LMFDB - Embedded newform 91.2.a.d.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,2,Mod(1,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, 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("91.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.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:	$0.726638658394$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.316.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 2 $ x^3 - x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.34292$ of defining polynomial
Character	$\chi$	$=$	91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.34292 q^{2} -1.14637 q^{3} +3.48929 q^{4} -1.34292 q^{5} -2.68585 q^{6} -1.00000 q^{7} +3.48929 q^{8} -1.68585 q^{9} +O(q^{10})$	\(q+2.34292 q^{2} -1.14637 q^{3} +3.48929 q^{4} -1.34292 q^{5} -2.68585 q^{6} -1.00000 q^{7} +3.48929 q^{8} -1.68585 q^{9} -3.14637 q^{10} +1.14637 q^{11} -4.00000 q^{12} +1.00000 q^{13} -2.34292 q^{14} +1.53948 q^{15} +1.19656 q^{16} +5.83221 q^{17} -3.94981 q^{18} -3.34292 q^{19} -4.68585 q^{20} +1.14637 q^{21} +2.68585 q^{22} -3.17513 q^{23} -4.00000 q^{24} -3.19656 q^{25} +2.34292 q^{26} +5.37169 q^{27} -3.48929 q^{28} +10.4893 q^{29} +3.60688 q^{30} +1.63565 q^{31} -4.17513 q^{32} -1.31415 q^{33} +13.6644 q^{34} +1.34292 q^{35} -5.88240 q^{36} +8.51806 q^{37} -7.83221 q^{38} -1.14637 q^{39} -4.68585 q^{40} -0.292731 q^{41} +2.68585 q^{42} -8.15371 q^{43} +4.00000 q^{44} +2.26396 q^{45} -7.43910 q^{46} -10.6142 q^{47} -1.37169 q^{48} +1.00000 q^{49} -7.48929 q^{50} -6.68585 q^{51} +3.48929 q^{52} -0.782020 q^{53} +12.5855 q^{54} -1.53948 q^{55} -3.48929 q^{56} +3.83221 q^{57} +24.5756 q^{58} +12.6430 q^{59} +5.37169 q^{60} -2.00000 q^{61} +3.83221 q^{62} +1.68585 q^{63} -12.1751 q^{64} -1.34292 q^{65} -3.07896 q^{66} -6.10038 q^{67} +20.3503 q^{68} +3.63986 q^{69} +3.14637 q^{70} +1.53948 q^{71} -5.88240 q^{72} -15.3001 q^{73} +19.9572 q^{74} +3.66442 q^{75} -11.6644 q^{76} -1.14637 q^{77} -2.68585 q^{78} +0.882404 q^{79} -1.60688 q^{80} -1.10038 q^{81} -0.685846 q^{82} -12.1292 q^{83} +4.00000 q^{84} -7.83221 q^{85} -19.1035 q^{86} -12.0246 q^{87} +4.00000 q^{88} +5.73604 q^{89} +5.30429 q^{90} -1.00000 q^{91} -11.0790 q^{92} -1.87506 q^{93} -24.8683 q^{94} +4.48929 q^{95} +4.78623 q^{96} -5.34292 q^{97} +2.34292 q^{98} -1.93260 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{2} - 2 q^{3} + 3 q^{4} + 2 q^{5} + 4 q^{6} - 3 q^{7} + 3 q^{8} + 7 q^{9}+O(q^{10}) $ 3 * q + q^2 - 2 * q^3 + 3 * q^4 + 2 * q^5 + 4 * q^6 - 3 * q^7 + 3 * q^8 + 7 * q^9	\( 3 q + q^{2} - 2 q^{3} + 3 q^{4} + 2 q^{5} + 4 q^{6} - 3 q^{7} + 3 q^{8} + 7 q^{9} - 8 q^{10} + 2 q^{11} - 12 q^{12} + 3 q^{13} - q^{14} - 6 q^{15} - q^{16} + 4 q^{17} - 15 q^{18} - 4 q^{19} - 2 q^{20} + 2 q^{21} - 4 q^{22} + 10 q^{23} - 12 q^{24} - 5 q^{25} + q^{26} - 8 q^{27} - 3 q^{28} + 24 q^{29} + 20 q^{30} - 4 q^{31} + 7 q^{32} - 16 q^{33} + 14 q^{34} - 2 q^{35} - q^{36} - 10 q^{38} - 2 q^{39} - 2 q^{40} + 2 q^{41} - 4 q^{42} + 10 q^{43} + 12 q^{44} + 22 q^{45} - 18 q^{46} - 8 q^{47} + 20 q^{48} + 3 q^{49} - 15 q^{50} - 8 q^{51} + 3 q^{52} + 8 q^{53} + 32 q^{54} + 6 q^{55} - 3 q^{56} - 2 q^{57} + 12 q^{58} - 4 q^{59} - 8 q^{60} - 6 q^{61} - 2 q^{62} - 7 q^{63} - 17 q^{64} + 2 q^{65} + 12 q^{66} - 12 q^{67} + 22 q^{68} - 6 q^{69} + 8 q^{70} - 6 q^{71} - q^{72} - 10 q^{73} + 30 q^{74} - 16 q^{75} - 8 q^{76} - 2 q^{77} + 4 q^{78} - 14 q^{79} - 14 q^{80} + 3 q^{81} + 10 q^{82} - 12 q^{83} + 12 q^{84} - 10 q^{85} - 26 q^{86} - 26 q^{87} + 12 q^{88} + 2 q^{89} - 28 q^{90} - 3 q^{91} - 12 q^{92} - 22 q^{93} - 10 q^{94} + 6 q^{95} - 4 q^{96} - 10 q^{97} + q^{98} + 14 q^{99}+O(q^{100}) \) 3 * q + q^2 - 2 * q^3 + 3 * q^4 + 2 * q^5 + 4 * q^6 - 3 * q^7 + 3 * q^8 + 7 * q^9 - 8 * q^10 + 2 * q^11 - 12 * q^12 + 3 * q^13 - q^14 - 6 * q^15 - q^16 + 4 * q^17 - 15 * q^18 - 4 * q^19 - 2 * q^20 + 2 * q^21 - 4 * q^22 + 10 * q^23 - 12 * q^24 - 5 * q^25 + q^26 - 8 * q^27 - 3 * q^28 + 24 * q^29 + 20 * q^30 - 4 * q^31 + 7 * q^32 - 16 * q^33 + 14 * q^34 - 2 * q^35 - q^36 - 10 * q^38 - 2 * q^39 - 2 * q^40 + 2 * q^41 - 4 * q^42 + 10 * q^43 + 12 * q^44 + 22 * q^45 - 18 * q^46 - 8 * q^47 + 20 * q^48 + 3 * q^49 - 15 * q^50 - 8 * q^51 + 3 * q^52 + 8 * q^53 + 32 * q^54 + 6 * q^55 - 3 * q^56 - 2 * q^57 + 12 * q^58 - 4 * q^59 - 8 * q^60 - 6 * q^61 - 2 * q^62 - 7 * q^63 - 17 * q^64 + 2 * q^65 + 12 * q^66 - 12 * q^67 + 22 * q^68 - 6 * q^69 + 8 * q^70 - 6 * q^71 - q^72 - 10 * q^73 + 30 * q^74 - 16 * q^75 - 8 * q^76 - 2 * q^77 + 4 * q^78 - 14 * q^79 - 14 * q^80 + 3 * q^81 + 10 * q^82 - 12 * q^83 + 12 * q^84 - 10 * q^85 - 26 * q^86 - 26 * q^87 + 12 * q^88 + 2 * q^89 - 28 * q^90 - 3 * q^91 - 12 * q^92 - 22 * q^93 - 10 * q^94 + 6 * q^95 - 4 * q^96 - 10 * q^97 + q^98 + 14 * 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 $

$2$	2.34292	1.65670	0.828348	−	0.560213i	$-0.189281\pi$
$2$	2.34292	1.65670	0.828348	+	0.560213i	$0.189281\pi$
$3$	−1.14637	−0.661854	−0.330927	−	0.943656i	$-0.607361\pi$
$3$	−1.14637	−0.661854	−0.330927	+	0.943656i	$0.607361\pi$
$4$	3.48929	1.74464
$5$	−1.34292	−0.600573	−0.300287	−	0.953849i	$-0.597082\pi$
$5$	−1.34292	−0.600573	−0.300287	+	0.953849i	$0.597082\pi$
$6$	−2.68585	−1.09649
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	3.48929	1.23365
$9$	−1.68585	−0.561949
$10$	−3.14637	−0.994968
$11$	1.14637	0.345642	0.172821	−	0.984953i	$-0.444712\pi$
$11$	1.14637	0.345642	0.172821	+	0.984953i	$0.444712\pi$
$12$	−4.00000	−1.15470
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−2.34292	−0.626173
$15$	1.53948	0.397492
$16$	1.19656	0.299139
$17$	5.83221	1.41452	0.707260	−	0.706954i	$-0.249931\pi$
$17$	5.83221	1.41452	0.707260	+	0.706954i	$0.249931\pi$
$18$	−3.94981	−0.930979
$19$	−3.34292	−0.766919	−0.383460	−	0.923558i	$-0.625267\pi$
$19$	−3.34292	−0.766919	−0.383460	+	0.923558i	$0.625267\pi$
$20$	−4.68585	−1.04779
$21$	1.14637	0.250157
$22$	2.68585	0.572624
$23$	−3.17513	−0.662061	−0.331031	−	0.943620i	$-0.607396\pi$
$23$	−3.17513	−0.662061	−0.331031	+	0.943620i	$0.607396\pi$
$24$	−4.00000	−0.816497
$25$	−3.19656	−0.639312
$26$	2.34292	0.459485
$27$	5.37169	1.03378
$28$	−3.48929	−0.659414
$29$	10.4893	1.94781	0.973906	−	0.226952i	$-0.0728760\pi$
$29$	10.4893	1.94781	0.973906	+	0.226952i	$0.0728760\pi$
