LMFDB - Embedded newform 731.2.a.f.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(1,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("731.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	731.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.172452 q^{2} -0.293380 q^{3} -1.97026 q^{4} -4.21864 q^{5} +0.0505941 q^{6} -4.31664 q^{7} +0.684680 q^{8} -2.91393 q^{9} +O(q^{10})$	\(q-0.172452 q^{2} -0.293380 q^{3} -1.97026 q^{4} -4.21864 q^{5} +0.0505941 q^{6} -4.31664 q^{7} +0.684680 q^{8} -2.91393 q^{9} +0.727513 q^{10} +0.176159 q^{11} +0.578036 q^{12} +5.17403 q^{13} +0.744414 q^{14} +1.23767 q^{15} +3.82245 q^{16} -1.00000 q^{17} +0.502513 q^{18} -6.05991 q^{19} +8.31182 q^{20} +1.26642 q^{21} -0.0303789 q^{22} +4.86324 q^{23} -0.200872 q^{24} +12.7969 q^{25} -0.892272 q^{26} +1.73503 q^{27} +8.50491 q^{28} -2.40862 q^{29} -0.213438 q^{30} -5.88376 q^{31} -2.02855 q^{32} -0.0516815 q^{33} +0.172452 q^{34} +18.2103 q^{35} +5.74120 q^{36} -1.32758 q^{37} +1.04504 q^{38} -1.51796 q^{39} -2.88842 q^{40} -5.62451 q^{41} -0.218396 q^{42} +1.00000 q^{43} -0.347078 q^{44} +12.2928 q^{45} -0.838677 q^{46} -7.90746 q^{47} -1.12143 q^{48} +11.6334 q^{49} -2.20685 q^{50} +0.293380 q^{51} -10.1942 q^{52} +0.862405 q^{53} -0.299210 q^{54} -0.743149 q^{55} -2.95552 q^{56} +1.77786 q^{57} +0.415372 q^{58} -11.4006 q^{59} -2.43852 q^{60} -1.41098 q^{61} +1.01467 q^{62} +12.5784 q^{63} -7.29507 q^{64} -21.8274 q^{65} +0.00891257 q^{66} +5.80029 q^{67} +1.97026 q^{68} -1.42678 q^{69} -3.14041 q^{70} +6.05586 q^{71} -1.99511 q^{72} -3.28780 q^{73} +0.228943 q^{74} -3.75436 q^{75} +11.9396 q^{76} -0.760413 q^{77} +0.261775 q^{78} +4.93040 q^{79} -16.1255 q^{80} +8.23276 q^{81} +0.969958 q^{82} +4.16319 q^{83} -2.49517 q^{84} +4.21864 q^{85} -0.172452 q^{86} +0.706642 q^{87} +0.120612 q^{88} +6.97457 q^{89} -2.11992 q^{90} -22.3344 q^{91} -9.58186 q^{92} +1.72618 q^{93} +1.36366 q^{94} +25.5646 q^{95} +0.595136 q^{96} +6.87277 q^{97} -2.00620 q^{98} -0.513313 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 2 q^{2} - q^{3} + 32 q^{4} - 3 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 34 q^{9}+O(q^{10}) $ 21 * q + 2 * q^2 - q^3 + 32 * q^4 - 3 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 34 * q^9	\( 21 q + 2 q^{2} - q^{3} + 32 q^{4} - 3 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 34 q^{9} + 12 q^{10} + 2 q^{11} - 5 q^{12} + 26 q^{13} - 3 q^{14} + 5 q^{15} + 62 q^{16} - 21 q^{17} - 10 q^{18} + 16 q^{19} - 27 q^{20} + 36 q^{21} - 14 q^{22} - q^{23} + 15 q^{24} + 40 q^{25} - 3 q^{26} - 16 q^{27} + 25 q^{28} + 15 q^{29} + 38 q^{30} + 18 q^{31} + 14 q^{32} + 14 q^{33} - 2 q^{34} - 5 q^{35} + 73 q^{36} + 12 q^{37} + 19 q^{38} - 11 q^{39} + 41 q^{40} - 45 q^{42} + 21 q^{43} - 34 q^{44} - 18 q^{45} + 28 q^{46} - q^{47} - 36 q^{48} + 40 q^{49} + 24 q^{50} + q^{51} + 23 q^{52} + 39 q^{53} - 83 q^{54} - 2 q^{55} - 10 q^{56} + 3 q^{57} + 19 q^{58} + 4 q^{59} - 35 q^{60} + 50 q^{61} + 5 q^{62} - 37 q^{63} + 120 q^{64} - 8 q^{65} - 37 q^{66} + 16 q^{67} - 32 q^{68} + 33 q^{69} - q^{70} + q^{71} - 54 q^{72} + 15 q^{73} + 52 q^{74} + 11 q^{75} - 15 q^{76} + 13 q^{77} - 100 q^{78} + 56 q^{79} - 100 q^{80} + 97 q^{81} - 11 q^{82} + 61 q^{84} + 3 q^{85} + 2 q^{86} - 8 q^{87} - 56 q^{88} + 5 q^{89} - 69 q^{90} - 4 q^{91} - 27 q^{92} + 17 q^{93} - 47 q^{94} - 9 q^{95} + 81 q^{96} - 28 q^{97} + 18 q^{98} - 19 q^{99}+O(q^{100}) \) 21 * q + 2 * q^2 - q^3 + 32 * q^4 - 3 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 34 * q^9 + 12 * q^10 + 2 * q^11 - 5 * q^12 + 26 * q^13 - 3 * q^14 + 5 * q^15 + 62 * q^16 - 21 * q^17 - 10 * q^18 + 16 * q^19 - 27 * q^20 + 36 * q^21 - 14 * q^22 - q^23 + 15 * q^24 + 40 * q^25 - 3 * q^26 - 16 * q^27 + 25 * q^28 + 15 * q^29 + 38 * q^30 + 18 * q^31 + 14 * q^32 + 14 * q^33 - 2 * q^34 - 5 * q^35 + 73 * q^36 + 12 * q^37 + 19 * q^38 - 11 * q^39 + 41 * q^40 - 45 * q^42 + 21 * q^43 - 34 * q^44 - 18 * q^45 + 28 * q^46 - q^47 - 36 * q^48 + 40 * q^49 + 24 * q^50 + q^51 + 23 * q^52 + 39 * q^53 - 83 * q^54 - 2 * q^55 - 10 * q^56 + 3 * q^57 + 19 * q^58 + 4 * q^59 - 35 * q^60 + 50 * q^61 + 5 * q^62 - 37 * q^63 + 120 * q^64 - 8 * q^65 - 37 * q^66 + 16 * q^67 - 32 * q^68 + 33 * q^69 - q^70 + q^71 - 54 * q^72 + 15 * q^73 + 52 * q^74 + 11 * q^75 - 15 * q^76 + 13 * q^77 - 100 * q^78 + 56 * q^79 - 100 * q^80 + 97 * q^81 - 11 * q^82 + 61 * q^84 + 3 * q^85 + 2 * q^86 - 8 * q^87 - 56 * q^88 + 5 * q^89 - 69 * q^90 - 4 * q^91 - 27 * q^92 + 17 * q^93 - 47 * q^94 - 9 * q^95 + 81 * q^96 - 28 * q^97 + 18 * q^98 - 19 * 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 $

$2$	−0.172452	−0.121942	−0.0609710	−	0.998140i	$-0.519420\pi$
$2$	−0.172452	−0.121942	−0.0609710	+	0.998140i	$0.519420\pi$
$3$	−0.293380	−0.169383	−0.0846916	−	0.996407i	$-0.526991\pi$
$3$	−0.293380	−0.169383	−0.0846916	+	0.996407i	$0.526991\pi$
$4$	−1.97026	−0.985130
$5$	−4.21864	−1.88663	−0.943316	−	0.331895i	$-0.892312\pi$
$5$	−4.21864	−1.88663	−0.943316	+	0.331895i	$0.892312\pi$
$6$	0.0505941	0.0206549
$7$	−4.31664	−1.63154	−0.815768	−	0.578379i	$-0.803686\pi$
$7$	−4.31664	−1.63154	−0.815768	+	0.578379i	$0.803686\pi$
$8$	0.684680	0.242071
$9$	−2.91393	−0.971309
$10$	0.727513	0.230060
$11$	0.176159	0.0531138	0.0265569	−	0.999647i	$-0.491546\pi$
$11$	0.176159	0.0531138	0.0265569	+	0.999647i	$0.491546\pi$
$12$	0.578036	0.166865
$13$	5.17403	1.43502	0.717509	−	0.696549i	$-0.245282\pi$
$13$	5.17403	1.43502	0.717509	+	0.696549i	$0.245282\pi$
$14$	0.744414	0.198953
$15$	1.23767	0.319564
$16$	3.82245	0.955612
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	0.502513	0.118443
$19$	−6.05991	−1.39024	−0.695120	−	0.718894i	$-0.744649\pi$
$19$	−6.05991	−1.39024	−0.695120	+	0.718894i	$0.744649\pi$
$20$	8.31182	1.85858
$21$	1.26642	0.276355
$22$	−0.0303789	−0.00647680
$23$	4.86324	1.01406	0.507028	−	0.861929i	$-0.330744\pi$
$23$	4.86324	1.01406	0.507028	+	0.861929i	$0.330744\pi$
$24$	−0.200872	−0.0410027
$25$	12.7969	2.55938
$26$	−0.892272	−0.174989
$27$	1.73503	0.333907
$28$	8.50491	1.60728
$29$	−2.40862	−0.447270	−0.223635	−	0.974673i	$-0.571792\pi$
$29$	−2.40862	−0.447270	−0.223635	+	0.974673i	$0.571792\pi$
$30$	−0.213438	−0.0389683
$31$	−5.88376	−1.05675	−0.528377	−	0.849010i	$-0.677199\pi$
