LMFDB - Embedded newform 6035.2.a.g.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("6035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.1897176198$
Analytic rank:	$0$
Dimension:	$58$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
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)

$f(q)$	$=$	$q-1.22218 q^{2} -2.16829 q^{3} -0.506288 q^{4} +1.00000 q^{5} +2.65003 q^{6} -1.52570 q^{7} +3.06312 q^{8} +1.70146 q^{9} +O(q^{10})$	\(q-1.22218 q^{2} -2.16829 q^{3} -0.506288 q^{4} +1.00000 q^{5} +2.65003 q^{6} -1.52570 q^{7} +3.06312 q^{8} +1.70146 q^{9} -1.22218 q^{10} +1.36364 q^{11} +1.09778 q^{12} -4.03684 q^{13} +1.86467 q^{14} -2.16829 q^{15} -2.73110 q^{16} +1.00000 q^{17} -2.07949 q^{18} +3.43089 q^{19} -0.506288 q^{20} +3.30816 q^{21} -1.66661 q^{22} -3.45978 q^{23} -6.64173 q^{24} +1.00000 q^{25} +4.93373 q^{26} +2.81560 q^{27} +0.772444 q^{28} +1.17126 q^{29} +2.65003 q^{30} +6.53982 q^{31} -2.78837 q^{32} -2.95677 q^{33} -1.22218 q^{34} -1.52570 q^{35} -0.861430 q^{36} +2.47264 q^{37} -4.19314 q^{38} +8.75303 q^{39} +3.06312 q^{40} -4.20597 q^{41} -4.04315 q^{42} -7.29130 q^{43} -0.690395 q^{44} +1.70146 q^{45} +4.22846 q^{46} +0.814588 q^{47} +5.92180 q^{48} -4.67224 q^{49} -1.22218 q^{50} -2.16829 q^{51} +2.04380 q^{52} +4.18387 q^{53} -3.44115 q^{54} +1.36364 q^{55} -4.67341 q^{56} -7.43914 q^{57} -1.43149 q^{58} +10.6756 q^{59} +1.09778 q^{60} -7.52132 q^{61} -7.99280 q^{62} -2.59593 q^{63} +8.87007 q^{64} -4.03684 q^{65} +3.61369 q^{66} +1.96847 q^{67} -0.506288 q^{68} +7.50180 q^{69} +1.86467 q^{70} +1.00000 q^{71} +5.21179 q^{72} -4.11228 q^{73} -3.02200 q^{74} -2.16829 q^{75} -1.73702 q^{76} -2.08051 q^{77} -10.6977 q^{78} +8.96779 q^{79} -2.73110 q^{80} -11.2094 q^{81} +5.14043 q^{82} -4.19715 q^{83} -1.67488 q^{84} +1.00000 q^{85} +8.91124 q^{86} -2.53964 q^{87} +4.17700 q^{88} +10.7285 q^{89} -2.07949 q^{90} +6.15902 q^{91} +1.75165 q^{92} -14.1802 q^{93} -0.995569 q^{94} +3.43089 q^{95} +6.04598 q^{96} -6.04849 q^{97} +5.71029 q^{98} +2.32019 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 58 q + q^{2} + 6 q^{3} + 69 q^{4} + 58 q^{5} + 10 q^{6} + 13 q^{7} - 3 q^{8} + 84 q^{9}+O(q^{10}) $ 58 * q + q^2 + 6 * q^3 + 69 * q^4 + 58 * q^5 + 10 * q^6 + 13 * q^7 - 3 * q^8 + 84 * q^9	\( 58 q + q^{2} + 6 q^{3} + 69 q^{4} + 58 q^{5} + 10 q^{6} + 13 q^{7} - 3 q^{8} + 84 q^{9} + q^{10} + 28 q^{11} + 18 q^{12} + 37 q^{13} + 28 q^{14} + 6 q^{15} + 83 q^{16} + 58 q^{17} - 12 q^{18} + 19 q^{19} + 69 q^{20} + 31 q^{21} + 13 q^{22} + 14 q^{23} + 13 q^{24} + 58 q^{25} + 18 q^{26} + 9 q^{27} + 8 q^{28} + 60 q^{29} + 10 q^{30} + 39 q^{31} - 30 q^{32} + 13 q^{33} + q^{34} + 13 q^{35} + 113 q^{36} + 60 q^{37} - q^{38} + 41 q^{39} - 3 q^{40} + 65 q^{41} - 30 q^{42} + 17 q^{43} + 69 q^{44} + 84 q^{45} + 24 q^{46} + 16 q^{47} + 14 q^{48} + 117 q^{49} + q^{50} + 6 q^{51} + 61 q^{52} + 5 q^{53} + 24 q^{54} + 28 q^{55} + 105 q^{56} + 8 q^{57} - 34 q^{58} + 22 q^{59} + 18 q^{60} + 113 q^{61} - 19 q^{62} + 8 q^{63} + 89 q^{64} + 37 q^{65} - 37 q^{66} + 19 q^{67} + 69 q^{68} + 75 q^{69} + 28 q^{70} + 58 q^{71} - 17 q^{72} + 49 q^{73} + 29 q^{74} + 6 q^{75} - 6 q^{76} + 17 q^{77} - 12 q^{78} + 7 q^{79} + 83 q^{80} + 134 q^{81} + 7 q^{82} - 12 q^{83} - 18 q^{84} + 58 q^{85} + 23 q^{86} - 36 q^{87} - 33 q^{88} + 52 q^{89} - 12 q^{90} + 31 q^{91} + 80 q^{92} - 37 q^{93} + 4 q^{94} + 19 q^{95} - 35 q^{96} + 26 q^{97} - 33 q^{98} + 57 q^{99}+O(q^{100}) \) 58 * q + q^2 + 6 * q^3 + 69 * q^4 + 58 * q^5 + 10 * q^6 + 13 * q^7 - 3 * q^8 + 84 * q^9 + q^10 + 28 * q^11 + 18 * q^12 + 37 * q^13 + 28 * q^14 + 6 * q^15 + 83 * q^16 + 58 * q^17 - 12 * q^18 + 19 * q^19 + 69 * q^20 + 31 * q^21 + 13 * q^22 + 14 * q^23 + 13 * q^24 + 58 * q^25 + 18 * q^26 + 9 * q^27 + 8 * q^28 + 60 * q^29 + 10 * q^30 + 39 * q^31 - 30 * q^32 + 13 * q^33 + q^34 + 13 * q^35 + 113 * q^36 + 60 * q^37 - q^38 + 41 * q^39 - 3 * q^40 + 65 * q^41 - 30 * q^42 + 17 * q^43 + 69 * q^44 + 84 * q^45 + 24 * q^46 + 16 * q^47 + 14 * q^48 + 117 * q^49 + q^50 + 6 * q^51 + 61 * q^52 + 5 * q^53 + 24 * q^54 + 28 * q^55 + 105 * q^56 + 8 * q^57 - 34 * q^58 + 22 * q^59 + 18 * q^60 + 113 * q^61 - 19 * q^62 + 8 * q^63 + 89 * q^64 + 37 * q^65 - 37 * q^66 + 19 * q^67 + 69 * q^68 + 75 * q^69 + 28 * q^70 + 58 * q^71 - 17 * q^72 + 49 * q^73 + 29 * q^74 + 6 * q^75 - 6 * q^76 + 17 * q^77 - 12 * q^78 + 7 * q^79 + 83 * q^80 + 134 * q^81 + 7 * q^82 - 12 * q^83 - 18 * q^84 + 58 * q^85 + 23 * q^86 - 36 * q^87 - 33 * q^88 + 52 * q^89 - 12 * q^90 + 31 * q^91 + 80 * q^92 - 37 * q^93 + 4 * q^94 + 19 * q^95 - 35 * q^96 + 26 * q^97 - 33 * q^98 + 57 * 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 $

$2$	−1.22218	−0.864208	−0.432104	−	0.901824i	$-0.642229\pi$
$2$	−1.22218	−0.864208	−0.432104	+	0.901824i	$0.642229\pi$
$3$	−2.16829	−1.25186	−0.625930	−	0.779879i	$-0.715281\pi$
$3$	−2.16829	−1.25186	−0.625930	+	0.779879i	$0.715281\pi$
$4$	−0.506288	−0.253144
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.65003	1.08187
$7$	−1.52570	−0.576661	−0.288330	−	0.957531i	$-0.593100\pi$
$7$	−1.52570	−0.576661	−0.288330	+	0.957531i	$0.593100\pi$
$8$	3.06312	1.08298
$9$	1.70146	0.567155
$10$	−1.22218	−0.386486
$11$	1.36364	0.411154	0.205577	−	0.978641i	$-0.434093\pi$
$11$	1.36364	0.411154	0.205577	+	0.978641i	$0.434093\pi$
$12$	1.09778	0.316901
$13$	−4.03684	−1.11962	−0.559810	−	0.828621i	$-0.689126\pi$
$13$	−4.03684	−1.11962	−0.559810	+	0.828621i	$0.689126\pi$
$14$	1.86467	0.498355
$15$	−2.16829	−0.559849
$16$	−2.73110	−0.682774
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.07949	−0.490140
$19$	3.43089	0.787099	0.393550	−	0.919303i	$-0.371247\pi$
$19$	3.43089	0.787099	0.393550	+	0.919303i	$0.371247\pi$
$20$	−0.506288	−0.113209
$21$	3.30816	0.721899
$22$	−1.66661	−0.355322
$23$	−3.45978	−0.721415	−0.360707	−	0.932679i	$-0.617465\pi$
$23$	−3.45978	−0.721415	−0.360707	+	0.932679i	$0.617465\pi$
$24$	−6.64173	−1.35574
$25$	1.00000	0.200000
$26$	4.93373	0.967584
$27$	2.81560	0.541862
$28$	0.772444	0.145978
$29$	1.17126	0.217498	0.108749	−	0.994069i	$-0.465315\pi$
$29$	1.17126	0.217498	0.108749	+	0.994069i	$0.465315\pi$
$30$	2.65003	0.483826
