LMFDB - Embedded newform 547.2.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,2,Mod(1,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("547.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	547.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:	$4.36781699056$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 4 x^{17} - 18 x^{16} + 84 x^{15} + 116 x^{14} - 708 x^{13} - 282 x^{12} + 3104 x^{11} + \cdots + 328 $ x^18 - 4x^17 - 18x^16 + 84x^15 + 116x^14 - 708x^13 - 282x^12 + 3104x^11 - 137x^10 - 7703x^9 + 2068x^8 + 11068x^7 - 4274x^6 - 9021x^5 + 4048x^4 + 3834x^3 - 1851x^2 - 654*x + 328
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.98431$ of defining polynomial
Character	$\chi$	$=$	547.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.98431 q^{2} -0.150114 q^{3} +1.93749 q^{4} +2.87852 q^{5} +0.297872 q^{6} -2.68467 q^{7} +0.124041 q^{8} -2.97747 q^{9} +O(q^{10})$	\(q-1.98431 q^{2} -0.150114 q^{3} +1.93749 q^{4} +2.87852 q^{5} +0.297872 q^{6} -2.68467 q^{7} +0.124041 q^{8} -2.97747 q^{9} -5.71188 q^{10} +0.368123 q^{11} -0.290844 q^{12} -2.43844 q^{13} +5.32721 q^{14} -0.432105 q^{15} -4.12111 q^{16} -3.34729 q^{17} +5.90822 q^{18} +0.377567 q^{19} +5.57710 q^{20} +0.403005 q^{21} -0.730471 q^{22} -0.915445 q^{23} -0.0186202 q^{24} +3.28588 q^{25} +4.83862 q^{26} +0.897299 q^{27} -5.20151 q^{28} -2.06894 q^{29} +0.857431 q^{30} +5.88622 q^{31} +7.92949 q^{32} -0.0552603 q^{33} +6.64207 q^{34} -7.72786 q^{35} -5.76881 q^{36} -7.95740 q^{37} -0.749211 q^{38} +0.366043 q^{39} +0.357054 q^{40} -1.24111 q^{41} -0.799687 q^{42} +5.58190 q^{43} +0.713235 q^{44} -8.57070 q^{45} +1.81653 q^{46} -12.4681 q^{47} +0.618636 q^{48} +0.207426 q^{49} -6.52020 q^{50} +0.502474 q^{51} -4.72445 q^{52} -11.7975 q^{53} -1.78052 q^{54} +1.05965 q^{55} -0.333009 q^{56} -0.0566780 q^{57} +4.10542 q^{58} -13.7347 q^{59} -0.837199 q^{60} +1.64414 q^{61} -11.6801 q^{62} +7.99350 q^{63} -7.49234 q^{64} -7.01909 q^{65} +0.109654 q^{66} +5.77093 q^{67} -6.48534 q^{68} +0.137421 q^{69} +15.3345 q^{70} -7.47759 q^{71} -0.369328 q^{72} -10.4002 q^{73} +15.7900 q^{74} -0.493255 q^{75} +0.731532 q^{76} -0.988288 q^{77} -0.726343 q^{78} +0.641853 q^{79} -11.8627 q^{80} +8.79770 q^{81} +2.46275 q^{82} +15.7053 q^{83} +0.780818 q^{84} -9.63525 q^{85} -11.0762 q^{86} +0.310576 q^{87} +0.0456624 q^{88} +4.77332 q^{89} +17.0069 q^{90} +6.54639 q^{91} -1.77367 q^{92} -0.883602 q^{93} +24.7406 q^{94} +1.08683 q^{95} -1.19032 q^{96} -15.9649 q^{97} -0.411598 q^{98} -1.09607 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 4 q^{2} - 10 q^{3} + 16 q^{4} - 27 q^{5} - 3 q^{6} - 11 q^{7} - 12 q^{8} + 14 q^{9}+O(q^{10}) $ 18 * q - 4 * q^2 - 10 * q^3 + 16 * q^4 - 27 * q^5 - 3 * q^6 - 11 * q^7 - 12 * q^8 + 14 * q^9	\( 18 q - 4 q^{2} - 10 q^{3} + 16 q^{4} - 27 q^{5} - 3 q^{6} - 11 q^{7} - 12 q^{8} + 14 q^{9} - 5 q^{10} + 2 q^{11} - 32 q^{12} - 25 q^{13} - 7 q^{14} + 9 q^{15} + 8 q^{16} - 30 q^{17} - 10 q^{18} + 4 q^{19} - 41 q^{20} - 16 q^{21} - 24 q^{22} - 26 q^{23} - 12 q^{24} + 31 q^{25} - 18 q^{26} - 37 q^{27} - 16 q^{28} - 18 q^{29} + 8 q^{30} - 5 q^{31} - 28 q^{32} - 10 q^{33} + 5 q^{34} - 9 q^{35} + 31 q^{36} - 18 q^{37} - 45 q^{38} + 7 q^{39} + 7 q^{40} - 17 q^{41} + 4 q^{42} + 8 q^{43} + 12 q^{44} - 44 q^{45} + 30 q^{46} - 52 q^{47} - 7 q^{48} + 29 q^{49} + 13 q^{50} + 19 q^{51} - 14 q^{52} - 60 q^{53} + 11 q^{54} + 11 q^{55} + 7 q^{56} + 4 q^{57} + 14 q^{58} - 8 q^{59} + 86 q^{60} - 26 q^{61} + 4 q^{62} - q^{63} + 44 q^{64} - 6 q^{65} + 18 q^{66} + 12 q^{67} - 61 q^{68} - 38 q^{69} + 35 q^{70} - q^{71} + 28 q^{72} - 2 q^{73} + 16 q^{74} - 17 q^{75} + 66 q^{76} - 73 q^{77} + 115 q^{78} + 18 q^{79} - 32 q^{80} + 18 q^{81} + 44 q^{82} - 43 q^{83} + 41 q^{84} + 51 q^{85} + 4 q^{86} + 3 q^{87} - 17 q^{88} - 28 q^{89} + 58 q^{90} - q^{91} - 68 q^{92} - 60 q^{93} + 78 q^{94} - 18 q^{95} + 29 q^{96} - 34 q^{97} + 34 q^{98} + 15 q^{99}+O(q^{100}) \) 18 * q - 4 * q^2 - 10 * q^3 + 16 * q^4 - 27 * q^5 - 3 * q^6 - 11 * q^7 - 12 * q^8 + 14 * q^9 - 5 * q^10 + 2 * q^11 - 32 * q^12 - 25 * q^13 - 7 * q^14 + 9 * q^15 + 8 * q^16 - 30 * q^17 - 10 * q^18 + 4 * q^19 - 41 * q^20 - 16 * q^21 - 24 * q^22 - 26 * q^23 - 12 * q^24 + 31 * q^25 - 18 * q^26 - 37 * q^27 - 16 * q^28 - 18 * q^29 + 8 * q^30 - 5 * q^31 - 28 * q^32 - 10 * q^33 + 5 * q^34 - 9 * q^35 + 31 * q^36 - 18 * q^37 - 45 * q^38 + 7 * q^39 + 7 * q^40 - 17 * q^41 + 4 * q^42 + 8 * q^43 + 12 * q^44 - 44 * q^45 + 30 * q^46 - 52 * q^47 - 7 * q^48 + 29 * q^49 + 13 * q^50 + 19 * q^51 - 14 * q^52 - 60 * q^53 + 11 * q^54 + 11 * q^55 + 7 * q^56 + 4 * q^57 + 14 * q^58 - 8 * q^59 + 86 * q^60 - 26 * q^61 + 4 * q^62 - q^63 + 44 * q^64 - 6 * q^65 + 18 * q^66 + 12 * q^67 - 61 * q^68 - 38 * q^69 + 35 * q^70 - q^71 + 28 * q^72 - 2 * q^73 + 16 * q^74 - 17 * q^75 + 66 * q^76 - 73 * q^77 + 115 * q^78 + 18 * q^79 - 32 * q^80 + 18 * q^81 + 44 * q^82 - 43 * q^83 + 41 * q^84 + 51 * q^85 + 4 * q^86 + 3 * q^87 - 17 * q^88 - 28 * q^89 + 58 * q^90 - q^91 - 68 * q^92 - 60 * q^93 + 78 * q^94 - 18 * q^95 + 29 * q^96 - 34 * q^97 + 34 * 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 $

$2$	−1.98431	−1.40312	−0.701560	−	0.712611i	$-0.747513\pi$
$2$	−1.98431	−1.40312	−0.701560	+	0.712611i	$0.747513\pi$
$3$	−0.150114	−0.0866682	−0.0433341	−	0.999061i	$-0.513798\pi$
$3$	−0.150114	−0.0866682	−0.0433341	+	0.999061i	$0.513798\pi$
$4$	1.93749	0.968745
$5$	2.87852	1.28731	0.643657	−	0.765314i	$-0.277417\pi$
$5$	2.87852	1.28731	0.643657	+	0.765314i	$0.277417\pi$
$6$	0.297872	0.121606
$7$	−2.68467	−1.01471	−0.507354	−	0.861738i	$-0.669376\pi$
$7$	−2.68467	−1.01471	−0.507354	+	0.861738i	$0.669376\pi$
$8$	0.124041	0.0438551
$9$	−2.97747	−0.992489
$10$	−5.71188	−1.80625
$11$	0.368123	0.110993	0.0554967	−	0.998459i	$-0.482326\pi$
$11$	0.368123	0.110993	0.0554967	+	0.998459i	$0.482326\pi$
$12$	−0.290844	−0.0839593
$13$	−2.43844	−0.676301	−0.338150	−	0.941092i	$-0.609801\pi$
$13$	−2.43844	−0.676301	−0.338150	+	0.941092i	$0.609801\pi$
$14$	5.32721	1.42376
$15$	−0.432105	−0.111569
$16$	−4.12111	−1.03028
$17$	−3.34729	−0.811838	−0.405919	−	0.913909i	$-0.633048\pi$
$17$	−3.34729	−0.811838	−0.405919	+	0.913909i	$0.633048\pi$
$18$	5.90822	1.39258
$19$	0.377567	0.0866199	0.0433099	−	0.999062i	$-0.486210\pi$
$19$	0.377567	0.0866199	0.0433099	+	0.999062i	$0.486210\pi$
