LMFDB - Embedded newform 6035.2.a.b.1.8

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:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
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)

$f(q)$	$=$	$q-1.63901 q^{2} +0.960813 q^{3} +0.686340 q^{4} +1.00000 q^{5} -1.57478 q^{6} +4.58027 q^{7} +2.15310 q^{8} -2.07684 q^{9} +O(q^{10})$	\(q-1.63901 q^{2} +0.960813 q^{3} +0.686340 q^{4} +1.00000 q^{5} -1.57478 q^{6} +4.58027 q^{7} +2.15310 q^{8} -2.07684 q^{9} -1.63901 q^{10} -3.05406 q^{11} +0.659445 q^{12} -2.91179 q^{13} -7.50709 q^{14} +0.960813 q^{15} -4.90162 q^{16} -1.00000 q^{17} +3.40395 q^{18} -5.62146 q^{19} +0.686340 q^{20} +4.40078 q^{21} +5.00563 q^{22} +1.25559 q^{23} +2.06872 q^{24} +1.00000 q^{25} +4.77245 q^{26} -4.87789 q^{27} +3.14362 q^{28} -1.71287 q^{29} -1.57478 q^{30} +8.18309 q^{31} +3.72759 q^{32} -2.93438 q^{33} +1.63901 q^{34} +4.58027 q^{35} -1.42542 q^{36} +3.67710 q^{37} +9.21361 q^{38} -2.79769 q^{39} +2.15310 q^{40} +12.2395 q^{41} -7.21291 q^{42} -9.45683 q^{43} -2.09613 q^{44} -2.07684 q^{45} -2.05791 q^{46} -0.692469 q^{47} -4.70954 q^{48} +13.9789 q^{49} -1.63901 q^{50} -0.960813 q^{51} -1.99848 q^{52} -3.94316 q^{53} +7.99490 q^{54} -3.05406 q^{55} +9.86176 q^{56} -5.40118 q^{57} +2.80740 q^{58} -3.23094 q^{59} +0.659445 q^{60} -9.57732 q^{61} -13.4121 q^{62} -9.51248 q^{63} +3.69370 q^{64} -2.91179 q^{65} +4.80947 q^{66} +5.76886 q^{67} -0.686340 q^{68} +1.20638 q^{69} -7.50709 q^{70} +1.00000 q^{71} -4.47163 q^{72} -1.79423 q^{73} -6.02679 q^{74} +0.960813 q^{75} -3.85824 q^{76} -13.9884 q^{77} +4.58543 q^{78} +0.429420 q^{79} -4.90162 q^{80} +1.54377 q^{81} -20.0606 q^{82} +4.91701 q^{83} +3.02044 q^{84} -1.00000 q^{85} +15.4998 q^{86} -1.64575 q^{87} -6.57569 q^{88} -13.1193 q^{89} +3.40395 q^{90} -13.3368 q^{91} +0.861759 q^{92} +7.86242 q^{93} +1.13496 q^{94} -5.62146 q^{95} +3.58152 q^{96} -3.64082 q^{97} -22.9114 q^{98} +6.34279 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{2} - 4 q^{3} + 23 q^{4} + 36 q^{5} - 2 q^{6} - 7 q^{7} - 3 q^{8} + 10 q^{9}+O(q^{10}) $ 36 * q - q^2 - 4 * q^3 + 23 * q^4 + 36 * q^5 - 2 * q^6 - 7 * q^7 - 3 * q^8 + 10 * q^9	\( 36 q - q^{2} - 4 q^{3} + 23 q^{4} + 36 q^{5} - 2 q^{6} - 7 q^{7} - 3 q^{8} + 10 q^{9} - q^{10} - 22 q^{11} - 14 q^{12} - 15 q^{13} - 28 q^{14} - 4 q^{15} + q^{16} - 36 q^{17} - 12 q^{18} - 23 q^{19} + 23 q^{20} - 21 q^{21} + 2 q^{23} - 13 q^{24} + 36 q^{25} - 18 q^{26} - 13 q^{27} - 20 q^{28} - 4 q^{29} - 2 q^{30} - 43 q^{31} - 2 q^{32} - 19 q^{33} + q^{34} - 7 q^{35} - 35 q^{36} - 30 q^{37} - 11 q^{38} - 20 q^{39} - 3 q^{40} - 39 q^{41} + 2 q^{42} - 7 q^{43} - 45 q^{44} + 10 q^{45} - 52 q^{46} - 12 q^{47} - 12 q^{48} - 15 q^{49} - q^{50} + 4 q^{51} - 19 q^{52} - 31 q^{53} + 48 q^{54} - 22 q^{55} - 30 q^{56} + 18 q^{57} - 12 q^{58} - 66 q^{59} - 14 q^{60} - 93 q^{61} - 7 q^{62} - 22 q^{63} - 41 q^{64} - 15 q^{65} - 21 q^{66} - 19 q^{67} - 23 q^{68} - 73 q^{69} - 28 q^{70} + 36 q^{71} - q^{72} - 47 q^{73} - 27 q^{74} - 4 q^{75} - 56 q^{76} - 9 q^{77} - 78 q^{78} - 21 q^{79} + q^{80} - 40 q^{81} - 15 q^{82} - 8 q^{83} - 54 q^{84} - 36 q^{85} - 17 q^{86} - 32 q^{87} - 13 q^{88} - 62 q^{89} - 12 q^{90} - 33 q^{91} + 42 q^{92} - 24 q^{93} - 40 q^{94} - 23 q^{95} + 21 q^{96} - 60 q^{97} + 11 q^{98} - 65 q^{99}+O(q^{100}) \) 36 * q - q^2 - 4 * q^3 + 23 * q^4 + 36 * q^5 - 2 * q^6 - 7 * q^7 - 3 * q^8 + 10 * q^9 - q^10 - 22 * q^11 - 14 * q^12 - 15 * q^13 - 28 * q^14 - 4 * q^15 + q^16 - 36 * q^17 - 12 * q^18 - 23 * q^19 + 23 * q^20 - 21 * q^21 + 2 * q^23 - 13 * q^24 + 36 * q^25 - 18 * q^26 - 13 * q^27 - 20 * q^28 - 4 * q^29 - 2 * q^30 - 43 * q^31 - 2 * q^32 - 19 * q^33 + q^34 - 7 * q^35 - 35 * q^36 - 30 * q^37 - 11 * q^38 - 20 * q^39 - 3 * q^40 - 39 * q^41 + 2 * q^42 - 7 * q^43 - 45 * q^44 + 10 * q^45 - 52 * q^46 - 12 * q^47 - 12 * q^48 - 15 * q^49 - q^50 + 4 * q^51 - 19 * q^52 - 31 * q^53 + 48 * q^54 - 22 * q^55 - 30 * q^56 + 18 * q^57 - 12 * q^58 - 66 * q^59 - 14 * q^60 - 93 * q^61 - 7 * q^62 - 22 * q^63 - 41 * q^64 - 15 * q^65 - 21 * q^66 - 19 * q^67 - 23 * q^68 - 73 * q^69 - 28 * q^70 + 36 * q^71 - q^72 - 47 * q^73 - 27 * q^74 - 4 * q^75 - 56 * q^76 - 9 * q^77 - 78 * q^78 - 21 * q^79 + q^80 - 40 * q^81 - 15 * q^82 - 8 * q^83 - 54 * q^84 - 36 * q^85 - 17 * q^86 - 32 * q^87 - 13 * q^88 - 62 * q^89 - 12 * q^90 - 33 * q^91 + 42 * q^92 - 24 * q^93 - 40 * q^94 - 23 * q^95 + 21 * q^96 - 60 * q^97 + 11 * q^98 - 65 * 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 $

$2$	−1.63901	−1.15895	−0.579476	−	0.814989i	$-0.696743\pi$
$2$	−1.63901	−1.15895	−0.579476	+	0.814989i	$0.696743\pi$
$3$	0.960813	0.554726	0.277363	−	0.960765i	$-0.410540\pi$
$3$	0.960813	0.554726	0.277363	+	0.960765i	$0.410540\pi$
$4$	0.686340	0.343170
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.57478	−0.642901
$7$	4.58027	1.73118	0.865590	−	0.500754i	$-0.166944\pi$
$7$	4.58027	1.73118	0.865590	+	0.500754i	$0.166944\pi$
$8$	2.15310	0.761234
$9$	−2.07684	−0.692279
$10$	−1.63901	−0.518299
$11$	−3.05406	−0.920835	−0.460417	−	0.887703i	$-0.652300\pi$
$11$	−3.05406	−0.920835	−0.460417	+	0.887703i	$0.652300\pi$
$12$	0.659445	0.190365
$13$	−2.91179	−0.807586	−0.403793	−	0.914850i	$-0.632308\pi$
$13$	−2.91179	−0.807586	−0.403793	+	0.914850i	$0.632308\pi$
$14$	−7.50709	−2.00635
$15$	0.960813	0.248081
$16$	−4.90162	−1.22540
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	3.40395	0.802319
$19$	−5.62146	−1.28965	−0.644826	−	0.764329i	$-0.723070\pi$
$19$	−5.62146	−1.28965	−0.644826	+	0.764329i	$0.723070\pi$
$20$	0.686340	0.153470
$21$	4.40078	0.960330
$22$	5.00563	1.06720
$23$	1.25559	0.261808	0.130904	−	0.991395i	$-0.458212\pi$
$23$	1.25559	0.261808	0.130904	+	0.991395i	$0.458212\pi$
$24$	2.06872	0.422276
$25$	1.00000	0.200000
$26$	4.77245	0.935954
$27$	−4.87789	−0.938751
$28$	3.14362	0.594089
$29$	−1.71287	−0.318072	−0.159036	−	0.987273i	$-0.550839\pi$
$29$	−1.71287	−0.318072	−0.159036	+	0.987273i	$0.550839\pi$
$30$	−1.57478	−0.287514
$31$	8.18309	1.46973	0.734863	−	0.678216i	$-0.237246\pi$
$31$	8.18309	1.46973	0.734863	+	0.678216i	$0.237246\pi$
$32$	3.72759	0.658951
$33$	−2.93438	−0.510811
