.467871
$506$	−0.230830	−0.0102617
$507$	−4.75101	−0.211000
$508$	41.9053	1.85925
$509$	4.34298	0.192499	0.0962496	−	0.995357i	$-0.469315\pi$
$509$	4.34298	0.192499	0.0962496	+	0.995357i	$0.469315\pi$
$510$	−0.106638	−0.00472201
$511$	−2.57515	−0.113918
$512$	11.6474	0.514749
$513$	3.48202	0.153735
$514$	−4.63816	−0.204580
$515$	−16.1691	−0.712495
$516$	2.83092	0.124624
$517$	−1.56113	−0.0686586
$518$	2.12471	0.0933542
$519$	3.74981	0.164598
$520$	3.46395	0.151904
$521$	−28.6305	−1.25432	−0.627162	−	0.778889i	$-0.715783\pi$
$521$	−28.6305	−1.25432	−0.627162	+	0.778889i	$0.715783\pi$
$522$	−1.44106	−0.0630736
$523$	−8.37479	−0.366204	−0.183102	−	0.983094i	$-0.558614\pi$
$523$	−8.37479	−0.366204	−0.183102	+	0.983094i	$0.558614\pi$
$524$	41.1700	1.79852
$525$	−0.624979	−0.0272763
$526$	−2.46572	−0.107511
$527$	−23.3558	−1.01739
$528$	−0.937002	−0.0407778
$529$	−20.7124	−0.900538
$530$	−2.02183	−0.0878228
$531$	14.8968	0.646468
$532$	−12.2926	−0.532953
$533$	34.5096	1.49478
$534$	−0.114533	−0.00495634
$535$	−1.11430	−0.0481755
$536$	3.25889	0.140762
$537$	2.63275	0.113611
$538$	−3.08212	−0.132880
$539$	−0.368623	−0.0158777
$540$	−2.85019	−0.122652
$541$	36.1008	1.55209	0.776047	−	0.630675i	$-0.217222\pi$
$541$	36.1008	1.55209	0.776047	+	0.630675i	$0.217222\pi$
$542$	−0.704798	−0.0302737
$543$	6.34027	0.272087
$544$	5.19102	0.222563
$545$	10.1587	0.435149
$546$	0.544394	0.0232979
$547$	−11.9713	−0.511855	−0.255927	−	0.966696i	$-0.582381\pi$
$547$	−11.9713	−0.511855	−0.255927	+	0.966696i	$0.582381\pi$
$548$	−7.13561	−0.304818
$549$	−15.6353	−0.667297
$550$	0.152616	0.00650756
$551$	7.75308	0.330292
$552$	−0.222782	−0.00948224
$553$	−15.7660	−0.670440
$554$	−3.26564	−0.138744
$555$	−1.31208	−0.0556948
$556$	1.93103	0.0818940
$557$	33.4237	1.41621	0.708105	−	0.706107i	$-0.249550\pi$
$557$	33.4237	1.41621	0.708105	+	0.706107i	$0.249550\pi$
$558$	3.64129	0.154148
$559$	−33.6798	−1.42450
$560$	9.94211	0.420131
$561$	−0.698735	−0.0295006
$562$	−2.90979	−0.122742
$563$	33.8827	1.42798	0.713992	−	0.700154i	$-0.246885\pi$
$563$	33.8827	1.42798	0.713992	+	0.700154i	$0.246885\pi$
$564$	−0.748939	−0.0315360
$565$	−1.27109	−0.0534751
$566$	1.34640	0.0565936
$567$	21.8201	0.916359
$568$	−5.69654	−0.239022
$569$	2.14970	0.0901201	0.0450600	−	0.998984i	$-0.485652\pi$
$569$	2.14970	0.0901201	0.0450600	+	0.998984i	$0.485652\pi$
$570$	−0.0894466	−0.00374650
$571$	−23.1217	−0.967612	−0.483806	−	0.875175i	$-0.660746\pi$
$571$	−23.1217	−0.967612	−0.483806	+	0.875175i	$0.660746\pi$
$572$	11.2821	0.471729
$573$	−6.42075	−0.268231
$574$	−2.37626	−0.0991830
$575$	−1.51249	−0.0630753
$576$	21.9006	0.912527
$577$	−23.7533	−0.988864	−0.494432	−	0.869216i	$-0.664624\pi$
$577$	−23.7533	−0.988864	−0.494432	+	0.869216i	$0.664624\pi$
$578$	−1.32945	−0.0552978
$579$	−5.02840	−0.208973
$580$	−6.34624	−0.263513
$581$	26.6660	1.10629
$582$	0.295244	0.0122383
$583$	−13.2479	−0.548670
$584$	0.606909	0.0251141
$585$	16.7864	0.694033
