LMFDB - Embedded newform 731.2.a.d.1.3

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:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 9x^{6} + 9x^{5} + 21x^{4} - 21x^{3} - 8x^{2} + 7x - 1 $ x^8 - x^7 - 9x^6 + 9x^5 + 21x^4 - 21x^3 - 8x^2 + 7x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.700276$ of defining polynomial
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)

$f(q)$	$=$	$q-0.700276 q^{2} -2.17405 q^{3} -1.50961 q^{4} -0.553685 q^{5} +1.52243 q^{6} -0.939298 q^{7} +2.45770 q^{8} +1.72649 q^{9} +O(q^{10})$	\(q-0.700276 q^{2} -2.17405 q^{3} -1.50961 q^{4} -0.553685 q^{5} +1.52243 q^{6} -0.939298 q^{7} +2.45770 q^{8} +1.72649 q^{9} +0.387732 q^{10} +4.19158 q^{11} +3.28197 q^{12} +2.15797 q^{13} +0.657768 q^{14} +1.20374 q^{15} +1.29816 q^{16} +1.00000 q^{17} -1.20902 q^{18} +1.29119 q^{19} +0.835850 q^{20} +2.04208 q^{21} -2.93526 q^{22} -5.86410 q^{23} -5.34315 q^{24} -4.69343 q^{25} -1.51118 q^{26} +2.76868 q^{27} +1.41798 q^{28} -6.74436 q^{29} -0.842948 q^{30} -1.18886 q^{31} -5.82447 q^{32} -9.11271 q^{33} -0.700276 q^{34} +0.520075 q^{35} -2.60633 q^{36} +10.1993 q^{37} -0.904188 q^{38} -4.69154 q^{39} -1.36079 q^{40} -7.21329 q^{41} -1.43002 q^{42} +1.00000 q^{43} -6.32767 q^{44} -0.955929 q^{45} +4.10649 q^{46} +6.83435 q^{47} -2.82227 q^{48} -6.11772 q^{49} +3.28670 q^{50} -2.17405 q^{51} -3.25771 q^{52} -0.839592 q^{53} -1.93884 q^{54} -2.32081 q^{55} -2.30851 q^{56} -2.80711 q^{57} +4.72291 q^{58} -2.69860 q^{59} -1.81718 q^{60} -9.70801 q^{61} +0.832529 q^{62} -1.62169 q^{63} +1.48241 q^{64} -1.19484 q^{65} +6.38141 q^{66} -0.826403 q^{67} -1.50961 q^{68} +12.7488 q^{69} -0.364196 q^{70} +8.41907 q^{71} +4.24318 q^{72} -9.01176 q^{73} -7.14232 q^{74} +10.2038 q^{75} -1.94920 q^{76} -3.93715 q^{77} +3.28537 q^{78} -9.88259 q^{79} -0.718772 q^{80} -11.1987 q^{81} +5.05129 q^{82} -13.1895 q^{83} -3.08275 q^{84} -0.553685 q^{85} -0.700276 q^{86} +14.6626 q^{87} +10.3016 q^{88} +17.6258 q^{89} +0.669414 q^{90} -2.02698 q^{91} +8.85253 q^{92} +2.58464 q^{93} -4.78593 q^{94} -0.714911 q^{95} +12.6627 q^{96} -17.8855 q^{97} +4.28409 q^{98} +7.23671 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 3 q^{3} + 3 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 5 q^{9}+O(q^{10}) $ 8 * q + q^2 - 3 * q^3 + 3 * q^4 - 7 * q^5 - q^6 - 5 * q^7 - 3 * q^8 + 5 * q^9	\( 8 q + q^{2} - 3 q^{3} + 3 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 5 q^{9} - 12 q^{10} - 4 q^{11} - 13 q^{12} - 12 q^{13} + q^{14} - 9 q^{15} - 3 q^{16} + 8 q^{17} + 5 q^{18} - 5 q^{20} - 20 q^{21} - 14 q^{22} - 9 q^{23} - q^{24} - 7 q^{25} - 17 q^{26} - 12 q^{27} + q^{28} - 27 q^{29} + 10 q^{30} - 12 q^{31} + 5 q^{32} + 10 q^{33} + q^{34} + 15 q^{35} - 4 q^{36} - 24 q^{37} - q^{38} + 3 q^{39} - 9 q^{40} - 8 q^{41} - 9 q^{42} + 8 q^{43} - 16 q^{44} + 10 q^{45} - 14 q^{46} + 15 q^{47} + 10 q^{48} - 7 q^{49} + 21 q^{50} - 3 q^{51} + q^{52} - 23 q^{53} - 19 q^{54} - 14 q^{55} - 20 q^{56} - 13 q^{57} - 7 q^{58} + 16 q^{59} - 3 q^{60} - 34 q^{61} + 15 q^{62} + 9 q^{63} - 25 q^{64} + 10 q^{65} + 15 q^{66} + 3 q^{68} - 19 q^{69} + 11 q^{70} - 3 q^{71} - 19 q^{72} - 3 q^{73} - 4 q^{74} + 27 q^{75} + 13 q^{76} - 3 q^{77} + 4 q^{78} - 24 q^{79} + 20 q^{80} - 8 q^{81} + 33 q^{82} - 8 q^{83} + 17 q^{84} - 7 q^{85} + q^{86} + 48 q^{87} + 16 q^{88} + 23 q^{89} + 11 q^{90} - 16 q^{91} + 49 q^{92} + 17 q^{93} - 11 q^{94} + 3 q^{95} + 37 q^{96} - 10 q^{97} + 29 q^{98} - 15 q^{99}+O(q^{100}) \) 8 * q + q^2 - 3 * q^3 + 3 * q^4 - 7 * q^5 - q^6 - 5 * q^7 - 3 * q^8 + 5 * q^9 - 12 * q^10 - 4 * q^11 - 13 * q^12 - 12 * q^13 + q^14 - 9 * q^15 - 3 * q^16 + 8 * q^17 + 5 * q^18 - 5 * q^20 - 20 * q^21 - 14 * q^22 - 9 * q^23 - q^24 - 7 * q^25 - 17 * q^26 - 12 * q^27 + q^28 - 27 * q^29 + 10 * q^30 - 12 * q^31 + 5 * q^32 + 10 * q^33 + q^34 + 15 * q^35 - 4 * q^36 - 24 * q^37 - q^38 + 3 * q^39 - 9 * q^40 - 8 * q^41 - 9 * q^42 + 8 * q^43 - 16 * q^44 + 10 * q^45 - 14 * q^46 + 15 * q^47 + 10 * q^48 - 7 * q^49 + 21 * q^50 - 3 * q^51 + q^52 - 23 * q^53 - 19 * q^54 - 14 * q^55 - 20 * q^56 - 13 * q^57 - 7 * q^58 + 16 * q^59 - 3 * q^60 - 34 * q^61 + 15 * q^62 + 9 * q^63 - 25 * q^64 + 10 * q^65 + 15 * q^66 + 3 * q^68 - 19 * q^69 + 11 * q^70 - 3 * q^71 - 19 * q^72 - 3 * q^73 - 4 * q^74 + 27 * q^75 + 13 * q^76 - 3 * q^77 + 4 * q^78 - 24 * q^79 + 20 * q^80 - 8 * q^81 + 33 * q^82 - 8 * q^83 + 17 * q^84 - 7 * q^85 + q^86 + 48 * q^87 + 16 * q^88 + 23 * q^89 + 11 * q^90 - 16 * q^91 + 49 * q^92 + 17 * q^93 - 11 * q^94 + 3 * q^95 + 37 * q^96 - 10 * q^97 + 29 * q^98 - 15 * 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 $

$2$	−0.700276	−0.495170	−0.247585	−	0.968866i	$-0.579637\pi$
$2$	−0.700276	−0.495170	−0.247585	+	0.968866i	$0.579637\pi$
$3$	−2.17405	−1.25519	−0.627594	−	0.778541i	$-0.715960\pi$
$3$	−2.17405	−1.25519	−0.627594	+	0.778541i	$0.715960\pi$
$4$	−1.50961	−0.754807
$5$	−0.553685	−0.247615	−0.123808	−	0.992306i	$-0.539511\pi$
$5$	−0.553685	−0.247615	−0.123808	+	0.992306i	$0.539511\pi$
$6$	1.52243	0.621531
$7$	−0.939298	−0.355021	−0.177511	−	0.984119i	$-0.556804\pi$
$7$	−0.939298	−0.355021	−0.177511	+	0.984119i	$0.556804\pi$
$8$	2.45770	0.868927
$9$	1.72649	0.575496
$10$	0.387732	0.122612
$11$	4.19158	1.26381	0.631905	−	0.775046i	$-0.282273\pi$
$11$	4.19158	1.26381	0.631905	+	0.775046i	$0.282273\pi$
$12$	3.28197	0.947424
$13$	2.15797	0.598514	0.299257	−	0.954173i	$-0.403261\pi$
$13$	2.15797	0.598514	0.299257	+	0.954173i	$0.403261\pi$
$14$	0.657768	0.175796
$15$	1.20374	0.310804
$16$	1.29816	0.324540
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.20902	−0.284968
$19$	1.29119	0.296219	0.148109	−	0.988971i	$-0.452681\pi$
$19$	1.29119	0.296219	0.148109	+	0.988971i	$0.452681\pi$
$20$	0.835850	0.186902
$21$	2.04208	0.445618
$22$	−2.93526	−0.625800
$23$	−5.86410	−1.22275	−0.611375	−	0.791341i	$-0.709383\pi$
$23$	−5.86410	−1.22275	−0.611375	+	0.791341i	$0.709383\pi$
$24$	−5.34315	−1.09067
$25$	−4.69343	−0.938687
$26$	−1.51118	−0.296366
$27$	2.76868	0.532832
$28$	1.41798	0.267972
$29$	−6.74436	−1.25240	−0.626199	−	0.779664i	$-0.715390\pi$
$29$	−6.74436	−1.25240	−0.626199	+	0.779664i	$0.715390\pi$
$30$	−0.842948	−0.153901