$20$	5.57710	1.24708
$21$	0.403005	0.0879429
$22$	−0.730471	−0.155737
$23$	−0.915445	−0.190884	−0.0954418	−	0.995435i	$-0.530426\pi$
$23$	−0.915445	−0.190884	−0.0954418	+	0.995435i	$0.530426\pi$
$24$	−0.0186202	−0.00380084
$25$	3.28588	0.657175
$26$	4.83862	0.948931
$27$	0.897299	0.172685
$28$	−5.20151	−0.982993
$29$	−2.06894	−0.384192	−0.192096	−	0.981376i	$-0.561529\pi$
$29$	−2.06894	−0.384192	−0.192096	+	0.981376i	$0.561529\pi$
$30$	0.857431	0.156545
$31$	5.88622	1.05720	0.528598	−	0.848872i	$-0.322718\pi$
$31$	5.88622	1.05720	0.528598	+	0.848872i	$0.322718\pi$
$32$	7.92949	1.40175
$33$	−0.0552603	−0.00961959
$34$	6.64207	1.13911
$35$	−7.72786	−1.30625
$36$	−5.76881	−0.961468
$37$	−7.95740	−1.30819	−0.654094	−	0.756413i	$-0.726950\pi$
$37$	−7.95740	−1.30819	−0.654094	+	0.756413i	$0.726950\pi$
$38$	−0.749211	−0.121538
$39$	0.366043	0.0586138
$40$	0.357054	0.0564553
$41$	−1.24111	−0.193829	−0.0969145	−	0.995293i	$-0.530897\pi$
$41$	−1.24111	−0.193829	−0.0969145	+	0.995293i	$0.530897\pi$
$42$	−0.799687	−0.123394
$43$	5.58190	0.851232	0.425616	−	0.904904i	$-0.360057\pi$
$43$	5.58190	0.851232	0.425616	+	0.904904i	$0.360057\pi$
$44$	0.713235	0.107524
$45$	−8.57070	−1.27764
$46$	1.81653	0.267832
$47$	−12.4681	−1.81866	−0.909329	−	0.416077i	$-0.863405\pi$
$47$	−12.4681	−1.81866	−0.909329	+	0.416077i	$0.863405\pi$
$48$	0.618636	0.0892924
$49$	0.207426	0.0296323
$50$	−6.52020	−0.922096
$51$	0.502474	0.0703605
$52$	−4.72445	−0.655163
$53$	−11.7975	−1.62052	−0.810258	−	0.586074i	$-0.800673\pi$
$53$	−11.7975	−1.62052	−0.810258	+	0.586074i	$0.800673\pi$
$54$	−1.78052	−0.242298
$55$	1.05965	0.142883
$56$	−0.333009	−0.0445001
$57$	−0.0566780	−0.00750719
$58$	4.10542	0.539068
$59$	−13.7347	−1.78810	−0.894051	−	0.447964i	$-0.852149\pi$
$59$	−13.7347	−1.78810	−0.894051	+	0.447964i	$0.852149\pi$
$60$	−0.837199	−0.108082
$61$	1.64414	0.210511	0.105255	−	0.994445i	$-0.466434\pi$
$61$	1.64414	0.210511	0.105255	+	0.994445i	$0.466434\pi$
$62$	−11.6801	−1.48337
$63$	7.99350	1.00709
$64$	−7.49234	−0.936543
$65$	−7.01909	−0.870611
$66$	0.109654	0.0134974
$67$	5.77093	0.705031	0.352515	−	0.935806i	$-0.385326\pi$
$67$	5.77093	0.705031	0.352515	+	0.935806i	$0.385326\pi$
$68$	−6.48534	−0.786463
$69$	0.137421	0.0165435
$70$	15.3345	1.83282
$71$	−7.47759	−0.887426	−0.443713	−	0.896169i	$-0.646339\pi$
$71$	−7.47759	−0.887426	−0.443713	+	0.896169i	$0.646339\pi$
$72$	−0.369328	−0.0435257
$73$	−10.4002	−1.21725	−0.608625	−	0.793458i	$-0.708279\pi$
$73$	−10.4002	−1.21725	−0.608625	+	0.793458i	$0.708279\pi$
$74$	15.7900	1.83555
$75$	−0.493255	−0.0569562
$76$	0.731532	0.0839125
$77$	−0.988288	−0.112626
$78$	−0.726343	−0.0822421
$79$	0.641853	0.0722141	0.0361070	−	0.999348i	$-0.488504\pi$
$79$	0.641853	0.0722141	0.0361070	+	0.999348i	$0.488504\pi$
$80$	−11.8627	−1.32629
$81$	8.79770	0.977522
$82$	2.46275	0.271965
$83$	15.7053	1.72388	0.861942	−	0.507006i	$-0.169248\pi$
$83$	15.7053	1.72388	0.861942	+	0.507006i	$0.169248\pi$
$84$	0.780818	0.0851942
$85$	−9.63525	−1.04509
$86$	−11.0762	−1.19438
$87$	0.310576	0.0332972
$88$	0.0456624	0.00486763
$89$	4.77332	0.505971	0.252986	−	0.967470i	$-0.418587\pi$
$89$	4.77332	0.505971	0.252986	+	0.967470i	$0.418587\pi$
$90$	17.0069	1.79269
$91$	6.54639	0.686248
$92$	−1.77367	−0.184917
$93$	−0.883602	−0.0916253
$94$	24.7406	2.55180
$95$	1.08683	0.111507
$96$	−1.19032	−0.121487
$97$	−15.9649	−1.62099	−0.810497	−	0.585742i	$-0.800803\pi$
$97$	−15.9649	−1.62099	−0.810497	+	0.585742i	$0.800803\pi$
$98$	−0.411598	−0.0415777
$99$	−1.09607	−0.110160
$100$	6.36635	0.636635
$101$	13.4395	1.33728	0.668642	−	0.743585i	$-0.266876\pi$
$101$	13.4395	1.33728	0.668642	+	0.743585i	$0.266876\pi$
$102$	−0.997065	−0.0987242
$103$	8.31399	0.819202	0.409601	−	0.912265i	$-0.365668\pi$
$103$	8.31399	0.819202	0.409601	+	0.912265i	$0.365668\pi$
$104$	−0.302466	−0.0296593
$105$	1.16006	0.113210
$106$	23.4100	2.27378
$107$	1.14891	0.111069	0.0555347	−	0.998457i	$-0.482314\pi$
$107$	1.14891	0.111069	0.0555347	+	0.998457i	$0.482314\pi$
$108$	1.73851	0.167288
$109$	8.92809	0.855156	0.427578	−	0.903978i	$-0.359367\pi$
$109$	8.92809	0.855156	0.427578	+	0.903978i	$0.359367\pi$
$110$	−2.10268	−0.200482
$111$	1.19451	0.113378
$112$	11.0638	1.04543
$113$	−8.71949	−0.820260	−0.410130	−	0.912027i	$-0.634517\pi$
$113$	−8.71949	−0.820260	−0.410130	+	0.912027i	$0.634517\pi$
$114$	0.112467	0.0105335
$115$	−2.63513	−0.245727
$116$	−4.00855	−0.372184
$117$	7.26037	0.671221
$118$	27.2539	2.50892
$119$	8.98636	0.823778
$120$	−0.0535988	−0.00489287
$121$	−10.8645	−0.987680
$122$	−3.26248	−0.295371
$123$	0.186308	0.0167988
$124$	11.4045	1.02415
$125$	−4.93414	−0.441323
$126$	−15.8616	−1.41306
$127$	−2.33627	−0.207310	−0.103655	−	0.994613i	$-0.533054\pi$
$127$	−2.33627	−0.207310	−0.103655	+	0.994613i	$0.533054\pi$
$128$	−0.991843	−0.0876674
$129$	−0.837920	−0.0737747
$130$	13.9281	1.22157
$131$	−1.82810	−0.159722	−0.0798610	−	0.996806i	$-0.525448\pi$
$131$	−1.82810	−0.159722	−0.0798610	+	0.996806i	$0.525448\pi$
$132$	−0.107066	−0.00931893
$133$	−1.01364	−0.0878939
$134$	−11.4513	−0.989243
$135$	2.58289	0.222300
$136$	−0.415202	−0.0356032
$137$	−13.2541	−1.13238	−0.566188	−	0.824276i	$-0.691582\pi$
$137$	−13.2541	−1.13238	−0.566188	+	0.824276i	$0.691582\pi$
$138$	−0.272686	−0.0232125
$139$	11.3648	0.963953	0.481976	−	0.876184i	$-0.339919\pi$
$139$	11.3648	0.963953	0.481976	+	0.876184i	$0.339919\pi$
$140$	−14.9726	−1.26542
$141$	1.87163	0.157620
$142$	14.8379	1.24516
$143$	−0.897646	−0.0750649
$144$	12.2705	1.02254
$145$	−5.95548	−0.494576
$146$	20.6372	1.70795
$147$	−0.0311375	−0.00256818
$148$	−15.4174	−1.26730
$149$	6.54097	0.535857	0.267929	−	0.963439i	$-0.413661\pi$
$149$	6.54097	0.535857	0.267929	+	0.963439i	$0.413661\pi$
$150$	0.978771	0.0799164
$151$	10.4153	0.847586	0.423793	−	0.905759i	$-0.360698\pi$
$151$	10.4153	0.847586	0.423793	+	0.905759i	$0.360698\pi$
$152$	0.0468338	0.00379872
$153$	9.96645	0.805740
$154$	1.96107	0.158028
$155$	16.9436	1.36094
$156$	0.709204	0.0567818
$157$	9.34946	0.746168	0.373084	−	0.927797i	$-0.378300\pi$
$157$	9.34946	0.746168	0.373084	+	0.927797i	$0.378300\pi$
$158$	−1.27364	−0.101325
$159$	1.77097	0.140447
$160$	22.8252	1.80449
$161$	2.45766	0.193691
$162$	−17.4574	−1.37158
$163$	7.10285	0.556338	0.278169	−	0.960532i	$-0.410272\pi$
