LMFDB - Embedded newform 51.3.g.a.8.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [51,3,Mod(2,51)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(51, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([4, 7])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("51.2"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 51 = 3 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	51.g (of order $8$, degree $4$, 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:	$1.38964934824$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			8.1
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	51.8
Dual form			51.3.g.a.32.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.292893 - 0.292893i) q^{2} +3.00000 q^{3} -3.82843i q^{4} +(-0.828427 + 2.00000i) q^{5} +(-0.878680 - 0.878680i) q^{6} +(1.82843 - 0.757359i) q^{7} +(-2.29289 + 2.29289i) q^{8} +9.00000 q^{9} +(0.828427 - 0.343146i) q^{10} +(-4.70711 + 1.94975i) q^{11} -11.4853i q^{12} +9.17157i q^{13} +(-0.757359 - 0.313708i) q^{14} +(-2.48528 + 6.00000i) q^{15} -13.9706 q^{16} +(-16.6066 + 3.63604i) q^{17} +(-2.63604 - 2.63604i) q^{18} +(-7.17157 + 7.17157i) q^{19} +(7.65685 + 3.17157i) q^{20} +(5.48528 - 2.27208i) q^{21} +(1.94975 + 0.807612i) q^{22} +(-19.7279 + 8.17157i) q^{23} +(-6.87868 + 6.87868i) q^{24} +(14.3640 + 14.3640i) q^{25} +(2.68629 - 2.68629i) q^{26} +27.0000 q^{27} +(-2.89949 - 7.00000i) q^{28} +(18.3848 - 44.3848i) q^{29} +(2.48528 - 1.02944i) q^{30} +(15.7279 - 37.9706i) q^{31} +(13.2635 + 13.2635i) q^{32} +(-14.1213 + 5.84924i) q^{33} +(5.92893 + 3.79899i) q^{34} +4.28427i q^{35} -34.4558i q^{36} +(3.17157 - 7.65685i) q^{37} +4.20101 q^{38} +27.5147i q^{39} +(-2.68629 - 6.48528i) q^{40} +(11.7782 + 28.4350i) q^{41} +(-2.27208 - 0.941125i) q^{42} +(-8.55635 - 8.55635i) q^{43} +(7.46447 + 18.0208i) q^{44} +(-7.45584 + 18.0000i) q^{45} +(8.17157 + 3.38478i) q^{46} +59.5391 q^{47} -41.9117 q^{48} +(-31.8787 + 31.8787i) q^{49} -8.41421i q^{50} +(-49.8198 + 10.9081i) q^{51} +35.1127 q^{52} +(-53.3553 - 53.3553i) q^{53} +(-7.90812 - 7.90812i) q^{54} -11.0294i q^{55} +(-2.45584 + 5.92893i) q^{56} +(-21.5147 + 21.5147i) q^{57} +(-18.3848 + 7.61522i) q^{58} +(79.2426 - 79.2426i) q^{59} +(22.9706 + 9.51472i) q^{60} +(-63.8995 + 26.4680i) q^{61} +(-15.7279 + 6.51472i) q^{62} +(16.4558 - 6.81623i) q^{63} +48.1127i q^{64} +(-18.3431 - 7.59798i) q^{65} +(5.84924 + 2.42284i) q^{66} +67.8995 q^{67} +(13.9203 + 63.5772i) q^{68} +(-59.1838 + 24.5147i) q^{69} +(1.25483 - 1.25483i) q^{70} +(-82.4975 - 34.1716i) q^{71} +(-20.6360 + 20.6360i) q^{72} +(-48.1630 - 19.9497i) q^{73} +(-3.17157 + 1.31371i) q^{74} +(43.0919 + 43.0919i) q^{75} +(27.4558 + 27.4558i) q^{76} +(-7.12994 + 7.12994i) q^{77} +(8.05887 - 8.05887i) q^{78} +(-32.8406 - 79.2843i) q^{79} +(11.5736 - 27.9411i) q^{80} +81.0000 q^{81} +(4.87868 - 11.7782i) q^{82} +(68.7817 + 68.7817i) q^{83} +(-8.69848 - 21.0000i) q^{84} +(6.48528 - 36.2254i) q^{85} +5.01219i q^{86} +(55.1543 - 133.154i) q^{87} +(6.32233 - 15.2635i) q^{88} -87.8406 q^{89} +(7.45584 - 3.08831i) q^{90} +(6.94618 + 16.7696i) q^{91} +(31.2843 + 75.5269i) q^{92} +(47.1838 - 113.912i) q^{93} +(-17.4386 - 17.4386i) q^{94} +(-8.40202 - 20.2843i) q^{95} +(39.7904 + 39.7904i) q^{96} +(122.418 + 50.7071i) q^{97} +18.6741 q^{98} +(-42.3640 + 17.5477i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 12 q^{3} + 8 q^{5} - 12 q^{6} - 4 q^{7} - 12 q^{8} + 36 q^{9} - 8 q^{10} - 16 q^{11} - 20 q^{14} + 24 q^{15} + 12 q^{16} - 24 q^{17} - 36 q^{18} - 40 q^{19} + 8 q^{20} - 12 q^{21} - 12 q^{22}+ \cdots - 144 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 + 12 * q^3 + 8 * q^5 - 12 * q^6 - 4 * q^7 - 12 * q^8 + 36 * q^9 - 8 * q^10 - 16 * q^11 - 20 * q^14 + 24 * q^15 + 12 * q^16 - 24 * q^17 - 36 * q^18 - 40 * q^19 + 8 * q^20 - 12 * q^21 - 12 * q^22 - 28 * q^23 - 36 * q^24 + 32 * q^25 + 56 * q^26 + 108 * q^27 + 28 * q^28 - 24 * q^30 + 12 * q^31 - 12 * q^32 - 48 * q^33 + 52 * q^34 + 24 * q^37 + 96 * q^38 - 56 * q^40 + 16 * q^41 - 60 * q^42 + 28 * q^43 + 44 * q^44 + 72 * q^45 + 44 * q^46 - 56 * q^47 + 36 * q^48 - 136 * q^49 - 72 * q^51 + 16 * q^52 - 72 * q^53 - 108 * q^54 + 92 * q^56 - 120 * q^57 + 300 * q^59 + 24 * q^60 - 216 * q^61 - 12 * q^62 - 36 * q^63 - 96 * q^65 - 36 * q^66 + 232 * q^67 - 32 * q^68 - 84 * q^69 - 176 * q^70 - 132 * q^71 - 108 * q^72 - 88 * q^73 - 24 * q^74 + 96 * q^75 + 8 * q^76 - 136 * q^77 + 168 * q^78 + 44 * q^79 + 216 * q^80 + 324 * q^81 + 28 * q^82 - 36 * q^83 + 84 * q^84 - 8 * q^85 + 96 * q^88 - 176 * q^89 - 72 * q^90 + 288 * q^91 + 12 * q^92 + 36 * q^93 + 264 * q^94 - 192 * q^95 - 36 * q^96 + 204 * q^97 + 284 * q^98 - 144 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/51\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$-1$	$e\left(\frac{5}{8}\right)$

Coefficient data

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

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

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

$2$	−0.292893	−	0.292893i	−0.146447	−	0.146447i	0.630082	−	0.776529i	$-0.283021\pi$
$2$	−0.292893	−	0.292893i	−0.146447	−	0.146447i	−0.776529	+	0.630082i	$0.783021\pi$
$3$	3.00000			1.00000
$3$	3.00000			1.00000
$4$		−	3.82843i		−	0.957107i
$5$	−0.828427	+	2.00000i	−0.165685	+	0.400000i	−0.984815	−	0.173609i	$-0.944457\pi$
$5$	−0.828427	+	2.00000i	−0.165685	+	0.400000i	0.819129	+	0.573609i	$0.194457\pi$
$6$	−0.878680	−	0.878680i	−0.146447	−	0.146447i
$7$	1.82843	−	0.757359i	0.261204	−	0.108194i	−0.248239	−	0.968699i	$-0.579852\pi$
$7$	1.82843	−	0.757359i	0.261204	−	0.108194i	0.509442	+	0.860505i	$0.329852\pi$
$8$	−2.29289	+	2.29289i	−0.286612	+	0.286612i
$9$	9.00000			1.00000
$10$	0.828427	−	0.343146i	0.0828427	−	0.0343146i
$11$	−4.70711	+	1.94975i	−0.427919	+	0.177250i	−0.586239	−	0.810138i	$-0.699392\pi$
$11$	−4.70711	+	1.94975i	−0.427919	+	0.177250i	0.158320	+	0.987388i	$0.449392\pi$
$12$		−	11.4853i		−	0.957107i
$13$			9.17157i			0.705506i	0.935717	+	0.352753i	$0.114754\pi$
$13$			9.17157i			0.705506i	−0.935717	+	0.352753i	$0.885246\pi$
$14$	−0.757359	−	0.313708i	−0.0540971	−	0.0224077i
$15$	−2.48528	+	6.00000i	−0.165685	+	0.400000i
$16$	−13.9706			−0.873160
$17$	−16.6066	+	3.63604i	−0.976859	+	0.213885i
$17$	−16.6066	+	3.63604i	−0.976859	+	0.213885i
$18$	−2.63604	−	2.63604i	−0.146447	−	0.146447i
$19$	−7.17157	+	7.17157i	−0.377451	+	0.377451i	−0.870182	−	0.492731i	$-0.835999\pi$
$19$	−7.17157	+	7.17157i	−0.377451	+	0.377451i	0.492731	+	0.870182i	$0.335999\pi$
$20$	7.65685	+	3.17157i	0.382843	+	0.158579i
$21$	5.48528	−	2.27208i	0.261204	−	0.108194i
$22$	1.94975	+	0.807612i	0.0886249	+	0.0367096i
$23$	−19.7279	+	8.17157i	−0.857736	+	0.355286i	−0.767822	−	0.640664i	$-0.778659\pi$
$23$	−19.7279	+	8.17157i	−0.857736	+	0.355286i	−0.0899142	+	0.995950i	$0.528659\pi$
$24$	−6.87868	+	6.87868i	−0.286612	+	0.286612i
$25$	14.3640	+	14.3640i	0.574558	+	0.574558i
$26$	2.68629	−	2.68629i	0.103319	−	0.103319i
$27$	27.0000			1.00000
$28$	−2.89949	−	7.00000i	−0.103553	−	0.250000i
$29$	18.3848	−	44.3848i	0.633958	−	1.53051i	−0.200649	−	0.979663i	$-0.564305\pi$
$29$	18.3848	−	44.3848i	0.633958	−	1.53051i	0.834607	−	0.550846i	$-0.185695\pi$
$30$	2.48528	−	1.02944i	0.0828427	−	0.0343146i
$31$	15.7279	−	37.9706i	0.507352	−	1.22486i	−0.438050	−	0.898951i	$-0.644331\pi$
$31$	15.7279	−	37.9706i	0.507352	−	1.22486i	0.945402	−	0.325906i	$-0.105669\pi$
$32$	13.2635	+	13.2635i	0.414483	+	0.414483i
$33$	−14.1213	+	5.84924i	−0.427919	+	0.177250i
$34$	5.92893	+	3.79899i	0.174380	+	0.111735i
$35$			4.28427i			0.122408i
$36$		−	34.4558i		−	0.957107i
$37$	3.17157	−	7.65685i	0.0857182	−	0.206942i	−0.875208	−	0.483747i	$-0.839276\pi$
$37$	3.17157	−	7.65685i	0.0857182	−	0.206942i	0.960926	+	0.276805i	$0.0892756\pi$
$38$	4.20101			0.110553
$39$			27.5147i			0.705506i
$40$	−2.68629	−	6.48528i	−0.0671573	−	0.162132i
$41$	11.7782	+	28.4350i	0.287273	+	0.693537i	0.999969	−	0.00793578i	$-0.00252606\pi$
$41$	11.7782	+	28.4350i	0.287273	+	0.693537i	−0.712696	+	0.701473i	$0.752526\pi$
$42$	−2.27208	−	0.941125i	−0.0540971	−	0.0224077i
$43$	−8.55635	−	8.55635i	−0.198985	−	0.198985i	0.600580	−	0.799565i	$-0.294936\pi$
$43$	−8.55635	−	8.55635i	−0.198985	−	0.198985i	−0.799565	+	0.600580i	$0.794936\pi$
$44$	7.46447	+	18.0208i	0.169647	+	0.409564i
$45$	−7.45584	+	18.0000i	−0.165685	+	0.400000i
$46$	8.17157	+	3.38478i	0.177643	+	0.0735821i
$47$	59.5391			1.26679			0.633395	−	0.773829i	$-0.281661\pi$
$47$	59.5391			1.26679			0.633395	+	0.773829i	$0.281661\pi$
$48$	−41.9117			−0.873160
$49$	−31.8787	+	31.8787i	−0.650585	+	0.650585i
$50$		−	8.41421i		−	0.168284i
$51$	−49.8198	+	10.9081i	−0.976859	+	0.213885i
$52$	35.1127			0.675244
$53$	−53.3553	−	53.3553i	−1.00670	−	1.00670i	−0.999977	−	0.00672714i	$-0.997859\pi$
$53$	−53.3553	−	53.3553i	−1.00670	−	1.00670i	−0.00672714	−	0.999977i	$-0.502141\pi$
$54$	−7.90812	−	7.90812i	−0.146447	−	0.146447i
$55$		−	11.0294i		−	0.200535i
$56$	−2.45584	+	5.92893i	−0.0438544	+	0.105874i
$57$	−21.5147	+	21.5147i	−0.377451	+	0.377451i
