LMFDB - Embedded newform 1690.2.e.t.991.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1690,2,Mod(191,1690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1690, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("1690.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1690 = 2 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1690.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:	$13.4947179416$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.22581504.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 $ x^8 - 4x^7 + 5x^6 + 2x^5 - 11x^4 + 4x^3 + 20x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			991.4
Root			$0.665665 - 1.24775i$ of defining polynomial
Character	$\chi$	$=$	1690.991
Dual form			1690.2.e.t.191.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.913419 + 1.58209i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-0.913419 + 1.58209i) q^{6} +(-1.99551 + 3.45632i) q^{7} -1.00000 q^{8} +(-0.168669 + 0.292144i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.913419 + 1.58209i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-0.913419 + 1.58209i) q^{6} +(-1.99551 + 3.45632i) q^{7} -1.00000 q^{8} +(-0.168669 + 0.292144i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-2.44811 - 4.24026i) q^{11} -1.82684 q^{12} -3.99102 q^{14} +(-0.913419 - 1.58209i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.31414 + 5.74026i) q^{17} -0.337339 q^{18} +(1.04739 - 1.81414i) q^{19} +(0.500000 - 0.866025i) q^{20} -7.29094 q^{21} +(2.44811 - 4.24026i) q^{22} +(0.495508 + 0.858244i) q^{23} +(-0.913419 - 1.58209i) q^{24} +1.00000 q^{25} +4.86425 q^{27} +(-1.99551 - 3.45632i) q^{28} +(-2.92163 - 5.06040i) q^{29} +(0.913419 - 1.58209i) q^{30} -10.8179 q^{31} +(0.500000 - 0.866025i) q^{32} +(4.47231 - 7.74627i) q^{33} -6.62828 q^{34} +(1.99551 - 3.45632i) q^{35} +(-0.168669 - 0.292144i) q^{36} +(-1.64996 - 2.85782i) q^{37} +2.09479 q^{38} +1.00000 q^{40} +(2.59030 + 4.48652i) q^{41} +(-3.64547 - 6.31414i) q^{42} +(-0.567874 + 0.983586i) q^{43} +4.89623 q^{44} +(0.168669 - 0.292144i) q^{45} +(-0.495508 + 0.858244i) q^{46} -1.61186 q^{47} +(0.913419 - 1.58209i) q^{48} +(-4.46410 - 7.73205i) q^{49} +(0.500000 + 0.866025i) q^{50} -12.1088 q^{51} -0.549905 q^{53} +(2.43213 + 4.21257i) q^{54} +(2.44811 + 4.24026i) q^{55} +(1.99551 - 3.45632i) q^{56} +3.82684 q^{57} +(2.92163 - 5.06040i) q^{58} +(1.73205 - 3.00000i) q^{59} +1.82684 q^{60} +(0.685861 - 1.18795i) q^{61} +(-5.40893 - 9.36854i) q^{62} +(-0.673162 - 1.16595i) q^{63} +1.00000 q^{64} +8.94462 q^{66} +(-1.81042 - 3.13575i) q^{67} +(-3.31414 - 5.74026i) q^{68} +(-0.905212 + 1.56787i) q^{69} +3.99102 q^{70} +(-3.00000 + 5.19615i) q^{71} +(0.168669 - 0.292144i) q^{72} -8.94462 q^{73} +(1.64996 - 2.85782i) q^{74} +(0.913419 + 1.58209i) q^{75} +(1.04739 + 1.81414i) q^{76} +19.5409 q^{77} +2.55231 q^{79} +(0.500000 + 0.866025i) q^{80} +(4.94911 + 8.57211i) q^{81} +(-2.59030 + 4.48652i) q^{82} +16.4207 q^{83} +(3.64547 - 6.31414i) q^{84} +(3.31414 - 5.74026i) q^{85} -1.13575 q^{86} +(5.33734 - 9.24454i) q^{87} +(2.44811 + 4.24026i) q^{88} +(1.72427 + 2.98652i) q^{89} +0.337339 q^{90} -0.991015 q^{92} +(-9.88124 - 17.1148i) q^{93} +(-0.805932 - 1.39592i) q^{94} +(-1.04739 + 1.81414i) q^{95} +1.82684 q^{96} +(-5.82606 + 10.0910i) q^{97} +(4.46410 - 7.73205i) q^{98} +1.65169 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 2 q^{3} - 4 q^{4} - 8 q^{5} + 2 q^{6} - 8 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^2 - 2 * q^3 - 4 * q^4 - 8 * q^5 + 2 * q^6 - 8 * q^8 - 4 * q^9	$ 8 q + 4 q^{2} - 2 q^{3} - 4 q^{4} - 8 q^{5} + 2 q^{6} - 8 q^{8} - 4 q^{9} - 4 q^{10} - 6 q^{11} + 4 q^{12} + 2 q^{15} - 4 q^{16} - 6 q^{17} - 8 q^{18} + 6 q^{19} + 4 q^{20} - 12 q^{21} + 6 q^{22} - 12 q^{23} + 2 q^{24} + 8 q^{25} + 40 q^{27} - 2 q^{30} - 36 q^{31} + 4 q^{32} - 6 q^{33} - 12 q^{34} - 4 q^{36} - 6 q^{37} + 12 q^{38} + 8 q^{40} - 6 q^{42} - 4 q^{43} + 12 q^{44} + 4 q^{45} + 12 q^{46} - 2 q^{48} - 8 q^{49} + 4 q^{50} + 60 q^{53} + 20 q^{54} + 6 q^{55} + 12 q^{57} - 4 q^{60} + 26 q^{61} - 18 q^{62} - 24 q^{63} + 8 q^{64} - 12 q^{66} - 24 q^{67} - 6 q^{68} - 12 q^{69} - 24 q^{71} + 4 q^{72} + 12 q^{73} + 6 q^{74} - 2 q^{75} + 6 q^{76} + 60 q^{77} + 20 q^{79} + 4 q^{80} - 28 q^{81} + 36 q^{83} + 6 q^{84} + 6 q^{85} - 8 q^{86} + 48 q^{87} + 6 q^{88} + 8 q^{90} + 24 q^{92} - 12 q^{93} - 6 q^{95} - 4 q^{96} + 18 q^{97} + 8 q^{98} + 84 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 - 2 * q^3 - 4 * q^4 - 8 * q^5 + 2 * q^6 - 8 * q^8 - 4 * q^9 - 4 * q^10 - 6 * q^11 + 4 * q^12 + 2 * q^15 - 4 * q^16 - 6 * q^17 - 8 * q^18 + 6 * q^19 + 4 * q^20 - 12 * q^21 + 6 * q^22 - 12 * q^23 + 2 * q^24 + 8 * q^25 + 40 * q^27 - 2 * q^30 - 36 * q^31 + 4 * q^32 - 6 * q^33 - 12 * q^34 - 4 * q^36 - 6 * q^37 + 12 * q^38 + 8 * q^40 - 6 * q^42 - 4 * q^43 + 12 * q^44 + 4 * q^45 + 12 * q^46 - 2 * q^48 - 8 * q^49 + 4 * q^50 + 60 * q^53 + 20 * q^54 + 6 * q^55 + 12 * q^57 - 4 * q^60 + 26 * q^61 - 18 * q^62 - 24 * q^63 + 8 * q^64 - 12 * q^66 - 24 * q^67 - 6 * q^68 - 12 * q^69 - 24 * q^71 + 4 * q^72 + 12 * q^73 + 6 * q^74 - 2 * q^75 + 6 * q^76 + 60 * q^77 + 20 * q^79 + 4 * q^80 - 28 * q^81 + 36 * q^83 + 6 * q^84 + 6 * q^85 - 8 * q^86 + 48 * q^87 + 6 * q^88 + 8 * q^90 + 24 * q^92 - 12 * q^93 - 6 * q^95 - 4 * q^96 + 18 * q^97 + 8 * q^98 + 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1690\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	0.913419	+	1.58209i	0.527363	+	0.913419i	0.999491	+	0.0318895i	$0.0101525\pi$
$3$	0.913419	+	1.58209i	0.527363	+	0.913419i	−0.472129	+	0.881530i	$0.656514\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−0.913419	+	1.58209i	−0.372902	+	0.645885i
$7$	−1.99551	+	3.45632i	−0.754231	+	1.30637i	0.191525	+	0.981488i	$0.438657\pi$
$7$	−1.99551	+	3.45632i	−0.754231	+	1.30637i	−0.945756	+	0.324879i	$0.894677\pi$
$8$	−1.00000			−0.353553
$9$	−0.168669	+	0.292144i	−0.0562231	+	0.0973812i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	−2.44811	−	4.24026i	−0.738134	−	1.27849i	−0.953335	−	0.301916i	$-0.902374\pi$
$11$	−2.44811	−	4.24026i	−0.738134	−	1.27849i	0.215200	−	0.976570i	$-0.430960\pi$
$12$	−1.82684			−0.527363
$13$		0			0
$13$		0			0
$14$	−3.99102			−1.06664
$15$	−0.913419	−	1.58209i	−0.235844	−	0.408493i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.31414	+	5.74026i	−0.803797	+	1.39222i	0.113303	+	0.993560i	$0.463857\pi$
$17$	−3.31414	+	5.74026i	−0.803797	+	1.39222i	−0.917100	+	0.398657i	$0.869477\pi$
$18$	−0.337339			−0.0795115
$19$	1.04739	−	1.81414i	0.240289	−	0.416192i	−0.720508	−	0.693447i	$-0.756091\pi$
$19$	1.04739	−	1.81414i	0.240289	−	0.416192i	0.960796	+	0.277255i	$0.0894246\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	−7.29094			−1.59101
$22$	2.44811	−	4.24026i	0.521940	−	0.904026i
$23$	0.495508	+	0.858244i	0.103320	+	0.178956i	0.913051	−	0.407846i	$-0.133720\pi$
$23$	0.495508	+	0.858244i	0.103320	+	0.178956i	−0.809730	+	0.586802i	$0.800387\pi$
$24$	−0.913419	−	1.58209i	−0.186451	−	0.322942i
$25$	1.00000			0.200000
$26$		0			0
$27$	4.86425			0.936126
$28$	−1.99551	−	3.45632i	−0.377115	−	0.653183i
$29$	−2.92163	−	5.06040i	−0.542532	−	0.939694i	−0.998758	−	0.0498293i	$-0.984132\pi$
$29$	−2.92163	−	5.06040i	−0.542532	−	0.939694i	0.456225	−	0.889864i	$-0.349201\pi$
$30$	0.913419	−	1.58209i	0.166767	−	0.288849i
$31$	−10.8179			−1.94294			−0.971472	−	0.237155i	$-0.923785\pi$
$31$	−10.8179			−1.94294			−0.971472	+	0.237155i	$0.923785\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	4.47231	−	7.74627i	0.778529	−	1.34845i
$34$	−6.62828			−1.13674
$35$	1.99551	−	3.45632i	0.337302	−	0.584225i
$36$	−0.168669	−	0.292144i	−0.0281115	−	0.0486906i
$37$	−1.64996	−	2.85782i	−0.271252	−	0.469822i	0.697931	−	0.716165i	$-0.254104\pi$
$37$	−1.64996	−	2.85782i	−0.271252	−	0.469822i	−0.969183	+	0.246343i	$0.920771\pi$
$38$	2.09479			0.339819
$39$		0			0
$40$	1.00000			0.158114
$41$	2.59030	+	4.48652i	0.404536	+	0.700677i	0.994267	−	0.106922i	$-0.0340996\pi$
$41$	2.59030	+	4.48652i	0.404536	+	0.700677i	−0.589731	+	0.807600i	$0.700766\pi$
$42$	−3.64547	−	6.31414i	−0.562508	−	0.974293i
$43$	−0.567874	+	0.983586i	−0.0866000	+	0.149996i	−0.906072	−	0.423124i	$-0.860934\pi$
$43$	−0.567874	+	0.983586i	−0.0866000	+	0.149996i	0.819472	+	0.573119i	$0.194267\pi$
$44$	4.89623			0.738134
$45$	0.168669	−	0.292144i	0.0251437	−	0.0435502i
$46$	−0.495508	+	0.858244i	−0.0730586	+	0.126541i
$47$	−1.61186			−0.235115			−0.117557	−	0.993066i	$-0.537506\pi$
$47$	−1.61186			−0.235115			−0.117557	+	0.993066i	$0.537506\pi$
$48$	0.913419	−	1.58209i	0.131841	−	0.228355i
$49$	−4.46410	−	7.73205i	−0.637729	−	1.10458i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	−12.1088			−1.69557
