LMFDB - Embedded newform 6034.2.a.r.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, 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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.74816 q^{3} +1.00000 q^{4} +3.57738 q^{5} -2.74816 q^{6} -1.00000 q^{7} +1.00000 q^{8} +4.55238 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.74816 q^{3} +1.00000 q^{4} +3.57738 q^{5} -2.74816 q^{6} -1.00000 q^{7} +1.00000 q^{8} +4.55238 q^{9} +3.57738 q^{10} -3.92498 q^{11} -2.74816 q^{12} -2.11896 q^{13} -1.00000 q^{14} -9.83123 q^{15} +1.00000 q^{16} +4.80431 q^{17} +4.55238 q^{18} -1.59988 q^{19} +3.57738 q^{20} +2.74816 q^{21} -3.92498 q^{22} -2.03624 q^{23} -2.74816 q^{24} +7.79768 q^{25} -2.11896 q^{26} -4.26620 q^{27} -1.00000 q^{28} -4.06726 q^{29} -9.83123 q^{30} -5.74306 q^{31} +1.00000 q^{32} +10.7865 q^{33} +4.80431 q^{34} -3.57738 q^{35} +4.55238 q^{36} +6.50695 q^{37} -1.59988 q^{38} +5.82325 q^{39} +3.57738 q^{40} -4.96400 q^{41} +2.74816 q^{42} +4.83825 q^{43} -3.92498 q^{44} +16.2856 q^{45} -2.03624 q^{46} +9.86161 q^{47} -2.74816 q^{48} +1.00000 q^{49} +7.79768 q^{50} -13.2030 q^{51} -2.11896 q^{52} +11.4104 q^{53} -4.26620 q^{54} -14.0412 q^{55} -1.00000 q^{56} +4.39673 q^{57} -4.06726 q^{58} +4.51796 q^{59} -9.83123 q^{60} -3.55751 q^{61} -5.74306 q^{62} -4.55238 q^{63} +1.00000 q^{64} -7.58035 q^{65} +10.7865 q^{66} -0.847040 q^{67} +4.80431 q^{68} +5.59591 q^{69} -3.57738 q^{70} +0.482083 q^{71} +4.55238 q^{72} +6.19145 q^{73} +6.50695 q^{74} -21.4293 q^{75} -1.59988 q^{76} +3.92498 q^{77} +5.82325 q^{78} +8.72558 q^{79} +3.57738 q^{80} -1.93296 q^{81} -4.96400 q^{82} -9.64214 q^{83} +2.74816 q^{84} +17.1869 q^{85} +4.83825 q^{86} +11.1775 q^{87} -3.92498 q^{88} +17.8210 q^{89} +16.2856 q^{90} +2.11896 q^{91} -2.03624 q^{92} +15.7829 q^{93} +9.86161 q^{94} -5.72339 q^{95} -2.74816 q^{96} -7.46416 q^{97} +1.00000 q^{98} -17.8680 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 31 q^{2} + 7 q^{3} + 31 q^{4} + 15 q^{5} + 7 q^{6} - 31 q^{7} + 31 q^{8} + 42 q^{9}+O(q^{10}) $ 31 * q + 31 * q^2 + 7 * q^3 + 31 * q^4 + 15 * q^5 + 7 * q^6 - 31 * q^7 + 31 * q^8 + 42 * q^9	\( 31 q + 31 q^{2} + 7 q^{3} + 31 q^{4} + 15 q^{5} + 7 q^{6} - 31 q^{7} + 31 q^{8} + 42 q^{9} + 15 q^{10} + 12 q^{11} + 7 q^{12} + 26 q^{13} - 31 q^{14} + 6 q^{15} + 31 q^{16} + 33 q^{17} + 42 q^{18} + 34 q^{19} + 15 q^{20} - 7 q^{21} + 12 q^{22} - 14 q^{23} + 7 q^{24} + 58 q^{25} + 26 q^{26} + 28 q^{27} - 31 q^{28} + 11 q^{29} + 6 q^{30} + 19 q^{31} + 31 q^{32} + 43 q^{33} + 33 q^{34} - 15 q^{35} + 42 q^{36} + 2 q^{37} + 34 q^{38} - 16 q^{39} + 15 q^{40} + 53 q^{41} - 7 q^{42} + 22 q^{43} + 12 q^{44} + 43 q^{45} - 14 q^{46} + 27 q^{47} + 7 q^{48} + 31 q^{49} + 58 q^{50} + 17 q^{51} + 26 q^{52} + 11 q^{53} + 28 q^{54} + 19 q^{55} - 31 q^{56} + 45 q^{57} + 11 q^{58} + 54 q^{59} + 6 q^{60} + 41 q^{61} + 19 q^{62} - 42 q^{63} + 31 q^{64} + 30 q^{65} + 43 q^{66} + 13 q^{67} + 33 q^{68} + 17 q^{69} - 15 q^{70} + 43 q^{71} + 42 q^{72} + 42 q^{73} + 2 q^{74} + 62 q^{75} + 34 q^{76} - 12 q^{77} - 16 q^{78} - 12 q^{79} + 15 q^{80} + 63 q^{81} + 53 q^{82} + 35 q^{83} - 7 q^{84} + 16 q^{85} + 22 q^{86} - 4 q^{87} + 12 q^{88} + 115 q^{89} + 43 q^{90} - 26 q^{91} - 14 q^{92} + q^{93} + 27 q^{94} - 13 q^{95} + 7 q^{96} + 32 q^{97} + 31 q^{98} + 34 q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 + 7 * q^3 + 31 * q^4 + 15 * q^5 + 7 * q^6 - 31 * q^7 + 31 * q^8 + 42 * q^9 + 15 * q^10 + 12 * q^11 + 7 * q^12 + 26 * q^13 - 31 * q^14 + 6 * q^15 + 31 * q^16 + 33 * q^17 + 42 * q^18 + 34 * q^19 + 15 * q^20 - 7 * q^21 + 12 * q^22 - 14 * q^23 + 7 * q^24 + 58 * q^25 + 26 * q^26 + 28 * q^27 - 31 * q^28 + 11 * q^29 + 6 * q^30 + 19 * q^31 + 31 * q^32 + 43 * q^33 + 33 * q^34 - 15 * q^35 + 42 * q^36 + 2 * q^37 + 34 * q^38 - 16 * q^39 + 15 * q^40 + 53 * q^41 - 7 * q^42 + 22 * q^43 + 12 * q^44 + 43 * q^45 - 14 * q^46 + 27 * q^47 + 7 * q^48 + 31 * q^49 + 58 * q^50 + 17 * q^51 + 26 * q^52 + 11 * q^53 + 28 * q^54 + 19 * q^55 - 31 * q^56 + 45 * q^57 + 11 * q^58 + 54 * q^59 + 6 * q^60 + 41 * q^61 + 19 * q^62 - 42 * q^63 + 31 * q^64 + 30 * q^65 + 43 * q^66 + 13 * q^67 + 33 * q^68 + 17 * q^69 - 15 * q^70 + 43 * q^71 + 42 * q^72 + 42 * q^73 + 2 * q^74 + 62 * q^75 + 34 * q^76 - 12 * q^77 - 16 * q^78 - 12 * q^79 + 15 * q^80 + 63 * q^81 + 53 * q^82 + 35 * q^83 - 7 * q^84 + 16 * q^85 + 22 * q^86 - 4 * q^87 + 12 * q^88 + 115 * q^89 + 43 * q^90 - 26 * q^91 - 14 * q^92 + q^93 + 27 * q^94 - 13 * q^95 + 7 * q^96 + 32 * q^97 + 31 * q^98 + 34 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.74816	−1.58665	−0.793325	−	0.608798i	$-0.791652\pi$
$3$	−2.74816	−1.58665	−0.793325	+	0.608798i	$0.791652\pi$
$4$	1.00000	0.500000
$5$	3.57738	1.59986	0.799928	−	0.600097i	$-0.204871\pi$
$5$	3.57738	1.59986	0.799928	+	0.600097i	$0.204871\pi$
$6$	−2.74816	−1.12193
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	4.55238	1.51746
$10$	3.57738	1.13127
$11$	−3.92498	−1.18343	−0.591713	−	0.806149i	$-0.701548\pi$
$11$	−3.92498	−1.18343	−0.591713	+	0.806149i	$0.701548\pi$
$12$	−2.74816	−0.793325
$13$	−2.11896	−0.587695	−0.293847	−	0.955852i	$-0.594936\pi$
$13$	−2.11896	−0.587695	−0.293847	+	0.955852i	$0.594936\pi$
$14$	−1.00000	−0.267261
$15$	−9.83123	−2.53841
$16$	1.00000	0.250000
$17$	4.80431	1.16522	0.582608	−	0.812753i	$-0.302032\pi$
$17$	4.80431	1.16522	0.582608	+	0.812753i	$0.302032\pi$
$18$	4.55238	1.07301
$19$	−1.59988	−0.367038	−0.183519	−	0.983016i	$-0.558749\pi$
$19$	−1.59988	−0.367038	−0.183519	+	0.983016i	$0.558749\pi$
$20$	3.57738	0.799928
$21$	2.74816	0.599698
$22$	−3.92498	−0.836809
$23$	−2.03624	−0.424585	−0.212293	−	0.977206i	$-0.568093\pi$
$23$	−2.03624	−0.424585	−0.212293	+	0.977206i	$0.568093\pi$
$24$	−2.74816	−0.560966
$25$	7.79768	1.55954
$26$	−2.11896	−0.415563
$27$	−4.26620	−0.821030
$28$	−1.00000	−0.188982
$29$	−4.06726	−0.755270	−0.377635	−	0.925954i	$-0.623263\pi$
$29$	−4.06726	−0.755270	−0.377635	+	0.925954i	$0.623263\pi$
$30$	−9.83123	−1.79493
$31$	−5.74306	−1.03148	−0.515742	−	0.856744i	$-0.672484\pi$
$31$	−5.74306	−1.03148	−0.515742	+	0.856744i	$0.672484\pi$
$32$	1.00000	0.176777