$31$	−5.88376	−1.05675	−0.528377	+	0.849010i	$0.677199\pi$
$32$	−2.02855	−0.358600
$33$	−0.0516815	−0.00899659
$34$	0.172452	0.0295753
$35$	18.2103	3.07811
$36$	5.74120	0.956866
$37$	−1.32758	−0.218252	−0.109126	−	0.994028i	$-0.534805\pi$
$37$	−1.32758	−0.218252	−0.109126	+	0.994028i	$0.534805\pi$
$38$	1.04504	0.169529
$39$	−1.51796	−0.243068
$40$	−2.88842	−0.456699
$41$	−5.62451	−0.878401	−0.439200	−	0.898389i	$-0.644738\pi$
$41$	−5.62451	−0.878401	−0.439200	+	0.898389i	$0.644738\pi$
$42$	−0.218396	−0.0336993
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−0.347078	−0.0523240
$45$	12.2928	1.83250
$46$	−0.838677	−0.123656
$47$	−7.90746	−1.15342	−0.576711	−	0.816949i	$-0.695664\pi$
$47$	−7.90746	−1.15342	−0.576711	+	0.816949i	$0.695664\pi$
$48$	−1.12143	−0.161865
$49$	11.6334	1.66191
$50$	−2.20685	−0.312096
$51$	0.293380	0.0410815
$52$	−10.1942	−1.41368
$53$	0.862405	0.118460	0.0592302	−	0.998244i	$-0.481135\pi$
$53$	0.862405	0.118460	0.0592302	+	0.998244i	$0.481135\pi$
$54$	−0.299210	−0.0407173
$55$	−0.743149	−0.100206
$56$	−2.95552	−0.394947
$57$	1.77786	0.235483
$58$	0.415372	0.0545410
$59$	−11.4006	−1.48423	−0.742117	−	0.670270i	$-0.766178\pi$
$59$	−11.4006	−1.48423	−0.742117	+	0.670270i	$0.766178\pi$
$60$	−2.43852	−0.314812
$61$	−1.41098	−0.180658	−0.0903290	−	0.995912i	$-0.528792\pi$
$61$	−1.41098	−0.180658	−0.0903290	+	0.995912i	$0.528792\pi$
$62$	1.01467	0.128863
$63$	12.5784	1.58473
$64$	−7.29507	−0.911883
$65$	−21.8274	−2.70735
$66$	0.00891257	0.00109706
$67$	5.80029	0.708618	0.354309	−	0.935128i	$-0.384716\pi$
$67$	5.80029	0.708618	0.354309	+	0.935128i	$0.384716\pi$
$68$	1.97026	0.238929
$69$	−1.42678	−0.171764
$70$	−3.14041	−0.375351
$71$	6.05586	0.718699	0.359349	−	0.933203i	$-0.382999\pi$
$71$	6.05586	0.718699	0.359349	+	0.933203i	$0.382999\pi$
$72$	−1.99511	−0.235126
$73$	−3.28780	−0.384808	−0.192404	−	0.981316i	$-0.561628\pi$
$73$	−3.28780	−0.384808	−0.192404	+	0.981316i	$0.561628\pi$
$74$	0.228943	0.0266141
$75$	−3.75436	−0.433517
$76$	11.9396	1.36957
$77$	−0.760413	−0.0866571
$78$	0.261775	0.0296402
$79$	4.93040	0.554713	0.277357	−	0.960767i	$-0.410542\pi$
$79$	4.93040	0.554713	0.277357	+	0.960767i	$0.410542\pi$
$80$	−16.1255	−1.80289
$81$	8.23276	0.914751
$82$	0.969958	0.107114
$83$	4.16319	0.456969	0.228485	−	0.973548i	$-0.426623\pi$
$83$	4.16319	0.456969	0.228485	+	0.973548i	$0.426623\pi$
$84$	−2.49517	−0.272246
$85$	4.21864	0.457576
$86$	−0.172452	−0.0185960
$87$	0.706642	0.0757600
$88$	0.120612	0.0128573
$89$	6.97457	0.739303	0.369652	−	0.929170i	$-0.379477\pi$
$89$	6.97457	0.739303	0.369652	+	0.929170i	$0.379477\pi$
$90$	−2.11992	−0.223459
$91$	−22.3344	−2.34128
$92$	−9.58186	−0.998978
$93$	1.72618	0.178996
$94$	1.36366	0.140651
$95$	25.5646	2.62287
$96$	0.595136	0.0607408
$97$	6.87277	0.697825	0.348912	−	0.937155i	$-0.386551\pi$
$97$	6.87277	0.697825	0.348912	+	0.937155i	$0.386551\pi$
$98$	−2.00620	−0.202657
$99$	−0.513313	−0.0515899
$100$	−25.2133	−2.52133
$101$	17.9421	1.78530	0.892652	−	0.450747i	$-0.148842\pi$
$101$	17.9421	1.78530	0.892652	+	0.450747i	$0.148842\pi$
$102$	−0.0505941	−0.00500956
$103$	11.9281	1.17531	0.587656	−	0.809111i	$-0.300051\pi$
$103$	11.9281	1.17531	0.587656	+	0.809111i	$0.300051\pi$
$104$	3.54255	0.347376
$105$	−5.34256	−0.521380
$106$	−0.148724	−0.0144453
$107$	−6.70930	−0.648612	−0.324306	−	0.945952i	$-0.605131\pi$
$107$	−6.70930	−0.648612	−0.324306	+	0.945952i	$0.605131\pi$
$108$	−3.41846	−0.328942
$109$	2.43203	0.232946	0.116473	−	0.993194i	$-0.462841\pi$
$109$	2.43203	0.232946	0.116473	+	0.993194i	$0.462841\pi$
$110$	0.128158	0.0122194
$111$	0.389485	0.0369683
$112$	−16.5001	−1.55912
$113$	−3.21822	−0.302745	−0.151372	−	0.988477i	$-0.548369\pi$
$113$	−3.21822	−0.302745	−0.151372	+	0.988477i	$0.548369\pi$
$114$	−0.306596	−0.0287153
$115$	−20.5163	−1.91315
$116$	4.74561	0.440619
$117$	−15.0768	−1.39385
$118$	1.96606	0.180991
$119$	4.31664	0.395706
$120$	0.847405	0.0773571
$121$	−10.9690	−0.997179
$122$	0.243327	0.0220298
$123$	1.65012	0.148786
$124$	11.5925	1.04104
$125$	−32.8924	−2.94198
$126$	−2.16917	−0.193245
$127$	14.7715	1.31076	0.655379	−	0.755300i	$-0.272509\pi$
$127$	14.7715	1.31076	0.655379	+	0.755300i	$0.272509\pi$
$128$	5.31514	0.469797
$129$	−0.293380	−0.0258307
$130$	3.76418	0.330140
$131$	−11.3189	−0.988940	−0.494470	−	0.869195i	$-0.664638\pi$
$131$	−11.3189	−0.988940	−0.494470	+	0.869195i	$0.664638\pi$
$132$	0.101826	0.00886281
$133$	26.1585	2.26823
$134$	−1.00027	−0.0864103
$135$	−7.31947	−0.629959
$136$	−0.684680	−0.0587108
$137$	−0.789636	−0.0674632	−0.0337316	−	0.999431i	$-0.510739\pi$
$137$	−0.789636	−0.0674632	−0.0337316	+	0.999431i	$0.510739\pi$
$138$	0.246051	0.0209453
$139$	16.3388	1.38584	0.692918	−	0.721016i	$-0.256325\pi$
$139$	16.3388	1.38584	0.692918	+	0.721016i	$0.256325\pi$
$140$	−35.8791	−3.03234
$141$	2.31989	0.195370
$142$	−1.04435	−0.0876396
$143$	0.911450	0.0762193
$144$	−11.1383	−0.928194
$145$	10.1611	0.843834
$146$	0.566988	0.0469242
$147$	−3.41301	−0.281500
$148$	2.61567	0.215007
$149$	17.8850	1.46520	0.732599	−	0.680660i	$-0.238307\pi$
$149$	17.8850	1.46520	0.732599	+	0.680660i	$0.238307\pi$
$150$	0.647448	0.0528639
$151$	22.1645	1.80372	0.901859	−	0.432030i	$-0.142203\pi$
$151$	22.1645	1.80372	0.901859	+	0.432030i	$0.142203\pi$
$152$	−4.14910	−0.336536
$153$	2.91393	0.235577
$154$	0.131135	0.0105671
$155$	24.8214	1.99371
$156$	2.99077	0.239454
$157$	1.67954	0.134042	0.0670208	−	0.997752i	$-0.478651\pi$
$157$	1.67954	0.134042	0.0670208	+	0.997752i	$0.478651\pi$
$158$	−0.850257	−0.0676428
$159$	−0.253013	−0.0200652
$160$	8.55771	0.676547
$161$	−20.9929	−1.65447
$162$	−1.41976	−0.111547
$163$	−14.7370	−1.15429	−0.577147	−	0.816641i	$-0.695834\pi$
$163$	−14.7370	−1.15429	−0.577147	+	0.816641i	$0.695834\pi$
$164$	11.0817	0.865339
$165$	0.218025	0.0169733
$166$	−0.717950	−0.0557237
$167$	3.34264	0.258661	0.129331	−	0.991602i	$-0.458717\pi$
$167$	3.34264	0.258661	0.129331	+	0.991602i	$0.458717\pi$
$168$	0.867090	0.0668975
$169$	13.7706	1.05928
$170$	−0.727513	−0.0557977
$171$	17.6582	1.35035
$172$	−1.97026	−0.150231
$173$	−18.8617	−1.43403	−0.717013	−	0.697060i	$-0.754491\pi$
$173$	−18.8617	−1.43403	−0.717013	+	0.697060i	$0.754491\pi$