$34$	1.63901	0.281087
$35$	4.58027	0.774207
$36$	−1.42542	−0.237570
$37$	3.67710	0.604512	0.302256	−	0.953227i	$-0.402260\pi$
$37$	3.67710	0.604512	0.302256	+	0.953227i	$0.402260\pi$
$38$	9.21361	1.49464
$39$	−2.79769	−0.447989
$40$	2.15310	0.340434
$41$	12.2395	1.91148	0.955741	−	0.294208i	$-0.0950558\pi$
$41$	12.2395	1.91148	0.955741	+	0.294208i	$0.0950558\pi$
$42$	−7.21291	−1.11298
$43$	−9.45683	−1.44215	−0.721077	−	0.692855i	$-0.756353\pi$
$43$	−9.45683	−1.44215	−0.721077	+	0.692855i	$0.756353\pi$
$44$	−2.09613	−0.316003
$45$	−2.07684	−0.309597
$46$	−2.05791	−0.303423
$47$	−0.692469	−0.101007	−0.0505035	−	0.998724i	$-0.516083\pi$
$47$	−0.692469	−0.101007	−0.0505035	+	0.998724i	$0.516083\pi$
$48$	−4.70954	−0.679763
$49$	13.9789	1.99698
$50$	−1.63901	−0.231790
$51$	−0.960813	−0.134541
$52$	−1.99848	−0.277140
$53$	−3.94316	−0.541634	−0.270817	−	0.962631i	$-0.587294\pi$
$53$	−3.94316	−0.541634	−0.270817	+	0.962631i	$0.587294\pi$
$54$	7.99490	1.08797
$55$	−3.05406	−0.411810
$56$	9.86176	1.31783
$57$	−5.40118	−0.715403
$58$	2.80740	0.368630
$59$	−3.23094	−0.420632	−0.210316	−	0.977633i	$-0.567449\pi$
$59$	−3.23094	−0.420632	−0.210316	+	0.977633i	$0.567449\pi$
$60$	0.659445	0.0851340
$61$	−9.57732	−1.22625	−0.613125	−	0.789986i	$-0.710088\pi$
$61$	−9.57732	−1.22625	−0.613125	+	0.789986i	$0.710088\pi$
$62$	−13.4121	−1.70334
$63$	−9.51248	−1.19846
$64$	3.69370	0.461712
$65$	−2.91179	−0.361164
$66$	4.80947	0.592005
$67$	5.76886	0.704778	0.352389	−	0.935854i	$-0.385369\pi$
$67$	5.76886	0.704778	0.352389	+	0.935854i	$0.385369\pi$
$68$	−0.686340	−0.0832310
$69$	1.20638	0.145231
$70$	−7.50709	−0.897269
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	−4.47163	−0.526987
$73$	−1.79423	−0.209998	−0.104999	−	0.994472i	$-0.533484\pi$
$73$	−1.79423	−0.209998	−0.104999	+	0.994472i	$0.533484\pi$
$74$	−6.02679	−0.700600
$75$	0.960813	0.110945
$76$	−3.85824	−0.442570
$77$	−13.9884	−1.59413
$78$	4.58543	0.519198
$79$	0.429420	0.0483135	0.0241567	−	0.999708i	$-0.492310\pi$
$79$	0.429420	0.0483135	0.0241567	+	0.999708i	$0.492310\pi$
$80$	−4.90162	−0.548018
$81$	1.54377	0.171530
$82$	−20.0606	−2.21532
$83$	4.91701	0.539712	0.269856	−	0.962901i	$-0.413024\pi$
$83$	4.91701	0.539712	0.269856	+	0.962901i	$0.413024\pi$
$84$	3.02044	0.329557
$85$	−1.00000	−0.108465
$86$	15.4998	1.67139
$87$	−1.64575	−0.176443
$88$	−6.57569	−0.700971
$89$	−13.1193	−1.39064	−0.695319	−	0.718701i	$-0.744737\pi$
$89$	−13.1193	−1.39064	−0.695319	+	0.718701i	$0.744737\pi$
$90$	3.40395	0.358808
$91$	−13.3368	−1.39808
$92$	0.861759	0.0898446
$93$	7.86242	0.815295
$94$	1.13496	0.117062
$95$	−5.62146	−0.576750
$96$	3.58152	0.365537
$97$	−3.64082	−0.369670	−0.184835	−	0.982770i	$-0.559175\pi$
$97$	−3.64082	−0.369670	−0.184835	+	0.982770i	$0.559175\pi$
$98$	−22.9114	−2.31441
$99$	6.34279	0.637475
$100$	0.686340	0.0686340
$101$	−6.62919	−0.659629	−0.329815	−	0.944046i	$-0.606986\pi$
$101$	−6.62919	−0.659629	−0.329815	+	0.944046i	$0.606986\pi$
$102$	1.57478	0.155926
$103$	−16.5796	−1.63364	−0.816818	−	0.576896i	$-0.804264\pi$
$103$	−16.5796	−1.63364	−0.816818	+	0.576896i	$0.804264\pi$
$104$	−6.26937	−0.614762
$105$	4.40078	0.429473
$106$	6.46285	0.627728
$107$	−1.03572	−0.100127	−0.0500635	−	0.998746i	$-0.515942\pi$
$107$	−1.03572	−0.100127	−0.0500635	+	0.998746i	$0.515942\pi$
$108$	−3.34790	−0.322151
$109$	−5.23047	−0.500988	−0.250494	−	0.968118i	$-0.580593\pi$
$109$	−5.23047	−0.500988	−0.250494	+	0.968118i	$0.580593\pi$
$110$	5.00563	0.477268
$111$	3.53301	0.335338
$112$	−22.4507	−2.12139
$113$	−4.73218	−0.445166	−0.222583	−	0.974914i	$-0.571449\pi$
$113$	−4.73218	−0.445166	−0.222583	+	0.974914i	$0.571449\pi$
$114$	8.85256	0.829118
$115$	1.25559	0.117084
$116$	−1.17561	−0.109153
$117$	6.04732	0.559075
$118$	5.29552	0.487493
$119$	−4.58027	−0.419873
$120$	2.06872	0.188848
$121$	−1.67270	−0.152064
$122$	15.6973	1.42117
$123$	11.7598	1.06035
$124$	5.61638	0.504366
$125$	1.00000	0.0894427
$126$	15.5910	1.38896
$127$	−0.0295666	−0.00262361	−0.00131181	−	0.999999i	$-0.500418\pi$
$127$	−0.0295666	−0.00262361	−0.00131181	+	0.999999i	$0.500418\pi$
$128$	−13.5092	−1.19405
$129$	−9.08625	−0.800000
$130$	4.77245	0.418571
$131$	4.06587	0.355237	0.177619	−	0.984099i	$-0.443161\pi$
$131$	4.06587	0.355237	0.177619	+	0.984099i	$0.443161\pi$
$132$	−2.01399	−0.175295
$133$	−25.7478	−2.23262
$134$	−9.45519	−0.816804
$135$	−4.87789	−0.419822
$136$	−2.15310	−0.184626
$137$	−18.3036	−1.56378	−0.781892	−	0.623414i	$-0.785745\pi$
$137$	−18.3036	−1.56378	−0.781892	+	0.623414i	$0.785745\pi$
$138$	−1.97727	−0.168316
$139$	9.68121	0.821149	0.410575	−	0.911827i	$-0.365328\pi$
$139$	9.68121	0.821149	0.410575	+	0.911827i	$0.365328\pi$
$140$	3.14362	0.265685
$141$	−0.665333	−0.0560312
$142$	−1.63901	−0.137542
$143$	8.89280	0.743653
$144$	10.1799	0.848322
$145$	−1.71287	−0.142246
$146$	2.94075	0.243378
$147$	13.4311	1.10778
$148$	2.52374	0.207450
$149$	5.13801	0.420922	0.210461	−	0.977602i	$-0.432504\pi$
$149$	5.13801	0.420922	0.210461	+	0.977602i	$0.432504\pi$
$150$	−1.57478	−0.128580
$151$	−10.4535	−0.850693	−0.425347	−	0.905030i	$-0.639848\pi$
$151$	−10.4535	−0.850693	−0.425347	+	0.905030i	$0.639848\pi$
$152$	−12.1035	−0.981727
$153$	2.07684	0.167902
$154$	22.9271	1.84752
$155$	8.18309	0.657281
$156$	−1.92017	−0.153736
$157$	−19.1542	−1.52867	−0.764335	−	0.644819i	$-0.776933\pi$
$157$	−19.1542	−1.52867	−0.764335	+	0.644819i	$0.776933\pi$
$158$	−0.703821	−0.0559930
$159$	−3.78864	−0.300458
$160$	3.72759	0.294692
$161$	5.75092	0.453236
$162$	−2.53025	−0.198795
$163$	−3.00740	−0.235557	−0.117779	−	0.993040i	$-0.537577\pi$
$163$	−3.00740	−0.235557	−0.117779	+	0.993040i	$0.537577\pi$
$164$	8.40044	0.655964
$165$	−2.93438	−0.228441
$166$	−8.05901	−0.625501
$167$	−5.03559	−0.389665	−0.194833	−	0.980836i	$-0.562416\pi$
$167$	−5.03559	−0.389665	−0.194833	+	0.980836i	$0.562416\pi$
$168$	9.47531	0.731036
$169$	−4.52146	−0.347804
$170$	1.63901	0.125706
$171$	11.6749	0.892799
$172$	−6.49061	−0.494904
$173$	−0.714035	−0.0542871	−0.0271436	−	0.999632i	$-0.508641\pi$
$173$	−0.714035	−0.0542871	−0.0271436	+	0.999632i	$0.508641\pi$
$174$	2.69739	0.204489
$175$	4.58027	0.346236