$31$	6.53982	1.17459	0.587293	−	0.809374i	$-0.300194\pi$
$31$	6.53982	1.17459	0.587293	+	0.809374i	$0.300194\pi$
$32$	−2.78837	−0.492918
$33$	−2.95677	−0.514707
$34$	−1.22218	−0.209601
$35$	−1.52570	−0.257891
$36$	−0.861430	−0.143572
$37$	2.47264	0.406500	0.203250	−	0.979127i	$-0.434850\pi$
$37$	2.47264	0.406500	0.203250	+	0.979127i	$0.434850\pi$
$38$	−4.19314	−0.680218
$39$	8.75303	1.40161
$40$	3.06312	0.484322
$41$	−4.20597	−0.656862	−0.328431	−	0.944528i	$-0.606520\pi$
$41$	−4.20597	−0.656862	−0.328431	+	0.944528i	$0.606520\pi$
$42$	−4.04315	−0.623871
$43$	−7.29130	−1.11191	−0.555956	−	0.831212i	$-0.687648\pi$
$43$	−7.29130	−1.11191	−0.555956	+	0.831212i	$0.687648\pi$
$44$	−0.690395	−0.104081
$45$	1.70146	0.253639
$46$	4.22846	0.623453
$47$	0.814588	0.118820	0.0594099	−	0.998234i	$-0.481078\pi$
$47$	0.814588	0.118820	0.0594099	+	0.998234i	$0.481078\pi$
$48$	5.92180	0.854738
$49$	−4.67224	−0.667462
$50$	−1.22218	−0.172842
$51$	−2.16829	−0.303621
$52$	2.04380	0.283425
$53$	4.18387	0.574699	0.287350	−	0.957826i	$-0.407226\pi$
$53$	4.18387	0.574699	0.287350	+	0.957826i	$0.407226\pi$
$54$	−3.44115	−0.468282
$55$	1.36364	0.183873
$56$	−4.67341	−0.624511
$57$	−7.43914	−0.985338
$58$	−1.43149	−0.187964
$59$	10.6756	1.38985	0.694923	−	0.719084i	$-0.255438\pi$
$59$	10.6756	1.38985	0.694923	+	0.719084i	$0.255438\pi$
$60$	1.09778	0.141722
$61$	−7.52132	−0.963006	−0.481503	−	0.876444i	$-0.659909\pi$
$61$	−7.52132	−0.963006	−0.481503	+	0.876444i	$0.659909\pi$
$62$	−7.99280	−1.01509
$63$	−2.59593	−0.327056
$64$	8.87007	1.10876
$65$	−4.03684	−0.500709
$66$	3.61369	0.444814
$67$	1.96847	0.240486	0.120243	−	0.992744i	$-0.461633\pi$
$67$	1.96847	0.240486	0.120243	+	0.992744i	$0.461633\pi$
$68$	−0.506288	−0.0613964
$69$	7.50180	0.903111
$70$	1.86467	0.222871
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	5.21179	0.614216
$73$	−4.11228	−0.481306	−0.240653	−	0.970611i	$-0.577362\pi$
$73$	−4.11228	−0.481306	−0.240653	+	0.970611i	$0.577362\pi$
$74$	−3.02200	−0.351301
$75$	−2.16829	−0.250372
$76$	−1.73702	−0.199249
$77$	−2.08051	−0.237096
$78$	−10.6977	−1.21128
$79$	8.96779	1.00896	0.504478	−	0.863425i	$-0.331685\pi$
$79$	8.96779	1.00896	0.504478	+	0.863425i	$0.331685\pi$
$80$	−2.73110	−0.305346
$81$	−11.2094	−1.24549
$82$	5.14043	0.567666
$83$	−4.19715	−0.460697	−0.230349	−	0.973108i	$-0.573987\pi$
$83$	−4.19715	−0.460697	−0.230349	+	0.973108i	$0.573987\pi$
$84$	−1.67488	−0.182744
$85$	1.00000	0.108465
$86$	8.91124	0.960924
$87$	−2.53964	−0.272277
$88$	4.17700	0.445270
$89$	10.7285	1.13721	0.568607	−	0.822609i	$-0.307482\pi$
$89$	10.7285	1.13721	0.568607	+	0.822609i	$0.307482\pi$
$90$	−2.07949	−0.219197
$91$	6.15902	0.645640
$92$	1.75165	0.182622
$93$	−14.1802	−1.47042
$94$	−0.995569	−0.102685
$95$	3.43089	0.352001
$96$	6.04598	0.617065
$97$	−6.04849	−0.614131	−0.307066	−	0.951688i	$-0.599347\pi$
$97$	−6.04849	−0.614131	−0.307066	+	0.951688i	$0.599347\pi$
$98$	5.71029	0.576826
$99$	2.32019	0.233188
$100$	−0.506288	−0.0506288
$101$	7.85700	0.781800	0.390900	−	0.920433i	$-0.372164\pi$
$101$	7.85700	0.781800	0.390900	+	0.920433i	$0.372164\pi$
$102$	2.65003	0.262392
$103$	1.19804	0.118046	0.0590231	−	0.998257i	$-0.481201\pi$
$103$	1.19804	0.118046	0.0590231	+	0.998257i	$0.481201\pi$
$104$	−12.3653	−1.21252
$105$	3.30816	0.322843
$106$	−5.11343	−0.496660
$107$	3.15469	0.304975	0.152488	−	0.988305i	$-0.451272\pi$
$107$	3.15469	0.304975	0.152488	+	0.988305i	$0.451272\pi$
$108$	−1.42550	−0.137169
$109$	−1.07716	−0.103173	−0.0515864	−	0.998669i	$-0.516428\pi$
$109$	−1.07716	−0.103173	−0.0515864	+	0.998669i	$0.516428\pi$
$110$	−1.66661	−0.158905
$111$	−5.36140	−0.508882
$112$	4.16684	0.393729
$113$	12.1096	1.13918	0.569588	−	0.821931i	$-0.307103\pi$
$113$	12.1096	1.13918	0.569588	+	0.821931i	$0.307103\pi$
$114$	9.09193	0.851538
$115$	−3.45978	−0.322626
$116$	−0.592997	−0.0550584
$117$	−6.86854	−0.634997
$118$	−13.0475	−1.20112
$119$	−1.52570	−0.139861
$120$	−6.64173	−0.606304
$121$	−9.14048	−0.830953
$122$	9.19237	0.832238
$123$	9.11975	0.822300
$124$	−3.31103	−0.297339
$125$	1.00000	0.0894427
$126$	3.17268	0.282644
$127$	−6.02321	−0.534473	−0.267237	−	0.963631i	$-0.586110\pi$
$127$	−6.02321	−0.534473	−0.267237	+	0.963631i	$0.586110\pi$
$128$	−5.26404	−0.465280
$129$	15.8096	1.39196
$130$	4.93373	0.432717
$131$	−19.4053	−1.69545	−0.847724	−	0.530437i	$-0.822028\pi$
$131$	−19.4053	−1.69545	−0.847724	+	0.530437i	$0.822028\pi$
$132$	1.49697	0.130295
$133$	−5.23451	−0.453889
$134$	−2.40581	−0.207830
$135$	2.81560	0.242328
$136$	3.06312	0.262661
$137$	−5.62274	−0.480383	−0.240192	−	0.970726i	$-0.577210\pi$
$137$	−5.62274	−0.480383	−0.240192	+	0.970726i	$0.577210\pi$
$138$	−9.16851	−0.780476
$139$	−21.5708	−1.82961	−0.914806	−	0.403894i	$-0.867657\pi$
$139$	−21.5708	−1.82961	−0.914806	+	0.403894i	$0.867657\pi$
$140$	0.772444	0.0652834
$141$	−1.76626	−0.148746
$142$	−1.22218	−0.102563
$143$	−5.50481	−0.460335
$144$	−4.64686	−0.387239
$145$	1.17126	0.0972682
$146$	5.02593	0.415949
$147$	10.1307	0.835570
$148$	−1.25187	−0.102903
$149$	12.3180	1.00913	0.504563	−	0.863375i	$-0.331654\pi$
$149$	12.3180	1.00913	0.504563	+	0.863375i	$0.331654\pi$
$150$	2.65003	0.216374
$151$	−17.8624	−1.45363	−0.726813	−	0.686836i	$-0.758999\pi$
$151$	−17.8624	−1.45363	−0.726813	+	0.686836i	$0.758999\pi$
$152$	10.5092	0.852411
$153$	1.70146	0.137555
$154$	2.54275	0.204900
$155$	6.53982	0.525291
$156$	−4.43155	−0.354808
$157$	−14.7628	−1.17820	−0.589098	−	0.808061i	$-0.700517\pi$
$157$	−14.7628	−1.17820	−0.589098	+	0.808061i	$0.700517\pi$
$158$	−10.9602	−0.871948
$159$	−9.07183	−0.719443
$160$	−2.78837	−0.220440
$161$	5.27860	0.416012
$162$	13.6999	1.07636
$163$	−5.14164	−0.402724	−0.201362	−	0.979517i	$-0.564537\pi$
$163$	−5.14164	−0.402724	−0.201362	+	0.979517i	$0.564537\pi$
$164$	2.12943	0.166281
$165$	−2.95677	−0.230184
$166$	5.12965	0.398138
$167$	−4.86221	−0.376249	−0.188124	−	0.982145i	$-0.560241\pi$
$167$	−4.86221	−0.376249	−0.188124	+	0.982145i	$0.560241\pi$
$168$	10.1333	0.781800
$169$	3.29611	0.253547
$170$	−1.22218	−0.0937366
$171$	5.83753	0.446407
$172$	3.69150	0.281474
$173$	−19.6072	−1.49070	−0.745352	−	0.666671i	$-0.767719\pi$
