LMFDB - Embedded newform 429.2.i.d.100.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(100,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("429.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.3118758597603.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{8} - 16x^{6} - 34x^{5} + 43x^{4} + 155x^{3} + 199x^{2} + 124x + 43 $ x^10 - 4x^8 - 16x^6 - 34x^5 + 43x^4 + 155x^3 + 199x^2 + 124*x + 43
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.2
Root			$-0.676693 - 0.583217i$ of defining polynomial
Character	$\chi$	$=$	429.100
Dual form			429.2.i.d.133.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.10097 + 1.90694i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-1.42428 - 2.46692i) q^{4} -0.484911 q^{5} +(1.10097 + 1.90694i) q^{6} +(0.958152 + 1.65957i) q^{7} +1.86848 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.10097 + 1.90694i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-1.42428 - 2.46692i) q^{4} -0.484911 q^{5} +(1.10097 + 1.90694i) q^{6} +(0.958152 + 1.65957i) q^{7} +1.86848 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.533873 - 0.924696i) q^{10} +(-0.500000 + 0.866025i) q^{11} -2.84856 q^{12} +(3.10980 + 1.82460i) q^{13} -4.21959 q^{14} +(-0.242455 + 0.419945i) q^{15} +(0.791418 - 1.37078i) q^{16} +(1.19065 + 2.06226i) q^{17} +2.20194 q^{18} +(2.05912 + 3.56651i) q^{19} +(0.690648 + 1.19624i) q^{20} +1.91630 q^{21} +(-1.10097 - 1.90694i) q^{22} +(-2.96811 + 5.14092i) q^{23} +(0.934238 - 1.61815i) q^{24} -4.76486 q^{25} +(-6.90320 + 3.92136i) q^{26} -1.00000 q^{27} +(2.72935 - 4.72737i) q^{28} +(-3.41117 + 5.90833i) q^{29} +(-0.533873 - 0.924696i) q^{30} +10.3099 q^{31} +(3.61113 + 6.25467i) q^{32} +(0.500000 + 0.866025i) q^{33} -5.24348 q^{34} +(-0.464618 - 0.804743i) q^{35} +(-1.42428 + 2.46692i) q^{36} +(-4.72586 + 8.18543i) q^{37} -9.06815 q^{38} +(3.13505 - 1.78086i) q^{39} -0.906044 q^{40} +(0.666734 - 1.15482i) q^{41} +(-2.10980 + 3.65428i) q^{42} +(-3.11976 - 5.40358i) q^{43} +2.84856 q^{44} +(0.242455 + 0.419945i) q^{45} +(-6.53561 - 11.3200i) q^{46} -1.23951 q^{47} +(-0.791418 - 1.37078i) q^{48} +(1.66389 - 2.88194i) q^{49} +(5.24598 - 9.08630i) q^{50} +2.38130 q^{51} +(0.0719280 - 10.2704i) q^{52} +8.17217 q^{53} +(1.10097 - 1.90694i) q^{54} +(0.242455 - 0.419945i) q^{55} +(1.79028 + 3.10086i) q^{56} +4.11825 q^{57} +(-7.51121 - 13.0098i) q^{58} +(-6.00722 - 10.4048i) q^{59} +1.38130 q^{60} +(-1.74095 - 3.01541i) q^{61} +(-11.3509 + 19.6604i) q^{62} +(0.958152 - 1.65957i) q^{63} -12.7374 q^{64} +(-1.50797 - 0.884768i) q^{65} -2.20194 q^{66} +(-1.80024 + 3.11811i) q^{67} +(3.39163 - 5.87448i) q^{68} +(2.96811 + 5.14092i) q^{69} +2.04613 q^{70} +(2.81972 + 4.88389i) q^{71} +(-0.934238 - 1.61815i) q^{72} +10.1156 q^{73} +(-10.4061 - 18.0239i) q^{74} +(-2.38243 + 4.12649i) q^{75} +(5.86553 - 10.1594i) q^{76} -1.91630 q^{77} +(-0.0556005 + 7.93903i) q^{78} -5.62348 q^{79} +(-0.383767 + 0.664704i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.46811 + 2.54284i) q^{82} +14.1891 q^{83} +(-2.72935 - 4.72737i) q^{84} +(-0.577358 - 1.00001i) q^{85} +13.7391 q^{86} +(3.41117 + 5.90833i) q^{87} +(-0.934238 + 1.61815i) q^{88} +(-0.222983 + 0.386217i) q^{89} -1.06775 q^{90} +(-0.0483879 + 6.90916i) q^{91} +16.9097 q^{92} +(5.15497 - 8.92866i) q^{93} +(1.36467 - 2.36368i) q^{94} +(-0.998492 - 1.72944i) q^{95} +7.22227 q^{96} +(4.32570 + 7.49233i) q^{97} +(3.66379 + 6.34587i) q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 5 q^{3} - 10 q^{4} - 4 q^{5} - 7 q^{7} + 6 q^{8} - 5 q^{9}+O(q^{10}) $ 10 * q + 5 * q^3 - 10 * q^4 - 4 * q^5 - 7 * q^7 + 6 * q^8 - 5 * q^9	\( 10 q + 5 q^{3} - 10 q^{4} - 4 q^{5} - 7 q^{7} + 6 q^{8} - 5 q^{9} - 7 q^{10} - 5 q^{11} - 20 q^{12} + 9 q^{13} + 2 q^{14} - 2 q^{15} - 4 q^{16} - 3 q^{17} - 7 q^{19} - 8 q^{20} - 14 q^{21} - 11 q^{23} + 3 q^{24} - 6 q^{25} - 4 q^{26} - 10 q^{27} - 5 q^{28} + 2 q^{29} + 7 q^{30} + 20 q^{31} + 9 q^{32} + 5 q^{33} + 58 q^{34} + 14 q^{35} - 10 q^{36} - 15 q^{37} - 38 q^{38} - 6 q^{39} + 30 q^{40} + 2 q^{41} + q^{42} - 7 q^{43} + 20 q^{44} + 2 q^{45} - 20 q^{46} + 36 q^{47} + 4 q^{48} - 14 q^{49} + 2 q^{50} - 6 q^{51} - 3 q^{52} + 30 q^{53} + 2 q^{55} - 3 q^{56} - 14 q^{57} - 5 q^{58} + 4 q^{59} - 16 q^{60} + 14 q^{61} - 46 q^{62} - 7 q^{63} - 74 q^{64} - 44 q^{65} + 5 q^{67} + 24 q^{68} + 11 q^{69} + 80 q^{70} + 13 q^{71} - 3 q^{72} + 56 q^{73} - 15 q^{74} - 3 q^{75} - 2 q^{76} + 14 q^{77} - 23 q^{78} + 32 q^{79} + 22 q^{80} - 5 q^{81} - 4 q^{82} + 24 q^{83} + 5 q^{84} - 13 q^{85} + 4 q^{86} - 2 q^{87} - 3 q^{88} + 6 q^{89} + 14 q^{90} - 29 q^{91} - 4 q^{92} + 10 q^{93} + 2 q^{94} + 21 q^{95} + 18 q^{96} - 9 q^{97} - 16 q^{98} + 10 q^{99}+O(q^{100}) \) 10 * q + 5 * q^3 - 10 * q^4 - 4 * q^5 - 7 * q^7 + 6 * q^8 - 5 * q^9 - 7 * q^10 - 5 * q^11 - 20 * q^12 + 9 * q^13 + 2 * q^14 - 2 * q^15 - 4 * q^16 - 3 * q^17 - 7 * q^19 - 8 * q^20 - 14 * q^21 - 11 * q^23 + 3 * q^24 - 6 * q^25 - 4 * q^26 - 10 * q^27 - 5 * q^28 + 2 * q^29 + 7 * q^30 + 20 * q^31 + 9 * q^32 + 5 * q^33 + 58 * q^34 + 14 * q^35 - 10 * q^36 - 15 * q^37 - 38 * q^38 - 6 * q^39 + 30 * q^40 + 2 * q^41 + q^42 - 7 * q^43 + 20 * q^44 + 2 * q^45 - 20 * q^46 + 36 * q^47 + 4 * q^48 - 14 * q^49 + 2 * q^50 - 6 * q^51 - 3 * q^52 + 30 * q^53 + 2 * q^55 - 3 * q^56 - 14 * q^57 - 5 * q^58 + 4 * q^59 - 16 * q^60 + 14 * q^61 - 46 * q^62 - 7 * q^63 - 74 * q^64 - 44 * q^65 + 5 * q^67 + 24 * q^68 + 11 * q^69 + 80 * q^70 + 13 * q^71 - 3 * q^72 + 56 * q^73 - 15 * q^74 - 3 * q^75 - 2 * q^76 + 14 * q^77 - 23 * q^78 + 32 * q^79 + 22 * q^80 - 5 * q^81 - 4 * q^82 + 24 * q^83 + 5 * q^84 - 13 * q^85 + 4 * q^86 - 2 * q^87 - 3 * q^88 + 6 * q^89 + 14 * q^90 - 29 * q^91 - 4 * q^92 + 10 * q^93 + 2 * q^94 + 21 * q^95 + 18 * q^96 - 9 * q^97 - 16 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$	−1.10097	+	1.90694i	−0.778505	+	1.34841i	0.154299	+	0.988024i	$0.450688\pi$
$2$	−1.10097	+	1.90694i	−0.778505	+	1.34841i	−0.932803	+	0.360386i	$0.882645\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−1.42428	−	2.46692i	−0.712139	−	1.23346i
$5$	−0.484911			−0.216859			−0.108429	−	0.994104i	$-0.534582\pi$
$5$	−0.484911			−0.216859			−0.108429	+	0.994104i	$0.534582\pi$
$6$	1.10097	+	1.90694i	0.449470	+	0.778505i
$7$	0.958152	+	1.65957i	0.362147	+	0.627258i	0.988314	−	0.152432i	$-0.0487104\pi$
$7$	0.958152	+	1.65957i	0.362147	+	0.627258i	−0.626167	+	0.779689i	$0.715377\pi$
$8$	1.86848			0.660606
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.533873	−	0.924696i	0.168826	−	0.292414i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	−2.84856			−0.822308
$13$	3.10980	+	1.82460i	0.862503	+	0.506053i
$13$	3.10980	+	1.82460i	0.862503	+	0.506053i
$14$	−4.21959			−1.12773
$15$	−0.242455	+	0.419945i	−0.0626017	+	0.108429i
$16$	0.791418	−	1.37078i	0.197854	−	0.342694i
$17$	1.19065	+	2.06226i	0.288775	+	0.500172i	0.973518	−	0.228612i	$-0.0734188\pi$
$17$	1.19065	+	2.06226i	0.288775	+	0.500172i	−0.684743	+	0.728785i	$0.740086\pi$
$18$	2.20194			0.519003
$19$	2.05912	+	3.56651i	0.472395	+	0.818213i	0.999501	−	0.0315869i	$-0.0100561\pi$
$19$	2.05912	+	3.56651i	0.472395	+	0.818213i	−0.527106	+	0.849800i	$0.676723\pi$
$20$	0.690648	+	1.19624i	0.154434	+	0.267487i
$21$	1.91630			0.418172
$22$	−1.10097	−	1.90694i	−0.234728	−	0.406561i
$23$	−2.96811	+	5.14092i	−0.618894	+	1.07196i	0.370794	+	0.928715i	$0.379086\pi$
$23$	−2.96811	+	5.14092i	−0.618894	+	1.07196i	−0.989688	+	0.143241i	$0.954248\pi$
$24$	0.934238	−	1.61815i	0.190701	−	0.330303i
$25$	−4.76486			−0.952972
$26$	−6.90320	+	3.92136i	−1.35383	+	0.769042i
$27$	−1.00000			−0.192450
$28$	2.72935	−	4.72737i	0.515799	−	0.893390i
$29$	−3.41117	+	5.90833i	−0.633439	+	1.09715i	0.353404	+	0.935471i	$0.385024\pi$
$29$	−3.41117	+	5.90833i	−0.633439	+	1.09715i	−0.986844	+	0.161678i	$0.948309\pi$
$30$	−0.533873	−	0.924696i	−0.0974715	−	0.168826i
$31$	10.3099			1.85172			0.925859	−	0.377869i	$-0.123343\pi$
$31$	10.3099			1.85172			0.925859	+	0.377869i	$0.123343\pi$
$32$	3.61113	+	6.25467i	0.638364	+	1.10568i
$33$	0.500000	+	0.866025i	0.0870388	+	0.150756i
$34$	−5.24348			−0.899250
$35$	−0.464618	−	0.804743i	−0.0785348	−	0.136026i
$36$	−1.42428	+	2.46692i	−0.237380	+	0.411154i
$37$	−4.72586	+	8.18543i	−0.776926	+	1.34568i	0.156779	+	0.987634i	$0.449889\pi$
$37$	−4.72586	+	8.18543i	−0.776926	+	1.34568i	−0.933705	+	0.358042i	$0.883444\pi$
$38$	−9.06815			−1.47105
$39$	3.13505	−	1.78086i	0.502009	−	0.285166i
$40$	−0.906044			−0.143258
$41$	0.666734	−	1.15482i	0.104126	−	0.180352i	−0.809255	−	0.587458i	$-0.800129\pi$
$41$	0.666734	−	1.15482i	0.104126	−	0.180352i	0.913381	+	0.407106i	$0.133462\pi$
$42$	−2.10980	+	3.65428i	−0.325549	+	0.563867i
$43$	−3.11976	−	5.40358i	−0.475758	−	0.824038i	0.523856	−	0.851807i	$-0.324493\pi$
$43$	−3.11976	−	5.40358i	−0.475758	−	0.824038i	−0.999614	+	0.0277692i	$0.991160\pi$
$44$	2.84856			0.429436
$45$	0.242455	+	0.419945i	0.0361431	+	0.0626017i
$46$	−6.53561	−	11.3200i	−0.963624	−	1.66905i
