LMFDB - Embedded newform 215.2.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [215,2,Mod(1,215)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(215, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("215.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 215 = 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	215.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:	$1.71678364346$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.1933097.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 7x^{3} + 13x^{2} + 5x - 4 $ x^5 - 2x^4 - 7x^3 + 13x^2 + 5x - 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.667116$ of defining polynomial
Character	$\chi$	$=$	215.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.667116 q^{2} -3.03868 q^{3} -1.55496 q^{4} +1.00000 q^{5} +2.02715 q^{6} -4.17800 q^{7} +2.37157 q^{8} +6.23360 q^{9} +O(q^{10})$	\(q-0.667116 q^{2} -3.03868 q^{3} -1.55496 q^{4} +1.00000 q^{5} +2.02715 q^{6} -4.17800 q^{7} +2.37157 q^{8} +6.23360 q^{9} -0.667116 q^{10} +2.70580 q^{11} +4.72502 q^{12} +4.36004 q^{13} +2.78721 q^{14} -3.03868 q^{15} +1.52780 q^{16} -2.58436 q^{17} -4.15854 q^{18} -2.83128 q^{19} -1.55496 q^{20} +12.6956 q^{21} -1.80508 q^{22} +5.69427 q^{23} -7.20645 q^{24} +1.00000 q^{25} -2.90865 q^{26} -9.82589 q^{27} +6.49661 q^{28} +5.24609 q^{29} +2.02715 q^{30} +4.64924 q^{31} -5.76236 q^{32} -8.22207 q^{33} +1.72407 q^{34} -4.17800 q^{35} -9.69298 q^{36} +1.95593 q^{37} +1.88879 q^{38} -13.2488 q^{39} +2.37157 q^{40} -10.0672 q^{41} -8.46945 q^{42} -1.00000 q^{43} -4.20740 q^{44} +6.23360 q^{45} -3.79874 q^{46} +8.44414 q^{47} -4.64251 q^{48} +10.4557 q^{49} -0.667116 q^{50} +7.85305 q^{51} -6.77967 q^{52} -5.41564 q^{53} +6.55501 q^{54} +2.70580 q^{55} -9.90841 q^{56} +8.60338 q^{57} -3.49975 q^{58} -3.03868 q^{59} +4.72502 q^{60} +10.7201 q^{61} -3.10158 q^{62} -26.0440 q^{63} +0.788558 q^{64} +4.36004 q^{65} +5.48508 q^{66} +13.3302 q^{67} +4.01856 q^{68} -17.3031 q^{69} +2.78721 q^{70} +9.52471 q^{71} +14.7834 q^{72} +10.1486 q^{73} -1.30483 q^{74} -3.03868 q^{75} +4.40252 q^{76} -11.3048 q^{77} +8.83847 q^{78} +11.2902 q^{79} +1.52780 q^{80} +11.1570 q^{81} +6.71598 q^{82} -9.02850 q^{83} -19.7411 q^{84} -2.58436 q^{85} +0.667116 q^{86} -15.9412 q^{87} +6.41699 q^{88} +2.08815 q^{89} -4.15854 q^{90} -18.2162 q^{91} -8.85434 q^{92} -14.1276 q^{93} -5.63322 q^{94} -2.83128 q^{95} +17.5100 q^{96} +14.5256 q^{97} -6.97515 q^{98} +16.8669 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 2 q^{2} - q^{3} + 8 q^{4} + 5 q^{5} - 12 q^{6} + 5 q^{7} + 3 q^{8} + 18 q^{9}+O(q^{10}) $ 5 * q + 2 * q^2 - q^3 + 8 * q^4 + 5 * q^5 - 12 * q^6 + 5 * q^7 + 3 * q^8 + 18 * q^9	\( 5 q + 2 q^{2} - q^{3} + 8 q^{4} + 5 q^{5} - 12 q^{6} + 5 q^{7} + 3 q^{8} + 18 q^{9} + 2 q^{10} - 6 q^{11} + 5 q^{13} + q^{14} - q^{15} + 14 q^{16} - 17 q^{17} - 5 q^{18} - 6 q^{19} + 8 q^{20} + 20 q^{21} - 8 q^{22} + q^{23} - 45 q^{24} + 5 q^{25} + 22 q^{26} - 22 q^{27} + 26 q^{28} + 6 q^{29} - 12 q^{30} + 6 q^{31} - 7 q^{32} - 20 q^{33} + 5 q^{35} + 36 q^{36} + 5 q^{37} - 16 q^{38} - 14 q^{39} + 3 q^{40} + 2 q^{41} - 58 q^{42} - 5 q^{43} - 15 q^{44} + 18 q^{45} - 14 q^{46} - 3 q^{48} + 18 q^{49} + 2 q^{50} - 10 q^{51} - 38 q^{52} - 23 q^{53} - 56 q^{54} - 6 q^{55} - 19 q^{56} + 28 q^{57} + 12 q^{58} - q^{59} + 20 q^{61} - 3 q^{62} + 26 q^{63} - 25 q^{64} + 5 q^{65} + 13 q^{66} + 21 q^{67} - 48 q^{68} + 10 q^{69} + q^{70} + 4 q^{71} + 20 q^{72} + 5 q^{73} + 24 q^{74} - q^{75} + 32 q^{76} - 26 q^{77} + 88 q^{78} + 41 q^{79} + 14 q^{80} + 41 q^{81} + 38 q^{82} - 7 q^{83} - 33 q^{84} - 17 q^{85} - 2 q^{86} - 40 q^{87} + 12 q^{88} + 20 q^{89} - 5 q^{90} - 42 q^{91} - 52 q^{92} - 36 q^{93} - 42 q^{94} - 6 q^{95} + 9 q^{96} + 37 q^{97} - 26 q^{98} + 12 q^{99}+O(q^{100}) \) 5 * q + 2 * q^2 - q^3 + 8 * q^4 + 5 * q^5 - 12 * q^6 + 5 * q^7 + 3 * q^8 + 18 * q^9 + 2 * q^10 - 6 * q^11 + 5 * q^13 + q^14 - q^15 + 14 * q^16 - 17 * q^17 - 5 * q^18 - 6 * q^19 + 8 * q^20 + 20 * q^21 - 8 * q^22 + q^23 - 45 * q^24 + 5 * q^25 + 22 * q^26 - 22 * q^27 + 26 * q^28 + 6 * q^29 - 12 * q^30 + 6 * q^31 - 7 * q^32 - 20 * q^33 + 5 * q^35 + 36 * q^36 + 5 * q^37 - 16 * q^38 - 14 * q^39 + 3 * q^40 + 2 * q^41 - 58 * q^42 - 5 * q^43 - 15 * q^44 + 18 * q^45 - 14 * q^46 - 3 * q^48 + 18 * q^49 + 2 * q^50 - 10 * q^51 - 38 * q^52 - 23 * q^53 - 56 * q^54 - 6 * q^55 - 19 * q^56 + 28 * q^57 + 12 * q^58 - q^59 + 20 * q^61 - 3 * q^62 + 26 * q^63 - 25 * q^64 + 5 * q^65 + 13 * q^66 + 21 * q^67 - 48 * q^68 + 10 * q^69 + q^70 + 4 * q^71 + 20 * q^72 + 5 * q^73 + 24 * q^74 - q^75 + 32 * q^76 - 26 * q^77 + 88 * q^78 + 41 * q^79 + 14 * q^80 + 41 * q^81 + 38 * q^82 - 7 * q^83 - 33 * q^84 - 17 * q^85 - 2 * q^86 - 40 * q^87 + 12 * q^88 + 20 * q^89 - 5 * q^90 - 42 * q^91 - 52 * q^92 - 36 * q^93 - 42 * q^94 - 6 * q^95 + 9 * q^96 + 37 * q^97 - 26 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−0.667116	−0.471722	−0.235861	−	0.971787i	$-0.575791\pi$
$2$	−0.667116	−0.471722	−0.235861	+	0.971787i	$0.575791\pi$
$3$	−3.03868	−1.75439	−0.877193	−	0.480139i	$-0.840586\pi$
$3$	−3.03868	−1.75439	−0.877193	+	0.480139i	$0.840586\pi$
$4$	−1.55496	−0.777478
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.02715	0.827582
$7$	−4.17800	−1.57914	−0.789568	−	0.613664i	$-0.789695\pi$
$7$	−4.17800	−1.57914	−0.789568	+	0.613664i	$0.789695\pi$
$8$	2.37157	0.838476
$9$	6.23360	2.07787
$10$	−0.667116	−0.210961
$11$	2.70580	0.815829	0.407915	−	0.913020i	$-0.366256\pi$
$11$	2.70580	0.815829	0.407915	+	0.913020i	$0.366256\pi$
$12$	4.72502	1.36400
$13$	4.36004	1.20926	0.604629	−	0.796508i	$-0.293322\pi$
$13$	4.36004	1.20926	0.604629	+	0.796508i	$0.293322\pi$
$14$	2.78721	0.744913
$15$	−3.03868	−0.784585
$16$	1.52780	0.381950
$17$	−2.58436	−0.626799	−0.313399	−	0.949621i	$-0.601468\pi$
$17$	−2.58436	−0.626799	−0.313399	+	0.949621i	$0.601468\pi$
$18$	−4.15854	−0.980176
$19$	−2.83128	−0.649541	−0.324770	−	0.945793i	$-0.605287\pi$
$19$	−2.83128	−0.649541	−0.324770	+	0.945793i	$0.605287\pi$
$20$	−1.55496	−0.347699
$21$	12.6956	2.77041
$22$	−1.80508	−0.384845
$23$	5.69427	1.18734	0.593669	−	0.804710i	$-0.297679\pi$
$23$	5.69427	1.18734	0.593669	+	0.804710i	$0.297679\pi$
$24$	−7.20645	−1.47101
$25$	1.00000	0.200000
