LMFDB - Embedded newform 4026.2.a.m.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4026,2,Mod(1,4026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4026, 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("4026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4026 = 2 \cdot 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4026.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:	$32.1477718538$
Analytic rank:	$1$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	4026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.23607 q^{5} -1.00000 q^{6} -1.61803 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.23607 q^{5} -1.00000 q^{6} -1.61803 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.23607 q^{10} +1.00000 q^{11} -1.00000 q^{12} -1.85410 q^{13} -1.61803 q^{14} -1.23607 q^{15} +1.00000 q^{16} -5.38197 q^{17} +1.00000 q^{18} -2.38197 q^{19} +1.23607 q^{20} +1.61803 q^{21} +1.00000 q^{22} +2.00000 q^{23} -1.00000 q^{24} -3.47214 q^{25} -1.85410 q^{26} -1.00000 q^{27} -1.61803 q^{28} +9.70820 q^{29} -1.23607 q^{30} -7.70820 q^{31} +1.00000 q^{32} -1.00000 q^{33} -5.38197 q^{34} -2.00000 q^{35} +1.00000 q^{36} +3.14590 q^{37} -2.38197 q^{38} +1.85410 q^{39} +1.23607 q^{40} -8.47214 q^{41} +1.61803 q^{42} -5.23607 q^{43} +1.00000 q^{44} +1.23607 q^{45} +2.00000 q^{46} +5.85410 q^{47} -1.00000 q^{48} -4.38197 q^{49} -3.47214 q^{50} +5.38197 q^{51} -1.85410 q^{52} -9.09017 q^{53} -1.00000 q^{54} +1.23607 q^{55} -1.61803 q^{56} +2.38197 q^{57} +9.70820 q^{58} -5.14590 q^{59} -1.23607 q^{60} -1.00000 q^{61} -7.70820 q^{62} -1.61803 q^{63} +1.00000 q^{64} -2.29180 q^{65} -1.00000 q^{66} -11.8541 q^{67} -5.38197 q^{68} -2.00000 q^{69} -2.00000 q^{70} +7.23607 q^{71} +1.00000 q^{72} -8.47214 q^{73} +3.14590 q^{74} +3.47214 q^{75} -2.38197 q^{76} -1.61803 q^{77} +1.85410 q^{78} +13.0902 q^{79} +1.23607 q^{80} +1.00000 q^{81} -8.47214 q^{82} +15.4164 q^{83} +1.61803 q^{84} -6.65248 q^{85} -5.23607 q^{86} -9.70820 q^{87} +1.00000 q^{88} -15.2361 q^{89} +1.23607 q^{90} +3.00000 q^{91} +2.00000 q^{92} +7.70820 q^{93} +5.85410 q^{94} -2.94427 q^{95} -1.00000 q^{96} -0.673762 q^{97} -4.38197 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - q^{7} + 2 q^{8} + 2 q^{9} - 2 q^{10} + 2 q^{11} - 2 q^{12} + 3 q^{13} - q^{14} + 2 q^{15} + 2 q^{16} - 13 q^{17} + 2 q^{18} - 7 q^{19} - 2 q^{20} + q^{21} + 2 q^{22} + 4 q^{23} - 2 q^{24} + 2 q^{25} + 3 q^{26} - 2 q^{27} - q^{28} + 6 q^{29} + 2 q^{30} - 2 q^{31} + 2 q^{32} - 2 q^{33} - 13 q^{34} - 4 q^{35} + 2 q^{36} + 13 q^{37} - 7 q^{38} - 3 q^{39} - 2 q^{40} - 8 q^{41} + q^{42} - 6 q^{43} + 2 q^{44} - 2 q^{45} + 4 q^{46} + 5 q^{47} - 2 q^{48} - 11 q^{49} + 2 q^{50} + 13 q^{51} + 3 q^{52} - 7 q^{53} - 2 q^{54} - 2 q^{55} - q^{56} + 7 q^{57} + 6 q^{58} - 17 q^{59} + 2 q^{60} - 2 q^{61} - 2 q^{62} - q^{63} + 2 q^{64} - 18 q^{65} - 2 q^{66} - 17 q^{67} - 13 q^{68} - 4 q^{69} - 4 q^{70} + 10 q^{71} + 2 q^{72} - 8 q^{73} + 13 q^{74} - 2 q^{75} - 7 q^{76} - q^{77} - 3 q^{78} + 15 q^{79} - 2 q^{80} + 2 q^{81} - 8 q^{82} + 4 q^{83} + q^{84} + 18 q^{85} - 6 q^{86} - 6 q^{87} + 2 q^{88} - 26 q^{89} - 2 q^{90} + 6 q^{91} + 4 q^{92} + 2 q^{93} + 5 q^{94} + 12 q^{95} - 2 q^{96} - 17 q^{97} - 11 q^{98} + 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - q^7 + 2 * q^8 + 2 * q^9 - 2 * q^10 + 2 * q^11 - 2 * q^12 + 3 * q^13 - q^14 + 2 * q^15 + 2 * q^16 - 13 * q^17 + 2 * q^18 - 7 * q^19 - 2 * q^20 + q^21 + 2 * q^22 + 4 * q^23 - 2 * q^24 + 2 * q^25 + 3 * q^26 - 2 * q^27 - q^28 + 6 * q^29 + 2 * q^30 - 2 * q^31 + 2 * q^32 - 2 * q^33 - 13 * q^34 - 4 * q^35 + 2 * q^36 + 13 * q^37 - 7 * q^38 - 3 * q^39 - 2 * q^40 - 8 * q^41 + q^42 - 6 * q^43 + 2 * q^44 - 2 * q^45 + 4 * q^46 + 5 * q^47 - 2 * q^48 - 11 * q^49 + 2 * q^50 + 13 * q^51 + 3 * q^52 - 7 * q^53 - 2 * q^54 - 2 * q^55 - q^56 + 7 * q^57 + 6 * q^58 - 17 * q^59 + 2 * q^60 - 2 * q^61 - 2 * q^62 - q^63 + 2 * q^64 - 18 * q^65 - 2 * q^66 - 17 * q^67 - 13 * q^68 - 4 * q^69 - 4 * q^70 + 10 * q^71 + 2 * q^72 - 8 * q^73 + 13 * q^74 - 2 * q^75 - 7 * q^76 - q^77 - 3 * q^78 + 15 * q^79 - 2 * q^80 + 2 * q^81 - 8 * q^82 + 4 * q^83 + q^84 + 18 * q^85 - 6 * q^86 - 6 * q^87 + 2 * q^88 - 26 * q^89 - 2 * q^90 + 6 * q^91 + 4 * q^92 + 2 * q^93 + 5 * q^94 + 12 * q^95 - 2 * q^96 - 17 * q^97 - 11 * q^98 + 2 * 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
$5$	1.23607	0.552786	0.276393	−	0.961045i	$-0.410861\pi$
$5$	1.23607	0.552786	0.276393	+	0.961045i	$0.410861\pi$
$6$	−1.00000	−0.408248
$7$	−1.61803	−0.611559	−0.305780	−	0.952102i	$-0.598917\pi$
$7$	−1.61803	−0.611559	−0.305780	+	0.952102i	$0.598917\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.23607	0.390879
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.00000	−0.288675
$13$	−1.85410	−0.514235	−0.257118	−	0.966380i	$-0.582773\pi$
$13$	−1.85410	−0.514235	−0.257118	+	0.966380i	$0.582773\pi$
$14$	−1.61803	−0.432438
$15$	−1.23607	−0.319151
$16$	1.00000	0.250000
$17$	−5.38197	−1.30532	−0.652659	−	0.757652i	$-0.726347\pi$
$17$	−5.38197	−1.30532	−0.652659	+	0.757652i	$0.726347\pi$
$18$	1.00000	0.235702
$19$	−2.38197	−0.546460	−0.273230	−	0.961949i	$-0.588092\pi$
$19$	−2.38197	−0.546460	−0.273230	+	0.961949i	$0.588092\pi$
$20$	1.23607	0.276393
$21$	1.61803	0.353084
$22$	1.00000	0.213201
$23$	2.00000	0.417029	0.208514	−	0.978019i	$-0.433137\pi$
$23$	2.00000	0.417029	0.208514	+	0.978019i	$0.433137\pi$
$24$	−1.00000	−0.204124
$25$	−3.47214	−0.694427
$26$	−1.85410	−0.363619
$27$	−1.00000	−0.192450
$28$	−1.61803	−0.305780
$29$	9.70820	1.80277	0.901384	−	0.433020i	$-0.142552\pi$
$29$	9.70820	1.80277	0.901384	+	0.433020i	$0.142552\pi$
$30$	−1.23607	−0.225674
$31$	−7.70820	−1.38443	−0.692217	−	0.721689i	$-0.743366\pi$
$31$	−7.70820	−1.38443	−0.692217	+	0.721689i	$0.743366\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	−5.38197	−0.923000
$35$	−2.00000	−0.338062
$36$	1.00000	0.166667
$37$	3.14590	0.517182	0.258591	−	0.965987i	$-0.416742\pi$
$37$	3.14590	0.517182	0.258591	+	0.965987i	$0.416742\pi$
$38$	−2.38197	−0.386406
$39$	1.85410	0.296894