$58$	−18.3848	+	7.61522i	−0.316979	+	0.131297i
$59$	79.2426	−	79.2426i	1.34310	−	1.34310i	0.450135	−	0.892960i	$-0.351376\pi$
$59$	79.2426	−	79.2426i	1.34310	−	1.34310i	0.892960	−	0.450135i	$-0.148624\pi$
$60$	22.9706	+	9.51472i	0.382843	+	0.158579i
$61$	−63.8995	+	26.4680i	−1.04753	+	0.433902i	−0.839010	−	0.544115i	$-0.816865\pi$
$61$	−63.8995	+	26.4680i	−1.04753	+	0.433902i	−0.208522	+	0.978018i	$0.566865\pi$
$62$	−15.7279	+	6.51472i	−0.253676	+	0.105076i
$63$	16.4558	−	6.81623i	0.261204	−	0.108194i
$64$			48.1127i			0.751761i
$65$	−18.3431	−	7.59798i	−0.282202	−	0.116892i
$66$	5.84924	+	2.42284i	0.0886249	+	0.0367096i
$67$	67.8995			1.01343			0.506713	−	0.862115i	$-0.330861\pi$
$67$	67.8995			1.01343			0.506713	+	0.862115i	$0.330861\pi$
$68$	13.9203	+	63.5772i	0.204710	+	0.934958i
$69$	−59.1838	+	24.5147i	−0.857736	+	0.355286i
$70$	1.25483	−	1.25483i	0.0179262	−	0.0179262i
$71$	−82.4975	−	34.1716i	−1.16194	−	0.481290i	−0.283417	−	0.958997i	$-0.591468\pi$
$71$	−82.4975	−	34.1716i	−1.16194	−	0.481290i	−0.878519	+	0.477707i	$0.841468\pi$
$72$	−20.6360	+	20.6360i	−0.286612	+	0.286612i
$73$	−48.1630	−	19.9497i	−0.659766	−	0.273284i	0.0275738	−	0.999620i	$-0.491222\pi$
$73$	−48.1630	−	19.9497i	−0.659766	−	0.273284i	−0.687340	+	0.726336i	$0.741222\pi$
$74$	−3.17157	+	1.31371i	−0.0428591	+	0.0177528i
$75$	43.0919	+	43.0919i	0.574558	+	0.574558i
$76$	27.4558	+	27.4558i	0.361261	+	0.361261i
$77$	−7.12994	+	7.12994i	−0.0925967	+	0.0925967i
$78$	8.05887	−	8.05887i	0.103319	−	0.103319i
$79$	−32.8406	−	79.2843i	−0.415704	−	1.00360i	−0.983578	−	0.180483i	$-0.942234\pi$
$79$	−32.8406	−	79.2843i	−0.415704	−	1.00360i	0.567874	−	0.823115i	$-0.307766\pi$
$80$	11.5736	−	27.9411i	0.144670	−	0.349264i
$81$	81.0000			1.00000
$82$	4.87868	−	11.7782i	0.0594961	−	0.143636i
$83$	68.7817	+	68.7817i	0.828696	+	0.828696i	0.987336	−	0.158641i	$-0.0507111\pi$
$83$	68.7817	+	68.7817i	0.828696	+	0.828696i	−0.158641	+	0.987336i	$0.550711\pi$
$84$	−8.69848	−	21.0000i	−0.103553	−	0.250000i
$85$	6.48528	−	36.2254i	0.0762974	−	0.426181i
$86$			5.01219i			0.0582813i
$87$	55.1543	−	133.154i	0.633958	−	1.53051i
$88$	6.32233	−	15.2635i	0.0718447	−	0.173448i
$89$	−87.8406			−0.986973			−0.493487	−	0.869753i	$-0.664278\pi$
$89$	−87.8406			−0.986973			−0.493487	+	0.869753i	$0.664278\pi$
$90$	7.45584	−	3.08831i	0.0828427	−	0.0343146i
$91$	6.94618	+	16.7696i	0.0763316	+	0.184281i
$92$	31.2843	+	75.5269i	0.340046	+	0.820945i
$93$	47.1838	−	113.912i	0.507352	−	1.22486i
$94$	−17.4386	−	17.4386i	−0.185517	−	0.185517i
$95$	−8.40202	−	20.2843i	−0.0884423	−	0.213519i
$96$	39.7904	+	39.7904i	0.414483	+	0.414483i
$97$	122.418	+	50.7071i	1.26204	+	0.522754i	0.910535	−	0.413433i	$-0.135670\pi$
$97$	122.418	+	50.7071i	1.26204	+	0.522754i	0.351504	+	0.936186i	$0.385670\pi$
$98$	18.6741			0.190552
$99$	−42.3640	+	17.5477i	−0.427919	+	0.177250i
$100$	54.9914	−	54.9914i	0.549914	−	0.549914i
$101$			95.5147i			0.945690i	0.881146	+	0.472845i	$0.156773\pi$
$101$			95.5147i			0.945690i	−0.881146	+	0.472845i	$0.843227\pi$
$102$	17.7868	+	11.3970i	0.174380	+	0.111735i
$103$	45.8234			0.444887			0.222444	−	0.974946i	$-0.428597\pi$
$103$	45.8234			0.444887			0.222444	+	0.974946i	$0.428597\pi$
$104$	−21.0294	−	21.0294i	−0.202206	−	0.202206i
$105$			12.8528i			0.122408i
$106$			31.2548i			0.294857i
$107$	−5.57716	+	13.4645i	−0.0521230	+	0.125836i	−0.947796	−	0.318877i	$-0.896694\pi$
$107$	−5.57716	+	13.4645i	−0.0521230	+	0.125836i	0.895673	+	0.444713i	$0.146694\pi$
$108$		−	103.368i		−	0.957107i
$109$	−92.6690	+	38.3848i	−0.850175	+	0.352154i	−0.764857	−	0.644200i	$-0.777190\pi$
$109$	−92.6690	+	38.3848i	−0.850175	+	0.352154i	−0.0853176	+	0.996354i	$0.527190\pi$
$110$	−3.23045	+	3.23045i	−0.0293677	+	0.0293677i
$111$	9.51472	−	22.9706i	0.0857182	−	0.206942i
$112$	−25.5442	+	10.5807i	−0.228073	+	0.0944709i
$113$	−33.3345	+	13.8076i	−0.294996	+	0.122191i	−0.525273	−	0.850934i	$-0.676037\pi$
$113$	−33.3345	+	13.8076i	−0.294996	+	0.122191i	0.230277	+	0.973125i	$0.426037\pi$
$114$	12.6030			0.110553
$115$		−	46.2254i		−	0.401960i
$116$	−169.924	−	70.3848i	−1.46486	−	0.606765i
$117$			82.5442i			0.705506i
$118$	−46.4193			−0.393384
$119$	−27.6102	+	19.2254i	−0.232018	+	0.161558i
$120$	−8.05887	−	19.4558i	−0.0671573	−	0.162132i
$121$	−67.2046	+	67.2046i	−0.555410	+	0.555410i
$122$	26.4680	+	10.9634i	0.216951	+	0.0898641i
$123$	35.3345	+	85.3051i	0.287273	+	0.693537i
$124$	−145.368	−	60.2132i	−1.17232	−	0.485590i
$125$	−90.6274	+	37.5391i	−0.725019	+	0.300313i
$126$	−6.81623	−	2.82338i	−0.0540971	−	0.0224077i
$127$	81.6985	+	81.6985i	0.643295	+	0.643295i	0.951364	−	0.308069i	$-0.0996827\pi$
$127$	81.6985	+	81.6985i	0.643295	+	0.643295i	−0.308069	+	0.951364i	$0.599683\pi$
$128$	67.1457	−	67.1457i	0.524576	−	0.524576i
$129$	−25.6690	−	25.6690i	−0.198985	−	0.198985i
$130$	3.14719	+	7.59798i	0.0242091	+	0.0584460i
$131$	38.6949	−	93.4178i	0.295381	−	0.713113i	−0.704613	−	0.709592i	$-0.748879\pi$
$131$	38.6949	−	93.4178i	0.295381	−	0.713113i	0.999994	−	0.00352085i	$-0.00112072\pi$
$132$	22.3934	+	54.0624i	0.169647	+	0.409564i
$133$	−7.68124	+	18.5442i	−0.0577537	+	0.139430i
$134$	−19.8873	−	19.8873i	−0.148413	−	0.148413i
$135$	−22.3675	+	54.0000i	−0.165685	+	0.400000i
$136$	29.7401	−	46.4142i	0.218677	−	0.341281i
$137$			15.0051i			0.109526i	0.998499	+	0.0547630i	$0.0174403\pi$
$137$			15.0051i			0.109526i	−0.998499	+	0.0547630i	$0.982560\pi$
$138$	24.5147	+	10.1543i	0.177643	+	0.0735821i
$139$	−23.6238	+	57.0330i	−0.169956	+	0.410309i	−0.985791	−	0.167974i	$-0.946277\pi$
$139$	−23.6238	+	57.0330i	−0.169956	+	0.410309i	0.815836	+	0.578284i	$0.196277\pi$
$140$	16.4020			0.117157
$141$	178.617			1.26679
$142$	14.1543	+	34.1716i	0.0996784	+	0.240645i
$143$	−17.8823	−	43.1716i	−0.125051	−	0.301899i
$144$	−125.735			−0.873160
$145$	73.5391	+	73.5391i	0.507166	+	0.507166i
$146$	8.26346	+	19.9497i	0.0565990	+	0.136642i
$147$	−95.6360	+	95.6360i	−0.650585	+	0.650585i
$148$	−29.3137	−	12.1421i	−0.198066	−	0.0820415i
$149$	51.9411			0.348598			0.174299	−	0.984693i	$-0.444234\pi$
$149$	51.9411			0.348598			0.174299	+	0.984693i	$0.444234\pi$
$150$		−	25.2426i		−	0.168284i
$151$	2.58579	−	2.58579i	0.0171244	−	0.0171244i	−0.698493	−	0.715617i	$-0.746146\pi$
$151$	2.58579	−	2.58579i	0.0171244	−	0.0171244i	0.715617	+	0.698493i	$0.246146\pi$
$152$		−	32.8873i		−	0.216364i
$153$	−149.459	+	32.7244i	−0.976859	+	0.213885i
$154$	4.17662			0.0271209
$155$	62.9117	+	62.9117i	0.405882	+	0.405882i
$156$	105.338			0.675244
$157$		−	254.770i		−	1.62274i	−0.584536	−	0.811368i	$-0.698723\pi$
$157$		−	254.770i		−	1.62274i	0.584536	−	0.811368i	$-0.301277\pi$
$158$	−13.6030	+	32.8406i	−0.0860951	+	0.207852i
$159$	−160.066	−	160.066i	−1.00670	−	1.00670i
$160$	−37.5147	+	15.5391i	−0.234467	+	0.0971194i
$161$	−29.8823	+	29.8823i	−0.185604	+	0.185604i
$162$	−23.7244	−	23.7244i	−0.146447	−	0.146447i
$163$	79.5355	−	32.9447i	0.487948	−	0.202115i	−0.125125	−	0.992141i	$-0.539933\pi$
$163$	79.5355	−	32.9447i	0.487948	−	0.202115i	0.613073	+	0.790026i	$0.289933\pi$
$164$	108.861	−	45.0919i	0.663789	−	0.274951i
$165$		−	33.0883i		−	0.200535i
$166$		−	40.2914i		−	0.242719i
$167$	196.681	+	81.4680i	1.17773	+	0.487833i	0.883741	−	0.467976i	$-0.155017\pi$
$167$	196.681	+	81.4680i	1.17773	+	0.487833i	0.293991	+	0.955808i	$0.405017\pi$
$168$	−7.36753	+	17.7868i	−0.0438544	+	0.105874i
$169$	84.8823			0.502262
$170$	−12.5097	+	8.71068i	−0.0735863	+	0.0512393i
$171$	−64.5442	+	64.5442i	−0.377451	+	0.377451i
$172$	−32.7574	+	32.7574i	−0.190450	+	0.190450i
$173$	64.3431	+	26.6518i	0.371926	+	0.154057i	0.560814	−	0.827942i	$-0.310488\pi$
$173$	64.3431	+	26.6518i	0.371926	+	0.154057i	−0.188888	+	0.981999i	$0.560488\pi$
$174$	−55.1543	+	22.8457i	−0.316979	+	0.131297i
$175$	37.1421	+	15.3848i	0.212241	+	0.0879130i
$176$	65.7609	−	27.2391i	0.373642	−	0.154767i
$177$	237.728	−	237.728i	1.34310	−	1.34310i
$178$	25.7279	+	25.7279i	0.144539	+	0.144539i
$179$	−28.2426	+	28.2426i	−0.157780	+	0.157780i	−0.781582	−	0.623802i	$-0.785587\pi$
$179$	−28.2426	+	28.2426i	−0.157780	+	0.157780i	0.623802	+	0.781582i	$0.285587\pi$
$180$	68.9117	+	28.5442i	0.382843	+	0.158579i
$181$	−54.8873	−	132.510i	−0.303245	−	0.732098i	−0.999892	−	0.0146839i	$-0.995326\pi$
$181$	−54.8873	−	132.510i	−0.303245	−	0.732098i	0.696647	−	0.717414i	$-0.254674\pi$
$182$	2.87720	−	6.94618i	0.0158088	−	0.0381658i
$183$	−191.698	+	79.4041i	−1.04753	+	0.433902i
$184$	26.4975	−	63.9706i	0.144008	−	0.347666i
$185$	12.6863	+	12.6863i	0.0685745	+	0.0685745i
$186$	−47.1838	+	19.5442i	−0.253676	+	0.105076i
$187$	71.0797	−	49.4939i	0.380105	−	0.264673i
$188$		−	227.941i		−	1.21245i
$189$	49.3675	−	20.4487i	0.261204	−	0.108194i
$190$	−3.48023	+	8.40202i	−0.0183170	+	0.0442212i
$191$	165.681			0.867441			0.433721	−	0.901047i	$-0.357201\pi$
$191$	165.681			0.867441			0.433721	+	0.901047i	$0.357201\pi$
$192$			144.338i			0.751761i
$193$	114.665	+	276.827i	0.594122	+	1.43434i	0.879489	+	0.475918i	$0.157884\pi$
