LMFDB - Embedded newform 637.2.k.g.569.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(459,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 1]))

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

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

chi := DirichletCharacter("637.459");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.k (of order $6$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.58891012706304.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 $ x^12 - 5x^10 - 2x^9 + 15x^8 + 2x^7 - 30x^6 + 4x^5 + 60x^4 - 16x^3 - 80*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			569.2
Root			$0.759479 - 1.19298i$ of defining polynomial
Character	$\chi$	$=$	637.569
Dual form			637.2.k.g.459.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.38595i q^{2} +(-1.41289 + 2.44719i) q^{3} +0.0791355 q^{4} +(-0.449430 - 0.259479i) q^{5} +(3.39169 + 1.95819i) q^{6} -2.88158i q^{8} +(-2.49250 - 4.31714i) q^{9} +O(q^{10})$	\(q-1.38595i q^{2} +(-1.41289 + 2.44719i) q^{3} +0.0791355 q^{4} +(-0.449430 - 0.259479i) q^{5} +(3.39169 + 1.95819i) q^{6} -2.88158i q^{8} +(-2.49250 - 4.31714i) q^{9} +(-0.359625 + 0.622889i) q^{10} +(-1.40656 - 0.812080i) q^{11} +(-0.111810 + 0.193660i) q^{12} +(-1.42641 - 3.31140i) q^{13} +(1.26999 - 0.733228i) q^{15} -3.83547 q^{16} +1.94825 q^{17} +(-5.98335 + 3.45449i) q^{18} +(2.15740 - 1.24558i) q^{19} +(-0.0355659 - 0.0205340i) q^{20} +(-1.12550 + 1.94943i) q^{22} +9.14058 q^{23} +(7.05179 + 4.07135i) q^{24} +(-2.36534 - 4.09689i) q^{25} +(-4.58944 + 1.97694i) q^{26} +5.60916 q^{27} +(2.61498 + 4.52928i) q^{29} +(-1.01622 - 1.76014i) q^{30} +(5.01767 - 2.89695i) q^{31} -0.447392i q^{32} +(3.97463 - 2.29475i) q^{33} -2.70019i q^{34} +(-0.197245 - 0.341639i) q^{36} -10.2293i q^{37} +(-1.72631 - 2.99006i) q^{38} +(10.1190 + 1.18792i) q^{39} +(-0.747709 + 1.29507i) q^{40} +(-3.64513 + 2.10452i) q^{41} +(-0.498655 + 0.863697i) q^{43} +(-0.111309 - 0.0642644i) q^{44} +2.58700i q^{45} -12.6684i q^{46} +(-3.91206 - 2.25863i) q^{47} +(5.41908 - 9.38612i) q^{48} +(-5.67810 + 3.27825i) q^{50} +(-2.75266 + 4.76775i) q^{51} +(-0.112880 - 0.262049i) q^{52} +(4.44825 + 7.70460i) q^{53} -7.77403i q^{54} +(0.421434 + 0.729946i) q^{55} +7.03944i q^{57} +(6.27736 - 3.62424i) q^{58} -6.20526i q^{59} +(0.100501 - 0.0580244i) q^{60} +(-6.73536 - 11.6660i) q^{61} +(-4.01504 - 6.95426i) q^{62} -8.29100 q^{64} +(-0.218163 + 1.85836i) q^{65} +(-3.18042 - 5.50865i) q^{66} +(7.25094 + 4.18633i) q^{67} +0.154176 q^{68} +(-12.9146 + 22.3688i) q^{69} +(-4.50168 - 2.59905i) q^{71} +(-12.4402 + 7.18234i) q^{72} +(10.2533 - 5.91976i) q^{73} -14.1773 q^{74} +13.3678 q^{75} +(0.170727 - 0.0985694i) q^{76} +(1.64640 - 14.0244i) q^{78} +(-0.491155 + 0.850705i) q^{79} +(1.72377 + 0.995221i) q^{80} +(-0.447609 + 0.775281i) q^{81} +(2.91676 + 5.05197i) q^{82} -8.91851i q^{83} +(-0.875603 - 0.505530i) q^{85} +(1.19704 + 0.691113i) q^{86} -14.7787 q^{87} +(-2.34008 + 4.05313i) q^{88} +12.0190i q^{89} +3.58546 q^{90} +0.723345 q^{92} +16.3723i q^{93} +(-3.13035 + 5.42193i) q^{94} -1.29280 q^{95} +(1.09485 + 0.632114i) q^{96} +(-3.82981 - 2.21114i) q^{97} +8.09643i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 8 q^{4} - 6 q^{5} + 18 q^{6} - 4 q^{9}+O(q^{10}) $ 12 * q - 8 * q^4 - 6 * q^5 + 18 * q^6 - 4 * q^9	$ 12 q - 8 q^{4} - 6 q^{5} + 18 q^{6} - 4 q^{9} - 12 q^{10} - 6 q^{11} - 2 q^{12} - 4 q^{13} + 6 q^{15} + 16 q^{16} - 8 q^{17} + 12 q^{18} + 12 q^{20} + 6 q^{22} + 24 q^{23} + 12 q^{24} + 10 q^{25} - 18 q^{26} - 12 q^{27} + 8 q^{29} + 8 q^{30} + 18 q^{31} - 30 q^{33} - 10 q^{36} + 2 q^{38} + 14 q^{39} + 46 q^{40} - 30 q^{41} + 2 q^{43} - 24 q^{44} + 42 q^{47} + 2 q^{48} - 18 q^{50} - 26 q^{51} + 28 q^{52} + 22 q^{53} + 6 q^{55} + 12 q^{58} - 66 q^{60} - 14 q^{61} + 4 q^{62} - 52 q^{64} - 18 q^{65} - 26 q^{66} + 24 q^{67} - 16 q^{68} - 4 q^{69} - 24 q^{71} - 60 q^{72} + 30 q^{73} - 12 q^{74} + 92 q^{75} + 18 q^{76} - 10 q^{78} + 28 q^{79} - 72 q^{80} + 2 q^{81} - 14 q^{82} - 48 q^{85} + 60 q^{86} - 4 q^{87} - 14 q^{88} - 24 q^{90} + 24 q^{92} - 4 q^{94} + 44 q^{95} + 6 q^{96} - 6 q^{97}+O(q^{100}) $ 12 * q - 8 * q^4 - 6 * q^5 + 18 * q^6 - 4 * q^9 - 12 * q^10 - 6 * q^11 - 2 * q^12 - 4 * q^13 + 6 * q^15 + 16 * q^16 - 8 * q^17 + 12 * q^18 + 12 * q^20 + 6 * q^22 + 24 * q^23 + 12 * q^24 + 10 * q^25 - 18 * q^26 - 12 * q^27 + 8 * q^29 + 8 * q^30 + 18 * q^31 - 30 * q^33 - 10 * q^36 + 2 * q^38 + 14 * q^39 + 46 * q^40 - 30 * q^41 + 2 * q^43 - 24 * q^44 + 42 * q^47 + 2 * q^48 - 18 * q^50 - 26 * q^51 + 28 * q^52 + 22 * q^53 + 6 * q^55 + 12 * q^58 - 66 * q^60 - 14 * q^61 + 4 * q^62 - 52 * q^64 - 18 * q^65 - 26 * q^66 + 24 * q^67 - 16 * q^68 - 4 * q^69 - 24 * q^71 - 60 * q^72 + 30 * q^73 - 12 * q^74 + 92 * q^75 + 18 * q^76 - 10 * q^78 + 28 * q^79 - 72 * q^80 + 2 * q^81 - 14 * q^82 - 48 * q^85 + 60 * q^86 - 4 * q^87 - 14 * q^88 - 24 * q^90 + 24 * q^92 - 4 * q^94 + 44 * q^95 + 6 * q^96 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$		−	1.38595i		−	0.980016i	−0.871718	−	0.490008i	$-0.836994\pi$
$2$		−	1.38595i		−	0.980016i	0.871718	−	0.490008i	$-0.163006\pi$
$3$	−1.41289	+	2.44719i	−0.815731	+	1.41289i	0.0930713	+	0.995659i	$0.470332\pi$
$3$	−1.41289	+	2.44719i	−0.815731	+	1.41289i	−0.908802	+	0.417228i	$0.863002\pi$
$4$	0.0791355			0.0395678
$5$	−0.449430	−	0.259479i	−0.200991	−	0.116042i	0.396127	−	0.918196i	$-0.370354\pi$
$5$	−0.449430	−	0.259479i	−0.200991	−	0.116042i	−0.597118	+	0.802154i	$0.703687\pi$
$6$	3.39169	+	1.95819i	1.38465	+	0.799429i
$7$		0			0
$7$		0			0
$8$		−	2.88158i		−	1.01879i
$9$	−2.49250	−	4.31714i	−0.830833	−	1.43905i
$10$	−0.359625	+	0.622889i	−0.113723	+	0.196975i
$11$	−1.40656	−	0.812080i	−0.424095	−	0.244851i	0.272733	−	0.962090i	$-0.412072\pi$
$11$	−1.40656	−	0.812080i	−0.424095	−	0.244851i	−0.696828	+	0.717239i	$0.745406\pi$
$12$	−0.111810	+	0.193660i	−0.0322766	+	0.0559048i
$13$	−1.42641	−	3.31140i	−0.395616	−	0.918416i
$13$	−1.42641	−	3.31140i	−0.395616	−	0.918416i
$14$		0			0
$15$	1.26999	−	0.733228i	0.327909	−	0.189319i
$16$	−3.83547			−0.958867
$17$	1.94825			0.472521			0.236260	−	0.971690i	$-0.424078\pi$
$17$	1.94825			0.472521			0.236260	+	0.971690i	$0.424078\pi$
$18$	−5.98335	+	3.45449i	−1.41029	+	0.814230i
$19$	2.15740	−	1.24558i	0.494942	−	0.285755i	−0.231680	−	0.972792i	$-0.574422\pi$
$19$	2.15740	−	1.24558i	0.494942	−	0.285755i	0.726622	+	0.687037i	$0.241089\pi$
$20$	−0.0355659	−	0.0205340i	−0.00795277	−	0.00459154i
$21$		0			0
$22$	−1.12550	+	1.94943i	−0.239958	+	0.415620i
$23$	9.14058			1.90594			0.952971	−	0.303060i	$-0.0980083\pi$
$23$	9.14058			1.90594			0.952971	+	0.303060i	$0.0980083\pi$
$24$	7.05179	+	4.07135i	1.43944	+	0.831061i
$25$	−2.36534	−	4.09689i	−0.473068	−	0.819378i
$26$	−4.58944	+	1.97694i	−0.900063	+	0.387710i
$27$	5.60916			1.07948
$28$		0			0
$29$	2.61498	+	4.52928i	0.485589	+	0.841065i	0.999863	−	0.0165608i	$-0.00527172\pi$
$29$	2.61498	+	4.52928i	0.485589	+	0.841065i	−0.514274	+	0.857626i	$0.671938\pi$
$30$	−1.01622	−	1.76014i	−0.185535	−	0.321357i
$31$	5.01767	−	2.89695i	0.901201	−	0.520308i	0.0236111	−	0.999721i	$-0.492484\pi$
$31$	5.01767	−	2.89695i	0.901201	−	0.520308i	0.877590	+	0.479413i	$0.159150\pi$
$32$		−	0.447392i		−	0.0790885i
$33$	3.97463	−	2.29475i	0.691894	−	0.399465i
$34$		−	2.70019i		−	0.463078i
$35$		0			0
$36$	−0.197245	−	0.341639i	−0.0328742	−	0.0569398i
$37$		−	10.2293i		−	1.68168i	−0.541284	−	0.840840i	$-0.682062\pi$
$37$		−	10.2293i		−	1.68168i	0.541284	−	0.840840i	$-0.317938\pi$
$38$	−1.72631	−	2.99006i	−0.280045	−	0.485052i
$39$	10.1190	+	1.18792i	1.62033	+	0.190219i
$40$	−0.747709	+	1.29507i	−0.118223	+	0.204769i
$41$	−3.64513	+	2.10452i	−0.569273	+	0.328670i	−0.756859	−	0.653578i	$-0.773267\pi$
$41$	−3.64513	+	2.10452i	−0.569273	+	0.328670i	0.187586	+	0.982248i	$0.439934\pi$
$42$		0			0
$43$	−0.498655	+	0.863697i	−0.0760442	+	0.131712i	−0.901540	−	0.432696i	$-0.857562\pi$
$43$	−0.498655	+	0.863697i	−0.0760442	+	0.131712i	0.825496	+	0.564408i	$0.190896\pi$
$44$	−0.111309	−	0.0642644i	−0.0167805	−	0.00968822i
$45$			2.58700i			0.385647i
$46$		−	12.6684i		−	1.86786i
$47$	−3.91206	−	2.25863i	−0.570632	−	0.329455i	0.186770	−	0.982404i	$-0.440198\pi$
$47$	−3.91206	−	2.25863i	−0.570632	−	0.329455i	−0.757402	+	0.652949i	$0.773532\pi$
$48$	5.41908	−	9.38612i	0.782177	−	1.35477i
$49$		0			0
$50$	−5.67810	+	3.27825i	−0.803004	+	0.463615i
$51$	−2.75266	+	4.76775i	−0.385450	+	0.667618i
$52$	−0.112880	−	0.262049i	−0.0156536	−	0.0363397i