$40$	1.23607	0.195440
$41$	−8.47214	−1.32313	−0.661563	−	0.749890i	$-0.730106\pi$
$41$	−8.47214	−1.32313	−0.661563	+	0.749890i	$0.730106\pi$
$42$	1.61803	0.249668
$43$	−5.23607	−0.798493	−0.399246	−	0.916844i	$-0.630728\pi$
$43$	−5.23607	−0.798493	−0.399246	+	0.916844i	$0.630728\pi$
$44$	1.00000	0.150756
$45$	1.23607	0.184262
$46$	2.00000	0.294884
$47$	5.85410	0.853909	0.426954	−	0.904273i	$-0.359587\pi$
$47$	5.85410	0.853909	0.426954	+	0.904273i	$0.359587\pi$
$48$	−1.00000	−0.144338
$49$	−4.38197	−0.625995
$50$	−3.47214	−0.491034
$51$	5.38197	0.753626
$52$	−1.85410	−0.257118
$53$	−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
$55$	1.23607	0.166671
$56$	−1.61803	−0.216219
$57$	2.38197	0.315499
$58$	9.70820	1.27475
$59$	−5.14590	−0.669939	−0.334969	−	0.942229i	$-0.608726\pi$
$59$	−5.14590	−0.669939	−0.334969	+	0.942229i	$0.608726\pi$
$60$	−1.23607	−0.159576
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	−7.70820	−0.978943
$63$	−1.61803	−0.203853
$64$	1.00000	0.125000
$65$	−2.29180	−0.284262
$66$	−1.00000	−0.123091
$67$	−11.8541	−1.44821	−0.724105	−	0.689690i	$-0.757747\pi$
$67$	−11.8541	−1.44821	−0.724105	+	0.689690i	$0.757747\pi$
$68$	−5.38197	−0.652659
$69$	−2.00000	−0.240772
$70$	−2.00000	−0.239046
$71$	7.23607	0.858763	0.429382	−	0.903123i	$-0.358732\pi$
$71$	7.23607	0.858763	0.429382	+	0.903123i	$0.358732\pi$
$72$	1.00000	0.117851
$73$	−8.47214	−0.991589	−0.495794	−	0.868440i	$-0.665123\pi$
$73$	−8.47214	−0.991589	−0.495794	+	0.868440i	$0.665123\pi$
$74$	3.14590	0.365703
$75$	3.47214	0.400928
$76$	−2.38197	−0.273230
$77$	−1.61803	−0.184392
$78$	1.85410	0.209936
$79$	13.0902	1.47276	0.736380	−	0.676569i	$-0.236534\pi$
$79$	13.0902	1.47276	0.736380	+	0.676569i	$0.236534\pi$
$80$	1.23607	0.138197
$81$	1.00000	0.111111
$82$	−8.47214	−0.935591
$83$	15.4164	1.69217	0.846085	−	0.533048i	$-0.178953\pi$
$83$	15.4164	1.69217	0.846085	+	0.533048i	$0.178953\pi$
$84$	1.61803	0.176542
$85$	−6.65248	−0.721562
$86$	−5.23607	−0.564620
$87$	−9.70820	−1.04083
$88$	1.00000	0.106600
$89$	−15.2361	−1.61502	−0.807510	−	0.589854i	$-0.799185\pi$
$89$	−15.2361	−1.61502	−0.807510	+	0.589854i	$0.799185\pi$
$90$	1.23607	0.130293
$91$	3.00000	0.314485
$92$	2.00000	0.208514
$93$	7.70820	0.799304
$94$	5.85410	0.603805
$95$	−2.94427	−0.302076
$96$	−1.00000	−0.102062
$97$	−0.673762	−0.0684102	−0.0342051	−	0.999415i	$-0.510890\pi$
$97$	−0.673762	−0.0684102	−0.0342051	+	0.999415i	$0.510890\pi$
$98$	−4.38197	−0.442645
$99$	1.00000	0.100504
$100$	−3.47214	−0.347214
$101$	−14.1803	−1.41100	−0.705498	−	0.708712i	$-0.749277\pi$
$101$	−14.1803	−1.41100	−0.705498	+	0.708712i	$0.749277\pi$
$102$	5.38197	0.532894
$103$	13.7984	1.35959	0.679797	−	0.733400i	$-0.262068\pi$
$103$	13.7984	1.35959	0.679797	+	0.733400i	$0.262068\pi$
$104$	−1.85410	−0.181810
$105$	2.00000	0.195180
$106$	−9.09017	−0.882915
$107$	−1.85410	−0.179243	−0.0896214	−	0.995976i	$-0.528566\pi$
$107$	−1.85410	−0.179243	−0.0896214	+	0.995976i	$0.528566\pi$
$108$	−1.00000	−0.0962250
$109$	−4.85410	−0.464939	−0.232469	−	0.972604i	$-0.574681\pi$
$109$	−4.85410	−0.464939	−0.232469	+	0.972604i	$0.574681\pi$
$110$	1.23607	0.117854
$111$	−3.14590	−0.298595
$112$	−1.61803	−0.152890
$113$	−1.67376	−0.157454	−0.0787271	−	0.996896i	$-0.525086\pi$
$113$	−1.67376	−0.157454	−0.0787271	+	0.996896i	$0.525086\pi$
$114$	2.38197	0.223092
$115$	2.47214	0.230528
$116$	9.70820	0.901384
$117$	−1.85410	−0.171412
$118$	−5.14590	−0.473718
$119$	8.70820	0.798280
$120$	−1.23607	−0.112837
$121$	1.00000	0.0909091
$122$	−1.00000	−0.0905357
$123$	8.47214	0.763907
$124$	−7.70820	−0.692217
$125$	−10.4721	−0.936656
$126$	−1.61803	−0.144146
$127$	9.70820	0.861464	0.430732	−	0.902480i	$-0.358255\pi$
$127$	9.70820	0.861464	0.430732	+	0.902480i	$0.358255\pi$
$128$	1.00000	0.0883883
$129$	5.23607	0.461010
$130$	−2.29180	−0.201004
$131$	−8.61803	−0.752961	−0.376481	−	0.926425i	$-0.622866\pi$
$131$	−8.61803	−0.752961	−0.376481	+	0.926425i	$0.622866\pi$
$132$	−1.00000	−0.0870388
$133$	3.85410	0.334193
$134$	−11.8541	−1.02404
$135$	−1.23607	−0.106384
$136$	−5.38197	−0.461500
$137$	3.61803	0.309110	0.154555	−	0.987984i	$-0.450606\pi$
$137$	3.61803	0.309110	0.154555	+	0.987984i	$0.450606\pi$
$138$	−2.00000	−0.170251
$139$	−14.7639	−1.25226	−0.626130	−	0.779719i	$-0.715362\pi$
$139$	−14.7639	−1.25226	−0.626130	+	0.779719i	$0.715362\pi$
$140$	−2.00000	−0.169031
$141$	−5.85410	−0.493004
$142$	7.23607	0.607237
$143$	−1.85410	−0.155048
$144$	1.00000	0.0833333
$145$	12.0000	0.996546
$146$	−8.47214	−0.701159
$147$	4.38197	0.361418
$148$	3.14590	0.258591
$149$	6.00000	0.491539	0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000	0.491539	0.245770	+	0.969328i	$0.420959\pi$
$150$	3.47214	0.283499
$151$	−7.56231	−0.615412	−0.307706	−	0.951482i	$-0.599561\pi$
$151$	−7.56231	−0.615412	−0.307706	+	0.951482i	$0.599561\pi$
$152$	−2.38197	−0.193203
$153$	−5.38197	−0.435106
$154$	−1.61803	−0.130385
$155$	−9.52786	−0.765296
$156$	1.85410	0.148447
$157$	13.7984	1.10123	0.550615	−	0.834759i	$-0.314393\pi$
$157$	13.7984	1.10123	0.550615	+	0.834759i	$0.314393\pi$
$158$	13.0902	1.04140
$159$	9.09017	0.720897
$160$	1.23607	0.0977198
$161$	−3.23607	−0.255038
$162$	1.00000	0.0785674
$163$	−20.9443	−1.64048	−0.820241	−	0.572018i	$-0.806161\pi$
$163$	−20.9443	−1.64048	−0.820241	+	0.572018i	$0.806161\pi$
$164$	−8.47214	−0.661563
$165$	−1.23607	−0.0962278
$166$	15.4164	1.19655
$167$	12.0000	0.928588	0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000	0.928588	0.464294	+	0.885681i	$0.346308\pi$
$168$	1.61803	0.124834
$169$	−9.56231	−0.735562
$170$	−6.65248	−0.510222
$171$	−2.38197	−0.182153
$172$	−5.23607	−0.399246
$173$	13.4164	1.02003	0.510015	−	0.860165i	$-0.329640\pi$
$173$	13.4164	1.02003	0.510015	+	0.860165i	$0.329640\pi$
$174$	−9.70820	−0.735977
$175$	5.61803	0.424683
$176$	1.00000	0.0753778
$177$	5.14590	0.386789
$178$	−15.2361	−1.14199
$179$	−14.0000	−1.04641	−0.523205	−	0.852207i	$-0.675264\pi$
$179$	−14.0000	−1.04641	−0.523205	+	0.852207i	$0.675264\pi$
$180$	1.23607	0.0921311
