LMFDB - Embedded newform 4522.2.a.bc.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4522,2,Mod(1,4522)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4522, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4522.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4522 = 2 \cdot 7 \cdot 17 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4522.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:	$36.1083517940$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 5 x^{10} - 9 x^{9} + 72 x^{8} - 8 x^{7} - 342 x^{6} + 246 x^{5} + 575 x^{4} - 613 x^{3} + \cdots - 80 $ x^11 - 5x^10 - 9x^9 + 72x^8 - 8x^7 - 342x^6 + 246x^5 + 575x^4 - 613x^3 - 147x^2 + 312x - 80
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.622180$ of defining polynomial
Character	$\chi$	$=$	4522.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.622180 q^{3} +1.00000 q^{4} +3.37396 q^{5} +0.622180 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.61289 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.622180 q^{3} +1.00000 q^{4} +3.37396 q^{5} +0.622180 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.61289 q^{9} -3.37396 q^{10} +3.58057 q^{11} -0.622180 q^{12} -4.13570 q^{13} -1.00000 q^{14} -2.09921 q^{15} +1.00000 q^{16} -1.00000 q^{17} +2.61289 q^{18} +1.00000 q^{19} +3.37396 q^{20} -0.622180 q^{21} -3.58057 q^{22} -7.47306 q^{23} +0.622180 q^{24} +6.38360 q^{25} +4.13570 q^{26} +3.49223 q^{27} +1.00000 q^{28} -2.88984 q^{29} +2.09921 q^{30} -7.51030 q^{31} -1.00000 q^{32} -2.22776 q^{33} +1.00000 q^{34} +3.37396 q^{35} -2.61289 q^{36} +4.45367 q^{37} -1.00000 q^{38} +2.57315 q^{39} -3.37396 q^{40} +0.227632 q^{41} +0.622180 q^{42} -1.88935 q^{43} +3.58057 q^{44} -8.81579 q^{45} +7.47306 q^{46} +0.272506 q^{47} -0.622180 q^{48} +1.00000 q^{49} -6.38360 q^{50} +0.622180 q^{51} -4.13570 q^{52} -6.74989 q^{53} -3.49223 q^{54} +12.0807 q^{55} -1.00000 q^{56} -0.622180 q^{57} +2.88984 q^{58} +3.28385 q^{59} -2.09921 q^{60} -15.1315 q^{61} +7.51030 q^{62} -2.61289 q^{63} +1.00000 q^{64} -13.9537 q^{65} +2.22776 q^{66} -9.58013 q^{67} -1.00000 q^{68} +4.64959 q^{69} -3.37396 q^{70} -10.2715 q^{71} +2.61289 q^{72} -9.08237 q^{73} -4.45367 q^{74} -3.97175 q^{75} +1.00000 q^{76} +3.58057 q^{77} -2.57315 q^{78} +7.71934 q^{79} +3.37396 q^{80} +5.66588 q^{81} -0.227632 q^{82} +4.58343 q^{83} -0.622180 q^{84} -3.37396 q^{85} +1.88935 q^{86} +1.79800 q^{87} -3.58057 q^{88} -12.0376 q^{89} +8.81579 q^{90} -4.13570 q^{91} -7.47306 q^{92} +4.67276 q^{93} -0.272506 q^{94} +3.37396 q^{95} +0.622180 q^{96} +7.34113 q^{97} -1.00000 q^{98} -9.35565 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 11 q^{2} - 5 q^{3} + 11 q^{4} - 2 q^{5} + 5 q^{6} + 11 q^{7} - 11 q^{8} + 10 q^{9}+O(q^{10}) $ 11 * q - 11 * q^2 - 5 * q^3 + 11 * q^4 - 2 * q^5 + 5 * q^6 + 11 * q^7 - 11 * q^8 + 10 * q^9	\( 11 q - 11 q^{2} - 5 q^{3} + 11 q^{4} - 2 q^{5} + 5 q^{6} + 11 q^{7} - 11 q^{8} + 10 q^{9} + 2 q^{10} - 9 q^{11} - 5 q^{12} - 11 q^{14} - 11 q^{15} + 11 q^{16} - 11 q^{17} - 10 q^{18} + 11 q^{19} - 2 q^{20} - 5 q^{21} + 9 q^{22} - 8 q^{23} + 5 q^{24} + 17 q^{25} - 14 q^{27} + 11 q^{28} - 17 q^{29} + 11 q^{30} - 9 q^{31} - 11 q^{32} - 7 q^{33} + 11 q^{34} - 2 q^{35} + 10 q^{36} - 14 q^{37} - 11 q^{38} - 6 q^{39} + 2 q^{40} - 16 q^{41} + 5 q^{42} + 3 q^{43} - 9 q^{44} + 5 q^{45} + 8 q^{46} - 12 q^{47} - 5 q^{48} + 11 q^{49} - 17 q^{50} + 5 q^{51} - 34 q^{53} + 14 q^{54} - q^{55} - 11 q^{56} - 5 q^{57} + 17 q^{58} - 23 q^{59} - 11 q^{60} + 12 q^{61} + 9 q^{62} + 10 q^{63} + 11 q^{64} - 28 q^{65} + 7 q^{66} - 11 q^{68} + 3 q^{69} + 2 q^{70} - 42 q^{71} - 10 q^{72} + 14 q^{73} + 14 q^{74} - 32 q^{75} + 11 q^{76} - 9 q^{77} + 6 q^{78} - 7 q^{79} - 2 q^{80} - 9 q^{81} + 16 q^{82} + q^{83} - 5 q^{84} + 2 q^{85} - 3 q^{86} - 10 q^{87} + 9 q^{88} - 6 q^{89} - 5 q^{90} - 8 q^{92} - 14 q^{93} + 12 q^{94} - 2 q^{95} + 5 q^{96} - 15 q^{97} - 11 q^{98} - 33 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - 5 * q^3 + 11 * q^4 - 2 * q^5 + 5 * q^6 + 11 * q^7 - 11 * q^8 + 10 * q^9 + 2 * q^10 - 9 * q^11 - 5 * q^12 - 11 * q^14 - 11 * q^15 + 11 * q^16 - 11 * q^17 - 10 * q^18 + 11 * q^19 - 2 * q^20 - 5 * q^21 + 9 * q^22 - 8 * q^23 + 5 * q^24 + 17 * q^25 - 14 * q^27 + 11 * q^28 - 17 * q^29 + 11 * q^30 - 9 * q^31 - 11 * q^32 - 7 * q^33 + 11 * q^34 - 2 * q^35 + 10 * q^36 - 14 * q^37 - 11 * q^38 - 6 * q^39 + 2 * q^40 - 16 * q^41 + 5 * q^42 + 3 * q^43 - 9 * q^44 + 5 * q^45 + 8 * q^46 - 12 * q^47 - 5 * q^48 + 11 * q^49 - 17 * q^50 + 5 * q^51 - 34 * q^53 + 14 * q^54 - q^55 - 11 * q^56 - 5 * q^57 + 17 * q^58 - 23 * q^59 - 11 * q^60 + 12 * q^61 + 9 * q^62 + 10 * q^63 + 11 * q^64 - 28 * q^65 + 7 * q^66 - 11 * q^68 + 3 * q^69 + 2 * q^70 - 42 * q^71 - 10 * q^72 + 14 * q^73 + 14 * q^74 - 32 * q^75 + 11 * q^76 - 9 * q^77 + 6 * q^78 - 7 * q^79 - 2 * q^80 - 9 * q^81 + 16 * q^82 + q^83 - 5 * q^84 + 2 * q^85 - 3 * q^86 - 10 * q^87 + 9 * q^88 - 6 * q^89 - 5 * q^90 - 8 * q^92 - 14 * q^93 + 12 * q^94 - 2 * q^95 + 5 * q^96 - 15 * q^97 - 11 * q^98 - 33 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−0.622180	−0.359216	−0.179608	−	0.983738i	$-0.557483\pi$
$3$	−0.622180	−0.359216	−0.179608	+	0.983738i	$0.557483\pi$
$4$	1.00000	0.500000
$5$	3.37396	1.50888	0.754440	−	0.656369i	$-0.227908\pi$
$5$	3.37396	1.50888	0.754440	+	0.656369i	$0.227908\pi$
$6$	0.622180	0.254004
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	−2.61289	−0.870964
$10$	−3.37396	−1.06694
$11$	3.58057	1.07958	0.539792	−	0.841799i	$-0.318503\pi$
$11$	3.58057	1.07958	0.539792	+	0.841799i	$0.318503\pi$
$12$	−0.622180	−0.179608
$13$	−4.13570	−1.14704	−0.573518	−	0.819193i	$-0.694422\pi$
$13$	−4.13570	−1.14704	−0.573518	+	0.819193i	$0.694422\pi$
$14$	−1.00000	−0.267261
$15$	−2.09921	−0.542014
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	2.61289	0.615865
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	3.37396	0.754440
$21$	−0.622180	−0.135771
$22$	−3.58057	−0.763381
$23$	−7.47306	−1.55824	−0.779120	−	0.626875i	$-0.784334\pi$
$23$	−7.47306	−1.55824	−0.779120	+	0.626875i	$0.784334\pi$
$24$	0.622180	0.127002
$25$	6.38360	1.27672
$26$	4.13570	0.811077
$27$	3.49223	0.672080
$28$	1.00000	0.188982
$29$	−2.88984	−0.536630	−0.268315	−	0.963331i	$-0.586467\pi$