$176$	14.9698	1.12839
$177$	−3.10433	−0.233335
$178$	21.5025	1.61168
$179$	1.47936	0.110573	0.0552864	−	0.998471i	$-0.482393\pi$
$179$	1.47936	0.110573	0.0552864	+	0.998471i	$0.482393\pi$
$180$	−1.42542	−0.106244
$181$	−4.15150	−0.308578	−0.154289	−	0.988026i	$-0.549309\pi$
$181$	−4.15150	−0.308578	−0.154289	+	0.988026i	$0.549309\pi$
$182$	21.8591	1.62030
$183$	−9.20202	−0.680233
$184$	2.70340	0.199297
$185$	3.67710	0.270346
$186$	−12.8866	−0.944888
$187$	3.05406	0.223335
$188$	−0.475269	−0.0346626
$189$	−22.3421	−1.62515
$190$	9.21361	0.668426
$191$	1.54877	0.112065	0.0560326	−	0.998429i	$-0.482155\pi$
$191$	1.54877	0.112065	0.0560326	+	0.998429i	$0.482155\pi$
$192$	3.54895	0.256124
$193$	−3.26029	−0.234680	−0.117340	−	0.993092i	$-0.537437\pi$
$193$	−3.26029	−0.234680	−0.117340	+	0.993092i	$0.537437\pi$
$194$	5.96733	0.428429
$195$	−2.79769	−0.200347
$196$	9.59426	0.685305
$197$	27.8250	1.98245	0.991224	−	0.132195i	$-0.0422024\pi$
$197$	27.8250	1.98245	0.991224	+	0.132195i	$0.0422024\pi$
$198$	−10.3959	−0.738803
$199$	20.3351	1.44152	0.720759	−	0.693185i	$-0.243793\pi$
$199$	20.3351	1.44152	0.720759	+	0.693185i	$0.243793\pi$
$200$	2.15310	0.152247
$201$	5.54280	0.390959
$202$	10.8653	0.764479
$203$	−7.84540	−0.550639
$204$	−0.659445	−0.0461704
$205$	12.2395	0.854841
$206$	27.1740	1.89331
$207$	−2.60765	−0.181244
$208$	14.2725	0.989620
$209$	17.1683	1.18756
$210$	−7.21291	−0.497738
$211$	−4.81915	−0.331764	−0.165882	−	0.986146i	$-0.553047\pi$
$211$	−4.81915	−0.331764	−0.165882	+	0.986146i	$0.553047\pi$
$212$	−2.70635	−0.185873
$213$	0.960813	0.0658338
$214$	1.69755	0.116042
$215$	−9.45683	−0.644951
$216$	−10.5026	−0.714609
$217$	37.4807	2.54436
$218$	8.57277	0.580621
$219$	−1.72392	−0.116492
$220$	−2.09613	−0.141321
$221$	2.91179	0.195868
$222$	−5.79062	−0.388641
$223$	−17.2991	−1.15843	−0.579215	−	0.815175i	$-0.696641\pi$
$223$	−17.2991	−1.15843	−0.579215	+	0.815175i	$0.696641\pi$
$224$	17.0734	1.14076
$225$	−2.07684	−0.138456
$226$	7.75607	0.515926
$227$	−17.8732	−1.18629	−0.593143	−	0.805097i	$-0.702113\pi$
$227$	−17.8732	−1.18629	−0.593143	+	0.805097i	$0.702113\pi$
$228$	−3.70705	−0.245505
$229$	−13.5420	−0.894882	−0.447441	−	0.894313i	$-0.647665\pi$
$229$	−13.5420	−0.894882	−0.447441	+	0.894313i	$0.647665\pi$
$230$	−2.05791	−0.135695
$231$	−13.4403	−0.884305
$232$	−3.68797	−0.242127
$233$	−12.7237	−0.833556	−0.416778	−	0.909008i	$-0.636841\pi$
$233$	−12.7237	−0.833556	−0.416778	+	0.909008i	$0.636841\pi$
$234$	−9.91160	−0.647942
$235$	−0.692469	−0.0451717
$236$	−2.21752	−0.144348
$237$	0.412592	0.0268007
$238$	7.50709	0.486612
$239$	7.06102	0.456740	0.228370	−	0.973574i	$-0.426660\pi$
$239$	7.06102	0.456740	0.228370	+	0.973574i	$0.426660\pi$
$240$	−4.70954	−0.303999
$241$	−28.3369	−1.82534	−0.912669	−	0.408700i	$-0.865982\pi$
$241$	−28.3369	−1.82534	−0.912669	+	0.408700i	$0.865982\pi$
$242$	2.74157	0.176235
$243$	16.1170	1.03390
$244$	−6.57330	−0.420813
$245$	13.9789	0.893077
$246$	−19.2744	−1.22889
$247$	16.3685	1.04151
$248$	17.6190	1.11881
$249$	4.72433	0.299392
$250$	−1.63901	−0.103660
$251$	15.0378	0.949178	0.474589	−	0.880207i	$-0.342597\pi$
$251$	15.0378	0.949178	0.474589	+	0.880207i	$0.342597\pi$
$252$	−6.52880	−0.411276
$253$	−3.83464	−0.241082
$254$	0.0484598	0.00304064
$255$	−0.960813	−0.0601685
$256$	14.7542	0.922138
$257$	20.6265	1.28665	0.643324	−	0.765594i	$-0.277555\pi$
$257$	20.6265	1.28665	0.643324	+	0.765594i	$0.277555\pi$
$258$	14.8924	0.927162
$259$	16.8421	1.04652
$260$	−1.99848	−0.123941
$261$	3.55735	0.220195
$262$	−6.66399	−0.411703
$263$	−19.2827	−1.18902	−0.594511	−	0.804087i	$-0.702654\pi$
$263$	−19.2827	−1.18902	−0.594511	+	0.804087i	$0.702654\pi$
$264$	−6.31801	−0.388847
$265$	−3.94316	−0.242226
$266$	42.2008	2.58750
$267$	−12.6052	−0.771423
$268$	3.95940	0.241859
$269$	−17.9756	−1.09599	−0.547994	−	0.836482i	$-0.684608\pi$
$269$	−17.9756	−1.09599	−0.547994	+	0.836482i	$0.684608\pi$
$270$	7.99490	0.486554
$271$	9.35711	0.568404	0.284202	−	0.958764i	$-0.408271\pi$
$271$	9.35711	0.568404	0.284202	+	0.958764i	$0.408271\pi$
$272$	4.90162	0.297204
$273$	−12.8142	−0.775549
$274$	29.9998	1.81235
$275$	−3.05406	−0.184167
$276$	0.827990	0.0498391
$277$	24.8078	1.49056	0.745278	−	0.666754i	$-0.232317\pi$
$277$	24.8078	1.49056	0.745278	+	0.666754i	$0.232317\pi$
$278$	−15.8676	−0.951673
$279$	−16.9949	−1.01746
$280$	9.86176	0.589353
$281$	−22.3810	−1.33514	−0.667570	−	0.744547i	$-0.732665\pi$
$281$	−22.3810	−1.33514	−0.667570	+	0.744547i	$0.732665\pi$
$282$	1.09048	0.0649374
$283$	−20.4317	−1.21454	−0.607268	−	0.794497i	$-0.707734\pi$
$283$	−20.4317	−1.21454	−0.607268	+	0.794497i	$0.707734\pi$
$284$	0.686340	0.0407268
$285$	−5.40118	−0.319938
$286$	−14.5754	−0.861859
$287$	56.0600	3.30912
$288$	−7.74160	−0.456178
$289$	1.00000	0.0588235
$290$	2.80740	0.164856
$291$	−3.49815	−0.205065
$292$	−1.23145	−0.0720652
$293$	29.0806	1.69891	0.849453	−	0.527665i	$-0.176932\pi$
$293$	29.0806	1.69891	0.849453	+	0.527665i	$0.176932\pi$
$294$	−22.0136	−1.28386
$295$	−3.23094	−0.188112
$296$	7.91715	0.460175
$297$	14.8974	0.864434
$298$	−8.42122	−0.487828
$299$	−3.65601	−0.211432
$300$	0.659445	0.0380731
$301$	−43.3149	−2.49663
$302$	17.1333	0.985913
$303$	−6.36942	−0.365913
$304$	27.5543	1.58035
$305$	−9.57732	−0.548396
$306$	−3.40395	−0.194591
$307$	−23.1977	−1.32396	−0.661981	−	0.749521i	$-0.730284\pi$
$307$	−23.1977	−1.32396	−0.661981	+	0.749521i	$0.730284\pi$
$308$	−9.60083	−0.547058
$309$	−15.9299	−0.906220
$310$	−13.4121	−0.761758
$311$	−32.1216	−1.82145	−0.910725	−	0.413014i	$-0.864476\pi$
$311$	−32.1216	−1.82145	−0.910725	+	0.413014i	$0.864476\pi$
$312$	−6.02370	−0.341025
$313$	−12.2631	−0.693154	−0.346577	−	0.938022i	$-0.612656\pi$
$313$	−12.2631	−0.693154	−0.346577	+	0.938022i	$0.612656\pi$
$314$	31.3938	1.77166
$315$	−9.51248	−0.535967
$316$	0.294728	0.0165797
$317$	14.5132	0.815144	0.407572	−	0.913173i	$-0.366376\pi$
$317$	14.5132	0.815144	0.407572	+	0.913173i	$0.366376\pi$
$318$	6.20960	0.348217
$319$	5.23121	0.292892
$320$	3.69370	0.206484
$321$	−0.995135	−0.0555430
$322$	−9.42579	−0.525279
$323$	5.62146	0.312787
$324$	1.05955	0.0588639