$586$	0.170035	0.00702408
$587$	36.1713	1.49295	0.746475	−	0.665414i	$-0.231745\pi$
$587$	36.1713	1.49295	0.746475	+	0.665414i	$0.231745\pi$
$588$	−0.176843	−0.00729289
$589$	−19.5905	−0.807214
$590$	−0.773009	−0.0318243
$591$	−3.10641	−0.127781
$592$	20.8725	0.857853
$593$	6.85953	0.281687	0.140844	−	0.990032i	$-0.455019\pi$
$593$	6.85953	0.281687	0.140844	+	0.990032i	$0.455019\pi$
$594$	0.220054	0.00902894
$595$	7.41397	0.303943
$596$	−9.20618	−0.377100
$597$	−2.90085	−0.118724
$598$	1.31747	0.0538754
$599$	−23.4725	−0.959062	−0.479531	−	0.877525i	$-0.659193\pi$
$599$	−23.4725	−0.959062	−0.479531	+	0.877525i	$0.659193\pi$
$600$	0.147295	0.00601328
$601$	−6.62505	−0.270241	−0.135121	−	0.990829i	$-0.543142\pi$
$601$	−6.62505	−0.270241	−0.135121	+	0.990829i	$0.543142\pi$
$602$	2.31911	0.0945200
$603$	15.7927	0.643127
$604$	35.3949	1.44020
$605$	1.00000	0.0406558
$606$	0.389435	0.0158197
$607$	9.06374	0.367886	0.183943	−	0.982937i	$-0.441114\pi$
$607$	9.06374	0.367886	0.183943	+	0.982937i	$0.441114\pi$
$608$	4.35416	0.176585
$609$	−2.00650	−0.0813075
$610$	0.811326	0.0328496
$611$	8.91022	0.360469
$612$	16.7379	0.676589
$613$	−16.5665	−0.669116	−0.334558	−	0.942375i	$-0.608587\pi$
$613$	−16.5665	−0.669116	−0.334558	+	0.942375i	$0.608587\pi$
$614$	−3.34775	−0.135104
$615$	1.46742	0.0591722
$616$	−1.56288	−0.0629702
$617$	−1.42775	−0.0574789	−0.0287394	−	0.999587i	$-0.509149\pi$
$617$	−1.42775	−0.0574789	−0.0287394	+	0.999587i	$0.509149\pi$
$618$	0.598892	0.0240910
$619$	35.9658	1.44559	0.722793	−	0.691064i	$-0.242858\pi$
$619$	35.9658	1.44559	0.722793	+	0.691064i	$0.242858\pi$
$620$	16.0357	0.644010
$621$	−2.18084	−0.0875141
$622$	4.94833	0.198410
$623$	7.96287	0.319026
$624$	5.34797	0.214090
$625$	1.00000	0.0400000
$626$	−0.213936	−0.00855060
$627$	−0.586090	−0.0234062
$628$	−8.41760	−0.335899
$629$	15.5649	0.620613
$630$	−1.15588	−0.0460512
$631$	0.127015	0.00505637	0.00252819	−	0.999997i	$-0.499195\pi$
$631$	0.127015	0.00505637	0.00252819	+	0.999997i	$0.499195\pi$
$632$	3.71573	0.147804
$633$	−3.09006	−0.122819
$634$	3.23887	0.128632
$635$	−21.1996	−0.841279
$636$	−6.35554	−0.252013
$637$	2.10392	0.0833605
$638$	0.489974	0.0193983
$639$	−27.6056	−1.09206
$640$	−4.74251	−0.187464
$641$	−26.4189	−1.04349	−0.521743	−	0.853103i	$-0.674718\pi$
$641$	−26.4189	−1.04349	−0.521743	+	0.853103i	$0.674718\pi$
$642$	0.0412731	0.00162892
$643$	23.2232	0.915833	0.457917	−	0.888995i	$-0.348596\pi$
$643$	23.2232	0.915833	0.457917	+	0.888995i	$0.348596\pi$
$644$	7.69906	0.303386
$645$	−1.43214	−0.0563903
$646$	1.06108	0.0417477
$647$	35.2623	1.38630	0.693152	−	0.720791i	$-0.256221\pi$
$647$	35.2623	1.38630	0.693152	+	0.720791i	$0.256221\pi$
$648$	−5.14255	−0.202019
$649$	−5.06506	−0.198821
$650$	−0.871060	−0.0341658
$651$	5.07004	0.198711
$652$	41.7324	1.63437
$653$	13.7781	0.539179	0.269590	−	0.962975i	$-0.413112\pi$
$653$	13.7781	0.539179	0.269590	+	0.962975i	$0.413112\pi$
$654$	−0.376270	−0.0147133
