LMFDB - Embedded newform 931.2.f.q.704.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [931,2,Mod(324,931)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(931, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("931.324");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 931 = 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	931.f (of order $3$, degree $2$, not minimal)

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:	no
Analytic conductor:	$7.43407242818$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 17 x^{18} - 22 x^{17} + 160 x^{16} - 182 x^{15} + 935 x^{14} - 842 x^{13} + \cdots + 49 $ x^20 - 2x^19 + 17x^18 - 22x^17 + 160x^16 - 182x^15 + 935x^14 - 842x^13 + 3745x^12 - 3060x^11 + 10134x^10 - 6552x^9 + 18447x^8 - 9966x^7 + 20249x^6 - 4174x^5 + 9686x^4 - 134x^3 + 3637x^2 + 406*x + 49
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			704.10
Root			$1.38026 + 2.39068i$ of defining polynomial
Character	$\chi$	$=$	931.704
Dual form			931.2.f.q.324.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38026 + 2.39068i) q^{2} +(0.0742045 - 0.128526i) q^{3} +(-2.81024 + 4.86748i) q^{4} +(-1.26728 - 2.19500i) q^{5} +0.409686 q^{6} -9.99440 q^{8} +(1.48899 + 2.57900i) q^{9} +O(q^{10})$	\(q+(1.38026 + 2.39068i) q^{2} +(0.0742045 - 0.128526i) q^{3} +(-2.81024 + 4.86748i) q^{4} +(-1.26728 - 2.19500i) q^{5} +0.409686 q^{6} -9.99440 q^{8} +(1.48899 + 2.57900i) q^{9} +(3.49836 - 6.05934i) q^{10} +(-0.791756 + 1.37136i) q^{11} +(0.417064 + 0.722377i) q^{12} -6.17112 q^{13} -0.376152 q^{15} +(-8.17440 - 14.1585i) q^{16} +(-1.51651 + 2.62668i) q^{17} +(-4.11038 + 7.11939i) q^{18} +(-0.500000 - 0.866025i) q^{19} +14.2455 q^{20} -4.37132 q^{22} +(-3.03609 - 5.25866i) q^{23} +(-0.741629 + 1.28454i) q^{24} +(-0.712018 + 1.23325i) q^{25} +(-8.51775 - 14.7532i) q^{26} +0.887185 q^{27} +1.46356 q^{29} +(-0.519188 - 0.899261i) q^{30} +(-3.73241 + 6.46472i) q^{31} +(12.5712 - 21.7740i) q^{32} +(0.117504 + 0.203522i) q^{33} -8.37274 q^{34} -16.7376 q^{36} +(0.246862 + 0.427578i) q^{37} +(1.38026 - 2.39068i) q^{38} +(-0.457924 + 0.793148i) q^{39} +(12.6657 + 21.9377i) q^{40} +6.46929 q^{41} +0.636828 q^{43} +(-4.45005 - 7.70771i) q^{44} +(3.77394 - 6.53666i) q^{45} +(8.38118 - 14.5166i) q^{46} +(1.78272 + 3.08775i) q^{47} -2.42631 q^{48} -3.93108 q^{50} +(0.225064 + 0.389823i) q^{51} +(17.3423 - 30.0378i) q^{52} +(-5.54175 + 9.59860i) q^{53} +(1.22455 + 2.12098i) q^{54} +4.01352 q^{55} -0.148409 q^{57} +(2.02009 + 3.49890i) q^{58} +(-6.86126 + 11.8841i) q^{59} +(1.05708 - 1.83091i) q^{60} +(-1.76806 - 3.06237i) q^{61} -20.6068 q^{62} +36.7086 q^{64} +(7.82056 + 13.5456i) q^{65} +(-0.324371 + 0.561828i) q^{66} +(2.38004 - 4.12235i) q^{67} +(-8.52353 - 14.7632i) q^{68} -0.901165 q^{69} -0.975752 q^{71} +(-14.8815 - 25.7756i) q^{72} +(0.631691 - 1.09412i) q^{73} +(-0.681468 + 1.18034i) q^{74} +(0.105670 + 0.183025i) q^{75} +5.62048 q^{76} -2.52822 q^{78} +(8.14490 + 14.1074i) q^{79} +(-20.7186 + 35.8856i) q^{80} +(-4.40113 + 7.62298i) q^{81} +(8.92930 + 15.4660i) q^{82} +0.284058 q^{83} +7.68741 q^{85} +(0.878988 + 1.52245i) q^{86} +(0.108603 - 0.188105i) q^{87} +(7.91313 - 13.7059i) q^{88} +(-3.08282 - 5.33959i) q^{89} +20.8361 q^{90} +34.1285 q^{92} +(0.553923 + 0.959423i) q^{93} +(-4.92123 + 8.52381i) q^{94} +(-1.26728 + 2.19500i) q^{95} +(-1.86568 - 3.23145i) q^{96} +13.9410 q^{97} -4.71566 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} - 4 q^{3} - 10 q^{4} - 16 q^{5} + 16 q^{6} - 12 q^{8} - 10 q^{9}+O(q^{10}) $ 20 * q + 2 * q^2 - 4 * q^3 - 10 * q^4 - 16 * q^5 + 16 * q^6 - 12 * q^8 - 10 * q^9	$ 20 q + 2 q^{2} - 4 q^{3} - 10 q^{4} - 16 q^{5} + 16 q^{6} - 12 q^{8} - 10 q^{9} + 12 q^{10} - 12 q^{12} + 24 q^{13} - 2 q^{16} - 16 q^{17} - 2 q^{18} - 10 q^{19} + 64 q^{20} + 8 q^{22} - 12 q^{23} + 8 q^{24} - 14 q^{25} - 24 q^{26} + 32 q^{27} - 24 q^{29} + 12 q^{30} - 8 q^{31} + 34 q^{32} + 4 q^{33} + 32 q^{34} - 12 q^{36} - 4 q^{37} + 2 q^{38} + 4 q^{39} + 20 q^{40} + 80 q^{41} + 8 q^{43} + 20 q^{44} - 24 q^{45} + 32 q^{46} - 16 q^{47} + 24 q^{48} - 68 q^{50} + 28 q^{51} + 40 q^{52} - 8 q^{54} + 32 q^{55} + 8 q^{57} + 8 q^{58} - 36 q^{59} - 32 q^{60} - 16 q^{61} - 32 q^{62} + 36 q^{64} - 8 q^{65} - 8 q^{66} + 28 q^{67} - 40 q^{68} + 96 q^{69} - 24 q^{71} - 34 q^{72} - 24 q^{74} + 32 q^{75} + 20 q^{76} + 56 q^{78} + 8 q^{79} - 8 q^{80} - 14 q^{81} + 8 q^{82} + 80 q^{85} + 52 q^{86} + 8 q^{87} + 4 q^{88} - 48 q^{89} - 128 q^{90} + 56 q^{92} - 40 q^{93} + 36 q^{94} - 16 q^{95} + 8 q^{96} - 32 q^{97} - 16 q^{99}+O(q^{100}) $ 20 * q + 2 * q^2 - 4 * q^3 - 10 * q^4 - 16 * q^5 + 16 * q^6 - 12 * q^8 - 10 * q^9 + 12 * q^10 - 12 * q^12 + 24 * q^13 - 2 * q^16 - 16 * q^17 - 2 * q^18 - 10 * q^19 + 64 * q^20 + 8 * q^22 - 12 * q^23 + 8 * q^24 - 14 * q^25 - 24 * q^26 + 32 * q^27 - 24 * q^29 + 12 * q^30 - 8 * q^31 + 34 * q^32 + 4 * q^33 + 32 * q^34 - 12 * q^36 - 4 * q^37 + 2 * q^38 + 4 * q^39 + 20 * q^40 + 80 * q^41 + 8 * q^43 + 20 * q^44 - 24 * q^45 + 32 * q^46 - 16 * q^47 + 24 * q^48 - 68 * q^50 + 28 * q^51 + 40 * q^52 - 8 * q^54 + 32 * q^55 + 8 * q^57 + 8 * q^58 - 36 * q^59 - 32 * q^60 - 16 * q^61 - 32 * q^62 + 36 * q^64 - 8 * q^65 - 8 * q^66 + 28 * q^67 - 40 * q^68 + 96 * q^69 - 24 * q^71 - 34 * q^72 - 24 * q^74 + 32 * q^75 + 20 * q^76 + 56 * q^78 + 8 * q^79 - 8 * q^80 - 14 * q^81 + 8 * q^82 + 80 * q^85 + 52 * q^86 + 8 * q^87 + 4 * q^88 - 48 * q^89 - 128 * q^90 + 56 * q^92 - 40 * q^93 + 36 * q^94 - 16 * q^95 + 8 * q^96 - 32 * q^97 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/931\mathbb{Z}\right)^\times$.

$n$	$248$	$344$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	1.38026	+	2.39068i	0.975992	+	1.69047i	0.676623	+	0.736329i	$0.263443\pi$
$2$	1.38026	+	2.39068i	0.975992	+	1.69047i	0.299368	+	0.954138i	$0.403224\pi$
$3$	0.0742045	−	0.128526i	0.0428420	−	0.0742045i	−0.843809	−	0.536643i	$-0.819692\pi$
$3$	0.0742045	−	0.128526i	0.0428420	−	0.0742045i	0.886651	+	0.462439i	$0.153025\pi$
$4$	−2.81024	+	4.86748i	−1.40512	+	2.43374i
$5$	−1.26728	−	2.19500i	−0.566747	−	0.981634i	−0.996885	−	0.0788709i	$-0.974868\pi$
$5$	−1.26728	−	2.19500i	−0.566747	−	0.981634i	0.430138	−	0.902763i	$-0.358465\pi$
$6$	0.409686			0.167254
$7$		0			0
$7$		0			0
$8$	−9.99440			−3.53355
$9$	1.48899	+	2.57900i	0.496329	+	0.859667i
$10$	3.49836	−	6.05934i	1.10628	−	1.91613i
$11$	−0.791756	+	1.37136i	−0.238724	+	0.413481i	−0.960348	−	0.278803i	$-0.910062\pi$
$11$	−0.791756	+	1.37136i	−0.238724	+	0.413481i	0.721625	+	0.692284i	$0.243396\pi$
$12$	0.417064	+	0.722377i	0.120396	+	0.208532i
$13$	−6.17112			−1.71156			−0.855780	−	0.517340i	$-0.826922\pi$
$13$	−6.17112			−1.71156			−0.855780	+	0.517340i	$0.826922\pi$
$14$		0			0
$15$	−0.376152			−0.0971221
$16$	−8.17440	−	14.1585i	−2.04360	−	3.53962i
$17$	−1.51651	+	2.62668i	−0.367809	+	0.637063i	−0.989223	−	0.146419i	$-0.953225\pi$
$17$	−1.51651	+	2.62668i	−0.367809	+	0.637063i	0.621414	+	0.783482i	$0.286559\pi$
$18$	−4.11038	+	7.11939i	−0.968826	+	1.67806i
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i
$20$	14.2455			3.18539
$21$		0			0
$22$	−4.37132			−0.931969
$23$	−3.03609	−	5.25866i	−0.633068	−	1.09651i	−0.986921	−	0.161205i	$-0.948462\pi$
$23$	−3.03609	−	5.25866i	−0.633068	−	1.09651i	0.353853	−	0.935301i	$-0.384871\pi$
$24$	−0.741629	+	1.28454i	−0.151384	+	0.262206i
$25$	−0.712018	+	1.23325i	−0.142404	+	0.246650i
$26$	−8.51775	−	14.7532i	−1.67047	−	2.89334i
$27$	0.887185			0.170739
$28$		0			0
$29$	1.46356			0.271776			0.135888	−	0.990724i	$-0.456611\pi$
$29$	1.46356			0.271776			0.135888	+	0.990724i	$0.456611\pi$
$30$	−0.519188	−	0.899261i	−0.0947904	−	0.164182i
$31$	−3.73241	+	6.46472i	−0.670361	+	1.16110i	0.307441	+	0.951567i	$0.400527\pi$
$31$	−3.73241	+	6.46472i	−0.670361	+	1.16110i	−0.977802	+	0.209532i	$0.932806\pi$
$32$	12.5712	−	21.7740i	2.22230	−	3.84913i
$33$	0.117504	+	0.203522i	0.0204548	+	0.0354287i
$34$	−8.37274			−1.43591
$35$		0			0
$36$	−16.7376			−2.78961
$37$	0.246862	+	0.427578i	0.0405839	+	0.0702934i	0.885604	−	0.464441i	$-0.153745\pi$
$37$	0.246862	+	0.427578i	0.0405839	+	0.0702934i	−0.845020	+	0.534735i	$0.820412\pi$
$38$	1.38026	−	2.39068i	0.223908	−	0.387820i
$39$	−0.457924	+	0.793148i	−0.0733266	+	0.127005i
$40$	12.6657	+	21.9377i	2.00263	+	3.46866i
$41$	6.46929			1.01033			0.505166	−	0.863022i	$-0.331431\pi$
