LMFDB - Embedded newform 1806.2.a.o.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1806,2,Mod(1,1806)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1806, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1806.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1806 = 2 \cdot 3 \cdot 7 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1806.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:	$14.4209826050$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	1806.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.618034 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.618034 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.618034 q^{10} +3.61803 q^{11} +1.00000 q^{12} +0.854102 q^{13} -1.00000 q^{14} -0.618034 q^{15} +1.00000 q^{16} +3.85410 q^{17} -1.00000 q^{18} +0.763932 q^{19} -0.618034 q^{20} +1.00000 q^{21} -3.61803 q^{22} +0.763932 q^{23} -1.00000 q^{24} -4.61803 q^{25} -0.854102 q^{26} +1.00000 q^{27} +1.00000 q^{28} +7.23607 q^{29} +0.618034 q^{30} -8.94427 q^{31} -1.00000 q^{32} +3.61803 q^{33} -3.85410 q^{34} -0.618034 q^{35} +1.00000 q^{36} -5.09017 q^{37} -0.763932 q^{38} +0.854102 q^{39} +0.618034 q^{40} +10.0902 q^{41} -1.00000 q^{42} +1.00000 q^{43} +3.61803 q^{44} -0.618034 q^{45} -0.763932 q^{46} -2.09017 q^{47} +1.00000 q^{48} +1.00000 q^{49} +4.61803 q^{50} +3.85410 q^{51} +0.854102 q^{52} -9.09017 q^{53} -1.00000 q^{54} -2.23607 q^{55} -1.00000 q^{56} +0.763932 q^{57} -7.23607 q^{58} +5.52786 q^{59} -0.618034 q^{60} +2.47214 q^{61} +8.94427 q^{62} +1.00000 q^{63} +1.00000 q^{64} -0.527864 q^{65} -3.61803 q^{66} +8.18034 q^{67} +3.85410 q^{68} +0.763932 q^{69} +0.618034 q^{70} +11.8541 q^{71} -1.00000 q^{72} +5.09017 q^{73} +5.09017 q^{74} -4.61803 q^{75} +0.763932 q^{76} +3.61803 q^{77} -0.854102 q^{78} +0.854102 q^{79} -0.618034 q^{80} +1.00000 q^{81} -10.0902 q^{82} +9.70820 q^{83} +1.00000 q^{84} -2.38197 q^{85} -1.00000 q^{86} +7.23607 q^{87} -3.61803 q^{88} -5.70820 q^{89} +0.618034 q^{90} +0.854102 q^{91} +0.763932 q^{92} -8.94427 q^{93} +2.09017 q^{94} -0.472136 q^{95} -1.00000 q^{96} +7.23607 q^{97} -1.00000 q^{98} +3.61803 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 2 * q^6 + 2 * q^7 - 2 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9} - q^{10} + 5 q^{11} + 2 q^{12} - 5 q^{13} - 2 q^{14} + q^{15} + 2 q^{16} + q^{17} - 2 q^{18} + 6 q^{19} + q^{20} + 2 q^{21} - 5 q^{22} + 6 q^{23} - 2 q^{24} - 7 q^{25} + 5 q^{26} + 2 q^{27} + 2 q^{28} + 10 q^{29} - q^{30} - 2 q^{32} + 5 q^{33} - q^{34} + q^{35} + 2 q^{36} + q^{37} - 6 q^{38} - 5 q^{39} - q^{40} + 9 q^{41} - 2 q^{42} + 2 q^{43} + 5 q^{44} + q^{45} - 6 q^{46} + 7 q^{47} + 2 q^{48} + 2 q^{49} + 7 q^{50} + q^{51} - 5 q^{52} - 7 q^{53} - 2 q^{54} - 2 q^{56} + 6 q^{57} - 10 q^{58} + 20 q^{59} + q^{60} - 4 q^{61} + 2 q^{63} + 2 q^{64} - 10 q^{65} - 5 q^{66} - 6 q^{67} + q^{68} + 6 q^{69} - q^{70} + 17 q^{71} - 2 q^{72} - q^{73} - q^{74} - 7 q^{75} + 6 q^{76} + 5 q^{77} + 5 q^{78} - 5 q^{79} + q^{80} + 2 q^{81} - 9 q^{82} + 6 q^{83} + 2 q^{84} - 7 q^{85} - 2 q^{86} + 10 q^{87} - 5 q^{88} + 2 q^{89} - q^{90} - 5 q^{91} + 6 q^{92} - 7 q^{94} + 8 q^{95} - 2 q^{96} + 10 q^{97} - 2 q^{98} + 5 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 2 * q^6 + 2 * q^7 - 2 * q^8 + 2 * q^9 - q^10 + 5 * q^11 + 2 * q^12 - 5 * q^13 - 2 * q^14 + q^15 + 2 * q^16 + q^17 - 2 * q^18 + 6 * q^19 + q^20 + 2 * q^21 - 5 * q^22 + 6 * q^23 - 2 * q^24 - 7 * q^25 + 5 * q^26 + 2 * q^27 + 2 * q^28 + 10 * q^29 - q^30 - 2 * q^32 + 5 * q^33 - q^34 + q^35 + 2 * q^36 + q^37 - 6 * q^38 - 5 * q^39 - q^40 + 9 * q^41 - 2 * q^42 + 2 * q^43 + 5 * q^44 + q^45 - 6 * q^46 + 7 * q^47 + 2 * q^48 + 2 * q^49 + 7 * q^50 + q^51 - 5 * q^52 - 7 * q^53 - 2 * q^54 - 2 * q^56 + 6 * q^57 - 10 * q^58 + 20 * q^59 + q^60 - 4 * q^61 + 2 * q^63 + 2 * q^64 - 10 * q^65 - 5 * q^66 - 6 * q^67 + q^68 + 6 * q^69 - q^70 + 17 * q^71 - 2 * q^72 - q^73 - q^74 - 7 * q^75 + 6 * q^76 + 5 * q^77 + 5 * q^78 - 5 * q^79 + q^80 + 2 * q^81 - 9 * q^82 + 6 * q^83 + 2 * q^84 - 7 * q^85 - 2 * q^86 + 10 * q^87 - 5 * q^88 + 2 * q^89 - q^90 - 5 * q^91 + 6 * q^92 - 7 * q^94 + 8 * q^95 - 2 * q^96 + 10 * q^97 - 2 * q^98 + 5 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−0.618034	−0.276393	−0.138197	−	0.990405i	$-0.544131\pi$
$5$	−0.618034	−0.276393	−0.138197	+	0.990405i	$0.544131\pi$
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0.618034	0.195440
$11$	3.61803	1.09088	0.545439	−	0.838150i	$-0.316363\pi$
$11$	3.61803	1.09088	0.545439	+	0.838150i	$0.316363\pi$
$12$	1.00000	0.288675
$13$	0.854102	0.236885	0.118443	−	0.992961i	$-0.462210\pi$
$13$	0.854102	0.236885	0.118443	+	0.992961i	$0.462210\pi$
$14$	−1.00000	−0.267261
$15$	−0.618034	−0.159576
$16$	1.00000	0.250000
$17$	3.85410	0.934757	0.467379	−	0.884057i	$-0.345199\pi$
$17$	3.85410	0.934757	0.467379	+	0.884057i	$0.345199\pi$
$18$	−1.00000	−0.235702
$19$	0.763932	0.175258	0.0876290	−	0.996153i	$-0.472071\pi$
$19$	0.763932	0.175258	0.0876290	+	0.996153i	$0.472071\pi$
$20$	−0.618034	−0.138197
$21$	1.00000	0.218218
$22$	−3.61803	−0.771367
$23$	0.763932	0.159291	0.0796454	−	0.996823i	$-0.474621\pi$
$23$	0.763932	0.159291	0.0796454	+	0.996823i	$0.474621\pi$
$24$	−1.00000	−0.204124
$25$	−4.61803	−0.923607
$26$	−0.854102	−0.167503
$27$	1.00000	0.192450
$28$	1.00000	0.188982
$29$	7.23607	1.34370	0.671852	−	0.740685i	$-0.265499\pi$
$29$	7.23607	1.34370	0.671852	+	0.740685i	$0.265499\pi$
$30$	0.618034	0.112837
$31$	−8.94427	−1.60644	−0.803219	−	0.595683i	$-0.796881\pi$
$31$	−8.94427	−1.60644	−0.803219	+	0.595683i	$0.796881\pi$
$32$	−1.00000	−0.176777
$33$	3.61803	0.629819
$34$	−3.85410	−0.660973
$35$	−0.618034	−0.104467
$36$	1.00000	0.166667
$37$	−5.09017	−0.836819	−0.418409	−	0.908259i	$-0.637412\pi$
$37$	−5.09017	−0.836819	−0.418409	+	0.908259i	$0.637412\pi$
$38$	−0.763932	−0.123926
$39$	0.854102	0.136766
$40$	0.618034	0.0977198
$41$	10.0902	1.57582	0.787910	−	0.615791i	$-0.211163\pi$
$41$	10.0902	1.57582	0.787910	+	0.615791i	$0.211163\pi$
$42$	−1.00000	−0.154303
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	3.61803	0.545439