$31$	−1.18886	−0.213525	−0.106763	−	0.994285i	$-0.534049\pi$
$31$	−1.18886	−0.213525	−0.106763	+	0.994285i	$0.534049\pi$
$32$	−5.82447	−1.02963
$33$	−9.11271	−1.58632
$34$	−0.700276	−0.120096
$35$	0.520075	0.0879087
$36$	−2.60633	−0.434388
$37$	10.1993	1.67675	0.838377	−	0.545090i	$-0.183505\pi$
$37$	10.1993	1.67675	0.838377	+	0.545090i	$0.183505\pi$
$38$	−0.904188	−0.146679
$39$	−4.69154	−0.751247
$40$	−1.36079	−0.215160
$41$	−7.21329	−1.12653	−0.563264	−	0.826277i	$-0.690454\pi$
$41$	−7.21329	−1.12653	−0.563264	+	0.826277i	$0.690454\pi$
$42$	−1.43002	−0.220657
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−6.32767	−0.953932
$45$	−0.955929	−0.142502
$46$	4.10649	0.605469
$47$	6.83435	0.996892	0.498446	−	0.866921i	$-0.333904\pi$
$47$	6.83435	0.996892	0.498446	+	0.866921i	$0.333904\pi$
$48$	−2.82227	−0.407359
$49$	−6.11772	−0.873960
$50$	3.28670	0.464809
$51$	−2.17405	−0.304428
$52$	−3.25771	−0.451763
$53$	−0.839592	−0.115327	−0.0576634	−	0.998336i	$-0.518365\pi$
$53$	−0.839592	−0.115327	−0.0576634	+	0.998336i	$0.518365\pi$
$54$	−1.93884	−0.263843
$55$	−2.32081	−0.312939
$56$	−2.30851	−0.308488
$57$	−2.80711	−0.371810
$58$	4.72291	0.620149
$59$	−2.69860	−0.351328	−0.175664	−	0.984450i	$-0.556207\pi$
$59$	−2.69860	−0.351328	−0.175664	+	0.984450i	$0.556207\pi$
$60$	−1.81718	−0.234597
$61$	−9.70801	−1.24298	−0.621491	−	0.783421i	$-0.713473\pi$
$61$	−9.70801	−1.24298	−0.621491	+	0.783421i	$0.713473\pi$
$62$	0.832529	0.105731
$63$	−1.62169	−0.204313
$64$	1.48241	0.185301
$65$	−1.19484	−0.148201
$66$	6.38141	0.785497
$67$	−0.826403	−0.100961	−0.0504806	−	0.998725i	$-0.516075\pi$
$67$	−0.826403	−0.100961	−0.0504806	+	0.998725i	$0.516075\pi$
$68$	−1.50961	−0.183068
$69$	12.7488	1.53478
$70$	−0.364196	−0.0435297
$71$	8.41907	0.999159	0.499580	−	0.866268i	$-0.333488\pi$
$71$	8.41907	0.999159	0.499580	+	0.866268i	$0.333488\pi$
$72$	4.24318	0.500064
$73$	−9.01176	−1.05475	−0.527374	−	0.849634i	$-0.676823\pi$
$73$	−9.01176	−1.05475	−0.527374	+	0.849634i	$0.676823\pi$
$74$	−7.14232	−0.830278
$75$	10.2038	1.17823
$76$	−1.94920	−0.223588
$77$	−3.93715	−0.448679
$78$	3.28537	0.371995
$79$	−9.88259	−1.11188	−0.555939	−	0.831223i	$-0.687641\pi$
$79$	−9.88259	−1.11188	−0.555939	+	0.831223i	$0.687641\pi$
$80$	−0.718772	−0.0803612
$81$	−11.1987	−1.24430
$82$	5.05129	0.557822
$83$	−13.1895	−1.44774	−0.723869	−	0.689937i	$-0.757638\pi$
$83$	−13.1895	−1.44774	−0.723869	+	0.689937i	$0.757638\pi$
$84$	−3.08275	−0.336356
$85$	−0.553685	−0.0600555
$86$	−0.700276	−0.0755127
$87$	14.6626	1.57199
$88$	10.3016	1.09816
$89$	17.6258	1.86833	0.934163	−	0.356845i	$-0.116148\pi$
$89$	17.6258	1.86833	0.934163	+	0.356845i	$0.116148\pi$
$90$	0.669414	0.0705624
$91$	−2.02698	−0.212485
$92$	8.85253	0.922940
$93$	2.58464	0.268014
$94$	−4.78593	−0.493631
$95$	−0.714911	−0.0733483
$96$	12.6627	1.29238
$97$	−17.8855	−1.81600	−0.907998	−	0.418974i	$-0.862390\pi$
$97$	−17.8855	−1.81600	−0.907998	+	0.418974i	$0.862390\pi$
$98$	4.28409	0.432759
$99$	7.23671	0.727317
$100$	7.08527	0.708527
$101$	−5.52361	−0.549620	−0.274810	−	0.961499i	$-0.588615\pi$
$101$	−5.52361	−0.549620	−0.274810	+	0.961499i	$0.588615\pi$
$102$	1.52243	0.150743
$103$	4.27021	0.420757	0.210378	−	0.977620i	$-0.432530\pi$
$103$	4.27021	0.420757	0.210378	+	0.977620i	$0.432530\pi$
$104$	5.30365	0.520065
$105$	−1.13067	−0.110342
$106$	0.587946	0.0571063
$107$	11.9042	1.15083	0.575413	−	0.817863i	$-0.304841\pi$
$107$	11.9042	1.15083	0.575413	+	0.817863i	$0.304841\pi$
$108$	−4.17964	−0.402186
$109$	−20.8344	−1.99557	−0.997786	−	0.0665039i	$-0.978816\pi$
$109$	−20.8344	−1.99557	−0.997786	+	0.0665039i	$0.978816\pi$
$110$	1.62521	0.154958
$111$	−22.1738	−2.10464
$112$	−1.21936	−0.115219
$113$	6.16876	0.580308	0.290154	−	0.956980i	$-0.406293\pi$
$113$	6.16876	0.580308	0.290154	+	0.956980i	$0.406293\pi$
$114$	1.96575	0.184109
$115$	3.24686	0.302771
$116$	10.1814	0.945318
$117$	3.72571	0.344442
$118$	1.88976	0.173967
$119$	−0.939298	−0.0861053
$120$	2.95842	0.270066
$121$	6.56937	0.597215
$122$	6.79828	0.615487
$123$	15.6820	1.41400
$124$	1.79472	0.161170
$125$	5.36710	0.480048
$126$	1.13563	0.101170
$127$	−3.44451	−0.305651	−0.152825	−	0.988253i	$-0.548837\pi$
$127$	−3.44451	−0.305651	−0.152825	+	0.988253i	$0.548837\pi$
$128$	10.6108	0.937874
$129$	−2.17405	−0.191414
$130$	0.836715	0.0733848
$131$	−13.7144	−1.19823	−0.599115	−	0.800663i	$-0.704481\pi$
$131$	−13.7144	−1.19823	−0.599115	+	0.800663i	$0.704481\pi$
$132$	13.7567	1.19736
$133$	−1.21281	−0.105164
$134$	0.578710	0.0499929
$135$	−1.53297	−0.131937
$136$	2.45770	0.210746
$137$	11.7562	1.00440	0.502201	−	0.864751i	$-0.332524\pi$
$137$	11.7562	1.00440	0.502201	+	0.864751i	$0.332524\pi$
$138$	−8.92770	−0.759977
$139$	17.1248	1.45250	0.726251	−	0.687429i	$-0.241261\pi$
$139$	17.1248	1.45250	0.726251	+	0.687429i	$0.241261\pi$
$140$	−0.785112	−0.0663541
$141$	−14.8582	−1.25129
$142$	−5.89567	−0.494753
$143$	9.04532	0.756408
$144$	2.24126	0.186772
$145$	3.73425	0.310113
$146$	6.31072	0.522279
$147$	13.3002	1.09698
$148$	−15.3970	−1.26563
$149$	−11.0882	−0.908382	−0.454191	−	0.890904i	$-0.650072\pi$
$149$	−11.0882	−0.908382	−0.454191	+	0.890904i	$0.650072\pi$
$150$	−7.14544	−0.583423
$151$	3.44058	0.279990	0.139995	−	0.990152i	$-0.455291\pi$
$151$	3.44058	0.279990	0.139995	+	0.990152i	$0.455291\pi$
$152$	3.17335	0.257393
$153$	1.72649	0.139578
$154$	2.75709	0.222172
$155$	0.658253	0.0528722
$156$	7.08241	0.567047
$157$	1.49893	0.119627	0.0598137	−	0.998210i	$-0.480949\pi$
$157$	1.49893	0.119627	0.0598137	+	0.998210i	$0.480949\pi$
$158$	6.92054	0.550569
$159$	1.82531	0.144757
$160$	3.22492	0.254952
$161$	5.50814	0.434102
$162$	7.84218	0.616140
$163$	−13.5122	−1.05835	−0.529177	−	0.848511i	$-0.677499\pi$
$163$	−13.5122	−1.05835	−0.529177	+	0.848511i	$0.677499\pi$
$164$	10.8893	0.850310
$165$	5.04556	0.392797
$166$	9.23631	0.716876
$167$	2.30380	0.178273	0.0891367	−	0.996019i	$-0.471589\pi$
$167$	2.30380	0.178273	0.0891367	+	0.996019i	$0.471589\pi$
$168$	5.01881	0.387210
$169$	−8.34315	−0.641781
$170$	0.387732	0.0297377
$171$	2.22922	0.170473
$172$	−1.50961	−0.115107
$173$	0.379987	0.0288899	0.0144449	−	0.999896i	$-0.495402\pi$
