LMFDB - Embedded newform 6022.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6022,2,Mod(1,6022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6022, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6022 = 2 \cdot 3011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6022.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:	$48.0859120972$
Analytic rank:	$2$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.80194$ of defining polynomial
Character	$\chi$	$=$	6022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.80194 q^{3} +1.00000 q^{4} -2.44504 q^{5} -2.80194 q^{6} +0.0489173 q^{7} +1.00000 q^{8} +4.85086 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.80194 q^{3} +1.00000 q^{4} -2.44504 q^{5} -2.80194 q^{6} +0.0489173 q^{7} +1.00000 q^{8} +4.85086 q^{9} -2.44504 q^{10} -5.80194 q^{11} -2.80194 q^{12} -4.44504 q^{13} +0.0489173 q^{14} +6.85086 q^{15} +1.00000 q^{16} -2.55496 q^{17} +4.85086 q^{18} -4.26875 q^{19} -2.44504 q^{20} -0.137063 q^{21} -5.80194 q^{22} -4.69202 q^{23} -2.80194 q^{24} +0.978230 q^{25} -4.44504 q^{26} -5.18598 q^{27} +0.0489173 q^{28} -2.70410 q^{29} +6.85086 q^{30} +6.89977 q^{31} +1.00000 q^{32} +16.2567 q^{33} -2.55496 q^{34} -0.119605 q^{35} +4.85086 q^{36} -4.89008 q^{37} -4.26875 q^{38} +12.4547 q^{39} -2.44504 q^{40} -5.52111 q^{41} -0.137063 q^{42} -8.12498 q^{43} -5.80194 q^{44} -11.8605 q^{45} -4.69202 q^{46} -3.26875 q^{47} -2.80194 q^{48} -6.99761 q^{49} +0.978230 q^{50} +7.15883 q^{51} -4.44504 q^{52} +0.423272 q^{53} -5.18598 q^{54} +14.1860 q^{55} +0.0489173 q^{56} +11.9608 q^{57} -2.70410 q^{58} +0.417895 q^{59} +6.85086 q^{60} -3.53319 q^{61} +6.89977 q^{62} +0.237291 q^{63} +1.00000 q^{64} +10.8683 q^{65} +16.2567 q^{66} -5.67025 q^{67} -2.55496 q^{68} +13.1468 q^{69} -0.119605 q^{70} -0.0827692 q^{71} +4.85086 q^{72} +2.91723 q^{73} -4.89008 q^{74} -2.74094 q^{75} -4.26875 q^{76} -0.283815 q^{77} +12.4547 q^{78} -13.3230 q^{79} -2.44504 q^{80} -0.0217703 q^{81} -5.52111 q^{82} +5.42758 q^{83} -0.137063 q^{84} +6.24698 q^{85} -8.12498 q^{86} +7.57673 q^{87} -5.80194 q^{88} +5.65279 q^{89} -11.8605 q^{90} -0.217440 q^{91} -4.69202 q^{92} -19.3327 q^{93} -3.26875 q^{94} +10.4373 q^{95} -2.80194 q^{96} -5.87263 q^{97} -6.99761 q^{98} -28.1444 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} - 4 q^{3} + 3 q^{4} - 7 q^{5} - 4 q^{6} - 9 q^{7} + 3 q^{8} + q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 - 4 * q^3 + 3 * q^4 - 7 * q^5 - 4 * q^6 - 9 * q^7 + 3 * q^8 + q^9	\( 3 q + 3 q^{2} - 4 q^{3} + 3 q^{4} - 7 q^{5} - 4 q^{6} - 9 q^{7} + 3 q^{8} + q^{9} - 7 q^{10} - 13 q^{11} - 4 q^{12} - 13 q^{13} - 9 q^{14} + 7 q^{15} + 3 q^{16} - 8 q^{17} + q^{18} - 5 q^{19} - 7 q^{20} + 5 q^{21} - 13 q^{22} - 9 q^{23} - 4 q^{24} + 6 q^{25} - 13 q^{26} - q^{27} - 9 q^{28} - 22 q^{29} + 7 q^{30} - 2 q^{31} + 3 q^{32} + 22 q^{33} - 8 q^{34} + 21 q^{35} + q^{36} - 14 q^{37} - 5 q^{38} + 15 q^{39} - 7 q^{40} - q^{41} + 5 q^{42} - 13 q^{44} - 9 q^{46} - 2 q^{47} - 4 q^{48} + 20 q^{49} + 6 q^{50} + 13 q^{51} - 13 q^{52} + 4 q^{53} - q^{54} + 28 q^{55} - 9 q^{56} + 23 q^{57} - 22 q^{58} + 7 q^{59} + 7 q^{60} - 14 q^{61} - 2 q^{62} + 18 q^{63} + 3 q^{64} + 35 q^{65} + 22 q^{66} - 15 q^{67} - 8 q^{68} + 12 q^{69} + 21 q^{70} - 7 q^{71} + q^{72} + 2 q^{73} - 14 q^{74} + 6 q^{75} - 5 q^{76} + 32 q^{77} + 15 q^{78} - 20 q^{79} - 7 q^{80} + 3 q^{81} - q^{82} + 5 q^{84} + 14 q^{85} + 20 q^{87} - 13 q^{88} - q^{89} + 39 q^{91} - 9 q^{92} - 16 q^{93} - 2 q^{94} - 7 q^{95} - 4 q^{96} - q^{97} + 20 q^{98} - 16 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - 4 * q^3 + 3 * q^4 - 7 * q^5 - 4 * q^6 - 9 * q^7 + 3 * q^8 + q^9 - 7 * q^10 - 13 * q^11 - 4 * q^12 - 13 * q^13 - 9 * q^14 + 7 * q^15 + 3 * q^16 - 8 * q^17 + q^18 - 5 * q^19 - 7 * q^20 + 5 * q^21 - 13 * q^22 - 9 * q^23 - 4 * q^24 + 6 * q^25 - 13 * q^26 - q^27 - 9 * q^28 - 22 * q^29 + 7 * q^30 - 2 * q^31 + 3 * q^32 + 22 * q^33 - 8 * q^34 + 21 * q^35 + q^36 - 14 * q^37 - 5 * q^38 + 15 * q^39 - 7 * q^40 - q^41 + 5 * q^42 - 13 * q^44 - 9 * q^46 - 2 * q^47 - 4 * q^48 + 20 * q^49 + 6 * q^50 + 13 * q^51 - 13 * q^52 + 4 * q^53 - q^54 + 28 * q^55 - 9 * q^56 + 23 * q^57 - 22 * q^58 + 7 * q^59 + 7 * q^60 - 14 * q^61 - 2 * q^62 + 18 * q^63 + 3 * q^64 + 35 * q^65 + 22 * q^66 - 15 * q^67 - 8 * q^68 + 12 * q^69 + 21 * q^70 - 7 * q^71 + q^72 + 2 * q^73 - 14 * q^74 + 6 * q^75 - 5 * q^76 + 32 * q^77 + 15 * q^78 - 20 * q^79 - 7 * q^80 + 3 * q^81 - q^82 + 5 * q^84 + 14 * q^85 + 20 * q^87 - 13 * q^88 - q^89 + 39 * q^91 - 9 * q^92 - 16 * q^93 - 2 * q^94 - 7 * q^95 - 4 * q^96 - q^97 + 20 * q^98 - 16 * 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
$3$	−2.80194	−1.61770	−0.808850	−	0.588015i	$-0.799909\pi$
$3$	−2.80194	−1.61770	−0.808850	+	0.588015i	$0.799909\pi$
$4$	1.00000	0.500000
$5$	−2.44504	−1.09346	−0.546728	−	0.837310i	$-0.684127\pi$
$5$	−2.44504	−1.09346	−0.546728	+	0.837310i	$0.684127\pi$
$6$	−2.80194	−1.14389
$7$	0.0489173	0.0184890	0.00924451	−	0.999957i	$-0.497057\pi$
$7$	0.0489173	0.0184890	0.00924451	+	0.999957i	$0.497057\pi$
$8$	1.00000	0.353553
$9$	4.85086	1.61695
$10$	−2.44504	−0.773190
$11$	−5.80194	−1.74935	−0.874675	−	0.484710i	$-0.838925\pi$
$11$	−5.80194	−1.74935	−0.874675	+	0.484710i	$0.838925\pi$
$12$	−2.80194	−0.808850
$13$	−4.44504	−1.23283	−0.616416	−	0.787420i	$-0.711416\pi$
$13$	−4.44504	−1.23283	−0.616416	+	0.787420i	$0.711416\pi$
$14$	0.0489173	0.0130737
$15$	6.85086	1.76888
$16$	1.00000	0.250000
$17$	−2.55496	−0.619668	−0.309834	−	0.950791i	$-0.600274\pi$
$17$	−2.55496	−0.619668	−0.309834	+	0.950791i	$0.600274\pi$
$18$	4.85086	1.14336
$19$	−4.26875	−0.979318	−0.489659	−	0.871914i	$-0.662879\pi$
$19$	−4.26875	−0.979318	−0.489659	+	0.871914i	$0.662879\pi$
$20$	−2.44504	−0.546728
$21$	−0.137063	−0.0299097
$22$	−5.80194	−1.23698
$23$	−4.69202	−0.978354	−0.489177	−	0.872185i	$-0.662703\pi$
$23$	−4.69202	−0.978354	−0.489177	+	0.872185i	$0.662703\pi$
$24$	−2.80194	−0.571943
$25$	0.978230	0.195646
$26$	−4.44504	−0.871744
$27$	−5.18598	−0.998042
$28$	0.0489173	0.00924451
$29$	−2.70410	−0.502139	−0.251070	−	0.967969i	$-0.580782\pi$
$29$	−2.70410	−0.502139	−0.251070	+	0.967969i	$0.580782\pi$
$30$	6.85086	1.25079