$655$	−20.8276	−0.813800
$656$	−23.3436	−0.911415
$657$	2.94110	0.114743
$658$	−0.613538	−0.0239182
$659$	−14.2777	−0.556182	−0.278091	−	0.960555i	$-0.589702\pi$
$659$	−14.2777	−0.556182	−0.278091	+	0.960555i	$0.589702\pi$
$660$	0.479741	0.0186739
$661$	−6.35944	−0.247354	−0.123677	−	0.992323i	$-0.539469\pi$
$661$	−6.35944	−0.247354	−0.123677	+	0.992323i	$0.539469\pi$
$662$	−2.74698	−0.106764
$663$	3.98805	0.154883
$664$	−6.28463	−0.243891
$665$	6.21874	0.241152
$666$	−2.42665	−0.0940306
$667$	−4.85587	−0.188020
$668$	−21.3622	−0.826529
$669$	0.777381	0.0300553
$670$	−0.819494	−0.0316598
$671$	5.31613	0.205227
$672$	−1.12686	−0.0434696
$673$	29.6901	1.14447	0.572234	−	0.820091i	$-0.306077\pi$
$673$	29.6901	1.14447	0.572234	+	0.820091i	$0.306077\pi$
$674$	3.72136	0.143342
$675$	1.44188	0.0554982
$676$	−38.6959	−1.48830
$677$	−44.2181	−1.69944	−0.849720	−	0.527234i	$-0.823229\pi$
$677$	−44.2181	−1.69944	−0.849720	+	0.527234i	$0.823229\pi$
$678$	0.0470803	0.00180811
$679$	−20.5267	−0.787744
$680$	−1.74732	−0.0670066
$681$	6.52809	0.250157
$682$	−1.23807	−0.0474082
$683$	23.7144	0.907406	0.453703	−	0.891153i	$-0.350103\pi$
$683$	23.7144	0.907406	0.453703	+	0.891153i	$0.350103\pi$
$684$	14.0395	0.536815
$685$	3.60984	0.137925
$686$	−2.89593	−0.110567
$687$	6.89326	0.262994
$688$	22.7823	0.868566
$689$	75.6126	2.88061
$690$	0.0560218	0.00213271
$691$	14.4117	0.548247	0.274123	−	0.961695i	$-0.411612\pi$
$691$	14.4117	0.548247	0.274123	+	0.961695i	$0.411612\pi$
$692$	30.5413	1.16101
$693$	−7.57376	−0.287703
$694$	−1.30463	−0.0495231
$695$	−0.976892	−0.0370556
$696$	0.472891	0.0179249
$697$	−17.4077	−0.659362
$698$	−5.18776	−0.196360
$699$	1.97605	0.0747411
$700$	−5.09031	−0.192396
$701$	29.6923	1.12146	0.560731	−	0.827998i	$-0.310520\pi$
$701$	29.6923	1.12146	0.560731	+	0.827998i	$0.310520\pi$
$702$	−1.25597	−0.0474034
$703$	13.0556	0.492402
$704$	−7.44641	−0.280647
$705$	0.378882	0.0142695
$706$	−2.93675	−0.110526
$707$	−27.0753	−1.01827
$708$	−2.42992	−0.0913218
$709$	25.0779	0.941819	0.470909	−	0.882182i	$-0.343926\pi$
$709$	25.0779	0.941819	0.470909	+	0.882182i	$0.343926\pi$
$710$	1.43248	0.0537599
$711$	18.0065	0.675298
$712$	−1.87668	−0.0703317
$713$	12.2699	0.459510
$714$	−0.274609	−0.0102770
$715$	−5.70753	−0.213450
$716$	21.4431	0.801367
$717$	−5.99693	−0.223960
$718$	−2.71397	−0.101284
$719$	41.2754	1.53931	0.769656	−	0.638459i	$-0.220428\pi$
$719$	41.2754	1.53931	0.769656	+	0.638459i	$0.220428\pi$
$720$	−11.3550	−0.423175
$721$	−41.6377	−1.55067
$722$	−2.00968	−0.0747925
$723$	−5.89626	−0.219284
$724$	51.6400	1.91919
$725$	3.21051	0.119235
$726$	−0.0370393	−0.00137466
$727$	12.1076	0.449046	0.224523	−	0.974469i	$-0.427918\pi$
$727$	12.1076	0.449046	0.224523	+	0.974469i	$0.427918\pi$
$728$	8.92018	0.330604
$729$	−23.8711	−0.884117
$730$	−0.152616	−0.00564856
$731$	16.9891	0.628363
$732$	2.55036	0.0942642
$733$	1.15567	0.0426856	0.0213428	−	0.999772i	$-0.493206\pi$
