LMFDB - Embedded newform 637.2.u.g.30.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(30,637)]

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([2, 1]))

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

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

chi := DirichletCharacter("637.30");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.u (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:	12.0.2346760387617129.1
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			30.4
Root			$-1.18541 + 0.771231i$ of defining polynomial
Character	$\chi$	$=$	637.30
Dual form			637.2.u.g.361.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.433001 - 0.249993i) q^{2} -0.849601 q^{3} +(-0.875007 + 1.51556i) q^{4} +(-0.902810 - 0.521238i) q^{5} +(-0.367878 + 0.212395i) q^{6} +1.87496i q^{8} -2.27818 q^{9} +O(q^{10})$	\(q+(0.433001 - 0.249993i) q^{2} -0.849601 q^{3} +(-0.875007 + 1.51556i) q^{4} +(-0.902810 - 0.521238i) q^{5} +(-0.367878 + 0.212395i) q^{6} +1.87496i q^{8} -2.27818 q^{9} -0.521224 q^{10} -3.96730i q^{11} +(0.743407 - 1.28762i) 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} +(-0.986453 + 0.569529i) q^{18} -5.50977i q^{19} +(1.57993 - 0.912173i) q^{20} +(-0.991800 - 1.71785i) q^{22} +(2.19549 + 3.80270i) q^{23} -1.59297i q^{24} +(-1.95662 - 3.38897i) q^{25} +(1.43097 - 1.09642i) q^{26} +4.48435 q^{27} +(4.19880 - 7.27253i) q^{29} +0.442832 q^{30} +(2.46516 - 1.42326i) q^{31} +(-4.35712 - 2.51558i) q^{32} +3.37063i q^{33} -0.0710158i q^{34} +(1.99342 - 3.45271i) q^{36} +(-0.730221 + 0.421593i) q^{37} +(-1.37740 - 2.38574i) q^{38} +(-3.03736 + 0.397695i) q^{39} +(0.977298 - 1.69273i) q^{40} +(-10.4766 - 6.04869i) q^{41} +(2.41161 + 4.17704i) q^{43} +(6.01267 + 3.47142i) q^{44} +(2.05676 + 1.18747i) q^{45} +(1.90130 + 1.09772i) q^{46} +(-3.94602 - 2.27824i) q^{47} +(1.08858 + 1.88548i) q^{48} +(-1.69444 - 0.978285i) q^{50} +(-0.0603367 + 0.104506i) q^{51} +(-2.41875 + 5.82776i) q^{52} +(0.139800 + 0.242141i) q^{53} +(1.94173 - 1.12106i) q^{54} +(-2.06791 + 3.58172i) q^{55} +4.68111i q^{57} -4.19868i q^{58} +(-9.33705 - 5.39075i) q^{59} +(-1.34231 + 0.774983i) q^{60} +5.86354 q^{61} +(0.711612 - 1.23255i) q^{62} +2.60963 q^{64} +(-3.47157 - 1.44084i) q^{65} +(0.842634 + 1.45949i) q^{66} -5.14447i q^{67} +(0.124282 + 0.215263i) q^{68} +(-1.86529 - 3.23078i) q^{69} +(-3.20326 + 1.84940i) q^{71} -4.27148i q^{72} +(5.72686 - 3.30640i) 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} +(-5.96135 + 10.3254i) q^{79} +2.67142i q^{80} +3.02462 q^{81} -6.04853 q^{82} +2.87321i q^{83} +(-0.128231 + 0.0740342i) q^{85} +(2.08846 + 1.20578i) q^{86} +(-3.56730 + 6.17875i) q^{87} +7.43852 q^{88} +(-1.51351 + 0.873824i) q^{89} +1.18744 q^{90} -7.68427 q^{92} +(-2.09440 + 1.20921i) q^{93} -2.27818 q^{94} +(-2.87190 + 4.97427i) q^{95} +(3.70181 + 2.13724i) q^{96} +(-2.34079 + 1.35145i) q^{97} +9.03822i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} + 4 q^{4} - 3 q^{5} + 9 q^{6} + 2 q^{9}+O(q^{10}) $ 12 * q - 6 * q^3 + 4 * q^4 - 3 * q^5 + 9 * q^6 + 2 * q^9	$ 12 q - 6 q^{3} + 4 q^{4} - 3 q^{5} + 9 q^{6} + 2 q^{9} + 24 q^{10} + q^{12} + 2 q^{13} - 12 q^{15} - 8 q^{16} - 17 q^{17} - 3 q^{18} + 3 q^{20} - 15 q^{22} + 3 q^{23} - 5 q^{25} + 9 q^{26} - 12 q^{27} - q^{29} - 22 q^{30} + 18 q^{31} + 18 q^{32} - 13 q^{36} + 15 q^{37} - 19 q^{38} - q^{39} + q^{40} + 6 q^{41} + 11 q^{43} + 33 q^{44} + 9 q^{45} - 30 q^{46} - 15 q^{47} - 19 q^{48} + 18 q^{50} + 4 q^{51} - 47 q^{52} - 8 q^{53} - 6 q^{54} + 15 q^{55} - 27 q^{59} + 30 q^{60} + 10 q^{61} - 41 q^{62} + 2 q^{64} - 3 q^{65} + 34 q^{66} + 11 q^{68} - 7 q^{69} + 30 q^{71} + 42 q^{73} - 33 q^{74} - q^{75} + 45 q^{76} + 44 q^{78} - 35 q^{79} - 28 q^{81} + 10 q^{82} - 21 q^{85} + 57 q^{86} - 10 q^{87} + 28 q^{88} - 48 q^{89} - 66 q^{92} - 81 q^{93} + 2 q^{94} + 2 q^{95} + 21 q^{96} + 3 q^{97}+O(q^{100}) $ 12 * q - 6 * q^3 + 4 * q^4 - 3 * q^5 + 9 * q^6 + 2 * q^9 + 24 * q^10 + q^12 + 2 * q^13 - 12 * q^15 - 8 * q^16 - 17 * q^17 - 3 * q^18 + 3 * q^20 - 15 * q^22 + 3 * q^23 - 5 * q^25 + 9 * q^26 - 12 * q^27 - q^29 - 22 * q^30 + 18 * q^31 + 18 * q^32 - 13 * q^36 + 15 * q^37 - 19 * q^38 - q^39 + q^40 + 6 * q^41 + 11 * q^43 + 33 * q^44 + 9 * q^45 - 30 * q^46 - 15 * q^47 - 19 * q^48 + 18 * q^50 + 4 * q^51 - 47 * q^52 - 8 * q^53 - 6 * q^54 + 15 * q^55 - 27 * q^59 + 30 * q^60 + 10 * q^61 - 41 * q^62 + 2 * q^64 - 3 * q^65 + 34 * q^66 + 11 * q^68 - 7 * q^69 + 30 * q^71 + 42 * q^73 - 33 * q^74 - q^75 + 45 * q^76 + 44 * q^78 - 35 * q^79 - 28 * q^81 + 10 * q^82 - 21 * q^85 + 57 * q^86 - 10 * q^87 + 28 * q^88 - 48 * q^89 - 66 * q^92 - 81 * q^93 + 2 * q^94 + 2 * q^95 + 21 * q^96 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.433001	−	0.249993i	0.306178	−	0.176772i	−0.339037	−	0.940773i	$-0.610101\pi$
$2$	0.433001	−	0.249993i	0.306178	−	0.176772i	0.645215	+	0.764001i	$0.276768\pi$
$3$	−0.849601			−0.490518			−0.245259	−	0.969458i	$-0.578873\pi$
$3$	−0.849601			−0.490518			−0.245259	+	0.969458i	$0.578873\pi$
$4$	−0.875007	+	1.51556i	−0.437503	+	0.757778i
$5$	−0.902810	−	0.521238i	−0.403749	−	0.233105i	0.284351	−	0.958720i	$-0.408222\pi$
$5$	−0.902810	−	0.521238i	−0.403749	−	0.233105i	−0.688100	+	0.725616i	$0.741555\pi$
$6$	−0.367878	+	0.212395i	−0.150186	+	0.0867098i
$7$		0			0
$7$		0			0
$8$			1.87496i			0.662897i
$9$	−2.27818			−0.759392
$10$	−0.521224			−0.164825
$11$		−	3.96730i		−	1.19619i	−0.801426	−	0.598094i	$-0.795925\pi$
$11$		−	3.96730i		−	1.19619i	0.801426	−	0.598094i	$-0.204075\pi$
$12$	0.743407	−	1.28762i	0.214603	−	0.371703i
$13$	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	$0.161184\pi$
$18$	−0.986453	+	0.569529i	−0.232509	+	0.134239i
$19$		−	5.50977i		−	1.26403i	−0.774957	−	0.632014i	$-0.782229\pi$
$19$		−	5.50977i		−	1.26403i	0.774957	−	0.632014i	$-0.217771\pi$
$20$	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	$0.681974\pi$
$24$		−	1.59297i		−	0.325163i
$25$	−1.95662	−	3.38897i	−0.391325	−	0.677794i
$26$	1.43097	−	1.09642i	0.280637	−	0.215026i
$27$	4.48435			0.863013
$28$		0			0
$29$	4.19880	−	7.27253i	0.779697	−	1.35047i	−0.152419	−	0.988316i	$-0.548706\pi$
$29$	4.19880	−	7.27253i	0.779697	−	1.35047i	0.932116	−	0.362159i	$-0.117960\pi$
$30$	0.442832			0.0808498
$31$	2.46516	−	1.42326i	0.442756	−	0.255625i	−0.262010	−	0.965065i	$-0.584385\pi$
$31$	2.46516	−	1.42326i	0.442756	−	0.255625i	0.704766	+	0.709440i	$0.251052\pi$
$32$	−4.35712	−	2.51558i	−0.770237	−	0.444696i
$33$			3.37063i			0.586751i
$34$		−	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	−0.558821	−	0.829288i	$-0.688746\pi$
$37$	−0.730221	+	0.421593i	−0.120048	+	0.0693095i	0.438774	+	0.898598i	$0.355413\pi$
$38$	−1.37740	−	2.38574i	−0.223445	−	0.387017i
$39$	−3.03736	+	0.397695i	−0.486366	+	0.0636822i
$40$	0.977298	−	1.69273i	0.154524	−	0.267644i
$41$	−10.4766	−	6.04869i	−1.63618	−	0.944647i	−0.982133	−	0.188190i	$-0.939738\pi$
$41$	−10.4766	−	6.04869i	−1.63618	−	0.944647i	−0.654044	−	0.756457i	$-0.726929\pi$
$42$		0			0
$43$	2.41161	+	4.17704i	0.367768	+	0.636993i	0.989216	−	0.146463i	$-0.0467888\pi$
$43$	2.41161	+	4.17704i	0.367768	+	0.636993i	−0.621448	+	0.783455i	$0.713455\pi$
$44$	6.01267	+	3.47142i	0.906444	+	0.523336i
$45$	2.05676	+	1.18747i	0.306604	+	0.177018i
$46$	1.90130	+	1.09772i	0.280331	+	0.161849i
$47$	−3.94602	−	2.27824i	−0.575587	−	0.332315i	0.183791	−	0.982965i	$-0.441163\pi$