$52$		0			0
$53$	−0.549905			−0.0755352			−0.0377676	−	0.999287i	$-0.512025\pi$
$53$	−0.549905			−0.0755352			−0.0377676	+	0.999287i	$0.512025\pi$
$54$	2.43213	+	4.21257i	0.330970	+	0.573258i
$55$	2.44811	+	4.24026i	0.330104	+	0.571756i
$56$	1.99551	−	3.45632i	0.266661	−	0.461870i
$57$	3.82684			0.506877
$58$	2.92163	−	5.06040i	0.383628	−	0.664464i
$59$	1.73205	−	3.00000i	0.225494	−	0.390567i	−0.730974	−	0.682406i	$-0.760934\pi$
$59$	1.73205	−	3.00000i	0.225494	−	0.390567i	0.956467	+	0.291839i	$0.0942671\pi$
$60$	1.82684			0.235844
$61$	0.685861	−	1.18795i	0.0878155	−	0.152101i	−0.818772	−	0.574119i	$-0.805345\pi$
$61$	0.685861	−	1.18795i	0.0878155	−	0.152101i	0.906587	+	0.422018i	$0.138678\pi$
$62$	−5.40893	−	9.36854i	−0.686934	−	1.18981i
$63$	−0.673162	−	1.16595i	−0.0848104	−	0.146896i
$64$	1.00000			0.125000
$65$		0			0
$66$	8.94462			1.10101
$67$	−1.81042	−	3.13575i	−0.221179	−	0.383093i	0.733988	−	0.679163i	$-0.237657\pi$
$67$	−1.81042	−	3.13575i	−0.221179	−	0.383093i	−0.955166	+	0.296070i	$0.904324\pi$
$68$	−3.31414	−	5.74026i	−0.401898	−	0.696108i
$69$	−0.905212	+	1.56787i	−0.108975	+	0.188750i
$70$	3.99102			0.477018
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	−0.987294	−	0.158901i	$-0.949205\pi$
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	0.631260	+	0.775571i	$0.282538\pi$
$72$	0.168669	−	0.292144i	0.0198779	−	0.0344295i
$73$	−8.94462			−1.04689			−0.523444	−	0.852060i	$-0.675353\pi$
$73$	−8.94462			−1.04689			−0.523444	+	0.852060i	$0.675353\pi$
$74$	1.64996	−	2.85782i	0.191804	−	0.332215i
$75$	0.913419	+	1.58209i	0.105473	+	0.182684i
$76$	1.04739	+	1.81414i	0.120144	+	0.208096i
$77$	19.5409			2.22689
$78$		0			0
$79$	2.55231			0.287158			0.143579	−	0.989639i	$-0.454139\pi$
$79$	2.55231			0.287158			0.143579	+	0.989639i	$0.454139\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	4.94911	+	8.57211i	0.549901	+	0.952456i
$82$	−2.59030	+	4.48652i	−0.286050	+	0.495454i
$83$	16.4207			1.80241			0.901205	−	0.433393i	$-0.142684\pi$
$83$	16.4207			1.80241			0.901205	+	0.433393i	$0.142684\pi$
$84$	3.64547	−	6.31414i	0.397753	−	0.688929i
$85$	3.31414	−	5.74026i	0.359469	−	0.622618i
$86$	−1.13575			−0.122471
$87$	5.33734	−	9.24454i	0.572223	−	0.991119i
$88$	2.44811	+	4.24026i	0.260970	+	0.452013i
$89$	1.72427	+	2.98652i	0.182772	+	0.316571i	0.942824	−	0.333292i	$-0.108160\pi$
$89$	1.72427	+	2.98652i	0.182772	+	0.316571i	−0.760051	+	0.649863i	$0.774826\pi$
$90$	0.337339			0.0355586
$91$		0			0
$92$	−0.991015			−0.103320
$93$	−9.88124	−	17.1148i	−1.02464	−	1.77472i
$94$	−0.805932	−	1.39592i	−0.0831256	−	0.143978i
$95$	−1.04739	+	1.81414i	−0.107460	+	0.186127i
$96$	1.82684			0.186451
$97$	−5.82606	+	10.0910i	−0.591547	+	1.02459i	0.402477	+	0.915430i	$0.368149\pi$
$97$	−5.82606	+	10.0910i	−0.591547	+	1.02459i	−0.994024	+	0.109159i	$0.965184\pi$
$98$	4.46410	−	7.73205i	0.450942	−	0.781055i
$99$	1.65169			0.166001
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−1.03961	−	1.80066i	−0.103445	−	0.179173i	0.809657	−	0.586904i	$-0.199653\pi$
$101$	−1.03961	−	1.80066i	−0.103445	−	0.179173i	−0.913102	+	0.407731i	$0.866320\pi$
$102$	−6.05440	−	10.4865i	−0.599475	−	1.03832i
$103$	2.26795			0.223468			0.111734	−	0.993738i	$-0.464360\pi$
$103$	2.26795			0.223468			0.111734	+	0.993738i	$0.464360\pi$
$104$		0			0
$105$	7.29094			0.711523
$106$	−0.274952	−	0.476231i	−0.0267057	−	0.0462557i
$107$	1.25076	+	2.16638i	0.120915	+	0.209431i	0.920129	−	0.391616i	$-0.128084\pi$
$107$	1.25076	+	2.16638i	0.120915	+	0.209431i	−0.799214	+	0.601047i	$0.794750\pi$
$108$	−2.43213	+	4.21257i	−0.234031	+	0.405354i
$109$	−15.6357			−1.49763			−0.748815	−	0.662780i	$-0.769377\pi$
$109$	−15.6357			−1.49763			−0.748815	+	0.662780i	$0.769377\pi$
$110$	−2.44811	+	4.24026i	−0.233418	+	0.404293i
$111$	3.01421	−	5.22077i	0.286097	−	0.495534i
$112$	3.99102			0.377115
$113$	−8.55889	+	14.8244i	−0.805153	+	1.39457i	0.111035	+	0.993816i	$0.464583\pi$
$113$	−8.55889	+	14.8244i	−0.805153	+	1.39457i	−0.916188	+	0.400749i	$0.868750\pi$
$114$	1.91342	+	3.31414i	0.179208	+	0.310398i
$115$	−0.495508	−	0.858244i	−0.0462063	−	0.0800317i
$116$	5.84325			0.542532
$117$		0			0
$118$	3.46410			0.318896
$119$	−13.2268	−	22.9095i	−1.21250	−	2.10011i
$120$	0.913419	+	1.58209i	0.0833834	+	0.144424i
$121$	−6.48652	+	11.2350i	−0.589684	+	1.02136i
$122$	1.37172			0.124190
$123$	−4.73205	+	8.19615i	−0.426675	+	0.739022i
$124$	5.40893	−	9.36854i	0.485736	−	0.841319i
$125$	−1.00000			−0.0894427
$126$	0.673162	−	1.16595i	0.0599700	−	0.103871i
$127$	−4.06218	−	7.03590i	−0.360460	−	0.624335i	0.627577	−	0.778555i	$-0.284047\pi$
$127$	−4.06218	−	7.03590i	−0.360460	−	0.624335i	−0.988037	+	0.154220i	$0.950714\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−2.07483			−0.182678
$130$		0			0
$131$	14.1773			1.23868			0.619340	−	0.785123i	$-0.287400\pi$
$131$	14.1773			1.23868			0.619340	+	0.785123i	$0.287400\pi$
$132$	4.47231	+	7.74627i	0.389264	+	0.674226i
$133$	4.18016	+	7.24026i	0.362466	+	0.627810i
$134$	1.81042	−	3.13575i	0.156397	−	0.270887i
$135$	−4.86425			−0.418648
$136$	3.31414	−	5.74026i	0.284185	−	0.492223i
$137$	−7.00821	+	12.1386i	−0.598752	+	1.03707i	0.394254	+	0.919001i	$0.371003\pi$
$137$	−7.00821	+	12.1386i	−0.598752	+	1.03707i	−0.993006	+	0.118067i	$0.962330\pi$
$138$	−1.81042			−0.154114
$139$	−7.99473	+	13.8473i	−0.678104	+	1.17451i	0.297447	+	0.954738i	$0.403865\pi$
$139$	−7.99473	+	13.8473i	−0.678104	+	1.17451i	−0.975551	+	0.219772i	$0.929469\pi$
$140$	1.99551	+	3.45632i	0.168651	+	0.292112i
$141$	−1.47231	−	2.55011i	−0.123991	−	0.214758i
$142$	−6.00000			−0.503509
$143$		0			0
$144$	0.337339			0.0281115
$145$	2.92163	+	5.06040i	0.242628	+	0.420244i
$146$	−4.47231	−	7.74627i	−0.370131	−	0.641085i
$147$	8.15519	−	14.1252i	0.672629	−	1.16503i
$148$	3.29992			0.271252
$149$	3.74846	−	6.49253i	0.307086	−	0.531889i	−0.670637	−	0.741785i	$-0.733979\pi$
$149$	3.74846	−	6.49253i	0.307086	−	0.531889i	0.977724	+	0.209896i	$0.0673127\pi$
$150$	−0.913419	+	1.58209i	−0.0745804	+	0.129177i
$151$	−4.24913			−0.345789			−0.172895	−	0.984940i	$-0.555312\pi$
$151$	−4.24913			−0.345789			−0.172895	+	0.984940i	$0.555312\pi$
$152$	−1.04739	+	1.81414i	−0.0849549	+	0.147146i
$153$	−1.11799	−	1.93641i	−0.0903839	−	0.156549i
$154$	9.77046	+	16.9229i	0.787326	+	1.36369i
$155$	10.8179			0.868911
$156$		0			0
$157$	−22.7526			−1.81586			−0.907929	−	0.419124i	$-0.862337\pi$
$157$	−22.7526			−1.81586			−0.907929	+	0.419124i	$0.862337\pi$
$158$	1.27616	+	2.21037i	0.101526	+	0.175847i
$159$	−0.502293	−	0.869998i	−0.0398345	−	0.0689953i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	−3.95516			−0.311710
$162$	−4.94911	+	8.57211i	−0.388839	+	0.673488i
$163$	−2.60749	+	4.51630i	−0.204234	+	0.353744i	−0.949888	−	0.312589i	$-0.898804\pi$
$163$	−2.60749	+	4.51630i	−0.204234	+	0.353744i	0.745654	+	0.666333i	$0.232137\pi$
$164$	−5.18059			−0.404536
$165$	−4.47231	+	7.74627i	−0.348169	+	0.603046i
$166$	8.21037	+	14.2208i	0.637248	+	1.10375i
$167$	−3.35224	−	5.80624i	−0.259404	−	0.449301i	0.706679	−	0.707535i	$-0.250193\pi$
$167$	−3.35224	−	5.80624i	−0.259404	−	0.449301i	−0.966082	+	0.258234i	$0.916859\pi$
$168$	7.29094			0.562508
$169$		0			0
$170$	6.62828			0.508366
$171$	0.353326	+	0.611979i	0.0270195	+	0.0467992i
$172$	−0.567874	−	0.983586i	−0.0433000	−	0.0749978i
$173$	−9.77046	+	16.9229i	−0.742834	+	1.28663i	0.208365	+	0.978051i	$0.433186\pi$
$173$	−9.77046	+	16.9229i	−0.742834	+	1.28663i	−0.951200	+	0.308576i	$0.900148\pi$
$174$	10.6747			0.809245
$175$	−1.99551	+	3.45632i	−0.150846	+	0.261273i
$176$	−2.44811	+	4.24026i	−0.184534	+	0.319621i
$177$	6.32835			0.475668
$178$	−1.72427	+	2.98652i	−0.129239	+	0.223849i
$179$	−4.48950	−	7.77604i	−0.335561	−	0.581209i	0.648031	−	0.761614i	$-0.275593\pi$
$179$	−4.48950	−	7.77604i	−0.335561	−	0.581209i	−0.983592	+	0.180405i	$0.942259\pi$
$180$	0.168669	+	0.292144i	0.0125719	+	0.0217751i
$181$	5.55648			0.413010			0.206505	−	0.978446i	$-0.433791\pi$
$181$	5.55648			0.413010			0.206505	+	0.978446i	$0.433791\pi$
$182$		0			0
$183$	2.50591			0.185242
$184$	−0.495508	−	0.858244i	−0.0365293	−	0.0632706i
$185$	1.64996	+	2.85782i	0.121308	+	0.210111i
$186$	9.88124	−	17.1148i	0.724527	−	1.25492i
$187$	32.4536			2.37324
$188$	0.805932	−	1.39592i	0.0587787	−	0.101808i
$189$	−9.70665	+	16.8124i	−0.706055	+	1.22292i
$190$	−2.09479			−0.151972
$191$	−5.09316	+	8.82161i	−0.368528	+	0.638309i	−0.989336	−	0.145654i	$-0.953471\pi$
$191$	−5.09316	+	8.82161i	−0.368528	+	0.638309i	0.620808	+	0.783963i	$0.286805\pi$
$192$	0.913419	+	1.58209i	0.0659204	+	0.114177i
$193$	4.06939	+	7.04839i	0.292921	+	0.507354i	0.974499	−	0.224391i	$-0.0720394\pi$