$31$	6.89977	1.23924	0.619618	−	0.784904i	$-0.287288\pi$
$31$	6.89977	1.23924	0.619618	+	0.784904i	$0.287288\pi$
$32$	1.00000	0.176777
$33$	16.2567	2.82992
$34$	−2.55496	−0.438172
$35$	−0.119605	−0.0202169
$36$	4.85086	0.808476
$37$	−4.89008	−0.803925	−0.401962	−	0.915656i	$-0.631672\pi$
$37$	−4.89008	−0.803925	−0.401962	+	0.915656i	$0.631672\pi$
$38$	−4.26875	−0.692483
$39$	12.4547	1.99435
$40$	−2.44504	−0.386595
$41$	−5.52111	−0.862252	−0.431126	−	0.902292i	$-0.641884\pi$
$41$	−5.52111	−0.862252	−0.431126	+	0.902292i	$0.641884\pi$
$42$	−0.137063	−0.0211493
$43$	−8.12498	−1.23905	−0.619524	−	0.784978i	$-0.712674\pi$
$43$	−8.12498	−1.23905	−0.619524	+	0.784978i	$0.712674\pi$
$44$	−5.80194	−0.874675
$45$	−11.8605	−1.76807
$46$	−4.69202	−0.691801
$47$	−3.26875	−0.476796	−0.238398	−	0.971168i	$-0.576622\pi$
$47$	−3.26875	−0.476796	−0.238398	+	0.971168i	$0.576622\pi$
$48$	−2.80194	−0.404425
$49$	−6.99761	−0.999658
$50$	0.978230	0.138343
$51$	7.15883	1.00244
$52$	−4.44504	−0.616416
$53$	0.423272	0.0581408	0.0290704	−	0.999577i	$-0.490745\pi$
$53$	0.423272	0.0581408	0.0290704	+	0.999577i	$0.490745\pi$
$54$	−5.18598	−0.705723
$55$	14.1860	1.91284
$56$	0.0489173	0.00653685
$57$	11.9608	1.58424
$58$	−2.70410	−0.355066
$59$	0.417895	0.0544053	0.0272026	−	0.999630i	$-0.491340\pi$
$59$	0.417895	0.0544053	0.0272026	+	0.999630i	$0.491340\pi$
$60$	6.85086	0.884442
$61$	−3.53319	−0.452378	−0.226189	−	0.974083i	$-0.572627\pi$
$61$	−3.53319	−0.452378	−0.226189	+	0.974083i	$0.572627\pi$
$62$	6.89977	0.876272
$63$	0.237291	0.0298958
$64$	1.00000	0.125000
$65$	10.8683	1.34805
$66$	16.2567	2.00106
$67$	−5.67025	−0.692731	−0.346366	−	0.938100i	$-0.612584\pi$
$67$	−5.67025	−0.692731	−0.346366	+	0.938100i	$0.612584\pi$
$68$	−2.55496	−0.309834
$69$	13.1468	1.58268
$70$	−0.119605	−0.0142955
$71$	−0.0827692	−0.00982290	−0.00491145	−	0.999988i	$-0.501563\pi$
$71$	−0.0827692	−0.00982290	−0.00491145	+	0.999988i	$0.501563\pi$
$72$	4.85086	0.571679
$73$	2.91723	0.341436	0.170718	−	0.985320i	$-0.445391\pi$
$73$	2.91723	0.341436	0.170718	+	0.985320i	$0.445391\pi$
$74$	−4.89008	−0.568461
$75$	−2.74094	−0.316496
$76$	−4.26875	−0.489659
$77$	−0.283815	−0.0323438
$78$	12.4547	1.41022
$79$	−13.3230	−1.49896	−0.749480	−	0.662027i	$-0.769696\pi$
$79$	−13.3230	−1.49896	−0.749480	+	0.662027i	$0.769696\pi$
$80$	−2.44504	−0.273364
$81$	−0.0217703	−0.00241892
$82$	−5.52111	−0.609704
$83$	5.42758	0.595755	0.297877	−	0.954604i	$-0.403721\pi$
$83$	5.42758	0.595755	0.297877	+	0.954604i	$0.403721\pi$
$84$	−0.137063	−0.0149548
$85$	6.24698	0.677580
$86$	−8.12498	−0.876139
$87$	7.57673	0.812311
$88$	−5.80194	−0.618489
$89$	5.65279	0.599195	0.299597	−	0.954066i	$-0.403148\pi$
$89$	5.65279	0.599195	0.299597	+	0.954066i	$0.403148\pi$
$90$	−11.8605	−1.25021
$91$	−0.217440	−0.0227939
$92$	−4.69202	−0.489177
$93$	−19.3327	−2.00471
$94$	−3.26875	−0.337146
$95$	10.4373	1.07084
$96$	−2.80194	−0.285972
$97$	−5.87263	−0.596275	−0.298137	−	0.954523i	$-0.596365\pi$
$97$	−5.87263	−0.596275	−0.298137	+	0.954523i	$0.596365\pi$
$98$	−6.99761	−0.706865
$99$	−28.1444	−2.82861
$100$	0.978230	0.0978230
$101$	−4.02177	−0.400181	−0.200091	−	0.979777i	$-0.564124\pi$
$101$	−4.02177	−0.400181	−0.200091	+	0.979777i	$0.564124\pi$
$102$	7.15883	0.708830
$103$	9.22282	0.908751	0.454376	−	0.890810i	$-0.349862\pi$
$103$	9.22282	0.908751	0.454376	+	0.890810i	$0.349862\pi$
$104$	−4.44504	−0.435872
$105$	0.335126	0.0327049
$106$	0.423272	0.0411118
$107$	7.59179	0.733926	0.366963	−	0.930235i	$-0.380397\pi$
$107$	7.59179	0.733926	0.366963	+	0.930235i	$0.380397\pi$
$108$	−5.18598	−0.499021
$109$	−18.3448	−1.75711	−0.878557	−	0.477637i	$-0.841493\pi$
$109$	−18.3448	−1.75711	−0.878557	+	0.477637i	$0.841493\pi$
$110$	14.1860	1.35258
$111$	13.7017	1.30051
$112$	0.0489173	0.00462225
$113$	−14.1129	−1.32763	−0.663815	−	0.747897i	$-0.731064\pi$
$113$	−14.1129	−1.32763	−0.663815	+	0.747897i	$0.731064\pi$
$114$	11.9608	1.12023
$115$	11.4722	1.06979
$116$	−2.70410	−0.251070
$117$	−21.5623	−1.99343
$118$	0.417895	0.0384703
$119$	−0.124982	−0.0114571
$120$	6.85086	0.625395
$121$	22.6625	2.06023
$122$	−3.53319	−0.319880
$123$	15.4698	1.39486
$124$	6.89977	0.619618
$125$	9.83340	0.879526
$126$	0.237291	0.0211396
$127$	−1.62565	−0.144253	−0.0721264	−	0.997396i	$-0.522978\pi$
$127$	−1.62565	−0.144253	−0.0721264	+	0.997396i	$0.522978\pi$
$128$	1.00000	0.0883883
$129$	22.7657	2.00441
$130$	10.8683	0.953214
$131$	11.8455	1.03494	0.517472	−	0.855700i	$-0.326873\pi$
$131$	11.8455	1.03494	0.517472	+	0.855700i	$0.326873\pi$
$132$	16.2567	1.41496
$133$	−0.208816	−0.0181066
$134$	−5.67025	−0.489835
$135$	12.6799	1.09132
$136$	−2.55496	−0.219086
$137$	18.1400	1.54981	0.774904	−	0.632078i	$-0.217798\pi$
$137$	18.1400	1.54981	0.774904	+	0.632078i	$0.217798\pi$
$138$	13.1468	1.11913
$139$	−9.37867	−0.795488	−0.397744	−	0.917496i	$-0.630207\pi$
$139$	−9.37867	−0.795488	−0.397744	+	0.917496i	$0.630207\pi$
$140$	−0.119605	−0.0101085
$141$	9.15883	0.771313
$142$	−0.0827692	−0.00694584
$143$	25.7899	2.15666
$144$	4.85086	0.404238
$145$	6.61165	0.549067
$146$	2.91723	0.241432
$147$	19.6069	1.61715
$148$	−4.89008	−0.401962
$149$	−20.3763	−1.66929	−0.834645	−	0.550789i	$-0.814327\pi$
$149$	−20.3763	−1.66929	−0.834645	+	0.550789i	$0.814327\pi$
$150$	−2.74094	−0.223797
$151$	−13.6679	−1.11227	−0.556137	−	0.831090i	$-0.687717\pi$
$151$	−13.6679	−1.11227	−0.556137	+	0.831090i	$0.687717\pi$
$152$	−4.26875	−0.346241
$153$	−12.3937	−1.00197
$154$	−0.283815	−0.0228705
$155$	−16.8702	−1.35505
$156$	12.4547	0.997177
$157$	−11.5767	−0.923924	−0.461962	−	0.886900i	$-0.652854\pi$
$157$	−11.5767	−0.923924	−0.461962	+	0.886900i	$0.652854\pi$
$158$	−13.3230	−1.05992
$159$	−1.18598	−0.0940544
$160$	−2.44504	−0.193298
$161$	−0.229521	−0.0180888
$162$	−0.0217703	−0.00171043
$163$	−5.20775	−0.407903	−0.203951	−	0.978981i	$-0.565378\pi$
$163$	−5.20775	−0.407903	−0.203951	+	0.978981i	$0.565378\pi$
$164$	−5.52111	−0.431126
$165$	−39.7482	−3.09440
$166$	5.42758	0.421262
$167$	19.2597	1.49036	0.745178	−	0.666865i	$-0.232364\pi$
$167$	19.2597	1.49036	0.745178	+	0.666865i	$0.232364\pi$
$168$	−0.137063	−0.0105747
$169$	6.75840	0.519877
$170$	6.24698	0.479121
$171$	−20.7071	−1.58351