$47$	−3.94602	−	2.27824i	−0.575587	−	0.332315i	−0.759378	+	0.650650i	$0.774496\pi$
$48$	1.08858	+	1.88548i	0.157123	+	0.272146i
$49$		0			0
$50$	−1.69444	−	0.978285i	−0.239630	−	0.138350i
$51$	−0.0603367	+	0.104506i	−0.00844883	+	0.0146338i
$52$	−2.41875	+	5.82776i	−0.335421	+	0.808164i
$53$	0.139800	+	0.242141i	0.0192030	+	0.0332606i	0.875467	−	0.483278i	$-0.160554\pi$
$53$	0.139800	+	0.242141i	0.0192030	+	0.0332606i	−0.856264	+	0.516538i	$0.827220\pi$
$54$	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
$58$		−	4.19868i		−	0.551314i
$59$	−9.33705	−	5.39075i	−1.21558	−	0.701815i	−0.251611	−	0.967829i	$-0.580960\pi$
$59$	−9.33705	−	5.39075i	−1.21558	−	0.701815i	−0.963969	+	0.266013i	$0.914294\pi$
$60$	−1.34231	+	0.774983i	−0.173292	+	0.100050i
$61$	5.86354			0.750749			0.375374	−	0.926873i	$-0.377514\pi$
$61$	5.86354			0.750749			0.375374	+	0.926873i	$0.377514\pi$
$62$	0.711612	−	1.23255i	0.0903748	−	0.156534i
$63$		0			0
$64$	2.60963			0.326204
$65$	−3.47157	−	1.44084i	−0.430595	−	0.178714i
$66$	0.842634	+	1.45949i	0.103721	+	0.179650i
$67$		−	5.14447i		−	0.628497i	−0.949341	−	0.314248i	$-0.898247\pi$
$67$		−	5.14447i		−	0.628497i	0.949341	−	0.314248i	$-0.101753\pi$
$68$	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	−0.677887	−	0.735167i	$-0.737104\pi$
$71$	−3.20326	+	1.84940i	−0.380157	+	0.219484i	0.297730	+	0.954650i	$0.403771\pi$
$72$		−	4.27148i		−	0.503399i
$73$	5.72686	−	3.30640i	0.670278	−	0.386985i	−0.125904	−	0.992042i	$-0.540183\pi$
$73$	5.72686	−	3.30640i	0.670278	−	0.386985i	0.796182	+	0.605057i	$0.206850\pi$
$74$	−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
$79$	−5.96135	+	10.3254i	−0.670705	+	1.16169i	0.307000	+	0.951710i	$0.400675\pi$
$79$	−5.96135	+	10.3254i	−0.670705	+	1.16169i	−0.977705	+	0.209985i	$0.932658\pi$
$80$			2.67142i			0.298674i
$81$	3.02462			0.336069
$82$	−6.04853			−0.667948
$83$			2.87321i			0.315376i	0.987489	+	0.157688i	$0.0504040\pi$
$83$			2.87321i			0.315376i	−0.987489	+	0.157688i	$0.949596\pi$
$84$		0			0
$85$	−0.128231	+	0.0740342i	−0.0139086	+	0.00803013i
$86$	2.08846	+	1.20578i	0.225205	+	0.130022i
$87$	−3.56730	+	6.17875i	−0.382455	+	0.662432i
$88$	7.43852			0.792949
$89$	−1.51351	+	0.873824i	−0.160432	+	0.0926252i	−0.578066	−	0.815990i	$-0.696193\pi$
$89$	−1.51351	+	0.873824i	−0.160432	+	0.0926252i	0.417635	+	0.908615i	$0.362859\pi$
$90$	1.18744			0.125167
$91$		0			0
$92$	−7.68427			−0.801141
$93$	−2.09440	+	1.20921i	−0.217180	+	0.125389i
$94$	−2.27818			−0.234976
$95$	−2.87190	+	4.97427i	−0.294650	+	0.510350i
$96$	3.70181	+	2.13724i	0.377815	+	0.218131i
$97$	−2.34079	+	1.35145i	−0.237671	+	0.137219i	−0.614106	−	0.789224i	$-0.710483\pi$
$97$	−2.34079	+	1.35145i	−0.237671	+	0.137219i	0.376435	+	0.926443i	$0.377150\pi$
$98$		0			0
$99$			9.03822i			0.908376i
$100$	6.84823			0.684823
$101$	11.4722			1.14153			0.570765	−	0.821114i	$-0.306647\pi$
$101$	11.4722			1.14153			0.570765	+	0.821114i	$0.306647\pi$
$102$			0.0603351i			0.00597407i
$103$	−2.08475	+	3.61090i	−0.205417	+	0.355792i	−0.950265	−	0.311441i	$-0.899188\pi$
$103$	−2.08475	+	3.61090i	−0.205417	+	0.355792i	0.744849	+	0.667233i	$0.232522\pi$
$104$	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
$109$	−5.56886	+	3.21518i	−0.533400	+	0.307958i	−0.742400	−	0.669957i	$-0.766312\pi$
$109$	−5.56886	+	3.21518i	−0.533400	+	0.307958i	0.209000	+	0.977916i	$0.432979\pi$
$110$			2.06785i			0.197162i
$111$	0.620397	−	0.358186i	0.0588855	−	0.0339975i
$112$		0			0
$113$	−5.48164	−	9.49448i	−0.515670	−	0.893166i	−0.999835	−	0.0181892i	$-0.994210\pi$
$113$	−5.48164	−	9.49448i	−0.515670	−	0.893166i	0.484165	−	0.874977i	$-0.339123\pi$
$114$	1.17025	+	2.02692i	0.109603	+	0.189839i
$115$		−	4.57749i		−	0.426853i
$116$	7.34795	+	12.7270i	0.682240	+	1.18167i
$117$	−8.14457	+	1.06641i	−0.752965	+	0.0985893i
$118$	−5.39060			−0.496245
$119$		0			0
$120$	−0.830314	+	1.43815i	−0.0757969	+	0.131284i
$121$	−4.73951			−0.430864
$122$	2.53892	−	1.46584i	0.229863	−	0.132711i
$123$	8.90097	+	5.13898i	0.802573	+	0.463366i
$124$			4.98145i			0.447348i
$125$			9.29184i			0.831087i
$126$		0			0
$127$	−1.00394	+	1.73887i	−0.0890849	+	0.154300i	−0.907125	−	0.420862i	$-0.861728\pi$
$127$	−1.00394	+	1.73887i	−0.0890849	+	0.154300i	0.818040	+	0.575162i	$0.195061\pi$
$128$	9.84421	−	5.68356i	0.870113	−	0.502360i
$129$	−2.04891	−	3.54882i	−0.180397	−	0.312456i
$130$	−1.86339	+	0.243983i	−0.163430	+	0.0213987i
$131$	−6.22511	+	10.7822i	−0.543890	+	0.942046i	0.454785	+	0.890601i	$0.349716\pi$
$131$	−6.22511	+	10.7822i	−0.543890	+	0.942046i	−0.998676	+	0.0514449i	$0.983617\pi$
$132$	−5.10838	−	2.94932i	−0.444627	−	0.256706i
$133$		0			0
$134$	−1.28608	−	2.22756i	−0.111101	−	0.192432i
$135$	−4.04851	−	2.33741i	−0.348441	−	0.201172i
$136$	0.230631	+	0.133155i	0.0197765	+	0.0114180i
$137$	4.54246	+	2.62259i	0.388088	+	0.224063i	0.681332	−	0.731975i	$-0.261401\pi$
$137$	4.54246	+	2.62259i	0.388088	+	0.224063i	−0.293243	+	0.956038i	$0.594735\pi$
$138$	−1.61535	−	0.932620i	−0.137507	−	0.0793899i
$139$	−10.3693	−	17.9601i	−0.879510	−	1.52336i	−0.851880	−	0.523737i	$-0.824537\pi$
$139$	−10.3693	−	17.9601i	−0.879510	−	1.52336i	−0.0276301	−	0.999618i	$-0.508796\pi$
$140$		0			0
$141$	3.35255	+	1.93559i	0.282335	+	0.163006i
$142$	−0.924676	+	1.60159i	−0.0775971	+	0.134402i
$143$	−1.85708	−	14.1833i	−0.155297	−	1.18606i
$144$	2.91900	+	5.05585i	0.243250	+	0.421321i
$145$	−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
$149$		−	0.0113760i		−	0.000931956i	−1.00000		0.000465978i	$-0.999852\pi$
$149$		−	0.0113760i		−	0.000931956i	1.00000		0.000465978i	$-0.000148325\pi$
$150$	1.43960	+	0.831153i	0.117543	+	0.0678633i
$151$	16.3726	−	9.45271i	1.33238	−	0.769251i	0.346717	−	0.937970i	$-0.387296\pi$
$151$	16.3726	−	9.45271i	1.33238	−	0.769251i	0.985664	+	0.168719i	$0.0539631\pi$
$152$	10.3306			0.837920
$153$	−0.161791	+	0.280230i	−0.0130800	+	0.0226553i
$154$		0			0
$155$	−2.96743			−0.238350
$156$	2.05498	−	4.95127i	0.164530	−	0.396419i
$157$	9.89687	+	17.1419i	0.789856	+	1.36807i	0.926054	+	0.377390i	$0.123178\pi$
$157$	9.89687	+	17.1419i	0.789856	+	1.36807i	−0.136198	+	0.990682i	$0.543488\pi$
$158$			5.96119i			0.474247i
$159$	−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
$163$		−	8.93255i		−	0.699651i	−0.936815	−	0.349825i	$-0.886241\pi$
$163$		−	8.93255i		−	0.699651i	0.936815	−	0.349825i	$-0.113759\pi$
$164$	18.3343	−	10.5853i	1.43167	−	0.826572i
$165$	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	0.280153	−	0.959955i	$-0.409615\pi$
$167$	−5.31279	−	3.06734i	−0.411116	−	0.237358i	−0.691269	+	0.722597i	$0.742948\pi$
$168$		0			0
$169$	12.5618	−	3.34692i	0.966290	−	0.257456i
$170$	−0.0370161	+	0.0641138i	−0.00283900	+	0.00491730i
$171$			12.5522i			0.959893i
$172$	−8.44072			−0.643599
$173$	24.2628			1.84466			0.922332	−	0.386399i	$-0.126281\pi$
$173$	24.2628			1.84466			0.922332	+	0.386399i	$0.126281\pi$
$174$			3.56721i			0.270429i
$175$		0			0
$176$	−8.80446	+	5.08325i	−0.663661	+	0.383165i
$177$	7.93277	+	4.57999i	0.596263	+	0.344253i
$178$	−0.436901	+	0.756734i	−0.0327471	+	0.0567196i
$179$	4.13675			0.309195			0.154598	−	0.987978i	$-0.450592\pi$
$179$	4.13675			0.309195			0.154598	+	0.987978i	$0.450592\pi$
$180$	−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
$185$	0.879001			0.0646254