$41$	6.46929			1.01033			0.505166	+	0.863022i	$0.331431\pi$
$42$		0			0
$43$	0.636828			0.0971153			0.0485576	−	0.998820i	$-0.484538\pi$
$43$	0.636828			0.0971153			0.0485576	+	0.998820i	$0.484538\pi$
$44$	−4.45005	−	7.70771i	−0.670870	−	1.16198i
$45$	3.77394	−	6.53666i	0.562586	−	0.974427i
$46$	8.38118	−	14.5166i	1.23574	−	2.14036i
$47$	1.78272	+	3.08775i	0.260036	+	0.450395i	0.966251	−	0.257602i	$-0.0829323\pi$
$47$	1.78272	+	3.08775i	0.260036	+	0.450395i	−0.706215	+	0.707997i	$0.749599\pi$
$48$	−2.42631			−0.350207
$49$		0			0
$50$	−3.93108			−0.555939
$51$	0.225064	+	0.389823i	0.0315153	+	0.0545861i
$52$	17.3423	−	30.0378i	2.40495	−	4.16549i
$53$	−5.54175	+	9.59860i	−0.761219	+	1.31847i	0.181004	+	0.983482i	$0.442065\pi$
$53$	−5.54175	+	9.59860i	−0.761219	+	1.31847i	−0.942223	+	0.334987i	$0.891268\pi$
$54$	1.22455	+	2.12098i	0.166640	+	0.288628i
$55$	4.01352			0.541183
$56$		0			0
$57$	−0.148409			−0.0196572
$58$	2.02009	+	3.49890i	0.265251	+	0.459429i
$59$	−6.86126	+	11.8841i	−0.893260	+	1.54717i	−0.0573177	+	0.998356i	$0.518255\pi$
$59$	−6.86126	+	11.8841i	−0.893260	+	1.54717i	−0.835943	+	0.548817i	$0.815079\pi$
$60$	1.05708	−	1.83091i	0.136468	−	0.236370i
$61$	−1.76806	−	3.06237i	−0.226377	−	0.392097i	0.730355	−	0.683068i	$-0.239355\pi$
$61$	−1.76806	−	3.06237i	−0.226377	−	0.392097i	−0.956732	+	0.290971i	$0.906022\pi$
$62$	−20.6068			−2.61707
$63$		0			0
$64$	36.7086			4.58857
$65$	7.82056	+	13.5456i	0.970021	+	1.68013i
$66$	−0.324371	+	0.561828i	−0.0399274	+	0.0691562i
$67$	2.38004	−	4.12235i	0.290768	−	0.503626i	−0.683223	−	0.730210i	$-0.739422\pi$
$67$	2.38004	−	4.12235i	0.290768	−	0.503626i	0.973992	+	0.226584i	$0.0727558\pi$
$68$	−8.52353	−	14.7632i	−1.03363	−	1.79030i
$69$	−0.901165			−0.108487
$70$		0			0
$71$	−0.975752			−0.115800			−0.0579002	−	0.998322i	$-0.518441\pi$
$71$	−0.975752			−0.115800			−0.0579002	+	0.998322i	$0.518441\pi$
$72$	−14.8815	−	25.7756i	−1.75381	−	3.03768i
$73$	0.631691	−	1.09412i	0.0739339	−	0.128057i	−0.826688	−	0.562660i	$-0.809778\pi$
$73$	0.631691	−	1.09412i	0.0739339	−	0.128057i	0.900622	+	0.434603i	$0.143111\pi$
$74$	−0.681468	+	1.18034i	−0.0792191	+	0.137212i
$75$	0.105670	+	0.183025i	0.0122017	+	0.0211340i
$76$	5.62048			0.644713
$77$		0			0
$78$	−2.52822			−0.286264
$79$	8.14490	+	14.1074i	0.916373	+	1.58720i	0.804879	+	0.593439i	$0.202230\pi$
$79$	8.14490	+	14.1074i	0.916373	+	1.58720i	0.111493	+	0.993765i	$0.464437\pi$
$80$	−20.7186	+	35.8856i	−2.31641	+	4.01214i
$81$	−4.40113	+	7.62298i	−0.489014	+	0.846998i
$82$	8.92930	+	15.4660i	0.986076	+	1.70793i
$83$	0.284058			0.0311794			0.0155897	−	0.999878i	$-0.495037\pi$
$83$	0.284058			0.0311794			0.0155897	+	0.999878i	$0.495037\pi$
$84$		0			0
$85$	7.68741			0.833817
$86$	0.878988	+	1.52245i	0.0947837	+	0.164170i
$87$	0.108603	−	0.188105i	0.0116434	−	0.0201670i
$88$	7.91313	−	13.7059i	0.843543	−	1.46106i
$89$	−3.08282	−	5.33959i	−0.326778	−	0.565996i	0.655093	−	0.755549i	$-0.272630\pi$
$89$	−3.08282	−	5.33959i	−0.326778	−	0.565996i	−0.981871	+	0.189553i	$0.939296\pi$
$90$	20.8361			2.19632
$91$		0			0
$92$	34.1285			3.55814
$93$	0.553923	+	0.959423i	0.0574391	+	0.0994875i
$94$	−4.92123	+	8.52381i	−0.507586	+	0.879164i
$95$	−1.26728	+	2.19500i	−0.130021	+	0.225202i
$96$	−1.86568	−	3.23145i	−0.190415	−	0.329809i
$97$	13.9410			1.41549			0.707747	−	0.706466i	$-0.249712\pi$
$97$	13.9410			1.41549			0.707747	+	0.706466i	$0.249712\pi$
$98$		0			0
$99$	−4.71566			−0.473942
$100$	−4.00188	−	6.93146i	−0.400188	−	0.693146i
$101$	−8.10764	+	14.0428i	−0.806740	+	1.39731i	0.108370	+	0.994111i	$0.465437\pi$
$101$	−8.10764	+	14.0428i	−0.806740	+	1.39731i	−0.915110	+	0.403204i	$0.867896\pi$
$102$	−0.621294	+	1.07611i	−0.0615173	+	0.106551i
$103$	−3.81393	−	6.60591i	−0.375797	−	0.650900i	0.614649	−	0.788801i	$-0.289298\pi$
$103$	−3.81393	−	6.60591i	−0.375797	−	0.650900i	−0.990446	+	0.137901i	$0.955964\pi$
$104$	61.6766			6.04789
$105$		0			0
$106$	−30.5963			−2.97177
$107$	−1.36246	−	2.35985i	−0.131714	−	0.228136i	0.792623	−	0.609712i	$-0.208715\pi$
$107$	−1.36246	−	2.35985i	−0.131714	−	0.228136i	−0.924337	+	0.381576i	$0.875381\pi$
$108$	−2.49320	+	4.31835i	−0.239908	+	0.415533i
$109$	−1.42275	+	2.46427i	−0.136275	+	0.236035i	−0.926084	−	0.377318i	$-0.876846\pi$
$109$	−1.42275	+	2.46427i	−0.136275	+	0.236035i	0.789809	+	0.613353i	$0.210180\pi$
$110$	5.53971	+	9.59505i	0.528190	+	0.914852i
$111$	0.0732731			0.00695478
$112$		0			0
$113$	−6.07066			−0.571080			−0.285540	−	0.958367i	$-0.592173\pi$
$113$	−6.07066			−0.571080			−0.285540	+	0.958367i	$0.592173\pi$
$114$	−0.204843	−	0.354798i	−0.0191853	−	0.0332299i
$115$	−7.69517	+	13.3284i	−0.717578	+	1.24288i
$116$	−4.11295	+	7.12384i	−0.381878	+	0.661432i
$117$	−9.18871	−	15.9153i	−0.849497	−	1.47137i
$118$	−37.8813			−3.48726
$119$		0			0
$120$	3.75942			0.343186
$121$	4.24624	+	7.35471i	0.386022	+	0.668610i
$122$	4.88077	−	8.45375i	0.441885	−	0.765366i
$123$	0.480050	−	0.831471i	0.0432846	−	0.0749712i
$124$	−20.9779	−	36.3348i	−1.88387	−	3.26296i
$125$	−9.06353			−0.810666
$126$		0			0
$127$	−11.4368			−1.01485			−0.507426	−	0.861695i	$-0.669403\pi$
$127$	−11.4368			−1.01485			−0.507426	+	0.861695i	$0.669403\pi$
$128$	25.5250	+	44.2105i	2.25611	+	3.90770i
$129$	0.0472554	−	0.0818488i	0.00416061	−	0.00720639i
$130$	−21.5888	+	37.3929i	−1.89346	+	3.27958i
$131$	5.96946	+	10.3394i	0.521554	+	0.903358i	0.999686	+	0.0250696i	$0.00798074\pi$
$131$	5.96946	+	10.3394i	0.521554	+	0.903358i	−0.478132	+	0.878288i	$0.658686\pi$
$132$	−1.32085			−0.114966
$133$		0			0
$134$	13.1403			1.13515
$135$	−1.12431	−	1.94737i	−0.0967656	−	0.167603i
$136$	15.1566	−	26.2521i	1.29967	−	2.25110i
$137$	4.63002	−	8.01942i	0.395569	−	0.685145i	−0.597605	−	0.801791i	$-0.703881\pi$
$137$	4.63002	−	8.01942i	0.395569	−	0.685145i	0.993174	+	0.116645i	$0.0372141\pi$
$138$	−1.24384	−	2.15440i	−0.105883	−	0.183395i
$139$	6.14306			0.521048			0.260524	−	0.965467i	$-0.416105\pi$
$139$	6.14306			0.521048			0.260524	+	0.965467i	$0.416105\pi$
$140$		0			0
$141$	0.529142			0.0445618
$142$	−1.34679	−	2.33271i	−0.113020	−	0.195757i
$143$	4.88602	−	8.46284i	0.408590	−	0.707698i
$144$	24.3432	−	42.1636i	2.02860	−	3.51363i
$145$	−1.85475	−	3.21251i	−0.154028	−	0.266785i
$146$	3.48759			0.288635
$147$		0			0
$148$	−2.77497			−0.228101
$149$	−6.03700	−	10.4564i	−0.494571	−	0.856621i	0.505410	−	0.862879i	$-0.331341\pi$
$149$	−6.03700	−	10.4564i	−0.494571	−	0.856621i	−0.999980	+	0.00625812i	$0.998008\pi$
$150$	−0.291704	+	0.505246i	−0.0238175	+	0.0412531i
$151$	−3.22555	+	5.58681i	−0.262491	+	0.454648i	−0.966903	−	0.255143i	$-0.917877\pi$
$151$	−3.22555	+	5.58681i	−0.262491	+	0.454648i	0.704412	+	0.709791i	$0.251211\pi$
$152$	4.99720	+	8.65541i	0.405327	+	0.702046i
$153$	−9.03228			−0.730217
$154$		0			0
$155$	18.9201			1.51970
$156$	−2.57375	−	4.45787i	−0.206065	−	0.356915i
$157$	−2.01092	+	3.48301i	−0.160489	+	0.277975i	−0.935044	−	0.354532i	$-0.884640\pi$
$157$	−2.01092	+	3.48301i	−0.160489	+	0.277975i	0.774555	+	0.632506i	$0.217974\pi$
$158$	−22.4842	+	38.9437i	−1.78874	+	3.09820i
$159$	0.822446	+	1.42452i	0.0652242	+	0.112972i
$160$	−63.7252			−5.03792
$161$		0			0
$162$	−24.2988			−1.90910
$163$	5.99000	+	10.3750i	0.469173	+	0.812631i	0.999379	−	0.0352376i	$-0.0112188\pi$
$163$	5.99000	+	10.3750i	0.469173	+	0.812631i	−0.530206	+	0.847869i	$0.677885\pi$
$164$	−18.1802	+	31.4891i	−1.41964	+	2.45889i
$165$	0.297821	−	0.515841i	0.0231853	−	0.0401582i
$166$	0.392073	+	0.679091i	0.0304308	+	0.0527077i
$167$	15.1250			1.17041			0.585204	−	0.810886i	$-0.301015\pi$
$167$	15.1250			1.17041			0.585204	+	0.810886i	$0.301015\pi$
$168$		0			0
$169$	25.0827			1.92944
$170$	10.6106	+	18.3782i	0.813799	+	1.40954i
$171$	1.48899	−	2.57900i	0.113866	−	0.197221i
$172$	−1.78964	+	3.09974i	−0.136459	+	0.236353i
$173$	−7.41365	−	12.8408i	−0.563649	−	0.976269i	−0.997174	−	0.0751277i	$-0.976064\pi$
$173$	−7.41365	−	12.8408i	−0.563649	−	0.976269i	0.433525	−	0.901142i	$-0.357270\pi$
$174$	0.599600			0.0454555
$175$		0			0
$176$	25.8885			1.95142
$177$	1.01827	+	1.76370i	0.0765381	+	0.132568i
$178$	8.51018	−	14.7401i	0.637865	−	1.10481i
$179$	8.14735	−	14.1116i	0.608961	−	1.05475i	−0.382451	−	0.923976i	$-0.624920\pi$
$179$	8.14735	−	14.1116i	0.608961	−	1.05475i	0.991412	−	0.130776i	$-0.0417469\pi$
