LMFDB - Embedded newform 637.2.q.i.491.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(491,637)]

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([0, 5]))

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

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

chi := DirichletCharacter("637.491");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.q (of order $6$, degree $2$, 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:	12.0.2346760387617129.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + \cdots + 64 $ x^12 - 3x^11 + x^10 + 10x^9 - 15x^8 - 10x^7 + 45x^6 - 20x^5 - 60x^4 + 80x^3 + 16x^2 - 96x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			491.3
Root			$-1.18541 + 0.771231i$ of defining polynomial
Character	$\chi$	$=$	637.491
Dual form			637.2.q.i.589.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.433001 + 0.249993i) q^{2} +(0.424801 + 0.735776i) q^{3} +(-0.875007 + 1.51556i) q^{4} -1.04248i q^{5} +(-0.367878 - 0.212395i) q^{6} -1.87496i q^{8} +(1.13909 - 1.97296i) q^{9} +O(q^{10})$	\(q+(-0.433001 + 0.249993i) q^{2} +(0.424801 + 0.735776i) q^{3} +(-0.875007 + 1.51556i) q^{4} -1.04248i q^{5} +(-0.367878 - 0.212395i) q^{6} -1.87496i q^{8} +(1.13909 - 1.97296i) q^{9} +(0.260612 + 0.451393i) q^{10} +(3.43579 - 1.98365i) q^{11} -1.48681 q^{12} +(3.57504 + 0.468096i) q^{13} +(0.767029 - 0.442844i) q^{15} +(-1.28129 - 2.21925i) q^{16} +(0.0710177 - 0.123006i) q^{17} +1.13906i q^{18} +(-4.77160 - 2.75488i) q^{19} +(1.57993 + 0.912173i) q^{20} +(-0.991800 + 1.71785i) q^{22} +(2.19549 + 3.80270i) q^{23} +(1.37955 - 0.796483i) q^{24} +3.91325 q^{25} +(-1.66502 + 0.691049i) q^{26} +4.48435 q^{27} +(4.19880 + 7.27253i) q^{29} +(-0.221416 + 0.383504i) q^{30} -2.84652i q^{31} +(4.35712 + 2.51558i) q^{32} +(2.91905 + 1.68531i) q^{33} +0.0710158i q^{34} +(1.99342 + 3.45271i) q^{36} +(0.730221 - 0.421593i) q^{37} +2.75481 q^{38} +(1.17426 + 2.82928i) q^{39} -1.95460 q^{40} +(-10.4766 + 6.04869i) q^{41} +(2.41161 - 4.17704i) q^{43} +6.94284i q^{44} +(-2.05676 - 1.18747i) q^{45} +(-1.90130 - 1.09772i) q^{46} -4.55648i q^{47} +(1.08858 - 1.88548i) q^{48} +(-1.69444 + 0.978285i) q^{50} +0.120673 q^{51} +(-3.83761 + 5.00858i) q^{52} -0.279600 q^{53} +(-1.94173 + 1.12106i) q^{54} +(-2.06791 - 3.58172i) q^{55} -4.68111i q^{57} +(-3.63617 - 2.09934i) q^{58} +(9.33705 + 5.39075i) q^{59} +1.54997i q^{60} +(-2.93177 + 5.07797i) q^{61} +(0.711612 + 1.23255i) q^{62} +2.60963 q^{64} +(0.487979 - 3.72689i) q^{65} -1.68527 q^{66} +(4.45524 - 2.57223i) q^{67} +(0.124282 + 0.215263i) q^{68} +(-1.86529 + 3.23078i) q^{69} +(-3.20326 - 1.84940i) q^{71} +(-3.69921 - 2.13574i) q^{72} -6.61281i q^{73} +(-0.210791 + 0.365101i) q^{74} +(1.66235 + 2.87927i) q^{75} +(8.35036 - 4.82108i) q^{76} +(-1.21576 - 0.931521i) q^{78} +11.9227 q^{79} +(-2.31352 + 1.33571i) q^{80} +(-1.51231 - 2.61940i) q^{81} +(3.02426 - 5.23818i) q^{82} -2.87321i q^{83} +(-0.128231 - 0.0740342i) q^{85} +2.41155i q^{86} +(-3.56730 + 6.17875i) q^{87} +(-3.71926 - 6.44195i) q^{88} +(1.51351 - 0.873824i) q^{89} +1.18744 q^{90} -7.68427 q^{92} +(2.09440 - 1.20921i) q^{93} +(1.13909 + 1.97296i) q^{94} +(-2.87190 + 4.97427i) q^{95} +4.27449i q^{96} +(-2.34079 - 1.35145i) q^{97} -9.03822i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{3} + 4 q^{4} + 9 q^{6} - q^{9}+O(q^{10}) $ 12 * q + 3 * q^3 + 4 * q^4 + 9 * q^6 - q^9	$ 12 q + 3 q^{3} + 4 q^{4} + 9 q^{6} - q^{9} - 12 q^{10} - 12 q^{11} - 2 q^{12} + 2 q^{13} - 12 q^{15} - 8 q^{16} - 17 q^{17} + 9 q^{19} + 3 q^{20} - 15 q^{22} + 3 q^{23} + 15 q^{24} + 10 q^{25} - 15 q^{26} - 12 q^{27} - q^{29} + 11 q^{30} - 18 q^{32} - 6 q^{33} - 13 q^{36} - 15 q^{37} + 38 q^{38} + 5 q^{39} - 2 q^{40} + 6 q^{41} + 11 q^{43} - 9 q^{45} + 30 q^{46} - 19 q^{48} + 18 q^{50} - 8 q^{51} + 40 q^{52} + 16 q^{53} + 6 q^{54} + 15 q^{55} + 24 q^{58} + 27 q^{59} - 5 q^{61} - 41 q^{62} + 2 q^{64} - 18 q^{65} - 68 q^{66} - 15 q^{67} + 11 q^{68} - 7 q^{69} + 30 q^{71} - 57 q^{72} - 33 q^{74} - q^{75} + 45 q^{76} + 44 q^{78} + 70 q^{79} - 63 q^{80} + 14 q^{81} - 5 q^{82} - 21 q^{85} - 10 q^{87} - 14 q^{88} + 48 q^{89} - 66 q^{92} + 81 q^{93} - q^{94} + 2 q^{95} + 3 q^{97}+O(q^{100}) $ 12 * q + 3 * q^3 + 4 * q^4 + 9 * q^6 - q^9 - 12 * q^10 - 12 * q^11 - 2 * q^12 + 2 * q^13 - 12 * q^15 - 8 * q^16 - 17 * q^17 + 9 * q^19 + 3 * q^20 - 15 * q^22 + 3 * q^23 + 15 * q^24 + 10 * q^25 - 15 * q^26 - 12 * q^27 - q^29 + 11 * q^30 - 18 * q^32 - 6 * q^33 - 13 * q^36 - 15 * q^37 + 38 * q^38 + 5 * q^39 - 2 * q^40 + 6 * q^41 + 11 * q^43 - 9 * q^45 + 30 * q^46 - 19 * q^48 + 18 * q^50 - 8 * q^51 + 40 * q^52 + 16 * q^53 + 6 * q^54 + 15 * q^55 + 24 * q^58 + 27 * q^59 - 5 * q^61 - 41 * q^62 + 2 * q^64 - 18 * q^65 - 68 * q^66 - 15 * q^67 + 11 * q^68 - 7 * q^69 + 30 * q^71 - 57 * q^72 - 33 * q^74 - q^75 + 45 * q^76 + 44 * q^78 + 70 * q^79 - 63 * q^80 + 14 * q^81 - 5 * q^82 - 21 * q^85 - 10 * q^87 - 14 * q^88 + 48 * q^89 - 66 * q^92 + 81 * q^93 - q^94 + 2 * q^95 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.433001	+	0.249993i	−0.306178	+	0.176772i	−0.645215	−	0.764001i	$-0.723232\pi$
$2$	−0.433001	+	0.249993i	−0.306178	+	0.176772i	0.339037	+	0.940773i	$0.389899\pi$
$3$	0.424801	+	0.735776i	0.245259	+	0.424801i	0.962204	−	0.272328i	$-0.0877937\pi$
$3$	0.424801	+	0.735776i	0.245259	+	0.424801i	−0.716946	+	0.697129i	$0.754460\pi$
$4$	−0.875007	+	1.51556i	−0.437503	+	0.757778i
$5$		−	1.04248i		−	0.466209i	−0.972452	−	0.233105i	$-0.925112\pi$
$5$		−	1.04248i		−	0.466209i	0.972452	−	0.233105i	$-0.0748884\pi$
$6$	−0.367878	−	0.212395i	−0.150186	−	0.0867098i
$7$		0			0
$7$		0			0
$8$		−	1.87496i		−	0.662897i
$9$	1.13909	−	1.97296i	0.379696	−	0.657653i
$10$	0.260612	+	0.451393i	0.0824127	+	0.142743i
$11$	3.43579	−	1.98365i	1.03593	−	0.598094i	0.117251	−	0.993102i	$-0.462592\pi$
$11$	3.43579	−	1.98365i	1.03593	−	0.598094i	0.918677	+	0.395009i	$0.129258\pi$
$12$	−1.48681			−0.429206
$13$	3.57504	+	0.468096i	0.991537	+	0.129827i
$13$	3.57504	+	0.468096i	0.991537	+	0.129827i
$14$		0			0
$15$	0.767029	−	0.442844i	0.198046	−	0.114342i
$16$	−1.28129	−	2.21925i	−0.320322	−	0.554813i
$17$	0.0710177	−	0.123006i	0.0172243	−	0.0298334i	−0.857285	−	0.514843i	$-0.827850\pi$
$17$	0.0710177	−	0.123006i	0.0172243	−	0.0298334i	0.874509	+	0.485009i	$0.161184\pi$
$18$			1.13906i			0.268479i
$19$	−4.77160	−	2.75488i	−1.09468	−	0.632014i	−0.159861	−	0.987140i	$-0.551105\pi$
$19$	−4.77160	−	2.75488i	−1.09468	−	0.632014i	−0.934818	+	0.355126i	$0.884438\pi$
$20$	1.57993	+	0.912173i	0.353283	+	0.203968i
$21$		0			0
$22$	−0.991800	+	1.71785i	−0.211452	+	0.366246i
$23$	2.19549	+	3.80270i	0.457791	+	0.792917i	0.998844	−	0.0480711i	$-0.0153074\pi$
$23$	2.19549	+	3.80270i	0.457791	+	0.792917i	−0.541053	+	0.840989i	$0.681974\pi$
$24$	1.37955	−	0.796483i	0.281599	−	0.162581i
$25$	3.91325			0.782649
$26$	−1.66502	+	0.691049i	−0.326536	+	0.135526i
$27$	4.48435			0.863013
$28$		0			0
$29$	4.19880	+	7.27253i	0.779697	+	1.35047i	0.932116	+	0.362159i	$0.117960\pi$
$29$	4.19880	+	7.27253i	0.779697	+	1.35047i	−0.152419	+	0.988316i	$0.548706\pi$
$30$	−0.221416	+	0.383504i	−0.0404249	+	0.0700179i
$31$		−	2.84652i		−	0.511251i	−0.966776	−	0.255625i	$-0.917719\pi$
$31$		−	2.84652i		−	0.511251i	0.966776	−	0.255625i	$-0.0822813\pi$
$32$	4.35712	+	2.51558i	0.770237	+	0.444696i
$33$	2.91905	+	1.68531i	0.508141	+	0.293376i
$34$			0.0710158i			0.0121791i
$35$		0			0
$36$	1.99342	+	3.45271i	0.332237	+	0.575451i
$37$	0.730221	−	0.421593i	0.120048	−	0.0693095i	−0.438774	−	0.898598i	$-0.644587\pi$
$37$	0.730221	−	0.421593i	0.120048	−	0.0693095i	0.558821	+	0.829288i	$0.311254\pi$
$38$	2.75481			0.446889
$39$	1.17426	+	2.82928i	0.188033	+	0.453047i
$40$	−1.95460			−0.309049
$41$	−10.4766	+	6.04869i	−1.63618	+	0.944647i	−0.654044	+	0.756457i	$0.726929\pi$
$41$	−10.4766	+	6.04869i	−1.63618	+	0.944647i	−0.982133	+	0.188190i	$0.939738\pi$
$42$		0			0
$43$	2.41161	−	4.17704i	0.367768	−	0.636993i	−0.621448	−	0.783455i	$-0.713455\pi$
$43$	2.41161	−	4.17704i	0.367768	−	0.636993i	0.989216	+	0.146463i	$0.0467888\pi$
$44$			6.94284i			1.04667i
$45$	−2.05676	−	1.18747i	−0.306604	−	0.177018i
$46$	−1.90130	−	1.09772i	−0.280331	−	0.161849i
$47$		−	4.55648i		−	0.664630i	−0.943168	−	0.332315i	$-0.892170\pi$
$47$		−	4.55648i		−	0.664630i	0.943168	−	0.332315i	$-0.107830\pi$
$48$	1.08858	−	1.88548i	0.157123	−	0.272146i
$49$		0			0
$50$	−1.69444	+	0.978285i	−0.239630	+	0.138350i
$51$	0.120673			0.0168977
$52$	−3.83761	+	5.00858i	−0.532180	+	0.694565i
$53$	−0.279600			−0.0384060			−0.0192030	−	0.999816i	$-0.506113\pi$
