LMFDB - Embedded newform 845.2.e.h.191.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(146,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("845.146");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			191.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	845.191
Dual form			845.2.e.h.146.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.20711 - 2.09077i) q^{2} +(0.707107 - 1.22474i) q^{3} +(-1.91421 - 3.31552i) q^{4} +1.00000 q^{5} +(-1.70711 - 2.95680i) q^{6} +(-2.41421 - 4.18154i) q^{7} -4.41421 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(1.20711 - 2.09077i) q^{2} +(0.707107 - 1.22474i) q^{3} +(-1.91421 - 3.31552i) q^{4} +1.00000 q^{5} +(-1.70711 - 2.95680i) q^{6} +(-2.41421 - 4.18154i) q^{7} -4.41421 q^{8} +(0.500000 + 0.866025i) q^{9} +(1.20711 - 2.09077i) q^{10} +(-1.70711 + 2.95680i) q^{11} -5.41421 q^{12} -11.6569 q^{14} +(0.707107 - 1.22474i) q^{15} +(-1.50000 + 2.59808i) q^{16} +(-0.414214 - 0.717439i) q^{17} +2.41421 q^{18} +(-0.292893 - 0.507306i) q^{19} +(-1.91421 - 3.31552i) q^{20} -6.82843 q^{21} +(4.12132 + 7.13834i) q^{22} +(-0.707107 + 1.22474i) q^{23} +(-3.12132 + 5.40629i) q^{24} +1.00000 q^{25} +5.65685 q^{27} +(-9.24264 + 16.0087i) q^{28} +(2.82843 - 4.89898i) q^{29} +(-1.70711 - 2.95680i) q^{30} +1.75736 q^{31} +(-0.792893 - 1.37333i) q^{32} +(2.41421 + 4.18154i) q^{33} -2.00000 q^{34} +(-2.41421 - 4.18154i) q^{35} +(1.91421 - 3.31552i) q^{36} +(4.24264 - 7.34847i) q^{37} -1.41421 q^{38} -4.41421 q^{40} +(1.58579 - 2.74666i) q^{41} +(-8.24264 + 14.2767i) q^{42} +(5.53553 + 9.58783i) q^{43} +13.0711 q^{44} +(0.500000 + 0.866025i) q^{45} +(1.70711 + 2.95680i) q^{46} -4.82843 q^{47} +(2.12132 + 3.67423i) q^{48} +(-8.15685 + 14.1281i) q^{49} +(1.20711 - 2.09077i) q^{50} -1.17157 q^{51} +2.48528 q^{53} +(6.82843 - 11.8272i) q^{54} +(-1.70711 + 2.95680i) q^{55} +(10.6569 + 18.4582i) q^{56} -0.828427 q^{57} +(-6.82843 - 11.8272i) q^{58} +(-0.878680 - 1.52192i) q^{59} -5.41421 q^{60} +(4.00000 + 6.92820i) q^{61} +(2.12132 - 3.67423i) q^{62} +(2.41421 - 4.18154i) q^{63} -9.82843 q^{64} +11.6569 q^{66} +(1.00000 - 1.73205i) q^{67} +(-1.58579 + 2.74666i) q^{68} +(1.00000 + 1.73205i) q^{69} -11.6569 q^{70} +(-5.94975 - 10.3053i) q^{71} +(-2.20711 - 3.82282i) q^{72} +8.48528 q^{73} +(-10.2426 - 17.7408i) q^{74} +(0.707107 - 1.22474i) q^{75} +(-1.12132 + 1.94218i) q^{76} +16.4853 q^{77} -8.48528 q^{79} +(-1.50000 + 2.59808i) q^{80} +(2.50000 - 4.33013i) q^{81} +(-3.82843 - 6.63103i) q^{82} -3.17157 q^{83} +(13.0711 + 22.6398i) q^{84} +(-0.414214 - 0.717439i) q^{85} +26.7279 q^{86} +(-4.00000 - 6.92820i) q^{87} +(7.53553 - 13.0519i) q^{88} +(-3.00000 + 5.19615i) q^{89} +2.41421 q^{90} +5.41421 q^{92} +(1.24264 - 2.15232i) q^{93} +(-5.82843 + 10.0951i) q^{94} +(-0.292893 - 0.507306i) q^{95} -2.24264 q^{96} +(3.82843 + 6.63103i) q^{97} +(19.6924 + 34.1082i) q^{98} -3.41421 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{7} - 12 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^7 - 12 * q^8 + 2 * q^9	$ 4 q + 2 q^{2} - 2 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{7} - 12 q^{8} + 2 q^{9} + 2 q^{10} - 4 q^{11} - 16 q^{12} - 24 q^{14} - 6 q^{16} + 4 q^{17} + 4 q^{18} - 4 q^{19} - 2 q^{20} - 16 q^{21} + 8 q^{22} - 4 q^{24} + 4 q^{25} - 20 q^{28} - 4 q^{30} + 24 q^{31} - 6 q^{32} + 4 q^{33} - 8 q^{34} - 4 q^{35} + 2 q^{36} - 12 q^{40} + 12 q^{41} - 16 q^{42} + 8 q^{43} + 24 q^{44} + 2 q^{45} + 4 q^{46} - 8 q^{47} - 10 q^{49} + 2 q^{50} - 16 q^{51} - 24 q^{53} + 16 q^{54} - 4 q^{55} + 20 q^{56} + 8 q^{57} - 16 q^{58} - 12 q^{59} - 16 q^{60} + 16 q^{61} + 4 q^{63} - 28 q^{64} + 24 q^{66} + 4 q^{67} - 12 q^{68} + 4 q^{69} - 24 q^{70} - 4 q^{71} - 6 q^{72} - 24 q^{74} + 4 q^{76} + 32 q^{77} - 6 q^{80} + 10 q^{81} - 4 q^{82} - 24 q^{83} + 24 q^{84} + 4 q^{85} + 56 q^{86} - 16 q^{87} + 16 q^{88} - 12 q^{89} + 4 q^{90} + 16 q^{92} - 12 q^{93} - 12 q^{94} - 4 q^{95} + 8 q^{96} + 4 q^{97} + 42 q^{98} - 8 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^7 - 12 * q^8 + 2 * q^9 + 2 * q^10 - 4 * q^11 - 16 * q^12 - 24 * q^14 - 6 * q^16 + 4 * q^17 + 4 * q^18 - 4 * q^19 - 2 * q^20 - 16 * q^21 + 8 * q^22 - 4 * q^24 + 4 * q^25 - 20 * q^28 - 4 * q^30 + 24 * q^31 - 6 * q^32 + 4 * q^33 - 8 * q^34 - 4 * q^35 + 2 * q^36 - 12 * q^40 + 12 * q^41 - 16 * q^42 + 8 * q^43 + 24 * q^44 + 2 * q^45 + 4 * q^46 - 8 * q^47 - 10 * q^49 + 2 * q^50 - 16 * q^51 - 24 * q^53 + 16 * q^54 - 4 * q^55 + 20 * q^56 + 8 * q^57 - 16 * q^58 - 12 * q^59 - 16 * q^60 + 16 * q^61 + 4 * q^63 - 28 * q^64 + 24 * q^66 + 4 * q^67 - 12 * q^68 + 4 * q^69 - 24 * q^70 - 4 * q^71 - 6 * q^72 - 24 * q^74 + 4 * q^76 + 32 * q^77 - 6 * q^80 + 10 * q^81 - 4 * q^82 - 24 * q^83 + 24 * q^84 + 4 * q^85 + 56 * q^86 - 16 * q^87 + 16 * q^88 - 12 * q^89 + 4 * q^90 + 16 * q^92 - 12 * q^93 - 12 * q^94 - 4 * q^95 + 8 * q^96 + 4 * q^97 + 42 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.20711	−	2.09077i	0.853553	−	1.47840i	−0.0244272	−	0.999702i	$-0.507776\pi$
$2$	1.20711	−	2.09077i	0.853553	−	1.47840i	0.877981	−	0.478696i	$-0.158890\pi$
$3$	0.707107	−	1.22474i	0.408248	−	0.707107i	−0.586445	−	0.809989i	$-0.699473\pi$
$3$	0.707107	−	1.22474i	0.408248	−	0.707107i	0.994694	+	0.102882i	$0.0328064\pi$
$4$	−1.91421	−	3.31552i	−0.957107	−	1.65776i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−1.70711	−	2.95680i	−0.696923	−	1.20711i
$7$	−2.41421	−	4.18154i	−0.912487	−	1.58047i	−0.810539	−	0.585684i	$-0.800826\pi$
$7$	−2.41421	−	4.18154i	−0.912487	−	1.58047i	−0.101947	−	0.994790i	$-0.532507\pi$
$8$	−4.41421			−1.56066
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	1.20711	−	2.09077i	0.381721	−	0.661160i
$11$	−1.70711	+	2.95680i	−0.514712	+	0.891507i	0.485142	+	0.874435i	$0.338768\pi$
$11$	−1.70711	+	2.95680i	−0.514712	+	0.891507i	−0.999854	+	0.0170722i	$0.994565\pi$
$12$	−5.41421			−1.56295
$13$		0			0
$13$		0			0
$14$	−11.6569			−3.11543
$15$	0.707107	−	1.22474i	0.182574	−	0.316228i
$16$	−1.50000	+	2.59808i	−0.375000	+	0.649519i
$17$	−0.414214	−	0.717439i	−0.100462	−	0.174005i	0.811413	−	0.584473i	$-0.198699\pi$
$17$	−0.414214	−	0.717439i	−0.100462	−	0.174005i	−0.911875	+	0.410468i	$0.865365\pi$
$18$	2.41421			0.569036
$19$	−0.292893	−	0.507306i	−0.0671943	−	0.116384i	0.830471	−	0.557062i	$-0.188071\pi$
$19$	−0.292893	−	0.507306i	−0.0671943	−	0.116384i	−0.897665	+	0.440678i	$0.854738\pi$
$20$	−1.91421	−	3.31552i	−0.428031	−	0.741372i
$21$	−6.82843			−1.49008
$22$	4.12132	+	7.13834i	0.878668	+	1.52190i
$23$	−0.707107	+	1.22474i	−0.147442	+	0.255377i	−0.930281	−	0.366847i	$-0.880437\pi$
$23$	−0.707107	+	1.22474i	−0.147442	+	0.255377i	0.782839	+	0.622224i	$0.213771\pi$
$24$	−3.12132	+	5.40629i	−0.637137	+	1.10355i
$25$	1.00000			0.200000
$26$		0			0
$27$	5.65685			1.08866
$28$	−9.24264	+	16.0087i	−1.74669	+	3.02536i
$29$	2.82843	−	4.89898i	0.525226	−	0.909718i	−0.474343	−	0.880340i	$-0.657314\pi$
$29$	2.82843	−	4.89898i	0.525226	−	0.909718i	0.999568	−	0.0293774i	$-0.00935245\pi$
$30$	−1.70711	−	2.95680i	−0.311674	−	0.539835i
$31$	1.75736			0.315631			0.157816	−	0.987469i	$-0.449555\pi$
$31$	1.75736			0.315631			0.157816	+	0.987469i	$0.449555\pi$
$32$	−0.792893	−	1.37333i	−0.140165	−	0.242773i
$33$	2.41421	+	4.18154i	0.420261	+	0.727913i
$34$	−2.00000			−0.342997
$35$	−2.41421	−	4.18154i	−0.408077	−	0.706809i
$36$	1.91421	−	3.31552i	0.319036	−	0.552586i
$37$	4.24264	−	7.34847i	0.697486	−	1.20808i	−0.271850	−	0.962340i	$-0.587635\pi$
$37$	4.24264	−	7.34847i	0.697486	−	1.20808i	0.969335	−	0.245741i	$-0.0790313\pi$
$38$	−1.41421			−0.229416
$39$		0			0
$40$	−4.41421			−0.697948
$41$	1.58579	−	2.74666i	0.247658	−	0.428957i	−0.715217	−	0.698902i	$-0.753672\pi$
$41$	1.58579	−	2.74666i	0.247658	−	0.428957i	0.962876	+	0.269945i	$0.0870057\pi$
$42$	−8.24264	+	14.2767i	−1.27187	+	2.20294i
$43$	5.53553	+	9.58783i	0.844161	+	1.46213i	0.886348	+	0.463020i	$0.153234\pi$
$43$	5.53553	+	9.58783i	0.844161	+	1.46213i	−0.0421868	+	0.999110i	$0.513432\pi$
$44$	13.0711			1.97054
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$	1.70711	+	2.95680i	0.251699	+	0.435956i
$47$	−4.82843			−0.704298			−0.352149	−	0.935944i	$-0.614549\pi$
$47$	−4.82843			−0.704298			−0.352149	+	0.935944i	$0.614549\pi$
$48$	2.12132	+	3.67423i	0.306186	+	0.530330i
$49$	−8.15685	+	14.1281i	−1.16526	+	2.01830i
$50$	1.20711	−	2.09077i	0.170711	−	0.295680i
$51$	−1.17157			−0.164053
$52$		0			0
$53$	2.48528			0.341380			0.170690	−	0.985325i	$-0.445400\pi$
$53$	2.48528			0.341380			0.170690	+	0.985325i	$0.445400\pi$
$54$	6.82843	−	11.8272i	0.929231	−	1.60948i