$180$	21.2113	+	36.7391i	1.58100	+	2.73837i
$181$	1.03994			0.0772982			0.0386491	−	0.999253i	$-0.487695\pi$
$181$	1.03994			0.0772982			0.0386491	+	0.999253i	$0.487695\pi$
$182$		0			0
$183$	−0.524792			−0.0387938
$184$	30.3439	+	52.5571i	2.23698	+	3.87456i
$185$	0.625689	−	1.08373i	0.0460016	−	0.0796771i
$186$	−1.52912	+	2.64851i	−0.112120	+	0.194198i
$187$	−2.40142	−	4.15938i	−0.175609	−	0.304164i
$188$	−20.0394			−1.46153
$189$		0			0
$190$	−6.99673			−0.507596
$191$	−1.88915	−	3.27211i	−0.136694	−	0.236762i	0.789549	−	0.613687i	$-0.210314\pi$
$191$	−1.88915	−	3.27211i	−0.136694	−	0.236762i	−0.926243	+	0.376926i	$0.876981\pi$
$192$	2.72394	−	4.71800i	0.196583	−	0.340492i
$193$	−5.23392	+	9.06541i	−0.376746	+	0.652543i	−0.990587	−	0.136887i	$-0.956290\pi$
$193$	−5.23392	+	9.06541i	−0.376746	+	0.652543i	0.613841	+	0.789430i	$0.289624\pi$
$194$	19.2422	+	33.3285i	1.38151	+	2.39285i
$195$	2.32128			0.166230
$196$		0			0
$197$	−13.4885			−0.961014			−0.480507	−	0.876991i	$-0.659547\pi$
$197$	−13.4885			−0.961014			−0.480507	+	0.876991i	$0.659547\pi$
$198$	−6.50884	−	11.2736i	−0.462563	−	0.801183i
$199$	8.96470	−	15.5273i	0.635491	−	1.10070i	−0.350920	−	0.936405i	$-0.614131\pi$
$199$	8.96470	−	15.5273i	0.635491	−	1.10070i	0.986411	−	0.164297i	$-0.0525355\pi$
$200$	7.11619	−	12.3256i	0.503191	−	0.871552i
$201$	−0.353219	−	0.611794i	−0.0249142	−	0.0431526i
$202$	−44.7626			−3.14949
$203$		0			0
$204$	−2.52994			−0.177131
$205$	−8.19842	−	14.2001i	−0.572603	−	0.991777i
$206$	10.5284	−	18.2358i	0.733550	−	1.27055i
$207$	9.04139	−	15.6601i	0.628420	−	1.08846i
$208$	50.4452	+	87.3736i	3.49774	+	6.05827i
$209$	1.58351			0.109534
$210$		0			0
$211$	7.90422			0.544149			0.272074	−	0.962276i	$-0.412290\pi$
$211$	7.90422			0.544149			0.272074	+	0.962276i	$0.412290\pi$
$212$	−31.1473	−	53.9487i	−2.13921	−	3.70521i
$213$	−0.0724051	+	0.125409i	−0.00496112	+	0.00859291i
$214$	3.76111	−	6.51443i	0.257104	−	0.445317i
$215$	−0.807041	−	1.39784i	−0.0550398	−	0.0953317i
$216$	−8.86688			−0.603315
$217$		0			0
$218$	−7.85506			−0.532012
$219$	−0.0937486	−	0.162377i	−0.00633494	−	0.0109724i
$220$	−11.2790	+	19.5357i	−0.760427	+	1.31710i
$221$	9.35858	−	16.2095i	0.629526	−	1.09037i
$222$	0.101136	+	0.175173i	0.00678780	+	0.0117568i
$223$	4.22024			0.282608			0.141304	−	0.989966i	$-0.454870\pi$
$223$	4.22024			0.282608			0.141304	+	0.989966i	$0.454870\pi$
$224$		0			0
$225$	−4.24074			−0.282716
$226$	−8.37910	−	14.5130i	−0.557369	−	0.965392i
$227$	8.05724	−	13.9556i	0.534778	−	0.926263i	−0.464396	−	0.885628i	$-0.653729\pi$
$227$	8.05724	−	13.9556i	0.534778	−	0.926263i	0.999174	−	0.0406350i	$-0.0129381\pi$
$228$	0.417064	−	0.722377i	0.0276208	−	0.0478406i
$229$	−6.62239	−	11.4703i	−0.437620	−	0.757980i	0.559885	−	0.828570i	$-0.310845\pi$
$229$	−6.62239	−	11.4703i	−0.437620	−	0.757980i	−0.997505	+	0.0705899i	$0.977512\pi$
$230$	−42.4854			−2.80140
$231$		0			0
$232$	−14.6274			−0.960336
$233$	−8.45371	−	14.6423i	−0.553821	−	0.959246i	−0.997994	−	0.0633050i	$-0.979836\pi$
$233$	−8.45371	−	14.6423i	−0.553821	−	0.959246i	0.444173	−	0.895941i	$-0.353497\pi$
$234$	25.3656	−	43.9346i	1.65820	−	2.87209i
$235$	4.51842	−	7.82613i	0.294749	−	0.510520i
$236$	−38.5636	−	66.7941i	−2.51027	−	4.34792i
$237$	2.41755			0.157037
$238$		0			0
$239$	−6.77655			−0.438338			−0.219169	−	0.975687i	$-0.570335\pi$
$239$	−6.77655			−0.438338			−0.219169	+	0.975687i	$0.570335\pi$
$240$	3.07482	+	5.32575i	0.198479	+	0.343776i
$241$	−11.3126	+	19.5940i	−0.728708	+	1.26216i	0.228721	+	0.973492i	$0.426546\pi$
$241$	−11.3126	+	19.5940i	−0.728708	+	1.26216i	−0.957429	+	0.288668i	$0.906788\pi$
$242$	−11.7218	+	20.3028i	−0.753509	+	1.30512i
$243$	1.98394	+	3.43629i	0.127270	+	0.220438i
$244$	19.8747			1.27235
$245$		0			0
$246$	2.65038			0.168982
$247$	3.08556	+	5.34434i	0.196329	+	0.340052i
$248$	37.3032	−	64.6111i	2.36876	−	4.10281i
$249$	0.0210783	−	0.0365087i	0.00133579	−	0.00231365i
$250$	−12.5100	−	21.6680i	−0.791204	−	1.37040i
$251$	11.3603			0.717053			0.358527	−	0.933520i	$-0.383279\pi$
$251$	11.3603			0.717053			0.358527	+	0.933520i	$0.383279\pi$
$252$		0			0
$253$	9.61537			0.604513
$254$	−15.7858	−	27.3417i	−0.990487	−	1.71557i
$255$	0.570440	−	0.988032i	0.0357224	−	0.0618729i
$256$	−33.7536	+	58.4630i	−2.10960	+	3.65394i
$257$	8.77044	+	15.1908i	0.547085	+	0.947579i	0.998472	+	0.0552511i	$0.0175959\pi$
$257$	8.77044	+	15.1908i	0.547085	+	0.947579i	−0.451387	+	0.892328i	$0.649071\pi$
$258$	0.260899			0.0162429
$259$		0			0
$260$	−87.9105			−5.45198
$261$	2.17922	+	3.77452i	0.134890	+	0.233637i
$262$	−16.4788	+	28.5421i	−1.01806	+	1.76334i
$263$	7.69993	−	13.3367i	0.474798	−	0.822374i	−0.524785	−	0.851235i	$-0.675854\pi$
$263$	7.69993	−	13.3367i	0.474798	−	0.822374i	0.999583	+	0.0288602i	$0.00918776\pi$
$264$	−1.17438	−	2.03408i	−0.0722781	−	0.125189i
$265$	28.0919			1.72567
$266$		0			0
$267$	−0.915035			−0.0559992
$268$	13.3770	+	23.1696i	0.817129	+	1.41531i
$269$	−3.96387	+	6.86563i	−0.241682	+	0.418605i	−0.961193	−	0.275875i	$-0.911032\pi$
$269$	−3.96387	+	6.86563i	−0.241682	+	0.418605i	0.719512	+	0.694480i	$0.244366\pi$
$270$	3.10370	−	5.37576i	0.188885	−	0.327158i
$271$	4.37663	+	7.58055i	0.265862	+	0.460486i	0.967789	−	0.251763i	$-0.0810103\pi$
$271$	4.37663	+	7.58055i	0.265862	+	0.460486i	−0.701927	+	0.712248i	$0.747677\pi$
$272$	49.5864			3.00662
$273$		0			0
$274$	25.5625			1.54429
$275$	−1.12749	−	1.95287i	−0.0679902	−	0.117762i
$276$	2.53249	−	4.38640i	0.152438	−	0.264030i
$277$	−9.23974	+	16.0037i	−0.555162	+	0.961569i	0.442729	+	0.896656i	$0.354010\pi$
$277$	−9.23974	+	16.0037i	−0.555162	+	0.961569i	−0.997891	+	0.0649133i	$0.979323\pi$
$278$	8.47903	+	14.6861i	0.508538	+	0.880814i
$279$	−22.2300			−1.33088
$280$		0			0
$281$	−3.48167			−0.207699			−0.103850	−	0.994593i	$-0.533116\pi$
$281$	−3.48167			−0.207699			−0.103850	+	0.994593i	$0.533116\pi$
$282$	0.730354	+	1.26501i	0.0434919	+	0.0753302i
$283$	5.65905	−	9.80176i	0.336395	−	0.582654i	−0.647356	−	0.762187i	$-0.724125\pi$
$283$	5.65905	−	9.80176i	0.336395	−	0.582654i	0.983752	+	0.179533i	$0.0574588\pi$
$284$	2.74209	−	4.74945i	0.162713	−	0.281828i
$285$	0.188076	+	0.325758i	0.0111407	+	0.0192962i
$286$	26.9759			1.59512
$287$		0			0
$288$	74.8735			4.41196
$289$	3.90037	+	6.75564i	0.229434	+	0.397391i
$290$	5.12006	−	8.86821i	0.300660	−	0.520759i
$291$	1.03448	−	1.79178i	0.0606425	−	0.105036i
$292$	3.55041	+	6.14948i	0.207772	+	0.359871i
$293$	−15.0868			−0.881381			−0.440691	−	0.897659i	$-0.645266\pi$
$293$	−15.0868			−0.881381			−0.440691	+	0.897659i	$0.645266\pi$
$294$		0			0
$295$	34.7807			2.02501
$296$	−2.46724	−	4.27339i	−0.143405	−	0.248386i
$297$	−0.702434	+	1.21665i	−0.0407594	+	0.0705973i
$298$	16.6653	−	28.8651i	0.965393	−	1.67211i
$299$	18.7360	+	32.4518i	1.08353	+	1.87674i
$300$	−1.18783			−0.0685793
$301$		0			0
$302$	−17.8084			−1.02476
$303$	1.20325	+	2.08408i	0.0691246	+	0.119727i
$304$	−8.17440	+	14.1585i	−0.468834	+	0.812045i
$305$	−4.48128	+	7.76180i	−0.256597	+	0.444439i
$306$	−12.4669	−	21.5933i	−0.712685	−	1.23441i
$307$	−6.07516			−0.346728			−0.173364	−	0.984858i	$-0.555464\pi$
$307$	−6.07516			−0.346728			−0.173364	+	0.984858i	$0.555464\pi$
$308$		0			0
$309$	−1.13204			−0.0643996
$310$	26.1147	+	45.2319i	1.48321	+	2.56900i
$311$	−9.25117	+	16.0235i	−0.524586	+	0.908609i	0.475004	+	0.879983i	$0.342446\pi$
$311$	−9.25117	+	16.0235i	−0.524586	+	0.908609i	−0.999590	+	0.0286258i	$0.990887\pi$
$312$	4.57668	−	7.92704i	0.259103	−	0.448780i
$313$	5.92908	+	10.2695i	0.335131	+	0.580464i	0.983510	−	0.180853i	$-0.0578860\pi$
$313$	5.92908	+	10.2695i	0.335131	+	0.580464i	−0.648379	+	0.761318i	$0.724553\pi$
$314$	−11.1024			−0.626543
$315$		0			0
$316$	−91.5564			−5.15045
$317$	1.14215	+	1.97826i	0.0641495	+	0.111110i	0.896316	−	0.443415i	$-0.146233\pi$
$317$	1.14215	+	1.97826i	0.0641495	+	0.111110i	−0.832167	+	0.554525i	$0.812900\pi$
$318$	−2.27038	+	3.93241i	−0.127317	+	0.220519i
$319$	−1.15878	+	2.00707i	−0.0648794	+	0.112374i
$320$	−46.5202	−	80.5753i	−2.60056	−	4.50430i
$321$	−0.404403			−0.0225716
$322$		0			0
$323$	3.03303			0.168762
$324$	−24.7364	−	42.8448i	−1.37425	−	2.38027i
$325$	4.39394	−	7.61053i	0.243732	−	0.422156i
$326$	−16.5355	+	28.6404i	−0.915817	+	1.58624i
$327$	0.211149	+	0.365720i	0.0116765	+	0.0202244i
$328$	−64.6567			−3.57007
