LMFDB - Embedded newform 4010.2.a.l.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4010,2,Mod(1,4010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4010, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4010 = 2 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4010.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.0200112105$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 3 x^{16} - 24 x^{15} + 70 x^{14} + 228 x^{13} - 638 x^{12} - 1075 x^{11} + 2854 x^{10} + \cdots - 2 $ x^17 - 3x^16 - 24x^15 + 70x^14 + 228x^13 - 638x^12 - 1075x^11 + 2854x^10 + 2544x^9 - 6415x^8 - 2573x^7 + 6456x^6 + 485x^5 - 1839x^4 + 67x^3 + 136x^2 - 8x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-1.70497$ of defining polynomial
Character	$\chi$	$=$	4010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.70497 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.70497 q^{6} -1.19610 q^{7} -1.00000 q^{8} -0.0930693 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.70497 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.70497 q^{6} -1.19610 q^{7} -1.00000 q^{8} -0.0930693 q^{9} +1.00000 q^{10} +5.50058 q^{11} -1.70497 q^{12} +5.99913 q^{13} +1.19610 q^{14} +1.70497 q^{15} +1.00000 q^{16} +4.84950 q^{17} +0.0930693 q^{18} +3.12006 q^{19} -1.00000 q^{20} +2.03931 q^{21} -5.50058 q^{22} +9.08141 q^{23} +1.70497 q^{24} +1.00000 q^{25} -5.99913 q^{26} +5.27360 q^{27} -1.19610 q^{28} +1.39561 q^{29} -1.70497 q^{30} -4.58360 q^{31} -1.00000 q^{32} -9.37834 q^{33} -4.84950 q^{34} +1.19610 q^{35} -0.0930693 q^{36} +7.24320 q^{37} -3.12006 q^{38} -10.2284 q^{39} +1.00000 q^{40} +1.08632 q^{41} -2.03931 q^{42} -4.46017 q^{43} +5.50058 q^{44} +0.0930693 q^{45} -9.08141 q^{46} -7.23466 q^{47} -1.70497 q^{48} -5.56935 q^{49} -1.00000 q^{50} -8.26826 q^{51} +5.99913 q^{52} -4.39298 q^{53} -5.27360 q^{54} -5.50058 q^{55} +1.19610 q^{56} -5.31962 q^{57} -1.39561 q^{58} -8.40462 q^{59} +1.70497 q^{60} -12.4754 q^{61} +4.58360 q^{62} +0.111320 q^{63} +1.00000 q^{64} -5.99913 q^{65} +9.37834 q^{66} +13.8349 q^{67} +4.84950 q^{68} -15.4836 q^{69} -1.19610 q^{70} +15.7136 q^{71} +0.0930693 q^{72} +16.9793 q^{73} -7.24320 q^{74} -1.70497 q^{75} +3.12006 q^{76} -6.57923 q^{77} +10.2284 q^{78} +6.62664 q^{79} -1.00000 q^{80} -8.71213 q^{81} -1.08632 q^{82} -9.63816 q^{83} +2.03931 q^{84} -4.84950 q^{85} +4.46017 q^{86} -2.37948 q^{87} -5.50058 q^{88} -0.103318 q^{89} -0.0930693 q^{90} -7.17555 q^{91} +9.08141 q^{92} +7.81490 q^{93} +7.23466 q^{94} -3.12006 q^{95} +1.70497 q^{96} +9.42084 q^{97} +5.56935 q^{98} -0.511935 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9}+O(q^{10}) $ 17 * q - 17 * q^2 + 3 * q^3 + 17 * q^4 - 17 * q^5 - 3 * q^6 + 4 * q^7 - 17 * q^8 + 6 * q^9	\( 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9} + 17 q^{10} - 8 q^{11} + 3 q^{12} + 14 q^{13} - 4 q^{14} - 3 q^{15} + 17 q^{16} - 8 q^{17} - 6 q^{18} + 7 q^{19} - 17 q^{20} - 11 q^{21} + 8 q^{22} + q^{23} - 3 q^{24} + 17 q^{25} - 14 q^{26} + 15 q^{27} + 4 q^{28} - 18 q^{29} + 3 q^{30} + 8 q^{31} - 17 q^{32} + 3 q^{33} + 8 q^{34} - 4 q^{35} + 6 q^{36} + 49 q^{37} - 7 q^{38} - 12 q^{39} + 17 q^{40} - 23 q^{41} + 11 q^{42} + 35 q^{43} - 8 q^{44} - 6 q^{45} - q^{46} + 11 q^{47} + 3 q^{48} + 27 q^{49} - 17 q^{50} - 16 q^{51} + 14 q^{52} - 3 q^{53} - 15 q^{54} + 8 q^{55} - 4 q^{56} + 9 q^{57} + 18 q^{58} - 6 q^{59} - 3 q^{60} + 6 q^{61} - 8 q^{62} + 10 q^{63} + 17 q^{64} - 14 q^{65} - 3 q^{66} + 55 q^{67} - 8 q^{68} - q^{69} + 4 q^{70} + 5 q^{71} - 6 q^{72} + 62 q^{73} - 49 q^{74} + 3 q^{75} + 7 q^{76} + 2 q^{77} + 12 q^{78} - 3 q^{79} - 17 q^{80} - 15 q^{81} + 23 q^{82} + 7 q^{83} - 11 q^{84} + 8 q^{85} - 35 q^{86} + 10 q^{87} + 8 q^{88} - 18 q^{89} + 6 q^{90} + 18 q^{91} + q^{92} + 33 q^{93} - 11 q^{94} - 7 q^{95} - 3 q^{96} + 63 q^{97} - 27 q^{98} - 11 q^{99}+O(q^{100}) \) 17 * q - 17 * q^2 + 3 * q^3 + 17 * q^4 - 17 * q^5 - 3 * q^6 + 4 * q^7 - 17 * q^8 + 6 * q^9 + 17 * q^10 - 8 * q^11 + 3 * q^12 + 14 * q^13 - 4 * q^14 - 3 * q^15 + 17 * q^16 - 8 * q^17 - 6 * q^18 + 7 * q^19 - 17 * q^20 - 11 * q^21 + 8 * q^22 + q^23 - 3 * q^24 + 17 * q^25 - 14 * q^26 + 15 * q^27 + 4 * q^28 - 18 * q^29 + 3 * q^30 + 8 * q^31 - 17 * q^32 + 3 * q^33 + 8 * q^34 - 4 * q^35 + 6 * q^36 + 49 * q^37 - 7 * q^38 - 12 * q^39 + 17 * q^40 - 23 * q^41 + 11 * q^42 + 35 * q^43 - 8 * q^44 - 6 * q^45 - q^46 + 11 * q^47 + 3 * q^48 + 27 * q^49 - 17 * q^50 - 16 * q^51 + 14 * q^52 - 3 * q^53 - 15 * q^54 + 8 * q^55 - 4 * q^56 + 9 * q^57 + 18 * q^58 - 6 * q^59 - 3 * q^60 + 6 * q^61 - 8 * q^62 + 10 * q^63 + 17 * q^64 - 14 * q^65 - 3 * q^66 + 55 * q^67 - 8 * q^68 - q^69 + 4 * q^70 + 5 * q^71 - 6 * q^72 + 62 * q^73 - 49 * q^74 + 3 * q^75 + 7 * q^76 + 2 * q^77 + 12 * q^78 - 3 * q^79 - 17 * q^80 - 15 * q^81 + 23 * q^82 + 7 * q^83 - 11 * q^84 + 8 * q^85 - 35 * q^86 + 10 * q^87 + 8 * q^88 - 18 * q^89 + 6 * q^90 + 18 * q^91 + q^92 + 33 * q^93 - 11 * q^94 - 7 * q^95 - 3 * q^96 + 63 * q^97 - 27 * q^98 - 11 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.70497	−0.984366	−0.492183	−	0.870492i	$-0.663801\pi$
$3$	−1.70497	−0.984366	−0.492183	+	0.870492i	$0.663801\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.70497	0.696052
$7$	−1.19610	−0.452082	−0.226041	−	0.974118i	$-0.572578\pi$
$7$	−1.19610	−0.452082	−0.226041	+	0.974118i	$0.572578\pi$
$8$	−1.00000	−0.353553
$9$	−0.0930693	−0.0310231
$10$	1.00000	0.316228
$11$	5.50058	1.65849	0.829244	−	0.558887i	$-0.188771\pi$
$11$	5.50058	1.65849	0.829244	+	0.558887i	$0.188771\pi$
$12$	−1.70497	−0.492183
$13$	5.99913	1.66386	0.831930	−	0.554881i	$-0.187236\pi$
$13$	5.99913	1.66386	0.831930	+	0.554881i	$0.187236\pi$
$14$	1.19610	0.319670
$15$	1.70497	0.440222
$16$	1.00000	0.250000
$17$	4.84950	1.17618	0.588088	−	0.808797i	$-0.299881\pi$
$17$	4.84950	1.17618	0.588088	+	0.808797i	$0.299881\pi$
$18$	0.0930693	0.0219367
$19$	3.12006	0.715791	0.357896	−	0.933762i	$-0.383494\pi$
$19$	3.12006	0.715791	0.357896	+	0.933762i	$0.383494\pi$
$20$	−1.00000	−0.223607
$21$	2.03931	0.445015
$22$	−5.50058	−1.17273
$23$	9.08141	1.89361	0.946803	−	0.321814i	$-0.104293\pi$
$23$	9.08141	1.89361	0.946803	+	0.321814i	$0.104293\pi$
$24$	1.70497	0.348026
$25$	1.00000	0.200000
$26$	−5.99913	−1.17653