$53$	−0.279600			−0.0384060			−0.0192030	+	0.999816i	$0.506113\pi$
$54$	−1.94173	+	1.12106i	−0.264236	+	0.152557i
$55$	−2.06791	−	3.58172i	−0.278837	−	0.482959i
$56$		0			0
$57$		−	4.68111i		−	0.620028i
$58$	−3.63617	−	2.09934i	−0.477452	−	0.275657i
$59$	9.33705	+	5.39075i	1.21558	+	0.701815i	0.963969	−	0.266013i	$-0.0857065\pi$
$59$	9.33705	+	5.39075i	1.21558	+	0.701815i	0.251611	+	0.967829i	$0.419040\pi$
$60$			1.54997i			0.200100i
$61$	−2.93177	+	5.07797i	−0.375374	+	0.650168i	−0.990383	−	0.138353i	$-0.955819\pi$
$61$	−2.93177	+	5.07797i	−0.375374	+	0.650168i	0.615009	+	0.788520i	$0.289153\pi$
$62$	0.711612	+	1.23255i	0.0903748	+	0.156534i
$63$		0			0
$64$	2.60963			0.326204
$65$	0.487979	−	3.72689i	0.0605263	−	0.462263i
$66$	−1.68527			−0.207442
$67$	4.45524	−	2.57223i	0.544294	−	0.314248i	−0.202523	−	0.979277i	$-0.564914\pi$
$67$	4.45524	−	2.57223i	0.544294	−	0.314248i	0.746818	+	0.665029i	$0.231581\pi$
$68$	0.124282	+	0.215263i	0.0150714	+	0.0261044i
$69$	−1.86529	+	3.23078i	−0.224555	+	0.388940i
$70$		0			0
$71$	−3.20326	−	1.84940i	−0.380157	−	0.219484i	0.297730	−	0.954650i	$-0.403771\pi$
$71$	−3.20326	−	1.84940i	−0.380157	−	0.219484i	−0.677887	+	0.735167i	$0.737104\pi$
$72$	−3.69921	−	2.13574i	−0.435956	−	0.251700i
$73$		−	6.61281i		−	0.773970i	−0.922086	−	0.386985i	$-0.873516\pi$
$73$		−	6.61281i		−	0.773970i	0.922086	−	0.386985i	$-0.126484\pi$
$74$	−0.210791	+	0.365101i	−0.0245040	+	0.0424421i
$75$	1.66235	+	2.87927i	0.191952	+	0.332470i
$76$	8.35036	−	4.82108i	0.957852	−	0.553016i
$77$		0			0
$78$	−1.21576	−	0.931521i	−0.137657	−	0.105474i
$79$	11.9227			1.34141			0.670705	−	0.741725i	$-0.265992\pi$
$79$	11.9227			1.34141			0.670705	+	0.741725i	$0.265992\pi$
$80$	−2.31352	+	1.33571i	−0.258659	+	0.149337i
$81$	−1.51231	−	2.61940i	−0.168035	−	0.291045i
$82$	3.02426	−	5.23818i	0.333974	−	0.578460i
$83$		−	2.87321i		−	0.315376i	−0.987489	−	0.157688i	$-0.949596\pi$
$83$		−	2.87321i		−	0.315376i	0.987489	−	0.157688i	$-0.0504040\pi$
$84$		0			0
$85$	−0.128231	−	0.0740342i	−0.0139086	−	0.00803013i
$86$			2.41155i			0.260044i
$87$	−3.56730	+	6.17875i	−0.382455	+	0.662432i
$88$	−3.71926	−	6.44195i	−0.396475	−	0.686714i
$89$	1.51351	−	0.873824i	0.160432	−	0.0926252i	−0.417635	−	0.908615i	$-0.637141\pi$
$89$	1.51351	−	0.873824i	0.160432	−	0.0926252i	0.578066	+	0.815990i	$0.303807\pi$
$90$	1.18744			0.125167
$91$		0			0
$92$	−7.68427			−0.801141
$93$	2.09440	−	1.20921i	0.217180	−	0.125389i
$94$	1.13909	+	1.97296i	0.117488	+	0.203495i
$95$	−2.87190	+	4.97427i	−0.294650	+	0.510350i
$96$			4.27449i			0.436263i
$97$	−2.34079	−	1.35145i	−0.237671	−	0.137219i	0.376435	−	0.926443i	$-0.377150\pi$
$97$	−2.34079	−	1.35145i	−0.237671	−	0.137219i	−0.614106	+	0.789224i	$0.710483\pi$
$98$		0			0
$99$		−	9.03822i		−	0.908376i
$100$	−3.42412	+	5.93074i	−0.342412	+	0.593074i
$101$	−5.73612	−	9.93524i	−0.570765	−	0.988594i	−0.996488	−	0.0837401i	$-0.973313\pi$
$101$	−5.73612	−	9.93524i	−0.570765	−	0.988594i	0.425723	−	0.904854i	$-0.360020\pi$
$102$	−0.0522517	+	0.0301676i	−0.00517369	+	0.00298703i
$103$	4.16950			0.410834			0.205417	−	0.978675i	$-0.434145\pi$
$103$	4.16950			0.410834			0.205417	+	0.978675i	$0.434145\pi$
$104$	0.877660	−	6.70304i	0.0860617	−	0.657287i
$105$		0			0
$106$	0.121067	−	0.0698982i	0.0117591	−	0.00678911i
$107$	−4.24371	−	7.35032i	−0.410255	−	0.710583i	0.584662	−	0.811277i	$-0.301227\pi$
$107$	−4.24371	−	7.35032i	−0.410255	−	0.710583i	−0.994917	+	0.100694i	$0.967894\pi$
$108$	−3.92383	+	6.79628i	−0.377571	+	0.653972i
$109$			6.43036i			0.615917i	0.951400	+	0.307958i	$0.0996458\pi$
$109$			6.43036i			0.615917i	−0.951400	+	0.307958i	$0.900354\pi$
$110$	1.79081	+	1.03393i	0.170747	+	0.0985810i
$111$	0.620397	+	0.358186i	0.0588855	+	0.0339975i
$112$		0			0
$113$	−5.48164	+	9.49448i	−0.515670	+	0.893166i	0.484165	+	0.874977i	$0.339123\pi$
$113$	−5.48164	+	9.49448i	−0.515670	+	0.893166i	−0.999835	+	0.0181892i	$0.994210\pi$
$114$	1.17025	+	2.02692i	0.109603	+	0.189839i
$115$	3.96422	−	2.28874i	0.369665	−	0.213426i
$116$	−14.6959			−1.36448
$117$	4.99582	−	6.52020i	0.461864	−	0.602793i
$118$	−5.39060			−0.496245
$119$		0			0
$120$	−0.830314	−	1.43815i	−0.0757969	−	0.131284i
$121$	2.36975	−	4.10453i	0.215432	−	0.373139i
$122$		−	2.93169i		−	0.265423i
$123$	−8.90097	−	5.13898i	−0.802573	−	0.463366i
$124$	4.31406	+	2.49073i	0.387414	+	0.223674i
$125$		−	9.29184i		−	0.831087i
$126$		0			0
$127$	−1.00394	−	1.73887i	−0.0890849	−	0.154300i	0.818040	−	0.575162i	$-0.195061\pi$
$127$	−1.00394	−	1.73887i	−0.0890849	−	0.154300i	−0.907125	+	0.420862i	$0.861728\pi$
$128$	−9.84421	+	5.68356i	−0.870113	+	0.502360i
$129$	4.09782			0.360793
$130$	0.720401	+	1.73574i	0.0631834	+	0.152234i
$131$	12.4502			1.08778			0.543890	−	0.839156i	$-0.316951\pi$
$131$	12.4502			1.08778			0.543890	+	0.839156i	$0.316951\pi$
$132$	−5.10838	+	2.94932i	−0.444627	+	0.256706i
$133$		0			0
$134$	−1.28608	+	2.22756i	−0.111101	+	0.192432i
$135$		−	4.67482i		−	0.402344i
$136$	−0.230631	−	0.133155i	−0.0197765	−	0.0114180i
$137$	−4.54246	−	2.62259i	−0.388088	−	0.224063i	0.293243	−	0.956038i	$-0.405265\pi$
$137$	−4.54246	−	2.62259i	−0.388088	−	0.224063i	−0.681332	+	0.731975i	$0.738599\pi$
$138$		−	1.86524i		−	0.158780i
$139$	−10.3693	+	17.9601i	−0.879510	+	1.52336i	−0.0276301	+	0.999618i	$0.508796\pi$
$139$	−10.3693	+	17.9601i	−0.879510	+	1.52336i	−0.851880	+	0.523737i	$0.824537\pi$
$140$		0			0
$141$	3.35255	−	1.93559i	0.282335	−	0.163006i
$142$	1.84935			0.155194
$143$	13.2116	−	5.48335i	1.10481	−	0.458541i
$144$	−5.83800			−0.486500
$145$	7.58143	−	4.37714i	0.629604	−	0.363502i
$146$	1.65316	+	2.86335i	0.136816	+	0.236973i
$147$		0			0
$148$			1.47559i			0.121293i
$149$	−0.00985188	−	0.00568799i	−0.000807098	−	0.000465978i	0.499596	−	0.866258i	$-0.333482\pi$
$149$	−0.00985188	−	0.00568799i	−0.000807098	−	0.000465978i	−0.500403	+	0.865792i	$0.666815\pi$
$150$	−1.43960	−	0.831153i	−0.117543	−	0.0678633i
$151$		−	18.9054i		−	1.53850i	−0.638947	−	0.769251i	$-0.720630\pi$
$151$		−	18.9054i		−	1.53850i	0.638947	−	0.769251i	$-0.279370\pi$
$152$	−5.16529	+	8.94654i	−0.418960	+	0.725660i
$153$	−0.161791	−	0.280230i	−0.0130800	−	0.0226553i
$154$		0			0
$155$	−2.96743			−0.238350
$156$	−5.31541	−	0.695972i	−0.425574	−	0.0557224i
$157$	−19.7937			−1.57971			−0.789856	−	0.613292i	$-0.789845\pi$
$157$	−19.7937			−1.57971			−0.789856	+	0.613292i	$0.789845\pi$
$158$	−5.16255	+	2.98060i	−0.410710	+	0.237124i
$159$	−0.118774	−	0.205723i	−0.00941942	−	0.0163149i
$160$	2.62243	−	4.54219i	0.207321	−	0.359091i
$161$		0			0
$162$	1.30967	+	0.756136i	0.102897	+	0.0594076i
$163$	−7.73581	−	4.46627i	−0.605915	−	0.349825i	0.165450	−	0.986218i	$-0.447092\pi$
$163$	−7.73581	−	4.46627i	−0.605915	−	0.349825i	−0.771365	+	0.636393i	$0.780426\pi$
$164$		−	21.1706i		−	1.65314i
$165$	1.75690	−	3.04304i	0.136774	−	0.236900i
$166$	0.718284	+	1.24410i	0.0557496	+	0.0965612i
$167$	−5.31279	+	3.06734i	−0.411116	+	0.237358i	−0.691269	−	0.722597i	$-0.742948\pi$
$167$	−5.31279	+	3.06734i	−0.411116	+	0.237358i	0.280153	+	0.959955i	$0.409615\pi$
$168$		0			0
$169$	12.5618	+	3.34692i	0.966290	+	0.257456i
$170$	0.0740322			0.00567801
$171$	−10.8705	+	6.27611i	−0.831291	+	0.479946i
$172$	4.22036	+	7.30987i	0.321799	+	0.557373i
$173$	−12.1314	+	21.0122i	−0.922332	+	1.59753i	−0.126535	+	0.991962i	$0.540386\pi$
$173$	−12.1314	+	21.0122i	−0.922332	+	1.59753i	−0.795797	+	0.605563i	$0.792948\pi$
$174$		−	3.56721i		−	0.270429i
$175$		0			0
$176$	−8.80446	−	5.08325i	−0.663661	−	0.383165i
$177$			9.15997i			0.688506i
$178$	−0.436901	+	0.756734i	−0.0327471	+	0.0567196i
$179$	−2.06838	−	3.58253i	−0.154598	−	0.267771i	0.778315	−	0.627874i	$-0.216075\pi$
$179$	−2.06838	−	3.58253i	−0.154598	−	0.267771i	−0.932912	+	0.360103i	$0.882741\pi$
$180$	3.59936	−	2.07809i	0.268280	−	0.154892i
$181$	7.86568			0.584651			0.292326	−	0.956319i	$-0.405571\pi$
$181$	7.86568			0.584651			0.292326	+	0.956319i	$0.405571\pi$
$182$		0			0
$183$	−4.98167			−0.368256
$184$	7.12989	−	4.11645i	0.525623	−	0.303468i
$185$	−0.439501	−	0.761237i	−0.0323127	−	0.0559673i
$186$	−0.604586	+	1.04717i	−0.0443304	+	0.0767825i
$187$		−	0.563498i		−	0.0412070i
$188$	6.90560	+	3.98695i	0.503642	+	0.290778i
$189$		0			0
$190$		−	2.87182i		−	0.208344i
$191$	3.23933	−	5.61069i	0.234390	−	0.405975i	−0.724705	−	0.689059i	$-0.758024\pi$
$191$	3.23933	−	5.61069i	0.234390	−	0.405975i	0.959095	+	0.283084i	$0.0913574\pi$
$192$	1.10857	+	1.92011i	0.0800044	+	0.138572i