$33$	10.7865	1.87768
$34$	4.80431	0.823932
$35$	−3.57738	−0.604688
$36$	4.55238	0.758731
$37$	6.50695	1.06974	0.534868	−	0.844935i	$-0.320361\pi$
$37$	6.50695	1.06974	0.534868	+	0.844935i	$0.320361\pi$
$38$	−1.59988	−0.259535
$39$	5.82325	0.932467
$40$	3.57738	0.565634
$41$	−4.96400	−0.775247	−0.387623	−	0.921818i	$-0.626704\pi$
$41$	−4.96400	−0.775247	−0.387623	+	0.921818i	$0.626704\pi$
$42$	2.74816	0.424050
$43$	4.83825	0.737826	0.368913	−	0.929464i	$-0.379730\pi$
$43$	4.83825	0.737826	0.368913	+	0.929464i	$0.379730\pi$
$44$	−3.92498	−0.591713
$45$	16.2856	2.42772
$46$	−2.03624	−0.300227
$47$	9.86161	1.43846	0.719232	−	0.694770i	$-0.244494\pi$
$47$	9.86161	1.43846	0.719232	+	0.694770i	$0.244494\pi$
$48$	−2.74816	−0.396663
$49$	1.00000	0.142857
$50$	7.79768	1.10276
$51$	−13.2030	−1.84879
$52$	−2.11896	−0.293847
$53$	11.4104	1.56733	0.783666	−	0.621182i	$-0.213347\pi$
$53$	11.4104	1.56733	0.783666	+	0.621182i	$0.213347\pi$
$54$	−4.26620	−0.580556
$55$	−14.0412	−1.89331
$56$	−1.00000	−0.133631
$57$	4.39673	0.582361
$58$	−4.06726	−0.534057
$59$	4.51796	0.588188	0.294094	−	0.955777i	$-0.404982\pi$
$59$	4.51796	0.588188	0.294094	+	0.955777i	$0.404982\pi$
$60$	−9.83123	−1.26921
$61$	−3.55751	−0.455493	−0.227746	−	0.973720i	$-0.573136\pi$
$61$	−3.55751	−0.455493	−0.227746	+	0.973720i	$0.573136\pi$
$62$	−5.74306	−0.729370
$63$	−4.55238	−0.573546
$64$	1.00000	0.125000
$65$	−7.58035	−0.940227
$66$	10.7865	1.32772
$67$	−0.847040	−0.103482	−0.0517412	−	0.998661i	$-0.516477\pi$
$67$	−0.847040	−0.103482	−0.0517412	+	0.998661i	$0.516477\pi$
$68$	4.80431	0.582608
$69$	5.59591	0.673668
$70$	−3.57738	−0.427579
$71$	0.482083	0.0572128	0.0286064	−	0.999591i	$-0.490893\pi$
$71$	0.482083	0.0572128	0.0286064	+	0.999591i	$0.490893\pi$
$72$	4.55238	0.536504
$73$	6.19145	0.724655	0.362327	−	0.932051i	$-0.381982\pi$
$73$	6.19145	0.724655	0.362327	+	0.932051i	$0.381982\pi$
$74$	6.50695	0.756418
$75$	−21.4293	−2.47444
$76$	−1.59988	−0.183519
$77$	3.92498	0.447293
$78$	5.82325	0.659354
$79$	8.72558	0.981704	0.490852	−	0.871243i	$-0.336686\pi$
$79$	8.72558	0.981704	0.490852	+	0.871243i	$0.336686\pi$
$80$	3.57738	0.399964
$81$	−1.93296	−0.214773
$82$	−4.96400	−0.548182
$83$	−9.64214	−1.05836	−0.529181	−	0.848509i	$-0.677501\pi$
$83$	−9.64214	−1.05836	−0.529181	+	0.848509i	$0.677501\pi$
$84$	2.74816	0.299849
$85$	17.1869	1.86418
$86$	4.83825	0.521722
$87$	11.1775	1.19835
$88$	−3.92498	−0.418404
$89$	17.8210	1.88902	0.944509	−	0.328484i	$-0.106538\pi$
$89$	17.8210	1.88902	0.944509	+	0.328484i	$0.106538\pi$
$90$	16.2856	1.71666
$91$	2.11896	0.222128
$92$	−2.03624	−0.212293
$93$	15.7829	1.63661
$94$	9.86161	1.01715
$95$	−5.72339	−0.587207
$96$	−2.74816	−0.280483
$97$	−7.46416	−0.757871	−0.378935	−	0.925423i	$-0.623710\pi$
$97$	−7.46416	−0.757871	−0.378935	+	0.925423i	$0.623710\pi$
$98$	1.00000	0.101015
$99$	−17.8680	−1.79580
$100$	7.79768	0.779768
$101$	12.2036	1.21431	0.607154	−	0.794584i	$-0.292311\pi$
$101$	12.2036	1.21431	0.607154	+	0.794584i	$0.292311\pi$
$102$	−13.2030	−1.30729
$103$	16.7376	1.64921	0.824603	−	0.565711i	$-0.191398\pi$
$103$	16.7376	1.64921	0.824603	+	0.565711i	$0.191398\pi$
$104$	−2.11896	−0.207782
$105$	9.83123	0.959429
$106$	11.4104	1.10827
$107$	15.0714	1.45701	0.728505	−	0.685040i	$-0.240215\pi$
$107$	15.0714	1.45701	0.728505	+	0.685040i	$0.240215\pi$
$108$	−4.26620	−0.410515
$109$	11.9337	1.14304	0.571521	−	0.820588i	$-0.306354\pi$
$109$	11.9337	1.14304	0.571521	+	0.820588i	$0.306354\pi$
$110$	−14.0412	−1.33877
$111$	−17.8822	−1.69730
$112$	−1.00000	−0.0944911
$113$	−10.0809	−0.948333	−0.474167	−	0.880435i	$-0.657251\pi$
$113$	−10.0809	−0.948333	−0.474167	+	0.880435i	$0.657251\pi$
$114$	4.39673	0.411791
$115$	−7.28441	−0.679275
$116$	−4.06726	−0.377635
$117$	−9.64634	−0.891804
$118$	4.51796	0.415912
$119$	−4.80431	−0.440410
$120$	−9.83123	−0.897464
$121$	4.40547	0.400498
$122$	−3.55751	−0.322082
$123$	13.6419	1.23005
$124$	−5.74306	−0.515742
$125$	10.0084	0.895177
$126$	−4.55238	−0.405559
$127$	−0.601841	−0.0534047	−0.0267024	−	0.999643i	$-0.508501\pi$
$127$	−0.601841	−0.0534047	−0.0267024	+	0.999643i	$0.508501\pi$
$128$	1.00000	0.0883883
$129$	−13.2963	−1.17067
$130$	−7.58035	−0.664841
$131$	−3.92792	−0.343184	−0.171592	−	0.985168i	$-0.554891\pi$
$131$	−3.92792	−0.343184	−0.171592	+	0.985168i	$0.554891\pi$
$132$	10.7865	0.938842
$133$	1.59988	0.138727
$134$	−0.847040	−0.0731731
$135$	−15.2618	−1.31353
$136$	4.80431	0.411966
$137$	−9.26900	−0.791904	−0.395952	−	0.918271i	$-0.629585\pi$
$137$	−9.26900	−0.791904	−0.395952	+	0.918271i	$0.629585\pi$
$138$	5.59591	0.476355
$139$	0.358362	0.0303959	0.0151980	−	0.999885i	$-0.495162\pi$
$139$	0.358362	0.0303959	0.0151980	+	0.999885i	$0.495162\pi$
$140$	−3.57738	−0.302344
$141$	−27.1013	−2.28234
$142$	0.482083	0.0404555
$143$	8.31689	0.695494
$144$	4.55238	0.379365
$145$	−14.5501	−1.20832
$146$	6.19145	0.512408
$147$	−2.74816	−0.226664
$148$	6.50695	0.534868
$149$	−8.39056	−0.687381	−0.343691	−	0.939083i	$-0.611677\pi$
$149$	−8.39056	−0.687381	−0.343691	+	0.939083i	$0.611677\pi$
$150$	−21.4293	−1.74969
$151$	−13.3490	−1.08632	−0.543162	−	0.839628i	$-0.682773\pi$
$151$	−13.3490	−1.08632	−0.543162	+	0.839628i	$0.682773\pi$
$152$	−1.59988	−0.129767
$153$	21.8711	1.76817
$154$	3.92498	0.316284
$155$	−20.5452	−1.65023
$156$	5.82325	0.466233
$157$	15.9854	1.27577	0.637887	−	0.770130i	$-0.279809\pi$
$157$	15.9854	1.27577	0.637887	+	0.770130i	$0.279809\pi$
$158$	8.72558	0.694170
$159$	−31.3575	−2.48681
$160$	3.57738	0.282817
$161$	2.03624	0.160478
$162$	−1.93296	−0.151867
$163$	−5.22917	−0.409581	−0.204790	−	0.978806i	$-0.565651\pi$
$163$	−5.22917	−0.409581	−0.204790	+	0.978806i	$0.565651\pi$
$164$	−4.96400	−0.387623
$165$	38.5874	3.00402
$166$	−9.64214	−0.748375
$167$	3.56348	0.275750	0.137875	−	0.990450i	$-0.455973\pi$
$167$	3.56348	0.275750	0.137875	+	0.990450i	$0.455973\pi$
$168$	2.74816	0.212025
$169$	−8.50999	−0.654615
$170$	17.1869	1.31817
$171$	−7.28327	−0.556965
$172$	4.83825	0.368913
$173$	−25.5973	−1.94613	−0.973064	−	0.230536i	$-0.925952\pi$
$173$	−25.5973	−1.94613	−0.973064	+	0.230536i	$0.925952\pi$
$174$	11.1775	0.847362
