LMFDB - Embedded newform 731.2.e.b.307.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(307,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("731.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.e (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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$58$
Relative dimension:	$29$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			307.1
Character	$\chi$	$=$	731.307
Dual form			731.2.e.b.681.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.61335 q^{2} +(1.52887 - 2.64809i) q^{3} +4.82960 q^{4} +(-0.766598 + 1.32779i) q^{5} +(-3.99548 + 6.92038i) q^{6} +(-0.834694 - 1.44573i) q^{7} -7.39472 q^{8} +(-3.17491 - 5.49911i) q^{9} +O(q^{10})$	\(q-2.61335 q^{2} +(1.52887 - 2.64809i) q^{3} +4.82960 q^{4} +(-0.766598 + 1.32779i) q^{5} +(-3.99548 + 6.92038i) q^{6} +(-0.834694 - 1.44573i) q^{7} -7.39472 q^{8} +(-3.17491 - 5.49911i) q^{9} +(2.00339 - 3.46997i) q^{10} -4.85965 q^{11} +(7.38384 - 12.7892i) q^{12} +(1.26987 + 2.19948i) q^{13} +(2.18135 + 3.77820i) q^{14} +(2.34406 + 4.06004i) q^{15} +9.66581 q^{16} +(-0.500000 - 0.866025i) q^{17} +(8.29715 + 14.3711i) q^{18} +(-3.12792 + 5.41771i) q^{19} +(-3.70236 + 6.41267i) q^{20} -5.10457 q^{21} +12.7000 q^{22} +(-1.99910 + 3.46254i) q^{23} +(-11.3056 + 19.5819i) q^{24} +(1.32466 + 2.29437i) q^{25} +(-3.31862 - 5.74802i) q^{26} -10.2429 q^{27} +(-4.03123 - 6.98230i) q^{28} +(-2.36654 - 4.09897i) q^{29} +(-6.12585 - 10.6103i) q^{30} +(1.99682 - 3.45859i) q^{31} -10.4707 q^{32} +(-7.42980 + 12.8688i) q^{33} +(1.30667 + 2.26323i) q^{34} +2.55950 q^{35} +(-15.3335 - 26.5585i) q^{36} +(-2.12628 + 3.68283i) q^{37} +(8.17434 - 14.1584i) q^{38} +7.76590 q^{39} +(5.66878 - 9.81861i) q^{40} -4.77403 q^{41} +13.3400 q^{42} +(-0.534635 + 6.53561i) q^{43} -23.4702 q^{44} +9.73552 q^{45} +(5.22435 - 9.04884i) q^{46} -2.43444 q^{47} +(14.7778 - 25.5959i) q^{48} +(2.10657 - 3.64869i) q^{49} +(-3.46179 - 5.99599i) q^{50} -3.05775 q^{51} +(6.13297 + 10.6226i) q^{52} +(-1.73938 + 3.01269i) q^{53} +26.7683 q^{54} +(3.72540 - 6.45258i) q^{55} +(6.17233 + 10.6908i) q^{56} +(9.56438 + 16.5660i) q^{57} +(6.18461 + 10.7121i) q^{58} +9.27106 q^{59} +(11.3209 + 19.6083i) q^{60} +(-6.89649 - 11.9451i) q^{61} +(-5.21838 + 9.03850i) q^{62} +(-5.30016 + 9.18014i) q^{63} +8.03195 q^{64} -3.89393 q^{65} +(19.4167 - 33.6306i) q^{66} +(-4.56843 + 7.91276i) q^{67} +(-2.41480 - 4.18255i) q^{68} +(6.11274 + 10.5876i) q^{69} -6.68886 q^{70} +(-0.528350 - 0.915128i) q^{71} +(23.4776 + 40.6644i) q^{72} +(-6.46472 - 11.1972i) q^{73} +(5.55672 - 9.62452i) q^{74} +8.10093 q^{75} +(-15.1066 + 26.1654i) q^{76} +(4.05632 + 7.02575i) q^{77} -20.2950 q^{78} +(-3.98971 - 6.91039i) q^{79} +(-7.40979 + 12.8341i) q^{80} +(-6.13538 + 10.6268i) q^{81} +12.4762 q^{82} +(-6.82937 + 11.8288i) q^{83} -24.6530 q^{84} +1.53320 q^{85} +(1.39719 - 17.0798i) q^{86} -14.4726 q^{87} +35.9358 q^{88} +(-3.32433 + 5.75792i) q^{89} -25.4423 q^{90} +(2.11991 - 3.67179i) q^{91} +(-9.65485 + 16.7227i) q^{92} +(-6.10576 - 10.5755i) q^{93} +6.36205 q^{94} +(-4.79571 - 8.30641i) q^{95} +(-16.0084 + 27.7273i) q^{96} +12.6719 q^{97} +(-5.50521 + 9.53531i) q^{98} +(15.4290 + 26.7237i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 58 q + 2 q^{2} - 5 q^{3} + 54 q^{4} - 3 q^{5} - 8 q^{6} - 13 q^{7} + 12 q^{8} - 30 q^{9}+O(q^{10}) $ 58 * q + 2 * q^2 - 5 * q^3 + 54 * q^4 - 3 * q^5 - 8 * q^6 - 13 * q^7 + 12 * q^8 - 30 * q^9	\( 58 q + 2 q^{2} - 5 q^{3} + 54 q^{4} - 3 q^{5} - 8 q^{6} - 13 q^{7} + 12 q^{8} - 30 q^{9} + 4 q^{10} - 8 q^{12} + 2 q^{13} + 5 q^{14} - 5 q^{15} + 30 q^{16} - 29 q^{17} + 16 q^{18} - 4 q^{19} - 7 q^{20} - 26 q^{21} - 10 q^{22} + 5 q^{23} - 28 q^{24} - 24 q^{25} - 8 q^{26} + 28 q^{27} - 25 q^{28} + 10 q^{29} - 5 q^{30} + 3 q^{31} + 16 q^{32} - 23 q^{33} - q^{34} - 26 q^{35} - 39 q^{36} - 16 q^{37} + q^{38} + 130 q^{39} + 15 q^{40} - 22 q^{41} + 112 q^{42} + 7 q^{43} + 24 q^{44} + 2 q^{45} - 61 q^{46} + 12 q^{47} + 22 q^{48} - 36 q^{49} - 17 q^{50} + 10 q^{51} - 35 q^{52} - 10 q^{53} - 10 q^{54} - 20 q^{55} - 4 q^{56} + 9 q^{57} - 17 q^{58} - 36 q^{59} + 22 q^{60} - 35 q^{61} + 3 q^{62} - 22 q^{63} + 28 q^{64} - 28 q^{65} + 14 q^{66} - 17 q^{67} - 27 q^{68} - 23 q^{69} + 10 q^{70} - 6 q^{71} + 17 q^{72} - 14 q^{73} + 21 q^{74} + 70 q^{75} - 44 q^{76} - 11 q^{77} - 184 q^{78} - 10 q^{79} + 8 q^{80} - 13 q^{81} + 184 q^{82} + 9 q^{83} - 36 q^{84} + 6 q^{85} - 76 q^{86} + 8 q^{87} + 50 q^{88} - 54 q^{89} - 34 q^{90} - 23 q^{91} - 66 q^{92} + 96 q^{94} - 3 q^{95} - 60 q^{96} + 36 q^{97} - 16 q^{98} + 20 q^{99}+O(q^{100}) \) 58 * q + 2 * q^2 - 5 * q^3 + 54 * q^4 - 3 * q^5 - 8 * q^6 - 13 * q^7 + 12 * q^8 - 30 * q^9 + 4 * q^10 - 8 * q^12 + 2 * q^13 + 5 * q^14 - 5 * q^15 + 30 * q^16 - 29 * q^17 + 16 * q^18 - 4 * q^19 - 7 * q^20 - 26 * q^21 - 10 * q^22 + 5 * q^23 - 28 * q^24 - 24 * q^25 - 8 * q^26 + 28 * q^27 - 25 * q^28 + 10 * q^29 - 5 * q^30 + 3 * q^31 + 16 * q^32 - 23 * q^33 - q^34 - 26 * q^35 - 39 * q^36 - 16 * q^37 + q^38 + 130 * q^39 + 15 * q^40 - 22 * q^41 + 112 * q^42 + 7 * q^43 + 24 * q^44 + 2 * q^45 - 61 * q^46 + 12 * q^47 + 22 * q^48 - 36 * q^49 - 17 * q^50 + 10 * q^51 - 35 * q^52 - 10 * q^53 - 10 * q^54 - 20 * q^55 - 4 * q^56 + 9 * q^57 - 17 * q^58 - 36 * q^59 + 22 * q^60 - 35 * q^61 + 3 * q^62 - 22 * q^63 + 28 * q^64 - 28 * q^65 + 14 * q^66 - 17 * q^67 - 27 * q^68 - 23 * q^69 + 10 * q^70 - 6 * q^71 + 17 * q^72 - 14 * q^73 + 21 * q^74 + 70 * q^75 - 44 * q^76 - 11 * q^77 - 184 * q^78 - 10 * q^79 + 8 * q^80 - 13 * q^81 + 184 * q^82 + 9 * q^83 - 36 * q^84 + 6 * q^85 - 76 * q^86 + 8 * q^87 + 50 * q^88 - 54 * q^89 - 34 * q^90 - 23 * q^91 - 66 * q^92 + 96 * q^94 - 3 * q^95 - 60 * q^96 + 36 * q^97 - 16 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.61335			−1.84792			−0.923959	−	0.382492i	$-0.875066\pi$
$2$	−2.61335			−1.84792			−0.923959	+	0.382492i	$0.875066\pi$
$3$	1.52887	−	2.64809i	0.882696	−	1.52887i	0.0343636	−	0.999409i	$-0.489060\pi$
$3$	1.52887	−	2.64809i	0.882696	−	1.52887i	0.848332	−	0.529464i	$-0.177607\pi$
$4$	4.82960			2.41480
$5$	−0.766598	+	1.32779i	−0.342833	+	0.593804i	−0.984958	−	0.172796i	$-0.944720\pi$
$5$	−0.766598	+	1.32779i	−0.342833	+	0.593804i	0.642125	+	0.766600i	$0.278053\pi$
$6$	−3.99548	+	6.92038i	−1.63115	+	2.82523i
$7$	−0.834694	−	1.44573i	−0.315485	−	0.546435i	0.664056	−	0.747683i	$-0.268834\pi$
$7$	−0.834694	−	1.44573i	−0.315485	−	0.546435i	−0.979540	+	0.201248i	$0.935500\pi$
$8$	−7.39472			−2.61443
$9$	−3.17491	−	5.49911i	−1.05830	−	1.83304i
$10$	2.00339	−	3.46997i	0.633527	−	1.09730i
$11$	−4.85965			−1.46524			−0.732620	−	0.680638i	$-0.761703\pi$
$11$	−4.85965			−1.46524			−0.732620	+	0.680638i	$0.761703\pi$
$12$	7.38384	−	12.7892i	2.13153	−	3.69192i
$13$	1.26987	+	2.19948i	0.352199	+	0.610027i	0.986635	−	0.162949i	$-0.0521006\pi$
$13$	1.26987	+	2.19948i	0.352199	+	0.610027i	−0.634435	+	0.772976i	$0.718767\pi$
$14$	2.18135	+	3.77820i	0.582989	+	1.00977i
$15$	2.34406	+	4.06004i	0.605234	+	1.04830i
$16$	9.66581			2.41645
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i
$18$	8.29715	+	14.3711i	1.95566	+	3.38730i
$19$	−3.12792	+	5.41771i	−0.717593	+	1.24291i	0.244357	+	0.969685i	$0.421423\pi$
$19$	−3.12792	+	5.41771i	−0.717593	+	1.24291i	−0.961951	+	0.273223i	$0.911910\pi$
$20$	−3.70236	+	6.41267i	−0.827872	+	1.43392i
$21$	−5.10457			−1.11391
$22$	12.7000			2.70764
$23$	−1.99910	+	3.46254i	−0.416841	+	0.721990i	−0.995620	−	0.0934946i	$-0.970196\pi$
$23$	−1.99910	+	3.46254i	−0.416841	+	0.721990i	0.578779	+	0.815485i	$0.303530\pi$
$24$	−11.3056	+	19.5819i	−2.30775	+	3.99713i
$25$	1.32466	+	2.29437i	0.264931	+	0.458874i
$26$	−3.31862	−	5.74802i	−0.650835	−	1.12728i
$27$	−10.2429			−1.97125
$28$	−4.03123	−	6.98230i	−0.761831	−	1.31953i
$29$	−2.36654	−	4.09897i	−0.439456	−	0.761160i	0.558191	−	0.829712i	$-0.311495\pi$
$29$	−2.36654	−	4.09897i	−0.439456	−	0.761160i	−0.997648	+	0.0685519i	$0.978162\pi$
$30$	−6.12585	−	10.6103i	−1.11842	−	1.93717i
$31$	1.99682	−	3.45859i	0.358639	−	0.621181i	−0.629095	−	0.777328i	$-0.716574\pi$
$31$	1.99682	−	3.45859i	0.358639	−	0.621181i	0.987734	+	0.156148i	$0.0499077\pi$
$32$	−10.4707			−1.85097
$33$	−7.42980	+	12.8688i	−1.29336	+	2.24017i
$34$	1.30667	+	2.26323i	0.224093	+	0.388140i
$35$	2.55950			0.432634
$36$	−15.3335	−	26.5585i	−2.55559	−	4.42641i
$37$	−2.12628	+	3.68283i	−0.349559	+	0.605454i	−0.986171	−	0.165730i	$-0.947002\pi$
$37$	−2.12628	+	3.68283i	−0.349559	+	0.605454i	0.636612	+	0.771184i	$0.280335\pi$
$38$	8.17434	−	14.1584i	1.32605	−	2.29679i
$39$	7.76590			1.24354
$40$	5.66878	−	9.81861i	0.896313	−	1.55246i
$41$	−4.77403			−0.745578			−0.372789	−	0.927916i	$-0.621598\pi$
$41$	−4.77403			−0.745578			−0.372789	+	0.927916i	$0.621598\pi$
$42$	13.3400			2.05841
$43$	−0.534635	+	6.53561i	−0.0815311	+	0.996671i