$29$	−2.88984	−0.536630	−0.268315	+	0.963331i	$0.586467\pi$
$30$	2.09921	0.383262
$31$	−7.51030	−1.34889	−0.674445	−	0.738325i	$-0.735617\pi$
$31$	−7.51030	−1.34889	−0.674445	+	0.738325i	$0.735617\pi$
$32$	−1.00000	−0.176777
$33$	−2.22776	−0.387803
$34$	1.00000	0.171499
$35$	3.37396	0.570303
$36$	−2.61289	−0.435482
$37$	4.45367	0.732179	0.366089	−	0.930580i	$-0.380696\pi$
$37$	4.45367	0.732179	0.366089	+	0.930580i	$0.380696\pi$
$38$	−1.00000	−0.162221
$39$	2.57315	0.412033
$40$	−3.37396	−0.533470
$41$	0.227632	0.0355502	0.0177751	−	0.999842i	$-0.494342\pi$
$41$	0.227632	0.0355502	0.0177751	+	0.999842i	$0.494342\pi$
$42$	0.622180	0.0960044
$43$	−1.88935	−0.288123	−0.144061	−	0.989569i	$-0.546016\pi$
$43$	−1.88935	−0.288123	−0.144061	+	0.989569i	$0.546016\pi$
$44$	3.58057	0.539792
$45$	−8.81579	−1.31418
$46$	7.47306	1.10184
$47$	0.272506	0.0397491	0.0198745	−	0.999802i	$-0.493673\pi$
$47$	0.272506	0.0397491	0.0198745	+	0.999802i	$0.493673\pi$
$48$	−0.622180	−0.0898039
$49$	1.00000	0.142857
$50$	−6.38360	−0.902778
$51$	0.622180	0.0871226
$52$	−4.13570	−0.573518
$53$	−6.74989	−0.927168	−0.463584	−	0.886053i	$-0.653437\pi$
$53$	−6.74989	−0.927168	−0.463584	+	0.886053i	$0.653437\pi$
$54$	−3.49223	−0.475232
$55$	12.0807	1.62896
$56$	−1.00000	−0.133631
$57$	−0.622180	−0.0824097
$58$	2.88984	0.379455
$59$	3.28385	0.427521	0.213761	−	0.976886i	$-0.431429\pi$
$59$	3.28385	0.427521	0.213761	+	0.976886i	$0.431429\pi$
$60$	−2.09921	−0.271007
$61$	−15.1315	−1.93739	−0.968696	−	0.248251i	$-0.920144\pi$
$61$	−15.1315	−1.93739	−0.968696	+	0.248251i	$0.920144\pi$
$62$	7.51030	0.953809
$63$	−2.61289	−0.329193
$64$	1.00000	0.125000
$65$	−13.9537	−1.73074
$66$	2.22776	0.274218
$67$	−9.58013	−1.17040	−0.585200	−	0.810889i	$-0.698984\pi$
$67$	−9.58013	−1.17040	−0.585200	+	0.810889i	$0.698984\pi$
$68$	−1.00000	−0.121268
$69$	4.64959	0.559744
$70$	−3.37396	−0.403265
$71$	−10.2715	−1.21901	−0.609504	−	0.792783i	$-0.708631\pi$
$71$	−10.2715	−1.21901	−0.609504	+	0.792783i	$0.708631\pi$
$72$	2.61289	0.307932
$73$	−9.08237	−1.06301	−0.531505	−	0.847055i	$-0.678373\pi$
$73$	−9.08237	−1.06301	−0.531505	+	0.847055i	$0.678373\pi$
$74$	−4.45367	−0.517728
$75$	−3.97175	−0.458618
$76$	1.00000	0.114708
$77$	3.58057	0.408044
$78$	−2.57315	−0.291352
$79$	7.71934	0.868493	0.434247	−	0.900794i	$-0.357015\pi$
$79$	7.71934	0.868493	0.434247	+	0.900794i	$0.357015\pi$
$80$	3.37396	0.377220
$81$	5.66588	0.629542
$82$	−0.227632	−0.0251378
$83$	4.58343	0.503097	0.251549	−	0.967845i	$-0.419060\pi$
$83$	4.58343	0.503097	0.251549	+	0.967845i	$0.419060\pi$
$84$	−0.622180	−0.0678854
$85$	−3.37396	−0.365957
$86$	1.88935	0.203734
$87$	1.79800	0.192766
$88$	−3.58057	−0.381690
$89$	−12.0376	−1.27599	−0.637993	−	0.770042i	$-0.720235\pi$
$89$	−12.0376	−1.27599	−0.637993	+	0.770042i	$0.720235\pi$
$90$	8.81579	0.929266
$91$	−4.13570	−0.433539
$92$	−7.47306	−0.779120
$93$	4.67276	0.484542
$94$	−0.272506	−0.0281068
$95$	3.37396	0.346161
$96$	0.622180	0.0635010
$97$	7.34113	0.745378	0.372689	−	0.927956i	$-0.378436\pi$
$97$	7.34113	0.745378	0.372689	+	0.927956i	$0.378436\pi$
$98$	−1.00000	−0.101015
$99$	−9.35565	−0.940278
$100$	6.38360	0.638360
$101$	18.2424	1.81518	0.907592	−	0.419853i	$-0.137918\pi$
$101$	18.2424	1.81518	0.907592	+	0.419853i	$0.137918\pi$
$102$	−0.622180	−0.0616050
$103$	−16.8574	−1.66101	−0.830506	−	0.557010i	$-0.811949\pi$
$103$	−16.8574	−1.66101	−0.830506	+	0.557010i	$0.811949\pi$
$104$	4.13570	0.405538
$105$	−2.09921	−0.204862
$106$	6.74989	0.655607
$107$	−6.56982	−0.635129	−0.317564	−	0.948237i	$-0.602865\pi$
$107$	−6.56982	−0.635129	−0.317564	+	0.948237i	$0.602865\pi$
$108$	3.49223	0.336040
$109$	−9.59943	−0.919459	−0.459729	−	0.888059i	$-0.652054\pi$
$109$	−9.59943	−0.919459	−0.459729	+	0.888059i	$0.652054\pi$
$110$	−12.0807	−1.15185
$111$	−2.77098	−0.263010
$112$	1.00000	0.0944911
$113$	−1.93098	−0.181651	−0.0908257	−	0.995867i	$-0.528951\pi$
$113$	−1.93098	−0.181651	−0.0908257	+	0.995867i	$0.528951\pi$
$114$	0.622180	0.0582725
$115$	−25.2138	−2.35120
$116$	−2.88984	−0.268315
$117$	10.8061	0.999027
$118$	−3.28385	−0.302303
$119$	−1.00000	−0.0916698
$120$	2.09921	0.191631
$121$	1.82050	0.165500
$122$	15.1315	1.36994
$123$	−0.141628	−0.0127702
$124$	−7.51030	−0.674445
$125$	4.66821	0.417538
$126$	2.61289	0.232775
$127$	3.74336	0.332169	0.166085	−	0.986111i	$-0.446887\pi$
$127$	3.74336	0.332169	0.166085	+	0.986111i	$0.446887\pi$
$128$	−1.00000	−0.0883883
$129$	1.17551	0.103498
$130$	13.9537	1.22382
$131$	12.9421	1.13075	0.565377	−	0.824832i	$-0.308731\pi$
$131$	12.9421	1.13075	0.565377	+	0.824832i	$0.308731\pi$
$132$	−2.22776	−0.193902
$133$	1.00000	0.0867110
$134$	9.58013	0.827597
$135$	11.7826	1.01409
$136$	1.00000	0.0857493
$137$	−2.86663	−0.244912	−0.122456	−	0.992474i	$-0.539077\pi$
$137$	−2.86663	−0.244912	−0.122456	+	0.992474i	$0.539077\pi$
$138$	−4.64959	−0.395799
$139$	4.13641	0.350846	0.175423	−	0.984493i	$-0.443871\pi$
$139$	4.13641	0.350846	0.175423	+	0.984493i	$0.443871\pi$
$140$	3.37396	0.285152
$141$	−0.169548	−0.0142785
$142$	10.2715	0.861969
$143$	−14.8082	−1.23832
$144$	−2.61289	−0.217741
$145$	−9.75020	−0.809710
$146$	9.08237	0.751662
$147$	−0.622180	−0.0513165
$148$	4.45367	0.366089
$149$	3.07979	0.252307	0.126153	−	0.992011i	$-0.459737\pi$
$149$	3.07979	0.252307	0.126153	+	0.992011i	$0.459737\pi$
$150$	3.97175	0.324292
$151$	−0.183537	−0.0149361	−0.00746803	−	0.999972i	$-0.502377\pi$
$151$	−0.183537	−0.0149361	−0.00746803	+	0.999972i	$0.502377\pi$
$152$	−1.00000	−0.0811107
$153$	2.61289	0.211240
$154$	−3.58057	−0.288531
$155$	−25.3394	−2.03531
$156$	2.57315	0.206017
$157$	0.905436	0.0722616	0.0361308	−	0.999347i	$-0.488497\pi$
$157$	0.905436	0.0722616	0.0361308	+	0.999347i	$0.488497\pi$
$158$	−7.71934	−0.614118
$159$	4.19964	0.333053
$160$	−3.37396	−0.266735
$161$	−7.47306	−0.588959
$162$	−5.66588	−0.445154
$163$	−9.06709	−0.710189	−0.355095	−	0.934830i	$-0.615551\pi$
$163$	−9.06709	−0.710189	−0.355095	+	0.934830i	$0.615551\pi$
$164$	0.227632	0.0177751
$165$	−7.51637	−0.585149
$166$	−4.58343	−0.355743
$167$	−8.58071	−0.663995	−0.331997	−	0.943280i	$-0.607723\pi$
$167$	−8.58071	−0.663995	−0.331997	+	0.943280i	$0.607723\pi$
