LMFDB - Embedded newform 6022.2.a.a.1.3

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			1.3
Root			$-1.24698$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +0.246980 q^{3} +1.00000 q^{4} -3.80194 q^{5} +0.246980 q^{6} -4.69202 q^{7} +1.00000 q^{8} -2.93900 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.246980 q^{3} +1.00000 q^{4} -3.80194 q^{5} +0.246980 q^{6} -4.69202 q^{7} +1.00000 q^{8} -2.93900 q^{9} -3.80194 q^{10} -2.75302 q^{11} +0.246980 q^{12} -5.80194 q^{13} -4.69202 q^{14} -0.939001 q^{15} +1.00000 q^{16} -1.19806 q^{17} -2.93900 q^{18} +5.89977 q^{19} -3.80194 q^{20} -1.15883 q^{21} -2.75302 q^{22} -4.35690 q^{23} +0.246980 q^{24} +9.45473 q^{25} -5.80194 q^{26} -1.46681 q^{27} -4.69202 q^{28} -9.13706 q^{29} -0.939001 q^{30} -5.63102 q^{31} +1.00000 q^{32} -0.679940 q^{33} -1.19806 q^{34} +17.8388 q^{35} -2.93900 q^{36} -7.60388 q^{37} +5.89977 q^{38} -1.43296 q^{39} -3.80194 q^{40} -5.87263 q^{41} -1.15883 q^{42} -2.37867 q^{43} -2.75302 q^{44} +11.1739 q^{45} -4.35690 q^{46} +6.89977 q^{47} +0.246980 q^{48} +15.0151 q^{49} +9.45473 q^{50} -0.295897 q^{51} -5.80194 q^{52} +10.2567 q^{53} -1.46681 q^{54} +10.4668 q^{55} -4.69202 q^{56} +1.45712 q^{57} -9.13706 q^{58} -1.96077 q^{59} -0.939001 q^{60} -10.6528 q^{61} -5.63102 q^{62} +13.7899 q^{63} +1.00000 q^{64} +22.0586 q^{65} -0.679940 q^{66} -13.8116 q^{67} -1.19806 q^{68} -1.07606 q^{69} +17.8388 q^{70} +6.36658 q^{71} -2.93900 q^{72} +9.36658 q^{73} -7.60388 q^{74} +2.33513 q^{75} +5.89977 q^{76} +12.9172 q^{77} -1.43296 q^{78} -10.6256 q^{79} -3.80194 q^{80} +8.45473 q^{81} -5.87263 q^{82} -12.1957 q^{83} -1.15883 q^{84} +4.55496 q^{85} -2.37867 q^{86} -2.25667 q^{87} -2.75302 q^{88} -5.18598 q^{89} +11.1739 q^{90} +27.2228 q^{91} -4.35690 q^{92} -1.39075 q^{93} +6.89977 q^{94} -22.4306 q^{95} +0.246980 q^{96} +10.3937 q^{97} +15.0151 q^{98} +8.09113 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.246980	0.142594	0.0712969	−	0.997455i	$-0.477286\pi$
$3$	0.246980	0.142594	0.0712969	+	0.997455i	$0.477286\pi$
$4$	1.00000	0.500000
$5$	−3.80194	−1.70028	−0.850139	−	0.526558i	$-0.823482\pi$
$5$	−3.80194	−1.70028	−0.850139	+	0.526558i	$0.823482\pi$
$6$	0.246980	0.100829
$7$	−4.69202	−1.77342	−0.886709	−	0.462329i	$-0.847014\pi$
$7$	−4.69202	−1.77342	−0.886709	+	0.462329i	$0.847014\pi$
$8$	1.00000	0.353553
$9$	−2.93900	−0.979667
$10$	−3.80194	−1.20228
$11$	−2.75302	−0.830067	−0.415033	−	0.909806i	$-0.636230\pi$
$11$	−2.75302	−0.830067	−0.415033	+	0.909806i	$0.636230\pi$
$12$	0.246980	0.0712969
$13$	−5.80194	−1.60917	−0.804584	−	0.593839i	$-0.797612\pi$
$13$	−5.80194	−1.60917	−0.804584	+	0.593839i	$0.797612\pi$
$14$	−4.69202	−1.25400
$15$	−0.939001	−0.242449
$16$	1.00000	0.250000
$17$	−1.19806	−0.290573	−0.145286	−	0.989390i	$-0.546410\pi$
$17$	−1.19806	−0.290573	−0.145286	+	0.989390i	$0.546410\pi$
$18$	−2.93900	−0.692729
$19$	5.89977	1.35350	0.676750	−	0.736213i	$-0.263388\pi$
$19$	5.89977	1.35350	0.676750	+	0.736213i	$0.263388\pi$
$20$	−3.80194	−0.850139
$21$	−1.15883	−0.252878
$22$	−2.75302	−0.586946
$23$	−4.35690	−0.908476	−0.454238	−	0.890880i	$-0.650088\pi$
$23$	−4.35690	−0.908476	−0.454238	+	0.890880i	$0.650088\pi$
$24$	0.246980	0.0504145
$25$	9.45473	1.89095
$26$	−5.80194	−1.13785
$27$	−1.46681	−0.282288
$28$	−4.69202	−0.886709
$29$	−9.13706	−1.69671	−0.848355	−	0.529428i	$-0.822407\pi$
$29$	−9.13706	−1.69671	−0.848355	+	0.529428i	$0.822407\pi$
$30$	−0.939001	−0.171437
$31$	−5.63102	−1.01136	−0.505681	−	0.862721i	$-0.668759\pi$
$31$	−5.63102	−1.01136	−0.505681	+	0.862721i	$0.668759\pi$
$32$	1.00000	0.176777
$33$	−0.679940	−0.118362
$34$	−1.19806	−0.205466
$35$	17.8388	3.01530
$36$	−2.93900	−0.489834
$37$	−7.60388	−1.25007	−0.625035	−	0.780597i	$-0.714915\pi$
$37$	−7.60388	−1.25007	−0.625035	+	0.780597i	$0.714915\pi$
$38$	5.89977	0.957069
$39$	−1.43296	−0.229457
$40$	−3.80194	−0.601139
$41$	−5.87263	−0.917150	−0.458575	−	0.888656i	$-0.651640\pi$
$41$	−5.87263	−0.917150	−0.458575	+	0.888656i	$0.651640\pi$
$42$	−1.15883	−0.178812
$43$	−2.37867	−0.362743	−0.181372	−	0.983415i	$-0.558054\pi$
$43$	−2.37867	−0.362743	−0.181372	+	0.983415i	$0.558054\pi$
$44$	−2.75302	−0.415033
$45$	11.1739	1.66571
$46$	−4.35690	−0.642389
$47$	6.89977	1.00644	0.503218	−	0.864160i	$-0.332149\pi$
$47$	6.89977	1.00644	0.503218	+	0.864160i	$0.332149\pi$
$48$	0.246980	0.0356484
$49$	15.0151	2.14501
$50$	9.45473	1.33710
$51$	−0.295897	−0.0414339
$52$	−5.80194	−0.804584
$53$	10.2567	1.40886	0.704431	−	0.709773i	$-0.251202\pi$
$53$	10.2567	1.40886	0.704431	+	0.709773i	$0.251202\pi$
$54$	−1.46681	−0.199608
$55$	10.4668	1.41134
$56$	−4.69202	−0.626998
$57$	1.45712	0.193001
$58$	−9.13706	−1.19976
$59$	−1.96077	−0.255271	−0.127635	−	0.991821i	$-0.540739\pi$
$59$	−1.96077	−0.255271	−0.127635	+	0.991821i	$0.540739\pi$
$60$	−0.939001	−0.121225
$61$	−10.6528	−1.36395	−0.681975	−	0.731375i	$-0.738879\pi$
$61$	−10.6528	−1.36395	−0.681975	+	0.731375i	$0.738879\pi$
$62$	−5.63102	−0.715141
$63$	13.7899	1.73736
$64$	1.00000	0.125000
$65$	22.0586	2.73603
$66$	−0.679940	−0.0836948
$67$	−13.8116	−1.68736	−0.843679	−	0.536847i	$-0.819615\pi$
$67$	−13.8116	−1.68736	−0.843679	+	0.536847i	$0.819615\pi$
$68$	−1.19806	−0.145286
$69$	−1.07606	−0.129543
$70$	17.8388	2.13214
$71$	6.36658	0.755575	0.377787	−	0.925892i	$-0.376685\pi$
$71$	6.36658	0.755575	0.377787	+	0.925892i	$0.376685\pi$
$72$	−2.93900	−0.346365
$73$	9.36658	1.09628	0.548138	−	0.836388i	$-0.315337\pi$
$73$	9.36658	1.09628	0.548138	+	0.836388i	$0.315337\pi$
$74$	−7.60388	−0.883933
