LMFDB - Embedded newform 399.2.j.g.58.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [399,2,Mod(58,399)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(399, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("399.58");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 399 = 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	399.j (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.18603104065$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 13 x^{14} - 2 x^{13} + 118 x^{12} - 16 x^{11} + 534 x^{10} - 21 x^{9} + 1743 x^{8} - 101 x^{7} + \cdots + 256 $ x^16 + 13x^14 - 2x^13 + 118x^12 - 16x^11 + 534x^10 - 21x^9 + 1743x^8 - 101x^7 + 2902x^6 - 401x^5 + 3427x^4 - 294x^3 + 1076x^2 + 96x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			58.3
Root			$0.624863 - 1.08229i$ of defining polynomial
Character	$\chi$	$=$	399.58
Dual form			399.2.j.g.172.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.624863 + 1.08229i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.219092 + 0.379479i) q^{4} +(-1.99797 + 3.46058i) q^{5} -1.24973 q^{6} +(2.16069 - 1.52690i) q^{7} -3.04706 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.624863 + 1.08229i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.219092 + 0.379479i) q^{4} +(-1.99797 + 3.46058i) q^{5} -1.24973 q^{6} +(2.16069 - 1.52690i) q^{7} -3.04706 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.49691 - 4.32477i) q^{10} +(1.18430 + 2.05127i) q^{11} +(-0.219092 + 0.379479i) q^{12} -2.18914 q^{13} +(0.302425 + 3.29260i) q^{14} -3.99593 q^{15} +(1.46581 - 2.53886i) q^{16} +(1.13610 + 1.96778i) q^{17} +(-0.624863 - 1.08229i) q^{18} +(0.500000 - 0.866025i) q^{19} -1.75095 q^{20} +(2.40268 + 1.10776i) q^{21} -2.96011 q^{22} +(4.29933 - 7.44667i) q^{23} +(-1.52353 - 2.63883i) q^{24} +(-5.48373 - 9.49810i) q^{25} +(1.36791 - 2.36929i) q^{26} -1.00000 q^{27} +(1.05282 + 0.485402i) q^{28} -0.735824 q^{29} +(2.49691 - 4.32477i) q^{30} +(4.95449 + 8.58143i) q^{31} +(-1.21520 - 2.10479i) q^{32} +(-1.18430 + 2.05127i) q^{33} -2.83963 q^{34} +(0.966988 + 10.5279i) q^{35} -0.438184 q^{36} +(-4.09719 + 7.09654i) q^{37} +(0.624863 + 1.08229i) q^{38} +(-1.09457 - 1.89585i) q^{39} +(6.08793 - 10.5446i) q^{40} -8.35871 q^{41} +(-2.70027 + 1.90821i) q^{42} -0.800311 q^{43} +(-0.518943 + 0.898836i) q^{44} +(-1.99797 - 3.46058i) q^{45} +(5.37299 + 9.30629i) q^{46} +(2.46065 - 4.26197i) q^{47} +2.93163 q^{48} +(2.33713 - 6.59832i) q^{49} +13.7063 q^{50} +(-1.13610 + 1.96778i) q^{51} +(-0.479623 - 0.830732i) q^{52} +(1.63914 + 2.83908i) q^{53} +(0.624863 - 1.08229i) q^{54} -9.46479 q^{55} +(-6.58375 + 4.65257i) q^{56} +1.00000 q^{57} +(0.459790 - 0.796379i) q^{58} +(1.78048 + 3.08389i) q^{59} +(-0.875477 - 1.51637i) q^{60} +(-1.37809 + 2.38693i) q^{61} -12.3835 q^{62} +(0.241993 + 2.63466i) q^{63} +8.90058 q^{64} +(4.37382 - 7.57568i) q^{65} +(-1.48005 - 2.56353i) q^{66} +(1.85054 + 3.20523i) q^{67} +(-0.497821 + 0.862252i) q^{68} +8.59867 q^{69} +(-11.9985 - 5.53194i) q^{70} +7.30367 q^{71} +(1.52353 - 2.63883i) q^{72} +(3.69123 + 6.39340i) q^{73} +(-5.12036 - 8.86873i) q^{74} +(5.48373 - 9.49810i) q^{75} +0.438184 q^{76} +(5.69100 + 2.62384i) q^{77} +2.73582 q^{78} +(-0.458446 + 0.794052i) q^{79} +(5.85729 + 10.1451i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.22305 - 9.04658i) q^{82} +4.91925 q^{83} +(0.106038 + 1.15447i) q^{84} -9.07955 q^{85} +(0.500085 - 0.866173i) q^{86} +(-0.367912 - 0.637243i) q^{87} +(-3.60865 - 6.25036i) q^{88} +(-8.85073 + 15.3299i) q^{89} +4.99382 q^{90} +(-4.73004 + 3.34260i) q^{91} +3.76780 q^{92} +(-4.95449 + 8.58143i) q^{93} +(3.07514 + 5.32630i) q^{94} +(1.99797 + 3.46058i) q^{95} +(1.21520 - 2.10479i) q^{96} +13.3590 q^{97} +(5.68093 + 6.65251i) q^{98} -2.36861 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{3} - 10 q^{4} + 5 q^{5} + q^{7} - 6 q^{8} - 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^3 - 10 * q^4 + 5 * q^5 + q^7 - 6 * q^8 - 8 * q^9	\( 16 q + 8 q^{3} - 10 q^{4} + 5 q^{5} + q^{7} - 6 q^{8} - 8 q^{9} + 3 q^{10} + 7 q^{11} + 10 q^{12} - 12 q^{13} - 12 q^{14} + 10 q^{15} - 10 q^{16} + 8 q^{19} - 32 q^{20} - q^{21} + 36 q^{22} + 9 q^{23} - 3 q^{24} - 15 q^{25} + 12 q^{26} - 16 q^{27} - 40 q^{28} + 8 q^{29} - 3 q^{30} + 11 q^{31} + 26 q^{32} - 7 q^{33} - 32 q^{34} - 7 q^{35} + 20 q^{36} - 17 q^{37} - 6 q^{39} + 3 q^{40} - 34 q^{41} - 9 q^{42} + 16 q^{43} + 31 q^{44} + 5 q^{45} - q^{46} + 29 q^{47} - 20 q^{48} + q^{49} + 60 q^{50} + 25 q^{52} + 6 q^{53} - 42 q^{55} - 54 q^{56} + 16 q^{57} + 37 q^{58} + 7 q^{59} - 16 q^{60} + 2 q^{61} - 78 q^{62} - 2 q^{63} + 58 q^{64} + 13 q^{65} + 18 q^{66} - 13 q^{67} - 14 q^{68} + 18 q^{69} - 81 q^{70} + 36 q^{71} + 3 q^{72} + 20 q^{73} + 26 q^{74} + 15 q^{75} - 20 q^{76} + 19 q^{77} + 24 q^{78} + 3 q^{79} + 35 q^{80} - 8 q^{81} + 5 q^{82} - 72 q^{83} - 29 q^{84} + 10 q^{85} + 51 q^{86} + 4 q^{87} - 53 q^{88} + q^{89} - 6 q^{90} - 9 q^{91} + 30 q^{92} - 11 q^{93} + 30 q^{94} - 5 q^{95} - 26 q^{96} + 6 q^{97} - 75 q^{98} - 14 q^{99}+O(q^{100}) \) 16 * q + 8 * q^3 - 10 * q^4 + 5 * q^5 + q^7 - 6 * q^8 - 8 * q^9 + 3 * q^10 + 7 * q^11 + 10 * q^12 - 12 * q^13 - 12 * q^14 + 10 * q^15 - 10 * q^16 + 8 * q^19 - 32 * q^20 - q^21 + 36 * q^22 + 9 * q^23 - 3 * q^24 - 15 * q^25 + 12 * q^26 - 16 * q^27 - 40 * q^28 + 8 * q^29 - 3 * q^30 + 11 * q^31 + 26 * q^32 - 7 * q^33 - 32 * q^34 - 7 * q^35 + 20 * q^36 - 17 * q^37 - 6 * q^39 + 3 * q^40 - 34 * q^41 - 9 * q^42 + 16 * q^43 + 31 * q^44 + 5 * q^45 - q^46 + 29 * q^47 - 20 * q^48 + q^49 + 60 * q^50 + 25 * q^52 + 6 * q^53 - 42 * q^55 - 54 * q^56 + 16 * q^57 + 37 * q^58 + 7 * q^59 - 16 * q^60 + 2 * q^61 - 78 * q^62 - 2 * q^63 + 58 * q^64 + 13 * q^65 + 18 * q^66 - 13 * q^67 - 14 * q^68 + 18 * q^69 - 81 * q^70 + 36 * q^71 + 3 * q^72 + 20 * q^73 + 26 * q^74 + 15 * q^75 - 20 * q^76 + 19 * q^77 + 24 * q^78 + 3 * q^79 + 35 * q^80 - 8 * q^81 + 5 * q^82 - 72 * q^83 - 29 * q^84 + 10 * q^85 + 51 * q^86 + 4 * q^87 - 53 * q^88 + q^89 - 6 * q^90 - 9 * q^91 + 30 * q^92 - 11 * q^93 + 30 * q^94 - 5 * q^95 - 26 * q^96 + 6 * q^97 - 75 * q^98 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/399\mathbb{Z}\right)^\times$.

$n$	$115$	$134$	$211$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.624863	+	1.08229i	−0.441845	+	0.765298i	−0.997826	−	0.0658968i	$-0.979009\pi$
$2$	−0.624863	+	1.08229i	−0.441845	+	0.765298i	0.555982	+	0.831195i	$0.312343\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.219092	+	0.379479i	0.109546	+	0.189739i
$5$	−1.99797	+	3.46058i	−0.893517	+	1.54762i	−0.0578880	+	0.998323i	$0.518437\pi$
$5$	−1.99797	+	3.46058i	−0.893517	+	1.54762i	−0.835629	+	0.549294i	$0.814897\pi$
$6$	−1.24973			−0.510199
$7$	2.16069	−	1.52690i	0.816663	−	0.577115i
$7$	2.16069	−	1.52690i	0.816663	−	0.577115i
$8$	−3.04706			−1.07730
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−2.49691	−	4.32477i	−0.789592	−	1.36761i
$11$	1.18430	+	2.05127i	0.357081	+	0.618482i	0.987472	−	0.157796i	$-0.0504387\pi$
$11$	1.18430	+	2.05127i	0.357081	+	0.618482i	−0.630391	+	0.776278i	$0.717105\pi$
$12$	−0.219092	+	0.379479i	−0.0632465	+	0.109546i
$13$	−2.18914			−0.607158			−0.303579	−	0.952806i	$-0.598182\pi$
$13$	−2.18914			−0.607158			−0.303579	+	0.952806i	$0.598182\pi$
$14$	0.302425	+	3.29260i	0.0808266	+	0.879986i
$15$	−3.99593			−1.03174
$16$	1.46581	−	2.53886i	0.366453	−	0.634716i
$17$	1.13610	+	1.96778i	0.275545	+	0.477257i	0.970272	−	0.242016i	$-0.0778085\pi$
$17$	1.13610	+	1.96778i	0.275545	+	0.477257i	−0.694728	+	0.719273i	$0.744475\pi$
$18$	−0.624863	−	1.08229i	−0.147282	−	0.255099i
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i
$20$	−1.75095			−0.391525
$21$	2.40268	+	1.10776i	0.524308	+	0.241733i
$22$	−2.96011			−0.631098
$23$	4.29933	−	7.44667i	0.896473	−	1.55274i	0.0645026	−	0.997918i	$-0.479454\pi$
$23$	4.29933	−	7.44667i	0.896473	−	1.55274i	0.831971	−	0.554820i	$-0.187213\pi$
$24$	−1.52353	−	2.63883i	−0.310990	−	0.538650i
$25$	−5.48373	−	9.49810i	−1.09675	−	1.89962i
$26$	1.36791	−	2.36929i	0.268270	−	0.464657i
$27$	−1.00000			−0.192450
$28$	1.05282	+	0.485402i	0.198964	+	0.0917324i
$29$	−0.735824			−0.136639			−0.0683196	−	0.997663i	$-0.521764\pi$
$29$	−0.735824			−0.136639			−0.0683196	+	0.997663i	$0.521764\pi$
$30$	2.49691	−	4.32477i	0.455871	−	0.789592i
$31$	4.95449	+	8.58143i	0.889853	+	1.54127i	0.840048	+	0.542511i	$0.182526\pi$
$31$	4.95449	+	8.58143i	0.889853	+	1.54127i	0.0498045	+	0.998759i	$0.484140\pi$
$32$	−1.21520	−	2.10479i	−0.214819	−	0.372077i
$33$	−1.18430	+	2.05127i	−0.206161	+	0.357081i
$34$	−2.83963			−0.486992
$35$	0.966988	+	10.5279i	0.163451	+	1.77954i
$36$	−0.438184			−0.0730307
$37$	−4.09719	+	7.09654i	−0.673574	+	1.16666i	0.303310	+	0.952892i	$0.401908\pi$
$37$	−4.09719	+	7.09654i	−0.673574	+	1.16666i	−0.976884	+	0.213772i	$0.931425\pi$
$38$	0.624863	+	1.08229i	0.101366	+	0.175571i
$39$	−1.09457	−	1.89585i	−0.175271	−	0.303579i
$40$	6.08793	−	10.5446i	0.962586	−	1.66725i
$41$	−8.35871			−1.30541			−0.652705	−	0.757612i	$-0.726366\pi$
$41$	−8.35871			−1.30541			−0.652705	+	0.757612i	$0.726366\pi$
$42$	−2.70027	+	1.90821i	−0.416660	+	0.294443i