$53$	4.44825	+	7.70460i	0.611015	+	1.05831i	0.991070	+	0.133344i	$0.0425717\pi$
$53$	4.44825	+	7.70460i	0.611015	+	1.05831i	−0.380055	+	0.924964i	$0.624095\pi$
$54$		−	7.77403i		−	1.05791i
$55$	0.421434	+	0.729946i	0.0568262	+	0.0984259i
$56$		0			0
$57$			7.03944i			0.932397i
$58$	6.27736	−	3.62424i	0.824258	−	0.475886i
$59$		−	6.20526i		−	0.807856i	−0.914791	−	0.403928i	$-0.867645\pi$
$59$		−	6.20526i		−	0.807856i	0.914791	−	0.403928i	$-0.132355\pi$
$60$	0.100501	−	0.0580244i	0.0129746	−	0.00749091i
$61$	−6.73536	−	11.6660i	−0.862375	−	1.49368i	−0.869630	−	0.493703i	$-0.835643\pi$
$61$	−6.73536	−	11.6660i	−0.862375	−	1.49368i	0.00725571	−	0.999974i	$-0.497690\pi$
$62$	−4.01504	−	6.95426i	−0.509911	−	0.883191i
$63$		0			0
$64$	−8.29100			−1.03637
$65$	−0.218163	+	1.85836i	−0.0270598	+	0.230502i
$66$	−3.18042	−	5.50865i	−0.391483	−	0.678068i
$67$	7.25094	+	4.18633i	0.885843	+	0.511442i	0.872580	−	0.488470i	$-0.162445\pi$
$67$	7.25094	+	4.18633i	0.885843	+	0.511442i	0.0132624	+	0.999912i	$0.495778\pi$
$68$	0.154176			0.0186966
$69$	−12.9146	+	22.3688i	−1.55474	+	2.69288i
$70$		0			0
$71$	−4.50168	−	2.59905i	−0.534251	−	0.308450i	0.208495	−	0.978023i	$-0.433144\pi$
$71$	−4.50168	−	2.59905i	−0.534251	−	0.308450i	−0.742746	+	0.669573i	$0.766477\pi$
$72$	−12.4402	+	7.18234i	−1.46609	+	0.846447i
$73$	10.2533	−	5.91976i	1.20006	−	0.692856i	0.239493	−	0.970898i	$-0.423019\pi$
$73$	10.2533	−	5.91976i	1.20006	−	0.692856i	0.960569	+	0.278042i	$0.0896855\pi$
$74$	−14.1773			−1.64807
$75$	13.3678			1.54359
$76$	0.170727	−	0.0985694i	0.0195838	−	0.0113067i
$77$		0			0
$78$	1.64640	−	14.0244i	0.186418	−	1.58795i
$79$	−0.491155	+	0.850705i	−0.0552592	+	0.0957118i	−0.892332	−	0.451380i	$-0.850932\pi$
$79$	−0.491155	+	0.850705i	−0.0552592	+	0.0957118i	0.837073	+	0.547092i	$0.184265\pi$
$80$	1.72377	+	0.995221i	0.192724	+	0.111269i
$81$	−0.447609	+	0.775281i	−0.0497343	+	0.0861423i
$82$	2.91676	+	5.05197i	0.322102	+	0.557897i
$83$		−	8.91851i		−	0.978934i	−0.872022	−	0.489467i	$-0.837191\pi$
$83$		−	8.91851i		−	0.978934i	0.872022	−	0.489467i	$-0.162809\pi$
$84$		0			0
$85$	−0.875603	−	0.505530i	−0.0949725	−	0.0548324i
$86$	1.19704	+	0.691113i	0.129080	+	0.0745246i
$87$	−14.7787			−1.58444
$88$	−2.34008	+	4.05313i	−0.249453	+	0.432065i
$89$			12.0190i			1.27401i	0.770860	+	0.637005i	$0.219827\pi$
$89$			12.0190i			1.27401i	−0.770860	+	0.637005i	$0.780173\pi$
$90$	3.58546			0.377941
$91$		0			0
$92$	0.723345			0.0754139
$93$			16.3723i			1.69773i
$94$	−3.13035	+	5.42193i	−0.322871	+	0.559229i
$95$	−1.29280			−0.132639
$96$	1.09485	+	0.632114i	0.111743	+	0.0645149i
$97$	−3.82981	−	2.21114i	−0.388858	−	0.224507i	0.292807	−	0.956172i	$-0.405411\pi$
$97$	−3.82981	−	2.21114i	−0.388858	−	0.224507i	−0.681665	+	0.731664i	$0.738744\pi$
$98$		0			0
$99$			8.09643i			0.813722i
$100$	−0.187183	−	0.324210i	−0.0187183	−	0.0324210i
$101$	−9.15132	+	15.8506i	−0.910591	+	1.57719i	−0.0973594	+	0.995249i	$0.531040\pi$
$101$	−9.15132	+	15.8506i	−0.910591	+	1.57719i	−0.813231	+	0.581940i	$0.802294\pi$
$102$	6.60787	+	3.81506i	0.654277	+	0.377747i
$103$	−2.51023	+	4.34784i	−0.247340	+	0.428406i	−0.962787	−	0.270262i	$-0.912890\pi$
$103$	−2.51023	+	4.34784i	−0.247340	+	0.428406i	0.715447	+	0.698667i	$0.246223\pi$
$104$	−9.54206	+	4.11033i	−0.935676	+	0.403051i
$105$		0			0
$106$	10.6782	−	6.16507i	1.03716	−	0.598804i
$107$	6.14456			0.594017			0.297008	−	0.954875i	$-0.404011\pi$
$107$	6.14456			0.594017			0.297008	+	0.954875i	$0.404011\pi$
$108$	0.443884			0.0427127
$109$	−10.3025	+	5.94812i	−0.986796	+	0.569727i	−0.904315	−	0.426866i	$-0.859618\pi$
$109$	−10.3025	+	5.94812i	−0.986796	+	0.569727i	−0.0824809	+	0.996593i	$0.526284\pi$
$110$	1.01167	−	0.584088i	0.0964590	−	0.0556906i
$111$	25.0330	+	14.4528i	2.37602	+	1.37180i
$112$		0			0
$113$	−1.77806	+	3.07969i	−0.167266	+	0.289713i	−0.937458	−	0.348099i	$-0.886827\pi$
$113$	−1.77806	+	3.07969i	−0.167266	+	0.289713i	0.770192	+	0.637812i	$0.220161\pi$
$114$	9.75633			0.913764
$115$	−4.10805	−	2.37178i	−0.383078	−	0.221170i
$116$	0.206938	+	0.358427i	0.0192137	+	0.0332791i
$117$	−10.7404	+	14.4117i	−0.992951	+	1.33236i
$118$	−8.60020			−0.791713
$119$		0			0
$120$	−2.11286	−	3.65957i	−0.192877	−	0.334072i
$121$	−4.18105	−	7.24180i	−0.380096	−	0.658345i
$122$	−16.1685	+	9.33489i	−1.46383	+	0.845141i
$123$		−	11.8938i		−	1.07243i
$124$	0.397076	−	0.229252i	0.0356585	−	0.0205874i
$125$			5.04981i			0.451668i
$126$		0			0
$127$	−0.711749	−	1.23279i	−0.0631575	−	0.109392i	0.832718	−	0.553698i	$-0.186784\pi$
$127$	−0.711749	−	1.23279i	−0.0631575	−	0.109392i	−0.895875	+	0.444306i	$0.853450\pi$
$128$			10.5961i			0.936576i
$129$	−1.40909	−	2.44061i	−0.124063	−	0.214884i
$130$	2.57560	+	0.302364i	0.225895	+	0.0265190i
$131$	4.33687	−	7.51168i	0.378914	−	0.656298i	−0.611990	−	0.790865i	$-0.709631\pi$
$131$	4.33687	−	7.51168i	0.378914	−	0.656298i	0.990905	+	0.134567i	$0.0429643\pi$
$132$	0.314535	−	0.181597i	0.0273767	−	0.0158060i
$133$		0			0
$134$	5.80205	−	10.0495i	0.501221	−	0.868141i
$135$	−2.52092	−	1.45546i	−0.216967	−	0.125266i
$136$		−	5.61405i		−	0.481401i
$137$		−	8.51784i		−	0.727728i	−0.931452	−	0.363864i	$-0.881457\pi$
$137$		−	8.51784i		−	0.727728i	0.931452	−	0.363864i	$-0.118543\pi$
$138$	31.0020	+	17.8990i	2.63907	+	1.52367i
$139$	−2.51922	+	4.36342i	−0.213677	+	0.370100i	−0.952863	−	0.303402i	$-0.901877\pi$
$139$	−2.51922	+	4.36342i	−0.213677	+	0.370100i	0.739185	+	0.673502i	$0.235211\pi$
$140$		0			0
$141$	11.0546	−	6.38237i	0.930964	−	0.537493i
$142$	−3.60215	+	6.23912i	−0.302286	+	0.523575i
$143$	−0.682776	+	5.81605i	−0.0570966	+	0.486363i
$144$	9.55990	+	16.5582i	0.796658	+	1.37985i
$145$		−	2.71412i		−	0.225396i
$146$	−8.20451	−	14.2106i	−0.679010	−	1.17608i
$147$		0			0
$148$		−	0.809498i		−	0.0665403i
$149$	−2.91409	+	1.68245i	−0.238732	+	0.137832i	−0.614594	−	0.788844i	$-0.710680\pi$
$149$	−2.91409	+	1.68245i	−0.238732	+	0.137832i	0.375862	+	0.926676i	$0.377347\pi$
$150$		−	18.5272i		−	1.51274i
$151$	10.9610	−	6.32831i	0.891990	−	0.514991i	0.0173971	−	0.999849i	$-0.494462\pi$
$151$	10.9610	−	6.32831i	0.891990	−	0.514991i	0.874593	+	0.484858i	$0.161129\pi$
$152$	−3.58924	−	6.21674i	−0.291125	−	0.504244i
$153$	−4.85602	−	8.41087i	−0.392586	−	0.679979i
$154$		0			0
$155$	−3.00679			−0.241511
$156$	0.800771	+	0.0940067i	0.0641130	+	0.00752656i
$157$	5.18457	+	8.97993i	0.413773	+	0.716677i	0.995299	−	0.0968517i	$-0.0308772\pi$
$157$	5.18457	+	8.97993i	0.413773	+	0.716677i	−0.581525	+	0.813528i	$0.697544\pi$
$158$	1.17904	+	0.680717i	0.0937992	+	0.0541550i
$159$	−25.1395			−1.99369
$160$	−0.116089	+	0.201071i	−0.00917761	+	0.0158961i
$161$		0			0
$162$	1.07450	+	0.620364i	0.0844209	+	0.0487404i
$163$	−13.6428	+	7.87669i	−1.06859	+	0.616950i	−0.927796	−	0.373089i	$-0.878299\pi$
$163$	−13.6428	+	7.87669i	−1.06859	+	0.616950i	−0.140794	+	0.990039i	$0.544965\pi$
$164$	−0.288459	+	0.166542i	−0.0225249	+	0.0130047i
$165$	−2.38176			−0.185420
$166$	−12.3606			−0.959371
$167$	14.2016	−	8.19930i	1.09895	−	0.634481i	0.163007	−	0.986625i	$-0.447881\pi$
$167$	14.2016	−	8.19930i	1.09895	−	0.634481i	0.935946	+	0.352144i	$0.114547\pi$
$168$		0			0
$169$	−8.93069	+	9.44684i	−0.686976	+	0.726680i
$170$	−0.700640	+	1.21354i	−0.0537367	+	0.0930746i
$171$	−10.7547	−	6.20920i	−0.822429	−	0.474830i
$172$	−0.0394614	+	0.0683491i	−0.00300890	+	0.00521157i
$173$	0.150677	+	0.260981i	0.0114558	+	0.0198420i	0.871696	−	0.490046i	$-0.163020\pi$
$173$	0.150677	+	0.260981i	0.0114558	+	0.0198420i	−0.860241	+	0.509888i	$0.829687\pi$
$174$			20.4825i			1.55278i
$175$		0			0
$176$	5.39483	+	3.11470i	0.406650	+	0.234780i
$177$	15.1855	+	8.76734i	1.14141	+	0.658993i
$178$	16.6577			1.24855
$179$	−4.90791	+	8.50075i	−0.366834	+	0.635376i	−0.989069	−	0.147455i	$-0.952892\pi$
$179$	−4.90791	+	8.50075i	−0.366834	+	0.635376i	0.622234	+	0.782831i	$0.286225\pi$
$180$			0.204724i			0.0152592i
$181$	−12.4320			−0.924062			−0.462031	−	0.886864i	$-0.652879\pi$
$181$	−12.4320			−0.924062			−0.462031	+	0.886864i	$0.652879\pi$
$182$		0			0
$183$	38.0652			2.81386
$184$		−	26.3393i		−	1.94176i
$185$	−2.65427	+	4.59733i	−0.195146	+	0.338003i
$186$	22.6912			1.66380
$187$	−2.74034	−	1.58214i	−0.200394	−	0.115697i
$188$	−0.309583	−	0.178738i	−0.0225786	−	0.0130358i
$189$		0			0
$190$			1.79176i			0.129988i
$191$	6.12346	+	10.6061i	0.443078	+	0.767434i	0.997916	−	0.0645248i	$-0.0205531\pi$
$191$	6.12346	+	10.6061i	0.443078	+	0.767434i	−0.554838	+	0.831958i	$0.687220\pi$
