LMFDB - Embedded newform 145.2.d.c.144.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [145,2,Mod(144,145)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(145, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("145.144"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 145 = 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	145.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.15783082931$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{17})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 5x^{2} + 4x + 16 $ x^4 - x^3 + 5x^2 + 4x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			144.1
Root			$-0.780776 - 1.35234i$ of defining polynomial
Character	$\chi$	$=$	145.144
Dual form			145.2.d.c.144.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} -2.56155 q^{3} -1.00000 q^{4} +(-0.280776 - 2.21837i) q^{5} -2.56155 q^{6} -3.46410i q^{7} -3.00000 q^{8} +3.56155 q^{9} +(-0.280776 - 2.21837i) q^{10} -0.972638i q^{11} +2.56155 q^{12} +4.43674i q^{13} -3.46410i q^{14} +(0.719224 + 5.68247i) q^{15} -1.00000 q^{16} -2.00000 q^{17} +3.56155 q^{18} -3.46410i q^{19} +(0.280776 + 2.21837i) q^{20} +8.87348i q^{21} -0.972638i q^{22} -3.46410i q^{23} +7.68466 q^{24} +(-4.84233 + 1.24573i) q^{25} +4.43674i q^{26} -1.43845 q^{27} +3.46410i q^{28} +(4.12311 + 3.46410i) q^{29} +(0.719224 + 5.68247i) q^{30} -7.90084i q^{31} +5.00000 q^{32} +2.49146i q^{33} -2.00000 q^{34} +(-7.68466 + 0.972638i) q^{35} -3.56155 q^{36} +7.12311 q^{37} -3.46410i q^{38} -11.3649i q^{39} +(0.842329 + 6.65511i) q^{40} -8.87348i q^{41} +8.87348i q^{42} +5.43845 q^{43} +0.972638i q^{44} +(-1.00000 - 7.90084i) q^{45} -3.46410i q^{46} -11.6847 q^{47} +2.56155 q^{48} -5.00000 q^{49} +(-4.84233 + 1.24573i) q^{50} +5.12311 q^{51} -4.43674i q^{52} -4.43674i q^{53} -1.43845 q^{54} +(-2.15767 + 0.273094i) q^{55} +10.3923i q^{56} +8.87348i q^{57} +(4.12311 + 3.46410i) q^{58} -1.12311 q^{59} +(-0.719224 - 5.68247i) q^{60} +1.94528i q^{61} -7.90084i q^{62} -12.3376i q^{63} +7.00000 q^{64} +(9.84233 - 1.24573i) q^{65} +2.49146i q^{66} +12.3376i q^{67} +2.00000 q^{68} +8.87348i q^{69} +(-7.68466 + 0.972638i) q^{70} -2.24621 q^{71} -10.6847 q^{72} -7.12311 q^{73} +7.12311 q^{74} +(12.4039 - 3.19101i) q^{75} +3.46410i q^{76} -3.36932 q^{77} -11.3649i q^{78} +14.8290i q^{79} +(0.280776 + 2.21837i) q^{80} -7.00000 q^{81} -8.87348i q^{82} -10.3923i q^{83} -8.87348i q^{84} +(0.561553 + 4.43674i) q^{85} +5.43845 q^{86} +(-10.5616 - 8.87348i) q^{87} +2.91791i q^{88} -8.87348i q^{89} +(-1.00000 - 7.90084i) q^{90} +15.3693 q^{91} +3.46410i q^{92} +20.2384i q^{93} -11.6847 q^{94} +(-7.68466 + 0.972638i) q^{95} -12.8078 q^{96} +8.24621 q^{97} -5.00000 q^{98} -3.46410i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 2 q^{3} - 4 q^{4} + 3 q^{5} - 2 q^{6} - 12 q^{8} + 6 q^{9} + 3 q^{10} + 2 q^{12} + 7 q^{15} - 4 q^{16} - 8 q^{17} + 6 q^{18} - 3 q^{20} + 6 q^{24} - 7 q^{25} - 14 q^{27} + 7 q^{30} + 20 q^{32}+ \cdots - 20 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 - 2 * q^3 - 4 * q^4 + 3 * q^5 - 2 * q^6 - 12 * q^8 + 6 * q^9 + 3 * q^10 + 2 * q^12 + 7 * q^15 - 4 * q^16 - 8 * q^17 + 6 * q^18 - 3 * q^20 + 6 * q^24 - 7 * q^25 - 14 * q^27 + 7 * q^30 + 20 * q^32 - 8 * q^34 - 6 * q^35 - 6 * q^36 + 12 * q^37 - 9 * q^40 + 30 * q^43 - 4 * q^45 - 22 * q^47 + 2 * q^48 - 20 * q^49 - 7 * q^50 + 4 * q^51 - 14 * q^54 - 21 * q^55 + 12 * q^59 - 7 * q^60 + 28 * q^64 + 27 * q^65 + 8 * q^68 - 6 * q^70 + 24 * q^71 - 18 * q^72 - 12 * q^73 + 12 * q^74 + 29 * q^75 + 36 * q^77 - 3 * q^80 - 28 * q^81 - 6 * q^85 + 30 * q^86 - 34 * q^87 - 4 * q^90 + 12 * q^91 - 22 * q^94 - 6 * q^95 - 10 * q^96 - 20 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/145\mathbb{Z}\right)^\times$.

$n$	$31$	$117$
$\chi(n)$	$-1$	$-1$

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 $

$2$	1.00000			0.707107			0.353553	−	0.935414i	$-0.384973\pi$
$2$	1.00000			0.707107			0.353553	+	0.935414i	$0.384973\pi$
$3$	−2.56155			−1.47891			−0.739457	−	0.673204i	$-0.764917\pi$
$3$	−2.56155			−1.47891			−0.739457	+	0.673204i	$0.764917\pi$
$4$	−1.00000			−0.500000
$5$	−0.280776	−	2.21837i	−0.125567	−	0.992085i
$5$	−0.280776	−	2.21837i	−0.125567	−	0.992085i
$6$	−2.56155			−1.04575
$7$		−	3.46410i		−	1.30931i	−0.755929	−	0.654654i	$-0.772814\pi$
$7$		−	3.46410i		−	1.30931i	0.755929	−	0.654654i	$-0.227186\pi$
$8$	−3.00000			−1.06066
$9$	3.56155			1.18718
$10$	−0.280776	−	2.21837i	−0.0887893	−	0.701510i
$11$		−	0.972638i		−	0.293261i	−0.989191	−	0.146631i	$-0.953157\pi$
$11$		−	0.972638i		−	0.293261i	0.989191	−	0.146631i	$-0.0468429\pi$
$12$	2.56155			0.739457
$13$			4.43674i			1.23053i	0.788320	+	0.615265i	$0.210951\pi$
$13$			4.43674i			1.23053i	−0.788320	+	0.615265i	$0.789049\pi$
$14$		−	3.46410i		−	0.925820i
$15$	0.719224	+	5.68247i	0.185703	+	1.46721i
$16$	−1.00000			−0.250000
$17$	−2.00000			−0.485071			−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000			−0.485071			−0.242536	+	0.970143i	$0.577979\pi$
$18$	3.56155			0.839466
$19$		−	3.46410i		−	0.794719i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$		−	3.46410i		−	0.794719i	0.917663	−	0.397360i	$-0.130073\pi$
$20$	0.280776	+	2.21837i	0.0627835	+	0.496043i
$21$			8.87348i			1.93635i
$22$		−	0.972638i		−	0.207367i
$23$		−	3.46410i		−	0.722315i	−0.932505	−	0.361158i	$-0.882382\pi$
$23$		−	3.46410i		−	0.722315i	0.932505	−	0.361158i	$-0.117618\pi$
$24$	7.68466			1.56862
$25$	−4.84233	+	1.24573i	−0.968466	+	0.249146i
$26$			4.43674i			0.870116i
$27$	−1.43845			−0.276829
$28$			3.46410i			0.654654i
$29$	4.12311	+	3.46410i	0.765641	+	0.643268i
$29$	4.12311	+	3.46410i	0.765641	+	0.643268i
$30$	0.719224	+	5.68247i	0.131312	+	1.03747i
$31$		−	7.90084i		−	1.41903i	−0.704689	−	0.709516i	$-0.748913\pi$
$31$		−	7.90084i		−	1.41903i	0.704689	−	0.709516i	$-0.251087\pi$
$32$	5.00000			0.883883
$33$			2.49146i			0.433708i
$34$	−2.00000			−0.342997
$35$	−7.68466	+	0.972638i	−1.29894	+	0.164406i
$36$	−3.56155			−0.593592
$37$	7.12311			1.17103			0.585516	−	0.810661i	$-0.300892\pi$
$37$	7.12311			1.17103			0.585516	+	0.810661i	$0.300892\pi$
$38$		−	3.46410i		−	0.561951i
$39$		−	11.3649i		−	1.81985i
$40$	0.842329	+	6.65511i	0.133184	+	1.05227i
$41$		−	8.87348i		−	1.38580i	−0.721031	−	0.692902i	$-0.756332\pi$
$41$		−	8.87348i		−	1.38580i	0.721031	−	0.692902i	$-0.243668\pi$
$42$			8.87348i			1.36921i
$43$	5.43845			0.829355			0.414678	−	0.909968i	$-0.363894\pi$
$43$	5.43845			0.829355			0.414678	+	0.909968i	$0.363894\pi$
$44$			0.972638i			0.146631i
$45$	−1.00000	−	7.90084i	−0.149071	−	1.17779i
$46$		−	3.46410i		−	0.510754i
$47$	−11.6847			−1.70438			−0.852191	−	0.523230i	$-0.824727\pi$
$47$	−11.6847			−1.70438			−0.852191	+	0.523230i	$0.824727\pi$
$48$	2.56155			0.369728
$49$	−5.00000			−0.714286
$50$	−4.84233	+	1.24573i	−0.684809	+	0.176173i
$51$	5.12311			0.717378
$52$		−	4.43674i		−	0.615265i
$53$		−	4.43674i		−	0.609433i	−0.952443	−	0.304717i	$-0.901438\pi$
$53$		−	4.43674i		−	0.609433i	0.952443	−	0.304717i	$-0.0985617\pi$
$54$	−1.43845			−0.195748
$55$	−2.15767	+	0.273094i	−0.290940	+	0.0368240i
$56$			10.3923i			1.38873i
$57$			8.87348i			1.17532i
$58$	4.12311	+	3.46410i	0.541390	+	0.454859i