$193$	−4.18228	+	2.41464i	−0.301047	+	0.173810i	−0.642913	−	0.765939i	$-0.722274\pi$
$193$	−4.18228	+	2.41464i	−0.301047	+	0.173810i	0.341866	+	0.939749i	$0.388941\pi$
$194$	1.35142			0.0970261
$195$	2.94945	−	1.22414i	0.211214	−	0.0876626i
$196$		0			0
$197$	−22.3748	+	12.9181i	−1.59414	+	0.920377i	−0.601554	+	0.798832i	$0.705452\pi$
$197$	−22.3748	+	12.9181i	−1.59414	+	0.920377i	−0.992586	+	0.121545i	$0.961215\pi$
$198$	2.25950	+	3.91356i	0.160575	+	0.278125i
$199$	−8.55731	+	14.8217i	−0.606612	+	1.05068i	0.385183	+	0.922840i	$0.374138\pi$
$199$	−8.55731	+	14.8217i	−0.606612	+	1.05068i	−0.991795	+	0.127842i	$0.959195\pi$
$200$		−	7.33717i		−	0.518816i
$201$	3.78518	+	2.18537i	0.266986	+	0.154144i
$202$	4.96749	+	2.86798i	0.349511	+	0.201790i
$203$		0			0
$204$	−0.105590	+	0.182887i	−0.00739278	+	0.0128047i
$205$	6.30561	+	10.9216i	0.440403	+	0.762800i
$206$	−1.80540	+	1.04235i	−0.125788	+	0.0726238i
$207$	10.0034			0.695286
$208$	−3.54182	−	8.53368i	−0.245581	−	0.591704i
$209$	−21.8589			−1.51201
$210$		0			0
$211$	−9.14557	−	15.8406i	−0.629607	−	1.09051i	−0.987631	−	0.156799i	$-0.949883\pi$
$211$	−9.14557	−	15.8406i	−0.629607	−	1.09051i	0.358024	−	0.933713i	$-0.383451\pi$
$212$	0.244652	−	0.423750i	0.0168028	−	0.0291032i
$213$		−	3.14251i		−	0.215321i
$214$	3.67506	+	2.12180i	0.251222	+	0.145043i
$215$	−4.35446	−	2.51405i	−0.296972	−	0.171457i
$216$		−	8.40796i		−	0.572089i
$217$		0			0
$218$	−1.60755	−	2.78435i	−0.108877	−	0.188580i
$219$	4.86555	−	2.80912i	0.328783	−	0.189823i
$220$	7.23773			0.487968
$221$	0.311470	−	0.406509i	0.0209517	−	0.0273447i
$222$	−0.358177			−0.0240392
$223$	9.96682	−	5.75435i	0.667428	−	0.385340i	−0.127674	−	0.991816i	$-0.540751\pi$
$223$	9.96682	−	5.75435i	0.667428	−	0.385340i	0.795101	+	0.606477i	$0.207418\pi$
$224$		0			0
$225$	4.45753	−	7.72067i	0.297169	−	0.514712i
$226$		−	5.48150i		−	0.364624i
$227$	15.5057	+	8.95223i	1.02915	+	0.594181i	0.916741	−	0.399481i	$-0.130810\pi$
$227$	15.5057	+	8.95223i	1.02915	+	0.594181i	0.112410	+	0.993662i	$0.464143\pi$
$228$	7.09448	+	4.09600i	0.469843	+	0.271264i
$229$		−	3.86350i		−	0.255307i	−0.991819	−	0.127654i	$-0.959255\pi$
$229$		−	3.86350i		−	0.255307i	0.991819	−	0.127654i	$-0.0407446\pi$
$230$	−1.14434	+	1.98206i	−0.0754556	+	0.130693i
$231$		0			0
$232$	13.6357	−	7.87256i	0.895226	−	0.516859i
$233$	−25.0642			−1.64201			−0.821004	−	0.570922i	$-0.806586\pi$
$233$	−25.0642			−1.64201			−0.821004	+	0.570922i	$0.806586\pi$
$234$	−0.533189	+	4.07217i	−0.0348556	+	0.266206i
$235$	−4.75001			−0.309857
$236$	−16.3400	+	9.43388i	−1.06364	+	0.614093i
$237$	5.06477	+	8.77245i	0.328992	+	0.569832i
$238$		0			0
$239$			7.80462i			0.504839i	0.967618	+	0.252419i	$0.0812263\pi$
$239$			7.80462i			0.504839i	−0.967618	+	0.252419i	$0.918774\pi$
$240$	−1.96557	−	1.13482i	−0.126877	−	0.0732524i
$241$	18.8493	+	10.8826i	1.21419	+	0.701012i	0.963669	−	0.267100i	$-0.0860655\pi$
$241$	18.8493	+	10.8826i	1.21419	+	0.701012i	0.250519	+	0.968112i	$0.419399\pi$
$242$			2.36969i			0.152329i
$243$	8.01138	−	13.8761i	0.513930	−	0.890154i
$244$	−5.13063	−	8.88652i	−0.328455	−	0.568901i
$245$		0			0
$246$	5.13884			0.327640
$247$	−15.7691	−	12.0824i	−1.00336	−	0.768783i
$248$	−5.33711			−0.338907
$249$	2.11404	−	1.22054i	0.133972	−	0.0773488i
$250$	2.32290	+	4.02338i	0.146913	+	0.254461i
$251$	−3.83990	+	6.65090i	−0.242372	+	0.419801i	−0.961390	−	0.275191i	$-0.911259\pi$
$251$	−3.83990	+	6.65090i	−0.242372	+	0.419801i	0.719017	+	0.694992i	$0.244592\pi$
$252$		0			0
$253$	15.0865	+	8.71017i	0.948478	+	0.547604i
$254$	0.869411	+	0.501955i	0.0545517	+	0.0314954i
$255$		−	0.125799i		−	0.00787784i
$256$	0.232070	−	0.401958i	0.0145044	−	0.0251224i
$257$	−6.81187	−	11.7985i	−0.424913	−	0.735971i	0.571499	−	0.820603i	$-0.306362\pi$
$257$	−6.81187	−	11.7985i	−0.424913	−	0.735971i	−0.996412	+	0.0846316i	$0.973029\pi$
$258$	−1.77436	+	1.02443i	−0.110467	+	0.0637781i
$259$		0			0
$260$	5.22132	+	4.00061i	0.323813	+	0.248107i
$261$	19.1312			1.18419
$262$	−5.39096	+	3.11247i	−0.333055	+	0.192289i
$263$	5.86158	+	10.1525i	0.361440	+	0.626033i	0.988198	−	0.153181i	$-0.0489518\pi$
$263$	5.86158	+	10.1525i	0.361440	+	0.626033i	−0.626758	+	0.779214i	$0.715618\pi$
$264$	3.15989	−	5.47309i	0.194478	−	0.336845i
$265$			0.291476i			0.0179052i
$266$		0			0
$267$	1.28588	+	0.742403i	0.0786945	+	0.0454343i
$268$			9.00289i			0.549939i
$269$	4.59938	−	7.96636i	0.280429	−	0.485717i	−0.691061	−	0.722796i	$-0.742857\pi$
$269$	4.59938	−	7.96636i	0.280429	−	0.485717i	0.971490	+	0.237079i	$0.0761899\pi$
$270$	1.16867	+	2.02420i	0.0711232	+	0.123189i
$271$	2.22022	−	1.28184i	0.134869	−	0.0778665i	−0.431048	−	0.902329i	$-0.641856\pi$
$271$	2.22022	−	1.28184i	0.134869	−	0.0778665i	0.565916	+	0.824463i	$0.308523\pi$
$272$	−0.363976			−0.0220693
$273$		0			0
$274$	2.62252			0.158432
$275$	13.4451	−	7.76252i	0.810769	−	0.468097i
$276$	−3.26428	−	5.65391i	−0.196487	−	0.340325i
$277$	−0.466941	+	0.808765i	−0.0280558	+	0.0485940i	−0.879712	−	0.475506i	$-0.842265\pi$
$277$	−0.466941	+	0.808765i	−0.0280558	+	0.0485940i	0.851657	+	0.524100i	$0.175598\pi$
$278$		−	10.3690i		−	0.621891i
$279$	−5.61607	−	3.24244i	−0.336226	−	0.194120i
$280$		0			0
$281$			6.45288i			0.384947i	0.981302	+	0.192473i	$0.0616509\pi$
$281$			6.45288i			0.384947i	−0.981302	+	0.192473i	$0.938349\pi$
$282$	−0.967771	+	1.67623i	−0.0576299	+	0.0998180i
$283$	−11.0873	−	19.2037i	−0.659071	−	1.14154i	−0.980857	−	0.194731i	$-0.937616\pi$
$283$	−11.0873	−	19.2037i	−0.659071	−	1.14154i	0.321786	−	0.946812i	$-0.395717\pi$
$284$	5.60575	−	3.23648i	0.332640	−	0.192050i
$285$	−4.87994			−0.289062
$286$	−4.34984	+	5.67711i	−0.257211	+	0.335695i
$287$		0			0
$288$	9.92629	−	5.73094i	0.584912	−	0.337699i
$289$	8.48991	+	14.7050i	0.499407	+	0.864998i
$290$	−2.18851	+	3.79061i	−0.128514	+	0.222593i
$291$		−	2.29639i		−	0.134617i
$292$	10.0221	+	5.78625i	0.586498	+	0.338615i
$293$	20.9600	+	12.1013i	1.22450	+	0.706964i	0.965874	−	0.259014i	$-0.0833976\pi$
$293$	20.9600	+	12.1013i	1.22450	+	0.706964i	0.258624	+	0.965978i	$0.416731\pi$
$294$		0			0
$295$	5.61972	−	9.73364i	0.327193	−	0.566714i
$296$	−0.790469	−	1.36913i	−0.0459451	−	0.0795792i
$297$	15.4073	−	8.89539i	0.894020	−	0.516163i
$298$	0.00568784			0.000329487
$299$	6.06892	+	14.6225i	0.350975	+	0.845640i
$300$	−5.81827			−0.335918
$301$		0			0
$302$	4.72623	+	8.18607i	0.271964	+	0.471055i
$303$	4.87341	−	8.44100i	0.279970	−	0.484923i
$304$			14.1192i			0.809791i
$305$	5.29366	+	3.05630i	0.303114	+	0.175003i
$306$	0.140111	+	0.0808933i	0.00800963	+	0.00462436i
$307$		−	24.2924i		−	1.38644i	−0.720726	−	0.693220i	$-0.756191\pi$
$307$		−	24.2924i		−	1.38644i	0.720726	−	0.693220i	$-0.243809\pi$
$308$		0			0
$309$	1.77121	+	3.06782i	0.100761	+	0.174522i
$310$	1.28490	−	0.741837i	0.0729774	−	0.0421335i
$311$	3.98711			0.226088			0.113044	−	0.993590i	$-0.463940\pi$
$311$	3.98711			0.226088			0.113044	+	0.993590i	$0.463940\pi$
$312$	5.30477	−	2.20169i	0.300323	−	0.124646i
$313$	−28.4754			−1.60953			−0.804763	−	0.593597i	$-0.797707\pi$
$313$	−28.4754			−1.60953			−0.804763	+	0.593597i	$0.797707\pi$
$314$	8.57071	−	4.94830i	0.483673	−	0.279249i
$315$		0			0
$316$	−10.4324	+	18.0695i	−0.586871	+	1.01649i
$317$			16.8161i			0.944487i	0.881468	+	0.472244i	$0.156556\pi$
$317$			16.8161i			0.944487i	−0.881468	+	0.472244i	$0.843444\pi$
$318$	0.102859	+	0.0593856i	0.00576804	+	0.00333018i
$319$	28.8523	+	16.6579i	1.61542	+	0.932664i
$320$		−	2.72048i		−	0.152079i
$321$	3.60546	−	6.24485i	0.201237	−	0.348553i
$322$		0			0
$323$	−0.677736	+	0.391291i	−0.0377102	+	0.0217720i
$324$	5.29313			0.294063
$325$	13.9900	+	1.83178i	0.776025	+	0.101609i
$326$	4.46615			0.247357
$327$	−4.73131	+	2.73162i	−0.261642	+	0.151059i
$328$	11.3410	+	19.6432i	0.626204	+	1.08462i
$329$		0			0
$330$			1.75685i			0.0967115i
$331$	−5.37730	−	3.10459i	−0.295563	−	0.170644i	0.344885	−	0.938645i	$-0.387918\pi$
$331$	−5.37730	−	3.10459i	−0.295563	−	0.170644i	−0.640448	+	0.768002i	$0.721251\pi$
$332$	4.35451	+	2.51408i	0.238985	+	0.137978i
$333$		−	1.92093i		−	0.105266i
$334$	1.53363	−	2.65633i	0.0839165	−	0.145348i
$335$	−2.68149	−	4.64448i	−0.146505	−	0.253755i
$336$		0			0
$337$	7.69650			0.419255			0.209628	−	0.977781i	$-0.432775\pi$
$337$	7.69650			0.419255			0.209628	+	0.977781i	$0.432775\pi$
$338$	−6.27597	+	1.69114i	−0.341368	+	0.0919858i
$339$	−9.31442			−0.505890
$340$	0.224406	−	0.129561i	0.0121701	−	0.00702642i
$341$	−5.64651	−	9.78005i	−0.305776	−	0.529619i
$342$	3.13797	−	5.43513i	0.169682	−	0.293898i
$343$		0			0