$47$	−1.23951			−0.180801			−0.0904007	−	0.995905i	$-0.528815\pi$
$47$	−1.23951			−0.180801			−0.0904007	+	0.995905i	$0.528815\pi$
$48$	−0.791418	−	1.37078i	−0.114231	−	0.197854i
$49$	1.66389	−	2.88194i	0.237698	−	0.411706i
$50$	5.24598	−	9.08630i	0.741893	−	1.28500i
$51$	2.38130			0.333448
$52$	0.0719280	−	10.2704i	0.00997461	−	1.42424i
$53$	8.17217			1.12253			0.561267	−	0.827635i	$-0.310314\pi$
$53$	8.17217			1.12253			0.561267	+	0.827635i	$0.310314\pi$
$54$	1.10097	−	1.90694i	0.149823	−	0.259502i
$55$	0.242455	−	0.419945i	0.0326927	−	0.0566254i
$56$	1.79028	+	3.10086i	0.239237	+	0.414370i
$57$	4.11825			0.545475
$58$	−7.51121	−	13.0098i	−0.986271	−	1.70827i
$59$	−6.00722	−	10.4048i	−0.782073	−	1.35459i	−0.930732	−	0.365702i	$-0.880829\pi$
$59$	−6.00722	−	10.4048i	−0.782073	−	1.35459i	0.148659	−	0.988889i	$-0.452504\pi$
$60$	1.38130			0.178325
$61$	−1.74095	−	3.01541i	−0.222905	−	0.386084i	0.732784	−	0.680462i	$-0.238221\pi$
$61$	−1.74095	−	3.01541i	−0.222905	−	0.386084i	−0.955689	+	0.294378i	$0.904887\pi$
$62$	−11.3509	+	19.6604i	−1.44157	+	2.49688i
$63$	0.958152	−	1.65957i	0.120716	−	0.209086i
$64$	−12.7374			−1.59217
$65$	−1.50797	−	0.884768i	−0.187041	−	0.109742i
$66$	−2.20194			−0.271041
$67$	−1.80024	+	3.11811i	−0.219935	+	0.380938i	−0.954788	−	0.297288i	$-0.903918\pi$
$67$	−1.80024	+	3.11811i	−0.219935	+	0.380938i	0.734853	+	0.678226i	$0.237251\pi$
$68$	3.39163	−	5.87448i	0.411296	−	0.712385i
$69$	2.96811	+	5.14092i	0.357319	+	0.618894i
$70$	2.04613			0.244559
$71$	2.81972	+	4.88389i	0.334639	+	0.579611i	0.983415	−	0.181368i	$-0.0580524\pi$
$71$	2.81972	+	4.88389i	0.334639	+	0.579611i	−0.648777	+	0.760979i	$0.724719\pi$
$72$	−0.934238	−	1.61815i	−0.110101	−	0.190701i
$73$	10.1156			1.18394			0.591969	−	0.805961i	$-0.298351\pi$
$73$	10.1156			1.18394			0.591969	+	0.805961i	$0.298351\pi$
$74$	−10.4061	−	18.0239i	−1.20968	−	2.09523i
$75$	−2.38243	+	4.12649i	−0.275099	+	0.476486i
$76$	5.86553	−	10.1594i	0.672823	−	1.16536i
$77$	−1.91630			−0.218383
$78$	−0.0556005	+	7.93903i	−0.00629552	+	0.898918i
$79$	−5.62348			−0.632691			−0.316346	−	0.948644i	$-0.602456\pi$
$79$	−5.62348			−0.632691			−0.316346	+	0.948644i	$0.602456\pi$
$80$	−0.383767	+	0.664704i	−0.0429065	+	0.0743162i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	1.46811	+	2.54284i	0.162126	+	0.280810i
$83$	14.1891			1.55745			0.778727	−	0.627364i	$-0.215866\pi$
$83$	14.1891			1.55745			0.778727	+	0.627364i	$0.215866\pi$
$84$	−2.72935	−	4.72737i	−0.297797	−	0.515799i
$85$	−0.577358	−	1.00001i	−0.0626233	−	0.108467i
$86$	13.7391			1.48152
$87$	3.41117	+	5.90833i	0.365716	+	0.633439i
$88$	−0.934238	+	1.61815i	−0.0995901	+	0.172495i
$89$	−0.222983	+	0.386217i	−0.0236361	+	0.0409390i	−0.877602	−	0.479391i	$-0.840858\pi$
$89$	−0.222983	+	0.386217i	−0.0236361	+	0.0409390i	0.853965	+	0.520330i	$0.174191\pi$
$90$	−1.06775			−0.112550
$91$	−0.0483879	+	6.90916i	−0.00507243	+	0.724277i
$92$	16.9097			1.76295
$93$	5.15497	−	8.92866i	0.534545	−	0.925859i
$94$	1.36467	−	2.36368i	0.140755	−	0.243795i
$95$	−0.998492	−	1.72944i	−0.102443	−	0.177437i
$96$	7.22227			0.737120
$97$	4.32570	+	7.49233i	0.439208	+	0.760730i	0.997629	−	0.0688275i	$-0.0219258\pi$
$97$	4.32570	+	7.49233i	0.439208	+	0.760730i	−0.558421	+	0.829558i	$0.688592\pi$
$98$	3.66379	+	6.34587i	0.370099	+	0.641030i
$99$	1.00000			0.100504
$100$	6.78649	+	11.7545i	0.678649	+	1.17545i
$101$	4.67375	−	8.09517i	0.465056	−	0.805500i	−0.534148	−	0.845391i	$-0.679368\pi$
$101$	4.67375	−	8.09517i	0.465056	−	0.805500i	0.999204	+	0.0398908i	$0.0127010\pi$
$102$	−2.62174	+	4.54099i	−0.259591	+	0.449625i
$103$	−12.4850			−1.23018			−0.615090	−	0.788457i	$-0.710881\pi$
$103$	−12.4850			−1.23018			−0.615090	+	0.788457i	$0.710881\pi$
$104$	5.81058	+	3.40922i	0.569774	+	0.334301i
$105$	−0.929237			−0.0906842
$106$	−8.99733	+	15.5838i	−0.873898	+	1.51364i
$107$	0.703898	−	1.21919i	0.0680484	−	0.117863i	−0.829994	−	0.557773i	$-0.811656\pi$
$107$	0.703898	−	1.21919i	0.0680484	−	0.117863i	0.898042	+	0.439909i	$0.144989\pi$
$108$	1.42428	+	2.46692i	0.137051	+	0.237380i
$109$	8.34052			0.798876			0.399438	−	0.916760i	$-0.369205\pi$
$109$	8.34052			0.798876			0.399438	+	0.916760i	$0.369205\pi$
$110$	0.533873	+	0.924696i	0.0509028	+	0.0881663i
$111$	4.72586	+	8.18543i	0.448559	+	0.776926i
$112$	3.03319			0.286610
$113$	−3.34147	−	5.78760i	−0.314339	−	0.544452i	0.664957	−	0.746881i	$-0.268450\pi$
$113$	−3.34147	−	5.78760i	−0.314339	−	0.544452i	−0.979297	+	0.202429i	$0.935116\pi$
$114$	−4.53408	+	7.85325i	−0.424655	+	0.735524i
$115$	1.43927	−	2.49289i	0.134213	−	0.232463i
$116$	19.4339			1.80439
$117$	0.0252507	−	3.60546i	0.00233442	−	0.333325i
$118$	26.4551			2.43539
$119$	−2.28164	+	3.95192i	−0.209158	+	0.362272i
$120$	−0.453022	+	0.784657i	−0.0413551	+	0.0716291i
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	7.66694			0.694132
$123$	−0.666734	−	1.15482i	−0.0601174	−	0.104126i
$124$	−14.6842	−	25.4338i	−1.31868	−	2.28402i
$125$	4.73509			0.423519
$126$	2.10980	+	3.65428i	0.187956	+	0.325549i
$127$	7.38377	−	12.7891i	0.655203	−	1.13485i	−0.326639	−	0.945149i	$-0.605916\pi$
$127$	7.38377	−	12.7891i	0.655203	−	1.13485i	0.981843	−	0.189697i	$-0.0607504\pi$
$128$	6.80121	−	11.7800i	0.601147	−	1.04122i
$129$	−6.23951			−0.549358
$130$	3.34744	−	1.90151i	0.293590	−	0.166774i
$131$	7.30254			0.638026			0.319013	−	0.947750i	$-0.396649\pi$
$131$	7.30254			0.638026			0.319013	+	0.947750i	$0.396649\pi$
$132$	1.42428	−	2.46692i	0.123968	−	0.214718i
$133$	−3.94591	+	6.83451i	−0.342154	+	0.592627i
$134$	−3.96403	−	6.86591i	−0.342440	−	0.593124i
$135$	0.484911			0.0417345
$136$	2.22470	+	3.85329i	0.190766	+	0.330417i
$137$	−2.69394	−	4.66604i	−0.230159	−	0.398647i	0.727696	−	0.685900i	$-0.240591\pi$
$137$	−2.69394	−	4.66604i	−0.230159	−	0.398647i	−0.957855	+	0.287253i	$0.907258\pi$
$138$	−13.0712			−1.11270
$139$	2.30517	+	3.99267i	0.195522	+	0.338654i	0.947072	−	0.321023i	$-0.104027\pi$
$139$	2.30517	+	3.99267i	0.195522	+	0.338654i	−0.751550	+	0.659677i	$0.770693\pi$
$140$	−1.32349	+	2.29236i	−0.111856	+	0.193739i
$141$	−0.619756	+	1.07345i	−0.0521929	+	0.0904007i
$142$	−12.4177			−1.04207
$143$	−3.13505	+	1.78086i	−0.262166	+	0.148923i
$144$	−1.58284			−0.131903
$145$	1.65412	−	2.86501i	0.137367	−	0.237926i
$146$	−11.1370	+	19.2898i	−0.921702	+	1.59643i
$147$	−1.66389	−	2.88194i	−0.137235	−	0.237698i
$148$	26.9238			2.21312
$149$	−7.28868	−	12.6244i	−0.597112	−	1.03423i	−0.993245	−	0.116035i	$-0.962982\pi$
$149$	−7.28868	−	12.6244i	−0.597112	−	1.03423i	0.396133	−	0.918193i	$-0.370352\pi$
$150$	−5.24598	−	9.08630i	−0.428332	−	0.741893i
$151$	−14.7218			−1.19804			−0.599022	−	0.800733i	$-0.704444\pi$
$151$	−14.7218			−1.19804			−0.599022	+	0.800733i	$0.704444\pi$
$152$	3.84742	+	6.66393i	0.312067	+	0.540516i
$153$	1.19065	−	2.06226i	0.0962582	−	0.166724i
$154$	2.10980	−	3.65428i	0.170012	−	0.294470i
$155$	−4.99940			−0.401561
$156$	−8.85844	−	5.19748i	−0.709242	−	0.416131i
$157$	14.3439			1.14477			0.572385	−	0.819985i	$-0.306018\pi$
$157$	14.3439			1.14477			0.572385	+	0.819985i	$0.306018\pi$
$158$	6.19130	−	10.7236i	0.492553	−	0.853127i
$159$	4.08609	−	7.07731i	0.324048	−	0.561267i
$160$	−1.75108	−	3.03296i	−0.138435	−	0.239776i
$161$	−11.3756			−0.896523
$162$	−1.10097	−	1.90694i	−0.0865005	−	0.149823i
$163$	−5.62355	−	9.74027i	−0.440470	−	0.762917i	0.557254	−	0.830342i	$-0.311855\pi$
$163$	−5.62355	−	9.74027i	−0.440470	−	0.762917i	−0.997724	+	0.0674250i	$0.978522\pi$
$164$	−3.79846			−0.296610
$165$	−0.242455	−	0.419945i	−0.0188751	−	0.0326927i
$166$	−15.6218	+	27.0577i	−1.21248	+	2.10008i
$167$	10.1791	−	17.6307i	0.787681	−	1.36430i	−0.139703	−	0.990193i	$-0.544615\pi$
$167$	10.1791	−	17.6307i	0.787681	−	1.36430i	0.927384	−	0.374110i	$-0.122052\pi$
$168$	3.58057			0.276247
$169$	6.34168	+	11.3483i	0.487821	+	0.872944i
$170$	2.54262			0.195010
$171$	2.05912	−	3.56651i	0.157465	−	0.272738i
$172$	−8.88680	+	15.3924i	−0.677613	+	1.17366i
$173$	5.37514	+	9.31002i	0.408665	+	0.707828i	0.994740	−	0.102428i	$-0.0326612\pi$
$173$	5.37514	+	9.31002i	0.408665	+	0.707828i	−0.586076	+	0.810256i	$0.699328\pi$
$174$	−15.0224			−1.13885
$175$	−4.56546	−	7.90761i	−0.345116	−	0.597759i
$176$	0.791418	+	1.37078i	0.0596554	+	0.103326i
$177$	−12.0144			−0.903060
$178$	−0.490996	−	0.850429i	−0.0368017	−	0.0637424i
$179$	−1.42636	+	2.47053i	−0.106611	+	0.184656i	−0.914395	−	0.404822i	$-0.867333\pi$
$179$	−1.42636	+	2.47053i	−0.106611	+	0.184656i	0.807784	+	0.589478i	$0.200667\pi$
$180$	0.690648	−	1.19624i	0.0514779	−	0.0891623i
$181$	8.36843			0.622020			0.311010	−	0.950407i	$-0.399333\pi$
$181$	8.36843			0.622020			0.311010	+	0.950407i	$0.399333\pi$
$182$	−13.1221	−	7.69907i	−0.972673	−	0.570693i
$183$	−3.48189			−0.257389
$184$	−5.54584	+	9.60568i	−0.408845	+	0.708140i
$185$	2.29162	−	3.96920i	0.168483	−	0.291822i
$186$	11.3509	+	19.6604i	0.832292	+	1.44157i
$187$	−2.38130			−0.174138