$192$	11.7142	−	20.2897i	0.845403	−	1.46428i
$193$	10.0752	+	5.81692i	0.725229	+	0.418711i	0.816674	−	0.577099i	$-0.195815\pi$
$193$	10.0752	+	5.81692i	0.725229	+	0.418711i	−0.0914452	+	0.995810i	$0.529149\pi$
$194$	−3.06454	+	5.30794i	−0.220021	+	0.381088i
$195$	−4.23953	−	3.15955i	−0.303599	−	0.226260i
$196$		0			0
$197$	−1.55984	+	0.900572i	−0.111134	+	0.0641631i	−0.554537	−	0.832159i	$-0.687104\pi$
$197$	−1.55984	+	0.900572i	−0.111134	+	0.0641631i	0.443403	+	0.896322i	$0.353771\pi$
$198$	11.2213			0.797461
$199$	6.59313			0.467375			0.233687	−	0.972312i	$-0.424921\pi$
$199$	6.59313			0.467375			0.233687	+	0.972312i	$0.424921\pi$
$200$	−11.8055	+	6.81593i	−0.834777	+	0.481959i
$201$	−20.4895	+	11.8296i	−1.44522	+	0.834397i
$202$	21.9681	+	12.6833i	1.54567	+	0.892394i
$203$		0			0
$204$	−0.217833	+	0.377298i	−0.0152514	+	0.0264162i
$205$	2.18431			0.152559
$206$	6.02590	+	3.47906i	0.419845	+	0.242397i
$207$	−22.7829	−	39.4611i	−1.58352	−	2.74274i
$208$	5.47096	+	12.7007i	0.379343	+	0.880638i
$209$	−4.04603			−0.279870
$210$		0			0
$211$	−5.35996	−	9.28373i	−0.368995	−	0.639118i	0.620414	−	0.784275i	$-0.286965\pi$
$211$	−5.35996	−	9.28373i	−0.368995	−	0.639118i	−0.989409	+	0.145157i	$0.953631\pi$
$212$	0.352015	+	0.609708i	0.0241765	+	0.0418749i
$213$	12.7207	−	7.34432i	0.871610	−	0.503224i
$214$		−	8.51607i		−	0.582146i
$215$	0.448221	−	0.258781i	0.0305684	−	0.0176487i
$216$		−	16.1633i		−	1.09977i
$217$		0			0
$218$	8.24382	+	14.2787i	0.558342	+	0.967076i
$219$			33.4558i			2.26074i
$220$	0.0333504	+	0.0577647i	0.00224849	+	0.00389449i
$221$	−2.77901	−	6.45144i	−0.186937	−	0.433971i
$222$	20.0309	−	34.6945i	1.34438	−	2.32854i
$223$	11.1612	−	6.44392i	0.747409	−	0.431517i	−0.0773480	−	0.997004i	$-0.524645\pi$
$223$	11.1612	−	6.44392i	0.747409	−	0.431517i	0.824757	+	0.565487i	$0.191312\pi$
$224$		0			0
$225$	−11.7912	+	20.4230i	−0.786082	+	1.36153i
$226$	4.26831	+	2.46431i	0.283924	+	0.163923i
$227$		−	0.699155i		−	0.0464045i	−0.999731	−	0.0232023i	$-0.992614\pi$
$227$		−	0.699155i		−	0.0464045i	0.999731	−	0.0232023i	$-0.00738617\pi$
$228$			0.557070i			0.0368929i
$229$	15.8369	+	9.14342i	1.04653	+	0.604214i	0.921676	−	0.387961i	$-0.126820\pi$
$229$	15.8369	+	9.14342i	1.04653	+	0.604214i	0.124854	+	0.992175i	$0.460154\pi$
$230$	−3.28718	+	5.69356i	−0.216750	+	0.375422i
$231$		0			0
$232$	13.0515	−	7.53528i	0.856872	−	0.494715i
$233$	13.3898	−	23.1918i	0.877194	−	1.51934i	0.0227864	−	0.999740i	$-0.492746\pi$
$233$	13.3898	−	23.1918i	0.877194	−	1.51934i	0.854407	−	0.519604i	$-0.173920\pi$
$234$	19.9739	+	14.8857i	1.30573	+	0.973109i
$235$	1.17213	+	2.03019i	0.0764614	+	0.132435i
$236$		−	0.491057i		−	0.0319651i
$237$	−1.38789	−	2.40390i	−0.0901533	−	0.156150i
$238$		0			0
$239$			16.6177i			1.07491i	0.843293	+	0.537454i	$0.180614\pi$
$239$			16.6177i			1.07491i	−0.843293	+	0.537454i	$0.819386\pi$
$240$	−4.87099	+	2.81227i	−0.314421	+	0.181531i
$241$			17.4129i			1.12166i	0.827931	+	0.560830i	$0.189518\pi$
$241$			17.4129i			1.12166i	−0.827931	+	0.560830i	$0.810482\pi$
$242$	−10.0368	+	5.79474i	−0.645189	+	0.372500i
$243$	7.14890	+	12.3823i	0.458602	+	0.794322i
$244$	−0.533007	−	0.923194i	−0.0341222	−	0.0591015i
$245$		0			0
$246$	−16.4842			−1.05099
$247$	−7.20195	−	5.36731i	−0.458249	−	0.341514i
$248$	−8.34782	−	14.4588i	−0.530087	−	0.918137i
$249$	21.8253	+	12.6008i	1.38312	+	0.798546i
$250$	6.99879			0.442642
$251$	3.22491	−	5.58571i	0.203554	−	0.352567i	−0.746117	−	0.665815i	$-0.768084\pi$
$251$	3.22491	−	5.58571i	0.203554	−	0.352567i	0.949671	+	0.313249i	$0.101417\pi$
$252$		0			0
$253$	−12.8568	−	7.42288i	−0.808300	−	0.466672i
$254$	−1.70858	+	0.986451i	−0.107206	+	0.0618954i
$255$	2.47426	−	1.42851i	0.154944	−	0.0894570i
$256$	−1.89624			−0.118515
$257$	−3.67156			−0.229025			−0.114513	−	0.993422i	$-0.536531\pi$
$257$	−3.67156			−0.229025			−0.114513	+	0.993422i	$0.536531\pi$
$258$	−3.38257	+	1.95293i	−0.210590	+	0.121584i
$259$		0			0
$260$	−0.0172645	+	0.147063i	−0.00107070	+	0.00912044i
$261$	13.0357	−	22.5784i	0.806887	−	1.39757i
$262$	−10.4108	−	6.01070i	−0.643183	−	0.371342i
$263$	−9.15964	+	15.8650i	−0.564807	+	0.978275i	0.432260	+	0.901749i	$0.357716\pi$
$263$	−9.15964	+	15.8650i	−0.564807	+	0.978275i	−0.997068	+	0.0765263i	$0.975617\pi$
$264$	−6.61252	−	11.4532i	−0.406973	−	0.704897i
$265$		−	4.61690i		−	0.283614i
$266$		0			0
$267$	−29.4128	−	16.9815i	−1.80003	−	1.03925i
$268$	0.573807	+	0.331287i	0.0350508	+	0.0202366i
$269$	−27.5429			−1.67932			−0.839661	−	0.543111i	$-0.817246\pi$
$269$	−27.5429			−1.67932			−0.839661	+	0.543111i	$0.817246\pi$
$270$	−2.01719	+	3.49388i	−0.122762	+	0.212631i
$271$		−	6.51923i		−	0.396015i	−0.980201	−	0.198007i	$-0.936553\pi$
$271$		−	6.51923i		−	0.396015i	0.980201	−	0.198007i	$-0.0634470\pi$
$272$	−7.47246			−0.453084
$273$		0			0
$274$	−11.8053			−0.713186
$275$			7.68338i			0.463325i
$276$	−1.02200	+	1.77016i	−0.0615174	+	0.106551i
$277$	−5.44186			−0.326970			−0.163485	−	0.986546i	$-0.552273\pi$
$277$	−5.44186			−0.326970			−0.163485	+	0.986546i	$0.552273\pi$
$278$	6.04749	+	3.49152i	0.362704	+	0.209407i
$279$	−25.0131	−	14.4413i	−1.49749	−	0.864579i
$280$		0			0
$281$			3.54237i			0.211320i	0.994402	+	0.105660i	$0.0336955\pi$
$281$			3.54237i			0.211320i	−0.994402	+	0.105660i	$0.966304\pi$
$282$	−8.84566	−	15.3211i	−0.526752	−	0.912360i
$283$	7.06956	−	12.2448i	0.420242	−	0.727880i	−0.575721	−	0.817646i	$-0.695279\pi$
$283$	7.06956	−	12.2448i	0.420242	−	0.727880i	0.995963	+	0.0897658i	$0.0286119\pi$
$284$	−0.356243	−	0.205677i	−0.0211391	−	0.0122047i
$285$	1.82658	−	3.16374i	0.108197	−	0.187404i
$286$	8.06077	+	0.946296i	0.476643	+	0.0559556i
$287$		0			0
$288$	−1.93145	+	1.11512i	−0.113812	+	0.0657093i
$289$	−13.2043			−0.776724
$290$	−3.76165			−0.220891
$291$	10.8222	−	6.24819i	0.634407	−	0.366275i
$292$	0.811403	−	0.468464i	0.0474838	−	0.0274148i
$293$	7.23071	+	4.17465i	0.422423	+	0.243886i	0.696113	−	0.717932i	$-0.254911\pi$
$293$	7.23071	+	4.17465i	0.422423	+	0.243886i	−0.273691	+	0.961818i	$0.588244\pi$
$294$		0			0
$295$	−1.61013	+	2.78883i	−0.0937455	+	0.162372i
$296$	−29.4765			−1.71328
$297$	−7.88964	−	4.55508i	−0.457803	−	0.264313i
$298$	2.33180	+	4.03879i	0.135077	+	0.233961i
$299$	−13.0382	−	30.2681i	−0.754021	−	1.75045i
$300$	1.05787			0.0610762
$301$		0			0
$302$	−8.77074	−	15.1914i	−0.504699	−	0.874165i
$303$	−25.8596	−	44.7901i	−1.48559	−	2.57312i
$304$	−8.27465	+	4.77737i	−0.474584	+	0.274001i
$305$			6.99073i			0.400288i
$306$	−11.6571	+	6.73021i	−0.666390	+	0.384741i
$307$			8.33362i			0.475625i	0.971311	+	0.237813i	$0.0764304\pi$
$307$			8.33362i			0.475625i	−0.971311	+	0.237813i	$0.923570\pi$
$308$		0			0
$309$	−7.09334	−	12.2860i	−0.403526	−	0.698927i
$310$			4.16727i			0.236685i
$311$	7.31134	+	12.6636i	0.414588	+	0.718088i	0.995385	−	0.0959606i	$-0.0305923\pi$
$311$	7.31134	+	12.6636i	0.414588	+	0.718088i	−0.580797	+	0.814048i	$0.697259\pi$
$312$	3.42309	−	29.1587i	0.193794	−	1.65079i
$313$	8.56641	−	14.8375i	0.484202	−	0.838663i	−0.515633	−	0.856809i	$-0.672443\pi$
$313$	8.56641	−	14.8375i	0.484202	−	0.838663i	0.999835	+	0.0181467i	$0.00577661\pi$
$314$	12.4458	−	7.18556i	0.702355	−	0.405505i
$315$		0			0
$316$	−0.0388678	+	0.0673210i	−0.00218649	+	0.00378710i
$317$	−12.1244	−	7.00002i	−0.680973	−	0.393160i	0.119248	−	0.992864i	$-0.461952\pi$
$317$	−12.1244	−	7.00002i	−0.680973	−	0.393160i	−0.800222	+	0.599704i	$0.795285\pi$
$318$			34.8422i			1.95385i
$319$		−	8.49428i		−	0.475589i
$320$	3.72622	+	2.15134i	0.208302	+	0.120263i
$321$	−8.68157	+	15.0369i	−0.484558	+	0.839279i
$322$		0			0
$323$	4.20317	−	2.42670i	0.233871	−	0.135025i
$324$	−0.0354217	+	0.0613523i	−0.00196787	+	0.00340846i
$325$	−10.1925	+	13.6764i	−0.565377	+	0.758633i
$326$	10.9167	+	18.9083i	0.604621	+	1.04724i
$327$		−	33.6161i		−	1.85897i
$328$	6.06434	+	10.5037i	0.334847	+	0.579972i
$329$		0			0
$330$			3.30100i			0.181714i
$331$	−5.99286	+	3.45998i	−0.329397	+	0.190178i	−0.655574	−	0.755131i	$-0.727573\pi$
$331$	−5.99286	+	3.45998i	−0.329397	+	0.190178i	0.326176	+	0.945309i	$0.394240\pi$
$332$		−	0.705771i		−	0.0387342i
$333$	−44.1611	+	25.4964i	−2.42001	+	1.39719i
$334$	−11.3638	−	19.6827i	−0.621801	−	1.07699i
$335$	−2.17253	−	3.76292i	−0.118698	−	0.205591i
$336$		0			0
$337$	11.1559			0.607703			0.303852	−	0.952719i	$-0.401727\pi$
$337$	11.1559			0.607703			0.303852	+	0.952719i	$0.401727\pi$
$338$	13.0929	+	12.3775i	0.712158	+	0.673248i
$339$	−5.02440	−	8.70251i	−0.272888	−	0.472656i