$733$	1.15567	0.0426856	0.0213428	+	0.999772i	$0.493206\pi$
$734$	−5.54445	−0.204650
$735$	0.0894634	0.00329991
$736$	−2.72708	−0.100521
$737$	−5.36965	−0.197794
$738$	2.71394	0.0999017
$739$	−0.481270	−0.0177038	−0.00885189	−	0.999961i	$-0.502818\pi$
$739$	−0.481270	−0.0177038	−0.00885189	+	0.999961i	$0.502818\pi$
$740$	−10.6866	−0.392848
$741$	3.34513	0.122886
$742$	−5.20652	−0.191137
$743$	11.6416	0.427089	0.213544	−	0.976933i	$-0.431499\pi$
$743$	11.6416	0.427089	0.213544	+	0.976933i	$0.431499\pi$
$744$	−1.19490	−0.0438073
$745$	4.65733	0.170631
$746$	4.63068	0.169541
$747$	−30.4555	−1.11431
$748$	−5.69104	−0.208085
$749$	−2.86949	−0.104849
$750$	−0.0370393	−0.00135249
$751$	−28.6183	−1.04430	−0.522148	−	0.852855i	$-0.674869\pi$
$751$	−28.6183	−1.04430	−0.522148	+	0.852855i	$0.674869\pi$
$752$	−6.02721	−0.219790
$753$	5.92773	0.216019
$754$	−2.79654	−0.101844
$755$	−17.9060	−0.651666
$756$	−7.33964	−0.266940
$757$	15.1907	0.552115	0.276058	−	0.961141i	$-0.410972\pi$
$757$	15.1907	0.552115	0.276058	+	0.961141i	$0.410972\pi$
$758$	−4.12631	−0.149874
$759$	0.367077	0.0133241
$760$	−1.46563	−0.0531639
$761$	−54.5541	−1.97759	−0.988793	−	0.149296i	$-0.952299\pi$
$761$	−54.5541	−1.97759	−0.988793	+	0.149296i	$0.952299\pi$
$762$	0.785217	0.0284454
$763$	26.1600	0.947056
$764$	−52.2956	−1.89199
$765$	−8.46756	−0.306145
$766$	0.974519	0.0352108
$767$	28.9090	1.04384
$768$	−3.43878	−0.124086
$769$	21.4428	0.773248	0.386624	−	0.922237i	$-0.373641\pi$
$769$	21.4428	0.773248	0.386624	+	0.922237i	$0.373641\pi$
$770$	0.393008	0.0141630
$771$	7.37581	0.265633
$772$	−40.9552	−1.47401
$773$	7.07653	0.254525	0.127263	−	0.991869i	$-0.459381\pi$
$773$	7.07653	0.254525	0.127263	+	0.991869i	$0.459381\pi$
$774$	−2.64868	−0.0952049
$775$	−8.11234	−0.291404
$776$	4.83773	0.173664
$777$	−3.37880	−0.121214
$778$	0.409480	0.0146806
$779$	−14.6013	−0.523147
$780$	−2.73813	−0.0980409
$781$	9.38616	0.335863
$782$	−0.664572	−0.0237650
$783$	4.62918	0.165433
$784$	−1.42318	−0.0508277
$785$	4.25839	0.151988
$786$	0.771440	0.0275163
$787$	−3.56317	−0.127013	−0.0635067	−	0.997981i	$-0.520228\pi$
$787$	−3.56317	−0.127013	−0.0635067	+	0.997981i	$0.520228\pi$
$788$	−25.3010	−0.901311
$789$	3.92110	0.139595
$790$	−0.934372	−0.0332435
$791$	−3.27324	−0.116383
$792$	1.78498	0.0634264
$793$	−30.3420	−1.07748
$794$	3.83500	0.136099
$795$	3.21521	0.114032
$796$	−23.6268	−0.837429
$797$	17.0747	0.604816	0.302408	−	0.953179i	$-0.402209\pi$
$797$	17.0747	0.604816	0.302408	+	0.953179i	$0.402209\pi$
$798$	−0.230338	−0.00815388
$799$	−4.49458	−0.159007
$800$	1.80304	0.0637469
$801$	−9.09447	−0.321337
$802$	−2.80831	−0.0991648
$803$	−1.00000	−0.0352892
$804$	−2.57604	−0.0908499
$805$	−3.89489	−0.137277
$806$	7.06633	0.248901
$807$	4.90133	0.172535
$808$	6.38109	0.224486
$809$	−12.2786	−0.431691	−0.215845	−	0.976428i	$-0.569251\pi$
$809$	−12.2786	−0.431691	−0.215845	+	0.976428i	$0.569251\pi$
$810$	1.29317	0.0454373
$811$	−34.0249	−1.19478	−0.597388	−	0.801952i	$-0.703795\pi$