$26$	−2.90865	−0.570434
$27$	−9.82589	−1.89099
$28$	6.49661	1.22774
$29$	5.24609	0.974174	0.487087	−	0.873354i	$-0.338060\pi$
$29$	5.24609	0.974174	0.487087	+	0.873354i	$0.338060\pi$
$30$	2.02715	0.370106
$31$	4.64924	0.835029	0.417514	−	0.908670i	$-0.362901\pi$
$31$	4.64924	0.835029	0.417514	+	0.908670i	$0.362901\pi$
$32$	−5.76236	−1.01865
$33$	−8.22207	−1.43128
$34$	1.72407	0.295675
$35$	−4.17800	−0.706211
$36$	−9.69298	−1.61550
$37$	1.95593	0.321552	0.160776	−	0.986991i	$-0.448600\pi$
$37$	1.95593	0.321552	0.160776	+	0.986991i	$0.448600\pi$
$38$	1.88879	0.306403
$39$	−13.2488	−2.12150
$40$	2.37157	0.374978
$41$	−10.0672	−1.57223	−0.786115	−	0.618080i	$-0.787911\pi$
$41$	−10.0672	−1.57223	−0.786115	+	0.618080i	$0.787911\pi$
$42$	−8.46945	−1.30686
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−4.20740	−0.634290
$45$	6.23360	0.929250
$46$	−3.79874	−0.560094
$47$	8.44414	1.23171	0.615853	−	0.787861i	$-0.288812\pi$
$47$	8.44414	1.23171	0.615853	+	0.787861i	$0.288812\pi$
$48$	−4.64251	−0.670088
$49$	10.4557	1.49367
$50$	−0.667116	−0.0943444
$51$	7.85305	1.09965
$52$	−6.77967	−0.940171
$53$	−5.41564	−0.743896	−0.371948	−	0.928254i	$-0.621310\pi$
$53$	−5.41564	−0.743896	−0.371948	+	0.928254i	$0.621310\pi$
$54$	6.55501	0.892024
$55$	2.70580	0.364850
$56$	−9.90841	−1.32407
$57$	8.60338	1.13954
$58$	−3.49975	−0.459539
$59$	−3.03868	−0.395603	−0.197801	−	0.980242i	$-0.563380\pi$
$59$	−3.03868	−0.395603	−0.197801	+	0.980242i	$0.563380\pi$
$60$	4.72502	0.609998
$61$	10.7201	1.37257	0.686283	−	0.727335i	$-0.259241\pi$
$61$	10.7201	1.37257	0.686283	+	0.727335i	$0.259241\pi$
$62$	−3.10158	−0.393902
$63$	−26.0440	−3.28123
$64$	0.788558	0.0985697
$65$	4.36004	0.540796
$66$	5.48508	0.675166
$67$	13.3302	1.62854	0.814271	−	0.580485i	$-0.197137\pi$
$67$	13.3302	1.62854	0.814271	+	0.580485i	$0.197137\pi$
$68$	4.01856	0.487322
$69$	−17.3031	−2.08305
$70$	2.78721	0.333135
$71$	9.52471	1.13038	0.565188	−	0.824962i	$-0.308804\pi$
$71$	9.52471	1.13038	0.565188	+	0.824962i	$0.308804\pi$
$72$	14.7834	1.74224
$73$	10.1486	1.18780	0.593902	−	0.804538i	$-0.297587\pi$
$73$	10.1486	1.18780	0.593902	+	0.804538i	$0.297587\pi$
$74$	−1.30483	−0.151683
$75$	−3.03868	−0.350877
$76$	4.40252	0.505004
$77$	−11.3048	−1.28830
$78$	8.83847	1.00076
$79$	11.2902	1.27024	0.635121	−	0.772413i	$-0.280950\pi$
$79$	11.2902	1.27024	0.635121	+	0.772413i	$0.280950\pi$
$80$	1.52780	0.170813
$81$	11.1570	1.23966
$82$	6.71598	0.741656
$83$	−9.02850	−0.991007	−0.495503	−	0.868606i	$-0.665016\pi$
$83$	−9.02850	−0.991007	−0.495503	+	0.868606i	$0.665016\pi$
$84$	−19.7411	−2.15393
$85$	−2.58436	−0.280313
$86$	0.667116	0.0719370
$87$	−15.9412	−1.70908
$88$	6.41699	0.684053
$89$	2.08815	0.221343	0.110672	−	0.993857i	$-0.464700\pi$
$89$	2.08815	0.221343	0.110672	+	0.993857i	$0.464700\pi$
$90$	−4.15854	−0.438348
$91$	−18.2162	−1.90958
$92$	−8.85434	−0.923129
$93$	−14.1276	−1.46496
$94$	−5.63322	−0.581023
$95$	−2.83128	−0.290484
$96$	17.5100	1.78711
$97$	14.5256	1.47485	0.737423	−	0.675431i	$-0.236042\pi$
$97$	14.5256	1.47485	0.737423	+	0.675431i	$0.236042\pi$
$98$	−6.97515	−0.704596
$99$	16.8669	1.69519
$100$	−1.55496	−0.155496
$101$	−2.76236	−0.274865	−0.137432	−	0.990511i	$-0.543885\pi$
$101$	−2.76236	−0.274865	−0.137432	+	0.990511i	$0.543885\pi$
$102$	−5.23889	−0.518728
$103$	2.24692	0.221396	0.110698	−	0.993854i	$-0.464691\pi$
$103$	2.24692	0.221396	0.110698	+	0.993854i	$0.464691\pi$
$104$	10.3401	1.01393
$105$	12.6956	1.23897
$106$	3.61286	0.350912
$107$	8.24288	0.796870	0.398435	−	0.917197i	$-0.369554\pi$
$107$	8.24288	0.796870	0.398435	+	0.917197i	$0.369554\pi$
$108$	15.2788	1.47021
$109$	−20.2540	−1.93998	−0.969992	−	0.243138i	$-0.921823\pi$
$109$	−20.2540	−1.93998	−0.969992	+	0.243138i	$0.921823\pi$
$110$	−1.80508	−0.172108
$111$	−5.94344	−0.564127
$112$	−6.38315	−0.603151
$113$	−3.95368	−0.371931	−0.185965	−	0.982556i	$-0.559541\pi$
$113$	−3.95368	−0.371931	−0.185965	+	0.982556i	$0.559541\pi$
$114$	−5.73945	−0.537549
$115$	5.69427	0.530993
$116$	−8.15743	−0.757399
$117$	27.1787	2.51268
$118$	2.02715	0.186615
$119$	10.7974	0.989800
$120$	−7.20645	−0.657856
$121$	−3.67865	−0.334422
$122$	−7.15154	−0.647470
$123$	30.5910	2.75830
$124$	−7.22937	−0.649217
$125$	1.00000	0.0894427
$126$	17.3744	1.54783
$127$	−4.27459	−0.379308	−0.189654	−	0.981851i	$-0.560737\pi$
$127$	−4.27459	−0.379308	−0.189654	+	0.981851i	$0.560737\pi$
$128$	10.9987	0.972153
$129$	3.03868	0.267541
$130$	−2.90865	−0.255106
$131$	0.301688	0.0263586	0.0131793	−	0.999913i	$-0.495805\pi$
$131$	0.301688	0.0263586	0.0131793	+	0.999913i	$0.495805\pi$
$132$	12.7850	1.11279
$133$	11.8291	1.02571
$134$	−8.89278	−0.768219
$135$	−9.82589	−0.845678
$136$	−6.12898	−0.525556
$137$	17.9858	1.53663	0.768314	−	0.640073i	$-0.221096\pi$
$137$	17.9858	1.53663	0.768314	+	0.640073i	$0.221096\pi$
$138$	11.5432	0.982620
$139$	−11.8659	−1.00645	−0.503227	−	0.864154i	$-0.667854\pi$
$139$	−11.8659	−1.00645	−0.503227	+	0.864154i	$0.667854\pi$
$140$	6.49661	0.549063
$141$	−25.6591	−2.16089
$142$	−6.35409	−0.533223
$143$	11.7974	0.986548
$144$	9.52371	0.793642
$145$	5.24609	0.435664
$146$	−6.77029	−0.560313
$147$	−31.7715	−2.62047
$148$	−3.04138	−0.250000
$149$	−15.3528	−1.25775	−0.628875	−	0.777506i	$-0.716484\pi$
$149$	−15.3528	−1.25775	−0.628875	+	0.777506i	$0.716484\pi$
$150$	2.02715	0.165516
$151$	−6.64271	−0.540576	−0.270288	−	0.962780i	$-0.587119\pi$
$151$	−6.64271	−0.540576	−0.270288	+	0.962780i	$0.587119\pi$
$152$	−6.71458	−0.544624
$153$	−16.1099	−1.30241
$154$	7.54163	0.607722
$155$	4.64924	0.373436
$156$	20.6013	1.64942
$157$	−24.0631	−1.92045	−0.960224	−	0.279231i	$-0.909921\pi$
$157$	−24.0631	−1.92045	−0.960224	+	0.279231i	$0.909921\pi$
$158$	−7.53185	−0.599201
$159$	16.4564	1.30508
$160$	−5.76236	−0.455554
$161$	−23.7907	−1.87497
$162$	−7.44300	−0.584778
$163$	4.95273	0.387927	0.193964	−	0.981009i	$-0.437866\pi$
$163$	4.95273	0.387927	0.193964	+	0.981009i	$0.437866\pi$
$164$	15.6540	1.22237
$165$	−8.22207	−0.640087
$166$	6.02306	0.467480
$167$	−14.8630	−1.15013	−0.575066	−	0.818107i	$-0.695024\pi$
$167$	−14.8630	−1.15013	−0.575066	+	0.818107i	$0.695024\pi$
$168$	30.1085	2.32292
$169$	6.00994	0.462303
$170$	1.72407	0.132230
$171$	−17.6491	−1.34966