$329$		0			0
$330$	1.64428			0.0905148
$331$	−10.6433	−	18.4348i	−0.585011	−	1.01327i	−0.994874	−	0.101121i	$-0.967757\pi$
$331$	−10.6433	−	18.4348i	−0.585011	−	1.01327i	0.409864	−	0.912147i	$-0.365576\pi$
$332$	−0.798269	+	1.38264i	−0.0438107	+	0.0758824i
$333$	−0.735150	+	1.27332i	−0.0402859	+	0.0697773i
$334$	20.8764	+	36.1591i	1.14231	+	1.97854i
$335$	−12.0648			−0.659168
$336$		0			0
$337$	17.1088			0.931978			0.465989	−	0.884791i	$-0.345699\pi$
$337$	17.1088			0.931978			0.465989	+	0.884791i	$0.345699\pi$
$338$	34.6206	+	59.9647i	1.88311	+	3.26165i
$339$	−0.450470	+	0.780237i	−0.0244662	+	0.0423767i
$340$	−21.6035	+	37.4183i	−1.17161	+	2.02929i
$341$	−5.91032	−	10.2370i	−0.320062	−	0.554363i
$342$	8.22076			0.444528
$343$		0			0
$344$	−6.36471			−0.343162
$345$	1.14203	+	1.97806i	0.0614849	+	0.106495i
$346$	20.4655	−	35.4474i	1.10023	−	1.90566i
$347$	−5.39958	+	9.35235i	−0.289865	+	0.502060i	−0.973777	−	0.227504i	$-0.926944\pi$
$347$	−5.39958	+	9.35235i	−0.289865	+	0.502060i	0.683913	+	0.729564i	$0.260277\pi$
$348$	0.610398	+	1.05724i	0.0327208	+	0.0566741i
$349$	−20.7117			−1.10867			−0.554336	−	0.832293i	$-0.687028\pi$
$349$	−20.7117			−1.10867			−0.554336	+	0.832293i	$0.687028\pi$
$350$		0			0
$351$	−5.47492			−0.292230
$352$	19.9067	+	34.4794i	1.06103	+	1.83776i
$353$	−8.45237	+	14.6399i	−0.449874	+	0.779205i	−0.998377	−	0.0569434i	$-0.981865\pi$
$353$	−8.45237	+	14.6399i	−0.449874	+	0.779205i	0.548503	+	0.836148i	$0.315198\pi$
$354$	−2.81096	+	4.86873i	−0.149401	+	0.258770i
$355$	1.23655	+	2.14178i	0.0656295	+	0.113674i
$356$	34.6538			1.83665
$357$		0			0
$358$	44.9819			2.37736
$359$	−7.75355	−	13.4295i	−0.409217	−	0.708784i	0.585586	−	0.810611i	$-0.300865\pi$
$359$	−7.75355	−	13.4295i	−0.409217	−	0.708784i	−0.994802	+	0.101827i	$0.967531\pi$
$360$	−37.7183	+	65.3300i	−1.98793	+	3.44319i
$361$	−0.500000	+	0.866025i	−0.0263158	+	0.0455803i
$362$	1.43539	+	2.48617i	0.0754423	+	0.130670i
$363$	1.26036			0.0661518
$364$		0			0
$365$	−3.20213			−0.167607
$366$	−0.724350	−	1.25461i	−0.0378624	−	0.0655796i
$367$	−1.35891	+	2.35370i	−0.0709343	+	0.122862i	−0.899311	−	0.437310i	$-0.855931\pi$
$367$	−1.35891	+	2.35370i	−0.0709343	+	0.122862i	0.828377	+	0.560171i	$0.189265\pi$
$368$	−49.6364	+	85.9728i	−2.58748	+	4.48164i
$369$	9.63269	+	16.6843i	0.501458	+	0.868550i
$370$	3.45446			0.179589
$371$		0			0
$372$	−6.22662			−0.322835
$373$	8.19582	+	14.1956i	0.424364	+	0.735019i	0.996361	−	0.0852362i	$-0.0271645\pi$
$373$	8.19582	+	14.1956i	0.424364	+	0.735019i	−0.571997	+	0.820256i	$0.693831\pi$
$374$	6.62917	−	11.4821i	0.342786	−	0.593723i
$375$	−0.672554	+	1.16490i	−0.0347305	+	0.0601551i
$376$	−17.8172	−	30.8603i	−0.918851	−	1.59150i
$377$	−9.03179			−0.465161
$378$		0			0
$379$	−26.4759			−1.35998			−0.679988	−	0.733223i	$-0.738015\pi$
$379$	−26.4759			−1.35998			−0.679988	+	0.733223i	$0.738015\pi$
$380$	−7.12274	−	12.3369i	−0.365389	−	0.632872i
$381$	−0.848661	+	1.46992i	−0.0434782	+	0.0753065i
$382$	5.21505	−	9.03273i	0.266825	−	0.462155i
$383$	4.48836	+	7.77407i	0.229345	+	0.397237i	0.957614	−	0.288054i	$-0.0930084\pi$
$383$	4.48836	+	7.77407i	0.229345	+	0.397237i	−0.728269	+	0.685291i	$0.759675\pi$
$384$	7.57627			0.386625
$385$		0			0
$386$	−28.8967			−1.47080
$387$	0.948228	+	1.64238i	0.0482011	+	0.0834868i
$388$	−39.1775	+	67.8575i	−1.98894	+	3.44494i
$389$	11.0078	−	19.0660i	0.558115	−	0.966684i	−0.439539	−	0.898224i	$-0.644858\pi$
$389$	11.0078	−	19.0660i	0.558115	−	0.966684i	0.997654	−	0.0684602i	$-0.0218086\pi$
$390$	3.20397	+	5.54944i	0.162239	+	0.281007i
$391$	18.4171			0.931391
$392$		0			0
$393$	1.77184			0.0893775
$394$	−18.6176	−	32.2467i	−0.937942	−	1.62456i
$395$	20.6438	−	35.7561i	1.03870	−	1.79908i
$396$	13.2521	−	22.9534i	0.665945	−	1.15345i
$397$	1.67742	+	2.90537i	0.0841872	+	0.145817i	0.905045	−	0.425317i	$-0.139837\pi$
$397$	1.67742	+	2.90537i	0.0841872	+	0.145817i	−0.820857	+	0.571133i	$0.806504\pi$
$398$	49.4945			2.48093
$399$		0			0
$400$	23.2813			1.16406
$401$	10.0549	+	17.4156i	0.502117	+	0.869692i	0.999997	+	0.00244597i	$0.000778576\pi$
$401$	10.0549	+	17.4156i	0.502117	+	0.869692i	−0.497880	+	0.867246i	$0.665888\pi$
$402$	0.975070	−	1.68887i	0.0486321	−	0.0842332i
$403$	23.0331	−	39.8946i	1.14736	−	1.98729i
$404$	−45.5688	−	78.9275i	−2.26713	−	3.92679i
$405$	22.3099			1.10859
$406$		0			0
$407$	−0.781819			−0.0387533
$408$	−2.24938	−	3.89604i	−0.111361	−	0.192883i
$409$	1.22413	−	2.12026i	0.0605294	−	0.104840i	−0.834173	−	0.551503i	$-0.814054\pi$
$409$	1.22413	−	2.12026i	0.0605294	−	0.104840i	0.894702	+	0.446663i	$0.147388\pi$
$410$	22.6319	−	39.1996i	1.11771	−	1.93593i
$411$	−0.687136	−	1.19015i	−0.0338939	−	0.0587059i
$412$	42.8722			2.11216
$413$		0			0
$414$	49.9179			2.45333
$415$	−0.359982	−	0.623506i	−0.0176708	−	0.0306067i
$416$	−77.5784	+	134.370i	−3.80359	+	6.58802i
$417$	0.455843	−	0.789542i	0.0223227	−	0.0386641i
$418$	2.18566	+	3.78567i	0.106904	+	0.185163i
$419$	−36.0307			−1.76022			−0.880108	−	0.474774i	$-0.842530\pi$
$419$	−36.0307			−1.76022			−0.880108	+	0.474774i	$0.842530\pi$
$420$		0			0
$421$	−21.2289			−1.03463			−0.517316	−	0.855795i	$-0.673069\pi$
$421$	−21.2289			−1.03463			−0.517316	+	0.855795i	$0.673069\pi$
$422$	10.9099	+	18.8965i	0.531085	+	0.919866i
$423$	−5.30888	+	9.19526i	−0.258127	+	0.447089i
$424$	55.3865	−	95.9323i	2.68981	−	4.65888i
$425$	−2.15957	−	3.74048i	−0.104755	−	0.181440i
$426$	−0.399752			−0.0193680
$427$		0			0
$428$	15.3154			0.740297
$429$	−0.725129	−	1.25596i	−0.0350096	−	0.0606383i
$430$	2.22785	−	3.85876i	0.107437	−	0.186086i
$431$	5.69055	−	9.85632i	0.274104	−	0.474762i	−0.695805	−	0.718231i	$-0.744952\pi$
$431$	5.69055	−	9.85632i	0.274104	−	0.474762i	0.969909	+	0.243469i	$0.0782854\pi$
$432$	−7.25221	−	12.5612i	−0.348922	−	0.604350i
$433$	23.1101			1.11060			0.555300	−	0.831650i	$-0.312604\pi$
$433$	23.1101			1.11060			0.555300	+	0.831650i	$0.312604\pi$
$434$		0			0
$435$	−0.550521			−0.0263955
$436$	−7.99653	−	13.8504i	−0.382964	−	0.663314i
$437$	−3.03609	+	5.25866i	−0.145236	+	0.251556i
$438$	0.258795	−	0.448246i	0.0123657	−	0.0214180i
$439$	13.9851	+	24.2229i	0.667472	+	1.15610i	0.978609	+	0.205730i	$0.0659569\pi$
$439$	13.9851	+	24.2229i	0.667472	+	1.15610i	−0.311137	+	0.950365i	$0.600710\pi$
$440$	−40.1127			−1.91230
$441$		0			0
$442$	51.6691			2.45765
$443$	−14.3176	−	24.7988i	−0.680249	−	1.17823i	−0.974905	−	0.222622i	$-0.928538\pi$
$443$	−14.3176	−	24.7988i	−0.680249	−	1.17823i	0.294656	−	0.955603i	$-0.404795\pi$
$444$	−0.205915	+	0.356655i	−0.00977229	+	0.0169261i
$445$	−7.81361	+	13.5336i	−0.370400	+	0.641552i
$446$	5.82503	+	10.0892i	0.275823	+	0.477740i
$447$	−1.79189			−0.0847535
$448$		0			0
$449$	1.51721			0.0716016			0.0358008	−	0.999359i	$-0.488602\pi$
$449$	1.51721			0.0716016			0.0358008	+	0.999359i	$0.488602\pi$
$450$	−5.85333	−	10.1383i	−0.275929	−	0.477922i
$451$	−5.12210	+	8.87174i	−0.241190	+	0.417754i
$452$	17.0600	−	29.5488i	0.802436	−	1.38986i
$453$	0.478700	+	0.829132i	0.0224913	+	0.0389560i
$454$	44.4844			2.08776
$455$		0			0
$456$	1.48326			0.0694599
$457$	−4.01202	−	6.94903i	−0.187675	−	0.325062i	0.756800	−	0.653647i	$-0.226762\pi$
$457$	−4.01202	−	6.94903i	−0.187675	−	0.325062i	−0.944474	+	0.328585i	$0.893428\pi$
$458$	18.2813	−	31.6641i	0.854227	−	1.47956i
$459$	−1.34543	+	2.33035i	−0.0627992	+	0.108771i
$460$	−43.2505	−	74.9121i	−2.01657	−	3.49279i
$461$	19.3393			0.900719			0.450360	−	0.892847i	$-0.351296\pi$
$461$	19.3393			0.900719			0.450360	+	0.892847i	$0.351296\pi$
$462$		0			0
$463$	32.2738			1.49989			0.749946	−	0.661499i	$-0.230080\pi$
$463$	32.2738			1.49989			0.749946	+	0.661499i	$0.230080\pi$
$464$	−11.9637	−	20.7218i	−0.555402	−	0.961984i
$465$	1.40396	−	2.43172i	0.0651069	−	0.112768i
$466$	23.3366	−	40.4202i	1.08105	−	1.87243i
$467$	−16.0840	−	27.8583i	−0.744278	−	1.28913i	−0.950531	−	0.310629i	$-0.899460\pi$
$467$	−16.0840	−	27.8583i	−0.744278	−	1.28913i	0.206253	−	0.978499i	$-0.433873\pi$
$468$	103.290			4.77458
$469$		0			0
$470$	24.9464			1.15069
$471$	0.298438	+	0.516910i	0.0137513	+	0.0238180i
$472$	68.5742	−	118.774i	3.15639	−	5.46702i
$473$	−0.504212	+	0.873321i	−0.0231837	+	0.0401554i
$474$	3.33685	+	5.77959i	0.153267	+	0.265465i
$475$	1.42404			0.0653392
$476$		0			0
$477$	−33.0064			−1.51126
$478$	−9.35340	−	16.2006i	−0.427815	−	0.740996i