$59$	−1.12311			−0.146216			−0.0731079	−	0.997324i	$-0.523292\pi$
$59$	−1.12311			−0.146216			−0.0731079	+	0.997324i	$0.523292\pi$
$60$	−0.719224	−	5.68247i	−0.0928514	−	0.733604i
$61$			1.94528i			0.249067i	0.992215	+	0.124534i	$0.0397434\pi$
$61$			1.94528i			0.249067i	−0.992215	+	0.124534i	$0.960257\pi$
$62$		−	7.90084i		−	1.00341i
$63$		−	12.3376i		−	1.55439i
$64$	7.00000			0.875000
$65$	9.84233	−	1.24573i	1.22079	−	0.154514i
$66$			2.49146i			0.306678i
$67$			12.3376i			1.50728i	0.657290	+	0.753638i	$0.271703\pi$
$67$			12.3376i			1.50728i	−0.657290	+	0.753638i	$0.728297\pi$
$68$	2.00000			0.242536
$69$			8.87348i			1.06824i
$70$	−7.68466	+	0.972638i	−0.918492	+	0.116252i
$71$	−2.24621			−0.266576			−0.133288	−	0.991077i	$-0.542554\pi$
$71$	−2.24621			−0.266576			−0.133288	+	0.991077i	$0.542554\pi$
$72$	−10.6847			−1.25920
$73$	−7.12311			−0.833696			−0.416848	−	0.908976i	$-0.636865\pi$
$73$	−7.12311			−0.833696			−0.416848	+	0.908976i	$0.636865\pi$
$74$	7.12311			0.828044
$75$	12.4039	−	3.19101i	1.43228	−	0.368466i
$76$			3.46410i			0.397360i
$77$	−3.36932			−0.383969
$78$		−	11.3649i		−	1.28683i
$79$			14.8290i			1.66840i	0.551464	+	0.834199i	$0.314070\pi$
$79$			14.8290i			1.66840i	−0.551464	+	0.834199i	$0.685930\pi$
$80$	0.280776	+	2.21837i	0.0313918	+	0.248021i
$81$	−7.00000			−0.777778
$82$		−	8.87348i		−	0.979912i
$83$		−	10.3923i		−	1.14070i	−0.821401	−	0.570352i	$-0.806807\pi$
$83$		−	10.3923i		−	1.14070i	0.821401	−	0.570352i	$-0.193193\pi$
$84$		−	8.87348i		−	0.968176i
$85$	0.561553	+	4.43674i	0.0609090	+	0.481232i
$86$	5.43845			0.586443
$87$	−10.5616	−	8.87348i	−1.13232	−	0.951337i
$88$			2.91791i			0.311051i
$89$		−	8.87348i		−	0.940587i	−0.882510	−	0.470293i	$-0.844148\pi$
$89$		−	8.87348i		−	0.940587i	0.882510	−	0.470293i	$-0.155852\pi$
$90$	−1.00000	−	7.90084i	−0.105409	−	0.832822i
$91$	15.3693			1.61114
$92$			3.46410i			0.361158i
$93$			20.2384i			2.09863i
$94$	−11.6847			−1.20518
$95$	−7.68466	+	0.972638i	−0.788429	+	0.0997906i
$96$	−12.8078			−1.30719
$97$	8.24621			0.837276			0.418638	−	0.908153i	$-0.362508\pi$
$97$	8.24621			0.837276			0.418638	+	0.908153i	$0.362508\pi$
$98$	−5.00000			−0.505076
$99$		−	3.46410i		−	0.348155i
$100$	4.84233	−	1.24573i	0.484233	−	0.124573i
$101$		−	6.92820i		−	0.689382i	−0.938716	−	0.344691i	$-0.887984\pi$
$101$		−	6.92820i		−	0.689382i	0.938716	−	0.344691i	$-0.112016\pi$
$102$	5.12311			0.507263
$103$			1.51883i			0.149654i	0.997197	+	0.0748272i	$0.0238405\pi$
$103$			1.51883i			0.149654i	−0.997197	+	0.0748272i	$0.976159\pi$
$104$		−	13.3102i		−	1.30517i
$105$	19.6847	−	2.49146i	1.92103	−	0.243142i
$106$		−	4.43674i		−	0.430934i
$107$		−	14.2829i		−	1.38078i	−0.723439	−	0.690388i	$-0.757440\pi$
$107$		−	14.2829i		−	1.38078i	0.723439	−	0.690388i	$-0.242560\pi$
$108$	1.43845			0.138415
$109$	−5.68466			−0.544492			−0.272246	−	0.962228i	$-0.587766\pi$
$109$	−5.68466			−0.544492			−0.272246	+	0.962228i	$0.587766\pi$
$110$	−2.15767	+	0.273094i	−0.205726	+	0.0260385i
$111$	−18.2462			−1.73185
$112$			3.46410i			0.327327i
$113$	5.36932			0.505103			0.252551	−	0.967583i	$-0.418730\pi$
$113$	5.36932			0.505103			0.252551	+	0.967583i	$0.418730\pi$
$114$			8.87348i			0.831077i
$115$	−7.68466	+	0.972638i	−0.716598	+	0.0906990i
$116$	−4.12311	−	3.46410i	−0.382821	−	0.321634i
$117$			15.8017i			1.46087i
$118$	−1.12311			−0.103390
$119$			6.92820i			0.635107i
$120$	−2.15767	−	17.0474i	−0.196967	−	1.55621i
$121$	10.0540			0.913998
$122$			1.94528i			0.176117i
$123$			22.7299i			2.04948i
$124$			7.90084i			0.709516i
$125$	4.12311	+	10.3923i	0.368782	+	0.929516i
$126$		−	12.3376i		−	1.09912i
$127$	−2.24621			−0.199319			−0.0996595	−	0.995022i	$-0.531775\pi$
$127$	−2.24621			−0.199319			−0.0996595	+	0.995022i	$0.531775\pi$
$128$	−3.00000			−0.265165
$129$	−13.9309			−1.22654
$130$	9.84233	−	1.24573i	0.863229	−	0.109258i
$131$			14.2829i			1.24790i	0.781465	+	0.623949i	$0.214473\pi$
$131$			14.2829i			1.24790i	−0.781465	+	0.623949i	$0.785527\pi$
$132$		−	2.49146i		−	0.216854i
$133$	−12.0000			−1.04053
$134$			12.3376i			1.06580i
$135$	0.403882	+	3.19101i	0.0347606	+	0.274638i
$136$	6.00000			0.514496
$137$	13.3693			1.14222			0.571109	−	0.820874i	$-0.306513\pi$
$137$	13.3693			1.14222			0.571109	+	0.820874i	$0.306513\pi$
$138$			8.87348i			0.755361i
$139$	19.3693			1.64288			0.821442	−	0.570292i	$-0.193170\pi$
$139$	19.3693			1.64288			0.821442	+	0.570292i	$0.193170\pi$
$140$	7.68466	−	0.972638i	0.649472	−	0.0822029i
$141$	29.9309			2.52063
$142$	−2.24621			−0.188498
$143$	4.31534			0.360867
$144$	−3.56155			−0.296796
$145$	6.52699	−	10.1192i	0.542037	−	0.840355i
$146$	−7.12311			−0.589512
$147$	12.8078			1.05637
$148$	−7.12311			−0.585516
$149$	−13.6847			−1.12109			−0.560545	−	0.828124i	$-0.689408\pi$
$149$	−13.6847			−1.12109			−0.560545	+	0.828124i	$0.689408\pi$
$150$	12.4039	−	3.19101i	1.01277	−	0.260545i
$151$	15.3693			1.25074			0.625369	−	0.780329i	$-0.284949\pi$
$151$	15.3693			1.25074			0.625369	+	0.780329i	$0.284949\pi$
$152$			10.3923i			0.842927i
$153$	−7.12311			−0.575869
$154$	−3.36932			−0.271507
$155$	−17.5270	+	2.21837i	−1.40780	+	0.178184i
$156$			11.3649i			0.909924i
$157$	22.4924			1.79509			0.897545	−	0.440922i	$-0.145349\pi$
$157$	22.4924			1.79509			0.897545	+	0.440922i	$0.145349\pi$
$158$			14.8290i			1.17974i
$159$			11.3649i			0.901299i
$160$	−1.40388	−	11.0918i	−0.110987	−	0.876888i
$161$	−12.0000			−0.945732
$162$	−7.00000			−0.549972
$163$	−5.43845			−0.425972			−0.212986	−	0.977055i	$-0.568319\pi$
$163$	−5.43845			−0.425972			−0.212986	+	0.977055i	$0.568319\pi$
$164$			8.87348i			0.692902i
$165$	5.52699	−	0.699544i	0.430275	−	0.0544594i
$166$		−	10.3923i		−	0.806599i
$167$		−	8.44703i		−	0.653651i	−0.945085	−	0.326825i	$-0.894021\pi$
$167$		−	8.44703i		−	0.653651i	0.945085	−	0.326825i	$-0.105979\pi$
$168$		−	26.6204i		−	2.05381i
$169$	−6.68466			−0.514204
$170$	0.561553	+	4.43674i	0.0430691	+	0.340282i
$171$		−	12.3376i		−	0.943478i
$172$	−5.43845			−0.414678
$173$			10.8188i			0.822535i	0.911515	+	0.411267i	$0.134914\pi$
$173$			10.8188i			0.822535i	−0.911515	+	0.411267i	$0.865086\pi$
$174$	−10.5616	−	8.87348i	−0.800669	−	0.672697i
$175$	4.31534	+	16.7743i	0.326209	+	1.26802i
$176$			0.972638i			0.0733153i
$177$	2.87689			0.216241
$178$		−	8.87348i		−	0.665095i
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$	1.00000	+	7.90084i	0.0745356	+	0.588894i
$181$	−13.6847			−1.01717			−0.508586	−	0.861011i	$-0.669832\pi$
$181$	−13.6847			−1.01717			−0.508586	+	0.861011i	$0.669832\pi$
$182$	15.3693			1.13925
$183$		−	4.98293i		−	0.368349i
$184$			10.3923i			0.766131i
$185$	−2.00000	−	15.8017i	−0.147043	−	1.16176i
$186$			20.2384i			1.48395i
$187$			1.94528i			0.142253i
$188$	11.6847			0.852191
$189$			4.98293i			0.362455i
$190$	−7.68466	+	0.972638i	−0.557504	+	0.0705626i
$191$			3.46410i			0.250654i	0.992116	+	0.125327i	$0.0399979\pi$
$191$			3.46410i			0.250654i	−0.992116	+	0.125327i	$0.960002\pi$
$192$	−17.9309			−1.29405
$193$	8.24621			0.593575			0.296788	−	0.954944i	$-0.404085\pi$
$193$	8.24621			0.593575			0.296788	+	0.954944i	$0.404085\pi$
$194$	8.24621			0.592043
$195$	−25.2116	+	3.19101i	−1.80544	+	0.228513i
$196$	5.00000			0.357143
