LMFDB - Embedded newform 8030.2.a.bc.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8030,2,Mod(1,8030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8030, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8030 = 2 \cdot 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8030.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:	$64.1198728231$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 5 x^{10} - 10 x^{9} + 71 x^{8} + 28 x^{7} - 360 x^{6} - 60 x^{5} + 788 x^{4} + 309 x^{3} + \cdots - 95 $ x^11 - 5x^10 - 10x^9 + 71x^8 + 28x^7 - 360x^6 - 60x^5 + 788x^4 + 309x^3 - 632x^2 - 503x - 95
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			1.7
Root			$-0.722992$ of defining polynomial
Character	$\chi$	$=$	8030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.722992 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.722992 q^{6} +3.72469 q^{7} -1.00000 q^{8} -2.47728 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.722992 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.722992 q^{6} +3.72469 q^{7} -1.00000 q^{8} -2.47728 q^{9} -1.00000 q^{10} +1.00000 q^{11} +0.722992 q^{12} -4.31205 q^{13} -3.72469 q^{14} +0.722992 q^{15} +1.00000 q^{16} -2.90707 q^{17} +2.47728 q^{18} +6.16965 q^{19} +1.00000 q^{20} +2.69292 q^{21} -1.00000 q^{22} -4.98195 q^{23} -0.722992 q^{24} +1.00000 q^{25} +4.31205 q^{26} -3.96003 q^{27} +3.72469 q^{28} -2.66421 q^{29} -0.722992 q^{30} +4.19085 q^{31} -1.00000 q^{32} +0.722992 q^{33} +2.90707 q^{34} +3.72469 q^{35} -2.47728 q^{36} -11.7125 q^{37} -6.16965 q^{38} -3.11757 q^{39} -1.00000 q^{40} -0.457121 q^{41} -2.69292 q^{42} -10.8371 q^{43} +1.00000 q^{44} -2.47728 q^{45} +4.98195 q^{46} +2.60179 q^{47} +0.722992 q^{48} +6.87328 q^{49} -1.00000 q^{50} -2.10179 q^{51} -4.31205 q^{52} +5.89430 q^{53} +3.96003 q^{54} +1.00000 q^{55} -3.72469 q^{56} +4.46060 q^{57} +2.66421 q^{58} +5.08934 q^{59} +0.722992 q^{60} -4.67979 q^{61} -4.19085 q^{62} -9.22710 q^{63} +1.00000 q^{64} -4.31205 q^{65} -0.722992 q^{66} -9.57915 q^{67} -2.90707 q^{68} -3.60191 q^{69} -3.72469 q^{70} -6.97368 q^{71} +2.47728 q^{72} -1.00000 q^{73} +11.7125 q^{74} +0.722992 q^{75} +6.16965 q^{76} +3.72469 q^{77} +3.11757 q^{78} -2.97753 q^{79} +1.00000 q^{80} +4.56878 q^{81} +0.457121 q^{82} +8.54904 q^{83} +2.69292 q^{84} -2.90707 q^{85} +10.8371 q^{86} -1.92620 q^{87} -1.00000 q^{88} +8.38429 q^{89} +2.47728 q^{90} -16.0610 q^{91} -4.98195 q^{92} +3.02995 q^{93} -2.60179 q^{94} +6.16965 q^{95} -0.722992 q^{96} -8.70981 q^{97} -6.87328 q^{98} -2.47728 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 11 q^{2} - 5 q^{3} + 11 q^{4} + 11 q^{5} + 5 q^{6} - q^{7} - 11 q^{8} + 12 q^{9}+O(q^{10}) $ 11 * q - 11 * q^2 - 5 * q^3 + 11 * q^4 + 11 * q^5 + 5 * q^6 - q^7 - 11 * q^8 + 12 * q^9	\( 11 q - 11 q^{2} - 5 q^{3} + 11 q^{4} + 11 q^{5} + 5 q^{6} - q^{7} - 11 q^{8} + 12 q^{9} - 11 q^{10} + 11 q^{11} - 5 q^{12} - 8 q^{13} + q^{14} - 5 q^{15} + 11 q^{16} - 15 q^{17} - 12 q^{18} + 5 q^{19} + 11 q^{20} - 11 q^{22} - 24 q^{23} + 5 q^{24} + 11 q^{25} + 8 q^{26} - 32 q^{27} - q^{28} + 10 q^{29} + 5 q^{30} + 7 q^{31} - 11 q^{32} - 5 q^{33} + 15 q^{34} - q^{35} + 12 q^{36} - 24 q^{37} - 5 q^{38} + 3 q^{39} - 11 q^{40} + 10 q^{41} - 14 q^{43} + 11 q^{44} + 12 q^{45} + 24 q^{46} - 8 q^{47} - 5 q^{48} - 18 q^{49} - 11 q^{50} + 22 q^{51} - 8 q^{52} - 30 q^{53} + 32 q^{54} + 11 q^{55} + q^{56} - 32 q^{57} - 10 q^{58} + 8 q^{59} - 5 q^{60} - 26 q^{61} - 7 q^{62} - 5 q^{63} + 11 q^{64} - 8 q^{65} + 5 q^{66} - 24 q^{67} - 15 q^{68} - 25 q^{69} + q^{70} + 16 q^{71} - 12 q^{72} - 11 q^{73} + 24 q^{74} - 5 q^{75} + 5 q^{76} - q^{77} - 3 q^{78} + 4 q^{79} + 11 q^{80} - 13 q^{81} - 10 q^{82} - 2 q^{83} - 15 q^{85} + 14 q^{86} - 17 q^{87} - 11 q^{88} - 11 q^{89} - 12 q^{90} - 41 q^{91} - 24 q^{92} - 15 q^{93} + 8 q^{94} + 5 q^{95} + 5 q^{96} - 37 q^{97} + 18 q^{98} + 12 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - 5 * q^3 + 11 * q^4 + 11 * q^5 + 5 * q^6 - q^7 - 11 * q^8 + 12 * q^9 - 11 * q^10 + 11 * q^11 - 5 * q^12 - 8 * q^13 + q^14 - 5 * q^15 + 11 * q^16 - 15 * q^17 - 12 * q^18 + 5 * q^19 + 11 * q^20 - 11 * q^22 - 24 * q^23 + 5 * q^24 + 11 * q^25 + 8 * q^26 - 32 * q^27 - q^28 + 10 * q^29 + 5 * q^30 + 7 * q^31 - 11 * q^32 - 5 * q^33 + 15 * q^34 - q^35 + 12 * q^36 - 24 * q^37 - 5 * q^38 + 3 * q^39 - 11 * q^40 + 10 * q^41 - 14 * q^43 + 11 * q^44 + 12 * q^45 + 24 * q^46 - 8 * q^47 - 5 * q^48 - 18 * q^49 - 11 * q^50 + 22 * q^51 - 8 * q^52 - 30 * q^53 + 32 * q^54 + 11 * q^55 + q^56 - 32 * q^57 - 10 * q^58 + 8 * q^59 - 5 * q^60 - 26 * q^61 - 7 * q^62 - 5 * q^63 + 11 * q^64 - 8 * q^65 + 5 * q^66 - 24 * q^67 - 15 * q^68 - 25 * q^69 + q^70 + 16 * q^71 - 12 * q^72 - 11 * q^73 + 24 * q^74 - 5 * q^75 + 5 * q^76 - q^77 - 3 * q^78 + 4 * q^79 + 11 * q^80 - 13 * q^81 - 10 * q^82 - 2 * q^83 - 15 * q^85 + 14 * q^86 - 17 * q^87 - 11 * q^88 - 11 * q^89 - 12 * q^90 - 41 * q^91 - 24 * q^92 - 15 * q^93 + 8 * q^94 + 5 * q^95 + 5 * q^96 - 37 * q^97 + 18 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.722992	0.417420	0.208710	−	0.977978i	$-0.433074\pi$
$3$	0.722992	0.417420	0.208710	+	0.977978i	$0.433074\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.722992	−0.295160
$7$	3.72469	1.40780	0.703899	−	0.710300i	$-0.251441\pi$
$7$	3.72469	1.40780	0.703899	+	0.710300i	$0.251441\pi$
$8$	−1.00000	−0.353553
$9$	−2.47728	−0.825761
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.722992	0.208710
$13$	−4.31205	−1.19595	−0.597973	−	0.801516i	$-0.704027\pi$
$13$	−4.31205	−1.19595	−0.597973	+	0.801516i	$0.704027\pi$
$14$	−3.72469	−0.995464
$15$	0.722992	0.186676
$16$	1.00000	0.250000
$17$	−2.90707	−0.705069	−0.352534	−	0.935799i	$-0.614680\pi$
$17$	−2.90707	−0.705069	−0.352534	+	0.935799i	$0.614680\pi$
$18$	2.47728	0.583901
$19$	6.16965	1.41541	0.707707	−	0.706506i	$-0.249730\pi$
$19$	6.16965	1.41541	0.707707	+	0.706506i	$0.249730\pi$
$20$	1.00000	0.223607
$21$	2.69292	0.587643
$22$	−1.00000	−0.213201
$23$	−4.98195	−1.03881	−0.519404	−	0.854529i	$-0.673846\pi$
$23$	−4.98195	−1.03881	−0.519404	+	0.854529i	$0.673846\pi$
$24$	−0.722992	−0.147580
$25$	1.00000	0.200000
$26$	4.31205	0.845662
$27$	−3.96003	−0.762108
$28$	3.72469	0.703899