$30$	3.60688	0.658524
$31$	1.63565	0.293772	0.146886	−	0.989153i	$-0.453075\pi$
$31$	1.63565	0.293772	0.146886	+	0.989153i	$0.453075\pi$
$32$	−4.17513	−0.738067
$33$	−1.31415	−0.228765
$34$	13.6644	2.34343
$35$	1.34292	0.226995
$36$	−5.88240	−0.980401
$37$	8.51806	1.40036	0.700180	−	0.713966i	$-0.253103\pi$
$37$	8.51806	1.40036	0.700180	+	0.713966i	$0.253103\pi$
$38$	−7.83221	−1.27055
$39$	−1.14637	−0.183565
$40$	−4.68585	−0.740897
$41$	−0.292731	−0.0457169	−0.0228584	−	0.999739i	$-0.507277\pi$
$41$	−0.292731	−0.0457169	−0.0228584	+	0.999739i	$0.507277\pi$
$42$	2.68585	0.414435
$43$	−8.15371	−1.24343	−0.621715	−	0.783244i	$-0.713564\pi$
$43$	−8.15371	−1.24343	−0.621715	+	0.783244i	$0.713564\pi$
$44$	4.00000	0.603023
$45$	2.26396	0.337491
$46$	−7.43910	−1.09683
$47$	−10.6142	−1.54824	−0.774122	−	0.633036i	$-0.781809\pi$
$47$	−10.6142	−1.54824	−0.774122	+	0.633036i	$0.781809\pi$
$48$	−1.37169	−0.197987
$49$	1.00000	0.142857
$50$	−7.48929	−1.05915
$51$	−6.68585	−0.936206
$52$	3.48929	0.483877
$53$	−0.782020	−0.107419	−0.0537093	−	0.998557i	$-0.517104\pi$
$53$	−0.782020	−0.107419	−0.0537093	+	0.998557i	$0.517104\pi$
$54$	12.5855	1.71266
$55$	−1.53948	−0.207584
$56$	−3.48929	−0.466276
$57$	3.83221	0.507589
$58$	24.5756	3.22693
$59$	12.6430	1.64598	0.822989	−	0.568057i	$-0.192305\pi$
$59$	12.6430	1.64598	0.822989	+	0.568057i	$0.192305\pi$
$60$	5.37169	0.693482
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	3.83221	0.486691
$63$	1.68585	0.212397
$64$	−12.1751	−1.52189
$65$	−1.34292	−0.166569
$66$	−3.07896	−0.378994
$67$	−6.10038	−0.745281	−0.372640	−	0.927976i	$-0.621547\pi$
$67$	−6.10038	−0.745281	−0.372640	+	0.927976i	$0.621547\pi$
$68$	20.3503	2.46783
$69$	3.63986	0.438188
$70$	3.14637	0.376063
$71$	1.53948	0.182703	0.0913514	−	0.995819i	$-0.470881\pi$
$71$	1.53948	0.182703	0.0913514	+	0.995819i	$0.470881\pi$
$72$	−5.88240	−0.693248
$73$	−15.3001	−1.79074	−0.895369	−	0.445324i	$-0.853088\pi$
$73$	−15.3001	−1.79074	−0.895369	+	0.445324i	$0.853088\pi$
$74$	19.9572	2.31997
$75$	3.66442	0.423131
$76$	−11.6644	−1.33800
$77$	−1.14637	−0.130640
$78$	−2.68585	−0.304112
$79$	0.882404	0.0992782	0.0496391	−	0.998767i	$-0.484193\pi$
$79$	0.882404	0.0992782	0.0496391	+	0.998767i	$0.484193\pi$
$80$	−1.60688	−0.179655
$81$	−1.10038	−0.122265
$82$	−0.685846	−0.0757390
$83$	−12.1292	−1.33135	−0.665674	−	0.746243i	$-0.731856\pi$
$83$	−12.1292	−1.33135	−0.665674	+	0.746243i	$0.731856\pi$
$84$	4.00000	0.436436
$85$	−7.83221	−0.849523
$86$	−19.1035	−2.05999
$87$	−12.0246	−1.28917
$88$	4.00000	0.426401
$89$	5.73604	0.608019	0.304009	−	0.952669i	$-0.401675\pi$
$89$	5.73604	0.608019	0.304009	+	0.952669i	$0.401675\pi$
$90$	5.30429	0.559121
$91$	−1.00000	−0.104828
$92$	−11.0790	−1.15506
$93$	−1.87506	−0.194434
$94$	−24.8683	−2.56497
$95$	4.48929	0.460591
$96$	4.78623	0.488493
$97$	−5.34292	−0.542492	−0.271246	−	0.962510i	$-0.587436\pi$
$97$	−5.34292	−0.542492	−0.271246	+	0.962510i	$0.587436\pi$
$98$	2.34292	0.236671
$99$	−1.93260	−0.194233
$100$	−11.1537	−1.11537
$101$	11.1464	1.10910	0.554552	−	0.832149i	$-0.312889\pi$
$101$	11.1464	1.10910	0.554552	+	0.832149i	$0.312889\pi$
$102$	−15.6644	−1.55101
$103$	−3.41454	−0.336444	−0.168222	−	0.985749i	$-0.553803\pi$
$103$	−3.41454	−0.336444	−0.168222	+	0.985749i	$0.553803\pi$
$104$	3.48929	0.342153
$105$	−1.53948	−0.150238
$106$	−1.83221	−0.177960
$107$	4.97858	0.481297	0.240649	−	0.970612i	$-0.422640\pi$
$107$	4.97858	0.481297	0.240649	+	0.970612i	$0.422640\pi$
$108$	18.7434	1.80358
$109$	−13.4966	−1.29274	−0.646372	−	0.763023i	$-0.723714\pi$
$109$	−13.4966	−1.29274	−0.646372	+	0.763023i	$0.723714\pi$
$110$	−3.60688	−0.343903
$111$	−9.76481	−0.926835
$112$	−1.19656	−0.113064
$113$	16.4464	1.54715	0.773576	−	0.633704i	$-0.218466\pi$
$113$	16.4464	1.54715	0.773576	+	0.633704i	$0.218466\pi$
$114$	8.97858	0.840921
$115$	4.26396	0.397616
$116$	36.6002	3.39824
$117$	−1.68585	−0.155857
$118$	29.6216	2.72689
$119$	−5.83221	−0.534638
$120$	5.37169	0.490366
$121$	−9.68585	−0.880531
$122$	−4.68585	−0.424237
$123$	0.335577	0.0302579
$124$	5.70727	0.512528
$125$	11.0073	0.984527
$126$	3.94981	0.351877
$127$	12.0575	1.06993	0.534967	−	0.844873i	$-0.320324\pi$
$127$	12.0575	1.06993	0.534967	+	0.844873i	$0.320324\pi$
$128$	−20.1751	−1.78325
$129$	9.34713	0.822969
$130$	−3.14637	−0.275955
$131$	−3.66442	−0.320162	−0.160081	−	0.987104i	$-0.551176\pi$
$131$	−3.66442	−0.320162	−0.160081	+	0.987104i	$0.551176\pi$
$132$	−4.58546	−0.399113
$133$	3.34292	0.289868
$134$	−14.2927	−1.23470
$135$	−7.21377	−0.620862
$136$	20.3503	1.74502
$137$	−13.1035	−1.11951	−0.559755	−	0.828658i	$-0.689105\pi$
$137$	−13.1035	−1.11951	−0.559755	+	0.828658i	$0.689105\pi$
$138$	8.52792	0.725945
$139$	7.49663	0.635856	0.317928	−	0.948115i	$-0.397013\pi$
$139$	7.49663	0.635856	0.317928	+	0.948115i	$0.397013\pi$
$140$	4.68585	0.396026
$141$	12.1678	1.02471
$142$	3.60688	0.302683
$143$	1.14637	0.0958639
$144$	−2.01721	−0.168101
$145$	−14.0863	−1.16980
$146$	−35.8469	−2.96671
$147$	−1.14637	−0.0945506
$148$	29.7220	2.44313
$149$	2.16779	0.177592	0.0887961	−	0.996050i	$-0.471698\pi$
$149$	2.16779	0.177592	0.0887961	+	0.996050i	$0.471698\pi$
$150$	8.58546	0.701000
$151$	14.9112	1.21345	0.606727	−	0.794910i	$-0.292482\pi$
$151$	14.9112	1.21345	0.606727	+	0.794910i	$0.292482\pi$
$152$	−11.6644	−0.946110
$153$	−9.83221	−0.794887
$154$	−2.68585	−0.216432
$155$	−2.19656	−0.176432
$156$	−4.00000	−0.320256
$157$	22.8683	1.82509	0.912546	−	0.408975i	$-0.134114\pi$
$157$	22.8683	1.82509	0.912546	+	0.408975i	$0.134114\pi$
$158$	2.06740	0.164474
$159$	0.896480	0.0710955
$160$	5.60688	0.443263
$161$	3.17513	0.250236
$162$	−2.57812	−0.202556
$163$	7.07896	0.554467	0.277234	−	0.960803i	$-0.410582\pi$
$163$	7.07896	0.554467	0.277234	+	0.960803i	$0.410582\pi$
$164$	−1.02142	−0.0797597
$165$	1.76481	0.137390
$166$	−28.4177	−2.20564
$167$	2.61423	0.202295	0.101148	−	0.994871i	$-0.467749\pi$
$167$	2.61423	0.202295	0.101148	+	0.994871i	$0.467749\pi$
$168$	4.00000	0.308607
$169$	1.00000	0.0769231
$170$	−18.3503	−1.40740
$171$	5.63565	0.430969
$172$	−28.4507	−2.16934
$173$	11.0031	0.836553	0.418276	−	0.908320i	$-0.362634\pi$
$173$	11.0031	0.836553	0.418276	+	0.908320i	$0.362634\pi$
$174$	−28.1726	−2.13576
$175$	3.19656	0.241637
$176$	1.37169	0.103395