$197$		−	10.8188i		−	0.770804i	−0.922749	−	0.385402i	$-0.874063\pi$
$197$		−	10.8188i		−	0.770804i	0.922749	−	0.385402i	$-0.125937\pi$
$198$		−	3.46410i		−	0.246183i
$199$	−15.3693			−1.08950			−0.544751	−	0.838598i	$-0.683376\pi$
$199$	−15.3693			−1.08950			−0.544751	+	0.838598i	$0.683376\pi$
$200$	14.5270	−	3.73720i	1.02721	−	0.264260i
$201$		−	31.6034i		−	2.22913i
$202$		−	6.92820i		−	0.487467i
$203$	12.0000	−	14.2829i	0.842235	−	1.00246i
$204$	−5.12311			−0.358689
$205$	−19.6847	+	2.49146i	−1.37484	+	0.174011i
$206$			1.51883i			0.105822i
$207$		−	12.3376i		−	0.857521i
$208$		−	4.43674i		−	0.307633i
$209$	−3.36932			−0.233061
$210$	19.6847	−	2.49146i	1.35837	−	0.171927i
$211$		−	14.8290i		−	1.02087i	−0.859915	−	0.510437i	$-0.829484\pi$
$211$		−	14.8290i		−	1.02087i	0.859915	−	0.510437i	$-0.170516\pi$
$212$			4.43674i			0.304717i
$213$	5.75379			0.394243
$214$		−	14.2829i		−	0.976356i
$215$	−1.52699	−	12.0645i	−0.104140	−	0.822791i
$216$	4.31534			0.293622
$217$	−27.3693			−1.85795
$218$	−5.68466			−0.385014
$219$	18.2462			1.23296
$220$	2.15767	−	0.273094i	0.145470	−	0.0184120i
$221$		−	8.87348i		−	0.596895i
$222$	−18.2462			−1.22461
$223$		−	12.3376i		−	0.826186i	−0.910689	−	0.413093i	$-0.864449\pi$
$223$		−	12.3376i		−	0.826186i	0.910689	−	0.413093i	$-0.135551\pi$
$224$		−	17.3205i		−	1.15728i
$225$	−17.2462	+	4.43674i	−1.14975	+	0.295783i
$226$	5.36932			0.357162
$227$			12.3376i			0.818874i	0.912338	+	0.409437i	$0.134275\pi$
$227$			12.3376i			0.818874i	−0.912338	+	0.409437i	$0.865725\pi$
$228$		−	8.87348i		−	0.587661i
$229$			15.8017i			1.04420i	0.852883	+	0.522102i	$0.174852\pi$
$229$			15.8017i			1.04420i	−0.852883	+	0.522102i	$0.825148\pi$
$230$	−7.68466	+	0.972638i	−0.506711	+	0.0641339i
$231$	8.63068			0.567857
$232$	−12.3693	−	10.3923i	−0.812085	−	0.682288i
$233$		−	2.49146i		−	0.163221i	−0.996664	−	0.0816106i	$-0.973994\pi$
$233$		−	2.49146i		−	0.163221i	0.996664	−	0.0816106i	$-0.0260064\pi$
$234$			15.8017i			1.03299i
$235$	3.28078	+	25.9209i	0.214014	+	1.69089i
$236$	1.12311			0.0731079
$237$		−	37.9854i		−	2.46742i
$238$			6.92820i			0.449089i
$239$	13.1231			0.848863			0.424432	−	0.905460i	$-0.360474\pi$
$239$	13.1231			0.848863			0.424432	+	0.905460i	$0.360474\pi$
$240$	−0.719224	−	5.68247i	−0.0464257	−	0.366802i
$241$	−1.68466			−0.108518			−0.0542592	−	0.998527i	$-0.517280\pi$
$241$	−1.68466			−0.108518			−0.0542592	+	0.998527i	$0.517280\pi$
$242$	10.0540			0.646294
$243$	22.2462			1.42710
$244$		−	1.94528i		−	0.124534i
$245$	1.40388	+	11.0918i	0.0896907	+	0.708632i
$246$			22.7299i			1.44920i
$247$	15.3693			0.977926
$248$			23.7025i			1.50511i
$249$			26.6204i			1.68700i
$250$	4.12311	+	10.3923i	0.260768	+	0.657267i
$251$			16.7743i			1.05879i	0.848377	+	0.529393i	$0.177580\pi$
$251$			16.7743i			1.05879i	−0.848377	+	0.529393i	$0.822420\pi$
$252$			12.3376i			0.777195i
$253$	−3.36932			−0.211827
$254$	−2.24621			−0.140940
$255$	−1.43845	−	11.3649i	−0.0900791	−	0.711700i
$256$	−17.0000			−1.06250
$257$			11.3649i			0.708926i	0.935070	+	0.354463i	$0.115336\pi$
$257$			11.3649i			0.708926i	−0.935070	+	0.354463i	$0.884664\pi$
$258$	−13.9309			−0.867298
$259$		−	24.6752i		−	1.53324i
$260$	−9.84233	+	1.24573i	−0.610395	+	0.0772570i
$261$	14.6847	+	12.3376i	0.908958	+	0.763677i
$262$			14.2829i			0.882398i
$263$	3.68466			0.227206			0.113603	−	0.993526i	$-0.463761\pi$
$263$	3.68466			0.227206			0.113603	+	0.993526i	$0.463761\pi$
$264$		−	7.47439i		−	0.460017i
$265$	−9.84233	+	1.24573i	−0.604609	+	0.0765247i
$266$	−12.0000			−0.735767
$267$			22.7299i			1.39105i
$268$		−	12.3376i		−	0.753638i
$269$		−	15.8017i		−	0.963446i	−0.876324	−	0.481723i	$-0.840011\pi$
$269$		−	15.8017i		−	0.963446i	0.876324	−	0.481723i	$-0.159989\pi$
$270$	0.403882	+	3.19101i	0.0245795	+	0.194199i
$271$			14.8290i			0.900800i	0.892827	+	0.450400i	$0.148719\pi$
$271$			14.8290i			0.900800i	−0.892827	+	0.450400i	$0.851281\pi$
$272$	2.00000			0.121268
$273$	−39.3693			−2.38274
$274$	13.3693			0.807670
$275$	1.21165	+	4.70983i	0.0730650	+	0.284014i
$276$		−	8.87348i		−	0.534121i
$277$		−	10.8188i		−	0.650036i	−0.945708	−	0.325018i	$-0.894630\pi$
$277$		−	10.8188i		−	0.650036i	0.945708	−	0.325018i	$-0.105370\pi$
$278$	19.3693			1.16169
$279$		−	28.1393i		−	1.68465i
$280$	23.0540	−	2.91791i	1.37774	−	0.174379i
$281$	13.6847			0.816358			0.408179	−	0.912902i	$-0.366164\pi$
$281$	13.6847			0.816358			0.408179	+	0.912902i	$0.366164\pi$
$282$	29.9309			1.78236
$283$		−	14.2829i		−	0.849028i	−0.905421	−	0.424514i	$-0.860445\pi$
$283$		−	14.2829i		−	0.849028i	0.905421	−	0.424514i	$-0.139555\pi$
$284$	2.24621			0.133288
$285$	19.6847	−	2.49146i	1.16602	−	0.147582i
$286$	4.31534			0.255171
$287$	−30.7386			−1.81444
$288$	17.8078			1.04933
$289$	−13.0000			−0.764706
$290$	6.52699	−	10.1192i	0.383278	−	0.594221i
$291$	−21.1231			−1.23826
$292$	7.12311			0.416848
$293$	1.36932			0.0799963			0.0399982	−	0.999200i	$-0.487265\pi$
$293$	1.36932			0.0799963			0.0399982	+	0.999200i	$0.487265\pi$
$294$	12.8078			0.746964
$295$	0.315342	+	2.49146i	0.0183599	+	0.145059i
$296$	−21.3693			−1.24207
$297$			1.39909i			0.0811833i
$298$	−13.6847			−0.792731
$299$	15.3693			0.888831
$300$	−12.4039	+	3.19101i	−0.716138	+	0.184233i
$301$		−	18.8393i		−	1.08588i
$302$	15.3693			0.884405
$303$			17.7470i			1.01954i
$304$			3.46410i			0.198680i
$305$	4.31534	−	0.546188i	0.247096	−	0.0312746i
$306$	−7.12311			−0.407201
$307$	3.19224			0.182191			0.0910953	−	0.995842i	$-0.470963\pi$
$307$	3.19224			0.182191			0.0910953	+	0.995842i	$0.470963\pi$
$308$	3.36932			0.191985
$309$		−	3.89055i		−	0.221326i
$310$	−17.5270	+	2.21837i	−0.995466	+	0.125995i
$311$		−	0.426450i		−	0.0241818i	−0.999927	−	0.0120909i	$-0.996151\pi$
$311$		−	0.426450i		−	0.0241818i	0.999927	−	0.0120909i	$-0.00384874\pi$
$312$			34.0948i			1.93024i
$313$		−	2.49146i		−	0.140826i	−0.997518	−	0.0704129i	$-0.977568\pi$
$313$		−	2.49146i		−	0.140826i	0.997518	−	0.0704129i	$-0.0224317\pi$
$314$	22.4924			1.26932
$315$	−27.3693	+	3.46410i	−1.54209	+	0.195180i
$316$		−	14.8290i		−	0.834199i
$317$	2.00000			0.112331			0.0561656	−	0.998421i	$-0.482113\pi$
$317$	2.00000			0.112331			0.0561656	+	0.998421i	$0.482113\pi$
$318$			11.3649i			0.637314i
$319$	3.36932	−	4.01029i	0.188646	−	0.224533i
$320$	−1.96543	−	15.5286i	−0.109871	−	0.868074i
$321$			36.5863i			2.04205i
$322$	−12.0000			−0.668734
$323$			6.92820i			0.385496i
$324$	7.00000			0.388889
$325$	−5.52699	−	21.4842i	−0.306582	−	1.19173i
$326$	−5.43845			−0.301208
$327$	14.5616			0.805256
$328$			26.6204i			1.46987i
$329$			40.4768i			2.23156i
$330$	5.52699	−	0.699544i	0.304251	−	0.0385086i
$331$		−	5.95557i		−	0.327347i	−0.986515	−	0.163674i	$-0.947666\pi$
$331$		−	5.95557i		−	0.327347i	0.986515	−	0.163674i	$-0.0523344\pi$
$332$			10.3923i			0.570352i
$333$	25.3693			1.39023
$334$		−	8.44703i		−	0.462201i
$335$	27.3693	−	3.46410i	1.49535	−	0.189264i
$336$		−	8.87348i		−	0.484088i
$337$	3.75379			0.204482			0.102241	−	0.994760i	$-0.467399\pi$
$337$	3.75379			0.204482			0.102241	+	0.994760i	$0.467399\pi$
$338$	−6.68466			−0.363597
$339$	−13.7538			−0.747003
$340$	−0.561553	−	4.43674i	−0.0304545	−	0.240616i
$341$	−7.68466			−0.416148
$342$		−	12.3376i		−	0.667140i