$29$	−2.66421	−0.494731	−0.247366	−	0.968922i	$-0.579565\pi$
$29$	−2.66421	−0.494731	−0.247366	+	0.968922i	$0.579565\pi$
$30$	−0.722992	−0.132000
$31$	4.19085	0.752699	0.376349	−	0.926478i	$-0.377179\pi$
$31$	4.19085	0.752699	0.376349	+	0.926478i	$0.377179\pi$
$32$	−1.00000	−0.176777
$33$	0.722992	0.125857
$34$	2.90707	0.498559
$35$	3.72469	0.629587
$36$	−2.47728	−0.412880
$37$	−11.7125	−1.92552	−0.962761	−	0.270353i	$-0.912860\pi$
$37$	−11.7125	−1.92552	−0.962761	+	0.270353i	$0.912860\pi$
$38$	−6.16965	−1.00085
$39$	−3.11757	−0.499211
$40$	−1.00000	−0.158114
$41$	−0.457121	−0.0713903	−0.0356951	−	0.999363i	$-0.511365\pi$
$41$	−0.457121	−0.0713903	−0.0356951	+	0.999363i	$0.511365\pi$
$42$	−2.69292	−0.415526
$43$	−10.8371	−1.65265	−0.826324	−	0.563195i	$-0.809572\pi$
$43$	−10.8371	−1.65265	−0.826324	+	0.563195i	$0.809572\pi$
$44$	1.00000	0.150756
$45$	−2.47728	−0.369291
$46$	4.98195	0.734549
$47$	2.60179	0.379510	0.189755	−	0.981832i	$-0.439231\pi$
$47$	2.60179	0.379510	0.189755	+	0.981832i	$0.439231\pi$
$48$	0.722992	0.104355
$49$	6.87328	0.981897
$50$	−1.00000	−0.141421
$51$	−2.10179	−0.294309
$52$	−4.31205	−0.597973
$53$	5.89430	0.809644	0.404822	−	0.914396i	$-0.367334\pi$
$53$	5.89430	0.809644	0.404822	+	0.914396i	$0.367334\pi$
$54$	3.96003	0.538892
$55$	1.00000	0.134840
$56$	−3.72469	−0.497732
$57$	4.46060	0.590821
$58$	2.66421	0.349828
$59$	5.08934	0.662576	0.331288	−	0.943530i	$-0.392517\pi$
$59$	5.08934	0.662576	0.331288	+	0.943530i	$0.392517\pi$
$60$	0.722992	0.0933379
$61$	−4.67979	−0.599186	−0.299593	−	0.954067i	$-0.596851\pi$
$61$	−4.67979	−0.599186	−0.299593	+	0.954067i	$0.596851\pi$
$62$	−4.19085	−0.532238
$63$	−9.22710	−1.16251
$64$	1.00000	0.125000
$65$	−4.31205	−0.534843
$66$	−0.722992	−0.0889942
$67$	−9.57915	−1.17028	−0.585140	−	0.810932i	$-0.698960\pi$
$67$	−9.57915	−1.17028	−0.585140	+	0.810932i	$0.698960\pi$
$68$	−2.90707	−0.352534
$69$	−3.60191	−0.433619
$70$	−3.72469	−0.445185
$71$	−6.97368	−0.827623	−0.413812	−	0.910363i	$-0.635803\pi$
$71$	−6.97368	−0.827623	−0.413812	+	0.910363i	$0.635803\pi$
$72$	2.47728	0.291951
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	11.7125	1.36155
$75$	0.722992	0.0834839
$76$	6.16965	0.707707
$77$	3.72469	0.424467
$78$	3.11757	0.352996
$79$	−2.97753	−0.334998	−0.167499	−	0.985872i	$-0.553569\pi$
$79$	−2.97753	−0.334998	−0.167499	+	0.985872i	$0.553569\pi$
$80$	1.00000	0.111803
$81$	4.56878	0.507642
$82$	0.457121	0.0504805
$83$	8.54904	0.938379	0.469189	−	0.883098i	$-0.344546\pi$
$83$	8.54904	0.938379	0.469189	+	0.883098i	$0.344546\pi$
$84$	2.69292	0.293821
$85$	−2.90707	−0.315316
$86$	10.8371	1.16860
$87$	−1.92620	−0.206511
$88$	−1.00000	−0.106600
$89$	8.38429	0.888733	0.444366	−	0.895845i	$-0.353429\pi$
$89$	8.38429	0.888733	0.444366	+	0.895845i	$0.353429\pi$
$90$	2.47728	0.261129
$91$	−16.0610	−1.68365
$92$	−4.98195	−0.519404
$93$	3.02995	0.314191
$94$	−2.60179	−0.268354
$95$	6.16965	0.632992
$96$	−0.722992	−0.0737901
$97$	−8.70981	−0.884347	−0.442174	−	0.896929i	$-0.645793\pi$
$97$	−8.70981	−0.884347	−0.442174	+	0.896929i	$0.645793\pi$
$98$	−6.87328	−0.694306
$99$	−2.47728	−0.248976
$100$	1.00000	0.100000
$101$	−3.92610	−0.390661	−0.195331	−	0.980737i	$-0.562578\pi$
$101$	−3.92610	−0.390661	−0.195331	+	0.980737i	$0.562578\pi$
$102$	2.10179	0.208108
$103$	2.37771	0.234283	0.117141	−	0.993115i	$-0.462627\pi$
$103$	2.37771	0.234283	0.117141	+	0.993115i	$0.462627\pi$
$104$	4.31205	0.422831
$105$	2.69292	0.262802
$106$	−5.89430	−0.572505
$107$	−5.64104	−0.545340	−0.272670	−	0.962108i	$-0.587907\pi$
$107$	−5.64104	−0.545340	−0.272670	+	0.962108i	$0.587907\pi$
$108$	−3.96003	−0.381054
$109$	4.15921	0.398380	0.199190	−	0.979961i	$-0.436169\pi$
$109$	4.15921	0.398380	0.199190	+	0.979961i	$0.436169\pi$
$110$	−1.00000	−0.0953463
$111$	−8.46804	−0.803751
$112$	3.72469	0.351950
$113$	6.88630	0.647808	0.323904	−	0.946090i	$-0.395004\pi$
$113$	6.88630	0.647808	0.323904	+	0.946090i	$0.395004\pi$
$114$	−4.46060	−0.417774
$115$	−4.98195	−0.464569
$116$	−2.66421	−0.247366
$117$	10.6822	0.987566
$118$	−5.08934	−0.468512
$119$	−10.8279	−0.992595
$120$	−0.722992	−0.0659998
$121$	1.00000	0.0909091
$122$	4.67979	0.423688
$123$	−0.330495	−0.0297997
$124$	4.19085	0.376349
$125$	1.00000	0.0894427
$126$	9.22710	0.822015
$127$	−18.7943	−1.66773	−0.833863	−	0.551972i	$-0.813875\pi$
$127$	−18.7943	−1.66773	−0.833863	+	0.551972i	$0.813875\pi$
$128$	−1.00000	−0.0883883
$129$	−7.83516	−0.689848
$130$	4.31205	0.378191
$131$	−12.2494	−1.07023	−0.535115	−	0.844779i	$-0.679732\pi$
$131$	−12.2494	−1.07023	−0.535115	+	0.844779i	$0.679732\pi$
$132$	0.722992	0.0629284
$133$	22.9800	1.99262
$134$	9.57915	0.827513
$135$	−3.96003	−0.340825
$136$	2.90707	0.249279
$137$	−14.0402	−1.19954	−0.599768	−	0.800174i	$-0.704740\pi$
$137$	−14.0402	−1.19954	−0.599768	+	0.800174i	$0.704740\pi$
$138$	3.60191	0.306615
$139$	−17.7748	−1.50764	−0.753818	−	0.657083i	$-0.771790\pi$
$139$	−17.7748	−1.50764	−0.753818	+	0.657083i	$0.771790\pi$
$140$	3.72469	0.314793
$141$	1.88107	0.158415
$142$	6.97368	0.585218
$143$	−4.31205	−0.360591
$144$	−2.47728	−0.206440
$145$	−2.66421	−0.221251
$146$	1.00000	0.0827606
$147$	4.96933	0.409863
$148$	−11.7125	−0.962761
$149$	10.0178	0.820690	0.410345	−	0.911930i	$-0.365408\pi$
$149$	10.0178	0.820690	0.410345	+	0.911930i	$0.365408\pi$
$150$	−0.722992	−0.0590320
$151$	−2.71631	−0.221050	−0.110525	−	0.993873i	$-0.535253\pi$
$151$	−2.71631	−0.221050	−0.110525	+	0.993873i	$0.535253\pi$
$152$	−6.16965	−0.500424
$153$	7.20164	0.582218
$154$	−3.72469	−0.300144
$155$	4.19085	0.336617
$156$	−3.11757	−0.249606
$157$	−22.1999	−1.77174	−0.885871	−	0.463931i	$-0.846438\pi$
$157$	−22.1999	−1.77174	−0.885871	+	0.463931i	$0.846438\pi$
$158$	2.97753	0.236879
$159$	4.26153	0.337961
$160$	−1.00000	−0.0790569
$161$	−18.5562	−1.46243
$162$	−4.56878	−0.358957
$163$	7.91208	0.619722	0.309861	−	0.950782i	$-0.399717\pi$
$163$	7.91208	0.619722	0.309861	+	0.950782i	$0.399717\pi$
$164$	−0.457121	−0.0356951
$165$	0.722992	0.0562848
$166$	−8.54904	−0.663534
$167$	1.95116	0.150985	0.0754925	−	0.997146i	$-0.475947\pi$
$167$	1.95116	0.150985	0.0754925	+	0.997146i	$0.475947\pi$
$168$	−2.69292	−0.207763
$169$	5.59374	0.430287
$170$	2.90707	0.222962
