LMFDB - Embedded newform 731.2.e.a.307.12

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			307.12
Character	$\chi$	$=$	731.307
Dual form			731.2.e.a.681.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.884748 q^{2} +(-1.14431 + 1.98200i) q^{3} -1.21722 q^{4} +(-1.47938 + 2.56236i) q^{5} +(1.01242 - 1.75357i) q^{6} +(-0.890904 - 1.54309i) q^{7} +2.84643 q^{8} +(-1.11888 - 1.93795i) q^{9} +O(q^{10})$	\(q-0.884748 q^{2} +(-1.14431 + 1.98200i) q^{3} -1.21722 q^{4} +(-1.47938 + 2.56236i) q^{5} +(1.01242 - 1.75357i) q^{6} +(-0.890904 - 1.54309i) q^{7} +2.84643 q^{8} +(-1.11888 - 1.93795i) q^{9} +(1.30888 - 2.26704i) q^{10} -5.91864 q^{11} +(1.39288 - 2.41253i) q^{12} +(-1.61336 - 2.79442i) q^{13} +(0.788225 + 1.36525i) q^{14} +(-3.38573 - 5.86425i) q^{15} -0.0839291 q^{16} +(0.500000 + 0.866025i) q^{17} +(0.989925 + 1.71460i) q^{18} +(1.92061 - 3.32660i) q^{19} +(1.80073 - 3.11896i) q^{20} +4.07787 q^{21} +5.23650 q^{22} +(-2.29863 + 3.98134i) q^{23} +(-3.25719 + 5.64162i) q^{24} +(-1.87712 - 3.25127i) q^{25} +(1.42741 + 2.47235i) q^{26} -1.74448 q^{27} +(1.08443 + 1.87828i) q^{28} +(3.37037 + 5.83765i) q^{29} +(2.99552 + 5.18839i) q^{30} +(-2.41125 + 4.17641i) q^{31} -5.61860 q^{32} +(6.77274 - 11.7307i) q^{33} +(-0.442374 - 0.766214i) q^{34} +5.27194 q^{35} +(1.36192 + 2.35892i) q^{36} +(3.72972 - 6.46006i) q^{37} +(-1.69926 + 2.94320i) q^{38} +7.38470 q^{39} +(-4.21095 + 7.29358i) q^{40} -5.27679 q^{41} -3.60789 q^{42} +(5.26744 + 3.90564i) q^{43} +7.20429 q^{44} +6.62098 q^{45} +(2.03371 - 3.52248i) q^{46} +3.01158 q^{47} +(0.0960407 - 0.166347i) q^{48} +(1.91258 - 3.31269i) q^{49} +(1.66078 + 2.87656i) q^{50} -2.28861 q^{51} +(1.96381 + 3.40142i) q^{52} +(2.64573 - 4.58255i) q^{53} +1.54342 q^{54} +(8.75591 - 15.1657i) q^{55} +(-2.53590 - 4.39230i) q^{56} +(4.39554 + 7.61330i) q^{57} +(-2.98193 - 5.16485i) q^{58} +4.48808 q^{59} +(4.12118 + 7.13810i) q^{60} +(7.30851 + 12.6587i) q^{61} +(2.13335 - 3.69507i) q^{62} +(-1.99363 + 3.45306i) q^{63} +5.13890 q^{64} +9.54706 q^{65} +(-5.99217 + 10.3787i) q^{66} +(-2.53867 + 4.39710i) q^{67} +(-0.608611 - 1.05414i) q^{68} +(-5.26067 - 9.11176i) q^{69} -4.66434 q^{70} +(-3.08476 - 5.34297i) q^{71} +(-3.18481 - 5.51625i) q^{72} +(-4.01874 - 6.96066i) q^{73} +(-3.29986 + 5.71553i) q^{74} +8.59203 q^{75} +(-2.33781 + 4.04920i) q^{76} +(5.27294 + 9.13300i) q^{77} -6.53360 q^{78} +(-8.45272 - 14.6405i) q^{79} +(0.124163 - 0.215056i) q^{80} +(5.35286 - 9.27142i) q^{81} +4.66863 q^{82} +(-7.37425 + 12.7726i) q^{83} -4.96367 q^{84} -2.95876 q^{85} +(-4.66036 - 3.45551i) q^{86} -15.4270 q^{87} -16.8470 q^{88} +(7.06642 - 12.2394i) q^{89} -5.85790 q^{90} +(-2.87469 + 4.97911i) q^{91} +(2.79794 - 4.84617i) q^{92} +(-5.51843 - 9.55819i) q^{93} -2.66449 q^{94} +(5.68262 + 9.84259i) q^{95} +(6.42941 - 11.1361i) q^{96} +3.75573 q^{97} +(-1.69215 + 2.93089i) q^{98} +(6.62224 + 11.4701i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9}+O(q^{10}) $ 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9	\( 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9} + 4 q^{10} + 16 q^{11} + 12 q^{12} + 2 q^{13} - 11 q^{14} + 7 q^{15} + 30 q^{16} + 29 q^{17} + 8 q^{18} + 8 q^{19} - 33 q^{20} - 26 q^{21} - 22 q^{22} - 5 q^{23} + 12 q^{24} - 36 q^{25} - 12 q^{27} + 15 q^{28} + 2 q^{29} + 11 q^{30} + 3 q^{31} - 40 q^{32} + 17 q^{33} - 3 q^{34} + 38 q^{35} - 7 q^{36} + 2 q^{37} + q^{38} - 54 q^{39} + 5 q^{40} + 14 q^{41} - 112 q^{42} + 31 q^{43} - 24 q^{44} - 46 q^{45} - 13 q^{46} - 28 q^{47} - 28 q^{49} - 13 q^{50} + 6 q^{51} + 85 q^{52} - 10 q^{53} + 34 q^{54} + 36 q^{55} - 54 q^{56} - 23 q^{57} + 3 q^{58} + 12 q^{59} + 2 q^{60} - q^{61} - q^{62} - 14 q^{63} + 28 q^{64} + 80 q^{65} - 74 q^{66} + 11 q^{67} + 27 q^{68} - 11 q^{69} + 2 q^{70} + 16 q^{71} + 21 q^{72} + 14 q^{73} + 21 q^{74} - 54 q^{75} + 44 q^{76} + 25 q^{77} + 88 q^{78} - 4 q^{79} - 112 q^{80} + 11 q^{81} - 176 q^{82} - 3 q^{83} + 100 q^{84} - 2 q^{85} + 44 q^{86} + 8 q^{87} - 106 q^{88} + 82 q^{89} + 54 q^{90} - 15 q^{91} + 42 q^{92} + 88 q^{94} + 29 q^{95} + 20 q^{96} + 20 q^{97} + 44 q^{98} - 54 q^{99}+O(q^{100}) \) 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9 + 4 * q^10 + 16 * q^11 + 12 * q^12 + 2 * q^13 - 11 * q^14 + 7 * q^15 + 30 * q^16 + 29 * q^17 + 8 * q^18 + 8 * q^19 - 33 * q^20 - 26 * q^21 - 22 * q^22 - 5 * q^23 + 12 * q^24 - 36 * q^25 - 12 * q^27 + 15 * q^28 + 2 * q^29 + 11 * q^30 + 3 * q^31 - 40 * q^32 + 17 * q^33 - 3 * q^34 + 38 * q^35 - 7 * q^36 + 2 * q^37 + q^38 - 54 * q^39 + 5 * q^40 + 14 * q^41 - 112 * q^42 + 31 * q^43 - 24 * q^44 - 46 * q^45 - 13 * q^46 - 28 * q^47 - 28 * q^49 - 13 * q^50 + 6 * q^51 + 85 * q^52 - 10 * q^53 + 34 * q^54 + 36 * q^55 - 54 * q^56 - 23 * q^57 + 3 * q^58 + 12 * q^59 + 2 * q^60 - q^61 - q^62 - 14 * q^63 + 28 * q^64 + 80 * q^65 - 74 * q^66 + 11 * q^67 + 27 * q^68 - 11 * q^69 + 2 * q^70 + 16 * q^71 + 21 * q^72 + 14 * q^73 + 21 * q^74 - 54 * q^75 + 44 * q^76 + 25 * q^77 + 88 * q^78 - 4 * q^79 - 112 * q^80 + 11 * q^81 - 176 * q^82 - 3 * q^83 + 100 * q^84 - 2 * q^85 + 44 * q^86 + 8 * q^87 - 106 * q^88 + 82 * q^89 + 54 * q^90 - 15 * q^91 + 42 * q^92 + 88 * q^94 + 29 * q^95 + 20 * q^96 + 20 * q^97 + 44 * q^98 - 54 * 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 $

$2$	−0.884748			−0.625611			−0.312806	−	0.949817i	$-0.601269\pi$
$2$	−0.884748			−0.625611			−0.312806	+	0.949817i	$0.601269\pi$
$3$	−1.14431	+	1.98200i	−0.660666	+	1.14431i	0.319775	+	0.947494i	$0.396393\pi$
$3$	−1.14431	+	1.98200i	−0.660666	+	1.14431i	−0.980441	+	0.196814i	$0.936941\pi$
$4$	−1.21722			−0.608611
$5$	−1.47938	+	2.56236i	−0.661598	+	1.14592i	0.318597	+	0.947890i	$0.396788\pi$
$5$	−1.47938	+	2.56236i	−0.661598	+	1.14592i	−0.980196	+	0.198032i	$0.936545\pi$
$6$	1.01242	−	1.75357i	0.413320	−	0.715891i
$7$	−0.890904	−	1.54309i	−0.336730	−	0.583234i	0.647086	−	0.762417i	$-0.275988\pi$
$7$	−0.890904	−	1.54309i	−0.336730	−	0.583234i	−0.983816	+	0.179184i	$0.942654\pi$
$8$	2.84643			1.00636
$9$	−1.11888	−	1.93795i	−0.372960	−	0.645985i
$10$	1.30888	−	2.26704i	0.413903	−	0.716902i
$11$	−5.91864			−1.78454			−0.892268	−	0.451506i	$-0.850887\pi$
$11$	−5.91864			−1.78454			−0.892268	+	0.451506i	$0.850887\pi$
$12$	1.39288	−	2.41253i	0.402089	−	0.696438i
$13$	−1.61336	−	2.79442i	−0.447465	−	0.775031i	0.550756	−	0.834666i	$-0.314340\pi$
$13$	−1.61336	−	2.79442i	−0.447465	−	0.775031i	−0.998220	+	0.0596352i	$0.981006\pi$
$14$	0.788225	+	1.36525i	0.210662	+	0.364877i
$15$	−3.38573	−	5.86425i	−0.874191	−	1.51414i
$16$	−0.0839291			−0.0209823
$17$	0.500000	+	0.866025i	0.121268	+	0.210042i
$17$	0.500000	+	0.866025i	0.121268	+	0.210042i
$18$	0.989925	+	1.71460i	0.233328	+	0.404135i
$19$	1.92061	−	3.32660i	0.440618	−	0.763174i	−0.557117	−	0.830434i	$-0.688093\pi$
$19$	1.92061	−	3.32660i	0.440618	−	0.763174i	0.997735	+	0.0672605i	$0.0214259\pi$
$20$	1.80073	−	3.11896i	0.402656	−	0.697420i
$21$	4.07787			0.889865
$22$	5.23650			1.11643
$23$	−2.29863	+	3.98134i	−0.479297	+	0.830167i	−0.999718	−	0.0237428i	$-0.992442\pi$
$23$	−2.29863	+	3.98134i	−0.479297	+	0.830167i	0.520421	+	0.853910i	$0.325775\pi$
$24$	−3.25719	+	5.64162i	−0.664871	+	1.15159i
$25$	−1.87712	−	3.25127i	−0.375425	−	0.650255i
$26$	1.42741	+	2.47235i	0.279939	+	0.484868i
$27$	−1.74448			−0.335725
$28$	1.08443	+	1.87828i	0.204938	+	0.354962i
$29$	3.37037	+	5.83765i	0.625862	+	1.08403i	0.988373	+	0.152046i	$0.0485861\pi$
$29$	3.37037	+	5.83765i	0.625862	+	1.08403i	−0.362511	+	0.931979i	$0.618081\pi$
$30$	2.99552	+	5.18839i	0.546904	+	0.947265i
$31$	−2.41125	+	4.17641i	−0.433074	+	0.750105i	−0.997136	−	0.0756266i	$-0.975904\pi$
$31$	−2.41125	+	4.17641i	−0.433074	+	0.750105i	0.564063	+	0.825732i	$0.309238\pi$
$32$	−5.61860			−0.993238
$33$	6.77274	−	11.7307i	1.17898	−	2.04206i
$34$	−0.442374	−	0.766214i	−0.0758665	−	0.131405i
$35$	5.27194			0.891120
$36$	1.36192	+	2.35892i	0.226987	+	0.393153i
$37$	3.72972	−	6.46006i	0.613162	−	1.06203i	−0.377542	−	0.925993i	$-0.623231\pi$
$37$	3.72972	−	6.46006i	0.613162	−	1.06203i	0.990704	−	0.136035i	$-0.0434361\pi$
$38$	−1.69926	+	2.94320i	−0.275656	+	0.477450i
$39$	7.38470			1.18250
$40$	−4.21095	+	7.29358i	−0.665809	+	1.15322i
$41$	−5.27679			−0.824096			−0.412048	−	0.911162i	$-0.635186\pi$
$41$	−5.27679			−0.824096			−0.412048	+	0.911162i	$0.635186\pi$
$42$	−3.60789			−0.556709
$43$	5.26744	+	3.90564i	0.803278	+	0.595605i
$43$	5.26744	+	3.90564i	0.803278	+	0.595605i
$44$	7.20429			1.08609
$45$	6.62098			0.986998
$46$	2.03371	−	3.52248i	0.299854	−	0.519362i
$47$	3.01158			0.439284			0.219642	−	0.975581i	$-0.429511\pi$
$47$	3.01158			0.439284			0.219642	+	0.975581i	$0.429511\pi$
$48$	0.0960407	−	0.166347i	0.0138623	−	0.0240102i
$49$	1.91258	−	3.31269i	0.273226	−	0.473241i
$50$	1.66078	+	2.87656i	0.234870	+	0.406807i