$168$	0.622180	0.0480022
$169$	4.10399	0.315691
$170$	3.37396	0.258771
$171$	−2.61289	−0.199813
$172$	−1.88935	−0.144061
$173$	13.4638	1.02364	0.511818	−	0.859094i	$-0.328972\pi$
$173$	13.4638	1.02364	0.511818	+	0.859094i	$0.328972\pi$
$174$	−1.79800	−0.136306
$175$	6.38360	0.482555
$176$	3.58057	0.269896
$177$	−2.04315	−0.153572
$178$	12.0376	0.902258
$179$	15.4409	1.15411	0.577053	−	0.816707i	$-0.304203\pi$
$179$	15.4409	1.15411	0.577053	+	0.816707i	$0.304203\pi$
$180$	−8.81579	−0.657090
$181$	4.99621	0.371365	0.185683	−	0.982610i	$-0.440550\pi$
$181$	4.99621	0.371365	0.185683	+	0.982610i	$0.440550\pi$
$182$	4.13570	0.306558
$183$	9.41452	0.695942
$184$	7.47306	0.550921
$185$	15.0265	1.10477
$186$	−4.67276	−0.342623
$187$	−3.58057	−0.261837
$188$	0.272506	0.0198745
$189$	3.49223	0.254022
$190$	−3.37396	−0.244773
$191$	5.22202	0.377852	0.188926	−	0.981991i	$-0.439499\pi$
$191$	5.22202	0.377852	0.188926	+	0.981991i	$0.439499\pi$
$192$	−0.622180	−0.0449020
$193$	11.5276	0.829774	0.414887	−	0.909873i	$-0.363821\pi$
$193$	11.5276	0.829774	0.414887	+	0.909873i	$0.363821\pi$
$194$	−7.34113	−0.527062
$195$	8.68170	0.621709
$196$	1.00000	0.0714286
$197$	12.9335	0.921477	0.460738	−	0.887536i	$-0.347585\pi$
$197$	12.9335	0.921477	0.460738	+	0.887536i	$0.347585\pi$
$198$	9.35565	0.664877
$199$	−5.45028	−0.386360	−0.193180	−	0.981163i	$-0.561880\pi$
$199$	−5.45028	−0.386360	−0.193180	+	0.981163i	$0.561880\pi$
$200$	−6.38360	−0.451389
$201$	5.96056	0.420426
$202$	−18.2424	−1.28353
$203$	−2.88984	−0.202827
$204$	0.622180	0.0435613
$205$	0.768022	0.0536410
$206$	16.8574	1.17451
$207$	19.5263	1.35717
$208$	−4.13570	−0.286759
$209$	3.58057	0.247673
$210$	2.09921	0.144859
$211$	8.61811	0.593295	0.296648	−	0.954987i	$-0.404131\pi$
$211$	8.61811	0.593295	0.296648	+	0.954987i	$0.404131\pi$
$212$	−6.74989	−0.463584
$213$	6.39075	0.437887
$214$	6.56982	0.449104
$215$	−6.37459	−0.434743
$216$	−3.49223	−0.237616
$217$	−7.51030	−0.509832
$218$	9.59943	0.650156
$219$	5.65087	0.381850
$220$	12.0807	0.814481
$221$	4.13570	0.278197
$222$	2.77098	0.185976
$223$	−1.93969	−0.129891	−0.0649457	−	0.997889i	$-0.520687\pi$
$223$	−1.93969	−0.129891	−0.0649457	+	0.997889i	$0.520687\pi$
$224$	−1.00000	−0.0668153
$225$	−16.6797	−1.11198
$226$	1.93098	0.128447
$227$	−4.36069	−0.289429	−0.144715	−	0.989473i	$-0.546226\pi$
$227$	−4.36069	−0.289429	−0.144715	+	0.989473i	$0.546226\pi$
$228$	−0.622180	−0.0412049
$229$	15.2558	1.00813	0.504064	−	0.863666i	$-0.331837\pi$
$229$	15.2558	1.00813	0.504064	+	0.863666i	$0.331837\pi$
$230$	25.2138	1.66255
$231$	−2.22776	−0.146576
$232$	2.88984	0.189727
$233$	6.39554	0.418986	0.209493	−	0.977810i	$-0.432819\pi$
$233$	6.39554	0.418986	0.209493	+	0.977810i	$0.432819\pi$
$234$	−10.8061	−0.706419
$235$	0.919424	0.0599766
$236$	3.28385	0.213761
$237$	−4.80282	−0.311977
$238$	1.00000	0.0648204
$239$	−3.99359	−0.258324	−0.129162	−	0.991624i	$-0.541229\pi$
$239$	−3.99359	−0.258324	−0.129162	+	0.991624i	$0.541229\pi$
$240$	−2.09921	−0.135503
$241$	−15.3324	−0.987646	−0.493823	−	0.869562i	$-0.664401\pi$
$241$	−15.3324	−0.987646	−0.493823	+	0.869562i	$0.664401\pi$
$242$	−1.82050	−0.117026
$243$	−14.0019	−0.898221
$244$	−15.1315	−0.968696
$245$	3.37396	0.215554
$246$	0.141628	0.00902989
$247$	−4.13570	−0.263148
$248$	7.51030	0.476904
$249$	−2.85172	−0.180720
$250$	−4.66821	−0.295244
$251$	−10.3931	−0.656010	−0.328005	−	0.944676i	$-0.606376\pi$
$251$	−10.3931	−0.656010	−0.328005	+	0.944676i	$0.606376\pi$
$252$	−2.61289	−0.164597
$253$	−26.7578	−1.68225
$254$	−3.74336	−0.234879
$255$	2.09921	0.131458
$256$	1.00000	0.0625000
$257$	−21.9471	−1.36902	−0.684512	−	0.729002i	$-0.739985\pi$
$257$	−21.9471	−1.36902	−0.684512	+	0.729002i	$0.739985\pi$
$258$	−1.17551	−0.0731844
$259$	4.45367	0.276737
$260$	−13.9537	−0.865370
$261$	7.55084	0.467385
$262$	−12.9421	−0.799564
$263$	3.28371	0.202482	0.101241	−	0.994862i	$-0.467719\pi$
$263$	3.28371	0.202482	0.101241	+	0.994862i	$0.467719\pi$
$264$	2.22776	0.137109
$265$	−22.7738	−1.39899
$266$	−1.00000	−0.0613139
$267$	7.48957	0.458354
$268$	−9.58013	−0.585200
$269$	18.4140	1.12272	0.561362	−	0.827571i	$-0.310278\pi$
$269$	18.4140	1.12272	0.561362	+	0.827571i	$0.310278\pi$
$270$	−11.7826	−0.717069
$271$	8.28268	0.503137	0.251569	−	0.967839i	$-0.419054\pi$
$271$	8.28268	0.503137	0.251569	+	0.967839i	$0.419054\pi$
$272$	−1.00000	−0.0606339
$273$	2.57315	0.155734
$274$	2.86663	0.173179
$275$	22.8570	1.37833
$276$	4.64959	0.279872
$277$	18.8387	1.13191	0.565954	−	0.824437i	$-0.308508\pi$
$277$	18.8387	1.13191	0.565954	+	0.824437i	$0.308508\pi$
$278$	−4.13641	−0.248086
$279$	19.6236	1.17483
$280$	−3.37396	−0.201633
$281$	−19.5252	−1.16478	−0.582389	−	0.812910i	$-0.697882\pi$
$281$	−19.5252	−1.16478	−0.582389	+	0.812910i	$0.697882\pi$
$282$	0.169548	0.0100964
$283$	−24.1174	−1.43363	−0.716816	−	0.697262i	$-0.754401\pi$
$283$	−24.1174	−1.43363	−0.716816	+	0.697262i	$0.754401\pi$
$284$	−10.2715	−0.609504
$285$	−2.09921	−0.124346
$286$	14.8082	0.875625
$287$	0.227632	0.0134367
$288$	2.61289	0.153966
$289$	1.00000	0.0588235
$290$	9.75020	0.572552
$291$	−4.56750	−0.267752
$292$	−9.08237	−0.531505
$293$	−4.42451	−0.258482	−0.129241	−	0.991613i	$-0.541254\pi$
$293$	−4.42451	−0.258482	−0.129241	+	0.991613i	$0.541254\pi$
$294$	0.622180	0.0362863
$295$	11.0796	0.645078
$296$	−4.45367	−0.258864
$297$	12.5042	0.725566
$298$	−3.07979	−0.178408
$299$	30.9063	1.78736
$300$	−3.97175	−0.229309
$301$	−1.88935	−0.108900
$302$	0.183537	0.0105614
$303$	−11.3500	−0.652043
$304$	1.00000	0.0573539
$305$	−51.0531	−2.92329
$306$	−2.61289	−0.149369
$307$	−22.4444	−1.28097	−0.640486	−	0.767970i	$-0.721267\pi$
$307$	−22.4444	−1.28097	−0.640486	+	0.767970i	$0.721267\pi$
$308$	3.58057	0.204022
$309$	10.4884	0.596662
$310$	25.3394	1.43918
$311$	−1.13252	−0.0642193	−0.0321096	−	0.999484i	$-0.510223\pi$
$311$	−1.13252	−0.0642193	−0.0321096	+	0.999484i	$0.510223\pi$
$312$	−2.57315	−0.145676
$313$	32.3895	1.83076	0.915382	−	0.402585i	$-0.131888\pi$
$313$	32.3895	1.83076	0.915382	+	0.402585i	$0.131888\pi$
$314$	−0.905436	−0.0510967
$315$	−8.81579	−0.496714
$316$	7.71934	0.434247
$317$	8.43453	0.473730	0.236865	−	0.971543i	$-0.423880\pi$
$317$	8.43453	0.473730	0.236865	+	0.971543i	$0.423880\pi$