$27$	5.27360	1.01490
$28$	−1.19610	−0.226041
$29$	1.39561	0.259159	0.129579	−	0.991569i	$-0.458637\pi$
$29$	1.39561	0.259159	0.129579	+	0.991569i	$0.458637\pi$
$30$	−1.70497	−0.311284
$31$	−4.58360	−0.823238	−0.411619	−	0.911356i	$-0.635037\pi$
$31$	−4.58360	−0.823238	−0.411619	+	0.911356i	$0.635037\pi$
$32$	−1.00000	−0.176777
$33$	−9.37834	−1.63256
$34$	−4.84950	−0.831682
$35$	1.19610	0.202177
$36$	−0.0930693	−0.0155116
$37$	7.24320	1.19077	0.595387	−	0.803439i	$-0.296999\pi$
$37$	7.24320	1.19077	0.595387	+	0.803439i	$0.296999\pi$
$38$	−3.12006	−0.506141
$39$	−10.2284	−1.63785
$40$	1.00000	0.158114
$41$	1.08632	0.169654	0.0848272	−	0.996396i	$-0.472966\pi$
$41$	1.08632	0.169654	0.0848272	+	0.996396i	$0.472966\pi$
$42$	−2.03931	−0.314673
$43$	−4.46017	−0.680169	−0.340085	−	0.940395i	$-0.610456\pi$
$43$	−4.46017	−0.680169	−0.340085	+	0.940395i	$0.610456\pi$
$44$	5.50058	0.829244
$45$	0.0930693	0.0138740
$46$	−9.08141	−1.33898
$47$	−7.23466	−1.05528	−0.527642	−	0.849467i	$-0.676924\pi$
$47$	−7.23466	−1.05528	−0.527642	+	0.849467i	$0.676924\pi$
$48$	−1.70497	−0.246092
$49$	−5.56935	−0.795622
$50$	−1.00000	−0.141421
$51$	−8.26826	−1.15779
$52$	5.99913	0.831930
$53$	−4.39298	−0.603422	−0.301711	−	0.953400i	$-0.597558\pi$
$53$	−4.39298	−0.603422	−0.301711	+	0.953400i	$0.597558\pi$
$54$	−5.27360	−0.717646
$55$	−5.50058	−0.741698
$56$	1.19610	0.159835
$57$	−5.31962	−0.704601
$58$	−1.39561	−0.183253
$59$	−8.40462	−1.09419	−0.547094	−	0.837071i	$-0.684266\pi$
$59$	−8.40462	−1.09419	−0.547094	+	0.837071i	$0.684266\pi$
$60$	1.70497	0.220111
$61$	−12.4754	−1.59731	−0.798657	−	0.601786i	$-0.794456\pi$
$61$	−12.4754	−1.59731	−0.798657	+	0.601786i	$0.794456\pi$
$62$	4.58360	0.582117
$63$	0.111320	0.0140250
$64$	1.00000	0.125000
$65$	−5.99913	−0.744101
$66$	9.37834	1.15439
$67$	13.8349	1.69020	0.845098	−	0.534611i	$-0.179542\pi$
$67$	13.8349	1.69020	0.845098	+	0.534611i	$0.179542\pi$
$68$	4.84950	0.588088
$69$	−15.4836	−1.86400
$70$	−1.19610	−0.142961
$71$	15.7136	1.86486	0.932428	−	0.361355i	$-0.117686\pi$
$71$	15.7136	1.86486	0.932428	+	0.361355i	$0.117686\pi$
$72$	0.0930693	0.0109683
$73$	16.9793	1.98727	0.993636	−	0.112635i	$-0.0359290\pi$
$73$	16.9793	1.98727	0.993636	+	0.112635i	$0.0359290\pi$
$74$	−7.24320	−0.842005
$75$	−1.70497	−0.196873
$76$	3.12006	0.357896
$77$	−6.57923	−0.749773
$78$	10.2284	1.15813
$79$	6.62664	0.745555	0.372778	−	0.927921i	$-0.378405\pi$
$79$	6.62664	0.745555	0.372778	+	0.927921i	$0.378405\pi$
$80$	−1.00000	−0.111803
$81$	−8.71213	−0.968014
$82$	−1.08632	−0.119964
$83$	−9.63816	−1.05793	−0.528963	−	0.848645i	$-0.677419\pi$
$83$	−9.63816	−1.05793	−0.528963	+	0.848645i	$0.677419\pi$
$84$	2.03931	0.222507
$85$	−4.84950	−0.526002
$86$	4.46017	0.480952
$87$	−2.37948	−0.255107
$88$	−5.50058	−0.586364
$89$	−0.103318	−0.0109517	−0.00547585	−	0.999985i	$-0.501743\pi$
$89$	−0.103318	−0.0109517	−0.00547585	+	0.999985i	$0.501743\pi$
$90$	−0.0930693	−0.00981037
$91$	−7.17555	−0.752202
$92$	9.08141	0.946803
$93$	7.81490	0.810368
$94$	7.23466	0.746198
$95$	−3.12006	−0.320111
$96$	1.70497	0.174013
$97$	9.42084	0.956541	0.478271	−	0.878212i	$-0.341264\pi$
$97$	9.42084	0.956541	0.478271	+	0.878212i	$0.341264\pi$
$98$	5.56935	0.562589
$99$	−0.511935	−0.0514514
$100$	1.00000	0.100000
$101$	0.845355	0.0841159	0.0420580	−	0.999115i	$-0.486609\pi$
$101$	0.845355	0.0841159	0.0420580	+	0.999115i	$0.486609\pi$
$102$	8.26826	0.818680
$103$	−6.46234	−0.636753	−0.318377	−	0.947964i	$-0.603138\pi$
$103$	−6.46234	−0.636753	−0.318377	+	0.947964i	$0.603138\pi$
$104$	−5.99913	−0.588263
$105$	−2.03931	−0.199017
$106$	4.39298	0.426683
$107$	12.6145	1.21949	0.609743	−	0.792599i	$-0.291273\pi$
$107$	12.6145	1.21949	0.609743	+	0.792599i	$0.291273\pi$
$108$	5.27360	0.507452
$109$	−14.1524	−1.35556	−0.677778	−	0.735266i	$-0.737057\pi$
$109$	−14.1524	−1.35556	−0.677778	+	0.735266i	$0.737057\pi$
$110$	5.50058	0.524460
$111$	−12.3495	−1.17216
$112$	−1.19610	−0.113021
$113$	−8.59617	−0.808660	−0.404330	−	0.914613i	$-0.632495\pi$
$113$	−8.59617	−0.808660	−0.404330	+	0.914613i	$0.632495\pi$
$114$	5.31962	0.498228
$115$	−9.08141	−0.846846
$116$	1.39561	0.129579
$117$	−0.558335	−0.0516181
$118$	8.40462	0.773708
$119$	−5.80047	−0.531728
$120$	−1.70497	−0.155642
$121$	19.2564	1.75058
$122$	12.4754	1.12947
$123$	−1.85214	−0.167002
$124$	−4.58360	−0.411619
$125$	−1.00000	−0.0894427
$126$	−0.111320	−0.00991717
$127$	6.14736	0.545490	0.272745	−	0.962086i	$-0.412069\pi$
$127$	6.14736	0.545490	0.272745	+	0.962086i	$0.412069\pi$
$128$	−1.00000	−0.0883883
$129$	7.60446	0.669535
$130$	5.99913	0.526159
$131$	21.2858	1.85975	0.929875	−	0.367876i	$-0.119915\pi$
$131$	21.2858	1.85975	0.929875	+	0.367876i	$0.119915\pi$
$132$	−9.37834	−0.816280
$133$	−3.73190	−0.323596
$134$	−13.8349	−1.19515
$135$	−5.27360	−0.453879
$136$	−4.84950	−0.415841
$137$	2.92733	0.250099	0.125049	−	0.992151i	$-0.460091\pi$
$137$	2.92733	0.250099	0.125049	+	0.992151i	$0.460091\pi$
$138$	15.4836	1.31805
$139$	−16.1465	−1.36953	−0.684766	−	0.728763i	$-0.740096\pi$
$139$	−16.1465	−1.36953	−0.684766	+	0.728763i	$0.740096\pi$
$140$	1.19610	0.101089
$141$	12.3349	1.03879
$142$	−15.7136	−1.31865
$143$	32.9987	2.75949
$144$	−0.0930693	−0.00775578
$145$	−1.39561	−0.115899
$146$	−16.9793	−1.40521
$147$	9.49559	0.783183
$148$	7.24320	0.595387
$149$	−14.9560	−1.22524	−0.612620	−	0.790377i	$-0.709885\pi$
$149$	−14.9560	−1.22524	−0.612620	+	0.790377i	$0.709885\pi$
$150$	1.70497	0.139210
$151$	5.36834	0.436870	0.218435	−	0.975852i	$-0.429905\pi$
$151$	5.36834	0.436870	0.218435	+	0.975852i	$0.429905\pi$
$152$	−3.12006	−0.253070
$153$	−0.451340	−0.0364886
$154$	6.57923	0.530169
$155$	4.58360	0.368163
$156$	−10.2284	−0.818924
$157$	6.02624	0.480946	0.240473	−	0.970656i	$-0.422697\pi$
$157$	6.02624	0.480946	0.240473	+	0.970656i	$0.422697\pi$
$158$	−6.62664	−0.527187
$159$	7.48990	0.593988
$160$	1.00000	0.0790569
$161$	−10.8623	−0.856066
$162$	8.71213	0.684490
$163$	12.2612	0.960372	0.480186	−	0.877167i	$-0.340569\pi$
$163$	12.2612	0.960372	0.480186	+	0.877167i	$0.340569\pi$
$164$	1.08632	0.0848272
$165$	9.37834	0.730103
$166$	9.63816	0.748067
$167$	−15.9373	−1.23327	−0.616633	−	0.787251i	$-0.711504\pi$
$167$	−15.9373	−1.23327	−0.616633	+	0.787251i	$0.711504\pi$