$479$	3.90899	−	6.77058i	0.178606	−	0.309356i	−0.762797	−	0.646638i	$-0.776174\pi$
$479$	3.90899	−	6.77058i	0.178606	−	0.309356i	0.941403	+	0.337283i	$0.109508\pi$
$480$	−4.72869	+	8.19033i	−0.215834	+	0.373836i
$481$	−1.52342	−	2.63863i	−0.0694618	−	0.120311i
$482$	−62.4573			−2.84485
$483$		0			0
$484$	−47.7318			−2.16963
$485$	−17.6672	−	30.6005i	−0.802226	−	1.38950i
$486$	−5.47672	+	9.48595i	−0.248429	+	0.430292i
$487$	14.8990	−	25.8058i	0.675137	−	1.16937i	−0.301292	−	0.953532i	$-0.597418\pi$
$487$	14.8990	−	25.8058i	0.675137	−	1.16937i	0.976429	−	0.215840i	$-0.0692489\pi$
$488$	17.6707	+	30.6066i	0.799916	+	1.38550i
$489$	1.77794			0.0804011
$490$		0			0
$491$	19.8290			0.894872			0.447436	−	0.894316i	$-0.352337\pi$
$491$	19.8290			0.894872			0.447436	+	0.894316i	$0.352337\pi$
$492$	2.69811	+	4.67326i	0.121640	+	0.210687i
$493$	−2.21951	+	3.84430i	−0.0999616	+	0.173139i
$494$	−8.51775	+	14.7532i	−0.383232	+	0.663777i
$495$	5.97608	+	10.3509i	0.268605	+	0.465237i
$496$	122.041			5.47980
$497$		0			0
$498$	0.116374			0.00521486
$499$	15.3361	+	26.5629i	0.686539	+	1.18912i	0.972950	+	0.231014i	$0.0742043\pi$
$499$	15.3361	+	26.5629i	0.686539	+	1.18912i	−0.286411	+	0.958107i	$0.592462\pi$
$500$	25.4707	−	44.1165i	1.13908	−	1.97295i
$501$	1.12234	−	1.94395i	0.0501426	−	0.0868495i
$502$	15.6801	+	27.1588i	0.699838	+	1.21215i
$503$	−36.5009			−1.62750			−0.813748	−	0.581218i	$-0.802576\pi$
$503$	−36.5009			−1.62750			−0.813748	+	0.581218i	$0.802576\pi$
$504$		0			0
$505$	41.0987			1.82887
$506$	13.2717	+	22.9873i	0.589999	+	1.02191i
$507$	1.86125	−	3.22377i	0.0826608	−	0.143173i
$508$	32.1401	−	55.6683i	1.42599	−	2.46988i
$509$	−2.47968	−	4.29494i	−0.109910	−	0.190370i	0.805824	−	0.592156i	$-0.201723\pi$
$509$	−2.47968	−	4.29494i	−0.109910	−	0.190370i	−0.915734	+	0.401786i	$0.868390\pi$
$510$	3.14943			0.139459
$511$		0			0
$512$	−84.2554			−3.72360
$513$	−0.443592	−	0.768324i	−0.0195851	−	0.0339224i
$514$	−24.2110	+	41.9347i	−1.06790	+	1.84966i
$515$	−9.66666	+	16.7431i	−0.425964	+	0.737791i
$516$	0.265598	+	0.460029i	0.0116923	+	0.0202517i
$517$	−5.64591			−0.248307
$518$		0			0
$519$	−2.20050			−0.0965914
$520$	−78.1618	−	135.380i	−3.42762	−	5.93681i
$521$	16.9400	−	29.3409i	0.742153	−	1.28545i	−0.209360	−	0.977839i	$-0.567138\pi$
$521$	16.9400	−	29.3409i	0.742153	−	1.28545i	0.951513	−	0.307608i	$-0.0995285\pi$
$522$	−6.01579	+	10.4196i	−0.263304	+	0.456056i
$523$	12.8544	+	22.2645i	0.562083	+	0.973557i	0.997314	+	0.0732383i	$0.0233334\pi$
$523$	12.8544	+	22.2645i	0.562083	+	0.973557i	−0.435231	+	0.900319i	$0.643333\pi$
$524$	−67.1024			−2.93138
$525$		0			0
$526$	42.5116			1.85360
$527$	−11.3205	−	19.6077i	−0.493129	−	0.854124i
$528$	1.92105	−	3.32735i	0.0836028	−	0.144804i
$529$	−6.93565	+	12.0129i	−0.301550	+	0.522300i
$530$	38.7742	+	67.1588i	1.68424	+	2.91719i
$531$	−40.8653			−1.77340
$532$		0			0
$533$	−39.9227			−1.72924
$534$	−1.26299	−	2.18756i	−0.0546548	−	0.0946648i
$535$	−3.45325	+	5.98121i	−0.149297	+	0.258590i
$536$	−23.7871	+	41.2005i	−1.02745	+	1.77959i
$537$	−1.20914	−	2.09429i	−0.0521782	−	0.0903753i
$538$	−21.8847			−0.943517
$539$		0			0
$540$	12.6384			0.543869
$541$	−10.8586	−	18.8077i	−0.466849	−	0.808606i	0.532434	−	0.846471i	$-0.321277\pi$
$541$	−10.8586	−	18.8077i	−0.466849	−	0.808606i	−0.999283	+	0.0378657i	$0.987944\pi$
$542$	−12.0818	+	20.9263i	−0.518957	+	0.898860i
$543$	0.0771682	−	0.133659i	0.00331160	−	0.00573587i
$544$	38.1288	+	66.0411i	1.63476	+	2.83149i
$545$	7.21211			0.308933
$546$		0			0
$547$	26.1501			1.11810			0.559049	−	0.829135i	$-0.311166\pi$
$547$	26.1501			1.11810			0.559049	+	0.829135i	$0.311166\pi$
$548$	26.0229	+	45.0730i	1.11164	+	1.92542i
$549$	5.26525	−	9.11967i	0.224715	−	0.389218i
$550$	3.11246	−	5.39094i	0.132716	−	0.229870i
$551$	−0.731780	−	1.26748i	−0.0311749	−	0.0539964i
$552$	9.00660			0.383346
$553$		0			0
$554$	−51.0130			−2.16733
$555$	−0.0928578	−	0.160835i	−0.00394160	−	0.00682704i
$556$	−17.2635	+	29.9012i	−0.732134	+	1.26809i
$557$	8.76751	−	15.1858i	0.371492	−	0.643442i	−0.618304	−	0.785939i	$-0.712180\pi$
$557$	8.76751	−	15.1858i	0.371492	−	0.643442i	0.989795	+	0.142497i	$0.0455131\pi$
$558$	−30.6833	−	53.1450i	−1.29893	−	2.24981i
$559$	−3.92994			−0.166219
$560$		0			0
$561$	−0.712784			−0.0300938
$562$	−4.80562	−	8.32357i	−0.202713	−	0.351109i
$563$	11.5155	−	19.9455i	0.485322	−	0.840603i	−0.514536	−	0.857469i	$-0.672036\pi$
$563$	11.5155	−	19.9455i	0.485322	−	0.840603i	0.999858	+	0.0168663i	$0.00536898\pi$
$564$	−1.48701	+	2.57559i	−0.0626146	+	0.108452i
$565$	7.69326	+	13.3251i	0.323658	+	0.560592i
$566$	31.2438			1.31328
$567$		0			0
$568$	9.75205			0.409187
$569$	20.6818	+	35.8220i	0.867027	+	1.50174i	0.865020	+	0.501737i	$0.167305\pi$
$569$	20.6818	+	35.8220i	0.867027	+	1.50174i	0.00200693	+	0.999998i	$0.499361\pi$
$570$	−0.519188	+	0.899261i	−0.0217464	+	0.0376659i
$571$	14.1453	−	24.5004i	0.591964	−	1.02531i	−0.402004	−	0.915638i	$-0.631686\pi$
$571$	14.1453	−	24.5004i	0.591964	−	1.02531i	0.993968	−	0.109673i	$-0.0349805\pi$
$572$	27.4618	+	47.5652i	1.14823	+	1.98880i
$573$	−0.560734			−0.0234250
$574$		0			0
$575$	8.64699			0.360604
$576$	54.6586	+	94.6715i	2.27744	+	3.94464i
$577$	−14.8699	+	25.7554i	−0.619041	+	1.07221i	0.370620	+	0.928785i	$0.379145\pi$
$577$	−14.8699	+	25.7554i	−0.619041	+	1.07221i	−0.989661	+	0.143426i	$0.954188\pi$
$578$	−10.7671	+	18.6491i	−0.447851	+	0.775700i
$579$	0.776760	+	1.34539i	0.0322810	+	0.0559124i
$580$	20.8491			0.865712
$581$		0			0
$582$	5.71143			0.236746
$583$	−8.77544	−	15.1995i	−0.363442	−	0.629499i
$584$	−6.31338	+	10.9351i	−0.261249	+	0.452497i
$585$	−23.2894	+	40.3385i	−0.962899	+	1.66779i
$586$	−20.8237	−	36.0678i	−0.860221	−	1.48995i
$587$	7.21249			0.297691			0.148846	−	0.988860i	$-0.452444\pi$
$587$	7.21249			0.297691			0.148846	+	0.988860i	$0.452444\pi$
$588$		0			0
$589$	7.46482			0.307583
$590$	48.0064	+	83.1495i	1.97639	+	3.42321i
$591$	−1.00091	+	1.73362i	−0.0411717	+	0.0713115i
$592$	4.03590	−	6.99039i	0.165875	−	0.287303i
$593$	−2.58063	−	4.46978i	−0.105974	−	0.183552i	0.808162	−	0.588960i	$-0.200463\pi$
$593$	−2.58063	−	4.46978i	−0.105974	−	0.183552i	−0.914136	+	0.405408i	$0.867129\pi$
$594$	−3.87817			−0.159123
$595$		0			0
$596$	67.8617			2.77972
$597$	−1.33044	−	2.30439i	−0.0544513	−	0.0943125i
$598$	−51.7212	+	89.5838i	−2.11504	+	3.66336i
$599$	−16.4009	+	28.4071i	−0.670121	+	1.16068i	0.307748	+	0.951468i	$0.400425\pi$
$599$	−16.4009	+	28.4071i	−0.670121	+	1.16068i	−0.977869	+	0.209216i	$0.932909\pi$
$600$	−1.05611	−	1.82923i	−0.0431154	−	0.0746780i
$601$	−24.6906			−1.00715			−0.503576	−	0.863951i	$-0.667983\pi$
$601$	−24.6906			−1.00715			−0.503576	+	0.863951i	$0.667983\pi$
$602$		0			0
$603$	14.1754			0.577267
$604$	−18.1291	−	31.4005i	−0.737663	−	1.27767i
$605$	10.7624	−	18.6410i	0.437553	−	0.757865i
$606$	−3.32158	+	5.75315i	−0.134930	+	0.233706i
$607$	8.71111	+	15.0881i	0.353573	+	0.612407i	0.986873	−	0.161500i	$-0.0516332\pi$
$607$	8.71111	+	15.0881i	0.353573	+	0.612407i	−0.633299	+	0.773907i	$0.718300\pi$
$608$	−25.1424			−1.01966
$609$		0			0
$610$	−24.7413			−1.00175
$611$	−11.0013	−	19.0549i	−0.445067	−	0.770878i
$612$	25.3829	−	43.9644i	1.02604	−	1.77716i
$613$	14.0165	−	24.2774i	0.566123	−	0.980554i	−0.430821	−	0.902437i	$-0.641776\pi$
$613$	14.0165	−	24.2774i	0.566123	−	0.980554i	0.996944	−	0.0781163i	$-0.0248906\pi$
$614$	−8.38530	−	14.5238i	−0.338403	−	0.586131i
$615$	−2.43344			−0.0981257
$616$		0			0
$617$	−7.79442			−0.313791			−0.156896	−	0.987615i	$-0.550149\pi$
$617$	−7.79442			−0.313791			−0.156896	+	0.987615i	$0.550149\pi$
$618$	−1.56251	−	2.70635i	−0.0628534	−	0.108865i
$619$	10.5543	−	18.2805i	0.424212	−	0.734757i	−0.572134	−	0.820160i	$-0.693884\pi$
$619$	10.5543	−	18.2805i	0.424212	−	0.734757i	0.996346	+	0.0854029i	$0.0272177\pi$
$620$	−53.1700	+	92.0931i	−2.13536	+	3.69855i
$621$	−2.69357	−	4.66540i	−0.108089	−	0.187216i
$622$	−51.0761			−2.04797
$623$		0			0
$624$	14.9730			0.599401
$625$	15.0462	+	26.0607i	0.601846	+	1.04243i
$626$	−16.3673	+	28.3491i	−0.654171	+	1.13306i
$627$	0.117504	−	0.203522i	0.00469265	−	0.00812790i
$628$	−11.3023	−	19.5762i	−0.451012	−	0.781175i
$629$	−1.49748			−0.0597084
$630$		0			0
$631$	27.8768			1.10976			0.554880	−	0.831931i	$-0.312764\pi$