$163$	7.10285	0.556338	0.278169	+	0.960532i	$0.410272\pi$
$164$	−2.40464	−0.187771
$165$	−0.159068	−0.0123834
$166$	−31.1643	−2.41882
$167$	−10.3824	−0.803411	−0.401705	−	0.915769i	$-0.631582\pi$
$167$	−10.3824	−0.803411	−0.401705	+	0.915769i	$0.631582\pi$
$168$	0.0499891	0.00385675
$169$	−7.05402	−0.542617
$170$	19.1193	1.46639
$171$	−1.12419	−0.0859692
$172$	10.8149	0.824626
$173$	−4.93534	−0.375227	−0.187614	−	0.982243i	$-0.560075\pi$
$173$	−4.93534	−0.375227	−0.187614	+	0.982243i	$0.560075\pi$
$174$	−0.616279	−0.0467200
$175$	−8.82148	−0.666841
$176$	−1.51708	−0.114354
$177$	2.06176	0.154972
$178$	−9.47175	−0.709938
$179$	17.2958	1.29275	0.646375	−	0.763020i	$-0.276284\pi$
$179$	17.2958	1.29275	0.646375	+	0.763020i	$0.276284\pi$
$180$	−16.6056	−1.23771
$181$	17.2065	1.27895	0.639476	−	0.768811i	$-0.279152\pi$
$181$	17.2065	1.27895	0.639476	+	0.768811i	$0.279152\pi$
$182$	−12.9901	−0.962888
$183$	−0.246808	−0.0182446
$184$	−0.113553	−0.00837122
$185$	−22.9055	−1.68405
$186$	1.75334	0.128561
$187$	−1.23222	−0.0901086
$188$	−24.1568	−1.76182
$189$	−2.40895	−0.175225
$190$	−2.15662	−0.156458
$191$	−0.969679	−0.0701635	−0.0350817	−	0.999384i	$-0.511169\pi$
$191$	−0.969679	−0.0701635	−0.0350817	+	0.999384i	$0.511169\pi$
$192$	1.12470	0.0811684
$193$	7.21747	0.519525	0.259763	−	0.965673i	$-0.416356\pi$
$193$	7.21747	0.519525	0.259763	+	0.965673i	$0.416356\pi$
$194$	31.6794	2.27445
$195$	1.05366	0.0754543
$196$	0.401886	0.0287062
$197$	−7.29036	−0.519417	−0.259708	−	0.965687i	$-0.583626\pi$
$197$	−7.29036	−0.519417	−0.259708	+	0.965687i	$0.583626\pi$
$198$	2.17495	0.154567
$199$	−6.97295	−0.494299	−0.247150	−	0.968977i	$-0.579494\pi$
$199$	−6.97295	−0.494299	−0.247150	+	0.968977i	$0.579494\pi$
$200$	0.407583	0.0288205
$201$	−0.866295	−0.0611037
$202$	−26.6682	−1.87637
$203$	5.55441	0.389843
$204$	0.973539	0.0681613
$205$	−3.57256	−0.249519
$206$	−16.4975	−1.14944
$207$	2.72571	0.189450
$208$	10.0491	0.696778
$209$	0.138991	0.00961423
$210$	−2.30192	−0.158847
$211$	2.25378	0.155157	0.0775784	−	0.996986i	$-0.475281\pi$
$211$	2.25378	0.155157	0.0775784	+	0.996986i	$0.475281\pi$
$212$	−22.8576	−1.56987
$213$	1.12249	0.0769116
$214$	−2.27979	−0.155844
$215$	16.0676	1.09580
$216$	0.111302	0.00757314
$217$	−15.8025	−1.07275
$218$	−17.7161	−1.19989
$219$	1.56121	0.105497
$220$	2.05306	0.138417
$221$	8.16217	0.549047
$222$	−2.37029	−0.159083
$223$	−5.31003	−0.355586	−0.177793	−	0.984068i	$-0.556896\pi$
$223$	−5.31003	−0.355586	−0.177793	+	0.984068i	$0.556896\pi$
$224$	−21.2880	−1.42237
$225$	−9.78359	−0.652239
$226$	17.3022	1.15092
$227$	−2.18872	−0.145271	−0.0726354	−	0.997359i	$-0.523141\pi$
$227$	−2.18872	−0.145271	−0.0726354	+	0.997359i	$0.523141\pi$
$228$	−0.109813	−0.00727254
$229$	4.87556	0.322186	0.161093	−	0.986939i	$-0.448498\pi$
$229$	4.87556	0.322186	0.161093	+	0.986939i	$0.448498\pi$
$230$	5.22891	0.344784
$231$	0.148356	0.00976108
$232$	−0.256633	−0.0168488
$233$	−15.8464	−1.03813	−0.519066	−	0.854734i	$-0.673720\pi$
$233$	−15.8464	−1.03813	−0.519066	+	0.854734i	$0.673720\pi$
$234$	−14.4068	−0.941803
$235$	−35.8897	−2.34118
$236$	−26.6108	−1.73221
$237$	−0.0963509	−0.00625866
$238$	−17.8317	−1.15586
$239$	24.8660	1.60845	0.804223	−	0.594328i	$-0.202582\pi$
$239$	24.8660	1.60845	0.804223	+	0.594328i	$0.202582\pi$
$240$	1.78075	0.114947
$241$	17.9529	1.15645	0.578223	−	0.815879i	$-0.303746\pi$
$241$	17.9529	1.15645	0.578223	+	0.815879i	$0.303746\pi$
$242$	21.5585	1.38583
$243$	−4.01255	−0.257405
$244$	3.18550	0.203931
$245$	0.597081	0.0381461
$246$	−0.369693	−0.0235707
$247$	−0.920674	−0.0585811
$248$	0.730133	0.0463635
$249$	−2.35759	−0.149406
$250$	9.79086	0.619228
$251$	1.86475	0.117702	0.0588509	−	0.998267i	$-0.481256\pi$
$251$	1.86475	0.117702	0.0588509	+	0.998267i	$0.481256\pi$
$252$	15.4873	0.975609
$253$	−0.336997	−0.0211868
$254$	4.63588	0.290881
$255$	1.44638	0.0905760
$256$	16.9528	1.05955
$257$	2.57803	0.160813	0.0804066	−	0.996762i	$-0.474378\pi$
$257$	2.57803	0.160813	0.0804066	+	0.996762i	$0.474378\pi$
$258$	1.66269	0.103515
$259$	21.3630	1.32743
$260$	−13.5994	−0.843400
$261$	6.16019	0.381306
$262$	3.62752	0.224109
$263$	5.06765	0.312484	0.156242	−	0.987719i	$-0.450062\pi$
$263$	5.06765	0.312484	0.156242	+	0.987719i	$0.450062\pi$
$264$	−0.00685455	−0.000421868 0
$265$	−33.9594	−2.08611
$266$	2.01138	0.123326
$267$	−0.716541	−0.0438516
$268$	11.1811	0.682995
$269$	−10.2521	−0.625082	−0.312541	−	0.949904i	$-0.601180\pi$
$269$	−10.2521	−0.625082	−0.312541	+	0.949904i	$0.601180\pi$
$270$	−5.12526	−0.311914
$271$	−26.7152	−1.62283	−0.811415	−	0.584470i	$-0.801302\pi$
$271$	−26.7152	−1.62283	−0.811415	+	0.584470i	$0.801302\pi$
$272$	13.7946	0.836419
$273$	−0.982703	−0.0594759
$274$	26.3003	1.58886
$275$	1.20961	0.0729421
$276$	0.266251	0.0160265
$277$	9.61574	0.577754	0.288877	−	0.957366i	$-0.406718\pi$
$277$	9.61574	0.577754	0.288877	+	0.957366i	$0.406718\pi$
$278$	−22.5514	−1.35254
$279$	−17.5260	−1.04926
$280$	−0.958572	−0.0572856
$281$	22.9906	1.37150	0.685751	−	0.727837i	$-0.259474\pi$
$281$	22.9906	1.37150	0.685751	+	0.727837i	$0.259474\pi$
$282$	−3.71390	−0.221159
$283$	8.48049	0.504113	0.252056	−	0.967713i	$-0.418893\pi$
$283$	8.48049	0.504113	0.252056	+	0.967713i	$0.418893\pi$
$284$	−14.4877	−0.859689
$285$	−0.163149	−0.00966410
$286$	1.78121	0.105325
$287$	3.33197	0.196680
$288$	−23.6098	−1.39122
$289$	−5.79563	−0.340919
$290$	11.8175	0.693949
$291$	2.39656	0.140489
$292$	−20.1503	−1.17921
$293$	−11.3819	−0.664937	−0.332468	−	0.943114i	$-0.607881\pi$
$293$	−11.3819	−0.664937	−0.332468	+	0.943114i	$0.607881\pi$
$294$	0.0617865	0.00360346
$295$	−39.5355	−2.30185
$296$	−0.987044	−0.0573708
$297$	0.330317	0.0191669
$298$	−12.9793	−0.751872
$299$	2.23226	0.129095
$300$	−0.955676	−0.0551760
$301$	−14.9855	−0.863752
$302$	−20.6672	−1.18927
$303$	−2.01746	−0.115900
$304$	−1.55600	−0.0892426
$305$	4.73269	0.270993
$306$	−19.7765	−1.13055
$307$	−5.38784	−0.307500	−0.153750	−	0.988110i	$-0.549135\pi$
$307$	−5.38784	−0.307500	−0.153750	+	0.988110i	$0.549135\pi$
$308$	−1.91480	−0.109106
$309$	−1.24804	−0.0709987
$310$	−33.6214	−1.90957
$311$	−20.0317	−1.13589	−0.567947	−	0.823065i	$-0.692262\pi$
$311$	−20.0317	−1.13589	−0.567947	+	0.823065i	$0.692262\pi$
$312$	0.0454043	0.00257051
$313$	27.9448	1.57953	0.789766	−	0.613408i	$-0.210202\pi$