$193$	4.06939	+	7.04839i	0.292921	+	0.507354i	−0.681578	+	0.731745i	$0.738706\pi$
$194$	−11.6521			−0.836574
$195$		0			0
$196$	8.92820			0.637729
$197$	−7.24026	−	12.5405i	−0.515847	−	0.893473i	−0.999831	−	0.0183962i	$-0.994144\pi$
$197$	−7.24026	−	12.5405i	−0.515847	−	0.893473i	0.483984	−	0.875077i	$-0.339189\pi$
$198$	0.825843	+	1.43040i	0.0586901	+	0.101654i
$199$	5.62828	−	9.74846i	0.398978	−	0.691050i	−0.594622	−	0.804005i	$-0.702698\pi$
$199$	5.62828	−	9.74846i	0.398978	−	0.691050i	0.993600	+	0.112955i	$0.0360316\pi$
$200$	−1.00000			−0.0707107
$201$	3.30735	−	5.72850i	0.233283	−	0.404058i
$202$	1.03961	−	1.80066i	0.0731469	−	0.126694i
$203$	23.3205			1.63678
$204$	6.05440	−	10.4865i	0.423893	−	0.734203i
$205$	−2.59030	−	4.48652i	−0.180914	−	0.313352i
$206$	1.13397	+	1.96410i	0.0790078	+	0.136845i
$207$	−0.334308			−0.0232360
$208$		0			0
$209$	−10.2566			−0.709461
$210$	3.64547	+	6.31414i	0.251561	+	0.435717i
$211$	−4.79257	−	8.30097i	−0.329934	−	0.571463i	0.652564	−	0.757733i	$-0.273693\pi$
$211$	−4.79257	−	8.30097i	−0.329934	−	0.571463i	−0.982498	+	0.186271i	$0.940360\pi$
$212$	0.274952	−	0.476231i	0.0188838	−	0.0327077i
$213$	−10.9610			−0.751037
$214$	−1.25076	+	2.16638i	−0.0855000	+	0.148090i
$215$	0.567874	−	0.983586i	0.0387287	−	0.0670800i
$216$	−4.86425			−0.330970
$217$	21.5871	−	37.3900i	1.46543	−	2.53820i
$218$	−7.81785	−	13.5409i	−0.529492	−	0.917107i
$219$	−8.17018	−	14.1512i	−0.552090	−	0.956248i
$220$	−4.89623			−0.330104
$221$		0			0
$222$	6.02843			0.404602
$223$	13.6058	+	23.5660i	0.911113	+	1.57809i	0.812495	+	0.582968i	$0.198109\pi$
$223$	13.6058	+	23.5660i	0.911113	+	1.57809i	0.0986181	+	0.995125i	$0.468558\pi$
$224$	1.99551	+	3.45632i	0.133330	+	0.230935i
$225$	−0.168669	+	0.292144i	−0.0112446	+	0.0194762i
$226$	−17.1178			−1.13866
$227$	3.16418	−	5.48052i	0.210014	−	0.363755i	−0.741705	−	0.670726i	$-0.765982\pi$
$227$	3.16418	−	5.48052i	0.210014	−	0.363755i	0.951719	+	0.306972i	$0.0993158\pi$
$228$	−1.91342	+	3.31414i	−0.126719	+	0.219484i
$229$	−2.50152			−0.165305			−0.0826524	−	0.996578i	$-0.526339\pi$
$229$	−2.50152			−0.165305			−0.0826524	+	0.996578i	$0.526339\pi$
$230$	0.495508	−	0.858244i	0.0326728	−	0.0565910i
$231$	17.8491	+	30.9155i	1.17438	+	2.03409i
$232$	2.92163	+	5.06040i	0.191814	+	0.332232i
$233$	−9.17903			−0.601339			−0.300669	−	0.953728i	$-0.597210\pi$
$233$	−9.17903			−0.601339			−0.300669	+	0.953728i	$0.597210\pi$
$234$		0			0
$235$	1.61186			0.105146
$236$	1.73205	+	3.00000i	0.112747	+	0.195283i
$237$	2.33133	+	4.03798i	0.151436	+	0.262295i
$238$	13.2268	−	22.9095i	0.857365	−	1.48500i
$239$	6.54030			0.423057			0.211528	−	0.977372i	$-0.432156\pi$
$239$	6.54030			0.423057			0.211528	+	0.977372i	$0.432156\pi$
$240$	−0.913419	+	1.58209i	−0.0589610	+	0.102123i
$241$	−4.54127	+	7.86571i	−0.292529	+	0.506675i	−0.974407	−	0.224791i	$-0.927830\pi$
$241$	−4.54127	+	7.86571i	−0.292529	+	0.506675i	0.681878	+	0.731466i	$0.261163\pi$
$242$	−12.9730			−0.833939
$243$	−1.74484	+	3.02216i	−0.111932	+	0.193872i
$244$	0.685861	+	1.18795i	0.0439077	+	0.0760504i
$245$	4.46410	+	7.73205i	0.285201	+	0.493983i
$246$	−9.46410			−0.603409
$247$		0			0
$248$	10.8179			0.686934
$249$	14.9990	+	25.9791i	0.950524	+	1.64636i
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	4.81414	−	8.33833i	0.303866	−	0.526311i	−0.673142	−	0.739513i	$-0.735056\pi$
$251$	4.81414	−	8.33833i	0.303866	−	0.526311i	0.977008	+	0.213202i	$0.0683892\pi$
$252$	1.34632			0.0848104
$253$	2.42612	−	4.20216i	0.152529	−	0.264188i
$254$	4.06218	−	7.03590i	0.254884	−	0.441472i
$255$	12.1088			0.758282
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.41113	+	12.8364i	0.462293	+	0.800716i	0.999075	−	0.0430058i	$-0.0136934\pi$
$257$	7.41113	+	12.8364i	0.462293	+	0.800716i	−0.536781	+	0.843721i	$0.680360\pi$
$258$	−1.03741	−	1.79685i	−0.0645866	−	0.111867i
$259$	13.1700			0.818347
$260$		0			0
$261$	1.97115			0.122011
$262$	7.08867	+	12.2779i	0.437939	+	0.758533i
$263$	−5.51673	−	9.55525i	−0.340176	−	0.589202i	0.644289	−	0.764782i	$-0.277153\pi$
$263$	−5.51673	−	9.55525i	−0.340176	−	0.589202i	−0.984465	+	0.175580i	$0.943820\pi$
$264$	−4.47231	+	7.74627i	−0.275252	+	0.476750i
$265$	0.549905			0.0337804
$266$	−4.18016	+	7.24026i	−0.256302	+	0.443929i
$267$	−3.14996	+	5.45589i	−0.192775	+	0.333895i
$268$	3.62085			0.221179
$269$	1.30515	−	2.26059i	0.0795767	−	0.137831i	−0.823491	−	0.567330i	$-0.807976\pi$
$269$	1.30515	−	2.26059i	0.0795767	−	0.137831i	0.903067	+	0.429499i	$0.141310\pi$
$270$	−2.43213	−	4.21257i	−0.148014	−	0.256369i
$271$	14.3448	+	24.8459i	0.871383	+	1.50928i	0.860567	+	0.509337i	$0.170109\pi$
$271$	14.3448	+	24.8459i	0.871383	+	1.50928i	0.0108156	+	0.999942i	$0.496557\pi$
$272$	6.62828			0.401898
$273$		0			0
$274$	−14.0164			−0.846763
$275$	−2.44811	−	4.24026i	−0.147627	−	0.255697i
$276$	−0.905212	−	1.56787i	−0.0544874	−	0.0943749i
$277$	−2.35035	+	4.07092i	−0.141219	+	0.244598i	−0.927956	−	0.372690i	$-0.878435\pi$
$277$	−2.35035	+	4.07092i	−0.141219	+	0.244598i	0.786737	+	0.617288i	$0.211769\pi$
$278$	−15.9895			−0.958984
$279$	1.82464	−	3.16037i	0.109238	−	0.189206i
$280$	−1.99551	+	3.45632i	−0.119254	+	0.206555i
$281$	−3.32418			−0.198304			−0.0991521	−	0.995072i	$-0.531613\pi$
$281$	−3.32418			−0.198304			−0.0991521	+	0.995072i	$0.531613\pi$
$282$	1.47231	−	2.55011i	0.0876747	−	0.151857i
$283$	−12.9886	−	22.4969i	−0.772093	−	1.33730i	−0.936414	−	0.350897i	$-0.885877\pi$
$283$	−12.9886	−	22.4969i	−0.772093	−	1.33730i	0.164322	−	0.986407i	$-0.447457\pi$
$284$	−3.00000	−	5.19615i	−0.178017	−	0.308335i
$285$	−3.82684			−0.226682
$286$		0			0
$287$	−20.6758			−1.22045
$288$	0.168669	+	0.292144i	0.00993893	+	0.0172147i
$289$	−13.4670	−	23.3256i	−0.792179	−	1.37209i
$290$	−2.92163	+	5.06040i	−0.171564	+	0.297157i
$291$	−21.2865			−1.24784
$292$	4.47231	−	7.74627i	0.261722	−	0.453316i
$293$	−0.476231	+	0.824857i	−0.0278217	+	0.0481886i	−0.879601	−	0.475712i	$-0.842190\pi$
$293$	−0.476231	+	0.824857i	−0.0278217	+	0.0481886i	0.851779	+	0.523901i	$0.175524\pi$
$294$	16.3104			0.951241
$295$	−1.73205	+	3.00000i	−0.100844	+	0.174667i
$296$	1.64996	+	2.85782i	0.0959021	+	0.166107i
$297$	−11.9082	−	20.6257i	−0.690986	−	1.19682i
$298$	7.49693			0.434285
$299$		0			0
$300$	−1.82684			−0.105473
$301$	−2.26639	−	3.92551i	−0.130633	−	0.226263i
$302$	−2.12456	−	3.67985i	−0.122255	−	0.211752i
$303$	1.89920	−	3.28952i	0.109106	−	0.188978i
$304$	−2.09479			−0.120144
$305$	−0.685861	+	1.18795i	−0.0392723	+	0.0680216i
$306$	1.11799	−	1.93641i	0.0639111	−	0.110697i
$307$	32.5819			1.85955			0.929773	−	0.368133i	$-0.120003\pi$
$307$	32.5819			1.85955			0.929773	+	0.368133i	$0.120003\pi$
$308$	−9.77046	+	16.9229i	−0.556724	+	0.964274i
$309$	2.07159	+	3.58810i	0.117849	+	0.204120i
$310$	5.40893	+	9.36854i	0.307206	+	0.532097i
$311$	−18.2831			−1.03674			−0.518370	−	0.855157i	$-0.673461\pi$
$311$	−18.2831			−1.03674			−0.518370	+	0.855157i	$0.673461\pi$
$312$		0			0
$313$	−16.0968			−0.909844			−0.454922	−	0.890531i	$-0.650333\pi$
$313$	−16.0968			−0.909844			−0.454922	+	0.890531i	$0.650333\pi$
$314$	−11.3763	−	19.7044i	−0.642003	−	1.11198i
$315$	0.673162	+	1.16595i	0.0379284	+	0.0656938i
$316$	−1.27616	+	2.21037i	−0.0717894	+	0.124343i
$317$	−7.38961			−0.415042			−0.207521	−	0.978231i	$-0.566540\pi$
$317$	−7.38961			−0.415042			−0.207521	+	0.978231i	$0.566540\pi$
$318$	0.502293	−	0.869998i	0.0281672	−	0.0487870i
$319$	−14.3049	+	24.7769i	−0.800923	+	1.38724i
$320$	−1.00000			−0.0559017
$321$	−2.28493	+	3.95762i	−0.127532	+	0.220893i
$322$	−1.97758	−	3.42527i	−0.110206	−	0.190883i
$323$	6.94242	+	12.0246i	0.386286	+	0.669068i
$324$	−9.89822			−0.549901
$325$		0			0
$326$	−5.21497			−0.288831
$327$	−14.2820	−	24.7371i	−0.789794	−	1.36796i
$328$	−2.59030	−	4.48652i	−0.143025	−	0.247727i
$329$	3.21649	−	5.57112i	0.177331	−	0.307146i
$330$	−8.94462			−0.492385
$331$	−9.74846	+	16.8848i	−0.535824	+	0.928074i	0.463299	+	0.886202i	$0.346666\pi$
$331$	−9.74846	+	16.8848i	−0.535824	+	0.928074i	−0.999123	+	0.0418724i	$0.986668\pi$
$332$	−8.21037	+	14.2208i	−0.450602	+	0.780466i
$333$	1.11319			0.0610025
$334$	3.35224	−	5.80624i	0.183426	−	0.317704i
$335$	1.81042	+	3.13575i	0.0989141	+	0.171324i
$336$	3.64547	+	6.31414i	0.198877	+	0.344465i
$337$	−27.8865			−1.51908			−0.759538	−	0.650463i	$-0.774575\pi$
$337$	−27.8865			−1.51908			−0.759538	+	0.650463i	$0.774575\pi$
$338$		0			0
$339$	−31.2714			−1.69843
$340$	3.31414	+	5.74026i	0.179734	+	0.311309i
$341$	26.4833	+	45.8705i	1.43415	+	2.48403i
$342$	−0.353326	+	0.611979i	−0.0191057	+	0.0330920i
$343$	7.69549			0.415517
$344$	0.567874	−	0.983586i	0.0306177	−	0.0530314i