$172$	−8.12498	−0.619524
$173$	9.52542	0.724204	0.362102	−	0.932138i	$-0.382059\pi$
$173$	9.52542	0.724204	0.362102	+	0.932138i	$0.382059\pi$
$174$	7.57673	0.574390
$175$	0.0478524	0.00361730
$176$	−5.80194	−0.437338
$177$	−1.17092	−0.0880114
$178$	5.65279	0.423695
$179$	9.30559	0.695532	0.347766	−	0.937581i	$-0.386940\pi$
$179$	9.30559	0.695532	0.347766	+	0.937581i	$0.386940\pi$
$180$	−11.8605	−0.884033
$181$	−5.08277	−0.377799	−0.188900	−	0.981996i	$-0.560492\pi$
$181$	−5.08277	−0.377799	−0.188900	+	0.981996i	$0.560492\pi$
$182$	−0.217440	−0.0161177
$183$	9.89977	0.731812
$184$	−4.69202	−0.345900
$185$	11.9565	0.879056
$186$	−19.3327	−1.41754
$187$	14.8237	1.08402
$188$	−3.26875	−0.238398
$189$	−0.253684	−0.0184528
$190$	10.4373	0.757199
$191$	−17.2010	−1.24462	−0.622312	−	0.782769i	$-0.713806\pi$
$191$	−17.2010	−1.24462	−0.622312	+	0.782769i	$0.713806\pi$
$192$	−2.80194	−0.202212
$193$	−19.4263	−1.39833	−0.699166	−	0.714959i	$-0.746445\pi$
$193$	−19.4263	−1.39833	−0.699166	+	0.714959i	$0.746445\pi$
$194$	−5.87263	−0.421630
$195$	−30.4523	−2.18074
$196$	−6.99761	−0.499829
$197$	−1.38835	−0.0989162	−0.0494581	−	0.998776i	$-0.515749\pi$
$197$	−1.38835	−0.0989162	−0.0494581	+	0.998776i	$0.515749\pi$
$198$	−28.1444	−2.00013
$199$	−5.21744	−0.369854	−0.184927	−	0.982752i	$-0.559205\pi$
$199$	−5.21744	−0.369854	−0.184927	+	0.982752i	$0.559205\pi$
$200$	0.978230	0.0691713
$201$	15.8877	1.12063
$202$	−4.02177	−0.282971
$203$	−0.132278	−0.00928406
$204$	7.15883	0.501219
$205$	13.4993	0.942835
$206$	9.22282	0.642584
$207$	−22.7603	−1.58195
$208$	−4.44504	−0.308208
$209$	24.7670	1.71317
$210$	0.335126	0.0231259
$211$	−10.7627	−0.740935	−0.370468	−	0.928845i	$-0.620803\pi$
$211$	−10.7627	−0.740935	−0.370468	+	0.928845i	$0.620803\pi$
$212$	0.423272	0.0290704
$213$	0.231914	0.0158905
$214$	7.59179	0.518964
$215$	19.8659	1.35484
$216$	−5.18598	−0.352861
$217$	0.337519	0.0229122
$218$	−18.3448	−1.24247
$219$	−8.17390	−0.552341
$220$	14.1860	0.956419
$221$	11.3569	0.763947
$222$	13.7017	0.919599
$223$	10.8726	0.728085	0.364042	−	0.931382i	$-0.381396\pi$
$223$	10.8726	0.728085	0.364042	+	0.931382i	$0.381396\pi$
$224$	0.0489173	0.00326843
$225$	4.74525	0.316350
$226$	−14.1129	−0.938776
$227$	−5.57971	−0.370339	−0.185169	−	0.982707i	$-0.559283\pi$
$227$	−5.57971	−0.370339	−0.185169	+	0.982707i	$0.559283\pi$
$228$	11.9608	0.792121
$229$	15.0411	0.993947	0.496974	−	0.867766i	$-0.334445\pi$
$229$	15.0411	0.993947	0.496974	+	0.867766i	$0.334445\pi$
$230$	11.4722	0.756454
$231$	0.795233	0.0523225
$232$	−2.70410	−0.177533
$233$	25.3163	1.65853	0.829264	−	0.558857i	$-0.188760\pi$
$233$	25.3163	1.65853	0.829264	+	0.558857i	$0.188760\pi$
$234$	−21.5623	−1.40957
$235$	7.99223	0.521356
$236$	0.417895	0.0272026
$237$	37.3303	2.42487
$238$	−0.124982	−0.00810136
$239$	25.4282	1.64481	0.822406	−	0.568901i	$-0.192631\pi$
$239$	25.4282	1.64481	0.822406	+	0.568901i	$0.192631\pi$
$240$	6.85086	0.442221
$241$	−14.9051	−0.960125	−0.480063	−	0.877234i	$-0.659386\pi$
$241$	−14.9051	−0.960125	−0.480063	+	0.877234i	$0.659386\pi$
$242$	22.6625	1.45680
$243$	15.6189	1.00196
$244$	−3.53319	−0.226189
$245$	17.1094	1.09308
$246$	15.4698	0.986318
$247$	18.9748	1.20734
$248$	6.89977	0.438136
$249$	−15.2078	−0.963752
$250$	9.83340	0.621919
$251$	−9.23191	−0.582713	−0.291357	−	0.956615i	$-0.594107\pi$
$251$	−9.23191	−0.582713	−0.291357	+	0.956615i	$0.594107\pi$
$252$	0.237291	0.0149479
$253$	27.2228	1.71148
$254$	−1.62565	−0.102002
$255$	−17.5036	−1.09612
$256$	1.00000	0.0625000
$257$	−18.2403	−1.13780	−0.568899	−	0.822408i	$-0.692630\pi$
$257$	−18.2403	−1.13780	−0.568899	+	0.822408i	$0.692630\pi$
$258$	22.7657	1.41733
$259$	−0.239210	−0.0148638
$260$	10.8683	0.674024
$261$	−13.1172	−0.811935
$262$	11.8455	0.731816
$263$	23.8702	1.47190	0.735951	−	0.677035i	$-0.236735\pi$
$263$	23.8702	1.47190	0.735951	+	0.677035i	$0.236735\pi$
$264$	16.2567	1.00053
$265$	−1.03492	−0.0635744
$266$	−0.208816	−0.0128033
$267$	−15.8388	−0.969317
$268$	−5.67025	−0.346366
$269$	−21.5743	−1.31541	−0.657705	−	0.753275i	$-0.728473\pi$
$269$	−21.5743	−1.31541	−0.657705	+	0.753275i	$0.728473\pi$
$270$	12.6799	0.771677
$271$	12.0653	0.732915	0.366458	−	0.930435i	$-0.380570\pi$
$271$	12.0653	0.732915	0.366458	+	0.930435i	$0.380570\pi$
$272$	−2.55496	−0.154917
$273$	0.609252	0.0368736
$274$	18.1400	1.09588
$275$	−5.67563	−0.342253
$276$	13.1468	0.791341
$277$	2.97584	0.178801	0.0894004	−	0.995996i	$-0.471505\pi$
$277$	2.97584	0.178801	0.0894004	+	0.995996i	$0.471505\pi$
$278$	−9.37867	−0.562495
$279$	33.4698	2.00378
$280$	−0.119605	−0.00714776
$281$	12.5211	0.746947	0.373473	−	0.927641i	$-0.378167\pi$
$281$	12.5211	0.746947	0.373473	+	0.927641i	$0.378167\pi$
$282$	9.15883	0.545401
$283$	0.354503	0.0210730	0.0105365	−	0.999944i	$-0.496646\pi$
$283$	0.354503	0.0210730	0.0105365	+	0.999944i	$0.496646\pi$
$284$	−0.0827692	−0.00491145
$285$	−29.2446	−1.73230
$286$	25.7899	1.52499
$287$	−0.270078	−0.0159422
$288$	4.85086	0.285839
$289$	−10.4722	−0.616011
$290$	6.61165	0.388249
$291$	16.4547	0.964593
$292$	2.91723	0.170718
$293$	0.826692	0.0482959	0.0241479	−	0.999708i	$-0.492313\pi$
$293$	0.826692	0.0482959	0.0241479	+	0.999708i	$0.492313\pi$
$294$	19.6069	1.14350
$295$	−1.02177	−0.0594898
$296$	−4.89008	−0.284230
$297$	30.0887	1.74593
$298$	−20.3763	−1.18037
$299$	20.8562	1.20615
$300$	−2.74094	−0.158248
$301$	−0.397452	−0.0229088
$302$	−13.6679	−0.786497
$303$	11.2687	0.647373
$304$	−4.26875	−0.244830
$305$	8.63879	0.494656
$306$	−12.3937	−0.708502
$307$	−4.69740	−0.268095	−0.134047	−	0.990975i	$-0.542797\pi$
$307$	−4.69740	−0.268095	−0.134047	+	0.990975i	$0.542797\pi$
$308$	−0.283815	−0.0161719
$309$	−25.8418	−1.47009
$310$	−16.8702	−0.958165
$311$	4.68532	0.265680	0.132840	−	0.991137i	$-0.457590\pi$
$311$	4.68532	0.265680	0.132840	+	0.991137i	$0.457590\pi$
$312$	12.4547	0.705110
$313$	−16.2131	−0.916420	−0.458210	−	0.888844i	$-0.651509\pi$
$313$	−16.2131	−0.916420	−0.458210	+	0.888844i	$0.651509\pi$
$314$	−11.5767	−0.653313
$315$	−0.580186	−0.0326898
$316$	−13.3230	−0.749480
$317$	19.5230	1.09652	0.548261	−	0.836307i	$-0.315290\pi$
$317$	19.5230	1.09652	0.548261	+	0.836307i	$0.315290\pi$
