LMFDB - Embedded newform 625.2.d.n.501.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [625,2,Mod(126,625)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(625, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("625.126");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 625 = 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	625.d (of order $5$, degree $4$, 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:	$4.99065012633$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 25x^{14} + 239x^{12} + 1165x^{10} + 3166x^{8} + 4820x^{6} + 3809x^{4} + 1205x^{2} + 1 $ x^16 + 25x^14 + 239x^12 + 1165x^10 + 3166x^8 + 4820x^6 + 3809x^4 + 1205*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			501.2
Root			$-3.18910i$ of defining polynomial
Character	$\chi$	$=$	625.501
Dual form			625.2.d.n.126.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.154814 - 0.476469i) q^{2} +(-2.50250 - 1.81817i) q^{3} +(1.41498 + 1.02804i) q^{4} +(-1.25372 + 0.910884i) q^{6} +0.0237879 q^{7} +(1.51951 - 1.10399i) q^{8} +(2.02970 + 6.24676i) q^{9} +O(q^{10})$	\(q+(0.154814 - 0.476469i) q^{2} +(-2.50250 - 1.81817i) q^{3} +(1.41498 + 1.02804i) q^{4} +(-1.25372 + 0.910884i) q^{6} +0.0237879 q^{7} +(1.51951 - 1.10399i) q^{8} +(2.02970 + 6.24676i) q^{9} +(1.10730 - 3.40791i) q^{11} +(-1.67182 - 5.14535i) q^{12} +(1.16681 + 3.59107i) q^{13} +(0.00368270 - 0.0113342i) q^{14} +(0.790173 + 2.43190i) q^{16} +(2.93109 - 2.12956i) q^{17} +3.29062 q^{18} +(1.96659 - 1.42881i) q^{19} +(-0.0595291 - 0.0432504i) q^{21} +(-1.45234 - 1.05519i) q^{22} +(0.530082 - 1.63143i) q^{23} -5.80980 q^{24} +1.89167 q^{26} +(3.41077 - 10.4973i) q^{27} +(0.0336593 + 0.0244549i) q^{28} +(-3.12065 - 2.26729i) q^{29} +(4.86202 - 3.53247i) q^{31} +5.03748 q^{32} +(-8.96717 + 6.51503i) q^{33} +(-0.560896 - 1.72626i) q^{34} +(-3.54996 + 10.9257i) q^{36} +(-0.114123 - 0.351233i) q^{37} +(-0.376328 - 1.15822i) q^{38} +(3.60924 - 11.1081i) q^{39} +(-2.41311 - 7.42680i) q^{41} +(-0.0298234 + 0.0216680i) q^{42} +0.174574 q^{43} +(5.07027 - 3.68377i) q^{44} +(-0.695260 - 0.505136i) q^{46} +(-6.31908 - 4.59108i) q^{47} +(2.44421 - 7.52250i) q^{48} -6.99943 q^{49} -11.2070 q^{51} +(-2.04076 + 6.28081i) q^{52} +(7.25837 + 5.27352i) q^{53} +(-4.47359 - 3.25025i) q^{54} +(0.0361458 - 0.0262615i) q^{56} -7.51920 q^{57} +(-1.56341 + 1.13589i) q^{58} +(-1.37678 - 4.23730i) q^{59} +(2.84729 - 8.76306i) q^{61} +(-0.930401 - 2.86348i) q^{62} +(0.0482822 + 0.148597i) q^{63} +(-0.800472 + 2.46360i) q^{64} +(1.71597 + 5.28120i) q^{66} +(3.61942 - 2.62967i) q^{67} +6.33671 q^{68} +(-4.29274 + 3.11886i) q^{69} +(7.84308 + 5.69833i) q^{71} +(9.98048 + 7.25125i) q^{72} +(-1.22181 + 3.76035i) q^{73} -0.185020 q^{74} +4.25156 q^{76} +(0.0263402 - 0.0810669i) q^{77} +(-4.73390 - 3.43938i) q^{78} +(7.83411 + 5.69181i) q^{79} +(-11.6798 + 8.48587i) q^{81} -3.91223 q^{82} +(7.24650 - 5.26489i) q^{83} +(-0.0397691 - 0.122397i) q^{84} +(0.0270266 - 0.0831794i) q^{86} +(3.68711 + 11.3478i) q^{87} +(-2.07974 - 6.40078i) q^{88} +(-5.25794 + 16.1823i) q^{89} +(0.0277559 + 0.0854239i) q^{91} +(2.42723 - 1.76349i) q^{92} -18.5898 q^{93} +(-3.16579 + 2.30008i) q^{94} +(-12.6063 - 9.15901i) q^{96} +(-2.23643 - 1.62486i) q^{97} +(-1.08361 + 3.33501i) q^{98} +23.5359 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 5 q^{3} - 8 q^{4} - 3 q^{6} + 20 q^{7} - 10 q^{8} + 3 q^{9}+O(q^{10}) $ 16 * q - 5 * q^3 - 8 * q^4 - 3 * q^6 + 20 * q^7 - 10 * q^8 + 3 * q^9	$ 16 q - 5 q^{3} - 8 q^{4} - 3 q^{6} + 20 q^{7} - 10 q^{8} + 3 q^{9} + 2 q^{11} - 25 q^{12} - 5 q^{13} + 9 q^{14} - 14 q^{16} + 10 q^{17} - 10 q^{18} + 7 q^{21} + 40 q^{22} - 15 q^{23} + 10 q^{24} + 22 q^{26} - 20 q^{27} - 30 q^{28} - 10 q^{29} + 17 q^{31} + 60 q^{32} - 5 q^{33} - q^{34} - 4 q^{36} + 15 q^{37} + 15 q^{38} - 9 q^{39} + 12 q^{41} + 45 q^{42} + 49 q^{44} - 33 q^{46} - 25 q^{47} + 20 q^{48} - 8 q^{49} - 28 q^{51} - 20 q^{52} - 30 q^{54} - 35 q^{56} - 20 q^{57} - 5 q^{58} + 20 q^{59} - 23 q^{61} - 15 q^{62} - 10 q^{63} - 28 q^{64} - 26 q^{66} + 80 q^{68} + 6 q^{69} + 22 q^{71} - 5 q^{72} - 40 q^{73} - 36 q^{74} - 20 q^{76} + 40 q^{77} + 25 q^{78} + 75 q^{79} + 11 q^{81} - 90 q^{82} - 25 q^{83} - 31 q^{84} + 17 q^{86} + 20 q^{87} + 5 q^{89} + 22 q^{91} - 60 q^{92} - 80 q^{93} - 51 q^{94} - 28 q^{96} - 40 q^{97} - 15 q^{98} - 44 q^{99}+O(q^{100}) $ 16 * q - 5 * q^3 - 8 * q^4 - 3 * q^6 + 20 * q^7 - 10 * q^8 + 3 * q^9 + 2 * q^11 - 25 * q^12 - 5 * q^13 + 9 * q^14 - 14 * q^16 + 10 * q^17 - 10 * q^18 + 7 * q^21 + 40 * q^22 - 15 * q^23 + 10 * q^24 + 22 * q^26 - 20 * q^27 - 30 * q^28 - 10 * q^29 + 17 * q^31 + 60 * q^32 - 5 * q^33 - q^34 - 4 * q^36 + 15 * q^37 + 15 * q^38 - 9 * q^39 + 12 * q^41 + 45 * q^42 + 49 * q^44 - 33 * q^46 - 25 * q^47 + 20 * q^48 - 8 * q^49 - 28 * q^51 - 20 * q^52 - 30 * q^54 - 35 * q^56 - 20 * q^57 - 5 * q^58 + 20 * q^59 - 23 * q^61 - 15 * q^62 - 10 * q^63 - 28 * q^64 - 26 * q^66 + 80 * q^68 + 6 * q^69 + 22 * q^71 - 5 * q^72 - 40 * q^73 - 36 * q^74 - 20 * q^76 + 40 * q^77 + 25 * q^78 + 75 * q^79 + 11 * q^81 - 90 * q^82 - 25 * q^83 - 31 * q^84 + 17 * q^86 + 20 * q^87 + 5 * q^89 + 22 * q^91 - 60 * q^92 - 80 * q^93 - 51 * q^94 - 28 * q^96 - 40 * q^97 - 15 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/625\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.154814	−	0.476469i	0.109470	−	0.336915i	−0.881283	−	0.472588i	$-0.843320\pi$
$2$	0.154814	−	0.476469i	0.109470	−	0.336915i	0.990754	+	0.135674i	$0.0433198\pi$
$3$	−2.50250	−	1.81817i	−1.44482	−	1.04972i	−0.987008	−	0.160671i	$-0.948634\pi$
$3$	−2.50250	−	1.81817i	−1.44482	−	1.04972i	−0.457809	−	0.889050i	$-0.651366\pi$
$4$	1.41498	+	1.02804i	0.707489	+	0.514021i
$5$		0			0
$5$		0			0
$6$	−1.25372	+	0.910884i	−0.511831	+	0.371867i
$7$	0.0237879			0.00899097			0.00449549	−	0.999990i	$-0.498569\pi$
$7$	0.0237879			0.00899097			0.00449549	+	0.999990i	$0.498569\pi$
$8$	1.51951	−	1.10399i	0.537227	−	0.390318i
$9$	2.02970	+	6.24676i	0.676566	+	2.08225i
$10$		0			0
$11$	1.10730	−	3.40791i	0.333863	−	1.02752i	−0.633417	−	0.773811i	$-0.718348\pi$
$11$	1.10730	−	3.40791i	0.333863	−	1.02752i	0.967280	−	0.253713i	$-0.0816517\pi$
$12$	−1.67182	−	5.14535i	−0.482614	−	1.48533i
$13$	1.16681	+	3.59107i	0.323614	+	0.995983i	0.972062	+	0.234724i	$0.0754185\pi$
$13$	1.16681	+	3.59107i	0.323614	+	0.995983i	−0.648448	+	0.761259i	$0.724582\pi$
$14$	0.00368270	−	0.0113342i	0.000984243	−	0.00302919i
$15$		0			0
$16$	0.790173	+	2.43190i	0.197543	+	0.607976i
$17$	2.93109	−	2.12956i	0.710894	−	0.516495i	−0.172568	−	0.984998i	$-0.555206\pi$
$17$	2.93109	−	2.12956i	0.710894	−	0.516495i	0.883462	+	0.468503i	$0.155206\pi$
$18$	3.29062			0.775606
$19$	1.96659	−	1.42881i	0.451166	−	0.327792i	−0.338890	−	0.940826i	$-0.610051\pi$
$19$	1.96659	−	1.42881i	0.451166	−	0.327792i	0.790056	+	0.613035i	$0.210051\pi$
$20$		0			0
$21$	−0.0595291	−	0.0432504i	−0.0129903	−	0.00943802i
$22$	−1.45234	−	1.05519i	−0.309640	−	0.224966i
$23$	0.530082	−	1.63143i	0.110530	−	0.340176i	−0.880459	−	0.474123i	$-0.842765\pi$
$23$	0.530082	−	1.63143i	0.110530	−	0.340176i	0.990988	+	0.133947i	$0.0427652\pi$
$24$	−5.80980			−1.18592
$25$		0			0
$26$	1.89167			0.370987
$27$	3.41077	−	10.4973i	0.656402	−	2.02020i
$28$	0.0336593	+	0.0244549i	0.00636102	+	0.00462155i
$29$	−3.12065	−	2.26729i	−0.579491	−	0.421025i	0.259050	−	0.965864i	$-0.416591\pi$
$29$	−3.12065	−	2.26729i	−0.579491	−	0.421025i	−0.838540	+	0.544839i	$0.816591\pi$
$30$		0			0
$31$	4.86202	−	3.53247i	0.873245	−	0.634449i	−0.0582109	−	0.998304i	$-0.518540\pi$
$31$	4.86202	−	3.53247i	0.873245	−	0.634449i	0.931456	+	0.363855i	$0.118540\pi$
$32$	5.03748			0.890510
$33$	−8.96717	+	6.51503i	−1.56098	+	1.13412i
$34$	−0.560896	−	1.72626i	−0.0961929	−	0.296051i
$35$		0			0
$36$	−3.54996	+	10.9257i	−0.591660	+	1.82094i
$37$	−0.114123	−	0.351233i	−0.0187616	−	0.0577424i	0.941237	−	0.337746i	$-0.109664\pi$
$37$	−0.114123	−	0.351233i	−0.0187616	−	0.0577424i	−0.959999	+	0.280003i	$0.909664\pi$
$38$	−0.376328	−	1.15822i	−0.0610485	−	0.187888i
$39$	3.60924	−	11.1081i	0.577941	−	1.77872i
$40$		0			0
$41$	−2.41311	−	7.42680i	−0.376865	−	1.15987i	−0.942212	−	0.335018i	$-0.891258\pi$
$41$	−2.41311	−	7.42680i	−0.376865	−	1.15987i	0.565347	−	0.824853i	$-0.308742\pi$
$42$	−0.0298234	+	0.0216680i	−0.00460186	+	0.00334345i
$43$	0.174574			0.0266224			0.0133112	−	0.999911i	$-0.495763\pi$
$43$	0.174574			0.0266224			0.0133112	+	0.999911i	$0.495763\pi$
$44$	5.07027	−	3.68377i	0.764373	−	0.555349i
$45$		0			0
$46$	−0.695260	−	0.505136i	−0.102510	−	0.0744782i
$47$	−6.31908	−	4.59108i	−0.921733	−	0.669678i	0.0222216	−	0.999753i	$-0.492926\pi$