$181$	−21.5623	−1.60271	−0.801357	−	0.598187i	$-0.795888\pi$
$181$	−21.5623	−1.60271	−0.801357	+	0.598187i	$0.795888\pi$
$182$	3.00000	0.222375
$183$	1.00000	0.0739221
$184$	2.00000	0.147442
$185$	3.88854	0.285891
$186$	7.70820	0.565193
$187$	−5.38197	−0.393568
$188$	5.85410	0.426954
$189$	1.61803	0.117695
$190$	−2.94427	−0.213600
$191$	17.4164	1.26021	0.630104	−	0.776511i	$-0.283012\pi$
$191$	17.4164	1.26021	0.630104	+	0.776511i	$0.283012\pi$
$192$	−1.00000	−0.0721688
$193$	21.9787	1.58206	0.791031	−	0.611776i	$-0.209545\pi$
$193$	21.9787	1.58206	0.791031	+	0.611776i	$0.209545\pi$
$194$	−0.673762	−0.0483733
$195$	2.29180	0.164119
$196$	−4.38197	−0.312998
$197$	−3.43769	−0.244926	−0.122463	−	0.992473i	$-0.539079\pi$
$197$	−3.43769	−0.244926	−0.122463	+	0.992473i	$0.539079\pi$
$198$	1.00000	0.0710669
$199$	3.32624	0.235791	0.117895	−	0.993026i	$-0.462385\pi$
$199$	3.32624	0.235791	0.117895	+	0.993026i	$0.462385\pi$
$200$	−3.47214	−0.245517
$201$	11.8541	0.836124
$202$	−14.1803	−0.997725
$203$	−15.7082	−1.10250
$204$	5.38197	0.376813
$205$	−10.4721	−0.731406
$206$	13.7984	0.961378
$207$	2.00000	0.139010
$208$	−1.85410	−0.128559
$209$	−2.38197	−0.164764
$210$	2.00000	0.138013
$211$	−20.1803	−1.38927	−0.694636	−	0.719361i	$-0.744435\pi$
$211$	−20.1803	−1.38927	−0.694636	+	0.719361i	$0.744435\pi$
$212$	−9.09017	−0.624315
$213$	−7.23607	−0.495807
$214$	−1.85410	−0.126744
$215$	−6.47214	−0.441396
$216$	−1.00000	−0.0680414
$217$	12.4721	0.846664
$218$	−4.85410	−0.328761
$219$	8.47214	0.572494
$220$	1.23607	0.0833357
$221$	9.97871	0.671241
$222$	−3.14590	−0.211139
$223$	−20.7639	−1.39046	−0.695228	−	0.718789i	$-0.744697\pi$
$223$	−20.7639	−1.39046	−0.695228	+	0.718789i	$0.744697\pi$
$224$	−1.61803	−0.108109
$225$	−3.47214	−0.231476
$226$	−1.67376	−0.111337
$227$	3.70820	0.246122	0.123061	−	0.992399i	$-0.460729\pi$
$227$	3.70820	0.246122	0.123061	+	0.992399i	$0.460729\pi$
$228$	2.38197	0.157750
$229$	−17.8885	−1.18211	−0.591054	−	0.806632i	$-0.701288\pi$
$229$	−17.8885	−1.18211	−0.591054	+	0.806632i	$0.701288\pi$
$230$	2.47214	0.163008
$231$	1.61803	0.106459
$232$	9.70820	0.637375
$233$	11.7984	0.772937	0.386469	−	0.922303i	$-0.373695\pi$
$233$	11.7984	0.772937	0.386469	+	0.922303i	$0.373695\pi$
$234$	−1.85410	−0.121206
$235$	7.23607	0.472029
$236$	−5.14590	−0.334969
$237$	−13.0902	−0.850298
$238$	8.70820	0.564469
$239$	−6.76393	−0.437522	−0.218761	−	0.975778i	$-0.570202\pi$
$239$	−6.76393	−0.437522	−0.218761	+	0.975778i	$0.570202\pi$
$240$	−1.23607	−0.0797878
$241$	−17.8885	−1.15230	−0.576151	−	0.817343i	$-0.695446\pi$
$241$	−17.8885	−1.15230	−0.576151	+	0.817343i	$0.695446\pi$
$242$	1.00000	0.0642824
$243$	−1.00000	−0.0641500
$244$	−1.00000	−0.0640184
$245$	−5.41641	−0.346042
$246$	8.47214	0.540164
$247$	4.41641	0.281009
$248$	−7.70820	−0.489471
$249$	−15.4164	−0.976975
$250$	−10.4721	−0.662316
$251$	−14.5066	−0.915647	−0.457824	−	0.889043i	$-0.651371\pi$
$251$	−14.5066	−0.915647	−0.457824	+	0.889043i	$0.651371\pi$
$252$	−1.61803	−0.101927
$253$	2.00000	0.125739
$254$	9.70820	0.609147
$255$	6.65248	0.416594
$256$	1.00000	0.0625000
$257$	−30.6869	−1.91420	−0.957099	−	0.289762i	$-0.906424\pi$
$257$	−30.6869	−1.91420	−0.957099	+	0.289762i	$0.906424\pi$
$258$	5.23607	0.325983
$259$	−5.09017	−0.316288
$260$	−2.29180	−0.142131
$261$	9.70820	0.600923
$262$	−8.61803	−0.532424
$263$	4.47214	0.275764	0.137882	−	0.990449i	$-0.455971\pi$
$263$	4.47214	0.275764	0.137882	+	0.990449i	$0.455971\pi$
$264$	−1.00000	−0.0615457
$265$	−11.2361	−0.690226
$266$	3.85410	0.236310
$267$	15.2361	0.932432
$268$	−11.8541	−0.724105
$269$	−10.0000	−0.609711	−0.304855	−	0.952399i	$-0.598608\pi$
$269$	−10.0000	−0.609711	−0.304855	+	0.952399i	$0.598608\pi$
$270$	−1.23607	−0.0752247
$271$	17.4164	1.05797	0.528986	−	0.848631i	$-0.322573\pi$
$271$	17.4164	1.05797	0.528986	+	0.848631i	$0.322573\pi$
$272$	−5.38197	−0.326330
$273$	−3.00000	−0.181568
$274$	3.61803	0.218573
$275$	−3.47214	−0.209378
$276$	−2.00000	−0.120386
$277$	1.81966	0.109333	0.0546664	−	0.998505i	$-0.482590\pi$
$277$	1.81966	0.109333	0.0546664	+	0.998505i	$0.482590\pi$
$278$	−14.7639	−0.885482
$279$	−7.70820	−0.461478
$280$	−2.00000	−0.119523
$281$	−0.381966	−0.0227862	−0.0113931	−	0.999935i	$-0.503627\pi$
$281$	−0.381966	−0.0227862	−0.0113931	+	0.999935i	$0.503627\pi$
$282$	−5.85410	−0.348607
$283$	7.90983	0.470191	0.235095	−	0.971972i	$-0.424460\pi$
$283$	7.90983	0.470191	0.235095	+	0.971972i	$0.424460\pi$
$284$	7.23607	0.429382
$285$	2.94427	0.174404
$286$	−1.85410	−0.109635
$287$	13.7082	0.809170
$288$	1.00000	0.0589256
$289$	11.9656	0.703856
$290$	12.0000	0.704664
$291$	0.673762	0.0394966
$292$	−8.47214	−0.495794
$293$	−15.7984	−0.922951	−0.461475	−	0.887153i	$-0.652680\pi$
$293$	−15.7984	−0.922951	−0.461475	+	0.887153i	$0.652680\pi$
$294$	4.38197	0.255561
$295$	−6.36068	−0.370333
$296$	3.14590	0.182852
$297$	−1.00000	−0.0580259
$298$	6.00000	0.347571
$299$	−3.70820	−0.214451
$300$	3.47214	0.200464
$301$	8.47214	0.488326
$302$	−7.56231	−0.435162
$303$	14.1803	0.814639
$304$	−2.38197	−0.136615
$305$	−1.23607	−0.0707770
$306$	−5.38197	−0.307667
$307$	2.76393	0.157746	0.0788730	−	0.996885i	$-0.474868\pi$
$307$	2.76393	0.157746	0.0788730	+	0.996885i	$0.474868\pi$
$308$	−1.61803	−0.0921960
$309$	−13.7984	−0.784962
$310$	−9.52786	−0.541146
$311$	−2.94427	−0.166954	−0.0834772	−	0.996510i	$-0.526603\pi$
$311$	−2.94427	−0.166954	−0.0834772	+	0.996510i	$0.526603\pi$
$312$	1.85410	0.104968
$313$	5.41641	0.306153	0.153077	−	0.988214i	$-0.451082\pi$
$313$	5.41641	0.306153	0.153077	+	0.988214i	$0.451082\pi$
$314$	13.7984	0.778687
$315$	−2.00000	−0.112687
$316$	13.0902	0.736380
$317$	30.3607	1.70523	0.852613	−	0.522543i	$-0.175017\pi$
$317$	30.3607	1.70523	0.852613	+	0.522543i	$0.175017\pi$
$318$	9.09017	0.509751
$319$	9.70820	0.543555
$320$	1.23607	0.0690983
$321$	1.85410	0.103486
$322$	−3.23607	−0.180339
$323$	12.8197	0.713305
$324$	1.00000	0.0555556
$325$	6.43769	0.357099
$326$	−20.9443	−1.16000
$327$	4.85410	0.268432
$328$	−8.47214	−0.467795