$340$	−0.0692913	−	0.0400054i	−0.00375785	−	0.00216960i
$341$	−9.41023			−0.509593
$342$	−8.60566	+	14.9054i	−0.465341	+	0.805994i
$343$		0			0
$344$	2.48881	+	1.43692i	0.134188	+	0.0774734i
$345$	11.6084	−	6.70213i	0.624977	−	0.360830i
$346$	0.361707	−	0.208832i	0.0194455	−	0.0112269i
$347$	−4.92511			−0.264393			−0.132197	−	0.991223i	$-0.542203\pi$
$347$	−4.92511			−0.264393			−0.132197	+	0.991223i	$0.542203\pi$
$348$	−1.16952			−0.0626928
$349$	−1.31926	+	0.761675i	−0.0706183	+	0.0407715i	−0.534893	−	0.844920i	$-0.679648\pi$
$349$	−1.31926	+	0.761675i	−0.0706183	+	0.0407715i	0.464275	+	0.885691i	$0.346315\pi$
$350$		0			0
$351$	−8.00098	−	18.5741i	−0.427061	−	0.991415i
$352$	−0.363318	+	0.629285i	−0.0193649	+	0.0335410i
$353$	15.5261	+	8.96401i	0.826372	+	0.477106i	0.852609	−	0.522550i	$-0.175019\pi$
$353$	15.5261	+	8.96401i	0.826372	+	0.477106i	−0.0262367	+	0.999656i	$0.508352\pi$
$354$	12.1511	−	21.0463i	0.645824	−	1.11860i
$355$	1.34879	+	2.33618i	0.0715865	+	0.123991i
$356$			0.951129i			0.0504097i
$357$		0			0
$358$	11.7816	+	6.80213i	0.622679	+	0.359504i
$359$	17.3217	+	10.0007i	0.914204	+	0.527816i	0.881781	−	0.471658i	$-0.156344\pi$
$359$	17.3217	+	10.0007i	0.914204	+	0.527816i	0.0324227	+	0.999474i	$0.489678\pi$
$360$	7.45466			0.392895
$361$	−6.39707	+	11.0801i	−0.336688	+	0.583161i
$362$			17.2301i			0.905596i
$363$	23.6294			1.24022
$364$		0			0
$365$	−6.14421			−0.321602
$366$		−	52.7566i		−	2.75763i
$367$	13.7078	−	23.7427i	0.715544	−	1.23936i	−0.247206	−	0.968963i	$-0.579512\pi$
$367$	13.7078	−	23.7427i	0.715544	−	1.23936i	0.962749	−	0.270395i	$-0.0871543\pi$
$368$	−35.0584			−1.82754
$369$	18.1710	+	10.4910i	0.945942	+	0.546140i
$370$	6.37169	+	3.67870i	0.331248	+	0.191246i
$371$		0			0
$372$			1.29563i			0.0671752i
$373$	7.94643	+	13.7636i	0.411451	+	0.712653i	0.995049	−	0.0993893i	$-0.0316889\pi$
$373$	7.94643	+	13.7636i	0.411451	+	0.712653i	−0.583598	+	0.812043i	$0.698356\pi$
$374$	−2.19277	+	3.79798i	−0.113385	+	0.196389i
$375$	−12.3578	−	7.13481i	−0.638156	−	0.368440i
$376$	−6.50842	+	11.2729i	−0.335646	+	0.581356i
$377$	11.2682	−	15.1199i	0.580341	−	0.778712i
$378$		0			0
$379$	7.60284	−	4.38950i	0.390532	−	0.225474i	−0.291859	−	0.956461i	$-0.594274\pi$
$379$	7.60284	−	4.38950i	0.390532	−	0.225474i	0.682390	+	0.730988i	$0.260940\pi$
$380$	−0.102307			−0.00524822
$381$	4.02249			0.206078
$382$	14.6996	−	8.48682i	0.752098	−	0.434224i
$383$	6.89562	−	3.98119i	0.352349	−	0.203429i	−0.313370	−	0.949631i	$-0.601458\pi$
$383$	6.89562	−	3.98119i	0.352349	−	0.203429i	0.665720	+	0.746202i	$0.268125\pi$
$384$	−25.9308	−	14.9712i	−1.32328	−	0.763994i
$385$		0			0
$386$	8.06198	−	13.9638i	0.410344	−	0.710736i
$387$	4.97159			0.252720
$388$	−0.303074	−	0.174980i	−0.0153863	−	0.00888326i
$389$	16.0217	+	27.7504i	0.812333	+	1.40700i	0.911227	+	0.411904i	$0.135136\pi$
$389$	16.0217	+	27.7504i	0.812333	+	1.40700i	−0.0988938	+	0.995098i	$0.531530\pi$
$390$	−4.37898	+	5.87579i	−0.221738	+	0.297532i
$391$	17.8082			0.900598
$392$		0			0
$393$	12.2550	+	21.2263i	0.618184	+	1.07073i
$394$	1.24815	+	2.16186i	0.0628809	+	0.108913i
$395$	0.441479	−	0.254888i	0.0222132	−	0.0128248i
$396$			0.640716i			0.0321972i
$397$	5.57251	−	3.21729i	0.279676	−	0.161471i	−0.353601	−	0.935396i	$-0.615043\pi$
$397$	5.57251	−	3.21729i	0.279676	−	0.161471i	0.633277	+	0.773925i	$0.281710\pi$
$398$		−	9.13777i		−	0.458035i
$399$		0			0
$400$	9.07219	+	15.7135i	0.453609	+	0.785675i
$401$		−	0.533577i		−	0.0266456i	−0.999911	−	0.0133228i	$-0.995759\pi$
$401$		−	0.533577i		−	0.0266456i	0.999911	−	0.0133228i	$-0.00424090\pi$
$402$	16.3953	+	28.3975i	0.817723	+	1.41634i
$403$	−16.7502	−	12.4832i	−0.834389	−	0.621835i
$404$	−0.724195	+	1.25434i	−0.0360301	+	0.0624059i
$405$	0.402337	−	0.232290i	0.0199923	−	0.0115426i
$406$		0			0
$407$	−8.30697	+	14.3881i	−0.411761	+	0.713191i
$408$	13.7387	+	7.93202i	0.680165	+	0.392694i
$409$		−	39.7528i		−	1.96565i	−0.184547	−	0.982824i	$-0.559082\pi$
$409$		−	39.7528i		−	1.96565i	0.184547	−	0.982824i	$-0.440918\pi$
$410$		−	3.02735i		−	0.149510i
$411$	20.8448	+	12.0347i	1.02820	+	0.593630i
$412$	−0.198648	+	0.344069i	−0.00978670	+	0.0169511i
$413$		0			0
$414$	−54.6913	+	31.5760i	−2.68793	+	1.55188i
$415$	−2.31416	+	4.00825i	−0.113598	+	0.196757i
$416$	−1.48149	+	0.638166i	−0.0726361	+	0.0312887i
$417$	−7.11875	−	12.3300i	−0.348607	−	0.603804i
$418$			5.60761i			0.274277i
$419$	11.9088	+	20.6266i	0.581783	+	1.00768i	0.995268	+	0.0971665i	$0.0309779\pi$
$419$	11.9088	+	20.6266i	0.581783	+	1.00768i	−0.413485	+	0.910511i	$0.635689\pi$
$420$		0			0
$421$		−	23.2419i		−	1.13274i	−0.824151	−	0.566370i	$-0.808347\pi$
$421$		−	23.2419i		−	1.13274i	0.824151	−	0.566370i	$-0.191653\pi$
$422$	−12.8668	+	7.42865i	−0.626346	+	0.361621i
$423$			22.5185i			1.09489i
$424$	22.2014	−	12.8180i	1.07820	−	0.622498i
$425$	−4.60828	−	7.98178i	−0.223535	−	0.387173i
$426$	−10.1789	−	17.6303i	−0.493168	−	0.854192i
$427$		0			0
$428$	0.486253			0.0235039
$429$	−13.2683	−	9.88831i	−0.640600	−	0.477412i
$430$	−0.358658	−	0.621214i	−0.0172960	−	0.0299576i
$431$	2.34424	+	1.35345i	0.112918	+	0.0651932i	0.555395	−	0.831586i	$-0.312567\pi$
$431$	2.34424	+	1.35345i	0.112918	+	0.0651932i	−0.442477	+	0.896780i	$0.645900\pi$
$432$	−21.5137			−1.03508
$433$	2.90945	−	5.03932i	0.139819	−	0.242174i	−0.787609	−	0.616176i	$-0.788681\pi$
$433$	2.90945	−	5.03932i	0.139819	−	0.242174i	0.927428	+	0.374002i	$0.122015\pi$
$434$		0			0
$435$	6.64198	+	3.83475i	0.318459	+	0.183862i
$436$	−0.815290	+	0.470708i	−0.0390453	+	0.0225428i
$437$	19.7199	−	11.3853i	0.943332	−	0.544633i
$438$	46.3682			2.21556
$439$	38.1702			1.82176			0.910882	−	0.412668i	$-0.135403\pi$
$439$	38.1702			1.82176			0.910882	+	0.412668i	$0.135403\pi$
$440$	2.10340	−	1.21440i	0.100276	−	0.0578942i
$441$		0			0
$442$	−8.94139	+	3.85158i	−0.425298	+	0.183201i
$443$	15.8370	−	27.4305i	0.752440	−	1.30326i	−0.194198	−	0.980962i	$-0.562210\pi$
$443$	15.8370	−	27.4305i	0.752440	−	1.30326i	0.946637	−	0.322301i	$-0.104456\pi$
$444$	1.98100	+	1.14373i	0.0940139	+	0.0542790i
$445$	3.11867	−	5.40169i	0.147839	−	0.256065i
$446$	−8.93097	−	15.4689i	−0.422894	−	0.732473i
$447$		−	9.50845i		−	0.449734i
$448$		0			0
$449$	27.1975	+	15.7025i	1.28353	+	0.741045i	0.977491	−	0.210975i	$-0.0676638\pi$
$449$	27.1975	+	15.7025i	1.28353	+	0.741045i	0.306036	+	0.952020i	$0.400997\pi$
$450$	28.3053	+	16.3421i	1.33433	+	0.770373i
$451$	6.83614			0.321901
$452$	−0.140708	+	0.243713i	−0.00661834	+	0.0114633i
$453$			35.7648i			1.68037i
$454$	−0.968995			−0.0454772
$455$		0			0
$456$	20.2847			0.949920
$457$			31.8281i			1.48886i	0.667702	+	0.744429i	$0.267278\pi$
$457$			31.8281i			1.48886i	−0.667702	+	0.744429i	$0.732722\pi$
$458$	12.6723	−	21.9491i	0.592140	−	1.02562i
$459$	10.9281			0.510078
$460$	−0.325093	−	0.187692i	−0.0151575	−	0.00875121i
$461$	−1.01005	−	0.583153i	−0.0470427	−	0.0271601i	0.476294	−	0.879286i	$-0.341980\pi$
$461$	−1.01005	−	0.583153i	−0.0470427	−	0.0271601i	−0.523337	+	0.852126i	$0.675313\pi$
$462$		0			0
$463$			20.3441i			0.945469i	0.881205	+	0.472734i	$0.156733\pi$
$463$			20.3441i			0.945469i	−0.881205	+	0.472734i	$0.843267\pi$
$464$	−10.0297	−	17.3719i	−0.465615	−	0.806470i
$465$	4.24825	−	7.35819i	0.197008	−	0.341228i
$466$	−32.1427	−	18.5576i	−1.48898	−	0.859664i
$467$	0.784697	−	1.35913i	0.0363114	−	0.0628932i	−0.847299	−	0.531117i	$-0.821773\pi$
$467$	0.784697	−	1.35913i	0.0363114	−	0.0628932i	0.883610	+	0.468224i	$0.155106\pi$
$468$	−0.849948	+	1.14048i	−0.0392889	+	0.0527185i
$469$		0			0
$470$	2.81375	−	1.62452i	0.129788	−	0.0749334i
$471$	−29.3008			−1.35011
$472$	−17.8810			−0.823039
$473$	1.40278	−	0.809896i	0.0644999	−	0.0372391i
$474$	−3.33169	+	1.92355i	−0.153030	+	0.0883517i
$475$	−10.2060	−	5.89243i	−0.468283	−	0.270363i
$476$		0			0
$477$	22.1745	−	38.4074i	1.01530	−	1.75856i
$478$	23.0313			1.05343
$479$	6.68501	+	3.85959i	0.305446	+	0.176349i	0.644887	−	0.764278i	$-0.276905\pi$
$479$	6.68501	+	3.85959i	0.305446	+	0.176349i	−0.339441	+	0.940627i	$0.610238\pi$
$480$	−0.328040	−	0.568182i	−0.0149729	−	0.0259338i
$481$	−33.8731	+	14.5911i	−1.54448	+	0.665299i
$482$	24.1334			1.09925
$483$		0			0
$484$	−0.330870	−	0.573083i	−0.0150395	−	0.0260492i
$485$	1.14749	+	1.98751i	0.0521047	+	0.0902481i
$486$	17.1612	−	9.90803i	0.778448	−	0.449437i
$487$			0.0761801i			0.00345205i	0.999999	+	0.00172602i	$0.000549411\pi$
$487$			0.0761801i			0.00345205i	−0.999999	+	0.00172602i	$0.999451\pi$