$47$	−6.31908	−	4.59108i	−0.921733	−	0.669678i	−0.943955	+	0.330075i	$0.892926\pi$
$48$	2.44421	−	7.52250i	0.352791	−	1.08578i
$49$	−6.99943			−0.999919
$50$		0			0
$51$	−11.2070			−1.56929
$52$	−2.04076	+	6.28081i	−0.283002	+	0.870992i
$53$	7.25837	+	5.27352i	0.997014	+	0.724373i	0.961446	−	0.274994i	$-0.0886759\pi$
$53$	7.25837	+	5.27352i	0.997014	+	0.724373i	0.0355683	+	0.999367i	$0.488676\pi$
$54$	−4.47359	−	3.25025i	−0.608778	−	0.442303i
$55$		0			0
$56$	0.0361458	−	0.0262615i	0.00483019	−	0.00350934i
$57$	−7.51920			−0.995943
$58$	−1.56341	+	1.13589i	−0.205286	+	0.149149i
$59$	−1.37678	−	4.23730i	−0.179242	−	0.551649i	0.820560	−	0.571560i	$-0.193662\pi$
$59$	−1.37678	−	4.23730i	−0.179242	−	0.551649i	−0.999802	+	0.0199113i	$0.993662\pi$
$60$		0			0
$61$	2.84729	−	8.76306i	0.364558	−	1.12199i	−0.585699	−	0.810529i	$-0.699180\pi$
$61$	2.84729	−	8.76306i	0.364558	−	1.12199i	0.950257	−	0.311466i	$-0.100820\pi$
$62$	−0.930401	−	2.86348i	−0.118161	−	0.363662i
$63$	0.0482822	+	0.148597i	0.00608298	+	0.0187215i
$64$	−0.800472	+	2.46360i	−0.100059	+	0.307950i
$65$		0			0
$66$	1.71597	+	5.28120i	0.211221	+	0.650070i
$67$	3.61942	−	2.62967i	0.442183	−	0.321265i	−0.344319	−	0.938853i	$-0.611890\pi$
$67$	3.61942	−	2.62967i	0.442183	−	0.321265i	0.786502	+	0.617588i	$0.211890\pi$
$68$	6.33671			0.768439
$69$	−4.29274	+	3.11886i	−0.516785	+	0.375466i
$70$		0			0
$71$	7.84308	+	5.69833i	0.930803	+	0.676268i	0.946189	−	0.323614i	$-0.104898\pi$
$71$	7.84308	+	5.69833i	0.930803	+	0.676268i	−0.0153866	+	0.999882i	$0.504898\pi$
$72$	9.98048	+	7.25125i	1.17621	+	0.854567i
$73$	−1.22181	+	3.76035i	−0.143002	+	0.440116i	−0.996749	−	0.0805732i	$-0.974325\pi$
$73$	−1.22181	+	3.76035i	−0.143002	+	0.440116i	0.853746	+	0.520689i	$0.174325\pi$
$74$	−0.185020			−0.0215081
$75$		0			0
$76$	4.25156			0.487687
$77$	0.0263402	−	0.0810669i	0.00300175	−	0.00923843i
$78$	−4.73390	−	3.43938i	−0.536009	−	0.389433i
$79$	7.83411	+	5.69181i	0.881406	+	0.640379i	0.933623	−	0.358257i	$-0.116629\pi$
$79$	7.83411	+	5.69181i	0.881406	+	0.640379i	−0.0522169	+	0.998636i	$0.516629\pi$
$80$		0			0
$81$	−11.6798	+	8.48587i	−1.29776	+	0.942875i
$82$	−3.91223			−0.432033
$83$	7.24650	−	5.26489i	0.795407	−	0.577897i	−0.114156	−	0.993463i	$-0.536416\pi$
$83$	7.24650	−	5.26489i	0.795407	−	0.577897i	0.909563	+	0.415566i	$0.136416\pi$
$84$	−0.0397691	−	0.122397i	−0.00433917	−	0.0133546i
$85$		0			0
$86$	0.0270266	−	0.0831794i	0.00291435	−	0.00896946i
$87$	3.68711	+	11.3478i	0.395300	+	1.21661i
$88$	−2.07974	−	6.40078i	−0.221701	−	0.682326i
$89$	−5.25794	+	16.1823i	−0.557341	+	1.71532i	0.132339	+	0.991205i	$0.457751\pi$
$89$	−5.25794	+	16.1823i	−0.557341	+	1.71532i	−0.689680	+	0.724115i	$0.742249\pi$
$90$		0			0
$91$	0.0277559	+	0.0854239i	0.00290961	+	0.00895485i
$92$	2.42723	−	1.76349i	0.253056	−	0.183856i
$93$	−18.5898			−1.92767
$94$	−3.16579	+	2.30008i	−0.326527	+	0.237236i
$95$		0			0
$96$	−12.6063	−	9.15901i	−1.28662	−	0.934787i
$97$	−2.23643	−	1.62486i	−0.227075	−	0.164979i	0.468431	−	0.883500i	$-0.344820\pi$
$97$	−2.23643	−	1.62486i	−0.227075	−	0.164979i	−0.695506	+	0.718521i	$0.744820\pi$
$98$	−1.08361	+	3.33501i	−0.109461	+	0.336887i
$99$	23.5359			2.36545
$100$		0			0
$101$	10.3526			1.03012			0.515062	−	0.857153i	$-0.327769\pi$
$101$	10.3526			1.03012			0.515062	+	0.857153i	$0.327769\pi$
$102$	−1.73500	+	5.33977i	−0.171790	+	0.528716i
$103$	−14.7980	−	10.7514i	−1.45809	−	1.05937i	−0.983855	−	0.178967i	$-0.942724\pi$
$103$	−14.7980	−	10.7514i	−1.45809	−	1.05937i	−0.474236	−	0.880398i	$-0.657276\pi$
$104$	5.73746	+	4.16851i	0.562604	+	0.408756i
$105$		0			0
$106$	3.63637	−	2.64198i	0.353195	−	0.256611i
$107$	15.8786			1.53504			0.767522	−	0.641023i	$-0.221490\pi$
$107$	15.8786			1.53504			0.767522	+	0.641023i	$0.221490\pi$
$108$	15.6178	−	11.3470i	1.50282	−	1.09186i
$109$	1.84208	+	5.66933i	0.176439	+	0.543024i	0.999696	−	0.0246449i	$-0.00784550\pi$
$109$	1.84208	+	5.66933i	0.176439	+	0.543024i	−0.823257	+	0.567669i	$0.807845\pi$
$110$		0			0
$111$	−0.353011	+	1.08645i	−0.0335063	+	0.103122i
$112$	0.0187965	+	0.0578498i	0.00177611	+	0.00546629i
$113$	0.750387	+	2.30945i	0.0705904	+	0.217255i	0.980128	−	0.198367i	$-0.0635639\pi$
$113$	0.750387	+	2.30945i	0.0705904	+	0.217255i	−0.909537	+	0.415622i	$0.863564\pi$
$114$	−1.16408	+	3.58267i	−0.109026	+	0.335548i
$115$		0			0
$116$	−2.08479	−	6.41632i	−0.193568	−	0.595741i
$117$	−20.0643	+	14.5776i	−1.85494	+	1.34770i
$118$	−2.23209			−0.205480
$119$	0.0697245	−	0.0506578i	0.00639163	−	0.00464379i
$120$		0			0
$121$	−1.48855	−	1.08149i	−0.135323	−	0.0983176i
$122$	−3.73453	−	2.71329i	−0.338108	−	0.245650i
$123$	−7.46438	+	22.9730i	−0.673041	+	2.07141i
$124$	10.5112			0.943932
$125$		0			0
$126$	0.0782768			0.00697345
$127$	−5.28644	+	16.2700i	−0.469096	+	1.44373i	0.384661	+	0.923058i	$0.374318\pi$
$127$	−5.28644	+	16.2700i	−0.469096	+	1.44373i	−0.853757	+	0.520672i	$0.825682\pi$
$128$	9.20073	+	6.68472i	0.813237	+	0.590851i
$129$	−0.436872	−	0.317406i	−0.0384645	−	0.0279461i
$130$		0			0
$131$	−3.87482	+	2.81522i	−0.338545	+	0.245967i	−0.744048	−	0.668127i	$-0.767096\pi$
$131$	−3.87482	+	2.81522i	−0.338545	+	0.245967i	0.405503	+	0.914094i	$0.367096\pi$
$132$	−19.3861			−1.68734
$133$	0.0467810	−	0.0339884i	0.00405642	−	0.00294716i
$134$	−0.692616	−	2.13165i	−0.0598329	−	0.184147i
$135$		0			0
$136$	2.10281	−	6.47177i	0.180314	−	0.554950i
$137$	3.95862	+	12.1834i	0.338207	+	1.04090i	0.965120	+	0.261806i	$0.0843181\pi$
$137$	3.95862	+	12.1834i	0.338207	+	1.04090i	−0.626913	+	0.779089i	$0.715682\pi$
$138$	0.821463	+	2.52820i	0.0699275	+	0.215215i
$139$	−2.45366	+	7.55158i	−0.208116	+	0.640516i	0.791455	+	0.611228i	$0.209324\pi$
$139$	−2.45366	+	7.55158i	−0.208116	+	0.640516i	−0.999571	+	0.0292885i	$0.990676\pi$
$140$		0			0
$141$	7.46612	+	22.9783i	0.628761	+	1.93513i
$142$	3.92930	−	2.85480i	0.329740	−	0.239570i
$143$	13.5300			1.13144
$144$	−13.5877	+	9.87205i	−1.13231	+	0.822671i
$145$		0			0
$146$	1.60254	+	1.16431i	0.132627	+	0.0963591i
$147$	17.5161	+	12.7262i	1.44470	+	1.04964i
$148$	0.199602	−	0.614310i	0.0164071	−	0.0504960i
$149$	−5.62724			−0.461002			−0.230501	−	0.973072i	$-0.574036\pi$
$149$	−5.62724			−0.461002			−0.230501	+	0.973072i	$0.574036\pi$
$150$		0			0
$151$	−7.36960			−0.599730			−0.299865	−	0.953982i	$-0.596942\pi$
$151$	−7.36960			−0.599730			−0.299865	+	0.953982i	$0.596942\pi$
$152$	1.41086	−	4.34217i	0.114436	−	0.352197i
$153$	19.2521	+	13.9875i	1.55644	+	1.13082i
$154$	−0.0345480	−	0.0251006i	−0.00278396	−	0.00202267i
$155$		0			0
$156$	16.5266	−	12.0073i	1.32319	−	0.961350i
$157$	8.63091			0.688822			0.344411	−	0.938819i	$-0.388079\pi$
$157$	8.63091			0.688822			0.344411	+	0.938819i	$0.388079\pi$
$158$	3.92481	−	2.85154i	0.312241	−	0.226856i
$159$	−8.57591	−	26.3939i	−0.680114	−	2.09317i
$160$		0			0
$161$	0.0126095	−	0.0388082i	0.000993770	−	0.00305851i
$162$	2.23506	+	6.87880i	0.175603	+	0.540450i
$163$	1.46772	+	4.51717i	0.114961	+	0.353812i	0.991939	−	0.126718i	$-0.0404443\pi$
$163$	1.46772	+	4.51717i	0.114961	+	0.353812i	−0.876978	+	0.480530i	$0.840444\pi$
$164$	4.22056	−	12.9895i	0.329570	−	1.01431i
$165$		0			0
$166$	−1.38670	−	4.26782i	−0.107629	−	0.331247i
$167$	−15.0451	+	10.9309i	−1.16422	+	0.845856i	−0.990306	−	0.138904i	$-0.955642\pi$
$167$	−15.0451	+	10.9309i	−1.16422	+	0.845856i	−0.173916	+	0.984761i	$0.555642\pi$
$168$	−0.138203			−0.0106626
$169$	−1.01710	+	0.738965i	−0.0782383	+	0.0568434i
$170$		0			0
$171$	12.9170	+	9.38476i	0.987789	+	0.717671i
$172$	0.247019	+	0.179470i	0.0188350	+	0.0136845i
$173$	4.88114	−	15.0226i	0.371106	−	1.14215i	−0.574963	−	0.818180i	$-0.694983\pi$
$173$	4.88114	−	15.0226i	0.371106	−	1.14215i	0.946068	−	0.323967i	$-0.105017\pi$
$174$	5.97767			0.453166
$175$		0			0
$176$	9.16266			0.690661
$177$	−4.25874	+	13.1070i	−0.320106	+	0.985186i
$178$	6.89636	+	5.01050i	0.516904	+	0.375553i
$179$	−7.58005	−	5.50723i	−0.566560	−	0.411630i	0.267294	−	0.963615i	$-0.413870\pi$
$179$	−7.58005	−	5.50723i	−0.566560	−	0.411630i	−0.833854	+	0.551985i	$0.813870\pi$
$180$		0			0
$181$	4.72975	−	3.43637i	0.351560	−	0.255423i	−0.397963	−	0.917401i	$-0.630283\pi$
$181$	4.72975	−	3.43637i	0.351560	−	0.255423i	0.749523	+	0.661978i	$0.230283\pi$
$182$	0.0449988			0.00333554
$183$	−23.0581	+	16.7527i	−1.70450	+	1.23839i
$184$	−0.995608	−	3.06417i	−0.0733972	−	0.225893i
$185$		0			0
$186$	−2.87797	+	8.85748i	−0.211023	+	0.649462i
$187$	−4.01177	−	12.3470i	−0.293369	−	0.902898i
$188$	−4.22154	−	12.9926i	−0.307888	−	0.947581i
$189$	0.0811349	−	0.249708i	0.00590170	−	0.0181636i
$190$		0			0
$191$	−6.76584	−	20.8231i	−0.489559	−	1.50671i	−0.825268	−	0.564741i	$-0.808976\pi$