$318$	−1.18598	−0.0665065
$319$	15.6890	0.878417
$320$	−2.44504	−0.136682
$321$	−21.2717	−1.18727
$322$	−0.229521	−0.0127907
$323$	10.9065	0.606853
$324$	−0.0217703	−0.00120946
$325$	−4.34827	−0.241199
$326$	−5.20775	−0.288431
$327$	51.4010	2.84248
$328$	−5.52111	−0.304852
$329$	−0.159899	−0.00881549
$330$	−39.7482	−2.18807
$331$	23.8702	1.31203	0.656013	−	0.754749i	$-0.272242\pi$
$331$	23.8702	1.31203	0.656013	+	0.754749i	$0.272242\pi$
$332$	5.42758	0.297877
$333$	−23.7211	−1.29991
$334$	19.2597	1.05384
$335$	13.8640	0.757471
$336$	−0.137063	−0.00747742
$337$	7.38165	0.402104	0.201052	−	0.979581i	$-0.435564\pi$
$337$	7.38165	0.402104	0.201052	+	0.979581i	$0.435564\pi$
$338$	6.75840	0.367608
$339$	39.5435	2.14771
$340$	6.24698	0.338790
$341$	−40.0320	−2.16786
$342$	−20.7071	−1.11971
$343$	−0.684726	−0.0369717
$344$	−8.12498	−0.438070
$345$	−32.1444	−1.73059
$346$	9.52542	0.512090
$347$	23.0881	1.23944	0.619718	−	0.784824i	$-0.287247\pi$
$347$	23.0881	1.23944	0.619718	+	0.784824i	$0.287247\pi$
$348$	7.57673	0.406155
$349$	22.2935	1.19334	0.596672	−	0.802485i	$-0.296489\pi$
$349$	22.2935	1.19334	0.596672	+	0.802485i	$0.296489\pi$
$350$	0.0478524	0.00255782
$351$	23.0519	1.23042
$352$	−5.80194	−0.309244
$353$	5.67994	0.302313	0.151156	−	0.988510i	$-0.451700\pi$
$353$	5.67994	0.302313	0.151156	+	0.988510i	$0.451700\pi$
$354$	−1.17092	−0.0622334
$355$	0.202374	0.0107409
$356$	5.65279	0.299597
$357$	0.350191	0.0185341
$358$	9.30559	0.491815
$359$	6.76702	0.357150	0.178575	−	0.983926i	$-0.442851\pi$
$359$	6.76702	0.357150	0.178575	+	0.983926i	$0.442851\pi$
$360$	−11.8605	−0.625106
$361$	−0.777775	−0.0409355
$362$	−5.08277	−0.267144
$363$	−63.4989	−3.33283
$364$	−0.217440	−0.0113969
$365$	−7.13275	−0.373345
$366$	9.89977	0.517469
$367$	21.3763	1.11583	0.557916	−	0.829897i	$-0.311601\pi$
$367$	21.3763	1.11583	0.557916	+	0.829897i	$0.311601\pi$
$368$	−4.69202	−0.244589
$369$	−26.7821	−1.39422
$370$	11.9565	0.621587
$371$	0.0207053	0.00107497
$372$	−19.3327	−1.00236
$373$	−18.7724	−0.971998	−0.485999	−	0.873959i	$-0.661544\pi$
$373$	−18.7724	−0.971998	−0.485999	+	0.873959i	$0.661544\pi$
$374$	14.8237	0.766516
$375$	−27.5526	−1.42281
$376$	−3.26875	−0.168573
$377$	12.0199	0.619054
$378$	−0.253684	−0.0130481
$379$	21.3153	1.09489	0.547446	−	0.836841i	$-0.315600\pi$
$379$	21.3153	1.09489	0.547446	+	0.836841i	$0.315600\pi$
$380$	10.4373	0.535421
$381$	4.55496	0.233358
$382$	−17.2010	−0.880082
$383$	−33.6752	−1.72072	−0.860360	−	0.509687i	$-0.829761\pi$
$383$	−33.6752	−1.72072	−0.860360	+	0.509687i	$0.829761\pi$
$384$	−2.80194	−0.142986
$385$	0.693940	0.0353665
$386$	−19.4263	−0.988770
$387$	−39.4131	−2.00348
$388$	−5.87263	−0.298137
$389$	23.2814	1.18041	0.590207	−	0.807252i	$-0.299046\pi$
$389$	23.2814	1.18041	0.590207	+	0.807252i	$0.299046\pi$
$390$	−30.4523	−1.54201
$391$	11.9879	0.606255
$392$	−6.99761	−0.353433
$393$	−33.1903	−1.67423
$394$	−1.38835	−0.0699443
$395$	32.5754	1.63905
$396$	−28.1444	−1.41431
$397$	1.44398	0.0724711	0.0362356	−	0.999343i	$-0.488463\pi$
$397$	1.44398	0.0724711	0.0362356	+	0.999343i	$0.488463\pi$
$398$	−5.21744	−0.261527
$399$	0.585089	0.0292911
$400$	0.978230	0.0489115
$401$	−26.9202	−1.34433	−0.672166	−	0.740401i	$-0.734636\pi$
$401$	−26.9202	−1.34433	−0.672166	+	0.740401i	$0.734636\pi$
$402$	15.8877	0.792406
$403$	−30.6698	−1.52777
$404$	−4.02177	−0.200091
$405$	0.0532292	0.00264498
$406$	−0.132278	−0.00656482
$407$	28.3720	1.40635
$408$	7.15883	0.354415
$409$	14.4179	0.712919	0.356460	−	0.934311i	$-0.383984\pi$
$409$	14.4179	0.712919	0.356460	+	0.934311i	$0.383984\pi$
$410$	13.4993	0.666685
$411$	−50.8273	−2.50712
$412$	9.22282	0.454376
$413$	0.0204423	0.00100590
$414$	−22.7603	−1.11861
$415$	−13.2707	−0.651432
$416$	−4.44504	−0.217936
$417$	26.2784	1.28686
$418$	24.7670	1.21139
$419$	−2.05993	−0.100634	−0.0503172	−	0.998733i	$-0.516023\pi$
$419$	−2.05993	−0.100634	−0.0503172	+	0.998733i	$0.516023\pi$
$420$	0.335126	0.0163525
$421$	12.8635	0.626930	0.313465	−	0.949600i	$-0.398510\pi$
$421$	12.8635	0.626930	0.313465	+	0.949600i	$0.398510\pi$
$422$	−10.7627	−0.523920
$423$	−15.8562	−0.770956
$424$	0.423272	0.0205559
$425$	−2.49934	−0.121236
$426$	0.231914	0.0112363
$427$	−0.172834	−0.00836403
$428$	7.59179	0.366963
$429$	−72.2616	−3.48882
$430$	19.8659	0.958020
$431$	−11.4668	−0.552337	−0.276168	−	0.961109i	$-0.589065\pi$
$431$	−11.4668	−0.552337	−0.276168	+	0.961109i	$0.589065\pi$
$432$	−5.18598	−0.249511
$433$	23.4698	1.12789	0.563943	−	0.825814i	$-0.309284\pi$
$433$	23.4698	1.12789	0.563943	+	0.825814i	$0.309284\pi$
$434$	0.337519	0.0162014
$435$	−18.5254	−0.888226
$436$	−18.3448	−0.878557
$437$	20.0291	0.958120
$438$	−8.17390	−0.390564
$439$	−32.5133	−1.55178	−0.775888	−	0.630870i	$-0.782698\pi$
$439$	−32.5133	−1.55178	−0.775888	+	0.630870i	$0.782698\pi$
$440$	14.1860	0.676290
$441$	−33.9444	−1.61640
$442$	11.3569	0.540192
$443$	−19.4843	−0.925726	−0.462863	−	0.886430i	$-0.653178\pi$
$443$	−19.4843	−0.925726	−0.462863	+	0.886430i	$0.653178\pi$
$444$	13.7017	0.650254
$445$	−13.8213	−0.655193
$446$	10.8726	0.514834
$447$	57.0930	2.70041
$448$	0.0489173	0.00231113
$449$	−25.5821	−1.20729	−0.603647	−	0.797252i	$-0.706286\pi$
$449$	−25.5821	−1.20729	−0.603647	+	0.797252i	$0.706286\pi$
$450$	4.74525	0.223693
$451$	32.0331	1.50838
$452$	−14.1129	−0.663815
$453$	38.2965	1.79933
$454$	−5.57971	−0.261869
$455$	0.531649	0.0249241
$456$	11.9608	0.560114
$457$	11.6431	0.544641	0.272321	−	0.962207i	$-0.412209\pi$
$457$	11.6431	0.544641	0.272321	+	0.962207i	$0.412209\pi$
$458$	15.0411	0.702827
$459$	13.2500	0.618455
$460$	11.4722	0.534894
$461$	1.26444	0.0588907	0.0294454	−	0.999566i	$-0.490626\pi$
$461$	1.26444	0.0588907	0.0294454	+	0.999566i	$0.490626\pi$
$462$	0.795233	0.0369976
$463$	−22.4892	−1.04516	−0.522580	−	0.852590i	$-0.675031\pi$
$463$	−22.4892	−1.04516	−0.522580	+	0.852590i	$0.675031\pi$
$464$	−2.70410	−0.125535
$465$	47.2693	2.19206
$466$	25.3163	1.17276
$467$	−3.29159	−0.152316	−0.0761582	−	0.997096i	$-0.524265\pi$
$467$	−3.29159	−0.152316	−0.0761582	+	0.997096i	$0.524265\pi$
$468$	−21.5623	−0.996716
$469$	−0.277374	−0.0128079
$470$	7.99223	0.368654
$471$	32.4373	1.49463
$472$	0.417895	0.0192352