$193$	114.665	+	276.827i	0.594122	+	1.43434i	−0.285368	+	0.958418i	$0.592116\pi$
$194$	−21.0036	−	50.7071i	−0.108266	−	0.261377i
$195$	−55.0294	−	22.7939i	−0.282202	−	0.116892i
$196$	122.045	+	122.045i	0.622680	+	0.622680i
$197$	−6.24264	−	15.0711i	−0.0316885	−	0.0765029i	0.907243	−	0.420607i	$-0.138183\pi$
$197$	−6.24264	−	15.0711i	−0.0316885	−	0.0765029i	−0.938932	+	0.344104i	$0.888183\pi$
$198$	17.5477	+	7.26851i	0.0886249	+	0.0367096i
$199$	−182.497	−	75.5929i	−0.917073	−	0.379864i	−0.126313	−	0.991990i	$-0.540314\pi$
$199$	−182.497	−	75.5929i	−0.917073	−	0.379864i	−0.790760	+	0.612126i	$0.790314\pi$
$200$	−65.8701			−0.329350
$201$	203.698			1.01343
$202$	27.9756	−	27.9756i	0.138493	−	0.138493i
$203$		−	95.0782i		−	0.468366i
$204$	41.7609	+	190.731i	0.204710	+	0.934958i
$205$	−66.6274			−0.325012
$206$	−13.4214	−	13.4214i	−0.0651522	−	0.0651522i
$207$	−177.551	+	73.5442i	−0.857736	+	0.355286i
$208$		−	128.132i		−	0.616019i
$209$	19.7746	−	47.7401i	0.0946153	−	0.228422i
$210$	3.76450	−	3.76450i	0.0179262	−	0.0179262i
$211$	−285.070	+	118.080i	−1.35104	+	0.559619i	−0.936582	−	0.350449i	$-0.886029\pi$
$211$	−285.070	+	118.080i	−1.35104	+	0.559619i	−0.414459	+	0.910068i	$0.636029\pi$
$212$	−204.267	+	204.267i	−0.963524	+	0.963524i
$213$	−247.492	−	102.515i	−1.16194	−	0.481290i
$214$	5.57716	−	2.31014i	0.0260615	−	0.0107950i
$215$	24.2010	−	10.0244i	0.112563	−	0.0466251i
$216$	−61.9081	+	61.9081i	−0.286612	+	0.286612i
$217$		−	81.3381i		−	0.374830i
$218$	38.3848	+	15.8995i	0.176077	+	0.0729335i
$219$	−144.489	−	59.8492i	−0.659766	−	0.273284i
$220$	−42.2254			−0.191934
$221$	−33.3482	−	152.309i	−0.150897	−	0.689179i
$222$	−9.51472	+	3.94113i	−0.0428591	+	0.0177528i
$223$	−231.740	+	231.740i	−1.03919	+	1.03919i	−0.0399934	+	0.999200i	$0.512734\pi$
$223$	−231.740	+	231.740i	−1.03919	+	1.03919i	−0.999200	+	0.0399934i	$0.987266\pi$
$224$	34.2965	+	14.2061i	0.153109	+	0.0634199i
$225$	129.276	+	129.276i	0.574558	+	0.574558i
$226$	13.8076	+	5.71930i	0.0610956	+	0.0253066i
$227$	162.945	−	67.4939i	0.717818	−	0.297330i	0.00628269	−	0.999980i	$-0.498000\pi$
$227$	162.945	−	67.4939i	0.717818	−	0.297330i	0.711535	+	0.702650i	$0.248000\pi$
$228$	82.3675	+	82.3675i	0.361261	+	0.361261i
$229$	13.5635	+	13.5635i	0.0592292	+	0.0592292i	0.736101	−	0.676872i	$-0.236665\pi$
$229$	13.5635	+	13.5635i	0.0592292	+	0.0592292i	−0.676872	+	0.736101i	$0.736665\pi$
$230$	−13.5391	+	13.5391i	−0.0588657	+	0.0588657i
$231$	−21.3898	+	21.3898i	−0.0925967	+	0.0925967i
$232$	59.6152	+	143.924i	0.256962	+	0.620362i
$233$	−116.761	+	281.886i	−0.501120	+	1.20981i	0.447755	+	0.894157i	$0.352224\pi$
$233$	−116.761	+	281.886i	−0.501120	+	1.20981i	−0.948874	+	0.315654i	$0.897776\pi$
$234$	24.1766	−	24.1766i	0.103319	−	0.103319i
$235$	−49.3238	+	119.078i	−0.209889	+	0.506716i
$236$	−303.375	−	303.375i	−1.28549	−	1.28549i
$237$	−98.5219	−	237.853i	−0.415704	−	1.00360i
$238$	13.7178	+	2.45584i	0.0576379	+	0.0103187i
$239$			178.250i			0.745815i	0.927869	+	0.372907i	$0.121639\pi$
$239$			178.250i			0.745815i	−0.927869	+	0.372907i	$0.878361\pi$
$240$	34.7208	−	83.8234i	0.144670	−	0.349264i
$241$	128.629	−	310.538i	0.533730	−	1.28854i	−0.395306	−	0.918549i	$-0.629362\pi$
$241$	128.629	−	310.538i	0.533730	−	1.28854i	0.929036	−	0.369989i	$-0.120638\pi$
$242$	39.3675			0.162676
$243$	243.000			1.00000
$244$	101.331	+	244.635i	0.415291	+	1.00260i
$245$	−37.3482	−	90.1665i	−0.152442	−	0.368027i
$246$	14.6360	−	35.3345i	0.0594961	−	0.143636i
$247$	−65.7746	−	65.7746i	−0.266294	−	0.266294i
$248$	51.0000	+	123.125i	0.205645	+	0.496471i
$249$	206.345	+	206.345i	0.828696	+	0.828696i
$250$	37.5391	+	15.5492i	0.150156	+	0.0621968i
$251$	−357.037			−1.42246			−0.711228	−	0.702961i	$-0.751861\pi$
$251$	−357.037			−1.42246			−0.711228	+	0.702961i	$0.751861\pi$
$252$	−26.0955	−	63.0000i	−0.103553	−	0.250000i
$253$	76.9289	−	76.9289i	0.304067	−	0.304067i
$254$		−	47.8579i		−	0.188417i
$255$	19.4558	−	108.676i	0.0762974	−	0.426181i
$256$	153.118			0.598116
$257$	137.770	+	137.770i	0.536068	+	0.536068i	0.922372	−	0.386303i	$-0.126248\pi$
$257$	137.770	+	137.770i	0.536068	+	0.536068i	−0.386303	+	0.922372i	$0.626248\pi$
$258$			15.0366i			0.0582813i
$259$		−	16.4020i		−	0.0633283i
$260$	−29.0883	+	70.2254i	−0.111878	+	0.270098i
$261$	165.463	−	399.463i	0.633958	−	1.53051i
$262$	−38.6949	+	16.0280i	−0.147691	+	0.0611754i
$263$	29.8162	−	29.8162i	0.113370	−	0.113370i	−0.648146	−	0.761516i	$-0.724455\pi$
$263$	29.8162	−	29.8162i	0.113370	−	0.113370i	0.761516	+	0.648146i	$0.224455\pi$
$264$	18.9670	−	45.7904i	0.0718447	−	0.173448i
$265$	150.912	−	62.5097i	0.569478	−	0.235886i
$266$	7.68124	−	3.18167i	0.0288768	−	0.0119612i
$267$	−263.522			−0.986973
$268$		−	259.948i		−	0.969956i
$269$	297.990	+	123.431i	1.10777	+	0.458853i	0.860169	−	0.510009i	$-0.170358\pi$
$269$	297.990	+	123.431i	1.10777	+	0.458853i	0.247600	+	0.968862i	$0.420358\pi$
$270$	22.3675	−	9.26494i	0.0828427	−	0.0343146i
$271$	149.848			0.552944			0.276472	−	0.961022i	$-0.410835\pi$
$271$	149.848			0.552944			0.276472	+	0.961022i	$0.410835\pi$
$272$	232.004	−	50.7975i	0.852954	−	0.186756i
$273$	20.8385	+	50.3087i	0.0763316	+	0.184281i
$274$	4.39488	−	4.39488i	0.0160397	−	0.0160397i
$275$	−95.6188	−	39.6066i	−0.347705	−	0.144024i
$276$	93.8528	+	226.581i	0.340046	+	0.820945i
$277$	−361.137	−	149.588i	−1.30374	−	0.540028i	−0.380691	−	0.924702i	$-0.624314\pi$
$277$	−361.137	−	149.588i	−1.30374	−	0.540028i	−0.923053	+	0.384674i	$0.874314\pi$
$278$	23.6238	−	9.78532i	0.0849779	−	0.0351990i
$279$	141.551	−	341.735i	0.507352	−	1.22486i
$280$	−9.82338	−	9.82338i	−0.0350835	−	0.0350835i
$281$	−375.571	+	375.571i	−1.33655	+	1.33655i	−0.437173	+	0.899378i	$0.644020\pi$
$281$	−375.571	+	375.571i	−1.33655	+	1.33655i	−0.899378	+	0.437173i	$0.855980\pi$
$282$	−52.3158	−	52.3158i	−0.185517	−	0.185517i
$283$	−118.329	−	285.673i	−0.418125	−	1.00944i	−0.982890	−	0.184192i	$-0.941033\pi$
$283$	−118.329	−	285.673i	−0.418125	−	1.00944i	0.564765	−	0.825252i	$-0.308967\pi$
$284$	−130.823	+	315.836i	−0.460646	+	1.11210i
$285$	−25.2061	−	60.8528i	−0.0884423	−	0.213519i
$286$	−7.40707	+	17.8823i	−0.0258988	+	0.0625254i
$287$	43.0711	+	43.0711i	0.150073	+	0.150073i
$288$	119.371	+	119.371i	0.414483	+	0.414483i
$289$	262.558	−	120.765i	0.908507	−	0.417870i
$290$		−	43.0782i		−	0.148546i
$291$	367.253	+	152.121i	1.26204	+	0.522754i
$292$	−76.3762	+	184.388i	−0.261562	+	0.631467i
$293$	−270.485			−0.923158			−0.461579	−	0.887099i	$-0.652717\pi$
$293$	−270.485			−0.923158			−0.461579	+	0.887099i	$0.652717\pi$
$294$	56.0223			0.190552
$295$	92.8385	+	224.132i	0.314707	+	0.759770i
$296$	10.2843	+	24.8284i	0.0347442	+	0.0838798i
$297$	−127.092	+	52.6432i	−0.427919	+	0.177250i
$298$	−15.2132	−	15.2132i	−0.0510510	−	0.0510510i
$299$	−74.9462	−	180.936i	−0.250656	−	0.605137i
$300$	164.974	−	164.974i	0.549914	−	0.549914i
$301$	−22.1249	−	9.16443i	−0.0735046	−	0.0304466i
$302$	−1.51472			−0.00501562
$303$			286.544i			0.945690i
$304$	100.191	−	100.191i	0.329575	−	0.329575i
$305$		−	149.726i		−	0.490904i
$306$	53.3604	+	34.1909i	0.174380	+	0.111735i
$307$	133.549			0.435014			0.217507	−	0.976059i	$-0.430208\pi$
$307$	133.549			0.435014			0.217507	+	0.976059i	$0.430208\pi$
$308$	27.2965	+	27.2965i	0.0886249	+	0.0886249i
$309$	137.470			0.444887
$310$		−	36.8528i		−	0.118880i
$311$	152.307	−	367.701i	0.489732	−	1.18232i	−0.465124	−	0.885246i	$-0.653990\pi$
$311$	152.307	−	367.701i	0.489732	−	1.18232i	0.954855	−	0.297071i	$-0.0960099\pi$
$312$	−63.0883	−	63.0883i	−0.202206	−	0.202206i
$313$	207.430	−	85.9203i	0.662716	−	0.274506i	−0.0258652	−	0.999665i	$-0.508234\pi$
$313$	207.430	−	85.9203i	0.662716	−	0.274506i	0.688581	+	0.725160i	$0.258234\pi$
$314$	−74.6203	+	74.6203i	−0.237644	+	0.237644i
$315$			38.5584i			0.122408i
$316$	−303.534	+	125.728i	−0.960551	+	0.397873i
$317$	−93.1127	+	38.5685i	−0.293731	+	0.121667i	−0.524683	−	0.851298i	$-0.675816\pi$
$317$	−93.1127	+	38.5685i	−0.293731	+	0.121667i	0.230952	+	0.972965i	$0.425816\pi$
$318$			93.7645i			0.294857i
$319$			244.770i			0.767303i
$320$	−96.2254	−	39.8579i	−0.300704	−	0.124556i
$321$	−16.7315	+	40.3934i	−0.0521230	+	0.125836i
$322$	17.5046			0.0543622
$323$	93.0193	−	145.172i	0.287986	−	0.449448i
$324$		−	310.103i		−	0.957107i
$325$	−131.740	+	131.740i	−0.405354	+	0.405354i
$326$	−32.9447	−	13.6461i	−0.101057	−	0.0418593i
$327$	−278.007	+	115.154i	−0.850175	+	0.352154i
$328$	−92.2046	−	38.1924i	−0.281112	−	0.116440i
$329$	108.863	−	45.0925i	0.330890	−	0.137059i
$330$	−9.69134	+	9.69134i	−0.0293677	+	0.0293677i
$331$	5.40916	+	5.40916i	0.0163419	+	0.0163419i	0.715231	−	0.698889i	$-0.246322\pi$
$331$	5.40916	+	5.40916i	0.0163419	+	0.0163419i	−0.698889	+	0.715231i	$0.746322\pi$
$332$	263.326	−	263.326i	0.793150	−	0.793150i
$333$	28.5442	−	68.9117i	0.0857182	−	0.206942i
$334$	−33.7452	−	81.4680i	−0.101033	−	0.243916i
$335$	−56.2498	+	135.799i	−0.167910	+	0.405370i
$336$	−76.6325	+	31.7422i	−0.228073	+	0.0944709i
$337$	−148.371	+	358.200i	−0.440270	+	1.06291i	0.535584	+	0.844482i	$0.320092\pi$