$191$	−6.76584	−	20.8231i	−0.489559	−	1.50671i	0.335709	−	0.941966i	$-0.391024\pi$
$192$	6.48242	−	4.70976i	0.467829	−	0.339897i
$193$	−25.2541			−1.81783			−0.908916	−	0.416980i	$-0.863089\pi$
$193$	−25.2541			−1.81783			−0.908916	+	0.416980i	$0.863089\pi$
$194$	−1.12043	+	0.814037i	−0.0804419	+	0.0584445i
$195$		0			0
$196$	−9.90405	−	7.19571i	−0.707432	−	0.513979i
$197$	−11.6934	−	8.49575i	−0.833120	−	0.605297i	0.0873202	−	0.996180i	$-0.472170\pi$
$197$	−11.6934	−	8.49575i	−0.833120	−	0.605297i	−0.920440	+	0.390883i	$0.872170\pi$
$198$	3.64369	−	11.2141i	0.258946	−	0.796953i
$199$	−3.77734			−0.267768			−0.133884	−	0.990997i	$-0.542745\pi$
$199$	−3.77734			−0.267768			−0.133884	+	0.990997i	$0.542745\pi$
$200$		0			0
$201$	−13.8388			−0.976112
$202$	1.60273	−	4.93270i	0.112768	−	0.347064i
$203$	−0.0742337	−	0.0539339i	−0.00521018	−	0.00378542i
$204$	−15.8576	−	11.5212i	−1.11025	−	0.806647i
$205$		0			0
$206$	−7.41364	+	5.38633i	−0.516533	+	0.375283i
$207$	11.2670			0.783113
$208$	−7.81115	+	5.67513i	−0.541605	+	0.393499i
$209$	−2.69166	−	8.28407i	−0.186186	−	0.573021i
$210$		0			0
$211$	−5.84061	+	17.9756i	−0.402084	+	1.23749i	0.521221	+	0.853422i	$0.325477\pi$
$211$	−5.84061	+	17.9756i	−0.402084	+	1.23749i	−0.923305	+	0.384067i	$0.874523\pi$
$212$	4.84904	+	14.9238i	0.333034	+	1.02497i
$213$	−9.26675	−	28.5201i	−0.634947	−	1.95417i
$214$	2.45824	−	7.56567i	0.168042	−	0.517179i
$215$		0			0
$216$	−6.40615	−	19.7161i	−0.435883	−	1.34151i
$217$	0.115657	−	0.0840299i	0.00785132	−	0.00570432i
$218$	2.98644			0.202267
$219$	9.89454	−	7.18881i	0.668611	−	0.485775i
$220$		0			0
$221$	11.0674	+	8.04095i	0.744476	+	0.540893i
$222$	0.463011	+	0.336397i	0.0310753	+	0.0225775i
$223$	−3.50907	+	10.7998i	−0.234984	+	0.723208i	0.762139	+	0.647413i	$0.224149\pi$
$223$	−3.50907	+	10.7998i	−0.234984	+	0.723208i	−0.997123	+	0.0757944i	$0.975851\pi$
$224$	0.119831			0.00800655
$225$		0			0
$226$	1.21655			0.0809239
$227$	3.46027	−	10.6496i	0.229666	−	0.706841i	−0.768118	−	0.640309i	$-0.778806\pi$
$227$	3.46027	−	10.6496i	0.229666	−	0.706841i	0.997784	−	0.0665322i	$-0.0211935\pi$
$228$	−10.6395	−	7.73006i	−0.704619	−	0.511936i
$229$	−7.80676	−	5.67194i	−0.515885	−	0.374813i	0.299166	−	0.954201i	$-0.403291\pi$
$229$	−7.80676	−	5.67194i	−0.515885	−	0.374813i	−0.815052	+	0.579388i	$0.803291\pi$
$230$		0			0
$231$	−0.213310	+	0.154979i	−0.0140348	+	0.0101968i
$232$	−7.24491			−0.475651
$233$	12.5608	−	9.12599i	0.822889	−	0.597864i	−0.0946499	−	0.995511i	$-0.530173\pi$
$233$	12.5608	−	9.12599i	0.822889	−	0.597864i	0.917538	+	0.397647i	$0.130173\pi$
$234$	3.83952	+	11.8168i	0.250997	+	0.772490i
$235$		0			0
$236$	2.40800	−	7.41107i	0.156748	−	0.482420i
$237$	−9.25615	−	28.4875i	−0.601252	−	1.85046i
$238$	−0.0133425	−	0.0410641i	−0.000864868	−	0.00266179i
$239$	4.42951	−	13.6326i	0.286521	−	0.881822i	−0.699417	−	0.714714i	$-0.746557\pi$
$239$	4.42951	−	13.6326i	0.286521	−	0.881822i	0.985938	−	0.167109i	$-0.0534430\pi$
$240$		0			0
$241$	7.82164	+	24.0725i	0.503836	+	1.55065i	0.802718	+	0.596359i	$0.203386\pi$
$241$	7.82164	+	24.0725i	0.503836	+	1.55065i	−0.298882	+	0.954290i	$0.596614\pi$
$242$	−0.745747	+	0.541817i	−0.0479384	+	0.0348293i
$243$	11.5450			0.740613
$244$	13.0377	−	9.47241i	0.834650	−	0.606409i
$245$		0			0
$246$	9.79034	+	7.11309i	0.624209	+	0.453514i
$247$	7.42558	+	5.39500i	0.472479	+	0.343276i
$248$	3.48808	−	10.7352i	0.221493	−	0.681687i
$249$	−27.7068			−1.75585
$250$		0			0
$251$	4.23698			0.267436			0.133718	−	0.991019i	$-0.457308\pi$
$251$	4.23698			0.267436			0.133718	+	0.991019i	$0.457308\pi$
$252$	−0.0844460	+	0.259898i	−0.00531960	+	0.0163720i
$253$	−4.97279	−	3.61294i	−0.312637	−	0.227144i
$254$	6.93374	+	5.03766i	0.435061	+	0.316091i
$255$		0			0
$256$	0.418140	−	0.303797i	0.0261338	−	0.0189873i
$257$	−20.4007			−1.27256			−0.636281	−	0.771458i	$-0.719528\pi$
$257$	−20.4007			−1.27256			−0.636281	+	0.771458i	$0.719528\pi$
$258$	−0.218868	+	0.159017i	−0.0136261	+	0.00989997i
$259$	−0.00271473	−	0.00835509i	−0.000168685	−	0.000519160i
$260$		0			0
$261$	7.82923	−	24.0959i	0.484617	−	1.49150i
$262$	0.741490	+	2.28207i	0.0458094	+	0.140987i
$263$	8.85883	+	27.2647i	0.546259	+	1.68121i	0.717978	+	0.696066i	$0.245068\pi$
$263$	8.85883	+	27.2647i	0.546259	+	1.68121i	−0.171719	+	0.985146i	$0.554932\pi$
$264$	−6.43317	+	19.7993i	−0.395934	+	1.21856i
$265$		0			0
$266$	−0.00895205	−	0.0275516i	−0.000548885	−	0.00168930i
$267$	42.5802	−	30.9363i	2.60586	−	1.89327i
$268$	7.82481			0.477977
$269$	−6.42887	+	4.67085i	−0.391975	+	0.284786i	−0.766264	−	0.642525i	$-0.777887\pi$
$269$	−6.42887	+	4.67085i	−0.391975	+	0.284786i	0.374289	+	0.927312i	$0.377887\pi$
$270$		0			0
$271$	−7.73005	−	5.61621i	−0.469567	−	0.341161i	0.327705	−	0.944780i	$-0.393725\pi$
$271$	−7.73005	−	5.61621i	−0.469567	−	0.341161i	−0.797273	+	0.603619i	$0.793725\pi$
$272$	7.49496	+	5.44541i	0.454449	+	0.330176i
$273$	0.0858561	−	0.264238i	0.00519625	−	0.0159924i
$274$	6.41785			0.387717
$275$		0			0
$276$	−9.28045			−0.558618
$277$	5.31213	−	16.3491i	0.319175	−	0.982320i	−0.654826	−	0.755779i	$-0.727258\pi$
$277$	5.31213	−	16.3491i	0.319175	−	0.982320i	0.974002	−	0.226541i	$-0.0727417\pi$
$278$	3.21823	+	2.33818i	0.193017	+	0.140235i
$279$	31.9349	+	23.2021i	1.91189	+	1.38907i
$280$		0			0
$281$	−22.0200	+	15.9985i	−1.31360	+	0.954388i	−0.313614	+	0.949550i	$0.601540\pi$
$281$	−22.0200	+	15.9985i	−1.31360	+	0.954388i	−0.999988	+	0.00483787i	$0.998460\pi$
$282$	12.1043			0.720803
$283$	2.81458	−	2.04491i	0.167309	−	0.121557i	−0.500980	−	0.865459i	$-0.667027\pi$
$283$	2.81458	−	2.04491i	0.167309	−	0.121557i	0.668289	+	0.743902i	$0.267027\pi$
$284$	5.23967	+	16.1260i	0.310917	+	0.956904i
$285$		0			0
$286$	2.09464	−	6.44664i	0.123859	−	0.381198i
$287$	−0.0574029	−	0.176668i	−0.00338838	−	0.0104284i
$288$	10.2246	+	31.4680i	0.602488	+	1.85427i
$289$	−1.19703	+	3.68407i	−0.0704134	+	0.216710i
$290$		0			0
$291$	2.64238	+	8.13241i	0.154899	+	0.476730i
$292$	−5.59464	+	4.06474i	−0.327401	+	0.237871i
$293$	23.4941			1.37254			0.686271	−	0.727346i	$-0.259246\pi$
$293$	23.4941			1.37254			0.686271	+	0.727346i	$0.259246\pi$
$294$	8.77536	−	6.37567i	0.511790	−	0.371837i
$295$		0			0
$296$	−0.561167	−	0.407712i	−0.0326172	−	0.0236978i
$297$	−31.9970	−	23.2472i	−1.85665	−	1.34894i
$298$	−0.871177	+	2.68121i	−0.0504659	+	0.155318i
$299$	6.47706			0.374578
$300$		0			0
$301$	0.00415276			0.000239361
$302$	−1.14092	+	3.51139i	−0.0656525	+	0.202058i
$303$	−25.9074	−	18.8228i	−1.48834	−	1.08134i
$304$	5.02867	+	3.65354i	0.288414	+	0.209545i
$305$		0			0
$306$	9.64510	−	7.00758i	0.551374	−	0.400596i
$307$	1.11253			0.0634952			0.0317476	−	0.999496i	$-0.489893\pi$
$307$	1.11253			0.0634952			0.0317476	+	0.999496i	$0.489893\pi$
$308$	0.120611	−	0.0876291i	0.00687245	−	0.00499313i
$309$	17.4841	+	53.8106i	0.994637	+	3.06118i
$310$		0			0
$311$	−4.55890	+	14.0308i	−0.258511	+	0.795616i	0.734606	+	0.678494i	$0.237367\pi$
$311$	−4.55890	+	14.0308i	−0.258511	+	0.795616i	−0.993117	+	0.117122i	$0.962633\pi$
$312$	−6.77892	−	20.8634i	−0.383781	−	1.18116i
$313$	1.52912	+	4.70615i	0.0864310	+	0.266007i	0.984926	−	0.172977i	$-0.0553385\pi$
$313$	1.52912	+	4.70615i	0.0864310	+	0.266007i	−0.898495	+	0.438984i	$0.855339\pi$
$314$	1.33619	−	4.11237i	0.0754055	−	0.232074i
$315$		0			0
$316$	5.23367	+	16.1076i	0.294417	+	0.906123i
$317$	−18.3530	+	13.3342i	−1.03080	+	0.748923i	−0.968470	−	0.249132i	$-0.919855\pi$
$317$	−18.3530	+	13.3342i	−1.03080	+	0.748923i	−0.0623350	+	0.998055i	$0.519855\pi$
$318$	−13.9036			−0.779673
$319$	−11.1822	+	8.12434i	−0.626083	+	0.454876i
$320$		0			0
$321$	−39.7362	−	28.8700i	−2.21786	−	1.61137i
$322$	−0.0165388	−	0.0120161i	−0.000921669	−	0.000669632i
$323$	2.72151	−	8.37595i	0.151429	−	0.466050i
$324$	−25.2505			−1.40281
$325$		0			0
$326$	2.37952			0.131789
$327$	5.69802	−	17.5367i	0.315101	−	0.969782i
$328$	−11.8658	−	8.62103i	−0.655181	−	0.476017i
$329$	−0.150318	−	0.109212i	−0.00828728	−	0.00602106i
$330$		0			0
$331$	−1.40169	+	1.01838i	−0.0770437	+	0.0559755i	−0.625640	−	0.780112i	$-0.715162\pi$
$331$	−1.40169	+	1.01838i	−0.0770437	+	0.0559755i	0.548597	+	0.836087i	$0.315162\pi$
$332$	15.6662			0.859793
$333$	1.96244	−	1.42579i	0.107541	−	0.0781330i
$334$	2.87904	+	8.86076i	0.157534	+	0.484839i
$335$		0			0
$336$	0.0581425	−	0.178944i	0.00317194	−	0.00976221i
$337$	4.32038	+	13.2968i	0.235346	+	0.724321i	0.997075	+	0.0764255i	$0.0243507\pi$
$337$	4.32038	+	13.2968i	0.235346	+	0.724321i	−0.761729	+	0.647896i	$0.775649\pi$
$338$	0.194633	+	0.599018i	0.0105866	+	0.0325823i
$339$	2.32114	−	7.14373i	0.126067	−	0.387994i