$343$		−	6.92820i		−	0.374088i
$344$	−16.3153			−0.879664
$345$	19.6847	−	2.49146i	1.05979	−	0.134136i
$346$			10.8188i			0.581620i
$347$			26.1940i			1.40617i	0.711107	+	0.703083i	$0.248194\pi$
$347$			26.1940i			1.40617i	−0.711107	+	0.703083i	$0.751806\pi$
$348$	10.5616	+	8.87348i	0.566159	+	0.475668i
$349$	10.3153			0.552168			0.276084	−	0.961134i	$-0.410963\pi$
$349$	10.3153			0.552168			0.276084	+	0.961134i	$0.410963\pi$
$350$	4.31534	+	16.7743i	0.230665	+	0.896625i
$351$		−	6.38202i		−	0.340647i
$352$		−	4.86319i		−	0.259209i
$353$		−	17.7470i		−	0.944575i	−0.881444	−	0.472288i	$-0.843428\pi$
$353$		−	17.7470i		−	0.944575i	0.881444	−	0.472288i	$-0.156572\pi$
$354$	2.87689			0.152905
$355$	0.630683	+	4.98293i	0.0334732	+	0.264466i
$356$			8.87348i			0.470293i
$357$		−	17.7470i		−	0.939269i
$358$	−12.0000			−0.634220
$359$		−	21.7572i		−	1.14830i	−0.818749	−	0.574152i	$-0.805332\pi$
$359$		−	21.7572i		−	1.14830i	0.818749	−	0.574152i	$-0.194668\pi$
$360$	3.00000	+	23.7025i	0.158114	+	1.24923i
$361$	7.00000			0.368421
$362$	−13.6847			−0.719250
$363$	−25.7538			−1.35172
$364$	−15.3693			−0.805571
$365$	2.00000	+	15.8017i	0.104685	+	0.827098i
$366$		−	4.98293i		−	0.260462i
$367$	−28.4924			−1.48729			−0.743646	−	0.668573i	$-0.766905\pi$
$367$	−28.4924			−1.48729			−0.743646	+	0.668573i	$0.766905\pi$
$368$			3.46410i			0.180579i
$369$		−	31.6034i		−	1.64521i
$370$	−2.00000	−	15.8017i	−0.103975	−	0.821490i
$371$	−15.3693			−0.797935
$372$		−	20.2384i		−	1.04931i
$373$			36.0401i			1.86609i	0.359765	+	0.933043i	$0.382857\pi$
$373$			36.0401i			1.86609i	−0.359765	+	0.933043i	$0.617143\pi$
$374$			1.94528i			0.100588i
$375$	−10.5616	−	26.6204i	−0.545396	−	1.37467i
$376$	35.0540			1.80777
$377$	−15.3693	+	18.2931i	−0.791560	+	0.942145i
$378$			4.98293i			0.256294i
$379$			0.426450i			0.0219053i	0.999940	+	0.0109526i	$0.00348640\pi$
$379$			0.426450i			0.0219053i	−0.999940	+	0.0109526i	$0.996514\pi$
$380$	7.68466	−	0.972638i	0.394215	−	0.0498953i
$381$	5.75379			0.294776
$382$			3.46410i			0.177239i
$383$		−	17.3205i		−	0.885037i	−0.896759	−	0.442518i	$-0.854085\pi$
$383$		−	17.3205i		−	0.885037i	0.896759	−	0.442518i	$-0.145915\pi$
$384$	7.68466			0.392156
$385$	0.946025	+	7.47439i	0.0482139	+	0.380930i
$386$	8.24621			0.419721
$387$	19.3693			0.984598
$388$	−8.24621			−0.418638
$389$			10.8188i			0.548533i	0.961654	+	0.274266i	$0.0884350\pi$
$389$			10.8188i			0.548533i	−0.961654	+	0.274266i	$0.911565\pi$
$390$	−25.2116	+	3.19101i	−1.27664	+	0.161583i
$391$			6.92820i			0.350374i
$392$	15.0000			0.757614
$393$		−	36.5863i		−	1.84553i
$394$		−	10.8188i		−	0.545041i
$395$	32.8963	−	4.16365i	1.65519	−	0.209496i
$396$			3.46410i			0.174078i
$397$		−	0.546188i		−	0.0274124i	−0.999906	−	0.0137062i	$-0.995637\pi$
$397$		−	0.546188i		−	0.0274124i	0.999906	−	0.0137062i	$-0.00436295\pi$
$398$	−15.3693			−0.770394
$399$	30.7386			1.53886
$400$	4.84233	−	1.24573i	0.242116	−	0.0622866i
$401$	15.9309			0.795550			0.397775	−	0.917483i	$-0.369783\pi$
$401$	15.9309			0.795550			0.397775	+	0.917483i	$0.369783\pi$
$402$		−	31.6034i		−	1.57623i
$403$	35.0540			1.74616
$404$			6.92820i			0.344691i
$405$	1.96543	+	15.5286i	0.0976632	+	0.771622i
$406$	12.0000	−	14.2829i	0.595550	−	0.708846i
$407$		−	6.92820i		−	0.343418i
$408$	−15.3693			−0.760895
$409$		−	3.89055i		−	0.192375i	−0.995363	−	0.0961877i	$-0.969335\pi$
$409$		−	3.89055i		−	0.192375i	0.995363	−	0.0961877i	$-0.0306649\pi$
$410$	−19.6847	+	2.49146i	−0.972156	+	0.123045i
$411$	−34.2462			−1.68924
$412$		−	1.51883i		−	0.0748272i
$413$			3.89055i			0.191442i
$414$		−	12.3376i		−	0.606359i
$415$	−23.0540	+	2.91791i	−1.13168	+	0.143235i
$416$			22.1837i			1.08765i
$417$	−49.6155			−2.42968
$418$	−3.36932			−0.164799
$419$	14.2462			0.695973			0.347986	−	0.937500i	$-0.386866\pi$
$419$	14.2462			0.695973			0.347986	+	0.937500i	$0.386866\pi$
$420$	−19.6847	+	2.49146i	−0.960513	+	0.121571i
$421$		−	37.4392i		−	1.82467i	−0.409439	−	0.912337i	$-0.634276\pi$
$421$		−	37.4392i		−	1.82467i	0.409439	−	0.912337i	$-0.365724\pi$
$422$		−	14.8290i		−	0.721867i
$423$	−41.6155			−2.02342
$424$			13.3102i			0.646401i
$425$	9.68466	−	2.49146i	0.469775	−	0.120854i
$426$	5.75379			0.278772
$427$	6.73863			0.326105
$428$			14.2829i			0.690388i
$429$	−11.0540			−0.533691
$430$	−1.52699	−	12.0645i	−0.0736379	−	0.581801i
$431$	8.63068			0.415725			0.207863	−	0.978158i	$-0.433349\pi$
$431$	8.63068			0.415725			0.207863	+	0.978158i	$0.433349\pi$
$432$	1.43845			0.0692073
$433$	16.8769			0.811052			0.405526	−	0.914084i	$-0.367088\pi$
$433$	16.8769			0.811052			0.405526	+	0.914084i	$0.367088\pi$
$434$	−27.3693			−1.31377
$435$	−16.7192	+	25.9209i	−0.801625	+	1.24281i
$436$	5.68466			0.272246
$437$	−12.0000			−0.574038
$438$	18.2462			0.871838
$439$	15.3693			0.733537			0.366769	−	0.930312i	$-0.380464\pi$
$439$	15.3693			0.733537			0.366769	+	0.930312i	$0.380464\pi$
$440$	6.47301	−	0.819281i	0.308589	−	0.0390577i
$441$	−17.8078			−0.847989
$442$		−	8.87348i		−	0.422068i
$443$	−4.00000			−0.190046			−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000			−0.190046			−0.0950229	+	0.995475i	$0.530292\pi$
$444$	18.2462			0.865927
$445$	−19.6847	+	2.49146i	−0.933142	+	0.118107i
$446$		−	12.3376i		−	0.584201i
$447$	35.0540			1.65800
$448$		−	24.2487i		−	1.14564i
$449$		−	17.7470i		−	0.837531i	−0.908094	−	0.418765i	$-0.862463\pi$
$449$		−	17.7470i		−	0.837531i	0.908094	−	0.418765i	$-0.137537\pi$
$450$	−17.2462	+	4.43674i	−0.812994	+	0.209150i
$451$	−8.63068			−0.406403
$452$	−5.36932			−0.252551
$453$	−39.3693			−1.84973
$454$			12.3376i			0.579031i
$455$	−4.31534	−	34.0948i	−0.202306	−	1.59839i
$456$		−	26.6204i		−	1.24662i
$457$		−	3.89055i		−	0.181992i	−0.995851	−	0.0909962i	$-0.970995\pi$
$457$		−	3.89055i		−	0.181992i	0.995851	−	0.0909962i	$-0.0290051\pi$
$458$			15.8017i			0.738364i
$459$	2.87689			0.134282
$460$	7.68466	−	0.972638i	0.358299	−	0.0453495i
$461$			34.6410i			1.61339i	0.590966	+	0.806696i	$0.298747\pi$
$461$			34.6410i			1.61339i	−0.590966	+	0.806696i	$0.701253\pi$
$462$	8.63068			0.401536
$463$		−	7.35465i		−	0.341800i	−0.985288	−	0.170900i	$-0.945333\pi$
$463$		−	7.35465i		−	0.341800i	0.985288	−	0.170900i	$-0.0546675\pi$
$464$	−4.12311	−	3.46410i	−0.191410	−	0.160817i
$465$	44.8963	−	5.68247i	2.08202	−	0.263518i
$466$		−	2.49146i		−	0.115415i
$467$	−8.31534			−0.384788			−0.192394	−	0.981318i	$-0.561625\pi$
$467$	−8.31534			−0.384788			−0.192394	+	0.981318i	$0.561625\pi$
$468$		−	15.8017i		−	0.730433i
$469$	42.7386			1.97349
$470$	3.28078	+	25.9209i	0.151331	+	1.19564i
$471$	−57.6155			−2.65478
$472$	3.36932			0.155085
$473$		−	5.28964i		−	0.243218i
$474$		−	37.9854i		−	1.74473i
$475$	4.31534	+	16.7743i	0.198001	+	0.769659i
$476$		−	6.92820i		−	0.317554i
$477$		−	15.8017i		−	0.723509i
$478$	13.1231			0.600237
$479$		−	2.91791i		−	0.133323i	−0.997776	−	0.0666614i	$-0.978765\pi$
$479$		−	2.91791i		−	0.133323i	0.997776	−	0.0666614i	$-0.0212347\pi$
$480$	3.59612	+	28.4124i	0.164140	+	1.29684i
$481$			31.6034i			1.44099i
$482$	−1.68466			−0.0767341
$483$	30.7386			1.39866
$484$	−10.0540			−0.456999
$485$	−2.31534	−	18.2931i	−0.105134	−	0.830649i
$486$	22.2462			1.00911