$329$	−9.47214	−0.522216
$330$	−1.23607	−0.0680433
$331$	19.3262	1.06227	0.531133	−	0.847288i	$-0.321766\pi$
$331$	19.3262	1.06227	0.531133	+	0.847288i	$0.321766\pi$
$332$	15.4164	0.846085
$333$	3.14590	0.172394
$334$	12.0000	0.656611
$335$	−14.6525	−0.800550
$336$	1.61803	0.0882710
$337$	−0.909830	−0.0495616	−0.0247808	−	0.999693i	$-0.507889\pi$
$337$	−0.909830	−0.0495616	−0.0247808	+	0.999693i	$0.507889\pi$
$338$	−9.56231	−0.520121
$339$	1.67376	0.0909063
$340$	−6.65248	−0.360781
$341$	−7.70820	−0.417423
$342$	−2.38197	−0.128802
$343$	18.4164	0.994393
$344$	−5.23607	−0.282310
$345$	−2.47214	−0.133095
$346$	13.4164	0.721271
$347$	−7.03444	−0.377629	−0.188814	−	0.982013i	$-0.560464\pi$
$347$	−7.03444	−0.377629	−0.188814	+	0.982013i	$0.560464\pi$
$348$	−9.70820	−0.520414
$349$	33.8885	1.81401	0.907006	−	0.421118i	$-0.138362\pi$
$349$	33.8885	1.81401	0.907006	+	0.421118i	$0.138362\pi$
$350$	5.61803	0.300297
$351$	1.85410	0.0989646
$352$	1.00000	0.0533002
$353$	−19.0344	−1.01310	−0.506551	−	0.862210i	$-0.669080\pi$
$353$	−19.0344	−1.01310	−0.506551	+	0.862210i	$0.669080\pi$
$354$	5.14590	0.273501
$355$	8.94427	0.474713
$356$	−15.2361	−0.807510
$357$	−8.70820	−0.460887
$358$	−14.0000	−0.739923
$359$	−14.1459	−0.746592	−0.373296	−	0.927712i	$-0.621772\pi$
$359$	−14.1459	−0.746592	−0.373296	+	0.927712i	$0.621772\pi$
$360$	1.23607	0.0651465
$361$	−13.3262	−0.701381
$362$	−21.5623	−1.13329
$363$	−1.00000	−0.0524864
$364$	3.00000	0.157243
$365$	−10.4721	−0.548137
$366$	1.00000	0.0522708
$367$	13.3820	0.698533	0.349266	−	0.937023i	$-0.386431\pi$
$367$	13.3820	0.698533	0.349266	+	0.937023i	$0.386431\pi$
$368$	2.00000	0.104257
$369$	−8.47214	−0.441042
$370$	3.88854	0.202156
$371$	14.7082	0.763612
$372$	7.70820	0.399652
$373$	27.8885	1.44401	0.722007	−	0.691886i	$-0.243220\pi$
$373$	27.8885	1.44401	0.722007	+	0.691886i	$0.243220\pi$
$374$	−5.38197	−0.278295
$375$	10.4721	0.540779
$376$	5.85410	0.301902
$377$	−18.0000	−0.927047
$378$	1.61803	0.0832227
$379$	19.7082	1.01234	0.506171	−	0.862433i	$-0.331060\pi$
$379$	19.7082	1.01234	0.506171	+	0.862433i	$0.331060\pi$
$380$	−2.94427	−0.151038
$381$	−9.70820	−0.497366
$382$	17.4164	0.891101
$383$	−10.6525	−0.544316	−0.272158	−	0.962253i	$-0.587737\pi$
$383$	−10.6525	−0.544316	−0.272158	+	0.962253i	$0.587737\pi$
$384$	−1.00000	−0.0510310
$385$	−2.00000	−0.101929
$386$	21.9787	1.11869
$387$	−5.23607	−0.266164
$388$	−0.673762	−0.0342051
$389$	−19.2148	−0.974228	−0.487114	−	0.873338i	$-0.661950\pi$
$389$	−19.2148	−0.974228	−0.487114	+	0.873338i	$0.661950\pi$
$390$	2.29180	0.116050
$391$	−10.7639	−0.544355
$392$	−4.38197	−0.221323
$393$	8.61803	0.434722
$394$	−3.43769	−0.173189
$395$	16.1803	0.814121
$396$	1.00000	0.0502519
$397$	−22.3607	−1.12225	−0.561125	−	0.827731i	$-0.689631\pi$
$397$	−22.3607	−1.12225	−0.561125	+	0.827731i	$0.689631\pi$
$398$	3.32624	0.166729
$399$	−3.85410	−0.192946
$400$	−3.47214	−0.173607
$401$	5.12461	0.255911	0.127955	−	0.991780i	$-0.459159\pi$
$401$	5.12461	0.255911	0.127955	+	0.991780i	$0.459159\pi$
$402$	11.8541	0.591229
$403$	14.2918	0.711925
$404$	−14.1803	−0.705498
$405$	1.23607	0.0614207
$406$	−15.7082	−0.779585
$407$	3.14590	0.155936
$408$	5.38197	0.266447
$409$	−3.14590	−0.155555	−0.0777773	−	0.996971i	$-0.524782\pi$
$409$	−3.14590	−0.155555	−0.0777773	+	0.996971i	$0.524782\pi$
$410$	−10.4721	−0.517182
$411$	−3.61803	−0.178464
$412$	13.7984	0.679797
$413$	8.32624	0.409707
$414$	2.00000	0.0982946
$415$	19.0557	0.935409
$416$	−1.85410	−0.0909048
$417$	14.7639	0.722993
$418$	−2.38197	−0.116506
$419$	32.7426	1.59958	0.799791	−	0.600278i	$-0.204943\pi$
$419$	32.7426	1.59958	0.799791	+	0.600278i	$0.204943\pi$
$420$	2.00000	0.0975900
$421$	22.7984	1.11112	0.555562	−	0.831475i	$-0.312503\pi$
$421$	22.7984	1.11112	0.555562	+	0.831475i	$0.312503\pi$
$422$	−20.1803	−0.982364
$423$	5.85410	0.284636
$424$	−9.09017	−0.441458
$425$	18.6869	0.906449
$426$	−7.23607	−0.350589
$427$	1.61803	0.0783022
$428$	−1.85410	−0.0896214
$429$	1.85410	0.0895169
$430$	−6.47214	−0.312114
$431$	18.6525	0.898458	0.449229	−	0.893417i	$-0.351699\pi$
$431$	18.6525	0.898458	0.449229	+	0.893417i	$0.351699\pi$
$432$	−1.00000	−0.0481125
$433$	18.4721	0.887714	0.443857	−	0.896098i	$-0.353610\pi$
$433$	18.4721	0.887714	0.443857	+	0.896098i	$0.353610\pi$
$434$	12.4721	0.598682
$435$	−12.0000	−0.575356
$436$	−4.85410	−0.232469
$437$	−4.76393	−0.227890
$438$	8.47214	0.404814
$439$	32.0000	1.52728	0.763638	−	0.645644i	$-0.223411\pi$
$439$	32.0000	1.52728	0.763638	+	0.645644i	$0.223411\pi$
$440$	1.23607	0.0589272
$441$	−4.38197	−0.208665
$442$	9.97871	0.474639
$443$	−18.3607	−0.872342	−0.436171	−	0.899864i	$-0.643666\pi$
$443$	−18.3607	−0.872342	−0.436171	+	0.899864i	$0.643666\pi$
$444$	−3.14590	−0.149298
$445$	−18.8328	−0.892761
$446$	−20.7639	−0.983201
$447$	−6.00000	−0.283790
$448$	−1.61803	−0.0764449
$449$	4.79837	0.226449	0.113225	−	0.993569i	$-0.463882\pi$
$449$	4.79837	0.226449	0.113225	+	0.993569i	$0.463882\pi$
$450$	−3.47214	−0.163678
$451$	−8.47214	−0.398937
$452$	−1.67376	−0.0787271
$453$	7.56231	0.355308
$454$	3.70820	0.174035
$455$	3.70820	0.173843
$456$	2.38197	0.111546
$457$	26.7984	1.25358	0.626788	−	0.779190i	$-0.284369\pi$
$457$	26.7984	1.25358	0.626788	+	0.779190i	$0.284369\pi$
$458$	−17.8885	−0.835877
$459$	5.38197	0.251209
$460$	2.47214	0.115264
$461$	−5.09017	−0.237073	−0.118536	−	0.992950i	$-0.537820\pi$
$461$	−5.09017	−0.237073	−0.118536	+	0.992950i	$0.537820\pi$
$462$	1.61803	0.0752778
$463$	−35.5623	−1.65272	−0.826360	−	0.563142i	$-0.809592\pi$
$463$	−35.5623	−1.65272	−0.826360	+	0.563142i	$0.809592\pi$
$464$	9.70820	0.450692
$465$	9.52786	0.441844
$466$	11.7984	0.546549
$467$	6.43769	0.297901	0.148950	−	0.988845i	$-0.452410\pi$
$467$	6.43769	0.297901	0.148950	+	0.988845i	$0.452410\pi$
$468$	−1.85410	−0.0857059
$469$	19.1803	0.885666
$470$	7.23607	0.333775
$471$	−13.7984	−0.635796
$472$	−5.14590	−0.236859
$473$	−5.23607	−0.240755
$474$	−13.0902	−0.601251
$475$	8.27051	0.379477
$476$	8.70820	0.399140
$477$	−9.09017	−0.416210
$478$	−6.76393	−0.309375