$188$	1.76541	+	3.05778i	0.128756	+	0.223012i
$189$	−0.958152	−	1.65957i	−0.0696953	−	0.120716i
$190$	4.39725			0.319010
$191$	−9.82009	−	17.0089i	−0.710557	−	1.23072i	−0.964648	−	0.263541i	$-0.915110\pi$
$191$	−9.82009	−	17.0089i	−0.710557	−	1.23072i	0.254091	−	0.967180i	$-0.418224\pi$
$192$	−6.36868	+	11.0309i	−0.459620	+	0.796085i
$193$	−9.29799	+	16.1046i	−0.669284	+	1.15923i	0.308821	+	0.951120i	$0.400066\pi$
$193$	−9.29799	+	16.1046i	−0.669284	+	1.15923i	−0.978105	+	0.208113i	$0.933268\pi$
$194$	−19.0499			−1.36770
$195$	−1.52022	+	0.863560i	−0.108865	+	0.0618408i
$196$	−9.47937			−0.677098
$197$	−8.86395	+	15.3528i	−0.631531	+	1.09384i	0.355708	+	0.934597i	$0.384240\pi$
$197$	−8.86395	+	15.3528i	−0.631531	+	1.09384i	−0.987239	+	0.159246i	$0.949094\pi$
$198$	−1.10097	+	1.90694i	−0.0782427	+	0.135520i
$199$	−9.00845	−	15.6031i	−0.638592	−	1.10607i	−0.985742	−	0.168264i	$-0.946184\pi$
$199$	−9.00845	−	15.6031i	−0.638592	−	1.10607i	0.347150	−	0.937810i	$-0.387150\pi$
$200$	−8.90303			−0.629539
$201$	1.80024	+	3.11811i	0.126979	+	0.219935i
$202$	10.2913	+	17.8251i	0.724096	+	1.25417i
$203$	−13.0737			−0.917593
$204$	−3.39163	−	5.87448i	−0.237462	−	0.411296i
$205$	−0.323307	+	0.559984i	−0.0225807	+	0.0391109i
$206$	13.7456	−	23.8081i	0.957702	−	1.65879i
$207$	5.93622			0.412596
$208$	4.96227	−	2.81881i	0.344071	−	0.195450i
$209$	−4.11825			−0.284865
$210$	1.02306	−	1.77200i	0.0705981	−	0.122279i
$211$	−8.44946	+	14.6349i	−0.581685	+	1.00751i	0.413595	+	0.910461i	$0.364273\pi$
$211$	−8.44946	+	14.6349i	−0.581685	+	1.00751i	−0.995280	+	0.0970468i	$0.969060\pi$
$212$	−11.6394	−	20.1601i	−0.799401	−	1.38460i
$213$	5.63943			0.386407
$214$	1.54994	+	2.68458i	0.105952	+	0.183514i
$215$	1.51280	+	2.62025i	0.103172	+	0.178700i
$216$	−1.86848			−0.127134
$217$	9.87848	+	17.1100i	0.670595	+	1.16150i
$218$	−9.18267	+	15.9049i	−0.621929	+	1.07721i
$219$	5.05779	−	8.76034i	0.341774	−	0.591969i
$220$	−1.38130			−0.0931270
$221$	−0.0601293	+	8.58568i	−0.00404474	+	0.577535i
$222$	−20.8121			−1.39682
$223$	9.13327	−	15.8193i	0.611609	−	1.05934i	−0.379360	−	0.925249i	$-0.623856\pi$
$223$	9.13327	−	15.8193i	0.611609	−	1.05934i	0.990969	−	0.134089i	$-0.0428107\pi$
$224$	−6.92003	+	11.9858i	−0.462364	+	0.800838i
$225$	2.38243	+	4.12649i	0.158829	+	0.275099i
$226$	14.7155			0.978859
$227$	−7.55145	−	13.0795i	−0.501207	−	0.868117i	−0.999999	−	0.00139467i	$-0.999556\pi$
$227$	−7.55145	−	13.0795i	−0.501207	−	0.868117i	0.498792	−	0.866722i	$-0.333777\pi$
$228$	−5.86553	−	10.1594i	−0.388454	−	0.672823i
$229$	−16.9082			−1.11732			−0.558661	−	0.829396i	$-0.688685\pi$
$229$	−16.9082			−1.11732			−0.558661	+	0.829396i	$0.688685\pi$
$230$	3.16919	+	5.48920i	0.208970	+	0.361947i
$231$	−0.958152	+	1.65957i	−0.0630418	+	0.109192i
$232$	−6.37370	+	11.0396i	−0.418454	+	0.724783i
$233$	6.71531			0.439935			0.219967	−	0.975507i	$-0.429405\pi$
$233$	6.71531			0.439935			0.219967	+	0.975507i	$0.429405\pi$
$234$	6.84760	+	4.01767i	0.447642	+	0.262643i
$235$	0.601053			0.0392084
$236$	−17.1119	+	29.6387i	−1.11389	+	1.92931i
$237$	−2.81174	+	4.87008i	−0.182642	+	0.316346i
$238$	−5.02405	−	8.70191i	−0.325661	−	0.564061i
$239$	−7.61739			−0.492728			−0.246364	−	0.969177i	$-0.579236\pi$
$239$	−7.61739			−0.492728			−0.246364	+	0.969177i	$0.579236\pi$
$240$	0.383767	+	0.664704i	0.0247721	+	0.0429065i
$241$	−2.66235	−	4.61133i	−0.171497	−	0.297042i	0.767446	−	0.641113i	$-0.221527\pi$
$241$	−2.66235	−	4.61133i	−0.171497	−	0.297042i	−0.938943	+	0.344071i	$0.888194\pi$
$242$	2.20194			0.141546
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−4.95919	+	8.58957i	−0.317479	+	0.549891i
$245$	−0.806838	+	1.39748i	−0.0515470	+	0.0892820i
$246$	2.93622			0.187207
$247$	−0.103988	+	14.8482i	−0.00661663	+	0.944768i
$248$	19.2639			1.22326
$249$	7.09454	−	12.2881i	0.449598	−	0.778727i
$250$	−5.21320	+	9.02953i	−0.329712	+	0.571077i
$251$	−5.37997	−	9.31839i	−0.339581	−	0.588171i	0.644773	−	0.764374i	$-0.276952\pi$
$251$	−5.37997	−	9.31839i	−0.339581	−	0.588171i	−0.984354	+	0.176203i	$0.943619\pi$
$252$	−5.45870			−0.343866
$253$	−2.96811	−	5.14092i	−0.186604	−	0.323207i
$254$	16.2586	+	28.1608i	1.02016	+	1.76697i
$255$	−1.15472			−0.0723112
$256$	2.23852	+	3.87723i	0.139907	+	0.242327i
$257$	9.15500	−	15.8569i	0.571073	−	0.989127i	−0.425383	−	0.905013i	$-0.639861\pi$
$257$	9.15500	−	15.8569i	0.571073	−	0.989127i	0.996456	−	0.0841141i	$-0.0268060\pi$
$258$	6.86953	−	11.8984i	0.427678	−	0.740760i
$259$	−18.1124			−1.12545
$260$	−0.0348787	+	4.98021i	−0.00216308	+	0.308860i
$261$	6.82235			0.422293
$262$	−8.03989	+	13.9255i	−0.496706	+	0.860321i
$263$	4.16958	−	7.22192i	0.257107	−	0.445323i	−0.708358	−	0.705853i	$-0.750564\pi$
$263$	4.16958	−	7.22192i	0.257107	−	0.445323i	0.965466	+	0.260530i	$0.0838973\pi$
$264$	0.934238	+	1.61815i	0.0574984	+	0.0995901i
$265$	−3.96277			−0.243431
$266$	−8.68867	−	15.0492i	−0.532736	−	0.922727i
$267$	0.222983	+	0.386217i	0.0136463	+	0.0236361i
$268$	10.2562			0.626497
$269$	2.37264	+	4.10954i	0.144663	+	0.250563i	0.929247	−	0.369459i	$-0.120457\pi$
$269$	2.37264	+	4.10954i	0.144663	+	0.250563i	−0.784584	+	0.620022i	$0.787124\pi$
$270$	−0.533873	+	0.924696i	−0.0324905	+	0.0562752i
$271$	−7.68594	+	13.3124i	−0.466887	+	0.808673i	−0.999284	−	0.0378220i	$-0.987958\pi$
$271$	−7.68594	+	13.3124i	−0.466887	+	0.808673i	0.532397	+	0.846495i	$0.321291\pi$
$272$	3.76920			0.228541
$273$	5.95932	+	3.49649i	0.360674	+	0.211617i
$274$	11.8638			0.716719
$275$	2.38243	−	4.12649i	0.143666	−	0.248837i
$276$	8.45483	−	14.6442i	0.508921	−	0.881477i
$277$	6.51786	+	11.2893i	0.391620	+	0.678306i	0.992663	−	0.120911i	$-0.0385814\pi$
$277$	6.51786	+	11.2893i	0.391620	+	0.678306i	−0.601043	+	0.799216i	$0.705248\pi$
$278$	−10.1517			−0.608859
$279$	−5.15497	−	8.92866i	−0.308620	−	0.534545i
$280$	−0.868128	−	1.50364i	−0.0518806	−	0.0898598i
$281$	−19.2082			−1.14587			−0.572933	−	0.819602i	$-0.694194\pi$
$281$	−19.2082			−1.14587			−0.572933	+	0.819602i	$0.694194\pi$
$282$	−1.36467	−	2.36368i	−0.0812648	−	0.140755i
$283$	−0.541092	+	0.937199i	−0.0321646	+	0.0557107i	−0.881660	−	0.471886i	$-0.843573\pi$
$283$	−0.541092	+	0.937199i	−0.0321646	+	0.0557107i	0.849495	+	0.527597i	$0.176907\pi$
$284$	8.03212	−	13.9120i	0.476619	−	0.825528i
$285$	−1.99698			−0.118291
$286$	0.0556005	−	7.93903i	0.00328773	−	0.469445i
$287$	2.55533			0.150836
$288$	3.61113	−	6.25467i	0.212788	−	0.368560i
$289$	5.66471	−	9.81157i	0.333218	−	0.577151i
$290$	3.64227	+	6.30860i	0.213881	+	0.370454i
$291$	8.65139			0.507154
$292$	−14.4074	−	24.9543i	−0.843129	−	1.46034i
$293$	13.5719	+	23.5073i	0.792882	+	1.37331i	0.924176	+	0.381968i	$0.124754\pi$
$293$	13.5719	+	23.5073i	0.792882	+	1.37331i	−0.131294	+	0.991343i	$0.541913\pi$
$294$	7.32758			0.427353
$295$	2.91297	+	5.04541i	0.169599	+	0.293755i
$296$	−8.83015	+	15.2943i	−0.513242	+	0.888961i
$297$	0.500000	−	0.866025i	0.0290129	−	0.0502519i
$298$	32.0985			1.85942
$299$	−18.6103	+	10.5716i	−1.07626	+	0.611372i
$300$	13.5730			0.783636
$301$	5.97840	−	10.3549i	0.344589	−	0.596846i
$302$	16.2083	−	28.0736i	0.932683	−	1.61545i
$303$	−4.67375	−	8.09517i	−0.268500	−	0.465056i
$304$	6.51851			0.373862
$305$	0.844204	+	1.46220i	0.0483390	+	0.0837256i
$306$	2.62174	+	4.54099i	0.149875	+	0.259591i
$307$	−12.3263			−0.703498			−0.351749	−	0.936094i	$-0.614413\pi$
$307$	−12.3263			−0.703498			−0.351749	+	0.936094i	$0.614413\pi$
$308$	2.72935	+	4.72737i	0.155519	+	0.269367i
$309$	−6.24249	+	10.8123i	−0.355123	+	0.615090i
$310$	5.50420	−	9.53355i	0.312617	−	0.541469i
$311$	22.3153			1.26538			0.632691	−	0.774404i	$-0.281950\pi$
$311$	22.3153			1.26538			0.632691	+	0.774404i	$0.281950\pi$
$312$	5.85776	−	3.32750i	0.331630	−	0.188383i
$313$	−9.81646			−0.554859			−0.277430	−	0.960746i	$-0.589483\pi$
$313$	−9.81646			−0.554859			−0.277430	+	0.960746i	$0.589483\pi$
$314$	−15.7923	+	27.3530i	−0.891209	+	1.54362i
$315$	−0.464618	+	0.804743i	−0.0261783	+	0.0453421i
$316$	8.00941	+	13.8727i	0.450564	+	0.780400i
$317$	32.5753			1.82961			0.914805	−	0.403895i	$-0.132344\pi$
$317$	32.5753			1.82961			0.914805	+	0.403895i	$0.132344\pi$
$318$	8.99733	+	15.5838i	0.504545	+	0.873898i
$319$	−3.41117	−	5.90833i	−0.190989	−	0.330803i
$320$	6.17648			0.345276
$321$	−0.703898	−	1.21919i	−0.0392878	−	0.0680484i
$322$	12.5242	−	21.6926i	0.697948	−	1.20888i
$323$	−4.90339	+	8.49291i	−0.272832	+	0.472558i
$324$	2.84856			0.158253
$325$	−14.8178	−	8.69396i	−0.821941	−	0.482254i
$326$	24.7655			1.37163
$327$	4.17026	−	7.22310i	0.230616	−	0.399438i
$328$	1.24578	−	2.15775i	0.0687865	−	0.119142i
$329$	−1.18764	−	2.05706i	−0.0654768	−	0.113409i
$330$	1.06775			0.0587775
$331$	−13.8819	−	24.0442i	−0.763021	−	1.32159i	−0.941287	−	0.337608i	$-0.890382\pi$
$331$	−13.8819	−	24.0442i	−0.763021	−	1.32159i	0.178266	−	0.983982i	$-0.442951\pi$
$332$	−20.2092	−	35.0033i	−1.10912	−	1.92106i
$333$	9.45172			0.517951
$334$	22.4138	+	38.8218i	1.22643	+	2.12423i