$325$	−2.91179	−0.161517
$326$	4.92914	0.273000
$327$	−5.02551	−0.277911
$328$	26.3527	1.45509
$329$	−3.17169	−0.174861
$330$	4.80947	0.264753
$331$	−31.7754	−1.74654	−0.873268	−	0.487240i	$-0.838004\pi$
$331$	−31.7754	−1.74654	−0.873268	+	0.487240i	$0.838004\pi$
$332$	3.37475	0.185213
$333$	−7.63674	−0.418491
$334$	8.25336	0.451604
$335$	5.76886	0.315186
$336$	−21.5710	−1.17679
$337$	32.8099	1.78727	0.893634	−	0.448796i	$-0.148147\pi$
$337$	32.8099	1.78727	0.893634	+	0.448796i	$0.148147\pi$
$338$	7.41069	0.403089
$339$	−4.54674	−0.246945
$340$	−0.686340	−0.0372220
$341$	−24.9917	−1.35337
$342$	−19.1352	−1.03471
$343$	31.9651	1.72595
$344$	−20.3615	−1.09782
$345$	1.20638	0.0649495
$346$	1.17031	0.0629162
$347$	−24.2582	−1.30225	−0.651125	−	0.758971i	$-0.725703\pi$
$347$	−24.2582	−1.30225	−0.651125	+	0.758971i	$0.725703\pi$
$348$	−1.12954	−0.0605499
$349$	1.34078	0.0717701	0.0358850	−	0.999356i	$-0.488575\pi$
$349$	1.34078	0.0717701	0.0358850	+	0.999356i	$0.488575\pi$
$350$	−7.50709	−0.401271
$351$	14.2034	0.758122
$352$	−11.3843	−0.606785
$353$	14.2320	0.757493	0.378746	−	0.925500i	$-0.376355\pi$
$353$	14.2320	0.757493	0.378746	+	0.925500i	$0.376355\pi$
$354$	5.08801	0.270425
$355$	1.00000	0.0530745
$356$	−9.00428	−0.477226
$357$	−4.40078	−0.232914
$358$	−2.42469	−0.128149
$359$	−17.3821	−0.917394	−0.458697	−	0.888593i	$-0.651684\pi$
$359$	−17.3821	−0.917394	−0.458697	+	0.888593i	$0.651684\pi$
$360$	−4.47163	−0.235676
$361$	12.6008	0.663202
$362$	6.80433	0.357628
$363$	−1.60715	−0.0843537
$364$	−9.15359	−0.479778
$365$	−1.79423	−0.0939142
$366$	15.0822	0.788357
$367$	−35.2028	−1.83757	−0.918785	−	0.394758i	$-0.870828\pi$
$367$	−35.2028	−1.83757	−0.918785	+	0.394758i	$0.870828\pi$
$368$	−6.15440	−0.320820
$369$	−25.4194	−1.32328
$370$	−6.02679	−0.313318
$371$	−18.0607	−0.937666
$372$	5.39630	0.279785
$373$	−1.63788	−0.0848061	−0.0424031	−	0.999101i	$-0.513501\pi$
$373$	−1.63788	−0.0848061	−0.0424031	+	0.999101i	$0.513501\pi$
$374$	−5.00563	−0.258835
$375$	0.960813	0.0496162
$376$	−1.49095	−0.0768899
$377$	4.98752	0.256870
$378$	36.6188	1.88347
$379$	−28.2984	−1.45359	−0.726794	−	0.686855i	$-0.758991\pi$
$379$	−28.2984	−1.45359	−0.726794	+	0.686855i	$0.758991\pi$
$380$	−3.85824	−0.197923
$381$	−0.0284080	−0.00145539
$382$	−2.53844	−0.129878
$383$	30.9644	1.58221	0.791105	−	0.611681i	$-0.209506\pi$
$383$	30.9644	1.58221	0.791105	+	0.611681i	$0.209506\pi$
$384$	−12.9798	−0.662372
$385$	−13.9884	−0.712916
$386$	5.34363	0.271983
$387$	19.6403	0.998373
$388$	−2.49884	−0.126860
$389$	20.0622	1.01720	0.508598	−	0.861004i	$-0.330164\pi$
$389$	20.0622	1.01720	0.508598	+	0.861004i	$0.330164\pi$
$390$	4.58543	0.232192
$391$	−1.25559	−0.0634977
$392$	30.0978	1.52017
$393$	3.90655	0.197059
$394$	−45.6053	−2.29756
$395$	0.429420	0.0216064
$396$	4.35332	0.218762
$397$	−7.86278	−0.394622	−0.197311	−	0.980341i	$-0.563221\pi$
$397$	−7.86278	−0.394622	−0.197311	+	0.980341i	$0.563221\pi$
$398$	−33.3294	−1.67065
$399$	−24.7388	−1.23849
$400$	−4.90162	−0.245081
$401$	11.5693	0.577743	0.288871	−	0.957368i	$-0.406720\pi$
$401$	11.5693	0.577743	0.288871	+	0.957368i	$0.406720\pi$
$402$	−9.08467	−0.453102
$403$	−23.8275	−1.18693
$404$	−4.54988	−0.226365
$405$	1.54377	0.0767105
$406$	12.8587	0.638165
$407$	−11.2301	−0.556655
$408$	−2.06872	−0.102417
$409$	−28.5129	−1.40987	−0.704935	−	0.709272i	$-0.749024\pi$
$409$	−28.5129	−1.40987	−0.704935	+	0.709272i	$0.749024\pi$
$410$	−20.0606	−0.990720
$411$	−17.5864	−0.867472
$412$	−11.3792	−0.560615
$413$	−14.7986	−0.728190
$414$	4.27395	0.210053
$415$	4.91701	0.241367
$416$	−10.8540	−0.532160
$417$	9.30183	0.455513
$418$	−28.1389	−1.37632
$419$	12.0041	0.586441	0.293220	−	0.956045i	$-0.405273\pi$
$419$	12.0041	0.586441	0.293220	+	0.956045i	$0.405273\pi$
$420$	3.02044	0.147382
$421$	20.0887	0.979065	0.489533	−	0.871985i	$-0.337167\pi$
$421$	20.0887	0.979065	0.489533	+	0.871985i	$0.337167\pi$
$422$	7.89862	0.384499
$423$	1.43814	0.0699250
$424$	−8.48999	−0.412310
$425$	−1.00000	−0.0485071
$426$	−1.57478	−0.0762983
$427$	−43.8667	−2.12286
$428$	−0.710857	−0.0343606
$429$	8.54432	0.412524
$430$	15.4998	0.747467
$431$	21.1091	1.01679	0.508396	−	0.861124i	$-0.330239\pi$
$431$	21.1091	1.01679	0.508396	+	0.861124i	$0.330239\pi$
$432$	23.9096	1.15035
$433$	17.8417	0.857416	0.428708	−	0.903443i	$-0.358969\pi$
$433$	17.8417	0.857416	0.428708	+	0.903443i	$0.358969\pi$
$434$	−61.4312	−2.94879
$435$	−1.64575	−0.0789076
$436$	−3.58988	−0.171924
$437$	−7.05823	−0.337641
$438$	2.82551	0.135008
$439$	21.9792	1.04901	0.524505	−	0.851407i	$-0.324250\pi$
$439$	21.9792	1.04901	0.524505	+	0.851407i	$0.324250\pi$
$440$	−6.57569	−0.313484
$441$	−29.0318	−1.38247
$442$	−4.77245	−0.227002
$443$	−19.8507	−0.943137	−0.471568	−	0.881829i	$-0.656312\pi$
$443$	−19.8507	−0.943137	−0.471568	+	0.881829i	$0.656312\pi$
$444$	2.42485	0.115078
$445$	−13.1193	−0.621913
$446$	28.3533	1.34257
$447$	4.93666	0.233496
$448$	16.9181	0.799306
$449$	9.55984	0.451157	0.225578	−	0.974225i	$-0.427573\pi$
$449$	9.55984	0.451157	0.225578	+	0.974225i	$0.427573\pi$
$450$	3.40395	0.160464
$451$	−37.3801	−1.76016
$452$	−3.24789	−0.152768
$453$	−10.0439	−0.471902
$454$	29.2943	1.37485
$455$	−13.3368	−0.625239
$456$	−11.6292	−0.544590
$457$	14.2273	0.665527	0.332763	−	0.943010i	$-0.392019\pi$
$457$	14.2273	0.665527	0.332763	+	0.943010i	$0.392019\pi$
$458$	22.1955	1.03713
$459$	4.87789	0.227681
$460$	0.861759	0.0401797
$461$	18.5806	0.865386	0.432693	−	0.901541i	$-0.357563\pi$
$461$	18.5806	0.865386	0.432693	+	0.901541i	$0.357563\pi$
$462$	22.0287	1.02487
$463$	−21.0100	−0.976416	−0.488208	−	0.872727i	$-0.662349\pi$
$463$	−21.0100	−0.976416	−0.488208	+	0.872727i	$0.662349\pi$
$464$	8.39583	0.389767
$465$	7.86242	0.364611
$466$	20.8542	0.966051
$467$	−18.8900	−0.874125	−0.437063	−	0.899431i	$-0.643981\pi$
$467$	−18.8900	−0.874125	−0.437063	+	0.899431i	$0.643981\pi$
$468$	4.15052	0.191858
$469$	26.4229	1.22010
$470$	1.13496	0.0523518
$471$	−18.4036	−0.847993
$472$	−6.95652	−0.320200
$473$	28.8818	1.32799
$474$	−0.676241	−0.0310608
$475$	−5.62146	−0.257930
$476$	−3.14362	−0.144088
$477$	8.18929	0.374962
$478$	−11.5731	−0.529339