$43$	−0.534635	+	6.53561i	−0.0815311	+	0.996671i
$44$	−23.4702			−3.53826
$45$	9.73552			1.45129
$46$	5.22435	−	9.04884i	0.770288	−	1.33418i
$47$	−2.43444			−0.355100			−0.177550	−	0.984112i	$-0.556817\pi$
$47$	−2.43444			−0.355100			−0.177550	+	0.984112i	$0.556817\pi$
$48$	14.7778	−	25.5959i	2.13299	−	3.69445i
$49$	2.10657	−	3.64869i	0.300939	−	0.521242i
$50$	−3.46179	−	5.99599i	−0.489571	−	0.847962i
$51$	−3.05775			−0.428170
$52$	6.13297	+	10.6226i	0.850490	+	1.47309i
$53$	−1.73938	+	3.01269i	−0.238922	+	0.413825i	−0.960405	−	0.278607i	$-0.910127\pi$
$53$	−1.73938	+	3.01269i	−0.238922	+	0.413825i	0.721483	+	0.692432i	$0.243461\pi$
$54$	26.7683			3.64270
$55$	3.72540	−	6.45258i	0.502333	−	0.870066i
$56$	6.17233	+	10.6908i	0.824812	+	1.42862i
$57$	9.56438	+	16.5660i	1.26683	+	2.19422i
$58$	6.18461	+	10.7121i	0.812079	+	1.40656i
$59$	9.27106			1.20699			0.603495	−	0.797367i	$-0.293774\pi$
$59$	9.27106			1.20699			0.603495	+	0.797367i	$0.293774\pi$
$60$	11.3209	+	19.6083i	1.46152	+	2.53142i
$61$	−6.89649	−	11.9451i	−0.883005	−	1.52941i	−0.847983	−	0.530023i	$-0.822183\pi$
$61$	−6.89649	−	11.9451i	−0.883005	−	1.52941i	−0.0350217	−	0.999387i	$-0.511150\pi$
$62$	−5.21838	+	9.03850i	−0.662735	+	1.14789i
$63$	−5.30016	+	9.18014i	−0.667757	+	1.15659i
$64$	8.03195			1.00399
$65$	−3.89393			−0.482982
$66$	19.4167	−	33.6306i	2.39003	−	4.13964i
$67$	−4.56843	+	7.91276i	−0.558123	+	0.966698i	0.439530	+	0.898228i	$0.355145\pi$
$67$	−4.56843	+	7.91276i	−0.558123	+	0.966698i	−0.997653	+	0.0684697i	$0.978188\pi$
$68$	−2.41480	−	4.18255i	−0.292837	−	0.507209i
$69$	6.11274	+	10.5876i	0.735888	+	1.27460i
$70$	−6.68886			−0.799472
$71$	−0.528350	−	0.915128i	−0.0627036	−	0.108606i	0.832969	−	0.553319i	$-0.186639\pi$
$71$	−0.528350	−	0.915128i	−0.0627036	−	0.108606i	−0.895673	+	0.444713i	$0.853306\pi$
$72$	23.4776	+	40.6644i	2.76686	+	4.79234i
$73$	−6.46472	−	11.1972i	−0.756638	−	1.31054i	−0.944556	−	0.328351i	$-0.893507\pi$
$73$	−6.46472	−	11.1972i	−0.756638	−	1.31054i	0.187918	−	0.982185i	$-0.439826\pi$
$74$	5.55672	−	9.62452i	0.645956	−	1.11883i
$75$	8.10093			0.935414
$76$	−15.1066	+	26.1654i	−1.73284	+	3.00137i
$77$	4.05632	+	7.02575i	0.462261	+	0.800659i
$78$	−20.2950			−2.29796
$79$	−3.98971	−	6.91039i	−0.448878	−	0.777479i	0.549435	−	0.835536i	$-0.314843\pi$
$79$	−3.98971	−	6.91039i	−0.448878	−	0.777479i	−0.998313	+	0.0580569i	$0.981510\pi$
$80$	−7.40979	+	12.8341i	−0.828439	+	1.43490i
$81$	−6.13538	+	10.6268i	−0.681709	+	1.18076i
$82$	12.4762			1.37777
$83$	−6.82937	+	11.8288i	−0.749620	+	1.29838i	0.198384	+	0.980124i	$0.436431\pi$
$83$	−6.82937	+	11.8288i	−0.749620	+	1.29838i	−0.948005	+	0.318256i	$0.896903\pi$
$84$	−24.6530			−2.68986
$85$	1.53320			0.166298
$86$	1.39719	−	17.0798i	0.150663	−	1.84177i
$87$	−14.4726			−1.55162
$88$	35.9358			3.83077
$89$	−3.32433	+	5.75792i	−0.352379	+	0.610338i	−0.986666	−	0.162760i	$-0.947960\pi$
$89$	−3.32433	+	5.75792i	−0.352379	+	0.610338i	0.634287	+	0.773098i	$0.281294\pi$
$90$	−25.4423			−2.68186
$91$	2.11991	−	3.67179i	0.222227	−	0.384908i
$92$	−9.65485	+	16.7227i	−1.00659	+	1.74346i
$93$	−6.10576	−	10.5755i	−0.633138	−	1.09663i
$94$	6.36205			0.656195
$95$	−4.79571	−	8.30641i	−0.492029	−	0.852220i
$96$	−16.0084	+	27.7273i	−1.63385	+	2.82990i
$97$	12.6719			1.28664			0.643318	−	0.765599i	$-0.277557\pi$
$97$	12.6719			1.28664			0.643318	+	0.765599i	$0.277557\pi$
$98$	−5.50521	+	9.53531i	−0.556110	+	0.963211i
$99$	15.4290	+	26.7237i	1.55067	+	2.68584i
$100$	6.39755	+	11.0809i	0.639755	+	1.10809i
$101$	7.32842	+	12.6932i	0.729205	+	1.26302i	0.957219	+	0.289363i	$0.0934434\pi$
$101$	7.32842	+	12.6932i	0.729205	+	1.26302i	−0.228014	+	0.973658i	$0.573223\pi$
$102$	7.99096			0.791223
$103$	−5.71931	−	9.90614i	−0.563540	−	0.976081i	−0.997184	−	0.0749961i	$-0.976106\pi$
$103$	−5.71931	−	9.90614i	−0.563540	−	0.976081i	0.433643	−	0.901085i	$-0.357228\pi$
$104$	−9.39036	−	16.2646i	−0.920800	−	1.59487i
$105$	3.91315	−	6.77777i	0.381884	−	0.661443i
$106$	4.54560	−	7.87321i	0.441508	−	0.764714i
$107$	−11.2064			−1.08336			−0.541682	−	0.840584i	$-0.682212\pi$
$107$	−11.2064			−1.08336			−0.541682	+	0.840584i	$0.682212\pi$
$108$	−49.4691			−4.76017
$109$	−8.39718	+	14.5443i	−0.804304	+	1.39310i	0.112455	+	0.993657i	$0.464128\pi$
$109$	−8.39718	+	14.5443i	−0.804304	+	1.39310i	−0.916760	+	0.399439i	$0.869205\pi$
$110$	−9.73577	+	16.8628i	−0.928269	+	1.60781i
$111$	6.50164	+	11.2612i	0.617108	+	1.06886i
$112$	−8.06799	−	13.9742i	−0.762353	−	1.32043i
$113$	11.1971			1.05333			0.526667	−	0.850071i	$-0.323441\pi$
$113$	11.1971			1.05333			0.526667	+	0.850071i	$0.323441\pi$
$114$	−24.9951	−	43.2927i	−2.34100	−	4.05474i
$115$	−3.06501	−	5.30876i	−0.285814	−	0.495044i
$116$	−11.4295	−	19.7964i	−1.06120	−	1.83805i
$117$	8.06347	−	13.9663i	0.745468	−	1.29119i
$118$	−24.2285			−2.23042
$119$	−0.834694	+	1.44573i	−0.0765162	+	0.132530i
$120$	−17.3337	−	30.0228i	−1.58234	−	2.74070i
$121$	12.6162			1.14693
$122$	18.0229	+	31.2166i	1.63172	+	2.82622i
$123$	−7.29889	+	12.6420i	−0.658118	+	1.13989i
$124$	9.64382	−	16.7036i	0.866040	−	1.50003i
$125$	−11.7279			−1.04897
$126$	13.8512	−	23.9909i	1.23396	−	2.13728i
$127$	4.68280			0.415531			0.207766	−	0.978179i	$-0.433381\pi$
$127$	4.68280			0.415531			0.207766	+	0.978179i	$0.433381\pi$
$128$	−0.0489137			−0.00432340
$129$	16.4895	+	11.4079i	1.45182	+	1.00441i
$130$	10.1762			0.892511
$131$	4.66528			0.407608			0.203804	−	0.979012i	$-0.434670\pi$
$131$	4.66528			0.407608			0.203804	+	0.979012i	$0.434670\pi$
$132$	−35.8829	+	62.1510i	−3.12321	+	5.40955i
$133$	10.4434			0.905559
$134$	11.9389	−	20.6788i	1.03137	−	1.78638i
$135$	7.85219	−	13.6004i	0.675809	−	1.17054i
$136$	3.69736	+	6.40402i	0.317046	+	0.549140i
$137$	11.6806			0.997943			0.498972	−	0.866618i	$-0.333711\pi$
$137$	11.6806			0.997943			0.498972	+	0.866618i	$0.333711\pi$
$138$	−15.9747	−	27.6691i	−1.35986	−	2.35535i
$139$	−5.94132	+	10.2907i	−0.503936	+	0.872843i	0.496053	+	0.868292i	$0.334782\pi$
$139$	−5.94132	+	10.2907i	−0.503936	+	0.872843i	−0.999990	+	0.00455131i	$0.998551\pi$
$140$	12.3613			1.04472
$141$	−3.72196	+	6.44662i	−0.313445	+	0.542903i
$142$	1.38076	+	2.39155i	0.115871	+	0.200694i
$143$	−6.17114	−	10.6887i	−0.516057	−	0.893837i
$144$	−30.6881	−	53.1533i	−2.55734	−	4.42944i
$145$	7.25675			0.602640
$146$	16.8946	+	29.2622i	1.39820	+	2.42176i
$147$	−6.44137	−	11.1568i	−0.531275	−	0.920196i
$148$	−10.2691	+	17.7866i	−0.844114	+	1.46205i
$149$	8.43381	−	14.6078i	0.690924	−	1.19672i	−0.280611	−	0.959822i	$-0.590537\pi$
$149$	8.43381	−	14.6078i	0.690924	−	1.19672i	0.971535	−	0.236894i	$-0.0761296\pi$
$150$	−21.1706			−1.72857
$151$	−18.2832			−1.48786			−0.743931	−	0.668256i	$-0.767041\pi$
$151$	−18.2832			−1.48786			−0.743931	+	0.668256i	$0.767041\pi$
$152$	23.1301	−	40.0625i	1.87610	−	3.24950i
$153$	−3.17491	+	5.49911i	−0.256676	+	0.444576i
$154$	−10.6006	−	18.3608i	−0.854220	−	1.47955i
$155$	3.06151	+	5.30269i	0.245906	+	0.425922i
$156$	37.5062			3.00290
$157$	2.78967	+	4.83186i	0.222640	+	0.385624i	0.955609	−	0.294638i	$-0.0951992\pi$
$157$	2.78967	+	4.83186i	0.222640	+	0.385624i	−0.732969	+	0.680262i	$0.761866\pi$
$158$	10.4265	+	18.0593i	0.829489	+	1.43672i
$159$	5.31858	+	9.21205i	0.421791	+	0.730563i
$160$	8.02680	−	13.9028i	0.634575	−	1.09912i
$161$	6.67454			0.526028
$162$	16.0339	−	27.7715i	1.25974	−	2.18194i
$163$	−10.0343	−	17.3799i	−0.785948	−	1.36130i	−0.928431	−	0.371505i	$-0.878842\pi$
$163$	−10.0343	−	17.3799i	−0.785948	−	1.36130i	0.142483	−	0.989797i	$-0.454491\pi$
$164$	−23.0566			−1.80042
$165$	−11.3913	−	19.7304i	−0.886814	−	1.53601i
$166$	17.8475	−	30.9128i	1.38524	−	2.39930i
$167$	−3.16194	+	5.47664i	−0.244678	+	0.423795i	−0.962041	−	0.272905i	$-0.912016\pi$
$167$	−3.16194	+	5.47664i	−0.244678	+	0.423795i	0.717363	+	0.696700i	$0.245349\pi$
$168$	37.7469			2.91223
$169$	3.27485	−	5.67220i	0.251911	−	0.436323i
$170$	−4.00678			−0.307306
$171$	39.7234			3.03773
$172$	−2.58207	+	31.5643i	−0.196881	+	2.40676i
$173$	−5.81565			−0.442156			−0.221078	−	0.975256i	$-0.570957\pi$
$173$	−5.81565			−0.442156			−0.221078	+	0.975256i	$0.570957\pi$
$174$	37.8219			2.86727
$175$	2.21136	−	3.83019i	0.167163	−	0.289535i
$176$	−46.9725			−3.54068
$177$	14.1743	−	24.5506i	1.06540	−	1.84533i
$178$	8.68765	−	15.0474i	0.651167	−	1.12785i
$179$	−12.8271	−	22.2171i	−0.958740	−	1.66059i	−0.725568	−	0.688151i	$-0.758423\pi$
$179$	−12.8271	−	22.2171i	−0.958740	−	1.66059i	−0.233172	−	0.972435i	$-0.574911\pi$
$180$	47.0186			3.50456
$181$	12.2986	+	21.3018i	0.914148	+	1.58335i	0.808144	+	0.588985i	$0.200472\pi$
$181$	12.2986	+	21.3018i	0.914148	+	1.58335i	0.106004	+	0.994366i	$0.466194\pi$
$182$	−5.54006	+	9.59567i	−0.410657	+	0.711279i
$183$	−42.1755			−3.11770
$184$	14.7828	−	25.6046i	1.08980	−	1.88759i