$340$		0			0
$341$	−6.65462	−	20.4808i	−0.360368	−	1.10910i
$342$	6.47129	−	4.70167i	0.349927	−	0.254237i
$343$	−0.333017			−0.0179812
$344$	0.265267	−	0.192728i	0.0143022	−	0.0103912i
$345$		0			0
$346$	−6.40213	−	4.65142i	−0.344181	−	0.250062i
$347$	−4.11121	−	2.98697i	−0.220701	−	0.160349i	0.471941	−	0.881630i	$-0.343553\pi$
$347$	−4.11121	−	2.98697i	−0.220701	−	0.160349i	−0.692642	+	0.721281i	$0.743553\pi$
$348$	−6.44879	+	19.8473i	−0.345691	+	1.06393i
$349$	−8.88643			−0.475680			−0.237840	−	0.971304i	$-0.576439\pi$
$349$	−8.88643			−0.475680			−0.237840	+	0.971304i	$0.576439\pi$
$350$		0			0
$351$	41.6761			2.22450
$352$	5.57799	−	17.1673i	0.297308	−	0.915020i
$353$	−7.61641	−	5.53364i	−0.405380	−	0.294526i	0.366349	−	0.930478i	$-0.380608\pi$
$353$	−7.61641	−	5.53364i	−0.405380	−	0.294526i	−0.771729	+	0.635952i	$0.780608\pi$
$354$	5.58579	+	4.05831i	0.296881	+	0.215697i
$355$		0			0
$356$	−24.0760	+	17.4922i	−1.27602	+	0.927085i
$357$	−0.266590			−0.0141094
$358$	−3.79752	+	2.75906i	−0.200705	+	0.145821i
$359$	2.81668	+	8.66886i	0.148659	+	0.457525i	0.997463	−	0.0711818i	$-0.0226770\pi$
$359$	2.81668	+	8.66886i	0.148659	+	0.457525i	−0.848804	+	0.528707i	$0.822677\pi$
$360$		0			0
$361$	−4.04535	+	12.4503i	−0.212913	+	0.655280i
$362$	−0.905090	−	2.78558i	−0.0475705	−	0.146407i
$363$	1.75875	+	5.41287i	0.0923103	+	0.284102i
$364$	−0.0485453	+	0.149407i	−0.00254447	+	0.00783106i
$365$		0			0
$366$	4.41241	+	13.5800i	0.230641	+	0.709839i
$367$	14.4639	−	10.5087i	0.755012	−	0.548548i	−0.142365	−	0.989814i	$-0.545471\pi$
$367$	14.4639	−	10.5087i	0.755012	−	0.548548i	0.897376	+	0.441266i	$0.145471\pi$
$368$	4.38633			0.228653
$369$	41.4956	−	30.1483i	2.16017	−	1.56946i
$370$		0			0
$371$	0.172661	+	0.125446i	0.00896413	+	0.00651282i
$372$	−26.3042	−	19.1111i	−1.36381	−	0.990865i
$373$	−0.949901	+	2.92350i	−0.0491840	+	0.151373i	−0.972632	−	0.232350i	$-0.925358\pi$
$373$	−0.949901	+	2.92350i	−0.0491840	+	0.151373i	0.923448	+	0.383723i	$0.125358\pi$
$374$	−6.50402			−0.336315
$375$		0			0
$376$	−14.6704			−0.756567
$377$	4.50077	−	13.8520i	0.231802	−	0.713412i
$378$	−0.106417	−	0.0773166i	−0.00547351	−	0.00397674i
$379$	−20.7000	−	15.0394i	−1.06329	−	0.772524i	−0.0885946	−	0.996068i	$-0.528238\pi$
$379$	−20.7000	−	15.0394i	−1.06329	−	0.772524i	−0.974694	+	0.223543i	$0.928238\pi$
$380$		0			0
$381$	42.8110	−	31.1040i	2.19327	−	1.59351i
$382$	−10.9690			−0.561224
$383$	1.80030	−	1.30799i	0.0919909	−	0.0668353i	−0.540839	−	0.841126i	$-0.681893\pi$
$383$	1.80030	−	1.30799i	0.0919909	−	0.0668353i	0.632830	+	0.774291i	$0.281893\pi$
$384$	−10.8708	−	33.4570i	−0.554750	−	1.70734i
$385$		0			0
$386$	−3.90970	+	12.0328i	−0.198998	+	0.612454i
$387$	0.354333	+	1.09053i	0.0180118	+	0.0554345i
$388$	−1.49407	−	4.59828i	−0.0758500	−	0.233442i
$389$	1.43511	−	4.41683i	0.0727632	−	0.223942i	−0.908061	−	0.418839i	$-0.862437\pi$
$389$	1.43511	−	4.41683i	0.0727632	−	0.223942i	0.980824	+	0.194897i	$0.0624372\pi$
$390$		0			0
$391$	−1.92050	−	5.91070i	−0.0971240	−	0.298917i
$392$	−10.6357	+	7.72728i	−0.537183	+	0.390287i
$393$	14.8153			0.747333
$394$	−5.85827	+	4.25628i	−0.295135	+	0.214428i
$395$		0			0
$396$	33.3028	+	24.1959i	1.67353	+	1.21589i
$397$	30.6983	+	22.3036i	1.54070	+	1.11939i	0.949892	+	0.312578i	$0.101193\pi$
$397$	30.6983	+	22.3036i	1.54070	+	1.11939i	0.590812	+	0.806809i	$0.298807\pi$
$398$	−0.584786	+	1.79979i	−0.0293127	+	0.0902151i
$399$	−0.178866			−0.00895449
$400$		0			0
$401$	−16.7187			−0.834890			−0.417445	−	0.908702i	$-0.637074\pi$
$401$	−16.7187			−0.834890			−0.417445	+	0.908702i	$0.637074\pi$
$402$	−2.14244	+	6.59375i	−0.106855	+	0.328866i
$403$	18.3584	+	13.3381i	0.914495	+	0.664420i
$404$	14.6487	+	10.6429i	0.728801	+	0.529505i
$405$		0			0
$406$	−0.0371903	+	0.0270203i	−0.00184572	+	0.00134100i
$407$	−1.32334			−0.0655955
$408$	−17.0291	+	12.3723i	−0.843064	+	0.612522i
$409$	0.146206	+	0.449975i	0.00722941	+	0.0222498i	0.954606	−	0.297871i	$-0.0962765\pi$
$409$	0.146206	+	0.449975i	0.00722941	+	0.0222498i	−0.947377	+	0.320121i	$0.896277\pi$
$410$		0			0
$411$	12.2450	−	37.6863i	0.604002	−	1.85893i
$412$	−9.88599	−	30.4259i	−0.487048	−	1.49898i
$413$	−0.0327507	−	0.100796i	−0.00161156	−	0.00495986i
$414$	1.74430	−	5.36840i	0.0857276	−	0.263842i
$415$		0			0
$416$	5.87778	+	18.0899i	0.288182	+	0.886932i
$417$	19.8703	−	14.4366i	0.973054	−	0.706965i
$418$	−4.36381			−0.213441
$419$	−19.6064	+	14.2449i	−0.957835	+	0.695908i	−0.952647	−	0.304078i	$-0.901651\pi$
$419$	−19.6064	+	14.2449i	−0.957835	+	0.695908i	−0.00518829	+	0.999987i	$0.501651\pi$
$420$		0			0
$421$	25.3612	+	18.4260i	1.23603	+	0.898028i	0.997327	−	0.0730653i	$-0.0232782\pi$
$421$	25.3612	+	18.4260i	1.23603	+	0.898028i	0.238702	+	0.971093i	$0.423278\pi$
$422$	7.66059	+	5.56574i	0.372912	+	0.270936i
$423$	15.8536	−	48.7923i	0.770828	−	2.37236i
$424$	16.8510			0.818359
$425$		0			0
$426$	−15.0236			−0.727895
$427$	0.0677310	−	0.208455i	0.00327773	−	0.0100878i
$428$	22.4679	+	16.3239i	1.08603	+	0.789045i
$429$	−33.8589	−	24.5999i	−1.63472	−	1.18769i
$430$		0			0
$431$	1.61857	−	1.17596i	0.0779639	−	0.0566441i	−0.548121	−	0.836399i	$-0.684657\pi$
$431$	1.61857	−	1.17596i	0.0779639	−	0.0566441i	0.626084	+	0.779755i	$0.284657\pi$
$432$	28.2234			1.35790
$433$	−5.72180	+	4.15713i	−0.274972	+	0.199779i	−0.716721	−	0.697360i	$-0.754358\pi$
$433$	−5.72180	+	4.15713i	−0.274972	+	0.199779i	0.441749	+	0.897138i	$0.354358\pi$
$434$	−0.0221323	−	0.0681161i	−0.00106238	−	0.00326968i
$435$		0			0
$436$	−3.22181	+	9.91572i	−0.154297	+	0.474877i
$437$	−1.28854	−	3.96573i	−0.0616394	−	0.189707i
$438$	−1.89343	−	5.82737i	−0.0904715	−	0.278443i
$439$	4.00549	−	12.3276i	0.191171	−	0.588365i	−0.808829	−	0.588045i	$-0.799898\pi$
$439$	4.00549	−	12.3276i	0.191171	−	0.588365i	1.00000		0.000320575i	$-0.000102042\pi$
$440$		0			0
$441$	−14.2067	−	43.7238i	−0.676511	−	2.08209i
$442$	5.54466	−	4.02843i	0.263733	−	0.191613i
$443$	21.8687			1.03901			0.519506	−	0.854467i	$-0.326116\pi$
$443$	21.8687			1.03901			0.519506	+	0.854467i	$0.326116\pi$
$444$	−1.61642	+	1.17440i	−0.0767121	+	0.0557346i
$445$		0			0
$446$	4.60252	+	3.34392i	0.217936	+	0.158339i
$447$	14.0822	+	10.2313i	0.666063	+	0.483923i
$448$	−0.0190415	+	0.0586038i	−0.000899628	+	0.00276877i
$449$	0.399626			0.0188595			0.00942976	−	0.999956i	$-0.496998\pi$
$449$	0.399626			0.0188595			0.00942976	+	0.999956i	$0.496998\pi$
$450$		0			0
$451$	−27.9819			−1.31762
$452$	−1.31243	+	4.03925i	−0.0617317	+	0.189991i
$453$	18.4424	+	13.3992i	0.866500	+	0.629549i
$454$	−4.53852	−	3.29743i	−0.213003	−	0.154756i
$455$		0			0
$456$	−11.4255	+	8.30110i	−0.535047	+	0.388735i
$457$	−35.2247			−1.64774			−0.823872	−	0.566777i	$-0.808190\pi$
$457$	−35.2247			−1.64774			−0.823872	+	0.566777i	$0.808190\pi$
$458$	−3.91110	+	2.84158i	−0.182754	+	0.132778i
$459$	−12.3573	−	38.0319i	−0.576790	−	1.77518i
$460$		0			0
$461$	−4.93238	+	15.1803i	−0.229724	+	0.707017i	0.768054	+	0.640385i	$0.221225\pi$
$461$	−4.93238	+	15.1803i	−0.229724	+	0.707017i	−0.997778	+	0.0666319i	$0.978775\pi$
$462$	0.0408192	+	0.125628i	0.00189908	+	0.00584477i
$463$	−9.41981	−	28.9912i	−0.437776	−	1.34734i	−0.890215	−	0.455540i	$-0.849446\pi$
$463$	−9.41981	−	28.9912i	−0.437776	−	1.34734i	0.452440	−	0.891795i	$-0.350554\pi$
$464$	3.04797	−	9.38067i	0.141498	−	0.435487i
$465$		0			0
$466$	−2.40366	−	7.39769i	−0.111347	−	0.342691i
$467$	−5.37719	+	3.90676i	−0.248827	+	0.180783i	−0.705207	−	0.709002i	$-0.749146\pi$
$467$	−5.37719	+	3.90676i	−0.248827	+	0.180783i	0.456380	+	0.889785i	$0.349146\pi$
$468$	−43.3769			−2.00510
$469$	0.0860984	−	0.0625542i	0.00397566	−	0.00288848i
$470$		0			0
$471$	−21.5988	−	15.6925i	−0.995222	−	0.723071i
$472$	−6.76995	−	4.91865i	−0.311612	−	0.226399i
$473$	0.193306	−	0.594934i	0.00888821	−	0.0273551i
$474$	−15.0064			−0.689267
$475$		0			0
$476$	0.150737			0.00690902
$477$	−18.2101	+	56.0450i	−0.833784	+	2.56612i
$478$	−5.80978	−	4.22105i	−0.265733	−	0.193067i
$479$	−17.9932	−	13.0728i	−0.822129	−	0.597312i	0.0951925	−	0.995459i	$-0.469653\pi$
$479$	−17.9932	−	13.0728i	−0.822129	−	0.597312i	−0.917322	+	0.398147i	$0.869653\pi$
$480$		0			0
$481$	1.12814	−	0.819644i	0.0514389	−	0.0373725i
$482$	12.6807			0.577591
$483$	−0.102115	+	0.0741910i	−0.00464640	+	0.00337581i
$484$	−0.994443	−	3.06058i	−0.0452020	−	0.139117i
$485$		0			0
$486$	1.78733	−	5.50084i	0.0810751	−	0.249523i
$487$	3.14737	+	9.68660i	0.142621	+	0.438942i	0.996697	−	0.0812055i	$-0.0258770\pi$
$487$	3.14737	+	9.68660i	0.142621	+	0.438942i	−0.854077	+	0.520147i	$0.825877\pi$
$488$	−5.34782	−	16.4589i	−0.242085	−	0.745060i