$479$	6.58287	0.300779	0.150390	−	0.988627i	$-0.451947\pi$
$479$	6.58287	0.300779	0.150390	+	0.988627i	$0.451947\pi$
$480$	3.58152	0.163473
$481$	−10.7070	−0.488195
$482$	46.4443	2.11548
$483$	5.52556	0.251422
$484$	−1.14804	−0.0521837
$485$	−3.64082	−0.165321
$486$	−26.4158	−1.19824
$487$	6.31940	0.286359	0.143180	−	0.989697i	$-0.454267\pi$
$487$	6.31940	0.286359	0.143180	+	0.989697i	$0.454267\pi$
$488$	−20.6209	−0.933464
$489$	−2.88955	−0.130670
$490$	−22.9114	−1.03503
$491$	−10.5644	−0.476767	−0.238383	−	0.971171i	$-0.576617\pi$
$491$	−10.5644	−0.476767	−0.238383	+	0.971171i	$0.576617\pi$
$492$	8.07125	0.363880
$493$	1.71287	0.0771437
$494$	−26.8281	−1.20705
$495$	6.34279	0.285087
$496$	−40.1104	−1.80101
$497$	4.58027	0.205453
$498$	−7.74321	−0.346981
$499$	−30.6377	−1.37153	−0.685767	−	0.727822i	$-0.740533\pi$
$499$	−30.6377	−1.37153	−0.685767	+	0.727822i	$0.740533\pi$
$500$	0.686340	0.0306941
$501$	−4.83826	−0.216157
$502$	−24.6471	−1.10005
$503$	−2.57619	−0.114867	−0.0574333	−	0.998349i	$-0.518292\pi$
$503$	−2.57619	−0.114867	−0.0574333	+	0.998349i	$0.518292\pi$
$504$	−20.4813	−0.912308
$505$	−6.62919	−0.294995
$506$	6.28499	0.279402
$507$	−4.34428	−0.192936
$508$	−0.0202928	−0.000900345 0
$509$	−30.0164	−1.33045	−0.665227	−	0.746641i	$-0.731665\pi$
$509$	−30.0164	−1.33045	−0.665227	+	0.746641i	$0.731665\pi$
$510$	1.57478	0.0697324
$511$	−8.21804	−0.363545
$512$	2.83609	0.125339
$513$	27.4209	1.21066
$514$	−33.8070	−1.49116
$515$	−16.5796	−0.730584
$516$	−6.23626	−0.274536
$517$	2.11484	0.0930107
$518$	−27.6043	−1.21286
$519$	−0.686055	−0.0301145
$520$	−6.26937	−0.274930
$521$	7.94559	0.348103	0.174051	−	0.984737i	$-0.444314\pi$
$521$	7.94559	0.348103	0.174051	+	0.984737i	$0.444314\pi$
$522$	−5.83052	−0.255195
$523$	−7.19810	−0.314751	−0.157376	−	0.987539i	$-0.550303\pi$
$523$	−7.19810	−0.314751	−0.157376	+	0.987539i	$0.550303\pi$
$524$	2.79057	0.121907
$525$	4.40078	0.192066
$526$	31.6045	1.37802
$527$	−8.18309	−0.356461
$528$	14.3832	0.625950
$529$	−21.4235	−0.931457
$530$	6.46285	0.280728
$531$	6.71013	0.291195
$532$	−17.6718	−0.766168
$533$	−35.6388	−1.54369
$534$	20.6599	0.894043
$535$	−1.03572	−0.0447781
$536$	12.4209	0.536501
$537$	1.42139	0.0613376
$538$	29.4620	1.27020
$539$	−42.6923	−1.83889
$540$	−3.34790	−0.144070
$541$	3.57242	0.153590	0.0767952	−	0.997047i	$-0.475531\pi$
$541$	3.57242	0.153590	0.0767952	+	0.997047i	$0.475531\pi$
$542$	−15.3364	−0.658753
$543$	−3.98882	−0.171176
$544$	−3.72759	−0.159819
$545$	−5.23047	−0.224049
$546$	21.0025	0.898824
$547$	−30.9984	−1.32540	−0.662698	−	0.748887i	$-0.730589\pi$
$547$	−30.9984	−1.32540	−0.662698	+	0.748887i	$0.730589\pi$
$548$	−12.5625	−0.536644
$549$	19.8905	0.848908
$550$	5.00563	0.213441
$551$	9.62883	0.410202
$552$	2.59746	0.110555
$553$	1.96686	0.0836393
$554$	−40.6601	−1.72748
$555$	3.53301	0.149968
$556$	6.64460	0.281794
$557$	12.3453	0.523086	0.261543	−	0.965192i	$-0.415769\pi$
$557$	12.3453	0.523086	0.261543	+	0.965192i	$0.415769\pi$
$558$	27.8548	1.17919
$559$	27.5364	1.16466
$560$	−22.4507	−0.948717
$561$	2.93438	0.123890
$562$	36.6826	1.54736
$563$	−9.11849	−0.384299	−0.192149	−	0.981366i	$-0.561546\pi$
$563$	−9.11849	−0.384299	−0.192149	+	0.981366i	$0.561546\pi$
$564$	−0.456645	−0.0192282
$565$	−4.73218	−0.199084
$566$	33.4876	1.40759
$567$	7.07088	0.296949
$568$	2.15310	0.0903419
$569$	−2.89963	−0.121559	−0.0607795	−	0.998151i	$-0.519359\pi$
$569$	−2.89963	−0.121559	−0.0607795	+	0.998151i	$0.519359\pi$
$570$	8.85256	0.370793
$571$	31.5979	1.32233	0.661165	−	0.750241i	$-0.270062\pi$
$571$	31.5979	1.32233	0.661165	+	0.750241i	$0.270062\pi$
$572$	6.10349	0.255200
$573$	1.48808	0.0621654
$574$	−91.8827	−3.83511
$575$	1.25559	0.0523615
$576$	−7.67121	−0.319634
$577$	17.1523	0.714061	0.357031	−	0.934093i	$-0.383789\pi$
$577$	17.1523	0.714061	0.357031	+	0.934093i	$0.383789\pi$
$578$	−1.63901	−0.0681737
$579$	−3.13253	−0.130183
$580$	−1.17561	−0.0488146
$581$	22.5212	0.934339
$582$	5.73349	0.237661
$583$	12.0426	0.498755
$584$	−3.86314	−0.159858
$585$	6.04732	0.250026
$586$	−47.6632	−1.96895
$587$	39.2755	1.62108	0.810538	−	0.585686i	$-0.199175\pi$
$587$	39.2755	1.62108	0.810538	+	0.585686i	$0.199175\pi$
$588$	9.21830	0.380156
$589$	−46.0009	−1.89544
$590$	5.29552	0.218013
$591$	26.7346	1.09971
$592$	−18.0237	−0.740771
$593$	−7.88138	−0.323649	−0.161825	−	0.986820i	$-0.551738\pi$
$593$	−7.88138	−0.323649	−0.161825	+	0.986820i	$0.551738\pi$
$594$	−24.4169	−1.00184
$595$	−4.58027	−0.187773
$596$	3.52642	0.144448
$597$	19.5383	0.799648
$598$	5.99222	0.245040
$599$	35.7660	1.46136	0.730680	−	0.682720i	$-0.239203\pi$
$599$	35.7660	1.46136	0.730680	+	0.682720i	$0.239203\pi$
$600$	2.06872	0.0844553
$601$	3.99843	0.163100	0.0815498	−	0.996669i	$-0.474013\pi$
$601$	3.99843	0.163100	0.0815498	+	0.996669i	$0.474013\pi$
$602$	70.9933	2.89347
$603$	−11.9810	−0.487903
$604$	−7.17466	−0.291933
$605$	−1.67270	−0.0680050
$606$	10.4395	0.424076
$607$	39.5395	1.60486	0.802430	−	0.596746i	$-0.203540\pi$
$607$	39.5395	1.60486	0.802430	+	0.596746i	$0.203540\pi$
$608$	−20.9545	−0.849817
$609$	−7.53797	−0.305454
$610$	15.6973	0.635565
$611$	2.01633	0.0815718
$612$	1.42542	0.0576191
$613$	−24.4095	−0.985891	−0.492946	−	0.870060i	$-0.664080\pi$
$613$	−24.4095	−0.985891	−0.492946	+	0.870060i	$0.664080\pi$
$614$	38.0211	1.53441
$615$	11.7598	0.474202
$616$	−30.1184	−1.21351
$617$	−11.3864	−0.458397	−0.229199	−	0.973380i	$-0.573611\pi$
$617$	−11.3864	−0.458397	−0.229199	+	0.973380i	$0.573611\pi$
$618$	26.1092	1.05027
$619$	0.430897	0.0173192	0.00865961	−	0.999963i	$-0.497244\pi$
$619$	0.430897	0.0173192	0.00865961	+	0.999963i	$0.497244\pi$
$620$	5.61638	0.225559
$621$	−6.12461	−0.245772
$622$	52.6475	2.11097
$623$	−60.0897	−2.40744
$624$	13.7132	0.548968
$625$	1.00000	0.0400000
$626$	20.0994	0.803332
$627$	16.4955	0.658768
$628$	−13.1463	−0.524594
$629$	−3.67710	−0.146616
$630$	15.5910	0.621161
$631$	24.5242	0.976294	0.488147	−	0.872761i	$-0.337673\pi$
$631$	24.5242	0.976294	0.488147	+	0.872761i	$0.337673\pi$
$632$	0.924582	0.0367779
$633$	−4.63030	−0.184038
$634$	−23.7873	−0.944713
$635$	−0.0295666	−0.00117331