$45$	−0.618034	−0.0921311
$46$	−0.763932	−0.112636
$47$	−2.09017	−0.304883	−0.152441	−	0.988313i	$-0.548714\pi$
$47$	−2.09017	−0.304883	−0.152441	+	0.988313i	$0.548714\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	4.61803	0.653089
$51$	3.85410	0.539682
$52$	0.854102	0.118443
$53$	−9.09017	−1.24863	−0.624315	−	0.781172i	$-0.714622\pi$
$53$	−9.09017	−1.24863	−0.624315	+	0.781172i	$0.714622\pi$
$54$	−1.00000	−0.136083
$55$	−2.23607	−0.301511
$56$	−1.00000	−0.133631
$57$	0.763932	0.101185
$58$	−7.23607	−0.950142
$59$	5.52786	0.719667	0.359833	−	0.933017i	$-0.382834\pi$
$59$	5.52786	0.719667	0.359833	+	0.933017i	$0.382834\pi$
$60$	−0.618034	−0.0797878
$61$	2.47214	0.316525	0.158262	−	0.987397i	$-0.449411\pi$
$61$	2.47214	0.316525	0.158262	+	0.987397i	$0.449411\pi$
$62$	8.94427	1.13592
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	−0.527864	−0.0654735
$66$	−3.61803	−0.445349
$67$	8.18034	0.999388	0.499694	−	0.866202i	$-0.333446\pi$
$67$	8.18034	0.999388	0.499694	+	0.866202i	$0.333446\pi$
$68$	3.85410	0.467379
$69$	0.763932	0.0919666
$70$	0.618034	0.0738692
$71$	11.8541	1.40682	0.703412	−	0.710783i	$-0.251659\pi$
$71$	11.8541	1.40682	0.703412	+	0.710783i	$0.251659\pi$
$72$	−1.00000	−0.117851
$73$	5.09017	0.595759	0.297880	−	0.954603i	$-0.403721\pi$
$73$	5.09017	0.595759	0.297880	+	0.954603i	$0.403721\pi$
$74$	5.09017	0.591720
$75$	−4.61803	−0.533245
$76$	0.763932	0.0876290
$77$	3.61803	0.412313
$78$	−0.854102	−0.0967080
$79$	0.854102	0.0960940	0.0480470	−	0.998845i	$-0.484700\pi$
$79$	0.854102	0.0960940	0.0480470	+	0.998845i	$0.484700\pi$
$80$	−0.618034	−0.0690983
$81$	1.00000	0.111111
$82$	−10.0902	−1.11427
$83$	9.70820	1.06561	0.532807	−	0.846237i	$-0.321137\pi$
$83$	9.70820	1.06561	0.532807	+	0.846237i	$0.321137\pi$
$84$	1.00000	0.109109
$85$	−2.38197	−0.258360
$86$	−1.00000	−0.107833
$87$	7.23607	0.775788
$88$	−3.61803	−0.385684
$89$	−5.70820	−0.605068	−0.302534	−	0.953139i	$-0.597833\pi$
$89$	−5.70820	−0.605068	−0.302534	+	0.953139i	$0.597833\pi$
$90$	0.618034	0.0651465
$91$	0.854102	0.0895342
$92$	0.763932	0.0796454
$93$	−8.94427	−0.927478
$94$	2.09017	0.215585
$95$	−0.472136	−0.0484401
$96$	−1.00000	−0.102062
$97$	7.23607	0.734711	0.367356	−	0.930081i	$-0.380263\pi$
$97$	7.23607	0.734711	0.367356	+	0.930081i	$0.380263\pi$
$98$	−1.00000	−0.101015
$99$	3.61803	0.363626
$100$	−4.61803	−0.461803
$101$	−10.1803	−1.01298	−0.506491	−	0.862245i	$-0.669058\pi$
$101$	−10.1803	−1.01298	−0.506491	+	0.862245i	$0.669058\pi$
$102$	−3.85410	−0.381613
$103$	3.23607	0.318859	0.159430	−	0.987209i	$-0.449034\pi$
$103$	3.23607	0.318859	0.159430	+	0.987209i	$0.449034\pi$
$104$	−0.854102	−0.0837516
$105$	−0.618034	−0.0603139
$106$	9.09017	0.882915
$107$	−8.00000	−0.773389	−0.386695	−	0.922208i	$-0.626383\pi$
$107$	−8.00000	−0.773389	−0.386695	+	0.922208i	$0.626383\pi$
$108$	1.00000	0.0962250
$109$	−0.472136	−0.0452224	−0.0226112	−	0.999744i	$-0.507198\pi$
$109$	−0.472136	−0.0452224	−0.0226112	+	0.999744i	$0.507198\pi$
$110$	2.23607	0.213201
$111$	−5.09017	−0.483138
$112$	1.00000	0.0944911
$113$	6.38197	0.600365	0.300182	−	0.953882i	$-0.402952\pi$
$113$	6.38197	0.600365	0.300182	+	0.953882i	$0.402952\pi$
$114$	−0.763932	−0.0715488
$115$	−0.472136	−0.0440269
$116$	7.23607	0.671852
$117$	0.854102	0.0789618
$118$	−5.52786	−0.508881
$119$	3.85410	0.353305
$120$	0.618034	0.0564185
$121$	2.09017	0.190015
$122$	−2.47214	−0.223817
$123$	10.0902	0.909800
$124$	−8.94427	−0.803219
$125$	5.94427	0.531672
$126$	−1.00000	−0.0890871
$127$	2.56231	0.227368	0.113684	−	0.993517i	$-0.463735\pi$
$127$	2.56231	0.227368	0.113684	+	0.993517i	$0.463735\pi$
$128$	−1.00000	−0.0883883
$129$	1.00000	0.0880451
$130$	0.527864	0.0462967
$131$	21.7984	1.90453	0.952266	−	0.305268i	$-0.0987461\pi$
$131$	21.7984	1.90453	0.952266	+	0.305268i	$0.0987461\pi$
$132$	3.61803	0.314909
$133$	0.763932	0.0662413
$134$	−8.18034	−0.706674
$135$	−0.618034	−0.0531919
$136$	−3.85410	−0.330487
$137$	−13.5623	−1.15871	−0.579353	−	0.815077i	$-0.696695\pi$
$137$	−13.5623	−1.15871	−0.579353	+	0.815077i	$0.696695\pi$
$138$	−0.763932	−0.0650302
$139$	−7.32624	−0.621403	−0.310702	−	0.950507i	$-0.600564\pi$
$139$	−7.32624	−0.621403	−0.310702	+	0.950507i	$0.600564\pi$
$140$	−0.618034	−0.0522334
$141$	−2.09017	−0.176024
$142$	−11.8541	−0.994774
$143$	3.09017	0.258413
$144$	1.00000	0.0833333
$145$	−4.47214	−0.371391
$146$	−5.09017	−0.421265
$147$	1.00000	0.0824786
$148$	−5.09017	−0.418409
$149$	10.1803	0.834006	0.417003	−	0.908905i	$-0.363080\pi$
$149$	10.1803	0.834006	0.417003	+	0.908905i	$0.363080\pi$
$150$	4.61803	0.377061
$151$	−0.291796	−0.0237460	−0.0118730	−	0.999930i	$-0.503779\pi$
$151$	−0.291796	−0.0237460	−0.0118730	+	0.999930i	$0.503779\pi$
$152$	−0.763932	−0.0619631
$153$	3.85410	0.311586
$154$	−3.61803	−0.291549
$155$	5.52786	0.444009
$156$	0.854102	0.0683829
$157$	17.4164	1.38998	0.694990	−	0.719019i	$-0.255409\pi$
$157$	17.4164	1.38998	0.694990	+	0.719019i	$0.255409\pi$
$158$	−0.854102	−0.0679487
$159$	−9.09017	−0.720897
$160$	0.618034	0.0488599
$161$	0.763932	0.0602063
$162$	−1.00000	−0.0785674
$163$	−13.5623	−1.06228	−0.531141	−	0.847284i	$-0.678237\pi$
$163$	−13.5623	−1.06228	−0.531141	+	0.847284i	$0.678237\pi$
$164$	10.0902	0.787910
$165$	−2.23607	−0.174078
$166$	−9.70820	−0.753503
$167$	−17.3262	−1.34074	−0.670372	−	0.742025i	$-0.733866\pi$
$167$	−17.3262	−1.34074	−0.670372	+	0.742025i	$0.733866\pi$
$168$	−1.00000	−0.0771517
$169$	−12.2705	−0.943885
$170$	2.38197	0.182688
$171$	0.763932	0.0584193
$172$	1.00000	0.0762493
$173$	19.4164	1.47620	0.738101	−	0.674690i	$-0.235723\pi$
$173$	19.4164	1.47620	0.738101	+	0.674690i	$0.235723\pi$
$174$	−7.23607	−0.548565
$175$	−4.61803	−0.349091
$176$	3.61803	0.272720
$177$	5.52786	0.415500
$178$	5.70820	0.427848
$179$	10.4721	0.782724	0.391362	−	0.920237i	$-0.372004\pi$
$179$	10.4721	0.782724	0.391362	+	0.920237i	$0.372004\pi$
$180$	−0.618034	−0.0460655
$181$	−14.5066	−1.07827	−0.539133	−	0.842221i	$-0.681248\pi$
$181$	−14.5066	−1.07827	−0.539133	+	0.842221i	$0.681248\pi$