$173$	−19.6072	−1.49070	−0.745352	+	0.666671i	$0.767719\pi$
$174$	3.10388	0.235304
$175$	−1.52570	−0.115332
$176$	−3.72424	−0.280725
$177$	−23.1478	−1.73989
$178$	−13.1121	−0.982791
$179$	−3.51877	−0.263005	−0.131503	−	0.991316i	$-0.541980\pi$
$179$	−3.51877	−0.263005	−0.131503	+	0.991316i	$0.541980\pi$
$180$	−0.861430	−0.0642072
$181$	19.0649	1.41709	0.708543	−	0.705668i	$-0.249353\pi$
$181$	19.0649	1.41709	0.708543	+	0.705668i	$0.249353\pi$
$182$	−7.52740	−0.557968
$183$	16.3084	1.20555
$184$	−10.5977	−0.781276
$185$	2.47264	0.181792
$186$	17.3307	1.27075
$187$	1.36364	0.0997194
$188$	−0.412416	−0.0300785
$189$	−4.29576	−0.312471
$190$	−4.19314	−0.304203
$191$	3.02121	0.218607	0.109304	−	0.994008i	$-0.465138\pi$
$191$	3.02121	0.218607	0.109304	+	0.994008i	$0.465138\pi$
$192$	−19.2328	−1.38801
$193$	4.87130	0.350644	0.175322	−	0.984511i	$-0.443903\pi$
$193$	4.87130	0.350644	0.175322	+	0.984511i	$0.443903\pi$
$194$	7.39231	0.530737
$195$	8.75303	0.626818
$196$	2.36550	0.168964
$197$	−4.06659	−0.289732	−0.144866	−	0.989451i	$-0.546275\pi$
$197$	−4.06659	−0.289732	−0.144866	+	0.989451i	$0.546275\pi$
$198$	−2.83568	−0.201523
$199$	11.9891	0.849888	0.424944	−	0.905220i	$-0.360294\pi$
$199$	11.9891	0.849888	0.424944	+	0.905220i	$0.360294\pi$
$200$	3.06312	0.216595
$201$	−4.26820	−0.301055
$202$	−9.60262	−0.675638
$203$	−1.78700	−0.125423
$204$	1.09778	0.0768597
$205$	−4.20597	−0.293758
$206$	−1.46421	−0.102017
$207$	−5.88670	−0.409154
$208$	11.0250	0.764447
$209$	4.67850	0.323619
$210$	−4.04315	−0.279004
$211$	−19.9325	−1.37221	−0.686104	−	0.727503i	$-0.740681\pi$
$211$	−19.9325	−1.37221	−0.686104	+	0.727503i	$0.740681\pi$
$212$	−2.11824	−0.145482
$213$	−2.16829	−0.148569
$214$	−3.85558	−0.263562
$215$	−7.29130	−0.497262
$216$	8.62452	0.586824
$217$	−9.97781	−0.677338
$218$	1.31647	0.0891628
$219$	8.91660	0.602528
$220$	−0.690395	−0.0465464
$221$	−4.03684	−0.271548
$222$	6.55257	0.439780
$223$	−16.4921	−1.10439	−0.552196	−	0.833714i	$-0.686210\pi$
$223$	−16.4921	−1.10439	−0.552196	+	0.833714i	$0.686210\pi$
$224$	4.25421	0.284247
$225$	1.70146	0.113431
$226$	−14.8001	−0.984485
$227$	−29.2000	−1.93807	−0.969035	−	0.246923i	$-0.920581\pi$
$227$	−29.2000	−1.93807	−0.969035	+	0.246923i	$0.920581\pi$
$228$	3.76635	0.249432
$229$	−1.38219	−0.0913377	−0.0456689	−	0.998957i	$-0.514542\pi$
$229$	−1.38219	−0.0913377	−0.0456689	+	0.998957i	$0.514542\pi$
$230$	4.22846	0.278817
$231$	4.51114	0.296811
$232$	3.58773	0.235546
$233$	9.44086	0.618491	0.309246	−	0.950982i	$-0.399923\pi$
$233$	9.44086	0.618491	0.309246	+	0.950982i	$0.399923\pi$
$234$	8.39457	0.548770
$235$	0.814588	0.0531379
$236$	−5.40493	−0.351831
$237$	−19.4447	−1.26307
$238$	1.86467	0.120869
$239$	−8.17391	−0.528726	−0.264363	−	0.964423i	$-0.585162\pi$
$239$	−8.17391	−0.528726	−0.264363	+	0.964423i	$0.585162\pi$
$240$	5.92180	0.382251
$241$	28.4862	1.83495	0.917477	−	0.397788i	$-0.130222\pi$
$241$	28.4862	1.83495	0.917477	+	0.397788i	$0.130222\pi$
$242$	11.1713	0.718116
$243$	15.8584	1.01732
$244$	3.80795	0.243779
$245$	−4.67224	−0.298498
$246$	−11.1459	−0.710639
$247$	−13.8499	−0.881251
$248$	20.0323	1.27205
$249$	9.10062	0.576729
$250$	−1.22218	−0.0772971
$251$	16.6095	1.04838	0.524190	−	0.851601i	$-0.324368\pi$
$251$	16.6095	1.04838	0.524190	+	0.851601i	$0.324368\pi$
$252$	1.31429	0.0827922
$253$	−4.71791	−0.296612
$254$	7.36141	0.461896
$255$	−2.16829	−0.135783
$256$	−11.3066	−0.706659
$257$	25.3809	1.58322	0.791608	−	0.611029i	$-0.209244\pi$
$257$	25.3809	1.58322	0.791608	+	0.611029i	$0.209244\pi$
$258$	−19.3221	−1.20294
$259$	−3.77252	−0.234413
$260$	2.04380	0.126751
$261$	1.99286	0.123355
$262$	23.7167	1.46522
$263$	−0.141150	−0.00870371	−0.00435185	−	0.999991i	$-0.501385\pi$
$263$	−0.141150	−0.00870371	−0.00435185	+	0.999991i	$0.501385\pi$
$264$	−9.05694	−0.557416
$265$	4.18387	0.257013
$266$	6.39748	0.392255
$267$	−23.2624	−1.42363
$268$	−0.996610	−0.0608776
$269$	29.5488	1.80162	0.900810	−	0.434214i	$-0.142974\pi$
$269$	29.5488	1.80162	0.900810	+	0.434214i	$0.142974\pi$
$270$	−3.44115	−0.209422
$271$	−16.2598	−0.987710	−0.493855	−	0.869544i	$-0.664413\pi$
$271$	−16.2598	−0.987710	−0.493855	+	0.869544i	$0.664413\pi$
$272$	−2.73110	−0.165597
$273$	−13.3545	−0.808252
$274$	6.87197	0.415151
$275$	1.36364	0.0822307
$276$	−3.79807	−0.228617
$277$	−15.4474	−0.928145	−0.464073	−	0.885797i	$-0.653612\pi$
$277$	−15.4474	−0.928145	−0.464073	+	0.885797i	$0.653612\pi$
$278$	26.3633	1.58117
$279$	11.1273	0.666172
$280$	−4.67341	−0.279290
$281$	7.50354	0.447624	0.223812	−	0.974632i	$-0.428150\pi$
$281$	7.50354	0.447624	0.223812	+	0.974632i	$0.428150\pi$
$282$	2.15868	0.128547
$283$	−8.72460	−0.518624	−0.259312	−	0.965794i	$-0.583496\pi$
$283$	−8.72460	−0.518624	−0.259312	+	0.965794i	$0.583496\pi$
$284$	−0.506288	−0.0300427
$285$	−7.43914	−0.440657
$286$	6.72784	0.397826
$287$	6.41706	0.378787
$288$	−4.74431	−0.279561
$289$	1.00000	0.0588235
$290$	−1.43149	−0.0840600
$291$	13.1149	0.768806
$292$	2.08200	0.121840
$293$	28.2610	1.65102	0.825511	−	0.564386i	$-0.190887\pi$
$293$	28.2610	1.65102	0.825511	+	0.564386i	$0.190887\pi$
$294$	−12.3815	−0.722106
$295$	10.6756	0.621558
$296$	7.57401	0.440231
$297$	3.83947	0.222788
$298$	−15.0547	−0.872095
$299$	13.9666	0.807710
$300$	1.09778	0.0633802
$301$	11.1243	0.641196
$302$	21.8310	1.25624
$303$	−17.0362	−0.978705
$304$	−9.37008	−0.537411
$305$	−7.52132	−0.430670
$306$	−2.07949	−0.118876
$307$	2.09087	0.119332	0.0596661	−	0.998218i	$-0.480996\pi$
$307$	2.09087	0.119332	0.0596661	+	0.998218i	$0.480996\pi$
$308$	1.05334	0.0600194
$309$	−2.59769	−0.147777
$310$	−7.99280	−0.453961
$311$	0.976329	0.0553625	0.0276813	−	0.999617i	$-0.491188\pi$
$311$	0.976329	0.0553625	0.0276813	+	0.999617i	$0.491188\pi$
$312$	26.8116	1.51791
$313$	1.32778	0.0750508	0.0375254	−	0.999296i	$-0.488052\pi$
$313$	1.32778	0.0750508	0.0375254	+	0.999296i	$0.488052\pi$
$314$	18.0427	1.01821
$315$	−2.59593	−0.146264
$316$	−4.54028	−0.255411
$317$	17.6204	0.989662	0.494831	−	0.868989i	$-0.335230\pi$
$317$	17.6204	0.989662	0.494831	+	0.868989i	$0.335230\pi$
$318$	11.0874	0.621749
$319$	1.59718	0.0894252
$320$	8.87007	0.495852
$321$	−6.84027	−0.381786
$322$	−6.45137	−0.359521