$55$	−1.70711	+	2.95680i	−0.230186	+	0.398694i
$56$	10.6569	+	18.4582i	1.42408	+	2.46658i
$57$	−0.828427			−0.109728
$58$	−6.82843	−	11.8272i	−0.896616	−	1.55299i
$59$	−0.878680	−	1.52192i	−0.114394	−	0.198137i	0.803143	−	0.595786i	$-0.203159\pi$
$59$	−0.878680	−	1.52192i	−0.114394	−	0.198137i	−0.917537	+	0.397649i	$0.869826\pi$
$60$	−5.41421			−0.698972
$61$	4.00000	+	6.92820i	0.512148	+	0.887066i	0.999901	+	0.0140840i	$0.00448323\pi$
$61$	4.00000	+	6.92820i	0.512148	+	0.887066i	−0.487753	+	0.872982i	$0.662183\pi$
$62$	2.12132	−	3.67423i	0.269408	−	0.466628i
$63$	2.41421	−	4.18154i	0.304162	−	0.526825i
$64$	−9.82843			−1.22855
$65$		0			0
$66$	11.6569			1.43486
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	−0.798454	−	0.602056i	$-0.794348\pi$
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	0.920623	+	0.390453i	$0.127682\pi$
$68$	−1.58579	+	2.74666i	−0.192305	+	0.333082i
$69$	1.00000	+	1.73205i	0.120386	+	0.208514i
$70$	−11.6569			−1.39326
$71$	−5.94975	−	10.3053i	−0.706105	−	1.22301i	−0.966291	−	0.257451i	$-0.917117\pi$
$71$	−5.94975	−	10.3053i	−0.706105	−	1.22301i	0.260186	−	0.965558i	$-0.416216\pi$
$72$	−2.20711	−	3.82282i	−0.260110	−	0.450524i
$73$	8.48528			0.993127			0.496564	−	0.868000i	$-0.334595\pi$
$73$	8.48528			0.993127			0.496564	+	0.868000i	$0.334595\pi$
$74$	−10.2426	−	17.7408i	−1.19068	−	2.06232i
$75$	0.707107	−	1.22474i	0.0816497	−	0.141421i
$76$	−1.12132	+	1.94218i	−0.128624	+	0.222784i
$77$	16.4853			1.87867
$78$		0			0
$79$	−8.48528			−0.954669			−0.477334	−	0.878722i	$-0.658397\pi$
$79$	−8.48528			−0.954669			−0.477334	+	0.878722i	$0.658397\pi$
$80$	−1.50000	+	2.59808i	−0.167705	+	0.290474i
$81$	2.50000	−	4.33013i	0.277778	−	0.481125i
$82$	−3.82843	−	6.63103i	−0.422779	−	0.732275i
$83$	−3.17157			−0.348125			−0.174063	−	0.984735i	$-0.555690\pi$
$83$	−3.17157			−0.348125			−0.174063	+	0.984735i	$0.555690\pi$
$84$	13.0711	+	22.6398i	1.42617	+	2.47020i
$85$	−0.414214	−	0.717439i	−0.0449278	−	0.0778172i
$86$	26.7279			2.88215
$87$	−4.00000	−	6.92820i	−0.428845	−	0.742781i
$88$	7.53553	−	13.0519i	0.803291	−	1.39134i
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	−0.980071	−	0.198650i	$-0.936344\pi$
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	0.662071	+	0.749441i	$0.269678\pi$
$90$	2.41421			0.254480
$91$		0			0
$92$	5.41421			0.564471
$93$	1.24264	−	2.15232i	0.128856	−	0.223185i
$94$	−5.82843	+	10.0951i	−0.601156	+	1.04123i
$95$	−0.292893	−	0.507306i	−0.0300502	−	0.0520485i
$96$	−2.24264			−0.228889
$97$	3.82843	+	6.63103i	0.388718	+	0.673279i	0.992277	−	0.124039i	$-0.0395847\pi$
$97$	3.82843	+	6.63103i	0.388718	+	0.673279i	−0.603559	+	0.797318i	$0.706251\pi$
$98$	19.6924	+	34.1082i	1.98923	+	3.44545i
$99$	−3.41421			−0.343141
$100$	−1.91421	−	3.31552i	−0.191421	−	0.331552i
$101$	1.82843	−	3.16693i	0.181935	−	0.315121i	−0.760604	−	0.649216i	$-0.775097\pi$
$101$	1.82843	−	3.16693i	0.181935	−	0.315121i	0.942540	+	0.334095i	$0.108431\pi$
$102$	−1.41421	+	2.44949i	−0.140028	+	0.242536i
$103$	14.5858			1.43718			0.718590	−	0.695434i	$-0.244788\pi$
$103$	14.5858			1.43718			0.718590	+	0.695434i	$0.244788\pi$
$104$		0			0
$105$	−6.82843			−0.666386
$106$	3.00000	−	5.19615i	0.291386	−	0.504695i
$107$	4.70711	−	8.15295i	0.455053	−	0.788175i	−0.543638	−	0.839320i	$-0.682954\pi$
$107$	4.70711	−	8.15295i	0.455053	−	0.788175i	0.998691	+	0.0511445i	$0.0162869\pi$
$108$	−10.8284	−	18.7554i	−1.04197	−	1.80474i
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$	4.12132	+	7.13834i	0.392952	+	0.680614i
$111$	−6.00000	−	10.3923i	−0.569495	−	0.986394i
$112$	14.4853			1.36873
$113$	4.41421	+	7.64564i	0.415254	+	0.719242i	0.995455	−	0.0952319i	$-0.0303593\pi$
$113$	4.41421	+	7.64564i	0.415254	+	0.719242i	−0.580201	+	0.814473i	$0.697026\pi$
$114$	−1.00000	+	1.73205i	−0.0936586	+	0.162221i
$115$	−0.707107	+	1.22474i	−0.0659380	+	0.114208i
$116$	−21.6569			−2.01079
$117$		0			0
$118$	−4.24264			−0.390567
$119$	−2.00000	+	3.46410i	−0.183340	+	0.317554i
$120$	−3.12132	+	5.40629i	−0.284936	+	0.493524i
$121$	−0.328427	−	0.568852i	−0.0298570	−	0.0517139i
$122$	19.3137			1.74858
$123$	−2.24264	−	3.88437i	−0.202212	−	0.350242i
$124$	−3.36396	−	5.82655i	−0.302093	−	0.523240i
$125$	1.00000			0.0894427
$126$	−5.82843	−	10.0951i	−0.519238	−	0.899346i
$127$	3.29289	−	5.70346i	0.292197	−	0.506100i	−0.682132	−	0.731229i	$-0.738947\pi$
$127$	3.29289	−	5.70346i	0.292197	−	0.506100i	0.974329	+	0.225129i	$0.0722804\pi$
$128$	−10.2782	+	17.8023i	−0.908471	+	1.57352i
$129$	15.6569			1.37851
$130$		0			0
$131$	−16.9706			−1.48272			−0.741362	−	0.671105i	$-0.765820\pi$
$131$	−16.9706			−1.48272			−0.741362	+	0.671105i	$0.765820\pi$
$132$	9.24264	−	16.0087i	0.804469	−	1.39338i
$133$	−1.41421	+	2.44949i	−0.122628	+	0.212398i
$134$	−2.41421	−	4.18154i	−0.208556	−	0.361230i
$135$	5.65685			0.486864
$136$	1.82843	+	3.16693i	0.156786	+	0.271562i
$137$	8.65685	+	14.9941i	0.739605	+	1.28103i	0.952673	+	0.303996i	$0.0983210\pi$
$137$	8.65685	+	14.9941i	0.739605	+	1.28103i	−0.213068	+	0.977037i	$0.568346\pi$
$138$	4.82843			0.411023
$139$	−2.24264	−	3.88437i	−0.190218	−	0.329468i	0.755104	−	0.655605i	$-0.227586\pi$
$139$	−2.24264	−	3.88437i	−0.190218	−	0.329468i	−0.945323	+	0.326137i	$0.894253\pi$
$140$	−9.24264	+	16.0087i	−0.781146	+	1.35298i
$141$	−3.41421	+	5.91359i	−0.287529	+	0.498014i
$142$	−28.7279			−2.41079
$143$		0			0
$144$	−3.00000			−0.250000
$145$	2.82843	−	4.89898i	0.234888	−	0.406838i
$146$	10.2426	−	17.7408i	0.847687	−	1.46824i
$147$	11.5355	+	19.9801i	0.951435	+	1.64793i
$148$	−32.4853			−2.67027
$149$	5.82843	+	10.0951i	0.477483	+	0.827025i	0.999667	−	0.0258077i	$-0.00821575\pi$
$149$	5.82843	+	10.0951i	0.477483	+	0.827025i	−0.522184	+	0.852833i	$0.674882\pi$
$150$	−1.70711	−	2.95680i	−0.139385	−	0.241421i
$151$	9.75736			0.794043			0.397021	−	0.917809i	$-0.370044\pi$
$151$	9.75736			0.794043			0.397021	+	0.917809i	$0.370044\pi$
$152$	1.29289	+	2.23936i	0.104867	+	0.181636i
$153$	0.414214	−	0.717439i	0.0334872	−	0.0580015i
$154$	19.8995	−	34.4669i	1.60355	−	2.77742i
$155$	1.75736			0.141154
$156$		0			0
$157$	18.0000			1.43656			0.718278	−	0.695756i	$-0.244931\pi$
$157$	18.0000			1.43656			0.718278	+	0.695756i	$0.244931\pi$
$158$	−10.2426	+	17.7408i	−0.814861	+	1.41138i
$159$	1.75736	−	3.04384i	0.139368	−	0.241392i
$160$	−0.792893	−	1.37333i	−0.0626837	−	0.108571i
$161$	6.82843			0.538155
$162$	−6.03553	−	10.4539i	−0.474196	−	0.821332i
$163$	−9.48528	−	16.4290i	−0.742945	−	1.28682i	−0.951149	−	0.308732i	$-0.900095\pi$
$163$	−9.48528	−	16.4290i	−0.742945	−	1.28682i	0.208204	−	0.978085i	$-0.433238\pi$
$164$	−12.1421			−0.948141
$165$	2.41421	+	4.18154i	0.187946	+	0.325532i
$166$	−3.82843	+	6.63103i	−0.297144	+	0.514668i
$167$	1.58579	−	2.74666i	0.122712	−	0.212543i	−0.798124	−	0.602493i	$-0.794174\pi$
$167$	1.58579	−	2.74666i	0.122712	−	0.212543i	0.920836	+	0.389950i	$0.127508\pi$
$168$	30.1421			2.32552
$169$		0			0
$170$	−2.00000			−0.153393
$171$	0.292893	−	0.507306i	0.0223981	−	0.0387947i
$172$	21.1924	−	36.7063i	1.61590	−	2.79883i
$173$	−8.41421	−	14.5738i	−0.639721	−	1.10803i	−0.985494	−	0.169711i	$-0.945717\pi$
$173$	−8.41421	−	14.5738i	−0.639721	−	1.10803i	0.345773	−	0.938318i	$-0.387617\pi$
$174$	−19.3137			−1.46417
$175$	−2.41421	−	4.18154i	−0.182497	−	0.316095i
$176$	−5.12132	−	8.87039i	−0.386034	−	0.668631i
$177$	−2.48528			−0.186805
$178$	7.24264	+	12.5446i	0.542859	+	0.940259i
$179$	−2.82843	+	4.89898i	−0.211407	+	0.366167i	−0.952155	−	0.305616i	$-0.901138\pi$
$179$	−2.82843	+	4.89898i	−0.211407	+	0.366167i	0.740748	+	0.671783i	$0.234471\pi$
$180$	1.91421	−	3.31552i	0.142677	−	0.247124i
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$		0			0
$183$	11.3137			0.836333
$184$	3.12132	−	5.40629i	0.230107	−	0.398557i
$185$	4.24264	−	7.34847i	0.311925	−	0.540270i
$186$	−3.00000	−	5.19615i	−0.219971	−	0.381000i
$187$	2.82843			0.206835
$188$	9.24264	+	16.0087i	0.674089	+	1.16756i
$189$	−13.6569	−	23.6544i	−0.993390	−	1.72060i
$190$	−1.41421			−0.102598
$191$	−1.17157	−	2.02922i	−0.0847720	−	0.146829i	0.820522	−	0.571615i	$-0.193683\pi$
$191$	−1.17157	−	2.02922i	−0.0847720	−	0.146829i	−0.905294	+	0.424785i	$0.860350\pi$
$192$	−6.94975	+	12.0373i	−0.501555	+	0.868718i
$193$	−2.17157	+	3.76127i	−0.156313	+	0.270742i	−0.933536	−	0.358483i	$-0.883294\pi$
$193$	−2.17157	+	3.76127i	−0.156313	+	0.270742i	0.777223	+	0.629225i	$0.216628\pi$
$194$	18.4853			1.32717
$195$		0			0
$196$	62.4558			4.46113
$197$	−5.48528	+	9.50079i	−0.390810	+	0.676903i	−0.992557	−	0.121784i	$-0.961138\pi$