$168$	−2.03931	−0.157336
$169$	22.9896	1.76843
$170$	4.84950	0.371940
$171$	−0.290382	−0.0222061
$172$	−4.46017	−0.340085
$173$	12.1842	0.926345	0.463172	−	0.886268i	$-0.346711\pi$
$173$	12.1842	0.926345	0.463172	+	0.886268i	$0.346711\pi$
$174$	2.37948	0.180388
$175$	−1.19610	−0.0904165
$176$	5.50058	0.414622
$177$	14.3296	1.07708
$178$	0.103318	0.00774402
$179$	−10.9880	−0.821279	−0.410639	−	0.911798i	$-0.634694\pi$
$179$	−10.9880	−0.821279	−0.410639	+	0.911798i	$0.634694\pi$
$180$	0.0930693	0.00693698
$181$	19.5903	1.45614	0.728068	−	0.685505i	$-0.240418\pi$
$181$	19.5903	1.45614	0.728068	+	0.685505i	$0.240418\pi$
$182$	7.17555	0.531887
$183$	21.2703	1.57234
$184$	−9.08141	−0.669491
$185$	−7.24320	−0.532531
$186$	−7.81490	−0.573017
$187$	26.6751	1.95067
$188$	−7.23466	−0.527642
$189$	−6.30774	−0.458820
$190$	3.12006	0.226353
$191$	−1.55475	−0.112498	−0.0562488	−	0.998417i	$-0.517914\pi$
$191$	−1.55475	−0.112498	−0.0562488	+	0.998417i	$0.517914\pi$
$192$	−1.70497	−0.123046
$193$	−21.0738	−1.51692	−0.758461	−	0.651718i	$-0.774048\pi$
$193$	−21.0738	−1.51692	−0.758461	+	0.651718i	$0.774048\pi$
$194$	−9.42084	−0.676377
$195$	10.2284	0.732468
$196$	−5.56935	−0.397811
$197$	−13.3624	−0.952034	−0.476017	−	0.879436i	$-0.657920\pi$
$197$	−13.3624	−0.952034	−0.476017	+	0.879436i	$0.657920\pi$
$198$	0.511935	0.0363817
$199$	16.0005	1.13424	0.567122	−	0.823634i	$-0.308057\pi$
$199$	16.0005	1.13424	0.567122	+	0.823634i	$0.308057\pi$
$200$	−1.00000	−0.0707107
$201$	−23.5880	−1.66377
$202$	−0.845355	−0.0594789
$203$	−1.66929	−0.117161
$204$	−8.26826	−0.578894
$205$	−1.08632	−0.0758718
$206$	6.46234	0.450253
$207$	−0.845201	−0.0587455
$208$	5.99913	0.415965
$209$	17.1621	1.18713
$210$	2.03931	0.140726
$211$	−20.8381	−1.43455	−0.717276	−	0.696789i	$-0.754611\pi$
$211$	−20.8381	−1.43455	−0.717276	+	0.696789i	$0.754611\pi$
$212$	−4.39298	−0.301711
$213$	−26.7912	−1.83570
$214$	−12.6145	−0.862306
$215$	4.46017	0.304181
$216$	−5.27360	−0.358823
$217$	5.48243	0.372171
$218$	14.1524	0.958523
$219$	−28.9492	−1.95620
$220$	−5.50058	−0.370849
$221$	29.0928	1.95699
$222$	12.3495	0.828841
$223$	3.50730	0.234866	0.117433	−	0.993081i	$-0.462533\pi$
$223$	3.50730	0.234866	0.117433	+	0.993081i	$0.462533\pi$
$224$	1.19610	0.0799176
$225$	−0.0930693	−0.00620462
$226$	8.59617	0.571809
$227$	−10.8130	−0.717687	−0.358844	−	0.933398i	$-0.616829\pi$
$227$	−10.8130	−0.717687	−0.358844	+	0.933398i	$0.616829\pi$
$228$	−5.31962	−0.352300
$229$	−0.855882	−0.0565583	−0.0282791	−	0.999600i	$-0.509003\pi$
$229$	−0.855882	−0.0565583	−0.0282791	+	0.999600i	$0.509003\pi$
$230$	9.08141	0.598811
$231$	11.2174	0.738051
$232$	−1.39561	−0.0916264
$233$	19.8892	1.30298	0.651491	−	0.758656i	$-0.274144\pi$
$233$	19.8892	1.30298	0.651491	+	0.758656i	$0.274144\pi$
$234$	0.558335	0.0364995
$235$	7.23466	0.471937
$236$	−8.40462	−0.547094
$237$	−11.2982	−0.733900
$238$	5.80047	0.375989
$239$	0.355451	0.0229922	0.0114961	−	0.999934i	$-0.496341\pi$
$239$	0.355451	0.0229922	0.0114961	+	0.999934i	$0.496341\pi$
$240$	1.70497	0.110055
$241$	−0.362915	−0.0233774	−0.0116887	−	0.999932i	$-0.503721\pi$
$241$	−0.362915	−0.0233774	−0.0116887	+	0.999932i	$0.503721\pi$
$242$	−19.2564	−1.23785
$243$	−0.966852	−0.0620236
$244$	−12.4754	−0.798657
$245$	5.56935	0.355813
$246$	1.85214	0.118088
$247$	18.7177	1.19098
$248$	4.58360	0.291059
$249$	16.4328	1.04139
$250$	1.00000	0.0632456
$251$	−13.6432	−0.861149	−0.430574	−	0.902555i	$-0.641689\pi$
$251$	−13.6432	−0.861149	−0.430574	+	0.902555i	$0.641689\pi$
$252$	0.111320	0.00701250
$253$	49.9530	3.14052
$254$	−6.14736	−0.385719
$255$	8.26826	0.517779
$256$	1.00000	0.0625000
$257$	−29.5636	−1.84412	−0.922062	−	0.387042i	$-0.873497\pi$
$257$	−29.5636	−1.84412	−0.922062	+	0.387042i	$0.873497\pi$
$258$	−7.60446	−0.473433
$259$	−8.66357	−0.538328
$260$	−5.99913	−0.372050
$261$	−0.129889	−0.00803991
$262$	−21.2858	−1.31504
$263$	−4.21888	−0.260147	−0.130074	−	0.991504i	$-0.541521\pi$
$263$	−4.21888	−0.260147	−0.130074	+	0.991504i	$0.541521\pi$
$264$	9.37834	0.577197
$265$	4.39298	0.269858
$266$	3.73190	0.228817
$267$	0.176155	0.0107805
$268$	13.8349	0.845098
$269$	−25.1969	−1.53628	−0.768140	−	0.640282i	$-0.778817\pi$
$269$	−25.1969	−1.53628	−0.768140	+	0.640282i	$0.778817\pi$
$270$	5.27360	0.320941
$271$	1.77939	0.108090	0.0540452	−	0.998538i	$-0.482789\pi$
$271$	1.77939	0.108090	0.0540452	+	0.998538i	$0.482789\pi$
$272$	4.84950	0.294044
$273$	12.2341	0.740442
$274$	−2.92733	−0.176847
$275$	5.50058	0.331697
$276$	−15.4836	−0.932001
$277$	8.50373	0.510940	0.255470	−	0.966817i	$-0.417770\pi$
$277$	8.50373	0.510940	0.255470	+	0.966817i	$0.417770\pi$
$278$	16.1465	0.968405
$279$	0.426592	0.0255394
$280$	−1.19610	−0.0714805
$281$	1.80918	0.107927	0.0539634	−	0.998543i	$-0.482815\pi$
$281$	1.80918	0.107927	0.0539634	+	0.998543i	$0.482815\pi$
$282$	−12.3349	−0.734532
$283$	19.9312	1.18479	0.592393	−	0.805649i	$-0.298183\pi$
$283$	19.9312	1.18479	0.592393	+	0.805649i	$0.298183\pi$
$284$	15.7136	0.932428
$285$	5.31962	0.315107
$286$	−32.9987	−1.95125
$287$	−1.29934	−0.0766978
$288$	0.0930693	0.00548416
$289$	6.51763	0.383390
$290$	1.39561	0.0819532
$291$	−16.0623	−0.941587
$292$	16.9793	0.993636
$293$	−13.6938	−0.800002	−0.400001	−	0.916515i	$-0.630990\pi$
$293$	−13.6938	−0.800002	−0.400001	+	0.916515i	$0.630990\pi$
$294$	−9.49559	−0.553794
$295$	8.40462	0.489336
$296$	−7.24320	−0.421002
$297$	29.0078	1.68321
$298$	14.9560	0.866376
$299$	54.4806	3.15069
$300$	−1.70497	−0.0984366
$301$	5.33479	0.307492
$302$	−5.36834	−0.308914
$303$	−1.44131	−0.0828009
$304$	3.12006	0.178948
$305$	12.4754	0.714341
$306$	0.451340	0.0258014
$307$	9.84525	0.561898	0.280949	−	0.959723i	$-0.409351\pi$
$307$	9.84525	0.561898	0.280949	+	0.959723i	$0.409351\pi$
$308$	−6.57923	−0.374886
$309$	11.0181	0.626798
$310$	−4.58360	−0.260331
$311$	−22.4636	−1.27379	−0.636897	−	0.770949i	$-0.719782\pi$
$311$	−22.4636	−1.27379	−0.636897	+	0.770949i	$0.719782\pi$
$312$	10.2284	0.579066
$313$	26.4811	1.49680	0.748399	−	0.663248i	$-0.230823\pi$
$313$	26.4811	1.49680	0.748399	+	0.663248i	$0.230823\pi$
$314$	−6.02624	−0.340080
$315$	−0.111320	−0.00627217
$316$	6.62664	0.372778