$177$	−14.4935	−1.08940
$178$	13.4391	1.00730
$179$	23.9614	1.79096	0.895478	−	0.445105i	$-0.146834\pi$
$179$	23.9614	1.79096	0.895478	+	0.445105i	$0.146834\pi$
$180$	7.89962	0.588803
$181$	6.56090	0.487668	0.243834	−	0.969817i	$-0.421595\pi$
$181$	6.56090	0.487668	0.243834	+	0.969817i	$0.421595\pi$
$182$	−2.34292	−0.173669
$183$	2.29273	0.169484
$184$	−11.0790	−0.816752
$185$	−11.4391	−0.841019
$186$	−4.39312	−0.322119
$187$	6.68585	0.488917
$188$	−37.0361	−2.70114
$189$	−5.37169	−0.390733
$190$	10.5181	0.763060
$191$	−4.39312	−0.317875	−0.158937	−	0.987289i	$-0.550807\pi$
$191$	−4.39312	−0.317875	−0.158937	+	0.987289i	$0.550807\pi$
$192$	13.9572	1.00727
$193$	−8.29273	−0.596924	−0.298462	−	0.954422i	$-0.596474\pi$
$193$	−8.29273	−0.596924	−0.298462	+	0.954422i	$0.596474\pi$
$194$	−12.5181	−0.898744
$195$	1.53948	0.110245
$196$	3.48929	0.249235
$197$	−3.17092	−0.225919	−0.112959	−	0.993600i	$-0.536033\pi$
$197$	−3.17092	−0.225919	−0.112959	+	0.993600i	$0.536033\pi$
$198$	−4.52792	−0.321786
$199$	−13.5970	−0.963867	−0.481934	−	0.876208i	$-0.660065\pi$
$199$	−13.5970	−0.963867	−0.481934	+	0.876208i	$0.660065\pi$
$200$	−11.1537	−0.788687
$201$	6.99327	0.493267
$202$	26.1151	1.83745
$203$	−10.4893	−0.736204
$204$	−23.3288	−1.63335
$205$	0.393115	0.0274564
$206$	−8.00000	−0.557386
$207$	5.35279	0.372045
$208$	1.19656	0.0829663
$209$	−3.83221	−0.265080
$210$	−3.60688	−0.248899
$211$	9.27552	0.638553	0.319277	−	0.947662i	$-0.396560\pi$
$211$	9.27552	0.638553	0.319277	+	0.947662i	$0.396560\pi$
$212$	−2.72869	−0.187407
$213$	−1.76481	−0.120923
$214$	11.6644	0.797364
$215$	10.9498	0.746771
$216$	18.7434	1.27533
$217$	−1.63565	−0.111035
$218$	−31.6216	−2.14168
$219$	17.5395	1.18521
$220$	−5.37169	−0.362159
$221$	5.83221	0.392317
$222$	−22.8782	−1.53548
$223$	−19.5928	−1.31203	−0.656016	−	0.754747i	$-0.727760\pi$
$223$	−19.5928	−1.31203	−0.656016	+	0.754747i	$0.727760\pi$
$224$	4.17513	0.278963
$225$	5.38890	0.359260
$226$	38.5328	2.56316
$227$	−19.6644	−1.30517	−0.652587	−	0.757714i	$-0.726316\pi$
$227$	−19.6644	−1.30517	−0.652587	+	0.757714i	$0.726316\pi$
$228$	13.3717	0.885562
$229$	7.76481	0.513113	0.256556	−	0.966529i	$-0.417412\pi$
$229$	7.76481	0.513113	0.256556	+	0.966529i	$0.417412\pi$
$230$	9.99013	0.658730
$231$	1.31415	0.0864650
$232$	36.6002	2.40292
$233$	12.1966	0.799023	0.399512	−	0.916728i	$-0.369180\pi$
$233$	12.1966	0.799023	0.399512	+	0.916728i	$0.369180\pi$
$234$	−3.94981	−0.258207
$235$	14.2541	0.929835
$236$	44.1151	2.87165
$237$	−1.01156	−0.0657077
$238$	−13.6644	−0.885733
$239$	−10.2927	−0.665781	−0.332891	−	0.942965i	$-0.608024\pi$
$239$	−10.2927	−0.665781	−0.332891	+	0.942965i	$0.608024\pi$
$240$	1.84208	0.118906
$241$	−4.02877	−0.259516	−0.129758	−	0.991546i	$-0.541420\pi$
$241$	−4.02877	−0.259516	−0.129758	+	0.991546i	$0.541420\pi$
$242$	−22.6932	−1.45877
$243$	−14.8536	−0.952861
$244$	−6.97858	−0.446758
$245$	−1.34292	−0.0857962
$246$	0.786230	0.0501282
$247$	−3.34292	−0.212705
$248$	5.70727	0.362412
$249$	13.9044	0.881158
$250$	25.7894	1.63106
$251$	2.91117	0.183752	0.0918758	−	0.995770i	$-0.470714\pi$
$251$	2.91117	0.183752	0.0918758	+	0.995770i	$0.470714\pi$
$252$	5.88240	0.370557
$253$	−3.63986	−0.228836
$254$	28.2499	1.77256
$255$	8.97858	0.562260
$256$	−22.9185	−1.43241
$257$	−19.5970	−1.22243	−0.611214	−	0.791465i	$-0.709319\pi$
$257$	−19.5970	−1.22243	−0.611214	+	0.791465i	$0.709319\pi$
$258$	21.8996	1.36341
$259$	−8.51806	−0.529286
$260$	−4.68585	−0.290604
$261$	−17.6833	−1.09457
$262$	−8.58546	−0.530412
$263$	7.56825	0.466678	0.233339	−	0.972395i	$-0.425035\pi$
$263$	7.56825	0.466678	0.233339	+	0.972395i	$0.425035\pi$
$264$	−4.58546	−0.282216
$265$	1.05019	0.0645128
$266$	7.83221	0.480224
$267$	−6.57560	−0.402420
$268$	−21.2860	−1.30025
$269$	−9.47208	−0.577523	−0.288761	−	0.957401i	$-0.593243\pi$
$269$	−9.47208	−0.577523	−0.288761	+	0.957401i	$0.593243\pi$
$270$	−16.9013	−1.02858
$271$	29.3717	1.78420	0.892102	−	0.451835i	$-0.149230\pi$
$271$	29.3717	1.78420	0.892102	+	0.451835i	$0.149230\pi$
$272$	6.97858	0.423138
$273$	1.14637	0.0693812
$274$	−30.7005	−1.85469
$275$	−3.66442	−0.220973
$276$	12.7005	0.764483
$277$	−1.90383	−0.114390	−0.0571949	−	0.998363i	$-0.518216\pi$
$277$	−1.90383	−0.114390	−0.0571949	+	0.998363i	$0.518216\pi$
$278$	17.5640	1.05342
$279$	−2.75746	−0.165085
$280$	4.68585	0.280033
$281$	−20.5756	−1.22744	−0.613719	−	0.789525i	$-0.710327\pi$
$281$	−20.5756	−1.22744	−0.613719	+	0.789525i	$0.710327\pi$
$282$	28.5082	1.69764
$283$	−26.9933	−1.60458	−0.802292	−	0.596932i	$-0.796386\pi$
$283$	−26.9933	−1.60458	−0.802292	+	0.596932i	$0.796386\pi$
$284$	5.37169	0.318751
$285$	−5.14637	−0.304844
$286$	2.68585	0.158817
$287$	0.292731	0.0172794
$288$	7.03863	0.414756
$289$	17.0147	1.00086
$290$	−33.0031	−1.93801
$291$	6.12494	0.359050
$292$	−53.3864	−3.12420
$293$	−14.9070	−0.870874	−0.435437	−	0.900219i	$-0.643406\pi$
$293$	−14.9070	−0.870874	−0.435437	+	0.900219i	$0.643406\pi$
$294$	−2.68585	−0.156642
$295$	−16.9786	−0.988531
$296$	29.7220	1.72755
$297$	6.15792	0.357319
$298$	5.07896	0.294216
$299$	−3.17513	−0.183623
$300$	12.7862	0.738213
$301$	8.15371	0.469972
$302$	34.9357	2.01033
$303$	−12.7778	−0.734066
$304$	−4.00000	−0.229416
$305$	2.68585	0.153791
$306$	−23.0361	−1.31689
$307$	26.0288	1.48554	0.742770	−	0.669546i	$-0.233512\pi$
$307$	26.0288	1.48554	0.742770	+	0.669546i	$0.233512\pi$
$308$	−4.00000	−0.227921
$309$	3.91431	0.222677
$310$	−5.14637	−0.292294
$311$	19.4966	1.10555	0.552776	−	0.833330i	$-0.313568\pi$
$311$	19.4966	1.10555	0.552776	+	0.833330i	$0.313568\pi$
$312$	−4.00000	−0.226455
$313$	−3.48194	−0.196811	−0.0984055	−	0.995146i	$-0.531374\pi$
$313$	−3.48194	−0.196811	−0.0984055	+	0.995146i	$0.531374\pi$
$314$	53.5787	3.02362
$315$	−2.26396	−0.127560
$316$	3.07896	0.173205
$317$	5.02142	0.282031	0.141016	−	0.990007i	$-0.454963\pi$
$317$	5.02142	0.282031	0.141016	+	0.990007i	$0.454963\pi$
$318$	2.10038	0.117784
$319$	12.0246	0.673246
$320$	16.3503	0.914008
$321$	−5.70727	−0.318549
$322$	7.43910	0.414565
$323$	−19.4966	−1.08482
$324$	−3.83956	−0.213309
$325$	−3.19656	−0.177313
$326$	16.5855	0.918584
$327$	15.4721	0.855608
$328$	−1.02142	−0.0563986
$329$	10.6142	0.585182
$330$	4.13481	0.227614