$345$	0.905212	−	1.56787i	0.0487350	−	0.0844115i
$346$	−19.5409			−1.05053
$347$	−10.0940	+	17.4833i	−0.541875	+	0.938555i	0.456922	+	0.889507i	$0.348952\pi$
$347$	−10.0940	+	17.4833i	−0.541875	+	0.938555i	−0.998796	+	0.0490478i	$0.984381\pi$
$348$	5.33734	+	9.24454i	0.286111	+	0.495559i
$349$	−17.8335	−	30.8885i	−0.954605	−	1.65342i	−0.735270	−	0.677774i	$-0.762945\pi$
$349$	−17.8335	−	30.8885i	−0.954605	−	1.65342i	−0.219335	−	0.975650i	$-0.570389\pi$
$350$	−3.99102			−0.213329
$351$		0			0
$352$	−4.89623			−0.260970
$353$	12.7886	+	22.1506i	0.680671	+	1.17896i	0.974776	+	0.223184i	$0.0716450\pi$
$353$	12.7886	+	22.1506i	0.680671	+	1.17896i	−0.294105	+	0.955773i	$0.595022\pi$
$354$	3.16418	+	5.48052i	0.168174	+	0.291286i
$355$	3.00000	−	5.19615i	0.159223	−	0.275783i
$356$	−3.44854			−0.182772
$357$	24.1632	−	41.8519i	1.27885	−	2.21504i
$358$	4.48950	−	7.77604i	0.237277	−	0.410977i
$359$	24.2487			1.27980			0.639899	−	0.768459i	$-0.278976\pi$
$359$	24.2487			1.27980			0.639899	+	0.768459i	$0.278976\pi$
$360$	−0.168669	+	0.292144i	−0.00888965	+	0.0153973i
$361$	7.30593	+	12.6542i	0.384523	+	0.666013i
$362$	2.77824	+	4.81205i	0.146021	+	0.252916i
$363$	−23.6997			−1.24391
$364$		0			0
$365$	8.94462			0.468183
$366$	1.25296	+	2.17018i	0.0654931	+	0.113437i
$367$	−1.47966	−	2.56285i	−0.0772378	−	0.133780i	0.824819	−	0.565396i	$-0.191277\pi$
$367$	−1.47966	−	2.56285i	−0.0772378	−	0.133780i	−0.902057	+	0.431616i	$0.857943\pi$
$368$	0.495508	−	0.858244i	0.0258301	−	0.0447391i
$369$	−1.74761			−0.0909771
$370$	−1.64996	+	2.85782i	−0.0857775	+	0.148571i
$371$	1.09734	−	1.90065i	0.0569710	−	0.0986766i
$372$	19.7625			1.02464
$373$	2.91179	−	5.04337i	0.150767	−	0.261136i	−0.780743	−	0.624853i	$-0.785159\pi$
$373$	2.91179	−	5.04337i	0.150767	−	0.261136i	0.931510	+	0.363717i	$0.118492\pi$
$374$	16.2268	+	28.1056i	0.839067	+	1.45331i
$375$	−0.913419	−	1.58209i	−0.0471688	−	0.0816987i
$376$	1.61186			0.0831256
$377$		0			0
$378$	−19.4133			−0.998513
$379$	0.290514	+	0.503185i	0.0149227	+	0.0258469i	0.873390	−	0.487021i	$-0.161916\pi$
$379$	0.290514	+	0.503185i	0.0149227	+	0.0258469i	−0.858468	+	0.512868i	$0.828583\pi$
$380$	−1.04739	−	1.81414i	−0.0537302	−	0.0930634i
$381$	7.42094	−	12.8534i	0.380186	−	0.658502i
$382$	−10.1863			−0.521177
$383$	−7.65070	+	13.2514i	−0.390933	+	0.677115i	−0.992573	−	0.121652i	$-0.961181\pi$
$383$	−7.65070	+	13.2514i	−0.390933	+	0.677115i	0.601640	+	0.798767i	$0.294514\pi$
$384$	−0.913419	+	1.58209i	−0.0466127	+	0.0807356i
$385$	−19.5409			−0.995897
$386$	−4.06939	+	7.04839i	−0.207126	+	0.358754i
$387$	−0.191566	−	0.331802i	−0.00973783	−	0.0168664i
$388$	−5.82606	−	10.0910i	−0.295773	−	0.512295i
$389$	19.7281			1.00025			0.500127	−	0.865952i	$-0.333287\pi$
$389$	19.7281			1.00025			0.500127	+	0.865952i	$0.333287\pi$
$390$		0			0
$391$	−6.56873			−0.332195
$392$	4.46410	+	7.73205i	0.225471	+	0.390528i
$393$	12.9498	+	22.4298i	0.653233	+	1.13143i
$394$	7.24026	−	12.5405i	0.364759	−	0.631781i
$395$	−2.55231			−0.128421
$396$	−0.825843	+	1.43040i	−0.0415002	+	0.0718804i
$397$	0.413419	−	0.716063i	0.0207489	−	0.0359382i	−0.855465	−	0.517861i	$-0.826728\pi$
$397$	0.413419	−	0.716063i	0.0207489	−	0.0359382i	0.876213	+	0.481923i	$0.160062\pi$
$398$	11.2566			0.564240
$399$	−7.63649	+	13.2268i	−0.382302	+	0.662167i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	15.8002	+	27.3668i	0.789026	+	1.36663i	0.926564	+	0.376137i	$0.122748\pi$
$401$	15.8002	+	27.3668i	0.789026	+	1.36663i	−0.137538	+	0.990496i	$0.543919\pi$
$402$	6.61471			0.329912
$403$		0			0
$404$	2.07923			0.103445
$405$	−4.94911	−	8.57211i	−0.245923	−	0.425951i
$406$	11.6603	+	20.1962i	0.578689	+	1.00232i
$407$	−8.07859	+	13.9925i	−0.400441	+	0.693584i
$408$	12.1088			0.599475
$409$	10.9668	−	18.9951i	0.542274	−	0.939247i	−0.456499	−	0.889724i	$-0.650897\pi$
$409$	10.9668	−	18.9951i	0.542274	−	0.939247i	0.998773	−	0.0495227i	$-0.0157700\pi$
$410$	2.59030	−	4.48652i	0.127926	−	0.221574i
$411$	−25.6057			−1.26304
$412$	−1.13397	+	1.96410i	−0.0558669	+	0.0967643i
$413$	6.91264	+	11.9730i	0.340149	+	0.589155i
$414$	−0.167154	−	0.289519i	−0.00821516	−	0.0142291i
$415$	−16.4207			−0.806062
$416$		0			0
$417$	−29.2102			−1.43043
$418$	−5.12828	−	8.88244i	−0.250832	−	0.434454i
$419$	15.2814	+	26.4681i	0.746545	+	1.29305i	0.949470	+	0.313859i	$0.101622\pi$
$419$	15.2814	+	26.4681i	0.746545	+	1.29305i	−0.202925	+	0.979194i	$0.565045\pi$
$420$	−3.64547	+	6.31414i	−0.177881	+	0.308098i
$421$	−21.4565			−1.04573			−0.522863	−	0.852417i	$-0.675136\pi$
$421$	−21.4565			−1.04573			−0.522863	+	0.852417i	$0.675136\pi$
$422$	4.79257	−	8.30097i	0.233299	−	0.404085i
$423$	0.271872	−	0.470896i	0.0132189	−	0.0228958i
$424$	0.549905			0.0267057
$425$	−3.31414	+	5.74026i	−0.160759	+	0.278443i
$426$	−5.48052	−	9.49253i	−0.265532	−	0.459915i
$427$	2.73728	+	4.74111i	0.132466	+	0.229438i
$428$	−2.50152			−0.120915
$429$		0			0
$430$	1.13575			0.0547706
$431$	4.58209	+	7.93641i	0.220711	+	0.382283i	0.955024	−	0.296528i	$-0.0958288\pi$
$431$	4.58209	+	7.93641i	0.220711	+	0.382283i	−0.734313	+	0.678811i	$0.762495\pi$
$432$	−2.43213	−	4.21257i	−0.117016	−	0.202677i
$433$	−5.04839	+	8.74407i	−0.242610	+	0.420213i	−0.961457	−	0.274955i	$-0.911337\pi$
$433$	−5.04839	+	8.74407i	−0.242610	+	0.420213i	0.718847	+	0.695168i	$0.244670\pi$
$434$	43.1742			2.07243
$435$	−5.33734	+	9.24454i	−0.255906	+	0.443242i
$436$	7.81785	−	13.5409i	0.374407	−	0.648492i
$437$	2.07597			0.0993069
$438$	8.17018	−	14.1512i	0.390387	−	0.676169i
$439$	−13.2648	−	22.9752i	−0.633093	−	1.09655i	−0.986916	−	0.161236i	$-0.948452\pi$
$439$	−13.2648	−	22.9752i	−0.633093	−	1.09655i	0.353823	−	0.935312i	$-0.384881\pi$
$440$	−2.44811	−	4.24026i	−0.116709	−	0.202146i
$441$	3.01183			0.143420
$442$		0			0
$443$	12.9851			0.616939			0.308469	−	0.951234i	$-0.400183\pi$
$443$	12.9851			0.616939			0.308469	+	0.951234i	$0.400183\pi$
$444$	3.01421	+	5.22077i	0.143048	+	0.247767i
$445$	−1.72427	−	2.98652i	−0.0817382	−	0.141575i
$446$	−13.6058	+	23.5660i	−0.644254	+	1.11588i
$447$	13.6957			0.647783
$448$	−1.99551	+	3.45632i	−0.0942789	+	0.163296i
$449$	15.8935	−	27.5283i	0.750059	−	1.29914i	−0.197734	−	0.980256i	$-0.563358\pi$
$449$	15.8935	−	27.5283i	0.750059	−	1.29914i	0.947793	−	0.318885i	$-0.103308\pi$
$450$	−0.337339			−0.0159023
$451$	12.6827	−	21.9670i	0.597204	−	1.03439i
$452$	−8.55889	−	14.8244i	−0.402576	−	0.697283i
$453$	−3.88124	−	6.72250i	−0.182356	−	0.315850i
$454$	6.32835			0.297004
$455$		0			0
$456$	−3.82684			−0.179208
$457$	3.70828	+	6.42293i	0.173466	+	0.300452i	0.939629	−	0.342194i	$-0.111170\pi$
$457$	3.70828	+	6.42293i	0.173466	+	0.300452i	−0.766163	+	0.642646i	$0.777837\pi$
$458$	−1.25076	−	2.16638i	−0.0584441	−	0.101228i
$459$	−16.1208	+	27.9221i	−0.752455	+	1.30329i
$460$	0.991015			0.0462063
$461$	−20.0296	+	34.6924i	−0.932873	+	1.61578i	−0.154491	+	0.987994i	$0.549374\pi$
$461$	−20.0296	+	34.6924i	−0.932873	+	1.61578i	−0.778383	+	0.627790i	$0.783960\pi$
$462$	−17.8491	+	30.9155i	−0.830413	+	1.43832i
$463$	22.6119			1.05086			0.525431	−	0.850836i	$-0.323904\pi$
$463$	22.6119			1.05086			0.525431	+	0.850836i	$0.323904\pi$
$464$	−2.92163	+	5.06040i	−0.135633	+	0.234923i
$465$	9.88124	+	17.1148i	0.458231	+	0.793680i
$466$	−4.58952	−	7.94928i	−0.212605	−	0.368243i
$467$	7.72244			0.357352			0.178676	−	0.983908i	$-0.442819\pi$
$467$	7.72244			0.357352			0.178676	+	0.983908i	$0.442819\pi$
$468$		0			0
$469$	14.4509			0.667279
$470$	0.805932	+	1.39592i	0.0371749	+	0.0643888i
$471$	−20.7827	−	35.9967i	−0.957616	−	1.65864i
$472$	−1.73205	+	3.00000i	−0.0797241	+	0.138086i
$473$	5.56088			0.255690
$474$	−2.33133	+	4.03798i	−0.107082	+	0.185471i
$475$	1.04739	−	1.81414i	0.0480577	−	0.0832384i
$476$	26.4536			1.21250
$477$	0.0927520	−	0.160651i	0.00424682	−	0.00735571i
$478$	3.27015	+	5.66406i	0.149573	+	0.259068i
$479$	2.49473	+	4.32100i	0.113987	+	0.197431i	0.917374	−	0.398025i	$-0.130304\pi$
$479$	2.49473	+	4.32100i	0.113987	+	0.197431i	−0.803387	+	0.595457i	$0.796971\pi$
$480$	−1.82684			−0.0833834
$481$		0			0
$482$	−9.08254			−0.413699
$483$	−3.61272	−	6.25741i	−0.164384	−	0.284722i
$484$	−6.48652	−	11.2350i	−0.294842	−	0.510681i
$485$	5.82606	−	10.0910i	0.264548	−	0.458210i
$486$	−3.48969			−0.158295
$487$	12.9177	−	22.3741i	0.585357	−	1.01387i	−0.409474	−	0.912322i	$-0.634288\pi$
$487$	12.9177	−	22.3741i	0.585357	−	1.01387i	0.994831	−	0.101546i	$-0.0323790\pi$
$488$	−0.685861	+	1.18795i	−0.0310475	+	0.0537758i
$489$	−9.52691			−0.430822
$490$	−4.46410	+	7.73205i	−0.201668	+	0.349298i
$491$	−8.75076	−	15.1568i	−0.394916	−	0.684015i	0.598174	−	0.801366i	$-0.295893\pi$