$75$	2.33513	0.269637
$76$	5.89977	0.676750
$77$	12.9172	1.47206
$78$	−1.43296	−0.162251
$79$	−10.6256	−1.19548	−0.597739	−	0.801691i	$-0.703934\pi$
$79$	−10.6256	−1.19548	−0.597739	+	0.801691i	$0.703934\pi$
$80$	−3.80194	−0.425070
$81$	8.45473	0.939415
$82$	−5.87263	−0.648523
$83$	−12.1957	−1.33865	−0.669324	−	0.742970i	$-0.733416\pi$
$83$	−12.1957	−1.33865	−0.669324	+	0.742970i	$0.733416\pi$
$84$	−1.15883	−0.126439
$85$	4.55496	0.494055
$86$	−2.37867	−0.256498
$87$	−2.25667	−0.241940
$88$	−2.75302	−0.293473
$89$	−5.18598	−0.549713	−0.274856	−	0.961485i	$-0.588630\pi$
$89$	−5.18598	−0.549713	−0.274856	+	0.961485i	$0.588630\pi$
$90$	11.1739	1.17783
$91$	27.2228	2.85373
$92$	−4.35690	−0.454238
$93$	−1.39075	−0.144214
$94$	6.89977	0.711657
$95$	−22.4306	−2.30133
$96$	0.246980	0.0252073
$97$	10.3937	1.05532	0.527662	−	0.849455i	$-0.323069\pi$
$97$	10.3937	1.05532	0.527662	+	0.849455i	$0.323069\pi$
$98$	15.0151	1.51675
$99$	8.09113	0.813189
$100$	9.45473	0.945473
$101$	4.45473	0.443262	0.221631	−	0.975131i	$-0.428862\pi$
$101$	4.45473	0.443262	0.221631	+	0.975131i	$0.428862\pi$
$102$	−0.295897	−0.0292982
$103$	−6.00538	−0.591727	−0.295864	−	0.955230i	$-0.595607\pi$
$103$	−6.00538	−0.591727	−0.295864	+	0.955230i	$0.595607\pi$
$104$	−5.80194	−0.568927
$105$	4.40581	0.429963
$106$	10.2567	0.996216
$107$	−5.27413	−0.509869	−0.254935	−	0.966958i	$-0.582054\pi$
$107$	−5.27413	−0.509869	−0.254935	+	0.966958i	$0.582054\pi$
$108$	−1.46681	−0.141144
$109$	−7.17092	−0.686849	−0.343425	−	0.939180i	$-0.611587\pi$
$109$	−7.17092	−0.686849	−0.343425	+	0.939180i	$0.611587\pi$
$110$	10.4668	0.997971
$111$	−1.87800	−0.178252
$112$	−4.69202	−0.443354
$113$	−1.59850	−0.150374	−0.0751871	−	0.997169i	$-0.523955\pi$
$113$	−1.59850	−0.150374	−0.0751871	+	0.997169i	$0.523955\pi$
$114$	1.45712	0.136472
$115$	16.5646	1.54466
$116$	−9.13706	−0.848355
$117$	17.0519	1.57645
$118$	−1.96077	−0.180504
$119$	5.62133	0.515307
$120$	−0.939001	−0.0857187
$121$	−3.42088	−0.310989
$122$	−10.6528	−0.964459
$123$	−1.45042	−0.130780
$124$	−5.63102	−0.505681
$125$	−16.9366	−1.51486
$126$	13.7899	1.22850
$127$	12.9487	1.14901	0.574505	−	0.818501i	$-0.305195\pi$
$127$	12.9487	1.14901	0.574505	+	0.818501i	$0.305195\pi$
$128$	1.00000	0.0883883
$129$	−0.587482	−0.0517249
$130$	22.0586	1.93467
$131$	−8.15644	−0.712632	−0.356316	−	0.934366i	$-0.615967\pi$
$131$	−8.15644	−0.712632	−0.356316	+	0.934366i	$0.615967\pi$
$132$	−0.679940	−0.0591812
$133$	−27.6819	−2.40032
$134$	−13.8116	−1.19314
$135$	5.57673	0.479968
$136$	−1.19806	−0.102733
$137$	9.36121	0.799782	0.399891	−	0.916563i	$-0.369048\pi$
$137$	9.36121	0.799782	0.399891	+	0.916563i	$0.369048\pi$
$138$	−1.07606	−0.0916007
$139$	3.50365	0.297176	0.148588	−	0.988899i	$-0.452527\pi$
$139$	3.50365	0.297176	0.148588	+	0.988899i	$0.452527\pi$
$140$	17.8388	1.50765
$141$	1.70410	0.143511
$142$	6.36658	0.534272
$143$	15.9729	1.33572
$144$	−2.93900	−0.244917
$145$	34.7385	2.88488
$146$	9.36658	0.775184
$147$	3.70841	0.305865
$148$	−7.60388	−0.625035
$149$	14.5187	1.18942	0.594710	−	0.803941i	$-0.297267\pi$
$149$	14.5187	1.18942	0.594710	+	0.803941i	$0.297267\pi$
$150$	2.33513	0.190662
$151$	0.203439	0.0165556	0.00827782	−	0.999966i	$-0.497365\pi$
$151$	0.203439	0.0165556	0.00827782	+	0.999966i	$0.497365\pi$
$152$	5.89977	0.478535
$153$	3.52111	0.284665
$154$	12.9172	1.04090
$155$	21.4088	1.71960
$156$	−1.43296	−0.114729
$157$	−1.74333	−0.139133	−0.0695665	−	0.997577i	$-0.522162\pi$
$157$	−1.74333	−0.139133	−0.0695665	+	0.997577i	$0.522162\pi$
$158$	−10.6256	−0.845331
$159$	2.53319	0.200895
$160$	−3.80194	−0.300570
$161$	20.4426	1.61111
$162$	8.45473	0.664266
$163$	6.98792	0.547336	0.273668	−	0.961824i	$-0.411763\pi$
$163$	6.98792	0.547336	0.273668	+	0.961824i	$0.411763\pi$
$164$	−5.87263	−0.458575
$165$	2.58509	0.201249
$166$	−12.1957	−0.946568
$167$	−7.47757	−0.578631	−0.289316	−	0.957234i	$-0.593428\pi$
$167$	−7.47757	−0.578631	−0.289316	+	0.957234i	$0.593428\pi$
$168$	−1.15883	−0.0894060
$169$	20.6625	1.58942
$170$	4.55496	0.349349
$171$	−17.3394	−1.32598
$172$	−2.37867	−0.181372
$173$	−17.5797	−1.33656	−0.668280	−	0.743909i	$-0.732969\pi$
$173$	−17.5797	−1.33656	−0.668280	+	0.743909i	$0.732969\pi$
$174$	−2.25667	−0.171078
$175$	−44.3618	−3.35344
$176$	−2.75302	−0.207517
$177$	−0.484271	−0.0364000
$178$	−5.18598	−0.388706
$179$	−12.3720	−0.924724	−0.462362	−	0.886691i	$-0.652998\pi$
$179$	−12.3720	−0.924724	−0.462362	+	0.886691i	$0.652998\pi$
$180$	11.1739	0.832853
$181$	1.36658	0.101577	0.0507887	−	0.998709i	$-0.483826\pi$
$181$	1.36658	0.101577	0.0507887	+	0.998709i	$0.483826\pi$
$182$	27.2228	2.01789
$183$	−2.63102	−0.194491
$184$	−4.35690	−0.321195
$185$	28.9095	2.12547
$186$	−1.39075	−0.101975
$187$	3.29829	0.241195
$188$	6.89977	0.503218
$189$	6.88231	0.500615
$190$	−22.4306	−1.62728
$191$	−10.4494	−0.756089	−0.378044	−	0.925787i	$-0.623403\pi$
$191$	−10.4494	−0.756089	−0.378044	+	0.925787i	$0.623403\pi$
$192$	0.246980	0.0178242
$193$	−19.4590	−1.40069	−0.700346	−	0.713803i	$-0.746971\pi$
$193$	−19.4590	−1.40069	−0.700346	+	0.713803i	$0.746971\pi$
$194$	10.3937	0.746226
$195$	5.44803	0.390141
$196$	15.0151	1.07250
$197$	26.7385	1.90504	0.952521	−	0.304472i	$-0.0984800\pi$
$197$	26.7385	1.90504	0.952521	+	0.304472i	$0.0984800\pi$
$198$	8.09113	0.575012
$199$	22.2228	1.57533	0.787667	−	0.616101i	$-0.211289\pi$
$199$	22.2228	1.57533	0.787667	+	0.616101i	$0.211289\pi$
$200$	9.45473	0.668550
$201$	−3.41119	−0.240607
$202$	4.45473	0.313434
$203$	42.8713	3.00898