$317$	−27.2550	−1.53079	−0.765397	−	0.643559i	$-0.777457\pi$
$317$	−27.2550	−1.53079	−0.765397	+	0.643559i	$0.777457\pi$
$318$	−7.48990	−0.420013
$319$	7.67668	0.429811
$320$	−1.00000	−0.0559017
$321$	−21.5073	−1.20042
$322$	10.8623	0.605330
$323$	15.1307	0.841896
$324$	−8.71213	−0.484007
$325$	5.99913	0.332772
$326$	−12.2612	−0.679086
$327$	24.1295	1.33436
$328$	−1.08632	−0.0599819
$329$	8.65336	0.477075
$330$	−9.37834	−0.516261
$331$	16.5643	0.910455	0.455228	−	0.890375i	$-0.349558\pi$
$331$	16.5643	0.910455	0.455228	+	0.890375i	$0.349558\pi$
$332$	−9.63816	−0.528963
$333$	−0.674120	−0.0369415
$334$	15.9373	0.872050
$335$	−13.8349	−0.755879
$336$	2.03931	0.111254
$337$	−17.9020	−0.975185	−0.487593	−	0.873071i	$-0.662125\pi$
$337$	−17.9020	−0.975185	−0.487593	+	0.873071i	$0.662125\pi$
$338$	−22.9896	−1.25047
$339$	14.6562	0.796017
$340$	−4.84950	−0.263001
$341$	−25.2124	−1.36533
$342$	0.290382	0.0157021
$343$	15.0342	0.811769
$344$	4.46017	0.240476
$345$	15.4836	0.833607
$346$	−12.1842	−0.655025
$347$	−9.73353	−0.522523	−0.261262	−	0.965268i	$-0.584139\pi$
$347$	−9.73353	−0.522523	−0.261262	+	0.965268i	$0.584139\pi$
$348$	−2.37948	−0.127554
$349$	−16.9695	−0.908355	−0.454178	−	0.890911i	$-0.650067\pi$
$349$	−16.9695	−0.908355	−0.454178	+	0.890911i	$0.650067\pi$
$350$	1.19610	0.0639341
$351$	31.6370	1.68866
$352$	−5.50058	−0.293182
$353$	−21.9750	−1.16961	−0.584805	−	0.811174i	$-0.698829\pi$
$353$	−21.9750	−1.16961	−0.584805	+	0.811174i	$0.698829\pi$
$354$	−14.3296	−0.761612
$355$	−15.7136	−0.833989
$356$	−0.103318	−0.00547585
$357$	9.88964	0.523415
$358$	10.9880	0.580732
$359$	11.6090	0.612698	0.306349	−	0.951919i	$-0.400893\pi$
$359$	11.6090	0.612698	0.306349	+	0.951919i	$0.400893\pi$
$360$	−0.0930693	−0.00490519
$361$	−9.26522	−0.487643
$362$	−19.5903	−1.02964
$363$	−32.8316	−1.72321
$364$	−7.17555	−0.376101
$365$	−16.9793	−0.888735
$366$	−21.2703	−1.11181
$367$	−6.63875	−0.346540	−0.173270	−	0.984874i	$-0.555433\pi$
$367$	−6.63875	−0.346540	−0.173270	+	0.984874i	$0.555433\pi$
$368$	9.08141	0.473401
$369$	−0.101103	−0.00526321
$370$	7.24320	0.376556
$371$	5.25443	0.272796
$372$	7.81490	0.405184
$373$	14.4904	0.750283	0.375142	−	0.926968i	$-0.377594\pi$
$373$	14.4904	0.750283	0.375142	+	0.926968i	$0.377594\pi$
$374$	−26.6751	−1.37933
$375$	1.70497	0.0880444
$376$	7.23466	0.373099
$377$	8.37246	0.431204
$378$	6.30774	0.324435
$379$	0.984048	0.0505472	0.0252736	−	0.999681i	$-0.491954\pi$
$379$	0.984048	0.0505472	0.0252736	+	0.999681i	$0.491954\pi$
$380$	−3.12006	−0.160056
$381$	−10.4811	−0.536962
$382$	1.55475	0.0795479
$383$	2.00553	0.102478	0.0512388	−	0.998686i	$-0.483683\pi$
$383$	2.00553	0.102478	0.0512388	+	0.998686i	$0.483683\pi$
$384$	1.70497	0.0870065
$385$	6.57923	0.335309
$386$	21.0738	1.07263
$387$	0.415105	0.0211010
$388$	9.42084	0.478271
$389$	−4.03764	−0.204716	−0.102358	−	0.994748i	$-0.532639\pi$
$389$	−4.03764	−0.204716	−0.102358	+	0.994748i	$0.532639\pi$
$390$	−10.2284	−0.517933
$391$	44.0403	2.22721
$392$	5.56935	0.281295
$393$	−36.2917	−1.83067
$394$	13.3624	0.673190
$395$	−6.62664	−0.333423
$396$	−0.511935	−0.0257257
$397$	3.48164	0.174739	0.0873693	−	0.996176i	$-0.472154\pi$
$397$	3.48164	0.174739	0.0873693	+	0.996176i	$0.472154\pi$
$398$	−16.0005	−0.802032
$399$	6.36278	0.318537
$400$	1.00000	0.0500000
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	23.5880	1.17646
$403$	−27.4976	−1.36975
$404$	0.845355	0.0420580
$405$	8.71213	0.432909
$406$	1.66929	0.0828454
$407$	39.8418	1.97489
$408$	8.26826	0.409340
$409$	−22.8143	−1.12810	−0.564048	−	0.825742i	$-0.690757\pi$
$409$	−22.8143	−1.12810	−0.564048	+	0.825742i	$0.690757\pi$
$410$	1.08632	0.0536495
$411$	−4.99102	−0.246189
$412$	−6.46234	−0.318377
$413$	10.0527	0.494663
$414$	0.845201	0.0415394
$415$	9.63816	0.473119
$416$	−5.99913	−0.294132
$417$	27.5294	1.34812
$418$	−17.1621	−0.839428
$419$	8.43839	0.412242	0.206121	−	0.978526i	$-0.433916\pi$
$419$	8.43839	0.412242	0.206121	+	0.978526i	$0.433916\pi$
$420$	−2.03931	−0.0995083
$421$	13.7144	0.668398	0.334199	−	0.942503i	$-0.391534\pi$
$421$	13.7144	0.668398	0.334199	+	0.942503i	$0.391534\pi$
$422$	20.8381	1.01438
$423$	0.673325	0.0327382
$424$	4.39298	0.213342
$425$	4.84950	0.235235
$426$	26.7912	1.29804
$427$	14.9218	0.722118
$428$	12.6145	0.609743
$429$	−56.2619	−2.71635
$430$	−4.46017	−0.215088
$431$	36.5496	1.76053	0.880265	−	0.474482i	$-0.157364\pi$
$431$	36.5496	1.76053	0.880265	+	0.474482i	$0.157364\pi$
$432$	5.27360	0.253726
$433$	2.01859	0.0970070	0.0485035	−	0.998823i	$-0.484555\pi$
$433$	2.01859	0.0970070	0.0485035	+	0.998823i	$0.484555\pi$
$434$	−5.48243	−0.263165
$435$	2.37948	0.114087
$436$	−14.1524	−0.677778
$437$	28.3346	1.35543
$438$	28.9492	1.38325
$439$	3.93872	0.187985	0.0939925	−	0.995573i	$-0.470037\pi$
$439$	3.93872	0.187985	0.0939925	+	0.995573i	$0.470037\pi$
$440$	5.50058	0.262230
$441$	0.518336	0.0246827
$442$	−29.0928	−1.38380
$443$	35.1878	1.67182	0.835912	−	0.548863i	$-0.184939\pi$
$443$	35.1878	1.67182	0.835912	+	0.548863i	$0.184939\pi$
$444$	−12.3495	−0.586079
$445$	0.103318	0.00489775
$446$	−3.50730	−0.166076
$447$	25.4995	1.20609
$448$	−1.19610	−0.0565103
$449$	1.56058	0.0736481	0.0368241	−	0.999322i	$-0.488276\pi$
$449$	1.56058	0.0736481	0.0368241	+	0.999322i	$0.488276\pi$
$450$	0.0930693	0.00438733
$451$	5.97538	0.281370
$452$	−8.59617	−0.404330
$453$	−9.15288	−0.430040
$454$	10.8130	0.507481
$455$	7.17555	0.336395
$456$	5.31962	0.249114
$457$	−23.2768	−1.08884	−0.544421	−	0.838812i	$-0.683251\pi$
$457$	−23.2768	−1.08884	−0.544421	+	0.838812i	$0.683251\pi$
$458$	0.855882	0.0399928
$459$	25.5743	1.19371
$460$	−9.08141	−0.423423
$461$	22.0027	1.02477	0.512384	−	0.858757i	$-0.328762\pi$
$461$	22.0027	1.02477	0.512384	+	0.858757i	$0.328762\pi$
$462$	−11.2174	−0.521881
$463$	3.41311	0.158621	0.0793103	−	0.996850i	$-0.474728\pi$
$463$	3.41311	0.158621	0.0793103	+	0.996850i	$0.474728\pi$
$464$	1.39561	0.0647897
$465$	−7.81490	−0.362407
$466$	−19.8892	−0.921348
$467$	3.58221	0.165765	0.0828825	−	0.996559i	$-0.473587\pi$
$467$	3.58221	0.165765	0.0828825	+	0.996559i	$0.473587\pi$
$468$	−0.558335	−0.0258091
$469$	−16.5478	−0.764108
$470$	−7.23466	−0.333710
$471$	−10.2746	−0.473427
$472$	8.40462	0.386854