$51$	−2.28861			−0.320470
$52$	1.96381	+	3.40142i	0.272332	+	0.471692i
$53$	2.64573	−	4.58255i	0.363420	−	0.629461i	−0.625102	−	0.780543i	$-0.714942\pi$
$53$	2.64573	−	4.58255i	0.363420	−	0.629461i	0.988521	+	0.151082i	$0.0482758\pi$
$54$	1.54342			0.210033
$55$	8.75591	−	15.1657i	1.18065	−	2.04494i
$56$	−2.53590	−	4.39230i	−0.338873	−	0.586946i
$57$	4.39554	+	7.61330i	0.582203	+	1.00841i
$58$	−2.98193	−	5.16485i	−0.391546	−	0.678178i
$59$	4.48808			0.584299			0.292149	−	0.956373i	$-0.405630\pi$
$59$	4.48808			0.584299			0.292149	+	0.956373i	$0.405630\pi$
$60$	4.12118	+	7.13810i	0.532042	+	0.921524i
$61$	7.30851	+	12.6587i	0.935759	+	1.62078i	0.773275	+	0.634071i	$0.218617\pi$
$61$	7.30851	+	12.6587i	0.935759	+	1.62078i	0.162484	+	0.986711i	$0.448049\pi$
$62$	2.13335	−	3.69507i	0.270936	−	0.469274i
$63$	−1.99363	+	3.45306i	−0.251173	+	0.435045i
$64$	5.13890			0.642363
$65$	9.54706			1.18417
$66$	−5.99217	+	10.3787i	−0.737585	+	1.27753i
$67$	−2.53867	+	4.39710i	−0.310148	+	0.537191i	−0.978394	−	0.206749i	$-0.933712\pi$
$67$	−2.53867	+	4.39710i	−0.310148	+	0.537191i	0.668247	+	0.743940i	$0.267045\pi$
$68$	−0.608611	−	1.05414i	−0.0738049	−	0.127834i
$69$	−5.26067	−	9.11176i	−0.633311	−	1.09693i
$70$	−4.66434			−0.557495
$71$	−3.08476	−	5.34297i	−0.366094	−	0.634094i	0.622857	−	0.782336i	$-0.285972\pi$
$71$	−3.08476	−	5.34297i	−0.366094	−	0.634094i	−0.988951	+	0.148242i	$0.952638\pi$
$72$	−3.18481	−	5.51625i	−0.375333	−	0.650096i
$73$	−4.01874	−	6.96066i	−0.470358	−	0.814684i	0.529067	−	0.848580i	$-0.322542\pi$
$73$	−4.01874	−	6.96066i	−0.470358	−	0.814684i	−0.999425	+	0.0338958i	$0.989209\pi$
$74$	−3.29986	+	5.71553i	−0.383601	+	0.664417i
$75$	8.59203			0.992122
$76$	−2.33781	+	4.04920i	−0.268165	+	0.464476i
$77$	5.27294	+	9.13300i	0.600907	+	1.04080i
$78$	−6.53360			−0.739784
$79$	−8.45272	−	14.6405i	−0.951005	−	1.64719i	−0.743255	−	0.669008i	$-0.766719\pi$
$79$	−8.45272	−	14.6405i	−0.951005	−	1.64719i	−0.207750	−	0.978182i	$-0.566614\pi$
$80$	0.124163	−	0.215056i	0.0138818	−	0.0240440i
$81$	5.35286	−	9.27142i	0.594762	−	1.03016i
$82$	4.66863			0.515564
$83$	−7.37425	+	12.7726i	−0.809429	+	1.40197i	0.103830	+	0.994595i	$0.466890\pi$
$83$	−7.37425	+	12.7726i	−0.809429	+	1.40197i	−0.913260	+	0.407378i	$0.866443\pi$
$84$	−4.96367			−0.541581
$85$	−2.95876			−0.320922
$86$	−4.66036	−	3.45551i	−0.502540	−	0.372617i
$87$	−15.4270			−1.65394
$88$	−16.8470			−1.79589
$89$	7.06642	−	12.2394i	0.749039	−	1.29737i	−0.199245	−	0.979950i	$-0.563849\pi$
$89$	7.06642	−	12.2394i	0.749039	−	1.29737i	0.948284	−	0.317423i	$-0.102818\pi$
$90$	−5.85790			−0.617477
$91$	−2.87469	+	4.97911i	−0.301350	+	0.521953i
$92$	2.79794	−	4.84617i	0.291705	−	0.505249i
$93$	−5.51843	−	9.55819i	−0.572234	−	0.991139i
$94$	−2.66449			−0.274821
$95$	5.68262	+	9.84259i	0.583025	+	1.00983i
$96$	6.42941	−	11.1361i	0.656199	−	1.13657i
$97$	3.75573			0.381336			0.190668	−	0.981655i	$-0.438935\pi$
$97$	3.75573			0.381336			0.190668	+	0.981655i	$0.438935\pi$
$98$	−1.69215	+	2.93089i	−0.170933	+	0.296065i
$99$	6.62224	+	11.4701i	0.665560	+	1.15278i
$100$	2.28488	+	3.95752i	0.228488	+	0.395752i
$101$	−1.81875	−	3.15016i	−0.180972	−	0.313453i	0.761240	−	0.648471i	$-0.224591\pi$
$101$	−1.81875	−	3.15016i	−0.180972	−	0.313453i	−0.942212	+	0.335018i	$0.891258\pi$
$102$	2.02485			0.200490
$103$	1.96481	+	3.40315i	0.193598	+	0.335322i	0.946440	−	0.322879i	$-0.104651\pi$
$103$	1.96481	+	3.40315i	0.193598	+	0.335322i	−0.752842	+	0.658202i	$0.771317\pi$
$104$	−4.59230	−	7.95411i	−0.450313	−	0.779964i
$105$	−6.03272	+	10.4490i	−0.588733	+	1.01972i
$106$	−2.34081	+	4.05440i	−0.227359	+	0.393798i
$107$	7.69252			0.743664			0.371832	−	0.928300i	$-0.378730\pi$
$107$	7.69252			0.743664			0.371832	+	0.928300i	$0.378730\pi$
$108$	2.12342			0.204326
$109$	0.506907	−	0.877989i	0.0485529	−	0.0840961i	−0.840728	−	0.541458i	$-0.817872\pi$
$109$	0.506907	−	0.877989i	0.0485529	−	0.0840961i	0.889280	+	0.457362i	$0.151206\pi$
$110$	−7.74677	+	13.4178i	−0.738625	+	1.27934i
$111$	8.53589	+	14.7846i	0.810191	+	1.40329i
$112$	0.0747727	+	0.129510i	0.00706536	+	0.0122376i
$113$	−5.07172			−0.477107			−0.238554	−	0.971129i	$-0.576673\pi$
$113$	−5.07172			−0.477107			−0.238554	+	0.971129i	$0.576673\pi$
$114$	−3.88894	−	6.73585i	−0.364233	−	0.630870i
$115$	−6.80108	−	11.7798i	−0.634204	−	1.09847i
$116$	−4.10249	−	7.10572i	−0.380906	−	0.659749i
$117$	−3.61030	+	6.25322i	−0.333772	+	0.578111i
$118$	−3.97082			−0.365544
$119$	0.890904	−	1.54309i	0.0816690	−	0.141455i
$120$	−9.63724	−	16.6922i	−0.879755	−	1.52378i
$121$	24.0303			2.18457
$122$	−6.46619	−	11.1998i	−0.585421	−	1.01398i
$123$	6.03827	−	10.4586i	0.544452	−	0.943019i
$124$	2.93503	−	5.08362i	0.263573	−	0.456522i
$125$	−3.68588			−0.329675
$126$	1.76386	−	3.05509i	0.157137	−	0.272169i
$127$	1.16768			0.103615			0.0518075	−	0.998657i	$-0.483502\pi$
$127$	1.16768			0.103615			0.0518075	+	0.998657i	$0.483502\pi$
$128$	6.69057			0.591369
$129$	−13.7685	+	5.97081i	−1.21225	+	0.525701i
$130$	−8.44674			−0.740828
$131$	−1.64480			−0.143707			−0.0718536	−	0.997415i	$-0.522891\pi$
$131$	−1.64480			−0.143707			−0.0718536	+	0.997415i	$0.522891\pi$
$132$	−8.24392	+	14.2789i	−0.717542	+	1.24282i
$133$	−6.84432			−0.593478
$134$	2.24608	−	3.89032i	0.194032	−	0.336073i
$135$	2.58075	−	4.46998i	0.222115	−	0.384715i
$136$	1.42321	+	2.46508i	0.122040	+	0.211379i
$137$	−6.00933			−0.513411			−0.256706	−	0.966490i	$-0.582637\pi$
$137$	−6.00933			−0.513411			−0.256706	+	0.966490i	$0.582637\pi$
$138$	4.65437	+	8.06161i	0.396206	+	0.686249i
$139$	7.81601	−	13.5377i	0.662945	−	1.14826i	−0.316893	−	0.948461i	$-0.602639\pi$
$139$	7.81601	−	13.5377i	0.662945	−	1.14826i	0.979838	−	0.199794i	$-0.0640272\pi$
$140$	−6.41712			−0.542345
$141$	−3.44617	+	5.96894i	−0.290220	+	0.502676i
$142$	2.72924	+	4.72718i	0.229033	+	0.396696i
$143$	9.54887	+	16.5391i	0.798517	+	1.38307i
$144$	0.0939064	+	0.162651i	0.00782554	+	0.0135542i
$145$	−19.9442			−1.65628
$146$	3.55557	+	6.15843i	0.294261	+	0.509675i
$147$	4.37716	+	7.58146i	0.361022	+	0.625308i
$148$	−4.53990	+	7.86333i	−0.373177	+	0.646362i
$149$	−1.44652	+	2.50545i	−0.118504	+	0.205254i	−0.919175	−	0.393850i	$-0.871143\pi$
$149$	−1.44652	+	2.50545i	−0.118504	+	0.205254i	0.800671	+	0.599104i	$0.204476\pi$
$150$	−7.60178			−0.620682
$151$	−23.2299			−1.89042			−0.945212	−	0.326457i	$-0.894145\pi$
$151$	−23.2299			−1.89042			−0.945212	+	0.326457i	$0.894145\pi$
$152$	5.46688	−	9.46892i	0.443423	−	0.768031i
$153$	1.11888	−	1.93795i	0.0904560	−	0.156674i
$154$	−4.66522	−	8.08040i	−0.375934	−	0.651137i
$155$	−7.13431	−	12.3570i	−0.573042	−	0.992537i
$156$	−8.98882			−0.719681
$157$	6.81926	+	11.8113i	0.544236	+	0.942645i	0.998655	+	0.0518566i	$0.0165139\pi$
$157$	6.81926	+	11.8113i	0.544236	+	0.942645i	−0.454418	+	0.890789i	$0.650153\pi$
$158$	7.47853	+	12.9532i	0.594960	+	1.03050i
$159$	6.05507	+	10.4877i	0.480198	+	0.831727i
$160$	8.31204	−	14.3969i	0.657125	−	1.13817i
$161$	8.19143			0.645575
$162$	−4.73593	+	8.20287i	−0.372090	+	0.644478i
$163$	−9.64261	−	16.7015i	−0.755267	−	1.30816i	−0.945241	−	0.326372i	$-0.894174\pi$
$163$	−9.64261	−	16.7015i	−0.755267	−	1.30816i	0.189974	−	0.981789i	$-0.439160\pi$
$164$	6.42302			0.501554
$165$	20.0389	+	34.7084i	1.56003	+	2.70204i
$166$	6.52435	−	11.3005i	0.506388	−	0.877090i
$167$	7.61294	−	13.1860i	0.589107	−	1.02036i	−0.405243	−	0.914209i	$-0.632813\pi$
$167$	7.61294	−	13.1860i	0.589107	−	1.02036i	0.994350	−	0.106154i	$-0.0338537\pi$
$168$	11.6074			0.895528
$169$	1.29416	−	2.24156i	0.0995510	−	0.172427i
$170$	2.61775			0.200773
$171$	−8.59572			−0.657331
$172$	−6.41165	−	4.75403i	−0.488883	−	0.362491i
$173$	1.66919			0.126906			0.0634531	−	0.997985i	$-0.479789\pi$
$173$	1.66919			0.126906			0.0634531	+	0.997985i	$0.479789\pi$
$174$	13.6490			1.03473
$175$	−3.34467	+	5.79315i	−0.252834	+	0.437921i
$176$	0.496746			0.0374436
$177$	−5.13575	+	8.89538i	−0.386026	+	0.668617i
$178$	−6.25200	+	10.8288i	−0.468607	+	0.811651i
$179$	−3.20258	−	5.54703i	−0.239372	−	0.414604i	0.721162	−	0.692766i	$-0.243608\pi$
$179$	−3.20258	−	5.54703i	−0.239372	−	0.414604i	−0.960534	+	0.278162i	$0.910275\pi$
$180$	−8.05920			−0.600697
$181$	−7.48635	−	12.9667i	−0.556456	−	0.963810i	−0.997789	−	0.0664662i	$-0.978828\pi$
$181$	−7.48635	−	12.9667i	−0.556456	−	0.963810i	0.441333	−	0.897343i	$-0.354506\pi$
$182$	2.54338	−	4.40526i	0.188528	−	0.326539i
$183$	−33.4527			−2.47290
$184$	−6.54288	+	11.3326i	−0.482348	+	0.835451i
$185$	11.0353	+	19.1138i	0.811334	+	1.40527i
$186$	4.88241	+	8.45659i	0.357996	+	0.620067i
$187$	−2.95932	−	5.12569i	−0.216407	−	0.374828i
$188$	−3.66576			−0.267353
$189$	1.55416	+	2.69189i	0.113049	+	0.195806i
$190$	−5.02769	−	8.70821i	−0.364747	−	0.631760i
$191$	9.95930	−	17.2500i	0.720630	−	1.24817i	−0.240118	−	0.970744i	$-0.577186\pi$