$186$	−0.604586	+	1.04717i	−0.0443304	+	0.0767825i
$187$	−0.488003	−	0.281749i	−0.0356863	−	0.0206035i
$188$	6.90560	−	3.98695i	0.503642	−	0.290778i
$189$		0			0
$190$			2.87182i			0.208344i
$191$	−6.47866			−0.468780			−0.234390	−	0.972143i	$-0.575309\pi$
$191$	−6.47866			−0.468780			−0.234390	+	0.972143i	$0.575309\pi$
$192$	−2.21715			−0.160009
$193$			4.82928i			0.347619i	0.984779	+	0.173810i	$0.0556077\pi$
$193$			4.82928i			0.347619i	−0.984779	+	0.173810i	$0.944392\pi$
$194$	−0.675708	+	1.17036i	−0.0485130	+	0.0840270i
$195$	2.94945	+	1.22414i	0.211214	+	0.0876626i
$196$		0			0
$197$	−22.3748	−	12.9181i	−1.59414	−	0.920377i	−0.992586	−	0.121545i	$-0.961215\pi$
$197$	−22.3748	−	12.9181i	−1.59414	−	0.920377i	−0.601554	−	0.798832i	$-0.705452\pi$
$198$	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	$0.959195\pi$
$200$	6.35417	−	3.66858i	0.449308	−	0.259408i
$201$			4.37075i			0.308289i
$202$	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
$206$			2.08470i			0.145248i
$207$	−5.00171	−	8.66322i	−0.347643	−	0.602136i
$208$	−5.61947	−	7.33415i	−0.389640	−	0.508532i
$209$	−21.8589			−1.51201
$210$		0			0
$211$	−9.14557	+	15.8406i	−0.629607	+	1.09051i	0.358024	+	0.933713i	$0.383451\pi$
$211$	−9.14557	+	15.8406i	−0.629607	+	1.09051i	−0.987631	+	0.156799i	$0.949883\pi$
$212$	−0.489304			−0.0336055
$213$	2.72149	−	1.57125i	0.186474	−	0.107661i
$214$	−3.67506	−	2.12180i	−0.251222	−	0.145043i
$215$		−	5.02810i		−	0.342913i
$216$			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
$220$	−3.61887	−	6.26806i	−0.243984	−	0.422593i
$221$	0.196312	−	0.472995i	0.0132054	−	0.0318171i
$222$	0.179088	−	0.310190i	0.0120196	−	0.0208186i
$223$	9.96682	+	5.75435i	0.667428	+	0.385340i	0.795101	−	0.606477i	$-0.207418\pi$
$223$	9.96682	+	5.75435i	0.667428	+	0.385340i	−0.127674	+	0.991816i	$0.540751\pi$
$224$		0			0
$225$	4.45753	+	7.72067i	0.297169	+	0.514712i
$226$	−4.74711	−	2.74075i	−0.315773	−	0.182312i
$227$	−15.5057	−	8.95223i	−1.02915	−	0.594181i	−0.112410	−	0.993662i	$-0.535857\pi$
$227$	−15.5057	−	8.95223i	−1.02915	−	0.594181i	−0.916741	+	0.399481i	$0.869190\pi$
$228$	−7.09448	−	4.09600i	−0.469843	−	0.271264i
$229$	−3.34589	−	1.93175i	−0.221103	−	0.127654i	0.385358	−	0.922767i	$-0.374078\pi$
$229$	−3.34589	−	1.93175i	−0.221103	−	0.127654i	−0.606461	+	0.795113i	$0.707411\pi$
$230$	−1.14434	−	1.98206i	−0.0754556	−	0.130693i
$231$		0			0
$232$	13.6357	+	7.87256i	0.895226	+	0.516859i
$233$	12.5321	−	21.7062i	0.821004	−	1.42202i	−0.0839312	−	0.996472i	$-0.526748\pi$
$233$	12.5321	−	21.7062i	0.821004	−	1.42202i	0.904935	−	0.425549i	$-0.139919\pi$
$234$	−3.26001	+	2.49784i	−0.213114	+	0.163289i
$235$	2.37501	+	4.11363i	0.154928	+	0.268344i
$236$	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	$-0.918774\pi$
$239$		−	7.80462i		−	0.504839i	0.967618	−	0.252419i	$-0.0812263\pi$
$240$		−	2.26964i		−	0.146505i
$241$	−18.8493	−	10.8826i	−1.21419	−	0.701012i	−0.250519	−	0.968112i	$-0.580601\pi$
$241$	−18.8493	−	10.8826i	−1.21419	−	0.701012i	−0.963669	+	0.267100i	$0.913935\pi$
$242$	−2.05221	+	1.18484i	−0.131921	+	0.0761647i
$243$	−16.0228			−1.02786
$244$	−5.13063	+	8.88652i	−0.328455	+	0.568901i
$245$		0			0
$246$	5.13884			0.327640
$247$	−2.57910	−	19.6976i	−0.164104	−	1.25333i
$248$	2.66855	+	4.62207i	0.169453	+	0.293502i
$249$		−	2.44109i		−	0.154698i
$250$	2.32290	+	4.02338i	0.146913	+	0.254461i
$251$	−3.83990	−	6.65090i	−0.242372	−	0.419801i	0.719017	−	0.694992i	$-0.244592\pi$
$251$	−3.83990	−	6.65090i	−0.242372	−	0.419801i	−0.961390	+	0.275191i	$0.911259\pi$
$252$		0			0
$253$	15.0865	−	8.71017i	0.948478	−	0.547604i
$254$			1.00391i			0.0629909i
$255$	0.108945	−	0.0628995i	0.00682241	−	0.00393892i
$256$	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
$261$	−9.56560	+	16.5681i	−0.592096	+	1.02554i
$262$			6.22494i			0.384578i
$263$	−11.7232			−0.722880			−0.361440	−	0.932395i	$-0.617715\pi$
$263$	−11.7232			−0.722880			−0.361440	+	0.932395i	$0.617715\pi$
$264$	−6.31978			−0.388956
$265$		−	0.291476i		−	0.0179052i
$266$		0			0
$267$	1.28588	−	0.742403i	0.0786945	−	0.0454343i
$268$	7.79673	+	4.50144i	0.476261	+	0.274970i
$269$	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	$0.0761899\pi$
$270$	−2.33735			−0.142246
$271$	−2.22022	+	1.28184i	−0.134869	+	0.0778665i	−0.565916	−	0.824463i	$-0.691477\pi$
$271$	−2.22022	+	1.28184i	−0.134869	+	0.0778665i	0.431048	+	0.902329i	$0.358144\pi$
$272$	−0.363976			−0.0220693
$273$		0			0
$274$	2.62252			0.158432
$275$	−13.4451	+	7.76252i	−0.810769	+	0.468097i
$276$	6.52857			0.392974
$277$	−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	$0.175598\pi$
$278$	−8.97981	−	5.18450i	−0.538573	−	0.310945i
$279$	−5.61607	+	3.24244i	−0.336226	+	0.194120i
$280$		0			0
$281$		−	6.45288i		−	0.384947i	−0.981302	−	0.192473i	$-0.938349\pi$
$281$		−	6.45288i		−	0.384947i	0.981302	−	0.192473i	$-0.0616509\pi$
$282$	1.93554			0.115260
$283$	22.1746			1.31814			0.659071	−	0.752081i	$-0.270950\pi$
$283$	22.1746			1.31814			0.659071	+	0.752081i	$0.270950\pi$
$284$		−	6.47296i		−	0.384099i
$285$	2.43997	−	4.22615i	0.144531	−	0.250335i
$286$	−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
$291$	1.98873	−	1.14820i	0.116582	−	0.0673085i
$292$			11.5725i			0.677229i
$293$	20.9600	−	12.1013i	1.22450	−	0.706964i	0.258624	−	0.965978i	$-0.416731\pi$
$293$	20.9600	−	12.1013i	1.22450	−	0.706964i	0.965874	+	0.259014i	$0.0833976\pi$
$294$		0			0
$295$	5.61972	+	9.73364i	0.327193	+	0.566714i
$296$	−0.790469	−	1.36913i	−0.0459451	−	0.0795792i
$297$		−	17.7908i		−	1.03233i
$298$	−0.00284392	−	0.00492581i	−0.000164744	−	0.000285345i
$299$	9.62898	+	12.5671i	0.556858	+	0.726773i
$300$	−5.81827			−0.335918
$301$		0			0
$302$	4.72623	−	8.18607i	0.271964	−	0.471055i
$303$	−9.74683			−0.559940
$304$	−12.2276	+	7.05959i	−0.701299	+	0.404895i
$305$	−5.29366	−	3.05630i	−0.303114	−	0.175003i
$306$			0.161787i			0.00924872i
$307$			24.2924i			1.38644i	0.720726	+	0.693220i	$0.243809\pi$
$307$			24.2924i			1.38644i	−0.720726	+	0.693220i	$0.756191\pi$
$308$		0			0
$309$	1.77121	−	3.06782i	0.100761	−	0.174522i
$310$	−1.28490	+	0.741837i	−0.0729774	+	0.0421335i
$311$	−1.99355	−	3.45294i	−0.113044	−	0.195798i	0.803952	−	0.594694i	$-0.202727\pi$
$311$	−1.99355	−	3.45294i	−0.113044	−	0.195798i	−0.916996	+	0.398896i	$0.869393\pi$
$312$	−0.745661	−	5.69491i	−0.0422148	−	0.322411i
$313$	14.2377	−	24.6604i	0.804763	−	1.39389i	−0.111688	−	0.993743i	$-0.535626\pi$
$313$	14.2377	−	24.6604i	0.804763	−	1.39389i	0.916451	−	0.400147i	$-0.131041\pi$
$314$	8.57071	+	4.94830i	0.483673	+	0.279249i
$315$		0			0
$316$	−10.4324	−	18.0695i	−0.586871	−	1.01649i
$317$	14.5632	+	8.40806i	0.817950	+	0.472244i	0.849709	−	0.527252i	$-0.176778\pi$
$317$	14.5632	+	8.40806i	0.817950	+	0.472244i	−0.0317591	+	0.999496i	$0.510111\pi$
$318$	−0.102859	−	0.0593856i	−0.00576804	−	0.00333018i
$319$	−28.8523	−	16.6579i	−1.61542	−	0.932664i
$320$	−2.35600	−	1.36024i	−0.131704	−	0.0760396i
$321$	3.60546	+	6.24485i	0.201237	+	0.348553i
$322$		0			0
$323$	−0.677736	−	0.391291i	−0.0377102	−	0.0217720i
$324$	−2.64657	+	4.58399i	−0.147031	+	0.254666i
$325$	−8.58136	−	11.1998i	−0.476008	−	0.621253i
$326$	−2.23308	−	3.86780i	−0.123679	−	0.214218i
$327$	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
$331$		−	6.20917i		−	0.341287i	−0.985333	−	0.170644i	$-0.945415\pi$