$43$	−0.800311			−0.122046			−0.0610232	−	0.998136i	$-0.519436\pi$
$43$	−0.800311			−0.122046			−0.0610232	+	0.998136i	$0.519436\pi$
$44$	−0.518943	+	0.898836i	−0.0782337	+	0.135505i
$45$	−1.99797	−	3.46058i	−0.297839	−	0.515872i
$46$	5.37299	+	9.30629i	0.792204	+	1.37214i
$47$	2.46065	−	4.26197i	0.358923	−	0.621673i	−0.628858	−	0.777520i	$-0.716477\pi$
$47$	2.46065	−	4.26197i	0.358923	−	0.621673i	0.987781	+	0.155847i	$0.0498108\pi$
$48$	2.93163			0.423144
$49$	2.33713	−	6.59832i	0.333876	−	0.942617i
$50$	13.7063			1.93837
$51$	−1.13610	+	1.96778i	−0.159086	+	0.275545i
$52$	−0.479623	−	0.830732i	−0.0665118	−	0.115202i
$53$	1.63914	+	2.83908i	0.225154	+	0.389978i	0.956366	−	0.292173i	$-0.0943783\pi$
$53$	1.63914	+	2.83908i	0.225154	+	0.389978i	−0.731212	+	0.682150i	$0.761045\pi$
$54$	0.624863	−	1.08229i	0.0850331	−	0.147282i
$55$	−9.46479			−1.27623
$56$	−6.58375	+	4.65257i	−0.879790	+	0.621726i
$57$	1.00000			0.132453
$58$	0.459790	−	0.796379i	0.0603733	−	0.104570i
$59$	1.78048	+	3.08389i	0.231799	+	0.401488i	0.958338	−	0.285638i	$-0.0922055\pi$
$59$	1.78048	+	3.08389i	0.231799	+	0.401488i	−0.726539	+	0.687126i	$0.758872\pi$
$60$	−0.875477	−	1.51637i	−0.113024	−	0.195763i
$61$	−1.37809	+	2.38693i	−0.176447	+	0.305615i	−0.940661	−	0.339348i	$-0.889794\pi$
$61$	−1.37809	+	2.38693i	−0.176447	+	0.305615i	0.764214	+	0.644962i	$0.223127\pi$
$62$	−12.3835			−1.57271
$63$	0.241993	+	2.63466i	0.0304883	+	0.331936i
$64$	8.90058			1.11257
$65$	4.37382	−	7.57568i	0.542506	−	0.939648i
$66$	−1.48005	−	2.56353i	−0.182182	−	0.315549i
$67$	1.85054	+	3.20523i	0.226080	+	0.391581i	0.956643	−	0.291264i	$-0.0940757\pi$
$67$	1.85054	+	3.20523i	0.226080	+	0.391581i	−0.730563	+	0.682845i	$0.760742\pi$
$68$	−0.497821	+	0.862252i	−0.0603697	+	0.104563i
$69$	8.59867			1.03516
$70$	−11.9985	−	5.53194i	−1.43410	−	0.661194i
$71$	7.30367			0.866786			0.433393	−	0.901205i	$-0.357316\pi$
$71$	7.30367			0.866786			0.433393	+	0.901205i	$0.357316\pi$
$72$	1.52353	−	2.63883i	0.179550	−	0.310990i
$73$	3.69123	+	6.39340i	0.432026	+	0.748291i	0.997048	−	0.0767854i	$-0.0244656\pi$
$73$	3.69123	+	6.39340i	0.432026	+	0.748291i	−0.565022	+	0.825076i	$0.691132\pi$
$74$	−5.12036	−	8.86873i	−0.595230	−	1.03097i
$75$	5.48373	−	9.49810i	0.633206	−	1.09675i
$76$	0.438184			0.0502632
$77$	5.69100	+	2.62384i	0.648550	+	0.299015i
$78$	2.73582			0.309771
$79$	−0.458446	+	0.794052i	−0.0515792	+	0.0893378i	−0.890662	−	0.454666i	$-0.849759\pi$
$79$	−0.458446	+	0.794052i	−0.0515792	+	0.0893378i	0.839083	+	0.544003i	$0.183092\pi$
$80$	5.85729	+	10.1451i	0.654864	+	1.13426i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	5.22305	−	9.04658i	0.576789	−	0.999028i
$83$	4.91925			0.539957			0.269979	−	0.962866i	$-0.412983\pi$
$83$	4.91925			0.539957			0.269979	+	0.962866i	$0.412983\pi$
$84$	0.106038	+	1.15447i	0.0115697	+	0.125963i
$85$	−9.07955			−0.984815
$86$	0.500085	−	0.866173i	0.0539256	−	0.0934018i
$87$	−0.367912	−	0.637243i	−0.0394443	−	0.0683196i
$88$	−3.60865	−	6.25036i	−0.384683	−	0.666291i
$89$	−8.85073	+	15.3299i	−0.938176	+	1.62497i	−0.169306	+	0.985564i	$0.554153\pi$
$89$	−8.85073	+	15.3299i	−0.938176	+	1.62497i	−0.768870	+	0.639405i	$0.779181\pi$
$90$	4.99382			0.526395
$91$	−4.73004	+	3.34260i	−0.495843	+	0.350400i
$92$	3.76780			0.392821
$93$	−4.95449	+	8.58143i	−0.513757	+	0.889853i
$94$	3.07514	+	5.32630i	0.317177	+	0.549366i
$95$	1.99797	+	3.46058i	0.204987	+	0.355048i
$96$	1.21520	−	2.10479i	0.124026	−	0.214819i
$97$	13.3590			1.35640			0.678201	−	0.734877i	$-0.262760\pi$
$97$	13.3590			1.35640			0.678201	+	0.734877i	$0.262760\pi$
$98$	5.68093	+	6.65251i	0.573861	+	0.672005i
$99$	−2.36861			−0.238054
$100$	2.40288	−	4.16192i	0.240288	−	0.416192i
$101$	5.63762	+	9.76464i	0.560964	+	0.971618i	0.997413	+	0.0718890i	$0.0229027\pi$
$101$	5.63762	+	9.76464i	0.560964	+	0.971618i	−0.436449	+	0.899729i	$0.643764\pi$
$102$	−1.41981	−	2.45919i	−0.140582	−	0.243496i
$103$	4.93999	−	8.55632i	0.486752	−	0.843079i	−0.513132	−	0.858310i	$-0.671515\pi$
$103$	4.93999	−	8.55632i	0.486752	−	0.843079i	0.999884	+	0.0152305i	$0.00484820\pi$
$104$	6.67044			0.654091
$105$	−8.63395	+	6.10140i	−0.842588	+	0.595435i
$106$	−4.09696			−0.397932
$107$	−3.46880	+	6.00814i	−0.335342	+	0.580829i	−0.983550	−	0.180634i	$-0.942185\pi$
$107$	−3.46880	+	6.00814i	−0.335342	+	0.580829i	0.648209	+	0.761463i	$0.275518\pi$
$108$	−0.219092	−	0.379479i	−0.0210822	−	0.0365154i
$109$	−1.84996	−	3.20423i	−0.177194	−	0.306909i	0.763724	−	0.645543i	$-0.223369\pi$
$109$	−1.84996	−	3.20423i	−0.177194	−	0.306909i	−0.940918	+	0.338633i	$0.890035\pi$
$110$	5.91420	−	10.2437i	0.563896	−	0.976697i
$111$	−8.19438			−0.777776
$112$	−0.709434	−	7.72384i	−0.0670352	−	0.729834i
$113$	−2.09680			−0.197250			−0.0986252	−	0.995125i	$-0.531445\pi$
$113$	−2.09680			−0.197250			−0.0986252	+	0.995125i	$0.531445\pi$
$114$	−0.624863	+	1.08229i	−0.0585238	+	0.101366i
$115$	17.1798	+	29.7564i	1.60203	+	2.77479i
$116$	−0.161213	−	0.279230i	−0.0149683	−	0.0259258i
$117$	1.09457	−	1.89585i	0.101193	−	0.175271i
$118$	−4.45023			−0.409677
$119$	5.45937	+	2.51705i	0.500459	+	0.230737i
$120$	12.1759			1.11150
$121$	2.69485	−	4.66762i	0.244986	−	0.424329i
$122$	−1.72224	−	2.98300i	−0.155924	−	0.270069i
$123$	−4.17935	−	7.23885i	−0.376840	−	0.652705i
$124$	−2.17098	+	3.76025i	−0.194960	+	0.337680i
$125$	23.8455			2.13281
$126$	−3.00269	−	1.38439i	−0.267501	−	0.123332i
$127$	10.7759			0.956206			0.478103	−	0.878304i	$-0.341325\pi$
$127$	10.7759			0.956206			0.478103	+	0.878304i	$0.341325\pi$
$128$	−3.13125	+	5.42348i	−0.276766	+	0.479372i
$129$	−0.400156	−	0.693090i	−0.0352317	−	0.0610232i
$130$	5.46608	+	9.46753i	0.479407	+	0.830357i
$131$	0.420271	−	0.727931i	0.0367192	−	0.0635996i	−0.847082	−	0.531463i	$-0.821643\pi$
$131$	0.420271	−	0.727931i	0.0367192	−	0.0635996i	0.883801	+	0.467863i	$0.154976\pi$
$132$	−1.03789			−0.0903364
$133$	−0.241993	−	2.63466i	−0.0209835	−	0.228454i
$134$	−4.62534			−0.399569
$135$	1.99797	−	3.46058i	0.171957	−	0.297839i
$136$	−3.46177	−	5.99596i	−0.296844	−	0.514149i
$137$	−1.28098	−	2.21873i	−0.109442	−	0.189559i	0.806102	−	0.591776i	$-0.201573\pi$
$137$	−1.28098	−	2.21873i	−0.109442	−	0.189559i	−0.915544	+	0.402217i	$0.868240\pi$
$138$	−5.37299	+	9.30629i	−0.457379	+	0.792204i
$139$	−10.8739			−0.922313			−0.461156	−	0.887319i	$-0.652565\pi$
$139$	−10.8739			−0.922313			−0.461156	+	0.887319i	$0.652565\pi$
$140$	−3.78326	+	2.67354i	−0.319744	+	0.225955i
$141$	4.92130			0.414449
$142$	−4.56379	+	7.90472i	−0.382985	+	0.663349i
$143$	−2.59260	−	4.49052i	−0.216804	−	0.375516i
$144$	1.46581	+	2.53886i	0.122151	+	0.211572i
$145$	1.47015	−	2.54638i	0.122089	−	0.211465i
$146$	−9.22605			−0.763554
$147$	6.88288	−	1.27514i	0.567690	−	0.105172i
$148$	−3.59065			−0.295149
$149$	11.0309	−	19.1060i	0.903684	−	1.56523i	0.0810093	−	0.996713i	$-0.474186\pi$
$149$	11.0309	−	19.1060i	0.903684	−	1.56523i	0.822674	−	0.568513i	$-0.192481\pi$
$150$	6.85316	+	11.8700i	0.559558	+	0.969183i
$151$	1.58958	+	2.75324i	0.129359	+	0.224056i	0.923428	−	0.383771i	$-0.125375\pi$
$151$	1.58958	+	2.75324i	0.129359	+	0.224056i	−0.794070	+	0.607827i	$0.792042\pi$
$152$	−1.52353	+	2.63883i	−0.123575	+	0.214038i
$153$	−2.27220			−0.183696
$154$	−6.39587	+	4.51980i	−0.515394	+	0.364216i
$155$	−39.5956			−3.18040
$156$	0.479623	−	0.830732i	0.0384006	−	0.0665118i
$157$	11.3194	+	19.6059i	0.903390	+	1.56472i	0.823064	+	0.567949i	$0.192263\pi$
$157$	11.3194	+	19.6059i	0.903390	+	1.56472i	0.0803267	+	0.996769i	$0.474404\pi$
$158$	−0.572932	−	0.992348i	−0.0455800	−	0.0789469i
$159$	−1.63914	+	2.83908i	−0.129993	+	0.225154i
$160$	9.71170			0.767777
$161$	−2.08082	−	22.6546i	−0.163992	−	1.78543i
$162$	1.24973			0.0981878
$163$	7.31481	−	12.6696i	0.572940	−	0.992362i	−0.423322	−	0.905980i	$-0.639136\pi$
$163$	7.31481	−	12.6696i	0.572940	−	0.992362i	0.996262	−	0.0863825i	$-0.0275307\pi$
$164$	−1.83133	−	3.17195i	−0.143003	−	0.247688i
$165$	−4.73239	−	8.19675i	−0.368416	−	0.638116i
$166$	−3.07385	+	5.32407i	−0.238577	+	0.413228i
$167$	−17.8027			−1.37762			−0.688808	−	0.724944i	$-0.741866\pi$
$167$	−17.8027			−1.37762			−0.688808	+	0.724944i	$0.741866\pi$
$168$	−7.32112	−	3.37541i	−0.564836	−	0.260418i
$169$	−8.20767			−0.631359
$170$	5.67347	−	9.82675i	0.435136	−	0.753677i
$171$	0.500000	+	0.866025i	0.0382360	+	0.0662266i
$172$	−0.175342	−	0.303701i	−0.0133697	−	0.0231570i
$173$	12.4672	−	21.5939i	0.947866	−	1.64175i	0.197957	−	0.980211i	$-0.436569\pi$
$173$	12.4672	−	21.5939i	0.947866	−	1.64175i	0.749909	−	0.661541i	$-0.230097\pi$
$174$	0.919579			0.0697131
$175$	−26.3513	−	12.1493i	−1.99197	−	0.918400i
$176$	6.94387			0.523414
$177$	−1.78048	+	3.08389i	−0.133829	+	0.231799i
$178$	−11.0610	−	19.1582i	−0.829057	−	1.43597i
$179$	−6.81705	−	11.8075i	−0.509530	−	0.882533i	−0.999939	−	0.0110399i	$-0.996486\pi$
$179$	−6.81705	−	11.8075i	−0.509530	−	0.882533i	0.490409	−	0.871493i	$-0.336848\pi$
$180$	0.875477	−	1.51637i	0.0652542	−	0.113024i
$181$	−3.79249			−0.281893			−0.140947	−	0.990017i	$-0.545015\pi$
$181$	−3.79249			−0.281893			−0.140947	+	0.990017i	$0.545015\pi$