$172$	1.55496	0.118564
$173$	−4.19048	−0.318596	−0.159298	−	0.987231i	$-0.550923\pi$
$173$	−4.19048	−0.318596	−0.159298	+	0.987231i	$0.550923\pi$
$174$	10.6346	0.806209
$175$	−4.17800	−0.315827
$176$	4.13393	0.311606
$177$	9.23360	0.694040
$178$	−1.39304	−0.104412
$179$	6.88559	0.514653	0.257327	−	0.966324i	$-0.417158\pi$
$179$	6.88559	0.514653	0.257327	+	0.966324i	$0.417158\pi$
$180$	−9.69298	−0.722472
$181$	14.7262	1.09459	0.547296	−	0.836939i	$-0.315657\pi$
$181$	14.7262	1.09459	0.547296	+	0.836939i	$0.315657\pi$
$182$	12.1523	0.900792
$183$	−32.5749	−2.40801
$184$	13.5044	0.995554
$185$	1.95593	0.143803
$186$	9.42474	0.691055
$187$	−6.99276	−0.511361
$188$	−13.1303	−0.957624
$189$	41.0526	2.98614
$190$	1.88879	0.137028
$191$	3.96616	0.286981	0.143491	−	0.989652i	$-0.454167\pi$
$191$	3.96616	0.286981	0.143491	+	0.989652i	$0.454167\pi$
$192$	−2.39618	−0.172929
$193$	10.9742	0.789940	0.394970	−	0.918694i	$-0.370755\pi$
$193$	10.9742	0.789940	0.394970	+	0.918694i	$0.370755\pi$
$194$	−9.69023	−0.695718
$195$	−13.2488	−0.948765
$196$	−16.2581	−1.16129
$197$	23.8477	1.69908	0.849538	−	0.527528i	$-0.176881\pi$
$197$	23.8477	1.69908	0.849538	+	0.527528i	$0.176881\pi$
$198$	−11.2522	−0.799657
$199$	−3.09135	−0.219140	−0.109570	−	0.993979i	$-0.534947\pi$
$199$	−3.09135	−0.219140	−0.109570	+	0.993979i	$0.534947\pi$
$200$	2.37157	0.167695
$201$	−40.5062	−2.85709
$202$	1.84281	0.129660
$203$	−21.9181	−1.53835
$204$	−12.2111	−0.854951
$205$	−10.0672	−0.703123
$206$	−1.49896	−0.104437
$207$	35.4958	2.46713
$208$	6.66127	0.461876
$209$	−7.66089	−0.529915
$210$	−8.46945	−0.584448
$211$	−2.58391	−0.177883	−0.0889417	−	0.996037i	$-0.528348\pi$
$211$	−2.58391	−0.177883	−0.0889417	+	0.996037i	$0.528348\pi$
$212$	8.42109	0.578363
$213$	−28.9426	−1.98311
$214$	−5.49896	−0.375901
$215$	−1.00000	−0.0681994
$216$	−23.3028	−1.58555
$217$	−19.4245	−1.31862
$218$	13.5118	0.915133
$219$	−30.8384	−2.08386
$220$	−4.20740	−0.283663
$221$	−11.2679	−0.757961
$222$	3.96497	0.266111
$223$	7.43466	0.497862	0.248931	−	0.968521i	$-0.419921\pi$
$223$	7.43466	0.497862	0.248931	+	0.968521i	$0.419921\pi$
$224$	24.0751	1.60859
$225$	6.23360	0.415573
$226$	2.63756	0.175448
$227$	−17.3002	−1.14825	−0.574127	−	0.818766i	$-0.694658\pi$
$227$	−17.3002	−1.14825	−0.574127	+	0.818766i	$0.694658\pi$
$228$	−13.3779	−0.885971
$229$	8.44574	0.558110	0.279055	−	0.960275i	$-0.409979\pi$
$229$	8.44574	0.558110	0.279055	+	0.960275i	$0.409979\pi$
$230$	−3.79874	−0.250481
$231$	34.3518	2.26018
$232$	12.4414	0.816821
$233$	−3.36343	−0.220346	−0.110173	−	0.993912i	$-0.535140\pi$
$233$	−3.36343	−0.220346	−0.110173	+	0.993912i	$0.535140\pi$
$234$	−18.1314	−1.18529
$235$	8.44414	0.550835
$236$	4.72502	0.307573
$237$	−34.3072	−2.22849
$238$	−7.20315	−0.466911
$239$	20.7483	1.34210	0.671049	−	0.741413i	$-0.265844\pi$
$239$	20.7483	1.34210	0.671049	+	0.741413i	$0.265844\pi$
$240$	−4.64251	−0.299672
$241$	19.9689	1.28631	0.643154	−	0.765737i	$-0.277626\pi$
$241$	19.9689	1.28631	0.643154	+	0.765737i	$0.277626\pi$
$242$	2.45408	0.157754
$243$	−4.42487	−0.283855
$244$	−16.6693	−1.06714
$245$	10.4557	0.667988
$246$	−20.4077	−1.30115
$247$	−12.3445	−0.785462
$248$	11.0260	0.700152
$249$	27.4348	1.73861
$250$	−0.667116	−0.0421921
$251$	−7.32749	−0.462507	−0.231254	−	0.972893i	$-0.574283\pi$
$251$	−7.32749	−0.462507	−0.231254	+	0.972893i	$0.574283\pi$
$252$	40.4972	2.55109
$253$	15.4076	0.968665
$254$	2.85165	0.178928
$255$	7.85305	0.491777
$256$	−8.91449	−0.557156
$257$	4.14720	0.258695	0.129348	−	0.991599i	$-0.458712\pi$
$257$	4.14720	0.258695	0.129348	+	0.991599i	$0.458712\pi$
$258$	−2.02715	−0.126205
$259$	−8.17186	−0.507775
$260$	−6.77967	−0.420457
$261$	32.7020	2.02420
$262$	−0.201261	−0.0124339
$263$	−8.18653	−0.504803	−0.252402	−	0.967623i	$-0.581220\pi$
$263$	−8.18653	−0.504803	−0.252402	+	0.967623i	$0.581220\pi$
$264$	−19.4992	−1.20009
$265$	−5.41564	−0.332680
$266$	−7.89138	−0.483852
$267$	−6.34522	−0.388321
$268$	−20.7279	−1.26616
$269$	−12.3576	−0.753455	−0.376728	−	0.926324i	$-0.622951\pi$
$269$	−12.3576	−0.753455	−0.376728	+	0.926324i	$0.622951\pi$
$270$	6.55501	0.398925
$271$	14.6972	0.892792	0.446396	−	0.894836i	$-0.352707\pi$
$271$	14.6972	0.892792	0.446396	+	0.894836i	$0.352707\pi$
$272$	−3.94839	−0.239406
$273$	55.3534	3.35014
$274$	−11.9986	−0.724862
$275$	2.70580	0.163166
$276$	26.9055	1.61952
$277$	25.8094	1.55074	0.775369	−	0.631508i	$-0.217564\pi$
$277$	25.8094	1.55074	0.775369	+	0.631508i	$0.217564\pi$
$278$	7.91595	0.474767
$279$	28.9815	1.73508
$280$	−9.90841	−0.592141
$281$	18.0836	1.07877	0.539387	−	0.842058i	$-0.318656\pi$
$281$	18.0836	1.07877	0.539387	+	0.842058i	$0.318656\pi$
$282$	17.1176	1.01934
$283$	16.7641	0.996520	0.498260	−	0.867028i	$-0.333972\pi$
$283$	16.7641	0.996520	0.498260	+	0.867028i	$0.333972\pi$
$284$	−14.8105	−0.878842
$285$	8.60338	0.509620
$286$	−7.87023	−0.465376
$287$	42.0607	2.48276
$288$	−35.9202	−2.11662
$289$	−10.3211	−0.607123
$290$	−3.49975	−0.205512
$291$	−44.1386	−2.58745
$292$	−15.7806	−0.923491
$293$	−16.4334	−0.960047	−0.480024	−	0.877255i	$-0.659372\pi$
$293$	−16.4334	−0.960047	−0.480024	+	0.877255i	$0.659372\pi$
$294$	21.1953	1.23613
$295$	−3.03868	−0.176919
$296$	4.63861	0.269614
$297$	−26.5869	−1.54273
$298$	10.2421	0.593309
$299$	24.8272	1.43580
$300$	4.72502	0.272799
$301$	4.17800	0.240816
$302$	4.43146	0.255002
$303$	8.39393	0.482219
$304$	−4.32564	−0.248092
$305$	10.7201	0.613830
$306$	10.7471	0.614373
$307$	−10.6830	−0.609710	−0.304855	−	0.952399i	$-0.598608\pi$
$307$	−10.6830	−0.609710	−0.304855	+	0.952399i	$0.598608\pi$
$308$	17.5785	1.00163
$309$	−6.82770	−0.388414
$310$	−3.10158	−0.176158
$311$	−15.8659	−0.899674	−0.449837	−	0.893111i	$-0.648518\pi$
$311$	−15.8659	−0.899674	−0.449837	+	0.893111i	$0.648518\pi$
$312$	−31.4204	−1.77883
$313$	4.80484	0.271586	0.135793	−	0.990737i	$-0.456642\pi$
$313$	4.80484	0.271586	0.135793	+	0.990737i	$0.456642\pi$
$314$	16.0529	0.905918
$315$	−26.0440	−1.46741
$316$	−17.5557	−0.987585
$317$	−10.8272	−0.608118	−0.304059	−	0.952653i	$-0.598342\pi$
$317$	−10.8272	−0.608118	−0.304059	+	0.952653i	$0.598342\pi$
$318$	−10.9783	−0.615635
$319$	14.1949	0.794759
$320$	0.788558	0.0440817
$321$	−25.0475	−1.39802