$174$	−0.121862	−0.00923833
$175$	−55.2397	−4.17573
$176$	0.673357	0.0507562
$177$	3.34472	0.251404
$178$	−1.20278	−0.0901521
$179$	−18.9337	−1.41517	−0.707584	−	0.706629i	$-0.750215\pi$
$179$	−18.9337	−1.41517	−0.707584	+	0.706629i	$0.750215\pi$
$180$	−24.2200	−1.80525
$181$	21.0234	1.56265	0.781327	−	0.624122i	$-0.214543\pi$
$181$	21.0234	1.56265	0.781327	+	0.624122i	$0.214543\pi$
$182$	3.85162	0.285501
$183$	0.413955	0.0306004
$184$	3.32976	0.245473
$185$	5.60057	0.411762
$186$	−0.297683	−0.0218272
$187$	−0.176159	−0.0128820
$188$	15.5797	1.13627
$189$	−7.48950	−0.544781
$190$	−4.40867	−0.319838
$191$	0.952155	0.0688955	0.0344478	−	0.999406i	$-0.489033\pi$
$191$	0.952155	0.0688955	0.0344478	+	0.999406i	$0.489033\pi$
$192$	2.14023	0.154458
$193$	−26.2637	−1.89051	−0.945253	−	0.326339i	$-0.894185\pi$
$193$	−26.2637	−1.89051	−0.945253	+	0.326339i	$0.894185\pi$
$194$	−1.18522	−0.0850941
$195$	6.40372	0.458580
$196$	−22.9208	−1.63720
$197$	−13.2195	−0.941853	−0.470926	−	0.882173i	$-0.656080\pi$
$197$	−13.2195	−0.941853	−0.470926	+	0.882173i	$0.656080\pi$
$198$	0.0885219	0.00629098
$199$	−10.2216	−0.724593	−0.362297	−	0.932063i	$-0.618007\pi$
$199$	−10.2216	−0.724593	−0.362297	+	0.932063i	$0.618007\pi$
$200$	8.76179	0.619552
$201$	−1.70169	−0.120028
$202$	−3.09415	−0.217704
$203$	10.3972	0.729737
$204$	−0.578036	−0.0404706
$205$	23.7278	1.65722
$206$	−2.05703	−0.143320
$207$	−14.1711	−0.984963
$208$	19.7775	1.37132
$209$	−1.06751	−0.0738409
$210$	0.921335	0.0635782
$211$	12.3549	0.850546	0.425273	−	0.905065i	$-0.360178\pi$
$211$	12.3549	0.850546	0.425273	+	0.905065i	$0.360178\pi$
$212$	−1.69916	−0.116699
$213$	−1.77667	−0.121736
$214$	1.15703	0.0790931
$215$	−4.21864	−0.287709
$216$	1.18794	0.0808291
$217$	25.3981	1.72413
$218$	−0.419409	−0.0284060
$219$	0.964576	0.0651800
$220$	1.46420	0.0987162
$221$	−5.17403	−0.348043
$222$	−0.0671675	−0.00450799
$223$	−13.8248	−0.925779	−0.462889	−	0.886416i	$-0.653187\pi$
$223$	−13.8248	−0.925779	−0.462889	+	0.886416i	$0.653187\pi$
$224$	8.75651	0.585069
$225$	−37.2893	−2.48595
$226$	0.554989	0.0369173
$227$	8.42885	0.559442	0.279721	−	0.960081i	$-0.409758\pi$
$227$	8.42885	0.559442	0.279721	+	0.960081i	$0.409758\pi$
$228$	−3.50285	−0.231982
$229$	0.840519	0.0555431	0.0277715	−	0.999614i	$-0.491159\pi$
$229$	0.840519	0.0555431	0.0277715	+	0.999614i	$0.491159\pi$
$230$	3.53807	0.233294
$231$	0.223090	0.0146783
$232$	−1.64913	−0.108271
$233$	−24.5186	−1.60626	−0.803132	−	0.595801i	$-0.796835\pi$
$233$	−24.5186	−1.60626	−0.803132	+	0.595801i	$0.796835\pi$
$234$	2.60002	0.169968
$235$	33.3587	2.17608
$236$	22.4622	1.46216
$237$	−1.44648	−0.0939591
$238$	−0.744414	−0.0482532
$239$	−20.5727	−1.33074	−0.665368	−	0.746516i	$-0.731725\pi$
$239$	−20.5727	−1.33074	−0.665368	+	0.746516i	$0.731725\pi$
$240$	4.73091	0.305379
$241$	11.8712	0.764692	0.382346	−	0.924019i	$-0.375116\pi$
$241$	11.8712	0.764692	0.382346	+	0.924019i	$0.375116\pi$
$242$	1.89162	0.121598
$243$	−7.62042	−0.488850
$244$	2.78000	0.177972
$245$	−49.0771	−3.13542
$246$	−0.284567	−0.0181433
$247$	−31.3542	−1.99502
$248$	−4.02849	−0.255809
$249$	−1.22140	−0.0774029
$250$	5.67236	0.358752
$251$	−8.09080	−0.510687	−0.255343	−	0.966850i	$-0.582189\pi$
$251$	−8.09080	−0.510687	−0.255343	+	0.966850i	$0.582189\pi$
$252$	−24.7827	−1.56116
$253$	0.856702	0.0538604
$254$	−2.54738	−0.159837
$255$	−1.23767	−0.0775056
$256$	13.6735	0.854595
$257$	−0.590185	−0.0368147	−0.0184074	−	0.999831i	$-0.505860\pi$
$257$	−0.590185	−0.0368147	−0.0184074	+	0.999831i	$0.505860\pi$
$258$	0.0505941	0.00314985
$259$	5.73067	0.356087
$260$	43.0056	2.66709
$261$	7.01855	0.434437
$262$	1.95197	0.120593
$263$	−5.58814	−0.344580	−0.172290	−	0.985046i	$-0.555117\pi$
$263$	−5.58814	−0.344580	−0.172290	+	0.985046i	$0.555117\pi$
$264$	−0.0353852	−0.00217781
$265$	−3.63818	−0.223491
$266$	−4.51108	−0.276592
$267$	−2.04620	−0.125226
$268$	−11.4281	−0.698081
$269$	12.0824	0.736678	0.368339	−	0.929692i	$-0.379927\pi$
$269$	12.0824	0.736678	0.368339	+	0.929692i	$0.379927\pi$
$270$	1.26226	0.0768185
$271$	−29.8454	−1.81298	−0.906490	−	0.422227i	$-0.861249\pi$
$271$	−29.8454	−1.81298	−0.906490	+	0.422227i	$0.861249\pi$
$272$	−3.82245	−0.231770
$273$	6.55248	0.396574
$274$	0.136174	0.00822659
$275$	2.25429	0.135939
$276$	2.81113	0.169210
$277$	32.2718	1.93903	0.969514	−	0.245037i	$-0.0788001\pi$
$277$	32.2718	1.93903	0.969514	+	0.245037i	$0.0788001\pi$
$278$	−2.81766	−0.168992
$279$	17.1448	1.02643
$280$	12.4683	0.745121
$281$	2.55054	0.152152	0.0760761	−	0.997102i	$-0.475761\pi$
$281$	2.55054	0.152152	0.0760761	+	0.997102i	$0.475761\pi$
$282$	−0.400070	−0.0238238
$283$	8.66349	0.514991	0.257496	−	0.966279i	$-0.417103\pi$
$283$	8.66349	0.514991	0.257496	+	0.966279i	$0.417103\pi$
$284$	−11.9316	−0.708012
$285$	−7.50015	−0.444271
$286$	−0.157181	−0.00929433
$287$	24.2790	1.43314
$288$	5.91104	0.348312
$289$	1.00000	0.0588235
$290$	−1.75230	−0.102899
$291$	−2.01634	−0.118200
$292$	6.47782	0.379086
$293$	12.4471	0.727166	0.363583	−	0.931562i	$-0.381553\pi$
$293$	12.4471	0.727166	0.363583	+	0.931562i	$0.381553\pi$
$294$	0.588580	0.0343267
$295$	48.0951	2.80021
$296$	−0.908965	−0.0528325
$297$	0.305640	0.0177351
$298$	−3.08431	−0.178669
$299$	25.1626	1.45519
$300$	7.39708	0.427070
$301$	−4.31664	−0.248807
$302$	−3.82231	−0.219949
$303$	−5.26385	−0.302401
$304$	−23.1637	−1.32853
$305$	5.95243	0.340835
$306$	−0.502513	−0.0287268
$307$	−19.8053	−1.13035	−0.565174	−	0.824972i	$-0.691191\pi$
$307$	−19.8053	−1.13035	−0.565174	+	0.824972i	$0.691191\pi$
$308$	1.49821	0.0853685
$309$	−3.49948	−0.199078
$310$	−4.28051	−0.243117
$311$	−18.6676	−1.05854	−0.529270	−	0.848453i	$-0.677534\pi$
$311$	−18.6676	−1.05854	−0.529270	+	0.848453i	$0.677534\pi$
$312$	−1.03932	−0.0588397
$313$	9.82978	0.555612	0.277806	−	0.960637i	$-0.410393\pi$
$313$	9.82978	0.555612	0.277806	+	0.960637i	$0.410393\pi$
$314$	−0.289639	−0.0163453
$315$	−53.0636	−2.98980
$316$	−9.71417	−0.546465
$317$	−31.6213	−1.77603	−0.888014	−	0.459816i	$-0.847915\pi$
$317$	−31.6213	−1.77603	−0.888014	+	0.459816i	$0.847915\pi$
$318$	0.0436326	0.00244679
$319$	−0.424299	−0.0237562
$320$	30.7752	1.72039
$321$	1.96838	0.109864
$322$	3.62027	0.201750
$323$	6.05991	0.337183
$324$	−16.2207	−0.901149