$313$	27.9448	1.57953	0.789766	+	0.613408i	$0.210202\pi$
$314$	−18.5522	−1.04696
$315$	23.0094	1.29644
$316$	1.24358	0.0699570
$317$	4.64368	0.260815	0.130408	−	0.991460i	$-0.458371\pi$
$317$	4.64368	0.260815	0.130408	+	0.991460i	$0.458371\pi$
$318$	−3.51416	−0.197064
$319$	−0.761625	−0.0426428
$320$	−21.5669	−1.20562
$321$	−0.172467	−0.00962618
$322$	−4.87677	−0.271772
$323$	−1.26383	−0.0703213
$324$	17.0454	0.946969
$325$	−8.01241	−0.444448
$326$	−14.0943	−0.780609
$327$	−1.34023	−0.0741148
$328$	−0.153949	−0.00850039
$329$	33.4727	1.84541
$330$	0.315640	0.0173754
$331$	6.20064	0.340818	0.170409	−	0.985373i	$-0.445491\pi$
$331$	6.20064	0.340818	0.170409	+	0.985373i	$0.445491\pi$
$332$	30.4289	1.67000
$333$	23.6929	1.29836
$334$	20.6018	1.12728
$335$	16.6117	0.907596
$336$	−1.66083	−0.0906057
$337$	−5.35112	−0.291494	−0.145747	−	0.989322i	$-0.546559\pi$
$337$	−5.35112	−0.291494	−0.145747	+	0.989322i	$0.546559\pi$
$338$	13.9974	0.761357
$339$	1.30891	0.0710905
$340$	−18.6682	−1.01242
$341$	2.16686	0.117342
$342$	2.23075	0.120625
$343$	18.2358	0.984640
$344$	0.692384	0.0373309
$345$	0.395569	0.0212967
$346$	9.79326	0.526489
$347$	−23.3962	−1.25597	−0.627987	−	0.778224i	$-0.716121\pi$
$347$	−23.3962	−1.25597	−0.627987	+	0.778224i	$0.716121\pi$
$348$	0.601738	0.0322565
$349$	15.4705	0.828119	0.414060	−	0.910250i	$-0.364111\pi$
$349$	15.4705	0.828119	0.414060	+	0.910250i	$0.364111\pi$
$350$	17.5046	0.935658
$351$	−2.18801	−0.116787
$352$	2.91903	0.155585
$353$	26.3066	1.40016	0.700079	−	0.714066i	$-0.253148\pi$
$353$	26.3066	1.40016	0.700079	+	0.714066i	$0.253148\pi$
$354$	−4.09118	−0.217444
$355$	−21.5244	−1.14240
$356$	9.24826	0.490157
$357$	−1.34898	−0.0713954
$358$	−34.3203	−1.81388
$359$	−36.8814	−1.94652	−0.973262	−	0.229698i	$-0.926226\pi$
$359$	−36.8814	−1.94652	−0.973262	+	0.229698i	$0.926226\pi$
$360$	−1.06312	−0.0560312
$361$	−18.8574	−0.992497
$362$	−34.1431	−1.79452
$363$	1.63091	0.0856005
$364$	12.6836	0.664799
$365$	−29.9372	−1.56698
$366$	0.489744	0.0255993
$367$	20.8701	1.08941	0.544706	−	0.838627i	$-0.316641\pi$
$367$	20.8701	1.08941	0.544706	+	0.838627i	$0.316641\pi$
$368$	3.77265	0.196663
$369$	3.69537	0.192373
$370$	45.4517	2.36292
$371$	31.6724	1.64435
$372$	−1.71197	−0.0887615
$373$	−18.4400	−0.954786	−0.477393	−	0.878690i	$-0.658418\pi$
$373$	−18.4400	−0.954786	−0.477393	+	0.878690i	$0.658418\pi$
$374$	2.44510	0.126433
$375$	0.740681	0.0382486
$376$	−1.54656	−0.0797575
$377$	5.04498	0.259830
$378$	4.78010	0.245862
$379$	13.2372	0.679947	0.339974	−	0.940435i	$-0.389582\pi$
$379$	13.2372	0.679947	0.339974	+	0.940435i	$0.389582\pi$
$380$	2.10573	0.108022
$381$	0.350706	0.0179672
$382$	1.92414	0.0984478
$383$	−3.10284	−0.158548	−0.0792738	−	0.996853i	$-0.525260\pi$
$383$	−3.10284	−0.158548	−0.0792738	+	0.996853i	$0.525260\pi$
$384$	0.148889	0.00759797
$385$	−2.84481	−0.144985
$386$	−14.3217	−0.728956
$387$	−16.6199	−0.844838
$388$	−30.9319	−1.57033
$389$	0.502131	0.0254591	0.0127295	−	0.999919i	$-0.495948\pi$
$389$	0.502131	0.0254591	0.0127295	+	0.999919i	$0.495948\pi$
$390$	−2.09079	−0.105871
$391$	3.06426	0.154966
$392$	0.0257294	0.00129953
$393$	0.274423	0.0138428
$394$	14.4663	0.728803
$395$	1.84759	0.0929622
$396$	−2.12363	−0.106717
$397$	−6.23481	−0.312916	−0.156458	−	0.987685i	$-0.550008\pi$
$397$	−6.23481	−0.312916	−0.156458	+	0.987685i	$0.550008\pi$
$398$	13.8365	0.693561
$399$	0.152161	0.00761760
$400$	−13.5415	−0.677074
$401$	−12.4398	−0.621216	−0.310608	−	0.950538i	$-0.600533\pi$
$401$	−12.4398	−0.621216	−0.310608	+	0.950538i	$0.600533\pi$
$402$	1.71900	0.0857359
$403$	−14.3532	−0.714983
$404$	26.0390	1.29549
$405$	25.3244	1.25838
$406$	−11.0217	−0.546996
$407$	−2.92931	−0.145200
$408$	0.0623274	0.00308567
$409$	20.4619	1.01178	0.505888	−	0.862599i	$-0.331165\pi$
$409$	20.4619	1.01178	0.505888	+	0.862599i	$0.331165\pi$
$410$	7.08908	0.350105
$411$	1.98962	0.0981409
$412$	16.1083	0.793597
$413$	36.8730	1.81440
$414$	−5.40865	−0.265821
$415$	45.2081	2.21918
$416$	−19.3356	−0.948004
$417$	−1.70602	−0.0835440
$418$	−0.275802	−0.0134899
$419$	28.1633	1.37587	0.687933	−	0.725774i	$-0.258518\pi$
$419$	28.1633	1.37587	0.687933	+	0.725774i	$0.258518\pi$
$420$	2.24760	0.109672
$421$	30.5281	1.48785	0.743924	−	0.668264i	$-0.232962\pi$
$421$	30.5281	1.48785	0.743924	+	0.668264i	$0.232962\pi$
$422$	−4.47220	−0.217703
$423$	37.1233	1.80500
$424$	−1.46338	−0.0710679
$425$	−10.9988	−0.533520
$426$	−2.22736	−0.107916
$427$	−4.41397	−0.213607
$428$	2.22600	0.107598
$429$	0.134749	0.00650574
$430$	−31.8831	−1.53754
$431$	25.7216	1.23897	0.619483	−	0.785010i	$-0.287342\pi$
$431$	25.7216	1.23897	0.619483	+	0.785010i	$0.287342\pi$
$432$	−3.69787	−0.177914
$433$	23.1151	1.11084	0.555420	−	0.831570i	$-0.312557\pi$
$433$	23.1151	1.11084	0.555420	+	0.831570i	$0.312557\pi$
$434$	31.3571	1.50519
$435$	0.893999	0.0428640
$436$	17.2981	0.828428
$437$	−0.345642	−0.0165343
$438$	−3.09793	−0.148025
$439$	−32.1881	−1.53626	−0.768128	−	0.640296i	$-0.778812\pi$
$439$	−32.1881	−1.53626	−0.768128	+	0.640296i	$0.778812\pi$
$440$	0.131440	0.00626616
$441$	−0.617605	−0.0294098
$442$	−16.1963	−0.770378
$443$	−3.71749	−0.176623	−0.0883117	−	0.996093i	$-0.528147\pi$
$443$	−3.71749	−0.176623	−0.0883117	+	0.996093i	$0.528147\pi$
$444$	2.31436	0.109835
$445$	13.7401	0.651343
$446$	10.5367	0.498929
$447$	−0.981889	−0.0464418
$448$	20.1144	0.950317
$449$	21.5153	1.01537	0.507686	−	0.861542i	$-0.330501\pi$
$449$	21.5153	1.01537	0.507686	+	0.861542i	$0.330501\pi$
$450$	19.4137	0.915170
$451$	−0.456882	−0.0215137
$452$	−16.8939	−0.794623
$453$	−1.56348	−0.0734588
$454$	4.34311	0.203832
$455$	18.8439	0.883416
$456$	−0.00703040	−0.000329228 0
$457$	−33.1622	−1.55126	−0.775630	−	0.631187i	$-0.782568\pi$
$457$	−33.1622	−1.55126	−0.775630	+	0.631187i	$0.782568\pi$
$458$	−9.67463	−0.452066
$459$	−3.00352	−0.140192
$460$	−5.10553	−0.238047
$461$	−24.3478	−1.13399	−0.566994	−	0.823722i	$-0.691894\pi$
$461$	−24.3478	−1.13399	−0.566994	+	0.823722i	$0.691894\pi$
$462$	−0.294383	−0.0136960
$463$	7.49196	0.348181	0.174090	−	0.984730i	$-0.444301\pi$
$463$	7.49196	0.348181	0.174090	+	0.984730i	$0.444301\pi$
$464$	8.52633	0.395825
$465$	−2.54347	−0.117950
$466$	31.4442	1.45662
$467$	−13.2796	−0.614504	−0.307252	−	0.951628i	$-0.599410\pi$
$467$	−13.2796	−0.614504	−0.307252	+	0.951628i	$0.599410\pi$