$322$	15.8711	0.884463
$323$	7.31705	0.407132
$324$	−17.3486	−0.963812
$325$	4.36004	0.241851
$326$	−3.30404	−0.182994
$327$	61.5456	3.40348
$328$	−23.8750	−1.31828
$329$	−35.2796	−1.94503
$330$	5.48508	0.301943
$331$	1.47399	0.0810180	0.0405090	−	0.999179i	$-0.487102\pi$
$331$	1.47399	0.0810180	0.0405090	+	0.999179i	$0.487102\pi$
$332$	14.0389	0.770486
$333$	12.1925	0.668143
$334$	9.91534	0.542543
$335$	13.3302	0.728306
$336$	19.3964	1.05816
$337$	32.6953	1.78102	0.890512	−	0.454959i	$-0.150346\pi$
$337$	32.6953	1.78102	0.890512	+	0.454959i	$0.150346\pi$
$338$	−4.00933	−0.218079
$339$	12.0140	0.652510
$340$	4.01856	0.217937
$341$	12.5799	0.681241
$342$	11.7740	0.636665
$343$	−14.4378	−0.779568
$344$	−2.37157	−0.127866
$345$	−17.3031	−0.931567
$346$	2.79554	0.150289
$347$	−16.3413	−0.877245	−0.438623	−	0.898671i	$-0.644533\pi$
$347$	−16.3413	−0.877245	−0.438623	+	0.898671i	$0.644533\pi$
$348$	24.7879	1.32877
$349$	−1.01986	−0.0545917	−0.0272959	−	0.999627i	$-0.508690\pi$
$349$	−1.01986	−0.0545917	−0.0272959	+	0.999627i	$0.508690\pi$
$350$	2.78721	0.148983
$351$	−42.8413	−2.28670
$352$	−15.5918	−0.831045
$353$	−19.4726	−1.03642	−0.518212	−	0.855252i	$-0.673402\pi$
$353$	−19.4726	−1.03642	−0.518212	+	0.855252i	$0.673402\pi$
$354$	−6.15988	−0.327394
$355$	9.52471	0.505519
$356$	−3.24698	−0.172089
$357$	−32.8100	−1.73649
$358$	−4.59349	−0.242773
$359$	3.90631	0.206167	0.103084	−	0.994673i	$-0.467129\pi$
$359$	3.90631	0.206167	0.103084	+	0.994673i	$0.467129\pi$
$360$	14.7834	0.779154
$361$	−10.9838	−0.578097
$362$	−9.82410	−0.516343
$363$	11.1782	0.586706
$364$	28.3255	1.48466
$365$	10.1486	0.531202
$366$	21.7313	1.13591
$367$	8.27672	0.432041	0.216021	−	0.976389i	$-0.430692\pi$
$367$	8.27672	0.432041	0.216021	+	0.976389i	$0.430692\pi$
$368$	8.69971	0.453504
$369$	−62.7548	−3.26689
$370$	−1.30483	−0.0678349
$371$	22.6265	1.17471
$372$	21.9678	1.13898
$373$	−24.3808	−1.26239	−0.631194	−	0.775625i	$-0.717435\pi$
$373$	−24.3808	−1.26239	−0.631194	+	0.775625i	$0.717435\pi$
$374$	4.66498	0.241220
$375$	−3.03868	−0.156917
$376$	20.0259	1.03276
$377$	22.8731	1.17803
$378$	−27.3868	−1.40863
$379$	29.5290	1.51680	0.758401	−	0.651788i	$-0.225981\pi$
$379$	29.5290	1.51680	0.758401	+	0.651788i	$0.225981\pi$
$380$	4.40252	0.225845
$381$	12.9891	0.665453
$382$	−2.64589	−0.135376
$383$	−32.1155	−1.64103	−0.820514	−	0.571627i	$-0.806313\pi$
$383$	−32.1155	−1.64103	−0.820514	+	0.571627i	$0.806313\pi$
$384$	−33.4214	−1.70553
$385$	−11.3048	−0.576147
$386$	−7.32106	−0.372632
$387$	−6.23360	−0.316872
$388$	−22.5866	−1.14666
$389$	23.1846	1.17551	0.587753	−	0.809041i	$-0.300013\pi$
$389$	23.1846	1.17551	0.587753	+	0.809041i	$0.300013\pi$
$390$	8.83847	0.447554
$391$	−14.7160	−0.744222
$392$	24.7963	1.25240
$393$	−0.916734	−0.0462431
$394$	−15.9092	−0.801492
$395$	11.2902	0.568070
$396$	−26.2273	−1.31797
$397$	−23.4162	−1.17523	−0.587613	−	0.809142i	$-0.699932\pi$
$397$	−23.4162	−1.17523	−0.587613	+	0.809142i	$0.699932\pi$
$398$	2.06229	0.103373
$399$	−35.9449	−1.79950
$400$	1.52780	0.0763901
$401$	10.9387	0.546250	0.273125	−	0.961979i	$-0.411943\pi$
$401$	10.9387	0.546250	0.273125	+	0.961979i	$0.411943\pi$
$402$	27.0224	1.34775
$403$	20.2709	1.00976
$404$	4.29534	0.213701
$405$	11.1570	0.554395
$406$	14.6219	0.725675
$407$	5.29235	0.262332
$408$	18.6240	0.922027
$409$	10.4441	0.516430	0.258215	−	0.966088i	$-0.416866\pi$
$409$	10.4441	0.516430	0.258215	+	0.966088i	$0.416866\pi$
$410$	6.71598	0.331679
$411$	−54.6531	−2.69584
$412$	−3.49387	−0.172131
$413$	12.6956	0.624711
$414$	−23.6798	−1.16380
$415$	−9.02850	−0.443192
$416$	−25.1241	−1.23181
$417$	36.0568	1.76571
$418$	5.11070	0.249973
$419$	20.0258	0.978322	0.489161	−	0.872193i	$-0.337303\pi$
$419$	20.0258	0.978322	0.489161	+	0.872193i	$0.337303\pi$
$420$	−19.7411	−0.963269
$421$	−2.85793	−0.139287	−0.0696435	−	0.997572i	$-0.522186\pi$
$421$	−2.85793	−0.139287	−0.0696435	+	0.997572i	$0.522186\pi$
$422$	1.72376	0.0839115
$423$	52.6374	2.55932
$424$	−12.8436	−0.623739
$425$	−2.58436	−0.125360
$426$	19.3081	0.935479
$427$	−44.7885	−2.16747
$428$	−12.8173	−0.619549
$429$	−35.8486	−1.73078
$430$	0.667116	0.0321712
$431$	−24.4570	−1.17805	−0.589027	−	0.808114i	$-0.700489\pi$
$431$	−24.4570	−1.17805	−0.589027	+	0.808114i	$0.700489\pi$
$432$	−15.0120	−0.722266
$433$	15.2128	0.731080	0.365540	−	0.930796i	$-0.380884\pi$
$433$	15.2128	0.731080	0.365540	+	0.930796i	$0.380884\pi$
$434$	12.9584	0.622024
$435$	−15.9412	−0.764322
$436$	31.4941	1.50829
$437$	−16.1221	−0.771224
$438$	20.5728	0.983005
$439$	5.90297	0.281733	0.140867	−	0.990029i	$-0.455011\pi$
$439$	5.90297	0.281733	0.140867	+	0.990029i	$0.455011\pi$
$440$	6.41699	0.305918
$441$	65.1765	3.10364
$442$	7.51700	0.357547
$443$	−24.3026	−1.15465	−0.577325	−	0.816514i	$-0.695904\pi$
$443$	−24.3026	−1.15465	−0.577325	+	0.816514i	$0.695904\pi$
$444$	9.24179	0.438596
$445$	2.08815	0.0989877
$446$	−4.95978	−0.234852
$447$	46.6523	2.20658
$448$	−3.29459	−0.155655
$449$	−3.64670	−0.172098	−0.0860492	−	0.996291i	$-0.527424\pi$
$449$	−3.64670	−0.172098	−0.0860492	+	0.996291i	$0.527424\pi$
$450$	−4.15854	−0.196035
$451$	−27.2398	−1.28267
$452$	6.14780	0.289168
$453$	20.1851	0.948379
$454$	11.5412	0.541657
$455$	−18.2162	−0.853990
$456$	20.4035	0.955481
$457$	−23.2754	−1.08878	−0.544388	−	0.838833i	$-0.683238\pi$
$457$	−23.2754	−1.08878	−0.544388	+	0.838833i	$0.683238\pi$
$458$	−5.63429	−0.263273
$459$	25.3936	1.18527
$460$	−8.85434	−0.412836
$461$	8.87536	0.413367	0.206683	−	0.978408i	$-0.433733\pi$
$461$	8.87536	0.413367	0.206683	+	0.978408i	$0.433733\pi$
$462$	−22.9166	−1.06618
$463$	6.86358	0.318978	0.159489	−	0.987200i	$-0.449015\pi$
$463$	6.86358	0.318978	0.159489	+	0.987200i	$0.449015\pi$
$464$	8.01498	0.372086
$465$	−14.1276	−0.655151
$466$	2.24380	0.103942
$467$	−21.3288	−0.986981	−0.493491	−	0.869751i	$-0.664279\pi$
$467$	−21.3288	−0.986981	−0.493491	+	0.869751i	$0.664279\pi$
$468$	−42.2618	−1.95355
$469$	−55.6935	−2.57169
$470$	−5.63322	−0.259841
$471$	73.1203	3.36921
$472$	−7.20645	−0.331704
$473$	−2.70580	−0.124413
$474$	22.8869	1.05123
$475$	−2.83128	−0.129908
$476$	−16.7896	−0.769548
$477$	−33.7590	−1.54572
$478$	−13.8415	−0.633097
$479$	−19.3177	−0.882649	−0.441324	−	0.897348i	$-0.645491\pi$