$171$	−15.2840	−1.16879
$172$	−10.8371	−0.826324
$173$	10.2435	0.778796	0.389398	−	0.921070i	$-0.372683\pi$
$173$	10.2435	0.778796	0.389398	+	0.921070i	$0.372683\pi$
$174$	1.92620	0.146025
$175$	3.72469	0.281560
$176$	1.00000	0.0753778
$177$	3.67955	0.276572
$178$	−8.38429	−0.628429
$179$	−14.7521	−1.10262	−0.551312	−	0.834299i	$-0.685873\pi$
$179$	−14.7521	−1.10262	−0.551312	+	0.834299i	$0.685873\pi$
$180$	−2.47728	−0.184646
$181$	−8.81861	−0.655482	−0.327741	−	0.944768i	$-0.606287\pi$
$181$	−8.81861	−0.655482	−0.327741	+	0.944768i	$0.606287\pi$
$182$	16.0610	1.19052
$183$	−3.38345	−0.250112
$184$	4.98195	0.367274
$185$	−11.7125	−0.861120
$186$	−3.02995	−0.222167
$187$	−2.90707	−0.212586
$188$	2.60179	0.189755
$189$	−14.7499	−1.07290
$190$	−6.16965	−0.447593
$191$	5.52058	0.399455	0.199728	−	0.979851i	$-0.435994\pi$
$191$	5.52058	0.399455	0.199728	+	0.979851i	$0.435994\pi$
$192$	0.722992	0.0521774
$193$	−1.92732	−0.138732	−0.0693658	−	0.997591i	$-0.522098\pi$
$193$	−1.92732	−0.138732	−0.0693658	+	0.997591i	$0.522098\pi$
$194$	8.70981	0.625328
$195$	−3.11757	−0.223254
$196$	6.87328	0.490949
$197$	16.2563	1.15821	0.579107	−	0.815251i	$-0.303401\pi$
$197$	16.2563	1.15821	0.579107	+	0.815251i	$0.303401\pi$
$198$	2.47728	0.176053
$199$	−26.2864	−1.86339	−0.931697	−	0.363237i	$-0.881671\pi$
$199$	−26.2864	−1.86339	−0.931697	+	0.363237i	$0.881671\pi$
$200$	−1.00000	−0.0707107
$201$	−6.92565	−0.488498
$202$	3.92610	0.276239
$203$	−9.92334	−0.696482
$204$	−2.10179	−0.147155
$205$	−0.457121	−0.0319267
$206$	−2.37771	−0.165663
$207$	12.3417	0.857808
$208$	−4.31205	−0.298987
$209$	6.16965	0.426763
$210$	−2.69292	−0.185829
$211$	−0.000584998 0	−4.02729e−5 0	−2.01365e−5	−	1.00000i	$-0.500006\pi$
$211$	−0.000584998 0	−4.02729e−5 0	−2.01365e−5		1.00000i	$0.500006\pi$
$212$	5.89430	0.404822
$213$	−5.04191	−0.345466
$214$	5.64104	0.385614
$215$	−10.8371	−0.739087
$216$	3.96003	0.269446
$217$	15.6096	1.05965
$218$	−4.15921	−0.281698
$219$	−0.722992	−0.0488553
$220$	1.00000	0.0674200
$221$	12.5354	0.843224
$222$	8.46804	0.568338
$223$	−10.6870	−0.715658	−0.357829	−	0.933787i	$-0.616483\pi$
$223$	−10.6870	−0.715658	−0.357829	+	0.933787i	$0.616483\pi$
$224$	−3.72469	−0.248866
$225$	−2.47728	−0.165152
$226$	−6.88630	−0.458070
$227$	−8.06212	−0.535102	−0.267551	−	0.963544i	$-0.586214\pi$
$227$	−8.06212	−0.535102	−0.267551	+	0.963544i	$0.586214\pi$
$228$	4.46060	0.295411
$229$	6.22502	0.411361	0.205680	−	0.978619i	$-0.434059\pi$
$229$	6.22502	0.411361	0.205680	+	0.978619i	$0.434059\pi$
$230$	4.98195	0.328500
$231$	2.69292	0.177181
$232$	2.66421	0.174914
$233$	−0.0577005	−0.00378008	−0.00189004	−	0.999998i	$-0.500602\pi$
$233$	−0.0577005	−0.00378008	−0.00189004	+	0.999998i	$0.500602\pi$
$234$	−10.6822	−0.698314
$235$	2.60179	0.169722
$236$	5.08934	0.331288
$237$	−2.15273	−0.139835
$238$	10.8279	0.701870
$239$	27.3101	1.76655	0.883273	−	0.468860i	$-0.155335\pi$
$239$	27.3101	1.76655	0.883273	+	0.468860i	$0.155335\pi$
$240$	0.722992	0.0466689
$241$	−15.5469	−1.00146	−0.500732	−	0.865603i	$-0.666936\pi$
$241$	−15.5469	−1.00146	−0.500732	+	0.865603i	$0.666936\pi$
$242$	−1.00000	−0.0642824
$243$	15.1833	0.974008
$244$	−4.67979	−0.299593
$245$	6.87328	0.439118
$246$	0.330495	0.0210716
$247$	−26.6038	−1.69276
$248$	−4.19085	−0.266119
$249$	6.18088	0.391698
$250$	−1.00000	−0.0632456
$251$	25.8058	1.62885	0.814424	−	0.580270i	$-0.197053\pi$
$251$	25.8058	1.62885	0.814424	+	0.580270i	$0.197053\pi$
$252$	−9.22710	−0.581253
$253$	−4.98195	−0.313213
$254$	18.7943	1.17926
$255$	−2.10179	−0.131619
$256$	1.00000	0.0625000
$257$	−25.0898	−1.56506	−0.782529	−	0.622615i	$-0.786070\pi$
$257$	−25.0898	−1.56506	−0.782529	+	0.622615i	$0.786070\pi$
$258$	7.83516	0.487796
$259$	−43.6254	−2.71075
$260$	−4.31205	−0.267422
$261$	6.60000	0.408530
$262$	12.2494	0.756768
$263$	−13.7359	−0.846990	−0.423495	−	0.905899i	$-0.639197\pi$
$263$	−13.7359	−0.846990	−0.423495	+	0.905899i	$0.639197\pi$
$264$	−0.722992	−0.0444971
$265$	5.89430	0.362084
$266$	−22.9800	−1.40899
$267$	6.06177	0.370975
$268$	−9.57915	−0.585140
$269$	23.0464	1.40517	0.702583	−	0.711602i	$-0.252030\pi$
$269$	23.0464	1.40517	0.702583	+	0.711602i	$0.252030\pi$
$270$	3.96003	0.241000
$271$	−19.2926	−1.17194	−0.585971	−	0.810332i	$-0.699287\pi$
$271$	−19.2926	−1.17194	−0.585971	+	0.810332i	$0.699287\pi$
$272$	−2.90707	−0.176267
$273$	−11.6120	−0.702789
$274$	14.0402	0.848200
$275$	1.00000	0.0603023
$276$	−3.60191	−0.216810
$277$	20.6134	1.23854	0.619270	−	0.785178i	$-0.287429\pi$
$277$	20.6134	1.23854	0.619270	+	0.785178i	$0.287429\pi$
$278$	17.7748	1.06606
$279$	−10.3819	−0.621549
$280$	−3.72469	−0.222593
$281$	−1.49881	−0.0894113	−0.0447056	−	0.999000i	$-0.514235\pi$
$281$	−1.49881	−0.0894113	−0.0447056	+	0.999000i	$0.514235\pi$
$282$	−1.88107	−0.112016
$283$	22.1090	1.31424	0.657122	−	0.753784i	$-0.271774\pi$
$283$	22.1090	1.31424	0.657122	+	0.753784i	$0.271774\pi$
$284$	−6.97368	−0.413812
$285$	4.46060	0.264223
$286$	4.31205	0.254977
$287$	−1.70263	−0.100503
$288$	2.47728	0.145975
$289$	−8.54893	−0.502878
$290$	2.66421	0.156448
$291$	−6.29712	−0.369144
$292$	−1.00000	−0.0585206
$293$	7.08375	0.413837	0.206918	−	0.978358i	$-0.433657\pi$
$293$	7.08375	0.413837	0.206918	+	0.978358i	$0.433657\pi$
$294$	−4.96933	−0.289817
$295$	5.08934	0.296313
$296$	11.7125	0.680775
$297$	−3.96003	−0.229784
$298$	−10.0178	−0.580316
$299$	21.4824	1.24236
$300$	0.722992	0.0417420
$301$	−40.3649	−2.32660
$302$	2.71631	0.156306
$303$	−2.83854	−0.163070
$304$	6.16965	0.353853
$305$	−4.67979	−0.267964
$306$	−7.20164	−0.411690
$307$	31.5670	1.80162	0.900811	−	0.434211i	$-0.142973\pi$
$307$	31.5670	1.80162	0.900811	+	0.434211i	$0.142973\pi$
$308$	3.72469	0.212234
$309$	1.71907	0.0977942
$310$	−4.19085	−0.238024
$311$	17.2135	0.976089	0.488044	−	0.872819i	$-0.337710\pi$
$311$	17.2135	0.976089	0.488044	+	0.872819i	$0.337710\pi$
$312$	3.11757	0.176498
$313$	12.3959	0.700657	0.350329	−	0.936627i	$-0.386070\pi$
$313$	12.3959	0.700657	0.350329	+	0.936627i	$0.386070\pi$
$314$	22.1999	1.25281
$315$	−9.22710	−0.519888
$316$	−2.97753	−0.167499
$317$	17.4769	0.981602	0.490801	−	0.871272i	$-0.336704\pi$
$317$	17.4769	0.981602	0.490801	+	0.871272i	$0.336704\pi$