$182$	−0.662051	−	7.20797i	−0.0490745	−	0.534290i
$183$	−2.75619			−0.203743
$184$	−13.1003	+	22.6905i	−0.965770	+	1.67276i
$185$	−16.3721	−	28.3573i	−1.20370	−	2.08487i
$186$	−6.19176	−	10.7244i	−0.454002	−	0.786354i
$187$	−2.69097	+	4.66090i	−0.196783	+	0.340839i
$188$	2.15644			0.157274
$189$	−2.16069	+	1.52690i	−0.157167	+	0.111066i
$190$	−4.99382			−0.362290
$191$	−5.01829	+	8.69194i	−0.363111	+	0.628926i	−0.988471	−	0.151410i	$-0.951619\pi$
$191$	−5.01829	+	8.69194i	−0.363111	+	0.628926i	0.625360	+	0.780336i	$0.284952\pi$
$192$	4.45029	+	7.70813i	0.321172	+	0.556286i
$193$	−9.49470	−	16.4453i	−0.683444	−	1.18376i	−0.973923	−	0.226878i	$-0.927148\pi$
$193$	−9.49470	−	16.4453i	−0.683444	−	1.18376i	0.290480	−	0.956881i	$-0.406185\pi$
$194$	−8.34755	+	14.4584i	−0.599319	+	1.03805i
$195$	8.74765			0.626432
$196$	3.01597	−	0.558747i	0.215426	−	0.0399105i
$197$	3.08525			0.219815			0.109908	−	0.993942i	$-0.464945\pi$
$197$	3.08525			0.219815			0.109908	+	0.993942i	$0.464945\pi$
$198$	1.48005	−	2.56353i	0.105183	−	0.182182i
$199$	9.42704	+	16.3281i	0.668266	+	1.15747i	0.978389	+	0.206773i	$0.0662963\pi$
$199$	9.42704	+	16.3281i	0.668266	+	1.15747i	−0.310123	+	0.950696i	$0.600370\pi$
$200$	16.7093	+	28.9413i	1.18152	+	2.04646i
$201$	−1.85054	+	3.20523i	−0.130527	+	0.226080i
$202$	−14.0910			−0.991436
$203$	−1.58989	+	1.12353i	−0.111588	+	0.0788565i
$204$	−0.995642			−0.0697089
$205$	16.7004	−	28.9260i	1.16641	−	2.02028i
$206$	6.17364	+	10.6931i	0.430138	+	0.745021i
$207$	4.29933	+	7.44667i	0.298824	+	0.517579i
$208$	−3.20887	+	5.55792i	−0.222495	+	0.385373i
$209$	2.36861			0.163840
$210$	−1.20847	−	13.1570i	−0.0833924	−	0.907921i
$211$	−19.9172			−1.37115			−0.685577	−	0.728000i	$-0.740450\pi$
$211$	−19.9172			−1.37115			−0.685577	+	0.728000i	$0.740450\pi$
$212$	−0.718247	+	1.24404i	−0.0493294	+	0.0854411i
$213$	3.65183	+	6.32516i	0.250220	+	0.433393i
$214$	−4.33505	−	7.50853i	−0.296338	−	0.513272i
$215$	1.59899	−	2.76954i	0.109050	−	0.188881i
$216$	3.04706			0.207326
$217$	23.8081	+	10.9768i	1.61620	+	0.745151i
$218$	4.62389			0.313169
$219$	−3.69123	+	6.39340i	−0.249430	+	0.432026i
$220$	−2.07366	−	3.59169i	−0.139806	−	0.242151i
$221$	−2.48708	−	4.30775i	−0.167299	−	0.289771i
$222$	5.12036	−	8.86873i	0.343656	−	0.595230i
$223$	12.3503			0.827040			0.413520	−	0.910495i	$-0.364299\pi$
$223$	12.3503			0.827040			0.413520	+	0.910495i	$0.364299\pi$
$224$	−5.83947	−	2.69229i	−0.390166	−	0.179886i
$225$	10.9675			0.731164
$226$	1.31021	−	2.26936i	0.0871541	−	0.150955i
$227$	−5.26897	−	9.12613i	−0.349714	−	0.605722i	0.636485	−	0.771289i	$-0.280388\pi$
$227$	−5.26897	−	9.12613i	−0.349714	−	0.605722i	−0.986199	+	0.165567i	$0.947055\pi$
$228$	0.219092	+	0.379479i	0.0145097	+	0.0251316i
$229$	−10.9731	+	19.0060i	−0.725126	+	1.25596i	0.233796	+	0.972286i	$0.424885\pi$
$229$	−10.9731	+	19.0060i	−0.725126	+	1.25596i	−0.958922	+	0.283669i	$0.908448\pi$
$230$	−42.9402			−2.83139
$231$	0.573187	+	6.24048i	0.0377129	+	0.410593i
$232$	2.24210			0.147201
$233$	3.30522	−	5.72481i	0.216532	−	0.375045i	−0.737213	−	0.675660i	$-0.763859\pi$
$233$	3.30522	−	5.72481i	0.216532	−	0.375045i	0.953745	+	0.300615i	$0.0971921\pi$
$234$	1.36791	+	2.36929i	0.0894232	+	0.154886i
$235$	9.83259	+	17.0305i	0.641408	+	1.11095i
$236$	−0.780180	+	1.35131i	−0.0507854	+	0.0879629i
$237$	−0.916892			−0.0595586
$238$	−6.13554	+	4.33583i	−0.397708	+	0.281050i
$239$	16.2362			1.05023			0.525115	−	0.851031i	$-0.324022\pi$
$239$	16.2362			1.05023			0.525115	+	0.851031i	$0.324022\pi$
$240$	−5.85729	+	10.1451i	−0.378086	+	0.654864i
$241$	−7.07793	−	12.2593i	−0.455929	−	0.789693i	0.542812	−	0.839854i	$-0.317360\pi$
$241$	−7.07793	−	12.2593i	−0.455929	−	0.789693i	−0.998741	+	0.0501617i	$0.984026\pi$
$242$	3.36783	+	5.83325i	0.216492	+	0.374975i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−1.20772			−0.0773162
$245$	18.1645	+	21.2710i	1.16049	+	1.35896i
$246$	10.4461			0.666019
$247$	−1.09457	+	1.89585i	−0.0696458	+	0.120630i
$248$	−15.0966	−	26.1482i	−0.958638	−	1.66041i
$249$	2.45962	+	4.26019i	0.155872	+	0.269979i
$250$	−14.9002	+	25.8079i	−0.942371	+	1.63224i
$251$	−14.5157			−0.916224			−0.458112	−	0.888895i	$-0.651474\pi$
$251$	−14.5157			−0.916224			−0.458112	+	0.888895i	$0.651474\pi$
$252$	−0.946779	+	0.669065i	−0.0596415	+	0.0421471i
$253$	20.3669			1.28045
$254$	−6.73346	+	11.6627i	−0.422495	+	0.731782i
$255$	−4.53977	−	7.86312i	−0.284292	−	0.492408i
$256$	4.98738	+	8.63839i	0.311711	+	0.539900i
$257$	−1.66506	+	2.88397i	−0.103864	+	0.179897i	−0.913273	−	0.407347i	$-0.866454\pi$
$257$	−1.66506	+	2.88397i	−0.103864	+	0.179897i	0.809410	+	0.587244i	$0.199787\pi$
$258$	1.00017			0.0622679
$259$	1.98298	+	21.5894i	0.123217	+	1.34150i
$260$	3.83308			0.237718
$261$	0.367912	−	0.637243i	0.0227732	−	0.0394443i
$262$	0.525224	+	0.909714i	0.0324484	+	0.0562023i
$263$	−11.9556	−	20.7076i	−0.737211	−	1.27689i	−0.953746	−	0.300612i	$-0.902809\pi$
$263$	−11.9556	−	20.7076i	−0.737211	−	1.27689i	0.216535	−	0.976275i	$-0.430524\pi$
$264$	3.60865	−	6.25036i	0.222097	−	0.384683i
$265$	−13.0998			−0.804715
$266$	3.00269	+	1.38439i	0.184107	+	0.0848827i
$267$	−17.7015			−1.08331
$268$	−0.810878	+	1.40448i	−0.0495323	+	0.0857924i
$269$	9.12904	+	15.8120i	0.556607	+	0.964072i	0.997777	+	0.0666484i	$0.0212306\pi$
$269$	9.12904	+	15.8120i	0.556607	+	0.964072i	−0.441169	+	0.897424i	$0.645436\pi$
$270$	2.49691	+	4.32477i	0.151957	+	0.263197i
$271$	4.55023	−	7.88123i	0.276407	−	0.478751i	−0.694082	−	0.719896i	$-0.744190\pi$
$271$	4.55023	−	7.88123i	0.276407	−	0.478751i	0.970489	+	0.241145i	$0.0775230\pi$
$272$	6.66124			0.403897
$273$	−5.25980	−	2.42504i	−0.318338	−	0.146770i
$274$	3.20176			0.193425
$275$	12.9888	−	22.4973i	0.783254	−	1.35664i
$276$	1.88390	+	3.26301i	0.113398	+	0.196410i
$277$	−6.45503	−	11.1804i	−0.387845	−	0.671768i	0.604314	−	0.796746i	$-0.293447\pi$
$277$	−6.45503	−	11.1804i	−0.387845	−	0.671768i	−0.992159	+	0.124978i	$0.960114\pi$
$278$	6.79470	−	11.7688i	0.407519	−	0.705844i
$279$	−9.90898			−0.593235
$280$	−2.94647	−	32.0792i	−0.176086	−	1.91710i
$281$	30.7965			1.83716			0.918582	−	0.395232i	$-0.129336\pi$
$281$	30.7965			1.83716			0.918582	+	0.395232i	$0.129336\pi$
$282$	−3.07514	+	5.32630i	−0.183122	+	0.317177i
$283$	−11.6351	−	20.1526i	−0.691635	−	1.19795i	−0.971302	−	0.237850i	$-0.923557\pi$
$283$	−11.6351	−	20.1526i	−0.691635	−	1.19795i	0.279666	−	0.960097i	$-0.409776\pi$
$284$	1.60018	+	2.77159i	0.0949530	+	0.164463i
$285$	−1.99797	+	3.46058i	−0.118349	+	0.204987i
$286$	6.48009			0.383176
$287$	−18.0605	+	12.7629i	−1.06608	+	0.753372i
$288$	2.43040			0.143213
$289$	5.91856	−	10.2512i	0.348150	−	0.603014i
$290$	1.83729	+	3.18227i	0.107889	+	0.186870i
$291$	6.67950	+	11.5692i	0.391559	+	0.678201i
$292$	−1.61744	+	2.80149i	−0.0946535	+	0.163945i
$293$	8.18298			0.478055			0.239027	−	0.971013i	$-0.423171\pi$
$293$	8.18298			0.478055			0.239027	+	0.971013i	$0.423171\pi$
$294$	−2.92078	+	8.24609i	−0.170343	+	0.480922i
$295$	−14.2294			−0.828466
$296$	12.4844	−	21.6236i	0.725640	−	1.25685i
$297$	−1.18430	−	2.05127i	−0.0687202	−	0.119027i
$298$	13.7856	+	23.8773i	0.798576	+	1.38317i
$299$	−9.41184	+	16.3018i	−0.544301	+	0.942757i
$300$	4.80577			0.277461
$301$	−1.72922	+	1.22200i	−0.0996707	+	0.0704348i
$302$	−3.97309			−0.228626
$303$	−5.63762	+	9.76464i	−0.323873	+	0.560964i
$304$	−1.46581	−	2.53886i	−0.0840701	−	0.145614i
$305$	−5.50676	−	9.53799i	−0.315316	−	0.546144i
$306$	1.41981	−	2.45919i	0.0811653	−	0.140582i
$307$	19.1256			1.09156			0.545778	−	0.837930i	$-0.316234\pi$
$307$	19.1256			1.09156			0.545778	+	0.837930i	$0.316234\pi$
$308$	0.251162	+	2.73448i	0.0143113	+	0.155811i
$309$	9.87999			0.562053
$310$	24.7418	−	42.8541i	1.40524	−	2.43395i
$311$	−17.1571	−	29.7170i	−0.972890	−	1.68510i	−0.686729	−	0.726914i	$-0.740954\pi$
$311$	−17.1571	−	29.7170i	−0.972890	−	1.68510i	−0.286161	−	0.958181i	$-0.592379\pi$
$312$	3.33522	+	5.77677i	0.188820	+	0.327045i
$313$	1.47774	−	2.55952i	0.0835269	−	0.144673i	−0.821236	−	0.570589i	$-0.806715\pi$
$313$	1.47774	−	2.55952i	0.0835269	−	0.144673i	0.904763	+	0.425916i	$0.140048\pi$
$314$	−28.2924			−1.59663
$315$	−9.60094	−	4.42652i	−0.540952	−	0.249406i
$316$	−0.401768			−0.0226012
$317$	6.26089	−	10.8442i	0.351646	−	0.609069i	−0.634892	−	0.772601i	$-0.718955\pi$
$317$	6.26089	−	10.8442i	0.351646	−	0.609069i	0.986538	+	0.163532i	$0.0522886\pi$
$318$	−2.04848	−	3.54807i	−0.114873	−	0.198966i
$319$	−0.871439	−	1.50938i	−0.0487912	−	0.0845089i
$320$	−17.7831	+	30.8011i	−0.994103	+	1.72184i
$321$	−6.93760			−0.387219
$322$	25.8192	+	11.9039i	1.43885	+	0.663381i
$323$	2.27220			0.126429
$324$	0.219092	−	0.379479i	0.0121718	−	0.0210822i
$325$	12.0046	+	20.7927i	0.665898	+	1.15337i
$326$	9.14152	+	15.8336i	0.506302	+	0.876940i
$327$	1.84996	−	3.20423i	0.102303	−	0.177194i
$328$	25.4695			1.40632
$329$	−1.19092	−	12.9660i	−0.0656577	−	0.714837i
$330$	11.8284			0.651132
$331$	−11.3692	+	19.6920i	−0.624906	+	1.08237i	0.363653	+	0.931535i	$0.381530\pi$
$331$	−11.3692	+	19.6920i	−0.624906	+	1.08237i	−0.988559	+	0.150835i	$0.951804\pi$