$173$	0.379987	0.0288899	0.0144449	+	0.999896i	$0.495402\pi$
$174$	−10.2678	−0.778403
$175$	4.40853	0.333254
$176$	5.44135	0.410157
$177$	5.86689	0.440982
$178$	−12.3429	−0.925139
$179$	−13.1384	−0.982007	−0.491004	−	0.871158i	$-0.663370\pi$
$179$	−13.1384	−0.982007	−0.491004	+	0.871158i	$0.663370\pi$
$180$	1.44308	0.107561
$181$	2.58726	0.192309	0.0961547	−	0.995366i	$-0.469346\pi$
$181$	2.58726	0.192309	0.0961547	+	0.995366i	$0.469346\pi$
$182$	1.41944	0.105216
$183$	21.1057	1.56018
$184$	−14.4122	−1.06248
$185$	−5.64720	−0.415190
$186$	−1.80996	−0.132713
$187$	4.19158	0.306519
$188$	−10.3172	−0.752461
$189$	−2.60061	−0.189167
$190$	0.500635	0.0363199
$191$	−17.5614	−1.27070	−0.635351	−	0.772224i	$-0.719144\pi$
$191$	−17.5614	−1.27070	−0.635351	+	0.772224i	$0.719144\pi$
$192$	−3.22283	−0.232588
$193$	−7.89542	−0.568324	−0.284162	−	0.958776i	$-0.591715\pi$
$193$	−7.89542	−0.568324	−0.284162	+	0.958776i	$0.591715\pi$
$194$	12.5248	0.899227
$195$	2.59763	0.186020
$196$	9.23539	0.659671
$197$	−17.2490	−1.22894	−0.614469	−	0.788941i	$-0.710630\pi$
$197$	−17.2490	−1.22894	−0.614469	+	0.788941i	$0.710630\pi$
$198$	−5.06770	−0.360145
$199$	−10.2317	−0.725303	−0.362652	−	0.931925i	$-0.618128\pi$
$199$	−10.2317	−0.725303	−0.362652	+	0.931925i	$0.618128\pi$
$200$	−11.5350	−0.815650
$201$	1.79664	0.126725
$202$	3.86805	0.272155
$203$	6.33497	0.444628
$204$	3.28197	0.229784
$205$	3.99389	0.278945
$206$	−2.99033	−0.208346
$207$	−10.1243	−0.703687
$208$	2.80140	0.194242
$209$	5.41212	0.374364
$210$	0.791779	0.0546380
$211$	11.0452	0.760385	0.380192	−	0.924907i	$-0.375858\pi$
$211$	11.0452	0.760385	0.380192	+	0.924907i	$0.375858\pi$
$212$	1.26746	0.0870495
$213$	−18.3035	−1.25413
$214$	−8.33625	−0.569855
$215$	−0.553685	−0.0377610
$216$	6.80458	0.462993
$217$	1.11669	0.0758061
$218$	14.5898	0.988147
$219$	19.5920	1.32391
$220$	3.50353	0.236208
$221$	2.15797	0.145161
$222$	15.5278	1.04215
$223$	−10.3166	−0.690848	−0.345424	−	0.938447i	$-0.612265\pi$
$223$	−10.3166	−0.690848	−0.345424	+	0.938447i	$0.612265\pi$
$224$	5.47091	0.365540
$225$	−8.10315	−0.540210
$226$	−4.31984	−0.287351
$227$	−13.7590	−0.913220	−0.456610	−	0.889667i	$-0.650936\pi$
$227$	−13.7590	−0.913220	−0.456610	+	0.889667i	$0.650936\pi$
$228$	4.23765	0.280645
$229$	−20.2272	−1.33665	−0.668325	−	0.743869i	$-0.732988\pi$
$229$	−20.2272	−1.33665	−0.668325	+	0.743869i	$0.732988\pi$
$230$	−2.27370	−0.149923
$231$	8.55954	0.563177
$232$	−16.5756	−1.08824
$233$	10.7951	0.707211	0.353606	−	0.935395i	$-0.384956\pi$
$233$	10.7951	0.707211	0.353606	+	0.935395i	$0.384956\pi$
$234$	−2.60903	−0.170557
$235$	−3.78407	−0.246846
$236$	4.07384	0.265185
$237$	21.4852	1.39562
$238$	0.657768	0.0426367
$239$	25.7910	1.66828	0.834139	−	0.551554i	$-0.185965\pi$
$239$	25.7910	1.66828	0.834139	+	0.551554i	$0.185965\pi$
$240$	1.56265	0.100868
$241$	−24.4736	−1.57648	−0.788242	−	0.615365i	$-0.789009\pi$
$241$	−24.4736	−1.57648	−0.788242	+	0.615365i	$0.789009\pi$
$242$	−4.60037	−0.295723
$243$	16.0405	1.02900
$244$	14.6553	0.938212
$245$	3.38729	0.216406
$246$	−10.9818	−0.700171
$247$	2.78635	0.177291
$248$	−2.92186	−0.185538
$249$	28.6747	1.81718
$250$	−3.75845	−0.237705
$251$	26.2281	1.65550	0.827751	−	0.561095i	$-0.189620\pi$
$251$	26.2281	1.65550	0.827751	+	0.561095i	$0.189620\pi$
$252$	2.44812	0.154217
$253$	−24.5799	−1.54532
$254$	2.41211	0.151349
$255$	1.20374	0.0753809
$256$	−10.3953	−0.649708
$257$	30.5054	1.90287	0.951436	−	0.307845i	$-0.0996079\pi$
$257$	30.5054	1.90287	0.951436	+	0.307845i	$0.0996079\pi$
$258$	1.52243	0.0947826
$259$	−9.58018	−0.595284
$260$	1.80374	0.111863
$261$	−11.6441	−0.720749
$262$	9.60383	0.593327
$263$	−5.97261	−0.368287	−0.184143	−	0.982899i	$-0.558951\pi$
$263$	−5.97261	−0.368287	−0.184143	+	0.982899i	$0.558951\pi$
$264$	−22.3963	−1.37840
$265$	0.464869	0.0285567
$266$	0.849302	0.0520740
$267$	−38.3193	−2.34510
$268$	1.24755	0.0762062
$269$	−26.0968	−1.59115	−0.795575	−	0.605855i	$-0.792831\pi$
$269$	−26.0968	−1.59115	−0.795575	+	0.605855i	$0.792831\pi$
$270$	1.07351	0.0653314
$271$	14.9787	0.909890	0.454945	−	0.890519i	$-0.349659\pi$
$271$	14.9787	0.909890	0.454945	+	0.890519i	$0.349659\pi$
$272$	1.29816	0.0787126
$273$	4.40675	0.266709
$274$	−8.23260	−0.497349
$275$	−19.6729	−1.18632
$276$	−19.2458	−1.15846
$277$	−18.8463	−1.13236	−0.566181	−	0.824281i	$-0.691580\pi$
$277$	−18.8463	−1.13236	−0.566181	+	0.824281i	$0.691580\pi$
$278$	−11.9920	−0.719235
$279$	−2.05255	−0.122883
$280$	1.27819	0.0763862
$281$	−6.12701	−0.365507	−0.182753	−	0.983159i	$-0.558501\pi$
$281$	−6.12701	−0.365507	−0.182753	+	0.983159i	$0.558501\pi$
$282$	10.4048	0.619599
$283$	−15.5410	−0.923816	−0.461908	−	0.886928i	$-0.652835\pi$
$283$	−15.5410	−0.923816	−0.461908	+	0.886928i	$0.652835\pi$
$284$	−12.7095	−0.754172
$285$	1.55425	0.0920659
$286$	−6.33422	−0.374550
$287$	6.77543	0.399941
$288$	−10.0559	−0.592548
$289$	1.00000	0.0588235
$290$	−2.61501	−0.153558
$291$	38.8839	2.27942
$292$	13.6043	0.796130
$293$	−5.55932	−0.324779	−0.162389	−	0.986727i	$-0.551920\pi$
$293$	−5.55932	−0.324779	−0.162389	+	0.986727i	$0.551920\pi$
$294$	−9.31382	−0.543193
$295$	1.49417	0.0869941
$296$	25.0668	1.45698
$297$	11.6051	0.673399
$298$	7.76481	0.449803
$299$	−12.6546	−0.731833
$300$	−15.4037	−0.889335
$301$	−0.939298	−0.0541402
$302$	−2.40935	−0.138643
$303$	12.0086	0.689876
$304$	1.67617	0.0961350
$305$	5.37517	0.307782
$306$	−1.20902	−0.0691149
$307$	22.5616	1.28766	0.643829	−	0.765170i	$-0.277345\pi$
$307$	22.5616	1.28766	0.643829	+	0.765170i	$0.277345\pi$
$308$	5.94357	0.338666
$309$	−9.28365	−0.528129
$310$	−0.460959	−0.0261807
$311$	5.39247	0.305779	0.152889	−	0.988243i	$-0.451142\pi$
$311$	5.39247	0.305779	0.152889	+	0.988243i	$0.451142\pi$
$312$	−11.5304	−0.652779
$313$	14.1115	0.797627	0.398814	−	0.917032i	$-0.369422\pi$
$313$	14.1115	0.797627	0.398814	+	0.917032i	$0.369422\pi$
$314$	−1.04966	−0.0592358
$315$	0.897902	0.0505911
$316$	14.9189	0.839254
$317$	−0.0796648	−0.00447442	−0.00223721	−	0.999997i	$-0.500712\pi$
$317$	−0.0796648	−0.00447442	−0.00223721	+	0.999997i	$0.500712\pi$
$318$	−1.27822	−0.0716792
$319$	−28.2696	−1.58279
$320$	−0.820787	−0.0458834
$321$	−25.8804	−1.44450