$487$			32.0298i			1.45141i	0.688006	+	0.725705i	$0.258486\pi$
$487$			32.0298i			1.45141i	−0.688006	+	0.725705i	$0.741514\pi$
$488$		−	5.83583i		−	0.264176i
$489$	13.9309			0.629976
$490$	1.40388	+	11.0918i	0.0634209	+	0.501079i
$491$			29.5384i			1.33305i	0.745484	+	0.666524i	$0.232218\pi$
$491$			29.5384i			1.33305i	−0.745484	+	0.666524i	$0.767782\pi$
$492$		−	22.7299i		−	1.02474i
$493$	−8.24621	−	6.92820i	−0.371391	−	0.312031i
$494$	15.3693			0.691498
$495$	−7.68466	+	0.972638i	−0.345400	+	0.0437168i
$496$			7.90084i			0.354758i
$497$			7.78110i			0.349030i
$498$			26.6204i			1.19289i
$499$	−4.63068			−0.207298			−0.103649	−	0.994614i	$-0.533052\pi$
$499$	−4.63068			−0.207298			−0.103649	+	0.994614i	$0.533052\pi$
$500$	−4.12311	−	10.3923i	−0.184391	−	0.464758i
$501$			21.6375i			0.966693i
$502$			16.7743i			0.748675i
$503$	4.94602			0.220532			0.110266	−	0.993902i	$-0.464830\pi$
$503$	4.94602			0.220532			0.110266	+	0.993902i	$0.464830\pi$
$504$			37.0127i			1.64868i
$505$	−15.3693	+	1.94528i	−0.683926	+	0.0865636i
$506$	−3.36932			−0.149784
$507$	17.1231			0.760464
$508$	2.24621			0.0996595
$509$	−29.0540			−1.28779			−0.643897	−	0.765112i	$-0.722684\pi$
$509$	−29.0540			−1.28779			−0.643897	+	0.765112i	$0.722684\pi$
$510$	−1.43845	−	11.3649i	−0.0636955	−	0.503248i
$511$			24.6752i			1.09156i
$512$	−11.0000			−0.486136
$513$			4.98293i			0.220002i
$514$			11.3649i			0.501286i
$515$	3.36932	−	0.426450i	0.148470	−	0.0187916i
$516$	13.9309			0.613272
$517$			11.3649i			0.499830i
$518$		−	24.6752i		−	1.08416i
$519$		−	27.7128i		−	1.21646i
$520$	−29.5270	+	3.73720i	−1.29484	+	0.163887i
$521$	22.3153			0.977653			0.488826	−	0.872381i	$-0.337425\pi$
$521$	22.3153			0.977653			0.488826	+	0.872381i	$0.337425\pi$
$522$	14.6847	+	12.3376i	0.642730	+	0.540001i
$523$			26.1940i			1.14538i	0.819771	+	0.572692i	$0.194101\pi$
$523$			26.1940i			1.14538i	−0.819771	+	0.572692i	$0.805899\pi$
$524$		−	14.2829i		−	0.623949i
$525$	−11.0540	−	42.9683i	−0.482435	−	1.87529i
$526$	3.68466			0.160659
$527$			15.8017i			0.688332i
$528$		−	2.49146i		−	0.108427i
$529$	11.0000			0.478261
$530$	−9.84233	+	1.24573i	−0.427523	+	0.0541111i
$531$	−4.00000			−0.173585
$532$	12.0000			0.520266
$533$	39.3693			1.70527
$534$			22.7299i			0.983618i
$535$	−31.6847	+	4.01029i	−1.36985	+	0.173380i
$536$		−	37.0127i		−	1.59871i
$537$	30.7386			1.32647
$538$		−	15.8017i		−	0.681259i
$539$			4.86319i			0.209472i
$540$	−0.403882	−	3.19101i	−0.0173803	−	0.137319i
$541$		−	38.5316i		−	1.65660i	−0.560284	−	0.828301i	$-0.689308\pi$
$541$		−	38.5316i		−	1.65660i	0.560284	−	0.828301i	$-0.310692\pi$
$542$			14.8290i			0.636962i
$543$	35.0540			1.50431
$544$	−10.0000			−0.428746
$545$	1.59612	+	12.6107i	0.0683702	+	0.540182i
$546$	−39.3693			−1.68485
$547$			7.35465i			0.314462i	0.987562	+	0.157231i	$0.0502568\pi$
$547$			7.35465i			0.314462i	−0.987562	+	0.157231i	$0.949743\pi$
$548$	−13.3693			−0.571109
$549$			6.92820i			0.295689i
$550$	1.21165	+	4.70983i	0.0516648	+	0.200828i
$551$	12.0000	−	14.2829i	0.511217	−	0.608470i
$552$		−	26.6204i		−	1.13304i
$553$	51.3693			2.18445
$554$		−	10.8188i		−	0.459645i
$555$	5.12311	+	40.4768i	0.217464	+	1.71815i
$556$	−19.3693			−0.821442
$557$		−	6.92820i		−	0.293557i	−0.989169	−	0.146779i	$-0.953109\pi$
$557$		−	6.92820i		−	0.293557i	0.989169	−	0.146779i	$-0.0468905\pi$
$558$		−	28.1393i		−	1.19123i
$559$			24.1290i			1.02055i
$560$	7.68466	−	0.972638i	0.324736	−	0.0411015i
$561$		−	4.98293i		−	0.210379i
$562$	13.6847			0.577252
$563$	−15.6847			−0.661030			−0.330515	−	0.943801i	$-0.607222\pi$
$563$	−15.6847			−0.661030			−0.330515	+	0.943801i	$0.607222\pi$
$564$	−29.9309			−1.26032
$565$	−1.50758	−	11.9111i	−0.0634243	−	0.501105i
$566$		−	14.2829i		−	0.600353i
$567$			24.2487i			1.01835i
$568$	6.73863			0.282747
$569$		−	3.89055i		−	0.163100i	−0.996669	−	0.0815502i	$-0.974013\pi$
$569$		−	3.89055i		−	0.163100i	0.996669	−	0.0815502i	$-0.0259871\pi$
$570$	19.6847	−	2.49146i	0.824500	−	0.104356i
$571$	28.0000			1.17176			0.585882	−	0.810397i	$-0.300748\pi$
$571$	28.0000			1.17176			0.585882	+	0.810397i	$0.300748\pi$
$572$	−4.31534			−0.180433
$573$		−	8.87348i		−	0.370695i
$574$	−30.7386			−1.28301
$575$	4.31534	+	16.7743i	0.179962	+	0.699538i
$576$	24.9309			1.03879
$577$	−44.2462			−1.84199			−0.920997	−	0.389570i	$-0.872624\pi$
$577$	−44.2462			−1.84199			−0.920997	+	0.389570i	$0.872624\pi$
$578$	−13.0000			−0.540729
$579$	−21.1231			−0.877846
$580$	−6.52699	+	10.1192i	−0.271018	+	0.420177i
$581$	−36.0000			−1.49353
$582$	−21.1231			−0.875581
$583$	−4.31534			−0.178723
$584$	21.3693			0.884269
$585$	35.0540	−	4.43674i	1.44930	−	0.183437i
$586$	1.36932			0.0565660
$587$			13.4300i			0.554314i	0.960825	+	0.277157i	$0.0893921\pi$
$587$			13.4300i			0.554314i	−0.960825	+	0.277157i	$0.910608\pi$
$588$	−12.8078			−0.528183
$589$	−27.3693			−1.12773
$590$	0.315342	+	2.49146i	0.0129824	+	0.102572i
$591$			27.7128i			1.13995i
$592$	−7.12311			−0.292758
$593$		−	6.38202i		−	0.262078i	−0.991377	−	0.131039i	$-0.958169\pi$
$593$		−	6.38202i		−	0.262078i	0.991377	−	0.131039i	$-0.0418313\pi$
$594$			1.39909i			0.0574053i
$595$	15.3693	−	1.94528i	0.630081	−	0.0797485i
$596$	13.6847			0.560545
$597$	39.3693			1.61128
$598$	15.3693			0.628498
$599$			0.972638i			0.0397409i	0.999803	+	0.0198705i	$0.00632538\pi$
$599$			0.972638i			0.0397409i	−0.999803	+	0.0198705i	$0.993675\pi$
$600$	−37.2116	+	9.57302i	−1.51916	+	0.390817i
$601$			8.87348i			0.361957i	0.983487	+	0.180978i	$0.0579264\pi$
$601$			8.87348i			0.361957i	−0.983487	+	0.180978i	$0.942074\pi$
$602$		−	18.8393i		−	0.767834i
$603$			43.9409i			1.78941i
$604$	−15.3693			−0.625369
$605$	−2.82292	−	22.3034i	−0.114768	−	0.906764i
$606$			17.7470i			0.720921i
$607$	0.177081			0.00718749			0.00359375	−	0.999994i	$-0.498856\pi$
$607$	0.177081			0.00718749			0.00359375	+	0.999994i	$0.498856\pi$
$608$		−	17.3205i		−	0.702439i
$609$	−30.7386	+	36.5863i	−1.24559	+	1.48255i
$610$	4.31534	−	0.546188i	0.174723	−	0.0221145i
$611$		−	51.8418i		−	2.09729i
$612$	7.12311			0.287934
$613$		−	14.4026i		−	0.581715i	−0.956766	−	0.290858i	$-0.906059\pi$
$613$		−	14.4026i		−	0.581715i	0.956766	−	0.290858i	$-0.0939406\pi$
$614$	3.19224			0.128828
$615$	50.4233	−	6.38202i	2.03326	−	0.257348i
$616$	10.1080			0.407261
$617$	13.3693			0.538228			0.269114	−	0.963108i	$-0.413269\pi$
$617$	13.3693			0.538228			0.269114	+	0.963108i	$0.413269\pi$
$618$		−	3.89055i		−	0.156501i
$619$		−	10.9385i		−	0.439655i	−0.975539	−	0.219828i	$-0.929451\pi$
$619$		−	10.9385i		−	0.439655i	0.975539	−	0.219828i	$-0.0705495\pi$
$620$	17.5270	−	2.21837i	0.703901	−	0.0890919i
$621$			4.98293i			0.199958i
$622$		−	0.426450i		−	0.0170991i
$623$	−30.7386			−1.23152
$624$			11.3649i			0.454962i
$625$	21.8963	−	12.0645i	0.875852	−	0.482579i
$626$		−	2.49146i		−	0.0995789i
$627$	8.63068			0.344676
$628$	−22.4924			−0.897545
$629$	−14.2462			−0.568034
$630$	−27.3693	+	3.46410i	−1.09042	+	0.138013i
$631$	−8.00000			−0.318475			−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000			−0.318475			−0.159237	+	0.987240i	$0.550904\pi$
$632$		−	44.4871i		−	1.76960i
$633$			37.9854i			1.50978i
$634$	2.00000			0.0794301