$185$	−3.26001	−	5.64650i	−0.239681	−	0.415139i
$186$	15.9565	+	27.6374i	1.16999	+	2.02648i
$187$	2.42983	+	4.20858i	0.177687	+	0.307762i
$188$	−11.7574			−0.857495
$189$	8.54969	+	14.8085i	0.621898	+	1.07716i
$190$	12.5329	+	21.7076i	0.909229	+	1.57483i
$191$	2.94035	−	5.09284i	0.212757	−	0.368505i	−0.739820	−	0.672805i	$-0.765089\pi$
$191$	2.94035	−	5.09284i	0.212757	−	0.368505i	0.952576	+	0.304300i	$0.0984225\pi$
$192$	12.2798	−	21.2693i	0.886221	−	1.53498i
$193$	−11.3668			−0.818200			−0.409100	−	0.912490i	$-0.634157\pi$
$193$	−11.3668			−0.818200			−0.409100	+	0.912490i	$0.634157\pi$
$194$	−33.1161			−2.37760
$195$	−5.95332	+	10.3115i	−0.426326	+	0.738419i
$196$	10.1739	−	17.6217i	0.726707	−	1.25869i
$197$	−4.46747	−	7.73789i	−0.318294	−	0.551302i	0.661838	−	0.749647i	$-0.269777\pi$
$197$	−4.46747	−	7.73789i	−0.318294	−	0.551302i	−0.980132	+	0.198345i	$0.936443\pi$
$198$	−40.3213	−	69.8385i	−2.86551	−	4.96321i
$199$	−19.0226			−1.34848			−0.674239	−	0.738513i	$-0.735528\pi$
$199$	−19.0226			−1.34848			−0.674239	+	0.738513i	$0.735528\pi$
$200$	−9.79546	−	16.9662i	−0.692644	−	1.19969i
$201$	13.9691	+	24.1952i	0.985306	+	1.70660i
$202$	−19.1517	−	33.1718i	−1.34751	−	2.33396i
$203$	−3.95068	+	6.84277i	−0.277283	+	0.480269i
$204$	−14.7677			−1.03394
$205$	3.65976	−	6.33889i	0.255609	−	0.442727i
$206$	14.9466	+	25.8882i	1.04138	+	1.80372i
$207$	25.3879			1.76458
$208$	12.2743	+	21.2598i	0.851073	+	1.47410i
$209$	15.2006	−	26.3282i	1.05145	−	1.82116i
$210$	−10.2264	+	17.7127i	−0.705690	+	1.22229i
$211$	9.84872			0.678014			0.339007	−	0.940784i	$-0.389909\pi$
$211$	9.84872			0.678014			0.339007	+	0.940784i	$0.389909\pi$
$212$	−8.40049	+	14.5501i	−0.576948	+	0.999303i
$213$	−3.23112			−0.221393
$214$	29.2862			2.00197
$215$	−8.26804	−	5.72006i	−0.563876	−	0.390105i
$216$	75.7435			5.15369
$217$	−6.66692			−0.452580
$218$	21.9448	−	38.0095i	1.48629	−	2.57433i
$219$	−39.5350			−2.67152
$220$	17.9922	−	31.1634i	1.21303	−	2.10103i
$221$	1.26987	−	2.19948i	0.0854209	−	0.147953i
$222$	−16.9911	−	29.4294i	−1.14036	−	1.97517i
$223$	−11.1065			−0.743748			−0.371874	−	0.928283i	$-0.621285\pi$
$223$	−11.1065			−0.743748			−0.371874	+	0.928283i	$0.621285\pi$
$224$	8.73981	+	15.1378i	0.583953	+	1.01144i
$225$	8.41133	−	14.5688i	0.560755	−	0.971256i
$226$	−29.2619			−1.94648
$227$	1.75450	−	3.03889i	0.116450	−	0.201698i	−0.801908	−	0.597447i	$-0.796182\pi$
$227$	1.75450	−	3.03889i	0.116450	−	0.201698i	0.918359	+	0.395749i	$0.129515\pi$
$228$	46.1921	+	80.0071i	3.05915	+	5.29860i
$229$	−2.96021	−	5.12723i	−0.195616	−	0.338817i	0.751486	−	0.659749i	$-0.229337\pi$
$229$	−2.96021	−	5.12723i	−0.195616	−	0.338817i	−0.947102	+	0.320932i	$0.896004\pi$
$230$	8.00995	+	13.8736i	0.528160	+	0.914800i
$231$	24.8064			1.63214
$232$	17.4999	+	30.3108i	1.14893	+	1.99000i
$233$	9.07658	+	15.7211i	0.594626	+	1.02992i	0.993600	+	0.112960i	$0.0360333\pi$
$233$	9.07658	+	15.7211i	0.594626	+	1.02992i	−0.398973	+	0.916963i	$0.630633\pi$
$234$	−21.0727	+	36.4989i	−1.37756	+	2.38601i
$235$	1.86624	−	3.23242i	0.121740	−	0.210860i
$236$	44.7755			2.91464
$237$	−24.3991			−1.58489
$238$	2.18135	−	3.77820i	0.141396	−	0.244904i
$239$	7.28767	−	12.6226i	0.471400	−	0.816489i	−0.528065	−	0.849204i	$-0.677082\pi$
$239$	7.28767	−	12.6226i	0.471400	−	0.816489i	0.999465	+	0.0327151i	$0.0104154\pi$
$240$	22.6573	+	39.2435i	1.46252	+	2.53316i
$241$	−9.74707	−	16.8824i	−0.627864	−	1.08749i	−0.987980	−	0.154585i	$-0.950596\pi$
$241$	−9.74707	−	16.8824i	−0.627864	−	1.08749i	0.360116	−	0.932908i	$-0.382737\pi$
$242$	−32.9706			−2.11943
$243$	3.39609	+	5.88221i	0.217859	+	0.377344i
$244$	−33.3073	−	57.6899i	−2.13228	−	3.69322i
$245$	3.22979	+	5.59416i	0.206344	+	0.357398i
$246$	19.0745	−	33.0381i	1.21615	−	2.10643i
$247$	−15.8882			−1.01094
$248$	−14.7659	+	25.5753i	−0.937636	+	1.62403i
$249$	20.8825	+	36.1695i	1.32337	+	2.29215i
$250$	30.6491			1.93842
$251$	−14.3935	−	24.9303i	−0.908511	−	1.57359i	−0.816133	−	0.577864i	$-0.803887\pi$
$251$	−14.3935	−	24.9303i	−0.908511	−	1.57359i	−0.0923780	−	0.995724i	$-0.529447\pi$
$252$	−25.5976	+	44.3364i	−1.61250	+	2.79293i
$253$	9.71493	−	16.8268i	0.610773	−	1.05789i
$254$	−12.2378			−0.767868
$255$	2.34406	−	4.06004i	0.146791	−	0.254249i
$256$	−15.9361			−0.996004
$257$	3.07876			0.192048			0.0960239	−	0.995379i	$-0.469387\pi$
$257$	3.07876			0.192048			0.0960239	+	0.995379i	$0.469387\pi$
$258$	−43.0927	−	29.8128i	−2.68284	−	1.85606i
$259$	7.09918			0.441122
$260$	−18.8061			−1.16630
$261$	−15.0271	+	26.0278i	−0.930156	+	1.61108i
$262$	−12.1920			−0.753225
$263$	−12.5381	+	21.7166i	−0.773132	+	1.33910i	0.162707	+	0.986674i	$0.447978\pi$
$263$	−12.5381	+	21.7166i	−0.773132	+	1.33910i	−0.935839	+	0.352429i	$0.885356\pi$
$264$	54.9413	−	95.1611i	3.38140	−	5.85676i
$265$	−2.66681	−	4.61904i	−0.163821	−	0.283746i
$266$	−27.2923			−1.67340
$267$	10.1650	+	17.6063i	0.622086	+	1.07749i
$268$	−22.0637	+	38.2154i	−1.34775	+	2.33438i
$269$	−26.7979			−1.63390			−0.816949	−	0.576710i	$-0.804336\pi$
$269$	−26.7979			−1.63390			−0.816949	+	0.576710i	$0.804336\pi$
$270$	−20.5205	+	35.5426i	−1.24884	+	2.16305i
$271$	−6.88138	−	11.9189i	−0.418014	−	0.724022i	0.577725	−	0.816231i	$-0.303940\pi$
$271$	−6.88138	−	11.9189i	−0.418014	−	0.724022i	−0.995740	+	0.0922092i	$0.970607\pi$
$272$	−4.83290	−	8.37083i	−0.293038	−	0.507556i
$273$	−6.48215	−	11.2274i	−0.392317	−	0.679514i
$274$	−30.5256			−1.84412
$275$	−6.43737	−	11.1498i	−0.388188	−	0.672361i
$276$	29.5221	+	51.1338i	1.77702	+	3.07789i
$277$	−6.32117	+	10.9486i	−0.379802	+	0.657837i	−0.991033	−	0.133616i	$-0.957341\pi$
$277$	−6.32117	+	10.9486i	−0.379802	+	0.657837i	0.611231	+	0.791452i	$0.290675\pi$
$278$	15.5268	−	26.8931i	0.931233	−	1.61294i
$279$	−25.3589			−1.51819
$280$	−18.9268			−1.13109
$281$	−9.15724	+	15.8608i	−0.546275	+	0.946177i	0.452250	+	0.891891i	$0.350621\pi$
$281$	−9.15724	+	15.8608i	−0.546275	+	0.946177i	−0.998525	+	0.0542856i	$0.982712\pi$
$282$	9.72677	−	16.8473i	0.579221	−	1.00324i
$283$	6.14269	+	10.6395i	0.365145	+	0.632450i	0.988799	−	0.149250i	$-0.0476860\pi$
$283$	6.14269	+	10.6395i	0.365145	+	0.632450i	−0.623654	+	0.781700i	$0.714353\pi$
$284$	−2.55172	−	4.41970i	−0.151416	−	0.262261i
$285$	−29.3281			−1.73725
$286$	16.1273	+	27.9334i	0.953630	+	1.65174i
$287$	3.98485	+	6.90196i	0.235218	+	0.407410i
$288$	33.2435	+	57.5794i	1.95889	+	3.39290i
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$	−18.9644			−1.11363
$291$	19.3737	−	33.5563i	1.13571	−	1.96711i
$292$	−31.2220	−	54.0780i	−1.82713	−	3.16468i
$293$	−0.112791			−0.00658930			−0.00329465	−	0.999995i	$-0.501049\pi$
$293$	−0.112791			−0.00658930			−0.00329465	+	0.999995i	$0.501049\pi$
$294$	16.8336	+	29.1566i	0.981753	+	1.70045i
$295$	−7.10718	+	12.3100i	−0.413796	+	0.716715i
$296$	15.7233	−	27.2335i	0.913897	−	1.58292i
$297$	49.7770			2.88835
$298$	−22.0405	+	38.1752i	−1.27677	+	2.21143i
$299$	−10.1544			−0.587245
$300$	39.1242			2.25884
$301$	9.89499	−	4.68229i	0.570338	−	0.269883i
$302$	47.7803			2.74945
$303$	44.8169			2.57467
$304$	−30.2338	+	52.3666i	−1.73403	+	3.00343i
$305$	21.1473			1.21089
$306$	8.29715	−	14.3711i	0.474317	−	0.821540i
$307$	−5.48803	+	9.50554i	−0.313218	+	0.542510i	−0.979057	−	0.203586i	$-0.934740\pi$
$307$	−5.48803	+	9.50554i	−0.313218	+	0.542510i	0.665839	+	0.746096i	$0.268074\pi$
$308$	19.5904	+	33.9316i	1.11627	+	1.93343i
$309$	−34.9764			−1.98974
$310$	−8.00079	−	13.8578i	−0.454415	−	0.787069i
$311$	10.6883	−	18.5127i	0.606079	−	1.04976i	−0.385801	−	0.922582i	$-0.626075\pi$
$311$	10.6883	−	18.5127i	0.606079	−	1.04976i	0.991880	−	0.127178i	$-0.0405918\pi$
$312$	−57.4267			−3.25115
$313$	−4.95444	+	8.58134i	−0.280042	+	0.485046i	−0.971395	−	0.237471i	$-0.923682\pi$
$313$	−4.95444	+	8.58134i	−0.280042	+	0.485046i	0.691353	+	0.722517i	$0.257015\pi$
$314$	−7.29039	−	12.6273i	−0.411421	−	0.712601i
$315$	−8.12617	−	14.0749i	−0.457858	−	0.793033i
$316$	−19.2687	−	33.3744i	−1.08395	−	1.87746i
$317$	−3.77742			−0.212161			−0.106080	−	0.994358i	$-0.533830\pi$
$317$	−3.77742			−0.212161			−0.106080	+	0.994358i	$0.533830\pi$
$318$	−13.8993	−	24.0743i	−0.779434	−	1.35002i
$319$	11.5006	+	19.9196i	0.643909	+	1.11528i
$320$	−6.15727	+	10.6647i	−0.344202	+	0.596175i
$321$	−17.1332	+	29.6755i	−0.956281	+	1.65633i
$322$	−17.4429			−0.972056
$323$	6.25583			0.348084
$324$	−29.6314	+	51.3231i	−1.64619	+	2.85129i
$325$	−3.36429	+	5.82712i	−0.186617	+	0.323230i
$326$	26.2232	+	45.4199i	1.45237	+	2.51557i
$327$	25.6765	+	44.4729i	1.41991	+	2.45936i
$328$	35.3026			1.94926
$329$	2.03201	+	3.51955i	0.112029	+	0.194039i
$330$	29.7695	+	51.5623i	1.63876	+	2.83841i
$331$	5.93884	+	10.2864i	0.326428	+	0.565390i	0.981800	−	0.189916i	$-0.0608215\pi$
$331$	5.93884	+	10.2864i	0.326428	+	0.565390i	−0.655372	+	0.755306i	$0.727488\pi$