$175$	−7.79768	−0.589449
$176$	−3.92498	−0.295857
$177$	−12.4161	−0.933249
$178$	17.8210	1.33574
$179$	1.01828	0.0761102	0.0380551	−	0.999276i	$-0.487884\pi$
$179$	1.01828	0.0761102	0.0380551	+	0.999276i	$0.487884\pi$
$180$	16.2856	1.21386
$181$	17.3069	1.28641	0.643207	−	0.765693i	$-0.277604\pi$
$181$	17.3069	1.28641	0.643207	+	0.765693i	$0.277604\pi$
$182$	2.11896	0.157068
$183$	9.77662	0.722708
$184$	−2.03624	−0.150113
$185$	23.2779	1.71142
$186$	15.7829	1.15726
$187$	−18.8568	−1.37895
$188$	9.86161	0.719232
$189$	4.26620	0.310320
$190$	−5.72339	−0.415218
$191$	−0.747688	−0.0541008	−0.0270504	−	0.999634i	$-0.508611\pi$
$191$	−0.747688	−0.0541008	−0.0270504	+	0.999634i	$0.508611\pi$
$192$	−2.74816	−0.198331
$193$	−13.4869	−0.970809	−0.485405	−	0.874290i	$-0.661328\pi$
$193$	−13.4869	−0.970809	−0.485405	+	0.874290i	$0.661328\pi$
$194$	−7.46416	−0.535896
$195$	20.8320	1.49181
$196$	1.00000	0.0714286
$197$	20.7514	1.47847	0.739237	−	0.673446i	$-0.235186\pi$
$197$	20.7514	1.47847	0.739237	+	0.673446i	$0.235186\pi$
$198$	−17.8680	−1.26982
$199$	18.7303	1.32775	0.663877	−	0.747842i	$-0.268910\pi$
$199$	18.7303	1.32775	0.663877	+	0.747842i	$0.268910\pi$
$200$	7.79768	0.551379
$201$	2.32780	0.164191
$202$	12.2036	0.858645
$203$	4.06726	0.285465
$204$	−13.2030	−0.924396
$205$	−17.7581	−1.24028
$206$	16.7376	1.16617
$207$	−9.26974	−0.644291
$208$	−2.11896	−0.146924
$209$	6.27950	0.434362
$210$	9.83123	0.678419
$211$	−19.7410	−1.35903	−0.679513	−	0.733663i	$-0.737809\pi$
$211$	−19.7410	−1.35903	−0.679513	+	0.733663i	$0.737809\pi$
$212$	11.4104	0.783666
$213$	−1.32484	−0.0907767
$214$	15.0714	1.03026
$215$	17.3083	1.18041
$216$	−4.26620	−0.290278
$217$	5.74306	0.389865
$218$	11.9337	0.808252
$219$	−17.0151	−1.14977
$220$	−14.0412	−0.946655
$221$	−10.1802	−0.684792
$222$	−17.8822	−1.20017
$223$	7.68148	0.514390	0.257195	−	0.966360i	$-0.417202\pi$
$223$	7.68148	0.514390	0.257195	+	0.966360i	$0.417202\pi$
$224$	−1.00000	−0.0668153
$225$	35.4980	2.36654
$226$	−10.0809	−0.670573
$227$	6.38279	0.423641	0.211820	−	0.977309i	$-0.432061\pi$
$227$	6.38279	0.423641	0.211820	+	0.977309i	$0.432061\pi$
$228$	4.39673	0.291180
$229$	12.6937	0.838826	0.419413	−	0.907795i	$-0.362236\pi$
$229$	12.6937	0.838826	0.419413	+	0.907795i	$0.362236\pi$
$230$	−7.28441	−0.480320
$231$	−10.7865	−0.709698
$232$	−4.06726	−0.267028
$233$	−15.3748	−1.00724	−0.503619	−	0.863926i	$-0.667998\pi$
$233$	−15.3748	−1.00724	−0.503619	+	0.863926i	$0.667998\pi$
$234$	−9.64634	−0.630601
$235$	35.2788	2.30133
$236$	4.51796	0.294094
$237$	−23.9793	−1.55762
$238$	−4.80431	−0.311417
$239$	17.8443	1.15425	0.577127	−	0.816654i	$-0.304174\pi$
$239$	17.8443	1.15425	0.577127	+	0.816654i	$0.304174\pi$
$240$	−9.83123	−0.634603
$241$	4.94676	0.318649	0.159325	−	0.987226i	$-0.449068\pi$
$241$	4.94676	0.318649	0.159325	+	0.987226i	$0.449068\pi$
$242$	4.40547	0.283195
$243$	18.1107	1.16180
$244$	−3.55751	−0.227746
$245$	3.57738	0.228551
$246$	13.6419	0.869774
$247$	3.39009	0.215706
$248$	−5.74306	−0.364685
$249$	26.4981	1.67925
$250$	10.0084	0.632986
$251$	16.9571	1.07032	0.535161	−	0.844750i	$-0.320251\pi$
$251$	16.9571	1.07032	0.535161	+	0.844750i	$0.320251\pi$
$252$	−4.55238	−0.286773
$253$	7.99220	0.502465
$254$	−0.601841	−0.0377628
$255$	−47.2323	−2.95780
$256$	1.00000	0.0625000
$257$	1.88940	0.117858	0.0589289	−	0.998262i	$-0.481231\pi$
$257$	1.88940	0.117858	0.0589289	+	0.998262i	$0.481231\pi$
$258$	−13.2963	−0.827790
$259$	−6.50695	−0.404322
$260$	−7.58035	−0.470113
$261$	−18.5157	−1.14609
$262$	−3.92792	−0.242668
$263$	−9.18365	−0.566288	−0.283144	−	0.959077i	$-0.591377\pi$
$263$	−9.18365	−0.566288	−0.283144	+	0.959077i	$0.591377\pi$
$264$	10.7865	0.663862
$265$	40.8192	2.50751
$266$	1.59988	0.0980949
$267$	−48.9749	−2.99721
$268$	−0.847040	−0.0517412
$269$	28.0857	1.71241	0.856206	−	0.516634i	$-0.172815\pi$
$269$	28.0857	1.71241	0.856206	+	0.516634i	$0.172815\pi$
$270$	−15.2618	−0.928806
$271$	−10.1598	−0.617166	−0.308583	−	0.951197i	$-0.599855\pi$
$271$	−10.1598	−0.617166	−0.308583	+	0.951197i	$0.599855\pi$
$272$	4.80431	0.291304
$273$	−5.82325	−0.352439
$274$	−9.26900	−0.559961
$275$	−30.6057	−1.84560
$276$	5.59591	0.336834
$277$	−17.3234	−1.04086	−0.520430	−	0.853904i	$-0.674228\pi$
$277$	−17.3234	−1.04086	−0.520430	+	0.853904i	$0.674228\pi$
$278$	0.358362	0.0214932
$279$	−26.1446	−1.56524
$280$	−3.57738	−0.213790
$281$	17.5808	1.04879	0.524393	−	0.851477i	$-0.324292\pi$
$281$	17.5808	1.04879	0.524393	+	0.851477i	$0.324292\pi$
$282$	−27.1013	−1.61386
$283$	−8.20644	−0.487822	−0.243911	−	0.969798i	$-0.578430\pi$
$283$	−8.20644	−0.487822	−0.243911	+	0.969798i	$0.578430\pi$
$284$	0.482083	0.0286064
$285$	15.7288	0.931693
$286$	8.31689	0.491788
$287$	4.96400	0.293016
$288$	4.55238	0.268252
$289$	6.08140	0.357729
$290$	−14.5501	−0.854414
$291$	20.5127	1.20248
$292$	6.19145	0.362327
$293$	13.4416	0.785264	0.392632	−	0.919696i	$-0.371565\pi$
$293$	13.4416	0.785264	0.392632	+	0.919696i	$0.371565\pi$
$294$	−2.74816	−0.160276
$295$	16.1625	0.941015
$296$	6.50695	0.378209
$297$	16.7447	0.971629
$298$	−8.39056	−0.486052
$299$	4.31472	0.249527
$300$	−21.4293	−1.23722
$301$	−4.83825	−0.278872
$302$	−13.3490	−0.768147
$303$	−33.5376	−1.92668
$304$	−1.59988	−0.0917594
$305$	−12.7266	−0.728723
$306$	21.8711	1.25029
$307$	19.2119	1.09648	0.548240	−	0.836321i	$-0.315298\pi$
$307$	19.2119	1.09648	0.548240	+	0.836321i	$0.315298\pi$
$308$	3.92498	0.223647
$309$	−45.9977	−2.61672
$310$	−20.5452	−1.16689
$311$	24.8047	1.40654	0.703272	−	0.710921i	$-0.251722\pi$
$311$	24.8047	1.40654	0.703272	+	0.710921i	$0.251722\pi$
$312$	5.82325	0.329677
$313$	13.4295	0.759079	0.379540	−	0.925175i	$-0.376082\pi$
$313$	13.4295	0.759079	0.379540	+	0.925175i	$0.376082\pi$
$314$	15.9854	0.902109
$315$	−16.2856	−0.917591
$316$	8.72558	0.490852
$317$	7.84084	0.440385	0.220193	−	0.975456i	$-0.429331\pi$
$317$	7.84084	0.440385	0.220193	+	0.975456i	$0.429331\pi$
$318$	−31.3575	−1.75844
$319$	15.9639	0.893807
$320$	3.57738	0.199982
$321$	−41.4187	−2.31177
$322$	2.03624	0.113475
$323$	−7.68632	−0.427678
$324$	−1.93296	−0.107386
$325$	−16.5230	−0.916532