$337$	−148.371	+	358.200i	−0.440270	+	1.06291i	−0.975854	+	0.218424i	$0.929908\pi$
$338$	−24.8614	−	24.8614i	−0.0735545	−	0.0735545i
$339$	−100.004	+	41.4228i	−0.294996	+	0.122191i
$340$	−138.686	−	24.8284i	−0.407901	−	0.0730248i
$341$			209.397i			0.614067i
$342$	37.8091			0.110553
$343$	−71.2548	+	172.024i	−0.207740	+	0.501529i
$344$	39.2376			0.114063
$345$		−	138.676i		−	0.401960i
$346$	−11.0395	−	26.6518i	−0.0319062	−	0.0770283i
$347$	−178.234	−	430.295i	−0.513643	−	1.24004i	−0.941750	−	0.336315i	$-0.890819\pi$
$347$	−178.234	−	430.295i	−0.513643	−	1.24004i	0.428107	−	0.903728i	$-0.359181\pi$
$348$	−509.772	−	211.154i	−1.46486	−	0.606765i
$349$	89.8751	+	89.8751i	0.257522	+	0.257522i	0.824045	−	0.566524i	$-0.191712\pi$
$349$	89.8751	+	89.8751i	0.257522	+	0.257522i	−0.566524	+	0.824045i	$0.691712\pi$
$350$	−6.37258	−	15.3848i	−0.0182074	−	0.0439565i
$351$			247.632i			0.705506i
$352$	−88.2929	−	36.5721i	−0.250832	−	0.103898i
$353$	−264.208			−0.748465			−0.374233	−	0.927335i	$-0.622094\pi$
$353$	−264.208			−0.748465			−0.374233	+	0.927335i	$0.622094\pi$
$354$	−139.258			−0.393384
$355$	136.686	−	136.686i	0.385032	−	0.385032i
$356$			336.291i			0.944639i
$357$	−82.8305	+	57.6762i	−0.232018	+	0.161558i
$358$	16.5442			0.0462127
$359$	387.127	+	387.127i	1.07835	+	1.07835i	0.996658	+	0.0816904i	$0.0260319\pi$
$359$	387.127	+	387.127i	1.07835	+	1.07835i	0.0816904	+	0.996658i	$0.473968\pi$
$360$	−24.1766	−	58.3675i	−0.0671573	−	0.162132i
$361$			258.137i			0.715061i
$362$	−22.7351	+	54.8873i	−0.0628040	+	0.151622i
$363$	−201.614	+	201.614i	−0.555410	+	0.555410i
$364$	64.2010	−	26.5929i	0.176376	−	0.0730575i
$365$	79.7990	−	79.7990i	0.218627	−	0.218627i
$366$	79.4041	+	32.8903i	0.216951	+	0.0898641i
$367$	−213.291	+	88.3482i	−0.581176	+	0.240731i	−0.653849	−	0.756625i	$-0.726847\pi$
$367$	−213.291	+	88.3482i	−0.581176	+	0.240731i	0.0726736	+	0.997356i	$0.476847\pi$
$368$	275.610	−	114.161i	0.748941	−	0.310221i
$369$	106.004	+	255.915i	0.287273	+	0.693537i
$370$		−	7.43146i		−	0.0200850i
$371$	−137.966	−	57.1472i	−0.371875	−	0.154036i
$372$	−436.103	−	180.640i	−1.17232	−	0.485590i
$373$	−11.3625			−0.0304624			−0.0152312	−	0.999884i	$-0.504848\pi$
$373$	−11.3625			−0.0304624			−0.0152312	+	0.999884i	$0.504848\pi$
$374$	−35.3152	−	6.32233i	−0.0944256	−	0.0169046i
$375$	−271.882	+	112.617i	−0.725019	+	0.300313i
$376$	−136.517	+	136.517i	−0.363077	+	0.363077i
$377$	407.078	+	168.617i	1.07978	+	0.447261i
$378$	−20.4487	−	8.47013i	−0.0540971	−	0.0224077i
$379$	86.4939	+	35.8269i	0.228216	+	0.0945302i	0.493861	−	0.869541i	$-0.335585\pi$
$379$	86.4939	+	35.8269i	0.228216	+	0.0945302i	−0.265645	+	0.964071i	$0.585585\pi$
$380$	−77.6569	+	32.1665i	−0.204360	+	0.0846487i
$381$	245.095	+	245.095i	0.643295	+	0.643295i
$382$	−48.5269	−	48.5269i	−0.127034	−	0.127034i
$383$	242.375	−	242.375i	0.632832	−	0.632832i	−0.315945	−	0.948777i	$-0.602322\pi$
$383$	242.375	−	242.375i	0.632832	−	0.632832i	0.948777	+	0.315945i	$0.102322\pi$
$384$	201.437	−	201.437i	0.524576	−	0.524576i
$385$	−8.35325	−	20.1665i	−0.0216967	−	0.0523806i
$386$	47.4960	−	114.665i	0.123047	−	0.297061i
$387$	−77.0071	−	77.0071i	−0.198985	−	0.198985i
$388$	194.128	−	468.668i	0.500331	−	1.20791i
$389$	171.799	+	171.799i	0.441643	+	0.441643i	0.892564	−	0.450921i	$-0.148904\pi$
$389$	171.799	+	171.799i	0.441643	+	0.441643i	−0.450921	+	0.892564i	$0.648904\pi$
$390$	9.44156	+	22.7939i	0.0242091	+	0.0584460i
$391$	297.902	−	207.434i	0.761897	−	0.530521i
$392$		−	146.189i		−	0.372931i
$393$	116.085	−	280.253i	0.295381	−	0.713113i
$394$	−2.58579	+	6.24264i	−0.00656291	+	0.0158443i
$395$	185.775			0.470315
$396$	67.1802	+	162.187i	0.169647	+	0.409564i
$397$	−105.019	−	253.539i	−0.264532	−	0.638638i	0.734676	−	0.678418i	$-0.237334\pi$
$397$	−105.019	−	253.539i	−0.264532	−	0.638638i	−0.999208	+	0.0397805i	$0.987334\pi$
$398$	31.3116	+	75.5929i	0.0786724	+	0.189932i
$399$	−23.0437	+	55.6325i	−0.0577537	+	0.139430i
$400$	−200.673	−	200.673i	−0.501682	−	0.501682i
$401$	−193.001	−	465.945i	−0.481298	−	1.16196i	−0.958993	−	0.283431i	$-0.908527\pi$
$401$	−193.001	−	465.945i	−0.481298	−	1.16196i	0.477694	−	0.878526i	$-0.341473\pi$
$402$	−59.6619	−	59.6619i	−0.148413	−	0.148413i
$403$	348.250	+	144.250i	0.864143	+	0.357940i
$404$	365.671			0.905127
$405$	−67.1026	+	162.000i	−0.165685	+	0.400000i
$406$	−27.8478	+	27.8478i	−0.0685905	+	0.0685905i
$407$			42.2254i			0.103748i
$408$	89.2203	−	139.243i	0.218677	−	0.341281i
$409$	352.340			0.861467			0.430734	−	0.902479i	$-0.358255\pi$
$409$	352.340			0.861467			0.430734	+	0.902479i	$0.358255\pi$
$410$	19.5147	+	19.5147i	0.0475969	+	0.0475969i
$411$			45.0152i			0.109526i
$412$		−	175.431i		−	0.425805i
$413$	84.8742	−	204.905i	0.205507	−	0.496137i
$414$	73.5442	+	30.4630i	0.177643	+	0.0735821i
$415$	−194.544	+	80.5828i	−0.468781	+	0.194175i
$416$	−121.647	+	121.647i	−0.292420	+	0.292420i
$417$	−70.8715	+	171.099i	−0.169956	+	0.410309i
$418$	−19.7746	+	8.19091i	−0.0473077	+	0.0195955i
$419$	−260.494	+	107.900i	−0.621704	+	0.257518i	−0.671224	−	0.741255i	$-0.734231\pi$
$419$	−260.494	+	107.900i	−0.621704	+	0.257518i	0.0495197	+	0.998773i	$0.484231\pi$
$420$	49.2061			0.117157
$421$		−	546.877i		−	1.29900i	−0.760363	−	0.649498i	$-0.774979\pi$
$421$		−	546.877i		−	1.29900i	0.760363	−	0.649498i	$-0.225021\pi$
$422$	118.080	+	48.9102i	0.279810	+	0.115901i
$423$	535.852			1.26679
$424$	244.676			0.577066
$425$	−290.765	−	186.309i	−0.684152	−	0.438373i
$426$	42.4630	+	102.515i	0.0996784	+	0.240645i
$427$	−96.7898	+	96.7898i	−0.226674	+	0.226674i
$428$	51.5477	+	21.3518i	0.120439	+	0.0498873i
$429$	−53.6468	−	129.515i	−0.125051	−	0.301899i
$430$	−10.0244	−	4.15224i	−0.0233125	−	0.00965636i
$431$	−1.71068	+	0.708586i	−0.00396909	+	0.00164405i	−0.384667	−	0.923055i	$-0.625684\pi$
$431$	−1.71068	+	0.708586i	−0.00396909	+	0.00164405i	0.380698	+	0.924699i	$0.375684\pi$
$432$	−377.205			−0.873160
$433$	132.794	+	132.794i	0.306683	+	0.306683i	0.843622	−	0.536938i	$-0.180419\pi$
$433$	132.794	+	132.794i	0.306683	+	0.306683i	−0.536938	+	0.843622i	$0.680419\pi$
$434$	−23.8234	+	23.8234i	−0.0548926	+	0.0548926i
$435$	220.617	+	220.617i	0.507166	+	0.507166i
$436$	146.953	+	354.777i	0.337049	+	0.813708i
$437$	82.8772	−	200.083i	0.189650	−	0.457856i
$438$	24.7904	+	59.8492i	0.0565990	+	0.136642i
$439$	106.466	−	257.032i	0.242519	−	0.585493i	−0.755012	−	0.655710i	$-0.772369\pi$
$439$	106.466	−	257.032i	0.242519	−	0.585493i	0.997532	+	0.0702172i	$0.0223692\pi$
$440$	25.2893	+	25.2893i	0.0574757	+	0.0574757i
$441$	−286.908	+	286.908i	−0.650585	+	0.650585i
$442$	−34.8427	+	54.3776i	−0.0788297	+	0.123026i
$443$			249.071i			0.562237i	0.959673	+	0.281119i	$0.0907054\pi$
$443$			249.071i			0.562237i	−0.959673	+	0.281119i	$0.909295\pi$
$444$	−87.9411	−	36.4264i	−0.198066	−	0.0820415i
$445$	72.7696	−	175.681i	0.163527	−	0.394789i
$446$	135.750			0.304373
$447$	155.823			0.348598
$448$	36.4386	+	87.9706i	0.0813362	+	0.196363i
$449$	6.69195	+	16.1558i	0.0149041	+	0.0359818i	0.931156	−	0.364620i	$-0.118801\pi$
$449$	6.69195	+	16.1558i	0.0149041	+	0.0359818i	−0.916252	+	0.400602i	$0.868801\pi$
$450$		−	75.7279i		−	0.168284i
$451$	−110.882	−	110.882i	−0.245859	−	0.245859i
$452$	52.8614	+	127.619i	0.116950	+	0.282342i
$453$	7.75736	−	7.75736i	0.0171244	−	0.0171244i
$454$	−67.4939	−	27.9569i	−0.148665	−	0.0615791i
$455$	−39.2935			−0.0863594
$456$		−	98.6619i		−	0.216364i
$457$	−570.098	+	570.098i	−1.24748	+	1.24748i	−0.290648	+	0.956830i	$0.593871\pi$
$457$	−570.098	+	570.098i	−1.24748	+	1.24748i	−0.956830	+	0.290648i	$0.906129\pi$
$458$		−	7.94531i		−	0.0173478i
$459$	−448.378	+	98.1731i	−0.976859	+	0.213885i
$460$	−176.971			−0.384719
$461$	−382.149	−	382.149i	−0.828957	−	0.828957i	0.158415	−	0.987373i	$-0.449362\pi$
$461$	−382.149	−	382.149i	−0.828957	−	0.828957i	−0.987373	+	0.158415i	$0.949362\pi$
$462$	12.5299			0.0271209
$463$		−	46.5097i		−	0.100453i	−0.998738	−	0.0502264i	$-0.984006\pi$
$463$		−	46.5097i		−	0.100453i	0.998738	−	0.0502264i	$-0.0159943\pi$
$464$	−256.846	+	620.080i	−0.553547	+	1.33638i
$465$	188.735	+	188.735i	0.405882	+	0.405882i
$466$	116.761	−	48.3640i	0.250560	−	0.103785i
$467$	249.394	−	249.394i	0.534034	−	0.534034i	−0.387736	−	0.921770i	$-0.626743\pi$
$467$	249.394	−	249.394i	0.534034	−	0.534034i	0.921770	+	0.387736i	$0.126743\pi$
$468$	316.014			0.675244
$469$	124.149	−	51.4243i	0.264711	−	0.109647i
$470$	49.3238	−	20.4306i	0.104944	−	0.0434693i
$471$		−	764.309i		−	1.62274i
$472$			363.390i			0.769894i
$473$	56.9584	+	23.5929i	0.120419	+	0.0498793i
$474$	−40.8091	+	98.5219i	−0.0860951	+	0.207852i
$475$	−206.024			−0.433736
$476$	73.6030	+	105.704i	0.154628	+	0.222066i
$477$	−480.198	−	480.198i	−1.00670	−	1.00670i
$478$	52.2082	−	52.2082i	0.109222	−	0.109222i
$479$	−509.683	−	211.118i	−1.06406	−	0.440747i	−0.219167	−	0.975687i	$-0.570334\pi$
$479$	−509.683	−	211.118i	−1.06406	−	0.440747i	−0.844890	+	0.534940i	$0.820334\pi$
$480$	−112.544	+	46.6173i	−0.234467	+	0.0971194i