$318$	−4.26153	−0.238975
$319$	−2.66421	−0.149167
$320$	1.00000	0.0559017
$321$	−4.07843	−0.227636
$322$	18.5562	1.03410
$323$	−17.9356	−0.997964
$324$	4.56878	0.253821
$325$	−4.31205	−0.239189
$326$	−7.91208	−0.438210
$327$	3.00708	0.166292
$328$	0.457121	0.0252403
$329$	9.69084	0.534273
$330$	−0.722992	−0.0397994
$331$	21.5994	1.18721	0.593604	−	0.804757i	$-0.297704\pi$
$331$	21.5994	1.18721	0.593604	+	0.804757i	$0.297704\pi$
$332$	8.54904	0.469189
$333$	29.0152	1.59002
$334$	−1.95116	−0.106763
$335$	−9.57915	−0.523365
$336$	2.69292	0.146911
$337$	13.7814	0.750722	0.375361	−	0.926879i	$-0.377519\pi$
$337$	13.7814	0.750722	0.375361	+	0.926879i	$0.377519\pi$
$338$	−5.59374	−0.304259
$339$	4.97874	0.270408
$340$	−2.90707	−0.157658
$341$	4.19085	0.226947
$342$	15.2840	0.826462
$343$	−0.471993	−0.0254852
$344$	10.8371	0.584299
$345$	−3.60191	−0.193920
$346$	−10.2435	−0.550692
$347$	−17.1806	−0.922301	−0.461151	−	0.887322i	$-0.652563\pi$
$347$	−17.1806	−0.922301	−0.461151	+	0.887322i	$0.652563\pi$
$348$	−1.92620	−0.103255
$349$	27.1320	1.45234	0.726171	−	0.687514i	$-0.241298\pi$
$349$	27.1320	1.45234	0.726171	+	0.687514i	$0.241298\pi$
$350$	−3.72469	−0.199093
$351$	17.0758	0.911441
$352$	−1.00000	−0.0533002
$353$	−20.5414	−1.09331	−0.546653	−	0.837359i	$-0.684098\pi$
$353$	−20.5414	−1.09331	−0.546653	+	0.837359i	$0.684098\pi$
$354$	−3.67955	−0.195566
$355$	−6.97368	−0.370124
$356$	8.38429	0.444366
$357$	−7.82851	−0.414328
$358$	14.7521	0.779673
$359$	−20.1198	−1.06188	−0.530942	−	0.847408i	$-0.678162\pi$
$359$	−20.1198	−1.06188	−0.530942	+	0.847408i	$0.678162\pi$
$360$	2.47728	0.130564
$361$	19.0645	1.00340
$362$	8.81861	0.463496
$363$	0.722992	0.0379472
$364$	−16.0610	−0.841826
$365$	−1.00000	−0.0523424
$366$	3.38345	0.176856
$367$	9.51159	0.496501	0.248251	−	0.968696i	$-0.420144\pi$
$367$	9.51159	0.496501	0.248251	+	0.968696i	$0.420144\pi$
$368$	−4.98195	−0.259702
$369$	1.13242	0.0589513
$370$	11.7125	0.608904
$371$	21.9544	1.13982
$372$	3.02995	0.157096
$373$	−31.1529	−1.61303	−0.806517	−	0.591211i	$-0.798650\pi$
$373$	−31.1529	−1.61303	−0.806517	+	0.591211i	$0.798650\pi$
$374$	2.90707	0.150321
$375$	0.722992	0.0373351
$376$	−2.60179	−0.134177
$377$	11.4882	0.591672
$378$	14.7499	0.758651
$379$	−28.4031	−1.45897	−0.729484	−	0.683998i	$-0.760240\pi$
$379$	−28.4031	−1.45897	−0.729484	+	0.683998i	$0.760240\pi$
$380$	6.16965	0.316496
$381$	−13.5881	−0.696141
$382$	−5.52058	−0.282457
$383$	22.0530	1.12685	0.563427	−	0.826166i	$-0.309483\pi$
$383$	22.0530	1.12685	0.563427	+	0.826166i	$0.309483\pi$
$384$	−0.722992	−0.0368950
$385$	3.72469	0.189828
$386$	1.92732	0.0980980
$387$	26.8467	1.36469
$388$	−8.70981	−0.442174
$389$	12.4869	0.633112	0.316556	−	0.948574i	$-0.397474\pi$
$389$	12.4869	0.633112	0.316556	+	0.948574i	$0.397474\pi$
$390$	3.11757	0.157864
$391$	14.4829	0.732431
$392$	−6.87328	−0.347153
$393$	−8.85618	−0.446735
$394$	−16.2563	−0.818981
$395$	−2.97753	−0.149816
$396$	−2.47728	−0.124488
$397$	14.0293	0.704108	0.352054	−	0.935980i	$-0.385483\pi$
$397$	14.0293	0.704108	0.352054	+	0.935980i	$0.385483\pi$
$398$	26.2864	1.31762
$399$	16.6143	0.831758
$400$	1.00000	0.0500000
$401$	2.19859	0.109792	0.0548962	−	0.998492i	$-0.482517\pi$
$401$	2.19859	0.109792	0.0548962	+	0.998492i	$0.482517\pi$
$402$	6.92565	0.345420
$403$	−18.0711	−0.900187
$404$	−3.92610	−0.195331
$405$	4.56878	0.227024
$406$	9.92334	0.492487
$407$	−11.7125	−0.580567
$408$	2.10179	0.104054
$409$	−0.132809	−0.00656701	−0.00328350	−	0.999995i	$-0.501045\pi$
$409$	−0.132809	−0.00656701	−0.00328350	+	0.999995i	$0.501045\pi$
$410$	0.457121	0.0225756
$411$	−10.1510	−0.500710
$412$	2.37771	0.117141
$413$	18.9562	0.932774
$414$	−12.3417	−0.606562
$415$	8.54904	0.419656
$416$	4.31205	0.211415
$417$	−12.8510	−0.629317
$418$	−6.16965	−0.301767
$419$	1.51521	0.0740228	0.0370114	−	0.999315i	$-0.488216\pi$
$419$	1.51521	0.0740228	0.0370114	+	0.999315i	$0.488216\pi$
$420$	2.69292	0.131401
$421$	−28.7154	−1.39950	−0.699751	−	0.714387i	$-0.746706\pi$
$421$	−28.7154	−1.39950	−0.699751	+	0.714387i	$0.746706\pi$
$422$	0.000584998 0	2.84773e−5 0
$423$	−6.44536	−0.313384
$424$	−5.89430	−0.286252
$425$	−2.90707	−0.141014
$426$	5.04191	0.244281
$427$	−17.4307	−0.843533
$428$	−5.64104	−0.272670
$429$	−3.11757	−0.150518
$430$	10.8371	0.522613
$431$	−3.48023	−0.167637	−0.0838185	−	0.996481i	$-0.526712\pi$
$431$	−3.48023	−0.167637	−0.0838185	+	0.996481i	$0.526712\pi$
$432$	−3.96003	−0.190527
$433$	17.5656	0.844151	0.422076	−	0.906561i	$-0.361302\pi$
$433$	17.5656	0.844151	0.422076	+	0.906561i	$0.361302\pi$
$434$	−15.6096	−0.749284
$435$	−1.92620	−0.0923543
$436$	4.15921	0.199190
$437$	−30.7369	−1.47034
$438$	0.722992	0.0345459
$439$	23.2165	1.10807	0.554033	−	0.832495i	$-0.313088\pi$
$439$	23.2165	1.10807	0.554033	+	0.832495i	$0.313088\pi$
$440$	−1.00000	−0.0476731
$441$	−17.0271	−0.810812
$442$	−12.5354	−0.596250
$443$	−25.6245	−1.21746	−0.608728	−	0.793379i	$-0.708320\pi$
$443$	−25.6245	−1.21746	−0.608728	+	0.793379i	$0.708320\pi$
$444$	−8.46804	−0.401875
$445$	8.38429	0.397453
$446$	10.6870	0.506046
$447$	7.24279	0.342572
$448$	3.72469	0.175975
$449$	−29.7656	−1.40473	−0.702363	−	0.711819i	$-0.747871\pi$
$449$	−29.7656	−1.40473	−0.702363	+	0.711819i	$0.747871\pi$
$450$	2.47728	0.116780
$451$	−0.457121	−0.0215250
$452$	6.88630	0.323904
$453$	−1.96387	−0.0922708
$454$	8.06212	0.378374
$455$	−16.0610	−0.752952
$456$	−4.46060	−0.208887
$457$	−13.7247	−0.642016	−0.321008	−	0.947076i	$-0.604022\pi$
$457$	−13.7247	−0.642016	−0.321008	+	0.947076i	$0.604022\pi$
$458$	−6.22502	−0.290876
$459$	11.5121	0.537339
$460$	−4.98195	−0.232285
$461$	36.9845	1.72254	0.861269	−	0.508150i	$-0.169670\pi$
$461$	36.9845	1.72254	0.861269	+	0.508150i	$0.169670\pi$
$462$	−2.69292	−0.125286
$463$	−0.305737	−0.0142088	−0.00710439	−	0.999975i	$-0.502261\pi$
$463$	−0.305737	−0.0142088	−0.00710439	+	0.999975i	$0.502261\pi$
$464$	−2.66421	−0.123683
$465$	3.02995	0.140511
$466$	0.0577005	0.00267292
$467$	−34.6469	−1.60327	−0.801633	−	0.597817i	$-0.796035\pi$
$467$	−34.6469	−1.60327	−0.801633	+	0.597817i	$0.796035\pi$
$468$	10.6822	0.493783
$469$	−35.6793	−1.64752
$470$	−2.60179	−0.120011
$471$	−16.0503	−0.739560
$472$	−5.08934	−0.234256