$204$	−0.295897	−0.0207169
$205$	22.3274	1.55941
$206$	−6.00538	−0.418414
$207$	12.8049	0.890004
$208$	−5.80194	−0.402292
$209$	−16.2422	−1.12350
$210$	4.40581	0.304030
$211$	2.78986	0.192062	0.0960308	−	0.995378i	$-0.469385\pi$
$211$	2.78986	0.192062	0.0960308	+	0.995378i	$0.469385\pi$
$212$	10.2567	0.704431
$213$	1.57242	0.107740
$214$	−5.27413	−0.360532
$215$	9.04354	0.616764
$216$	−1.46681	−0.0998039
$217$	26.4209	1.79357
$218$	−7.17092	−0.485676
$219$	2.31336	0.156322
$220$	10.4668	0.705672
$221$	6.95108	0.467580
$222$	−1.87800	−0.126043
$223$	−5.39373	−0.361191	−0.180595	−	0.983557i	$-0.557802\pi$
$223$	−5.39373	−0.361191	−0.180595	+	0.983557i	$0.557802\pi$
$224$	−4.69202	−0.313499
$225$	−27.7875	−1.85250
$226$	−1.59850	−0.106331
$227$	14.0543	0.932816	0.466408	−	0.884570i	$-0.345548\pi$
$227$	14.0543	0.932816	0.466408	+	0.884570i	$0.345548\pi$
$228$	1.45712	0.0965004
$229$	−23.9245	−1.58098	−0.790489	−	0.612477i	$-0.790173\pi$
$229$	−23.9245	−1.58098	−0.790489	+	0.612477i	$0.790173\pi$
$230$	16.5646	1.09224
$231$	3.19029	0.209906
$232$	−9.13706	−0.599878
$233$	28.0629	1.83846	0.919231	−	0.393718i	$-0.128811\pi$
$233$	28.0629	1.83846	0.919231	+	0.393718i	$0.128811\pi$
$234$	17.0519	1.11472
$235$	−26.2325	−1.71122
$236$	−1.96077	−0.127635
$237$	−2.62432	−0.170468
$238$	5.62133	0.364377
$239$	−24.0084	−1.55297	−0.776486	−	0.630135i	$-0.783000\pi$
$239$	−24.0084	−1.55297	−0.776486	+	0.630135i	$0.783000\pi$
$240$	−0.939001	−0.0606123
$241$	−14.5864	−0.939594	−0.469797	−	0.882775i	$-0.655673\pi$
$241$	−14.5864	−0.939594	−0.469797	+	0.882775i	$0.655673\pi$
$242$	−3.42088	−0.219902
$243$	6.48858	0.416243
$244$	−10.6528	−0.681975
$245$	−57.0863	−3.64711
$246$	−1.45042	−0.0924753
$247$	−34.2301	−2.17801
$248$	−5.63102	−0.357570
$249$	−3.01208	−0.190883
$250$	−16.9366	−1.07117
$251$	−10.5724	−0.667325	−0.333663	−	0.942693i	$-0.608285\pi$
$251$	−10.5724	−0.667325	−0.333663	+	0.942693i	$0.608285\pi$
$252$	13.7899	0.868679
$253$	11.9946	0.754095
$254$	12.9487	0.812473
$255$	1.12498	0.0704491
$256$	1.00000	0.0625000
$257$	−21.9922	−1.37184	−0.685919	−	0.727678i	$-0.740599\pi$
$257$	−21.9922	−1.37184	−0.685919	+	0.727678i	$0.740599\pi$
$258$	−0.587482	−0.0365750
$259$	35.6775	2.21689
$260$	22.0586	1.36802
$261$	26.8538	1.66221
$262$	−8.15644	−0.503907
$263$	−14.4088	−0.888484	−0.444242	−	0.895907i	$-0.646527\pi$
$263$	−14.4088	−0.888484	−0.444242	+	0.895907i	$0.646527\pi$
$264$	−0.679940	−0.0418474
$265$	−38.9952	−2.39546
$266$	−27.6819	−1.69728
$267$	−1.28083	−0.0783856
$268$	−13.8116	−0.843679
$269$	10.2717	0.626279	0.313139	−	0.949707i	$-0.398619\pi$
$269$	10.2717	0.626279	0.313139	+	0.949707i	$0.398619\pi$
$270$	5.57673	0.339389
$271$	−13.3642	−0.811817	−0.405908	−	0.913914i	$-0.633045\pi$
$271$	−13.3642	−0.811817	−0.405908	+	0.913914i	$0.633045\pi$
$272$	−1.19806	−0.0726432
$273$	6.72348	0.406924
$274$	9.36121	0.565531
$275$	−26.0291	−1.56961
$276$	−1.07606	−0.0647715
$277$	−10.5603	−0.634509	−0.317255	−	0.948340i	$-0.602761\pi$
$277$	−10.5603	−0.634509	−0.317255	+	0.948340i	$0.602761\pi$
$278$	3.50365	0.210135
$279$	16.5496	0.990798
$280$	17.8388	1.06607
$281$	12.8726	0.767916	0.383958	−	0.923350i	$-0.374561\pi$
$281$	12.8726	0.767916	0.383958	+	0.923350i	$0.374561\pi$
$282$	1.70410	0.101478
$283$	−26.0640	−1.54934	−0.774671	−	0.632364i	$-0.782085\pi$
$283$	−26.0640	−1.54934	−0.774671	+	0.632364i	$0.782085\pi$
$284$	6.36658	0.377787
$285$	−5.53989	−0.328155
$286$	15.9729	0.944495
$287$	27.5545	1.62649
$288$	−2.93900	−0.173182
$289$	−15.5646	−0.915567
$290$	34.7385	2.03992
$291$	2.56704	0.150483
$292$	9.36658	0.548138
$293$	−20.4993	−1.19758	−0.598792	−	0.800905i	$-0.704352\pi$
$293$	−20.4993	−1.19758	−0.598792	+	0.800905i	$0.704352\pi$
$294$	3.70841	0.216279
$295$	7.45473	0.434031
$296$	−7.60388	−0.441966
$297$	4.03816	0.234318
$298$	14.5187	0.841046
$299$	25.2784	1.46189
$300$	2.33513	0.134819
$301$	11.1608	0.643295
$302$	0.203439	0.0117066
$303$	1.10023	0.0632064
$304$	5.89977	0.338375
$305$	40.5013	2.31910
$306$	3.52111	0.201288
$307$	−16.5743	−0.945947	−0.472974	−	0.881077i	$-0.656819\pi$
$307$	−16.5743	−0.945947	−0.472974	+	0.881077i	$0.656819\pi$
$308$	12.9172	0.736028
$309$	−1.48321	−0.0843766
$310$	21.4088	1.21594
$311$	9.79417	0.555376	0.277688	−	0.960671i	$-0.410432\pi$
$311$	9.79417	0.555376	0.277688	+	0.960671i	$0.410432\pi$
$312$	−1.43296	−0.0811254
$313$	−16.2295	−0.917347	−0.458673	−	0.888605i	$-0.651675\pi$
$313$	−16.2295	−0.917347	−0.458673	+	0.888605i	$0.651675\pi$
$314$	−1.74333	−0.0983819
$315$	−52.4282	−2.95399
$316$	−10.6256	−0.597739
$317$	−29.5948	−1.66221	−0.831104	−	0.556117i	$-0.812291\pi$
$317$	−29.5948	−1.66221	−0.831104	+	0.556117i	$0.812291\pi$
$318$	2.53319	0.142054
$319$	25.1545	1.40838
$320$	−3.80194	−0.212535
$321$	−1.30260	−0.0727041
$322$	20.4426	1.13922
$323$	−7.06829	−0.393290
$324$	8.45473	0.469707
$325$	−54.8558	−3.04285
$326$	6.98792	0.387025
$327$	−1.77107	−0.0979404
$328$	−5.87263	−0.324261
$329$	−32.3739	−1.78483
$330$	2.58509	0.142304
$331$	−14.4088	−0.791979	−0.395990	−	0.918255i	$-0.629598\pi$
$331$	−14.4088	−0.791979	−0.395990	+	0.918255i	$0.629598\pi$
$332$	−12.1957	−0.669324
$333$	22.3478	1.22465
$334$	−7.47757	−0.409154
$335$	52.5109	2.86898
$336$	−1.15883	−0.0632196
$337$	−15.3013	−0.833513	−0.416757	−	0.909018i	$-0.636833\pi$
$337$	−15.3013	−0.833513	−0.416757	+	0.909018i	$0.636833\pi$
$338$	20.6625	1.12389
$339$	−0.394797	−0.0214424
$340$	4.55496	0.247027
$341$	15.5023	0.839498
$342$	−17.3394	−0.937609
$343$	−37.6069	−2.03058