$811$	−34.0249	−1.19478	−0.597388	+	0.801952i	$0.703795\pi$
$812$	−16.3425	−0.573509
$813$	1.12080	0.0393083
$814$	0.825082	0.0289191
$815$	−21.1121	−0.739524
$816$	−2.69767	−0.0944374
$817$	14.2502	0.498552
$818$	4.94893	0.173035
$819$	43.2275	1.51049
$820$	11.9518	0.417376
$821$	−2.25573	−0.0787254	−0.0393627	−	0.999225i	$-0.512533\pi$
$821$	−2.25573	−0.0787254	−0.0393627	+	0.999225i	$0.512533\pi$
$822$	−0.133706	−0.00466354
$823$	32.6411	1.13780	0.568898	−	0.822408i	$-0.307370\pi$
$823$	32.6411	1.13780	0.568898	+	0.822408i	$0.307370\pi$
$824$	9.81315	0.341857
$825$	−0.242697	−0.00844961
$826$	−1.99061	−0.0692622
$827$	31.4297	1.09292	0.546459	−	0.837486i	$-0.315976\pi$
$827$	31.4297	1.09292	0.546459	+	0.837486i	$0.315976\pi$
$828$	−8.79317	−0.305584
$829$	−34.0674	−1.18321	−0.591606	−	0.806227i	$-0.701506\pi$
$829$	−34.0674	−1.18321	−0.591606	+	0.806227i	$0.701506\pi$
$830$	1.58036	0.0548551
$831$	5.19318	0.180149
$832$	42.5006	1.47344
$833$	−1.06128	−0.0367712
$834$	0.0361835	0.00125293
$835$	10.8070	0.373990
$836$	−4.77357	−0.165097
$837$	−11.6971	−0.404309
$838$	−5.61373	−0.193923
$839$	16.5819	0.572472	0.286236	−	0.958159i	$-0.407596\pi$
$839$	16.5819	0.572472	0.286236	+	0.958159i	$0.407596\pi$
$840$	0.379305	0.0130873
$841$	−18.6926	−0.644574
$842$	4.41385	0.152111
$843$	4.62727	0.159372
$844$	−25.1678	−0.866312
$845$	19.5759	0.673432
$846$	0.700728	0.0240915
$847$	2.57515	0.0884831
$848$	−51.1472	−1.75640
$849$	−2.14111	−0.0734829
$850$	0.439388	0.0150709
$851$	−8.17694	−0.280302
$852$	4.50292	0.154268
$853$	19.0594	0.652582	0.326291	−	0.945269i	$-0.394201\pi$
$853$	19.0594	0.652582	0.326291	+	0.945269i	$0.394201\pi$
$854$	2.08928	0.0714938
$855$	−7.10248	−0.242900
$856$	0.676280	0.0231148
$857$	36.7950	1.25689	0.628446	−	0.777853i	$-0.283691\pi$
$857$	36.7950	1.25689	0.628446	+	0.777853i	$0.283691\pi$
$858$	0.211403	0.00721719
$859$	24.4012	0.832557	0.416278	−	0.909237i	$-0.363334\pi$
$859$	24.4012	0.832557	0.416278	+	0.909237i	$0.363334\pi$
$860$	−11.6644	−0.397754
$861$	3.77883	0.128782
$862$	1.84611	0.0628786
$863$	−41.3178	−1.40647	−0.703237	−	0.710955i	$-0.748263\pi$
$863$	−41.3178	−1.40647	−0.703237	+	0.710955i	$0.748263\pi$
$864$	2.59977	0.0884459
$865$	−15.4506	−0.525336
$866$	1.00020	0.0339883
$867$	2.11415	0.0718003
$868$	41.2943	1.40162
$869$	−6.12238	−0.207688
$870$	−0.118915	−0.00403160
$871$	30.6475	1.03845
$872$	−6.16537	−0.208786
$873$	23.4438	0.793451
$874$	−0.557434	−0.0188555
$875$	2.57515	0.0870558
$876$	−0.479741	−0.0162089
$877$	12.6114	0.425857	0.212928	−	0.977068i	$-0.431700\pi$
$877$	12.6114	0.425857	0.212928	+	0.977068i	$0.431700\pi$
$878$	1.52613	0.0515044
$879$	−0.270397	−0.00912027
$880$	3.86079	0.130147
$881$	0.487933	0.0164389	0.00821944	−	0.999966i	$-0.497384\pi$
$881$	0.487933	0.0164389	0.00821944	+	0.999966i	$0.497384\pi$
$882$	0.165459	0.00557130
$883$	46.0458	1.54957	0.774783	−	0.632228i	$-0.217859\pi$