$191$	9.95930	−	17.2500i	0.720630	−	1.24817i	0.960748	−	0.277423i	$-0.0894805\pi$
$192$	−5.88049	+	10.1853i	−0.424388	+	0.735061i
$193$	−6.90060			−0.496716			−0.248358	−	0.968668i	$-0.579891\pi$
$193$	−6.90060			−0.496716			−0.248358	+	0.968668i	$0.579891\pi$
$194$	−3.32287			−0.238568
$195$	−10.9248	+	18.9223i	−0.782339	+	1.35505i
$196$	−2.32803	+	4.03227i	−0.166288	+	0.288019i
$197$	3.21595	+	5.57019i	0.229127	+	0.396860i	0.957550	−	0.288268i	$-0.0930795\pi$
$197$	3.21595	+	5.57019i	0.229127	+	0.396860i	−0.728422	+	0.685128i	$0.759746\pi$
$198$	−5.85901	−	10.1481i	−0.416382	−	0.721194i
$199$	12.6847			0.899194			0.449597	−	0.893231i	$-0.351568\pi$
$199$	12.6847			0.899194			0.449597	+	0.893231i	$0.351568\pi$
$200$	−5.34310	−	9.25452i	−0.377814	−	0.654394i
$201$	−5.81003	−	10.0633i	−0.409808	−	0.709808i
$202$	1.60913	+	2.78710i	0.113218	+	0.196100i
$203$	6.00535	−	10.4016i	0.421493	−	0.730048i
$204$	2.78575			0.195042
$205$	7.80637	−	13.5210i	0.545221	−	0.944350i
$206$	−1.73836	−	3.01093i	−0.121117	−	0.209781i
$207$	10.2875			0.715034
$208$	0.135408	+	0.234533i	0.00938882	+	0.0162619i
$209$	−11.3674	+	19.6889i	−0.786300	+	1.36191i
$210$	5.33743	−	9.24471i	0.368318	−	0.637945i
$211$	−10.5626			−0.727160			−0.363580	−	0.931563i	$-0.618446\pi$
$211$	−10.5626			−0.727160			−0.363580	+	0.931563i	$0.618446\pi$
$212$	−3.22044	+	5.57797i	−0.221181	+	0.383097i
$213$	14.1197			0.967464
$214$	−6.80594			−0.465244
$215$	−17.8002	+	7.71917i	−1.21396	+	0.526443i
$216$	−4.96554			−0.337862
$217$	8.59277			0.583316
$218$	−0.448485	+	0.776799i	−0.0303752	+	0.0526115i
$219$	18.3947			1.24300
$220$	−10.6579	+	18.4600i	−0.718554	+	1.24457i
$221$	1.61336	−	2.79442i	0.108526	−	0.187973i
$222$	−7.55211	−	13.0806i	−0.506864	−	0.877915i
$223$	−27.8701			−1.86632			−0.933162	−	0.359457i	$-0.882962\pi$
$223$	−27.8701			−1.86632			−0.933162	+	0.359457i	$0.882962\pi$
$224$	5.00564	+	8.67001i	0.334453	+	0.579290i
$225$	−4.20055	+	7.27556i	−0.280037	+	0.485037i
$226$	4.48719			0.298484
$227$	3.99015	−	6.91114i	0.264836	−	0.458709i	−0.702685	−	0.711501i	$-0.748016\pi$
$227$	3.99015	−	6.91114i	0.264836	−	0.458709i	0.967521	+	0.252792i	$0.0813490\pi$
$228$	−5.35034	−	9.26707i	−0.354335	−	0.613727i
$229$	2.01000	+	3.48142i	0.132824	+	0.230059i	0.924764	−	0.380540i	$-0.124262\pi$
$229$	2.01000	+	3.48142i	0.132824	+	0.230059i	−0.791940	+	0.610599i	$0.790929\pi$
$230$	6.01724	+	10.4222i	0.396765	+	0.687218i
$231$	−24.1354			−1.58800
$232$	9.59352	+	16.6165i	0.629846	+	1.09092i
$233$	4.12138	+	7.13843i	0.270000	+	0.467654i	0.968862	−	0.247603i	$-0.0796428\pi$
$233$	4.12138	+	7.13843i	0.270000	+	0.467654i	−0.698861	+	0.715257i	$0.746310\pi$
$234$	3.19420	−	5.53252i	0.208812	−	0.361672i
$235$	−4.45526	+	7.71674i	−0.290629	+	0.503385i
$236$	−5.46299			−0.355610
$237$	38.6900			2.51319
$238$	−0.788225	+	1.36525i	−0.0510931	+	0.0884958i
$239$	8.01667	−	13.8853i	0.518556	−	0.898164i	−0.481212	−	0.876604i	$-0.659803\pi$
$239$	8.01667	−	13.8853i	0.518556	−	0.898164i	0.999768	−	0.0215603i	$-0.00686338\pi$
$240$	0.284161	+	0.492181i	0.0183425	+	0.0317702i
$241$	−3.83986	−	6.65083i	−0.247347	−	0.428418i	0.715442	−	0.698672i	$-0.246225\pi$
$241$	−3.83986	−	6.65083i	−0.247347	−	0.428418i	−0.962789	+	0.270255i	$0.912892\pi$
$242$	−21.2607			−1.36669
$243$	9.63391	+	16.6864i	0.618015	+	1.07043i
$244$	−8.89608	−	15.4085i	−0.569513	−	0.986425i
$245$	5.65886	+	9.80144i	0.361531	+	0.626191i
$246$	−5.34235	+	9.25321i	−0.340615	+	0.589963i
$247$	−12.3945			−0.788644
$248$	−6.86346	+	11.8879i	−0.435830	+	0.754880i
$249$	−16.8768	−	29.2315i	−1.06953	−	1.85247i
$250$	3.26107			0.206248
$251$	5.21413	+	9.03113i	0.329113	+	0.570040i	0.982336	−	0.187125i	$-0.0599171\pi$
$251$	5.21413	+	9.03113i	0.329113	+	0.570040i	−0.653223	+	0.757165i	$0.726584\pi$
$252$	2.42669	−	4.20314i	0.152867	−	0.264773i
$253$	13.6047	−	23.5641i	0.855323	−	1.48146i
$254$	−1.03310			−0.0648228
$255$	3.38573	−	5.86425i	0.212023	−	0.367234i
$256$	−16.1973			−1.01233
$257$	20.8134			1.29831			0.649153	−	0.760658i	$-0.275124\pi$
$257$	20.8134			1.29831			0.649153	+	0.760658i	$0.275124\pi$
$258$	12.1817	−	5.28266i	0.758399	−	0.328884i
$259$	−13.2913			−0.825881
$260$	−11.6209			−0.720697
$261$	7.54207	−	13.0633i	0.466843	−	0.808595i
$262$	1.45524			0.0899049
$263$	15.1872	−	26.3050i	0.936483	−	1.62204i	0.164515	−	0.986375i	$-0.447394\pi$
$263$	15.1872	−	26.3050i	0.936483	−	1.62204i	0.771968	−	0.635662i	$-0.219273\pi$
$264$	19.2781	−	33.3907i	1.18649	−	2.05506i
$265$	7.82809	+	13.5586i	0.480876	+	0.832901i
$266$	6.05550			0.371286
$267$	16.1723	+	28.0113i	0.989729	+	1.71426i
$268$	3.09012	−	5.35225i	0.188759	−	0.326940i
$269$	−4.36699			−0.266260			−0.133130	−	0.991099i	$-0.542503\pi$
$269$	−4.36699			−0.266260			−0.133130	+	0.991099i	$0.542503\pi$
$270$	−2.28331	+	3.95481i	−0.138958	+	0.240682i
$271$	0.804729	+	1.39383i	0.0488838	+	0.0846692i	0.889432	−	0.457068i	$-0.151100\pi$
$271$	0.804729	+	1.39383i	0.0488838	+	0.0846692i	−0.840548	+	0.541737i	$0.817767\pi$
$272$	−0.0419645	−	0.0726847i	−0.00254447	−	0.00440716i
$273$	−6.57906	−	11.3953i	−0.398183	−	0.689673i
$274$	5.31674			0.321196
$275$	11.1100	+	19.2431i	0.669959	+	1.16040i
$276$	6.40341	+	11.0910i	0.385440	+	0.667601i
$277$	−0.204446	+	0.354112i	−0.0122840	+	0.0212765i	−0.872102	−	0.489324i	$-0.837244\pi$
$277$	−0.204446	+	0.354112i	−0.0122840	+	0.0212765i	0.859818	+	0.510601i	$0.170577\pi$
$278$	−6.91520	+	11.9775i	−0.414746	+	0.718361i
$279$	10.7916			0.646076
$280$	15.0062			0.896792
$281$	−5.49996	+	9.52621i	−0.328100	+	0.568286i	−0.982135	−	0.188178i	$-0.939742\pi$
$281$	−5.49996	+	9.52621i	−0.328100	+	0.568286i	0.654035	+	0.756465i	$0.273075\pi$
$282$	3.04899	−	5.28101i	0.181565	−	0.314479i
$283$	6.94125	+	12.0226i	0.412614	+	0.714669i	0.995175	−	0.0981184i	$-0.0312824\pi$
$283$	6.94125	+	12.0226i	0.412614	+	0.714669i	−0.582560	+	0.812787i	$0.697949\pi$
$284$	3.75484	+	6.50357i	0.222809	+	0.385916i
$285$	−26.0107			−1.54074
$286$	−8.44834	−	14.6330i	−0.499561	−	0.865265i
$287$	4.70111	+	8.14257i	0.277498	+	0.480641i
$288$	6.28653	+	10.8886i	0.370438	+	0.641617i
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$	17.6456			1.03619
$291$	−4.29771	+	7.44385i	−0.251936	+	0.436366i
$292$	4.89170	+	8.47267i	0.286265	+	0.495825i
$293$	24.4827			1.43029			0.715146	−	0.698975i	$-0.246360\pi$
$293$	24.4827			1.43029			0.715146	+	0.698975i	$0.246360\pi$
$294$	−3.87268	−	6.70768i	−0.225859	−	0.391200i
$295$	−6.63958	+	11.5001i	−0.386571	+	0.669561i
$296$	10.6164	−	18.3881i	0.617065	−	1.06879i
$297$	10.3249			0.599114
$298$	1.27981	−	2.21669i	0.0741372	−	0.128409i
$299$	14.8340			0.857874
$300$	−10.4584			−0.603816
$301$	1.33397	−	11.6077i	0.0768888	−	0.669057i
$302$	20.5526			1.18267
$303$	8.32483			0.478249
$304$	−0.161195	+	0.279198i	−0.00924517	+	0.0160131i
$305$	−43.2482			−2.47639
$306$	−0.989925	+	1.71460i	−0.0565903	+	0.0980172i
$307$	−16.5499	+	28.6653i	−0.944554	+	1.63602i	−0.187912	+	0.982186i	$0.560172\pi$
$307$	−16.5499	+	28.6653i	−0.944554	+	1.63602i	−0.756642	+	0.653829i	$0.773161\pi$
$308$	−6.41833	−	11.1169i	−0.365718	−	0.633443i
$309$	−8.99338			−0.511615
$310$	6.31206	+	10.9328i	0.358501	+	0.620942i
$311$	1.55444	−	2.69236i	0.0881441	−	0.152670i	−0.818583	−	0.574389i	$-0.805240\pi$
$311$	1.55444	−	2.69236i	0.0881441	−	0.152670i	0.906727	+	0.421719i	$0.138573\pi$
$312$	21.0200			1.19003
$313$	13.9714	−	24.1992i	0.789711	−	1.36782i	−0.136433	−	0.990649i	$-0.543564\pi$
$313$	13.9714	−	24.1992i	0.789711	−	1.36782i	0.926144	−	0.377171i	$-0.123103\pi$
$314$	−6.03333	−	10.4500i	−0.340480	−	0.589729i
$315$	−5.89866	−	10.2168i	−0.332352	−	0.575650i
$316$	10.2888	+	17.8208i	0.578792	+	1.00250i
$317$	3.61564			0.203074			0.101537	−	0.994832i	$-0.467624\pi$
$317$	3.61564			0.203074			0.101537	+	0.994832i	$0.467624\pi$
$318$	−5.35721	−	9.27895i	−0.300417	−	0.520338i
$319$	−19.9480	−	34.5510i	−1.11687	−	1.93448i
$320$	−7.60239	+	13.1677i	−0.424986	+	0.736098i
$321$	−8.80260	+	15.2466i	−0.491313	+	0.850980i
$322$	−7.24735			−0.403879
$323$	3.84122			0.213731
$324$	−6.51561	+	11.2854i	−0.361978	+	0.626965i
$325$	−6.05694	+	10.4909i	−0.335979	+	0.581932i
$326$	8.53128	+	14.7766i	0.472504	+	0.818400i
$327$	1.16012	+	2.00938i	0.0641545	+	0.111119i
$328$	−15.0200			−0.829341
$329$	−2.68303	−	4.64714i	−0.147920	−	0.256205i
$330$	−17.7294	−	30.7082i	−0.975970	−	1.69043i
$331$	−10.0168	−	17.3495i	−0.550571	−	0.953616i	−0.998233	−	0.0594137i	$-0.981077\pi$
$331$	−10.0168	−	17.3495i	−0.550571	−	0.953616i	0.447663	−	0.894202i	$-0.352256\pi$
$332$	8.97610	−	15.5471i	0.492627	−	0.853256i
$333$	−16.6924			−0.914739
$334$	−6.73553	+	11.6663i	−0.368552	+	0.638351i
$335$	−7.51130	−	13.0100i	−0.410386	−	0.710810i
$336$	−0.342252			−0.0186714