$325$	66.2117	3.67276
$326$	2.54143	0.140757
$327$	−0.713510	−0.0394572
$328$	−3.85099	−0.212635
$329$	34.1337	1.88185
$330$	−0.0375989	−0.00206975
$331$	−16.6799	−0.916812	−0.458406	−	0.888743i	$-0.651579\pi$
$331$	−16.6799	−0.916812	−0.458406	+	0.888743i	$0.651579\pi$
$332$	−8.20256	−0.450174
$333$	3.86846	0.211990
$334$	−0.576446	−0.0315417
$335$	−24.4693	−1.33690
$336$	4.84081	0.264088
$337$	23.6322	1.28733	0.643663	−	0.765309i	$-0.277414\pi$
$337$	23.6322	1.28733	0.643663	+	0.765309i	$0.277414\pi$
$338$	−2.37477	−0.129170
$339$	0.944162	0.0512799
$340$	−8.31182	−0.450772
$341$	−1.03647	−0.0561282
$342$	−3.04519	−0.164665
$343$	−20.0007	−1.07993
$344$	0.684680	0.0369155
$345$	6.01907	0.324056
$346$	3.25273	0.174868
$347$	8.02618	0.430868	0.215434	−	0.976518i	$-0.430883\pi$
$347$	8.02618	0.430868	0.215434	+	0.976518i	$0.430883\pi$
$348$	−1.39227	−0.0746335
$349$	22.8355	1.22235	0.611177	−	0.791494i	$-0.290696\pi$
$349$	22.8355	1.22235	0.611177	+	0.791494i	$0.290696\pi$
$350$	9.52620	0.509197
$351$	8.97710	0.479162
$352$	−0.357346	−0.0190466
$353$	12.1637	0.647406	0.323703	−	0.946159i	$-0.395072\pi$
$353$	12.1637	0.647406	0.323703	+	0.946159i	$0.395072\pi$
$354$	−0.576804	−0.0306568
$355$	−25.5475	−1.35592
$356$	−13.7417	−0.728310
$357$	−1.26642	−0.0670259
$358$	3.26515	0.172568
$359$	2.51862	0.132928	0.0664638	−	0.997789i	$-0.478828\pi$
$359$	2.51862	0.132928	0.0664638	+	0.997789i	$0.478828\pi$
$360$	8.41664	0.443596
$361$	17.7226	0.932766
$362$	−3.62552	−0.190553
$363$	3.21808	0.168905
$364$	44.0046	2.30647
$365$	13.8700	0.725991
$366$	−0.0713874	−0.00373148
$367$	26.7729	1.39753	0.698766	−	0.715350i	$-0.253733\pi$
$367$	26.7729	1.39753	0.698766	+	0.715350i	$0.253733\pi$
$368$	18.5895	0.969044
$369$	16.3894	0.853199
$370$	−0.965829	−0.0502111
$371$	−3.72269	−0.193273
$372$	−3.40102	−0.176335
$373$	32.2151	1.66804	0.834018	−	0.551737i	$-0.186035\pi$
$373$	32.2151	1.66804	0.834018	+	0.551737i	$0.186035\pi$
$374$	0.0303789	0.00157086
$375$	9.64998	0.498323
$376$	−5.41407	−0.279210
$377$	−12.4623	−0.641840
$378$	1.29158	0.0664317
$379$	25.5117	1.31045	0.655223	−	0.755436i	$-0.272575\pi$
$379$	25.5117	1.31045	0.655223	+	0.755436i	$0.272575\pi$
$380$	−50.3689	−2.58387
$381$	−4.33367	−0.222021
$382$	−0.164201	−0.00840126
$383$	21.1600	1.08123	0.540614	−	0.841271i	$-0.318192\pi$
$383$	21.1600	1.08123	0.540614	+	0.841271i	$0.318192\pi$
$384$	−1.55936	−0.0795757
$385$	3.20791	0.163490
$386$	4.52924	0.230532
$387$	−2.91393	−0.148123
$388$	−13.5412	−0.687448
$389$	−2.41995	−0.122696	−0.0613481	−	0.998116i	$-0.519540\pi$
$389$	−2.41995	−0.122696	−0.0613481	+	0.998116i	$0.519540\pi$
$390$	−1.10434	−0.0559202
$391$	−4.86324	−0.245945
$392$	7.96514	0.402300
$393$	3.32075	0.167510
$394$	2.27974	0.114851
$395$	−20.7996	−1.04654
$396$	1.01136	0.0508228
$397$	29.0531	1.45813	0.729066	−	0.684444i	$-0.239955\pi$
$397$	29.0531	1.45813	0.729066	+	0.684444i	$0.239955\pi$
$398$	1.76274	0.0883583
$399$	−7.67438	−0.384200
$400$	48.9155	2.44578
$401$	21.6639	1.08184	0.540921	−	0.841073i	$-0.318076\pi$
$401$	21.6639	1.08184	0.540921	+	0.841073i	$0.318076\pi$
$402$	0.293460	0.0146365
$403$	−30.4427	−1.51646
$404$	−35.3506	−1.75876
$405$	−34.7310	−1.72580
$406$	−1.79301	−0.0889856
$407$	−0.233864	−0.0115922
$408$	0.200872	0.00994462
$409$	−2.07539	−0.102621	−0.0513106	−	0.998683i	$-0.516340\pi$
$409$	−2.07539	−0.102621	−0.0513106	+	0.998683i	$0.516340\pi$
$410$	−4.09190	−0.202085
$411$	0.231664	0.0114271
$412$	−23.5015	−1.15784
$413$	49.2124	2.42158
$414$	2.44384	0.120108
$415$	−17.5630	−0.862133
$416$	−10.4958	−0.514598
$417$	−4.79348	−0.234738
$418$	0.184094	0.00900431
$419$	−9.28687	−0.453693	−0.226847	−	0.973930i	$-0.572842\pi$
$419$	−9.28687	−0.453693	−0.226847	+	0.973930i	$0.572842\pi$
$420$	10.5262	0.513628
$421$	3.21476	0.156678	0.0783390	−	0.996927i	$-0.475038\pi$
$421$	3.21476	0.156678	0.0783390	+	0.996927i	$0.475038\pi$
$422$	−2.13063	−0.103717
$423$	23.0418	1.12033
$424$	0.590471	0.0286758
$425$	−12.7969	−0.620742
$426$	0.306391	0.0148447
$427$	6.09071	0.294750
$428$	13.2191	0.638967
$429$	−0.267401	−0.0129103
$430$	0.727513	0.0350838
$431$	−27.1337	−1.30699	−0.653493	−	0.756933i	$-0.726697\pi$
$431$	−27.1337	−1.30699	−0.653493	+	0.756933i	$0.726697\pi$
$432$	6.63206	0.319085
$433$	−34.0466	−1.63617	−0.818087	−	0.575094i	$-0.804965\pi$
$433$	−34.0466	−1.63617	−0.818087	+	0.575094i	$0.804965\pi$
$434$	−4.37995	−0.210244
$435$	−2.98107	−0.142931
$436$	−4.79174	−0.229483
$437$	−29.4708	−1.40978
$438$	−0.166343	−0.00794818
$439$	−12.0634	−0.575755	−0.287877	−	0.957667i	$-0.592950\pi$
$439$	−12.0634	−0.575755	−0.287877	+	0.957667i	$0.592950\pi$
$440$	−0.508819	−0.0242570
$441$	−33.8988	−1.61423
$442$	0.892272	0.0424411
$443$	25.7412	1.22300	0.611500	−	0.791245i	$-0.290567\pi$
$443$	25.7412	1.22300	0.611500	+	0.791245i	$0.290567\pi$
$444$	−0.767387	−0.0364186
$445$	−29.4232	−1.39479
$446$	2.38412	0.112891
$447$	−5.24712	−0.248180
$448$	31.4902	1.48777
$449$	33.3622	1.57446	0.787231	−	0.616659i	$-0.211514\pi$
$449$	33.3622	1.57446	0.787231	+	0.616659i	$0.211514\pi$
$450$	6.43062	0.303142
$451$	−0.990805	−0.0466552
$452$	6.34073	0.298243
$453$	−6.50262	−0.305520
$454$	−1.45357	−0.0682195
$455$	94.2209	4.41714
$456$	1.21726	0.0570036
$457$	34.6806	1.62229	0.811145	−	0.584845i	$-0.198845\pi$
$457$	34.6806	1.62229	0.811145	+	0.584845i	$0.198845\pi$
$458$	−0.144949	−0.00677303
$459$	−1.73503	−0.0809843
$460$	40.4224	1.88470
$461$	26.3078	1.22528	0.612638	−	0.790363i	$-0.290108\pi$
$461$	26.3078	1.22528	0.612638	+	0.790363i	$0.290108\pi$
$462$	−0.0384724	−0.00178990
$463$	−23.9992	−1.11534	−0.557668	−	0.830064i	$-0.688304\pi$
$463$	−23.9992	−1.11534	−0.557668	+	0.830064i	$0.688304\pi$
$464$	−9.20683	−0.427416
$465$	−7.28212	−0.337700
$466$	4.22828	0.195871
$467$	−8.63167	−0.399426	−0.199713	−	0.979854i	$-0.564001\pi$
$467$	−8.63167	−0.399426	−0.199713	+	0.979854i	$0.564001\pi$
$468$	29.7051	1.37312
$469$	−25.0378	−1.15614
$470$	−5.75278	−0.265356
$471$	−0.492743	−0.0227044
$472$	−7.80577	−0.359290
$473$	0.176159	0.00809978
$474$	0.249449	0.0114576
$475$	−77.5482	−3.55816
$476$	−8.50491	−0.389822
$477$	−2.51299	−0.115062
$478$	3.54780	0.162273