$489$	4.54003	−	13.9728i	0.205307	−	0.631871i
$490$		0			0
$491$	2.05189	+	6.31505i	0.0926003	+	0.284994i	0.986621	−	0.163032i	$-0.0521272\pi$
$491$	2.05189	+	6.31505i	0.0926003	+	0.284994i	−0.894021	+	0.448026i	$0.852127\pi$
$492$	−34.1792	+	24.8326i	−1.54092	+	1.11954i
$493$	−13.9752			−0.629413
$494$	3.72014	−	2.70284i	0.167377	−	0.121606i
$495$		0			0
$496$	12.4325	+	9.03270i	0.558234	+	0.405580i
$497$	0.186570	+	0.135551i	0.00836882	+	0.00608030i
$498$	−4.28941	+	13.2014i	−0.192213	+	0.591571i
$499$	1.08397			0.0485253			0.0242626	−	0.999706i	$-0.492276\pi$
$499$	1.08397			0.0485253			0.0242626	+	0.999706i	$0.492276\pi$
$500$		0			0
$501$	57.5244			2.57000
$502$	0.655945	−	2.01879i	0.0292762	−	0.0901030i
$503$	1.60673	+	1.16736i	0.0716405	+	0.0520498i	0.623029	−	0.782199i	$-0.285902\pi$
$503$	1.60673	+	1.16736i	0.0716405	+	0.0520498i	−0.551389	+	0.834249i	$0.685902\pi$
$504$	0.237415	+	0.172492i	0.0105753	+	0.00768339i
$505$		0			0
$506$	−2.49132	+	1.81005i	−0.110752	+	0.0804664i
$507$	3.88885			0.172710
$508$	−24.2065	+	17.5870i	−1.07399	+	0.780298i
$509$	0.713568	+	2.19614i	0.0316283	+	0.0973420i	0.965624	−	0.259941i	$-0.0837031\pi$
$509$	0.713568	+	2.19614i	0.0316283	+	0.0973420i	−0.933996	+	0.357283i	$0.883703\pi$
$510$		0			0
$511$	−0.0290643	+	0.0894508i	−0.00128573	+	0.00395707i
$512$	6.94871	+	21.3859i	0.307093	+	0.945134i
$513$	−8.29102	−	25.5171i	−0.366057	−	1.12661i
$514$	−3.15832	+	9.72031i	−0.139308	+	0.428744i
$515$		0			0
$516$	−0.291858	−	0.898246i	−0.0128483	−	0.0395431i
$517$	−22.6431	+	16.4512i	−0.995842	+	0.723522i
$518$	−0.00440122			−0.000193379
$519$	−39.5287	+	28.7193i	−1.73512	+	1.26064i
$520$		0			0
$521$	8.93539	+	6.49194i	0.391467	+	0.284417i	0.766056	−	0.642774i	$-0.222216\pi$
$521$	8.93539	+	6.49194i	0.391467	+	0.284417i	−0.374590	+	0.927191i	$0.622216\pi$
$522$	−10.2689	−	7.46077i	−0.449456	−	0.326549i
$523$	8.03522	−	24.7299i	0.351356	−	1.08136i	−0.606737	−	0.794903i	$-0.707522\pi$
$523$	8.03522	−	24.7299i	0.351356	−	1.08136i	0.958093	−	0.286459i	$-0.0924781\pi$
$524$	−8.37696			−0.365949
$525$		0			0
$526$	14.3623			0.626224
$527$	6.72842	−	20.7080i	0.293095	−	0.902053i
$528$	−22.9295	−	16.6593i	−0.997880	−	0.725002i
$529$	16.2268	+	11.7895i	0.705514	+	0.512586i
$530$		0			0
$531$	23.6749	−	17.2009i	1.02741	−	0.746453i
$532$	0.101136			0.00438478
$533$	23.8545	−	17.3313i	1.03325	−	0.750702i
$534$	−8.14818	−	25.0775i	−0.352606	−	1.08521i
$535$		0			0
$536$	2.59663	−	7.99159i	0.112157	−	0.345184i
$537$	8.95597	+	27.5637i	0.386479	+	1.18946i
$538$	1.23023	+	3.78627i	0.0530392	+	0.163238i
$539$	−7.75045	+	23.8534i	−0.333836	+	1.02744i
$540$		0			0
$541$	−0.00563620	−	0.0173465i	−0.000242319	−	0.000745782i	0.950935	−	0.309390i	$-0.100125\pi$
$541$	−0.00563620	−	0.0173465i	−0.000242319	−	0.000745782i	−0.951178	+	0.308644i	$0.900125\pi$
$542$	−3.87267	+	2.81366i	−0.166346	+	0.120857i
$543$	−18.0841			−0.776063
$544$	14.7653	−	10.7276i	0.633058	−	0.459944i
$545$		0			0
$546$	−0.112609	−	0.0818156i	−0.00481924	−	0.00350138i
$547$	8.05820	+	5.85462i	0.344544	+	0.250326i	0.746576	−	0.665300i	$-0.231696\pi$
$547$	8.05820	+	5.85462i	0.344544	+	0.250326i	−0.402033	+	0.915625i	$0.631696\pi$
$548$	−6.92366	+	21.3088i	−0.295764	+	0.910268i
$549$	60.5199			2.58293
$550$		0			0
$551$	−9.37656			−0.399455
$552$	−3.07967	+	9.47825i	−0.131080	+	0.403421i
$553$	0.186357	+	0.135396i	0.00792470	+	0.00575763i
$554$	−6.96743	−	5.06214i	−0.296018	−	0.215070i
$555$		0			0
$556$	−11.2352	+	8.16286i	−0.476479	+	0.346182i
$557$	−34.9291			−1.47999			−0.739996	−	0.672611i	$-0.765173\pi$
$557$	−34.9291			−1.47999			−0.739996	+	0.672611i	$0.765173\pi$
$558$	15.9990	−	11.6240i	0.677294	−	0.492083i
$559$	0.203695	+	0.626909i	0.00861538	+	0.0265154i
$560$		0			0
$561$	−12.4094	+	38.1923i	−0.523926	+	1.61248i
$562$	4.21377	+	12.9686i	0.177747	+	0.547049i
$563$	4.88059	+	15.0209i	0.205692	+	0.633055i	0.999684	+	0.0251273i	$0.00799911\pi$
$563$	4.88059	+	15.0209i	0.205692	+	0.633055i	−0.793992	+	0.607928i	$0.792001\pi$
$564$	−13.0583	+	40.1894i	−0.549854	+	1.69228i
$565$		0			0
$566$	−0.538601	−	1.65764i	−0.0226391	−	0.0696759i
$567$	−0.277838	+	0.201861i	−0.0116681	+	0.00847736i
$568$	18.2085			0.764012
$569$	11.7797	−	8.55845i	0.493831	−	0.358789i	−0.312825	−	0.949811i	$-0.601275\pi$
$569$	11.7797	−	8.55845i	0.493831	−	0.358789i	0.806656	+	0.591022i	$0.201275\pi$
$570$		0			0
$571$	−22.3401	−	16.2310i	−0.934903	−	0.679246i	0.0122857	−	0.999925i	$-0.496089\pi$
$571$	−22.3401	−	16.2310i	−0.934903	−	0.679246i	−0.947188	+	0.320678i	$0.896089\pi$
$572$	19.1447	+	13.9094i	0.800480	+	0.581583i
$573$	−20.9285	+	64.4112i	−0.874299	+	2.69082i
$574$	−0.0930636			−0.00388440
$575$		0			0
$576$	−17.0142			−0.708927
$577$	−8.39043	+	25.8231i	−0.349298	+	1.07503i	0.609944	+	0.792444i	$0.291192\pi$
$577$	−8.39043	+	25.8231i	−0.349298	+	1.07503i	−0.959242	+	0.282585i	$0.908808\pi$
$578$	1.57003	+	1.14069i	0.0653047	+	0.0474466i
$579$	63.1984	+	45.9163i	2.62643	+	1.90822i
$580$		0			0
$581$	0.172379	−	0.125241i	0.00715148	−	0.00519586i
$582$	4.28392			0.177574
$583$	26.0088	−	18.8965i	1.07718	−	0.782614i
$584$	2.29483	+	7.06275i	0.0949605	+	0.292258i
$585$		0			0
$586$	3.63723	−	11.1942i	0.150253	−	0.462430i
$587$	−3.30761	−	10.1798i	−0.136520	−	0.420165i	0.859304	−	0.511466i	$-0.170897\pi$
$587$	−3.30761	−	10.1798i	−0.136520	−	0.420165i	−0.995823	+	0.0913013i	$0.970897\pi$
$588$	11.7018	+	36.0145i	0.482575	+	1.48521i
$589$	4.51437	−	13.8938i	0.186011	−	0.572484i
$590$		0			0
$591$	13.8160	+	42.5212i	0.568313	+	1.74909i
$592$	0.763989	−	0.555070i	0.0313997	−	0.0228132i
$593$	−3.84629			−0.157948			−0.0789740	−	0.996877i	$-0.525164\pi$
$593$	−3.84629			−0.157948			−0.0789740	+	0.996877i	$0.525164\pi$
$594$	−16.0301	+	11.6466i	−0.657725	+	0.477865i
$595$		0			0
$596$	−7.96242	−	5.78504i	−0.326154	−	0.236964i
$597$	9.45278	+	6.86784i	0.386876	+	0.281082i
$598$	1.00274	−	3.08612i	0.0410051	−	0.126201i
$599$	46.1423			1.88532			0.942662	−	0.333750i	$-0.108314\pi$
$599$	46.1423			1.88532			0.942662	+	0.333750i	$0.108314\pi$
$600$		0			0
$601$	−13.3119			−0.543005			−0.271503	−	0.962438i	$-0.587521\pi$
$601$	−13.3119			−0.543005			−0.271503	+	0.962438i	$0.587521\pi$
$602$	0.000642906	−	0.00197866i	2.62029e−5	−	8.06442e-5i
$603$	23.7732	+	17.2723i	0.968121	+	0.703381i
$604$	−10.4278	−	7.57626i	−0.424302	−	0.308274i
$605$		0			0
$606$	−12.9793	+	9.43003i	−0.527249	+	0.383069i
$607$	34.0838			1.38342			0.691709	−	0.722176i	$-0.256858\pi$
$607$	34.0838			1.38342			0.691709	+	0.722176i	$0.256858\pi$
$608$	9.90666	−	7.19761i	0.401768	−	0.291902i
$609$	0.0877085	+	0.269939i	0.00355413	+	0.0109385i
$610$		0			0
$611$	9.11373	−	28.0492i	0.368702	−	1.13475i
$612$	12.8616	+	39.5839i	0.519900	+	1.60009i
$613$	7.87404	+	24.2338i	0.318029	+	0.978794i	0.974490	+	0.224433i	$0.0720530\pi$
$613$	7.87404	+	24.2338i	0.318029	+	0.978794i	−0.656460	+	0.754361i	$0.727947\pi$
$614$	0.172235	−	0.530084i	0.00695083	−	0.0213924i
$615$		0			0
$616$	−0.0494726	−	0.152261i	−0.00199331	−	0.00613477i
$617$	21.7992	−	15.8381i	0.877604	−	0.637617i	−0.0550123	−	0.998486i	$-0.517520\pi$
$617$	21.7992	−	15.8381i	0.877604	−	0.637617i	0.932617	+	0.360869i	$0.117520\pi$
$618$	28.3459			1.14024
$619$	−31.8178	+	23.1170i	−1.27886	+	0.929149i	−0.999518	−	0.0310417i	$-0.990118\pi$
$619$	−31.8178	+	23.1170i	−1.27886	+	0.929149i	−0.279346	+	0.960191i	$0.590118\pi$
$620$		0			0
$621$	−15.3175	−	11.1288i	−0.614671	−	0.446584i
$622$	5.97948	+	4.34435i	0.239755	+	0.174193i
$623$	−0.125075	+	0.384942i	−0.00501104	+	0.0154224i
$624$	29.8657			1.19559
$625$		0			0
$626$	2.47906			0.0990833
$627$	−8.32599	+	25.6248i	−0.332508	+	1.02335i
$628$	12.2126	+	8.87294i	0.487334	+	0.354069i
$629$	−1.08248	−	0.786466i	−0.0431612	−	0.0313584i
$630$		0			0
$631$	−9.09686	+	6.60926i	−0.362140	+	0.263110i	−0.753944	−	0.656938i	$-0.771851\pi$
$631$	−9.09686	+	6.60926i	−0.362140	+	0.263110i	0.391804	+	0.920049i	$0.371851\pi$
$632$	18.1877			0.723467
$633$	47.2988	−	34.3646i	1.87996	−	1.36587i
$634$	3.51204	+	10.8089i	0.139481	+	0.429278i
$635$		0			0
$636$	14.9993	−	46.1632i	0.594763	−	1.83049i
$637$	−8.16700	−	25.1354i	−0.323588	−	0.995902i
$638$	2.13983	+	6.58573i	0.0847169	+	0.260732i
$639$	−19.6771	+	60.5598i	−0.778413	+	2.39571i
$640$		0			0
$641$	5.40078	+	16.6219i	0.213318	+	0.656525i	0.999269	+	0.0382358i	$0.0121738\pi$
$641$	5.40078	+	16.6219i	0.213318	+	0.656525i	−0.785951	+	0.618289i	$0.787826\pi$
$642$	−19.9074	+	14.4636i	−0.785683	+	0.570832i
$643$	−8.72320			−0.344009			−0.172005	−	0.985096i	$-0.555024\pi$
$643$	−8.72320			−0.344009			−0.172005	+	0.985096i	$0.555024\pi$