$479$	−22.8328	−1.04326	−0.521629	−	0.853172i	$-0.674675\pi$
$479$	−22.8328	−1.04326	−0.521629	+	0.853172i	$0.674675\pi$
$480$	−1.23607	−0.0564185
$481$	−5.83282	−0.265954
$482$	−17.8885	−0.814801
$483$	3.23607	0.147246
$484$	1.00000	0.0454545
$485$	−0.832816	−0.0378162
$486$	−1.00000	−0.0453609
$487$	5.61803	0.254577	0.127289	−	0.991866i	$-0.459373\pi$
$487$	5.61803	0.254577	0.127289	+	0.991866i	$0.459373\pi$
$488$	−1.00000	−0.0452679
$489$	20.9443	0.947133
$490$	−5.41641	−0.244688
$491$	17.5623	0.792576	0.396288	−	0.918126i	$-0.370298\pi$
$491$	17.5623	0.792576	0.396288	+	0.918126i	$0.370298\pi$
$492$	8.47214	0.381953
$493$	−52.2492	−2.35319
$494$	4.41641	0.198704
$495$	1.23607	0.0555571
$496$	−7.70820	−0.346109
$497$	−11.7082	−0.525185
$498$	−15.4164	−0.690826
$499$	37.3050	1.67000	0.834999	−	0.550251i	$-0.185468\pi$
$499$	37.3050	1.67000	0.834999	+	0.550251i	$0.185468\pi$
$500$	−10.4721	−0.468328
$501$	−12.0000	−0.536120
$502$	−14.5066	−0.647460
$503$	34.5410	1.54011	0.770054	−	0.637979i	$-0.220229\pi$
$503$	34.5410	1.54011	0.770054	+	0.637979i	$0.220229\pi$
$504$	−1.61803	−0.0720730
$505$	−17.5279	−0.779980
$506$	2.00000	0.0889108
$507$	9.56231	0.424677
$508$	9.70820	0.430732
$509$	37.7426	1.67291	0.836457	−	0.548033i	$-0.184623\pi$
$509$	37.7426	1.67291	0.836457	+	0.548033i	$0.184623\pi$
$510$	6.65248	0.294577
$511$	13.7082	0.606415
$512$	1.00000	0.0441942
$513$	2.38197	0.105166
$514$	−30.6869	−1.35354
$515$	17.0557	0.751565
$516$	5.23607	0.230505
$517$	5.85410	0.257463
$518$	−5.09017	−0.223649
$519$	−13.4164	−0.588915
$520$	−2.29180	−0.100502
$521$	−23.7082	−1.03868	−0.519338	−	0.854569i	$-0.673821\pi$
$521$	−23.7082	−1.03868	−0.519338	+	0.854569i	$0.673821\pi$
$522$	9.70820	0.424917
$523$	37.4164	1.63611	0.818053	−	0.575143i	$-0.195054\pi$
$523$	37.4164	1.63611	0.818053	+	0.575143i	$0.195054\pi$
$524$	−8.61803	−0.376481
$525$	−5.61803	−0.245191
$526$	4.47214	0.194994
$527$	41.4853	1.80713
$528$	−1.00000	−0.0435194
$529$	−19.0000	−0.826087
$530$	−11.2361	−0.488064
$531$	−5.14590	−0.223313
$532$	3.85410	0.167097
$533$	15.7082	0.680398
$534$	15.2361	0.659329
$535$	−2.29180	−0.0990830
$536$	−11.8541	−0.512019
$537$	14.0000	0.604145
$538$	−10.0000	−0.431131
$539$	−4.38197	−0.188745
$540$	−1.23607	−0.0531919
$541$	−33.7082	−1.44923	−0.724614	−	0.689154i	$-0.757982\pi$
$541$	−33.7082	−1.44923	−0.724614	+	0.689154i	$0.757982\pi$
$542$	17.4164	0.748099
$543$	21.5623	0.925327
$544$	−5.38197	−0.230750
$545$	−6.00000	−0.257012
$546$	−3.00000	−0.128388
$547$	−23.8885	−1.02140	−0.510700	−	0.859759i	$-0.670614\pi$
$547$	−23.8885	−1.02140	−0.510700	+	0.859759i	$0.670614\pi$
$548$	3.61803	0.154555
$549$	−1.00000	−0.0426790
$550$	−3.47214	−0.148052
$551$	−23.1246	−0.985142
$552$	−2.00000	−0.0851257
$553$	−21.1803	−0.900680
$554$	1.81966	0.0773100
$555$	−3.88854	−0.165059
$556$	−14.7639	−0.626130
$557$	−22.6525	−0.959816	−0.479908	−	0.877319i	$-0.659330\pi$
$557$	−22.6525	−0.959816	−0.479908	+	0.877319i	$0.659330\pi$
$558$	−7.70820	−0.326314
$559$	9.70820	0.410613
$560$	−2.00000	−0.0845154
$561$	5.38197	0.227227
$562$	−0.381966	−0.0161123
$563$	−10.2705	−0.432850	−0.216425	−	0.976299i	$-0.569440\pi$
$563$	−10.2705	−0.432850	−0.216425	+	0.976299i	$0.569440\pi$
$564$	−5.85410	−0.246502
$565$	−2.06888	−0.0870386
$566$	7.90983	0.332475
$567$	−1.61803	−0.0679510
$568$	7.23607	0.303619
$569$	−10.0000	−0.419222	−0.209611	−	0.977785i	$-0.567220\pi$
$569$	−10.0000	−0.419222	−0.209611	+	0.977785i	$0.567220\pi$
$570$	2.94427	0.123322
$571$	10.8328	0.453339	0.226670	−	0.973972i	$-0.427216\pi$
$571$	10.8328	0.453339	0.226670	+	0.973972i	$0.427216\pi$
$572$	−1.85410	−0.0775239
$573$	−17.4164	−0.727581
$574$	13.7082	0.572169
$575$	−6.94427	−0.289596
$576$	1.00000	0.0416667
$577$	15.2361	0.634286	0.317143	−	0.948378i	$-0.397277\pi$
$577$	15.2361	0.634286	0.317143	+	0.948378i	$0.397277\pi$
$578$	11.9656	0.497702
$579$	−21.9787	−0.913404
$580$	12.0000	0.498273
$581$	−24.9443	−1.03486
$582$	0.673762	0.0279283
$583$	−9.09017	−0.376476
$584$	−8.47214	−0.350579
$585$	−2.29180	−0.0947541
$586$	−15.7984	−0.652625
$587$	12.3607	0.510180	0.255090	−	0.966917i	$-0.417895\pi$
$587$	12.3607	0.510180	0.255090	+	0.966917i	$0.417895\pi$
$588$	4.38197	0.180709
$589$	18.3607	0.756539
$590$	−6.36068	−0.261865
$591$	3.43769	0.141408
$592$	3.14590	0.129296
$593$	−12.7426	−0.523278	−0.261639	−	0.965166i	$-0.584263\pi$
$593$	−12.7426	−0.523278	−0.261639	+	0.965166i	$0.584263\pi$
$594$	−1.00000	−0.0410305
$595$	10.7639	0.441278
$596$	6.00000	0.245770
$597$	−3.32624	−0.136134
$598$	−3.70820	−0.151640
$599$	−31.3050	−1.27909	−0.639543	−	0.768755i	$-0.720876\pi$
$599$	−31.3050	−1.27909	−0.639543	+	0.768755i	$0.720876\pi$
$600$	3.47214	0.141749
$601$	13.4164	0.547267	0.273633	−	0.961834i	$-0.411775\pi$
$601$	13.4164	0.547267	0.273633	+	0.961834i	$0.411775\pi$
$602$	8.47214	0.345298
$603$	−11.8541	−0.482736
$604$	−7.56231	−0.307706
$605$	1.23607	0.0502533
$606$	14.1803	0.576037
$607$	29.7082	1.20582	0.602909	−	0.797810i	$-0.294008\pi$
$607$	29.7082	1.20582	0.602909	+	0.797810i	$0.294008\pi$
$608$	−2.38197	−0.0966015
$609$	15.7082	0.636529
$610$	−1.23607	−0.0500469
$611$	−10.8541	−0.439110
$612$	−5.38197	−0.217553
$613$	38.1459	1.54070	0.770349	−	0.637622i	$-0.220082\pi$
$613$	38.1459	1.54070	0.770349	+	0.637622i	$0.220082\pi$
$614$	2.76393	0.111543
$615$	10.4721	0.422277
$616$	−1.61803	−0.0651924
$617$	17.1246	0.689411	0.344705	−	0.938711i	$-0.387979\pi$
$617$	17.1246	0.689411	0.344705	+	0.938711i	$0.387979\pi$
$618$	−13.7984	−0.555052
$619$	−11.0557	−0.444367	−0.222184	−	0.975005i	$-0.571318\pi$
$619$	−11.0557	−0.444367	−0.222184	+	0.975005i	$0.571318\pi$
$620$	−9.52786	−0.382648
$621$	−2.00000	−0.0802572
$622$	−2.94427	−0.118055
$623$	24.6525	0.987681
$624$	1.85410	0.0742235
$625$	4.41641	0.176656
$626$	5.41641	0.216483
$627$	2.38197	0.0951266
$628$	13.7984	0.550615
$629$	−16.9311	−0.675088
$630$	−2.00000	−0.0796819
$631$	−8.18034	−0.325654	−0.162827	−	0.986655i	$-0.552061\pi$
$631$	−8.18034	−0.325654	−0.162827	+	0.986655i	$0.552061\pi$