$479$	−19.3177	−0.882649	−0.441324	+	0.897348i	$0.645491\pi$
$480$	17.5100	0.799218
$481$	8.52792	0.388839
$482$	−13.3215	−0.606780
$483$	72.2923	3.28941
$484$	5.72013	0.260006
$485$	14.5256	0.659571
$486$	2.95190	0.133901
$487$	1.05482	0.0477982	0.0238991	−	0.999714i	$-0.492392\pi$
$487$	1.05482	0.0477982	0.0238991	+	0.999714i	$0.492392\pi$
$488$	25.4234	1.15086
$489$	−15.0498	−0.680574
$490$	−6.97515	−0.315105
$491$	13.3031	0.600360	0.300180	−	0.953883i	$-0.402953\pi$
$491$	13.3031	0.600360	0.300180	+	0.953883i	$0.402953\pi$
$492$	−47.5677	−2.14452
$493$	−13.5578	−0.610611
$494$	8.23522	0.370520
$495$	16.8669	0.758110
$496$	7.10312	0.318940
$497$	−39.7942	−1.78502
$498$	−18.3022	−0.820140
$499$	16.6442	0.745097	0.372549	−	0.928013i	$-0.378484\pi$
$499$	16.6442	0.745097	0.372549	+	0.928013i	$0.378484\pi$
$500$	−1.55496	−0.0695398
$501$	45.1639	2.01778
$502$	4.88829	0.218175
$503$	0.626638	0.0279404	0.0139702	−	0.999902i	$-0.495553\pi$
$503$	0.626638	0.0279404	0.0139702	+	0.999902i	$0.495553\pi$
$504$	−61.7651	−2.75124
$505$	−2.76236	−0.122923
$506$	−10.2786	−0.456941
$507$	−18.2623	−0.811057
$508$	6.64680	0.294904
$509$	−6.26851	−0.277847	−0.138923	−	0.990303i	$-0.544364\pi$
$509$	−6.26851	−0.277847	−0.138923	+	0.990303i	$0.544364\pi$
$510$	−5.23889	−0.231982
$511$	−42.4008	−1.87570
$512$	−16.0503	−0.709330
$513$	27.8199	1.22828
$514$	−2.76666	−0.122032
$515$	2.24692	0.0990113
$516$	−4.72502	−0.208007
$517$	22.8482	1.00486
$518$	5.45158	0.239529
$519$	12.7336	0.558941
$520$	10.3401	0.453445
$521$	13.0619	0.572252	0.286126	−	0.958192i	$-0.407632\pi$
$521$	13.0619	0.572252	0.286126	+	0.958192i	$0.407632\pi$
$522$	−21.8160	−0.954862
$523$	−2.34385	−0.102490	−0.0512448	−	0.998686i	$-0.516319\pi$
$523$	−2.34385	−0.102490	−0.0512448	+	0.998686i	$0.516319\pi$
$524$	−0.469111	−0.0204932
$525$	12.6956	0.554082
$526$	5.46137	0.238127
$527$	−12.0153	−0.523395
$528$	−12.5617	−0.546678
$529$	9.42472	0.409770
$530$	3.61286	0.156933
$531$	−18.9419	−0.822010
$532$	−18.3937	−0.797469
$533$	−43.8933	−1.90123
$534$	4.23300	0.183180
$535$	8.24288	0.356371
$536$	31.6135	1.36549
$537$	−20.9231	−0.902900
$538$	8.24394	0.355422
$539$	28.2910	1.21858
$540$	15.2788	0.657496
$541$	−27.6634	−1.18934	−0.594671	−	0.803969i	$-0.702718\pi$
$541$	−27.6634	−1.18934	−0.594671	+	0.803969i	$0.702718\pi$
$542$	−9.80474	−0.421150
$543$	−44.7483	−1.92033
$544$	14.8920	0.638489
$545$	−20.2540	−0.867587
$546$	−36.9271	−1.58034
$547$	24.1791	1.03383	0.516913	−	0.856038i	$-0.327081\pi$
$547$	24.1791	1.03383	0.516913	+	0.856038i	$0.327081\pi$
$548$	−27.9671	−1.19470
$549$	66.8247	2.85201
$550$	−1.80508	−0.0769690
$551$	−14.8532	−0.632766
$552$	−41.0355	−1.74659
$553$	−47.1703	−2.00588
$554$	−17.2179	−0.731518
$555$	−5.94344	−0.252285
$556$	18.4510	0.782497
$557$	−21.9737	−0.931055	−0.465528	−	0.885033i	$-0.654135\pi$
$557$	−21.9737	−0.931055	−0.465528	+	0.885033i	$0.654135\pi$
$558$	−19.3340	−0.818475
$559$	−4.36004	−0.184410
$560$	−6.38315	−0.269737
$561$	21.2488	0.897124
$562$	−12.0638	−0.508882
$563$	−1.06155	−0.0447391	−0.0223695	−	0.999750i	$-0.507121\pi$
$563$	−1.06155	−0.0447391	−0.0223695	+	0.999750i	$0.507121\pi$
$564$	39.8988	1.68004
$565$	−3.95368	−0.166333
$566$	−11.1836	−0.470081
$567$	−46.6139	−1.95760
$568$	22.5885	0.947793
$569$	28.6235	1.19996	0.599980	−	0.800015i	$-0.295175\pi$
$569$	28.6235	1.19996	0.599980	+	0.800015i	$0.295175\pi$
$570$	−5.73945	−0.240399
$571$	26.6889	1.11690	0.558449	−	0.829539i	$-0.311397\pi$
$571$	26.6889	1.11690	0.558449	+	0.829539i	$0.311397\pi$
$572$	−18.3444	−0.767019
$573$	−12.0519	−0.503476
$574$	−28.0594	−1.17118
$575$	5.69427	0.237468
$576$	4.91556	0.204815
$577$	−3.26004	−0.135717	−0.0678587	−	0.997695i	$-0.521617\pi$
$577$	−3.26004	−0.135717	−0.0678587	+	0.997695i	$0.521617\pi$
$578$	6.88537	0.286393
$579$	−33.3471	−1.38586
$580$	−8.15743	−0.338719
$581$	37.7211	1.56493
$582$	29.4455	1.22056
$583$	−14.6536	−0.606892
$584$	24.0681	0.995945
$585$	27.1787	1.12370
$586$	10.9630	0.452876
$587$	−32.9611	−1.36045	−0.680225	−	0.733004i	$-0.738118\pi$
$587$	−32.9611	−1.36045	−0.680225	+	0.733004i	$0.738118\pi$
$588$	49.4033	2.03736
$589$	−13.1633	−0.542385
$590$	2.02715	0.0834566
$591$	−72.4655	−2.98083
$592$	2.98827	0.122817
$593$	16.3019	0.669440	0.334720	−	0.942318i	$-0.391358\pi$
$593$	16.3019	0.669440	0.334720	+	0.942318i	$0.391358\pi$
$594$	17.7366	0.727739
$595$	10.7974	0.442652
$596$	23.8729	0.977873
$597$	9.39363	0.384456
$598$	−16.5627	−0.677297
$599$	−15.5570	−0.635642	−0.317821	−	0.948151i	$-0.602951\pi$
$599$	−15.5570	−0.635642	−0.317821	+	0.948151i	$0.602951\pi$
$600$	−7.20645	−0.294202
$601$	0.0149762	0.000610890 0	0.000305445	−	1.00000i	$-0.499903\pi$
$601$	0.0149762	0.000610890 0	0.000305445		1.00000i	$0.499903\pi$
$602$	−2.78721	−0.113598
$603$	83.0951	3.38389
$604$	10.3291	0.420286
$605$	−3.67865	−0.149558
$606$	−5.59973	−0.227473
$607$	27.4196	1.11293	0.556465	−	0.830871i	$-0.312157\pi$
$607$	27.4196	1.11293	0.556465	+	0.830871i	$0.312157\pi$
$608$	16.3149	0.661655
$609$	66.6023	2.69886
$610$	−7.15154	−0.289557
$611$	36.8168	1.48945
$612$	25.0501	1.01259
$613$	31.4158	1.26887	0.634436	−	0.772975i	$-0.281232\pi$
$613$	31.4158	1.26887	0.634436	+	0.772975i	$0.281232\pi$
$614$	7.12679	0.287614
$615$	30.5910	1.23355
$616$	−26.8102	−1.08021
$617$	27.4600	1.10550	0.552748	−	0.833348i	$-0.313579\pi$
$617$	27.4600	1.10550	0.552748	+	0.833348i	$0.313579\pi$
$618$	4.55486	0.183224
$619$	−8.94419	−0.359498	−0.179749	−	0.983713i	$-0.557528\pi$
$619$	−8.94419	−0.359498	−0.179749	+	0.983713i	$0.557528\pi$
$620$	−7.22937	−0.290338
$621$	−55.9513	−2.24525
$622$	10.5844	0.424396
$623$	−8.72428	−0.349531
$624$	−20.2415	−0.810309
$625$	1.00000	0.0400000
$626$	−3.20539	−0.128113
$627$	23.2790	0.929674
$628$	37.4171	1.49311
$629$	−5.05482	−0.201549
$630$	17.3744	0.692211
$631$	−0.678048	−0.0269927	−0.0134963	−	0.999909i	$-0.504296\pi$
$631$	−0.678048	−0.0269927	−0.0134963	+	0.999909i	$0.504296\pi$
$632$	26.7754	1.06507
$633$	7.85167	0.312076
$634$	7.22303	0.286863
$635$	−4.27459	−0.169632
$636$	−25.5890	−1.01467
$637$	45.5871	1.80623
$638$	−9.46962	−0.374906
$639$	59.3733	2.34877
$640$	10.9987	0.434760