$318$	−4.19964	−0.235504
$319$	−10.3473	−0.579337
$320$	3.37396	0.188610
$321$	4.08761	0.228148
$322$	7.47306	0.416457
$323$	−1.00000	−0.0556415
$324$	5.66588	0.314771
$325$	−26.4006	−1.46444
$326$	9.06709	0.502180
$327$	5.97257	0.330284
$328$	−0.227632	−0.0125689
$329$	0.272506	0.0150237
$330$	7.51637	0.413763
$331$	23.2717	1.27913	0.639565	−	0.768737i	$-0.279114\pi$
$331$	23.2717	1.27913	0.639565	+	0.768737i	$0.279114\pi$
$332$	4.58343	0.251549
$333$	−11.6370	−0.637701
$334$	8.58071	0.469515
$335$	−32.3230	−1.76599
$336$	−0.622180	−0.0339427
$337$	−30.2410	−1.64733	−0.823667	−	0.567074i	$-0.808075\pi$
$337$	−30.2410	−1.64733	−0.823667	+	0.567074i	$0.808075\pi$
$338$	−4.10399	−0.223228
$339$	1.20142	0.0652520
$340$	−3.37396	−0.182979
$341$	−26.8912	−1.45624
$342$	2.61289	0.141289
$343$	1.00000	0.0539949
$344$	1.88935	0.101867
$345$	15.6875	0.844587
$346$	−13.4638	−0.723819
$347$	−12.3737	−0.664257	−0.332129	−	0.943234i	$-0.607767\pi$
$347$	−12.3737	−0.664257	−0.332129	+	0.943234i	$0.607767\pi$
$348$	1.79800	0.0963830
$349$	33.9693	1.81834	0.909169	−	0.416428i	$-0.136718\pi$
$349$	33.9693	1.81834	0.909169	+	0.416428i	$0.136718\pi$
$350$	−6.38360	−0.341218
$351$	−14.4428	−0.770900
$352$	−3.58057	−0.190845
$353$	−34.4604	−1.83414	−0.917071	−	0.398725i	$-0.869453\pi$
$353$	−34.4604	−1.83414	−0.917071	+	0.398725i	$0.869453\pi$
$354$	2.04315	0.108592
$355$	−34.6558	−1.83934
$356$	−12.0376	−0.637993
$357$	0.622180	0.0329293
$358$	−15.4409	−0.816076
$359$	−4.63018	−0.244371	−0.122186	−	0.992507i	$-0.538990\pi$
$359$	−4.63018	−0.244371	−0.122186	+	0.992507i	$0.538990\pi$
$360$	8.81579	0.464633
$361$	1.00000	0.0526316
$362$	−4.99621	−0.262595
$363$	−1.13268	−0.0594503
$364$	−4.13570	−0.216769
$365$	−30.6435	−1.60396
$366$	−9.41452	−0.492105
$367$	23.8615	1.24556	0.622779	−	0.782398i	$-0.286003\pi$
$367$	23.8615	1.24556	0.622779	+	0.782398i	$0.286003\pi$
$368$	−7.47306	−0.389560
$369$	−0.594779	−0.0309629
$370$	−15.0265	−0.781190
$371$	−6.74989	−0.350437
$372$	4.67276	0.242271
$373$	1.72988	0.0895699	0.0447849	−	0.998997i	$-0.485740\pi$
$373$	1.72988	0.0895699	0.0447849	+	0.998997i	$0.485740\pi$
$374$	3.58057	0.185147
$375$	−2.90447	−0.149986
$376$	−0.272506	−0.0140534
$377$	11.9515	0.615534
$378$	−3.49223	−0.179621
$379$	−24.4407	−1.25544	−0.627718	−	0.778441i	$-0.716011\pi$
$379$	−24.4407	−1.25544	−0.627718	+	0.778441i	$0.716011\pi$
$380$	3.37396	0.173080
$381$	−2.32904	−0.119320
$382$	−5.22202	−0.267182
$383$	−16.8335	−0.860153	−0.430076	−	0.902792i	$-0.641513\pi$
$383$	−16.8335	−0.860153	−0.430076	+	0.902792i	$0.641513\pi$
$384$	0.622180	0.0317505
$385$	12.0807	0.615690
$386$	−11.5276	−0.586738
$387$	4.93666	0.250945
$388$	7.34113	0.372689
$389$	8.02037	0.406649	0.203324	−	0.979111i	$-0.434825\pi$
$389$	8.02037	0.406649	0.203324	+	0.979111i	$0.434825\pi$
$390$	−8.68170	−0.439615
$391$	7.47306	0.377929
$392$	−1.00000	−0.0505076
$393$	−8.05230	−0.406185
$394$	−12.9335	−0.651582
$395$	26.0447	1.31045
$396$	−9.35565	−0.470139
$397$	16.3477	0.820466	0.410233	−	0.911981i	$-0.365447\pi$
$397$	16.3477	0.820466	0.410233	+	0.911981i	$0.365447\pi$
$398$	5.45028	0.273198
$399$	−0.622180	−0.0311480
$400$	6.38360	0.319180
$401$	−31.5716	−1.57661	−0.788306	−	0.615284i	$-0.789042\pi$
$401$	−31.5716	−1.57661	−0.788306	+	0.615284i	$0.789042\pi$
$402$	−5.96056	−0.297286
$403$	31.0603	1.54722
$404$	18.2424	0.907592
$405$	19.1165	0.949904
$406$	2.88984	0.143420
$407$	15.9467	0.790448
$408$	−0.622180	−0.0308025
$409$	−21.6931	−1.07266	−0.536328	−	0.844009i	$-0.680189\pi$
$409$	−21.6931	−1.07266	−0.536328	+	0.844009i	$0.680189\pi$
$410$	−0.768022	−0.0379299
$411$	1.78356	0.0879764
$412$	−16.8574	−0.830506
$413$	3.28385	0.161588
$414$	−19.5263	−0.959665
$415$	15.4643	0.759114
$416$	4.13570	0.202769
$417$	−2.57359	−0.126029
$418$	−3.58057	−0.175132
$419$	−21.8699	−1.06842	−0.534208	−	0.845353i	$-0.679390\pi$
$419$	−21.8699	−1.06842	−0.534208	+	0.845353i	$0.679390\pi$
$420$	−2.09921	−0.102431
$421$	5.79071	0.282222	0.141111	−	0.989994i	$-0.454933\pi$
$421$	5.79071	0.282222	0.141111	+	0.989994i	$0.454933\pi$
$422$	−8.61811	−0.419523
$423$	−0.712029	−0.0346200
$424$	6.74989	0.327803
$425$	−6.38360	−0.309650
$426$	−6.39075	−0.309633
$427$	−15.1315	−0.732265
$428$	−6.56982	−0.317564
$429$	9.21334	0.444824
$430$	6.37459	0.307410
$431$	−8.32441	−0.400973	−0.200486	−	0.979697i	$-0.564252\pi$
$431$	−8.32441	−0.400973	−0.200486	+	0.979697i	$0.564252\pi$
$432$	3.49223	0.168020
$433$	25.9981	1.24939	0.624694	−	0.780870i	$-0.285224\pi$
$433$	25.9981	1.24939	0.624694	+	0.780870i	$0.285224\pi$
$434$	7.51030	0.360506
$435$	6.06638	0.290861
$436$	−9.59943	−0.459729
$437$	−7.47306	−0.357485
$438$	−5.65087	−0.270009
$439$	−7.59139	−0.362318	−0.181159	−	0.983454i	$-0.557985\pi$
$439$	−7.59139	−0.362318	−0.181159	+	0.983454i	$0.557985\pi$
$440$	−12.0807	−0.575925
$441$	−2.61289	−0.124423
$442$	−4.13570	−0.196715
$443$	−28.0966	−1.33491	−0.667455	−	0.744650i	$-0.732616\pi$
$443$	−28.0966	−1.33491	−0.667455	+	0.744650i	$0.732616\pi$
$444$	−2.77098	−0.131505
$445$	−40.6145	−1.92531
$446$	1.93969	0.0918471
$447$	−1.91619	−0.0906325
$448$	1.00000	0.0472456
$449$	1.31196	0.0619152	0.0309576	−	0.999521i	$-0.490144\pi$
$449$	1.31196	0.0619152	0.0309576	+	0.999521i	$0.490144\pi$
$450$	16.6797	0.786287
$451$	0.815054	0.0383794
$452$	−1.93098	−0.0908257
$453$	0.114193	0.00536527
$454$	4.36069	0.204658
$455$	−13.9537	−0.654158
$456$	0.622180	0.0291362
$457$	−10.3510	−0.484198	−0.242099	−	0.970252i	$-0.577836\pi$
$457$	−10.3510	−0.484198	−0.242099	+	0.970252i	$0.577836\pi$
$458$	−15.2558	−0.712855
$459$	−3.49223	−0.163003
$460$	−25.2138	−1.17560
$461$	−24.0062	−1.11808	−0.559041	−	0.829140i	$-0.688831\pi$
$461$	−24.0062	−1.11808	−0.559041	+	0.829140i	$0.688831\pi$
$462$	2.22776	0.103645
$463$	−34.7485	−1.61490	−0.807450	−	0.589936i	$-0.799153\pi$
$463$	−34.7485	−1.61490	−0.807450	+	0.589936i	$0.799153\pi$
$464$	−2.88984	−0.134157
$465$	15.7657	0.731116
$466$	−6.39554	−0.296268
$467$	19.7236	0.912701	0.456350	−	0.889800i	$-0.349156\pi$
$467$	19.7236	0.912701	0.456350	+	0.889800i	$0.349156\pi$
$468$	10.8061	0.499514
$469$	−9.58013	−0.442369
$470$	−0.919424	−0.0424099