$326$	−5.22917	−0.289617
$327$	−32.7957	−1.81361
$328$	−4.96400	−0.274091
$329$	−9.86161	−0.543688
$330$	38.5874	2.12416
$331$	19.9705	1.09768	0.548839	−	0.835928i	$-0.315070\pi$
$331$	19.9705	1.09768	0.548839	+	0.835928i	$0.315070\pi$
$332$	−9.64214	−0.529181
$333$	29.6222	1.62328
$334$	3.56348	0.194985
$335$	−3.03019	−0.165557
$336$	2.74816	0.149924
$337$	18.3331	0.998665	0.499333	−	0.866410i	$-0.333579\pi$
$337$	18.3331	0.998665	0.499333	+	0.866410i	$0.333579\pi$
$338$	−8.50999	−0.462882
$339$	27.7040	1.50467
$340$	17.1869	0.932089
$341$	22.5414	1.22069
$342$	−7.28327	−0.393834
$343$	−1.00000	−0.0539949
$344$	4.83825	0.260861
$345$	20.0187	1.07777
$346$	−25.5973	−1.37612
$347$	−3.72888	−0.200177	−0.100088	−	0.994979i	$-0.531913\pi$
$347$	−3.72888	−0.200177	−0.100088	+	0.994979i	$0.531913\pi$
$348$	11.1775	0.599175
$349$	24.2300	1.29700	0.648501	−	0.761213i	$-0.275396\pi$
$349$	24.2300	1.29700	0.648501	+	0.761213i	$0.275396\pi$
$350$	−7.79768	−0.416804
$351$	9.03992	0.482515
$352$	−3.92498	−0.209202
$353$	−15.8785	−0.845127	−0.422564	−	0.906333i	$-0.638870\pi$
$353$	−15.8785	−0.845127	−0.422564	+	0.906333i	$0.638870\pi$
$354$	−12.4161	−0.659907
$355$	1.72460	0.0915321
$356$	17.8210	0.944509
$357$	13.2030	0.698778
$358$	1.01828	0.0538180
$359$	−16.8381	−0.888678	−0.444339	−	0.895859i	$-0.646561\pi$
$359$	−16.8381	−0.888678	−0.444339	+	0.895859i	$0.646561\pi$
$360$	16.2856	0.858328
$361$	−16.4404	−0.865283
$362$	17.3069	0.909632
$363$	−12.1069	−0.635450
$364$	2.11896	0.111064
$365$	22.1492	1.15934
$366$	9.77662	0.511032
$367$	−7.69238	−0.401539	−0.200770	−	0.979639i	$-0.564344\pi$
$367$	−7.69238	−0.401539	−0.200770	+	0.979639i	$0.564344\pi$
$368$	−2.03624	−0.106146
$369$	−22.5980	−1.17641
$370$	23.2779	1.21016
$371$	−11.4104	−0.592396
$372$	15.7829	0.818303
$373$	31.6456	1.63855	0.819273	−	0.573404i	$-0.194377\pi$
$373$	31.6456	1.63855	0.819273	+	0.573404i	$0.194377\pi$
$374$	−18.8568	−0.975063
$375$	−27.5046	−1.42033
$376$	9.86161	0.508574
$377$	8.61837	0.443869
$378$	4.26620	0.219430
$379$	21.6077	1.10991	0.554957	−	0.831879i	$-0.312735\pi$
$379$	21.6077	1.10991	0.554957	+	0.831879i	$0.312735\pi$
$380$	−5.72339	−0.293603
$381$	1.65395	0.0847347
$382$	−0.747688	−0.0382550
$383$	17.6869	0.903759	0.451880	−	0.892079i	$-0.350754\pi$
$383$	17.6869	0.903759	0.451880	+	0.892079i	$0.350754\pi$
$384$	−2.74816	−0.140241
$385$	14.0412	0.715604
$386$	−13.4869	−0.686466
$387$	22.0256	1.11962
$388$	−7.46416	−0.378935
$389$	−6.15885	−0.312266	−0.156133	−	0.987736i	$-0.549903\pi$
$389$	−6.15885	−0.312266	−0.156133	+	0.987736i	$0.549903\pi$
$390$	20.8320	1.05487
$391$	−9.78272	−0.494734
$392$	1.00000	0.0505076
$393$	10.7945	0.544513
$394$	20.7514	1.04544
$395$	31.2147	1.57058
$396$	−17.8680	−0.897902
$397$	2.67101	0.134054	0.0670270	−	0.997751i	$-0.478649\pi$
$397$	2.67101	0.134054	0.0670270	+	0.997751i	$0.478649\pi$
$398$	18.7303	0.938864
$399$	−4.39673	−0.220112
$400$	7.79768	0.389884
$401$	−33.9573	−1.69575	−0.847874	−	0.530198i	$-0.822118\pi$
$401$	−33.9573	−1.69575	−0.847874	+	0.530198i	$0.822118\pi$
$402$	2.32780	0.116100
$403$	12.1693	0.606198
$404$	12.2036	0.607154
$405$	−6.91492	−0.343605
$406$	4.06726	0.201855
$407$	−25.5397	−1.26595
$408$	−13.2030	−0.653647
$409$	15.7522	0.778895	0.389448	−	0.921049i	$-0.372666\pi$
$409$	15.7522	0.778895	0.389448	+	0.921049i	$0.372666\pi$
$410$	−17.7581	−0.877012
$411$	25.4727	1.25648
$412$	16.7376	0.824603
$413$	−4.51796	−0.222314
$414$	−9.26974	−0.455583
$415$	−34.4936	−1.69323
$416$	−2.11896	−0.103891
$417$	−0.984837	−0.0482277
$418$	6.27950	0.307140
$419$	8.23693	0.402400	0.201200	−	0.979550i	$-0.435516\pi$
$419$	8.23693	0.402400	0.201200	+	0.979550i	$0.435516\pi$
$420$	9.83123	0.479715
$421$	−17.6368	−0.859564	−0.429782	−	0.902933i	$-0.641410\pi$
$421$	−17.6368	−0.859564	−0.429782	+	0.902933i	$0.641410\pi$
$422$	−19.7410	−0.960977
$423$	44.8938	2.18281
$424$	11.4104	0.554136
$425$	37.4625	1.81720
$426$	−1.32484	−0.0641888
$427$	3.55751	0.172160
$428$	15.0714	0.728505
$429$	−22.8562	−1.10351
$430$	17.3083	0.834679
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	−4.26620	−0.205258
$433$	−0.689093	−0.0331157	−0.0165578	−	0.999863i	$-0.505271\pi$
$433$	−0.689093	−0.0331157	−0.0165578	+	0.999863i	$0.505271\pi$
$434$	5.74306	0.275676
$435$	39.9861	1.91719
$436$	11.9337	0.571521
$437$	3.25774	0.155839
$438$	−17.0151	−0.813013
$439$	4.74138	0.226294	0.113147	−	0.993578i	$-0.463907\pi$
$439$	4.74138	0.226294	0.113147	+	0.993578i	$0.463907\pi$
$440$	−14.0412	−0.669386
$441$	4.55238	0.216780
$442$	−10.1802	−0.484221
$443$	−0.804752	−0.0382349	−0.0191175	−	0.999817i	$-0.506086\pi$
$443$	−0.804752	−0.0382349	−0.0191175	+	0.999817i	$0.506086\pi$
$444$	−17.8822	−0.848649
$445$	63.7525	3.02216
$446$	7.68148	0.363729
$447$	23.0586	1.09063
$448$	−1.00000	−0.0472456
$449$	−11.1635	−0.526840	−0.263420	−	0.964681i	$-0.584851\pi$
$449$	−11.1635	−0.526840	−0.263420	+	0.964681i	$0.584851\pi$
$450$	35.4980	1.67339
$451$	19.4836	0.917447
$452$	−10.0809	−0.474167
$453$	36.6851	1.72362
$454$	6.38279	0.299559
$455$	7.58035	0.355372
$456$	4.39673	0.205896
$457$	34.3207	1.60545	0.802727	−	0.596346i	$-0.203381\pi$
$457$	34.3207	1.60545	0.802727	+	0.596346i	$0.203381\pi$
$458$	12.6937	0.593140
$459$	−20.4961	−0.956678
$460$	−7.28441	−0.339637
$461$	25.0235	1.16546	0.582730	−	0.812666i	$-0.301985\pi$
$461$	25.0235	1.16546	0.582730	+	0.812666i	$0.301985\pi$
$462$	−10.7865	−0.501832
$463$	23.5189	1.09301	0.546507	−	0.837454i	$-0.315957\pi$
$463$	23.5189	1.09301	0.546507	+	0.837454i	$0.315957\pi$
$464$	−4.06726	−0.188818
$465$	56.4614	2.61833
$466$	−15.3748	−0.712225
$467$	−17.9546	−0.830840	−0.415420	−	0.909630i	$-0.636365\pi$
$467$	−17.9546	−0.830840	−0.415420	+	0.909630i	$0.636365\pi$
$468$	−9.64634	−0.445902
$469$	0.847040	0.0391127
$470$	35.2788	1.62729
$471$	−43.9305	−2.02421
$472$	4.51796	0.207956
$473$	−18.9900	−0.873162
$474$	−23.9793	−1.10140
$475$	−12.4754	−0.572408
$476$	−4.80431	−0.220205
$477$	51.9443	2.37837
$478$	17.8443	0.816181
$479$	2.13545	0.0975713	0.0487856	−	0.998809i	$-0.484465\pi$
$479$	2.13545	0.0975713	0.0487856	+	0.998809i	$0.484465\pi$