$636$	−2.60029	−0.103108
$637$	−40.7036	−1.61273
$638$	−8.57398	−0.339447
$639$	−2.07684	−0.0821584
$640$	−13.5092	−0.533997
$641$	15.9906	0.631590	0.315795	−	0.948827i	$-0.397729\pi$
$641$	15.9906	0.631590	0.315795	+	0.948827i	$0.397729\pi$
$642$	1.63103	0.0643717
$643$	3.57065	0.140813	0.0704064	−	0.997518i	$-0.477570\pi$
$643$	3.57065	0.140813	0.0704064	+	0.997518i	$0.477570\pi$
$644$	3.94709	0.155537
$645$	−9.08625	−0.357771
$646$	−9.21361	−0.362505
$647$	19.4095	0.763064	0.381532	−	0.924356i	$-0.375397\pi$
$647$	19.4095	0.763064	0.381532	+	0.924356i	$0.375397\pi$
$648$	3.32388	0.130574
$649$	9.86748	0.387333
$650$	4.77245	0.187191
$651$	36.0120	1.41142
$652$	−2.06410	−0.0808363
$653$	17.8146	0.697141	0.348570	−	0.937283i	$-0.386667\pi$
$653$	17.8146	0.697141	0.348570	+	0.937283i	$0.386667\pi$
$654$	8.23683	0.322086
$655$	4.06587	0.158867
$656$	−59.9932	−2.34234
$657$	3.72632	0.145378
$658$	5.19842	0.202656
$659$	−7.16048	−0.278933	−0.139466	−	0.990227i	$-0.544539\pi$
$659$	−7.16048	−0.278933	−0.139466	+	0.990227i	$0.544539\pi$
$660$	−2.01399	−0.0783943
$661$	33.9466	1.32037	0.660184	−	0.751104i	$-0.270478\pi$
$661$	33.9466	1.32037	0.660184	+	0.751104i	$0.270478\pi$
$662$	52.0801	2.02415
$663$	2.79769	0.108653
$664$	10.5868	0.410848
$665$	−25.7478	−0.998457
$666$	12.5167	0.485011
$667$	−2.15065	−0.0832736
$668$	−3.45613	−0.133722
$669$	−16.6212	−0.642611
$670$	−9.45519	−0.365286
$671$	29.2497	1.12917
$672$	16.4043	0.632810
$673$	10.2833	0.396392	0.198196	−	0.980162i	$-0.436492\pi$
$673$	10.2833	0.396392	0.198196	+	0.980162i	$0.436492\pi$
$674$	−53.7756	−2.07136
$675$	−4.87789	−0.187750
$676$	−3.10326	−0.119356
$677$	10.6676	0.409989	0.204995	−	0.978763i	$-0.434282\pi$
$677$	10.6676	0.409989	0.204995	+	0.978763i	$0.434282\pi$
$678$	7.45213	0.286197
$679$	−16.6759	−0.639964
$680$	−2.15310	−0.0825675
$681$	−17.1728	−0.658064
$682$	40.9615	1.56850
$683$	−35.0975	−1.34297	−0.671484	−	0.741019i	$-0.734343\pi$
$683$	−35.0975	−1.34297	−0.671484	+	0.741019i	$0.734343\pi$
$684$	8.01293	0.306382
$685$	−18.3036	−0.699346
$686$	−52.3910	−2.00030
$687$	−13.0114	−0.496414
$688$	46.3538	1.76722
$689$	11.4817	0.437416
$690$	−1.97727	−0.0752733
$691$	4.05213	0.154150	0.0770751	−	0.997025i	$-0.475442\pi$
$691$	4.05213	0.154150	0.0770751	+	0.997025i	$0.475442\pi$
$692$	−0.490071	−0.0186297
$693$	29.0517	1.10358
$694$	39.7594	1.50925
$695$	9.68121	0.367229
$696$	−3.54345	−0.134314
$697$	−12.2395	−0.463603
$698$	−2.19754	−0.0831781
$699$	−12.2251	−0.462395
$700$	3.14362	0.118818
$701$	32.8762	1.24172	0.620859	−	0.783922i	$-0.286784\pi$
$701$	32.8762	1.24172	0.620859	+	0.783922i	$0.286784\pi$
$702$	−23.2795	−0.878628
$703$	−20.6707	−0.779610
$704$	−11.2808	−0.425160
$705$	−0.665333	−0.0250579
$706$	−23.3263	−0.877898
$707$	−30.3635	−1.14194
$708$	−2.13063	−0.0800738
$709$	43.4330	1.63116	0.815581	−	0.578643i	$-0.196418\pi$
$709$	43.4330	1.63116	0.815581	+	0.578643i	$0.196418\pi$
$710$	−1.63901	−0.0615108
$711$	−0.891835	−0.0334464
$712$	−28.2470	−1.05860
$713$	10.2746	0.384785
$714$	7.21291	0.269936
$715$	8.89280	0.332572
$716$	1.01535	0.0379453
$717$	6.78433	0.253365
$718$	28.4894	1.06322
$719$	12.3459	0.460423	0.230212	−	0.973141i	$-0.426058\pi$
$719$	12.3459	0.460423	0.230212	+	0.973141i	$0.426058\pi$
$720$	10.1799	0.379381
$721$	−75.9390	−2.82812
$722$	−20.6529	−0.768620
$723$	−27.2264	−1.01256
$724$	−2.84934	−0.105895
$725$	−1.71287	−0.0636144
$726$	2.63413	0.0977619
$727$	22.3180	0.827730	0.413865	−	0.910338i	$-0.364179\pi$
$727$	22.3180	0.827730	0.413865	+	0.910338i	$0.364179\pi$
$728$	−28.7154	−1.06426
$729$	10.8541	0.402003
$730$	2.94075	0.108842
$731$	9.45683	0.349774
$732$	−6.31572	−0.233436
$733$	−9.24516	−0.341478	−0.170739	−	0.985316i	$-0.554615\pi$
$733$	−9.24516	−0.341478	−0.170739	+	0.985316i	$0.554615\pi$
$734$	57.6976	2.12966
$735$	13.4311	0.495413
$736$	4.68031	0.172518
$737$	−17.6185	−0.648984
$738$	41.6625	1.53362
$739$	−43.7922	−1.61092	−0.805460	−	0.592650i	$-0.798082\pi$
$739$	−43.7922	−1.61092	−0.805460	+	0.592650i	$0.798082\pi$
$740$	2.52374	0.0927747
$741$	15.7271	0.577750
$742$	29.6016	1.08671
$743$	49.4480	1.81407	0.907035	−	0.421054i	$-0.138340\pi$
$743$	49.4480	1.81407	0.907035	+	0.421054i	$0.138340\pi$
$744$	16.9285	0.620631
$745$	5.13801	0.188242
$746$	2.68449	0.0982863
$747$	−10.2118	−0.373632
$748$	2.09613	0.0766420
$749$	−4.74388	−0.173338
$750$	−1.57478	−0.0575028
$751$	20.5427	0.749613	0.374807	−	0.927103i	$-0.377709\pi$
$751$	20.5427	0.749613	0.374807	+	0.927103i	$0.377709\pi$
$752$	3.39422	0.123774
$753$	14.4485	0.526534
$754$	−8.17458	−0.297701
$755$	−10.4535	−0.380442
$756$	−15.3343	−0.557702
$757$	−12.3203	−0.447788	−0.223894	−	0.974613i	$-0.571877\pi$
$757$	−12.3203	−0.447788	−0.223894	+	0.974613i	$0.571877\pi$
$758$	46.3812	1.68464
$759$	−3.68437	−0.133734
$760$	−12.1035	−0.439042
$761$	−2.10734	−0.0763909	−0.0381955	−	0.999270i	$-0.512161\pi$
$761$	−2.10734	−0.0763909	−0.0381955	+	0.999270i	$0.512161\pi$
$762$	0.0465609	0.00168672
$763$	−23.9570	−0.867300
$764$	1.06298	0.0384574
$765$	2.07684	0.0750882
$766$	−50.7509	−1.83370
$767$	9.40782	0.339697
$768$	14.1760	0.511534
$769$	−52.3618	−1.88822	−0.944108	−	0.329636i	$-0.893074\pi$
$769$	−52.3618	−1.88822	−0.944108	+	0.329636i	$0.893074\pi$
$770$	22.9271	0.826236
$771$	19.8182	0.713737
$772$	−2.23767	−0.0805354
$773$	−26.5180	−0.953786	−0.476893	−	0.878961i	$-0.658237\pi$
$773$	−26.5180	−0.953786	−0.476893	+	0.878961i	$0.658237\pi$
$774$	−32.1906	−1.15707
$775$	8.18309	0.293945
$776$	−7.83904	−0.281405
$777$	16.1821	0.580531
$778$	−32.8821	−1.17888
$779$	−68.8037	−2.46515
$780$	−1.92017	−0.0687530
$781$	−3.05406	−0.109283
$782$	2.05791	0.0735908
$783$	8.35519	0.298590
$784$	−68.5191	−2.44711
$785$	−19.1542	−0.683642
$786$	−6.40285	−0.228382
$787$	−12.8019	−0.456338	−0.228169	−	0.973622i	$-0.573274\pi$
$787$	−12.8019	−0.456338	−0.228169	+	0.973622i	$0.573274\pi$
$788$	19.0974	0.680317
$789$	−18.5271	−0.659581
$790$	−0.703821	−0.0250408
$791$	−21.6747	−0.770662
$792$	13.6566	0.485268
$793$	27.8872	0.990303
$794$	12.8872	0.457348
$795$	−3.78864	−0.134369
$796$	13.9568	0.494686