$491$	−8.75076	−	15.1568i	−0.394916	−	0.684015i	−0.993090	+	0.117351i	$0.962560\pi$
$492$	−4.73205	−	8.19615i	−0.213337	−	0.369511i
$493$	38.7307			1.74434
$494$		0			0
$495$	−1.65169			−0.0742378
$496$	5.40893	+	9.36854i	0.242868	+	0.420660i
$497$	−11.9730	−	20.7379i	−0.537065	−	0.930223i
$498$	−14.9990	+	25.9791i	−0.672122	+	1.16415i
$499$	−19.0519			−0.852878			−0.426439	−	0.904516i	$-0.640232\pi$
$499$	−19.0519			−0.852878			−0.426439	+	0.904516i	$0.640232\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$	6.12399	−	10.6071i	0.273600	−	0.473889i
$502$	9.62828			0.429731
$503$	1.96384	−	3.40148i	0.0875635	−	0.151664i	−0.818917	−	0.573912i	$-0.805425\pi$
$503$	1.96384	−	3.40148i	0.0875635	−	0.151664i	0.906481	+	0.422247i	$0.138759\pi$
$504$	0.673162	+	1.16595i	0.0299850	+	0.0519355i
$505$	1.03961	+	1.80066i	0.0462622	+	0.0801284i
$506$	4.85224			0.215708
$507$		0			0
$508$	8.12436			0.360460
$509$	21.3170	+	36.9221i	0.944858	+	1.63654i	0.756036	+	0.654530i	$0.227134\pi$
$509$	21.3170	+	36.9221i	0.944858	+	1.63654i	0.188822	+	0.982011i	$0.439533\pi$
$510$	6.05440	+	10.4865i	0.268093	+	0.464351i
$511$	17.8491	−	30.9155i	0.789596	−	1.36762i
$512$	−1.00000			−0.0441942
$513$	5.09479	−	8.82443i	0.224940	−	0.389608i
$514$	−7.41113	+	12.8364i	−0.326891	+	0.566191i
$515$	−2.26795			−0.0999378
$516$	1.03741	−	1.79685i	0.0456696	−	0.0791021i
$517$	3.94603	+	6.83472i	0.173546	+	0.300591i
$518$	6.58502	+	11.4056i	0.289329	+	0.501133i
$519$	−35.6981			−1.56697
$520$		0			0
$521$	32.4921			1.42351			0.711753	−	0.702430i	$-0.247902\pi$
$521$	32.4921			1.42351			0.711753	+	0.702430i	$0.247902\pi$
$522$	0.985577	+	1.70707i	0.0431375	+	0.0747164i
$523$	−5.31194	−	9.20055i	−0.232275	−	0.402312i	0.726202	−	0.687481i	$-0.241284\pi$
$523$	−5.31194	−	9.20055i	−0.232275	−	0.402312i	−0.958477	+	0.285169i	$0.907950\pi$
$524$	−7.08867	+	12.2779i	−0.309670	+	0.536364i
$525$	−7.29094			−0.318203
$526$	5.51673	−	9.55525i	0.240541	−	0.416629i
$527$	35.8519	−	62.0973i	1.56173	−	2.70500i
$528$	−8.94462			−0.389264
$529$	11.0089	−	19.0681i	0.478650	−	0.829046i
$530$	0.274952	+	0.476231i	0.0119432	+	0.0206862i
$531$	0.584287	+	1.01202i	0.0253559	+	0.0439177i
$532$	−8.36033			−0.362466
$533$		0			0
$534$	−6.29992			−0.272624
$535$	−1.25076	−	2.16638i	−0.0540750	−	0.0936606i
$536$	1.81042	+	3.13575i	0.0781984	+	0.135444i
$537$	8.20159	−	14.2056i	0.353925	−	0.613016i
$538$	2.61031			0.112538
$539$	−21.8573	+	37.8579i	−0.941459	+	1.63065i
$540$	2.43213	−	4.21257i	0.104662	−	0.181280i
$541$	36.2860			1.56006			0.780029	−	0.625743i	$-0.215204\pi$
$541$	36.2860			1.56006			0.780029	+	0.625743i	$0.215204\pi$
$542$	−14.3448	+	24.8459i	−0.616161	+	1.06722i
$543$	5.07540	+	8.79085i	0.217806	+	0.377251i
$544$	3.31414	+	5.74026i	0.142093	+	0.246112i
$545$	15.6357			0.669760
$546$		0			0
$547$	−21.3774			−0.914030			−0.457015	−	0.889459i	$-0.651081\pi$
$547$	−21.3774			−0.914030			−0.457015	+	0.889459i	$0.651081\pi$
$548$	−7.00821	−	12.1386i	−0.299376	−	0.518534i
$549$	0.231367	+	0.400740i	0.00987451	+	0.0171032i
$550$	2.44811	−	4.24026i	0.104388	−	0.180805i
$551$	−12.2404			−0.521457
$552$	0.905212	−	1.56787i	0.0385284	−	0.0667331i
$553$	−5.09316	+	8.82161i	−0.216583	+	0.375133i
$554$	−4.70070			−0.199714
$555$	−3.01421	+	5.22077i	−0.127946	+	0.221609i
$556$	−7.99473	−	13.8473i	−0.339052	−	0.587255i
$557$	14.4684	+	25.0600i	0.613045	+	1.06183i	0.990724	+	0.135889i	$0.0433890\pi$
$557$	14.4684	+	25.0600i	0.613045	+	1.06183i	−0.377679	+	0.925937i	$0.623278\pi$
$558$	3.64928			0.154486
$559$		0			0
$560$	−3.99102			−0.168651
$561$	29.6437	+	51.3444i	1.25156	+	2.16776i
$562$	−1.66209	−	2.87883i	−0.0701111	−	0.121436i
$563$	9.18717	−	15.9126i	0.387193	−	0.670638i	−0.604878	−	0.796318i	$-0.706778\pi$
$563$	9.18717	−	15.9126i	0.387193	−	0.670638i	0.992071	+	0.125680i	$0.0401114\pi$
$564$	2.94462			0.123991
$565$	8.55889	−	14.8244i	0.360075	−	0.623668i
$566$	12.9886	−	22.4969i	0.545952	−	0.945616i
$567$	−39.5039			−1.65901
$568$	3.00000	−	5.19615i	0.125877	−	0.218026i
$569$	1.40280	+	2.42973i	0.0588086	+	0.101860i	0.893931	−	0.448205i	$-0.147936\pi$
$569$	1.40280	+	2.42973i	0.0588086	+	0.101860i	−0.835122	+	0.550064i	$0.814603\pi$
$570$	−1.91342	−	3.31414i	−0.0801443	−	0.138814i
$571$	0.119334			0.00499398			0.00249699	−	0.999997i	$-0.499205\pi$
$571$	0.119334			0.00499398			0.00249699	+	0.999997i	$0.499205\pi$
$572$		0			0
$573$	−18.6088			−0.777392
$574$	−10.3379	−	17.9058i	−0.431496	−	0.747373i
$575$	0.495508	+	0.858244i	0.0206641	+	0.0357913i
$576$	−0.168669	+	0.292144i	−0.00702789	+	0.0121727i
$577$	27.6701			1.15192			0.575960	−	0.817478i	$-0.304628\pi$
$577$	27.6701			1.15192			0.575960	+	0.817478i	$0.304628\pi$
$578$	13.4670	−	23.3256i	0.560155	−	0.970217i
$579$	−7.43412	+	12.8763i	−0.308951	+	0.535119i
$580$	−5.84325			−0.242628
$581$	−32.7677	+	56.7553i	−1.35943	+	2.35461i
$582$	−10.6433	−	18.4347i	−0.441178	−	0.764142i
$583$	1.34623	+	2.33174i	0.0557551	+	0.0965707i
$584$	8.94462			0.370131
$585$		0			0
$586$	−0.952463			−0.0393459
$587$	−8.96018	−	15.5195i	−0.369826	−	0.640558i	0.619712	−	0.784829i	$-0.287249\pi$
$587$	−8.96018	−	15.5195i	−0.369826	−	0.640558i	−0.989538	+	0.144272i	$0.953916\pi$
$588$	8.15519	+	14.1252i	0.336314	+	0.582514i
$589$	−11.3306	+	19.6251i	−0.466867	+	0.808638i
$590$	−3.46410			−0.142615
$591$	13.2268	−	22.9095i	0.544077	−	0.942369i
$592$	−1.64996	+	2.85782i	−0.0678130	+	0.117456i
$593$	−22.0640			−0.906058			−0.453029	−	0.891496i	$-0.649657\pi$
$593$	−22.0640			−0.906058			−0.453029	+	0.891496i	$0.649657\pi$
$594$	11.9082	−	20.6257i	0.488601	−	0.846282i
$595$	13.2268	+	22.9095i	0.542245	+	0.939196i
$596$	3.74846	+	6.49253i	0.153543	+	0.265944i
$597$	20.5639			0.841625
$598$		0			0
$599$	47.3354			1.93407			0.967035	−	0.254642i	$-0.0819577\pi$
$599$	47.3354			1.93407			0.967035	+	0.254642i	$0.0819577\pi$
$600$	−0.913419	−	1.58209i	−0.0372902	−	0.0645885i
$601$	13.4610	+	23.3152i	0.549087	+	0.951046i	0.998337	+	0.0576406i	$0.0183577\pi$
$601$	13.4610	+	23.3152i	0.549087	+	0.951046i	−0.449251	+	0.893406i	$0.648309\pi$
$602$	2.26639	−	3.92551i	0.0923713	−	0.159992i
$603$	1.22145			0.0497414
$604$	2.12456	−	3.67985i	0.0864473	−	0.149731i
$605$	6.48652	−	11.2350i	0.263715	−	0.456767i
$606$	3.79841			0.154300
$607$	−9.85548	+	17.0702i	−0.400022	+	0.692858i	−0.993728	−	0.111824i	$-0.964331\pi$
$607$	−9.85548	+	17.0702i	−0.400022	+	0.692858i	0.593706	+	0.804682i	$0.297664\pi$
$608$	−1.04739	−	1.81414i	−0.0424774	−	0.0735731i
$609$	21.3014	+	36.8951i	0.863176	+	1.49507i
$610$	−1.37172			−0.0555394
$611$		0			0
$612$	2.23597			0.0903839
$613$	−7.32308	−	12.6840i	−0.295777	−	0.512300i	0.679389	−	0.733779i	$-0.262245\pi$
$613$	−7.32308	−	12.6840i	−0.295777	−	0.512300i	−0.975165	+	0.221479i	$0.928912\pi$
$614$	16.2909	+	28.2167i	0.657449	+	1.13873i
$615$	4.73205	−	8.19615i	0.190815	−	0.330501i
$616$	−19.5409			−0.787326
$617$	−2.36033	+	4.08821i	−0.0950233	+	0.164585i	−0.909618	−	0.415445i	$-0.863626\pi$
$617$	−2.36033	+	4.08821i	−0.0950233	+	0.164585i	0.814595	+	0.580030i	$0.196959\pi$
$618$	−2.07159	+	3.58810i	−0.0833315	+	0.144334i
$619$	25.6874			1.03246			0.516231	−	0.856449i	$-0.327335\pi$
$619$	25.6874			1.03246			0.516231	+	0.856449i	$0.327335\pi$
$620$	−5.40893	+	9.36854i	−0.217228	+	0.376249i
$621$	2.41027	+	4.17472i	0.0967210	+	0.167526i
$622$	−9.14155	−	15.8336i	−0.366543	−	0.634870i
$623$	−13.7632			−0.551410
$624$		0			0
$625$	1.00000			0.0400000
$626$	−8.04839	−	13.9402i	−0.321678	−	0.557163i
$627$	−9.36854	−	16.2268i	−0.374143	−	0.648035i
$628$	11.3763	−	19.7044i	0.453964	−	0.786290i
$629$	21.8728			0.872126
$630$	−0.673162	+	1.16595i	−0.0268194	+	0.0464526i
$631$	−14.0678	+	24.3662i	−0.560032	+	0.970003i	0.437461	+	0.899237i	$0.355878\pi$
$631$	−14.0678	+	24.3662i	−0.560032	+	0.970003i	−0.997493	+	0.0707660i	$0.977456\pi$
$632$	−2.55231			−0.101526
$633$	8.75525	−	15.1645i	0.347990	−	0.602736i
$634$	−3.69481	−	6.39959i	−0.146739	−	0.254160i
$635$	4.06218	+	7.03590i	0.161203	+	0.279211i
$636$	1.00459			0.0398345
$637$		0			0
$638$	−28.6099			−1.13268
$639$	−1.01202	−	1.75286i	−0.0400347	−	0.0693422i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−6.86874	+	11.8970i	−0.271299	+	0.469904i	−0.969195	−	0.246296i	$-0.920787\pi$
$641$	−6.86874	+	11.8970i	−0.271299	+	0.469904i	0.697896	+	0.716199i	$0.254120\pi$
$642$	−4.56986			−0.180358
$643$	5.82308	−	10.0859i	0.229640	−	0.397748i	−0.728061	−	0.685512i	$-0.759578\pi$
$643$	5.82308	−	10.0859i	0.229640	−	0.397748i	0.957701	+	0.287764i	$0.0929118\pi$
$644$	1.97758	−	3.42527i	0.0779275	−	0.134974i
$645$	2.07483			0.0816963
$646$	−6.94242	+	12.0246i	−0.273146	+	0.473102i