$480$	−9.83123	−0.448732
$481$	−13.7880	−0.628679
$482$	4.94676	0.225319
$483$	−5.59591	−0.254623
$484$	4.40547	0.200249
$485$	−26.7022	−1.21248
$486$	18.1107	0.821516
$487$	−13.1994	−0.598120	−0.299060	−	0.954234i	$-0.596673\pi$
$487$	−13.1994	−0.598120	−0.299060	+	0.954234i	$0.596673\pi$
$488$	−3.55751	−0.161041
$489$	14.3706	0.649861
$490$	3.57738	0.161610
$491$	5.79224	0.261400	0.130700	−	0.991422i	$-0.458277\pi$
$491$	5.79224	0.261400	0.130700	+	0.991422i	$0.458277\pi$
$492$	13.6419	0.615023
$493$	−19.5404	−0.880054
$494$	3.39009	0.152527
$495$	−63.9208	−2.87303
$496$	−5.74306	−0.257871
$497$	−0.482083	−0.0216244
$498$	26.4981	1.18741
$499$	10.3205	0.462010	0.231005	−	0.972953i	$-0.425799\pi$
$499$	10.3205	0.462010	0.231005	+	0.972953i	$0.425799\pi$
$500$	10.0084	0.447588
$501$	−9.79301	−0.437519
$502$	16.9571	0.756833
$503$	−37.1427	−1.65611	−0.828055	−	0.560647i	$-0.810553\pi$
$503$	−37.1427	−1.65611	−0.828055	+	0.560647i	$0.810553\pi$
$504$	−4.55238	−0.202779
$505$	43.6571	1.94272
$506$	7.99220	0.355297
$507$	23.3868	1.03864
$508$	−0.601841	−0.0267024
$509$	−23.8847	−1.05867	−0.529336	−	0.848413i	$-0.677559\pi$
$509$	−23.8847	−1.05867	−0.529336	+	0.848413i	$0.677559\pi$
$510$	−47.2323	−2.09148
$511$	−6.19145	−0.273894
$512$	1.00000	0.0441942
$513$	6.82540	0.301349
$514$	1.88940	0.0833381
$515$	59.8769	2.63849
$516$	−13.2963	−0.585336
$517$	−38.7066	−1.70232
$518$	−6.50695	−0.285899
$519$	70.3455	3.08783
$520$	−7.58035	−0.332420
$521$	−41.1734	−1.80384	−0.901919	−	0.431906i	$-0.857841\pi$
$521$	−41.1734	−1.80384	−0.901919	+	0.431906i	$0.857841\pi$
$522$	−18.5157	−0.810411
$523$	6.50309	0.284360	0.142180	−	0.989841i	$-0.454589\pi$
$523$	6.50309	0.284360	0.142180	+	0.989841i	$0.454589\pi$
$524$	−3.92792	−0.171592
$525$	21.4293	0.935250
$526$	−9.18365	−0.400426
$527$	−27.5915	−1.20190
$528$	10.7865	0.469421
$529$	−18.8537	−0.819728
$530$	40.8192	1.77307
$531$	20.5675	0.892552
$532$	1.59988	0.0693636
$533$	10.5185	0.455609
$534$	−48.9749	−2.11935
$535$	53.9163	2.33101
$536$	−0.847040	−0.0365866
$537$	−2.79841	−0.120760
$538$	28.0857	1.21086
$539$	−3.92498	−0.169061
$540$	−15.2618	−0.656765
$541$	−7.24346	−0.311421	−0.155710	−	0.987803i	$-0.549767\pi$
$541$	−7.24346	−0.311421	−0.155710	+	0.987803i	$0.549767\pi$
$542$	−10.1598	−0.436402
$543$	−47.5622	−2.04109
$544$	4.80431	0.205983
$545$	42.6914	1.82870
$546$	−5.82325	−0.249212
$547$	15.0423	0.643163	0.321582	−	0.946882i	$-0.395786\pi$
$547$	15.0423	0.643163	0.321582	+	0.946882i	$0.395786\pi$
$548$	−9.26900	−0.395952
$549$	−16.1952	−0.691193
$550$	−30.6057	−1.30503
$551$	6.50712	0.277213
$552$	5.59591	0.238178
$553$	−8.72558	−0.371049
$554$	−17.3234	−0.736000
$555$	−63.9713	−2.71543
$556$	0.358362	0.0151980
$557$	−39.5450	−1.67557	−0.837787	−	0.545997i	$-0.816151\pi$
$557$	−39.5450	−1.67557	−0.837787	+	0.545997i	$0.816151\pi$
$558$	−26.1446	−1.10679
$559$	−10.2521	−0.433616
$560$	−3.57738	−0.151172
$561$	51.8216	2.18791
$562$	17.5808	0.741603
$563$	2.52645	0.106477	0.0532385	−	0.998582i	$-0.483046\pi$
$563$	2.52645	0.106477	0.0532385	+	0.998582i	$0.483046\pi$
$564$	−27.1013	−1.14117
$565$	−36.0633	−1.51720
$566$	−8.20644	−0.344942
$567$	1.93296	0.0811765
$568$	0.482083	0.0202278
$569$	−14.1378	−0.592687	−0.296344	−	0.955081i	$-0.595767\pi$
$569$	−14.1378	−0.592687	−0.296344	+	0.955081i	$0.595767\pi$
$570$	15.7288	0.658806
$571$	23.7452	0.993706	0.496853	−	0.867835i	$-0.334489\pi$
$571$	23.7452	0.993706	0.496853	+	0.867835i	$0.334489\pi$
$572$	8.31689	0.347747
$573$	2.05477	0.0858391
$574$	4.96400	0.207193
$575$	−15.8779	−0.662156
$576$	4.55238	0.189683
$577$	24.2612	1.01001	0.505004	−	0.863117i	$-0.331491\pi$
$577$	24.2612	1.01001	0.505004	+	0.863117i	$0.331491\pi$
$578$	6.08140	0.252953
$579$	37.0642	1.54034
$580$	−14.5501	−0.604162
$581$	9.64214	0.400023
$582$	20.5127	0.850279
$583$	−44.7854	−1.85482
$584$	6.19145	0.256204
$585$	−34.5087	−1.42676
$586$	13.4416	0.555265
$587$	24.9078	1.02805	0.514027	−	0.857774i	$-0.328153\pi$
$587$	24.9078	1.02805	0.514027	+	0.857774i	$0.328153\pi$
$588$	−2.74816	−0.113332
$589$	9.18821	0.378594
$590$	16.1625	0.665398
$591$	−57.0281	−2.34582
$592$	6.50695	0.267434
$593$	−2.18122	−0.0895719	−0.0447860	−	0.998997i	$-0.514261\pi$
$593$	−2.18122	−0.0895719	−0.0447860	+	0.998997i	$0.514261\pi$
$594$	16.7447	0.687045
$595$	−17.1869	−0.704593
$596$	−8.39056	−0.343691
$597$	−51.4738	−2.10668
$598$	4.31472	0.176442
$599$	21.7918	0.890388	0.445194	−	0.895434i	$-0.353135\pi$
$599$	21.7918	0.890388	0.445194	+	0.895434i	$0.353135\pi$
$600$	−21.4293	−0.874847
$601$	−24.0944	−0.982832	−0.491416	−	0.870925i	$-0.663521\pi$
$601$	−24.0944	−0.982832	−0.491416	+	0.870925i	$0.663521\pi$
$602$	−4.83825	−0.197192
$603$	−3.85605	−0.157031
$604$	−13.3490	−0.543162
$605$	15.7601	0.640738
$606$	−33.5376	−1.36237
$607$	−13.9574	−0.566513	−0.283256	−	0.959044i	$-0.591415\pi$
$607$	−13.9574	−0.566513	−0.283256	+	0.959044i	$0.591415\pi$
$608$	−1.59988	−0.0648837
$609$	−11.1775	−0.452934
$610$	−12.7266	−0.515285
$611$	−20.8964	−0.845378
$612$	21.8711	0.884085
$613$	−22.6500	−0.914823	−0.457412	−	0.889255i	$-0.651223\pi$
$613$	−22.6500	−0.914823	−0.457412	+	0.889255i	$0.651223\pi$
$614$	19.2119	0.775329
$615$	48.8022	1.96789
$616$	3.92498	0.158142
$617$	−16.2326	−0.653499	−0.326749	−	0.945111i	$-0.605953\pi$
$617$	−16.2326	−0.653499	−0.326749	+	0.945111i	$0.605953\pi$
$618$	−45.9977	−1.85030
$619$	−2.39475	−0.0962530	−0.0481265	−	0.998841i	$-0.515325\pi$
$619$	−2.39475	−0.0962530	−0.0481265	+	0.998841i	$0.515325\pi$
$620$	−20.5452	−0.825113
$621$	8.68700	0.348597
$622$	24.8047	0.994577
$623$	−17.8210	−0.713982
$624$	5.82325	0.233117
$625$	−3.18457	−0.127383
$626$	13.4295	0.536750
$627$	−17.2571	−0.689181
$628$	15.9854	0.637887
$629$	31.2614	1.24647
$630$	−16.2856	−0.648835
$631$	−12.1642	−0.484247	−0.242124	−	0.970245i	$-0.577844\pi$
$631$	−12.1642	−0.484247	−0.242124	+	0.970245i	$0.577844\pi$
$632$	8.72558	0.347085
$633$	54.2514	2.15630
$634$	7.84084	0.311400
$635$	−2.15302	−0.0854398
$636$	−31.3575	−1.24340
$637$	−2.11896	−0.0839564
$638$	15.9639	0.632017
$639$	2.19463	0.0868181