$323$	3.43089	0.190900
$324$	5.67519	0.315288
$325$	−4.03684	−0.223924
$326$	6.28398	0.348037
$327$	2.33558	0.129158
$328$	−12.8834	−0.711367
$329$	−1.24282	−0.0685188
$330$	3.61369	0.198927
$331$	23.2480	1.27782	0.638912	−	0.769280i	$-0.279385\pi$
$331$	23.2480	1.27782	0.638912	+	0.769280i	$0.279385\pi$
$332$	2.12497	0.116623
$333$	4.20712	0.230549
$334$	5.94247	0.325157
$335$	1.96847	0.107549
$336$	−9.03490	−0.492894
$337$	24.7260	1.34691	0.673457	−	0.739227i	$-0.264809\pi$
$337$	24.7260	1.34691	0.673457	+	0.739227i	$0.264809\pi$
$338$	−4.02842	−0.219117
$339$	−26.2571	−1.42609
$340$	−0.506288	−0.0274573
$341$	8.91797	0.482935
$342$	−7.13448	−0.385789
$343$	17.8083	0.961560
$344$	−22.3341	−1.20418
$345$	7.50180	0.403883
$346$	23.9634	1.28828
$347$	−19.0824	−1.02440	−0.512199	−	0.858867i	$-0.671169\pi$
$347$	−19.0824	−1.02440	−0.512199	+	0.858867i	$0.671169\pi$
$348$	1.28579	0.0689254
$349$	21.6006	1.15625	0.578127	−	0.815947i	$-0.303784\pi$
$349$	21.6006	1.15625	0.578127	+	0.815947i	$0.303784\pi$
$350$	1.86467	0.0996710
$351$	−11.3661	−0.606679
$352$	−3.80233	−0.202665
$353$	12.7854	0.680497	0.340249	−	0.940336i	$-0.389489\pi$
$353$	12.7854	0.680497	0.340249	+	0.940336i	$0.389489\pi$
$354$	28.2906	1.50363
$355$	1.00000	0.0530745
$356$	−5.43169	−0.287879
$357$	3.30816	0.175086
$358$	4.30055	0.227291
$359$	13.9002	0.733622	0.366811	−	0.930295i	$-0.380450\pi$
$359$	13.9002	0.733622	0.366811	+	0.930295i	$0.380450\pi$
$360$	5.21179	0.274686
$361$	−7.22903	−0.380475
$362$	−23.3007	−1.22466
$363$	19.8192	1.04024
$364$	−3.11824	−0.163440
$365$	−4.11228	−0.215247
$366$	−19.9317	−1.04185
$367$	10.6560	0.556239	0.278119	−	0.960547i	$-0.410289\pi$
$367$	10.6560	0.556239	0.278119	+	0.960547i	$0.410289\pi$
$368$	9.44901	0.492563
$369$	−7.15631	−0.372543
$370$	−3.02200	−0.157107
$371$	−6.38334	−0.331407
$372$	7.17926	0.372227
$373$	29.4711	1.52596	0.762978	−	0.646425i	$-0.223737\pi$
$373$	29.4711	1.52596	0.762978	+	0.646425i	$0.223737\pi$
$374$	−1.66661	−0.0861783
$375$	−2.16829	−0.111970
$376$	2.49518	0.128679
$377$	−4.72821	−0.243515
$378$	5.25017	0.270040
$379$	17.8622	0.917519	0.458759	−	0.888561i	$-0.348294\pi$
$379$	17.8622	0.917519	0.458759	+	0.888561i	$0.348294\pi$
$380$	−1.73702	−0.0891070
$381$	13.0600	0.669086
$382$	−3.69245	−0.188922
$383$	−7.01023	−0.358206	−0.179103	−	0.983830i	$-0.557320\pi$
$383$	−7.01023	−0.358206	−0.179103	+	0.983830i	$0.557320\pi$
$384$	11.4139	0.582466
$385$	−2.08051	−0.106033
$386$	−5.95359	−0.303030
$387$	−12.4059	−0.630626
$388$	3.06228	0.155464
$389$	16.1850	0.820610	0.410305	−	0.911948i	$-0.365422\pi$
$389$	16.1850	0.820610	0.410305	+	0.911948i	$0.365422\pi$
$390$	−10.6977	−0.541701
$391$	−3.45978	−0.174969
$392$	−14.3116	−0.722847
$393$	42.0762	2.12246
$394$	4.97008	0.250389
$395$	8.96779	0.451219
$396$	−1.17468	−0.0590300
$397$	−14.4129	−0.723361	−0.361680	−	0.932302i	$-0.617797\pi$
$397$	−14.4129	−0.723361	−0.361680	+	0.932302i	$0.617797\pi$
$398$	−14.6528	−0.734480
$399$	11.3499	0.568206
$400$	−2.73110	−0.136555
$401$	−16.5678	−0.827354	−0.413677	−	0.910424i	$-0.635756\pi$
$401$	−16.5678	−0.827354	−0.413677	+	0.910424i	$0.635756\pi$
$402$	5.21648	0.260175
$403$	−26.4002	−1.31509
$404$	−3.97790	−0.197908
$405$	−11.2094	−0.557000
$406$	2.18403	0.108391
$407$	3.37180	0.167134
$408$	−6.64173	−0.328814
$409$	12.5945	0.622759	0.311380	−	0.950286i	$-0.399209\pi$
$409$	12.5945	0.622759	0.311380	+	0.950286i	$0.399209\pi$
$410$	5.14043	0.253868
$411$	12.1917	0.601373
$412$	−0.606553	−0.0298827
$413$	−16.2878	−0.801470
$414$	7.19458	0.353594
$415$	−4.19715	−0.206030
$416$	11.2562	0.551881
$417$	46.7717	2.29042
$418$	−5.71795	−0.279674
$419$	23.9386	1.16948	0.584738	−	0.811222i	$-0.301197\pi$
$419$	23.9386	1.16948	0.584738	+	0.811222i	$0.301197\pi$
$420$	−1.67488	−0.0817257
$421$	20.2803	0.988400	0.494200	−	0.869348i	$-0.335461\pi$
$421$	20.2803	0.988400	0.494200	+	0.869348i	$0.335461\pi$
$422$	24.3610	1.18587
$423$	1.38599	0.0673892
$424$	12.8157	0.622386
$425$	1.00000	0.0485071
$426$	2.65003	0.128394
$427$	11.4753	0.555328
$428$	−1.59718	−0.0772026
$429$	11.9360	0.576276
$430$	8.91124	0.429738
$431$	−15.0256	−0.723756	−0.361878	−	0.932226i	$-0.617864\pi$
$431$	−15.0256	−0.723756	−0.361878	+	0.932226i	$0.617864\pi$
$432$	−7.68967	−0.369969
$433$	17.4036	0.836365	0.418183	−	0.908363i	$-0.362667\pi$
$433$	17.4036	0.836365	0.418183	+	0.908363i	$0.362667\pi$
$434$	12.1946	0.585361
$435$	−2.53964	−0.121766
$436$	0.545351	0.0261176
$437$	−11.8701	−0.567825
$438$	−10.8976	−0.520710
$439$	−12.1896	−0.581780	−0.290890	−	0.956756i	$-0.593951\pi$
$439$	−12.1896	−0.581780	−0.290890	+	0.956756i	$0.593951\pi$
$440$	4.17700	0.199131
$441$	−7.94964	−0.378554
$442$	4.93373	0.234674
$443$	−7.04787	−0.334854	−0.167427	−	0.985884i	$-0.553546\pi$
$443$	−7.04787	−0.334854	−0.167427	+	0.985884i	$0.553546\pi$
$444$	2.71441	0.128820
$445$	10.7285	0.508578
$446$	20.1562	0.954425
$447$	−26.7089	−1.26329
$448$	−13.5331	−0.639377
$449$	18.9081	0.892326	0.446163	−	0.894952i	$-0.352790\pi$
$449$	18.9081	0.892326	0.446163	+	0.894952i	$0.352790\pi$
$450$	−2.07949	−0.0980280
$451$	−5.73544	−0.270071
$452$	−6.13094	−0.288375
$453$	38.7309	1.81974
$454$	35.6875	1.67490
$455$	6.15902	0.288739
$456$	−22.7870	−1.06710
$457$	34.3997	1.60915	0.804575	−	0.593850i	$-0.202393\pi$
$457$	34.3997	1.60915	0.804575	+	0.593850i	$0.202393\pi$
$458$	1.68928	0.0789348
$459$	2.81560	0.131421
$460$	1.75165	0.0816709
$461$	−10.7757	−0.501876	−0.250938	−	0.968003i	$-0.580739\pi$
$461$	−10.7757	−0.501876	−0.250938	+	0.968003i	$0.580739\pi$
$462$	−5.51341	−0.256507
$463$	−29.0892	−1.35189	−0.675946	−	0.736951i	$-0.736265\pi$
$463$	−29.0892	−1.35189	−0.675946	+	0.736951i	$0.736265\pi$
$464$	−3.19884	−0.148502
$465$	−14.1802	−0.657591
$466$	−11.5384	−0.534505
$467$	−3.91443	−0.181138	−0.0905692	−	0.995890i	$-0.528869\pi$
$467$	−3.91443	−0.181138	−0.0905692	+	0.995890i	$0.528869\pi$
$468$	3.47746	0.160746
$469$	−3.00329	−0.138679
$470$	−0.995569	−0.0459222
$471$	32.0099	1.47494
$472$	32.7007	1.50517
$473$	−9.94272	−0.457167
$474$	23.7649	1.09156
$475$	3.43089	0.157420
$476$	0.772444	0.0354049
$477$	7.11871	0.325943