$797$	18.8478	0.667624	0.333812	−	0.942640i	$-0.391665\pi$
$797$	18.8478	0.667624	0.333812	+	0.942640i	$0.391665\pi$
$798$	40.5471	1.43535
$799$	0.692469	0.0244978
$800$	3.72759	0.131790
$801$	27.2466	0.962710
$802$	−18.9621	−0.669576
$803$	5.47968	0.193374
$804$	3.80424	0.134165
$805$	5.75092	0.202693
$806$	39.0534	1.37560
$807$	−17.2712	−0.607973
$808$	−14.2733	−0.502132
$809$	35.1004	1.23406	0.617032	−	0.786938i	$-0.288335\pi$
$809$	35.1004	1.23406	0.617032	+	0.786938i	$0.288335\pi$
$810$	−2.53025	−0.0889038
$811$	23.2823	0.817550	0.408775	−	0.912635i	$-0.365956\pi$
$811$	23.2823	0.817550	0.408775	+	0.912635i	$0.365956\pi$
$812$	−5.38462	−0.188963
$813$	8.99043	0.315308
$814$	18.4062	0.645137
$815$	−3.00740	−0.105344
$816$	4.70954	0.164867
$817$	53.1612	1.85988
$818$	46.7327	1.63397
$819$	27.6984	0.967859
$820$	8.40044	0.293356
$821$	−42.3523	−1.47810	−0.739052	−	0.673648i	$-0.764726\pi$
$821$	−42.3523	−1.47810	−0.739052	+	0.673648i	$0.764726\pi$
$822$	28.8242	1.00536
$823$	−25.6597	−0.894442	−0.447221	−	0.894423i	$-0.647586\pi$
$823$	−25.6597	−0.894442	−0.447221	+	0.894423i	$0.647586\pi$
$824$	−35.6974	−1.24358
$825$	−2.93438	−0.102162
$826$	24.2549	0.843937
$827$	−57.0740	−1.98466	−0.992329	−	0.123626i	$-0.960548\pi$
$827$	−57.0740	−1.98466	−0.992329	+	0.123626i	$0.960548\pi$
$828$	−1.78973	−0.0621975
$829$	−30.3330	−1.05351	−0.526755	−	0.850017i	$-0.676591\pi$
$829$	−30.3330	−1.05351	−0.526755	+	0.850017i	$0.676591\pi$
$830$	−8.05901	−0.279732
$831$	23.8357	0.826850
$832$	−10.7553	−0.372872
$833$	−13.9789	−0.484339
$834$	−15.2458	−0.527917
$835$	−5.03559	−0.174264
$836$	11.7833	0.407534
$837$	−39.9162	−1.37971
$838$	−19.6749	−0.679657
$839$	−43.4477	−1.49998	−0.749990	−	0.661449i	$-0.769942\pi$
$839$	−43.4477	−1.49998	−0.749990	+	0.661449i	$0.769942\pi$
$840$	9.47531	0.326929
$841$	−26.0661	−0.898830
$842$	−32.9256	−1.13469
$843$	−21.5040	−0.740637
$844$	−3.30758	−0.113852
$845$	−4.52146	−0.155543
$846$	−2.35713	−0.0810397
$847$	−7.66142	−0.263250
$848$	19.3278	0.663721
$849$	−19.6310	−0.673734
$850$	1.63901	0.0562174
$851$	4.61692	0.158266
$852$	0.659445	0.0225922
$853$	23.1042	0.791074	0.395537	−	0.918450i	$-0.370559\pi$
$853$	23.1042	0.791074	0.395537	+	0.918450i	$0.370559\pi$
$854$	71.8978	2.46029
$855$	11.6749	0.399272
$856$	−2.23001	−0.0762201
$857$	19.2439	0.657361	0.328680	−	0.944441i	$-0.393396\pi$
$857$	19.2439	0.657361	0.328680	+	0.944441i	$0.393396\pi$
$858$	−14.0042	−0.478095
$859$	−24.5578	−0.837901	−0.418951	−	0.908009i	$-0.637602\pi$
$859$	−24.5578	−0.837901	−0.418951	+	0.908009i	$0.637602\pi$
$860$	−6.49061	−0.221328
$861$	53.8632	1.83565
$862$	−34.5980	−1.17841
$863$	6.13016	0.208673	0.104337	−	0.994542i	$-0.466728\pi$
$863$	6.13016	0.208673	0.104337	+	0.994542i	$0.466728\pi$
$864$	−18.1828	−0.618591
$865$	−0.714035	−0.0242779
$866$	−29.2426	−0.993704
$867$	0.960813	0.0326309
$868$	25.7246	0.873148
$869$	−1.31147	−0.0444887
$870$	2.69739	0.0914501
$871$	−16.7977	−0.569169
$872$	−11.2617	−0.381369
$873$	7.56140	0.255915
$874$	11.5685	0.391309
$875$	4.58027	0.154841
$876$	−1.18319	−0.0399764
$877$	−35.2444	−1.19012	−0.595059	−	0.803682i	$-0.702871\pi$
$877$	−35.2444	−1.19012	−0.595059	+	0.803682i	$0.702871\pi$
$878$	−36.0241	−1.21575
$879$	27.9410	0.942427
$880$	14.9698	0.504633
$881$	−16.4830	−0.555326	−0.277663	−	0.960679i	$-0.589560\pi$
$881$	−16.4830	−0.555326	−0.277663	+	0.960679i	$0.589560\pi$
$882$	47.5834	1.60222
$883$	−9.87811	−0.332425	−0.166212	−	0.986090i	$-0.553154\pi$
$883$	−9.87811	−0.332425	−0.166212	+	0.986090i	$0.553154\pi$
$884$	1.99848	0.0672162
$885$	−3.10433	−0.104351
$886$	32.5355	1.09305
$887$	24.6300	0.826993	0.413496	−	0.910506i	$-0.364307\pi$
$887$	24.6300	0.826993	0.413496	+	0.910506i	$0.364307\pi$
$888$	7.60691	0.255271
$889$	−0.135423	−0.00454194
$890$	21.5025	0.720767
$891$	−4.71477	−0.157951
$892$	−11.8730	−0.397539
$893$	3.89269	0.130264
$894$	−8.09122	−0.270611
$895$	1.47936	0.0494497
$896$	−61.8756	−2.06712
$897$	−3.51274	−0.117287
$898$	−15.6686	−0.522869
$899$	−14.0166	−0.467478
$900$	−1.42542	−0.0475139
$901$	3.94316	0.131366
$902$	61.2662	2.03994
$903$	−41.6175	−1.38494
$904$	−10.1888	−0.338876
$905$	−4.15150	−0.138000
$906$	16.4619	0.546911
$907$	13.1052	0.435152	0.217576	−	0.976043i	$-0.430185\pi$
$907$	13.1052	0.435152	0.217576	+	0.976043i	$0.430185\pi$
$908$	−12.2671	−0.407098
$909$	13.7678	0.456648
$910$	21.8591	0.724622
$911$	−51.5286	−1.70722	−0.853609	−	0.520914i	$-0.825591\pi$
$911$	−51.5286	−1.70722	−0.853609	+	0.520914i	$0.825591\pi$
$912$	26.4745	0.876658
$913$	−15.0169	−0.496986
$914$	−23.3187	−0.771314
$915$	−9.20202	−0.304209
$916$	−9.29444	−0.307097
$917$	18.6228	0.614979
$918$	−7.99490	−0.263871
$919$	10.0572	0.331758	0.165879	−	0.986146i	$-0.446954\pi$
$919$	10.0572	0.331758	0.165879	+	0.986146i	$0.446954\pi$
$920$	2.70340	0.0891283
$921$	−22.2886	−0.734435
$922$	−30.4537	−1.00294
$923$	−2.91179	−0.0958429
$924$	−9.22460	−0.303467
$925$	3.67710	0.120902
$926$	34.4355	1.13162
$927$	34.4331	1.13093
$928$	−6.38487	−0.209594
$929$	−53.8353	−1.76628	−0.883139	−	0.469111i	$-0.844575\pi$
$929$	−53.8353	−1.76628	−0.883139	+	0.469111i	$0.844575\pi$
$930$	−12.8866	−0.422567
$931$	−78.5817	−2.57541
$932$	−8.73278	−0.286052
$933$	−30.8629	−1.01040
$934$	30.9608	1.01307
$935$	3.05406	0.0998785
$936$	13.0205	0.425587
$937$	1.44457	0.0471922	0.0235961	−	0.999722i	$-0.492488\pi$
$937$	1.44457	0.0471922	0.0235961	+	0.999722i	$0.492488\pi$
$938$	−43.3073	−1.41403
$939$	−11.7826	−0.384510
$940$	−0.475269	−0.0155016
$941$	−12.2889	−0.400607	−0.200304	−	0.979734i	$-0.564193\pi$
$941$	−12.2889	−0.400607	−0.200304	+	0.979734i	$0.564193\pi$
$942$	30.1636	0.982783
$943$	15.3677	0.500441
$944$	15.8368	0.515444
$945$	−22.3421	−0.726787
$946$	−47.3374	−1.53907
$947$	20.7123	0.673060	0.336530	−	0.941673i	$-0.390747\pi$
$947$	20.7123	0.673060	0.336530	+	0.941673i	$0.390747\pi$
$948$	0.283179	0.00919722
$949$	5.22442	0.169592
$950$	9.21361	0.298929
$951$	13.9445	0.452181
$952$	−9.86176	−0.319621
$953$	−56.5318	−1.83124	−0.915622	−	0.402041i	$-0.868301\pi$
$953$	−56.5318	−1.83124	−0.915622	+	0.402041i	$0.868301\pi$
$954$	−13.4223	−0.434563