$335$	0.872958	−	1.51201i	0.0476948	−	0.0826098i
$336$	1.51660	−	2.62682i	0.0827372	−	0.143305i
$337$	18.8793			1.02842			0.514210	−	0.857664i	$-0.328085\pi$
$337$	18.8793			1.02842			0.514210	+	0.857664i	$0.328085\pi$
$338$	−28.6225	−	0.400931i	−1.55686	−	0.0218078i
$339$	−6.68295			−0.362968
$340$	−1.64464	+	2.84860i	−0.0891930	+	0.154487i
$341$	−5.15497	+	8.92866i	−0.279157	+	0.483514i
$342$	4.53408	+	7.85325i	0.245175	+	0.424655i
$343$	19.7912			1.06862
$344$	−5.82919	−	10.0965i	−0.314289	−	0.544364i
$345$	−1.43927	−	2.49289i	−0.0774877	−	0.134213i
$346$	−23.6715			−1.27259
$347$	2.79721	+	4.84490i	0.150162	+	0.260088i	0.931287	−	0.364287i	$-0.118687\pi$
$347$	2.79721	+	4.84490i	0.150162	+	0.260088i	−0.781125	+	0.624375i	$0.785354\pi$
$348$	9.71693	−	16.8302i	0.520882	−	0.902194i
$349$	−6.88677	+	11.9282i	−0.368641	+	0.638504i	−0.989353	−	0.145534i	$-0.953510\pi$
$349$	−6.88677	+	11.9282i	−0.368641	+	0.638504i	0.620713	+	0.784038i	$0.286843\pi$
$350$	20.1058			1.07470
$351$	−3.10980	−	1.82460i	−0.165989	−	0.0973899i
$352$	−7.22227			−0.384948
$353$	−1.02915	+	1.78254i	−0.0547760	+	0.0948749i	−0.892113	−	0.451812i	$-0.850778\pi$
$353$	−1.02915	+	1.78254i	−0.0547760	+	0.0948749i	0.837337	+	0.546687i	$0.184111\pi$
$354$	13.2276	−	22.9108i	0.703037	−	1.21770i
$355$	−1.36731	−	2.36825i	−0.0725693	−	0.125694i
$356$	1.27036			0.0673289
$357$	2.28164	+	3.95192i	0.120757	+	0.209158i
$358$	−3.14077	−	5.43997i	−0.165995	−	0.287511i
$359$	29.1390			1.53790			0.768948	−	0.639311i	$-0.220780\pi$
$359$	29.1390			1.53790			0.768948	+	0.639311i	$0.220780\pi$
$360$	0.453022	+	0.784657i	0.0238764	+	0.0413551i
$361$	1.02002	−	1.76672i	0.0536851	−	0.0929853i
$362$	−9.21340	+	15.9581i	−0.484246	+	0.838738i
$363$	−1.00000			−0.0524864
$364$	17.1133	−	9.72120i	0.896980	−	0.509530i
$365$	−4.90515			−0.256747
$366$	3.83347	−	6.63976i	0.200379	−	0.347066i
$367$	6.31869	−	10.9443i	0.329833	−	0.571287i	−0.652646	−	0.757663i	$-0.726341\pi$
$367$	6.31869	−	10.9443i	0.329833	−	0.571287i	0.982478	+	0.186376i	$0.0596743\pi$
$368$	4.69803	+	8.13723i	0.244902	+	0.424183i
$369$	−1.33347			−0.0694176
$370$	5.04602	+	8.73996i	0.262330	+	0.454369i
$371$	7.83018	+	13.5623i	0.406523	+	0.704118i
$372$	−29.3684			−1.52268
$373$	11.5123	+	19.9400i	0.596087	+	1.03245i	0.993393	+	0.114766i	$0.0366119\pi$
$373$	11.5123	+	19.9400i	0.596087	+	1.03245i	−0.397306	+	0.917686i	$0.630055\pi$
$374$	2.62174	−	4.54099i	0.135567	−	0.234809i
$375$	2.36754	−	4.10071i	0.122259	−	0.211760i
$376$	−2.31600			−0.119439
$377$	−21.3884	+	12.1497i	−1.10156	+	0.625740i
$378$	4.21959			0.217033
$379$	−5.46195	+	9.46037i	−0.280561	+	0.485946i	−0.971523	−	0.236945i	$-0.923854\pi$
$379$	−5.46195	+	9.46037i	−0.280561	+	0.485946i	0.690962	+	0.722891i	$0.257187\pi$
$380$	−2.84426	+	4.92640i	−0.145908	+	0.252719i
$381$	−7.38377	−	12.7891i	−0.378282	−	0.655203i
$382$	43.2466			2.21269
$383$	2.08366	+	3.60900i	0.106470	+	0.184411i	0.914338	−	0.404952i	$-0.132712\pi$
$383$	2.08366	+	3.60900i	0.106470	+	0.184411i	−0.807868	+	0.589364i	$0.799379\pi$
$384$	−6.80121	−	11.7800i	−0.347073	−	0.601147i
$385$	0.929237			0.0473583
$386$	−20.4736	−	35.4614i	−1.04208	−	1.80494i
$387$	−3.11976	+	5.40358i	−0.158586	+	0.274679i
$388$	12.3220	−	21.3423i	0.625554	−	1.08349i
$389$	−31.8025			−1.61245			−0.806225	−	0.591609i	$-0.798493\pi$
$389$	−31.8025			−1.61245			−0.806225	+	0.591609i	$0.798493\pi$
$390$	0.0269613	−	3.84972i	0.00136524	−	0.194938i
$391$	−14.1359			−0.714884
$392$	3.10894	−	5.38484i	0.157025	−	0.271975i
$393$	3.65127	−	6.32419i	0.184182	−	0.319013i
$394$	−19.5179	−	33.8060i	−0.983299	−	1.70312i
$395$	2.72689			0.137205
$396$	−1.42428	−	2.46692i	−0.0715727	−	0.123968i
$397$	17.3069	+	29.9764i	0.868607	+	1.50447i	0.863420	+	0.504485i	$0.168318\pi$
$397$	17.3069	+	29.9764i	0.868607	+	1.50447i	0.00518680	+	0.999987i	$0.498349\pi$
$398$	39.6722			1.98859
$399$	3.94591	+	6.83451i	0.197542	+	0.342154i
$400$	−3.77100	+	6.53156i	−0.188550	+	0.326578i
$401$	−3.58380	+	6.20732i	−0.178966	+	0.309979i	−0.941527	−	0.336938i	$-0.890609\pi$
$401$	−3.58380	+	6.20732i	−0.178966	+	0.309979i	0.762560	+	0.646917i	$0.223942\pi$
$402$	−7.92807			−0.395416
$403$	32.0618	+	18.8115i	1.59711	+	0.937067i
$404$	−26.6269			−1.32474
$405$	0.242455	−	0.419945i	0.0120477	−	0.0208672i
$406$	14.3938	−	24.9307i	0.714351	−	1.23729i
$407$	−4.72586	−	8.18543i	−0.234252	−	0.405737i
$408$	4.44939			0.220278
$409$	9.20827	+	15.9492i	0.455320	+	0.788637i	0.998707	−	0.0508455i	$-0.0161916\pi$
$409$	9.20827	+	15.9492i	0.455320	+	0.788637i	−0.543387	+	0.839482i	$0.682858\pi$
$410$	−0.711903	−	1.23305i	−0.0351584	−	0.0608961i
$411$	−5.38788			−0.265764
$412$	17.7821	+	30.7995i	0.876060	+	1.51738i
$413$	11.5117	−	19.9388i	0.566452	−	0.981123i
$414$	−6.53561	+	11.3200i	−0.321208	+	0.556348i
$415$	−6.88044			−0.337747
$416$	−0.182367	+	26.0396i	−0.00894128	+	1.27670i
$417$	4.61034			0.225769
$418$	4.53408	−	7.85325i	0.221769	−	0.384115i
$419$	−2.14992	+	3.72377i	−0.105030	+	0.181918i	−0.913751	−	0.406275i	$-0.866827\pi$
$419$	−2.14992	+	3.72377i	−0.105030	+	0.181918i	0.808720	+	0.588194i	$0.200161\pi$
$420$	1.32349	+	2.29236i	0.0645798	+	0.111856i
$421$	−24.9023			−1.21366			−0.606831	−	0.794831i	$-0.707560\pi$
$421$	−24.9023			−1.21366			−0.606831	+	0.794831i	$0.707560\pi$
$422$	−18.6052	−	32.2252i	−0.905689	−	1.56870i
$423$	0.619756	+	1.07345i	0.0301336	+	0.0521929i
$424$	15.2695			0.741553
$425$	−5.67327	−	9.82640i	−0.275194	−	0.476650i
$426$	−6.20886	+	10.7541i	−0.300820	+	0.521036i
$427$	3.33618	−	5.77844i	0.161449	−	0.279638i
$428$	−4.01019			−0.193840
$429$	−0.0252507	+	3.60546i	−0.00121911	+	0.174073i
$430$	−6.66222			−0.321281
$431$	9.62279	−	16.6672i	0.463514	−	0.802829i	−0.535619	−	0.844459i	$-0.679922\pi$
$431$	9.62279	−	16.6672i	0.463514	−	0.802829i	0.999133	+	0.0416303i	$0.0132552\pi$
$432$	−0.791418	+	1.37078i	−0.0380771	+	0.0659515i
$433$	−13.8448	−	23.9799i	−0.665338	−	1.15240i	−0.979194	−	0.202928i	$-0.934954\pi$
$433$	−13.8448	−	23.9799i	−0.665338	−	1.15240i	0.313856	−	0.949471i	$-0.398379\pi$
$434$	−43.5037			−2.08825
$435$	−1.65412	−	2.86501i	−0.0793088	−	0.137367i
$436$	−11.8792	−	20.5754i	−0.568911	−	0.985383i
$437$	−24.4468			−1.16945
$438$	11.1370	+	19.2898i	0.532145	+	0.921702i
$439$	−0.754602	+	1.30701i	−0.0360152	+	0.0623801i	−0.883471	−	0.468486i	$-0.844800\pi$
$439$	−0.754602	+	1.30701i	−0.0360152	+	0.0623801i	0.847456	+	0.530866i	$0.178133\pi$
$440$	0.453022	−	0.784657i	0.0215970	−	0.0374071i
$441$	−3.32778			−0.158466
$442$	−16.3062	−	9.56725i	−0.775605	−	0.455068i
$443$	8.99290			0.427266			0.213633	−	0.976914i	$-0.431470\pi$
$443$	8.99290			0.427266			0.213633	+	0.976914i	$0.431470\pi$
$444$	13.4619	−	23.3167i	0.638872	−	1.10656i
$445$	0.108127	−	0.187281i	0.00512570	−	0.00887797i
$446$	20.1109	+	34.8332i	0.952281	+	1.64940i
$447$	−14.5774			−0.689485
$448$	−12.2043	−	21.1385i	−0.576600	−	0.998701i
$449$	7.06475	+	12.2365i	0.333406	+	0.577476i	0.983177	−	0.182654i	$-0.0584687\pi$
$449$	7.06475	+	12.2365i	0.333406	+	0.577476i	−0.649771	+	0.760130i	$0.725135\pi$
$450$	−10.4920			−0.494596
$451$	0.666734	+	1.15482i	0.0313953	+	0.0543782i
$452$	−9.51838	+	16.4863i	−0.447707	+	0.775451i
$453$	−7.36091	+	12.7495i	−0.345846	+	0.599022i
$454$	33.2557			1.56077
$455$	0.0234638	−	3.35033i	0.00110000	−	0.157066i
$456$	7.69485			0.360344
$457$	−18.2673	+	31.6399i	−0.854509	+	1.48005i	0.0225902	+	0.999745i	$0.492809\pi$
$457$	−18.2673	+	31.6399i	−0.854509	+	1.48005i	−0.877100	+	0.480309i	$0.840525\pi$
$458$	18.6154	−	32.2428i	0.869841	−	1.50661i
$459$	−1.19065	−	2.06226i	−0.0555747	−	0.0962582i
$460$	−8.19968			−0.382312
$461$	14.5176	+	25.1452i	0.676152	+	1.17113i	0.976131	+	0.217184i	$0.0696872\pi$
$461$	14.5176	+	25.1452i	0.676152	+	1.17113i	−0.299978	+	0.953946i	$0.596979\pi$
$462$	−2.10980	−	3.65428i	−0.0981566	−	0.170012i
$463$	35.2485			1.63813			0.819067	−	0.573697i	$-0.194491\pi$
$463$	35.2485			1.63813			0.819067	+	0.573697i	$0.194491\pi$
$464$	5.39933	+	9.35191i	0.250658	+	0.434152i
$465$	−2.49970	+	4.32961i	−0.115921	+	0.200781i
$466$	−7.39337	+	12.8057i	−0.342491	+	0.593212i
$467$	−29.6955			−1.37414			−0.687072	−	0.726590i	$-0.741104\pi$
$467$	−29.6955			−1.37414			−0.687072	+	0.726590i	$0.741104\pi$
$468$	−8.93036	+	5.07289i	−0.412806	+	0.234495i
$469$	−6.89963			−0.318595
$470$	−0.661743	+	1.14617i	−0.0305239	+	0.0528690i
$471$	7.17197	−	12.4222i	0.330467	−	0.572385i
$472$	−11.2243	−	19.4411i	−0.516642	−	0.894851i
$473$	6.23951			0.286893
$474$	−6.19130	−	10.7236i	−0.284376	−	0.492553i
$475$	−9.81144	−	16.9939i	−0.450180	−	0.779734i
$476$	12.9988			0.595798
$477$	−4.08609	−	7.07731i	−0.187089	−	0.324048i
$478$	8.38653	−	14.5259i	0.383591	−	0.664399i
$479$	1.57603	−	2.72976i	0.0720106	−	0.124726i	−0.827772	−	0.561065i	$-0.810392\pi$
$479$	1.57603	−	2.72976i	0.0720106	−	0.124726i	0.899782	+	0.436339i	$0.143725\pi$
$480$	−3.50216			−0.159851