$647$	−17.2324	−	29.8473i	−0.677474	−	1.17342i	−0.975739	−	0.218936i	$-0.929741\pi$
$647$	−17.2324	−	29.8473i	−0.677474	−	1.17342i	0.298265	−	0.954483i	$-0.403592\pi$
$648$	−4.94911	−	8.57211i	−0.194419	−	0.336744i
$649$	−16.9610			−0.665779
$650$		0			0
$651$	78.8723			3.09125
$652$	−2.60749	−	4.51630i	−0.102117	−	0.176872i
$653$	2.43255	+	4.21330i	0.0951931	+	0.164879i	0.909689	−	0.415290i	$-0.136320\pi$
$653$	2.43255	+	4.21330i	0.0951931	+	0.164879i	−0.814496	+	0.580169i	$0.802986\pi$
$654$	14.2820	−	24.7371i	0.558469	−	0.967296i
$655$	−14.1773			−0.553954
$656$	2.59030	−	4.48652i	0.101134	−	0.175169i
$657$	1.50868	−	2.61311i	0.0588593	−	0.101947i
$658$	6.43298			0.250784
$659$	8.82145	−	15.2792i	0.343635	−	0.595193i	−0.641470	−	0.767148i	$-0.721675\pi$
$659$	8.82145	−	15.2792i	0.343635	−	0.595193i	0.985105	+	0.171955i	$0.0550083\pi$
$660$	−4.47231	−	7.74627i	−0.174084	−	0.301523i
$661$	1.82762	+	3.16552i	0.0710860	+	0.123125i	0.899378	−	0.437173i	$-0.144020\pi$
$661$	1.82762	+	3.16552i	0.0710860	+	0.123125i	−0.828292	+	0.560297i	$0.810687\pi$
$662$	−19.4969			−0.757770
$663$		0			0
$664$	−16.4207			−0.637248
$665$	−4.18016	−	7.24026i	−0.162100	−	0.280765i
$666$	0.556596	+	0.964052i	0.0215677	+	0.0373563i
$667$	2.89538	−	5.01494i	0.112109	−	0.194179i
$668$	6.70447			0.259404
$669$	−24.8556	+	43.0512i	−0.960974	+	1.66446i
$670$	−1.81042	+	3.13575i	−0.0699428	+	0.121145i
$671$	−6.71626			−0.259278
$672$	−3.64547	+	6.31414i	−0.140627	+	0.243573i
$673$	−15.4685	−	26.7922i	−0.596267	−	1.03276i	−0.993367	−	0.114989i	$-0.963317\pi$
$673$	−15.4685	−	26.7922i	−0.596267	−	1.03276i	0.397100	−	0.917775i	$-0.370017\pi$
$674$	−13.9433	−	24.1505i	−0.537075	−	0.930241i
$675$	4.86425			0.187225
$676$		0			0
$677$	−25.6685			−0.986522			−0.493261	−	0.869881i	$-0.664195\pi$
$677$	−25.6685			−0.986522			−0.493261	+	0.869881i	$0.664195\pi$
$678$	−15.6357	−	27.0818i	−0.600486	−	1.04007i
$679$	−23.2519	−	40.2735i	−0.892326	−	1.54555i
$680$	−3.31414	+	5.74026i	−0.127091	+	0.220129i
$681$	11.5609			0.443014
$682$	−26.4833	+	45.8705i	−1.01410	+	1.75647i
$683$	15.2290	−	26.3774i	0.582721	−	1.00930i	−0.412435	−	0.910987i	$-0.635321\pi$
$683$	15.2290	−	26.3774i	0.582721	−	1.00930i	0.995155	−	0.0983147i	$-0.0313452\pi$
$684$	−0.706653			−0.0270195
$685$	7.00821	−	12.1386i	0.267770	−	0.463791i
$686$	3.84774	+	6.66449i	0.146908	+	0.254451i
$687$	−2.28493	−	3.95762i	−0.0871756	−	0.150993i
$688$	1.13575			0.0433000
$689$		0			0
$690$	1.81042			0.0689217
$691$	3.12662	+	5.41546i	0.118942	+	0.206014i	0.919349	−	0.393444i	$-0.128716\pi$
$691$	3.12662	+	5.41546i	0.118942	+	0.206014i	−0.800407	+	0.599458i	$0.795383\pi$
$692$	−9.77046	−	16.9229i	−0.371417	−	0.643313i
$693$	−3.29595	+	5.70876i	−0.125203	+	0.216858i
$694$	−20.1880			−0.766327
$695$	7.99473	−	13.8473i	0.303257	−	0.525257i
$696$	−5.33734	+	9.24454i	−0.202311	+	0.350413i
$697$	−34.3384			−1.30066
$698$	17.8335	−	30.8885i	0.675008	−	1.16915i
$699$	−8.38431	−	14.5220i	−0.317124	−	0.549274i
$700$	−1.99551	−	3.45632i	−0.0754231	−	0.130637i
$701$	−9.17903			−0.346687			−0.173344	−	0.984861i	$-0.555457\pi$
$701$	−9.17903			−0.346687			−0.173344	+	0.984861i	$0.555457\pi$
$702$		0			0
$703$	−6.91264			−0.260715
$704$	−2.44811	−	4.24026i	−0.0922668	−	0.159811i
$705$	1.47231	+	2.55011i	0.0554503	+	0.0960428i
$706$	−12.7886	+	22.1506i	−0.481307	+	0.833648i
$707$	8.29822			0.312087
$708$	−3.16418	+	5.48052i	−0.118917	+	0.205970i
$709$	−17.3506	+	30.0521i	−0.651614	+	1.12863i	0.331117	+	0.943590i	$0.392575\pi$
$709$	−17.3506	+	30.0521i	−0.651614	+	1.12863i	−0.982731	+	0.185039i	$0.940759\pi$
$710$	6.00000			0.225176
$711$	−0.430497	+	0.745642i	−0.0161449	+	0.0279638i
$712$	−1.72427	−	2.98652i	−0.0646197	−	0.111925i
$713$	−5.36033	−	9.28436i	−0.200746	−	0.347702i
$714$	48.3264			1.80857
$715$		0			0
$716$	8.97900			0.335561
$717$	5.97403	+	10.3473i	0.223104	+	0.386428i
$718$	12.1244	+	21.0000i	0.452477	+	0.783713i
$719$	−9.12761	+	15.8095i	−0.340403	+	0.589595i	−0.984507	−	0.175343i	$-0.943897\pi$
$719$	−9.12761	+	15.8095i	−0.340403	+	0.589595i	0.644105	+	0.764937i	$0.277230\pi$
$720$	−0.337339			−0.0125719
$721$	−4.52571	+	7.83876i	−0.168546	+	0.291931i
$722$	−7.30593	+	12.6542i	−0.271899	+	0.470942i
$723$	−16.5923			−0.617076
$724$	−2.77824	+	4.81205i	−0.103253	+	0.178839i
$725$	−2.92163	−	5.06040i	−0.108506	−	0.187939i
$726$	−11.8498	−	20.5245i	−0.439788	−	0.761736i
$727$	−4.76025			−0.176548			−0.0882740	−	0.996096i	$-0.528135\pi$
$727$	−4.76025			−0.176548			−0.0882740	+	0.996096i	$0.528135\pi$
$728$		0			0
$729$	23.3196			0.863687
$730$	4.47231	+	7.74627i	0.165528	+	0.286702i
$731$	−3.76403	−	6.51948i	−0.139218	−	0.241132i
$732$	−1.25296	+	2.17018i	−0.0463106	+	0.0802123i
$733$	1.44352			0.0533176			0.0266588	−	0.999645i	$-0.491513\pi$
$733$	1.44352			0.0533176			0.0266588	+	0.999645i	$0.491513\pi$
$734$	1.47966	−	2.56285i	0.0546154	−	0.0945966i
$735$	−8.15519	+	14.1252i	−0.300809	+	0.521016i
$736$	0.991015			0.0365293
$737$	−8.86425	+	15.3533i	−0.326519	+	0.565547i
$738$	−0.873806	−	1.51348i	−0.0321653	−	0.0557119i
$739$	−15.5949	−	27.0111i	−0.573667	−	0.993621i	−0.996185	−	0.0872663i	$-0.972187\pi$
$739$	−15.5949	−	27.0111i	−0.573667	−	0.993621i	0.422518	−	0.906355i	$-0.361146\pi$
$740$	−3.29992			−0.121308
$741$		0			0
$742$	2.19468			0.0805691
$743$	12.0430	+	20.8591i	0.441815	+	0.765246i	0.997824	−	0.0659301i	$-0.0210014\pi$
$743$	12.0430	+	20.8591i	0.441815	+	0.765246i	−0.556009	+	0.831176i	$0.687668\pi$
$744$	9.88124	+	17.1148i	0.362264	+	0.627459i
$745$	−3.74846	+	6.49253i	−0.137333	+	0.237868i
$746$	5.82358			0.213216
$747$	−2.76967	+	4.79721i	−0.101337	+	0.175521i
$748$	−16.2268	+	28.1056i	−0.593310	+	1.02764i
$749$	−9.98359			−0.364792
$750$	0.913419	−	1.58209i	0.0333534	−	0.0577697i
$751$	0.944617	+	1.63612i	0.0344696	+	0.0597030i	0.882746	−	0.469851i	$-0.155692\pi$
$751$	0.944617	+	1.63612i	0.0344696	+	0.0597030i	−0.848276	+	0.529554i	$0.822359\pi$
$752$	0.805932	+	1.39592i	0.0293893	+	0.0509038i
$753$	17.5893			0.640990
$754$		0			0
$755$	4.24913			0.154642
$756$	−9.70665	−	16.8124i	−0.353028	−	0.611462i
$757$	11.7385	+	20.3317i	0.426642	+	0.738966i	0.996572	−	0.0827270i	$-0.0263629\pi$
$757$	11.7385	+	20.3317i	0.426642	+	0.738966i	−0.569930	+	0.821693i	$0.693030\pi$
$758$	−0.290514	+	0.503185i	−0.0105520	+	0.0182765i
$759$	8.86425			0.321752
$760$	1.04739	−	1.81414i	0.0379930	−	0.0658057i
$761$	11.8218	−	20.4760i	0.428540	−	0.742253i	−0.568204	−	0.822888i	$-0.692361\pi$
$761$	11.8218	−	20.4760i	0.428540	−	0.742253i	0.996744	+	0.0806347i	$0.0256947\pi$
$762$	14.8419			0.537665
$763$	31.2012	−	54.0420i	1.12956	−	1.95645i
$764$	−5.09316	−	8.82161i	−0.184264	−	0.319155i
$765$	1.11799	+	1.93641i	0.0404209	+	0.0700111i
$766$	−15.3014			−0.552862
$767$		0			0
$768$	−1.82684			−0.0659204
$769$	−19.3738	−	33.5563i	−0.698636	−	1.21007i	−0.968940	−	0.247298i	$-0.920457\pi$
$769$	−19.3738	−	33.5563i	−0.698636	−	1.21007i	0.270304	−	0.962775i	$-0.412876\pi$
$770$	−9.77046	−	16.9229i	−0.352103	−	0.609860i
$771$	−13.5389	+	23.4501i	−0.487593	+	0.844535i
$772$	−8.13878			−0.292921
$773$	−3.55660	+	6.16020i	−0.127922	+	0.221567i	−0.922871	−	0.385109i	$-0.874164\pi$
$773$	−3.55660	+	6.16020i	−0.127922	+	0.221567i	0.794949	+	0.606676i	$0.207497\pi$
$774$	0.191566	−	0.331802i	0.00688569	−	0.0119264i
$775$	−10.8179			−0.388589
$776$	5.82606	−	10.0910i	0.209143	−	0.362247i
$777$	12.0298	+	20.8362i	0.431566	+	0.747494i
$778$	9.86404	+	17.0850i	0.353643	+	0.612528i
$779$	10.8522			0.388822
$780$		0			0
$781$	29.3774			1.05120
$782$	−3.28436	−	5.68868i	−0.117449	−	0.203427i
$783$	−14.2115	−	24.6151i	−0.507878	−	0.879671i
$784$	−4.46410	+	7.73205i	−0.159432	+	0.276145i
$785$	22.7526			0.812076
$786$	−12.9498	+	22.4298i	−0.461906	+	0.800044i
$787$	−1.31655	+	2.28033i	−0.0469298	+	0.0812848i	−0.888536	−	0.458807i	$-0.848277\pi$
$787$	−1.31655	+	2.28033i	−0.0469298	+	0.0812848i	0.841606	+	0.540092i	$0.181610\pi$
$788$	14.4805			0.515847
$789$	10.0782	−	17.4559i	0.358792	−	0.621446i
$790$	−1.27616	−	2.21037i	−0.0454036	−	0.0786413i
$791$	−34.1587	−	59.1645i	−1.21454	−	2.10365i
$792$	−1.65169			−0.0586901
$793$		0			0
$794$	0.826838			0.0293434
$795$	0.502293	+	0.869998i	0.0178145	+	0.0308556i
$796$	5.62828	+	9.74846i	0.199489	+	0.345525i
$797$	1.25953	−	2.18158i	0.0446150	−	0.0772754i	−0.842856	−	0.538140i	$-0.819127\pi$
$797$	1.25953	−	2.18158i	0.0446150	−	0.0772754i	0.887471	+	0.460864i	$0.152461\pi$
$798$	−15.2730			−0.540657
$799$	5.34194	−	9.25252i	0.188984	−	0.327331i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−1.16333			−0.0411041
$802$	−15.8002	+	27.3668i	−0.557926	+	0.966356i
$803$	21.8974	+	37.9275i	0.772744	+	1.33843i