$481$	70.2254	+	29.0883i	0.145999	+	0.0604747i
$482$	−128.629	+	53.2798i	−0.266865	+	0.110539i
$483$	−89.6468	+	89.6468i	−0.185604	+	0.185604i
$484$	257.288	+	257.288i	0.531586	+	0.531586i
$485$	−202.828	+	202.828i	−0.418203	+	0.418203i
$486$	−71.1731	−	71.1731i	−0.146447	−	0.146447i
$487$	−202.436	−	488.723i	−0.415679	−	1.00354i	−0.983585	−	0.180444i	$-0.942246\pi$
$487$	−202.436	−	488.723i	−0.415679	−	1.00354i	0.567906	−	0.823093i	$-0.307754\pi$
$488$	85.8263	−	207.203i	0.175874	−	0.424597i
$489$	238.607	−	98.8341i	0.487948	−	0.202115i
$490$	−15.4701	+	37.3482i	−0.0315717	+	0.0762208i
$491$	−110.350	−	110.350i	−0.224746	−	0.224746i	0.585748	−	0.810494i	$-0.300801\pi$
$491$	−110.350	−	110.350i	−0.224746	−	0.224746i	−0.810494	+	0.585748i	$0.800801\pi$
$492$	326.584	−	135.276i	0.663789	−	0.274951i
$493$	−143.924	+	803.928i	−0.291935	+	1.63069i
$494$			38.5299i			0.0779957i
$495$		−	99.2649i		−	0.200535i
$496$	−219.728	+	530.470i	−0.443000	+	1.06950i
$497$	−176.721			−0.355575
$498$		−	120.874i		−	0.242719i
$499$	−214.724	−	518.390i	−0.430309	−	1.03886i	−0.979188	−	0.202956i	$-0.934945\pi$
$499$	−214.724	−	518.390i	−0.430309	−	1.03886i	0.548878	−	0.835902i	$-0.315055\pi$
$500$	143.716	+	346.960i	0.287431	+	0.693921i
$501$	590.044	+	244.404i	1.17773	+	0.487833i
$502$	104.574	+	104.574i	0.208314	+	0.208314i
$503$	345.767	+	834.754i	0.687409	+	1.65955i	0.749938	+	0.661508i	$0.230083\pi$
$503$	345.767	+	834.754i	0.687409	+	1.65955i	−0.0625291	+	0.998043i	$0.519917\pi$
$504$	−22.1026	+	53.3604i	−0.0438544	+	0.105874i
$505$	−191.029	−	79.1270i	−0.378276	−	0.156687i
$506$	−45.0639			−0.0890591
$507$	254.647			0.502262
$508$	312.777	−	312.777i	0.615702	−	0.615702i
$509$		−	543.651i		−	1.06808i	−0.845460	−	0.534038i	$-0.820674\pi$
$509$		−	543.651i		−	1.06808i	0.845460	−	0.534038i	$-0.179326\pi$
$510$	−37.5290	+	26.1320i	−0.0735863	+	0.0512393i
$511$	−103.172			−0.201901
$512$	−313.430	−	313.430i	−0.612168	−	0.612168i
$513$	−193.632	+	193.632i	−0.377451	+	0.377451i
$514$		−	80.7035i		−	0.157011i
$515$	−37.9613	+	91.6468i	−0.0737113	+	0.177955i
$516$	−98.2721	+	98.2721i	−0.190450	+	0.190450i
$517$	−280.257	+	116.086i	−0.542083	+	0.224538i
$518$	−4.80404	+	4.80404i	−0.00927421	+	0.00927421i
$519$	193.029	+	79.9554i	0.371926	+	0.154057i
$520$	59.4802	−	24.6375i	0.114385	−	0.0473798i
$521$	−301.957	+	125.075i	−0.579572	+	0.240066i	−0.653157	−	0.757222i	$-0.726556\pi$
$521$	−301.957	+	125.075i	−0.579572	+	0.240066i	0.0735853	+	0.997289i	$0.476556\pi$
$522$	−165.463	+	68.5370i	−0.316979	+	0.131297i
$523$			779.561i			1.49056i	0.666754	+	0.745278i	$0.267683\pi$
$523$			779.561i			1.49056i	−0.666754	+	0.745278i	$0.732317\pi$
$524$	−357.643	−	148.141i	−0.682525	−	0.282711i
$525$	111.426	+	46.1543i	0.212241	+	0.0879130i
$526$	−17.4659			−0.0332052
$527$	−123.125	+	687.749i	−0.233634	+	1.30503i
$528$	197.283	−	81.7172i	0.373642	−	0.154767i
$529$	−51.6432	+	51.6432i	−0.0976242	+	0.0976242i
$530$	−62.5097	−	25.8924i	−0.117943	−	0.0488535i
$531$	713.184	−	713.184i	1.34310	−	1.34310i
$532$	70.9949	+	29.4071i	0.133449	+	0.0552764i
$533$	−260.794	+	108.024i	−0.489294	+	0.202672i
$534$	77.1838	+	77.1838i	0.144539	+	0.144539i
$535$	−22.3087	−	22.3087i	−0.0416984	−	0.0416984i
$536$	−155.686	+	155.686i	−0.290459	+	0.290459i
$537$	−84.7279	+	84.7279i	−0.157780	+	0.157780i
$538$	−51.1270	−	123.431i	−0.0950316	−	0.229427i
$539$	87.9010	−	212.212i	0.163082	−	0.393714i
$540$	206.735	+	85.6325i	0.382843	+	0.158579i
$541$	133.019	−	321.137i	0.245877	−	0.593599i	−0.751969	−	0.659198i	$-0.770896\pi$
$541$	133.019	−	321.137i	0.245877	−	0.593599i	0.997846	+	0.0655991i	$0.0208958\pi$
$542$	−43.8894	−	43.8894i	−0.0809767	−	0.0809767i
$543$	−164.662	−	397.529i	−0.303245	−	0.732098i
$544$	−268.487	−	172.034i	−0.493543	−	0.316240i
$545$		−	217.137i		−	0.398417i
$546$	8.63160	−	20.8385i	0.0158088	−	0.0381658i
$547$	383.971	−	926.988i	0.701958	−	1.69468i	−0.0172201	−	0.999852i	$-0.505482\pi$
$547$	383.971	−	926.988i	0.701958	−	1.69468i	0.719178	−	0.694825i	$-0.244518\pi$
$548$	57.4457			0.104828
$549$	−575.095	+	238.212i	−1.04753	+	0.433902i
$550$	16.4056	+	39.6066i	0.0298283	+	0.0720120i
$551$	186.461	+	450.156i	0.338405	+	0.816981i
$552$	79.4924	−	191.912i	0.144008	−	0.347666i
$553$	−120.093	−	120.093i	−0.217167	−	0.217167i
$554$	61.9613	+	149.588i	0.111844	+	0.270014i
$555$	38.0589	+	38.0589i	0.0685745	+	0.0685745i
$556$	218.347	+	90.4422i	0.392710	+	0.162666i
$557$	953.823			1.71243			0.856215	−	0.516620i	$-0.172810\pi$
$557$	953.823			1.71243			0.856215	+	0.516620i	$0.172810\pi$
$558$	−141.551	+	58.6325i	−0.253676	+	0.105076i
$559$	78.4752	−	78.4752i	0.140385	−	0.140385i
$560$		−	59.8537i		−	0.106882i
$561$	213.239	−	148.482i	0.380105	−	0.264673i
$562$	220.004			0.391467
$563$	−680.973	−	680.973i	−1.20954	−	1.20954i	−0.971175	−	0.238368i	$-0.923388\pi$
$563$	−680.973	−	680.973i	−1.20954	−	1.20954i	−0.238368	−	0.971175i	$-0.576612\pi$
$564$		−	683.823i		−	1.21245i
$565$		−	78.1076i		−	0.138244i
$566$	−49.0137	+	118.329i	−0.0865966	+	0.209063i
$567$	148.103	−	61.3461i	0.261204	−	0.108194i
$568$	267.510	−	110.806i	0.470968	−	0.195081i
$569$	181.378	−	181.378i	0.318766	−	0.318766i	−0.529527	−	0.848293i	$-0.677631\pi$
$569$	181.378	−	181.378i	0.318766	−	0.318766i	0.848293	+	0.529527i	$0.177631\pi$
$570$	−10.4407	+	25.2061i	−0.0183170	+	0.0442212i
$571$	61.8837	−	25.6331i	0.108378	−	0.0448916i	−0.327836	−	0.944735i	$-0.606319\pi$
$571$	61.8837	−	25.6331i	0.108378	−	0.0448916i	0.436214	+	0.899843i	$0.356319\pi$
$572$	−165.279	+	68.4609i	−0.288950	+	0.119687i
$573$	497.044			0.867441
$574$		−	25.2304i		−	0.0439555i
$575$	−400.747	−	165.995i	−0.696952	−	0.288687i
$576$			433.014i			0.751761i
$577$	213.937			0.370775			0.185387	−	0.982666i	$-0.440646\pi$
$577$	213.937			0.370775			0.185387	+	0.982666i	$0.440646\pi$
$578$	−112.273	−	41.5305i	−0.194243	−	0.0718520i
$579$	343.996	+	830.481i	0.594122	+	1.43434i
$580$	281.539	−	281.539i	0.485412	−	0.485412i
$581$	177.855	+	73.6699i	0.306119	+	0.126798i
$582$	−63.0107	−	152.121i	−0.108266	−	0.261377i
$583$	355.179	+	147.120i	0.609226	+	0.252350i
$584$	156.175	−	64.6899i	0.267423	−	0.110770i
$585$	−165.088	−	68.3818i	−0.282202	−	0.116892i
$586$	79.2233	+	79.2233i	0.135193	+	0.135193i
$587$	252.524	−	252.524i	0.430194	−	0.430194i	−0.458500	−	0.888694i	$-0.651613\pi$
$587$	252.524	−	252.524i	0.430194	−	0.430194i	0.888694	+	0.458500i	$0.151613\pi$
$588$	366.136	+	366.136i	0.622680	+	0.622680i
$589$	159.515	+	385.103i	0.270823	+	0.653824i
$590$	38.4550	−	92.8385i	0.0651779	−	0.157353i
$591$	−18.7279	−	45.2132i	−0.0316885	−	0.0765029i
$592$	−44.3087	+	106.971i	−0.0748457	+	0.180694i
$593$	547.715	+	547.715i	0.923634	+	0.923634i	0.997284	−	0.0736503i	$-0.0234649\pi$
$593$	547.715	+	547.715i	0.923634	+	0.923634i	−0.0736503	+	0.997284i	$0.523465\pi$
$594$	52.6432	+	21.8055i	0.0886249	+	0.0367096i
$595$	−15.5778	−	71.1472i	−0.0261811	−	0.119575i
$596$		−	198.853i		−	0.333646i
$597$	−547.492	−	226.779i	−0.917073	−	0.379864i
$598$	−31.0437	+	74.9462i	−0.0519126	+	0.125328i
$599$	197.456			0.329642			0.164821	−	0.986323i	$-0.447295\pi$
$599$	197.456			0.329642			0.164821	+	0.986323i	$0.447295\pi$
$600$	−197.610			−0.329350
$601$	−106.891	−	258.057i	−0.177855	−	0.429380i	0.809661	−	0.586898i	$-0.199651\pi$
$601$	−106.891	−	258.057i	−0.177855	−	0.429380i	−0.987516	+	0.157518i	$0.949651\pi$
$602$	3.79603	+	9.16443i	0.00630570	+	0.0152233i
$603$	611.095			1.01343
$604$	−9.89949	−	9.89949i	−0.0163899	−	0.0163899i
$605$	−78.7351	−	190.083i	−0.130141	−	0.314187i
$606$	83.9268	−	83.9268i	0.138493	−	0.138493i
$607$	56.2893	+	23.3158i	0.0927336	+	0.0384115i	0.428568	−	0.903510i	$-0.359018\pi$
$607$	56.2893	+	23.3158i	0.0927336	+	0.0384115i	−0.335834	+	0.941921i	$0.609018\pi$
$608$	−190.240			−0.312894
$609$		−	285.235i		−	0.468366i
$610$	−43.8537	+	43.8537i	−0.0718913	+	0.0718913i
$611$			546.067i			0.893727i
$612$	125.283	+	572.194i	0.204710	+	0.934958i
$613$	−763.040			−1.24476			−0.622381	−	0.782714i	$-0.713835\pi$
$613$	−763.040			−1.24476			−0.622381	+	0.782714i	$0.713835\pi$
$614$	−39.1157	−	39.1157i	−0.0637063	−	0.0637063i
$615$	−199.882			−0.325012
$616$		−	32.6964i		−	0.0530786i
$617$	−112.410	+	271.381i	−0.182188	+	0.439840i	−0.988417	−	0.151763i	$-0.951505\pi$
$617$	−112.410	+	271.381i	−0.182188	+	0.439840i	0.806229	+	0.591603i	$0.201505\pi$
$618$	−40.2641	−	40.2641i	−0.0651522	−	0.0651522i
$619$	15.1924	−	6.29289i	0.0245434	−	0.0101662i	−0.370378	−	0.928881i	$-0.620772\pi$
$619$	15.1924	−	6.29289i	0.0245434	−	0.0101662i	0.394921	+	0.918715i	$0.370772\pi$
$620$	240.853	−	240.853i	0.388472	−	0.388472i
$621$	−532.654	+	220.632i	−0.857736	+	0.355286i
$622$	−152.307	+	63.0874i	−0.244866	+	0.101427i
$623$	−160.610	+	66.5269i	−0.257801	+	0.106785i
$624$		−	384.396i		−	0.616019i
$625$			295.489i			0.472783i
$626$	−85.9203	−	35.5894i	−0.137253	−	0.0568520i
$627$	59.3238	−	143.220i	0.0946153	−	0.228422i
$628$	−975.367			−1.55313
$629$	−24.8284	+	138.686i	−0.0394729	+	0.220487i