$197$	−5.48528	+	9.50079i	−0.390810	+	0.676903i	0.601746	+	0.798687i	$0.294472\pi$
$198$	−4.12132	+	7.13834i	−0.292889	+	0.507299i
$199$	−2.00000	−	3.46410i	−0.141776	−	0.245564i	0.786389	−	0.617731i	$-0.211948\pi$
$199$	−2.00000	−	3.46410i	−0.141776	−	0.245564i	−0.928166	+	0.372168i	$0.878615\pi$
$200$	−4.41421			−0.312132
$201$	−1.41421	−	2.44949i	−0.0997509	−	0.172774i
$202$	−4.41421	−	7.64564i	−0.310583	−	0.537946i
$203$	−27.3137			−1.91705
$204$	2.24264	+	3.88437i	0.157016	+	0.271960i
$205$	1.58579	−	2.74666i	0.110756	−	0.191835i
$206$	17.6066	−	30.4955i	1.22671	−	2.12472i
$207$	−1.41421			−0.0982946
$208$		0			0
$209$	2.00000			0.138343
$210$	−8.24264	+	14.2767i	−0.568796	+	0.985184i
$211$	−1.65685	+	2.86976i	−0.114063	+	0.197562i	−0.917405	−	0.397956i	$-0.869720\pi$
$211$	−1.65685	+	2.86976i	−0.114063	+	0.197562i	0.803342	+	0.595518i	$0.203053\pi$
$212$	−4.75736	−	8.23999i	−0.326737	−	0.565925i
$213$	−16.8284			−1.15306
$214$	−11.3640	−	19.6830i	−0.776824	−	1.34550i
$215$	5.53553	+	9.58783i	0.377520	+	0.653884i
$216$	−24.9706			−1.69903
$217$	−4.24264	−	7.34847i	−0.288009	−	0.498847i
$218$	−2.41421	+	4.18154i	−0.163511	+	0.283210i
$219$	6.00000	−	10.3923i	0.405442	−	0.702247i
$220$	13.0711			0.881251
$221$		0			0
$222$	−28.9706			−1.94438
$223$	−4.75736	+	8.23999i	−0.318576	+	0.551790i	−0.980191	−	0.198053i	$-0.936538\pi$
$223$	−4.75736	+	8.23999i	−0.318576	+	0.551790i	0.661615	+	0.749844i	$0.269871\pi$
$224$	−3.82843	+	6.63103i	−0.255798	+	0.443054i
$225$	0.500000	+	0.866025i	0.0333333	+	0.0577350i
$226$	21.3137			1.41777
$227$	8.17157	+	14.1536i	0.542366	+	0.939406i	0.998768	+	0.0496320i	$0.0158048\pi$
$227$	8.17157	+	14.1536i	0.542366	+	0.939406i	−0.456401	+	0.889774i	$0.650862\pi$
$228$	1.58579	+	2.74666i	0.105021	+	0.181902i
$229$	−4.82843			−0.319071			−0.159536	−	0.987192i	$-0.551000\pi$
$229$	−4.82843			−0.319071			−0.159536	+	0.987192i	$0.551000\pi$
$230$	1.70711	+	2.95680i	0.112563	+	0.194965i
$231$	11.6569	−	20.1903i	0.766965	−	1.32842i
$232$	−12.4853	+	21.6251i	−0.819699	+	1.41976i
$233$	−20.6274			−1.35135			−0.675674	−	0.737201i	$-0.736147\pi$
$233$	−20.6274			−1.35135			−0.675674	+	0.737201i	$0.736147\pi$
$234$		0			0
$235$	−4.82843			−0.314972
$236$	−3.36396	+	5.82655i	−0.218975	+	0.379276i
$237$	−6.00000	+	10.3923i	−0.389742	+	0.675053i
$238$	4.82843	+	8.36308i	0.312980	+	0.542098i
$239$	−3.41421			−0.220847			−0.110424	−	0.993885i	$-0.535221\pi$
$239$	−3.41421			−0.220847			−0.110424	+	0.993885i	$0.535221\pi$
$240$	2.12132	+	3.67423i	0.136931	+	0.237171i
$241$	7.24264	+	12.5446i	0.466539	+	0.808070i	0.999270	−	0.0382151i	$-0.0121672\pi$
$241$	7.24264	+	12.5446i	0.466539	+	0.808070i	−0.532730	+	0.846285i	$0.678834\pi$
$242$	−1.58579			−0.101938
$243$	4.94975	+	8.57321i	0.317526	+	0.549972i
$244$	15.3137	−	26.5241i	0.980360	−	1.69803i
$245$	−8.15685	+	14.1281i	−0.521122	+	0.902610i
$246$	−10.8284			−0.690395
$247$		0			0
$248$	−7.75736			−0.492593
$249$	−2.24264	+	3.88437i	−0.142122	+	0.246162i
$250$	1.20711	−	2.09077i	0.0763441	−	0.132232i
$251$	−9.89949	−	17.1464i	−0.624851	−	1.08227i	−0.988570	−	0.150764i	$-0.951827\pi$
$251$	−9.89949	−	17.1464i	−0.624851	−	1.08227i	0.363719	−	0.931509i	$-0.381507\pi$
$252$	−18.4853			−1.16446
$253$	−2.41421	−	4.18154i	−0.151780	−	0.262891i
$254$	−7.94975	−	13.7694i	−0.498812	−	0.863967i
$255$	−1.17157			−0.0733667
$256$	14.9853	+	25.9553i	0.936580	+	1.62220i
$257$	−13.8284	+	23.9515i	−0.862594	+	1.49406i	0.00682332	+	0.999977i	$0.497828\pi$
$257$	−13.8284	+	23.9515i	−0.862594	+	1.49406i	−0.869417	+	0.494079i	$0.835505\pi$
$258$	18.8995	−	32.7349i	1.17663	−	2.03798i
$259$	−40.9706			−2.54579
$260$		0			0
$261$	5.65685			0.350150
$262$	−20.4853	+	35.4815i	−1.26558	+	2.19206i
$263$	5.29289	−	9.16756i	0.326374	−	0.565296i	−0.655416	−	0.755268i	$-0.727507\pi$
$263$	5.29289	−	9.16756i	0.326374	−	0.565296i	0.981789	+	0.189972i	$0.0608399\pi$
$264$	−10.6569	−	18.4582i	−0.655884	−	1.13602i
$265$	2.48528			0.152670
$266$	3.41421	+	5.91359i	0.209339	+	0.362586i
$267$	4.24264	+	7.34847i	0.259645	+	0.449719i
$268$	−7.65685			−0.467717
$269$	12.6569	+	21.9223i	0.771702	+	1.33663i	0.936630	+	0.350321i	$0.113928\pi$
$269$	12.6569	+	21.9223i	0.771702	+	1.33663i	−0.164928	+	0.986306i	$0.552739\pi$
$270$	6.82843	−	11.8272i	0.415565	−	0.719779i
$271$	−13.3640	+	23.1471i	−0.811803	+	1.40608i	0.0997982	+	0.995008i	$0.468180\pi$
$271$	−13.3640	+	23.1471i	−0.811803	+	1.40608i	−0.911601	+	0.411076i	$0.865153\pi$
$272$	2.48528			0.150692
$273$		0			0
$274$	41.7990			2.52517
$275$	−1.70711	+	2.95680i	−0.102942	+	0.178301i
$276$	3.82843	−	6.63103i	0.230444	−	0.399141i
$277$	6.41421	+	11.1097i	0.385393	+	0.667520i	0.991824	−	0.127616i	$-0.0407326\pi$
$277$	6.41421	+	11.1097i	0.385393	+	0.667520i	−0.606431	+	0.795136i	$0.707399\pi$
$278$	−10.8284			−0.649446
$279$	0.878680	+	1.52192i	0.0526052	+	0.0911148i
$280$	10.6569	+	18.4582i	0.636869	+	1.10309i
$281$	21.7990			1.30042			0.650209	−	0.759755i	$-0.274681\pi$
$281$	21.7990			1.30042			0.650209	+	0.759755i	$0.274681\pi$
$282$	8.24264	+	14.2767i	0.490842	+	0.850163i
$283$	8.36396	−	14.4868i	0.497186	−	0.861151i	−0.502809	−	0.864398i	$-0.667700\pi$
$283$	8.36396	−	14.4868i	0.497186	−	0.861151i	0.999995	+	0.00324643i	$0.00103337\pi$
$284$	−22.7782	+	39.4530i	−1.35164	+	2.34110i
$285$	−0.828427			−0.0490718
$286$		0			0
$287$	−15.3137			−0.903940
$288$	0.792893	−	1.37333i	0.0467217	−	0.0809243i
$289$	8.15685	−	14.1281i	0.479815	−	0.831064i
$290$	−6.82843	−	11.8272i	−0.400979	−	0.694516i
$291$	10.8284			0.634774
$292$	−16.2426	−	28.1331i	−0.950529	−	1.64636i
$293$	−13.0711	−	22.6398i	−0.763620	−	1.32263i	−0.940973	−	0.338481i	$-0.890087\pi$
$293$	−13.0711	−	22.6398i	−0.763620	−	1.32263i	0.177353	−	0.984147i	$-0.443247\pi$
$294$	55.6985			3.24840
$295$	−0.878680	−	1.52192i	−0.0511587	−	0.0886095i
$296$	−18.7279	+	32.4377i	−1.08854	+	1.88540i
$297$	−9.65685	+	16.7262i	−0.560348	+	0.970550i
$298$	28.1421			1.63023
$299$		0			0
$300$	−5.41421			−0.312590
$301$	26.7279	−	46.2941i	1.54057	−	2.66835i
$302$	11.7782	−	20.4004i	0.677758	−	1.17391i
$303$	−2.58579	−	4.47871i	−0.148550	−	0.257295i
$304$	1.75736			0.100791
$305$	4.00000	+	6.92820i	0.229039	+	0.396708i
$306$	−1.00000	−	1.73205i	−0.0571662	−	0.0990148i
$307$	24.8284			1.41703			0.708517	−	0.705694i	$-0.249365\pi$
$307$	24.8284			1.41703			0.708517	+	0.705694i	$0.249365\pi$
$308$	−31.5563	−	54.6572i	−1.79809	−	3.11438i
$309$	10.3137	−	17.8639i	0.586726	−	1.01624i
$310$	2.12132	−	3.67423i	0.120483	−	0.208683i
$311$	8.48528			0.481156			0.240578	−	0.970630i	$-0.422663\pi$
$311$	8.48528			0.481156			0.240578	+	0.970630i	$0.422663\pi$
$312$		0			0
$313$	−4.82843			−0.272919			−0.136459	−	0.990646i	$-0.543572\pi$
$313$	−4.82843			−0.272919			−0.136459	+	0.990646i	$0.543572\pi$
$314$	21.7279	−	37.6339i	1.22618	−	2.12380i
$315$	2.41421	−	4.18154i	0.136026	−	0.235603i
$316$	16.2426	+	28.1331i	0.913720	+	1.58261i
$317$	−2.14214			−0.120314			−0.0601572	−	0.998189i	$-0.519160\pi$
$317$	−2.14214			−0.120314			−0.0601572	+	0.998189i	$0.519160\pi$
$318$	−4.24264	−	7.34847i	−0.237915	−	0.412082i
$319$	9.65685	+	16.7262i	0.540680	+	0.936485i
$320$	−9.82843			−0.549426
$321$	−6.65685	−	11.5300i	−0.371549	−	0.643542i
$322$	8.24264	−	14.2767i	0.459344	−	0.795608i
$323$	−0.242641	+	0.420266i	−0.0135009	+	0.0233842i
$324$	−19.1421			−1.06345
$325$		0			0
$326$	−45.7990			−2.53657
$327$	−1.41421	+	2.44949i	−0.0782062	+	0.135457i
$328$	−7.00000	+	12.1244i	−0.386510	+	0.669456i
$329$	11.6569	+	20.1903i	0.642663	+	1.11313i
$330$	11.6569			0.641689
$331$	13.0208	+	22.5527i	0.715689	+	1.23961i	0.962693	+	0.270595i	$0.0872204\pi$
$331$	13.0208	+	22.5527i	0.715689	+	1.23961i	−0.247005	+	0.969014i	$0.579446\pi$
$332$	6.07107	+	10.5154i	0.333193	+	0.577107i
$333$	8.48528			0.464991
$334$	−3.82843	−	6.63103i	−0.209482	−	0.362834i
$335$	1.00000	−	1.73205i	0.0546358	−	0.0946320i
$336$	10.2426	−	17.7408i	0.558782	−	0.967839i
$337$	12.8284			0.698809			0.349404	−	0.936972i	$-0.386384\pi$
$337$	12.8284			0.698809			0.349404	+	0.936972i	$0.386384\pi$
$338$		0			0
$339$	12.4853			0.678107
$340$	−1.58579	+	2.74666i	−0.0860013	+	0.148959i
$341$	−3.00000	+	5.19615i	−0.162459	+	0.281387i
$342$	−0.707107	−	1.22474i	−0.0382360	−	0.0662266i
$343$	44.9706			2.42818
$344$	−24.4350	−	42.3227i	−1.31745	−	2.28189i
$345$	1.00000	+	1.73205i	0.0538382	+	0.0932505i
$346$	−40.6274			−2.18414
$347$	2.12132	+	3.67423i	0.113878	+	0.197243i	0.917331	−	0.398126i	$-0.130339\pi$
$347$	2.12132	+	3.67423i	0.113878	+	0.197243i	−0.803452	+	0.595369i	$0.797006\pi$