$344$	−2.37867	−0.128249
$345$	4.09113	0.220259
$346$	−17.5797	−0.945091
$347$	28.8509	1.54880	0.774398	−	0.632699i	$-0.218053\pi$
$347$	28.8509	1.54880	0.774398	+	0.632699i	$0.218053\pi$
$348$	−2.25667	−0.120970
$349$	−6.15213	−0.329316	−0.164658	−	0.986351i	$-0.552652\pi$
$349$	−6.15213	−0.329316	−0.164658	+	0.986351i	$0.552652\pi$
$350$	−44.3618	−2.37124
$351$	8.51035	0.454249
$352$	−2.75302	−0.146736
$353$	−1.42327	−0.0757531	−0.0378766	−	0.999282i	$-0.512059\pi$
$353$	−1.42327	−0.0757531	−0.0378766	+	0.999282i	$0.512059\pi$
$354$	−0.484271	−0.0257387
$355$	−24.2054	−1.28469
$356$	−5.18598	−0.274856
$357$	1.38835	0.0734795
$358$	−12.3720	−0.653878
$359$	−34.2422	−1.80723	−0.903617	−	0.428341i	$-0.859098\pi$
$359$	−34.2422	−1.80723	−0.903617	+	0.428341i	$0.859098\pi$
$360$	11.1739	0.588916
$361$	15.8073	0.831964
$362$	1.36658	0.0718261
$363$	−0.844887	−0.0443451
$364$	27.2228	1.42686
$365$	−35.6112	−1.86397
$366$	−2.63102	−0.137526
$367$	−13.5187	−0.705671	−0.352836	−	0.935685i	$-0.614782\pi$
$367$	−13.5187	−0.705671	−0.352836	+	0.935685i	$0.614782\pi$
$368$	−4.35690	−0.227119
$369$	17.2597	0.898502
$370$	28.9095	1.50293
$371$	−48.1245	−2.49850
$372$	−1.39075	−0.0721069
$373$	10.0248	0.519062	0.259531	−	0.965735i	$-0.416432\pi$
$373$	10.0248	0.519062	0.259531	+	0.965735i	$0.416432\pi$
$374$	3.29829	0.170551
$375$	−4.18300	−0.216009
$376$	6.89977	0.355829
$377$	53.0127	2.73029
$378$	6.88231	0.353988
$379$	−15.6069	−0.801671	−0.400835	−	0.916150i	$-0.631280\pi$
$379$	−15.6069	−0.801671	−0.400835	+	0.916150i	$0.631280\pi$
$380$	−22.4306	−1.15066
$381$	3.19806	0.163842
$382$	−10.4494	−0.534635
$383$	17.4534	0.891827	0.445914	−	0.895076i	$-0.352879\pi$
$383$	17.4534	0.891827	0.445914	+	0.895076i	$0.352879\pi$
$384$	0.246980	0.0126036
$385$	−49.1105	−2.50290
$386$	−19.4590	−0.990439
$387$	6.99090	0.355368
$388$	10.3937	0.527662
$389$	−11.9323	−0.604991	−0.302496	−	0.953151i	$-0.597820\pi$
$389$	−11.9323	−0.604991	−0.302496	+	0.953151i	$0.597820\pi$
$390$	5.44803	0.275872
$391$	5.21983	0.263978
$392$	15.0151	0.758375
$393$	−2.01447	−0.101617
$394$	26.7385	1.34707
$395$	40.3980	2.03265
$396$	8.09113	0.406595
$397$	−36.8678	−1.85034	−0.925172	−	0.379548i	$-0.876079\pi$
$397$	−36.8678	−1.85034	−0.925172	+	0.379548i	$0.876079\pi$
$398$	22.2228	1.11393
$399$	−6.83685	−0.342271
$400$	9.45473	0.472737
$401$	−23.5690	−1.17698	−0.588489	−	0.808505i	$-0.700277\pi$
$401$	−23.5690	−1.17698	−0.588489	+	0.808505i	$0.700277\pi$
$402$	−3.41119	−0.170135
$403$	32.6708	1.62745
$404$	4.45473	0.221631
$405$	−32.1444	−1.59727
$406$	42.8713	2.12767
$407$	20.9336	1.03764
$408$	−0.295897	−0.0146491
$409$	12.0392	0.595302	0.297651	−	0.954675i	$-0.403797\pi$
$409$	12.0392	0.595302	0.297651	+	0.954675i	$0.403797\pi$
$410$	22.3274	1.10267
$411$	2.31203	0.114044
$412$	−6.00538	−0.295864
$413$	9.19998	0.452701
$414$	12.8049	0.629328
$415$	46.3672	2.27608
$416$	−5.80194	−0.284463
$417$	0.865330	0.0423754
$418$	−16.2422	−0.794432
$419$	35.5816	1.73828	0.869138	−	0.494569i	$-0.164674\pi$
$419$	35.5816	1.73828	0.869138	+	0.494569i	$0.164674\pi$
$420$	4.40581	0.214982
$421$	−19.9715	−0.973353	−0.486676	−	0.873582i	$-0.661791\pi$
$421$	−19.9715	−0.973353	−0.486676	+	0.873582i	$0.661791\pi$
$422$	2.78986	0.135808
$423$	−20.2784	−0.985971
$424$	10.2567	0.498108
$425$	−11.3274	−0.549457
$426$	1.57242	0.0761838
$427$	49.9831	2.41885
$428$	−5.27413	−0.254935
$429$	3.94497	0.190465
$430$	9.04354	0.436118
$431$	−4.34721	−0.209398	−0.104699	−	0.994504i	$-0.533388\pi$
$431$	−4.34721	−0.209398	−0.104699	+	0.994504i	$0.533388\pi$
$432$	−1.46681	−0.0705720
$433$	6.54958	0.314753	0.157376	−	0.987539i	$-0.449696\pi$
$433$	6.54958	0.314753	0.157376	+	0.987539i	$0.449696\pi$
$434$	26.4209	1.26824
$435$	8.57971	0.411366
$436$	−7.17092	−0.343425
$437$	−25.7047	−1.22962
$438$	2.31336	0.110536
$439$	1.35988	0.0649035	0.0324518	−	0.999473i	$-0.489668\pi$
$439$	1.35988	0.0649035	0.0324518	+	0.999473i	$0.489668\pi$
$440$	10.4668	0.498986
$441$	−44.1293	−2.10139
$442$	6.95108	0.330629
$443$	−31.3448	−1.48924	−0.744619	−	0.667490i	$-0.767369\pi$
$443$	−31.3448	−1.48924	−0.744619	+	0.667490i	$0.767369\pi$
$444$	−1.87800	−0.0891260
$445$	19.7168	0.934665
$446$	−5.39373	−0.255401
$447$	3.58583	0.169604
$448$	−4.69202	−0.221677
$449$	−27.9608	−1.31955	−0.659775	−	0.751463i	$-0.729348\pi$
$449$	−27.9608	−1.31955	−0.659775	+	0.751463i	$0.729348\pi$
$450$	−27.7875	−1.30991
$451$	16.1675	0.761296
$452$	−1.59850	−0.0751871
$453$	0.0502453	0.00236073
$454$	14.0543	0.659601
$455$	−103.499	−4.85213
$456$	1.45712	0.0682361
$457$	16.0489	0.750737	0.375368	−	0.926876i	$-0.377516\pi$
$457$	16.0489	0.750737	0.375368	+	0.926876i	$0.377516\pi$
$458$	−23.9245	−1.11792
$459$	1.75733	0.0820252
$460$	16.5646	0.772331
$461$	18.5526	0.864079	0.432040	−	0.901855i	$-0.357794\pi$
$461$	18.5526	0.864079	0.432040	+	0.901855i	$0.357794\pi$
$462$	3.19029	0.148426
$463$	24.9202	1.15814	0.579070	−	0.815278i	$-0.303416\pi$
$463$	24.9202	1.15814	0.579070	+	0.815278i	$0.303416\pi$
$464$	−9.13706	−0.424178
$465$	5.28754	0.245204
$466$	28.0629	1.29999
$467$	−24.3153	−1.12518	−0.562588	−	0.826737i	$-0.690194\pi$
$467$	−24.3153	−1.12518	−0.562588	+	0.826737i	$0.690194\pi$
$468$	17.0519	0.788224
$469$	64.8044	2.99239
$470$	−26.2325	−1.21002
$471$	−0.430567	−0.0198395
$472$	−1.96077	−0.0902518
$473$	6.54852	0.301101
$474$	−2.62432	−0.120539
$475$	55.7808	2.55940
$476$	5.62133	0.257653
$477$	−30.1444	−1.38022
$478$	−24.0084	−1.09812
$479$	−18.6165	−0.850612	−0.425306	−	0.905050i	$-0.639833\pi$