$331$	−6.14950	−0.338007	−0.169004	−	0.985615i	$-0.554055\pi$
$331$	−6.14950	−0.338007	−0.169004	+	0.985615i	$0.554055\pi$
$332$	−42.3221	−2.32273
$333$	−14.3601	−0.786931
$334$	6.12494	0.335142
$335$	8.19235	0.447596
$336$	1.37169	0.0748320
$337$	−25.6258	−1.39593	−0.697963	−	0.716134i	$-0.745910\pi$
$337$	−25.6258	−1.39593	−0.697963	+	0.716134i	$0.745910\pi$
$338$	2.34292	0.127438
$339$	−18.8536	−1.02399
$340$	−27.3288	−1.48211
$341$	1.87506	0.101540
$342$	13.2039	0.713985
$343$	−1.00000	−0.0539949
$344$	−28.4507	−1.53396
$345$	−4.88806	−0.263164
$346$	25.7795	1.38591
$347$	−16.7005	−0.896532	−0.448266	−	0.893900i	$-0.647958\pi$
$347$	−16.7005	−0.896532	−0.448266	+	0.893900i	$0.647958\pi$
$348$	−41.9572	−2.24914
$349$	−23.5500	−1.26060	−0.630300	−	0.776351i	$-0.717068\pi$
$349$	−23.5500	−1.26060	−0.630300	+	0.776351i	$0.717068\pi$
$350$	7.48929	0.400319
$351$	5.37169	0.286720
$352$	−4.78623	−0.255107
$353$	−7.64973	−0.407154	−0.203577	−	0.979059i	$-0.565257\pi$
$353$	−7.64973	−0.407154	−0.203577	+	0.979059i	$0.565257\pi$
$354$	−33.9572	−1.80480
$355$	−2.06740	−0.109726
$356$	20.0147	1.06078
$357$	6.68585	0.353853
$358$	56.1396	2.96707
$359$	18.3748	0.969786	0.484893	−	0.874573i	$-0.338858\pi$
$359$	18.3748	0.969786	0.484893	+	0.874573i	$0.338858\pi$
$360$	7.89962	0.416346
$361$	−7.82487	−0.411835
$362$	15.3717	0.807918
$363$	11.1035	0.582784
$364$	−3.48929	−0.182888
$365$	20.5468	1.07547
$366$	5.37169	0.280783
$367$	5.33871	0.278679	0.139339	−	0.990245i	$-0.455502\pi$
$367$	5.33871	0.278679	0.139339	+	0.990245i	$0.455502\pi$
$368$	−3.79923	−0.198049
$369$	0.493499	0.0256906
$370$	−26.8009	−1.39331
$371$	0.782020	0.0406004
$372$	−6.54262	−0.339219
$373$	21.5212	1.11433	0.557163	−	0.830403i	$-0.311890\pi$
$373$	21.5212	1.11433	0.557163	+	0.830403i	$0.311890\pi$
$374$	15.6644	0.809988
$375$	−12.6184	−0.651614
$376$	−37.0361	−1.90999
$377$	10.4893	0.540226
$378$	−12.5855	−0.647326
$379$	4.61002	0.236801	0.118400	−	0.992966i	$-0.462223\pi$
$379$	4.61002	0.236801	0.118400	+	0.992966i	$0.462223\pi$
$380$	15.6644	0.803568
$381$	−13.8223	−0.708140
$382$	−10.2927	−0.526622
$383$	−8.33558	−0.425928	−0.212964	−	0.977060i	$-0.568312\pi$
$383$	−8.33558	−0.425928	−0.212964	+	0.977060i	$0.568312\pi$
$384$	23.1281	1.18025
$385$	1.53948	0.0784592
$386$	−19.4292	−0.988922
$387$	13.7459	0.698744
$388$	−18.6430	−0.946455
$389$	−6.44223	−0.326634	−0.163317	−	0.986574i	$-0.552219\pi$
$389$	−6.44223	−0.326634	−0.163317	+	0.986574i	$0.552219\pi$
$390$	3.60688	0.182642
$391$	−18.5181	−0.936498
$392$	3.48929	0.176236
$393$	4.20077	0.211901
$394$	−7.42923	−0.374279
$395$	−1.18500	−0.0596238
$396$	−6.74338	−0.338868
$397$	1.40046	0.0702872	0.0351436	−	0.999382i	$-0.488811\pi$
$397$	1.40046	0.0702872	0.0351436	+	0.999382i	$0.488811\pi$
$398$	−31.8568	−1.59684
$399$	−3.83221	−0.191851
$400$	−3.82487	−0.191243
$401$	−6.97858	−0.348494	−0.174247	−	0.984702i	$-0.555749\pi$
$401$	−6.97858	−0.348494	−0.174247	+	0.984702i	$0.555749\pi$
$402$	16.3847	0.817194
$403$	1.63565	0.0814777
$404$	38.8929	1.93499
$405$	1.47773	0.0734291
$406$	−24.5756	−1.21967
$407$	9.76481	0.484024
$408$	−23.3288	−1.15495
$409$	−18.3790	−0.908785	−0.454392	−	0.890802i	$-0.650144\pi$
$409$	−18.3790	−0.908785	−0.454392	+	0.890802i	$0.650144\pi$
$410$	0.921039	0.0454869
$411$	15.0214	0.740952
$412$	−11.9143	−0.586976
$413$	−12.6430	−0.622121
$414$	12.5412	0.616365
$415$	16.2885	0.799572
$416$	−4.17513	−0.204703
$417$	−8.59388	−0.420844
$418$	−8.97858	−0.439157
$419$	−30.0393	−1.46751	−0.733757	−	0.679412i	$-0.762235\pi$
$419$	−30.0393	−1.46751	−0.733757	+	0.679412i	$0.762235\pi$
$420$	−5.37169	−0.262112
$421$	−8.31729	−0.405360	−0.202680	−	0.979245i	$-0.564965\pi$
$421$	−8.31729	−0.405360	−0.202680	+	0.979245i	$0.564965\pi$
$422$	21.7318	1.05789
$423$	17.8940	0.870034
$424$	−2.72869	−0.132517
$425$	−18.6430	−0.904318
$426$	−4.13481	−0.200332
$427$	2.00000	0.0967868
$428$	17.3717	0.839692
$429$	−1.31415	−0.0634479
$430$	25.6546	1.23717
$431$	9.64973	0.464811	0.232406	−	0.972619i	$-0.425340\pi$
$431$	9.64973	0.464811	0.232406	+	0.972619i	$0.425340\pi$
$432$	6.42754	0.309245
$433$	26.3074	1.26425	0.632127	−	0.774865i	$-0.282182\pi$
$433$	26.3074	1.26425	0.632127	+	0.774865i	$0.282182\pi$
$434$	−3.83221	−0.183952
$435$	16.1481	0.774240
$436$	−47.0937	−2.25538
$437$	10.6142	0.507748
$438$	41.0937	1.96353
$439$	33.8139	1.61385	0.806925	−	0.590654i	$-0.201130\pi$
$439$	33.8139	1.61385	0.806925	+	0.590654i	$0.201130\pi$
$440$	−5.37169	−0.256085
$441$	−1.68585	−0.0802784
$442$	13.6644	0.649950
$443$	26.4464	1.25651	0.628254	−	0.778008i	$-0.283770\pi$
$443$	26.4464	1.25651	0.628254	+	0.778008i	$0.283770\pi$
$444$	−34.0722	−1.61700
$445$	−7.70306	−0.365160
$446$	−45.9044	−2.17364
$447$	−2.48508	−0.117540
$448$	12.1751	0.575221
$449$	2.64300	0.124731	0.0623655	−	0.998053i	$-0.480136\pi$
$449$	2.64300	0.124731	0.0623655	+	0.998053i	$0.480136\pi$
$450$	12.6258	0.595185
$451$	−0.335577	−0.0158017
$452$	57.3864	2.69923
$453$	−17.0937	−0.803130
$454$	−46.0722	−2.16228
$455$	1.34292	0.0629572
$456$	13.3717	0.626187
$457$	−33.6890	−1.57590	−0.787952	−	0.615737i	$-0.788859\pi$
$457$	−33.6890	−1.57590	−0.787952	+	0.615737i	$0.788859\pi$
$458$	18.1923	0.850073
$459$	31.3288	1.46231
$460$	14.8782	0.693699
$461$	33.0790	1.54064	0.770320	−	0.637657i	$-0.220096\pi$
$461$	33.0790	1.54064	0.770320	+	0.637657i	$0.220096\pi$
$462$	3.07896	0.143246
$463$	−2.51806	−0.117024	−0.0585120	−	0.998287i	$-0.518636\pi$
$463$	−2.51806	−0.117024	−0.0585120	+	0.998287i	$0.518636\pi$
$464$	12.5510	0.582667
$465$	2.51806	0.116772
$466$	28.5756	1.32374
$467$	2.57560	0.119184	0.0595922	−	0.998223i	$-0.481020\pi$
$467$	2.57560	0.119184	0.0595922	+	0.998223i	$0.481020\pi$
$468$	−5.88240	−0.271914
$469$	6.10038	0.281690
$470$	33.3963	1.54045
$471$	−26.2155	−1.20794
$472$	44.1151	2.03056
$473$	−9.34713	−0.429782
$474$	−2.37000	−0.108858
$475$	10.6858	0.490300
$476$	−20.3503	−0.932753
$477$	1.31836	0.0603638
$478$	−24.1151	−1.10300
$479$	0.513847	0.0234783	0.0117391	−	0.999931i	$-0.496263\pi$
$479$	0.513847	0.0234783	0.0117391	+	0.999931i	$0.496263\pi$
$480$	−6.42754	−0.293376
$481$	8.51806	0.388390
$482$	−9.43910	−0.429939
$483$	−3.63986	−0.165620
$484$	−33.7967	−1.53621
$485$	7.17513	0.325806
$486$	−34.8009	−1.57860