$632$	13.0902	0.520699
$633$	20.1803	0.802097
$634$	30.3607	1.20578
$635$	12.0000	0.476205
$636$	9.09017	0.360449
$637$	8.12461	0.321909
$638$	9.70820	0.384351
$639$	7.23607	0.286254
$640$	1.23607	0.0488599
$641$	−33.1246	−1.30834	−0.654172	−	0.756346i	$-0.726983\pi$
$641$	−33.1246	−1.30834	−0.654172	+	0.756346i	$0.726983\pi$
$642$	1.85410	0.0731756
$643$	17.3820	0.685478	0.342739	−	0.939431i	$-0.388645\pi$
$643$	17.3820	0.685478	0.342739	+	0.939431i	$0.388645\pi$
$644$	−3.23607	−0.127519
$645$	6.47214	0.254840
$646$	12.8197	0.504383
$647$	13.3475	0.524745	0.262373	−	0.964967i	$-0.415495\pi$
$647$	13.3475	0.524745	0.262373	+	0.964967i	$0.415495\pi$
$648$	1.00000	0.0392837
$649$	−5.14590	−0.201994
$650$	6.43769	0.252507
$651$	−12.4721	−0.488822
$652$	−20.9443	−0.820241
$653$	12.1459	0.475306	0.237653	−	0.971350i	$-0.423622\pi$
$653$	12.1459	0.475306	0.237653	+	0.971350i	$0.423622\pi$
$654$	4.85410	0.189810
$655$	−10.6525	−0.416227
$656$	−8.47214	−0.330781
$657$	−8.47214	−0.330530
$658$	−9.47214	−0.369262
$659$	−25.9230	−1.00982	−0.504908	−	0.863173i	$-0.668474\pi$
$659$	−25.9230	−1.00982	−0.504908	+	0.863173i	$0.668474\pi$
$660$	−1.23607	−0.0481139
$661$	−40.4721	−1.57418	−0.787092	−	0.616836i	$-0.788414\pi$
$661$	−40.4721	−1.57418	−0.787092	+	0.616836i	$0.788414\pi$
$662$	19.3262	0.751136
$663$	−9.97871	−0.387541
$664$	15.4164	0.598273
$665$	4.76393	0.184737
$666$	3.14590	0.121901
$667$	19.4164	0.751806
$668$	12.0000	0.464294
$669$	20.7639	0.802780
$670$	−14.6525	−0.566075
$671$	−1.00000	−0.0386046
$672$	1.61803	0.0624170
$673$	−13.4164	−0.517165	−0.258582	−	0.965989i	$-0.583255\pi$
$673$	−13.4164	−0.517165	−0.258582	+	0.965989i	$0.583255\pi$
$674$	−0.909830	−0.0350453
$675$	3.47214	0.133643
$676$	−9.56231	−0.367781
$677$	−6.47214	−0.248744	−0.124372	−	0.992236i	$-0.539692\pi$
$677$	−6.47214	−0.248744	−0.124372	+	0.992236i	$0.539692\pi$
$678$	1.67376	0.0642804
$679$	1.09017	0.0418369
$680$	−6.65248	−0.255111
$681$	−3.70820	−0.142099
$682$	−7.70820	−0.295162
$683$	−9.12461	−0.349144	−0.174572	−	0.984644i	$-0.555854\pi$
$683$	−9.12461	−0.349144	−0.174572	+	0.984644i	$0.555854\pi$
$684$	−2.38197	−0.0910767
$685$	4.47214	0.170872
$686$	18.4164	0.703142
$687$	17.8885	0.682491
$688$	−5.23607	−0.199623
$689$	16.8541	0.642090
$690$	−2.47214	−0.0941126
$691$	45.8885	1.74568	0.872841	−	0.488004i	$-0.162275\pi$
$691$	45.8885	1.74568	0.872841	+	0.488004i	$0.162275\pi$
$692$	13.4164	0.510015
$693$	−1.61803	−0.0614640
$694$	−7.03444	−0.267024
$695$	−18.2492	−0.692233
$696$	−9.70820	−0.367989
$697$	45.5967	1.72710
$698$	33.8885	1.28270
$699$	−11.7984	−0.446255
$700$	5.61803	0.212342
$701$	−18.2918	−0.690872	−0.345436	−	0.938442i	$-0.612269\pi$
$701$	−18.2918	−0.690872	−0.345436	+	0.938442i	$0.612269\pi$
$702$	1.85410	0.0699786
$703$	−7.49342	−0.282620
$704$	1.00000	0.0376889
$705$	−7.23607	−0.272526
$706$	−19.0344	−0.716371
$707$	22.9443	0.862908
$708$	5.14590	0.193395
$709$	−42.7426	−1.60523	−0.802617	−	0.596495i	$-0.796560\pi$
$709$	−42.7426	−1.60523	−0.802617	+	0.596495i	$0.796560\pi$
$710$	8.94427	0.335673
$711$	13.0902	0.490920
$712$	−15.2361	−0.570996
$713$	−15.4164	−0.577349
$714$	−8.70820	−0.325896
$715$	−2.29180	−0.0857083
$716$	−14.0000	−0.523205
$717$	6.76393	0.252604
$718$	−14.1459	−0.527920
$719$	15.4508	0.576219	0.288110	−	0.957597i	$-0.406973\pi$
$719$	15.4508	0.576219	0.288110	+	0.957597i	$0.406973\pi$
$720$	1.23607	0.0460655
$721$	−22.3262	−0.831473
$722$	−13.3262	−0.495951
$723$	17.8885	0.665282
$724$	−21.5623	−0.801357
$725$	−33.7082	−1.25189
$726$	−1.00000	−0.0371135
$727$	27.5066	1.02016	0.510081	−	0.860126i	$-0.329615\pi$
$727$	27.5066	1.02016	0.510081	+	0.860126i	$0.329615\pi$
$728$	3.00000	0.111187
$729$	1.00000	0.0370370
$730$	−10.4721	−0.387591
$731$	28.1803	1.04229
$732$	1.00000	0.0369611
$733$	−11.7295	−0.433239	−0.216619	−	0.976256i	$-0.569503\pi$
$733$	−11.7295	−0.433239	−0.216619	+	0.976256i	$0.569503\pi$
$734$	13.3820	0.493937
$735$	5.41641	0.199787
$736$	2.00000	0.0737210
$737$	−11.8541	−0.436651
$738$	−8.47214	−0.311864
$739$	−5.12461	−0.188512	−0.0942559	−	0.995548i	$-0.530047\pi$
$739$	−5.12461	−0.188512	−0.0942559	+	0.995548i	$0.530047\pi$
$740$	3.88854	0.142946
$741$	−4.41641	−0.162241
$742$	14.7082	0.539955
$743$	20.0000	0.733729	0.366864	−	0.930274i	$-0.380431\pi$
$743$	20.0000	0.733729	0.366864	+	0.930274i	$0.380431\pi$
$744$	7.70820	0.282596
$745$	7.41641	0.271716
$746$	27.8885	1.02107
$747$	15.4164	0.564057
$748$	−5.38197	−0.196784
$749$	3.00000	0.109618
$750$	10.4721	0.382388
$751$	−28.7984	−1.05087	−0.525434	−	0.850834i	$-0.676097\pi$
$751$	−28.7984	−1.05087	−0.525434	+	0.850834i	$0.676097\pi$
$752$	5.85410	0.213477
$753$	14.5066	0.528649
$754$	−18.0000	−0.655521
$755$	−9.34752	−0.340191
$756$	1.61803	0.0588473
$757$	−15.8885	−0.577479	−0.288739	−	0.957408i	$-0.593236\pi$
$757$	−15.8885	−0.577479	−0.288739	+	0.957408i	$0.593236\pi$
$758$	19.7082	0.715834
$759$	−2.00000	−0.0725954
$760$	−2.94427	−0.106800
$761$	−19.9230	−0.722208	−0.361104	−	0.932526i	$-0.617600\pi$
$761$	−19.9230	−0.722208	−0.361104	+	0.932526i	$0.617600\pi$
$762$	−9.70820	−0.351691
$763$	7.85410	0.284338
$764$	17.4164	0.630104
$765$	−6.65248	−0.240521
$766$	−10.6525	−0.384890
$767$	9.54102	0.344506
$768$	−1.00000	−0.0360844
$769$	51.3050	1.85010	0.925052	−	0.379841i	$-0.124021\pi$
$769$	51.3050	1.85010	0.925052	+	0.379841i	$0.124021\pi$
$770$	−2.00000	−0.0720750
$771$	30.6869	1.10516
$772$	21.9787	0.791031
$773$	39.4853	1.42019	0.710094	−	0.704107i	$-0.248653\pi$
$773$	39.4853	1.42019	0.710094	+	0.704107i	$0.248653\pi$
$774$	−5.23607	−0.188207
$775$	26.7639	0.961389
$776$	−0.673762	−0.0241866
$777$	5.09017	0.182609
$778$	−19.2148	−0.688883
$779$	20.1803	0.723036
$780$	2.29180	0.0820595
$781$	7.23607	0.258927
$782$	−10.7639	−0.384917
$783$	−9.70820	−0.346943
$784$	−4.38197	−0.156499
$785$	17.0557	0.608745
$786$	8.61803	0.307395
$787$	29.8885	1.06541	0.532706	−	0.846301i	$-0.321175\pi$
$787$	29.8885	1.06541	0.532706	+	0.846301i	$0.321175\pi$