$337$	−4.35288	−	7.53940i	−0.237116	−	0.410697i	0.722769	−	0.691089i	$-0.242869\pi$
$337$	−4.35288	−	7.53940i	−0.237116	−	0.410697i	−0.959886	+	0.280392i	$0.909536\pi$
$338$	−1.14501	+	1.98321i	−0.0622802	+	0.107872i
$339$	5.80361	−	10.0521i	0.315209	−	0.545957i
$340$	3.60146			0.195317
$341$	14.2713	−	24.7187i	0.772836	−	1.33859i
$342$	7.60505			0.411234
$343$	−19.2884			−1.04147
$344$	14.9934	+	11.1171i	0.808390	+	0.599395i
$345$	31.1301			1.67599
$346$	−1.47681			−0.0793940
$347$	−16.2399	+	28.1284i	−0.871806	+	1.51001i	−0.0116784	+	0.999932i	$0.503717\pi$
$347$	−16.2399	+	28.1284i	−0.871806	+	1.51001i	−0.860127	+	0.510080i	$0.829616\pi$
$348$	18.7780			1.00661
$349$	15.3539	−	26.5938i	0.821877	−	1.42353i	−0.0824052	−	0.996599i	$-0.526260\pi$
$349$	15.3539	−	26.5938i	0.821877	−	1.42353i	0.904283	−	0.426934i	$-0.140406\pi$
$350$	2.95919	−	5.12547i	0.158176	−	0.273968i
$351$	2.81447	+	4.87480i	0.150225	+	0.260198i
$352$	33.2545			1.77247
$353$	0.525182	+	0.909642i	0.0279526	+	0.0484154i	0.879663	−	0.475597i	$-0.157768\pi$
$353$	0.525182	+	0.909642i	0.0279526	+	0.0484154i	−0.851711	+	0.524012i	$0.824435\pi$
$354$	4.54384	−	7.87016i	0.241502	−	0.418294i
$355$	18.2541			0.968829
$356$	−8.60139	+	14.8980i	−0.455873	+	0.789595i
$357$	2.03894	+	3.53154i	0.107912	+	0.186909i
$358$	2.83347	+	4.90772i	0.149754	+	0.259381i
$359$	−10.5878	−	18.3386i	−0.558802	−	0.967873i	−0.997597	−	0.0692857i	$-0.977928\pi$
$359$	−10.5878	−	18.3386i	−0.558802	−	0.967873i	0.438795	−	0.898587i	$-0.355405\pi$
$360$	18.8462			0.993280
$361$	2.12251	+	3.67629i	0.111711	+	0.193489i
$362$	6.62353	+	11.4723i	0.348125	+	0.602970i
$363$	−27.4980	+	47.6280i	−1.44327	+	2.49982i
$364$	3.49914	−	6.06068i	0.183405	−	0.317666i
$365$	23.7810			1.24475
$366$	29.5972			1.54707
$367$	12.0588	−	20.8865i	0.629465	−	1.09026i	−0.358195	−	0.933647i	$-0.616608\pi$
$367$	12.0588	−	20.8865i	0.629465	−	1.09026i	0.987659	−	0.156618i	$-0.0500591\pi$
$368$	0.192922	−	0.334150i	0.0100567	−	0.0174188i
$369$	5.90409	+	10.2262i	0.307355	+	0.532354i
$370$	−9.76349	−	16.9109i	−0.507580	−	0.879154i
$371$	−9.42838			−0.489497
$372$	6.71715	+	11.6344i	0.348268	+	0.603218i
$373$	12.6331	+	21.8812i	0.654117	+	1.13296i	0.982114	+	0.188286i	$0.0602931\pi$
$373$	12.6331	+	21.8812i	0.654117	+	1.13296i	−0.327997	+	0.944679i	$0.606374\pi$
$374$	2.61825	+	4.53494i	0.135387	+	0.234496i
$375$	4.21778	−	7.30541i	0.217805	−	0.377250i
$376$	8.57224			0.442080
$377$	10.8752	−	18.8364i	0.560102	−	0.970126i
$378$	−1.37504	−	2.38164i	−0.0707246	−	0.122499i
$379$	11.2354			0.577124			0.288562	−	0.957461i	$-0.406823\pi$
$379$	11.2354			0.577124			0.288562	+	0.957461i	$0.406823\pi$
$380$	−6.91701	−	11.9806i	−0.354835	−	0.614593i
$381$	−1.33619	+	2.31435i	−0.0684550	+	0.118568i
$382$	−8.81147	+	15.2619i	−0.450834	+	0.780867i
$383$	−17.7309			−0.906005			−0.453003	−	0.891509i	$-0.649647\pi$
$383$	−17.7309			−0.906005			−0.453003	+	0.891509i	$0.649647\pi$
$384$	−7.65607	+	13.2607i	−0.390697	+	0.676707i
$385$	−31.2027			−1.59024
$386$	6.10529			0.310751
$387$	1.67532	−	14.5780i	0.0851614	−	0.741042i
$388$	−4.57155			−0.232085
$389$	−4.69744			−0.238170			−0.119085	−	0.992884i	$-0.537996\pi$
$389$	−4.69744			−0.238170			−0.119085	+	0.992884i	$0.537996\pi$
$390$	9.66567	−	16.7414i	0.489440	−	0.847735i
$391$	−4.59726			−0.232493
$392$	5.44402	−	9.42933i	0.274965	−	0.476253i
$393$	1.88216	−	3.26000i	0.0949425	−	0.164445i
$394$	−2.84531	−	4.92822i	−0.143345	−	0.248280i
$395$	50.0191			2.51673
$396$	−8.06073	−	13.9616i	−0.405067	−	0.701596i
$397$	4.83915	−	8.38165i	0.242870	−	0.420663i	−0.718661	−	0.695361i	$-0.755245\pi$
$397$	4.83915	−	8.38165i	0.242870	−	0.420663i	0.961531	+	0.274698i	$0.0885779\pi$
$398$	−11.2228			−0.562546
$399$	7.83201	−	13.5654i	0.392091	−	0.679121i
$400$	0.157545	+	0.272876i	0.00787726	+	0.0136438i
$401$	−5.91103	−	10.2382i	−0.295183	−	0.511272i	0.679845	−	0.733356i	$-0.262047\pi$
$401$	−5.91103	−	10.2382i	−0.295183	−	0.511272i	−0.975027	+	0.222084i	$0.928714\pi$
$402$	5.14041	+	8.90345i	0.256380	+	0.444064i
$403$	15.5608			0.775140
$404$	2.21382	+	3.83445i	0.110142	+	0.190771i
$405$	15.8378	+	27.4319i	0.786987	+	1.36310i
$406$	−5.31322	+	9.20277i	−0.263691	+	0.456726i
$407$	−22.0749	+	38.2348i	−1.09421	+	1.89523i
$408$	−6.51438			−0.322510
$409$	−19.5934			−0.968829			−0.484415	−	0.874839i	$-0.660967\pi$
$409$	−19.5934			−0.968829			−0.484415	+	0.874839i	$0.660967\pi$
$410$	−6.90667	+	11.9627i	−0.341096	+	0.590796i
$411$	6.87652	−	11.9105i	0.339194	−	0.587500i
$412$	−2.39161	−	4.14238i	−0.117826	−	0.204081i
$413$	−3.99845	−	6.92552i	−0.196751	−	0.340783i
$414$	−9.10188			−0.447333
$415$	−21.8186	−	37.7910i	−1.07103	−	1.85509i
$416$	9.06481	+	15.7007i	0.444439	+	0.769791i
$417$	17.8878	+	30.9826i	0.875971	+	1.51723i
$418$	10.0573	−	17.4197i	0.491918	−	0.852027i
$419$	−32.5125			−1.58834			−0.794169	−	0.607697i	$-0.792093\pi$
$419$	−32.5125			−1.58834			−0.794169	+	0.607697i	$0.792093\pi$
$420$	7.34315	−	12.7187i	0.358309	−	0.620610i
$421$	0.299567	+	0.518866i	0.0146000	+	0.0252880i	0.873233	−	0.487303i	$-0.162019\pi$
$421$	0.299567	+	0.518866i	0.0146000	+	0.0252880i	−0.858633	+	0.512591i	$0.828686\pi$
$422$	9.34525			0.454920
$423$	−3.36959	−	5.83630i	−0.163835	−	0.283771i
$424$	7.53090	−	13.0439i	0.365733	−	0.633468i
$425$	1.87712	−	3.25127i	0.0910539	−	0.157710i
$426$	−12.4923			−0.605256
$427$	13.0224	−	22.5554i	0.630196	−	1.09153i
$428$	−9.36350			−0.452602
$429$	−43.7074			−2.11021
$430$	15.7487	−	6.82951i	0.759469	−	0.329348i
$431$	−7.08237			−0.341146			−0.170573	−	0.985345i	$-0.554562\pi$
$431$	−7.08237			−0.341146			−0.170573	+	0.985345i	$0.554562\pi$
$432$	0.146413			0.00704428
$433$	14.9415	−	25.8795i	0.718045	−	1.24369i	−0.243729	−	0.969843i	$-0.578371\pi$
$433$	14.9415	−	25.8795i	0.718045	−	1.24369i	0.961773	−	0.273846i	$-0.0882960\pi$
$434$	−7.60244			−0.364929
$435$	22.8223	−	39.5294i	1.09425	−	1.89529i
$436$	−0.617018	+	1.06871i	−0.0295498	+	0.0511818i
$437$	8.82954	+	15.2932i	0.422374	+	0.731574i
$438$	−16.2747			−0.777634
$439$	−13.2687	−	22.9821i	−0.633283	−	1.09688i	−0.986876	−	0.161479i	$-0.948374\pi$
$439$	−13.2687	−	22.9821i	−0.633283	−	1.09688i	0.353594	−	0.935399i	$-0.384960\pi$
$440$	24.9231	−	43.1680i	1.18816	−	2.05795i
$441$	−8.55978			−0.407609
$442$	−1.42741	+	2.47235i	−0.0678951	+	0.117598i
$443$	0.0865349	+	0.149883i	0.00411140	+	0.00712115i	0.868074	−	0.496435i	$-0.165358\pi$
$443$	0.0865349	+	0.149883i	0.00411140	+	0.00712115i	−0.863962	+	0.503556i	$0.832025\pi$
$444$	−10.3901	−	17.9961i	−0.493091	−	0.854059i
$445$	20.9078	+	36.2134i	0.991125	+	1.71668i
$446$	24.6580			1.16759
$447$	−3.31053	−	5.73401i	−0.156583	−	0.271209i
$448$	−4.57827	−	7.92980i	−0.216303	−	0.374648i
$449$	−6.12943	+	10.6165i	−0.289266	+	0.501023i	−0.973635	−	0.228113i	$-0.926744\pi$
$449$	−6.12943	+	10.6165i	−0.289266	+	0.501023i	0.684369	+	0.729136i	$0.260078\pi$
$450$	3.71643	−	6.43704i	0.175194	−	0.303445i
$451$	31.2314			1.47063
$452$	6.17341			0.290373
$453$	26.5822	−	46.0417i	1.24894	−	2.16323i
$454$	−3.53028	+	6.11462i	−0.165684	+	0.286973i
$455$	−8.50551	−	14.7320i	−0.398745	−	0.690646i
$456$	12.5116	+	21.6707i	0.585909	+	1.01482i
$457$	−23.0440			−1.07795			−0.538977	−	0.842320i	$-0.681189\pi$
$457$	−23.0440			−1.07795			−0.538977	+	0.842320i	$0.681189\pi$
$458$	−1.77834	−	3.08018i	−0.0830965	−	0.143927i
$459$	−0.872240	−	1.51076i	−0.0407127	−	0.0705164i
$460$	8.27843	+	14.3387i	0.385984	+	0.668543i
$461$	13.8615	−	24.0089i	0.645596	−	1.11821i	−0.338567	−	0.940942i	$-0.609942\pi$
$461$	13.8615	−	24.0089i	0.645596	−	1.11821i	0.984163	−	0.177263i	$-0.0567244\pi$
$462$	21.3538			0.993468
$463$	−18.6633	+	32.3257i	−0.867355	+	1.50230i	−0.00266633	+	0.999996i	$0.500849\pi$
$463$	−18.6633	+	32.3257i	−0.867355	+	1.50230i	−0.864689	+	0.502307i	$0.832485\pi$
$464$	−0.282872	−	0.489949i	−0.0131320	−	0.0227453i
$465$	32.6554			1.51436
$466$	−3.64638	−	6.31571i	−0.168915	−	0.292570i
$467$	−11.0720	+	19.1773i	−0.512351	+	0.887418i	0.487546	+	0.873097i	$0.337892\pi$
$467$	−11.0720	+	19.1773i	−0.512351	+	0.887418i	−0.999897	+	0.0143211i	$0.995441\pi$
$468$	4.39453	−	7.61156i	0.203137	−	0.351844i
$469$	9.04683			0.417744
$470$	3.94179	−	6.82737i	0.181821	−	0.314923i
$471$	−31.2133			−1.43823
$472$	12.7750			0.588018
$473$	−31.1761	−	23.1161i	−1.43348	−	1.06288i
$474$	−34.2309			−1.57228
$475$	−14.4209			−0.661676
$476$	−1.08443	+	1.87828i	−0.0497046	+	0.0860910i
$477$	−11.8410			−0.542163
$478$	−7.09273	+	12.2850i	−0.324414	+	0.561902i
$479$	3.29848	−	5.71314i	0.150712	−	0.261040i	−0.780778	−	0.624809i	$-0.785177\pi$
$479$	3.29848	−	5.71314i	0.150712	−	0.261040i	0.931489	+	0.363769i	$0.118510\pi$
$480$	19.0231	+	32.9489i	0.868280	+	1.50391i
$481$	−24.0695			−1.09747
$482$	3.39731	+	5.88431i	0.154743	+	0.268023i