$473$	−24.5335	−1.12805
$474$	11.2982	0.518945
$475$	3.12006	0.143158
$476$	−5.80047	−0.265864
$477$	0.408851	0.0187200
$478$	−0.355451	−0.0162580
$479$	20.3528	0.929945	0.464972	−	0.885325i	$-0.346064\pi$
$479$	20.3528	0.929945	0.464972	+	0.885325i	$0.346064\pi$
$480$	−1.70497	−0.0778210
$481$	43.4529	1.98128
$482$	0.362915	0.0165303
$483$	18.5198	0.842682
$484$	19.2564	0.875290
$485$	−9.42084	−0.427778
$486$	0.966852	0.0438573
$487$	−12.4334	−0.563411	−0.281706	−	0.959501i	$-0.590900\pi$
$487$	−12.4334	−0.563411	−0.281706	+	0.959501i	$0.590900\pi$
$488$	12.4754	0.564736
$489$	−20.9050	−0.945358
$490$	−5.56935	−0.251598
$491$	19.1497	0.864212	0.432106	−	0.901823i	$-0.357771\pi$
$491$	19.1497	0.864212	0.432106	+	0.901823i	$0.357771\pi$
$492$	−1.85214	−0.0835011
$493$	6.76802	0.304816
$494$	−18.7177	−0.842147
$495$	0.511935	0.0230098
$496$	−4.58360	−0.205810
$497$	−18.7950	−0.843069
$498$	−16.4328	−0.736371
$499$	24.0890	1.07837	0.539187	−	0.842186i	$-0.318732\pi$
$499$	24.0890	1.07837	0.539187	+	0.842186i	$0.318732\pi$
$500$	−1.00000	−0.0447214
$501$	27.1727	1.21399
$502$	13.6432	0.608924
$503$	−19.4938	−0.869186	−0.434593	−	0.900627i	$-0.643108\pi$
$503$	−19.4938	−0.869186	−0.434593	+	0.900627i	$0.643108\pi$
$504$	−0.111320	−0.00495859
$505$	−0.845355	−0.0376178
$506$	−49.9530	−2.22068
$507$	−39.1966	−1.74078
$508$	6.14736	0.272745
$509$	−9.12398	−0.404413	−0.202207	−	0.979343i	$-0.564811\pi$
$509$	−9.12398	−0.404413	−0.202207	+	0.979343i	$0.564811\pi$
$510$	−8.26826	−0.366125
$511$	−20.3089	−0.898411
$512$	−1.00000	−0.0441942
$513$	16.4539	0.726459
$514$	29.5636	1.30399
$515$	6.46234	0.284765
$516$	7.60446	0.334768
$517$	−39.7948	−1.75017
$518$	8.66357	0.380656
$519$	−20.7737	−0.911862
$520$	5.99913	0.263079
$521$	−0.530267	−0.0232314	−0.0116157	−	0.999933i	$-0.503697\pi$
$521$	−0.530267	−0.0232314	−0.0116157	+	0.999933i	$0.503697\pi$
$522$	0.129889	0.00568507
$523$	1.77844	0.0777657	0.0388828	−	0.999244i	$-0.487620\pi$
$523$	1.77844	0.0777657	0.0388828	+	0.999244i	$0.487620\pi$
$524$	21.2858	0.929875
$525$	2.03931	0.0890029
$526$	4.21888	0.183952
$527$	−22.2281	−0.968273
$528$	−9.37834	−0.408140
$529$	59.4721	2.58574
$530$	−4.39298	−0.190819
$531$	0.782212	0.0339451
$532$	−3.73190	−0.161798
$533$	6.51697	0.282281
$534$	−0.176155	−0.00762295
$535$	−12.6145	−0.545370
$536$	−13.8349	−0.597575
$537$	18.7342	0.808439
$538$	25.1969	1.08631
$539$	−30.6347	−1.31953
$540$	−5.27360	−0.226940
$541$	19.2892	0.829306	0.414653	−	0.909980i	$-0.363903\pi$
$541$	19.2892	0.829306	0.414653	+	0.909980i	$0.363903\pi$
$542$	−1.77939	−0.0764314
$543$	−33.4009	−1.43337
$544$	−4.84950	−0.207921
$545$	14.1524	0.606223
$546$	−12.2341	−0.523571
$547$	42.5411	1.81892	0.909462	−	0.415786i	$-0.136494\pi$
$547$	42.5411	1.81892	0.909462	+	0.415786i	$0.136494\pi$
$548$	2.92733	0.125049
$549$	1.16108	0.0495537
$550$	−5.50058	−0.234546
$551$	4.35439	0.185503
$552$	15.4836	0.659024
$553$	−7.92611	−0.337052
$554$	−8.50373	−0.361289
$555$	12.3495	0.524205
$556$	−16.1465	−0.684766
$557$	7.66531	0.324789	0.162395	−	0.986726i	$-0.448078\pi$
$557$	7.66531	0.324789	0.162395	+	0.986726i	$0.448078\pi$
$558$	−0.426592	−0.0180591
$559$	−26.7571	−1.13171
$560$	1.19610	0.0505443
$561$	−45.4802	−1.92018
$562$	−1.80918	−0.0763157
$563$	28.9724	1.22104	0.610520	−	0.792001i	$-0.290960\pi$
$563$	28.9724	1.22104	0.610520	+	0.792001i	$0.290960\pi$
$564$	12.3349	0.519393
$565$	8.59617	0.361644
$566$	−19.9312	−0.837770
$567$	10.4206	0.437622
$568$	−15.7136	−0.659326
$569$	−34.8262	−1.45999	−0.729995	−	0.683453i	$-0.760478\pi$
$569$	−34.8262	−1.45999	−0.729995	+	0.683453i	$0.760478\pi$
$570$	−5.31962	−0.222814
$571$	7.94387	0.332441	0.166220	−	0.986089i	$-0.446844\pi$
$571$	7.94387	0.332441	0.166220	+	0.986089i	$0.446844\pi$
$572$	32.9987	1.37975
$573$	2.65080	0.110739
$574$	1.29934	0.0542335
$575$	9.08141	0.378721
$576$	−0.0930693	−0.00387789
$577$	−2.20712	−0.0918835	−0.0459417	−	0.998944i	$-0.514629\pi$
$577$	−2.20712	−0.0918835	−0.0459417	+	0.998944i	$0.514629\pi$
$578$	−6.51763	−0.271098
$579$	35.9302	1.49321
$580$	−1.39561	−0.0579496
$581$	11.5282	0.478270
$582$	16.0623	0.665803
$583$	−24.1639	−1.00077
$584$	−16.9793	−0.702607
$585$	0.558335	0.0230843
$586$	13.6938	0.565687
$587$	11.7984	0.486970	0.243485	−	0.969905i	$-0.421709\pi$
$587$	11.7984	0.486970	0.243485	+	0.969905i	$0.421709\pi$
$588$	9.49559	0.391592
$589$	−14.3011	−0.589266
$590$	−8.40462	−0.346013
$591$	22.7826	0.937150
$592$	7.24320	0.297694
$593$	34.8854	1.43257	0.716286	−	0.697806i	$-0.245840\pi$
$593$	34.8854	1.43257	0.716286	+	0.697806i	$0.245840\pi$
$594$	−29.0078	−1.19021
$595$	5.80047	0.237796
$596$	−14.9560	−0.612620
$597$	−27.2804	−1.11651
$598$	−54.4806	−2.22788
$599$	10.4970	0.428897	0.214449	−	0.976735i	$-0.431205\pi$
$599$	10.4970	0.428897	0.214449	+	0.976735i	$0.431205\pi$
$600$	1.70497	0.0696052
$601$	32.8562	1.34023	0.670115	−	0.742257i	$-0.266245\pi$
$601$	32.8562	1.34023	0.670115	+	0.742257i	$0.266245\pi$
$602$	−5.33479	−0.217430
$603$	−1.28760	−0.0524352
$604$	5.36834	0.218435
$605$	−19.2564	−0.782884
$606$	1.44131	0.0585491
$607$	21.5122	0.873151	0.436576	−	0.899668i	$-0.356191\pi$
$607$	21.5122	0.873151	0.436576	+	0.899668i	$0.356191\pi$
$608$	−3.12006	−0.126535
$609$	2.84609	0.115329
$610$	−12.4754	−0.505115
$611$	−43.4017	−1.75584
$612$	−0.451340	−0.0182443
$613$	−45.5965	−1.84163	−0.920813	−	0.390004i	$-0.872474\pi$
$613$	−45.5965	−1.84163	−0.920813	+	0.390004i	$0.872474\pi$
$614$	−9.84525	−0.397322
$615$	1.85214	0.0746856
$616$	6.57923	0.265085
$617$	−16.9519	−0.682459	−0.341230	−	0.939980i	$-0.610843\pi$
$617$	−16.9519	−0.682459	−0.341230	+	0.939980i	$0.610843\pi$
$618$	−11.0181	−0.443213
$619$	6.12969	0.246373	0.123187	−	0.992384i	$-0.460689\pi$
$619$	6.12969	0.246373	0.123187	+	0.992384i	$0.460689\pi$
$620$	4.58360	0.184082
$621$	47.8917	1.92183
$622$	22.4636	0.900708
$623$	0.123579	0.00495107
$624$	−10.2284	−0.409462
$625$	1.00000	0.0400000
$626$	−26.4811	−1.05840
$627$	−29.2610	−1.16857
$628$	6.02624	0.240473
$629$	35.1259	1.40056
$630$	0.111320	0.00443510
$631$	−19.5720	−0.779147	−0.389574	−	0.920995i	$-0.627378\pi$
$631$	−19.5720	−0.779147	−0.389574	+	0.920995i	$0.627378\pi$
$632$	−6.62664	−0.263594