$182$	−0.854102	−0.0633102
$183$	2.47214	0.182746
$184$	−0.763932	−0.0563178
$185$	3.14590	0.231291
$186$	8.94427	0.655826
$187$	13.9443	1.01971
$188$	−2.09017	−0.152441
$189$	1.00000	0.0727393
$190$	0.472136	0.0342523
$191$	−21.7984	−1.57727	−0.788637	−	0.614858i	$-0.789213\pi$
$191$	−21.7984	−1.57727	−0.788637	+	0.614858i	$0.789213\pi$
$192$	1.00000	0.0721688
$193$	−3.09017	−0.222435	−0.111218	−	0.993796i	$-0.535475\pi$
$193$	−3.09017	−0.222435	−0.111218	+	0.993796i	$0.535475\pi$
$194$	−7.23607	−0.519519
$195$	−0.527864	−0.0378011
$196$	1.00000	0.0714286
$197$	17.3262	1.23444	0.617222	−	0.786789i	$-0.288258\pi$
$197$	17.3262	1.23444	0.617222	+	0.786789i	$0.288258\pi$
$198$	−3.61803	−0.257122
$199$	21.5066	1.52456	0.762280	−	0.647247i	$-0.224080\pi$
$199$	21.5066	1.52456	0.762280	+	0.647247i	$0.224080\pi$
$200$	4.61803	0.326544
$201$	8.18034	0.576997
$202$	10.1803	0.716286
$203$	7.23607	0.507872
$204$	3.85410	0.269841
$205$	−6.23607	−0.435546
$206$	−3.23607	−0.225468
$207$	0.763932	0.0530969
$208$	0.854102	0.0592213
$209$	2.76393	0.191185
$210$	0.618034	0.0426484
$211$	7.41641	0.510567	0.255283	−	0.966866i	$-0.417831\pi$
$211$	7.41641	0.510567	0.255283	+	0.966866i	$0.417831\pi$
$212$	−9.09017	−0.624315
$213$	11.8541	0.812230
$214$	8.00000	0.546869
$215$	−0.618034	−0.0421496
$216$	−1.00000	−0.0680414
$217$	−8.94427	−0.607177
$218$	0.472136	0.0319771
$219$	5.09017	0.343962
$220$	−2.23607	−0.150756
$221$	3.29180	0.221430
$222$	5.09017	0.341630
$223$	−2.43769	−0.163240	−0.0816200	−	0.996664i	$-0.526009\pi$
$223$	−2.43769	−0.163240	−0.0816200	+	0.996664i	$0.526009\pi$
$224$	−1.00000	−0.0668153
$225$	−4.61803	−0.307869
$226$	−6.38197	−0.424522
$227$	−25.0344	−1.66159	−0.830797	−	0.556575i	$-0.812115\pi$
$227$	−25.0344	−1.66159	−0.830797	+	0.556575i	$0.812115\pi$
$228$	0.763932	0.0505926
$229$	−11.0902	−0.732859	−0.366430	−	0.930446i	$-0.619420\pi$
$229$	−11.0902	−0.732859	−0.366430	+	0.930446i	$0.619420\pi$
$230$	0.472136	0.0311317
$231$	3.61803	0.238049
$232$	−7.23607	−0.475071
$233$	−4.32624	−0.283421	−0.141711	−	0.989908i	$-0.545260\pi$
$233$	−4.32624	−0.283421	−0.141711	+	0.989908i	$0.545260\pi$
$234$	−0.854102	−0.0558344
$235$	1.29180	0.0842675
$236$	5.52786	0.359833
$237$	0.854102	0.0554799
$238$	−3.85410	−0.249824
$239$	−3.41641	−0.220989	−0.110495	−	0.993877i	$-0.535243\pi$
$239$	−3.41641	−0.220989	−0.110495	+	0.993877i	$0.535243\pi$
$240$	−0.618034	−0.0398939
$241$	20.3820	1.31292	0.656459	−	0.754362i	$-0.272054\pi$
$241$	20.3820	1.31292	0.656459	+	0.754362i	$0.272054\pi$
$242$	−2.09017	−0.134361
$243$	1.00000	0.0641500
$244$	2.47214	0.158262
$245$	−0.618034	−0.0394847
$246$	−10.0902	−0.643326
$247$	0.652476	0.0415160
$248$	8.94427	0.567962
$249$	9.70820	0.615232
$250$	−5.94427	−0.375949
$251$	−7.52786	−0.475155	−0.237577	−	0.971369i	$-0.576353\pi$
$251$	−7.52786	−0.475155	−0.237577	+	0.971369i	$0.576353\pi$
$252$	1.00000	0.0629941
$253$	2.76393	0.173767
$254$	−2.56231	−0.160773
$255$	−2.38197	−0.149164
$256$	1.00000	0.0625000
$257$	5.23607	0.326617	0.163308	−	0.986575i	$-0.447783\pi$
$257$	5.23607	0.326617	0.163308	+	0.986575i	$0.447783\pi$
$258$	−1.00000	−0.0622573
$259$	−5.09017	−0.316288
$260$	−0.527864	−0.0327367
$261$	7.23607	0.447901
$262$	−21.7984	−1.34671
$263$	5.38197	0.331866	0.165933	−	0.986137i	$-0.446936\pi$
$263$	5.38197	0.331866	0.165933	+	0.986137i	$0.446936\pi$
$264$	−3.61803	−0.222675
$265$	5.61803	0.345113
$266$	−0.763932	−0.0468397
$267$	−5.70820	−0.349336
$268$	8.18034	0.499694
$269$	13.8885	0.846799	0.423400	−	0.905943i	$-0.360837\pi$
$269$	13.8885	0.846799	0.423400	+	0.905943i	$0.360837\pi$
$270$	0.618034	0.0376124
$271$	2.76393	0.167897	0.0839485	−	0.996470i	$-0.473247\pi$
$271$	2.76393	0.167897	0.0839485	+	0.996470i	$0.473247\pi$
$272$	3.85410	0.233689
$273$	0.854102	0.0516926
$274$	13.5623	0.819329
$275$	−16.7082	−1.00754
$276$	0.763932	0.0459833
$277$	−1.38197	−0.0830343	−0.0415171	−	0.999138i	$-0.513219\pi$
$277$	−1.38197	−0.0830343	−0.0415171	+	0.999138i	$0.513219\pi$
$278$	7.32624	0.439399
$279$	−8.94427	−0.535480
$280$	0.618034	0.0369346
$281$	20.7639	1.23867	0.619336	−	0.785126i	$-0.287402\pi$
$281$	20.7639	1.23867	0.619336	+	0.785126i	$0.287402\pi$
$282$	2.09017	0.124468
$283$	−8.50658	−0.505664	−0.252832	−	0.967510i	$-0.581362\pi$
$283$	−8.50658	−0.505664	−0.252832	+	0.967510i	$0.581362\pi$
$284$	11.8541	0.703412
$285$	−0.472136	−0.0279669
$286$	−3.09017	−0.182726
$287$	10.0902	0.595604
$288$	−1.00000	−0.0589256
$289$	−2.14590	−0.126229
$290$	4.47214	0.262613
$291$	7.23607	0.424186
$292$	5.09017	0.297880
$293$	−13.2361	−0.773259	−0.386630	−	0.922235i	$-0.626361\pi$
$293$	−13.2361	−0.773259	−0.386630	+	0.922235i	$0.626361\pi$
$294$	−1.00000	−0.0583212
$295$	−3.41641	−0.198911
$296$	5.09017	0.295860
$297$	3.61803	0.209940
$298$	−10.1803	−0.589731
$299$	0.652476	0.0377337
$300$	−4.61803	−0.266622
$301$	1.00000	0.0576390
$302$	0.291796	0.0167910
$303$	−10.1803	−0.584845
$304$	0.763932	0.0438145
$305$	−1.52786	−0.0874852
$306$	−3.85410	−0.220324
$307$	16.0000	0.913168	0.456584	−	0.889680i	$-0.349073\pi$
$307$	16.0000	0.913168	0.456584	+	0.889680i	$0.349073\pi$
$308$	3.61803	0.206157
$309$	3.23607	0.184093
$310$	−5.52786	−0.313962
$311$	5.27051	0.298863	0.149432	−	0.988772i	$-0.452256\pi$
$311$	5.27051	0.298863	0.149432	+	0.988772i	$0.452256\pi$
$312$	−0.854102	−0.0483540
$313$	12.5066	0.706914	0.353457	−	0.935451i	$-0.385006\pi$
$313$	12.5066	0.706914	0.353457	+	0.935451i	$0.385006\pi$
$314$	−17.4164	−0.982865
$315$	−0.618034	−0.0348223
$316$	0.854102	0.0480470
$317$	−15.7984	−0.887325	−0.443663	−	0.896194i	$-0.646321\pi$
$317$	−15.7984	−0.887325	−0.443663	+	0.896194i	$0.646321\pi$
$318$	9.09017	0.509751
$319$	26.1803	1.46582
$320$	−0.618034	−0.0345492
$321$	−8.00000	−0.446516
$322$	−0.763932	−0.0425723
$323$	2.94427	0.163824
$324$	1.00000	0.0555556
$325$	−3.94427	−0.218789
$326$	13.5623	0.751147
$327$	−0.472136	−0.0261092
$328$	−10.0902	−0.557136
$329$	−2.09017	−0.115235
$330$	2.23607	0.123091
$331$	−20.3820	−1.12029	−0.560147	−	0.828393i	$-0.689255\pi$