$483$	−9.37351	+	16.2354i	−0.426510	+	0.738736i
$484$	−29.2502			−1.32955
$485$	−5.55614	+	9.62352i	−0.252292	+	0.436982i
$486$	−8.52358	−	14.7633i	−0.386637	−	0.669676i
$487$	19.0839	+	33.0543i	0.864775	+	1.49783i	0.867270	+	0.497838i	$0.165873\pi$
$487$	19.0839	+	33.0543i	0.864775	+	1.49783i	−0.00249455	+	0.999997i	$0.500794\pi$
$488$	20.8032	+	36.0321i	0.941715	+	1.63110i
$489$	44.1364			1.99592
$490$	−5.00667	−	8.67180i	−0.226178	−	0.391752i
$491$	−14.7992	−	25.6329i	−0.667877	−	1.15680i	−0.978497	−	0.206262i	$-0.933870\pi$
$491$	−14.7992	−	25.6329i	−0.667877	−	1.15680i	0.310620	−	0.950534i	$-0.399463\pi$
$492$	−7.34991	+	12.7304i	−0.331360	+	0.573932i
$493$	−3.37037	+	5.83765i	−0.151794	+	0.262915i
$494$	10.9660			0.493385
$495$	−39.1872			−1.76133
$496$	0.202374	−	0.350522i	0.00908687	−	0.0157389i
$497$	−5.49646	+	9.52014i	−0.246550	+	0.427037i
$498$	14.9317	+	25.8625i	0.669107	+	1.15893i
$499$	4.01808	+	6.95952i	0.179874	+	0.311551i	0.941837	−	0.336069i	$-0.109098\pi$
$499$	4.01808	+	6.95952i	0.179874	+	0.311551i	−0.761963	+	0.647620i	$0.775764\pi$
$500$	4.48653			0.200644
$501$	17.4231	+	30.1777i	0.778406	+	1.34824i
$502$	−4.61319	−	7.99027i	−0.205897	−	0.356623i
$503$	−1.14464	−	1.98258i	−0.0510370	−	0.0883987i	0.839378	−	0.543548i	$-0.182919\pi$
$503$	−1.14464	−	1.98258i	−0.0510370	−	0.0883987i	−0.890415	+	0.455149i	$0.849586\pi$
$504$	−5.67472	+	9.82890i	−0.252772	+	0.437814i
$505$	10.7625			0.478924
$506$	−12.0368	+	20.8483i	−0.535100	+	0.926820i
$507$	2.96184	+	5.13006i	0.131540	+	0.227834i
$508$	−1.42133			−0.0630613
$509$	−8.25621	−	14.3002i	−0.365950	−	0.633844i	0.622978	−	0.782239i	$-0.285923\pi$
$509$	−8.25621	−	14.3002i	−0.365950	−	0.633844i	−0.988928	+	0.148395i	$0.952589\pi$
$510$	−2.99552	+	5.18839i	−0.132644	+	0.229746i
$511$	−7.16062	+	12.4026i	−0.316767	+	0.548657i
$512$	0.949361			0.0419562
$513$	−3.35047	+	5.80318i	−0.147927	+	0.256217i
$514$	−18.4146			−0.812234
$515$	−11.6268			−0.512337
$516$	16.7594	−	7.26780i	0.737790	−	0.319947i
$517$	−17.8244			−0.783918
$518$	11.7594			0.516680
$519$	−1.91007	+	3.30834i	−0.0838427	+	0.145220i
$520$	27.1750			1.19170
$521$	5.15304	−	8.92532i	0.225759	−	0.391025i	−0.730788	−	0.682604i	$-0.760847\pi$
$521$	5.15304	−	8.92532i	0.225759	−	0.391025i	0.956547	+	0.291579i	$0.0941806\pi$
$522$	−6.67283	+	11.5577i	−0.292062	+	0.505866i
$523$	16.1741	+	28.0144i	0.707245	+	1.22498i	0.965875	+	0.259008i	$0.0833957\pi$
$523$	16.1741	+	28.0144i	0.707245	+	1.22498i	−0.258630	+	0.965977i	$0.583271\pi$
$524$	2.00209			0.0874618
$525$	−7.65467	−	13.2583i	−0.334077	−	0.578639i
$526$	−13.4368	+	23.2733i	−0.585874	+	1.01476i
$527$	−4.82250			−0.210072
$528$	−0.568430	+	0.984549i	−0.0247377	+	0.0428470i
$529$	0.932616	+	1.61534i	0.0405485	+	0.0702321i
$530$	−6.92588	−	11.9960i	−0.300841	−	0.521072i
$531$	−5.02162	−	8.69770i	−0.217920	−	0.377448i
$532$	8.33105			0.361197
$533$	8.51334	+	14.7455i	0.368754	+	0.638700i
$534$	−14.3084	−	24.7829i	−0.619185	−	1.07246i
$535$	−11.3801	+	19.7110i	−0.492007	+	0.852181i
$536$	−7.22614	+	12.5160i	−0.312122	+	0.540610i
$537$	14.6589			0.632580
$538$	3.86369			0.166575
$539$	−11.3199	+	19.6066i	−0.487581	+	0.844516i
$540$	−3.14134	+	5.44096i	−0.135182	+	0.234142i
$541$	13.3471	+	23.1179i	0.573838	+	0.993917i	0.996167	+	0.0874741i	$0.0278795\pi$
$541$	13.3471	+	23.1179i	0.573838	+	0.993917i	−0.422329	+	0.906443i	$0.638787\pi$
$542$	−0.711982	−	1.23319i	−0.0305822	−	0.0529700i
$543$	34.2667			1.47053
$544$	−2.80930	−	4.86585i	−0.120448	−	0.208622i
$545$	1.49982	+	2.59776i	0.0642450	+	0.111276i
$546$	5.82081	+	10.0819i	0.249108	+	0.431467i
$547$	−11.1370	+	19.2899i	−0.476185	+	0.824776i	−0.999628	−	0.0272848i	$-0.991314\pi$
$547$	−11.1370	+	19.2899i	−0.476185	+	0.824776i	0.523443	+	0.852061i	$0.324647\pi$
$548$	7.31468			0.312468
$549$	16.3547	−	28.3271i	0.698000	−	1.20897i
$550$	−9.82956	−	17.0253i	−0.419134	−	0.725961i
$551$	25.8927			1.10307
$552$	−14.9741	−	25.9360i	−0.637342	−	1.10391i
$553$	−15.0611	+	26.0866i	−0.640464	+	1.10932i
$554$	0.180884	−	0.313299i	0.00768500	−	0.0133108i
$555$	−50.5113			−2.14408
$556$	−9.51382	+	16.4784i	−0.403476	+	0.698840i
$557$	−10.3391			−0.438082			−0.219041	−	0.975716i	$-0.570293\pi$
$557$	−10.3391			−0.438082			−0.219041	+	0.975716i	$0.570293\pi$
$558$	−9.54784			−0.404192
$559$	2.41571	−	21.0206i	0.102174	−	0.889077i
$560$	−0.442469			−0.0186977
$561$	13.5455			0.571891
$562$	4.86608	−	8.42830i	0.205263	−	0.355526i
$563$	−25.7885			−1.08686			−0.543429	−	0.839455i	$-0.682874\pi$
$563$	−25.7885			−1.08686			−0.543429	+	0.839455i	$0.682874\pi$
$564$	4.19475	−	7.26552i	0.176631	−	0.305934i
$565$	7.50300	−	12.9956i	0.315653	−	0.546728i
$566$	−6.14125	−	10.6370i	−0.258136	−	0.447105i
$567$	−19.0755			−0.801097
$568$	−8.78056	−	15.2084i	−0.368424	−	0.638129i
$569$	−18.8913	+	32.7207i	−0.791965	+	1.37172i	0.132784	+	0.991145i	$0.457608\pi$
$569$	−18.8913	+	32.7207i	−0.791965	+	1.37172i	−0.924749	+	0.380578i	$0.875725\pi$
$570$	23.0129			0.963904
$571$	19.1637	−	33.1924i	0.801974	−	1.38906i	−0.116341	−	0.993209i	$-0.537117\pi$
$571$	19.1637	−	33.1924i	0.801974	−	1.38906i	0.918315	−	0.395851i	$-0.129550\pi$
$572$	−11.6231	−	20.1318i	−0.485986	−	0.841752i
$573$	22.7930	+	39.4786i	0.952191	+	1.64924i
$574$	−4.15930	−	7.20412i	−0.173606	−	0.300694i
$575$	17.2592			0.719760
$576$	−5.74981	−	9.95896i	−0.239575	−	0.414957i
$577$	5.36843	+	9.29839i	0.223491	+	0.387097i	0.955866	−	0.293805i	$-0.0949215\pi$
$577$	5.36843	+	9.29839i	0.223491	+	0.387097i	−0.732375	+	0.680902i	$0.761588\pi$
$578$	0.442374	−	0.766214i	0.0184003	−	0.0318703i
$579$	7.89640	−	13.6770i	0.328163	−	0.568395i
$580$	24.2765			1.00803
$581$	26.2790			1.09024
$582$	3.80239	−	6.58593i	0.157614	−	0.272995i
$583$	−15.6591	+	27.1224i	−0.648535	+	1.12330i
$584$	−11.4391	−	19.8130i	−0.473352	−	0.819869i
$585$	−10.6820	−	18.5018i	−0.441646	−	0.764954i
$586$	−21.6610			−0.894807
$587$	16.8698	+	29.2194i	0.696292	+	1.20601i	0.969743	+	0.244127i	$0.0785015\pi$
$587$	16.8698	+	29.2194i	0.696292	+	1.20601i	−0.273451	+	0.961886i	$0.588165\pi$
$588$	−5.32797	−	9.22832i	−0.219722	−	0.380569i
$589$	9.26215	+	16.0425i	0.381640	+	0.661021i
$590$	5.87435	−	10.1747i	0.241843	−	0.418885i
$591$	−14.7202			−0.605506
$592$	−0.313032	+	0.542187i	−0.0128655	+	0.0222838i
$593$	−1.03037	−	1.78465i	−0.0423122	−	0.0732868i	0.844094	−	0.536196i	$-0.180139\pi$
$593$	−1.03037	−	1.78465i	−0.0423122	−	0.0732868i	−0.886406	+	0.462909i	$0.846806\pi$
$594$	−9.13497			−0.374812
$595$	2.63597	+	4.56563i	0.108064	+	0.187173i
$596$	1.76074	−	3.04969i	0.0721226	−	0.124920i
$597$	−14.5152	+	25.1411i	−0.594067	+	1.02895i
$598$	−13.1244			−0.536695
$599$	−12.3540	+	21.3978i	−0.504771	+	0.874290i	0.495213	+	0.868771i	$0.335090\pi$
$599$	−12.3540	+	21.3978i	−0.504771	+	0.874290i	−0.999985	+	0.00551824i	$0.998243\pi$
$600$	24.4566			0.998436
$601$	7.70294			0.314210			0.157105	−	0.987582i	$-0.449784\pi$
$601$	7.70294			0.314210			0.157105	+	0.987582i	$0.449784\pi$
$602$	−1.18023	+	10.2699i	−0.0481025	+	0.418569i
$603$	11.3618			0.462690
$604$	28.2760			1.15053
$605$	−35.5499	+	61.5742i	−1.44531	+	2.50335i
$606$	−7.36537			−0.299198
$607$	9.65038	−	16.7150i	0.391697	−	0.678439i	−0.600977	−	0.799267i	$-0.705222\pi$
$607$	9.65038	−	16.7150i	0.391697	−	0.678439i	0.992674	+	0.120828i	$0.0385548\pi$
$608$	−10.7912	+	18.6908i	−0.437639	+	0.758013i
$609$	13.7439	+	23.8052i	0.556933	+	0.964636i
$610$	38.2638			1.54925
$611$	−4.85875	−	8.41560i	−0.196564	−	0.340459i
$612$	−1.36192	+	2.35892i	−0.0550525	+	0.0953537i
$613$	4.94444			0.199704			0.0998520	−	0.995002i	$-0.468163\pi$
$613$	4.94444			0.199704			0.0998520	+	0.995002i	$0.468163\pi$
$614$	14.6425	−	25.3616i	0.590923	−	1.02351i
$615$	17.8658	+	30.9444i	0.720418	+	1.24780i
$616$	15.0090	+	25.9964i	0.604732	+	1.04743i
$617$	12.0895	+	20.9397i	0.486707	+	0.843000i	0.999883	−	0.0152825i	$-0.00486477\pi$
$617$	12.0895	+	20.9397i	0.486707	+	0.843000i	−0.513177	+	0.858283i	$0.671531\pi$
$618$	7.95687			0.320072
$619$	12.3448	+	21.3819i	0.496181	+	0.859410i	0.999990	−	0.00440460i	$-0.00140203\pi$
$619$	12.3448	+	21.3819i	0.496181	+	0.859410i	−0.503810	+	0.863815i	$0.668069\pi$
$620$	8.68403	+	15.0412i	0.348759	+	0.604069i
$621$	4.00991	−	6.94537i	0.160912	−	0.278708i
$622$	−1.37528	+	2.38206i	−0.0551439	+	0.0955120i
$623$	−25.1820			−1.00890
$624$	−0.619791			−0.0248115
$625$	14.8384	−	25.7009i	0.593537	−	1.02804i
$626$	−12.3612	+	21.4102i	−0.494052	+	0.855723i
$627$	−26.0156	−	45.0603i	−1.03896	−	1.79954i
$628$	−8.30055	−	14.3770i	−0.331228	−	0.573704i
$629$	7.45944			0.297427
$630$	5.21883	+	9.03927i	0.207923	+	0.360133i
$631$	0.911709	+	1.57913i	0.0362946	+	0.0628641i	0.883602	−	0.468239i	$-0.155111\pi$
$631$	0.911709	+	1.57913i	0.0362946	+	0.0628641i	−0.847308	+	0.531103i	$0.821778\pi$