$487$	36.0575	1.63392	0.816962	−	0.576692i	$-0.195657\pi$
$487$	36.0575	1.63392	0.816962	+	0.576692i	$0.195657\pi$
$488$	−6.97858	−0.315905
$489$	−8.11508	−0.366976
$490$	−3.14637	−0.142138
$491$	−9.22846	−0.416475	−0.208237	−	0.978078i	$-0.566773\pi$
$491$	−9.22846	−0.416475	−0.208237	+	0.978078i	$0.566773\pi$
$492$	1.17092	0.0527893
$493$	61.1758	2.75522
$494$	−7.83221	−0.352388
$495$	2.59533	0.116651
$496$	1.95715	0.0878788
$497$	−1.53948	−0.0690551
$498$	32.5770	1.45981
$499$	1.00314	0.0449065	0.0224533	−	0.999748i	$-0.492852\pi$
$499$	1.00314	0.0449065	0.0224533	+	0.999748i	$0.492852\pi$
$500$	38.4078	1.71765
$501$	−2.99686	−0.133890
$502$	6.82065	0.304421
$503$	−30.3503	−1.35325	−0.676626	−	0.736327i	$-0.736559\pi$
$503$	−30.3503	−1.35325	−0.676626	+	0.736327i	$0.736559\pi$
$504$	5.88240	0.262023
$505$	−14.9687	−0.666099
$506$	−8.52792	−0.379112
$507$	−1.14637	−0.0509119
$508$	42.0722	1.86665
$509$	10.5995	0.469816	0.234908	−	0.972018i	$-0.424521\pi$
$509$	10.5995	0.469816	0.234908	+	0.972018i	$0.424521\pi$
$510$	21.0361	0.931495
$511$	15.3001	0.676836
$512$	−13.3461	−0.589818
$513$	−17.9572	−0.792828
$514$	−45.9143	−2.02519
$515$	4.58546	0.202060
$516$	32.6148	1.43579
$517$	−12.1678	−0.535139
$518$	−19.9572	−0.876867
$519$	−12.6136	−0.553676
$520$	−4.68585	−0.205488
$521$	−16.2646	−0.712564	−0.356282	−	0.934378i	$-0.615956\pi$
$521$	−16.2646	−0.712564	−0.356282	+	0.934378i	$0.615956\pi$
$522$	−41.4307	−1.81337
$523$	7.22219	0.315804	0.157902	−	0.987455i	$-0.449527\pi$
$523$	7.22219	0.315804	0.157902	+	0.987455i	$0.449527\pi$
$524$	−12.7862	−0.558569
$525$	−3.66442	−0.159929
$526$	17.7318	0.773144
$527$	9.53948	0.415546
$528$	−1.57246	−0.0684326
$529$	−12.9185	−0.561675
$530$	2.46052	0.106878
$531$	−21.3142	−0.924955
$532$	11.6644	0.505717
$533$	−0.292731	−0.0126796
$534$	−15.4061	−0.666688
$535$	−6.68585	−0.289054
$536$	−21.2860	−0.919415
$537$	−27.4685	−1.18535
$538$	−22.1923	−0.956780
$539$	1.14637	0.0493775
$540$	−25.1709	−1.08318
$541$	17.3534	0.746081	0.373041	−	0.927815i	$-0.378315\pi$
$541$	17.3534	0.746081	0.373041	+	0.927815i	$0.378315\pi$
$542$	68.8156	2.95588
$543$	−7.52119	−0.322765
$544$	−24.3503	−1.04401
$545$	18.1249	0.776387
$546$	2.68585	0.114944
$547$	−34.1109	−1.45848	−0.729238	−	0.684261i	$-0.760125\pi$
$547$	−34.1109	−1.45848	−0.729238	+	0.684261i	$0.760125\pi$
$548$	−45.7220	−1.95315
$549$	3.37169	0.143900
$550$	−8.58546	−0.366085
$551$	−35.0649	−1.49381
$552$	12.7005	0.540571
$553$	−0.882404	−0.0375236
$554$	−4.46052	−0.189509
$555$	13.1134	0.556632
$556$	26.1579	1.10934
$557$	−13.2222	−0.560242	−0.280121	−	0.959965i	$-0.590375\pi$
$557$	−13.2222	−0.560242	−0.280121	+	0.959965i	$0.590375\pi$
$558$	−6.46052	−0.273496
$559$	−8.15371	−0.344865
$560$	1.60688	0.0679033
$561$	−7.66442	−0.323592
$562$	−48.2070	−2.03349
$563$	−41.3717	−1.74361	−0.871804	−	0.489854i	$-0.837050\pi$
$563$	−41.3717	−1.74361	−0.871804	+	0.489854i	$0.837050\pi$
$564$	42.4569	1.78776
$565$	−22.0863	−0.929178
$566$	−63.2432	−2.65831
$567$	1.10038	0.0462118
$568$	5.37169	0.225391
$569$	−2.68164	−0.112420	−0.0562100	−	0.998419i	$-0.517902\pi$
$569$	−2.68164	−0.112420	−0.0562100	+	0.998419i	$0.517902\pi$
$570$	−12.0575	−0.505035
$571$	−28.9315	−1.21075	−0.605373	−	0.795942i	$-0.706976\pi$
$571$	−28.9315	−1.21075	−0.605373	+	0.795942i	$0.706976\pi$
$572$	4.00000	0.167248
$573$	5.03612	0.210387
$574$	0.685846	0.0286267
$575$	10.1495	0.423263
$576$	20.5254	0.855225
$577$	37.5296	1.56238	0.781189	−	0.624294i	$-0.214613\pi$
$577$	37.5296	1.56238	0.781189	+	0.624294i	$0.214613\pi$
$578$	39.8641	1.65813
$579$	9.50650	0.395077
$580$	−49.1512	−2.04089
$581$	12.1292	0.503202
$582$	14.3503	0.594838
$583$	−0.896480	−0.0371284
$584$	−53.3864	−2.20914
$585$	2.26396	0.0936033
$586$	−34.9259	−1.44277
$587$	23.0649	0.951990	0.475995	−	0.879448i	$-0.342088\pi$
$587$	23.0649	0.951990	0.475995	+	0.879448i	$0.342088\pi$
$588$	−4.00000	−0.164957
$589$	−5.46787	−0.225299
$590$	−39.7795	−1.63770
$591$	3.63504	0.149525
$592$	10.1923	0.418903
$593$	−11.0502	−0.453777	−0.226889	−	0.973921i	$-0.572855\pi$
$593$	−11.0502	−0.453777	−0.226889	+	0.973921i	$0.572855\pi$
$594$	14.4275	0.591969
$595$	7.83221	0.321089
$596$	7.56404	0.309835
$597$	15.5872	0.637940
$598$	−7.43910	−0.304207
$599$	−44.6044	−1.82248	−0.911242	−	0.411870i	$-0.864876\pi$
$599$	−44.6044	−1.82248	−0.911242	+	0.411870i	$0.864876\pi$
$600$	12.7862	0.521996
$601$	47.8715	1.95272	0.976359	−	0.216156i	$-0.0693520\pi$
$601$	47.8715	1.95272	0.976359	+	0.216156i	$0.0693520\pi$
$602$	19.1035	0.778601
$603$	10.2843	0.418809
$604$	52.0294	2.11705
$605$	13.0073	0.528824
$606$	−29.9374	−1.21612
$607$	45.0691	1.82930	0.914649	−	0.404249i	$-0.132467\pi$
$607$	45.0691	1.82930	0.914649	+	0.404249i	$0.132467\pi$
$608$	13.9572	0.566037
$609$	12.0246	0.487260
$610$	6.29273	0.254785
$611$	−10.6142	−0.429406
$612$	−34.3074	−1.38680
$613$	−25.5212	−1.03079	−0.515396	−	0.856952i	$-0.672355\pi$
$613$	−25.5212	−1.03079	−0.515396	+	0.856952i	$0.672355\pi$
$614$	60.9834	2.46109
$615$	−0.450654	−0.0181721
$616$	−4.00000	−0.161165
$617$	29.2432	1.17729	0.588643	−	0.808393i	$-0.299663\pi$
$617$	29.2432	1.17729	0.588643	+	0.808393i	$0.299663\pi$
$618$	9.17092	0.368909
$619$	4.78623	0.192375	0.0961874	−	0.995363i	$-0.469335\pi$
$619$	4.78623	0.192375	0.0961874	+	0.995363i	$0.469335\pi$
$620$	−7.66442	−0.307811
$621$	−17.0558	−0.684428
$622$	45.6791	1.83157
$623$	−5.73604	−0.229810
$624$	−1.37169	−0.0549116
$625$	1.20077	0.0480307
$626$	−8.15792	−0.326056
$627$	4.39312	0.175444
$628$	79.7942	3.18413
$629$	49.6791	1.98084
$630$	−5.30429	−0.211328
$631$	−28.3931	−1.13031	−0.565156	−	0.824984i	$-0.691184\pi$
$631$	−28.3931	−1.13031	−0.565156	+	0.824984i	$0.691184\pi$
$632$	3.07896	0.122475
$633$	−10.6331	−0.422629
$634$	11.7648	0.467240
$635$	−16.1923	−0.642574
$636$	3.12808	0.124036
$637$	1.00000	0.0396214
$638$	28.1726	1.11536
$639$	−2.59533	−0.102670
$640$	27.0937	1.07097
$641$	5.96137	0.235460	0.117730	−	0.993046i	$-0.462438\pi$
$641$	5.96137	0.235460	0.117730	+	0.993046i	$0.462438\pi$
$642$	−13.3717	−0.527739
$643$	31.1940	1.23017	0.615086	−	0.788460i	$-0.289121\pi$
$643$	31.1940	1.23017	0.615086	+	0.788460i	$0.289121\pi$
$644$	11.0790	0.436572
$645$	−12.5525	−0.494253
$646$	−45.6791	−1.79722