$640$	3.57738	0.141409
$641$	−17.3642	−0.685843	−0.342922	−	0.939364i	$-0.611416\pi$
$641$	−17.3642	−0.685843	−0.342922	+	0.939364i	$0.611416\pi$
$642$	−41.4187	−1.63467
$643$	−42.0603	−1.65870	−0.829348	−	0.558733i	$-0.811288\pi$
$643$	−42.0603	−1.65870	−0.829348	+	0.558733i	$0.811288\pi$
$644$	2.03624	0.0802390
$645$	−47.5659	−1.87291
$646$	−7.68632	−0.302414
$647$	−6.50073	−0.255570	−0.127785	−	0.991802i	$-0.540787\pi$
$647$	−6.50073	−0.255570	−0.127785	+	0.991802i	$0.540787\pi$
$648$	−1.93296	−0.0759336
$649$	−17.7329	−0.696077
$650$	−16.5230	−0.648086
$651$	−15.7829	−0.618579
$652$	−5.22917	−0.204790
$653$	−35.7417	−1.39868	−0.699341	−	0.714788i	$-0.746523\pi$
$653$	−35.7417	−1.39868	−0.699341	+	0.714788i	$0.746523\pi$
$654$	−32.7957	−1.28241
$655$	−14.0517	−0.549044
$656$	−4.96400	−0.193812
$657$	28.1859	1.09964
$658$	−9.86161	−0.384446
$659$	−1.43448	−0.0558793	−0.0279396	−	0.999610i	$-0.508895\pi$
$659$	−1.43448	−0.0558793	−0.0279396	+	0.999610i	$0.508895\pi$
$660$	38.5874	1.50201
$661$	21.0731	0.819648	0.409824	−	0.912165i	$-0.365590\pi$
$661$	21.0731	0.819648	0.409824	+	0.912165i	$0.365590\pi$
$662$	19.9705	0.776175
$663$	27.9767	1.08653
$664$	−9.64214	−0.374187
$665$	5.72339	0.221943
$666$	29.6222	1.14784
$667$	8.28190	0.320677
$668$	3.56348	0.137875
$669$	−21.1099	−0.816157
$670$	−3.03019	−0.117066
$671$	13.9632	0.539042
$672$	2.74816	0.106013
$673$	39.4154	1.51935	0.759677	−	0.650301i	$-0.225357\pi$
$673$	39.4154	1.51935	0.759677	+	0.650301i	$0.225357\pi$
$674$	18.3331	0.706163
$675$	−33.2665	−1.28043
$676$	−8.50999	−0.327307
$677$	3.53747	0.135956	0.0679780	−	0.997687i	$-0.478345\pi$
$677$	3.53747	0.135956	0.0679780	+	0.997687i	$0.478345\pi$
$678$	27.7040	1.06397
$679$	7.46416	0.286448
$680$	17.1869	0.659086
$681$	−17.5409	−0.672170
$682$	22.5414	0.863156
$683$	7.97266	0.305065	0.152533	−	0.988298i	$-0.451257\pi$
$683$	7.97266	0.305065	0.152533	+	0.988298i	$0.451257\pi$
$684$	−7.28327	−0.278483
$685$	−33.1588	−1.26693
$686$	−1.00000	−0.0381802
$687$	−34.8844	−1.33092
$688$	4.83825	0.184456
$689$	−24.1781	−0.921114
$690$	20.0187	0.762100
$691$	30.1152	1.14563	0.572817	−	0.819683i	$-0.305850\pi$
$691$	30.1152	1.14563	0.572817	+	0.819683i	$0.305850\pi$
$692$	−25.5973	−0.973064
$693$	17.8680	0.678750
$694$	−3.72888	−0.141546
$695$	1.28200	0.0486290
$696$	11.1775	0.423681
$697$	−23.8486	−0.903330
$698$	24.2300	0.917120
$699$	42.2525	1.59813
$700$	−7.79768	−0.294725
$701$	26.0541	0.984051	0.492025	−	0.870581i	$-0.336257\pi$
$701$	26.0541	0.984051	0.492025	+	0.870581i	$0.336257\pi$
$702$	9.03992	0.341190
$703$	−10.4103	−0.392634
$704$	−3.92498	−0.147928
$705$	−96.9517	−3.65141
$706$	−15.8785	−0.597595
$707$	−12.2036	−0.458965
$708$	−12.4161	−0.466624
$709$	14.4040	0.540953	0.270476	−	0.962727i	$-0.412819\pi$
$709$	14.4040	0.540953	0.270476	+	0.962727i	$0.412819\pi$
$710$	1.72460	0.0647230
$711$	39.7222	1.48970
$712$	17.8210	0.667869
$713$	11.6942	0.437953
$714$	13.2030	0.494110
$715$	29.7527	1.11269
$716$	1.01828	0.0380551
$717$	−49.0391	−1.83140
$718$	−16.8381	−0.628391
$719$	2.79084	0.104081	0.0520403	−	0.998645i	$-0.483428\pi$
$719$	2.79084	0.104081	0.0520403	+	0.998645i	$0.483428\pi$
$720$	16.2856	0.606929
$721$	−16.7376	−0.623342
$722$	−16.4404	−0.611848
$723$	−13.5945	−0.505585
$724$	17.3069	0.643207
$725$	−31.7152	−1.17787
$726$	−12.1069	−0.449331
$727$	−13.2019	−0.489632	−0.244816	−	0.969570i	$-0.578727\pi$
$727$	−13.2019	−0.489632	−0.244816	+	0.969570i	$0.578727\pi$
$728$	2.11896	0.0785340
$729$	−43.9721	−1.62860
$730$	22.1492	0.819779
$731$	23.2444	0.859727
$732$	9.77662	0.361354
$733$	−44.2633	−1.63490	−0.817450	−	0.575999i	$-0.804613\pi$
$733$	−44.2633	−1.63490	−0.817450	+	0.575999i	$0.804613\pi$
$734$	−7.69238	−0.283931
$735$	−9.83123	−0.362630
$736$	−2.03624	−0.0750567
$737$	3.32462	0.122464
$738$	−22.5980	−0.831845
$739$	−27.6427	−1.01685	−0.508427	−	0.861105i	$-0.669773\pi$
$739$	−27.6427	−1.01685	−0.508427	+	0.861105i	$0.669773\pi$
$740$	23.2779	0.855712
$741$	−9.31651	−0.342250
$742$	−11.4104	−0.418887
$743$	−22.2907	−0.817765	−0.408883	−	0.912587i	$-0.634081\pi$
$743$	−22.2907	−0.817765	−0.408883	+	0.912587i	$0.634081\pi$
$744$	15.7829	0.578628
$745$	−30.0163	−1.09971
$746$	31.6456	1.15863
$747$	−43.8947	−1.60602
$748$	−18.8568	−0.689474
$749$	−15.0714	−0.550698
$750$	−27.5046	−1.00433
$751$	4.42534	0.161483	0.0807415	−	0.996735i	$-0.474271\pi$
$751$	4.42534	0.161483	0.0807415	+	0.996735i	$0.474271\pi$
$752$	9.86161	0.359616
$753$	−46.6008	−1.69823
$754$	8.61837	0.313863
$755$	−47.7544	−1.73796
$756$	4.26620	0.155160
$757$	7.70690	0.280112	0.140056	−	0.990144i	$-0.455272\pi$
$757$	7.70690	0.280112	0.140056	+	0.990144i	$0.455272\pi$
$758$	21.6077	0.784828
$759$	−21.9638	−0.797237
$760$	−5.72339	−0.207609
$761$	−30.1921	−1.09446	−0.547231	−	0.836982i	$-0.684318\pi$
$761$	−30.1921	−1.09446	−0.547231	+	0.836982i	$0.684318\pi$
$762$	1.65395	0.0599164
$763$	−11.9337	−0.432029
$764$	−0.747688	−0.0270504
$765$	78.2412	2.82882
$766$	17.6869	0.639054
$767$	−9.57339	−0.345675
$768$	−2.74816	−0.0991657
$769$	39.6807	1.43092	0.715462	−	0.698652i	$-0.246216\pi$
$769$	39.6807	1.43092	0.715462	+	0.698652i	$0.246216\pi$
$770$	14.0412	0.506009
$771$	−5.19239	−0.186999
$772$	−13.4869	−0.485405
$773$	27.7853	0.999369	0.499685	−	0.866207i	$-0.333449\pi$
$773$	27.7853	0.999369	0.499685	+	0.866207i	$0.333449\pi$
$774$	22.0256	0.791692
$775$	−44.7826	−1.60864
$776$	−7.46416	−0.267948
$777$	17.8822	0.641519
$778$	−6.15885	−0.220805
$779$	7.94180	0.284545
$780$	20.8320	0.745906
$781$	−1.89217	−0.0677071
$782$	−9.78272	−0.349829
$783$	17.3517	0.620100
$784$	1.00000	0.0357143
$785$	57.1859	2.04105
$786$	10.7945	0.385029
$787$	−30.7777	−1.09711	−0.548553	−	0.836116i	$-0.684821\pi$
$787$	−30.7777	−1.09711	−0.548553	+	0.836116i	$0.684821\pi$
$788$	20.7514	0.739237
$789$	25.2381	0.898502
$790$	31.2147	1.11057
$791$	10.0809	0.358436
$792$	−17.8680	−0.634912
$793$	7.53824	0.267691
$794$	2.67101	0.0947904
$795$	−112.178	−3.97854
$796$	18.7303	0.663877
$797$	−18.5485	−0.657023	−0.328512	−	0.944500i	$-0.606547\pi$
$797$	−18.5485	−0.657023	−0.328512	+	0.944500i	$0.606547\pi$