$478$	9.98995	0.456930
$479$	14.8520	0.678607	0.339304	−	0.940677i	$-0.389809\pi$
$479$	14.8520	0.678607	0.339304	+	0.940677i	$0.389809\pi$
$480$	6.04598	0.275960
$481$	−9.98168	−0.455125
$482$	−34.8151	−1.58578
$483$	−11.4455	−0.520789
$484$	4.62771	0.210351
$485$	−6.04849	−0.274648
$486$	−19.3818	−0.879175
$487$	27.6406	1.25252	0.626258	−	0.779616i	$-0.284586\pi$
$487$	27.6406	1.25252	0.626258	+	0.779616i	$0.284586\pi$
$488$	−23.0387	−1.04291
$489$	11.1485	0.504154
$490$	5.71029	0.257965
$491$	−12.8248	−0.578775	−0.289388	−	0.957212i	$-0.593452\pi$
$491$	−12.8248	−0.578775	−0.289388	+	0.957212i	$0.593452\pi$
$492$	−4.61722	−0.208160
$493$	1.17126	0.0527511
$494$	16.9271	0.761585
$495$	2.32019	0.104285
$496$	−17.8609	−0.801977
$497$	−1.52570	−0.0684370
$498$	−11.1226	−0.498414
$499$	29.6371	1.32674	0.663370	−	0.748292i	$-0.269126\pi$
$499$	29.6371	1.32674	0.663370	+	0.748292i	$0.269126\pi$
$500$	−0.506288	−0.0226419
$501$	10.5427	0.471011
$502$	−20.2997	−0.906019
$503$	−36.8635	−1.64366	−0.821831	−	0.569731i	$-0.807047\pi$
$503$	−36.8635	−1.64366	−0.821831	+	0.569731i	$0.807047\pi$
$504$	−7.95164	−0.354194
$505$	7.85700	0.349632
$506$	5.76611	0.256335
$507$	−7.14691	−0.317405
$508$	3.04948	0.135299
$509$	−6.79991	−0.301401	−0.150700	−	0.988579i	$-0.548153\pi$
$509$	−6.79991	−0.301401	−0.150700	+	0.988579i	$0.548153\pi$
$510$	2.65003	0.117345
$511$	6.27411	0.277550
$512$	24.3467	1.07598
$513$	9.65999	0.426499
$514$	−31.0199	−1.36823
$515$	1.19804	0.0527919
$516$	−8.00422	−0.352366
$517$	1.11081	0.0488532
$518$	4.61068	0.202581
$519$	42.5139	1.86615
$520$	−12.3653	−0.542256
$521$	42.4915	1.86158	0.930792	−	0.365548i	$-0.119118\pi$
$521$	42.4915	1.86158	0.930792	+	0.365548i	$0.119118\pi$
$522$	−2.43563	−0.106605
$523$	−18.3253	−0.801309	−0.400654	−	0.916229i	$-0.631217\pi$
$523$	−18.3253	−0.801309	−0.400654	+	0.916229i	$0.631217\pi$
$524$	9.82466	0.429192
$525$	3.30816	0.144380
$526$	0.172511	0.00752182
$527$	6.53982	0.284879
$528$	8.07522	0.351429
$529$	−11.0299	−0.479561
$530$	−5.11343	−0.222113
$531$	18.1642	0.788258
$532$	2.65017	0.114899
$533$	16.9789	0.735436
$534$	28.4307	1.23032
$535$	3.15469	0.136389
$536$	6.02965	0.260441
$537$	7.62970	0.329246
$538$	−36.1138	−1.55697
$539$	−6.37126	−0.274430
$540$	−1.42550	−0.0613439
$541$	−26.1113	−1.12261	−0.561306	−	0.827609i	$-0.689701\pi$
$541$	−26.1113	−1.12261	−0.561306	+	0.827609i	$0.689701\pi$
$542$	19.8723	0.853588
$543$	−41.3382	−1.77399
$544$	−2.78837	−0.119550
$545$	−1.07716	−0.0461403
$546$	16.3216	0.698498
$547$	24.9017	1.06472	0.532359	−	0.846519i	$-0.321306\pi$
$547$	24.9017	1.06472	0.532359	+	0.846519i	$0.321306\pi$
$548$	2.84672	0.121606
$549$	−12.7973	−0.546174
$550$	−1.66661	−0.0710645
$551$	4.01847	0.171193
$552$	22.9789	0.978048
$553$	−13.6822	−0.581825
$554$	18.8795	0.802111
$555$	−5.36140	−0.227579
$556$	10.9210	0.463155
$557$	−15.9513	−0.675877	−0.337938	−	0.941168i	$-0.609730\pi$
$557$	−15.9513	−0.675877	−0.337938	+	0.941168i	$0.609730\pi$
$558$	−13.5995	−0.575711
$559$	29.4338	1.24492
$560$	4.16684	0.176081
$561$	−2.95677	−0.124835
$562$	−9.17064	−0.386840
$563$	−30.7161	−1.29453	−0.647264	−	0.762266i	$-0.724087\pi$
$563$	−30.7161	−1.29453	−0.647264	+	0.762266i	$0.724087\pi$
$564$	0.894236	0.0376541
$565$	12.1096	0.509455
$566$	10.6630	0.448199
$567$	17.1022	0.718225
$568$	3.06312	0.128526
$569$	37.4527	1.57010	0.785050	−	0.619432i	$-0.212637\pi$
$569$	37.4527	1.57010	0.785050	+	0.619432i	$0.212637\pi$
$570$	9.09193	0.380819
$571$	36.1308	1.51203	0.756014	−	0.654556i	$-0.227144\pi$
$571$	36.1308	1.51203	0.756014	+	0.654556i	$0.227144\pi$
$572$	2.78702	0.116531
$573$	−6.55086	−0.273666
$574$	−7.84277	−0.327351
$575$	−3.45978	−0.144283
$576$	15.0921	0.628837
$577$	24.7694	1.03116	0.515581	−	0.856841i	$-0.327576\pi$
$577$	24.7694	1.03116	0.515581	+	0.856841i	$0.327576\pi$
$578$	−1.22218	−0.0508358
$579$	−10.5624	−0.438957
$580$	−0.592997	−0.0246228
$581$	6.40360	0.265666
$582$	−16.0286	−0.664409
$583$	5.70531	0.236290
$584$	−12.5964	−0.521243
$585$	−6.86854	−0.283979
$586$	−34.5398	−1.42683
$587$	1.05183	0.0434138	0.0217069	−	0.999764i	$-0.493090\pi$
$587$	1.05183	0.0434138	0.0217069	+	0.999764i	$0.493090\pi$
$588$	−5.12907	−0.211519
$589$	22.4374	0.924515
$590$	−13.0475	−0.537156
$591$	8.81753	0.362705
$592$	−6.75303	−0.277548
$593$	18.6638	0.766431	0.383215	−	0.923659i	$-0.374817\pi$
$593$	18.6638	0.766431	0.383215	+	0.923659i	$0.374817\pi$
$594$	−4.69250	−0.192536
$595$	−1.52570	−0.0625476
$596$	−6.23643	−0.255454
$597$	−25.9959	−1.06394
$598$	−17.0696	−0.698030
$599$	−17.2778	−0.705951	−0.352976	−	0.935633i	$-0.614830\pi$
$599$	−17.2778	−0.705951	−0.352976	+	0.935633i	$0.614830\pi$
$600$	−6.64173	−0.271147
$601$	−37.2878	−1.52100	−0.760501	−	0.649337i	$-0.775046\pi$
$601$	−37.2878	−1.52100	−0.760501	+	0.649337i	$0.775046\pi$
$602$	−13.5959	−0.554127
$603$	3.34927	0.136393
$604$	9.04354	0.367976
$605$	−9.14048	−0.371613
$606$	20.8212	0.845805
$607$	−34.0586	−1.38239	−0.691197	−	0.722666i	$-0.742916\pi$
$607$	−34.0586	−1.38239	−0.691197	+	0.722666i	$0.742916\pi$
$608$	−9.56657	−0.387975
$609$	3.87472	0.157012
$610$	9.19237	0.372188
$611$	−3.28836	−0.133033
$612$	−0.861430	−0.0348213
$613$	−2.18059	−0.0880734	−0.0440367	−	0.999030i	$-0.514022\pi$
$613$	−2.18059	−0.0880734	−0.0440367	+	0.999030i	$0.514022\pi$
$614$	−2.55541	−0.103128
$615$	9.11975	0.367744
$616$	−6.37286	−0.256770
$617$	47.1104	1.89659	0.948297	−	0.317384i	$-0.102804\pi$
$617$	47.1104	1.89659	0.948297	+	0.317384i	$0.102804\pi$
$618$	3.17483	0.127711
$619$	9.68633	0.389326	0.194663	−	0.980870i	$-0.437639\pi$
$619$	9.68633	0.389326	0.194663	+	0.980870i	$0.437639\pi$
$620$	−3.31103	−0.132974
$621$	−9.74136	−0.390907
$622$	−1.19324	−0.0478448
$623$	−16.3684	−0.655787
$624$	−23.9054	−0.956981
$625$	1.00000	0.0400000
$626$	−1.62279	−0.0648595
$627$	−10.1443	−0.405125
$628$	7.47420	0.298253
$629$	2.47264	0.0985908
$630$	3.17268	0.126402
$631$	33.3216	1.32651	0.663257	−	0.748392i	$-0.269174\pi$
$631$	33.3216	1.32651	0.663257	+	0.748392i	$0.269174\pi$
$632$	27.4695	1.09268
$633$	43.2193	1.71781
$634$	−21.5353	−0.855274
$635$	−6.02321	−0.239024
$636$	4.59296	0.182123