$331$		−	6.20917i		−	0.341287i	0.985333	−	0.170644i	$-0.0545846\pi$
$332$	−4.35451	−	2.51408i	−0.238985	−	0.137978i
$333$	1.66357	−	0.960464i	0.0911632	−	0.0526331i
$334$	−3.06726			−0.167833
$335$	−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	$0.432775\pi$
$338$	4.60255	−	4.58958i	0.250346	−	0.249640i
$339$	4.65721	+	8.06653i	0.252945	+	0.438114i
$340$		−	0.259122i		−	0.0140528i
$341$	−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
$345$			3.88904i			0.209379i
$346$	10.5058	−	6.06553i	0.564795	−	0.326085i
$347$	−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	0.825349	−	0.564623i	$-0.190978\pi$
$349$	13.9933	+	8.07906i	0.749046	+	0.432462i	−0.0763028	+	0.997085i	$0.524312\pi$
$350$		0			0
$351$	16.0317	−	2.09911i	0.855709	−	0.112042i
$352$	−9.98008	+	17.2860i	−0.531940	+	0.921347i
$353$			11.8424i			0.630306i	0.949041	+	0.315153i	$0.102056\pi$
$353$			11.8424i			0.630306i	−0.949041	+	0.315153i	$0.897944\pi$
$354$	4.57986			0.243417
$355$	3.85591			0.204651
$356$		−	3.05841i		−	0.162095i
$357$		0			0
$358$	1.79122	−	1.03416i	0.0946688	−	0.0546571i
$359$	27.1631	+	15.6826i	1.43362	+	0.827698i	0.997394	−	0.0721417i	$-0.0229834\pi$
$359$	27.1631	+	15.6826i	1.43362	+	0.827698i	0.436221	+	0.899840i	$0.356317\pi$
$360$	−2.22646	+	3.85634i	−0.117345	+	0.203247i
$361$	−11.3575			−0.597765
$362$	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
$367$	−24.0774			−1.25683			−0.628415	−	0.777878i	$-0.716296\pi$
$367$	−24.0774			−1.25683			−0.628415	+	0.777878i	$0.716296\pi$
$368$	5.62610	−	9.74470i	0.293281	−	0.507977i
$369$	23.8676	+	13.7800i	1.24250	+	0.717358i
$370$	0.380608	−	0.219744i	0.0197869	−	0.0114240i
$371$		0			0
$372$		−	4.23225i		−	0.219432i
$373$	−18.3922			−0.952314			−0.476157	−	0.879360i	$-0.657971\pi$
$373$	−18.3922			−0.952314			−0.476157	+	0.879360i	$0.657971\pi$
$374$	−0.281741			−0.0145685
$375$		−	7.89436i		−	0.407663i
$376$	4.27160	−	7.39862i	0.220291	−	0.381555i
$377$	11.6066	−	27.9650i	0.597771	−	1.44027i
$378$		0			0
$379$	−7.04719	−	4.06870i	−0.361990	−	0.208995i	0.307963	−	0.951398i	$-0.400353\pi$
$379$	−7.04719	−	4.06870i	−0.361990	−	0.208995i	−0.669953	+	0.742403i	$0.733686\pi$
$380$	−5.02586	−	8.70504i	−0.257821	−	0.446559i
$381$	0.852946	−	1.47735i	0.0436977	−	0.0756867i
$382$	−2.80527	+	1.61962i	−0.143530	+	0.0828671i
$383$		−	22.3711i		−	1.14311i	−0.820564	−	0.571555i	$-0.806340\pi$
$383$		−	22.3711i		−	1.14311i	0.820564	−	0.571555i	$-0.193660\pi$
$384$	−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
$388$		−	4.73012i		−	0.240136i
$389$	−10.6973	−	18.5283i	−0.542374	−	0.939420i	−0.998767	−	0.0496415i	$-0.984192\pi$
$389$	−10.6973	−	18.5283i	−0.542374	−	0.939420i	0.456393	−	0.889778i	$-0.349141\pi$
$390$	1.58314	−	0.207288i	0.0801655	−	0.0104964i
$391$	0.623674			0.0315406
$392$		0			0
$393$	5.28886	−	9.16058i	0.266788	−	0.462090i
$394$	−12.9178			−0.650788
$395$	10.7639	−	6.21456i	0.541592	−	0.312689i
$396$	−13.6979	−	7.90851i	−0.688347	−	0.397417i
$397$			1.19673i			0.0600622i	0.999549	+	0.0300311i	$0.00956063\pi$
$397$			1.19673i			0.0600622i	−0.999549	+	0.0300311i	$0.990439\pi$
$398$			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	$-0.305982\pi$
$401$	31.4150	−	18.1375i	1.56879	−	0.905741i	0.996310	−	0.0858220i	$-0.0273516\pi$
$402$	1.09266	+	1.89254i	0.0544968	+	0.0943913i
$403$	8.14682	−	6.24214i	0.405822	−	0.310943i
$404$	−10.0383	+	17.3868i	−0.499423	+	0.865026i
$405$	−2.73066	−	1.57655i	−0.135688	−	0.0783393i
$406$		0			0
$407$	1.67259	+	2.89701i	0.0829072	+	0.143599i
$408$	−0.195945	−	0.113129i	−0.00970071	−	0.00560071i
$409$	12.7066	+	7.33616i	0.628301	+	0.362750i	0.780094	−	0.625662i	$-0.215171\pi$
$409$	12.7066	+	7.33616i	0.628301	+	0.362750i	−0.151793	+	0.988412i	$0.548505\pi$
$410$	5.46067	+	3.15272i	0.269683	+	0.155702i
$411$	−3.85928	−	2.22816i	−0.190364	−	0.109907i
$412$	−3.64834	−	6.31912i	−0.179741	−	0.311321i
$413$		0			0
$414$	−4.33150	−	2.50079i	−0.212881	−	0.122907i
$415$	1.49763	−	2.59397i	0.0735156	−	0.127333i
$416$	−16.7544	−	6.95375i	−0.821451	−	0.340936i
$417$	8.80975	+	15.2589i	0.431415	+	0.747233i
$418$	−9.46494	+	5.46458i	−0.462945	+	0.267282i
$419$	−2.96674	+	5.13855i	−0.144935	+	0.251034i	−0.929349	−	0.369203i	$-0.879631\pi$
$419$	−2.96674	+	5.13855i	−0.144935	+	0.251034i	0.784414	+	0.620238i	$0.212964\pi$
$420$		0			0
$421$			2.63174i			0.128263i	0.997941	+	0.0641317i	$0.0204278\pi$
$421$			2.63174i			0.128263i	−0.997941	+	0.0641317i	$0.979572\pi$
$422$			9.14532i			0.445187i
$423$	8.98974	+	5.19023i	0.437096	+	0.252358i
$424$	−0.454004	+	0.262119i	−0.0220484	+	0.0127296i
$425$	−0.555819			−0.0269612
$426$	0.785606	−	1.36071i	0.0380628	−	0.0659266i
$427$		0			0
$428$	14.8531			0.717952
$429$	1.57778	+	12.0501i	0.0761759	+	0.581785i
$430$	−1.25699	−	2.17717i	−0.0606175	−	0.104993i
$431$			18.8377i			0.907378i	0.891160	+	0.453689i	$0.149892\pi$
$431$			18.8377i			0.907378i	−0.891160	+	0.453689i	$0.850108\pi$
$432$	−5.74573	−	9.95190i	−0.276442	−	0.478811i
$433$	−9.56773	−	16.5718i	−0.459796	−	0.796389i	0.539154	−	0.842207i	$-0.318744\pi$
$433$	−9.56773	−	16.5718i	−0.459796	−	0.796389i	−0.998950	+	0.0458176i	$0.985411\pi$
$434$		0			0
$435$	6.44119	−	3.71883i	0.308832	−	0.178304i
$436$		−	11.2532i		−	0.538931i
$437$	20.9520	−	12.0966i	1.00227	−	0.578660i
$438$	−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
$443$	10.4696	−	18.1339i	0.497426	−	0.861568i	−0.502569	−	0.864537i	$-0.667612\pi$
$443$	10.4696	−	18.1339i	0.497426	−	0.861568i	0.999996	+	0.00296930i	$0.000945159\pi$
$444$			1.25366i			0.0594961i
$445$	1.82188			0.0863654
$446$	5.75419			0.272469
$447$			0.00966505i			0.000457141i
$448$		0			0
$449$	15.4700	−	8.93162i	0.730075	−	0.421509i	−0.0883746	−	0.996087i	$-0.528167\pi$
$449$	15.4700	−	8.93162i	0.730075	−	0.421509i	0.818450	+	0.574578i	$0.194834\pi$
$450$	3.86023	+	2.22871i	0.181973	+	0.105062i
$451$	−23.9970	+	41.5640i	−1.12997	+	1.95717i
$452$	19.1859			0.902429
$453$	−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	−0.627066	−	0.778966i	$-0.715744\pi$
$457$	−5.68629	+	3.28298i	−0.265994	+	0.153571i	0.361072	+	0.932538i	$0.382411\pi$
$458$	−1.93170			−0.0902624
$459$	0.318468	−	0.551603i	0.0148648	−	0.0257466i
$460$	6.93744	+	4.00533i	0.323460	+	0.186749i
$461$	4.42854	−	2.55682i	0.206258	−	0.119083i	−0.393313	−	0.919404i	$-0.628671\pi$
$461$	4.42854	−	2.55682i	0.206258	−	0.119083i	0.599571	+	0.800322i	$0.295338\pi$
$462$		0			0
$463$			33.3239i			1.54869i	0.632761	+	0.774347i	$0.281921\pi$
$463$			33.3239i			1.54869i	−0.632761	+	0.774347i	$0.718079\pi$
$464$	−21.5194			−0.999015
$465$	2.52113			0.116915
$466$		−	12.5317i		−	0.580522i
$467$	6.47472	−	11.2145i	0.299614	−	0.518947i	−0.676433	−	0.736504i	$-0.736475\pi$
$467$	6.47472	−	11.2145i	0.299614	−	0.518947i	0.976048	+	0.217557i	$0.0698087\pi$
$468$	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
$473$	16.5716	−	9.56761i	0.761962	−	0.439919i
$474$		−	5.06464i		−	0.232627i
$475$	−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
$479$		−	27.0119i		−	1.23421i	−0.786882	−	0.617104i	$-0.788306\pi$
$479$		−	27.0119i		−	1.23421i	0.786882	−	0.617104i	$-0.211694\pi$
$480$	−2.22802	−	3.85905i	−0.101695	−	0.176141i
$481$	−2.41322	+	1.84903i	−0.110033	+	0.0843083i
$482$	−10.8823			−0.495677
$483$		0			0
$484$	4.14710	−	7.18299i	0.188505	−	0.326499i
$485$	2.81771			0.127946