$798$	−4.39673	−0.155642
$799$	47.3783	1.67612
$800$	7.79768	0.275690
$801$	81.1279	2.86651
$802$	−33.9573	−1.19907
$803$	−24.3013	−0.857575
$804$	2.32780	0.0820953
$805$	7.28441	0.256742
$806$	12.1693	0.428647
$807$	−77.1839	−2.71700
$808$	12.2036	0.429323
$809$	0.0217052	0.000763113 0	0.000381557	−	1.00000i	$-0.499879\pi$
$809$	0.0217052	0.000763113 0	0.000381557		1.00000i	$0.499879\pi$
$810$	−6.91492	−0.242966
$811$	−54.5747	−1.91638	−0.958189	−	0.286136i	$-0.907629\pi$
$811$	−54.5747	−1.91638	−0.958189	+	0.286136i	$0.907629\pi$
$812$	4.06726	0.142733
$813$	27.9209	0.979227
$814$	−25.5397	−0.895165
$815$	−18.7068	−0.655269
$816$	−13.2030	−0.462198
$817$	−7.74061	−0.270810
$818$	15.7522	0.550762
$819$	9.64634	0.337070
$820$	−17.7581	−0.620141
$821$	25.7095	0.897268	0.448634	−	0.893716i	$-0.351911\pi$
$821$	25.7095	0.897268	0.448634	+	0.893716i	$0.351911\pi$
$822$	25.4727	0.888463
$823$	36.5001	1.27231	0.636157	−	0.771559i	$-0.280523\pi$
$823$	36.5001	1.27231	0.636157	+	0.771559i	$0.280523\pi$
$824$	16.7376	0.583083
$825$	84.1095	2.92832
$826$	−4.51796	−0.157200
$827$	11.6855	0.406345	0.203173	−	0.979143i	$-0.434875\pi$
$827$	11.6855	0.406345	0.203173	+	0.979143i	$0.434875\pi$
$828$	−9.26974	−0.322146
$829$	2.76756	0.0961213	0.0480606	−	0.998844i	$-0.484696\pi$
$829$	2.76756	0.0961213	0.0480606	+	0.998844i	$0.484696\pi$
$830$	−34.4936	−1.19729
$831$	47.6074	1.65148
$832$	−2.11896	−0.0734619
$833$	4.80431	0.166459
$834$	−0.984837	−0.0341021
$835$	12.7479	0.441160
$836$	6.27950	0.217181
$837$	24.5011	0.846880
$838$	8.23693	0.284540
$839$	25.6785	0.886519	0.443260	−	0.896393i	$-0.353822\pi$
$839$	25.6785	0.886519	0.443260	+	0.896393i	$0.353822\pi$
$840$	9.83123	0.339210
$841$	−12.4574	−0.429567
$842$	−17.6368	−0.607804
$843$	−48.3150	−1.66406
$844$	−19.7410	−0.679513
$845$	−30.4435	−1.04729
$846$	44.8938	1.54348
$847$	−4.40547	−0.151374
$848$	11.4104	0.391833
$849$	22.5526	0.774003
$850$	37.4625	1.28495
$851$	−13.2497	−0.454194
$852$	−1.32484	−0.0453883
$853$	−22.8449	−0.782193	−0.391097	−	0.920350i	$-0.627904\pi$
$853$	−22.8449	−0.782193	−0.391097	+	0.920350i	$0.627904\pi$
$854$	3.55751	0.121736
$855$	−26.0550	−0.891064
$856$	15.0714	0.515131
$857$	−26.6506	−0.910366	−0.455183	−	0.890398i	$-0.650426\pi$
$857$	−26.6506	−0.910366	−0.455183	+	0.890398i	$0.650426\pi$
$858$	−22.8562	−0.780296
$859$	53.5119	1.82580	0.912902	−	0.408179i	$-0.133836\pi$
$859$	53.5119	1.82580	0.912902	+	0.408179i	$0.133836\pi$
$860$	17.3083	0.590207
$861$	−13.6419	−0.464914
$862$	−1.00000	−0.0340601
$863$	−39.7801	−1.35413	−0.677065	−	0.735923i	$-0.736748\pi$
$863$	−39.7801	−1.35413	−0.677065	+	0.735923i	$0.736748\pi$
$864$	−4.26620	−0.145139
$865$	−91.5714	−3.11352
$866$	−0.689093	−0.0234163
$867$	−16.7127	−0.567592
$868$	5.74306	0.194932
$869$	−34.2477	−1.16177
$870$	39.9861	1.35566
$871$	1.79485	0.0608161
$872$	11.9337	0.404126
$873$	−33.9797	−1.15004
$874$	3.25774	0.110195
$875$	−10.0084	−0.338345
$876$	−17.0151	−0.574887
$877$	11.1608	0.376872	0.188436	−	0.982085i	$-0.439658\pi$
$877$	11.1608	0.376872	0.188436	+	0.982085i	$0.439658\pi$
$878$	4.74138	0.160014
$879$	−36.9395	−1.24594
$880$	−14.0412	−0.473328
$881$	47.8391	1.61174	0.805870	−	0.592093i	$-0.201698\pi$
$881$	47.8391	1.61174	0.805870	+	0.592093i	$0.201698\pi$
$882$	4.55238	0.153287
$883$	3.77274	0.126963	0.0634814	−	0.997983i	$-0.479780\pi$
$883$	3.77274	0.126963	0.0634814	+	0.997983i	$0.479780\pi$
$884$	−10.1802	−0.342396
$885$	−44.4171	−1.49306
$886$	−0.804752	−0.0270362
$887$	−22.3592	−0.750749	−0.375374	−	0.926873i	$-0.622486\pi$
$887$	−22.3592	−0.750749	−0.375374	+	0.926873i	$0.622486\pi$
$888$	−17.8822	−0.600086
$889$	0.601841	0.0201851
$890$	63.7525	2.13699
$891$	7.58681	0.254168
$892$	7.68148	0.257195
$893$	−15.7774	−0.527970
$894$	23.0586	0.771195
$895$	3.64280	0.121765
$896$	−1.00000	−0.0334077
$897$	−11.8575	−0.395911
$898$	−11.1635	−0.372532
$899$	23.3585	0.779050
$900$	35.4980	1.18327
$901$	54.8189	1.82628
$902$	19.4836	0.648733
$903$	13.2963	0.442472
$904$	−10.0809	−0.335286
$905$	61.9135	2.05808
$906$	36.6851	1.21878
$907$	−30.4111	−1.00978	−0.504892	−	0.863182i	$-0.668468\pi$
$907$	−30.4111	−1.00978	−0.504892	+	0.863182i	$0.668468\pi$
$908$	6.38279	0.211820
$909$	55.5557	1.84267
$910$	7.58035	0.251286
$911$	5.24925	0.173915	0.0869577	−	0.996212i	$-0.472285\pi$
$911$	5.24925	0.173915	0.0869577	+	0.996212i	$0.472285\pi$
$912$	4.39673	0.145590
$913$	37.8452	1.25249
$914$	34.3207	1.13523
$915$	34.9747	1.15623
$916$	12.6937	0.419413
$917$	3.92792	0.129711
$918$	−20.4961	−0.676473
$919$	−5.06126	−0.166955	−0.0834777	−	0.996510i	$-0.526603\pi$
$919$	−5.06126	−0.166955	−0.0834777	+	0.996510i	$0.526603\pi$
$920$	−7.28441	−0.240160
$921$	−52.7974	−1.73973
$922$	25.0235	0.824104
$923$	−1.02152	−0.0336237
$924$	−10.7865	−0.354849
$925$	50.7392	1.66829
$926$	23.5189	0.772878
$927$	76.1961	2.50261
$928$	−4.06726	−0.133514
$929$	48.0412	1.57618	0.788091	−	0.615559i	$-0.211070\pi$
$929$	48.0412	1.57618	0.788091	+	0.615559i	$0.211070\pi$
$930$	56.4614	1.85144
$931$	−1.59988	−0.0524339
$932$	−15.3748	−0.503619
$933$	−68.1672	−2.23169
$934$	−17.9546	−0.587493
$935$	−67.4581	−2.20612
$936$	−9.64634	−0.315300
$937$	−27.4189	−0.895736	−0.447868	−	0.894100i	$-0.647817\pi$
$937$	−27.4189	−0.895736	−0.447868	+	0.894100i	$0.647817\pi$
$938$	0.847040	0.0276569
$939$	−36.9064	−1.20439
$940$	35.2788	1.15067
$941$	35.5158	1.15778	0.578890	−	0.815405i	$-0.303486\pi$
$941$	35.5158	1.15778	0.578890	+	0.815405i	$0.303486\pi$
$942$	−43.9305	−1.43133
$943$	10.1079	0.329158
$944$	4.51796	0.147047
$945$	15.2618	0.496467
$946$	−18.9900	−0.617419
$947$	−47.4242	−1.54108	−0.770540	−	0.637392i	$-0.780013\pi$
$947$	−47.4242	−1.54108	−0.770540	+	0.637392i	$0.780013\pi$
$948$	−23.9793	−0.778811
$949$	−13.1195	−0.425876
$950$	−12.4754	−0.404754
$951$	−21.5479	−0.698738
$952$	−4.80431	−0.155709
$953$	−5.70164	−0.184694	−0.0923471	−	0.995727i	$-0.529437\pi$
$953$	−5.70164	−0.184694	−0.0923471	+	0.995727i	$0.529437\pi$
$954$	51.9443	1.68176
$955$	−2.67477	−0.0865534
$956$	17.8443	0.577127
$957$	−43.8714	−1.41816
$958$	2.13545	0.0689933