$883$	46.0458	1.54957	0.774783	+	0.632228i	$0.217859\pi$
$884$	32.4818	1.09248
$885$	1.22927	0.0413216
$886$	−1.85915	−0.0624595
$887$	24.2846	0.815397	0.407698	−	0.913117i	$-0.366331\pi$
$887$	24.2846	0.815397	0.407698	+	0.913117i	$0.366331\pi$
$888$	0.796314	0.0267226
$889$	−54.5919	−1.83095
$890$	0.471919	0.0158188
$891$	8.47335	0.283868
$892$	6.33159	0.211997
$893$	−3.76999	−0.126158
$894$	−0.172504	−0.00576941
$895$	−10.8479	−0.362605
$896$	−12.2127	−0.407996
$897$	−2.09510	−0.0699535
$898$	1.06503	0.0355405
$899$	−26.0447	−0.868640
$900$	5.81369	0.193790
$901$	−38.1412	−1.27067
$902$	−0.922765	−0.0307247
$903$	−3.68796	−0.122728
$904$	0.771434	0.0256575
$905$	−26.1243	−0.868400
$906$	0.663227	0.0220342
$907$	46.0733	1.52984	0.764920	−	0.644126i	$-0.222779\pi$
$907$	46.0733	1.52984	0.764920	+	0.644126i	$0.222779\pi$
$908$	53.1698	1.76450
$909$	30.9230	1.02565
$910$	−2.24311	−0.0743582
$911$	−5.93708	−0.196704	−0.0983522	−	0.995152i	$-0.531357\pi$
$911$	−5.93708	−0.196704	−0.0983522	+	0.995152i	$0.531357\pi$
$912$	−2.26277	−0.0749279
$913$	10.3551	0.342705
$914$	3.91712	0.129567
$915$	−1.29021	−0.0426529
$916$	56.1440	1.85505
$917$	−53.6340	−1.77115
$918$	0.633547	0.0209102
$919$	−50.9198	−1.67969	−0.839845	−	0.542827i	$-0.817354\pi$
$919$	−50.9198	−1.67969	−0.839845	+	0.542827i	$0.817354\pi$
$920$	0.917945	0.0302638
$921$	5.32375	0.175423
$922$	2.55024	0.0839878
$923$	−53.5718	−1.76334
$924$	1.23540	0.0406417
$925$	5.40627	0.177757
$926$	5.05180	0.166012
$927$	47.5549	1.56191
$928$	5.78866	0.190022
$929$	−20.2466	−0.664268	−0.332134	−	0.943232i	$-0.607769\pi$
$929$	−20.2466	−0.664268	−0.332134	+	0.943232i	$0.607769\pi$
$930$	0.300476	0.00985298
$931$	−0.890189	−0.0291748
$932$	16.0945	0.527192
$933$	−7.86906	−0.257622
$934$	4.50981	0.147565
$935$	2.87905	0.0941549
$936$	−10.1878	−0.332999
$937$	57.0438	1.86354	0.931769	−	0.363051i	$-0.118265\pi$
$937$	57.0438	1.86354	0.931769	+	0.363051i	$0.118265\pi$
$938$	−2.11032	−0.0689042
$939$	0.340211	0.0111024
$940$	3.08591	0.100651
$941$	−37.6145	−1.22620	−0.613099	−	0.790006i	$-0.710077\pi$
$941$	−37.6145	−1.22620	−0.613099	+	0.790006i	$0.710077\pi$
$942$	−0.157728	−0.00513906
$943$	9.14503	0.297803
$944$	−19.5552	−0.636466
$945$	3.71306	0.120786
$946$	0.900576	0.0292802
$947$	28.1399	0.914423	0.457212	−	0.889358i	$-0.348848\pi$
$947$	28.1399	0.914423	0.457212	+	0.889358i	$0.348848\pi$
$948$	−2.93716	−0.0953944
$949$	5.70753	0.185274
$950$	0.368553	0.0119574
$951$	−5.15060	−0.167020
$952$	−4.49960	−0.145833
$953$	−46.6049	−1.50968	−0.754841	−	0.655908i	$-0.772286\pi$
$953$	−46.6049	−1.50968	−0.754841	+	0.655908i	$0.772286\pi$
$954$	5.94641	0.192522
$955$	26.4559	0.856092
$956$	−48.8437	−1.57972
$957$	−0.779179	−0.0251873
$958$	2.62760	0.0848940
$959$	9.29587	0.300179
$960$	1.80722	0.0583278
$961$	34.8100	1.12290
$962$	−4.70918	−0.151830
$963$	3.27727	0.105609
$964$	−48.0237	−1.54674
$965$	20.7189	0.666965
$966$	0.144264	0.00464162