$322$	−3.85722	−0.214954
$323$	1.29119	0.0718437
$324$	16.9057	0.939207
$325$	−10.1283	−0.561817
$326$	9.46224	0.524065
$327$	45.2950	2.50482
$328$	−17.7281	−0.978870
$329$	−6.41949	−0.353918
$330$	−3.53329	−0.194501
$331$	6.94268	0.381604	0.190802	−	0.981629i	$-0.438891\pi$
$331$	6.94268	0.381604	0.190802	+	0.981629i	$0.438891\pi$
$332$	19.9111	1.09276
$333$	17.6090	0.964965
$334$	−1.61330	−0.0882756
$335$	0.457567	0.0249995
$336$	2.65095	0.144621
$337$	−35.2679	−1.92117	−0.960584	−	0.277991i	$-0.910331\pi$
$337$	−35.2679	−1.92117	−0.960584	+	0.277991i	$0.910331\pi$
$338$	5.84251	0.317790
$339$	−13.4112	−0.728396
$340$	0.835850	0.0453303
$341$	−4.98320	−0.269856
$342$	−1.56107	−0.0844130
$343$	12.3214	0.665296
$344$	2.45770	0.132510
$345$	−7.05884	−0.380035
$346$	−0.266096	−0.0143054
$347$	−11.0825	−0.594938	−0.297469	−	0.954731i	$-0.596143\pi$
$347$	−11.0825	−0.594938	−0.297469	+	0.954731i	$0.596143\pi$
$348$	−22.1348	−1.18655
$349$	20.7909	1.11291	0.556457	−	0.830876i	$-0.312160\pi$
$349$	20.7909	1.11291	0.556457	+	0.830876i	$0.312160\pi$
$350$	−3.08719	−0.165017
$351$	5.97473	0.318908
$352$	−24.4137	−1.30126
$353$	17.5850	0.935957	0.467979	−	0.883740i	$-0.344982\pi$
$353$	17.5850	0.935957	0.467979	+	0.883740i	$0.344982\pi$
$354$	−4.10844	−0.218361
$355$	−4.66151	−0.247407
$356$	−26.6081	−1.41023
$357$	2.04208	0.108078
$358$	9.20047	0.486260
$359$	−35.3016	−1.86315	−0.931574	−	0.363551i	$-0.881564\pi$
$359$	−35.3016	−1.86315	−0.931574	+	0.363551i	$0.881564\pi$
$360$	−2.34939	−0.123823
$361$	−17.3328	−0.912254
$362$	−1.81179	−0.0952258
$363$	−14.2821	−0.749617
$364$	3.05996	0.160385
$365$	4.98967	0.261171
$366$	−14.7798	−0.772552
$367$	23.1009	1.20586	0.602929	−	0.797795i	$-0.294000\pi$
$367$	23.1009	1.20586	0.602929	+	0.797795i	$0.294000\pi$
$368$	−7.61255	−0.396832
$369$	−12.4537	−0.648311
$370$	3.95459	0.205590
$371$	0.788627	0.0409435
$372$	−3.90181	−0.202299
$373$	−19.4372	−1.00642	−0.503211	−	0.864163i	$-0.667848\pi$
$373$	−19.4372	−1.00642	−0.503211	+	0.864163i	$0.667848\pi$
$374$	−2.93526	−0.151779
$375$	−11.6683	−0.602551
$376$	16.7968	0.866227
$377$	−14.5542	−0.749577
$378$	1.82115	0.0936697
$379$	−30.1016	−1.54622	−0.773108	−	0.634274i	$-0.781299\pi$
$379$	−30.1016	−1.54622	−0.773108	+	0.634274i	$0.781299\pi$
$380$	1.07924	0.0553638
$381$	7.48853	0.383649
$382$	12.2979	0.629213
$383$	18.1092	0.925337	0.462669	−	0.886531i	$-0.346892\pi$
$383$	18.1092	0.925337	0.462669	+	0.886531i	$0.346892\pi$
$384$	−23.0685	−1.17721
$385$	2.17994	0.111100
$386$	5.52897	0.281417
$387$	1.72649	0.0877623
$388$	27.0002	1.37073
$389$	−5.86498	−0.297366	−0.148683	−	0.988885i	$-0.547503\pi$
$389$	−5.86498	−0.297366	−0.148683	+	0.988885i	$0.547503\pi$
$390$	−1.81906	−0.0921116
$391$	−5.86410	−0.296560
$392$	−15.0355	−0.759408
$393$	29.8157	1.50400
$394$	12.0790	0.608533
$395$	5.47184	0.275318
$396$	−10.9246	−0.548984
$397$	18.1107	0.908948	0.454474	−	0.890760i	$-0.349827\pi$
$397$	18.1107	0.908948	0.454474	+	0.890760i	$0.349827\pi$
$398$	7.16498	0.359148
$399$	2.63671	0.132001
$400$	−6.09284	−0.304642
$401$	20.3594	1.01670	0.508350	−	0.861151i	$-0.330256\pi$
$401$	20.3594	1.01670	0.508350	+	0.861151i	$0.330256\pi$
$402$	−1.25814	−0.0627505
$403$	−2.56553	−0.127798
$404$	8.33852	0.414857
$405$	6.20055	0.308108
$406$	−4.43622	−0.220166
$407$	42.7512	2.11910
$408$	−5.34315	−0.264526
$409$	−2.72391	−0.134689	−0.0673443	−	0.997730i	$-0.521453\pi$
$409$	−2.72391	−0.134689	−0.0673443	+	0.997730i	$0.521453\pi$
$410$	−2.79682	−0.138125
$411$	−25.5586	−1.26071
$412$	−6.44638	−0.317590
$413$	2.53479	0.124729
$414$	7.08980	0.348445
$415$	7.30284	0.358482
$416$	−12.5690	−0.616248
$417$	−37.2300	−1.82316
$418$	−3.78998	−0.185374
$419$	−1.59875	−0.0781042	−0.0390521	−	0.999237i	$-0.512434\pi$
$419$	−1.59875	−0.0781042	−0.0390521	+	0.999237i	$0.512434\pi$
$420$	1.70687	0.0832868
$421$	−20.3781	−0.993170	−0.496585	−	0.867988i	$-0.665413\pi$
$421$	−20.3781	−0.993170	−0.496585	+	0.867988i	$0.665413\pi$
$422$	−7.73470	−0.376520
$423$	11.7994	0.573707
$424$	−2.06346	−0.100211
$425$	−4.69343	−0.227665
$426$	12.8175	0.621008
$427$	9.11871	0.441285
$428$	−17.9708	−0.868652
$429$	−19.6650	−0.949434
$430$	0.387732	0.0186981
$431$	−13.5942	−0.654812	−0.327406	−	0.944884i	$-0.606174\pi$
$431$	−13.5942	−0.654812	−0.327406	+	0.944884i	$0.606174\pi$
$432$	3.59419	0.172926
$433$	−7.63983	−0.367147	−0.183573	−	0.983006i	$-0.558766\pi$
$433$	−7.63983	−0.367147	−0.183573	+	0.983006i	$0.558766\pi$
$434$	−0.781993	−0.0375369
$435$	−8.11844	−0.389250
$436$	31.4519	1.50627
$437$	−7.57166	−0.362202
$438$	−13.7198	−0.655558
$439$	4.71833	0.225194	0.112597	−	0.993641i	$-0.464083\pi$
$439$	4.71833	0.225194	0.112597	+	0.993641i	$0.464083\pi$
$440$	−5.70386	−0.271921
$441$	−10.5622	−0.502960
$442$	−1.51118	−0.0718793
$443$	−7.29643	−0.346664	−0.173332	−	0.984863i	$-0.555453\pi$
$443$	−7.29643	−0.346664	−0.173332	+	0.984863i	$0.555453\pi$
$444$	33.4738	1.58860
$445$	−9.75911	−0.462626
$446$	7.22444	0.342087
$447$	24.1063	1.14019
$448$	−1.39242	−0.0657858
$449$	−21.4156	−1.01066	−0.505332	−	0.862925i	$-0.668630\pi$
$449$	−21.4156	−1.01066	−0.505332	+	0.862925i	$0.668630\pi$
$450$	5.67444	0.267496
$451$	−30.2351	−1.42372
$452$	−9.31245	−0.438021
$453$	−7.47998	−0.351440
$454$	9.63512	0.452199
$455$	1.12231	0.0526146
$456$	−6.89902	−0.323076
$457$	28.3217	1.32484	0.662418	−	0.749135i	$-0.269530\pi$
$457$	28.3217	1.32484	0.662418	+	0.749135i	$0.269530\pi$
$458$	14.1646	0.661869
$459$	2.76868	0.129231
$460$	−4.90151	−0.228534
$461$	−13.7596	−0.640849	−0.320425	−	0.947274i	$-0.603826\pi$
$461$	−13.7596	−0.640849	−0.320425	+	0.947274i	$0.603826\pi$
$462$	−5.99404	−0.278868
$463$	0.0623073	0.00289567	0.00144783	−	0.999999i	$-0.499539\pi$
$463$	0.0623073	0.00289567	0.00144783	+	0.999999i	$0.499539\pi$
$464$	−8.75528	−0.406453
$465$	−1.43107	−0.0663645
$466$	−7.55955	−0.350189
$467$	39.9364	1.84804	0.924018	−	0.382348i	$-0.124885\pi$
$467$	39.9364	1.84804	0.924018	+	0.382348i	$0.124885\pi$
$468$	−5.62439	−0.259987
$469$	0.776239	0.0358434
$470$	2.64989	0.122231
$471$	−3.25874	−0.150155
$472$	−6.63234	−0.305278
$473$	4.19158	0.192729
$474$	−15.0456	−0.691067
$475$	−6.06011	−0.278057