$644$	0.0577386	−	0.0419496i	0.00227522	−	0.00165304i
$645$		0			0
$646$	−3.56955	−	2.59343i	−0.140442	−	0.102037i
$647$	−20.2783	−	14.7330i	−0.797222	−	0.579216i	0.112876	−	0.993609i	$-0.463994\pi$
$647$	−20.2783	−	14.7330i	−0.797222	−	0.579216i	−0.910098	+	0.414393i	$0.863994\pi$
$648$	−8.37925	+	25.7887i	−0.329168	+	1.01308i
$649$	−15.9648			−0.626674
$650$		0			0
$651$	−0.442212			−0.0173317
$652$	−2.56705	+	7.90058i	−0.100534	+	0.309411i
$653$	−24.2525	−	17.6205i	−0.949073	−	0.689542i	0.00151446	−	0.999999i	$-0.499518\pi$
$653$	−24.2525	−	17.6205i	−0.949073	−	0.689542i	−0.950587	+	0.310457i	$0.899518\pi$
$654$	−7.47357	−	5.42986i	−0.292240	−	0.212324i
$655$		0			0
$656$	16.1545	−	11.7369i	0.630727	−	0.458250i
$657$	−25.9699			−1.01318
$658$	−0.0753075	+	0.0547141i	−0.00293579	+	0.00213298i
$659$	−1.34917	−	4.15233i	−0.0525563	−	0.161752i	0.921333	−	0.388773i	$-0.127101\pi$
$659$	−1.34917	−	4.15233i	−0.0525563	−	0.161752i	−0.973890	+	0.227022i	$0.927101\pi$
$660$		0			0
$661$	−6.01126	+	18.5008i	−0.233811	+	0.719596i	0.763466	+	0.645848i	$0.223496\pi$
$661$	−6.01126	+	18.5008i	−0.233811	+	0.719596i	−0.997277	+	0.0737481i	$0.976504\pi$
$662$	0.268228	+	0.825521i	0.0104250	+	0.0320848i
$663$	−13.0764	−	40.2449i	−0.507844	−	1.56298i
$664$	5.19874	−	16.0001i	0.201750	−	0.620924i
$665$		0			0
$666$	−0.375534	−	1.15577i	−0.0145516	−	0.0447853i
$667$	−5.35311	+	3.88926i	−0.207273	+	0.150593i
$668$	−32.5258			−1.25846
$669$	28.4173	−	20.6464i	1.09868	−	0.798235i
$670$		0			0
$671$	−26.7109	−	19.4066i	−1.03116	−	0.749184i
$672$	−0.299877	−	0.217873i	−0.0115680	−	0.00840465i
$673$	−11.1949	+	34.4544i	−0.431532	+	1.32812i	0.465067	+	0.885276i	$0.346030\pi$
$673$	−11.1949	+	34.4544i	−0.431532	+	1.32812i	−0.896599	+	0.442844i	$0.853970\pi$
$674$	7.00436			0.269798
$675$		0			0
$676$	−2.19886			−0.0845715
$677$	0.630538	−	1.94060i	0.0242336	−	0.0745832i	−0.938208	−	0.346071i	$-0.887516\pi$
$677$	0.630538	−	1.94060i	0.0242336	−	0.0745832i	0.962442	+	0.271488i	$0.0875156\pi$
$678$	−3.04442	−	2.21190i	−0.116920	−	0.0849476i
$679$	−0.0531999	−	0.0386520i	−0.00204162	−	0.00148333i
$680$		0			0
$681$	−28.0222	+	20.3593i	−1.07381	+	0.780170i
$682$	−10.7887			−0.413121
$683$	−12.8719	+	9.35197i	−0.492529	+	0.357843i	−0.806156	−	0.591703i	$-0.798456\pi$
$683$	−12.8719	+	9.35197i	−0.492529	+	0.357843i	0.313627	+	0.949546i	$0.398456\pi$
$684$	8.62937	+	26.5585i	0.329952	+	1.01549i
$685$		0			0
$686$	−0.0515557	+	0.158672i	−0.00196841	+	0.00605814i
$687$	9.22384	+	28.3880i	0.351911	+	1.08307i
$688$	0.137944	+	0.424548i	0.00525907	+	0.0161857i
$689$	−10.4684	+	32.2185i	−0.398815	+	1.22743i
$690$		0			0
$691$	−1.20568	−	3.71070i	−0.0458662	−	0.141162i	0.925501	−	0.378746i	$-0.123644\pi$
$691$	−1.20568	−	3.71070i	−0.0458662	−	0.141162i	−0.971367	+	0.237584i	$0.923644\pi$
$692$	22.3506	−	16.2386i	0.849641	−	0.617300i
$693$	0.559869			0.0212677
$694$	−2.05967	+	1.49644i	−0.0781840	+	0.0568040i
$695$		0			0
$696$	18.1304	+	13.1725i	0.687230	+	0.499301i
$697$	−22.8889	−	16.6298i	−0.866979	−	0.629897i
$698$	−1.37575	+	4.23411i	−0.0520728	+	0.160264i
$699$	−48.0261			−1.81651
$700$		0			0
$701$	30.3587			1.14663			0.573316	−	0.819335i	$-0.305657\pi$
$701$	30.3587			1.14663			0.573316	+	0.819335i	$0.305657\pi$
$702$	6.45205	−	19.8574i	0.243517	−	0.749468i
$703$	−0.726278	−	0.527672i	−0.0273921	−	0.0199015i
$704$	7.50936	+	5.45587i	0.283020	+	0.205626i
$705$		0			0
$706$	−3.81574	+	2.77230i	−0.143607	+	0.104337i
$707$	0.246267			0.00926181
$708$	−19.5006	+	14.1680i	−0.732878	+	0.532467i
$709$	−15.0082	−	46.1906i	−0.563646	−	1.73472i	−0.671940	−	0.740606i	$-0.734539\pi$
$709$	−15.0082	−	46.1906i	−0.563646	−	1.73472i	0.108293	−	0.994119i	$-0.465461\pi$
$710$		0			0
$711$	−19.6546	+	60.4905i	−0.737103	+	2.26857i
$712$	9.87554	+	30.3938i	0.370102	+	1.13906i
$713$	−3.18568	−	9.80452i	−0.119305	−	0.367182i
$714$	−0.0412719	+	0.127022i	−0.00154456	+	0.00475367i
$715$		0			0
$716$	−5.06395	−	15.5852i	−0.189249	−	0.582447i
$717$	−35.8713	+	26.0620i	−1.33964	+	0.973305i
$718$	4.56651			0.170421
$719$	−3.85284	+	2.79925i	−0.143687	+	0.104395i	−0.657306	−	0.753623i	$-0.728304\pi$
$719$	−3.85284	+	2.79925i	−0.143687	+	0.104395i	0.513620	+	0.858018i	$0.328304\pi$
$720$		0			0
$721$	−0.352013	−	0.255753i	−0.0131097	−	0.00952472i
$722$	5.30591	+	3.85497i	0.197466	+	0.143467i
$723$	24.1944	−	74.4626i	0.899798	−	2.76929i
$724$	10.2252			0.380018
$725$		0			0
$726$	2.85135			0.105823
$727$	−1.04661	+	3.22114i	−0.0388167	+	0.119466i	−0.968587	−	0.248674i	$-0.920005\pi$
$727$	−1.04661	+	3.22114i	−0.0388167	+	0.119466i	0.929770	+	0.368140i	$0.120005\pi$
$728$	0.136482	+	0.0991600i	0.00505836	+	0.00367511i
$729$	6.14803	+	4.46681i	0.227705	+	0.165437i
$730$		0			0
$731$	0.511694	−	0.371767i	0.0189257	−	0.0137503i
$732$	−49.8491			−1.84248
$733$	−12.4596	+	9.05244i	−0.460207	+	0.334360i	−0.793612	−	0.608424i	$-0.791802\pi$
$733$	−12.4596	+	9.05244i	−0.460207	+	0.334360i	0.333406	+	0.942783i	$0.391802\pi$
$734$	−2.76783	−	8.51852i	−0.102163	−	0.314424i
$735$		0			0
$736$	2.67028	−	8.21828i	0.0984279	−	0.302930i
$737$	−4.95388	−	15.2465i	−0.182479	−	0.561612i
$738$	−7.94063	−	24.4388i	−0.292299	−	0.899603i
$739$	3.08543	−	9.49596i	0.113499	−	0.349315i	−0.878132	−	0.478419i	$-0.841210\pi$
$739$	3.08543	−	9.49596i	0.113499	−	0.349315i	0.991631	+	0.129104i	$0.0412101\pi$
$740$		0			0
$741$	−8.77347	−	27.0020i	−0.322301	−	0.991942i
$742$	0.0865015	−	0.0628470i	0.00317557	−	0.00230719i
$743$	−41.4419			−1.52036			−0.760178	−	0.649715i	$-0.774888\pi$
$743$	−41.4419			−1.52036			−0.760178	+	0.649715i	$0.774888\pi$
$744$	−28.2474	+	20.5229i	−1.03560	+	0.752406i
$745$		0			0
$746$	1.24590	+	0.905198i	0.0456156	+	0.0331416i
$747$	47.5967	+	34.5811i	1.74147	+	1.26525i
$748$	7.01662	−	21.5949i	0.256553	−	0.789589i
$749$	0.377719			0.0138015
$750$		0			0
$751$	21.1036			0.770082			0.385041	−	0.922900i	$-0.374187\pi$
$751$	21.1036			0.770082			0.385041	+	0.922900i	$0.374187\pi$
$752$	6.17190	−	18.9952i	0.225066	−	0.692682i
$753$	−10.6030	−	7.70355i	−0.386396	−	0.280733i
$754$	−5.90325	−	4.28896i	−0.214984	−	0.156195i
$755$		0			0
$756$	0.371514	−	0.269921i	0.0135118	−	0.00981692i
$757$	40.7168			1.47988			0.739938	−	0.672675i	$-0.234855\pi$
$757$	40.7168			1.47988			0.739938	+	0.672675i	$0.234855\pi$
$758$	−10.3705	+	7.53460i	−0.376673	+	0.273669i
$759$	5.87545	+	18.0828i	0.213265	+	0.656363i
$760$		0			0
$761$	−1.56877	+	4.82817i	−0.0568678	+	0.175021i	−0.975456	−	0.220196i	$-0.929330\pi$
$761$	−1.56877	+	4.82817i	−0.0568678	+	0.175021i	0.918588	+	0.395217i	$0.129330\pi$
$762$	−8.19234	−	25.2134i	−0.296777	−	0.913387i
$763$	0.0438191	+	0.134861i	0.00158636	+	0.00488231i
$764$	11.8335	−	36.4198i	0.428121	−	1.31762i
$765$		0			0
$766$	−0.344506	−	1.06028i	−0.0124475	−	0.0383095i
$767$	13.6100	−	9.88822i	0.491428	−	0.357043i
$768$	−1.59875			−0.0576899
$769$	37.8367	−	27.4899i	1.36442	−	0.991312i	0.366275	−	0.930507i	$-0.380633\pi$
$769$	37.8367	−	27.4899i	1.36442	−	0.991312i	0.998150	−	0.0608058i	$-0.0193670\pi$
$770$		0			0
$771$	51.0527	+	37.0920i	1.83862	+	1.33583i
$772$	−35.7340	−	25.9623i	−1.28610	−	0.934404i
$773$	5.90031	−	18.1593i	0.212219	−	0.653144i	−0.787120	−	0.616800i	$-0.788429\pi$
$773$	5.90031	−	18.1593i	0.212219	−	0.653144i	0.999339	−	0.0363441i	$-0.0115712\pi$
$774$	0.574458			0.0206485
$775$		0			0
$776$	−5.19209			−0.186385
$777$	−0.00839737	+	0.0258445i	−0.000301254	+	0.000927165i
$778$	−1.88231	−	1.36757i	−0.0674839	−	0.0490299i
$779$	−15.3571	−	11.1576i	−0.550225	−	0.399762i
$780$		0			0
$781$	28.1040	−	20.4188i	1.00564	−	0.730641i
$782$	−3.11359			−0.111342
$783$	−34.4441	+	25.0251i	−1.23093	+	0.894325i
$784$	−5.53077	−	17.0219i	−0.197527	−	0.607927i
$785$		0			0
$786$	2.29362	−	7.05903i	0.0818106	−	0.251787i
$787$	−1.24383	−	3.82813i	−0.0443379	−	0.136458i	0.926437	−	0.376450i	$-0.122855\pi$
$787$	−1.24383	−	3.82813i	−0.0443379	−	0.136458i	−0.970775	+	0.239992i	$0.922855\pi$
$788$	−7.81192	−	24.0426i	−0.278288	−	0.856483i
$789$	27.4026	−	84.3366i	0.975560	−	3.00246i
$790$		0			0
$791$	0.0178501	+	0.0549370i	0.000634677	+	0.00195333i
$792$	35.7629	−	25.9833i	1.27078	−	0.923276i
$793$	34.7910			1.23546
$794$	15.3795	−	11.1739i	0.545799	−	0.396546i
$795$		0			0
$796$	−5.34485	−	3.88326i	−0.189443	−	0.137639i
$797$	12.9319	+	9.39554i	0.458070	+	0.332807i	0.792774	−	0.609516i	$-0.208636\pi$
$797$	12.9319	+	9.39554i	0.458070	+	0.332807i	−0.334704	+	0.942323i	$0.608636\pi$
$798$	−0.0276910	+	0.0852241i	−0.000980250	+	0.00301690i
$799$	−28.2988			−1.00114
$800$		0			0
$801$	−111.759			−3.94881
$802$	−2.58829	+	7.96592i	−0.0913955	+	0.281287i