$332$	−32.9831	+	57.1284i	−1.81018	+	3.13533i
$333$	27.0030			1.47976
$334$	8.26325	−	14.3124i	0.452145	−	0.783138i
$335$	−7.00430	−	12.1318i	−0.382686	−	0.662832i
$336$	−49.3397			−2.69170
$337$	6.16785	+	10.6830i	0.335984	+	0.581942i	0.983673	−	0.179963i	$-0.0575977\pi$
$337$	6.16785	+	10.6830i	0.335984	+	0.581942i	−0.647689	+	0.761905i	$0.724264\pi$
$338$	−8.55832	+	14.8234i	−0.465511	+	0.806289i
$339$	17.1190	−	29.6509i	0.929774	−	1.61042i
$340$	7.40472			0.401577
$341$	−9.70383	+	16.8075i	−0.525492	+	0.910179i
$342$	−103.811			−5.61347
$343$	−18.7191			−1.01074
$344$	3.95348	−	48.3290i	0.213157	−	2.60573i
$345$	−18.7441			−1.00915
$346$	15.1983			0.817067
$347$	13.4585	−	23.3109i	0.722492	−	1.25139i	−0.237507	−	0.971386i	$-0.576330\pi$
$347$	13.4585	−	23.3109i	0.722492	−	1.25139i	0.959998	−	0.280006i	$-0.0903365\pi$
$348$	−69.8968			−3.74686
$349$	14.6716	−	25.4119i	0.785352	−	1.36027i	−0.143436	−	0.989660i	$-0.545815\pi$
$349$	14.6716	−	25.4119i	0.785352	−	1.36027i	0.928788	−	0.370610i	$-0.120851\pi$
$350$	−5.77907	+	10.0096i	−0.308904	+	0.535038i
$351$	−13.0072	−	22.5291i	−0.694273	−	1.20252i
$352$	50.8839			2.71212
$353$	−5.81331	−	10.0689i	−0.309411	−	0.535916i	0.668823	−	0.743422i	$-0.266799\pi$
$353$	−5.81331	−	10.0689i	−0.309411	−	0.535916i	−0.978234	+	0.207506i	$0.933465\pi$
$354$	−37.0424	+	64.1593i	−1.96878	+	3.41003i
$355$	1.62013			0.0859874
$356$	−16.0552	+	27.8084i	−0.850924	+	1.47384i
$357$	2.55228	+	4.42068i	0.135081	+	0.233967i
$358$	33.5216	+	58.0611i	1.77167	+	3.06863i
$359$	7.50574	+	13.0003i	0.396138	+	0.686131i	0.993246	−	0.116030i	$-0.0370169\pi$
$359$	7.50574	+	13.0003i	0.396138	+	0.686131i	−0.597108	+	0.802161i	$0.703684\pi$
$360$	−71.9915			−3.79428
$361$	−10.0677	−	17.4378i	−0.529881	−	0.917780i
$362$	−32.1406	−	55.6691i	−1.68927	−	2.92590i
$363$	19.2886	−	33.4089i	1.01239	−	1.75351i
$364$	10.2383	−	17.7333i	0.536633	−	0.929476i
$365$	19.8234			1.03760
$366$	110.219			5.76125
$367$	−3.76254	+	6.51691i	−0.196403	+	0.340180i	−0.947360	−	0.320172i	$-0.896259\pi$
$367$	−3.76254	+	6.51691i	−0.196403	+	0.340180i	0.750957	+	0.660352i	$0.229593\pi$
$368$	−19.3229	+	33.4683i	−1.00728	+	1.74465i
$369$	15.1571	+	26.2529i	0.789048	+	1.36667i
$370$	8.51954	+	14.7563i	0.442910	+	0.767142i
$371$	5.80739			0.301505
$372$	−29.4884	−	51.0753i	−1.52890	−	2.64813i
$373$	−11.6351	−	20.1526i	−0.602444	−	1.04346i	−0.992450	−	0.122652i	$-0.960860\pi$
$373$	−11.6351	−	20.1526i	−0.602444	−	1.04346i	0.390005	−	0.920813i	$-0.372473\pi$
$374$	−6.34999	−	10.9985i	−0.328350	−	0.568719i
$375$	−17.9305	+	31.0565i	−0.925925	+	1.60375i
$376$	18.0020			0.928384
$377$	6.01042	−	10.4104i	0.309552	−	0.536160i
$378$	−22.3433	−	38.6998i	−1.14922	−	1.99050i
$379$	9.74533			0.500584			0.250292	−	0.968170i	$-0.419473\pi$
$379$	9.74533			0.500584			0.250292	+	0.968170i	$0.419473\pi$
$380$	−23.1613	−	40.1166i	−1.18815	−	2.05794i
$381$	7.15941	−	12.4005i	0.366788	−	0.635295i
$382$	−7.68417	+	13.3094i	−0.393157	+	0.680967i
$383$	−13.2584			−0.677475			−0.338737	−	0.940881i	$-0.610000\pi$
$383$	−13.2584			−0.677475			−0.338737	+	0.940881i	$0.610000\pi$
$384$	−0.0747829	+	0.129528i	−0.00381625	+	0.00660994i
$385$	−12.4383			−0.633913
$386$	29.7054			1.51197
$387$	37.6374	−	17.8100i	1.91322	−	0.905331i
$388$	61.2002			3.10697
$389$	17.6257			0.893659			0.446830	−	0.894619i	$-0.352553\pi$
$389$	17.6257			0.893659			0.446830	+	0.894619i	$0.352553\pi$
$390$	15.5581	−	26.9474i	0.787816	−	1.36454i
$391$	3.99820			0.202198
$392$	−15.5775	+	26.9811i	−0.786784	+	1.36275i
$393$	7.13263	−	12.3541i	0.359794	−	0.623181i
$394$	11.6751	+	20.2218i	0.588182	+	1.01876i
$395$	12.2340			0.615560
$396$	74.5157	+	129.065i	3.74455	+	6.48576i
$397$	4.34398	−	7.52400i	0.218018	−	0.377619i	−0.736184	−	0.676782i	$-0.763374\pi$
$397$	4.34398	−	7.52400i	0.218018	−	0.377619i	0.954202	+	0.299163i	$0.0967074\pi$
$398$	49.7128			2.49188
$399$	15.9667	−	27.6551i	0.799333	−	1.38448i
$400$	12.8039	+	22.1769i	0.640193	+	1.10885i
$401$	1.31338	+	2.27485i	0.0655873	+	0.113600i	0.896954	−	0.442123i	$-0.145775\pi$
$401$	1.31338	+	2.27485i	0.0655873	+	0.113600i	−0.831367	+	0.555724i	$0.812441\pi$
$402$	−36.5062	−	63.2306i	−1.82076	−	3.15365i
$403$	10.1428			0.505249
$404$	35.3933	+	61.3030i	1.76088	+	3.04994i
$405$	−9.40674	−	16.2930i	−0.467425	−	0.809604i
$406$	10.3245	−	17.8826i	0.512396	−	0.887497i
$407$	10.3330	−	17.8973i	0.512188	−	0.887135i
$408$	22.6112			1.11942
$409$	24.8589			1.22919			0.614597	−	0.788841i	$-0.289319\pi$
$409$	24.8589			1.22919			0.614597	+	0.788841i	$0.289319\pi$
$410$	−9.56423	+	16.5657i	−0.472344	+	0.818123i
$411$	17.8582	−	30.9313i	0.880880	−	1.52573i
$412$	−27.6220	−	47.8426i	−1.36084	−	2.35704i
$413$	−7.73850	−	13.4035i	−0.380787	−	0.659542i
$414$	−66.3474			−3.26079
$415$	−10.4708	−	18.1359i	−0.513989	−	0.890255i
$416$	−13.2964	−	23.0301i	−0.651912	−	1.12914i
$417$	18.1671	+	31.4663i	0.889645	+	1.54091i
$418$	−39.7245	+	68.8048i	−1.94299	+	3.36535i
$419$	−25.4148			−1.24159			−0.620797	−	0.783971i	$-0.713191\pi$
$419$	−25.4148			−1.24159			−0.620797	+	0.783971i	$0.713191\pi$
$420$	18.8989	−	32.7339i	0.922173	−	1.59725i
$421$	−4.88942	−	8.46873i	−0.238296	−	0.412740i	0.721930	−	0.691967i	$-0.243255\pi$
$421$	−4.88942	−	8.46873i	−0.238296	−	0.412740i	−0.960225	+	0.279226i	$0.909922\pi$
$422$	−25.7382			−1.25291
$423$	7.72914	+	13.3873i	0.375804	+	0.650911i
$424$	12.8622	−	22.2780i	0.624644	−	1.08192i
$425$	1.32466	−	2.29437i	0.0642552	−	0.111293i
$426$	8.44405			0.409115
$427$	−11.5129	+	19.9409i	−0.557149	+	0.965010i
$428$	−54.1224			−2.61610
$429$	−37.7396			−1.82208
$430$	21.6073	+	14.9485i	1.04200	+	0.720882i
$431$	2.75657			0.132780			0.0663898	−	0.997794i	$-0.478852\pi$
$431$	2.75657			0.132780			0.0663898	+	0.997794i	$0.478852\pi$
$432$	−99.0060			−4.76343
$433$	−4.50797	+	7.80803i	−0.216639	+	0.375230i	−0.953778	−	0.300511i	$-0.902843\pi$
$433$	−4.50797	+	7.80803i	−0.216639	+	0.375230i	0.737139	+	0.675741i	$0.236176\pi$
$434$	17.4230			0.836330
$435$	11.0947	−	19.2165i	0.531948	−	0.921361i
$436$	−40.5550	+	70.2433i	−1.94223	+	3.36405i
$437$	−12.5060	−	21.6611i	−0.598245	−	1.03619i
$438$	103.319			4.93676
$439$	−15.5858	−	26.9954i	−0.743868	−	1.28842i	−0.950722	−	0.310046i	$-0.899656\pi$
$439$	−15.5858	−	26.9954i	−0.743868	−	1.28842i	0.206853	−	0.978372i	$-0.433678\pi$
$440$	−27.5483	+	47.7151i	−1.31331	+	2.27473i
$441$	−26.7527			−1.27394
$442$	−3.31862	+	5.74802i	−0.157851	+	0.273405i
$443$	−2.14053	−	3.70751i	−0.101700	−	0.176149i	0.810685	−	0.585482i	$-0.199095\pi$
$443$	−2.14053	−	3.70751i	−0.101700	−	0.176149i	−0.912385	+	0.409333i	$0.865761\pi$
$444$	31.4003	+	54.3869i	1.49019	+	2.58109i
$445$	−5.09685	−	8.82801i	−0.241614	−	0.418488i
$446$	29.0252			1.37438
$447$	−25.7885	−	44.6669i	−1.21975	−	2.11267i
$448$	−6.70421	−	11.6120i	−0.316744	−	0.548617i
$449$	14.1656	−	24.5355i	0.668514	−	1.15790i	−0.309806	−	0.950800i	$-0.600264\pi$
$449$	14.1656	−	24.5355i	0.668514	−	1.15790i	0.978320	−	0.207100i	$-0.0664025\pi$
$450$	−21.9817	+	38.0735i	−1.03623	+	1.79480i
$451$	23.2001			1.09245
$452$	54.0775			2.54359
$453$	−27.9526	+	48.4154i	−1.31333	+	2.27475i
$454$	−4.58513	+	7.94168i	−0.215191	+	0.372721i
$455$	3.25024	+	5.62957i	0.152373	+	0.263918i
$456$	−70.7260	−	122.501i	−3.31205	−	5.73663i
$457$	15.7153			0.735133			0.367566	−	0.929997i	$-0.380191\pi$
$457$	15.7153			0.735133			0.367566	+	0.929997i	$0.380191\pi$
$458$	7.73605	+	13.3992i	0.361482	+	0.626105i
$459$	5.12145	+	8.87062i	0.239049	+	0.414045i
$460$	−14.8028	−	25.6391i	−0.690183	−	1.19543i
$461$	7.65469	−	13.2583i	0.356515	−	0.617502i	−0.630861	−	0.775896i	$-0.717298\pi$
$461$	7.65469	−	13.2583i	0.356515	−	0.617502i	0.987376	+	0.158394i	$0.0506316\pi$
$462$	−64.8278			−3.01606
$463$	−16.3045	+	28.2402i	−0.757733	+	1.31243i	0.186272	+	0.982498i	$0.440360\pi$
$463$	−16.3045	+	28.2402i	−0.757733	+	1.31243i	−0.944004	+	0.329933i	$0.892974\pi$
$464$	−22.8746	−	39.6199i	−1.06192	−	1.83931i
$465$	18.7226			0.868242
$466$	−23.7203	−	41.0847i	−1.09882	−	1.90321i
$467$	4.35923	−	7.55041i	0.201721	−	0.349391i	−0.747362	−	0.664417i	$-0.768680\pi$
$467$	4.35923	−	7.55041i	0.201721	−	0.349391i	0.949083	+	0.315026i	$0.102013\pi$
$468$	38.9433	−	67.4517i	1.80015	−	3.11796i
$469$	15.2530			0.704317
$470$	−4.87713	+	8.44744i	−0.224965	+	0.389651i
$471$	17.0602			0.786094
$472$	−68.5569			−3.15559
$473$	2.59814	−	31.7608i	0.119463	−	1.46036i
$474$	63.7633			2.92875
$475$	−16.5737			−0.760451
$476$	−4.03123	+	6.98230i	−0.184771	+	0.320033i
$477$	22.0895			1.01141
$478$	−19.0452	+	32.9873i	−0.871109	+	1.50880i
$479$	−17.2596	+	29.8945i	−0.788611	+	1.36591i	0.138207	+	0.990403i	$0.455866\pi$
$479$	−17.2596	+	29.8945i	−0.788611	+	1.36591i	−0.926818	+	0.375511i	$0.877467\pi$