$331$	−20.3820	−1.12029	−0.560147	+	0.828393i	$0.689255\pi$
$332$	9.70820	0.532807
$333$	−5.09017	−0.278940
$334$	17.3262	0.948050
$335$	−5.05573	−0.276224
$336$	1.00000	0.0545545
$337$	13.2705	0.722891	0.361445	−	0.932393i	$-0.382283\pi$
$337$	13.2705	0.722891	0.361445	+	0.932393i	$0.382283\pi$
$338$	12.2705	0.667428
$339$	6.38197	0.346621
$340$	−2.38197	−0.129180
$341$	−32.3607	−1.75243
$342$	−0.763932	−0.0413087
$343$	1.00000	0.0539949
$344$	−1.00000	−0.0539164
$345$	−0.472136	−0.0254189
$346$	−19.4164	−1.04383
$347$	−15.4164	−0.827596	−0.413798	−	0.910369i	$-0.635798\pi$
$347$	−15.4164	−0.827596	−0.413798	+	0.910369i	$0.635798\pi$
$348$	7.23607	0.387894
$349$	−10.2918	−0.550907	−0.275454	−	0.961314i	$-0.588828\pi$
$349$	−10.2918	−0.550907	−0.275454	+	0.961314i	$0.588828\pi$
$350$	4.61803	0.246844
$351$	0.854102	0.0455886
$352$	−3.61803	−0.192842
$353$	−26.9443	−1.43410	−0.717049	−	0.697022i	$-0.754508\pi$
$353$	−26.9443	−1.43410	−0.717049	+	0.697022i	$0.754508\pi$
$354$	−5.52786	−0.293803
$355$	−7.32624	−0.388836
$356$	−5.70820	−0.302534
$357$	3.85410	0.203981
$358$	−10.4721	−0.553470
$359$	−8.29180	−0.437624	−0.218812	−	0.975767i	$-0.570218\pi$
$359$	−8.29180	−0.437624	−0.218812	+	0.975767i	$0.570218\pi$
$360$	0.618034	0.0325733
$361$	−18.4164	−0.969285
$362$	14.5066	0.762449
$363$	2.09017	0.109705
$364$	0.854102	0.0447671
$365$	−3.14590	−0.164664
$366$	−2.47214	−0.129221
$367$	−18.6525	−0.973651	−0.486826	−	0.873499i	$-0.661845\pi$
$367$	−18.6525	−0.973651	−0.486826	+	0.873499i	$0.661845\pi$
$368$	0.763932	0.0398227
$369$	10.0902	0.525273
$370$	−3.14590	−0.163547
$371$	−9.09017	−0.471938
$372$	−8.94427	−0.463739
$373$	−28.3820	−1.46956	−0.734781	−	0.678304i	$-0.762715\pi$
$373$	−28.3820	−1.46956	−0.734781	+	0.678304i	$0.762715\pi$
$374$	−13.9443	−0.721041
$375$	5.94427	0.306961
$376$	2.09017	0.107792
$377$	6.18034	0.318304
$378$	−1.00000	−0.0514344
$379$	−23.8885	−1.22707	−0.613536	−	0.789667i	$-0.710253\pi$
$379$	−23.8885	−1.22707	−0.613536	+	0.789667i	$0.710253\pi$
$380$	−0.472136	−0.0242201
$381$	2.56231	0.131271
$382$	21.7984	1.11530
$383$	−21.5967	−1.10354	−0.551771	−	0.833996i	$-0.686048\pi$
$383$	−21.5967	−1.10354	−0.551771	+	0.833996i	$0.686048\pi$
$384$	−1.00000	−0.0510310
$385$	−2.23607	−0.113961
$386$	3.09017	0.157286
$387$	1.00000	0.0508329
$388$	7.23607	0.367356
$389$	35.7771	1.81397	0.906985	−	0.421163i	$-0.138378\pi$
$389$	35.7771	1.81397	0.906985	+	0.421163i	$0.138378\pi$
$390$	0.527864	0.0267294
$391$	2.94427	0.148898
$392$	−1.00000	−0.0505076
$393$	21.7984	1.09958
$394$	−17.3262	−0.872883
$395$	−0.527864	−0.0265597
$396$	3.61803	0.181813
$397$	−28.4721	−1.42898	−0.714488	−	0.699648i	$-0.753340\pi$
$397$	−28.4721	−1.42898	−0.714488	+	0.699648i	$0.753340\pi$
$398$	−21.5066	−1.07803
$399$	0.763932	0.0382444
$400$	−4.61803	−0.230902
$401$	25.1246	1.25466	0.627332	−	0.778752i	$-0.284147\pi$
$401$	25.1246	1.25466	0.627332	+	0.778752i	$0.284147\pi$
$402$	−8.18034	−0.407998
$403$	−7.63932	−0.380542
$404$	−10.1803	−0.506491
$405$	−0.618034	−0.0307104
$406$	−7.23607	−0.359120
$407$	−18.4164	−0.912867
$408$	−3.85410	−0.190806
$409$	−33.7426	−1.66847	−0.834233	−	0.551412i	$-0.814089\pi$
$409$	−33.7426	−1.66847	−0.834233	+	0.551412i	$0.814089\pi$
$410$	6.23607	0.307977
$411$	−13.5623	−0.668979
$412$	3.23607	0.159430
$413$	5.52786	0.272008
$414$	−0.763932	−0.0375452
$415$	−6.00000	−0.294528
$416$	−0.854102	−0.0418758
$417$	−7.32624	−0.358767
$418$	−2.76393	−0.135188
$419$	−16.1459	−0.788779	−0.394389	−	0.918943i	$-0.629044\pi$
$419$	−16.1459	−0.788779	−0.394389	+	0.918943i	$0.629044\pi$
$420$	−0.618034	−0.0301570
$421$	−1.05573	−0.0514530	−0.0257265	−	0.999669i	$-0.508190\pi$
$421$	−1.05573	−0.0514530	−0.0257265	+	0.999669i	$0.508190\pi$
$422$	−7.41641	−0.361025
$423$	−2.09017	−0.101628
$424$	9.09017	0.441458
$425$	−17.7984	−0.863348
$426$	−11.8541	−0.574333
$427$	2.47214	0.119635
$428$	−8.00000	−0.386695
$429$	3.09017	0.149195
$430$	0.618034	0.0298042
$431$	−13.1246	−0.632190	−0.316095	−	0.948727i	$-0.602372\pi$
$431$	−13.1246	−0.632190	−0.316095	+	0.948727i	$0.602372\pi$
$432$	1.00000	0.0481125
$433$	20.4721	0.983828	0.491914	−	0.870644i	$-0.336297\pi$
$433$	20.4721	0.983828	0.491914	+	0.870644i	$0.336297\pi$
$434$	8.94427	0.429339
$435$	−4.47214	−0.214423
$436$	−0.472136	−0.0226112
$437$	0.583592	0.0279170
$438$	−5.09017	−0.243218
$439$	−2.47214	−0.117989	−0.0589943	−	0.998258i	$-0.518789\pi$
$439$	−2.47214	−0.117989	−0.0589943	+	0.998258i	$0.518789\pi$
$440$	2.23607	0.106600
$441$	1.00000	0.0476190
$442$	−3.29180	−0.156575
$443$	−20.9098	−0.993456	−0.496728	−	0.867906i	$-0.665465\pi$
$443$	−20.9098	−0.993456	−0.496728	+	0.867906i	$0.665465\pi$
$444$	−5.09017	−0.241569
$445$	3.52786	0.167237
$446$	2.43769	0.115428
$447$	10.1803	0.481514
$448$	1.00000	0.0472456
$449$	22.2148	1.04838	0.524190	−	0.851601i	$-0.324368\pi$
$449$	22.2148	1.04838	0.524190	+	0.851601i	$0.324368\pi$
$450$	4.61803	0.217696
$451$	36.5066	1.71903
$452$	6.38197	0.300182
$453$	−0.291796	−0.0137098
$454$	25.0344	1.17492
$455$	−0.527864	−0.0247466
$456$	−0.763932	−0.0357744
$457$	−29.7082	−1.38969	−0.694846	−	0.719159i	$-0.744527\pi$
$457$	−29.7082	−1.38969	−0.694846	+	0.719159i	$0.744527\pi$
$458$	11.0902	0.518210
$459$	3.85410	0.179894
$460$	−0.472136	−0.0220135
$461$	−21.8885	−1.01945	−0.509726	−	0.860337i	$-0.670253\pi$
$461$	−21.8885	−1.01945	−0.509726	+	0.860337i	$0.670253\pi$
$462$	−3.61803	−0.168326
$463$	−17.7082	−0.822970	−0.411485	−	0.911417i	$-0.634990\pi$
$463$	−17.7082	−0.822970	−0.411485	+	0.911417i	$0.634990\pi$
$464$	7.23607	0.335926
$465$	5.52786	0.256349
$466$	4.32624	0.200409
$467$	1.38197	0.0639498	0.0319749	−	0.999489i	$-0.489820\pi$
$467$	1.38197	0.0639498	0.0319749	+	0.999489i	$0.489820\pi$
$468$	0.854102	0.0394809
$469$	8.18034	0.377733
$470$	−1.29180	−0.0595861
$471$	17.4164	0.802506
$472$	−5.52786	−0.254441
$473$	3.61803	0.166357
$474$	−0.854102	−0.0392302
$475$	−3.52786	−0.161870
$476$	3.85410	0.176652
$477$	−9.09017	−0.416210
$478$	3.41641	0.156263
$479$	0.944272	0.0431449	0.0215724	−	0.999767i	$-0.493133\pi$