$471$	−0.563344	−0.0259575
$472$	−3.28385	−0.151152
$473$	−6.76495	−0.311053
$474$	4.80282	0.220601
$475$	6.38360	0.292900
$476$	−1.00000	−0.0458349
$477$	17.6367	0.807530
$478$	3.99359	0.182663
$479$	−6.26318	−0.286172	−0.143086	−	0.989710i	$-0.545703\pi$
$479$	−6.26318	−0.286172	−0.143086	+	0.989710i	$0.545703\pi$
$480$	2.09921	0.0958154
$481$	−18.4190	−0.839835
$482$	15.3324	0.698371
$483$	4.64959	0.211563
$484$	1.82050	0.0827502
$485$	24.7687	1.12469
$486$	14.0019	0.635138
$487$	2.61228	0.118374	0.0591868	−	0.998247i	$-0.481149\pi$
$487$	2.61228	0.118374	0.0591868	+	0.998247i	$0.481149\pi$
$488$	15.1315	0.684971
$489$	5.64136	0.255111
$490$	−3.37396	−0.152420
$491$	−19.6949	−0.888819	−0.444410	−	0.895824i	$-0.646586\pi$
$491$	−19.6949	−0.888819	−0.444410	+	0.895824i	$0.646586\pi$
$492$	−0.141628	−0.00638510
$493$	2.88984	0.130152
$494$	4.13570	0.186074
$495$	−31.5656	−1.41877
$496$	−7.51030	−0.337222
$497$	−10.2715	−0.460742
$498$	2.85172	0.127789
$499$	−14.5188	−0.649953	−0.324976	−	0.945722i	$-0.605356\pi$
$499$	−14.5188	−0.649953	−0.324976	+	0.945722i	$0.605356\pi$
$500$	4.66821	0.208769
$501$	5.33874	0.238517
$502$	10.3931	0.463869
$503$	−38.7671	−1.72854	−0.864270	−	0.503028i	$-0.832219\pi$
$503$	−38.7671	−1.72854	−0.864270	+	0.503028i	$0.832219\pi$
$504$	2.61289	0.116387
$505$	61.5490	2.73890
$506$	26.7578	1.18953
$507$	−2.55342	−0.113401
$508$	3.74336	0.166085
$509$	38.9570	1.72674	0.863369	−	0.504573i	$-0.168350\pi$
$509$	38.9570	1.72674	0.863369	+	0.504573i	$0.168350\pi$
$510$	−2.09921	−0.0929546
$511$	−9.08237	−0.401780
$512$	−1.00000	−0.0441942
$513$	3.49223	0.154186
$514$	21.9471	0.968046
$515$	−56.8763	−2.50627
$516$	1.17551	0.0517492
$517$	0.975727	0.0429124
$518$	−4.45367	−0.195683
$519$	−8.37692	−0.367706
$520$	13.9537	0.611909
$521$	−18.2915	−0.801363	−0.400682	−	0.916217i	$-0.631227\pi$
$521$	−18.2915	−0.801363	−0.400682	+	0.916217i	$0.631227\pi$
$522$	−7.55084	−0.330491
$523$	−36.9897	−1.61745	−0.808724	−	0.588189i	$-0.799841\pi$
$523$	−36.9897	−1.61745	−0.808724	+	0.588189i	$0.799841\pi$
$524$	12.9421	0.565377
$525$	−3.97175	−0.173341
$526$	−3.28371	−0.143176
$527$	7.51030	0.327154
$528$	−2.22776	−0.0969508
$529$	32.8466	1.42811
$530$	22.7738	0.989232
$531$	−8.58035	−0.372355
$532$	1.00000	0.0433555
$533$	−0.941418	−0.0407774
$534$	−7.48957	−0.324105
$535$	−22.1663	−0.958334
$536$	9.58013	0.413799
$537$	−9.60701	−0.414573
$538$	−18.4140	−0.793885
$539$	3.58057	0.154226
$540$	11.7826	0.507044
$541$	27.9156	1.20019	0.600094	−	0.799930i	$-0.295130\pi$
$541$	27.9156	1.20019	0.600094	+	0.799930i	$0.295130\pi$
$542$	−8.28268	−0.355772
$543$	−3.10854	−0.133400
$544$	1.00000	0.0428746
$545$	−32.3881	−1.38735
$546$	−2.57315	−0.110121
$547$	−41.5888	−1.77821	−0.889105	−	0.457703i	$-0.848672\pi$
$547$	−41.5888	−1.77821	−0.889105	+	0.457703i	$0.848672\pi$
$548$	−2.86663	−0.122456
$549$	39.5370	1.68740
$550$	−22.8570	−0.974624
$551$	−2.88984	−0.123111
$552$	−4.64959	−0.197900
$553$	7.71934	0.328260
$554$	−18.8387	−0.800380
$555$	−9.34918	−0.396851
$556$	4.13641	0.175423
$557$	12.0223	0.509402	0.254701	−	0.967020i	$-0.418023\pi$
$557$	12.0223	0.509402	0.254701	+	0.967020i	$0.418023\pi$
$558$	−19.6236	−0.830733
$559$	7.81377	0.330487
$560$	3.37396	0.142576
$561$	2.22776	0.0940561
$562$	19.5252	0.823622
$563$	−24.6705	−1.03974	−0.519870	−	0.854246i	$-0.674020\pi$
$563$	−24.6705	−1.03974	−0.519870	+	0.854246i	$0.674020\pi$
$564$	−0.169548	−0.00713925
$565$	−6.51505	−0.274090
$566$	24.1174	1.01373
$567$	5.66588	0.237945
$568$	10.2715	0.430985
$569$	1.38521	0.0580710	0.0290355	−	0.999578i	$-0.490756\pi$
$569$	1.38521	0.0580710	0.0290355	+	0.999578i	$0.490756\pi$
$570$	2.09921	0.0879262
$571$	27.6248	1.15606	0.578030	−	0.816015i	$-0.303822\pi$
$571$	27.6248	1.15606	0.578030	+	0.816015i	$0.303822\pi$
$572$	−14.8082	−0.619160
$573$	−3.24904	−0.135730
$574$	−0.227632	−0.00950119
$575$	−47.7050	−1.98944
$576$	−2.61289	−0.108871
$577$	15.3080	0.637279	0.318640	−	0.947876i	$-0.396774\pi$
$577$	15.3080	0.637279	0.318640	+	0.947876i	$0.396774\pi$
$578$	−1.00000	−0.0415945
$579$	−7.17223	−0.298068
$580$	−9.75020	−0.404855
$581$	4.58343	0.190153
$582$	4.56750	0.189329
$583$	−24.1685	−1.00096
$584$	9.08237	0.375831
$585$	36.4594	1.50741
$586$	4.42451	0.182775
$587$	26.9993	1.11438	0.557191	−	0.830384i	$-0.311879\pi$
$587$	26.9993	1.11438	0.557191	+	0.830384i	$0.311879\pi$
$588$	−0.622180	−0.0256583
$589$	−7.51030	−0.309456
$590$	−11.0796	−0.456139
$591$	−8.04699	−0.331009
$592$	4.45367	0.183045
$593$	−32.7285	−1.34400	−0.671999	−	0.740552i	$-0.734564\pi$
$593$	−32.7285	−1.34400	−0.671999	+	0.740552i	$0.734564\pi$
$594$	−12.5042	−0.513053
$595$	−3.37396	−0.138319
$596$	3.07979	0.126153
$597$	3.39106	0.138787
$598$	−30.9063	−1.26385
$599$	23.1827	0.947220	0.473610	−	0.880735i	$-0.342951\pi$
$599$	23.1827	0.947220	0.473610	+	0.880735i	$0.342951\pi$
$600$	3.97175	0.162146
$601$	−4.98376	−0.203292	−0.101646	−	0.994821i	$-0.532411\pi$
$601$	−4.98376	−0.203292	−0.101646	+	0.994821i	$0.532411\pi$
$602$	1.88935	0.0770041
$603$	25.0318	1.01938
$604$	−0.183537	−0.00746803
$605$	6.14230	0.249720
$606$	11.3500	0.461064
$607$	6.49760	0.263729	0.131865	−	0.991268i	$-0.457904\pi$
$607$	6.49760	0.263729	0.131865	+	0.991268i	$0.457904\pi$
$608$	−1.00000	−0.0405554
$609$	1.79800	0.0728587
$610$	51.0531	2.06708
$611$	−1.12700	−0.0455936
$612$	2.61289	0.105620
$613$	−15.6331	−0.631415	−0.315708	−	0.948857i	$-0.602242\pi$
$613$	−15.6331	−0.631415	−0.315708	+	0.948857i	$0.602242\pi$
$614$	22.4444	0.905784
$615$	−0.477848	−0.0192687
$616$	−3.58057	−0.144265
$617$	17.6426	0.710266	0.355133	−	0.934816i	$-0.384436\pi$
$617$	17.6426	0.710266	0.355133	+	0.934816i	$0.384436\pi$
$618$	−10.4884	−0.421903
$619$	12.4235	0.499341	0.249670	−	0.968331i	$-0.419678\pi$
$619$	12.4235	0.499341	0.249670	+	0.968331i	$0.419678\pi$
$620$	−25.3394	−1.01766
$621$	−26.0976	−1.04726
$622$	1.13252	0.0454099
$623$	−12.0376	−0.482277
$624$	2.57315	0.103008
$625$	−16.1676	−0.646706
$626$	−32.3895	−1.29455
$627$	−2.22776	−0.0889682
$628$	0.905436	0.0361308
$629$	−4.45367	−0.177579
$630$	8.81579	0.351230
$631$	−9.03215	−0.359564	−0.179782	−	0.983706i	$-0.557539\pi$
$631$	−9.03215	−0.359564	−0.179782	+	0.983706i	$0.557539\pi$