$788$	−3.43769	−0.122463
$789$	−4.47214	−0.159212
$790$	16.1803	0.575671
$791$	2.70820	0.0962926
$792$	1.00000	0.0355335
$793$	1.85410	0.0658411
$794$	−22.3607	−0.793551
$795$	11.2361	0.398502
$796$	3.32624	0.117895
$797$	9.88854	0.350270	0.175135	−	0.984544i	$-0.443964\pi$
$797$	9.88854	0.350270	0.175135	+	0.984544i	$0.443964\pi$
$798$	−3.85410	−0.136434
$799$	−31.5066	−1.11462
$800$	−3.47214	−0.122759
$801$	−15.2361	−0.538340
$802$	5.12461	0.180956
$803$	−8.47214	−0.298975
$804$	11.8541	0.418062
$805$	−4.00000	−0.140981
$806$	14.2918	0.503407
$807$	10.0000	0.352017
$808$	−14.1803	−0.498863
$809$	12.0000	0.421898	0.210949	−	0.977497i	$-0.432345\pi$
$809$	12.0000	0.421898	0.210949	+	0.977497i	$0.432345\pi$
$810$	1.23607	0.0434310
$811$	16.0000	0.561836	0.280918	−	0.959732i	$-0.409361\pi$
$811$	16.0000	0.561836	0.280918	+	0.959732i	$0.409361\pi$
$812$	−15.7082	−0.551250
$813$	−17.4164	−0.610820
$814$	3.14590	0.110264
$815$	−25.8885	−0.906836
$816$	5.38197	0.188406
$817$	12.4721	0.436345
$818$	−3.14590	−0.109994
$819$	3.00000	0.104828
$820$	−10.4721	−0.365703
$821$	18.1803	0.634498	0.317249	−	0.948342i	$-0.397241\pi$
$821$	18.1803	0.634498	0.317249	+	0.948342i	$0.397241\pi$
$822$	−3.61803	−0.126193
$823$	−54.4721	−1.89878	−0.949390	−	0.314101i	$-0.898297\pi$
$823$	−54.4721	−1.89878	−0.949390	+	0.314101i	$0.898297\pi$
$824$	13.7984	0.480689
$825$	3.47214	0.120884
$826$	8.32624	0.289707
$827$	39.7426	1.38199	0.690994	−	0.722861i	$-0.257173\pi$
$827$	39.7426	1.38199	0.690994	+	0.722861i	$0.257173\pi$
$828$	2.00000	0.0695048
$829$	28.5410	0.991271	0.495635	−	0.868531i	$-0.334935\pi$
$829$	28.5410	0.991271	0.495635	+	0.868531i	$0.334935\pi$
$830$	19.0557	0.661434
$831$	−1.81966	−0.0631233
$832$	−1.85410	−0.0642794
$833$	23.5836	0.817123
$834$	14.7639	0.511233
$835$	14.8328	0.513311
$836$	−2.38197	−0.0823820
$837$	7.70820	0.266435
$838$	32.7426	1.13108
$839$	24.9230	0.860437	0.430219	−	0.902725i	$-0.358437\pi$
$839$	24.9230	0.860437	0.430219	+	0.902725i	$0.358437\pi$
$840$	2.00000	0.0690066
$841$	65.2492	2.24997
$842$	22.7984	0.785684
$843$	0.381966	0.0131556
$844$	−20.1803	−0.694636
$845$	−11.8197	−0.406609
$846$	5.85410	0.201268
$847$	−1.61803	−0.0555963
$848$	−9.09017	−0.312158
$849$	−7.90983	−0.271465
$850$	18.6869	0.640956
$851$	6.29180	0.215680
$852$	−7.23607	−0.247904
$853$	30.9443	1.05951	0.529756	−	0.848150i	$-0.322284\pi$
$853$	30.9443	1.05951	0.529756	+	0.848150i	$0.322284\pi$
$854$	1.61803	0.0553680
$855$	−2.94427	−0.100692
$856$	−1.85410	−0.0633719
$857$	−17.5967	−0.601093	−0.300547	−	0.953767i	$-0.597169\pi$
$857$	−17.5967	−0.601093	−0.300547	+	0.953767i	$0.597169\pi$
$858$	1.85410	0.0632980
$859$	−27.7771	−0.947742	−0.473871	−	0.880594i	$-0.657144\pi$
$859$	−27.7771	−0.947742	−0.473871	+	0.880594i	$0.657144\pi$
$860$	−6.47214	−0.220698
$861$	−13.7082	−0.467174
$862$	18.6525	0.635306
$863$	−22.2705	−0.758097	−0.379048	−	0.925377i	$-0.623749\pi$
$863$	−22.2705	−0.758097	−0.379048	+	0.925377i	$0.623749\pi$
$864$	−1.00000	−0.0340207
$865$	16.5836	0.563859
$866$	18.4721	0.627709
$867$	−11.9656	−0.406372
$868$	12.4721	0.423332
$869$	13.0902	0.444054
$870$	−12.0000	−0.406838
$871$	21.9787	0.744720
$872$	−4.85410	−0.164381
$873$	−0.673762	−0.0228034
$874$	−4.76393	−0.161142
$875$	16.9443	0.572821
$876$	8.47214	0.286247
$877$	13.0557	0.440861	0.220430	−	0.975403i	$-0.429254\pi$
$877$	13.0557	0.440861	0.220430	+	0.975403i	$0.429254\pi$
$878$	32.0000	1.07995
$879$	15.7984	0.532866
$880$	1.23607	0.0416678
$881$	45.8673	1.54531	0.772654	−	0.634828i	$-0.218929\pi$
$881$	45.8673	1.54531	0.772654	+	0.634828i	$0.218929\pi$
$882$	−4.38197	−0.147548
$883$	43.6869	1.47018	0.735091	−	0.677969i	$-0.237139\pi$
$883$	43.6869	1.47018	0.735091	+	0.677969i	$0.237139\pi$
$884$	9.97871	0.335620
$885$	6.36068	0.213812
$886$	−18.3607	−0.616839
$887$	−50.0902	−1.68186	−0.840932	−	0.541141i	$-0.817992\pi$
$887$	−50.0902	−1.68186	−0.840932	+	0.541141i	$0.817992\pi$
$888$	−3.14590	−0.105569
$889$	−15.7082	−0.526836
$890$	−18.8328	−0.631277
$891$	1.00000	0.0335013
$892$	−20.7639	−0.695228
$893$	−13.9443	−0.466627
$894$	−6.00000	−0.200670
$895$	−17.3050	−0.578441
$896$	−1.61803	−0.0540547
$897$	3.70820	0.123813
$898$	4.79837	0.160124
$899$	−74.8328	−2.49581
$900$	−3.47214	−0.115738
$901$	48.9230	1.62986
$902$	−8.47214	−0.282091
$903$	−8.47214	−0.281935
$904$	−1.67376	−0.0556685
$905$	−26.6525	−0.885958
$906$	7.56231	0.251241
$907$	37.0344	1.22971	0.614854	−	0.788641i	$-0.289215\pi$
$907$	37.0344	1.22971	0.614854	+	0.788641i	$0.289215\pi$
$908$	3.70820	0.123061
$909$	−14.1803	−0.470332
$910$	3.70820	0.122926
$911$	−39.9787	−1.32455	−0.662277	−	0.749259i	$-0.730410\pi$
$911$	−39.9787	−1.32455	−0.662277	+	0.749259i	$0.730410\pi$
$912$	2.38197	0.0788748
$913$	15.4164	0.510209
$914$	26.7984	0.886411
$915$	1.23607	0.0408631
$916$	−17.8885	−0.591054
$917$	13.9443	0.460480
$918$	5.38197	0.177631
$919$	−34.5410	−1.13940	−0.569702	−	0.821852i	$-0.692941\pi$
$919$	−34.5410	−1.13940	−0.569702	+	0.821852i	$0.692941\pi$
$920$	2.47214	0.0815039
$921$	−2.76393	−0.0910747
$922$	−5.09017	−0.167636
$923$	−13.4164	−0.441606
$924$	1.61803	0.0532294
$925$	−10.9230	−0.359146
$926$	−35.5623	−1.16865
$927$	13.7984	0.453198
$928$	9.70820	0.318687
$929$	−48.3820	−1.58736	−0.793680	−	0.608335i	$-0.791838\pi$
$929$	−48.3820	−1.58736	−0.793680	+	0.608335i	$0.791838\pi$
$930$	9.52786	0.312431
$931$	10.4377	0.342082
$932$	11.7984	0.386469
$933$	2.94427	0.0963911
$934$	6.43769	0.210648
$935$	−6.65248	−0.217559
$936$	−1.85410	−0.0606032
$937$	36.7214	1.19963	0.599817	−	0.800137i	$-0.295240\pi$
$937$	36.7214	1.19963	0.599817	+	0.800137i	$0.295240\pi$
$938$	19.1803	0.626260
$939$	−5.41641	−0.176758
$940$	7.23607	0.236015
$941$	10.7639	0.350894	0.175447	−	0.984489i	$-0.443863\pi$
$941$	10.7639	0.350894	0.175447	+	0.984489i	$0.443863\pi$
$942$	−13.7984	−0.449575
$943$	−16.9443	−0.551781
$944$	−5.14590	−0.167485
$945$	2.00000	0.0650600
$946$	−5.23607	−0.170239
$947$	−20.6180	−0.669996	−0.334998	−	0.942219i	$-0.608736\pi$