$332$	1.07777	+	1.86675i	0.0591502	+	0.102451i
$333$	−4.09719	−	7.09654i	−0.224525	−	0.388888i
$334$	11.1243	−	19.2678i	0.608693	−	1.05429i
$335$	−14.7893			−0.808024
$336$	6.33432	−	4.47631i	0.345566	−	0.244203i
$337$	4.05805			0.221056			0.110528	−	0.993873i	$-0.464746\pi$
$337$	4.05805			0.221056			0.110528	+	0.993873i	$0.464746\pi$
$338$	5.12867	−	8.88312i	0.278963	−	0.483178i
$339$	−1.04840	−	1.81588i	−0.0569413	−	0.0986252i
$340$	−1.98926	−	3.44550i	−0.107883	−	0.186858i
$341$	−11.7352	+	20.3260i	−0.635499	+	1.10072i
$342$	−1.24973			−0.0675775
$343$	−5.02517	−	17.8255i	−0.271334	−	0.962485i
$344$	2.43860			0.131480
$345$	−17.1798	+	29.7564i	−0.924932	+	1.60203i
$346$	15.5806	+	26.9864i	0.837619	+	1.45080i
$347$	11.5526	+	20.0097i	0.620175	+	1.07417i	0.989453	+	0.144855i	$0.0462717\pi$
$347$	11.5526	+	20.0097i	0.620175	+	1.07417i	−0.369278	+	0.929319i	$0.620395\pi$
$348$	0.161213	−	0.279230i	0.00864195	−	0.0149683i
$349$	17.9043			0.958394			0.479197	−	0.877707i	$-0.340928\pi$
$349$	17.9043			0.958394			0.479197	+	0.877707i	$0.340928\pi$
$350$	29.6151	−	20.9282i	1.58299	−	1.11866i
$351$	2.18914			0.116848
$352$	2.87833	−	4.98541i	0.153415	−	0.265723i
$353$	4.45601	+	7.71803i	0.237169	+	0.410790i	0.959901	−	0.280339i	$-0.0904470\pi$
$353$	4.45601	+	7.71803i	0.237169	+	0.410790i	−0.722732	+	0.691129i	$0.757114\pi$
$354$	−2.22512	−	3.85401i	−0.118264	−	0.204838i
$355$	−14.5925	+	25.2749i	−0.774488	+	1.34145i
$356$	−7.75651			−0.411094
$357$	0.549857	+	5.98647i	0.0291015	+	0.316838i
$358$	17.0389			0.900534
$359$	−6.11826	+	10.5971i	−0.322909	+	0.559295i	−0.981087	−	0.193567i	$-0.937994\pi$
$359$	−6.11826	+	10.5971i	−0.322909	+	0.559295i	0.658178	+	0.752863i	$0.271328\pi$
$360$	6.08793	+	10.5446i	0.320862	+	0.555749i
$361$	−0.500000	−	0.866025i	−0.0263158	−	0.0455803i
$362$	2.36978	−	4.10459i	0.124553	−	0.215732i
$363$	5.38970			0.282886
$364$	−2.30476	−	1.06261i	−0.120802	−	0.0556961i
$365$	−29.4998			−1.54409
$366$	1.72224	−	2.98300i	0.0900229	−	0.155924i
$367$	0.178424	+	0.309040i	0.00931366	+	0.0161317i	0.870645	−	0.491912i	$-0.163702\pi$
$367$	0.178424	+	0.309040i	0.00931366	+	0.0161317i	−0.861331	+	0.508044i	$0.830369\pi$
$368$	−12.6040	−	21.8308i	−0.657031	−	1.13801i
$369$	4.17935	−	7.23885i	0.217568	−	0.376840i
$370$	40.9212			2.12739
$371$	7.87667	+	3.63155i	0.408937	+	0.188541i
$372$	−4.34196			−0.225120
$373$	6.24199	−	10.8115i	0.323198	−	0.559796i	−0.657948	−	0.753063i	$-0.728575\pi$
$373$	6.24199	−	10.8115i	0.323198	−	0.559796i	0.981146	+	0.193268i	$0.0619086\pi$
$374$	−3.36298	−	5.82485i	−0.173896	−	0.301196i
$375$	11.9228	+	20.6508i	0.615689	+	1.06641i
$376$	−7.49776	+	12.9865i	−0.386667	+	0.669728i
$377$	1.61082			0.0829616
$378$	−0.302425	−	3.29260i	−0.0155551	−	0.169353i
$379$	17.4065			0.894111			0.447056	−	0.894506i	$-0.352473\pi$
$379$	17.4065			0.894111			0.447056	+	0.894506i	$0.352473\pi$
$380$	−0.875477	+	1.51637i	−0.0449110	+	0.0777882i
$381$	5.38795	+	9.33220i	0.276033	+	0.478103i
$382$	−6.27149	−	10.8625i	−0.320877	−	0.555776i
$383$	13.4769	−	23.3426i	0.688636	−	1.19275i	−0.283643	−	0.958930i	$-0.591543\pi$
$383$	13.4769	−	23.3426i	0.688636	−	1.19275i	0.972279	−	0.233823i	$-0.0751236\pi$
$384$	−6.26250			−0.319582
$385$	−20.4504	+	14.4518i	−1.04225	+	0.736532i
$386$	23.7316			1.20790
$387$	0.400156	−	0.693090i	0.0203411	−	0.0352317i
$388$	2.92685	+	5.06946i	0.148588	+	0.257363i
$389$	17.3066	+	29.9760i	0.877481	+	1.51984i	0.854096	+	0.520116i	$0.174111\pi$
$389$	17.3066	+	29.9760i	0.877481	+	1.51984i	0.0233855	+	0.999727i	$0.492555\pi$
$390$	−5.46608	+	9.46753i	−0.276786	+	0.479407i
$391$	19.5379			0.988073
$392$	−7.12140	+	20.1055i	−0.359685	+	1.01548i
$393$	0.840542			0.0423997
$394$	−1.92786	+	3.33915i	−0.0971242	+	0.168224i
$395$	−1.83192	−	3.17298i	−0.0921738	−	0.159650i
$396$	−0.518943	−	0.898836i	−0.0260779	−	0.0451682i
$397$	8.83972	−	15.3108i	0.443653	−	0.768429i	−0.554304	−	0.832314i	$-0.687016\pi$
$397$	8.83972	−	15.3108i	0.443653	−	0.768429i	0.997957	+	0.0638847i	$0.0203490\pi$
$398$	−23.5624			−1.18108
$399$	2.16069	−	1.52690i	0.108170	−	0.0764408i
$400$	−32.1525			−1.60762
$401$	6.99922	−	12.1230i	0.349524	−	0.605394i	−0.636641	−	0.771160i	$-0.719677\pi$
$401$	6.99922	−	12.1230i	0.349524	−	0.605394i	0.986165	+	0.165767i	$0.0530099\pi$
$402$	−2.31267	−	4.00566i	−0.115345	−	0.199784i
$403$	−10.8461	−	18.7859i	−0.540281	−	0.935795i
$404$	−2.47032	+	4.27871i	−0.122903	+	0.212874i
$405$	3.99593			0.198559
$406$	−0.222532	−	2.42278i	−0.0110441	−	0.120241i
$407$	−19.4093			−0.962081
$408$	3.46177	−	5.99596i	0.171383	−	0.296844i
$409$	−15.2732	−	26.4540i	−0.755213	−	1.30807i	−0.945269	−	0.326294i	$-0.894200\pi$
$409$	−15.2732	−	26.4540i	−0.755213	−	1.30807i	0.190056	−	0.981773i	$-0.439133\pi$
$410$	20.8709	+	36.1495i	1.03074	+	1.78530i
$411$	1.28098	−	2.21873i	0.0631863	−	0.109442i
$412$	4.32926			0.213287
$413$	8.55586	+	3.94469i	0.421006	+	0.194105i
$414$	−10.7460			−0.528136
$415$	−9.82848	+	17.0234i	−0.482461	+	0.835647i
$416$	2.66024	+	4.60767i	0.130429	+	0.225910i
$417$	−5.43695	−	9.41708i	−0.266249	−	0.461156i
$418$	−1.48005	+	2.56353i	−0.0723918	+	0.125386i
$419$	17.2075			0.840640			0.420320	−	0.907376i	$-0.361918\pi$
$419$	17.2075			0.840640			0.420320	+	0.907376i	$0.361918\pi$
$420$	−4.20698	−	1.93963i	−0.205280	−	0.0946445i
$421$	−9.71684			−0.473570			−0.236785	−	0.971562i	$-0.576094\pi$
$421$	−9.71684			−0.473570			−0.236785	+	0.971562i	$0.576094\pi$
$422$	12.4455	−	21.5562i	0.605838	−	1.04934i
$423$	2.46065	+	4.26197i	0.119641	+	0.207224i
$424$	−4.99457	−	8.65085i	−0.242558	−	0.420123i
$425$	12.4601	−	21.5816i	0.604405	−	1.04686i
$426$	−9.12759			−0.442233
$427$	0.666978	+	7.26162i	0.0322774	+	0.351414i
$428$	−3.03995			−0.146941
$429$	2.59260	−	4.49052i	0.125172	−	0.216804i
$430$	1.99830	+	3.46117i	0.0963668	+	0.166912i
$431$	9.28764	+	16.0867i	0.447370	+	0.774868i	0.998214	−	0.0597406i	$-0.0190274\pi$
$431$	9.28764	+	16.0867i	0.447370	+	0.774868i	−0.550844	+	0.834608i	$0.685694\pi$
$432$	−1.46581	+	2.53886i	−0.0705239	+	0.122151i
$433$	−16.8441			−0.809474			−0.404737	−	0.914433i	$-0.632637\pi$
$433$	−16.8441			−0.809474			−0.404737	+	0.914433i	$0.632637\pi$
$434$	−26.7569	+	18.9084i	−1.28437	+	0.907633i
$435$	2.94030			0.140977
$436$	0.810624	−	1.40404i	0.0388219	−	0.0672414i
$437$	−4.29933	−	7.44667i	−0.205665	−	0.356222i
$438$	−4.61303	−	7.99000i	−0.220419	−	0.381777i
$439$	0.188178	−	0.325933i	0.00898123	−	0.0155559i	−0.861500	−	0.507758i	$-0.830474\pi$
$439$	0.188178	−	0.325933i	0.00898123	−	0.0155559i	0.870481	+	0.492202i	$0.163808\pi$
$440$	28.8398			1.37488
$441$	4.54574	+	5.32318i	0.216464	+	0.253485i
$442$	6.21634			0.295681
$443$	16.2975	−	28.2280i	0.774316	−	1.34115i	−0.160863	−	0.986977i	$-0.551428\pi$
$443$	16.2975	−	28.2280i	0.774316	−	1.34115i	0.935178	−	0.354177i	$-0.115239\pi$
$444$	−1.79532	−	3.10959i	−0.0852023	−	0.147575i
$445$	−35.3669	−	61.2573i	−1.67655	−	2.90387i
$446$	−7.71728	+	13.3667i	−0.365424	+	0.632932i
$447$	22.0617			1.04348
$448$	19.2314	−	13.5903i	0.908597	−	0.642082i
$449$	16.7178			0.788964			0.394482	−	0.918904i	$-0.370924\pi$
$449$	16.7178			0.788964			0.394482	+	0.918904i	$0.370924\pi$
$450$	−6.85316	+	11.8700i	−0.323061	+	0.559558i
$451$	−9.89924	−	17.1460i	−0.466137	−	0.807373i
$452$	−0.459393	−	0.795692i	−0.0216080	−	0.0374262i
$453$	−1.58958	+	2.75324i	−0.0746852	+	0.129359i
$454$	13.1695			0.618077
$455$	−2.11687	−	23.0471i	−0.0992405	−	1.08046i
$456$	−3.04706			−0.142692
$457$	−8.79534	+	15.2340i	−0.411428	+	0.712615i	−0.995046	−	0.0994135i	$-0.968303\pi$
$457$	−8.79534	+	15.2340i	−0.411428	+	0.712615i	0.583618	+	0.812029i	$0.301637\pi$
$458$	−13.7134	−	23.7524i	−0.640786	−	1.10987i
$459$	−1.13610	−	1.96778i	−0.0530286	−	0.0918482i
$460$	−7.52794	+	13.0388i	−0.350992	+	0.607936i
$461$	−1.81881			−0.0847103			−0.0423552	−	0.999103i	$-0.513486\pi$
$461$	−1.81881			−0.0847103			−0.0423552	+	0.999103i	$0.513486\pi$
$462$	−7.11220	−	3.27909i	−0.330889	−	0.152557i
$463$	−1.35124			−0.0627976			−0.0313988	−	0.999507i	$-0.509996\pi$
$463$	−1.35124			−0.0627976			−0.0313988	+	0.999507i	$0.509996\pi$
$464$	−1.07858	+	1.86816i	−0.0500719	+	0.0867270i
$465$	−19.7978	−	34.2908i	−0.918101	−	1.59020i
$466$	4.13062	+	7.15444i	0.191347	+	0.331423i
$467$	7.99872	−	13.8542i	0.370137	−	0.641095i	−0.619450	−	0.785036i	$-0.712644\pi$
$467$	7.99872	−	13.8542i	0.370137	−	0.641095i	0.989586	+	0.143941i	$0.0459775\pi$
$468$	0.959247			0.0443412
$469$	8.89252	+	4.09990i	0.410618	+	0.189316i
$470$	−24.5761			−1.13361
$471$	−11.3194	+	19.6059i	−0.521573	+	0.903390i
$472$	−5.42524	−	9.39679i	−0.249717	−	0.432523i
$473$	−0.947811	−	1.64166i	−0.0435804	−	0.0754835i
$474$	0.572932	−	0.992348i	0.0263156	−	0.0455800i
$475$	−10.9675			−0.503221
$476$	0.240939	+	2.62318i	0.0110434	+	0.120233i
$477$	−3.27829			−0.150102
$478$	−10.1454	+	17.5723i	−0.464039	+	0.803739i
$479$	7.18238	+	12.4403i	0.328171	+	0.568410i	0.982149	−	0.188104i	$-0.0602343\pi$
$479$	7.18238	+	12.4403i	0.328171	+	0.568410i	−0.653978	+	0.756514i	$0.726901\pi$
$480$	4.85585	+	8.41058i	0.221638	+	0.383889i