$486$	−6.93788	+	4.00558i	−0.314708	+	0.181697i
$487$	27.7854	+	16.0419i	1.25908	+	0.726928i	0.972895	−	0.231247i	$-0.0742805\pi$
$487$	27.7854	+	16.0419i	1.25908	+	0.726928i	0.286182	+	0.958175i	$0.407614\pi$
$488$			10.9939i			0.497669i
$489$			7.58910i			0.343191i
$490$		0			0
$491$	−14.3020	+	24.7718i	−0.645440	+	1.11793i	0.338760	+	0.940873i	$0.389992\pi$
$491$	−14.3020	+	24.7718i	−0.645440	+	1.11793i	−0.984200	+	0.177061i	$0.943341\pi$
$492$	−15.5768	+	8.99328i	−0.702257	+	0.405448i
$493$	−0.596378	−	1.03296i	−0.0268595	−	0.0465220i
$494$	−6.04103	−	7.88433i	−0.271799	−	0.354733i
$495$	4.71106	−	8.15980i	0.211746	−	0.366756i
$496$	−6.31716	−	3.64721i	−0.283649	−	0.163765i
$497$		0			0
$498$	−0.610255	−	1.05699i	−0.0273462	−	0.0473650i
$499$	−1.55726	−	0.899082i	−0.0697123	−	0.0402484i	0.464739	−	0.885448i	$-0.346148\pi$
$499$	−1.55726	−	0.899082i	−0.0697123	−	0.0402484i	−0.534451	+	0.845199i	$0.679482\pi$
$500$	−14.0823	−	8.13042i	−0.629780	−	0.363603i
$501$	4.51376	+	2.60602i	0.201660	+	0.116428i
$502$	−3.32536	−	1.91990i	−0.148418	−	0.0856893i
$503$	14.5386	+	25.1816i	0.648245	+	1.12279i	0.983542	+	0.180681i	$0.0578300\pi$
$503$	14.5386	+	25.1816i	0.648245	+	1.12279i	−0.335297	+	0.942112i	$0.608837\pi$
$504$		0			0
$505$	−10.3572	−	5.97976i	−0.460891	−	0.266096i
$506$	4.35497	−	7.54303i	0.193602	−	0.335329i
$507$	−10.6725	+	2.84355i	−0.473982	+	0.126287i
$508$	−1.75690	−	3.04304i	−0.0779499	−	0.135013i
$509$	−20.0843	+	11.5957i	−0.890220	+	0.513969i	−0.874014	−	0.485900i	$-0.838492\pi$
$509$	−20.0843	+	11.5957i	−0.890220	+	0.513969i	−0.0162054	+	0.999869i	$0.505159\pi$
$510$	0.0314489	−	0.0544711i	0.00139258	−	0.00241202i
$511$		0			0
$512$			22.5022i			0.994464i
$513$		−	24.7077i		−	1.09087i
$514$	−5.89910	−	3.40585i	−0.260198	−	0.150225i
$515$	3.76427	−	2.17330i	0.165874	−	0.0957671i
$516$	7.17125			0.315696
$517$	−9.03847	+	15.6551i	−0.397511	+	0.688510i
$518$		0			0
$519$	−20.6137			−0.904840
$520$	2.70151	−	6.50904i	0.118469	−	0.285440i
$521$	16.6255	+	28.7962i	0.728376	+	1.26158i	0.957569	+	0.288203i	$0.0930579\pi$
$521$	16.6255	+	28.7962i	0.728376	+	1.26158i	−0.229193	+	0.973381i	$0.573609\pi$
$522$			9.56535i			0.418664i
$523$	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
$527$		−	0.404307i		−	0.0176119i
$528$	7.48028	−	4.31874i	0.325537	−	0.187949i
$529$	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
$534$	0.371191	−	0.642922i	0.0160630	−	0.0278220i
$535$			8.84793i			0.382529i
$536$	9.64566			0.416629
$537$	−3.51459			−0.151666
$538$		−	4.59926i		−	0.198288i
$539$		0			0
$540$	7.08495	−	4.09050i	0.304888	−	0.176027i
$541$	19.6306	+	11.3337i	0.843986	+	0.487275i	0.858617	−	0.512618i	$-0.171324\pi$
$541$	19.6306	+	11.3337i	0.843986	+	0.487275i	−0.0146313	+	0.999893i	$0.504657\pi$
$542$	−0.640905	+	1.11008i	−0.0275292	+	0.0476820i
$543$	−6.68269			−0.286782
$544$	−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
$549$	−13.3582			−0.570113
$550$	−3.88116	+	6.72236i	−0.165493	+	0.286642i
$551$	−40.0699	−	23.1344i	−1.70704	−	0.985558i
$552$	6.05757	−	3.49734i	0.257827	−	0.148857i
$553$		0			0
$554$			0.466928i			0.0198379i
$555$	−0.746801			−0.0316999
$556$	36.2927			1.53915
$557$			11.3281i			0.479986i	0.970775	+	0.239993i	$0.0771451\pi$
$557$			11.3281i			0.479986i	−0.970775	+	0.239993i	$0.922855\pi$
$558$	−1.62118	+	2.80796i	−0.0686299	+	0.118871i
$559$	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	$0.925253\pi$
$564$	−5.86700	+	3.38732i	−0.247045	+	0.142632i
$565$			11.4290i			0.480820i
$566$	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	$0.571065\pi$
$570$		−	2.43990i		−	0.102196i
$571$	13.1273	+	22.7371i	0.549360	+	0.951519i	0.998319	+	0.0579663i	$0.0184616\pi$
$571$	13.1273	+	22.7371i	0.549360	+	0.951519i	−0.448959	+	0.893552i	$0.648205\pi$
$572$	23.1205	+	9.59594i	0.966716	+	0.401226i
$573$	5.50428			0.229945
$574$		0			0
$575$	8.59149	−	14.8809i	0.358290	−	0.620576i
$576$	−5.94520			−0.247717
$577$	21.2806	−	12.2863i	0.885922	−	0.511487i	0.0133154	−	0.999911i	$-0.495761\pi$
$577$	21.2806	−	12.2863i	0.885922	−	0.511487i	0.872606	+	0.488424i	$0.162428\pi$
$578$	7.35228	+	4.24484i	0.305815	+	0.176562i
$579$		−	4.10296i		−	0.170513i
$580$		−	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
$584$	6.19936	+	10.7376i	0.256531	+	0.444325i
$585$	7.90885	+	3.28249i	0.326991	+	0.135714i
$586$	6.05048	−	10.4797i	0.249943	−	0.432914i
$587$	−17.7777	−	10.2640i	−0.733765	−	0.423639i	0.0860331	−	0.996292i	$-0.472581\pi$
$587$	−17.7777	−	10.2640i	−0.733765	−	0.423639i	−0.819798	+	0.572653i	$0.805914\pi$
$588$		0			0
$589$	−7.84184	−	13.5825i	−0.323117	−	0.559656i
$590$	4.86669	+	2.80978i	0.200358	+	0.115677i
$591$	19.0097	+	10.9752i	0.781954	+	0.451461i
$592$	1.87124	+	1.08036i	0.0769077	+	0.0444027i
$593$	33.1545	+	19.1417i	1.36149	+	0.786057i	0.989822	−	0.142308i	$-0.0454524\pi$
$593$	33.1545	+	19.1417i	1.36149	+	0.786057i	0.371669	+	0.928365i	$0.378786\pi$
$594$	−4.44757	−	7.70342i	−0.182486	−	0.316075i
$595$		0			0
$596$	0.0172409	+	0.00995405i	0.000706216	+	0.000407734i
$597$	7.27030	−	12.5925i	0.297554	−	0.515378i
$598$	7.31105	+	3.03438i	0.298971	+	0.124085i
$599$	−7.03567	−	12.1861i	−0.287470	−	0.497912i	0.685735	−	0.727851i	$-0.259481\pi$
$599$	−7.03567	−	12.1861i	−0.287470	−	0.497912i	−0.973205	+	0.229939i	$0.926147\pi$
$600$	−5.39851	+	3.11683i	−0.220393	+	0.127244i
$601$	−10.1171	+	17.5233i	−0.412685	+	0.714791i	−0.995182	−	0.0980417i	$-0.968742\pi$
$601$	−10.1171	+	17.5233i	−0.412685	+	0.714791i	0.582498	+	0.812832i	$0.302075\pi$
$602$		0			0
$603$			11.7200i			0.477276i
$604$			33.0847i			1.34620i
$605$	4.27887	+	2.47041i	0.173961	+	0.100436i
$606$	−4.22039	+	2.43664i	−0.171441	+	0.0989818i
$607$	−6.55127			−0.265908			−0.132954	−	0.991122i	$-0.542446\pi$
$607$	−6.55127			−0.265908			−0.132954	+	0.991122i	$0.542446\pi$
$608$	−13.8603	+	24.0067i	−0.562108	+	0.973600i
$609$		0			0
$610$	−3.05621			−0.123742
$611$	−15.1736	−	6.29767i	−0.613859	−	0.254776i
$612$	−0.283136	−	0.490406i	−0.0114451	−	0.0198235i
$613$			33.3244i			1.34596i	0.739660	+	0.672980i	$0.234986\pi$
$613$			33.3244i			1.34596i	−0.739660	+	0.672980i	$0.765014\pi$
$614$	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	−0.377499	−	0.926010i	$-0.623216\pi$
$617$	5.85466	−	3.38019i	0.235700	−	0.136081i	0.613199	+	0.789929i	$0.289883\pi$
$618$		−	1.77116i		−	0.0712466i
$619$	15.2582	−	8.80931i	0.613278	−	0.354076i	−0.160970	−	0.986959i	$-0.551462\pi$
$619$	15.2582	−	8.80931i	0.613278	−	0.354076i	0.774247	+	0.632883i	$0.218129\pi$
$620$	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
$625$	−4.93986	+	8.55609i	−0.197594	+	0.342244i
$626$		−	14.2373i		−	0.569038i
$627$	18.5714			0.741669
$628$	−34.6393			−1.38226
$629$			0.119762i			0.00477524i
$630$		0			0
$631$	13.6416	−	7.87596i	0.543062	−	0.313537i	−0.203257	−	0.979125i	$-0.565153\pi$
$631$	13.6416	−	7.87596i	0.543062	−	0.313537i	0.746319	+	0.665588i	$0.231819\pi$
$632$	−19.3596	−	11.1773i	−0.770084	−	0.444608i
$633$	7.77009	−	13.4582i	0.308833	−	0.534915i
$634$	8.40783			0.333918
$635$	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
$640$	−11.8499			−0.468410
$641$	−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	$0.302378\pi$
$642$	3.12234	+	1.80268i	0.123229	+	0.0711463i
$643$	16.3952	−	9.46576i	0.646563	−	0.373293i	−0.140575	−	0.990070i	$-0.544895\pi$