$804$	3.30735	+	5.72850i	0.116641	+	0.202029i
$805$	3.95516			0.139401
$806$		0			0
$807$	4.76861			0.167863
$808$	1.03961	+	1.80066i	0.0365735	+	0.0633471i
$809$	−4.35078	−	7.53576i	−0.152965	−	0.264943i	0.779351	−	0.626587i	$-0.215549\pi$
$809$	−4.35078	−	7.53576i	−0.152965	−	0.264943i	−0.932316	+	0.361644i	$0.882216\pi$
$810$	4.94911	−	8.57211i	0.173894	−	0.301193i
$811$	40.3063			1.41535			0.707673	−	0.706540i	$-0.249745\pi$
$811$	40.3063			1.41535			0.707673	+	0.706540i	$0.249745\pi$
$812$	−11.6603	+	20.1962i	−0.409195	+	0.708746i
$813$	−26.2056	+	45.3894i	−0.919070	+	1.59188i
$814$	−16.1572			−0.566309
$815$	2.60749	−	4.51630i	0.0913363	−	0.158199i
$816$	6.05440	+	10.4865i	0.211946	+	0.367102i
$817$	1.18958	+	2.06040i	0.0416180	+	0.0720844i
$818$	21.9336			0.766892
$819$		0			0
$820$	5.18059			0.180914
$821$	−16.9095	−	29.2880i	−0.590144	−	1.02216i	−0.994213	−	0.107431i	$-0.965738\pi$
$821$	−16.9095	−	29.2880i	−0.590144	−	1.02216i	0.404068	−	0.914729i	$-0.367596\pi$
$822$	−12.8029	−	22.1752i	−0.446551	−	0.773449i
$823$	24.1874	−	41.8938i	0.843119	−	1.46033i	−0.0441253	−	0.999026i	$-0.514050\pi$
$823$	24.1874	−	41.8938i	0.843119	−	1.46033i	0.887245	−	0.461299i	$-0.152617\pi$
$824$	−2.26795			−0.0790078
$825$	4.47231	−	7.74627i	0.155706	−	0.269690i
$826$	−6.91264	+	11.9730i	−0.240522	+	0.416596i
$827$	15.1331			0.526228			0.263114	−	0.964765i	$-0.415250\pi$
$827$	15.1331			0.526228			0.263114	+	0.964765i	$0.415250\pi$
$828$	0.167154	−	0.289519i	0.00580900	−	0.0100615i
$829$	4.22458	+	7.31719i	0.146726	+	0.254137i	0.930015	−	0.367520i	$-0.119793\pi$
$829$	4.22458	+	7.31719i	0.146726	+	0.254137i	−0.783290	+	0.621657i	$0.786460\pi$
$830$	−8.21037	−	14.2208i	−0.284986	−	0.493610i
$831$	−8.58742			−0.297894
$832$		0			0
$833$	59.1786			2.05042
$834$	−14.6051	−	25.2967i	−0.505733	−	0.875954i
$835$	3.35224	+	5.80624i	0.116009	+	0.200933i
$836$	5.12828	−	8.88244i	0.177365	−	0.307206i
$837$	−52.6208			−1.81884
$838$	−15.2814	+	26.4681i	−0.527887	+	0.914327i
$839$	9.11014	−	15.7792i	0.314517	−	0.544759i	−0.664818	−	0.747006i	$-0.731491\pi$
$839$	9.11014	−	15.7792i	0.314517	−	0.544759i	0.979335	+	0.202246i	$0.0648241\pi$
$840$	−7.29094			−0.251561
$841$	−2.57180	+	4.45448i	−0.0886826	+	0.153603i
$842$	−10.7282	−	18.5819i	−0.369720	−	0.640373i
$843$	−3.03637	−	5.25915i	−0.104578	−	0.181135i
$844$	9.58514			0.329934
$845$		0			0
$846$	0.543744			0.0186943
$847$	−25.8878	−	44.8390i	−0.889516	−	1.54069i
$848$	0.274952	+	0.476231i	0.00944190	+	0.0163538i
$849$	23.7281	−	41.0983i	0.814346	−	1.41049i
$850$	−6.62828			−0.227348
$851$	1.63514	−	2.83214i	0.0560518	−	0.0970846i
$852$	5.48052	−	9.49253i	0.187759	−	0.325209i
$853$	−37.4425			−1.28201			−0.641003	−	0.767539i	$-0.721481\pi$
$853$	−37.4425			−1.28201			−0.641003	+	0.767539i	$0.721481\pi$
$854$	−2.73728	+	4.74111i	−0.0936678	+	0.162237i
$855$	−0.353326	−	0.611979i	−0.0120835	−	0.0209292i
$856$	−1.25076	−	2.16638i	−0.0427500	−	0.0740452i
$857$	28.6086			0.977251			0.488626	−	0.872494i	$-0.337498\pi$
$857$	28.6086			0.977251			0.488626	+	0.872494i	$0.337498\pi$
$858$		0			0
$859$	−22.4266			−0.765186			−0.382593	−	0.923917i	$-0.624969\pi$
$859$	−22.4266			−0.765186			−0.382593	+	0.923917i	$0.624969\pi$
$860$	0.567874	+	0.983586i	0.0193643	+	0.0335400i
$861$	−18.8857	−	32.7110i	−0.643622	−	1.11479i
$862$	−4.58209	+	7.93641i	−0.156067	+	0.270315i
$863$	−3.08381			−0.104974			−0.0524871	−	0.998622i	$-0.516715\pi$
$863$	−3.08381			−0.104974			−0.0524871	+	0.998622i	$0.516715\pi$
$864$	2.43213	−	4.21257i	0.0827426	−	0.143314i
$865$	9.77046	−	16.9229i	0.332206	−	0.575397i
$866$	−10.0968			−0.343102
$867$	24.6021	−	42.6121i	0.835531	−	1.44718i
$868$	21.5871	+	37.3900i	0.732714	+	1.26910i
$869$	−6.24835	−	10.8225i	−0.211961	−	0.367127i
$870$	−10.6747			−0.361905
$871$		0			0
$872$	15.6357			0.529492
$873$	−1.96535	−	3.40409i	−0.0665172	−	0.115211i
$874$	1.03798	+	1.79784i	0.0351103	+	0.0608128i
$875$	1.99551	−	3.45632i	0.0674605	−	0.116845i
$876$	16.3404			0.552090
$877$	19.0864	−	33.0587i	0.644503	−	1.11631i	−0.339913	−	0.940457i	$-0.610398\pi$
$877$	19.0864	−	33.0587i	0.644503	−	1.11631i	0.984416	−	0.175855i	$-0.0562689\pi$
$878$	13.2648	−	22.9752i	0.447664	−	0.775377i
$879$	−1.74000			−0.0586886
$880$	2.44811	−	4.24026i	0.0825259	−	0.142939i
$881$	11.9835	+	20.7561i	0.403736	+	0.699291i	0.994173	−	0.107792i	$-0.0343781\pi$
$881$	11.9835	+	20.7561i	0.403736	+	0.699291i	−0.590438	+	0.807083i	$0.701045\pi$
$882$	1.50591	+	2.60832i	0.0507067	+	0.0878267i
$883$	−19.7537			−0.664765			−0.332383	−	0.943145i	$-0.607853\pi$
$883$	−19.7537			−0.664765			−0.332383	+	0.943145i	$0.607853\pi$
$884$		0			0
$885$	−6.32835			−0.212725
$886$	6.49253	+	11.2454i	0.218121	+	0.377796i
$887$	−10.0846	−	17.4670i	−0.338608	−	0.586486i	0.645563	−	0.763707i	$-0.276623\pi$
$887$	−10.0846	−	17.4670i	−0.338608	−	0.586486i	−0.984171	+	0.177221i	$0.943289\pi$
$888$	−3.01421	+	5.22077i	−0.101150	+	0.175198i
$889$	32.4244			1.08748
$890$	1.72427	−	2.98652i	0.0577977	−	0.100108i
$891$	24.2320	−	41.9710i	0.811801	−	1.40608i
$892$	−27.2116			−0.911113
$893$	−1.68826	+	2.92415i	−0.0564954	+	0.0978529i
$894$	6.84784	+	11.8608i	0.229026	+	0.396685i
$895$	4.48950	+	7.77604i	0.150067	+	0.259924i
$896$	−3.99102			−0.133330
$897$		0			0
$898$	31.7869			1.06074
$899$	31.6057	+	54.7427i	1.05411	+	1.82577i
$900$	−0.168669	−	0.292144i	−0.00562231	−	0.00973812i
$901$	1.82246	−	3.15659i	0.0607150	−	0.105161i
$902$	25.3654			0.844574
$903$	4.14033	−	7.17127i	0.137782	−	0.238645i
$904$	8.55889	−	14.8244i	0.284664	−	0.493053i
$905$	−5.55648			−0.184704
$906$	3.88124	−	6.72250i	0.128945	−	0.223340i
$907$	11.9528	+	20.7029i	0.396887	+	0.687428i	0.993340	−	0.115220i	$-0.0367571\pi$
$907$	11.9528	+	20.7029i	0.396887	+	0.687428i	−0.596453	+	0.802648i	$0.703424\pi$
$908$	3.16418	+	5.48052i	0.105007	+	0.181877i
$909$	0.701403			0.0232641
$910$		0			0
$911$	−26.3025			−0.871439			−0.435720	−	0.900082i	$-0.643506\pi$
$911$	−26.3025			−0.871439			−0.435720	+	0.900082i	$0.643506\pi$
$912$	−1.91342	−	3.31414i	−0.0633596	−	0.109742i
$913$	−40.1998	−	69.6281i	−1.33042	−	2.30436i
$914$	−3.70828	+	6.42293i	−0.122659	+	0.212452i
$915$	−2.50591			−0.0828429
$916$	1.25076	−	2.16638i	0.0413262	−	0.0715791i
$917$	−28.2910	+	49.0014i	−0.934250	+	1.61817i
$918$	−32.2416			−1.06413
$919$	−12.8564	+	22.2679i	−0.424094	+	0.734552i	−0.996335	−	0.0855332i	$-0.972741\pi$
$919$	−12.8564	+	22.2679i	−0.424094	+	0.734552i	0.572242	+	0.820085i	$0.306074\pi$
$920$	0.495508	+	0.858244i	0.0163364	+	0.0282955i
$921$	29.7609	+	51.5474i	0.980655	+	1.69855i
$922$	−40.0593			−1.31928
$923$		0			0
$924$	−35.6981			−1.17438
$925$	−1.64996	−	2.85782i	−0.0542504	−	0.0939645i
$926$	11.3059	+	19.5824i	0.371536	+	0.643519i
$927$	−0.382533	+	0.662567i	−0.0125640	+	0.0217616i
$928$	−5.84325			−0.191814
$929$	13.2566	−	22.9610i	0.434934	−	0.753327i	−0.562357	−	0.826895i	$-0.690105\pi$
$929$	13.2566	−	22.9610i	0.434934	−	0.753327i	0.997290	+	0.0735678i	$0.0234385\pi$
$930$	−9.88124	+	17.1148i	−0.324018	+	0.561216i
$931$	−18.7027			−0.612956
$932$	4.58952	−	7.94928i	0.150335	−	0.260387i
$933$	−16.7001	−	28.9255i	−0.546738	−	0.946977i
$934$	3.86122	+	6.68783i	0.126343	+	0.218833i
$935$	−32.4536			−1.06134
$936$		0			0
$937$	24.3940			0.796918			0.398459	−	0.917186i	$-0.369545\pi$
$937$	24.3940			0.796918			0.398459	+	0.917186i	$0.369545\pi$
$938$	7.22543	+	12.5148i	0.235919	+	0.408623i
$939$	−14.7031	−	25.4665i	−0.479818	−	0.831069i
$940$	−0.805932	+	1.39592i	−0.0262866	+	0.0455298i
$941$	3.13575			0.102222			0.0511112	−	0.998693i	$-0.483724\pi$
$941$	3.13575			0.102222			0.0511112	+	0.998693i	$0.483724\pi$
$942$	20.7827	−	35.9967i	0.677137	−	1.17284i
$943$	−2.56702	+	4.44621i	−0.0835937	+	0.144789i
$944$	−3.46410			−0.112747
$945$	9.70665	−	16.8124i	0.315757	−	0.546908i
$946$	2.78044	+	4.81586i	0.0903999	+	0.156577i
$947$	9.39450	+	16.2718i	0.305280	+	0.528761i	0.977324	−	0.211751i	$-0.0679165\pi$
$947$	9.39450	+	16.2718i	0.305280	+	0.528761i	−0.672043	+	0.740512i	$0.734583\pi$
$948$	−4.66266			−0.151436
$949$		0			0
$950$	2.09479			0.0679639
$951$	−6.74981	−	11.6910i	−0.218878	−	0.379107i
$952$	13.2268	+	22.9095i	0.428682	+	0.742500i
$953$	3.80667	−	6.59335i	0.123310	−	0.213579i	−0.797761	−	0.602974i	$-0.793982\pi$
$953$	3.80667	−	6.59335i	0.123310	−	0.213579i	0.921071	+	0.389394i	$0.127316\pi$
$954$	0.185504			0.00600591
$955$	5.09316	−	8.82161i	0.164811	−	0.285461i
$956$	−3.27015	+	5.66406i	−0.105764	+	0.183189i
$957$	−52.2656			−1.68951
$958$	−2.49473	+	4.32100i	−0.0806011	+	0.139605i
$959$	−27.9699	−	48.4452i	−0.903194	−	1.56438i
$960$	−0.913419	−	1.58209i	−0.0294805	−	0.0510617i