$348$	−15.3137	+	26.5241i	−0.820901	+	1.42184i
$349$	−9.24264	+	16.0087i	−0.494747	+	0.856927i	−0.999982	−	0.00605481i	$-0.998073\pi$
$349$	−9.24264	+	16.0087i	−0.494747	+	0.856927i	0.505234	+	0.862982i	$0.331406\pi$
$350$	−11.6569			−0.623085
$351$		0			0
$352$	5.41421			0.288579
$353$	−7.41421	+	12.8418i	−0.394619	+	0.683500i	−0.993052	−	0.117673i	$-0.962457\pi$
$353$	−7.41421	+	12.8418i	−0.394619	+	0.683500i	0.598434	+	0.801172i	$0.295790\pi$
$354$	−3.00000	+	5.19615i	−0.159448	+	0.276172i
$355$	−5.94975	−	10.3053i	−0.315780	−	0.546947i
$356$	22.9706			1.21744
$357$	2.82843	+	4.89898i	0.149696	+	0.259281i
$358$	6.82843	+	11.8272i	0.360894	+	0.625086i
$359$	−8.10051			−0.427528			−0.213764	−	0.976885i	$-0.568572\pi$
$359$	−8.10051			−0.427528			−0.213764	+	0.976885i	$0.568572\pi$
$360$	−2.20711	−	3.82282i	−0.116325	−	0.201480i
$361$	9.32843	−	16.1573i	0.490970	−	0.850385i
$362$		0			0
$363$	−0.928932			−0.0487563
$364$		0			0
$365$	8.48528			0.444140
$366$	13.6569	−	23.6544i	0.713855	−	1.23643i
$367$	−17.7782	+	30.7927i	−0.928013	+	1.60737i	−0.141371	+	0.989957i	$0.545151\pi$
$367$	−17.7782	+	30.7927i	−0.928013	+	1.60737i	−0.786642	+	0.617409i	$0.788182\pi$
$368$	−2.12132	−	3.67423i	−0.110581	−	0.191533i
$369$	3.17157			0.165105
$370$	−10.2426	−	17.7408i	−0.532490	−	0.922299i
$371$	−6.00000	−	10.3923i	−0.311504	−	0.539542i
$372$	−9.51472			−0.493315
$373$	1.34315	+	2.32640i	0.0695455	+	0.120456i	0.898701	−	0.438561i	$-0.144512\pi$
$373$	1.34315	+	2.32640i	0.0695455	+	0.120456i	−0.829156	+	0.559018i	$0.811178\pi$
$374$	3.41421	−	5.91359i	0.176545	−	0.305785i
$375$	0.707107	−	1.22474i	0.0365148	−	0.0632456i
$376$	21.3137			1.09917
$377$		0			0
$378$	−65.9411			−3.39165
$379$	−14.5355	+	25.1763i	−0.746640	+	1.29322i	0.202784	+	0.979223i	$0.435001\pi$
$379$	−14.5355	+	25.1763i	−0.746640	+	1.29322i	−0.949425	+	0.313995i	$0.898332\pi$
$380$	−1.12132	+	1.94218i	−0.0575225	+	0.0996319i
$381$	−4.65685	−	8.06591i	−0.238578	−	0.413229i
$382$	−5.65685			−0.289430
$383$	14.5563	+	25.2123i	0.743795	+	1.28829i	0.950756	+	0.309941i	$0.100309\pi$
$383$	14.5563	+	25.2123i	0.743795	+	1.28829i	−0.206961	+	0.978349i	$0.566357\pi$
$384$	14.5355	+	25.1763i	0.741763	+	1.28477i
$385$	16.4853			0.840168
$386$	5.24264	+	9.08052i	0.266843	+	0.462186i
$387$	−5.53553	+	9.58783i	−0.281387	+	0.487377i
$388$	14.6569	−	25.3864i	0.744089	−	1.28880i
$389$	28.6274			1.45147			0.725734	−	0.687976i	$-0.241500\pi$
$389$	28.6274			1.45147			0.725734	+	0.687976i	$0.241500\pi$
$390$		0			0
$391$	1.17157			0.0592490
$392$	36.0061	−	62.3644i	1.81858	−	3.14988i
$393$	−12.0000	+	20.7846i	−0.605320	+	1.04844i
$394$	13.2426	+	22.9369i	0.667155	+	1.15555i
$395$	−8.48528			−0.426941
$396$	6.53553	+	11.3199i	0.328423	+	0.568845i
$397$	−5.89949	−	10.2182i	−0.296087	−	0.512838i	0.679150	−	0.733999i	$-0.262349\pi$
$397$	−5.89949	−	10.2182i	−0.296087	−	0.512838i	−0.975237	+	0.221161i	$0.929015\pi$
$398$	−9.65685			−0.484054
$399$	2.00000	+	3.46410i	0.100125	+	0.173422i
$400$	−1.50000	+	2.59808i	−0.0750000	+	0.129904i
$401$	2.65685	−	4.60181i	0.132677	−	0.229803i	−0.792031	−	0.610481i	$-0.790976\pi$
$401$	2.65685	−	4.60181i	0.132677	−	0.229803i	0.924708	+	0.380678i	$0.124309\pi$
$402$	−6.82843			−0.340571
$403$		0			0
$404$	−14.0000			−0.696526
$405$	2.50000	−	4.33013i	0.124226	−	0.215166i
$406$	−32.9706	+	57.1067i	−1.63630	+	2.83416i
$407$	14.4853	+	25.0892i	0.718009	+	1.24363i
$408$	5.17157			0.256031
$409$	−3.58579	−	6.21076i	−0.177306	−	0.307103i	0.763651	−	0.645629i	$-0.223405\pi$
$409$	−3.58579	−	6.21076i	−0.177306	−	0.307103i	−0.940957	+	0.338527i	$0.890071\pi$
$410$	−3.82843	−	6.63103i	−0.189073	−	0.327483i
$411$	24.4853			1.20777
$412$	−27.9203	−	48.3594i	−1.37553	−	2.38250i
$413$	−4.24264	+	7.34847i	−0.208767	+	0.361595i
$414$	−1.70711	+	2.95680i	−0.0838997	+	0.145319i
$415$	−3.17157			−0.155686
$416$		0			0
$417$	−6.34315			−0.310625
$418$	2.41421	−	4.18154i	0.118083	−	0.204526i
$419$	−5.41421	+	9.37769i	−0.264502	+	0.458130i	−0.967433	−	0.253127i	$-0.918541\pi$
$419$	−5.41421	+	9.37769i	−0.264502	+	0.458130i	0.702931	+	0.711258i	$0.251874\pi$
$420$	13.0711	+	22.6398i	0.637803	+	1.10471i
$421$	−34.9706			−1.70436			−0.852180	−	0.523248i	$-0.824720\pi$
$421$	−34.9706			−1.70436			−0.852180	+	0.523248i	$0.824720\pi$
$422$	4.00000	+	6.92820i	0.194717	+	0.337260i
$423$	−2.41421	−	4.18154i	−0.117383	−	0.203313i
$424$	−10.9706			−0.532778
$425$	−0.414214	−	0.717439i	−0.0200923	−	0.0348009i
$426$	−20.3137	+	35.1844i	−0.984202	+	1.70469i
$427$	19.3137	−	33.4523i	0.934656	−	1.61887i
$428$	−36.0416			−1.74214
$429$		0			0
$430$	26.7279			1.28893
$431$	−20.1924	+	34.9742i	−0.972633	+	1.68465i	−0.285099	+	0.958498i	$0.592026\pi$
$431$	−20.1924	+	34.9742i	−0.972633	+	1.68465i	−0.687534	+	0.726152i	$0.741307\pi$
$432$	−8.48528	+	14.6969i	−0.408248	+	0.707107i
$433$	−3.82843	−	6.63103i	−0.183982	−	0.318667i	0.759251	−	0.650798i	$-0.225566\pi$
$433$	−3.82843	−	6.63103i	−0.183982	−	0.318667i	−0.943233	+	0.332131i	$0.892232\pi$
$434$	−20.4853			−0.983325
$435$	−4.00000	−	6.92820i	−0.191785	−	0.332182i
$436$	3.82843	+	6.63103i	0.183348	+	0.317569i
$437$	0.828427			0.0396290
$438$	−14.4853	−	25.0892i	−0.692134	−	1.19881i
$439$	−0.485281	+	0.840532i	−0.0231612	+	0.0401164i	−0.877374	−	0.479808i	$-0.840706\pi$
$439$	−0.485281	+	0.840532i	−0.0231612	+	0.0401164i	0.854212	+	0.519924i	$0.174040\pi$
$440$	7.53553	−	13.0519i	0.359242	−	0.622226i
$441$	−16.3137			−0.776843
$442$		0			0
$443$	−9.41421			−0.447283			−0.223641	−	0.974671i	$-0.571794\pi$
$443$	−9.41421			−0.447283			−0.223641	+	0.974671i	$0.571794\pi$
$444$	−22.9706	+	39.7862i	−1.09013	+	1.88817i
$445$	−3.00000	+	5.19615i	−0.142214	+	0.246321i
$446$	11.4853	+	19.8931i	0.543844	+	0.941965i
$447$	16.4853			0.779727
$448$	23.7279	+	41.0980i	1.12104	+	1.94170i
$449$	16.5563	+	28.6764i	0.781342	+	1.35332i	0.931160	+	0.364611i	$0.118798\pi$
$449$	16.5563	+	28.6764i	0.781342	+	1.35332i	−0.149817	+	0.988714i	$0.547869\pi$
$450$	2.41421			0.113807
$451$	5.41421	+	9.37769i	0.254945	+	0.441578i
$452$	16.8995	−	29.2708i	0.794885	−	1.37678i
$453$	6.89949	−	11.9503i	0.324167	−	0.561473i
$454$	39.4558			1.85175
$455$		0			0
$456$	3.65685			0.171248
$457$	9.00000	−	15.5885i	0.421002	−	0.729197i	−0.575036	−	0.818128i	$-0.695012\pi$
$457$	9.00000	−	15.5885i	0.421002	−	0.729197i	0.996038	+	0.0889312i	$0.0283451\pi$
$458$	−5.82843	+	10.0951i	−0.272345	+	0.471715i
$459$	−2.34315	−	4.05845i	−0.109369	−	0.189432i
$460$	5.41421			0.252439
$461$	−4.75736	−	8.23999i	−0.221572	−	0.383775i	0.733713	−	0.679459i	$-0.237786\pi$
$461$	−4.75736	−	8.23999i	−0.221572	−	0.383775i	−0.955286	+	0.295685i	$0.904452\pi$
$462$	−28.1421	−	48.7436i	−1.30929	−	2.26776i
$463$	−4.34315			−0.201843			−0.100922	−	0.994894i	$-0.532179\pi$
$463$	−4.34315			−0.201843			−0.100922	+	0.994894i	$0.532179\pi$
$464$	8.48528	+	14.6969i	0.393919	+	0.682288i
$465$	1.24264	−	2.15232i	0.0576261	−	0.0998113i
$466$	−24.8995	+	43.1272i	−1.15345	+	1.99783i
$467$	−13.4142			−0.620736			−0.310368	−	0.950617i	$-0.600452\pi$
$467$	−13.4142			−0.620736			−0.310368	+	0.950617i	$0.600452\pi$
$468$		0			0
$469$	−9.65685			−0.445912
$470$	−5.82843	+	10.0951i	−0.268845	+	0.465654i
$471$	12.7279	−	22.0454i	0.586472	−	1.01580i
$472$	3.87868	+	6.71807i	0.178531	+	0.309224i
$473$	−37.7990			−1.73800
$474$	14.4853	+	25.0892i	0.665331	+	1.15239i
$475$	−0.292893	−	0.507306i	−0.0134389	−	0.0232768i
$476$	15.3137			0.701903
$477$	1.24264	+	2.15232i	0.0568966	+	0.0985478i
$478$	−4.12132	+	7.13834i	−0.188505	+	0.326500i
$479$	15.3640	−	26.6112i	0.701997	−	1.21589i	−0.265767	−	0.964037i	$-0.585625\pi$
$479$	15.3640	−	26.6112i	0.701997	−	1.21589i	0.967764	−	0.251858i	$-0.0810415\pi$
$480$	−2.24264			−0.102362
$481$		0			0
$482$	34.9706			1.59287
$483$	4.82843	−	8.36308i	0.219701	−	0.380533i
$484$	−1.25736	+	2.17781i	−0.0571527	+	0.0989914i
$485$	3.82843	+	6.63103i	0.173840	+	0.301100i
$486$	23.8995			1.08410
$487$	5.48528	+	9.50079i	0.248562	+	0.430522i	0.963127	−	0.269047i	$-0.0867088\pi$
$487$	5.48528	+	9.50079i	0.248562	+	0.430522i	−0.714565	+	0.699569i	$0.753375\pi$
$488$	−17.6569	−	30.5826i	−0.799288	−	1.38441i
$489$	−26.8284			−1.21322
$490$	19.6924	+	34.1082i	0.889611	+	1.54085i
$491$	−2.58579	+	4.47871i	−0.116695	+	0.202122i	−0.918456	−	0.395523i	$-0.870563\pi$
$491$	−2.58579	+	4.47871i	−0.116695	+	0.202122i	0.801761	+	0.597645i	$0.203897\pi$
$492$	−8.58579	+	14.8710i	−0.387077	+	0.670437i
$493$	−4.68629			−0.211060
$494$		0			0
$495$	−3.41421			−0.153457
$496$	−2.63604	+	4.56575i	−0.118362	+	0.205008i