$637$	18.8611	0.747304
$638$	−1.95204	−0.0772820
$639$	1.70146	0.0673089
$640$	−5.26404	−0.208080
$641$	−6.37699	−0.251876	−0.125938	−	0.992038i	$-0.540194\pi$
$641$	−6.37699	−0.251876	−0.125938	+	0.992038i	$0.540194\pi$
$642$	8.36000	0.329943
$643$	46.5851	1.83714	0.918569	−	0.395261i	$-0.129346\pi$
$643$	46.5851	1.83714	0.918569	+	0.395261i	$0.129346\pi$
$644$	−2.67249	−0.105311
$645$	15.8096	0.622503
$646$	−4.19314	−0.164977
$647$	−18.3187	−0.720181	−0.360091	−	0.932917i	$-0.617254\pi$
$647$	−18.3187	−0.720181	−0.360091	+	0.932917i	$0.617254\pi$
$648$	−34.3358	−1.34884
$649$	14.5577	0.571440
$650$	4.93373	0.193517
$651$	21.6347	0.847932
$652$	2.60315	0.101947
$653$	13.9417	0.545581	0.272790	−	0.962073i	$-0.412053\pi$
$653$	13.9417	0.545581	0.272790	+	0.962073i	$0.412053\pi$
$654$	−2.85449	−0.111619
$655$	−19.4053	−0.758228
$656$	11.4869	0.448489
$657$	−6.99690	−0.272975
$658$	1.51894	0.0592145
$659$	31.2007	1.21541	0.607703	−	0.794164i	$-0.292091\pi$
$659$	31.2007	1.21541	0.607703	+	0.794164i	$0.292091\pi$
$660$	1.49697	0.0582697
$661$	−29.0837	−1.13123	−0.565613	−	0.824671i	$-0.691360\pi$
$661$	−29.0837	−1.13123	−0.565613	+	0.824671i	$0.691360\pi$
$662$	−28.4131	−1.10431
$663$	8.75303	0.339940
$664$	−12.8564	−0.498925
$665$	−5.23451	−0.202985
$666$	−5.14183	−0.199242
$667$	−4.05232	−0.156906
$668$	2.46168	0.0952451
$669$	35.7596	1.38255
$670$	−2.40581	−0.0929445
$671$	−10.2564	−0.395944
$672$	−9.22435	−0.355837
$673$	−12.1621	−0.468816	−0.234408	−	0.972138i	$-0.575315\pi$
$673$	−12.1621	−0.468816	−0.234408	+	0.972138i	$0.575315\pi$
$674$	−30.2196	−1.16401
$675$	2.81560	0.108372
$676$	−1.66878	−0.0641839
$677$	9.80860	0.376975	0.188488	−	0.982076i	$-0.439641\pi$
$677$	9.80860	0.376975	0.188488	+	0.982076i	$0.439641\pi$
$678$	32.0907	1.23244
$679$	9.22819	0.354145
$680$	3.06312	0.117465
$681$	63.3139	2.42619
$682$	−10.8993	−0.417357
$683$	20.1615	0.771458	0.385729	−	0.922612i	$-0.373950\pi$
$683$	20.1615	0.771458	0.385729	+	0.922612i	$0.373950\pi$
$684$	−2.95547	−0.113005
$685$	−5.62274	−0.214834
$686$	−21.7649	−0.830988
$687$	2.99698	0.114342
$688$	19.9132	0.759185
$689$	−16.8896	−0.643444
$690$	−9.16851	−0.349039
$691$	23.2173	0.883230	0.441615	−	0.897205i	$-0.354406\pi$
$691$	23.2173	0.883230	0.441615	+	0.897205i	$0.354406\pi$
$692$	9.92686	0.377363
$693$	−3.53991	−0.134470
$694$	23.3221	0.885294
$695$	−21.5708	−0.818227
$696$	−7.77921	−0.294870
$697$	−4.20597	−0.159313
$698$	−26.3997	−0.999245
$699$	−20.4705	−0.774265
$700$	0.772444	0.0291956
$701$	10.1567	0.383615	0.191807	−	0.981433i	$-0.438565\pi$
$701$	10.1567	0.383615	0.191807	+	0.981433i	$0.438565\pi$
$702$	13.8914	0.524297
$703$	8.48336	0.319956
$704$	12.0956	0.455870
$705$	−1.76626	−0.0665212
$706$	−15.6260	−0.588091
$707$	−11.9874	−0.450834
$708$	11.7194	0.440444
$709$	−14.8019	−0.555897	−0.277948	−	0.960596i	$-0.589654\pi$
$709$	−14.8019	−0.555897	−0.277948	+	0.960596i	$0.589654\pi$
$710$	−1.22218	−0.0458674
$711$	15.2584	0.572234
$712$	32.8626	1.23158
$713$	−22.6264	−0.847364
$714$	−4.04315	−0.151311
$715$	−5.50481	−0.205868
$716$	1.78151	0.0665781
$717$	17.7234	0.661892
$718$	−16.9884	−0.634003
$719$	2.04583	0.0762965	0.0381483	−	0.999272i	$-0.487854\pi$
$719$	2.04583	0.0762965	0.0381483	+	0.999272i	$0.487854\pi$
$720$	−4.64686	−0.173178
$721$	−1.82785	−0.0680727
$722$	8.83514	0.328810
$723$	−61.7661	−2.29711
$724$	−9.65235	−0.358727
$725$	1.17126	0.0434997
$726$	−24.2225	−0.898981
$727$	−13.5075	−0.500966	−0.250483	−	0.968121i	$-0.580589\pi$
$727$	−13.5075	−0.500966	−0.250483	+	0.968121i	$0.580589\pi$
$728$	18.8658	0.699214
$729$	−0.757350	−0.0280500
$730$	5.02593	0.186018
$731$	−7.29130	−0.269678
$732$	−8.25673	−0.305178
$733$	−37.2140	−1.37453	−0.687266	−	0.726406i	$-0.741189\pi$
$733$	−37.2140	−1.37453	−0.687266	+	0.726406i	$0.741189\pi$
$734$	−13.0235	−0.480706
$735$	10.1307	0.373678
$736$	9.64714	0.355598
$737$	2.68428	0.0988768
$738$	8.74626	0.321954
$739$	15.8339	0.582460	0.291230	−	0.956653i	$-0.405936\pi$
$739$	15.8339	0.582460	0.291230	+	0.956653i	$0.405936\pi$
$740$	−1.25187	−0.0460196
$741$	30.0306	1.10320
$742$	7.80156	0.286404
$743$	17.4356	0.639649	0.319825	−	0.947477i	$-0.396376\pi$
$743$	17.4356	0.639649	0.319825	+	0.947477i	$0.396376\pi$
$744$	−43.4357	−1.59243
$745$	12.3180	0.451295
$746$	−36.0188	−1.31874
$747$	−7.14130	−0.261287
$748$	−0.690395	−0.0252434
$749$	−4.81311	−0.175867
$750$	2.65003	0.0967652
$751$	47.6774	1.73977	0.869887	−	0.493252i	$-0.164192\pi$
$751$	47.6774	1.73977	0.869887	+	0.493252i	$0.164192\pi$
$752$	−2.22472	−0.0811271
$753$	−36.0141	−1.31243
$754$	5.77870	0.210448
$755$	−17.8624	−0.650081
$756$	2.17489	0.0791000
$757$	−18.2129	−0.661958	−0.330979	−	0.943638i	$-0.607379\pi$
$757$	−18.2129	−0.661958	−0.330979	+	0.943638i	$0.607379\pi$
$758$	−21.8307	−0.792927
$759$	10.2298	0.371317
$760$	10.5092	0.381210
$761$	−32.7124	−1.18582	−0.592912	−	0.805267i	$-0.702022\pi$
$761$	−32.7124	−1.18582	−0.592912	+	0.805267i	$0.702022\pi$
$762$	−15.9616	−0.578229
$763$	1.64342	0.0594957
$764$	−1.52960	−0.0553391
$765$	1.70146	0.0615166
$766$	8.56773	0.309565
$767$	−43.0958	−1.55610
$768$	24.5158	0.884639
$769$	17.2451	0.621874	0.310937	−	0.950431i	$-0.399357\pi$
$769$	17.2451	0.621874	0.310937	+	0.950431i	$0.399357\pi$
$770$	2.54275	0.0916343
$771$	−55.0330	−1.98197
$772$	−2.46628	−0.0887634
$773$	−41.6468	−1.49793	−0.748965	−	0.662610i	$-0.769449\pi$
$773$	−41.6468	−1.49793	−0.748965	+	0.662610i	$0.769449\pi$
$774$	15.1622	0.544993
$775$	6.53982	0.234917
$776$	−18.5273	−0.665090
$777$	8.17989	0.293452
$778$	−19.7809	−0.709178
$779$	−14.4302	−0.517016
$780$	−4.43155	−0.158675
$781$	1.36364	0.0487950
$782$	4.22846	0.151209
$783$	3.29781	0.117854
$784$	12.7603	0.455726
$785$	−14.7628	−0.526905
$786$	−51.4245	−1.83425
$787$	−9.10191	−0.324448	−0.162224	−	0.986754i	$-0.551867\pi$
$787$	−9.10191	−0.324448	−0.162224	+	0.986754i	$0.551867\pi$
$788$	2.05886	0.0733440
$789$	0.306054	0.0108958
$790$	−10.9602	−0.389947
$791$	−18.4756	−0.656918
$792$	7.10702	0.252537
$793$	30.3624	1.07820
$794$	17.6150	0.625135
$795$	−9.07183	−0.321745
$796$	−6.06996	−0.215144
$797$	−6.01105	−0.212922	−0.106461	−	0.994317i	$-0.533952\pi$