$632$	−7.71934	−0.307059
$633$	−5.36202	−0.213121
$634$	−8.43453	−0.334978
$635$	12.6299	0.501204
$636$	4.19964	0.166527
$637$	−4.13570	−0.163862
$638$	10.3473	0.409653
$639$	26.8384	1.06171
$640$	−3.37396	−0.133367
$641$	39.5070	1.56043	0.780216	−	0.625510i	$-0.215109\pi$
$641$	39.5070	1.56043	0.780216	+	0.625510i	$0.215109\pi$
$642$	−4.08761	−0.161325
$643$	−28.8926	−1.13941	−0.569706	−	0.821848i	$-0.692943\pi$
$643$	−28.8926	−1.13941	−0.569706	+	0.821848i	$0.692943\pi$
$644$	−7.47306	−0.294480
$645$	3.96614	0.156167
$646$	1.00000	0.0393445
$647$	−47.1649	−1.85424	−0.927121	−	0.374762i	$-0.877724\pi$
$647$	−47.1649	−1.85424	−0.927121	+	0.374762i	$0.877724\pi$
$648$	−5.66588	−0.222577
$649$	11.7581	0.461545
$650$	26.4006	1.03552
$651$	4.67276	0.183140
$652$	−9.06709	−0.355095
$653$	39.2186	1.53474	0.767372	−	0.641202i	$-0.221564\pi$
$653$	39.2186	1.53474	0.767372	+	0.641202i	$0.221564\pi$
$654$	−5.97257	−0.233546
$655$	43.6660	1.70617
$656$	0.227632	0.00888755
$657$	23.7312	0.925844
$658$	−0.272506	−0.0106234
$659$	−46.1930	−1.79942	−0.899712	−	0.436484i	$-0.856223\pi$
$659$	−46.1930	−1.79942	−0.899712	+	0.436484i	$0.856223\pi$
$660$	−7.51637	−0.292574
$661$	47.7823	1.85852	0.929259	−	0.369429i	$-0.120447\pi$
$661$	47.7823	1.85852	0.929259	+	0.369429i	$0.120447\pi$
$662$	−23.2717	−0.904482
$663$	−2.57315	−0.0999328
$664$	−4.58343	−0.177872
$665$	3.37396	0.130837
$666$	11.6370	0.450923
$667$	21.5959	0.836198
$668$	−8.58071	−0.331997
$669$	1.20684	0.0466590
$670$	32.3230	1.24875
$671$	−54.1795	−2.09158
$672$	0.622180	0.0240011
$673$	29.2734	1.12841	0.564203	−	0.825636i	$-0.309184\pi$
$673$	29.2734	1.12841	0.564203	+	0.825636i	$0.309184\pi$
$674$	30.2410	1.16484
$675$	22.2930	0.858058
$676$	4.10399	0.157846
$677$	3.12575	0.120132	0.0600661	−	0.998194i	$-0.480869\pi$
$677$	3.12575	0.120132	0.0600661	+	0.998194i	$0.480869\pi$
$678$	−1.20142	−0.0461401
$679$	7.34113	0.281727
$680$	3.37396	0.129385
$681$	2.71314	0.103968
$682$	26.8912	1.02972
$683$	37.9370	1.45162	0.725809	−	0.687896i	$-0.241465\pi$
$683$	37.9370	1.45162	0.725809	+	0.687896i	$0.241465\pi$
$684$	−2.61289	−0.0999064
$685$	−9.67188	−0.369544
$686$	−1.00000	−0.0381802
$687$	−9.49182	−0.362136
$688$	−1.88935	−0.0720307
$689$	27.9155	1.06350
$690$	−15.6875	−0.597213
$691$	16.6057	0.631712	0.315856	−	0.948807i	$-0.397708\pi$
$691$	16.6057	0.631712	0.315856	+	0.948807i	$0.397708\pi$
$692$	13.4638	0.511818
$693$	−9.35565	−0.355392
$694$	12.3737	0.469701
$695$	13.9561	0.529385
$696$	−1.79800	−0.0681530
$697$	−0.227632	−0.00862219
$698$	−33.9693	−1.28576
$699$	−3.97918	−0.150506
$700$	6.38360	0.241277
$701$	−37.5304	−1.41750	−0.708751	−	0.705459i	$-0.750741\pi$
$701$	−37.5304	−1.41750	−0.708751	+	0.705459i	$0.750741\pi$
$702$	14.4428	0.545108
$703$	4.45367	0.167973
$704$	3.58057	0.134948
$705$	−0.572047	−0.0215445
$706$	34.4604	1.29693
$707$	18.2424	0.686075
$708$	−2.04315	−0.0767861
$709$	43.5512	1.63560	0.817800	−	0.575503i	$-0.195194\pi$
$709$	43.5512	1.63560	0.817800	+	0.575503i	$0.195194\pi$
$710$	34.6558	1.30061
$711$	−20.1698	−0.756427
$712$	12.0376	0.451129
$713$	56.1249	2.10189
$714$	−0.622180	−0.0232845
$715$	−49.9621	−1.86848
$716$	15.4409	0.577053
$717$	2.48473	0.0927940
$718$	4.63018	0.172797
$719$	24.4558	0.912047	0.456024	−	0.889968i	$-0.349273\pi$
$719$	24.4558	0.912047	0.456024	+	0.889968i	$0.349273\pi$
$720$	−8.81579	−0.328545
$721$	−16.8574	−0.627803
$722$	−1.00000	−0.0372161
$723$	9.53951	0.354778
$724$	4.99621	0.185683
$725$	−18.4476	−0.685126
$726$	1.13268	0.0420377
$727$	−38.5771	−1.43074	−0.715372	−	0.698743i	$-0.753743\pi$
$727$	−38.5771	−1.43074	−0.715372	+	0.698743i	$0.753743\pi$
$728$	4.13570	0.153279
$729$	−8.28595	−0.306887
$730$	30.6435	1.13417
$731$	1.88935	0.0698801
$732$	9.41452	0.347971
$733$	45.3796	1.67613	0.838066	−	0.545568i	$-0.183686\pi$
$733$	45.3796	1.67613	0.838066	+	0.545568i	$0.183686\pi$
$734$	−23.8615	−0.880743
$735$	−2.09921	−0.0774305
$736$	7.47306	0.275461
$737$	−34.3024	−1.26354
$738$	0.594779	0.0218941
$739$	34.0201	1.25145	0.625726	−	0.780043i	$-0.284803\pi$
$739$	34.0201	1.25145	0.625726	+	0.780043i	$0.284803\pi$
$740$	15.0265	0.552385
$741$	2.57315	0.0945269
$742$	6.74989	0.247796
$743$	6.88125	0.252448	0.126224	−	0.992002i	$-0.459714\pi$
$743$	6.88125	0.252448	0.126224	+	0.992002i	$0.459714\pi$
$744$	−4.67276	−0.171312
$745$	10.3911	0.380700
$746$	−1.72988	−0.0633355
$747$	−11.9760	−0.438180
$748$	−3.58057	−0.130919
$749$	−6.56982	−0.240056
$750$	2.90447	0.106056
$751$	−24.9523	−0.910522	−0.455261	−	0.890358i	$-0.650454\pi$
$751$	−24.9523	−0.910522	−0.455261	+	0.890358i	$0.650454\pi$
$752$	0.272506	0.00993727
$753$	6.46641	0.235649
$754$	−11.9515	−0.435248
$755$	−0.619248	−0.0225367
$756$	3.49223	0.127011
$757$	27.1822	0.987954	0.493977	−	0.869475i	$-0.335543\pi$
$757$	27.1822	0.987954	0.493977	+	0.869475i	$0.335543\pi$
$758$	24.4407	0.887727
$759$	16.6482	0.604291
$760$	−3.37396	−0.122386
$761$	−21.7469	−0.788325	−0.394162	−	0.919041i	$-0.628965\pi$
$761$	−21.7469	−0.788325	−0.394162	+	0.919041i	$0.628965\pi$
$762$	2.32904	0.0843723
$763$	−9.59943	−0.347523
$764$	5.22202	0.188926
$765$	8.81579	0.318736
$766$	16.8335	0.608220
$767$	−13.5810	−0.490382
$768$	−0.622180	−0.0224510
$769$	−14.8607	−0.535890	−0.267945	−	0.963434i	$-0.586345\pi$
$769$	−14.8607	−0.535890	−0.267945	+	0.963434i	$0.586345\pi$
$770$	−12.0807	−0.435358
$771$	13.6551	0.491775
$772$	11.5276	0.414887
$773$	26.1046	0.938916	0.469458	−	0.882955i	$-0.344449\pi$
$773$	26.1046	0.938916	0.469458	+	0.882955i	$0.344449\pi$
$774$	−4.93666	−0.177445
$775$	−47.9427	−1.72215
$776$	−7.34113	−0.263531
$777$	−2.77098	−0.0994085
$778$	−8.02037	−0.287544
$779$	0.227632	0.00815577
$780$	8.68170	0.310855
$781$	−36.7780	−1.31602
$782$	−7.47306	−0.267236
$783$	−10.0920	−0.360658
$784$	1.00000	0.0357143
$785$	3.05490	0.109034
$786$	8.05230	0.287216
$787$	35.2372	1.25607	0.628035	−	0.778185i	$-0.283859\pi$
$787$	35.2372	1.25607	0.628035	+	0.778185i	$0.283859\pi$
$788$	12.9335	0.460738
$789$	−2.04306	−0.0727348
$790$	−26.0447	−0.926630
$791$	−1.93098	−0.0686577
$792$	9.35565	0.332439
$793$	62.5793	2.22226
$794$	−16.3477	−0.580157
$795$	14.1694	0.502538
$796$	−5.45028	−0.193180