$481$	−29.6316	+	16.8322i	−1.35108	+	0.767483i
$482$	11.7247			0.534045
$483$	−5.68780	+	9.85156i	−0.258804	+	0.448262i
$484$	−1.42428	+	2.46692i	−0.0647399	+	0.112133i
$485$	−2.09758	−	3.63311i	−0.0952461	−	0.164971i
$486$	−2.20194			−0.0998822
$487$	−20.4574	−	35.4332i	−0.927011	−	1.60563i	−0.788294	−	0.615298i	$-0.789036\pi$
$487$	−20.4574	−	35.4332i	−0.927011	−	1.60563i	−0.138717	−	0.990332i	$-0.544298\pi$
$488$	−3.25292	−	5.63422i	−0.147253	−	0.255049i
$489$	−11.2471			−0.508611
$490$	−1.77661	−	3.07718i	−0.0802592	−	0.139013i
$491$	14.9399	−	25.8766i	0.674227	−	1.16780i	−0.302467	−	0.953160i	$-0.597810\pi$
$491$	14.9399	−	25.8766i	0.674227	−	1.16780i	0.976694	−	0.214636i	$-0.0688566\pi$
$492$	−1.89923	+	3.28956i	−0.0856239	+	0.148305i
$493$	−16.2460			−0.731685
$494$	−28.2001	−	16.5457i	−1.26878	−	0.744428i
$495$	−0.484911			−0.0217951
$496$	8.15946	−	14.1326i	0.366371	−	0.634573i
$497$	−5.40343	+	9.35902i	−0.242377	+	0.419809i
$498$	15.6218	+	27.0577i	0.700028	+	1.21248i
$499$	−13.0261			−0.583126			−0.291563	−	0.956552i	$-0.594175\pi$
$499$	−13.0261			−0.583126			−0.291563	+	0.956552i	$0.594175\pi$
$500$	−6.74408	−	11.6811i	−0.301605	−	0.522395i
$501$	−10.1791	−	17.6307i	−0.454768	−	0.787681i
$502$	23.6928			1.05746
$503$	−5.43549	−	9.41455i	−0.242357	−	0.419774i	0.719028	−	0.694981i	$-0.244587\pi$
$503$	−5.43549	−	9.41455i	−0.242357	−	0.419774i	−0.961385	+	0.275207i	$0.911254\pi$
$504$	1.79028	−	3.10086i	0.0797456	−	0.138123i
$505$	−2.26635	+	3.92544i	−0.100851	+	0.174680i
$506$	13.0712			0.581087
$507$	12.9987	+	0.182081i	0.577294	+	0.00808649i
$508$	−42.0662			−1.86638
$509$	1.85301	−	3.20950i	0.0821332	−	0.142259i	−0.822033	−	0.569440i	$-0.807160\pi$
$509$	1.85301	−	3.20950i	0.0821332	−	0.142259i	0.904166	+	0.427181i	$0.140493\pi$
$510$	1.27131	−	2.20197i	0.0562946	−	0.0975051i
$511$	9.69226	+	16.7875i	0.428760	+	0.742635i
$512$	17.3466			0.766621
$513$	−2.05912	−	3.56651i	−0.0909125	−	0.157465i
$514$	20.1588	+	34.9160i	0.889166	+	1.54008i
$515$	6.05410			0.266776
$516$	8.88680	+	15.3924i	0.391220	+	0.677613i
$517$	0.619756	−	1.07345i	0.0272569	−	0.0472102i
$518$	19.9412	−	34.5392i	0.876166	−	1.51756i
$519$	10.7503			0.471885
$520$	−2.81761	−	1.65317i	−0.123561	−	0.0724962i
$521$	5.99603			0.262691			0.131345	−	0.991337i	$-0.458070\pi$
$521$	5.99603			0.262691			0.131345	+	0.991337i	$0.458070\pi$
$522$	−7.51121	+	13.0098i	−0.328757	+	0.569424i
$523$	−7.54314	+	13.0651i	−0.329839	+	0.571297i	−0.982480	−	0.186370i	$-0.940328\pi$
$523$	−7.54314	+	13.0651i	−0.329839	+	0.571297i	0.652641	+	0.757667i	$0.273661\pi$
$524$	−10.4009	−	18.0148i	−0.454363	−	0.786981i
$525$	−9.13092			−0.398506
$526$	9.18118	+	15.9023i	0.400318	+	0.693372i
$527$	12.2755	+	21.2618i	0.534729	+	0.926178i
$528$	1.58284			0.0688841
$529$	−6.11937	−	10.5991i	−0.266059	−	0.460829i
$530$	4.36290	−	7.55677i	0.189512	−	0.328245i
$531$	−6.00722	+	10.4048i	−0.260691	+	0.451530i
$532$	22.4803			0.974644
$533$	4.18049	−	2.37473i	0.181077	−	0.102861i
$534$	−0.981991			−0.0424949
$535$	−0.341328	+	0.591197i	−0.0147569	+	0.0255597i
$536$	−3.36371	+	5.82612i	−0.145290	+	0.251650i
$537$	1.42636	+	2.47053i	0.0615520	+	0.106611i
$538$	−10.4489			−0.450482
$539$	1.66389	+	2.88194i	0.0716688	+	0.124134i
$540$	−0.690648	−	1.19624i	−0.0297208	−	0.0514779i
$541$	37.3311			1.60499			0.802494	−	0.596660i	$-0.203506\pi$
$541$	37.3311			1.60499			0.802494	+	0.596660i	$0.203506\pi$
$542$	−16.9240	−	29.3132i	−0.726948	−	1.25911i
$543$	4.18421	−	7.24727i	0.179562	−	0.311010i
$544$	−8.59918	+	14.8942i	−0.368687	+	0.638584i
$545$	−4.04441			−0.173243
$546$	−13.2286	+	7.51452i	−0.566133	+	0.321592i
$547$	−35.6488			−1.52423			−0.762116	−	0.647440i	$-0.775840\pi$
$547$	−35.6488			−1.52423			−0.762116	+	0.647440i	$0.775840\pi$
$548$	−7.67384	+	13.2915i	−0.327810	+	0.567784i
$549$	−1.74095	+	3.01541i	−0.0743018	+	0.128695i
$550$	5.24598	+	9.08630i	0.223689	+	0.387441i
$551$	−28.0961			−1.19694
$552$	5.54584	+	9.60568i	0.236047	+	0.408845i
$553$	−5.38815	−	9.33255i	−0.229127	−	0.396860i
$554$	−28.7039			−1.21951
$555$	−2.29162	−	3.96920i	−0.0972739	−	0.168483i
$556$	6.56641	−	11.3734i	0.278478	−	0.482338i
$557$	16.3999	−	28.4055i	0.694886	−	1.20358i	−0.275333	−	0.961349i	$-0.588788\pi$
$557$	16.3999	−	28.4055i	0.694886	−	1.20358i	0.970219	−	0.242229i	$-0.0778785\pi$
$558$	22.7019			0.961048
$559$	0.157552	−	22.4963i	0.00666373	−	0.951493i
$560$	−1.47083			−0.0621539
$561$	−1.19065	+	2.06226i	−0.0502692	+	0.0870688i
$562$	21.1477	−	36.6289i	0.892062	−	1.54510i
$563$	17.9277	+	31.0516i	0.755561	+	1.30867i	0.945095	+	0.326796i	$0.105969\pi$
$563$	17.9277	+	31.0516i	0.755561	+	1.30867i	−0.189534	+	0.981874i	$0.560698\pi$
$564$	3.53082			0.148674
$565$	1.62032	+	2.80647i	0.0681673	+	0.118069i
$566$	−1.19145	−	2.06366i	−0.0500806	−	0.0867421i
$567$	−1.91630			−0.0804772
$568$	5.26857	+	9.12543i	0.221064	+	0.382895i
$569$	11.9496	−	20.6973i	0.500953	−	0.867677i	−0.499046	−	0.866575i	$-0.666316\pi$
$569$	11.9496	−	20.6973i	0.500953	−	0.867677i	0.999999	−	0.00110116i	$-0.000350510\pi$
$570$	2.19862	−	3.80813i	0.0920902	−	0.159505i
$571$	−28.9193			−1.21023			−0.605117	−	0.796136i	$-0.706874\pi$
$571$	−28.9193			−1.21023			−0.605117	+	0.796136i	$0.706874\pi$
$572$	8.85844	+	5.19748i	0.370390	+	0.217317i
$573$	−19.6402			−0.820481
$574$	−2.81335	+	4.87286i	−0.117427	+	0.203389i
$575$	14.1426	−	24.4958i	0.589789	−	1.02154i
$576$	6.36868	+	11.0309i	0.265362	+	0.459620i
$577$	−12.7234			−0.529681			−0.264841	−	0.964292i	$-0.585319\pi$
$577$	−12.7234			−0.529681			−0.264841	+	0.964292i	$0.585319\pi$
$578$	12.4734	+	21.6045i	0.518824	+	0.898630i
$579$	9.29799	+	16.1046i	0.386411	+	0.669284i
$580$	−9.42369			−0.391297
$581$	13.5953	+	23.5477i	0.564028	+	0.976924i
$582$	−9.52494	+	16.4977i	−0.394821	+	0.683851i
$583$	−4.08609	+	7.07731i	−0.169228	+	0.293112i
$584$	18.9007			0.782117
$585$	−0.0122443	+	1.74833i	−0.000506240	+	0.0722845i
$586$	−59.7693			−2.46905
$587$	−15.4785	+	26.8096i	−0.638868	+	1.10655i	0.346814	+	0.937934i	$0.387263\pi$
$587$	−15.4785	+	26.8096i	−0.638868	+	1.10655i	−0.985682	+	0.168617i	$0.946070\pi$
$588$	−4.73968	+	8.20937i	−0.195461	+	0.338549i
$589$	21.2294	+	36.7705i	0.874743	+	1.51510i
$590$	−12.8284			−0.528136
$591$	8.86395	+	15.3528i	0.364614	+	0.631531i
$592$	7.48026	+	12.9562i	0.307437	+	0.532496i
$593$	−2.60071			−0.106798			−0.0533992	−	0.998573i	$-0.517006\pi$
$593$	−2.60071			−0.106798			−0.0533992	+	0.998573i	$0.517006\pi$
$594$	1.10097	+	1.90694i	0.0451734	+	0.0782427i
$595$	1.10639	−	1.91633i	0.0453577	−	0.0785619i
$596$	−20.7622	+	35.9612i	−0.850453	+	1.47303i
$597$	−18.0169			−0.737383
$598$	0.330057	−	47.1278i	0.0134970	−	1.92720i
$599$	43.3096			1.76958			0.884792	−	0.465986i	$-0.154300\pi$
$599$	43.3096			1.76958			0.884792	+	0.465986i	$0.154300\pi$
$600$	−4.45151	+	7.71025i	−0.181732	+	0.314770i
$601$	19.4264	−	33.6475i	0.792418	−	1.37251i	−0.132047	−	0.991243i	$-0.542155\pi$
$601$	19.4264	−	33.6475i	0.792418	−	1.37251i	0.924466	−	0.381265i	$-0.124512\pi$
$602$	13.1641	+	22.8009i	0.536529	+	0.929295i
$603$	3.60049			0.146623
$604$	20.9680	+	36.3176i	0.853174	+	1.47774i
$605$	0.242455	+	0.419945i	0.00985722	+	0.0170732i
$606$	20.5827			0.836114
$607$	3.76237	+	6.51662i	0.152710	+	0.264502i	0.932223	−	0.361885i	$-0.117867\pi$
$607$	3.76237	+	6.51662i	0.152710	+	0.264502i	−0.779513	+	0.626386i	$0.784533\pi$
$608$	−14.8715	+	25.7583i	−0.603121	+	1.04464i
$609$	−6.53685	+	11.3222i	−0.264886	+	0.458797i
$610$	−3.71778			−0.150529
$611$	−3.85463	−	2.26161i	−0.155942	−	0.0914951i
$612$	−6.78326			−0.274197
$613$	9.24184	−	16.0073i	0.373274	−	0.646530i	−0.616793	−	0.787126i	$-0.711568\pi$
$613$	9.24184	−	16.0073i	0.373274	−	0.646530i	0.990067	+	0.140595i	$0.0449016\pi$
$614$	13.5709	−	23.5055i	0.547677	−	0.948604i
$615$	0.323307	+	0.559984i	0.0130370	+	0.0225807i
$616$	−3.58057			−0.144265
$617$	1.20338	+	2.08432i	0.0484464	+	0.0839117i	0.889232	−	0.457457i	$-0.151240\pi$
$617$	1.20338	+	2.08432i	0.0484464	+	0.0839117i	−0.840785	+	0.541369i	$0.817906\pi$
$618$	−13.7456	−	23.8081i	−0.552929	−	0.957702i
$619$	44.3837			1.78393			0.891965	−	0.452104i	$-0.149326\pi$
$619$	44.3837			1.78393			0.891965	+	0.452104i	$0.149326\pi$
$620$	7.12054	+	12.3331i	0.285968	+	0.495311i
$621$	2.96811	−	5.14092i	0.119106	−	0.206298i
$622$	−24.5685	+	42.5538i	−0.985106	+	1.70625i
$623$	−0.854606			−0.0342390
$624$	0.0399677	−	5.70686i	0.00159999	−	0.228457i
$625$	21.5282			0.861128
$626$	10.8077	−	18.7194i	0.431961	−	0.748178i
$627$	−2.05912	+	3.56651i	−0.0822335	+	0.142433i
$628$	−20.4298	−	35.3854i	−0.815236	−	1.41203i
$629$	−22.5073			−0.897426
$630$	−1.02306	−	1.77200i	−0.0407598	−	0.0705981i
$631$	−2.96964	−	5.14356i	−0.118219	−	0.204762i	0.800843	−	0.598875i	$-0.204385\pi$
$631$	−2.96964	−	5.14356i	−0.118219	−	0.204762i	−0.919062	+	0.394113i	$0.871052\pi$
$632$	−10.5073			−0.417960
$633$	8.44946	+	14.6349i	0.335836	+	0.581685i