$481$	8.96931	−	15.5353i	0.408966	−	0.708349i
$482$	17.6909			0.805800
$483$	18.5790	−	13.1293i	0.845375	−	0.597405i
$484$	2.36168			0.107349
$485$	−26.6908	+	46.2299i	−1.21197	+	2.09919i
$486$	0.624863	+	1.08229i	0.0283444	+	0.0490939i
$487$	7.84788	+	13.5929i	0.355621	+	0.615954i	0.987224	−	0.159338i	$-0.0509359\pi$
$487$	7.84788	+	13.5929i	0.355621	+	0.615954i	−0.631603	+	0.775292i	$0.717603\pi$
$488$	4.19914	−	7.27312i	0.190086	−	0.329238i
$489$	14.6296			0.661575
$490$	−34.3718	+	6.36782i	−1.55276	+	0.287669i
$491$	38.8742			1.75437			0.877183	−	0.480156i	$-0.159420\pi$
$491$	38.8742			1.75437			0.877183	+	0.480156i	$0.159420\pi$
$492$	1.83133	−	3.17195i	0.0825626	−	0.143003i
$493$	−0.835970	−	1.44794i	−0.0376502	−	0.0652120i
$494$	−1.36791	−	2.36929i	−0.0615453	−	0.106600i
$495$	4.73239	−	8.19675i	0.212705	−	0.368416i
$496$	29.0494			1.30436
$497$	15.7809	−	11.1520i	0.707872	−	0.500235i
$498$	−6.14771			−0.275485
$499$	−21.9808	+	38.0719i	−0.983997	+	1.70433i	−0.337684	+	0.941260i	$0.609644\pi$
$499$	−21.9808	+	38.0719i	−0.983997	+	1.70433i	−0.646313	+	0.763073i	$0.723690\pi$
$500$	5.22437	+	9.04888i	0.233641	+	0.404678i
$501$	−8.90136	−	15.4176i	−0.397683	−	0.688808i
$502$	9.07033	−	15.7103i	0.404829	−	0.701184i
$503$	−23.9459			−1.06770			−0.533848	−	0.845580i	$-0.679255\pi$
$503$	−23.9459			−1.06770			−0.533848	+	0.845580i	$0.679255\pi$
$504$	−0.737369	−	8.02798i	−0.0328450	−	0.357595i
$505$	−45.0551			−2.00492
$506$	−12.7265	+	22.0429i	−0.565762	+	0.979929i
$507$	−4.10384	−	7.10805i	−0.182258	−	0.315680i
$508$	2.36091	+	4.08922i	0.104749	+	0.181430i
$509$	9.19234	−	15.9216i	0.407444	−	0.705713i	−0.587159	−	0.809472i	$-0.699754\pi$
$509$	9.19234	−	15.9216i	0.407444	−	0.705713i	0.994602	+	0.103759i	$0.0330870\pi$
$510$	11.3469			0.502451
$511$	17.7377	+	8.17798i	0.784669	+	0.361773i
$512$	−24.9907			−1.10444
$513$	−0.500000	+	0.866025i	−0.0220755	+	0.0382360i
$514$	−2.08087	−	3.60418i	−0.0917833	−	0.158973i
$515$	19.7399	+	34.1905i	0.869843	+	1.50661i
$516$	0.175342	−	0.303701i	0.00771900	−	0.0133697i
$517$	11.6566			0.512658
$518$	−24.6052	−	11.3442i	−1.08109	−	0.498438i
$519$	24.9345			1.09450
$520$	−13.3273	+	23.0836i	−0.584441	+	1.01228i
$521$	−0.710069	−	1.22988i	−0.0311087	−	0.0538819i	0.850052	−	0.526699i	$-0.176570\pi$
$521$	−0.710069	−	1.22988i	−0.0311087	−	0.0538819i	−0.881161	+	0.472817i	$0.843237\pi$
$522$	0.459790	+	0.796379i	0.0201244	+	0.0348566i
$523$	−11.6918	+	20.2507i	−0.511245	+	0.885503i	0.488670	+	0.872469i	$0.337482\pi$
$523$	−11.6918	+	20.2507i	−0.511245	+	0.885503i	−0.999915	+	0.0130338i	$0.995851\pi$
$524$	0.368312			0.0160898
$525$	−2.65405	−	28.8955i	−0.115832	−	1.26110i
$526$	29.8823			1.30293
$527$	−11.2576	+	19.4987i	−0.490388	+	0.849378i
$528$	3.47193	+	6.01357i	0.151097	+	0.261707i
$529$	−25.4686	−	44.1128i	−1.10733	−	1.91795i
$530$	8.18558	−	14.1778i	0.355559	−	0.615846i
$531$	−3.56096			−0.154533
$532$	0.946779	−	0.669065i	0.0410481	−	0.0290077i
$533$	18.2984			0.792591
$534$	11.0610	−	19.1582i	0.478656	−	0.829057i
$535$	−13.8611	−	24.0081i	−0.599267	−	1.03796i
$536$	−5.63872	−	9.76654i	−0.243555	−	0.421850i
$537$	6.81705	−	11.8075i	0.294178	−	0.509530i
$538$	−22.8176			−0.983737
$539$	16.3028	−	3.02031i	0.702213	−	0.130094i
$540$	1.75095			0.0753491
$541$	−17.9064	+	31.0148i	−0.769856	+	1.33343i	0.167785	+	0.985824i	$0.446339\pi$
$541$	−17.9064	+	31.0148i	−0.769856	+	1.33343i	−0.937641	+	0.347606i	$0.886995\pi$
$542$	5.68654	+	9.84938i	0.244258	+	0.423067i
$543$	−1.89624	−	3.28439i	−0.0813756	−	0.140947i
$544$	2.76117	−	4.78249i	0.118384	−	0.205048i
$545$	14.7846			0.633304
$546$	5.91126	−	4.17734i	0.252979	−	0.178774i
$547$	13.7734			0.588909			0.294455	−	0.955665i	$-0.404862\pi$
$547$	13.7734			0.588909			0.294455	+	0.955665i	$0.404862\pi$
$548$	0.561308	−	0.972213i	0.0239779	−	0.0415309i
$549$	−1.37809	−	2.38693i	−0.0588156	−	0.101872i
$550$	16.2324	+	28.1154i	0.692154	+	1.19885i
$551$	−0.367912	+	0.637243i	−0.0156736	+	0.0271474i
$552$	−26.2007			−1.11518
$553$	0.221882	+	2.41570i	0.00943537	+	0.102726i
$554$	16.1340			0.685470
$555$	16.3721	−	28.3573i	0.694956	−	1.20370i
$556$	−2.38239	−	4.12642i	−0.101036	−	0.174999i
$557$	−5.88752	−	10.1975i	−0.249462	−	0.432081i	0.713914	−	0.700233i	$-0.246921\pi$
$557$	−5.88752	−	10.1975i	−0.249462	−	0.432081i	−0.963377	+	0.268152i	$0.913587\pi$
$558$	6.19176	−	10.7244i	0.262118	−	0.454002i
$559$	1.75199			0.0741014
$560$	28.1464	+	12.9769i	1.18940	+	0.548375i
$561$	−5.38195			−0.227226
$562$	−19.2436	+	33.3308i	−0.811741	+	1.40598i
$563$	−5.79905	−	10.0443i	−0.244401	−	0.423315i	0.717562	−	0.696495i	$-0.245258\pi$
$563$	−5.79905	−	10.0443i	−0.244401	−	0.423315i	−0.961963	+	0.273180i	$0.911925\pi$
$564$	1.07822	+	1.86753i	0.0454012	+	0.0786372i
$565$	4.18934	−	7.25614i	0.176247	−	0.305268i
$566$	29.0814			1.22238
$567$	−2.40268	−	1.10776i	−0.100903	−	0.0465215i
$568$	−22.2547			−0.933788
$569$	−8.10322	+	14.0352i	−0.339705	+	0.588386i	−0.984377	−	0.176073i	$-0.943660\pi$
$569$	−8.10322	+	14.0352i	−0.339705	+	0.588386i	0.644673	+	0.764459i	$0.276994\pi$
$570$	−2.49691	−	4.32477i	−0.104584	−	0.181145i
$571$	8.99591	+	15.5814i	0.376467	+	0.652060i	0.990545	−	0.137185i	$-0.0438054\pi$
$571$	8.99591	+	15.5814i	0.376467	+	0.652060i	−0.614078	+	0.789245i	$0.710472\pi$
$572$	1.13604	−	1.96768i	0.0475002	−	0.0822727i
$573$	−10.0366			−0.419284
$574$	−2.52789	−	27.5219i	−0.105512	−	1.14874i
$575$	−94.3055			−3.93281
$576$	−4.45029	+	7.70813i	−0.185429	+	0.321172i
$577$	11.9506	+	20.6990i	0.497509	+	0.861712i	0.999996	−	0.00287352i	$-0.000914671\pi$
$577$	11.9506	+	20.6990i	0.497509	+	0.861712i	−0.502486	+	0.864585i	$0.667581\pi$
$578$	7.39657	+	12.8112i	0.307657	+	0.532877i
$579$	9.49470	−	16.4453i	0.394586	−	0.683444i
$580$	1.28840			0.0534977
$581$	10.6289	−	7.51121i	0.440963	−	0.311618i
$582$	−16.6951			−0.692034
$583$	−3.88249	+	6.72466i	−0.160796	+	0.278507i
$584$	−11.2474	−	19.4811i	−0.465421	−	0.806133i
$585$	4.37382	+	7.57568i	0.180835	+	0.313216i
$586$	−5.11324	+	8.85640i	−0.211226	+	0.365854i
$587$	−15.6293			−0.645091			−0.322545	−	0.946554i	$-0.604539\pi$
$587$	−15.6293			−0.645091			−0.322545	+	0.946554i	$0.604539\pi$
$588$	1.99187	+	2.33253i	0.0821435	+	0.0961921i
$589$	9.90898			0.408293
$590$	8.89141	−	15.4004i	0.366053	−	0.634023i
$591$	1.54263	+	2.67191i	0.0634552	+	0.109908i
$592$	12.0114	+	20.8044i	0.493666	+	0.855055i
$593$	−4.12431	+	7.14351i	−0.169365	+	0.293349i	−0.938197	−	0.346102i	$-0.887505\pi$
$593$	−4.12431	+	7.14351i	−0.169365	+	0.293349i	0.768832	+	0.639451i	$0.220838\pi$
$594$	2.96011			0.121455
$595$	−19.6181	+	13.8636i	−0.804262	+	0.568352i
$596$	9.66711			0.395980
$597$	−9.42704	+	16.3281i	−0.385823	+	0.668266i
$598$	−11.7622	−	20.3728i	−0.480993	−	0.833105i
$599$	4.20849	+	7.28931i	0.171954	+	0.297833i	0.939103	−	0.343636i	$-0.111659\pi$
$599$	4.20849	+	7.28931i	0.171954	+	0.297833i	−0.767149	+	0.641469i	$0.778325\pi$
$600$	−16.7093	+	28.9413i	−0.682153	+	1.18152i
$601$	−15.3330			−0.625446			−0.312723	−	0.949844i	$-0.601241\pi$
$601$	−15.3330			−0.625446			−0.312723	+	0.949844i	$0.601241\pi$
$602$	−0.242034	−	2.63511i	−0.00986459	−	0.107399i
$603$	−3.70108			−0.150720
$604$	−0.696531	+	1.20643i	−0.0283415	+	0.0490888i
$605$	10.7684	+	18.6515i	0.437799	+	0.758291i
$606$	−7.04548	−	12.2031i	−0.286203	−	0.495718i
$607$	1.88178	−	3.25934i	0.0763790	−	0.132292i	−0.825306	−	0.564686i	$-0.808997\pi$
$607$	1.88178	−	3.25934i	0.0763790	−	0.132292i	0.901685	+	0.432393i	$0.142331\pi$
$608$	−2.43040			−0.0985656
$609$	−1.76795	−	0.815116i	−0.0716410	−	0.0330301i
$610$	13.7639			0.557284
$611$	−5.38671	+	9.33005i	−0.217923	+	0.377454i
$612$	−0.497821	−	0.862252i	−0.0201232	−	0.0348545i
$613$	−8.76287	−	15.1777i	−0.353929	−	0.613023i	0.633005	−	0.774148i	$-0.281821\pi$
$613$	−8.76287	−	15.1777i	−0.353929	−	0.613023i	−0.986934	+	0.161125i	$0.948488\pi$
$614$	−11.9509	+	20.6996i	−0.482299	+	0.835366i
$615$	33.4008			1.34685
$616$	−17.3408	−	7.99502i	−0.698683	−	0.322128i
$617$	−12.0057			−0.483330			−0.241665	−	0.970360i	$-0.577694\pi$
$617$	−12.0057			−0.483330			−0.241665	+	0.970360i	$0.577694\pi$
$618$	−6.17364	+	10.6931i	−0.248340	+	0.430138i
$619$	−13.9364	−	24.1385i	−0.560150	−	0.970209i	−0.997483	−	0.0709089i	$-0.977410\pi$
$619$	−13.9364	−	24.1385i	−0.560150	−	0.970209i	0.437332	−	0.899300i	$-0.355923\pi$
$620$	−8.67509	−	15.0257i	−0.348400	−	0.603446i
$621$	−4.29933	+	7.44667i	−0.172526	+	0.298824i
$622$	42.8834			1.71947
$623$	4.28364	+	46.6374i	0.171620	+	1.86849i
$624$	−6.41774			−0.256915
$625$	−20.2239	+	35.0289i	−0.808957	+	1.40115i
$626$	1.84677	+	3.19870i	0.0738118	+	0.127846i
$627$	1.18430	+	2.05127i	0.0472965	+	0.0819200i
$628$	−4.96001	+	8.59098i	−0.197926	+	0.342818i
$629$	−18.6193			−0.742398
$630$	10.7901	−	7.62508i	0.429887	−	0.303790i
$631$	46.7972			1.86297			0.931483	−	0.363784i	$-0.118515\pi$
$631$	46.7972			1.86297			0.931483	+	0.363784i	$0.118515\pi$
$632$	1.39691	−	2.41953i	0.0555663	−	0.0962436i
$633$	−9.95858	−	17.2488i	−0.395818	−	0.685577i
$634$	7.82439	+	13.5522i	0.310746	+	0.538228i