$630$	11.2935	−	11.2935i	0.0179262	−	0.0179262i
$631$	831.543	−	831.543i	1.31782	−	1.31782i	0.402318	−	0.915500i	$-0.368204\pi$
$631$	831.543	−	831.543i	1.31782	−	1.31782i	0.915500	−	0.402318i	$-0.131796\pi$
$632$	257.090	+	106.490i	0.406789	+	0.168497i
$633$	−855.209	+	354.239i	−1.35104	+	0.559619i
$634$	38.5685	+	15.9756i	0.0608337	+	0.0251981i
$635$	−231.078	+	95.7157i	−0.363903	+	0.150733i
$636$	−612.801	+	612.801i	−0.963524	+	0.963524i
$637$	−292.378	−	292.378i	−0.458992	−	0.458992i
$638$	71.6913	−	71.6913i	0.112369	−	0.112369i
$639$	−742.477	−	307.544i	−1.16194	−	0.481290i
$640$	78.6661	+	189.917i	0.122916	+	0.296745i
$641$	273.587	−	660.498i	0.426813	−	1.03042i	−0.553479	−	0.832863i	$-0.686700\pi$
$641$	273.587	−	660.498i	0.426813	−	1.03042i	0.980292	−	0.197555i	$-0.0633001\pi$
$642$	16.7315	−	6.93041i	0.0260615	−	0.0107950i
$643$	−80.3152	+	193.898i	−0.124907	+	0.301552i	−0.973947	−	0.226777i	$-0.927181\pi$
$643$	−80.3152	+	193.898i	−0.124907	+	0.301552i	0.849040	+	0.528329i	$0.177181\pi$
$644$	114.402	+	114.402i	0.177643	+	0.177643i
$645$	72.6030	−	30.0732i	0.112563	−	0.0466251i
$646$	−69.7645	+	15.2750i	−0.107995	+	0.0236456i
$647$			66.6173i			0.102963i	0.998674	+	0.0514817i	$0.0163944\pi$
$647$			66.6173i			0.102963i	−0.998674	+	0.0514817i	$0.983606\pi$
$648$	−185.724	+	185.724i	−0.286612	+	0.286612i
$649$	−218.500	+	527.507i	−0.336672	+	0.812799i
$650$	77.1716			0.118725
$651$		−	244.014i		−	0.374830i
$652$	−126.126	−	304.496i	−0.193445	−	0.467018i
$653$	238.679	+	576.222i	0.365512	+	0.882423i	0.994474	+	0.104987i	$0.0334802\pi$
$653$	238.679	+	576.222i	0.365512	+	0.882423i	−0.628962	+	0.777436i	$0.716520\pi$
$654$	115.154	+	47.6985i	0.176077	+	0.0729335i
$655$	154.780	+	154.780i	0.236305	+	0.236305i
$656$	−164.548	−	397.253i	−0.250835	−	0.605569i
$657$	−433.467	−	179.548i	−0.659766	−	0.273284i
$658$	−45.0925	−	18.6779i	−0.0685296	−	0.0283859i
$659$	632.278			0.959451			0.479726	−	0.877419i	$-0.340736\pi$
$659$	632.278			0.959451			0.479726	+	0.877419i	$0.340736\pi$
$660$	−126.676			−0.191934
$661$	−559.487	+	559.487i	−0.846426	+	0.846426i	−0.989685	−	0.143259i	$-0.954242\pi$
$661$	−559.487	+	559.487i	−0.846426	+	0.846426i	0.143259	+	0.989685i	$0.454242\pi$
$662$		−	3.16861i		−	0.00478643i
$663$	−100.045	−	456.926i	−0.150897	−	0.689179i
$664$	−315.418			−0.475028
$665$	−30.7250	−	30.7250i	−0.0462030	−	0.0462030i
$666$	−28.5442	+	11.8234i	−0.0428591	+	0.0177528i
$667$			1025.85i			1.53801i
$668$	311.894	−	752.980i	0.466908	−	1.12722i
$669$	−695.220	+	695.220i	−1.03919	+	1.03919i
$670$	56.2498	−	23.2994i	0.0839549	−	0.0347753i
$671$	249.176	−	249.176i	0.371350	−	0.371350i
$672$	102.889	+	42.6182i	0.153109	+	0.0634199i
$673$	383.827	−	158.986i	0.570322	−	0.236235i	−0.0788372	−	0.996888i	$-0.525121\pi$
$673$	383.827	−	158.986i	0.570322	−	0.236235i	0.649160	+	0.760652i	$0.275121\pi$
$674$	148.371	−	61.4573i	0.220135	−	0.0911830i
$675$	387.827	+	387.827i	0.574558	+	0.574558i
$676$		−	324.966i		−	0.480718i
$677$	−253.203	−	104.880i	−0.374008	−	0.154919i	0.187758	−	0.982215i	$-0.439878\pi$
$677$	−253.203	−	104.880i	−0.374008	−	0.154919i	−0.561766	+	0.827296i	$0.689878\pi$
$678$	41.4228	+	17.1579i	0.0610956	+	0.0253066i
$679$	262.235			0.386208
$680$	68.1909	+	97.9310i	0.100281	+	0.144016i
$681$	488.834	−	202.482i	0.717818	−	0.297330i
$682$	61.3310	−	61.3310i	0.0899281	−	0.0899281i
$683$	−507.390	−	210.168i	−0.742885	−	0.307713i	−0.0210502	−	0.999778i	$-0.506701\pi$
$683$	−507.390	−	210.168i	−0.742885	−	0.307713i	−0.721835	+	0.692065i	$0.756701\pi$
$684$	247.103	+	247.103i	0.361261	+	0.361261i
$685$	−30.0101	−	12.4306i	−0.0438104	−	0.0181468i
$686$	71.2548	−	29.5147i	0.103870	−	0.0430244i
$687$	40.6905	+	40.6905i	0.0592292	+	0.0592292i
$688$	119.537	+	119.537i	0.173746	+	0.173746i
$689$	489.352	−	489.352i	0.710236	−	0.710236i
$690$	−40.6173	+	40.6173i	−0.0588657	+	0.0588657i
$691$	260.559	+	629.045i	0.377075	+	0.910340i	0.992511	+	0.122153i	$0.0389800\pi$
$691$	260.559	+	629.045i	0.377075	+	0.910340i	−0.615436	+	0.788187i	$0.711020\pi$
$692$	102.034	−	246.333i	0.147449	−	0.355973i
$693$	−64.1695	+	64.1695i	−0.0925967	+	0.0925967i
$694$	−73.8269	+	178.234i	−0.106379	+	0.256821i
$695$	−94.4954	−	94.4954i	−0.135965	−	0.135965i
$696$	178.846	+	431.772i	0.256962	+	0.620362i
$697$	−298.986	−	429.383i	−0.428962	−	0.616045i
$698$		−	52.6476i		−	0.0754264i
$699$	−350.283	+	845.657i	−0.501120	+	1.20981i
$700$	58.8995	−	142.196i	0.0841421	−	0.203137i
$701$	−531.391			−0.758047			−0.379024	−	0.925387i	$-0.623740\pi$
$701$	−531.391			−0.758047			−0.379024	+	0.925387i	$0.623740\pi$
$702$	72.5299	−	72.5299i	0.103319	−	0.103319i
$703$	32.1665	+	77.6569i	0.0457561	+	0.110465i
$704$	−93.8076	−	226.472i	−0.133249	−	0.321693i
$705$	−147.971	+	357.235i	−0.209889	+	0.506716i
$706$	77.3848	+	77.3848i	0.109610	+	0.109610i
$707$	72.3390	+	174.642i	0.102318	+	0.247018i
$708$	−910.124	−	910.124i	−1.28549	−	1.28549i
$709$	537.026	+	222.444i	0.757442	+	0.313743i	0.727774	−	0.685817i	$-0.240555\pi$
$709$	537.026	+	222.444i	0.757442	+	0.313743i	0.0296681	+	0.999560i	$0.490555\pi$
$710$	−80.0690			−0.112773
$711$	−295.566	−	713.558i	−0.415704	−	1.00360i
$712$	201.409	−	201.409i	0.282878	−	0.282878i
$713$			877.602i			1.23086i
$714$	41.1535	+	7.36753i	0.0576379	+	0.0103187i
$715$	101.157			0.141479
$716$	108.125	+	108.125i	0.151012	+	0.151012i
$717$			534.749i			0.745815i
$718$		−	226.774i		−	0.315841i
$719$	−25.4823	+	61.5198i	−0.0354413	+	0.0855630i	−0.940609	−	0.339491i	$-0.889745\pi$
$719$	−25.4823	+	61.5198i	−0.0354413	+	0.0855630i	0.905168	+	0.425054i	$0.139745\pi$
$720$	104.162	−	251.470i	0.144670	−	0.349264i
$721$	83.7847	−	34.7048i	0.116206	−	0.0481342i
$722$	75.6066	−	75.6066i	0.104718	−	0.104718i
$723$	385.887	−	931.613i	0.533730	−	1.28854i
$724$	−507.304	+	210.132i	−0.700696	+	0.290238i
$725$	901.619	−	373.463i	1.24361	−	0.515121i
$726$	118.103			0.162676
$727$		−	443.304i		−	0.609771i	−0.952389	−	0.304886i	$-0.901382\pi$
$727$		−	443.304i		−	0.609771i	0.952389	−	0.304886i	$-0.0986182\pi$
$728$	−54.3776	−	22.5240i	−0.0746946	−	0.0309395i
$729$	729.000			1.00000
$730$	−46.7452			−0.0640345
$731$	173.203	+	110.981i	0.236940	+	0.151820i
$732$	303.993	+	733.904i	0.415291	+	1.00260i
$733$	472.302	−	472.302i	0.644340	−	0.644340i	−0.307279	−	0.951619i	$-0.599418\pi$
$733$	472.302	−	472.302i	0.644340	−	0.644340i	0.951619	+	0.307279i	$0.0994185\pi$
$734$	88.3482	+	36.5950i	0.120365	+	0.0498570i
$735$	−112.045	−	270.500i	−0.152442	−	0.368027i
$736$	−370.044	−	153.277i	−0.502777	−	0.208257i
$737$	−319.610	+	132.387i	−0.433664	+	0.179629i
$738$	43.9081	−	106.004i	0.0594961	−	0.143636i
$739$	−824.285	−	824.285i	−1.11541	−	1.11541i	−0.992407	−	0.123000i	$-0.960749\pi$
$739$	−824.285	−	824.285i	−1.11541	−	1.11541i	−0.123000	−	0.992407i	$-0.539251\pi$
$740$	48.5685	−	48.5685i	0.0656332	−	0.0656332i
$741$	−197.324	−	197.324i	−0.266294	−	0.266294i
$742$	23.6711	+	57.1472i	0.0319018	+	0.0770178i
$743$	−169.593	+	409.434i	−0.228254	+	0.551055i	−0.995965	−	0.0897419i	$-0.971396\pi$
$743$	−169.593	+	409.434i	−0.228254	+	0.551055i	0.767711	+	0.640797i	$0.221396\pi$
$744$	153.000	+	369.375i	0.205645	+	0.496471i
$745$	−43.0294	+	103.882i	−0.0577576	+	0.139439i
$746$	3.32799	+	3.32799i	0.00446112	+	0.00446112i
$747$	619.036	+	619.036i	0.828696	+	0.828696i
$748$	−189.484	−	272.123i	−0.253321	−	0.363801i
$749$			28.8427i			0.0385083i
$750$	112.617	+	46.6476i	0.150156	+	0.0621968i
$751$	−66.0366	+	159.426i	−0.0879315	+	0.212285i	−0.961728	−	0.274007i	$-0.911651\pi$
$751$	−66.0366	+	159.426i	−0.0879315	+	0.212285i	0.873796	+	0.486292i	$0.161651\pi$
$752$	−831.795			−1.10611
$753$	−1071.11			−1.42246
$754$	−69.8436	−	168.617i	−0.0926307	−	0.223630i
$755$	3.02944	+	7.31371i	0.00401250	+	0.00968703i
$756$	−78.2864	−	189.000i	−0.103553	−	0.250000i
$757$	504.686	+	504.686i	0.666693	+	0.666693i	0.956949	−	0.290256i	$-0.0937406\pi$
$757$	504.686	+	504.686i	0.666693	+	0.666693i	−0.290256	+	0.956949i	$0.593741\pi$
$758$	−14.8400	−	35.8269i	−0.0195778	−	0.0472651i
$759$	230.787	−	230.787i	0.304067	−	0.304067i
$760$	65.7746	+	27.2447i	0.0865455	+	0.0358483i
$761$	333.495			0.438232			0.219116	−	0.975699i	$-0.429683\pi$
$761$	333.495			0.438232			0.219116	+	0.975699i	$0.429683\pi$
$762$		−	143.574i		−	0.188417i
$763$	−140.368	+	140.368i	−0.183968	+	0.183968i
$764$		−	634.299i		−	0.830234i
$765$	58.3675	−	326.029i	0.0762974	−	0.426181i
$766$	−141.980			−0.185352
$767$	726.780	+	726.780i	0.947561	+	0.947561i
$768$	459.353			0.598116
$769$			222.073i			0.288782i	0.989521	+	0.144391i	$0.0461223\pi$
$769$			222.073i			0.288782i	−0.989521	+	0.144391i	$0.953878\pi$
$770$	−3.46003	+	8.35325i	−0.00449354	+	0.0108484i
$771$	413.309	+	413.309i	0.536068	+	0.536068i
$772$	1059.81	−	438.988i	1.37281	−	0.568638i
$773$	−283.377	+	283.377i	−0.366593	+	0.366593i	−0.866233	−	0.499640i	$-0.833466\pi$
$773$	−283.377	+	283.377i	−0.366593	+	0.366593i	0.499640	+	0.866233i	$0.333466\pi$
$774$			45.1097i			0.0582813i