$473$	−10.8371	−0.498292
$474$	2.15273	0.0988780
$475$	6.16965	0.283083
$476$	−10.8279	−0.496297
$477$	−14.6018	−0.668572
$478$	−27.3101	−1.24914
$479$	−38.5076	−1.75946	−0.879728	−	0.475477i	$-0.842275\pi$
$479$	−38.5076	−1.75946	−0.879728	+	0.475477i	$0.842275\pi$
$480$	−0.722992	−0.0329999
$481$	50.5048	2.30282
$482$	15.5469	0.708142
$483$	−13.4160	−0.610448
$484$	1.00000	0.0454545
$485$	−8.70981	−0.395492
$486$	−15.1833	−0.688728
$487$	11.8255	0.535864	0.267932	−	0.963438i	$-0.413660\pi$
$487$	11.8255	0.535864	0.267932	+	0.963438i	$0.413660\pi$
$488$	4.67979	0.211844
$489$	5.72037	0.258684
$490$	−6.87328	−0.310503
$491$	−22.3606	−1.00912	−0.504559	−	0.863377i	$-0.668345\pi$
$491$	−22.3606	−1.00912	−0.504559	+	0.863377i	$0.668345\pi$
$492$	−0.330495	−0.0148998
$493$	7.74505	0.348820
$494$	26.6038	1.19696
$495$	−2.47728	−0.111346
$496$	4.19085	0.188175
$497$	−25.9748	−1.16513
$498$	−6.18088	−0.276972
$499$	−35.8063	−1.60291	−0.801454	−	0.598056i	$-0.795940\pi$
$499$	−35.8063	−1.60291	−0.801454	+	0.598056i	$0.795940\pi$
$500$	1.00000	0.0447214
$501$	1.41067	0.0630241
$502$	−25.8058	−1.15177
$503$	−2.65582	−0.118417	−0.0592085	−	0.998246i	$-0.518858\pi$
$503$	−2.65582	−0.118417	−0.0592085	+	0.998246i	$0.518858\pi$
$504$	9.22710	0.411008
$505$	−3.92610	−0.174709
$506$	4.98195	0.221475
$507$	4.04423	0.179610
$508$	−18.7943	−0.833863
$509$	−8.38887	−0.371830	−0.185915	−	0.982566i	$-0.559525\pi$
$509$	−8.38887	−0.371830	−0.185915	+	0.982566i	$0.559525\pi$
$510$	2.10179	0.0930688
$511$	−3.72469	−0.164770
$512$	−1.00000	−0.0441942
$513$	−24.4320	−1.07870
$514$	25.0898	1.10666
$515$	2.37771	0.104774
$516$	−7.83516	−0.344924
$517$	2.60179	0.114426
$518$	43.6254	1.91679
$519$	7.40594	0.325085
$520$	4.31205	0.189096
$521$	12.7085	0.556771	0.278386	−	0.960469i	$-0.410201\pi$
$521$	12.7085	0.556771	0.278386	+	0.960469i	$0.410201\pi$
$522$	−6.60000	−0.288874
$523$	35.8825	1.56903	0.784517	−	0.620108i	$-0.212911\pi$
$523$	35.8825	1.56903	0.784517	+	0.620108i	$0.212911\pi$
$524$	−12.2494	−0.535115
$525$	2.69292	0.117529
$526$	13.7359	0.598912
$527$	−12.1831	−0.530704
$528$	0.722992	0.0314642
$529$	1.81984	0.0791235
$530$	−5.89430	−0.256032
$531$	−12.6077	−0.547129
$532$	22.9800	0.996309
$533$	1.97113	0.0853789
$534$	−6.06177	−0.262319
$535$	−5.64104	−0.243883
$536$	9.57915	0.413756
$537$	−10.6656	−0.460257
$538$	−23.0464	−0.993602
$539$	6.87328	0.296053
$540$	−3.96003	−0.170413
$541$	−13.2102	−0.567952	−0.283976	−	0.958831i	$-0.591654\pi$
$541$	−13.2102	−0.567952	−0.283976	+	0.958831i	$0.591654\pi$
$542$	19.2926	0.828688
$543$	−6.37579	−0.273611
$544$	2.90707	0.124640
$545$	4.15921	0.178161
$546$	11.6120	0.496947
$547$	−32.9359	−1.40824	−0.704119	−	0.710082i	$-0.748658\pi$
$547$	−32.9359	−1.40824	−0.704119	+	0.710082i	$0.748658\pi$
$548$	−14.0402	−0.599768
$549$	11.5932	0.494784
$550$	−1.00000	−0.0426401
$551$	−16.4372	−0.700250
$552$	3.60191	0.153307
$553$	−11.0903	−0.471609
$554$	−20.6134	−0.875779
$555$	−8.46804	−0.359448
$556$	−17.7748	−0.753818
$557$	−12.5331	−0.531045	−0.265522	−	0.964105i	$-0.585544\pi$
$557$	−12.5331	−0.531045	−0.265522	+	0.964105i	$0.585544\pi$
$558$	10.3819	0.439502
$559$	46.7302	1.97648
$560$	3.72469	0.157397
$561$	−2.10179	−0.0887376
$562$	1.49881	0.0632233
$563$	19.5867	0.825480	0.412740	−	0.910849i	$-0.364572\pi$
$563$	19.5867	0.825480	0.412740	+	0.910849i	$0.364572\pi$
$564$	1.88107	0.0792074
$565$	6.88630	0.289709
$566$	−22.1090	−0.929310
$567$	17.0173	0.714658
$568$	6.97368	0.292609
$569$	31.0848	1.30314	0.651571	−	0.758588i	$-0.274110\pi$
$569$	31.0848	1.30314	0.651571	+	0.758588i	$0.274110\pi$
$570$	−4.46060	−0.186834
$571$	0.283602	0.0118684	0.00593419	−	0.999982i	$-0.498111\pi$
$571$	0.283602	0.0118684	0.00593419	+	0.999982i	$0.498111\pi$
$572$	−4.31205	−0.180296
$573$	3.99133	0.166740
$574$	1.70263	0.0710664
$575$	−4.98195	−0.207762
$576$	−2.47728	−0.103220
$577$	2.04116	0.0849745	0.0424873	−	0.999097i	$-0.486472\pi$
$577$	2.04116	0.0849745	0.0424873	+	0.999097i	$0.486472\pi$
$578$	8.54893	0.355589
$579$	−1.39344	−0.0579093
$580$	−2.66421	−0.110625
$581$	31.8425	1.32105
$582$	6.29712	0.261024
$583$	5.89430	0.244117
$584$	1.00000	0.0413803
$585$	10.6822	0.441653
$586$	−7.08375	−0.292627
$587$	−13.2015	−0.544883	−0.272441	−	0.962172i	$-0.587831\pi$
$587$	−13.2015	−0.544883	−0.272441	+	0.962172i	$0.587831\pi$
$588$	4.96933	0.204932
$589$	25.8561	1.06538
$590$	−5.08934	−0.209525
$591$	11.7532	0.483461
$592$	−11.7125	−0.481381
$593$	22.6378	0.929622	0.464811	−	0.885410i	$-0.346122\pi$
$593$	22.6378	0.929622	0.464811	+	0.885410i	$0.346122\pi$
$594$	3.96003	0.162482
$595$	−10.8279	−0.443902
$596$	10.0178	0.410345
$597$	−19.0049	−0.777817
$598$	−21.4824	−0.878481
$599$	−13.6008	−0.555713	−0.277856	−	0.960623i	$-0.589624\pi$
$599$	−13.6008	−0.555713	−0.277856	+	0.960623i	$0.589624\pi$
$600$	−0.722992	−0.0295160
$601$	−3.63997	−0.148478	−0.0742388	−	0.997240i	$-0.523653\pi$
$601$	−3.63997	−0.148478	−0.0742388	+	0.997240i	$0.523653\pi$
$602$	40.3649	1.64515
$603$	23.7303	0.966371
$604$	−2.71631	−0.110525
$605$	1.00000	0.0406558
$606$	2.83854	0.115308
$607$	24.3617	0.988809	0.494405	−	0.869232i	$-0.335386\pi$
$607$	24.3617	0.988809	0.494405	+	0.869232i	$0.335386\pi$
$608$	−6.16965	−0.250212
$609$	−7.17450	−0.290725
$610$	4.67979	0.189479
$611$	−11.2190	−0.453873
$612$	7.20164	0.291109
$613$	−6.91416	−0.279260	−0.139630	−	0.990204i	$-0.544591\pi$
$613$	−6.91416	−0.279260	−0.139630	+	0.990204i	$0.544591\pi$
$614$	−31.5670	−1.27394
$615$	−0.330495	−0.0133268
$616$	−3.72469	−0.150072
$617$	−38.6145	−1.55456	−0.777281	−	0.629153i	$-0.783402\pi$
$617$	−38.6145	−1.55456	−0.777281	+	0.629153i	$0.783402\pi$
$618$	−1.71907	−0.0691510
$619$	13.3964	0.538446	0.269223	−	0.963078i	$-0.413233\pi$
$619$	13.3964	0.538446	0.269223	+	0.963078i	$0.413233\pi$
$620$	4.19085	0.168309
$621$	19.7287	0.791685
$622$	−17.2135	−0.690199
$623$	31.2288	1.25116
$624$	−3.11757	−0.124803
$625$	1.00000	0.0400000
$626$	−12.3959	−0.495440
$627$	4.46060	0.178139
$628$	−22.1999	−0.885871
$629$	34.0491	1.35763
$630$	9.22710	0.367616
$631$	14.4174	0.573948	0.286974	−	0.957938i	$-0.407351\pi$
$631$	14.4174	0.573948	0.286974	+	0.957938i	$0.407351\pi$
$632$	2.97753	0.118440