$473$	47.1406	2.16753
$474$	37.3303	1.71464
$475$	−4.17582	−0.191600
$476$	−0.124982	−0.00572853
$477$	2.05323	0.0940109
$478$	25.4282	1.16306
$479$	25.0901	1.14639	0.573197	−	0.819417i	$-0.305703\pi$
$479$	25.0901	1.14639	0.573197	+	0.819417i	$0.305703\pi$
$480$	6.85086	0.312697
$481$	21.7366	0.991105
$482$	−14.9051	−0.678911
$483$	0.643104	0.0292623
$484$	22.6625	1.03011
$485$	14.3588	0.652000
$486$	15.6189	0.708490
$487$	−8.57912	−0.388757	−0.194379	−	0.980927i	$-0.562269\pi$
$487$	−8.57912	−0.388757	−0.194379	+	0.980927i	$0.562269\pi$
$488$	−3.53319	−0.159940
$489$	14.5918	0.659864
$490$	17.1094	0.772926
$491$	−33.6238	−1.51742	−0.758711	−	0.651427i	$-0.774171\pi$
$491$	−33.6238	−1.51742	−0.758711	+	0.651427i	$0.774171\pi$
$492$	15.4698	0.697432
$493$	6.90887	0.311160
$494$	18.9748	0.853715
$495$	68.8141	3.09297
$496$	6.89977	0.309809
$497$	−0.00404885	−0.000181616 0
$498$	−15.2078	−0.681476
$499$	0.515729	0.0230872	0.0115436	−	0.999933i	$-0.496325\pi$
$499$	0.515729	0.0230872	0.0115436	+	0.999933i	$0.496325\pi$
$500$	9.83340	0.439763
$501$	−53.9643	−2.41095
$502$	−9.23191	−0.412040
$503$	−29.4946	−1.31510	−0.657548	−	0.753412i	$-0.728407\pi$
$503$	−29.4946	−1.31510	−0.657548	+	0.753412i	$0.728407\pi$
$504$	0.237291	0.0105698
$505$	9.83340	0.437580
$506$	27.2228	1.21020
$507$	−18.9366	−0.841004
$508$	−1.62565	−0.0721264
$509$	10.3026	0.456655	0.228327	−	0.973584i	$-0.426674\pi$
$509$	10.3026	0.456655	0.228327	+	0.973584i	$0.426674\pi$
$510$	−17.5036	−0.775075
$511$	0.142703	0.00631282
$512$	1.00000	0.0441942
$513$	22.1377	0.977401
$514$	−18.2403	−0.804544
$515$	−22.5502	−0.993679
$516$	22.7657	1.00220
$517$	18.9651	0.834083
$518$	−0.239210	−0.0105103
$519$	−26.6896	−1.17154
$520$	10.8683	0.476607
$521$	4.51679	0.197884	0.0989422	−	0.995093i	$-0.468454\pi$
$521$	4.51679	0.197884	0.0989422	+	0.995093i	$0.468454\pi$
$522$	−13.1172	−0.574125
$523$	6.91962	0.302574	0.151287	−	0.988490i	$-0.451658\pi$
$523$	6.91962	0.302574	0.151287	+	0.988490i	$0.451658\pi$
$524$	11.8455	0.517472
$525$	−0.134079	−0.00585171
$526$	23.8702	1.04079
$527$	−17.6286	−0.767915
$528$	16.2567	0.707481
$529$	−0.984935	−0.0428232
$530$	−1.03492	−0.0449539
$531$	2.02715	0.0879707
$532$	−0.208816	−0.00905332
$533$	24.5415	1.06301
$534$	−15.8388	−0.685411
$535$	−18.5623	−0.802516
$536$	−5.67025	−0.244918
$537$	−26.0737	−1.12516
$538$	−21.5743	−0.930136
$539$	40.5997	1.74875
$540$	12.6799	0.545658
$541$	−37.4862	−1.61166	−0.805829	−	0.592149i	$-0.798280\pi$
$541$	−37.4862	−1.61166	−0.805829	+	0.592149i	$0.798280\pi$
$542$	12.0653	0.518249
$543$	14.2416	0.611166
$544$	−2.55496	−0.109543
$545$	44.8538	1.92133
$546$	0.609252	0.0260736
$547$	10.3327	0.441796	0.220898	−	0.975297i	$-0.429101\pi$
$547$	10.3327	0.441796	0.220898	+	0.975297i	$0.429101\pi$
$548$	18.1400	0.774904
$549$	−17.1390	−0.731474
$550$	−5.67563	−0.242010
$551$	11.5431	0.491754
$552$	13.1468	0.559563
$553$	−0.651728	−0.0277143
$554$	2.97584	0.126431
$555$	−33.5013	−1.42205
$556$	−9.37867	−0.397744
$557$	−45.0907	−1.91055	−0.955276	−	0.295715i	$-0.904442\pi$
$557$	−45.0907	−1.91055	−0.955276	+	0.295715i	$0.904442\pi$
$558$	33.4698	1.41689
$559$	36.1159	1.52754
$560$	−0.119605	−0.00505423
$561$	−41.5351	−1.75361
$562$	12.5211	0.528171
$563$	20.9202	0.881682	0.440841	−	0.897585i	$-0.354680\pi$
$563$	20.9202	0.881682	0.440841	+	0.897585i	$0.354680\pi$
$564$	9.15883	0.385656
$565$	34.5066	1.45170
$566$	0.354503	0.0149009
$567$	−0.00106494	−4.47234e−5 0
$568$	−0.0827692	−0.00347292
$569$	−30.3220	−1.27116	−0.635582	−	0.772034i	$-0.719240\pi$
$569$	−30.3220	−1.27116	−0.635582	+	0.772034i	$0.719240\pi$
$570$	−29.2446	−1.22492
$571$	−38.7832	−1.62302	−0.811512	−	0.584335i	$-0.801355\pi$
$571$	−38.7832	−1.62302	−0.811512	+	0.584335i	$0.801355\pi$
$572$	25.7899	1.07833
$573$	48.1963	2.01343
$574$	−0.270078	−0.0112728
$575$	−4.58987	−0.191411
$576$	4.85086	0.202119
$577$	−35.2804	−1.46874	−0.734370	−	0.678749i	$-0.762522\pi$
$577$	−35.2804	−1.46874	−0.734370	+	0.678749i	$0.762522\pi$
$578$	−10.4722	−0.435586
$579$	54.4312	2.26208
$580$	6.61165	0.274534
$581$	0.265503	0.0110149
$582$	16.4547	0.682071
$583$	−2.45580	−0.101709
$584$	2.91723	0.120716
$585$	52.7206	2.17973
$586$	0.826692	0.0341503
$587$	22.0315	0.909336	0.454668	−	0.890661i	$-0.349758\pi$
$587$	22.0315	0.909336	0.454668	+	0.890661i	$0.349758\pi$
$588$	19.6069	0.808573
$589$	−29.4534	−1.21361
$590$	−1.02177	−0.0420656
$591$	3.89008	0.160017
$592$	−4.89008	−0.200981
$593$	30.2513	1.24227	0.621136	−	0.783703i	$-0.286672\pi$
$593$	30.2513	1.24227	0.621136	+	0.783703i	$0.286672\pi$
$594$	30.0887	1.23456
$595$	0.305586	0.0125278
$596$	−20.3763	−0.834645
$597$	14.6189	0.598313
$598$	20.8562	0.852875
$599$	11.7888	0.481677	0.240838	−	0.970565i	$-0.422578\pi$
$599$	11.7888	0.481677	0.240838	+	0.970565i	$0.422578\pi$
$600$	−2.74094	−0.111898
$601$	2.09916	0.0856266	0.0428133	−	0.999083i	$-0.486368\pi$
$601$	2.09916	0.0856266	0.0428133	+	0.999083i	$0.486368\pi$
$602$	−0.397452	−0.0161990
$603$	−27.5056	−1.12011
$604$	−13.6679	−0.556137
$605$	−55.4107	−2.25277
$606$	11.2687	0.457762
$607$	11.0911	0.450175	0.225088	−	0.974339i	$-0.427733\pi$
$607$	11.0911	0.450175	0.225088	+	0.974339i	$0.427733\pi$
$608$	−4.26875	−0.173121
$609$	0.370633	0.0150188
$610$	8.63879	0.349774
$611$	14.5297	0.587810
$612$	−12.3937	−0.500987
$613$	−15.8750	−0.641186	−0.320593	−	0.947217i	$-0.603882\pi$
$613$	−15.8750	−0.641186	−0.320593	+	0.947217i	$0.603882\pi$
$614$	−4.69740	−0.189572
$615$	−37.8243	−1.52522
$616$	−0.283815	−0.0114352
$617$	−32.2989	−1.30030	−0.650152	−	0.759804i	$-0.725295\pi$
$617$	−32.2989	−1.30030	−0.650152	+	0.759804i	$0.725295\pi$
$618$	−25.8418	−1.03951
$619$	−17.3720	−0.698238	−0.349119	−	0.937078i	$-0.613519\pi$
$619$	−17.3720	−0.698238	−0.349119	+	0.937078i	$0.613519\pi$
$620$	−16.8702	−0.677525
$621$	24.3327	0.976439
$622$	4.68532	0.187864
$623$	0.276520	0.0110785
$624$	12.4547	0.498588
$625$	−28.9342	−1.15737
$626$	−16.2131	−0.648007
$627$	−69.3957	−2.77140
$628$	−11.5767	−0.461962
$629$	12.4940	0.498167
$630$	−0.580186	−0.0231152
$631$	1.47411	0.0586833	0.0293417	−	0.999569i	$-0.490659\pi$
$631$	1.47411	0.0586833	0.0293417	+	0.999569i	$0.490659\pi$