$967$	−11.1299	−0.357913	−0.178957	−	0.983857i	$-0.557272\pi$
$967$	−11.1299	−0.357913	−0.178957	+	0.983857i	$0.557272\pi$
$968$	−0.606909	−0.0195068
$969$	−1.68738	−0.0542065
$970$	−1.21651	−0.0390599
$971$	−0.296008	−0.00949936	−0.00474968	−	0.999989i	$-0.501512\pi$
$971$	−0.296008	−0.00949936	−0.00474968	+	0.999989i	$0.501512\pi$
$972$	12.6156	0.404645
$973$	−2.51564	−0.0806477
$974$	2.56814	0.0822886
$975$	1.38520	0.0443619
$976$	20.5245	0.656973
$977$	13.1681	0.421285	0.210643	−	0.977563i	$-0.432444\pi$
$977$	13.1681	0.421285	0.210643	+	0.977563i	$0.432444\pi$
$978$	0.781978	0.0250049
$979$	3.09220	0.0988272
$980$	0.728659	0.0232762
$981$	−29.8776	−0.953918
$982$	4.22854	0.134938
$983$	−50.8860	−1.62301	−0.811505	−	0.584345i	$-0.801352\pi$
$983$	−50.8860	−1.62301	−0.811505	+	0.584345i	$0.801352\pi$
$984$	−0.890592	−0.0283910
$985$	12.7996	0.407828
$986$	1.41066	0.0449245
$987$	0.975676	0.0310561
$988$	27.2453	0.866788
$989$	−8.92512	−0.283802
$990$	−0.448858	−0.0142656
$991$	36.1290	1.14768	0.573838	−	0.818969i	$-0.305454\pi$
$991$	36.1290	1.14768	0.573838	+	0.818969i	$0.305454\pi$
$992$	−14.6268	−0.464402
$993$	4.36838	0.138626
$994$	3.68884	0.117003
$995$	11.9526	0.378923
$996$	4.96778	0.157410
$997$	−8.05846	−0.255214	−0.127607	−	0.991825i	$-0.540730\pi$
$997$	−8.05846	−0.255214	−0.127607	+	0.991825i	$0.540730\pi$
$998$	−2.01246	−0.0637032
$999$	7.79521	0.246630

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.b.1.13	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.b.1.13	✓	23	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:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q+0.152616 q^{2} -0.242697 q^{3} -1.97671 q^{4} +1.00000 q^{5} -0.0370393 q^{6} +2.57515 q^{7} -0.606909 q^{8} -2.94110 q^{9} +O(q^{10})\)	\(q+0.152616 q^{2} -0.242697 q^{3} -1.97671 q^{4} +1.00000 q^{5} -0.0370393 q^{6} +2.57515 q^{7} -0.606909 q^{8} -2.94110 q^{9} +0.152616 q^{10} +1.00000 q^{11} +0.479741 q^{12} -5.70753 q^{13} +0.393008 q^{14} -0.242697 q^{15} +3.86079 q^{16} +2.87905 q^{17} -0.448858 q^{18} +2.41491 q^{19} -1.97671 q^{20} -0.624979 q^{21} +0.152616 q^{22} -1.51249 q^{23} +0.147295 q^{24} +1.00000 q^{25} -0.871060 q^{26} +1.44188 q^{27} -5.09031 q^{28} +3.21051 q^{29} -0.0370393 q^{30} -8.11234 q^{31} +1.80304 q^{32} -0.242697 q^{33} +0.439388 q^{34} +2.57515 q^{35} +5.81369 q^{36} +5.40627 q^{37} +0.368553 q^{38} +1.38520 q^{39} -0.606909 q^{40} -6.04633 q^{41} -0.0953817 q^{42} +5.90093 q^{43} -1.97671 q^{44} -2.94110 q^{45} -0.230830 q^{46} -1.56113 q^{47} -0.937002 q^{48} -0.368623 q^{49} +0.152616 q^{50} -0.698735 q^{51} +11.2821 q^{52} -13.2479 q^{53} +0.220054 q^{54} +1.00000 q^{55} -1.56288 q^{56} -0.586090 q^{57} +0.489974 q^{58} -5.06506 q^{59} +0.479741 q^{60} +5.31613 q^{61} -1.23807 q^{62} -7.57376 q^{63} -7.44641 q^{64} -5.70753 q^{65} -0.0370393 q^{66} -5.36965 q^{67} -5.69104 q^{68} +0.367077 q^{69} +0.393008 q^{70} +9.38616 q^{71} +1.78498 q^{72} -1.00000 q^{73} +0.825082 