$479$	−18.6165	−0.850612	−0.425306	+	0.905050i	$0.639833\pi$
$480$	−0.939001	−0.0428593
$481$	44.1172	2.01157
$482$	−14.5864	−0.664393
$483$	5.04892	0.229734
$484$	−3.42088	−0.155494
$485$	−39.5163	−1.79434
$486$	6.48858	0.294328
$487$	−20.7584	−0.940653	−0.470326	−	0.882493i	$-0.655864\pi$
$487$	−20.7584	−0.940653	−0.470326	+	0.882493i	$0.655864\pi$
$488$	−10.6528	−0.482229
$489$	1.72587	0.0780467
$490$	−57.0863	−2.57890
$491$	34.7764	1.56944	0.784720	−	0.619851i	$-0.212807\pi$
$491$	34.7764	1.56944	0.784720	+	0.619851i	$0.212807\pi$
$492$	−1.45042	−0.0653899
$493$	10.9468	0.493018
$494$	−34.2301	−1.54009
$495$	−30.7620	−1.38265
$496$	−5.63102	−0.252840
$497$	−29.8722	−1.33995
$498$	−3.01208	−0.134975
$499$	−11.3448	−0.507864	−0.253932	−	0.967222i	$-0.581724\pi$
$499$	−11.3448	−0.507864	−0.253932	+	0.967222i	$0.581724\pi$
$500$	−16.9366	−0.757428
$501$	−1.84681	−0.0825092
$502$	−10.5724	−0.471870
$503$	5.70278	0.254274	0.127137	−	0.991885i	$-0.459421\pi$
$503$	5.70278	0.254274	0.127137	+	0.991885i	$0.459421\pi$
$504$	13.7899	0.614249
$505$	−16.9366	−0.753669
$506$	11.9946	0.533226
$507$	5.10321	0.226642
$508$	12.9487	0.574505
$509$	−1.57434	−0.0697812	−0.0348906	−	0.999391i	$-0.511108\pi$
$509$	−1.57434	−0.0697812	−0.0348906	+	0.999391i	$0.511108\pi$
$510$	1.12498	0.0498150
$511$	−43.9482	−1.94415
$512$	1.00000	0.0441942
$513$	−8.65386	−0.382077
$514$	−21.9922	−0.970036
$515$	22.8321	1.00610
$516$	−0.587482	−0.0258625
$517$	−18.9952	−0.835409
$518$	35.6775	1.56758
$519$	−4.34183	−0.190585
$520$	22.0586	0.967334
$521$	32.3250	1.41618	0.708091	−	0.706121i	$-0.249557\pi$
$521$	32.3250	1.41618	0.708091	+	0.706121i	$0.249557\pi$
$522$	26.8538	1.17536
$523$	35.3817	1.54713	0.773566	−	0.633716i	$-0.218471\pi$
$523$	35.3817	1.54713	0.773566	+	0.633716i	$0.218471\pi$
$524$	−8.15644	−0.356316
$525$	−10.9565	−0.478179
$526$	−14.4088	−0.628253
$527$	6.74632	0.293874
$528$	−0.679940	−0.0295906
$529$	−4.01746	−0.174672
$530$	−38.9952	−1.69384
$531$	5.76271	0.250080
$532$	−27.6819	−1.20016
$533$	34.0726	1.47585
$534$	−1.28083	−0.0554270
$535$	20.0519	0.866919
$536$	−13.8116	−0.596571
$537$	−3.05562	−0.131860
$538$	10.2717	0.442846
$539$	−41.3368	−1.78050
$540$	5.57673	0.239984
$541$	0.122589	0.00527051	0.00263525	−	0.999997i	$-0.499161\pi$
$541$	0.122589	0.00527051	0.00263525	+	0.999997i	$0.499161\pi$
$542$	−13.3642	−0.574041
$543$	0.337519	0.0144843
$544$	−1.19806	−0.0513665
$545$	27.2634	1.16783
$546$	6.72348	0.287738
$547$	−7.60925	−0.325348	−0.162674	−	0.986680i	$-0.552012\pi$
$547$	−7.60925	−0.325348	−0.162674	+	0.986680i	$0.552012\pi$
$548$	9.36121	0.399891
$549$	31.3086	1.33622
$550$	−26.0291	−1.10988
$551$	−53.9066	−2.29650
$552$	−1.07606	−0.0458003
$553$	49.8558	2.12008
$554$	−10.5603	−0.448666
$555$	7.14005	0.303078
$556$	3.50365	0.148588
$557$	30.4292	1.28933	0.644664	−	0.764466i	$-0.276997\pi$
$557$	30.4292	1.28933	0.644664	+	0.764466i	$0.276997\pi$
$558$	16.5496	0.700600
$559$	13.8009	0.583715
$560$	17.8388	0.753826
$561$	0.814610	0.0343929
$562$	12.8726	0.542999
$563$	17.5690	0.740443	0.370222	−	0.928943i	$-0.379282\pi$
$563$	17.5690	0.740443	0.370222	+	0.928943i	$0.379282\pi$
$564$	1.70410	0.0717557
$565$	6.07739	0.255678
$566$	−26.0640	−1.09555
$567$	−39.6698	−1.66597
$568$	6.36658	0.267136
$569$	12.0441	0.504916	0.252458	−	0.967608i	$-0.418761\pi$
$569$	12.0441	0.504916	0.252458	+	0.967608i	$0.418761\pi$
$570$	−5.53989	−0.232041
$571$	−34.4101	−1.44002	−0.720009	−	0.693964i	$-0.755863\pi$
$571$	−34.4101	−1.44002	−0.720009	+	0.693964i	$0.755863\pi$
$572$	15.9729	0.667859
$573$	−2.58078	−0.107814
$574$	27.5545	1.15010
$575$	−41.1933	−1.71788
$576$	−2.93900	−0.122458
$577$	39.6021	1.64866	0.824328	−	0.566113i	$-0.191553\pi$
$577$	39.6021	1.64866	0.824328	+	0.566113i	$0.191553\pi$
$578$	−15.5646	−0.647404
$579$	−4.80599	−0.199730
$580$	34.7385	1.44244
$581$	57.2223	2.37398
$582$	2.56704	0.106407
$583$	−28.2368	−1.16945
$584$	9.36658	0.387592
$585$	−64.8303	−2.68040
$586$	−20.4993	−0.846820
$587$	−1.68963	−0.0697384	−0.0348692	−	0.999392i	$-0.511101\pi$
$587$	−1.68963	−0.0697384	−0.0348692	+	0.999392i	$0.511101\pi$
$588$	3.70841	0.152932
$589$	−33.2218	−1.36888
$590$	7.45473	0.306906
$591$	6.60388	0.271647
$592$	−7.60388	−0.312517
$593$	1.10262	0.0452792	0.0226396	−	0.999744i	$-0.492793\pi$
$593$	1.10262	0.0452792	0.0226396	+	0.999744i	$0.492793\pi$
$594$	4.03816	0.165688
$595$	−21.3720	−0.876165
$596$	14.5187	0.594710
$597$	5.48858	0.224633
$598$	25.2784	1.03371
$599$	−37.6969	−1.54025	−0.770127	−	0.637890i	$-0.779807\pi$
$599$	−37.6969	−1.54025	−0.770127	+	0.637890i	$0.779807\pi$
$600$	2.33513	0.0953311
$601$	−25.0388	−1.02135	−0.510676	−	0.859773i	$-0.670605\pi$
$601$	−25.0388	−1.02135	−0.510676	+	0.859773i	$0.670605\pi$
$602$	11.1608	0.454878
$603$	40.5924	1.65305
$604$	0.203439	0.00827782
$605$	13.0060	0.528768
$606$	1.10023	0.0446937
$607$	7.05323	0.286282	0.143141	−	0.989702i	$-0.454280\pi$
$607$	7.05323	0.286282	0.143141	+	0.989702i	$0.454280\pi$
$608$	5.89977	0.239267
$609$	10.5883	0.429061
$610$	40.5013	1.63985
$611$	−40.0320	−1.61952
$612$	3.52111	0.142332
$613$	−21.6213	−0.873277	−0.436639	−	0.899637i	$-0.643831\pi$
$613$	−21.6213	−0.873277	−0.436639	+	0.899637i	$0.643831\pi$
$614$	−16.5743	−0.668886
$615$	5.51440	0.222362
$616$	12.9172	0.520450
$617$	−16.0653	−0.646765	−0.323383	−	0.946268i	$-0.604820\pi$
$617$	−16.0653	−0.646765	−0.323383	+	0.946268i	$0.604820\pi$
$618$	−1.48321	−0.0596633
$619$	−9.93362	−0.399266	−0.199633	−	0.979871i	$-0.563975\pi$