$647$	14.9112	0.586219	0.293109	−	0.956079i	$-0.405310\pi$
$647$	14.9112	0.586219	0.293109	+	0.956079i	$0.405310\pi$
$648$	−3.83956	−0.150832
$649$	14.4935	0.568920
$650$	−7.48929	−0.293754
$651$	1.87506	0.0734893
$652$	24.7005	0.967348
$653$	−3.57246	−0.139801	−0.0699006	−	0.997554i	$-0.522268\pi$
$653$	−3.57246	−0.139801	−0.0699006	+	0.997554i	$0.522268\pi$
$654$	36.2499	1.41748
$655$	4.92104	0.192281
$656$	−0.350269	−0.0136757
$657$	25.7936	1.00630
$658$	24.8683	0.969468
$659$	−3.90383	−0.152071	−0.0760357	−	0.997105i	$-0.524226\pi$
$659$	−3.90383	−0.152071	−0.0760357	+	0.997105i	$0.524226\pi$
$660$	6.15792	0.239697
$661$	13.7936	0.536508	0.268254	−	0.963348i	$-0.413553\pi$
$661$	13.7936	0.536508	0.268254	+	0.963348i	$0.413553\pi$
$662$	−14.4078	−0.559975
$663$	−6.68585	−0.259657
$664$	−42.3221	−1.64242
$665$	−4.48929	−0.174087
$666$	−33.6447	−1.30371
$667$	−33.3049	−1.28957
$668$	9.12181	0.352933
$669$	22.4605	0.868374
$670$	19.1940	0.741530
$671$	−2.29273	−0.0885099
$672$	−4.78623	−0.184633
$673$	5.70306	0.219837	0.109918	−	0.993941i	$-0.464941\pi$
$673$	5.70306	0.219837	0.109918	+	0.993941i	$0.464941\pi$
$674$	−60.0393	−2.31263
$675$	−17.1709	−0.660909
$676$	3.48929	0.134203
$677$	35.2614	1.35521	0.677604	−	0.735427i	$-0.263019\pi$
$677$	35.2614	1.35521	0.677604	+	0.735427i	$0.263019\pi$
$678$	−44.1726	−1.69644
$679$	5.34292	0.205043
$680$	−27.3288	−1.04801
$681$	22.5426	0.863835
$682$	4.39312	0.168221
$683$	1.03612	0.0396459	0.0198229	−	0.999804i	$-0.493690\pi$
$683$	1.03612	0.0396459	0.0198229	+	0.999804i	$0.493690\pi$
$684$	19.6644	0.751888
$685$	17.5970	0.672348
$686$	−2.34292	−0.0894532
$687$	−8.90131	−0.339606
$688$	−9.75639	−0.371959
$689$	−0.782020	−0.0297926
$690$	−11.4523	−0.435983
$691$	3.67850	0.139937	0.0699684	−	0.997549i	$-0.477710\pi$
$691$	3.67850	0.139937	0.0699684	+	0.997549i	$0.477710\pi$
$692$	38.3931	1.45949
$693$	1.93260	0.0734132
$694$	−39.1281	−1.48528
$695$	−10.0674	−0.381878
$696$	−41.9572	−1.59038
$697$	−1.70727	−0.0646674
$698$	−55.1758	−2.08843
$699$	−13.9817	−0.528837
$700$	11.1537	0.421571
$701$	−0.0617493	−0.00233224	−0.00116612	−	0.999999i	$-0.500371\pi$
$701$	−0.0617493	−0.00233224	−0.00116612	+	0.999999i	$0.500371\pi$
$702$	12.5855	0.475008
$703$	−28.4752	−1.07396
$704$	−13.9572	−0.526030
$705$	−16.3404	−0.615415
$706$	−17.9227	−0.674531
$707$	−11.1464	−0.419202
$708$	−50.5720	−1.90061
$709$	−42.9834	−1.61428	−0.807138	−	0.590363i	$-0.798985\pi$
$709$	−42.9834	−1.61428	−0.807138	+	0.590363i	$0.798985\pi$
$710$	−4.84377	−0.181783
$711$	−1.48760	−0.0557892
$712$	20.0147	0.750082
$713$	−5.19342	−0.194495
$714$	15.6644	0.586226
$715$	−1.53948	−0.0575733
$716$	83.6081	3.12458
$717$	11.7992	0.440650
$718$	43.0508	1.60664
$719$	17.6546	0.658404	0.329202	−	0.944260i	$-0.393220\pi$
$719$	17.6546	0.658404	0.329202	+	0.944260i	$0.393220\pi$
$720$	2.70896	0.100957
$721$	3.41454	0.127164
$722$	−18.3331	−0.682286
$723$	4.61844	0.171762
$724$	22.8929	0.850807
$725$	−33.5296	−1.24526
$726$	26.0147	0.965496
$727$	−23.8077	−0.882977	−0.441488	−	0.897267i	$-0.645549\pi$
$727$	−23.8077	−0.882977	−0.441488	+	0.897267i	$0.645549\pi$
$728$	−3.48929	−0.129322
$729$	20.3288	0.752920
$730$	48.1396	1.78173
$731$	−47.5542	−1.75885
$732$	8.00000	0.295689
$733$	31.3492	1.15791	0.578954	−	0.815360i	$-0.303461\pi$
$733$	31.3492	1.15791	0.578954	+	0.815360i	$0.303461\pi$
$734$	12.5082	0.461686
$735$	1.53948	0.0567846
$736$	13.2566	0.488645
$737$	−6.99327	−0.257600
$738$	1.15623	0.0425615
$739$	−24.8108	−0.912680	−0.456340	−	0.889806i	$-0.650840\pi$
$739$	−24.8108	−0.912680	−0.456340	+	0.889806i	$0.650840\pi$
$740$	−39.9143	−1.46728
$741$	3.83221	0.140780
$742$	1.83221	0.0672626
$743$	21.3717	0.784051	0.392026	−	0.919954i	$-0.371774\pi$
$743$	21.3717	0.784051	0.392026	+	0.919954i	$0.371774\pi$
$744$	−6.54262	−0.239864
$745$	−2.91117	−0.106657
$746$	50.4225	1.84610
$747$	20.4479	0.748149
$748$	23.3288	0.852987
$749$	−4.97858	−0.181913
$750$	−29.5640	−1.07953
$751$	19.2243	0.701503	0.350751	−	0.936469i	$-0.385926\pi$
$751$	19.2243	0.701503	0.350751	+	0.936469i	$0.385926\pi$
$752$	−12.7005	−0.463141
$753$	−3.33727	−0.121617
$754$	24.5756	0.894990
$755$	−20.0246	−0.728768
$756$	−18.7434	−0.681690
$757$	−19.8610	−0.721860	−0.360930	−	0.932593i	$-0.617541\pi$
$757$	−19.8610	−0.721860	−0.360930	+	0.932593i	$0.617541\pi$
$758$	10.8009	0.392307
$759$	4.17262	0.151456
$760$	15.6644	0.568208
$761$	6.12073	0.221876	0.110938	−	0.993827i	$-0.464614\pi$
$761$	6.12073	0.221876	0.110938	+	0.993827i	$0.464614\pi$
$762$	−32.3847	−1.17317
$763$	13.4966	0.488611
$764$	−15.3288	−0.554578
$765$	13.2039	0.477388
$766$	−19.5296	−0.705634
$767$	12.6430	0.456512
$768$	26.2730	0.948045
$769$	3.82800	0.138041	0.0690206	−	0.997615i	$-0.478013\pi$
$769$	3.82800	0.138041	0.0690206	+	0.997615i	$0.478013\pi$
$770$	3.60688	0.129983
$771$	22.4653	0.809070
$772$	−28.9357	−1.04142
$773$	−6.53635	−0.235096	−0.117548	−	0.993067i	$-0.537503\pi$
$773$	−6.53635	−0.235096	−0.117548	+	0.993067i	$0.537503\pi$
$774$	32.2056	1.15761
$775$	−5.22846	−0.187812
$776$	−18.6430	−0.669245
$777$	9.76481	0.350311
$778$	−15.0937	−0.541134
$779$	0.978577	0.0350612
$780$	5.37169	0.192337
$781$	1.76481	0.0631498
$782$	−43.3864	−1.55149
$783$	56.3452	2.01361
$784$	1.19656	0.0427342
$785$	−30.7104	−1.09610
$786$	9.84208	0.351055
$787$	30.8066	1.09814	0.549068	−	0.835778i	$-0.314983\pi$
$787$	30.8066	1.09814	0.549068	+	0.835778i	$0.314983\pi$
$788$	−11.0643	−0.394148
$789$	−8.67598	−0.308873
$790$	−2.77636	−0.0987786
$791$	−16.4464	−0.584768
$792$	−6.74338	−0.239616
$793$	−2.00000	−0.0710221
$794$	3.28117	0.116444
$795$	−1.20390	−0.0426981
$796$	−47.4439	−1.68161
$797$	−38.8156	−1.37492	−0.687460	−	0.726222i	$-0.741274\pi$
$797$	−38.8156	−1.37492	−0.687460	+	0.726222i	$0.741274\pi$
$798$	−8.97858	−0.317838
$799$	−61.9044	−2.19002
$800$	13.3461	0.471854
$801$	−9.67008	−0.341675
$802$	−16.3503	−0.577348
$803$	−17.5395	−0.618955
$804$	24.4015	0.860576
$805$	−4.26396	−0.150285
$806$	3.83221	0.134984
$807$	10.8585	0.382236
$808$	38.8929	1.36825
$809$	1.04033	0.0365759	0.0182880	−	0.999833i	$-0.494178\pi$
$809$	1.04033	0.0365759	0.0182880	+	0.999833i	$0.494178\pi$
$810$	3.46221	0.121650
$811$	12.6712	0.444944	0.222472	−	0.974939i	$-0.428587\pi$