$803$	11.4620	+	8.32765i	0.404486	+	0.293876i
$804$	−19.5816	−	14.2268i	−0.690589	−	0.501742i
$805$		0			0
$806$	9.19735	−	6.68226i	0.323963	−	0.235373i
$807$	24.5806			0.865279
$808$	15.7309	−	11.4291i	0.553410	−	0.402076i
$809$	−9.02377	−	27.7723i	−0.317259	−	0.976422i	−0.974815	−	0.223016i	$-0.928410\pi$
$809$	−9.02377	−	27.7723i	−0.317259	−	0.976422i	0.657556	−	0.753406i	$-0.271590\pi$
$810$		0			0
$811$	2.19933	−	6.76885i	0.0772290	−	0.237686i	−0.904988	−	0.425438i	$-0.860120\pi$
$811$	2.19933	−	6.76885i	0.0772290	−	0.237686i	0.982217	+	0.187752i	$0.0601200\pi$
$812$	−0.0495927	−	0.152631i	−0.00174036	−	0.00535629i
$813$	9.13320	+	28.1091i	0.320315	+	0.985829i
$814$	−0.204872	+	0.630530i	−0.00718075	+	0.0221001i
$815$		0			0
$816$	−8.85544	−	27.2542i	−0.310002	−	0.954089i
$817$	0.343316	−	0.249434i	0.0120111	−	0.00872658i
$818$	0.237034			0.00828770
$819$	−0.477287	+	0.346769i	−0.0166777	+	0.0121171i
$820$		0			0
$821$	26.3765	+	19.1637i	0.920547	+	0.668816i	0.943660	−	0.330917i	$-0.107358\pi$
$821$	26.3765	+	19.1637i	0.920547	+	0.668816i	−0.0231135	+	0.999733i	$0.507358\pi$
$822$	−16.0607	−	11.6687i	−0.560180	−	0.406994i
$823$	8.38552	−	25.8080i	0.292301	−	0.899609i	−0.691814	−	0.722076i	$-0.743188\pi$
$823$	8.38552	−	25.8080i	0.292301	−	0.899609i	0.984115	−	0.177533i	$-0.0568118\pi$
$824$	−34.3551			−1.19681
$825$		0			0
$826$	−0.0530966			−0.00184747
$827$	−16.9413	+	52.1400i	−0.589107	+	1.81308i	−0.00699443	+	0.999976i	$0.502226\pi$
$827$	−16.9413	+	52.1400i	−0.589107	+	1.81308i	−0.582112	+	0.813108i	$0.697774\pi$
$828$	15.9426	+	11.5830i	0.554044	+	0.402537i
$829$	−0.381831	−	0.277416i	−0.0132615	−	0.00963506i	0.581135	−	0.813807i	$-0.302609\pi$
$829$	−0.381831	−	0.277416i	−0.0132615	−	0.00963506i	−0.594396	+	0.804172i	$0.702609\pi$
$830$		0			0
$831$	−43.0190	+	31.2551i	−1.49231	+	1.08423i
$832$	−9.78095			−0.339093
$833$	−20.5160	+	14.9057i	−0.710837	+	0.516453i
$834$	−3.80240	−	11.7026i	−0.131666	−	0.405228i
$835$		0			0
$836$	4.70773	−	14.4889i	0.162820	−	0.501110i
$837$	−20.4980	−	63.0863i	−0.708514	−	2.18058i
$838$	3.75190	+	11.5472i	0.129607	+	0.398890i
$839$	−11.8890	+	36.5906i	−0.410454	+	1.26325i	0.505799	+	0.862651i	$0.331198\pi$
$839$	−11.8890	+	36.5906i	−0.410454	+	1.26325i	−0.916254	+	0.400598i	$0.868802\pi$
$840$		0			0
$841$	−4.36361	−	13.4298i	−0.150469	−	0.463097i
$842$	12.7057	−	9.23122i	0.437867	−	0.318129i
$843$	84.1929			2.89976
$844$	−26.7440	+	19.4306i	−0.920566	+	0.668830i
$845$		0			0
$846$	−20.7937	−	15.1075i	−0.714902	−	0.519406i
$847$	−0.0354094	−	0.0257264i	−0.00121668	−	0.000883971i
$848$	−7.08931	+	21.8187i	−0.243448	+	0.749256i
$849$	−10.7615			−0.369333
$850$		0			0
$851$	−0.633505			−0.0217163
$852$	16.2076	−	49.8820i	0.555264	−	1.70893i
$853$	29.0066	+	21.0745i	0.993167	+	0.721578i	0.960612	−	0.277892i	$-0.0896357\pi$
$853$	29.0066	+	21.0745i	0.993167	+	0.721578i	0.0325548	+	0.999470i	$0.489636\pi$
$854$	−0.0888365	−	0.0645435i	−0.00303992	−	0.00220863i
$855$		0			0
$856$	24.1277	−	17.5298i	0.824667	−	0.599155i
$857$	0.386299			0.0131957			0.00659786	−	0.999978i	$-0.497900\pi$
$857$	0.386299			0.0131957			0.00659786	+	0.999978i	$0.497900\pi$
$858$	−16.9629	+	12.3243i	−0.579105	+	0.420744i
$859$	6.88765	+	21.1980i	0.235003	+	0.723266i	0.997121	+	0.0758275i	$0.0241598\pi$
$859$	6.88765	+	21.1980i	0.235003	+	0.723266i	−0.762117	+	0.647439i	$0.775840\pi$
$860$		0			0
$861$	−0.177562	+	0.546479i	−0.00605129	+	0.0186240i
$862$	−0.309731	−	0.953255i	−0.0105495	−	0.0324680i
$863$	2.87327	+	8.84300i	0.0978071	+	0.301019i	0.987975	−	0.154613i	$-0.0494131\pi$
$863$	2.87327	+	8.84300i	0.0978071	+	0.301019i	−0.890168	+	0.455633i	$0.849413\pi$
$864$	17.1817	−	52.8798i	0.584533	−	1.79901i
$865$		0			0
$866$	1.09493	+	3.36984i	0.0372072	+	0.114512i
$867$	9.69383	−	7.04298i	0.329220	−	0.239192i
$868$	0.250039			0.00848686
$869$	28.0719	−	20.3954i	0.952273	−	0.691867i
$870$		0			0
$871$	13.6665	+	9.92928i	0.463071	+	0.336441i
$872$	9.05792	+	6.58096i	0.306740	+	0.222860i
$873$	5.61085	−	17.2684i	0.189898	−	0.584447i
$874$	−2.08903			−0.0706626
$875$		0			0
$876$	21.3910			0.722734
$877$	9.01669	−	27.7505i	0.304472	−	0.937069i	−0.675402	−	0.737450i	$-0.736030\pi$
$877$	9.01669	−	27.7505i	0.304472	−	0.937069i	0.979874	−	0.199618i	$-0.0639703\pi$
$878$	−5.25362	−	3.81698i	−0.177301	−	0.128817i
$879$	−58.7940	−	42.7164i	−1.98307	−	1.44079i
$880$		0			0
$881$	32.4203	−	23.5548i	1.09227	−	0.793580i	0.112488	−	0.993653i	$-0.464118\pi$
$881$	32.4203	−	23.5548i	1.09227	−	0.793580i	0.979781	+	0.200073i	$0.0641180\pi$
$882$	−23.0325			−0.775543
$883$	−24.9452	+	18.1237i	−0.839471	+	0.609912i	−0.922223	−	0.386658i	$-0.873629\pi$
$883$	−24.9452	+	18.1237i	−0.839471	+	0.609912i	0.0827515	+	0.996570i	$0.473629\pi$
$884$	7.39373	+	22.7556i	0.248678	+	0.765352i
$885$		0			0
$886$	3.38558	−	10.4198i	0.113741	−	0.350058i
$887$	−11.9135	−	36.6659i	−0.400016	−	1.23112i	−0.924986	−	0.380001i	$-0.875924\pi$
$887$	−11.9135	−	36.6659i	−0.400016	−	1.23112i	0.524971	−	0.851120i	$-0.324076\pi$
$888$	0.663029	+	2.04059i	0.0222498	+	0.0684779i
$889$	−0.125753	+	0.387029i	−0.00421763	+	0.0129805i
$890$		0			0
$891$	15.9861	+	49.2001i	0.535554	+	1.64826i
$892$	−16.0679	+	11.6740i	−0.537993	+	0.390875i
$893$	−18.9868			−0.635370
$894$	7.05501	−	5.12576i	0.235955	−	0.171431i
$895$		0			0
$896$	0.218866	+	0.159015i	0.00731179	+	0.00531233i
$897$	−16.2088	−	11.7764i	−0.541197	−	0.393203i
$898$	0.0618678	−	0.190410i	0.00206456	−	0.00635405i
$899$	−23.1818			−0.773156
$900$		0			0
$901$	32.5052			1.08291
$902$	−4.33199	+	13.3325i	−0.144240	+	0.443924i
$903$	−0.0103923	−	0.00755042i	−0.000345833	−	0.000251262i
$904$	3.68982	+	2.68081i	0.122722	+	0.0891625i
$905$		0			0
$906$	9.23945	−	6.71285i	0.306960	−	0.223020i
$907$	−4.77670			−0.158608			−0.0793038	−	0.996850i	$-0.525270\pi$
$907$	−4.77670			−0.158608			−0.0793038	+	0.996850i	$0.525270\pi$
$908$	15.8445	−	11.5117i	0.525818	−	0.382029i
$909$	21.0127	+	64.6703i	0.696946	+	2.14498i
$910$		0			0
$911$	−3.56395	+	10.9687i	−0.118079	+	0.363410i	−0.992577	−	0.121620i	$-0.961191\pi$
$911$	−3.56395	+	10.9687i	−0.118079	+	0.363410i	0.874498	+	0.485029i	$0.161191\pi$
$912$	−5.94147	−	18.2860i	−0.196742	−	0.605509i
$913$	−9.91824	−	30.5252i	−0.328246	−	1.01024i
$914$	−5.45329	+	16.7835i	−0.180379	+	0.555149i
$915$		0			0
$916$	−5.21540	−	16.0514i	−0.172322	−	0.530352i
$917$	−0.0921738	+	0.0669682i	−0.00304385	+	0.00221148i
$918$	−20.0341			−0.661224
$919$	33.4341	−	24.2913i	1.10289	−	0.801296i	0.121360	−	0.992609i	$-0.461274\pi$
$919$	33.4341	−	24.2913i	1.10289	−	0.801296i	0.981529	+	0.191313i	$0.0612745\pi$
$920$		0			0
$921$	−2.78409	−	2.02276i	−0.0917389	−	0.0666522i
$922$	6.46934	+	4.70025i	0.213057	+	0.154795i
$923$	−11.3117	+	34.8139i	−0.372330	+	1.14591i
$924$	−0.461153			−0.0151708
$925$		0			0
$926$	−15.2717			−0.501860
$927$	37.1259	−	114.262i	1.21937	−	3.75285i
$928$	−15.7202	−	11.4214i	−0.516042	−	0.374927i
$929$	10.8549	+	7.88657i	0.356139	+	0.258750i	0.751440	−	0.659802i	$-0.229360\pi$
$929$	10.8549	+	7.88657i	0.356139	+	0.258750i	−0.395301	+	0.918552i	$0.629360\pi$
$930$		0			0
$931$	−13.7650	+	10.0009i	−0.451130	+	0.327765i
$932$	27.1552			0.889499
$933$	36.9191	−	26.8233i	1.20868	−	0.878155i
$934$	1.02898	+	3.16689i	0.0336694	+	0.103624i
$935$		0			0
$936$	−14.3944	+	44.3014i	−0.470496	+	1.44804i
$937$	12.9765	+	39.9376i	0.423924	+	1.30470i	0.904021	+	0.427488i	$0.140602\pi$
$937$	12.9765	+	39.9376i	0.423924	+	1.30470i	−0.480097	+	0.877215i	$0.659398\pi$
$938$	−0.0164759	−	0.0507075i	−0.000537956	−	0.00165566i
$939$	4.72996	−	14.5573i	0.154356	−	0.475060i
$940$		0			0
$941$	12.3781	+	38.0960i	0.403515	+	1.24189i	0.922129	+	0.386884i	$0.126449\pi$
$941$	12.3781	+	38.0960i	0.403515	+	1.24189i	−0.518613	+	0.855009i	$0.673551\pi$
$942$	−10.8208	+	7.86176i	−0.352560	+	0.256150i
$943$	−13.3954			−0.436215
$944$	9.21680	−	6.69639i	0.299981	−	0.217949i
$945$		0			0
$946$	−0.253541	−	0.184208i	−0.00824334	−	0.00598913i
$947$	−35.5766	−	25.8479i	−1.15608	−	0.839944i	−0.166806	−	0.985990i	$-0.553345\pi$
$947$	−35.5766	−	25.8479i	−1.15608	−	0.839944i	−0.989278	+	0.146046i	$0.953345\pi$
$948$	16.1891	−	49.8249i	0.525797	−	1.61824i
$949$	−14.9293			−0.484625
$950$		0			0
$951$	70.1721			2.27549
$952$	0.0500213	−	0.153950i	0.00162120	−	0.00498954i
$953$	−32.8600	−	23.8742i	−1.06444	−	0.773360i	−0.0895340	−	0.995984i	$-0.528538\pi$
$953$	−32.8600	−	23.8742i	−1.06444	−	0.773360i	−0.974904	+	0.222624i	$0.928538\pi$
$954$	23.8845	+	17.3531i	0.773290	+	0.561828i
$955$		0			0
$956$	20.2826	−	14.7362i	0.655986	−	0.476602i
$957$	42.7548			1.38207