$643$	16.3952	−	9.46576i	0.646563	−	0.373293i	0.787138	+	0.616777i	$0.211562\pi$
$644$		0			0
$645$			4.27188i			0.168205i
$646$	−0.391280			−0.0153947
$647$	−37.6768			−1.48123			−0.740614	−	0.671930i	$-0.765465\pi$
$647$	−37.6768			−1.48123			−0.740614	+	0.671930i	$0.765465\pi$
$648$			5.67104i			0.222779i
$649$	−21.3867	+	37.0429i	−0.839503	+	1.45406i
$650$	−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
$655$	11.2402	−	6.48952i	0.439190	−	0.253567i
$656$			31.0004i			1.21036i
$657$	−13.0468	+	7.53257i	−0.509004	+	0.293874i
$658$		0			0
$659$	0.709152	+	1.22829i	0.0276247	+	0.0478473i	0.879507	−	0.475886i	$-0.157872\pi$
$659$	0.709152	+	1.22829i	0.0276247	+	0.0478473i	−0.851883	+	0.523733i	$0.824539\pi$
$660$	3.07459	+	5.32535i	0.119678	+	0.207289i
$661$			4.59298i			0.178646i	0.996003	+	0.0893231i	$0.0284704\pi$
$661$			4.59298i			0.178646i	−0.996003	+	0.0893231i	$0.971530\pi$
$662$	−1.55225	−	2.68858i	−0.0603300	−	0.104495i
$663$	−0.166787	+	0.401857i	−0.00647747	+	0.0156068i
$664$	−5.38715			−0.209062
$665$		0			0
$666$	0.480219	−	0.831764i	0.0186081	−	0.0322302i
$667$	36.8736			1.42775
$668$	9.29746	−	5.36789i	0.359730	−	0.207690i
$669$	−8.46782	−	4.88890i	−0.327385	−	0.189016i
$670$			2.68142i			0.103592i
$671$		−	23.2624i		−	0.898036i
$672$		0			0
$673$	−2.10111	+	3.63924i	−0.0809920	+	0.140282i	−0.903676	−	0.428216i	$-0.859142\pi$
$673$	−2.10111	+	3.63924i	−0.0809920	+	0.140282i	0.822684	+	0.568499i	$0.192475\pi$
$674$	3.33259	−	1.92407i	0.128367	−	0.0741126i
$675$	−8.77418	−	15.1973i	−0.337718	−	0.584945i
$676$	−5.91919	+	21.9666i	−0.227661	+	0.844871i
$677$	4.04354	−	7.00361i	0.155406	−	0.269171i	−0.777801	−	0.628511i	$-0.783665\pi$
$677$	4.04354	−	7.00361i	0.155406	−	0.269171i	0.933207	+	0.359340i	$0.116998\pi$
$678$	4.03316	+	2.32854i	0.154892	+	0.0894272i
$679$		0			0
$680$	−0.138811	−	0.240427i	−0.00532315	−	0.00921997i
$681$	13.1737	+	7.60583i	0.504817	+	0.291456i
$682$	−4.88989	−	2.82318i	−0.187244	−	0.108105i
$683$	21.3792	+	12.3433i	0.818051	+	0.472302i	0.849744	−	0.527196i	$-0.176757\pi$
$683$	21.3792	+	12.3433i	0.818051	+	0.472302i	−0.0316929	+	0.999498i	$0.510090\pi$
$684$	−19.0236	−	10.9833i	−0.727386	−	0.419956i
$685$	−2.73398	−	4.73540i	−0.104460	−	0.180930i
$686$		0			0
$687$	2.84267	+	1.64122i	0.108455	+	0.0626164i
$688$	6.17994	−	10.7040i	0.235608	−	0.408085i
$689$	0.613136	+	0.800222i	0.0233586	+	0.0304860i
$690$	0.972234	+	1.68396i	0.0370123	+	0.0641072i
$691$	9.74859	−	5.62835i	0.370854	−	0.214113i	−0.302978	−	0.952998i	$-0.597981\pi$
$691$	9.74859	−	5.62835i	0.370854	−	0.214113i	0.673831	+	0.738885i	$0.264647\pi$
$692$	−21.2301	+	36.7716i	−0.807047	+	1.39785i
$693$		0			0
$694$			15.2043i			0.577147i
$695$			21.6194i			0.820071i
$696$	−11.5849	−	6.68854i	−0.439124	−	0.253528i
$697$	−1.48805	+	0.859128i	−0.0563640	+	0.0325418i
$698$	8.07884			0.305789
$699$	−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	$0.362094\pi$
$702$	6.41698	−	4.91673i	0.242193	−	0.185570i
$703$	2.32288	+	4.02335i	0.0876091	+	0.151743i
$704$		−	10.3532i		−	0.390201i
$705$	−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
$709$		−	23.7741i		−	0.892854i	−0.894820	−	0.446427i	$-0.852696\pi$
$709$		−	23.7741i		−	0.892854i	0.894820	−	0.446427i	$-0.147304\pi$
$710$	1.66961	−	0.963952i	0.0626595	−	0.0361765i
$711$	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
$716$	−3.61969	+	6.26948i	−0.135274	+	0.234301i
$717$			6.63082i			0.247632i
$718$	15.6822			0.585255
$719$	20.7808			0.774992			0.387496	−	0.921871i	$-0.373340\pi$
$719$	20.7808			0.774992			0.387496	+	0.921871i	$0.373340\pi$
$720$		−	6.08597i		−	0.226811i
$721$		0			0
$722$	−4.91782	+	2.83931i	−0.183022	+	0.105668i
$723$	16.0144	+	9.24589i	0.595580	+	0.343859i
$724$	−6.88252	+	11.9209i	−0.255787	+	0.443036i
$725$	−32.8618			−1.22046
$726$	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
$731$	0.685069			0.0253382
$732$	4.35899	−	7.55000i	0.161113	−	0.279056i
$733$	4.55224	+	2.62824i	0.168141	+	0.0970761i	0.581709	−	0.813397i	$-0.302384\pi$
$733$	4.55224	+	2.62824i	0.168141	+	0.0970761i	−0.413568	+	0.910473i	$0.635718\pi$
$734$	−10.4255	+	6.01919i	−0.384814	+	0.222172i
$735$		0			0
$736$		−	22.0917i		−	0.814312i
$737$	−20.4097			−0.751800
$738$	13.7796			0.507235
$739$			7.15001i			0.263017i	0.991315	+	0.131509i	$0.0419821\pi$
$739$			7.15001i			0.263017i	−0.991315	+	0.131509i	$0.958018\pi$
$740$	−0.769132	+	1.33218i	−0.0282738	+	0.0489717i
$741$	2.19121	+	16.7351i	0.0804960	+	0.614780i
$742$		0			0
$743$	−0.618032	−	0.356821i	−0.0226734	−	0.0130905i	0.488620	−	0.872496i	$-0.337500\pi$
$743$	−0.618032	−	0.356821i	−0.0226734	−	0.0130905i	−0.511294	+	0.859406i	$0.670834\pi$
$744$	−2.26721	−	3.92692i	−0.0831198	−	0.143968i
$745$	−0.00592959	+	0.0102703i	−0.000217243	+	0.000376276i
$746$	−7.96386	+	4.59794i	−0.291578	+	0.168342i
$747$		−	6.54569i		−	0.239494i
$748$	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	$0.988693\pi$
$752$			11.6763i			0.425791i
$753$	3.26238	+	5.65062i	0.118888	+	0.205920i
$754$	−1.96539	−	15.0104i	−0.0715752	−	0.546648i
$755$	−19.7084			−0.717263
$756$		0			0
$757$	−8.19425	+	14.1928i	−0.297825	+	0.515848i	−0.975638	−	0.219386i	$-0.929594\pi$
$757$	−8.19425	+	14.1928i	−0.297825	+	0.515848i	0.677813	+	0.735234i	$0.262928\pi$
$758$	−4.06859			−0.147778
$759$	−12.8175	+	7.40018i	−0.465245	+	0.268609i
$760$	−9.32654	−	5.38468i	−0.338309	−	0.195323i
$761$			8.31998i			0.301599i	0.988564	+	0.150800i	$0.0481848\pi$
$761$			8.31998i			0.301599i	−0.988564	+	0.150800i	$0.951815\pi$
$762$		−	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
$766$	−5.59263	−	9.68671i	−0.202070	−	0.349995i
$767$	−35.9037	−	14.9015i	−1.29641	−	0.538061i
$768$	−0.197167	+	0.341504i	−0.00711466	+	0.0123230i
$769$	−22.1346	−	12.7794i	−0.798194	−	0.460838i	0.0446452	−	0.999003i	$-0.485784\pi$
$769$	−22.1346	−	12.7794i	−0.798194	−	0.460838i	−0.842839	+	0.538165i	$0.819118\pi$
$770$		0			0
$771$	5.78738	+	10.0240i	0.208427	+	0.361007i
$772$	−7.31905	−	4.22565i	−0.263418	−	0.152085i
$773$	−7.27528	−	4.20038i	−0.261674	−	0.151077i	0.363424	−	0.931624i	$-0.381608\pi$
$773$	−7.27528	−	4.20038i	−0.261674	−	0.151077i	−0.625098	+	0.780546i	$0.714941\pi$
$774$	−4.75789	−	2.74697i	−0.171019	−	0.0987378i
$775$	−9.64678	−	5.56957i	−0.346523	−	0.200065i
$776$	−2.53392	−	4.38887i	−0.0909623	−	0.157551i
$777$		0			0
$778$	−9.26388	−	5.34850i	−0.332126	−	0.191753i
$779$	−33.3269	+	57.7238i	−1.19406	+	2.06817i
$780$	−4.43604	+	3.39892i	−0.158836	+	0.121701i
$781$	7.33714	+	12.7083i	0.262544	+	0.454739i
$782$	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
$786$		−	5.28872i		−	0.188642i
$787$	30.3667	+	17.5322i	1.08246	+	0.624956i	0.931558	−	0.363593i	$-0.118450\pi$
$787$	30.3667	+	17.5322i	1.08246	+	0.624956i	0.150898	+	0.988549i	$0.451784\pi$
$788$	39.1562	−	22.6069i	1.39488	−	0.805336i
$789$	9.96001			0.354586
$790$	3.10720	−	5.38182i	0.110549	−	0.191477i
$791$		0			0
$792$	−16.9463			−0.602160
$793$	20.9624	−	2.74470i	0.744395	−	0.0974671i
$794$	0.299175	+	0.518186i	0.0106173	+	0.0183897i
$795$			0.247639i			0.00878284i
$796$	−14.9754	−	25.9382i	−0.530789	−	0.919354i
$797$	12.2876	+	21.2828i	0.435250	+	0.753875i	0.997316	−	0.0732173i	$-0.0233267\pi$
$797$	12.2876	+	21.2828i	0.435250	+	0.753875i	−0.562066	+	0.827092i	$0.689993\pi$
$798$		0			0