$775$	771.323	−	319.492i	0.995255	−	0.412248i
$776$	−396.957	+	164.425i	−0.511542	+	0.211888i
$777$		−	49.2061i		−	0.0633283i
$778$		−	100.638i		−	0.129354i
$779$	−288.392	−	119.456i	−0.370208	−	0.153345i
$780$	−87.2649	+	210.676i	−0.111878	+	0.270098i
$781$	454.950			0.582523
$782$	−148.009	−	26.4975i	−0.189270	−	0.0338842i
$783$	496.389	−	1198.39i	0.633958	−	1.53051i
$784$	445.363	−	445.363i	0.568065	−	0.568065i
$785$	509.539	+	211.058i	0.649094	+	0.268864i
$786$	−116.085	+	48.0839i	−0.147691	+	0.0611754i
$787$	1185.72	+	491.140i	1.50663	+	0.624066i	0.974859	−	0.222823i	$-0.0715273\pi$
$787$	1185.72	+	491.140i	1.50663	+	0.624066i	0.531769	+	0.846889i	$0.321527\pi$
$788$	−57.6985	+	23.8995i	−0.0732214	+	0.0303293i
$789$	89.4487	−	89.4487i	0.113370	−	0.113370i
$790$	−54.4121	−	54.4121i	−0.0688761	−	0.0688761i
$791$	−50.4924	+	50.4924i	−0.0638337	+	0.0638337i
$792$	56.9010	−	137.371i	0.0718447	−	0.173448i
$793$	−242.754	−	586.059i	−0.306120	−	0.739040i
$794$	−43.5004	+	105.019i	−0.0547864	+	0.132266i
$795$	452.735	−	187.529i	0.569478	−	0.235886i
$796$	−289.402	+	698.678i	−0.363570	+	0.877737i
$797$	−77.0812	−	77.0812i	−0.0967141	−	0.0967141i	0.657094	−	0.753808i	$-0.271785\pi$
$797$	−77.0812	−	77.0812i	−0.0967141	−	0.0967141i	−0.753808	+	0.657094i	$0.771785\pi$
$798$	23.0437	−	9.54502i	0.0288768	−	0.0119612i
$799$	−988.742	+	216.487i	−1.23747	+	0.270947i
$800$			381.032i			0.476289i
$801$	−790.566			−0.986973
$802$	−79.9435	+	193.001i	−0.0996801	+	0.240649i
$803$	265.605			0.330766
$804$		−	779.845i		−	0.969956i
$805$	−35.0092	−	84.5198i	−0.0434897	−	0.104994i
$806$	−59.7502	−	144.250i	−0.0741318	−	0.178970i
$807$	893.970	+	370.294i	1.10777	+	0.458853i
$808$	−219.005	−	219.005i	−0.271046	−	0.271046i
$809$	−287.561	−	694.233i	−0.355452	−	0.858137i	−0.995927	−	0.0901586i	$-0.971263\pi$
$809$	−287.561	−	694.233i	−0.355452	−	0.858137i	0.640475	−	0.767979i	$-0.278737\pi$
$810$	67.1026	−	27.7948i	0.0828427	−	0.0343146i
$811$	−602.614	−	249.611i	−0.743050	−	0.307781i	−0.0211478	−	0.999776i	$-0.506732\pi$
$811$	−602.614	−	249.611i	−0.743050	−	0.307781i	−0.721902	+	0.691995i	$0.756732\pi$
$812$	−364.000			−0.448276
$813$	449.543			0.552944
$814$	12.3675	−	12.3675i	0.0151935	−	0.0151935i
$815$			186.363i			0.228667i
$816$	696.011	−	152.393i	0.852954	−	0.186756i
$817$	122.725			0.150214
$818$	−103.198	−	103.198i	−0.126159	−	0.126159i
$819$	62.5156	+	150.926i	0.0763316	+	0.184281i
$820$			255.078i			0.311071i
$821$	−282.247	+	681.404i	−0.343784	+	0.829968i	0.653542	+	0.756890i	$0.273282\pi$
$821$	−282.247	+	681.404i	−0.343784	+	0.829968i	−0.997326	+	0.0730782i	$0.976718\pi$
$822$	13.1846	−	13.1846i	0.0160397	−	0.0160397i
$823$	−412.331	+	170.793i	−0.501010	+	0.207525i	−0.618852	−	0.785507i	$-0.712402\pi$
$823$	−412.331	+	170.793i	−0.501010	+	0.207525i	0.117843	+	0.993032i	$0.462402\pi$
$824$	−105.068	+	105.068i	−0.127510	+	0.127510i
$825$	−286.856	−	118.820i	−0.347705	−	0.144024i
$826$	−84.8742	+	35.1561i	−0.102753	+	0.0425618i
$827$	−730.907	+	302.752i	−0.883806	+	0.366084i	−0.777972	−	0.628300i	$-0.783751\pi$
$827$	−730.907	+	302.752i	−0.883806	+	0.366084i	−0.105834	+	0.994384i	$0.533751\pi$
$828$	281.558	+	679.742i	0.340046	+	0.820945i
$829$			465.176i			0.561129i	0.959835	+	0.280564i	$0.0905216\pi$
$829$			465.176i			0.561129i	−0.959835	+	0.280564i	$0.909478\pi$
$830$	80.5828	+	33.3785i	0.0970877	+	0.0402151i
$831$	−1083.41	−	448.764i	−1.30374	−	0.540028i
$832$	−441.269			−0.530372
$833$	413.484	−	645.309i	0.496380	−	0.774680i
$834$	70.8715	−	29.3560i	0.0849779	−	0.0351990i
$835$	−325.872	+	325.872i	−0.390266	+	0.390266i
$836$	−182.770	−	75.7056i	−0.218624	−	0.0905570i
$837$	424.654	−	1025.21i	0.507352	−	1.22486i
$838$	107.900	+	44.6937i	0.128759	+	0.0533338i
$839$	−376.092	+	155.783i	−0.448263	+	0.185677i	−0.595383	−	0.803442i	$-0.703000\pi$
$839$	−376.092	+	155.783i	−0.448263	+	0.185677i	0.147120	+	0.989119i	$0.453000\pi$
$840$	−29.4701	−	29.4701i	−0.0350835	−	0.0350835i
$841$	−1037.33	−	1037.33i	−1.23345	−	1.23345i
$842$	−160.177	+	160.177i	−0.190234	+	0.190234i
$843$	−1126.71	+	1126.71i	−1.33655	+	1.33655i
$844$	452.059	+	1091.37i	0.535616	+	1.29309i
$845$	−70.3188	+	169.765i	−0.0832175	+	0.200905i
$846$	−156.947	−	156.947i	−0.185517	−	0.185517i
$847$	−71.9807	+	173.777i	−0.0849831	+	0.205167i
$848$	745.404	+	745.404i	0.879014	+	0.879014i
$849$	−354.988	−	857.018i	−0.418125	−	1.00944i
$850$	30.5944	+	139.731i	0.0359934	+	0.164390i
$851$			176.971i			0.207956i
$852$	−392.470	+	947.507i	−0.460646	+	1.11210i
$853$	199.765	−	482.274i	0.234191	−	0.565386i	−0.762472	−	0.647022i	$-0.776014\pi$
$853$	199.765	−	482.274i	0.234191	−	0.565386i	0.996662	+	0.0816356i	$0.0260144\pi$
$854$	56.6981			0.0663912
$855$	−75.6182	−	182.558i	−0.0884423	−	0.213519i
$856$	−18.0847	−	43.6604i	−0.0211270	−	0.0510052i
$857$	−167.607	−	404.640i	−0.195575	−	0.472159i	0.795420	−	0.606058i	$-0.207250\pi$
$857$	−167.607	−	404.640i	−0.195575	−	0.472159i	−0.990995	+	0.133899i	$0.957250\pi$
$858$	−22.2212	+	53.6468i	−0.0258988	+	0.0625254i
$859$	−231.551	−	231.551i	−0.269559	−	0.269559i	0.559363	−	0.828923i	$-0.311046\pi$
$859$	−231.551	−	231.551i	−0.269559	−	0.269559i	−0.828923	+	0.559363i	$0.811046\pi$
$860$	−38.3776	−	92.6518i	−0.0446252	−	0.107735i
$861$	129.213	+	129.213i	0.150073	+	0.150073i
$862$	0.708586	+	0.293506i	0.000822026	+	0.000340494i
$863$	−1473.72			−1.70767			−0.853835	−	0.520543i	$-0.825730\pi$
$863$	−1473.72			−1.70767			−0.853835	+	0.520543i	$0.825730\pi$
$864$	358.113	+	358.113i	0.414483	+	0.414483i
$865$	−106.607	+	106.607i	−0.123245	+	0.123245i
$866$		−	77.7889i		−	0.0898255i
$867$	787.675	−	362.294i	0.908507	−	0.417870i
$868$	−311.397			−0.358752
$869$	309.169	+	309.169i	0.355775	+	0.355775i
$870$		−	129.235i		−	0.148546i
$871$			622.745i			0.714977i
$872$	124.468	−	300.492i	0.142739	−	0.344601i
$873$	1101.76	+	456.364i	1.26204	+	0.522754i
$874$	−82.8772	+	34.3289i	−0.0948252	+	0.0392779i
$875$	−137.275	+	137.275i	−0.156886	+	0.156886i
$876$	−229.128	+	553.165i	−0.261562	+	0.631467i
$877$	433.130	−	179.408i	0.493877	−	0.204570i	−0.121822	−	0.992552i	$-0.538874\pi$
$877$	433.130	−	179.408i	0.493877	−	0.204570i	0.615699	+	0.787981i	$0.288874\pi$
$878$	−106.466	+	44.0996i	−0.121260	+	0.0502274i
$879$	−811.456			−0.923158
$880$			154.087i			0.175099i
$881$	487.378	+	201.879i	0.553210	+	0.229147i	0.641735	−	0.766927i	$-0.278215\pi$
$881$	487.378	+	201.879i	0.553210	+	0.229147i	−0.0885243	+	0.996074i	$0.528215\pi$
$882$	168.067			0.190552
$883$	−548.169			−0.620803			−0.310402	−	0.950605i	$-0.600464\pi$
$883$	−548.169			−0.620803			−0.310402	+	0.950605i	$0.600464\pi$
$884$	−583.103	+	127.671i	−0.659618	+	0.144424i
$885$	278.516	+	672.396i	0.314707	+	0.759770i
$886$	72.9512	−	72.9512i	0.0823377	−	0.0823377i
$887$	−886.966	−	367.393i	−0.999961	−	0.414197i	−0.178178	−	0.983998i	$-0.557020\pi$
$887$	−886.966	−	367.393i	−0.999961	−	0.414197i	−0.821783	+	0.569801i	$0.807020\pi$
$888$	30.8528	+	74.4853i	0.0347442	+	0.0838798i
$889$	211.255	+	87.5046i	0.237632	+	0.0984304i
$890$	−72.7696	+	30.1421i	−0.0817635	+	0.0338676i
$891$	−381.276	+	157.930i	−0.427919	+	0.177250i
$892$	887.200	+	887.200i	0.994619	+	0.994619i
$893$	−426.989	+	426.989i	−0.478151	+	0.478151i
$894$	−45.6396	−	45.6396i	−0.0510510	−	0.0510510i
$895$	−33.0883	−	79.8823i	−0.0369702	−	0.0892539i
$896$	71.9176	−	173.624i	0.0802652	−	0.193777i
$897$	−224.839	−	542.808i	−0.250656	−	0.605137i
$898$	2.77190	−	6.69195i	0.00308675	−	0.00745207i
$899$	−1396.16	−	1396.16i	−1.55302	−	1.55302i
$900$	494.922	−	494.922i	0.549914	−	0.549914i
$901$	1080.05	+	692.049i	1.19873	+	0.768090i
$902$			64.9533i			0.0720103i
$903$	−66.3747	−	27.4933i	−0.0735046	−	0.0304466i
$904$	44.7731	−	108.092i	0.0495278	−	0.119571i
$905$	310.489			0.343082
$906$	−4.54416			−0.00501562
$907$	−153.671	−	370.993i	−0.169427	−	0.409034i	0.816245	−	0.577706i	$-0.196052\pi$
$907$	−153.671	−	370.993i	−0.169427	−	0.409034i	−0.985672	+	0.168672i	$0.946052\pi$
$908$	−258.395	−	623.822i	−0.284577	−	0.687029i
$909$			859.632i			0.945690i
$910$	11.5088	+	11.5088i	0.0126470	+	0.0126470i
$911$	412.710	+	996.370i	0.453029	+	1.09371i	0.971164	+	0.238411i	$0.0766265\pi$
$911$	412.710	+	996.370i	0.453029	+	1.09371i	−0.518135	+	0.855299i	$0.673373\pi$
$912$	300.573	−	300.573i	0.329575	−	0.329575i
$913$	−457.870	−	189.656i	−0.501501	−	0.207728i
$914$	333.955			0.365378
$915$		−	449.177i		−	0.490904i
$916$	51.9268	−	51.9268i	0.0566887	−	0.0566887i
$917$		−	200.114i		−	0.218226i
$918$	160.081	+	102.573i	0.174380	+	0.111735i
$919$	−1163.94			−1.26652			−0.633262	−	0.773938i	$-0.718284\pi$
$919$	−1163.94			−1.26652			−0.633262	+	0.773938i	$0.718284\pi$
$920$	105.990	+	105.990i	0.115206	+	0.115206i
$921$	400.648			0.435014
$922$			223.858i			0.242796i
$923$	313.407	−	756.632i	0.339553	−	0.819753i
$924$	81.8894	+	81.8894i	0.0886249	+	0.0886249i
$925$	155.539	−	64.4264i	0.168150	−	0.0696502i
$926$	−13.6224	+	13.6224i	−0.0147110	+	0.0147110i
$927$	412.410			0.444887