$479$	−28.7535	−1.31378	−0.656891	−	0.753985i	$-0.728129\pi$
$479$	−28.7535	−1.31378	−0.656891	+	0.753985i	$0.728129\pi$
$480$	−2.51066	−0.114596
$481$	−6.86892	−0.313196
$482$	−2.04722	−0.0932481
$483$	6.15890	0.280240
$484$	21.6117	0.982351
$485$	−28.9938	−1.31654
$486$	1.31416	0.0596114
$487$	11.3394	0.513838	0.256919	−	0.966433i	$-0.417293\pi$
$487$	11.3394	0.513838	0.256919	+	0.966433i	$0.417293\pi$
$488$	−0.966072	−0.0437320
$489$	4.32356	0.195518
$490$	8.46344	0.382339
$491$	19.4765	0.878962	0.439481	−	0.898252i	$-0.355162\pi$
$491$	19.4765	0.878962	0.439481	+	0.898252i	$0.355162\pi$
$492$	−3.25117	−0.146574
$493$	2.40862	0.108479
$494$	5.40709	0.243277
$495$	2.16548	0.0973313
$496$	−22.4903	−1.00985
$497$	−26.1410	−1.17258
$498$	0.210632	0.00943867
$499$	14.2589	0.638314	0.319157	−	0.947702i	$-0.396600\pi$
$499$	14.2589	0.638314	0.319157	+	0.947702i	$0.396600\pi$
$500$	64.8066	2.89824
$501$	−0.980666	−0.0438129
$502$	1.39528	0.0622742
$503$	0.468086	0.0208709	0.0104355	−	0.999946i	$-0.496678\pi$
$503$	0.468086	0.0208709	0.0104355	+	0.999946i	$0.496678\pi$
$504$	8.61216	0.383616
$505$	−75.6912	−3.36821
$506$	−0.147740	−0.00656785
$507$	−4.04002	−0.179424
$508$	−29.1037	−1.29127
$509$	34.3459	1.52235	0.761177	−	0.648544i	$-0.224622\pi$
$509$	34.3459	1.52235	0.761177	+	0.648544i	$0.224622\pi$
$510$	0.213438	0.00945120
$511$	14.1922	0.627828
$512$	−12.9883	−0.574008
$513$	−10.5141	−0.464210
$514$	0.101779	0.00448926
$515$	−50.3204	−2.21738
$516$	0.578036	0.0254466
$517$	−1.39297	−0.0612626
$518$	−0.988266	−0.0434219
$519$	5.53364	0.242900
$520$	−14.9448	−0.655371
$521$	−18.5075	−0.810828	−0.405414	−	0.914133i	$-0.632873\pi$
$521$	−18.5075	−0.810828	−0.405414	+	0.914133i	$0.632873\pi$
$522$	−1.21036	−0.0529762
$523$	−13.8951	−0.607591	−0.303795	−	0.952737i	$-0.598254\pi$
$523$	−13.8951	−0.607591	−0.303795	+	0.952737i	$0.598254\pi$
$524$	22.3012	0.974234
$525$	16.2062	0.707298
$526$	0.963686	0.0420187
$527$	5.88376	0.256300
$528$	−0.197550	−0.00859724
$529$	0.651149	0.0283108
$530$	0.627411	0.0272530
$531$	33.2206	1.44165
$532$	−51.5390	−2.23450
$533$	−29.1014	−1.26052
$534$	0.352872	0.0152703
$535$	28.3041	1.22369
$536$	3.97134	0.171536
$537$	5.55476	0.239706
$538$	−2.08364	−0.0898320
$539$	2.04932	0.0882705
$540$	14.4213	0.620592
$541$	−9.31863	−0.400639	−0.200320	−	0.979731i	$-0.564198\pi$
$541$	−9.31863	−0.400639	−0.200320	+	0.979731i	$0.564198\pi$
$542$	5.14691	0.221079
$543$	−6.16784	−0.264687
$544$	2.02855	0.0869733
$545$	−10.2599	−0.439484
$546$	−1.12999	−0.0483591
$547$	−0.567210	−0.0242521	−0.0121261	−	0.999926i	$-0.503860\pi$
$547$	−0.567210	−0.0242521	−0.0121261	+	0.999926i	$0.503860\pi$
$548$	1.55579	0.0664600
$549$	4.11150	0.175475
$550$	−0.388756	−0.0165766
$551$	14.5960	0.621812
$552$	−0.976888	−0.0415791
$553$	−21.2828	−0.905035
$554$	−5.56535	−0.236449
$555$	−1.64310	−0.0697455
$556$	−32.1916	−1.36523
$557$	−3.94707	−0.167243	−0.0836213	−	0.996498i	$-0.526649\pi$
$557$	−3.94707	−0.167243	−0.0836213	+	0.996498i	$0.526649\pi$
$558$	−2.95666	−0.125166
$559$	5.17403	0.218838
$560$	69.6081	2.94148
$561$	0.0516815	0.00218199
$562$	−0.439845	−0.0185537
$563$	−39.8211	−1.67826	−0.839129	−	0.543933i	$-0.816935\pi$
$563$	−39.8211	−1.67826	−0.839129	+	0.543933i	$0.816935\pi$
$564$	−4.57079	−0.192465
$565$	13.5765	0.571168
$566$	−1.49404	−0.0627990
$567$	−35.5379	−1.49245
$568$	4.14633	0.173976
$569$	−23.5468	−0.987132	−0.493566	−	0.869708i	$-0.664307\pi$
$569$	−23.5468	−0.987132	−0.493566	+	0.869708i	$0.664307\pi$
$570$	1.29342	0.0541752
$571$	28.1467	1.17790	0.588951	−	0.808168i	$-0.299541\pi$
$571$	28.1467	1.17790	0.588951	+	0.808168i	$0.299541\pi$
$572$	−1.79579	−0.0750859
$573$	−0.279344	−0.0116697
$574$	−4.18696	−0.174760
$575$	62.2345	2.59536
$576$	21.2573	0.885721
$577$	−22.2525	−0.926383	−0.463191	−	0.886258i	$-0.653296\pi$
$577$	−22.2525	−0.926383	−0.463191	+	0.886258i	$0.653296\pi$
$578$	−0.172452	−0.00717306
$579$	7.70527	0.320220
$580$	−20.0200	−0.831286
$581$	−17.9710	−0.745562
$582$	0.347722	0.0144135
$583$	0.151920	0.00629188
$584$	−2.25109	−0.0931507
$585$	63.6034	2.62968
$586$	−2.14652	−0.0886720
$587$	2.71305	0.111979	0.0559897	−	0.998431i	$-0.482169\pi$
$587$	2.71305	0.111979	0.0559897	+	0.998431i	$0.482169\pi$
$588$	6.72451	0.277314
$589$	35.6551	1.46914
$590$	−8.29410	−0.341463
$591$	3.87835	0.159534
$592$	−5.07459	−0.208564
$593$	−10.2512	−0.420966	−0.210483	−	0.977598i	$-0.567504\pi$
$593$	−10.2512	−0.420966	−0.210483	+	0.977598i	$0.567504\pi$
$594$	−0.0527083	−0.00216265
$595$	−18.2103	−0.746552
$596$	−35.2382	−1.44341
$597$	2.99883	0.122734
$598$	−4.33934	−0.177449
$599$	32.3635	1.32234	0.661168	−	0.750238i	$-0.270061\pi$
$599$	32.3635	1.32234	0.661168	+	0.750238i	$0.270061\pi$
$600$	−2.57054	−0.104942
$601$	−1.48983	−0.0607716	−0.0303858	−	0.999538i	$-0.509674\pi$
$601$	−1.48983	−0.0607716	−0.0303858	+	0.999538i	$0.509674\pi$
$602$	0.744414	0.0303400
$603$	−16.9016	−0.688287
$604$	−43.6698	−1.77690
$605$	46.2741	1.88131
$606$	0.907763	0.0368753
$607$	−39.1723	−1.58995	−0.794977	−	0.606640i	$-0.792517\pi$
$607$	−39.1723	−1.58995	−0.794977	+	0.606640i	$0.792517\pi$
$608$	12.2928	0.498540
$609$	−3.05032	−0.123605
$610$	−1.02651	−0.0415621
$611$	−40.9134	−1.65518
$612$	−5.74120	−0.232074
$613$	5.85102	0.236320	0.118160	−	0.992995i	$-0.462300\pi$
$613$	5.85102	0.236320	0.118160	+	0.992995i	$0.462300\pi$
$614$	3.41547	0.137837
$615$	−6.96126	−0.280705
$616$	−0.520639	−0.0209772
$617$	−2.81791	−0.113445	−0.0567224	−	0.998390i	$-0.518065\pi$
$617$	−2.81791	−0.113445	−0.0567224	+	0.998390i	$0.518065\pi$
$618$	0.603492	0.0242760
$619$	6.68906	0.268856	0.134428	−	0.990923i	$-0.457080\pi$
$619$	6.68906	0.268856	0.134428	+	0.990923i	$0.457080\pi$
$620$	−48.9047	−1.96406
$621$	8.43788	0.338600
$622$	3.21926	0.129081
$623$	−30.1067	−1.20620
$624$	−5.80232	−0.232279
$625$	74.7765	2.99106
$626$	−1.69517	−0.0677525
$627$	0.313185	0.0125074
$628$	−3.30912	−0.132048
$629$	1.32758	0.0529339
$630$	9.15094	0.364582
$631$	24.7710	0.986119	0.493059	−	0.869996i	$-0.335879\pi$
$631$	24.7710	0.986119	0.493059	+	0.869996i	$0.335879\pi$
$632$	3.37574	0.134280
$633$	−3.62468	−0.144068
$634$	5.45315	0.216572
$635$	−62.3156	−2.47292
$636$	0.498501	0.0197668
$637$	60.1915	2.38487