$468$	14.0669	0.650242
$469$	−15.4930	−0.715401
$470$	71.2163	3.28496
$471$	−1.40348	−0.0646690
$472$	−1.70366	−0.0784174
$473$	2.05483	0.0944811
$474$	0.191190	0.00878165
$475$	1.24064	0.0569244
$476$	17.4110	0.798031
$477$	35.1268	1.60834
$478$	−49.3418	−2.25684
$479$	12.1494	0.555122	0.277561	−	0.960708i	$-0.410474\pi$
$479$	12.1494	0.555122	0.277561	+	0.960708i	$0.410474\pi$
$480$	−3.42637	−0.156392
$481$	19.4036	0.884729
$482$	−35.6241	−1.62263
$483$	−0.368929	−0.0167869
$484$	−21.0498	−0.956810
$485$	−45.9554	−2.08673
$486$	7.96215	0.361171
$487$	−10.7245	−0.485974	−0.242987	−	0.970029i	$-0.578127\pi$
$487$	−10.7245	−0.485974	−0.242987	+	0.970029i	$0.578127\pi$
$488$	0.203941	0.00923196
$489$	−1.06623	−0.0482168
$490$	−1.18479	−0.0535235
$491$	−28.6725	−1.29397	−0.646985	−	0.762503i	$-0.723970\pi$
$491$	−28.6725	−1.29397	−0.646985	+	0.762503i	$0.723970\pi$
$492$	0.360969	0.0162738
$493$	6.92534	0.311902
$494$	1.82690	0.0821963
$495$	−3.15507	−0.141810
$496$	−24.2578	−1.08921
$497$	20.0748	0.900478
$498$	4.67818	0.209634
$499$	−10.6822	−0.478203	−0.239102	−	0.970995i	$-0.576853\pi$
$499$	−10.6822	−0.478203	−0.239102	+	0.970995i	$0.576853\pi$
$500$	−9.55984	−0.427529
$501$	1.55853	0.0696301
$502$	−3.70024	−0.165150
$503$	33.7672	1.50561	0.752803	−	0.658245i	$-0.228701\pi$
$503$	33.7672	1.50561	0.752803	+	0.658245i	$0.228701\pi$
$504$	0.991521	0.0441659
$505$	38.6860	1.72150
$506$	0.668706	0.0297276
$507$	1.05891	0.0470276
$508$	−4.52650	−0.200831
$509$	−16.5306	−0.732704	−0.366352	−	0.930476i	$-0.619393\pi$
$509$	−16.5306	−0.732704	−0.366352	+	0.930476i	$0.619393\pi$
$510$	−2.87007	−0.127089
$511$	27.9210	1.23515
$512$	−31.6560	−1.39901
$513$	0.338791	0.0149580
$514$	−5.11562	−0.225640
$515$	23.9320	1.05457
$516$	−1.62346	−0.0714688
$517$	−4.58980	−0.201859
$518$	−42.3908	−1.86254
$519$	0.740863	0.0325203
$520$	−0.870655	−0.0381808
$521$	−30.3577	−1.33000	−0.664999	−	0.746845i	$-0.731568\pi$
$521$	−30.3577	−1.33000	−0.664999	+	0.746845i	$0.731568\pi$
$522$	−12.2237	−0.535019
$523$	−16.6911	−0.729851	−0.364925	−	0.931037i	$-0.618905\pi$
$523$	−16.6911	−0.729851	−0.364925	+	0.931037i	$0.618905\pi$
$524$	−3.54193	−0.154730
$525$	1.32422	0.0577939
$526$	−10.0558	−0.438453
$527$	−19.7029	−0.858272
$528$	0.227734	0.00991086
$529$	−22.1620	−0.963563
$530$	67.3861	2.92706
$531$	40.8945	1.77467
$532$	−1.96392	−0.0851467
$533$	3.02637	0.131087
$534$	1.42184	0.0615290
$535$	3.30716	0.142981
$536$	0.715831	0.0309192
$537$	−2.59634	−0.112040
$538$	20.3434	0.877065
$539$	0.0763585	0.00328899
$540$	5.00433	0.215352
$541$	−36.1017	−1.55213	−0.776067	−	0.630650i	$-0.782788\pi$
$541$	−36.1017	−1.55213	−0.776067	+	0.630650i	$0.782788\pi$
$542$	53.0112	2.27702
$543$	−2.58294	−0.110844
$544$	−26.5423	−1.13799
$545$	25.6997	1.10085
$546$	1.94999	0.0834517
$547$	−1.00000	−0.0427569
$547$	−1.00000	−0.0427569
$548$	−25.6797	−1.09698
$549$	−4.89537	−0.208929
$550$	−2.40024	−0.102347
$551$	−0.781163	−0.0332787
$552$	0.0170458	0.000725518 0
$553$	−1.72316	−0.0732762
$554$	−19.0806	−0.810658
$555$	3.43844	0.145953
$556$	22.0192	0.933824
$557$	2.18856	0.0927321	0.0463661	−	0.998925i	$-0.485236\pi$
$557$	2.18856	0.0927321	0.0463661	+	0.998925i	$0.485236\pi$
$558$	34.7771	1.47223
$559$	−13.6111	−0.575689
$560$	31.8474	1.34580
$561$	0.184973	0.00780955
$562$	−45.6204	−1.92438
$563$	−23.1881	−0.977260	−0.488630	−	0.872491i	$-0.662503\pi$
$563$	−23.1881	−0.977260	−0.488630	+	0.872491i	$0.662503\pi$
$564$	3.62627	0.152693
$565$	−25.0992	−1.05593
$566$	−16.8279	−0.707331
$567$	−23.6189	−0.991900
$568$	−0.927527	−0.0389182
$569$	−7.55092	−0.316551	−0.158276	−	0.987395i	$-0.550593\pi$
$569$	−7.55092	−0.316551	−0.158276	+	0.987395i	$0.550593\pi$
$570$	0.323738	0.0135599
$571$	−2.22139	−0.0929621	−0.0464810	−	0.998919i	$-0.514801\pi$
$571$	−2.22139	−0.0929621	−0.0464810	+	0.998919i	$0.514801\pi$
$572$	−1.73918	−0.0727187
$573$	0.145562	0.00608094
$574$	−6.61166	−0.275965
$575$	−3.00804	−0.125444
$576$	22.3082	0.929508
$577$	23.8362	0.992314	0.496157	−	0.868233i	$-0.334744\pi$
$577$	23.8362	0.992314	0.496157	+	0.868233i	$0.334744\pi$
$578$	11.5003	0.478351
$579$	−1.08344	−0.0450263
$580$	−11.5387	−0.479118
$581$	−42.1636	−1.74924
$582$	−4.75551	−0.197122
$583$	−4.34295	−0.179866
$584$	−1.29005	−0.0533827
$585$	20.8991	0.864072
$586$	22.5852	0.932986
$587$	29.6166	1.22241	0.611204	−	0.791473i	$-0.290685\pi$
$587$	29.6166	1.22241	0.611204	+	0.791473i	$0.290685\pi$
$588$	−0.0603286	−0.00248791
$589$	2.22244	0.0915742
$590$	78.4508	3.22977
$591$	1.09438	0.0450169
$592$	32.7934	1.34780
$593$	−40.2054	−1.65104	−0.825520	−	0.564373i	$-0.809118\pi$
$593$	−40.2054	−1.65104	−0.825520	+	0.564373i	$0.809118\pi$
$594$	−0.655451	−0.0268935
$595$	25.8674	1.06046
$596$	12.6731	0.519109
$597$	1.04673	0.0428400
$598$	−4.42949	−0.181135
$599$	−24.9569	−1.01971	−0.509856	−	0.860259i	$-0.670301\pi$
$599$	−24.9569	−1.01971	−0.509856	+	0.860259i	$0.670301\pi$
$600$	−0.0611839	−0.00249782
$601$	−30.2445	−1.23370	−0.616850	−	0.787081i	$-0.711591\pi$
$601$	−30.2445	−1.23370	−0.616850	+	0.787081i	$0.711591\pi$
$602$	29.7360	1.21195
$603$	−17.1827	−0.699735
$604$	20.1796	0.821095
$605$	−31.2736	−1.27145
$606$	4.00326	0.162621
$607$	18.6504	0.756998	0.378499	−	0.925602i	$-0.376440\pi$
$607$	18.6504	0.756998	0.378499	+	0.925602i	$0.376440\pi$
$608$	2.99392	0.121419
$609$	−0.833793	−0.0337870
$610$	−9.39113	−0.380236
$611$	30.4027	1.22996
$612$	19.3099	0.780556
$613$	12.7148	0.513545	0.256773	−	0.966472i	$-0.417341\pi$
$613$	12.7148	0.513545	0.256773	+	0.966472i	$0.417341\pi$
$614$	10.6912	0.431460
$615$	0.536291	0.0216253
$616$	−0.122588	−0.00493922
$617$	−9.36487	−0.377016	−0.188508	−	0.982072i	$-0.560365\pi$
$617$	−9.36487	−0.377016	−0.188508	+	0.982072i	$0.560365\pi$
$618$	2.47651	0.0996197
$619$	4.28108	0.172071	0.0860355	−	0.996292i	$-0.472580\pi$
$619$	4.28108	0.172071	0.0860355	+	0.996292i	$0.472580\pi$
$620$	32.8281	1.31841
$621$	−0.821429	−0.0329628
$622$	39.7492	1.59380
$623$	−12.8148	−0.513413
$624$	−1.50850	−0.0603885
$625$	−30.6324	−1.22530
$626$	−55.4511	−2.21627
$627$	−0.0208645	−0.000833248 0
$628$	18.1145	0.722847
$629$	26.6358	1.06204
$630$	−45.6579	−1.81905
$631$	−39.5061	−1.57271	−0.786357	−	0.617772i	$-0.788035\pi$
$631$	−39.5061	−1.57271	−0.786357	+	0.617772i	$0.788035\pi$