$811$	12.6712	0.444944	0.222472	+	0.974939i	$0.428587\pi$
$812$	−36.6002	−1.28441
$813$	−33.6707	−1.18088
$814$	22.8782	0.801880
$815$	−9.50650	−0.332998
$816$	−8.00000	−0.280056
$817$	27.2572	0.953610
$818$	−43.0607	−1.50558
$819$	1.68585	0.0589082
$820$	1.37169	0.0479016
$821$	27.0361	0.943567	0.471783	−	0.881714i	$-0.343610\pi$
$821$	27.0361	0.943567	0.471783	+	0.881714i	$0.343610\pi$
$822$	35.1940	1.22753
$823$	−31.6363	−1.10277	−0.551386	−	0.834251i	$-0.685901\pi$
$823$	−31.6363	−1.10277	−0.551386	+	0.834251i	$0.685901\pi$
$824$	−11.9143	−0.415055
$825$	4.20077	0.146252
$826$	−29.6216	−1.03067
$827$	56.4800	1.96400	0.982002	−	0.188872i	$-0.0604832\pi$
$827$	56.4800	1.96400	0.982002	+	0.188872i	$0.0604832\pi$
$828$	18.6774	0.649085
$829$	−42.6760	−1.48220	−0.741099	−	0.671396i	$-0.765695\pi$
$829$	−42.6760	−1.48220	−0.741099	+	0.671396i	$0.765695\pi$
$830$	38.1627	1.32465
$831$	2.18248	0.0757094
$832$	−12.1751	−0.422097
$833$	5.83221	0.202074
$834$	−20.1348	−0.697211
$835$	−3.51071	−0.121493
$836$	−13.3717	−0.462470
$837$	8.78623	0.303697
$838$	−70.3797	−2.43122
$839$	−40.1642	−1.38662	−0.693311	−	0.720639i	$-0.743849\pi$
$839$	−40.1642	−1.38662	−0.693311	+	0.720639i	$0.743849\pi$
$840$	−5.37169	−0.185341
$841$	81.0252	2.79397
$842$	−19.4868	−0.671558
$843$	23.5872	0.812385
$844$	32.3650	1.11405
$845$	−1.34292	−0.0461980
$846$	41.9242	1.44138
$847$	9.68585	0.332810
$848$	−0.935731	−0.0321331
$849$	30.9442	1.06200
$850$	−43.6791	−1.49818
$851$	−27.0460	−0.927124
$852$	−6.15792	−0.210967
$853$	19.6932	0.674282	0.337141	−	0.941454i	$-0.390540\pi$
$853$	19.6932	0.674282	0.337141	+	0.941454i	$0.390540\pi$
$854$	4.68585	0.160346
$855$	−7.56825	−0.258829
$856$	17.3717	0.593752
$857$	1.66442	0.0568556	0.0284278	−	0.999596i	$-0.490950\pi$
$857$	1.66442	0.0568556	0.0284278	+	0.999596i	$0.490950\pi$
$858$	−3.07896	−0.105114
$859$	−41.2944	−1.40895	−0.704474	−	0.709730i	$-0.748817\pi$
$859$	−41.2944	−1.40895	−0.704474	+	0.709730i	$0.748817\pi$
$860$	38.2070	1.30285
$861$	−0.335577	−0.0114364
$862$	22.6086	0.770051
$863$	−31.3288	−1.06645	−0.533223	−	0.845975i	$-0.679019\pi$
$863$	−31.3288	−1.06645	−0.533223	+	0.845975i	$0.679019\pi$
$864$	−22.4275	−0.763000
$865$	−14.7764	−0.502411
$866$	61.6363	2.09449
$867$	−19.5051	−0.662426
$868$	−5.70727	−0.193717
$869$	1.01156	0.0343147
$870$	37.8337	1.28268
$871$	−6.10038	−0.206704
$872$	−47.0937	−1.59479
$873$	9.00735	0.304852
$874$	24.8683	0.841184
$875$	−11.0073	−0.372116
$876$	61.2003	2.06777
$877$	−53.8041	−1.81683	−0.908417	−	0.418065i	$-0.862708\pi$
$877$	−53.8041	−1.81683	−0.908417	+	0.418065i	$0.862708\pi$
$878$	79.2234	2.67366
$879$	17.0888	0.576392
$880$	−1.84208	−0.0620964
$881$	8.09196	0.272625	0.136313	−	0.990666i	$-0.456475\pi$
$881$	8.09196	0.272625	0.136313	+	0.990666i	$0.456475\pi$
$882$	−3.94981	−0.132997
$883$	−27.0705	−0.910996	−0.455498	−	0.890237i	$-0.650539\pi$
$883$	−27.0705	−0.910996	−0.455498	+	0.890237i	$0.650539\pi$
$884$	20.3503	0.684454
$885$	19.4637	0.654264
$886$	61.9620	2.08165
$887$	−38.4935	−1.29249	−0.646243	−	0.763132i	$-0.723661\pi$
$887$	−38.4935	−1.29249	−0.646243	+	0.763132i	$0.723661\pi$
$888$	−34.0722	−1.14339
$889$	−12.0575	−0.404397
$890$	−18.0477	−0.604959
$891$	−1.26144	−0.0422599
$892$	−68.3650	−2.28903
$893$	35.4826	1.18738
$894$	−5.82235	−0.194728
$895$	−32.1783	−1.07560
$896$	20.1751	0.674004
$897$	3.63986	0.121532
$898$	6.19235	0.206641
$899$	17.1568	0.572213
$900$	18.8034	0.626781
$901$	−4.56090	−0.151946
$902$	−0.786230	−0.0261786
$903$	−9.34713	−0.311053
$904$	57.3864	1.90864
$905$	−8.81079	−0.292881
$906$	−40.0491	−1.33054
$907$	15.7031	0.521411	0.260706	−	0.965418i	$-0.416045\pi$
$907$	15.7031	0.521411	0.260706	+	0.965418i	$0.416045\pi$
$908$	−68.6148	−2.27706
$909$	−18.7911	−0.623260
$910$	3.14637	0.104301
$911$	44.9399	1.48893	0.744463	−	0.667663i	$-0.232705\pi$
$911$	44.9399	1.48893	0.744463	+	0.667663i	$0.232705\pi$
$912$	4.58546	0.151840
$913$	−13.9044	−0.460170
$914$	−78.9307	−2.61080
$915$	−3.07896	−0.101787
$916$	27.0937	0.895200
$917$	3.66442	0.121010
$918$	73.4011	2.42260
$919$	−27.2432	−0.898669	−0.449334	−	0.893364i	$-0.648339\pi$
$919$	−27.2432	−0.898669	−0.449334	+	0.893364i	$0.648339\pi$
$920$	14.8782	0.490519
$921$	−29.8385	−0.983211
$922$	77.5015	2.55237
$923$	1.53948	0.0506726
$924$	4.58546	0.150851
$925$	−27.2285	−0.895266
$926$	−5.89962	−0.193873
$927$	5.75639	0.189065
$928$	−43.7942	−1.43761
$929$	−17.1422	−0.562416	−0.281208	−	0.959647i	$-0.590735\pi$
$929$	−17.1422	−0.562416	−0.281208	+	0.959647i	$0.590735\pi$
$930$	5.89962	0.193456
$931$	−3.34292	−0.109560
$932$	42.5573	1.39401
$933$	−22.3503	−0.731715
$934$	6.03442	0.197452
$935$	−8.97858	−0.293631
$936$	−5.88240	−0.192272
$937$	−51.5197	−1.68308	−0.841538	−	0.540197i	$-0.818350\pi$
$937$	−51.5197	−1.68308	−0.841538	+	0.540197i	$0.818350\pi$
$938$	14.2927	0.466674
$939$	3.99158	0.130260
$940$	49.7367	1.62223
$941$	32.7575	1.06786	0.533931	−	0.845528i	$-0.320714\pi$
$941$	32.7575	1.06786	0.533931	+	0.845528i	$0.320714\pi$
$942$	−61.4208	−2.00120
$943$	0.929460	0.0302674
$944$	15.1281	0.492377
$945$	7.21377	0.234664
$946$	−21.8996	−0.712018
$947$	20.9295	0.680116	0.340058	−	0.940404i	$-0.389553\pi$
$947$	20.9295	0.680116	0.340058	+	0.940404i	$0.389553\pi$
$948$	−3.52962	−0.114637
$949$	−15.3001	−0.496662
$950$	25.0361	0.812279
$951$	−5.75639	−0.186664
$952$	−20.3503	−0.659556
$953$	46.4120	1.50343	0.751716	−	0.659487i	$-0.229226\pi$
$953$	46.4120	1.50343	0.751716	+	0.659487i	$0.229226\pi$
$954$	3.08883	0.100004
$955$	5.89962	0.190907
$956$	−35.9143	−1.16155
$957$	−13.7845	−0.445591
$958$	1.20390	0.0388964
$959$	13.1035	0.423135
$960$	−18.7434	−0.604940
$961$	−28.3246	−0.913698
$962$	19.9572	0.643444
$963$	−8.39312	−0.270464
$964$	−14.0575	−0.452763
$965$	11.1365	0.358497
$966$	−8.52792	−0.274381
$967$	−23.2186	−0.746660	−0.373330	−	0.927699i	$-0.621784\pi$
$967$	−23.2186	−0.746660	−0.373330	+	0.927699i	$0.621784\pi$
$968$	−33.7967	−1.08627
$969$	22.3503	0.717994
$970$	16.8108	0.539762
$971$	−14.1004	−0.452503	−0.226251	−	0.974069i	$-0.572647\pi$
$971$	−14.1004	−0.452503	−0.226251	+	0.974069i	$0.572647\pi$
$972$	−51.8286	−1.66240
$973$	−7.49663	−0.240331
$974$	84.4800	2.70692
$975$	3.66442	0.117355
$976$	−2.39312	−0.0766018