$633$	−0.000422949 0	−1.68107e−5 0
$634$	−17.4769	−0.694098
$635$	−18.7943	−0.745829
$636$	4.26153	0.168981
$637$	−29.6379	−1.17430
$638$	2.66421	0.105477
$639$	17.2758	0.683419
$640$	−1.00000	−0.0395285
$641$	−17.3494	−0.685258	−0.342629	−	0.939471i	$-0.611317\pi$
$641$	−17.3494	−0.685258	−0.342629	+	0.939471i	$0.611317\pi$
$642$	4.07843	0.160963
$643$	−11.2913	−0.445286	−0.222643	−	0.974900i	$-0.571468\pi$
$643$	−11.2913	−0.445286	−0.222643	+	0.974900i	$0.571468\pi$
$644$	−18.5562	−0.731217
$645$	−7.83516	−0.308509
$646$	17.9356	0.705667
$647$	6.04009	0.237461	0.118730	−	0.992927i	$-0.462118\pi$
$647$	6.04009	0.237461	0.118730	+	0.992927i	$0.462118\pi$
$648$	−4.56878	−0.179479
$649$	5.08934	0.199774
$650$	4.31205	0.169132
$651$	11.2856	0.442318
$652$	7.91208	0.309861
$653$	−24.0348	−0.940556	−0.470278	−	0.882518i	$-0.655846\pi$
$653$	−24.0348	−0.940556	−0.470278	+	0.882518i	$0.655846\pi$
$654$	−3.00708	−0.117586
$655$	−12.2494	−0.478622
$656$	−0.457121	−0.0178476
$657$	2.47728	0.0966480
$658$	−9.69084	−0.377788
$659$	35.7310	1.39188	0.695941	−	0.718099i	$-0.254988\pi$
$659$	35.7310	1.39188	0.695941	+	0.718099i	$0.254988\pi$
$660$	0.722992	0.0281424
$661$	−0.867877	−0.0337565	−0.0168782	−	0.999858i	$-0.505373\pi$
$661$	−0.867877	−0.0337565	−0.0168782	+	0.999858i	$0.505373\pi$
$662$	−21.5994	−0.839483
$663$	9.06301	0.351978
$664$	−8.54904	−0.331767
$665$	22.9800	0.891126
$666$	−29.0152	−1.12431
$667$	13.2730	0.513931
$668$	1.95116	0.0754925
$669$	−7.72665	−0.298730
$670$	9.57915	0.370075
$671$	−4.67979	−0.180661
$672$	−2.69292	−0.103882
$673$	16.9613	0.653812	0.326906	−	0.945057i	$-0.393994\pi$
$673$	16.9613	0.653812	0.326906	+	0.945057i	$0.393994\pi$
$674$	−13.7814	−0.530840
$675$	−3.96003	−0.152422
$676$	5.59374	0.215144
$677$	−9.70265	−0.372903	−0.186452	−	0.982464i	$-0.559699\pi$
$677$	−9.70265	−0.372903	−0.186452	+	0.982464i	$0.559699\pi$
$678$	−4.97874	−0.191207
$679$	−32.4413	−1.24498
$680$	2.90707	0.111481
$681$	−5.82885	−0.223362
$682$	−4.19085	−0.160476
$683$	16.2995	0.623684	0.311842	−	0.950134i	$-0.399054\pi$
$683$	16.2995	0.623684	0.311842	+	0.950134i	$0.399054\pi$
$684$	−15.2840	−0.584397
$685$	−14.0402	−0.536449
$686$	0.471993	0.0180208
$687$	4.50064	0.171710
$688$	−10.8371	−0.413162
$689$	−25.4165	−0.968290
$690$	3.60191	0.137122
$691$	47.2918	1.79907	0.899533	−	0.436852i	$-0.143907\pi$
$691$	47.2918	1.79907	0.899533	+	0.436852i	$0.143907\pi$
$692$	10.2435	0.389398
$693$	−9.22710	−0.350508
$694$	17.1806	0.652165
$695$	−17.7748	−0.674235
$696$	1.92620	0.0730125
$697$	1.32888	0.0503350
$698$	−27.1320	−1.02696
$699$	−0.0417170	−0.00157788
$700$	3.72469	0.140780
$701$	−0.834534	−0.0315199	−0.0157600	−	0.999876i	$-0.505017\pi$
$701$	−0.834534	−0.0315199	−0.0157600	+	0.999876i	$0.505017\pi$
$702$	−17.0758	−0.644486
$703$	−72.2620	−2.72541
$704$	1.00000	0.0376889
$705$	1.88107	0.0708452
$706$	20.5414	0.773084
$707$	−14.6235	−0.549972
$708$	3.67955	0.138286
$709$	−50.5797	−1.89956	−0.949781	−	0.312915i	$-0.898694\pi$
$709$	−50.5797	−1.89956	−0.949781	+	0.312915i	$0.898694\pi$
$710$	6.97368	0.261717
$711$	7.37617	0.276628
$712$	−8.38429	−0.314215
$713$	−20.8786	−0.781910
$714$	7.82851	0.292974
$715$	−4.31205	−0.161261
$716$	−14.7521	−0.551312
$717$	19.7450	0.737391
$718$	20.1198	0.750866
$719$	−44.0483	−1.64273	−0.821363	−	0.570406i	$-0.806786\pi$
$719$	−44.0483	−1.64273	−0.821363	+	0.570406i	$0.806786\pi$
$720$	−2.47728	−0.0923229
$721$	8.85622	0.329823
$722$	−19.0645	−0.709508
$723$	−11.2403	−0.418030
$724$	−8.81861	−0.327741
$725$	−2.66421	−0.0989463
$726$	−0.722992	−0.0268327
$727$	−28.7938	−1.06790	−0.533952	−	0.845515i	$-0.679294\pi$
$727$	−28.7938	−1.06790	−0.533952	+	0.845515i	$0.679294\pi$
$728$	16.0610	0.595261
$729$	−2.72894	−0.101072
$730$	1.00000	0.0370117
$731$	31.5043	1.16523
$732$	−3.38345	−0.125056
$733$	8.11075	0.299577	0.149789	−	0.988718i	$-0.452141\pi$
$733$	8.11075	0.299577	0.149789	+	0.988718i	$0.452141\pi$
$734$	−9.51159	−0.351079
$735$	4.96933	0.183296
$736$	4.98195	0.183637
$737$	−9.57915	−0.352853
$738$	−1.13242	−0.0416849
$739$	−34.1150	−1.25494	−0.627470	−	0.778640i	$-0.715910\pi$
$739$	−34.1150	−1.25494	−0.627470	+	0.778640i	$0.715910\pi$
$740$	−11.7125	−0.430560
$741$	−19.2343	−0.706591
$742$	−21.9544	−0.805971
$743$	−3.34089	−0.122565	−0.0612826	−	0.998120i	$-0.519519\pi$
$743$	−3.34089	−0.122565	−0.0612826	+	0.998120i	$0.519519\pi$
$744$	−3.02995	−0.111083
$745$	10.0178	0.367024
$746$	31.1529	1.14059
$747$	−21.1784	−0.774876
$748$	−2.90707	−0.106293
$749$	−21.0111	−0.767729
$750$	−0.722992	−0.0263999
$751$	26.8419	0.979475	0.489737	−	0.871870i	$-0.337093\pi$
$751$	26.8419	0.979475	0.489737	+	0.871870i	$0.337093\pi$
$752$	2.60179	0.0948774
$753$	18.6574	0.679913
$754$	−11.4882	−0.418375
$755$	−2.71631	−0.0988568
$756$	−14.7499	−0.536448
$757$	−40.8554	−1.48491	−0.742457	−	0.669894i	$-0.766340\pi$
$757$	−40.8554	−1.48491	−0.742457	+	0.669894i	$0.766340\pi$
$758$	28.4031	1.03165
$759$	−3.60191	−0.130741
$760$	−6.16965	−0.223797
$761$	37.3611	1.35434	0.677169	−	0.735827i	$-0.263206\pi$
$761$	37.3611	1.35434	0.677169	+	0.735827i	$0.263206\pi$
$762$	13.5881	0.492246
$763$	15.4918	0.560839
$764$	5.52058	0.199728
$765$	7.20164	0.260376
$766$	−22.0530	−0.796806
$767$	−21.9455	−0.792405
$768$	0.722992	0.0260887
$769$	−31.9981	−1.15388	−0.576941	−	0.816786i	$-0.695754\pi$
$769$	−31.9981	−1.15388	−0.576941	+	0.816786i	$0.695754\pi$
$770$	−3.72469	−0.134228
$771$	−18.1397	−0.653286
$772$	−1.92732	−0.0693658
$773$	−27.0486	−0.972870	−0.486435	−	0.873717i	$-0.661703\pi$
$773$	−27.0486	−0.972870	−0.486435	+	0.873717i	$0.661703\pi$
$774$	−26.8467	−0.964983
$775$	4.19085	0.150540
$776$	8.70981	0.312664
$777$	−31.5408	−1.13152
$778$	−12.4869	−0.447678
$779$	−2.82027	−0.101047
$780$	−3.11757	−0.111627
$781$	−6.97368	−0.249538
$782$	−14.4829	−0.517907
$783$	10.5504	0.377039
$784$	6.87328	0.245474
$785$	−22.1999	−0.792347
$786$	8.85618	0.315890
$787$	−36.1436	−1.28838	−0.644190	−	0.764866i	$-0.722805\pi$
$787$	−36.1436	−1.28838	−0.644190	+	0.764866i	$0.722805\pi$
$788$	16.2563	0.579107
$789$	−9.93092	−0.353550
$790$	2.97753	0.105936
$791$	25.6493	0.911984
$792$	2.47728	0.0880264
$793$	20.1795	0.716594