$344$	−7.83177	−	4.52167i	−0.422261	−	0.243792i
$345$	3.36801	+	1.94452i	0.181327	+	0.104689i
$346$		−	12.1311i		−	0.652170i
$347$	−15.2047	+	26.3353i	−0.816231	+	1.41375i	0.0922088	+	0.995740i	$0.470607\pi$
$347$	−15.2047	+	26.3353i	−0.816231	+	1.41375i	−0.908440	+	0.418015i	$0.862726\pi$
$348$	−6.24283	−	10.8129i	−0.334651	−	0.579632i
$349$	13.9933	−	8.07906i	0.749046	−	0.432462i	−0.0763028	−	0.997085i	$-0.524312\pi$
$349$	13.9933	−	8.07906i	0.749046	−	0.432462i	0.825349	+	0.564623i	$0.190978\pi$
$350$		0			0
$351$	16.0317	+	2.09911i	0.855709	+	0.112042i
$352$	19.9602			1.06388
$353$	−10.2558	+	5.92119i	−0.545861	+	0.315153i	−0.747451	−	0.664317i	$-0.768723\pi$
$353$	−10.2558	+	5.92119i	−0.545861	+	0.315153i	0.201590	+	0.979470i	$0.435389\pi$
$354$	−2.28993	−	3.96628i	−0.121709	−	0.210805i
$355$	−1.92796	+	3.33932i	−0.102325	+	0.177233i
$356$			3.05841i			0.162095i
$357$		0			0
$358$	1.79122	+	1.03416i	0.0946688	+	0.0546571i
$359$			31.3653i			1.65540i	0.561174	+	0.827698i	$0.310350\pi$
$359$			31.3653i			1.65540i	−0.561174	+	0.827698i	$0.689650\pi$
$360$	−2.22646	+	3.85634i	−0.117345	+	0.203247i
$361$	5.67876	+	9.83591i	0.298882	+	0.517679i
$362$	−3.40585	+	1.96637i	−0.179007	+	0.103350i
$363$	4.02669			0.211346
$364$		0			0
$365$	−6.89369			−0.360832
$366$	2.15707	−	1.24538i	0.112752	−	0.0650973i
$367$	12.0387	+	20.8517i	0.628415	+	1.08845i	0.987870	+	0.155285i	$0.0496295\pi$
$367$	12.0387	+	20.8517i	0.628415	+	1.08845i	−0.359454	+	0.933163i	$0.617037\pi$
$368$	5.62610	−	9.74470i	0.293281	−	0.507977i
$369$			27.5600i			1.43472i
$370$	0.380608	+	0.219744i	0.0197869	+	0.0114240i
$371$		0			0
$372$			4.23225i			0.219432i
$373$	9.19612	−	15.9281i	0.476157	−	0.824728i	−0.523470	−	0.852044i	$-0.675363\pi$
$373$	9.19612	−	15.9281i	0.476157	−	0.824728i	0.999627	+	0.0273160i	$0.00869604\pi$
$374$	0.140871	+	0.243995i	0.00728425	+	0.0126167i
$375$	6.83672	−	3.94718i	0.353046	−	0.203831i
$376$	−8.54320			−0.440582
$377$	11.6066	+	27.9650i	0.597771	+	1.44027i
$378$		0			0
$379$	−7.04719	+	4.06870i	−0.361990	+	0.208995i	−0.669953	−	0.742403i	$-0.733686\pi$
$379$	−7.04719	+	4.06870i	−0.361990	+	0.208995i	0.307963	+	0.951398i	$0.400353\pi$
$380$	−5.02586	−	8.70504i	−0.257821	−	0.446559i
$381$	0.852946	−	1.47735i	0.0436977	−	0.0756867i
$382$			3.23925i			0.165734i
$383$	−19.3739	−	11.1856i	−0.989962	−	0.571555i	−0.0846992	−	0.996407i	$-0.526993\pi$
$383$	−19.3739	−	11.1856i	−0.989962	−	0.571555i	−0.905263	+	0.424852i	$0.860326\pi$
$384$	−8.36365	−	4.82876i	−0.426806	−	0.246417i
$385$		0			0
$386$	1.20729	−	2.09108i	0.0614493	−	0.106433i
$387$	−5.49409	−	9.51604i	−0.279280	−	0.483727i
$388$	4.09641	−	2.36506i	0.207963	−	0.120068i
$389$	21.3946			1.08475			0.542374	−	0.840137i	$-0.317525\pi$
$389$	21.3946			1.08475			0.542374	+	0.840137i	$0.317525\pi$
$390$	−0.971088	+	1.26740i	−0.0491729	+	0.0641771i
$391$	0.623674			0.0315406
$392$		0			0
$393$	5.28886	+	9.16058i	0.266788	+	0.462090i
$394$	6.45888	−	11.1871i	0.325394	−	0.563599i
$395$		−	12.4291i		−	0.625377i
$396$	13.6979	+	7.90851i	0.688347	+	0.397417i
$397$	1.03640	+	0.598365i	0.0520154	+	0.0300311i	0.525782	−	0.850619i	$-0.323773\pi$
$397$	1.03640	+	0.598365i	0.0520154	+	0.0300311i	−0.473767	+	0.880650i	$0.657106\pi$
$398$		−	8.55708i		−	0.428928i
$399$		0			0
$400$	−5.01399	−	8.68449i	−0.250699	−	0.434224i
$401$	−31.4150	+	18.1375i	−1.56879	+	0.905741i	−0.572479	+	0.819919i	$0.694018\pi$
$401$	−31.4150	+	18.1375i	−1.56879	+	0.905741i	−0.996310	+	0.0858220i	$0.972648\pi$
$402$	−2.18532			−0.108994
$403$	1.33245	−	10.1764i	0.0663739	−	0.506924i
$404$	20.0766			0.998846
$405$	−2.73066	+	1.57655i	−0.135688	+	0.0783393i
$406$		0			0
$407$	1.67259	−	2.89701i	0.0829072	−	0.143599i
$408$		−	0.226257i		−	0.0112014i
$409$	−12.7066	−	7.33616i	−0.628301	−	0.362750i	0.151793	−	0.988412i	$-0.451495\pi$
$409$	−12.7066	−	7.33616i	−0.628301	−	0.362750i	−0.780094	+	0.625662i	$0.784829\pi$
$410$	−5.46067	−	3.15272i	−0.269683	−	0.155702i
$411$		−	4.45631i		−	0.219814i
$412$	−3.64834	+	6.31912i	−0.179741	+	0.311321i
$413$		0			0
$414$	−4.33150	+	2.50079i	−0.212881	+	0.122907i
$415$	−2.99525			−0.147031
$416$	14.3993	+	11.0329i	0.705985	+	0.540930i
$417$	−17.6195			−0.862830
$418$	9.46494	−	5.46458i	0.462945	−	0.267282i
$419$	−2.96674	−	5.13855i	−0.144935	−	0.251034i	0.784414	−	0.620238i	$-0.212964\pi$
$419$	−2.96674	−	5.13855i	−0.144935	−	0.251034i	−0.929349	+	0.369203i	$0.879631\pi$
$420$		0			0
$421$		−	2.63174i		−	0.128263i	−0.997941	−	0.0641317i	$-0.979572\pi$
$421$		−	2.63174i		−	0.128263i	0.997941	−	0.0641317i	$-0.0204278\pi$
$422$	7.92008	+	4.57266i	0.385544	+	0.222594i
$423$	−8.98974	−	5.19023i	−0.437096	−	0.252358i
$424$			0.524238i			0.0254593i
$425$	0.277910	−	0.481354i	0.0134806	−	0.0233491i
$426$	0.785606	+	1.36071i	0.0380628	+	0.0659266i
$427$		0			0
$428$	14.8531			0.717952
$429$	9.64682	+	7.39146i	0.465753	+	0.356863i
$430$	2.51398			0.121235
$431$	−16.3139	+	9.41883i	−0.785812	+	0.453689i	−0.838486	−	0.544923i	$-0.816559\pi$
$431$	−16.3139	+	9.41883i	−0.785812	+	0.453689i	0.0526738	+	0.998612i	$0.483226\pi$
$432$	−5.74573	−	9.95190i	−0.276442	−	0.478811i
$433$	−9.56773	+	16.5718i	−0.459796	+	0.796389i	−0.998950	−	0.0458176i	$-0.985411\pi$
$433$	−9.56773	+	16.5718i	−0.459796	+	0.796389i	0.539154	+	0.842207i	$0.318744\pi$
$434$		0			0
$435$	6.44119	+	3.71883i	0.308832	+	0.178304i
$436$	−9.74557	−	5.62661i	−0.466728	−	0.269466i
$437$		−	24.1933i		−	1.15732i
$438$	−1.40452	+	2.43271i	−0.0671108	+	0.116239i
$439$	0.632554	+	1.09561i	0.0301901	+	0.0522908i	0.880726	−	0.473627i	$-0.157055\pi$
$439$	0.632554	+	1.09561i	0.0301901	+	0.0522908i	−0.850536	+	0.525918i	$0.823722\pi$
$440$	−6.71557	+	3.87724i	−0.320152	+	0.184840i
$441$		0			0
$442$	−0.0332422	+	0.253884i	−0.00158117	+	0.0120760i
$443$	−20.9392			−0.994853			−0.497426	−	0.867506i	$-0.665722\pi$
$443$	−20.9392			−0.994853			−0.497426	+	0.867506i	$0.665722\pi$
$444$	−1.08570	+	0.626831i	−0.0515252	+	0.0297481i
$445$	−0.910940	−	1.57779i	−0.0431827	−	0.0747946i
$446$	−2.87710	+	4.98328i	−0.136234	+	0.235965i
$447$		−	0.00966505i		−	0.000457141i
$448$		0			0
$449$	15.4700	+	8.93162i	0.730075	+	0.421509i	0.818450	−	0.574578i	$-0.194834\pi$
$449$	15.4700	+	8.93162i	0.730075	+	0.421509i	−0.0883746	+	0.996087i	$0.528167\pi$
$450$			4.45741i			0.210125i
$451$	−23.9970	+	41.5640i	−1.12997	+	1.95717i
$452$	−9.59295	−	16.6155i	−0.451214	−	0.781526i
$453$	13.9102	−	8.03104i	0.653557	−	0.377331i
$454$	−8.95199			−0.420138
$455$		0			0
$456$	−8.77687			−0.411015
$457$	5.68629	−	3.28298i	0.265994	−	0.153571i	−0.361072	−	0.932538i	$-0.617589\pi$
$457$	5.68629	−	3.28298i	0.265994	−	0.153571i	0.627066	+	0.778966i	$0.284256\pi$
$458$	0.965850	+	1.67290i	0.0451312	+	0.0781695i
$459$	0.318468	−	0.551603i	0.0148648	−	0.0257466i
$460$			8.01066i			0.373499i
$461$	4.42854	+	2.55682i	0.206258	+	0.119083i	0.599571	−	0.800322i	$-0.295338\pi$
$461$	4.42854	+	2.55682i	0.206258	+	0.119083i	−0.393313	+	0.919404i	$0.628671\pi$
$462$		0			0
$463$		−	33.3239i		−	1.54869i	−0.632761	−	0.774347i	$-0.718079\pi$
$463$		−	33.3239i		−	1.54869i	0.632761	−	0.774347i	$-0.281921\pi$
$464$	10.7597	−	18.6364i	0.499508	−	0.865173i
$465$	−1.26057	−	2.18336i	−0.0584574	−	0.101251i
$466$	10.8528	−	6.26587i	0.502747	−	0.290261i
$467$	−12.9494			−0.599229			−0.299614	−	0.954060i	$-0.596858\pi$
$467$	−12.9494			−0.599229			−0.299614	+	0.954060i	$0.596858\pi$
$468$	5.51035	+	13.2767i	0.254716	+	0.613714i
$469$		0			0
$470$	2.05676	−	1.18747i	0.0948713	−	0.0547740i
$471$	−8.40840	−	14.5638i	−0.387439	−	0.671063i
$472$	10.1074	−	17.5066i	0.465231	−	0.805805i
$473$		−	19.1352i		−	0.879838i
$474$	−4.38611	−	2.53232i	−0.201461	−	0.116313i
$475$	−18.6724	−	10.7805i	−0.856750	−	0.494645i
$476$		0			0
$477$	−0.318489	+	0.551640i	−0.0145826	+	0.0252578i
$478$	−1.95110	−	3.37941i	−0.0892414	−	0.154571i
$479$	23.3930	−	13.5060i	1.06885	−	0.617104i	0.140987	−	0.990012i	$-0.454973\pi$
$479$	23.3930	−	13.5060i	1.06885	−	0.617104i	0.927868	+	0.372908i	$0.121639\pi$
$480$	4.45605			0.203390
$481$	2.80791	−	1.16540i	0.128030	−	0.0531376i
$482$	−10.8823			−0.495677
$483$		0			0
$484$	4.14710	+	7.18299i	0.188505	+	0.326499i
$485$	−1.40886	+	2.44021i	−0.0639729	+	0.110804i
$486$			8.01117i			0.363394i
$487$	−27.7854	−	16.0419i	−1.25908	−	0.726928i	−0.286182	−	0.958175i	$-0.592386\pi$
$487$	−27.7854	−	16.0419i	−1.25908	−	0.726928i	−0.972895	+	0.231247i	$0.925720\pi$
$488$	9.52097	+	5.49694i	0.430994	+	0.248835i
$489$		−	7.58910i		−	0.343191i
$490$		0			0