$632$	−24.0601	−	41.6733i	−0.957058	−	1.65767i
$633$	12.0869	−	20.9351i	0.480410	−	0.832095i
$634$	−3.19892			−0.127046
$635$	−1.72745	+	2.99202i	−0.0685516	+	0.118735i
$636$	−7.37036	−	12.7658i	−0.292254	−	0.506198i
$637$	−12.3427			−0.489035
$638$	17.6490	+	30.5689i	0.698729	+	1.21023i
$639$	−6.90295	+	11.9563i	−0.273077	+	0.472982i
$640$	−9.89789	+	17.1436i	−0.391248	+	0.677662i
$641$	−31.6504			−1.25012			−0.625058	−	0.780578i	$-0.714925\pi$
$641$	−31.6504			−1.25012			−0.625058	+	0.780578i	$0.714925\pi$
$642$	7.78808	−	13.4894i	0.307371	−	0.532383i
$643$	36.1224			1.42453			0.712264	−	0.701912i	$-0.247670\pi$
$643$	36.1224			1.42453			0.712264	+	0.701912i	$0.247670\pi$
$644$	−9.97078			−0.392904
$645$	5.06953	−	44.1131i	0.199612	−	1.73695i
$646$	−3.39851			−0.133713
$647$	−40.2037			−1.58057			−0.790284	−	0.612740i	$-0.790067\pi$
$647$	−40.2037			−1.58057			−0.790284	+	0.612740i	$0.790067\pi$
$648$	15.2365	−	26.3904i	0.598547	−	1.03671i
$649$	−26.5633			−1.04270
$650$	5.35886	−	9.28182i	0.210192	−	0.364063i
$651$	−9.83278	+	17.0309i	−0.385377	+	0.667492i
$652$	11.7372	+	20.3294i	0.459664	+	0.796161i
$653$	−34.8497			−1.36378			−0.681888	−	0.731457i	$-0.738841\pi$
$653$	−34.8497			−1.36378			−0.681888	+	0.731457i	$0.738841\pi$
$654$	−1.02641	−	1.77779i	−0.0401358	−	0.0695172i
$655$	2.43329	−	4.21458i	0.0950765	−	0.164677i
$656$	0.442876			0.0172914
$657$	−8.99297	+	15.5763i	−0.350849	+	0.607688i
$658$	2.37380	+	4.11154i	0.0925404	+	0.160285i
$659$	−8.35401	−	14.4696i	−0.325426	−	0.563655i	0.656172	−	0.754611i	$-0.272174\pi$
$659$	−8.35401	−	14.4696i	−0.325426	−	0.563655i	−0.981599	+	0.190956i	$0.938841\pi$
$660$	−24.3918	−	42.2478i	−0.949449	−	1.64449i
$661$	−23.3107			−0.906683			−0.453341	−	0.891337i	$-0.649768\pi$
$661$	−23.3107			−0.906683			−0.453341	+	0.891337i	$0.649768\pi$
$662$	8.86230	+	15.3500i	0.344443	+	0.596593i
$663$	3.69235	+	6.39534i	0.143399	+	0.248374i
$664$	−20.9903	+	36.3562i	−0.814581	+	1.41090i
$665$	10.1253	−	17.5376i	0.392644	−	0.680079i
$666$	14.7686			0.572271
$667$	−30.9889			−1.19990
$668$	−9.26663	+	16.0503i	−0.358537	+	0.621004i
$669$	31.8920	−	55.2386i	1.23302	−	2.13565i
$670$	6.64561	+	11.5105i	0.256742	+	0.444691i
$671$	−43.2564	−	74.9223i	−1.66990	−	2.89234i
$672$	−22.9119			−0.883847
$673$	2.17009	+	3.75870i	0.0836507	+	0.144887i	0.904815	−	0.425804i	$-0.140009\pi$
$673$	2.17009	+	3.75870i	0.0836507	+	0.144887i	−0.821165	+	0.570691i	$0.806675\pi$
$674$	3.85120	+	6.67047i	0.148343	+	0.256937i
$675$	3.27461	+	5.67178i	0.126040	+	0.218307i
$676$	−1.57528	+	2.72847i	−0.0605878	+	0.104941i
$677$	35.9756			1.38266			0.691328	−	0.722541i	$-0.257026\pi$
$677$	35.9756			1.38266			0.691328	+	0.722541i	$0.257026\pi$
$678$	−5.13473	+	8.89361i	−0.197198	+	0.341557i
$679$	−3.34599	−	5.79543i	−0.128407	−	0.222408i
$680$	−8.42190			−0.322965
$681$	9.13192	+	15.8169i	0.349936	+	0.606107i
$682$	−12.6265	+	21.8698i	−0.483494	+	0.837437i
$683$	−8.97636	+	15.5475i	−0.343471	+	0.594909i	−0.985075	−	0.172127i	$-0.944936\pi$
$683$	−8.97636	+	15.5475i	−0.343471	+	0.594909i	0.641604	+	0.767036i	$0.278269\pi$
$684$	10.4629			0.400059
$685$	8.89007	−	15.3981i	0.339672	−	0.588329i
$686$	17.0653			0.651557
$687$	−9.20023			−0.351010
$688$	−0.442092	−	0.327797i	−0.0168546	−	0.0124971i
$689$	−17.0741			−0.650470
$690$	−27.5423			−1.04852
$691$	9.68869	−	16.7813i	0.368575	−	0.638391i	−0.620768	−	0.783994i	$-0.713179\pi$
$691$	9.68869	−	16.7813i	0.368575	−	0.638391i	0.989343	+	0.145603i	$0.0465124\pi$
$692$	−2.03178			−0.0772365
$693$	11.7996	−	20.4374i	0.448228	−	0.776354i
$694$	14.3682	−	24.8865i	0.545411	−	0.944680i
$695$	23.1257	+	40.0549i	0.877207	+	1.51937i
$696$	−43.9118			−1.66447
$697$	−2.63840	−	4.56983i	−0.0999363	−	0.173095i
$698$	−13.5844	+	23.5288i	−0.514176	+	0.890578i
$699$	−18.8645			−0.713520
$700$	4.07121	−	7.05154i	0.153877	−	0.266523i
$701$	−8.54187	−	14.7949i	−0.322622	−	0.558797i	0.658406	−	0.752663i	$-0.271231\pi$
$701$	−8.54187	−	14.7949i	−0.322622	−	0.558797i	−0.981028	+	0.193865i	$0.937898\pi$
$702$	−2.49009	−	4.31297i	−0.0939825	−	0.162783i
$703$	−14.3267	−	24.8145i	−0.540341	−	0.935898i
$704$	−30.4153			−1.14632
$705$	−10.1964	−	17.6607i	−0.384018	−	0.665139i
$706$	−0.464654	−	0.804804i	−0.0174875	−	0.0302892i
$707$	−3.24066	+	5.61299i	−0.121878	+	0.211098i
$708$	6.25134	−	10.8276i	0.234940	−	0.406928i
$709$	−2.03338			−0.0763653			−0.0381827	−	0.999271i	$-0.512157\pi$
$709$	−2.03338			−0.0763653			−0.0381827	+	0.999271i	$0.512157\pi$
$710$	−16.1503			−0.606110
$711$	−18.9151	+	32.7620i	−0.709373	+	1.22867i
$712$	20.1141	−	34.8386i	0.753806	−	1.30563i
$713$	−11.0851	−	19.2000i	−0.415142	−	0.719047i
$714$	−1.80394	−	3.12452i	−0.0675109	−	0.116932i
$715$	−56.5056			−2.11319
$716$	3.89825	+	6.75196i	0.145684	+	0.252333i
$717$	18.3471	+	31.7781i	0.685184	+	1.18677i
$718$	9.36751	+	16.2250i	0.349593	+	0.605512i
$719$	5.00777	−	8.67370i	0.186758	−	0.323475i	−0.757409	−	0.652940i	$-0.773535\pi$
$719$	5.00777	−	8.67370i	0.186758	−	0.323475i	0.944168	+	0.329466i	$0.106869\pi$
$720$	−0.555693			−0.0207095
$721$	3.50091	−	6.06376i	0.130381	−	0.225826i
$722$	−1.87788	−	3.25259i	−0.0698875	−	0.121049i
$723$	17.5759			0.653655
$724$	9.11254	+	15.7834i	0.338665	+	0.586585i
$725$	12.6532	−	21.9160i	0.469928	−	0.813940i
$726$	24.3288	−	42.1387i	0.902927	−	1.56391i
$727$	12.8775			0.477598			0.238799	−	0.971069i	$-0.423246\pi$
$727$	12.8775			0.477598			0.238799	+	0.971069i	$0.423246\pi$
$728$	−8.18261	+	14.1727i	−0.303268	+	0.525275i
$729$	−11.9795			−0.443684
$730$	−21.0402			−0.778731
$731$	−0.748661	+	6.51456i	−0.0276902	+	0.240950i
$732$	40.7194			1.50503
$733$	−36.4849			−1.34760			−0.673801	−	0.738913i	$-0.735339\pi$
$733$	−36.4849			−1.34760			−0.673801	+	0.738913i	$0.735339\pi$
$734$	−10.6690	+	18.4793i	−0.393800	+	0.682082i
$735$	−25.9019			−0.955406
$736$	12.9151	−	22.3696i	0.476056	−	0.824553i
$737$	15.0255	−	26.0248i	0.553470	−	0.958637i
$738$	−5.22363	−	9.04759i	−0.192284	−	0.333046i
$739$	−29.7323			−1.09372			−0.546861	−	0.837223i	$-0.684177\pi$
$739$	−29.7323			−1.09372			−0.546861	+	0.837223i	$0.684177\pi$
$740$	−13.4325	−	23.2657i	−0.493787	−	0.855264i
$741$	14.1831	−	24.5659i	0.521031	−	0.902452i
$742$	8.34174			0.306235
$743$	10.2325	−	17.7232i	0.375395	−	0.650203i	−0.614991	−	0.788534i	$-0.710841\pi$
$743$	10.2325	−	17.7232i	0.375395	−	0.650203i	0.990386	+	0.138331i	$0.0441738\pi$
$744$	−15.7078	−	27.2067i	−0.575876	−	0.997447i
$745$	−4.27991	−	7.41302i	−0.156804	−	0.271592i
$746$	−11.1771	−	19.3593i	−0.409223	−	0.708795i
$747$	33.0036			1.20754
$748$	3.60215	+	6.23910i	0.131708	+	0.228124i
$749$	−6.85329	−	11.8703i	−0.250414	−	0.433730i
$750$	−3.73167	+	6.46344i	−0.136261	+	0.236011i
$751$	−5.34838	+	9.26367i	−0.195165	+	0.338036i	−0.946955	−	0.321367i	$-0.895858\pi$
$751$	−5.34838	+	9.26367i	−0.195165	+	0.338036i	0.751789	+	0.659403i	$0.229191\pi$
$752$	−0.252759			−0.00921717
$753$	−23.8663			−0.869735
$754$	−9.62183	+	16.6655i	−0.350406	+	0.606921i
$755$	34.3659	−	59.5234i	1.25070	−	2.16628i
$756$	−1.89176	−	3.27663i	−0.0688027	−	0.119170i
$757$	−14.3441	−	24.8447i	−0.521344	−	0.902995i	−0.999692	−	0.0248240i	$-0.992097\pi$
$757$	−14.3441	−	24.8447i	−0.521344	−	0.902995i	0.478348	−	0.878171i	$-0.341236\pi$
$758$	−9.94050			−0.361055
$759$	31.1360	+	53.9292i	1.13017	+	1.95751i
$760$	16.1752	+	28.0162i	0.586736	+	1.01626i
$761$	−15.1393	−	26.2220i	−0.548798	−	0.950547i	−0.998357	−	0.0572959i	$-0.981752\pi$
$761$	−15.1393	−	26.2220i	−0.548798	−	0.950547i	0.449559	−	0.893251i	$-0.351581\pi$
$762$	1.18219	−	2.04761i	0.0428262	−	0.0741772i
$763$	−1.80642			−0.0653969
$764$	−12.1227	+	20.9971i	−0.438583	+	0.759648i
$765$	3.31049	+	5.73394i	0.119691	+	0.207311i
$766$	15.6874			0.566807
$767$	−7.24088	−	12.5416i	−0.261453	−	0.452850i
$768$	18.5347	−	32.1030i	0.668812	−	1.15842i
$769$	−20.2425	+	35.0611i	−0.729964	+	1.26433i	0.226935	+	0.973910i	$0.427130\pi$
$769$	−20.2425	+	35.0611i	−0.729964	+	1.26433i	−0.956898	+	0.290424i	$0.906204\pi$
$770$	27.6065			0.994870
$771$	−23.8170	+	41.2522i	−0.857747	+	1.48566i
$772$	8.39955			0.302307
$773$	−8.35871			−0.300642			−0.150321	−	0.988637i	$-0.548031\pi$
$773$	−8.35871			−0.300642			−0.150321	+	0.988637i	$0.548031\pi$
$774$	−1.48224	+	12.8979i	−0.0532779	+	0.463604i
$775$	18.1049			0.650346
$776$	10.6904			0.383764
$777$	15.2093	−	26.3433i	0.545631	−	0.945061i
$778$	4.15605			0.149002
$779$	−10.1347	+	17.5537i	−0.363112	+	0.628928i
$780$	13.2979	−	23.0326i	0.476140	−	0.824699i
$781$	18.2576	+	31.6231i	0.653308	+	1.13156i
$782$	4.06741			0.145450
$783$	−5.87954	−	10.1837i	−0.210118	−	0.363935i
$784$	−0.160521	+	0.278031i	−0.00573290	+	0.00992967i
$785$	−40.3531			−1.44026
$786$	−1.66524	+	2.88428i	−0.0593971	+	0.102879i