$794$	−14.0293	−0.497880
$795$	4.26153	0.151141
$796$	−26.2864	−0.931697
$797$	−32.0600	−1.13562	−0.567812	−	0.823158i	$-0.692210\pi$
$797$	−32.0600	−1.13562	−0.567812	+	0.823158i	$0.692210\pi$
$798$	−16.6143	−0.588141
$799$	−7.56358	−0.267580
$800$	−1.00000	−0.0353553
$801$	−20.7703	−0.733881
$802$	−2.19859	−0.0776350
$803$	−1.00000	−0.0352892
$804$	−6.92565	−0.244249
$805$	−18.5562	−0.654020
$806$	18.0711	0.636528
$807$	16.6624	0.586543
$808$	3.92610	0.138120
$809$	50.6866	1.78205	0.891023	−	0.453957i	$-0.149988\pi$
$809$	50.6866	1.78205	0.891023	+	0.453957i	$0.149988\pi$
$810$	−4.56878	−0.160530
$811$	34.6962	1.21835	0.609174	−	0.793037i	$-0.291501\pi$
$811$	34.6962	1.21835	0.609174	+	0.793037i	$0.291501\pi$
$812$	−9.92334	−0.348241
$813$	−13.9484	−0.489192
$814$	11.7125	0.410523
$815$	7.91208	0.277148
$816$	−2.10179	−0.0735774
$817$	−66.8613	−2.33918
$818$	0.132809	0.00464357
$819$	39.7877	1.39029
$820$	−0.457121	−0.0159633
$821$	20.8934	0.729183	0.364592	−	0.931167i	$-0.381209\pi$
$821$	20.8934	0.729183	0.364592	+	0.931167i	$0.381209\pi$
$822$	10.1510	0.354055
$823$	−54.5691	−1.90216	−0.951079	−	0.308947i	$-0.900023\pi$
$823$	−54.5691	−1.90216	−0.951079	+	0.308947i	$0.900023\pi$
$824$	−2.37771	−0.0828315
$825$	0.722992	0.0251713
$826$	−18.9562	−0.659571
$827$	−31.9117	−1.10968	−0.554840	−	0.831957i	$-0.687220\pi$
$827$	−31.9117	−1.10968	−0.554840	+	0.831957i	$0.687220\pi$
$828$	12.3417	0.428904
$829$	−2.95117	−0.102498	−0.0512492	−	0.998686i	$-0.516320\pi$
$829$	−2.95117	−0.102498	−0.0512492	+	0.998686i	$0.516320\pi$
$830$	−8.54904	−0.296741
$831$	14.9033	0.516990
$832$	−4.31205	−0.149493
$833$	−19.9811	−0.692305
$834$	12.8510	0.444994
$835$	1.95116	0.0675226
$836$	6.16965	0.213382
$837$	−16.5959	−0.573638
$838$	−1.51521	−0.0523421
$839$	43.7866	1.51168	0.755840	−	0.654756i	$-0.227229\pi$
$839$	43.7866	1.51168	0.755840	+	0.654756i	$0.227229\pi$
$840$	−2.69292	−0.0929145
$841$	−21.9020	−0.755241
$842$	28.7154	0.989598
$843$	−1.08362	−0.0373220
$844$	−0.000584998 0	−2.01365e−5 0
$845$	5.59374	0.192430
$846$	6.44536	0.221596
$847$	3.72469	0.127982
$848$	5.89430	0.202411
$849$	15.9846	0.548591
$850$	2.90707	0.0997118
$851$	58.3511	2.00025
$852$	−5.04191	−0.172733
$853$	9.58240	0.328095	0.164048	−	0.986452i	$-0.447545\pi$
$853$	9.58240	0.328095	0.164048	+	0.986452i	$0.447545\pi$
$854$	17.4307	0.596468
$855$	−15.2840	−0.522700
$856$	5.64104	0.192807
$857$	28.7614	0.982469	0.491235	−	0.871027i	$-0.336546\pi$
$857$	28.7614	0.982469	0.491235	+	0.871027i	$0.336546\pi$
$858$	3.11757	0.106432
$859$	17.9607	0.612810	0.306405	−	0.951901i	$-0.400874\pi$
$859$	17.9607	0.612810	0.306405	+	0.951901i	$0.400874\pi$
$860$	−10.8371	−0.369543
$861$	−1.23099	−0.0419520
$862$	3.48023	0.118537
$863$	5.35437	0.182265	0.0911325	−	0.995839i	$-0.470951\pi$
$863$	5.35437	0.182265	0.0911325	+	0.995839i	$0.470951\pi$
$864$	3.96003	0.134723
$865$	10.2435	0.348288
$866$	−17.5656	−0.596905
$867$	−6.18081	−0.209911
$868$	15.6096	0.529824
$869$	−2.97753	−0.101006
$870$	1.92620	0.0653044
$871$	41.3057	1.39959
$872$	−4.15921	−0.140849
$873$	21.5767	0.730259
$874$	30.7369	1.03969
$875$	3.72469	0.125917
$876$	−0.722992	−0.0244276
$877$	51.2392	1.73023	0.865113	−	0.501577i	$-0.167247\pi$
$877$	51.2392	1.73023	0.865113	+	0.501577i	$0.167247\pi$
$878$	−23.2165	−0.783520
$879$	5.12149	0.172744
$880$	1.00000	0.0337100
$881$	31.4647	1.06007	0.530036	−	0.847975i	$-0.322178\pi$
$881$	31.4647	1.06007	0.530036	+	0.847975i	$0.322178\pi$
$882$	17.0271	0.573331
$883$	23.7413	0.798959	0.399480	−	0.916742i	$-0.369191\pi$
$883$	23.7413	0.798959	0.399480	+	0.916742i	$0.369191\pi$
$884$	12.5354	0.421612
$885$	3.67955	0.123687
$886$	25.6245	0.860871
$887$	−3.46149	−0.116225	−0.0581127	−	0.998310i	$-0.518508\pi$
$887$	−3.46149	−0.116225	−0.0581127	+	0.998310i	$0.518508\pi$
$888$	8.46804	0.284169
$889$	−70.0029	−2.34782
$890$	−8.38429	−0.281042
$891$	4.56878	0.153060
$892$	−10.6870	−0.357829
$893$	16.0521	0.537163
$894$	−7.24279	−0.242235
$895$	−14.7521	−0.493108
$896$	−3.72469	−0.124433
$897$	15.5316	0.518585
$898$	29.7656	0.993291
$899$	−11.1653	−0.372384
$900$	−2.47728	−0.0825761
$901$	−17.1351	−0.570854
$902$	0.457121	0.0152205
$903$	−29.1835	−0.971166
$904$	−6.88630	−0.229035
$905$	−8.81861	−0.293141
$906$	1.96387	0.0652453
$907$	−7.02781	−0.233355	−0.116677	−	0.993170i	$-0.537224\pi$
$907$	−7.02781	−0.233355	−0.116677	+	0.993170i	$0.537224\pi$
$908$	−8.06212	−0.267551
$909$	9.72605	0.322593
$910$	16.0610	0.532417
$911$	−18.1463	−0.601215	−0.300607	−	0.953748i	$-0.597189\pi$
$911$	−18.1463	−0.601215	−0.300607	+	0.953748i	$0.597189\pi$
$912$	4.46060	0.147705
$913$	8.54904	0.282932
$914$	13.7247	0.453974
$915$	−3.38345	−0.111853
$916$	6.22502	0.205680
$917$	−45.6250	−1.50667
$918$	−11.5121	−0.379956
$919$	43.1058	1.42193	0.710964	−	0.703228i	$-0.248259\pi$
$919$	43.1058	1.42193	0.710964	+	0.703228i	$0.248259\pi$
$920$	4.98195	0.164250
$921$	22.8227	0.752032
$922$	−36.9845	−1.21802
$923$	30.0708	0.989793
$924$	2.69292	0.0885905
$925$	−11.7125	−0.385105
$926$	0.305737	0.0100471
$927$	−5.89026	−0.193462
$928$	2.66421	0.0874570
$929$	−33.2937	−1.09233	−0.546165	−	0.837678i	$-0.683913\pi$
$929$	−33.2937	−1.09233	−0.546165	+	0.837678i	$0.683913\pi$
$930$	−3.02995	−0.0993560
$931$	42.4057	1.38979
$932$	−0.0577005	−0.00189004
$933$	12.4452	0.407439
$934$	34.6469	1.13368
$935$	−2.90707	−0.0950714
$936$	−10.6822	−0.349157
$937$	29.9882	0.979670	0.489835	−	0.871815i	$-0.337057\pi$
$937$	29.9882	0.979670	0.489835	+	0.871815i	$0.337057\pi$
$938$	35.6793	1.16497
$939$	8.96213	0.292468
$940$	2.60179	0.0848609
$941$	5.72872	0.186751	0.0933755	−	0.995631i	$-0.470234\pi$
$941$	5.72872	0.186751	0.0933755	+	0.995631i	$0.470234\pi$
$942$	16.0503	0.522948
$943$	2.27735	0.0741608
$944$	5.08934	0.165644
$945$	−14.7499	−0.479813
$946$	10.8371	0.352346
$947$	−45.8217	−1.48900	−0.744502	−	0.667620i	$-0.767313\pi$
$947$	−45.8217	−1.48900	−0.744502	+	0.667620i	$0.767313\pi$
$948$	−2.15273	−0.0699173
$949$	4.31205	0.139975
$950$	−6.16965	−0.200170
$951$	12.6357	0.409740
$952$	10.8279	0.350935
$953$	−7.25476	−0.235005	−0.117502	−	0.993073i	$-0.537489\pi$
$953$	−7.25476	−0.235005	−0.117502	+	0.993073i	$0.537489\pi$