$497$	−28.7279	+	49.7582i	−1.28862	+	2.23196i
$498$	5.41421	+	9.37769i	0.242617	+	0.420224i
$499$	41.5563			1.86032			0.930159	−	0.367157i	$-0.119669\pi$
$499$	41.5563			1.86032			0.930159	+	0.367157i	$0.119669\pi$
$500$	−1.91421	−	3.31552i	−0.0856062	−	0.148274i
$501$	−2.24264	−	3.88437i	−0.100194	−	0.173541i
$502$	−47.7990			−2.13337
$503$	−18.9497	−	32.8219i	−0.844927	−	1.46346i	−0.885684	−	0.464288i	$-0.846310\pi$
$503$	−18.9497	−	32.8219i	−0.844927	−	1.46346i	0.0407567	−	0.999169i	$-0.487023\pi$
$504$	−10.6569	+	18.4582i	−0.474694	+	0.822194i
$505$	1.82843	−	3.16693i	0.0813639	−	0.140926i
$506$	−11.6569			−0.518210
$507$		0			0
$508$	−25.2132			−1.11866
$509$	−20.5563	+	35.6046i	−0.911144	+	1.57815i	−0.0986936	+	0.995118i	$0.531466\pi$
$509$	−20.5563	+	35.6046i	−0.911144	+	1.57815i	−0.812451	+	0.583030i	$0.801867\pi$
$510$	−1.41421	+	2.44949i	−0.0626224	+	0.108465i
$511$	−20.4853	−	35.4815i	−0.906215	−	1.56961i
$512$	31.2426			1.38074
$513$	−1.65685	−	2.86976i	−0.0731519	−	0.126703i
$514$	33.3848	+	57.8241i	1.47254	+	2.55051i
$515$	14.5858			0.642727
$516$	−29.9706	−	51.9105i	−1.31938	−	2.28523i
$517$	8.24264	−	14.2767i	0.362511	−	0.627887i
$518$	−49.4558	+	85.6600i	−2.17297	+	3.76369i
$519$	−23.7990			−1.04466
$520$		0			0
$521$	−17.6569			−0.773561			−0.386780	−	0.922172i	$-0.626413\pi$
$521$	−17.6569			−0.773561			−0.386780	+	0.922172i	$0.626413\pi$
$522$	6.82843	−	11.8272i	0.298872	−	0.517662i
$523$	9.87868	−	17.1104i	0.431965	−	0.748184i	−0.565078	−	0.825038i	$-0.691154\pi$
$523$	9.87868	−	17.1104i	0.431965	−	0.748184i	0.997042	+	0.0768531i	$0.0244872\pi$
$524$	32.4853	+	56.2662i	1.41913	+	2.45800i
$525$	−6.82843			−0.298017
$526$	−12.7782	−	22.1324i	−0.557155	−	0.965021i
$527$	−0.727922	−	1.26080i	−0.0317088	−	0.0549212i
$528$	−14.4853			−0.630391
$529$	10.5000	+	18.1865i	0.456522	+	0.790719i
$530$	3.00000	−	5.19615i	0.130312	−	0.225706i
$531$	0.878680	−	1.52192i	0.0381314	−	0.0660456i
$532$	10.8284			0.469472
$533$		0			0
$534$	20.4853			0.886485
$535$	4.70711	−	8.15295i	0.203506	−	0.352483i
$536$	−4.41421	+	7.64564i	−0.190665	+	0.330241i
$537$	4.00000	+	6.92820i	0.172613	+	0.298974i
$538$	61.1127			2.63476
$539$	−27.8492	−	48.2363i	−1.19955	−	2.07768i
$540$	−10.8284	−	18.7554i	−0.465981	−	0.807103i
$541$	−7.17157			−0.308330			−0.154165	−	0.988045i	$-0.549269\pi$
$541$	−7.17157			−0.308330			−0.154165	+	0.988045i	$0.549269\pi$
$542$	32.2635	+	55.8819i	1.38583	+	2.40034i
$543$		0			0
$544$	−0.656854	+	1.13770i	−0.0281624	+	0.0487787i
$545$	−2.00000			−0.0856706
$546$		0			0
$547$	13.2132			0.564956			0.282478	−	0.959274i	$-0.408844\pi$
$547$	13.2132			0.564956			0.282478	+	0.959274i	$0.408844\pi$
$548$	33.1421	−	57.4039i	1.41576	−	2.45217i
$549$	−4.00000	+	6.92820i	−0.170716	+	0.295689i
$550$	4.12132	+	7.13834i	0.175734	+	0.304380i
$551$	−3.31371			−0.141169
$552$	−4.41421	−	7.64564i	−0.187881	−	0.325420i
$553$	20.4853	+	35.4815i	0.871123	+	1.50883i
$554$	30.9706			1.31581
$555$	−6.00000	−	10.3923i	−0.254686	−	0.441129i
$556$	−8.58579	+	14.8710i	−0.364118	+	0.630672i
$557$	17.8995	−	31.0028i	0.758426	−	1.31363i	−0.185227	−	0.982696i	$-0.559302\pi$
$557$	17.8995	−	31.0028i	0.758426	−	1.31363i	0.943653	−	0.330937i	$-0.107365\pi$
$558$	4.24264			0.179605
$559$		0			0
$560$	14.4853			0.612115
$561$	2.00000	−	3.46410i	0.0844401	−	0.146254i
$562$	26.3137	−	45.5767i	1.10998	−	1.92254i
$563$	3.87868	+	6.71807i	0.163467	+	0.283133i	0.936110	−	0.351708i	$-0.114399\pi$
$563$	3.87868	+	6.71807i	0.163467	+	0.283133i	−0.772643	+	0.634841i	$0.781066\pi$
$564$	26.1421			1.10078
$565$	4.41421	+	7.64564i	0.185707	+	0.321655i
$566$	−20.1924	−	34.9742i	−0.848749	−	1.47008i
$567$	−24.1421			−1.01387
$568$	26.2635	+	45.4896i	1.10199	+	1.90870i
$569$	5.17157	−	8.95743i	0.216804	−	0.375515i	−0.737025	−	0.675865i	$-0.763770\pi$
$569$	5.17157	−	8.95743i	0.216804	−	0.375515i	0.953829	+	0.300350i	$0.0971035\pi$
$570$	−1.00000	+	1.73205i	−0.0418854	+	0.0725476i
$571$	−11.5147			−0.481876			−0.240938	−	0.970541i	$-0.577455\pi$
$571$	−11.5147			−0.481876			−0.240938	+	0.970541i	$0.577455\pi$
$572$		0			0
$573$	−3.31371			−0.138432
$574$	−18.4853	+	32.0174i	−0.771561	+	1.33638i
$575$	−0.707107	+	1.22474i	−0.0294884	+	0.0510754i
$576$	−4.91421	−	8.51167i	−0.204759	−	0.354653i
$577$	−34.8284			−1.44993			−0.724963	−	0.688788i	$-0.758143\pi$
$577$	−34.8284			−1.44993			−0.724963	+	0.688788i	$0.758143\pi$
$578$	−19.6924	−	34.1082i	−0.819095	−	1.41871i
$579$	3.07107	+	5.31925i	0.127629	+	0.221060i
$580$	−21.6569			−0.899252
$581$	7.65685	+	13.2621i	0.317660	+	0.550203i
$582$	13.0711	−	22.6398i	0.541813	−	0.938448i
$583$	−4.24264	+	7.34847i	−0.175712	+	0.304342i
$584$	−37.4558			−1.54993
$585$		0			0
$586$	−63.1127			−2.60716
$587$	−10.1716	+	17.6177i	−0.419826	+	0.727160i	−0.995922	−	0.0902226i	$-0.971242\pi$
$587$	−10.1716	+	17.6177i	−0.419826	+	0.727160i	0.576096	+	0.817382i	$0.304575\pi$
$588$	44.1630	−	76.4925i	1.82125	−	3.15450i
$589$	−0.514719	−	0.891519i	−0.0212086	−	0.0367344i
$590$	−4.24264			−0.174667
$591$	7.75736	+	13.4361i	0.319095	+	0.552689i
$592$	12.7279	+	22.0454i	0.523114	+	0.906061i
$593$	−24.6274			−1.01133			−0.505663	−	0.862731i	$-0.668752\pi$
$593$	−24.6274			−1.01133			−0.505663	+	0.862731i	$0.668752\pi$
$594$	23.3137	+	40.3805i	0.956573	+	1.65683i
$595$	−2.00000	+	3.46410i	−0.0819920	+	0.142014i
$596$	22.3137	−	38.6485i	0.914005	−	1.58310i
$597$	−5.65685			−0.231520
$598$		0			0
$599$	25.4558			1.04010			0.520049	−	0.854137i	$-0.325914\pi$
$599$	25.4558			1.04010			0.520049	+	0.854137i	$0.325914\pi$
$600$	−3.12132	+	5.40629i	−0.127427	+	0.220711i
$601$	22.3137	−	38.6485i	0.910195	−	1.57650i	0.0964075	−	0.995342i	$-0.469265\pi$
$601$	22.3137	−	38.6485i	0.910195	−	1.57650i	0.813788	−	0.581162i	$-0.197402\pi$
$602$	−64.5269	−	111.764i	−2.62992	−	4.55516i
$603$	2.00000			0.0814463
$604$	−18.6777	−	32.3507i	−0.759984	−	1.31633i
$605$	−0.328427	−	0.568852i	−0.0133525	−	0.0231271i
$606$	−12.4853			−0.507180
$607$	−15.8787	−	27.5027i	−0.644496	−	1.11630i	−0.984418	−	0.175846i	$-0.943734\pi$
$607$	−15.8787	−	27.5027i	−0.644496	−	1.11630i	0.339922	−	0.940454i	$-0.389599\pi$
$608$	−0.464466	+	0.804479i	−0.0188366	+	0.0326259i
$609$	−19.3137	+	33.4523i	−0.782631	+	1.35556i
$610$	19.3137			0.781989
$611$		0			0
$612$	−3.17157			−0.128203
$613$	7.34315	−	12.7187i	0.296587	−	0.513704i	−0.678766	−	0.734355i	$-0.737485\pi$
$613$	7.34315	−	12.7187i	0.296587	−	0.513704i	0.975353	+	0.220651i	$0.0708182\pi$
$614$	29.9706	−	51.9105i	1.20951	−	2.09494i
$615$	−2.24264	−	3.88437i	−0.0904320	−	0.156633i
$616$	−72.7696			−2.93197
$617$	−5.48528	−	9.50079i	−0.220829	−	0.382487i	0.734231	−	0.678900i	$-0.237543\pi$
$617$	−5.48528	−	9.50079i	−0.220829	−	0.382487i	−0.955060	+	0.296413i	$0.904210\pi$
$618$	−24.8995	−	43.1272i	−1.00160	−	1.73483i
$619$	1.75736			0.0706342			0.0353171	−	0.999376i	$-0.488756\pi$
$619$	1.75736			0.0706342			0.0353171	+	0.999376i	$0.488756\pi$
$620$	−3.36396	−	5.82655i	−0.135100	−	0.234000i
$621$	−4.00000	+	6.92820i	−0.160514	+	0.278019i
$622$	10.2426	−	17.7408i	0.410692	−	0.711340i
$623$	28.9706			1.16068
$624$		0			0
$625$	1.00000			0.0400000
$626$	−5.82843	+	10.0951i	−0.232951	+	0.403483i
$627$	1.41421	−	2.44949i	0.0564782	−	0.0978232i
$628$	−34.4558	−	59.6793i	−1.37494	−	2.38146i
$629$	−7.02944			−0.280282
$630$	−5.82843	−	10.0951i	−0.232210	−	0.402200i
$631$	4.87868	+	8.45012i	0.194217	+	0.336394i	0.946644	−	0.322282i	$-0.104450\pi$
$631$	4.87868	+	8.45012i	0.194217	+	0.336394i	−0.752426	+	0.658676i	$0.771117\pi$
$632$	37.4558			1.48991
$633$	2.34315	+	4.05845i	0.0931317	+	0.161309i
$634$	−2.58579	+	4.47871i	−0.102695	+	0.177872i
$635$	3.29289	−	5.70346i	0.130674	−	0.226335i
$636$	−13.4558			−0.533559
$637$		0			0
$638$	46.6274			1.84600
$639$	5.94975	−	10.3053i	0.235368	−	0.407670i
$640$	−10.2782	+	17.8023i	−0.406281	+	0.703699i
$641$	−23.8284	−	41.2720i	−0.941166	−	1.63015i	−0.763251	−	0.646102i	$-0.776398\pi$
$641$	−23.8284	−	41.2720i	−0.941166	−	1.63015i	−0.177915	−	0.984046i	$-0.556935\pi$
$642$	−32.1421			−1.26855
$643$	−4.75736	−	8.23999i	−0.187612	−	0.324953i	0.756842	−	0.653598i	$-0.226741\pi$
$643$	−4.75736	−	8.23999i	−0.187612	−	0.324953i	−0.944454	+	0.328645i	$0.893408\pi$
$644$	−13.0711	−	22.6398i	−0.515072	−	0.892131i
$645$	15.6569			0.616488
$646$	0.585786	+	1.01461i	0.0230475	+	0.0399194i
$647$	−4.70711	+	8.15295i	−0.185055	+	0.320525i	−0.943595	−	0.331101i	$-0.892580\pi$
$647$	−4.70711	+	8.15295i	−0.185055	+	0.320525i	0.758540	+	0.651627i	$0.225913\pi$
$648$	−11.0355	+	19.1141i	−0.433517	+	0.750873i