$635$	0.630683	+	4.98293i	0.0250279	+	0.197741i
$636$		−	11.3649i		−	0.450649i
$637$		−	22.1837i		−	0.878950i
$638$	3.36932	−	4.01029i	0.133393	−	0.158769i
$639$	−8.00000			−0.316475
$640$	0.842329	+	6.65511i	0.0332960	+	0.263066i
$641$		−	4.98293i		−	0.196814i	−0.995146	−	0.0984069i	$-0.968625\pi$
$641$		−	4.98293i		−	0.196814i	0.995146	−	0.0984069i	$-0.0313747\pi$
$642$			36.5863i			1.44395i
$643$			35.0675i			1.38293i	0.722412	+	0.691463i	$0.243033\pi$
$643$			35.0675i			1.38293i	−0.722412	+	0.691463i	$0.756967\pi$
$644$	12.0000			0.472866
$645$	3.91146	+	30.9038i	0.154014	+	1.21684i
$646$			6.92820i			0.272587i
$647$		−	48.9239i		−	1.92340i	−0.274111	−	0.961698i	$-0.588384\pi$
$647$		−	48.9239i		−	1.92340i	0.274111	−	0.961698i	$-0.411616\pi$
$648$	21.0000			0.824958
$649$			1.09238i			0.0428795i
$650$	−5.52699	−	21.4842i	−0.216786	−	0.842678i
$651$	70.1080			2.74775
$652$	5.43845			0.212986
$653$	−28.7386			−1.12463			−0.562315	−	0.826923i	$-0.690089\pi$
$653$	−28.7386			−1.12463			−0.562315	+	0.826923i	$0.690089\pi$
$654$	14.5616			0.569402
$655$	31.6847	−	4.01029i	1.23802	−	0.156695i
$656$			8.87348i			0.346451i
$657$	−25.3693			−0.989751
$658$			40.4768i			1.57795i
$659$			35.6137i			1.38731i	0.720307	+	0.693655i	$0.244001\pi$
$659$			35.6137i			1.38731i	−0.720307	+	0.693655i	$0.755999\pi$
$660$	−5.52699	+	0.699544i	−0.215138	+	0.0272297i
$661$	−24.7386			−0.962221			−0.481111	−	0.876660i	$-0.659766\pi$
$661$	−24.7386			−0.962221			−0.481111	+	0.876660i	$0.659766\pi$
$662$		−	5.95557i		−	0.231470i
$663$			22.7299i			0.882756i
$664$			31.1769i			1.20990i
$665$	3.36932	+	26.6204i	0.130657	+	1.03230i
$666$	25.3693			0.983041
$667$	12.0000	−	14.2829i	0.464642	−	0.553034i
$668$			8.44703i			0.326825i
$669$			31.6034i			1.22186i
$670$	27.3693	−	3.46410i	1.05737	−	0.133830i
$671$	1.89205			0.0730418
$672$			44.3674i			1.71151i
$673$		−	29.1119i		−	1.12218i	−0.827754	−	0.561091i	$-0.810382\pi$
$673$		−	29.1119i		−	1.12218i	0.827754	−	0.561091i	$-0.189618\pi$
$674$	3.75379			0.144591
$675$	6.96543	−	1.79192i	0.268100	−	0.0689710i
$676$	6.68466			0.257102
$677$	−13.3693			−0.513825			−0.256912	−	0.966435i	$-0.582705\pi$
$677$	−13.3693			−0.513825			−0.256912	+	0.966435i	$0.582705\pi$
$678$	−13.7538			−0.528211
$679$		−	28.5657i		−	1.09625i
$680$	−1.68466	−	13.3102i	−0.0646037	−	0.510424i
$681$		−	31.6034i		−	1.21104i
$682$	−7.68466			−0.294261
$683$			16.2281i			0.620952i	0.950581	+	0.310476i	$0.100488\pi$
$683$			16.2281i			0.620952i	−0.950581	+	0.310476i	$0.899512\pi$
$684$			12.3376i			0.471739i
$685$	−3.75379	−	29.6581i	−0.143425	−	1.13318i
$686$		−	6.92820i		−	0.264520i
$687$		−	40.4768i		−	1.54429i
$688$	−5.43845			−0.207339
$689$	19.6847			0.749926
$690$	19.6847	−	2.49146i	0.749382	−	0.0948484i
$691$	18.7386			0.712851			0.356426	−	0.934324i	$-0.383995\pi$
$691$	18.7386			0.712851			0.356426	+	0.934324i	$0.383995\pi$
$692$		−	10.8188i		−	0.411267i
$693$	−12.0000			−0.455842
$694$			26.1940i			0.994310i
$695$	−5.43845	−	42.9683i	−0.206292	−	1.62988i
$696$	31.6847	+	26.6204i	1.20100	+	1.00905i
$697$			17.7470i			0.672214i
$698$	10.3153			0.390441
$699$			6.38202i			0.241390i
$700$	−4.31534	−	16.7743i	−0.163105	−	0.634010i
$701$	−50.8078			−1.91898			−0.959491	−	0.281738i	$-0.909089\pi$
$701$	−50.8078			−1.91898			−0.959491	+	0.281738i	$0.909089\pi$
$702$		−	6.38202i		−	0.240874i
$703$		−	24.6752i		−	0.930641i
$704$		−	6.80847i		−	0.256604i
$705$	−8.40388	−	66.3977i	−0.316509	−	2.50068i
$706$		−	17.7470i		−	0.667916i
$707$	−24.0000			−0.902613
$708$	−2.87689			−0.108120
$709$	−6.31534			−0.237178			−0.118589	−	0.992943i	$-0.537837\pi$
$709$	−6.31534			−0.237178			−0.118589	+	0.992943i	$0.537837\pi$
$710$	0.630683	+	4.98293i	0.0236691	+	0.187006i
$711$			52.8144i			1.98070i
$712$			26.6204i			0.997643i
$713$	−27.3693			−1.02499
$714$		−	17.7470i		−	0.664163i
$715$	−1.21165	−	9.57302i	−0.0453130	−	0.358011i
$716$	12.0000			0.448461
$717$	−33.6155			−1.25539
$718$		−	21.7572i		−	0.811973i
$719$	26.2462			0.978819			0.489409	−	0.872054i	$-0.337212\pi$
$719$	26.2462			0.978819			0.489409	+	0.872054i	$0.337212\pi$
$720$	1.00000	+	7.90084i	0.0372678	+	0.294447i
$721$	5.26137			0.195944
$722$	7.00000			0.260513
$723$	4.31534			0.160489
$724$	13.6847			0.508586
$725$	−24.2808	−	11.6380i	−0.901765	−	0.432226i
$726$	−25.7538			−0.955813
$727$	−4.49242			−0.166615			−0.0833074	−	0.996524i	$-0.526548\pi$
$727$	−4.49242			−0.166615			−0.0833074	+	0.996524i	$0.526548\pi$
$728$	−46.1080			−1.70887
$729$	−35.9848			−1.33277
$730$	2.00000	+	15.8017i	0.0740233	+	0.584847i
$731$	−10.8769			−0.402296
$732$			4.98293i			0.184174i
$733$	−16.8769			−0.623362			−0.311681	−	0.950187i	$-0.600892\pi$
$733$	−16.8769			−0.623362			−0.311681	+	0.950187i	$0.600892\pi$
$734$	−28.4924			−1.05167
$735$	−3.59612	−	28.4124i	−0.132645	−	1.04801i
$736$		−	17.3205i		−	0.638442i
$737$	12.0000			0.442026
$738$		−	31.6034i		−	1.16334i
$739$		−	27.5931i		−	1.01503i	−0.861644	−	0.507514i	$-0.830565\pi$
$739$		−	27.5931i		−	1.01503i	0.861644	−	0.507514i	$-0.169435\pi$
$740$	2.00000	+	15.8017i	0.0735215	+	0.580881i
$741$	−39.3693			−1.44627
$742$	−15.3693			−0.564225
$743$	−32.0000			−1.17397			−0.586983	−	0.809599i	$-0.699684\pi$
$743$	−32.0000			−1.17397			−0.586983	+	0.809599i	$0.699684\pi$
$744$		−	60.7153i		−	2.22593i
$745$	3.84233	+	30.3576i	0.140772	+	1.11222i
$746$			36.0401i			1.31952i
$747$		−	37.0127i		−	1.35423i
$748$		−	1.94528i		−	0.0711263i
$749$	−49.4773			−1.80786
$750$	−10.5616	−	26.6204i	−0.385653	−	0.972041i
$751$		−	6.50175i		−	0.237252i	−0.992939	−	0.118626i	$-0.962151\pi$
$751$		−	6.50175i		−	0.237252i	0.992939	−	0.118626i	$-0.0378490\pi$
$752$	11.6847			0.426096
$753$		−	42.9683i		−	1.56585i
$754$	−15.3693	+	18.2931i	−0.559718	+	0.666197i
$755$	−4.31534	−	34.0948i	−0.157051	−	1.24084i
$756$		−	4.98293i		−	0.181227i
$757$	15.7538			0.572581			0.286291	−	0.958143i	$-0.407578\pi$
$757$	15.7538			0.572581			0.286291	+	0.958143i	$0.407578\pi$
$758$			0.426450i			0.0154894i
$759$	8.63068			0.313274
$760$	23.0540	−	2.91791i	0.836256	−	0.105844i
$761$	−1.50758			−0.0546496			−0.0273248	−	0.999627i	$-0.508699\pi$
$761$	−1.50758			−0.0546496			−0.0273248	+	0.999627i	$0.508699\pi$
$762$	5.75379			0.208438
$763$			19.6922i			0.712907i
$764$		−	3.46410i		−	0.125327i
$765$	2.00000	+	15.8017i	0.0723102	+	0.571311i
$766$		−	17.3205i		−	0.625815i
$767$		−	4.98293i		−	0.179923i
$768$	43.5464			1.57135
$769$		−	32.6957i		−	1.17904i	−0.807754	−	0.589519i	$-0.799317\pi$
$769$		−	32.6957i		−	1.17904i	0.807754	−	0.589519i	$-0.200683\pi$
$770$	0.946025	+	7.47439i	0.0340924	+	0.269358i
$771$		−	29.1119i		−	1.04844i
$772$	−8.24621			−0.296788
$773$	26.0000			0.935155			0.467578	−	0.883952i	$-0.345127\pi$
$773$	26.0000			0.935155			0.467578	+	0.883952i	$0.345127\pi$
$774$	19.3693			0.696216
$775$	9.84233	+	38.2585i	0.353547	+	1.37428i
$776$	−24.7386			−0.888065
$777$			63.2067i			2.26753i
$778$			10.8188i			0.387871i
$779$	−30.7386			−1.10133
$780$	25.2116	−	3.19101i	0.902722	−	0.114256i
$781$			2.18475i			0.0781765i
$782$			6.92820i			0.247752i
$783$	−5.93087	−	4.98293i	−0.211952	−	0.178075i
$784$	5.00000			0.178571
$785$	−6.31534	−	49.8965i	−0.225404	−	1.78088i