$947$	−20.6180	−0.669996	−0.334998	+	0.942219i	$0.608736\pi$
$948$	−13.0902	−0.425149
$949$	15.7082	0.509910
$950$	8.27051	0.268331
$951$	−30.3607	−0.984512
$952$	8.70820	0.282235
$953$	−18.4934	−0.599061	−0.299530	−	0.954087i	$-0.596830\pi$
$953$	−18.4934	−0.599061	−0.299530	+	0.954087i	$0.596830\pi$
$954$	−9.09017	−0.294305
$955$	21.5279	0.696625
$956$	−6.76393	−0.218761
$957$	−9.70820	−0.313822
$958$	−22.8328	−0.737695
$959$	−5.85410	−0.189039
$960$	−1.23607	−0.0398939
$961$	28.4164	0.916658
$962$	−5.83282	−0.188058
$963$	−1.85410	−0.0597476
$964$	−17.8885	−0.576151
$965$	27.1672	0.874543
$966$	3.23607	0.104119
$967$	9.63932	0.309980	0.154990	−	0.987916i	$-0.450466\pi$
$967$	9.63932	0.309980	0.154990	+	0.987916i	$0.450466\pi$
$968$	1.00000	0.0321412
$969$	−12.8197	−0.411827
$970$	−0.832816	−0.0267401
$971$	47.1246	1.51230	0.756150	−	0.654398i	$-0.227078\pi$
$971$	47.1246	1.51230	0.756150	+	0.654398i	$0.227078\pi$
$972$	−1.00000	−0.0320750
$973$	23.8885	0.765832
$974$	5.61803	0.180013
$975$	−6.43769	−0.206171
$976$	−1.00000	−0.0320092
$977$	−49.2837	−1.57672	−0.788362	−	0.615212i	$-0.789071\pi$
$977$	−49.2837	−1.57672	−0.788362	+	0.615212i	$0.789071\pi$
$978$	20.9443	0.669724
$979$	−15.2361	−0.486947
$980$	−5.41641	−0.173021
$981$	−4.85410	−0.154980
$982$	17.5623	0.560436
$983$	48.2492	1.53891	0.769456	−	0.638700i	$-0.220528\pi$
$983$	48.2492	1.53891	0.769456	+	0.638700i	$0.220528\pi$
$984$	8.47214	0.270082
$985$	−4.24922	−0.135392
$986$	−52.2492	−1.66395
$987$	9.47214	0.301501
$988$	4.41641	0.140505
$989$	−10.4721	−0.332995
$990$	1.23607	0.0392848
$991$	5.96556	0.189502	0.0947511	−	0.995501i	$-0.469794\pi$
$991$	5.96556	0.189502	0.0947511	+	0.995501i	$0.469794\pi$
$992$	−7.70820	−0.244736
$993$	−19.3262	−0.613300
$994$	−11.7082	−0.371362
$995$	4.11146	0.130342
$996$	−15.4164	−0.488488
$997$	−25.4164	−0.804946	−0.402473	−	0.915432i	$-0.631849\pi$
$997$	−25.4164	−0.804946	−0.402473	+	0.915432i	$0.631849\pi$
$998$	37.3050	1.18087
$999$	−3.14590	−0.0995318

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.m.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.m.1.2	✓	2	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:	\( N \)	\(=\)	\( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.23607 q^{5} -1.00000 q^{6} -1.61803 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.23607 q^{5} -1.00000 q^{6} -1.61803 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.23607 q^{10} +1.00000 q^{11} -1.00000 q^{12} -1.85410 q^{13} -1.61803 q^{14} -1.23607 q^{15} +1.00000 q^{16} -5.38197 q^{17} +1.00000 q^{18} -2.38197 q^{19} +1.23607 q^{20} +1.61803 q^{21} +1.00000 q^{22} +2.00000 q^{23} -1.00000 q^{24} -3.47214 q^{25} -1.85410 q^{26} -1.00000 q^{27} -1.61803 q^{28} +9.70820 q^{29} -1.23607 q^{30} -7.70820 q^{31} +1.00000 q^{32} -1.00000 q^{33} -5.38197 q^{34} -2.00000 q^{35} +1.00000 q^{36} +3.14590 q^{37} -2.38197 q^{38} +1.85410 q^{39} +1.23607 q^{40} -8.47214 q^{41} +1.61803 q^{42} -5.23607 q^{43} +1.00000 q^{44} +1.23607 q^{45} +2.00000 q^{46} +5.85410 q^{47} -1.00000 q^{48} -4.38197 q^{49} -3.47214 q^{50} +5.38197 q^{51} -1.85410 q^{52} -9.09017 q^{53} -1.00000 q^{54} +1.23607 q^{55} -1.61803 q^{56} +2.38197 q^{57} +9.70820 q^{58} -5.14590 q^{59} -1.23607 q^{60} -1.00000 q^{61} -7.70820 q^{62} -1.61803 q^{63} +1.00000 q^{64} -2.29180 q^{65} -1.00000 q^{66} -11.8541 q^{67} -5.38197 q^{68} -2.00000 q^{69} -2.00000 q^{70} +7.23607 q^{71} +1.00000 q^{72} -8.47214 q^{73} +3.14590 q^{74} +3.47214 q^{75} -2.38197 q^{76} -1.61803 q^{77} +1.85410 q^{78} +13.0902 q^{79} +1.23607 q^{80} +1.00000 q^{81} -8.47214 q^{82} +15.4164 q^{83} +1.61803 q^{84} -6.65248 q^{85} -5.23607 q^{86} -9.70820 q^{87} +1.00000 q^{88} -15.2361 q^{89} +1.23607 q^{90} +3.00000 q^{91} +2.00000 q^{92} +7.70820 q^{93} +5.85410 q^{94} -2.94427 q^{95} -1.00000 q^{96} -0.673762 q^{97} -4.38197 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - q^{7} + 2 q^{8} + 2 q^{9} - 2 q^{10} + 2 q^{11} - 2 q^{12} + 3 q^{13} - q^{14} + 2 q^{15} + 2 q^{16} - 13 q^{17} + 2 q^{18} - 7 q^{19} - 2 q^{20} + q^{21} + 2 q^{22} + 4 q^{23} - 2 q^{24} + 2 q^{25} + 3 q^{26} - 2 q^{27} - q^{28} + 6 q^{29} + 2 q^{30} - 2 q^{31} + 2 q^{32} - 2 q^{33} - 13 q^{34} - 4 q^{35} + 2 q^{36} + 13 q^{37} - 7 q^{38} - 3 q^{39} - 2 q^{40} - 8 q^{41} + q^{42} - 6 q^{43} + 2 q^{44} - 2 q^{45} + 4 q^{46} + 5 q^{47} - 2 q^{48} - 11 q^{49} + 2 q^{50} + 13 q^{51} + 3 q^{52} - 7 q^{53} - 2 q^{54} - 2 q^{55} - q^{56} + 7 q^{57} + 6 q^{58} - 17 q^{59} + 2 q^{60} - 2 q^{61} - 2 q^{62} - q^{63} + 2 q^{64} - 18 q^{65} - 2 q^{66} - 17 q^{67} - 13 q^{68} - 4 q^{69} - 4 q^{70} + 10 q^{71} + 2 q^{72} - 8 q^{73} + 13 q^{74} - 2 q^{75} - 7 q^{76} - q^{77} - 3 q^{78} + 15 q^{79} - 2 q^{80} + 2 q^{81} - 8 q^{82} + 4 q^{83} + q^{84} + 18 q^{85} - 6 q^{86} - 6 q^{87} + 2 q^{88} - 26 q^{89} - 2 q^{90} + 6 q^{91} + 4 q^{92} + 2 q^{93} + 5 q^{94} + 12 q^{95} - 2 q^{96} - 17 q^{97} - 11 q^{98} + 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - q^7 + 2 * q^8 + 2 * q^9 - 2 * q^10 + 2 * q^11 - 2 * q^12 + 3 * q^13 - q^14 + 2 * q^15 + 2 * q^16 - 13 * q^17 + 2 * q^18 - 7 * q^19 - 2 * q^20 + q^21 + 2 * q^22 + 4 * q^23 - 2 * q^24 + 2 * q^25 + 3 * q^26 - 2 * q^27 - q^28 + 6 * q^29 + 2 * q^30 - 2 * q^31 + 2 * q^32 - 2 * q^33 - 13 * q^34 - 4 * q^35 + 2 * q^36 + 13 * q^37 - 7 * q^38 - 3 * q^39 - 2 * q^40 - 8 * q^41 + q^42 - 6 * q^43 + 2 * q^44 - 2 * q^45 + 4 * q^46 + 5 * q^47 - 2 * q^48 - 11 * q^49 + 2 * q^50 + 13 * q^51 + 3 * q^52 - 7 * q^53 - 2 * q^54 - 2 * q^55 - q^56 + 7 * q^57 + 6 * q^58 - 17 * q^59 + 2 * q^60 - 2 * q^61 - 2 * q^62 - q^63 + 2 * q^64 - 18 * q^65 - 2 * q^66 - 17 * q^67 - 13 * q^68 - 4 * q^69 - 4 * q^70 + 10 * q^71 + 2 * q^72 - 8 * q^73 + 13 * q^74 - 2 * q^75 - 7 * q^76 - q^77 - 3 * q^78 + 15 * q^79 - 2 * q^80 + 2 * q^81 - 8 * q^82 + 4 * q^83 + q^84 + 18 * q^85 - 6 * q^86 - 6 * q^87 + 2 * q^88 - 26 * q^89 - 2 * q^90 + 6 * q^91 + 4 * q^92 + 2 * q^93 + 5 * q^94 + 12 * q^95 - 2 * q^96 - 17 * q^97 - 11 * q^98 + 2 * q^99

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