$632$	0.0796161	0.00316696
$633$	−0.338324	−0.0134472
$634$	−9.21451	−0.365955
$635$	−6.72500	−0.266873
$636$	3.43124	0.136057
$637$	−0.505796	−0.0200404
$638$	1.51130	0.0598329
$639$	22.2643	0.880760
$640$	−2.85504	−0.112855
$641$	18.2383	0.720369	0.360184	−	0.932881i	$-0.382714\pi$
$641$	18.2383	0.720369	0.360184	+	0.932881i	$0.382714\pi$
$642$	0.342228	0.0135067
$643$	−36.2895	−1.43112	−0.715559	−	0.698552i	$-0.753828\pi$
$643$	−36.2895	−1.43112	−0.715559	+	0.698552i	$0.753828\pi$
$644$	4.76170	0.187637
$645$	−2.41197	−0.0949712
$646$	2.50783	0.0986692
$647$	−33.5029	−1.31714	−0.658568	−	0.752522i	$-0.728837\pi$
$647$	−33.5029	−1.31714	−0.658568	+	0.752522i	$0.728837\pi$
$648$	1.09128	0.0428694
$649$	−5.05606	−0.198468
$650$	15.8991	0.623614
$651$	2.37218	0.0929729
$652$	13.7617	0.538950
$653$	−15.9755	−0.625170	−0.312585	−	0.949890i	$-0.601195\pi$
$653$	−15.9755	−0.625170	−0.312585	+	0.949890i	$0.601195\pi$
$654$	2.65943	0.103992
$655$	−5.26223	−0.205612
$656$	5.11476	0.199698
$657$	30.9662	1.20811
$658$	−66.4202	−2.58933
$659$	40.3580	1.57213	0.786063	−	0.618147i	$-0.212116\pi$
$659$	40.3580	1.57213	0.786063	+	0.618147i	$0.212116\pi$
$660$	−0.308193	−0.0119964
$661$	−15.5296	−0.604032	−0.302016	−	0.953303i	$-0.597660\pi$
$661$	−15.5296	−0.604032	−0.302016	+	0.953303i	$0.597660\pi$
$662$	−12.3040	−0.478209
$663$	−1.22525	−0.0475849
$664$	1.94811	0.0756012
$665$	−2.91779	−0.113147
$666$	−47.0141	−1.82176
$667$	1.89400	0.0733360
$668$	−20.1157	−0.778300
$669$	0.797108	0.0308180
$670$	−32.9628	−1.27347
$671$	0.605246	0.0233653
$672$	3.19562	0.123274
$673$	−43.0979	−1.66130	−0.830652	−	0.556792i	$-0.812032\pi$
$673$	−43.0979	−1.66130	−0.830652	+	0.556792i	$0.812032\pi$
$674$	10.6183	0.409001
$675$	2.94842	0.113485
$676$	−13.6671	−0.525657
$677$	−23.0443	−0.885663	−0.442831	−	0.896605i	$-0.646026\pi$
$677$	−23.0443	−0.885663	−0.442831	+	0.896605i	$0.646026\pi$
$678$	−2.59729	−0.0997484
$679$	42.8605	1.64484
$680$	−1.19517	−0.0458325
$681$	0.328557	0.0125903
$682$	−4.29971	−0.164645
$683$	−45.7310	−1.74985	−0.874923	−	0.484261i	$-0.839088\pi$
$683$	−45.7310	−1.74985	−0.874923	+	0.484261i	$0.839088\pi$
$684$	−2.17811	−0.0832822
$685$	−38.1522	−1.45772
$686$	−36.1855	−1.38157
$687$	−0.731888	−0.0279233
$688$	−23.0036	−0.877006
$689$	28.7676	1.09596
$690$	−0.784931	−0.0298818
$691$	2.00105	0.0761236	0.0380618	−	0.999275i	$-0.487882\pi$
$691$	2.00105	0.0761236	0.0380618	+	0.999275i	$0.487882\pi$
$692$	−9.56218	−0.363499
$693$	2.94259	0.111780
$694$	46.4253	1.76228
$695$	32.7139	1.24091
$696$	0.0385242	0.00146025
$697$	4.15436	0.157358
$698$	−30.6984	−1.16195
$699$	2.37876	0.0899729
$700$	−17.0915	−0.645999
$701$	−36.9644	−1.39613	−0.698063	−	0.716036i	$-0.745954\pi$
$701$	−36.9644	−1.39613	−0.698063	+	0.716036i	$0.745954\pi$
$702$	4.34169	0.163867
$703$	−3.00445	−0.113315
$704$	−2.75811	−0.103950
$705$	5.38753	0.202906
$706$	−52.2004	−1.96459
$707$	−36.0806	−1.35695
$708$	3.99464	0.150128
$709$	−16.4717	−0.618609	−0.309305	−	0.950963i	$-0.600096\pi$
$709$	−16.4717	−0.618609	−0.309305	+	0.950963i	$0.600096\pi$
$710$	42.7111	1.60292
$711$	−1.91110	−0.0716717
$712$	0.592087	0.0221894
$713$	−5.38851	−0.201801
$714$	2.67679	0.100176
$715$	−2.58389	−0.0966321
$716$	33.5104	1.25234
$717$	−3.73272	−0.139401
$718$	73.1841	2.73121
$719$	1.45386	0.0542200	0.0271100	−	0.999632i	$-0.491370\pi$
$719$	1.45386	0.0542200	0.0271100	+	0.999632i	$0.491370\pi$
$720$	35.3208	1.31633
$721$	−22.3203	−0.831250
$722$	37.4190	1.39259
$723$	−2.69497	−0.100227
$724$	33.3375	1.23898
$725$	−6.79828	−0.252482
$726$	−3.23623	−0.120108
$727$	33.1204	1.22837	0.614184	−	0.789163i	$-0.289485\pi$
$727$	33.1204	1.22837	0.614184	+	0.789163i	$0.289485\pi$
$728$	0.812021	0.0300955
$729$	−25.7908	−0.955213
$730$	59.4046	2.19866
$731$	−18.6843	−0.691062
$732$	−0.478188	−0.0176743
$733$	5.43027	0.200572	0.100286	−	0.994959i	$-0.468024\pi$
$733$	5.43027	0.200572	0.100286	+	0.994959i	$0.468024\pi$
$734$	−41.4129	−1.52858
$735$	−0.0896300	−0.00330605
$736$	−7.25901	−0.267571
$737$	2.12441	0.0782537
$738$	−7.33276	−0.269922
$739$	−14.1862	−0.521847	−0.260924	−	0.965359i	$-0.584027\pi$
$739$	−14.1862	−0.521847	−0.260924	+	0.965359i	$0.584027\pi$
$740$	−44.3792	−1.63141
$741$	0.138206	0.00507712
$742$	−62.8479	−2.30722
$743$	−18.3288	−0.672417	−0.336209	−	0.941788i	$-0.609145\pi$
$743$	−18.3288	−0.672417	−0.336209	+	0.941788i	$0.609145\pi$
$744$	−0.109603	−0.00401824
$745$	18.8283	0.689816
$746$	36.5906	1.33968
$747$	−46.7621	−1.71094
$748$	−2.38741	−0.0872922
$749$	−3.08444	−0.112703
$750$	−1.46974	−0.0536674
$751$	−4.60177	−0.167921	−0.0839605	−	0.996469i	$-0.526757\pi$
$751$	−4.60177	−0.167921	−0.0839605	+	0.996469i	$0.526757\pi$
$752$	51.3825	1.87373
$753$	−0.279924	−0.0102010
$754$	−10.0108	−0.364572
$755$	29.9807	1.09111
$756$	−4.66731	−0.169748
$757$	31.7533	1.15409	0.577047	−	0.816711i	$-0.304205\pi$
$757$	31.7533	1.15409	0.577047	+	0.816711i	$0.304205\pi$
$758$	−26.2666	−0.954048
$759$	0.0505878	0.00183622
$760$	0.134812	0.00489015
$761$	10.3955	0.376837	0.188418	−	0.982089i	$-0.439664\pi$
$761$	10.3955	0.376837	0.188418	+	0.982089i	$0.439664\pi$
$762$	−0.695909	−0.0252101
$763$	−23.9689	−0.867734
$764$	−1.87874	−0.0679705
$765$	28.6886	1.03724
$766$	6.15699	0.222461
$767$	33.4912	1.20930
$768$	−2.54485	−0.0918293
$769$	31.1538	1.12344	0.561718	−	0.827329i	$-0.310141\pi$
$769$	31.1538	1.12344	0.561718	+	0.827329i	$0.310141\pi$
$770$	5.64498	0.203431
$771$	−0.386998	−0.0139374
$772$	13.9838	0.503287
$773$	3.74734	0.134782	0.0673912	−	0.997727i	$-0.478532\pi$
$773$	3.74734	0.134782	0.0673912	+	0.997727i	$0.478532\pi$
$774$	32.9791	1.18541
$775$	19.3414	0.694764
$776$	−1.98031	−0.0710889
$777$	−3.20687	−0.115046
$778$	−0.996384	−0.0357221
$779$	−0.468603	−0.0167894
$780$	2.04146	0.0730959
$781$	−2.75267	−0.0984984
$782$	−6.08045	−0.217436
$783$	−1.85646	−0.0663444
$784$	−0.854828	−0.0305296
$785$	26.9126	0.960552
$786$	−0.544541	−0.0194231
$787$	50.4938	1.79991	0.899955	−	0.435983i	$-0.143599\pi$
$787$	50.4938	1.79991	0.899955	+	0.435983i	$0.143599\pi$
$788$	−14.1250	−0.503182
$789$	−0.760723	−0.0270825
$790$	−3.66619	−0.130437
$791$	23.4089	0.832325
$792$	−0.135958	−0.00483106
$793$	−4.00913	−0.142368
$794$	12.3718	0.439059
$795$	5.09778	0.180799
$796$	−13.5100	−0.478850