$631$	27.8768			1.10976			0.554880	+	0.831931i	$0.312764\pi$
$632$	−81.4034	−	140.995i	−3.23805	−	5.60847i
$633$	0.586528	−	1.01590i	0.0233124	−	0.0403783i
$634$	−3.15293	+	5.46103i	−0.125219	+	0.216885i
$635$	14.4937	+	25.1038i	0.575164	+	0.996213i
$636$	−9.24507			−0.366591
$637$		0			0
$638$	−6.39769			−0.253287
$639$	−1.45288	−	2.51647i	−0.0574751	−	0.0995498i
$640$	64.6948	−	112.055i	2.55729	−	4.42935i
$641$	−11.2764	+	19.5312i	−0.445390	+	0.771438i	−0.998079	−	0.0619495i	$-0.980268\pi$
$641$	−11.2764	+	19.5312i	−0.445390	+	0.771438i	0.552690	+	0.833387i	$0.313602\pi$
$642$	−0.558182	−	0.966799i	−0.0220297	−	0.0381565i
$643$	16.1900			0.638472			0.319236	−	0.947675i	$-0.396574\pi$
$643$	16.1900			0.638472			0.319236	+	0.947675i	$0.396574\pi$
$644$		0			0
$645$	−0.239544			−0.00943205
$646$	4.18637	+	7.25100i	0.164710	+	0.285287i
$647$	14.6616	−	25.3947i	0.576408	−	0.998368i	−0.419479	−	0.907765i	$-0.637787\pi$
$647$	14.6616	−	25.3947i	0.576408	−	0.998368i	0.995887	−	0.0906030i	$-0.0288794\pi$
$648$	43.9867	−	76.1871i	1.72796	−	2.99291i
$649$	−10.8649	−	18.8186i	−0.426485	−	0.738693i
$650$	24.2592			0.951522
$651$		0			0
$652$	−67.3333			−2.63697
$653$	3.14438	+	5.44623i	0.123049	+	0.213127i	0.920969	−	0.389637i	$-0.127399\pi$
$653$	3.14438	+	5.44623i	0.123049	+	0.213127i	−0.797920	+	0.602764i	$0.794066\pi$
$654$	−0.582880	+	1.00958i	−0.0227924	+	0.0394776i
$655$	15.1300	−	26.2059i	0.591178	−	1.02395i
$656$	−52.8826	−	91.5953i	−2.06472	−	3.57619i
$657$	3.76232			0.146782
$658$		0			0
$659$	−8.10004			−0.315533			−0.157766	−	0.987476i	$-0.550429\pi$
$659$	−8.10004			−0.315533			−0.157766	+	0.987476i	$0.550429\pi$
$660$	1.67390	+	2.89927i	0.0651563	+	0.112854i
$661$	4.97706	−	8.62052i	0.193585	−	0.335299i	−0.752851	−	0.658191i	$-0.771322\pi$
$661$	4.97706	−	8.62052i	0.193585	−	0.335299i	0.946436	+	0.322892i	$0.104655\pi$
$662$	29.3811	−	50.8896i	1.14193	−	1.97788i
$663$	−1.38890	−	2.40564i	−0.0539403	−	0.0934273i
$664$	−2.83899			−0.110174
$665$		0			0
$666$	−4.05879			−0.157275
$667$	−4.44349	−	7.69636i	−0.172053	−	0.298004i
$668$	−42.5049	+	73.6206i	−1.64456	+	2.84847i
$669$	0.313160	−	0.542410i	0.0121075	−	0.0209708i
$670$	−16.6525	−	28.8430i	−0.643342	−	1.11430i
$671$	5.59950			0.216166
$672$		0			0
$673$	−35.7331			−1.37741			−0.688704	−	0.725042i	$-0.741820\pi$
$673$	−35.7331			−1.37741			−0.688704	+	0.725042i	$0.741820\pi$
$674$	23.6147	+	40.9018i	0.909602	+	1.57548i
$675$	−0.631691	+	1.09412i	−0.0243138	+	0.0421127i
$676$	−70.4883	+	122.089i	−2.71109	+	4.69574i
$677$	−2.71740	−	4.70667i	−0.104438	−	0.180892i	0.809070	−	0.587712i	$-0.199971\pi$
$677$	−2.71740	−	4.70667i	−0.104438	−	0.180892i	−0.913508	+	0.406820i	$0.866638\pi$
$678$	−2.48707			−0.0955152
$679$		0			0
$680$	−76.8311			−2.94634
$681$	−1.19577	−	2.07113i	−0.0458219	−	0.0793658i
$682$	16.3156	−	28.2594i	0.624755	−	1.08211i
$683$	−10.4794	+	18.1508i	−0.400982	+	0.694520i	−0.993845	−	0.110783i	$-0.964664\pi$
$683$	−10.4794	+	18.1508i	−0.400982	+	0.694520i	0.592863	+	0.805303i	$0.297998\pi$
$684$	8.36882	+	14.4952i	0.319990	+	0.554239i
$685$	−23.4702			−0.896749
$686$		0			0
$687$	−1.96564			−0.0749940
$688$	−5.20568	−	9.01651i	−0.198465	−	0.343751i
$689$	34.1988	−	59.2341i	1.30287	−	2.25664i
$690$	−3.15260	+	5.46047i	−0.120018	+	0.207876i
$691$	−20.5313	−	35.5613i	−0.781049	−	1.35282i	−0.931331	−	0.364173i	$-0.881352\pi$
$691$	−20.5313	−	35.5613i	−0.781049	−	1.35282i	0.150283	−	0.988643i	$-0.451982\pi$
$692$	83.3365			3.16798
$693$		0			0
$694$	−29.8113			−1.13162
$695$	−7.78500	−	13.4840i	−0.295302	−	0.511478i
$696$	−1.08542	+	1.88000i	−0.0411427	+	0.0712612i
$697$	−9.81076	+	16.9927i	−0.371609	+	0.643646i
$698$	−28.5875	−	49.5151i	−1.08205	−	1.87417i
$699$	−2.50921			−0.0949071
$700$		0			0
$701$	−39.6574			−1.49784			−0.748920	−	0.662661i	$-0.769427\pi$
$701$	−39.6574			−1.49784			−0.748920	+	0.662661i	$0.769427\pi$
$702$	−7.55682	−	13.0888i	−0.285214	−	0.494004i
$703$	0.246862	−	0.427578i	0.00931059	−	0.0161264i
$704$	−29.0642	+	50.3408i	−1.09540	+	1.89729i
$705$	−0.670573	−	1.16147i	−0.0252552	−	0.0437434i
$706$	−46.6659			−1.75629
$707$		0			0
$708$	−11.4464			−0.430180
$709$	19.3514	+	33.5176i	0.726757	+	1.25878i	0.958247	+	0.285943i	$0.0923068\pi$
$709$	19.3514	+	33.5176i	0.726757	+	1.25878i	−0.231489	+	0.972837i	$0.574360\pi$
$710$	−3.41353	+	5.91242i	−0.128108	+	0.221889i
$711$	−24.2553	+	42.0114i	−0.909645	+	1.57555i
$712$	30.8109	+	53.3661i	1.15469	+	1.99998i
$713$	45.3277			1.69754
$714$		0			0
$715$	−24.7679			−0.926267
$716$	45.7920	+	79.3140i	1.71133	+	2.96410i
$717$	−0.502850	+	0.870962i	−0.0187793	+	0.0325267i
$718$	21.4038	−	37.0725i	0.798784	−	1.38353i
$719$	−12.7472	−	22.0788i	−0.475390	−	0.823400i	0.524212	−	0.851588i	$-0.324360\pi$
$719$	−12.7472	−	22.0788i	−0.475390	−	0.823400i	−0.999603	+	0.0281872i	$0.991027\pi$
$720$	−123.399			−4.59880
$721$		0			0
$722$	−2.76052			−0.102736
$723$	1.67889	+	2.90792i	0.0624386	+	0.108147i
$724$	−2.92248	+	5.06188i	−0.108613	+	0.188123i
$725$	−1.04208	+	1.80494i	−0.0387019	+	0.0670336i
$726$	1.73963	+	3.01312i	0.0645636	+	0.111827i
$727$	22.6721			0.840860			0.420430	−	0.907325i	$-0.361879\pi$
$727$	22.6721			0.840860			0.420430	+	0.907325i	$0.361879\pi$
$728$		0			0
$729$	−25.8179			−0.956219
$730$	−4.41977	−	7.65527i	−0.163583	−	0.283334i
$731$	−0.965758	+	1.67274i	−0.0357198	+	0.0618686i
$732$	1.47479	−	2.55441i	0.0545099	−	0.0944139i
$733$	4.75217	+	8.23099i	0.175525	+	0.304019i	0.940343	−	0.340228i	$-0.110504\pi$
$733$	4.75217	+	8.23099i	0.175525	+	0.304019i	−0.764818	+	0.644247i	$0.777171\pi$
$734$	−7.50258			−0.276925
$735$		0			0
$736$	−152.669			−5.62746
$737$	3.76883	+	6.52780i	0.138827	+	0.240455i
$738$	−26.5912	+	46.0574i	−0.978837	+	1.69540i
$739$	−7.11433	+	12.3224i	−0.261705	+	0.453286i	−0.966695	−	0.255931i	$-0.917618\pi$
$739$	−7.11433	+	12.3224i	−0.261705	+	0.453286i	0.704990	+	0.709217i	$0.250951\pi$
$740$	3.51667	+	6.09105i	0.129275	+	0.223912i
$741$	0.915849			0.0336445
$742$		0			0
$743$	−32.0267			−1.17494			−0.587472	−	0.809244i	$-0.699877\pi$
$743$	−32.0267			−1.17494			−0.587472	+	0.809244i	$0.699877\pi$
$744$	−5.53613	−	9.58886i	−0.202964	−	0.351545i
$745$	−15.3012	+	26.5024i	−0.560592	+	0.970974i
$746$	−22.6247	+	39.1872i	−0.828351	+	1.43475i
$747$	0.422958	+	0.732585i	0.0154752	+	0.0268039i
$748$	26.9942			0.987007
$749$		0			0
$750$	−3.71320			−0.135587
$751$	3.77679	+	6.54159i	0.137817	+	0.238706i	0.926670	−	0.375876i	$-0.122658\pi$
$751$	3.77679	+	6.54159i	0.137817	+	0.238706i	−0.788853	+	0.614582i	$0.789325\pi$
$752$	29.1453	−	50.4811i	1.06282	−	1.84086i
$753$	0.842982	−	1.46009i	0.0307200	−	0.0532085i
$754$	−12.4662	−	21.5921i	−0.453993	−	0.786339i
$755$	16.3507			0.595064
$756$		0			0
$757$	−25.3179			−0.920193			−0.460097	−	0.887869i	$-0.652185\pi$
$757$	−25.3179			−0.920193			−0.460097	+	0.887869i	$0.652185\pi$
$758$	−36.5436	−	63.2954i	−1.32732	−	2.29899i
$759$	0.713503	−	1.23582i	0.0258985	−	0.0448575i
$760$	12.6657	−	21.9377i	0.459435	−	0.795765i
$761$	−2.57472	−	4.45955i	−0.0933337	−	0.161659i	0.815578	−	0.578647i	$-0.196419\pi$
$761$	−2.57472	−	4.45955i	−0.0933337	−	0.161659i	−0.908912	+	0.416988i	$0.863086\pi$
$762$	−4.68549			−0.169738
$763$		0			0
$764$	21.2359			0.768287
$765$	11.4465	+	19.8259i	0.413848	+	0.716805i
$766$	−12.3902	+	21.4605i	−0.447677	+	0.775399i
$767$	42.3417	−	73.3379i	1.52887	−	2.64808i
$768$	5.00934	+	8.67643i	0.180759	+	0.313084i
$769$	−30.5976			−1.10338			−0.551689	−	0.834050i	$-0.686017\pi$
$769$	−30.5976			−1.10338			−0.551689	+	0.834050i	$0.686017\pi$
$770$		0			0
$771$	2.60322			0.0937528
$772$	−29.4171	−	50.9519i	−1.05874	−	1.83380i
$773$	−24.8448	+	43.0325i	−0.893606	+	1.54777i	−0.0580865	+	0.998312i	$0.518500\pi$
$773$	−24.8448	+	43.0325i	−0.893606	+	1.54777i	−0.835520	+	0.549460i	$0.814833\pi$
$774$	−2.61760	+	4.53382i	−0.0940878	+	0.162965i
$775$	−5.31509	−	9.20600i	−0.190923	−	0.330689i
$776$	−139.332			−5.00173
$777$		0			0
$778$	60.7743			2.17886
$779$	−3.23464	−	5.60257i	−0.115893	−	0.200733i
$780$	−6.52335	+	11.2988i	−0.233573	+	0.404561i
$781$	0.772558	−	1.33811i	0.0276443	−	0.0478813i
$782$	25.4204	+	44.0293i	0.909030	+	1.57449i
$783$	1.29845			0.0464027
$784$		0			0
$785$	10.1936			0.363826
$786$	2.44560	+	4.23591i	0.0872317	+	0.151090i