$786$		−	36.5863i		−	1.30499i
$787$			12.3376i			0.439787i	0.975524	+	0.219894i	$0.0705710\pi$
$787$			12.3376i			0.439787i	−0.975524	+	0.219894i	$0.929429\pi$
$788$			10.8188i			0.385402i
$789$	−9.43845			−0.336018
$790$	32.8963	−	4.16365i	1.17040	−	0.148136i
$791$		−	18.5999i		−	0.661335i
$792$			10.3923i			0.369274i
$793$	−8.63068			−0.306485
$794$		−	0.546188i		−	0.0193835i
$795$	25.2116	−	3.19101i	0.894165	−	0.113173i
$796$	15.3693			0.544751
$797$	34.0000			1.20434			0.602171	−	0.798367i	$-0.294303\pi$
$797$	34.0000			1.20434			0.602171	+	0.798367i	$0.294303\pi$
$798$	30.7386			1.08814
$799$	23.3693			0.826747
$800$	−24.2116	+	6.22866i	−0.856011	+	0.220216i
$801$		−	31.6034i		−	1.11665i
$802$	15.9309			0.562539
$803$			6.92820i			0.244491i
$804$			31.6034i			1.11456i
$805$	3.36932	+	26.6204i	0.118753	+	0.938247i
$806$	35.0540			1.23472
$807$			40.4768i			1.42485i
$808$			20.7846i			0.731200i
$809$			31.6034i			1.11112i	0.831478	+	0.555558i	$0.187495\pi$
$809$			31.6034i			1.11112i	−0.831478	+	0.555558i	$0.812505\pi$
$810$	1.96543	+	15.5286i	0.0690583	+	0.545619i
$811$	4.63068			0.162605			0.0813026	−	0.996689i	$-0.474092\pi$
$811$	4.63068			0.162605			0.0813026	+	0.996689i	$0.474092\pi$
$812$	−12.0000	+	14.2829i	−0.421117	+	0.501230i
$813$		−	37.9854i		−	1.33221i
$814$		−	6.92820i		−	0.242833i
$815$	1.52699	+	12.0645i	0.0534880	+	0.422601i
$816$	−5.12311			−0.179345
$817$		−	18.8393i		−	0.659105i
$818$		−	3.89055i		−	0.136030i
$819$	54.7386			1.91272
$820$	19.6847	−	2.49146i	0.687418	−	0.0870057i
$821$	47.7926			1.66797			0.833987	−	0.551784i	$-0.186053\pi$
$821$	47.7926			1.66797			0.833987	+	0.551784i	$0.186053\pi$
$822$	−34.2462			−1.19447
$823$	−21.7538			−0.758289			−0.379145	−	0.925337i	$-0.623782\pi$
$823$	−21.7538			−0.758289			−0.379145	+	0.925337i	$0.623782\pi$
$824$		−	4.55648i		−	0.158732i
$825$	−3.10370	−	12.0645i	−0.108057	−	0.420032i
$826$			3.89055i			0.135370i
$827$	−15.0540			−0.523478			−0.261739	−	0.965139i	$-0.584296\pi$
$827$	−15.0540			−0.523478			−0.261739	+	0.965139i	$0.584296\pi$
$828$			12.3376i			0.428761i
$829$		−	23.5828i		−	0.819064i	−0.912296	−	0.409532i	$-0.865692\pi$
$829$		−	23.5828i		−	0.819064i	0.912296	−	0.409532i	$-0.134308\pi$
$830$	−23.0540	+	2.91791i	−0.800215	+	0.101282i
$831$			27.7128i			0.961347i
$832$			31.0572i			1.07671i
$833$	10.0000			0.346479
$834$	−49.6155			−1.71805
$835$	−18.7386	+	2.37173i	−0.648477	+	0.0820770i
$836$	3.36932			0.116530
$837$			11.3649i			0.392830i
$838$	14.2462			0.492127
$839$			18.7196i			0.646272i	0.946352	+	0.323136i	$0.104737\pi$
$839$			18.7196i			0.646272i	−0.946352	+	0.323136i	$0.895263\pi$
$840$	−59.0540	+	7.47439i	−2.03756	+	0.257891i
$841$	5.00000	+	28.5657i	0.172414	+	0.985025i
$842$		−	37.4392i		−	1.29024i
$843$	−35.0540			−1.20732
$844$			14.8290i			0.510437i
$845$	1.87689	+	14.8290i	0.0645671	+	0.510135i
$846$	−41.6155			−1.43077
$847$		−	34.8280i		−	1.19670i
$848$			4.43674i			0.152358i
$849$			36.5863i			1.25564i
$850$	9.68466	−	2.49146i	0.332181	−	0.0854565i
$851$		−	24.6752i		−	0.845854i
$852$	−5.75379			−0.197122
$853$	37.8617			1.29636			0.648181	−	0.761487i	$-0.275530\pi$
$853$	37.8617			1.29636			0.648181	+	0.761487i	$0.275530\pi$
$854$	6.73863			0.230591
$855$	−27.3693	+	3.46410i	−0.936011	+	0.118470i
$856$			42.8486i			1.46453i
$857$			20.2384i			0.691331i	0.938358	+	0.345666i	$0.112347\pi$
$857$			20.2384i			0.691331i	−0.938358	+	0.345666i	$0.887653\pi$
$858$	−11.0540			−0.377376
$859$			52.2682i			1.78337i	0.452657	+	0.891685i	$0.350476\pi$
$859$			52.2682i			1.78337i	−0.452657	+	0.891685i	$0.649524\pi$
$860$	1.52699	+	12.0645i	0.0520698	+	0.411396i
$861$	78.7386			2.68341
$862$	8.63068			0.293962
$863$			15.3752i			0.523379i	0.965152	+	0.261689i	$0.0842796\pi$
$863$			15.3752i			0.523379i	−0.965152	+	0.261689i	$0.915720\pi$
$864$	−7.19224			−0.244685
$865$	24.0000	−	3.03765i	0.816024	−	0.103283i
$866$	16.8769			0.573500
$867$	33.3002			1.13093
$868$	27.3693			0.928975
$869$	14.4233			0.489277
$870$	−16.7192	+	25.9209i	−0.566835	+	0.878801i
$871$	−54.7386			−1.85475
$872$	17.0540			0.577520
$873$	29.3693			0.994001
$874$	−12.0000			−0.405906
$875$	36.0000	−	14.2829i	1.21702	−	0.482849i
$876$	−18.2462			−0.616482
$877$		−	41.0230i		−	1.38525i	−0.721298	−	0.692625i	$-0.756454\pi$
$877$		−	41.0230i		−	1.38525i	0.721298	−	0.692625i	$-0.243546\pi$
$878$	15.3693			0.518689
$879$	−3.50758			−0.118308
$880$	2.15767	−	0.273094i	0.0727351	−	0.00920599i
$881$			45.4598i			1.53158i	0.643092	+	0.765789i	$0.277651\pi$
$881$			45.4598i			1.53158i	−0.643092	+	0.765789i	$0.722349\pi$
$882$	−17.8078			−0.599619
$883$		−	35.9204i		−	1.20882i	−0.796675	−	0.604408i	$-0.793410\pi$
$883$		−	35.9204i		−	1.20882i	0.796675	−	0.604408i	$-0.206590\pi$
$884$			8.87348i			0.298447i
$885$	−0.807764	−	6.38202i	−0.0271527	−	0.214529i
$886$	−4.00000			−0.134383
$887$	−3.68466			−0.123719			−0.0618594	−	0.998085i	$-0.519703\pi$
$887$	−3.68466			−0.123719			−0.0618594	+	0.998085i	$0.519703\pi$
$888$	54.7386			1.83691
$889$			7.78110i			0.260970i
$890$	−19.6847	+	2.49146i	−0.659831	+	0.0835141i
$891$			6.80847i			0.228092i
$892$			12.3376i			0.413093i
$893$			40.4768i			1.35451i
$894$	35.0540			1.17238
$895$	3.36932	+	26.6204i	0.112624	+	0.889823i
$896$			10.3923i			0.347183i
$897$	−39.3693			−1.31450
$898$		−	17.7470i		−	0.592224i
$899$	27.3693	−	32.5760i	0.912818	−	1.08647i
$900$	17.2462	−	4.43674i	0.574874	−	0.147891i
$901$			8.87348i			0.295618i
$902$	−8.63068			−0.287370
$903$			48.2579i			1.60592i
$904$	−16.1080			−0.535742
$905$	3.84233	+	30.3576i	0.127723	+	1.00912i
$906$	−39.3693			−1.30796
$907$	−40.4924			−1.34453			−0.672264	−	0.740311i	$-0.734678\pi$
$907$	−40.4924			−1.34453			−0.672264	+	0.740311i	$0.734678\pi$
$908$		−	12.3376i		−	0.409437i
$909$		−	24.6752i		−	0.818423i
$910$	−4.31534	−	34.0948i	−0.143052	−	1.13023i
$911$			9.84612i			0.326216i	0.986608	+	0.163108i	$0.0521520\pi$
$911$			9.84612i			0.326216i	−0.986608	+	0.163108i	$0.947848\pi$
$912$		−	8.87348i		−	0.293830i
$913$	−10.1080			−0.334524
$914$		−	3.89055i		−	0.128688i
$915$	−11.0540	+	1.39909i	−0.365433	+	0.0462524i
$916$		−	15.8017i		−	0.522102i
$917$	49.4773			1.63388
$918$	2.87689			0.0949517
$919$	−24.0000			−0.791687			−0.395843	−	0.918318i	$-0.629548\pi$
$919$	−24.0000			−0.791687			−0.395843	+	0.918318i	$0.629548\pi$
$920$	23.0540	−	2.91791i	0.760067	−	0.0962008i
$921$	−8.17708			−0.269444
$922$			34.6410i			1.14084i
$923$		−	9.96585i		−	0.328030i
$924$	−8.63068			−0.283929
$925$	−34.4924	+	8.87348i	−1.13410	+	0.291758i
$926$		−	7.35465i		−	0.241689i
$927$			5.40938i			0.177667i
$928$	20.6155	+	17.3205i	0.676738	+	0.568574i
$929$	48.7386			1.59906			0.799531	−	0.600624i	$-0.205081\pi$
$929$	48.7386			1.59906			0.799531	+	0.600624i	$0.205081\pi$
$930$	44.8963	−	5.68247i	1.47221	−	0.186336i
$931$			17.3205i			0.567657i
$932$			2.49146i			0.0816106i
$933$			1.09238i			0.0357628i
$934$	−8.31534			−0.272086
$935$	4.31534	−	0.546188i	0.141127	−	0.0178622i
$936$		−	47.4050i		−	1.54948i
$937$			31.6034i			1.03244i	0.856457	+	0.516218i	$0.172661\pi$
$937$			31.6034i			1.03244i	−0.856457	+	0.516218i	$0.827339\pi$
$938$	42.7386			1.39547