$479$	0.944272	0.0431449	0.0215724	+	0.999767i	$0.493133\pi$
$480$	0.618034	0.0282093
$481$	−4.34752	−0.198230
$482$	−20.3820	−0.928373
$483$	0.763932	0.0347601
$484$	2.09017	0.0950077
$485$	−4.47214	−0.203069
$486$	−1.00000	−0.0453609
$487$	−29.3820	−1.33142	−0.665712	−	0.746209i	$-0.731872\pi$
$487$	−29.3820	−1.33142	−0.665712	+	0.746209i	$0.731872\pi$
$488$	−2.47214	−0.111908
$489$	−13.5623	−0.613309
$490$	0.618034	0.0279199
$491$	17.2361	0.777853	0.388926	−	0.921269i	$-0.372846\pi$
$491$	17.2361	0.777853	0.388926	+	0.921269i	$0.372846\pi$
$492$	10.0902	0.454900
$493$	27.8885	1.25604
$494$	−0.652476	−0.0293563
$495$	−2.23607	−0.100504
$496$	−8.94427	−0.401610
$497$	11.8541	0.531729
$498$	−9.70820	−0.435035
$499$	−21.2705	−0.952199	−0.476099	−	0.879391i	$-0.657950\pi$
$499$	−21.2705	−0.952199	−0.476099	+	0.879391i	$0.657950\pi$
$500$	5.94427	0.265836
$501$	−17.3262	−0.774079
$502$	7.52786	0.335985
$503$	−23.2361	−1.03605	−0.518023	−	0.855367i	$-0.673332\pi$
$503$	−23.2361	−1.03605	−0.518023	+	0.855367i	$0.673332\pi$
$504$	−1.00000	−0.0445435
$505$	6.29180	0.279981
$506$	−2.76393	−0.122872
$507$	−12.2705	−0.544952
$508$	2.56231	0.113684
$509$	−17.5279	−0.776909	−0.388454	−	0.921468i	$-0.626991\pi$
$509$	−17.5279	−0.776909	−0.388454	+	0.921468i	$0.626991\pi$
$510$	2.38197	0.105475
$511$	5.09017	0.225176
$512$	−1.00000	−0.0441942
$513$	0.763932	0.0337284
$514$	−5.23607	−0.230953
$515$	−2.00000	−0.0881305
$516$	1.00000	0.0440225
$517$	−7.56231	−0.332590
$518$	5.09017	0.223649
$519$	19.4164	0.852286
$520$	0.527864	0.0231484
$521$	36.4721	1.59787	0.798937	−	0.601415i	$-0.205396\pi$
$521$	36.4721	1.59787	0.798937	+	0.601415i	$0.205396\pi$
$522$	−7.23607	−0.316714
$523$	17.0557	0.745795	0.372897	−	0.927873i	$-0.378364\pi$
$523$	17.0557	0.745795	0.372897	+	0.927873i	$0.378364\pi$
$524$	21.7984	0.952266
$525$	−4.61803	−0.201548
$526$	−5.38197	−0.234665
$527$	−34.4721	−1.50163
$528$	3.61803	0.157455
$529$	−22.4164	−0.974626
$530$	−5.61803	−0.244032
$531$	5.52786	0.239889
$532$	0.763932	0.0331207
$533$	8.61803	0.373288
$534$	5.70820	0.247018
$535$	4.94427	0.213760
$536$	−8.18034	−0.353337
$537$	10.4721	0.451906
$538$	−13.8885	−0.598778
$539$	3.61803	0.155840
$540$	−0.618034	−0.0265959
$541$	23.3050	1.00196	0.500979	−	0.865459i	$-0.332973\pi$
$541$	23.3050	1.00196	0.500979	+	0.865459i	$0.332973\pi$
$542$	−2.76393	−0.118721
$543$	−14.5066	−0.622537
$544$	−3.85410	−0.165243
$545$	0.291796	0.0124992
$546$	−0.854102	−0.0365522
$547$	−30.1803	−1.29042	−0.645209	−	0.764006i	$-0.723230\pi$
$547$	−30.1803	−1.29042	−0.645209	+	0.764006i	$0.723230\pi$
$548$	−13.5623	−0.579353
$549$	2.47214	0.105508
$550$	16.7082	0.712440
$551$	5.52786	0.235495
$552$	−0.763932	−0.0325151
$553$	0.854102	0.0363201
$554$	1.38197	0.0587141
$555$	3.14590	0.133536
$556$	−7.32624	−0.310702
$557$	−39.9230	−1.69159	−0.845796	−	0.533507i	$-0.820874\pi$
$557$	−39.9230	−1.69159	−0.845796	+	0.533507i	$0.820874\pi$
$558$	8.94427	0.378641
$559$	0.854102	0.0361247
$560$	−0.618034	−0.0261167
$561$	13.9443	0.588728
$562$	−20.7639	−0.875874
$563$	18.8328	0.793709	0.396854	−	0.917882i	$-0.370102\pi$
$563$	18.8328	0.793709	0.396854	+	0.917882i	$0.370102\pi$
$564$	−2.09017	−0.0880120
$565$	−3.94427	−0.165937
$566$	8.50658	0.357558
$567$	1.00000	0.0419961
$568$	−11.8541	−0.497387
$569$	−44.1803	−1.85214	−0.926068	−	0.377356i	$-0.876833\pi$
$569$	−44.1803	−1.85214	−0.926068	+	0.377356i	$0.876833\pi$
$570$	0.472136	0.0197756
$571$	−12.9787	−0.543142	−0.271571	−	0.962418i	$-0.587543\pi$
$571$	−12.9787	−0.543142	−0.271571	+	0.962418i	$0.587543\pi$
$572$	3.09017	0.129206
$573$	−21.7984	−0.910640
$574$	−10.0902	−0.421156
$575$	−3.52786	−0.147122
$576$	1.00000	0.0416667
$577$	19.2016	0.799374	0.399687	−	0.916652i	$-0.369119\pi$
$577$	19.2016	0.799374	0.399687	+	0.916652i	$0.369119\pi$
$578$	2.14590	0.0892576
$579$	−3.09017	−0.128423
$580$	−4.47214	−0.185695
$581$	9.70820	0.402764
$582$	−7.23607	−0.299945
$583$	−32.8885	−1.36210
$584$	−5.09017	−0.210633
$585$	−0.527864	−0.0218245
$586$	13.2361	0.546777
$587$	−25.9787	−1.07226	−0.536128	−	0.844137i	$-0.680114\pi$
$587$	−25.9787	−1.07226	−0.536128	+	0.844137i	$0.680114\pi$
$588$	1.00000	0.0412393
$589$	−6.83282	−0.281541
$590$	3.41641	0.140651
$591$	17.3262	0.712706
$592$	−5.09017	−0.209205
$593$	25.7082	1.05571	0.527855	−	0.849335i	$-0.322997\pi$
$593$	25.7082	1.05571	0.527855	+	0.849335i	$0.322997\pi$
$594$	−3.61803	−0.148450
$595$	−2.38197	−0.0976511
$596$	10.1803	0.417003
$597$	21.5066	0.880206
$598$	−0.652476	−0.0266817
$599$	−28.7639	−1.17526	−0.587631	−	0.809129i	$-0.699939\pi$
$599$	−28.7639	−1.17526	−0.587631	+	0.809129i	$0.699939\pi$
$600$	4.61803	0.188530
$601$	−13.4164	−0.547267	−0.273633	−	0.961834i	$-0.588225\pi$
$601$	−13.4164	−0.547267	−0.273633	+	0.961834i	$0.588225\pi$
$602$	−1.00000	−0.0407570
$603$	8.18034	0.333129
$604$	−0.291796	−0.0118730
$605$	−1.29180	−0.0525190
$606$	10.1803	0.413548
$607$	−30.6738	−1.24501	−0.622505	−	0.782616i	$-0.713885\pi$
$607$	−30.6738	−1.24501	−0.622505	+	0.782616i	$0.713885\pi$
$608$	−0.763932	−0.0309815
$609$	7.23607	0.293220
$610$	1.52786	0.0618614
$611$	−1.78522	−0.0722222
$612$	3.85410	0.155793
$613$	40.1803	1.62287	0.811434	−	0.584444i	$-0.198687\pi$
$613$	40.1803	1.62287	0.811434	+	0.584444i	$0.198687\pi$
$614$	−16.0000	−0.645707
$615$	−6.23607	−0.251463
$616$	−3.61803	−0.145775
$617$	12.6525	0.509369	0.254685	−	0.967024i	$-0.418028\pi$
$617$	12.6525	0.509369	0.254685	+	0.967024i	$0.418028\pi$
$618$	−3.23607	−0.130174
$619$	34.5623	1.38918	0.694588	−	0.719408i	$-0.255587\pi$
$619$	34.5623	1.38918	0.694588	+	0.719408i	$0.255587\pi$
$620$	5.52786	0.222004
$621$	0.763932	0.0306555
$622$	−5.27051	−0.211328
$623$	−5.70820	−0.228694
$624$	0.854102	0.0341914
$625$	19.4164	0.776656
$626$	−12.5066	−0.499863
$627$	2.76393	0.110381
$628$	17.4164	0.694990
$629$	−19.6180	−0.782222
$630$	0.618034	0.0246231
$631$	18.0000	0.716569	0.358284	−	0.933613i	$-0.383362\pi$
$631$	18.0000	0.716569	0.358284	+	0.933613i	$0.383362\pi$
$632$	−0.854102	−0.0339744