$649$	6.00000			0.235521
$650$		0			0
$651$	−12.0000			−0.470317
$652$	−36.3137	+	62.8972i	−1.42215	+	2.46324i
$653$	−23.4853	+	40.6777i	−0.919050	+	1.59184i	−0.118189	+	0.992991i	$0.537709\pi$
$653$	−23.4853	+	40.6777i	−0.919050	+	1.59184i	−0.800861	+	0.598850i	$0.795624\pi$
$654$	3.41421	+	5.91359i	0.133506	+	0.231240i
$655$	−16.9706			−0.663095
$656$	4.75736	+	8.23999i	0.185744	+	0.321717i
$657$	4.24264	+	7.34847i	0.165521	+	0.286691i
$658$	56.2843			2.19419
$659$	−8.92893	−	15.4654i	−0.347822	−	0.602445i	0.638040	−	0.770003i	$-0.279745\pi$
$659$	−8.92893	−	15.4654i	−0.347822	−	0.602445i	−0.985862	+	0.167558i	$0.946412\pi$
$660$	9.24264	−	16.0087i	0.359769	−	0.623139i
$661$	−14.7990	+	25.6326i	−0.575614	+	0.996993i	0.420361	+	0.907357i	$0.361904\pi$
$661$	−14.7990	+	25.6326i	−0.575614	+	0.996993i	−0.995975	+	0.0896356i	$0.971430\pi$
$662$	62.8701			2.44351
$663$		0			0
$664$	14.0000			0.543305
$665$	−1.41421	+	2.44949i	−0.0548408	+	0.0949871i
$666$	10.2426	−	17.7408i	0.396894	−	0.687441i
$667$	4.00000	+	6.92820i	0.154881	+	0.268261i
$668$	−12.1421			−0.469793
$669$	6.72792	+	11.6531i	0.260116	+	0.450535i
$670$	−2.41421	−	4.18154i	−0.0932692	−	0.161547i
$671$	−27.3137			−1.05443
$672$	5.41421	+	9.37769i	0.208858	+	0.361752i
$673$	−3.24264	+	5.61642i	−0.124995	+	0.216497i	−0.921731	−	0.387830i	$-0.873225\pi$
$673$	−3.24264	+	5.61642i	−0.124995	+	0.216497i	0.796736	+	0.604327i	$0.206558\pi$
$674$	15.4853	−	26.8213i	0.596471	−	1.03312i
$675$	5.65685			0.217732
$676$		0			0
$677$	−20.1421			−0.774125			−0.387063	−	0.922053i	$-0.626510\pi$
$677$	−20.1421			−0.774125			−0.387063	+	0.922053i	$0.626510\pi$
$678$	15.0711	−	26.1039i	0.578801	−	1.00251i
$679$	18.4853	−	32.0174i	0.709400	−	1.22872i
$680$	1.82843	+	3.16693i	0.0701170	+	0.121446i
$681$	23.1127			0.885681
$682$	7.24264	+	12.5446i	0.277335	+	0.480358i
$683$	−5.34315	−	9.25460i	−0.204450	−	0.354117i	0.745507	−	0.666497i	$-0.232207\pi$
$683$	−5.34315	−	9.25460i	−0.204450	−	0.354117i	−0.949957	+	0.312380i	$0.898874\pi$
$684$	−2.24264			−0.0857495
$685$	8.65685	+	14.9941i	0.330761	+	0.572896i
$686$	54.2843	−	94.0231i	2.07258	−	3.58982i
$687$	−3.41421	+	5.91359i	−0.130260	+	0.225618i
$688$	−33.2132			−1.26624
$689$		0			0
$690$	4.82843			0.183815
$691$	−3.46447	+	6.00063i	−0.131795	+	0.228275i	−0.924368	−	0.381501i	$-0.875407\pi$
$691$	−3.46447	+	6.00063i	−0.131795	+	0.228275i	0.792574	+	0.609776i	$0.208741\pi$
$692$	−32.2132	+	55.7949i	−1.22456	+	2.12100i
$693$	8.24264	+	14.2767i	0.313112	+	0.542326i
$694$	10.2426			0.388805
$695$	−2.24264	−	3.88437i	−0.0850682	−	0.147342i
$696$	17.6569	+	30.5826i	0.669281	+	1.15923i
$697$	−2.62742			−0.0995205
$698$	22.3137	+	38.6485i	0.844586	+	1.46287i
$699$	−14.5858	+	25.2633i	−0.551685	+	0.955547i
$700$	−9.24264	+	16.0087i	−0.349339	+	0.605073i
$701$	14.6863			0.554694			0.277347	−	0.960770i	$-0.410545\pi$
$701$	14.6863			0.554694			0.277347	+	0.960770i	$0.410545\pi$
$702$		0			0
$703$	−4.97056			−0.187468
$704$	16.7782	−	29.0607i	0.632351	−	1.09526i
$705$	−3.41421	+	5.91359i	−0.128587	+	0.222719i
$706$	17.8995	+	31.0028i	0.673656	+	1.16681i
$707$	−17.6569			−0.664054
$708$	4.75736	+	8.23999i	0.178793	+	0.309678i
$709$	−22.5563	−	39.0687i	−0.847121	−	1.46726i	−0.883766	−	0.467929i	$-0.845000\pi$
$709$	−22.5563	−	39.0687i	−0.847121	−	1.46726i	0.0366445	−	0.999328i	$-0.488333\pi$
$710$	−28.7279			−1.07814
$711$	−4.24264	−	7.34847i	−0.159111	−	0.275589i
$712$	13.2426	−	22.9369i	0.496289	−	0.859598i
$713$	−1.24264	+	2.15232i	−0.0465373	+	0.0806049i
$714$	13.6569			0.511095
$715$		0			0
$716$	21.6569			0.809355
$717$	−2.41421	+	4.18154i	−0.0901605	+	0.156162i
$718$	−9.77817	+	16.9363i	−0.364918	+	0.632057i
$719$	−14.4853	−	25.0892i	−0.540210	−	0.935671i	−0.998892	−	0.0470703i	$-0.985012\pi$
$719$	−14.4853	−	25.0892i	−0.540210	−	0.935671i	0.458682	−	0.888601i	$-0.348322\pi$
$720$	−3.00000			−0.111803
$721$	−35.2132	−	60.9911i	−1.31141	−	2.27143i
$722$	−22.5208	−	39.0072i	−0.838138	−	1.45170i
$723$	20.4853			0.761856
$724$		0			0
$725$	2.82843	−	4.89898i	0.105045	−	0.181944i
$726$	−1.12132	+	1.94218i	−0.0416161	+	0.0720812i
$727$	−51.3553			−1.90466			−0.952332	−	0.305063i	$-0.901322\pi$
$727$	−51.3553			−1.90466			−0.952332	+	0.305063i	$0.901322\pi$
$728$		0			0
$729$	29.0000			1.07407
$730$	10.2426	−	17.7408i	0.379097	−	0.656616i
$731$	4.58579	−	7.94282i	0.169611	−	0.293776i
$732$	−21.6569	−	37.5108i	−0.800460	−	1.38644i
$733$	21.3137			0.787240			0.393620	−	0.919273i	$-0.371223\pi$
$733$	21.3137			0.787240			0.393620	+	0.919273i	$0.371223\pi$
$734$	42.9203	+	74.3402i	1.58422	+	2.74395i
$735$	11.5355	+	19.9801i	0.425495	+	0.736978i
$736$	2.24264			0.0826648
$737$	3.41421	+	5.91359i	0.125764	+	0.217830i
$738$	3.82843	−	6.63103i	0.140926	−	0.244092i
$739$	−2.63604	+	4.56575i	−0.0969683	+	0.167954i	−0.910428	−	0.413667i	$-0.864248\pi$
$739$	−2.63604	+	4.56575i	−0.0969683	+	0.167954i	0.813460	+	0.581621i	$0.197581\pi$
$740$	−32.4853			−1.19418
$741$		0			0
$742$	−28.9706			−1.06354
$743$	10.7574	−	18.6323i	0.394649	−	0.683553i	−0.598407	−	0.801192i	$-0.704199\pi$
$743$	10.7574	−	18.6323i	0.394649	−	0.683553i	0.993056	+	0.117640i	$0.0375328\pi$
$744$	−5.48528	+	9.50079i	−0.201100	+	0.348316i
$745$	5.82843	+	10.0951i	0.213537	+	0.369857i
$746$	6.48528			0.237443
$747$	−1.58579	−	2.74666i	−0.0580209	−	0.100495i
$748$	−5.41421	−	9.37769i	−0.197963	−	0.342882i
$749$	−45.4558			−1.66092
$750$	−1.70711	−	2.95680i	−0.0623347	−	0.107967i
$751$	13.7574	−	23.8284i	0.502013	−	0.869512i	−0.497984	−	0.867186i	$-0.665926\pi$
$751$	13.7574	−	23.8284i	0.502013	−	0.869512i	0.999997	−	0.00232617i	$-0.000740444\pi$
$752$	7.24264	−	12.5446i	0.264112	−	0.457455i
$753$	−28.0000			−1.02038
$754$		0			0
$755$	9.75736			0.355107
$756$	−52.2843	+	90.5590i	−1.90156	+	3.29360i
$757$	12.0711	−	20.9077i	0.438730	−	0.759903i	−0.558861	−	0.829261i	$-0.688762\pi$
$757$	12.0711	−	20.9077i	0.438730	−	0.759903i	0.997592	+	0.0693577i	$0.0220950\pi$
$758$	35.0919	+	60.7809i	1.27459	+	2.20766i
$759$	−6.82843			−0.247856
$760$	1.29289	+	2.23936i	0.0468982	+	0.0812300i
$761$	−4.31371	−	7.47156i	−0.156372	−	0.270844i	0.777186	−	0.629271i	$-0.216646\pi$
$761$	−4.31371	−	7.47156i	−0.156372	−	0.270844i	−0.933558	+	0.358427i	$0.883313\pi$
$762$	−22.4853			−0.814556
$763$	4.82843	+	8.36308i	0.174801	+	0.302764i
$764$	−4.48528	+	7.76874i	−0.162272	+	0.281063i
$765$	0.414214	−	0.717439i	0.0149759	−	0.0259391i
$766$	70.2843			2.53947
$767$		0			0
$768$	42.3848			1.52943
$769$	11.4853	−	19.8931i	0.414170	−	0.717363i	−0.581171	−	0.813781i	$-0.697405\pi$
$769$	11.4853	−	19.8931i	0.414170	−	0.717363i	0.995341	+	0.0964182i	$0.0307386\pi$
$770$	19.8995	−	34.4669i	0.717128	−	1.24210i
$771$	19.5563	+	33.8726i	0.704305	+	1.21989i
$772$	16.6274			0.598434
$773$	11.0711	+	19.1757i	0.398199	+	0.689700i	0.993504	−	0.113799i	$-0.0363021\pi$
$773$	11.0711	+	19.1757i	0.398199	+	0.689700i	−0.595305	+	0.803500i	$0.702969\pi$
$774$	13.3640	+	23.1471i	0.480358	+	0.832004i
$775$	1.75736			0.0631262
$776$	−16.8995	−	29.2708i	−0.606657	−	1.05076i
$777$	−28.9706	+	50.1785i	−1.03931	+	1.80014i
$778$	34.5563	−	59.8534i	1.23891	−	2.14585i
$779$	−1.85786			−0.0665649
$780$		0			0
$781$	40.6274			1.45376
$782$	1.41421	−	2.44949i	0.0505722	−	0.0875936i
$783$	16.0000	−	27.7128i	0.571793	−	0.990375i
$784$	−24.4706	−	42.3843i	−0.873949	−	1.51372i
$785$	18.0000			0.642448
$786$	28.9706	+	50.1785i	1.03335	+	1.78981i
$787$	−11.2426	−	19.4728i	−0.400757	−	0.694131i	0.593061	−	0.805158i	$-0.297919\pi$
$787$	−11.2426	−	19.4728i	−0.400757	−	0.694131i	−0.993817	+	0.111027i	$0.964586\pi$
$788$	42.0000			1.49619
$789$	−7.48528	−	12.9649i	−0.266483	−	0.461562i
$790$	−10.2426	+	17.7408i	−0.364417	+	0.631188i
$791$	21.3137	−	36.9164i	0.757828	−	1.31260i
$792$	15.0711			0.535527
$793$		0			0
$794$	−28.4853			−1.01090
$795$	1.75736	−	3.04384i	0.0623271	−	0.107954i
$796$	−7.65685	+	13.2621i	−0.271390	+	0.470061i
$797$	11.4853	+	19.8931i	0.406830	+	0.704649i	0.994533	−	0.104427i	$-0.0333010\pi$
$797$	11.4853	+	19.8931i	0.406830	+	0.704649i	−0.587703	+	0.809077i	$0.699968\pi$
$798$	9.65685			0.341849
$799$	2.00000	+	3.46410i	0.0707549	+	0.122551i
$800$	−0.792893	−	1.37333i	−0.0280330	−	0.0485546i
$801$	−6.00000			−0.212000
$802$	−6.41421	−	11.1097i	−0.226494	−	0.392299i
$803$	−14.4853	+	25.0892i	−0.511174	+	0.885380i
$804$	−5.41421	+	9.37769i	−0.190945	+	0.330726i
$805$	6.82843			0.240670
$806$		0			0
$807$	35.7990			1.26018
$808$	−8.07107	+	13.9795i	−0.283939	+	0.491797i
$809$	−22.6274	+	39.1918i	−0.795538	+	1.37791i	0.126960	+	0.991908i	$0.459478\pi$