$632$	−13.3230	−0.529962
$633$	30.1564	1.19861
$634$	19.5230	0.775358
$635$	3.97477	0.157734
$636$	−1.18598	−0.0470272
$637$	31.1047	1.23241
$638$	15.6890	0.621135
$639$	−0.401501	−0.0158831
$640$	−2.44504	−0.0966488
$641$	−35.8834	−1.41731	−0.708654	−	0.705556i	$-0.750697\pi$
$641$	−35.8834	−1.41731	−0.708654	+	0.705556i	$0.750697\pi$
$642$	−21.2717	−0.839528
$643$	−39.1396	−1.54351	−0.771757	−	0.635917i	$-0.780622\pi$
$643$	−39.1396	−1.54351	−0.771757	+	0.635917i	$0.780622\pi$
$644$	−0.229521	−0.00904440
$645$	−55.6631	−2.19173
$646$	10.9065	0.429110
$647$	13.7245	0.539568	0.269784	−	0.962921i	$-0.413048\pi$
$647$	13.7245	0.539568	0.269784	+	0.962921i	$0.413048\pi$
$648$	−0.0217703	−0.000855217 0
$649$	−2.42460	−0.0951739
$650$	−4.34827	−0.170553
$651$	−0.945706	−0.0370651
$652$	−5.20775	−0.203951
$653$	−30.2838	−1.18510	−0.592549	−	0.805535i	$-0.701878\pi$
$653$	−30.2838	−1.18510	−0.592549	+	0.805535i	$0.701878\pi$
$654$	51.4010	2.00994
$655$	−28.9627	−1.13167
$656$	−5.52111	−0.215563
$657$	14.1511	0.552086
$658$	−0.159899	−0.00623349
$659$	−21.9138	−0.853639	−0.426820	−	0.904337i	$-0.640366\pi$
$659$	−21.9138	−0.853639	−0.426820	+	0.904337i	$0.640366\pi$
$660$	−39.7482	−1.54720
$661$	−41.1704	−1.60134	−0.800672	−	0.599103i	$-0.795524\pi$
$661$	−41.1704	−1.60134	−0.800672	+	0.599103i	$0.795524\pi$
$662$	23.8702	0.927743
$663$	−31.8213	−1.23584
$664$	5.42758	0.210631
$665$	0.510564	0.0197988
$666$	−23.7211	−0.919173
$667$	12.6877	0.491270
$668$	19.2597	0.745178
$669$	−30.4644	−1.17782
$670$	13.8640	0.535613
$671$	20.4993	0.791368
$672$	−0.137063	−0.00528733
$673$	−24.8474	−0.957797	−0.478898	−	0.877870i	$-0.658964\pi$
$673$	−24.8474	−0.957797	−0.478898	+	0.877870i	$0.658964\pi$
$674$	7.38165	0.284331
$675$	−5.07308	−0.195263
$676$	6.75840	0.259938
$677$	−4.50125	−0.172997	−0.0864986	−	0.996252i	$-0.527568\pi$
$677$	−4.50125	−0.172997	−0.0864986	+	0.996252i	$0.527568\pi$
$678$	39.5435	1.51866
$679$	−0.287273	−0.0110245
$680$	6.24698	0.239561
$681$	15.6340	0.599096
$682$	−40.0320	−1.53291
$683$	−49.2954	−1.88624	−0.943118	−	0.332457i	$-0.892122\pi$
$683$	−49.2954	−1.88624	−0.943118	+	0.332457i	$0.892122\pi$
$684$	−20.7071	−0.791755
$685$	−44.3532	−1.69465
$686$	−0.684726	−0.0261429
$687$	−42.1444	−1.60791
$688$	−8.12498	−0.309762
$689$	−1.88146	−0.0716779
$690$	−32.1444	−1.22371
$691$	−26.1594	−0.995151	−0.497576	−	0.867421i	$-0.665776\pi$
$691$	−26.1594	−0.995151	−0.497576	+	0.867421i	$0.665776\pi$
$692$	9.52542	0.362102
$693$	−1.37675	−0.0522983
$694$	23.0881	0.876414
$695$	22.9312	0.869831
$696$	7.57673	0.287195
$697$	14.1062	0.534310
$698$	22.2935	0.843822
$699$	−70.9348	−2.68300
$700$	0.0478524	0.00180865
$701$	−6.06398	−0.229033	−0.114517	−	0.993421i	$-0.536532\pi$
$701$	−6.06398	−0.229033	−0.114517	+	0.993421i	$0.536532\pi$
$702$	23.0519	0.870038
$703$	20.8745	0.787298
$704$	−5.80194	−0.218669
$705$	−22.3937	−0.843397
$706$	5.67994	0.213767
$707$	−0.196734	−0.00739895
$708$	−1.17092	−0.0440057
$709$	3.49396	0.131218	0.0656092	−	0.997845i	$-0.479101\pi$
$709$	3.49396	0.131218	0.0656092	+	0.997845i	$0.479101\pi$
$710$	0.202374	0.00759497
$711$	−64.6282	−2.42375
$712$	5.65279	0.211847
$713$	−32.3739	−1.21241
$714$	0.350191	0.0131056
$715$	−63.0573	−2.35821
$716$	9.30559	0.347766
$717$	−71.2482	−2.66081
$718$	6.76702	0.252543
$719$	35.4687	1.32276	0.661380	−	0.750051i	$-0.269971\pi$
$719$	35.4687	1.32276	0.661380	+	0.750051i	$0.269971\pi$
$720$	−11.8605	−0.442016
$721$	0.451156	0.0168019
$722$	−0.777775	−0.0289458
$723$	41.7633	1.55319
$724$	−5.08277	−0.188900
$725$	−2.64523	−0.0982415
$726$	−63.4989	−2.35666
$727$	−23.4825	−0.870917	−0.435458	−	0.900209i	$-0.643414\pi$
$727$	−23.4825	−0.870917	−0.435458	+	0.900209i	$0.643414\pi$
$728$	−0.217440	−0.00805885
$729$	−43.6980	−1.61844
$730$	−7.13275	−0.263995
$731$	20.7590	0.767799
$732$	9.89977	0.365906
$733$	−41.9245	−1.54852	−0.774259	−	0.632869i	$-0.781877\pi$
$733$	−41.9245	−1.54852	−0.774259	+	0.632869i	$0.781877\pi$
$734$	21.3763	0.789013
$735$	−47.9396	−1.76828
$736$	−4.69202	−0.172950
$737$	32.8984	1.21183
$738$	−26.7821	−0.985862
$739$	−17.5961	−0.647283	−0.323642	−	0.946180i	$-0.604907\pi$
$739$	−17.5961	−0.647283	−0.323642	+	0.946180i	$0.604907\pi$
$740$	11.9565	0.439528
$741$	−53.1661	−1.95311
$742$	0.0207053	0.000760116 0
$743$	−1.31575	−0.0482701	−0.0241351	−	0.999709i	$-0.507683\pi$
$743$	−1.31575	−0.0482701	−0.0241351	+	0.999709i	$0.507683\pi$
$744$	−19.3327	−0.708772
$745$	49.8208	1.82529
$746$	−18.7724	−0.687306
$747$	26.3284	0.963307
$748$	14.8237	0.542008
$749$	0.371370	0.0135696
$750$	−27.5526	−1.00608
$751$	46.9439	1.71301	0.856504	−	0.516141i	$-0.172632\pi$
$751$	46.9439	1.71301	0.856504	+	0.516141i	$0.172632\pi$
$752$	−3.26875	−0.119199
$753$	25.8672	0.942655
$754$	12.0199	0.437737
$755$	33.4185	1.21622
$756$	−0.253684	−0.00922641
$757$	40.7918	1.48260	0.741301	−	0.671173i	$-0.234209\pi$
$757$	40.7918	1.48260	0.741301	+	0.671173i	$0.234209\pi$
$758$	21.3153	0.774206
$759$	−76.2766	−2.76867
$760$	10.4373	0.378600
$761$	−19.9433	−0.722945	−0.361472	−	0.932383i	$-0.617726\pi$
$761$	−19.9433	−0.722945	−0.361472	+	0.932383i	$0.617726\pi$
$762$	4.55496	0.165009
$763$	−0.897380	−0.0324873
$764$	−17.2010	−0.622312
$765$	30.3032	1.09561
$766$	−33.6752	−1.21673
$767$	−1.85756	−0.0670726
$768$	−2.80194	−0.101106
$769$	7.35988	0.265404	0.132702	−	0.991156i	$-0.457635\pi$
$769$	7.35988	0.265404	0.132702	+	0.991156i	$0.457635\pi$
$770$	0.693940	0.0250079
$771$	51.1081	1.84061
$772$	−19.4263	−0.699166
$773$	−2.88040	−0.103601	−0.0518003	−	0.998657i	$-0.516496\pi$
$773$	−2.88040	−0.103601	−0.0518003	+	0.998657i	$0.516496\pi$
$774$	−39.4131	−1.41667
$775$	6.74956	0.242451
$776$	−5.87263	−0.210815
$777$	0.670251	0.0240451
$778$	23.2814	0.834679
$779$	23.5682	0.844419
$780$	−30.4523	−1.09037
$781$	0.480222	0.0171837
$782$	11.9879	0.428687
$783$	14.0234	0.501156
$784$	−6.99761	−0.249915
$785$	28.3056	1.01027
$786$	−33.1903	−1.18386
$787$	18.0234	0.642466	0.321233	−	0.947000i	$-0.395903\pi$
$787$	18.0234	0.642466	0.321233	+	0.947000i	$0.395903\pi$
$788$	−1.38835	−0.0494581
$789$	−66.8829	−2.38109
$790$	32.5754	1.15898
$791$	−0.690366	−0.0245466
$792$	−28.1444	−1.00007