$939$			6.38202i			0.208269i
$940$	−3.28078	−	25.9209i	−0.107007	−	0.845446i
$941$	32.4233			1.05697			0.528485	−	0.848943i	$-0.322760\pi$
$941$	32.4233			1.05697			0.528485	+	0.848943i	$0.322760\pi$
$942$	−57.6155			−1.87722
$943$	−30.7386			−1.00099
$944$	1.12311			0.0365540
$945$	11.0540	−	1.39909i	0.359586	−	0.0455123i
$946$		−	5.28964i		−	0.171981i
$947$	23.6847			0.769648			0.384824	−	0.922990i	$-0.374262\pi$
$947$	23.6847			0.769648			0.384824	+	0.922990i	$0.374262\pi$
$948$			37.9854i			1.23371i
$949$		−	31.6034i		−	1.02589i
$950$	4.31534	+	16.7743i	0.140008	+	0.544231i
$951$	−5.12311			−0.166128
$952$		−	20.7846i		−	0.673633i
$953$		−	10.2726i		−	0.332761i	−0.986062	−	0.166381i	$-0.946792\pi$
$953$		−	10.2726i		−	0.332761i	0.986062	−	0.166381i	$-0.0532080\pi$
$954$		−	15.8017i		−	0.511598i
$955$	7.68466	−	0.972638i	0.248670	−	0.0314738i
$956$	−13.1231			−0.424432
$957$	−8.63068	+	10.2726i	−0.278990	+	0.332065i
$958$		−	2.91791i		−	0.0942735i
$959$		−	46.3127i		−	1.49551i
$960$	5.03457	+	39.7773i	0.162490	+	1.28381i
$961$	−31.4233			−1.01365
$962$			31.6034i			1.01893i
$963$		−	50.8691i		−	1.63924i
$964$	1.68466			0.0542592
$965$	−2.31534	−	18.2931i	−0.0745335	−	0.588877i
$966$	30.7386			0.988999
$967$	45.9309			1.47704			0.738519	−	0.674233i	$-0.235526\pi$
$967$	45.9309			1.47704			0.738519	+	0.674233i	$0.235526\pi$
$968$	−30.1619			−0.969441
$969$		−	17.7470i		−	0.570114i
$970$	−2.31534	−	18.2931i	−0.0743411	−	0.587358i
$971$			45.8862i			1.47256i	0.676678	+	0.736279i	$0.263419\pi$
$971$			45.8862i			1.47256i	−0.676678	+	0.736279i	$0.736581\pi$
$972$	−22.2462			−0.713548
$973$		−	67.0973i		−	2.15104i
$974$			32.0298i			1.02630i
$975$	14.1577	+	55.0328i	0.453408	+	1.76246i
$976$		−	1.94528i		−	0.0622668i
$977$		−	6.38202i		−	0.204179i	−0.994775	−	0.102089i	$-0.967447\pi$
$977$		−	6.38202i		−	0.204179i	0.994775	−	0.102089i	$-0.0325528\pi$
$978$	13.9309			0.445460
$979$	−8.63068			−0.275838
$980$	−1.40388	−	11.0918i	−0.0448454	−	0.354316i
$981$	−20.2462			−0.646412
$982$			29.5384i			0.942607i
$983$	27.0540			0.862888			0.431444	−	0.902140i	$-0.358004\pi$
$983$	27.0540			0.862888			0.431444	+	0.902140i	$0.358004\pi$
$984$		−	68.1897i		−	2.17381i
$985$	−24.0000	+	3.03765i	−0.764704	+	0.0967876i
$986$	−8.24621	−	6.92820i	−0.262613	−	0.220639i
$987$		−	103.684i		−	3.30028i
$988$	−15.3693			−0.488963
$989$		−	18.8393i		−	0.599056i
$990$	−7.68466	+	0.972638i	−0.244234	+	0.0309125i
$991$	−30.7386			−0.976445			−0.488222	−	0.872719i	$-0.662355\pi$
$991$	−30.7386			−0.976445			−0.488222	+	0.872719i	$0.662355\pi$
$992$		−	39.5042i		−	1.25426i
$993$			15.2555i			0.484118i
$994$			7.78110i			0.246802i
$995$	4.31534	+	34.0948i	0.136806	+	1.08088i
$996$		−	26.6204i		−	0.843501i
$997$	59.6155			1.88804			0.944021	−	0.329884i	$-0.107010\pi$
$997$	59.6155			1.88804			0.944021	+	0.329884i	$0.107010\pi$
$998$	−4.63068			−0.146582
$999$	−10.2462			−0.324176

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	145.2.d.c.144.1	yes	4
3.2	odd	2		1305.2.f.e.289.4		4
4.3	odd	2		2320.2.j.c.289.3		4
5.2	odd	4		725.2.c.f.376.8		8
5.3	odd	4		725.2.c.f.376.1		8
5.4	even	2		145.2.d.a.144.4	yes	4
15.14	odd	2		1305.2.f.i.289.3		4
20.19	odd	2		2320.2.j.a.289.2		4
29.28	even	2		145.2.d.a.144.3	✓	4
87.86	odd	2		1305.2.f.i.289.4		4
116.115	odd	2		2320.2.j.a.289.1		4
145.28	odd	4		725.2.c.f.376.7		8
145.57	odd	4		725.2.c.f.376.2		8
145.144	even	2	inner	145.2.d.c.144.2	yes	4
435.434	odd	2		1305.2.f.e.289.3		4
580.579	odd	2		2320.2.j.c.289.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.2.d.a.144.3	✓	4	29.28	even	2
145.2.d.a.144.4	yes	4	5.4	even	2
145.2.d.c.144.1	yes	4	1.1	even	1	trivial
145.2.d.c.144.2	yes	4	145.144	even	2	inner
725.2.c.f.376.1		8	5.3	odd	4
725.2.c.f.376.2		8	145.57	odd	4
725.2.c.f.376.7		8	145.28	odd	4
725.2.c.f.376.8		8	5.2	odd	4
1305.2.f.e.289.3		4	435.434	odd	2
1305.2.f.e.289.4		4	3.2	odd	2
1305.2.f.i.289.3		4	15.14	odd	2
1305.2.f.i.289.4		4	87.86	odd	2
2320.2.j.a.289.1		4	116.115	odd	2
2320.2.j.a.289.2		4	20.19	odd	2
2320.2.j.c.289.3		4	4.3	odd	2
2320.2.j.c.289.4		4	580.579	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 145 = 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	145.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.56155 q^{3} -1.00000 q^{4} +(-0.280776 - 2.21837i) q^{5} -2.56155 q^{6} -3.46410i q^{7} -3.00000 q^{8} +3.56155 q^{9} +(-0.280776 - 2.21837i) q^{10} -0.972638i q^{11} +2.56155 q^{12} +4.43674i q^{13} -3.46410i q^{14} +(0.719224 + 5.68247i) q^{15} -1.00000 q^{16} -2.00000 q^{17} +3.56155 q^{18} -3.46410i q^{19} +(0.280776 + 2.21837i) q^{20} +8.87348i q^{21} -0.972638i q^{22} -3.46410i q^{23} +7.68466 q^{24} +(-4.84233 + 1.24573i) q^{25} +4.43674i q^{26} -1.43845 q^{27} +3.46410i q^{28} +(4.12311 + 3.46410i) q^{29} +(0.719224 + 5.68247i) q^{30} -7.90084i q^{31} +5.00000 q^{32} +2.49146i q^{33} -2.00000 q^{34} +(-7.68466 + 0.972638i) q^{35} -3.56155 q^{36} +7.12311 q^{37} -3.46410i q^{38} -11.3649i q^{39} +(0.842329 + 6.65511i) q^{40} -8.87348i q^{41} +8.87348i q^{42} +5.43845 q^{43} +0.972638i q^{44} +(-1.00000 - 7.90084i) q^{45} -3.46410i q^{46} -11.6847 q^{47} +2.56155 q^{48} -5.00000 q^{49} +(-4.84233 + 1.24573i) q^{50} +5.12311 q^{51} -4.43674i q^{52} -4.43674i q^{53} -1.43845 q^{54} +(-2.15767 + 0.273094i) q^{55} +10.3923i q^{56} +8.87348i q^{57} +(4.12311 + 3.46410i) q^{58} -1.12311 q^{59} +(-0.719224 - 5.68247i) q^{60} +1.94528i q^{61} -7.90084i q^{62} -12.3376i q^{63} +7.00000 q^{64} +(9.84233 - 1.24573i) q^{65} +2.49146i q^{66} +12.3376i q^{67} +2.00000 q^{68} +8.87348i q^{69} +(-7.68466 + 0.972638i) q^{70} -2.24621 q^{71} -10.6847 q^{72} -7.12311 q^{73} +7.12311 q^{74} +(12.4039 - 3.19101i) q^{75} +3.46410i q^{76} -3.36932 q^{77} -11.3649i q^{78} +14.8290i q^{79} +(0.280776 + 2.21837i) q^{80} -7.00000 q^{81} -8.87348i q^{82} -10.3923i q^{83} -8.87348i q^{84} +(0.561553 + 4.43674i) q^{85} +5.43845 q^{86} +(-10.5616 - 8.87348i) q^{87} +2.91791i q^{88} -8.87348i q^{89} +(-1.00000 - 7.90084i) q^{90} +15.3693 q^{91} +3.46410i q^{92} +20.2384i q^{93} -11.6847 q^{94} +(-7.68466 + 0.972638i) q^{95} -12.8078 q^{96} +8.24621 q^{97} -5.00000 q^{98} -3.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 2 q^{3} - 4 q^{4} + 3 q^{5} - 2 q^{6} - 12 q^{8} + 6 q^{9} + 3 q^{10} + 2 q^{12} + 7 q^{15} - 4 q^{16} - 8 q^{17} + 6 q^{18} - 3 q^{20} + 6 q^{24} - 7 q^{25} - 14 q^{27} + 7 q^{30} + 20 q^{32}+ \cdots - 20 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 - 2 * q^3 - 4 * q^4 + 3 * q^5 - 2 * q^6 - 12 * q^8 + 6 * q^9 + 3 * q^10 + 2 * q^12 + 7 * q^15 - 4 * q^16 - 8 * q^17 + 6 * q^18 - 3 * q^20 + 6 * q^24 - 7 * q^25 - 14 * q^27 + 7 * q^30 + 20 * q^32 - 8 * q^34 - 6 * q^35 - 6 * q^36 + 12 * q^37 - 9 * q^40 + 30 * q^43 - 4 * q^45 - 22 * q^47 + 2 * q^48 - 20 * q^49 - 7 * q^50 + 4 * q^51 - 14 * q^54 - 21 * q^55 + 12 * q^59 - 7 * q^60 + 28 * q^64 + 27 * q^65 + 8 * q^68 - 6 * q^70 + 24 * q^71 - 18 * q^72 - 12 * q^73 + 12 * q^74 + 29 * q^75 + 36 * q^77 - 3 * q^80 - 28 * q^81 - 6 * q^85 + 30 * q^86 - 34 * q^87 - 4 * q^90 + 12 * q^91 - 22 * q^94 - 6 * q^95 - 10 * q^96 - 20 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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