$955$	1.54877	0.0501170
$956$	4.84627	0.156739
$957$	5.02622	0.162474
$958$	−10.7894	−0.348589
$959$	−83.8356	−2.70719
$960$	3.54895	0.114542
$961$	35.9629	1.16009
$962$	17.5488	0.565795
$963$	2.15103	0.0693158
$964$	−19.4487	−0.626401
$965$	−3.26029	−0.104952
$966$	−9.05643	−0.291386
$967$	50.0182	1.60848	0.804238	−	0.594307i	$-0.202574\pi$
$967$	50.0182	1.60848	0.804238	+	0.594307i	$0.202574\pi$
$968$	−3.60149	−0.115756
$969$	5.40118	0.173511
$970$	5.96733	0.191599
$971$	−14.9899	−0.481048	−0.240524	−	0.970643i	$-0.577319\pi$
$971$	−14.9899	−0.481048	−0.240524	+	0.970643i	$0.577319\pi$
$972$	11.0617	0.354805
$973$	44.3425	1.42156
$974$	−10.3575	−0.331877
$975$	−2.79769	−0.0895978
$976$	46.9444	1.50265
$977$	39.7301	1.27108	0.635538	−	0.772069i	$-0.280778\pi$
$977$	39.7301	1.27108	0.635538	+	0.772069i	$0.280778\pi$
$978$	4.73598	0.151440
$979$	40.0670	1.28055
$980$	9.59426	0.306477
$981$	10.8628	0.346824
$982$	17.3152	0.552550
$983$	25.0661	0.799484	0.399742	−	0.916628i	$-0.369100\pi$
$983$	25.0661	0.799484	0.399742	+	0.916628i	$0.369100\pi$
$984$	25.3201	0.807174
$985$	27.8250	0.886578
$986$	−2.80740	−0.0894059
$987$	−3.04740	−0.0970000
$988$	11.2344	0.357414
$989$	−11.8739	−0.377567
$990$	−10.3959	−0.330403
$991$	13.3213	0.423165	0.211583	−	0.977360i	$-0.432138\pi$
$991$	13.3213	0.423165	0.211583	+	0.977360i	$0.432138\pi$
$992$	30.5032	0.968477
$993$	−30.5303	−0.968849
$994$	−7.50709	−0.238110
$995$	20.3351	0.644667
$996$	3.24250	0.102743
$997$	−7.85769	−0.248856	−0.124428	−	0.992229i	$-0.539710\pi$
$997$	−7.85769	−0.248856	−0.124428	+	0.992229i	$0.539710\pi$
$998$	50.2154	1.58954
$999$	−17.9365	−0.567486

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6035.2.a.b.1.8	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6035.2.a.b.1.8	✓	36	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)

\(f(q)\)	\(=\)	\(q-1.63901 q^{2} +0.960813 q^{3} +0.686340 q^{4} +1.00000 q^{5} -1.57478 q^{6} +4.58027 q^{7} +2.15310 q^{8} -2.07684 q^{9} +O(q^{10})\)	\(q-1.63901 q^{2} +0.960813 q^{3} +0.686340 q^{4} +1.00000 q^{5} -1.57478 q^{6} +4.58027 q^{7} +2.15310 q^{8} -2.07684 q^{9} -1.63901 q^{10} -3.05406 q^{11} +0.659445 q^{12} -2.91179 q^{13} -7.50709 q^{14} +0.960813 q^{15} -4.90162 q^{16} -1.00000 q^{17} +3.40395 q^{18} -5.62146 q^{19} +0.686340 q^{20} +4.40078 q^{21} +5.00563 q^{22} +1.25559 q^{23} +2.06872 q^{24} +1.00000 q^{25} +4.77245 q^{26} -4.87789 q^{27} +3.14362 q^{28} -1.71287 q^{29} -1.57478 q^{30} +8.18309 q^{31} +3.72759 q^{32} -2.93438 q^{33} +1.63901 q^{34} +4.58027 q^{35} -1.42542 q^{36} +3.67710 q^{37} +9.21361 q^{38} -2.79769 q^{39} +2.15310 q^{40} +12.2395 q^{41} -7.21291 q^{42} -9.45683 q^{43} -2.09613 q^{44} -2.07684 q^{45} -2.05791 q^{46} -0.692469 q^{47} -4.70954 q^{48} +13.9789 q^{49} -1.63901 q^{50} -0.960813 q^{51} -1.99848 q^{52} -3.94316 q^{53} +7.99490 q^{54} -3.05406 q^{55} +9.86176 q^{56} -5.40118 q^{57} +2.80740 q^{58} -3.23094 q^{59} +0.659445 q^{60} -9.57732 q^{61} -13.4121 q^{62} -9.51248 q^{63} +3.69370 q^{64} -2.91179 q^{65} +4.80947 q^{66} +5.76886 q^{67} -0.686340 q^{68} +1.20638 q^{69} -7.50709 q^{70} +1.00000 q^{71} -4.47163 q^{72} -1.79423 q^{73} -6.02679 q^{74} +0.960813 q^{75} -3.85824 q^{76} -13.9884 q^{77} +4.58543 q^{78} +0.429420 q^{79} -4.90162 q^{80} +1.54377 q^{81} -20.0606 q^{82} +4.91701 q^{83} +3.02044 q^{84} -1.00000 q^{85} +15.4998 q^{86} -1.64575 q^{87} -6.57569 q^{88} -13.1193 q^{89} +3.40395 q^{90} -13.3368 q^{91} +0.861759 q^{92} +7.86242 q^{93} +1.13496 q^{94} -5.62146 q^{95} +3.58152 q^{96} -3.64082 q^{97} -22.9114 q^{98} +6.34279 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{2} - 4 q^{3} + 23 q^{4} + 36 q^{5} - 2 q^{6} - 7 q^{7} - 3 q^{8} + 10 q^{9}+O(q^{10}) \) 36 * q - q^2 - 4 * q^3 + 23 * q^4 + 36 * q^5 - 2 * q^6 - 7 * q^7 - 3 * q^8 + 10 * q^9	\( 36 q - q^{2} - 4 q^{3} + 23 q^{4} + 36 q^{5} - 2 q^{6} - 7 q^{7} - 3 q^{8} + 10 q^{9} - q^{10} - 22 q^{11} - 14 q^{12} - 15 q^{13} - 28 q^{14} - 4 q^{15} + q^{16} - 36 q^{17} - 12 q^{18} - 23 q^{19} + 23 q^{20} - 21 q^{21} + 2 q^{23} - 13 q^{24} + 36 q^{25} - 18 q^{26} - 13 q^{27} - 20 q^{28} - 4 q^{29} - 2 q^{30} - 43 q^{31} - 2 q^{32} - 19 q^{33} + q^{34} - 7 q^{35} - 35 q^{36} - 30 q^{37} - 11 q^{38} - 20 q^{39} - 3 q^{40} - 39 q^{41} + 2 q^{42} - 7 q^{43} - 45 q^{44} + 10 q^{45} - 52 q^{46} - 12 q^{47} - 12 q^{48} - 15 q^{49} - q^{50} + 4 q^{51} - 19 q^{52} - 31 q^{53} + 48 q^{54} - 22 q^{55} - 30 q^{56} + 18 q^{57} - 12 q^{58} - 66 q^{59} - 14 q^{60} - 93 q^{61} - 7 q^{62} - 22 q^{63} - 41 q^{64} - 15 q^{65} - 21 q^{66} - 19 q^{67} - 23 q^{68} - 73 q^{69} - 28 q^{70} + 36 q^{71} - q^{72} - 47 q^{73} - 27 q^{74} - 4 q^{75} - 56 q^{76} - 9 q^{77} - 78 q^{78} - 21 q^{79} + q^{80} - 40 q^{81} - 15 q^{82} - 8 q^{83} - 54 q^{84} - 36 q^{85} - 17 q^{86} - 32 q^{87} - 13 q^{88} - 62 q^{89} - 12 q^{90} - 33 q^{91} + 42 q^{92} - 24 q^{93} - 40 q^{94} - 23 q^{95} + 21 q^{96} - 60 q^{97} + 11 q^{98} - 65 q^{99}+O(q^{100}) \) 36 * q - q^2 - 4 * q^3 + 23 * q^4 + 36 * q^5 - 2 * q^6 - 7 * q^7 - 3 * q^8 + 10 * q^9 - q^10 - 22 * q^11 - 14 * q^12 - 15 * q^13 - 28 * q^14 - 4 * q^15 + q^16 - 36 * q^17 - 12 * q^18 - 23 * q^19 + 23 * q^20 - 21 * q^21 + 2 * q^23 - 13 * q^24 + 36 * q^25 - 18 * q^26 - 13 * q^27 - 20 * q^28 - 4 * q^29 - 2 * q^30 - 43 * q^31 - 2 * q^32 - 19 * q^33 + q^34 - 7 * q^35 - 35 * q^36 - 30 * q^37 - 11 * q^38 - 20 * q^39 - 3 * q^40 - 39 * q^41 + 2 * q^42 - 7 * q^43 - 45 * q^44 + 10 * q^45 - 52 * q^46 - 12 * q^47 - 12 * q^48 - 15 * q^49 - q^50 + 4 * q^51 - 19 * q^52 - 31 * q^53 + 48 * q^54 - 22 * q^55 - 30 * q^56 + 18 * q^57 - 12 * q^58 - 66 * q^59 - 14 * q^60 - 93 * q^61 - 7 * q^62 - 22 * q^63 - 41 * q^64 - 15 * q^65 - 21 * q^66 - 19 * q^67 - 23 * q^68 - 73 * q^69 - 28 * q^70 + 36 * q^71 - q^72 - 47 * q^73 - 27 * q^74 - 4 * q^75 - 56 * q^76 - 9 * q^77 - 78 * q^78 - 21 * q^79 + q^80 - 40 * q^81 - 15 * q^82 - 8 * q^83 - 54 * q^84 - 36 * q^85 - 17 * q^86 - 32 * q^87 - 13 * q^88 - 62 * q^89 - 12 * q^90 - 33 * q^91 + 42 * q^92 - 24 * q^93 - 40 * q^94 - 23 * q^95 + 21 * q^96 - 60 * q^97 + 11 * q^98 - 65 * q^99

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