$787$	−19.8845	−	34.4410i	−0.708807	−	1.22769i	−0.965300	−	0.261144i	$-0.915900\pi$
$787$	−19.8845	−	34.4410i	−0.708807	−	1.22769i	0.256493	−	0.966546i	$-0.417433\pi$
$788$	−3.91453	−	6.78016i	−0.139449	−	0.241533i
$789$	34.7577	+	60.2020i	1.23741	+	2.14325i
$790$	−44.2543			−1.57450
$791$	4.51842	+	7.82613i	0.160656	+	0.278265i
$792$	18.8497	+	32.6487i	0.669796	+	1.16012i
$793$	23.5825	−	40.8460i	0.837438	−	1.45048i
$794$	−4.28142	+	7.41565i	−0.151942	+	0.263171i
$795$	−35.8310			−1.27079
$796$	−15.4401			−0.547259
$797$	−2.47770	+	4.29151i	−0.0877648	+	0.152013i	−0.906566	−	0.422064i	$-0.861306\pi$
$797$	−2.47770	+	4.29151i	−0.0877648	+	0.152013i	0.818801	+	0.574077i	$0.194639\pi$
$798$	−6.92935	+	12.0020i	−0.245296	+	0.424866i
$799$	1.50579	+	2.60810i	0.0532710	+	0.0922680i
$800$	10.5468	+	18.2676i	0.372886	+	0.645858i
$801$	−31.6258			−1.11744
$802$	5.22977	+	9.05823i	0.184670	+	0.319857i
$803$	23.7855	+	41.1976i	0.839371	+	1.45383i
$804$	7.07209	+	12.2492i	0.249414	+	0.431997i
$805$	−12.1182	+	20.9894i	−0.427111	+	0.739779i
$806$	−13.7674			−0.484936
$807$	4.99718	−	8.65537i	0.175909	−	0.304683i
$808$	−5.17694	−	8.96672i	−0.182124	−	0.315448i
$809$	−25.8772			−0.909792			−0.454896	−	0.890545i	$-0.650324\pi$
$809$	−25.8772			−0.909792			−0.454896	+	0.890545i	$0.650324\pi$
$810$	−14.0125	−	24.2703i	−0.492348	−	0.852771i
$811$	10.4194	−	18.0470i	0.365875	−	0.633714i	−0.623041	−	0.782189i	$-0.714103\pi$
$811$	10.4194	−	18.0470i	0.365875	−	0.633714i	0.988916	+	0.148475i	$0.0474364\pi$
$812$	−7.30985	+	12.6610i	−0.256525	+	0.444315i
$813$	−3.68343			−0.129183
$814$	19.5307	−	33.8281i	0.684550	−	1.18568i
$815$	57.0603			1.99873
$816$	0.192081			0.00672419
$817$	23.1092	−	10.0214i	0.808489	−	0.350606i
$818$	17.3352			0.606110
$819$	12.8657			0.449565
$820$	−9.50208	+	16.4581i	−0.331827	+	0.574741i
$821$	−13.9075			−0.485376			−0.242688	−	0.970104i	$-0.578029\pi$
$821$	−13.9075			−0.485376			−0.242688	+	0.970104i	$0.578029\pi$
$822$	−6.08398	+	10.5378i	−0.212203	+	0.367547i
$823$	22.7891	−	39.4720i	0.794380	−	1.37591i	−0.128853	−	0.991664i	$-0.541129\pi$
$823$	22.7891	−	39.4720i	0.794380	−	1.37591i	0.923232	−	0.384242i	$-0.125537\pi$
$824$	5.59269	+	9.68682i	0.194831	+	0.337456i
$825$	−50.8531			−1.77048
$826$	3.53762	+	6.12734i	0.123090	+	0.213197i
$827$	22.1899	−	38.4341i	0.771619	−	1.33648i	−0.165056	−	0.986284i	$-0.552780\pi$
$827$	22.1899	−	38.4341i	0.771619	−	1.33648i	0.936675	−	0.350200i	$-0.113886\pi$
$828$	−12.5222			−0.435177
$829$	−12.5580	+	21.7510i	−0.436156	+	0.755445i	−0.997389	−	0.0722130i	$-0.976994\pi$
$829$	−12.5580	+	21.7510i	−0.436156	+	0.755445i	0.561233	+	0.827658i	$0.310327\pi$
$830$	19.3040	+	33.4355i	0.670051	+	1.16056i
$831$	−0.467899	−	0.810425i	−0.0162312	−	0.0281133i
$832$	−8.29088	−	14.3602i	−0.287435	−	0.497851i
$833$	3.82516			0.132534
$834$	−15.8262	−	27.4118i	−0.548017	−	0.949194i
$835$	22.5248	+	39.0142i	0.779504	+	1.35014i
$836$	13.8366	−	23.9658i	0.478550	−	0.828874i
$837$	4.20638	−	7.28566i	0.145394	−	0.251829i
$838$	28.7653			0.993681
$839$	18.2028			0.628430			0.314215	−	0.949352i	$-0.398259\pi$
$839$	18.2028			0.628430			0.314215	+	0.949352i	$0.398259\pi$
$840$	−17.1717	+	29.7423i	−0.592480	+	1.02621i
$841$	−8.21880	+	14.2354i	−0.283407	+	0.490875i
$842$	−0.265042	−	0.459065i	−0.00913393	−	0.0158204i
$843$	−12.5873	−	21.8018i	−0.433529	−	0.750895i
$844$	12.8570			0.442558
$845$	3.82911	+	6.63222i	0.131726	+	0.228155i
$846$	2.98124	+	5.16365i	0.102497	+	0.177530i
$847$	−21.4087	−	37.0809i	−0.735610	−	1.27411i
$848$	−0.222054	+	0.384609i	−0.00762537	+	0.0132075i
$849$	−31.7717			−1.09040
$850$	−1.66078	+	2.87656i	−0.0569643	+	0.0986651i
$851$	17.1465	+	29.6986i	0.587774	+	1.01805i
$852$	−17.1868			−0.588809
$853$	17.3666	+	30.0798i	0.594620	+	1.02991i	0.993600	+	0.112952i	$0.0360306\pi$
$853$	17.3666	+	30.0798i	0.594620	+	1.02991i	−0.398981	+	0.916959i	$0.630636\pi$
$854$	−11.5215	+	19.9558i	−0.394258	+	0.682875i
$855$	12.7163	−	22.0253i	0.434889	−	0.753250i
$856$	21.8962			0.748397
$857$	−11.5491	+	20.0037i	−0.394510	+	0.683312i	−0.993039	−	0.117790i	$-0.962419\pi$
$857$	−11.5491	+	20.0037i	−0.394510	+	0.683312i	0.598528	+	0.801102i	$0.295752\pi$
$858$	38.6700			1.32017
$859$	40.5821			1.38464			0.692322	−	0.721589i	$-0.256588\pi$
$859$	40.5821			1.38464			0.692322	+	0.721589i	$0.256588\pi$
$860$	21.6668	−	9.39593i	0.738831	−	0.320399i
$861$	−21.5181			−0.733334
$862$	6.26611			0.213425
$863$	−10.9241	+	18.9210i	−0.371859	+	0.644079i	−0.989852	−	0.142105i	$-0.954613\pi$
$863$	−10.9241	+	18.9210i	−0.371859	+	0.644079i	0.617992	+	0.786184i	$0.287946\pi$
$864$	9.80154			0.333455
$865$	−2.46937	+	4.27707i	−0.0839610	+	0.145425i
$866$	−13.2195	+	22.8968i	−0.449217	+	0.778066i
$867$	−1.14431	−	1.98200i	−0.0388627	−	0.0673122i
$868$	−10.4593			−0.355012
$869$	50.0286	+	86.6521i	1.69710	+	2.93947i
$870$	−20.1920	+	34.9736i	−0.684573	+	1.18571i
$871$	16.3831			0.555120
$872$	1.44288	−	2.49913i	0.0488619	−	0.0846313i
$873$	−4.20220	−	7.27843i	−0.142223	−	0.246338i
$874$	−7.81192	−	13.5306i	−0.264242	−	0.457681i
$875$	3.28376	+	5.68765i	0.111011	+	0.192278i
$876$	−22.3904			−0.756502
$877$	−8.09911	−	14.0281i	−0.273488	−	0.473694i	0.696265	−	0.717785i	$-0.254844\pi$
$877$	−8.09911	−	14.0281i	−0.273488	−	0.473694i	−0.969752	+	0.244091i	$0.921511\pi$
$878$	11.7395	+	20.3334i	0.396189	+	0.686219i
$879$	−28.0157	+	48.5246i	−0.944946	+	1.63669i
$880$	−0.734875	+	1.27284i	−0.0247726	+	0.0429075i
$881$	24.1516			0.813689			0.406844	−	0.913497i	$-0.366629\pi$
$881$	24.1516			0.813689			0.406844	+	0.913497i	$0.366629\pi$
$882$	7.57325			0.255004
$883$	5.89103	−	10.2036i	0.198249	−	0.343378i	−0.749712	−	0.661765i	$-0.769808\pi$
$883$	5.89103	−	10.2036i	0.198249	−	0.343378i	0.947961	+	0.318387i	$0.103141\pi$
$884$	−1.96381	+	3.40142i	−0.0660501	+	0.114402i
$885$	−15.1954	−	26.3193i	−0.510789	−	0.884712i
$886$	−0.0765615	−	0.132608i	−0.00257214	−	0.00445507i
$887$	14.9530			0.502073			0.251036	−	0.967978i	$-0.419229\pi$
$887$	14.9530			0.502073			0.251036	+	0.967978i	$0.419229\pi$
$888$	24.2968	+	42.0833i	0.815348	+	1.41222i
$889$	−1.04029	−	1.80184i	−0.0348903	−	0.0604318i
$890$	−18.4981	−	32.0397i	−0.620059	−	1.07397i
$891$	−31.6816	+	54.8742i	−1.06137	+	1.83835i
$892$	33.9241			1.13586
$893$	5.78407	−	10.0183i	0.193557	−	0.335250i
$894$	2.92899	+	5.07315i	0.0979599	+	0.169672i
$895$	18.9513			0.633472
$896$	−5.96066	−	10.3242i	−0.199132	−	0.344906i
$897$	−16.9747	+	29.4010i	−0.566768	+	0.981671i
$898$	5.42300	−	9.39291i	0.180968	−	0.313445i
$899$	−32.5073			−1.08418
$900$	5.11300	−	8.85597i	0.170433	−	0.295199i
$901$	5.29147			0.176284
$902$	−27.6319			−0.920042
$903$	21.4800	+	15.9267i	0.714808	+	0.530007i
$904$	−14.4363			−0.480144
$905$	44.3006			1.47260
$906$	−23.5185	+	40.7353i	−0.781350	+	1.35334i
$907$	−10.6484			−0.353573			−0.176787	−	0.984249i	$-0.556570\pi$
$907$	−10.6484			−0.353573			−0.176787	+	0.984249i	$0.556570\pi$
$908$	−4.85690	+	8.41239i	−0.161182	+	0.279175i
$909$	−4.06992	+	7.04930i	−0.134991	+	0.233811i
$910$	7.52523	+	13.0341i	0.249459	+	0.432076i
$911$	40.7942			1.35157			0.675786	−	0.737098i	$-0.263804\pi$
$911$	40.7942			1.35157			0.675786	+	0.737098i	$0.263804\pi$
$912$	−0.368914	−	0.638977i	−0.0122159	−	0.0211586i
$913$	43.6455	−	75.5963i	1.44446	−	2.50187i
$914$	20.3882			0.674380
$915$	49.4893	−	85.7179i	1.63606	−	2.83375i
$916$	−2.44661	−	4.23766i	−0.0808384	−	0.140016i
$917$	1.46536	+	2.53808i	0.0483906	+	0.0838149i
$918$	0.771712	+	1.33664i	0.0254703	+	0.0441159i
$919$	−18.7927			−0.619915			−0.309957	−	0.950750i	$-0.600315\pi$
$919$	−18.7927			−0.619915			−0.309957	+	0.950750i	$0.600315\pi$
$920$	−19.3588	−	33.5304i	−0.638241	−	1.10547i
$921$	−37.8764	−	65.6038i	−1.24807	−	2.16172i
$922$	−12.2640	+	21.2418i	−0.403892	+	0.699562i
$923$	−9.95365	+	17.2402i	−0.327628	+	0.567469i
$924$	29.3782			0.966471
$925$	−28.0046			−0.920785
$926$	16.5123	−	28.6001i	0.542627	−	0.939858i
$927$	4.39676	−	7.61542i	0.144409	−	0.250123i
$928$	−18.9368	−	32.7995i	−0.621630	−	1.07669i
$929$	2.95710	+	5.12185i	0.0970193	+	0.168042i	0.910450	−	0.413620i	$-0.135736\pi$
$929$	2.95710	+	5.12185i	0.0970193	+	0.168042i	−0.813430	+	0.581662i	$0.802402\pi$
$930$	−28.8918			−0.947398
$931$	−7.34665	−	12.7248i	−0.240777	−	0.417037i
$932$	−5.01663	−	8.68905i	−0.164325	−	0.284619i
$933$	3.55751	+	6.16179i	0.116468	+	0.201728i
$934$	9.79593	−	16.9670i	0.320533	−	0.555179i
$935$	17.5118			0.572698
$936$	−10.2765	+	17.7994i	−0.335897	+	0.581790i
$937$	−8.39578	−	14.5419i	−0.274278	−	0.475064i	0.695675	−	0.718357i	$-0.255106\pi$
$937$	−8.39578	−	14.5419i	−0.274278	−	0.475064i	−0.969953	+	0.243293i	$0.921772\pi$
$938$	−8.00417			−0.261345
$939$	31.9752	+	55.3827i	1.04347	+	1.80734i
$940$	5.42304	−	9.39299i	0.176880	−	0.306365i