$977$	−2.95402	−0.0945074	−0.0472537	−	0.998883i	$-0.515047\pi$
$977$	−2.95402	−0.0945074	−0.0472537	+	0.998883i	$0.515047\pi$
$978$	−19.0130	−0.607969
$979$	6.57560	0.210157
$980$	−4.68585	−0.149684
$981$	22.7533	0.726455
$982$	−21.6216	−0.689972
$983$	−35.0367	−1.11750	−0.558749	−	0.829337i	$-0.688719\pi$
$983$	−35.0367	−1.11750	−0.558749	+	0.829337i	$0.688719\pi$
$984$	1.17092	0.0373277
$985$	4.25831	0.135681
$986$	143.330	4.56456
$987$	−12.1678	−0.387305
$988$	−11.6644	−0.371095
$989$	25.8891	0.823227
$990$	6.08065	0.193256
$991$	47.9718	1.52388	0.761938	−	0.647650i	$-0.224248\pi$
$991$	47.9718	1.52388	0.761938	+	0.647650i	$0.224248\pi$
$992$	−6.82908	−0.216823
$993$	7.04958	0.223712
$994$	−3.60688	−0.114403
$995$	18.2598	0.578873
$996$	48.5166	1.53731
$997$	−38.4422	−1.21748	−0.608739	−	0.793371i	$-0.708324\pi$
$997$	−38.4422	−1.21748	−0.608739	+	0.793371i	$0.708324\pi$
$998$	2.35027	0.0743965
$999$	45.7564	1.44767

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.2.a.d.1.3	✓	3
3.2	odd	2		819.2.a.i.1.1		3
4.3	odd	2		1456.2.a.t.1.2		3
5.4	even	2		2275.2.a.m.1.1		3
7.2	even	3		637.2.e.j.508.1		6
7.3	odd	6		637.2.e.i.79.1		6
7.4	even	3		637.2.e.j.79.1		6
7.5	odd	6		637.2.e.i.508.1		6
7.6	odd	2		637.2.a.j.1.3		3
8.3	odd	2		5824.2.a.bs.1.2		3
8.5	even	2		5824.2.a.by.1.2		3
13.5	odd	4		1183.2.c.f.337.1		6
13.8	odd	4		1183.2.c.f.337.6		6
13.12	even	2		1183.2.a.i.1.1		3
21.20	even	2		5733.2.a.x.1.1		3
91.90	odd	2		8281.2.a.bg.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.a.d.1.3	✓	3	1.1	even	1	trivial
637.2.a.j.1.3		3	7.6	odd	2
637.2.e.i.79.1		6	7.3	odd	6
637.2.e.i.508.1		6	7.5	odd	6
637.2.e.j.79.1		6	7.4	even	3
637.2.e.j.508.1		6	7.2	even	3
819.2.a.i.1.1		3	3.2	odd	2
1183.2.a.i.1.1		3	13.12	even	2
1183.2.c.f.337.1		6	13.5	odd	4
1183.2.c.f.337.6		6	13.8	odd	4
1456.2.a.t.1.2		3	4.3	odd	2
2275.2.a.m.1.1		3	5.4	even	2
5733.2.a.x.1.1		3	21.20	even	2
5824.2.a.bs.1.2		3	8.3	odd	2
5824.2.a.by.1.2		3	8.5	even	2
8281.2.a.bg.1.1		3	91.90	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.a (trivial)

\(f(q)\)	\(=\)	\(q+2.34292 q^{2} -1.14637 q^{3} +3.48929 q^{4} -1.34292 q^{5} -2.68585 q^{6} -1.00000 q^{7} +3.48929 q^{8} -1.68585 q^{9} +O(q^{10})\)	\(q+2.34292 q^{2} -1.14637 q^{3} +3.48929 q^{4} -1.34292 q^{5} -2.68585 q^{6} -1.00000 q^{7} +3.48929 q^{8} -1.68585 q^{9} -3.14637 q^{10} +1.14637 q^{11} -4.00000 q^{12} +1.00000 q^{13} -2.34292 q^{14} +1.53948 q^{15} +1.19656 q^{16} +5.83221 q^{17} -3.94981 q^{18} -3.34292 q^{19} -4.68585 q^{20} +1.14637 q^{21} +2.68585 q^{22} -3.17513 q^{23} -4.00000 q^{24} -3.19656 q^{25} +2.34292 q^{26} +5.37169 q^{27} -3.48929 q^{28} +10.4893 q^{29} +3.60688 q^{30} +1.63565 q^{31} -4.17513 q^{32} -1.31415 q^{33} +13.6644 q^{34} +1.34292 q^{35} -5.88240 q^{36} +8.51806 q^{37} -7.83221 q^{38} -1.14637 q^{39} -4.68585 q^{40} -0.292731 q^{41} +2.68585 q^{42} -8.15371 q^{43} +4.00000 q^{44} +2.26396 q^{45} -7.43910 q^{46} -10.6142 q^{47} -1.37169 q^{48} +1.00000 q^{49} -7.48929 q^{50} -6.68585 q^{51} +3.48929 q^{52} -0.782020 q^{53} +12.5855 q^{54} -1.53948 q^{55} -3.48929 q^{56} +3.83221 q^{57} +24.5756 q^{58} +12.6430 q^{59} +5.37169 q^{60} -2.00000 q^{61} +3.83221 q^{62} +1.68585 q^{63} -12.1751 q^{64} -1.34292 q^{65} -3.07896 q^{66} -6.10038 q^{67} +20.3503 q^{68} +3.63986 q^{69} +3.14637 q^{70} +1.53948 q^{71} -5.88240 q^{72} -15.3001 q^{73} +19.9572 q^{74} +3.66442 q^{75} -11.6644 q^{76} -1.14637 q^{77} -2.68585 q^{78} +0.882404 q^{79} -1.60688 q^{80} -1.10038 q^{81} -0.685846 q^{82} -12.1292 q^{83} +4.00000 q^{84} -7.83221 q^{85} -19.1035 q^{86} -12.0246 q^{87} +4.00000 q^{88} +5.73604 q^{89} +5.30429 q^{90} -1.00000 q^{91} -11.0790 q^{92} -1.87506 q^{93} -24.8683 q^{94} +4.48929 q^{95} +4.78623 q^{96} -5.34292 q^{97} +2.34292 q^{98} -1.93260 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} - 2 q^{3} + 3 q^{4} + 2 q^{5} + 4 q^{6} - 3 q^{7} + 3 q^{8} + 7 q^{9}+O(q^{10}) \) 3 * q + q^2 - 2 * q^3 + 3 * q^4 + 2 * q^5 + 4 * q^6 - 3 * q^7 + 3 * q^8 + 7 * q^9	\( 3 q + q^{2} - 2 q^{3} + 3 q^{4} + 2 q^{5} + 4 q^{6} - 3 q^{7} + 3 q^{8} + 7 q^{9} - 8 q^{10} + 2 q^{11} - 12 q^{12} + 3 q^{13} - q^{14} - 6 q^{15} - q^{16} + 4 q^{17} - 15 q^{18} - 4 q^{19} - 2 q^{20} + 2 q^{21} - 4 q^{22} + 10 q^{23} - 12 q^{24} - 5 q^{25} + q^{26} - 8 q^{27} - 3 q^{28} + 24 q^{29} + 20 q^{30} - 4 q^{31} + 7 q^{32} - 16 q^{33} + 14 q^{34} - 2 q^{35} - q^{36} - 10 q^{38} - 2 q^{39} - 2 q^{40} + 2 q^{41} - 4 q^{42} + 10 q^{43} + 12 q^{44} + 22 q^{45} - 18 q^{46} - 8 q^{47} + 20 q^{48} + 3 q^{49} - 15 q^{50} - 8 q^{51} + 3 q^{52} + 8 q^{53} + 32 q^{54} + 6 q^{55} - 3 q^{56} - 2 q^{57} + 12 q^{58} - 4 q^{59} - 8 q^{60} - 6 q^{61} - 2 q^{62} - 7 q^{63} - 17 q^{64} + 2 q^{65} + 12 q^{66} - 12 q^{67} + 22 q^{68} - 6 q^{69} + 8 q^{70} - 6 q^{71} - q^{72} - 10 q^{73} + 30 q^{74} - 16 q^{75} - 8 q^{76} - 2 q^{77} + 4 q^{78} - 14 q^{79} - 14 q^{80} + 3 q^{81} + 10 q^{82} - 12 q^{83} + 12 q^{84} - 10 q^{85} - 26 q^{86} - 26 q^{87} + 12 q^{88} + 2 q^{89} - 28 q^{90} - 3 q^{91} - 12 q^{92} - 22 q^{93} - 10 q^{94} + 6 q^{95} - 4 q^{96} - 10 q^{97} + q^{98} + 14 q^{99}+O(q^{100}) \) 3 * q + q^2 - 2 * q^3 + 3 * q^4 + 2 * q^5 + 4 * q^6 - 3 * q^7 + 3 * q^8 + 7 * q^9 - 8 * q^10 + 2 * q^11 - 12 * q^12 + 3 * q^13 - q^14 - 6 * q^15 - q^16 + 4 * q^17 - 15 * q^18 - 4 * q^19 - 2 * q^20 + 2 * q^21 - 4 * q^22 + 10 * q^23 - 12 * q^24 - 5 * q^25 + q^26 - 8 * q^27 - 3 * q^28 + 24 * q^29 + 20 * q^30 - 4 * q^31 + 7 * q^32 - 16 * q^33 + 14 * q^34 - 2 * q^35 - q^36 - 10 * q^38 - 2 * q^39 - 2 * q^40 + 2 * q^41 - 4 * q^42 + 10 * q^43 + 12 * q^44 + 22 * q^45 - 18 * q^46 - 8 * q^47 + 20 * q^48 + 3 * q^49 - 15 * q^50 - 8 * q^51 + 3 * q^52 + 8 * q^53 + 32 * q^54 + 6 * q^55 - 3 * q^56 - 2 * q^57 + 12 * q^58 - 4 * q^59 - 8 * q^60 - 6 * q^61 - 2 * q^62 - 7 * q^63 - 17 * q^64 + 2 * q^65 + 12 * q^66 - 12 * q^67 + 22 * q^68 - 6 * q^69 + 8 * q^70 - 6 * q^71 - q^72 - 10 * q^73 + 30 * q^74 - 16 * q^75 - 8 * q^76 - 2 * q^77 + 4 * q^78 - 14 * q^79 - 14 * q^80 + 3 * q^81 + 10 * q^82 - 12 * q^83 + 12 * q^84 - 10 * q^85 - 26 * q^86 - 26 * q^87 + 12 * q^88 + 2 * q^89 - 28 * q^90 - 3 * q^91 - 12 * q^92 - 22 * q^93 - 10 * q^94 + 6 * q^95 - 4 * q^96 - 10 * q^97 + q^98 + 14 * q^99

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