$797$	−48.9797	−1.73495	−0.867475	−	0.497481i	$-0.834258\pi$
$797$	−48.9797	−1.73495	−0.867475	+	0.497481i	$0.834258\pi$
$798$	−0.301936	−0.0106884
$799$	41.7344	1.47646
$800$	26.0553	0.921195
$801$	−14.2124	−0.502171
$802$	24.6845	0.871641
$803$	−3.82855	−0.135107
$804$	−1.67844	−0.0591939
$805$	7.07444	0.249341
$806$	28.4812	1.00321
$807$	1.53898	0.0541747
$808$	1.66705	0.0586467
$809$	−24.6489	−0.866611	−0.433305	−	0.901247i	$-0.642653\pi$
$809$	−24.6489	−0.866611	−0.433305	+	0.901247i	$0.642653\pi$
$810$	−50.2514	−1.76565
$811$	31.9192	1.12083	0.560417	−	0.828210i	$-0.310641\pi$
$811$	31.9192	1.12083	0.560417	+	0.828210i	$0.310641\pi$
$812$	10.7616	0.377658
$813$	4.01031	0.140648
$814$	5.81265	0.203733
$815$	20.4457	0.716182
$816$	−2.07075	−0.0724909
$817$	2.10754	0.0737336
$818$	−40.6028	−1.41964
$819$	−19.4916	−0.681093
$820$	−6.92180	−0.241720
$821$	10.1931	0.355740	0.177870	−	0.984054i	$-0.443079\pi$
$821$	10.1931	0.355740	0.177870	+	0.984054i	$0.443079\pi$
$822$	−3.94803	−0.137703
$823$	34.6165	1.20666	0.603328	−	0.797493i	$-0.293841\pi$
$823$	34.6165	1.20666	0.603328	+	0.797493i	$0.293841\pi$
$824$	1.03128	0.0359262
$825$	−0.181579	−0.00632176
$826$	−73.1675	−2.54582
$827$	37.5580	1.30602	0.653010	−	0.757349i	$-0.273506\pi$
$827$	37.5580	1.30602	0.653010	+	0.757349i	$0.273506\pi$
$828$	5.28103	0.183528
$829$	24.0820	0.836401	0.418200	−	0.908355i	$-0.362661\pi$
$829$	24.0820	0.836401	0.418200	+	0.908355i	$0.362661\pi$
$830$	−89.7070	−3.11377
$831$	−1.44345	−0.0500729
$832$	18.2696	0.633385
$833$	−0.694317	−0.0240567
$834$	3.38527	0.117222
$835$	−29.8858	−1.03424
$836$	0.269294	0.00931373
$837$	5.28170	0.182562
$838$	−55.8847	−1.93051
$839$	−34.4662	−1.18991	−0.594953	−	0.803761i	$-0.702829\pi$
$839$	−34.4662	−1.18991	−0.594953	+	0.803761i	$0.702829\pi$
$840$	0.143895	0.00496484
$841$	−24.7195	−0.852396
$842$	−60.5772	−2.08763
$843$	−3.45120	−0.118866
$844$	4.36668	0.150307
$845$	−20.3051	−0.698518
$846$	−73.6642	−2.53263
$847$	29.1675	1.00221
$848$	48.6190	1.66958
$849$	−1.27304	−0.0436905
$850$	21.8250	0.748592
$851$	7.28457	0.249712
$852$	2.17481	0.0745077
$853$	8.14117	0.278748	0.139374	−	0.990240i	$-0.455491\pi$
$853$	8.14117	0.278748	0.139374	+	0.990240i	$0.455491\pi$
$854$	8.75868	0.299716
$855$	−3.23601	−0.110669
$856$	0.142512	0.00487096
$857$	57.4729	1.96324	0.981618	−	0.190854i	$-0.0611258\pi$
$857$	57.4729	1.96324	0.981618	+	0.190854i	$0.0611258\pi$
$858$	−0.267384	−0.00912833
$859$	38.5381	1.31490	0.657451	−	0.753497i	$-0.271635\pi$
$859$	38.5381	1.31490	0.657451	+	0.753497i	$0.271635\pi$
$860$	31.1308	1.06155
$861$	−0.500174	−0.0170459
$862$	−51.0397	−1.73842
$863$	41.0444	1.39717	0.698584	−	0.715529i	$-0.253814\pi$
$863$	41.0444	1.39717	0.698584	+	0.715529i	$0.253814\pi$
$864$	7.11513	0.242061
$865$	−14.2065	−0.483035
$866$	−45.8675	−1.55864
$867$	0.870003	0.0295469
$868$	−30.6172	−1.03922
$869$	0.236281	0.00801528
$870$	−1.77397	−0.0601433
$871$	−14.0720	−0.476813
$872$	1.10745	0.0375030
$873$	47.5351	1.60882
$874$	0.685861	0.0231996
$875$	13.2465	0.447814
$876$	3.02483	0.102200
$877$	9.31493	0.314543	0.157271	−	0.987555i	$-0.449730\pi$
$877$	9.31493	0.314543	0.157271	+	0.987555i	$0.449730\pi$
$878$	63.8713	2.15555
$879$	1.70858	0.0576288
$880$	−4.36694	−0.147210
$881$	−29.9630	−1.00948	−0.504739	−	0.863272i	$-0.668411\pi$
$881$	−29.9630	−1.00948	−0.504739	+	0.863272i	$0.668411\pi$
$882$	1.22552	0.0412654
$883$	−45.4522	−1.52959	−0.764794	−	0.644275i	$-0.777159\pi$
$883$	−45.4522	−1.52959	−0.764794	+	0.644275i	$0.777159\pi$
$884$	15.8141	0.531886
$885$	5.93483	0.199497
$886$	7.37666	0.247824
$887$	−31.0703	−1.04324	−0.521620	−	0.853178i	$-0.674672\pi$
$887$	−31.0703	−1.04324	−0.521620	+	0.853178i	$0.674672\pi$
$888$	0.148169	0.00497222
$889$	6.27210	0.210359
$890$	−27.2646	−0.913912
$891$	3.23864	0.108498
$892$	−10.2881	−0.344472
$893$	−4.70754	−0.157532
$894$	1.94837	0.0651633
$895$	49.7863	1.66417
$896$	2.66277	0.0889568
$897$	−0.335092	−0.0111884
$898$	−42.6931	−1.42469
$899$	−12.1782	−0.406167
$900$	−18.9556	−0.631853
$901$	39.4898	1.31560
$902$	0.906596	0.0301863
$903$	2.24953	0.0748598
$904$	−1.08157	−0.0359726
$905$	49.5293	1.64641
$906$	3.10243	0.103071
$907$	27.4635	0.911910	0.455955	−	0.890003i	$-0.349298\pi$
$907$	27.4635	0.911910	0.455955	+	0.890003i	$0.349298\pi$
$908$	−4.24063	−0.140730
$909$	−40.0158	−1.32724
$910$	−37.3922	−1.23954
$911$	−8.25357	−0.273453	−0.136727	−	0.990609i	$-0.543658\pi$
$911$	−8.25357	−0.273453	−0.136727	+	0.990609i	$0.543658\pi$
$912$	0.233577	0.00773449
$913$	5.78150	0.191340
$914$	65.8040	2.17660
$915$	−0.710442	−0.0234865
$916$	9.44635	0.312116
$917$	4.90784	0.162071
$918$	5.95992	0.196707
$919$	−40.7751	−1.34505	−0.672524	−	0.740075i	$-0.734790\pi$
$919$	−40.7751	−1.34505	−0.672524	+	0.740075i	$0.734790\pi$
$920$	−0.326864	−0.0107764
$921$	0.808789	0.0266505
$922$	48.3135	1.59112
$923$	18.2336	0.600167
$924$	0.287437	0.00945599
$925$	−26.1470	−0.859710
$926$	−14.8664	−0.488539
$927$	−24.7546	−0.813048
$928$	−16.4056	−0.538541
$929$	−49.6880	−1.63021	−0.815104	−	0.579314i	$-0.803321\pi$
$929$	−49.6880	−1.63021	−0.815104	+	0.579314i	$0.803321\pi$
$930$	5.04703	0.165499
$931$	0.0783174	0.00256675
$932$	−30.7022	−1.00568
$933$	3.00704	0.0984459
$934$	26.3508	0.862223
$935$	−3.54696	−0.115998
$936$	0.900583	0.0294365
$937$	−11.8945	−0.388575	−0.194288	−	0.980945i	$-0.562239\pi$
$937$	−11.8945	−0.388575	−0.194288	+	0.980945i	$0.562239\pi$
$938$	30.7429	1.00379
$939$	−4.19489	−0.136895
$940$	−69.5358	−2.26801
$941$	−23.3867	−0.762386	−0.381193	−	0.924496i	$-0.624487\pi$
$941$	−23.3867	−0.762386	−0.381193	+	0.924496i	$0.624487\pi$
$942$	2.78494	0.0907384
$943$	1.13617	0.0369988
$944$	56.6022	1.84224
$945$	−6.93421	−0.225570
$946$	−4.07742	−0.132568
$947$	3.24137	0.105330	0.0526651	−	0.998612i	$-0.483228\pi$
$947$	3.24137	0.105330	0.0526651	+	0.998612i	$0.483228\pi$
$948$	−0.186679	−0.00606305
$949$	25.3602	0.823228
$950$	−2.46181	−0.0798718
$951$	−0.697080	−0.0226044
$952$	1.11468	0.0361269
$953$	55.4588	1.79649	0.898244	−	0.439498i	$-0.144844\pi$
$953$	55.4588	1.79649	0.898244	+	0.439498i	$0.144844\pi$
$954$	−69.7024	−2.25670
$955$	−2.79124	−0.0903224
$956$	48.1775	1.55817
$957$	0.114330	0.00369577
$958$	−24.1082	−0.778902
$959$	35.5829	1.14903
$960$	3.23748	0.104489
$961$	3.64761	0.117665