$793$	15.7052	0.557707
$794$	1.44398	0.0512448
$795$	2.89977	0.102844
$796$	−5.21744	−0.184927
$797$	−11.5851	−0.410365	−0.205182	−	0.978724i	$-0.565779\pi$
$797$	−11.5851	−0.410365	−0.205182	+	0.978724i	$0.565779\pi$
$798$	0.585089	0.0207119
$799$	8.35152	0.295456
$800$	0.978230	0.0345856
$801$	27.4209	0.968869
$802$	−26.9202	−0.950586
$803$	−16.9256	−0.597291
$804$	15.8877	0.560316
$805$	0.561189	0.0197793
$806$	−30.6698	−1.08030
$807$	60.4499	2.12794
$808$	−4.02177	−0.141485
$809$	−6.08085	−0.213791	−0.106896	−	0.994270i	$-0.534091\pi$
$809$	−6.08085	−0.213791	−0.106896	+	0.994270i	$0.534091\pi$
$810$	0.0532292	0.00187028
$811$	−0.771807	−0.0271018	−0.0135509	−	0.999908i	$-0.504314\pi$
$811$	−0.771807	−0.0271018	−0.0135509	+	0.999908i	$0.504314\pi$
$812$	−0.132278	−0.00464203
$813$	−33.8062	−1.18564
$814$	28.3720	0.994437
$815$	12.7332	0.446023
$816$	7.15883	0.250609
$817$	34.6835	1.21342
$818$	14.4179	0.504110
$819$	−1.05477	−0.0368566
$820$	13.4993	0.471417
$821$	−31.1511	−1.08718	−0.543590	−	0.839351i	$-0.682935\pi$
$821$	−31.1511	−1.08718	−0.543590	+	0.839351i	$0.682935\pi$
$822$	−50.8273	−1.77281
$823$	−34.0863	−1.18818	−0.594088	−	0.804400i	$-0.702487\pi$
$823$	−34.0863	−1.18818	−0.594088	+	0.804400i	$0.702487\pi$
$824$	9.22282	0.321292
$825$	15.9028	0.553663
$826$	0.0204423	0.000711279 0
$827$	−40.8769	−1.42143	−0.710715	−	0.703480i	$-0.751629\pi$
$827$	−40.8769	−1.42143	−0.710715	+	0.703480i	$0.751629\pi$
$828$	−22.7603	−0.790976
$829$	−0.836855	−0.0290652	−0.0145326	−	0.999894i	$-0.504626\pi$
$829$	−0.836855	−0.0290652	−0.0145326	+	0.999894i	$0.504626\pi$
$830$	−13.2707	−0.460632
$831$	−8.33811	−0.289246
$832$	−4.44504	−0.154104
$833$	17.8786	0.619457
$834$	26.2784	0.909948
$835$	−47.0907	−1.62964
$836$	24.7670	0.856585
$837$	−35.7821	−1.23681
$838$	−2.05993	−0.0711592
$839$	−10.0175	−0.345841	−0.172921	−	0.984936i	$-0.555320\pi$
$839$	−10.0175	−0.345841	−0.172921	+	0.984936i	$0.555320\pi$
$840$	0.335126	0.0115629
$841$	−21.6878	−0.747856
$842$	12.8635	0.443306
$843$	−35.0834	−1.20834
$844$	−10.7627	−0.370468
$845$	−16.5246	−0.568462
$846$	−15.8562	−0.545148
$847$	1.10859	0.0380915
$848$	0.423272	0.0145352
$849$	−0.993295	−0.0340898
$850$	−2.49934	−0.0857265
$851$	22.9444	0.786523
$852$	0.231914	0.00794525
$853$	−30.1008	−1.03063	−0.515316	−	0.857000i	$-0.672326\pi$
$853$	−30.1008	−1.03063	−0.515316	+	0.857000i	$0.672326\pi$
$854$	−0.172834	−0.00591426
$855$	50.6297	1.73150
$856$	7.59179	0.259482
$857$	−42.1299	−1.43913	−0.719565	−	0.694425i	$-0.755659\pi$
$857$	−42.1299	−1.43913	−0.719565	+	0.694425i	$0.755659\pi$
$858$	−72.2616	−2.46697
$859$	16.6213	0.567113	0.283556	−	0.958956i	$-0.408486\pi$
$859$	16.6213	0.567113	0.283556	+	0.958956i	$0.408486\pi$
$860$	19.8659	0.677422
$861$	0.756741	0.0257897
$862$	−11.4668	−0.390561
$863$	33.3623	1.13566	0.567832	−	0.823144i	$-0.307782\pi$
$863$	33.3623	1.13566	0.567832	+	0.823144i	$0.307782\pi$
$864$	−5.18598	−0.176431
$865$	−23.2900	−0.791885
$866$	23.4698	0.797536
$867$	29.3424	0.996521
$868$	0.337519	0.0114561
$869$	77.2995	2.62220
$870$	−18.5254	−0.628070
$871$	25.2045	0.854022
$872$	−18.3448	−0.621234
$873$	−28.4873	−0.964147
$874$	20.0291	0.677493
$875$	0.481024	0.0162616
$876$	−8.17390	−0.276170
$877$	20.4015	0.688910	0.344455	−	0.938803i	$-0.388064\pi$
$877$	20.4015	0.688910	0.344455	+	0.938803i	$0.388064\pi$
$878$	−32.5133	−1.09727
$879$	−2.31634	−0.0781282
$880$	14.1860	0.478209
$881$	−23.1728	−0.780713	−0.390356	−	0.920664i	$-0.627648\pi$
$881$	−23.1728	−0.780713	−0.390356	+	0.920664i	$0.627648\pi$
$882$	−33.9444	−1.14297
$883$	2.47411	0.0832604	0.0416302	−	0.999133i	$-0.486745\pi$
$883$	2.47411	0.0832604	0.0416302	+	0.999133i	$0.486745\pi$
$884$	11.3569	0.381974
$885$	2.86294	0.0962366
$886$	−19.4843	−0.654587
$887$	−4.60952	−0.154772	−0.0773862	−	0.997001i	$-0.524657\pi$
$887$	−4.60952	−0.154772	−0.0773862	+	0.997001i	$0.524657\pi$
$888$	13.7017	0.459799
$889$	−0.0795223	−0.00266709
$890$	−13.8213	−0.463292
$891$	0.126310	0.00423153
$892$	10.8726	0.364042
$893$	13.9535	0.466935
$894$	57.0930	1.90948
$895$	−22.7525	−0.760534
$896$	0.0489173	0.00163421
$897$	−58.4379	−1.95118
$898$	−25.5821	−0.853686
$899$	−18.6577	−0.622269
$900$	4.74525	0.158175
$901$	−1.08144	−0.0360280
$902$	32.0331	1.06659
$903$	1.11364	0.0370595
$904$	−14.1129	−0.469388
$905$	12.4276	0.413107
$906$	38.2965	1.27232
$907$	−52.8799	−1.75585	−0.877924	−	0.478799i	$-0.841072\pi$
$907$	−52.8799	−1.75585	−0.877924	+	0.478799i	$0.841072\pi$
$908$	−5.57971	−0.185169
$909$	−19.5090	−0.647074
$910$	0.531649	0.0176240
$911$	21.5730	0.714746	0.357373	−	0.933962i	$-0.383673\pi$
$911$	21.5730	0.714746	0.357373	+	0.933962i	$0.383673\pi$
$912$	11.9608	0.396061
$913$	−31.4905	−1.04218
$914$	11.6431	0.385120
$915$	−24.2054	−0.800204
$916$	15.0411	0.496974
$917$	0.579449	0.0191351
$918$	13.2500	0.437314
$919$	−42.2030	−1.39215	−0.696074	−	0.717970i	$-0.745071\pi$
$919$	−42.2030	−1.39215	−0.696074	+	0.717970i	$0.745071\pi$
$920$	11.4722	0.378227
$921$	13.1618	0.433697
$922$	1.26444	0.0416420
$923$	0.367913	0.0121100
$924$	0.795233	0.0261612
$925$	−4.78363	−0.157285
$926$	−22.4892	−0.739040
$927$	44.7385	1.46941
$928$	−2.70410	−0.0887665
$929$	27.0519	0.887544	0.443772	−	0.896140i	$-0.353640\pi$
$929$	27.0519	0.887544	0.443772	+	0.896140i	$0.353640\pi$
$930$	47.2693	1.55002
$931$	29.8710	0.978984
$932$	25.3163	0.829264
$933$	−13.1280	−0.429790
$934$	−3.29159	−0.107704
$935$	−36.2446	−1.18532
$936$	−21.5623	−0.704784
$937$	−32.4058	−1.05865	−0.529326	−	0.848419i	$-0.677555\pi$
$937$	−32.4058	−1.05865	−0.529326	+	0.848419i	$0.677555\pi$
$938$	−0.277374	−0.00905657
$939$	45.4282	1.48249
$940$	7.99223	0.260678
$941$	−15.2895	−0.498422	−0.249211	−	0.968449i	$-0.580171\pi$
$941$	−15.2895	−0.498422	−0.249211	+	0.968449i	$0.580171\pi$
$942$	32.4373	1.05686
$943$	25.9051	0.843588
$944$	0.417895	0.0136013
$945$	0.620269	0.0201773
$946$	47.1406	1.53267
$947$	12.0304	0.390935	0.195468	−	0.980710i	$-0.437378\pi$
$947$	12.0304	0.390935	0.195468	+	0.980710i	$0.437378\pi$
$948$	37.3303	1.21243
$949$	−12.9672	−0.420934
$950$	−4.17582	−0.135481
$951$	−54.7023	−1.77384
$952$	−0.124982	−0.00405068