$476$	1.41798	0.0649929
$477$	−1.44954	−0.0663701
$478$	−18.0608	−0.826081
$479$	−21.9351	−1.00224	−0.501121	−	0.865377i	$-0.667079\pi$
$479$	−21.9351	−1.00224	−0.501121	+	0.865377i	$0.667079\pi$
$480$	−7.01113	−0.320013
$481$	22.0098	1.00356
$482$	17.1383	0.780627
$483$	−11.9750	−0.544879
$484$	−9.91721	−0.450782
$485$	9.90292	0.449669
$486$	−11.2328	−0.509529
$487$	15.9045	0.720700	0.360350	−	0.932817i	$-0.382657\pi$
$487$	15.9045	0.720700	0.360350	+	0.932817i	$0.382657\pi$
$488$	−23.8593	−1.08006
$489$	29.3761	1.32843
$490$	−2.37203	−0.107158
$491$	17.0933	0.771409	0.385704	−	0.922622i	$-0.373958\pi$
$491$	17.0933	0.771409	0.385704	+	0.922622i	$0.373958\pi$
$492$	−23.6738	−1.06730
$493$	−6.74436	−0.303751
$494$	−1.95121	−0.0877893
$495$	−4.00686	−0.180095
$496$	−1.54333	−0.0692976
$497$	−7.90801	−0.354723
$498$	−20.0802	−0.899814
$499$	0.137869	0.00617185	0.00308593	−	0.999995i	$-0.499018\pi$
$499$	0.137869	0.00617185	0.00308593	+	0.999995i	$0.499018\pi$
$500$	−8.10226	−0.362344
$501$	−5.00857	−0.223767
$502$	−18.3669	−0.819755
$503$	35.3666	1.57692	0.788459	−	0.615088i	$-0.210879\pi$
$503$	35.3666	1.57692	0.788459	+	0.615088i	$0.210879\pi$
$504$	−3.98561	−0.177533
$505$	3.05834	0.136094
$506$	17.2127	0.765197
$507$	18.1384	0.805555
$508$	5.19988	0.230707
$509$	0.392665	0.0174046	0.00870229	−	0.999962i	$-0.497230\pi$
$509$	0.392665	0.0174046	0.00870229	+	0.999962i	$0.497230\pi$
$510$	−0.842948	−0.0373264
$511$	8.46473	0.374458
$512$	−13.9421	−0.616159
$513$	3.57489	0.157835
$514$	−21.3622	−0.942245
$515$	−2.36435	−0.104186
$516$	3.28197	0.144481
$517$	28.6467	1.25988
$518$	6.70877	0.294766
$519$	−0.826111	−0.0362622
$520$	−2.93655	−0.128776
$521$	36.1058	1.58183	0.790913	−	0.611929i	$-0.209606\pi$
$521$	36.1058	1.58183	0.790913	+	0.611929i	$0.209606\pi$
$522$	8.15405	0.356893
$523$	12.8979	0.563987	0.281993	−	0.959416i	$-0.409004\pi$
$523$	12.8979	0.563987	0.281993	+	0.959416i	$0.409004\pi$
$524$	20.7034	0.904432
$525$	−9.58436	−0.418296
$526$	4.18247	0.182365
$527$	−1.18886	−0.0517875
$528$	−11.8298	−0.514824
$529$	11.3877	0.495117
$530$	−0.325536	−0.0141404
$531$	−4.65910	−0.202188
$532$	1.83088	0.0793785
$533$	−15.5661	−0.674242
$534$	26.8340	1.16122
$535$	−6.59120	−0.284962
$536$	−2.03105	−0.0877280
$537$	28.5634	1.23260
$538$	18.2750	0.787889
$539$	−25.6429	−1.10452
$540$	2.31420	0.0995873
$541$	−17.9465	−0.771581	−0.385790	−	0.922586i	$-0.626071\pi$
$541$	−17.9465	−0.771581	−0.385790	+	0.922586i	$0.626071\pi$
$542$	−10.4892	−0.450550
$543$	−5.62483	−0.241384
$544$	−5.82447	−0.249722
$545$	11.5357	0.494134
$546$	−3.08594	−0.132066
$547$	3.80795	0.162816	0.0814082	−	0.996681i	$-0.474058\pi$
$547$	3.80795	0.162816	0.0814082	+	0.996681i	$0.474058\pi$
$548$	−17.7474	−0.758129
$549$	−16.7607	−0.715331
$550$	13.7765	0.587430
$551$	−8.70825	−0.370984
$552$	31.3328	1.33361
$553$	9.28270	0.394741
$554$	13.1976	0.560712
$555$	12.2773	0.521141
$556$	−25.8518	−1.09636
$557$	6.48077	0.274599	0.137300	−	0.990530i	$-0.456158\pi$
$557$	6.48077	0.274599	0.137300	+	0.990530i	$0.456158\pi$
$558$	1.43735	0.0608479
$559$	2.15797	0.0912725
$560$	0.675141	0.0285299
$561$	−9.11271	−0.384739
$562$	4.29060	0.180988
$563$	16.1665	0.681335	0.340667	−	0.940184i	$-0.389347\pi$
$563$	16.1665	0.681335	0.340667	+	0.940184i	$0.389347\pi$
$564$	22.4301	0.944480
$565$	−3.41555	−0.143693
$566$	10.8830	0.457446
$567$	10.5189	0.441753
$568$	20.6915	0.868197
$569$	22.3046	0.935059	0.467529	−	0.883978i	$-0.345144\pi$
$569$	22.3046	0.935059	0.467529	+	0.883978i	$0.345144\pi$
$570$	−1.08840	−0.0455883
$571$	−42.3553	−1.77251	−0.886256	−	0.463195i	$-0.846703\pi$
$571$	−42.3553	−1.77251	−0.886256	+	0.463195i	$0.846703\pi$
$572$	−13.6549	−0.570942
$573$	38.1794	1.59497
$574$	−4.74467	−0.198039
$575$	27.5228	1.14778
$576$	2.55936	0.106640
$577$	−32.1544	−1.33860	−0.669302	−	0.742990i	$-0.733407\pi$
$577$	−32.1544	−1.33860	−0.669302	+	0.742990i	$0.733407\pi$
$578$	−0.700276	−0.0291276
$579$	17.1650	0.713354
$580$	−5.63728	−0.234075
$581$	12.3889	0.513978
$582$	−27.2295	−1.12870
$583$	−3.51922	−0.145751
$584$	−22.1482	−0.916499
$585$	−2.06287	−0.0852892
$586$	3.89306	0.160821
$587$	−10.6688	−0.440349	−0.220174	−	0.975461i	$-0.570663\pi$
$587$	−10.6688	−0.440349	−0.220174	+	0.975461i	$0.570663\pi$
$588$	−20.0782	−0.828011
$589$	−1.53504	−0.0632503
$590$	−1.04633	−0.0430769
$591$	37.5001	1.54255
$592$	13.2403	0.544175
$593$	10.1504	0.416826	0.208413	−	0.978041i	$-0.433170\pi$
$593$	10.1504	0.416826	0.208413	+	0.978041i	$0.433170\pi$
$594$	−8.12680	−0.333447
$595$	0.520075	0.0213210
$596$	16.7389	0.685653
$597$	22.2441	0.910391
$598$	8.86169	0.362381
$599$	−16.9844	−0.693963	−0.346981	−	0.937872i	$-0.612793\pi$
$599$	−16.9844	−0.693963	−0.346981	+	0.937872i	$0.612793\pi$
$600$	25.0777	1.02379
$601$	32.6786	1.33299	0.666494	−	0.745510i	$-0.267794\pi$
$601$	32.6786	1.33299	0.666494	+	0.745510i	$0.267794\pi$
$602$	0.657768	0.0268086
$603$	−1.42677	−0.0581028
$604$	−5.19394	−0.211339
$605$	−3.63736	−0.147880
$606$	−8.40933	−0.341606
$607$	−16.2109	−0.657980	−0.328990	−	0.944333i	$-0.606708\pi$
$607$	−16.2109	−0.657980	−0.328990	+	0.944333i	$0.606708\pi$
$608$	−7.52048	−0.304996
$609$	−13.7725	−0.558091
$610$	−3.76410	−0.152404
$611$	14.7483	0.596654
$612$	−2.60633	−0.105355
$613$	38.1170	1.53953	0.769765	−	0.638327i	$-0.220373\pi$
$613$	38.1170	1.53953	0.769765	+	0.638327i	$0.220373\pi$
$614$	−15.7993	−0.637609
$615$	−8.68291	−0.350129
$616$	−9.67631	−0.389870
$617$	−12.7294	−0.512465	−0.256233	−	0.966615i	$-0.582481\pi$
$617$	−12.7294	−0.512465	−0.256233	+	0.966615i	$0.582481\pi$
$618$	6.50112	0.261513
$619$	−24.1930	−0.972400	−0.486200	−	0.873847i	$-0.661617\pi$
$619$	−24.1930	−0.972400	−0.486200	+	0.873847i	$0.661617\pi$
$620$	−0.993708	−0.0399083
$621$	−16.2358	−0.651521
$622$	−3.77621	−0.151412
$623$	−16.5558	−0.663296
$624$	−6.09038	−0.243810
$625$	20.4955	0.819819
$626$	−9.88192	−0.394961
$627$	−11.7662	−0.469898
$628$	−2.26280	−0.0902955
$629$	10.1993	0.406673
$630$	−0.628779	−0.0250512
$631$	−17.0869	−0.680218	−0.340109	−	0.940386i	$-0.610464\pi$
$631$	−17.0869	−0.680218	−0.340109	+	0.940386i	$0.610464\pi$
$632$	−24.2884	−0.966142