$962$	−38.5028	−1.24138
$963$	−3.42084	−0.110235
$964$	34.7835	1.12030
$965$	20.7756	0.668792
$966$	0.732070	0.0235540
$967$	−19.5302	−0.628048	−0.314024	−	0.949415i	$-0.601677\pi$
$967$	−19.5302	−0.628048	−0.314024	+	0.949415i	$0.601677\pi$
$968$	−1.34764	−0.0433148
$969$	0.189718	0.00609462
$970$	91.1898	2.92793
$971$	−14.9189	−0.478770	−0.239385	−	0.970925i	$-0.576946\pi$
$971$	−14.9189	−0.478770	−0.239385	+	0.970925i	$0.576946\pi$
$972$	−7.77428	−0.249360
$973$	−30.5108	−0.978130
$974$	21.2808	0.681880
$975$	1.20277	0.0385195
$976$	−6.77569	−0.216885
$977$	−38.6671	−1.23707	−0.618536	−	0.785757i	$-0.712274\pi$
$977$	−38.6671	−1.23707	−0.618536	+	0.785757i	$0.712274\pi$
$978$	2.11574	0.0676540
$979$	1.75717	0.0561594
$980$	1.15684	0.0369538
$981$	−26.5831	−0.848733
$982$	56.8951	1.81559
$983$	−43.8743	−1.39937	−0.699687	−	0.714449i	$-0.746677\pi$
$983$	−43.8743	−1.39937	−0.699687	+	0.714449i	$0.746677\pi$
$984$	0.0231098	0.000736714 0
$985$	−20.9854	−0.668652
$986$	−13.7420	−0.437636
$987$	−5.02470	−0.159938
$988$	−1.78380	−0.0567501
$989$	−5.10992	−0.162486
$990$	6.26064	0.198976
$991$	7.55457	0.239979	0.119989	−	0.992775i	$-0.461714\pi$
$991$	7.55457	0.239979	0.119989	+	0.992775i	$0.461714\pi$
$992$	46.6747	1.48192
$993$	−0.930801	−0.0295381
$994$	−39.8347	−1.26348
$995$	−20.0718	−0.636318
$996$	−4.56780	−0.144736
$997$	−0.872251	−0.0276245	−0.0138122	−	0.999905i	$-0.504397\pi$
$997$	−0.872251	−0.0276245	−0.0138122	+	0.999905i	$0.504397\pi$
$998$	21.1969	0.670976
$999$	−7.14017	−0.225905

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.a.b.1.4	✓	18
3.2	odd	2		4923.2.a.l.1.15		18
4.3	odd	2		8752.2.a.s.1.8		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.a.b.1.4	✓	18	1.1	even	1	trivial
4923.2.a.l.1.15		18	3.2	odd	2
8752.2.a.s.1.8		18	4.3	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:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	547.a (trivial)

\(f(q)\)	\(=\)	\(q-1.98431 q^{2} -0.150114 q^{3} +1.93749 q^{4} +2.87852 q^{5} +0.297872 q^{6} -2.68467 q^{7} +0.124041 q^{8} -2.97747 q^{9} +O(q^{10})\)	\(q-1.98431 q^{2} -0.150114 q^{3} +1.93749 q^{4} +2.87852 q^{5} +0.297872 q^{6} -2.68467 q^{7} +0.124041 q^{8} -2.97747 q^{9} -5.71188 q^{10} +0.368123 q^{11} -0.290844 q^{12} -2.43844 q^{13} +5.32721 q^{14} -0.432105 q^{15} -4.12111 q^{16} -3.34729 q^{17} +5.90822 q^{18} +0.377567 q^{19} +5.57710 q^{20} +0.403005 q^{21} -0.730471 q^{22} -0.915445 q^{23} -0.0186202 q^{24} +3.28588 q^{25} +4.83862 q^{26} +0.897299 q^{27} -5.20151 q^{28} -2.06894 q^{29} +0.857431 q^{30} +5.88622 q^{31} +7.92949 q^{32} -0.0552603 q^{33} +6.64207 q^{34} -7.72786 q^{35} -5.76881 q^{36} -7.95740 q^{37} -0.749211 q^{38} +0.366043 q^{39} +0.357054 q^{40} -1.24111 q^{41} -0.799687 q^{42} +5.58190 q^{43} +0.713235 q^{44} -8.57070 q^{45} +1.81653 q^{46} -12.4681 q^{47} +0.618636 q^{48} +0.207426 q^{49} -6.52020 q^{50} +0.502474 q^{51} -4.72445 q^{52} -11.7975 q^{53} -1.78052 q^{54} +1.05965 q^{55} -0.333009 q^{56} -0.0566780 q^{57} +4.10542 q^{58} -13.7347 q^{59} -0.837199 q^{60} +1.64414 q^{61} -11.6801 q^{62} +7.99350 q^{63} -7.49234 q^{64} -7.01909 q^{65} +0.109654 q^{66} +5.77093 q^{67} -6.48534 q^{68} +0.137421 q^{69} +15.3345 q^{70} -7.47759 q^{71} -0.369328 q^{72} -10.4002 q^{73} +15.7900 q^{74} -0.493255 q^{75} +0.731532 q^{76} -0.988288 q^{77} -0.726343 q^{78} +0.641853 q^{79} -11.8627 q^{80} +8.79770 q^{81} +2.46275 q^{82} +15.7053 q^{83} +0.780818 q^{84} -9.63525 q^{85} -11.0762 q^{86} +0.310576 q^{87} +0.0456624 q^{88} +4.77332 q^{89} +17.0069 q^{90} +6.54639 q^{91} -1.77367 q^{92} -0.883602 q^{93} +24.7406 q^{94} +1.08683 q^{95} -1.19032 q^{96} -15.9649 q^{97} -0.411598 q^{98} -1.09607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 4 q^{2} - 10 q^{3} + 16 q^{4} - 27 q^{5} - 3 q^{6} - 11 q^{7} - 12 q^{8} + 14 q^{9}+O(q^{10}) \) 18 * q - 4 * q^2 - 10 * q^3 + 16 * q^4 - 27 * q^5 - 3 * q^6 - 11 * q^7 - 12 * q^8 + 14 * q^9	\( 18 q - 4 q^{2} - 10 q^{3} + 16 q^{4} - 27 q^{5} - 3 q^{6} - 11 q^{7} - 12 q^{8} + 14 q^{9} - 5 q^{10} + 2 q^{11} - 32 q^{12} - 25 q^{13} - 7 q^{14} + 9 q^{15} + 8 q^{16} - 30 q^{17} - 10 q^{18} + 4 q^{19} - 41 q^{20} - 16 q^{21} - 24 q^{22} - 26 q^{23} - 12 q^{24} + 31 q^{25} - 18 q^{26} - 37 q^{27} - 16 q^{28} - 18 q^{29} + 8 q^{30} - 5 q^{31} - 28 q^{32} - 10 q^{33} + 5 q^{34} - 9 q^{35} + 31 q^{36} - 18 q^{37} - 45 q^{38} + 7 q^{39} + 7 q^{40} - 17 q^{41} + 4 q^{42} + 8 q^{43} + 12 q^{44} - 44 q^{45} + 30 q^{46} - 52 q^{47} - 7 q^{48} + 29 q^{49} + 13 q^{50} + 19 q^{51} - 14 q^{52} - 60 q^{53} + 11 q^{54} + 11 q^{55} + 7 q^{56} + 4 q^{57} + 14 q^{58} - 8 q^{59} + 86 q^{60} - 26 q^{61} + 4 q^{62} - q^{63} + 44 q^{64} - 6 q^{65} + 18 q^{66} + 12 q^{67} - 61 q^{68} - 38 q^{69} + 35 q^{70} - q^{71} + 28 q^{72} - 2 q^{73} + 16 q^{74} - 17 q^{75} + 66 q^{76} - 73 q^{77} + 115 q^{78} + 18 q^{79} - 32 q^{80} + 18 q^{81} + 44 q^{82} - 43 q^{83} + 41 q^{84} + 51 q^{85} + 4 q^{86} + 3 q^{87} - 17 q^{88} - 28 q^{89} + 58 q^{90} - q^{91} - 68 q^{92} - 60 q^{93} + 78 q^{94} - 18 q^{95} + 29 q^{96} - 34 q^{97} + 34 q^{98} + 15 q^{99}+O(q^{100}) \) 18 * q - 4 * q^2 - 10 * q^3 + 16 * q^4 - 27 * q^5 - 3 * q^6 - 11 * q^7 - 12 * q^8 + 14 * q^9 - 5 * q^10 + 2 * q^11 - 32 * q^12 - 25 * q^13 - 7 * q^14 + 9 * q^15 + 8 * q^16 - 30 * q^17 - 10 * q^18 + 4 * q^19 - 41 * q^20 - 16 * q^21 - 24 * q^22 - 26 * q^23 - 12 * q^24 + 31 * q^25 - 18 * q^26 - 37 * q^27 - 16 * q^28 - 18 * q^29 + 8 * q^30 - 5 * q^31 - 28 * q^32 - 10 * q^33 + 5 * q^34 - 9 * q^35 + 31 * q^36 - 18 * q^37 - 45 * q^38 + 7 * q^39 + 7 * q^40 - 17 * q^41 + 4 * q^42 + 8 * q^43 + 12 * q^44 - 44 * q^45 + 30 * q^46 - 52 * q^47 - 7 * q^48 + 29 * q^49 + 13 * q^50 + 19 * q^51 - 14 * q^52 - 60 * q^53 + 11 * q^54 + 11 * q^55 + 7 * q^56 + 4 * q^57 + 14 * q^58 - 8 * q^59 + 86 * q^60 - 26 * q^61 + 4 * q^62 - q^63 + 44 * q^64 - 6 * q^65 + 18 * q^66 + 12 * q^67 - 61 * q^68 - 38 * q^69 + 35 * q^70 - q^71 + 28 * q^72 - 2 * q^73 + 16 * q^74 - 17 * q^75 + 66 * q^76 - 73 * q^77 + 115 * q^78 + 18 * q^79 - 32 * q^80 + 18 * q^81 + 44 * q^82 - 43 * q^83 + 41 * q^84 + 51 * q^85 + 4 * q^86 + 3 * q^87 - 17 * q^88 - 28 * q^89 + 58 * q^90 - q^91 - 68 * q^92 - 60 * q^93 + 78 * q^94 - 18 * q^95 + 29 * q^96 - 34 * q^97 + 34 * q^98 + 15 * q^99

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