$491$	−14.3020	−	24.7718i	−0.645440	−	1.11793i	−0.984200	−	0.177061i	$-0.943341\pi$
$491$	−14.3020	−	24.7718i	−0.645440	−	1.11793i	0.338760	−	0.940873i	$-0.389992\pi$
$492$	15.5768	−	8.99328i	0.702257	−	0.405448i
$493$	1.19276			0.0537190
$494$	9.84854	+	1.28952i	0.443107	+	0.0580181i
$495$	−9.42212			−0.423493
$496$	−6.31716	+	3.64721i	−0.283649	+	0.163765i
$497$		0			0
$498$	−0.610255	+	1.05699i	−0.0273462	+	0.0473650i
$499$		−	1.79816i		−	0.0804969i	−0.999190	−	0.0402484i	$-0.987185\pi$
$499$		−	1.79816i		−	0.0804969i	0.999190	−	0.0402484i	$-0.0128149\pi$
$500$	14.0823	+	8.13042i	0.629780	+	0.363603i
$501$	−4.51376	−	2.60602i	−0.201660	−	0.116428i
$502$		−	3.83980i		−	0.171379i
$503$	14.5386	−	25.1816i	0.648245	−	1.12279i	−0.335297	−	0.942112i	$-0.608837\pi$
$503$	14.5386	−	25.1816i	0.648245	−	1.12279i	0.983542	−	0.180681i	$-0.0578300\pi$
$504$		0			0
$505$	−10.3572	+	5.97976i	−0.460891	+	0.266096i
$506$	−8.70994			−0.387204
$507$	2.87366	+	10.6644i	0.127624	+	0.473624i
$508$	3.51380			0.155900
$509$	20.0843	−	11.5957i	0.890220	−	0.513969i	0.0162054	−	0.999869i	$-0.494841\pi$
$509$	20.0843	−	11.5957i	0.890220	−	0.513969i	0.874014	+	0.485900i	$0.161508\pi$
$510$	0.0314489	+	0.0544711i	0.00139258	+	0.00241202i
$511$		0			0
$512$		−	22.5022i		−	0.994464i
$513$	−21.3975	−	12.3539i	−0.944723	−	0.545436i
$514$	5.89910	+	3.40585i	0.260198	+	0.150225i
$515$		−	4.34660i		−	0.191534i
$516$	−3.58562	+	6.21048i	−0.157848	+	0.273401i
$517$	−9.03847	−	15.6551i	−0.397511	−	0.688510i
$518$		0			0
$519$	−20.6137			−0.904840
$520$	−6.98775	−	0.914939i	−0.306433	−	0.0401227i
$521$	−33.2510			−1.45675			−0.728376	−	0.685178i	$-0.759725\pi$
$521$	−33.2510			−1.45675			−0.728376	+	0.685178i	$0.759725\pi$
$522$	−8.28383	+	4.78267i	−0.362574	+	0.209332i
$523$	19.3560	+	33.5256i	0.846380	+	1.46597i	0.884417	+	0.466697i	$0.154556\pi$
$523$	19.3560	+	33.5256i	0.846380	+	1.46597i	−0.0380367	+	0.999276i	$0.512110\pi$
$524$	−10.8940	+	18.8690i	−0.475908	+	0.824296i
$525$		0			0
$526$	−5.07614	−	2.93071i	−0.221330	−	0.127785i
$527$	−0.350140	−	0.202153i	−0.0152523	−	0.00880594i
$528$		−	8.63748i		−	0.375898i
$529$	1.85966	−	3.22102i	0.0808546	−	0.140044i
$530$	−0.0728671	−	0.126210i	−0.00316514	−	0.00548219i
$531$	21.2714	−	12.2811i	0.923102	−	0.532953i
$532$		0			0
$533$	−40.2857	+	16.7202i	−1.74497	+	0.724233i
$534$	−0.742383			−0.0321260
$535$	−7.66253	+	4.42396i	−0.331280	+	0.191265i
$536$	−4.82283	−	8.35338i	−0.208314	−	0.360811i
$537$	1.75730	−	3.04372i	0.0758329	−	0.131346i
$538$			4.59926i			0.198288i
$539$		0			0
$540$	7.08495	+	4.09050i	0.304888	+	0.176027i
$541$			22.6675i			0.974551i	0.873248	+	0.487275i	$0.162009\pi$
$541$			22.6675i			0.974551i	−0.873248	+	0.487275i	$0.837991\pi$
$542$	−0.640905	+	1.11008i	−0.0275292	+	0.0476820i
$543$	3.34135	+	5.78738i	0.143391	+	0.248360i
$544$	0.618865	−	0.357302i	0.0265336	−	0.0153192i
$545$	6.70349			0.287146
$546$		0			0
$547$	−9.21134			−0.393848			−0.196924	−	0.980419i	$-0.563095\pi$
$547$	−9.21134			−0.393848			−0.196924	+	0.980419i	$0.563095\pi$
$548$	7.94936	−	4.58957i	0.339580	−	0.196057i
$549$	6.67909	+	11.5685i	0.285056	+	0.493732i
$550$	−3.88116	+	6.72236i	−0.165493	+	0.286642i
$551$		−	46.2688i		−	1.97112i
$552$	6.05757	+	3.49734i	0.257827	+	0.148857i
$553$		0			0
$554$		−	0.466928i		−	0.0198379i
$555$	0.373400	−	0.646748i	0.0158500	−	0.0274529i
$556$	−18.1464	−	31.4304i	−0.769577	−	1.33295i
$557$	−9.81039	+	5.66403i	−0.415680	+	0.239993i	−0.693227	−	0.720719i	$-0.743812\pi$
$557$	−9.81039	+	5.66403i	−0.415680	+	0.239993i	0.277547	+	0.960712i	$0.410478\pi$
$558$	3.24236			0.137260
$559$	10.5769	−	13.8042i	0.447354	−	0.583855i
$560$		0			0
$561$	0.414608	−	0.239374i	0.0175048	−	0.0101064i
$562$	−1.61318	−	2.79411i	−0.0680478	−	0.117862i
$563$	−16.3193	+	28.2659i	−0.687777	+	1.19127i	0.284778	+	0.958594i	$0.408080\pi$
$563$	−16.3193	+	28.2659i	−0.687777	+	1.19127i	−0.972555	+	0.232672i	$0.925253\pi$
$564$			6.77463i			0.285264i
$565$	9.89776	+	5.71448i	0.416402	+	0.240410i
$566$	9.60161	+	5.54349i	0.403586	+	0.233010i
$567$		0			0
$568$	−3.46755	+	6.00597i	−0.145495	+	0.252005i
$569$	17.5045	+	30.3188i	0.733829	+	1.27103i	0.955235	+	0.295847i	$0.0956019\pi$
$569$	17.5045	+	30.3188i	0.733829	+	1.27103i	−0.221407	+	0.975182i	$0.571065\pi$
$570$	2.11302	−	1.21995i	0.0885046	−	0.0510981i
$571$	−26.2546			−1.09872			−0.549360	−	0.835586i	$-0.685128\pi$
$571$	−26.2546			−1.09872			−0.549360	+	0.835586i	$0.685128\pi$
$572$	−3.24992	+	24.8209i	−0.135886	+	1.03781i
$573$	5.50428			0.229945
$574$		0			0
$575$	8.59149	+	14.8809i	0.358290	+	0.620576i
$576$	2.97260	−	5.14870i	0.123858	−	0.214529i
$577$		−	24.5727i		−	1.02297i	−0.859291	−	0.511487i	$-0.829095\pi$
$577$		−	24.5727i		−	1.02297i	0.859291	−	0.511487i	$-0.170905\pi$
$578$	−7.35228	−	4.24484i	−0.305815	−	0.176562i
$579$	−3.55327	−	2.05148i	−0.147669	−	0.0852567i
$580$			15.3201i			0.636133i
$581$		0			0
$582$	0.574083	+	0.994341i	0.0237965	+	0.0412167i
$583$	−0.960646	+	0.554629i	−0.0397859	+	0.0229704i
$584$	−12.3987			−0.513063
$585$	−6.79714	−	5.20802i	−0.281027	−	0.215325i
$586$	−12.1010			−0.499886
$587$	−17.7777	+	10.2640i	−0.733765	+	0.423639i	−0.819798	−	0.572653i	$-0.805914\pi$
$587$	−17.7777	+	10.2640i	−0.733765	+	0.423639i	0.0860331	+	0.996292i	$0.472581\pi$
$588$		0			0
$589$	−7.84184	+	13.5825i	−0.323117	+	0.559656i
$590$			5.61957i			0.231354i
$591$	−19.0097	−	10.9752i	−0.781954	−	0.451461i
$592$	−1.87124	−	1.08036i	−0.0769077	−	0.0444027i
$593$			38.2835i			1.57211i	0.618154	+	0.786057i	$0.287881\pi$
$593$			38.2835i			1.57211i	−0.618154	+	0.786057i	$0.712119\pi$
$594$	−4.44757	+	7.70342i	−0.182486	+	0.316075i
$595$		0			0
$596$	0.0172409	−	0.00995405i	0.000706216	−	0.000407734i
$597$	−14.5406			−0.595107
$598$	−6.28338	−	4.81436i	−0.256946	−	0.196874i
$599$	14.0713			0.574939			0.287470	−	0.957790i	$-0.407186\pi$
$599$	14.0713			0.574939			0.287470	+	0.957790i	$0.407186\pi$
$600$	5.39851	−	3.11683i	0.220393	−	0.127244i
$601$	−10.1171	−	17.5233i	−0.412685	−	0.714791i	0.582498	−	0.812832i	$-0.302075\pi$
$601$	−10.1171	−	17.5233i	−0.412685	−	0.714791i	−0.995182	+	0.0980417i	$0.968742\pi$
$602$		0			0
$603$		−	11.7200i		−	0.477276i
$604$	28.6522	+	16.5424i	1.16584	+	0.673099i
$605$	−4.27887	−	2.47041i	−0.173961	−	0.100436i
$606$			4.87328i			0.197964i
$607$	3.27563	−	5.67356i	0.132954	−	0.230283i	−0.791860	−	0.610703i	$-0.790887\pi$
$607$	3.27563	−	5.67356i	0.132954	−	0.230283i	0.924814	+	0.380420i	$0.124220\pi$
$608$	−13.8603	−	24.0067i	−0.562108	−	0.973600i
$609$		0			0
$610$	−3.05621			−0.123742
$611$	2.13287	−	16.2896i	0.0862867	−	0.659005i
$612$	0.566272			0.0228902
$613$	−28.8598	+	16.6622i	−1.16564	+	0.672980i	−0.952648	−	0.304075i	$-0.901653\pi$
$613$	−28.8598	+	16.6622i	−1.16564	+	0.672980i	−0.212988	+	0.977055i	$0.568319\pi$
$614$	6.07294	+	10.5186i	0.245084	+	0.424498i
$615$	−5.35726	+	9.27904i	−0.216025	+	0.374167i
$616$		0			0
$617$	5.85466	+	3.38019i	0.235700	+	0.136081i	0.613199	−	0.789929i	$-0.289883\pi$
$617$	5.85466	+	3.38019i	0.235700	+	0.136081i	−0.377499	+	0.926010i	$0.623216\pi$
$618$	−1.53387	−	0.885581i	−0.0617013	−	0.0356233i
$619$		−	17.6186i		−	0.708152i	−0.935217	−	0.354076i	$-0.884795\pi$
$619$		−	17.6186i		−	0.708152i	0.935217	−	0.354076i	$-0.115205\pi$
$620$	2.59652	−	4.49731i	0.104279	−	0.180616i
$621$	9.84534	+	17.0526i	0.395080	+	0.684298i
$622$	−1.72642	+	0.996751i	−0.0692233	+	0.0399661i
$623$		0			0
$624$	4.77431	−	6.23110i	0.191125	−	0.249444i
$625$	9.87972			0.395189
$626$	12.3299	−	7.11866i	0.492801	−	0.284519i
$627$	−9.28569	−	16.0833i	−0.370835	−	0.642304i
$628$	17.3197	−	29.9985i	0.691130	−	1.19707i
$629$		−	0.119762i		−	0.00477524i
$630$		0			0
$631$	13.6416	+	7.87596i	0.543062	+	0.313537i	0.746319	−	0.665588i	$-0.231819\pi$
$631$	13.6416	+	7.87596i	0.543062	+	0.313537i	−0.203257	+	0.979125i	$0.565153\pi$
$632$		−	22.3546i		−	0.889216i
$633$	7.77009	−	13.4582i	0.308833	−	0.534915i
$634$	−4.20392	−	7.28140i	−0.166959	−	0.289181i
$635$	−1.81273	+	1.04658i	−0.0719359	+	0.0415322i
$636$	0.415713			0.0164841
$637$		0			0
$638$	−16.6575			−0.659475
$639$	−7.29759	+	4.21327i	−0.288688	+	0.166674i
$640$	5.92497	+	10.2623i	0.234205	+	0.405655i
$641$	−10.4702	+	18.1350i	−0.413550	+	0.716289i	−0.995275	−	0.0970962i	$-0.969045\pi$
$641$	−10.4702	+	18.1350i	−0.413550	+	0.716289i	0.581725	+	0.813385i	$0.302378\pi$
$642$			3.60537i			0.142293i
$643$	16.3952	+	9.46576i	0.646563	+	0.373293i	0.787138	−	0.616777i	$-0.211562\pi$