$633$	−24.0129	−0.954426
$634$	0.0557873	0.00221560
$635$	1.90717	0.0756838
$636$	−2.75552	−0.109263
$637$	−13.2019	−0.523077
$638$	19.7965	0.783751
$639$	14.5354	0.575012
$640$	−5.87506	−0.232232
$641$	34.8664	1.37714	0.688570	−	0.725170i	$-0.258239\pi$
$641$	34.8664	1.37714	0.688570	+	0.725170i	$0.258239\pi$
$642$	18.1234	0.715274
$643$	24.2777	0.957420	0.478710	−	0.877973i	$-0.341104\pi$
$643$	24.2777	0.957420	0.478710	+	0.877973i	$0.341104\pi$
$644$	−8.31516	−0.327663
$645$	1.20374	0.0473971
$646$	−0.904188	−0.0355748
$647$	15.5151	0.609961	0.304981	−	0.952359i	$-0.401350\pi$
$647$	15.5151	0.609961	0.304981	+	0.952359i	$0.401350\pi$
$648$	−27.5230	−1.08121
$649$	−11.3114	−0.444012
$650$	7.09261	0.278195
$651$	−2.42774	−0.0951508
$652$	20.3982	0.798853
$653$	−31.0833	−1.21638	−0.608191	−	0.793791i	$-0.708105\pi$
$653$	−31.0833	−1.21638	−0.608191	+	0.793791i	$0.708105\pi$
$654$	−31.7190	−1.24031
$655$	7.59343	0.296700
$656$	−9.36402	−0.365604
$657$	−15.5587	−0.607002
$658$	4.49541	0.175249
$659$	31.3231	1.22017	0.610087	−	0.792335i	$-0.291135\pi$
$659$	31.3231	1.22017	0.610087	+	0.792335i	$0.291135\pi$
$660$	−7.61685	−0.296486
$661$	22.6922	0.882625	0.441313	−	0.897353i	$-0.354513\pi$
$661$	22.6922	0.882625	0.441313	+	0.897353i	$0.354513\pi$
$662$	−4.86179	−0.188959
$663$	−4.69154	−0.182204
$664$	−32.4159	−1.25798
$665$	0.671515	0.0260402
$666$	−12.3311	−0.477822
$667$	39.5496	1.53137
$668$	−3.47785	−0.134562
$669$	22.4287	0.867144
$670$	−0.320423	−0.0123790
$671$	−40.6919	−1.57089
$672$	−11.8940	−0.458822
$673$	−12.5137	−0.482369	−0.241184	−	0.970479i	$-0.577536\pi$
$673$	−12.5137	−0.482369	−0.241184	+	0.970479i	$0.577536\pi$
$674$	24.6973	0.951304
$675$	−12.9946	−0.500163
$676$	12.5949	0.484421
$677$	37.5287	1.44234	0.721172	−	0.692756i	$-0.243604\pi$
$677$	37.5287	1.44234	0.721172	+	0.692756i	$0.243604\pi$
$678$	9.39153	0.360680
$679$	16.7998	0.644717
$680$	−1.36079	−0.0521839
$681$	29.9128	1.14626
$682$	3.48962	0.133624
$683$	9.80794	0.375290	0.187645	−	0.982237i	$-0.439914\pi$
$683$	9.80794	0.375290	0.187645	+	0.982237i	$0.439914\pi$
$684$	−3.36526	−0.128674
$685$	−6.50924	−0.248705
$686$	−8.62841	−0.329434
$687$	43.9749	1.67775
$688$	1.29816	0.0494920
$689$	−1.81182	−0.0690247
$690$	4.94313	0.188182
$691$	25.8848	0.984705	0.492352	−	0.870396i	$-0.336137\pi$
$691$	25.8848	0.984705	0.492352	+	0.870396i	$0.336137\pi$
$692$	−0.573634	−0.0218063
$693$	−6.79743	−0.258213
$694$	7.76079	0.294595
$695$	−9.48171	−0.359662
$696$	36.0362	1.36595
$697$	−7.21329	−0.273223
$698$	−14.5594	−0.551081
$699$	−23.4691	−0.887682
$700$	−6.65518	−0.251542
$701$	8.38827	0.316820	0.158410	−	0.987373i	$-0.449363\pi$
$701$	8.38827	0.316820	0.158410	+	0.987373i	$0.449363\pi$
$702$	−4.18396	−0.157913
$703$	13.1692	0.496687
$704$	6.21364	0.234185
$705$	8.22676	0.309838
$706$	−12.3144	−0.463458
$707$	5.18831	0.195127
$708$	−8.85674	−0.332857
$709$	8.19225	0.307667	0.153833	−	0.988097i	$-0.450838\pi$
$709$	8.19225	0.307667	0.153833	+	0.988097i	$0.450838\pi$
$710$	3.26434	0.122509
$711$	−17.0622	−0.639881
$712$	43.3188	1.62344
$713$	6.97159	0.261088
$714$	−1.43002	−0.0535171
$715$	−5.00826	−0.187298
$716$	19.8338	0.741226
$717$	−56.0708	−2.09400
$718$	24.7209	0.922575
$719$	5.51098	0.205525	0.102762	−	0.994706i	$-0.467232\pi$
$719$	5.51098	0.205525	0.102762	+	0.994706i	$0.467232\pi$
$720$	−1.24095	−0.0462475
$721$	−4.01100	−0.149378
$722$	12.1378	0.451721
$723$	53.2068	1.97878
$724$	−3.90576	−0.145156
$725$	31.6542	1.17561
$726$	10.0014	0.371188
$727$	−34.4942	−1.27932	−0.639660	−	0.768658i	$-0.720925\pi$
$727$	−34.4942	−1.27932	−0.639660	+	0.768658i	$0.720925\pi$
$728$	−4.98170	−0.184634
$729$	−1.27669	−0.0472848
$730$	−3.49415	−0.129324
$731$	1.00000	0.0369863
$732$	−31.8614	−1.17763
$733$	26.0248	0.961247	0.480623	−	0.876927i	$-0.340410\pi$
$733$	26.0248	0.961247	0.480623	+	0.876927i	$0.340410\pi$
$734$	−16.1770	−0.597105
$735$	−7.36413	−0.271630
$736$	34.1553	1.25898
$737$	−3.46394	−0.127596
$738$	8.72099	0.321024
$739$	18.0501	0.663982	0.331991	−	0.943283i	$-0.392280\pi$
$739$	18.0501	0.663982	0.331991	+	0.943283i	$0.392280\pi$
$740$	8.52509	0.313388
$741$	−6.05766	−0.222534
$742$	−0.552256	−0.0202740
$743$	3.48202	0.127743	0.0638715	−	0.997958i	$-0.479655\pi$
$743$	3.48202	0.127743	0.0638715	+	0.997958i	$0.479655\pi$
$744$	6.35226	0.232885
$745$	6.13938	0.224929
$746$	13.6114	0.498350
$747$	−22.7715	−0.833167
$748$	−6.32767	−0.231363
$749$	−11.1816	−0.408568
$750$	8.17106	0.298365
$751$	37.8965	1.38286	0.691432	−	0.722441i	$-0.256980\pi$
$751$	37.8965	1.38286	0.691432	+	0.722441i	$0.256980\pi$
$752$	8.87209	0.323532
$753$	−57.0212	−2.07797
$754$	10.1919	0.371168
$755$	−1.90499	−0.0693299
$756$	3.92592	0.142784
$757$	−15.5903	−0.566638	−0.283319	−	0.959026i	$-0.591435\pi$
$757$	−15.5903	−0.566638	−0.283319	+	0.959026i	$0.591435\pi$
$758$	21.0794	0.765640
$759$	53.4378	1.93967
$760$	−1.75704	−0.0637344
$761$	15.5200	0.562598	0.281299	−	0.959620i	$-0.409235\pi$
$761$	15.5200	0.562598	0.281299	+	0.959620i	$0.409235\pi$
$762$	−5.24404	−0.189971
$763$	19.5697	0.708471
$764$	26.5110	0.959134
$765$	−0.955929	−0.0345617
$766$	−12.6814	−0.458199
$767$	−5.82351	−0.210275
$768$	22.6000	0.815506
$769$	−18.2942	−0.659705	−0.329852	−	0.944033i	$-0.606999\pi$
$769$	−18.2942	−0.659705	−0.329852	+	0.944033i	$0.606999\pi$
$770$	−1.52656	−0.0550133
$771$	−66.3202	−2.38846
$772$	11.9190	0.428975
$773$	1.00257	0.0360598	0.0180299	−	0.999837i	$-0.494261\pi$
$773$	1.00257	0.0360598	0.0180299	+	0.999837i	$0.494261\pi$
$774$	−1.20902	−0.0434572
$775$	5.57983	0.200433
$776$	−43.9571	−1.57797
$777$	20.8278	0.747193
$778$	4.10710	0.147247
$779$	−9.31372	−0.333699
$780$	−3.92142	−0.140409
$781$	35.2892	1.26275
$782$	4.10649	0.146848
$783$	−18.6730	−0.667318
$784$	−7.94179	−0.283635
$785$	−0.829932	−0.0296215
$786$	−20.8792	−0.744736
$787$	−4.76054	−0.169695	−0.0848475	−	0.996394i	$-0.527040\pi$
$787$	−4.76054	−0.169695	−0.0848475	+	0.996394i	$0.527040\pi$
$788$	26.0393	0.927611
$789$	12.9847	0.462269
$790$	−3.83180	−0.136329
$791$	−5.79431	−0.206022
$792$	17.7857	0.631986
$793$	−20.9496	−0.743943
$794$	−12.6825	−0.450083
$795$	−1.01065	−0.0358440