$634$	−35.8645	+	62.1191i	−1.42436	+	2.46706i
$635$	−3.58047	+	6.20155i	−0.142087	+	0.246101i
$636$	−23.2789			−0.923068
$637$	10.4327	−	5.92632i	0.413360	−	0.234809i
$638$	15.0224			0.594744
$639$	2.81972	−	4.88389i	0.111546	−	0.193204i
$640$	−3.29798	+	5.71227i	−0.130364	+	0.225797i
$641$	9.16253	+	15.8700i	0.361898	+	0.626826i	0.988273	−	0.152696i	$-0.0487955\pi$
$641$	9.16253	+	15.8700i	0.361898	+	0.626826i	−0.626375	+	0.779522i	$0.715462\pi$
$642$	3.09989			0.122343
$643$	−5.06300	−	8.76936i	−0.199665	−	0.345830i	0.748755	−	0.662847i	$-0.230652\pi$
$643$	−5.06300	−	8.76936i	−0.199665	−	0.345830i	−0.948420	+	0.317017i	$0.897319\pi$
$644$	16.2020	+	28.0627i	0.638450	+	1.10583i
$645$	3.02561			0.119133
$646$	−10.7970	−	18.7009i	−0.424801	−	0.735778i
$647$	19.7005	−	34.1222i	0.774505	−	1.34148i	−0.160567	−	0.987025i	$-0.551332\pi$
$647$	19.7005	−	34.1222i	0.774505	−	1.34148i	0.935072	−	0.354458i	$-0.115335\pi$
$648$	−0.934238	+	1.61815i	−0.0367003	+	0.0635668i
$649$	12.0144			0.471608
$650$	32.8928	−	18.6847i	1.29016	−	0.732876i
$651$	19.7570			0.774337
$652$	−16.0190	+	27.7457i	−0.627353	+	1.08661i
$653$	6.04670	−	10.4732i	0.236626	−	0.409848i	−0.723118	−	0.690724i	$-0.757292\pi$
$653$	6.04670	−	10.4732i	0.236626	−	0.409848i	0.959744	+	0.280877i	$0.0906252\pi$
$654$	9.18267	+	15.9049i	0.359071	+	0.621929i
$655$	−3.54108			−0.138362
$656$	−1.05533	−	1.82789i	−0.0412037	−	0.0713670i
$657$	−5.05779	−	8.76034i	−0.197323	−	0.341774i
$658$	5.23024			0.203896
$659$	0.879116	+	1.52267i	0.0342455	+	0.0593149i	0.882640	−	0.470049i	$-0.155764\pi$
$659$	0.879116	+	1.52267i	0.0342455	+	0.0593149i	−0.848395	+	0.529364i	$0.822431\pi$
$660$	−0.690648	+	1.19624i	−0.0268834	+	0.0465635i
$661$	7.63266	−	13.2202i	0.296876	−	0.514205i	−0.678543	−	0.734560i	$-0.737388\pi$
$661$	7.63266	−	13.2202i	0.296876	−	0.514205i	0.975420	+	0.220356i	$0.0707218\pi$
$662$	61.1345			2.37606
$663$	7.40535	+	4.34491i	0.287600	+	0.168742i
$664$	26.5119			1.02886
$665$	1.91341	−	3.31413i	0.0741990	−	0.128516i
$666$	−10.4061	+	18.0239i	−0.403227	+	0.698410i
$667$	−20.2495	−	35.0731i	−0.784063	−	1.35804i
$668$	−57.9914			−2.24375
$669$	−9.13327	−	15.8193i	−0.353113	−	0.611609i
$670$	1.92220	+	3.32935i	0.0742612	+	0.128624i
$671$	3.48189			0.134417
$672$	6.92003	+	11.9858i	0.266946	+	0.462364i
$673$	0.281370	−	0.487348i	0.0108460	−	0.0187859i	−0.860551	−	0.509364i	$-0.829881\pi$
$673$	0.281370	−	0.487348i	0.0108460	−	0.0187859i	0.871397	+	0.490578i	$0.163214\pi$
$674$	−20.7856	+	36.0016i	−0.800630	+	1.38673i
$675$	4.76486			0.183400
$676$	18.9630	−	31.8075i	0.729346	−	1.22337i
$677$	45.6749			1.75543			0.877715	−	0.479183i	$-0.159067\pi$
$677$	45.6749			1.75543			0.877715	+	0.479183i	$0.159067\pi$
$678$	7.35774	−	12.7440i	0.282572	−	0.489429i
$679$	−8.28935	+	14.3576i	−0.318116	+	0.550993i
$680$	−1.07878	−	1.86850i	−0.0413693	−	0.0716538i
$681$	−15.1029			−0.578744
$682$	−11.3509	−	19.6604i	−0.434650	−	0.752836i
$683$	12.1933	+	21.1194i	0.466563	+	0.808111i	0.999271	−	0.0381885i	$-0.0121587\pi$
$683$	12.1933	+	21.1194i	0.466563	+	0.808111i	−0.532707	+	0.846299i	$0.678825\pi$
$684$	−11.7311			−0.448549
$685$	1.30632	+	2.26261i	0.0499119	+	0.0864500i
$686$	−21.7895	+	37.7406i	−0.831928	+	1.44094i
$687$	−8.45408	+	14.6429i	−0.322543	+	0.558661i
$688$	−9.87612			−0.376524
$689$	25.4138	+	14.9109i	0.968188	+	0.568061i
$690$	6.33838			0.241298
$691$	0.566322	−	0.980898i	0.0215439	−	0.0373151i	−0.855052	−	0.518542i	$-0.826475\pi$
$691$	0.566322	−	0.980898i	0.0215439	−	0.0373151i	0.876596	+	0.481226i	$0.159809\pi$
$692$	15.3114	−	26.5201i	0.582052	−	1.00814i
$693$	0.958152	+	1.65957i	0.0363972	+	0.0630418i
$694$	−12.3186			−0.467607
$695$	−1.11780	−	1.93609i	−0.0424007	−	0.0734401i
$696$	6.37370	+	11.0396i	0.241594	+	0.418454i
$697$	3.17538			0.120276
$698$	−15.1643	−	26.2653i	−0.573977	−	0.994157i
$699$	3.35766	−	5.81563i	0.126998	−	0.219967i
$700$	−13.0050	+	22.5253i	−0.491542	+	0.851376i
$701$	−29.1864			−1.10235			−0.551177	−	0.834388i	$-0.685821\pi$
$701$	−29.1864			−1.10235			−0.551177	+	0.834388i	$0.685821\pi$
$702$	6.90320	−	3.92136i	0.260544	−	0.148002i
$703$	−38.9245			−1.46807
$704$	6.36868	−	11.0309i	0.240029	−	0.415742i
$705$	0.300527	−	0.520527i	0.0113185	−	0.0196042i
$706$	−2.26613	−	3.92505i	−0.0852868	−	0.147721i
$707$	17.9127			0.673675
$708$	17.1119	+	29.6387i	0.643105	+	1.11389i
$709$	7.62396	+	13.2051i	0.286324	+	0.495927i	0.972929	−	0.231103i	$-0.0742334\pi$
$709$	7.62396	+	13.2051i	0.286324	+	0.495927i	−0.686606	+	0.727030i	$0.740900\pi$
$710$	6.02148			0.225982
$711$	2.81174	+	4.87008i	0.105449	+	0.182642i
$712$	−0.416638	+	0.721638i	−0.0156142	+	0.0270445i
$713$	−30.6010	+	53.0025i	−1.14602	+	1.98496i
$714$	−10.0481			−0.376041
$715$	1.52022	−	0.863560i	0.0568530	−	0.0322953i
$716$	8.12614			0.303688
$717$	−3.80869	+	6.59685i	−0.142238	+	0.246364i
$718$	−32.0812	+	55.5663i	−1.19726	+	2.07371i
$719$	13.0599	+	22.6205i	0.487054	+	0.843602i	0.999889	−	0.0148849i	$-0.00473820\pi$
$719$	13.0599	+	22.6205i	0.487054	+	0.843602i	−0.512835	+	0.858487i	$0.671405\pi$
$720$	0.767534			0.0286043
$721$	−11.9625	−	20.7197i	−0.445507	−	0.771640i
$722$	2.24602	+	3.89022i	0.0835882	+	0.144779i
$723$	−5.32470			−0.198028
$724$	−11.9190	−	20.6443i	−0.442965	−	0.767238i
$725$	16.2538	−	28.1524i	0.603650	−	1.04555i
$726$	1.10097	−	1.90694i	0.0408609	−	0.0707732i
$727$	−42.1911			−1.56478			−0.782390	−	0.622789i	$-0.786000\pi$
$727$	−42.1911			−1.56478			−0.782390	+	0.622789i	$0.786000\pi$
$728$	−0.0904117	+	12.9096i	−0.00335088	+	0.478462i
$729$	1.00000			0.0370370
$730$	5.40044	−	9.35383i	0.199879	−	0.346201i
$731$	7.42907	−	12.8675i	0.274774	−	0.475922i
$732$	4.95919	+	8.58957i	0.183297	+	0.317479i
$733$	23.1746			0.855974			0.427987	−	0.903785i	$-0.359223\pi$
$733$	23.1746			0.855974			0.427987	+	0.903785i	$0.359223\pi$
$734$	13.9134	+	24.0987i	0.513553	+	0.889499i
$735$	0.806838	+	1.39748i	0.0297607	+	0.0515470i
$736$	−42.8730			−1.58032
$737$	−1.80024	−	3.11811i	−0.0663128	−	0.114857i
$738$	1.46811	−	2.54284i	0.0540419	−	0.0936034i
$739$	−14.1456	+	24.5009i	−0.520354	+	0.901280i	0.479366	+	0.877615i	$0.340867\pi$
$739$	−14.1456	+	24.5009i	−0.520354	+	0.901280i	−0.999720	+	0.0236647i	$0.992467\pi$
$740$	−13.0556			−0.479934
$741$	12.8069	+	7.51415i	0.470474	+	0.276039i
$742$	−34.4832			−1.26592
$743$	−3.34664	+	5.79655i	−0.122776	+	0.212655i	−0.920862	−	0.389890i	$-0.872513\pi$
$743$	−3.34664	+	5.79655i	−0.122776	+	0.212655i	0.798085	+	0.602545i	$0.205846\pi$
$744$	9.63193	−	16.6830i	0.353124	−	0.611628i
$745$	3.53436	+	6.12169i	0.129489	+	0.224281i
$746$	−50.6991			−1.85623
$747$	−7.09454	−	12.2881i	−0.259576	−	0.449598i
$748$	3.39163	+	5.87448i	0.124010	+	0.214792i
$749$	2.69776			0.0985742
$750$	5.21320	+	9.02953i	0.190359	+	0.329712i
$751$	10.9480	−	18.9625i	0.399499	−	0.691953i	−0.594165	−	0.804343i	$-0.702517\pi$
$751$	10.9480	−	18.9625i	0.399499	−	0.691953i	0.993664	+	0.112390i	$0.0358507\pi$
$752$	−0.980972	+	1.69909i	−0.0357724	+	0.0619596i
$753$	−10.7599			−0.392114
$754$	0.379326	−	54.1628i	0.0138142	−	1.97249i
$755$	7.13877			0.259806
$756$	−2.72935	+	4.72737i	−0.0992655	+	0.171933i
$757$	11.9728	−	20.7374i	0.435157	−	0.753715i	−0.562151	−	0.827035i	$-0.690026\pi$
$757$	11.9728	−	20.7374i	0.435157	−	0.753715i	0.997308	+	0.0733199i	$0.0233594\pi$
$758$	−12.0269	−	20.8312i	−0.436837	−	0.756623i
$759$	−5.93622			−0.215471
$760$	−1.86566	−	3.23141i	−0.0676745	−	0.117216i
$761$	−3.20137	−	5.54493i	−0.116049	−	0.201004i	0.802149	−	0.597124i	$-0.203690\pi$
$761$	−3.20137	−	5.54493i	−0.116049	−	0.201004i	−0.918199	+	0.396120i	$0.870356\pi$
$762$	32.5173			1.17798
$763$	7.99148	+	13.8417i	0.289311	+	0.501101i
$764$	−27.9731	+	48.4508i	−1.01203	+	1.75289i
$765$	−0.577358	+	1.00001i	−0.0208744	+	0.0361556i
$766$	−9.17619			−0.331549
$767$	0.303372	−	43.3176i	0.0109541	−	1.56411i
$768$	4.47703			0.161551
$769$	0.101103	−	0.175115i	0.00364586	−	0.00631482i	−0.864197	−	0.503154i	$-0.832173\pi$
$769$	0.101103	−	0.175115i	0.00364586	−	0.00631482i	0.867843	+	0.496839i	$0.165506\pi$
$770$	−1.02306	+	1.77200i	−0.0368687	+	0.0638584i
$771$	−9.15500	−	15.8569i	−0.329709	−	0.571073i
$772$	52.9717			1.90649
$773$	−9.51598	−	16.4822i	−0.342266	−	0.592822i	0.642587	−	0.766213i	$-0.277861\pi$
$773$	−9.51598	−	16.4822i	−0.342266	−	0.592822i	−0.984853	+	0.173391i	$0.944528\pi$
$774$	−6.86953	−	11.8984i	−0.246920	−	0.427678i
$775$	−49.1254			−1.76464
$776$	8.08246	+	13.9992i	0.290143	+	0.502543i
$777$	−9.05618	+	15.6858i	−0.324889	+	0.562724i
$778$	35.0136	−	60.6454i	1.25530	−	2.17424i
$779$	5.49155			0.196755
$780$	4.29555	+	2.52031i	0.153805	+	0.0902417i
$781$	−5.63943			−0.201795
$782$	15.5632	−	26.9563i	0.556540	−	0.963956i
$783$	3.41117	−	5.90833i	0.121905	−	0.211146i
$784$	−2.63366	−	4.56164i	−0.0940594	−	0.162916i
$785$	−6.95553			−0.248254
$786$	8.03989	+	13.9255i	0.286774	+	0.496706i