$480$	−24.5439	−	42.5114i	−1.12027	−	1.94037i
$481$	−10.8004			−0.492458
$482$	25.4725	+	44.1197i	1.16024	+	2.00960i
$483$	10.2045	−	17.6748i	0.464323	−	0.804230i
$484$	60.9313			2.76960
$485$	−9.71425	+	16.8256i	−0.441101	+	0.764010i
$486$	−8.87518	−	15.3723i	−0.402586	−	0.697300i
$487$	3.17499	+	5.49925i	0.143873	+	0.249195i	0.928952	−	0.370201i	$-0.120711\pi$
$487$	3.17499	+	5.49925i	0.143873	+	0.249195i	−0.785079	+	0.619395i	$0.787378\pi$
$488$	50.9976	+	88.3305i	2.30855	+	3.99853i
$489$	−61.3648			−2.77501
$490$	−8.44057	−	14.6195i	−0.381306	−	0.660441i
$491$	3.91294	+	6.77742i	0.176589	+	0.305861i	0.940710	−	0.339212i	$-0.110160\pi$
$491$	3.91294	+	6.77742i	0.176589	+	0.305861i	−0.764121	+	0.645073i	$0.776827\pi$
$492$	−35.2507	+	61.0559i	−1.58922	+	2.75261i
$493$	−2.36654	+	4.09897i	−0.106584	+	0.184609i
$494$	41.5215			1.86814
$495$	−47.3112			−2.12648
$496$	19.3008	−	33.4300i	0.866633	−	1.50105i
$497$	−0.882020	+	1.52770i	−0.0395640	+	0.0685269i
$498$	−54.5732	−	94.5236i	−2.44548	−	4.23570i
$499$	9.16628	+	15.8765i	0.410339	+	0.710728i	0.994927	−	0.100602i	$-0.0320770\pi$
$499$	9.16628	+	15.8765i	0.410339	+	0.710728i	−0.584588	+	0.811331i	$0.698744\pi$
$500$	−56.6410			−2.53306
$501$	9.66841	+	16.7462i	0.431953	+	0.748164i
$502$	37.6153	+	65.1516i	1.67885	+	2.90786i
$503$	−11.2530	−	19.4908i	−0.501748	−	0.869053i	−0.999998	−	0.00201973i	$-0.999357\pi$
$503$	−11.2530	−	19.4908i	−0.501748	−	0.869053i	0.498250	−	0.867034i	$-0.333976\pi$
$504$	39.1932	−	67.8846i	1.74580	−	3.02382i
$505$	−22.4718			−0.999982
$506$	−25.3885	+	43.9742i	−1.12866	+	1.95489i
$507$	−10.0137	−	17.3442i	−0.444722	−	0.770281i
$508$	22.6160			1.00342
$509$	7.20210	+	12.4744i	0.319227	+	0.552918i	0.980327	−	0.197380i	$-0.0632433\pi$
$509$	7.20210	+	12.4744i	0.319227	+	0.552918i	−0.661100	+	0.750298i	$0.729910\pi$
$510$	−6.12585	+	10.6103i	−0.271257	+	0.469832i
$511$	−10.7921	+	18.6925i	−0.477415	+	0.826907i
$512$	41.7443			1.84486
$513$	32.0390	−	55.4931i	1.41456	−	2.45008i
$514$	−8.04587			−0.354888
$515$	17.5376			0.772801
$516$	79.6375	+	55.0955i	3.50584	+	2.42544i
$517$	11.8305			0.520307
$518$	−18.5526			−0.815156
$519$	−8.89140	+	15.4003i	−0.390289	+	0.676000i
$520$	28.7945			1.26272
$521$	2.47461	−	4.28616i	0.108415	−	0.187780i	−0.806713	−	0.590943i	$-0.798756\pi$
$521$	2.47461	−	4.28616i	0.108415	−	0.187780i	0.915128	+	0.403163i	$0.132089\pi$
$522$	39.2711	−	68.0196i	1.71885	−	2.97714i
$523$	10.7775	+	18.6671i	0.471265	+	0.816256i	0.999460	−	0.0328680i	$-0.0104641\pi$
$523$	10.7775	+	18.6671i	0.471265	+	0.816256i	−0.528194	+	0.849123i	$0.677131\pi$
$524$	22.5314			0.984290
$525$	−6.76179	−	11.7118i	−0.295109	−	0.511143i
$526$	32.7664	−	56.7531i	1.42868	−	2.47455i
$527$	−3.99363			−0.173965
$528$	−71.8150	+	124.387i	−3.12535	+	5.41326i
$529$	3.50720	+	6.07464i	0.152487	+	0.264115i
$530$	6.96930	+	12.0712i	0.302727	+	0.524338i
$531$	−29.4348	−	50.9826i	−1.27736	−	2.21245i
$532$	50.4375			2.18674
$533$	−6.06241	−	10.5004i	−0.262592	−	0.454823i
$534$	−26.5646	−	46.0113i	−1.14956	−	1.99110i
$535$	8.59080	−	14.8797i	0.371413	−	0.643306i
$536$	33.7823	−	58.5127i	1.45917	−	2.52736i
$537$	−78.4439			−3.38510
$538$	70.0323			3.01931
$539$	−10.2372	+	17.7314i	−0.440948	+	0.763744i
$540$	37.9229	−	65.6844i	1.63194	−	2.82661i
$541$	5.57746	+	9.66044i	0.239794	+	0.415335i	0.960655	−	0.277745i	$-0.0895869\pi$
$541$	5.57746	+	9.66044i	0.239794	+	0.415335i	−0.720861	+	0.693079i	$0.756254\pi$
$542$	17.9835	+	31.1483i	0.772456	+	1.33793i
$543$	75.2121			3.22766
$544$	5.23534	+	9.06788i	0.224463	+	0.388782i
$545$	−12.8745	−	22.2993i	−0.551484	−	0.955198i
$546$	16.9401	+	29.3411i	0.724970	+	1.25569i
$547$	−6.02575	+	10.4369i	−0.257642	+	0.446250i	−0.965610	−	0.259995i	$-0.916279\pi$
$547$	−6.02575	+	10.4369i	−0.257642	+	0.446250i	0.707968	+	0.706245i	$0.249612\pi$
$548$	56.4127			2.40983
$549$	−43.7915	+	75.8491i	−1.86897	+	3.23716i
$550$	16.8231	+	29.1384i	0.717339	+	1.24247i
$551$	29.6094			1.26140
$552$	−45.2021	−	78.2923i	−1.92393	−	3.33234i
$553$	−6.66038	+	11.5361i	−0.283228	+	0.490565i
$554$	16.5194	−	28.6125i	0.701843	−	1.21563i
$555$	−19.9366			−0.846260
$556$	−28.6942	+	49.6998i	−1.21690	+	2.10774i
$557$	20.2539			0.858186			0.429093	−	0.903260i	$-0.358833\pi$
$557$	20.2539			0.858186			0.429093	+	0.903260i	$0.358833\pi$
$558$	66.2715			2.80550
$559$	−15.0539	+	7.12347i	−0.636711	+	0.301291i
$560$	24.7396			1.04544
$561$	14.8596			0.627372
$562$	23.9311	−	41.4498i	1.00947	−	1.74846i
$563$	−7.05765			−0.297444			−0.148722	−	0.988879i	$-0.547516\pi$
$563$	−7.05765			−0.297444			−0.148722	+	0.988879i	$0.547516\pi$
$564$	−17.9755	+	31.1346i	−0.756907	+	1.31100i
$565$	−8.58367	+	14.8674i	−0.361118	+	0.625475i
$566$	−16.0530	−	27.8046i	−0.674758	−	1.16871i
$567$	20.4847			0.860275
$568$	3.90700	+	6.76712i	0.163934	+	0.283942i
$569$	−0.527849	+	0.914262i	−0.0221286	+	0.0383278i	−0.876878	−	0.480714i	$-0.840378\pi$
$569$	−0.527849	+	0.914262i	−0.0221286	+	0.0383278i	0.854749	+	0.519041i	$0.173711\pi$
$570$	76.6447			3.21029
$571$	−4.58584	+	7.94290i	−0.191911	+	0.332400i	−0.945884	−	0.324506i	$-0.894802\pi$
$571$	−4.58584	+	7.94290i	−0.191911	+	0.332400i	0.753972	+	0.656906i	$0.228135\pi$
$572$	−29.8041	−	51.6223i	−1.24617	−	2.15843i
$573$	−8.99086	−	15.5726i	−0.375599	−	0.650556i
$574$	−10.4138	−	18.0372i	−0.434664	−	0.752860i
$575$	−10.5925			−0.441737
$576$	−25.5007	−	44.1685i	−1.06253	−	1.84036i
$577$	−1.62716	−	2.81832i	−0.0677395	−	0.117328i	0.830166	−	0.557516i	$-0.188245\pi$
$577$	−1.62716	−	2.81832i	−0.0677395	−	0.117328i	−0.897906	+	0.440187i	$0.854912\pi$
$578$	1.30667	−	2.26323i	0.0543505	−	0.0941378i
$579$	−17.3784	+	30.1003i	−0.722222	+	1.25092i
$580$	35.0472			1.45525
$581$	22.8017			0.945974
$582$	−50.6304	+	87.6943i	−2.09870	+	3.63505i
$583$	8.45277	−	14.6406i	0.350078	−	0.606353i
$584$	47.8048	+	82.8003i	1.97818	+	3.42630i
$585$	12.3629	+	21.4131i	0.511142	+	0.885323i
$586$	0.294761			0.0121765
$587$	21.1919	+	36.7055i	0.874685	+	1.51500i	0.857098	+	0.515154i	$0.172265\pi$
$587$	21.1919	+	36.7055i	0.874685	+	1.51500i	0.0175871	+	0.999845i	$0.494402\pi$
$588$	−31.1092	−	53.8827i	−1.28292	−	2.22209i
$589$	12.4918	+	21.6363i	0.514714	+	0.891510i
$590$	18.5735	−	32.1703i	0.764660	−	1.32443i
$591$	−27.3208			−1.12383
$592$	−20.5522	+	35.5975i	−0.844692	+	1.46305i
$593$	−3.18455	−	5.51580i	−0.130774	−	0.226507i	0.793201	−	0.608959i	$-0.208413\pi$
$593$	−3.18455	−	5.51580i	−0.130774	−	0.226507i	−0.923975	+	0.382453i	$0.875079\pi$
$594$	−130.085			−5.33744
$595$	−1.27975	−	2.21659i	−0.0524646	−	0.0908713i
$596$	40.7319	−	70.5497i	1.66844	−	2.88983i
$597$	−29.0832	+	50.3736i	−1.19030	+	2.06165i
$598$	26.5370			1.08518
$599$	−1.71254	+	2.96621i	−0.0699727	+	0.121196i	−0.898889	−	0.438176i	$-0.855625\pi$
$599$	−1.71254	+	2.96621i	−0.0699727	+	0.121196i	0.828916	+	0.559373i	$0.188958\pi$
$600$	−59.9041			−2.44558
$601$	0.355316			0.0144936			0.00724681	−	0.999974i	$-0.497693\pi$
$601$	0.355316			0.0144936			0.00724681	+	0.999974i	$0.497693\pi$
$602$	−25.8591	+	12.2365i	−1.05394	+	0.498721i
$603$	58.0175			2.36265
$604$	−88.3003			−3.59289
$605$	−9.67157	+	16.7517i	−0.393205	+	0.681051i
$606$	−117.122			−4.75777
$607$	8.67033	−	15.0175i	0.351918	−	0.609540i	−0.634668	−	0.772785i	$-0.718863\pi$
$607$	8.67033	−	15.0175i	0.351918	−	0.609540i	0.986585	+	0.163246i	$0.0521963\pi$
$608$	32.7514	−	56.7272i	1.32825	−	2.30059i
$609$	12.0802	+	20.9235i	0.489513	+	0.847862i
$610$	−55.2654			−2.23763
$611$	−3.09143	−	5.35452i	−0.125066	−	0.216621i
$612$	−15.3335	+	26.5585i	−0.619821	+	1.07356i
$613$	15.9479			0.644131			0.322066	−	0.946717i	$-0.395623\pi$
$613$	15.9479			0.644131			0.322066	+	0.946717i	$0.395623\pi$
$614$	14.3421	−	24.8413i	0.578801	−	1.00251i
$615$	−11.1906	−	19.3827i	−0.451249	−	0.781587i
$616$	−29.9954	−	51.9535i	−1.20855	−	2.09327i
$617$	16.8100	+	29.1158i	0.676745	+	1.17216i	0.975956	+	0.217970i	$0.0699434\pi$
$617$	16.8100	+	29.1158i	0.676745	+	1.17216i	−0.299211	+	0.954187i	$0.596723\pi$
$618$	91.4056			3.67687
$619$	−2.20302	−	3.81575i	−0.0885470	−	0.153368i	0.818350	−	0.574720i	$-0.194889\pi$
$619$	−2.20302	−	3.81575i	−0.0885470	−	0.153368i	−0.906897	+	0.421352i	$0.861556\pi$
$620$	14.7859	+	25.6099i	0.593814	+	1.02852i
$621$	20.4766	−	35.4665i	0.821698	−	1.42322i
$622$	−27.9323	+	48.3802i	−1.11998	+	1.93987i
$623$	11.0992			0.444680
$624$	75.0637			3.00495
$625$	2.36730	−	4.10028i	0.0946918	−	0.164011i
$626$	12.9477	−	22.4261i	0.517494	−	0.896325i
$627$	−46.4796	−	80.5050i	−1.85622	−	3.21506i
$628$	13.4730	+	23.3359i	0.537631	+	0.931204i
$629$	4.25257			0.169561
$630$	21.2365	+	36.7828i	0.846084	+	1.46546i
$631$	−24.5686	−	42.5541i	−0.978061	−	1.69405i	−0.669439	−	0.742867i	$-0.733466\pi$
$631$	−24.5686	−	42.5541i	−0.978061	−	1.69405i	−0.308622	−	0.951185i	$-0.599868\pi$