$928$	832.541	−	344.850i	0.897135	−	0.371605i
$929$	1590.26	−	658.706i	1.71179	−	0.709049i	0.711817	−	0.702365i	$-0.247872\pi$
$929$	1590.26	−	658.706i	1.71179	−	0.709049i	0.999978	−	0.00668405i	$-0.00212761\pi$
$930$		−	110.558i		−	0.118880i
$931$		−	457.241i		−	0.491128i
$932$	1079.18	+	447.011i	1.15792	+	0.479625i
$933$	456.920	−	1103.10i	0.489732	−	1.18232i
$934$	−146.092			−0.156415
$935$	40.1035	+	183.161i	0.0428914	+	0.195895i
$936$	−189.265	−	189.265i	−0.202206	−	0.202206i
$937$	992.125	−	992.125i	1.05883	−	1.05883i	0.0606736	−	0.998158i	$-0.480675\pi$
$937$	992.125	−	992.125i	1.05883	−	1.05883i	0.998158	−	0.0606736i	$-0.0193249\pi$
$938$	−51.4243	−	21.3006i	−0.0548234	−	0.0227086i
$939$	622.290	−	257.761i	0.662716	−	0.274506i
$940$	455.882	+	188.833i	0.484981	+	0.200886i
$941$	1655.90	−	685.895i	1.75972	−	0.728900i	0.763145	−	0.646228i	$-0.223654\pi$
$941$	1655.90	−	685.895i	1.75972	−	0.728900i	0.996577	−	0.0826726i	$-0.0263456\pi$
$942$	−223.861	+	223.861i	−0.237644	+	0.237644i
$943$	−464.718	−	464.718i	−0.492808	−	0.492808i
$944$	−1107.06	+	1107.06i	−1.17274	+	1.17274i
$945$			115.675i			0.122408i
$946$	−9.77251	−	23.5929i	−0.0103304	−	0.0249397i
$947$	−464.994	+	1122.60i	−0.491018	+	1.18542i	0.463184	+	0.886262i	$0.346707\pi$
$947$	−464.994	+	1122.60i	−0.491018	+	1.18542i	−0.954203	+	0.299161i	$0.903293\pi$
$948$	−910.602	+	377.184i	−0.960551	+	0.397873i
$949$	182.971	−	441.730i	0.192804	−	0.465469i
$950$	60.3431	+	60.3431i	0.0635191	+	0.0635191i
$951$	−279.338	+	115.706i	−0.293731	+	0.121667i
$952$	19.2254	−	107.389i	0.0201947	−	0.112804i
$953$		−	1552.12i		−	1.62867i	−0.580398	−	0.814333i	$-0.697103\pi$
$953$		−	1552.12i		−	1.62867i	0.580398	−	0.814333i	$-0.302897\pi$
$954$			281.294i			0.294857i
$955$	−137.255	+	331.362i	−0.143722	+	0.346976i
$956$	682.416			0.713825
$957$			734.309i			0.767303i
$958$	87.4478	+	211.118i	0.0912817	+	0.220373i
$959$	11.3642	+	27.4356i	0.0118501	+	0.0286086i
$960$	−288.676	−	119.574i	−0.300704	−	0.124556i
$961$	−514.866	−	514.866i	−0.535761	−	0.535761i
$962$	−12.0488	−	29.0883i	−0.0125247	−	0.0302373i
$963$	−50.1945	+	121.180i	−0.0521230	+	0.125836i
$964$	−1188.87	−	492.446i	−1.23327	−	0.510836i
$965$	−648.646			−0.672172
$966$	52.5139			0.0543622
$967$	449.474	−	449.474i	0.464813	−	0.464813i	−0.435416	−	0.900229i	$-0.643399\pi$
$967$	449.474	−	449.474i	0.464813	−	0.464813i	0.900229	+	0.435416i	$0.143399\pi$
$968$		−	308.186i		−	0.318374i
$969$	279.058	−	435.515i	0.287986	−	0.449448i
$970$	118.814			0.122489
$971$	68.4428	+	68.4428i	0.0704869	+	0.0704869i	0.741471	−	0.670984i	$-0.234128\pi$
$971$	68.4428	+	68.4428i	0.0704869	+	0.0704869i	−0.670984	+	0.741471i	$0.734128\pi$
$972$		−	930.308i		−	0.957107i
$973$			122.172i			0.125563i
$974$	−83.8516	+	202.436i	−0.0860899	+	0.207839i
$975$	−395.220	+	395.220i	−0.405354	+	0.405354i
$976$	892.712	−	369.773i	0.914664	−	0.378866i
$977$	−1043.58	+	1043.58i	−1.06814	+	1.06814i	−0.0706425	+	0.997502i	$0.522505\pi$
$977$	−1043.58	+	1043.58i	−1.06814	+	1.06814i	−0.997502	+	0.0706425i	$0.977495\pi$
$978$	−98.8341	−	40.9384i	−0.101057	−	0.0418593i
$979$	413.475	−	171.267i	0.422344	−	0.174941i
$980$	−345.196	+	142.985i	−0.352241	+	0.145903i
$981$	−834.021	+	345.463i	−0.850175	+	0.352154i
$982$			64.6417i			0.0658266i
$983$	1317.22	+	545.610i	1.34000	+	0.555046i	0.933491	−	0.358601i	$-0.116746\pi$
$983$	1317.22	+	545.610i	1.34000	+	0.555046i	0.406509	+	0.913647i	$0.366746\pi$
$984$	−276.614	−	114.577i	−0.281112	−	0.116440i
$985$	35.3137			0.0358515
$986$	277.619	−	193.311i	0.281561	−	0.196056i
$987$	326.589	−	135.277i	0.330890	−	0.137059i
$988$	−251.813	+	251.813i	−0.254872	+	0.254872i
$989$	238.718	+	98.8802i	0.241373	+	0.0999799i
$990$	−29.0740	+	29.0740i	−0.0293677	+	0.0293677i
$991$	44.0812	+	18.2590i	0.0444815	+	0.0184248i	0.404813	−	0.914399i	$-0.367337\pi$
$991$	44.0812	+	18.2590i	0.0444815	+	0.0184248i	−0.360332	+	0.932824i	$0.617337\pi$
$992$	712.227	−	295.014i	0.717971	−	0.297393i
$993$	16.2275	+	16.2275i	0.0163419	+	0.0163419i
$994$	51.7603	+	51.7603i	0.0520728	+	0.0520728i
$995$	302.372	−	302.372i	0.303891	−	0.303891i
$996$	789.978	−	789.978i	0.793150	−	0.793150i
$997$	377.727	+	911.914i	0.378864	+	0.914658i	0.992179	+	0.124820i	$0.0398353\pi$
$997$	377.727	+	911.914i	0.378864	+	0.914658i	−0.613316	+	0.789838i	$0.710165\pi$
$998$	−88.9417	+	214.724i	−0.0891200	+	0.215155i
$999$	85.6325	−	206.735i	0.0857182	−	0.206942i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	51.3.g.a.8.1	✓	4
3.2	odd	2		51.3.g.b.8.1	yes	4
17.15	even	8		51.3.g.b.32.1	yes	4
51.32	odd	8	inner	51.3.g.a.32.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.3.g.a.8.1	✓	4	1.1	even	1	trivial
51.3.g.a.32.1	yes	4	51.32	odd	8	inner
51.3.g.b.8.1	yes	4	3.2	odd	2
51.3.g.b.32.1	yes	4	17.15	even	8

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:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	51.g (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.292893 - 0.292893i) q^{2} +3.00000 q^{3} -3.82843i q^{4} +(-0.828427 + 2.00000i) q^{5} +(-0.878680 - 0.878680i) q^{6} +(1.82843 - 0.757359i) q^{7} +(-2.29289 + 2.29289i) q^{8} +9.00000 q^{9} +(0.828427 - 0.343146i) q^{10} +(-4.70711 + 1.94975i) q^{11} -11.4853i q^{12} +9.17157i q^{13} +(-0.757359 - 0.313708i) q^{14} +(-2.48528 + 6.00000i) q^{15} -13.9706 q^{16} +(-16.6066 + 3.63604i) q^{17} +(-2.63604 - 2.63604i) q^{18} +(-7.17157 + 7.17157i) q^{19} +(7.65685 + 3.17157i) q^{20} +(5.48528 - 2.27208i) q^{21} +(1.94975 + 0.807612i) q^{22} +(-19.7279 + 8.17157i) q^{23} +(-6.87868 + 6.87868i) q^{24} +(14.3640 + 14.3640i) q^{25} +(2.68629 - 2.68629i) q^{26} +27.0000 q^{27} +(-2.89949 - 7.00000i) q^{28} +(18.3848 - 44.3848i) q^{29} +(2.48528 - 1.02944i) q^{30} +(15.7279 - 37.9706i) q^{31} +(13.2635 + 13.2635i) q^{32} +(-14.1213 + 5.84924i) q^{33} +(5.92893 + 3.79899i) q^{34} +4.28427i q^{35} -34.4558i q^{36} +(3.17157 - 7.65685i) q^{37} +4.20101 q^{38} +27.5147i q^{39} +(-2.68629 - 6.48528i) q^{40} +(11.7782 + 28.4350i) q^{41} +(-2.27208 - 0.941125i) q^{42} +(-8.55635 - 8.55635i) q^{43} +(7.46447 + 18.0208i) q^{44} +(-7.45584 + 18.0000i) q^{45} +(8.17157 + 3.38478i) q^{46} +59.5391 q^{47} -41.9117 q^{48} +(-31.8787 + 31.8787i) q^{49} -8.41421i q^{50} +(-49.8198 + 10.9081i) q^{51} +35.1127 q^{52} +(-53.3553 - 53.3553i) q^{53} +(-7.90812 - 7.90812i) q^{54} -11.0294i q^{55} +(-2.45584 + 5.92893i) q^{56} +(-21.5147 + 21.5147i) q^{57} +(-18.3848 + 7.61522i) q^{58} +(79.2426 - 79.2426i) q^{59} +(22.9706 + 9.51472i) q^{60} +(-63.8995 + 26.4680i) q^{61} +(-15.7279 + 6.51472i) q^{62} +(16.4558 - 6.81623i) q^{63} +48.1127i q^{64} +(-18.3431 - 7.59798i) q^{65} +(5.84924 + 2.42284i) q^{66} +67.8995 q^{67} +(13.9203 + 63.5772i) q^{68} +(-59.1838 + 24.5147i) q^{69} +(1.25483 - 1.25483i) q^{70} +(-82.4975 - 34.1716i) q^{71} +(-20.6360 + 20.6360i) q^{72} +(-48.1630 - 19.9497i) q^{73} +(-3.17157 + 1.31371i) q^{74} +(43.0919 + 43.0919i) q^{75} +(27.4558 + 27.4558i) q^{76} +(-7.12994 + 7.12994i) q^{77} +(8.05887 - 8.05887i) q^{78} +(-32.8406 - 79.2843i) q^{79} +(11.5736 - 27.9411i) q^{80} +81.0000 q^{81} +(4.87868 - 11.7782i) q^{82} +(68.7817 + 68.7817i) q^{83} +(-8.69848 - 21.0000i) q^{84} +(6.48528 - 36.2254i) q^{85} +5.01219i q^{86} +(55.1543 - 133.154i) q^{87} +(6.32233 - 15.2635i) q^{88} -87.8406 q^{89} +(7.45584 - 3.08831i) q^{90} +(6.94618 + 16.7696i) q^{91} +(31.2843 + 75.5269i) q^{92} +(47.1838 - 113.912i) q^{93} +(-17.4386 - 17.4386i) q^{94} +(-8.40202 - 20.2843i) q^{95} +(39.7904 + 39.7904i) q^{96} +(122.418 + 50.7071i) q^{97} +18.6741 q^{98} +(-42.3640 + 17.5477i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 12 q^{3} + 8 q^{5} - 12 q^{6} - 4 q^{7} - 12 q^{8} + 36 q^{9} - 8 q^{10} - 16 q^{11} - 20 q^{14} + 24 q^{15} + 12 q^{16} - 24 q^{17} - 36 q^{18} - 40 q^{19} + 8 q^{20} - 12 q^{21} - 12 q^{22}+ \cdots - 144 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 12 * q^3 + 8 * q^5 - 12 * q^6 - 4 * q^7 - 12 * q^8 + 36 * q^9 - 8 * q^10 - 16 * q^11 - 20 * q^14 + 24 * q^15 + 12 * q^16 - 24 * q^17 - 36 * q^18 - 40 * q^19 + 8 * q^20 - 12 * q^21 - 12 * q^22 - 28 * q^23 - 36 * q^24 + 32 * q^25 + 56 * q^26 + 108 * q^27 + 28 * q^28 - 24 * q^30 + 12 * q^31 - 12 * q^32 - 48 * q^33 + 52 * q^34 + 24 * q^37 + 96 * q^38 - 56 * q^40 + 16 * q^41 - 60 * q^42 + 28 * q^43 + 44 * q^44 + 72 * q^45 + 44 * q^46 - 56 * q^47 + 36 * q^48 - 136 * q^49 - 72 * q^51 + 16 * q^52 - 72 * q^53 - 108 * q^54 + 92 * q^56 - 120 * q^57 + 300 * q^59 + 24 * q^60 - 216 * q^61 - 12 * q^62 - 36 * q^63 - 96 * q^65 - 36 * q^66 + 232 * q^67 - 32 * q^68 - 84 * q^69 - 176 * q^70 - 132 * q^71 - 108 * q^72 - 88 * q^73 - 24 * q^74 + 96 * q^75 + 8 * q^76 - 136 * q^77 + 168 * q^78 + 44 * q^79 + 216 * q^80 + 324 * q^81 + 28 * q^82 - 36 * q^83 + 84 * q^84 - 8 * q^85 + 96 * q^88 - 176 * q^89 - 72 * q^90 + 288 * q^91 + 12 * q^92 + 36 * q^93 + 264 * q^94 - 192 * q^95 - 36 * q^96 + 204 * q^97 + 284 * q^98 - 144 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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