$941$	15.4867	−	26.8237i	0.504852	−	0.874429i	−0.495133	−	0.868817i	$-0.664881\pi$
$941$	15.4867	−	26.8237i	0.504852	−	0.874429i	0.999984	−	0.00561124i	$-0.00178612\pi$
$942$	27.6159			0.899775
$943$	12.1294	−	21.0087i	0.394987	−	0.684137i
$944$	−0.376681			−0.0122599
$945$	−9.19679			−0.299172
$946$	27.5830	+	20.4519i	0.896800	+	0.664948i
$947$	9.57496			0.311144			0.155572	−	0.987825i	$-0.450278\pi$
$947$	9.57496			0.311144			0.155572	+	0.987825i	$0.450278\pi$
$948$	−47.0944			−1.52955
$949$	−12.9673	+	22.4601i	−0.420937	+	0.729084i
$950$	12.7589			0.413952
$951$	−4.13740	+	7.16618i	−0.134164	+	0.232379i
$952$	2.53590	−	4.39230i	0.0821888	−	0.142355i
$953$	−8.27797	−	14.3379i	−0.268150	−	0.464449i	0.700234	−	0.713913i	$-0.253079\pi$
$953$	−8.27797	−	14.3379i	−0.268150	−	0.464449i	−0.968384	+	0.249464i	$0.919746\pi$
$954$	10.4763			0.339183
$955$	29.4672	+	51.0386i	0.953535	+	1.65157i
$956$	−9.75807	+	16.9015i	−0.315598	+	0.546633i
$957$	91.3066			2.95152
$958$	−2.91833	+	5.05469i	−0.0942869	+	0.163310i
$959$	5.35373	+	9.27294i	0.172881	+	0.299439i
$960$	−17.3989	−	30.1358i	−0.561548	−	0.972630i
$961$	3.87173	+	6.70603i	0.124895	+	0.216324i
$962$	21.2954			0.686592
$963$	−8.60699	−	14.9078i	−0.277357	−	0.480396i
$964$	4.67396	+	8.09553i	0.150538	+	0.260740i
$965$	10.2086	−	17.6818i	0.328626	−	0.569197i
$966$	8.29319	−	14.3642i	0.266829	−	0.462162i
$967$	13.6478			0.438882			0.219441	−	0.975626i	$-0.429577\pi$
$967$	13.6478			0.438882			0.219441	+	0.975626i	$0.429577\pi$
$968$	68.4005			2.19847
$969$	−4.39554	+	7.61330i	−0.141205	+	0.244574i
$970$	4.91579	−	8.51439i	0.157836	−	0.273381i
$971$	−2.35077	−	4.07165i	−0.0754398	−	0.130665i	0.825838	−	0.563908i	$-0.190703\pi$
$971$	−2.35077	−	4.07165i	−0.0754398	−	0.130665i	−0.901277	+	0.433242i	$0.857369\pi$
$972$	−11.7266	−	20.3111i	−0.376131	−	0.651478i
$973$	−27.8533			−0.892934
$974$	−16.8845	−	29.2447i	−0.541013	−	0.937062i
$975$	−13.8620	−	24.0097i	−0.443939	−	0.768926i
$976$	−0.613397	−	1.06243i	−0.0196343	−	0.0340077i
$977$	−19.8223	+	34.3333i	−0.634172	+	1.09842i	0.352518	+	0.935805i	$0.385326\pi$
$977$	−19.8223	+	34.3333i	−0.634172	+	1.09842i	−0.986690	+	0.162613i	$0.948008\pi$
$978$	−39.0496			−1.24867
$979$	−41.8236	+	72.4405i	−1.33669	+	2.31521i
$980$	−6.88809	−	11.9305i	−0.220032	−	0.381106i
$981$	−2.26867			−0.0724331
$982$	13.0935	+	22.6786i	0.417831	+	0.723705i
$983$	0.969961	−	1.68002i	0.0309370	−	0.0535844i	−0.850142	−	0.526553i	$-0.823484\pi$
$983$	0.969961	−	1.68002i	0.0309370	−	0.0535844i	0.881079	+	0.472968i	$0.156818\pi$
$984$	17.1875	−	29.7696i	0.547918	−	0.949021i
$985$	−19.0305			−0.606361
$986$	2.98193	−	5.16485i	0.0949639	−	0.164482i
$987$	12.2808			0.390903
$988$	15.0869			0.479977
$989$	−27.6576	+	11.9939i	−0.879460	+	0.381383i
$990$	34.6708			1.10191
$991$	44.5170			1.41413			0.707064	−	0.707150i	$-0.250019\pi$
$991$	44.5170			1.41413			0.707064	+	0.707150i	$0.250019\pi$
$992$	13.5479	−	23.4656i	0.430145	−	0.745033i
$993$	45.8490			1.45497
$994$	4.86298	−	8.42292i	0.154244	−	0.267159i
$995$	−18.7655	+	32.5028i	−0.594906	+	1.03041i
$996$	20.5428	+	35.5812i	0.650924	+	1.12743i
$997$	−21.9532			−0.695265			−0.347632	−	0.937631i	$-0.613014\pi$
$997$	−21.9532			−0.695265			−0.347632	+	0.937631i	$0.613014\pi$
$998$	−3.55499	−	6.15742i	−0.112531	−	0.194910i
$999$	−6.50642	+	11.2695i	−0.205854	+	0.356550i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.e.a.307.12	✓	58
43.36	even	3	inner	731.2.e.a.681.12	yes	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.e.a.307.12	✓	58	1.1	even	1	trivial
731.2.e.a.681.12	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)

\(f(q)\)	\(=\)	\(q-0.884748 q^{2} +(-1.14431 + 1.98200i) q^{3} -1.21722 q^{4} +(-1.47938 + 2.56236i) q^{5} +(1.01242 - 1.75357i) q^{6} +(-0.890904 - 1.54309i) q^{7} +2.84643 q^{8} +(-1.11888 - 1.93795i) q^{9} +O(q^{10})\)	\(q-0.884748 q^{2} +(-1.14431 + 1.98200i) q^{3} -1.21722 q^{4} +(-1.47938 + 2.56236i) q^{5} +(1.01242 - 1.75357i) q^{6} +(-0.890904 - 1.54309i) q^{7} +2.84643 q^{8} +(-1.11888 - 1.93795i) q^{9} +(1.30888 - 2.26704i) q^{10} -5.91864 q^{11} +(1.39288 - 2.41253i) q^{12} +(-1.61336 - 2.79442i) q^{13} +(0.788225 + 1.36525i) q^{14} +(-3.38573 - 5.86425i) q^{15} -0.0839291 q^{16} +(0.500000 + 0.866025i) q^{17} +(0.989925 + 1.71460i) q^{18} +(1.92061 - 3.32660i) q^{19} +(1.80073 - 3.11896i) q^{20} +4.07787 q^{21} +5.23650 q^{22} +(-2.29863 + 3.98134i) q^{23} +(-3.25719 + 5.64162i) q^{24} +(-1.87712 - 3.25127i) q^{25} +(1.42741 + 2.47235i) q^{26} -1.74448 q^{27} +(1.08443 + 1.87828i) q^{28} +(3.37037 + 5.83765i) q^{29} +(2.99552 + 5.18839i) q^{30} +(-2.41125 + 4.17641i) q^{31} -5.61860 q^{32} +(6.77274 - 11.7307i) q^{33} +(-0.442374 - 0.766214i) q^{34} +5.27194 q^{35} +(1.36192 + 2.35892i) q^{36} +(3.72972 - 6.46006i) q^{37} +(-1.69926 + 2.94320i) q^{38} +7.38470 q^{39} +(-4.21095 + 7.29358i) q^{40} -5.27679 q^{41} -3.60789 q^{42} +(5.26744 + 3.90564i) q^{43} +7.20429 q^{44} +6.62098 q^{45} +(2.03371 - 3.52248i) q^{46} +3.01158 q^{47} +(0.0960407 - 0.166347i) q^{48} +(1.91258 - 3.31269i) q^{49} +(1.66078 + 2.87656i) q^{50} -2.28861 q^{51} +(1.96381 + 3.40142i) q^{52} +(2.64573 - 4.58255i) q^{53} +1.54342 q^{54} +(8.75591 - 15.1657i) q^{55} +(-2.53590 - 4.39230i) q^{56} +(4.39554 + 7.61330i) q^{57} +(-2.98193 - 5.16485i) q^{58} +4.48808 q^{59} +(4.12118 + 7.13810i) q^{60} +(7.30851 + 12.6587i) q^{61} +(2.13335 - 3.69507i) q^{62} +(-1.99363 + 3.45306i) q^{63} +5.13890 q^{64} +9.54706 q^{65} +(-5.99217 + 10.3787i) q^{66} +(-2.53867 + 4.39710i) q^{67} +(-0.608611 - 1.05414i) q^{68} +(-5.26067 - 9.11176i) q^{69} -4.66434 q^{70} +(-3.08476 - 5.34297i) q^{71} +(-3.18481 - 5.51625i) q^{72} +(-4.01874 - 6.96066i) q^{73} +(-3.29986 + 5.71553i) q^{74} +8.59203 q^{75} +(-2.33781 + 4.04920i) q^{76} +(5.27294 + 9.13300i) q^{77} -6.53360 q^{78} +(-8.45272 - 14.6405i) q^{79} +(0.124163 - 0.215056i) q^{80} +(5.35286 - 9.27142i) q^{81} +4.66863 q^{82} +(-7.37425 + 12.7726i) q^{83} -4.96367 q^{84} -2.95876 q^{85} +(-4.66036 - 3.45551i) q^{86} -15.4270 q^{87} -16.8470 q^{88} +(7.06642 - 12.2394i) q^{89} -5.85790 q^{90} +(-2.87469 + 4.97911i) q^{91} +(2.79794 - 4.84617i) q^{92} +(-5.51843 - 9.55819i) q^{93} -2.66449 q^{94} +(5.68262 + 9.84259i) q^{95} +(6.42941 - 11.1361i) q^{96} +3.75573 q^{97} +(-1.69215 + 2.93089i) q^{98} +(6.62224 + 11.4701i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9}+O(q^{10}) \) 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9	\( 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9} + 4 q^{10} + 16 q^{11} + 12 q^{12} + 2 q^{13} - 11 q^{14} + 7 q^{15} + 30 q^{16} + 29 q^{17} + 8 q^{18} + 8 q^{19} - 33 q^{20} - 26 q^{21} - 22 q^{22} - 5 q^{23} + 12 q^{24} - 36 q^{25} - 12 q^{27} + 15 q^{28} + 2 q^{29} + 11 q^{30} + 3 q^{31} - 40 q^{32} + 17 q^{33} - 3 q^{34} + 38 q^{35} - 7 q^{36} + 2 q^{37} + q^{38} - 54 q^{39} + 5 q^{40} + 14 q^{41} - 112 q^{42} + 31 q^{43} - 24 q^{44} - 46 q^{45} - 13 q^{46} - 28 q^{47} - 28 q^{49} - 13 q^{50} + 6 q^{51} + 85 q^{52} - 10 q^{53} + 34 q^{54} + 36 q^{55} - 54 q^{56} - 23 q^{57} + 3 q^{58} + 12 q^{59} + 2 q^{60} - q^{61} - q^{62} - 14 q^{63} + 28 q^{64} + 80 q^{65} - 74 q^{66} + 11 q^{67} + 27 q^{68} - 11 q^{69} + 2 q^{70} + 16 q^{71} + 21 q^{72} + 14 q^{73} + 21 q^{74} - 54 q^{75} + 44 q^{76} + 25 q^{77} + 88 q^{78} - 4 q^{79} - 112 q^{80} + 11 q^{81} - 176 q^{82} - 3 q^{83} + 100 q^{84} - 2 q^{85} + 44 q^{86} + 8 q^{87} - 106 q^{88} + 82 q^{89} + 54 q^{90} - 15 q^{91} + 42 q^{92} + 88 q^{94} + 29 q^{95} + 20 q^{96} + 20 q^{97} + 44 q^{98} - 54 q^{99}+O(q^{100}) \) 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9 + 4 * q^10 + 16 * q^11 + 12 * q^12 + 2 * q^13 - 11 * q^14 + 7 * q^15 + 30 * q^16 + 29 * q^17 + 8 * q^18 + 8 * q^19 - 33 * q^20 - 26 * q^21 - 22 * q^22 - 5 * q^23 + 12 * q^24 - 36 * q^25 - 12 * q^27 + 15 * q^28 + 2 * q^29 + 11 * q^30 + 3 * q^31 - 40 * q^32 + 17 * q^33 - 3 * q^34 + 38 * q^35 - 7 * q^36 + 2 * q^37 + q^38 - 54 * q^39 + 5 * q^40 + 14 * q^41 - 112 * q^42 + 31 * q^43 - 24 * q^44 - 46 * q^45 - 13 * q^46 - 28 * q^47 - 28 * q^49 - 13 * q^50 + 6 * q^51 + 85 * q^52 - 10 * q^53 + 34 * q^54 + 36 * q^55 - 54 * q^56 - 23 * q^57 + 3 * q^58 + 12 * q^59 + 2 * q^60 - q^61 - q^62 - 14 * q^63 + 28 * q^64 + 80 * q^65 - 74 * q^66 + 11 * q^67 + 27 * q^68 - 11 * q^69 + 2 * q^70 + 16 * q^71 + 21 * q^72 + 14 * q^73 + 21 * q^74 - 54 * q^75 + 44 * q^76 + 25 * q^77 + 88 * q^78 - 4 * q^79 - 112 * q^80 + 11 * q^81 - 176 * q^82 - 3 * q^83 + 100 * q^84 - 2 * q^85 + 44 * q^86 + 8 * q^87 - 106 * q^88 + 82 * q^89 + 54 * q^90 - 15 * q^91 + 42 * q^92 + 88 * q^94 + 29 * q^95 + 20 * q^96 + 20 * q^97 + 44 * q^98 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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