$632$	29.5028	+	51.1004i	1.17356	+	2.03266i
$633$	15.0575	−	26.0803i	0.598480	−	1.03660i
$634$	9.87171			0.392056
$635$	−3.58982	+	6.21776i	−0.142458	+	0.246744i
$636$	25.6866	+	44.4905i	1.01854	+	1.76416i
$637$	10.7003			0.423962
$638$	−30.0550	−	52.0569i	−1.18989	−	2.06095i
$639$	−3.35493	+	5.81090i	−0.132719	+	0.229876i
$640$	0.0374971	−	0.0649470i	0.00148220	−	0.00256725i
$641$	−0.346148			−0.0136720			−0.00683601	−	0.999977i	$-0.502176\pi$
$641$	−0.346148			−0.0136720			−0.00683601	+	0.999977i	$0.502176\pi$
$642$	44.7750	−	77.5525i	1.76713	−	3.06075i
$643$	23.8235			0.939508			0.469754	−	0.882797i	$-0.344343\pi$
$643$	23.8235			0.939508			0.469754	+	0.882797i	$0.344343\pi$
$644$	32.2354			1.27025
$645$	−27.7880	+	13.1492i	−1.09415	+	0.517751i
$646$	−16.3487			−0.643230
$647$	25.2998			0.994638			0.497319	−	0.867568i	$-0.334318\pi$
$647$	25.2998			0.994638			0.497319	+	0.867568i	$0.334318\pi$
$648$	45.3695	−	78.5822i	1.78228	−	3.08700i
$649$	−45.0541			−1.76853
$650$	8.79206	−	15.2283i	0.344853	−	0.597303i
$651$	−10.1929	+	17.6546i	−0.399490	+	0.691938i
$652$	−48.4617	−	83.9381i	−1.89791	−	3.28727i
$653$	7.87441			0.308149			0.154075	−	0.988059i	$-0.450760\pi$
$653$	7.87441			0.308149			0.154075	+	0.988059i	$0.450760\pi$
$654$	−67.1016	−	116.223i	−2.62388	−	4.54469i
$655$	−3.57640	+	6.19450i	−0.139741	+	0.242039i
$656$	−46.1448			−1.80165
$657$	−41.0498	+	71.1003i	−1.60151	+	2.77389i
$658$	−5.31036	−	9.19782i	−0.207019	−	0.358568i
$659$	−10.2173	−	17.6968i	−0.398008	−	0.689371i	0.595472	−	0.803376i	$-0.296965\pi$
$659$	−10.2173	−	17.6968i	−0.398008	−	0.689371i	−0.993480	+	0.114006i	$0.963632\pi$
$660$	−55.0155	−	95.2897i	−2.14148	−	3.70915i
$661$	−8.12319			−0.315955			−0.157978	−	0.987443i	$-0.550497\pi$
$661$	−8.12319			−0.315955			−0.157978	+	0.987443i	$0.550497\pi$
$662$	−15.5203	−	26.8819i	−0.603212	−	1.04479i
$663$	−3.88295	−	6.72547i	−0.150801	−	0.261196i
$664$	50.5013	−	87.4708i	1.95983	−	3.39452i
$665$	−8.00589	+	13.8666i	−0.310455	+	0.537724i
$666$	−70.5684			−2.73447
$667$	18.9238			0.732734
$668$	−15.2709	+	26.4499i	−0.590848	+	1.02338i
$669$	−16.9805	+	29.4111i	−0.656503	+	1.13710i
$670$	18.3047	+	31.7047i	0.707172	+	1.22486i
$671$	33.5145	+	58.0489i	1.29381	+	2.24095i
$672$	53.4483			2.06181
$673$	8.40280	+	14.5541i	0.323904	+	0.561018i	0.981290	−	0.192536i	$-0.0616711\pi$
$673$	8.40280	+	14.5541i	0.323904	+	0.561018i	−0.657386	+	0.753554i	$0.728338\pi$
$674$	−16.1188	−	27.9185i	−0.620871	−	1.07538i
$675$	−13.5683	−	23.5010i	−0.522245	−	0.904555i
$676$	15.8162	−	27.3944i	0.608315	−	1.05363i
$677$	−13.5106			−0.519256			−0.259628	−	0.965709i	$-0.583600\pi$
$677$	−13.5106			−0.519256			−0.259628	+	0.965709i	$0.583600\pi$
$678$	−44.7378	+	77.4882i	−1.71815	+	2.97592i
$679$	−10.5772	−	18.3202i	−0.405914	−	0.703064i
$680$	−11.3376			−0.434775
$681$	−5.36483	−	9.29215i	−0.205581	−	0.356076i
$682$	25.3595	−	43.9240i	0.971066	−	1.68194i
$683$	8.17693	−	14.1629i	0.312881	−	0.541926i	−0.666104	−	0.745859i	$-0.732039\pi$
$683$	8.17693	−	14.1629i	0.312881	−	0.541926i	0.978985	+	0.203933i	$0.0653724\pi$
$684$	191.848			7.33550
$685$	−8.95434	+	15.5094i	−0.342128	+	0.592583i
$686$	48.9195			1.86776
$687$	−18.1031			−0.690677
$688$	−5.16768	+	63.1719i	−0.197016	+	2.40841i
$689$	−8.83515			−0.336593
$690$	48.9848			1.86482
$691$	−11.7128	+	20.2872i	−0.445577	+	0.771761i	−0.998092	−	0.0617413i	$-0.980335\pi$
$691$	−11.7128	+	20.2872i	−0.445577	+	0.771761i	0.552516	+	0.833503i	$0.313668\pi$
$692$	−28.0872			−1.06772
$693$	25.7569	−	44.6123i	0.978424	−	1.69468i
$694$	−35.1718	+	60.9194i	−1.33510	+	2.31247i
$695$	−9.10921	−	15.7776i	−0.345532	−	0.598479i
$696$	107.021			4.05661
$697$	2.38701	+	4.13443i	0.0904146	+	0.156603i
$698$	−38.3420	+	66.4103i	−1.45127	+	2.51367i
$699$	55.5078			2.09950
$700$	10.6800	−	18.4983i	0.403666	−	0.699170i
$701$	19.8386	+	34.3614i	0.749292	+	1.29781i	0.948162	+	0.317786i	$0.102939\pi$
$701$	19.8386	+	34.3614i	0.749292	+	1.29781i	−0.198870	+	0.980026i	$0.563727\pi$
$702$	33.9923	+	58.8765i	1.28296	+	2.22215i
$703$	−13.3017	−	23.0392i	−0.501682	−	0.868939i
$704$	−39.0325			−1.47109
$705$	−5.70649	−	9.88392i	−0.214919	−	0.372250i
$706$	15.1922	+	26.3137i	0.571766	+	0.990328i
$707$	12.2340	−	21.1899i	0.460106	−	0.796927i
$708$	68.4561	−	118.569i	2.57274	−	4.45611i
$709$	−9.60688			−0.360794			−0.180397	−	0.983594i	$-0.557738\pi$
$709$	−9.60688			−0.360794			−0.180397	+	0.983594i	$0.557738\pi$
$710$	−4.23396			−0.158898
$711$	−25.3340	+	43.8797i	−0.950098	+	1.64562i
$712$	24.5825	−	42.5782i	0.921269	−	1.59569i
$713$	7.98367	+	13.8281i	0.298991	+	0.517867i
$714$	−6.67001	−	11.5528i	−0.249619	−	0.432352i
$715$	18.9231			0.707685
$716$	−61.9496	−	107.300i	−2.31516	−	4.00998i
$717$	−22.2839	−	38.5968i	−0.832206	−	1.44142i
$718$	−19.6151	−	33.9744i	−0.732030	−	1.26791i
$719$	5.86238	−	10.1539i	0.218630	−	0.378678i	−0.735759	−	0.677243i	$-0.763175\pi$
$719$	5.86238	−	10.1539i	0.218630	−	0.378678i	0.954389	+	0.298565i	$0.0965079\pi$
$720$	94.1016			3.50696
$721$	−9.54774	+	16.5372i	−0.355577	+	0.615877i
$722$	26.3105	+	45.5711i	0.979176	+	1.69598i
$723$	−59.6082			−2.21685
$724$	59.3973	+	102.879i	2.20748	+	3.82347i
$725$	6.26971	−	10.8595i	0.232851	−	0.403310i
$726$	−50.4079	+	87.3090i	−1.87081	+	3.24034i
$727$	53.0854			1.96883			0.984415	−	0.175862i	$-0.0562713\pi$
$727$	53.0854			1.96883			0.984415	+	0.175862i	$0.0562713\pi$
$728$	−15.6761	+	27.1519i	−0.580997	+	1.00632i
$729$	−16.0435			−0.594204
$730$	−51.8053			−1.91740
$731$	5.92732	−	2.80480i	0.219230	−	0.103739i
$732$	−203.690			−7.52861
$733$	−44.0507			−1.62705			−0.813525	−	0.581530i	$-0.802454\pi$
$733$	−44.0507			−1.62705			−0.813525	+	0.581530i	$0.802454\pi$
$734$	9.83283	−	17.0310i	0.362936	−	0.628624i
$735$	19.7518			0.728555
$736$	20.9319	−	36.2552i	0.771562	−	1.33638i
$737$	22.2010	−	38.4533i	0.817785	−	1.41644i
$738$	−39.6108	−	68.6080i	−1.45809	−	2.52549i
$739$	−8.54980			−0.314510			−0.157255	−	0.987558i	$-0.550264\pi$
$739$	−8.54980			−0.314510			−0.157255	+	0.987558i	$0.550264\pi$
$740$	−15.7445	−	27.2703i	−0.578780	−	1.00248i
$741$	−24.2911	+	42.0734i	−0.892356	+	1.54561i
$742$	−15.1767			−0.557156
$743$	−5.52047	+	9.56174i	−0.202526	+	0.350786i	−0.949342	−	0.314245i	$-0.898249\pi$
$743$	−5.52047	+	9.56174i	−0.202526	+	0.350786i	0.746815	+	0.665031i	$0.231582\pi$
$744$	45.1504	+	78.2028i	1.65529	+	2.86705i
$745$	12.9307	+	22.3966i	0.473743	+	0.820547i
$746$	30.4067	+	52.6659i	1.11327	+	1.92824i
$747$	86.7305			3.17330
$748$	11.7351	+	20.3258i	0.429077	+	0.743183i
$749$	9.35391	+	16.2015i	0.341784	+	0.591988i
$750$	46.8586	−	81.1614i	1.71103	−	2.96360i
$751$	4.90996	−	8.50431i	0.179167	−	0.310327i	−0.762428	−	0.647073i	$-0.775993\pi$
$751$	4.90996	−	8.50431i	0.179167	−	0.310327i	0.941596	+	0.336746i	$0.109326\pi$
$752$	−23.5309			−0.858082
$753$	−88.0235			−3.20776
$754$	−15.7073	+	27.2059i	−0.572027	+	0.990780i
$755$	14.0158	−	24.2761i	0.510088	−	0.883498i
$756$	41.2916	+	71.5191i	1.50176	+	2.60112i
$757$	−8.49950	−	14.7216i	−0.308920	−	0.535065i	0.669207	−	0.743076i	$-0.266634\pi$
$757$	−8.49950	−	14.7216i	−0.308920	−	0.535065i	−0.978126	+	0.208012i	$0.933301\pi$
$758$	−25.4680			−0.925038
$759$	−29.7058	−	51.4520i	−1.07825	−	1.86759i
$760$	35.4629	+	61.4236i	1.28638	+	2.22807i
$761$	−7.73895	−	13.4043i	−0.280537	−	0.485904i	0.690980	−	0.722874i	$-0.257179\pi$
$761$	−7.73895	−	13.4043i	−0.280537	−	0.485904i	−0.971517	+	0.236970i	$0.923846\pi$
$762$	−18.7100	+	32.4067i	−0.677793	+	1.17397i
$763$	28.0363			1.01498
$764$	14.2007	−	24.5964i	0.513764	−	0.889866i
$765$	−4.86776	−	8.43121i	−0.175994	−	0.304831i
$766$	34.6490			1.25192
$767$	11.7731	+	20.3916i	0.425101	+	0.736296i
$768$	−24.3642	+	42.2001i	−0.879168	+	1.52276i
$769$	−6.98322	+	12.0953i	−0.251821	+	0.436167i	−0.964027	−	0.265803i	$-0.914363\pi$
$769$	−6.98322	+	12.0953i	−0.251821	+	0.436167i	0.712206	+	0.701970i	$0.247696\pi$
$770$	32.5055			1.17142
$771$	4.70703	−	8.15282i	0.169520	−	0.293617i
$772$	−54.8970			−1.97579
$773$	−4.33604			−0.155957			−0.0779783	−	0.996955i	$-0.524846\pi$
$773$	−4.33604			−0.155957			−0.0779783	+	0.996955i	$0.524846\pi$
$774$	−98.3597	+	46.5436i	−3.53547	+	1.67298i
$775$	10.5804			0.380058
$776$	−93.7052			−3.36382
$777$	10.8538	−	18.7992i	0.389376	−	0.674419i
$778$	−46.0621			−1.65141
$779$	14.9328	−	25.8643i	0.535022	−	0.926685i
$780$	−28.7521	+	49.8002i	−1.02949	+	1.78313i
$781$	2.56760	+	4.44721i	0.0918758	+	0.159134i
$782$	−10.4487			−0.373645
$783$	24.2403	+	41.9854i	0.866277	+	1.50044i
$784$	20.3617	−	35.2676i	0.727205	−	1.25956i
$785$	−8.55423			−0.305313
$786$	−18.6401	+	32.2855i	−0.664869	+	1.15159i
$787$	−20.9919	−	36.3591i	−0.748281	−	1.29606i	−0.948646	−	0.316340i	$-0.897546\pi$