$799$	−0.560475	+	0.323590i	−0.0198282	+	0.0114478i
$800$			19.6882i			0.696083i
$801$	3.44804	−	1.99073i	0.121831	−	0.0703389i
$802$	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
$807$	−3.90764	+	6.76823i	−0.137555	+	0.238253i
$808$			21.5099i			0.756717i
$809$	−31.8012			−1.11807			−0.559035	−	0.829144i	$-0.688828\pi$
$809$	−31.8012			−1.11807			−0.559035	+	0.829144i	$0.688828\pi$
$810$	−1.57651			−0.0553927
$811$			10.3633i			0.363905i	0.983307	+	0.181953i	$0.0582418\pi$
$811$			10.3633i			0.363905i	−0.983307	+	0.181953i	$0.941758\pi$
$812$		0			0
$813$	1.88630	−	1.08906i	0.0661555	−	0.0381949i
$814$	1.44847	+	0.836272i	0.0507687	+	0.0293113i
$815$	−4.65598	+	8.06439i	−0.163092	+	0.282483i
$816$	0.309235			0.0108254
$817$	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	−0.437452	−	0.899242i	$-0.644119\pi$
$821$	3.51253	−	2.02796i	0.122588	−	0.0707762i	0.560040	+	0.828465i	$0.310786\pi$
$822$	−2.22810			−0.0777138
$823$	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	$0.118119\pi$
$824$	−6.77027	−	3.90882i	−0.235854	−	0.136170i
$825$	11.4230	−	6.59505i	0.397696	−	0.229610i
$826$		0			0
$827$			23.5788i			0.819915i	0.912105	+	0.409957i	$0.134456\pi$
$827$			23.5788i			0.819915i	−0.912105	+	0.409957i	$0.865544\pi$
$828$	17.5061			0.608380
$829$	−29.0406			−1.00862			−0.504311	−	0.863522i	$-0.668253\pi$
$829$	−29.0406			−1.00862			−0.504311	+	0.863522i	$0.668253\pi$
$830$		−	1.49759i		−	0.0519820i
$831$	0.396714	−	0.687128i	0.0137618	−	0.0238362i
$832$	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
$837$	11.0546	−	6.38240i	0.382104	−	0.220608i
$838$			2.96666i			0.102482i
$839$	10.0090	−	5.77871i	0.345550	−	0.199503i	−0.317174	−	0.948367i	$-0.602734\pi$
$839$	10.0090	−	5.77871i	0.345550	−	0.199503i	0.662723	+	0.748864i	$0.269400\pi$
$840$		0			0
$841$	−20.7598	−	35.9570i	−0.715855	−	1.23990i
$842$	0.657918	+	1.13955i	0.0226734	+	0.0392714i
$843$			5.48238i			0.188823i
$844$	−16.0049	−	27.7212i	−0.550910	−	0.954205i
$845$	−13.0854	−	3.52603i	−0.450153	−	0.121299i
$846$	5.19009			0.178439
$847$		0			0
$848$	0.358248	−	0.620504i	0.0123023	−	0.0213082i
$849$	−18.8395			−0.646572
$850$	−0.240670	+	0.138951i	−0.00825493	+	0.00476598i
$851$	−3.20638	−	1.85121i	−0.109913	−	0.0634586i
$852$			5.49943i			0.188408i
$853$		−	1.51845i		−	0.0519906i	−0.999662	−	0.0259953i	$-0.991725\pi$
$853$		−	1.51845i		−	0.0519906i	0.999662	−	0.0259953i	$-0.00827550\pi$
$854$		0			0
$855$	6.54269	−	11.3323i	0.223755	−	0.387556i
$856$	13.7815	−	7.95678i	0.471043	−	0.271957i
$857$	3.00060	+	5.19718i	0.102498	+	0.177532i	0.912713	−	0.408600i	$-0.133983\pi$
$857$	3.00060	+	5.19718i	0.102498	+	0.177532i	−0.810215	+	0.586133i	$0.800650\pi$
$858$	3.69563	+	4.82328i	0.126167	+	0.164664i
$859$	0.838021	−	1.45150i	0.0285929	−	0.0495244i	−0.851375	−	0.524558i	$-0.824231\pi$
$859$	0.838021	−	1.45150i	0.0285929	−	0.0495244i	0.879968	+	0.475033i	$0.157564\pi$
$860$	7.62036	+	4.39962i	0.259852	+	0.150026i
$861$		0			0
$862$	4.70929	+	8.15673i	0.160399	+	0.277819i
$863$	−36.4167	−	21.0252i	−1.23964	−	0.715706i	−0.270619	−	0.962687i	$-0.587228\pi$
$863$	−36.4167	−	21.0252i	−1.23964	−	0.715706i	−0.969021	+	0.246980i	$0.920562\pi$
$864$	−19.5388	−	11.2807i	−0.664724	−	0.383779i
$865$	−21.9047	−	12.6467i	−0.744781	−	0.429999i
$866$	−8.28567	−	4.78374i	−0.281559	−	0.162558i
$867$	−7.21304	−	12.4934i	−0.244968	−	0.424297i
$868$		0			0
$869$	40.9639	+	23.6505i	1.38960	+	0.802288i
$870$	1.85936	−	3.22051i	0.0630383	−	0.109186i
$871$	−2.40811	−	18.3917i	−0.0815956	−	0.623178i
$872$	−6.02832	−	10.4414i	−0.204145	−	0.353589i
$873$	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
$877$		−	30.8630i		−	1.04217i	−0.853505	−	0.521084i	$-0.825528\pi$
$877$		−	30.8630i		−	1.04217i	0.853505	−	0.521084i	$-0.174472\pi$
$878$	0.547793	+	0.316268i	0.0184871	+	0.0106735i
$879$	−17.8077	+	10.2813i	−0.600638	+	0.346778i
$880$	10.5983			0.357270
$881$	27.8669	−	48.2669i	0.938860	−	1.62615i	0.171260	−	0.985226i	$-0.445216\pi$
$881$	27.8669	−	48.2669i	0.938860	−	1.62615i	0.767601	−	0.640928i	$-0.221450\pi$
$882$		0			0
$883$	−2.92007			−0.0982681			−0.0491341	−	0.998792i	$-0.515646\pi$
$883$	−2.92007			−0.0982681			−0.0491341	+	0.998792i	$0.515646\pi$
$884$	0.545076	+	0.711396i	0.0183329	+	0.0239268i
$885$	−4.77452	−	8.26971i	−0.160494	−	0.277983i
$886$		−	10.4693i		−	0.351724i
$887$	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
$891$		−	11.9996i		−	0.402002i
$892$	−17.4421	+	10.0702i	−0.584004	+	0.337175i
$893$	−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
$898$	4.46569	−	7.73480i	0.149022	−	0.258114i
$899$		−	23.9039i		−	0.797241i
$900$	−15.6015			−0.520050
$901$	0.0397131			0.00132304
$902$			23.9964i			0.798991i
$903$		0			0
$904$	17.8017	−	10.2778i	0.592077	−	0.341836i
$905$	−7.10121	−	4.09989i	−0.236052	−	0.136285i
$906$	−4.01541	+	6.95490i	−0.133403	+	0.231061i
$907$	35.6164			1.18262			0.591311	−	0.806444i	$-0.298611\pi$
$907$	35.6164			1.18262			0.591311	+	0.806444i	$0.298611\pi$
$908$	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
$913$	11.3989			0.377249
$914$	−1.64145	+	2.84307i	−0.0542943	+	0.0940404i
$915$	4.49750	+	2.59663i	0.148683	+	0.0858420i
$916$	5.85535	−	3.38059i	0.193466	−	0.111698i
$917$		0			0
$918$		−	0.318459i		−	0.0105107i
$919$	26.1128			0.861382			0.430691	−	0.902499i	$-0.358270\pi$
$919$	26.1128			0.861382			0.430691	+	0.902499i	$0.358270\pi$
$920$	8.58259			0.282959
$921$		−	20.6389i		−	0.680074i
$922$	1.27838	−	2.21421i	0.0421010	−	0.0729211i
$923$	−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
$928$	−36.5893	+	21.1248i	−1.20110	+	0.693457i
$929$		−	10.0231i		−	0.328849i	−0.986390	−	0.164424i	$-0.947423\pi$
$929$		−	10.0231i		−	0.328849i	0.986390	−	0.164424i	$-0.0525766\pi$
$930$	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
$934$		−	6.47455i		−	0.211854i
$935$	0.293716	+	0.508731i	0.00960554	+	0.0166373i
$936$	−1.99947	−	15.2707i	−0.0653546	−	0.499139i
$937$	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
$940$	−8.31259			−0.271127
$941$	−14.8001	+	8.54482i	−0.482468	+	0.278553i	−0.721445	−	0.692472i	$-0.756522\pi$
$941$	−14.8001	+	8.54482i	−0.482468	+	0.278553i	0.238976	+	0.971025i	$0.423188\pi$
$942$	−7.28169	−	4.20409i	−0.237250	−	0.136977i
$943$		−	53.1193i		−	1.72980i
$944$			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	−0.161600	−	0.986856i	$-0.551665\pi$
$947$	18.8408	−	10.8777i	0.612243	−	0.353479i	0.773843	+	0.633378i	$0.218332\pi$
$948$	8.86342	+	15.3519i	0.287871	+	0.498607i
$949$	18.9260	−	14.5012i	0.614364	−	0.470730i
$950$	−5.39012	+	9.33597i	−0.174879	+	0.302899i
$951$	−12.3729	−	7.14350i	−0.401219	−	0.231644i
$952$		0			0
$953$	−8.90406	−	15.4223i	−0.288431	−	0.499577i	0.685005	−	0.728539i	$-0.259800\pi$
$953$	−8.90406	−	15.4223i	−0.288431	−	0.499577i	−0.973435	+	0.228962i	$0.926467\pi$
$954$	−0.275812	−	0.159240i	−0.00892976	−	0.00515560i
$955$	5.84900	+	3.37692i	0.189269	+	0.109275i
$956$	11.8283	+	6.82909i	0.382556	+	0.220869i
$957$	24.5130	+	14.1526i	0.792392	+	0.457488i
$958$	−6.75281	−	11.6962i	−0.218173	−	0.377887i
$959$		0			0
$960$	2.00166	+	1.15566i	0.0646034	+	0.0372988i
$961$	−11.4487	+	19.8297i	−0.369311	+	0.639666i
$962$	−0.582683	+	1.40392i	−0.0187865	+	0.0452642i
$963$	9.66793	+	16.7453i	0.311545	+	0.539611i
$964$	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	$-0.807372\pi$