$787$	−6.73224	+	11.6606i	−0.239978	+	0.415655i	−0.960708	−	0.277562i	$-0.910474\pi$
$787$	−6.73224	+	11.6606i	−0.239978	+	0.415655i	0.720729	+	0.693217i	$0.243807\pi$
$788$	37.9058	−	65.6548i	1.35034	−	2.33886i
$789$	−1.14274	−	1.97928i	−0.0406826	−	0.0704643i
$790$	113.975			4.05506
$791$		0			0
$792$	47.1302			1.67470
$793$	10.9109	+	18.8983i	0.387458	+	0.671097i
$794$	−4.63055	+	8.02035i	−0.164332	+	0.284631i
$795$	2.08454	−	3.61054i	0.0739312	−	0.128053i
$796$	50.3859	+	87.2709i	1.78588	+	3.09324i
$797$	10.9902			0.389293			0.194647	−	0.980873i	$-0.437644\pi$
$797$	10.9902			0.389293			0.194647	+	0.980873i	$0.437644\pi$
$798$		0			0
$799$	−10.8141			−0.382574
$800$	17.9018	+	31.0069i	0.632926	+	1.09626i
$801$	9.18055	−	15.9012i	0.324379	−	0.561840i
$802$	−27.7567	+	48.0760i	−0.980124	+	1.69762i
$803$	1.00029	+	1.73256i	0.0352995	+	0.0611406i
$804$	3.97052			0.140030
$805$		0			0
$806$	127.167			4.47926
$807$	0.588274	+	1.01892i	0.0207082	+	0.0358677i
$808$	81.0310	−	140.350i	2.85066	−	4.93749i
$809$	−10.0318	+	17.3755i	−0.352698	+	0.610891i	−0.986721	−	0.162423i	$-0.948069\pi$
$809$	−10.0318	+	17.3755i	−0.352698	+	0.610891i	0.634023	+	0.773314i	$0.281402\pi$
$810$	30.7935	+	53.3359i	1.08197	+	1.87403i
$811$	1.57184			0.0551948			0.0275974	−	0.999619i	$-0.491214\pi$
$811$	1.57184			0.0551948			0.0275974	+	0.999619i	$0.491214\pi$
$812$		0			0
$813$	1.29906			0.0455601
$814$	−1.07911	−	1.86908i	−0.0378229	−	0.0655112i
$815$	15.1821	−	26.2961i	0.531804	−	0.921112i
$816$	3.67953	−	6.37313i	0.128809	−	0.223104i
$817$	−0.318414	−	0.551509i	−0.0111399	−	0.0192949i
$818$	6.75848			0.236305
$819$		0			0
$820$	92.1581			3.21830
$821$	−1.54080	−	2.66874i	−0.0537742	−	0.0931396i	0.837885	−	0.545846i	$-0.183792\pi$
$821$	−1.54080	−	2.66874i	−0.0537742	−	0.0931396i	−0.891659	+	0.452707i	$0.850458\pi$
$822$	1.89685	−	3.28544i	0.0661603	−	0.114593i
$823$	−24.7002	+	42.7820i	−0.860996	+	1.49129i	0.00997316	+	0.999950i	$0.496825\pi$
$823$	−24.7002	+	42.7820i	−0.860996	+	1.49129i	−0.870969	+	0.491338i	$0.836508\pi$
$824$	38.1179	+	66.0222i	1.32790	+	2.29999i
$825$	−0.334659			−0.0116513
$826$		0			0
$827$	19.8375			0.689817			0.344909	−	0.938636i	$-0.387910\pi$
$827$	19.8375			0.689817			0.344909	+	0.938636i	$0.387910\pi$
$828$	50.8169	+	88.0175i	1.76601	+	3.05882i
$829$	−20.3268	+	35.2071i	−0.705979	+	1.22279i	0.260358	+	0.965512i	$0.416159\pi$
$829$	−20.3268	+	35.2071i	−0.705979	+	1.22279i	−0.966337	+	0.257280i	$0.917174\pi$
$830$	0.993737	−	1.72120i	0.0344931	−	0.0597438i
$831$	1.37126	+	2.37509i	0.0475685	+	0.0823910i
$832$	−226.533			−7.85361
$833$		0			0
$834$	2.51673			0.0871471
$835$	−19.1677	−	33.1994i	−0.663325	−	1.14891i
$836$	−4.45005	+	7.70771i	−0.153908	+	0.266577i
$837$	−3.31134	+	5.73540i	−0.114457	+	0.198245i
$838$	−49.7318	−	86.1379i	−1.71796	−	2.97559i
$839$	21.7950			0.752448			0.376224	−	0.926529i	$-0.377222\pi$
$839$	21.7950			0.752448			0.376224	+	0.926529i	$0.377222\pi$
$840$		0			0
$841$	−26.8580			−0.926138
$842$	−29.3014	−	50.7515i	−1.00979	−	1.74901i
$843$	−0.258356	+	0.447485i	−0.00889824	+	0.0154122i
$844$	−22.2127	+	38.4736i	−0.764594	+	1.32432i
$845$	−31.7869	−	55.0565i	−1.09350	−	1.89400i
$846$	−29.3106			−1.00772
$847$		0			0
$848$	181.202			6.22251
$849$	−0.839853	−	1.45467i	−0.0288237	−	0.0499241i
$850$	5.96154	−	10.3257i	0.204479	−	0.354168i
$851$	1.49899	−	2.59633i	0.0513847	−	0.0890010i
$852$	−0.406951	−	0.704860i	−0.0139419	−	0.0241481i
$853$	52.6727			1.80348			0.901740	−	0.432280i	$-0.142291\pi$
$853$	52.6727			1.80348			0.901740	+	0.432280i	$0.142291\pi$
$854$		0			0
$855$	−7.54788			−0.258132
$856$	13.6170	+	23.5853i	0.465419	+	0.806130i
$857$	−12.9687	+	22.4625i	−0.443003	+	0.767304i	−0.997911	−	0.0646078i	$-0.979420\pi$
$857$	−12.9687	+	22.4625i	−0.443003	+	0.767304i	0.554907	+	0.831912i	$0.312754\pi$
$858$	2.00173	−	3.46710i	0.0683381	−	0.118365i
$859$	20.8030	+	36.0319i	0.709791	+	1.22939i	0.964935	+	0.262490i	$0.0845438\pi$
$859$	20.8030	+	36.0319i	0.709791	+	1.22939i	−0.255144	+	0.966903i	$0.582123\pi$
$860$	9.07191			0.309350
$861$		0			0
$862$	31.4178			1.07009
$863$	−13.3223	−	23.0748i	−0.453495	−	0.785477i	0.545105	−	0.838368i	$-0.316490\pi$
$863$	−13.3223	−	23.0748i	−0.453495	−	0.785477i	−0.998600	+	0.0528911i	$0.983156\pi$
$864$	11.1530	−	19.3175i	0.379432	−	0.657196i
$865$	−18.7904	+	32.5459i	−0.638893	+	1.10659i
$866$	31.8979	+	55.2488i	1.08394	+	1.87743i
$867$	1.15770			0.0393175
$868$		0			0
$869$	−25.7951			−0.875039
$870$	−0.759863	−	1.31612i	−0.0257618	−	0.0446207i
$871$	−14.6875	+	25.4395i	−0.497667	+	0.861985i
$872$	14.2195	−	24.6290i	0.481534	−	0.834042i
$873$	20.7580	+	35.9539i	0.702551	+	1.21685i
$874$	−16.7624			−0.566995
$875$		0			0
$876$	1.05382			0.0356054
$877$	10.8160	+	18.7339i	0.365230	+	0.632598i	0.988813	−	0.149160i	$-0.0476569\pi$
$877$	10.8160	+	18.7339i	0.365230	+	0.632598i	−0.623583	+	0.781757i	$0.714324\pi$
$878$	−38.6061	+	66.8678i	−1.30289	+	2.25668i
$879$	−1.11951	+	1.93905i	−0.0377601	+	0.0654024i
$880$	−32.8081	−	56.8254i	−1.10596	−	1.91558i
$881$	−36.3647			−1.22516			−0.612579	−	0.790409i	$-0.709868\pi$
$881$	−36.3647			−1.22516			−0.612579	+	0.790409i	$0.709868\pi$
$882$		0			0
$883$	−45.8156			−1.54182			−0.770908	−	0.636946i	$-0.780197\pi$
$883$	−45.8156			−1.54182			−0.770908	+	0.636946i	$0.780197\pi$
$884$	52.5997	+	91.1053i	1.76912	+	3.06420i
$885$	2.58088	−	4.47022i	0.0867554	−	0.150265i
$886$	39.5240	−	68.4575i	1.32783	−	2.29988i
$887$	10.3126	+	17.8619i	0.346263	+	0.599745i	0.985582	−	0.169196i	$-0.0541172\pi$
$887$	10.3126	+	17.8619i	0.346263	+	0.599745i	−0.639320	+	0.768941i	$0.720784\pi$
$888$	−0.732321			−0.0245751
$889$		0			0
$890$	−43.1393			−1.44603
$891$	−6.96924	−	12.0711i	−0.233478	−	0.404397i
$892$	−11.8599	+	20.5419i	−0.397098	+	0.687794i
$893$	1.78272	−	3.08775i	0.0596563	−	0.103328i
$894$	−2.47327	−	4.28384i	−0.0827187	−	0.143273i
$895$	−41.3000			−1.38051
$896$		0			0
$897$	5.56119			0.185683
$898$	2.09415	+	3.62717i	0.0698825	+	0.121040i
$899$	−5.46260	+	9.46151i	−0.182188	+	0.315559i
$900$	11.9175	−	20.6417i	0.397250	−	0.688057i
$901$	−16.8083	−	29.1128i	−0.559965	−	0.969889i
$902$	−28.2793			−0.941599
$903$		0			0
$904$	60.6727			2.01794
$905$	−1.31790	−	2.28267i	−0.0438085	−	0.0758785i
$906$	−1.32146	+	2.28884i	−0.0439026	+	0.0760415i
$907$	−4.27045	+	7.39664i	−0.141798	+	0.245601i	−0.928174	−	0.372147i	$-0.878622\pi$
$907$	−4.27045	+	7.39664i	−0.141798	+	0.245601i	0.786376	+	0.617749i	$0.211955\pi$
$908$	45.2855	+	78.4369i	1.50285	+	2.60302i
$909$	−48.2887			−1.60163
$910$		0			0
$911$	−43.6287			−1.44548			−0.722742	−	0.691118i	$-0.757119\pi$
$911$	−43.6287			−1.44548			−0.722742	+	0.691118i	$0.757119\pi$
$912$	1.21315	+	2.10124i	0.0401715	+	0.0695792i
$913$	−0.224904	+	0.389546i	−0.00744325	+	0.0128921i
$914$	11.0753	−	19.1829i	0.366337	−	0.634515i
$915$	0.665061	+	1.15192i	0.0219862	+	0.0380813i
$916$	74.4420			2.45963
$917$		0			0
$918$	−7.42816			−0.245166
$919$	24.9033	+	43.1338i	0.821484	+	1.42285i	0.904577	+	0.426311i	$0.140187\pi$
$919$	24.9033	+	43.1338i	0.821484	+	1.42285i	−0.0830925	+	0.996542i	$0.526480\pi$
$920$	76.9086	−	133.210i	2.53560	−	4.39179i
$921$	−0.450804	+	0.780815i	−0.0148545	+	0.0257287i
$922$	26.6932	+	46.2340i	0.879094	+	1.52264i
$923$	6.02148			0.198199
$924$		0			0
$925$	−0.703081			−0.0231172
$926$	44.5463	+	77.1564i	1.46388	+	2.53552i
$927$	11.3578	−	19.6722i	0.373038	−	0.646121i
$928$	18.3987	−	31.8675i	0.603967	−	1.04610i
$929$	−22.2948	−	38.6157i	−0.731467	−	1.26694i	−0.956256	−	0.292531i	$-0.905502\pi$
$929$	−22.2948	−	38.6157i	−0.731467	−	1.26694i	0.224789	−	0.974408i	$-0.427831\pi$
$930$	7.75130			0.254175
$931$		0			0
$932$	95.0277			3.11274
$933$	1.37296	+	2.37803i	0.0449486	+	0.0778532i
$934$	44.4002	−	76.9034i	1.45282	−	2.51636i
$935$	−6.08656	+	10.5422i	−0.199052	+	0.344768i
$936$	91.8357	+	159.064i	3.00174	+	5.19917i
$937$	−52.7172			−1.72219			−0.861097	−	0.508440i	$-0.830222\pi$
$937$	−52.7172			−1.72219			−0.861097	+	0.508440i	$0.830222\pi$
$938$		0			0
$939$	1.75986			0.0574307
$940$	25.3956	+	43.9866i	0.828315	+	1.43468i
$941$	−7.53757	+	13.0555i	−0.245718	+	0.425596i	−0.962333	−	0.271873i	$-0.912357\pi$
$941$	−7.53757	+	13.0555i	−0.245718	+	0.425596i	0.716615	+	0.697469i	$0.245690\pi$
$942$	−0.823845	+	1.42694i	−0.0268423	+	0.0464923i