$959$	9.26900	0.299312
$960$	−9.83123	−0.317301
$961$	1.98279	0.0639609
$962$	−13.7880	−0.444543
$963$	68.6109	2.21096
$964$	4.94676	0.159325
$965$	−48.2479	−1.55315
$966$	−5.59591	−0.180045
$967$	−30.2022	−0.971238	−0.485619	−	0.874171i	$-0.661406\pi$
$967$	−30.2022	−0.971238	−0.485619	+	0.874171i	$0.661406\pi$
$968$	4.40547	0.141597
$969$	21.1232	0.678576
$970$	−26.7022	−0.857355
$971$	40.3481	1.29483	0.647415	−	0.762137i	$-0.275850\pi$
$971$	40.3481	1.29483	0.647415	+	0.762137i	$0.275850\pi$
$972$	18.1107	0.580900
$973$	−0.358362	−0.0114886
$974$	−13.1994	−0.422935
$975$	45.4079	1.45422
$976$	−3.55751	−0.113873
$977$	10.4624	0.334723	0.167362	−	0.985896i	$-0.446475\pi$
$977$	10.4624	0.334723	0.167362	+	0.985896i	$0.446475\pi$
$978$	14.3706	0.459521
$979$	−69.9470	−2.23551
$980$	3.57738	0.114275
$981$	54.3268	1.73452
$982$	5.79224	0.184838
$983$	58.9621	1.88060	0.940299	−	0.340348i	$-0.110545\pi$
$983$	58.9621	1.88060	0.940299	+	0.340348i	$0.110545\pi$
$984$	13.6419	0.434887
$985$	74.2356	2.36534
$986$	−19.5404	−0.622292
$987$	27.1013	0.862644
$988$	3.39009	0.107853
$989$	−9.85182	−0.313270
$990$	−63.9208	−2.03154
$991$	−36.5503	−1.16106	−0.580529	−	0.814239i	$-0.697154\pi$
$991$	−36.5503	−1.16106	−0.580529	+	0.814239i	$0.697154\pi$
$992$	−5.74306	−0.182342
$993$	−54.8821	−1.74163
$994$	−0.482083	−0.0152908
$995$	67.0054	2.12421
$996$	26.4981	0.839626
$997$	−34.6727	−1.09809	−0.549047	−	0.835791i	$-0.685009\pi$
$997$	−34.6727	−1.09809	−0.549047	+	0.835791i	$0.685009\pi$
$998$	10.3205	0.326691
$999$	−27.7600	−0.878286

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.r.1.3	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.r.1.3	✓	31	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.74816 q^{3} +1.00000 q^{4} +3.57738 q^{5} -2.74816 q^{6} -1.00000 q^{7} +1.00000 q^{8} +4.55238 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.74816 q^{3} +1.00000 q^{4} +3.57738 q^{5} -2.74816 q^{6} -1.00000 q^{7} +1.00000 q^{8} +4.55238 q^{9} +3.57738 q^{10} -3.92498 q^{11} -2.74816 q^{12} -2.11896 q^{13} -1.00000 q^{14} -9.83123 q^{15} +1.00000 q^{16} +4.80431 q^{17} +4.55238 q^{18} -1.59988 q^{19} +3.57738 q^{20} +2.74816 q^{21} -3.92498 q^{22} -2.03624 q^{23} -2.74816 q^{24} +7.79768 q^{25} -2.11896 q^{26} -4.26620 q^{27} -1.00000 q^{28} -4.06726 q^{29} -9.83123 q^{30} -5.74306 q^{31} +1.00000 q^{32} +10.7865 q^{33} +4.80431 q^{34} -3.57738 q^{35} +4.55238 q^{36} +6.50695 q^{37} -1.59988 q^{38} +5.82325 q^{39} +3.57738 q^{40} -4.96400 q^{41} +2.74816 q^{42} +4.83825 q^{43} -3.92498 q^{44} +16.2856 q^{45} -2.03624 q^{46} +9.86161 q^{47} -2.74816 q^{48} +1.00000 q^{49} +7.79768 q^{50} -13.2030 q^{51} -2.11896 q^{52} +11.4104 q^{53} -4.26620 q^{54} -14.0412 q^{55} -1.00000 q^{56} +4.39673 q^{57} -4.06726 q^{58} +4.51796 q^{59} -9.83123 q^{60} -3.55751 q^{61} -5.74306 q^{62} -4.55238 q^{63} +1.00000 q^{64} -7.58035 q^{65} +10.7865 q^{66} -0.847040 q^{67} +4.80431 q^{68} +5.59591 q^{69} -3.57738 q^{70} +0.482083 q^{71} +4.55238 q^{72} +6.19145 q^{73} +6.50695 q^{74} -21.4293 q^{75} -1.59988 q^{76} +3.92498 q^{77} +5.82325 q^{78} +8.72558 q^{79} +3.57738 q^{80} -1.93296 q^{81} -4.96400 q^{82} -9.64214 q^{83} +2.74816 q^{84} +17.1869 q^{85} +4.83825 q^{86} +11.1775 q^{87} -3.92498 q^{88} +17.8210 q^{89} +16.2856 q^{90} +2.11896 q^{91} -2.03624 q^{92} +15.7829 q^{93} +9.86161 q^{94} -5.72339 q^{95} -2.74816 q^{96} -7.46416 q^{97} +1.00000 q^{98} -17.8680 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 31 q^{2} + 7 q^{3} + 31 q^{4} + 15 q^{5} + 7 q^{6} - 31 q^{7} + 31 q^{8} + 42 q^{9}+O(q^{10}) \) 31 * q + 31 * q^2 + 7 * q^3 + 31 * q^4 + 15 * q^5 + 7 * q^6 - 31 * q^7 + 31 * q^8 + 42 * q^9	\( 31 q + 31 q^{2} + 7 q^{3} + 31 q^{4} + 15 q^{5} + 7 q^{6} - 31 q^{7} + 31 q^{8} + 42 q^{9} + 15 q^{10} + 12 q^{11} + 7 q^{12} + 26 q^{13} - 31 q^{14} + 6 q^{15} + 31 q^{16} + 33 q^{17} + 42 q^{18} + 34 q^{19} + 15 q^{20} - 7 q^{21} + 12 q^{22} - 14 q^{23} + 7 q^{24} + 58 q^{25} + 26 q^{26} + 28 q^{27} - 31 q^{28} + 11 q^{29} + 6 q^{30} + 19 q^{31} + 31 q^{32} + 43 q^{33} + 33 q^{34} - 15 q^{35} + 42 q^{36} + 2 q^{37} + 34 q^{38} - 16 q^{39} + 15 q^{40} + 53 q^{41} - 7 q^{42} + 22 q^{43} + 12 q^{44} + 43 q^{45} - 14 q^{46} + 27 q^{47} + 7 q^{48} + 31 q^{49} + 58 q^{50} + 17 q^{51} + 26 q^{52} + 11 q^{53} + 28 q^{54} + 19 q^{55} - 31 q^{56} + 45 q^{57} + 11 q^{58} + 54 q^{59} + 6 q^{60} + 41 q^{61} + 19 q^{62} - 42 q^{63} + 31 q^{64} + 30 q^{65} + 43 q^{66} + 13 q^{67} + 33 q^{68} + 17 q^{69} - 15 q^{70} + 43 q^{71} + 42 q^{72} + 42 q^{73} + 2 q^{74} + 62 q^{75} + 34 q^{76} - 12 q^{77} - 16 q^{78} - 12 q^{79} + 15 q^{80} + 63 q^{81} + 53 q^{82} + 35 q^{83} - 7 q^{84} + 16 q^{85} + 22 q^{86} - 4 q^{87} + 12 q^{88} + 115 q^{89} + 43 q^{90} - 26 q^{91} - 14 q^{92} + q^{93} + 27 q^{94} - 13 q^{95} + 7 q^{96} + 32 q^{97} + 31 q^{98} + 34 q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 + 7 * q^3 + 31 * q^4 + 15 * q^5 + 7 * q^6 - 31 * q^7 + 31 * q^8 + 42 * q^9 + 15 * q^10 + 12 * q^11 + 7 * q^12 + 26 * q^13 - 31 * q^14 + 6 * q^15 + 31 * q^16 + 33 * q^17 + 42 * q^18 + 34 * q^19 + 15 * q^20 - 7 * q^21 + 12 * q^22 - 14 * q^23 + 7 * q^24 + 58 * q^25 + 26 * q^26 + 28 * q^27 - 31 * q^28 + 11 * q^29 + 6 * q^30 + 19 * q^31 + 31 * q^32 + 43 * q^33 + 33 * q^34 - 15 * q^35 + 42 * q^36 + 2 * q^37 + 34 * q^38 - 16 * q^39 + 15 * q^40 + 53 * q^41 - 7 * q^42 + 22 * q^43 + 12 * q^44 + 43 * q^45 - 14 * q^46 + 27 * q^47 + 7 * q^48 + 31 * q^49 + 58 * q^50 + 17 * q^51 + 26 * q^52 + 11 * q^53 + 28 * q^54 + 19 * q^55 - 31 * q^56 + 45 * q^57 + 11 * q^58 + 54 * q^59 + 6 * q^60 + 41 * q^61 + 19 * q^62 - 42 * q^63 + 31 * q^64 + 30 * q^65 + 43 * q^66 + 13 * q^67 + 33 * q^68 + 17 * q^69 - 15 * q^70 + 43 * q^71 + 42 * q^72 + 42 * q^73 + 2 * q^74 + 62 * q^75 + 34 * q^76 - 12 * q^77 - 16 * q^78 - 12 * q^79 + 15 * q^80 + 63 * q^81 + 53 * q^82 + 35 * q^83 - 7 * q^84 + 16 * q^85 + 22 * q^86 - 4 * q^87 + 12 * q^88 + 115 * q^89 + 43 * q^90 - 26 * q^91 - 14 * q^92 + q^93 + 27 * q^94 - 13 * q^95 + 7 * q^96 + 32 * q^97 + 31 * q^98 + 34 * q^99

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