$809$	−22.6274	+	39.1918i	−0.795538	+	1.37791i	−0.922497	+	0.386004i	$0.873855\pi$
$810$	−6.03553	−	10.4539i	−0.212067	−	0.367311i
$811$	−28.3848			−0.996724			−0.498362	−	0.866969i	$-0.666065\pi$
$811$	−28.3848			−0.996724			−0.498362	+	0.866969i	$0.666065\pi$
$812$	52.2843	+	90.5590i	1.83482	+	3.17800i
$813$	18.8995	+	32.7349i	0.662834	+	1.14806i
$814$	69.9411			2.45144
$815$	−9.48528	−	16.4290i	−0.332255	−	0.575482i
$816$	1.75736	−	3.04384i	0.0615199	−	0.106556i
$817$	3.24264	−	5.61642i	0.113446	−	0.196494i
$818$	−17.3137			−0.605360
$819$		0			0
$820$	−12.1421			−0.424022
$821$	25.6274	−	44.3880i	0.894403	−	1.54915i	0.0598613	−	0.998207i	$-0.480934\pi$
$821$	25.6274	−	44.3880i	0.894403	−	1.54915i	0.834542	−	0.550945i	$-0.185733\pi$
$822$	29.5563	−	51.1931i	1.03090	−	1.78556i
$823$	1.19239	+	2.06528i	0.0415640	+	0.0719910i	0.886059	−	0.463572i	$-0.153433\pi$
$823$	1.19239	+	2.06528i	0.0415640	+	0.0719910i	−0.844495	+	0.535563i	$0.820099\pi$
$824$	−64.3848			−2.24295
$825$	2.41421	+	4.18154i	0.0840521	+	0.145583i
$826$	10.2426	+	17.7408i	0.356387	+	0.617280i
$827$	56.1421			1.95225			0.976127	−	0.217202i	$-0.0696930\pi$
$827$	56.1421			1.95225			0.976127	+	0.217202i	$0.0696930\pi$
$828$	2.70711	+	4.68885i	0.0940785	+	0.162949i
$829$	−20.4853	+	35.4815i	−0.711483	+	1.23233i	0.252817	+	0.967514i	$0.418643\pi$
$829$	−20.4853	+	35.4815i	−0.711483	+	1.23233i	−0.964300	+	0.264811i	$0.914690\pi$
$830$	−3.82843	+	6.63103i	−0.132887	+	0.230166i
$831$	18.1421			0.629344
$832$		0			0
$833$	13.5147			0.468257
$834$	−7.65685	+	13.2621i	−0.265135	+	0.459228i
$835$	1.58579	−	2.74666i	0.0548784	−	0.0950522i
$836$	−3.82843	−	6.63103i	−0.132409	−	0.229339i
$837$	9.94113			0.343616
$838$	13.0711	+	22.6398i	0.451533	+	0.782077i
$839$	−3.36396	−	5.82655i	−0.116137	−	0.201155i	0.802097	−	0.597194i	$-0.203718\pi$
$839$	−3.36396	−	5.82655i	−0.116137	−	0.201155i	−0.918234	+	0.396039i	$0.870384\pi$
$840$	30.1421			1.04000
$841$	−1.50000	−	2.59808i	−0.0517241	−	0.0895888i
$842$	−42.2132	+	73.1154i	−1.45476	+	2.51972i
$843$	15.4142	−	26.6982i	0.530894	−	0.919535i
$844$	12.6863			0.436680
$845$		0			0
$846$	−11.6569			−0.400771
$847$	−1.58579	+	2.74666i	−0.0544883	+	0.0943764i
$848$	−3.72792	+	6.45695i	−0.128017	+	0.221733i
$849$	−11.8284	−	20.4874i	−0.405951	−	0.703127i
$850$	−2.00000			−0.0685994
$851$	6.00000	+	10.3923i	0.205677	+	0.356244i
$852$	32.2132	+	55.7949i	1.10361	+	1.91150i
$853$	−13.4558			−0.460719			−0.230360	−	0.973106i	$-0.573990\pi$
$853$	−13.4558			−0.460719			−0.230360	+	0.973106i	$0.573990\pi$
$854$	−46.6274	−	80.7611i	−1.59556	−	2.76359i
$855$	0.292893	−	0.507306i	0.0100167	−	0.0173495i
$856$	−20.7782	+	35.9889i	−0.710183	+	1.23007i
$857$	11.6569			0.398191			0.199095	−	0.979980i	$-0.436200\pi$
$857$	11.6569			0.398191			0.199095	+	0.979980i	$0.436200\pi$
$858$		0			0
$859$	−27.7990			−0.948489			−0.474245	−	0.880393i	$-0.657279\pi$
$859$	−27.7990			−0.948489			−0.474245	+	0.880393i	$0.657279\pi$
$860$	21.1924	−	36.7063i	0.722654	−	1.25167i
$861$	−10.8284	+	18.7554i	−0.369032	+	0.639182i
$862$	48.7487	+	84.4353i	1.66039	+	2.87588i
$863$	−31.4558			−1.07077			−0.535385	−	0.844608i	$-0.679833\pi$
$863$	−31.4558			−1.07077			−0.535385	+	0.844608i	$0.679833\pi$
$864$	−4.48528	−	7.76874i	−0.152592	−	0.264298i
$865$	−8.41421	−	14.5738i	−0.286092	−	0.495526i
$866$	−18.4853			−0.628155
$867$	−11.5355	−	19.9801i	−0.391767	−	0.678561i
$868$	−16.2426	+	28.1331i	−0.551311	+	0.954899i
$869$	14.4853	−	25.0892i	0.491380	−	0.851094i
$870$	−19.3137			−0.654796
$871$		0			0
$872$	8.82843			0.298968
$873$	−3.82843	+	6.63103i	−0.129573	+	0.224426i
$874$	1.00000	−	1.73205i	0.0338255	−	0.0585875i
$875$	−2.41421	−	4.18154i	−0.0816153	−	0.141362i
$876$	−45.9411			−1.55221
$877$	−12.6569	−	21.9223i	−0.427392	−	0.740264i	0.569249	−	0.822165i	$-0.307234\pi$
$877$	−12.6569	−	21.9223i	−0.427392	−	0.740264i	−0.996640	+	0.0819013i	$0.973901\pi$
$878$	1.17157	+	2.02922i	0.0395387	+	0.0684830i
$879$	−36.9706			−1.24699
$880$	−5.12132	−	8.87039i	−0.172640	−	0.299021i
$881$	−9.51472	+	16.4800i	−0.320559	+	0.555225i	−0.980603	−	0.196002i	$-0.937204\pi$
$881$	−9.51472	+	16.4800i	−0.320559	+	0.555225i	0.660044	+	0.751227i	$0.270537\pi$
$882$	−19.6924	+	34.1082i	−0.663077	+	1.14848i
$883$	−23.7574			−0.799499			−0.399749	−	0.916624i	$-0.630903\pi$
$883$	−23.7574			−0.799499			−0.399749	+	0.916624i	$0.630903\pi$
$884$		0			0
$885$	−2.48528			−0.0835418
$886$	−11.3640	+	19.6830i	−0.381780	+	0.661262i
$887$	11.1924	−	19.3858i	0.375804	−	0.650911i	−0.614643	−	0.788805i	$-0.710700\pi$
$887$	11.1924	−	19.3858i	0.375804	−	0.650911i	0.990447	+	0.137894i	$0.0440334\pi$
$888$	26.4853	+	45.8739i	0.888788	+	1.53943i
$889$	−31.7990			−1.06650
$890$	7.24264	+	12.5446i	0.242774	+	0.420497i
$891$	8.53553	+	14.7840i	0.285951	+	0.495282i
$892$	36.4264			1.21965
$893$	1.41421	+	2.44949i	0.0473249	+	0.0819690i
$894$	19.8995	−	34.4669i	0.665539	−	1.15275i
$895$	−2.82843	+	4.89898i	−0.0945439	+	0.163755i
$896$	99.2548			3.31587
$897$		0			0
$898$	79.9411			2.66767
$899$	4.97056	−	8.60927i	0.165778	−	0.287135i
$900$	1.91421	−	3.31552i	0.0638071	−	0.110517i
$901$	−1.02944	−	1.78304i	−0.0342955	−	0.0594016i
$902$	26.1421			0.870438
$903$	−37.7990	−	65.4698i	−1.25787	−	2.17870i
$904$	−19.4853	−	33.7495i	−0.648071	−	1.12249i
$905$		0			0
$906$	−16.6569	−	28.8505i	−0.553387	−	0.958494i
$907$	−4.60660	+	7.97887i	−0.152960	+	0.264934i	−0.932314	−	0.361649i	$-0.882214\pi$
$907$	−4.60660	+	7.97887i	−0.152960	+	0.264934i	0.779355	+	0.626583i	$0.215547\pi$
$908$	31.2843	−	54.1859i	1.03821	−	1.79822i
$909$	3.65685			0.121290
$910$		0			0
$911$	−12.0000			−0.397578			−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000			−0.397578			−0.198789	+	0.980042i	$0.563701\pi$
$912$	1.24264	−	2.15232i	0.0411479	−	0.0712703i
$913$	5.41421	−	9.37769i	0.179184	−	0.310356i
$914$	−21.7279	−	37.6339i	−0.718696	−	1.24482i
$915$	11.3137			0.374020
$916$	9.24264	+	16.0087i	0.305385	+	0.528943i
$917$	40.9706	+	70.9631i	1.35297	+	2.34341i
$918$	−11.3137			−0.373408
$919$	−0.242641	−	0.420266i	−0.00800398	−	0.0138633i	0.861996	−	0.506916i	$-0.169214\pi$
$919$	−0.242641	−	0.420266i	−0.00800398	−	0.0138633i	−0.870000	+	0.493052i	$0.835881\pi$
$920$	3.12132	−	5.40629i	0.102907	−	0.178240i
$921$	17.5563	−	30.4085i	0.578501	−	1.00199i
$922$	−22.9706			−0.756495
$923$		0			0
$924$	−89.2548			−2.93627
$925$	4.24264	−	7.34847i	0.139497	−	0.241616i
$926$	−5.24264	+	9.08052i	−0.172284	+	0.298404i
$927$	7.29289	+	12.6317i	0.239530	+	0.414878i
$928$	−8.97056			−0.294473
$929$	−8.41421	−	14.5738i	−0.276061	−	0.478152i	0.694341	−	0.719646i	$-0.255696\pi$
$929$	−8.41421	−	14.5738i	−0.276061	−	0.478152i	−0.970402	+	0.241494i	$0.922363\pi$
$930$	−3.00000	−	5.19615i	−0.0983739	−	0.170389i
$931$	9.55635			0.313197
$932$	39.4853	+	68.3905i	1.29338	+	2.24021i
$933$	6.00000	−	10.3923i	0.196431	−	0.340229i
$934$	−16.1924	+	28.0460i	−0.529831	+	0.917694i
$935$	2.82843			0.0924995
$936$		0			0
$937$	−22.9706			−0.750416			−0.375208	−	0.926941i	$-0.622429\pi$
$937$	−22.9706			−0.750416			−0.375208	+	0.926941i	$0.622429\pi$
$938$	−11.6569	+	20.1903i	−0.380610	+	0.659235i
$939$	−3.41421	+	5.91359i	−0.111419	+	0.192983i
$940$	9.24264	+	16.0087i	0.301462	+	0.522147i
$941$	18.7696			0.611870			0.305935	−	0.952052i	$-0.401031\pi$
$941$	18.7696			0.611870			0.305935	+	0.952052i	$0.401031\pi$
$942$	−30.7279	−	53.2223i	−1.00117	−	1.73408i
$943$	2.24264	+	3.88437i	0.0730304	+	0.126492i
$944$	5.27208			0.171592
$945$	−13.6569	−	23.6544i	−0.444258	−	0.769477i
$946$	−45.6274	+	79.0290i	−1.48348	+	2.56945i
$947$	−8.55635	+	14.8200i	−0.278044	+	0.481586i	−0.970899	−	0.239491i	$-0.923019\pi$
$947$	−8.55635	+	14.8200i	−0.278044	+	0.481586i	0.692855	+	0.721077i	$0.256353\pi$
$948$	45.9411			1.49210
$949$		0			0
$950$	−1.41421			−0.0458831
$951$	−1.51472	+	2.62357i	−0.0491181	+	0.0850751i
$952$	8.82843	−	15.2913i	0.286131	−	0.495593i
$953$	−17.6274	−	30.5316i	−0.571008	−	0.989015i	−0.996463	−	0.0840352i	$-0.973219\pi$
$953$	−17.6274	−	30.5316i	−0.571008	−	0.989015i	0.425455	−	0.904980i	$-0.360114\pi$
$954$	6.00000			0.194257
$955$	−1.17157	−	2.02922i	−0.0379112	−	0.0656641i
$956$	6.53553	+	11.3199i	0.211374	+	0.366111i
$957$	27.3137			0.882927
$958$	−37.0919	−	64.2450i	−1.19838	−	2.07566i
$959$	41.7990	−	72.3980i	1.34976	−	2.33785i
$960$	−6.94975	+	12.0373i	−0.224302	+	0.388503i
$961$	−27.9117			−0.900377
$962$		0			0
$963$	9.41421			0.303369
$964$	27.7279	−	48.0262i	0.893056	−	1.54682i