$488$	−33.6165	+	19.4085i	−1.52175	+	0.878582i
$489$		−	44.5155i		−	2.01306i
$490$		0			0
$491$	0.893574	+	1.54772i	0.0403264	+	0.0698474i	0.885484	−	0.464670i	$-0.153827\pi$
$491$	0.893574	+	1.54772i	0.0403264	+	0.0698474i	−0.845158	+	0.534517i	$0.820494\pi$
$492$		−	0.941220i		−	0.0424335i
$493$	5.09464	+	8.82418i	0.229451	+	0.397421i
$494$	−7.43884	+	9.98156i	−0.334689	+	0.449092i
$495$	2.10085	−	3.63878i	0.0944262	−	0.163551i
$496$	−19.2451	+	11.1112i	−0.864131	+	0.498906i
$497$		0			0
$498$	17.4642	−	30.2488i	0.782589	−	1.35548i
$499$	7.21826	+	4.16747i	0.323134	+	0.186561i	0.652789	−	0.757540i	$-0.273599\pi$
$499$	7.21826	+	4.16747i	0.323134	+	0.186561i	−0.329655	+	0.944102i	$0.606932\pi$
$500$			0.399619i			0.0178715i
$501$			46.3387i			2.07026i
$502$	−7.74152	−	4.46957i	−0.345521	−	0.199487i
$503$	0.720238	−	1.24749i	0.0321138	−	0.0556228i	−0.849522	−	0.527554i	$-0.823109\pi$
$503$	0.720238	−	1.24749i	0.0321138	−	0.0556228i	0.881636	+	0.471931i	$0.156443\pi$
$504$		0			0
$505$	8.22576	−	4.74914i	0.366041	−	0.211334i
$506$	−10.2878	+	17.8189i	−0.457347	+	0.792148i
$507$	−10.5002	−	35.2024i	−0.466329	−	1.56339i
$508$	−0.0563247	−	0.0975572i	−0.00249900	−	0.00432840i
$509$		−	14.8256i		−	0.657135i	−0.944480	−	0.328568i	$-0.893434\pi$
$509$		−	14.8256i		−	0.657135i	0.944480	−	0.328568i	$-0.106566\pi$
$510$	−1.97985	−	3.42920i	−0.0876693	−	0.151848i
$511$		0			0
$512$			23.8204i			1.05272i
$513$	12.1012	−	6.98664i	0.534282	−	0.308468i
$514$			5.08860i			0.224449i
$515$	2.25634	−	1.30270i	0.0994264	−	0.0574038i
$516$	−0.111509	−	0.193139i	−0.00490891	−	0.00850248i
$517$	3.66837	+	6.35380i	0.161335	+	0.279440i
$518$		0			0
$519$	−0.851561			−0.0373794
$520$	5.35503	+	0.628655i	0.234834	+	0.0275683i
$521$	−0.167194	−	0.289588i	−0.00732489	−	0.0126871i	0.862340	−	0.506330i	$-0.168998\pi$
$521$	−0.167194	−	0.289588i	−0.00732489	−	0.0126871i	−0.869665	+	0.493643i	$0.835665\pi$
$522$	−31.2926	−	18.0668i	−1.36964	−	0.790763i
$523$	32.5065			1.42141			0.710705	−	0.703490i	$-0.248376\pi$
$523$	32.5065			1.42141			0.710705	+	0.703490i	$0.248376\pi$
$524$	0.343201	−	0.594441i	0.0149928	−	0.0259683i
$525$		0			0
$526$	21.9881	+	12.6948i	0.958726	+	0.553521i
$527$	9.77570	−	5.64400i	0.425836	−	0.245857i
$528$	−15.2446	+	8.80145i	−0.663434	+	0.383034i
$529$	60.5502			2.63262
$530$	−6.39881			−0.277947
$531$	−26.7890	+	15.4666i	−1.16254	+	0.671194i
$532$		0			0
$533$	12.1683	+	9.06855i	0.527070	+	0.392803i
$534$	−23.5355	+	40.7647i	−1.01848	+	1.76406i
$535$	−2.76155	−	1.59438i	−0.119392	−	0.0689311i
$536$	12.0633	−	20.8942i	0.521053	−	0.902491i
$537$	−13.8686	−	24.0212i	−0.598476	−	1.03659i
$538$			38.1732i			1.64576i
$539$		0			0
$540$	−0.199495	−	0.115178i	−0.00858488	−	0.00495649i
$541$	−9.18120	−	5.30077i	−0.394731	−	0.227898i	0.289477	−	0.957185i	$-0.406519\pi$
$541$	−9.18120	−	5.30077i	−0.394731	−	0.227898i	−0.684208	+	0.729287i	$0.739852\pi$
$542$	−9.03534			−0.388101
$543$	17.5650	−	30.4235i	0.753786	−	1.30560i
$544$		−	0.871633i		−	0.0373709i
$545$	6.17364			0.264450
$546$		0			0
$547$	10.2327			0.437519			0.218760	−	0.975779i	$-0.429799\pi$
$547$	10.2327			0.437519			0.218760	+	0.975779i	$0.429799\pi$
$548$		−	0.674064i		−	0.0287946i
$549$	−33.5758	+	58.1549i	−1.43298	+	2.48199i
$550$	10.6488			0.454067
$551$	11.2831	+	6.51432i	0.480677	+	0.277519i
$552$	64.4574	+	37.2145i	2.74349	+	1.58396i
$553$		0			0
$554$			7.54216i			0.320436i
$555$	−7.50037	−	12.9910i	−0.318373	−	0.551438i
$556$	−0.199360	+	0.345301i	−0.00845474	+	0.0146440i
$557$	−27.7067	−	15.9965i	−1.17397	−	0.677793i	−0.219359	−	0.975644i	$-0.570397\pi$
$557$	−27.7067	−	15.9965i	−1.17397	−	0.677793i	−0.954612	+	0.297851i	$0.903730\pi$
$558$	−20.0150	+	34.6670i	−0.847302	+	1.46757i
$559$	3.57133	+	0.419257i	0.151051	+	0.0177327i
$560$		0			0
$561$	7.74359	−	4.47076i	0.326934	−	0.188756i
$562$	4.90956			0.207097
$563$	10.7913			0.454800			0.227400	−	0.973801i	$-0.426978\pi$
$563$	10.7913			0.454800			0.227400	+	0.973801i	$0.426978\pi$
$564$	0.874811	−	0.505072i	0.0368362	−	0.0212674i
$565$	1.59823	−	0.922737i	0.0672380	−	0.0388199i
$566$	−16.9708	−	9.79808i	−0.713335	−	0.411844i
$567$		0			0
$568$	−7.48937	+	12.9720i	−0.314247	+	0.544292i
$569$	24.6014			1.03134			0.515672	−	0.856786i	$-0.327542\pi$
$569$	24.6014			1.03134			0.515672	+	0.856786i	$0.327542\pi$
$570$	−4.38479	−	2.53156i	−0.183659	−	0.106035i
$571$	8.28621	+	14.3521i	0.346767	+	0.600618i	0.985673	−	0.168667i	$-0.0539461\pi$
$571$	8.28621	+	14.3521i	0.346767	+	0.600618i	−0.638906	+	0.769285i	$0.720613\pi$
$572$	−0.0540319	+	0.460256i	−0.00225919	+	0.0192443i
$573$	−34.6070			−1.44573
$574$		0			0
$575$	−21.6206	−	37.4480i	−0.901641	−	1.56169i
$576$	20.6653	+	35.7934i	0.861054	+	1.49139i
$577$	12.6969	−	7.33053i	0.528577	−	0.305174i	−0.211860	−	0.977300i	$-0.567952\pi$
$577$	12.6969	−	7.33053i	0.528577	−	0.305174i	0.740437	+	0.672126i	$0.234619\pi$
$578$			18.3005i			0.761202i
$579$	−28.4702	+	16.4373i	−1.18318	+	0.683111i
$580$		−	0.214784i		−	0.00891840i
$581$		0			0
$582$	−8.65969	−	14.9990i	−0.358956	−	0.621730i
$583$		−	14.4493i		−	0.598431i
$584$	−17.0583	−	29.5458i	−0.705877	−	1.22262i
$585$	8.56658	−	3.69013i	0.354185	−	0.152568i
$586$	5.78587	−	10.0214i	0.239012	−	0.413981i
$587$	−30.5998	+	17.6668i	−1.26299	+	0.729186i	−0.973652	−	0.228041i	$-0.926768\pi$
$587$	−30.5998	+	17.6668i	−1.26299	+	0.729186i	−0.289336	+	0.957227i	$0.593435\pi$
$588$		0			0
$589$	7.21676	−	12.4998i	0.297362	−	0.515045i
$590$	3.86519	+	2.23157i	0.159127	+	0.0918722i
$591$		−	5.08963i		−	0.209359i
$592$			39.2340i			1.61251i
$593$	14.2283	+	8.21471i	0.584286	+	0.337338i	0.762835	−	0.646593i	$-0.223807\pi$
$593$	14.2283	+	8.21471i	0.584286	+	0.337338i	−0.178549	+	0.983931i	$0.557140\pi$
$594$	−6.31313	+	10.9347i	−0.259031	+	0.448655i
$595$		0			0
$596$	−0.230608	+	0.133142i	−0.00944608	+	0.00545370i
$597$	−9.31535	+	16.1347i	−0.381252	+	0.660348i
$598$	−41.9501	+	18.0704i	−1.71547	+	0.738953i
$599$	−6.04094	−	10.4632i	−0.246826	−	0.427516i	0.715817	−	0.698288i	$-0.246054\pi$
$599$	−6.04094	−	10.4632i	−0.246826	−	0.427516i	−0.962644	+	0.270772i	$0.912721\pi$
$600$		−	38.5206i		−	1.57259i
$601$	3.90743	+	6.76787i	0.159387	+	0.276067i	0.934648	−	0.355574i	$-0.115715\pi$
$601$	3.90743	+	6.76787i	0.159387	+	0.276067i	−0.775261	+	0.631642i	$0.782381\pi$
$602$		0			0
$603$		−	41.7377i		−	1.69969i
$604$	0.867401	−	0.500794i	0.0352941	−	0.0203770i
$605$			4.33957i			0.176429i
$606$	−62.0770	+	35.8401i	−2.52170	+	1.45591i
$607$	17.7825	+	30.8001i	0.721768	+	1.25014i	0.960291	+	0.279002i	$0.0900035\pi$
$607$	17.7825	+	30.8001i	0.721768	+	1.25014i	−0.238523	+	0.971137i	$0.576663\pi$
$608$	−0.557261	−	0.965205i	−0.0225999	−	0.0391442i
$609$		0			0
$610$	9.68882			0.392289
$611$	−1.89900	+	16.1761i	−0.0768252	+	0.654415i
$612$	−0.384284	−	0.665599i	−0.0155338	−	0.0269052i
$613$	10.3376	+	5.96839i	0.417530	+	0.241061i	0.694020	−	0.719956i	$-0.255838\pi$
$613$	10.3376	+	5.96839i	0.417530	+	0.241061i	−0.276490	+	0.961017i	$0.589171\pi$
$614$	11.5500			0.466120
$615$	−3.08618	+	5.34542i	−0.124447	+	0.215548i
$616$		0			0
$617$	−20.4124	−	11.7851i	−0.821772	−	0.474450i	0.0292550	−	0.999572i	$-0.490687\pi$
$617$	−20.4124	−	11.7851i	−0.821772	−	0.474450i	−0.851027	+	0.525122i	$0.824020\pi$
$618$	−17.0278	+	9.83103i	−0.684960	+	0.395462i
$619$	−24.7312	+	14.2786i	−0.994031	+	0.573904i	−0.906477	−	0.422256i	$-0.861238\pi$
$619$	−24.7312	+	14.2786i	−0.994031	+	0.573904i	−0.0875541	+	0.996160i	$0.527905\pi$
$620$	−0.237944			−0.00955606
$621$	51.2710			2.05743
$622$	17.5512	−	10.1332i	0.703738	−	0.406303i
$623$		0			0
$624$	−38.8110	−	4.55623i	−1.55368	−	0.182395i
$625$	−10.5164	+	18.2149i	−0.420656	+	0.728597i
$626$	−20.5640	−	11.8726i	−0.821903	−	0.474526i
$627$	5.71659	−	9.90142i	0.228298	−	0.395425i
$628$	0.410283	+	0.710632i	0.0163721	+	0.0283573i
$629$		−	19.9292i		−	0.794628i
$630$		0			0
$631$	−38.9646	−	22.4962i	−1.55116	−	0.895561i	−0.998048	−	0.0624526i	$-0.980108\pi$
$631$	−38.9646	−	22.4962i	−1.55116	−	0.895561i	−0.553109	−	0.833109i	$-0.686559\pi$
$632$	2.45138	+	1.41530i	0.0975106	+	0.0562978i
$633$	30.2921			1.20400
$634$	−9.70169	+	16.8038i	−0.385303	+	0.667365i
$635$			0.738735i			0.0293158i
$636$	−1.98943			−0.0788860
$637$		0			0
$638$	−11.7727			−0.466085
$639$			25.9125i			1.02508i
$640$	2.74947	−	4.76222i	0.108682	−	0.188243i
$641$	2.53300			0.100048			0.0500238	−	0.998748i	$-0.484070\pi$