$797$	−41.7090	−1.47741	−0.738705	−	0.674029i	$-0.764562\pi$
$797$	−41.7090	−1.47741	−0.738705	+	0.674029i	$0.764562\pi$
$798$	0.622180	0.0220249
$799$	−0.272506	−0.00964057
$800$	−6.38360	−0.225694
$801$	31.4530	1.11134
$802$	31.5716	1.11483
$803$	−32.5201	−1.14761
$804$	5.96056	0.210213
$805$	−25.2138	−0.888669
$806$	−31.0603	−1.09405
$807$	−11.4568	−0.403300
$808$	−18.2424	−0.641765
$809$	−5.39779	−0.189776	−0.0948881	−	0.995488i	$-0.530249\pi$
$809$	−5.39779	−0.189776	−0.0948881	+	0.995488i	$0.530249\pi$
$810$	−19.1165	−0.671684
$811$	9.05795	0.318068	0.159034	−	0.987273i	$-0.449162\pi$
$811$	9.05795	0.318068	0.159034	+	0.987273i	$0.449162\pi$
$812$	−2.88984	−0.101414
$813$	−5.15332	−0.180735
$814$	−15.9467	−0.558931
$815$	−30.5920	−1.07159
$816$	0.622180	0.0217807
$817$	−1.88935	−0.0660999
$818$	21.6931	0.758483
$819$	10.8061	0.377597
$820$	0.768022	0.0268205
$821$	25.4499	0.888206	0.444103	−	0.895976i	$-0.353522\pi$
$821$	25.4499	0.888206	0.444103	+	0.895976i	$0.353522\pi$
$822$	−1.78356	−0.0622087
$823$	52.5687	1.83243	0.916215	−	0.400687i	$-0.131229\pi$
$823$	52.5687	1.83243	0.916215	+	0.400687i	$0.131229\pi$
$824$	16.8574	0.587256
$825$	−14.2211	−0.495116
$826$	−3.28385	−0.114260
$827$	0.0207156	0.000720354 0	0.000360177	−	1.00000i	$-0.499885\pi$
$827$	0.0207156	0.000720354 0	0.000360177		1.00000i	$0.499885\pi$
$828$	19.5263	0.678586
$829$	39.5920	1.37509	0.687544	−	0.726143i	$-0.258689\pi$
$829$	39.5920	1.37509	0.687544	+	0.726143i	$0.258689\pi$
$830$	−15.4643	−0.536774
$831$	−11.7211	−0.406599
$832$	−4.13570	−0.143379
$833$	−1.00000	−0.0346479
$834$	2.57359	0.0891163
$835$	−28.9510	−1.00189
$836$	3.58057	0.123837
$837$	−26.2277	−0.906561
$838$	21.8699	0.755484
$839$	−21.2377	−0.733208	−0.366604	−	0.930377i	$-0.619480\pi$
$839$	−21.2377	−0.733208	−0.366604	+	0.930377i	$0.619480\pi$
$840$	2.09921	0.0724296
$841$	−20.6488	−0.712028
$842$	−5.79071	−0.199561
$843$	12.1482	0.418406
$844$	8.61811	0.296648
$845$	13.8467	0.476341
$846$	0.712029	0.0244800
$847$	1.82050	0.0625532
$848$	−6.74989	−0.231792
$849$	15.0054	0.514983
$850$	6.38360	0.218956
$851$	−33.2825	−1.14091
$852$	6.39075	0.218944
$853$	−12.7429	−0.436310	−0.218155	−	0.975914i	$-0.570004\pi$
$853$	−12.7429	−0.436310	−0.218155	+	0.975914i	$0.570004\pi$
$854$	15.1315	0.517790
$855$	−8.81579	−0.301494
$856$	6.56982	0.224552
$857$	35.6488	1.21774	0.608869	−	0.793271i	$-0.291623\pi$
$857$	35.6488	1.21774	0.608869	+	0.793271i	$0.291623\pi$
$858$	−9.21334	−0.314538
$859$	43.6023	1.48769	0.743845	−	0.668352i	$-0.233000\pi$
$859$	43.6023	1.48769	0.743845	+	0.668352i	$0.233000\pi$
$860$	−6.37459	−0.217372
$861$	−0.141628	−0.00482668
$862$	8.32441	0.283530
$863$	−54.0972	−1.84149	−0.920746	−	0.390164i	$-0.872418\pi$
$863$	−54.0972	−1.84149	−0.920746	+	0.390164i	$0.872418\pi$
$864$	−3.49223	−0.118808
$865$	45.4264	1.54454
$866$	−25.9981	−0.883450
$867$	−0.622180	−0.0211303
$868$	−7.51030	−0.254916
$869$	27.6397	0.937611
$870$	−6.06638	−0.205670
$871$	39.6205	1.34249
$872$	9.59943	0.325078
$873$	−19.1816	−0.649198
$874$	7.47306	0.252780
$875$	4.66821	0.157814
$876$	5.65087	0.190925
$877$	−32.8237	−1.10838	−0.554189	−	0.832391i	$-0.686971\pi$
$877$	−32.8237	−1.10838	−0.554189	+	0.832391i	$0.686971\pi$
$878$	7.59139	0.256197
$879$	2.75284	0.0928510
$880$	12.0807	0.407241
$881$	14.2689	0.480731	0.240365	−	0.970682i	$-0.422733\pi$
$881$	14.2689	0.480731	0.240365	+	0.970682i	$0.422733\pi$
$882$	2.61289	0.0879807
$883$	38.1353	1.28336	0.641678	−	0.766974i	$-0.278239\pi$
$883$	38.1353	1.28336	0.641678	+	0.766974i	$0.278239\pi$
$884$	4.13570	0.139099
$885$	−6.89349	−0.231722
$886$	28.0966	0.943924
$887$	0.982976	0.0330051	0.0165025	−	0.999864i	$-0.494747\pi$
$887$	0.982976	0.0330051	0.0165025	+	0.999864i	$0.494747\pi$
$888$	2.77098	0.0929881
$889$	3.74336	0.125548
$890$	40.6145	1.36140
$891$	20.2871	0.679644
$892$	−1.93969	−0.0649457
$893$	0.272506	0.00911906
$894$	1.91619	0.0640868
$895$	52.0969	1.74141
$896$	−1.00000	−0.0334077
$897$	−19.2293	−0.642047
$898$	−1.31196	−0.0437806
$899$	21.7036	0.723854
$900$	−16.6797	−0.555989
$901$	6.74989	0.224871
$902$	−0.815054	−0.0271383
$903$	1.17551	0.0391187
$904$	1.93098	0.0642234
$905$	16.8570	0.560346
$906$	−0.114193	−0.00379382
$907$	31.8203	1.05658	0.528288	−	0.849065i	$-0.322834\pi$
$907$	31.8203	1.05658	0.528288	+	0.849065i	$0.322834\pi$
$908$	−4.36069	−0.144715
$909$	−47.6654	−1.58096
$910$	13.9537	0.462560
$911$	−2.99186	−0.0991249	−0.0495625	−	0.998771i	$-0.515783\pi$
$911$	−2.99186	−0.0991249	−0.0495625	+	0.998771i	$0.515783\pi$
$912$	−0.622180	−0.0206024
$913$	16.4113	0.543135
$914$	10.3510	0.342379
$915$	31.7642	1.05009
$916$	15.2558	0.504064
$917$	12.9421	0.427385
$918$	3.49223	0.115261
$919$	−35.4561	−1.16959	−0.584794	−	0.811182i	$-0.698825\pi$
$919$	−35.4561	−1.16959	−0.584794	+	0.811182i	$0.698825\pi$
$920$	25.2138	0.831274
$921$	13.9645	0.460145
$922$	24.0062	0.790604
$923$	42.4800	1.39825
$924$	−2.22776	−0.0732879
$925$	28.4304	0.934787
$926$	34.7485	1.14191
$927$	44.0466	1.44668
$928$	2.88984	0.0948637
$929$	17.2650	0.566447	0.283224	−	0.959054i	$-0.408596\pi$
$929$	17.2650	0.566447	0.283224	+	0.959054i	$0.408596\pi$
$930$	−15.7657	−0.516977
$931$	1.00000	0.0327737
$932$	6.39554	0.209493
$933$	0.704630	0.0230686
$934$	−19.7236	−0.645377
$935$	−12.0807	−0.395081
$936$	−10.8061	−0.353209
$937$	−5.15138	−0.168288	−0.0841441	−	0.996454i	$-0.526816\pi$
$937$	−5.15138	−0.168288	−0.0841441	+	0.996454i	$0.526816\pi$
$938$	9.58013	0.312802
$939$	−20.1521	−0.657640
$940$	0.919424	0.0299883
$941$	3.73802	0.121856	0.0609280	−	0.998142i	$-0.480594\pi$
$941$	3.73802	0.121856	0.0609280	+	0.998142i	$0.480594\pi$
$942$	0.563344	0.0183547
$943$	−1.70111	−0.0553957
$944$	3.28385	0.106880
$945$	11.7826	0.383289
$946$	6.76495	0.219948
$947$	−46.6508	−1.51595	−0.757974	−	0.652285i	$-0.773810\pi$
$947$	−46.6508	−1.51595	−0.757974	+	0.652285i	$0.773810\pi$
$948$	−4.80282	−0.155988
$949$	37.5619	1.21931
$950$	−6.38360	−0.207111
$951$	−5.24780	−0.170171
$952$	1.00000	0.0324102
$953$	−1.90704	−0.0617751	−0.0308876	−	0.999523i	$-0.509833\pi$
$953$	−1.90704	−0.0617751	−0.0308876	+	0.999523i	$0.509833\pi$
$954$	−17.6367	−0.571010
$955$	17.6189	0.570134