$633$	35.5283	1.41212
$634$	27.2550	1.08243
$635$	−6.14736	−0.243950
$636$	7.48990	0.296994
$637$	−33.4113	−1.32380
$638$	−7.67668	−0.303923
$639$	−1.46245	−0.0578537
$640$	1.00000	0.0395285
$641$	−39.7130	−1.56857	−0.784284	−	0.620402i	$-0.786969\pi$
$641$	−39.7130	−1.56857	−0.784284	+	0.620402i	$0.786969\pi$
$642$	21.5073	0.848825
$643$	5.19385	0.204826	0.102413	−	0.994742i	$-0.467344\pi$
$643$	5.19385	0.204826	0.102413	+	0.994742i	$0.467344\pi$
$644$	−10.8623	−0.428033
$645$	−7.60446	−0.299425
$646$	−15.1307	−0.595311
$647$	−11.8361	−0.465327	−0.232663	−	0.972557i	$-0.574744\pi$
$647$	−11.8361	−0.465327	−0.232663	+	0.972557i	$0.574744\pi$
$648$	8.71213	0.342245
$649$	−46.2303	−1.81470
$650$	−5.99913	−0.235305
$651$	−9.34739	−0.366353
$652$	12.2612	0.480186
$653$	1.73645	0.0679526	0.0339763	−	0.999423i	$-0.489183\pi$
$653$	1.73645	0.0679526	0.0339763	+	0.999423i	$0.489183\pi$
$654$	−24.1295	−0.943538
$655$	−21.2858	−0.831705
$656$	1.08632	0.0424136
$657$	−1.58025	−0.0616514
$658$	−8.65336	−0.337343
$659$	−38.5400	−1.50130	−0.750652	−	0.660698i	$-0.770261\pi$
$659$	−38.5400	−1.50130	−0.750652	+	0.660698i	$0.770261\pi$
$660$	9.37834	0.365051
$661$	−22.8573	−0.889046	−0.444523	−	0.895767i	$-0.646627\pi$
$661$	−22.8573	−0.889046	−0.444523	+	0.895767i	$0.646627\pi$
$662$	−16.5643	−0.643789
$663$	−49.6024	−1.92640
$664$	9.63816	0.374033
$665$	3.73190	0.144717
$666$	0.674120	0.0261216
$667$	12.6741	0.490744
$668$	−15.9373	−0.616633
$669$	−5.97986	−0.231195
$670$	13.8349	0.534487
$671$	−68.6221	−2.64913
$672$	−2.03931	−0.0786682
$673$	−10.5177	−0.405429	−0.202714	−	0.979238i	$-0.564976\pi$
$673$	−10.5177	−0.405429	−0.202714	+	0.979238i	$0.564976\pi$
$674$	17.9020	0.689560
$675$	5.27360	0.202981
$676$	22.9896	0.884215
$677$	−35.8186	−1.37662	−0.688311	−	0.725416i	$-0.741648\pi$
$677$	−35.8186	−1.37662	−0.688311	+	0.725416i	$0.741648\pi$
$678$	−14.6562	−0.562869
$679$	−11.2682	−0.432435
$680$	4.84950	0.185970
$681$	18.4359	0.706467
$682$	25.2124	0.965434
$683$	5.65921	0.216543	0.108272	−	0.994121i	$-0.465468\pi$
$683$	5.65921	0.216543	0.108272	+	0.994121i	$0.465468\pi$
$684$	−0.290382	−0.0111030
$685$	−2.92733	−0.111848
$686$	−15.0342	−0.574007
$687$	1.45926	0.0556741
$688$	−4.46017	−0.170042
$689$	−26.3540	−1.00401
$690$	−15.4836	−0.589449
$691$	23.9433	0.910846	0.455423	−	0.890275i	$-0.349488\pi$
$691$	23.9433	0.910846	0.455423	+	0.890275i	$0.349488\pi$
$692$	12.1842	0.463172
$693$	0.612325	0.0232603
$694$	9.73353	0.369480
$695$	16.1465	0.612473
$696$	2.37948	0.0901940
$697$	5.26810	0.199544
$698$	16.9695	0.642304
$699$	−33.9105	−1.28261
$700$	−1.19610	−0.0452082
$701$	5.09161	0.192308	0.0961538	−	0.995366i	$-0.469346\pi$
$701$	5.09161	0.192308	0.0961538	+	0.995366i	$0.469346\pi$
$702$	−31.6370	−1.19406
$703$	22.5992	0.852346
$704$	5.50058	0.207311
$705$	−12.3349	−0.464559
$706$	21.9750	0.827040
$707$	−1.01113	−0.0380273
$708$	14.3296	0.538541
$709$	33.9602	1.27540	0.637702	−	0.770283i	$-0.279885\pi$
$709$	33.9602	1.27540	0.637702	+	0.770283i	$0.279885\pi$
$710$	15.7136	0.589719
$711$	−0.616737	−0.0231295
$712$	0.103318	0.00387201
$713$	−41.6255	−1.55889
$714$	−9.88964	−0.370111
$715$	−32.9987	−1.23408
$716$	−10.9880	−0.410639
$717$	−0.606035	−0.0226328
$718$	−11.6090	−0.433243
$719$	−43.3196	−1.61555	−0.807775	−	0.589491i	$-0.799328\pi$
$719$	−43.3196	−1.61555	−0.807775	+	0.589491i	$0.799328\pi$
$720$	0.0930693	0.00346849
$721$	7.72959	0.287865
$722$	9.26522	0.344816
$723$	0.618759	0.0230119
$724$	19.5903	0.728068
$725$	1.39561	0.0518317
$726$	32.8316	1.21850
$727$	−29.5054	−1.09430	−0.547148	−	0.837036i	$-0.684287\pi$
$727$	−29.5054	−1.09430	−0.547148	+	0.837036i	$0.684287\pi$
$728$	7.17555	0.265943
$729$	27.7848	1.02907
$730$	16.9793	0.628431
$731$	−21.6296	−0.799999
$732$	21.2703	0.786171
$733$	8.69610	0.321198	0.160599	−	0.987020i	$-0.448657\pi$
$733$	8.69610	0.321198	0.160599	+	0.987020i	$0.448657\pi$
$734$	6.63875	0.245041
$735$	−9.49559	−0.350250
$736$	−9.08141	−0.334745
$737$	76.0997	2.80317
$738$	0.101103	0.00372165
$739$	−48.3732	−1.77944	−0.889719	−	0.456509i	$-0.849100\pi$
$739$	−48.3732	−1.77944	−0.889719	+	0.456509i	$0.849100\pi$
$740$	−7.24320	−0.266265
$741$	−31.9131	−1.17236
$742$	−5.25443	−0.192896
$743$	35.4577	1.30082	0.650408	−	0.759585i	$-0.274598\pi$
$743$	35.4577	1.30082	0.650408	+	0.759585i	$0.274598\pi$
$744$	−7.81490	−0.286508
$745$	14.9560	0.547944
$746$	−14.4904	−0.530530
$747$	0.897018	0.0328202
$748$	26.6751	0.975337
$749$	−15.0881	−0.551308
$750$	−1.70497	−0.0622568
$751$	18.2548	0.666126	0.333063	−	0.942905i	$-0.391918\pi$
$751$	18.2548	0.666126	0.333063	+	0.942905i	$0.391918\pi$
$752$	−7.23466	−0.263821
$753$	23.2612	0.847686
$754$	−8.37246	−0.304907
$755$	−5.36834	−0.195374
$756$	−6.30774	−0.229410
$757$	0.986222	0.0358449	0.0179224	−	0.999839i	$-0.494295\pi$
$757$	0.986222	0.0358449	0.0179224	+	0.999839i	$0.494295\pi$
$758$	−0.984048	−0.0357422
$759$	−85.1686	−3.09142
$760$	3.12006	0.113176
$761$	−13.6656	−0.495378	−0.247689	−	0.968840i	$-0.579671\pi$
$761$	−13.6656	−0.495378	−0.247689	+	0.968840i	$0.579671\pi$
$762$	10.4811	0.379689
$763$	16.9277	0.612823
$764$	−1.55475	−0.0562488
$765$	0.451340	0.0163182
$766$	−2.00553	−0.0724626
$767$	−50.4204	−1.82058
$768$	−1.70497	−0.0615229
$769$	−8.35506	−0.301291	−0.150646	−	0.988588i	$-0.548135\pi$
$769$	−8.35506	−0.301291	−0.150646	+	0.988588i	$0.548135\pi$
$770$	−6.57923	−0.237099
$771$	50.4050	1.81529
$772$	−21.0738	−0.758461
$773$	−29.9800	−1.07830	−0.539152	−	0.842208i	$-0.681255\pi$
$773$	−29.9800	−1.07830	−0.539152	+	0.842208i	$0.681255\pi$
$774$	−0.415105	−0.0149206
$775$	−4.58360	−0.164648
$776$	−9.42084	−0.338188
$777$	14.7712	0.529912
$778$	4.03764	0.144756
$779$	3.38938	0.121437
$780$	10.2284	0.366234
$781$	86.4337	3.09284
$782$	−44.0403	−1.57488
$783$	7.35990	0.263021
$784$	−5.56935	−0.198905
$785$	−6.02624	−0.215086
$786$	36.2917	1.29448
$787$	9.57778	0.341411	0.170706	−	0.985322i	$-0.445395\pi$
$787$	9.57778	0.341411	0.170706	+	0.985322i	$0.445395\pi$
$788$	−13.3624	−0.476017
$789$	7.19307	0.256080
$790$	6.62664	0.235765
$791$	10.2819	0.365581
$792$	0.511935	0.0181908
$793$	−74.8417	−2.65771
$794$	−3.48164	−0.123559
$795$	−7.48990	−0.265639
$796$	16.0005	0.567122