$641$	2.53300			0.100048			0.0500238	+	0.998748i	$0.484070\pi$
$642$	20.8405	+	12.0322i	0.822507	+	0.474875i
$643$	−15.9150	−	9.18853i	−0.627627	−	0.362360i	0.152206	−	0.988349i	$-0.451362\pi$
$643$	−15.9150	−	9.18853i	−0.627627	−	0.362360i	−0.779832	+	0.625988i	$0.784696\pi$
$644$		0			0
$645$			1.46251i			0.0575863i
$646$	−3.36329	−	5.82539i	−0.132327	−	0.229197i
$647$	−10.4643	+	18.1248i	−0.411396	+	0.712558i	−0.995043	−	0.0994494i	$-0.968292\pi$
$647$	−10.4643	+	18.1248i	−0.411396	+	0.712558i	0.583647	+	0.812008i	$0.301625\pi$
$648$	2.23404	+	1.28982i	0.0877612	+	0.0506690i
$649$	−5.03917	+	8.72810i	−0.197805	+	0.342608i
$650$	18.9549	+	14.1263i	0.743473	+	0.554079i
$651$		0			0
$652$	−1.07963	+	0.623326i	−0.0422817	+	0.0244113i
$653$	−48.1160			−1.88292			−0.941461	−	0.337121i	$-0.890547\pi$
$653$	−48.1160			−1.88292			−0.941461	+	0.337121i	$0.890547\pi$
$654$	−46.5903			−1.82183
$655$	−3.89824	+	2.25065i	−0.152317	+	0.0879401i
$656$	13.9808	−	8.07180i	0.545857	−	0.315151i
$657$	−51.1129	−	29.5100i	−1.99410	−	1.15130i
$658$		0			0
$659$	1.10819	−	1.91944i	0.0431690	−	0.0747708i	−0.843634	−	0.536919i	$-0.819588\pi$
$659$	1.10819	−	1.91944i	0.0431690	−	0.0747708i	0.886803	+	0.462148i	$0.152921\pi$
$660$	−0.188482			−0.00733664
$661$	−0.552034	−	0.318717i	−0.0214716	−	0.0123966i	0.489226	−	0.872157i	$-0.337279\pi$
$661$	−0.552034	−	0.318717i	−0.0214716	−	0.0123966i	−0.510697	+	0.859761i	$0.670613\pi$
$662$	4.79537	+	8.30582i	0.186377	+	0.322815i
$663$	19.7143	+	2.31437i	0.765642	+	0.0898827i
$664$	−25.6994			−0.997331
$665$		0			0
$666$	35.3368	+	61.2052i	1.36927	+	2.37165i
$667$	23.9024	+	41.4002i	0.925506	+	1.60302i
$668$	1.12385	−	0.648856i	0.0434831	−	0.0251050i
$669$			36.4181i			1.40801i
$670$	−5.21523	+	3.01102i	−0.201482	+	0.116326i
$671$			21.8786i			0.844614i
$672$		0			0
$673$	7.70343	+	13.3427i	0.296945	+	0.514324i	0.975436	−	0.220285i	$-0.0706988\pi$
$673$	7.70343	+	13.3427i	0.296945	+	0.514324i	−0.678490	+	0.734609i	$0.737365\pi$
$674$		−	15.4616i		−	0.595559i
$675$	−13.2676	−	22.9801i	−0.510669	−	0.884505i
$676$	−0.706735	+	0.747581i	−0.0271821	+	0.0287531i
$677$	−5.84060	+	10.1162i	−0.224473	+	0.388798i	−0.956161	−	0.292841i	$-0.905399\pi$
$677$	−5.84060	+	10.1162i	−0.224473	+	0.388798i	0.731689	+	0.681639i	$0.238733\pi$
$678$	−12.0613	+	6.96358i	−0.463210	+	0.267435i
$679$		0			0
$680$	−1.45673	+	2.52312i	−0.0558629	+	0.0967574i
$681$	1.71097	+	0.987826i	0.0655643	+	0.0378536i
$682$			13.0421i			0.499409i
$683$		−	22.9114i		−	0.876680i	−0.898809	−	0.438340i	$-0.855567\pi$
$683$		−	22.9114i		−	0.876680i	0.898809	−	0.438340i	$-0.144433\pi$
$684$	−0.851075	−	0.491369i	−0.0325417	−	0.0187879i
$685$	−2.21020	+	3.82817i	−0.0844473	+	0.146267i
$686$		0			0
$687$	−44.7514	+	25.8372i	−1.70737	+	0.985752i
$688$	1.91258	−	3.31268i	0.0729163	−	0.126295i
$689$	19.1679	−	25.7199i	0.730240	−	0.979849i
$690$	−9.28883	−	16.0887i	−0.353620	−	0.612487i
$691$			47.2325i			1.79681i	0.439167	+	0.898405i	$0.355274\pi$
$691$			47.2325i			1.79681i	−0.439167	+	0.898405i	$0.644726\pi$
$692$	0.0119239	+	0.0206529i	0.000453280	+	0.000785104i
$693$		0			0
$694$			6.82596i			0.259110i
$695$	2.26443	−	1.30737i	0.0858946	−	0.0495913i
$696$			42.5860i			1.61422i
$697$	−7.10163	+	4.10013i	−0.268994	+	0.155303i
$698$	1.05565	+	1.82843i	0.0399568	+	0.0692071i
$699$	37.8365	+	65.5347i	1.43111	+	2.47875i
$700$		0			0
$701$	12.2098			0.461158			0.230579	−	0.973054i	$-0.425938\pi$
$701$	12.2098			0.461158			0.230579	+	0.973054i	$0.425938\pi$
$702$	−25.7429	+	11.0890i	−0.971603	+	0.418527i
$703$	−12.7413	−	22.0686i	−0.480548	−	0.832334i
$704$	11.6618	+	6.73295i	0.439521	+	0.253758i
$705$	−6.62435			−0.249488
$706$	12.4237	−	21.5185i	0.467572	−	0.809858i
$707$		0			0
$708$	1.20171	+	0.693808i	0.0451630	+	0.0260749i
$709$	15.4910	−	8.94374i	0.581777	−	0.335889i	−0.180062	−	0.983655i	$-0.557630\pi$
$709$	15.4910	−	8.94374i	0.581777	−	0.335889i	0.761839	+	0.647766i	$0.224297\pi$
$710$	3.23783	−	1.86936i	0.121514	−	0.0701560i
$711$	4.89681			0.183645
$712$	34.6337			1.29795
$713$	45.8644	−	26.4798i	1.71764	−	0.991678i
$714$		0			0
$715$	1.81600	−	2.43674i	0.0679146	−	0.0911290i
$716$	−0.388390	+	0.672711i	−0.0145148	+	0.0251404i
$717$	−40.6667	−	23.4789i	−1.51872	−	0.876836i
$718$	13.8605	−	24.0070i	0.517268	−	0.895935i
$719$	−4.56317	−	7.90364i	−0.170178	−	0.294756i	0.768304	−	0.640085i	$-0.221101\pi$
$719$	−4.56317	−	7.90364i	−0.170178	−	0.294756i	−0.938482	+	0.345329i	$0.887767\pi$
$720$		−	9.92235i		−	0.369784i
$721$		0			0
$722$	15.3564	+	8.86604i	0.571507	+	0.329960i
$723$	−42.6126	−	24.6024i	−1.58478	−	0.914973i
$724$	−0.983812			−0.0365631
$725$	12.3706	−	21.4266i	0.459434	−	0.795763i
$726$		−	32.7493i		−	1.21544i
$727$	−33.6859			−1.24934			−0.624670	−	0.780889i	$-0.714767\pi$
$727$	−33.6859			−1.24934			−0.624670	+	0.780889i	$0.714767\pi$
$728$		0			0
$729$	−43.0880			−1.59585
$730$			8.51558i			0.315176i
$731$	−0.971507	+	1.68270i	−0.0359325	+	0.0622369i
$732$	3.01231			0.111338
$733$	−40.2134	−	23.2172i	−1.48532	−	0.857547i	−0.485455	−	0.874262i	$-0.661346\pi$
$733$	−40.2134	−	23.2172i	−1.48532	−	0.857547i	−0.999860	+	0.0167147i	$0.994679\pi$
$734$	−32.9062	−	18.9984i	−1.21459	−	0.701245i
$735$		0			0
$736$		−	4.08942i		−	0.150738i
$737$	−6.79927	−	11.7767i	−0.250454	−	0.433799i
$738$	14.5400	−	25.1841i	0.535226	−	0.927039i
$739$	1.60237	+	0.925127i	0.0589440	+	0.0340314i	0.529182	−	0.848508i	$-0.322499\pi$
$739$	1.60237	+	0.925127i	0.0589440	+	0.0340314i	−0.470238	+	0.882539i	$0.655832\pi$
$740$	−0.210047	+	0.363813i	−0.00772149	+	0.0133740i
$741$	23.3104	−	10.0412i	0.856328	−	0.368871i
$742$		0			0
$743$	28.7095	−	16.5755i	1.05325	−	0.608094i	0.129693	−	0.991554i	$-0.458601\pi$
$743$	28.7095	−	16.5755i	1.05325	−	0.608094i	0.923558	+	0.383460i	$0.125268\pi$
$744$	47.1781			1.72963
$745$	1.74624			0.0639773
$746$	19.0757	−	11.0134i	0.698412	−	0.403228i
$747$	−38.5024	+	22.2294i	−1.40873	+	0.813331i
$748$	−0.216858	−	0.125203i	−0.00792913	−	0.00457788i
$749$		0			0
$750$	−9.88850	+	17.1274i	−0.361077	+	0.625404i
$751$	20.7743			0.758064			0.379032	−	0.925384i	$-0.376257\pi$
$751$	20.7743			0.758064			0.379032	+	0.925384i	$0.376257\pi$
$752$	15.0046	+	8.66289i	0.547160	+	0.315903i
$753$	9.11286	+	15.7839i	0.332091	+	0.575199i
$754$	−20.9554	−	15.6172i	−0.763150	−	0.568744i
$755$	−6.56824			−0.239043
$756$		0			0
$757$	−21.8075	−	37.7717i	−0.792607	−	1.37283i	−0.924348	−	0.381551i	$-0.875390\pi$
$757$	−21.8075	−	37.7717i	−0.792607	−	1.37283i	0.131741	−	0.991284i	$-0.457943\pi$
$758$	−6.08364	−	10.5372i	−0.220968	−	0.382727i
$759$	36.3304	−	20.9754i	1.31871	−	0.761358i
$760$			3.72532i			0.135131i
$761$	10.7302	−	6.19511i	0.388971	−	0.224573i	−0.292743	−	0.956191i	$-0.594568\pi$
$761$	10.7302	−	6.19511i	0.388971	−	0.224573i	0.681714	+	0.731619i	$0.261235\pi$
$762$		−	5.57497i		−	0.201960i
$763$		0			0
$764$	0.484583	+	0.839323i	0.0175316	+	0.0303656i
$765$			5.04013i			0.182226i
$766$	−5.51773	−	9.55700i	−0.199364	−	0.345308i
$767$	−20.5481	+	8.85127i	−0.741948	+	0.319601i
$768$	2.67917	−	4.64046i	0.0966763	−	0.167448i
$769$	4.80955	−	2.77680i	0.173437	−	0.100134i	−0.410769	−	0.911740i	$-0.634740\pi$
$769$	4.80955	−	2.77680i	0.173437	−	0.100134i	0.584205	+	0.811606i	$0.301406\pi$
$770$		0			0
$771$	5.18750	−	8.98501i	0.186823	−	0.323587i
$772$	0.797307	+	0.460325i	0.0286957	+	0.0165675i
$773$			43.8042i			1.57553i	0.615977	+	0.787764i	$0.288761\pi$
$773$			43.8042i			1.57553i	−0.615977	+	0.787764i	$0.711239\pi$
$774$		−	6.89039i		−	0.247670i
$775$	−23.7370	−	13.7046i	−0.852659	−	0.492283i
$776$	−6.37159	+	11.0359i	−0.228727	+	0.396166i
$777$		0			0
$778$	38.4608	−	22.2053i	1.37889	−	0.796100i
$779$	−5.24267	+	9.08058i	−0.187838	+	0.325346i
$780$	−0.335498	−	0.250032i	−0.0120128	−	0.00895260i
$781$	4.22127	+	7.31145i	0.151049	+	0.261624i
$782$		−	24.6813i		−	0.882600i
$783$	14.6678	+	25.4054i	0.524185	+	0.907916i
$784$		0			0
$785$		−	5.38113i		−	0.192061i
$786$	29.4187	−	16.9849i	1.04933	−	0.605830i
$787$			24.8009i			0.884057i	0.897001	+	0.442029i	$0.145741\pi$
$787$			24.8009i			0.884057i	−0.897001	+	0.442029i	$0.854259\pi$
$788$	−0.123439	+	0.0712673i	−0.00439732	+	0.00253879i
$789$	−25.8831	−	44.8308i	−0.921462	−	1.59602i
$790$	−0.353263	−	0.611870i	−0.0125685	−	0.0217693i
$791$		0			0
$792$	23.3305			0.829015
$793$	−29.0233	+	38.9440i	−1.03065	+	1.38294i
$794$	−4.45901	−	7.72323i	−0.158244	−	0.274087i
$795$	11.2985	+	6.52316i	0.400715	+	0.231353i
$796$	0.521751			0.0184930