$956$	−3.99359	−0.129162
$957$	6.43787	0.208107
$958$	6.26318	0.202354
$959$	−2.86663	−0.0925682
$960$	−2.09921	−0.0677517
$961$	25.4046	0.819502
$962$	18.4190	0.593853
$963$	17.1662	0.553174
$964$	−15.3324	−0.493823
$965$	38.8936	1.25203
$966$	−4.64959	−0.149598
$967$	−43.6226	−1.40281	−0.701405	−	0.712763i	$-0.747443\pi$
$967$	−43.6226	−1.40281	−0.701405	+	0.712763i	$0.747443\pi$
$968$	−1.82050	−0.0585132
$969$	0.622180	0.0199873
$970$	−24.7687	−0.795274
$971$	4.31205	0.138380	0.0691902	−	0.997603i	$-0.477958\pi$
$971$	4.31205	0.138380	0.0691902	+	0.997603i	$0.477958\pi$
$972$	−14.0019	−0.449111
$973$	4.13641	0.132607
$974$	−2.61228	−0.0837027
$975$	16.4259	0.526051
$976$	−15.1315	−0.484348
$977$	17.1778	0.549568	0.274784	−	0.961506i	$-0.411394\pi$
$977$	17.1778	0.549568	0.274784	+	0.961506i	$0.411394\pi$
$978$	−5.64136	−0.180391
$979$	−43.1016	−1.37753
$980$	3.37396	0.107777
$981$	25.0823	0.800816
$982$	19.6949	0.628490
$983$	−30.4967	−0.972693	−0.486347	−	0.873766i	$-0.661671\pi$
$983$	−30.4967	−0.972693	−0.486347	+	0.873766i	$0.661671\pi$
$984$	0.141628	0.00451494
$985$	43.6372	1.39040
$986$	−2.88984	−0.0920313
$987$	−0.169548	−0.00539676
$988$	−4.13570	−0.131574
$989$	14.1192	0.448965
$990$	31.5656	1.00322
$991$	9.36076	0.297354	0.148677	−	0.988886i	$-0.452498\pi$
$991$	9.36076	0.297354	0.148677	+	0.988886i	$0.452498\pi$
$992$	7.51030	0.238452
$993$	−14.4792	−0.459484
$994$	10.2715	0.325794
$995$	−18.3890	−0.582971
$996$	−2.85172	−0.0903602
$997$	−41.7650	−1.32271	−0.661355	−	0.750073i	$-0.730018\pi$
$997$	−41.7650	−1.32271	−0.661355	+	0.750073i	$0.730018\pi$
$998$	14.5188	0.459586
$999$	15.5532	0.492082

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4522.2.a.bc.1.6	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4522.2.a.bc.1.6	✓	11	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4522 = 2 \cdot 7 \cdot 17 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4522.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.622180 q^{3} +1.00000 q^{4} +3.37396 q^{5} +0.622180 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.61289 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.622180 q^{3} +1.00000 q^{4} +3.37396 q^{5} +0.622180 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.61289 q^{9} -3.37396 q^{10} +3.58057 q^{11} -0.622180 q^{12} -4.13570 q^{13} -1.00000 q^{14} -2.09921 q^{15} +1.00000 q^{16} -1.00000 q^{17} +2.61289 q^{18} +1.00000 q^{19} +3.37396 q^{20} -0.622180 q^{21} -3.58057 q^{22} -7.47306 q^{23} +0.622180 q^{24} +6.38360 q^{25} +4.13570 q^{26} +3.49223 q^{27} +1.00000 q^{28} -2.88984 q^{29} +2.09921 q^{30} -7.51030 q^{31} -1.00000 q^{32} -2.22776 q^{33} +1.00000 q^{34} +3.37396 q^{35} -2.61289 q^{36} +4.45367 q^{37} -1.00000 q^{38} +2.57315 q^{39} -3.37396 q^{40} +0.227632 q^{41} +0.622180 q^{42} -1.88935 q^{43} +3.58057 q^{44} -8.81579 q^{45} +7.47306 q^{46} +0.272506 q^{47} -0.622180 q^{48} +1.00000 q^{49} -6.38360 q^{50} +0.622180 q^{51} -4.13570 q^{52} -6.74989 q^{53} -3.49223 q^{54} +12.0807 q^{55} -1.00000 q^{56} -0.622180 q^{57} +2.88984 q^{58} +3.28385 q^{59} -2.09921 q^{60} -15.1315 q^{61} +7.51030 q^{62} -2.61289 q^{63} +1.00000 q^{64} -13.9537 q^{65} +2.22776 q^{66} -9.58013 q^{67} -1.00000 q^{68} +4.64959 q^{69} -3.37396 q^{70} -10.2715 q^{71} +2.61289 q^{72} -9.08237 q^{73} -4.45367 q^{74} -3.97175 q^{75} +1.00000 q^{76} +3.58057 q^{77} -2.57315 q^{78} +7.71934 q^{79} +3.37396 q^{80} +5.66588 q^{81} -0.227632 q^{82} +4.58343 q^{83} -0.622180 q^{84} -3.37396 q^{85} +1.88935 q^{86} +1.79800 q^{87} -3.58057 q^{88} -12.0376 q^{89} +8.81579 q^{90} -4.13570 q^{91} -7.47306 q^{92} +4.67276 q^{93} -0.272506 q^{94} +3.37396 q^{95} +0.622180 q^{96} +7.34113 q^{97} -1.00000 q^{98} -9.35565 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} - 5 q^{3} + 11 q^{4} - 2 q^{5} + 5 q^{6} + 11 q^{7} - 11 q^{8} + 10 q^{9}+O(q^{10}) \) 11 * q - 11 * q^2 - 5 * q^3 + 11 * q^4 - 2 * q^5 + 5 * q^6 + 11 * q^7 - 11 * q^8 + 10 * q^9	\( 11 q - 11 q^{2} - 5 q^{3} + 11 q^{4} - 2 q^{5} + 5 q^{6} + 11 q^{7} - 11 q^{8} + 10 q^{9} + 2 q^{10} - 9 q^{11} - 5 q^{12} - 11 q^{14} - 11 q^{15} + 11 q^{16} - 11 q^{17} - 10 q^{18} + 11 q^{19} - 2 q^{20} - 5 q^{21} + 9 q^{22} - 8 q^{23} + 5 q^{24} + 17 q^{25} - 14 q^{27} + 11 q^{28} - 17 q^{29} + 11 q^{30} - 9 q^{31} - 11 q^{32} - 7 q^{33} + 11 q^{34} - 2 q^{35} + 10 q^{36} - 14 q^{37} - 11 q^{38} - 6 q^{39} + 2 q^{40} - 16 q^{41} + 5 q^{42} + 3 q^{43} - 9 q^{44} + 5 q^{45} + 8 q^{46} - 12 q^{47} - 5 q^{48} + 11 q^{49} - 17 q^{50} + 5 q^{51} - 34 q^{53} + 14 q^{54} - q^{55} - 11 q^{56} - 5 q^{57} + 17 q^{58} - 23 q^{59} - 11 q^{60} + 12 q^{61} + 9 q^{62} + 10 q^{63} + 11 q^{64} - 28 q^{65} + 7 q^{66} - 11 q^{68} + 3 q^{69} + 2 q^{70} - 42 q^{71} - 10 q^{72} + 14 q^{73} + 14 q^{74} - 32 q^{75} + 11 q^{76} - 9 q^{77} + 6 q^{78} - 7 q^{79} - 2 q^{80} - 9 q^{81} + 16 q^{82} + q^{83} - 5 q^{84} + 2 q^{85} - 3 q^{86} - 10 q^{87} + 9 q^{88} - 6 q^{89} - 5 q^{90} - 8 q^{92} - 14 q^{93} + 12 q^{94} - 2 q^{95} + 5 q^{96} - 15 q^{97} - 11 q^{98} - 33 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - 5 * q^3 + 11 * q^4 - 2 * q^5 + 5 * q^6 + 11 * q^7 - 11 * q^8 + 10 * q^9 + 2 * q^10 - 9 * q^11 - 5 * q^12 - 11 * q^14 - 11 * q^15 + 11 * q^16 - 11 * q^17 - 10 * q^18 + 11 * q^19 - 2 * q^20 - 5 * q^21 + 9 * q^22 - 8 * q^23 + 5 * q^24 + 17 * q^25 - 14 * q^27 + 11 * q^28 - 17 * q^29 + 11 * q^30 - 9 * q^31 - 11 * q^32 - 7 * q^33 + 11 * q^34 - 2 * q^35 + 10 * q^36 - 14 * q^37 - 11 * q^38 - 6 * q^39 + 2 * q^40 - 16 * q^41 + 5 * q^42 + 3 * q^43 - 9 * q^44 + 5 * q^45 + 8 * q^46 - 12 * q^47 - 5 * q^48 + 11 * q^49 - 17 * q^50 + 5 * q^51 - 34 * q^53 + 14 * q^54 - q^55 - 11 * q^56 - 5 * q^57 + 17 * q^58 - 23 * q^59 - 11 * q^60 + 12 * q^61 + 9 * q^62 + 10 * q^63 + 11 * q^64 - 28 * q^65 + 7 * q^66 - 11 * q^68 + 3 * q^69 + 2 * q^70 - 42 * q^71 - 10 * q^72 + 14 * q^73 + 14 * q^74 - 32 * q^75 + 11 * q^76 - 9 * q^77 + 6 * q^78 - 7 * q^79 - 2 * q^80 - 9 * q^81 + 16 * q^82 + q^83 - 5 * q^84 + 2 * q^85 - 3 * q^86 - 10 * q^87 + 9 * q^88 - 6 * q^89 - 5 * q^90 - 8 * q^92 - 14 * q^93 + 12 * q^94 - 2 * q^95 + 5 * q^96 - 15 * q^97 - 11 * q^98 - 33 * q^99

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