$953$	6.05370	0.196099	0.0980493	−	0.995182i	$-0.468740\pi$
$953$	6.05370	0.196099	0.0980493	+	0.995182i	$0.468740\pi$
$954$	2.05323	0.0664758
$955$	42.0573	1.36094
$956$	25.4282	0.822406
$957$	−43.9597	−1.42102
$958$	25.0901	0.810623
$959$	0.887363	0.0286544
$960$	6.85086	0.221110
$961$	16.6069	0.535705
$962$	21.7366	0.700817
$963$	36.8267	1.18672
$964$	−14.9051	−0.480063
$965$	47.4980	1.52901
$966$	0.643104	0.0206915
$967$	57.1460	1.83769	0.918846	−	0.394616i	$-0.129122\pi$
$967$	57.1460	1.83769	0.918846	+	0.394616i	$0.129122\pi$
$968$	22.6625	0.728400
$969$	−30.5593	−0.981705
$970$	14.3588	0.461034
$971$	6.06292	0.194568	0.0972841	−	0.995257i	$-0.468984\pi$
$971$	6.06292	0.194568	0.0972841	+	0.995257i	$0.468984\pi$
$972$	15.6189	0.500978
$973$	−0.458779	−0.0147078
$974$	−8.57912	−0.274893
$975$	12.1836	0.390187
$976$	−3.53319	−0.113095
$977$	−15.5754	−0.498301	−0.249151	−	0.968465i	$-0.580151\pi$
$977$	−15.5754	−0.498301	−0.249151	+	0.968465i	$0.580151\pi$
$978$	14.5918	0.466594
$979$	−32.7972	−1.04820
$980$	17.1094	0.546541
$981$	−88.9880	−2.84117
$982$	−33.6238	−1.07298
$983$	25.4620	0.812113	0.406056	−	0.913848i	$-0.366904\pi$
$983$	25.4620	0.812113	0.406056	+	0.913848i	$0.366904\pi$
$984$	15.4698	0.493159
$985$	3.39459	0.108160
$986$	6.90887	0.220023
$987$	0.448026	0.0142608
$988$	18.9748	0.603668
$989$	38.1226	1.21223
$990$	68.8141	2.18706
$991$	14.7842	0.469636	0.234818	−	0.972039i	$-0.424551\pi$
$991$	14.7842	0.469636	0.234818	+	0.972039i	$0.424551\pi$
$992$	6.89977	0.219068
$993$	−66.8829	−2.12246
$994$	−0.00404885	−0.000128422 0
$995$	12.7569	0.404420
$996$	−15.2078	−0.481876
$997$	−8.54719	−0.270692	−0.135346	−	0.990798i	$-0.543215\pi$
$997$	−8.54719	−0.270692	−0.135346	+	0.990798i	$0.543215\pi$
$998$	0.515729	0.0163251
$999$	25.3599	0.802351

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6022.2.a.a.1.1	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6022.2.a.a.1.1	✓	3	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:	\( N \)	\(=\)	\( 6022 = 2 \cdot 3011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.80194 q^{3} +1.00000 q^{4} -2.44504 q^{5} -2.80194 q^{6} +0.0489173 q^{7} +1.00000 q^{8} +4.85086 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.80194 q^{3} +1.00000 q^{4} -2.44504 q^{5} -2.80194 q^{6} +0.0489173 q^{7} +1.00000 q^{8} +4.85086 q^{9} -2.44504 q^{10} -5.80194 q^{11} -2.80194 q^{12} -4.44504 q^{13} +0.0489173 q^{14} +6.85086 q^{15} +1.00000 q^{16} -2.55496 q^{17} +4.85086 q^{18} -4.26875 q^{19} -2.44504 q^{20} -0.137063 q^{21} -5.80194 q^{22} -4.69202 q^{23} -2.80194 q^{24} +0.978230 q^{25} -4.44504 q^{26} -5.18598 q^{27} +0.0489173 q^{28} -2.70410 q^{29} +6.85086 q^{30} +6.89977 q^{31} +1.00000 q^{32} +16.2567 q^{33} -2.55496 q^{34} -0.119605 q^{35} +4.85086 q^{36} -4.89008 q^{37} -4.26875 q^{38} +12.4547 q^{39} -2.44504 q^{40} -5.52111 q^{41} -0.137063 q^{42} -8.12498 q^{43} -5.80194 q^{44} -11.8605 q^{45} -4.69202 q^{46} -3.26875 q^{47} -2.80194 q^{48} -6.99761 q^{49} +0.978230 q^{50} +7.15883 q^{51} -4.44504 q^{52} +0.423272 q^{53} -5.18598 q^{54} +14.1860 q^{55} +0.0489173 q^{56} +11.9608 q^{57} -2.70410 q^{58} +0.417895 q^{59} +6.85086 q^{60} -3.53319 q^{61} +6.89977 q^{62} +0.237291 q^{63} +1.00000 q^{64} +10.8683 q^{65} +16.2567 q^{66} -5.67025 q^{67} -2.55496 q^{68} +13.1468 q^{69} -0.119605 q^{70} -0.0827692 q^{71} +4.85086 q^{72} +2.91723 q^{73} -4.89008 q^{74} -2.74094 q^{75} -4.26875 q^{76} -0.283815 q^{77} +12.4547 q^{78} -13.3230 q^{79} -2.44504 q^{80} -0.0217703 q^{81} -5.52111 q^{82} +5.42758 q^{83} -0.137063 q^{84} +6.24698 q^{85} -8.12498 q^{86} +7.57673 q^{87} -5.80194 q^{88} +5.65279 q^{89} -11.8605 q^{90} -0.217440 q^{91} -4.69202 q^{92} -19.3327 q^{93} -3.26875 q^{94} +10.4373 q^{95} -2.80194 q^{96} -5.87263 q^{97} -6.99761 q^{98} -28.1444 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - 4 q^{3} + 3 q^{4} - 7 q^{5} - 4 q^{6} - 9 q^{7} + 3 q^{8} + q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 - 4 * q^3 + 3 * q^4 - 7 * q^5 - 4 * q^6 - 9 * q^7 + 3 * q^8 + q^9	\( 3 q + 3 q^{2} - 4 q^{3} + 3 q^{4} - 7 q^{5} - 4 q^{6} - 9 q^{7} + 3 q^{8} + q^{9} - 7 q^{10} - 13 q^{11} - 4 q^{12} - 13 q^{13} - 9 q^{14} + 7 q^{15} + 3 q^{16} - 8 q^{17} + q^{18} - 5 q^{19} - 7 q^{20} + 5 q^{21} - 13 q^{22} - 9 q^{23} - 4 q^{24} + 6 q^{25} - 13 q^{26} - q^{27} - 9 q^{28} - 22 q^{29} + 7 q^{30} - 2 q^{31} + 3 q^{32} + 22 q^{33} - 8 q^{34} + 21 q^{35} + q^{36} - 14 q^{37} - 5 q^{38} + 15 q^{39} - 7 q^{40} - q^{41} + 5 q^{42} - 13 q^{44} - 9 q^{46} - 2 q^{47} - 4 q^{48} + 20 q^{49} + 6 q^{50} + 13 q^{51} - 13 q^{52} + 4 q^{53} - q^{54} + 28 q^{55} - 9 q^{56} + 23 q^{57} - 22 q^{58} + 7 q^{59} + 7 q^{60} - 14 q^{61} - 2 q^{62} + 18 q^{63} + 3 q^{64} + 35 q^{65} + 22 q^{66} - 15 q^{67} - 8 q^{68} + 12 q^{69} + 21 q^{70} - 7 q^{71} + q^{72} + 2 q^{73} - 14 q^{74} + 6 q^{75} - 5 q^{76} + 32 q^{77} + 15 q^{78} - 20 q^{79} - 7 q^{80} + 3 q^{81} - q^{82} + 5 q^{84} + 14 q^{85} + 20 q^{87} - 13 q^{88} - q^{89} + 39 q^{91} - 9 q^{92} - 16 q^{93} - 2 q^{94} - 7 q^{95} - 4 q^{96} - q^{97} + 20 q^{98} - 16 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - 4 * q^3 + 3 * q^4 - 7 * q^5 - 4 * q^6 - 9 * q^7 + 3 * q^8 + q^9 - 7 * q^10 - 13 * q^11 - 4 * q^12 - 13 * q^13 - 9 * q^14 + 7 * q^15 + 3 * q^16 - 8 * q^17 + q^18 - 5 * q^19 - 7 * q^20 + 5 * q^21 - 13 * q^22 - 9 * q^23 - 4 * q^24 + 6 * q^25 - 13 * q^26 - q^27 - 9 * q^28 - 22 * q^29 + 7 * q^30 - 2 * q^31 + 3 * q^32 + 22 * q^33 - 8 * q^34 + 21 * q^35 + q^36 - 14 * q^37 - 5 * q^38 + 15 * q^39 - 7 * q^40 - q^41 + 5 * q^42 - 13 * q^44 - 9 * q^46 - 2 * q^47 - 4 * q^48 + 20 * q^49 + 6 * q^50 + 13 * q^51 - 13 * q^52 + 4 * q^53 - q^54 + 28 * q^55 - 9 * q^56 + 23 * q^57 - 22 * q^58 + 7 * q^59 + 7 * q^60 - 14 * q^61 - 2 * q^62 + 18 * q^63 + 3 * q^64 + 35 * q^65 + 22 * q^66 - 15 * q^67 - 8 * q^68 + 12 * q^69 + 21 * q^70 - 7 * q^71 + q^72 + 2 * q^73 - 14 * q^74 + 6 * q^75 - 5 * q^76 + 32 * q^77 + 15 * q^78 - 20 * q^79 - 7 * q^80 + 3 * q^81 - q^82 + 5 * q^84 + 14 * q^85 + 20 * q^87 - 13 * q^88 - q^89 + 39 * q^91 - 9 * q^92 - 16 * q^93 - 2 * q^94 - 7 * q^95 - 4 * q^96 - q^97 + 20 * q^98 - 16 * q^99

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