$619$	−9.93362	−0.399266	−0.199633	+	0.979871i	$0.563975\pi$
$620$	21.4088	0.859798
$621$	6.39075	0.256452
$622$	9.79417	0.392710
$623$	24.3327	0.974870
$624$	−1.43296	−0.0573643
$625$	17.1183	0.684731
$626$	−16.2295	−0.648662
$627$	−4.01149	−0.160204
$628$	−1.74333	−0.0695665
$629$	9.10992	0.363236
$630$	−52.4282	−2.08879
$631$	−42.9028	−1.70793	−0.853966	−	0.520329i	$-0.825809\pi$
$631$	−42.9028	−1.70793	−0.853966	+	0.520329i	$0.825809\pi$
$632$	−10.6256	−0.422665
$633$	0.689038	0.0273868
$634$	−29.5948	−1.17536
$635$	−49.2301	−1.95364
$636$	2.53319	0.100447
$637$	−87.1165	−3.45168
$638$	25.1545	0.995877
$639$	−18.7114	−0.740211
$640$	−3.80194	−0.150285
$641$	−44.0411	−1.73952	−0.869760	−	0.493474i	$-0.835727\pi$
$641$	−44.0411	−1.73952	−0.869760	+	0.493474i	$0.835727\pi$
$642$	−1.30260	−0.0514096
$643$	41.1213	1.62166	0.810832	−	0.585279i	$-0.199015\pi$
$643$	41.1213	1.62166	0.810832	+	0.585279i	$0.199015\pi$
$644$	20.4426	0.805553
$645$	2.23357	0.0879467
$646$	−7.06829	−0.278098
$647$	29.3370	1.15336	0.576679	−	0.816971i	$-0.304348\pi$
$647$	29.3370	1.15336	0.576679	+	0.816971i	$0.304348\pi$
$648$	8.45473	0.332133
$649$	5.39804	0.211892
$650$	−54.8558	−2.15162
$651$	6.52542	0.255751
$652$	6.98792	0.273668
$653$	−17.0828	−0.668500	−0.334250	−	0.942484i	$-0.608483\pi$
$653$	−17.0828	−0.668500	−0.334250	+	0.942484i	$0.608483\pi$
$654$	−1.77107	−0.0692543
$655$	31.0103	1.21167
$656$	−5.87263	−0.229287
$657$	−27.5284	−1.07399
$658$	−32.3739	−1.26207
$659$	33.3183	1.29790	0.648948	−	0.760833i	$-0.275209\pi$
$659$	33.3183	1.29790	0.648948	+	0.760833i	$0.275209\pi$
$660$	2.58509	0.100624
$661$	30.9982	1.20569	0.602845	−	0.797858i	$-0.294034\pi$
$661$	30.9982	1.20569	0.602845	+	0.797858i	$0.294034\pi$
$662$	−14.4088	−0.560014
$663$	1.71678	0.0666740
$664$	−12.1957	−0.473284
$665$	105.245	4.08121
$666$	22.3478	0.865960
$667$	39.8092	1.54142
$668$	−7.47757	−0.289316
$669$	−1.33214	−0.0515036
$670$	52.5109	2.02867
$671$	29.3274	1.13217
$672$	−1.15883	−0.0447030
$673$	44.6238	1.72012	0.860061	−	0.510191i	$-0.170425\pi$
$673$	44.6238	1.72012	0.860061	+	0.510191i	$0.170425\pi$
$674$	−15.3013	−0.589383
$675$	−13.8683	−0.533792
$676$	20.6625	0.794711
$677$	36.1400	1.38897	0.694487	−	0.719505i	$-0.255631\pi$
$677$	36.1400	1.38897	0.694487	+	0.719505i	$0.255631\pi$
$678$	−0.394797	−0.0151621
$679$	−48.7676	−1.87153
$680$	4.55496	0.174675
$681$	3.47112	0.133014
$682$	15.5023	0.593615
$683$	28.6195	1.09510	0.547548	−	0.836774i	$-0.315561\pi$
$683$	28.6195	1.09510	0.547548	+	0.836774i	$0.315561\pi$
$684$	−17.3394	−0.662990
$685$	−35.5907	−1.35985
$686$	−37.6069	−1.43584
$687$	−5.90887	−0.225437
$688$	−2.37867	−0.0906858
$689$	−59.5086	−2.26710
$690$	4.09113	0.155747
$691$	13.1086	0.498674	0.249337	−	0.968417i	$-0.419787\pi$
$691$	13.1086	0.498674	0.249337	+	0.968417i	$0.419787\pi$
$692$	−17.5797	−0.668280
$693$	−37.9638	−1.44212
$694$	28.8509	1.09516
$695$	−13.3207	−0.505281
$696$	−2.25667	−0.0855388
$697$	7.03577	0.266499
$698$	−6.15213	−0.232862
$699$	6.93097	0.262153
$700$	−44.3618	−1.67672
$701$	1.70948	0.0645662	0.0322831	−	0.999479i	$-0.489722\pi$
$701$	1.70948	0.0645662	0.0322831	+	0.999479i	$0.489722\pi$
$702$	8.51035	0.321203
$703$	−44.8611	−1.69197
$704$	−2.75302	−0.103758
$705$	−6.47889	−0.244009
$706$	−1.42327	−0.0535655
$707$	−20.9017	−0.786089
$708$	−0.484271	−0.0182000
$709$	0.109916	0.00412799	0.00206400	−	0.999998i	$-0.499343\pi$
$709$	0.109916	0.00412799	0.00206400	+	0.999998i	$0.499343\pi$
$710$	−24.2054	−0.908411
$711$	31.2288	1.17117
$712$	−5.18598	−0.194353
$713$	24.5338	0.918797
$714$	1.38835	0.0519579
$715$	−60.7278	−2.27109
$716$	−12.3720	−0.462362
$717$	−5.92958	−0.221444
$718$	−34.2422	−1.27791
$719$	−21.1202	−0.787650	−0.393825	−	0.919185i	$-0.628848\pi$
$719$	−21.1202	−0.787650	−0.393825	+	0.919185i	$0.628848\pi$
$720$	11.1739	0.416427
$721$	28.1774	1.04938
$722$	15.8073	0.588287
$723$	−3.60255	−0.133980
$724$	1.36658	0.0507887
$725$	−86.3885	−3.20839
$726$	−0.844887	−0.0313567
$727$	18.4829	0.685494	0.342747	−	0.939428i	$-0.388643\pi$
$727$	18.4829	0.685494	0.342747	+	0.939428i	$0.388643\pi$
$728$	27.2228	1.00894
$729$	−23.7616	−0.880061
$730$	−35.6112	−1.31803
$731$	2.84979	0.105403
$732$	−2.63102	−0.0972454
$733$	−11.1166	−0.410602	−0.205301	−	0.978699i	$-0.565817\pi$
$733$	−11.1166	−0.410602	−0.205301	+	0.978699i	$0.565817\pi$
$734$	−13.5187	−0.498985
$735$	−14.0992	−0.520055
$736$	−4.35690	−0.160597
$737$	38.0237	1.40062
$738$	17.2597	0.635337
$739$	22.7265	0.836007	0.418003	−	0.908446i	$-0.362730\pi$
$739$	22.7265	0.836007	0.418003	+	0.908446i	$0.362730\pi$
$740$	28.9095	1.06273
$741$	−8.45414	−0.310571
$742$	−48.1245	−1.76671
$743$	−35.8756	−1.31615	−0.658074	−	0.752953i	$-0.728629\pi$
$743$	−35.8756	−1.31615	−0.658074	+	0.752953i	$0.728629\pi$
$744$	−1.39075	−0.0509873
$745$	−55.1992	−2.02234
$746$	10.0248	0.367032
$747$	35.8431	1.31143
$748$	3.29829	0.120597
$749$	24.7463	0.904211
$750$	−4.18300	−0.152741
$751$	−14.3532	−0.523755	−0.261877	−	0.965101i	$-0.584342\pi$
$751$	−14.3532	−0.523755	−0.261877	+	0.965101i	$0.584342\pi$
$752$	6.89977	0.251609
$753$	−2.61117	−0.0951564
$754$	53.0127	1.93061
$755$	−0.773463	−0.0281492
$756$	6.88231	0.250307
$757$	−18.4946	−0.672196	−0.336098	−	0.941827i	$-0.609107\pi$
$757$	−18.4946	−0.672196	−0.336098	+	0.941827i	$0.609107\pi$
$758$	−15.6069	−0.566867
$759$	2.96243	0.107529
$760$	−22.4306	−0.813642
$761$	9.54048	0.345842	0.172921	−	0.984936i	$-0.444679\pi$
$761$	9.54048	0.345842	0.172921	+	0.984936i	$0.444679\pi$