$638$	0.0731713	0.00289688
$639$	−17.6463	−0.698079
$640$	−22.4227	−0.886334
$641$	46.5248	1.83762	0.918809	−	0.394702i	$-0.129152\pi$
$641$	46.5248	1.83762	0.918809	+	0.394702i	$0.129152\pi$
$642$	−0.339450	−0.0133970
$643$	−34.4894	−1.36013	−0.680064	−	0.733153i	$-0.738048\pi$
$643$	−34.4894	−1.36013	−0.680064	+	0.733153i	$0.738048\pi$
$644$	41.3614	1.62987
$645$	1.23767	0.0487330
$646$	−1.04504	−0.0411167
$647$	−21.8630	−0.859525	−0.429762	−	0.902942i	$-0.641403\pi$
$647$	−21.8630	−0.859525	−0.429762	+	0.902942i	$0.641403\pi$
$648$	5.63680	0.221435
$649$	−2.00832	−0.0788333
$650$	−11.4183	−0.447864
$651$	−7.45129	−0.292039
$652$	29.0358	1.13713
$653$	47.2757	1.85004	0.925021	−	0.379916i	$-0.124047\pi$
$653$	47.2757	1.85004	0.925021	+	0.379916i	$0.124047\pi$
$654$	0.123046	0.00481149
$655$	47.7505	1.86577
$656$	−21.4994	−0.839410
$657$	9.58041	0.373767
$658$	−5.88642	−0.229476
$659$	4.83729	0.188434	0.0942170	−	0.995552i	$-0.469965\pi$
$659$	4.83729	0.188434	0.0942170	+	0.995552i	$0.469965\pi$
$660$	−0.429567	−0.0167209
$661$	33.5838	1.30626	0.653130	−	0.757246i	$-0.273455\pi$
$661$	33.5838	1.30626	0.653130	+	0.757246i	$0.273455\pi$
$662$	2.87649	0.111798
$663$	1.51796	0.0589527
$664$	2.85045	0.110619
$665$	−110.353	−4.27931
$666$	−0.667124	−0.0258505
$667$	−11.7137	−0.453557
$668$	−6.58587	−0.254815
$669$	4.05593	0.156811
$670$	4.21979	0.163025
$671$	−0.248557	−0.00959543
$672$	−2.56899	−0.0991009
$673$	23.6150	0.910293	0.455146	−	0.890417i	$-0.349587\pi$
$673$	23.6150	0.910293	0.455146	+	0.890417i	$0.349587\pi$
$674$	−4.07542	−0.156979
$675$	22.2030	0.854595
$676$	−27.1317	−1.04353
$677$	−4.74249	−0.182269	−0.0911343	−	0.995839i	$-0.529049\pi$
$677$	−4.74249	−0.182269	−0.0911343	+	0.995839i	$0.529049\pi$
$678$	−0.162823	−0.00625317
$679$	−29.6673	−1.13853
$680$	2.88842	0.110766
$681$	−2.47286	−0.0947602
$682$	0.178742	0.00684439
$683$	−22.1555	−0.847756	−0.423878	−	0.905719i	$-0.639332\pi$
$683$	−22.1555	−0.847756	−0.423878	+	0.905719i	$0.639332\pi$
$684$	−34.7912	−1.33027
$685$	3.33119	0.127278
$686$	3.44916	0.131689
$687$	−0.246592	−0.00940806
$688$	3.82245	0.145729
$689$	4.46211	0.169993
$690$	−1.03800	−0.0395160
$691$	1.58833	0.0604231	0.0302115	−	0.999544i	$-0.490382\pi$
$691$	1.58833	0.0604231	0.0302115	+	0.999544i	$0.490382\pi$
$692$	37.1624	1.41270
$693$	2.21579	0.0841709
$694$	−1.38413	−0.0525409
$695$	−68.9274	−2.61457
$696$	0.483824	0.0183393
$697$	5.62451	0.213043
$698$	−3.93802	−0.149056
$699$	7.19326	0.272074
$700$	108.837	4.11364
$701$	−39.8473	−1.50501	−0.752505	−	0.658586i	$-0.771155\pi$
$701$	−39.8473	−1.50501	−0.752505	+	0.658586i	$0.771155\pi$
$702$	−1.54812	−0.0584300
$703$	8.04500	0.303423
$704$	−1.28509	−0.0484336
$705$	−9.78679	−0.368592
$706$	−2.09765	−0.0789460
$707$	−77.4495	−2.91279
$708$	−6.58997	−0.247666
$709$	34.7626	1.30554	0.652768	−	0.757558i	$-0.273608\pi$
$709$	34.7626	1.30554	0.652768	+	0.757558i	$0.273608\pi$
$710$	4.40572	0.165344
$711$	−14.3668	−0.538798
$712$	4.77535	0.178964
$713$	−28.6141	−1.07161
$714$	0.218396	0.00817328
$715$	−3.84508	−0.143798
$716$	37.3042	1.39412
$717$	6.03562	0.225404
$718$	−0.434341	−0.0162095
$719$	−27.2621	−1.01670	−0.508352	−	0.861149i	$-0.669745\pi$
$719$	−27.2621	−1.01670	−0.508352	+	0.861149i	$0.669745\pi$
$720$	46.9886	1.75116
$721$	−51.4894	−1.91757
$722$	−3.05629	−0.113743
$723$	−3.48278	−0.129526
$724$	−41.4215	−1.53942
$725$	−30.8229	−1.14474
$726$	−0.554965	−0.0205967
$727$	−4.05340	−0.150332	−0.0751662	−	0.997171i	$-0.523949\pi$
$727$	−4.05340	−0.150332	−0.0751662	+	0.997171i	$0.523949\pi$
$728$	−15.2919	−0.566757
$729$	−22.4626	−0.831948
$730$	−2.39192	−0.0885288
$731$	−1.00000	−0.0369863
$732$	−0.815599	−0.0301454
$733$	9.16733	0.338603	0.169302	−	0.985564i	$-0.445849\pi$
$733$	9.16733	0.338603	0.169302	+	0.985564i	$0.445849\pi$
$734$	−4.61703	−0.170418
$735$	14.3982	0.531087
$736$	−9.86533	−0.363641
$737$	1.02177	0.0376374
$738$	−2.82639	−0.104041
$739$	50.2919	1.85002	0.925009	−	0.379945i	$-0.124057\pi$
$739$	50.2919	1.85002	0.925009	+	0.379945i	$0.124057\pi$
$740$	−11.0346	−0.405639
$741$	9.19870	0.337923
$742$	0.641986	0.0235681
$743$	22.4728	0.824449	0.412224	−	0.911082i	$-0.364752\pi$
$743$	22.4728	0.824449	0.412224	+	0.911082i	$0.364752\pi$
$744$	1.18188	0.0433298
$745$	−75.4505	−2.76429
$746$	−5.55557	−0.203404
$747$	−12.1312	−0.443858
$748$	0.347078	0.0126904
$749$	28.9616	1.05823
$750$	−1.66416	−0.0607665
$751$	−12.6276	−0.460788	−0.230394	−	0.973097i	$-0.574001\pi$
$751$	−12.6276	−0.460788	−0.230394	+	0.973097i	$0.574001\pi$
$752$	−30.2258	−1.10222
$753$	2.37368	0.0865018
$754$	2.14915	0.0782673
$755$	−93.5039	−3.40295
$756$	14.7563	0.536680
$757$	−19.9122	−0.723720	−0.361860	−	0.932232i	$-0.617858\pi$
$757$	−19.9122	−0.723720	−0.361860	+	0.932232i	$0.617858\pi$
$758$	−4.39954	−0.159798
$759$	−0.251340	−0.00912305
$760$	17.5036	0.634921
$761$	40.6930	1.47512	0.737561	−	0.675281i	$-0.235978\pi$
$761$	40.6930	1.47512	0.737561	+	0.675281i	$0.235978\pi$
$762$	0.747350	0.0270736
$763$	−10.4982	−0.380061
$764$	−1.87599	−0.0678711
$765$	−12.2928	−0.444448
$766$	−3.64909	−0.131847
$767$	−58.9872	−2.12990
$768$	−4.01154	−0.144754
$769$	24.9465	0.899594	0.449797	−	0.893131i	$-0.351496\pi$
$769$	24.9465	0.899594	0.449797	+	0.893131i	$0.351496\pi$
$770$	−0.553210	−0.0199363
$771$	0.173149	0.00623580
$772$	51.7464	1.86239
$773$	15.3405	0.551759	0.275879	−	0.961192i	$-0.411031\pi$
$773$	15.3405	0.551759	0.275879	+	0.961192i	$0.411031\pi$
$774$	0.502513	0.0180625
$775$	−75.2939	−2.70464
$776$	4.70565	0.168923
$777$	−1.68127	−0.0603151
$778$	0.417325	0.0149618
$779$	34.0840	1.22119
$780$	−12.6170	−0.451761
$781$	1.06679	0.0381728
$782$	0.838677	0.0299910
$783$	−4.17903	−0.149346
$784$	44.4680	1.58814
$785$	−7.08536	−0.252887
$786$	−0.572671	−0.0204265
$787$	20.9783	0.747795	0.373898	−	0.927470i	$-0.378021\pi$
$787$	20.9783	0.747795	0.373898	+	0.927470i	$0.378021\pi$
$788$	26.0459	0.927848
$789$	1.63945	0.0583660
$790$	3.58693	0.127617
$791$	13.8919	0.493939
$792$	−0.351455	−0.0124884
$793$	−7.30047	−0.259247
$794$	−5.01026	−0.177808
$795$	1.06737	0.0378557
$796$	20.1393	0.713818
$797$	0.267596	0.00947874	0.00473937	−	0.999989i	$-0.498491\pi$
$797$	0.267596	0.00947874	0.00473937	+	0.999989i	$0.498491\pi$