$797$	−18.7374	−0.663712	−0.331856	−	0.943330i	$-0.607675\pi$
$797$	−18.7374	−0.663712	−0.331856	+	0.943330i	$0.607675\pi$
$798$	−6.36278	−0.225240
$799$	−35.0845	−1.24120
$800$	−1.00000	−0.0353553
$801$	0.00961575	0.000339756 0
$802$	−1.00000	−0.0353112
$803$	93.3958	3.29587
$804$	−23.5880	−0.831886
$805$	10.8623	0.382844
$806$	27.4976	0.968561
$807$	42.9599	1.51226
$808$	−0.845355	−0.0297395
$809$	29.9832	1.05415	0.527077	−	0.849818i	$-0.323288\pi$
$809$	29.9832	1.05415	0.527077	+	0.849818i	$0.323288\pi$
$810$	−8.71213	−0.306113
$811$	−15.0603	−0.528838	−0.264419	−	0.964408i	$-0.585180\pi$
$811$	−15.0603	−0.528838	−0.264419	+	0.964408i	$0.585180\pi$
$812$	−1.66929	−0.0585805
$813$	−3.03381	−0.106400
$814$	−39.8418	−1.39645
$815$	−12.2612	−0.429491
$816$	−8.26826	−0.289447
$817$	−13.9160	−0.486859
$818$	22.8143	0.797684
$819$	0.667823	0.0233356
$820$	−1.08632	−0.0379359
$821$	−35.5925	−1.24219	−0.621094	−	0.783736i	$-0.713311\pi$
$821$	−35.5925	−1.24219	−0.621094	+	0.783736i	$0.713311\pi$
$822$	4.99102	0.174082
$823$	−39.8581	−1.38936	−0.694682	−	0.719317i	$-0.744455\pi$
$823$	−39.8581	−1.38936	−0.694682	+	0.719317i	$0.744455\pi$
$824$	6.46234	0.225126
$825$	−9.37834	−0.326512
$826$	−10.0527	−0.349780
$827$	−39.9309	−1.38853	−0.694267	−	0.719718i	$-0.744271\pi$
$827$	−39.9309	−1.38853	−0.694267	+	0.719718i	$0.744271\pi$
$828$	−0.845201	−0.0293728
$829$	5.51909	0.191686	0.0958429	−	0.995396i	$-0.469445\pi$
$829$	5.51909	0.191686	0.0958429	+	0.995396i	$0.469445\pi$
$830$	−9.63816	−0.334546
$831$	−14.4986	−0.502952
$832$	5.99913	0.207982
$833$	−27.0086	−0.935791
$834$	−27.5294	−0.953265
$835$	15.9373	0.551533
$836$	17.1621	0.593565
$837$	−24.1720	−0.835508
$838$	−8.43839	−0.291499
$839$	−32.7731	−1.13145	−0.565726	−	0.824593i	$-0.691404\pi$
$839$	−32.7731	−1.13145	−0.565726	+	0.824593i	$0.691404\pi$
$840$	2.03931	0.0703630
$841$	−27.0523	−0.932837
$842$	−13.7144	−0.472629
$843$	−3.08460	−0.106239
$844$	−20.8381	−0.717276
$845$	−22.9896	−0.790866
$846$	−0.673325	−0.0231494
$847$	−23.0325	−0.791407
$848$	−4.39298	−0.150855
$849$	−33.9821	−1.16626
$850$	−4.84950	−0.166336
$851$	65.7785	2.25486
$852$	−26.7912	−0.917851
$853$	9.20862	0.315297	0.157649	−	0.987495i	$-0.449609\pi$
$853$	9.20862	0.315297	0.157649	+	0.987495i	$0.449609\pi$
$854$	−14.9218	−0.510614
$855$	0.290382	0.00993086
$856$	−12.6145	−0.431153
$857$	37.3542	1.27600	0.637998	−	0.770038i	$-0.279763\pi$
$857$	37.3542	1.27600	0.637998	+	0.770038i	$0.279763\pi$
$858$	56.2619	1.92075
$859$	−25.2691	−0.862172	−0.431086	−	0.902311i	$-0.641869\pi$
$859$	−25.2691	−0.862172	−0.431086	+	0.902311i	$0.641869\pi$
$860$	4.46017	0.152090
$861$	2.21534	0.0754987
$862$	−36.5496	−1.24488
$863$	28.2280	0.960892	0.480446	−	0.877024i	$-0.340475\pi$
$863$	28.2280	0.960892	0.480446	+	0.877024i	$0.340475\pi$
$864$	−5.27360	−0.179411
$865$	−12.1842	−0.414274
$866$	−2.01859	−0.0685943
$867$	−11.1124	−0.377396
$868$	5.48243	0.186086
$869$	36.4504	1.23649
$870$	−2.37948	−0.0806719
$871$	82.9971	2.81225
$872$	14.1524	0.479262
$873$	−0.876792	−0.0296749
$874$	−28.3346	−0.958431
$875$	1.19610	0.0404355
$876$	−28.9492	−0.978102
$877$	41.6783	1.40738	0.703688	−	0.710509i	$-0.251535\pi$
$877$	41.6783	1.40738	0.703688	+	0.710509i	$0.251535\pi$
$878$	−3.93872	−0.132925
$879$	23.3476	0.787495
$880$	−5.50058	−0.185425
$881$	28.4633	0.958954	0.479477	−	0.877555i	$-0.340826\pi$
$881$	28.4633	0.958954	0.479477	+	0.877555i	$0.340826\pi$
$882$	−0.518336	−0.0174533
$883$	32.4949	1.09354	0.546771	−	0.837282i	$-0.315857\pi$
$883$	32.4949	1.09354	0.546771	+	0.837282i	$0.315857\pi$
$884$	29.0928	0.978496
$885$	−14.3296	−0.481686
$886$	−35.1878	−1.18216
$887$	−14.3753	−0.482674	−0.241337	−	0.970441i	$-0.577586\pi$
$887$	−14.3753	−0.482674	−0.241337	+	0.970441i	$0.577586\pi$
$888$	12.3495	0.414421
$889$	−7.35284	−0.246606
$890$	−0.103318	−0.00346323
$891$	−47.9218	−1.60544
$892$	3.50730	0.117433
$893$	−22.5726	−0.755362
$894$	−25.4995	−0.852831
$895$	10.9880	0.367287
$896$	1.19610	0.0399588
$897$	−92.8879	−3.10144
$898$	−1.56058	−0.0520771
$899$	−6.39692	−0.213349
$900$	−0.0930693	−0.00310231
$901$	−21.3037	−0.709730
$902$	−5.97538	−0.198958
$903$	−9.09568	−0.302685
$904$	8.59617	0.285904
$905$	−19.5903	−0.651204
$906$	9.15288	0.304084
$907$	55.2137	1.83334	0.916670	−	0.399644i	$-0.130866\pi$
$907$	55.2137	1.83334	0.916670	+	0.399644i	$0.130866\pi$
$908$	−10.8130	−0.358844
$909$	−0.0786766	−0.00260954
$910$	−7.17555	−0.237867
$911$	45.9673	1.52296	0.761482	−	0.648186i	$-0.224472\pi$
$911$	45.9673	1.52296	0.761482	+	0.648186i	$0.224472\pi$
$912$	−5.31962	−0.176150
$913$	−53.0155	−1.75456
$914$	23.2768	0.769928
$915$	−21.2703	−0.703173
$916$	−0.855882	−0.0282791
$917$	−25.4599	−0.840760
$918$	−25.5743	−0.844078
$919$	−24.3208	−0.802268	−0.401134	−	0.916019i	$-0.631384\pi$
$919$	−24.3208	−0.802268	−0.401134	+	0.916019i	$0.631384\pi$
$920$	9.08141	0.299405
$921$	−16.7859	−0.553113
$922$	−22.0027	−0.724620
$923$	94.2677	3.10286
$924$	11.2174	0.369026
$925$	7.24320	0.238155
$926$	−3.41311	−0.112162
$927$	0.601446	0.0197541
$928$	−1.39561	−0.0458132
$929$	−34.9847	−1.14781	−0.573905	−	0.818922i	$-0.694572\pi$
$929$	−34.9847	−1.14781	−0.573905	+	0.818922i	$0.694572\pi$
$930$	7.81490	0.256261
$931$	−17.3767	−0.569499
$932$	19.8892	0.651491
$933$	38.2998	1.25388
$934$	−3.58221	−0.117213
$935$	−26.6751	−0.872368
$936$	0.558335	0.0182498
$937$	−22.0632	−0.720775	−0.360387	−	0.932803i	$-0.617356\pi$
$937$	−22.0632	−0.720775	−0.360387	+	0.932803i	$0.617356\pi$
$938$	16.5478	0.540306
$939$	−45.1495	−1.47340
$940$	7.23466	0.235969
$941$	−34.6093	−1.12823	−0.564116	−	0.825695i	$-0.690783\pi$
$941$	−34.6093	−1.12823	−0.564116	+	0.825695i	$0.690783\pi$
$942$	10.2746	0.334764
$943$	9.86531	0.321259
$944$	−8.40462	−0.273547
$945$	6.30774	0.205191
$946$	24.5335	0.797653
$947$	−13.3406	−0.433512	−0.216756	−	0.976226i	$-0.569548\pi$
$947$	−13.3406	−0.433512	−0.216756	+	0.976226i	$0.569548\pi$
$948$	−11.2982	−0.366950
$949$	101.861	3.30654
$950$	−3.12006	−0.101228
$951$	46.4690	1.50686
$952$	5.80047	0.187994
$953$	−54.0452	−1.75069	−0.875347	−	0.483495i	$-0.839367\pi$
$953$	−54.0452	−1.75069	−0.875347	+	0.483495i	$0.839367\pi$
$954$	−0.408851	−0.0132371