$633$	7.41641	0.294776
$634$	15.7984	0.627434
$635$	−1.58359	−0.0628429
$636$	−9.09017	−0.360449
$637$	0.854102	0.0338408
$638$	−26.1803	−1.03649
$639$	11.8541	0.468941
$640$	0.618034	0.0244299
$641$	32.6869	1.29106	0.645528	−	0.763737i	$-0.276637\pi$
$641$	32.6869	1.29106	0.645528	+	0.763737i	$0.276637\pi$
$642$	8.00000	0.315735
$643$	−38.6869	−1.52566	−0.762832	−	0.646597i	$-0.776191\pi$
$643$	−38.6869	−1.52566	−0.762832	+	0.646597i	$0.776191\pi$
$644$	0.763932	0.0301031
$645$	−0.618034	−0.0243351
$646$	−2.94427	−0.115841
$647$	6.47214	0.254446	0.127223	−	0.991874i	$-0.459394\pi$
$647$	6.47214	0.254446	0.127223	+	0.991874i	$0.459394\pi$
$648$	−1.00000	−0.0392837
$649$	20.0000	0.785069
$650$	3.94427	0.154707
$651$	−8.94427	−0.350554
$652$	−13.5623	−0.531141
$653$	6.47214	0.253274	0.126637	−	0.991949i	$-0.459582\pi$
$653$	6.47214	0.253274	0.126637	+	0.991949i	$0.459582\pi$
$654$	0.472136	0.0184620
$655$	−13.4721	−0.526400
$656$	10.0902	0.393955
$657$	5.09017	0.198586
$658$	2.09017	0.0814833
$659$	−46.4508	−1.80947	−0.904734	−	0.425977i	$-0.859931\pi$
$659$	−46.4508	−1.80947	−0.904734	+	0.425977i	$0.859931\pi$
$660$	−2.23607	−0.0870388
$661$	24.8541	0.966713	0.483356	−	0.875424i	$-0.339418\pi$
$661$	24.8541	0.966713	0.483356	+	0.875424i	$0.339418\pi$
$662$	20.3820	0.792168
$663$	3.29180	0.127843
$664$	−9.70820	−0.376751
$665$	−0.472136	−0.0183086
$666$	5.09017	0.197240
$667$	5.52786	0.214040
$668$	−17.3262	−0.670372
$669$	−2.43769	−0.0942467
$670$	5.05573	0.195320
$671$	8.94427	0.345290
$672$	−1.00000	−0.0385758
$673$	8.29180	0.319625	0.159813	−	0.987147i	$-0.448911\pi$
$673$	8.29180	0.319625	0.159813	+	0.987147i	$0.448911\pi$
$674$	−13.2705	−0.511161
$675$	−4.61803	−0.177748
$676$	−12.2705	−0.471943
$677$	9.41641	0.361902	0.180951	−	0.983492i	$-0.442082\pi$
$677$	9.41641	0.361902	0.180951	+	0.983492i	$0.442082\pi$
$678$	−6.38197	−0.245098
$679$	7.23607	0.277695
$680$	2.38197	0.0913442
$681$	−25.0344	−0.959322
$682$	32.3607	1.23915
$683$	10.8541	0.415321	0.207660	−	0.978201i	$-0.433415\pi$
$683$	10.8541	0.415321	0.207660	+	0.978201i	$0.433415\pi$
$684$	0.763932	0.0292097
$685$	8.38197	0.320258
$686$	−1.00000	−0.0381802
$687$	−11.0902	−0.423116
$688$	1.00000	0.0381246
$689$	−7.76393	−0.295782
$690$	0.472136	0.0179739
$691$	41.9574	1.59614	0.798068	−	0.602568i	$-0.205856\pi$
$691$	41.9574	1.59614	0.798068	+	0.602568i	$0.205856\pi$
$692$	19.4164	0.738101
$693$	3.61803	0.137438
$694$	15.4164	0.585199
$695$	4.52786	0.171752
$696$	−7.23607	−0.274282
$697$	38.8885	1.47301
$698$	10.2918	0.389550
$699$	−4.32624	−0.163633
$700$	−4.61803	−0.174545
$701$	−19.8541	−0.749879	−0.374940	−	0.927049i	$-0.622337\pi$
$701$	−19.8541	−0.749879	−0.374940	+	0.927049i	$0.622337\pi$
$702$	−0.854102	−0.0322360
$703$	−3.88854	−0.146659
$704$	3.61803	0.136360
$705$	1.29180	0.0486519
$706$	26.9443	1.01406
$707$	−10.1803	−0.382871
$708$	5.52786	0.207750
$709$	−0.291796	−0.0109586	−0.00547932	−	0.999985i	$-0.501744\pi$
$709$	−0.291796	−0.0109586	−0.00547932	+	0.999985i	$0.501744\pi$
$710$	7.32624	0.274949
$711$	0.854102	0.0320313
$712$	5.70820	0.213924
$713$	−6.83282	−0.255891
$714$	−3.85410	−0.144236
$715$	−1.90983	−0.0714236
$716$	10.4721	0.391362
$717$	−3.41641	−0.127588
$718$	8.29180	0.309447
$719$	−24.9230	−0.929471	−0.464735	−	0.885450i	$-0.653851\pi$
$719$	−24.9230	−0.929471	−0.464735	+	0.885450i	$0.653851\pi$
$720$	−0.618034	−0.0230328
$721$	3.23607	0.120517
$722$	18.4164	0.685388
$723$	20.3820	0.758013
$724$	−14.5066	−0.539133
$725$	−33.4164	−1.24105
$726$	−2.09017	−0.0775735
$727$	−3.67376	−0.136252	−0.0681261	−	0.997677i	$-0.521702\pi$
$727$	−3.67376	−0.136252	−0.0681261	+	0.997677i	$0.521702\pi$
$728$	−0.854102	−0.0316551
$729$	1.00000	0.0370370
$730$	3.14590	0.116435
$731$	3.85410	0.142549
$732$	2.47214	0.0913728
$733$	−16.3607	−0.604295	−0.302148	−	0.953261i	$-0.597704\pi$
$733$	−16.3607	−0.604295	−0.302148	+	0.953261i	$0.597704\pi$
$734$	18.6525	0.688475
$735$	−0.618034	−0.0227965
$736$	−0.763932	−0.0281589
$737$	29.5967	1.09021
$738$	−10.0902	−0.371424
$739$	−43.2148	−1.58968	−0.794841	−	0.606818i	$-0.792446\pi$
$739$	−43.2148	−1.58968	−0.794841	+	0.606818i	$0.792446\pi$
$740$	3.14590	0.115646
$741$	0.652476	0.0239693
$742$	9.09017	0.333711
$743$	17.2148	0.631549	0.315775	−	0.948834i	$-0.397736\pi$
$743$	17.2148	0.631549	0.315775	+	0.948834i	$0.397736\pi$
$744$	8.94427	0.327913
$745$	−6.29180	−0.230514
$746$	28.3820	1.03914
$747$	9.70820	0.355205
$748$	13.9443	0.509853
$749$	−8.00000	−0.292314
$750$	−5.94427	−0.217054
$751$	−2.36068	−0.0861424	−0.0430712	−	0.999072i	$-0.513714\pi$
$751$	−2.36068	−0.0861424	−0.0430712	+	0.999072i	$0.513714\pi$
$752$	−2.09017	−0.0762207
$753$	−7.52786	−0.274331
$754$	−6.18034	−0.225075
$755$	0.180340	0.00656324
$756$	1.00000	0.0363696
$757$	−9.32624	−0.338968	−0.169484	−	0.985533i	$-0.554210\pi$
$757$	−9.32624	−0.338968	−0.169484	+	0.985533i	$0.554210\pi$
$758$	23.8885	0.867671
$759$	2.76393	0.100324
$760$	0.472136	0.0171262
$761$	29.1246	1.05577	0.527883	−	0.849317i	$-0.322986\pi$
$761$	29.1246	1.05577	0.527883	+	0.849317i	$0.322986\pi$
$762$	−2.56231	−0.0928225
$763$	−0.472136	−0.0170925
$764$	−21.7984	−0.788637
$765$	−2.38197	−0.0861202
$766$	21.5967	0.780322
$767$	4.72136	0.170478
$768$	1.00000	0.0360844
$769$	33.8885	1.22205	0.611026	−	0.791610i	$-0.290757\pi$
$769$	33.8885	1.22205	0.611026	+	0.791610i	$0.290757\pi$
$770$	2.23607	0.0805823
$771$	5.23607	0.188572
$772$	−3.09017	−0.111218
$773$	−22.7426	−0.817996	−0.408998	−	0.912535i	$-0.634122\pi$
$773$	−22.7426	−0.817996	−0.408998	+	0.912535i	$0.634122\pi$
$774$	−1.00000	−0.0359443
$775$	41.3050	1.48372
$776$	−7.23607	−0.259760
$777$	−5.09017	−0.182609
$778$	−35.7771	−1.28267
$779$	7.70820	0.276175
$780$	−0.527864	−0.0189006
$781$	42.8885	1.53467
$782$	−2.94427	−0.105287
$783$	7.23607	0.258596
$784$	1.00000	0.0357143
$785$	−10.7639	−0.384181
$786$	−21.7984	−0.777522
$787$	24.3607	0.868364	0.434182	−	0.900825i	$-0.357037\pi$
$787$	24.3607	0.868364	0.434182	+	0.900825i	$0.357037\pi$
$788$	17.3262	0.617222
$789$	5.38197	0.191603