$796$	15.4459	0.547464
$797$	32.0355	1.13476	0.567378	−	0.823457i	$-0.307958\pi$
$797$	32.0355	1.13476	0.567378	+	0.823457i	$0.307958\pi$
$798$	−1.84642	−0.0653627
$799$	6.83435	0.241782
$800$	27.3367	0.966500
$801$	30.4306	1.07521
$802$	−14.2572	−0.503439
$803$	−37.7736	−1.33300
$804$	−2.71223	−0.0956531
$805$	−3.04977	−0.107490
$806$	1.79658	0.0632817
$807$	56.7357	1.99719
$808$	−13.5754	−0.477579
$809$	−18.7547	−0.659380	−0.329690	−	0.944089i	$-0.606944\pi$
$809$	−18.7547	−0.659380	−0.329690	+	0.944089i	$0.606944\pi$
$810$	−4.34209	−0.152566
$811$	−44.7483	−1.57133	−0.785663	−	0.618655i	$-0.787678\pi$
$811$	−44.7483	−1.57133	−0.785663	+	0.618655i	$0.787678\pi$
$812$	−9.56335	−0.335608
$813$	−32.5644	−1.14208
$814$	−29.9376	−1.04931
$815$	7.48148	0.262065
$816$	−2.82227	−0.0987991
$817$	1.29119	0.0451730
$818$	1.90749	0.0666937
$819$	−3.49955	−0.122284
$820$	−6.02923	−0.210550
$821$	−39.6622	−1.38422	−0.692111	−	0.721791i	$-0.743319\pi$
$821$	−39.6622	−1.38422	−0.692111	+	0.721791i	$0.743319\pi$
$822$	17.8981	0.624267
$823$	−18.2603	−0.636516	−0.318258	−	0.948004i	$-0.603098\pi$
$823$	−18.2603	−0.636516	−0.318258	+	0.948004i	$0.603098\pi$
$824$	10.4949	0.365607
$825$	42.7699	1.48906
$826$	−1.77505	−0.0617620
$827$	45.1739	1.57085	0.785426	−	0.618956i	$-0.212444\pi$
$827$	45.1739	1.57085	0.785426	+	0.618956i	$0.212444\pi$
$828$	15.2838	0.531148
$829$	3.32014	0.115313	0.0576566	−	0.998336i	$-0.481637\pi$
$829$	3.32014	0.115313	0.0576566	+	0.998336i	$0.481637\pi$
$830$	−5.11400	−0.177510
$831$	40.9727	1.42133
$832$	3.19900	0.110905
$833$	−6.11772	−0.211966
$834$	26.0713	0.902775
$835$	−1.27558	−0.0441432
$836$	−8.17022	−0.282573
$837$	−3.29157	−0.113773
$838$	1.11957	0.0386748
$839$	9.34904	0.322765	0.161382	−	0.986892i	$-0.448405\pi$
$839$	9.34904	0.322765	0.161382	+	0.986892i	$0.448405\pi$
$840$	−2.77884	−0.0958791
$841$	16.4865	0.568498
$842$	14.2703	0.491788
$843$	13.3204	0.458780
$844$	−16.6740	−0.573944
$845$	4.61947	0.158915
$846$	−8.26284	−0.284082
$847$	−6.17059	−0.212024
$848$	−1.08993	−0.0374282
$849$	33.7869	1.15956
$850$	3.28670	0.112733
$851$	−59.8097	−2.05025
$852$	27.6312	0.946628
$853$	20.1506	0.689944	0.344972	−	0.938613i	$-0.387888\pi$
$853$	20.1506	0.689944	0.344972	+	0.938613i	$0.387888\pi$
$854$	−6.38561	−0.218511
$855$	−1.23429	−0.0422117
$856$	29.2570	0.999985
$857$	−38.8098	−1.32572	−0.662858	−	0.748745i	$-0.730657\pi$
$857$	−38.8098	−1.32572	−0.662858	+	0.748745i	$0.730657\pi$
$858$	13.7709	0.470131
$859$	−27.6769	−0.944322	−0.472161	−	0.881512i	$-0.656526\pi$
$859$	−27.6769	−0.944322	−0.472161	+	0.881512i	$0.656526\pi$
$860$	0.835850	0.0285022
$861$	−14.7301	−0.502001
$862$	9.51972	0.324243
$863$	−5.47473	−0.186362	−0.0931810	−	0.995649i	$-0.529704\pi$
$863$	−5.47473	−0.186362	−0.0931810	+	0.995649i	$0.529704\pi$
$864$	−16.1261	−0.548620
$865$	−0.210393	−0.00715358
$866$	5.34999	0.181800
$867$	−2.17405	−0.0738346
$868$	−1.68578	−0.0572189
$869$	−41.4237	−1.40520
$870$	5.68515	0.192745
$871$	−1.78336	−0.0604267
$872$	−51.2046	−1.73401
$873$	−30.8791	−1.04510
$874$	5.30225	0.179351
$875$	−5.04131	−0.170427
$876$	−29.5764	−0.999293
$877$	−44.3872	−1.49885	−0.749424	−	0.662090i	$-0.769669\pi$
$877$	−44.3872	−1.49885	−0.749424	+	0.662090i	$0.769669\pi$
$878$	−3.30413	−0.111509
$879$	12.0862	0.407658
$880$	−3.01279	−0.101561
$881$	31.6932	1.06777	0.533885	−	0.845557i	$-0.320731\pi$
$881$	31.6932	1.06777	0.533885	+	0.845557i	$0.320731\pi$
$882$	7.39643	0.249051
$883$	−12.2593	−0.412557	−0.206279	−	0.978493i	$-0.566135\pi$
$883$	−12.2593	−0.412557	−0.206279	+	0.978493i	$0.566135\pi$
$884$	−3.25771	−0.109569
$885$	−3.24841	−0.109194
$886$	5.10952	0.171658
$887$	−28.4728	−0.956024	−0.478012	−	0.878353i	$-0.658642\pi$
$887$	−28.4728	−0.956024	−0.478012	+	0.878353i	$0.658642\pi$
$888$	−54.4964	−1.82878
$889$	3.23542	0.108513
$890$	6.83407	0.229079
$891$	−46.9403	−1.57256
$892$	15.5740	0.521457
$893$	8.82443	0.295298
$894$	−16.8811	−0.564588
$895$	7.27451	0.243160
$896$	−9.96674	−0.332965
$897$	27.5117	0.918587
$898$	14.9968	0.500450
$899$	8.01810	0.267419
$900$	12.2326	0.407754
$901$	−0.839592	−0.0279709
$902$	21.1729	0.704981
$903$	2.04208	0.0679561
$904$	15.1610	0.504246
$905$	−1.43253	−0.0476187
$906$	5.23805	0.174023
$907$	1.57734	0.0523748	0.0261874	−	0.999657i	$-0.491663\pi$
$907$	1.57734	0.0523748	0.0261874	+	0.999657i	$0.491663\pi$
$908$	20.7708	0.689305
$909$	−9.53644	−0.316304
$910$	−0.785925	−0.0260531
$911$	−31.0624	−1.02914	−0.514571	−	0.857448i	$-0.672049\pi$
$911$	−31.0624	−1.02914	−0.514571	+	0.857448i	$0.672049\pi$
$912$	−3.64408	−0.120668
$913$	−55.2850	−1.82967
$914$	−19.8330	−0.656018
$915$	−11.6859	−0.386324
$916$	30.5352	1.00891
$917$	12.8819	0.425397
$918$	−1.93884	−0.0639912
$919$	41.9471	1.38371	0.691854	−	0.722038i	$-0.256794\pi$
$919$	41.9471	1.38371	0.691854	+	0.722038i	$0.256794\pi$
$920$	7.97981	0.263086
$921$	−49.0500	−1.61625
$922$	9.63553	0.317329
$923$	18.1681	0.598011
$924$	−12.9216	−0.425090
$925$	−47.8697	−1.57395
$926$	−0.0436323	−0.00143385
$927$	7.37247	0.242144
$928$	39.2823	1.28951
$929$	−14.4493	−0.474066	−0.237033	−	0.971502i	$-0.576175\pi$
$929$	−14.4493	−0.474066	−0.237033	+	0.971502i	$0.576175\pi$
$930$	1.00215	0.0328617
$931$	−7.89913	−0.258884
$932$	−16.2964	−0.533808
$933$	−11.7235	−0.383810
$934$	−27.9665	−0.915092
$935$	−2.32081	−0.0758988
$936$	9.15668	0.299295
$937$	−24.8435	−0.811602	−0.405801	−	0.913961i	$-0.633007\pi$
$937$	−24.8435	−0.811602	−0.405801	+	0.913961i	$0.633007\pi$
$938$	−0.543581	−0.0177486
$939$	−30.6790	−1.00117
$940$	5.71249	0.186321
$941$	−42.7216	−1.39268	−0.696342	−	0.717711i	$-0.745190\pi$
$941$	−42.7216	−1.39268	−0.696342	+	0.717711i	$0.745190\pi$
$942$	2.28202	0.0743521
$943$	42.2995	1.37746
$944$	−3.50322	−0.114020
$945$	1.43992	0.0468406
$946$	−2.93526	−0.0954337
$947$	−44.6064	−1.44951	−0.724756	−	0.689006i	$-0.758048\pi$
$947$	−44.6064	−1.44951	−0.724756	+	0.689006i	$0.758048\pi$
$948$	−32.4344	−1.05342
$949$	−19.4471	−0.631281
$950$	4.24375	0.137685
$951$	0.173195	0.00561624
$952$	−2.30851	−0.0748192
$953$	7.52427	0.243735	0.121868	−	0.992546i	$-0.461112\pi$
$953$	7.52427	0.243735	0.121868	+	0.992546i	$0.461112\pi$