$762$	3.19806	0.115854
$763$	33.6461	1.21807
$764$	−10.4494	−0.378044
$765$	−13.3870	−0.484009
$766$	17.4534	0.630617
$767$	11.3763	0.410773
$768$	0.246980	0.00891211
$769$	−6.84654	−0.246893	−0.123446	−	0.992351i	$-0.539395\pi$
$769$	−6.84654	−0.246893	−0.123446	+	0.992351i	$0.539395\pi$
$770$	−49.1105	−1.76982
$771$	−5.43163	−0.195615
$772$	−19.4590	−0.700346
$773$	−20.8388	−0.749519	−0.374759	−	0.927122i	$-0.622275\pi$
$773$	−20.8388	−0.749519	−0.374759	+	0.927122i	$0.622275\pi$
$774$	6.99090	0.251283
$775$	−53.2398	−1.91243
$776$	10.3937	0.373113
$777$	8.81163	0.316115
$778$	−11.9323	−0.427794
$779$	−34.6472	−1.24136
$780$	5.44803	0.195071
$781$	−17.5273	−0.627177
$782$	5.21983	0.186661
$783$	13.4024	0.478961
$784$	15.0151	0.536252
$785$	6.62804	0.236565
$786$	−2.01447	−0.0718539
$787$	17.4024	0.620327	0.310163	−	0.950683i	$-0.399616\pi$
$787$	17.4024	0.620327	0.310163	+	0.950683i	$0.399616\pi$
$788$	26.7385	0.952521
$789$	−3.55868	−0.126692
$790$	40.3980	1.43730
$791$	7.50019	0.266676
$792$	8.09113	0.287506
$793$	61.8068	2.19483
$794$	−36.8678	−1.30839
$795$	−9.63102	−0.341577
$796$	22.2228	0.787667
$797$	−4.16315	−0.147466	−0.0737331	−	0.997278i	$-0.523491\pi$
$797$	−4.16315	−0.147466	−0.0737331	+	0.997278i	$0.523491\pi$
$798$	−6.83685	−0.242022
$799$	−8.26636	−0.292443
$800$	9.45473	0.334275
$801$	15.2416	0.538536
$802$	−23.5690	−0.832249
$803$	−25.7864	−0.909982
$804$	−3.41119	−0.120303
$805$	−77.7217	−2.73933
$806$	32.6708	1.15078
$807$	2.53691	0.0893034
$808$	4.45473	0.156717
$809$	−49.1008	−1.72629	−0.863146	−	0.504954i	$-0.831510\pi$
$809$	−49.1008	−1.72629	−0.863146	+	0.504954i	$0.831510\pi$
$810$	−32.1444	−1.12944
$811$	−3.78794	−0.133012	−0.0665062	−	0.997786i	$-0.521185\pi$
$811$	−3.78794	−0.133012	−0.0665062	+	0.997786i	$0.521185\pi$
$812$	42.8713	1.50449
$813$	−3.30068	−0.115760
$814$	20.9336	0.733723
$815$	−26.5676	−0.930624
$816$	−0.295897	−0.0103585
$817$	−14.0336	−0.490973
$818$	12.0392	0.420942
$819$	−80.0079	−2.79570
$820$	22.3274	0.779705
$821$	10.5284	0.367444	0.183722	−	0.982978i	$-0.441185\pi$
$821$	10.5284	0.367444	0.183722	+	0.982978i	$0.441185\pi$
$822$	2.31203	0.0806412
$823$	13.9769	0.487204	0.243602	−	0.969875i	$-0.421671\pi$
$823$	13.9769	0.487204	0.243602	+	0.969875i	$0.421671\pi$
$824$	−6.00538	−0.209207
$825$	−6.42865	−0.223817
$826$	9.19998	0.320108
$827$	2.84607	0.0989675	0.0494838	−	0.998775i	$-0.484242\pi$
$827$	2.84607	0.0989675	0.0494838	+	0.998775i	$0.484242\pi$
$828$	12.8049	0.445002
$829$	−35.7482	−1.24159	−0.620794	−	0.783974i	$-0.713190\pi$
$829$	−35.7482	−1.24159	−0.620794	+	0.783974i	$0.713190\pi$
$830$	46.3672	1.60943
$831$	−2.60819	−0.0904770
$832$	−5.80194	−0.201146
$833$	−17.9890	−0.623281
$834$	0.865330	0.0299639
$835$	28.4292	0.983834
$836$	−16.2422	−0.561748
$837$	8.25965	0.285495
$838$	35.5816	1.22915
$839$	−28.9976	−1.00111	−0.500554	−	0.865705i	$-0.666870\pi$
$839$	−28.9976	−1.00111	−0.500554	+	0.865705i	$0.666870\pi$
$840$	4.40581	0.152015
$841$	54.4859	1.87883
$842$	−19.9715	−0.688264
$843$	3.17928	0.109500
$844$	2.78986	0.0960308
$845$	−78.5575	−2.70246
$846$	−20.2784	−0.697187
$847$	16.0508	0.551513
$848$	10.2567	0.352215
$849$	−6.43727	−0.220927
$850$	−11.3274	−0.388525
$851$	33.1293	1.13566
$852$	1.57242	0.0538701
$853$	−10.8183	−0.370413	−0.185206	−	0.982700i	$-0.559295\pi$
$853$	−10.8183	−0.370413	−0.185206	+	0.982700i	$0.559295\pi$
$854$	49.9831	1.71039
$855$	65.9235	2.25453
$856$	−5.27413	−0.180266
$857$	22.8864	0.781783	0.390892	−	0.920437i	$-0.372167\pi$
$857$	22.8864	0.781783	0.390892	+	0.920437i	$0.372167\pi$
$858$	3.94497	0.134679
$859$	29.5036	1.00665	0.503326	−	0.864097i	$-0.332110\pi$
$859$	29.5036	1.00665	0.503326	+	0.864097i	$0.332110\pi$
$860$	9.04354	0.308382
$861$	6.80540	0.231927
$862$	−4.34721	−0.148066
$863$	41.1685	1.40139	0.700696	−	0.713460i	$-0.252873\pi$
$863$	41.1685	1.40139	0.700696	+	0.713460i	$0.252873\pi$
$864$	−1.46681	−0.0499020
$865$	66.8370	2.27253
$866$	6.54958	0.222564
$867$	−3.84415	−0.130554
$868$	26.4209	0.896783
$869$	29.2526	0.992327
$870$	8.57971	0.290879
$871$	80.1342	2.71524
$872$	−7.17092	−0.242838
$873$	−30.5472	−1.03387
$874$	−25.7047	−0.869474
$875$	79.4669	2.68647
$876$	2.31336	0.0781610
$877$	38.7114	1.30719	0.653596	−	0.756844i	$-0.273260\pi$
$877$	38.7114	1.30719	0.653596	+	0.756844i	$0.273260\pi$
$878$	1.35988	0.0458937
$879$	−5.06292	−0.170768
$880$	10.4668	0.352836
$881$	26.9831	0.909085	0.454542	−	0.890725i	$-0.349803\pi$
$881$	26.9831	0.909085	0.454542	+	0.890725i	$0.349803\pi$
$882$	−44.1293	−1.48591
$883$	−41.9028	−1.41014	−0.705070	−	0.709138i	$-0.749084\pi$
$883$	−41.9028	−1.41014	−0.705070	+	0.709138i	$0.749084\pi$
$884$	6.95108	0.233790
$885$	1.84117	0.0618901
$886$	−31.3448	−1.05305
$887$	46.6010	1.56471	0.782354	−	0.622834i	$-0.214019\pi$
$887$	46.6010	1.56471	0.782354	+	0.622834i	$0.214019\pi$
$888$	−1.87800	−0.0630216
$889$	−60.7555	−2.03768
$890$	19.7168	0.660908
$891$	−23.2760	−0.779777
$892$	−5.39373	−0.180595
$893$	40.7071	1.36221
$894$	3.58583	0.119928
$895$	47.0374	1.57229
$896$	−4.69202	−0.156749
$897$	6.24326	0.208456
$898$	−27.9608	−0.933063
$899$	51.4510	1.71599
$900$	−27.7875	−0.926249
$901$	−12.2881	−0.409377
$902$	16.1675	0.538317
$903$	2.75648	0.0917299
$904$	−1.59850	−0.0531653
$905$	−5.19567	−0.172710
$906$	0.0502453	0.00166929
$907$	0.643695	0.0213735	0.0106868	−	0.999943i	$-0.496598\pi$
$907$	0.643695	0.0213735	0.0106868	+	0.999943i	$0.496598\pi$
$908$	14.0543	0.466408
$909$	−13.0925	−0.434249
$910$	−103.499	−3.43097