$641$	24.7590	0.977922	0.488961	−	0.872306i	$-0.337376\pi$
$641$	24.7590	0.977922	0.488961	+	0.872306i	$0.337376\pi$
$642$	16.7096	0.659475
$643$	−13.3021	−0.524583	−0.262291	−	0.964989i	$-0.584478\pi$
$643$	−13.3021	−0.524583	−0.262291	+	0.964989i	$0.584478\pi$
$644$	36.9934	1.45775
$645$	3.03868	0.119648
$646$	−4.88132	−0.192053
$647$	−38.4734	−1.51255	−0.756273	−	0.654257i	$-0.772982\pi$
$647$	−38.4734	−1.51255	−0.756273	+	0.654257i	$0.772982\pi$
$648$	26.4595	1.03943
$649$	−8.22207	−0.322745
$650$	−2.90865	−0.114087
$651$	59.0250	2.31337
$652$	−7.70127	−0.301605
$653$	−47.7958	−1.87040	−0.935198	−	0.354125i	$-0.884779\pi$
$653$	−47.7958	−1.87040	−0.935198	+	0.354125i	$0.884779\pi$
$654$	−41.0580	−1.60550
$655$	0.301688	0.0117879
$656$	−15.3807	−0.600514
$657$	63.2623	2.46810
$658$	23.5356	0.917513
$659$	0.962771	0.0375042	0.0187521	−	0.999824i	$-0.494031\pi$
$659$	0.962771	0.0375042	0.0187521	+	0.999824i	$0.494031\pi$
$660$	12.7850	0.497654
$661$	21.5317	0.837486	0.418743	−	0.908105i	$-0.362471\pi$
$661$	21.5317	0.837486	0.418743	+	0.908105i	$0.362471\pi$
$662$	−0.983324	−0.0382180
$663$	34.2396	1.32976
$664$	−21.4117	−0.830936
$665$	11.8291	0.458713
$666$	−8.13379	−0.315178
$667$	29.8726	1.15667
$668$	23.1113	0.894203
$669$	−22.5916	−0.873441
$670$	−8.89278	−0.343558
$671$	29.0064	1.11978
$672$	−73.1567	−2.82208
$673$	−17.8883	−0.689541	−0.344771	−	0.938687i	$-0.612043\pi$
$673$	−17.8883	−0.689541	−0.344771	+	0.938687i	$0.612043\pi$
$674$	−21.8115	−0.840149
$675$	−9.82589	−0.378199
$676$	−9.34519	−0.359430
$677$	8.85919	0.340486	0.170243	−	0.985402i	$-0.445545\pi$
$677$	8.85919	0.340486	0.170243	+	0.985402i	$0.445545\pi$
$678$	−8.01472	−0.307803
$679$	−60.6877	−2.32898
$680$	−6.12898	−0.235036
$681$	52.5698	2.01448
$682$	−8.39227	−0.321357
$683$	−28.8869	−1.10533	−0.552664	−	0.833404i	$-0.686389\pi$
$683$	−28.8869	−1.10533	−0.552664	+	0.833404i	$0.686389\pi$
$684$	27.4436	1.04933
$685$	17.9858	0.687201
$686$	9.63169	0.367740
$687$	−25.6639	−0.979140
$688$	−1.52780	−0.0582469
$689$	−23.6124	−0.899561
$690$	11.5432	0.439441
$691$	−43.8504	−1.66815	−0.834073	−	0.551654i	$-0.813997\pi$
$691$	−43.8504	−1.66815	−0.834073	+	0.551654i	$0.813997\pi$
$692$	6.51602	0.247702
$693$	−70.4698	−2.67693
$694$	10.9015	0.413816
$695$	−11.8659	−0.450100
$696$	−37.8056	−1.43302
$697$	26.0172	0.985472
$698$	0.680363	0.0257521
$699$	10.2204	0.386571
$700$	6.49661	0.245549
$701$	21.8597	0.825629	0.412815	−	0.910815i	$-0.364546\pi$
$701$	21.8597	0.825629	0.412815	+	0.910815i	$0.364546\pi$
$702$	28.5801	1.07869
$703$	−5.53778	−0.208861
$704$	2.13368	0.0804161
$705$	−25.6591	−0.966377
$706$	12.9905	0.488904
$707$	11.5411	0.434049
$708$	−14.3578	−0.539601
$709$	−35.0273	−1.31548	−0.657740	−	0.753245i	$-0.728487\pi$
$709$	−35.0273	−1.31548	−0.657740	+	0.753245i	$0.728487\pi$
$710$	−6.35409	−0.238465
$711$	70.3784	2.63939
$712$	4.95218	0.185591
$713$	26.4741	0.991461
$714$	21.8881	0.819141
$715$	11.7974	0.441198
$716$	−10.7068	−0.400132
$717$	−63.0476	−2.35456
$718$	−2.60596	−0.0972536
$719$	0.792596	0.0295589	0.0147794	−	0.999891i	$-0.495295\pi$
$719$	0.792596	0.0295589	0.0147794	+	0.999891i	$0.495295\pi$
$720$	9.52371	0.354928
$721$	−9.38765	−0.349614
$722$	7.32749	0.272701
$723$	−60.6791	−2.25668
$724$	−22.8986	−0.851021
$725$	5.24609	0.194835
$726$	−7.45718	−0.276762
$727$	11.3417	0.420639	0.210320	−	0.977633i	$-0.432550\pi$
$727$	11.3417	0.420639	0.210320	+	0.977633i	$0.432550\pi$
$728$	−43.2010	−1.60114
$729$	−20.0252	−0.741673
$730$	−6.77029	−0.250580
$731$	2.58436	0.0955859
$732$	50.6526	1.87217
$733$	−30.5953	−1.13006	−0.565031	−	0.825069i	$-0.691136\pi$
$733$	−30.5953	−1.13006	−0.565031	+	0.825069i	$0.691136\pi$
$734$	−5.52153	−0.203803
$735$	−31.7715	−1.17191
$736$	−32.8124	−1.20948
$737$	36.0688	1.32861
$738$	41.8648	1.54106
$739$	−14.0643	−0.517364	−0.258682	−	0.965963i	$-0.583288\pi$
$739$	−14.0643	−0.517364	−0.258682	+	0.965963i	$0.583288\pi$
$740$	−3.04138	−0.111803
$741$	37.5111	1.37800
$742$	−15.0945	−0.554138
$743$	−2.26441	−0.0830730	−0.0415365	−	0.999137i	$-0.513225\pi$
$743$	−2.26441	−0.0830730	−0.0415365	+	0.999137i	$0.513225\pi$
$744$	−33.5045	−1.22834
$745$	−15.3528	−0.562483
$746$	16.2648	0.595496
$747$	−56.2801	−2.05918
$748$	10.8734	0.397572
$749$	−34.4388	−1.25836
$750$	2.02715	0.0740212
$751$	29.0652	1.06060	0.530302	−	0.847809i	$-0.322079\pi$
$751$	29.0652	1.06060	0.530302	+	0.847809i	$0.322079\pi$
$752$	12.9010	0.470450
$753$	22.2659	0.811416
$754$	−15.2590	−0.555701
$755$	−6.64271	−0.241753
$756$	−63.8350	−2.32165
$757$	−35.3092	−1.28333	−0.641667	−	0.766983i	$-0.721757\pi$
$757$	−35.3092	−1.28333	−0.641667	+	0.766983i	$0.721757\pi$
$758$	−19.6993	−0.715510
$759$	−46.8187	−1.69941
$760$	−6.71458	−0.243563
$761$	−33.6653	−1.22036	−0.610182	−	0.792261i	$-0.708904\pi$
$761$	−33.6653	−1.22036	−0.610182	+	0.792261i	$0.708904\pi$
$762$	−8.66525	−0.313909
$763$	84.6213	3.06350
$764$	−6.16721	−0.223122
$765$	−16.1099	−0.582453
$766$	21.4248	0.774109
$767$	−13.2488	−0.478386
$768$	27.0883	0.977466
$769$	2.70131	0.0974117	0.0487059	−	0.998813i	$-0.484490\pi$
$769$	2.70131	0.0974117	0.0487059	+	0.998813i	$0.484490\pi$
$770$	7.54163	0.271782
$771$	−12.6020	−0.453851
$772$	−17.0644	−0.614161
$773$	−3.35121	−0.120535	−0.0602673	−	0.998182i	$-0.519195\pi$
$773$	−3.35121	−0.120535	−0.0602673	+	0.998182i	$0.519195\pi$
$774$	4.15854	0.149475
$775$	4.64924	0.167006
$776$	34.4483	1.23662
$777$	24.8317	0.890832
$778$	−15.4668	−0.554512
$779$	28.5031	1.02123
$780$	20.6013	0.737644
$781$	25.7720	0.922194
$782$	9.81730	0.351066
$783$	−51.5475	−1.84216
$784$	15.9742	0.570507
$785$	−24.0631	−0.858851
$786$	0.611568	0.0218139
$787$	38.2795	1.36452	0.682259	−	0.731111i	$-0.260998\pi$
$787$	38.2795	1.36452	0.682259	+	0.731111i	$0.260998\pi$
$788$	−37.0821	−1.32099
$789$	24.8763	0.885619
$790$	−7.53185	−0.267971
$791$	16.5185	0.587329
$792$	40.0010	1.42137
$793$	46.7400	1.65978
$794$	15.6213	0.554380
$795$	16.4564	0.583649
$796$	4.80691	0.170376
$797$	0.585709	0.0207469	0.0103734	−	0.999946i	$-0.496698\pi$
$797$	0.585709	0.0207469	0.0103734	+	0.999946i	$0.496698\pi$
$798$	23.9794	0.848862
$799$	−21.8227	−0.772031
$800$	−5.76236	−0.203730
$801$	13.0167	0.459922
$802$	−7.29735	−0.257678