$797$	−6.01105	−0.212922	−0.106461	+	0.994317i	$0.533952\pi$
$798$	−13.8716	−0.491048
$799$	0.814588	0.0288180
$800$	−2.78837	−0.0985836
$801$	18.2541	0.644977
$802$	20.2487	0.715006
$803$	−5.60768	−0.197891
$804$	2.16094	0.0762103
$805$	5.27860	0.186046
$806$	32.2657	1.13651
$807$	−64.0702	−2.25538
$808$	24.0669	0.846672
$809$	−37.4679	−1.31730	−0.658651	−	0.752448i	$-0.728873\pi$
$809$	−37.4679	−1.31730	−0.658651	+	0.752448i	$0.728873\pi$
$810$	13.6999	0.481364
$811$	26.6716	0.936565	0.468282	−	0.883579i	$-0.344873\pi$
$811$	26.6716	0.936565	0.468282	+	0.883579i	$0.344873\pi$
$812$	0.904736	0.0317500
$813$	35.2558	1.23648
$814$	−4.12093	−0.144439
$815$	−5.14164	−0.180104
$816$	5.92180	0.207304
$817$	−25.0156	−0.875185
$818$	−15.3927	−0.538194
$819$	10.4793	0.366178
$820$	2.12943	0.0743630
$821$	−54.3186	−1.89573	−0.947865	−	0.318671i	$-0.896764\pi$
$821$	−54.3186	−1.89573	−0.947865	+	0.318671i	$0.896764\pi$
$822$	−14.9004	−0.519711
$823$	−4.22040	−0.147114	−0.0735570	−	0.997291i	$-0.523435\pi$
$823$	−4.22040	−0.147114	−0.0735570	+	0.997291i	$0.523435\pi$
$824$	3.66974	0.127841
$825$	−2.95677	−0.102941
$826$	19.9065	0.692637
$827$	19.7192	0.685705	0.342853	−	0.939389i	$-0.388607\pi$
$827$	19.7192	0.685705	0.342853	+	0.939389i	$0.388607\pi$
$828$	2.98036	0.103575
$829$	−9.09454	−0.315866	−0.157933	−	0.987450i	$-0.550483\pi$
$829$	−9.09454	−0.315866	−0.157933	+	0.987450i	$0.550483\pi$
$830$	5.12965	0.178053
$831$	33.4944	1.16191
$832$	−35.8071	−1.24139
$833$	−4.67224	−0.161883
$834$	−57.1632	−1.97940
$835$	−4.86221	−0.168264
$836$	−2.36867	−0.0819221
$837$	18.4135	0.636463
$838$	−29.2571	−1.01067
$839$	54.8216	1.89265	0.946326	−	0.323213i	$-0.104763\pi$
$839$	54.8216	1.89265	0.946326	+	0.323213i	$0.104763\pi$
$840$	10.1333	0.349632
$841$	−27.6281	−0.952695
$842$	−24.7860	−0.854184
$843$	−16.2698	−0.560362
$844$	10.0916	0.347366
$845$	3.29611	0.113390
$846$	−1.69392	−0.0582383
$847$	13.9456	0.479178
$848$	−11.4266	−0.392390
$849$	18.9174	0.649245
$850$	−1.22218	−0.0419203
$851$	−8.55481	−0.293255
$852$	1.09778	0.0376092
$853$	50.6592	1.73454	0.867268	−	0.497841i	$-0.165874\pi$
$853$	50.6592	1.73454	0.867268	+	0.497841i	$0.165874\pi$
$854$	−14.0248	−0.479919
$855$	5.83753	0.199639
$856$	9.66320	0.330281
$857$	−28.5345	−0.974721	−0.487360	−	0.873201i	$-0.662040\pi$
$857$	−28.5345	−0.974721	−0.487360	+	0.873201i	$0.662040\pi$
$858$	−14.5879	−0.498022
$859$	31.1665	1.06339	0.531694	−	0.846937i	$-0.321556\pi$
$859$	31.1665	1.06339	0.531694	+	0.846937i	$0.321556\pi$
$860$	3.69150	0.125879
$861$	−13.9140	−0.474188
$862$	18.3639	0.625476
$863$	35.8746	1.22119	0.610593	−	0.791944i	$-0.290931\pi$
$863$	35.8746	1.22119	0.610593	+	0.791944i	$0.290931\pi$
$864$	−7.85092	−0.267094
$865$	−19.6072	−0.666663
$866$	−21.2703	−0.722794
$867$	−2.16829	−0.0736389
$868$	5.05164	0.171464
$869$	12.2289	0.414836
$870$	3.10388	0.105231
$871$	−7.94639	−0.269253
$872$	−3.29946	−0.111734
$873$	−10.2913	−0.348307
$874$	14.5074	0.490719
$875$	−1.52570	−0.0515781
$876$	−4.51436	−0.152526
$877$	20.0696	0.677703	0.338852	−	0.940840i	$-0.389962\pi$
$877$	20.0696	0.677703	0.338852	+	0.940840i	$0.389962\pi$
$878$	14.8979	0.502779
$879$	−61.2778	−2.06685
$880$	−3.72424	−0.125544
$881$	3.56871	0.120233	0.0601164	−	0.998191i	$-0.480853\pi$
$881$	3.56871	0.120233	0.0601164	+	0.998191i	$0.480853\pi$
$882$	9.71585	0.327150
$883$	40.9256	1.37726	0.688628	−	0.725115i	$-0.258213\pi$
$883$	40.9256	1.37726	0.688628	+	0.725115i	$0.258213\pi$
$884$	2.04380	0.0687406
$885$	−23.1478	−0.778104
$886$	8.61373	0.289384
$887$	4.78320	0.160604	0.0803020	−	0.996771i	$-0.474412\pi$
$887$	4.78320	0.160604	0.0803020	+	0.996771i	$0.474412\pi$
$888$	−16.4226	−0.551107
$889$	9.18961	0.308210
$890$	−13.1121	−0.439517
$891$	−15.2856	−0.512088
$892$	8.34975	0.279570
$893$	2.79476	0.0935230
$894$	32.6429	1.09174
$895$	−3.51877	−0.117619
$896$	8.03136	0.268309
$897$	−30.2836	−1.01114
$898$	−23.1090	−0.771156
$899$	7.65985	0.255470
$900$	−0.861430	−0.0287143
$901$	4.18387	0.139385
$902$	7.00971	0.233398
$903$	−24.1208	−0.802688
$904$	37.0932	1.23370
$905$	19.0649	0.633740
$906$	−47.3359	−1.57263
$907$	−23.2264	−0.771220	−0.385610	−	0.922662i	$-0.626009\pi$
$907$	−23.2264	−0.771220	−0.385610	+	0.922662i	$0.626009\pi$
$908$	14.7836	0.490611
$909$	13.3684	0.443402
$910$	−7.52740	−0.249531
$911$	33.8044	1.11999	0.559995	−	0.828496i	$-0.310803\pi$
$911$	33.8044	1.11999	0.559995	+	0.828496i	$0.310803\pi$
$912$	20.3170	0.672764
$913$	−5.72341	−0.189417
$914$	−42.0425	−1.39064
$915$	16.3084	0.539138
$916$	0.699786	0.0231216
$917$	29.6067	0.977699
$918$	−3.44115	−0.113575
$919$	−9.84517	−0.324762	−0.162381	−	0.986728i	$-0.551917\pi$
$919$	−9.84517	−0.324762	−0.162381	+	0.986728i	$0.551917\pi$
$920$	−10.5977	−0.349397
$921$	−4.53360	−0.149387
$922$	13.1698	0.433725
$923$	−4.03684	−0.132874
$924$	−2.28394	−0.0751360
$925$	2.47264	0.0813000
$926$	35.5522	1.16832
$927$	2.03842	0.0669505
$928$	−3.26591	−0.107209
$929$	−16.6815	−0.547301	−0.273650	−	0.961829i	$-0.588231\pi$
$929$	−16.6815	−0.547301	−0.273650	+	0.961829i	$0.588231\pi$
$930$	17.3307	0.568295
$931$	−16.0299	−0.525359
$932$	−4.77979	−0.156567
$933$	−2.11696	−0.0693061
$934$	4.78412	0.156541
$935$	1.36364	0.0445959
$936$	−21.0392	−0.687688
$937$	48.6867	1.59053	0.795263	−	0.606264i	$-0.207333\pi$
$937$	48.6867	1.59053	0.795263	+	0.606264i	$0.207333\pi$
$938$	3.67055	0.119848
$939$	−2.87902	−0.0939531
$940$	−0.412416	−0.0134515
$941$	45.3144	1.47721	0.738603	−	0.674140i	$-0.235486\pi$
$941$	45.3144	1.47721	0.738603	+	0.674140i	$0.235486\pi$
$942$	−39.1217	−1.27465
$943$	14.5518	0.473870
$944$	−29.1561	−0.948952
$945$	−4.29576	−0.139741
$946$	12.1517	0.395087
$947$	−26.8881	−0.873747	−0.436873	−	0.899523i	$-0.643914\pi$
$947$	−26.8881	−0.873747	−0.436873	+	0.899523i	$0.643914\pi$
$948$	9.84464	0.319739
$949$	16.6006	0.538879
$950$	−4.19314	−0.136044
$951$	−38.2061	−1.23892
$952$	−4.67341	−0.151466
$953$	−56.1023	−1.81733	−0.908665	−	0.417525i	$-0.862898\pi$
$953$	−56.1023	−1.81733	−0.908665	+	0.417525i	$0.862898\pi$
$954$	−8.70031	−0.281683
$955$	3.02121	0.0977642
$956$	4.13835	0.133844
$957$	−3.46315	−0.111948