$787$	−20.9919	−	36.3591i	−0.748281	−	1.29606i	0.200365	−	0.979721i	$-0.435787\pi$
$788$	−21.5761	−	37.3709i	−0.768617	−	1.33128i
$789$	38.3383	+	66.4039i	1.36488	+	2.36404i
$790$	−31.9718			−1.13750
$791$	−9.34615	−	16.1880i	−0.332311	−	0.575579i
$792$	−114.093	−	197.615i	−4.05412	−	7.02193i
$793$	17.5153	−	30.3374i	0.621988	−	1.07731i
$794$	−11.3523	+	19.6628i	−0.402880	+	0.697808i
$795$	−16.3088			−0.578415
$796$	−91.8716			−3.25630
$797$	17.2579	−	29.8915i	0.611305	−	1.05881i	−0.379716	−	0.925103i	$-0.623978\pi$
$797$	17.2579	−	29.8915i	0.611305	−	1.05881i	0.991021	−	0.133708i	$-0.0426883\pi$
$798$	−41.7265	+	72.2723i	−1.47710	+	2.55841i
$799$	1.21722	+	2.10829i	0.0430622	+	0.0745859i
$800$	−13.8701	−	24.0236i	−0.490380	−	0.849364i
$801$	42.2179			1.49169
$802$	−3.43233	−	5.94497i	−0.121200	−	0.209924i
$803$	31.4163	+	54.4146i	1.10866	+	1.92025i
$804$	67.4652	+	116.853i	2.37931	+	4.12109i
$805$	−5.11669	+	8.86237i	−0.180340	+	0.312357i
$806$	−26.5067			−0.933659
$807$	−40.9706	+	70.9632i	−1.44223	+	2.49802i
$808$	−54.1917	−	93.8627i	−1.90646	−	3.30208i
$809$	−11.8629			−0.417078			−0.208539	−	0.978014i	$-0.566871\pi$
$809$	−11.8629			−0.417078			−0.208539	+	0.978014i	$0.566871\pi$
$810$	24.5831	+	42.5792i	0.863762	+	1.49608i
$811$	14.7633	−	25.5709i	0.518411	−	0.897915i	−0.481360	−	0.876523i	$-0.659857\pi$
$811$	14.7633	−	25.5709i	0.518411	−	0.897915i	0.999771	−	0.0213916i	$-0.00680966\pi$
$812$	−19.0802	+	33.0478i	−0.669583	+	1.15975i
$813$	−42.0831			−1.47592
$814$	−27.0037	+	46.7718i	−0.946480	+	1.63935i
$815$	30.7691			1.07780
$816$	−29.5556			−1.03465
$817$	−33.7357	−	23.3393i	−1.18026	−	0.816540i
$818$	−64.9650			−2.27145
$819$	−26.9221			−0.940734
$820$	17.6752	−	30.6143i	0.617243	−	1.06910i
$821$	−38.9859			−1.36062			−0.680308	−	0.732926i	$-0.738154\pi$
$821$	−38.9859			−1.36062			−0.680308	+	0.732926i	$0.738154\pi$
$822$	−46.6697	+	80.8344i	−1.62779	+	2.81942i
$823$	7.90805	−	13.6971i	0.275657	−	0.477452i	−0.694643	−	0.719354i	$-0.744438\pi$
$823$	7.90805	−	13.6971i	0.275657	−	0.477452i	0.970301	+	0.241902i	$0.0777712\pi$
$824$	42.2927	+	73.2532i	1.47334	+	2.55189i
$825$	−39.3677			−1.37061
$826$	20.2234	+	35.0280i	0.703662	+	1.21878i
$827$	16.9421	−	29.3445i	0.589133	−	1.02041i	−0.405213	−	0.914222i	$-0.632803\pi$
$827$	16.9421	−	29.3445i	0.589133	−	1.02041i	0.994346	−	0.106186i	$-0.0338639\pi$
$828$	122.613			4.26110
$829$	−9.70466	+	16.8090i	−0.337057	+	0.583800i	−0.983878	−	0.178842i	$-0.942765\pi$
$829$	−9.70466	+	16.8090i	−0.337057	+	0.583800i	0.646821	+	0.762642i	$0.276098\pi$
$830$	27.3637	+	47.3954i	0.949809	+	1.64512i
$831$	19.3285	+	33.4780i	0.670499	+	1.16134i
$832$	10.1996	+	17.6661i	0.353606	+	0.612463i
$833$	−4.21315			−0.145977
$834$	−47.4769	−	82.2324i	−1.64399	−	2.84747i
$835$	−4.84787	−	8.39676i	−0.167767	−	0.290582i
$836$	73.4127	−	127.155i	2.53903	−	4.39773i
$837$	−20.4532	+	35.4260i	−0.706966	+	1.22450i
$838$	66.4178			2.29436
$839$	50.2389			1.73444			0.867220	−	0.497926i	$-0.165905\pi$
$839$	50.2389			1.73444			0.867220	+	0.497926i	$0.165905\pi$
$840$	−28.9367	+	50.1197i	−0.998409	+	1.72930i
$841$	3.29894	−	5.71393i	0.113757	−	0.197032i
$842$	12.7778	+	22.1317i	0.440351	+	0.762710i
$843$	28.0005	+	48.4984i	0.964390	+	1.67037i
$844$	47.5654			1.63727
$845$	5.02098	+	8.69659i	0.172727	+	0.299172i
$846$	−20.1989	−	34.9856i	−0.694454	−	1.20283i
$847$	−10.5307	−	18.2397i	−0.361839	−	0.626723i
$848$	−16.8125	+	29.1201i	−0.577343	+	0.999988i
$849$	37.5656			1.28925
$850$	−3.46179	+	5.99599i	−0.118738	+	0.205661i
$851$	−8.50131	−	14.7247i	−0.291421	−	0.504756i
$852$	−15.6050			−0.534619
$853$	14.5329	+	25.1717i	0.497596	+	0.861862i	0.999996	−	0.00277342i	$-0.000882809\pi$
$853$	14.5329	+	25.1717i	0.497596	+	0.861862i	−0.502400	+	0.864635i	$0.667549\pi$
$854$	30.0873	−	52.1127i	1.02956	−	1.78326i
$855$	−30.4519	+	52.7442i	−1.04143	+	1.80381i
$856$	82.8682			2.83238
$857$	−26.6371	+	46.1369i	−0.909907	+	1.57601i	−0.0957153	+	0.995409i	$0.530514\pi$
$857$	−26.6371	+	46.1369i	−0.909907	+	1.57601i	−0.814192	+	0.580596i	$0.802819\pi$
$858$	98.6267			3.36706
$859$	−12.3368			−0.420926			−0.210463	−	0.977602i	$-0.567497\pi$
$859$	−12.3368			−0.420926			−0.210463	+	0.977602i	$0.567497\pi$
$860$	−39.9313	−	27.6256i	−1.36165	−	0.942025i
$861$	24.3693			0.830505
$862$	−7.20389			−0.245366
$863$	−17.8596	+	30.9338i	−0.607948	+	1.05300i	0.383630	+	0.923487i	$0.374674\pi$
$863$	−17.8596	+	30.9338i	−0.607948	+	1.05300i	−0.991578	+	0.129511i	$0.958659\pi$
$864$	107.250			3.64873
$865$	4.45826	−	7.72194i	0.151586	−	0.262554i
$866$	11.7809	−	20.4051i	0.400331	−	0.693394i
$867$	1.52887	+	2.64809i	0.0519233	+	0.0899338i
$868$	−32.1985			−1.09289
$869$	19.3886	+	33.5821i	0.657714	+	1.13919i
$870$	−28.9942	+	50.2194i	−0.982996	+	1.70260i
$871$	−23.2053			−0.786282
$872$	62.0949	−	107.551i	2.10280	−	3.64215i
$873$	−40.2322	−	69.6841i	−1.36165	−	2.35845i
$874$	32.6827	+	56.6080i	1.10551	+	1.91479i
$875$	9.78919	+	16.9554i	0.330935	+	0.573197i
$876$	−190.938			−6.45119
$877$	7.08161	+	12.2657i	0.239129	+	0.414183i	0.960465	−	0.278402i	$-0.0898048\pi$
$877$	7.08161	+	12.2657i	0.239129	+	0.414183i	−0.721336	+	0.692586i	$0.756471\pi$
$878$	40.7311	+	70.5483i	1.37461	+	2.38089i
$879$	−0.172443	+	0.298679i	−0.00581635	+	0.0100742i
$880$	36.0090	−	62.3694i	1.21386	−	2.10247i
$881$	3.56239			0.120020			0.0600100	−	0.998198i	$-0.480887\pi$
$881$	3.56239			0.120020			0.0600100	+	0.998198i	$0.480887\pi$
$882$	69.9142			2.35413
$883$	−9.47534	+	16.4118i	−0.318870	+	0.552300i	−0.980253	−	0.197749i	$-0.936637\pi$
$883$	−9.47534	+	16.4118i	−0.318870	+	0.552300i	0.661382	+	0.750049i	$0.269970\pi$
$884$	6.13297	−	10.6226i	0.206274	−	0.357277i
$885$	21.7320	+	37.6408i	0.730512	+	1.26528i
$886$	5.59395	+	9.68901i	0.187933	+	0.325509i
$887$	16.7724			0.563162			0.281581	−	0.959538i	$-0.409141\pi$
$887$	16.7724			0.563162			0.281581	+	0.959538i	$0.409141\pi$
$888$	−48.0778	−	83.2732i	−1.61339	−	2.79447i
$889$	−3.90870	−	6.77007i	−0.131094	−	0.227061i
$890$	13.3199	+	23.0707i	0.446483	+	0.773331i
$891$	29.8158	−	51.6425i	0.998868	−	1.73009i
$892$	−53.6400			−1.79600
$893$	7.61474	−	13.1891i	0.254817	−	0.441357i
$894$	67.3942	+	116.730i	2.25400	+	3.90404i
$895$	39.3328			1.31475
$896$	0.0408280	+	0.0707161i	0.00136397	+	0.00236246i
$897$	−15.5248	+	26.8898i	−0.518359	+	0.897823i
$898$	−37.0195	+	64.1197i	−1.23536	+	2.13970i
$899$	−18.9022			−0.630424
$900$	40.6233	−	70.3616i	1.35411	−	2.34539i
$901$	3.47876			0.115894
$902$	−60.6300			−2.01876
$903$	2.72908	−	33.3614i	0.0908181	−	1.11020i
$904$	−82.7995			−2.75387
$905$	−37.7123			−1.25360
$906$	73.0500	−	126.526i	2.42692	−	4.20356i
$907$	−10.3776			−0.344581			−0.172290	−	0.985046i	$-0.555117\pi$
$907$	−10.3776			−0.344581			−0.172290	+	0.985046i	$0.555117\pi$
$908$	8.47354	−	14.6766i	0.281204	−	0.487060i
$909$	46.5342	−	80.5996i	1.54344	−	2.67332i
$910$	−8.49400	−	14.7120i	−0.281573	−	0.487699i
$911$	−24.8387			−0.822942			−0.411471	−	0.911423i	$-0.634985\pi$
$911$	−24.8387			−0.822942			−0.411471	+	0.911423i	$0.634985\pi$
$912$	92.4475	+	160.124i	3.06124	+	5.30223i
$913$	33.1883	−	57.4839i	1.09837	−	1.90244i
$914$	−41.0697			−1.35846
$915$	32.3316	−	56.0000i	1.06885	−	1.85130i
$916$	−14.2966	−	24.7624i	−0.472373	−	0.818174i
$917$	−3.89408	−	6.74475i	−0.128594	−	0.222731i
$918$	−13.3842	−	23.1820i	−0.441743	−	0.765121i
$919$	−4.21558			−0.139059			−0.0695296	−	0.997580i	$-0.522150\pi$
$919$	−4.21558			−0.139059			−0.0695296	+	0.997580i	$0.522150\pi$
$920$	22.6649	+	39.2568i	0.747240	+	1.29426i
$921$	16.7810	+	29.0655i	0.552953	+	0.957742i
$922$	−20.0044	+	34.6486i	−0.658810	+	1.14109i
$923$	1.34187	−	2.32419i	0.0441683	−	0.0765018i
$924$	119.805			3.94129
$925$	−11.2664			−0.370436
$926$	42.6093	−	73.8014i	1.40023	−	2.42526i
$927$	−36.3166	+	62.9022i	−1.19279	+	2.06598i
$928$	24.7793	+	42.9191i	0.813421	+	1.40889i
$929$	−13.9883	−	24.2284i	−0.458941	−	0.794909i	0.539964	−	0.841688i	$-0.318438\pi$
$929$	−13.9883	−	24.2284i	−0.458941	−	0.794909i	−0.998905	+	0.0467789i	$0.985104\pi$
$930$	−48.9288			−1.60444
$931$	13.1784	+	22.8256i	0.431904	+	0.748079i
$932$	43.8362	+	75.9265i	1.43590	+	2.48706i
$933$	−32.6822	−	56.6072i	−1.06997	−	1.85324i
$934$	−11.3922	+	19.7319i	−0.372764	+	0.645646i
$935$	−7.45080			−0.243667
$936$	−59.6271	+	103.277i	−1.94897	+	3.37572i
$937$	13.8767	+	24.0352i	0.453332	+	0.785194i	0.998591	−	0.0530737i	$-0.0169018\pi$
$937$	13.8767	+	24.0352i	0.453332	+	0.785194i	−0.545258	+	0.838268i	$0.683568\pi$
$938$	−39.8613			−1.30152
$939$	15.1494	+	26.2396i	0.494383	+	0.856297i
$940$	9.01318	−	15.6113i	0.293977	−	0.509184i
$941$	4.91221	−	8.50819i	0.160133	−	0.277359i	−0.774783	−	0.632227i	$-0.782141\pi$
$941$	4.91221	−	8.50819i	0.160133	−	0.277359i	0.934916	+	0.354868i	$0.115474\pi$
$942$	−44.5844			−1.45264