$798$	1.32346	0.0468501
$799$	7.90746	0.279746
$800$	−25.9592	−0.917795
$801$	−20.3234	−0.718092
$802$	−3.73598	−0.131922
$803$	−0.579174	−0.0204386
$804$	3.35277	0.118243
$805$	88.5614	3.12138
$806$	5.24991	0.184920
$807$	−3.54474	−0.124781
$808$	12.2846	0.432170
$809$	−29.4591	−1.03573	−0.517864	−	0.855463i	$-0.673273\pi$
$809$	−29.4591	−1.03573	−0.517864	+	0.855463i	$0.673273\pi$
$810$	5.98944	0.210447
$811$	−37.1346	−1.30397	−0.651986	−	0.758231i	$-0.726064\pi$
$811$	−37.1346	−1.30397	−0.651986	+	0.758231i	$0.726064\pi$
$812$	−20.4851	−0.718886
$813$	8.75606	0.307089
$814$	0.0403303	0.00141358
$815$	62.1702	2.17773
$816$	1.12143	0.0392579
$817$	−6.05991	−0.212010
$818$	0.357905	0.0125138
$819$	65.0809	2.27411
$820$	−46.7499	−1.63258
$821$	37.7936	1.31901	0.659503	−	0.751702i	$-0.270767\pi$
$821$	37.7936	1.31901	0.659503	+	0.751702i	$0.270767\pi$
$822$	−0.0399509	−0.00139345
$823$	28.8414	1.00535	0.502675	−	0.864476i	$-0.332349\pi$
$823$	28.8414	1.00535	0.502675	+	0.864476i	$0.332349\pi$
$824$	8.16694	0.284509
$825$	−0.661363	−0.0230257
$826$	−8.48678	−0.295293
$827$	−9.35284	−0.325230	−0.162615	−	0.986690i	$-0.551993\pi$
$827$	−9.35284	−0.325230	−0.162615	+	0.986690i	$0.551993\pi$
$828$	27.9208	0.970316
$829$	7.95786	0.276388	0.138194	−	0.990405i	$-0.455870\pi$
$829$	7.95786	0.276388	0.138194	+	0.990405i	$0.455870\pi$
$830$	3.02877	0.105130
$831$	−9.46793	−0.328439
$832$	−37.7449	−1.30857
$833$	−11.6334	−0.403073
$834$	0.826645	0.0286244
$835$	−14.1014	−0.487999
$836$	2.10326	0.0727429
$837$	−10.2085	−0.352857
$838$	1.60154	0.0553243
$839$	−26.7280	−0.922752	−0.461376	−	0.887205i	$-0.652644\pi$
$839$	−26.7280	−0.922752	−0.461376	+	0.887205i	$0.652644\pi$
$840$	−3.65794	−0.126211
$841$	−23.1985	−0.799950
$842$	−0.554392	−0.0191056
$843$	−0.748277	−0.0257720
$844$	−24.3424	−0.837898
$845$	−58.0932	−1.99847
$846$	−3.97360	−0.136615
$847$	47.3491	1.62693
$848$	3.29650	0.113202
$849$	−2.54170	−0.0872308
$850$	2.20685	0.0756945
$851$	−6.45633	−0.221320
$852$	3.50050	0.119925
$853$	−9.81495	−0.336057	−0.168029	−	0.985782i	$-0.553740\pi$
$853$	−9.81495	−0.336057	−0.168029	+	0.985782i	$0.553740\pi$
$854$	−1.05036	−0.0359424
$855$	−74.4934	−2.54762
$856$	−4.59372	−0.157010
$857$	−15.4154	−0.526579	−0.263289	−	0.964717i	$-0.584807\pi$
$857$	−15.4154	−0.526579	−0.263289	+	0.964717i	$0.584807\pi$
$858$	0.0461139	0.00157430
$859$	−40.8037	−1.39220	−0.696102	−	0.717943i	$-0.745084\pi$
$859$	−40.8037	−1.39220	−0.696102	+	0.717943i	$0.745084\pi$
$860$	8.31182	0.283431
$861$	−7.12298	−0.242750
$862$	4.67927	0.159376
$863$	20.9368	0.712697	0.356348	−	0.934353i	$-0.384022\pi$
$863$	20.9368	0.712697	0.356348	+	0.934353i	$0.384022\pi$
$864$	−3.51959	−0.119739
$865$	79.5705	2.70548
$866$	5.87140	0.199518
$867$	−0.293380	−0.00996372
$868$	−50.0408	−1.69849
$869$	0.868532	0.0294629
$870$	0.514092	0.0174293
$871$	30.0109	1.01688
$872$	1.66516	0.0563895
$873$	−20.0268	−0.677803
$874$	5.08231	0.171912
$875$	141.985	4.79996
$876$	−1.90047	−0.0642108
$877$	13.1568	0.444273	0.222136	−	0.975016i	$-0.428697\pi$
$877$	13.1568	0.444273	0.222136	+	0.975016i	$0.428697\pi$
$878$	2.08036	0.0702087
$879$	−3.65173	−0.123170
$880$	−2.84065	−0.0957582
$881$	−49.4757	−1.66688	−0.833440	−	0.552610i	$-0.813632\pi$
$881$	−49.4757	−1.66688	−0.833440	+	0.552610i	$0.813632\pi$
$882$	5.84593	0.196843
$883$	1.64401	0.0553252	0.0276626	−	0.999617i	$-0.491194\pi$
$883$	1.64401	0.0553252	0.0276626	+	0.999617i	$0.491194\pi$
$884$	10.1942	0.342868
$885$	−14.1102	−0.474308
$886$	−4.43912	−0.149135
$887$	−13.7314	−0.461054	−0.230527	−	0.973066i	$-0.574045\pi$
$887$	−13.7314	−0.461054	−0.230527	+	0.973066i	$0.574045\pi$
$888$	0.266672	0.00894894
$889$	−63.7632	−2.13855
$890$	5.07409	0.170084
$891$	1.45027	0.0485859
$892$	27.2385	0.912013
$893$	47.9185	1.60353
$894$	0.904876	0.0302636
$895$	79.8743	2.66990
$896$	−22.9436	−0.766491
$897$	−7.38221	−0.246485
$898$	−5.75339	−0.191993
$899$	14.1717	0.472654
$900$	73.4696	2.44899
$901$	−0.862405	−0.0287309
$902$	0.170866	0.00568923
$903$	1.26642	0.0421437
$904$	−2.20345	−0.0732856
$905$	−88.6900	−2.94815
$906$	1.12139	0.0372557
$907$	−30.0990	−0.999419	−0.499710	−	0.866193i	$-0.666560\pi$
$907$	−30.0990	−0.999419	−0.499710	+	0.866193i	$0.666560\pi$
$908$	−16.6070	−0.551123
$909$	−52.2819	−1.73408
$910$	−16.2486	−0.538636
$911$	50.1830	1.66264	0.831318	−	0.555797i	$-0.187587\pi$
$911$	50.1830	1.66264	0.831318	+	0.555797i	$0.187587\pi$
$912$	6.79577	0.225031
$913$	0.733381	0.0242714
$914$	−5.98074	−0.197825
$915$	−1.74633	−0.0577318
$916$	−1.65604	−0.0547171
$917$	48.8598	1.61349
$918$	0.299210	0.00987539
$919$	7.23483	0.238655	0.119327	−	0.992855i	$-0.461926\pi$
$919$	7.23483	0.238655	0.119327	+	0.992855i	$0.461926\pi$
$920$	−14.0471	−0.463118
$921$	5.81049	0.191462
$922$	−4.53683	−0.149413
$923$	31.3332	1.03135
$924$	−0.439546	−0.0144600
$925$	−16.9889	−0.558591
$926$	4.13871	0.136006
$927$	−34.7577	−1.14159
$928$	4.88600	0.160391
$929$	56.8159	1.86407	0.932034	−	0.362371i	$-0.118033\pi$
$929$	56.8159	1.86407	0.932034	+	0.362371i	$0.118033\pi$
$930$	1.25582	0.0411799
$931$	−70.4973	−2.31046
$932$	48.3079	1.58238
$933$	5.47669	0.179299
$934$	1.48855	0.0487068
$935$	0.743149	0.0243036
$936$	−10.3227	−0.337410
$937$	12.2614	0.400563	0.200282	−	0.979738i	$-0.435814\pi$
$937$	12.2614	0.400563	0.200282	+	0.979738i	$0.435814\pi$
$938$	4.31781	0.140982
$939$	−2.88386	−0.0941114
$940$	−65.7253	−2.14372
$941$	56.7052	1.84854	0.924269	−	0.381742i	$-0.124676\pi$
$941$	56.7052	1.84854	0.924269	+	0.381742i	$0.124676\pi$
$942$	0.0849745	0.00276862
$943$	−27.3534	−0.890748
$944$	−43.5783	−1.41835
$945$	31.5955	1.02780
$946$	−0.0303789	−0.000987703 0
$947$	40.6424	1.32070	0.660350	−	0.750958i	$-0.270408\pi$
$947$	40.6424	1.32070	0.660350	+	0.750958i	$0.270408\pi$
$948$	2.84995	0.0925619
$949$	−17.0112	−0.552206
$950$	13.3734	0.433889
$951$	9.27706	0.300829
$952$	2.95552	0.0957888
$953$	16.9551	0.549230	0.274615	−	0.961554i	$-0.411450\pi$
$953$	16.9551	0.549230	0.274615	+	0.961554i	$0.411450\pi$
$954$	0.433370	0.0140309
$955$	−4.01680	−0.129981
$956$	40.5335	1.31095
$957$	0.124481	0.00402390
$958$	4.95861	0.160205
$959$	3.40857	0.110069
$960$	−9.02885	−0.291405