$803$	27.4601	0.969045
$804$	62.9854	2.22132
$805$	−23.7907	−0.838510
$806$	−13.5230	−0.476328
$807$	37.5508	1.32185
$808$	−6.55112	−0.230468
$809$	−45.1595	−1.58772	−0.793861	−	0.608099i	$-0.791932\pi$
$809$	−45.1595	−1.58772	−0.793861	+	0.608099i	$0.791932\pi$
$810$	−7.44300	−0.261520
$811$	−17.4128	−0.611446	−0.305723	−	0.952121i	$-0.598898\pi$
$811$	−17.4128	−0.611446	−0.305723	+	0.952121i	$0.598898\pi$
$812$	34.0817	1.19603
$813$	−44.6602	−1.56630
$814$	−3.53061	−0.123748
$815$	4.95273	0.173486
$816$	11.9979	0.420010
$817$	2.83128	0.0990541
$818$	−6.96746	−0.243611
$819$	−113.553	−3.96785
$820$	15.6540	0.546663
$821$	−36.2816	−1.26624	−0.633119	−	0.774055i	$-0.718225\pi$
$821$	−36.2816	−1.26624	−0.633119	+	0.774055i	$0.718225\pi$
$822$	36.4600	1.27169
$823$	−50.3506	−1.75511	−0.877557	−	0.479473i	$-0.840828\pi$
$823$	−50.3506	−1.75511	−0.877557	+	0.479473i	$0.840828\pi$
$824$	5.32874	0.185635
$825$	−8.22207	−0.286256
$826$	−8.46945	−0.294690
$827$	0.00449454	0.000156291 0	7.81453e−5	−	1.00000i	$-0.499975\pi$
$827$	0.00449454	0.000156291 0	7.81453e−5		1.00000i	$0.499975\pi$
$828$	−55.1944	−1.91814
$829$	7.34740	0.255186	0.127593	−	0.991827i	$-0.459275\pi$
$829$	7.34740	0.255186	0.127593	+	0.991827i	$0.459275\pi$
$830$	6.02306	0.209063
$831$	−78.4267	−2.72059
$832$	3.43814	0.119196
$833$	−27.0212	−0.936229
$834$	−24.0541	−0.832924
$835$	−14.8630	−0.514355
$836$	11.9123	0.411997
$837$	−45.6830	−1.57903
$838$	−13.3595	−0.461496
$839$	37.6999	1.30155	0.650773	−	0.759272i	$-0.274445\pi$
$839$	37.6999	1.30155	0.650773	+	0.759272i	$0.274445\pi$
$840$	30.1085	1.03884
$841$	−1.47859	−0.0509859
$842$	1.90657	0.0657048
$843$	−54.9502	−1.89259
$844$	4.01786	0.138300
$845$	6.00994	0.206748
$846$	−35.1153	−1.20729
$847$	15.3694	0.528098
$848$	−8.27402	−0.284131
$849$	−50.9407	−1.74828
$850$	1.72407	0.0591350
$851$	11.1376	0.381791
$852$	45.0045	1.54183
$853$	−30.3162	−1.03801	−0.519004	−	0.854772i	$-0.673697\pi$
$853$	−30.3162	−1.03801	−0.519004	+	0.854772i	$0.673697\pi$
$854$	29.8791	1.02244
$855$	−17.6491	−0.603586
$856$	19.5486	0.668156
$857$	1.69382	0.0578597	0.0289299	−	0.999581i	$-0.490790\pi$
$857$	1.69382	0.0578597	0.0289299	+	0.999581i	$0.490790\pi$
$858$	23.9151	0.816450
$859$	11.9716	0.408464	0.204232	−	0.978922i	$-0.434530\pi$
$859$	11.9716	0.408464	0.204232	+	0.978922i	$0.434530\pi$
$860$	1.55496	0.0530236
$861$	−127.809	−4.35572
$862$	16.3157	0.555714
$863$	22.9766	0.782134	0.391067	−	0.920362i	$-0.372106\pi$
$863$	22.9766	0.782134	0.391067	+	0.920362i	$0.372106\pi$
$864$	56.6203	1.92626
$865$	−4.19048	−0.142481
$866$	−10.1487	−0.344867
$867$	31.3625	1.06513
$868$	30.2043	1.02520
$869$	30.5489	1.03630
$870$	10.6346	0.360548
$871$	58.1201	1.96933
$872$	−48.0338	−1.62663
$873$	90.5465	3.06454
$874$	10.7553	0.363804
$875$	−4.17800	−0.141242
$876$	47.9523	1.62016
$877$	19.8240	0.669410	0.334705	−	0.942323i	$-0.391363\pi$
$877$	19.8240	0.669410	0.334705	+	0.942323i	$0.391363\pi$
$878$	−3.93796	−0.132900
$879$	49.9358	1.68429
$880$	4.13393	0.139355
$881$	−23.2616	−0.783703	−0.391852	−	0.920028i	$-0.628165\pi$
$881$	−23.2616	−0.783703	−0.391852	+	0.920028i	$0.628165\pi$
$882$	−43.4803	−1.46406
$883$	0.416638	0.0140210	0.00701049	−	0.999975i	$-0.497768\pi$
$883$	0.416638	0.0140210	0.00701049	+	0.999975i	$0.497768\pi$
$884$	17.5211	0.589298
$885$	9.23360	0.310384
$886$	16.2126	0.544674
$887$	0.146654	0.00492417	0.00246208	−	0.999997i	$-0.499216\pi$
$887$	0.146654	0.00492417	0.00246208	+	0.999997i	$0.499216\pi$
$888$	−14.0953	−0.473007
$889$	17.8592	0.598979
$890$	−1.39304	−0.0466947
$891$	30.1886	1.01136
$892$	−11.5606	−0.387076
$893$	−23.9078	−0.800043
$894$	−31.1225	−1.04089
$895$	6.88559	0.230160
$896$	−45.9524	−1.53516
$897$	−75.4421	−2.51894
$898$	2.43277	0.0811826
$899$	24.3903	0.813463
$900$	−9.69298	−0.323099
$901$	13.9960	0.466273
$902$	18.1721	0.605065
$903$	−12.6956	−0.422484
$904$	−9.37642	−0.311855
$905$	14.7262	0.489516
$906$	−13.4658	−0.447371
$907$	48.5718	1.61280	0.806400	−	0.591371i	$-0.201413\pi$
$907$	48.5718	1.61280	0.806400	+	0.591371i	$0.201413\pi$
$908$	26.9010	0.892742
$909$	−17.2194	−0.571133
$910$	12.1523	0.402846
$911$	46.1787	1.52997	0.764984	−	0.644049i	$-0.222747\pi$
$911$	46.1787	1.52997	0.764984	+	0.644049i	$0.222747\pi$
$912$	13.1442	0.435250
$913$	−24.4293	−0.808493
$914$	15.5274	0.513600
$915$	−32.5749	−1.07689
$916$	−13.1327	−0.433918
$917$	−1.26045	−0.0416238
$918$	−16.9405	−0.559120
$919$	−25.9487	−0.855968	−0.427984	−	0.903786i	$-0.640776\pi$
$919$	−25.9487	−0.855968	−0.427984	+	0.903786i	$0.640776\pi$
$920$	13.5044	0.445225
$921$	32.4622	1.06967
$922$	−5.92089	−0.194994
$923$	41.5281	1.36691
$924$	−53.4156	−1.75724
$925$	1.95593	0.0643105
$926$	−4.57881	−0.150469
$927$	14.0064	0.460032
$928$	−30.2298	−0.992342
$929$	43.5930	1.43024	0.715120	−	0.699002i	$-0.246372\pi$
$929$	43.5930	1.43024	0.715120	+	0.699002i	$0.246372\pi$
$930$	9.42474	0.309049
$931$	−29.6030	−0.970198
$932$	5.22999	0.171314
$933$	48.2115	1.57837
$934$	14.2288	0.465581
$935$	−6.99276	−0.228688
$936$	64.4562	2.10682
$937$	−23.2125	−0.758318	−0.379159	−	0.925332i	$-0.623787\pi$
$937$	−23.2125	−0.758318	−0.379159	+	0.925332i	$0.623787\pi$
$938$	37.1540	1.21312
$939$	−14.6004	−0.476466
$940$	−13.1303	−0.428262
$941$	−19.2543	−0.627673	−0.313837	−	0.949477i	$-0.601614\pi$
$941$	−19.2543	−0.627673	−0.313837	+	0.949477i	$0.601614\pi$
$942$	−48.7797	−1.58933
$943$	−57.3253	−1.86677
$944$	−4.64251	−0.151101
$945$	41.0526	1.33544
$946$	1.80508	0.0586883
$947$	2.25602	0.0733109	0.0366555	−	0.999328i	$-0.488330\pi$
$947$	2.25602	0.0733109	0.0366555	+	0.999328i	$0.488330\pi$
$948$	53.3462	1.73261
$949$	44.2483	1.43636
$950$	1.88879	0.0612806
$951$	32.9006	1.06687
$952$	25.6069	0.829924
$953$	−32.7387	−1.06051	−0.530256	−	0.847838i	$-0.677904\pi$
$953$	−32.7387	−1.06051	−0.530256	+	0.847838i	$0.677904\pi$
$954$	22.5211	0.729149
$955$	3.96616	0.128342
$956$	−32.2627	−1.04345
$957$	−43.1337	−1.39431
$958$	12.8872	0.416365
$959$	−75.1446	−2.42654
$960$	−2.39618	−0.0773363
$961$	−9.38454	−0.302727
$962$	−5.68911	−0.183424
$963$	51.3829	1.65579
$964$	−31.0507	−1.00008
$965$	10.9742	0.353272
$966$	−48.2273	−1.55169
$967$	−5.89512	−0.189574	−0.0947872	−	0.995498i	$-0.530217\pi$