$967$		−	35.3813i		−	1.13779i	0.822412	−	0.568893i	$-0.192628\pi$
$968$		−	8.88637i		−	0.285619i
$969$	0.575805	+	0.332441i	0.0184975	+	0.0106796i
$970$	1.22007	−	0.704409i	0.0391742	−	0.0226172i
$971$	−49.7067			−1.59516			−0.797582	−	0.603211i	$-0.793888\pi$
$971$	−49.7067			−1.59516			−0.797582	+	0.603211i	$0.793888\pi$
$972$	14.0200	−	24.2834i	0.449693	−	0.778890i
$973$		0			0
$974$	16.0415			0.514002
$975$	7.29074	+	9.51537i	0.233490	+	0.304736i
$976$	−7.51287	−	13.0127i	−0.240481	−	0.416526i
$977$		−	61.2801i		−	1.96052i	−0.197702	−	0.980262i	$-0.563348\pi$
$977$		−	61.2801i		−	1.96052i	0.197702	−	0.980262i	$-0.436652\pi$
$978$	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
$982$			14.3016i			0.456383i
$983$	−6.05318	+	3.49481i	−0.193067	+	0.111467i	−0.593417	−	0.804895i	$-0.702222\pi$
$983$	−6.05318	+	3.49481i	−0.193067	+	0.111467i	0.400351	+	0.916362i	$0.368888\pi$
$984$	−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
$989$	−10.5893	+	18.3413i	−0.336722	+	0.583219i
$990$		−	4.71094i		−	0.149723i
$991$	−32.7341			−1.03983			−0.519917	−	0.854217i	$-0.674037\pi$
$991$	−32.7341			−1.03983			−0.519917	+	0.854217i	$0.674037\pi$
$992$	−14.3213			−0.454703
$993$			5.27532i			0.167407i
$994$		0			0
$995$	15.4512	−	8.92078i	0.489838	−	0.282808i
$996$	3.69960	+	2.13597i	0.117226	+	0.0676807i
$997$	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	$-0.201229\pi$
$998$	−0.899058			−0.0284592
$999$	−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.u.g.30.4		12
7.2	even	3		637.2.q.i.589.3		12
7.3	odd	6		91.2.k.b.4.4	✓	12
7.4	even	3		637.2.k.i.459.4		12
7.5	odd	6		637.2.q.g.589.3		12
7.6	odd	2		91.2.u.b.30.4	yes	12
13.10	even	6		637.2.k.i.569.3		12
21.17	even	6		819.2.bm.f.550.3		12
21.20	even	2		819.2.do.e.667.3		12
91.6	even	12		1183.2.e.j.170.5		24
91.10	odd	6		91.2.u.b.88.4	yes	12
91.19	even	12		8281.2.a.cp.1.8		12
91.20	even	12		1183.2.e.j.170.8		24
91.23	even	6		637.2.q.i.491.3		12
91.33	even	12		8281.2.a.cp.1.5		12
91.45	even	12		1183.2.e.j.508.5		24
91.58	odd	12		8281.2.a.co.1.8		12
91.59	even	12		1183.2.e.j.508.8		24
91.62	odd	6		91.2.k.b.23.3	yes	12
91.72	odd	12		8281.2.a.co.1.5		12
91.75	odd	6		637.2.q.g.491.3		12
91.88	even	6	inner	637.2.u.g.361.4		12
273.62	even	6		819.2.bm.f.478.4		12
273.101	even	6		819.2.do.e.361.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.b.4.4	✓	12	7.3	odd	6
91.2.k.b.23.3	yes	12	91.62	odd	6
91.2.u.b.30.4	yes	12	7.6	odd	2
91.2.u.b.88.4	yes	12	91.10	odd	6
637.2.k.i.459.4		12	7.4	even	3
637.2.k.i.569.3		12	13.10	even	6
637.2.q.g.491.3		12	91.75	odd	6
637.2.q.g.589.3		12	7.5	odd	6
637.2.q.i.491.3		12	91.23	even	6
637.2.q.i.589.3		12	7.2	even	3
637.2.u.g.30.4		12	1.1	even	1	trivial
637.2.u.g.361.4		12	91.88	even	6	inner
819.2.bm.f.478.4		12	273.62	even	6
819.2.bm.f.550.3		12	21.17	even	6
819.2.do.e.361.3		12	273.101	even	6
819.2.do.e.667.3		12	21.20	even	2
1183.2.e.j.170.5		24	91.6	even	12
1183.2.e.j.170.8		24	91.20	even	12
1183.2.e.j.508.5		24	91.45	even	12
1183.2.e.j.508.8		24	91.59	even	12
8281.2.a.co.1.5		12	91.72	odd	12
8281.2.a.co.1.8		12	91.58	odd	12
8281.2.a.cp.1.5		12	91.33	even	12
8281.2.a.cp.1.8		12	91.19	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.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.433001 - 0.249993i) q^{2} -0.849601 q^{3} +(-0.875007 + 1.51556i) q^{4} +(-0.902810 - 0.521238i) q^{5} +(-0.367878 + 0.212395i) q^{6} +1.87496i q^{8} -2.27818 q^{9} +O(q^{10})\)	\(q+(0.433001 - 0.249993i) q^{2} -0.849601 q^{3} +(-0.875007 + 1.51556i) q^{4} +(-0.902810 - 0.521238i) q^{5} +(-0.367878 + 0.212395i) q^{6} +1.87496i q^{8} -2.27818 q^{9} -0.521224 q^{10} -3.96730i q^{11} +(0.743407 - 1.28762i) 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} +(-0.986453 + 0.569529i) q^{18} -5.50977i q^{19} +(1.57993 - 0.912173i) q^{20} +(-0.991800 - 1.71785i) q^{22} +(2.19549 + 3.80270i) q^{23} -1.59297i q^{24} +(-1.95662 - 3.38897i) q^{25} +(1.43097 - 1.09642i) q^{26} +4.48435 q^{27} +(4.19880 - 7.27253i) q^{29} +0.442832 q^{30} +(2.46516 - 1.42326i) q^{31} +(-4.35712 - 2.51558i) q^{32} +3.37063i q^{33} -0.0710158i q^{34} +(1.99342 - 3.45271i) q^{36} +(-0.730221 + 0.421593i) q^{37} +(-1.37740 - 2.38574i) q^{38} +(-3.03736 + 0.397695i) q^{39} +(0.977298 - 1.69273i) q^{40} +(-10.4766 - 6.04869i) q^{41} +(2.41161 + 4.17704i) q^{43} +(6.01267 + 3.47142i) q^{44} +(2.05676 + 1.18747i) q^{45} +(1.90130 + 1.09772i) q^{46} +(-3.94602 - 2.27824i) q^{47} +(1.08858 + 1.88548i) q^{48} +(-1.69444 - 0.978285i) q^{50} +(-0.0603367 + 0.104506i) q^{51} +(-2.41875 + 5.82776i) q^{52} +(0.139800 + 0.242141i) q^{53} +(1.94173 - 1.12106i) q^{54} +(-2.06791 + 3.58172i) q^{55} +4.68111i q^{57} -4.19868i q^{58} +(-9.33705 - 5.39075i) q^{59} +(-1.34231 + 0.774983i) q^{60} +5.86354 q^{61} +(0.711612 - 1.23255i) q^{62} +2.60963 q^{64} +(-3.47157 - 1.44084i) q^{65} +(0.842634 + 1.45949i) q^{66} -5.14447i q^{67} +(0.124282 + 0.215263i) q^{68} +(-1.86529 - 3.23078i) q^{69} +(-3.20326 + 1.84940i) q^{71} -4.27148i q^{72} +(5.72686 - 3.30640i) 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} +(-5.96135 + 10.3254i) q^{79} +2.67142i q^{80} +3.02462 q^{81} -6.04853 q^{82} +2.87321i q^{83} +(-0.128231 + 0.0740342i) q^{85} +(2.08846 + 1.20578i) q^{86} +(-3.56730 + 6.17875i) q^{87} +7.43852 q^{88} +(-1.51351 + 0.873824i) q^{89} +1.18744 q^{90} -7.68427 q^{92} +(-2.09440 + 1.20921i) q^{93} -2.27818 q^{94} +(-2.87190 + 4.97427i) q^{95} +(3.70181 + 2.13724i) q^{96} +(-2.34079 + 1.35145i) q^{97} +9.03822i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} + 4 q^{4} - 3 q^{5} + 9 q^{6} + 2 q^{9}+O(q^{10}) \) 12 * q - 6 * q^3 + 4 * q^4 - 3 * q^5 + 9 * q^6 + 2 * q^9	\( 12 q - 6 q^{3} + 4 q^{4} - 3 q^{5} + 9 q^{6} + 2 q^{9} + 24 q^{10} + q^{12} + 2 q^{13} - 12 q^{15} - 8 q^{16} - 17 q^{17} - 3 q^{18} + 3 q^{20} - 15 q^{22} + 3 q^{23} - 5 q^{25} + 9 q^{26} - 12 q^{27} - q^{29} - 22 q^{30} + 18 q^{31} + 18 q^{32} - 13 q^{36} + 15 q^{37} - 19 q^{38} - q^{39} + q^{40} + 6 q^{41} + 11 q^{43} + 33 q^{44} + 9 q^{45} - 30 q^{46} - 15 q^{47} - 19 q^{48} + 18 q^{50} + 4 q^{51} - 47 q^{52} - 8 q^{53} - 6 q^{54} + 15 q^{55} - 27 q^{59} + 30 q^{60} + 10 q^{61} - 41 q^{62} + 2 q^{64} - 3 q^{65} + 34 q^{66} + 11 q^{68} - 7 q^{69} + 30 q^{71} + 42 q^{73} - 33 q^{74} - q^{75} + 45 q^{76} + 44 q^{78} - 35 q^{79} - 28 q^{81} + 10 q^{82} - 21 q^{85} + 57 q^{86} - 10 q^{87} + 28 q^{88} - 48 q^{89} - 66 q^{92} - 81 q^{93} + 2 q^{94} + 2 q^{95} + 21 q^{96} + 3 q^{97}+O(q^{100}) \) 12 * q - 6 * q^3 + 4 * q^4 - 3 * q^5 + 9 * q^6 + 2 * q^9 + 24 * q^10 + q^12 + 2 * q^13 - 12 * q^15 - 8 * q^16 - 17 * q^17 - 3 * q^18 + 3 * q^20 - 15 * q^22 + 3 * q^23 - 5 * q^25 + 9 * q^26 - 12 * q^27 - q^29 - 22 * q^30 + 18 * q^31 + 18 * q^32 - 13 * q^36 + 15 * q^37 - 19 * q^38 - q^39 + q^40 + 6 * q^41 + 11 * q^43 + 33 * q^44 + 9 * q^45 - 30 * q^46 - 15 * q^47 - 19 * q^48 + 18 * q^50 + 4 * q^51 - 47 * q^52 - 8 * q^53 - 6 * q^54 + 15 * q^55 - 27 * q^59 + 30 * q^60 + 10 * q^61 - 41 * q^62 + 2 * q^64 - 3 * q^65 + 34 * q^66 + 11 * q^68 - 7 * q^69 + 30 * q^71 + 42 * q^73 - 33 * q^74 - q^75 + 45 * q^76 + 44 * q^78 - 35 * q^79 - 28 * q^81 + 10 * q^82 - 21 * q^85 + 57 * q^86 - 10 * q^87 + 28 * q^88 - 48 * q^89 - 66 * q^92 - 81 * q^93 + 2 * q^94 + 2 * q^95 + 21 * q^96 + 3 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more