$635$	−21.5299	+	37.2908i	−0.854386	+	1.47984i
$636$	−1.43649			−0.0569607
$637$	−5.11631	+	14.4446i	−0.202716	+	0.572317i
$638$	2.17812			0.0862326
$639$	−3.65183	+	6.32516i	−0.144464	+	0.250220i
$640$	−12.5122	−	21.6718i	−0.494590	−	0.856655i
$641$	−8.86536	−	15.3553i	−0.350161	−	0.606496i	0.636117	−	0.771593i	$-0.280540\pi$
$641$	−8.86536	−	15.3553i	−0.350161	−	0.606496i	−0.986277	+	0.165097i	$0.947206\pi$
$642$	4.33505	−	7.50853i	0.171091	−	0.296338i
$643$	−42.2257			−1.66522			−0.832609	−	0.553862i	$-0.813154\pi$
$643$	−42.2257			−1.66522			−0.832609	+	0.553862i	$0.813154\pi$
$644$	8.14104	−	5.75307i	0.320802	−	0.226703i
$645$	3.19799			0.125921
$646$	−1.41981	+	2.45919i	−0.0558618	+	0.0967555i
$647$	20.2952	+	35.1523i	0.797886	+	1.38198i	0.920990	+	0.389586i	$0.127382\pi$
$647$	20.2952	+	35.1523i	0.797886	+	1.38198i	−0.123104	+	0.992394i	$0.539285\pi$
$648$	1.52353	+	2.63883i	0.0598500	+	0.103663i
$649$	−4.21726	+	7.30451i	−0.165542	+	0.286727i
$650$	−30.0050			−1.17689
$651$	2.39791	+	26.1068i	0.0939814	+	1.02321i
$652$	6.41048			0.251054
$653$	−4.32081	+	7.48386i	−0.169086	+	0.292866i	−0.938099	−	0.346368i	$-0.887415\pi$
$653$	−4.32081	+	7.48386i	−0.169086	+	0.292866i	0.769013	+	0.639234i	$0.220748\pi$
$654$	2.31194	+	4.00441i	0.0904042	+	0.156585i
$655$	1.67937	+	2.90876i	0.0656186	+	0.113655i
$656$	−12.2523	+	21.2216i	−0.478372	+	0.828564i
$657$	−7.38246			−0.288017
$658$	14.7772	+	6.81303i	0.576074	+	0.265599i
$659$	−43.2307			−1.68403			−0.842015	−	0.539454i	$-0.818631\pi$
$659$	−43.2307			−1.68403			−0.842015	+	0.539454i	$0.818631\pi$
$660$	2.07366	−	3.59169i	0.0807172	−	0.139806i
$661$	−4.37679	−	7.58083i	−0.170237	−	0.294860i	0.768265	−	0.640132i	$-0.221120\pi$
$661$	−4.37679	−	7.58083i	−0.170237	−	0.294860i	−0.938503	+	0.345272i	$0.887787\pi$
$662$	−14.2084	−	24.6096i	−0.552223	−	0.956479i
$663$	2.48708	−	4.30775i	0.0965902	−	0.167299i
$664$	−14.9893			−0.581696
$665$	9.60094	+	4.42652i	0.372309	+	0.171653i
$666$	10.2407			0.396820
$667$	−3.16356	+	5.47944i	−0.122493	+	0.212165i
$668$	−3.90044	−	6.75576i	−0.150912	−	0.261388i
$669$	6.17517	+	10.6957i	0.238746	+	0.413520i
$670$	9.24127	−	16.0063i	0.357021	−	0.618379i
$671$	−6.52832			−0.252023
$672$	−0.588140	−	6.40327i	−0.0226880	−	0.247012i
$673$	0.331699			0.0127861			0.00639304	−	0.999980i	$-0.497965\pi$
$673$	0.331699			0.0127861			0.00639304	+	0.999980i	$0.497965\pi$
$674$	−2.53573	+	4.39201i	−0.0976726	+	0.169174i
$675$	5.48373	+	9.49810i	0.211069	+	0.365582i
$676$	−1.79824	−	3.11464i	−0.0691630	−	0.119794i
$677$	13.9315	−	24.1301i	0.535432	−	0.927395i	−0.463711	−	0.885987i	$-0.653482\pi$
$677$	13.9315	−	24.1301i	0.535432	−	0.927395i	0.999142	−	0.0414081i	$-0.0131844\pi$
$678$	2.62043			0.100637
$679$	28.8646	−	20.3979i	1.10772	−	0.782799i
$680$	27.6660			1.06094
$681$	5.26897	−	9.12613i	0.201907	−	0.349714i
$682$	−14.6658	−	25.4020i	−0.561584	−	0.972692i
$683$	−8.38990	−	14.5317i	−0.321031	−	0.556042i	0.659670	−	0.751555i	$-0.270696\pi$
$683$	−8.38990	−	14.5317i	−0.321031	−	0.556042i	−0.980701	+	0.195514i	$0.937363\pi$
$684$	−0.219092	+	0.379479i	−0.00837720	+	0.0145097i
$685$	10.2374			0.391153
$686$	22.4325	+	5.69976i	0.856475	+	0.217618i
$687$	−21.9463			−0.837303
$688$	−1.17311	+	2.03188i	−0.0447243	+	0.0774647i
$689$	−3.58831	−	6.21514i	−0.136704	−	0.236778i
$690$	−21.4701	−	37.1873i	−0.817353	−	1.41570i
$691$	12.9029	−	22.3485i	0.490850	−	0.850177i	−0.509095	−	0.860711i	$-0.670020\pi$
$691$	12.9029	−	22.3485i	0.490850	−	0.850177i	0.999945	+	0.0105336i	$0.00335300\pi$
$692$	10.9259			0.415340
$693$	−5.11782	+	3.61663i	−0.194410	+	0.137385i
$694$	−28.8751			−1.09608
$695$	21.7257	−	37.6300i	0.824102	−	1.42739i
$696$	1.12105	+	1.94172i	0.0424934	+	0.0736006i
$697$	−9.49632	−	16.4481i	−0.359699	−	0.623017i
$698$	−11.1877	+	19.3777i	−0.423461	+	0.733457i
$699$	6.61044			0.250030
$700$	−1.16296	−	12.6616i	−0.0439559	−	0.478563i
$701$	14.8949			0.562573			0.281287	−	0.959624i	$-0.409239\pi$
$701$	14.8949			0.562573			0.281287	+	0.959624i	$0.409239\pi$
$702$	−1.36791	+	2.36929i	−0.0516285	+	0.0894232i
$703$	4.09719	+	7.09654i	0.154528	+	0.267651i
$704$	10.5410	+	18.2575i	0.397278	+	0.688106i
$705$	−9.83259	+	17.0305i	−0.370317	+	0.641408i
$706$	−11.1376			−0.419168
$707$	27.0908	+	12.4902i	1.01885	+	0.469744i
$708$	−1.56036			−0.0586419
$709$	−3.29447	+	5.70619i	−0.123726	+	0.214300i	−0.921234	−	0.389008i	$-0.872818\pi$
$709$	−3.29447	+	5.70619i	−0.123726	+	0.214300i	0.797508	+	0.603308i	$0.206151\pi$
$710$	−18.2366	−	31.5867i	−0.684407	−	1.18543i
$711$	−0.458446	−	0.794052i	−0.0171931	−	0.0297793i
$712$	26.9687	−	46.7112i	1.01070	−	1.75058i
$713$	85.2041			3.19092
$714$	−6.82271	−	3.14562i	−0.255334	−	0.117722i
$715$	20.7197			0.774874
$716$	2.98713	−	5.17385i	0.111634	−	0.193356i
$717$	8.11809	+	14.0609i	0.303176	+	0.525115i
$718$	−7.64615	−	13.2435i	−0.285352	−	0.494244i
$719$	16.4386	−	28.4724i	0.613055	−	1.06184i	−0.377667	−	0.925942i	$-0.623274\pi$
$719$	16.4386	−	28.4724i	0.613055	−	1.06184i	0.990722	−	0.135902i	$-0.0433931\pi$
$720$	−11.7146			−0.436576
$721$	−2.39089	−	26.0304i	−0.0890414	−	0.969423i
$722$	1.24973			0.0465100
$723$	7.07793	−	12.2593i	0.263231	−	0.455929i
$724$	−0.830904	−	1.43917i	−0.0308803	−	0.0534863i
$725$	4.03506	+	6.98893i	0.149858	+	0.259562i
$726$	−3.36783	+	5.83325i	−0.124992	+	0.216492i
$727$	−15.7724			−0.584966			−0.292483	−	0.956271i	$-0.594481\pi$
$727$	−15.7724			−0.584966			−0.292483	+	0.956271i	$0.594481\pi$
$728$	14.4127	−	10.1851i	0.534172	−	0.377486i
$729$	1.00000			0.0370370
$730$	18.4333	−	31.9275i	0.682248	−	1.18169i
$731$	−0.909233	−	1.57484i	−0.0336292	−	0.0582475i
$732$	−0.603859	−	1.04591i	−0.0223193	−	0.0386581i
$733$	−2.99896	+	5.19434i	−0.110769	+	0.191857i	−0.916081	−	0.400994i	$-0.868665\pi$
$733$	−2.99896	+	5.19434i	−0.110769	+	0.191857i	0.805312	+	0.592852i	$0.201998\pi$
$734$	−0.445962			−0.0164608
$735$	−9.33903	+	26.3664i	−0.344475	+	0.972540i
$736$	−20.8982			−0.770317
$737$	−4.38320	+	7.59193i	−0.161457	+	0.279652i
$738$	5.22305	+	9.04658i	0.192263	+	0.333009i
$739$	−5.50327	−	9.53195i	−0.202441	−	0.350638i	0.746873	−	0.664966i	$-0.231554\pi$
$739$	−5.50327	−	9.53195i	−0.202441	−	0.350638i	−0.949314	+	0.314328i	$0.898221\pi$
$740$	7.17399	−	12.4257i	0.263721	−	0.456778i
$741$	−2.18914			−0.0804200
$742$	−8.85225	+	6.25566i	−0.324976	+	0.229653i
$743$	23.7308			0.870598			0.435299	−	0.900286i	$-0.356643\pi$
$743$	23.7308			0.870598			0.435299	+	0.900286i	$0.356643\pi$
$744$	15.0966	−	26.1482i	0.553470	−	0.958638i
$745$	44.0786	+	76.3463i	1.61491	+	2.79711i
$746$	7.80078	+	13.5114i	0.285607	+	0.494686i
$747$	−2.45962	+	4.26019i	−0.0899929	+	0.155872i
$748$	−2.35829			−0.0862274
$749$	1.67885	+	18.2782i	0.0613439	+	0.667872i
$750$	−29.8004			−1.08816
$751$	16.2986	−	28.2300i	0.594745	−	1.03013i	−0.398838	−	0.917021i	$-0.630586\pi$
$751$	16.2986	−	28.2300i	0.594745	−	1.03013i	0.993583	−	0.113107i	$-0.0360803\pi$
$752$	−7.21371	−	12.4945i	−0.263057	−	0.455628i
$753$	−7.25786	−	12.5710i	−0.264491	−	0.458112i
$754$	−1.00654	+	1.74338i	−0.0366561	+	0.0634903i
$755$	−12.7037			−0.462336
$756$	−1.05282	−	0.485402i	−0.0382906	−	0.0176539i
$757$	−15.3780			−0.558923			−0.279461	−	0.960157i	$-0.590156\pi$
$757$	−15.3780			−0.558923			−0.279461	+	0.960157i	$0.590156\pi$
$758$	−10.8767	+	18.8389i	−0.395059	+	0.684261i
$759$	10.1834	+	17.6382i	0.369635	+	0.640227i
$760$	−6.08793	−	10.5446i	−0.220832	−	0.382493i
$761$	−23.2625	+	40.2919i	−0.843266	+	1.46058i	0.0438521	+	0.999038i	$0.486037\pi$
$761$	−23.2625	+	40.2919i	−0.843266	+	1.46058i	−0.887118	+	0.461542i	$0.847296\pi$
$762$	−13.4669			−0.487855
$763$	−8.88973	−	4.09862i	−0.321830	−	0.148380i
$764$	−4.39788			−0.159110
$765$	4.53977	−	7.86312i	0.164136	−	0.284292i
$766$	16.8424	+	29.1719i	0.608541	+	1.05402i
$767$	−3.89772	−	6.75106i	−0.140739	−	0.243766i
$768$	−4.98738	+	8.63839i	−0.179967	+	0.311711i
$769$	−41.6203			−1.50086			−0.750432	−	0.660947i	$-0.770155\pi$
$769$	−41.6203			−1.50086			−0.750432	+	0.660947i	$0.770155\pi$
$770$	−2.86239	−	31.1638i	−0.103153	−	1.12307i
$771$	−3.33012			−0.119932
$772$	4.16043	−	7.20608i	0.149737	−	0.259352i
$773$	−6.51547	−	11.2851i	−0.234345	−	0.405898i	0.724737	−	0.689026i	$-0.241961\pi$
$773$	−6.51547	−	11.2851i	−0.234345	−	0.405898i	−0.959082	+	0.283128i	$0.908628\pi$
$774$	0.500085	+	0.866173i	0.0179752	+	0.0311339i
$775$	54.3382	−	94.1165i	1.95188	−	3.38076i
$776$	−40.7057			−1.46125
$777$	−17.7055	+	12.5120i	−0.635181	+	0.448866i
$778$	−43.2571			−1.55084
$779$	−4.17935	+	7.23885i	−0.149741	+	0.259359i
$780$	1.91654	+	3.31955i	0.0686232	+	0.118859i
$781$	8.64976	+	14.9818i	0.309513	+	0.536092i
$782$	−12.2085	+	21.1458i	−0.436575	+	0.756171i
$783$	0.735824			0.0262962
$784$	−13.3264	−	15.6056i	−0.475943	−	0.557341i
$785$	−90.4634			−3.22878
$786$	−0.525224	+	0.909714i	−0.0187341	+	0.0324484i
$787$	−5.41229	−	9.37436i	−0.192927	−	0.334160i	0.753292	−	0.657686i	$-0.228465\pi$
$787$	−5.41229	−	9.37436i	−0.192927	−	0.334160i	−0.946219	+	0.323527i	$0.895131\pi$
$788$	0.675955	+	1.17079i	0.0240799	+	0.0417076i