$790$	0.527864	0.0187806
$791$	6.38197	0.226917
$792$	−3.61803	−0.128561
$793$	2.11146	0.0749800
$794$	28.4721	1.01044
$795$	5.61803	0.199251
$796$	21.5066	0.762280
$797$	12.7639	0.452122	0.226061	−	0.974113i	$-0.427415\pi$
$797$	12.7639	0.452122	0.226061	+	0.974113i	$0.427415\pi$
$798$	−0.763932	−0.0270429
$799$	−8.05573	−0.284991
$800$	4.61803	0.163272
$801$	−5.70820	−0.201689
$802$	−25.1246	−0.887181
$803$	18.4164	0.649901
$804$	8.18034	0.288498
$805$	−0.472136	−0.0166406
$806$	7.63932	0.269084
$807$	13.8885	0.488900
$808$	10.1803	0.358143
$809$	33.2361	1.16852	0.584259	−	0.811567i	$-0.301385\pi$
$809$	33.2361	1.16852	0.584259	+	0.811567i	$0.301385\pi$
$810$	0.618034	0.0217155
$811$	38.9443	1.36752	0.683759	−	0.729708i	$-0.260344\pi$
$811$	38.9443	1.36752	0.683759	+	0.729708i	$0.260344\pi$
$812$	7.23607	0.253936
$813$	2.76393	0.0969353
$814$	18.4164	0.645495
$815$	8.38197	0.293607
$816$	3.85410	0.134921
$817$	0.763932	0.0267266
$818$	33.7426	1.17978
$819$	0.854102	0.0298447
$820$	−6.23607	−0.217773
$821$	−37.6869	−1.31528	−0.657641	−	0.753331i	$-0.728446\pi$
$821$	−37.6869	−1.31528	−0.657641	+	0.753331i	$0.728446\pi$
$822$	13.5623	0.473040
$823$	27.1459	0.946247	0.473123	−	0.880996i	$-0.343127\pi$
$823$	27.1459	0.946247	0.473123	+	0.880996i	$0.343127\pi$
$824$	−3.23607	−0.112734
$825$	−16.7082	−0.581705
$826$	−5.52786	−0.192339
$827$	−30.1459	−1.04828	−0.524138	−	0.851633i	$-0.675612\pi$
$827$	−30.1459	−1.04828	−0.524138	+	0.851633i	$0.675612\pi$
$828$	0.763932	0.0265485
$829$	−26.8328	−0.931942	−0.465971	−	0.884800i	$-0.654295\pi$
$829$	−26.8328	−0.931942	−0.465971	+	0.884800i	$0.654295\pi$
$830$	6.00000	0.208263
$831$	−1.38197	−0.0479399
$832$	0.854102	0.0296107
$833$	3.85410	0.133537
$834$	7.32624	0.253687
$835$	10.7082	0.370573
$836$	2.76393	0.0955926
$837$	−8.94427	−0.309159
$838$	16.1459	0.557751
$839$	−23.7082	−0.818498	−0.409249	−	0.912423i	$-0.634209\pi$
$839$	−23.7082	−0.818498	−0.409249	+	0.912423i	$0.634209\pi$
$840$	0.618034	0.0213242
$841$	23.3607	0.805541
$842$	1.05573	0.0363828
$843$	20.7639	0.715148
$844$	7.41641	0.255283
$845$	7.58359	0.260884
$846$	2.09017	0.0718615
$847$	2.09017	0.0718191
$848$	−9.09017	−0.312158
$849$	−8.50658	−0.291945
$850$	17.7984	0.610479
$851$	−3.88854	−0.133298
$852$	11.8541	0.406115
$853$	41.6312	1.42542	0.712712	−	0.701456i	$-0.247466\pi$
$853$	41.6312	1.42542	0.712712	+	0.701456i	$0.247466\pi$
$854$	−2.47214	−0.0845948
$855$	−0.472136	−0.0161467
$856$	8.00000	0.273434
$857$	3.79837	0.129750	0.0648750	−	0.997893i	$-0.479335\pi$
$857$	3.79837	0.129750	0.0648750	+	0.997893i	$0.479335\pi$
$858$	−3.09017	−0.105497
$859$	27.0557	0.923130	0.461565	−	0.887107i	$-0.347288\pi$
$859$	27.0557	0.923130	0.461565	+	0.887107i	$0.347288\pi$
$860$	−0.618034	−0.0210748
$861$	10.0902	0.343872
$862$	13.1246	0.447026
$863$	−0.450850	−0.0153471	−0.00767355	−	0.999971i	$-0.502443\pi$
$863$	−0.450850	−0.0153471	−0.00767355	+	0.999971i	$0.502443\pi$
$864$	−1.00000	−0.0340207
$865$	−12.0000	−0.408012
$866$	−20.4721	−0.695671
$867$	−2.14590	−0.0728785
$868$	−8.94427	−0.303588
$869$	3.09017	0.104827
$870$	4.47214	0.151620
$871$	6.98684	0.236740
$872$	0.472136	0.0159885
$873$	7.23607	0.244904
$874$	−0.583592	−0.0197403
$875$	5.94427	0.200953
$876$	5.09017	0.171981
$877$	−31.1246	−1.05100	−0.525502	−	0.850793i	$-0.676122\pi$
$877$	−31.1246	−1.05100	−0.525502	+	0.850793i	$0.676122\pi$
$878$	2.47214	0.0834305
$879$	−13.2361	−0.446441
$880$	−2.23607	−0.0753778
$881$	33.1459	1.11671	0.558357	−	0.829601i	$-0.311432\pi$
$881$	33.1459	1.11671	0.558357	+	0.829601i	$0.311432\pi$
$882$	−1.00000	−0.0336718
$883$	1.23607	0.0415970	0.0207985	−	0.999784i	$-0.493379\pi$
$883$	1.23607	0.0415970	0.0207985	+	0.999784i	$0.493379\pi$
$884$	3.29180	0.110715
$885$	−3.41641	−0.114841
$886$	20.9098	0.702479
$887$	6.47214	0.217313	0.108657	−	0.994079i	$-0.465345\pi$
$887$	6.47214	0.217313	0.108657	+	0.994079i	$0.465345\pi$
$888$	5.09017	0.170815
$889$	2.56231	0.0859370
$890$	−3.52786	−0.118254
$891$	3.61803	0.121209
$892$	−2.43769	−0.0816200
$893$	−1.59675	−0.0534331
$894$	−10.1803	−0.340481
$895$	−6.47214	−0.216340
$896$	−1.00000	−0.0334077
$897$	0.652476	0.0217855
$898$	−22.2148	−0.741317
$899$	−64.7214	−2.15858
$900$	−4.61803	−0.153934
$901$	−35.0344	−1.16717
$902$	−36.5066	−1.21554
$903$	1.00000	0.0332779
$904$	−6.38197	−0.212261
$905$	8.96556	0.298025
$906$	0.291796	0.00969428
$907$	−6.29180	−0.208916	−0.104458	−	0.994529i	$-0.533311\pi$
$907$	−6.29180	−0.208916	−0.104458	+	0.994529i	$0.533311\pi$
$908$	−25.0344	−0.830797
$909$	−10.1803	−0.337661
$910$	0.527864	0.0174985
$911$	−2.47214	−0.0819055	−0.0409528	−	0.999161i	$-0.513039\pi$
$911$	−2.47214	−0.0819055	−0.0409528	+	0.999161i	$0.513039\pi$
$912$	0.763932	0.0252963
$913$	35.1246	1.16245
$914$	29.7082	0.982660
$915$	−1.52786	−0.0505096
$916$	−11.0902	−0.366430
$917$	21.7984	0.719846
$918$	−3.85410	−0.127204
$919$	21.1591	0.697973	0.348986	−	0.937128i	$-0.386526\pi$
$919$	21.1591	0.697973	0.348986	+	0.937128i	$0.386526\pi$
$920$	0.472136	0.0155659
$921$	16.0000	0.527218
$922$	21.8885	0.720861
$923$	10.1246	0.333256
$924$	3.61803	0.119025
$925$	23.5066	0.772892
$926$	17.7082	0.581928
$927$	3.23607	0.106286
$928$	−7.23607	−0.237536
$929$	−18.5836	−0.609708	−0.304854	−	0.952399i	$-0.598608\pi$
$929$	−18.5836	−0.609708	−0.304854	+	0.952399i	$0.598608\pi$
$930$	−5.52786	−0.181266
$931$	0.763932	0.0250369
$932$	−4.32624	−0.141711
$933$	5.27051	0.172549
$934$	−1.38197	−0.0452193
$935$	−8.61803	−0.281840
$936$	−0.854102	−0.0279172
$937$	−11.7984	−0.385436	−0.192718	−	0.981254i	$-0.561730\pi$
$937$	−11.7984	−0.385436	−0.192718	+	0.981254i	$0.561730\pi$
$938$	−8.18034	−0.267098
$939$	12.5066	0.408137
$940$	1.29180	0.0421337
$941$	15.8197	0.515706	0.257853	−	0.966184i	$-0.416985\pi$
$941$	15.8197	0.515706	0.257853	+	0.966184i	$0.416985\pi$
$942$	−17.4164	−0.567457
$943$	7.70820	0.251014
$944$	5.52786	0.179917
$945$	−0.618034	−0.0201046
$946$	−3.61803	−0.117632
$947$	24.6869	0.802217	0.401109	−	0.916031i	$-0.368625\pi$
$947$	24.6869	0.802217	0.401109	+	0.916031i	$0.368625\pi$