$643$	16.3952	+	9.46576i	0.646563	+	0.373293i	−0.140575	+	0.990070i	$0.544895\pi$
$644$		0			0
$645$		−	4.27188i		−	0.168205i
$646$	0.195640	−	0.338859i	0.00769736	−	0.0133322i
$647$	18.8384	+	32.6291i	0.740614	+	1.28278i	0.952216	+	0.305426i	$0.0987988\pi$
$647$	18.8384	+	32.6291i	0.740614	+	1.28278i	−0.211601	+	0.977356i	$0.567868\pi$
$648$	−4.91126	+	2.83552i	−0.192933	+	0.111390i
$649$	42.7735			1.67901
$650$	−6.51562	+	2.70424i	−0.255563	+	0.106069i
$651$		0			0
$652$	13.5378	−	7.81604i	0.530180	−	0.306100i
$653$	−14.5163	−	25.1430i	−0.568066	−	0.983920i	−0.996757	−	0.0804686i	$-0.974358\pi$
$653$	−14.5163	−	25.1430i	−0.568066	−	0.983920i	0.428691	−	0.903451i	$-0.358975\pi$
$654$	1.36577	−	2.36559i	0.0534060	−	0.0925019i
$655$		−	12.9790i		−	0.507133i
$656$	26.8472	+	15.5002i	1.04821	+	0.605182i
$657$	−13.0468	−	7.53257i	−0.509004	−	0.293874i
$658$		0			0
$659$	0.709152	−	1.22829i	0.0276247	−	0.0478473i	−0.851883	−	0.523733i	$-0.824539\pi$
$659$	0.709152	−	1.22829i	0.0276247	−	0.0478473i	0.879507	+	0.475886i	$0.157872\pi$
$660$	3.07459	+	5.32535i	0.119678	+	0.207289i
$661$	−3.97764	+	2.29649i	−0.154712	+	0.0893231i	−0.575357	−	0.817902i	$-0.695137\pi$
$661$	−3.97764	+	2.29649i	−0.154712	+	0.0893231i	0.420645	+	0.907225i	$0.361804\pi$
$662$	3.10450			0.120660
$663$	0.431412	+	0.0564868i	0.0167547	+	0.00219377i
$664$	−5.38715			−0.209062
$665$		0			0
$666$	0.480219	+	0.831764i	0.0186081	+	0.0322302i
$667$	−18.4368	+	31.9335i	−0.713877	+	1.23647i
$668$		−	10.7358i		−	0.415380i
$669$	8.46782	+	4.88890i	0.327385	+	0.189016i
$670$	2.32218	+	1.34071i	0.0897135	+	0.0517961i
$671$			23.2624i			0.898036i
$672$		0			0
$673$	−2.10111	−	3.63924i	−0.0809920	−	0.140282i	0.822684	−	0.568499i	$-0.192475\pi$
$673$	−2.10111	−	3.63924i	−0.0809920	−	0.140282i	−0.903676	+	0.428216i	$0.859142\pi$
$674$	−3.33259	+	1.92407i	−0.128367	+	0.0741126i
$675$	17.5484			0.675436
$676$	−16.0641	+	16.1095i	−0.617849	+	0.619596i
$677$	−8.08708			−0.310812			−0.155406	−	0.987851i	$-0.549669\pi$
$677$	−8.08708			−0.310812			−0.155406	+	0.987851i	$0.549669\pi$
$678$	4.03316	−	2.32854i	0.154892	−	0.0894272i
$679$		0			0
$680$	−0.138811	+	0.240427i	−0.00532315	+	0.00921997i
$681$			15.2117i			0.582912i
$682$	4.88989	+	2.82318i	0.187244	+	0.108105i
$683$	−21.3792	−	12.3433i	−0.818051	−	0.472302i	0.0316929	−	0.999498i	$-0.489910\pi$
$683$	−21.3792	−	12.3433i	−0.818051	−	0.472302i	−0.849744	+	0.527196i	$0.823243\pi$
$684$		−	21.9666i		−	0.839912i
$685$	−2.73398	+	4.73540i	−0.104460	+	0.180930i
$686$		0			0
$687$	2.84267	−	1.64122i	0.108455	−	0.0626164i
$688$	−12.3599			−0.471216
$689$	−0.999581	−	0.130880i	−0.0380810	−	0.00498612i
$690$	−1.94447			−0.0740246
$691$	−9.74859	+	5.62835i	−0.370854	+	0.214113i	−0.673831	−	0.738885i	$-0.735353\pi$
$691$	−9.74859	+	5.62835i	−0.370854	+	0.214113i	0.302978	+	0.952998i	$0.402019\pi$
$692$	−21.2301	−	36.7716i	−0.807047	−	1.39785i
$693$		0			0
$694$		−	15.2043i		−	0.577147i
$695$	18.7230	+	10.8097i	0.710202	+	0.410035i
$696$	11.5849	+	6.68854i	0.439124	+	0.253528i
$697$			1.71826i			0.0650836i
$698$	−4.03942	+	6.99648i	−0.152894	+	0.264821i
$699$	−10.6473	−	18.4416i	−0.402717	−	0.697526i
$700$		0			0
$701$	22.2305			0.839635			0.419818	−	0.907608i	$-0.362094\pi$
$701$	22.2305			0.839635			0.419818	+	0.907608i	$0.362094\pi$
$702$	−7.46651	+	3.09890i	−0.281805	+	0.116961i
$703$	−4.64576			−0.175218
$704$	8.96614	−	5.17660i	0.337924	−	0.195101i
$705$	−2.01781	−	3.49495i	−0.0759951	−	0.131627i
$706$	2.96052	−	5.12776i	0.111420	−	0.192986i
$707$		0			0
$708$	−13.8825	−	8.01504i	−0.521734	−	0.301224i
$709$	−20.5889	−	11.8870i	−0.773234	−	0.446427i	0.0607929	−	0.998150i	$-0.480637\pi$
$709$	−20.5889	−	11.8870i	−0.773234	−	0.446427i	−0.834027	+	0.551723i	$0.813970\pi$
$710$		−	1.92790i		−	0.0723530i
$711$	13.5810	−	23.5230i	0.509328	−	0.882182i
$712$	−1.63838	−	2.83776i	−0.0614010	−	0.106350i
$713$	10.8245	−	6.24951i	0.405380	−	0.234046i
$714$		0			0
$715$	−5.71626	−	13.7728i	−0.213776	−	0.515072i
$716$	7.23937			0.270548
$717$	−5.74246	+	3.31541i	−0.214456	+	0.123816i
$718$	−7.84111	−	13.5812i	−0.292628	−	0.506846i
$719$	−10.3904	+	17.9967i	−0.387496	+	0.671163i	−0.992112	−	0.125354i	$-0.959993\pi$
$719$	−10.3904	+	17.9967i	−0.387496	+	0.671163i	0.604616	+	0.796517i	$0.293327\pi$
$720$			6.08597i			0.226811i
$721$		0			0
$722$	−4.91782	−	2.83931i	−0.183022	−	0.105668i
$723$			18.4918i			0.687717i
$724$	−6.88252	+	11.9209i	−0.255787	+	0.443036i
$725$	16.4309	+	28.4592i	0.610229	+	1.05695i
$726$	−1.74356	+	1.00665i	−0.0647097	+	0.0373601i
$727$	26.7719			0.992915			0.496457	−	0.868061i	$-0.334634\pi$
$727$	26.7719			0.992915			0.496457	+	0.868061i	$0.334634\pi$
$728$		0			0
$729$	4.53910			0.168115
$730$	2.98497	−	1.72338i	0.110479	−	0.0637850i
$731$	−0.342535	−	0.593287i	−0.0126691	−	0.0219435i
$732$	4.35899	−	7.55000i	0.161113	−	0.279056i
$733$			5.25647i			0.194152i	0.995277	+	0.0970761i	$0.0309490\pi$
$733$			5.25647i			0.194152i	−0.995277	+	0.0970761i	$0.969051\pi$
$734$	−10.4255	−	6.01919i	−0.384814	−	0.222172i
$735$		0			0
$736$			22.0917i			0.814312i
$737$	10.2048	−	17.6753i	0.375900	−	0.651078i
$738$	−6.88981	−	11.9335i	−0.253617	−	0.439278i
$739$	−6.19209	+	3.57501i	−0.227780	+	0.131509i	−0.609547	−	0.792750i	$-0.708649\pi$
$739$	−6.19209	+	3.57501i	−0.227780	+	0.131509i	0.381768	+	0.924258i	$0.375315\pi$
$740$	1.53826			0.0565477
$741$	2.19121	−	16.7351i	0.0804960	−	0.614780i
$742$		0			0
$743$	−0.618032	+	0.356821i	−0.0226734	+	0.0130905i	−0.511294	−	0.859406i	$-0.670834\pi$
$743$	−0.618032	+	0.356821i	−0.0226734	+	0.0130905i	0.488620	+	0.872496i	$0.337500\pi$
$744$	−2.26721	−	3.92692i	−0.0831198	−	0.143968i
$745$	−0.00592959	+	0.0102703i	−0.000217243	+	0.000376276i
$746$			9.19587i			0.336685i
$747$	−5.66873	−	3.27284i	−0.207408	−	0.119747i
$748$	0.854012	+	0.493064i	0.0312258	+	0.0180282i
$749$		0			0
$750$	−1.97354	+	3.41827i	−0.0720634	+	0.124817i
$751$	−12.8507	−	22.2580i	−0.468927	−	0.812205i	0.530442	−	0.847721i	$-0.322026\pi$
$751$	−12.8507	−	22.2580i	−0.468927	−	0.812205i	−0.999369	+	0.0355158i	$0.988693\pi$
$752$	−10.1120	+	5.83815i	−0.368746	+	0.212896i
$753$	−6.52477			−0.237776
$754$	−12.0167	−	9.20730i	−0.437624	−	0.335310i
$755$	−19.7084			−0.717263
$756$		0			0
$757$	−8.19425	−	14.1928i	−0.297825	−	0.515848i	0.677813	−	0.735234i	$-0.262928\pi$
$757$	−8.19425	−	14.1928i	−0.297825	−	0.515848i	−0.975638	+	0.219386i	$0.929594\pi$
$758$	2.03430	−	3.52350i	0.0738889	−	0.127979i
$759$			14.8004i			0.537219i
$760$	9.32654	+	5.38468i	0.338309	+	0.195323i
$761$	7.20531	+	4.15999i	0.261192	+	0.150800i	0.624878	−	0.780722i	$-0.285149\pi$
$761$	7.20531	+	4.15999i	0.261192	+	0.150800i	−0.363686	+	0.931522i	$0.618482\pi$
$762$			0.852923i			0.0308981i
$763$		0			0
$764$	5.66888	+	9.81878i	0.205093	+	0.355231i
$765$	−0.292133	+	0.168663i	−0.0105621	+	0.00609802i
$766$	11.1853			0.404140
$767$	30.8569	+	23.6428i	1.11418	+	0.853690i
$768$	0.394335			0.0142293
$769$	−22.1346	+	12.7794i	−0.798194	+	0.460838i	−0.842839	−	0.538165i	$-0.819118\pi$
$769$	−22.1346	+	12.7794i	−0.798194	+	0.460838i	0.0446452	+	0.999003i	$0.485784\pi$
$770$		0			0
$771$	5.78738	−	10.0240i	0.208427	−	0.361007i
$772$		−	8.45131i		−	0.304169i
$773$	7.27528	+	4.20038i	0.261674	+	0.151077i	0.625098	−	0.780546i	$-0.285059\pi$
$773$	7.27528	+	4.20038i	0.261674	+	0.151077i	−0.363424	+	0.931624i	$0.618392\pi$
$774$	4.75789	+	2.74697i	0.171019	+	0.0987378i
$775$		−	11.1391i		−	0.400130i
$776$	−2.53392	+	4.38887i	−0.0909623	+	0.157551i
$777$		0			0
$778$	−9.26388	+	5.34850i	−0.332126	+	0.191753i
$779$	66.6537			2.38812
$780$	−0.725534	+	5.54119i	−0.0259783	+	0.198406i
$781$	−14.6743			−0.525087
$782$	−0.270052	+	0.155914i	−0.00965703	+	0.00557549i
$783$	18.8289	+	32.6125i	0.672889	+	1.16548i
$784$		0			0
$785$			20.6345i			0.736476i
$786$	−4.58017	−	2.64436i	−0.163369	−	0.0943212i
$787$	−30.3667	−	17.5322i	−1.08246	−	0.624956i	−0.150898	−	0.988549i	$-0.548216\pi$
$787$	−30.3667	−	17.5322i	−1.08246	−	0.624956i	−0.931558	+	0.363593i	$0.881550\pi$
$788$		−	45.2137i		−	1.61067i
$789$	−4.98000	+	8.62562i	−0.177293	+	0.307080i
$790$	3.10720	+	5.38182i	0.110549	+	0.191477i
$791$		0			0
$792$	−16.9463			−0.602160
$793$	−12.8582	+	16.7816i	−0.456607	+	0.595931i
$794$	−0.598349			−0.0212346
$795$	−0.214461	+	0.123819i	−0.00760616	+	0.00439142i
$796$	−14.9754	−	25.9382i	−0.530789	−	0.919354i
$797$	12.2876	−	21.2828i	0.435250	−	0.753875i	−0.562066	−	0.827092i	$-0.689993\pi$
$797$	12.2876	−	21.2828i	0.435250	−	0.753875i	0.997316	+	0.0732173i	$0.0233267\pi$