q^{74} -0.242697 q^{75} -4.77357 q^{76} +2.57515 q^{77} +0.211403 q^{78} -6.12238 q^{79} +3.86079 q^{80} +8.47335 q^{81} -0.922765 q^{82} +10.3551 q^{83} +1.23540 q^{84} +2.87905 q^{85} +0.900576 q^{86} -0.779179 q^{87} -0.606909 q^{88} +3.09220 q^{89} -0.448858 q^{90} -14.6977 q^{91} +2.98976 q^{92} +1.96884 q^{93} -0.238254 q^{94} +2.41491 q^{95} -0.437591 q^{96} -7.97109 q^{97} -0.0562576 q^{98} -2.94110 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 5 q^{2} - 3 q^{3} + 15 q^{4} + 23 q^{5} - 15 q^{6} - 10 q^{7} - 12 q^{8} + 8 q^{9}+O(q^{10}) \) 23 * q - 5 * q^2 - 3 * q^3 + 15 * q^4 + 23 * q^5 - 15 * q^6 - 10 * q^7 - 12 * q^8 + 8 * q^9	\( 23 q - 5 q^{2} - 3 q^{3} + 15 q^{4} + 23 q^{5} - 15 q^{6} - 10 q^{7} - 12 q^{8} + 8 q^{9} - 5 q^{10} + 23 q^{11} + 4 q^{12} - 19 q^{13} - 5 q^{14} - 3 q^{15} - q^{16} - 26 q^{17} + 5 q^{18} - 34 q^{19} + 15 q^{20} - 26 q^{21} - 5 q^{22} - 4 q^{23} - 23 q^{24} + 23 q^{25} - 13 q^{26} - 3 q^{27} - 28 q^{28} - 36 q^{29} - 15 q^{30} - 24 q^{31} - 19 q^{32} - 3 q^{33} - 4 q^{34} - 10 q^{35} - 14 q^{36} + 4 q^{37} - 15 q^{38} - 34 q^{39} - 12 q^{40} - 74 q^{41} + 7 q^{42} - 15 q^{43} + 15 q^{44} + 8 q^{45} + 3 q^{46} + q^{47} + 29 q^{48} + q^{49} - 5 q^{50} - 47 q^{51} - 23 q^{52} - 6 q^{53} - 11 q^{54} + 23 q^{55} - 20 q^{56} - 19 q^{57} + 22 q^{58} - 17 q^{59} + 4 q^{60} - 59 q^{61} + 38 q^{62} - 21 q^{63} - 18 q^{64} - 19 q^{65} - 15 q^{66} + 12 q^{67} + 5 q^{68} - 8 q^{69} - 5 q^{70} - 34 q^{71} + 21 q^{72} - 23 q^{73} - 9 q^{74} - 3 q^{75} - 53 q^{76} - 10 q^{77} + 23 q^{78} - 62 q^{79} - q^{80} + 7 q^{81} + 24 q^{82} - 8 q^{83} + 46 q^{84} - 26 q^{85} - 11 q^{86} + q^{87} - 12 q^{88} - 77 q^{89} + 5 q^{90} - 6 q^{91} + 47 q^{92} - 32 q^{94} - 34 q^{95} - 53 q^{96} - 21 q^{97} - 3 q^{98} + 8 q^{99}+O(q^{100}) \) 23 * q - 5 * q^2 - 3 * q^3 + 15 * q^4 + 23 * q^5 - 15 * q^6 - 10 * q^7 - 12 * q^8 + 8 * q^9 - 5 * q^10 + 23 * q^11 + 4 * q^12 - 19 * q^13 - 5 * q^14 - 3 * q^15 - q^16 - 26 * q^17 + 5 * q^18 - 34 * q^19 + 15 * q^20 - 26 * q^21 - 5 * q^22 - 4 * q^23 - 23 * q^24 + 23 * q^25 - 13 * q^26 - 3 * q^27 - 28 * q^28 - 36 * q^29 - 15 * q^30 - 24 * q^31 - 19 * q^32 - 3 * q^33 - 4 * q^34 - 10 * q^35 - 14 * q^36 + 4 * q^37 - 15 * q^38 - 34 * q^39 - 12 * q^40 - 74 * q^41 + 7 * q^42 - 15 * q^43 + 15 * q^44 + 8 * q^45 + 3 * q^46 + q^47 + 29 * q^48 + q^49 - 5 * q^50 - 47 * q^51 - 23 * q^52 - 6 * q^53 - 11 * q^54 + 23 * q^55 - 20 * q^56 - 19 * q^57 + 22 * q^58 - 17 * q^59 + 4 * q^60 - 59 * q^61 + 38 * q^62 - 21 * q^63 - 18 * q^64 - 19 * q^65 - 15 * q^66 + 12 * q^67 + 5 * q^68 - 8 * q^69 - 5 * q^70 - 34 * q^71 + 21 * q^72 - 23 * q^73 - 9 * q^74 - 3 * q^75 - 53 * q^76 - 10 * q^77 + 23 * q^78 - 62 * q^79 - q^80 + 7 * q^81 + 24 * q^82 - 8 * q^83 + 46 * q^84 - 26 * q^85 - 11 * q^86 + q^87 - 12 * q^88 - 77 * q^89 + 5 * q^90 - 6 * q^91 + 47 * q^92 - 32 * q^94 - 34 * q^95 - 53 * q^96 - 21 * q^97 - 3 * q^98 + 8 * q^99

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