$954$	14.6018	0.472752
$955$	5.52058	0.178642
$956$	27.3101	0.883273
$957$	−1.92620	−0.0622653
$958$	38.5076	1.24412
$959$	−52.2954	−1.68870
$960$	0.722992	0.0233345
$961$	−13.4368	−0.433445
$962$	−50.5048	−1.62834
$963$	13.9745	0.450320
$964$	−15.5469	−0.500732
$965$	−1.92732	−0.0620426
$966$	13.4160	0.431652
$967$	32.6021	1.04841	0.524206	−	0.851592i	$-0.324362\pi$
$967$	32.6021	1.04841	0.524206	+	0.851592i	$0.324362\pi$
$968$	−1.00000	−0.0321412
$969$	−12.9673	−0.416570
$970$	8.70981	0.279655
$971$	10.3600	0.332467	0.166234	−	0.986086i	$-0.446839\pi$
$971$	10.3600	0.332467	0.166234	+	0.986086i	$0.446839\pi$
$972$	15.1833	0.487004
$973$	−66.2054	−2.12245
$974$	−11.8255	−0.378913
$975$	−3.11757	−0.0998423
$976$	−4.67979	−0.149796
$977$	40.8250	1.30611	0.653053	−	0.757312i	$-0.273488\pi$
$977$	40.8250	1.30611	0.653053	+	0.757312i	$0.273488\pi$
$978$	−5.72037	−0.182917
$979$	8.38429	0.267963
$980$	6.87328	0.219559
$981$	−10.3035	−0.328967
$982$	22.3606	0.713554
$983$	23.2927	0.742923	0.371462	−	0.928448i	$-0.378857\pi$
$983$	23.2927	0.742923	0.371462	+	0.928448i	$0.378857\pi$
$984$	0.330495	0.0105358
$985$	16.2563	0.517969
$986$	−7.74505	−0.246653
$987$	7.00640	0.223016
$988$	−26.6038	−0.846379
$989$	53.9901	1.71678
$990$	2.47728	0.0787332
$991$	−7.06823	−0.224530	−0.112265	−	0.993678i	$-0.535810\pi$
$991$	−7.06823	−0.224530	−0.112265	+	0.993678i	$0.535810\pi$
$992$	−4.19085	−0.133060
$993$	15.6162	0.495564
$994$	25.9748	0.823869
$995$	−26.2864	−0.833335
$996$	6.18088	0.195849
$997$	29.2063	0.924972	0.462486	−	0.886627i	$-0.346958\pi$
$997$	29.2063	0.924972	0.462486	+	0.886627i	$0.346958\pi$
$998$	35.8063	1.13343
$999$	46.3819	1.46746

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.bc.1.7	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.bc.1.7	✓	11	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8030 = 2 \cdot 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8030.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.722992 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.722992 q^{6} +3.72469 q^{7} -1.00000 q^{8} -2.47728 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.722992 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.722992 q^{6} +3.72469 q^{7} -1.00000 q^{8} -2.47728 q^{9} -1.00000 q^{10} +1.00000 q^{11} +0.722992 q^{12} -4.31205 q^{13} -3.72469 q^{14} +0.722992 q^{15} +1.00000 q^{16} -2.90707 q^{17} +2.47728 q^{18} +6.16965 q^{19} +1.00000 q^{20} +2.69292 q^{21} -1.00000 q^{22} -4.98195 q^{23} -0.722992 q^{24} +1.00000 q^{25} +4.31205 q^{26} -3.96003 q^{27} +3.72469 q^{28} -2.66421 q^{29} -0.722992 q^{30} +4.19085 q^{31} -1.00000 q^{32} +0.722992 q^{33} +2.90707 q^{34} +3.72469 q^{35} -2.47728 q^{36} -11.7125 q^{37} -6.16965 q^{38} -3.11757 q^{39} -1.00000 q^{40} -0.457121 q^{41} -2.69292 q^{42} -10.8371 q^{43} +1.00000 q^{44} -2.47728 q^{45} +4.98195 q^{46} +2.60179 q^{47} +0.722992 q^{48} +6.87328 q^{49} -1.00000 q^{50} -2.10179 q^{51} -4.31205 q^{52} +5.89430 q^{53} +3.96003 q^{54} +1.00000 q^{55} -3.72469 q^{56} +4.46060 q^{57} +2.66421 q^{58} +5.08934 q^{59} +0.722992 q^{60} -4.67979 q^{61} -4.19085 q^{62} -9.22710 q^{63} +1.00000 q^{64} -4.31205 q^{65} -0.722992 q^{66} -9.57915 q^{67} -2.90707 q^{68} -3.60191 q^{69} -3.72469 q^{70} -6.97368 q^{71} +2.47728 q^{72} -1.00000 q^{73} +11.7125 q^{74} +0.722992 q^{75} +6.16965 q^{76} +3.72469 q^{77} +3.11757 q^{78} -2.97753 q^{79} +1.00000 q^{80} +4.56878 q^{81} +0.457121 q^{82} +8.54904 q^{83} +2.69292 q^{84} -2.90707 q^{85} +10.8371 q^{86} -1.92620 q^{87} -1.00000 q^{88} +8.38429 q^{89} +2.47728 q^{90} -16.0610 q^{91} -4.98195 q^{92} +3.02995 q^{93} -2.60179 q^{94} +6.16965 q^{95} -0.722992 q^{96} -8.70981 q^{97} -6.87328 q^{98} -2.47728 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} - 5 q^{3} + 11 q^{4} + 11 q^{5} + 5 q^{6} - q^{7} - 11 q^{8} + 12 q^{9}+O(q^{10}) \) 11 * q - 11 * q^2 - 5 * q^3 + 11 * q^4 + 11 * q^5 + 5 * q^6 - q^7 - 11 * q^8 + 12 * q^9	\( 11 q - 11 q^{2} - 5 q^{3} + 11 q^{4} + 11 q^{5} + 5 q^{6} - q^{7} - 11 q^{8} + 12 q^{9} - 11 q^{10} + 11 q^{11} - 5 q^{12} - 8 q^{13} + q^{14} - 5 q^{15} + 11 q^{16} - 15 q^{17} - 12 q^{18} + 5 q^{19} + 11 q^{20} - 11 q^{22} - 24 q^{23} + 5 q^{24} + 11 q^{25} + 8 q^{26} - 32 q^{27} - q^{28} + 10 q^{29} + 5 q^{30} + 7 q^{31} - 11 q^{32} - 5 q^{33} + 15 q^{34} - q^{35} + 12 q^{36} - 24 q^{37} - 5 q^{38} + 3 q^{39} - 11 q^{40} + 10 q^{41} - 14 q^{43} + 11 q^{44} + 12 q^{45} + 24 q^{46} - 8 q^{47} - 5 q^{48} - 18 q^{49} - 11 q^{50} + 22 q^{51} - 8 q^{52} - 30 q^{53} + 32 q^{54} + 11 q^{55} + q^{56} - 32 q^{57} - 10 q^{58} + 8 q^{59} - 5 q^{60} - 26 q^{61} - 7 q^{62} - 5 q^{63} + 11 q^{64} - 8 q^{65} + 5 q^{66} - 24 q^{67} - 15 q^{68} - 25 q^{69} + q^{70} + 16 q^{71} - 12 q^{72} - 11 q^{73} + 24 q^{74} - 5 q^{75} + 5 q^{76} - q^{77} - 3 q^{78} + 4 q^{79} + 11 q^{80} - 13 q^{81} - 10 q^{82} - 2 q^{83} - 15 q^{85} + 14 q^{86} - 17 q^{87} - 11 q^{88} - 11 q^{89} - 12 q^{90} - 41 q^{91} - 24 q^{92} - 15 q^{93} + 8 q^{94} + 5 q^{95} + 5 q^{96} - 37 q^{97} + 18 q^{98} + 12 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - 5 * q^3 + 11 * q^4 + 11 * q^5 + 5 * q^6 - q^7 - 11 * q^8 + 12 * q^9 - 11 * q^10 + 11 * q^11 - 5 * q^12 - 8 * q^13 + q^14 - 5 * q^15 + 11 * q^16 - 15 * q^17 - 12 * q^18 + 5 * q^19 + 11 * q^20 - 11 * q^22 - 24 * q^23 + 5 * q^24 + 11 * q^25 + 8 * q^26 - 32 * q^27 - q^28 + 10 * q^29 + 5 * q^30 + 7 * q^31 - 11 * q^32 - 5 * q^33 + 15 * q^34 - q^35 + 12 * q^36 - 24 * q^37 - 5 * q^38 + 3 * q^39 - 11 * q^40 + 10 * q^41 - 14 * q^43 + 11 * q^44 + 12 * q^45 + 24 * q^46 - 8 * q^47 - 5 * q^48 - 18 * q^49 - 11 * q^50 + 22 * q^51 - 8 * q^52 - 30 * q^53 + 32 * q^54 + 11 * q^55 + q^56 - 32 * q^57 - 10 * q^58 + 8 * q^59 - 5 * q^60 - 26 * q^61 - 7 * q^62 - 5 * q^63 + 11 * q^64 - 8 * q^65 + 5 * q^66 - 24 * q^67 - 15 * q^68 - 25 * q^69 + q^70 + 16 * q^71 - 12 * q^72 - 11 * q^73 + 24 * q^74 - 5 * q^75 + 5 * q^76 - q^77 - 3 * q^78 + 4 * q^79 + 11 * q^80 - 13 * q^81 - 10 * q^82 - 2 * q^83 - 15 * q^85 + 14 * q^86 - 17 * q^87 - 11 * q^88 - 11 * q^89 - 12 * q^90 - 41 * q^91 - 24 * q^92 - 15 * q^93 + 8 * q^94 + 5 * q^95 + 5 * q^96 - 37 * q^97 + 18 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more