$958$	−9.01439	+	6.54934i	−0.291242	+	0.211599i
$959$	0.0941671	+	0.289817i	0.00304081	+	0.00935866i
$960$		0			0
$961$	1.58141	−	4.86709i	0.0510133	−	0.157003i
$962$	−0.215882	−	0.664418i	−0.00696033	−	0.0214217i
$963$	32.2288	+	99.1900i	1.03856	+	3.19635i
$964$	−13.6801	+	42.1031i	−0.440607	+	1.35605i
$965$		0			0
$966$	0.0195409	+	0.0601406i	0.000628717	+	0.00193499i
$967$	12.9444	−	9.40466i	0.416264	−	0.302433i	−0.359869	−	0.933003i	$-0.617179\pi$
$967$	12.9444	−	9.40466i	0.416264	−	0.302433i	0.776133	+	0.630569i	$0.217179\pi$
$968$	−3.45581			−0.111074
$969$	−22.0395	+	16.0126i	−0.708010	+	0.514399i
$970$		0			0
$971$	−44.9167	−	32.6339i	−1.44145	−	1.04727i	−0.987738	−	0.156122i	$-0.950101\pi$
$971$	−44.9167	−	32.6339i	−1.44145	−	1.04727i	−0.453708	−	0.891150i	$-0.649899\pi$
$972$	16.3360	+	11.8688i	0.523976	+	0.380691i
$973$	−0.0583673	+	0.179636i	−0.00187117	+	0.00575887i
$974$	5.10263			0.163499
$975$		0			0
$976$	23.5608			0.754162
$977$	1.95465	−	6.01580i	0.0625348	−	0.192462i	−0.914908	−	0.403662i	$-0.867737\pi$
$977$	1.95465	−	6.01580i	0.0625348	−	0.192462i	0.977443	+	0.211200i	$0.0677371\pi$
$978$	−5.95474	−	4.32637i	−0.190411	−	0.138342i
$979$	49.3257	+	35.8372i	1.57645	+	1.14536i
$980$		0			0
$981$	−31.6761	+	23.0141i	−1.01134	+	0.734782i
$982$	3.32659			0.106156
$983$	−39.3524	+	28.5912i	−1.25515	+	0.911916i	−0.998509	−	0.0545918i	$-0.982614\pi$
$983$	−39.3524	+	28.5912i	−1.25515	+	0.911916i	−0.256636	+	0.966508i	$0.582614\pi$
$984$	14.0197	+	43.1482i	0.446932	+	1.37551i
$985$		0			0
$986$	−2.16357	+	6.65877i	−0.0689020	+	0.212059i
$987$	0.177603	+	0.546606i	0.00565317	+	0.0173987i
$988$	4.96075	+	15.2676i	0.157823	+	0.485728i
$989$	0.0925388	−	0.284805i	0.00294256	−	0.00905628i
$990$		0			0
$991$	−13.6512	−	42.0141i	−0.433645	−	1.33462i	−0.894469	−	0.447131i	$-0.852446\pi$
$991$	−13.6512	−	42.0141i	−0.433645	−	1.33462i	0.460823	−	0.887492i	$-0.347554\pi$
$992$	24.4924	−	17.7947i	0.777633	−	0.564984i
$993$	5.35931			0.170073
$994$	0.0934697	−	0.0679097i	0.00296468	−	0.00215397i
$995$		0			0
$996$	−39.2046	−	28.4838i	−1.24224	−	0.902543i
$997$	−32.5437	−	23.6444i	−1.03067	−	0.748825i	−0.0622265	−	0.998062i	$-0.519820\pi$
$997$	−32.5437	−	23.6444i	−1.03067	−	0.748825i	−0.968442	+	0.249237i	$0.919820\pi$
$998$	0.167814	−	0.516479i	0.00531207	−	0.0163489i
$999$	−4.07623			−0.128966

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.d.n.501.2		16
5.2	odd	4		625.2.e.k.124.5		32
5.3	odd	4		625.2.e.k.124.4		32
5.4	even	2		625.2.d.p.501.3		16
25.2	odd	20		625.2.e.j.249.5		32
25.3	odd	20		625.2.e.j.374.5		32
25.4	even	10		625.2.d.q.251.2		16
25.6	even	5	inner	625.2.d.n.126.2		16
25.8	odd	20		625.2.e.k.499.5		32
25.9	even	10		625.2.a.e.1.5	✓	8
25.11	even	5		625.2.d.m.376.3		16
25.12	odd	20		625.2.b.d.624.10		16
25.13	odd	20		625.2.b.d.624.7		16
25.14	even	10		625.2.d.q.376.2		16
25.16	even	5		625.2.a.g.1.4	yes	8
25.17	odd	20		625.2.e.k.499.4		32
25.19	even	10		625.2.d.p.126.3		16
25.21	even	5		625.2.d.m.251.3		16
25.22	odd	20		625.2.e.j.374.4		32
25.23	odd	20		625.2.e.j.249.4		32
75.41	odd	10		5625.2.a.s.1.5		8
75.59	odd	10		5625.2.a.be.1.4		8
100.59	odd	10		10000.2.a.bn.1.8		8
100.91	odd	10		10000.2.a.be.1.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
625.2.a.e.1.5	✓	8	25.9	even	10
625.2.a.g.1.4	yes	8	25.16	even	5
625.2.b.d.624.7		16	25.13	odd	20
625.2.b.d.624.10		16	25.12	odd	20
625.2.d.m.251.3		16	25.21	even	5
625.2.d.m.376.3		16	25.11	even	5
625.2.d.n.126.2		16	25.6	even	5	inner
625.2.d.n.501.2		16	1.1	even	1	trivial
625.2.d.p.126.3		16	25.19	even	10
625.2.d.p.501.3		16	5.4	even	2
625.2.d.q.251.2		16	25.4	even	10
625.2.d.q.376.2		16	25.14	even	10
625.2.e.j.249.4		32	25.23	odd	20
625.2.e.j.249.5		32	25.2	odd	20
625.2.e.j.374.4		32	25.22	odd	20
625.2.e.j.374.5		32	25.3	odd	20
625.2.e.k.124.4		32	5.3	odd	4
625.2.e.k.124.5		32	5.2	odd	4
625.2.e.k.499.4		32	25.17	odd	20
625.2.e.k.499.5		32	25.8	odd	20
5625.2.a.s.1.5		8	75.41	odd	10
5625.2.a.be.1.4		8	75.59	odd	10
10000.2.a.be.1.1		8	100.91	odd	10
10000.2.a.bn.1.8		8	100.59	odd	10

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:	\( N \)	\(=\)	\( 625 = 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	625.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.154814 - 0.476469i) q^{2} +(-2.50250 - 1.81817i) q^{3} +(1.41498 + 1.02804i) q^{4} +(-1.25372 + 0.910884i) q^{6} +0.0237879 q^{7} +(1.51951 - 1.10399i) q^{8} +(2.02970 + 6.24676i) q^{9} +O(q^{10})\)	\(q+(0.154814 - 0.476469i) q^{2} +(-2.50250 - 1.81817i) q^{3} +(1.41498 + 1.02804i) q^{4} +(-1.25372 + 0.910884i) q^{6} +0.0237879 q^{7} +(1.51951 - 1.10399i) q^{8} +(2.02970 + 6.24676i) q^{9} +(1.10730 - 3.40791i) q^{11} +(-1.67182 - 5.14535i) q^{12} +(1.16681 + 3.59107i) q^{13} +(0.00368270 - 0.0113342i) q^{14} +(0.790173 + 2.43190i) q^{16} +(2.93109 - 2.12956i) q^{17} +3.29062 q^{18} +(1.96659 - 1.42881i) q^{19} +(-0.0595291 - 0.0432504i) q^{21} +(-1.45234 - 1.05519i) q^{22} +(0.530082 - 1.63143i) q^{23} -5.80980 q^{24} +1.89167 q^{26} +(3.41077 - 10.4973i) q^{27} +(0.0336593 + 0.0244549i) q^{28} +(-3.12065 - 2.26729i) q^{29} +(4.86202 - 3.53247i) q^{31} +5.03748 q^{32} +(-8.96717 + 6.51503i) q^{33} +(-0.560896 - 1.72626i) q^{34} +(-3.54996 + 10.9257i) q^{36} +(-0.114123 - 0.351233i) q^{37} +(-0.376328 - 1.15822i) q^{38} +(3.60924 - 11.1081i) q^{39} +(-2.41311 - 7.42680i) q^{41} +(-0.0298234 + 0.0216680i) q^{42} +0.174574 q^{43} +(5.07027 - 3.68377i) q^{44} +(-0.695260 - 0.505136i) q^{46} +(-6.31908 - 4.59108i) q^{47} +(2.44421 - 7.52250i) q^{48} -6.99943 q^{49} -11.2070 q^{51} +(-2.04076 + 6.28081i) q^{52} +(7.25837 + 5.27352i) q^{53} +(-4.47359 - 3.25025i) q^{54} +(0.0361458 - 0.0262615i) q^{56} -7.51920 q^{57} +(-1.56341 + 1.13589i) q^{58} +(-1.37678 - 4.23730i) q^{59} +(2.84729 - 8.76306i) q^{61} +(-0.930401 - 2.86348i) q^{62} +(0.0482822 + 0.148597i) q^{63} +(-0.800472 + 2.46360i) q^{64} +(1.71597 + 5.28120i) q^{66} +(3.61942 - 2.62967i) q^{67} +6.33671 q^{68} +(-4.29274 + 3.11886i) q^{69} +(7.84308 + 5.69833i) q^{71} +(9.98048 + 7.25125i) q^{72} +(-1.22181 + 3.76035i) q^{73} -0.185020 q^{74} +4.25156 q^{76} +(0.0263402 - 0.0810669i) q^{77} +(-4.73390 - 3.43938i) q^{78} +(7.83411 + 5.69181i) q^{79} +(-11.6798 + 8.48587i) q^{81} -3.91223 q^{82} +(7.24650 - 5.26489i) q^{83} +(-0.0397691 - 0.122397i) q^{84} +(0.0270266 - 0.0831794i) q^{86} +(3.68711 + 11.3478i) q^{87} +(-2.07974 - 6.40078i) q^{88} +(-5.25794 + 16.1823i) q^{89} +(0.0277559 + 0.0854239i) q^{91} +(2.42723 - 1.76349i) q^{92} -18.5898 q^{93} +(-3.16579 + 2.30008i) q^{94} +(-12.6063 - 9.15901i) q^{96} +(-2.23643 - 1.62486i) q^{97} +(-1.08361 + 3.33501i) q^{98} +23.5359 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 5 q^{3} - 8 q^{4} - 3 q^{6} + 20 q^{7} - 10 q^{8} + 3 q^{9}+O(q^{10}) \) 16 * q - 5 * q^3 - 8 * q^4 - 3 * q^6 + 20 * q^7 - 10 * q^8 + 3 * q^9	\( 16 q - 5 q^{3} - 8 q^{4} - 3 q^{6} + 20 q^{7} - 10 q^{8} + 3 q^{9} + 2 q^{11} - 25 q^{12} - 5 q^{13} + 9 q^{14} - 14 q^{16} + 10 q^{17} - 10 q^{18} + 7 q^{21} + 40 q^{22} - 15 q^{23} + 10 q^{24} + 22 q^{26} - 20 q^{27} - 30 q^{28} - 10 q^{29} + 17 q^{31} + 60 q^{32} - 5 q^{33} - q^{34} - 4 q^{36} + 15 q^{37} + 15 q^{38} - 9 q^{39} + 12 q^{41} + 45 q^{42} + 49 q^{44} - 33 q^{46} - 25 q^{47} + 20 q^{48} - 8 q^{49} - 28 q^{51} - 20 q^{52} - 30 q^{54} - 35 q^{56} - 20 q^{57} - 5 q^{58} + 20 q^{59} - 23 q^{61} - 15 q^{62} - 10 q^{63} - 28 q^{64} - 26 q^{66} + 80 q^{68} + 6 q^{69} + 22 q^{71} - 5 q^{72} - 40 q^{73} - 36 q^{74} - 20 q^{76} + 40 q^{77} + 25 q^{78} + 75 q^{79} + 11 q^{81} - 90 q^{82} - 25 q^{83} - 31 q^{84} + 17 q^{86} + 20 q^{87} + 5 q^{89} + 22 q^{91} - 60 q^{92} - 80 q^{93} - 51 q^{94} - 28 q^{96} - 40 q^{97} - 15 q^{98} - 44 q^{99}+O(q^{100}) \) 16 * q - 5 * q^3 - 8 * q^4 - 3 * q^6 + 20 * q^7 - 10 * q^8 + 3 * q^9 + 2 * q^11 - 25 * q^12 - 5 * q^13 + 9 * q^14 - 14 * q^16 + 10 * q^17 - 10 * q^18 + 7 * q^21 + 40 * q^22 - 15 * q^23 + 10 * q^24 + 22 * q^26 - 20 * q^27 - 30 * q^28 - 10 * q^29 + 17 * q^31 + 60 * q^32 - 5 * q^33 - q^34 - 4 * q^36 + 15 * q^37 + 15 * q^38 - 9 * q^39 + 12 * q^41 + 45 * q^42 + 49 * q^44 - 33 * q^46 - 25 * q^47 + 20 * q^48 - 8 * q^49 - 28 * q^51 - 20 * q^52 - 30 * q^54 - 35 * q^56 - 20 * q^57 - 5 * q^58 + 20 * q^59 - 23 * q^61 - 15 * q^62 - 10 * q^63 - 28 * q^64 - 26 * q^66 + 80 * q^68 + 6 * q^69 + 22 * q^71 - 5 * q^72 - 40 * q^73 - 36 * q^74 - 20 * q^76 + 40 * q^77 + 25 * q^78 + 75 * q^79 + 11 * q^81 - 90 * q^82 - 25 * q^83 - 31 * q^84 + 17 * q^86 + 20 * q^87 + 5 * q^89 + 22 * q^91 - 60 * q^92 - 80 * q^93 - 51 * q^94 - 28 * q^96 - 40 * q^97 - 15 * q^98 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more