$797$	8.23575	−	14.2647i	0.291725	−	0.505283i	−0.682492	−	0.730893i	$-0.739104\pi$
$797$	8.23575	−	14.2647i	0.291725	−	0.505283i	0.974218	+	0.225610i	$0.0724373\pi$
$798$		0			0
$799$	−7.62168	−	4.40038i	−0.269636	−	0.155674i
$800$	−1.83292	+	1.05823i	−0.0648034	+	0.0374142i
$801$	51.8876	−	29.9573i	1.83336	−	1.05849i
$802$	−0.739513			−0.0261131
$803$	−19.2293			−0.678587
$804$	−1.62145	+	0.936144i	−0.0571841	+	0.0330152i
$805$		0			0
$806$	−17.3012	+	23.2150i	−0.609408	+	0.817715i
$807$	38.9151	−	67.4028i	1.36987	−	2.37269i
$808$	45.6747	+	26.3703i	1.60683	+	0.927704i
$809$	−0.690968	+	1.19679i	−0.0242932	+	0.0420770i	−0.877916	−	0.478814i	$-0.841067\pi$
$809$	−0.690968	+	1.19679i	−0.0242932	+	0.0420770i	0.853623	+	0.520891i	$0.174400\pi$
$810$	−0.321942	−	0.557621i	−0.0113119	−	0.0195928i
$811$		−	6.83571i		−	0.240034i	−0.992772	−	0.120017i	$-0.961705\pi$
$811$		−	6.83571i		−	0.240034i	0.992772	−	0.120017i	$-0.0382950\pi$
$812$		0			0
$813$	15.9538	+	9.21093i	0.559524	+	0.323041i
$814$	19.9412	+	11.5131i	0.698939	+	0.403533i
$815$	8.17533			0.286369
$816$	10.5577	−	18.2865i	0.369595	−	0.640157i
$817$			2.48446i			0.0869201i
$818$	−55.0954			−1.92637
$819$		0			0
$820$	0.172856			0.00603640
$821$		−	10.5425i		−	0.367936i	−0.982932	−	0.183968i	$-0.941106\pi$
$821$		−	10.5425i		−	0.367936i	0.982932	−	0.183968i	$-0.0588943\pi$
$822$	16.6796	−	28.8899i	0.581767	−	1.00765i
$823$	−14.8330			−0.517047			−0.258524	−	0.966005i	$-0.583236\pi$
$823$	−14.8330			−0.517047			−0.258524	+	0.966005i	$0.583236\pi$
$824$	12.5287	+	7.23343i	0.436457	+	0.251988i
$825$	−18.8027	−	10.8558i	−0.654627	−	0.377949i
$826$		0			0
$827$			55.6758i			1.93604i	0.250879	+	0.968018i	$0.419280\pi$
$827$			55.6758i			1.93604i	−0.250879	+	0.968018i	$0.580720\pi$
$828$	−1.80294	−	3.12278i	−0.0626564	−	0.108524i
$829$	0.0232424	−	0.0402570i	0.000807242	−	0.00139818i	−0.865622	−	0.500699i	$-0.833076\pi$
$829$	0.0232424	−	0.0402570i	0.000807242	−	0.00139818i	0.866429	+	0.499301i	$0.166410\pi$
$830$	5.55524	+	3.20732i	0.192825	+	0.111328i
$831$	7.68873	−	13.3173i	0.266719	−	0.461971i
$832$	11.8264	+	27.4548i	0.410006	+	0.951823i
$833$		0			0
$834$	−17.0888	+	9.86624i	−0.591738	+	0.341640i
$835$	−8.51016			−0.294506
$836$	−0.320185			−0.0110738
$837$	28.1449	−	16.2495i	0.972831	−	0.561664i
$838$	28.5875	−	16.5050i	0.987540	−	0.570157i
$839$	−22.1248	−	12.7738i	−0.763833	−	0.440999i	0.0668370	−	0.997764i	$-0.478709\pi$
$839$	−22.1248	−	12.7738i	−0.763833	−	0.440999i	−0.830670	+	0.556765i	$0.812043\pi$
$840$		0			0
$841$	0.823775	−	1.42682i	0.0284060	−	0.0492007i
$842$	−32.2121			−1.11010
$843$	−8.66886	−	5.00497i	−0.298572	−	0.172380i
$844$	−0.424164	−	0.734673i	−0.0146003	−	0.0252885i
$845$	6.46497	−	1.92837i	0.222402	−	0.0663380i
$846$	31.2096			1.07301
$847$		0			0
$848$	−17.0611	−	29.5507i	−0.585881	−	1.01478i
$849$	19.9770	+	34.6012i	0.685609	+	1.18751i
$850$	−11.0624	+	6.38686i	−0.379436	+	0.219068i
$851$		−	93.5013i		−	3.20518i
$852$	1.00666	−	0.581197i	0.0344877	−	0.0199115i
$853$			22.6671i			0.776105i	0.921637	+	0.388053i	$0.126852\pi$
$853$			22.6671i			0.776105i	−0.921637	+	0.388053i	$0.873148\pi$
$854$		0			0
$855$	3.22231	+	5.58120i	0.110201	+	0.190873i
$856$		−	17.7061i		−	0.605181i
$857$	18.5268	+	32.0893i	0.632862	+	1.09615i	0.986964	+	0.160943i	$0.0514534\pi$
$857$	18.5268	+	32.0893i	0.632862	+	1.09615i	−0.354101	+	0.935207i	$0.615213\pi$
$858$	−13.7047	+	18.3892i	−0.467872	+	0.627798i
$859$	−2.12169	+	3.67488i	−0.0723912	+	0.125385i	−0.899949	−	0.435996i	$-0.856396\pi$
$859$	−2.12169	+	3.67488i	−0.0723912	+	0.125385i	0.827558	+	0.561381i	$0.189730\pi$
$860$	0.0354702	−	0.0204788i	0.00120953	−	0.000698320i
$861$		0			0
$862$	1.87581	−	3.24900i	0.0638904	−	0.110661i
$863$	−6.49563	−	3.75025i	−0.221114	−	0.127660i	0.385352	−	0.922770i	$-0.374080\pi$
$863$	−6.49563	−	3.75025i	−0.221114	−	0.127660i	−0.606466	+	0.795110i	$0.707413\pi$
$864$		−	2.50949i		−	0.0853746i
$865$		−	0.156390i		−	0.00531743i
$866$	−6.98425	−	4.03236i	−0.237335	−	0.137025i
$867$	18.6562	−	32.3135i	0.633598	−	1.09742i
$868$		0			0
$869$	1.38168	−	0.797714i	0.0468703	−	0.0270606i
$870$	5.31478	−	9.20547i	0.180188	−	0.312095i
$871$	3.51976	−	29.9822i	0.119263	−	1.01591i
$872$	17.1400	+	29.6874i	0.580434	+	1.00534i
$873$			22.0451i			0.746113i
$874$	−15.7795	−	27.3309i	−0.533749	−	0.924481i
$875$		0			0
$876$			2.64755i			0.0894523i
$877$	24.4996	−	14.1448i	0.827291	−	0.477637i	−0.0256330	−	0.999671i	$-0.508160\pi$
$877$	24.4996	−	14.1448i	0.827291	−	0.477637i	0.852924	+	0.522035i	$0.174827\pi$
$878$		−	52.9021i		−	1.78536i
$879$	−20.4324	+	11.7966i	−0.689166	+	0.397890i
$880$	−1.61640	−	2.79968i	−0.0544888	−	0.0943773i
$881$	19.7860	+	34.2704i	0.666609	+	1.15460i	0.978846	+	0.204596i	$0.0655882\pi$
$881$	19.7860	+	34.2704i	0.666609	+	1.15460i	−0.312238	+	0.950004i	$0.601079\pi$
$882$		0			0
$883$	−28.3609			−0.954419			−0.477209	−	0.878790i	$-0.658352\pi$
$883$	−28.3609			−0.954419			−0.477209	+	0.878790i	$0.658352\pi$
$884$	−0.219919	−	0.510538i	−0.00739667	−	0.0171713i
$885$	−4.54987	−	7.88061i	−0.152942	−	0.264904i
$886$	−38.0174	−	21.9494i	−1.27722	−	0.737403i
$887$	43.7186			1.46793			0.733963	−	0.679189i	$-0.237669\pi$
$887$	43.7186			1.46793			0.733963	+	0.679189i	$0.237669\pi$
$888$	41.6469	−	72.1345i	1.39758	−	2.42068i
$889$		0			0
$890$	−7.48649	−	4.32233i	−0.250948	−	0.144885i
$891$	1.25918	−	0.726988i	0.0421841	−	0.0243550i
$892$	0.883247	−	0.509943i	0.0295733	−	0.0170742i
$893$	−11.2532			−0.376573
$894$	−13.1783			−0.440747
$895$	4.41152	−	2.54699i	0.147461	−	0.0851366i
$896$		0			0
$897$	92.4934	+	10.8583i	3.08826	+	0.362547i
$898$	21.7629	−	37.6944i	0.726236	−	1.25788i
$899$	26.2422	+	15.1509i	0.875227	+	0.505312i
$900$	−0.933105	+	1.61619i	−0.0311035	+	0.0538728i
$901$	8.66632	+	15.0105i	0.288717	+	0.500073i
$902$		−	9.47456i		−	0.315468i
$903$		0			0
$904$	8.87439	+	5.12363i	0.295158	+	0.170409i
$905$	5.58731	+	3.22583i	0.185728	+	0.107230i
$906$	49.5683			1.64679
$907$	−18.3493	+	31.7818i	−0.609277	+	1.05530i	0.382083	+	0.924128i	$0.375207\pi$
$907$	−18.3493	+	31.7818i	−0.609277	+	1.05530i	−0.991360	+	0.131171i	$0.958126\pi$
$908$		−	0.0553280i		−	0.00183612i
$909$	91.2387			3.02620
$910$		0			0
$911$	−35.5211			−1.17686			−0.588432	−	0.808546i	$-0.700255\pi$
$911$	−35.5211			−1.17686			−0.588432	+	0.808546i	$0.700255\pi$
$912$		−	26.9995i		−	0.894044i
$913$	−7.24254	+	12.5444i	−0.239693	+	0.415161i
$914$	44.1123			1.45911
$915$	−17.1077	−	9.87711i	−0.565562	−	0.326527i
$916$	1.25326	+	0.723569i	0.0414088	+	0.0239074i
$917$		0			0
$918$		−	15.1458i		−	0.499885i
$919$	−10.9667	−	18.9949i	−0.361758	−	0.626583i	0.626492	−	0.779428i	$-0.284490\pi$
$919$	−10.9667	−	18.9949i	−0.361758	−	0.626583i	−0.988250	+	0.152844i	$0.951157\pi$
$920$	−6.83449	+	11.8377i	−0.225327	+	0.390277i
$921$	−20.3940	−	11.7745i	−0.672005	−	0.387982i
$922$	−0.808222	+	1.39988i	−0.0266174	+	0.0461026i
$923$	−2.18521	+	18.6142i	−0.0719272	+	0.612693i
$924$		0			0
$925$	−41.9082	+	24.1957i	−1.37793	+	0.795549i
$926$	28.1959			0.926575
$927$	25.0270			0.821993
$928$	2.02636	−	1.16992i	0.0665186	−	0.0384045i
$929$	−13.4383	+	7.75858i	−0.440895	+	0.254551i	−0.703977	−	0.710223i	$-0.748594\pi$
$929$	−13.4383	+	7.75858i	−0.440895	+	0.254551i	0.263082	+	0.964773i	$0.415261\pi$
$930$	−10.1981	−	5.88788i	−0.334409	−	0.193071i
$931$		0			0
$932$	1.05961	−	1.83529i	0.0347086	−	0.0601171i
$933$	−41.3204			−1.35277
$934$	−1.88370	−	1.08755i	−0.0616364	−	0.0355858i
$935$	0.821061	+	1.42212i	0.0268516	+	0.0465083i
$936$	41.5284	+	30.9494i	1.35740	+	1.01161i
$937$	−40.8110			−1.33324			−0.666618	−	0.745399i	$-0.732259\pi$
$937$	−40.8110			−1.33324			−0.666618	+	0.745399i	$0.732259\pi$
$938$		0			0
$939$	24.2067	+	41.9273i	0.789957	+	1.36825i
$940$	0.0927572	+	0.160660i	0.00302541	+	0.00524016i
$941$	−44.6814	+	25.7968i	−1.45657	+	0.840952i	−0.998841	−	0.0481384i	$-0.984671\pi$
$941$	−44.6814	+	25.7968i	−1.45657	+	0.840952i	−0.457731	+	0.889091i	$0.651338\pi$
$942$			40.6096i			1.32313i
$943$	−33.3186	+	19.2365i	−1.08500	+	0.626427i
$944$			23.8001i			0.774627i
$945$		0			0
$946$	−1.12248	−	1.94419i	−0.0364949	−	0.0632110i
$947$		−	4.98209i		−	0.161896i	−0.996718	−	0.0809482i	$-0.974205\pi$
$947$		−	4.98209i		−	0.161896i	0.996718	−	0.0809482i	$-0.0257948\pi$
$948$	−0.109832	−	0.190234i	−0.00356717	−	0.00617851i
$949$	−34.2282	−	25.5088i	−1.11109	−	0.828051i
$950$	−8.16663	+	14.1450i	−0.264961	+	0.458925i