$955$	1.55475	0.0503105
$956$	0.355451	0.0114961
$957$	−13.0885	−0.423092
$958$	−20.3528	−0.657570
$959$	−3.50137	−0.113065
$960$	1.70497	0.0550277
$961$	−9.99065	−0.322279
$962$	−43.4529	−1.40098
$963$	−1.17402	−0.0378322
$964$	−0.362915	−0.0116887
$965$	21.0738	0.678388
$966$	−18.5198	−0.595866
$967$	−11.5758	−0.372253	−0.186127	−	0.982526i	$-0.559594\pi$
$967$	−11.5758	−0.372253	−0.186127	+	0.982526i	$0.559594\pi$
$968$	−19.2564	−0.618924
$969$	−25.7975	−0.828734
$970$	9.42084	0.302485
$971$	14.4804	0.464697	0.232349	−	0.972633i	$-0.425359\pi$
$971$	14.4804	0.464697	0.232349	+	0.972633i	$0.425359\pi$
$972$	−0.966852	−0.0310118
$973$	19.3128	0.619141
$974$	12.4334	0.398392
$975$	−10.2284	−0.327569
$976$	−12.4754	−0.399329
$977$	−27.9598	−0.894515	−0.447257	−	0.894405i	$-0.647599\pi$
$977$	−27.9598	−0.894515	−0.447257	+	0.894405i	$0.647599\pi$
$978$	20.9050	0.668469
$979$	−0.568310	−0.0181633
$980$	5.56935	0.177906
$981$	1.31716	0.0420536
$982$	−19.1497	−0.611090
$983$	−0.798824	−0.0254785	−0.0127393	−	0.999919i	$-0.504055\pi$
$983$	−0.798824	−0.0254785	−0.0127393	+	0.999919i	$0.504055\pi$
$984$	1.85214	0.0590442
$985$	13.3624	0.425763
$986$	−6.76802	−0.215538
$987$	−14.7537	−0.469616
$988$	18.7177	0.595488
$989$	−40.5046	−1.28797
$990$	−0.511935	−0.0162704
$991$	−15.5151	−0.492852	−0.246426	−	0.969162i	$-0.579256\pi$
$991$	−15.5151	−0.492852	−0.246426	+	0.969162i	$0.579256\pi$
$992$	4.58360	0.145529
$993$	−28.2416	−0.896221
$994$	18.7950	0.596140
$995$	−16.0005	−0.507249
$996$	16.4328	0.520693
$997$	14.0015	0.443432	0.221716	−	0.975111i	$-0.428834\pi$
$997$	14.0015	0.443432	0.221716	+	0.975111i	$0.428834\pi$
$998$	−24.0890	−0.762525
$999$	38.1977	1.20852

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.l.1.5	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.l.1.5	✓	17	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:	\( N \)	\(=\)	\( 4010 = 2 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4010.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.70497 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.70497 q^{6} -1.19610 q^{7} -1.00000 q^{8} -0.0930693 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.70497 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.70497 q^{6} -1.19610 q^{7} -1.00000 q^{8} -0.0930693 q^{9} +1.00000 q^{10} +5.50058 q^{11} -1.70497 q^{12} +5.99913 q^{13} +1.19610 q^{14} +1.70497 q^{15} +1.00000 q^{16} +4.84950 q^{17} +0.0930693 q^{18} +3.12006 q^{19} -1.00000 q^{20} +2.03931 q^{21} -5.50058 q^{22} +9.08141 q^{23} +1.70497 q^{24} +1.00000 q^{25} -5.99913 q^{26} +5.27360 q^{27} -1.19610 q^{28} +1.39561 q^{29} -1.70497 q^{30} -4.58360 q^{31} -1.00000 q^{32} -9.37834 q^{33} -4.84950 q^{34} +1.19610 q^{35} -0.0930693 q^{36} +7.24320 q^{37} -3.12006 q^{38} -10.2284 q^{39} +1.00000 q^{40} +1.08632 q^{41} -2.03931 q^{42} -4.46017 q^{43} +5.50058 q^{44} +0.0930693 q^{45} -9.08141 q^{46} -7.23466 q^{47} -1.70497 q^{48} -5.56935 q^{49} -1.00000 q^{50} -8.26826 q^{51} +5.99913 q^{52} -4.39298 q^{53} -5.27360 q^{54} -5.50058 q^{55} +1.19610 q^{56} -5.31962 q^{57} -1.39561 q^{58} -8.40462 q^{59} +1.70497 q^{60} -12.4754 q^{61} +4.58360 q^{62} +0.111320 q^{63} +1.00000 q^{64} -5.99913 q^{65} +9.37834 q^{66} +13.8349 q^{67} +4.84950 q^{68} -15.4836 q^{69} -1.19610 q^{70} +15.7136 q^{71} +0.0930693 q^{72} +16.9793 q^{73} -7.24320 q^{74} -1.70497 q^{75} +3.12006 q^{76} -6.57923 q^{77} +10.2284 q^{78} +6.62664 q^{79} -1.00000 q^{80} -8.71213 q^{81} -1.08632 q^{82} -9.63816 q^{83} +2.03931 q^{84} -4.84950 q^{85} +4.46017 q^{86} -2.37948 q^{87} -5.50058 q^{88} -0.103318 q^{89} -0.0930693 q^{90} -7.17555 q^{91} +9.08141 q^{92} +7.81490 q^{93} +7.23466 q^{94} -3.12006 q^{95} +1.70497 q^{96} +9.42084 q^{97} +5.56935 q^{98} -0.511935 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9}+O(q^{10}) \) 17 * q - 17 * q^2 + 3 * q^3 + 17 * q^4 - 17 * q^5 - 3 * q^6 + 4 * q^7 - 17 * q^8 + 6 * q^9	\( 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9} + 17 q^{10} - 8 q^{11} + 3 q^{12} + 14 q^{13} - 4 q^{14} - 3 q^{15} + 17 q^{16} - 8 q^{17} - 6 q^{18} + 7 q^{19} - 17 q^{20} - 11 q^{21} + 8 q^{22} + q^{23} - 3 q^{24} + 17 q^{25} - 14 q^{26} + 15 q^{27} + 4 q^{28} - 18 q^{29} + 3 q^{30} + 8 q^{31} - 17 q^{32} + 3 q^{33} + 8 q^{34} - 4 q^{35} + 6 q^{36} + 49 q^{37} - 7 q^{38} - 12 q^{39} + 17 q^{40} - 23 q^{41} + 11 q^{42} + 35 q^{43} - 8 q^{44} - 6 q^{45} - q^{46} + 11 q^{47} + 3 q^{48} + 27 q^{49} - 17 q^{50} - 16 q^{51} + 14 q^{52} - 3 q^{53} - 15 q^{54} + 8 q^{55} - 4 q^{56} + 9 q^{57} + 18 q^{58} - 6 q^{59} - 3 q^{60} + 6 q^{61} - 8 q^{62} + 10 q^{63} + 17 q^{64} - 14 q^{65} - 3 q^{66} + 55 q^{67} - 8 q^{68} - q^{69} + 4 q^{70} + 5 q^{71} - 6 q^{72} + 62 q^{73} - 49 q^{74} + 3 q^{75} + 7 q^{76} + 2 q^{77} + 12 q^{78} - 3 q^{79} - 17 q^{80} - 15 q^{81} + 23 q^{82} + 7 q^{83} - 11 q^{84} + 8 q^{85} - 35 q^{86} + 10 q^{87} + 8 q^{88} - 18 q^{89} + 6 q^{90} + 18 q^{91} + q^{92} + 33 q^{93} - 11 q^{94} - 7 q^{95} - 3 q^{96} + 63 q^{97} - 27 q^{98} - 11 q^{99}+O(q^{100}) \) 17 * q - 17 * q^2 + 3 * q^3 + 17 * q^4 - 17 * q^5 - 3 * q^6 + 4 * q^7 - 17 * q^8 + 6 * q^9 + 17 * q^10 - 8 * q^11 + 3 * q^12 + 14 * q^13 - 4 * q^14 - 3 * q^15 + 17 * q^16 - 8 * q^17 - 6 * q^18 + 7 * q^19 - 17 * q^20 - 11 * q^21 + 8 * q^22 + q^23 - 3 * q^24 + 17 * q^25 - 14 * q^26 + 15 * q^27 + 4 * q^28 - 18 * q^29 + 3 * q^30 + 8 * q^31 - 17 * q^32 + 3 * q^33 + 8 * q^34 - 4 * q^35 + 6 * q^36 + 49 * q^37 - 7 * q^38 - 12 * q^39 + 17 * q^40 - 23 * q^41 + 11 * q^42 + 35 * q^43 - 8 * q^44 - 6 * q^45 - q^46 + 11 * q^47 + 3 * q^48 + 27 * q^49 - 17 * q^50 - 16 * q^51 + 14 * q^52 - 3 * q^53 - 15 * q^54 + 8 * q^55 - 4 * q^56 + 9 * q^57 + 18 * q^58 - 6 * q^59 - 3 * q^60 + 6 * q^61 - 8 * q^62 + 10 * q^63 + 17 * q^64 - 14 * q^65 - 3 * q^66 + 55 * q^67 - 8 * q^68 - q^69 + 4 * q^70 + 5 * q^71 - 6 * q^72 + 62 * q^73 - 49 * q^74 + 3 * q^75 + 7 * q^76 + 2 * q^77 + 12 * q^78 - 3 * q^79 - 17 * q^80 - 15 * q^81 + 23 * q^82 + 7 * q^83 - 11 * q^84 + 8 * q^85 - 35 * q^86 + 10 * q^87 + 8 * q^88 - 18 * q^89 + 6 * q^90 + 18 * q^91 + q^92 + 33 * q^93 - 11 * q^94 - 7 * q^95 - 3 * q^96 + 63 * q^97 - 27 * q^98 - 11 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more