$961$	3.61858	0.116728
$962$	1.18456	0.0381917
$963$	19.5504	0.630003
$964$	−23.3894	−0.753321
$965$	110.797	3.56669
$966$	−1.06211	−0.0341730
$967$	0.778315	0.0250289	0.0125145	−	0.999922i	$-0.496016\pi$
$967$	0.778315	0.0250289	0.0125145	+	0.999922i	$0.496016\pi$
$968$	−7.51023	−0.241388
$969$	−1.77786	−0.0571131
$970$	5.00003	0.160541
$971$	56.8332	1.82386	0.911932	−	0.410342i	$-0.134591\pi$
$971$	56.8332	1.82386	0.911932	+	0.410342i	$0.134591\pi$
$972$	15.0142	0.481581
$973$	−70.5286	−2.26104
$974$	−1.95551	−0.0626584
$975$	−19.4252	−0.622104
$976$	−5.39341	−0.172639
$977$	6.35287	0.203246	0.101623	−	0.994823i	$-0.467596\pi$
$977$	6.35287	0.203246	0.101623	+	0.994823i	$0.467596\pi$
$978$	−0.745606	−0.0238419
$979$	1.22863	0.0392672
$980$	96.6946	3.08880
$981$	−7.08677	−0.226263
$982$	−3.35876	−0.107182
$983$	18.1096	0.577607	0.288803	−	0.957388i	$-0.406743\pi$
$983$	18.1096	0.577607	0.288803	+	0.957388i	$0.406743\pi$
$984$	1.12980	0.0360168
$985$	55.7684	1.77693
$986$	−0.415372	−0.0132281
$987$	−10.0141	−0.318754
$988$	61.7759	1.96535
$989$	4.86324	0.154642
$990$	−0.373442	−0.0118688
$991$	39.0786	1.24137	0.620687	−	0.784058i	$-0.286854\pi$
$991$	39.0786	1.24137	0.620687	+	0.784058i	$0.286854\pi$
$992$	11.9355	0.378952
$993$	4.89356	0.155293
$994$	4.50807	0.142987
$995$	43.1214	1.36704
$996$	2.40647	0.0762519
$997$	−23.7235	−0.751331	−0.375666	−	0.926755i	$-0.622586\pi$
$997$	−23.7235	−0.751331	−0.375666	+	0.926755i	$0.622586\pi$
$998$	−2.45897	−0.0778373
$999$	−2.30339	−0.0728759

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.a.f.1.10	✓	21
3.2	odd	2		6579.2.a.u.1.12		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.a.f.1.10	✓	21	1.1	even	1	trivial
6579.2.a.u.1.12		21	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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.a (trivial)

\(f(q)\)	\(=\)	\(q-0.172452 q^{2} -0.293380 q^{3} -1.97026 q^{4} -4.21864 q^{5} +0.0505941 q^{6} -4.31664 q^{7} +0.684680 q^{8} -2.91393 q^{9} +O(q^{10})\)	\(q-0.172452 q^{2} -0.293380 q^{3} -1.97026 q^{4} -4.21864 q^{5} +0.0505941 q^{6} -4.31664 q^{7} +0.684680 q^{8} -2.91393 q^{9} +0.727513 q^{10} +0.176159 q^{11} +0.578036 q^{12} +5.17403 q^{13} +0.744414 q^{14} +1.23767 q^{15} +3.82245 q^{16} -1.00000 q^{17} +0.502513 q^{18} -6.05991 q^{19} +8.31182 q^{20} +1.26642 q^{21} -0.0303789 q^{22} +4.86324 q^{23} -0.200872 q^{24} +12.7969 q^{25} -0.892272 q^{26} +1.73503 q^{27} +8.50491 q^{28} -2.40862 q^{29} -0.213438 q^{30} -5.88376 q^{31} -2.02855 q^{32} -0.0516815 q^{33} +0.172452 q^{34} +18.2103 q^{35} +5.74120 q^{36} -1.32758 q^{37} +1.04504 q^{38} -1.51796 q^{39} -2.88842 q^{40} -5.62451 q^{41} -0.218396 q^{42} +1.00000 q^{43} -0.347078 q^{44} +12.2928 q^{45} -0.838677 q^{46} -7.90746 q^{47} -1.12143 q^{48} +11.6334 q^{49} -2.20685 q^{50} +0.293380 q^{51} -10.1942 q^{52} +0.862405 q^{53} -0.299210 q^{54} -0.743149 q^{55} -2.95552 q^{56} +1.77786 q^{57} +0.415372 q^{58} -11.4006 q^{59} -2.43852 q^{60} -1.41098 q^{61} +1.01467 q^{62} +12.5784 q^{63} -7.29507 q^{64} -21.8274 q^{65} +0.00891257 q^{66} +5.80029 q^{67} +1.97026 q^{68} -1.42678 q^{69} -3.14041 q^{70} +6.05586 q^{71} -1.99511 q^{72} -3.28780 q^{73} +0.228943 q^{74} -3.75436 q^{75} +11.9396 q^{76} -0.760413 q^{77} +0.261775 q^{78} +4.93040 q^{79} -16.1255 q^{80} +8.23276 q^{81} +0.969958 q^{82} +4.16319 q^{83} -2.49517 q^{84} +4.21864 q^{85} -0.172452 q^{86} +0.706642 q^{87} +0.120612 q^{88} +6.97457 q^{89} -2.11992 q^{90} -22.3344 q^{91} -9.58186 q^{92} +1.72618 q^{93} +1.36366 q^{94} +25.5646 q^{95} +0.595136 q^{96} +6.87277 q^{97} -2.00620 q^{98} -0.513313 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 2 q^{2} - q^{3} + 32 q^{4} - 3 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 34 q^{9}+O(q^{10}) \) 21 * q + 2 * q^2 - q^3 + 32 * q^4 - 3 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 34 * q^9	\( 21 q + 2 q^{2} - q^{3} + 32 q^{4} - 3 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 34 q^{9} + 12 q^{10} + 2 q^{11} - 5 q^{12} + 26 q^{13} - 3 q^{14} + 5 q^{15} + 62 q^{16} - 21 q^{17} - 10 q^{18} + 16 q^{19} - 27 q^{20} + 36 q^{21} - 14 q^{22} - q^{23} + 15 q^{24} + 40 q^{25} - 3 q^{26} - 16 q^{27} + 25 q^{28} + 15 q^{29} + 38 q^{30} + 18 q^{31} + 14 q^{32} + 14 q^{33} - 2 q^{34} - 5 q^{35} + 73 q^{36} + 12 q^{37} + 19 q^{38} - 11 q^{39} + 41 q^{40} - 45 q^{42} + 21 q^{43} - 34 q^{44} - 18 q^{45} + 28 q^{46} - q^{47} - 36 q^{48} + 40 q^{49} + 24 q^{50} + q^{51} + 23 q^{52} + 39 q^{53} - 83 q^{54} - 2 q^{55} - 10 q^{56} + 3 q^{57} + 19 q^{58} + 4 q^{59} - 35 q^{60} + 50 q^{61} + 5 q^{62} - 37 q^{63} + 120 q^{64} - 8 q^{65} - 37 q^{66} + 16 q^{67} - 32 q^{68} + 33 q^{69} - q^{70} + q^{71} - 54 q^{72} + 15 q^{73} + 52 q^{74} + 11 q^{75} - 15 q^{76} + 13 q^{77} - 100 q^{78} + 56 q^{79} - 100 q^{80} + 97 q^{81} - 11 q^{82} + 61 q^{84} + 3 q^{85} + 2 q^{86} - 8 q^{87} - 56 q^{88} + 5 q^{89} - 69 q^{90} - 4 q^{91} - 27 q^{92} + 17 q^{93} - 47 q^{94} - 9 q^{95} + 81 q^{96} - 28 q^{97} + 18 q^{98} - 19 q^{99}+O(q^{100}) \) 21 * q + 2 * q^2 - q^3 + 32 * q^4 - 3 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 34 * q^9 + 12 * q^10 + 2 * q^11 - 5 * q^12 + 26 * q^13 - 3 * q^14 + 5 * q^15 + 62 * q^16 - 21 * q^17 - 10 * q^18 + 16 * q^19 - 27 * q^20 + 36 * q^21 - 14 * q^22 - q^23 + 15 * q^24 + 40 * q^25 - 3 * q^26 - 16 * q^27 + 25 * q^28 + 15 * q^29 + 38 * q^30 + 18 * q^31 + 14 * q^32 + 14 * q^33 - 2 * q^34 - 5 * q^35 + 73 * q^36 + 12 * q^37 + 19 * q^38 - 11 * q^39 + 41 * q^40 - 45 * q^42 + 21 * q^43 - 34 * q^44 - 18 * q^45 + 28 * q^46 - q^47 - 36 * q^48 + 40 * q^49 + 24 * q^50 + q^51 + 23 * q^52 + 39 * q^53 - 83 * q^54 - 2 * q^55 - 10 * q^56 + 3 * q^57 + 19 * q^58 + 4 * q^59 - 35 * q^60 + 50 * q^61 + 5 * q^62 - 37 * q^63 + 120 * q^64 - 8 * q^65 - 37 * q^66 + 16 * q^67 - 32 * q^68 + 33 * q^69 - q^70 + q^71 - 54 * q^72 + 15 * q^73 + 52 * q^74 + 11 * q^75 - 15 * q^76 + 13 * q^77 - 100 * q^78 + 56 * q^79 - 100 * q^80 + 97 * q^81 - 11 * q^82 + 61 * q^84 + 3 * q^85 + 2 * q^86 - 8 * q^87 - 56 * q^88 + 5 * q^89 - 69 * q^90 - 4 * q^91 - 27 * q^92 + 17 * q^93 - 47 * q^94 - 9 * q^95 + 81 * q^96 - 28 * q^97 + 18 * q^98 - 19 * q^99

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