$911$	7.38298	0.244609	0.122304	−	0.992493i	$-0.460972\pi$
$911$	7.38298	0.244609	0.122304	+	0.992493i	$0.460972\pi$
$912$	1.45712	0.0482502
$913$	33.5749	1.11117
$914$	16.0489	0.530851
$915$	10.0030	0.330688
$916$	−23.9245	−0.790489
$917$	38.2702	1.26379
$918$	1.75733	0.0580006
$919$	14.0180	0.462413	0.231206	−	0.972905i	$-0.425733\pi$
$919$	14.0180	0.462413	0.231206	+	0.972905i	$0.425733\pi$
$920$	16.5646	0.546120
$921$	−4.09352	−0.134886
$922$	18.5526	0.610996
$923$	−36.9385	−1.21585
$924$	3.19029	0.104953
$925$	−71.8926	−2.36381
$926$	24.9202	0.818929
$927$	17.6498	0.579696
$928$	−9.13706	−0.299939
$929$	12.5104	0.410451	0.205226	−	0.978715i	$-0.434207\pi$
$929$	12.5104	0.410451	0.205226	+	0.978715i	$0.434207\pi$
$930$	5.28754	0.173385
$931$	88.5855	2.90327
$932$	28.0629	0.919231
$933$	2.41896	0.0791932
$934$	−24.3153	−0.795620
$935$	−12.5399	−0.410098
$936$	17.0519	0.557359
$937$	−23.2591	−0.759840	−0.379920	−	0.925019i	$-0.624049\pi$
$937$	−23.2591	−0.759840	−0.379920	+	0.925019i	$0.624049\pi$
$938$	64.8044	2.11594
$939$	−4.00836	−0.130808
$940$	−26.2325	−0.855610
$941$	43.0243	1.40255	0.701276	−	0.712890i	$-0.252614\pi$
$941$	43.0243	1.40255	0.701276	+	0.712890i	$0.252614\pi$
$942$	−0.430567	−0.0140286
$943$	25.5864	0.833208
$944$	−1.96077	−0.0638177
$945$	−26.1661	−0.851184
$946$	6.54852	0.212911
$947$	−51.3594	−1.66896	−0.834478	−	0.551041i	$-0.814231\pi$
$947$	−51.3594	−1.66896	−0.834478	+	0.551041i	$0.814231\pi$
$948$	−2.62432	−0.0852339
$949$	−54.3443	−1.76409
$950$	55.7808	1.80977
$951$	−7.30931	−0.237021
$952$	5.62133	0.182188
$953$	45.3381	1.46865	0.734323	−	0.678801i	$-0.237500\pi$
$953$	45.3381	1.46865	0.734323	+	0.678801i	$0.237500\pi$
$954$	−30.1444	−0.975960
$955$	39.7278	1.28556
$956$	−24.0084	−0.776486
$957$	6.21265	0.200827
$958$	−18.6165	−0.601473
$959$	−43.9230	−1.41835
$960$	−0.939001	−0.0303061
$961$	0.708415	0.0228521
$962$	44.1172	1.42240
$963$	15.5007	0.499502
$964$	−14.5864	−0.469797
$965$	73.9821	2.38157
$966$	5.04892	0.162446
$967$	28.7660	0.925051	0.462525	−	0.886606i	$-0.346943\pi$
$967$	28.7660	0.925051	0.462525	+	0.886606i	$0.346943\pi$
$968$	−3.42088	−0.109951
$969$	−1.74572	−0.0560808
$970$	−39.5163	−1.26879
$971$	−41.3793	−1.32792	−0.663962	−	0.747767i	$-0.731126\pi$
$971$	−41.3793	−1.32792	−0.663962	+	0.747767i	$0.731126\pi$
$972$	6.48858	0.208121
$973$	−16.4392	−0.527016
$974$	−20.7584	−0.665142
$975$	−13.5483	−0.433891
$976$	−10.6528	−0.340988
$977$	−23.3980	−0.748570	−0.374285	−	0.927314i	$-0.622112\pi$
$977$	−23.3980	−0.748570	−0.374285	+	0.927314i	$0.622112\pi$
$978$	1.72587	0.0551873
$979$	14.2771	0.456298
$980$	−57.0863	−1.82356
$981$	21.0753	0.672883
$982$	34.7764	1.10976
$983$	−25.6829	−0.819158	−0.409579	−	0.912275i	$-0.634324\pi$
$983$	−25.6829	−0.819158	−0.409579	+	0.912275i	$0.634324\pi$
$984$	−1.45042	−0.0462377
$985$	−101.658	−3.23910
$986$	10.9468	0.348616
$987$	−7.99569	−0.254506
$988$	−34.2301	−1.08900
$989$	10.3636	0.329543
$990$	−30.7620	−0.977680
$991$	50.0799	1.59084	0.795420	−	0.606058i	$-0.207250\pi$
$991$	50.0799	1.59084	0.795420	+	0.606058i	$0.207250\pi$
$992$	−5.63102	−0.178785
$993$	−3.55868	−0.112931
$994$	−29.8722	−0.947487
$995$	−84.4898	−2.67851
$996$	−3.01208	−0.0954415
$997$	27.0344	0.856189	0.428095	−	0.903734i	$-0.359185\pi$
$997$	27.0344	0.856189	0.428095	+	0.903734i	$0.359185\pi$
$998$	−11.3448	−0.359114
$999$	11.1535	0.352880

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6022.2.a.a.1.3	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6022.2.a.a.1.3	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.246980 q^{3} +1.00000 q^{4} -3.80194 q^{5} +0.246980 q^{6} -4.69202 q^{7} +1.00000 q^{8} -2.93900 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.246980 q^{3} +1.00000 q^{4} -3.80194 q^{5} +0.246980 q^{6} -4.69202 q^{7} +1.00000 q^{8} -2.93900 q^{9} -3.80194 q^{10} -2.75302 q^{11} +0.246980 q^{12} -5.80194 q^{13} -4.69202 q^{14} -0.939001 q^{15} +1.00000 q^{16} -1.19806 q^{17} -2.93900 q^{18} +5.89977 q^{19} -3.80194 q^{20} -1.15883 q^{21} -2.75302 q^{22} -4.35690 q^{23} +0.246980 q^{24} +9.45473 q^{25} -5.80194 q^{26} -1.46681 q^{27} -4.69202 q^{28} -9.13706 q^{29} -0.939001 q^{30} -5.63102 q^{31} +1.00000 q^{32} -0.679940 q^{33} -1.19806 q^{34} +17.8388 q^{35} -2.93900 q^{36} -7.60388 q^{37} +5.89977 q^{38} -1.43296 q^{39} -3.80194 q^{40} -5.87263 q^{41} -1.15883 q^{42} -2.37867 q^{43} -2.75302 q^{44} +11.1739 q^{45} -4.35690 q^{46} +6.89977 q^{47} +0.246980 q^{48} +15.0151 q^{49} +9.45473 q^{50} -0.295897 q^{51} -5.80194 q^{52} +10.2567 q^{53} -1.46681 q^{54} +10.4668 q^{55} -4.69202 q^{56} +1.45712 q^{57} -9.13706 q^{58} -1.96077 q^{59} -0.939001 q^{60} -10.6528 q^{61} -5.63102 q^{62} +13.7899 q^{63} +1.00000 q^{64} +22.0586 q^{65} -0.679940 q^{66} -13.8116 q^{67} -1.19806 q^{68} -1.07606 q^{69} +17.8388 q^{70} +6.36658 q^{71} -2.93900 q^{72} +9.36658 q^{73} -7.60388 q^{74} +2.33513 q^{75} +5.89977 q^{76} +12.9172 q^{77} -1.43296 q^{78} -10.6256 q^{79} -3.80194 q^{80} +8.45473 q^{81} -5.87263 q^{82} -12.1957 q^{83} -1.15883 q^{84} +4.55496 q^{85} -2.37867 q^{86} -2.25667 q^{87} -2.75302 q^{88} -5.18598 q^{89} +11.1739 q^{90} +27.2228 q^{91} -4.35690 q^{92} -1.39075 q^{93} +6.89977 q^{94} -22.4306 q^{95} +0.246980 q^{96} +10.3937 q^{97} +15.0151 q^{98} +8.09113 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - 4 q^{3} + 3 q^{4} - 7 q^{5} - 4 q^{6} - 9 q^{7} + 3 q^{8} + q^{9}+O(q^{10}) \) 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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