$787$	−2.34992	−	4.07019i	−0.0837658	−	0.145087i	0.821099	−	0.570786i	$-0.193361\pi$
$787$	−2.34992	−	4.07019i	−0.0837658	−	0.145087i	−0.904865	+	0.425699i	$0.860028\pi$
$788$	50.4990			1.79895
$789$	−4.16958	−	7.22192i	−0.148441	−	0.257107i
$790$	−3.00223	+	5.20001i	−0.106814	+	0.185008i
$791$	6.40328	−	11.0908i	0.227674	−	0.394344i
$792$	1.86848			0.0663934
$793$	0.0879201	−	12.5538i	0.00312214	−	0.445800i
$794$	−76.2175			−2.70486
$795$	−1.98139	+	3.43186i	−0.0702726	+	0.121716i
$796$	−25.6611	+	44.4463i	−0.909533	+	1.57536i
$797$	−16.8724	−	29.2238i	−0.597650	−	1.03516i	−0.993167	−	0.116701i	$-0.962768\pi$
$797$	−16.8724	−	29.2238i	−0.597650	−	1.03516i	0.395517	−	0.918459i	$-0.370565\pi$
$798$	−17.3773			−0.615151
$799$	−1.47582	−	2.55620i	−0.0522109	−	0.0904319i
$800$	−17.2066	−	29.8026i	−0.608343	−	1.05368i
$801$	0.445966			0.0157574
$802$	−7.89133	−	13.6682i	−0.278652	−	0.482640i
$803$	−5.05779	+	8.76034i	−0.178485	+	0.309146i
$804$	5.12810	−	8.88212i	0.180854	−	0.313248i
$805$	5.51616			0.194419
$806$	−71.1715	+	40.4290i	−2.50691	+	1.42405i
$807$	4.74529			0.167042
$808$	8.73279	−	15.1256i	0.307218	−	0.532118i
$809$	8.14038	−	14.0996i	0.286201	−	0.495714i	−0.686699	−	0.726942i	$-0.740941\pi$
$809$	8.14038	−	14.0996i	0.286201	−	0.495714i	0.972900	+	0.231228i	$0.0742743\pi$
$810$	0.533873	+	0.924696i	0.0187584	+	0.0324905i
$811$	2.43125			0.0853727			0.0426864	−	0.999089i	$-0.486408\pi$
$811$	2.43125			0.0853727			0.0426864	+	0.999089i	$0.486408\pi$
$812$	18.6206	+	32.2518i	0.653454	+	1.13182i
$813$	7.68594	+	13.3124i	0.269558	+	0.466887i
$814$	20.8121			0.729465
$815$	2.72692	+	4.72317i	0.0955199	+	0.165445i
$816$	1.88460	−	3.26422i	0.0659742	−	0.114271i
$817$	12.8479	−	22.2533i	0.449492	−	0.778543i
$818$	−40.5522			−1.41787
$819$	6.00770	−	3.41268i	0.209926	−	0.119249i
$820$	1.84192			0.0643225
$821$	3.18467	−	5.51601i	0.111146	−	0.192510i	−0.805087	−	0.593157i	$-0.797881\pi$
$821$	3.18467	−	5.51601i	0.111146	−	0.192510i	0.916232	+	0.400647i	$0.131215\pi$
$822$	5.93190	−	10.2744i	0.206899	−	0.358359i
$823$	−6.74276	−	11.6788i	−0.235038	−	0.407098i	0.724246	−	0.689542i	$-0.242188\pi$
$823$	−6.74276	−	11.6788i	−0.235038	−	0.407098i	−0.959284	+	0.282444i	$0.908855\pi$
$824$	−23.3279			−0.812665
$825$	−2.38243	−	4.12649i	−0.0829456	−	0.143666i
$826$	25.3480	+	43.9041i	0.881971	+	1.52762i
$827$	25.3516			0.881561			0.440780	−	0.897615i	$-0.354702\pi$
$827$	25.3516			0.881561			0.440780	+	0.897615i	$0.354702\pi$
$828$	−8.45483	−	14.6442i	−0.293826	−	0.508921i
$829$	10.4605	−	18.1181i	0.363307	−	0.629267i	−0.625196	−	0.780468i	$-0.714981\pi$
$829$	10.4605	−	18.1181i	0.363307	−	0.629267i	0.988503	+	0.151201i	$0.0483142\pi$
$830$	7.57517	−	13.1206i	0.262938	−	0.455422i
$831$	13.0357			0.452204
$832$	−39.6106	−	23.2406i	−1.37325	−	0.805722i
$833$	7.92443			0.274565
$834$	−5.07586	+	8.79164i	−0.175763	+	0.304430i
$835$	−4.93595	+	8.54931i	−0.170816	+	0.295861i
$836$	5.86553	+	10.1594i	0.202864	+	0.351370i
$837$	−10.3099			−0.356363
$838$	−4.73400	−	8.19954i	−0.163533	−	0.283248i
$839$	−24.4435	−	42.3374i	−0.843884	−	1.46165i	−0.886586	−	0.462563i	$-0.846930\pi$
$839$	−24.4435	−	42.3374i	−0.843884	−	1.46165i	0.0427020	−	0.999088i	$-0.486403\pi$
$840$	−1.73626			−0.0599065
$841$	−8.77222	−	15.1939i	−0.302490	−	0.523929i
$842$	27.4167	−	47.4871i	0.944842	−	1.63651i
$843$	−9.60411	+	16.6348i	−0.330783	+	0.572933i
$844$	48.1376			1.65696
$845$	−3.07515	−	5.50290i	−0.105788	−	0.189305i
$846$	−2.72934			−0.0938365
$847$	0.958152	−	1.65957i	0.0329225	−	0.0570234i
$848$	6.46760	−	11.2022i	0.222098	−	0.384686i
$849$	0.541092	+	0.937199i	0.0185702	+	0.0321646i
$850$	24.9845			0.856960
$851$	−28.0537	−	48.5905i	−0.961670	−	1.66566i
$852$	−8.03212	−	13.9120i	−0.275176	−	0.476619i
$853$	4.75187			0.162701			0.0813505	−	0.996686i	$-0.474077\pi$
$853$	4.75187			0.162701			0.0813505	+	0.996686i	$0.474077\pi$
$854$	7.34609	+	12.7238i	0.251378	+	0.435400i
$855$	−0.998492	+	1.72944i	−0.0341477	+	0.0591455i
$856$	1.31522	−	2.27802i	0.0449532	−	0.0778612i
$857$	−25.3024			−0.864315			−0.432157	−	0.901798i	$-0.642248\pi$
$857$	−25.3024			−0.864315			−0.432157	+	0.901798i	$0.642248\pi$
$858$	−6.84760	−	4.01767i	−0.233773	−	0.137161i
$859$	20.5107			0.699817			0.349909	−	0.936784i	$-0.386213\pi$
$859$	20.5107			0.699817			0.349909	+	0.936784i	$0.386213\pi$
$860$	4.30931	−	7.46394i	0.146946	−	0.254518i
$861$	1.27767	−	2.21298i	0.0435427	−	0.0754182i
$862$	21.1889	+	36.7002i	0.721695	+	1.25001i
$863$	34.2383			1.16548			0.582742	−	0.812657i	$-0.301980\pi$
$863$	34.2383			1.16548			0.582742	+	0.812657i	$0.301980\pi$
$864$	−3.61113	−	6.25467i	−0.122853	−	0.212788i
$865$	−2.60647	−	4.51453i	−0.0886225	−	0.153499i
$866$	60.9709			2.07187
$867$	−5.66471	−	9.81157i	−0.192384	−	0.333218i
$868$	28.1394	−	48.7389i	0.955114	−	1.65431i
$869$	2.81174	−	4.87008i	0.0953818	−	0.165206i
$870$	7.28454			0.246969
$871$	−11.2877	+	6.41197i	−0.382469	+	0.217261i
$872$	15.5841			0.527743
$873$	4.32570	−	7.49233i	0.146403	−	0.253577i
$874$	26.9153	−	46.6186i	0.910423	−	1.57690i
$875$	4.53693	+	7.85820i	0.153376	+	0.265656i
$876$	−28.8148			−0.973562
$877$	16.8118	+	29.1190i	0.567696	+	0.983278i	0.996793	+	0.0800196i	$0.0254983\pi$
$877$	16.8118	+	29.1190i	0.567696	+	0.983278i	−0.429098	+	0.903258i	$0.641168\pi$
$878$	−1.66159	−	2.87796i	−0.0560760	−	0.0971264i
$879$	27.1439			0.915541
$880$	−0.383767	−	0.664704i	−0.0129368	−	0.0224072i
$881$	−27.3761	+	47.4168i	−0.922324	+	1.59751i	−0.126514	+	0.991965i	$0.540379\pi$
$881$	−27.3761	+	47.4168i	−0.922324	+	1.59751i	−0.795809	+	0.605547i	$0.792954\pi$
$882$	3.66379	−	6.34587i	0.123366	−	0.213677i
$883$	29.0149			0.976430			0.488215	−	0.872723i	$-0.337648\pi$
$883$	29.0149			0.976430			0.488215	+	0.872723i	$0.337648\pi$
$884$	21.2658	−	12.0801i	0.715248	−	0.406296i
$885$	5.82593			0.195837
$886$	−9.90093	+	17.1489i	−0.332628	+	0.576129i
$887$	−23.7874	+	41.2011i	−0.798704	+	1.38340i	0.121756	+	0.992560i	$0.461147\pi$
$887$	−23.7874	+	41.2011i	−0.798704	+	1.38340i	−0.920460	+	0.390836i	$0.872186\pi$
$888$	8.83015	+	15.2943i	0.296320	+	0.513242i
$889$	28.2991			0.949121
$890$	0.238089	+	0.412382i	0.00798077	+	0.0138231i
$891$	−0.500000	−	0.866025i	−0.0167506	−	0.0290129i
$892$	−52.0333			−1.74220
$893$	−2.55231	−	4.42073i	−0.0854098	−	0.147934i
$894$	16.0493	−	27.7981i	0.536768	−	0.929709i
$895$	0.691658	−	1.19799i	0.0231196	−	0.0400443i
$896$	26.0664			0.870816
$897$	−0.149894	+	21.4028i	−0.00500480	+	0.714620i
$898$	−31.1124			−1.03823
$899$	−35.1690	+	60.9145i	−1.17295	+	2.03161i
$900$	6.78649	−	11.7545i	0.226216	−	0.391818i
$901$	9.73018	+	16.8532i	0.324159	+	0.561460i
$902$	−2.93622			−0.0977655
$903$	−5.97840	−	10.3549i	−0.198949	−	0.344589i
$904$	−6.24346	−	10.8140i	−0.207654	−	0.359668i
$905$	−4.05794			−0.134891
$906$	−16.2083	−	28.0736i	−0.538485	−	0.932683i
$907$	−10.1525	+	17.5846i	−0.337108	+	0.583889i	−0.983888	−	0.178789i	$-0.942782\pi$
$907$	−10.1525	+	17.5846i	−0.337108	+	0.583889i	0.646779	+	0.762677i	$0.276116\pi$
$908$	−21.5107	+	37.2577i	−0.713859	+	1.23644i
$909$	−9.34750			−0.310037
$910$	6.36304	+	3.73336i	0.210933	+	0.123760i
$911$	−3.84391			−0.127354			−0.0636772	−	0.997971i	$-0.520283\pi$
$911$	−3.84391			−0.127354			−0.0636772	+	0.997971i	$0.520283\pi$
$912$	3.25926	−	5.64520i	0.107925	−	0.186931i
$913$	−7.09454	+	12.2881i	−0.234795	+	0.406677i
$914$	−40.2236	−	69.6694i	−1.33048	−	2.30446i
$915$	1.68841			0.0558171
$916$	24.0819	+	41.7111i	0.795689	+	1.37817i
$917$	6.99695	+	12.1191i	0.231059	+	0.400207i
$918$	5.24348			0.173061
$919$	−13.8916	−	24.0610i	−0.458243	−	0.793700i	0.540625	−	0.841264i	$-0.318188\pi$
$919$	−13.8916	−	24.0610i	−0.458243	−	0.793700i	−0.998868	+	0.0475632i	$0.984854\pi$
$920$	2.68924	−	4.65790i	0.0886616	−	0.153566i
$921$	−6.16314	+	10.6749i	−0.203082	+	0.351749i
$922$	−63.9339			−2.10555
$923$	−0.142399	+	20.3328i	−0.00468713	+	0.669261i
$924$	5.45870			0.179578
$925$	22.5181	−	39.0024i	0.740389	−	1.28239i
$926$	−38.8076	+	67.2167i	−1.27530	+	2.20888i
$927$	6.24249	+	10.8123i	0.205030	+	0.355123i
$928$	−49.2728			−1.61746
$929$	19.5863	+	33.9244i	0.642604	+	1.11302i	0.984849	+	0.173413i	$0.0554794\pi$
$929$	19.5863	+	33.9244i	0.642604	+	1.11302i	−0.342245	+	0.939611i	$0.611187\pi$
$930$	−5.50420	−	9.53355i	−0.180490	−	0.312617i
$931$	13.7046			0.449151
$932$	−9.56448	−	16.5662i	−0.313295	−	0.542643i
$933$	11.1576	−	19.3256i	0.365284	−	0.632691i
$934$	32.6939	−	56.6275i	1.06978	−	1.85291i
$935$	1.15472			0.0377633
$936$	0.0471802	−	6.73672i	0.00154213	−	0.220197i
$937$	−3.22613			−0.105393			−0.0526965	−	0.998611i	$-0.516782\pi$
$937$	−3.22613			−0.105393			−0.0526965	+	0.998611i	$0.516782\pi$
$938$	7.59629	−	13.1572i	0.248028	−	0.429597i
$939$	−4.90823	+	8.50131i	−0.160174	+	0.277430i
$940$	−0.856067	−	1.48275i	−0.0279218	−	0.0483620i
$941$	−53.7920			−1.75357			−0.876785	−	0.480882i	$-0.840316\pi$
$941$	−53.7920			−1.75357			−0.876785	+	0.480882i	$0.840316\pi$