$798$		0			0
$799$	−0.560475	−	0.323590i	−0.0198282	−	0.0114478i
$800$	17.0505	+	9.84409i	0.602825	+	0.348041i
$801$		−	3.98145i		−	0.140678i
$802$	9.06848	−	15.7071i	0.320219	−	0.554636i
$803$	−13.1175	−	22.7202i	−0.462907	−	0.801778i
$804$	−6.62411	+	3.82443i	−0.233615	+	0.134877i
$805$		0			0
$806$	1.96709	+	4.73951i	0.0692877	+	0.166942i
$807$	7.81528			0.275111
$808$	−18.6282	+	10.7550i	−0.655336	+	0.378358i
$809$	15.9006	+	27.5406i	0.559035	+	0.968277i	0.997577	+	0.0695667i	$0.0221617\pi$
$809$	15.9006	+	27.5406i	0.559035	+	0.968277i	−0.438542	+	0.898711i	$0.644505\pi$
$810$	0.788253	−	1.36529i	0.0276964	−	0.0479715i
$811$		−	10.3633i		−	0.363905i	−0.983307	−	0.181953i	$-0.941758\pi$
$811$		−	10.3633i		−	0.363905i	0.983307	−	0.181953i	$-0.0582418\pi$
$812$		0			0
$813$	1.88630	+	1.08906i	0.0661555	+	0.0381949i
$814$			1.67254i			0.0586226i
$815$	−4.65598	+	8.06439i	−0.163092	+	0.282483i
$816$	−0.154617	−	0.267805i	−0.00541269	−	0.00937505i
$817$	−23.0145	+	13.2874i	−0.805176	+	0.464868i
$818$	7.33597			0.256496
$819$		0			0
$820$	−22.0698			−0.770711
$821$	−3.51253	+	2.02796i	−0.122588	+	0.0707762i	−0.560040	−	0.828465i	$-0.689214\pi$
$821$	−3.51253	+	2.02796i	−0.122588	+	0.0707762i	0.437452	+	0.899242i	$0.355881\pi$
$822$	1.11405	+	1.92959i	0.0388569	+	0.0673021i
$823$	4.35848	−	7.54912i	0.151927	−	0.263146i	−0.780009	−	0.625769i	$-0.784785\pi$
$823$	4.35848	−	7.54912i	0.151927	−	0.263146i	0.931936	+	0.362623i	$0.118119\pi$
$824$		−	7.81764i		−	0.272340i
$825$	11.4230	+	6.59505i	0.397696	+	0.229610i
$826$		0			0
$827$		−	23.5788i		−	0.819915i	−0.912105	−	0.409957i	$-0.865544\pi$
$827$		−	23.5788i		−	0.819915i	0.912105	−	0.409957i	$-0.134456\pi$
$828$	−8.75307	+	15.1608i	−0.304190	+	0.526873i
$829$	14.5203	+	25.1499i	0.504311	+	0.873492i	0.999988	+	0.00498467i	$0.00158668\pi$
$829$	14.5203	+	25.1499i	0.504311	+	0.873492i	−0.495677	+	0.868507i	$0.665080\pi$
$830$	1.29695	−	0.748793i	0.0450177	−	0.0259910i
$831$	−0.793427			−0.0275237
$832$	9.32953	+	1.22156i	0.323443	+	0.0423499i
$833$		0			0
$834$	7.62926	−	4.40475i	0.264180	−	0.152524i
$835$	3.19763	+	5.53846i	0.110659	+	0.191666i
$836$	19.1267	−	33.1284i	0.661511	−	1.14577i
$837$		−	12.7648i		−	0.441216i
$838$	2.56921	+	1.48333i	0.0887517	+	0.0512408i
$839$	10.0090	+	5.77871i	0.345550	+	0.199503i	0.662723	−	0.748864i	$-0.269400\pi$
$839$	10.0090	+	5.77871i	0.345550	+	0.199503i	−0.317174	+	0.948367i	$0.602734\pi$
$840$		0			0
$841$	−20.7598	+	35.9570i	−0.715855	+	1.23990i
$842$	0.657918	+	1.13955i	0.0226734	+	0.0392714i
$843$	−4.74788	+	2.74119i	−0.163526	+	0.0944116i
$844$	32.0097			1.10182
$845$	3.48908	−	13.0953i	0.120028	−	0.450493i
$846$	5.19009			0.178439
$847$		0			0
$848$	0.358248	+	0.620504i	0.0123023	+	0.0213082i
$849$	9.41977	−	16.3155i	0.323286	−	0.559947i
$850$			0.277902i			0.00953197i
$851$	3.20638	+	1.85121i	0.109913	+	0.0634586i
$852$	4.76265	+	2.74972i	0.163166	+	0.0942038i
$853$			1.51845i			0.0519906i	0.999662	+	0.0259953i	$0.00827550\pi$
$853$			1.51845i			0.0519906i	−0.999662	+	0.0259953i	$0.991725\pi$
$854$		0			0
$855$	6.54269	+	11.3323i	0.223755	+	0.387556i
$856$	−13.7815	+	7.95678i	−0.471043	+	0.271957i
$857$	−6.00119			−0.204997			−0.102498	−	0.994733i	$-0.532684\pi$
$857$	−6.00119			−0.204997			−0.102498	+	0.994733i	$0.532684\pi$
$858$	−6.02490	−	0.788868i	−0.205687	−	0.0269315i
$859$	−1.67604			−0.0571858			−0.0285929	−	0.999591i	$-0.509103\pi$
$859$	−1.67604			−0.0571858			−0.0285929	+	0.999591i	$0.509103\pi$
$860$	7.62036	−	4.39962i	0.259852	−	0.150026i
$861$		0			0
$862$	4.70929	−	8.15673i	0.160399	−	0.277819i
$863$		−	42.0504i		−	1.43141i	−0.698401	−	0.715706i	$-0.746105\pi$
$863$		−	42.0504i		−	1.43141i	0.698401	−	0.715706i	$-0.253895\pi$
$864$	19.5388	+	11.2807i	0.664724	+	0.383779i
$865$	21.9047	+	12.6467i	0.744781	+	0.429999i
$866$		−	9.56747i		−	0.325116i
$867$	−7.21304	+	12.4934i	−0.244968	+	0.424297i
$868$		0			0
$869$	40.9639	−	23.6505i	1.38960	−	0.802288i
$870$	−3.71873			−0.126077
$871$	17.1317	−	7.11035i	0.580486	−	0.240925i
$872$	12.0566			0.408290
$873$	−5.33272	+	3.07885i	−0.180485	+	0.104203i
$874$	6.04815	+	10.4757i	0.204582	+	0.354346i
$875$		0			0
$876$			9.83201i			0.332193i
$877$	−26.7281	−	15.4315i	−0.902545	−	0.521084i	−0.0245198	−	0.999699i	$-0.507806\pi$
$877$	−26.7281	−	15.4315i	−0.902545	−	0.521084i	−0.878025	+	0.478615i	$0.841139\pi$
$878$	−0.547793	−	0.316268i	−0.0184871	−	0.0106735i
$879$			20.5625i			0.693557i
$880$	−5.29917	+	9.17843i	−0.178635	+	0.309405i
$881$	27.8669	+	48.2669i	0.938860	+	1.62615i	0.767601	+	0.640928i	$0.221450\pi$
$881$	27.8669	+	48.2669i	0.938860	+	1.62615i	0.171260	+	0.985226i	$0.445216\pi$
$882$		0			0
$883$	−2.92007			−0.0982681			−0.0491341	−	0.998792i	$-0.515646\pi$
$883$	−2.92007			−0.0982681			−0.0491341	+	0.998792i	$0.515646\pi$
$884$	0.343549	+	0.827747i	0.0115548	+	0.0278402i
$885$	9.54904			0.320988
$886$	9.06671	−	5.23467i	0.304602	−	0.175862i
$887$	0.939545	+	1.62734i	0.0315468	+	0.0546407i	0.881368	−	0.472431i	$-0.156623\pi$
$887$	0.939545	+	1.62734i	0.0315468	+	0.0546407i	−0.849821	+	0.527071i	$0.823290\pi$
$888$	0.671584	−	1.16322i	0.0225369	−	0.0390350i
$889$		0			0
$890$	0.788876	+	0.455458i	0.0264432	+	0.0152670i
$891$	−10.3920	−	5.99980i	−0.348144	−	0.201001i
$892$			20.1404i			0.674349i
$893$	−12.5526	+	21.7417i	−0.420055	+	0.727557i
$894$	0.00241620	+	0.00418498i	8.08097e−5	+	0.000139967i
$895$	−3.73470	+	2.15623i	−0.124837	+	0.0720748i
$896$		0			0
$897$	−8.18080	+	10.6770i	−0.273149	+	0.356495i
$898$	−8.93138			−0.298044
$899$	20.7014	−	11.9520i	0.690431	−	0.398621i
$900$	7.80074	+	13.5113i	0.260025	+	0.450376i
$901$	−0.0198566	+	0.0343926i	−0.000661518	+	0.00114578i
$902$		−	23.9964i		−	0.798991i
$903$		0			0
$904$	17.8017	+	10.2778i	0.592077	+	0.341836i
$905$		−	8.19978i		−	0.272570i
$906$	−4.01541	+	6.95490i	−0.133403	+	0.231061i
$907$	−17.8082	−	30.8447i	−0.591311	−	1.02418i	−0.994056	−	0.108868i	$-0.965277\pi$
$907$	−17.8082	−	30.8447i	−0.591311	−	1.02418i	0.402745	−	0.915312i	$-0.368056\pi$
$908$	−27.1352	+	15.6665i	−0.900514	+	0.519912i
$909$	−26.1358			−0.866869
$910$		0			0
$911$	44.2844			1.46721			0.733604	−	0.679577i	$-0.237837\pi$
$911$	44.2844			1.46721			0.733604	+	0.679577i	$0.237837\pi$
$912$	−10.3886	+	5.99784i	−0.344000	+	0.198608i
$913$	−5.69946	−	9.87175i	−0.188624	−	0.326707i
$914$	−1.64145	+	2.84307i	−0.0542943	+	0.0940404i
$915$			5.19327i			0.171684i
$916$	5.85535	+	3.38059i	0.193466	+	0.111698i
$917$		0			0
$918$			0.318459i			0.0105107i
$919$	−13.0564	+	22.6144i	−0.430691	+	0.745979i	−0.996933	−	0.0782603i	$-0.975063\pi$
$919$	−13.0564	+	22.6144i	−0.430691	+	0.745979i	0.566242	+	0.824239i	$0.308397\pi$
$920$	−4.29129	−	7.43274i	−0.141480	−	0.245050i
$921$	17.8738	−	10.3194i	0.588961	−	0.340037i
$922$	−2.55675			−0.0842021
$923$	−10.5861	−	8.11111i	−0.348445	−	0.266981i
$924$		0			0
$925$	2.85753	−	1.64980i	0.0939551	−	0.0542450i
$926$	8.33076	+	14.4293i	0.273766	+	0.474176i
$927$	4.74944	−	8.22626i	0.155992	−	0.270186i
$928$			42.2497i			1.38691i
$929$	−8.68030	−	5.01157i	−0.284791	−	0.164424i	0.350799	−	0.936451i	$-0.385910\pi$
$929$	−8.68030	−	5.01157i	−0.284791	−	0.164424i	−0.635591	+	0.772026i	$0.719243\pi$
$930$	1.09165	+	0.630266i	0.0357967	+	0.0206672i
$931$		0			0
$932$	21.9313	−	37.9861i	0.718384	−	1.24428i
$933$	1.69373	+	2.93362i	0.0554501	+	0.0960425i
$934$	5.60712	−	3.23727i	0.183471	−	0.105927i
$935$	−0.587432			−0.0192111
$936$	−12.2251	−	9.36694i	−0.399590	−	0.306168i
$937$	0.916838			0.0299518			0.0149759	−	0.999888i	$-0.495233\pi$
$937$	0.916838			0.0299518			0.0149759	+	0.999888i	$0.495233\pi$
$938$		0			0
$939$	−12.0964	−	20.9515i	−0.394750	−	0.683728i
$940$	4.15629	−	7.19891i	0.135563	−	0.234803i
$941$			17.0896i			0.557107i	0.960421	+	0.278553i	$0.0898549\pi$
$941$			17.0896i			0.557107i	−0.960421	+	0.278553i	$0.910145\pi$
$942$	7.28169	+	4.20409i	0.237250	+	0.136977i
$943$	−46.0027	−	26.5597i	−1.49805	−	0.864902i
$944$		−	27.6284i		−	0.899227i
$945$		0			0
$946$	4.78368	+	8.28557i	0.155531	+	0.269387i
$947$	−18.8408	+	10.8777i	−0.612243	+	0.353479i	−0.773843	−	0.633378i	$-0.781668\pi$
$947$	−18.8408	+	10.8777i	−0.612243	+	0.353479i	0.161600	+	0.986856i	$0.448335\pi$
$948$	−17.7268			−0.575741
$949$	3.09543	−	23.6410i	0.100482	−	0.767420i
$950$	10.7802			0.349757
$951$	−12.3729	+	7.14350i	−0.401219	+	0.231644i
$952$		0			0
$953$	−8.90406	+	15.4223i	−0.288431	+	0.499577i	−0.973435	−	0.228962i	$-0.926467\pi$