$954$	1.01508	0.0328645
$955$	9.72350	0.314645
$956$	−38.9344	−1.25923
$957$	61.4594	1.98670
$958$	15.3606	0.496280
$959$	−11.0426	−0.356584
$960$	1.78443	0.0575923
$961$	−29.5866	−0.954407
$962$	−15.4129	−0.496933
$963$	20.5525	0.662296
$964$	36.9457	1.18994
$965$	4.37157	0.140726
$966$	8.38577	0.269808
$967$	−41.3671	−1.33028	−0.665138	−	0.746720i	$-0.731627\pi$
$967$	−41.3671	−1.33028	−0.665138	+	0.746720i	$0.731627\pi$
$968$	16.1455	0.518937
$969$	−2.80711	−0.0901773
$970$	−6.93478	−0.222662
$971$	−23.9472	−0.768503	−0.384251	−	0.923229i	$-0.625540\pi$
$971$	−23.9472	−0.768503	−0.384251	+	0.923229i	$0.625540\pi$
$972$	−24.2149	−0.776695
$973$	−16.0852	−0.515669
$974$	−11.1375	−0.356869
$975$	22.0194	0.705186
$976$	−12.6026	−0.403398
$977$	22.7839	0.728922	0.364461	−	0.931219i	$-0.381253\pi$
$977$	22.7839	0.728922	0.364461	+	0.931219i	$0.381253\pi$
$978$	−20.5714	−0.657800
$979$	73.8798	2.36121
$980$	−5.11350	−0.163345
$981$	−35.9703	−1.14844
$982$	−11.9700	−0.381978
$983$	−21.4244	−0.683331	−0.341665	−	0.939822i	$-0.610991\pi$
$983$	−21.4244	−0.683331	−0.341665	+	0.939822i	$0.610991\pi$
$984$	38.5417	1.22867
$985$	9.55048	0.304304
$986$	4.72291	0.150408
$987$	13.9563	0.444233
$988$	−4.20631	−0.133821
$989$	−5.86410	−0.186468
$990$	2.80590	0.0891775
$991$	52.0310	1.65282	0.826410	−	0.563069i	$-0.190380\pi$
$991$	52.0310	1.65282	0.826410	+	0.563069i	$0.190380\pi$
$992$	6.92447	0.219852
$993$	−15.0937	−0.478985
$994$	5.53779	0.175648
$995$	5.66511	0.179596
$996$	−43.2877	−1.37162
$997$	30.5484	0.967477	0.483738	−	0.875213i	$-0.339279\pi$
$997$	30.5484	0.967477	0.483738	+	0.875213i	$0.339279\pi$
$998$	−0.0965462	−0.00305612
$999$	28.2386	0.893430

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.a.d.1.3	✓	8
3.2	odd	2		6579.2.a.k.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.a.d.1.3	✓	8	1.1	even	1	trivial
6579.2.a.k.1.6		8	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)

\(f(q)\)	\(=\)	\(q-0.700276 q^{2} -2.17405 q^{3} -1.50961 q^{4} -0.553685 q^{5} +1.52243 q^{6} -0.939298 q^{7} +2.45770 q^{8} +1.72649 q^{9} +O(q^{10})\)	\(q-0.700276 q^{2} -2.17405 q^{3} -1.50961 q^{4} -0.553685 q^{5} +1.52243 q^{6} -0.939298 q^{7} +2.45770 q^{8} +1.72649 q^{9} +0.387732 q^{10} +4.19158 q^{11} +3.28197 q^{12} +2.15797 q^{13} +0.657768 q^{14} +1.20374 q^{15} +1.29816 q^{16} +1.00000 q^{17} -1.20902 q^{18} +1.29119 q^{19} +0.835850 q^{20} +2.04208 q^{21} -2.93526 q^{22} -5.86410 q^{23} -5.34315 q^{24} -4.69343 q^{25} -1.51118 q^{26} +2.76868 q^{27} +1.41798 q^{28} -6.74436 q^{29} -0.842948 q^{30} -1.18886 q^{31} -5.82447 q^{32} -9.11271 q^{33} -0.700276 q^{34} +0.520075 q^{35} -2.60633 q^{36} +10.1993 q^{37} -0.904188 q^{38} -4.69154 q^{39} -1.36079 q^{40} -7.21329 q^{41} -1.43002 q^{42} +1.00000 q^{43} -6.32767 q^{44} -0.955929 q^{45} +4.10649 q^{46} +6.83435 q^{47} -2.82227 q^{48} -6.11772 q^{49} +3.28670 q^{50} -2.17405 q^{51} -3.25771 q^{52} -0.839592 q^{53} -1.93884 q^{54} -2.32081 q^{55} -2.30851 q^{56} -2.80711 q^{57} +4.72291 q^{58} -2.69860 q^{59} -1.81718 q^{60} -9.70801 q^{61} +0.832529 q^{62} -1.62169 q^{63} +1.48241 q^{64} -1.19484 q^{65} +6.38141 q^{66} -0.826403 q^{67} -1.50961 q^{68} +12.7488 q^{69} -0.364196 q^{70} +8.41907 q^{71} +4.24318 q^{72} -9.01176 q^{73} -7.14232 q^{74} +10.2038 q^{75} -1.94920 q^{76} -3.93715 q^{77} +3.28537 q^{78} -9.88259 q^{79} -0.718772 q^{80} -11.1987 q^{81} +5.05129 q^{82} -13.1895 q^{83} -3.08275 q^{84} -0.553685 q^{85} -0.700276 q^{86} +14.6626 q^{87} +10.3016 q^{88} +17.6258 q^{89} +0.669414 q^{90} -2.02698 q^{91} +8.85253 q^{92} +2.58464 q^{93} -4.78593 q^{94} -0.714911 q^{95} +12.6627 q^{96} -17.8855 q^{97} +4.28409 q^{98} +7.23671 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 3 q^{3} + 3 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 5 q^{9}+O(q^{10}) \) 8 * q + q^2 - 3 * q^3 + 3 * q^4 - 7 * q^5 - q^6 - 5 * q^7 - 3 * q^8 + 5 * q^9	\( 8 q + q^{2} - 3 q^{3} + 3 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 5 q^{9} - 12 q^{10} - 4 q^{11} - 13 q^{12} - 12 q^{13} + q^{14} - 9 q^{15} - 3 q^{16} + 8 q^{17} + 5 q^{18} - 5 q^{20} - 20 q^{21} - 14 q^{22} - 9 q^{23} - q^{24} - 7 q^{25} - 17 q^{26} - 12 q^{27} + q^{28} - 27 q^{29} + 10 q^{30} - 12 q^{31} + 5 q^{32} + 10 q^{33} + q^{34} + 15 q^{35} - 4 q^{36} - 24 q^{37} - q^{38} + 3 q^{39} - 9 q^{40} - 8 q^{41} - 9 q^{42} + 8 q^{43} - 16 q^{44} + 10 q^{45} - 14 q^{46} + 15 q^{47} + 10 q^{48} - 7 q^{49} + 21 q^{50} - 3 q^{51} + q^{52} - 23 q^{53} - 19 q^{54} - 14 q^{55} - 20 q^{56} - 13 q^{57} - 7 q^{58} + 16 q^{59} - 3 q^{60} - 34 q^{61} + 15 q^{62} + 9 q^{63} - 25 q^{64} + 10 q^{65} + 15 q^{66} + 3 q^{68} - 19 q^{69} + 11 q^{70} - 3 q^{71} - 19 q^{72} - 3 q^{73} - 4 q^{74} + 27 q^{75} + 13 q^{76} - 3 q^{77} + 4 q^{78} - 24 q^{79} + 20 q^{80} - 8 q^{81} + 33 q^{82} - 8 q^{83} + 17 q^{84} - 7 q^{85} + q^{86} + 48 q^{87} + 16 q^{88} + 23 q^{89} + 11 q^{90} - 16 q^{91} + 49 q^{92} + 17 q^{93} - 11 q^{94} + 3 q^{95} + 37 q^{96} - 10 q^{97} + 29 q^{98} - 15 q^{99}+O(q^{100}) \) 8 * q + q^2 - 3 * q^3 + 3 * q^4 - 7 * q^5 - q^6 - 5 * q^7 - 3 * q^8 + 5 * q^9 - 12 * q^10 - 4 * q^11 - 13 * q^12 - 12 * q^13 + q^14 - 9 * q^15 - 3 * q^16 + 8 * q^17 + 5 * q^18 - 5 * q^20 - 20 * q^21 - 14 * q^22 - 9 * q^23 - q^24 - 7 * q^25 - 17 * q^26 - 12 * q^27 + q^28 - 27 * q^29 + 10 * q^30 - 12 * q^31 + 5 * q^32 + 10 * q^33 + q^34 + 15 * q^35 - 4 * q^36 - 24 * q^37 - q^38 + 3 * q^39 - 9 * q^40 - 8 * q^41 - 9 * q^42 + 8 * q^43 - 16 * q^44 + 10 * q^45 - 14 * q^46 + 15 * q^47 + 10 * q^48 - 7 * q^49 + 21 * q^50 - 3 * q^51 + q^52 - 23 * q^53 - 19 * q^54 - 14 * q^55 - 20 * q^56 - 13 * q^57 - 7 * q^58 + 16 * q^59 - 3 * q^60 - 34 * q^61 + 15 * q^62 + 9 * q^63 - 25 * q^64 + 10 * q^65 + 15 * q^66 + 3 * q^68 - 19 * q^69 + 11 * q^70 - 3 * q^71 - 19 * q^72 - 3 * q^73 - 4 * q^74 + 27 * q^75 + 13 * q^76 - 3 * q^77 + 4 * q^78 - 24 * q^79 + 20 * q^80 - 8 * q^81 + 33 * q^82 - 8 * q^83 + 17 * q^84 - 7 * q^85 + q^86 + 48 * q^87 + 16 * q^88 + 23 * q^89 + 11 * q^90 - 16 * q^91 + 49 * q^92 + 17 * q^93 - 11 * q^94 + 3 * q^95 + 37 * q^96 - 10 * q^97 + 29 * q^98 - 15 * q^99

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