$789$	11.9556	−	20.7076i	0.425629	−	0.737211i
$790$	4.57879			0.162906
$791$	−4.53053	+	3.20161i	−0.161087	+	0.113836i
$792$	7.21729			0.256455
$793$	3.01684	−	5.22531i	0.107131	−	0.185556i
$794$	11.0472	+	19.1344i	0.392052	+	0.679053i
$795$	−6.54990	−	11.3448i	−0.232301	−	0.402357i
$796$	−4.13078	+	7.15473i	−0.146412	+	0.253593i
$797$	1.01586			0.0359836			0.0179918	−	0.999838i	$-0.494273\pi$
$797$	1.01586			0.0359836			0.0179918	+	0.999838i	$0.494273\pi$
$798$	0.302425	+	3.29260i	0.0107057	+	0.116557i
$799$	11.1822			0.395597
$800$	−13.3276	+	23.0841i	−0.471203	+	0.816148i
$801$	−8.85073	−	15.3299i	−0.312725	−	0.541656i
$802$	8.74710	+	15.1504i	0.308871	+	0.534980i
$803$	−8.74307	+	15.1434i	−0.308536	+	0.534401i
$804$	−1.62176			−0.0571950
$805$	82.5553	+	38.0622i	2.90969	+	1.34152i
$806$	27.1092			0.954882
$807$	−9.12904	+	15.8120i	−0.321357	+	0.556607i
$808$	−17.1782	−	29.7535i	−0.604326	−	1.04672i
$809$	7.26173	+	12.5777i	0.255309	+	0.442208i	0.964979	−	0.262326i	$-0.0844896\pi$
$809$	7.26173	+	12.5777i	0.255309	+	0.442208i	−0.709671	+	0.704534i	$0.751156\pi$
$810$	−2.49691	+	4.32477i	−0.0877324	+	0.151957i
$811$	−8.72354			−0.306325			−0.153162	−	0.988201i	$-0.548946\pi$
$811$	−8.72354			−0.306325			−0.153162	+	0.988201i	$0.548946\pi$
$812$	−0.774689	−	0.357171i	−0.0271862	−	0.0125342i
$813$	9.10046			0.319167
$814$	12.1281	−	21.0065i	0.425091	−	0.736278i
$815$	29.2295	+	50.6270i	1.02386	+	1.77339i
$816$	3.33062	+	5.76880i	0.116595	+	0.201948i
$817$	−0.400156	+	0.693090i	−0.0139997	+	0.0242481i
$818$	38.1747			1.33475
$819$	−0.529757	−	5.76764i	−0.0185112	−	0.201538i
$820$	14.6357			0.511101
$821$	11.9249	−	20.6545i	0.416181	−	0.720846i	−0.579371	−	0.815064i	$-0.696702\pi$
$821$	11.9249	−	20.6545i	0.416181	−	0.720846i	0.995552	+	0.0942181i	$0.0300351\pi$
$822$	1.60088	+	2.77281i	0.0558371	+	0.0967127i
$823$	12.2249	+	21.1742i	0.426134	+	0.738085i	0.996526	−	0.0832873i	$-0.0265419\pi$
$823$	12.2249	+	21.1742i	0.426134	+	0.738085i	−0.570392	+	0.821373i	$0.693209\pi$
$824$	−15.0525	+	26.0716i	−0.524378	+	0.908249i
$825$	25.9776			0.904424
$826$	−9.61556	+	6.79507i	−0.334568	+	0.236431i
$827$	−17.8924			−0.622179			−0.311090	−	0.950381i	$-0.600694\pi$
$827$	−17.8924			−0.622179			−0.311090	+	0.950381i	$0.600694\pi$
$828$	−1.88390	+	3.26301i	−0.0654701	+	0.113398i
$829$	−7.77612	−	13.4686i	−0.270076	−	0.467785i	0.698805	−	0.715312i	$-0.253715\pi$
$829$	−7.77612	−	13.4686i	−0.270076	−	0.467785i	−0.968881	+	0.247527i	$0.920382\pi$
$830$	−12.2829	−	21.2746i	−0.426346	−	0.738453i
$831$	6.45503	−	11.1804i	0.223923	−	0.387845i
$832$	−19.4846			−0.675507
$833$	15.6393	−	2.89737i	0.541869	−	0.100388i
$834$	13.5894			0.470563
$835$	35.5692	−	61.6077i	1.23092	−	2.13202i
$836$	0.518943	+	0.898836i	0.0179480	+	0.0310869i
$837$	−4.95449	−	8.58143i	−0.171252	−	0.296618i
$838$	−10.7523	+	18.6236i	−0.371433	+	0.643340i
$839$	−2.07381			−0.0715959			−0.0357979	−	0.999359i	$-0.511397\pi$
$839$	−2.07381			−0.0715959			−0.0357979	+	0.999359i	$0.511397\pi$
$840$	26.3082	−	18.5913i	0.907719	−	0.641462i
$841$	−28.4586			−0.981330
$842$	6.07169	−	10.5165i	0.209244	−	0.362422i
$843$	15.3982	+	26.6705i	0.530343	+	0.918582i
$844$	−4.36370	−	7.55815i	−0.150205	−	0.260162i
$845$	16.3986	−	28.4033i	0.564130	−	0.977102i
$846$	−6.15028			−0.211451
$847$	−1.30427	−	14.2000i	−0.0448153	−	0.487919i
$848$	9.61071			0.330033
$849$	11.6351	−	20.1526i	0.399316	−	0.691635i
$850$	15.5717	+	26.9710i	0.534106	+	0.925099i
$851$	35.2304	+	61.0208i	1.20768	+	2.09177i
$852$	−1.60018	+	2.77159i	−0.0548212	+	0.0949530i
$853$	14.2407			0.487594			0.243797	−	0.969826i	$-0.421607\pi$
$853$	14.2407			0.487594			0.243797	+	0.969826i	$0.421607\pi$
$854$	−8.27598	−	3.81565i	−0.283198	−	0.130569i
$855$	−3.99593			−0.136658
$856$	10.5697	−	18.3072i	0.361263	−	0.625726i
$857$	−12.6943	−	21.9872i	−0.433630	−	0.751070i	0.563552	−	0.826080i	$-0.309434\pi$
$857$	−12.6943	−	21.9872i	−0.433630	−	0.751070i	−0.997183	+	0.0750106i	$0.976101\pi$
$858$	3.24005	+	5.61192i	0.110613	+	0.191588i
$859$	19.5613	−	33.8811i	0.667421	−	1.15601i	−0.311201	−	0.950344i	$-0.600731\pi$
$859$	19.5613	−	33.8811i	0.667421	−	1.15601i	0.978623	−	0.205664i	$-0.0659353\pi$
$860$	1.40131			0.0477842
$861$	−20.0833	−	9.25943i	−0.684437	−	0.315560i
$862$	−23.2140			−0.790673
$863$	−0.817785	+	1.41645i	−0.0278377	+	0.0482164i	−0.879609	−	0.475698i	$-0.842196\pi$
$863$	−0.817785	+	1.41645i	−0.0278377	+	0.0482164i	0.851771	+	0.523914i	$0.175529\pi$
$864$	1.21520	+	2.10479i	0.0413419	+	0.0716063i
$865$	49.8182	+	86.2876i	1.69387	+	2.93387i
$866$	10.5252	−	18.2302i	0.357662	−	0.619489i
$867$	11.8371			0.402009
$868$	1.05073	+	11.4396i	0.0356640	+	0.388285i
$869$	−2.17176			−0.0736718
$870$	−1.83729	+	3.18227i	−0.0622899	+	0.107889i
$871$	−4.05109	−	7.01670i	−0.137266	−	0.237752i
$872$	5.63695	+	9.76348i	0.190891	+	0.330633i
$873$	−6.67950	+	11.5692i	−0.226067	+	0.391559i
$874$	10.7460			0.363488
$875$	51.5228	−	36.4098i	1.74179	−	1.23088i
$876$	−3.23488			−0.109296
$877$	2.61968	−	4.53741i	0.0884602	−	0.153218i	−0.818400	−	0.574649i	$-0.805139\pi$
$877$	2.61968	−	4.53741i	0.0884602	−	0.153218i	0.906860	+	0.421431i	$0.138472\pi$
$878$	0.235171	+	0.407327i	0.00793662	+	0.0137466i
$879$	4.09149	+	7.08667i	0.138003	+	0.239027i
$880$	−13.8736	+	24.0298i	−0.467679	+	0.810044i
$881$	−23.6123			−0.795520			−0.397760	−	0.917489i	$-0.630212\pi$
$881$	−23.6123			−0.795520			−0.397760	+	0.917489i	$0.630212\pi$
$882$	−8.60171	+	1.59358i	−0.289635	+	0.0536585i
$883$	−22.5324			−0.758277			−0.379138	−	0.925340i	$-0.623780\pi$
$883$	−22.5324			−0.758277			−0.379138	+	0.925340i	$0.623780\pi$
$884$	1.08980	−	1.88759i	0.0366539	−	0.0634865i
$885$	−7.11468	−	12.3230i	−0.239157	−	0.414233i
$886$	20.3674	+	35.2773i	0.684255	+	1.18516i
$887$	−9.56395	+	16.5652i	−0.321126	+	0.556206i	−0.980721	−	0.195415i	$-0.937395\pi$
$887$	−9.56395	+	16.5652i	−0.321126	+	0.556206i	0.659595	+	0.751621i	$0.270728\pi$
$888$	24.9688			0.837897
$889$	23.2833	−	16.4537i	0.780898	−	0.551841i
$890$	88.3979			2.96311
$891$	1.18430	−	2.05127i	0.0396757	−	0.0687202i
$892$	2.70587	+	4.68670i	0.0905991	+	0.156922i
$893$	−2.46065	−	4.26197i	−0.0823426	−	0.142622i
$894$	−13.7856	+	23.8773i	−0.461058	+	0.798576i
$895$	54.4809			1.82110
$896$	1.51548	+	16.4996i	0.0506287	+	0.551211i
$897$	−18.8237			−0.628504
$898$	−10.4464	+	18.0936i	−0.348600	+	0.603792i
$899$	−3.64564	−	6.31443i	−0.121589	−	0.210598i
$900$	2.40288	+	4.16192i	0.0800962	+	0.138731i
$901$	−3.72446	+	6.45095i	−0.124080	+	0.214912i
$902$	24.7427			0.823841
$903$	−1.92289	−	0.886551i	−0.0639898	−	0.0295026i
$904$	6.38909			0.212498
$905$	7.57726	−	13.1242i	0.251877	−	0.436263i
$906$	−1.98655	−	3.44080i	−0.0659986	−	0.114313i
$907$	11.8397	+	20.5070i	0.393132	+	0.680924i	0.992861	−	0.119279i	$-0.0380583\pi$
$907$	11.8397	+	20.5070i	0.393132	+	0.680924i	−0.599729	+	0.800203i	$0.704725\pi$
$908$	2.30878	−	3.99893i	0.0766196	−	0.132709i
$909$	−11.2752			−0.373976
$910$	26.2665	+	12.1102i	0.870726	+	0.401449i
$911$	−55.7299			−1.84641			−0.923207	−	0.384302i	$-0.874442\pi$
$911$	−55.7299			−1.84641			−0.923207	+	0.384302i	$0.874442\pi$
$912$	1.46581	−	2.53886i	0.0485379	−	0.0840701i
$913$	5.82588	+	10.0907i	0.192808	+	0.333954i
$914$	−10.9918	−	19.0383i	−0.363575	−	0.629731i
$915$	5.50676	−	9.53799i	0.182048	−	0.315316i
$916$	−9.61653			−0.317739
$917$	−0.203406	−	2.21454i	−0.00671704	−	0.0731307i
$918$	2.83963			0.0937216
$919$	9.01041	−	15.6065i	0.297226	−	0.514811i	−0.678274	−	0.734809i	$-0.737272\pi$
$919$	9.01041	−	15.6065i	0.297226	−	0.514811i	0.975500	+	0.219998i	$0.0706052\pi$
$920$	−52.3481	−	90.6695i	−1.72586	−	2.98928i
$921$	9.56281	+	16.5633i	0.315105	+	0.545778i
$922$	1.13651	−	1.96849i	0.0374288	−	0.0648286i
$923$	−15.9887			−0.526276
$924$	−2.24255	+	1.58475i	−0.0737744	+	0.0521345i
$925$	89.8715			2.95496
$926$	0.844342	−	1.46244i	0.0277468	−	0.0480589i
$927$	4.93999	+	8.55632i	0.162251	+	0.281026i
$928$	0.894173	+	1.54875i	0.0293527	+	0.0508403i
$929$	−6.27043	+	10.8607i	−0.205726	+	0.356328i	−0.950364	−	0.311141i	$-0.899289\pi$
$929$	−6.27043	+	10.8607i	−0.205726	+	0.356328i	0.744638	+	0.667469i	$0.232622\pi$
$930$	49.4837			1.62263
$931$	−4.54574	−	5.32318i	−0.148981	−	0.174460i
$932$	2.89659			0.0948810
$933$	17.1571	−	29.7170i	0.561698	−	0.972890i
$934$	9.99621	+	17.3139i	0.327086	+	0.566530i
$935$	−10.7529	−	18.6246i	−0.351659	−	0.609091i
$936$	−3.33522	+	5.77677i	−0.109015	+	0.188820i
$937$	−31.4153			−1.02629			−0.513147	−	0.858301i	$-0.671520\pi$
$937$	−31.4153			−1.02629			−0.513147	+	0.858301i	$0.671520\pi$
$938$	−9.99391	+	7.06244i	−0.326313	+	0.230597i
$939$	2.95548			0.0964485
$940$	−4.30849	+	7.46252i	−0.140527	+	0.243401i
$941$	−7.45006	−	12.9039i	−0.242865	−	0.420654i	0.718664	−	0.695357i	$-0.244754\pi$
$941$	−7.45006	−	12.9039i	−0.242865	−	0.420654i	−0.961529	+	0.274703i	$0.911421\pi$
$942$	−14.1462	−	24.5020i	−0.460908	−	0.798317i
$943$	−35.9369	+	62.2445i	−1.17027	+	2.02696i
$944$	10.4394			0.339774
$945$	−0.966988	−	10.5279i	−0.0314561	−	0.342473i
$946$	2.36901			0.0770231