$951$	34.2608	−	19.7805i	1.11098	−	0.641426i
$952$		0			0
$953$	15.1163	−	26.1822i	0.489664	−	0.848123i	−0.510265	−	0.860017i	$-0.670453\pi$
$953$	15.1163	−	26.1822i	0.489664	−	0.848123i	0.999929	+	0.0118941i	$0.00378608\pi$
$954$	−53.2309	−	30.7329i	−1.72341	−	0.995013i
$955$		−	6.35562i		−	0.205663i
$956$			1.31505i			0.0425317i
$957$	20.7871	+	12.0015i	0.671953	+	0.387952i
$958$	5.34921	−	9.26511i	0.172825	−	0.299342i
$959$		0			0
$960$	−10.5295	+	6.07919i	−0.339837	+	0.196205i
$961$	1.28469	−	2.22516i	0.0414418	−	0.0717792i
$962$	20.2226	+	46.9465i	0.652004	+	1.51362i
$963$	−15.3153	−	26.5269i	−0.493529	−	0.854817i
$964$			1.37798i			0.0443816i
$965$	−3.01873	−	5.22860i	−0.0971764	−	0.168315i
$966$		0			0
$967$			29.9990i			0.964703i	0.875978	+	0.482352i	$0.160217\pi$
$967$			29.9990i			0.964703i	−0.875978	+	0.482352i	$0.839783\pi$
$968$	−20.8678	+	12.0481i	−0.670718	+	0.387239i
$969$			13.7146i			0.440577i
$970$	2.75459	−	1.59036i	0.0884446	−	0.0510635i
$971$	22.0620	+	38.2125i	0.708003	+	1.22630i	0.965597	+	0.260044i	$0.0837371\pi$
$971$	22.0620	+	38.2125i	0.708003	+	1.22630i	−0.257594	+	0.966253i	$0.582930\pi$
$972$	0.565732	+	0.979876i	0.0181459	+	0.0314295i
$973$		0			0
$974$	0.105582			0.00338306
$975$	−19.0681	−	44.2662i	−0.610667	−	1.41765i
$976$	25.8333	+	44.7445i	0.826902	+	1.43224i
$977$	12.9925	+	7.50121i	0.415666	+	0.239985i	0.693221	−	0.720725i	$-0.256191\pi$
$977$	12.9925	+	7.50121i	0.415666	+	0.239985i	−0.277555	+	0.960710i	$0.589524\pi$
$978$	−61.6964			−1.97283
$979$	9.76037	−	16.9055i	0.311943	−	0.540301i
$980$		0			0
$981$	51.3577	+	29.6514i	1.63973	+	0.946696i
$982$	2.14506	−	1.23845i	0.0684516	−	0.0395206i
$983$	5.21223	−	3.00928i	0.166244	−	0.0959812i	−0.414569	−	0.910018i	$-0.636068\pi$
$983$	5.21223	−	3.00928i	0.166244	−	0.0959812i	0.580814	+	0.814037i	$0.302734\pi$
$984$	−34.2729			−1.09258
$985$	0.934717			0.0297825
$986$	12.2299	−	7.06093i	0.389479	−	0.224866i
$987$		0			0
$988$	−0.569930	−	0.424745i	−0.0181319	−	0.0135129i
$989$	−4.55800	+	7.89469i	−0.144936	+	0.251036i
$990$	−5.04318	−	2.91168i	−0.160283	−	0.0925392i
$991$	−16.9200	+	29.3063i	−0.537482	+	0.930946i	0.461557	+	0.887111i	$0.347291\pi$
$991$	−16.9200	+	29.3063i	−0.537482	+	0.930946i	−0.999039	+	0.0438356i	$0.986042\pi$
$992$	−1.29607	−	2.24487i	−0.0411504	−	0.0712746i
$993$		−	19.5542i		−	0.620535i
$994$		0			0
$995$	−2.96315	−	1.71078i	−0.0939382	−	0.0542353i
$996$	1.72716	+	0.997175i	0.0547271	+	0.0315967i
$997$	−26.3215			−0.833610			−0.416805	−	0.908996i	$-0.636850\pi$
$997$	−26.3215			−0.833610			−0.416805	+	0.908996i	$0.636850\pi$
$998$	5.77591	−	10.0042i	0.182833	−	0.316676i
$999$		−	57.3775i		−	1.81534i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.k.g.569.2		12
7.2	even	3		637.2.q.h.491.2		12
7.3	odd	6		637.2.u.h.361.5		12
7.4	even	3		637.2.u.i.361.5		12
7.5	odd	6		91.2.q.a.36.2	✓	12
7.6	odd	2		637.2.k.h.569.2		12
13.4	even	6		637.2.u.i.30.5		12
21.5	even	6		819.2.ct.a.127.5		12
28.19	even	6		1456.2.cc.c.673.1		12
91.2	odd	12		8281.2.a.ch.1.1		6
91.4	even	6	inner	637.2.k.g.459.5		12
91.17	odd	6		637.2.k.h.459.5		12
91.30	even	6		637.2.q.h.589.2		12
91.37	odd	12		8281.2.a.by.1.6		6
91.54	even	12		1183.2.a.p.1.1		6
91.68	odd	6		1183.2.c.i.337.3		12
91.69	odd	6		637.2.u.h.30.5		12
91.75	odd	6		1183.2.c.i.337.10		12
91.82	odd	6		91.2.q.a.43.2	yes	12
91.89	even	12		1183.2.a.m.1.6		6
273.173	even	6		819.2.ct.a.316.5		12
364.355	even	6		1456.2.cc.c.225.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.2	✓	12	7.5	odd	6
91.2.q.a.43.2	yes	12	91.82	odd	6
637.2.k.g.459.5		12	91.4	even	6	inner
637.2.k.g.569.2		12	1.1	even	1	trivial
637.2.k.h.459.5		12	91.17	odd	6
637.2.k.h.569.2		12	7.6	odd	2
637.2.q.h.491.2		12	7.2	even	3
637.2.q.h.589.2		12	91.30	even	6
637.2.u.h.30.5		12	91.69	odd	6
637.2.u.h.361.5		12	7.3	odd	6
637.2.u.i.30.5		12	13.4	even	6
637.2.u.i.361.5		12	7.4	even	3
819.2.ct.a.127.5		12	21.5	even	6
819.2.ct.a.316.5		12	273.173	even	6
1183.2.a.m.1.6		6	91.89	even	12
1183.2.a.p.1.1		6	91.54	even	12
1183.2.c.i.337.3		12	91.68	odd	6
1183.2.c.i.337.10		12	91.75	odd	6
1456.2.cc.c.225.1		12	364.355	even	6
1456.2.cc.c.673.1		12	28.19	even	6
8281.2.a.by.1.6		6	91.37	odd	12
8281.2.a.ch.1.1		6	91.2	odd	12

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.38595i q^{2} +(-1.41289 + 2.44719i) q^{3} +0.0791355 q^{4} +(-0.449430 - 0.259479i) q^{5} +(3.39169 + 1.95819i) q^{6} -2.88158i q^{8} +(-2.49250 - 4.31714i) q^{9} +O(q^{10})\)	\(q-1.38595i q^{2} +(-1.41289 + 2.44719i) q^{3} +0.0791355 q^{4} +(-0.449430 - 0.259479i) q^{5} +(3.39169 + 1.95819i) q^{6} -2.88158i q^{8} +(-2.49250 - 4.31714i) q^{9} +(-0.359625 + 0.622889i) q^{10} +(-1.40656 - 0.812080i) q^{11} +(-0.111810 + 0.193660i) q^{12} +(-1.42641 - 3.31140i) q^{13} +(1.26999 - 0.733228i) q^{15} -3.83547 q^{16} +1.94825 q^{17} +(-5.98335 + 3.45449i) q^{18} +(2.15740 - 1.24558i) q^{19} +(-0.0355659 - 0.0205340i) q^{20} +(-1.12550 + 1.94943i) q^{22} +9.14058 q^{23} +(7.05179 + 4.07135i) q^{24} +(-2.36534 - 4.09689i) q^{25} +(-4.58944 + 1.97694i) q^{26} +5.60916 q^{27} +(2.61498 + 4.52928i) q^{29} +(-1.01622 - 1.76014i) q^{30} +(5.01767 - 2.89695i) q^{31} -0.447392i q^{32} +(3.97463 - 2.29475i) q^{33} -2.70019i q^{34} +(-0.197245 - 0.341639i) q^{36} -10.2293i q^{37} +(-1.72631 - 2.99006i) q^{38} +(10.1190 + 1.18792i) q^{39} +(-0.747709 + 1.29507i) q^{40} +(-3.64513 + 2.10452i) q^{41} +(-0.498655 + 0.863697i) q^{43} +(-0.111309 - 0.0642644i) q^{44} +2.58700i q^{45} -12.6684i q^{46} +(-3.91206 - 2.25863i) q^{47} +(5.41908 - 9.38612i) q^{48} +(-5.67810 + 3.27825i) q^{50} +(-2.75266 + 4.76775i) q^{51} +(-0.112880 - 0.262049i) q^{52} +(4.44825 + 7.70460i) q^{53} -7.77403i q^{54} +(0.421434 + 0.729946i) q^{55} +7.03944i q^{57} +(6.27736 - 3.62424i) q^{58} -6.20526i q^{59} +(0.100501 - 0.0580244i) q^{60} +(-6.73536 - 11.6660i) q^{61} +(-4.01504 - 6.95426i) q^{62} -8.29100 q^{64} +(-0.218163 + 1.85836i) q^{65} +(-3.18042 - 5.50865i) q^{66} +(7.25094 + 4.18633i) q^{67} +0.154176 q^{68} +(-12.9146 + 22.3688i) q^{69} +(-4.50168 - 2.59905i) q^{71} +(-12.4402 + 7.18234i) q^{72} +(10.2533 - 5.91976i) q^{73} -14.1773 q^{74} +13.3678 q^{75} +(0.170727 - 0.0985694i) q^{76} +(1.64640 - 14.0244i) q^{78} +(-0.491155 + 0.850705i) q^{79} +(1.72377 + 0.995221i) q^{80} +(-0.447609 + 0.775281i) q^{81} +(2.91676 + 5.05197i) q^{82} -8.91851i q^{83} +(-0.875603 - 0.505530i) q^{85} +(1.19704 + 0.691113i) q^{86} -14.7787 q^{87} +(-2.34008 + 4.05313i) q^{88} +12.0190i q^{89} +3.58546 q^{90} +0.723345 q^{92} +16.3723i q^{93} +(-3.13035 + 5.42193i) q^{94} -1.29280 q^{95} +(1.09485 + 0.632114i) q^{96} +(-3.82981 - 2.21114i) q^{97} +8.09643i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 8 q^{4} - 6 q^{5} + 18 q^{6} - 4 q^{9}+O(q^{10}) \) 12 * q - 8 * q^4 - 6 * q^5 + 18 * q^6 - 4 * q^9	\( 12 q - 8 q^{4} - 6 q^{5} + 18 q^{6} - 4 q^{9} - 12 q^{10} - 6 q^{11} - 2 q^{12} - 4 q^{13} + 6 q^{15} + 16 q^{16} - 8 q^{17} + 12 q^{18} + 12 q^{20} + 6 q^{22} + 24 q^{23} + 12 q^{24} + 10 q^{25} - 18 q^{26} - 12 q^{27} + 8 q^{29} + 8 q^{30} + 18 q^{31} - 30 q^{33} - 10 q^{36} + 2 q^{38} + 14 q^{39} + 46 q^{40} - 30 q^{41} + 2 q^{43} - 24 q^{44} + 42 q^{47} + 2 q^{48} - 18 q^{50} - 26 q^{51} + 28 q^{52} + 22 q^{53} + 6 q^{55} + 12 q^{58} - 66 q^{60} - 14 q^{61} + 4 q^{62} - 52 q^{64} - 18 q^{65} - 26 q^{66} + 24 q^{67} - 16 q^{68} - 4 q^{69} - 24 q^{71} - 60 q^{72} + 30 q^{73} - 12 q^{74} + 92 q^{75} + 18 q^{76} - 10 q^{78} + 28 q^{79} - 72 q^{80} + 2 q^{81} - 14 q^{82} - 48 q^{85} + 60 q^{86} - 4 q^{87} - 14 q^{88} - 24 q^{90} + 24 q^{92} - 4 q^{94} + 44 q^{95} + 6 q^{96} - 6 q^{97}+O(q^{100}) \) 12 * q - 8 * q^4 - 6 * q^5 + 18 * q^6 - 4 * q^9 - 12 * q^10 - 6 * q^11 - 2 * q^12 - 4 * q^13 + 6 * q^15 + 16 * q^16 - 8 * q^17 + 12 * q^18 + 12 * q^20 + 6 * q^22 + 24 * q^23 + 12 * q^24 + 10 * q^25 - 18 * q^26 - 12 * q^27 + 8 * q^29 + 8 * q^30 + 18 * q^31 - 30 * q^33 - 10 * q^36 + 2 * q^38 + 14 * q^39 + 46 * q^40 - 30 * q^41 + 2 * q^43 - 24 * q^44 + 42 * q^47 + 2 * q^48 - 18 * q^50 - 26 * q^51 + 28 * q^52 + 22 * q^53 + 6 * q^55 + 12 * q^58 - 66 * q^60 - 14 * q^61 + 4 * q^62 - 52 * q^64 - 18 * q^65 - 26 * q^66 + 24 * q^67 - 16 * q^68 - 4 * q^69 - 24 * q^71 - 60 * q^72 + 30 * q^73 - 12 * q^74 + 92 * q^75 + 18 * q^76 - 10 * q^78 + 28 * q^79 - 72 * q^80 + 2 * q^81 - 14 * q^82 - 48 * q^85 + 60 * q^86 - 4 * q^87 - 14 * q^88 - 24 * q^90 + 24 * q^92 - 4 * q^94 + 44 * q^95 + 6 * q^96 - 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more