$948$	0.854102	0.0277399
$949$	4.34752	0.141127
$950$	3.52786	0.114459
$951$	−15.7984	−0.512297
$952$	−3.85410	−0.124912
$953$	37.7771	1.22372	0.611860	−	0.790966i	$-0.290422\pi$
$953$	37.7771	1.22372	0.611860	+	0.790966i	$0.290422\pi$
$954$	9.09017	0.294305
$955$	13.4721	0.435948
$956$	−3.41641	−0.110495
$957$	26.1803	0.846290
$958$	−0.944272	−0.0305080
$959$	−13.5623	−0.437950
$960$	−0.618034	−0.0199470
$961$	49.0000	1.58065
$962$	4.34752	0.140170
$963$	−8.00000	−0.257796
$964$	20.3820	0.656459
$965$	1.90983	0.0614796
$966$	−0.763932	−0.0245791
$967$	−12.6738	−0.407561	−0.203780	−	0.979017i	$-0.565323\pi$
$967$	−12.6738	−0.407561	−0.203780	+	0.979017i	$0.565323\pi$
$968$	−2.09017	−0.0671806
$969$	2.94427	0.0945836
$970$	4.47214	0.143592
$971$	−17.8885	−0.574071	−0.287035	−	0.957920i	$-0.592670\pi$
$971$	−17.8885	−0.574071	−0.287035	+	0.957920i	$0.592670\pi$
$972$	1.00000	0.0320750
$973$	−7.32624	−0.234868
$974$	29.3820	0.941459
$975$	−3.94427	−0.126318
$976$	2.47214	0.0791311
$977$	−24.7639	−0.792268	−0.396134	−	0.918193i	$-0.629648\pi$
$977$	−24.7639	−0.792268	−0.396134	+	0.918193i	$0.629648\pi$
$978$	13.5623	0.433675
$979$	−20.6525	−0.660056
$980$	−0.618034	−0.0197424
$981$	−0.472136	−0.0150741
$982$	−17.2361	−0.550025
$983$	−44.1803	−1.40913	−0.704567	−	0.709637i	$-0.748859\pi$
$983$	−44.1803	−1.40913	−0.704567	+	0.709637i	$0.748859\pi$
$984$	−10.0902	−0.321663
$985$	−10.7082	−0.341192
$986$	−27.8885	−0.888152
$987$	−2.09017	−0.0665308
$988$	0.652476	0.0207580
$989$	0.763932	0.0242916
$990$	2.23607	0.0710669
$991$	40.1803	1.27637	0.638185	−	0.769883i	$-0.279685\pi$
$991$	40.1803	1.27637	0.638185	+	0.769883i	$0.279685\pi$
$992$	8.94427	0.283981
$993$	−20.3820	−0.646802
$994$	−11.8541	−0.375989
$995$	−13.2918	−0.421378
$996$	9.70820	0.307616
$997$	−1.93112	−0.0611591	−0.0305795	−	0.999532i	$-0.509735\pi$
$997$	−1.93112	−0.0611591	−0.0305795	+	0.999532i	$0.509735\pi$
$998$	21.2705	0.673306
$999$	−5.09017	−0.161046

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1806.2.a.o.1.1	✓	2
3.2	odd	2		5418.2.a.bf.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1806.2.a.o.1.1	✓	2	1.1	even	1	trivial
5418.2.a.bf.1.2		2	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1806 = 2 \cdot 3 \cdot 7 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1806.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.618034 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.618034 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.618034 q^{10} +3.61803 q^{11} +1.00000 q^{12} +0.854102 q^{13} -1.00000 q^{14} -0.618034 q^{15} +1.00000 q^{16} +3.85410 q^{17} -1.00000 q^{18} +0.763932 q^{19} -0.618034 q^{20} +1.00000 q^{21} -3.61803 q^{22} +0.763932 q^{23} -1.00000 q^{24} -4.61803 q^{25} -0.854102 q^{26} +1.00000 q^{27} +1.00000 q^{28} +7.23607 q^{29} +0.618034 q^{30} -8.94427 q^{31} -1.00000 q^{32} +3.61803 q^{33} -3.85410 q^{34} -0.618034 q^{35} +1.00000 q^{36} -5.09017 q^{37} -0.763932 q^{38} +0.854102 q^{39} +0.618034 q^{40} +10.0902 q^{41} -1.00000 q^{42} +1.00000 q^{43} +3.61803 q^{44} -0.618034 q^{45} -0.763932 q^{46} -2.09017 q^{47} +1.00000 q^{48} +1.00000 q^{49} +4.61803 q^{50} +3.85410 q^{51} +0.854102 q^{52} -9.09017 q^{53} -1.00000 q^{54} -2.23607 q^{55} -1.00000 q^{56} +0.763932 q^{57} -7.23607 q^{58} +5.52786 q^{59} -0.618034 q^{60} +2.47214 q^{61} +8.94427 q^{62} +1.00000 q^{63} +1.00000 q^{64} -0.527864 q^{65} -3.61803 q^{66} +8.18034 q^{67} +3.85410 q^{68} +0.763932 q^{69} +0.618034 q^{70} +11.8541 q^{71} -1.00000 q^{72} +5.09017 q^{73} +5.09017 q^{74} -4.61803 q^{75} +0.763932 q^{76} +3.61803 q^{77} -0.854102 q^{78} +0.854102 q^{79} -0.618034 q^{80} +1.00000 q^{81} -10.0902 q^{82} +9.70820 q^{83} +1.00000 q^{84} -2.38197 q^{85} -1.00000 q^{86} +7.23607 q^{87} -3.61803 q^{88} -5.70820 q^{89} +0.618034 q^{90} +0.854102 q^{91} +0.763932 q^{92} -8.94427 q^{93} +2.09017 q^{94} -0.472136 q^{95} -1.00000 q^{96} +7.23607 q^{97} -1.00000 q^{98} +3.61803 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 2 * q^6 + 2 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9} - q^{10} + 5 q^{11} + 2 q^{12} - 5 q^{13} - 2 q^{14} + q^{15} + 2 q^{16} + q^{17} - 2 q^{18} + 6 q^{19} + q^{20} + 2 q^{21} - 5 q^{22} + 6 q^{23} - 2 q^{24} - 7 q^{25} + 5 q^{26} + 2 q^{27} + 2 q^{28} + 10 q^{29} - q^{30} - 2 q^{32} + 5 q^{33} - q^{34} + q^{35} + 2 q^{36} + q^{37} - 6 q^{38} - 5 q^{39} - q^{40} + 9 q^{41} - 2 q^{42} + 2 q^{43} + 5 q^{44} + q^{45} - 6 q^{46} + 7 q^{47} + 2 q^{48} + 2 q^{49} + 7 q^{50} + q^{51} - 5 q^{52} - 7 q^{53} - 2 q^{54} - 2 q^{56} + 6 q^{57} - 10 q^{58} + 20 q^{59} + q^{60} - 4 q^{61} + 2 q^{63} + 2 q^{64} - 10 q^{65} - 5 q^{66} - 6 q^{67} + q^{68} + 6 q^{69} - q^{70} + 17 q^{71} - 2 q^{72} - q^{73} - q^{74} - 7 q^{75} + 6 q^{76} + 5 q^{77} + 5 q^{78} - 5 q^{79} + q^{80} + 2 q^{81} - 9 q^{82} + 6 q^{83} + 2 q^{84} - 7 q^{85} - 2 q^{86} + 10 q^{87} - 5 q^{88} + 2 q^{89} - q^{90} - 5 q^{91} + 6 q^{92} - 7 q^{94} + 8 q^{95} - 2 q^{96} + 10 q^{97} - 2 q^{98} + 5 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 2 * q^6 + 2 * q^7 - 2 * q^8 + 2 * q^9 - q^10 + 5 * q^11 + 2 * q^12 - 5 * q^13 - 2 * q^14 + q^15 + 2 * q^16 + q^17 - 2 * q^18 + 6 * q^19 + q^20 + 2 * q^21 - 5 * q^22 + 6 * q^23 - 2 * q^24 - 7 * q^25 + 5 * q^26 + 2 * q^27 + 2 * q^28 + 10 * q^29 - q^30 - 2 * q^32 + 5 * q^33 - q^34 + q^35 + 2 * q^36 + q^37 - 6 * q^38 - 5 * q^39 - q^40 + 9 * q^41 - 2 * q^42 + 2 * q^43 + 5 * q^44 + q^45 - 6 * q^46 + 7 * q^47 + 2 * q^48 + 2 * q^49 + 7 * q^50 + q^51 - 5 * q^52 - 7 * q^53 - 2 * q^54 - 2 * q^56 + 6 * q^57 - 10 * q^58 + 20 * q^59 + q^60 - 4 * q^61 + 2 * q^63 + 2 * q^64 - 10 * q^65 - 5 * q^66 - 6 * q^67 + q^68 + 6 * q^69 - q^70 + 17 * q^71 - 2 * q^72 - q^73 - q^74 - 7 * q^75 + 6 * q^76 + 5 * q^77 + 5 * q^78 - 5 * q^79 + q^80 + 2 * q^81 - 9 * q^82 + 6 * q^83 + 2 * q^84 - 7 * q^85 - 2 * q^86 + 10 * q^87 - 5 * q^88 + 2 * q^89 - q^90 - 5 * q^91 + 6 * q^92 - 7 * q^94 + 8 * q^95 - 2 * q^96 + 10 * q^97 - 2 * q^98 + 5 * q^99

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