$947$	−4.68806	+	8.11996i	−0.152342	+	0.263863i	−0.932088	−	0.362232i	$-0.882015\pi$
$947$	−4.68806	+	8.11996i	−0.152342	+	0.263863i	0.779746	+	0.626096i	$0.215348\pi$
$948$	−0.200884	−	0.347941i	−0.00652441	−	0.0113006i
$949$	−8.08062	−	13.9960i	−0.262308	−	0.454331i
$950$	6.85316	−	11.8700i	0.222346	−	0.385114i
$951$	12.5218			0.406046
$952$	−16.6350	−	7.66960i	−0.539145	−	0.248573i
$953$	−11.0785			−0.358868			−0.179434	−	0.983770i	$-0.557427\pi$
$953$	−11.0785			−0.358868			−0.179434	+	0.983770i	$0.557427\pi$
$954$	2.04848	−	3.54807i	0.0663220	−	0.114873i
$955$	−20.0527	−	34.7324i	−0.648892	−	1.12391i
$956$	3.55722	+	6.16129i	0.115049	+	0.199270i
$957$	0.871439	−	1.50938i	0.0281696	−	0.0487912i
$958$	−17.9520			−0.580004
$959$	−6.15559	−	2.83804i	−0.198774	−	0.0916452i
$960$	−35.5661			−1.14789
$961$	−33.5940	+	58.1865i	−1.08368	+	1.87698i
$962$	11.2092	+	19.4149i	0.361399	+	0.625961i
$963$	−3.46880	−	6.00814i	−0.111781	−	0.193610i
$964$	3.10144	−	5.37185i	0.0998906	−	0.173016i
$965$	75.8803			2.44267
$966$	2.60046	+	28.3120i	0.0836683	+	0.910924i
$967$	51.5512			1.65778			0.828888	−	0.559415i	$-0.188974\pi$
$967$	51.5512			1.65778			0.828888	+	0.559415i	$0.188974\pi$
$968$	−8.21138	+	14.2225i	−0.263924	+	0.457129i
$969$	1.13610	+	1.96778i	0.0364968	+	0.0632143i
$970$	−33.3562	−	57.7747i	−1.07100	−	1.85503i
$971$	6.76322	−	11.7142i	0.217042	−	0.375928i	−0.736860	−	0.676045i	$-0.763692\pi$
$971$	6.76322	−	11.7142i	0.217042	−	0.375928i	0.953902	+	0.300117i	$0.0970258\pi$
$972$	0.438184			0.0140548
$973$	−23.4951	+	16.6034i	−0.753218	+	0.532280i
$974$	−19.6154			−0.628518
$975$	−12.0046	+	20.7927i	−0.384456	+	0.665898i
$976$	4.04005	+	6.99758i	0.129319	+	0.223987i
$977$	22.2791	+	38.5885i	0.712771	+	1.23455i	0.963813	+	0.266579i	$0.0858932\pi$
$977$	22.2791	+	38.5885i	0.712771	+	1.23455i	−0.251043	+	0.967976i	$0.580773\pi$
$978$	−9.14152	+	15.8336i	−0.292313	+	0.506302i
$979$	−41.9278			−1.34002
$980$	−4.09222	+	11.5534i	−0.130721	+	0.369058i
$981$	3.69992			0.118129
$982$	−24.2910	+	42.0733i	−0.775158	+	1.34261i
$983$	5.10725	+	8.84601i	0.162896	+	0.282144i	0.935906	−	0.352250i	$-0.114583\pi$
$983$	5.10725	+	8.84601i	0.162896	+	0.282144i	−0.773010	+	0.634394i	$0.781250\pi$
$984$	12.7348	+	22.0572i	0.405969	+	0.703159i
$985$	−6.16423	+	10.6768i	−0.196409	+	0.340190i
$986$	2.08947			0.0665422
$987$	10.6334	−	7.51435i	0.338465	−	0.239184i
$988$	−0.959247			−0.0305177
$989$	−3.44081	+	5.95965i	−0.109411	+	0.189506i
$990$	5.91420	+	10.2437i	0.187965	+	0.325566i
$991$	9.45937	+	16.3841i	0.300487	+	0.520459i	0.976246	−	0.216664i	$-0.0695175\pi$
$991$	9.45937	+	16.3841i	0.300487	+	0.520459i	−0.675759	+	0.737122i	$0.736184\pi$
$992$	12.0414	−	20.8563i	0.382314	−	0.662188i
$993$	−22.7383			−0.721580
$994$	2.20881	+	24.0481i	0.0700593	+	0.762759i
$995$	−75.3396			−2.38843
$996$	−1.07777	+	1.86675i	−0.0341504	+	0.0591502i
$997$	−7.67167	−	13.2877i	−0.242964	−	0.420826i	0.718593	−	0.695431i	$-0.244786\pi$
$997$	−7.67167	−	13.2877i	−0.242964	−	0.420826i	−0.961557	+	0.274605i	$0.911453\pi$
$998$	−27.4700	−	47.5794i	−0.869548	−	1.50610i
$999$	4.09719	−	7.09654i	0.129629	−	0.224525i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	399.2.j.g.58.3	✓	16
3.2	odd	2		1197.2.j.m.856.6		16
7.2	even	3		2793.2.a.bm.1.6		8
7.4	even	3	inner	399.2.j.g.172.3	yes	16
7.5	odd	6		2793.2.a.bn.1.6		8
21.2	odd	6		8379.2.a.cr.1.3		8
21.5	even	6		8379.2.a.cq.1.3		8
21.11	odd	6		1197.2.j.m.172.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
399.2.j.g.58.3	✓	16	1.1	even	1	trivial
399.2.j.g.172.3	yes	16	7.4	even	3	inner
1197.2.j.m.172.6		16	21.11	odd	6
1197.2.j.m.856.6		16	3.2	odd	2
2793.2.a.bm.1.6		8	7.2	even	3
2793.2.a.bn.1.6		8	7.5	odd	6
8379.2.a.cq.1.3		8	21.5	even	6
8379.2.a.cr.1.3		8	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 399 = 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	399.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.624863 + 1.08229i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.219092 + 0.379479i) q^{4} +(-1.99797 + 3.46058i) q^{5} -1.24973 q^{6} +(2.16069 - 1.52690i) q^{7} -3.04706 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.624863 + 1.08229i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.219092 + 0.379479i) q^{4} +(-1.99797 + 3.46058i) q^{5} -1.24973 q^{6} +(2.16069 - 1.52690i) q^{7} -3.04706 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.49691 - 4.32477i) q^{10} +(1.18430 + 2.05127i) q^{11} +(-0.219092 + 0.379479i) q^{12} -2.18914 q^{13} +(0.302425 + 3.29260i) q^{14} -3.99593 q^{15} +(1.46581 - 2.53886i) q^{16} +(1.13610 + 1.96778i) q^{17} +(-0.624863 - 1.08229i) q^{18} +(0.500000 - 0.866025i) q^{19} -1.75095 q^{20} +(2.40268 + 1.10776i) q^{21} -2.96011 q^{22} +(4.29933 - 7.44667i) q^{23} +(-1.52353 - 2.63883i) q^{24} +(-5.48373 - 9.49810i) q^{25} +(1.36791 - 2.36929i) q^{26} -1.00000 q^{27} +(1.05282 + 0.485402i) q^{28} -0.735824 q^{29} +(2.49691 - 4.32477i) q^{30} +(4.95449 + 8.58143i) q^{31} +(-1.21520 - 2.10479i) q^{32} +(-1.18430 + 2.05127i) q^{33} -2.83963 q^{34} +(0.966988 + 10.5279i) q^{35} -0.438184 q^{36} +(-4.09719 + 7.09654i) q^{37} +(0.624863 + 1.08229i) q^{38} +(-1.09457 - 1.89585i) q^{39} +(6.08793 - 10.5446i) q^{40} -8.35871 q^{41} +(-2.70027 + 1.90821i) q^{42} -0.800311 q^{43} +(-0.518943 + 0.898836i) q^{44} +(-1.99797 - 3.46058i) q^{45} +(5.37299 + 9.30629i) q^{46} +(2.46065 - 4.26197i) q^{47} +2.93163 q^{48} +(2.33713 - 6.59832i) q^{49} +13.7063 q^{50} +(-1.13610 + 1.96778i) q^{51} +(-0.479623 - 0.830732i) q^{52} +(1.63914 + 2.83908i) q^{53} +(0.624863 - 1.08229i) q^{54} -9.46479 q^{55} +(-6.58375 + 4.65257i) q^{56} +1.00000 q^{57} +(0.459790 - 0.796379i) q^{58} +(1.78048 + 3.08389i) q^{59} +(-0.875477 - 1.51637i) q^{60} +(-1.37809 + 2.38693i) q^{61} -12.3835 q^{62} +(0.241993 + 2.63466i) q^{63} +8.90058 q^{64} +(4.37382 - 7.57568i) q^{65} +(-1.48005 - 2.56353i) q^{66} +(1.85054 + 3.20523i) q^{67} +(-0.497821 + 0.862252i) q^{68} +8.59867 q^{69} +(-11.9985 - 5.53194i) q^{70} +7.30367 q^{71} +(1.52353 - 2.63883i) q^{72} +(3.69123 + 6.39340i) q^{73} +(-5.12036 - 8.86873i) q^{74} +(5.48373 - 9.49810i) q^{75} +0.438184 q^{76} +(5.69100 + 2.62384i) q^{77} +2.73582 q^{78} +(-0.458446 + 0.794052i) q^{79} +(5.85729 + 10.1451i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.22305 - 9.04658i) q^{82} +4.91925 q^{83} +(0.106038 + 1.15447i) q^{84} -9.07955 q^{85} +(0.500085 - 0.866173i) q^{86} +(-0.367912 - 0.637243i) q^{87} +(-3.60865 - 6.25036i) q^{88} +(-8.85073 + 15.3299i) q^{89} +4.99382 q^{90} +(-4.73004 + 3.34260i) q^{91} +3.76780 q^{92} +(-4.95449 + 8.58143i) q^{93} +(3.07514 + 5.32630i) q^{94} +(1.99797 + 3.46058i) q^{95} +(1.21520 - 2.10479i) q^{96} +13.3590 q^{97} +(5.68093 + 6.65251i) q^{98} -2.36861 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} - 10 q^{4} + 5 q^{5} + q^{7} - 6 q^{8} - 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^3 - 10 * q^4 + 5 * q^5 + q^7 - 6 * q^8 - 8 * q^9	\( 16 q + 8 q^{3} - 10 q^{4} + 5 q^{5} + q^{7} - 6 q^{8} - 8 q^{9} + 3 q^{10} + 7 q^{11} + 10 q^{12} - 12 q^{13} - 12 q^{14} + 10 q^{15} - 10 q^{16} + 8 q^{19} - 32 q^{20} - q^{21} + 36 q^{22} + 9 q^{23} - 3 q^{24} - 15 q^{25} + 12 q^{26} - 16 q^{27} - 40 q^{28} + 8 q^{29} - 3 q^{30} + 11 q^{31} + 26 q^{32} - 7 q^{33} - 32 q^{34} - 7 q^{35} + 20 q^{36} - 17 q^{37} - 6 q^{39} + 3 q^{40} - 34 q^{41} - 9 q^{42} + 16 q^{43} + 31 q^{44} + 5 q^{45} - q^{46} + 29 q^{47} - 20 q^{48} + q^{49} + 60 q^{50} + 25 q^{52} + 6 q^{53} - 42 q^{55} - 54 q^{56} + 16 q^{57} + 37 q^{58} + 7 q^{59} - 16 q^{60} + 2 q^{61} - 78 q^{62} - 2 q^{63} + 58 q^{64} + 13 q^{65} + 18 q^{66} - 13 q^{67} - 14 q^{68} + 18 q^{69} - 81 q^{70} + 36 q^{71} + 3 q^{72} + 20 q^{73} + 26 q^{74} + 15 q^{75} - 20 q^{76} + 19 q^{77} + 24 q^{78} + 3 q^{79} + 35 q^{80} - 8 q^{81} + 5 q^{82} - 72 q^{83} - 29 q^{84} + 10 q^{85} + 51 q^{86} + 4 q^{87} - 53 q^{88} + q^{89} - 6 q^{90} - 9 q^{91} + 30 q^{92} - 11 q^{93} + 30 q^{94} - 5 q^{95} - 26 q^{96} + 6 q^{97} - 75 q^{98} - 14 q^{99}+O(q^{100}) \) 16 * q + 8 * q^3 - 10 * q^4 + 5 * q^5 + q^7 - 6 * q^8 - 8 * q^9 + 3 * q^10 + 7 * q^11 + 10 * q^12 - 12 * q^13 - 12 * q^14 + 10 * q^15 - 10 * q^16 + 8 * q^19 - 32 * q^20 - q^21 + 36 * q^22 + 9 * q^23 - 3 * q^24 - 15 * q^25 + 12 * q^26 - 16 * q^27 - 40 * q^28 + 8 * q^29 - 3 * q^30 + 11 * q^31 + 26 * q^32 - 7 * q^33 - 32 * q^34 - 7 * q^35 + 20 * q^36 - 17 * q^37 - 6 * q^39 + 3 * q^40 - 34 * q^41 - 9 * q^42 + 16 * q^43 + 31 * q^44 + 5 * q^45 - q^46 + 29 * q^47 - 20 * q^48 + q^49 + 60 * q^50 + 25 * q^52 + 6 * q^53 - 42 * q^55 - 54 * q^56 + 16 * q^57 + 37 * q^58 + 7 * q^59 - 16 * q^60 + 2 * q^61 - 78 * q^62 - 2 * q^63 + 58 * q^64 + 13 * q^65 + 18 * q^66 - 13 * q^67 - 14 * q^68 + 18 * q^69 - 81 * q^70 + 36 * q^71 + 3 * q^72 + 20 * q^73 + 26 * q^74 + 15 * q^75 - 20 * q^76 + 19 * q^77 + 24 * q^78 + 3 * q^79 + 35 * q^80 - 8 * q^81 + 5 * q^82 - 72 * q^83 - 29 * q^84 + 10 * q^85 + 51 * q^86 + 4 * q^87 - 53 * q^88 + q^89 - 6 * q^90 - 9 * q^91 + 30 * q^92 - 11 * q^93 + 30 * q^94 - 5 * q^95 - 26 * q^96 + 6 * q^97 - 75 * q^98 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more