$943$	9.54376	−	16.5303i	0.310788	−	0.538300i
$944$	89.6123			2.91663
$945$	−26.2167			−0.852829
$946$	−6.78985	+	83.0020i	−0.220757	+	2.69863i
$947$	39.9848			1.29933			0.649666	−	0.760219i	$-0.274909\pi$
$947$	39.9848			1.29933			0.649666	+	0.760219i	$0.274909\pi$
$948$	−117.838			−3.82719
$949$	16.4187	−	28.4381i	0.532975	−	0.923139i
$950$	43.3128			1.40525
$951$	−5.77519	+	10.0029i	−0.187273	+	0.324367i
$952$	6.17233	−	10.6908i	0.200046	−	0.346490i
$953$	−12.2771	−	21.2646i	−0.397696	−	0.688829i	0.595746	−	0.803173i	$-0.296857\pi$
$953$	−12.2771	−	21.2646i	−0.397696	−	0.688829i	−0.993441	+	0.114344i	$0.963523\pi$
$954$	−57.7275			−1.86900
$955$	4.50814	+	7.80832i	0.145880	+	0.252671i
$956$	35.1965	−	60.9621i	1.13834	−	1.97166i
$957$	70.3318			2.27350
$958$	45.1054	−	78.1248i	1.45729	−	2.52410i
$959$	−9.74975	−	16.8871i	−0.314836	−	0.545311i
$960$	18.8274	+	32.6100i	0.607651	+	1.05248i
$961$	7.52545	+	13.0345i	0.242756	+	0.420467i
$962$	28.2253			0.910021
$963$	35.5793	+	61.6252i	1.14653	+	1.98584i
$964$	−47.0744	−	81.5353i	−1.51616	−	2.62607i
$965$	8.71376	−	15.0927i	0.280506	−	0.485850i
$966$	−26.6680	+	46.1904i	−0.858030	+	1.48615i
$967$	14.1494			0.455014			0.227507	−	0.973776i	$-0.426943\pi$
$967$	14.1494			0.455014			0.227507	+	0.973776i	$0.426943\pi$
$968$	−93.2935			−2.99857
$969$	9.56438	−	16.5660i	0.307252	−	0.532176i
$970$	25.3867	−	43.9711i	0.815119	−	1.41183i
$971$	24.7113	+	42.8012i	0.793022	+	1.37355i	0.924088	+	0.382181i	$0.124827\pi$
$971$	24.7113	+	42.8012i	0.793022	+	1.37355i	−0.131066	+	0.991374i	$0.541840\pi$
$972$	16.4018	+	28.4087i	0.526087	+	0.911209i
$973$	19.8367			0.635937
$974$	−8.29736	−	14.3715i	−0.265865	−	0.460491i
$975$	10.2871	+	17.8179i	0.329452	+	0.570628i
$976$	−66.6601	−	115.459i	−2.13374	−	3.69574i
$977$	8.84281	−	15.3162i	0.282907	−	0.490008i	−0.689193	−	0.724578i	$-0.742035\pi$
$977$	8.84281	−	15.3162i	0.282907	−	0.490008i	0.972099	+	0.234570i	$0.0753680\pi$
$978$	160.368			5.12799
$979$	16.1551	−	27.9815i	0.516320	−	0.894292i
$980$	15.5986	+	27.0175i	0.498278	+	0.863043i
$981$	106.641			3.40479
$982$	−10.2259	−	17.7118i	−0.326321	−	0.565205i
$983$	−15.6491	+	27.1051i	−0.499130	+	0.864518i	−0.999999	−	0.00100446i	$-0.999680\pi$
$983$	−15.6491	+	27.1051i	−0.499130	+	0.864518i	0.500870	+	0.865523i	$0.333014\pi$
$984$	53.9732	−	93.4844i	1.72060	−	2.98017i
$985$	13.6990			0.436487
$986$	6.18461	−	10.7121i	0.196958	−	0.341141i
$987$	12.4268			0.395549
$988$	−76.7337			−2.44123
$989$	−21.5610	−	14.9165i	−0.685601	−	0.474318i
$990$	123.641			3.92956
$991$	2.41895			0.0768405			0.0384202	−	0.999262i	$-0.487767\pi$
$991$	2.41895			0.0768405			0.0384202	+	0.999262i	$0.487767\pi$
$992$	−20.9080	+	36.2138i	−0.663831	+	1.14979i
$993$	36.3190			1.15255
$994$	2.30503	−	3.99242i	0.0731110	−	0.126632i
$995$	14.5827	−	25.2580i	0.462303	−	0.800732i
$996$	100.854	+	174.684i	3.19568	+	5.53508i
$997$	24.4513			0.774380			0.387190	−	0.922000i	$-0.373446\pi$
$997$	24.4513			0.774380			0.387190	+	0.922000i	$0.373446\pi$
$998$	−23.9547	−	41.4907i	−0.758273	−	1.31337i
$999$	21.7793	−	37.7229i	0.689067	−	1.19350i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.e.b.307.1	✓	58
43.36	even	3	inner	731.2.e.b.681.1	yes	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.e.b.307.1	✓	58	1.1	even	1	trivial
731.2.e.b.681.1	yes	58	43.36	even	3	inner

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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.61335 q^{2} +(1.52887 - 2.64809i) q^{3} +4.82960 q^{4} +(-0.766598 + 1.32779i) q^{5} +(-3.99548 + 6.92038i) q^{6} +(-0.834694 - 1.44573i) q^{7} -7.39472 q^{8} +(-3.17491 - 5.49911i) q^{9} +O(q^{10})\)	\(q-2.61335 q^{2} +(1.52887 - 2.64809i) q^{3} +4.82960 q^{4} +(-0.766598 + 1.32779i) q^{5} +(-3.99548 + 6.92038i) q^{6} +(-0.834694 - 1.44573i) q^{7} -7.39472 q^{8} +(-3.17491 - 5.49911i) q^{9} +(2.00339 - 3.46997i) q^{10} -4.85965 q^{11} +(7.38384 - 12.7892i) q^{12} +(1.26987 + 2.19948i) q^{13} +(2.18135 + 3.77820i) q^{14} +(2.34406 + 4.06004i) q^{15} +9.66581 q^{16} +(-0.500000 - 0.866025i) q^{17} +(8.29715 + 14.3711i) q^{18} +(-3.12792 + 5.41771i) q^{19} +(-3.70236 + 6.41267i) q^{20} -5.10457 q^{21} +12.7000 q^{22} +(-1.99910 + 3.46254i) q^{23} +(-11.3056 + 19.5819i) q^{24} +(1.32466 + 2.29437i) q^{25} +(-3.31862 - 5.74802i) q^{26} -10.2429 q^{27} +(-4.03123 - 6.98230i) q^{28} +(-2.36654 - 4.09897i) q^{29} +(-6.12585 - 10.6103i) q^{30} +(1.99682 - 3.45859i) q^{31} -10.4707 q^{32} +(-7.42980 + 12.8688i) q^{33} +(1.30667 + 2.26323i) q^{34} +2.55950 q^{35} +(-15.3335 - 26.5585i) q^{36} +(-2.12628 + 3.68283i) q^{37} +(8.17434 - 14.1584i) q^{38} +7.76590 q^{39} +(5.66878 - 9.81861i) q^{40} -4.77403 q^{41} +13.3400 q^{42} +(-0.534635 + 6.53561i) q^{43} -23.4702 q^{44} +9.73552 q^{45} +(5.22435 - 9.04884i) q^{46} -2.43444 q^{47} +(14.7778 - 25.5959i) q^{48} +(2.10657 - 3.64869i) q^{49} +(-3.46179 - 5.99599i) q^{50} -3.05775 q^{51} +(6.13297 + 10.6226i) q^{52} +(-1.73938 + 3.01269i) q^{53} +26.7683 q^{54} +(3.72540 - 6.45258i) q^{55} +(6.17233 + 10.6908i) q^{56} +(9.56438 + 16.5660i) q^{57} +(6.18461 + 10.7121i) q^{58} +9.27106 q^{59} +(11.3209 + 19.6083i) q^{60} +(-6.89649 - 11.9451i) q^{61} +(-5.21838 + 9.03850i) q^{62} +(-5.30016 + 9.18014i) q^{63} +8.03195 q^{64} -3.89393 q^{65} +(19.4167 - 33.6306i) q^{66} +(-4.56843 + 7.91276i) q^{67} +(-2.41480 - 4.18255i) q^{68} +(6.11274 + 10.5876i) q^{69} -6.68886 q^{70} +(-0.528350 - 0.915128i) q^{71} +(23.4776 + 40.6644i) q^{72} +(-6.46472 - 11.1972i) q^{73} +(5.55672 - 9.62452i) q^{74} +8.10093 q^{75} +(-15.1066 + 26.1654i) q^{76} +(4.05632 + 7.02575i) q^{77} -20.2950 q^{78} +(-3.98971 - 6.91039i) q^{79} +(-7.40979 + 12.8341i) q^{80} +(-6.13538 + 10.6268i) q^{81} +12.4762 q^{82} +(-6.82937 + 11.8288i) q^{83} -24.6530 q^{84} +1.53320 q^{85} +(1.39719 - 17.0798i) q^{86} -14.4726 q^{87} +35.9358 q^{88} +(-3.32433 + 5.75792i) q^{89} -25.4423 q^{90} +(2.11991 - 3.67179i) q^{91} +(-9.65485 + 16.7227i) q^{92} +(-6.10576 - 10.5755i) q^{93} +6.36205 q^{94} +(-4.79571 - 8.30641i) q^{95} +(-16.0084 + 27.7273i) q^{96} +12.6719 q^{97} +(-5.50521 + 9.53531i) q^{98} +(15.4290 + 26.7237i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 58 q + 2 q^{2} - 5 q^{3} + 54 q^{4} - 3 q^{5} - 8 q^{6} - 13 q^{7} + 12 q^{8} - 30 q^{9}+O(q^{10}) \) 58 * q + 2 * q^2 - 5 * q^3 + 54 * q^4 - 3 * q^5 - 8 * q^6 - 13 * q^7 + 12 * q^8 - 30 * q^9	\( 58 q + 2 q^{2} - 5 q^{3} + 54 q^{4} - 3 q^{5} - 8 q^{6} - 13 q^{7} + 12 q^{8} - 30 q^{9} + 4 q^{10} - 8 q^{12} + 2 q^{13} + 5 q^{14} - 5 q^{15} + 30 q^{16} - 29 q^{17} + 16 q^{18} - 4 q^{19} - 7 q^{20} - 26 q^{21} - 10 q^{22} + 5 q^{23} - 28 q^{24} - 24 q^{25} - 8 q^{26} + 28 q^{27} - 25 q^{28} + 10 q^{29} - 5 q^{30} + 3 q^{31} + 16 q^{32} - 23 q^{33} - q^{34} - 26 q^{35} - 39 q^{36} - 16 q^{37} + q^{38} + 130 q^{39} + 15 q^{40} - 22 q^{41} + 112 q^{42} + 7 q^{43} + 24 q^{44} + 2 q^{45} - 61 q^{46} + 12 q^{47} + 22 q^{48} - 36 q^{49} - 17 q^{50} + 10 q^{51} - 35 q^{52} - 10 q^{53} - 10 q^{54} - 20 q^{55} - 4 q^{56} + 9 q^{57} - 17 q^{58} - 36 q^{59} + 22 q^{60} - 35 q^{61} + 3 q^{62} - 22 q^{63} + 28 q^{64} - 28 q^{65} + 14 q^{66} - 17 q^{67} - 27 q^{68} - 23 q^{69} + 10 q^{70} - 6 q^{71} + 17 q^{72} - 14 q^{73} + 21 q^{74} + 70 q^{75} - 44 q^{76} - 11 q^{77} - 184 q^{78} - 10 q^{79} + 8 q^{80} - 13 q^{81} + 184 q^{82} + 9 q^{83} - 36 q^{84} + 6 q^{85} - 76 q^{86} + 8 q^{87} + 50 q^{88} - 54 q^{89} - 34 q^{90} - 23 q^{91} - 66 q^{92} + 96 q^{94} - 3 q^{95} - 60 q^{96} + 36 q^{97} - 16 q^{98} + 20 q^{99}+O(q^{100}) \) 58 * q + 2 * q^2 - 5 * q^3 + 54 * q^4 - 3 * q^5 - 8 * q^6 - 13 * q^7 + 12 * q^8 - 30 * q^9 + 4 * q^10 - 8 * q^12 + 2 * q^13 + 5 * q^14 - 5 * q^15 + 30 * q^16 - 29 * q^17 + 16 * q^18 - 4 * q^19 - 7 * q^20 - 26 * q^21 - 10 * q^22 + 5 * q^23 - 28 * q^24 - 24 * q^25 - 8 * q^26 + 28 * q^27 - 25 * q^28 + 10 * q^29 - 5 * q^30 + 3 * q^31 + 16 * q^32 - 23 * q^33 - q^34 - 26 * q^35 - 39 * q^36 - 16 * q^37 + q^38 + 130 * q^39 + 15 * q^40 - 22 * q^41 + 112 * q^42 + 7 * q^43 + 24 * q^44 + 2 * q^45 - 61 * q^46 + 12 * q^47 + 22 * q^48 - 36 * q^49 - 17 * q^50 + 10 * q^51 - 35 * q^52 - 10 * q^53 - 10 * q^54 - 20 * q^55 - 4 * q^56 + 9 * q^57 - 17 * q^58 - 36 * q^59 + 22 * q^60 - 35 * q^61 + 3 * q^62 - 22 * q^63 + 28 * q^64 - 28 * q^65 + 14 * q^66 - 17 * q^67 - 27 * q^68 - 23 * q^69 + 10 * q^70 - 6 * q^71 + 17 * q^72 - 14 * q^73 + 21 * q^74 + 70 * q^75 - 44 * q^76 - 11 * q^77 - 184 * q^78 - 10 * q^79 + 8 * q^80 - 13 * q^81 + 184 * q^82 + 9 * q^83 - 36 * q^84 + 6 * q^85 - 76 * q^86 + 8 * q^87 + 50 * q^88 - 54 * q^89 - 34 * q^90 - 23 * q^91 - 66 * q^92 + 96 * q^94 - 3 * q^95 - 60 * q^96 + 36 * q^97 - 16 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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