$961$	86.0260			2.77503
$962$		0			0
$963$	−0.843858			−0.0271929
$964$	−4.54127	−	7.86571i	−0.146265	−	0.253338i
$965$	−4.06939	−	7.04839i	−0.130998	−	0.226896i
$966$	3.61272	−	6.25741i	0.116237	−	0.201329i
$967$	22.5849			0.726282			0.363141	−	0.931734i	$-0.381704\pi$
$967$	22.5849			0.726282			0.363141	+	0.931734i	$0.381704\pi$
$968$	6.48652	−	11.2350i	0.208485	−	0.361106i
$969$	−12.6827	+	21.9670i	−0.407426	+	0.705683i
$970$	11.6521			0.374127
$971$	16.3491	−	28.3174i	0.524666	−	0.908748i	−0.474921	−	0.880028i	$-0.657524\pi$
$971$	16.3491	−	28.3174i	0.524666	−	0.908748i	0.999587	−	0.0287200i	$-0.00914313\pi$
$972$	−1.74484	−	3.02216i	−0.0559659	−	0.0969358i
$973$	−31.9071	−	55.2647i	−1.02289	−	1.77170i
$974$	25.8354			0.827820
$975$		0			0
$976$	−1.37172			−0.0439077
$977$	−24.4258	−	42.3066i	−0.781449	−	1.35351i	−0.931098	−	0.364770i	$-0.881147\pi$
$977$	−24.4258	−	42.3066i	−0.781449	−	1.35351i	0.149648	−	0.988739i	$-0.452186\pi$
$978$	−4.76346	−	8.25055i	−0.152319	−	0.263823i
$979$	8.44242	−	14.6227i	0.269821	−	0.467343i
$980$	−8.92820			−0.285201
$981$	2.63726	−	4.56787i	0.0842013	−	0.145841i
$982$	8.75076	−	15.1568i	0.279248	−	0.483672i
$983$	−16.3881			−0.522700			−0.261350	−	0.965244i	$-0.584168\pi$
$983$	−16.3881			−0.522700			−0.261350	+	0.965244i	$0.584168\pi$
$984$	4.73205	−	8.19615i	0.150852	−	0.261284i
$985$	7.24026	+	12.5405i	0.230694	+	0.399573i
$986$	19.3654	+	33.5418i	0.616718	+	1.06819i
$987$	11.7520			0.374071
$988$		0			0
$989$	−1.12554			−0.0357902
$990$	−0.825843	−	1.43040i	−0.0262470	−	0.0454612i
$991$	21.8977	+	37.9279i	0.695603	+	1.20482i	0.969977	+	0.243197i	$0.0781962\pi$
$991$	21.8977	+	37.9279i	0.695603	+	1.20482i	−0.274373	+	0.961623i	$0.588470\pi$
$992$	−5.40893	+	9.36854i	−0.171734	+	0.297451i
$993$	−35.6177			−1.13029
$994$	11.9730	−	20.7379i	0.379762	−	0.657767i
$995$	−5.62828	+	9.74846i	−0.178428	+	0.309047i
$996$	−29.9980			−0.950524
$997$	22.5569	−	39.0697i	0.714384	−	1.23735i	−0.248812	−	0.968552i	$-0.580040\pi$
$997$	22.5569	−	39.0697i	0.714384	−	1.23735i	0.963196	−	0.268798i	$-0.0866265\pi$
$998$	−9.52593	−	16.4994i	−0.301538	−	0.522279i
$999$	−8.02583	−	13.9012i	−0.253926	−	0.439813i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1690.2.e.t.991.4		8
13.2	odd	12		1690.2.d.k.1351.5		8
13.3	even	3		1690.2.a.t.1.1		4
13.4	even	6		1690.2.e.s.191.4		8
13.5	odd	4		1690.2.l.j.361.4		8
13.6	odd	12		130.2.l.b.121.2	yes	8
13.7	odd	12		1690.2.l.j.1161.4		8
13.8	odd	4		130.2.l.b.101.2	✓	8
13.9	even	3	inner	1690.2.e.t.191.4		8
13.10	even	6		1690.2.a.u.1.1		4
13.11	odd	12		1690.2.d.k.1351.1		8
13.12	even	2		1690.2.e.s.991.4		8
39.8	even	4		1170.2.bs.g.361.4		8
39.32	even	12		1170.2.bs.g.901.4		8
52.19	even	12		1040.2.da.d.641.1		8
52.47	even	4		1040.2.da.d.881.1		8
65.8	even	4		650.2.n.e.49.2		8
65.19	odd	12		650.2.m.c.251.3		8
65.29	even	6		8450.2.a.cm.1.4		4
65.32	even	12		650.2.n.e.199.2		8
65.34	odd	4		650.2.m.c.101.3		8
65.47	even	4		650.2.n.d.49.3		8
65.49	even	6		8450.2.a.ci.1.4		4
65.58	even	12		650.2.n.d.199.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.l.b.101.2	✓	8	13.8	odd	4
130.2.l.b.121.2	yes	8	13.6	odd	12
650.2.m.c.101.3		8	65.34	odd	4
650.2.m.c.251.3		8	65.19	odd	12
650.2.n.d.49.3		8	65.47	even	4
650.2.n.d.199.3		8	65.58	even	12
650.2.n.e.49.2		8	65.8	even	4
650.2.n.e.199.2		8	65.32	even	12
1040.2.da.d.641.1		8	52.19	even	12
1040.2.da.d.881.1		8	52.47	even	4
1170.2.bs.g.361.4		8	39.8	even	4
1170.2.bs.g.901.4		8	39.32	even	12
1690.2.a.t.1.1		4	13.3	even	3
1690.2.a.u.1.1		4	13.10	even	6
1690.2.d.k.1351.1		8	13.11	odd	12
1690.2.d.k.1351.5		8	13.2	odd	12
1690.2.e.s.191.4		8	13.4	even	6
1690.2.e.s.991.4		8	13.12	even	2
1690.2.e.t.191.4		8	13.9	even	3	inner
1690.2.e.t.991.4		8	1.1	even	1	trivial
1690.2.l.j.361.4		8	13.5	odd	4
1690.2.l.j.1161.4		8	13.7	odd	12
8450.2.a.ci.1.4		4	65.49	even	6
8450.2.a.cm.1.4		4	65.29	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:	\( N \)	\(=\)	\( 1690 = 2 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1690.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.913419 + 1.58209i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-0.913419 + 1.58209i) q^{6} +(-1.99551 + 3.45632i) q^{7} -1.00000 q^{8} +(-0.168669 + 0.292144i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.913419 + 1.58209i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-0.913419 + 1.58209i) q^{6} +(-1.99551 + 3.45632i) q^{7} -1.00000 q^{8} +(-0.168669 + 0.292144i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-2.44811 - 4.24026i) q^{11} -1.82684 q^{12} -3.99102 q^{14} +(-0.913419 - 1.58209i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.31414 + 5.74026i) q^{17} -0.337339 q^{18} +(1.04739 - 1.81414i) q^{19} +(0.500000 - 0.866025i) q^{20} -7.29094 q^{21} +(2.44811 - 4.24026i) q^{22} +(0.495508 + 0.858244i) q^{23} +(-0.913419 - 1.58209i) q^{24} +1.00000 q^{25} +4.86425 q^{27} +(-1.99551 - 3.45632i) q^{28} +(-2.92163 - 5.06040i) q^{29} +(0.913419 - 1.58209i) q^{30} -10.8179 q^{31} +(0.500000 - 0.866025i) q^{32} +(4.47231 - 7.74627i) q^{33} -6.62828 q^{34} +(1.99551 - 3.45632i) q^{35} +(-0.168669 - 0.292144i) q^{36} +(-1.64996 - 2.85782i) q^{37} +2.09479 q^{38} +1.00000 q^{40} +(2.59030 + 4.48652i) q^{41} +(-3.64547 - 6.31414i) q^{42} +(-0.567874 + 0.983586i) q^{43} +4.89623 q^{44} +(0.168669 - 0.292144i) q^{45} +(-0.495508 + 0.858244i) q^{46} -1.61186 q^{47} +(0.913419 - 1.58209i) q^{48} +(-4.46410 - 7.73205i) q^{49} +(0.500000 + 0.866025i) q^{50} -12.1088 q^{51} -0.549905 q^{53} +(2.43213 + 4.21257i) q^{54} +(2.44811 + 4.24026i) q^{55} +(1.99551 - 3.45632i) q^{56} +3.82684 q^{57} +(2.92163 - 5.06040i) q^{58} +(1.73205 - 3.00000i) q^{59} +1.82684 q^{60} +(0.685861 - 1.18795i) q^{61} +(-5.40893 - 9.36854i) q^{62} +(-0.673162 - 1.16595i) q^{63} +1.00000 q^{64} +8.94462 q^{66} +(-1.81042 - 3.13575i) q^{67} +(-3.31414 - 5.74026i) q^{68} +(-0.905212 + 1.56787i) q^{69} +3.99102 q^{70} +(-3.00000 + 5.19615i) q^{71} +(0.168669 - 0.292144i) q^{72} -8.94462 q^{73} +(1.64996 - 2.85782i) q^{74} +(0.913419 + 1.58209i) q^{75} +(1.04739 + 1.81414i) q^{76} +19.5409 q^{77} +2.55231 q^{79} +(0.500000 + 0.866025i) q^{80} +(4.94911 + 8.57211i) q^{81} +(-2.59030 + 4.48652i) q^{82} +16.4207 q^{83} +(3.64547 - 6.31414i) q^{84} +(3.31414 - 5.74026i) q^{85} -1.13575 q^{86} +(5.33734 - 9.24454i) q^{87} +(2.44811 + 4.24026i) q^{88} +(1.72427 + 2.98652i) q^{89} +0.337339 q^{90} -0.991015 q^{92} +(-9.88124 - 17.1148i) q^{93} +(-0.805932 - 1.39592i) q^{94} +(-1.04739 + 1.81414i) q^{95} +1.82684 q^{96} +(-5.82606 + 10.0910i) q^{97} +(4.46410 - 7.73205i) q^{98} +1.65169 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 2 q^{3} - 4 q^{4} - 8 q^{5} + 2 q^{6} - 8 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^2 - 2 * q^3 - 4 * q^4 - 8 * q^5 + 2 * q^6 - 8 * q^8 - 4 * q^9	\( 8 q + 4 q^{2} - 2 q^{3} - 4 q^{4} - 8 q^{5} + 2 q^{6} - 8 q^{8} - 4 q^{9} - 4 q^{10} - 6 q^{11} + 4 q^{12} + 2 q^{15} - 4 q^{16} - 6 q^{17} - 8 q^{18} + 6 q^{19} + 4 q^{20} - 12 q^{21} + 6 q^{22} - 12 q^{23} + 2 q^{24} + 8 q^{25} + 40 q^{27} - 2 q^{30} - 36 q^{31} + 4 q^{32} - 6 q^{33} - 12 q^{34} - 4 q^{36} - 6 q^{37} + 12 q^{38} + 8 q^{40} - 6 q^{42} - 4 q^{43} + 12 q^{44} + 4 q^{45} + 12 q^{46} - 2 q^{48} - 8 q^{49} + 4 q^{50} + 60 q^{53} + 20 q^{54} + 6 q^{55} + 12 q^{57} - 4 q^{60} + 26 q^{61} - 18 q^{62} - 24 q^{63} + 8 q^{64} - 12 q^{66} - 24 q^{67} - 6 q^{68} - 12 q^{69} - 24 q^{71} + 4 q^{72} + 12 q^{73} + 6 q^{74} - 2 q^{75} + 6 q^{76} + 60 q^{77} + 20 q^{79} + 4 q^{80} - 28 q^{81} + 36 q^{83} + 6 q^{84} + 6 q^{85} - 8 q^{86} + 48 q^{87} + 6 q^{88} + 8 q^{90} + 24 q^{92} - 12 q^{93} - 6 q^{95} - 4 q^{96} + 18 q^{97} + 8 q^{98} + 84 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 - 2 * q^3 - 4 * q^4 - 8 * q^5 + 2 * q^6 - 8 * q^8 - 4 * q^9 - 4 * q^10 - 6 * q^11 + 4 * q^12 + 2 * q^15 - 4 * q^16 - 6 * q^17 - 8 * q^18 + 6 * q^19 + 4 * q^20 - 12 * q^21 + 6 * q^22 - 12 * q^23 + 2 * q^24 + 8 * q^25 + 40 * q^27 - 2 * q^30 - 36 * q^31 + 4 * q^32 - 6 * q^33 - 12 * q^34 - 4 * q^36 - 6 * q^37 + 12 * q^38 + 8 * q^40 - 6 * q^42 - 4 * q^43 + 12 * q^44 + 4 * q^45 + 12 * q^46 - 2 * q^48 - 8 * q^49 + 4 * q^50 + 60 * q^53 + 20 * q^54 + 6 * q^55 + 12 * q^57 - 4 * q^60 + 26 * q^61 - 18 * q^62 - 24 * q^63 + 8 * q^64 - 12 * q^66 - 24 * q^67 - 6 * q^68 - 12 * q^69 - 24 * q^71 + 4 * q^72 + 12 * q^73 + 6 * q^74 - 2 * q^75 + 6 * q^76 + 60 * q^77 + 20 * q^79 + 4 * q^80 - 28 * q^81 + 36 * q^83 + 6 * q^84 + 6 * q^85 - 8 * q^86 + 48 * q^87 + 6 * q^88 + 8 * q^90 + 24 * q^92 - 12 * q^93 - 6 * q^95 - 4 * q^96 + 18 * q^97 + 8 * q^98 + 84 * q^99

Introduction

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