$943$	−19.6413	−	34.0198i	−0.639609	−	1.10784i
$944$	224.347			7.30187
$945$		0			0
$946$	−2.78378			−0.0905084
$947$	6.46080	+	11.1904i	0.209948	+	0.363640i	0.951698	−	0.307036i	$-0.0993373\pi$
$947$	6.46080	+	11.1904i	0.209948	+	0.363640i	−0.741750	+	0.670676i	$0.766004\pi$
$948$	−6.79389	+	11.7674i	−0.220655	+	0.382186i
$949$	−3.89824	+	6.75195i	−0.126542	+	0.219178i
$950$	1.96554	+	3.40442i	0.0637705	+	0.110454i
$951$	0.339010			0.0109932
$952$		0			0
$953$	−16.3314			−0.529026			−0.264513	−	0.964382i	$-0.585211\pi$
$953$	−16.3314			−0.529026			−0.264513	+	0.964382i	$0.585211\pi$
$954$	−45.5574	−	78.9078i	−1.47498	−	2.55473i
$955$	−4.78819	+	8.29338i	−0.154942	+	0.268368i
$956$	19.0437	−	32.9847i	0.615918	−	1.06680i
$957$	0.171974	+	0.297867i	0.00555912	+	0.00962867i
$958$	21.5817			0.697274
$959$		0			0
$960$	−13.8080			−0.445652
$961$	−12.3618	−	21.4112i	−0.398767	−	0.690685i
$962$	4.20542	−	7.28400i	0.135588	−	0.234846i
$963$	4.05738	−	7.02759i	0.130747	−	0.226461i
$964$	−63.5822	−	110.128i	−2.04784	−	3.54697i
$965$	26.5314			0.854077
$966$		0			0
$967$	56.7625			1.82536			0.912679	−	0.408678i	$-0.134010\pi$
$967$	56.7625			1.82536			0.912679	+	0.408678i	$0.134010\pi$
$968$	−42.4387	−	73.5059i	−1.36403	−	2.36257i
$969$	0.225064	−	0.389823i	0.00723010	−	0.0125229i
$970$	48.7707	−	84.4733i	1.56593	−	2.71227i
$971$	3.36778	+	5.83316i	0.108077	+	0.187195i	0.914991	−	0.403474i	$-0.132197\pi$
$971$	3.36778	+	5.83316i	0.108077	+	0.187195i	−0.806914	+	0.590669i	$0.798864\pi$
$972$	−22.3014			−0.715318
$973$		0			0
$974$	82.2579			2.63571
$975$	−0.652100	−	1.12947i	−0.0208839	−	0.0361720i
$976$	−28.9057	+	50.0662i	−0.925249	+	1.60258i
$977$	−10.6586	+	18.4612i	−0.340999	+	0.590627i	−0.984618	−	0.174719i	$-0.944098\pi$
$977$	−10.6586	+	18.4612i	−0.340999	+	0.590627i	0.643620	+	0.765345i	$0.277432\pi$
$978$	2.45402	+	4.25048i	0.0784708	+	0.135915i
$979$	9.76336			0.312038
$980$		0			0
$981$	−8.47382			−0.270548
$982$	27.3692	+	47.4049i	0.873388	+	1.51275i
$983$	10.6318	−	18.4149i	0.339103	−	0.587344i	−0.645161	−	0.764047i	$-0.723210\pi$
$983$	10.6318	−	18.4149i	0.339103	−	0.587344i	0.984264	+	0.176703i	$0.0565431\pi$
$984$	−4.79781	+	8.31005i	−0.152949	+	0.264915i
$985$	17.0937	+	29.6072i	0.544652	+	0.943364i
$986$	−12.2540			−0.390247
$987$		0			0
$988$	−34.6846			−1.10346
$989$	−1.93346	−	3.34886i	−0.0614806	−	0.106487i
$990$	−16.4971	+	28.5738i	−0.524312	+	0.908136i
$991$	21.8178	−	37.7895i	0.693065	−	1.20042i	−0.277764	−	0.960649i	$-0.589593\pi$
$991$	21.8178	−	37.7895i	0.693065	−	1.20042i	0.970829	−	0.239774i	$-0.0770735\pi$
$992$	93.8418	+	162.539i	2.97948	+	5.16061i
$993$	−3.15913			−0.100252
$994$		0			0
$995$	−45.4433			−1.44065
$996$	0.118470	+	0.205197i	0.00375387	+	0.00650190i
$997$	−25.8886	+	44.8404i	−0.819901	+	1.42011i	0.0858539	+	0.996308i	$0.472638\pi$
$997$	−25.8886	+	44.8404i	−0.819901	+	1.42011i	−0.905755	+	0.423802i	$0.860695\pi$
$998$	−42.3357	+	73.3276i	−1.34011	+	2.32114i
$999$	0.219012	+	0.379341i	0.00692925	+	0.0120018i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.f.q.704.10		20
7.2	even	3	inner	931.2.f.q.324.10		20
7.3	odd	6		931.2.a.p.1.1	✓	10
7.4	even	3		931.2.a.q.1.1	yes	10
7.5	odd	6		931.2.f.r.324.10		20
7.6	odd	2		931.2.f.r.704.10		20
21.11	odd	6		8379.2.a.cs.1.10		10
21.17	even	6		8379.2.a.ct.1.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
931.2.a.p.1.1	✓	10	7.3	odd	6
931.2.a.q.1.1	yes	10	7.4	even	3
931.2.f.q.324.10		20	7.2	even	3	inner
931.2.f.q.704.10		20	1.1	even	1	trivial
931.2.f.r.324.10		20	7.5	odd	6
931.2.f.r.704.10		20	7.6	odd	2
8379.2.a.cs.1.10		10	21.11	odd	6
8379.2.a.ct.1.10		10	21.17	even	6

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:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.38026 + 2.39068i) q^{2} +(0.0742045 - 0.128526i) q^{3} +(-2.81024 + 4.86748i) q^{4} +(-1.26728 - 2.19500i) q^{5} +0.409686 q^{6} -9.99440 q^{8} +(1.48899 + 2.57900i) q^{9} +O(q^{10})\)	\(q+(1.38026 + 2.39068i) q^{2} +(0.0742045 - 0.128526i) q^{3} +(-2.81024 + 4.86748i) q^{4} +(-1.26728 - 2.19500i) q^{5} +0.409686 q^{6} -9.99440 q^{8} +(1.48899 + 2.57900i) q^{9} +(3.49836 - 6.05934i) q^{10} +(-0.791756 + 1.37136i) q^{11} +(0.417064 + 0.722377i) q^{12} -6.17112 q^{13} -0.376152 q^{15} +(-8.17440 - 14.1585i) q^{16} +(-1.51651 + 2.62668i) q^{17} +(-4.11038 + 7.11939i) q^{18} +(-0.500000 - 0.866025i) q^{19} +14.2455 q^{20} -4.37132 q^{22} +(-3.03609 - 5.25866i) q^{23} +(-0.741629 + 1.28454i) q^{24} +(-0.712018 + 1.23325i) q^{25} +(-8.51775 - 14.7532i) q^{26} +0.887185 q^{27} +1.46356 q^{29} +(-0.519188 - 0.899261i) q^{30} +(-3.73241 + 6.46472i) q^{31} +(12.5712 - 21.7740i) q^{32} +(0.117504 + 0.203522i) q^{33} -8.37274 q^{34} -16.7376 q^{36} +(0.246862 + 0.427578i) q^{37} +(1.38026 - 2.39068i) q^{38} +(-0.457924 + 0.793148i) q^{39} +(12.6657 + 21.9377i) q^{40} +6.46929 q^{41} +0.636828 q^{43} +(-4.45005 - 7.70771i) q^{44} +(3.77394 - 6.53666i) q^{45} +(8.38118 - 14.5166i) q^{46} +(1.78272 + 3.08775i) q^{47} -2.42631 q^{48} -3.93108 q^{50} +(0.225064 + 0.389823i) q^{51} +(17.3423 - 30.0378i) q^{52} +(-5.54175 + 9.59860i) q^{53} +(1.22455 + 2.12098i) q^{54} +4.01352 q^{55} -0.148409 q^{57} +(2.02009 + 3.49890i) q^{58} +(-6.86126 + 11.8841i) q^{59} +(1.05708 - 1.83091i) q^{60} +(-1.76806 - 3.06237i) q^{61} -20.6068 q^{62} +36.7086 q^{64} +(7.82056 + 13.5456i) q^{65} +(-0.324371 + 0.561828i) q^{66} +(2.38004 - 4.12235i) q^{67} +(-8.52353 - 14.7632i) q^{68} -0.901165 q^{69} -0.975752 q^{71} +(-14.8815 - 25.7756i) q^{72} +(0.631691 - 1.09412i) q^{73} +(-0.681468 + 1.18034i) q^{74} +(0.105670 + 0.183025i) q^{75} +5.62048 q^{76} -2.52822 q^{78} +(8.14490 + 14.1074i) q^{79} +(-20.7186 + 35.8856i) q^{80} +(-4.40113 + 7.62298i) q^{81} +(8.92930 + 15.4660i) q^{82} +0.284058 q^{83} +7.68741 q^{85} +(0.878988 + 1.52245i) q^{86} +(0.108603 - 0.188105i) q^{87} +(7.91313 - 13.7059i) q^{88} +(-3.08282 - 5.33959i) q^{89} +20.8361 q^{90} +34.1285 q^{92} +(0.553923 + 0.959423i) q^{93} +(-4.92123 + 8.52381i) q^{94} +(-1.26728 + 2.19500i) q^{95} +(-1.86568 - 3.23145i) q^{96} +13.9410 q^{97} -4.71566 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} - 4 q^{3} - 10 q^{4} - 16 q^{5} + 16 q^{6} - 12 q^{8} - 10 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 - 4 * q^3 - 10 * q^4 - 16 * q^5 + 16 * q^6 - 12 * q^8 - 10 * q^9	\( 20 q + 2 q^{2} - 4 q^{3} - 10 q^{4} - 16 q^{5} + 16 q^{6} - 12 q^{8} - 10 q^{9} + 12 q^{10} - 12 q^{12} + 24 q^{13} - 2 q^{16} - 16 q^{17} - 2 q^{18} - 10 q^{19} + 64 q^{20} + 8 q^{22} - 12 q^{23} + 8 q^{24} - 14 q^{25} - 24 q^{26} + 32 q^{27} - 24 q^{29} + 12 q^{30} - 8 q^{31} + 34 q^{32} + 4 q^{33} + 32 q^{34} - 12 q^{36} - 4 q^{37} + 2 q^{38} + 4 q^{39} + 20 q^{40} + 80 q^{41} + 8 q^{43} + 20 q^{44} - 24 q^{45} + 32 q^{46} - 16 q^{47} + 24 q^{48} - 68 q^{50} + 28 q^{51} + 40 q^{52} - 8 q^{54} + 32 q^{55} + 8 q^{57} + 8 q^{58} - 36 q^{59} - 32 q^{60} - 16 q^{61} - 32 q^{62} + 36 q^{64} - 8 q^{65} - 8 q^{66} + 28 q^{67} - 40 q^{68} + 96 q^{69} - 24 q^{71} - 34 q^{72} - 24 q^{74} + 32 q^{75} + 20 q^{76} + 56 q^{78} + 8 q^{79} - 8 q^{80} - 14 q^{81} + 8 q^{82} + 80 q^{85} + 52 q^{86} + 8 q^{87} + 4 q^{88} - 48 q^{89} - 128 q^{90} + 56 q^{92} - 40 q^{93} + 36 q^{94} - 16 q^{95} + 8 q^{96} - 32 q^{97} - 16 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 - 4 * q^3 - 10 * q^4 - 16 * q^5 + 16 * q^6 - 12 * q^8 - 10 * q^9 + 12 * q^10 - 12 * q^12 + 24 * q^13 - 2 * q^16 - 16 * q^17 - 2 * q^18 - 10 * q^19 + 64 * q^20 + 8 * q^22 - 12 * q^23 + 8 * q^24 - 14 * q^25 - 24 * q^26 + 32 * q^27 - 24 * q^29 + 12 * q^30 - 8 * q^31 + 34 * q^32 + 4 * q^33 + 32 * q^34 - 12 * q^36 - 4 * q^37 + 2 * q^38 + 4 * q^39 + 20 * q^40 + 80 * q^41 + 8 * q^43 + 20 * q^44 - 24 * q^45 + 32 * q^46 - 16 * q^47 + 24 * q^48 - 68 * q^50 + 28 * q^51 + 40 * q^52 - 8 * q^54 + 32 * q^55 + 8 * q^57 + 8 * q^58 - 36 * q^59 - 32 * q^60 - 16 * q^61 - 32 * q^62 + 36 * q^64 - 8 * q^65 - 8 * q^66 + 28 * q^67 - 40 * q^68 + 96 * q^69 - 24 * q^71 - 34 * q^72 - 24 * q^74 + 32 * q^75 + 20 * q^76 + 56 * q^78 + 8 * q^79 - 8 * q^80 - 14 * q^81 + 8 * q^82 + 80 * q^85 + 52 * q^86 + 8 * q^87 + 4 * q^88 - 48 * q^89 - 128 * q^90 + 56 * q^92 - 40 * q^93 + 36 * q^94 - 16 * q^95 + 8 * q^96 - 32 * q^97 - 16 * q^99

Introduction

L-functions

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