$942$	15.7923	+	27.3530i	0.514540	+	0.891209i
$943$	3.95788	+	6.85525i	0.128886	+	0.223238i
$944$	−19.0169			−0.618947
$945$	0.464618	+	0.804743i	0.0151140	+	0.0261783i
$946$	−6.86953	+	11.8984i	−0.223348	+	0.386849i
$947$	−26.2297	+	45.4312i	−0.852351	+	1.47631i	0.0267303	+	0.999643i	$0.491490\pi$
$947$	−26.2297	+	45.4312i	−0.852351	+	1.47631i	−0.879081	+	0.476672i	$0.841843\pi$
$948$	16.0188			0.520267
$949$	31.4574	+	18.4569i	1.02115	+	0.599135i
$950$	43.2085			1.40187
$951$	16.2876	−	28.2110i	0.528163	−	0.914805i
$952$	−4.26320	+	7.38407i	−0.138171	+	0.239319i
$953$	4.40217	+	7.62479i	0.142600	+	0.246991i	0.928475	−	0.371395i	$-0.121120\pi$
$953$	4.40217	+	7.62479i	0.142600	+	0.246991i	−0.785875	+	0.618386i	$0.787787\pi$
$954$	17.9947			0.582599
$955$	4.76187	+	8.24780i	0.154091	+	0.266893i
$956$	10.8493	+	18.7915i	0.350891	+	0.607761i
$957$	−6.82235			−0.220535
$958$	3.47033	+	6.01078i	0.112121	+	0.194199i
$959$	5.16241	−	8.94155i	0.166703	−	0.288738i
$960$	3.08824	−	5.34899i	0.0996726	−	0.172638i
$961$	75.2947			2.42886
$962$	0.525521	−	75.0374i	0.0169435	−	2.41930i
$963$	−1.40780			−0.0453656
$964$	−7.58386	+	13.1356i	−0.244260	+	0.423070i
$965$	4.50870	−	7.80929i	0.145140	−	0.251390i
$966$	−12.5242	−	21.6926i	−0.402960	−	0.697948i
$967$	30.2813			0.973780			0.486890	−	0.873463i	$-0.338131\pi$
$967$	30.2813			0.973780			0.486890	+	0.873463i	$0.338131\pi$
$968$	−0.934238	−	1.61815i	−0.0300275	−	0.0520092i
$969$	4.90339	+	8.49291i	0.157519	+	0.272832i
$970$	9.23750			0.296598
$971$	−3.19282	−	5.53012i	−0.102462	−	0.177470i	0.810236	−	0.586103i	$-0.199339\pi$
$971$	−3.19282	−	5.53012i	−0.102462	−	0.177470i	−0.912699	+	0.408633i	$0.866005\pi$
$972$	1.42428	−	2.46692i	0.0456838	−	0.0791266i
$973$	−4.41741	+	7.65117i	−0.141616	+	0.245285i
$974$	90.0919			2.88673
$975$	−14.9381	+	8.48557i	−0.478401	+	0.271756i
$976$	−5.51127			−0.176411
$977$	−16.2192	+	28.0924i	−0.518897	+	0.898755i	0.480862	+	0.876796i	$0.340324\pi$
$977$	−16.2192	+	28.0924i	−0.518897	+	0.898755i	−0.999759	+	0.0219592i	$0.993010\pi$
$978$	12.3827	−	21.4475i	0.395956	−	0.685817i
$979$	−0.222983	−	0.386217i	−0.00712656	−	0.0123436i
$980$	4.59665			0.146835
$981$	−4.17026	−	7.22310i	−0.133146	−	0.230616i
$982$	32.8968	+	56.9789i	1.04978	+	1.81827i
$983$	2.62989			0.0838804			0.0419402	−	0.999120i	$-0.486646\pi$
$983$	2.62989			0.0838804			0.0419402	+	0.999120i	$0.486646\pi$
$984$	−1.24578	−	2.15775i	−0.0397139	−	0.0687865i
$985$	4.29823	−	7.44475i	0.136953	−	0.237209i
$986$	17.8864	−	30.9802i	0.569620	−	0.986611i
$987$	−2.37528			−0.0756061
$988$	36.7775	−	20.8914i	1.17005	−	0.664645i
$989$	37.0391			1.17778
$990$	0.533873	−	0.924696i	0.0169676	−	0.0293888i
$991$	12.0638	−	20.8952i	0.383220	−	0.663757i	−0.608300	−	0.793707i	$-0.708148\pi$
$991$	12.0638	−	20.8952i	0.383220	−	0.663757i	0.991521	+	0.129950i	$0.0414817\pi$
$992$	37.2305	+	64.4852i	1.18207	+	2.04741i
$993$	−27.7639			−0.881060
$994$	−11.8981	−	20.6080i	−0.377383	−	0.653647i
$995$	4.36830	+	7.56611i	0.138484	+	0.239862i
$996$	−40.4184			−1.28071
$997$	−24.0951	−	41.7339i	−0.763098	−	1.32172i	−0.941246	−	0.337721i	$-0.890344\pi$
$997$	−24.0951	−	41.7339i	−0.763098	−	1.32172i	0.178148	−	0.984004i	$-0.442989\pi$
$998$	14.3413	−	24.8399i	0.453967	−	0.786293i
$999$	4.72586	−	8.18543i	0.149520	−	0.258975i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.i.d.100.2	✓	10
13.3	even	3	inner	429.2.i.d.133.2	yes	10
13.4	even	6		5577.2.a.s.1.2		5
13.9	even	3		5577.2.a.r.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.i.d.100.2	✓	10	1.1	even	1	trivial
429.2.i.d.133.2	yes	10	13.3	even	3	inner
5577.2.a.r.1.4		5	13.9	even	3
5577.2.a.s.1.2		5	13.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.10097 + 1.90694i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-1.42428 - 2.46692i) q^{4} -0.484911 q^{5} +(1.10097 + 1.90694i) q^{6} +(0.958152 + 1.65957i) q^{7} +1.86848 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.10097 + 1.90694i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-1.42428 - 2.46692i) q^{4} -0.484911 q^{5} +(1.10097 + 1.90694i) q^{6} +(0.958152 + 1.65957i) q^{7} +1.86848 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.533873 - 0.924696i) q^{10} +(-0.500000 + 0.866025i) q^{11} -2.84856 q^{12} +(3.10980 + 1.82460i) q^{13} -4.21959 q^{14} +(-0.242455 + 0.419945i) q^{15} +(0.791418 - 1.37078i) q^{16} +(1.19065 + 2.06226i) q^{17} +2.20194 q^{18} +(2.05912 + 3.56651i) q^{19} +(0.690648 + 1.19624i) q^{20} +1.91630 q^{21} +(-1.10097 - 1.90694i) q^{22} +(-2.96811 + 5.14092i) q^{23} +(0.934238 - 1.61815i) q^{24} -4.76486 q^{25} +(-6.90320 + 3.92136i) q^{26} -1.00000 q^{27} +(2.72935 - 4.72737i) q^{28} +(-3.41117 + 5.90833i) q^{29} +(-0.533873 - 0.924696i) q^{30} +10.3099 q^{31} +(3.61113 + 6.25467i) q^{32} +(0.500000 + 0.866025i) q^{33} -5.24348 q^{34} +(-0.464618 - 0.804743i) q^{35} +(-1.42428 + 2.46692i) q^{36} +(-4.72586 + 8.18543i) q^{37} -9.06815 q^{38} +(3.13505 - 1.78086i) q^{39} -0.906044 q^{40} +(0.666734 - 1.15482i) q^{41} +(-2.10980 + 3.65428i) q^{42} +(-3.11976 - 5.40358i) q^{43} +2.84856 q^{44} +(0.242455 + 0.419945i) q^{45} +(-6.53561 - 11.3200i) q^{46} -1.23951 q^{47} +(-0.791418 - 1.37078i) q^{48} +(1.66389 - 2.88194i) q^{49} +(5.24598 - 9.08630i) q^{50} +2.38130 q^{51} +(0.0719280 - 10.2704i) q^{52} +8.17217 q^{53} +(1.10097 - 1.90694i) q^{54} +(0.242455 - 0.419945i) q^{55} +(1.79028 + 3.10086i) q^{56} +4.11825 q^{57} +(-7.51121 - 13.0098i) q^{58} +(-6.00722 - 10.4048i) q^{59} +1.38130 q^{60} +(-1.74095 - 3.01541i) q^{61} +(-11.3509 + 19.6604i) q^{62} +(0.958152 - 1.65957i) q^{63} -12.7374 q^{64} +(-1.50797 - 0.884768i) q^{65} -2.20194 q^{66} +(-1.80024 + 3.11811i) q^{67} +(3.39163 - 5.87448i) q^{68} +(2.96811 + 5.14092i) q^{69} +2.04613 q^{70} +(2.81972 + 4.88389i) q^{71} +(-0.934238 - 1.61815i) q^{72} +10.1156 q^{73} +(-10.4061 - 18.0239i) q^{74} +(-2.38243 + 4.12649i) q^{75} +(5.86553 - 10.1594i) q^{76} -1.91630 q^{77} +(-0.0556005 + 7.93903i) q^{78} -5.62348 q^{79} +(-0.383767 + 0.664704i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.46811 + 2.54284i) q^{82} +14.1891 q^{83} +(-2.72935 - 4.72737i) q^{84} +(-0.577358 - 1.00001i) q^{85} +13.7391 q^{86} +(3.41117 + 5.90833i) q^{87} +(-0.934238 + 1.61815i) q^{88} +(-0.222983 + 0.386217i) q^{89} -1.06775 q^{90} +(-0.0483879 + 6.90916i) q^{91} +16.9097 q^{92} +(5.15497 - 8.92866i) q^{93} +(1.36467 - 2.36368i) q^{94} +(-0.998492 - 1.72944i) q^{95} +7.22227 q^{96} +(4.32570 + 7.49233i) q^{97} +(3.66379 + 6.34587i) q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 5 q^{3} - 10 q^{4} - 4 q^{5} - 7 q^{7} + 6 q^{8} - 5 q^{9}+O(q^{10}) \) 10 * q + 5 * q^3 - 10 * q^4 - 4 * q^5 - 7 * q^7 + 6 * q^8 - 5 * q^9	\( 10 q + 5 q^{3} - 10 q^{4} - 4 q^{5} - 7 q^{7} + 6 q^{8} - 5 q^{9} - 7 q^{10} - 5 q^{11} - 20 q^{12} + 9 q^{13} + 2 q^{14} - 2 q^{15} - 4 q^{16} - 3 q^{17} - 7 q^{19} - 8 q^{20} - 14 q^{21} - 11 q^{23} + 3 q^{24} - 6 q^{25} - 4 q^{26} - 10 q^{27} - 5 q^{28} + 2 q^{29} + 7 q^{30} + 20 q^{31} + 9 q^{32} + 5 q^{33} + 58 q^{34} + 14 q^{35} - 10 q^{36} - 15 q^{37} - 38 q^{38} - 6 q^{39} + 30 q^{40} + 2 q^{41} + q^{42} - 7 q^{43} + 20 q^{44} + 2 q^{45} - 20 q^{46} + 36 q^{47} + 4 q^{48} - 14 q^{49} + 2 q^{50} - 6 q^{51} - 3 q^{52} + 30 q^{53} + 2 q^{55} - 3 q^{56} - 14 q^{57} - 5 q^{58} + 4 q^{59} - 16 q^{60} + 14 q^{61} - 46 q^{62} - 7 q^{63} - 74 q^{64} - 44 q^{65} + 5 q^{67} + 24 q^{68} + 11 q^{69} + 80 q^{70} + 13 q^{71} - 3 q^{72} + 56 q^{73} - 15 q^{74} - 3 q^{75} - 2 q^{76} + 14 q^{77} - 23 q^{78} + 32 q^{79} + 22 q^{80} - 5 q^{81} - 4 q^{82} + 24 q^{83} + 5 q^{84} - 13 q^{85} + 4 q^{86} - 2 q^{87} - 3 q^{88} + 6 q^{89} + 14 q^{90} - 29 q^{91} - 4 q^{92} + 10 q^{93} + 2 q^{94} + 21 q^{95} + 18 q^{96} - 9 q^{97} - 16 q^{98} + 10 q^{99}+O(q^{100}) \) 10 * q + 5 * q^3 - 10 * q^4 - 4 * q^5 - 7 * q^7 + 6 * q^8 - 5 * q^9 - 7 * q^10 - 5 * q^11 - 20 * q^12 + 9 * q^13 + 2 * q^14 - 2 * q^15 - 4 * q^16 - 3 * q^17 - 7 * q^19 - 8 * q^20 - 14 * q^21 - 11 * q^23 + 3 * q^24 - 6 * q^25 - 4 * q^26 - 10 * q^27 - 5 * q^28 + 2 * q^29 + 7 * q^30 + 20 * q^31 + 9 * q^32 + 5 * q^33 + 58 * q^34 + 14 * q^35 - 10 * q^36 - 15 * q^37 - 38 * q^38 - 6 * q^39 + 30 * q^40 + 2 * q^41 + q^42 - 7 * q^43 + 20 * q^44 + 2 * q^45 - 20 * q^46 + 36 * q^47 + 4 * q^48 - 14 * q^49 + 2 * q^50 - 6 * q^51 - 3 * q^52 + 30 * q^53 + 2 * q^55 - 3 * q^56 - 14 * q^57 - 5 * q^58 + 4 * q^59 - 16 * q^60 + 14 * q^61 - 46 * q^62 - 7 * q^63 - 74 * q^64 - 44 * q^65 + 5 * q^67 + 24 * q^68 + 11 * q^69 + 80 * q^70 + 13 * q^71 - 3 * q^72 + 56 * q^73 - 15 * q^74 - 3 * q^75 - 2 * q^76 + 14 * q^77 - 23 * q^78 + 32 * q^79 + 22 * q^80 - 5 * q^81 - 4 * q^82 + 24 * q^83 + 5 * q^84 - 13 * q^85 + 4 * q^86 - 2 * q^87 - 3 * q^88 + 6 * q^89 + 14 * q^90 - 29 * q^91 - 4 * q^92 + 10 * q^93 + 2 * q^94 + 21 * q^95 + 18 * q^96 - 9 * q^97 - 16 * q^98 + 10 * q^99

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