$953$	−8.90406	+	15.4223i	−0.288431	+	0.499577i	0.685005	+	0.728539i	$0.259800\pi$
$954$		−	0.318481i		−	0.0103112i
$955$	−5.84900	−	3.37692i	−0.189269	−	0.109275i
$956$	−11.8283	−	6.82909i	−0.382556	−	0.220869i
$957$			28.3052i			0.914976i
$958$	−6.75281	+	11.6962i	−0.218173	+	0.377887i
$959$		0			0
$960$	2.00166	−	1.15566i	0.0646034	−	0.0372988i
$961$	22.8973			0.738623
$962$	−0.924488	+	1.20658i	−0.0298067	+	0.0389016i
$963$	−19.3359			−0.623089
$964$	−32.9865	+	19.0447i	−1.06242	+	0.613390i
$965$	2.51720	+	4.35992i	0.0810316	+	0.140351i
$966$		0			0
$967$			35.3813i			1.13779i	0.822412	+	0.568893i	$0.192628\pi$
$967$			35.3813i			1.13779i	−0.822412	+	0.568893i	$0.807372\pi$
$968$	−7.69582	−	4.44318i	−0.247353	−	0.142809i
$969$	−0.575805	−	0.332441i	−0.0184975	−	0.0106796i
$970$		−	1.40882i		−	0.0452344i
$971$	24.8533	−	43.0472i	0.797582	−	1.38145i	−0.123605	−	0.992331i	$-0.539446\pi$
$971$	24.8533	−	43.0472i	0.797582	−	1.38145i	0.921187	−	0.389120i	$-0.127221\pi$
$972$	14.0200	+	24.2834i	0.449693	+	0.778890i
$973$		0			0
$974$	16.0415			0.514002
$975$	4.59518	+	11.0716i	0.147164	+	0.354577i
$976$	15.0257			0.480962
$977$	53.0701	−	30.6401i	1.69786	−	0.980262i	0.750081	−	0.661346i	$-0.230014\pi$
$977$	53.0701	−	30.6401i	1.69786	−	0.980262i	0.947783	−	0.318917i	$-0.103319\pi$
$978$	1.89723	+	3.28609i	0.0606666	+	0.105078i
$979$	3.46673	−	6.00455i	0.110797	−	0.191906i
$980$		0			0
$981$	12.6868	+	7.32475i	0.405060	+	0.233861i
$982$	12.3856	+	7.15080i	0.395239	+	0.228191i
$983$			6.98962i			0.222934i	0.993768	+	0.111467i	$0.0355550\pi$
$983$			6.98962i			0.222934i	−0.993768	+	0.111467i	$0.964445\pi$
$984$	−9.63536	+	16.6889i	−0.307164	+	0.532024i
$985$	13.4668	+	23.3252i	0.429088	+	0.743203i
$986$	−0.516464	+	0.298181i	−0.0164476	+	0.00949601i
$987$		0			0
$988$	32.1096	−	13.3268i	1.02154	−	0.423981i
$989$	21.1787			0.673443
$990$	4.07979	−	2.35547i	0.129664	−	0.0748617i
$991$	16.3671	+	28.3486i	0.519917	+	0.900522i	0.999732	+	0.0231525i	$0.00737033\pi$
$991$	16.3671	+	28.3486i	0.519917	+	0.900522i	−0.479815	+	0.877370i	$0.659296\pi$
$992$	7.16066	−	12.4026i	0.227351	−	0.393784i
$993$		−	5.27532i		−	0.167407i
$994$		0			0
$995$	15.4512	+	8.92078i	0.489838	+	0.282808i
$996$			4.27193i			0.135361i
$997$	28.8948	−	50.0473i	0.915109	−	1.58502i	0.108367	−	0.994111i	$-0.465438\pi$
$997$	28.8948	−	50.0473i	0.915109	−	1.58502i	0.806742	−	0.590904i	$-0.201229\pi$
$998$	0.449529	+	0.778607i	0.0142296	+	0.0246464i
$999$	3.27456	−	1.89057i	0.103603	−	0.0598150i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.q.i.491.3		12
7.2	even	3		637.2.u.g.361.4		12
7.3	odd	6		91.2.k.b.23.3	yes	12
7.4	even	3		637.2.k.i.569.3		12
7.5	odd	6		91.2.u.b.88.4	yes	12
7.6	odd	2		637.2.q.g.491.3		12
13.2	odd	12		8281.2.a.co.1.5		12
13.4	even	6	inner	637.2.q.i.589.3		12
13.11	odd	12		8281.2.a.co.1.8		12
21.5	even	6		819.2.do.e.361.3		12
21.17	even	6		819.2.bm.f.478.4		12
91.4	even	6		637.2.u.g.30.4		12
91.17	odd	6		91.2.u.b.30.4	yes	12
91.24	even	12		1183.2.e.j.170.5		24
91.30	even	6		637.2.k.i.459.4		12
91.41	even	12		8281.2.a.cp.1.5		12
91.54	even	12		1183.2.e.j.508.8		24
91.69	odd	6		637.2.q.g.589.3		12
91.76	even	12		8281.2.a.cp.1.8		12
91.80	even	12		1183.2.e.j.170.8		24
91.82	odd	6		91.2.k.b.4.4	✓	12
91.89	even	12		1183.2.e.j.508.5		24
273.17	even	6		819.2.do.e.667.3		12
273.173	even	6		819.2.bm.f.550.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.b.4.4	✓	12	91.82	odd	6
91.2.k.b.23.3	yes	12	7.3	odd	6
91.2.u.b.30.4	yes	12	91.17	odd	6
91.2.u.b.88.4	yes	12	7.5	odd	6
637.2.k.i.459.4		12	91.30	even	6
637.2.k.i.569.3		12	7.4	even	3
637.2.q.g.491.3		12	7.6	odd	2
637.2.q.g.589.3		12	91.69	odd	6
637.2.q.i.491.3		12	1.1	even	1	trivial
637.2.q.i.589.3		12	13.4	even	6	inner
637.2.u.g.30.4		12	91.4	even	6
637.2.u.g.361.4		12	7.2	even	3
819.2.bm.f.478.4		12	21.17	even	6
819.2.bm.f.550.3		12	273.173	even	6
819.2.do.e.361.3		12	21.5	even	6
819.2.do.e.667.3		12	273.17	even	6
1183.2.e.j.170.5		24	91.24	even	12
1183.2.e.j.170.8		24	91.80	even	12
1183.2.e.j.508.5		24	91.89	even	12
1183.2.e.j.508.8		24	91.54	even	12
8281.2.a.co.1.5		12	13.2	odd	12
8281.2.a.co.1.8		12	13.11	odd	12
8281.2.a.cp.1.5		12	91.41	even	12
8281.2.a.cp.1.8		12	91.76	even	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.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.433001 + 0.249993i) q^{2} +(0.424801 + 0.735776i) q^{3} +(-0.875007 + 1.51556i) q^{4} -1.04248i q^{5} +(-0.367878 - 0.212395i) q^{6} -1.87496i q^{8} +(1.13909 - 1.97296i) q^{9} +O(q^{10})\)	\(q+(-0.433001 + 0.249993i) q^{2} +(0.424801 + 0.735776i) q^{3} +(-0.875007 + 1.51556i) q^{4} -1.04248i q^{5} +(-0.367878 - 0.212395i) q^{6} -1.87496i q^{8} +(1.13909 - 1.97296i) q^{9} +(0.260612 + 0.451393i) q^{10} +(3.43579 - 1.98365i) q^{11} -1.48681 q^{12} +(3.57504 + 0.468096i) q^{13} +(0.767029 - 0.442844i) q^{15} +(-1.28129 - 2.21925i) q^{16} +(0.0710177 - 0.123006i) q^{17} +1.13906i q^{18} +(-4.77160 - 2.75488i) q^{19} +(1.57993 + 0.912173i) q^{20} +(-0.991800 + 1.71785i) q^{22} +(2.19549 + 3.80270i) q^{23} +(1.37955 - 0.796483i) q^{24} +3.91325 q^{25} +(-1.66502 + 0.691049i) q^{26} +4.48435 q^{27} +(4.19880 + 7.27253i) q^{29} +(-0.221416 + 0.383504i) q^{30} -2.84652i q^{31} +(4.35712 + 2.51558i) q^{32} +(2.91905 + 1.68531i) q^{33} +0.0710158i q^{34} +(1.99342 + 3.45271i) q^{36} +(0.730221 - 0.421593i) q^{37} +2.75481 q^{38} +(1.17426 + 2.82928i) q^{39} -1.95460 q^{40} +(-10.4766 + 6.04869i) q^{41} +(2.41161 - 4.17704i) q^{43} +6.94284i q^{44} +(-2.05676 - 1.18747i) q^{45} +(-1.90130 - 1.09772i) q^{46} -4.55648i q^{47} +(1.08858 - 1.88548i) q^{48} +(-1.69444 + 0.978285i) q^{50} +0.120673 q^{51} +(-3.83761 + 5.00858i) q^{52} -0.279600 q^{53} +(-1.94173 + 1.12106i) q^{54} +(-2.06791 - 3.58172i) q^{55} -4.68111i q^{57} +(-3.63617 - 2.09934i) q^{58} +(9.33705 + 5.39075i) q^{59} +1.54997i q^{60} +(-2.93177 + 5.07797i) q^{61} +(0.711612 + 1.23255i) q^{62} +2.60963 q^{64} +(0.487979 - 3.72689i) q^{65} -1.68527 q^{66} +(4.45524 - 2.57223i) q^{67} +(0.124282 + 0.215263i) q^{68} +(-1.86529 + 3.23078i) q^{69} +(-3.20326 - 1.84940i) q^{71} +(-3.69921 - 2.13574i) q^{72} -6.61281i q^{73} +(-0.210791 + 0.365101i) q^{74} +(1.66235 + 2.87927i) q^{75} +(8.35036 - 4.82108i) q^{76} +(-1.21576 - 0.931521i) q^{78} +11.9227 q^{79} +(-2.31352 + 1.33571i) q^{80} +(-1.51231 - 2.61940i) q^{81} +(3.02426 - 5.23818i) q^{82} -2.87321i q^{83} +(-0.128231 - 0.0740342i) q^{85} +2.41155i q^{86} +(-3.56730 + 6.17875i) q^{87} +(-3.71926 - 6.44195i) q^{88} +(1.51351 - 0.873824i) q^{89} +1.18744 q^{90} -7.68427 q^{92} +(2.09440 - 1.20921i) q^{93} +(1.13909 + 1.97296i) q^{94} +(-2.87190 + 4.97427i) q^{95} +4.27449i q^{96} +(-2.34079 - 1.35145i) q^{97} -9.03822i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{3} + 4 q^{4} + 9 q^{6} - q^{9}+O(q^{10}) \) 12 * q + 3 * q^3 + 4 * q^4 + 9 * q^6 - q^9	\( 12 q + 3 q^{3} + 4 q^{4} + 9 q^{6} - q^{9} - 12 q^{10} - 12 q^{11} - 2 q^{12} + 2 q^{13} - 12 q^{15} - 8 q^{16} - 17 q^{17} + 9 q^{19} + 3 q^{20} - 15 q^{22} + 3 q^{23} + 15 q^{24} + 10 q^{25} - 15 q^{26} - 12 q^{27} - q^{29} + 11 q^{30} - 18 q^{32} - 6 q^{33} - 13 q^{36} - 15 q^{37} + 38 q^{38} + 5 q^{39} - 2 q^{40} + 6 q^{41} + 11 q^{43} - 9 q^{45} + 30 q^{46} - 19 q^{48} + 18 q^{50} - 8 q^{51} + 40 q^{52} + 16 q^{53} + 6 q^{54} + 15 q^{55} + 24 q^{58} + 27 q^{59} - 5 q^{61} - 41 q^{62} + 2 q^{64} - 18 q^{65} - 68 q^{66} - 15 q^{67} + 11 q^{68} - 7 q^{69} + 30 q^{71} - 57 q^{72} - 33 q^{74} - q^{75} + 45 q^{76} + 44 q^{78} + 70 q^{79} - 63 q^{80} + 14 q^{81} - 5 q^{82} - 21 q^{85} - 10 q^{87} - 14 q^{88} + 48 q^{89} - 66 q^{92} + 81 q^{93} - q^{94} + 2 q^{95} + 3 q^{97}+O(q^{100}) \) 12 * q + 3 * q^3 + 4 * q^4 + 9 * q^6 - q^9 - 12 * q^10 - 12 * q^11 - 2 * q^12 + 2 * q^13 - 12 * q^15 - 8 * q^16 - 17 * q^17 + 9 * q^19 + 3 * q^20 - 15 * q^22 + 3 * q^23 + 15 * q^24 + 10 * q^25 - 15 * q^26 - 12 * q^27 - q^29 + 11 * q^30 - 18 * q^32 - 6 * q^33 - 13 * q^36 - 15 * q^37 + 38 * q^38 + 5 * q^39 - 2 * q^40 + 6 * q^41 + 11 * q^43 - 9 * q^45 + 30 * q^46 - 19 * q^48 + 18 * q^50 - 8 * q^51 + 40 * q^52 + 16 * q^53 + 6 * q^54 + 15 * q^55 + 24 * q^58 + 27 * q^59 - 5 * q^61 - 41 * q^62 + 2 * q^64 - 18 * q^65 - 68 * q^66 - 15 * q^67 + 11 * q^68 - 7 * q^69 + 30 * q^71 - 57 * q^72 - 33 * q^74 - q^75 + 45 * q^76 + 44 * q^78 + 70 * q^79 - 63 * q^80 + 14 * q^81 - 5 * q^82 - 21 * q^85 - 10 * q^87 - 14 * q^88 + 48 * q^89 - 66 * q^92 + 81 * q^93 - q^94 + 2 * q^95 + 3 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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