$958$	−18.1518	−0.586458
$959$	8.57862	0.277018
$960$	−19.2328	−0.620737
$961$	11.7692	0.379652
$962$	12.1994	0.393323
$963$	5.36759	0.172968
$964$	−14.4222	−0.464508
$965$	4.87130	0.156813
$966$	13.9884	0.450070
$967$	47.8374	1.53835	0.769173	−	0.639041i	$-0.220668\pi$
$967$	47.8374	1.53835	0.769173	+	0.639041i	$0.220668\pi$
$968$	−27.9984	−0.899903
$969$	−7.43914	−0.238980
$970$	7.39231	0.237353
$971$	0.431514	0.0138480	0.00692398	−	0.999976i	$-0.497796\pi$
$971$	0.431514	0.0138480	0.00692398	+	0.999976i	$0.497796\pi$
$972$	−8.02892	−0.257528
$973$	32.9106	1.05507
$974$	−33.7817	−1.08243
$975$	8.75303	0.280321
$976$	20.5415	0.657516
$977$	45.2375	1.44728	0.723638	−	0.690180i	$-0.242468\pi$
$977$	45.2375	1.44728	0.723638	+	0.690180i	$0.242468\pi$
$978$	−13.6255	−0.435694
$979$	14.6298	0.467570
$980$	2.36550	0.0755630
$981$	−1.83274	−0.0585149
$982$	15.6742	0.500183
$983$	−29.5893	−0.943751	−0.471876	−	0.881665i	$-0.656423\pi$
$983$	−29.5893	−0.943751	−0.471876	+	0.881665i	$0.656423\pi$
$984$	27.9349	0.890532
$985$	−4.06659	−0.129572
$986$	−1.43149	−0.0455879
$987$	2.69478	0.0857759
$988$	7.01206	0.223083
$989$	25.2263	0.802150
$990$	−2.83568	−0.0901237
$991$	−1.49677	−0.0475465	−0.0237733	−	0.999717i	$-0.507568\pi$
$991$	−1.49677	−0.0475465	−0.0237733	+	0.999717i	$0.507568\pi$
$992$	−18.2354	−0.578975
$993$	−50.4082	−1.59966
$994$	1.86467	0.0591439
$995$	11.9891	0.380081
$996$	−4.60753	−0.145995
$997$	19.8453	0.628507	0.314254	−	0.949339i	$-0.398246\pi$
$997$	19.8453	0.628507	0.314254	+	0.949339i	$0.398246\pi$
$998$	−36.2218	−1.14658
$999$	6.96197	0.220267

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6035.2.a.g.1.20	✓	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6035.2.a.g.1.20	✓	58	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)

\(f(q)\)	\(=\)	\(q-1.22218 q^{2} -2.16829 q^{3} -0.506288 q^{4} +1.00000 q^{5} +2.65003 q^{6} -1.52570 q^{7} +3.06312 q^{8} +1.70146 q^{9} +O(q^{10})\)	\(q-1.22218 q^{2} -2.16829 q^{3} -0.506288 q^{4} +1.00000 q^{5} +2.65003 q^{6} -1.52570 q^{7} +3.06312 q^{8} +1.70146 q^{9} -1.22218 q^{10} +1.36364 q^{11} +1.09778 q^{12} -4.03684 q^{13} +1.86467 q^{14} -2.16829 q^{15} -2.73110 q^{16} +1.00000 q^{17} -2.07949 q^{18} +3.43089 q^{19} -0.506288 q^{20} +3.30816 q^{21} -1.66661 q^{22} -3.45978 q^{23} -6.64173 q^{24} +1.00000 q^{25} +4.93373 q^{26} +2.81560 q^{27} +0.772444 q^{28} +1.17126 q^{29} +2.65003 q^{30} +6.53982 q^{31} -2.78837 q^{32} -2.95677 q^{33} -1.22218 q^{34} -1.52570 q^{35} -0.861430 q^{36} +2.47264 q^{37} -4.19314 q^{38} +8.75303 q^{39} +3.06312 q^{40} -4.20597 q^{41} -4.04315 q^{42} -7.29130 q^{43} -0.690395 q^{44} +1.70146 q^{45} +4.22846 q^{46} +0.814588 q^{47} +5.92180 q^{48} -4.67224 q^{49} -1.22218 q^{50} -2.16829 q^{51} +2.04380 q^{52} +4.18387 q^{53} -3.44115 q^{54} +1.36364 q^{55} -4.67341 q^{56} -7.43914 q^{57} -1.43149 q^{58} +10.6756 q^{59} +1.09778 q^{60} -7.52132 q^{61} -7.99280 q^{62} -2.59593 q^{63} +8.87007 q^{64} -4.03684 q^{65} +3.61369 q^{66} +1.96847 q^{67} -0.506288 q^{68} +7.50180 q^{69} +1.86467 q^{70} +1.00000 q^{71} +5.21179 q^{72} -4.11228 q^{73} -3.02200 q^{74} -2.16829 q^{75} -1.73702 q^{76} -2.08051 q^{77} -10.6977 q^{78} +8.96779 q^{79} -2.73110 q^{80} -11.2094 q^{81} +5.14043 q^{82} -4.19715 q^{83} -1.67488 q^{84} +1.00000 q^{85} +8.91124 q^{86} -2.53964 q^{87} +4.17700 q^{88} +10.7285 q^{89} -2.07949 q^{90} +6.15902 q^{91} +1.75165 q^{92} -14.1802 q^{93} -0.995569 q^{94} +3.43089 q^{95} +6.04598 q^{96} -6.04849 q^{97} +5.71029 q^{98} +2.32019 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 58 q + q^{2} + 6 q^{3} + 69 q^{4} + 58 q^{5} + 10 q^{6} + 13 q^{7} - 3 q^{8} + 84 q^{9}+O(q^{10}) \) 58 * q + q^2 + 6 * q^3 + 69 * q^4 + 58 * q^5 + 10 * q^6 + 13 * q^7 - 3 * q^8 + 84 * q^9	\( 58 q + q^{2} + 6 q^{3} + 69 q^{4} + 58 q^{5} + 10 q^{6} + 13 q^{7} - 3 q^{8} + 84 q^{9} + q^{10} + 28 q^{11} + 18 q^{12} + 37 q^{13} + 28 q^{14} + 6 q^{15} + 83 q^{16} + 58 q^{17} - 12 q^{18} + 19 q^{19} + 69 q^{20} + 31 q^{21} + 13 q^{22} + 14 q^{23} + 13 q^{24} + 58 q^{25} + 18 q^{26} + 9 q^{27} + 8 q^{28} + 60 q^{29} + 10 q^{30} + 39 q^{31} - 30 q^{32} + 13 q^{33} + q^{34} + 13 q^{35} + 113 q^{36} + 60 q^{37} - q^{38} + 41 q^{39} - 3 q^{40} + 65 q^{41} - 30 q^{42} + 17 q^{43} + 69 q^{44} + 84 q^{45} + 24 q^{46} + 16 q^{47} + 14 q^{48} + 117 q^{49} + q^{50} + 6 q^{51} + 61 q^{52} + 5 q^{53} + 24 q^{54} + 28 q^{55} + 105 q^{56} + 8 q^{57} - 34 q^{58} + 22 q^{59} + 18 q^{60} + 113 q^{61} - 19 q^{62} + 8 q^{63} + 89 q^{64} + 37 q^{65} - 37 q^{66} + 19 q^{67} + 69 q^{68} + 75 q^{69} + 28 q^{70} + 58 q^{71} - 17 q^{72} + 49 q^{73} + 29 q^{74} + 6 q^{75} - 6 q^{76} + 17 q^{77} - 12 q^{78} + 7 q^{79} + 83 q^{80} + 134 q^{81} + 7 q^{82} - 12 q^{83} - 18 q^{84} + 58 q^{85} + 23 q^{86} - 36 q^{87} - 33 q^{88} + 52 q^{89} - 12 q^{90} + 31 q^{91} + 80 q^{92} - 37 q^{93} + 4 q^{94} + 19 q^{95} - 35 q^{96} + 26 q^{97} - 33 q^{98} + 57 q^{99}+O(q^{100}) \) 58 * q + q^2 + 6 * q^3 + 69 * q^4 + 58 * q^5 + 10 * q^6 + 13 * q^7 - 3 * q^8 + 84 * q^9 + q^10 + 28 * q^11 + 18 * q^12 + 37 * q^13 + 28 * q^14 + 6 * q^15 + 83 * q^16 + 58 * q^17 - 12 * q^18 + 19 * q^19 + 69 * q^20 + 31 * q^21 + 13 * q^22 + 14 * q^23 + 13 * q^24 + 58 * q^25 + 18 * q^26 + 9 * q^27 + 8 * q^28 + 60 * q^29 + 10 * q^30 + 39 * q^31 - 30 * q^32 + 13 * q^33 + q^34 + 13 * q^35 + 113 * q^36 + 60 * q^37 - q^38 + 41 * q^39 - 3 * q^40 + 65 * q^41 - 30 * q^42 + 17 * q^43 + 69 * q^44 + 84 * q^45 + 24 * q^46 + 16 * q^47 + 14 * q^48 + 117 * q^49 + q^50 + 6 * q^51 + 61 * q^52 + 5 * q^53 + 24 * q^54 + 28 * q^55 + 105 * q^56 + 8 * q^57 - 34 * q^58 + 22 * q^59 + 18 * q^60 + 113 * q^61 - 19 * q^62 + 8 * q^63 + 89 * q^64 + 37 * q^65 - 37 * q^66 + 19 * q^67 + 69 * q^68 + 75 * q^69 + 28 * q^70 + 58 * q^71 - 17 * q^72 + 49 * q^73 + 29 * q^74 + 6 * q^75 - 6 * q^76 + 17 * q^77 - 12 * q^78 + 7 * q^79 + 83 * q^80 + 134 * q^81 + 7 * q^82 - 12 * q^83 - 18 * q^84 + 58 * q^85 + 23 * q^86 - 36 * q^87 - 33 * q^88 + 52 * q^89 - 12 * q^90 + 31 * q^91 + 80 * q^92 - 37 * q^93 + 4 * q^94 + 19 * q^95 - 35 * q^96 + 26 * q^97 - 33 * q^98 + 57 * q^99

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