$967$	−5.89512	−0.189574	−0.0947872	+	0.995498i	$0.530217\pi$
$968$	−8.72416	−0.280405
$969$	−22.2342	−0.714266
$970$	−9.69023	−0.311135
$971$	−9.73071	−0.312273	−0.156137	−	0.987735i	$-0.549904\pi$
$971$	−9.73071	−0.312273	−0.156137	+	0.987735i	$0.549904\pi$
$972$	6.88048	0.220691
$973$	49.5758	1.58933
$974$	−0.703684	−0.0225475
$975$	−13.2488	−0.424301
$976$	16.3781	0.524252
$977$	−57.7248	−1.84678	−0.923390	−	0.383864i	$-0.874593\pi$
$977$	−57.7248	−1.84678	−0.923390	+	0.383864i	$0.874593\pi$
$978$	10.0399	0.321042
$979$	5.65011	0.180578
$980$	−16.2581	−0.519346
$981$	−126.256	−4.03103
$982$	−8.87470	−0.283203
$983$	44.1150	1.40705	0.703526	−	0.710670i	$-0.251608\pi$
$983$	44.1150	1.40705	0.703526	+	0.710670i	$0.251608\pi$
$984$	72.5486	2.31277
$985$	23.8477	0.759850
$986$	9.04460	0.288039
$987$	107.204	3.41233
$988$	19.1952	0.610680
$989$	−5.69427	−0.181067
$990$	−11.2522	−0.357617
$991$	9.65909	0.306831	0.153416	−	0.988162i	$-0.450973\pi$
$991$	9.65909	0.306831	0.153416	+	0.988162i	$0.450973\pi$
$992$	−26.7906	−0.850602
$993$	−4.47900	−0.142137
$994$	26.5474	0.842032
$995$	−3.09135	−0.0980023
$996$	−42.6599	−1.35173
$997$	−8.30193	−0.262925	−0.131462	−	0.991321i	$-0.541967\pi$
$997$	−8.30193	−0.262925	−0.131462	+	0.991321i	$0.541967\pi$
$998$	−11.1036	−0.351479
$999$	−19.2187	−0.608054

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	215.2.a.c.1.2	✓	5
3.2	odd	2		1935.2.a.u.1.4		5
4.3	odd	2		3440.2.a.w.1.4		5
5.2	odd	4		1075.2.b.h.474.4		10
5.3	odd	4		1075.2.b.h.474.7		10
5.4	even	2		1075.2.a.m.1.4		5
15.14	odd	2		9675.2.a.ch.1.2		5
43.42	odd	2		9245.2.a.l.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
215.2.a.c.1.2	✓	5	1.1	even	1	trivial
1075.2.a.m.1.4		5	5.4	even	2
1075.2.b.h.474.4		10	5.2	odd	4
1075.2.b.h.474.7		10	5.3	odd	4
1935.2.a.u.1.4		5	3.2	odd	2
3440.2.a.w.1.4		5	4.3	odd	2
9245.2.a.l.1.4		5	43.42	odd	2
9675.2.a.ch.1.2		5	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 215 = 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	215.a (trivial)

\(f(q)\)	\(=\)	\(q-0.667116 q^{2} -3.03868 q^{3} -1.55496 q^{4} +1.00000 q^{5} +2.02715 q^{6} -4.17800 q^{7} +2.37157 q^{8} +6.23360 q^{9} +O(q^{10})\)	\(q-0.667116 q^{2} -3.03868 q^{3} -1.55496 q^{4} +1.00000 q^{5} +2.02715 q^{6} -4.17800 q^{7} +2.37157 q^{8} +6.23360 q^{9} -0.667116 q^{10} +2.70580 q^{11} +4.72502 q^{12} +4.36004 q^{13} +2.78721 q^{14} -3.03868 q^{15} +1.52780 q^{16} -2.58436 q^{17} -4.15854 q^{18} -2.83128 q^{19} -1.55496 q^{20} +12.6956 q^{21} -1.80508 q^{22} +5.69427 q^{23} -7.20645 q^{24} +1.00000 q^{25} -2.90865 q^{26} -9.82589 q^{27} +6.49661 q^{28} +5.24609 q^{29} +2.02715 q^{30} +4.64924 q^{31} -5.76236 q^{32} -8.22207 q^{33} +1.72407 q^{34} -4.17800 q^{35} -9.69298 q^{36} +1.95593 q^{37} +1.88879 q^{38} -13.2488 q^{39} +2.37157 q^{40} -10.0672 q^{41} -8.46945 q^{42} -1.00000 q^{43} -4.20740 q^{44} +6.23360 q^{45} -3.79874 q^{46} +8.44414 q^{47} -4.64251 q^{48} +10.4557 q^{49} -0.667116 q^{50} +7.85305 q^{51} -6.77967 q^{52} -5.41564 q^{53} +6.55501 q^{54} +2.70580 q^{55} -9.90841 q^{56} +8.60338 q^{57} -3.49975 q^{58} -3.03868 q^{59} +4.72502 q^{60} +10.7201 q^{61} -3.10158 q^{62} -26.0440 q^{63} +0.788558 q^{64} +4.36004 q^{65} +5.48508 q^{66} +13.3302 q^{67} +4.01856 q^{68} -17.3031 q^{69} +2.78721 q^{70} +9.52471 q^{71} +14.7834 q^{72} +10.1486 q^{73} -1.30483 q^{74} -3.03868 q^{75} +4.40252 q^{76} -11.3048 q^{77} +8.83847 q^{78} +11.2902 q^{79} +1.52780 q^{80} +11.1570 q^{81} +6.71598 q^{82} -9.02850 q^{83} -19.7411 q^{84} -2.58436 q^{85} +0.667116 q^{86} -15.9412 q^{87} +6.41699 q^{88} +2.08815 q^{89} -4.15854 q^{90} -18.2162 q^{91} -8.85434 q^{92} -14.1276 q^{93} -5.63322 q^{94} -2.83128 q^{95} +17.5100 q^{96} +14.5256 q^{97} -6.97515 q^{98} +16.8669 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 2 q^{2} - q^{3} + 8 q^{4} + 5 q^{5} - 12 q^{6} + 5 q^{7} + 3 q^{8} + 18 q^{9}+O(q^{10}) \) 5 * q + 2 * q^2 - q^3 + 8 * q^4 + 5 * q^5 - 12 * q^6 + 5 * q^7 + 3 * q^8 + 18 * q^9	\( 5 q + 2 q^{2} - q^{3} + 8 q^{4} + 5 q^{5} - 12 q^{6} + 5 q^{7} + 3 q^{8} + 18 q^{9} + 2 q^{10} - 6 q^{11} + 5 q^{13} + q^{14} - q^{15} + 14 q^{16} - 17 q^{17} - 5 q^{18} - 6 q^{19} + 8 q^{20} + 20 q^{21} - 8 q^{22} + q^{23} - 45 q^{24} + 5 q^{25} + 22 q^{26} - 22 q^{27} + 26 q^{28} + 6 q^{29} - 12 q^{30} + 6 q^{31} - 7 q^{32} - 20 q^{33} + 5 q^{35} + 36 q^{36} + 5 q^{37} - 16 q^{38} - 14 q^{39} + 3 q^{40} + 2 q^{41} - 58 q^{42} - 5 q^{43} - 15 q^{44} + 18 q^{45} - 14 q^{46} - 3 q^{48} + 18 q^{49} + 2 q^{50} - 10 q^{51} - 38 q^{52} - 23 q^{53} - 56 q^{54} - 6 q^{55} - 19 q^{56} + 28 q^{57} + 12 q^{58} - q^{59} + 20 q^{61} - 3 q^{62} + 26 q^{63} - 25 q^{64} + 5 q^{65} + 13 q^{66} + 21 q^{67} - 48 q^{68} + 10 q^{69} + q^{70} + 4 q^{71} + 20 q^{72} + 5 q^{73} + 24 q^{74} - q^{75} + 32 q^{76} - 26 q^{77} + 88 q^{78} + 41 q^{79} + 14 q^{80} + 41 q^{81} + 38 q^{82} - 7 q^{83} - 33 q^{84} - 17 q^{85} - 2 q^{86} - 40 q^{87} + 12 q^{88} + 20 q^{89} - 5 q^{90} - 42 q^{91} - 52 q^{92} - 36 q^{93} - 42 q^{94} - 6 q^{95} + 9 q^{96} + 37 q^{97} - 26 q^{98} + 12 q^{99}+O(q^{100}) \) 5 * q + 2 * q^2 - q^3 + 8 * q^4 + 5 * q^5 - 12 * q^6 + 5 * q^7 + 3 * q^8 + 18 * q^9 + 2 * q^10 - 6 * q^11 + 5 * q^13 + q^14 - q^15 + 14 * q^16 - 17 * q^17 - 5 * q^18 - 6 * q^19 + 8 * q^20 + 20 * q^21 - 8 * q^22 + q^23 - 45 * q^24 + 5 * q^25 + 22 * q^26 - 22 * q^27 + 26 * q^28 + 6 * q^29 - 12 * q^30 + 6 * q^31 - 7 * q^32 - 20 * q^33 + 5 * q^35 + 36 * q^36 + 5 * q^37 - 16 * q^38 - 14 * q^39 + 3 * q^40 + 2 * q^41 - 58 * q^42 - 5 * q^43 - 15 * q^44 + 18 * q^45 - 14 * q^46 - 3 * q^48 + 18 * q^49 + 2 * q^50 - 10 * q^51 - 38 * q^52 - 23 * q^53 - 56 * q^54 - 6 * q^55 - 19 * q^56 + 28 * q^57 + 12 * q^58 - q^59 + 20 * q^61 - 3 * q^62 + 26 * q^63 - 25 * q^64 + 5 * q^65 + 13 * q^66 + 21 * q^67 - 48 * q^68 + 10 * q^69 + q^70 + 4 * q^71 + 20 * q^72 + 5 * q^73 + 24 * q^74 - q^75 + 32 * q^76 - 26 * q^77 + 88 * q^78 + 41 * q^79 + 14 * q^80 + 41 * q^81 + 38 * q^82 - 7 * q^83 - 33 * q^84 - 17 * q^85 - 2 * q^86 - 40 * q^87 + 12 * q^88 + 20 * q^89 - 5 * q^90 - 42 * q^91 - 52 * q^92 - 36 * q^93 - 42 * q^94 - 6 * q^95 + 9 * q^96 + 37 * q^97 - 26 * q^98 + 12 * q^99

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