$965$	−2.17157	+	3.76127i	−0.0699054	+	0.121080i
$966$	−11.6569	−	20.1903i	−0.375053	−	0.649611i
$967$	47.9411			1.54168			0.770841	−	0.637027i	$-0.219836\pi$
$967$	47.9411			1.54168			0.770841	+	0.637027i	$0.219836\pi$
$968$	1.44975	+	2.51104i	0.0465966	+	0.0807078i
$969$	0.343146	+	0.594346i	0.0110234	+	0.0190931i
$970$	18.4853			0.593527
$971$	−22.1421	−	38.3513i	−0.710575	−	1.23075i	−0.964642	−	0.263565i	$-0.915102\pi$
$971$	−22.1421	−	38.3513i	−0.710575	−	1.23075i	0.254067	−	0.967187i	$-0.418232\pi$
$972$	18.9497	−	32.8219i	0.607813	−	1.05276i
$973$	−10.8284	+	18.7554i	−0.347143	+	0.601270i
$974$	26.4853			0.848643
$975$		0			0
$976$	−24.0000			−0.768221
$977$	19.7574	−	34.2208i	0.632094	−	1.09482i	−0.355029	−	0.934855i	$-0.615529\pi$
$977$	19.7574	−	34.2208i	0.632094	−	1.09482i	0.987123	−	0.159964i	$-0.0511377\pi$
$978$	−32.3848	+	56.0921i	−1.03555	+	1.79363i
$979$	−10.2426	−	17.7408i	−0.327356	−	0.566998i
$980$	62.4558			1.99508
$981$	−1.00000	−	1.73205i	−0.0319275	−	0.0553001i
$982$	6.24264	+	10.8126i	0.199211	+	0.345043i
$983$	−1.02944			−0.0328339			−0.0164170	−	0.999865i	$-0.505226\pi$
$983$	−1.02944			−0.0328339			−0.0164170	+	0.999865i	$0.505226\pi$
$984$	9.89949	+	17.1464i	0.315584	+	0.546608i
$985$	−5.48528	+	9.50079i	−0.174776	+	0.302720i
$986$	−5.65685	+	9.79796i	−0.180151	+	0.312031i
$987$	32.9706			1.04946
$988$		0			0
$989$	−15.6569			−0.497859
$990$	−4.12132	+	7.13834i	−0.130984	+	0.226871i
$991$	−24.4853	+	42.4098i	−0.777801	+	1.34719i	0.155406	+	0.987851i	$0.450331\pi$
$991$	−24.4853	+	42.4098i	−0.777801	+	1.34719i	−0.933207	+	0.359340i	$0.883002\pi$
$992$	−1.39340	−	2.41344i	−0.0442404	−	0.0766267i
$993$	36.8284			1.16871
$994$	69.3553	+	120.127i	2.19982	+	3.81020i
$995$	−2.00000	−	3.46410i	−0.0634043	−	0.109819i
$996$	17.1716			0.544102
$997$	−14.4142	−	24.9662i	−0.456503	−	0.790686i	0.542271	−	0.840204i	$-0.317565\pi$
$997$	−14.4142	−	24.9662i	−0.456503	−	0.790686i	−0.998773	+	0.0495181i	$0.984231\pi$
$998$	50.1630	−	86.8848i	1.58788	−	2.75029i
$999$	24.0000	−	41.5692i	0.759326	−	1.31519i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.e.h.191.2		4
13.2	odd	12		845.2.m.f.361.4		8
13.3	even	3	inner	845.2.e.h.146.2		4
13.4	even	6		845.2.a.g.1.2		2
13.5	odd	4		845.2.m.f.316.1		8
13.6	odd	12		845.2.c.b.506.4		4
13.7	odd	12		845.2.c.b.506.1		4
13.8	odd	4		845.2.m.f.316.4		8
13.9	even	3		65.2.a.b.1.1	✓	2
13.10	even	6		845.2.e.c.146.1		4
13.11	odd	12		845.2.m.f.361.1		8
13.12	even	2		845.2.e.c.191.1		4
39.17	odd	6		7605.2.a.x.1.1		2
39.35	odd	6		585.2.a.m.1.2		2
52.35	odd	6		1040.2.a.j.1.2		2
65.4	even	6		4225.2.a.r.1.1		2
65.9	even	6		325.2.a.i.1.2		2
65.22	odd	12		325.2.b.f.274.1		4
65.48	odd	12		325.2.b.f.274.4		4
91.48	odd	6		3185.2.a.j.1.1		2
104.35	odd	6		4160.2.a.z.1.1		2
104.61	even	6		4160.2.a.bf.1.2		2
143.87	odd	6		7865.2.a.j.1.2		2
156.35	even	6		9360.2.a.cd.1.1		2
195.74	odd	6		2925.2.a.u.1.1		2
195.113	even	12		2925.2.c.r.2224.1		4
195.152	even	12		2925.2.c.r.2224.4		4
260.139	odd	6		5200.2.a.bu.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.a.b.1.1	✓	2	13.9	even	3
325.2.a.i.1.2		2	65.9	even	6
325.2.b.f.274.1		4	65.22	odd	12
325.2.b.f.274.4		4	65.48	odd	12
585.2.a.m.1.2		2	39.35	odd	6
845.2.a.g.1.2		2	13.4	even	6
845.2.c.b.506.1		4	13.7	odd	12
845.2.c.b.506.4		4	13.6	odd	12
845.2.e.c.146.1		4	13.10	even	6
845.2.e.c.191.1		4	13.12	even	2
845.2.e.h.146.2		4	13.3	even	3	inner
845.2.e.h.191.2		4	1.1	even	1	trivial
845.2.m.f.316.1		8	13.5	odd	4
845.2.m.f.316.4		8	13.8	odd	4
845.2.m.f.361.1		8	13.11	odd	12
845.2.m.f.361.4		8	13.2	odd	12
1040.2.a.j.1.2		2	52.35	odd	6
2925.2.a.u.1.1		2	195.74	odd	6
2925.2.c.r.2224.1		4	195.113	even	12
2925.2.c.r.2224.4		4	195.152	even	12
3185.2.a.j.1.1		2	91.48	odd	6
4160.2.a.z.1.1		2	104.35	odd	6
4160.2.a.bf.1.2		2	104.61	even	6
4225.2.a.r.1.1		2	65.4	even	6
5200.2.a.bu.1.1		2	260.139	odd	6
7605.2.a.x.1.1		2	39.17	odd	6
7865.2.a.j.1.2		2	143.87	odd	6
9360.2.a.cd.1.1		2	156.35	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.20711 - 2.09077i) q^{2} +(0.707107 - 1.22474i) q^{3} +(-1.91421 - 3.31552i) q^{4} +1.00000 q^{5} +(-1.70711 - 2.95680i) q^{6} +(-2.41421 - 4.18154i) q^{7} -4.41421 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.20711 - 2.09077i) q^{2} +(0.707107 - 1.22474i) q^{3} +(-1.91421 - 3.31552i) q^{4} +1.00000 q^{5} +(-1.70711 - 2.95680i) q^{6} +(-2.41421 - 4.18154i) q^{7} -4.41421 q^{8} +(0.500000 + 0.866025i) q^{9} +(1.20711 - 2.09077i) q^{10} +(-1.70711 + 2.95680i) q^{11} -5.41421 q^{12} -11.6569 q^{14} +(0.707107 - 1.22474i) q^{15} +(-1.50000 + 2.59808i) q^{16} +(-0.414214 - 0.717439i) q^{17} +2.41421 q^{18} +(-0.292893 - 0.507306i) q^{19} +(-1.91421 - 3.31552i) q^{20} -6.82843 q^{21} +(4.12132 + 7.13834i) q^{22} +(-0.707107 + 1.22474i) q^{23} +(-3.12132 + 5.40629i) q^{24} +1.00000 q^{25} +5.65685 q^{27} +(-9.24264 + 16.0087i) q^{28} +(2.82843 - 4.89898i) q^{29} +(-1.70711 - 2.95680i) q^{30} +1.75736 q^{31} +(-0.792893 - 1.37333i) q^{32} +(2.41421 + 4.18154i) q^{33} -2.00000 q^{34} +(-2.41421 - 4.18154i) q^{35} +(1.91421 - 3.31552i) q^{36} +(4.24264 - 7.34847i) q^{37} -1.41421 q^{38} -4.41421 q^{40} +(1.58579 - 2.74666i) q^{41} +(-8.24264 + 14.2767i) q^{42} +(5.53553 + 9.58783i) q^{43} +13.0711 q^{44} +(0.500000 + 0.866025i) q^{45} +(1.70711 + 2.95680i) q^{46} -4.82843 q^{47} +(2.12132 + 3.67423i) q^{48} +(-8.15685 + 14.1281i) q^{49} +(1.20711 - 2.09077i) q^{50} -1.17157 q^{51} +2.48528 q^{53} +(6.82843 - 11.8272i) q^{54} +(-1.70711 + 2.95680i) q^{55} +(10.6569 + 18.4582i) q^{56} -0.828427 q^{57} +(-6.82843 - 11.8272i) q^{58} +(-0.878680 - 1.52192i) q^{59} -5.41421 q^{60} +(4.00000 + 6.92820i) q^{61} +(2.12132 - 3.67423i) q^{62} +(2.41421 - 4.18154i) q^{63} -9.82843 q^{64} +11.6569 q^{66} +(1.00000 - 1.73205i) q^{67} +(-1.58579 + 2.74666i) q^{68} +(1.00000 + 1.73205i) q^{69} -11.6569 q^{70} +(-5.94975 - 10.3053i) q^{71} +(-2.20711 - 3.82282i) q^{72} +8.48528 q^{73} +(-10.2426 - 17.7408i) q^{74} +(0.707107 - 1.22474i) q^{75} +(-1.12132 + 1.94218i) q^{76} +16.4853 q^{77} -8.48528 q^{79} +(-1.50000 + 2.59808i) q^{80} +(2.50000 - 4.33013i) q^{81} +(-3.82843 - 6.63103i) q^{82} -3.17157 q^{83} +(13.0711 + 22.6398i) q^{84} +(-0.414214 - 0.717439i) q^{85} +26.7279 q^{86} +(-4.00000 - 6.92820i) q^{87} +(7.53553 - 13.0519i) q^{88} +(-3.00000 + 5.19615i) q^{89} +2.41421 q^{90} +5.41421 q^{92} +(1.24264 - 2.15232i) q^{93} +(-5.82843 + 10.0951i) q^{94} +(-0.292893 - 0.507306i) q^{95} -2.24264 q^{96} +(3.82843 + 6.63103i) q^{97} +(19.6924 + 34.1082i) q^{98} -3.41421 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{7} - 12 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^7 - 12 * q^8 + 2 * q^9	\( 4 q + 2 q^{2} - 2 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{7} - 12 q^{8} + 2 q^{9} + 2 q^{10} - 4 q^{11} - 16 q^{12} - 24 q^{14} - 6 q^{16} + 4 q^{17} + 4 q^{18} - 4 q^{19} - 2 q^{20} - 16 q^{21} + 8 q^{22} - 4 q^{24} + 4 q^{25} - 20 q^{28} - 4 q^{30} + 24 q^{31} - 6 q^{32} + 4 q^{33} - 8 q^{34} - 4 q^{35} + 2 q^{36} - 12 q^{40} + 12 q^{41} - 16 q^{42} + 8 q^{43} + 24 q^{44} + 2 q^{45} + 4 q^{46} - 8 q^{47} - 10 q^{49} + 2 q^{50} - 16 q^{51} - 24 q^{53} + 16 q^{54} - 4 q^{55} + 20 q^{56} + 8 q^{57} - 16 q^{58} - 12 q^{59} - 16 q^{60} + 16 q^{61} + 4 q^{63} - 28 q^{64} + 24 q^{66} + 4 q^{67} - 12 q^{68} + 4 q^{69} - 24 q^{70} - 4 q^{71} - 6 q^{72} - 24 q^{74} + 4 q^{76} + 32 q^{77} - 6 q^{80} + 10 q^{81} - 4 q^{82} - 24 q^{83} + 24 q^{84} + 4 q^{85} + 56 q^{86} - 16 q^{87} + 16 q^{88} - 12 q^{89} + 4 q^{90} + 16 q^{92} - 12 q^{93} - 12 q^{94} - 4 q^{95} + 8 q^{96} + 4 q^{97} + 42 q^{98} - 8 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^7 - 12 * q^8 + 2 * q^9 + 2 * q^10 - 4 * q^11 - 16 * q^12 - 24 * q^14 - 6 * q^16 + 4 * q^17 + 4 * q^18 - 4 * q^19 - 2 * q^20 - 16 * q^21 + 8 * q^22 - 4 * q^24 + 4 * q^25 - 20 * q^28 - 4 * q^30 + 24 * q^31 - 6 * q^32 + 4 * q^33 - 8 * q^34 - 4 * q^35 + 2 * q^36 - 12 * q^40 + 12 * q^41 - 16 * q^42 + 8 * q^43 + 24 * q^44 + 2 * q^45 + 4 * q^46 - 8 * q^47 - 10 * q^49 + 2 * q^50 - 16 * q^51 - 24 * q^53 + 16 * q^54 - 4 * q^55 + 20 * q^56 + 8 * q^57 - 16 * q^58 - 12 * q^59 - 16 * q^60 + 16 * q^61 + 4 * q^63 - 28 * q^64 + 24 * q^66 + 4 * q^67 - 12 * q^68 + 4 * q^69 - 24 * q^70 - 4 * q^71 - 6 * q^72 - 24 * q^74 + 4 * q^76 + 32 * q^77 - 6 * q^80 + 10 * q^81 - 4 * q^82 - 24 * q^83 + 24 * q^84 + 4 * q^85 + 56 * q^86 - 16 * q^87 + 16 * q^88 - 12 * q^89 + 4 * q^90 + 16 * q^92 - 12 * q^93 - 12 * q^94 - 4 * q^95 + 8 * q^96 + 4 * q^97 + 42 * q^98 - 8 * q^99

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